characterization of the ductility of bolted end plate - CMM

CHARACTERIZATION OF THE DUCTILITY OF
BOLTED END PLATE BEAM-TO-COLUMN
STEEL CONNECTIONS
Ana Margarida Girão Coelho
Thesis presented in fulfilment of the requirements for the degree
of Doctor of Philosophy in Civil Engineering under the
scientific advising of Prof. Dr. Luís Simões da Silva and
Prof. Ir. Frans S. K. Bijlaard.
Tese apresentada para obtenção do grau de doutor em
Engenharia Civil sob orientação científica do Prof. Dr. Luís
Simões da Silva e do Prof. Frans S. K. Bijlaard.
Universidade de Coimbra
July 2004

O trabalho apresentado nesta tese de doutoramento foi financiado pelo
Ministério da Ciência e Ensino Superior, ao abrigo do programa PRODEP
(Concurso Público 4/5.3/PRODEP/2000) e com apoio da Fundação para a
Ciência e Tecnologia (Bolsa de Doutoramento SFRH/BD/5125/2001).
Coimbra, 2004.

To Miguel, my son
and Encarnação and Hermínio, my parents.

ACKNOWLEDGEMENTS
The author would like to express her sincere gratitude to Prof. Dr. Luís A. P.
Simões da Silva (University of Coimbra) and Prof. Ir. Frans S. K. Bijlaard (Delft
University of Technology). Prof. Simões da Silva and Prof. Bijlaard are a model
for their technical expertise, professionalism, scientific knowledge and ethics.
Financial support from the Portuguese Ministry of Science and Higher Education
(Ministério da Ciência e Ensino Superior) under contract grants from
PRODEP (Concurso Público 4/5.3/PRODEP/2000) and Fundação para a
Ciência e Tecnologia (Grant SFRH/BD/5125/2001) is gratefully acknowledged.
The assistance provided by Mr. Nol Gresnigt, Mr. Henk Kolstein and Mr.
Edwin Scharp from the Department of Steel and Timber Structures of the Delft
University of Technology is most appreciated. To Corrie van der Wouden and Jan
Willem van de Kuilen, thank you for your friendship. This research project was
also made possible by the assistance of several people at the Department of Civil
Engineering of the Faculty of Science and Technology of the University of Coimbra.
Thank you Aldina Santiago, Luciano Lima, Luís Borges, Luís Neves, Pedro
Simão, Rui Simões and Sandra Jordão.
The friendship and support of my sister Rita and all my friends is also very
much appreciated. Thank you all. To Carina, a special word of appreciation for the
works with the cover of this thesis.
To Cláudio, thank you for your patience, love and understanding.

TABLE OF CONTENTS
ABSTRACT
RESUMO (Portuguese abstract)
NOTATION
PART I
STATE-OF-THE-ART AND LITERATURE REVIEW
1 MODELLING OF THE MOMENT-ROTATION CHARACTERISTICS OF
BOLTED JOINTS: BACKGROUND REVIEW
1.1 General introduction 3
1.1.1 Literature review 4
1.1.2 Scope of the work, objectives and research approach 7
1.1.3 Outline of the dissertation 9
1.2 Definitions 10
1.3 Methods for modelling the rotational behaviour of beam-tocolumn
joints
12
1.3.1 Generality 12
1.3.2 The component method 12
1.4 Characterization of basic components of bolted joints in terms
of plastic resistance and initial stiffness
14
1.4.1 T-stub model for characterization of the tension zone
of bolted joints
15
1.4.1.1 Plastic resistance of single T-stub connections
15
1.4.1.2 Initial stiffness of single T-stub connections
19
1.4.2 Characterization of the several joint components 24
1.5 Characterization of the post-limit behaviour of basic components
of bolted joints
29
1.5.1 Column web in shear (component with high ductility)
30
1.5.2 Column flange in bending, end plate in bending
and bolts in tension (T-stub idealization)
32
1.5.3 Column web in compression (component with
limited ductility)
32
1
3

1.5.4 Column web in tension (component with limited
ductility)
34
1.6 Evaluation of the moment-rotation response of bolted joints
by means of component models
34
1.6.1 Eurocode 3 component model 37
1.6.1.1 Model for stiffness evaluation 37
1.6.1.2 Model for resistance evaluation 38
1.6.1.3 Idealization of the moment-rotation curve 39
1.6.2 Guidelines for evaluation of the ductility of bolted
joints
39
1.7 References 44
Appendix A: Design provisions for characterization of resistance
and stiffness of T-stubs
50
A.1 Basic formulations for prediction of plastic resistance of
bolted T-stubs
50
A.1.1 Type-1 mechanism 50
A.1.2 Type-2 mechanism 50
A.1.3 Type-3 mechanism 51
A.1.4 Supplementary mechanism 51
A.2 Influence of the moment-shear interaction on resistance formulations
51
A.2.1 Type-1 mechanism 52
A.2.2 Type-2 mechanism 53
A.3 Influence of the bolt dimensions on resistance formulations 54
A.4 Formulations for prediction of elastic stiffness of bolted Tstubs
56
A.4.1 Elastic theory for the evaluation of the elastic stiffness
of a bolted T-stub
56
A.4.2 Simplification of the stiffness coefficients for inclusion
in design codes
57
PART II
FURTHER DEVELOPMENTS ON THE T-STUB MODEL
2 IMPROVEMENTS ON THE T-STUB MODEL: INTRODUCTION 61
2.1 Introduction 61
2.2 Failure modes 62
2.3 References 65
3 EXPERIMENTAL ASSESSMENT OF THE BEHAVIOUR OF T-STUB CON-
NECTIONS
3.1 Introduction 67
3.2 Description of the experimental programme 67
3.2.1 Geometrical properties of the specimens 67
3.2.2 Mechanical properties of the specimens 69
59
67

3.2.2.1 Tension tests on the bolts 69
3.2.2.2 Tension tests on the structural steel 73
3.2.3 Testing procedure 75
3.2.4 Aspects related to the welding procedure 78
3.3 Experimental results 82
3.3.1 Reference test series WT1 82
3.3.2 Failure modes and general characteristics of the 87
overall behaviour of the test specimens
3.4 Concluding remarks 90
3.5 References 92
4 NUMERICAL ASSESSMENT OF THE BEHAVIOUR OF T-STUB CONNEC-
TIONS
4.1 Introduction 93
4.2 Previous research 94
4.3 Description of the model 96
4.4 Calibration of the finite element model 99
4.4.1 Geometry 100
4.4.2 Boundary and load conditions 101
4.4.3 Mechanical properties of steel components 102
4.4.4 Specimen discretization 102
4.4.5 Contact analysis 104
4.5 Failure criteria 104
4.6 Numerical results for HR T-stub T1 106
4.7 Numerical results for WP T-stub WT1 110
4.8 Considerations on the numerical modelling of the heat affected
zone in WP T-stubs
113
4.9 Concluding remarks 115
4.10 References 116
Appendix B: Preliminary study for calibration of the finite element
model (e.g. HR-T-stub T1)
119
B.1 Mesh convergence study 119
B.2 Influence of the definition of the constitutive law and element
formulation on the overall behaviour
121
B.3 Calibration of the joint element stiffness 121
Appendix C: Stress and strain numerical results for HR-T-stub T1 123
C.1 Load steps for stress and strain contours 123
C.2 Von Mises equivalent stresses, σeq 123
C.3 Stresses σxx and strains εxx 124
C.4 Stresses σyy 126
C.5 Stresses σzz 128
C.6 Principal stresses and strains, σ11 and ε11 128
C.7 Displacement results in xy cross-section 132
93

5 PARAMETRIC STUDY 135
5.1 Description of the specimens 135
5.2 Influence of the assembly type and the weld throat thickness 135
5.3 Influence of geometric parameters 147
5.3.1 Gauge of the bolts 149
5.3.2 Pitch of the bolts and end distance 149
5.3.3 Edge distance and flange thickness 151
5.4 Influence of the bolt and flange steel grade 158
5.5 Experimental results for the stiffened test specimens and the 169
rotated configurations
5.5.1 Influence of a transverse stiffener 169
5.5.2 Influence of the T-stub orientation 174
5.6 Summary of the parametric study and concluding remarks 175
5.7 References 178
6 SIMPLIFIED METHODOLOGIES FOR ASSESSMENT OF THE BEHAVIOUR
OF SINGLE T-STUB CONNECTIONS
6.1 Introduction 179
6.2 Previous research 179
6.2.1 Jaspart proposal (1991) 180
6.2.2 Faella and co-workers model (2000) 181
6.2.3 Swanson model (1999) 182
6.2.4 Beg and co-workers proposals for evaluation of
the deformation capacity (2002)
185
6.2.5 Examples 186
6.2.5.1 Evaluation of initial stiffness 186
6.2.5.2 Evaluation of plastic resistance 187
6.2.5.3 Piecewise multilinear approximation of the
overall response and evaluation of the
deformation capacity and ultimate resistance
187
6.2.5.4 Summary 193
6.3 Proposal and validation of a beam model for characterization
of the force-deformation response of T-stubs
194
6.3.1 Description of the model 194
6.3.1.1 Fracture conditions 196
6.3.1.2 Bolt deformation behaviour 196
6.3.1.3 Flange constitutive law 197
6.3.2 Analysis of the model in the elastic range 199
6.3.3 Analysis of the model in the elastoplastic range 204
6.3.4 Sophistication of the proposed method: modelling
of the bolt action as a distributed load
214
6.3.5 Influence of the distance m for the WP T-stubs 215
6.4 Concluding remarks 216
6.5 References 218
179

Appendix D: Detailed results obtained from application of the simplified
methods for assessment of the force-deformation response of
single T-stub connections
219
D.1 Geometrical and mechanical characteristics of the specimens 219
D.2 Previous research: exemplification 219
D.2.1 Evaluation of initial stiffness 219
D.2.2 Piecewise multilinear approximation of the overall
response and evaluation of the deformation capacity
and ultimate resistance
219
D.3 Application of the proposed model: results for HR-T-stub T1 235
D.4 Application of the proposed model: results for WP-T-stub
WT1
239
D.5 Prediction of the nonlinear response of the above connections
using the nominal stress-strain characteristics
241
D.6 Comparative graphs: simple beam model and sophisticated
beam model accounting for the bolt action
255
D.7 Comparative graphs: influence of the distance m for the WP-
T-stubs
264
PART III
MONOTONIC BEHAVIOUR OF BEAM-TO-COLUMN BOLTED END
PLATE CONNECTIONS
7 EXPERIMENTAL TESTS ON BOLTED END PLATE CONNECTIONS 275
7.1 Introduction 275
7.2 Description of the test programme 275
7.2.1 Test details 275
7.2.2 Geometrical properties 277
7.2.3 Mechanical properties 277
7.2.3.1 Tension tests on the bolts 277
7.2.3.2 Tension tests of the structural steel 278
7.2.4 Test arrangement and instrumentation 280
7.2.5 Testing procedure 284
7.3 Test results 284
7.3.1 Moment-rotation curves 288
7.3.2 Behaviour of the tension zone 294
7.3.2.1 End plate deformation behaviour 294
7.3.2.2 Yield line patterns 299
7.3.2.3 Bolt elongation behaviour 299
7.3.2.4 Strain behaviour 300
7.4 Discussion of test results 302
7.4.1 Plastic flexural resistance 303
7.4.2 Initial rotational stiffness 304
7.4.3 Rotation capacity 304
7.5 Concluding remarks 305
273

7.6 References 306
8 DUCTILITY OF BOLTED END PLATE CONNECTIONS 307
8.1 Introduction 307
8.2 Modelling of bolt row behaviour through equivalent T-stubs 310
8.3 Application to bolted extended end plate connections 310
8.3.1 Component characterization 310
8.3.2 Evaluation of the nonlinear moment-rotation response
318
8.3.3 Evaluation of the rotation capacity according to 326
other authors
8.3.4 Characterization of the joint ductility 328
8.4 Discussion 330
8.5 References 332
9 CONCLUSIONS AND RECOMMENDATIONS 333
9.1 Conclusions 333
9.2 Future research 336
9.3 References 338
LIST OF REFERENCES 339

ABSTRACT
The analysis of steel-framed building structures with full strength beam-tocolumn
joints is quite standard nowadays. Buildings utilizing such framing
systems are widely used in design practice. However, there is growing recognition
of significant benefits in designing joints as partial strength, semi-rigid.
The design of joints within this partial strength/semi-rigid approach is becoming
more and more popular. It requires however the knowledge of the full
nonlinear moment-rotation behaviour of the joint, which is also a design parameter.
Additionally, the joint failure must be ductile, i.e. the joint must have
sufficient rotation capacity as the first plastic hinges occur in the joints rather
than in the connected members. The research work reported in this thesis deals
with this issue and gives particular attention to the characterization of the joint
ductility, which is particularly important in the partial strength/semi-rigid joint
scenario.
The experimental and numerical results of sixty one individual T-stub tests
and eight full-scale bolted end plate connection tests are presented and assessed
based on their resistance, stiffness and ductility characteristics. The results
are used to compare existing resistance and stiffness models and to develop
a simple methodology for evaluation of ductility properties.
The T-stub model has been used for many years to model the tension zone
of bolted joints. Previous research was mainly concentrated on rolled profiles
as T-stub elements. In the case of end plate connections, the T-stub on the end
plate side comprises welded plates as T-stub elements. This research also provides
insight into the behaviour of this different type of assembly, in terms of
resistance, stiffness, deformation capacity and failure modes, in particular. It
also explores the main features of the individual T-stub as a standalone configuration
and evaluates quantitatively and qualitatively the influence of the
main geometrical and mechanical parameters on the overall behaviour.
A simplified two-dimensional beam model for the assessment of the deformation
response of individual T-stubs is developed based on the experimental
observations and the results of the finite element investigation. The model is
based on the Eurocode 3 approach and includes the deformations from tension
bolt elongation and bending of the T-stub flange. It is able to predict the deformation
capacity of a T-stub with a satisfactory degree of accuracy.
This study on individual T-stubs is part of the investigation of end plate
behaviour. The outcomes are used to validate a methodology based on the socalled
component model to determine the rotational behaviour of bolted end
plate connections. Since most of the joint rotation in thin end plates comes

from the end plate deformation, the characterization of bolt row behaviour
through equivalent T-stubs is of the utmost importance. A spring model that
includes the T-stub idealization of the tension zone is used to derive the
nonlinear moment-rotation of the joint. Special attention is given to the characterization
of the joint ductility. Comparisons of the joint ductility and the corresponding
equivalent T-stub for the end plate side are drawn. Finally, some
recommendations for the required ductility expressed in terms of a ductility
index are given.

RESUMO
O projecto de estruturas metálicas para edifícios porticados com ligações
viga-pilar de resistência total é relativamente comum. No entanto, tem-se
vindo a reconhecer os benefícios que decorrem da modelação semi-rígida e de
resistência parcial das ligações. Esta abordagem tem-se generalizado no
dimensionamento das ligações metálicas. Para o efeito, é necessário avaliar o
comportamento momento-rotação real das ligações. Adicionalmente, a rotura
das ligações tem de ser dúctil, isto é, as ligações têm de exibir capacidade de
rotação suficiente, uma vez que as primeiras rótulas plásticas se formam no nó
de ligação e não nos elementos (viga ou pilar). O trabalho de investigação
apresentado nesta tese foca este aspecto e dá ênfase à caracterização da
ductilidade das ligações, que é particularmente relevante na modelação semirígida/resistência
parcial.
Descrevem-se e discutem-se os resultados experimentais e numéricos de
sessenta e um testes em ligações em duplo T (T-stubs) individuais e oito
ligações viga-pilar aparafusadas com placa de extremidade. A análise destes
resultados inclui a caracterização das propriedades de resistência, rigidez e
ductilidade das ligações e a sua confrontação com modelos correntes de avaliação
de resistência e rigidez. Em termos de ductilidade, é proposta uma metodologia
simplificada para a caracterização desta propriedade das ligações.
O modelo do T-stub é utilizado na idealização da zona traccionada de
ligações aparafusadas. Os trabalhos de investigação anteriores centraram a
análise desta ligação mais simples em elementos que utilizam perfis laminados
a quente. No caso de ligações com placa de extremidade, os T-stubs equivalentes
na zona da placa englobam elementos soldados. Neste trabalho
procura-se descrever o comportamento deste tipo de T-stub, focando os modos
de rotura, a resistência, a rigidez e a ductilidade, em particular. Exploram-se
também as principais características do T-stub isolado e avalia-se
qualitativa e quantitativamente a influência dos principais parâmetros geométricos
e mecânicos no comportamento global.
Com base nos resultados experimentais e numéricos (elementos finitos)
propõe-se um modelo de viga bidimensional simplificado para caracterização
do comportamento força-deformação de T-stubs. O modelo baseia-se na
abordagem do Eurocódigo 3 e inclui a deformação do parafuso traccionado e
do banzo do T-stub em flexão e permite prever a capacidade de deformação
com um grau de precisão satisfatório.
Este estudo em T-stubs isolados constitui uma parte do trabalho de investigação
do comportamento da placa de extremidade. As conclusões deste es-

tudo são utilizadas na validação de uma metodologia baseada no método das
componentes para avaliação do comportamento rotacional de ligações aparafusadas
com placa de extremidade. Uma vez que a rotação da ligação provém
essencialmente da deformação da placa de extremidade, no caso de placas
finas, a idealização do seu comportamento por meio de T-stubs equivalentes
é particularmente relevante. Um modelo mecânico de molas e bielas rígidas
que inclui a idealização da zona traccionada por intermédio de T-stubs
é utilizado para a caracterização da resposta momento-rotação da ligação,
com particular ênfase na avaliação da sua ductilidade. Estabelecem-se comparações
entre a ductilidade da ligação e os correspondentes T-stubs equivalentes
na zona da placa de extremidade. Finalmente, são propostas algumas
recomendações para a ductilidade mínima da ligação, expressa em termos de
um índice de ductilidade.

NOTATION
Lower cases
a’ Effective edge distance according to the Kulak’s prying model
aep Throat thickness of a fillet weld at the end plate side
aw Throat thickness of a fillet weld
a Total displacements
b Width; actual width of a T-stub tributary to a bolt row
b’ Distance between the inside edge of the bolt shank to 50% distance
into profile root
beff Effective width; effective width of a T-stub tributary to a bolt row
for resistance calculations
b′ eff Effective width of a T-stub tributary to a bolt-row for stiffness
calculations
d Length between the bolt axis and the face of the T-stub web
dc Clear depth of the column web
dw Bolt head, nut or washer diameter, as appropriate
d0 Bolt hole clearance
e Edge distance
ecomp End plate distance
e1 End distance (from the centre of the bolt hole to the adjacent edge)
fu Ultimate or tensile stress
fy Yield stress
h Depth
hmrn Height of the resultant tension force above the neutral axis at
maximum strain
hr Distance of bolt row r to the centre of compression
hyfn Height of the flush bolt row above the neutral axis at yield
k Empirical factor
ke Initial axial stiffness of a spring-component
keff.r Effective stiffness coefficient for bolt row r
ki Auxiliary length values for definition of the bolt conventional
(i=1→4) length, according to Aggerskov
ki Joint element stiffness modulus (1: normal direction; 2,3: tangen-
(i=1→3) tial direction)
kp-l Post-limit axial stiffness of a spring-component
lHAZ Width of the heat affected zone
m Distance from bolt centre to 20% distance into profile root or weld
mf Average distance from each bolt to the adjacent web and flange
welds below the tension flange

mpl Plastic moment of a plate per unit length
n Effective edge distance; number of bolt rows in tension; ratio between
the axial force in the column and the corresponding plastic
level
nth Number of threads per unit length of the bolt
p Pitch of the bolts
pi-j Distance between bolt rows i and j
q Parameter
qb Uniformly distributed bolt action, statically equivalent to B
qee Initial prying gradient
qij,k Prying gradient
r Fillet radius of the flange-to-web connection
s Length
sp Length obtained by dispersion at 45º through the end plate
sx Ratio transverse stress/yield stress in the column web
t Thickness
u Degree-of-freedom
v Degree-of-freedom
w Horizontal distance between bolt axis centrelines (gauge); degreeof-freedom
x Cartesian axis; distance
xi Distance of the joint row to the tip of the flanges
y Cartesian axis
z Lever arm; cartesian axis
zi Distance between the ith bolt row to the centre of compression
z1 Distance in [mm] between the first bolt row from the tension
flange and the centre of compression
Upper cases
Ab Nominal area of the bolt shank
As Bolt tensile stress area
Avc Shear area of a column profile
B Bolt force
E Young modulus
Eh Strain hardening modulus
Eu Modulus of the stress-strain curve before collapse
F Force; resistance; load; applied load per bolt row in a T-stub
FQi Contact force associated to a joint row
FRd Full “plastic” (design) resistance
Fti Potential resistance of bolt row i in the tension zone
Fu Ultimate resistance
Fv Vertical forces
F 1. Rd .0 Ratio between the design resistance of mechanism type-1 accounting
for shear and that corresponding to the basic formulation
G Tangential modulus of elasticity
Height of the column below the end plate
Hc.low

Hc.up Height of the column above the end plate
I Moment of inertia
K Spring axial stiffness (generic)
Kb Bolt elastic stiffness according to the Swanson’s bolt model
Kcws.h Residual stiffness (Krawinkler et al. model for characterization of
the behaviour of the “column web in shear”)
K(flex) Stiffness for the flexible beam approach
K(rig) Stiffness for the rigid beam approach
L Length; cantilever length
Lb Bolt conventional length
*
L b
Clamping length of the bolts
Lbeam Length of the beam
Lcomp Length of the end plate below the compression beam flange
Lg Grip length
Linfluence.i Influence length of a joint row
Lload Distance between the load application point and the face of the
end plate
Ls Bolt shank length
Ltg Bolt threaded length included in the grip length
M Bending moment
Mj.Ed
Mj.Rd
N
Bending moment (lower than Mj.Rd) acting in the joint
Joint flexural plastic (design) resistance
Axial force
P Concentrated force
Q Prying force
R Norm of external forces
Sj.ini Initial rotational stiffness of a joint
S0 Bolt preload
V Shear force
Parameter
Zf
Greek letters
α Coefficient obtained from an abacus provided in Eurocode 3;
parameter that represents a ductility limit
αf Parameter
β Transformation parameter; ratio flexural resistance of flanges /axial
resistance of the bolts; parameter that represents a ductility limit
βa; βb Coefficients that account for the shear deformations
βu.lim Limit value for the β-ratio to have a collapse failure mode governed
by cracking of the flange material
χ Curvature
δ Relative displacement; elongation
δ(flex) Displacement of a flexible beam at mid-span
δ(rig) Displacement of a rigid beam at mid-span
Deformation capacity of half T-stub
δu

δ Non-dimensional displacement
δ a Norm of the iterative displacements
∆ Axial deformation; elongation
∆ a Total displacements for a certain increment
∆ FRd
Deformation corresponding to the component plastic resistance
∆u Deformation capacity
ε
ε
Strain; engineering strain; parameter
e
Elastic deformation (strain)
εh Strain at the strain hardening point
εhs Engineering strain at which the maximum engineering stress is
reached
εn
ε
Natural or logarithmic strain
p
Plastic deformation (strain)
εu Ultimate strain
εuni Uniform strain
ε0 Ultimate transverse strain acting in the column web in the case
that the axial force in the column is absent
φ Connection rotational deformation; bolt diameter
Φ Joint rotation
φCd Rotation capacity of a connection
ΦCd Rotation capacity of a joint
Φ Joint rotation at which the moment deteriorates back to Mj.Rd after
*
Cd
reaching a moment above Mj.Rd through deformation beyond ΦXd
φ Rotation of the connection at maximum load
M max
Φ Rotation of the joint at maximum load
M max
φXd
ΦXd
Connection rotation value at which the moment resistance first
reaches Mj.Rd
Joint rotation value at which the moment resistance first reaches
Mj.Rd
γ Shear deformation of the column web panel
γd Euclidean displacement norm
γdt Euclidean iterative displacement norm
Coefficients
γi
(i=1→3)
γM
Partial safety coefficients (γM0, γM1, γM2)
γw Work norm
γψ Euclidean residual norm
η Stiffness modification factor
ϕi Component ductility index
ϑj Joint ductility index
λ Ratio between n and m
λ Plate slenderness
p
κN
κwc
Parameter that reflects the influence of the level of axial force in
the column
Reduction factor to account for the effect of axial force in the col-

umn
µ Friction coefficient; ratio between characteristic strain values;
stiffness ratio
θ Rotation
ρ Reduction factor for plate buckling
ρy Yield ratio
*
ρ Alternative definition of the yield ratio
y
σ Stress; nominal or conventional stress
σeq Von Mises equivalent stress
σn True stress
σx Transverse stress acting in the column web
τ Shear stress
Γ Parameter
τy Yield shear stress
υ Poisson’s ratio
ω Reduction factor to allow for possible effects of interaction with
shear in the column web panel (ω 1, ω2: parameters for computation
of ω)
ξ Coefficient
ψ Norm of residuals
ψi Component ductility index
ζ Coefficient taken as 0.8 in Eurocode 3
Subscripts
av average
b Beam; bolt
bfc Beam web and flange in compression
bot Bottom T-stub
bt Bolts in tension
bwt Beam web in tension
c Column; compression
cfb Column flange in bending
cp Circular yield line patterns
cwc Column web in compression
cws Column web in shear
cwt Column web in tension
e/el Elastic
ep End plate
epb End plate in bending
f Flange
fract Fracture
h Bolt head; strain hardening
j Joint
l Lower T-stub element
m Strain hardening range and before collapse
max Maximum

min Minimum
n Bolt nut
nc Non-circular yield line patterns
p/pl Plastic
p-l Post-limit
red Reduced
ri Bolt row i
Rd Pure plastic conditions; design conditions
s Stiffener
t Tension
top Top T-stub
T T-stub element
u Ultimate conditions; upper T-stub element
w Web; weld
wp Web panel
wsh Washer
X Extension of the end plate above the tension beam flange
y Yield
0 T-stub component
1 Type-1 plastic failure mechanism of a T-stub; bolt row 1
11 Principal direction 1 for a stress state
2 Type-2 “plastic” failure mechanism of a T-stub; bolt row 2
3 Type-3 “plastic” failure mechanism of a T-stub; bolt row 3
* Supplementary plastic failure mechanism of a T-stub
Abbreviations
B Back (from eye position)
BF Basic formulation of resistance
BM Base metal
DTi Reference to a LVDT i
F Front (from eye position)
FBA Resistance formulation accounting for the bolt action
FE Finite element
FT Full-threaded bolt
HAZ Heat affected zone
HR Hot-rolled profile
L Left (from eye position)
LVDT Linear variable displacement transducer
K-R Knee-range of a deformability curve
R Right (from eye position)
SG Strain gauge
ST Short-threaded bolt
WM Weld metal
WP Welded plates
HP Reference to a specific LVDT

PART I: STATE-OF-THE-ART AND LITERATURE REVIEW
1

1 MODELLING OF THE MOMENT-ROTATION CHARACTER-
ISTICS OF BOLTED JOINTS: BACKGROUND REVIEW
1.1 GENERAL INTRODUCTION
Structural joints, particularly bolted and welded connections found in common
steel constructions, exhibit a distinctively nonlinear behaviour. This nonlinearity
arises because a joint is an assemblage of several components that interact
differently at distinct levels of applied loads. The interaction between the elemental
parts includes elastoplastic deformations, contact, slip and separation
phenomena. The analysis of this complex behaviour is usually approximate in
nature with drastic simplifications. Tests (both experimental and numerical) are
frequently carried out to obtain the actual response, which is then modelled approximately
by mathematical expressions that relate the main structural joint
properties.
Beam-to-column joints in steel-framed building structures have to transfer
the beam and floor loads to the columns. Generally, the forces transmitted
through the joints can be axial and shear forces, bending and torsion moments.
The bending deformations are predominant in most cases, when compared to
axial and shear deformations that are hence neglected. The effect of torsion is
also negligible in planar frames. Typical beam-to-column moment-resisting
joints in steel-framed structures include bolted end plate connections, bolted
connections with (flange and/or web) angle cleats and welded connections.
Their behaviour is represented by a moment vs. rotation curve (M-Φ) that describes
the relationship between the applied bending moment, M and the corresponding
rotation between the members, Φ. This curve defines three main
structural properties: (i) moment resistance, (ii) rotational stiffness and (iii) rotation
capacity. Historically, moment-resisting joints have been designed for
strength and stiffness with little regard to rotational capacity. There is growing
recognition that in many situations this practice is questionable and so guidance
is urged to help designers.
Joints can be grouped according to their structural properties. The European
code of practice for the design of structural steel joints in buildings, Eurocode 3
[1.1], classifies joints by strength (full strength, partial strength or nominally
pinned) and stiffness (rigid, semi-rigid or nominally pinned). A full strength
joint exhibits a moment resistance at least equal to that of the connected members
whilst partial strength joints have lower strength than the members. Nominally
pinned joints are sufficiently flexible to be regarded as a pin for analysis
purposes, i.e. they are not moment resisting and have no rotational stiffness. A
rigid joint is stiff enough for the effect of its deformation on the distribution of
3

State-of-the-art and literature review
internal forces and bending moments in the structure to be neglected. A semirigid
joint does not meet the criteria for a rigid joint or a pin. Naturally, nominally
pinned joints have to be ductile, i.e. they have to rotate plastically at some
stage of the loading cycle without failure. The semi-rigid/partial strength design
philosophy of joints usually leads to more economic and simple solutions.
The use of this joint category in steel frames, however, is only feasible if they
develop sufficient rotation capacity in order that the intended failure mechanism
of the whole structure can be formed prior to fracture of the joint.
End plate bolted connections that are widely used in steel-frames as moment-resistant
connections between steel members usually fall in the semirigid/partial
strength category. The simplicity and economy associated to their
fabrication and erection made this joint typology quite popular in steel-framed
structures. In Europe, steel bolted partial strength extended end plate connections
are typical for low-rise buildings erected using welding at the shop and
bolting on site. Rules for prediction of strength and stiffness of this joint configuration
have been included in modern design codes as the Eurocode 3. Yet,
no quantitative guidance for characterization of the ductility is available.
The main topics of this research work are moment-resisting bolted (major
axis) connections joining I-sections in steel-framed structures and the characterization
of their rotational behaviour. Special emphasis is given on extended
end plate connections similar to that shown in Fig. 1.1. The main source of deformability
of this connection type is often the tension zone that can be modelled
with the T-stub approach [1.1-1.5]. The evaluation of the deformation behaviour
of single T-stubs is therefore very important and is also focused on in
this work.
(a) Three-dimensional view. (b) Section. (c) Elevation.
Fig. 1.1 Unstiffened bolted end plate connection.
1.1.1 Literature review
Bolted end plate beam-to-column steel connections have been widely studied
over the years. The emphasis in most of the previous research on this subject
4

Modelling of the M-Φ characteristics of bolted joints: background review
was mainly placed on full strength end plate connections and therefore only the
resistance and stiffness properties were fully characterized. Thoroughly conducted
experimental tests were carried out for prediction of the M-Φ curve.
However, the information extracted from those experiments was limited to the
joint typology that had been tested and could not be extrapolated to other joint
configurations. Analytical methodologies based on finite element (FE) analyses
can be regarded as an alternative tool for investigation and understanding of
joint behaviour, provided that the requirements for a reliable simulation are totally
fulfilled. Many researchers used both approaches in conjunction.
Douty and McGuire [1.6] conducted monotonic experimental tests on end
plate connections to study their performance, design and use in plastically designed
structures. They identified the effect of prying action in increasing the
tension bolt force and recognized the importance of material strain hardening.
The effect of prying action was further investigated by Aggerskov [1.4,1.7]
who carried out a series of fifteen tests on extended end plates.
Zoetemeijer [1.2,1.8-1.10] reported on detailed series of tests performed at
the Delft University of Technology to propose and validate yield line models
for the strength design of the tension region. This zone of end plate connections
includes the following basic elemental parts: column flange, end plate and the
bolts in tension. Zoetemeijer also proposed some criteria and simple empirical
expressions for the estimation of a joint deformation capacity based on a series
of experiments described in [1.10]. Packer and Morris [1.3] and Mann and
Morris [1.11] focused on this subject too. Similar to Zoetemeijer, they also idealized
the tension region as a T-stub. Fig. 1.2 identifies the T-stub which accounts
for the deformation of the column flange and the end plate in bending in
the particular case of an extended end plate bolted connection. In this particular
case, since the column flange is unstiffened, the T-stub on the column side is
orientated at right angles to the end plate T-stub [1.5]. Different investigators
also carried out various studies focusing on mechanisms in T-stubs rather than
whole plates, particularly to assess the resistance properties of this simple connection
[1.5,1.12-1.15].
Jenkins et al. [1.16] contributed to a better understanding of end plate behaviour
and proposed standardized end plate connection types to permit a generalization
of joint characteristics obtained from numerical modelling. They
performed FE analysis to determine the complete M-Φ curve of some joints
that was compared with experimental results. This experimental programme
included eighteen tests. The principal objective of the programme was to obtain
M-Φ relationships but they also directed attention at other features as the
evaluation of the axial forces in the bolts.
The characterization of the initial rotational stiffness of beam-to-column
joints was the main research topic of Davison et al. [1.17] who did various tests
on end plate connections with different thickness and identical beam and column
sizes. The researchers also investigated the effect of lack of fit [1.18] and
concluded that it was negligible.
5

State-of-the-art and literature review
6
Equivalent
T-stub
M
T-stub
T-stub
(a) Unstiffened extended end plate connection: T-stub identification and orientation.
External load
External load
Stiffener
Weld toe
External load
External load
(b) Model for the column flange side. (c) Model for the end plate side.
Fig. 1.2 T-stub identification and representation.
Janss and co-workers [1.19] completed a series of tests that were later used
by Jaspart [1.20] to propose a methodology for evaluation of plastic resistance
and initial rotational stiffness of moment joints.
Aggarwal [1.21] and Bose et al. [1.22] carried out comparative tests on end
plate connections for which they characterized the moment carrying behaviour.
In particular, Bose et al. [1.22] described the observed failure modes that involved
end plate failure, bolt fracture, bolt stripping, weld fracture and column
web buckling. They used these test results to validate finite element models for
the analysis of this joint type. In their tests, most of the specimens were full
strength joints but they also tested partial strength joints.
More recently, Adegoke and Kemp [1.23] reported on three tests on thin
end plate partial strength joints that use a similar column/beam set and different
plate thickness. These tests provide insight into the joint resistance and ductility
properties. The observed failure modes included failure of the end plate and
bolt, development of cracks in the end plate along the weld to the beam web in
the tension zone that led to fracture of the end plate in the thinner plates [1.23].
Fracture of the bolt in tension below the tension flange determined collapse for

Modelling of the M-Φ characteristics of bolted joints: background review
the thicker plate [1.23]. The test results were compared with a bilinear M-Φ relationship
proposed by the authors. They also identified the influence of the
plate thickness on the membrane effect and material strain hardening.
Amongst those researchers focusing exclusively on the end plate behaviour,
Zandonini and Zanon [1.24] performed five static tests on extended end plate
connections with four bolts in tension and different plate thickness. In order to
isolate the end plate behaviour, the specimens were connected to a counter
beam with minor deformability. The moment capacity of the connection in all
tests was greater than the plastic moment of the beam. Bursi [1.25] used these
test results to evaluate the plastic failure moment capacity of the tested connections
by means of numerical modelling. He compared the yield line paths and
failure mechanism models defined numerically with experimental evidence and
found a good agreement between both.
The numerical simulation of bolted connections also represents a significant
part of the research work devoted to end plate behaviour. Krishnamurthy and
co-workers [1.26-1.28] carried out a comprehensive research programme to investigate
the rotational response of this joint type by means of FE analyses.
The objective of their research was the development of rotational design criteria
applicable to end plate connections. They performed three-dimensional FE
analyses on bolted connections and correlated the results to previous twodimensional
analyses to enable the prediction of the more accurate threedimensional
values from the less expensive two-dimensional results. Having
validated the computer analyses, they proposed equations to predict the general
rotational behaviour. However, they overlooked some important phenomena as
the flexibility of the column flange, bolt head and nut, or plasticity of the material.
Kukreti and collaborators [1.29-1.31] focused on a similar topic. They developed
an analytical methodology based on FE results to characterize the M-Φ
behaviour of this joint type. Experimental tests were also carried out to verify
the methodology. Bahaari and Sherbourne [1.32-1.36] did a series of FE analyses
to propose analytical expressions for the design of end plate connections. In
their models they considered all major influences on the overall response, including
column, beam, bolt components, material plasticity, strain hardening
and contact phenomena. Bursi and Jaspart [1.37-1.38] gave some recommendations
on FE modelling of end plate behaviour. Choi and Chung [1.39] developed
a refined three-dimensional FE model for the detailed investigation of the
behaviour of end plate connections. Their model accounted for different types
of nonlinearities, such as elastoplasticity and contact. They made a thorough
description of the contact regions of the joints with increasing loading.
1.1.2 Scope of the work, objectives and research approach
The research work reported herein focuses on the characterization of the rotational
behaviour of bolted beam-to-column joints with an extended end plate,
7

State-of-the-art and literature review
similar to that shown in Fig. 1.1. In this joint type, the main source of deformability
is the tension zone that can be idealized by means of equivalent T-stubs,
which correspond to two T-shaped elements connected through the flanges by
means of one or more bolt rows. This idealization is also adopted in modern
design codes, as the Eurocode 3. The models for the column and the end plate
sides are different. The T-stub elements on the column flange side are generally
hot rolled profiles, whilst on the end plate side such elements comprise two
welded plates, the end plate and the beam flange, and a further additional stiffener
that corresponds to the beam web (Fig. 1.2c). The first model (HR-T-stub)
has been extensively studied over the past years and was the aim of several research
programmes that are reported in technical literature. The current approach
to account for the behaviour of T-stubs made up of welded plates (WP-
T-stub) consists in a mere extrapolation of the existing rules for the other assembly
type. This assumption can be erroneous and can lead to unsafe estimations
of the characteristic properties. To deal with this problem, a research project
was devised to increase the knowledge and understanding of end plate behaviour
and contribute towards the improvement of its design.
Simultaneously, the issue of available ductility is also addressed in this
work. The knowledge of the plastic rotation capacity of beams is particularly
important in the case of full strength beam-to-column joints, because yielding
occurs at the member ends. In the case of partial strength joints, there is significant
yielding of the connection and the evaluation of its ductility becomes
crucial. The ductility of a joint reflects the length of the yield plateau of the M-
Φ response and is intrinsically linked to the rotational capacity of the joint.
The research described in this dissertation is divided into experimental,
numerical (FE modelling) and analytical works. Reliable test results are essential
and support the validity of analytical and numerical work. Numerical
analyses are important as they provide a means of carrying out wide-ranging
parametric studies to complement existing experimental results. Analytical
work allows the development of relatively simple design models that can be
used in practice.
The experimental programme was conducted at the Delft University of
Technology and included the (monotonic) testing of thirty-two individual Tstub
connections made up of welded plates and eight full-scale single sided
beam-to-column joints. The primary intent of the first series of tests on isolated
T-stubs was to provide insight into the actual behaviour of this type of connection,
failure modes and deformation capacity. The parameters affecting the deformation
response of bolted T-stubs were identified and their influence on the
overall behaviour of the connection was qualitatively and quantitatively assessed.
In addition, the role of the welding and the presence of transverse stiffeners
were tackled. For the follow up study on extended end plate connections,
the main objective was the analysis of the ultimate behaviour of the assembly
end plate in bending-bolts and eventually the proposal of sound design rules for
this elemental part within the framework of the so-called component method
[1.1,1.40].
8

Modelling of the M-Φ characteristics of bolted joints: background review
The numerical part of the work included the assessment of the loadcarrying
behaviour of single T-stubs and the exploration of other model features,
namely the prying effect and the variation of contact flange surfaces
within the course of loading. In this context, two T-stub connections representative
of HR- and WP-T-stubs were modelled and calibrated against experimental
results. Having validated a three-dimensional FE model for the individual
T-stubs, a parametric study was conducted in order to provide a better understanding
of the overall behaviour and to evaluate the influence of the main
parameters on the connection deformability.
The analytical approach of the research involved:
(i) The proposal of a simplified beam model for the characterization of the T-stub
response. With this simplification some information and features of the T-stub
model may be lost. However, this methodology overcomes the complexity of
the above approaches and is less time-consuming.
(ii) The assessment of the global M-Φ response of an end plate connection based
on the component method. A software tool developed at the University of
Coimbra [1.41] was used for this assessment. The outcomes were validated
through comparison with experimental evidence.
1.1.3 Outline of the dissertation
The dissertation is divided into three parts.
Part 1 (Chapter 1) presents background material on extended end plate connections.
References to previous research work on the characterization of the
rotational behaviour of this joint type are made. Special emphasis is given to
the component method for the evaluation of the M-Φ response.
Part 2 contains five chapters and includes further developments on the Tstub
model. Chapter 2 is a brief introduction. Chapter 3 describes the experimental
programme on isolated T-stub connections made up of welded plates.
Chapter 4 includes the numerical evaluation of the force-deformation (F-∆) response
of T-stubs. A three-dimensional FE model is recommended for that
purpose. In both chapters, detailed results are given for benchmark specimens
and the approaches are validated. A parametric study is described in Chapter 5.
It provides insight into the main behavioural features of T-stub connections and
highlights the parameters that affect their deformability. A two-dimensional
simplified model that provides analytical solutions for the F-∆ response is proposed
in Chapter 6. Because ductility is such an important characteristic of
connection performance, this chapter emphasises the evaluation of deformation
capacity of isolated T-stubs.
Part 3 contains Chapters 7 and 8. Chapter 7 is entirely dedicated to the experiments
on extended end plates connections. All the test details are provided
and the results are thoroughly analysed. Chapter 8 presents a ductility analysis
where the experimental results for the overall end plate connection are con-
9

State-of-the-art and literature review
fronted with the component tests. For that purpose, a procedure based on the
component methodology is recommended. Comparisons with other proposals
from the literature are also drawn.
Finally, conclusions and recommendations are summarized in Chapter 9.
1.2 DEFINITIONS
Beam-to-column joints consist of a web panel and one or two connections (single-
or double-sided joint configuration) – Fig. 1.3. The web panel zone includes
the column web and the flange(s) of the column for the height of the
connected beam profile(s). The connection is the location where two members
are interconnected and the means of interconnection, i.e. the set of physical
components that mechanically fasten the connected elements.
The behaviour of a steel beam-to-column joint is represented by a M-Φ
curve, as already explained. The rotational deformation of a joint, Φ, results
from the in-plane bending, M, and is the sum of the shear deformation of the
column web panel zone, γ, and the connection deformation, φ. The deformation
of the connection includes the deformation of the fastening elements (bolts, end
plate, etc.) and the load-introduction deformation of the column web. It results
in a relative rotation between the beam and column axes, θb and θc, which is
equal to:
φ = θb − θc
(1.1)
according to Fig 1.4, and provides a flexural deformability curve M-φ. This deformability
is only due to the couple of forces Fb transferred by the flanges of
the beam that are statically equivalent to the bending moment M acting on the
beam. In this figure, z is the lever arm.
The shear deformation of the column web panel is associated with the force
Vwp acting in this panel and leads to a relative rotation γ between the beam and
column axes. A shear deformability curve Vwp-γ may then be established. For a
Joint
Fig. 1.3 Parts of a beam-to-column joint (single-sided configuration).
10
Web panel
Connection

Modelling of the M-Φ characteristics of bolted joints: background review
single-sided joint configuration (see Fig. 1.5), the shear action in the panel is
related to the internal actions on the joint as follows:
M ⎡ z ⎤ M
Vwp = ⎢1+ ( Vc1 + Vc2)
= β
2
⎥
(1.2)
z ⎣ M ⎦ z
The transformation parameter β relates the web panel shear force, Vwp, with the
internal actions. Conservative values for the transformation parameter β, neglecting
the effect of the shear force in the column, are suggested in Eurocode
3: (i) β = 1, in the case of single-sided joints, (ii) β = 2, in the case of doublesided
joints with equal but unbalanced end bending moments and (iii) β = 0, in
the case of double-sided joints with balanced end bending moments.
The global M-Φ response of the joint is obtained by summing the contribu-
θc
Fig. 1.4 Sources of connection deformability.
Mc1
Nc2
Nc1
Vc2
Mc2
Vc1
θb
Fb
Fb
Vb
M
z
Nb Mb = M
Fig. 1.5 Internal forces acting on the joint (single-sided configuration).
11

State-of-the-art and literature review
tions of rotation of the connection (φ) and of the shear panel (γ), as illustrated
in Fig. 1.6. The M-γ curve is obtained from the Vwp-γ by means of the transformation
parameter β.
M
φi φ
γi γ
Fig. 1.6 Global moment-rotation response of a joint.
12
Mi
+
M
Mi
=
M
Mi
Φi (= φi + γi)
1.3 METHODS FOR MODELLING THE ROTATIONAL BEHAVIOUR OF BEAM-
TO-COLUMN JOINTS
1.3.1 Generality
The characterization of the M-Φ curve can be ascertained by experimental testing
or mathematical models based on the geometrical and mechanical properties
of the joint. Full-scale experimental tests are naturally the most reliable
method of description of the rotational behaviour of structural joints. However,
they are time consuming, expensive and cannot certainly be regarded as a design
tool. In addition, the data gathered from tests of prototype joints are few
and generally limited to displacement and surface measurements, as strain
measurements, for instance. Therefore the results cannot be extended to different
joint configurations. Nonetheless, tests provide accurate information on the
joint response that is used to validate mathematical models of prediction of the
M-Φ curve. Mathematical models for representation of the curve include: (i)
curve fitting to test results by regression analysis, (ii) simplified analytical
models, (iii) mechanical models that take into account the various sources of
joint deformability and (iv) numerical models. For a review of different methods,
the reader should refer to Nethercot and Zandonini [1.42].
Mechanical models are the most effective solution for an accurate description
of the complex nature of bolted joint behaviour. These models use a set of
rigid and flexible elements to simulate the overall joint. The interplay between
these elements results in different mechanical models, as explained below.
1.3.2 The component method
Current design practice adopts the so-called component method for the prediction
of the rotational behaviour of beam-to-column joints. For the purposes of
Φ

Modelling of the M-Φ characteristics of bolted joints: background review
simplicity, any joint can be subdivided into three different zones: tension,
compression and shear. Within each zone, several sources of deformability can
be identified, which are simple elemental parts (or “components”) that contribute
to the overall response of the joint. From a theoretical point of view, this
methodology can be applied to any joint configuration and loading conditions
provided that the basic components are properly characterized. Essentially, the
method comprises three basic steps: (i) identification of the active components
for a given structural joint, (ii) characterization of the individual component F-
∆ response and (iii) assembly of those elements into a mechanical model made
up of extensional springs and rigid links. This spring assembly is treated as a
structure, whose F-∆ behaviour is used to generate the M-Φ curve of the full
joint.
The method is illustrated in Fig. 1.7 for the particular case of a bolted extended
end plate connection (with two bolt rows in tension). For the computation
of the joint rotational stiffness, the active joint components for this configuration,
according to Eurocode 3, are: column web in shear (cws), column
web in compression (cwc), column web in tension (cwt), column flange in
bending (cfb), end plate in bending (epb), and bolts in tension (bt). The welds
connecting the end plate and the beam are not taken into account for computation
of the rotational stiffness, as well as components beam web and flange in
compression (bfc) and beam web in tension (bwt). Each component is characterized
by a nonlinear F-∆ response, which can be obtained by means of experimental
tests or analytical models. These individual components are assembled
into a mechanical model in order to evaluate the M-Φ response of the
whole joint. The Eurocode 3 spring model is represented in Fig. 1.7 [1.40]. Alternative
spring and rigid link models are proposed in literature, as the “Innsbruck
model” proposed by Huber and Tschemmernegg [1.43]. Essentially, they
share the same basic components but assume different component interplay.
M
(cws)
(cwc)
(cwt.1) (cfb.1) (epb.1) (bt.1)
(cwt.2) (cfb.2) (epb.2) (bt.2)
Fig. 1.7 Component method: active components and mechanical model adopted
by Eurocode 3 for characterization of the joint rotational stiffness.
Φ
M
13

State-of-the-art and literature review
1.4 CHARACTERIZATION OF BASIC COMPONENTS OF BOLTED JOINTS IN
TERMS OF PLASTIC RESISTANCE AND INITIAL STIFFNESS
Within the framework of the component method, the basic joint components
are modelled by means of nonlinear extensional springs (Fig. 1.8a; K: spring
axial stiffness). This complex behaviour can be approximated with simple relationships
without significant loss of accuracy. The elastic-perfectly plastic response
is one of the simplest possible idealizations. Following the Eurocode 3
approach for idealization of the flexural joint spring nonlinear behaviour, this
response is characterized by a secant stiffness, ke/η, and a full plastic resistance,
FRd (Fig. 1.8b). ke is the initial stiffness of the component and η is a
stiffness modification coefficient. Eurocode 3 defines this coefficient for different
types of connections. For a single component, similar values can be
adopted. The post-limit stiffness, kp-l is taken as zero, which means that strain
hardening and geometric nonlinear effects are neglected. Regarding the component
ductility, i.e. the extension of the plastic plateau, the code [1.1] presents
some qualitative principles that are however insufficient. For instance, the
component column web in shear has very high ductility and therefore the deformation
capacity is taken as infinite; on the other hand, the bolts in tension
are brittle components with no plastic plateau.
The following sections present the formulations adopted in Eurocode 3 for
prediction of the plastic resistance and initial stiffness of the basic components
of bolted joints. Particular attention is devoted to the T-stub model that is used
to idealize the tension zone of this joint typology. Then, the remaining components
are briefly analysed.
F
(a) Extensional spring representing a generic component.
F
14
FRd
ke/η
K
∆
(b) Actual behaviour and elastic-plastic response.
Fig. 1.8 Modelling of a component subjected to compression.
∆
Actual behaviour
Elastic-plastic approximation

Modelling of the M-Φ characteristics of bolted joints: background review
1.4.1 T-stub model for characterization of the tension zone of bolted joints
The equivalent T-stub corresponds to two T-shaped elements connected
through the flanges by means of one or more bolt rows as depicted in Fig. 1.9.
The main behavioural aspects of the T-stub as a standalone configuration have
been widely investigated over the past thirty years, both experimentally and
theoretically. As a result, the structural response of this kind of connection is
thoroughly known in elastic and plastic ranges, and appropriate design rules for
prediction of the elastic-plastic F-∆ curve have been assessed.
e
Transverse view
Fig. 1.9 Equivalent T-stub (one bolt row).
w
bf
e
e1
b
0.5p
1.4.1.1 Plastic resistance of single T-stub connections
Lateral view
Plan
The evaluation of the plastic (design) resistance of bolted T-stub connections is
based on the well-known yield line principle. The works of Zoetemeijer [1.2],
Packer and Morris [1.3] and Mann and Morris [1.11] form the basis of the procedure
presented below. Zoetemeijer suggests that the determination of the
plastic resistance of such a connection type is based on the plastic behaviour of
15

State-of-the-art and literature review
the flanges and the bolts, and assumes that the yielding is large enough to allow
the adoption of the most favourable static equilibrium [1.2]. For the purposes
of simplicity, consider a bolted T-stub with one bolt row only. This simple connection
can fail according to three possible “plastic” collapse mechanisms, as
illustrated in Fig. 1.10. Type-1 mechanism is characterized by the formation of
four plastic hinges: two hinges are located at the bolt axes, due to the bending
moment caused by the prying forces, Q and the other two hinges are located at
the flange-to-web connection. The formation of two plastic hinges at the
flange-to-web connection and the failure of the bolts typify type-2 mechanism.
The third collapse mechanism involves bolt failure only. A fourth supplementary
mechanism corresponds to the metal shear tearing around the bolt head or
washer but is not relevant in most cases. The resistance corresponding to each
collapse mechanism is easily computed by establishing the equilibrium equations
in the plastic conditions (cf. Appendix A). The plastic (design) resistance
of the T-stub, FRd.0, corresponds to the smallest value among the examined
“plastic” modes, i.e. FRd.0 = min (F1.Rd.0, F2.Rd.0, F3.Rd.0), where:
4M f . Rd
F1.
Rd .0
=
m
(1.3)
2M f. Rd+ 2BRdn 2M f . Rd⎡ ( 2 − β Rd ) λ ⎤
F2.
Rd .0 = = ⎢1+ ⎥
m+ n m ⎢⎣ βRd ( 1+
λ ) ⎥⎦
(1.4)
F3. Rd.0 = 2BRd
(1.5)
The plastic flexural resistance of the T-flanges, Mf.Rd, is given by:
2
t f
M f . Rd= 4
fy. fbeff (1.6)
where beff is the effective width tributary to one bolt row, tf is the flange thick-
Q
16
B
F1.Rd.0
B
n m m n
(a) Type-1:
⎛ 2λ
⎞
⎜βRd ≤ ⎟
⎝ 2λ+ 1⎠
.
Q
b
(=F1.Rd.0/2+Q)
Mf.Rd
Mf.Rd
Q
BRd
F2.Rd.0
n m m n
BRd
Q
(b) Type-2 (ξ ≤ 1.0):
⎛ 2λ
⎞
⎜ < βRd
≤ 2⎟
⎝2λ+ 1 ⎠ .
b
Mf.Rd
ξMf.Rd
Fig. 1.10 “Plastic” collapse mechanisms of bolted T-stubs.
BRd
F3.Rd.0
n m m n
BRd
b
ξMf.Rd
(c) Type-3 (ξ ≤ 1.0):
β > 2 .
( )
Rd

Modelling of the M-Φ characteristics of bolted joints: background review
ness and fy.f is the yield stress of the flanges. The length m represents the distance
between the bolt axis and the section corresponding to the plastic hinge at
the flange-to-web connection. According to Eurocode 3, m= d − ζ s,
where d
represents the length between the bolt axis and the face of the T-stub element
web, ζ is a coefficient taken as 0.8 and s = r or s = 2aw , for hot rolled profiles
or welded plates as T-stub, respectively; r is the fillet radius of the flangeto-web
connection and aw is the throat thickness of the fillet weld. The geometrical
parameter λ is defined as the ratio n/m, being n the effective edge distance.
In Eurocode 3, n is taken as the minimum value of e (distance between
the bolt axis and the tip of the flanges) and 1.25m, i.e. n = min (e,1.25m). BRd is
the “plastic” (design) resistance of a single bolt in tension.
The β-ratio is the relation between the flexural resistance of the flanges and
the axial resistance of the bolts and governs the occurrence of a given (“plastic”)
collapse mode (Fig. 1.11). At plastic conditions, this parameter, βRd, is the
ratio between the plastic resistances corresponding to type-1 mechanism and
that corresponding to a type-3 mechanism:
2M f. Rd
β Rd = (1.7)
BRd m
The basic formulations presented above do not cater for the influence of the
moment-shear interaction on the resistance of bolted T-stubs that can lead to a
decrease in the plastic resistance. Faella et al. [1.44] assume that such interaction
can be taken into account under the Von Mises yield criterion. Analytical
expressions for type-1 and type-2 mechanisms allowing for moment-shear interaction
are derived in Appendix A and are reproduced below:
F
2
8⎛m⎞ ⎡ 3 ⎤ M
= ⎜ 1+ −1
⎜
⎟
t ⎟ ⎢ ⎥
⎝ ⎠ ⎢ ( mtf
) ⎥ m
⎣ ⎦
1. Rd .0 2
3 f
F
2B
Rd
1
2λ
2λ+ 1
Type-1
2λ
2λ+ 1
Type-2
f. Rd
1 2
Non-circular yield line patterns
Circular yield line patterns
Type-3
βRd
(1.8)
Fig. 1.11 Influence of βRd on the “plastic” collapse mechanism of bolted T-stubs.
17

State-of-the-art and literature review
and:
2
16 ⎛m⎞ ⎡ ⎤
3 2λβRd + 1 M f. Rd
F2.
Rd .0 = ⎜ ⎟ ( 1+ λ ) ⎢ 1+ −1⎥
(1.9)
2 2
3 ⎜t ⎟ ⎢
f
4 ( mtf
) ( 1+
λ ) ⎥
⎝ ⎠ m
⎢⎣ ⎥⎦
Naturally, the “plastic” resistance for mechanism type-3 is not affected by this
interaction.
Regarding mechanism type-1, a significant increase in resistance can be expected
due to the influence of the bolt action on a finite contact area. Jaspart
[1.20] suggests an alternative formulation to cater for this effect (Appendix A):
( 32n−2dw) M f . Rd 32λm−2d M w f . Rd
F1.
Rd .0 = =
(1.10)
8mn − dw( m + n) 8λm− dw( 1+
λ)
m
whereby dw is the bolt head, nut or washer diameter, as appropriate.
By combining both effects for type-1 mechanism, the plastic resistance can
be expressed as:
18
2
16 ⎛ m ⎞
F1.
Rd .0 = ⎜
3 ⎜
⎟
t ⎟
⎝ f ⎠
⎡
Γ ⎢
⎢
⎣
3
1+ 2
2
4Γ
( mtf
)
⎤ M
−1⎥
⎥ m
⎦
λm
8 − ( 1+
λ )
dw
Γ=
λm
16 −1
d
w
f. Rd
(1.11)
(1.12)
as derived in Appendix A.
The effective width of the T-element flange, beff, that appears explicitly in
the above formulae is a notional width and does not necessarily represent any
physical length of the flange. beff represents the width of the flange plate that
contributes to load transmission. Zoetmeijer has successfully introduced this
concept in [1.2]. It accounts for all possible yield line mechanisms of the Tstub
flange and cannot exceed the actual flange width. This effective length has
to be defined by establishing the equivalence, in the plastic collapse condition,
between the beam model and the actual plate behaviour where collapse occurs
due to the development of a yield line mechanism [1.44].
In the case of a bolted T-stub with one bolt row, three possible yield line
mechanisms are considered: (i) circular pattern (Fig. 1.12a): beff.1 = 2πm, (ii)
non-circular pattern (Fig. 1.12b): beff.2 = 4m + 1.25e and (iii) beam pattern (Fig.
1.12c): beff.3 = b.
Regarding the circular pattern, beff is determined from the equivalence between
the failure load that corresponds to the collapse mechanism of a simply
supported plate (P = 2πmpl, mpl = tf 2 fy/4) and that of the equivalent beam model.
By equating both relationships, the following expression is determined for beff.1:
2
t f 4m1 beff .1 = 2πfy= 2πm
(1.13)
2
4 t f
f
y

Modelling of the M-Φ characteristics of bolted joints: background review
(a) Circular pattern. (b) Non-circular pattern. (c) Beam pattern.
Fig. 1.12 Yield line mechanisms of bolted T-stubs with one bolt row.
(a) Circular pattern. (b) Non-circular pattern. (c) Beam pattern.
(d) “Circular” pattern. (e) “Non-circular” pattern.
Fig. 1.13 Yield line mechanisms of bolted T-stubs with two bolt rows.
Referring now to the non-circular pattern, Zoetemeijer provides a simplified
expression for the evaluation of the effective width associated to this mechanism
[1.2]. For the beam pattern, the computation of this length is quite
straightforward. The effective width of the equivalent T-stub corresponds to
the smallest value of the above, i.e., beff = min (beff.1, beff.2, beff.3).
Now, consider the case of multiple bolt rows. Depending on the pitch of the
bolts, p, they may behave as a single bolt row or as a bolt group. For the particular
case of two bolt rows illustrated in Fig. 1.13, the behaviour is such of a
group in cases c, d and e and of an individual bolt in the remaining. The effective
width of each bolt row is taken as the minimum among the five cases: (i)
individual bolt (Fig. 1.13a): beff.1 = 2πm, (ii) individual bolt (Fig. 1.13b): beff.2 =
4m + 1.25e, (iii) bolt group (Fig. 1.13c): beff.3 = b, (iv) bolt group, (Fig. 1.13d):
beff.4 = πm + 0.5p and (v) bolt group (Fig. 1.13e): beff.5 = 2m + 0.625e + 0.5p.
Again, beff = min (beff.1, beff.2, beff.3, beff.4, beff.5).
1.4.1.2 Initial stiffness of single T-stub connections
The evaluation of the initial stiffness of a T-stub, ke.0, is based on the analysis
19

State-of-the-art and literature review
of the elastic response of the connection, which has been analysed for the first
time by Aggerskov [1.7] and later by Holmes and Martin [1.45] to accommodate
the effect of the prying forces on the bolt behaviour. Yee and Melchers
[1.5] adopted a similar procedure for the evaluation of the elastic deformation
of this type of connection. The single T-stub element is modelled as a simply
supported beam, the supports corresponding to the location of the prying
forces. This system is loaded by a concentrated force applied at the mid-span
section, equivalent to the force applied on the T-stub through the web and the
bolt force acting at the bolt axes (Fig. 1.14). The analysis of the T-stub is carried
out by taking the interaction of the two T-stub elements and the bolts into
consideration as well as the compatibility requirements to cater for the bolt deformation.
Jaspart [1.20] applies the same approach with a slight modification
concerning the position of the prying forces. This location depends on the relative
stiffness of the flange and the bolts, i.e. the flange cross-section dimensions
and the bolt diameter, as well as the degree of bolt preloading. Yee and
Melchers [1.5] assume that the prying forces are located at the edge of the
flange (n = e ≤ 1.25m). Jaspart [1.20] uses the distribution proposed by Douty
and McGuire [1.6] (n = 0.75e ≤ 0.75×1.25m = 0.9375m).
The elastic deformation of the bolted T-stub is determined from the following
expressions (subscripts u and l refer to the upper and lower T-stub element,
respectively):
Z fu . / l⎡1 qu/
l⎛3
3 ⎞⎤
∆ e.0. u/ l = α f . u/ l 2α
f . u/ l F
E
⎢ − ⎜ − ⎟
4 2 2
⎥
(1.14)
⎣ ⎝ ⎠⎦
E is the Young modulus of steel. The other parameters that appear explicitly in
the above expression are defined as follows:
3
21.5 ( α f − 2α
f ) Z f
q =
(1.15)
2 3 Lb
26 ( α f − 8α
f ) Z f +
2A
Z
f
20
( ) 3
m+ n
⎡2⎤ =
⎣ ⎦
b′ t
3
eff f
s
(1.16)
n
α f =
(1.17)
2(
m+ n)
b′ eff is the effective width for stiffness calculations, computed per bolt row. As
is the bolt tensile stress area and Lb is the conventional bolt length. Eurocode 3
defines this length as:
Lb = tf. u + tf. l + 2twsh + 0.5(
tn + th)
(1.18)
where th, twsh and tn represent the bolt head, washer and nut thickness, respectively
(Fig. 1.15). Aggerskov [1.7] defines a different conventional bolt length
and distinguishes between the cases of snug-tightened and preloaded bolts. According
to the author:

Modelling of the M-Φ characteristics of bolted joints: background review
B
F
n m m
Fig. 1.14 Equivalent (half-) model for the flange flexural elastic behaviour.
L s
L tg
B
n
th
twsh
tf.u
tf.l
twsh
tn Fig. 1.15 Bolt geometrical properties (including washer).
⎧k1
+ 2k4 ⇐snug-tightened
bolts
⎪
Lb= ⎨ k2k3 ⎪
⇐ preloaded bolts
⎩(
k2 + k3)
where (see Fig. 1.15):
(1.19)
k1 = Ls + 1.43Ltg + 0.71tn
tfu . + tfl
.
k3
=
5
(1.20)
k2 = Ls+ 1.43Ltg + 0.91tn+ 0.8twsh k4 = 0.1tn+ 0.4twsh
The initial stiffness coefficients ke.0.u and ke.0.l, which include the bolt deformation,
are defined as the ratio between the applied force F and the corresponding
deformation:
F
ke.0.
u/ l =
∆e.0. u/ l
E
=
⎡1 qu/
l⎛3
3 ⎞⎤
Z fu . / l⎢ − ⎜ α fu . / l−2α fu . / l ⎟
4 2 2
⎥
⎣ ⎝ ⎠⎦
(1.21)
The initial stiffness of the bolted T-stub is then given by:
1
ke.0
=
1 1
+
ke.0. u ke.0.
l
(1.22)
The expressions presented above are lengthy and therefore they are not
suitable for practical design. Jaspart proposes a simplified approach for the
prediction of the axial stiffness of bolted T-stubs in [1.46]. This approach relies
21

State-of-the-art and literature review
on two major assumptions: (i) the distance n is taken as 1.25m (see Fig. 1.16b)
and (ii) the bolt deformability is dissociated from that of the T-stub (Fig.
1.16c).
Under these assumptions, the initial stiffness coefficients of the single Tstub
elements may be simplified to the following expressions (cf. Appendix A;
subscripts f and b refer to the flange and the bolt, respectively):
3
Eb′ eff t f . u / l
keT
. . u/ l = (1.23)
3
mu/
l
and the axial stiffness of a snug-tightened bolt row is equal to:
EAs
kebt
. = 1.6
(1.24)
L b
The stiffness coefficient ke.bt from Eq. (1.24) characterizes the deformation of a
snug-tightened bolt row in tension and is determined assuming that the bolt
force is increased from 0.5F to 0.63F due to the prying effect (cf. Appendix A).
The initial stiffness of the overall connection is computed by means of the fol-
(a) Actual behaviour.
Q
22
B
(1)
F
Q
n m m n
n = 1.25m
B
B = 0.63F
F
B
n m m n
Q = 0.13F
(b) T-stub element alone. (c) Bolts alone.
Fig. 1.16 Elastic deformation of the T-stub.
B
Q
b
F
B = 0.63F

Modelling of the M-Φ characteristics of bolted joints: background review
lowing relationship:
keo
. =
1
k
1
1
+
k
1
+
k
eT . . u eT . . l ebt .
(1.25)
Referring to Eqs. (1.16) and (1.23), the effective length b′ eff represents a
new effective length for stiffness calculations, slightly different from the effective
width beff for resistance calculations defined above. This new length may
be taken as (cf. Appendix A):
b′ eff = 0.9beff
(1.26)
Faella et al. [1.44] also adopt a procedure that neglects the compatibility
requirements between the axial deformation of the bolts and the deformation of
the T-stub flanges and neglects the effect of prying action. The bolt deformability
is again separated from that of the T-stub. They derive the initial stiffness
of the single T-stub by means of a flexible beam model, i.e. the bolt restraining
action is modelled as simple supports at the bolt axis (Fig. 1.17a). In
this case (I: moment of inertia of the beam section):
( )
( )
3
3
F 2m 2Fm
δ = =
(1.27)
flex
3
48EI
Eb′ t
eff f
δ(flex)
B B
(a) Flexible beam approach.
B
m m
F
F
δ(rig)
m m
(b) Rigid beam approach.
Fig. 1.17 Behavioural schemes of the equivalent T-stub modelled as a beam.
B
23

State-of-the-art and literature review
and so:
F
K(
) = flex
δ(
flex)
3
0.5Eb′ eff t f
= 3
m
(1.28)
If the bolt acts as a fixed edge (Fig. 1.17b), then the beam is fully restrained at
the bolt line (rigid beam approach) and the displacement is evaluated as follows:
3 3
Fm 0.5Fm
δ ( rig ) = =
3
24EI
Eb′ t
(1.29)
24
eff f
3
2Eb′ eff t f
3
F
K(
rig ) = = (1.30)
δ(
rig ) m
In reality, the restraining action of the bolts lies in between these two limit
situations. In fact, the Eurocode 3 adopts an expression that yields results in between
these two boundaries (see Eq. (1.23)). By adopting a nomenclature similar
to the above, according to Faella et al. [1.44], the axial stiffness of a single
T-element is determined from the following relationship:
3
Eb′ eff t f
ke. T . u / l = K(
flex)
= 0.5
(1.31)
3
m
For the bolt stiffness they propose the expression from Eurocode 3 – Eqs.
(1.18) and (1.24). The effective width b′ eff is now defined as follows:
b′ eff = 2m+
dh≤ b
(1.32)
where dh is the bolt head diameter and b is the actual width of the T-stub. This
new width is obtained by consideration of a 45º spreading of the bolt action
starting from the bolt head edge (Fig. 1.18) [1.47]. The accuracy of such an assumption
is confirmed by experimental evidence in [1.44].
b’eff
45º
Fig. 1.18 Effective width for stiffness calculations [1.47].
1.4.2 Characterization of the several joint components
The Eurocode 3 formulations for prediction of the full plastic resistance and
initial stiffness for each component are summarized in Table 1.1. In this table,
fy is the yield stress, fu is the ultimate stress, Avc is the shear area of the column
dh
m

Modelling of the M-Φ characteristics of bolted joints: background review
profile, dc is the clear depth of the column web, β is the transformation parameter
defined in §1.2, γM are partial safety factors, Mb.Rd is the moment resistance
of the beam cross-section and subscripts b, c, ep, f and w refer to the beam, the
column, the end plate, the flange and the web, respectively. The partial safety
factors for design purposes are taken as γM0 = 1.1 = γM1 and γM2 = 1.25, for the
resistance of cross-sections and bolts, respectively [1.1]. The geometric parameters
are defined in Table 1.2 and Fig. 1.19 for bolted joints.
Regarding the evaluation of the plastic resistance of the components column
web in compression and column web in tension, the reduction factors for
plate buckling and interaction with shear in the column web panel, ρ and ω, respectively,
are defined below:
⎪
⎧1.0 if λp
≤ 0.72
beff. cwcdcfy. wc
ρ = ⎨
with λ
2
p = 0.932
(1.33)
2
⎪⎩ ( λp − 0.2 ) λp if λp
> 0.72
Etwc
⎧1 if 0 ≤ β ≤0.5
⎪
ω = ⎨ω1+
21 ( −β)( 1 − ω1) if 0.5< β ≤1
(1.34)
⎪
⎩ω1−(
1 −β)( ω2 − ω1) if 1< β ≤ 2
with:
1
1
ω 1 =
and ω 2 =
(1.35)
2
2
⎛beff . cwctwc ⎞
⎛beff . cwctwc⎞ 1+ 1.3⎜
⎟
1+ 5.2⎜
⎟
⎝ Avc
⎠
⎝ Avc
⎠
0.8rc
mc
ec
rc
aep.w
mep
eep
( )
n = min e , e ,1.25m
c c ep c
( )
n = min e , e ,1.25m
ep c ep ep
0.8 2 aep.w
(a) Column flange and end plate between beam
flanges.
aep.f
LX
bep
eep eep w
mep
eX
mX
p1-2
m2
p2-3
aep.w
m = L −e − 0.8 2a
X X X ep. f
(b) End plate extension.
Fig. 1.19 Definition of the geometric parameters m and n for the column
flange and end plate (particular case of a hot rolled column section).
25

State-of-the-art and literature review
κwc is a reduction factor to account for the effect of an axial force in the column.
Generally, this reduction factor is unitary [1.1].
As mentioned above, the components column flange in bending and end
plate in bending are modelled by means of equivalent T-stubs, provided that
the effective width is properly defined (Table 1.2 – e1 is the end distance from
the centre of the bolt hole to the adjacent edge, α is a coefficient obtained from
an abacus provided by Eurocode 3). The design resistance associated to each of
the three possible failure modes is thus obtained from Eqs. (1.3-1.5) by introduction
of the appropriate geometric and mechanic parameters and partial
safety coefficients, γM0, γM1 or γM2.
Table 1.1 Synthesis of the code formulations for evaluation of the properties
of basic bolted joint components.
Component Plastic resistance Initial stiffness
cws
0.9 f ywc . Avc
Fcws.
Rd =
3γ
M 0
0.38EAvc kecws
. =
β z
cwc
ωκwcbeff.
cwctwcfy. wc
Fcwc.
Rd = , but:
γ M 0
ωκ wcρbeff. cwctwc fy.
wc
Fcwc.
Rd ≤
γ M 1
0.7Ebeff . cwctwc kecwc
. =
dc
cwt
ωκ wcbeff. cwttwcfy. wc
Fcwt.
Rd =
γ M 0
0.7Ebeff . cwttwc kecwc
. =
dc
cfb Fcfb. Rd = min ( Fcfb.1. Rd , Fcfb.2. Rd , Fcfb.3.
Rd )
3
Eb′ eff . cfbt fc
kecfb
. = 3
mc
and:
b′ eff . cfb= 0.9beff.
cfb
k
Eb′ t
26
epb Fcfb. Rd = min ( Fepb.1. Rd , Fepb.2. Rd , Fepb.3.
Rd )
bfc
bwt
bt
F
F
bfc. Rd
M bRd .
=
hb − tfb
b t f
3
eff . epb ep
eepb . = 3
mep
and:
b′ = 0.9b
eff . epb eff . epb
k ebfc . = ∞
bwt. Rd =
eff . bwt wb
γ M 0
y. wb
ebwt .
bt. Rd = Rd
0.9 fub . As
=
γ M 2
kebt
.
F B
k = ∞
1.6As =
L
b

Modelling of the M-Φ characteristics of bolted joints: background review
With respect to the effective widths of the two above components, the
equivalence between the column flange in transverse bending and the T-stub
model is quite straightforward. In fact, for an unstiffened column flange, the effective
width is obtained directly from Fig. 1.13 by changing the geometry accordingly,
except for the beam pattern that is unlikely to develop. In the case of
a stiffened column flange or the end plate in bending, the groups of bolt rows at
each side of a stiffener are treated as separate equivalent T-stubs. The exten-
Table 1.2 Definition of geometric parameters that appear explicitly in the
above formulae.
Component Geometric parameters
beff . cwc = tfb + 2 2aep+ 5(
tfc + s) + sp
c hot-rolled profile column section
cwc
⎧⎪ r ⇐
s = ⎨
⎪⎩ 2ac ⇐ welded profile column section
sp: length obtained by dispersion at 45º through the end plate
b = b
cwt eff . cwt eff . cfb
cfb
⎧⎪ beff. nc but beff. cfb ≤beff . cp ⇐ type-1 mechanism
beff
. cfb = ⎨
, whereby
⎪⎩ beff
. nc ⇐ type-2 mechanism
subscript cp refers to circular yield line patterns and nc to noncircular
yield line patterns.
Bolt row
location
Inner bolt
row
End bolt
row
Bolt row
adjacent to
a stiffener
Inner bolt
row
End bolt
row
Bolt row
adjacent to
a stiffener
Circular pattern Non-circ. pattern
Bolt row considered individually
2 c m π 4mc + 1.25ec
min ( 2 πmc, π mc + 2e1)
min ( 4mc + 1.25 ec,
2m + 0.625e
+ e
π c m α
2 c m
c c
Bolt row as part of a group of bolt rows
2 p p
( π m + p e + p)
min , 2
π mc+ p
c
1
(
min e1+ 0.5 p,
2mc + 0.625ec + 0.5p
0.5p+
αmc−
− 2m +
0.625e
( )
c c
1
)
)
27

State-of-the-art and literature review
Table 1.2 Definition of geometric parameters that appear explicitly in the
above formulae (cont.).
Component Geometric parameters
⎧⎪ beff. nc but beff . epb ≤beff . cp ⇐ type-1 mechanism
beff
. epb = ⎨
⎪⎩ beff
. nc ⇐ type-2 mechanism
28
epb
Bolt row
location
Bolt row
outside
tension
flange of
beam
1 st row
below
tension
flange of
beam
Other inner
bolt
row
Other end
bolt row
Bolt row
outside
tension
flange of
beam
1 st row
below
tension
flange of
beam
Other inner
bolt
row
Other end
bolt row
b =
b
bwt eff . bwt eff . epb
Circular pattern Non-circ. pattern
Bolt row considered individually
min ( 4mX+ 1.25 eX ,0.5 bep,
min ( 2 πmX, πmX
+ w,
2mX + 0.625 eX + eep,
π mX + 2eep)
2m + 0.625e + 0.5w
π ep m α
2 ep m
X c
2 ep m π 4m + 1.25e
ep ep
2 ep m π 4m + 1.25e
ep ep
Bolt row as part of a group of bolt rows
⎯⎯⎯ ⎯⎯⎯
π mep + p
2 p
0.5p+
αm
−
ep
( 2mep 0.625eep)
− +
π mep + p
2mep + 0.625eep + 0.5 p
p
)

Modelling of the M-Φ characteristics of bolted joints: background review
sion of an end plate and the portion between the beam flanges are also modelled
as two separate equivalent T-stubs [1.1] and the resistance and plastic
failure modes are determined separately.
1.5 CHARACTERIZATION OF THE POST-LIMIT BEHAVIOUR OF BASIC
COMPONENTS OF BOLTED JOINTS
Design codes as the Eurocode 3 do not give an accurate description of the postlimit
response of the individual joint components and their deformation capacity,
in particular. Within the framework of the component method, the overall
joint behaviour is determined by the behaviour of its elementary parts. As a
consequence, the rotation capacity of a joint is bound by the deformation capacity
of the single components. In terms of characterization of the post-limit
component behaviour with a bilinear approximation, two main properties have
to be fully described: the post-limit stiffness, kp-l and deformation capacity, ∆u.
Jaspart [1.20] and Jaspart and Maquoi [1.48] assume that this behaviour can
be approximated by a linear relationship (Fig. 1.20) and propose a general,
simple methodology for characterization of both properties for all components.
kp-l is taken as the strain hardening stiffness since the effects of material strain
hardening after yielding of the component are dominant. It is defined below:
Eh
kp− l = ke
(1.36)
E
for components column web in compression, column web in tension, column
flange in bending, end plate in bending and:
21 ( + υ ) Eh
k = k
(1.37)
p−l e
3
E
for component column web in shear. Eh is the strain hardening modulus of the
material and υ is the Poisson’s ratio. For the bolts in tension kp-l is taken as zero
since this is a brittle component. Components beam web in tension and beam
flange and web in compression are disregarded since they only provide a limitation
to the joint flexural resistance [1.1]. They also suggest expressions for
computation of the ultimate resistance, Fu, and, consequently, ∆u. Fu is readily
determined by formally equivalent expressions to those listed in Table 1.1, by
replacing fy with fu, the ultimate stress of the structural steel. The deformation
capacity is determined from the intersection of the post-limit behaviour with
Fu:
FRd Fu − FRd
∆ u = + (1.38)
ke kp−l From a qualitative point of view, the basic components can be grouped according
to three ductility classes that reflect this post-limit behaviour [1.49].
The component ductility reflects the “length” of the post-limit response and
can be quantified by means of an index ϕ i for each component i. The author
29

State-of-the-art and literature review
30
F
Fu
FRd
ke
kp-l
∆u
Post-limit linear approximation
Actual behaviour
Elastic-plastic approximation
(using the component initial
stiffness)
Fig. 1.20 Bilinear approximation of the component behaviour as proposed by
Jaspart [1.20] and Jaspart and Maquoi [1.48].
proposes the following expression for the definition of ϕ i:
∆u
ϕi
= (1.39)
∆ FRd
whereby ∆u is the component deformation capacity and ∆ F = F
Rd Rd ke
is the
deformation value corresponding to the component plastic resistance, FRd.
Kuhlmann et al. [1.49] propose three ductility classes: (i) components with
high ductility (ϕi ≥ α) (e.g. cws, cfb, epb), (ii) components with limited ductility
(β ≤ ϕi < α) (e.g. cwc, cwt) and (iii) components with brittle failure (ϕi < β)
(e.g. bt, welds). α and β represent ductility limits. Simões da Silva et al. [1.50]
propose α = 20 and β = 3. The ductility behaviour of the several joint components
is analysed in the following sub-sections according to alternative procedures
from the literature.
1.5.1 Column web in shear (component with high ductility)
For the web panel subjected to shear, literature proposes an alternative model,
the Krawinkler et al. model that can be used to predict the contribution of this
component to the overall joint response [1.44]. This model was developed
based on experimental observations regarding the significant post-yield resistance
of the panel zone. Fig. 1.21 illustrates this model in terms of a global Vwpγ
response. This curve is easily converted into a Vwp-∆wp response by means of
the following simplified relationship:
∆ ∆ wp ( cws)
γ = = (1.40)
z z
∆

Modelling of the M-Φ characteristics of bolted joints: background review
Vwp
Vwp.p
Vwp.y
γy
4γy
Fig. 1.21 Krawinkler et al. trilinear model.
Kcws.h
This relation was derived by idealizing the web panel as a short column stub of
height z, subjected to a shear force Vwp [1.5,1.20]. There are two swivel points
in the model corresponding to: (i) first yielding of the panel zone, (Vwp.y,γy) and
(ii) first yielding of the column flanges, (Vwp.p,4γy). According to Krawinkler et
al., the rotational behaviour of the panel after yielding can be attributed to the
bending of the column flanges [1.44]. The co-ordinates at the swivel points of
this curve are given by [1.44]:
f y twchchb Vwp.
y = (1.41)
3 β z
E f y
γ y =
(1.42)
21+ υ 3
( )
⎛ bt ⎞
2
c fc
Vwp. p = Vwp.
y ⎜1+ 3.12 ⎟
(1.43)
⎜ hht ⎟
⎝ c b wc ⎠
whereby hc and hb are the column and beam depth, respectively. The residual
stiffness Kcws.h is given by [1.44]:
Eh twchchb Kcws.
h =
(1.44)
21 ( + υ) βz
This model imposes no limits on the deformation capacity of this component.
Beg and co-workers [1.51-1.52] present some expressions to limit the ultimate
shear panel rotation, γu:
⎧⎛ d 1 ⎞ c
⎪⎜28−0.38 ⎟κNif
0 ≤ n ≤0.10
⎪⎝
twc
ε ⎠
γ u[%]
= ⎨ (1.45)
⎪⎡
dc 1 ⎛ dc
1⎞
⎤
⎪⎢28 −0.38−⎜55−0.81 ⎟(
n− 0.1 ) ⎥κNif
n>
0.10
⎩⎢⎣
twc ε ⎝ twc
ε ⎠ ⎥⎦
γ
31

State-of-the-art and literature review
with:
N
n =
N
(1.46)
32
pl
235
ε = (1.47)
f y
The influence of the level of axial force in the column, N, can be assessed by
means of the following parameter κN:
2
hc n
κ N = 1 if hb hc
≥ 1 and κ N = 1 − if hb hc
< 1
(1.48)
h 0.4
b
1.5.2 Column flange in bending, end plate in bending and bolts in tension
(T-stub idealization)
These three components can be idealized with the equivalent T-stub approach.
The deformation capacity of a T-stub mainly depends on the plate/bolt resistance
ratio. It has been well established that the best way to accomplish deformation
capacity is a design in the type-1 situation [1.8], i.e. βRd < 2λ/(2λ+1). In
type-1, the deformation can be regarded as “indefinitely large” because yielding
occurs in the flange. The only limitations are the membrane stresses in the
plate that develop with large deformations. In a type-3 mechanism (βRd > 2), the
deformations are mainly determined by bolt tension elongation, which leads to
a brittle failure. A thorough analysis of the post-limit behaviour of isolated Tstub
connections is carried out later in the text (Chapter 6). Previous research
work of several authors on this subject is also reviewed, namely the work of
Jaspart [1.20], Faella et al. [1.44], Beg et al. [1.51-1.52] and Swanson [1.53].
1.5.3 Column web in compression (component with limited ductility)
Aribert and co-workers opened up the elastoplastic studies of web profiles subjected
to local compression forces [1.54-1.56]. Their studies mainly focused on
resistance evaluation rather than a full description of the overall deformation
behaviour.
The component column web in compression in particular was extensively
studied by Kuhlmann and Kühnemund [1.57-1.58] and Kühnemund [1.59].
They performed numerous tests on this component and characterized its F-∆
behaviour in detail (model depicted in Fig. 1.22). The elastic-plastic response is
easily determined from the Eurocode 3 proposals (see Tables 1.1-1.2). The
post-limit behaviour is described by two distinct branches. The first branch is
defined between the plastic resistance and the maximum resistance, Fcwc.u. The
second (softening) branch follows on until fracture. In this phase they redefine

Modelling of the M-Φ characteristics of bolted joints: background review
Fcwc
Fcwc.u
Fcwc.Rd
2/3Fcwc.Rd
ke.cwc
∆e.cwc
4.5∆e.cwc
∆u.cwc
Fig. 1.22 Kuhlmann and Kühnemund model.
∆cwc
the effective width beff.cwc. The procedure for assessment of the relevant ordinates
of the curve in this post-limit regime can be found in [1.59].
Other authors also looked into the behaviour of this component. Huber and
Tschemmernegg [1.60] suggested values for the deformation capacity for this
component for different standard shapes of the column section (Table 1.3). Beg
and co-workers [1.51-1.52] carried out a numerical analysis of the component
and proposed expressions for evaluation of the deformation capacity that depend
on the level of axial force in the column. These expressions are defined in
a non-dimensional form below:
⎧ dc 1 dc
1
⎪18.5
− 0.75 if < 20
⎪
twc ε twcε
⎪ dc 1 dc
1
δucwc
. [%] = ⎨5.7
−0.11 if 20 ≤ < 33 for n = 0 (1.49)
⎪ twc ε twc
ε
⎪ dc
1
⎪2.07
if ≥ 33
⎪⎩ twc
ε
and:
⎧ d 1 ⎛ c d 1⎞ c dc
1
⎪9.4 − 0.34 + ⎜15−0.75 ⎟(
0.5 − n)
if < 20
⎪ twcε ⎝ twc ε ⎠ twc
ε
⎪ dc 1 dc
1
δucwc
. [%] = ⎨4.8
−0.11 if 20 ≤ < 33
(1.50)
⎪ twc ε twc
ε
⎪ dc
1
⎪1.17
if ≥ 33
⎪⎩
twc
ε
33

State-of-the-art and literature review
for n ≥ 0.1. n and ε are defined in Eqs. (1.46) and (1.47), respectively. The deformation
capacity of the column web in compression, ∆u.cwc, is computed
from:
d δ ∆ = (1.51)
34
ucwc . ucwc . c
Table 1.3 Deformation capacity of the column web in compression according
to Huber and Tschemmernegg [1.60].
Column profile IPE HEA HEB HEM
∆u.cwc (mm) 1.5 3.0 5.0 7.5
1.5.4 Column web in tension (component with limited ductility)
Witteveen et al. [1.61] suggest a very simple expression for evaluation of the
deformation capacity of the column web subjected to tension:
ucwt . 0.025 c h
∆ = (1.52)
This limit value is also adopted in Eurocode 3.
Beg et al. [1.51-1.52] also studied this component and derived an analytical
expression for evaluation of the ultimate deformation:
u. cwt u. cwt c d δ ∆ = (1.53)
with:
2
⎛ 2
4−3sx −s⎞
x
δucwt . = ε ⎜ ⎟
0
(1.54)
⎜ 2 ⎟
⎝ ⎠
sx is defined below (σx: transverse stress):
σ x
sx
= (1.55)
f ywc .
and ε0 is the ultimate transverse strain in the case that the axial force in the column
is absent. They suggest that this value should be set as equal to 0.1.
1.6 EVALUATION OF THE MOMENT-ROTATION RESPONSE OF BOLTED
JOINTS BY MEANS OF COMPONENT MODELS
Mechanical (component) models use a set of rigid and flexible parts (springs)
to simulate the interaction between the various sources of joint deformation.
The springs are combined in series or in parallel depending on the way they interplay
with each other. Springs in series are subjected to the same force whilst
parallel springs undergo the same deformation.
The active components of a joint are grouped according to their type of
loading (tension, compression or shear). They can also be distinguished be-

Modelling of the M-Φ characteristics of bolted joints: background review
tween those linked to the web panel, the load-introduction into the column web
panel and the connection. A sophisticated component interplay as assumed in
the Innsbruck model [1.43,1.62] allows separate representation of the behaviour
of the web panel in shear, the load-introduction and the connection elements
(Fig. 1.23). Due to its complexity, this model is not easily implemented
in a design code, as it requires successive iterations within the component assembly
[1.62]. This is why a simplified component model, as depicted in Fig.
1.7, is desirable.
Huber highlights the two main differences between the two component
models [1.62]. In the Eurocode 3 model there is no separation between the
panel and connecting zone, which may lead to a non-straight deformation of
the column front in contradiction with experimental evidence. Also, the stiff
separation bar between tension and compression components (see Fig. 1.7)
prevents the interaction between these components within the web panel that
exists in reality. However, this simplified model yields analytical solutions
rather than iterative, making it a simpler tool for daily design practice.
Aribert et al. propose an alternative component model that is yet restricted
to the case of internal flush end plate joints under balanced loading, i.e. the
web panel is not subjected to shear forces [1.63]. Basically they assume the
same components but introduce an additional component at the level of the tension
beam flange. This new component corresponds to the part of the end plate
located between the tension beam flange and the first bolt row and is subjected
to longitudinal bending. Also, they assume a sophisticated component interplay
since they do not separate the components under compression from the tensile
zone as in Eurocode 3 (see Fig. 1.7).
Finally, reference is made to the component model commonly used at the
University of Coimbra (Fig. 1.24). This model assumes a sophisticated component
interplay since it does not establish the equivalence of all tensile components
into a single equivalent spring as in Eurocode 3. This equivalence is explained
below. For further reference, this model is designated by UC model.
For illustration of the differences between the alternative spring models,
consider the evaluation of the initial stiffness of a (single-sided) bolted ex-
(cwt.1)
(cwt.2)
(cfb.2)
(cws) (cwc) (bfc)
(cfb.1) (epb.1) (bt.1)
(epb.2)
(bwt.2)
(bt.2)
Fig. 1.23 Innsbruck spring model (single-sided steel joint configuration).
Φ
M
35

State-of-the-art and literature review
36
(cwt.1) (cfb.1) (epb.1) (bt.1)
(cwt.2)
(cfb.2)
(epb.2)
(cws) (cwc) (bfc)
(bwt.2)
(bt.2)
Fig. 1.24 UC spring model (single-sided steel joint configuration).
30 100
30
Φ
30
35
35
165
Fig. 1.25 Illustrative example: connection geometry.
tended end plate connection. The column is made up of a HE240B profile and
the beam profile is IPE240. Bolts M20 fasten the elements. The end plate dimensions
are 315×160 mm 2 and 15 mm thickness. The continuous fillet welds
between the beam and the end plate have a throat thickness aw = 8 mm. The geometry
of the connection is depicted in Fig. 1.25. For all components, E = 210
GPa. The characterization of the elastic stiffness of the single components is
based on the Eurocode 3 proposals (Tables 1.1-1.2). The following results are
obtained: (i) Eurocode 3 model: Sj.ini = 23.82 kNm/mrad, (ii) Innsbruck model:
Sj.ini = 23.12 kNm/mrad (difference of -2.94% in comparison with the Eurocode
3 model) and (iii) UC model: Sj.ini = 24.25 kNm/mrad (difference of 1.81% in
comparison with the Eurocode 3 model).
50
M

Modelling of the M-Φ characteristics of bolted joints: background review
1.6.1 Eurocode 3 component model
Fig. 1.26a depicts the Eurocode 3 mechanical model for the particular case of a
bolted extended end plate connection, with two bolt rows in tension, which allows
for characterization of the rotational behaviour of such a joint type. The
model assumes that the compressive springs are located at the centre of compression,
which corresponds to the centre of the lower beam flange, and the
tensile springs are positioned at the corresponding bolt row level. The bolt row
deformations are proportional to the distance to the centre of compression and
the forces acting in each row depend on the component stiffness [1.40].
1.6.1.1 Model for stiffness evaluation
For evaluation of the initial rotational stiffness, Sj.ini, the model (Fig. 1.26a) is
simplified by replacing each assembly of springs in series with an equivalent
spring, which retains all the relevant characteristics (Fig. 1.26b). Weynand further
simplifies this model by establishing the equivalence between the parallel
spring assembly t.1 and t.2 and the spring t (Fig. 1.26c) [1.64]. By means of
simple equilibrium considerations and compatibility requirements, the follow-
(cws)
(cwc) (bfc)
(cwt.1) (cfb.1) (epb.1) (bt.1)
(cwt.2)
(cfb.2)
(epb.2)
(bwt.2)
(a) Eurocode 3 spring model: active components for a bolted extended end
plate connection with two bolt rows in tension (see Fig. 1.7).
(c)
(t.2)
(t.1)
Φ M
(c)
(bt.2)
Φ
(t)
M
Φ M
(b) Eurocode 3 equivalent model. (c) Eurocode 3 simplified model.
Fig. 1.26 Eurocode 3 spring model and simplifications.
37

State-of-the-art and literature review
ing expression for initial stiffness is derived in [1.64]:
M 2 kecket Sjini . = = z
Φ kec + ket
(1.56)
The elastic stiffness of each equivalent spring t.i and c, corresponding to a
spring assembly in series, are readily obtained as follows (Fig. 1.26a):
kec
=
1
k
1
1
+
k
1
+
k
(1.57)
38
ecws . ecwc . ebfc .
and:
ket.
i =
1
k
1
+
k
1
1
+
k
1
+
k
1
+
k
ecwti . . ecfbi . . eepbi . . ebwti . . ebti . .
The lever arm z is given by [1.64]:
z =
n
∑
i=
1
n
∑
i=
1
k z
2
et. i i
k z
et. i i
whereby zi is the distance from bolt row i to the centre of compression.
1.6.1.2 Model for resistance evaluation
(1.58)
(1.59)
For evaluation of the joint flexural resistance, Mj.Rd, simple equilibrium equations
yield:
n
M = ∑ F z
(1.60)
j. Rd ti. Rd i
i=
1
in the absence of an axial force. Fti.Rd is the potential resistance of bolt row i in
the tension zone and zi is the distance of the i-th bolt row from the centre of
compression. Fti.Rd is taken as the least of the following values:
Fti. Rd = min ( Fcwt. i. Rd , Fcfb. i. Rd , Fepb. i. Rd , Fbwt. i. Rd , Fbt.
i. Rd )
(1.61)
The values of Fti.Rd are calculated starting at the top row and working down.
Bolt rows below the current row are ignored. Each bolt row is analysed first in
isolation and then in combination with the successive rows above it. The procedure
can be summarized as follows [1.1]:
(i) Compute the plastic resistance of bolt row 1 omitting the bolt rows below:
Ft1. Rd = min ( Fcws. Rd β , Fcwc. Rd , Fbfc. Rd , Fcwt.1. Rd , Fcfb.1. Rd , Fepb.1. Rd , Fbt.1.
Rd ) (1.62)
(ii) Compute the plastic resistance of bolt row 2 omitting the bolt rows below:
min F β −F , F −F , F −
F , F ,
F t2. Rd = ( cws. Rd t1. Rd cwc. Rd t1. Rd bfc. Rd t1. Rd cwt.2. Rd

Modelling of the M-Φ characteristics of bolted joints: background review
F , F , F , F , F F ,
cfb.2. Rd epb.2. Rd bwt.2. Rd bt.2. Rd .1 ( 2. ) −
cwt + Rd t1. Rd
cfb.1 ( + 2. ) Rd t1. Rd, bt.1 ( + 2. ) Rd t1. Rd)
F −F F − F
(1.63)
(iii) Compute the plastic resistance of bolt row 2 omitting the bolt rows below:
F t3. Rd = min ( Fcws. Rd β −Ft1. Rd −Ft2. Rd , Fcwc. Rd −Ft1. Rd − Ft2.
Rd ,
F −F − F , F , F , F , F , F ,
bfc. Rd t1. Rd t 2. Rd cwt.3. Rd cfb.3. Rd epb.3. Rd bwt.3. Rd bt.3. Rd
F −F , F −F , F − F ,
cwt.2 ( + 3. ) Rd t2. Rd cfb.2 ( + 3. ) Rd t2. Rd epb.2 ( + 3. ) Rd t2. Rd
cwt.1 ( + 2+ 3. ) Rd t2. Rd t1. Rd, cfb.1 ( + 2+ 3. ) Rd t2. Rd t1. Rd)
F
and so forth.
−F −F F −F − F (1.64)
1.6.1.3 Idealization of the moment-rotation curve
The conversion of the F-∆ curves of the individual active joint components into
a global M-Φ curve is based on the spring model so that the compatibility and
equilibrium requirements are met. Depending on the desired level of accuracy
and available software, the rotational joint behaviour can be fully characterized
(full nonlinear shape) or approximated by nonlinear or multilinear simplifications.
The characterization of the actual nonlinear M-Φ curve is not easily open
to simple analytical formulations and therefore the simplified approximations
are preferred for hand calculations. Recently, the author proposed an energy
approach for evaluation of the multilinear M-Φ response from component
models in closed-form solutions. It also allows the identification of the yielding
sequence of the individual components and the corresponding levels of deformation
[1.65-1.70].
The Eurocode 3 adopts two possible idealizations of the M-Φ curve, bilinear
(elastic-plastic curve) and nonlinear, as depicted in Fig. 1.27. The stiffness
modification factor, η, (Fig. 1.27a) depends on the joint type and configuration
and is defined in the code [1.1]. For bolted end plate beam-to-column joints
this factor is taken as 2. The stiffness ratio µ that is used to define the nonlinear
part of the idealized M-Φ curve in Fig. 1.27b is defined as follows:
Ψ
⎛1.5M ⎞ jEd . 2
µ = ⎜ ⎟ for M jRd . < M jEd . ≤ M jRd .
(1.65)
⎜ M ⎟
⎝ jRd . ⎠ 3
and Ψ is a coefficient that depends on the type of connection. For bolted end
plate connections, this coefficient is taken as 2.7.
1.6.2 Guidelines for evaluation of the ductility of bolted joints
The ductility of a joint can be defined as the amount of a plastic rotation that
39

State-of-the-art and literature review
40
Bending moment (kNm)
180
150
120
90
60
30
Sj.ini/η
0
0 15 30 45 60 75 90 105 120
Joint rotation (mrad)
(a) Bilinear idealization of the moment-rotation curve.
Bending moment (kNm)
180
150
120
90
2/3Mj.Rd
60
30
Sj.ini
Sj.ini/µ
Actual response
Mj.Rd
0
0 15 30 45 60 75 90 105 120
Joint rotation (mrad)
Actual response
Mj.Rd
(b) Nonlinear idealization of the moment-rotation curve.
Fig. 1.27 Eurocode 3 idealizations of the actual rotational response.
can be sustained while maintaining a certain percentage of its ultimate resistance
[1.53]. It reflects the length of the yield plateau of the M-Φ response.
This property can be quantified by means of an index ϑj that relates the rotation
capacity of the joint, ΦCd to the rotation value corresponding to the joint plastic
resistance [1.46,1.50]. In this work, the following relationship is proposed:
ΦCd
ϑ j = (1.66)
ΦM
Rd
similarly to Eq. (1.39). This index allows a direct classification of a joint in
terms of ductility, similarly to the basic joint components (§1.5). ΦM is the
Rd
“analytical” rotation value corresponding to Mj.Rd and is given by the ratio
M S (Fig. 1.28). Fig. 1.28 presents other distinctive rotation values. ΦXd
j. Rd j. ini

Modelling of the M-Φ characteristics of bolted joints: background review
M
Mmax
Mj.Rd
Φ MRd
ΦXd
Fig. 1.28 Definitions of joint rotation.
*
Φ Cd ΦCd
Mmax
Φ
Φ
*
Φ Cd is the rotation
is the rotation at which the moment first reaches Mj.Rd and
at which the moment deteriorates back to Mj.Rd after reaching a moment above
Mj.Rd through deformation beyond ΦXd. Φ M is the rotation at which the mo-
max
ment resistance is maximum.
Jaspart [1.46] classifies the joints in terms of available rotation capacity. He
groups structural joints into three classes: (i) class 1 joints, which have a sufficiently
good rotation capacity to allow a plastic frame analysis (high ductility),
(ii) class 2 joints, with a limited rotation capacity (limited ductility) and (iii)
class 3 joints, for which brittle failure or instability phenomena limits the rotation
capacity.
Literature reports several procedures for characterization of the available
rotation capacity. Zoetemeijer [1.10] proposes some criteria and simple empirical
expressions for the estimation of a joint deformation capacity based on a series
of experiments. He concluded that considerable rotation capacity was obtained
from the tension side of a joint if βRd < 2λ/(2λ+1), within the T-stub idealization
of the region. This means that the tension zone fails according to a
type-1 mechanism, with complete yielding of one of the plate components
(column flange or end plate). If βRd > 2, then the joint behaves elastically up to
failure of the bolts without deformation of the plate(s). In this case, the bolt
elongation mainly supplies the joint deformation. To prevent this situation,
Zoetemeijer suggests that the condition βRd < 1.75 should always be satisfied
[1.10]. For the intermediate situations, i.e. 2λ/(2λ+1) < βRd ≤ 1.75, the joint rotational
deformation remains limited since the bolt is also engaged in the collapse
mode. In the latter situation, Zoetemeijer suggests an expression for
evaluation of the rotation capacity, ΦCd [1.10]:
41

State-of-the-art and literature review
10.6 − 4β
Rd
Φ Cd = (1.67)
1.3z1
whereby z1 is the distance in [mm] between the first bolt row from the tension
flange and the centre of compression.
Later, Jaspart [1.46] extended the above criteria for inclusion in Eurocode
3. The code states that a bolted end plate joint may be assumed to have sufficient
rotation capacity for plastic analysis, provided that both of the following
conditions are satisfied: (i) the moment resistance of the joint is governed by
the resistance of either the column flange in bending or the end plate in bending
and (ii) the thickness t of either the column flange or the end plate (not necessarily
the same basic component as in (i)) satisfies:
fub
.
t ≤ 0.36φ
(1.68)
f y
where φ is the bolt diameter, fu.b is the tensile strength of the bolt and fy is the
yield strength of the relevant basic component. This expression is derived in
[1.46]. These guidelines are yet insufficient to ensure adequate ductility in partial
strength joints.
More recently, Adegoke and Kemp [1.23] performed an experimental/analytical
study on thin extended end plates and realized that most of the
connection rotation in these cases came from the end plate deformation. From
these observations, they proposed a simple expression for evaluation of the
connection ultimate rotation:
2
mf fy. ep mfmX fy.
ep
φ Cd = 1.4 + 40
(1.69)
Etephyfn Etephmrn In this expression, the first part corresponds to the connection rotation when
the yield lines in the extended and flush zones of the end plate (above and below
the top tension beam flange, respectively) are fully developed and is based
on the elastic flexibility of the stronger flush bolt lines [1.23]. mf represents the
average distance from each bolt to the adjacent web and flange welds below
the tension flange, i.e.:
mep + m2
m f = (1.70)
2
(see Fig. 1.19). hyfn is the height of the flush bolt row above the neutral axis at
yield and hmrn is the height of the resultant tension force above the neutral axis
at maximum strain. They assumed that the rotation capacity was attained when
fracture of the end plate occurred. This would happen when the maximum
strain would be thirty times the yield strain.
In the context of the component method, several researchers have developed
simplified approaches to quantify the overall rotation capacity. Since in
many cases the most important sources of deformability in bolted joints can be
idealized by means of the equivalent T-stub in tension, special attention has
been devoted to the evaluation of the deformation capacity of this individual
42

Modelling of the M-Φ characteristics of bolted joints: background review
component. Swanson [1.53] developed a methodology for characterization of
the ductility of T-stub connections. Faella and co-workers [1.44,1.71-1.72] set
up a procedure for computation of the deformation capacity of the isolated Tstub
and the overall joint. Other components have also been studied within this
framework. Kuhlmann and Kuhnemund [1.57] performed tests on the component
column web under transverse compression and proposed design rules for
this component from the point of view of resistance and deformation capacity.
The researchers also conducted a series of full-scale tests that are reported in
[1.58-1.59]. The study was restricted to joints under balanced loading. The
dominant component of all tests was the column web in compression. They
also developed a procedure based on the component method to determine the
rotation capacity of the joint for those cases where the critical component was
the column web under compression. Beg et al. [1.51] set up a methodology
based on a simplified component model for characterization of the rotational
response to include the evaluation of rotation capacity. They analysed different
components, the column web, the bolts in tension, the column flange and the
end plate in bending, and proposed simple expressions for evaluation of their
deformation capacity based on numerical evidence, as already mentioned
above (see §1.5). Yet, there was no calibration of this work. For this reason,
this methodology is questionable and should be used with special care. They
then established a simple mechanical model to mimic the joint rotational behaviour
(Fig. 1.29). This model is composed of bilinear springs that represent
the response of all relevant components. The overall joint rotation results from
the contribution of all components and can be readily determined as follows
(Fig. 1.29):
∆ cwt +∆ 0 +∆cwc
Φ= + γ
(1.71)
z
The rotation capacity mainly depends on the deformation capacity of the weakest
component, i.e. the component with lower resistance. In Fig. 1.29 the Tstub
that represents the tension zone is the governing component. Consequently:
∆ cwt. R +∆ 0. u +∆cwc.
R
Φ = + γ
(1.72)
Cd R
z
It is worth mentioning that this procedure is identical to the proposals of Faella
and co-workers [1.44]. They also proposed a similar expression for evaluation
of the rotation capacity, though they mainly focused on the study of the tension
zone idealized as a T-stub.
Finally, and in the framework of the component method, the author’s proposals
for evaluation of the rotation capacity are also referred [1.65-1.70]. By
means of an elastic analogy of the nonlinear behaviour, the author proposed an
elastic equivalence for the spring models mentioned above (Figs. 1.7 and 1.24).
The basic building block of an equivalent model corresponds to replacing each
nonlinear spring with an equivalent elastic spring consisting of a set of linear
elastic springs with specific properties. Such equivalent models provide closed-
43

State-of-the-art and literature review
form solutions to an otherwise numerical problem and allow for the identification
of the yielding sequence of the components and, ultimately, the computation
of the joint rotation capacity.
F
FR
44
z
∆cwt.R
cwt
cws
∆
F
cwt T-stub
idealization
cwc
T-stub
M
∆0.u
∆
F
(cws)
∆cwc.R
cwc
(cwt) (T-stub)
(cwc)
Fig. 1.29 Computation of the joint rotation capacity according to Beg et al.
[1.51].
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Φ
M
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γ

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large capacity moment end plates. Journal of Structural Engineering
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[1.32] Bahaari MR, Sherbourne AN. Computer modelling of an extended endplate
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[1.33] Sherbourne AN , Bahaari MR. 3D simulation of end-plate bolted connections.
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unstiffened columns-II: Extended endplate connections. Journal of Constructional
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end plate steel connections. Journal of Constructional Steel Research;
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for end plate connection. Journal of Structural Engineering ASCE;
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and Design (Eds.: R. Bjorhovde, A. Colson and R. Zandonini), Trento,
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[1.41] Borges LAC. Probabilistic evaluation of the rotation capacity of steel
joints. MSc thesis. University of Coimbra, Coimbra, Portugal, 2003.
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beam-to-column connections, Chapter 2 in Structural connections, stability
and strength (Ed.: R. Narayanan). Elsevier Applied Science, London,
UK; 23-62, 1989.
[1.43] Huber G, Tschemmernegg F. Modelling of beam-to-column joints.
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[1.44] Faella C, Piluso V, Rizzano G. Structural semi-rigid connections – theory,
design and software. CRC Press, USA, 2000.
[1.45] Holmes M, Martin LH. Analysis and design of structural connections:
reinforced concrete and steel. Ellis Horwood Limited, Chichester, UK,
1983.
[1.46] Jaspart JP. Contributions to recent advances in the field of steel joints –
column bases and further configurations for beam-to-column joints and
beam splices. Aggregation thesis. University of Liège, Liège, Belgium,
1997.
[1.47] Ballio G, Mazzolani FM. Theory and design of steel structures. Chapman
and Hall, London, UK, 1983.
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properties of structural joints. In: Proceedings of the Annual Technical
Meeting on Structural Stability Research, Lehigh, USA; 177-191, 1994.
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the Semi-Rigid Behaviour of Civil Engineering Structural Connections
(Ed.: R. Maquoi), Liège, Belgium; 167-176, 1998.
[1.50] Simões da Silva L, Santiago A, Vila Real P. Post-limit stiffness and
ductility of end plate beam-to-column steel joints. Computers and Structures;
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[1.51] Beg D, Zupančič E, Vayas I. On the rotation capacity of moment con-
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[1.52] Zupančič E, Beg D, Vayas I. Deformation capacity of components of
moment resistant connections. European Convention for Constructional
Steelwork – Technical Committee 10, Structural Connections (ECCS-
TC10), Document ECCS-TWG 10.2-02-005, 2002.
[1.53] Swanson JA. Characterization of the strength, stiffness and ductility behavior
of T-stub connections. PhD dissertation, Georgia Institute of
Technology, Atlanta, USA, 1999.
[1.54] Aribert JM, Lachal A. Étude élasto-plastique par analyse des contraintes
de la compression locale sur l’âme d’un profilé. Construction Métallique;
4:51-66, 1977.
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la résistance d’un profilé en compression locale. Construction Métallique;
2:3-26, 1981.
[1.56] Aribert JM, Lachal A, Moheissen M. Interaction du voilement et de la
résistance plastique de l’âme d’un profilé laminé soumis à une double
compression locale (nuance dácier allant jusqu’à FeE460. Construction
Métallique; 2:3-23, 1990.
[1.57] Kuhlmann U, Kühnemund F. Rotation capacity of steel joints: verification
procedure and component tests. In: Proceedings of the NATO Advanced
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response of structures (Eds.: C.C. Baniotopoulos and F. Wald),
Nato Science series, Kluwer Academic Publishers, Dordrecht, The Netherlands;
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Proceedings of the International Colloquium on Stability and Ductility
of Steel Structures (SDSS 2002) (Ed.: M. Ivanyi), Budapest, Hungary;
363-370, 2002.
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joints in steel structures. PhD Thesis (in German), University of Stuttgart,
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[1.60] Huber G, Tschemmernegg F. Component characteristics, Chapter 4 in
Composite steel-concrete joints in braced frames for buildings (Ed.: D.
Anderson), COST C1, Brussels, Luxembourg; 4.1-4.49, 1996.
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bolted beam-to-column connections. Journal of the Structural Division
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[1.62] Huber G. Nicht-lineare berechnungen von verbundquerschnitten und
biegeweichen knoten. PhD Thesis (in English), University of Innsbruck,
Innsbruck, Austria, 1999.
[1.63] Aribert JM, Lachal A, Dinga ON. Modélisation du comportement
d’assemblages métalliques semi-rigides de type pouter-pouteau boulonnés
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anwendung nachgiebiger anschlüsse im stahlbau. PhD thesis (in Ger-
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man). University of Aachen, Aachen, Germany, 1996.
[1.65] Girão Coelho AM. Equivalent elastic models for the analysis of steel
joints. MSc thesis (in Portuguese). University of Coimbra, Coimbra,
Portugal, 1999.
[1.66] Simões da Silva LAP, Girão Coelho AM, Neto EL. Equivalent postbuckling
models for the flexural behaviour of steel connections. Computers
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connections. Journal of Constructional Steel Research; 57:45-70, 2001.
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Evaluation of the moment-rotation response of beam-to-column composite
joints under static loading. Steel and Composite Structures;
1(2):245-268, 2001.
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models for steel and steel-concrete composite structural connections.
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Model validation. Journal of Structural Engineering ASCE; 127(6):694-
704, 2001.
49

State-of-the-art and literature review
APPENDIX A: DESIGN PROVISIONS FOR CHARACTERIZATION OF RESIS-
TANCE AND STIFFNESS OF T-STUBS
A.1 Basic formulations for prediction of plastic resistance of bolted Tstubs
The equilibrium conditions of the mechanisms illustrated in Fig. 1.10 provide
the equations for the evaluation of the corresponding “plastic” resistance, FRd.0.
A.1.1 Type-1 mechanism
Regarding type-1 mechanism, the three equilibrium equations yield the following
relationships:
F1.
Rd .0
∑ Fv= 0 ⇔ Q = B−
2
(A.1)
(1)
∑ M = M f. Rd⇔ Bm− Q( n+ m) = M f. Rd
(A.2)
and:
(2)
∑ M = M f. Rd⇔ Qn= M f. Rd
(A.3)
Section (1) corresponds to the critical section at the flange-to-web connection
and section (2) is the section at the bolt axis.
By equating Eqs. (A.2-A.3), the bolt force is computed as:
2n+
m
B = M f . Rd
(A.4)
mn
Eqs. (A.1), (A.3) and (A.4) provide:
⎛ M f . Rd⎞ 4M
f . Rd
F1. Rd .0 = 2⎜B−
⎟=
(A.5)
⎝ n ⎠ m
A.1.2 Type-2 mechanism
For the second mechanism, the equilibrium equations are written as follows:
F2.
Rd .0
∑ Fv= 0 ⇔ Q = B−
2
and:
(A.6)
(1)
∑ M = M f. Rd⇔ Bm− Q( n+ m) = M f . Rd
(A.7)
This mechanism involves bolt fracture. Therefore, the bolt force at “plastic”
conditions is equal to
B = B
(A.8)
50
Rd

Modelling of the M-Φ characteristics of bolted joints: background review
The plastic resistance F2.Rd.0 is then calculated by means of the following relationship:
⎛ 2m⎞ 2 2Mf. Rd+ 2nBRd
F2. Rd .0 = ⎜2− ⎟BRd+
M f . Rd =
(A.9)
⎝ m+ n⎠ m+ n m+ n
By inserting the parameter λ = nmin
Eq. (A.9), F2.Rd.0 is re-written as follows:
2λ
1+
2M f . Rd β 2M f. Rd⎡ ( 2 − β Rd
Rd ) λ ⎤
F2.
Rd .0 = = ⎢1+ ⎥
(A.10)
m 1+ λ m ⎢⎣ βRd ( 1+
λ)
⎥⎦
A.1.3 Type-3 mechanism
Type-3 mechanism is characterized by bolt fracture only. The force equilibrium
equation yields:
∑ Fv = 0⇔ F3. Rd.0 = 2BRd
(A.11)
A.1.4 Supplementary mechanism
Supplementary plastic mechanisms corresponding to the metal shear tearing
around the bolt head or the washer should also be taken into account, though
they are not relevant in most cases. The yielding condition in this case provides
the following relationship:
*
FRd = 2πdwτ
y. ftf (A.12)
whereby τy.f is the yield shear stress of the flanges.
A.2 Influence of the moment-shear interaction on resistance formulations
The moment-shear interaction can be approximately assessed by assuming that
the external fibres take the bending moment stresses and the internal ones the
shear stresses, as illustrated in Fig. A.1 (see reference [1.44]). The reduced
plastic flexural resistance of the flanges is given by:
M f = ∫ σ dS= xt ( f
S
−xb
) eff fy.
f
(A.13)
and the reduced plastic shear resistance is defined as:
Vf = ∫ τ dS = ( tf S
−2x)
beffτy.
f
(A.14)
Under of the Von Mises criterion, the yield shear stress is computed as:
51

State-of-the-art and literature review
52
tf
Fig. A.1 Distribution of internal stresses in the plastic condition under combined
bending moment and shear force.
τ y =
f y
3
(A.15)
From Eqs. (A.13-A.15), the distance x is derived:
tf x = −
2
3 Vf
2 beff fy.
f
(A.16)
Substitution of x into Eq. (A.13) yields:
M f
2
3 V f
= M f. Rd −
4 b f
(A.17)
eff y. f
where Mf.Rd is given by Eq. (1.6). The pure plastic shear resistance, Vf.Rd, is ex-
pressed by the following relationship:
t f
Vf . Rd= befffy. f
(A.18)
3
Therefore, Mf.Rd and Vf.Rd are related by means of:
M f . Rd
2
t f
befffy. f
3
tfVf . Rd
=
4
=
4
(A.19)
Eqs. (A.17-A.19) provide the following yielding condition:
2
M ⎛ f V ⎞ f
+ ⎜ = 1
M ⎜
⎟
f . Rd V ⎟
⎝ f. Rd⎠
The shear force in the T-stub flange is given by:
(A.20)
Vf FRd.0
= B− Q =
2
(A.21)
A.2.1 Type-1 mechanism
Regarding type-1 mechanism, the equilibrium condition provides (§A.1.1):
4M f
F1.
Rd .0 =
m
(A.22)
S
x
x
fy
Mf
τy
Vf

Modelling of the M-Φ characteristics of bolted joints: background review
Mf and Vf are related by means of the following relationship that derives from
Eqs. (A.21-A.22):
Vf F1. Rd.0
= ⇔ M f
2
m
= Vf
2
(A.23)
The yielding condition brings:
2
M ⎛ f V ⎞ f
+ ⎜ = 1⇔1− M ⎜
⎟
f . Rd V ⎟
⎝ f . Rd⎠ 2
2 m V ⎛ f V ⎞ f
− ⎜ = 0
3 tfV ⎜
⎟
f . Rd V ⎟
⎝ f. Rd⎠
(A.24)
that has the positive solution:
( ) 2
V f
Vf . Rd
=
⎡
1 m ⎢
3 t ⎢
f ⎢⎣ ⎤
3
1+ −1⎥
mt
⎥
f ⎥⎦
(A.25)
By equating Eqs. (1.6), (A.18) and (A.23-A.25), the following relationship
is obtained for the plastic resistance associated with type-1 mechanism:
⎡
2
F1. Rd .0 = m⎢ 3 ⎢
⎢⎣ ⎤
3
1+ − 1⎥b 2 eff fy.
f
( mt
⎥
f ) ⎥⎦ 2
8⎛ m ⎞
⎡
= ⎜ ⎢
3⎜
⎟
t ⎟ ⎢
⎝ f ⎠ ⎢⎣ ⎤
3 M f . Rd
1+ −1⎥
(A.26)
2
( mt
⎥
f ) m
⎥⎦
A.2.2 Type-2 mechanism
With reference to type-2 mechanism (§A.1.2), the plastic resistance F2.Rd.0 is
given by Eqs. (A.9-A.10). From Eq. (A.21), Mf and Vf are correlated by means
of the following relationship:
Vf F2.
Rd.0
= ⇔ M f
2
= ( m+ n) Vf − nBRd
(A.27)
The yielding condition provides:
M f
M f . Rd
2
⎛ V ⎞ f
+ ⎜ = 1⇔ 1+ ⎜
⎟
V ⎟
⎝ f . Rd⎠ 4 BRd 3Vf. Rd
−
4 m+ n Vf 3 tfVf. Rd
2
⎛ V ⎞ f
− ⎜ ⎟ = 0
⎜V ⎟
⎝ f. Rd⎠
(A.28)
The ratio BRd Vf. Rd can be written:
BRd
Vf . Rd
=
3 t f 1
2 m βRd
(A.29)
by taking Eqs. (1.6-1.7) and (A.18) into account. Thus, from Eq. (A.28), the
following condition is obtained:
2λ 1+ −
β Rd
2
4 m(
1+
λ ) V ⎛ f V ⎞ f
− ⎜ = 0
3 tfV ⎜
⎟
f . Rd V ⎟
⎝ f . Rd ⎠
(A.30)
The positive solution for Eq. (A.30) is:
53

State-of-the-art and literature review
V f
Vf . Rd
=
⎡
⎢
2 m ⎢
( 1+ λ ) ⎢
3 tf⎢
⎢
⎢⎣ ⎤
2λ
+ 1
⎥
3 β ⎥
Rd
1+ −1
2 ⎥
4 ⎛m⎞ 2 ⎥
⎜ ⎟ ( 1+
λ
⎜ ) ⎥
t ⎟
⎝ f ⎠
⎥⎦
(A.31)
and, therefore, by means of Eqs. (A.7), (A.18) and (A.21), F2.Rd.0 is given by:
⎡
⎢ 2
16 ⎛m⎞ ⎢
F2.
Rd .0 = ⎜ ( 1+ λ )
3 ⎜
⎟
t ⎟
⎢
⎝ f ⎠ ⎢
⎢
⎢⎣ ⎤
2λ
+ 1
⎥
3 β ⎥ M
Rd
f . Rd
1+ −1
2 ⎥
4⎛m⎞
m
2 ⎥
⎜ ⎟ ( 1+
λ
⎜ ) ⎥
t ⎟
⎝ f ⎠ ⎥⎦
(A.32)
A.3 Influence of the bolt dimensions on resistance formulations
To cater for the influence of the bolt finite size on the plastic resistance for
type-1 mechanism, Jaspart (see reference [1.20]) provides an alternative formulation
that assumes that the bolt action is uniformly distributed under the
washer, the bolt head or the nut, as appropriate. Consider the half T-stub represented
in Fig. A.2, whereby qb is the uniformly distributed bolt action, which is
statically equivalent to B, and dw is the diameter of the washer, the bolt head or
nut, as suitable. Equilibrium conditions provide the following relationships:
F1.
Rd.0
∑ Fv = 0 ⇔ Q = qdw
−
(A.33)
2
(1)
∑ M = M f. Rd⇔ qbdwm− Q( n+ m) = M f . Rd
(A.34)
and:
2
(2)
dw
∑ M = M f. Rd⇔Qn− qb= M f. Rd
(A.35)
8
By solving this system of equations, the prying force, the bolt force and the
plastic resistance are obtained:
( 8m+
dw) M f. Rd
Q =
(A.36)
8mn
− m + n d
B = qd =
and:
54
w
( ) w
8( m+ 2n)
M
8 − ( + )
f . Rd
mn m n d
( )
w
( 32n−2d ) M
8 − ( + )
w f . Rd
(A.37)
F1. Rd .0 = 2 B− Q =
mn m n dw
(A.38)
The previous relationships do not allow for moment-shear interaction. By

Modelling of the M-Φ characteristics of bolted joints: background review
Q
e m
n
(2)
B
(1)
F1.Rd.0
qb
B
Q
tf
Mf.Rd
Mf.Rd
Fig. A.2 Influence of the bolt-finite size on the T-stub resistance.
applying a similar procedure to §A.2.1, the following relationships are derived
for the plastic resistance. The plastic T-stub resistance is now given by:
( 32n−2dw) M f
F1.
Rd .0 =
8mn
− ( m + n) dw
From Eq. (A.21),
(A.39)
Vf F1.
Rd.0
= ⇔ M f
2
8mn
− ( m + n) dw
=
Vf
16n−dw
(A.40)
By re-arranging the equations, the positive solution for the yielding condition
is written as follows:
( ) 2
V f
Vf . Rd
with:
=
⎡
2 m
Γ ⎢
3 t ⎢
f ⎢⎣ ⎤
3
1+ −1⎥
2
4Γ
mt
⎥
f ⎥⎦
(A.41)
55

State-of-the-art and literature review
56
( )
8λm− 1+
λ dw
Γ=
16λm−dw
Thus:
2
16 ⎛ m ⎞
⎡ ⎤
3 M .
F1.
Rd .0 = ⎜ Γ ⎢ 1+ −1⎥
2
2
3 ⎜
⎟
t ⎟ ⎢
f 4 ( mt
⎥
⎝ ⎠ Γ f ) m
⎢⎣ ⎥⎦
A.4 Formulations for prediction of elastic stiffness of bolted T-stubs
A.4.1 Elastic theory for evaluation of the elastic stiffness of a bolted T-stub
f Rd
(A.42)
(A.43)
The elastic stiffness of a bolted T-stub can be computed by means of the theoretical
model shown in Fig. 1.14. From simple elastic bending theory, applying
the double integration method, the deflection of the T-stub web, ∆e.0.u/l is computed
as:
2
1 ⎧⎪ n⎡ 2 n ⎤
∆ = y ( x = m)
( )
e.0. u/ l
2
=− ⎨ ⎢ m+ n − ⎥B−
EI f ⎪⎩ 2⎣ 3 ⎦
2 3
⎡n⎡ 2
2 n ⎤ m ⎤ F⎫⎪
−⎢ ⎢m − ( m+ n)
− ⎥−
⎥ ⎬
⎣2⎣ 3 ⎦ 3 ⎦ 2⎭⎪
If represents the flange inertia and is defined as follows:
(A.44)
I f
3
b′ eff tf
=
12
(A.45)
where b′ eff is the effective width for stiffness calculations, computed per bolt
row. Eq. (A.44) can be re-written in a simpler form by bringing in the parame-
ters Zf and αf defined in Eqs. (1.16-1.17):
Z f ⎡F⎛33⎞⎤ ∆ e.0. u/ l = 2B
α f α f
E
⎢ − ⎜ − ⎟
4 4
⎥
⎣ ⎝ ⎠⎦
(A.46)
The bolt-elastic deformation, ∆e.bt, is given by:
BLb
∆ ebt . = (A.47)
EAs
The compatibility requirement between the bolt and the flange deformation at
the bolt centreline yields:
∆ Z eb .
f ⎡F⎛33⎞ 2 3 ⎤ BLb
= y( x1= n) = α f 2α f B(
6α f 8α
f )
2 E
⎢ ⎜ − ⎟−
− =
2 2
⎥
(A.48)
⎣ ⎝ ⎠
⎦ 2EAs
Thus:

Modelling of the M-Φ characteristics of bolted joints: background review
⎛33⎞ ⎜ α f − 2α
f ⎟Z
fF
2
B =
⎝ ⎠
2 3 Lb
26 ( α f − 8α
f ) +
2As
q
= F
2
(A.49)
where q is defined by Eq. (1.15). From Eqs. (A.46-A.49) the deformation of
the upper (u) or the lower (l) T-stub element is given by:
Z f ⎡1 q ⎛3 3 ⎞⎤
∆ e.0. u/ l = α f 2α
f F
E
⎢ − ⎜ − ⎟
4 2 2
⎥
⎣ ⎝ ⎠⎦
and the total deformation:
(A.50)
Z f ⎡1 ⎛3 3 ⎞⎤
∆ e.0 = ∆ e.0. u +∆ e.0. l = q α f 2α
f F
E
⎢ − ⎜ − ⎟
2 2
⎥
⎣ ⎝ ⎠⎦
The elastic axial stiffness of the bolted T-stub is then defined as:
(A.51)
F
ke.0
= =
∆e.0 Z f
E
⎡1 ⎛3 3 ⎞⎤
⎢ −q⎜ α f −2α
f ⎟
2 2
⎥
⎣ ⎝ ⎠⎦
(A.52)
A.4.2 Simplification of the stiffness coefficients for inclusion in design codes
As already mentioned above, Jaspart (see reference [1.46]) simplifies the complex
above formulae for inclusion in Eurocode 3 – cf. §1.4.1.2. By supposing
that the analysis of the T-elements and the bolts is carried out separately, ke.T is
derived by means of Eq. (A.52) adopting A s ≈ ∞ in Eq. (1.16). Further, if n is
taken as equal to 1.25m, as explained in the text, then:
n 1.25m
α f = = = 0.278
(A.53)
2 m+ n 2 m+ 1.25m
( ) ( )
( + ) ( + )
3 3
⎡2m n ⎤
Z f =
⎣ ⎦
3
b′ eff tf and:
⎡2 =
⎣ m 1.25m
⎤⎦
3
b′ eff tf 3
m
= 91.125 3
b′ eff tf
(A.54)
⎛3 3⎞ 2⎜ α f − 2α f ⎟Z f
2
q =
⎝ ⎠
2 3 Lb 26 ( α f − 8α f ) Z f +
2As
⎛3 3⎞
2⎜ × 0.278 − 2× 0.278 ⎟Z
f
2
=
⎝ ⎠
2 3 Lb
26 ( × 0.278− 8× 0.278)
Z f +
∞
= 1.28(A.55)
By replacing the above results in Eq. (A.52):
k
eT .
3 3
E ⎛m⎞ 0.5E⎛
m⎞
= ⎜ ⎟ ≈ ⎜ ⎟
1.936b′
⎜
eff t ⎟
f b ⎜
eff t ⎟
⎝ ⎠
′
⎝ f ⎠
(A.56)
57

State-of-the-art and literature review
The effective width for stiffness calculations, b′ eff , is related to the effective
width for strength calculations, beff as explained below. With reference to Fig.
1.16, the elastic bending moment at the T-stub flange (section (1)) is evaluated
as follows:
( 1)
M = (0.63 − 0.13× 2.25) Fm = 0.3375Fm
(A.57)
If the maximum elastic load corresponds to the formation of a plastic hinge at
section (1), then from internal equilibrium conditions and Eq. (A.57) the following
relationship is obtained:
2
1 (1) 1 b′ eff tf
F = M = f
(A.58)
58
el max y. f
0.3375m 0.3375m 4
The maximum elastic load, Fel, corresponds to 2/3 of the plastic resistance, FRd,
as in Eurocode 3 (see reference [1.1]), being FRd given by Eq. (A.5). As the Tstub
flange is fixed at the bolt centreline, the only possible collapse mode of
the T-stub is that of the complete yielding of the flange (type-1 mechanism).
Then, the maximum elastic moment is given by:
2
2 2beff
tf
Fel = F1. Rd .0 = fy.
f
(A.59)
3 3 m
by taking Eqs. (A.5) and (1.6) into consideration. By equating Eqs. (A.57-
A.58), b′ eff is computed as follows:
2 2
1 b′ eff tf 2beff tf
2
f ′
y. f = fy. f ⇔ beff= × 0.3375× 4beff= 0.9beff(A.60)
0.3375m 4 3 m
3
The bolt elastic deformation can be computed by means of Eq. (A.47) and
assuming that the prying effect increases the bolt force from 0.5F to 0.63F. The
bolt elastic stiffness is expressed as the ratio between the tensile force F and
∆e.bt:
F F EAs
kebt
. = = ≈1.6
(A.61)
∆ 0.63FL
L
ebt .
b
b
EAs

PART II: FURTHER DEVELOPMENTS ON THE T-STUB MODEL
59

2 IMPROVEMENTS ON THE T-STUB MODEL: INTRODUCTION
2.1 INTRODUCTION
The T-stub model is widely accepted as a simplified model for the characterization
of the behaviour of the tension zone of a bolted joint, which is often the
most important source of deformability of the whole joint. Within the framework
of the component method, this connection behaviour is modelled by
means of a F-∆ response that is intrinsically nonlinear, due to mechanical and
geometrical nonlinearities and contact phenomena. Current design specifications
based on the T-stub model rely on pure plastic yield line mechanisms and
do not allow for a complete characterization of the deformation capacity at ultimate
conditions.
Modern design codes, as the Eurocode 3 [2.1], approximate the nonlinear
component behaviour by means of a linearized response, characterized by a full
“plastic” resistance, FRd.0 and initial stiffness, ke.0. The design rules for the prediction
of both parameters are given in §1.4.1. Fig. 2.1 illustrates the bilinear
approximation of the actual behaviour of an isolated T-stub connection tested
by Bursi and Jaspart [2.2]. In this particular case, the plastic mechanism of the
connection is of type-1, which corresponds to double curvature of the flange,
owing to the formation of plastic hinges at the bolt axes and at the flange-toweb
connection. Therefore, the connection has considerable deformation capacity
[2.3]. No quantitative guidance is given in the code to evaluate this
property though, and therefore no limits are imposed to the extension of the
plastic plateau.
This part of the research work is devoted to the characterization of the full
nonlinear (monotonic) behaviour of isolated T-stub connections, in order to
provide insight into the actual component behaviour, failure modes and deformation
capacity. Tests, both experimental and numerical, were hence carried
out at the Delft University of Technology and at the University of Coimbra to
fulfil those objectives. Additionally, this test programme clarified some aspects
related to the differences between the assembly types. The T-stub assemblage
may comprise hot rolled profiles or welded plates as T-stub elements, denominated
HR-T-stubs and WP-T-stubs, respectively. The current approach to account
for the behaviour of T-stubs made up of welded plates consists in a mere
extrapolation of the existing rules for the other assembly type. This assumption
can be erroneous and can lead to unsafe estimations of the characteristic properties,
as reported earlier by the author in technical literature [2.4-2.5].
The following sections present and discuss the results of thirty-two experimental
tests and three numerical tests on WP-T-stubs, and twenty-six numerical
tests on HR-T-stubs. The experimental programme is described in Chapter
61

Further developments on the T-stub model
62
Total applied load (kN)
210
180
150
120
90
60
30
Actual response
Eurocode 3 bilinear approximation
0
0 1 2 3 4 5 6 7 8 9 10
Total deformation (mm)
Fig. 2.1 Simplified approximations of the response of a bolted T-stub connection.
3. Detailed results for the benchmark specimen are also provided. The numerical
model is fully described in Chapter 4 where the calibration procedure is
also explained. Chapter 5 is completely devoted to the parametric study that
highlights the main parameters affecting the deformation capacity of bolted Tstubs
and assesses, both qualitatively and quantitatively, their influence on the
overall behaviour of the connection. Moreover, this study adds further examples
to a database for future validation of a simplified analytical (beam) model
that is addressed in Chapter 6. This model attempts at filling in some code gaps
on the characterization of the component behaviour, namely post-limit stiffness,
kp-l.0 and deformation capacity, ∆u.0.
2.2 FAILURE MODES
In this work, two categories of failure modes are considered: plastic mechanisms,
that rely on pure “plastic” conditions and ultimate conditions, which
correspond to cracking of the material. “Plastic” failure mechanisms indicate
the strength of connections for design purposes whereas ultimate conditions indicate
failure of the connection after certain deformation. The three possible
“plastic” failure mechanisms have been briefly described in §1.4.1 and correspond
to: (i) type-1: complete yielding of the flange, with the development of
four plastic hinges (double curvature bending), (ii) type-2: partial yielding of
the flange with bolt “plastic” failure, with the development of two plastic
hinges at the flange-to-web connection (single curvature bending) and (iii)
type-3: bolt “plastic” failure without yielding of the flanges (the flange remains
virtually undeformed). With respect to ultimate conditions, four different typologies
for the failure modes of a bolted T-stub connection are defined: (i)
type-11, characterized by a plastic type-1 mode and cracking of the flange ma-

Improvements on the T-stub model: introduction
terial at ultimate conditions, (ii) type-13, also a type-1 plastic mechanism but
with fracture of the bolt at limit conditions, (iii) type-23, where the plastic
mode involves both flange and bolt and the deformation capacity is governed
by the bolt itself and (iv) type-33, a type-3 “plastic” mode and deformation capacity
determined by bolt fracture.
The failure mechanism typology, in both cases, is governed by the β-ratio,
which is a resistance-based parameter that expresses the ratio between the flexural
resistance of the flanges and the axial strength of the bolts. It depends exclusively
on geometric and mechanic characteristics of the connection. In plastic
conditions, this parameter is defined by Eq. (1.7). With reference to ultimate
conditions, the β-ratio, βu, is given by:
2M fu .
β u = (2.1)
Bm u
whereby Mf.u is the ultimate flexural resistance of the T-stub flanges and Bu is
the tensile strength of the bolts. According to Piluso et al. [2.6], the limit value
for this parameter to have a collapse failure mode governed by cracking of the
flange material is:
2λ
⎡ dw
⎤
βu.lim = 1− ( 1+
λ)
2λ+ 1
⎢
8n
⎥
⎣ ⎦ (2.2)
Otherwise (βu > βu.lim), bolt fracture is likely to determine the ultimate conditions.
Table 2.1 summarizes the various failure mechanism types.
The ultimate tensile strength of a bolt subjected to an axial loading is evaluated
by assuming that tension fracture of the bolt occurs before stripping of the
threads. Therefore, the axial ultimate strength is calculated as the ultimate
strength of the bolt material multiplied by the effective tensile area:
Bu = fu. bAs (2.3)
For computation of the ultimate flexural resistance of the flange, two alternative
expressions are suggested. Gioncu et al. [2.7] propose the following relationship:
M f . Rd
M fu . = (2.4)
ρ
y
Table 2.1 Failure mechanisms typologies.
“Plastic” conditions Ultimate conditions
Typology βRd Typology βu
2λ
Type-11 ≤ βu.lim
Type-1 ≤
2λ+ 1
Type-13
Type-2
2λ
>
2λ+ 1
but 2 ≤ Type-23
Type-3 > 2
Type-33
>
βu.lim
63

Further developments on the T-stub model
being ρ y = fy fu
the yield ratio and Mf.Rd the full plastic flexural resistance of
the T-stub flanges, defined in Eq. (1.6). Faella and co-authors [2.6,2.8] present
an alternative expression that derives from simple equilibrium equations between
internal stresses and the external moment. They assumed that the flange
behaves as a rectangular compact section of width beff and thickness tf. The
flange constitutive law is approximated by means of a quadrilinear model (Fig.
2.2). The following relationship is therefore obtained:
M f . y⎡ 1 E ⎛ h µ ⎞⎛ h µ ⎞ h
M fu . = ⎢3− + 2 ( µ u−µ h)
⎜1− ⎟⎜2+ ⎟−
2 ⎢⎣ µ u E ⎝ µ u ⎠⎝ µ u ⎠
Eh − E ⎛ u µ ⎞⎛ m µ ⎞⎤
m
− ( µ u −µ m)
⎜1− ⎟⎜2+ ⎟⎥ E
⎝ µ u ⎠⎝ µ u ⎠⎦⎥
(2.5)
whereby Mf.y is the bending moment corresponding to first yielding of the
flange:
2
t f
M f . y= 6
and:
fy. fbeff 2
= M f . Rd
3
(2.6)
ε h µ h =
ε y
εm µ m =
εy εu
µ u =
εy
(2.7)
The ratio M fu . M fy . is a parameter that also depends exclusively on the mechanical
properties of the flange material and can be written in a formally
equivalent expression to Eq. (2.4):
M f . Rd
M fu . = *
ρ
(2.8)
64
y
σ
fy
E
Eh
εy εh εm εu
Fig. 2.2 Flange piecewise material constitutive law (qaudrilinear approximation
proposed by Faella and co-authors [2.8]).
Eu
ε

with (cf. Eqs. (2.5-2.6)):
* 4⎡1 E ⎛ h µ ⎞⎛ h µ ⎞ h
ρ y = ⎢3− + 2 ( µ u −µ h)
⎜1− ⎟⎜2+ ⎟−
3 ⎢⎣ µ u E ⎝ µ u ⎠⎝ µ u ⎠
−1
Eh − E ⎛ u µ ⎞⎛ m µ ⎞⎤
m
− ( µ u −µ m)
⎜1− ⎟⎜2+ ⎟⎥ E
⎝ µ u ⎠⎝ µ u ⎠⎦⎥
2.3 REFERENCES
Improvements on the T-stub model: introduction
(2.9)
[2.1] European Committee for Standardization (CEN). PrEN 1993-1-8:2003,
Eurocode 3: Design of steel structures, Part 1.8: Design of joints, Stage
49 draft, May 2003, Brussels, 2003.
[2.2] Bursi OS, Jaspart JP. Benchmarks for finite element modelling of bolted
steel connections. Journal of Constructional Steel Research; 43(1):17-
42, 1997.
[2.3] Zoetemeijer P. Summary of the research on bolted beam-to-column
connections. Report 25-6-90-2. Faculty of Civil Engineering, Stevin
Laboratory – Steel Structures, Delft University of Technology. 1990.
[2.4] Girão Coelho AM, Bijlaard F, Simões da Silva L. On the deformation
capacity of beam-to-column bolted connections. Document ECCS-
TWG 10.2-02-003, European Convention for Constructional Steelwork
– Technical Committee 10, Structural connections (ECCS-TC10), 2002.
[2.5] Girão Coelho AM, Bijlaard F, Simões da Silva L. On the behaviour of
bolted end plate connections modelled by welded T-stubs. In: Proceedings
of the Third European Conference on Steel Structures (Eurosteel)
(Eds.: A. Lamas and L. Simões da Silva), Coimbra, Portugal, 907-918,
2002.
[2.6] Piluso V, Faella C, Rizzano G. Ultimate behavior of bolted T-stubs – I:
Theoretical model. Journal of Structural Engineering ASCE;
127(6):686-693, 2001.
[2.7] Gioncu V, Mateescu G, Petcu D, Anastasiadis A. Prediction of available
ductility by means of local plastic mechanism method: DUCTROT
computer program, Chapter 2.1 in Moment resistant connections of steel
frames in seismic areas (Ed.: F. Mazzolani). E&FN Spon, London, UK;
95-146, 2000.
[2.8] Faella C, Piluso V, Rizzano G. Structural semi-rigid connections – theory,
design and software. CRC Press, USA, 2000.
65

3 EXPERIMENTAL ASSESSMENT OF THE BEHAVIOUR OF T-
STUB CONNECTIONS
3.1 INTRODUCTION
A series of thirty-two tests on bolted T-stub connections made up of welded
plates is presented in this chapter. Although T-stubs have been used for many
years to model the tension zone of bolted joints, the research was mainly concentrated
on rolled profiles as T-stub elements. To extend this model to the
case of welded plates as T-stub elements, a test programme was undertaken at
the Delft University of Technology. It provides insight into the behaviour of
this different type of assembly, in terms of resistance, stiffness, deformation
capacity and failure modes, in particular. The key variables tested include the
weld throat thickness, the size of the T-stub, the type and diameter of the bolts,
the steel grade, the presence of transverse stiffeners and the T-stub orientation.
The results show that the welding procedure is particularly important to ensure
a ductile behaviour of the connection. Most of the T-stubs failed by tension
fracture of the bolts after significant yielding of the flanges. However,
some of the specimens have shown early damage of the plate material near the
weld toe due to the effect of the welding consumable that induced premature
cracking and reduced the overall deformation capacity. A solution to this problem
was given by setting requirements to the weld metal to be used.
This chapter describes the main collapse modes observed and gives detailed
information on the benchmark specimen WT1 (eight tests). The remaining results
are discussed in Chapter 5, as part of the parametric study presented.
3.2 DESCRIPTION OF THE EXPERIMENTAL PROGRAMME
3.2.1 Geometrical properties of the specimens
The basic configuration of the test specimens comprised two plates of 10 mm
thickness. The plates were welded together by means of a continuous 45º-fillet
weld with similar plate characteristics. Snug-tightened high-strength bolts fastened
the T-stub elements. The unstiffened specimens were designed to fail according
to a plastic collapse mode 1 that ensures a good ductility of the connection
[3.1].
The general characteristics of the specimens are given in Table 3.1. For notation
the reader should refer to Fig. 3.1. Both nominal and actual properties
are reported. The actual geometry was measured before testing the specimens
and is listed in Table 3.1 as an average value of the several T-elements from
67

Further developments on the T-stub model
each series. In series WT7 and WT57, the T-stub elements were fastened by
means of one bolt row only due to equipment limitation. The two T-stubs for
most series were symmetrical. For series WT64A and WT64B, the T-stub elements
included a stiffener only on one side of the connection.
Table 3.1 Tests description [dimensions (nominal and averaged actual values
– in bold) in mm; //: T-stub elements parallel, ⊥: T-stub elements
orientated at right angles].
Test ID #
Geometry
WT1 8
tf
10
10.32
tw
10
10.93
b
45
45.05
p
50
49.8
e1
20
20.1
w
90
89.7
e
30
30.0
aw
5
WT2A
WT2B
WT4A
2
2
2
10
10.27
10
10.29
10
10.39
10
10.54
10
10.69
10
11.00
45
45.0
45
44.95
75
74.85
50
49.9
50
49.9
90
89.6
20
20.0
20
20.0
30
30.1
90
89.9
90
89.9
90
89.7
30
29.9
30
29.9
30
30.0
3
7
5
WT4B 1
10
10.37
10
10.92
75
74.8
90
89.8
30
29.9
90
89.8
30
29.9
5
WT51
WT53C
2
1
10
9.98
10
10.09
10
10.01
10
10.10
45
45.0
45
45.05
50
50.7
50
50.0
20
19.6
20
20.0
90
90.1
90
90.1
30
30.2
30
30.0
5
5
WT53D 1
10
10.14
10
10.22
45
45.0
50
49.9
20
20.0
90
90.0
30
30.0
5
WT53E
WT61
1
2
10
10.09
10
10.31
10
10.17
10
10.93
45
44.65
45
45.1
50
49.2
50
49.9
20
20.0
20
20.1
90
90.0
90
89.8
30
30.1
30
29.4
5
5
WT64A 1
10
10.28
10
10.94
75
74.95
90
90.0
30
29.9
90
89.7
30
29.8
5
WT64B
WT64C
2
1
10
10.42
10
10.30
10
10.82
10
10.84
75
74.9
75
75.1
90
89.9
90
89.7
30
29.9
30
30.2
90
89.7
90
89.8
30
30.0
30
29.9
5
5
WT7_M12 1
10
10.33
10
10.84
75
75.6
30 90 30
⎯
30.0 89.9 29.9
5
WT7_M16 1
10
10.33
10
10.81
75
74.9
30 90 30
⎯
WT7_M20 1
10
10.33
10
10.87
75
75.2
30.0
30
89.9
90
29.8
30
5
⎯
WT57_M12 1
10
10.09
10
10.18
75
75.0
29.9
30
89.8
90
29.7
30
5
⎯
30.0 89.7 30.2
5
WT57_M16 1
10
10.16
10
10.18
75
75.3
30 90 30
⎯
WT57_M20 1
10
10.15
10
10.15
75
75.1
30.0
30
90.0
90
30.1
30
5
⎯
30.0 90.0 30.2
5
68

Experimental assessment of the behaviour of T-stub connections
3.2.2 Mechanical properties of the specimens
3.2.2.1 Tension tests on the bolts
In order to characterize the mechanical properties of the M12, grade 8.8 and
10.9 bolts, two series of experiments were performed. In the first series, the ac-
Table 3.1 Tests description (cont.).
Test ID # Bolt Materials Stiff. Orient.
φ # Type Plate Bolt
WT1 8
12
11.8
4 ST S355 8.8 No //
WT2A
WT2B
WT4A
2
2
2
12
11.8
12
11.8
12
11.8
4
4
4
ST
ST
ST
S355
S355
S355
8.8
8.8
8.8
No
No
No
//
//
//
WT4B 1
12
11.8
4 ST S355 8.8 No ⊥
WT51
WT53C
2
1
12
11.8
12
⎯
4
4
ST
FT
S690
S690
8.8
8.8
No
No
//
//
WT53D 1
12
11.9
4 ST S690 10.9 No //
WT53E
WT61
1
2
12
⎯
12
11.9
4
4
FT
ST
S690
S355
10.9
8.8
No
Yes
//
//
WT64A 1
12
11.8
4 ST S355 8.8 Yes //
WT64B
WT64C
2
1
12
11.8
12
11.8
4
4
ST
ST
S355
S355
8.8
8.8
Yes
Yes
⊥
//
WT7_M12 1
12
11.9
2 ST S355 8.8 No //
WT7_M16
WT7_M20
WT57_M12
1
1
1
16
⎯
20
⎯
12
2
2
2
FT
FT
FT
S355
S355
S690
8.8
8.8
8.8
No
No
No
//
//
//
WT57_M16
WT57_M20
1
1
16
⎯
20
⎯
2
2
FT
FT
S690
S690
8.8
8.8
No
No
//
//
69

Further developments on the T-stub model
70
Section xx
x x
e w
bf
aw
Fig. 3.1 T-stub geometry: notation.
e
e1
p
e1
b
b
Plan
tual bolt (short-threaded, ST or full-threaded, FT) was tested under tension
(Fig. 3.2a). Failure always occurred in the threaded region. This type of test did
not provide enough data to determine the Young modulus and the proof
strength of the bolt. Then, in a second test series, the bolts were machined so
that the threads within the bolt grip were removed and a constant diameter was
obtained (Fig. 3.2b). This procedure was not expected to introduce major influences
on the bolt behaviour since the removal of the material was limited to the
threads, even though the bolt mechanical properties were not uniform.
Both specimen types were tested in tension under displacement control in a
special test rig as shown in Fig. 3.3. The elongation behaviour of the bolt was
measured by means of a measuring bracket (or horseshoe device, also illustrated
in Fig. 3.3) in the first series of tests and by means of internal strain
gauges in the second. The strain gauges (TML-BTM-6C) could measure strains
up to 6000 µm/m. The graphs from Fig. 3.4a plot the bolt elongation curve for

Experimental assessment of the behaviour of T-stub connections
one of the short-threaded M12 grade 8.8 (group 2) tested bolts. The graph includes
the load cell displacement results and the measuring bracket data up to
its removal in the elastic range. Clearly, the results obtained from the measuring
bracket are stiffer since the displacement of the actuator also includes the
slippery of the clamps. Fig. 3.4b traces the force-strain results obtained for an
identical bolt type (now chosen from the second test series). Naturally, the
Group 1 (8.8) Group 3 (10.9) Group 2 (8.8) Group 4 (10.9)
(i) Full-threaded specimens.
(a) First series: “actual” bolts.
(ii) Short-threaded specimens.
Group 1 (8.8) Group 3 (10.9) Group 2 (8.8) Group 4 (10.9)
(i) Full-threaded specimens.
(b) Second series: machined bolts.
(ii) Short-threaded specimens.
Fig. 3.2 Bolt specimens: two series of tests.
Fig. 3.3 Test rig for the bolt tensile testing and horseshoe device.
71

Further developments on the T-stub model
72
Applied load (kN)
80
70
60
50
40
30
(a) Bolt elongation behaviour.
Applied load (kN)
20
Results from the load cell
10
0
Results from the measuring bracket
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
80
70
60
50
40
30
(b) Bolt strain behaviour.
Applied load (kN)
Deformation (mm)
20
10
0
0 600 1200 1800 2400 3000 3600 4200 4800 5400 6000 6600
80
70
60
50
40
30
20
10
Strain (µm/m)
Maximum load
Results from the measuring bracket
Results from the strain gauge
0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
Bolt elongation (mm)
(c) Comparison of the bolt experimental (elastic) results for both test series.
Fig. 3.4 Bolt tensile response (e.g. bolt from group 2).

Experimental assessment of the behaviour of T-stub connections
maximum load level in the latter case decreases, as the bolt tensile area is
smaller. To verify the accuracy of the special bolt-measuring bracket, Fig. 3.4c
compares the elastic deformation of two bolts from the same group 2, representing
each bolt series. The bolt elongation is given by ∆b = εbLg, in the case
of the strain measurements, being εb the bolt strain and Lg the grip length. The
results are identical for both series, which means that the measuring bracket
that is much simpler to attach can be used to assess the bolt elongation behaviour
in future tests.
Bolts M16 and M20 used in series WT7 and WT57 have not been tested.
Table 3.2 summarizes the average relevant characteristics for the tested
bolts. Usually, for the bolts, the following parameters are measured: Young
modulus, E, ultimate or tensile stress, fu and ultimate strain, εu.
Table 3.2 Average characteristic values for the bolts.
Bolt grade Type Group E (MPa) fu (MPa) εu
8.8
FT
ST
1
2
216942
221886
968.36
919.91
0.20
0.13
10.9
FT
ST
3
4
217060
217824
1196.37
1165.97
0.14
0.11
3.2.2.2 Tension tests on the structural steel
The test programme included two different steel grades: S355 and S690. According
to the European Standards EN 10025 [3.2] and EN 10204 [3.3], the
steel qualities were S355J0 (ordinary steel) and N-A-XTRA M70 (highstrength
steel for plates), respectively. Table 3.3 summarizes the chemical
composition for the two steel grades.
The coupon tension testing of the structural steel material was performed
according to the RILEM procedures [3.4]. The plate coupon specimens were of
a standard type for flat materials and were of full thickness of the product [3.4].
Fig. 3.5 depicts the test arrangements for the standard tensile test. The experiments
were driven under displacement control. The engineering stress-strain
relation for the web and flange strips is represented in Fig. 3.6, for one of the
tested strip-coupons. The four typical regions of the stress-strain curve of a low
carbon structural steel are very clear: linear elastic region, yield plateau, strain
hardening region and strain softening or necking portion, after reaching the
maximum load.
The average characteristics are set out in Table 3.4. In this table the values
for the Young modulus, E, the strain hardening modulus, Eh, the static yield
and tensile stresses, fy and fu, the yield ratio, ρy the strain at the strain hardening
point, εh, the uniform strain, εuni, and the ultimate strain, εu, are given. The
stress values indicated in the table correspond to the static stresses, which are
the stress values obtained at zero strain rate, i.e. during a hold on of the defor-
73

Further developments on the T-stub model
(a) Test set up. (b) Detail of the
extensometer.
Fig. 3.5 Tensile coupon tests.
74
Stress (MPa)
900
750
600
450
(a) Steel grade S355.
Stress (MPa)
(c) Coupon
necking.
300
Web strip coupon
150
Flange strip coupon
0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
900
750
600
450
Strain (m/m)
300
Web strip coupon
150
Flange strip coupon
0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Strain (m/m)
(b) Steel grade S690.
Fig. 3.6 Engineering stress-strain relation.
(d) S355 coupons after
failure.

Experimental assessment of the behaviour of T-stub connections
mation driven experiment. It has been observed that the static stresses were
reached after a hold on of circa one minute. The total hold on lasted for three
minutes. The yield ratio gives an idea on the material ductility. Gioncu and
Mazzolani suggest that a good ductility is ensured if 0.5 ≤ ρy ≤ 0.7 [3.5]. High
strength steel grades with ρy > 0.9 show a rather poor structural ductility [3.5].
That is the case of the steel grade S690 (Table 3.4). In the author’s opinion,
these values are rather conservative. Eurocode 3 indicates that a good material
ductility is guaranteed if ρy ≤ 0.83 (recommended value for steel grades up to
S460). The assurance of a good material ductility does not necessarily imply
that the whole structure is ductile. The structural ductility depends on the yield
ratio but especially on the structural discontinuities.
Table 3.3 Chemical composition of the structural steels according to the
European standards.
%C %Mn %Si %P %S %N %CEV
max. max. max. max. max. max. max.
S355J0 0.20 1.60 0.55 0.040 0.045 0.009 0.40
0.20 1.60 0.80 0.020 0.010 ⎯ 0.48
N-A-XTRA
M70
Table 3.4 Average characteristic values for the structural steels.
Steel
grade
Strip # E
(MPa)
Eh
(MPa)
fy
(MPa)
fu
(MPa)
ρy
S355
Web
Flange
2
2
209211
209856
2145
2264
391.54
340.12
493.80
480.49
0.793
0.708
S690
Web
Flange
2
2
208895
204462
2201
2495
706.31
698.55
742.96
741.28
0.950
0.940
Steel
grade
Strip # εh εuni εu
S355
Web
Flange
2
2
0.019
0.015
0.163
0.224
0.300
0.361
S690
Web
Flange
2
2
0.018
0.014
0.082
0.075
0.160
0.174
3.2.3 Testing procedure
The specimens were subjected to monotonic tensile force, which was applied to
the webs that were clamped to the testing machine (Schenck, maximum test
load 600 kN, maximum piston stroke ±125 mm) as shown in Fig. 3.7. The tests
were carried out under displacement control with a speed of 0.01 mm/s up to
collapse of the specimens. Two different ultimate failure modes were observed,
75

Further developments on the T-stub model
as explained below in the text: (i) fracture of the bolts and (ii) cracking of the
flange near the weld toe.
The gap of the flanges was measured at opposite sides of the specimen, in
the centreline of the webs by means of Linear Variable Displacement Transducers
(LVDTs). The bolt elongation was measured with a measuring bracket
that was removed prior to collapse, as before, so that it was not damaged. In
some of the specimens, internal strain gauges similar to those used in the tension
tests were attached to the bolts. Strain gauges TML (maximum strain
30000 µm/m) were used to monitor strains in the flange. Due to cost restrictions
not all specimens have been instrumented with strain gauges. For illustration,
Fig. 3.8 shows the instrumentation of some of the specimens.
Before installation of the specimens into the testing machine, the dimensions
of the plates were recorded and the bolts were hand-tightened and measured.
The specimen was next placed into the machine and aligned, so that the
clamping devices were centred with respect to the webs. The bolts were subsequently
fastened by using an ordinary spanner (45º turn) and measured. After
that, the measurement devices and strain gauges, if any, were connected. The
test itself then started with loading of the specimen up to 2/3FRd.0, which corresponded
to the theoretical elastic limit. FRd.0 was determined according to
Eurocode 3. Complete unloading followed on and the specimen was then reloaded
up to collapse. In this third phase the test was interrupted at the load
(a) Unstiffened specimen. (b) Stif. spec. (T-stubs orientated at 90º).
(c) Detail of the measuring devices.
Fig. 3.7 Test set up for testing WP-T-stubs.
76

30.0 mm
Experimental assessment of the behaviour of T-stub connections
Left side Right side
5.0 mm
SG5
SG4
SG3
SG2
SG1
90.0 mm
SG6
SG7
30.0 mm
20.0 mm
50.0 mm
20.0 mm
Left side Right side
30.0 mm
SG4
SG6z
SG6x
SG3
SG2
90.0 mm
(a) Specimens WT1b/c/d/h, WT51a. (b) Specimen WT51b.
Left side Right side
LB RB
30.0 mm
SG3
SG2
LF RF
SG1
90.0 mm
30.0 mm
30.0 mm
90.0 mm
30.0 mm
HP3
SG7z
SG7x
30.0 mm
Left side Right side
HP1
30.0 mm
LB
SG6 SG5
LF
SG4
HP2
90.0 mm
(i) Upper profile. (ii) Lower profile.
(c) Specimen WT64Bb.
HP3
14.0
Left side Right side
SG4
SG2
SG3
40.0
30.0 mm
SG5
16.0
SG7
SG6
SG1
48.0
90.0 mm
HP1
HP2
30.0 mm
30.0 mm
90.0 mm
30.0 mm
RB
RF
30.0 mm
20.0 mm
50.0 mm
20.0 mm
30.0 mm
HP4 90.0 mm
30.0 mm
(d) Specimen WT64C (upper profile; lower profile not instrumented).
Fig. 3.8 Instrumentation of some of the tested specimens (SG: strain gauge;
L: left; R: right; B: back; F: front; HP: LVDT).
77

Further developments on the T-stub model
levels of 2/3FRd.0, FRd.0, at the knee-range and after this level each six minutes,
equivalent to an actuator displacement of 3.6 mm. The knee-range of the F-∆
curve (K-R) corresponds to the transition from the stiff to the soft part. The
hold on of the test lasted for three minutes and intended to record the quasistatic
forces.
Regarding the stiffened specimens, the former load levels were taken as
equal to the parent unstiffened cases. For the rotated configurations, the lower
hydraulic actuator was rotated 90º so that the T-stub element was orientated at
a right angle to the upper element (Fig. 3.7b).
3.2.4 Aspects related to the welding procedure
In this type of T-stub assembly, two plates, web and flange, are welded together
by means of a continuous 45º-fillet weld. The fillet welds were done in
the shop in a down-hand position. The procedure involved manual metal arc
welding in which a consumable electrode was used. Three main zones could be
identified after the welding process [3.6]: the weld metal (WM), the heat affected
zone (HAZ) and the base metal (BM), which is the part of the parent
plate that is not influenced by the heat input. The HAZ is the portion of the
plate on either side of the weld affected by the heat in which metal suffers
thermal disturbances and therefore structural modifications that may include
re-crystallization, refining and grain growth [3.7]. The hot WM causes the plate
to bend up due to shrinkage during cooling down and so considerable force is
exerted to do this [3.7]. Residual stresses can then be expected in the HAZ.
Obviously, this will influence the overall behaviour of the connection.
The composition of the WM deposited with the electrode compared to that
of the BM is of great importance, since this will naturally alter the properties of
the steel at and near the weld toe [3.7]. For each steel quality there are often a
large number of electrode types to choose from. In this test programme two different
types of carbon steel covered electrodes were used: rutile and basic (Table
3.5). The distinction between them lies in the type of covering that result in
different performances. Rutile electrodes have high titanium oxide content and
produce easy striking with a stable arc and low spatter. They are commonly
known as general-purpose electrodes. The mechanical strength is generally
classed as moderate. This type of consumable normally has high hydrogen content
(higher than 10 ml/100 g all-WM). Basic electrodes offer improved mechanical
properties and superior weld penetration. The mechanical strength is
generally classed as good to high and the resistance to cracking is enhanced.
They have a high proportion of calcium carbonate and calcium fluoride in the
coating, which makes it more fluid than rutile coatings and also fast freezing.
The hydrogen content is generally lower, which reduces the cracking problem.
Table 3.5 summarizes the main characteristics of the various electrodes.
The classification indicated in the table complies with the European standard
EN 499 [3.8]. Regarding this classification standard, the first two digits desig-
78

Experimental assessment of the behaviour of T-stub connections
nate the minimum yield strength of the deposited WM and also refer to the
limit boundaries of the tensile strength and the minimum elongation of the
WM. For instance, the Kardo electrode (E35) has a minimum yield stress of
350 MPa (measured value: 396 MPa), the tensile strength varies between 440
and 570 MPa (measured value: 453 MPa) and a minimum elongation of 22%.
The latter value decreases as the strength of the WM increases [3.8], thus reducing
the deformation capacity of the weld.
Table 3.6 lists the electrodes used in the welding of each specimen. Clearly,
the Kardo and the Conarc 70G were the most utilized electrode types. These
are soft, low hydrogen electrodes. The experiences on the consumable performance
were carried out in test series WT1. Fig. 3.9 shows the influence of
the deposited WM on the global behaviour of the eight specimens from series
WT1. Essentially, such behaviour mainly depends on the mismatch in mechanical
properties between the three different zones and the hydrogen content
[3.6-3.7]. In the elastic range, the deformation behaviour is not too much dependent
on the WM properties. However, when the connection is plastically
deformed, the choice of the electrode type becomes crucial. The graphs show
that the deformation capacity of the joint was greatly influenced by the depos-
Table 3.5 Characteristics of the electrodes and mechanical properties of the
deposited weld metal.
Brand Type Classif. Actual mech. prop.
name (EN 499) fy (MPa) fu (MPa)
Cumulo Rutile E38 O R12 Not provided.
Conarc 51 Basic E42 4 B12 H5 Not provided.
Kardo Basic E35 4 B32 H5 396 453
Conarc 70G Basic E55 4 B32 H5 600 655
Brand Chemical composition
name %C %Mn %Si %P %S %Ni
Cumulo 0.06 0.50 0.30 ⎯ ⎯ ⎯
Conarc 51 Not provided.
Kardo 0.016 0.30 0.21 0.010 0.008 0.03
Conarc 70G 0.06 1.2 0.4 0.014 0.009 1.0
Table 3.6 Types of electrode used in the tests.
Test ID Electrode Test ID Electrode
WT1a/b/c Cumulo Series WT51 Conarc 70G
WT1d Conarc 51 Series WT53 Conarc 70G
WT1e/f Cumulo Series WT61 Kardo
WTg/h Kardo Series WT64 Kardo
Series WT2 Kardo Series WT7 Kardo
Series WT4 Kardo Series WT57 Conarc 70G
79

Further developments on the T-stub model
80
Total applied load (kN)
210
180
150
120
90
60
30
(a) Cumulo electrode (rutile).
Total applied load (kN)
WT1f
WT1e WT1a
WT1b
WT1c
0
0 2 4 6 8 10 12 14 16 18 20 22
210
180
150
120
90
60
30
Deformation (mm)
WT1d
WT1c
0
0 2 4 6 8 10 12 14 16 18 20 22
Deformation (mm)
(b) Conarc 51 and Cumulo electrodes (basic and rutile, respectively).
Total applied load (kN)
210
180
150
120
90
60
30
WT1d
WT1c
0
0 2 4 6 8 10 12 14 16 18 20 22
Deformation (mm)
WT1g
WT1h
(c) Kardo electrode (basic).
Fig. 3.9 Performance of the different electrode types for steel grade S355.

Experimental assessment of the behaviour of T-stub connections
(i) Deformation at failure (WT1e). (ii) Detail: typical crack (WT1a).
(a) Cumulo electrode (rutile).
(i) Deformation at failure. (ii) Detail: crack.
(iii) Detail: bolts (no bending deformations).
(b) Cumulo electrode (rutile) and aw = 8.0 mm (WT1f).
(c) Conarc 51 electrode (basic) (WT1d). (d) Kardo electrode (basic) (WT1h).
Fig. 3.10 Illustration: specimens (series WT1) after failure for comparison of the
effect of the deposited WM with different electrode-types.
81

Further developments on the T-stub model
ited WM mechanical properties. Both Cumulo and Conarc 51 electrodes induced
an early cracking of the plates at the HAZ, limiting the deformation capacity
of the T-stub and did not allow for the effective use of the bolts (Figs.
3.9 and 3.10a-c). Also, the scatter of the responses was not acceptable (Fig.
3.9a). Note that the load-carrying behaviour of WT1f deviates even more from
the remaining tests because, by mistake, the actual weld throat thickness was
8.0 mm instead of the specified value of 5.0 mm. The electrode that provided
the best ductility to the overall connection (steel grade S355) is the Kardo
(Figs. 3.9-3.10). Therefore, it was the most suitable consumable and it was
used in the rest of the specimens to weld the plates. This electrode is classified
as an evenmatch electrode as the nominal properties of the WM and the BM
are identical.
Finally, regarding the welding of the plates made up of S690, the electrode
Conarc 70G, specified by the distributor as the proper electrode type for that
steel quality, guaranteed a performance identical to the Kardo for S355.
3.3 EXPERIMENTAL RESULTS
3.3.1 Reference test series WT1
Test series WT1 includes eight specimens that differ in the electrode type used
in the welding procedure, as explained above. It has been shown previously
that the Kardo electrode seemed to be the most suitable in terms of overall
connection performance (Fig. 3.9). For further analysis consider specimens
WT1g/h whose collapse was determined by bolt fracture with some damage of
the plate in the HAZ in the first case, as well (Figs. 3.10d and 3.11).
The load-carrying behaviour of the above specimens is compared with the
Eurocode 3 [3.1] predictions for elastic stiffness and plastic resistance in Fig.
3.12 (results in Tables 3.7-3.8). Notice that the experimental F-∆ curves depicted
throughout the text correspond to the third part of the test – reloading up
to collapse (cf. §3.2.3). Eurocode 3 often underestimates both properties – see
also Table 3.8. The experimental global elastic stiffness is computed by means
of a regression analysis of the unloading portion of the F-∆ curve (which is not
traced in the graphs). By comparing the results, there is a ratio between the experiments
and the code predictions of 1.58 and 1.48 for WT1g and WT1h, respectively.
In addition, if the lower bound of the knee-range of the F-∆ curve is
compared with FRd.0 predicted by Eurocode 3, deviations of 0.84 (WT1g) and
0.81 (WT1h) are observed.
The remaining characteristics of the F-∆ response (post-limit stiffness and
deformation capacity) cannot be compared with any code provisions since it
does not cover the post-limit behaviour. Table 3.8 sets out the values of maximum
load, Fmax, post-limit stiffness (also determined by means of a regression
analysis of the post-limit response) and deformation capacity, taken as the de-
82

Experimental assessment of the behaviour of T-stub connections
formation level corresponding to Fmax.
Table 3.8 summarizes the results for the eight tests, corroborating the
above-mentioned scatter of results between the six initial specimens. Figs.
3.13-3.14 show other results also obtained in this test series. The results of the
(a) Detail of WT1h.
(b) WT1g: front view. (c) WT1g: top view.
Fig. 3.11 Specimens WT1g/h after failure.
Table 3.7 Eurocode 3 predictions of (global) initial stiffness and plastic resistance
(evaluated using the average real dimensions of the specimens).
Test ID ke.0
(kN/mm)
FRd.0
(kN)
Test ID ke.0
(kN/mm)
FRd.0
(kN)
WT1 217.28 96.66 WT53D 194.16 190.66
WT2A 175.78 88.88 WT53E 189.84 187.23
WT2B 254.24 102.18 WT57_M12 151.69 107.49
WT4A 343.86 163.47 WT57_M16 163.02 159.18
WT7_M12 168.64 81.00 WT57_M20 166.89 158.41
WT7_M16 179.58 80.22 WT61 380.92 153.19
WT7_M20 186.44 80.73 WT64A 388.02 172.85
WT51 184.16 178.90 WT64C 425.46 182.45
WT53C 190.10 187.35
83

Further developments on the T-stub model
bolt elongation behaviour for specimen WT1h are given in Fig. 3.13. The
graph does not apply up to collapse since the bolt deformation was measured
by means of the horseshoe device that was removed before the maximum load
was reached. The graph shows that the results are alike for the four bolts and,
consequently, the four curves are nearly indistinguishable. Specimen WT1h
was also instrumented with strain gauges (see Fig. 3.8a). These were attached
close to the fillet weld, near the theoretical location of the expected yield line.
Table 3.8 Main characteristics of the force-deformation curves for the unstiffened
specimens [The elastic stiffness is quantified by using the
average deformation values. The deformation capacity here is
taken as the average deformation, from the two opposite LVDTs,
corresponding to the maximum load. Italic values for def. capacity
refer to the readings of HP1].
Test ID Resistance (kN)
K-R Fmax ke.0
Stiffness (kN/mm)
kp-l.0 ke.0/ kp-l.0
∆u.0
(mm)
WT1a 125-140 157.65 96.28 5.97 16.13 6.24
WT1b 140-155 182.08 109.88 4.63 23.73 10.37
WT1c 135-145 166.37 128.63 4.89 26.30 8.12
WT1d 137-145 150.08 120.42 7.91 15.22 4.46
WT1e 140-150 168.12 134.25 6.80 19.74 4.97
WT1f 168-180 184.99 118.46 2.37 50.00 4.90
WT1g 115-135 182.66 137.16 4.22 32.50 14.10
WT1h 119-139 184.99 147.17 4.14 35.55 14.55
WT2Aa 103-124 162.01 128.63 6.47 19.88 ⎯
WT2Ab 106-130 173.64 123.65 3.80 32.54 17.98
WT2Ba 118-156 191.97 127.15 6.47 19.65 10.09
WT2Bb 123-160 195.75 159.49 4.43 36.00 13.09
WT4Aa 118-209 216.40 150.15 5.50 27.30 5.35
WT4Ab 140-196 206.51 173.91 8.74 19.90 4.33
WT7_M12 60-96 100.64 91.18 3.78 24.12 4.60
WT7_M16 80-104 132.34 116.09 5.08 22.85 11.47
WT7_M20 88-118 145.72 137.70 5.61 24.55 9.12
WT51a 155-188 193.71 119.24 3.47 34.36 4.10
WT51b 158-189 194.59 123.67 3.98 31.07 3.82
WT53C 166-192 197.79 128.46 4.75 27.04 4.24
WT53D 185-218 234.72 105.79 9.52 11.11 5.54
WT53E 178-215 230.07 129.63 8.25 15.71 5.26
WT57_M12 75-119 121.87 85.78 1.14 75.25 4.33
WT57_M16 104-165 173.64 110.43 6.99 15.80 5.88
WT57_M20 126-204 241.71 150.96 6.32 23.89 15.98
WT61a 128-180 203.89 164.65 9.75 16.89 6.18
WT61b 119-177 213.20 152.05 11.09 13.71 7.96
WT64A 121-200 220.47 164.04 9.39 17.47 4.60
WT64C 118-214 236.47 172.45 8.84 19.51 4.59
84

Experimental assessment of the behaviour of T-stub connections
Total applied load (kN)
210
180
150
120
90
60
EC3: Initial
stiffness
30
0
WT1g WT1h
0 2 4 6 8 10 12 14 16 18 20 22
Deformation (mm)
EC3: Plastic resistance
Fig. 3.12 Experimental load-carrying behaviour of specimens WT1g/h and
comparison with Eurocode 3 (EC3) predictions.
Total applied load (kN)
210
180
150
120
90
60
Bolt RB Bolt LB
30
0
Bolt LF Bolt RF
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
Bolt elongation (mm)
Fig. 3.13 Experimental results for the bolt elongation behaviour (WT1h).
Total applied load (kN)
210
180
150
120
90
60
30
0
SG1 SG3 SG5
0 4000 8000 12000 16000 20000 24000 28000 32000
Strain (µm/m)
(a) Strain gauges SG1, SG3 and SG5.
Fig. 3.14 Experimental results for the flange strain behaviour (WT1h).
85

Further developments on the T-stub model
86
Total applied load (kN)
210
180
150
120
90
60
(b) Strain gauges SG4 and SG6.
Total applied load (kN)
30
0
SG4 SG6
0 4000 8000 12000 16000 20000 24000 28000 32000
210
180
150
120
90
60
(c) Strain gauges SG2 and SG7.
Total applied load (kN)
Strain (µm/m)
30
0
SG2 SG7
0 4000 8000 12000 16000 20000 24000 28000 32000
210
180
150
120
90
60
Strain (µm/m)
30
0
SG2 SG3 SG4
0 4000 8000 12000 16000 20000 24000 28000 32000
Strain (µm/m)
(d) Strain gauges SG2, SG3 and SG4.
Fig. 3.14 Experimental results for the flange strain behaviour (WT1h) (cont.).

Experimental assessment of the behaviour of T-stub connections
The force-strain results are shown in Fig. 3.14. In particular, Fig.3.14a compares
the results for the edge strain gauges (SG1, SG5) and the one attached at
mid length of the specimen (SG3). The results are very similar. Figs. 3.14b-c
depict symmetry. The results are analogous but not exactly the same for symmetric
strain gauges, since they may not be placed exactly on the same spot.
Finally, Fig. 3.14d compares the strain results for the remaining strain gauges
that are also alike.
3.3.2 Failure modes and general characteristics of the overall behaviour
of the test specimens
The deformation capacity of a bolted T-stub connection made up of welded
plates primarily depends on the plate/bolt strength ratio and the weld resistance
that is associated to the consumable type and properties. Collapse is eventually
governed by brittle fracture of the bolts or the welds, or cracking of the plate
material near the weld toe. Most of the tested specimens failed by tension rupture
of the bolts after bending deformation of the flange. The degree of plastic
deformation of the flange depends first and foremost on the geometric characteristics
of the connection and the mechanical properties of the elements. However,
the collapse of some specimens was due to cracking of the plate material
in the HAZ.
In this T-stub assembly type, the collapse mode involving rupture of the
plate was also affected by residual stresses and modified microstructure in the
HAZ. This could lead to a reduction of the ultimate material strain with respect
to the unaffected material and thus to an earlier failure of the whole connection.
It was also observed that the extent of the properties variations in the HAZ,
which were inherent to the welding procedure, was highly dependent on the
electrode type and the hydrogen content, in particular.
The observed failure modes involved combined bending and tension bolt
fracture (type-13 or -23) in nineteen specimens, stripping of the nut threads
bolt fracture (type-23B) in one specimen (WT57_M16), cracking of the plate
material in the HAZ (type-11) in ten specimens and combined collapse modes
11 and 13 (type-1(1+3)) in the remaining cases. Notice that the stiffened specimens
failed in a combined bending and tension bolt fracture mode. Table 3.9
summarizes the collapse modes of the several tests.
Depending on the failure mode and naturally on the connection configuration,
a similar behaviour was observed between related specimens. The most
significant characteristic describing the overall behaviour of the connection is
the F-∆ response. Fig. 3.15 plots the load-carrying behaviour of six selected
examples that illustrate the five above-mentioned collapse modes. For the parallel
T-stub elements specimens, the deformation corresponds to the average
value measured by the two opposite LVDTs at each specimen. For specimen
WT64B that includes a stiffener and where the two T-stubs are orientated at
right angles, the results for LVDTs HP1 and HP2 (see Fig. 3.8c) are shown.
87

Further developments on the T-stub model
Table 3.9 Observed failure modes.
Test ID Failure Test ID Failure Test ID Failure
mode
mode
mode
Type # Type # Type #
13 1 WT4A 13 2 WT64B “23” 2
WT1 11 6 WT4B “13” 1 WT64C 23 1
1(1+3) 1 WT51 23 2 WT7_M12 13 1
WT2A
13
1(1+3)
1
1
WT53C
WT53D
23
13
1
1
WT7_M16
WT7_M20
11
11
1
1
WT2B
13
1(1+3)
1
1
WT53E
WT61
13
23
1
2
WT57_M12
WT57_M16
23
23B
1
1
WT64A 23 1 WT57_M20 1(1+3) 1
88
Total applied load (kN)
240
210
180
150
120
90
60
30
WT64Bb (HP1)
WT64Bb (HP2)
WT61b
WT57_M16
WT2Ba
0
-2 0 2 4 6 8 10 12 14 16 18 20 22
Deformation (mm)
WT1g
WT7_M16
Fig. 3.15 Force-deformation characteristics of some of the tested specimens.
Figs. 3.11b-c and 3.16 depict the six above specimens at collapse conditions
[WT1g: collapse type-1(1+3)].
First, consider specimens WT1g, WT7_M16, WT2Ba and WT61b, which
exhibit failure modes type-1(1+3), type-11, type-13 and type-23, respectively
(Figs. 3.11b-c and 3.16a-c). An elastic branch, with slope ke.0, that develops until
yielding of the flange begins, characterizes the F-∆ curves. A loss of stiffness
then follows on and at a certain load level a quasi-linear branch with slope
kp-l.0 arises. This post-limit region is longer for specimens WT1g and
WT7_M16 that develop large bending deformations of the flange, when compared
to tests WT2Ba and WT61b. For these latter specimens, fracture of the
bolts determined collapse. In the specific case of WT61b, which was stiffened
on one side, the bolts at the stiffened side fractured. Therefore, at failure, there
was a sudden drop of load with constant deformation, which characterizes a
brittle failure type. Regarding specimen WT7_M16, the failure mechanism was

Experimental assessment of the behaviour of T-stub connections
(a) Specimen WT7_M16 (collapse type-
11).
(b) Specimen WT2Ba (collapse
type-13).
(c) Specimen WT61b (collapse type-23). (d) Specimen WT64Bb (collapse
type-“23”).
(e) Specimen WT57_M16 (collapse type-23B).
Fig. 3.16 Specimens at failure.
very ductile and after the maximum load was reached, at a deformation of
about 12 mm, the drop of load was very smooth and proceeded with increasing
deformation between the flanges. This test was stopped at ∆ ≈ 16 mm because
the webs started to bend and twist excessively and that would damage the
equipment. If the test had continued, the behavioural tendency would have
been the same. Finally, with respect to specimen WT1g that exhibits a combined
failure mechanism, the maximum load was reached for a deformation of
14 mm, after which it started decreasing. This decrease was smooth and corresponded
to the beginning of cracking of the flange plate close to the weld toe.
89

Further developments on the T-stub model
Eventually, at ∆≈20 mm, there was a sudden drop of load that coincided with
the bolt fracture. Notice that bolt rupture took place at opposite side of plate
cracking. Apparently, a larger deformation capacity would be expected for
specimen WT7_M16, when compared to WT1g, because the bolt did not govern
the collapse. However, since the T-stub width tributary to a bolt row was
higher in specimen WT7_M16, smaller deformation capacity was expected
[3.9].
Specimen WT64Bb tried to mimic the actual configuration of the tension
side of a bolted connection: elements orientated at right angles, one T-element
stiffened and the other unstiffened. When this assembly was subjected to a tensile
force, the plates became in contact except at the stiffener-web contact, as
clearly shown in Fig. 3.16d. Therefore, the F-∆ response depicted in Fig. 3.15
shows that the two flanges are opening at the stiffener side (HP2) and closing
at the opposite side (HP1). The characteristics of the curve for LVDT HP2 are
very similar to those described for WT61b, where bolt fracture at the stiffener
side also governs the ultimate condition.
Finally, type-23B failure that occurs in specimen WT57_M16 (and is not
common) is a brittle rupture mode. The specimen at collapse is illustrated in
Fig. 3.16e and the corresponding load-carrying behaviour is shown in the graph
from Fig. 3.15.
3.4 CONCLUDING REMARKS
The experiments presented above can be regarded as a reliable database for the
characterization of the behaviour of the T-stub assembly made up of welded
plates. The test procedure and the instrumentation set up adopted for the programme
were satisfactory, as evidenced by the identical results obtained from
the various sets of tests from one series (Figs. 3.17-3.18, for illustration). Detailed
information on the experimental results is given in Table 3.8, which set
out the main characteristics of the load-carrying behaviour of the various specimens,
and later in Chapter 5. Reference [3.10] also provides a thorough description
of this experimental programme.
The programme provides insight into the assessment of failure modes and
available deformation capacity of bolted T-stub connections. The major contributions
of the overall T-stub deformation are the flange deformation and the
tension bolt elongation. Usually, a higher deformation capacity of the T-stub is
expected if the flange cracking governs the collapse instead of bolt fracture.
However, in this type of assembly this statement is not so straightforward. The
cracking associated to the flange mechanism, in this case, depends on structural
constraint conditions and modifications in the mechanical properties in the
HAZ, particularly those linked to the presence of residual stresses. Therefore,
the selection of the electrodes and welding procedures is of the utmost importance
in this connection type to ensure a ductile behaviour. It has been found
out that soft, low hydrogen, mismatch (or evenmatch) electrodes prevent an
90

Total applied load (kN)
Experimental assessment of the behaviour of T-stub connections
210
180
150
120
90
60
WT2Aa WT2Ab
30
0
WT2Ba WT2Bb
0 2 4 6 8 10 12 14 16 18 20 22
Deformation (mm)
Fig. 3.17 (Experimental) load-carrying behaviour for test series WT2.
Total applied load (kN)
240
210
180
Bolt RB
150
Bolt LB
120
90
Bolt LF
60
Bolt RF
30
0
Removal of measuring
brackets
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Bolt elongation (mm)
Fig. 3.18 Experimental results for the bolt elongation behaviour (specimen
WT4Ab).
early cracking of the flange thus enhancing the overall deformation capacity.
Regarding the definition of “deformation capacity”, some clarification
seems appropriate: “Which criterion should be considered to define the deformation
capacity?”. This question has been addressed previously by the author
[3.11] since the designation adopted so far (deformation capacity taken as the
deformation level at maximum load) seems very conservative (e.g.: WT1g,
WT7_M16, among others). In many examples, there is a long plateau in the F-
∆ response after the maximum load level is reached that cannot be disregarded.
Then, some guidelines on this specific issue are desirable.
91

Further developments on the T-stub model
3.5 REFERENCES
[3.1] European Committee for Standardization (CEN). prEN 1993-1-8:2003,
Part 1.8: Design of joints, Eurocode 3: Design of steel structures. Stage
49 draft, May 2003, Brussels, 2003.
[3.2] European Committee for Standardization (CEN). prEN 10025:2000E:
Hot rolled products of structural steels, September 2000, Brussels, 2000.
[3.3] European Committee for Standardization (CEN). EN 10204:1995E: Metallic
products, October 1995, Brussels, 1995.
[3.4] RILEM draft recommendation. Tension testing of metallic structural
materials for determining stress-strain relations under monotonic and
uniaxial tensile loading. Materials and Structures; 23:35-46, 1990.
[3.5] Gioncu V, Mazzolani FM. Ductility of seismic resistant steel structures.
Spon Press, London, UK, 2002.
[3.6] Rodrigues DM, Menezes LF, Loureiro A, Fernandes JV. Numerical
study of the plastic behaviour in tension of welds in high strength steels.
International Journal of Plasticity; 20:1-18, 2004.
[3.7] Davies AC. The science and practice of welding – welding science and
technology – Vol. I. Cambridge University Press, Cambridge, UK,
1992.
[3.8] European Committee for Standardization (CEN). EN 499:1994E: Welding
consumables – Covered electrodes for manual metal arc welding of
non alloy and fine grain steels - Classification, December 1994, Brussels,
1994.
[3.9] Girão Coelho AM, Simões da Silva L. Numerical evaluation of the ductility
of a bolted T-stub connection. In: Proceedings of the third international
conference on advances in steel structures (ICASS’02) (Eds.: S.L.
Chan, F.G. Teng and K.F.Chung), Hong Kong, China, 277-284, 2002.
[3.10] Girão Coelho AM, Bijlaard F, Gresnigt N, Simões da Silva L. Experimental
assessment of the behaviour of bolted T-stub connections made
up of welded plates. Journal of Constructional Steel Research; 60:269-
311, 2004.
[3.11] Girão Coelho AM, Bijlaard F, Simões da Silva L. Experimental research
work on T-stub connections made up of welded plates. Document
ECCS-TWG 10.2-217, European Convention for Constructional
Steelwork – Technical Committee 10, Structural Connections (ECCS-
TC10), 2002.
92

4 NUMERICAL ASSESSMENT OF THE BEHAVIOUR OF T-STUB
CONNECTIONS
4.1 INTRODUCTION
The behaviour of a bolted T-stub connection can be predicted with numerical
simulations. The numerical modelling of this type of problem is complex since
it requires an adequate representation of the connection geometry, the materials
constitutive laws, boundary and load conditions [4.1]. Today, the FE method is
widely accepted as the most expedite technique for obtaining numerical solutions
for structural mechanical problems [4.2]. The basic steps of this method
are [4.3]: (i) the continuum is divided into non-overlapping discrete elements,
over which the main variables are interpolated, (ii) these elements are interconnected
at a number of points along their periphery (the nodal points), (iii) the
solution strategy can be obtained using implicit or explicit solvers and (iv) subsidiary
quantities, such as stresses and strains, are evaluated for each element.
Regarding the solution technique, the implicit method is based on static equilibrium
and is characterized by the assembly of a global stiffness matrix, followed
by simultaneous solution of the set of linear equations [4.4]. The resulting
system of equations is solved for the nodal variables and so the nodal displacements
are computed directly, i.e. implicitly. The explicit method is based
on dynamic equilibrium.
The FE model allows complex geometry to be modelled fairly accurately.
Material and geometrical nonlinearities are also adequately simulated, as well
as the boundary and load conditions. In terms of geometry modelling, the numerical
model must reproduce the global behaviour of the connection. Such
behaviour is three-dimensional in nature. The choice of elements must then be
made among three-dimensional elements: solid or shell elements. Several attempts
of a two-dimensional approach were made in the past but proved to be
unsatisfactory. Shell elements behave in a three-dimensional fashion and are
able to reproduce the collapse mechanisms but are not suitable for element interfacing,
in particular for bolt/plate contact simulation. For that purpose, solid
elements are accurate and therefore this type of elements was used in the numeric
simulations. Regarding the material properties, for steel components the
modelling of elastoplasticity is fundamental. In elasticity type problems, no
permanent deformations occur. The plastic behaviour is characterized by a
time-independent irreversible straining that can only be sustained once a certain
stress level has been reached [4.5]. The elastoplastic material response is
taken into account through dissociation of the elastic and plastic deformations
(ε e and ε p , respectively). The total strain ε is thus defined as the sum
93

Further developments on the T-stub model
ε ε ε
the yield stress is reached, the stress continues to increase with strain but with a
reduced modulus of elasticity. The plasticity formulations are based on three
fundamental concepts [4.6]: (i) a yield condition to specify the onset of plastic
deformation, (ii) a flow rule to define the plastic straining and (iii) a hardening
rule to define the evolution of the yield surface with plastic straining. For steel
components the yield condition is usually defined under the Von Mises yield
criterion. The flow rule defines the direction of the plastic straining. In most
cases, the direction of the plastic strain vector is orthogonal to the yield surface
(associated flow).
With respect to the element-interfacing phenomenon, in FE analysis the
element penetration in contact zones is avoided by adding special interface or
contact elements. Generally, it is not possible to define a priori the zones that
come into contact because of the different load stages and corresponding deformations.
This means that contact may not be attained for the same element
under different loading conditions. As a result, the simulation of contact behaviour
between the connection components is rather complex. Contact phenomenon
is intrinsically nonlinear: the contact zones are very stiff (compression)
whilst non-contacting zones are very flexible (tension). The interfacing forces
that are developed when two parts come into contact transmit the applied
forces. These contact forces are normal to the interface direction and the frictional
forces are developed along the tangential direction of the interface. The
distribution of the interface stresses and the contact conditions (sticking or sliding)
are also unknown. Most FE packages offer some facilities for dealing with
the unilateral contact problem with friction.
The modelling of a bolted T-stub connection is therefore highly nonlinear,
involving complex phenomena such as material plasticity, second-order effects
and unilateral contact boundary conditions. In the following sections, the procedures
for the implementation of a FE model using the commercial FE package
LUSAS [4.7-4.8] for the analysis of this type of problem are described.
This numerical model is validated through comparison with experimental evidence.
94
e p
= + . In general, plasticity is modelled with strain hardening, i.e. once
4.2 PREVIOUS RESEARCH
The FE modelling of an individual T-stub connection has been performed by a
number of authors from different research centres. In the framework of the
Numerical Simulation Working Group of the European Research Project
COST C1 “Civil Engineering Structural Connections”, this task was proposed
as a benchmark for FE modelling of bolted steel connections. Jaspart provided
the necessary experimental data for those simulations (T-stub T1) [4.9]. Bursi
[4.10] and Bursi and Jaspart [4.11-4.12] developed and calibrated a threedimensional
nonlinear model to mimic the experimental load-carrying response

Numerical assessment of the behaviour of T-stub connections
of the given example (T1). Later, they extended the method to another T-stub
configuration to investigate another connection representative of a different
collapse mode [4.11-4.12]. The models are proposed as benchmarks in the
validation process of FE software packages. The simulations of the individual
connections were performed by means of solids and contact elements. The F-∆
response as well as the bolt behaviour (elongation, preloading effects) and prying
effects were addressed. The proposed model was satisfactory, in general.
Gomes et al. [4.13] implemented a three-dimensional model as well for the
simulation of the test T1 but used shell elements instead of solids. Their model
allowed for the assessment of second order effects and nonlinear material behaviour
with strain hardening. The agreement between results was rather poor.
Mistakidis et al. proposed a two-dimensional FE model capable of describing
plasticity, large displacements and unilateral contact effects [4.14-4.15]. Although
the model encompasses all the essential characteristics and dominant
plastification mechanisms, the numerical results are much stiffer than the actual
response. In general, the FE results do not compare well to the experiments.
Zajdel also carried out a three-dimensional FE analysis of the benchmark
problem and proposed a reliable model that accounted for most of the Tstub
features [4.16].
Wanzek and Gebbeken [4.17] validated a three-dimensional numerical
model against experimental results performed in Munich [4.18]. They used
other experimental results (e.g. strain results, bolts measurements) for calibration
of the model. The agreement between responses was very good.
More recently, Swanson [4.19] and Swanson et al. [4.20] performed tests
on individual T-stubs and proposed a robust FE model to supplement their research.
This sophisticated model provided insight into the characteristics of the
T-stub behaviour and stress distributions (namely, contact stresses). The results
of this robust model were used to validate a simpler two-dimensional model.
The main criticism to their approach lies in the input of the material properties.
They used nominal properties instead of actual properties. This procedure is
questionable. Naturally, this validation process was only applicable within the
range analysis, which was limited to a single example. The authors explored
many features of the T-stub model, as the bolt response and the prying effect.
They discussed the conclusions drawn from the FE analyses but they did not
broaden the scope of their analysis to conclude about the mechanisms and parameters
that influence (and how) the T-stub behaviour.
The main concern of all above models was the accomplishment of a reliable
FE model that was calibrated against experiments to obtain the F-∆ response.
Furthermore, only the case of HR-T-stubs was addressed. These models afforded
some basis for the implementation of the FE models described below.
Several model features have already been highlighted by these authors. However,
some aspects still have to be looked into. Additionally, this research also
proposes a FE model for WP-T-stubs that necessarily includes specific aspects,
namely the influence of the welding of the plates.
95

Further developments on the T-stub model
4.3 DESCRIPTION OF THE MODEL
The T-stub connection was generated with three-dimensional elements, solid
and joint elements. In particular, the solid elements were hexahedral bricks and
were used to model the continuum. The joint elements were employed in the
simulation of element contact.
In the FE library of the commercial package LUSAS [4.21] there are three
types of hexahedral solid elements: the eight-node brick (HX8(M)), the sixteen-node
brick (HX16) and the twenty-node brick (HX20). These elements
belong to a family of serendipity isoparametric elements, i.e. they have no inside
nodes and the geometry and displacement interpolation are carried out by
means of the same shape functions. The elements have three degrees-offreedom
per node (u, v and w) and are numerically integrated. The complete
formulation of this element type is detailed in the literature [4.2-4.3]. The
choice of one or another type of brick depends on their application. In linear
elastic problems, the higher order elements (sixteen and twenty nodes) are
more accurate than the eight-node brick. For nonlinear problems, involving
plasticity and contact phenomenon, in particular, the eight-node element, which
has no mid-side nodes, leads to improved numerical solutions since they allow
for a better representation of the discontinuities at element edges and of the
strain field. The FE code LUSAS implements two eight-node bricks, HX8 e
HX8M, as already pointed out. The element HX8M exhibits improved accuracy
in coarse meshes when compared with the parent element HX8, particularly
in bending dominated problems [4.22]. In addition, the element does not
suffer from shear locking in the nearly incompressible limit. The element formulation
is based on the works of Simo and Rifai [4.23]. It includes an assumed
“enhanced” strain field related to the internal degrees-of-freedom that
are eliminated at the element level before assembly of the structure stiffness
matrix. Thereby, the eight-node brick with enhanced strains, HX8M, and full
integration (2×2×2 Gauss points) was chosen for the numerical analysis.
The kinematic description of solid elements in nonlinear geometrical analysis
is based on three different formulations: (i) the total Lagrangian formulation,
that accounts for large displacements and small strains; in this formulation
all variables are referred to the undeformed configuration, (ii) the updated Lagrangian
formulation that accounts for large displacements and moderately
large strains; all variables are referred to the last converged solution configuration
and (iii) the Eulerian formulation catering for large displacements and
large strains; in each iteration at the same load increment, the deformed configuration
is updated and it corresponds to the reference configuration for the
subsequent iteration. In the total Lagrangian formulation stresses and strains
are output in terms of the “second Piola-Kirchoff stresses” and “Green-
Lagrange strains”, with reference to the undeformed configuration [4.22]. The
stresses and strains output for the updated Lagrangian and Eulerian formulations
are the “Cauchy (or true) stresses” and the “natural (or logarithmic)
strains” [4.22]. For elements with no rotational degrees-of-freedom of the
96

Numerical assessment of the behaviour of T-stub connections
nodes, in which the internal displacement field is defined in terms of nodal
displacements only, the three types of formulations yield identical results for
arbitrarily large displacements, provided that the strains are small. In the FE
code LUSAS, the Lagrangian approach is preferred in structural problems
[4.22]. Consequently, the updated Lagrangian nonlinear formulation was employed.
For the material nonlinearity, an elastoplastic constitutive law based on the
Von Mises yield criterion was adopted. A plastic potential defined the flow
rule [4.5]. The constitutive model was integrated by means of the explicit forward
Euler algorithm [4.5]. For this algorithm the hardening data and direction
of the plastic flow are evaluated at the point at which the elastic stress increment
crosses the yield surface.
In order for an element formulation to be applicable to a specific response
prediction, both kinematic and constitutive descriptions must be appropriate
[4.2]. In a materially nonlinear only analysis, the configuration and volume of
the body under consideration are constant. In this type of analysis, both displacements
and rotations are assumed infinitesimally small. Then, the engineering
stress-strain constitutive law describes the material behaviour in a
proper way. In a large displacement and strain elastoplastic analysis, the configuration
and volume of the body do not remain constant. The Lagrangian
formulation includes the kinematic nonlinear effects due to large displacements
and strains, but whether the large strain behaviour is modelled accurately depends
on the constitutive relations specified. This requires the use of a true
stress-logarithmic strain measure (σn – εn) for the definition of the uniaxial material
response, instead of the classic engineering constitutive law (σ – ε). These
quantities are defined with respect to the current length and cross-sectional area
of the coupon and are related to the engineering values by means of the following
relationships:
σ n = σ ( 1+
ε)
and ε n = ln ( 1+
ε )
(4.1)
Node-to-node nonlinear contact friction elements simulated the interface
boundary conditions. The contact between two bodies was modelled with a
joint mesh interface, which used a “master” and “slave” connection to tie the
two surfaces together at their nodes. The sliding and sticking conditions are
reproduced with the classic isotropic Coulomb friction law. The selected element
from LUSAS FE package for the contact analysis was the threedimensional
joint element JNT4 [4.21] that connected two adjacent nodes by
means of springs with adequate properties. This element is compatible with the
brick HX8M, comprising three nodal degrees-of-freedom (u, v and w). The
element has four nodes: two active nodes, a third and fourth auxiliary nodes for
definition of the local xy-plane. The two active nodes are connected with extensional
springs in the three local directions x, y and z.
The friction model was able to represent frictional and gap connections
between adjacent nodes whereby on the closure of a specified initial gap, frictional
forces were allowed to develop. In the proposed numerical model, this
97

Further developments on the T-stub model
initial gap was set as equal to zero. In order to model the nonlinear relation
between stresses F and relative displacements δ, the linear stiffness moduli
have to be specified. The local element stiffness matrix is formulated directly
from user input stiffness coefficients and is then transformed to the global Cartesian
system. The normal stiffness modulus, k1, should be set as equal to infinity,
i.e. its value should be the biggest possible. However, a stiffness value too
large could induce poor conditioning of the stiffness matrix. The optimum
value was found when the change in the results for an additional increase in the
stiffness value was negligible or when the penetration between the bodies in
contact reached a certain limit [4.11]. Concerning the tangential stiffness
moduli, k2 and k3, their value must be non-zero, otherwise the bodies in contact
would have an unrealistic infinite movement in these directions at the commencement
of loading. The location and magnitude of the contact forces can be
ascertained by the joint elements arrangement, since a zero force means separation
of the flanges whilst a compressive force implies contact between the
plates at that location.
The joint element possesses no geometrically nonlinear terms in its formulation.
However, it may be used in geometrically nonlinear analysis but it remains
geometrically linear.
To determine the structural response of the nonlinear problem an implicit
solution strategy was used, which is suitable for problems involving smooth
nonlinear analyses. A load stepping routine was hence used. There was no restriction
on the magnitude of the load step as the procedure was unconditionally
stable. The increment size followed from accuracy and convergence criteria.
Within each increment, the equilibrium equations were solved by means of
the Newton-Raphson iterations, which is stable and converges quadratically. In
the Newton-Raphson method, for each load step, the residuals are eliminated
by an iterative scheme. In each iteration, the load level remains constant and
the structure is analysed with a redefined tangent stiffness matrix. The accuracy
of the solution is measured by means of appropriate convergence criteria. Their
selection is of the utmost importance: too tight convergence criteria may lead
to an unnecessary number of iterations and a consequent waste of computer
resources, whilst a loose tolerance may result in incorrect solutions. Generally
speaking, in nonlinear geometrical analysis relatively tight tolerances are required,
while in nonlinear material problems slack tolerances are admitted,
since high local residuals are not easy to eliminate. The FE code LUSAS disposes
of six different convergence criteria [4.22]: (i) Euclidean residual norm,
γψ, defined by the norm of the residuals, ψ , as a percentage of the norm of the
external forces, R : γψψ R
2 2
98
= × 100 , (ii) Euclidean displacement norm,
γd, defined by the norm of the iterative displacements, δ a , as a percentage of
the total displacements, a : 2 2 100
γ d = δa
a × , (iii) Euclidean iterative displacement
norm, γdt, defined by the norm of the iterative displacements, δ a , as

Numerical assessment of the behaviour of T-stub connections
a percentage of the total displacements ∆ a for a certain increment: γ dt =
2 2 100
a a δ = ∆ × , (iv) work norm, γw, corresponding to the work done by
the residuals forces on the current iteration as the percentage of the work done
() i
T
() i
γ w = ⎡ψ ⎤
⎣ ⎦
δa (0)
T
(0)
⎡R ⎤
⎣ ⎦
δa
×
by the external forces on iteration zero, ( )
× 100 , (v) root mean square of residuals and (vi) maximum absolute residual.
Based on nonlinear numerical analysis from literature [4.24-4.26], it was
concluded that establishing displacement-based convergence criteria was
enough. Nevertheless, Crisfield [4.25] suggests that any displacement constraint
must be coupled with a force limitation. The following convergence
criteria were hence used. LUSAS [4.22] suggests the following values as limit
tolerances:
⎧slack
: 5.
0 −1.
0
⎪
(i) Euclidean displacement norm ⎨tight
: 0.
1−
0.
001
⎪
⎩reasonable
: 0.
1−
1.
0
⎧slack
: 5.
0 −1.
0
⎪
(ii) Euclidean incremental norm ⎨tight
: 0.
1−
0.
001
⎪
⎩reasonable
: 0.
1−
1.
0
⎧slack
: 0.
1−
0.
001
⎪
−6
−9
(iii) Work norm ⎨tight
: 10 −10
⎪
−6
⎩reasonable
: 0.
001−
10
For predominantly materially nonlinear problems, where high local residuals
have to be tolerated, slack convergence criteria are usually more effective
[4.22]. As a consequence, the following slack tolerance values were used: γd =
3.0, γdt = 3.0 and γw= 0.05.
With respect to the incremental method, a load curve was defined. Loads
were applied to the specimen in a displacement-control fashion that enforced a
better conditioning of the tangent stiffness matrix when compared to the classical
load-control procedure.
4.4 CALIBRATION OF THE FINITE ELEMENT MODEL
The FE model for both T-stub assembly-types was identical. The only difference
lied in the representation of the flange-to-web connection. For the HR-Tstub,
flange and web were connected by means of a fillet radius, r, that ensured
the continuity between both plates. In the case of WP-T-stubs, a continuous
45º-fillet weld (throat thickness aw) linked the flange and the web, though the
two plates were not necessarily in contact.
99

Further developments on the T-stub model
The calibration of the FE model for the HR-T-sub was based on the experimental
test programme carried out by Bursi and Jaspart [4.11-4.12]. The
specimen T1, which was obtained from an IPE300 beam profile, with snugtightened
bolts was selected for the following study. Regarding the WP-T-stub,
the approach was validated with experimental evidence from the series of tests
WT1 reported in Chapter 3.
4.4.1 Geometry
The general geometrical characteristics of the specimens are specified in Table
4.1 for the two specimens reported herein. By adopting the adequate boundary
conditions only one eighth of the T-stub was modelled, owing to symmetry
considerations (Fig. 4.1). The xy and yz planes are geometrical planes of symmetry.
Although the xz plane does not meet such criterion, since the bolt elongation
behaviour is not symmetrical along the y direction, some authors propose
numerical models that account for a symmetric behaviour of an “equivalent
bolt” complying with the requirements for symmetry in the xz plane
[4.11,4.17]. If the “equivalent bolt” is defined in such a way that its geometrical
stiffness is identical to that of the actual bolt, i.e. the elongation of the
“equivalent bolt” represents half of the elongation behaviour of the actual bolt,
only one eight of the T-stub has to be considered. This approach can be very
useful in terms of FE analysis, since the number of elements is significantly
reduced. In this case, the xz symmetry plane between the two flanges was modelled
by contact elements on a rigid foundation (Fig. 4.1). The interface
boundaries between flanges and washer or bolt head and between web and
flange plates in the case of WP-T-stubs were also modelled by means of contact
elements. In order to reduce the number of contact planes the bolt head or
nut and the washer, if any, were assumed fully connected. This simplification
led to slightly stiffer deformation behaviour, but the overall response was not
greatly influenced, as already shown in the literature [4.12,4.16-4.17].
The bolt modelling in this type of connection is very important since the
overall response of the T-stub is greatly influenced by the bolt behaviour. The
bolt is composed of head, nut and shank (threaded and non-threaded part).
Each of these components constitutes a source of flexibility that must be taken
into account when modelling the bolt. Bursi and Jaspart [4.12-4.16] defined the
above-mentioned “equivalent bolt” by means of the Aggerskov model [4.27]
Table 4.1 Nominal geometrical properties of the various specimens (dimensions
in [mm]; ST: short-threaded, FT: full-threaded).
Test ID T-elements geometry Bolt characteristics
tf tw w e p/2 e1 r/aw φ Washer Type #
T1 10.7 7.1 90 30 20 20 15 12 Yes ST 4
WT1 10.0 10.0 90 30 25 20 5 12 No ST 4
100

y
z
x
Numerical assessment of the behaviour of T-stub connections
External load
External load
‘Equivalent’ bolt
M12, short-threaded
Plan
10.7 mm
x
y
Rigid foundation
x
d0 = 14.0 mm
30.0 mm 26.45 mm
Section xx
Contact plane
15.0 mm
3.55 mm
¼ external load
Boundary geometric
conditions
x
20.0 mm
20.0 mm
150.0 mm
Fig. 4.1 Finite element geometry model assuming symmetry in the xy, xz and
yz planes: particular specimen T1.
and reproduced the bolt shank with a cylinder of cross-sectional area As (tensile
stress area of the bolt). In the proposed numerical model, a different approach
was implemented. The “equivalent bolt” had half of the conventional bolt
length, as defined in Eurocode 3 [4.28] and the “equivalent shank” has a
threaded part (cross-sectional area As) and a non-threaded portion (actual bolt
diameter). The length of these parts was proportional to that of the real bolt.
4.4.2 Boundary and load conditions
The nodes in the symmetry planes xy and yz were fixed with symmetric geo-
101

Further developments on the T-stub model
metrical boundary conditions (Fig. 4.1): in plane xy, the nodes were fixed in the
z direction on one side and in plane yz in the x direction, along the back of the
half of the web. The nodes in plane xz between the two flanges and between the
washers and the flanges were restrained with contact elements. The boundary
conditions for the second model were identical except for the symmetry plane
xz between the two flanges. This plane was modelled by contact elements on a
rigid foundation (Fig. 4.1). The nodes on this rigid base were fully restrained.
Complying with geometrical symmetry, the bottom bolt nodes were also fixed
in the y direction.
No friction was assumed between the flanges interface because of the Telements
symmetric behaviour. For the flange-washer and flange-web (in the
case of welded profiles) interfaces a non-zero friction coefficient, µ, was assumed.
A value of 0.25 for this type of contact surface was suggested by Vasarhelyi
and Chiang [4.29], who carried out an experimental study for supplying
reliable values for this parameter. This value was adopted in the model.
A uniform total prescribed displacement of 0.1 mm was applied at the top
of the upper T-element in positive y direction (Fig. 4.1). In the nonlinear analysis,
the total load factor was increased from 1.0 to the collapse, as explained
below. A final remark concerning the nodal restraints must be made: in LU-
SAS FE package, when applying total prescribed displacements in a certain
direction, the corresponding nodes must be fixed in the same direction.
4.4.3 Mechanical properties of steel components
For a good correlation with experimental results, the full actual stress-strain
relationship of the materials must be adopted in the numerical simulation. For
both models a rate and temperature independent plasticity law with hardening
was used for the T-stub profile and the high strength bolt. The constitutive laws
were reproduced with a piecewise linear model [4.11-4.12,4.30]. As already
pointed out, to perform realistic simulations, the conventional constitutive law
had to be converted into a constitutive true law (Fig. 4.2). The material properties
for the rigid foundation were also defined. Since it is a rigid element, a
linear elastic material was assumed, with E = 10 15 MPa and υ = 0.45.
4.4.4 Specimen discretization
A FE mesh must be sufficiently refined to produce accurate results but the
number of elements and nodes should be kept as small as possible in order to
limit the processing time needed for the analysis.
The behaviour of a bolted T-stub connection is dominated by the flexural
deformation of the flange. Particular attention must then be devoted to the discretization
of this part. Based on the study performed by Wanzek and Gebbeken
[4.17], the flange discretization with HX8M elements was analysed with
102

True stress (MPa)
Numerical assessment of the behaviour of T-stub connections
1200
1000
800
600
(a) HR-T-stub specimen T1 [4.11].
True stress (MPa)
400
Bolt (fy=893MPa)
200
0
T-flange (fy=431MPa)
T-web (fy=496MPa)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
1200
1000
800
600
Logarithmic strain
400
Bolt (fy=803MPa)
200
0
T-flange (fy=340MPa)
T-web (fy=391MPa)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Logarithmic strain
(b) WP-T-stub specimen WT1.
Fig. 4.2 Stress-strain true laws for specimens T1 and WT1.
respect to two parameters: (i) degree of discretization in order to represent the
bending dominated problem and (ii) number of elements through thickness to
check the capability of representing the yielding lines.
The FE mesh depicted in Fig. 4.3a complies with the requirements for a
reliable simulation and satisfies the mesh convergence study that was performed
within the framework of this research work (cf. Appendix B).
For the bolt discretization, in order to simulate the complex state of stress in
the bolt, a reasonably refined mesh was essential. In a T-stub connection the
bolt works in tension and bending due to the deformation of the T-stub flanges.
The overall response of the T-stub is greatly influenced by the bolt behaviour.
As a result, the bolt modelling is crucial. The bolt is composed of head, nut and
shank (threaded and non-threaded part). Each of these components constitutes
a source of flexibility that has to be taken into account when modelling the
bolt. The number of elements was determined decisively by the discretization
103

Further developments on the T-stub model
(a) Flange discretization. (b) Bolt discretization. (c) Global mesh.
Fig. 4.3 Flange discretization adopted for further analysis (e.g. T1).
of the circumference of the bolt. Technical literature suggests a minimum of 12
to 16 nodes around the circular hole [4.1]. The bolt mesh represented in Fig.
4.3b also complied with the requests for an accurate modelling. In the proposed
numerical model, a different approach was implemented. As already explained,
the “equivalent bolt” has half of the conventional bolt length, Lb, defined in Eq.
(1.18) and the “equivalent shank” a threaded part (cross-sectional As) and a
non-threaded part (actual bolt diameter), whose lengths were proportional to
those of the real bolt.
Fig. 4.3c shows specimen T1 global mesh that comprises 3588 elements
and 5680 nodes. For the welded specimen, similar discretization was adopted.
The global mesh in this case included 4164 elements and 6618 nodes.
4.4.5 Contact analysis
Appendix B describes the models used for the calibration of the joint elements
stiffness coefficients ki in the interface behaviour.
4.5 FAILURE CRITERIA
The deformation capacity of a T-stub is related to the plate/bolt resistance ratio
and is eventually determined by bolt fracture or cracking of the plate material,
as already mentioned. In both situations, the modelling of the failure condition
104

Numerical assessment of the behaviour of T-stub connections
can be ascertained by assuming that cracking occurs when the ultimate strain εu
is attained, either at the bolt or at the T-stub critical sections [4.31-4.32]. Due
to the nature of the materials, the bolt deformation supply is substantially less
than the plate. Whilst for high strength bolts the ultimate strain is circa 5%-6%,
for constructional steels, ultimate strains of 25%-30%, at least, can be expected
[4.33]. As a result, bolt fracture is likely to govern most ultimate conditions
and its assessment is of primary importance.
The potential failure mechanisms of a bolt under axial loading are: (i) tension
failure, (ii) stripping of the bolt threads and (iii) stripping of the nut
threads. Swanson [4.19] points out that high-strength fasteners are designed so
that tension failure of the bolt occurs before stripping of the threads. The stripping
phenomena should not be expected in most cases. Additionally, such a
failure type is not easily opened to a numerical or analytical implementation.
Therefore, the ultimate deformation of the bolt is frequently governed by tension
failure. A comprehensive numerical study on the behaviour of a single
bolt in tension was hence carried out to evaluate its maximum deformation
capacity and has been recently reported by the author [4.34].
Based on the study of a single bolt in tension, a failure criterion for the assessment
of the T-stub collapse is now proposed. As a component of the T-stub
connection, the bolt is subjected to combined tension and bending. In this case,
the strain distribution at the bolt critical section changes from the symmetric
case depicted in Fig. 4.4a to the case illustrated in Fig. 4.4b. The bolt axis direction
is no longer a principal direction. However, if a similar failure criterion
εmax
εmin
ε11.av = εy.av
Bolt cross-section
Bolt cross-section
(a) Bolt under pure axial tension. (b) Bolt under combined tension and
bending.
Fig. 4.4 Sketch of the strain distribution within a bolt cross-section.
εmin
εmax
105

Further developments on the T-stub model
is adopted to the single bolt in tension respecting to the maximum average
principal strain, i.e. ε11. av = εu.
b , the deformation capacity of the bolt in com-
bined tension and bending can be determined. It has been concluded that since
the bolt, as a T-stub element, is subjected to combined tension and bending
deformations, failure should be assessed by comparison of the maximum average
principal strain, ε11.av.b with εu.b.
Should the flange section be critical, a similar criterion based on the maximum
principal strain, i.e. ε11.av.f = εu.f, seems appropriate.
4.6 NUMERICAL RESULTS FOR HR T-STUB T1
The most significant characteristic describing the overall behaviour of the model
is the F-∆ curve. The implementation of the above FE model yields the
results shown in Fig. 4.5. The numerical results are compliant with the experimental
response [4.12] showing that the proposed model is rather accurate. The
end of the numerical curve, i.e. the deformation capacity of the connection is
established by application of the above failure criteria.
For the T-stub specimen T1, experimental observations indicated that the
collapse is due to inelastic phenomena in the bolts and significant flange yielding
[4.11]. Under the above failure criterion, the ultimate conditions are governed
by bolt fracture. The maximum average bolt strain ε11.av.b equals εu.b for a
global deformation of 9.20 mm. This value is very close to the experiments
(9.49 mm; ratio = 0.97).
Fig. 4.5 compares the actual T-stub behaviour with the FE model. The
curves in this case include the web deformation. However, the real gap between
the two flanges does not account for the web deformation. This response
is depicted in Fig. 4.6a. The “real” flange deformation, ∆ is smaller than the
total deformation due to the contribution of the web. Therefore, the “real” F-∆
106
Total applied load (kN)
210
180
150
120
90
60
30
Experimental results
Numerical results LUSAS
0
0 1 2 3 4 5 6 7 8 9 10
Total deformation (mm)
Fig. 4.5 Global response of specimen T1: numerical and experimental results.

Total applied load (kN)
Numerical assessment of the behaviour of T-stub connections
210
180
150
120
(a) Load-deformation behaviour.
Ratio
90
Num. - Total def.
60
Num. - Real def.
Def. capacity (bolt)
30
0
Bolt elongation
0 1 2 3 4 5 6 7 8 9 10
1.0
0.8
0.6
0.4
Deformation (mm)
0.2
Prying force, Q Bolt force, B
0.0
0 15 30 45 60 75 90 105
Applied load F, per bolt row (kN)
(b) Bolt and prying force.
Fig. 4.6 Numerical results for specimen T1.
curve is stiffer, showing a deviation of nearly 25% in the elastic regime and 8%
in the post-limit range. Fig. 4.6a also plots the bolt elongation behaviour
against the applied load until collapse. The evolution of the ratios of prying and
bolt forces with the applied load per bolt row, F, Q/F and B/F, respectively, is
illustrated in Fig. 4.6b showing an increase of such ratios with plastic straining
in the flange. The yielding of the flange starts at a load level of 96.29 kN (Fig.
4.7a). The ratio Q/F for this load level is 0.22; at collapse (2F = 207.98 kN) it
increases to 0.34, which means an enlargement of 1.5 times. This information
on the contact pressures provided by the FE model is very useful and cannot be
obtained from experiments. Furthermore, the model gives detailed results for
the bolt behaviour, particularly in terms of bolt elongation behaviour (curve Bδb)
– Fig. 4.8.
The evolution of the flange yielding is represented in Fig. 4.7. The beam
pattern governs the kinematic mechanism: two yield lines develop in the
flange, one near the bolt hole and another close to the flange-to-web connections
(see also Appendix C). This means that the flange is in double curvature,
107

Further developments on the T-stub model
(a) 2F=96.29kN;
∆=0.61mm.
(d) 2F=146.45kN;
∆=1.10mm.
(g) 2F=179.08kN;
∆=3.04mm.
108
(b) 2F=117.44kN;
∆=0.76mm.
(e) 2F=159.55 kN;
∆=1.43mm.
(h) 2F=190.85kN;
∆=4.82mm.
Fig. 4.7 Flange yielding evolution with the applied load.
(c) 2F=134.20kN;
∆=0.93 mm.
(f) 2F=166.25kN;
∆=1.69mm.
(i) 2F=207.98kN;
∆=8.70mm.
as Fig. 4.7c clearly shows.
The location of the prying forces changes during the course of loading. Fig.
4.9 shows the evolution of the contact area with the applied load. Clearly, as
the load increases, the contact area spreads to the bolt axis. Let n be the distance
between the prying forces and the bolt axis. The ratio n/e is plotted
against the external load in Fig. 4.10. Two cases are taken into account: (i) the
overall contact area and (ii) the flange cross-section at the horizontal bolt axis
x. In both cases, n is computed as follows:
∑ FQi Linfluence. i × number of active joints×
xi
i
n = e−
(4.2)
F L × number of active joints
∑
i
Qi influence. i

Bolt internal force (kN)
Numerical assessment of the behaviour of T-stub connections
90
75
60
45
30
15
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Bolt deformation (mm)
Fig. 4.8 Bolt elongation behaviour.
(a) 2F = 96.29kN;
∆ = 0.61mm.
(d) 2F = 174.46kN;
∆ = 2.45mm.
(b) 2F = 159.55kN;
∆ = 1.43mm.
(e) 2F = 179.08kN;
∆ = 3.04mm.
Fig. 4.9 Evolution of the contact area with the applied load.
Ratio n/e
1.00
0.96
0.92
0.88
0.84
0.80
0.76
Whole contact area
Joint elements at the bolt x axis
(c) 2F = 171.00kN;
∆ = 2.06mm.
(f) 2F ≥ 183.40kN;
∆ ≥ 3.63mm.
0.72
0 15 30 45 60 75 90 105
Applied load F, per bolt row (kN)
Fig. 4.10 Evolution of the ratio n/e with the applied load per bolt row.
109

Further developments on the T-stub model
where FQi is the force associated to a joint row (in the y direction), Linfluence.i is
the influence length of each of those joint rows and xi is the distance of the
joint row to the tip of the flanges. Clearly, as the load increases, Q is shifted
inside, from the tip of the flanges. Such situation is even more evident in the
second case.
4.7 NUMERICAL RESULTS FOR WP T-STUB WT1
The first series of tests WT1 included eight different specimens for analysis of
the adequate electrode for the welding procedure (cf. §3.3.1). The criterion for
the choice of one or another electrode type was based on the ductility provided
to the connection. It was seen experimentally that basic electrodes with low
hydrogen content ensured enhanced deformation capacity of the T-stub connection.
Two tests (WT1g/h) from this series were performed with this electrode
type and are used for further comparisons. Fig. 4.11a compares the loadcarrying
behaviour from the numerical model with the experiments. In the FE
modelling, the average real dimensions are used. Exception is made for the
fillet weld throat thickness, as it was not measured. Therefore, the nominal
value (aw = 5 mm) was used in the model. This can lead to some differences
since the F-∆ response is sensitive to the value of m.
The measurement of the gap between the two flanges in the test was performed
by means of two LVDTs at opposite sides of the web. The numerical
results that appear in the graph correspond to the location of those LVDTs. Fig.
4.11b shows the bolt elongation response for specimen WT1h, for the broken
bolts (LB: left back and LF: left front) – see also Figs. 3.10d and 3.11. The
graph of Fig. 4.11b does not display the experimental results of the bolt elongation
behaviour up to collapse since the measuring device was removed before
the collapse.
The FE model yields stiffer results than the experiments, though the agreement
is good. The differences may derive from the insufficient geometrical and
mechanical characterization of the fillet weld and also because of the modelling
of the HAZ, near the weld toe. In fact, some authors [4.35] have already
highlighted the fact that due to the welding process, the connection behaviour
and the cracking of material, in particular, are influenced by the presence of
residual stresses and modified microstructures in the HAZ. It is very difficult to
quantify these effects and therefore they were not included in the simulations.
However, it should be borne in mind that if cracking of material governs the
collapse model, a reduction of the ultimate strain with respect to the unaffected
material is advised. For both specimens WT1g/h, bolt fracture determines the
failure mode. Yet, for specimen WT1g there was a combined failure type involving
cracking of the flange in the HAZ and bolt fracture. Figs. 3.11b-c illustrate
the specimen at failure. The graph from Fig. 4.11a also shows this type of
fracture: at a deformation level of circa 14 mm there is a smooth drop of load
that follows on until fracture of the bolt at 20.5 mm. Numerically and under the
110

Total applied load (kN)
Numerical assessment of the behaviour of T-stub connections
210
180
150
(a) Load-deformation behaviour.
Total applied load (kN)
120
90
Experimental results: WT1g
Experimental results: WT1h
60
Numerical results LUSAS
30
0
Def. capacity (bolt - num. assessment)
0 2 4 6 8 10 12 14 16 18 20 22
210
180
150
120
Deformation (mm)
90
60
Experimental results: bolt LB
Experimental results: bolt LF
30
0
Numerical results LUSAS
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Bolt elongation (mm)
(b) Bolt elongation behaviour.
Fig. 4.11 Global response of specimen WT1: numerical and experimental results.
above proposed failure criterion, it was established that bolt determines collapse.
This was in line with experimental observations and the numerical prediction
(13.98 mm) matches the experimental results for WT1h (15.11 mm at
maximum load). The average maximum principal strain level in the HAZ is
6.8% with a local maximum of 14% (FE results). For the flange plate, the
maximum (natural) strain measured in standard material tensile testing was
30.8%.
Finally, Fig. 4.12 plots the strains in the flange, close to the fillet weld.
Specimen WT1h was instrumented with five strain gauges on one side of the
connection near the weld toe (Figs. 3.8a and 3.10d): (i) SG1 and SG5 are located
near the flange edge, (ii) SG2 and SG4 are placed at the bolt x axis crosssection
and (iii) SG3 is attached at the T-stub half width. The good correspondence
between results is a valid statement of the reliability of the procedure.
Regarding the ratios Q/F and n/e for the specimen WT1, Fig. 4.13 shows
111

Further developments on the T-stub model
112
Total applied load (kN)
210
180
150
120
90
60
30
(a) Strain gauges SG1 and SG5.
Total applied load (kN)
0
0.0% 0.6% 1.2% 1.8% 2.4% 3.0% 3.6% 4.2% 4.8% 5.4% 6.0%
210
180
150
120
90
60
(b) Strain gauges SG2 and SG4.
Total applied load (kN)
Strain
Experimental results SG1
Experimental results SG5
Numerical results LUSAS
30
Numerical results LUSAS
0
0.0% 0.6% 1.2% 1.8% 2.4% 3.0% 3.6% 4.2% 4.8% 5.4% 6.0%
210
180
150
120
90
60
30
Strain
Experimental results SG2
Experimental results SG4
0
0.0% 0.6% 1.2% 1.8% 2.4% 3.0% 3.6% 4.2% 4.8% 5.4% 6.0%
Strain
Experimental results SG3
Numerical results LUSAS
(c) Strain gauge SG3.
Fig. 4.12 Force-strain in the x direction, εxx, response for specimen WT1.

Ratio
Numerical assessment of the behaviour of T-stub connections
1.0
0.8
0.6
0.4
(a) Ratio Q/F and B/F.
Ratio n/e
0.2
Prying force, Q Bolt force, B
0.0
0 15 30 45 60 75 90 105
1.00
0.94
0.88
0.82
0.76
0.70
0.64
0.58
Applied load F, per bolt row (kN)
Whole contact area
Joint elements at the bolt axis
0.52
0 15 30 45 60 75 90 105
Applied load F, per bolt row (kN)
(b) Evolution of the ratio n/e with the applied load per bolt row.
Fig. 4.13 Numerical results for the prying forces (specimen WT1).
their evolution with the external load. In the elastic regime Q/F = 0.26 and n/e =
0.73 at the bolt horizontal axis; at failure, Q/F = 0.37 and n/e = 0.58 at the same
section. There is an amplification in Q/F of 1.42 and the prying force shifts to
the bolt vertical axis as the load increases.
4.8 CONSIDERATIONS ON THE NUMERICAL MODELLING OF THE HEAT
AFFECTED ZONE IN WP T-STUBS
The numerical results presented above for WP-T-stub specimen WT1 do not
account for the specific behaviour of the HAZ. The characterization of the mechanical
properties of this zone is very complex and uncertain due to its heterogeneity
and small size. Nevertheless, most of the high strength steels that
113

Further developments on the T-stub model
have a high carbon content and various alloying elements as chromium, copper,
nickel, etc. present a marked loss of hardness and strength in the HAZ that
may affect the performance of the T-stub connection [4.36]. Moreover, localized
heating from the welding process and subsequent rapid cooling induce a
local triaxial residual tensile stress field in the HAZ and the constraint conditions
affect the failure ductility of the metal in the zone. These effects are not
easily modelled.
However, there is evidence that when soft electrodes are used (cf. §3.2.4),
the strength of the weld is slightly affected and the installed residual stress field
is not significant [4.36]. As the fine microstructure is lost during the weld thermal
cycle, the HAZ strength and toughness are expected to decrease below
those of the BM [4.37], i.e. the HAZ softens. This softening effect, which depends
on the heat input, can be so severe that fracture can occur in the HAZ
instead of the BM, as seen in the previous chapter 3. Bang and Kim [4.37] estimate
the degree of HAZ softening in 20% at 6 kJ/mm. This means that the
strength properties in this zone should be reduced to a maximum of 80% in
relation to those of the BM.
Another aspect that must be considered in the modelling of the HAZ is the
width itself, lHAZ. Rodrigues et al. show that the ratio lHAZ/tf is an important
parameter in the characterization of the change of strength in the zone [4.38].
They studied the influence of the HAZ size in the geometrical constraint effect
and consequent influence behaviour of the joint. The study covered the range
of lHAZ/tf 1/6-1 and it demonstrated that this influence is negligible if the WM
tensile strength evenmatches the BM. This is the case of the tested specimens.
Taking these considerations into account, a FE model was implemented for
specimen WT1 in order to analyse the influence of the HAZ properties on the
overall behaviour. The width of the zone was taken as 5 mm, which corresponds
to lHAZ/tf = 0.5. The model assumed a degree of softening of 15%,
slightly below the maximum, as there was no information on the heat input
during the welding process. The results are illustrated in Fig. 4.14. Compari-
114
Total applied load (kN)
210
180
150
120
90
Experimental results: WT1h
60
Numerical results (mechanical properties of the
HAZ equal to those of the BM)
30
0
Numerical results (strength mechanical
properties of the HAZ reduced in 15%)
0 2 4 6 8 10 12 14 16 18 20 22
Deformation (mm)
Fig. 4.14 Numerical results for specimen WT1 accounting for a reduction of
15% in the strength properties of the HAZ.

Numerical assessment of the behaviour of T-stub connections
sons with the original numerical model and experimental results are also set.
The correspondence between the FE results and the experiments improves
when compared to the model described earlier. There is a slight drop in the
load-carrying behaviour in the post-limit domain (circa 7% in the load and 10%
in the deformation capacity). These differences, however, can be considered
insignificant. Therefore, for future analyses, the influence of the softening of
the HAZ is disregarded.
4.9 CONCLUDING REMARKS
The three-dimensional FE model presented above provides accurate deformation
predictions (up to fracture) of the T-stub response. It allows for a complete
characterization of the load-carrying behaviour of both types of T-stub assemblies.
Table 4.2 compares the main characteristics of the F-∆ curve as ascertained
numerically and experimentally. The results are very close, which means
that the FE model is valid and reliable.
The characterization of the T-stub collapse failure modes and corresponding
ductility levels can be performed by means of this numerical procedure in
order to clarify some code deficiencies. Additionally, the numerical model allows
the evaluation of the prying forces, thus opening the way to more reliable
design rules. Further, the parameters affecting the deformation capacity of
bolted T-stubs can be highlighted and their influence on the overall behaviour
of the connection can be assessed both qualitatively and quantitatively. It is
easy to recognize that the deformation capacity of isolated bolted T-stub connections
mainly depends on the mechanical properties of the materials and on
some geometrical parameters. The next logical step forward is the implementation
of a parametric study based on the above procedures, in order to get insight
on this particular aspect. The following chapter is devoted to such a
study, presenting an experimental/numerical investigation that allows for a
complete understanding of the main influences on the T-stub ultimate behaviour.
Table 4.2 Results for the two specimens [values in bold correspond to averaged
experimental results; underlined values include the web deformation;
K-R refers to the knee-range of the curve].
Spec. Stiffness (kN/mm) Strength (kN) ∆u Q/F
T1
WT1
ke.0 kpl.0 ke.0/kpl.0 K-R Fu (mm) K-R Ult.
83.54 2.68 29.60 65-85 103.99 8.70 0.24 0.34
49.00 1.73 28.32 58-87 102.81 9.49 ⎯ ⎯
69.29 1.57 44.24 55-76 94.98 14.20 0.27 0.37
71.09 2.09 34.01 58-69 183.83 14.33 ⎯ ⎯
115

Further developments on the T-stub model
4.10 REFERENCES
[4.1] Virdi KS. Guidance on good practice in simulation of semi-rigid connections
by the finite element method. In: Numerical simulation of
semi-rigid connections by the finite element method (Ed.: K.S. Virdi).
COST C1, Report of working group 6 – Numerical simulation, Brussels;
1-12, 1999.
[4.2] Bathe KJ. Finite element procedures in engineering analysis. Prentice-
Hall, Englewood Cliffs, New Jersey, USA, 1982.
[4.3] Hinton E, Owen DR. An introduction to finite element computations.
Pineridge Press Limited, Swansea, UK, 1979.
[4.4] van der Vegte GJ, Makino Y, Sakimoto T. Numerical research on single-bolted
connections using implicit and explicit solution techniques.
Memoirs of the Faculty of Engineering Kumamoto University;
XXXXVII(1):19-44, 2002.
[4.5] Owen DRJ, Hinton E. Finite elements in plasticity, theory and practice.
Pineridge Press Limited, Swansea, UK, 1980.
[4.6] Bathe KJ, Wilson EL. Numerical methods in finite element analysis.
Prentice-Hall, Englewood Cliffs, New Jersey, USA, 1976.
[4.7] Lusas 13. Modeller reference manual. Finite element analysis Ltd, Version
13.2. Surrey, UK, 2001.
[4.8] Lusas 13. Solver reference manual. Finite element analysis Ltd, Version
13.2. Surrey, UK, 2001.
[4.9] Jaspart JP. Numerical simulation of a T-stub – experimental data. Cost
C1, Numerical simulation group, Doc. C1WD6/94-09, 1994.
[4.10] Bursi OS. A refined finite element model for T-stub steel connections.
Cost C1, Numerical simulation group, Doc. C1WD6/95-07, 1995.
[4.11] Bursi OS, Jaspart JP. Benchmarks for finite element modelling of bolted
steel connections. Journal of Constructional Steel Research; 43(1):17-
42, 1997.
[4.12] Bursi OS, Jaspart JP. Basic issues in the finite element simulation of
extended end-plate connections. Computers and Structures; 69:361-382,
1998.
[4.13] Gomes FCT, Neves LFC, Silva LAPS, Simões RAD. Numerical simulation
of a T-stub. Cost C1, Numerical simulation group, Doc.
C1WG6/95-, 1995.
[4.14] Mistakidis ES, Baniotopoulos CC, Bisbos CD, Panagiotopoulos PD. A
2-D numerical model for the analysis of steel T-stub connections. Cost
C1, Numerical simulation group, Doc. C1WD6/96-09, 1996.
[4.15] Mistakidis ES, Baniotopoulos CC, Bisbos CD, Panagiotopoulos PD.
Steel T-stub connections under static loading: an effective 2-D numerical
model. Journal of Constructional Steel Research; 44(1-2):51-67,
1997.
[4.16] Zajdel M. Numerical analysis of bolted tee-stub connections. TNO-
Report 97-CON-R-1123, 1997.
116

Numerical assessment of the behaviour of T-stub connections
[4.17] Wanzek T, Gebbeken N. Numerical aspects for the simulation of end
plate connections. In: Numerical simulation of semi-rigid connections
by the finite element method (Ed.: K.S. Virdi). COST C1, Report of
working group 6 – Numerical simulation, Brussels; 13-31, 1999.
[4.18] Gebbeken N, Wanzek T, Petersen, C. Semi-rigid connections, T-stub
model – Report on experimental investigations. Report 97/2. Institut für
Mechanik und Static, Universität des Bundeswehr München, Munich,
Germany, 1997.
[4.19] Swanson JA. Characterization of the strength, stiffness and ductility
behavior of T-stub connections. PhD dissertation, Georgia Institute of
Technology, Atlanta, USA, 1999.
[4.20] Swanson JA, Kokan DS, Leon RT. Advanced finite element modelling
of bolted T-stub connection components. Journal of Constructional
Steel Research; 58:1015-1031, 2002.
[4.21] Lusas 13. Element reference manual. Finite element analysis Ltd, Version
13.2. Surrey, UK, 2001.
[4.22] Lusas 13. Theory manual. Finite element analysis Ltd, Version 13.2.
Surrey, UK, 2001.
[4.23] Simo JC, Rifai MS. A class of mixed assumed strain methods and the
method of incompatible modes. International Journal for Numerical
Methods in Engineering; 29:1595-1638, 1990.
[4.24] Crisfield M. Large deflection elasto-plastic buckling analysis of plates
using finite elements. TRRL Report LR 593, Transport and Road Research
Laboratory, Department of the Environment, Crowthorne, UK,
1973.
[4.25] Crisfield M. Non-linear finite element analysis of solids and structures,
Volume 1 – Essentials. John Wiley & Sons Ltd., Chichester, UK, 1997.
[4.26] Crisfield M. Non-linear finite element analysis of solids and structures,
Volume 2 – Advanced topics. John Wiley & Sons Ltd., Chichester, UK,
1997.
[4.27] Aggerskov H. High-strength bolted connections subjected to prying.
Journal of Structural Division ASCE; 102(ST1):161-175, 1976.
[4.28] European Committee for Standardization (CEN). prEN 1993-1-8:2003,
Part 1.8: Design of joints, Eurocode 3: Design of steel structures. Stage
49 draft, May 2003, Brussels, 2003.
[4.29] Vasarhelyi DD, Chiang KC. Coefficient of friction in joints of various
steel. Journal of Structural Division ASCE; 93(ST4):227-243, 1967.
[4.30] Girão Coelho AM. Material data of the plate sections of the welded Tstub
specimens. Internal report, Steel and Timber Section, Faculty of
Civil Engineering, Delft University of Technology, 2002.
[4.31] Faella C, Piluso V, Rizzano G. Structural semi-rigid connections – theory,
design and software, CRC Press, USA, 2000.
[4.32] Gioncu V, Mateescu G, Petcu D, Anastasiadis A. Prediction of available
ductility by means of local plastic mechanism method: DUCTROT
computer program, Chapter 2.1 in Moment resistant connections of steel
117

Further developments on the T-stub model
frames in seismic areas (Ed.: F. Mazzolani). E&FN Spon, London, UK;
95-146, 2000.
[4.33] Hirt MA, Bez R. Construction métallique – Notions fondamentales et
methods de dimensionnement. Traité de Génie Civil de l’École
polytechnique fédérale de Lausanne, Volume 10. Presses Polytechniques et
Universitaires Romandes, Lausanne, Switzerland, 1994.
[4.34] Girão Coelho AM, Bijlaard F, Simões da Silva L. On the deformation
capacity of beam-to-column bolted connections. Document ECCS-
TWG 10.2-02-003, European Convention for Constructional Steelwork
– Technical Committee 10, Structural connections (ECCS-TC10), 2002.
[4.35] Piluso V, Faella C, Rizzano G. Ultimate behavior of bolted T-stubs. II:
model validation. Journal of Structural Engineering ASCE; 127(6):694-
704, 2001.
[4.36] Loureiro AJR. Effect of heat input on plastic deformation of undermathed
welds. Journal of Materials Processing Technology; 128:240-
249, 2002.
[4.37] Bang KS, Kim WY. Estimation and prediction of the HAZ softening in
thermomechanically controlled-rolled and accelerated-cooled steel.
Welding Journal; 81(8):174S-179S, 2002.
[4.38] Rodrigues DM, Menezes LF, Loureiro A, Fernandes JV. Numerical
study of the plastic behaviour in tension of welds in high strength steels.
International Journal of Plasticity; 20:1-18, 2004.
118

Numerical assessment of the behaviour of T-stub connections
APPENDIX B: PRELIMINARY STUDY FOR CALIBRATION OF THE FINITE ELE-
MENT MODEL (E.G. HR-T-STUB T1)
B.1 Mesh convergence study
As mentioned in §4.4.4, the flange mesh discretization with HX8M elements is
analysed with respect to two parameters: (i) x: degree of discretization in order
to represent the bending dominated problem and (ii) y: number of elements
through thickness to check the capability of representing the yielding lines. The
various discretizations are labelled ‘FxTy’, concerning the two above parameters,
respectively (Fig. B1). The material properties adopted in these simulations
are those from Fig. 4.2a.
Fig. B2 depicts the F-∆ response of discretization F0Ty, with y = 1, 2, 3, 4
and 5. The deformation behaviour of F0T1 is stiffer than the other models because
shear locking occurs. The remaining models yield identical solutions in
the elastic domain but slightly different solutions in the plastic domain. Model
F0T2 is more flexible than F0T3, F0T4 and F0T5, which show very small deviations.
For future analysis, the model with three layers of HX8M is adopted.
(a) F0T1. (b) F0T4. (c) F1T2.
(d) F1T3. (e) F2T3.
Fig. B1 Flange discretization: analysed models FxTy.
119

Further developments on the T-stub model
To assess the influence of the degree of the flange discretization, the F-∆ behaviour
of models F0T3, F1T3 and F2T3 is compared (Fig. B3). In the elastic
domain, the three models yield identical stiffness. The model F1T3 is stiffer
than model F2T3 in the plastic regime, but the post-limit stiffness is identical
for both models. For model F0T3 the slope of the F-∆ curve is smaller than the
corresponding value for the finer meshes. Fig. B4 compares the curves for
models F1Ty, y = 2, 3 and 4 and F2T3. Again, the model with two layers of
elements shows a weaker response than the remainders. This situation, again, is
due to the shear locking effect, which is compensated in this particular case by
a weaker plastic response. Comparison of models F1T3 and F1T4 shows that
the lesser the number of elements across flange thickness, the stiffer the response.
F1T4 and F2T3, however, yield similar results.
Model F2T3 (11910 nodes and 7722 elements) satisfies convergence requirements
but demands greater computation effort. Model F1T3 (5680 nodes
and 3588 elements) shows small deviations from F2T3 and is not as timeconsuming.
Therefore, it will be used extensively in future comparisons.
120
Total applied load (kN)
210
195
180
165
150
135
120
F0T1
F0T4
F0T2
F0T5
F0T3
0 1 2 3 4 5 6 7 8
Total deformation (mm)
Fig. B2 Comparison of the deformation behaviour of models F0Ty.
Total applied load (kN)
200
190
180
170
160
150
140
F0T3 F1T3 F2T3
0 1 2 3 4 5 6 7 8
Total deformation (mm)
Fig. B3 Comparison of the deformation behaviour of models FxT3.

Total applied load (kN)
Numerical assessment of the behaviour of T-stub connections
200
190
180
170
160
150
140
F1T2
F1T4
F1T3
F2T3
0 1 2 3 4 5 6 7 8
Total deformation (mm)
Fig. B4 Comparison of the deformation behaviour of models F1T2, F1T3,
F1T4 and F2T3.
B.2 Influence of the definition of the constitutive law and element formulation
on the overall behaviour
Fig. B5a compares the F-∆ curve for the different material stress-strain relationships.
As expected, this relation does not influence the elastic behaviour,
but the post-limit behaviour is rather stiffer in the case of true stresslogarithmic
strain relation and closer to the experimental behaviour. Fig. B5b
depicts the F-∆ characteristics for two different element formulations: total
Lagrangian and updated Lagrangian formulations. Again, the elastic part of the
curve is not affected by the different element HX8M formulation. However, in
the plastic range, the updated Lagrangian formulation yields closer results to
the experimental curve. Therefore, to perform realistic simulations, a true
stress-logarithmic strain relation must describe the constitutive material laws
and the updated Lagrangian element formulation must be used.
B.3 Calibration of the joint element stiffness
Regarding the joint element stiffness, three cases are analysed in Fig. B6. The
stiffer the elements, the stiffer the global T-stub response. From the stiffness
values, it can be concluded that the results for the stiffness coefficient k1 =
8000 N/mm/mm 2 are more realistic than the higher values. In terms of elastic
stiffness and ultimate resistance, the three curves fit each other. However, in
the knee-range of the global response, this model is more compliant and accurate
than the remaining.
The joint element stiffness k1 is hence taken as equal to 8000 N/mm/mm 2
and the tangential stiffness coefficients are taken as k2 = k3 = 1000 N/mm/mm 2 .
121

Further developments on the T-stub model
122
Total applied load (kN)
210
180
150
120
(a) Stress-strain relationships.
Total applied load (kN)
90
60
Experimental results
Num. res.: Nominal law
30
0
Num. res.: True law
0 1 2 3 4 5 6 7 8 9 10
210
180
150
120
Total deformation (mm)
90
60
Experimental results
Num. res.: total lagrangian formulation
30
0
Num. res.: update lagrangian formulation
0 1 2 3 4 5 6 7 8 9 10
Total deformation (mm)
(b) Total and updated Lagrangian formulation.
Fig. B5 Influence of constitutive laws and element formulation on the overall
behaviour.
Total applied load (kN)
210
180
150
120
90
Experimental results
60
Num. res.: k1=8000
Num. res.: k1=20000
30
0
Num. res.: k1=2000000
0 1 2 3 4 5 6 7 8 9 10
Total deformation (mm)
Fig. B6 Influence of contact element stiffness coefficients on the overall
behaviour.

Numerical assessment of the behaviour of T-stub connections
APPENDIX C: STRESS AND STRAIN NUMERICAL RESULTS FOR HR-T-STUB T1
C.1 Load steps for stress and strain contours
To illustrate the stress and strain contour results, four load steps are chosen
(Fig. C1) as follows: (i) 2F = 96.29 kN (load case 4) for the elastic regime, (ii)
2F = 159.55 kN (load case 9) for the knee-range, (iii) 2F = 190.85 kN (load
case 25) for the subsequent linear part (in the post-limit regime) and (iv) 2F =
207.98 kN (load case 46) for the collapse (maximum deformation).
C.2 Von Mises equivalent stresses, σeq
The Von Mises equivalent stress, σeq, combines the individual component
stresses at a node according to the classical Von Mises failure criterion. The
stress distribution within the T-stub flange is well reproduced with the generalized
stress σeq. Fig. C2 illustrates the σeq contours in the three-dimensional
view, for the four load levels. The bending of the flange is well reproduced.
The peak equivalent stress values are located at the bolt axis and at the flangeto-web
connection, where the yield lines develop. Fig. C3 depicts the equivalent
stresses in xy cross-section corresponding to the bolt axis.
Regarding the bolt behaviour, Fig. C4 shows the equivalent stresses for the
chosen load levels. The bending of the bolt is clearly present from the commencement
of loading. For the first load stage, no yielding occurs. As the load
increases, the bolt stresses and strains magnify and so do the yielded portions.
The compression and tension zones of the bolt are also noticeable: the bolt area
near the web is subjected to tension whilst the zone near the tips of the flange is
in compression.
Total applied load (kN)
210
180
150
120
90
60
30
96.29 kN
159.55 kN
190.85 kN
Experimental results
Numerical results LUSAS
0
0 1 2 3 4 5 6 7 8 9 10
Total deformation (mm)
207.98 kN
Fig. C1 Selected load levels for stress and strain analyses.
123

Further developments on the T-stub model
(a) Elastic regime. (b) Knee-range.
(c) Post-limit regime. (d) Collapse.
Fig. C2 Von Mises equivalent stresses in the T-stub flange.
(a) Elastic regime. (b) Knee-range.
Fig. C3 Von Mises equivalent stresses in xy cross-section.
C.3 Stresses σxx and strains εxx
The stress component in the x direction, σxx, represents the bending of the T-
element flanges along this axis. The development of σxx is illustrated in Fig.
124

Numerical assessment of the behaviour of T-stub connections
C5. The double curvature bending of the T-stub flange is clear. The high values
of tension (positive values) occur in the upper part of the flange-to-web connection
and on the lower part of the flange near the bolt axis. Conversely, the
high values of compression are located on the opposite parts. Fig. C6 presents
the strain results for the same load levels.
(c) Post-limit regime. (d) Collapse.
Fig. C3 Von Mises equivalent stresses in xy cross-section (cont.).
(a) Elastic regime. (b) Knee-range.
(c) Post-limit regime. (d) Collapse.
Fig. C4 Von Mises equivalent stresses in the bolt.
125

Further developments on the T-stub model
C.4 Stresses σyy
The stress component along the y direction, σyy, is depicted in Figs. C.7-C.8 for
the T-stub flange, three-dimensional and bottom xz plane views, respectively.
(a) Elastic regime. (b) Knee-range.
(c) Post-limit regime. (d) Collapse.
Fig. C5 Stresses σxx in the T-stub flange.
(a) Elastic regime. (b) Knee-range.
Fig. C6 Strains εxx in the T-stub flange.
126

Numerical assessment of the behaviour of T-stub connections
(c) Post-limit regime. (d) Collapse.
Fig. C6 Strains εxx in the T-stub flange (cont.).
(a) Elastic regime. (b) Knee-range.
(c) Post-limit regime. (d) Collapse.
Fig. C7 Stresses σyy in the T-stub flange.
The positive stress σyy is quite uniform in the flange in the elastic areas. The
stress uniform transfer between the flange and the web is also clear in Fig. C7
(red contour). The concentration of negative stress σyy occurs at the contact
127

Further developments on the T-stub model
areas: the washer/flange and the flange/rigid foundation contact planes (Figs.
C7-C8, respectively). In the latter, the stress concentration is quite distinct in
the middle of the flange-to-web connection, due to the bending of the flanges
and at the tips of the flanges, where the prying effect takes place.
C.5 Stresses σzz
The stress component on the z-axis, σzz, represents the deformation behaviour
along the T-stub width. The distribution of the stress is not uniform and the
peak values occur at the washer/flange contact plane, due to sliding (Fig. C9).
C.6 Principal stresses and strains, σ11 and ε11
The principal stress σ11 and the principal strain ε11 represent the maximum
stress and strain values, respectively. The maximum values of stress in the Tstub
flange (Fig. C10) occur at the bolt axis and at the flange-to-web connection.
Fig. C11 shows the corresponding strain contours.
Figs. C12-C13 illustrate the principal stresses and strains in the bolt, respectively.
The maximum strain ε11 in the bolt corresponds to the maximum allowed
strain and therefore once it is attained, collapse occurs. The distribution
(a) Elastic regime. (b) Knee-range.
(c) Post-limit regime. (d) Collapse.
Fig. C8 Stresses σyy in the T-stub flange/rigid foundation contact plane.
128

Numerical assessment of the behaviour of T-stub connections
(a) Elastic regime. (b) Knee-range.
(c) Post-limit regime. (d) Collapse.
Fig. C9 Stresses σzz in the T-stub flange.
(a) Elastic regime. (b) Knee-range.
Fig. C10 Principal stresses σ11 in the T-stub flange.
of principal stresses in the bolt shank is not uniform as the applied load increases.
The maximum contour area enlarges with the increasing of load. The
principal strain contours in the xy cross-section are illustrated in Fig. C14.
129

Further developments on the T-stub model
(c) Post-limit regime. (d) Collapse.
Fig. C10 Principal stresses σ11 in the T-stub flange (cont.).
(a) Elastic regime. (b) Knee-range.
(c) Post-limit regime. (d) Collapse.
Fig. C11 Principal strains ε11 in the T-stub flange.
130

Numerical assessment of the behaviour of T-stub connections
(a) Elastic regime. (b) Knee-range.
(c) Post-limit regime. (d) Collapse.
Fig. C12 Principal stresses σ11 in the bolt.
(a) Elastic regime. (b) Knee-range.
Fig. C13 Principal strains ε11 in the bolt.
131

Further developments on the T-stub model
(c) Post-limit regime. (d) Collapse.
Fig. C13 Principal strains ε11 in the bolt (cont.).
(a) Elastic regime. (b) Knee-range.
(c) Post-limit regime. (d) Collapse.
Fig. C14 Principal strains ε11 in xy cross-section.
C.7 Displacement results in xy cross-section
Finally, the displacement contour in the x and y directions are illustrated in
Figs. C15-C16 for the middle xy cross-section. The results are presented in the
deformed configuration (magnification factor = 1.0). Fig. C15 shows that no
penetration occurs between the bolt and the flange at collapse conditions.
132

Numerical assessment of the behaviour of T-stub connections
(a) Elastic regime. (b) Knee-range.
(c) Post-limit regime. (d) Collapse.
Fig. C15 Horizontal displacement contours in xy cross-section.
(a) Elastic regime. (b) Knee-range.
Fig. C16 Vertical displacement contours in xy cross-section.
133

Further developments on the T-stub model
(c) Post-limit regime. (d) Collapse.
Fig. C16 Vertical displacement contours in xy cross-section (cont.).
134

5 PARAMETRIC STUDY
5.1 DESCRIPTION OF THE SPECIMENS
A parametric analysis was undertaken in order to identify the dependence of
the T-stub behaviour on the main geometrical and mechanical variables. The
basic HR specimen is T1 from the previous section and the study on this assembly
type was performed numerically. For the WP specimens, an experimental
programme was devised along with a FE analysis. Three supplementary
WP-T-stubs derived from HR-T-stub T1 were also considered to compare the
behaviour of the two assembly types. The main geometric parameters that were
varied in the study are: (i) weld throat thickness, aw, for WP-T-stubs (ii) gauge
of the bolts, w, (iii) pitch of the bolts, p, (iv) end distance, e1, (v) edge distance,
e, and (vi) flange thickness, tf. The influence of the bolt is analysed by varying:
(i) the diameter, φ, (ii) the thread length (spec. P24: FT bolt) and (iii) the preload,
S0 (spec. P25). The steel constitutive law is the mechanical variable in the
study. Additionally, the question of the number of bolt rows is also tackled.
Tables 3.1 and 5.1 sum up the main characteristics of the several specimens.
In the following sections the load-carrying behaviour of the several specimens
is compared to assess the influence of the main parameters. For some
specimens other results are also included to get insight into other behaviour parameters.
5.2 INFLUENCE OF THE ASSEMBLY TYPE AND THE WELD THROAT THICK-
NESS
Having validated the numerical procedure for both T-stub assemblies, in this
section the influence of welding and of the size of the fillet weld on the overall
behaviour are analysed. For that purpose, HR-T-stub specimen T1 is selected.
The equivalent WP-T-stub (generally labelled Weld_T1 hereafter) is identical
to T1 in terms of geometrical and mechanical properties. The flange-to-web
connection radius is thus replaced with a continuous 45º-fillet weld of throat
thickness (i) aw = 0.5tw = 3.55 mm [Weld_T1(i)], (ii) aw = tw
= 7.1mm
[Weld_T1(ii)] and (iii) a w = 10 mm [Weld_T1(iii)]. The values for aw are chosen
to meet the Eurocode 3 requirements [5.1]. The first value, aw = 0.5tw,
complies with the minimum dimension prescribed in the code (3.0 mm) and is
commonly used in practice. The value aw = tw
can be regarded, in design practice,
as an upper value for the size of the fillet weld. Finally, the latter value
135

Further developments on the T-stub model
yields a distance m similar to the one in the HR specimen T1. For T1, m =
41.45 − 0.8× 15 = 29.45 mm and for Weld_T1(iii), m = 41.45 − 0.8 2 × 10 =
30.14 mm.
The numerical results for both specimens T1 and Weld_T1 are compared in
Figs. 5.1-5.3. Concerning the overall behaviour, the connections clearly yield
different responses. Bolt fracture determines collapse of all T-stubs. Comparison
of the F-∆ responses of the welded specimens shows that as the weld throat
thickness increases, the stiffness and resistance improve but the deformation
capacity significantly decreases (Fig. 5.1). It should be noted that the increase
Table 5.1 Details of the parametric numerical study [dimensions in mm;
yield stress in MPa] (see Figs. 1.9 and 3.1 for notation).
Type Test Profile
T-stub elements geometry
HR specimens
WP
spec.
136
ID
b p e1 w e r/aw tf tw
P1 IPE300 40 40 20 100 25 15 10.7 7.1
P2 IPE300 40 40 20 80 35 15 10.7 7.1
P3 IPE300 35 30 20 90 30 15 10.7 7.1
P4 IPE300 52.5 65 20 90 30 15 10.7 7.1
P5 IPE300 60 80 20 90 30 15 10.7 7.1
P6 IPE300 35 40 15 90 30 15 10.7 7.1
P7 IPE300 45 40 25 90 30 15 10.7 7.1
P8 HEA220 40 40 20 90 65 18 11.0 7.0
P9 HEB180 40 40 20 90 45 15 14.0 8.5
P10 HEAA160+ 40 40 20 90 30 15 7.0 4.5
P11 HEB180 40 40 20 90 30 15 14.0 8.5
P12 IPE300 40 40 20 90 30 15 10.7 7.1
P13 IPE300 40 40 20 90 30 15 10.7 7.1
P14 IPE300 40 40 20 90 30 15 10.7 7.1
P15 IPE300 40 40 20 80 35 15 10.7 7.1
P16 IPE300 70 70 35 90 30 15 10.7 7.1
P17 IPE300 70 70 35 90 30 15 10.7 7.1
P18 IPE300 70 70 35 90 30 15 10.7 7.1
P19 IPE300 70 90 25 90 30 15 10.7 7.1
P20 HEB180 70 70 35 90 30 15 14.0 8.5
P21 IPE300 92.5 115 35 90 30 15 10.7 7.1
P22 UB457×
152×67
P23 UB457×
152×82
70 70 35 90 30 10.2 15.0 9.0
70 70 35 90 30 10.2 18.9 10.5
P24 IPE300 40 40 20 90 30 15 10.7 7.1
P25 IPE300 40 40 20 90 30 15 10.7 7.1
Weld_T1(i) 40 40 20 90 30 3.55 10.7 7.1
Weld_T1(ii) 40 40 20 90 30 7.1 10.7 7.1
Weld_T1(iii) 40 40 20 90 30 10 10.7 7.1

HR specimens
Parametric study
Table 5.1 Details of the parametric numerical study (cont.).
Type Test
ID
Profile
φ
Bolt
# Type
Material (fy)
Flange Bolt
P1 IPE300 12 4 ST 431 893
P2 IPE300 12 4 ST 431 893
P3 IPE300 12 4 ST 431 893
P4 IPE300 12 4 ST 431 893
P5 IPE300 12 4 ST 431 893
P6 IPE300 12 4 ST 431 893
P7 IPE300 12 4 ST 431 893
P8 HEA220 12 4 ST 431 893
P9 HEB180 12 4 ST 431 893
P10 HEAA160+ 12 4 ST 431 893
P11 HEB180 12 4 ST 431 893
P12 IPE300 16 4 ST 431 893
P13 IPE300 12 4 ST 355 893
P14 IPE300 12 4 ST 275 893
P15 IPE300 16 4 ST 431 893
P16 IPE300 12 4 ST 431 893
P17 IPE300 16 4 ST 431 893
P18 IPE300 20 4 ST 431 893
P19 IPE300 16 4 ST 431 893
P20 HEB180 16 4 ST 431 893
P21 IPE300 20 4 ST 431 893
P22
UB457×
152×67
20
4 ST
431 893
P23
UB457×
152×82
20
4 ST
431 893
P24 IPE300 12 4 FT 431 893
P25 IPE300 12 4 ST 431 893
Weld_T1(i) 12 4 ST 431 893
Weld_T1(ii) 12 4 ST 431 893
Weld_T1(iii) 12 4 ST 431 893
WP
spec.
Table 5.2 Numerical results (per bolt row) for T1 and weld-equiv. Weld_T1.
Test ID Stiffness (kN/mm) Resistance (kN) ∆u.0 Q/F
ke.0 kp-l.0 ke.0/kp-l.0 K-R Fu.0 (mm) K-R Ult.
T1 83.54 2.68 29.60 65-85 103.99 8.70 0.24 0.34
Weld
_T1(i)
Weld
_T1(ii)
Weld
_T1(iii)
73.50 1.70 43.12 50-78 92.02 10.85 0.34 0.45
88.04 2.51 35.07 60-87 102.75 8.01 0.27 0.36
107.29 3.31 32.41 75-97 113.10 6.22 0.22 0.28
137

Further developments on the T-stub model
138
Total applied load (kN)
240
210
180
150
120
90
60
30
0
T1 Weld_T1(i)
Weld_T1(ii) Weld_T1(iii)
0 1 2 3 4 5 6 7 8 9 10 11
Deformation (mm)
Fig 5.1 Overall response of specimens T1 and Weld_T1.
(a) Ratio B/F.
Ratio B/F
Ratio Q/F
1.0
0.8
0.6
0.4
0.2
T1 Weld_T1(i)
0.0
Weld_T1(ii) Weld_T1(iii)
0 15 30 45 60 75 90 105 120
1.0
0.8
0.6
0.4
0.2
Applied load F, per bolt row (kN)
T1 Weld_T1(i)
Weld_T1(ii) Weld_T1(iii)
0.0
0 15 30 45 60 75 90 105 120
Applied load F, per bolt row (kN)
b) Ratio Q/F.
Fig. 5.2 Bolt and prying force ratios for specimens T1 and Weld_T1.

Ratio n/e
1.00
0.96
0.92
0.88
0.84
0.80
0.76
(a) Whole contact area.
Ratio n/e
T1 Weld_T1(i)
Weld_T1(ii) Weld_T1(iii)
0.72
0 15 30 45 60 75 90 105 120
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
Applied load F, per bolt row (kN)
T1 Weld_T1(i)
Weld_T1(ii) Weld_T1(iii)
0.60
0 15 30 45 60 75 90 105 120
Applied load F, per bolt row (kN)
(b) Joint elements at the bolt x axis.
Fig. 5.3 Evolution of the ratios n/e for specimens T1 and Weld_T1.
Total applied load (kN)
240
210
180
150
120
90
60
30
0
157.95 kN
(Ld cs 6)
140.11 kN
(Ld cs 9)
205.50 kN
(Ld cs 29)
184.05 kN
(Ld cs 57)
Weld_T1(i) Weld_T1(ii)
0 1 2 3 4 5 6 7 8 9 10 11
Deformation (mm)
Parametric study
Fig. 5.4 Selected load levels for stress and strain analyses of specimens
Weld_T1.
139

Further developments on the T-stub model
(i) Knee-range. (ii) Collapse.
(a) Specimen T1.
(i) Knee-range. (ii) Collapse.
(b) Specimen Weld_T1(i).
(i) Knee-range. (ii) Collapse.
(c) Specimen Weld_T1(ii).
Fig. 5.5 Von Mises equivalent stresses in the T-stub flange.
140

(i) Knee-range. (ii) Collapse.
(a) Specimen T1.
(i) Knee-range. (ii) Collapse.
(b) Specimen Weld_T1(i).
(i) Knee-range. (ii) Collapse.
(c) Specimen Weld_T1(ii).
Fig. 5.6 Von Mises equivalent stresses in xy cross-section.
Parametric study
in aw leads to a decrease in m. To conclude about the influence of welding itself,
the comparisons have to be made between specimen T1 and Weld_T1(iii)
that have similar values of the distance m. Clearly, if the flange-to-web connection
radius is replaced with a fillet weld, the stiffness and the resistance of the
connection improve, but the deformation capacity is greatly reduced: it drops
141

Further developments on the T-stub model
(i) Knee-range. (ii) Collapse.
(a) Specimen T1.
(i) Knee-range. (ii) Collapse.
(b) Specimen Weld_T1(i).
(i) Knee-range.
(c) Specimen Weld_T1(ii).
(ii) Collapse.
Fig. 5.7 Stresses σxx in the T-stub flange.
142

(i) Knee-range.
(a) Specimen T1.
(ii) Collapse.
Fig. 5.8 Strains εxx in the T-stub flange.
Parametric study
from a gap between flanges of 8.70 mm to 6.22 mm. For specimens T1 and
Weld_T1(ii), the F-∆ curves are surprisingly coincident. However, in the
welded case, the ductility is smaller. Table 5.2 sets out the main characteristics
of the four F-∆ curves.
Regarding the bolt force and the prying forces, their magnitude in relation
to the applied load is higher for smaller weld throat thickness, in the case of the
welded specimen for all course of loading (Fig. 5.2). The location of the contact
forces also changes with the increasing of loading (Fig. 5.3). For the WP
specimen Weld_T1(i), with smaller aw, Q is closer to the bolt axis than in the
remaining specimens. Concerning the influence of the assembly type, Fig. 5.2
shows that in the elastic regime the ratios B/F and Q/F for specimens T1 and
Weld_T1(iii) are coincident but as the load increases the same ratios decrease
in the welded case. Worth mentioning is the fact that even if T1 and
Weld_T1(ii) yield identical F-∆ behaviour, the evolution of B/F and Q/F with
the course of loading is different (Fig. 5.2). With respect to the location of the
prying forces, Fig. 5.3 shows that for the welded specimen Weld_T1(iii) there
is a almost constant relationship of n/e from the commencement of loading to
failure, with a slight increase near collapse. For specimen T1, the variation of
143

Further developments on the T-stub model
(i) Knee-range.
(b) Specimen Weld_T1(i).
(ii) Collapse.
Fig. 5.8 Strains εxx in the T-stub flange (cont.).
Q with the applied load is more evident and Q is shifted to the bolt axis near
collapse failure.
The magnitude of the difference in performance of the HP-T-stub T1 and
the welded equivalents Weld_T1 is rather surprising. In terms of the overall deformation
behaviour, the differences can arise due to the redefinition of the
length m that slightly increases in the welded case. This accounts for the decrease
in stiffness and resistance. Regarding the deformation capacity, as it will
also be shown in the following section, the increase in the same distance m improves
the ultimate deformation of the connection, ∆u. With respect to the prying
effect, the disparity of results was not expected.
To compare the stress and strain contour results for the above specimens,
two load steps are chosen (Fig. 5.4), corresponding to the knee-range of the
curves and collapse (maximum deformation). For specimen T1 the reader
should refer to Fig. C1 from Appendix C for indication of the analogous levels.
As the contour results for the welded specimens are identical, only the results
for specimens Weld_T1(i-ii) are shown. For the two selected load steps, Figs.
5.5-5.6 show the Von Mises equivalent stress contours in the T-stub flange and
in xy cross-section at the bolt axis. The figures show that the higher stress values
in the flange concentrate at the bolt axis and near the flange-to-web con-
144

(i) Knee-range.
(c) Specimen Weld_T1(ii).
(ii) Collapse.
Fig. 5.8 Strains εxx in the T-stub flange (cont.).
Parametric study
nection. In particular, in the case of WP specimens, such concentration takes
place at the “potential” HAZ rather than at the weld toe. The stress distribution
in the bolt is identical in all three cases.
Figs. 5.7-5.10 illustrate the stress and strain contours in the x direction.
They clearly show the double curvature of the flange in the three cases and
confirm the previous conclusions related to the location of yield lines and potential
fracture lines. Finally, Figs. 5.11-5.14 display identical results with respect
to the principal direction 1.
The experimental programme also included the analysis of the influence of
the fillet weld throat thickness, aw on the overall behaviour (series WT2 – cf.
Table 3.1). Bolt fracture is still the determinant factor of collapse, though some
damage in the HAZ has been observed in specimens WT2Aa and WT2Ba. In
these specimens the weld quality was inferior to the expected and this may explain
such plate damage. Fig. 5.15a shows that if aw decreases, the resistance
slightly decreases, whilst the deformation capacity improves, with little variation
of stiffness. On the other hand, if aw increases, the deformation capacity is
reduced, resistance increases and there is still small change in the slope of the
two characteristic branches of the F-∆ curve (Fig. 5.15b; see also Table 3.8).
The main (experimental) characteristics of the tests also confirm the above
145

Further developments on the T-stub model
(i) Knee-range. (ii) Collapse.
(a) Specimen T1.
(i) Knee-range. (ii) Collapse.
(b) Specimen Weld_T1(i).
(i) Knee-range.
(c) Specimen Weld_T1(ii).
(ii) Collapse.
Fig. 5.9 Stresses σxx in xy cross-section.
statements related to the influence of the fillet weld throat thickness.
In series WT2Aa there was a malfunctioning of the LVDTs and there is
only a record of the deformation behaviour until ∆ ≈ 4.5 mm.
146

(i) Knee-range. (ii) Collapse.
(a) Specimen T1.
(i) Knee-range. (ii) Collapse.
(b) Specimen Weld_T1(i).
(i) Knee-range. (ii) Collapse.
(c) Specimen Weld_T1(ii).
Fig. 5.10 Strains εxx in xy cross-section.
5.3 INFLUENCE OF GEOMETRIC PARAMETERS
Parametric study
The main geometric connection parameters that were varied in this parametric
study are indicated in §5.1.
147

Further developments on the T-stub model
(i) Knee-range. (ii) Collapse
(a) Specimen T1.
(i) Knee-range. (ii) Collapse.
(b) Specimen Weld_T1(i).
(i) Knee-range. (ii) Collapse.
(c) Specimen Weld_T1(ii).
Fig. 5.11 Principal stresses σ11 in the T-stub flange.
148

(i) Knee-range. (ii) Collapse.
(a) Specimen T1.
Fig. 5.12 Principal strains ε11 in the T-stub flange.
5.3.1 Gauge of the bolts
Parametric study
To assess the influence of the variation of the distance w, two HR specimens,
P1 and P2, were obtained from T1 by shifting the bolt axis centreline (Table
5.1). Naturally, this will also alter the distance m between yield lines. Note that
in all three cases the determinant plastic failure mechanism was of type-1. Yet,
the collapse condition of the several specimens was determined by bolt fracture
(black circles).
Fig. 5.16 shows that if the gauge of the bolts increases, consequently increasing
the distance m between plastic hinges, the connection strength and
stiffness decrease but the deformation capacity improves. These results can be
found in Table 5.3.
5.3.2 Pitch of the bolts and end distance
The enlargement of the pitch of the bolts and/or the end distance implies larger
T-stub widths and therefore higher stiffness and resistance values but reduced
deformation capacity (Figs. 5.17-5.18). As the T-stub width increases, the ef-
149

Further developments on the T-stub model
(i) Knee-range. (ii) Collapse.
(b) Specimen Weld_T1(i).
Fig. 5.12 Principal strains ε11 in the T-stub flange (cont.).
fective width also increases, since the beam pattern governs the plastic mechanisms.
Therefore, the flexural resistance of the flanges is enhanced and so βRd
assumes larger values. For a certain ratio λ, then the starting governing plastic
mechanism type-1 changes into type-2 and eventually into type-3, as beff grows.
This transition of plastic modes is associated with the increase in resistance and
initial stiffness and the reduction of deformation capacity. For all the analysed
specimens, bolt determined collapse and the plastic mechanism was of type-1
(flange yielding). For specimen WT4A, however, βRd was very close to the
boundary limit of type-2. This is rather evident in Fig. 5.19a that shows
WT4Ab at collapse conditions. Apparently, the flange is in single bending curvature.
Table 5.3 sets out the main characteristics of the above F-∆ responses and
confirms the above statements concerning the major influences of the T-stub
width on the overall behaviour of T-stubs. For better understanding, part of Table
3.8 for the welded specimens is included here. The results in Table 5.3 are
presented for a bolt row. This means that the previous experimental results for
stiffness and resistance are divided by 2.
With respect to the experiments, Fig. 5.18c compares the results for the two
tests in this series with WT1h. The connection ductility clearly decreases.
150

(i) Knee-range. (ii) Collapse.
(c) Specimen Weld_T1(ii).
Fig. 5.12 Principal strains ε11 in the T-stub flange (cont.).
Parametric study
When comparing specimens WT1g/h and WT4Aa/b, the reduction of ∆u.0 is, on
average, 66%. Bolt determined collapse in all cases. In particular, for WT4Aa,
only bolt RB did not fail and for specimen WT4Ab, for which there is a record
of the bolt elongation behaviour up to collapse (Fig. 5.20), the bolts on the left
hand side were broken (Fig. 5.19 – the specimen is rotated in this figure). In
fact, the graph from Fig. 5.20 shows that the bolts on the right hand side
yielded smaller deformation than the others. Fig. 5.19b shows that the bolts
were highly deformed at collapse. In this figure, an unbroken bolt is shown and
the combined bending and tension deformations are very clear. It should be
stressed that the bolt measurement up to collapse has only been carried out in
this specific specimen as an experiment. Unfortunately, it was observed that
the measuring brackets were damaged in the end and therefore they had to be
replaced prior to collapse.
5.3.3 Edge distance and flange thickness
The variation of the edge distance e is analysed in Fig. 5.21 that depicts the F-
∆ behaviour of specimens T1, P8, P9 and P11. For these specimens not only
151

Further developments on the T-stub model
(i) Knee-range. (ii) Collapse.
(a) Specimen T1.
(i) Knee-range. (ii) Collapse.
(b) Specimen Weld_T1(i).
(i) Knee-range. (ii) Collapse.
(c) Specimen Weld_T1(ii).
Fig. 5.13 Principal stresses σ11 in xy cross-section.
the edge distance was varied, but also the flange thickness and the distance m
were slightly different, as the beam profiles changed (P8: tf = 11.0 mm; P9-11: tf
= 14.0 mm). To conclude about the single effect of e, only specimens P9 and
P11 can be compared. Clearly, both stiffness and resistance are identical and
the deformation capacity does not vary significantly either. If e is bigger, ∆u.0 is
152

(i) Knee-range. (ii) Collapse.
(a) Specimen T1.
(i) Knee-range. (ii) Collapse.
(b) Specimen Weld_T1(i).
(i) Knee-range. (ii) Collapse.
(c) Specimen Weld_T1(ii).
Fig. 5.14 Principal strains ε11 in xy cross-section.
Parametric study
somewhat improved. Fig. 5.22 depicts the influence of the flange thickness on
the overall behaviour (the distance m also varies as the profile changes). From
the graphs it can be concluded that as the flange thickness decreases and all the
153

Further developments on the T-stub model
154
Total applied load (kN)
210
180
150
120
90
60
30
0
WT1h WT2Aa WT2Ab
0 2 4 6 8 10 12 14 16 18 20 22
Deformation (mm)
(a) Series WT2A: smaller weld throat thickness.
Total applied load (kN)
210
180
150
120
90
60
30
0
WT1h WT2Ba WT2Bb
0 2 4 6 8 10 12 14 16 18 20 22
Deformation (mm)
(b) Series WT2B: smaller weld throat thickness.
Fig. 5.15 Experimental load-carrying behaviour of specimen series WT2 and
comparison with WT1h.
Total applied load (kN)
280
240
200
160
120
80
40
0
T1 P1 P2
0 1 2 3 4 5 6 7 8 9 10 11
Deformation (mm)
Fig. 5.16 Influence of the gauge of the bolts on the overall behaviour.

Total applied load (kN)
280
240
200
160
120
80
40
T1 P3 P4 P5
0
0 1 2 3 4 5 6 7 8 9 10 11
Deformation (mm)
(a) Pitch of the bolts, p.
Total applied load (kN)
280
240
200
160
120
80
40
0
T1 P6 P7
Parametric study
0 1 2 3 4 5 6 7 8 9 10 11
Deformation (mm)
(b) End distance, e1.
Fig. 5.17 Influence of the T-stub width on the overall behaviour: single effects
of the pitch and end distance.
Total applied load (kN)
280
240
200
160
120
80
40
T1 P16
0
0 1 2 3 4 5 6 7 8 9 10 11
Deformation (mm)
(a) Numerical results for HR specimens.
Fig. 5.18 Influence of the T-stub width on the overall behaviour: combined effects
of the pitch and end distance.
155

Further developments on the T-stub model
156
Total applied load (kN)
240
210
180
150
120
90
Experimental results: WT4Aa
60
Experimental results: WT4Ab
30
0
Numerical results LUSAS
0.0 0.7 1.4 2.1 2.8 3.5 4.2 4.9 5.6 6.3 7.0
Total deformation (mm)
(b) Experimental and numerical load-carrying behaviour of WP specimen
WT4A.
Total applied load (kN)
240
210
180
150
120
90
60
30
0
WT1h WT4Aa WT4Ab
0 2 4 6 8 10 12 14 16 18 20 22
Deformation (mm)
(c) Comparison of the responses of the original specimen WT1 and WT4A: experimental
assessment.
Total applied load (kN)
240
200
160
120
80
40
0
WT1 WT4A
0 2 4 6 8 10 12 14 16
Deformation (mm)
(d) Comparison of the responses of the original specimen WT1 and WT4A:
numerical assessment.
Fig. 5.18 Influence of the T-stub width on the overall behaviour: combined effects
of the pitch and end distance (cont.).

Parametric study
(a) Deformation at failure. (b) Detail of an unbroken bolt
after failure of the connection.
Fig. 5.19 Specimen WT4Ab at collapse conditions.
Total applied load (kN)
240
210
180
150
120
90
Experimental results: bolt LF
60
Experimental results: bolt LB
30
0
Numerical results LUSAS
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Bolt deformation (mm)
(a) Comparison of the numerical results with experimental evidence.
Total applied load (kN)
240
210
180
150
120
90
60
Bolt RB Bolt LB
30
0
Bolt LF Bolt RF
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Bolt elongation (mm)
(b) Experimental results.
Fig. 5.20 Bolt elongation behaviour for specimen WT4Ab.
157

Further developments on the T-stub model
Table 5.3 Synthesis of the characteristic results (per bolt row) of the curves
comparing the effect of the geometric parameters on the overall
behaviour [underlined values correspond to experimental results].
Test
ID
Stiffness (kN/mm)
ke.0 kp-l.0 ke.0/kp-l.0
Resistance (kN)
K-R Fu.0
∆u.0
(mm)
Q/F
K-R Ult.
T1 83.54 2.68 29.60 65-85 103.99 8.70 0.24 0.34
P1 63.27 2.01 31.48 60-73 91.76 10.77 0.33 0.44
P2 117.06 3.49 33.54 70-100 116.72 6.18 0.18 0.25
P3 72.62 2.30 31.62 60-75 95.41 10.17 0.26 0.40
P4 97.86 4.24 23.08 70-103 115.97 4.68 0.20 0.26
P5 101.23 6.00 16.88 90-120 130.20 3.63 0.18 0.18
P6 76.56 2.36 32.44 55-75 95.53 10.06 0.26 0.42
P7 91.45 2.97 30.79 70-93 111.34 7.56 0.22 0.29
P8 95.12 3.06 31.04 75-93 112.71 8.08 0.19 0.28
P9 128.47 6.19 20.76 85-120 131.43 3.31 0.13 0.16
P10 43.88 0.90 48.63 40-47 76.79 32.75 0.56 0.77
P11 122.80 6.82 18.01 90-110 121.15 2.94 0.20 0.21
P16 111.23 8.44 13.18 85-112 125.69 3.06 0.19 0.20
WT1 69.29 1.57 44.24 55-76 94.98 14.20 0.27 0.37
WT1g 68.58 2.11 32.50 58-68 91.33 14.10 ⎯ ⎯
WT1h 73.58 2.07 35.55 60-70 92.50 14.55 ⎯ ⎯
WT4A 85.95 3.84 22.38 67-99 107.95 5.18 0.22 0.27
WT4Aa 75.08 2.75 27.30 59-105 108.20 5.35 ⎯ ⎯
WT4Ab 86.96 4.37 19.90 70-98 103.26 4.33 ⎯ ⎯
other parameters remain the same, the component ductility improves considerably,
whilst stiffness and resistance decrease. In this case, the flange-bolt
stiffness decreases and, consequently, the degree of plastic deformation in the
flange increases.
5.4 INFLUENCE OF THE BOLT AND FLANGE STEEL GRADE
Fig. 5.23 illustrates the influence of the bolt diameter on the overall behaviour
of HR-T-stubs. Essentially, if the bolt diameter is bigger, the initial stiffness,
the strength and the ductility improve greatly but the post-limit stiffness decreases.
For a given geometry, the bolt ceases to be the determining factor of
collapse. The bolt-threaded length has an effect on the overall response if the
bolt governs the specimen collapse. In that case, if the threaded portion of the
bolt is longer, the deformation capacity of the whole connection increases. The
remaining properties do not change much (Fig. 5.24). The effect of a bolt preloading
is the enhancement of the initial stiffness (Fig. 5.25). The quantification
of the observed behaviour variations is summarized in Table 5.4.
158

Total applied load (kN)
280
240
200
160
120
80
40
0
T1 P8 P9 P11
0 1 2 3 4 5 6 7 8 9 10 11
Deformation (mm)
Fig. 5.21 Influence of the edge distance on the overall behaviour.
Total applied load (kN)
280
240
200
160
120
80
40
0
T1 P9 P10 P11
0 3 6 9 12 15 18 21 24 27 30 33
Deformation (mm)
Fig. 5.22 Influence of the flange thickness on the overall behaviour.
Parametric study
Fig. 5.26 compares the behaviour of the specimens with larger bolts (M16
and M20), confirming the previous considerations on the influence of the bolt
diameter. This conclusion is also supported by experimental evidence (Fig.
5.27). Surprisingly, if the deformation capacity of the connection is evaluated
at the maximum load level, specimen WT7_M16 yields a higher value when
compared to WT7_M20 (Fig. 5.27). However, the ductile branch after collapse
starts is longer in the latter case. These conclusions can also be taken from Table
5.4 that repeats part of the information contained in Table 3.8 for this test
series. For illustration, Fig. 5.28 shows the specimens from the experiments at
failure conditions.
For specimen WT7_M20 whose failure mode is of type-11 (cracking of the
material at the HAZ – Fig. 5.28c), a numerical model was also implemented.
159

Further developments on the T-stub model
160
Total applied load (kN)
350
300
250
200
150
100
50
(a) Geometry from T1.
Total applied load (kN)
0
350
300
250
200
150
100
50
(b) Geometry from P2.
Total applied load (kN)
0
600
500
400
300
200
100
0
T1 P12
0 3 6 9 12 15 18 21 24 27
Deformation (mm)
P2 P12 P15
0 3 6 9 12 15 18 21 24 27
Deformation (mm)
P16 P17 P18
0 3 6 9 12 15 18 21 24 27
Deformation (mm)
(c) Geometry from P16.
Fig. 5.23 Influence of the bolt diameter on the overall behaviour: numerical
results.

Total applied load (kN)
240
210
180
150
120
90
60
30
0
T1 P24
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Deformation (mm)
Parametric study
Fig. 5.24 Influence of the bolt threaded length on the overall behaviour.
Total applied load (kN)
240
210
180
150
120
90
60
30
0
T1 P25
0 1 2 3 4 5 6 7 8 9 10
Deformation (mm)
Fig. 5.25 Influence of a bolt preloading on the overall behaviour.
Again, this model does not cater for the specific behaviour of the HAZ, as already
mentioned in §4.8. The differences between the two F-∆ responses
shown in Fig. 5.29 derive from this simplification. In particular, the failure
ductility of the metal in this HAZ is clearly reduced. Experimentally, the deformation
of the T-stub flange at maximum load is 9.12 mm, whilst numerically
a total deformation of 25.37 mm is reached. However, since the softening
branch is sufficiently large, this numerical value is comparable to the maximum
deformation of 18.70 mm that was reached in the experiments. At this
displacement level, the test was stopped to prevent damage of the equipment.
The numerical deformation capacity was established by setting the maximum
average principal strain, at the critical zone, ε11.av.f, as equal to the ultimate
strain of the flange material, εu.f (cf. §4.5). In this specific case, since the critical
section is located at the HAZ, the deformation of the flanges was also
161

Further developments on the T-stub model
162
Total applied load (kN)
490
420
350
280
210
140
70
(a) Specimens with bolt M16.
Total applied load (kN)
0
700
600
500
400
300
200
100
0
P17 P19 P20
0 1 2 3 4 5 6 7 8 9 10
Deformation (mm)
P18 P21 P22 P23
0 3 6 9 12 15 18 21 24 27
Deformation (mm)
(b) Specimens with bolt M20.
Fig. 5.26 Influence of some geometric variations for bolts M16 and M20 and
the corresponding geometries P17 and P18 (HR-T-stub series).
Total applied load (kN)
150
125
100
75
50
25
0
WT7_M20 WT7_M16 WT7_M20
0 2 4 6 8 10 12 14 16 18 20
Total deformation (mm)
Fig. 5.27 Influence of the bolt diameter on the overall behaviour: experimental
results (series WT7).

Parametric study
(a) Spec. WT7_M12. (b) Spec. WT7_M16. (c) Spec. WT7_M20.
Fig. 5.28 Deformation of specimens WT7 at failure.
Table 5.4 Synthesis of the characteristic results (per bolt row) of the curves
comparing the effect of the bolt on the overall behaviour [underlined
values correspond to experimental results].
Test ID Stiffness (kN/mm)
ke.0 kpl.0 ke.0/kpl.0
Strength (kN)
K-R Fu
∆u
(mm)
Q/F
K-R Ult.
T1 83.54 2.68 29.60 65-85 103.99 8.70 0.24 0.34
P12 102.05 2.19 46.68 80-103 154.06 24.22 0.29 0.57
P24 80.46 1.89 42.51 65-87 108.14 13.80 0.24 0.31
P25 127.66 2.59 49.29 65-85 104.26 8.72 0.32 0.34
P2 117.06 3.49 33.54 70-100 116.72 6.18 0.18 0.25
P12 102.05 2.19 46.68 80-103 154.06 24.22 0.29 0.57
P15 128.41 2.71 47.47 80-120 171.08 18.02 0.21 0.48
P16 111.23 8.44 13.18 85-112 125.69 3.06 0.19 0.20
P17 138.31 3.86 35.81 115-165 192.01 9.29 0.22 0.36
P18 171.57 2.56 66.96 150-200 266.57 26.07 0.27 0.44
P19 127.27 3.93 32.36 115-160 186.52 9.29 0.22 0.38
P20 181.68 9.73 18.67 160-200 225.94 4.06 0.18 0.23
P21 168.61 3.22 52.38 155-230 281.33 17.67 0.23 0.42
P22 250.69 7.08 32.07 190-270 305.21 6.40 0.21 0.34
P23 322.09 9.61 33.53 275-305 346.01 5.22 0.20 0.24
WT4Aa 75.08 2.75 27.30 59-105 108.20 5.35 ⎯ ⎯
WT4Ab 86.96 4.37 19.90 70-98 103.26 4.33 ⎯ ⎯
WT7_M12 91.18 3.78 24.12 60-96 100.64 3.86 ⎯ ⎯
WT7_M16 116.09 5.08 17.54 80-104 132.34 5.88 ⎯ ⎯
WT7_M20 142.80 2.86 49.93 90-131 177.53 25.37 0.30 0.45
WT7_M20 137.70 5.61 16.33 88-118 145.72 15.98 ⎯ ⎯
evaluated for other flange strain levels, as indicated in Fig. 5.29 (e.g.: for an
ε11.av.f = 0.15, corresponding to 0.5εu.f, ∆ = 12.21 mm).
Another comparison that can be performed with the experimental test series
163

Further developments on the T-stub model
164
Total applied load (kN)
180
150
120
90
Numerical results
60
Experimental results
E11.p = 0.15 (def. = 12.21 mm)
30
0
E11.p = 0.20 (def. = 16.60 mm)
E11.p = 0.25 (def. = 20.98 mm)
0 3 6 9 12 15 18 21 24 27
Deformation (mm)
Fig. 5.29 Global response of specimen WT7_M20: numerical and experimental
results.
Applied load per bolt row (kN)
120
100
80
60
40
20
0
WT4Aa WT4Ab WT7_M12
0 1 2 3 4 5 6 7
Deformation (mm)
Fig. 5.30 Experimental load-carrying behaviour of specimen WT7_M12 and
comparison with series WT4Aa (per bolt row): assessment of the influence
of number of bolt rows for identical geometries.
WT7 (specimen WT7_M12, more specifically) and series WT4A relates to the
influence of the number of bolts fastening the T-stub elements. Fig. 5.30 compares
the F-∆ response, per bolt row, for the three specimens, and shows a
good agreement. This means that the symmetric behaviour is valid. This graph
also shows that for specimen WT7_M12 at a load level of 58 kN some slippage
occurred, resulting in a sharp decrease of stiffness in the response. Identical
situation is observed in WT4Aa.
Regarding the effect of the flange steel grade, Fig. 5.31 shows that the initial
stiffness is not affected by the steel properties (as long as the Young

Total applied load (kN)
240
200
160
120
80
40
(a) Numerical results.
Total applied load (kN)
0
210
180
150
120
90
60
T1 P13 P14
0 3 6 9 12 15 18 21 24 27
Deformation (mm)
30
0
WT1h WT51a WT51b
0 2 4 6 8 10 12 14 16 18 20 22
Deformation (mm)
(b) Experimental results.
Fig. 5.31 Influence of the flange steel grade on the overall behaviour.
Parametric study
modulus is constant) but as the yield stress of the flange, fy.f increases the resistance
and the post-limit stiffness also increase and the deformation capacity
decreases. Table 5.5 confirms these conclusions.
The FE models of P13 and P14 were obtained from the original specimen
T1 by reducing the stress values of the flange mechanical properties and maintaining
the strain ordinates. Both new specimens exhibit a type-1 plastic failure
mechanism. The flexural resistance of the flanges increases with the flange yield
stress and so βRd becomes greater. This explains the improvement in the resistance
properties despite a reduction in the deformation capacity. In the above case,
specimen P14, whose flange is steel grade S275, is typified by a failure type-
11, i.e. cracking of the flange material is the determining factor of collapse. For
the other two specimens, bolt failure governs the ultimate conditions.
Test series WT51 comprises the testing of two specimens geometrically
165

Further developments on the T-stub model
Table 5.5 Synthesis of the characteristic numerical results (per bolt row) of
the curves comparing the effect of the flange steel grade.
Test ID
166
Stiffness (kN/mm) Strength (kN) ∆u Q/F
ke.0 kpl.0 ke.0/kpl.0 K-R Fu (mm) K-R Ult.
T1 83.54 2.68 29.60 65-85 103.99 8.70 0.24 0.34
P13 81.31 2.19 37.17 55-72 93.71 11.38 0.24 0.42
P14 81.97 1.07 76.69 45-65 86.57 24.15 0.24 0.53
identical to the original test series WT1 and whose T-stub elements are made
up of high-strength steel S690. According to Eurocode 3, these specimens exhibit
a type-2 plastic mechanism. Bolt governs collapse in the three cases and
the deformation capacity is far reduced in series WT51 because the bolts are
engaged in collapse of the specimen at an earlier stage. The knee-range of the
F-∆ response of specimens WT51 develops for higher loads in comparison to
WT1h. The slope of the post-limit part of these curves is lower than in the
original case. Here, the single curvature of the flange is evident (Fig. 5.32) and
the deformation of the flanges is far less than in series WT1 (see Fig. 3.11, for
instance). This is also clear in Fig. 5.33a where the strains for WT1h and
WT51b are compared for SG3, on the same location in both specimens (Figs.
3.8a-b). Fig. 5.33b plots the force-strain results for the two T-rosettes attached
to specimen WT51b. It shows that the flange strain level there at collapse is
rather low. Symmetry of results is also rather obvious.
Now consider test series WT53 to assess the influence of the bolt type on
the overall response. Naturally, since the actual bolt properties also vary (Table
3.2), the global results will include not only the effect of the bolt type (short- or
full-threaded) but also their mechanical properties. Fig. 5.34 depicts the F-∆ response
of identical T-stub elements connected by means of the four different
M12 bolt types tested (cf. §3.2.2.1). The graphs show that if higher strength
bolts are used (WT53D/E), since bolt determines failure in the four cases, the
maximum load reached is also higher (see Table 3.8). For the four specimens
compared in this figure, the initial stiffness is identical because the Young
modulus, which is one of the main parameters used in the computation of ke.0,
is identical for the four bolt types (Table 3.2).
If bolt governs the failure mode of the T-stub, the overall deformation capacity
mainly depends on the maximum elongation of the bolt, or, in other
words, on the ultimate strain values. Table 3.2 shows that full-threaded bolts
exhibit higher values of εu (though for bolt grade 10.9 that difference is
smaller) and higher bolt grades exhibit smaller deformations, i.e. the failure
type is more brittle. When taking into account the T-stubs WT51b and
WT53C/D/E, the above considerations are still valid. Specimen WT53C is
more ductile than the remaining since the fasteners are full-threaded M12 grade
8.8, even though the deformation level at Fmax is lower (Table 3.8). For this
specimen, the plateau that follows Fmax is far longer than in the other cases

Parametric study
(a) Deformation at failure (WT51b). (b) Detail of a broken bolt (WT51a).
Fig. 5.32 Deformation of specimens WT51 at failure.
Total applied load (kN)
210
180
150
120
90
60
30
0
WT1h WT51b
0 4000 8000 12000 16000 20000 24000 28000 32000
Strain (µm/m)
(a) Comparison of the results for SG3 in specimens WT1h and WT51b.
Total applied load (kN)
210
180
150
120
90
60
30
0
SG6x
SG7x
SG6z
SG7z
-4000 -3200 -2400 -1600 -800 0 800 1600 2400
Strain (µm/m)
(b) Results for the rosettes.
Fig. 5.33 Experimental results for the flange strain behaviour (specimen
WT51b).
167

Further developments on the T-stub model
168
Total applied load (kN)
240
210
180
150
120
90
60
WT51b WT53C
30
0
WT53D WT53E
0 1 2 3 4 5 6 7 8 9 10
Deformation (mm)
Fig. 5.34 Experimental load-carrying behaviour of specimen series WT53 and
comparison with WT51b.
Fig. 5.35 Comparison of the deformation of specimens WT51, WT53C,
WT53D and WT53E (from left to right) at failure.
(Fig. 5.34). Surprisingly, the deformation capacity for both tests WT53D/E that
use bolt grade 10.9 is identical. These conclusions are also indicated in Table
3.8. Fig. 5.35 illustrates the four specimens after failure.
Having analysed the influence of the steel grade on the overall T-stub behaviour
(mainly: increase of strength and decrease of ductility for higher
strength steel grades), the response obtained for series WT57 and WT7 can be
compared. In series WT57, when using bolts M12 and M16, the plastic resistance
of the specimens, as determined according to Eurocode 3 (Table 3.7) corresponds
to that of a plastic mechanism type-2 whilst for M20 it corresponds to
a type-1 plastic mechanism. This is evident in the graphs from Fig. 5.36 where
the responses of the three specimens are shown. For comparison, WT7_M20 is
also included. It is worth mentioning that the bolt is also engaged in collapse in
the case of the high-strength steel (WT57_M20) since the specimen fails in a
combined failure mode (type-13), whilst in WT7_M20 collapse is governed by
plate cracking near the weld toe only. Basically, the conclusions drawn above
are supported with this series of experiments (summary in Table 3.8).

Total applied load (kN)
270
240
210
180
150
120
90
60
WT7_M20 WT57_M12
30
0
WT57_M16 WT57_M20
0 2 4 6 8 10 12 14 16 18 20 22 24
Parametric study
Deformation (mm)
Fig. 5.36 Experimental load-carrying behaviour of specimen series WT57 and
comparison with WT7_M20.
5.5 EXPERIMENTAL RESULTS FOR THE STIFFENED TEST SPECIMENS AND
THE ROTATED CONFIGURATIONS
The experimental programme included the test of some transversely stiffened
specimens and T-stub connections with the elements orientated at right angles,
in order to simulate the actual behaviour in tension of the components modelling
the end plate side. The results obtained for those cases are discussed in this
section. For complete description of the specimens and the characteristic results
of the load-carrying behaviour, the reader should refer to Chapter 3.
5.5.1 Influence of a transverse stiffener
If a transverse stiffener is added to a T-stub connection, stiffness and resistance
properties improve and deformation capacity decreases. To support this statement,
first consider series WT61 that is obtained from the original WT1 by including
a transverse stiffener in order to simulate the T-stub model for the end
plate side (Fig. 1.8c). The load-carrying behaviour of the two specimens included
in this series is compared with specimen WT1h and the code predictions
[5.1] in Fig. 5.37 and Tables 3.7-3.8. The collapse of the specimens is determined
by bolt fracture at the stiffener side (Fig. 3.16c) – labelled “left side”.
Fig. 5.38 plots the bolt elongation behaviour against the overall deformation
for specimens WT61a and WT1h. Whilst for WT61a the record of the bolt
elongation was carried out nearly until collapse, for WT1h, the measuring
brackets were removed at an earlier stage. Therefore, the loss of stiffness in
this response, which is evident for WT61a, is not plotted in the graph. This loss
of stiffness does not occur for the unbroken bolt RB (unstiffened side), of
which the response is very close to the bolts from WT1h.
169

Further developments on the T-stub model
170
Total applied load (kN)
240
210
180
150
120
90
60
EC3: Init.
stiffness
30
0
WT1h WT61a WT61b
0 2 4 6 8 10 12 14 16 18 20 22
Deformation (mm)
EC3: Plastic resistance
Fig. 5.37 Experimental load-carrying behaviour of specimen series WT61 and
comparison with WT1h and Eurocode 3 predictions.
Deformation (mm)
24
21
18
15
12
9
6
3
Bolt RB (WT61a) Bolt LF (WT61a)
Bolt RB (WT1h) Bolt LF (WT1h)
WT1h: max. deformation
WT61a: max. deformation
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
Bolt elongation (mm)
Fig. 5.38 Comparison of the overall deformation-bolt elongation response for
bolts LF and RB in specimens WT1h and WT61a.
Now consider the stiffened specimen WT64C that derives from series
WT4A by inclusion of the stiffeners. The above conclusions are not so obvious
in this case. Fig. 5.39 and Table 3.8 show that both the initial and the post-limit
stiffness values are identical for the two series. Nevertheless, resistance is still
higher in the stiffened case. With respect to the ductility properties, if the absolute
maximum deformation is taken into account, then WT64C shows improved
ductility. If the deformation capacity is assumed as the level corresponding
to Fmax instead, the same conclusion applies. For specimen WT64C
some strain results are given in Fig. 5.40 (see Fig. 3.8d for an indication of the
strain gauges nomenclature) and they prove that the flange is not engaged in
collapse, as the strain level is low at failure conditions. Fig. 5.41 compares the
strains at equivalent strain gauges in WT4A and WT64C. At the bolt axis, the

Total applied load (kN)
240
210
180
150
120
90
60
30
0
WT4Ab WT64C
0 1 2 3 4 5 6 7 8
Parametric study
Deformation (mm)
Fig. 5.39 Experimental load-carrying behaviour of specimen series WT64C
and comparison with WT4Ab.
Total applied load (kN)
240
210
180
150
120
90
60
30
0
SG1 SG6 SG7
0 4000 8000 12000 16000 20000 24000 28000 32000
Strain (µm/m)
(a) Strain gauges SG1, SG6 and SG7.
Total applied load (kN)
240
210
180
150
120
90
Limit of the strain gauges
60
30
0
SG2
SG4
SG3
SG5
0 4000 8000 12000 16000 20000 24000 28000 32000
Strain (µm/m)
(b) Strain gauges SG2, SG3, SG4 and SG5.
Fig. 5.40 Experimental results for flange behaviour (specimen WT64C).
Limit of the strain gauges
171

Further developments on the T-stub model
172
Total applied load (kN)
240
210
180
150
120
90
60
30
0
SG1 SG2
0 600 1200 1800 2400 3000 3600 4200 4800 5400 6000
Strain (µm/m)
(c) Strain gauges SG1 and SG2.
Fig. 5.40 Experimental results for flange behaviour (specimen WT64C) (cont.).
Deformation (mm)
8
7
6
5
4
3
2
SG2 (WT64C)
1
0
SG4 (WT64C)
SG6z (WT4Aa)
0 1200 2400 3600 4800 6000 7200 8400 9600
Strain (µm/m)
(a) Strain gauges SG2 and SG2 from WT64C and SG6 from WT4Aa.
Deformation (mm)
8
7
6
5
4
3
2
SG1 (WT64C)
1
0
SG7 (WT64C)
SG2 (WT4Ab)
0 1500 3000 4500 6000 7500 9000 10500 12000 13500
Strain (µm/m)
(b) Strain gauges SG1 and SG7 from WT64C and SG2 from WT4Aa.
Fig. 5.41 Experimental results for the flange behaviour: comparison between
specimens WT64C and WT4Ab.

Parametric study
strain level is higher in WT64C (Fig. 5.41a), whilst at the weld toe the strains
are higher in WT4Aa (Fig. 5.41b).
Finally, series WT64A is identical to WT64C but only one of the T-stub
elements is stiffened. The results for both specimens are analogous (Fig. 5.42,
Table 3.8). The deformation behaviour is illustrated at two different load stages
in Fig. 5.43.
The main effect of the transverse stiffness is in fact the increase of stiffness
and resistance and decrease of ductility of the connection. The two stiffened
specimen series also indicate that a trilinear curve best fits the experiments
rather than a bilinear approximation as suggested for the other cases.
A final remark concerns the evaluation of ke.0 and FRd for these specimens,
according to Eurocode 3. A simplification has been introduced: both properties
are evaluated for full stiffened and unstiffened specimens and then the average
value is taken (Table 3.7).
Total applied load (kN)
240
210
180
150
120
90
60
30
0
WT64A WT64C
0 1 2 3 4 5 6 7 8
(a) Average gap (LVDTs HP1 and HP2).
Total applied load (kN)
240
210
180
150
120
90
60
Deformation (mm)
30
0
WT64A WT64C
-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0
Deformation measured by HP3 (mm)
(b) LVDT HP3.
Fig. 5.42 Experimental load-carrying behaviour of specimen series WT64A
and comparison with WT64C.
173

Further developments on the T-stub model
(i) WT64A (F = 214 kN; ∆ = 4.46
mm).
(a) After removal of the measuring brackets.
174
(ii) WT64C (F = 231 kN; ∆ = 4.49
mm).
(i) WT64A. (ii) WT64C.
(b) After failure.
Fig. 5.43 Deformation of the specimens WT64A and WT64C at two different
load stages.
5.5.2 Influence of the T-stub orientation
To assess the influence of the T-stub orientation, consider series WT4B and
WT64B. They are identical to specimens WT4A and WT64A, respectively, by
rotating 90º one of the T-stubs. In these tests the flanges are bent in two directions
with double curvature in the plan (x and z directions) – Figs. 3.16d and
5.44. Contrary to the previous tests, here there is no gap between the flanges,
except at the stiffener side in WT64B (Fig. 3.16d). For WT4B, both flanges are
bent as a whole until the bolt starts deforming excessively. At this time, at the
bolt centrelines, the flanges start opening and the maximum deformation at the
web is nearly equal to the bolt deformation capacity. Fig. 5.45 illustrates the F-
∆ response. It shows results for HP1, HP2 and HP3. HP1 (at the back, from the
eye position) shows that the two plates on this side are compressed and their
displacement is negative. HP2 and HP3, located at the front and left sides, respectively,
show that the plates are compressed until a certain load level is
reached, but then they start “opening” and there is an inversion of the deforma-

Parametric study
tion. That inversion starts at a lower load level for HP3 and becomes positive
closer to the maximum load. For comparison, Fig. 5.45 also plots the deformation
of WT4B against the average gap of specimen WT4Ab. Clearly, no resemblance
between results is observed. The maximum load for specimen
WT4B (223.67 kN) is close to the maximum load of WT4Aa, but a bit higher
though.
For specimen WT64B similar conclusions are drawn (Figs. 5.46a-b) except
at the stiffener side where the two flange plates “open” from the commencement
of loading.
The results for LVDTs HP2 and HP3 for both specimens WT4B and
WT64B are compared in Fig. 5.46c. They are identical apart from the influence
of the stiffener. The F-∆ response, as given by HP2, for WT64Bb and WT64A
is compared in Fig. 5.46d. A similar behaviour is observed.
It should be noted though that some perturbations might have occurred in
the measurement by means of the LVDTs in these series since the devices are
not so easily attached here.
Fig. 5.44 Deformation of specimen WT4B at failure (two different views).
5.6 SUMMARY OF THE PARAMETRIC STUDY AND CONCLUDING REMARKS
The experimental/numerical investigation presented in this chapter provides
accurate deformation predictions (up to failure) of the T-stub response. Particular
emphasis on the identification of the main parameters affecting the deformation
capacity of bolted T-stubs has been given. Their influence on the overall
behaviour of the connection has been assessed both qualitatively and quantitatively.
The main conclusions drawn from this study are listed below and summarized
in Table 5.6:
1. The enlargement of the weld throat thickness improves stiffness and resistance
but decreases the deformation capacity;
2. The effect of the width of the T-stub is identical to the above;
3. The increase of the distance m leads to lower stiffness and resistance values
and improves the deformation capacity;
4. Long-threaded bolts increase the overall deformation capacity of a T-stub
175

Further developments on the T-stub model
176
Total applied load (kN)
240
210
180
150
120
90
WT4B (HP1)
60
WT4B (HP2)
30
0
WT4B (HP3)
WTAb (av.def.)
-2.1 -1.4 -0.7 0.0 0.7 1.4 2.1 2.8 3.5 4.2 4.9 5.6
Deformation (mm)
Fig. 5.45 Experimental load-carrying behaviour of specimen series WT4B and
comparison with WT4A.
Total applied load (kN)
240
210
180
150
120
90
WT64Ba (HP1)
60
WT64Ba (HP2)
30
0
WT64Bb (HP1)
WT64Bb (HP2)
-2.1 -1.4 -0.7 0.0 0.7 1.4 2.1 2.8 3.5 4.2 4.9 5.6
Deformation (mm)
(a) Results measured by LVDTs HP1 and HP2 for the two tests WT64B.
Total applied load (kN)
240
210
180
150
120
90
60
30
0
HP3 HP4
-2.1 -1.4 -0.7 0.0 0.7 1.4 2.1 2.8 3.5 4.2 4.9 5.6
Deformation (mm)
HP1 HP2
(b) Results measured by the four LVDTs for test WT64Bb.
Fig. 5.46 Experimental load-carrying behaviour of specimen series WT64B
and comparison with other test series.

Total applied load (kN)
240
210
180
150
120
90
WT64Bb (HP2)
60
WT64Bb (HP3)
30
0
WT4B (HP2)
WT4B (HP3)
-2.1 -1.4 -0.7 0.0 0.7 1.4 2.1 2.8 3.5 4.2 4.9 5.6
Deformation (mm)
Parametric study
(c) Comparison of the results from WT64Bb with WT4B (measured with
LVDT HP2 and HP3).
Total applied load (kN)
240
210
180
150
120
90
60
30
0
0.0 0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0
Deformation (mm)
WT64Bb (HP2)
WT64A (HP2)
(d) Comparison of the results from WT64Bb with WT64A (measured with
LVDT HP2).
Fig. 5.46 Experimental load-carrying behaviour of specimen series WT64B
and comparison with other test series (cont.).
connection when compared to short-threaded equivalent bolts, if collapse is
governed by bolt fracture;
5. Higher bolt diameters increase the strength of the bolt and therefore enhance
the three characteristic properties of the load-carrying behaviour of the connection:
resistance, stiffness and ductility;
6. Identical T-stubs yield higher resistance and lower deformation capacity for
higher steel grades.
Regarding the influence of the stiffener, its main effect is the decrease of
the deformation capacity (note that, for the stiffened specimens, a trilinear approximation
for simplified calculations best fits the experimental results rather
177

Further developments on the T-stub model
than the classical bilinear approximation. Moreover, for stiffened T-stubs, the
influence of the elements orientation is not relevant at the stiffener side; in the
case of unstiffened specimens it has been shown that the two plates become in
contact when the connection is subjected to tension.
Table 5.6 Summary of the main conclusions drawn from the parametric
study [Notation: x↑ ⇒ y↑ means that if x increases then y also increases;
similarly, x↑ ⇒ y↓ means that if x increases then y decreases].
Strength Stiffness Ductility
FRd Fu ke.0
Assembly type
kpl.0 ∆u
WP Rd F ⇒ ↑ WP u F ⇒ ↑ WP e.0
k ⇒ ↑ WP ⇒kpl.0 ↑ WP ⇒∆u ↓
Throat thickness (WP-T-stubs only)
aw aw ↑⇒ FRd
↑ aw ↑⇒ Fu
↑ aw ↑⇒ke.0 ↑ aw ↑⇒kpl.0 ↑ aw ↑⇒∆u ↓
Connection geometry
w w FRd
p p FRd
e1
tf
↑⇒ ↓
↑⇒ ↑
e1↑⇒ FRd
↑
tf ↑⇒ FRd
↑
w↑⇒ Fu↓
p ↑⇒ Fu
↑
e1↑⇒ Fu↑
tf ↑⇒ Fu
↑
w↑⇒ ke.0
↓
p↑⇒ke.0 ↑
e1 ↑⇒ke.0 ↑
tf ↑⇒ke.0 ↑
w↑⇒kpl.0 ↓
p↑⇒kpl.0 ↑
e1 ↑⇒kpl.0 ↑
tf ↑⇒ kpl.0
↑
w ↑⇒∆u ↑
p ↑⇒∆u ↓
e1 ↑⇒∆u ↓
t f ↑⇒∆u ↓
Bolt characteristics
φ Rd F φ ↑⇒ ↑ u F φ ↑⇒ ↑ φ ↑⇒ke.0 ↑ φ ↑⇒kpl.0 ↓ φ ↑⇒∆u ↑
Ltg
S0 No influence
No influence
S0 ↑⇒ke.0 ↑
Plate material
Lt ↑⇒∆u ↑
No influence
fyf . ↑⇒ FRd↑
f y. f ↑⇒ Fu
↑ No influence
fyf . ↑⇒kpl.0 ↑ f y. f ↑⇒∆u↓ 5.7 REFERENCES
[5.1] European Committee for Standardization (CEN). prEN 1993-1-8:2003,
Part 1.8: Design of joints, Eurocode 3: Design of steel structures. Stage
49 draft, May 2003, Brussels, 2003.
178

6 SIMPLIFIED METHODOLOGIES FOR ASSESSMENT OF THE
BEHAVIOUR OF SINGLE T-STUB CONNECTIONS
6.1 INTRODUCTION
Previous chapters deal with the characterization of the overall behaviour of
single T-stub connections by means of experimental tests or numerical threedimensional
models. Both approaches provide a complete definition of the F-∆
response up to collapse of the connection. From a practical point of view, neither
of the above methods seems appropriate. Therefore, a simple methodology
for prediction of the connection response up to collapse is desired. As already
pointed out, the collapse is governed by fracture of the bolts and/or cracking of
the T-stub material. Because of the emphasis placed on connection ductility,
the methodology must be able to predict the response of the T-stub well into its
plastic and strain hardening range with a reasonable degree of accuracy.
This chapter presents simplified methods for determining the monotonic deformation
response of T-stubs. First, existing models from the literature are
discussed. Next, a two-dimensional beam model is proposed and calibrated
against test results from the database compiled previously. Some recommendations
for modifications are also given. Finally, conclusions are drawn.
6.2 PREVIOUS RESEARCH
The analytical prediction of the overall response of bolted T-stub connections
is very complex. The behaviour of this type of connections is intrinsically
three-dimensional and involves both geometrical and material nonlinearities. It
includes the bending deformations of the flange and the combined axial and
bending deformations of the bolts.
Several theoretical approaches for the characterization of the behaviour of
T-stubs have already been proposed in the literature. Essentially, they use the
same basic prying mechanism, which is also the model implemented in Eurocode
3 [6.1] (Fig. 6.1). The model is two-dimensional, i.e. the threedimensional
effects are not accounted for. The system is statically indeterminate
to the first degree. It is loaded by applying a vertical force F/2 to the support
(1), which corresponds to the critical section at the flange-to-web connection.
Only one quarter-model is taken into account due to symmetry considerations.
The contact points at the tips of the flange are modelled with a pinned
support and reproduce the effect of the prying forces. The T-stub flange behaves
as a rectangular cross-section of width beff and depth tf. Such width, beff,
represents the flange plate width tributary to a bolt row that contributes to load
transmission. This width varies with increasing loading but cannot exceed the ac-
179

Further developments on the T-stub model
180
F
2
F
2
(1)
F ⎛∆⎞ ⎜ ⎟
2⎝ 2⎠
Fig. 6.1 Typical T-stub prying model.
∆
tual flange width, b. At pure plastic conditions and for evaluation of the plastic
(design) resistance, it accounts for all possible yield line mechanisms of the T-stub
flange. Despite these major simplifications, the nonlinear analysis of this prying
model is still very complex and requires an incremental procedure. Therefore,
it is not intended for hand computation unless some simplifications that reduce
the model complexity to a reasonable level are assumed.
In this section three alternative simplified models developed by Jaspart
[6.2], Faella and co-workers [6.3-6.5] and Swanson [6.6] are briefly addressed.
These models yield a piecewise F-∆ relationship for characterization of the
connection response. In addition, the proposals of Beg et al. [6.7] for assessment
of the deformation capacity are also reviewed.
6.2.1 Jaspart proposal (1991)
Jaspart approximates the nonlinear T-stub behaviour to a bilinear response
[6.2]. The characteristics of this bilinear behaviour are summarized as follows:
(i) The initial elastic region has a slope ke.0 that is evaluated by application of
Eqs. (1.21-1.22) (later, Jaspart simplified this expression for inclusion in
Eurocode 3 in [6.8] – cf. Eqs. (1.23-1.25), in Chapter 1).
B
(2)
Q

Simplified methodologies: assessment of the behaviour of T-stub connections
(ii) The swivel point in the bilinear relationship represents the full development
of the yield lines and the correponding force is FRd.0. This “plastic” resistance
is is determined from the above prying model as explained in Chapter 1 –
Eqs. (1.3-1.5,1.10).
(iii) In the plastic region, above the swivel point, the effects of material strain
hardening are dominant. The slope of this second linear region is given by:
Eh
k = k
(6.1)
p− l.0 e.0
E
whereby Eh is the strain hardening modulus of the flange material.
(iv) The point of maximum force, Fu.0, is determined by formally equivalent
expressions to FRd.0, by replacing the plastic conditions (index Rd) with
ultimate conditions (index u). This means that these expressions are based on
the same geometric characteristics but the plastic moment of the flange, Mf.Rd
is replaced with:
2
M fu . = 0.25tffuf
. beff
(6.2)
which is an identical expression to Eq. (1.6) and BRd is replaced with:
Bu = fu. bAs (6.3)
The following expressions are then obtained for Fu.0:
Fu.0 = min ( F1. u.0; F2. u.0; F3.
u.0
)
(6.4)
and:
4M
fu .
F1.
u.0
= ( basic formulation)
m
(6.5)
( 32n−2dw) M f . u
F1.
u.0
=
( formulation accounting for the bolt)
8mn
− d m + n
w
( )
( − )
β ( 1 λ )
2M fu . + 2Bun 2M fu . ⎡
F2.
u.0
= = ⎢1+ m+ n m ⎢⎣ 2
u
βu +
λ ⎤
⎥
⎥⎦
(6.6)
F3. u.0 = 2Bu = 2fu.
bAs (6.7)
The deformation capacity is readily determined by intersection of the plastic
region, with slope kp-l.0, with the maximum resistance, Fu.0, i.e.:
FRd.0 Fu.0 − FRd.0
∆ u.0
= +
(6.8)
ke.0 kp−l.0
This methodology can be easily extended to a nonlinear idealization of the F-∆
response, similar to that proposed in Eurocode 3 for the joint overall M-Φ response
(cf. §1.6.1.3), provided that the transition portion of the two straight curves is well
established.
6.2.2 Faella and co-workers model (2000)
Faella and co-workers [6.3-6.5] developed a procedure based on the resem-
181

Further developments on the T-stub model
blance of the distribution of internal forces at plastic and ultimate conditions
(Figs. 1.10 and 6.2). They assumed the following simplifications [6.4]: (i)
geometrical nonlinearities are neglected, (ii) compatibility between bolt and
flange deformation is not considered, (iii) the shear interaction is disregarded,
(iv) prying forces are located at the tip of the flanges, (v) bending of the bolts is
neglected and (vi) cracking of the material is modelled by assuming the cracking
condition as the occurrence of the ultimate strain in the extreme fibres of
the T-stub flanges. The plastic deformation of the flange is computed from the
corresponding moment-curvature (M-χ) diagram. This is obtained from simple
internal equilibrium conditions of the section and by assuming that the material
constitutive law can be approximated by a quadrilinear relationship (see Fig.
2.2). This stress-strain relationship is defined in natural coordinates. The basic
formulations for computation of plastic deformations are derived from the integration
of the M-χ diagram over a certain length, the cantilever length, L, that
remains unchanged during the loading process and equal to that occurring at ultimate
conditions [6.3].
This simple model yields a multilinear F-∆ curve for the behaviour of the
T-stub. The characteristic coordinates of this curve are determined according to
the potential failure mode (Fig. 6.2). In particular, for the evaluation of the
characteristic force coordinates, they use the same expression as the Eurocode
3 for plastic conditions (cf. Chapter 1 and [6.3-6.5]).
Q
182
F1.u.0
B B
Q
(=F1.u/2+Q)
n m m n
(a) Flange fracture
mechanism:
β ≤ β .
( )
u u.lim
b
Mf.u
Mf.u
Q
Bu
F2.u.0
Bu
n m m n
Q
b
Mf.u
ξMf.u
(b) Combined
bolt/flange mechanism:
β < β ≤ 2 .
( )
u.lim u
Bu
F3.u.0
Bu
n m m n
b
ξMf.u
(c) Bolt fracture mecha-
β > 2 .
nism: ( )
Fig. 6.2 Collapse mechanism typologies of a single T-stub prying at ultimate
conditions according to Faella et al. [6.3].
6.2.3 Swanson model (1999)
Swanson developed a prying model that uses the geometrical properties defined
in Fig. 6.3a, which is consistent with the strength model proposed by Ku-
u

Simplified methodologies: assessment of the behaviour of T-stub connections
lak et al. [6.6]. The author uses the following dimensions:
b′ = d −0.5r− 0.5φ
(6.9)
( )
a′ = min 1.25 b′ ; e+ 0.5φ
(6.10)
For comparison, Fig. 6.3b shows the dimensions used in Eurocode 3:
m= d − 0.8r
(6.11)
n= min ( 1.25 m; e)
(6.12)
The model includes: (i) nonlinear material properties, (ii) a variable bolt
stiffness that captures the changing behaviour of the bolts as a function of the
loads they are subjected to, (iii) partially plastic hinges in the flange and (iv)
second order membrane behaviour of thin flanges [6.6].
The bolt behaviour is incorporated by means of an extensional spring located
at the inside edge of the bolt shank. This spring is characterized by a
piecewise linear force-deformation, B-δb, response. Swanson [6.6] proposes an
analytical model for the characterization of the bolt deformation behaviour
similar to that depicted in Fig. 6.4. The multilinear curve refers to handtightened
bolts and its characteristic coordinates are set out in Table 6.1. The
bolt elastic stiffness, Kb is evaluated as follows [6.6]:
Eb
Kb
=
(6.13)
L A + L A
s b tg s
whereby Ls and Ltg are the shank and threaded lengths of the bolt included in
0.5r
F
2
B-δb
0.5φ
B-δb
b’ a’
m n
(a) Dimensions used by Swanson. (b) Dimensions used in Eurocode 3.
Fig. 6.3 T-stub prying model proposed by Swanson [6.6].
0.8r
F
2
183

Further developments on the T-stub model
184
B
0.90Bu
0.85Bu
Yielding,
0.1Kb
Elastic, Kb
δb.1 δb.2
Plastic,
0.02Kb
Bolt fracture
δb.fract
δb
Fig. 6.4 Bolt force-deformation model according to Swanson.
the grip length, respectively, Ab is the nominal area of the bolt shank, Ab = πφ 2 /4
and φ is the bolt nominal diameter.
Based on mechanistic considerations, the deformation capacity of the single
bolt in tension, δb.fract, is easily assessed as follows [6.6]:
0.90BL ⎛ u s
2 ⎞
δbfract . = + εub
. ⎜Ltg+ ⎟
(6.14)
AbEb ⎝ nth
⎠
being nth the number of threads per unit length of the bolt. These predictions are
based on the assumption that the bolt shank remains elastic with inelastic deformation
concentrated in the threads that are included in the grip length [6.6]. It is also
recognized that a portion of the bolt inside the nut will deform inelastically. As a
result, two of the threads within the nut are included in the predictions.
The flange mechanistic model assumes an elastic-yielding-plastic constitutive
relationship for the steel. It also accommodates the shear deformations as
well as the membrane effect, which can be particularly relevant for flexible
flanges. Plastic hinges will develop at the flange-to-web connection and at the
bolt axis and their length is taken as equal to the flange thickness. Strain hardening
is assumed to start immediately following the formation of a plastic
hinge and was modelled with rotational springs [6.6]. The partially plastic
states were incorporated in the model in a simplified way, as reported in [6.6].
Swanson derived the stiffness coefficients and corresponding prying gradients,
qij,k = ∂Q/∂∆, by using the direct stiffness method. Both parameters are
used in an incremental solution technique. First, the initial stiffness and the initial
prying gradient, qee, are determined:
12EI ( 3EI + Kbγ
3 )
ke.0
= (6.15)
γ ee
2
9EI ( Kba′′ b βb
− 2EI)
qee
= (6.16)
γ
ee

Simplified methodologies: assessment of the behaviour of T-stub connections
Table 6.1 Characteristic coordinates of the bolt deformation response.
Bolt force, B Bolt stiffness, Kb Bolt elongation, δb
0≤ B< 0.85Bub K 0.85Bu δ b.1
=
Kb
0.85Bu ≤ B < 0.90Bu
0.10K b
0.05Bu
δb.2 = δb.1+
0.10Kb
0.90Bu ≤ B≤ Bfract
0.02K b
δ .
0.90BL u s
= + ε . L
AE
whereby:
3
beff tf
bfract ub tg
b b
I =
12
(6.17)
is the inertia of the flange cross-section and the remaining coefficients are defined
below:
γ ee = 12EIγ1+
Kbγ2
3 2 2 3
γ1= a′ βa + ( 3a′ b′ + 3ab
′ ′ + b′
) βb
(6.18)
(6.19)
3 3 2 4 2
γ2= 4a′ b′ βaβb + 3a′
b′
βb
(6.20)
3 2
γ3= a′ βa + 3a′
b′
βb
(6.21)
12EI βa = 1+ 2
Gb′ t a′ 12EI
βb
= 1+
2
Gb′ t b′
(6.22)
eff f eff f
The coefficients βa and βb account for shear deformations.
Next, several checks are made to determine which limit is reached first
(bolt force or flange internal stresses limits). Incremental deformations are then
calculated for each of the potential limits with the smallest value governing.
The F-∆ curve can yield up to nine linear branches, with different stiffness, before
failure. Swanson states that the strength and the deformation capacity of
the flange are not always predicted accurately because of sensitivities of the
model to strain hardening parameters and bolt ductility [6.6]. It should be
stressed that this model is not intended for hand calculations and it will not be
used for further comparisons.
6.2.4 Beg and co-workers proposals for evaluation of the deformation capacity
(2002)
Beg et al. developed a set of simple analytical expressions for evaluation of the
deformation capacity of single T-stub connections [6.7]. They also assumed
two alternative cracking conditions: (i) attainment of the ultimate strain at the
185

Further developments on the T-stub model
outer fibre of the flange section and (ii) fracture of the bolt. The maximum
strain allowed at the flange section is 0.20 and the fracture of the bolt is assessed
as follows:
*
ub . 2 ub . b L δ = ε
(6.23)
whereby εu.b is taken as 0.10 for full-threaded bolts and 0.02-0.05 for small-
threaded bolts, and
186
L is the clamping length of bolts, i.e. thickness of clamped
*
b
plates including thickness of washers [6.7]. Factor 2 results from symmetry.
For each potential plastic failure mode (see Fig. 1.10) the authors propose the
following relationships (δu is the deformation capacity of a half-T-stub):
(i) Mode 1:
δu = 0.4m⇒∆ u.0 = 2δ u = 0.8m
(6.24)
(ii) Mode 2:
δub
. ⎛ m⎞ ⎛ m⎞
δu = ⎜1+ k ⎟⇒ ∆ u.0 = 2δu = δu.
b⎜1+
k ⎟
2 ⎝ n ⎠ ⎝ n ⎠ (6.25)
whereby k is an empirical factor varying from 3.0 to 4.0 [6.7].
(iii) Mode 3:
ub .
*
u u.0 2 u. b b
2
L
δ
δ = ⇒∆ = ε
(6.26)
These expressions account for the dependence of the deformation capacity
of a T-stub on the fracture elongation of the bolts, on the ultimate strain of the
steel and on the geometrical parameters m and n. However, the dependence on
the flange thickness is neglected. In Chapter 5 it has been shown evidenced the
strong dependence of the deformation behaviour on this geometrical parameter.
For identical geometry connections that fail according to a plastic mechanism
of type-1, the T-stub with thicker flanges exhibits a lower deformation capacity
than the thinner flange. Eq. (6.24) does not account for this effect.
6.2.5 Examples
To illustrate the alternative procedures, the T-stub (unstiffened) specimens referred
in Chapters 3, 4 and 5 are used. These specimens constitute a database
for exemplification of the procedures presented in this section. Later, the same
specimens will be used for validation of an alternative model for characterization
of the behaviour of isolated T-stub connections.
6.2.5.1 Evaluation of initial stiffness
Chapter 1 already presented some procedures for evaluation of the initial stiffness
of single T-stub connections, namely, the Yee and Melchers standard proposals
[6.9-6.10] and the subsequent modifications suggested by Jaspart in
[6.2]. The Eurocode 3 simple expressions were also derived. These are the

Simplified methodologies: assessment of the behaviour of T-stub connections
same expressions adopted by Jaspart in his simple methodology [6.2] (§6.2.1).
Faella et al. presented an alternative formulation for the definition of ke.0 in
[6.3] (cf. Chapter 1).
Table 6.2 compares the initial stiffness predictions (per bolt row) of some
T-stub specimens by application of two of the above procedures: Faella et al.
formulation and Eurocode 3. Identical tables for the other methodologies are
shown in Appendix D. The specimens were grouped according to the assembly
type (hot rolled profiles or welded plates). The results do not differ substantially.
The ratio value in the tables is given by:
Ratio = Predicted value Actual value (6.27)
As a general conclusion, it can be stated that the procedures proposed by
Faella et al. provide the best prediction for evaluation of ke.0 (third column in
Table 6.2). Eurocode 3 overestimates ke.0 (fifth column Table 6.2). Regarding
the remaining methods, the following conclusions are also drawn (Appendix
D): (i) the location of the prying forces for application of the Yee and Melchers
procedures does not introduce major differences within the limits analysed and
(ii) the Swanson model is more accurate in the elastic domain if the geometrical
dimensions from Eurocode 3 are used. In both cases, however, the average
error is systematically over 100%.
6.2.5.2 Evaluation of plastic resistance
The alternative methodologies analysed in this work use the same approach as
the Eurocode 3 for evaluation of the “plastic” resistance, FRd.0 (see Chapter 1).
Table 6.3 summarizes the predictions for FRd.0 using the expressions from
Eurocode 3. The potential plastic mode is also indicated. For those specimens
failing according to a plastic collapse mode 1, both results from application of
the basic formulation and the formulation accounting for the bolt action are
given. In some cases, if the latter formulation is taken into account, the collapse
type-2 may become critical (specimens P4, WT4, for instance). In those cases,
the values for type-2 are shown in bold/italic.
These predictions are compared with the knee-range of the actual F-∆ (numerical
or experimental) response since the definition of FRd.0 in this case is not
straightforward. The predictions of FRd.0 are within these limits, which means
that the Eurocode proposals are accurate.
6.2.5.3 Piecewise multilinear approximation of the overall response and evaluation
of the deformation capacity and ultimate resistance
The global F-∆ response of a T-stub is characterized in this section by using
the bilinear approximation suggested by Jaspart and the multilinear model proposed
by Faella and co-workers. The same examples from above are used for
187

Further developments on the T-stub model
Table 6.2 Prediction of axial stiffness by application of the Faella, Piluso and
Rizzano procedures and the Eurocode 3.
Test ID Num./Exp.
stiffness
188
Faella et al. predictions
Eurocode 3 predictions
ke.0 Ratio ke.0 Ratio
T1 83.54 87.77 1.05 144.36 1.73
P1 63.27 57.38 0.91 97.27 1.54
P2 117.06 140.95 1.20 220.29 1.88
P3 72.62 77.95 1.07 129.45 1.78
P4 97.86 111.10 1.14 178.63 1.83
P5 101.23 124.32 1.23 197.37 1.95
P9 128.47 173.54 1.35 255.91 1.99
P10 43.88 23.85 0.54 42.08 0.96
P12 102.05 92.09 0.90 156.40 1.53
P14 81.97 87.77 1.07 144.36 1.76
P15 128.41 152.41 1.19 249.63 1.94
P16 111.23 141.11 1.27 220.51 1.98
P18 171.57 158.73 0.93 266.81 1.56
P20 181.68 300.54 1.65 441.03 2.43
P23 322.09 487.19 1.51 675.18 2.10
Average 1.13 1.80
Coefficient of variation
0.24
0.18
Weld_T1(i) 73.50 45.50 0.62 78.07 1.06
Weld_T1(ii) 88.04 62.40 0.71 105.25 1.20
Weld_T1(iii) 107.29 82.56 0.77 136.49 1.27
WT1g 68.58 63.38 0.92 108.64 1.58
WT1h 73.58 63.38 0.86 108.64 1.48
WT2Aa 64.32 50.79 0.79 87.89 1.37
WT2Ab 61.75 50.79 0.82 87.89 1.42
WT2Ba 63.58 74.80 1.18 127.12 2.00
WT2Bb 79.75 74.80 0.94 127.12 1.59
WT4Aa 75.08 103.38 1.38 171.93 2.29
WT4Ab 86.96 103.38 1.19 171.93 1.98
WT7_M12 91.18 101.21 1.11 168.64 1.85
WT7_M16 116.09 104.59 0.90 179.58 1.55
WT7_M20 137.70 107.38 0.78 186.44 1.35
WT51a 59.62 53.27 0.89 92.08 1.54
WT51b 61.84 53.27 0.86 92.08 1.49
WT53C 64.23 55.13 0.86 95.05 1.48
WT53D 52.90 56.36 1.07 97.08 1.84
WT53E 64.82 55.05 0.85 94.92 1.46
WT57_M12 42.89 90.34 2.11 151.69 3.54
WT57_M16 55.22 94.71 1.72 163.02 2.95
WT57_M20 75.48 95.72 1.27 166.89 2.21
Average 1.03 1.75
Coefficient of variation
0.34 0.33

Simplified methodologies: assessment of the behaviour of T-stub connections
Table 6.3 Prediction of the plastic resistance Eurocode 3 (per bolt row).
Test ID Num./Exp.
Eurocode 3 predictions
kneerange
Potential plastic
mode
FRd.0 (kN)
Basic for- Formul. accountmulationing
for the bolt
T1 65 - 85 1 67.02 79.78
P1 60 - 73 1 57.29 67.92
P2 70 - 100 1 80.73 98.53
P3 60 - 75 1 58.64 69.80
P4 70 - 103 1 or 2 87.97 96.37
P5 90 - 120 2 99.48 ⎯
P9 85 - 120 2 108.23 ⎯
P10 40 - 47 1 27.47 32.52
P12 80 - 103 1 67.02 84.04
P14 45 - 65 1 42.76 50.90
P15 80 - 120 1 80.73 104.67
P16 85 - 112 2 103.63 ⎯
P18 150 - 200 1 117.29 157.16
P20 160 - 200 2 190.88 ⎯
P23 275 - 305 2 296.71 ⎯
Weld_T1(i) 50 - 78 1 57.23 61.10
Weld_T1(ii) 60 - 87 1 59.07 69.26
Weld_T1(iii) 75 - 97 1 65.50 77.73
WT1g 58 - 68 1 48.33 55.77
WT1h 60 - 70 1 48.33 44.44
WT2Aa 52 - 62 1 44.44 50.94
WT2Ab 53 - 65 1 44.44 50.94
WT2Ba 59 - 78 1 51.09 59.35
WT2Bb 62 - 80 1 51.09 59.35
WT4Aa 89 - 105 1 or 2 81.62 87.34
WT4Ab 70 - 98 1 or 2 81.62 87.34
WT7_M12 60 - 96 1 or 2 81.00 86.96
WT7_M16 80 - 104 1 80.22 96.14
WT7_M20 88 - 118 1 80.73 100.79
WT51a 78 - 94 2 89.48 ⎯
WT51b 79 - 95 2 89.48 ⎯
WT53C 79 - 94 1 or 2 93.19 93.38
WT53D 83 - 96 1 or 2 94.31 107.76
WT53E 93 - 109 1 92.59 106.67
WT57_M12 75 - 119 2 110.48 ⎯
WT57_M16 104 - 165 1 or 2 158.52 163.78
WT57_M20 126 - 204 1 157.72 196.15
189

Further developments on the T-stub model
comparison with the simple methodology of Jaspart. For application of the
Faella et al. procedures only six examples are considered. As already stated
above, the Swanson proposals are not illustrated herein.
a) Methodology recommended by Jaspart
Fig. 6.5 illustrates the bilinear approximation of the F-∆ response of some selected
specimens, as proposed by Jaspart. The graphs compare the actual response
with four alternative approaches of the methodology, regarding the mechanical
properties of the T-stub flange, the resistance formulation and a combination
of both. The two alternative resistance formulations are the basic formulations
(BF) and the formulation accounting for the bolt action (FBA) when
applicable. The complete characterization of the actual material properties of
the various specimens from the database was given in Chapters 3, 4 and 5. The
190
Load, F (kN)
120
105
(a) HR-T-stub T1 (fy.f = 430 MPa).
Load, F (kN)
90
75
60
Actual response
45
Bilinear response (actual Eh and BF)
30
Bilinear response (actual Eh and FBA)
15
0
Bilinear response (nominal Eh and BF)
Bilinear response (nominal Eh and FBA)
0 2 4 6 8 10 12 14 16 18 20 22 24
90
80
70
60
50
40
30
20
10
(b) HR-T-stub P14 (fy.f = 275 MPa).
Deformation, ∆ (mm)
Actual response
Bilinear response (actual Eh and BF)
Bilinear response (actual Eh and FBA)
Bilinear response (nominal Eh and BF)
Bilinear response (nominal Eh and FBA)
0
0 2 4 6 8 10 12 14 16 18 20 22 24 26
Deformation, ∆ (mm)
Fig. 6.5 Illustration of the methodology proposed by Jaspart.

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
105
90
75
60
45
Actual response
30
Bilinear response (actual Eh and BF)
Bilinear response (actual Eh and FBA)
15
0
Bilinear response (nominal Eh and BF)
Bilinear response (nominal Eh and FBA)
0 2 4 6 8 10 12 14 16 18 20 22
(c) WP-T-stub WT1 (fy.f = 340 MPa).
Load, F (kN)
105
90
75
60
45
Deformation, ∆ (mm)
30
Actual response
15
0
Bilinear response (actual Eh and FBA)
0 1 2 3 4 5 6 7 8 9 10
(d) WP-T-stub WT51 (fy.f = 698 MPa).
Deformation, ∆ (mm)
Fig. 6.5 Illustration of the methodology proposed by Jaspart (cont.).
actual strain hardening modulus, Eh, for these specimens however is always
lower than the nominal properties [6.3,6.11]. For steel grade S355, Eh = E/48.2
and for S275, Eh = E/42.8. No quantitative guidance is given in neither references
for steel grade S690. Hence, both actual and nominal values for Eh are
taken into account for those specimens where steel grade S355 and S275 was
employed (S275 was used in specimen P14).
For further details on this methodology, the reader should refer to Appendix
D. Generally speaking, the bilinear approximation proposed by this author reproduces
well the actual behaviour for those specimens made up of S690, with
an overestimation of the deformation capacity. For the remaining cases, the
predictions are fine provided that the nominal value of the strain hardening
modulus is used. If the actual value of Eh is used instead, then the predictions
are not so good.
191

Further developments on the T-stub model
b) Methodology recommended by Faella, Piluso and Rizzano
Fig. 6.6 shows the overall F-∆ response for some T-stub specimens that were
chosen to illustrate the different failure modes. The graphs trace the response
for actual and nominal flange mechanical properties and include the compatibility
of the deformations of the flange and the bolt (Appendix D). In general,
this model does not provide an accurate modelling of the deformation behaviour.
c) Methodology recommended by Beg, Zupančič and Vayas
The procedures for a direct computation of the deformation capacity from Beg
et al. [6.7] are illustrated in Appendix D for the various specimens. The predictions
are not satisfactory though, particularly for those specimens that fail ac-
192
Load, F (kN)
135
120
105
90
75
60
Actual response
45
Quadrilinear approximation (BF: type-2
30
15
0
governs failure)
Quadrilinear approximation(FBA: (BF: type-1
governs failure)
0 1 2 3 4 5 6 7 8 9 10 11
Deformation, ∆ (mm)
(a) HR-specimen T1 (actual material properties).
Load, F (kN)
270
240
210
180
150
120
90
60
30
0
Actual response
Quadrilinear approximation (actual mat. prop.)
Quadrilinear approximation (nominal mat. prop.)
0 3 6 9 12 15 18 21 24 27 30
Deformation, ∆ (mm)
(b) HR-specimen P18.
Fig. 6.6 Illustration of the methodology proposed by Faella, Piluso and Rizzano.

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
120
105
(c) WP-T-stub specimen WT4A.
Load, F (kN)
90
75
60
45
30
Actual response
15
0
Quadrilinear approximation (actual mat. prop.)
Quadrilinear approximation (nominal mat. prop.)
0 1 2 3 4 5 6 7 8 9 10
105
(d) WP-T-stub specimen WT51.
90
75
60
45
Deformation, ∆ (mm)
30
Actual response
15
Quadrilinear approximation (actual mat. prop.)
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5
Deformation, ∆ (mm)
Fig. 6.6 Illustration of the methodology proposed by Faella, Piluso and Rizzano
(cont.).
cording to a plastic mode 1. The average ratios of the actual numerical or experimental
predictions are 2.10 for HR-T-stubs and 3.55 for WP-T-stubs, with
coefficients of variation of 0.50 and 0.48, respectively. Again, it is noted that
this methodology only gives an estimation of the T-stub deformation capacity,
rather than a description of the full nonlinear behaviour.
6.2.5.4 Summary
This section described and illustrated several methodologies for the assessment
of the F-∆ response of T-stubs (or some of its characteristics). Table 6.4 compares
the different methods from a statistical point of view, in terms of average
ratios of the sample of examples and coefficient of variation. The examples are
divided according to the assembly type (HR-T-stub or WP-T-stub). The pa-
193

Further developments on the T-stub model
Table 6.4 Summary of the different proposals from a statistical point of view
(average ratios and coefficients of variation, the latter in italic) for
evaluation of the force-deformation characteristics.
Methodology T-stub
assembly
194
Stiffness Ultimate resistance
Deformation
capacity
ke.0 Fu.0 ∆u.0
Beg et al.
HR
WP
⎯
⎯
⎯
⎯
2.10 (0.50)
3.55 (0.48)
Eurocode 3
HR
WP
1.80 (0.18)
1.75 (0.33)
⎯
⎯
⎯
⎯
Faella et al.
HR
WP
1.13 (0.24)
1.03 (0.34)
0.80 (0.46)
0.95 (0.23)
0.73 (0.54)
1.16 (0.36)
Jaspart
HR
WP
2.30 (0.21)
2.30 (0.31)
0.96 (0.11)
0.93 (0.08)
0.91 (0.35)
1.13 (0.30)
Swanson
HR
WP
2.35 (0.26)
3.08 (0.37)
⎯
⎯
⎯
⎯
Yee and
HR 2.32 (0.18) ⎯ ⎯
Melchers WP 2.23 (0.32) ⎯ ⎯
rameters chosen for comparison are the initial stiffness, the ultimate resistance
and the deformation capacity.
The best approach for characterization of the initial stiffness is that proposed
by Faella et al. [6.3], though the coefficient of variation of the sample is
slightly higher than for the Eurocode 3. Regarding the evaluation of the deformation
capacity, Jaspart [6.2] gives accurate predictions. The scatter of results
for the deformation capacity is rather high when compared to the other properties
as shown by the coefficient of variation. The results shown for the methodology
proposed by Faella and co-authors, in terms of ultimate resistance and
deformation capacity, are merely illustrative since the sample is not big enough
for a statistical analysis of this type.
6.3 PROPOSAL AND VALIDATION OF A BEAM MODEL FOR CHARACTERI-
ZATION OF THE FORCE-DEFORMATION RESPONSE OF T-STUBS
6.3.1 Description of the model
The models described above afford some basis for the development of an analytical
method for the evaluation of the deformation capacity and the loadcarrying
capacity of single T-stub connections. The mechanical model is similar
to that depicted in Fig. 6.3b. A model that uses geometrical and mechanical

Simplified methodologies: assessment of the behaviour of T-stub connections
properties consistent with the Eurocode 3 prying model is desired so as to
make implementation easier.
The prying model is analysed up to collapse. From static equilibrium (Fig.
6.7):
F
B = + Q
(6.28)
2
() 1 F
M = Qn − m
(6.29)
2
( 2)
M = Qn
(6.30)
being (1) the section at the flange-to-web connection and (2) the flange section
at the bolt line. Normally, M1 ≥ M2. However, Swanson points out that in some
cases this inequality may not be observed due to the effect of the removal of
flange material at the bolt line when the holes are drilled for the bolts [6.6].
The deflected shape and the moment diagram of one side of the flange in pure
elastic conditions and after separation at the bolt axis are as shown in Fig. 6.8a
[6.12]. If the bolt is strong enough, a stage of loading will be reached when the
plastic moment of the flange, Mf.p, is attained at the flange-to-web connection
(Fig. 6.8b, [6.12]). Any additional load will cause further flange deflection that
results in strain hardening of the flange and an increase in the internal moment
at that section. The zone of full plastification spreads into the flange. With continued
loading, a similar condition may develop at the bolt axis. When the most
(1)
F
2
(1*)
0.2r or 0.2 2a w
Fig. 6.7 Internal forces.
(2)
m n
M1 = Qn - 0.5Fm
B
M2 = Qn
Q
195

Further developments on the T-stub model
highly strained flange fibres are strained to the breaking point (εu) and fracture,
the ultimate resisting moment of the flange, Mf.u, is also reached and the ultimate
conditions (subscript u) are attained (Fig. 6.8c, [6.12]). In this figure, Bu
is not necessarily the tensile strength of the bolt.
For common steels, Mf.u is significantly higher than Mf.p [6.3,6.11,6.13]. If
simple plastic theory is applied, the limit resistance and the deformation would
be determined by Mf.p. Therefore, consideration of strain hardening is crucial to
carry out an ultimate analysis of the system up to a fracture condition.
M (1)
196
B
0.5F
M (1) = Qn-0.5Fm
Q
M (2) = Qn
m n
(a) Pure elastic conditions.
Mf.p
B
0.5F
M (1) = Mf.p
Mf.y
Q
M (2) = Qn
m n
(b) Full plastification of
section (1).
Fig. 6.8 Effect of material strain hardening.
6.3.1.1 Fracture conditions
Mf.u
Bu
M (1) 0.5Fu
= Mf.u
Mf.p
Mf.y
Mf.y
Mf.p
Qu
M (2) = Qun
m n
(c) Fracture of section
(1).
The two possible ultimate fracture conditions are: (i) fracture of the bolt and
(ii) cracking of material of the flange near the web as already explained in
Chapter 2.
In the context of a two-dimensional model, where the flange is modelled as
a rectangular cross-section, this latter condition may be too severe. Critical section
(1) is defined at a distance m from the bolt axis, where the flange thickness
is higher than tf owing to the fillet weld or radius that provide some extra material
thickness. Therefore, the imposition of cracking of the material should also
be checked at the end of this fillet, section (1*) – Fig. 6.7, i.e. at a distance m * =
d – r or m * = d – 2 aw for HR- and WP-T-stubs, respectively.
6.3.1.2 Bolt deformation behaviour
The bolt elongation response is based on the Swanson’s proposals. Its influence

Simplified methodologies: assessment of the behaviour of T-stub connections
on the overall response is accounted for by means of an extensional spring with
similar characteristics to the Swanson bolt model, as just explained (Fig. 6.4
and Table 6.1). For the computation of the bolt deformation at fracture, however,
the parameter nth that appears in Eq. (6.14) is disregarded.
For design calculations, the nominal material characteristics of the bolts
have to be defined. The parameters given in Table 6.5 are suggested by Hirt
and Bez [6.14] for high-strength bolts.
Table 6.5 Minimum mechanical properties of high-strength bolts.
Bolt grade fy fu εu
(MPa) (MPa)
8.8 640 800 0.12
10.9 900 1000 0.09
6.3.1.3 Flange constitutive law
The flange material constitutive law is modelled by means of a piecewise linear
curve, that accounts for the strain hardening effects. This law is a true stresslogarithmic
strain relationship, i.e. it is defined in natural coordinates in order
to capture the actual material behaviour. Faella et al., in fact, adopted the same
approach since the prediction of the plastic deformation capacity of compact
sections is more accurate if natural stress-strain coordinates are used [6.3].
The above model is not suitable for a hand calculation. Instead, a numerical
FE method is used to determine the structural response. Consequently, the
piecewise constitutive law may contain numerous branches. It should be
stressed that many FE codes do not allow for an elastoplastic analysis with
strain hardening for beam elements. The FE code LUSAS [6.15] implements a
beam element that belongs to the Kirchoff beams group (with quadrilateral
cross-section) [6.15]. Shear deformations are excluded in this element formulation.
It has a quadrilateral cross-section.
From a design point of view, the constitutive law should be of a standard
type though. The stress-strain curve can be idealized by means of a multilinear
model with a straight line for hardening range, as suggested in [6.13] (Fig. 6.9).
The maximum stress is reached for a strain value:
fu − fy
εhs = εh+
(6.31)
Eh
With reference to Fig. 6.9, Gioncu and Mazzolani give no guidance on the
characterization of the softening branch of this curve [6.13]. For current structural
steel grades, the characteristic coordinates are set out in Table 6.6, for
plate thickness smaller than 40 mm [6.13]. These coordinates are transformed
into a true stress-logarithmic strain curve by means of Eq. (4.1), which is reproduced
below:
197

Further developments on the T-stub model
198
= ( 1+
) and ε ln ( 1 ε )
σ n σ ε
n = + (6.32)
The stress-strain characteristics in natural coordinates for the three above steel
grades are depicted in Fig. 6.10. The fifth linear part of the curve in natural coordinates
has a slope of Eu = fu, according to Faella et al. [6.3].
σ
fu
fy
E
Eh
εy εh εhs εuni εu
Fig. 6.9 Idealization of the stress-strain diagram with a multi-linear model.
True stress (MPa)
700
600
500
400
300
200
100
0
0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24
Logarithmic strain
S355
S275
S235
Fig. 6.10 True stress-logarithmic strain characteristics for steel grades S235,
S275 and S355.
Table 6.6 Characteristics of the stress-strain curve (stress values in [MPa]).
Steel
grade
fy fu εy εh εhs εuni εu Eh Eu
S235 235 360 0.001 0.014 0.037 0.140 0.250 5500 360
S275 275 430 0.001 0.015 0.047 0.120 0.220 4800 430
S355 355 510 0.002 0.017 0.053 0.110 0.200 4250 510
ε

Simplified methodologies: assessment of the behaviour of T-stub connections
6.3.2 Analysis of the model in the elastic range
First, the proposed model is analysed and validated in the elastic domain by using
the specimens from the author’s database. The initial stiffness of a T-stub
connection is evaluated and compared with the actual predictions, corresponding
to experimental or (three-dimensional) numerical values.
In order to assess the importance of the shear deformability on the flange
rectangular cross-section, two beam elements are tested: thin beam and thick
beam. The thick beam element includes the shear deformations in its formulation
but does not allow for a material nonlinear analysis with strain hardening.
The results are compared in Table 6.7 for fifteen selected examples that represent
the three different failure types. Clearly, the thick beam model provides a
better agreement with the actual results (second column of Table 6.7), which
indicates that the shear deformation in the elastic domain may be significant.
From the analysis of the average ratio to the actual values, the model with a
thin beam element was re-analysed with a reduced Young modulus for the
flange material. This reduction was taken as half of the actual E since the earlier
results were nearly twice as much as the actual. This factor of reduction
may be slightly increased in order to best fit the actual results (unitary average
ratio). However, the calibration of this factor should be based on a larger sam-
Table 6.7 Influence of shear deformations on the initial stiffness of some of
the tested T-stubs (stiffness values in [kN/mm]).
Test
ID
Num.
res.
Thick beam model
(Thin) Beam model predictions
Actual Young Reduced Young
modulus modulus (0.5E)
ke.0 Ratio ke.0 Ratio ke.0 Ratio
T1 83.54 149.35 1.79 175.06 2.10 99.68 1.19
P1 63.27 108.03 1.71 124.27 1.96 69.86 1.10
P2 117.06 215.72 1.84 259.43 2.22 153.84 1.31
P3 72.62 133.92 1.84 157.91 2.17 88.80 1.22
P4 97.86 184.95 1.89 214.04 2.19 125.31 1.28
P5 101.23 204.49 2.02 235.17 2.32 139.71 1.38
P9 128.47 262.74 2.05 292.60 2.28 185.87 1.45
P10 43.88 49.35 1.12 54.57 1.24 28.14 0.64
P12 102.05 162.51 1.59 194.79 1.91 106.02 1.04
P14 81.97 149.35 1.82 175.06 2.14 99.68 1.22
P15 128.41 240.45 1.87 298.29 2.32 167.26 1.30
P16 111.23 228.71 2.06 261.17 2.35 157.91 1.42
P18 171.57 279.74 1.63 333.71 1.95 183.33 1.07
P20 181.68 422.05 2.32 509.64 2.81 328.23 1.81
P23 322.09 605.32 1.88 775.43 2.41 522.49 1.62
Average 1.83 2.16 1.27
Coeff. variation
0.15
0.16
0.21
199

Further developments on the T-stub model
ple of examples, which also includes other connections beyond those from the
author. The results for this reduced modulus of elasticity are set out in Table
6.7 as well. As expected, the initial stiffness values decrease. These values will
improve further if an additional correction of the Young modulus for shear is
introduced. It is desirable to obtain this correction by means of a simple formula
rather than an empirical correction. In Appendix A of Chapter 1, the
shear interaction was already taken into consideration for resistance purposes.
In mode-1 plastic failure types the ratio between the design resistance of
mechanism type-1 accounting for shear and that corresponding to the basic
formulation is given by (cf. Appendix A):
2
2⎛ m ⎞ ⎡ 3 ⎤4Mf.
Rd
⎜ 1+ −1
2
3 ⎜
⎟
t ⎟ ⎢ ⎥
2
⎝ f ⎠ ⎢ ( mtf ) ⎥ m
2⎛m⎞ ⎡ 3 ⎤
F1.
Rd .0 =
⎣ ⎦
= ⎜ ⎟ 1 1 2
4M ⎢ + − ⎥ (6.33)
f . Rd 3 ⎜t⎟ ⎝ f ⎠ ⎢ ( mt
⎣ f ) ⎥
⎦
m
The above relationship depends exclusively on the ratio m/tf. Fig. 6.11 plots
that relationship and shows that lim F1.
Rd .0 = 1.
The value of F 1. Rd .0 is signifi-
cant for mtf 2.5( F1.
Rd.0
0.9)
200
mtf
→∞
≤ < . If the analysis of the T-stub elements and the
bolts is carried out separately, the T-flange is fixed at the bolt centreline.
Therefore, the only possible collapse mode is of type-1 and so the above relationship
applies. The following expression is then proposed for determining the
reduced modulus to employ in the beam model:
2 2
2⎛m⎞ ⎡ 3 ⎤ E⎛m⎞ ⎡ 3 ⎤
Ered = 0.5E× ⎜ ⎟ ⎢ 1+ − 1 1 1
2 ⎥ = ⎜ ⎟ ⎢ + − 2 ⎥ (6.34)
3⎜t ⎟
f ( mt ) 3 ⎜t ⎟
⎝ ⎠ ⎢ f ⎥ f ⎢ ( mt
⎣ ⎦
⎝ ⎠
⎣ f ) ⎥
⎦
This reduction does not have much influence at ultimate conditions. In fact, the
effect of shear on the moment resistance of the flange is apparently beneficial
[6.12].
1.0
0.9
0.8
0.7
0.6
F 0.5
1.Rd.0
0.4
0.3
0.2
0.1
0.0
0 1 2 3 4 5 6 7 8 9 10 11 12
Fig. 6.11 Interaction F 1. Rd.0
vs. mt f .
m/tf

Simplified methodologies: assessment of the behaviour of T-stub connections
Table 6.8 shows the results for initial stiffness obtained through application
of the above expression, as well as the reduced Young modulus. In this table
both the ratio to the actual stiffness values (eighth column – Act.) and to the
beam model with the simple reduction (ninth column – 0.5E) are calculated.
The difference between the two approaches is 8% on average. The results obtained
with Ered as in Eq. (6.34) show a good agreement with the actual predictions
(error of 17%, on average).
This value of Ered is then used onwards. It is important to stress that this
value has little influence at ultimate conditions, as already explained. The beam
model referred hereafter is hence the model that employs the thin beam model
and Ered for the flange material.
Table 6.9 evaluates the initial stiffness for other T-stubs from the database.
The results are in line with the previous predictions. Additionally and in the
elastic behaviour domain, a set of sixteen T-stub connections tested by Faella
et al. [6.3] are considered. Unfortunately, these specimens cannot be used for
further comparisons due to lack of data. The geometrical and mechanical characteristics
of the latter specimens are set out in Table 6.10. The initial stiffness
predictions by application of this model are summarized in Table 6.11 along
with the reductions to be applied. In this table these results are also compared
with the experiments and the beam model with the simple reduction, as before.
Table 6.8 Values of the reduced Young modulus accounting for shear.
Test
ID
E
(MPa)
m/tf F 1. Rd .0 0.5F 1. Rd.0
Ered
(MPa)
Beam model predictions
Reduced Young modulus
( Ered = 0.5EF1.
Rd.0
)
ke.0 Ratio
kN/mm Act. 0.5E
T1 2.75 0.92 0.46 95416 92.48 1.11 0.93
P1 3.22 0.94 0.47 97472 65.96 1.04 0.94
P2 2.29 0.89 0.44 92315 139.46 1.19 0.91
P3 2.75 0.92 0.46 95416 82.29 1.13 0.93
P4 2.75 0.92 0.46 95416 116.60 1.19 0.93
P5 2.75 0.92 0.46 95416 130.20 1.29 0.93
P9 2.05 0.87 0.43 90180 167.39 1.30 0.90
P10 4.39 0.96 0.48 100318 27.16 0.62 0.96
P12 2.75 0.92 0.46 95416 97.94 0.96 0.92
P14 2.75 0.92 0.46 95416 92.48 1.13 0.93
P15 2.29 0.89 0.44 92315 154.94 1.21 0.93
P16 2.75 0.92 0.46 95416 147.44 1.33 0.93
P18 2.75 0.92 0.46 95416 169.58 0.99 0.93
P20 2.05 0.87 0.43 90180 296.64 1.63 0.90
P23 1.67 0.82 0.41 85306 461.22 1.43 0.88
Average 1.17 0.92
Coeff. variation 0.20 0.02
208153
201

Further developments on the T-stub model
Table 6.9 Validation of the approach with further examples from the database:
comparison of initial stiffness predictions (Young modulus
in [MPa] stiffness values in [kN/mm]).
Test
ID
E m/tf F1.
Rd .0
2
Beam model predictions
0.5E Ered = 0.5EF1.
Rd.0
Ratio
Actual
ke.0
ke.0 Ra- ke.0
tio
Act. 0.5E
HR-T-stubs
P6 2.75 0.46 76.68 88.80 1.16 82.29 1.07 0.93
P7 2.75 0.46 91.72 110.19 1.20 102.35 1.12 0.93
P8 2.46 0.45 95.19 127.28 1.34 116.44 1.22 0.91
P11 2.05 0.43 122.93 188.83 1.54 170.56 1.39 0.90
P13 2.75 0.46 83.46 99.68 1.19 92.48 1.11 0.93
P17 2.75 0.46 138.60 172.19 1.24 159.89 1.15 0.93
P19 2.75 0.46 130.47 172.19 1.32 159.89 1.23 0.93
P21 2.75 0.46 174.25 228.11 1.31 211.79 1.22 0.93
P22
2.16 0.44 253.74 328.89 1.30 296.85 1.17 0.90
202
208153
Average 1.29 1.19 0.92
0.09
0.08 0.01
209856
204462
Coeff. variation
WP-T-stubs
Weld_
T1(i)
3.50 0.47 73.77 55.10 0.75 52.36 0.71 0.95
Weld_
T1(ii)
3.12 0.47 89.12 73.19 0.82 68.82 0.77 0.94
Weld_
T1(iii)
2.82 0.46 107.29 94.26 0.88 87.68 0.82 0.93
WT1
WT2A
WT2B
WT4A
3.27
3.53
3.08
3.24
0.47
0.47
0.47
0.47
71.08
61.83
79.75
86.96
75.96
62.09
88.19
122.66
1.07
1.00
1.11
1.41
71.61
58.97
82.62
115.86
1.01
0.95
1.04
1.33
0.94
0.95
0.94
0.94
WT51
WT53C
WT53D
WT53E
3.45
3.40
3.38
3.40
0.47
0.47
0.47
0.47
60.73
64.23
52.90
64.82
64.11
65.60
67.77
65.44
1.06
1.02
1.28
1.01
60.73
62.12
64.08
61.94
1.00
0.97
1.21
0.96
0.95
0.95
0.95
0.95
WT7_
M12
3.28 0.47 91.18 120.34 1.32 113.79 1.25 0.95
WT7_
M16
3.28 0.47 116.09 124.29 1.07 117.27 1.01 0.94
WT7_
M20
3.27 0.47 137.70 128.08 0.93 120.60 0.88 0.94
WT57_
M12
3.38 0.47 85.78 105.35 1.23 99.95 1.17 0.95
WT57_
M16
3.37 0.47 110.43 113.07 1.02 106.94 0.97 0.95
WT57_
M20
3.38 0.47 150.96 115.51 0.77 109.09 0.72 0.94
208153
209856
204462
Average 1.04 0.99 0.94
0.18
0.18 0.01
Coeff. variation

Simplified methodologies: assessment of the behaviour of T-stub connections
Table 6.10 Geometric characteristics of the specimens tested by Faella et al.
Test ID Geometric characteristics (dimensions in [mm])
b beff tf m n λ φ
Kb
(kN/mm)
TS1 189.0 90.70 11.40 28.35 35.44 1.25 20 1.79×10 6
TS2 189.0 116.03 11.00 41.01 49.85 1.22 20 1.84×10 6
TS3 189.0 64.05 9.10 30.03 34.10 1.14 20 2.13×10 6
TS4 189.0 96.33 9.35 31.16 33.10 1.06 20 2.09×10 6
TS5 189.0 98.13 13.75 32.06 32.21 1.00 20 1.54×10 6
TS6 189.0 95.50 13.45 30.75 32.98 1.07 20 1.57×10 6
TS7 188.0 80.28 14.85 29.99 37.48 1.25 12 5.10×10 5
TS8 189.0 77.12 14.90 28.41 35.51 1.25 12 5.09×10 5
TS9 189.0 78.65 16.50 29.18 36.47 1.25 12 4.66×10 5
TS10 189.0 78.15 15.50 28.93 36.16 1.25 12 4.92×10 5
TS11 189.5 101.55 11.05 40.63 50.25 1.24 12 6.53×10 5
TS12 189.5 76.50 10.70 28.10 35.13 1.25 12 6.71×10 5
TS13 189.0 79.45 12.65 29.58 36.97 1.25 12 5.84×10 5
TS14 189.0 80.65 12.70 30.18 37.72 1.25 12 5.82×10 5
TS15 189.0 84.20 13.80 31.95 39.94 1.25 12 5.43×10 5
TS16 189.5 82.65 13.45 31.18 38.97 1.25 12 5.55×10 5
Table 6.11 Validation of the approach with further examples tested by Faella,
Piluso and Rizzano [6.3]: comparison of initial stiffness predictions
(Young modulus in [MPa]; stiffness values in [kN/mm]).
Test
ID
E m/tf 0.5F 1. Rd.0
Exp.
ke.0
Beam model predictions
0.5E Ered = 0.5EF1.
Rd.0
ke.0 Ratio
ke.0 Ratio
Act. 0.5E
TS1 2.49 0.45 167 290.59 1.74 265.65 1.59 0.91
TS2 3.73 0.48 112 122.13 1.09 116.51 1.04 0.95
TS3 3.30 0.47 99 145.17 1.47 136.88 1.38 0.94
TS4 3.33 0.47 103 146.62 1.42 138.43 1.34 0.94
TS5 2.33 0.45 229 364.25 1.59 347.20 1.52 0.95
TS6 2.29 0.44 214 372.57 1.74 338.93 1.58 0.91
TS7 2.02 0.43 237 295.17 1.25 270.92 1.14 0.92
TS8 1.91 0.43 213 317.39 1.49 289.89 1.36 0.91
TS9 1.77 0.42 214 346.13 1.62 315.21 1.47 0.91
TS10 1.87 0.42 266 325.77 1.22 297.45 1.12 0.91
TS11 3.68 0.47 82 101.57 1.24 97.15 1.18 0.96
TS12 2.63 0.45 168 184.66 1.10 171.63 1.02 0.93
TS13 2.34 0.45 163 234.90 1.44 217.04 1.33 0.92
TS14 2.38 0.45 156 229.40 1.47 212.29 1.36 0.93
TS15 2.32 0.44 192 242.82 1.26 224.84 1.17 0.93
TS16 2.32 0.44 179 241.14 1.35 223.10 1.25 0.93
Average 1.41 1.30 0.93
Coeff. variation
0.14 0.14 0.02
210000
203

Further developments on the T-stub model
Regarding the latter specimens, the Young modulus of the flange crosssection
was taken as equal to 210 GPa, since this particular parameter was not
defined by the authors. And since the characteristics of the bolts were not provided
as well, the following assumptions were made to define the bolt elastic
elongation behaviour: (i) Eb = 210 GPa, (ii) bolts are full-threaded, (iii) two
washers per bolt with twsh = 2.95 mm for M20 bolts and twsh = 2.50 mm for
M12 bolts, (iv) th = 13.10 mm for M20 bolts and th = 8.90 mm for M12 bolts
and (v) tn = 16.00 mm for M20 bolts and tn = 11.90 mm for M12 bolts.
Finally, a remark concerning the two values of b and beff that appear in Table
6.10 is required. The beam model employs beff for the definition of the
cross-section width, which is kept constant throughout the load history. As
mentioned earlier, this width accounts for all possible yield line mechanisms of
the T-stub flange and cannot exceed the actual flange width, b. For the examples
from the database, beff = b; however, for the set of examples tested by
Faella and co-authors, b > beff and so the smallest value governs.
Physically, it is quite clear that the section width that contributes to load
transmission expands with the loading provided that the actual flange width is
not exceeded. The assumption of a constant flange width of beff seems appropriate
until strain hardening begins (the reduction at elastic conditions can be
done indirectly with the reduction of the Young modulus, for instance), but it
may be too conservative at ultimate conditions.
6.3.3 Analysis of the model in the elastoplastic range
Having carried out the full nonlinear analysis of the beam model, numerous results
can be extracted, namely: (i) load-carrying behaviour, (ii) evolution of the
prying forces, (iii) flange moment diagram, (iv) flange plastic strain diagram,
etc. Thorough results for specimens T1 and WT1 are given in Appendix D to
illustrate the capacities of the model. In this section, the F-∆ response of the
specimens from the database is characterized up to collapse in the framework
of the proposed methodology. This simplified load-carrying behaviour is compared
with the actual response and the bilinear approximation proposed by Jaspart.
Firstly, the collapse modes are defined. Table 6.12 sets out the actual determining
fracture element: bolt or T-stub flange. The prediction of the failure
modes as described in Chapter 2, which is based on a force criterion, is also
given. These predictions are generally in line with the observed failure modes,
except for specimens P13, WT53D and WT53E. Such situation may derive
from the fact that the fracture criterion for the numerical three-dimensional
model and for the beam model is based on a deformation condition. This may
introduce some differences. This table also indicates the fracture element that is
determinant in the two-dimensional model. Here, the differences are more frequent
(underlined specimens). The critical section (1*) that is referred to in the
table is the critical section right at the end of the fillet weld or radius. After
204

Simplified methodologies: assessment of the behaviour of T-stub connections
Table 6.12 Prediction of the failure modes.
Test ID Actual deter- Predicted poten- Determining fracture
mining fracture tial failure mode. element in the beam
element Mf.u Eq.
(2.4)
Mf.u Eq.
(2.5)
model
T1 Bolt 13 13 Bolt
P1 Bolt 13 13 Bolt
P2 Bolt 13 13 Bolt
P3 Bolt 13 13 Flange, at (1*)
P4 Bolt 13 13 Bolt
P5 Bolt 23 23 Bolt
P6 Bolt 13 13 Bolt
P7 Bolt 13 13 Bolt
P8 Bolt 13 13 Bolt
P9 Bolt 23 23 Bolt
P10 Flange 11 11 Flange, at (1*)
P11 Bolt 23 23 Bolt
P12 Flange 11 11 Flange, at (1*)
P13 Bolt 11 11 Flange, at (1*)
P14 Flange 11 11 Flange, at (1*)
P15 Flange 11 11 Flange, at (1*)
P16 Bolt 23 23 Bolt
P17 Bolt 13 13
Bolt and flange at
(1*) (simultaneously)
P18 Flange 11 11 Flange, at (1*)
P19 Bolt 13 13
Bolt and flange at
(1*) (simultaneously)
P20 Bolt 23 23 Bolt
P21 Bolt 13 13 Flange at the bolt axis
P22 Bolt 13 13 Bolt
P23 Bolt 23 23 Bolt
Weld_T1(i) Bolt 11 11 Flange, at (1*)
Weld_T1(ii) Bolt 13 13 Flange, at (1*)
Weld_T1(iii) Bolt 13 13 Bolt
WT1 Bolt and flange 11 13 Flange, at (1*)
WT2A Bolt and flange 11 13 Flange, at (1*)
WT2B Bolt and flange 11 13 Flange, at (1*)
WT4A Bolt 13 13 Bolt
WT51 Bolt 23 23 Flange, at (1*)
WT53C Bolt 13 13 Flange, at (1*)
WT53D Bolt 11 13 Flange, at (1*)
WT53E Bolt 11 13 Flange, at (1*)
WT7_M12 Bolt 13 13 Bolt
WT7_M16 Flange 11 13 Flange, at (1*)
WT7_M20 Flange 11 11 Flange, at (1*)
WT57_M12 Bolt 23 23 Flange, at (1*)
WT57_M16 Bolt (stripping) 13 13 Flange, at (1*)
WT57_M20 Bolt and flange 11 11 Flange, at (1*)
205

Further developments on the T-stub model
application of the model and within the process of calibration of the model, it
was observed that the imposition of cracking of the material at section (1), at
the flange-to-web connection, as an ultimate condition was a too severe condition
indeed (§6.3.1.1). Therefore, collapse occurs when either or both of the
following conditions are verified: (i) fracture of the bolt and (ii) cracking of
material of the flange at the end of the fillet weld or radius, section (1*).
Table 6.13 summarizes the predictions of deformation capacity and ultimate
resistance of the proposed model. The predictions are compared with the
actual results. The ultimate resistance is well estimated and the scatter of results
is lower since the variation is also low (coefficient of variation of 0.13 for
HR-T-stubs and 0.15 for WP-T-stubs). Regarding the deformation capacity, the
differences are more relevant. However, this disparity has to be accepted
within reasonable limits due to all the simplifications inherent to this twodimensional
approach. In this table the specimens are separated according to
their assembly type. Table 6.14 presents identical results but with specimens
grouped according to the potential failure type (Mf.u from Eq. (2.4)). The specimens
whose actual failure type was not well predicted were excluded from this
table. If now the specimens are analysed in this context, the following conclusions
may be drawn: (i) for specimens that fail according to type-23, both predictions
of deformation and resistance at ultimate conditions are good, with average
errors smaller than 10%, (ii) identical conclusions are valid for specimens
of type-11 failure, regarding the evaluation of deformation capacity, (iii)
for these latter specimens the ultimate resistance prediction is conservative, (iv)
for those specimens failing according to a type-13 mode, the predictions for resistance
are good and (v) the evaluation of deformation capacity for these
specimens is rather weak. It should be noted that the deformation capacity, ∆u.0,
that appears in the above tables corresponds to the deformation of the T-stub
when the maximum load is reached. This definition may be quite conservative
when the experimental results are taken for comparison since the softening
branches sometimes can be quite extended (specimen WT7_M20, for example).
Figs. 6.12-6.14 illustrate the load-carrying behaviour for some specimens
that represent the various collapse modes. The curves are compared with the
actual response and the bilinear approximation of Jaspart. This bilinear approximation
was defined using the formulation accounting for the bolt action
for specimens of failure type-11 and the actual material strain hardening
modulus. It becomes clear from these curves that the beam model provides a
better agreement with the real F-∆ response and in general these two curves fit
well. Finally, Fig. 6.15 compares the responses for those specimens whose
failure mode was not well predicted by the beam model. Nonetheless, the
agreement is surprisingly good.
Fig. 6.15e traces the F-∆ behaviour of specimen WT57_M12. For this
specimen the flange plates are fastened by means of two full-threaded bolts. At collapse,
the bolt model estimates a fracture elongation of 4 mm – Eq. (6.14). Since
206

Simplified methodologies: assessment of the behaviour of T-stub connections
Table 6.13 Prediction of deformation capacity and ultimate resistance.
Test ID Potential
failure
Actual results Beam model predictions
Fmax ∆u.0 Fu.0 Ratio ∆u.0 Ratio
type (kN) (mm) (kN) (mm)
T1 13 103.99 8.70 114.45 1.10 16.76 1.93
P1 13 91.76 10.77 103.25 1.13 25.34 2.35
P2 13 116.72 6.18 124.34 1.07 8.75 1.42
P3 13 95.41 10.17 111.96 1.17 24.17 2.38
P4 13 115.97 4.68 120.25 1.04 7.23 1.55
P5 23 130.20 3.63 123.76 0.95 4.63 1.28
P6 13 95.53 10.06 111.96 1.17 24.17 2.40
P7 13 111.34 7.56 116.43 1.05 11.66 1.54
P8 13 112.71 8.08 124.24 1.10 12.20 1.51
P9 23 131.43 3.31 137.48 1.05 3.67 1.11
P10 11 76.79 32.75 50.25 0.65 32.40 0.99
P11 23 121.15 2.94 134.34 1.11 3.47 1.18
P12 11 154.06 24.22 122.43 0.79 19.67 0.81
P13 11 93.71 11.38 97.44 1.04 18.57 1.63
P14 11 86.57 24.15 79.54 0.92 20.49 0.85
P15 11 171.08 18.02 153.17 0.90 16.48 0.91
P16 23 125.69 3.06 127.98 1.02 3.00 0.98
P17 13 192.01 9.29 212.18 1.11 20.67 2.22
P18 11 266.57 26.07 215.75 0.81 20.18 0.77
P19 13 186.52 9.29 212.18 1.14 20.67 2.23
P20 23 225.94 4.06 246.14 1.09 4.03 0.99
P21 13 281.33 17.67 285.70 1.02 20.61 1.17
P22 13 305.21 6.40 345.44 1.13 13.75 2.15
P23 23 346.01 5.22 408.62 1.18 5.24 1.00
Average 1.03 1.47
Coefficient of variation 0.13 0.38
Weld_T1(i) 11 92.02 10.85 84.80 0.92 18.27 1.68
Weld_T1(ii) 13 102.75 8.01 101.03 0.98 20.00 2.50
Weld_T1(iii) 13 113.10 6.22 114.21 1.01 18.82 3.02
WT1 11 91.91 14.32 85.60 0.93 18.51 1.29
WT2A 11 86.82 17.98 75.16 0.87 16.51 0.92
WT2B 11 97.88 13.09 92.51 0.95 19.18 1.47
WT4A 13 103.26 4.33 124.40 1.20 10.77 2.49
WT51 23 97.08 3.96 112.86 1.16 9.43 2.38
WT53C 13 98.90 4.24 114.45 1.16 8.50 2.00
WT53D 11 117.36 5.54 117.02 1.00 8.23 1.49
WT53E 11 115.04 5.26 116.04 1.01 9.03 1.72
WT7_M12 13 100.34 4.60 123.83 1.23 11.00 2.39
WT7_M16 11 132.34 11.47 140.79 1.06 17.78 1.55
WT7_M20 11 145.72 9.12 141.17 0.97 17.87 1.96
WT57_M12 23 121.87 4.33 174.51 1.43 8.07 1.86
WT57_M16 13 173.64 5.88 196.62 1.13 9.13 1.55
WT57_M20 11 241.71 15.98 196.77 0.81 8.36 0.52
Average 1.05 1.81
Coefficient of variation
0.15
0.34
207

Further developments on the T-stub model
Table 6.14 Prediction of deformation capacity and ultimate resistance: specimens
organized by failure type group.
208
Test ID Potential
failure
Actual results Beam model predictions
Fmax ∆u.0 Fu.0 Ratio ∆u.0 Ratio
type (kN) (mm) (kN) (mm)
T1 13 103.99 8.70 114.45 1.10 16.76 1.93
P1 13 91.76 10.77 103.25 1.13 25.34 2.35
P2 13 116.72 6.18 124.34 1.07 8.75 1.42
P4 13 115.97 4.68 120.25 1.04 7.23 1.55
P6 13 95.53 10.06 111.96 1.17 24.17 2.40
P7 13 111.34 7.56 116.43 1.05 11.66 1.54
P8 13 112.71 8.08 124.24 1.10 12.20 1.51
P17 13 192.01 9.29 212.18 1.11 20.67 2.22
P19 13 186.52 9.29 212.18 1.14 20.67 2.23
P22 13 305.21 6.40 345.44 1.13 13.75 2.15
Weld_T1(iii) 13 113.10 6.22 114.21 1.01 18.82 3.02
WT4A 13 103.26 4.33 124.40 1.20 10.77 2.49
WT7_M12 13 100.34 4.60 123.83 1.23 11.00 2.39
Average 1.11 2.09
Coefficient of variation 0.06 0.23
P10 11 76.79 32.75 50.25 0.65 32.40 0.99
P12 11 154.06 24.22 122.43 0.79 19.67 0.81
P14 11 86.57 24.15 79.54 0.92 20.49 0.85
P15 11 171.08 18.02 153.17 0.90 16.48 0.91
P18 11 266.57 26.07 215.75 0.81 20.18 0.77
WT7_M16 11 132.34 11.47 140.79 1.06 17.78 1.55
WT7_M20 11 145.72 9.12 141.17 0.97 17.87 1.96
WT57_M20 11 241.71 15.98 196.77 0.81 8.36 0.52
Average 0.86 1.05
Coefficient of variation 0.14 0.45
P5 23 130.20 3.63 123.76 0.95 4.63 1.28
P9 23 131.43 3.31 137.48 1.05 3.67 1.11
P11 23 121.15 2.94 134.34 1.11 3.47 1.18
P16 23 125.69 3.06 127.98 1.02 3.00 0.98
P20 23 225.94 4.06 246.14 1.09 4.03 0.99
P23 23 346.01 5.22 408.62 1.18 5.24 1.00
Average 1.07 1.09
Coefficient of variation
0.07
0.11
bolt governs fracture of this specimen, the post-limit behaviour proceeds until this
deformation of 4 mm is attained, leading to an overall deformation of 8.1 mm and
ultimate resistance of 174.5 kN, corresponding to 1.43 times the maximum resis-

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
(a) Specimen P1.
Load, F (kN)
(b) Specimen P2.
Load, F (kN)
120
105
90
75
60
45
Actual response
30
Simplified response (Beam model)
15
0
Bilinear approximation (Jaspart)
0 3 6 9 12 15 18 21 24 27 30 33
Deformation, ∆ (mm)
135
120
105
90
75
60
45
Actual response
30
Simplified response (Beam model)
15
0
Bilinear approximation (Jaspart)
0 1 2 3 4 5 6 7 8 9 10 11 12 13
120
105
90
75
60
45
30
15
Deformation, ∆ (mm)
Actual response
Simplified response (Beam model)
Bilinear approximation (Jaspart)
0
0 2 4 6 8 10 12 14 16 18 20 22 24 26
Deformation, ∆ (mm)
(c) Specimen Weld_T1(iii).
Fig. 6.12 Specimens that fail according to type-13: comparison of the actual
response with the beam model predictions.
209

Further developments on the T-stub model
210
Load, F (kN)
(a) Specimen P10.
Load, F (kN)
(b) Specimen P18.
Load, F (kN)
80
70
60
50
40
30
Actual response
20
Simplified response (Beam model)
10
0
Bilinear approximation
0 3 6 9 12 15 18 21 24 27 30 33 36
280
240
200
160
Deformation, ∆ (mm)
120
Actual response
80
Simplified response (Beam model)
40
0
Bilinear approximation (Jaspart)
0 3 6 9 12 15 18 21 24 27 30
160
140
120
100
80
Deformation, ∆ (mm)
60
Actual response
40
Simplified response (Beam model)
20
0
Bilinear approximation (Jaspart)
0 2 4 6 8 10 12 14 16 18 20 22 24
Deformation, ∆ (mm)
(c) Specimen WT7_M20.
Fig. 6.13 Specimens that fail according to type-11: comparison of the actual
response with the beam model predictions.

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
(a) Specimen P5.
Load, F (kN)
(b) Specimen P16.
Load, F (kN)
140
120
100
80
60
40
Actual response
Simplified response (Beam model)
20
0
Bilinear approximation (Jaspart)
0 1 2 3 4 5 6 7 8 9 10 11 12
140
120
100
80
Deformation, ∆ (mm)
60
Actual response
40
Simplified response (Beam model)
20
0
Bilinear approximation (Jaspart)
0 1 2 3 4 5 6 7 8 9 10 11
450
400
350
300
250
200
150
100
Deformation, ∆ (mm)
Actual response
Simplified response (Beam model)
50
0
Bilinear approximation (Jaspart)
0 1 2 3 4 5 6 7 8 9 10 11
Deformation, ∆ (mm)
(c) Specimen P23.
Fig. 6.14 Specimens that fail according to type-23: comparison of the actual
response with the beam model predictions.
211

Further developments on the T-stub model
212
Load, F (kN)
(a) Specimen Weld_T1(i).
Load, F (kN)
100
90
80
70
60
50
40
30
Actual response
20
Simplified response (Beam model)
10
0
Bilinear approximation (Jaspart)
0 3 6 9 12 15 18 21 24 27 30 33 36 39
105
90
75
60
45
30
15
(b) Specimen WT2B.
Load, F (kN)
Deformation, ∆ (mm)
Actual response
Simplified response (Beam model)
Bilinear approximation (Jaspart)
0
0 2 4 6 8 10 12 14 16 18 20
120
105
90
75
60
45
30
15
Deformation, ∆ (mm)
Actual response
Simplified response (Beam model)
Bilinear approximation (Jaspart)
0
0 1 2 3 4 5 6 7 8 9 10
Deformation, ∆ (mm)
(c) Specimen WT51.
Fig. 6.15 WP-T-stub specimens whose observed failure types are not coincident
with the predictions.

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
120
105
90
75
60
(d) Specimen WT53D.
Load, F (kN)
45
Actual response
30
Simplified response (Beam model)
15
0
Bilinear approximation (Jaspart)
0 1 2 3 4 5 6 7 8 9 10
180
160
140
120
100
80
60
40
(e) Specimen WT57_M12.
Load, F (kN)
Deformation, ∆ (mm)
Actual response
Simplified response (Beam model)
20
0
Bilinear approximation (Jaspart)
0 1 2 3 4 5 6 7 8 9 10
210
180
150
120
90
60
30
Deformation, ∆ (mm)
Actual response
Simplified response (Beam model)
Bilinear approximation (Jaspart)
0
0 1 2 3 4 5 6 7 8 9 10
Deformation, ∆ (mm)
(f) Specimen WT57_M16.
Fig. 6.15 WP-T-stub specimens whose observed failure types are not coincident
with the predictions (cont.).
213

Further developments on the T-stub model
tance from the tests. With reference to Eq. (6.14) derived for δb.fract, it was developed
for short-threaded bolts [6.6]. If a full-threaded bolt is considered instead,
this expression seems to overestimate the bolt fracture deformation. Consequently,
some guidelines concerning this matter are required.
In terms of design calculations, the characterization of the behaviour of the
above specimens should be based in nominal properties, as already mentioned.
The results obtained by this procedure are fully described and analysed in Appendix
D.
6.3.4 Sophistication of the proposed method: modelling of the bolt action
as a distributed load
Jaspart has shown that a significant increase in the resistance of single T-stubs
that fail according to a plastic mechanism type-1 can be expected due to the influence
of the bolt action on a finite contact area [6.2]. This effect is taken into
account in the beam model in this section. The bolt is then modelled as a spring
assembly in parallel, as shown in Fig. 6.16. The length of this assembly is the
bolt diameter. The behaviour of this spring assembly is the same as the original
single spring, i.e. the spring stiffness and force values are divided by the number
of springs in the assembly.
Eleven examples were chosen to illustrate this modification, five examples
from type-11 group and three examples from each of the other two groups. The
analysis of the first group is quite straightforward as the bolt is not engaged in
the failure mode. For those specimens whose fracture is governed by the bolt
itself, the fracture condition has to be redefined. Below, this condition is imposed
at two different sections and the results are then compared: (i) section (2)
from above, at mid- bolt section and (ii) section (2*), located at ¼ of the inside
bolt edge, from section (2). For those specimens that fail according to a type-23
(1)
mechanism, when the bolt fractures, ε p < ε pu . , specimens belonging to type-
(1)
13 failure mode may exhibit ε > ε when the bolt fracture but
(1*) (2)
ε p , ε p < ε p. u .
214
p pu .
Table 6.15 summarizes the predicted resistance and deformation values at
collapse when this modification is introduced. The examples are grouped according
to the failure mode. The underlined connections, again, refer to those
cases where the predicted failure mode does not match the observed type. For
evaluation of ratios to actual values these examples are not taken into consideration.
The fracture condition here was identical to the above.
The application of this modified model provides a significant enhancement of
results in terms of resistance, particularly for the evaluation of Fu.0. So are the predictions
of deformation capacity for specimens from type-11 group. Specimens
that fail according to a type-23 mechanism show worse predictions of deformation
capacity. For specimens belonging to type-13 fracture mode, these predict-

Simplified methodologies: assessment of the behaviour of T-stub connections
0.8r
F
2
B-δb
φ
m n
Fig. 6.16 Beam model accounting for the bolt action on a finite area.
ions improve but are still distant from the actual deformation values. Further
comparisons are carried out in Appendix D.
It is worth mentioning that this sophistication enforced the “correct” fracture
element to be critical in specimens P3 and Weld_T1(ii), for instance. Nevertheless,
the beam model is not yet able to simulate the fracture of the bolt simultaneously
to cracking of the flange material in some WP-T-stubs.
6.3.5 Influence of the distance m for the WP-T-stubs
Distance m is one of the geometrical parameters that most influences the deformation
behaviour of T-stub connections. For HR-T-stubs, this distance is
well established and there is experimental and numerical evidence for its definition.
Common procedures for WP-T-stubs consisted in extrapolating the design
rules defined for HR-T-stubs. Parameter m defines the location of the potential
yield line at the flange-to-web connection with respect to the bolt line.
In previous chapters, it has been shown that this procedure may not be accurate
enough. In fact, there is evidence that in some cases the yield line at the flangeto-web
connection develops in the flange at the end of the fillet root, i.e. for a
distance m defined as follows:
m = d − 2aw (6.35)
215

Further developments on the T-stub model
Table 6.15 Prediction of deformation capacity and ultimate resistance by applying
the sophisticated beam model accounting for bolt action:
specimens organized by failure type group.
216
Test ID Potential
failure
type
Actual results Sophisticated beam model predictions
Fmax ∆ u.0 Fu.0 Ratio ∆ u.0 Ratio
(kN) (mm) (kN) (mm)
T1 13 103.99 8.70 113.87 1.09 12.74 1.46
P1 13 91.76 10.77 103.27 1.13 19.88 1.85
P3 13 95.41 10.17 108.18 1.13 16.06 1.58
Weld_T1(ii) 13 102.75 8.01 104.18 1.01 17.61 2.20
Weld_T1(iii) 13 113.10 6.22 113.33 1.00 14.16 2.27
WT57_M16 13 173.64 5.88 212.19 1.22 8.35 1.42
Average 1.07 1.87
Coefficient of variation 0.06 0.19
P10 11 76.79 32.75 59.17 0.77 27.79 0.85
P12 11 154.06 24.22 149.02 0.97 19.22 0.79
P14 11 86.57 24.15 88.79 1.03 19.87 0.82
P15 11 171.08 18.02 187.94 1.10 16.16 0.90
P18 11 266.57 26.07 280.34 1.05 18.69 0.72
Weld_T1(i) 11 92.02 10.85 88.57 0.96 17.17 1.58
WT1 11 91.91 14.32 90.37 0.98 15.67 1.09
WT2A 11 86.82 17.98 81.50 0.94 16.11 0.90
WT2B 11 97.88 13.09 102.67 1.05 19.83 1.10
WT7_M16 11 132.34 11.47 158.47 1.20 16.24 1.42
WT7_M20 11 145.72 9.12 177.93 1.22 14.71 1.61
WT57_M20 11 241.71 15.98 233.41 0.97 7.56 0.47
Average 1.02 0.97
Coefficient of variation 0.12 0.33
P5 23 130.20 3.63 121.71 0.93 3.37 0.93
P20 23 225.94 4.06 247.76 1.10 3.51 0.87
P23 23 346.01 5.22 399.89 1.16 4.00 0.77
WT51 23 97.08 3.96 119.08 1.23 9.00 2.27
Average 1.06 0.85
Coefficient of variation
0.11
0.10
The influence of this distance is further detailed in Appendix D. Generally
speaking, if m from Eq. (6.35) is adopted, there is an increase on resistance and
stiffness and decrease on ductility.
6.4 CONCLUDING REMARKS
The proposed beam model yields an accurate prediction of the F-∆ response of
bolted T-stub connections, despite the simplifications inherent to a two-

Simplified methodologies: assessment of the behaviour of T-stub connections
dimensional modelling of the behaviour. These reduced the model complexity
to a more reasonable level, when compared to the three-dimensional FE modelling.
However, to obtain the F-∆ curve, a numerical incremental procedure is
still required and, consequently, the model is not suitable for hand calculations.
The dominant effects in both approaches are the strain hardening of the flange
and the bolt elongation behaviour, as confirmed by experimental evidence. Another
important simplification of the beam model corresponds to the beam section
width, which is kept constant with the course of loading. As the load increases,
the flange width tributary to load transmission also increases. The
analysis of this variation was not carried out and the implementation of such
phenomenon is not straightforward neither. Nevertheless, for those specimens
failing according to a type-11 mode, this issue can be particularly relevant.
The applicability of the model was well demonstrated within the range of
examples shown above. The behaviour predicted by this model is rather good
in terms of resistance. With respect to ductility, it reflects an overestimation of
test results that is within an acceptable error. Table 6.16 summarizes the statistical
parameters (average and coefficient of variation) corresponding to the
sample of connections that were analysed above. Two approaches in terms of
material properties are taken into account: actual properties (Table 6.13) and
nominal properties (Table D.17 in Appendix D).
If the results are analysed in terms of failure types (cf. Table 6.14), the predictions
for resistance are accurate for those specimens whose fracture is determined
by the bolt. For those specimens failing according to a type-11, the results
seem rather conservative. Concerning the predictions for deformation capacity,
these are quite good for failure modes type-11 and -23, even though the scatter of
results for specimens of failure type-11 is high (coefficient of variation of 0.45).
For the remaining case (type-23 failure), there is an overestimation of results.
The modification for inclusion of the bolt action provides an enhancement of
results but introduces an additional complexity. From a design point of view, the
methodology should be further simplified so that it can be used in an expedite way,
as Jaspart’s simple proposal. This can be achieved by modelling plasticity phenomena
in the flange by means of rotational springs at the critical sections that capture
the overall behaviour.
Table 6.16 Summary of the proposed beam model from a statistical point of
view (average ratios and coefficients of variation, the latter in
italic) for evaluation of the force-deformation characteristics.
T-stub assembly
Ultimate resistance
Fu.0
Deformation capacity
HR
WP
Actual material properties
1.03 (0.13)
1.05 (0.15)
1.47 (0.38)
1.81 (0.34)
HR Nominal material proper- 0.98 (0.17) 1.73 (0.38)
WP
ties 0.94 (0.23) 1.18 (0.53)
∆u.0
217

Further developments on the T-stub model
6.5 REFERENCES
[6.1] European Committee for Standardization (CEN). prEN 1993-1-8:2003,
Part 1.8: Design of joints, Eurocode 3: Design of steel structures. Stage
49 draft, May 2003, Brussels, 2003.
[6.2] Jaspart JP. Study of the semi-rigid behaviour of beam-to-column joints
and of its influence on the stability and strength of steel building frames.
PhD thesis (in French). University of Liège, Liège, Belgium, 1991.
[6.3] Faella C, Piluso V, Rizzano G. Structural semi-rigid connections – theory,
design and software. CRC Press, USA, 2000.
[6.4] Piluso V, Faella C, Rizzano G. Ultimate behavior of bolted T-stubs. I:
theoretical model. Journal of Structural Engineering ASCE; 127(6):686-
693, 2001.
[6.5] Piluso V, Faella C, Rizzano G. Ultimate behavior of bolted T-stubs. II:
model validation. Journal of Structural Engineering ASCE; 127(6):694-
704, 2001.
[6.6] Swanson JA. Characterization of the strength, stiffness and ductility behavior
of T-stub connections. PhD dissertation, Georgia Institute of
Technology, Atlanta, USA, 1999.
[6.7] Beg D, Zupančič E, Vayas I. On the rotation capacity of moment connections.
Journal of Constructional Steel Research; 60:601-620, 2004.
[6.8] Jaspart JP. Contributions to recent advances in the field of steel joints – column
bases and further configurations for beam-to-column joints and beam
splices. Aggregation thesis. University of Liège, Liège, Belgium, 1997.
[6.9] Yee YL, Melchers RE. Moment-rotation curves for bolted connections.
Journal of Structural Engineering ASCE; 112(3):615-635, 1986.
[6.10] Maquoi R, Jaspart JP. Moment-rotation curves for bolted connections:
Discussion of the paper by Yee YL and Melchers RE. Journal of Structural
Engineering ASCE; 113(10):2324-2329, 1986.
[6.11] Gioncu V, Mateescu G, Petcu D, Anastasiadis A. Prediction of available
ductility by means of local plastic mechanism method: DUCTROT
computer program, Chapter 2.1 in Moment resistant connections of steel
frames in seismic areas (Ed.: F. Mazzolani). E&FN Spon, London, UK;
95-146, 2000.
[6.12] McGuire W. Steel structures. Prentice-Hall International series in Theoretical
and Applied Mechanics (Eds.: NM Newmark and WJ Hall).
Englewood Cliffs, N.J., USA, 1968.
[6.13] Gioncu V, Mazzolani FM. Ductility of seismic resistant steel structures.
Spon Press, London, 2002.
[6.14] Hirt MA, Bez R. Construction métallique – Notions fondamentales et
methods de dimensionnement. Traité de Génie Civil de l’École
polytechnique fédérale de Lausanne, Volume 10. Presses Polytechniques et
Universitaires Romandes, Lausanne, Switzerland, 1994.
[6.15] Lusas 13. Theory manual. Finite element analysis Ltd, Version 13.5.
Surrey, UK, 2003.
218

APPENDIX D: DETAILED RESULTS OBTAINED FROM APPLICATION OF THE
SIMPLIFIED METHODS FOR ASSESSMENT OF THE FORCE-
DEFORMATION RESPONSE OF SINGLE T-STUB CONNECTIONS
D.1 Geometrical and mechanical characteristics of the specimens
This appendix gives detailed results that were obtained from application of the
simplified methods for assessment of the F-∆ response of single T-stub connections.
For illustration of the various methodologies presented in Chapter 6,
the specimens from the database compiled in Chapters 3-5 are employed. The
relevant geometrical and mechanical characteristics of those specimens are
summarized in Tables D.1 and D.2, respectively.
D.2 Previous research: exemplification
D.2.1 Evaluation of initial stiffness
Table D.3 sets out the predictions of initial stiffness of the above specimens by
application of the procedures proposed by Yee and Melchers [6.9] and subsequently
modified by Jaspart [6.2]. The results show that the two approaches
(which differ essentially in the location of the prying forces) yield identical
results, with consistent errors of 130%, which seem too high. The table also
shows that the scatter of results is higher for the WP-T-stubs. This result however
may not be significant because in these cases most of the specimens were
tested experimentally. Thus, the determination of the experimental initial stiffness
is not as straightforward as for the specimens tested numerically. It should
be noted that the values of ke.0 contained in this table were computed using the
bolt conventional length as defined by Aggerskov – Eq (1.19).
The results after application of the Swanson’s procedures are summarized
in Table D.4. Again, the errors are excessive. Errors well above 100% are not
acceptable. This table also shows that in spite of the deviations from the actual
results, the Eurocode 3 prying model yields better results than the Kulak
model, also adopted by Swanson. Both models are illustrated in Fig. 6.3. The
two models differ in the geometry of the beam model.
D.2.2 Piecewise multilinear approximation of the overall response and evaluation
of the deformation capacity and ultimate resistance
a) Methodology recommended by Jaspart
Table D.5 indicates the predictions of the different observed failure modes. The
predicted potential failure type is defined according to the expressions pre-
219

Further developments on the T-stub model
Table D.1 Geometrical characteristics of the specimens.
Test ID Potential Geometric characteristics (dimensions in [mm])
failure
type
beff tf m m/tf n λ φ
T1 13 40.0 10.7 29.45 2.75 30.00 1.02 12
P1 13 40.0 10.7 34.45 3.22 25.00 0.73 12
P2 13 40.0 10.7 24.45 2.29 30.56 1.25 12
P3 13 35.0 10.7 29.45 2.75 30.00 1.02 12
P4 13 52.5 10.7 29.45 2.75 30.00 1.02 12
P5 23 60.0 10.7 29.45 2.75 30.00 1.02 12
P6 13 35.0 10.7 29.45 2.75 30.00 1.02 12
P7 13 45.0 10.7 29.45 2.75 30.00 1.02 12
P8 13 40.0 11.0 27.10 2.46 33.88 1.25 12
P9 23 40.0 14.0 28.75 2.05 35.94 1.25 12
P10 11 40.0 7.0 30.75 4.39 30.00 0.98 12
P11 23 40.0 14.0 28.75 2.05 30.00 1.04 12
P12 11 40.0 10.7 29.45 2.75 30.00 1.02 16
P13 11 40.0 10.7 29.45 2.75 30.00 1.02 12
P14 11 40.0 10.7 29.45 2.75 30.00 1.02 12
P15 11 40.0 10.7 24.45 2.29 30.56 1.25 16
P16 23 70.0 10.7 29.45 2.75 30.00 1.02 12
P17 13 70.0 10.7 29.45 2.75 30.00 1.02 16
P18 11 70.0 10.7 29.45 2.75 30.00 1.02 20
P19 13 70.0 10.7 29.45 2.75 30.00 1.02 16
P20 23 70.0 14.0 28.75 2.05 30.00 1.04 16
P21 13 92.5 10.7 29.45 2.75 30.00 1.02 20
P22 13 70.0 15.0 32.34 2.16 30.00 0.93 20
P23 23 70.0 18.9 31.59 1.67 30.00 0.95 20
Weld_T1(i) 11 40.0 10.7 37.43 3.50 30.00 0.80 12
Weld_T1(ii) 13 40.0 10.7 33.42 3.12 30.00 0.90 12
Weld_T1(iii) 13 40.0 10.7 30.14 2.82 30.00 1.00 12
WT1 11 45.1 10.3 33.73 3.27 30.00 0.89 12
WT2A 11 45.0 10.3 36.29 3.53 29.90 0.82 12
WT2B 11 45.0 10.3 31.69 3.08 29.90 0.94 12
WT4A 13 74.9 10.4 33.69 3.24 30.00 0.89 12
WT51 23 45.0 10.0 34.39 3.45 30.20 0.88 12
WT53C 13 45.1 10.1 34.34 3.40 30.00 0.87 12
WT53D 11 45.0 10.1 34.24 3.38 30.00 0.88 12
WT53E 11 44.7 10.1 34.26 3.40 30.10 0.88 12
WT7_M12 13 75.6 10.3 33.87 3.28 29.90 0.88 12
WT7_M16 11 74.9 10.3 33.89 3.28 29.80 0.88 16
WT7_M20 11 75.2 10.3 33.81 3.27 29.70 0.88 20
WT57_M12 23 75.0 10.1 34.11 3.38 30.20 0.89 12
WT57_M16 13 75.3 10.2 34.26 3.37 30.10 0.88 16
WT57_M20 11 75.1 10.2 34.27 3.38 30.20 0.88 20
220

Simplified methodologies: assessment of the behaviour of T-stub connections
Table D.2 Mechanical characteristics of the specimens.
Test ID Potential Flange Bolt
failure
type
fy.f
(MPa)
εp.u.f fu.b
(MPa)
δu.b
(mm)
Kb
(N/mm)
T1 13 431.0 0.284 974.0 0.97 6.92×10 5
P1 13 431.0 0.284 974.0 0.97 6.92×10 5
P2 13 431.0 0.284 974.0 0.97 6.92×10 5
P3 13 431.0 0.284 974.0 0.97 6.92×10 5
P4 13 431.0 0.284 974.0 0.97 6.92×10 5
P5 23 431.0 0.284 974.0 0.97 6.92×10 5
P6 13 431.0 0.284 974.0 0.97 6.92×10 5
P7 13 431.0 0.284 974.0 0.97 6.92×10 5
P8 13 431.0 0.284 974.0 0.98 6.78×10 5
P9 23 431.0 0.284 974.0 1.36 5.45×10 5
P10 11 431.0 0.284 974.0 0.75 9.37×10 5
P11 23 431.0 0.284 974.0 1.20 5.57×10 5
P12 11 431.0 0.284 974.0 1.01 1.19×10 6
P13 11 355.0 0.284 974.0 0.97 6.92×10 5
P14 11 275.0 0.284 974.0 0.97 6.92×10 5
P15 11 431.0 0.284 974.0 1.01 1.19×10 6
P16 23 431.0 0.284 974.0 0.97 6.52×10 5
P17 13 431.0 0.284 974.0 1.09 1.11×10 6
P18 11 431.0 0.284 974.0 1.09 1.73×10 6
P19 13 431.0 0.284 974.0 1.09 1.11×10 6
P20 23 431.0 0.284 974.0 1.37 9.54×10 5
P21 13 431.0 0.284 974.0 1.37 1.49×10 6
P22 13 431.0 0.284 974.0 1.52 1.40×10 6
P23 23 431.0 0.284 974.0 1.98 1.14×10 6
Weld_T1(i) 11 431.0 0.284 974.0 0.97 6.92×10 5
Weld_T1(ii) 13 431.0 0.284 974.0 0.97 6.92×10 5
Weld_T1(iii) 13 431.0 0.284 974.0 0.97 6.92×10 5
WT1 11 340.1 0.361 919.9 1.14 1.10×10 6
WT2A 11 340.1 0.361 919.9 1.14 1.10×10 6
WT2B 11 340.1 0.361 919.9 1.14 1.10×10 6
WT4A 13 340.1 0.361 919.9 1.14 1.10×10 6
WT51 23 698.6 0.174 919.9 1.14 1.10×10 6
WT53C 13 698.6 0.174 968.4 4.00 9.14×10 5
WT53D 11 698.6 0.174 1166.0 0.98 1.08×10 6
WT53E 11 698.6 0.174 1196.4 2.80 9.15×10 5
WT7_M12 13 340.1 0.361 919.9 1.14 1.10×10 6
WT7_M16 11 340.1 0.361 919.9 2.60 1.65×10 6
WT7_M20 11 340.1 0.361 919.9 2.60 2.57×10 6
WT57_M12 23 698.6 0.174 919.9 4.00 9.14×10 5
WT57_M16 13 698.6 0.174 919.9 2.60 1.65×10 6
WT57_M20 11 698.6 0.174 919.9 2.60 2.57×10 6
221

Further developments on the T-stub model
Table D.3 Prediction of axial stiffness by application of the standard Yee and
Melchers procedures and the modified proposal of Jaspart.
Test ID Num./Exp.
stiffness
222
Yee and Melchers
standard procedure
Modified Yee and
Melchers procedures
ke.0 Ratio ke.0 Ratio
T1 83.54 185.18 2.22 190.80 2.28
P1 63.27 131.03 2.07 133.36 2.11
P2 117.06 280.41 2.40 286.85 2.45
P3 72.62 165.74 2.28 171.77 2.37
P4 97.86 230.23 2.35 234.19 2.39
P5 101.23 255.09 2.52 257.74 2.55
P9 128.47 329.76 2.57 328.23 2.55
P10 43.88 54.04 1.23 58.19 1.33
P12 102.05 201.90 1.98 121.96 1.20
P14 81.97 185.18 2.26 190.80 2.33
P15 128.41 315.17 2.45 330.88 2.58
P16 111.23 287.85 2.59 288.86 2.60
P18 171.57 343.17 2.00 358.98 2.09
P20 181.68 578.78 3.19 565.31 3.11
P23 322.09 870.01 2.70 825.15 2.56
Average 2.32 2.30
Coefficient of variation
0.18
0.21
Weld_T1(i) 73.50 104.27 1.42 108.31 1.47
Weld_T1(ii) 88.04 137.43 1.56 142.29 1.62
Weld_T1(iii) 107.29 175.52 1.64 181.03 1.69
WT1g 68.58 138.88 2.03 144.34 2.10
WT1h 73.58 138.88 1.89 144.34 1.96
WT2Aa 64.32 114.67 1.78 119.46 1.86
WT2Ab 61.75 114.67 1.86 119.46 1.93
WT2Ba 63.58 160.23 2.52 166.22 2.61
WT2Bb 79.75 160.23 2.01 166.22 2.08
WT4Aa 75.08 216.22 2.88 219.37 2.92
WT4Ab 86.96 216.22 2.49 219.37 2.52
WT7_M12 91.18 212.53 2.33 215.74 2.37
WT7_M16 116.09 226.41 1.95 234.29 2.02
WT7_M20 137.70 239.59 1.74 251.42 1.83
WT51a 59.62 118.33 1.98 123.71 2.07
WT51b 61.84 118.33 1.91 123.71 2.00
WT53C 64.23 120.20 1.87 124.73 1.94
WT53D 52.90 124.75 2.36 130.04 2.46
WT53E 64.82 119.92 1.85 124.52 1.92
WT57_M12 42.89 186.75 4.35 189.45 4.42
WT57_M16 55.22 206.87 3.75 214.82 3.89
WT57_M20 75.48 214.57 2.84 225.89 2.99
Average 2.23 2.30
Coefficient of variation
0.32
0.31

Simplified methodologies: assessment of the behaviour of T-stub connections
Table D.4 Prediction of axial stiffness by application of the Swanson procedures.
Test ID Num./Exp.
stiffness
Prediction with b’
from Eq. (6.9)
Prediction with m
from Eq. (6.11)
ke.0 Ratio ke.0 Ratio
T1 83.54 186.06 2.23 164.67 1.97
P1 63.27 136.36 2.16 118.51 1.87
P2 117.06 235.18 2.01 219.72 1.88
P3 72.62 172.30 2.37 152.37 2.10
P4 97.86 214.84 2.20 190.54 1.95
P5 101.23 229.15 2.26 203.48 2.01
P9 128.47 222.73 1.73 213.20 1.66
P10 43.88 83.97 1.91 73.10 1.67
P12 102.05 256.91 2.52 201.46 1.97
P14 81.97 341.76 4.17 280.41 3.42
P15 128.41 237.49 1.85 211.38 1.65
P16 111.23 343.25 3.09 277.12 2.49
P18 171.57 467.64 2.73 331.66 1.93
P20 181.68 412.57 2.27 353.66 1.95
P23 322.09 565.93 1.76 452.25 1.40
Average 2.35 1.99
Coefficient of variation
0.26 0.23
Weld_T1(i) 73.50 135.46 1.84 105.75 1.44
Weld_T1(ii) 88.04 149.68 1.70 131.78 1.50
Weld_T1(iii) 107.29 162.48 1.51 158.40 1.48
WT1g 68.58 189.06 2.76 154.29 2.25
WT1h 73.58 189.06 2.57 154.29 2.10
WT2Aa 64.32 172.50 2.68 130.81 2.03
WT2Ab 61.75 172.50 2.79 130.81 2.12
WT2Ba 63.58 197.38 3.10 173.86 2.73
WT2Bb 79.75 197.38 2.47 173.86 2.18
WT4Aa 75.08 266.10 3.54 218.87 2.92
WT4Ab 86.96 266.10 3.06 218.87 2.52
WT7_M12 91.18 263.26 2.89 215.78 2.37
WT7_M16 116.09 345.88 2.98 246.96 2.13
WT7_M20 137.70 452.30 3.28 279.81 2.03
WT51a 59.62 167.26 2.81 136.37 2.29
WT51b 61.84 167.26 2.70 136.37 2.21
WT53C 64.23 163.52 2.55 132.76 2.07
WT53D 52.90 174.20 3.29 141.15 2.67
WT53E 64.82 163.49 2.52 132.71 2.05
WT57_M12 42.89 229.31 5.35 187.65 4.38
WT57_M16 55.22 324.57 5.88 231.40 4.19
WT57_M20 75.48 417.33 5.53 257.03 3.41
Average 3.08 2.41
Coefficient of variation
0.37
0.31
223

Further developments on the T-stub model
Table D.5 Prediction of failure modes.
Test Pot. Critical resis- Test ID Pot. Critical resis-
ID failure tance formula
failure tance formula
type Plst. Ultm.
type Plst. Ultm.
T1 13 1 1 or 2 P21 13 1 1
P1 13 1 1 or 2 P22 13 1 or 2 1 or 2
P2 13 1 1 P23 23 2 2
P3 13 1 1 or 2 Weld_T1(i) 11 1 1
P4 13 1 or 2 2 Weld_T1(ii) 13 1 1
P5 23 2 2 Weld_T1(iii) 13 1 1 or 2
P6 13 1 1 WT1 11 1 1
P7 13 1 1 or 2 WT2A 11 1 1
P8 13 1 1 or 2 WT2B 11 1 1
P9 23 2 2 WT4A 13 1 or 2 2
P10 11 1 1 WT7_M12 13 1 or 2 2
P11 23 2 2 WT7_M16 11 1 1
P12 11 1 1 WT7_M20 11 1 1
P13 11 1 1 WT51 23 2 1 or 2
P14 11 1 1 WT53C 13 1 or 2
P15 11 1 1 WT53D 11 1 or 2 1
P16 23 2 2 WT53E 11 1 1
P17 13 1 1 or 2 WT57_M12 23 2 2
P18 11 1 1 WT57_M16 13 1 or 2 1 or 2
P19 13 1 1 or 2 WT57_M20 11 1 1
P20 23 2 2
sented in Chapter 2. For computation of Mf.u, Eq. (2.4) recommended by
Gioncu et al. is employed [6.11]. This table also indicates the critical resistance
formula according to the Jaspart methodology (cf. 6.2.1). For application of the
procedures, four different cases are considered regarding the resistance formulation
(BF or FBA) and the mechanical properties of the T-stub material. The
complete characterization of the actual material properties of the various
specimens from the database was given in Chapters 3, 4 and 5. The actual
strain hardening modulus, Eh, for these specimens however is always lower
than the nominal properties [6.3,6.13]. For steel grade S355, Eh = E/48.2 and
for S275, Eh = E/42.8. No quantitative guidance is given in any of the references
for steel grade S690. Hence, both actual and nominal values for Eh are
taken into account for those specimens where steel grade S355 and S275 was
employed (S275 was used in specimen P14).
This variation combined with the two alternative resistance formulations
yields four different approaches that are summarized in Tables D.6-D.9. The
specimens are divided according to the assembly type (HR-T-stubs and WP-T-
stubs).
224

Simplified methodologies: assessment of the behaviour of T-stub connections
Table D.6 Prediction of ultimate resistance and deformation capacity by using
the actual strain hardening modulus of the flange material and
the basic formulation for computation of resistance (HR-T-stubs).
Test ID Numerical results Jaspart methodology (Actual Eh; BF)
Ratio
Ratio
Fmax ∆u.0 Fu.0 ∆u.0
(kN) (mm) (kN)
(mm)
T1 103.99 8.70 92.53 0.89 21.54 2.47
P1 91.76 10.77 79.10 0.86 27.33 2.54
P2 116.72 6.18 111.45 0.95 17.00 2.75
P3 95.41 10.17 80.96 0.85 21.02 2.07
P4 115.97 4.68 112.95 0.97 17.17 3.67
P5 130.20 3.63 117.24 0.90 11.24 3.10
P6 95.53 10.06 80.96 0.85 21.02 2.09
P7 111.34 7.56 104.09 0.93 22.06 2.92
P8 112.71 8.08 106.27 0.94 19.18 2.37
P9 131.43 3.31 127.29 0.97 9.31 2.82
P10 76.79 32.75 37.93 0.49 30.29 0.93
P11 121.15 2.94 123.56 1.02 9.42 3.20
P12 154.06 24.22 92.53 0.60 19.88 0.82
P13 93.71 11.38 79.31 0.85 20.30 1.78
P14 86.57 24.15 66.87 0.77 20.21 0.84
P15 171.08 18.02 111.45 0.65 15.00 0.83
P16 125.69 3.06 122.97 0.98 10.93 3.57
P17 192.01 9.29 161.92 0.84 21.77 2.34
P18 266.57 26.07 161.92 0.61 20.39 0.78
P19 186.52 9.29 161.92 0.87 21.77 2.34
P20 225.94 4.06 225.65 1.00 9.84 2.42
P21 281.33 17.67 213.96 0.76 21.37 1.21
P22 305.21 6.40 298.54 0.98 20.76 3.25
P23 346.01 5.22 353.25 1.02 10.43 2.00
Average 0.86 2.21
Coefficient of variation
0.17
0.41
For identical assembly types, the tables show that the model yields identical
results, in terms of average ratios. The ultimate resistance predictions are more
accurate if the formulation accounting for the bolt finite size is employed. Note
that for those specimens whose collapse mode is determined from Eq. (6.6) this
formulation does not apply.
With respect to the evaluation of deformation capacity, the best predictions
are obtained through application of the basic formulation and assuming the
nominal strain hardening modulus (Table D.8). The models where the actual
strain hardening modulus was used provided an overestimation of this property.
On the other hand, if the nominal strain hardening modulus is considered
the approximation improves significantly.
225

Further developments on the T-stub model
Table D.6 Prediction of ultimate resistance and deformation capacity (WP-Tstubs)
(cont.).
Test ID Num. or Exp. results
Jaspart methodology (Actual Eh; BF)
Fmax ∆u.0 Fu.0 Ratio ∆u.0 Ratio
(kN) (mm) (kN)
(mm)
Weld_T1(i) 92.02 10.85 72.79 0.79 31.33 2.89
Weld_T1(ii) 102.75 8.01 81.54 0.79 26.03 3.25
Weld_T1(iii) 113.10 6.22 81.54 0.72 22.26 3.58
WT1(h) 91.91 14.32 68.28 0.74 18.41 1.29
WT2A(b) 86.82 17.98 62.78 0.72 20.92 1.16
WT2B(b) 97.88 13.09 72.17 0.74 16.63 1.27
WT4A(b) 103.26 4.33 103.55 1.00 12.95 2.99
WT7_M12 100.34 4.60 103.11 1.03 13.30 2.89
WT7_M16 132.34 11.47 113.32 0.86 18.48 1.61
WT7_M20 145.72 9.12 114.05 0.78 17.92 1.96
WT51(b) 97.08 3.96 96.51 0.99 7.87 1.99
WT53C 98.90 4.24 98.89 1.00 6.40 1.51
WT53D 117.36 5.54 100.08 0.85 6.34 1.14
WT53E 115.04 5.26 98.25 0.85 6.36 1.21
WT57_M12 121.87 4.33 120.69 0.99 6.80 1.57
WT57_M16 173.64 5.88 168.21 0.97 6.34 1.08
WT57_M20 241.71 15.98 167.36 0.69 6.17 0.39
Average 0.85 1.87
Coefficient of variation
0.14
0.49
b) Methodology recommended by Faella, Piluso and Rizzano
To illustrate the methodology proposed by Faella et al. [6.3-6.5], six examples
were selected: T1, P16, P18, WT4A, WT7_M20 and WT51. These examples
typify the three different failure modes (Type-11, -13 and -23) as well as the
two assembly types (HR- and WP-T-stubs). In the framework of this methodology,
however, the potential collapse mode is defined differently. As already
mentioned in §6.2.2, Faella et al. assume the occurrence of three alternative
collapse modes, termed: (i) type-1 if cracking of the flange material occurs at
the two critical sections, at the flange-to-web connection, (1) and at the bolt
line, (ii) type-2 if cracking of the flange material occurs at critical section (1)
and, simultaneously, bolt fracture also takes place and (iii) type-3 if a bolt fracture
mechanism arises. The boundaries for the occurrence of a given mechanism
are indicated in Fig. 6.2. The coefficient βu, which is defined in Eq. (2.1),
with Mf.u given by Eq. (2.5), is compared with βu.lim. Faella et al. suggest two
alternative expressions for βu.lim:
226

Simplified methodologies: assessment of the behaviour of T-stub connections
Table D.7 Prediction of ultimate resistance and deformation capacity by using
the actual strain hardening modulus of the flange material and
the formulation accounting for the bolt for computation of resistance
(HR-T-stubs).
Test ID Numerical results Jaspart methodology (Actual Eh; FBA)
Fmax ∆u.0 Fu.0 Ratio ∆u.0 Ratio
(kN) (mm) (kN)
(mm)
T1 103.99 8.70 105.79 1.02 22.05 2.53
P1 91.76 10.77 91.97 1.00 30.19 2.80
P2 116.72 6.18 119.60 1.02 12.35 2.00
P3 95.41 10.17 96.36 1.01 25.01 2.46
P4 115.97 4.68 112.95 0.97 11.61 2.48
P5 130.20 3.63 117.24 0.90 11.24 3.10
P6 95.53 10.06 96.36 1.01 25.01 2.49
P7 111.34 7.56 108.65 0.98 14.79 1.96
P8 112.71 8.08 114.85 1.02 15.21 1.88
P9 131.43 3.31 127.29 0.97 9.31 2.82
P10 76.79 32.75 44.90 0.58 35.86 1.10
P11 121.15 2.94 123.56 1.02 9.42 3.20
P12 154.06 24.22 116.02 0.75 24.93 1.03
P13 93.71 11.38 94.40 1.01 24.16 2.12
P14 86.57 24.15 79.59 0.92 24.06 1.00
P15 171.08 18.02 144.50 0.84 19.45 1.08
P16 125.69 3.06 122.97 0.98 10.93 3.57
P17 192.01 9.29 194.44 1.01 23.20 2.50
P18 266.57 26.07 216.96 0.81 27.33 1.05
P19 186.52 9.29 194.44 1.04 23.20 2.50
P20 225.94 4.06 225.65 1.00 9.84 2.42
P21 281.33 17.67 286.69 1.02 28.63 1.62
P22 305.21 6.40 309.55 1.01 11.50 1.80
P23 346.01 5.22 353.25 1.02 10.43 2.00
Average 0.96 2.15
Coefficient of variation
0.11
0.34
2λ
βu
.lim =
(D.1)
2λ+ 1
in [6.3] and later [6.4]:
2λ
⎡ dw
⎤
βu.lim = 1− ( 1+
λ)
2λ+ 1
⎢
8n
⎥
⎣ ⎦ (D.2)
which is the same as in Eq. (2.2). Table D.10 sets out the predictions of the
failure modes by using the two above expressions. For further comparisons,
reference is made to Eq. (D.2) – last column in Table D.10. Specimen T1 is the
only case where a change in the collapse mode is observed. For compari-
227

Further developments on the T-stub model
Table D.7 Prediction of ultimate resistance and deformation capacity (WP-Tstubs)
(cont.).
Test ID Num. or Exp. results
Jaspart methodology (Actual Eh; FBA)
Fmax ∆u.0 Fu.0 Ratio ∆u.0 Ratio
(kN) (mm) (kN)
(mm)
Weld_T1(i) 92.02 10.85 84.35 0.92 36.31 3.35
Weld_T1(ii) 102.75 8.01 95.61 0.93 30.52 3.81
Weld_T1(iii) 113.10 6.22 104.58 0.92 24.03 3.86
WT1(h) 91.91 14.32 78.79 0.86 21.24 1.48
WT2A(b) 86.82 17.98 71.97 0.83 23.98 1.33
WT2B(b) 97.88 13.09 83.84 0.86 19.32 1.48
WT4A(b) 103.26 4.33 103.55 1.00 9.73 2.25
WT7_M12 100.34 4.60 103.11 1.03 9.88 2.15
WT7_M16 132.34 11.47 135.81 1.03 22.15 1.93
WT7_M20 145.72 9.12 142.39 0.98 22.37 2.45
WT51(b) 97.08 3.96 98.21 1.01 9.54 2.41
WT53C 98.90 4.24 102.51 1.04 9.66 2.28
WT53D 117.36 5.54 115.33 0.98 8.15 1.47
WT53E 115.04 5.26 113.19 0.98 7.33 1.39
WT57_M12 121.87 4.33 120.69 0.99 6.80 1.57
WT57_M16 173.64 5.88 179.87 1.04 9.92 1.69
WT57_M20 241.71 15.98 208.15 0.86 7.67 0.48
Average 0.96 2.08
Coefficient of variation
0.07
0.44
son, the table also includes the critical modes for the same examples according
to the author (second column) and Jaspart (third and fourth columns).
The application of the method proposed by these authors requires, in the
first place, the approximation of the steel flange constitutive law by a quadrilinear
relationship. The actual material properties for the example specimens
were defined in terms of a piecewise σ-ε law earlier in Chapters 3 and 4. Fig.
D.1 shows those laws in terms of natural coordinates and the corresponding
quadrilinear approximations.
Next, the F-∆ response may be fully characterized. In terms of ultimate
conditions, the predictions of resistance and deformation capacity are summarized
and compared with the actual results for the various specimens in Table
D.11. These results are obtained by application of the basic formulation for
evaluation of the resistance of specimens failing according to a type-1 mechanism.
For those specimens whose failure mode is of type-2, the bolt is also
subjected to plasticity. In this table, the bolt plastic deformations, δb.p.u, are
evaluated. It should be noted that, so far, the compatibility requirements between
flange and bolt deformations have been disregarded. For specimen T1,
228

Simplified methodologies: assessment of the behaviour of T-stub connections
Table D.8 Prediction of ultimate resistance and deformation capacity by using
the nominal strain hardening modulus of the flange material
and the basic formulation for computation of resistance.
Test ID Numerical results Jaspart methodology (Nominal Eh; BF)
Fmax ∆u.0 Fu.0 Ratio ∆u.0 Ratio
(kN) (mm) (kN)
(mm)
T1 103.99 8.70 92.53 0.89 8.98 1.03
P1 91.76 10.77 79.10 0.86 11.39 1.06
P2 116.72 6.18 111.45 0.95 7.09 1.15
P3 95.41 10.17 80.96 0.85 8.76 0.86
P4 115.97 4.68 112.95 0.97 7.23 1.55
P5 130.20 3.63 117.24 0.90 4.84 1.33
P6 95.53 10.06 80.96 0.85 8.76 0.87
P7 111.34 7.56 104.09 0.93 9.20 1.22
P8 112.71 8.08 106.27 0.94 8.00 0.99
P9 131.43 3.31 127.29 0.97 4.01 1.21
P10 76.79 32.75 37.93 0.49 12.63 0.39
P11 121.15 2.94 123.56 1.02 4.05 1.38
P12 154.06 24.22 92.53 0.60 8.29 0.34
P13 93.71 11.38 79.31 0.85 8.43 0.74
P14 86.57 24.15 66.87 0.77 7.44 0.31
P15 171.08 18.02 111.45 0.65 6.25 0.35
P16 125.69 3.06 122.97 0.98 4.70 1.53
P17 192.01 9.29 161.92 0.84 9.08 0.98
P18 266.57 26.07 161.92 0.61 8.50 0.33
P19 186.52 9.29 161.92 0.87 9.08 0.98
P20 225.94 4.06 225.65 1.00 4.23 1.04
P21 281.33 17.67 213.96 0.76 8.91 0.50
P22 305.21 6.40 298.54 0.98 8.66 1.35
P23 346.01 5.22 353.25 1.02 4.48 0.86
Average 0.86 0.93
Coefficient of variation 0.17 0.42
Weld_T1(i) 92.02 10.85 72.79 0.79 13.06 1.20
Weld_T1(ii) 102.75 8.01 81.54 0.79 10.85 1.35
Weld_T1(iii) 113.10 6.22 90.42 0.80 9.28 1.49
WT1(h) 91.91 14.32 68.28 0.74 9.29 0.65
WT2A(b) 86.82 17.98 62.78 0.72 10.56 0.59
WT2B(b) 97.88 13.09 72.17 0.74 8.40 0.64
WT4A(b) 103.26 4.33 103.55 1.00 6.62 1.53
WT7_M12 100.34 4.60 103.11 1.03 6.80 1.48
WT7_M16 132.34 11.47 113.32 0.86 9.33 0.81
WT7_M20 145.72 9.12 114.05 0.78 9.05 0.99
Average 0.83 1.07
Coefficient of variation
0.13
0.36
229

Further developments on the T-stub model
Table D.9 Prediction of ultimate resistance and deformation capacity by using
the nominal strain hardening modulus of the flange material
and the formulation accounting for the bolt for computation of resistance.
Test ID Numerical results
Fmax ∆u.0
Jaspart methodology (Nominal Eh; FBA)
Fu.0 Ratio ∆u.0 Ratio
(kN) (mm) (kN)
(mm)
T1 103.99 8.70 105.79 1.02 9.24 1.06
P1 91.76 10.77 91.97 1.00 12.62 1.17
P2 116.72 6.18 119.60 1.02 5.25 0.85
P3 95.41 10.17 96.36 1.01 10.43 1.03
P4 115.97 4.68 112.95 0.97 5.01 1.07
P5 130.20 3.63 117.24 0.90 4.84 1.33
P6 95.53 10.06 96.36 1.01 10.43 1.04
P7 111.34 7.56 108.65 0.98 6.31 0.83
P8 112.71 8.08 114.85 1.02 6.44 0.80
P9 131.43 3.31 127.29 0.97 4.01 1.21
P10 76.79 32.75 44.90 0.58 14.95 0.46
P11 121.15 2.94 123.56 1.02 4.05 1.38
P12 154.06 24.22 116.02 0.75 10.39 0.43
P13 93.71 11.38 94.40 1.01 10.03 0.88
P14 86.57 24.15 79.59 0.92 8.86 0.37
P15 171.08 18.02 144.50 0.84 8.11 0.45
P16 125.69 3.06 122.97 0.98 4.70 1.53
P17 192.01 9.29 194.44 1.01 9.72 1.05
P18 266.57 26.07 216.96 0.81 11.39 0.44
P19 186.52 9.29 194.44 1.04 9.72 1.05
P20 225.94 4.06 225.65 1.00 4.23 1.04
P21 281.33 17.67 286.69 1.02 11.94 0.68
P22 305.21 6.40 309.55 1.01 4.97 0.78
P23 346.01 5.22 353.25 1.02 4.48 0.86
Average 0.96 0.91
Coefficient of variation 0.11
0.35
Weld_T1(i) 92.02 10.85 84.35 0.92 15.14 1.39
Weld_T1(ii) 102.75 8.01 95.61 0.93 12.73 1.59
Weld_T1(iii) 113.10 6.22 104.58 0.92 10.05 1.61
WT1(h) 91.91 14.32 78.79 0.86 10.73 0.75
WT2A(b) 86.82 17.98 71.97 0.83 12.11 0.67
WT2B(b) 97.88 13.09 83.84 0.86 9.75 0.75
WT4A(b) 103.26 4.33 103.55 1.00 5.05 1.17
WT7_M12 100.34 4.60 103.11 1.03 5.13 1.12
WT7_M16 132.34 11.47 135.81 1.03 11.18 0.98
WT7_M20 145.72 9.12 142.39 0.98 11.29 1.24
Average 0.93 1.13
Coefficient of variation
0.08
0.30
230

Simplified methodologies: assessment of the behaviour of T-stub connections
Stress (MPa)
900
750
600
450
300
150
0
Actual piecewise true law
Quadrilinear true law
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Strain
(a) Flange steel grade S355 (fy.f = 430 MPa) for specimens T1, P16 and P18.
Stress (MPa)
900
750
600
450
300
150
0
Actual piecewise true law
Quadrilinear true law
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Strain
(b) Flange steel grade S355 (fy.f = 340 MPa) for specimens WT4A and
WT7_M20.
Stress (MPa)
900
750
600
450
300
150
0
Actual piecewise true law
Quadrilinear true law
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35
Strain
(c) Flange steel grade S690 (fy.f = 698 MPa) for specimen WT51.
Fig. D.1 Quadrilinear approximation of the actual piecewise flange material
law for application of the method recommended by Faella, Piluso and
Rizzano.
231

Further developments on the T-stub model
failing according to a type-2 mechanism, the application of the formulae provided
by Faella et al. yields a negative bolt plastic deformation, which has no
physical meaning.
If now the formulation accounting for the bolt action for type-1 is considered,
the ultimate resistance prediction improves (specimens P18 and
WT7_M20) as well as the deformation capacity – Table D.12. In this table, the
results for specimen T1 are computed by assuming that mode 1 governs collapse,
as ascertained by Eq. (D.1). The results are not so different from those in
Table D.11. With respect to the remaining specimens illustrating type-2 collapse
mode, in Table D.12 the compatibility requirements between bolt and
flange deformations are accounted for. The actual bolt deformation at fracture
is known. If this value is imposed, a new value for the overall T-stub deformation
can be calculated by means of linear interpolation. By doing so, the predictions
improve.
So far, the actual material properties for the flange have been employed. As
before, the nominal properties for the strain hardening range are also taken into
consideration (Table D.13). For this analysis, specimen WT51 that uses S690 is
Table D.10 Prediction of failure modes according to Faella and co-authors.
Test ID Potential Crit. resistance formula Pot. failure type ac-
failure type according to Jaspart cording to Faella et al.
Plastic Ultimate Eq. (D.1) Eq. (D.2)
T1 13 1 1 or 2 2 1
P16 23 2 2 2 2
P18 11 1 1 1 1
WT4A 13 1 or 2 2 2 2
WT7_M20 11 1 1 1 1
WT51 23 2 1 or 2 2 2
Table D.11 Prediction of ultimate resistance and deformation capacity by using
the basic formulation for computation of resistance and neglecting
the compatibility requirements between flange and bolt
deformations.
Test ID Num. or Exp. results Faella et al. methodology
Fmax ∆u Fu.0 Ratio ∆u.0 Ratio δb.p.u
(kN) (mm) (kN) (mm) (mm)
T1 103.99 8.70 109.17 1.05 9.64 1.11 -12.79
P16 125.69 3.06 128.89 1.03 26.18 8.56 12.82
P18 266.57 26.07 106.19 0.40 9.86 0.38 0.00
WT4A 103.26 4.33 108.07 1.05 25.32 5.85 11.14
WT7_M20 145.72 9.12 130.96 0.90 12.15 1.33 0.00
WT51 97.08 3.96 100.90 1.04 6.46 1.63 1.27
232

Simplified methodologies: assessment of the behaviour of T-stub connections
Table D.12 Prediction of ultimate resistance and deformation capacity by using
the formulation accounting for bolt finite size for computation
of resistance of specimens failing according to mode 1 and catering
for compatibility requirements between flange and bolt deformations
(specimens from type-2 collapse mode).
Test ID Num. or Exp. results Faella et al. methodology
Fmax ∆u.0 δb.p.fract Fu.0 Ratio ∆u.0 Ratio
(kN) (mm) (mm) (kN)
(mm)
T1 103.99 8.70 0.87 126.39 1.22 10.19 1.17
P16 125.69 3.06 0.87 83.24 0.66 1.96 0.64
P18 266.57 26.07 ⎯ 142.28 0.53 10.24 0.39
WT4A 103.26 4.33 1.08 71.89 0.70 2.95 0.68
WT7_M20 145.72 9.12 ⎯ 163.51 1.12 12.45 1.37
WT51 97.08 3.96 1.08 98.99 1.02 5.71 1.44
Table D.13 Actual properties of the flange steel grade and nominal properties
according to Faella and co-authors [S355(1) is the steel grade from
specimens T1, P16 and P18; S355(2) is the steel grade from
specimens WT4A and WT7_M20].
Steel
fy E Eh Eu
(MPa) (GPa) (GPa) (GPa)
εy εh εm εu
S355(1) 430 208 1.74 0.67 0.0021 0.0200 0.1545 0.2872
S355(2) 340 210 2.15 0.48 0.0016 0.0150 0.2240 0.3610
S355 355 210 4.36 0.51 0.0017 0.0166 0.0521 0.8100
Table D.14 Prediction of ultimate resistance and deformation capacity with
nominal steel properties by using the formulation accounting for
bolt finite size for computation of resistance of specimens failing
according to mode 1.
Test ID Potential
failure type
Fmax
(kN)
∆u.0
(mm)
δb.p.u
(mm)
T1 2 112.08 28.23 -10.60
P16 2 64.83 1.70 0.87
P18 1 158.05 27.38 ⎯
WT4A 2 60.60 2.53 1.08
WT7_M20 1 224.79 37.21 ⎯
neglected. The results for this new approach are given in Table D.14 (bolt and
flange compatibility is also accounted for). Again, for specimen T1 the results
are poor. For the remaining cases, the results do not improve considerably.
233

Further developments on the T-stub model
c) Methodology recommended by Beg, Zupančič and Vayas for evaluation of
the deformation capacity
Beg and co-authors proposed simple formulae for the assessment of the deformation
capacity of single T-stubs in [6.7]. For the examples under analysis,
Table D.15 sets out the predictions of their proposals. For the specimens failing
according to a type-2 plastic mechanism, a value of k = 3.5 is assumed (see Eq.
(6.25)). In general, the predictions are not satisfactory. For those specimens
failing according to a type-2 plastic mode, the predictions improve, but for the
remaining cases the deviations are not acceptable.
Table D.15 Prediction of deformation capacity by means of Beg et al. methodology.
Test ID Num. or exp. results
Beg et al. methodology
∆u.0
(mm)
Potential plastic
failure mode
∆u.0
(mm)
Ratio
T1 8.70 1 23.56 2.71
P1 10.77 1 27.56 2.56
P2 6.18 1 19.56 3.17
P3 10.17 1 23.56 2.32
P4 4.68 1 23.56 5.03
P5 3.63 2 4.30 1.18
P6 10.06 1 23.56 2.34
P7 7.56 1 23.56 3.12
P8 8.08 1 21.68 2.68
P9 3.31 2 5.16 1.56
P10 32.75 1 24.60 0.75
P11 2.94 2 5.24 1.78
P12 24.22 1 23.56 0.97
P13 11.38 1 23.56 2.07
P14 24.15 1 23.56 0.98
P15 18.02 1 19.56 1.09
P16 3.06 2 4.32 1.41
P17 9.29 1 23.56 2.54
P18 26.07 1 23.56 0.90
P19 9.29 1 23.56 2.54
P20 4.06 2 5.95 1.46
P21 17.67 1 23.56 1.33
P22 6.40 1 25.87 4.04
P23 5.22 2 9.27 1.78
Average 2.10
Coefficient of variation
0.50
234

Simplified methodologies: assessment of the behaviour of T-stub connections
Table D.15 Prediction of deformation capacity by means of Beg et al. methodology
(cont.).
Test ID Num. or exp. results
Beg et al. methodology
∆u.0
(mm)
Potential plastic
failure mode
∆u.0
(mm)
Ratio
Weld_T1(i) 10.85 1 29.95 2.76
Weld_T1(ii) 8.01 1 26.73 3.34
Weld_T1(iii) 6.22 1 24.11 3.87
WT1 14.32 1 26.98 1.88
WT2A 17.98 1 29.03 1.61
WT2B 13.09 1 25.35 1.94
WT4A 4.33 1 26.96 6.23
WT51 3.96 2 5.67 1.43
WT53C 4.24 1 27.47 6.48
WT53D 5.54 1 27.39 4.94
WT53E 5.26 1 27.41 5.21
WT7_M12 4.60 1 27.10 5.89
WT7_M16 11.47 1 27.11 2.36
WT7_M20 9.12 1 27.05 2.97
WT57_M12 4.33 2 12.88 2.97
WT57_M16 5.88 1 27.40 4.66
WT57_M20 15.98 1 27.41 1.72
Average 3.55
Coefficient of variation
0.48
D.3 Application of the proposed model: results for HR-T-stub T1
Specimen T1 was selected for illustration of the results obtained when the proposed
model was applied. The geometrical and mechanical characteristics for
this connection are indicated in Tables D.1-D.2.
First, the overall F-∆ response is shown in Fig. D.2. The actual behaviour,
obtained from the three-dimensional numerical model, is plotted against the
simplified response from the proposed beam model. Both curves fit well
though the simplified curve yields larger ductility than the real behaviour. This
graph also traces the bilinear approximation of Jaspart. For this approximation,
the FBA was employed for resistance computation (this specimen fails according
to a failure type-13). The actual value for the strain hardening modulus was
used. This response deviates significantly from the real behaviour. The predictions
from Faella and co-workers are also included (results from Table D.11).
Fig. D.3 shows the bolt response. The trilinear model fits the numerical
results well. The prying force is plotted against the total flange deformation in
Fig. D.4 for both approaches. The two models yield different responses. The
235

Further developments on the T-stub model
beam model gives lower results for the prying force. The ratios B/F and Q/F
are shown in Fig. D.5. Figs. D.6-D.9 trace the beam diagrams of bending moment,
flange deformation, flange rotation and plastic strain, respectively. Four
load levels were chosen: (i) F = 36.0 kN, corresponding to yielding of the
flange at the flange-to-web connection; (ii) F = 60.0 kN, corresponding to first
yielding at the bolt axis (the section at the flange-to-web connection is not engaged
in the strain hardening domain yet); (iii) F = 88.9 kN, corresponding to
first yielding of the bolt and (iv) F = 114.5 kN, corresponding to fracture of the
bolt. Fig. D.6 shows that, at ultimate conditions, the bending moments acting at
sections (1) and (2) are similar. Again, the plastic deformation of the flange is
restricted to an area close to the critical sections, as shown in Figs. D.8-D.9.
Fig. D.10 traces the variation of the applied load with the parameter L/m.
236
Load, F (kN)
120
105
90
75
60
45
30
Actual response
Simplified response (Beam model)
15
0
Bilinear approximation (Jaspart)
Quadrilinear approximation (Faella and co-authors)
0 2 4 6 8 10 12 14 16 18 20 22 24
Deformation, ∆ (mm)
Fig. D.2 Specimen T1: force-deformation behaviour as ascertained by the
different approaches.
Bolt force, B (kN)
90
80
70
60
50
40
30
20
"Actual" response (3-dim. FE model)
10
0
Simplified response (Beam model)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Bolt elongation, δ b (mm)
Fig. D.3 Specimen T1: bolt elongation behaviour.

Simplified methodologies: assessment of the behaviour of T-stub connections
Prying force, Q (kN)
40
35
30
25
20
15
10
5
"Actual" response (3-dim. FE model)
Simplified response (Beam model)
0
0 2 4 6 8 10 12 14 16 18
Deformation, ∆ (mm)
Fig. D.4 Specimen T1: prying force behaviour.
Ratio B/F, Q/F
1.2
1.0
0.8
0.6
0.4
0.2
B/F (3-dim. FE model) Q/F (3-dim. FE model)
B/F (Beam model) Q/F (Beam model)
0.0
0 15 30 45 60 75 90 105 120
Load, F (kN)
Fig. D.5 Specimen T1: ratio B/F and Q/F.
Mz (Nmm)
1.0E+06
8.0E+05
6.0E+05
4.0E+05
2.0E+05
0.0E+00
-2.0E+05
-4.0E+05
-6.0E+05
-8.0E+05
-1.0E+06
0 5 10 15 20 25 30 35 40 45 50 55 60
Beam length (mm)
Fig. D.6 Specimen T1: flange moment diagram.
F = 36.0 kN F = 60.0 kN
F = 88.9 kN F = 114.5 kN
Mp
Mp
237

Further developments on the T-stub model
238
∆/2 (mm)
9
8
7
6
5
4
3
2
1
0
F = 36.0 kN
F = 88.9 kN
F = 60.0 kN
F = 114.5 kN
0 5 10 15 20 25 30 35 40 45 50 55 60
Beam length (mm)
Fig. D.7 Specimen T1: flange (half-) deformation diagram.
θz (rad)
0.03
0.00
-0.03
-0.06
-0.09
-0.12
-0.15
-0.18
-0.21
-0.24
-0.27
-0.30
-0.33
0 5 10 15 20 25 30 35 40 45 50 55 60
Beam length (mm)
Fig. D.8 Specimen T1: flange rotation diagram.
Plastic strain
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
-0.5
εp.u
F = 36.0 kN
F = 60.0 kN
F = 88.9 kN
F = 114.5 kN
0 5 10 15 20 25 30 35 40 45 50 55 60
Beam length (mm)
Fig. D.9 Specimen T1: flange plastic strain diagram.
F = 36.0 kN
F = 60.0 kN
F = 88.9 kN
F = 114.5 kN
εp.u

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
120
105
90
75
60
45
30
15
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
L/m
Fig. D.10 Specimen T1: length of the equivalent cantilever.
D.4 Application of the proposed model: results for WP-T-stub WT1
Specimen WT1 was also selected for further detail of the results extracted from
the proposed model. The geometrical and mechanical characteristics for this
connection are indicated in Tables D.1-D.2, as well.
Identical results to the above are shown in this section. Fig. D.11 plots the
alternative predictions for the deformation behaviour and compares those with
the actual test (experimental) results. The agreement between the Faella et al.
quadrilinear approximation and the real response is very good. As for the beam
model and the simple approximation of Jaspart, the results are good but clearly
underestimate the resistance predictions. The ductility is also overestimated.
Figs. D.12-D.14 show the bolt response and the prying behaviour as ascertained
by the beam model. No comparisons are established with the test results
Load, F (kN)
105
90
75
60
45
30 Actual response (WT1h)
Simplified response (Beam model)
15
0
Bilinear approximation (Jaspart)
Quadrilinear approximation (Faella and co-authors)
0 2 4 6 8 10 12 14 16 18 20 22 24
Deformation, ∆ (mm)
Fig. D.11 Specimen WT1: force-deformation behaviour as ascertained by the
different approaches.
239

Further developments on the T-stub model
240
Bolt force, B (kN)
90
80
70
60
50
40
30
20
10
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Bolt elongation, δ b (mm)
Fig. D.12 Specimen WT1: bolt elongation behaviour.
Prying force, Q (kN)
30
25
20
15
10
5
0
0 2 4 6 8 10 12 14 16 18 20
Deformation, ∆ (mm)
Fig. D.13 Specimen WT1: prying force behaviour.
Ratio B/F, Q/F
1.2
1.0
0.8
0.6
0.4
0.2
B/F (Beam model) Q/F (Beam model)
0.0
0 10 20 30 40 50 60 70 80 90 100
Load, F (kN)
Fig. D.14 Specimen WT1: ratio B/F and Q/F.

Simplified methodologies: assessment of the behaviour of T-stub connections
since these values were not determined experimentally.
Fig. D.15-D.18 give results for the flange bending moment, flange deformation,
flange rotation and plastic strain at four different load levels: (i) F =
26.0 kN, corresponding to yielding of the flange at the flange-to-web connection,
(ii) F = 42.0 kN, corresponding to first yielding at the bolt axis, (iii) F =
78.0 kN, corresponding to first yielding of the bolt and cracking of the flange
material at section (1) and (iv) F = 85.6 kN, corresponding to cracking of the
flange material at section (1*). Finally, Fig. D.19 shows the evolution of the
non-dimensional parameter L/m with increasing loading.
D.5 Prediction of the nonlinear response of the above connections using
the nominal stress-strain characteristics
If the nominal mechanical properties of the bolt and flange plates are input, the
Mz (Nmm)
8.0E+05
6.0E+05
4.0E+05
2.0E+05
0.0E+00
-2.0E+05
-4.0E+05
-6.0E+05
F = 26.0 kN F = 42.0 kN
F = 78.0 kN F = 85.6 kN
-8.0E+05
0 5 10 15 20 25 30 35 40 45 50 55 60 65
Beam length (mm)
Fig. D.15 Specimen WT1: flange moment diagram.
∆/2 (mm)
10
9
8
7
6
5
4
3
2
1
0
0 5 10 15 20 25 30 35 40 45 50 55 60 65
Beam length (mm)
Fig. D.16 Specimen WT1: flange gap diagram.
F = 26.0 kN F = 42.0 kN
F = 78.0 kN F = 85.6 kN
Mp
Mp
241

Further developments on the T-stub model
242
θz (mm)
0.03
0.00
-0.03
-0.06
-0.09
-0.12
-0.15
-0.18
-0.21
-0.24
-0.27
-0.30
-0.33
0 5 10 15 20 25 30 35 40 45 50 55 60 65
Beam length (mm)
Fig. D.17 Specimen WT1: flange rotation diagram.
Plastic strain
0.7
0.5
0.3
0.1
-0.1
-0.3
-0.5
εp.u
F = 26.0 kN
F = 42.0 kN
F = 78.0 kN
F = 85.6 kN
-0.7
0 5 10 15 20 25 30 35 40 45 50 55 60 65
Beam length (mm)
Fig. D.18 Specimen WT1: flange plastic strain diagram.
Load, F (kN)
90
75
60
45
30
15
F = 26.0 kN
F = 42.0 kN
F = 78.0 kN
F = 85.6 kN
εp.u
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
L/m
Fig. D.19 Specimen WT1: length of the equivalent cantilever.

Simplified methodologies: assessment of the behaviour of T-stub connections
Table D.16 Prediction of the failure modes.
Test ID Actual determiningfracture
element
Predicted potential
failure
mode.
Mu Eq. Mu Eq.
(2.4)
(2.5)
Determining fracture element
in the beam model
(nominal mech. Properties)
T1 Bolt 13 13 Flange, at (1*)
P1 Bolt 13 13 Flange, at (1*)
P2 Bolt 13 13 Bolt
P3 Bolt 13 13 Flange, at (1*)
P4 Bolt 13 13 Bolt
P5 Bolt 23 23 Bolt
P6 Bolt 13 13 Flange, at (1*)
P7 Bolt 13 13 Flange, at (1*)
P8 Bolt 13 13 Flange, at (1*)
P9 Bolt 23 23 Bolt
P10 Flange 11 11 Flange, at (1*)
P11 Bolt 23 23 Bolt
P12 Flange 11 11 Flange, at (1*)
P13 Bolt 13 13 Flange, at (1*)
P14 Flange 11 11 Flange, at (1*)
P15 Flange 11 11 Flange, at (1*)
P16 Bolt 23 23 Bolt
P17 Bolt 13 13 Flange, at (1*)
P18 Flange 11 11 Flange, at (1*)
P19 Bolt 13 13 Flange, at (1*)
P20 Bolt 23 23 Bolt
P21 Bolt 13 13 Flange, at (1*)
P22 Bolt 13 13 Flange, at (1*)
P23 Bolt 23 23 Bolt
Weld_T1(i) Bolt 11 11 Flange, at (1*)
Weld_T1(ii) Bolt 13 13 Flange, at (1*)
Weld_T1(iii) Bolt 13 13 Flange, at (1*)
WT1
Bolt and
flange 11 13
Flange, at (1*)
WT2A
Bolt and
flange 11 13
Flange, at (1*)
WT2B
Bolt and
Flange, at (1*)
flange 13 13
WT4A Bolt 23 23 Bolt
WT7_M12 Bolt 23 23 Bolt
WT7_M16 Flange 11 13 Flange, at (1*)
WT7_M20 Flange 11 11 Flange, at (1*)
243

Further developments on the T-stub model
predicted failure modes may slightly change (Tables 6.12 and D.16 – see T-
stubs T1, P1, P6-P8, P22 and Weld_T1(iii)). The responses for this new approach
are traced in Figs. D.20-D.53. These graphs also trace the actual response
as well as the prediction by using the actual material properties. For
most specimens whose failure is determined by the bolt (black circle), the predictions
of deformation capacity improve. If the flange governs ultimate collapse
(black square in the graphs), then the maximum deformation decreases
since the nominal ultimate strain is lower than the actual value. In terms of
strength, the ultimate resistance is lower now when compared to the actual
properties. However, it can be seen from the graphs that the (nominal) ultimate
resistance is identical to the value predicted by the actual mechanical properties
if the bolt is determinant.
These new predictions at ultimate conditions are summarized in Table D.17
for the various specimens. From a design point of view, and on average, the
244
Load, F (kN)
120
105
90
75
60
45
Actual response
30
Simplified response (Simple beam model)
15
0
Simplified response with nominal properties
0.0 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 13.5 15.0 16.5 18.0
Deformation, ∆ (mm)
Fig. D.20 Specimen T1: force-deformation behaviour (nominal properties).
Load, F (kN)
105
90
75
60
45
30
Actual response
Simplified response (Simple beam model)
15
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20 22 24
Deformation, ∆ (mm)
Fig. D.21 Specimen P1: force-deformation behaviour (nominal properties).

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
135
120
105
90
75
60
45
Actual response
30
Simplified response (Simple beam model)
15
0
Simplified response with nominal properties
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Deformation, ∆ (mm)
Fig. D.22 Specimen P2: force-deformation behaviour (nominal properties).
Load, F (kN)
120
105
90
75
60
45
Actual response
30
Simplified response (Simple beam model)
15
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20 22
Deformation, ∆ (mm)
Fig. D.23 Specimen P3: force-deformation behaviour (nominal properties).
Load, F (kN)
135
120
105
90
75
60
45
Actual response
30
Simplified response (Simple beam model)
15
0
Simplified response with nominal properties
0.0 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 13.5 15.0
Deformation, ∆ (mm)
Fig. D.24 Specimen P4: force-deformation behaviour (nominal properties).
245

Further developments on the T-stub model
246
Load, F (kN)
135
120
105
90
75
60
45
Actual response
30
Simplified response (Simple beam model)
15
0
Simplified response with nominal properties
0 1 2 3 4 5 6 7 8 9 10 11 12
Deformation, ∆ (mm)
Fig. D.25 Specimen P5: force-deformation behaviour (nominal properties).
Load, F (kN)
120
105
90
75
60
45
Actual response
30
Simplified response (Simple beam model)
15
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20 22 24
Deformation, ∆ (mm)
Fig. D.26 Specimen P6: force-deformation behaviour (nominal properties).
Load, F (kN)
135
120
105
90
75
60
45
Actual response
30
Simplified response (Simple beam model)
15
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20
Deformation, ∆ (mm)
Fig. D.27 Specimen P7: force-deformation behaviour (nominal properties).

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
135
120
105
90
75
60
45
Actual response
30
Simplified response (Simple beam model)
15
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20
Deformation, ∆ (mm)
Fig. D.28 Specimen P8: force-deformation behaviour (nominal properties).
Load, F (kN)
160
140
120
100
80
60
Actual response
40
Simplified response (Simple beam model)
20
0
Simplified response with nominal properties
0 1 2 3 4 5 6 7 8 9 10
Deformation, ∆ (mm)
Fig. D.29 Specimen P9: force-deformation behaviour (nominal properties).
Load, F (kN)
80
70
60
50
40
30
20
Actual response
10
0
Simplified response (Simple beam model)
Simplified response with nominal properties
0 3 6 9 12 15 18 21 24 27 30 33 36
Deformation, ∆ (mm)
Fig. D.30 Specimen P10: force-deformation behaviour (nominal properties).
247

Further developments on the T-stub model
248
Load, F (kN)
160
140
120
100
80
60
Actual response
40
Simplified response (Simple beam model)
20
0
Simplified response with nominal properties
0 1 2 3 4 5 6 7 8 9 10
Deformation, ∆ (mm)
Fig. D.31 Specimen P11: force-deformation behaviour (nominal properties).
Load, F (kN)
160
140
120
100
80
60
Actual response
40
Simplified response (Simple beam model)
20
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20 22 24 26
Deformation, ∆ (mm)
Fig. D.32 Specimen P12: force-deformation behaviour (nominal properties).
Load, F (kN)
135
120
105
90
75
60
45
Actual response
30
Simplified response (Simple beam model)
15
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20
Deformation, ∆ (mm)
Fig. D.33 Specimen P13: force-deformation behaviour (nominal properties).

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
90
80
70
60
50
40
30
Actual response
20
Simplified response (Simple beam model)
10
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20 22 24 26
Deformation, ∆ (mm)
Fig. D.34 Specimen P14: force-deformation behaviour (nominal properties).
Load, F (kN)
180
160
140
120
100
80
60
40
Actual response
Simplified response (Simple beam model)
20
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20
Deformation, ∆ (mm)
Fig. D.35 Specimen P15: force-deformation behaviour (nominal properties).
Load, F (kN)
160
140
120
100
80
60
Actual response
40
Simplified response (Simple beam model)
20
0
Simplified response with nominal properties
0 1 2 3 4 5 6 7 8 9 10
Deformation, ∆ (mm)
Fig. D.36 Specimen P16: force-deformation behaviour (nominal properties).
249

Further developments on the T-stub model
250
Load, F (kN)
240
210
180
150
120
90
Actual response
60
Simplified response (Simple beam model)
30
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20 22
Deformation, ∆ (mm)
Fig. D.37 Specimen P17: force-deformation behaviour (nominal properties).
Load, F (kN)
280
240
200
160
120
80
Actual response
Simplified response (Simple beam model)
40
0
Simplified response with nominal properties
0 3 6 9 12 15 18 21 24 27 30
Deformation, ∆ (mm)
Fig. D.38 Specimen P18: force-deformation behaviour (nominal properties).
Load, F (kN)
240
210
180
150
120
90
Actual response
60
Simplified response (Simple beam model)
30
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20 22
Deformation, ∆ (mm)
Fig. D.39 Specimen P19: force-deformation behaviour (nominal properties).

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
270
240
210
180
150
120
90
Actual response
60
Simplified response (Simple beam model)
30
0
Simplified response with nominal properties
0 1 2 3 4 5 6 7 8 9 10
Deformation, ∆ (mm)
Fig. D.40 Specimen P20: force-deformation behaviour (nominal properties).
Load, F (kN)
320
280
240
200
160
120
Actual response
80
Simplified response (Simple beam model)
40
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20 22
Deformation, ∆ (mm)
Fig. D.41 Specimen P21: force-deformation behaviour (nominal properties).
Load, F (kN)
400
350
300
250
200
150
Actual response
100
Simplified response (Simple beam model)
50
0
Simplified response with nominal properties
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Deformation, ∆ (mm)
Fig. D.42 Specimen P22: force-deformation behaviour (nominal properties).
251

Further developments on the T-stub model
252
Load, F (kN)
450
400
350
300
250
200
150
Actual response
100
Simplified response (Simple beam model)
50
0
Simplified response with nominal properties
0 1 2 3 4 5 6 7 8 9 10 11 12
Deformation, ∆ (mm)
Fig. D.43 Specimen P23: force-deformation behaviour (nominal properties).
Load, F (kN)
120
105
90
75
60
45
Actual response
30
Simplified response (Simple beam model)
15
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20 22
Deformation, ∆ (mm)
Fig. D.44 Specimen Weld_T1(i): force-deformation behaviour (nominal properties).
Load, F (kN)
120
105
90
75
60
45
Actual response
30
Simplified response (Simple beam model)
15
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20 22
Deformation, ∆ (mm)
Fig. D.45 Specimen Weld_T1(ii): force-deformation behaviour (nominal properties).

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
120
105
90
75
60
45
Actual response
30
Simplified response (Simple beam model)
15
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20 22
Deformation, ∆ (mm)
Fig. D.46 Specimen Weld_T1(iii): force-deformation behaviour (nominal
properties).
Load, F (kN)
105
90
75
60
45
30
Actual response
15
0
Simplified response (Simple beam model)
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20
Deformation, ∆ (mm)
Fig. D.47 Specimen WT1: force-deformation behaviour (nominal properties).
Load, F (kN)
105
90
75
60
45
30
Actual response
15
0
Simplified response (Simple beam model)
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20
Deformation, ∆ (mm)
Fig. D.48 Specimen WT2A: force-deformation behaviour (nominal properties).
253

Further developments on the T-stub model
254
Load, F (kN)
105
90
75
60
45
30
Actual response
15
0
Simplified response (Simple beam model)
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20
Deformation, ∆ (mm)
Fig. D.49 Specimen WT2B: force-deformation behaviour (nominal properties).
Load, F (kN)
135
120
105
90
75
60
45
Actual response
30
Simplified response (Simple beam model)
15
0
Simplified response with nominal properties
0 1 2 3 4 5 6 7 8 9 10 11 12
Deformation, ∆ (mm)
Fig. D.50 Specimen WT4A: force-deformation behaviour (nominal properties).
Load, F (kN)
135
120
105
90
75
60
45
Actual response
30
Simplified response (Simple beam model)
15
0
Simplified response with nominal properties
0 1 2 3 4 5 6 7 8 9 10 11 12
Deformation, ∆ (mm)
Fig. D.51 Specimen WT7_M12: force-deformation behaviour (nominal properties).

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
160
140
120
100
80
60
Actual response
40
Simplified response (Simple beam model)
20
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20
Deformation, ∆ (mm)
Fig. D.52 Specimen WT7_M16: force-deformation behaviour (nominal properties).
Load, F (kN)
160
140
120
100
80
60
Actual response
40
Simplified response (Simple beam model)
20
0
Simplified response with nominal properties
0 2 4 6 8 10 12 14 16 18 20
Deformation, ∆ (mm)
Fig. D.53 Specimen WT7_M20: force-deformation behaviour (nominal properties).
predictions for resistance are very good (ratios of 0.96 approximately) but they
overestimate the deformation capacity. In addition, the predicted failure type
does not always correspond to the actual mode. The reason for the good resistance
predictions derives from the mechanical σ-ε law, which differs significantly
at yielding conditions from the nominal law but approximates it at ultimate
conditions.
D.6 Comparative graphs: simple beam model and sophisticated beam
model accounting for the bolt action
Figs. D.54-D.75 compare the actual response of the several T-stubs with the
255

Further developments on the T-stub model
Table D.17 Prediction of deformation capacity and ultimate resistance (nominal
properties of steel).
256
Test ID Potential
failure
Actual results Beam model predictions
Fmax ∆u.0 Fu.0 Ratio ∆u.0 Ratio
type (kN) (mm) (kN) (mm)
T1 13 103.99 8.70 104.13 1.00 16.92 1.94
P1 13 91.76 10.77 87.94 0.96 19.30 1.79
P2 13 116.72 6.18 126.50 1.08 14.30 2.31
P3 13 95.41 10.17 91.54 0.96 16.34 1.61
P4 13 115.97 4.68 124.12 1.07 12.42 2.65
P5 23 130.20 3.63 129.04 0.99 9.19 2.53
P6 13 95.53 10.06 91.54 0.96 16.34 1.62
P7 13 111.34 7.56 117.31 1.05 18.03 2.38
P8 13 112.71 8.08 120.92 1.07 16.48 2.04
P9 23 131.43 3.31 144.71 1.10 8.04 2.43
P10 11 76.79 32.75 42.69 0.56 24.44 0.75
P11 23 121.15 2.94 138.24 1.14 6.87 2.34
P12 11 154.06 24.22 104.58 0.68 15.29 0.63
P13 13 93.71 11.38 104.13 1.11 16.92 1.49
P14 11 86.57 24.15 86.88 1.00 17.12 0.71
P15 11 171.08 18.02 130.79 0.76 13.75 0.76
P16 23 125.69 3.06 131.06 1.04 5.99 1.96
P17 13 192.01 9.29 183.01 0.95 17.06 1.84
P18 11 266.57 26.07 184.10 0.69 15.83 0.61
P19 13 186.52 9.29 183.01 0.98 17.06 1.84
P20 23 225.94 4.06 255.70 1.13 8.28 2.04
P21 13 281.33 17.67 243.84 0.87 16.60 0.94
P22 13 305.21 6.40 317.41 1.04 14.35 2.24
P23 23 346.01 5.22 427.41 1.24 10.59 2.03
Average 0.98 1.73
Coefficient of variation 0.17 0.38
Weld_T1(i) 11 92.02 10.85 70.00 0.76 9.84 0.91
Weld_T1(ii) 13 102.75 8.01 84.42 0.82 12.41 1.55
Weld_T1(iii) 13 113.10 6.22 101.77 0.90 17.43 2.80
WT1 11 91.91 14.32 84.39 0.92 10.74 0.75
WT2A 11 86.82 17.98 75.00 0.86 9.93 0.55
WT2B 13 97.88 13.09 93.44 0.95 12.63 0.96
WT4A 23 103.26 4.33 112.20 1.09 5.12 1.18
WT7_M12 23 100.34 4.60 111.31 1.11 5.13 1.11
WT7_M16 11 132.34 11.47 140.10 1.06 10.34 0.90
WT7_M20 11 145.72 9.12 140.33 0.96 10.25 1.12
Average 0.94 1.18
Coefficient of variation
0.12 0.53

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
120
105
90
75
60
Fig. D.54 Specimen T1.
Load, F (kN)
45
Actual response
30 Simplified response (Simple beam model)
15
0
Simplified response accounting for the bolt action
0 2 4 6 8 10 12 14 16 18 20
105
90
75
60
Fig. D.55 Specimen P1.
Load, F (kN)
Deformation, ∆ (mm)
45
30
Actual response
Simplified response (Simple beam model)
15
0
Simplified response accounting for the bolt action
0 2 4 6 8 10 12 14 16 18 20 22 24
120
105
90
75
60
Fig. D.56 Specimen P3.
Deformation, ∆ (mm)
45
Actual response
30 Simplified response (Simple beam model)
15
0
Simplified response accounting for the bolt action
0 2 4 6 8 10 12 14 16 18 20 22
Deformation, ∆ (mm)
257

Further developments on the T-stub model
258
Load, F (kN)
Fig. D.57 Specimen P5.
Load, F (kN)
135
120
105
90
75
60
Actual response
45
30
15
0
Simplified response (Simple
beam model)
Simplified response accounting
for the bolt action
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
80
70
60
50
40
Fig. D.58 Specimen P10.
Load, F (kN)
Deformation, ∆ (mm)
30
20
Actual response
Simplified response (Simple beam model)
10
0
Simplified response accounting for the bolt action
0 3 6 9 12 15 18 21 24 27 30 33 36
160
140
120
100
80
Fig. D.59 Specimen P12.
Deformation, ∆ (mm)
60
Actual response
40 Simplified response (Simple beam model)
20
0
Simplified response accounting for the bolt action
0 2 4 6 8 10 12 14 16 18 20 22 24 26
Deformation, ∆ (mm)

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
Fig. D.60 Specimen P14.
Load, F (kN)
90
80
70
60
50
40
30 Actual response
20 Simplified response (Simple beam model)
10
0
Simplified response accounting for the bolt action
0 2 4 6 8 10 12 14 16 18 20 22 24 26
210
180
150
120
Fig. D.61 Specimen P15.
Load, F (kN)
Deformation, ∆ (mm)
90
60
Actual response
Simplified response (Simple beam model)
30
0
Simplified response accounting for the bolt action
0 2 4 6 8 10 12 14 16 18 20
300
250
200
150
Fig. D.62 Specimen P18.
Deformation, ∆ (mm)
100
Actual response
50
0
Simplified response (Simple beam model)
Simplified response accounting for the bolt action
0 3 6 9 12 15 18 21 24 27 30
Deformation, ∆ (mm)
259

Further developments on the T-stub model
260
Load, F (kN)
Fig. D.63 Specimen P20.
Load, F (kN)
Fig. D.64 Specimen 23.
Load, F (kN)
270
240
210
180
150
120
Actual response
90
60
30
0
Simplified response (Simple
beam model)
Simplified response accounting
for the bolt action
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Deformation, ∆ (mm)
450
400
350
300
250
200
Actual response
150
Simplified response (Simple
100
50
0
beam model)
Simplified response accounting
for the bolt action
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
120
105
Fig. D.65 Specimen Weld_T1(i).
90
75
60
Deformation, ∆ (mm)
45
Actual response
30 Simplified response (Simple beam model)
15
0
Simplified response accounting for the bolt action
0 2 4 6 8 10 12 14 16 18 20 22
Deformation, ∆ (mm)

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
120
105
Fig. D.66 Specimen Weld_T1(ii).
Load, F (kN)
90
75
60
45
Actual response
30 Simplified response (Simple beam model)
15
0
Simplified response accounting for the bolt action
0 2 4 6 8 10 12 14 16 18 20 22
120
105
Fig. D.67 Specimen Weld_T1(iii).
Load, F (kN)
90
75
60
Deformation, ∆ (mm)
45
Actual response
30 Simplified response (Simple beam model)
15
0
Simplified response accounting for the bolt action
0 2 4 6 8 10 12 14 16 18 20 22
105
90
75
60
Fig. D.68 Specimen WT1.
Deformation, ∆ (mm)
45
30
Actual response
Simplified response (Simple beam model)
15
0
Simplified response accounting for the bolt action
0 2 4 6 8 10 12 14 16 18 20
Deformation, ∆ (mm)
261

Further developments on the T-stub model
262
Load, F (kN)
105
90
75
60
Fig. D.69 Specimen WT2A.
Load, F (kN)
45
30
Actual response
Simplified response (Simple beam model)
15
0
Simplified response accounting for the bolt action
0 2 4 6 8 10 12 14 16 18 20
105
90
75
60
Fig. D.70 Specimen WT2B.
Load, F (kN)
Deformation, ∆ (mm)
45
30
Actual response
Simplified response (Simple beam model)
15
0
Simplified response accounting for the bolt action
0 2 4 6 8 10 12 14 16 18 20
120
105
90
75
60
Fig. D.71 Specimen WT51.
Deformation, ∆ (mm)
Actual response
45
Simplified response (Simple
30
beam model)
15
0
Simplified response accounting
for the bolt action
0 1 2 3 4 5 6 7 8 9 10
Deformation, ∆ (mm)

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
175
150
125
100
Fig. D.72 Specimen WT7_M16.
Load, F (kN)
75
50
Actual response
Simplified response (Simple beam model)
25
0
Simplified response accounting for the bolt action
0 2 4 6 8 10 12 14 16 18 20
200
175
150
125
100
Fig. D.73 Specimen WT7_M20.
Load, F (kN)
Deformation, ∆ (mm)
75
Actual response
50 Simplified response (Simple beam model)
25
0
Simplified response accounting for the bolt action
0 2 4 6 8 10 12 14 16 18 20
240
210
180
150
120
Fig. D.74 Specimen WT57_M16.
Deformation, ∆ (mm)
Actual response
90
Simplified response (Simple
60
beam model)
30
0
Simplified response accounting
for the bolt action
0 1 2 3 4 5 6 7 8 9 10
Deformation, ∆ (mm)
263

Further developments on the T-stub model
264
Load, F (kN)
Fig. D.75 Specimen WT57_M20.
270
240
210
180
150
120
90 Actual response
60 Simplified response (Simple beam model)
30
0
Simplified response accounting for the bolt action
0 2 4 6 8 10 12 14 16 18 20 22 24
Deformation, ∆ (mm)
predictions from the simplified approach (bolt modelled as a single extensional
spring) and with a sophistication of the beam model. This sophistication consists
in assuming that the bolt effect can be reproduced with a set of extensional
springs along a certain length here taken as the bolt diameter. The figures
clearly show that such sophistication improved the agreement of the results
with the actual predictions, in most cases. Table D.18 gives the actual results
for resistance and deformation capacity and compare them with the aforementioned
two-dimensional approaches. Four alternative ultimate conditions are
imposed for the sophisticated approach. The determinant conditions however
are either fracture of the bolt at mid-section or cracking of the material at section
(1*) – values in bold.
D.7 Comparative graphs: influence of the distance m for the WP-T-stubs
The influence of the geometrical parameter m is evident in the graphs from
Figs. D.76-D.89. These graphs compare the actual response with the beam
model predictions and highlight the effect of m: increase on resistance and
stiffness (see also Table D.19) and decrease on ductility. Tables 6.13 and D.20
set out the predictions of deformation capacity and show that for the original
distance there is an average ratio between experiments and analytical predictions
of 1.81 (coefficient of variation of 0.34). If the “new” m is adopted, the
average ratio drops to 1.02 with a coefficient of variation of 0.47. In general,
for WP-T-stubs, the new value of m gives a better agreement with the experiments,
particularly for specimens made up of S355.

Simplified methodologies: assessment of the behaviour of T-stub connections
Table D.18 Comparison of the predicted values for ultimate resistance and
deformation capacity by applying the simple beam model and the
sophisticated beam model accounting for the bolt action.
Test
ID
T1
P1
P3
P5
P10
P12
P14
P15
P18
P
20
P
23
Num. or Exp.
results
Simple beam
model predictions
Beam model accounting
for bolt action
Fmax ∆u.0 Fmax ∆u.0 Fmax
Ratio
∆u.0
(kN) (mm) (kN) (mm) (kN) (mm)
103.99
91.76
95.41
130.20
76.79
154.06
86.57
171.08
266.57
225.94
346.01
8.70
10.77
10.17
3.63
32.75
24.22
24.15
18.02
26.07
4.06
5.22
114.45
103.25
111.96
123.76
50.25
122.43
79.54
153.17
215.75
246.14
408.62
16.76
25.34
24.17
4.63
32.40
19.67
20.49
16.48
20.18
4.03
5.24
Ratio
Ultimate
conditions
98.21 0.94 6.35 0.73 Bolt 1/4
104.04 1.00 8.54 0.98 Flange (1)
113.87 1.09 12.74 1.46 Bolt 1/2
129.79 1.25 20.69 2.38 Flange (1*)
85.78 0.93 8.79 0.82 Bolt 1/4
91.55 1.00 12.10 1.12 Flange (1)
103.27 1.13 19.88 1.85 Bolt 1/2
109.08 1.19 24.23 2.25 Flange (1*)
90.54 0.95 7.42 0.73 Bolt 1/4
94.37 0.99 9.11 0.90 Flange (1)
108.18 1.13 16.06 1.58 Bolt 1/2
116.14 1.22 20.65 2.03 Flange (1*)
117.91 0.91 2.88 0.79 Bolt 1/4
121.71 0.93 3.37 0.93 Bolt 1/2
154.84 1.19 11.82 3.25 Flange (1)
188.42 1.45 23.75 6.54 Flange (1*)
48.36 0.63 12.87 0.39 Flange (1)
52.29 0.68 17.72 0.54 Bolt 1/4
59.17 0.77 27.79 0.85 Flange (1*)
112.97 1.47 134.63 4.11 Bolt 1/2
119.29 0.77 8.02 0.33 Flange (1)
125.30 0.81 10.00 0.41 Bolt 1/4
149.02 0.97 19.22 0.79 Flange (1*)
186.85 1.21 37.05 1.53 Bolt 1/2
72.08 0.83 8.62 0.36 Flange (1)
75.04 0.87 10.31 0.43 Bolt 1/4
88.79 1.03 19.87 0.82 Flange (1*)
95.75 1.11 25.57 1.06 Bolt 1/2
142.15 0.83 5.46 0.30 Flange (1)
146.01 0.85 6.20 0.34 Bolt 1/4
187.94 1.10 16.16 0.90 Flange (1*)
199.91 1.17 19.47 1.08 Bolt 1/2
217.87 0.82 7.42 0.28 Flange (1)
244.55 0.92 11.69 0.45 Bolt 1/4
280.34 1.05 18.69 0.72 Flange (1*)
241.83 1.07 3.03 0.75 Bolt 1/4
247.76 1.10 3.51 0.87 Bolt 1/2
373.18 1.08 3.41 0.65 Bolt 1/4
399.89 1.16 4.00 0.77 Bolt 1/2
265

Further developments on the T-stub model
Table D.18 Comparison of the predicted values for ultimate resistance and
deformation capacity by applying the simple beam model and the
sophisticated beam model accounting for the bolt action (cont.).
Test
ID
Weld_
T1(i)
Weld_
T1(ii)
Weld_
T1(iii)
WT1
WT2A
WT2B
WT51
WT7
M16
WT7
M20
WT5
7_M
16
WT5
7_M
20
266
Num. or Exp.
results
Simple beam
model predictions
Beam model accounting
for bolt action
Fmax ∆u.0 Fmax ∆u.0 Fmax
Ratio
∆u.0
(kN) (mm) (kN) (mm) (kN) (mm)
92.02
102.75
113.10
91.91
86.82
97.88
97.08
132.34
145.72
173.64
241.71
10.85
8.01
6.22
14.32
17.98
13.09
3.96
11.47
9.12
5.88
15.98
84.80
101.03
114.21
85.60
75.16
92.51
112.86
140.79
141.17
196.62
196.77
18.27
20.00
18.82
18.51
16.51
19.18
9.43
17.78
17.87
9.13
8.36
Ratio
Ultimate
conditions
80.57 0.88 11.11 1.02 Bolt 1/4
84.55 0.92 14.00 1.29 Flange (1)
88.57 0.96 17.17 1.58 Flange (1*)
96.38 1.05 23.93 2.20 Bolt 1/2
88.34 0.86 8.39 1.05 Bolt 1/4
94.29 0.92 11.55 1.44 Flange (1)
104.18 1.01 17.61 2.20 Bolt 1/2
106.21 1.03 18.97 2.37 Flange (1*)
95.74 0.85 6.44 1.04 Bolt 1/4
103.47 0.91 9.57 1.54 Flange (1)
113.33 1.00 14.16 2.27 Bolt 1/2
125.23 1.11 20.46 3.29 Flange (1*)
82.72 0.90 10.40 0.73 Flange (1)
84.56 0.92 11.53 0.81 Bolt 1/4
90.37 0.98 15.67 1.09 Flange (1*)
111.79 1.22 40.67 2.84 Bolt 1/2
77.64 0.89 12.88 0.72 Flange (1)
79.60 0.92 14.44 0.80 Bolt 1/4
81.50 0.94 16.11 0.90 Flange (1*)
112.53 1.30 69.47 3.86 Bolt 1/2
87.31 0.89 9.42 0.52 Flange (1)
89.21 0.91 10.40 0.58 Bolt 1/4
102.67 1.05 19.83 1.10 Flange (1*)
114.33 1.17 31.74 1.77 Bolt 1/2
104.11 1.07 3.80 0.96 Flange (1)
111.82 1.15 5.07 1.28 Bolt 1/4
119.08 1.23 9.00 2.27 Flange (1*)
124.81 1.29 13.01 3.29 Bolt 1/2
142.96 1.08 10.13 0.88 Flange (1)
158.47 1.20 16.24 1.42 Flange (1*)
176.09 1.33 25.98 2.26 Bolt 1/4
157.51 1.08 8.27 0.91 Flange (1)
177.93 1.22 14.71 1.61 Flange (1*)
183.04 1.05 3.49 0.59 Flange (1)
212.19 1.22 8.35 1.42 Flange (1*)
230.02 1.32 15.13 2.57 Bolt 1/4
210.60 0.87 2.97 0.19 Flange (1)
233.41 0.97 7.56 0.47 Flange (1*)
310.09 1.28 45.68 2.86 Bolt 1/4

Simplified methodologies: assessment of the behaviour of T-stub connections
Table D.19 Prediction of axial stiffness by using the modified proposal for m.
Test ID Num./Exp. Standard m Modified m
stiffness ke.0 Ratio ke.0 Ratio
Weld_T1(i) 73.77 52.36 0.71 59.00 0.80
Weld_T1(ii) 89.12 68.82 0.77 85.26 0.96
Weld_T1(iii) 107.29 87.68 0.82 119.32 1.11
WT1g/h (av.) 71.08 71.61 1.01 84.68 1.19
WT2Aa/b (av.) 61.83 58.97 0.95 66.00 1.07
WT2Ba/b (av.) 79.75 82.62 1.04 103.73 1.30
WT4Aa/b (av.) 86.96 115.86 1.33 136.22 1.57
WT7_M16 60.73 60.73 1.00 71.39 1.18
WT7_M20 64.23 62.12 0.97 72.98 1.14
WT51a/b (av.) 52.90 64.08 1.21 75.47 1.43
WT53C 116.09 117.27 1.01 138.40 1.19
WT53D 137.70 120.60 0.88 142.93 1.04
WT57_M12 85.78 99.95 1.17 116.81 1.36
WT57_M20 150.96 109.09 0.72 128.83 0.85
Average 0.97 1.16
Coefficient of variation
0.19
0.18
Table D.20 Prediction of ultimate resistance and deformation capacity (WP-Tstubs)
by using the modified proposal for m.
Test ID
Num. or Exp. results Modified m
Fmax ∆u.0 Fmax Ratio ∆u.0 Ratio
(kN) (mm) (kN)
(mm)
Weld_T1(i) 92.02 10.85 83.42 0.91 14.57 1.34
Weld_T1(ii) 102.75 8.01 95.86 0.93 10.99 1.37
Weld_T1(iii) 113.10 6.22 108.05 0.96 8.46 1.36
WT1g/h (av.) 91.91 14.32 80.56 0.88 10.27 0.72
WT2Aa/b (av.) 86.82 17.98 74.12 0.85 13.23 0.74
WT2Ba/b (av.) 97.88 13.09 86.75 0.89 8.85 0.68
WT4Aa/b (av.) 103.26 4.33 127.24 1.23 9.36 2.16
WT7_M16 97.08 3.96 107.02 1.10 3.78 0.95
WT7_M20 98.90 4.24 108.12 1.09 3.49 0.82
WT51a/b (av.) 117.36 5.54 111.74 0.95 3.04 0.55
WT53C 132.34 11.47 134.63 1.02 10.74 0.94
WT53D 145.72 9.12 134.73 0.92 10.68 1.17
WT57_M12 121.87 4.33 162.92 1.34 5.38 1.24
WT57_M20 241.71 15.98 185.74 0.77 2.83 0.18
Average 0.99 1.02
Coefficient of variation
0.16
0.47
267

Further developments on the T-stub model
268
Load, F (kN)
120
105
Fig. D.76 Specimen Weld_T1(i).
Load, F (kN)
90
75
60
45
30
Actual response
Simplified response (Simple beam model)
15
0
Simplified response with new m
0 2 4 6 8 10 12 14 16 18 20 22
120
105
Fig. D.77 Specimen Weld_T1(ii).
Load, F (kN)
90
75
60
Deformation, ∆ (mm)
45
30
Actual response
Simplified response (Simple beam model)
15
0
Simplified response with new m
0 2 4 6 8 10 12 14 16 18 20 22
120
105
Fig. D.78 Specimen Weld_T1(iii).
90
75
60
Deformation, ∆ (mm)
45
Actual response
30
Simplified response (Simple beam model)
15
0
Simplified response with new m
0 2 4 6 8 10 12 14 16 18 20 22
Deformation, ∆ (mm)

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
105
90
75
60
Fig. D.79 Specimen WT1.
Load, F (kN)
45
30
Actual response
15
0
Simplified response (Simple beam model)
Simplified response with new m
0 2 4 6 8 10 12 14 16 18 20
105
90
75
60
Fig. D.80 Specimen WT2A.
Load, F (kN)
Deformation, ∆ (mm)
45
30
Actual response
15
0
Simplified response (Simple beam model)
Simplified response with new m
0 2 4 6 8 10 12 14 16 18 20
105
90
75
60
Fig. D.81 Specimen WT2B.
Deformation, ∆ (mm)
45
30
Actual response
15
0
Simplified response (Simple beam model)
Simplified response with new m
0 2 4 6 8 10 12 14 16 18 20
Deformation, ∆ (mm)
269

Further developments on the T-stub model
270
Load, F (kN)
Fig. D.82 Specimen WT4A.
Load, F (kN)
135
120
105
90
75
60
45
Actual response
30
Simplified response (Simple beam model)
15
0
Simplified response with new m
0 1 2 3 4 5 6 7 8 9 10 11 12
160
140
120
100
Fig. D.83 Specimen WT7_M16.
Load, F (kN)
80
Deformation, ∆ (mm)
60
Actual response
40
Simplified response (Simple beam model)
20
0
Simplified response with new m
0 2 4 6 8 10 12 14 16 18 20
160
140
120
100
Fig. D.84 Specimen WT7_M20.
80
Deformation, ∆ (mm)
60
Actual response
40
Simplified response (Simple beam model)
20
0
Simplified response with new m
0 2 4 6 8 10 12 14 16 18 20
Deformation, ∆ (mm)

Simplified methodologies: assessment of the behaviour of T-stub connections
Load, F (kN)
120
100
80
60
Fig. D.85 Specimen WT51.
Load, F (kN)
40
Actual response
20
0
Simplified response (Simple beam model)
Simplified response with new m
0 1 2 3 4 5 6 7 8 9 10
120
100
80
60
Fig. D.86 Specimen WT53C.
Load, F (kN)
Deformation, ∆ (mm)
40
Actual response
20
0
Simplified response (Simple beam model)
Simplified response with new m
0 1 2 3 4 5 6 7 8 9 10
120
100
80
60
Fig. D.87 Specimen WT53D.
Deformation, ∆ (mm)
40
Actual response
20
0
Simplified response (Simple beam model)
Simplified response with new m
0 1 2 3 4 5 6 7 8 9 10
Deformation, ∆ (mm)
271

Further developments on the T-stub model
272
Load, F (kN)
210
180
150
120
Fig. D.88 Specimen WT57_M12.
Load, F (kN)
90
60
Actual response
30
0
Simplified response (Simple beam model)
Simplified response with new m
0 1 2 3 4 5 6 7 8 9 10
280
240
200
160
Fig. D.89 Specimen WT57_M20.
Deformation, ∆ (mm)
120
80
Actual response
40
0
Simplified response (Simple beam model)
Simplified response with new m
0 2 4 6 8 10 12 14 16 18 20 22 24
Deformation, ∆ (mm)

PART III: MONOTONIC BEHAVIOUR OF BEAM-TO-COLUMN
BOLTED END PLATE CONNECTIONS
273

7 EXPERIMENTAL TESTS ON BOLTED END PLATE CONNEC-
TIONS
7.1 INTRODUCTION
An experimental investigation of eight statically loaded extended end plate
moment connections undertaken at the Delft University of Technology is described
in this chapter. It provides a better understanding of the behaviour of
this joint type up to collapse and complements the study on welded T-stubs reported
in Chapter 3.
The specimens were designed to confine failure to the end plate and/or
bolts without development of the full plastic moment capacity of the beam
(partial strength joint). The parameters investigated were the end plate thickness
and steel grade. The main objective was the analysis of the ultimate behaviour
of the components end plate in bending and bolts and eventually the
proposal of sound design rules for this elemental part within the framework of
the so-called component method. The description of this test programme and
results is given below. Comparisons with the code predictions [7.1] are also
drawn.
7.2 DESCRIPTION OF THE TEST PROGRAMME
7.2.1 Test details
The experimental programme essentially comprised four test details (two
specimens for each testing type) on the above joint configuration. Two main
parameters were varied in the four sets: the end plate thickness, tp and the end
plate steel grade. The specimens were fabricated from one column/beam set, as
detailed in Table 7.1. The steel grade specified for the beams was S355. Unfortunately,
due to a laboratory misunderstanding, steel grade S235 was ordered
instead. This brought a problem in terms of the beam resistance that was naturally
lower than expected. Therefore, for the critical cases, the beam flanges
were stiffened with continuous plates in order to increase the beam flange
thickness and minimize the chance of premature failure. End plates were connected
to the beam-ends by full strength 45º-continuous fillet welds. The fillet
welds were done in the shop in a down-hand position. The procedure involved
manual metal arc welding in which consumable electrodes were used. Basic,
soft, low hydrogen electrodes were used in the process. Hand tightened fullthreaded
M20 grade 8.8 bolts in 22 mm diameter drilled holes were employed
in all sets. Two different batches of bolts were employed. The first batch of
275

Monotonic behaviour of beam-to-column bolted end plate connections
bolts were employed in tests FS1a-b, FS2a-b and FS3a in both tension and
compression zones. The second batch of bolts were used to fasten the end plate
and the beam in the tension zone in the remaining tests.
The geometry of the specimens is depicted in Figs. 7.1-7.2. The column had
a section profile HE340M that was chosen so that it behaves almost as a rigid
element. In addition, for the available column, the clearance above and below
the end plate was less than 400 mm. However, since this is a rigid column, this
limitation proved not to be severe. Regarding the joint geometry, the top bolt
Table 7.1 Details of the test specimens.
Test # Column Beam End Plate
ID Profile Steel
grade
Profile Steel
grade
tp
(mm)
Steel
grade
FS1 2 HE340M S355 IPE300 S235 10 S355
FS2 2 HE340M S355 IPE300 S235 15 S355
FS3 2 HE340M S355 IPE300 S235 20 S355
FS4 2 HE340M S355 IPE300 S235 10 S690
hp = 400 Hc.up = 400
1200
276
Hc.low = 400
bc = 309
HE340M
hc = 377
tp = 10, 15, 20
5.5 ~ 6
3.5 ~ 4
Lstiffened ~ 500
ts ~ 10
IPE300
ts = 10
Lload = 1000 200
Lbeam = 1200
Fig. 7.1 Geometry of the specimens (dimensions in [mm]).
hb = 300
bb = 150

LX =
69.65
aw = 5.5 ~ 6
d0 =
22
aw = 3.5 ~ 4
Lcomp =
30.35
bp = 150
e = 30 w = 90 30
1 2
3 4
5 6
Experimental tests on bolted end plate connections
eX =
30
p = 90
p2-3 = 205
hp = 400
ecomp =
75
aw = 5
aw = 5
150
(a) Detail of the end plate. (b) Detail of the stiffener.
Fig. 7.2 Details of the specimens (dimensions in [mm]).
row corresponds to specimen WT7_M20 (refer to Chapter 3) from the former
test series on isolated T-stubs. All the end plate specimens were designed complying
with the Eurocode 3 requirements [7.1] so that the components end plate
and bolts in the tension zone were the determining factor of collapse.
7.2.2 Geometrical properties
The actual geometry of the various connection elements was recorded before
starting the test. For the various specimens the profiles and plates actual dimensions
and connection geometry are summarized in Table 7.2. These values
are given as an average value of the several measurements from each series.
Table 7.3 indicates the bolts measurements for each test.
7.2.3 Mechanical properties
7.2.3.1 Tension tests on the bolts
Two different batches of bolts were used in the experiments. Having performed
tests from series FS1 and FS2 and test FS3a, it was decided to use a different
batch of bolts, from another manufacturer as explained later in the text. Three
machined bolts from each group were tested in tension in order to determine
the mechanical properties of the bolt material, in accordance with ISO 898-
1:1999(E) [7.2]. The average properties are set out in Table 7.4.
300
277

Monotonic behaviour of beam-to-column bolted end plate connections
Table 7.2 Actual geometry of the connection (averaged dimensions, [mm]).
Test ID Column profile Stif.
278
hc bc tfc Hc.up Hc.low ts
FS1 175.00 219.00 10.76
FS2
FS3
376.00 307.50 40.21
174.50
177.50
219.50
216.50
10.50
10.46
FS4
174.50 219.50 10.42
Beam profile
hb bb tfb twb Lbeam Lload
FS1 300.45 150.50 10.76 7.20 1200.00 1002.50
FS2 301.40 149.60 10.67 7.01 1200.38 1000.25
FS3 301.46 149.75 10.57 7.03 1191.50 992.63
FS4 300.66 149.54 11.86 7.03 1218.75 991.88
End plate and connection geometry
hp bp tp e w
FS1 401.04 149.84 10.40 30.01 89.91
FS2 400.84 149.41 15.01 29.76 89.89
FS3 401.40 150.47 20.02 30.27 89.93
FS4 401.69 149.76 10.06 29.94 89.88
eX LX p p2-3 ecomp.
FS1 29.90 69.35 90.03 205.90 76.45
FS2 30.10 69.30 89.98 205.04 75.44
FS3 29.74 68.90 90.14 204.84 76.82
FS4 29.83 69.86 89.95 205.28 76.13
7.2.3.2 Tension tests of the structural steel
The test programme included two different steel grades for the end plate: S355
and S690. According to the European Standards EN 10025 [7.3] and EN 10204
[7.4], the steel qualities are S355J0 (ordinary steel) and N-A-XTRA M70
(high-strength steel for plates), respectively. For the beam profile, steel grade
S235JR was ordered. Table 7.5 summarizes the chemical composition of the
different steel grades.
The coupon tension testing of the structural steel material was performed
according to the RILEM procedures [7.5]. The average characteristics are set
out in Table 7.6. In this table the values for the Young modulus, E, the strain
hardening modulus, Est, the static yield and tensile stresses, fy and fu, the yield
ratio, ρy, the strain at the strain hardening point, εst, the uniform strain, εuni, and
the ultimate strain, εu are given. Note that for the 10 mm thickness end plates,
the structural steel is the same that had been used in the testing of the isolated
T-stub connections (cf. Chapter 3).

Experimental tests on bolted end plate connections
Table 7.3 Bolt hole clearance and length (dimensions in [mm]; H-tght:
Hand-tightening; Aft. clps.: after collapse).
Test
ID
#1 #2 #3 #4 #5 #6
d0 21.93 21.98 21.98 21.75 21.98 21.93
FS1a
Bolt
length
Initial
H-tght
Aft.
clps.
94.00
94.00
94.65
94.00
94.00
94.40
94.10
94.10
94.50
94.25
94.25
94.90
93.00
93.10
93.00
92.90
93.00
93.10
d0 22.05 22.00 22.03 22.05 22.10 21.90
FS1b
Bolt
length
Initial
H-tght
Aft.
clps.
94.00
94.00
94.95
94.25
94.25
96.00
94.40
94.40
95.40
94.05
94.05
94.85
93.15
93.15
93.00
93.20
93.20
93.15
d0 21.93 22.08 22.00 22.08 22.03 22.03
FS2a
Bolt
length
Initial
H-tght
Aft.
clps.
94.00
94.02
95.70
93.90
93.94
96.18
94.20
94.20
102.06
93.85
93.85
96.62
92.90
92.94
93.24
92.90
92.96
93.78
d0 22.00 21.93 22.00 21.98 22.00 21.95
FS2b
Bolt
length
Initial
H-tght
Aft.
clps.
93.90
93.90
95.16
94.30
94.40
97.02
93.90
93.90
101.30
94.12
94.12
96.52
92.86
92.94
93.28
92.78
92.90
93.04
d0 22.95 22.88 22.95 22.98 23.03 22.93
FS3a
Bolt
length
Initial
H-tght
Aft.
clps.
94.04
94.10
95.56
94.00
94.00
95.10
93.74
93.80
96.04
94.10
94.16
96.12
93.16
93.16
93.48
62.90
92.90
93.44
d0 22.05 21.90 22.00 22.03 21.95 22.03
FS3b
Bolt
length
Initial
H-tght
Aft.
clps.
92.54
92.54
95.30
92.52
92.52
95.00
92.56
92.56
95.25
92.50
92.50
99.22
92.78
93.00
93.24
93.14
93.14
93.24
d0 22.08 22.00 22.05 21.93 22.00 22.05
FS4a
Bolt
length
Initial
H-tght
Aft.
clps.
92.46
92.50
94.40
92.45
92.48
93.94
92.54
92.56
99.62
92.52
92.54
102.62
92.70
92.74
93.06
92.68
92.70
93.10
d0 22.03 22.08 21.98 22.00 21.98 22.03
FS4b
Bolt
length
Initial
H-tght
Aft.
clps.
92.40
92.42
94.16
92.38
92.40
94.82
92.32
92.34
100.94
92.38
92.42
100.26
93.04
93.06
93.26
93.06
93.08
93.38
279

Monotonic behaviour of beam-to-column bolted end plate connections
Table 7.4 Average characteristic values for the bolts.
Batch E (MPa) fy (MPa) fu (MPa) εu
1 223166 857.33 913.78 0.184
2 222982 854.31 916.81 0.156
Table 7.5 Chemical composition of the structural steels according to the
European standards.
% max. C Mn Si P S N CEV
S235JR 0.17 1.40 ⎯ 0.045 0.045 0.012 0.35
S355J0 0.20 1.60 0.55 0.040 0.045 0.009 0.40
N-A-XTRA M70 0.20 1.60 0.80 0.020 0.010 ⎯ 0.48
Table 7.6 Average characteristic values for the structural steels.
280
Specimen Steel
grade
End
plate
Beam
E
(MPa)
Est
(MPa)
fy
(MPa)
fu
(MPa)
tp = 10 S355 209856 2264 340.12 480.49 0.708
tp = 15 S355 208538 2901 342.82 507.85 0.675
tp = 20 S355 208622 2771 342.62 502.59 0.682
tp = 10 S690 204462 2495 698.55 741.28 0.940
Web S235 208332 1856 299.12 446.25 0.670
Flange S235 209496 1933 316.24 462.28 0.684
Specimen Steel
grade
εst εuni εu
End
plate
Beam
tp = 10 S355 0.015 0.224 0.361
tp = 15 S355 0.020 0.198 0.475
tp = 20 S355 0.017 0.196 0.457
tp = 10 S690 0.014 0.075 0.174
Web S235 0.016 0.235 0.464
Flange S235 0.016 0.235 0.299
7.2.4 Test arrangement and instrumentation
The main features of the test apparatus are illustrated in Figs. 7.3a-b. Concerning
the T arrangement depicted in Figs. 7.1-7.2, the actual connection was rotated
180º for practical reasons. The column was bolted to a reaction wall. The
reader should bear in mind that the goal of these tests was the study of the end
plate in the tension zone and therefore it had to be ensured that the column was
not governing any failure mode.
The load was applied by a 400 kN testing machine (hydraulic jack with
maximum piston stroke of ±200 mm), through a purpose-built device (Fig.
ρy

(a) Test apparatus (illustration
with specimen FS2a).
(c) Detail of the load application device.
Fig. 7.3 Equipment and test specimen.
Experimental tests on bolted end plate connections
(b) Detail of the beam and connection zone (illustration
with specimen FS1a).
7.3c) that was clamped to the beam at 200 mm from the free end. A beam
guidance device near the loading point was provided to prevent lateral torsional
buckling of the beam with the course of loading. For that purpose, a special device
located at 250 mm from the load point was attached to the specimens
(Figs. 7.3a-b).
The length of the beam was chosen to ensure a realistic stress pattern developed
at the connection, on one hand, and to ensure that fracture of the several
specimens, i.e. ultimate load, was attained with the specific testing machine.
The instrumentation plan is described in Figs. 7.4-7.6 below. The primary
requirements of the instrumentation were the measurement of the applied load,
the relevant displacements of the connection (e.g. vertical displacement of the
beam, horizontal displacement of the assembly end plate-tensile beam flange)
and bolt elongation. The record of all measurements was made automatically
with intervals of 1 second. The displacements were measured by means of
281

Monotonic behaviour of beam-to-column bolted end plate connections
LVDTs located as indicated in Fig. 7.4. These were attached to the elements
with special glue. Four LVDTs with an accuracy of 0.5% were used to measure
the beam vertical displacements (DT1-4). The range of these transducers is 480
mm for DT1, 425 mm for DT2 and 200 mm for both DT3 and DT4. The horizontal
displacements of the assembly end plate-beam flanges were measured
with 50 mm LVDTs with a precision of 0.5% (DT6-7, compression side, DT9-
10, tension side). In order to measure the end plate vertical displacement due to
elongation of the bolt holes, an additional 35 mm LVDT (DT5 – accuracy of
0.5%) was attached to the lower part of the end plate (tension side), as illustrated
in Fig. 7.4. To ensure that the displacements of the column could be neglected,
two LVDTs (DT8,11) were attached to the back side of the column.
These transducers could measure up to 1.5 mm displacement with an accuracy
of 0.5% as well. This was the precision of the electrical components connected
to the data logger.
The bolts deformations were measured with special measuring brackets,
MBs (horseshoe device), as common practice in the Stevin Laboratory of the
Delft University of Technology. These devices were attached to the bolts only
282
Top
DT8
DT11
HE340M
Bottom
Bolts 1/3/5
DT8/11
DT6/7
DT9/10
DT4
DT5
100 200
DT6/9
1000
IPE300
DT3 DT2 DT1
Load
300 300 300
DT5 DT4
DT7/10
DT3 DT2 DT1
Bolts 2/4/6
Fig. 7.4 Location of the displacement transducers.
Front
Back

Experimental tests on bolted end plate connections
Fig. 7.5 MBs 1,3 and LVDTs 6,9 (illustration with specimen FS4a).
10
19
SG3
SG2
SG1
Back
30 45 45 30
11 13
2 12 1
4 5 6
7 8
4
3
9
14
10
15
Top
3
6 5
30
90
30
250
19
19
Unidirectional strain gauges
xy strain gauges
30
45
13
11 2 12
4 5 6
7 8
14
4
15
9
10
5 19
(a) Sketch of the location of the strain gauges on the beam and end plate.
(b) Strain gauges located at the beam
and end plate extension.
Fig. 7.6 Location of the strain gauges.
30
90
30
(c) Strain gauges located at the end
plate.
283

Monotonic behaviour of beam-to-column bolted end plate connections
on the tension side. They could only measure up to 2 mm of displacement.
However, they were removed before collapse to prevent damage. Fig. 7.5
shows these devices for bolts 1 and 3.
Finally, strain gauges, SGs, TML (maximum strain 21000 µm/m) were
added to the end plate (back side) in the tension zone to provide insight into the
strain distribution in this zone (Fig. 7.6). In addition, the specimens were provided
with strain gauges at the top of the tension beam flange.
For good comparison of the results, all specimens used the same arrangement
for the location of the strain gauges and measuring devices.
7.2.5 Testing procedure
Before installation of the specimens into the testing rig, the dimensions of the
plates were recorded and the bolts were hand-tightened and measured. The
specimens were then placed into the machine and aligned. The bolts were fastened
with an ordinary spanner (45º turn) and measured.
In order to sketch the yield line patterns the specimens were painted with
chalk. The measurement devices and strain gauges were then connected. Electronic
records started and all the equipment was verified.
The specimens were subjected to monotonic tensile force, which was applied
to the beam as explained before. The tests were carried out under displacement
control with a constant speed of 0.02 mm/s up to collapse of the
specimens. The test itself then started with loading of the specimen up to
2/3Mj.Rd, which corresponds to the theoretical elastic limit. Mj.Rd is the full plastic
resistance and is determined according to Eurocode 3. Complete unloading
followed on and the specimen was then reloaded up to collapse. In this third
phase, the test was interrupted at the load levels corresponding to 2/3Mj.Rd,
Mj.Rd, at the knee-range and after this level each six minutes, equivalent to an
actuator displacement of 7.2 mm. The hold on of the test lasted for three minutes.
The testing procedures adopted for the full-scale tests were identical to
those described in Chapter 3 for the individual T-stubs.
Four collapse failure modes or a combination of those were observed in the
test: (i) weld cracking, (ii) plate cracking, (iii) bolt fracture and (iv) bolt nut
stripping (see Table 7.7). After collapse, the bolts were measured again (Table
7.3).
7.3 TEST RESULTS
The results presented in the following sections relate to the third phase of the
tests, after elimination of slippery and after settlement of the connecting parts.
The plotted graphs refer to the applied load, displacement and strain direct
readings and to the corresponding bending moment and deformations.
The bending moment, M, acting on the connection corresponds to the ap-
284

Experimental tests on bolted end plate connections
Table 7.7 Description of failure types.
Test ID Mode of failure
FS1a Weld failure of the assembly beam-end plate, both at the flange and
web sides.
FS1b Weld failure of the assembly beam-end plate, both at the flange and
web sides and plate cracking at opposite sides.
FS2a Nut stripping of bolt #4 and weld failure along the whole end plate
extension width but not at the inner part.
FS2b Nut stripping of bolts #1 and #4 with no plate cracking or weld failure.
FS3a Nut stripping of bolts #3 and #4 and some weld failure close to bolt
#3 but without development of a crack.
FS3b Nut stripping of bolt #3.
FS4a Fracture of bolt #4 and some weld failure at the end plate extension
close to bolt #1 but without development of a complete crack.
FS4b Fracture of bolt #3.
plied load, “Load” multiplied by the distance between the load application
point and the face of the end plate, Lload:
M = Load × Lload
(7.1)
The rotational deformation of the joint, Φ, is the sum of the shear deformation
of the column web panel zone, γ and the connection rotational deformation,
φ, that is defined as the change in angle between the centrelines of beam
and column, θb and θc. In these tests, the column hardly deforms as it behaves
as a rigid element. This statement will be validated later in the text. Then, both
γ and θc are nought and so:
Φ= φ = θb
(7.2)
The beam rotation is approximately given by (Fig. 7.4):
δDT1 δDT2δDT3
θb = arctan − θb. el = arctan − θb. el = arctan − θb.
el =
900 600 300
(7.3)
δ DT4
= arctan −θbel
.
100
where δDTi are the vertical displacements at LVDT DTi and θb.el is the beam
elastic rotation. The above expression disregards the effect of shear deforma-
tion in the beam and assumes that the vertical displacements of the end plate
are negligible, i.e. δ DT5 ≈ 0 . Some differences in the results from DT4 are expected
when compared to the remaining LVDTs since it is located closer to the
end plate. In this region, the beam theory is not valid and the stress distribution
is not smooth.
By using the above relationships, the M-φ curve of the connection can be
characterized. The main features of this curve are: resistance, stiffness and ro-
285

Monotonic behaviour of beam-to-column bolted end plate connections
tation capacity. In particular, for the different tests the following characteristics
are assessed [7.6]: the knee-range of the M-φ curve, the plastic flexural resistance,
Mj.Rd, the maximum bending moment, Mmax, the initial stiffness, Sj.ini, the
post-limit stiffness, Sj.p-l, the rotation corresponding to the maximum load level,
φ and the rotation capacity, φCd (see Figs. 1.28 and 7.7). The stiffness values
M max
are computed by means of linear regression analysis of the quasi-elastic
branches before and after the knee-range.
A brief summary of the observed collapse failure modes is given in Table
7.7 and some illustrations are given in Fig. 7.8. Failure occurred due to a variety
of reasons, but the collapse modes always involved the components end
plate and bolts in the tension zone.
286
Bending moment, M (kNm)
200
160
120
80
Mj.Rd
Sj.p-l
Knee-range
40
Sj.ini
0
Φ MRd Φ Xd
Φ Cd
0 10 20 30 40 50 60 70
Connection rotation φ (mrad)
Fig. 7.7 Moment-rotation characteristics from tests.
(i) General view. (ii) Detail: weld failure,
front side.
Mmax
(iii) Detail: bolts #2-#4
after failure (notice the
bending of bolt #2).
(a) Specimen FS1b.
Fig. 7.8 Illustration of the various failure types observed in the experiments.

(iv) Detail: end plate cracking (extension),
back side.
(a) Specimen FS1b (cont.).
Experimental tests on bolted end plate connections
(v) Elongation of the bolt holes
in the tension zone.
(i) General view of the end plate. (ii) Nut stripping of bolt #4
(column side).
(iii) Detail of the weld fracture in the tension
zone.
(iv) Detail of tension bolts
(bolt #3 nearly fractures).
(b) Specimen FS2a.
Fig. 7.8 Illustration of the various failure types observed in the experiments
(cont.).
287

Monotonic behaviour of beam-to-column bolted end plate connections
288
(i) Bolt #3.
(ii) Bolt #4.
(c) Specimen FS3a. (d) Specimen FS4b.
Fig. 7.8 Illustration of the various failure types observed in the experiments
(cont.).
7.3.1 Moment-rotation curves
As explained above, the M-φ curves for the different connections are obtained
from the beam vertical displacement readings and the applied load. For illustration,
Fig. 7.9 plots the load vs. vertical displacement of the beam for specimen
FS1a. This curve can be converted into a moment-“gross beam rotation” curve
by application of Eqs. (7.1) and (7.3) excluding θel, as shown in Fig. 7.10a for
the four LVDTs DT1-4. Examination of these four curves indicates a good
agreement of the results obtained for DT1-3 and some deviation for DT4.
These differences have already been explained earlier in the text. Therefore,
the results from DT1 are kept for further analysis. If now the beam elastic deformation
is subtracted from the “gross rotation” (see Eq. (7.3)), the connection
rotation can be completely characterized (Fig. 7.10b). This value is taken as
equal to the beam rotation because the column rotation, θc, can be disregarded
in comparison with θb (see Fig. 7.11) and also because the end plate vertical
deformation due to the bolt hole elongation can be neglected when compared to
the δDT1 (see Fig. 7.12). Note that for specimen FS1a the slippery at circa 110
kN has to be disregarded.
The M-φ responses for the eight connection details are reported in Fig. 7.13.
Almost identical responses are obtained for each set over the entire elastoplastic
range. This proves that the test procedure and the instrumentation setup
adopted for the programme were satisfactory. The main features of the eight
curves are summarized in Table 7.8. All characteristic values are referred to the
readings from LVDT DT1. In all cases, the knee-range domain of the curves is
alike for the same connection detail. The maximum resistance is also similar,

Total applied load (kN)
160
140
120
100
80
60
40
20
Experimental tests on bolted end plate connections
DT4 DT3
DT2
DT1
0
0 10 20 30 40 50 60 70
Vertical displacement of the beam (mm)
Fig. 7.9 Beam vertical displacement readings of LVDTs DT1-4 for specimen
FS1a.
Bending moment (kNm)
160
140
120
100
80
60
40
20
DT1
DT4
DT3
DT2
0
0 10 20 30 40 50 60 70 80 90 100
Beam rotation includ. elastic def. (mrad)
(a) Beam rotation computed from the displacement readings of LVDTs DT1-4
[arctan(δDTi/LDTi)].
Bending moment (kNm)
160
140
120
100
80
60
Beam rotation including the beam elastic
40
deformation
20
0
Connection rotation (equal to the beam
rotation)
0 10 20 30 40 50 60 70 80 90 100
Beam rotation θb (mrad)
(b) Beam rotation computed by means of Eq. (7.3) from the readings of DT1.
Fig. 7.10 Beam rotation for specimen FS1a.
289

Monotonic behaviour of beam-to-column bolted end plate connections
290
Total applied load (kN)
160
140
120
100
80
60
40
20
DT8 (compression
side)
(a) Column horizontal displacements.
Bending moment (kNm)
DT11 (tension
side)
0
-0.20 -0.16 -0.12 -0.08 -0.04 0.00 0.04 0.08 0.12 0.16 0.20
160
140
120
100
80
60
40
20
Horizontal displac. (column side) (mm)
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Column rotation θc (mrad)
⎛ ⎛ δDT8 + δ ⎞⎞
DT11
(b) Corresponding column rotations ⎜θc= arctan ⎜ ⎟⎟.
⎜ ⎜ hb − t ⎟⎟
⎝ ⎝ fb ⎠⎠
Bending moment (kNm)
160
140
120
100
80
60
40
20
0
0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.30
θc/θ b
(c) Ratio between column rotation and beam rotation.
Fig.7.11 Column rotation for specimen FS1a.

Total applied load (kN)
210
180
150
120
90
60
30
Experimental tests on bolted end plate connections
FS1a
FS4b
0
-7 -6 -5 -4 -3 -2 -1 0 1
Vertical displac. of the end plate (δ DT5) (mm)
Fig. 7.12 End plate vertical displacement for specimens FS1a and FS4b.
(a) Series FS1.
Bending moment (kNm)
Bending moment (kNm)
240
210
180
150
120
90
60
30
0
0 10 20 30 40 50 60 70 80 90 100 110 120
240
210
180
150
120
90
60
30
Connection rotation φ (mrad)
FS1a FS1b
0
0 10 20 30 40 50 60 70 80 90 100 110 120
Connection rotation φ (mrad)
FS2a FS2b
(b) Series FS2.
Fig. 7.13 Moment-rotation curves for the four test series.
291

Monotonic behaviour of beam-to-column bolted end plate connections
(c) Series FS3.
292
Bending moment (kNm)
Bending moment (kNm)
240
210
180
150
120
90
60
30
240
210
180
150
120
0
0 10 20 30 40 50 60 70 80 90 100 110 120
90
60
30
Connection rotation φ (mrad)
FS3a FS3b
0
0 10 20 30 40 50 60 70 80 90 100 110 120
Connection rotation φ (mrad)
FS4a FS4b
(d) Series FS4.
Fig. 7.13 Moment-rotation curves for the four test series (cont.).
though in series FS1 and FS3 some differences were observed. In series FS1,
experimental observations show that the welding quality in set FS1a is poor,
i.e. the welding procedure resulted in a glue weld instead of a burnt-in weld.
This induced premature cracking of the specimen. Regarding series FS3, the
discrepancies arise because different bolts were employed in the two sets and
also because there was a disturbance in test FS3a at a load level of 190 kN that
may have had some effect on the final results. In terms of rotational stiffness,
some differences arise, particularly for Sj.ini in the case of series FS1 and Sj.p-l
for series FS3. Identical values of the ratio Sj.ini/Sj.p-l are obtained for the four
test types. Exception is made for joint FS3a, which shows some disturbance in
the post-limit regime, and therefore the results are not reliable in this domain.
Now, in terms of maximum rotation, the values at Mmax are close for all sets
(again, the results for FS3a are not reliable in the post-limit domain), particularly
for specimen FS2. Higher deviations appear for φCd, especially for series

Experimental tests on bolted end plate connections
Table 7.8 Main characteristics of the moment-rotation curves.
Test ID
Resistance [kNm]
Knee-range Mj.Rd Mmax
FS1a 65-112 105.60 ( M Rd
5.81 mrad)
FS1b 68-120 109.30 ( M Rd
6.49 mrad)
FS2a 120-174 165.65 ( M Rd
7.08 mrad)
FS2b 117-181 170.22 ( M Rd
7.74 mrad)
FS3a 112-186 172.27 ( M Rd
7.47 mrad)
FS3b 122-200 192.66 ( M Rd
8.94 mrad)
FS4a 110-170 165.60 ( M Rd
10.24 mrad)
FS4b 110-170 163.52 ( M 9.53 mrad)
φ = 142.76
φ = 161.17
φ = 193.06
φ = 197.31
φ = 202.91
φ = 214.35
φ = 185.32
φ =
Rd
Stiffness [kNm/mrad]
187.67
Ratio
Sj.ini Sj.p-l
FS1a
2 18.19 ( R = 0.9717)
0.84 ( )
FS1b
2 16.84 ( R = 0.9921)
0.74 ( 2
0.9681)
FS2a
2 23.39 ( R = 0.9925)
0.84 ( 2
0.8611)
FS2b
2 22.00 ( R = 0.9968)
0.92 ( 2
0.8405)
FS3a
2 23.23 ( R = 0.9905)
1.81 ( 2
0.8629)
FS3b
2 21.56 ( R = 0.9972)
1.03 ( 2
0.8003)
FS4a
2 16.18 ( R = 0.9936)
0.78 ( 2
0.8004)
FS4b
2 17.15 ( R = 0.9956)
0.74 ( 2
0.8681)
2
R = 0.9384
Sj.ini/Sj.p-l
21.55
R = 22.78
R = 27.93
R = 23.91
R = 12.82
R = 20.96
R = 20.61
R =
Rotation [mrad]
23.29
φXd φCd Mmax
FS1a 18.23 68.91 ( Cd
127.71 kNm)
FS1b 20.00 111.22 ( Cd
70.29 kNm)
FS2a 17.45 82.88 ( Cd
66.00 kNm)
FS2b 19.17 60.89 ( Cd
147.93 kNm)
FS3a 13.75 42.76 ( Cd
108.16 kNm)
FS3b 18.25 48.74 ( Cd
153.10 kNm)
FS4a 19.25 61.69 ( Cd
150.25 kNm)
FS4b 18.33 64.24 ( 158.09 kNm)
φ
M φ = 61.55
M φ = 77.05
M φ = 41.72
M φ = 40.30
M φ = 25.00
M φ = 29.99
M φ = 37.70
M φ = 43.85
Cd
293

Monotonic behaviour of beam-to-column bolted end plate connections
FS1 and FS2. The differences that are observed in series FS1 have already been
explained above. For series FS2 and FS3, φCd is not well defined since it corresponds
to the beginning of final unloading of the test. No actual rupture was
observed in this case. The test was stopped because the deformations were already
too high and there was fear of damaging the equipment if the test went
on any further.
One connection from each set is now chosen for the purpose of a comparative
study. In all the cases, the assembly end plate-bolts is the main source of
connection deformability. Fig. 7.14 compares the rotational behaviour of the
four test types and shows an increase in resistance and rotational stiffness and a
loss of rotation capacity with the end plate thickness (FS1, FS2 and FS3). The
effect of the steel grade is identical (FS1 and FS4).
294
Bending moment (kNm)
240
210
180
150
120
90
60
30
FS3b
FS4b
FS2a
0
0 10 20 30 40 50 60 70 80 90 100 110 120
Connection rotation φ (mrad)
FS1b
Fig. 7.14 Comparison of the moment-rotation curves for the four test series.
7.3.2 Behaviour of the tension zone
7.3.2.1 End plate deformation behaviour
The most significant characteristic describing the overall end plate deformation
behaviour in the tension zone is the F-∆ response. The test setup does not allow
a direct measurement of the force at the component level but the information
gathered from LVDTs DT9 and DT10 permits a full characterization of the end
plate deformation behaviour. These transducers are attached to the beam flange
and they measure the gap between the end plate and the column flange (see
Fig. 7.4). As an example, Fig. 7.15a traces the moment-gap response obtained
for DT9 and DT10 for specimens FS1b and FS4a and indicates a good agreement
over the whole loading history. For comparison, Fig. 7.15b shows that
these measurements are also identical for the two sets from one test type.

Bending moment (kNm)
210
180
150
120
90
60
30
Experimental tests on bolted end plate connections
FS1b: DT9 FS1b: DT10
FS4a: DT9 FS4a: DT10
0
0 3 6 9 12 15 18 21 24 27 30 33
End plate (horiz.) deformation (δ DT9-10) (mm)
(a) Comparison of the responses for the two devices (DT9, DT10) for tests
FS1b and FS4a.
Bending moment (kNm)
180
160
140
120
100
80
60
40
20
0
FS1a FS1b
0 3 6 9 12 15 18 21 24 27 30 33
Horizontal displac. (tension side) (mm)
(b) Comparison of the responses for the two tests from series FS1 (deformations
from DT9).
Fig. 7.15 End plate deformation in the tension zone for several specimens.
Bending moment (kNm)
240
210
180
150
120
90
60
30
FS3b
FS4b
FS2a
FS1b
0
0 3 6 9 12 15 18 21 24 27 30 33
End plate (horiz.) deformation (δ DT9) (mm)
Fig. 7.16 Comparison of the moment-end plate deformation curves for the
four test series.
295

Monotonic behaviour of beam-to-column bolted end plate connections
Fig. 7.16 compares the end plate deformation behaviour for the four connection
details. The deformability of the end plate increases for smaller values
of tp and lower steel grades. This behaviour is identical to the connection rotation,
as expected, since the components end plate and bolts are the main
sources of connection deformability. Fig. 7.17 illustrates the evolution of the
end plate deformation response with the applied load for the specific case of
FS4b and Figs. 7.17d and 7.18 compare the collapse conditions for the four test
types.
A comparative analysis of the influence of the end plate deformability over
the connection rotational behaviour is plotted in the graph of Fig. 7.19. For series
FS2, FS3 and FS4 where the bolts mainly determine failure, either by fracture
or by stripping, the shape of the curves is identical. In series FS1 where
end plate cracking and weld fracture are engaged in the collapse mode, the
shape of the curve is slightly different. Even so, these curves clearly demonstrate
that the ratio between end plate deformation behaviour is higher for
lower end plate thickness values and lower steel grades.
(i) General view. (ii) Tension zone.
(a) Load = 80 kN (theoretical elastic limit; elastic branch of the M-φ curve).
(i) General view. (ii) Tension zone.
(b) Load = 120 kN (theoretical plastic resistance; knee-range branch of the M-φ
curve).
Fig. 7.17 Evolution of the end plate deformations until failure conditions for
test series FS4b.
296

Experimental tests on bolted end plate connections
(i) General view. (ii) Tension zone.
(c) Load = 162 kN (post-limit branch of the M-φ curve).
(i) General view. (ii) Tension zone.
(d) Load = 188 kN (maximum load attained during the test).
(i) General view. (ii) Tension zone.
(e) Collapse conditions.
Fig. 7.17 Evolution of the end plate deformations until failure conditions for
test series FS4b (cont.).
Finally, Fig. 7.20 shows an alternative procedure for computation of the
connection deformation from the readings of the horizontal LVDTs, in the
compression and tension zone of the end plate (e.g. specimen FS1a). As expected,
the agreement between both procedures is excellent.
297

Monotonic behaviour of beam-to-column bolted end plate connections
(a) Specimen FS1a. (b) Specimen FS2a. (c) Specimen FS3b.
Fig. 7.18 Comparison of the end plate deformations at failure conditions for
test series FS1-3.
298
Bending moment (kNm)
240
210
180
150
120
90
60
30
FS3b
FS2a
FS4b
FS1b
0
0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.30
Ratio δ DT9/φ (mm/mrad)
Fig. 7.19 Comparison of the ratio end plate deformation vs. connection rotation
for the four test series.
Bending moment (kNm)
160
140
120
100
80
60
40
Connection rotation as defined above
Connection rotation computed from DT9
20
0
Connection rotation computed from DT10
0 10 20 30 40 50 60 70 80 90 100
Connection rotation (mrad)
Fig. 7.20 Comparison of the moment-rotation curve for test FS1a by using alternative
definitions of connection rotation.

7.3.2.2 Yield line patterns
Experimental tests on bolted end plate connections
Figs. 7.21 and 7.22 depict the yield line patterns of the inner tension bolt #3 for
specimens FS1b and FS2b at collapse conditions. These patterns could be
sketched because the specimens were painted with chalk. Clearly, for series
FS1 the yielding of the end plate in this area spreads to the compression bolt,
whilst for FS2, with a thicker plate, there is a small amount of plasticity in the
end plate.
(a) Load = 93 kN. (b) Load = 151 kN. (c) Collapse
conditions.
Fig. 7.21 Yield line patterns around the inner tension bolt for different load
levels (e.g. specimen FS1b).
(a) Load = 130 kN. (b) Load = 188 kN. (c) Near collapse conditions.
Fig. 7.22 Yield line patterns around the inner tension bolt for different load
levels (e.g. specimen FS2b).
7.3.2.3 Bolt elongation behaviour
The experimental results demonstrate that the two rows of tension bolts carry
unequal forces (Fig. 7.23): the inner tension bolts carry a larger proportion of
the load than the outer bolts. This conclusion is also supported by the graphs
299

Monotonic behaviour of beam-to-column bolted end plate connections
shown in Fig. 7.24 that compare the ratio between the bolt elongation and the
gap end plate-column flange. This ratio increases for the inner tension bolts.
The graphs also highlight the influence of the bolt tension deformation on the
overall behaviour with the increase of tp and steel grade. This conclusion is in
line with the above observations.
300
Total applied load (kN)
210
180
150
120
90
60
MB1 MB2
30
0
MB3 MB4
0.00 0.15 0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50
(Tension) Bolt elongation (mm)
Fig. 7.23 Bolt elongation behaviour (e.g. specimen FS4b).
End pl. (hor.) def. (δ DT9) (mm)
14
12
10
8
6
4
2
FS1b
FS4b
FS2b
FS3a
0
0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.30
δ b/δ DT9 (mm/mm)
(a) Bolt #1.
Fig. 7.24 Comparison of the “nondimensional” bolt elongation behaviour for
the four specimen types.
7.3.2.4 Strain behaviour
This section illustrates some of the experimental strain results. Unfortunately,
the travel range of the gauges used for recording the strains was often exceeded
before the connection failure occurred and in many specimens, the gauges were
damaged in early stages of loading. In some cases, the strain gauges were not

(b) Bolt #2.
(c) Bolt #3.
End pl. (hor.) def. (δ DT9) (mm)
End pl. (hor.) def. (δ DT9) (mm)
End pl. (hor.) def. (δ DT9) (mm)
14
12
10
8
6
4
2
Experimental tests on bolted end plate connections
FS1b
FS4b
FS2b
FS3a
0
0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.30
14
12
10
8
6
4
2
FS1b
δ b/δ DT9 (mm/mm)
FS4b
FS2b
0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
14
12
10
8
6
4
2
FS1b
δ b/δ DT9 (mm/mm)
FS4b
FS2b
FS3a
0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
δ b/δ DT9 (mm/mm)
(d) Bolt #4.
Fig. 7.24 Comparison of the “nondimensional” bolt elongation behaviour for
the four specimen types (cont.).
FS3a
301

Monotonic behaviour of beam-to-column bolted end plate connections
attached correctly and consequently their results are not trustworthy.
Anyhow, some results can be retained for future comparisons. Fig. 7.25
shows the results obtained in different gauges (for their location, please refer to
Fig. 7.6). These results also allow an assessment of the yield line patterns
(hogging, SG11 and sagging yield lines, SG5, 7 and 9).
302
Total applied load (kN)
240
210
180
150
120
90
60
30
FS2a
FS3b
FS4b
FS1b
0
0 3000 6000 9000 12000 15000 18000 21000 24000
Strain (SG5) (µm/m)
(a) Strains at SG5, located at the end plate extension.
Total applied load (kN)
240
210
180
150
120
90
60
30
0
FS3b
FS1b
FS4b
FS2a
Limit of the strain gauges
Limit of the strain gauges
0 3000 6000 9000 12000 15000 18000 21000 24000
Strain (SG7) (µm/m)
(b) Strains at SG7, located at the inner end plate side, near the beam tension
flange.
Fig. 7.25 Comparison of some strain results obtained for the four specimen
types at different strain gauges.
7.4 DISCUSSION OF TEST RESULTS
Eurocode 3 gives quantitative rules for the prediction of the joint flexural plastic
resistance and initial rotational stiffness. These structural properties are
evaluated below by using the actual geometrical characteristics from Table 7.2

Total applied load (kN)
240
210
180
150
120
90
60
30
Experimental tests on bolted end plate connections
FS3b
FS4b
FS2a
0
0 3000 6000 9000 12000 15000 18000 21000 24000
Strain (SG9) (µm/m)
FS1b
(c) Strains at SG9, located at the inner end plate side, near the beam web.
Total applied load (kN)
240
210
180
150
120
90
60
30
Limit of the strain gauges
Limit of the strain gauges
0
-24000 -21000 -18000 -15000 -12000 -9000 -6000 -3000 0
Strain (SG11) (µm/m)
(d) Strains at SG11, located at the bolt axis (end plate extension).
Fig. 7.25 Comparison of some strain results obtained for the four specimen
types at different strain gauges (cont.).
and the mechanical properties from Tables 7.4 and 7.6. The recommendations
on rotation capacity are also verified to investigate if there is enough rotation
capacity according to the code. The provisions are compared with the test results.
7.4.1 Plastic flexural resistance
According to Eurocode 3, the joint plastic flexural resistance is evaluated by
means of Eq. (1.60). As the overall connection behaviour was dominated by
the end plate and bolts, the computation of Fti.Rd relies on the T-stub idealization
of the tension zone that can fail according to the three possible plastic collapse
mechanisms.
FS4b
FS1b
FS3b
FS2a
303

Monotonic behaviour of beam-to-column bolted end plate connections
Table 7.9 Evaluation of the resistance of the test specimens (the experimental
values correspond to the average of the two tests per connection
detail; Ratio = [Theory/Experiments]).
Test
ID
304
Row 1 Row 2
h1 Ft1.Rd Plastic h2 Ft2.Rd Plastic
Mj.Rd
(mm) (kN) mode (mm) (kN) mode (kNm)
Ratio
FS1 334.52 83.86 Type-1 244.49 202.34 Type-1 77.52 0.72
FS2 335.26 176.07 Type-1 245.28 297.87 Type-2 132.09 0.79
FS3 335.34 274.06 Type-2 245.20 389.01 Type-2 187.29 1.03
FS4 334.76 161.16 Type-1 244.81 287.94 Type-2 124.44 0.76
Application of the procedure detailed in §1.6.1.2 provides the results presented
in Table 7.9. It is worth mentioning that the predicted yield line patterns
(double curvature for the bolt row located at the end plate extension and side
yielding near the beam flange) are in line with the experimental observations
(cf. Figs. 7.22-7.23 for the inner bolt row, for instance). By comparing the code
predictions with the experiments, they are within the knee-range bounds but
below the experimental values of flexural resistance.
7.4.2 Initial rotational stiffness
The initial rotational stiffness was evaluated according to the Eurocode 3 procedure,
as explained in §1.6.1.1. For simplicity, z was taken as equal to the distance
from the centre of compression to a mid point between the two bolt rows
in tension [7.1].
Table 7.10 sets out the predicted values for the initial stiffness and compares
them with the experiments. The ratio between the predicted values and
the experiments shows that Eurocode overestimates this property. The differences
may derive from the fact that the expression as presented in the code was
calibrated for a certain range of joints. The particular joints that were tested
were not ‘balanced’, i.e. there was a much weaker component than the remaining
ones. This situation is unlikely to occur in common joints for which the expression
was calibrated.
7.4.3 Rotation capacity
The experimental values of rotation capacity and corresponding moment values
for the various tests are set out in Table 7.8. It can be easily seen that test FS1,
which employs a thinner end plate and steel grade S355, presents higher ductility
than the remaining tests.
Application of the Eurocode 3 guidelines to the characterization of the rota-

Experimental tests on bolted end plate connections
Table 7.10 Evaluation of the initial rotational stiffness of the test specimens
(the experimental values correspond to the average of the two tests
per connection detail; Ratio = [Theory/Experiments]).
Test ID keff.1 keff.2 keq
(kN/mm)
kcws kcwc
FS1 225.023 333.57 541.95 2718.64 4867.62
FS2 375.03 453.37 816.22 2717.60 4983.72
FS3 2453.12 496.04 942.50 2711.50 5052.06
FS4 202.18 315.65 500.25 2710.23 4857.34
Test ID z
(mm)
Sj.ini
(kNm/mrad)
Ratio
FS1 289.51 34.66 1.98
FS2 289.62 46.76 2.06
FS3 290.27 51.76 2.31
FS4 290.41 32.77 1.97
Table 7.11 Verification of the recommendations for rotation capacity.
Test ID tp
(mm)
Maximum tp
(mm)
FS1 10.40 11.80 Yes.
FS2 15.01 11.75 No.
FS3 20.02 11.76 No.
FS4 10.06 8.25 No.
tion capacity [7.1] – cf. §1.6.2 – shows that the first condition is guaranteed for
all specimens (the joint moment resistance is governed by the resistance of the
end plate in bending), whilst the second condition (Eq. (1.68)) is only fulfilled
for specimens FS1 (Table 7.11). Though these recommendations are only valid
for steel grades up to S460, they were also applied to series FS4 that includes
end plates from grade S690.
7.5 CONCLUDING REMARKS
Tests on eight extended end plate moment connections were conducted under
static loading. All specimens were designed to trigger failure in the end plate
rather than in the beam or the column. The following conclusions can be drawn
from the test programme:
1. The joint moment resistance increases with the increase of end plate thickness
and with the yield stress of the plate;
305

Monotonic behaviour of beam-to-column bolted end plate connections
2. The joint initial rotational stiffness also increases with the end plate thickness,
but the sensitivity to the thickness variation is not as noticeable as for resistance.
The steel grade has little influence if any on this property;
3. The joint post-limit rotational stiffness is identical for all specimens, i.e. the
variation with end plate thickness or steel grade is not significant;
4. The Eurocode 3 proposals give safe approaches for the prediction of the joint
resistance but overestimate the joint initial stiffness in this particular case;
5. The available rotation capacity and hence the joint ductility decreases with
the plate thickness (series FS1, FS2 and FS3) and with the plate steel grade
(FS1 and FS4);
6. In terms of the verification of sufficient rotation capacity, Eurocode 3 gives
safe criteria but perhaps too conservative [7.7]. For instance, in terms of overall
rotation capacity, specimens from series FS2 and FS4 exhibit rotation values of
40 mrad.
7.6 REFERENCES
[7.1] European Committee for Standardization (CEN). PrEN 1993-1-8:2003,
Eurocode 3: Design of steel structures, Part 1.8: Design of joints, Stage
49 draft, May 2003, Brussels, 2003.
[7.2] International Standard ISO 898-1:1999(E). Mechanical properties of
fasteners made of carbon steel and alloy steel – Part 1: Bolts, screws and
studs, August 1999, Switzerland, 1999.
[7.3] European Committee for Standardization (CEN). PrEN 10025:2000E:
Hot rolled products of structural steels, September 2000, Brussels, 2000.
[7.4] European Committee for Standardization (CEN). EN 10204:1995E: Metallic
products, October 1995, Brussels, 1995.
[7.5] RILEM draft recommendation. Tension testing of metallic structural
materials for determining stress-strain relations under monotonic and
uniaxial tensile loading. Materials and Structures; 23:35-46, 1990.
[7.6] Weynand K. Sicherheits-und Wirtsschaftlichkeitsuntersuchungen zur
anwendung nachgiebiger anschlüsse im stahlbau. PhD thesis (in German).
University of Aachen, Aachen, Germany, 1996.
[7.7] Girão Coelho AM, Bijlaard F, Simões da Silva L. Experimental assessment
of the ductility of extended end plate connections. Engineering
Structures (in print), 2004.
306

8 DUCTILITY OF BOLTED END PLATE CONNECTIONS
8.1 INTRODUCTION
The methodology developed in this chapter provides a characterization of the
full nonlinear M-Φ behaviour of bolted end plate connections. The assessment
of the available joint rotation is addressed in particular. Kuhlmann and Kühnemund
[8.1] assume that the available joint rotation should be taken as the total
joint rotation or rotation capacity, ΦCd. In the context of the component
method, for a direct computation of the joint rotation capacity the following
steps have to be fulfilled [8.2-8.3]: (i) the F-∆ curve of each joint component
up to failure is modelled, (ii) the weakest joint component, i.e. the component
with lower resistance, is identified, (iii) the plastic engagement of the remaining
components is determined, (iv) the global displacements of the individual
components at the level of maximum resistance are evaluated to finally (v) determine
ΦCd.
Literature suggests that most of the joint rotation in thin end plates comes
from the end plate deformation [8.4-8.5]. The tests described in Chapter 7 confirm
this statement. For really thin end plates, the end plate deformation would
be sufficient to characterize the M-Φ curve since it becomes the weakest joint
component. In general, extended end plate connections are characterized by the
participation of two or more components to the joint plastic deformation, as
highlighted by Faella et al. [8.2]. In the framework of the component method,
in this joint configuration the following sources of deformability for characterization
of the rotation capacity are identified (Fig. 8.1): column web in shear
(cws), column web in compression (cwc), column web in tension (cwt), column
flange in bending (cfb), end plate in bending (epb) and bolts in tension
(bt). Components beam web and flange in compression (bfc) and beam web in
tension (bwt) are not taken into account in the model since they basically provide
a resistance limitation [8.6]. Components column flange in bending, end
plate in bending and bolts in tension are modelled as equivalent T-stubs, as already
explained. The full M-Φ response is characterized from the F-∆ curve of
the joint components, which are assembled into an appropriate mechanical
model. Chapter 1 (§1.6) discusses alternative component models that are illustrated
in Fig. 8.2. If most of the joint rotation comes in fact from the subassembly
end plate-bolts, the several models yield identical solutions since the
only deformable components are the end plate in bending and the bolts in tension
(Fig. 8.3). Consequently, the component models illustrated above are
equivalent, as shown in Fig. 8.3. This is the case of the tested joints that were
reported in Chapter 7.
307

Monotonic behaviour of beam-to-column bolted end plate connections
308
cws
cwt
cwc
T-stub idealization
Fig. 8.1 Basic joint components of an extended end plate connection with
two bolt rows in tension.
z
(cws)
(cwc)
(cwt.1)
(cwt.2)
T-stubs (row 1)
(cfb.1)
(cfb.2)
(epb.1)
(epb.2)
T-stubs
(row 2)
(bt.1)
(bt.2)
Φ
Φ
M
bwt
bfc
M
(cwt.1)
(cwt.2)
z
T-stubs (row 1)
(cfb.1)
(cfb.2)
(epb.1)
(epb.2)
T-stubs
(row 2)
(cws) (cwc)
(a) Mechanical model adopted in Eurocode 3. (b) UC component model.
(cwt.1)
(cwt.2)
(cws) (cwc)
T-stubs (row 1)
(cfb.1)
(cfb.2)
(epb.1)
(epb.2)
T-stubs
(row 2)
(c) Innsbruck mechanical model.
Fig. 8.2 Alternative component models for analysis of the rotational behaviour
of an extended end plate connection (two bolt rows in tension).
(bt.1)
(bt.2)
Φ
Φ
M
(bt.1)
(bt.2)
Φ
Φ
M

Ductility of bolted end plate connections
The following sections address the characterization of the rotational behaviour
of extended end plate connections up to failure. The full M-Φ curve is derived
by using a computational tool, NASCon [8.7]. This software allows for a
multilinear definition of the deformation behaviour of components and uses the
spring model illustrated in Fig. 8.2b. Since ductility is such an important property
in a partial strength scenario, particular attention is given to this issue.
The available experimental tests (Chapter 7) were basically aimed at the investigation
of the end plate behaviour. Therefore, the proposed methodology is
illustrated and validated only for this connection type. However, from a theoretical
point of view, the procedure can be applied to any beam-to-column joint
configuration, as long as the F-∆ response of each component can be predicted
with sufficient accuracy. This research work focuses on those components
(cws)
(cwt.1)
(cwt.2)
(cfb.1)
(cfb.2)
(cwc)
(epb.1)
(epb.2)
(cws) (cwc)
(cwt.1)
(cwt.2)
(cws) (cwc)
(bt.1)
(bt.2)
(cwt.1)
(cwt.2)
Φ
Φ
(cfb.1)
(cfb.2)
M
(epb.1)
(epb.2)
(cfb.1)
(cfb.2)
(bt.1)
(bt.2)
(epb.1)
(epb.2)
(bt.1)
(bt.2)
Φ
Φ
M
Φ
Φ
M
T-stub (row 1)
(epb.1) (bt.1)
(epb.2) (bt.2)
T-stub (row 2)
Fig. 8.3 Equivalence of component models for analysis of the rotational behaviour
of tested joints.
Φ
Φ
M
309

Monotonic behaviour of beam-to-column bolted end plate connections
modelled by equivalent T-stubs. Chapter 3 describes some experiments performed
on WP-T-stubs. A three-dimensional FE model has been proposed in
Chapter 4 for the assessment of the F-∆ behaviour of this component. Chapter
6 proposes a simplified beam model for the assessment of the overall deformation
behaviour of individual T-stubs and also describes alternative simplified
methods recommended by other authors. These methodologies are used below
for characterization of the end plate behaviour.
8.2 MODELLING OF BOLT ROW BEHAVIOUR THROUGH EQUIVALENT T-
STUBS
The T-stub idealization of the tension zone of a connection consists is substituting
this zone for T-stub sections of appropriate effective length (Fig. 8.4).
These T-stub sections are connected by their flange to a rigid foundation (halfmodel)
and subjected to a uniformly distributed force acting in the web plate
[8.6]. The extension of the end plate and the portion between the beam flanges
are modelled as two separate equivalent T-stubs (Fig. 8.4). On the column side,
two situations have to be analysed: (i) the bolt rows act individually or (ii) the
bolt rows act in combination (Fig. 8.4).
To define the effective length, the complex pattern of yield lines that occurs
around the bolts is converted into a simple equivalent T-stub. This effective
length does not represent any actual length of the connection. The typical observed
yield-line pattern in thin end plates is shown in Figs. 8.5 and 8.6, for
two different cases: (i) end plate with one bolt row below the tension beam
flange and (ii) end plate with two bolt rows below the flush line, respectively.
For thicker end plates, the patterns may not develop fully as the bolt elongation
behaviour may govern the overall behaviour. For end plates with more than
one bolt row below the flush line, the cases of individual and combined bolt
row behaviour have to be taken into consideration, as illustrated in Fig. 8.6.
8.3 APPLICATION TO BOLTED EXTENDED END PLATE CONNECTIONS
The above procedures are applied to the extended end plate connections from
Chapter 7 that were tested monotonically up to failure. In these examples, the
tension zone on the end plate side that is idealized as a T-stub was always critical.
The remaining joint components behaved elastically until collapse.
8.3.1 Component characterization
The four joint configurations FS1-FS4 comprise two bolt rows in tension. For
each test detail, on the end plate side, two equivalent T-stubs are identified
(Figs. 8.4-8.5). For further reference, these two T-stubs are designated by “T-
310

eff.ep.r1
Bolt
row 1
End plate side
beff.cf.r(1+2)
Bolt row 2
Ductility of bolted end plate connections
Bolt rows 1
and 2
beff.ep.r2
Bolt row
1, individually
Bolt row
2, individually
Column side
Fig. 8.4 T-stub idealization of an extended end plate bolted connection with
two bolt rows in tension.
stub top” and “T-stub bottom”, for bolt rows 1 and 2, respectively (cf. Figs.
8.4-8.5). The characterization of these components in terms of F-∆ behaviour is
performed by means of four alternative procedures (Table 8.1): (i) experimentally,
(ii) numerically (three-dimensional FE model), (iii) analytically (simple
beam model) and (iv) simplified bilinear approximation proposed by Jaspart
[8.8]. The experimental results are not available for all equivalent T-stubs and
the numerical model is not implemented for all T-stubs, as shown in Table 8.1.
For the equivalent T-stubs top from joints FS1 and FS4, the tests on WT7_M20
and WT57_M20, respectively, provide an experimental F-∆ curve that can be
beff.fc.r1
beff.fc.r2
311

Monotonic behaviour of beam-to-column bolted end plate connections
312
Bolt row 1 beff .1 r = bep
2
Bolt row 2 b . 2=
αm
eff r ep
Hogging yield-line
Sagging yield-line
(a) Plot. (b) Illustration: spec. FS1b.
Fig. 8.5 Typical yield-line pattern in thin extended end plates with two bolt
rows in tension.
p2-3
Bolt row 1
Bolt row 2
Hogging yield-line
Sagging yield-line
p2-3
beff.r1
acting in
combination
Influence of
bolt row 2
(0.5beff.r2 + 0.5p)
beff.r(2+3)
Influence of
bolt row 3
(0.5beff.r3 + 0.5p)
Fig. 8.6 T-stub idealization of an extended end plate with three bolt rows in tension
with the bolts below the tension beam flange acting in combination.

Ductility of bolted end plate connections
Table 8.1 Alternative procedures for characterization of the T-stub response.
Test ID Equivalent
Characterization procedures
T-stub Experimental Numerical Beam Jaspart
model approximation
Top �
� � �
FS1
(WT7_M20)
Bot. ⎯ ⎯ � �
FS2
Top
Bot.
⎯
⎯
⎯
⎯
�
�
�
�
FS3
Top
Bot.
⎯
⎯
⎯
⎯
�
�
�
�
Top �
⎯ � �
FS4
(WT57_M20)
Bot. ⎯ ⎯ � �
used for component characterization. The individual T-stub specimens do not
correspond exactly to the equivalent T-stubs top as the bolt properties are different.
However, no major differences are expected. For application of the recommendations
of Jaspart [8.8], the bolt deformability is associated to that of
the end plate.
The effective length of the different components is defined according to
Eurocode 3 [8.6] and is summarized in Table 8.2. The actual geometric properties
of the joints are used (Table 7.2). Figs. 8.7-8.10 illustrate the T-stub responses
for the various configurations and with the alternative methodologies.
Table 8.3 sets out the predictions of ultimate resistance and deformation capacity
of the above equivalent T-stubs, as ascertained by the different procedures.
The experimental results correspond in fact to experimental failure (see Figs.
8.7a and 8.10a). Concerning the numerical predictions for the equivalent Tstub
top for joint FS1, the values that are indicated in the table do not account
for any reduction of the failure ductility of the HAZ (see also §5.4).
The graphs in Figs. 8.7-8.10 also plot the experimental end plate deformation
behaviour, which is obtained directly from the measurement of the displacement
of the tension beam flange with the course of loading. The corresponding
force level is evaluated indirectly, Ft = M/z, whereby z is the lever
arm determined from Eq. (1.59). In these graphs, this force Ft acting at the
level of the tension beam flange was divided equally by the two bolt rows. This
procedure gives a reasonable agreement with the predictions for the T-stub top
but deviates from the predicted behaviour for the T-stub bottom in the same
case (e.g. specimen FS2, Fig. 8.8). In fact, the division of the tensile force by
the two bolt rows modelled as two equivalent T-stubs seems more appropriate
for the top T-stub, rather than the bottom T-stub. The equivalent T-stub top
shares the tensile beam flange whereas the T-stub bottom shares the beam web.
313

Monotonic behaviour of beam-to-column bolted end plate connections
Therefore, the force acting at the web of the T-stub top is directly related to the
tensile force Ft. This is not true for the bottom T-stub. Furthermore, the assumption
of an equal division of Ft by the two bolt rows is questionable. Consequently,
the graphs that were traced are merely illustrative and should be regarded
as such.
The experimental deformation of the end plate at the tensile beam flange
level is obtained from the readings of the LVDTs. Table 8.3 indicates these
values at failure (in bold). They are directly related to the equivalent T-stub top
Table 8.2 Effective length of the equivalent T-stubs.
beff
Test ID
(mm) FS1 FS2 FS3 FS4
T-stub top 74.92 74.71 75.24 74.88
T-stub bot. 205.77 202.67 202.73 206.42
(a) T-stub top.
314
Fep.r1 (kN)
Fep.r2 (kN)
270
225
180
135
90
End plate deformation (exp.)
Exp. results WT7_M20
45
0
Numerical FE results
Beam model
Jaspart approximation
0 2 4 6 8 10 12 14 16 18 20
400
350
300
250
200
∆ep.r1 (mm)
150
100
.
End plate deformation (exp.)
Beam model
50
0
Jaspart approximation
0 2 4 6 8 10 12 14 16 18 20
(b) T-stub bottom.
Fig. 8.7 Equivalent T-stubs for joint FS1.
∆ep.r2 (mm)

(a) T-stub top.
Fep.r1 (kN)
Fep.r2 (kN)
350
300
250
200
Ductility of bolted end plate connections
150
100
End plate deformation (exp.)
Beam model
50
0
Jaspart approximation
0.0 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 13.5 15.0
700
600
500
400
∆ep.r1 (mm)
300
200
.
End plate deformation (exp.)
100
0
Beam model
Jaspart approximation
0.0 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 13.5 15.0
(b) T-stub bottom.
Fig. 8.8 Equivalent T-stubs for joint FS2.
Fep.r1 (kN)
600
500
400
300
∆ep.r2 (mm)
200
End plate deformation (exp.)
100
0
Beam model
Jaspart approximation
0 1 2 3 4 5 6 7 8 9 10 11 12
(a) T-stub top.
Fig. 8.9 Equivalent T-stubs for joint FS3.
∆ep.r1 (mm)
315

Monotonic behaviour of beam-to-column bolted end plate connections
316
Fep.r2 (kN)
900
800
700
600
500
400
300
.
200
End plate deformation (exp.)
100
0
Beam model
Jaspart approximation
0 1 2 3 4 5 6 7 8 9 10 11 12
∆ep.r2 (mm)
(b) T-stub bottom.
Fig. 8.9 Equivalent T-stubs for joint FS3 (cont.).
(a) T-stub top.
Fep.r1 (kN)
Fep.r2 (kN)
350
300
250
200
150
End plate deformation (exp.)
100
Exp. results WT57_M20
Beam model
50
0
Jaspart approximation
0.0 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 13.5 15.0 16.5
480
400
320
240
∆ep.r1 (mm)
160
.
End plate deformation (exp.)
80
0
Beam model
Jaspart approximation
0.0 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 13.5 15.0 16.5
∆ep.r2 (mm)
(b) T-stub bottom.
Fig. 8.10 Equivalent T-stubs for joint FS4.

Ductility of bolted end plate connections
Table 8.3 Assessment of the ultimate conditions of the equivalent T-stubs by
means of the proposed alternative characterization procedures.
Test ID Equiva-
Characterization procedures
lent Experimental Numeri- Beam Jaspart
T-stub
cal model approx.
Evaluation of Fep.ri.u (kN)
FS1
Top
Bot.
105.29
⎯
177.53
⎯
137.80
360.18
137.68
275.70
FS2
Top
Bot.
⎯
⎯
⎯
⎯
316.00
375.79
273.52
366.47
FS3
Top
Bot.
⎯
⎯
⎯
⎯
526.93
865.40
324.28
448.49
FS4
Top
Bot.
207.97
⎯
⎯
⎯
182.99
439.82
195.17
310.90
Evaluation of ∆ep.ri.u (kN)
FS1
Top
Bot.
27.42
⎯
9.35
⎯
12.68
⎯
9.35
10.20
7.04
4.62
FS2
Top
Bot.
14.55
⎯
⎯
⎯
⎯
⎯
8.87
10.83
5.87
4.83
FS3
Top
Bot.
11.79
⎯
⎯
⎯
⎯
⎯
11.21
10.69
3.77
3.77
FS4
Top
Bot.
16.03
⎯
11.76
⎯
⎯
⎯
4.02
7.53
4.39
5.34
deformation capacity. The predictions do not compare well to the experiments
as they clearly underestimate the deformation capacity, particularly for the
thinner end plates (ratios between the beam model predictions and the actual
results from the LVDTs range from 3 to 4 for FS1 and FS4). For the thicker
end plates the agreement improves considerably. In fact, for specimen FS3 the
beam model predictions are quite accurate.
The nondimensional analysis of these equivalent T-stubs, at the top bolt
row, at failure, i.e. in terms of the component ductility index, ϕep.r1, is summarized
in Table 8.4 (BM: beam model; JBA: Jaspart approximation; Num: Numerical
results for T-stub top and beam model for T-stub bottom; Exp: Experimental
results for T-stub top and beam model for T-stub bottom). These
indexes are evaluated from Eq. (1.39). The values in italic correspond to the ratios
to the experimental results for the end plate deformation, at the beam
flange level. Generally speaking, the predictions given by the beam model are
good, showing a pronounced underestimation for FS4, which uses S690, and a
clear overestimation for FS3. The average error is 14% but the coefficient of
variation is significant (0.75). Jaspart [8.8], on the other hand, gives estimations
with an average error of 25% but the scatter of results is lower, with a co-
317

Monotonic behaviour of beam-to-column bolted end plate connections
efficient of variation of 0.26. The experimental results for the single T-stub are
available for specimens FS1 (WT7_M20) and FS4 (WT57_M20). The corresponding
indexes show some deviations from the actual joint results.
The results just described are again analysed in the following sections in
order to establish some criteria regarding the ductility requirements for the
overall joint behaviour.
Table 8.4 Evaluation of the equivalent “T-stub top” component ductility index
(characterization of the T-stubs for evaluation of the analytical
response: BM – beam model, JBA – Jaspart bilinear approximation,
Num – numerical FE model, Exp – T-stubs top characterized
experimentally).
ϕep.r1
Test ID
Average Coeff.
FS1 FS2 FS3 FS4
var.
Experimental 27.98 15.99 16.15 11.06 ⎯ ⎯
BM
18.33
(0.66)
13.86
(0.87)
25.48
(1.58)
3.72
(0.34) 0.86 0.75
JBA
20.71
(0.74)
16.31
(1.02)
11.42
(0.71)
6.01
(0.54) 0.75 0.26
Num
23.92
(0.86)
⎯ ⎯ ⎯
⎯ ⎯
Exp
18.33
(0.66)
⎯ ⎯ 15.08
(1.36) 1.01 0.50
Analytical
8.3.2 Evaluation of the nonlinear moment-rotation response
The full M-Φ joint response is evaluated using the software NASCon [8.7].
This software is a computational implementation of the component method.
The model file is written by means of the user-friendly “Connection Assistant”
tool. All the details of the joint and joint components are specified in this file
(see Fig. 8.11 for illustration). The multilinear component behaviour is input in
this file. The model is then imported by NASCon to generate the M-Φ curve
(Fig. 8.12). A displacement control-based strategy was selected (Fig. 8.13). Finally,
the overall M-Φ curve can be visualized (Fig. 8.14).
The various curves are shown in the graphs from Figs. 8.15-8.18 and are
compared with the experiments. The graphs trace the responses obtained in
NASCon for the different characterization processes described in the previous
section. The critical component is also indicated in the graphs as well as the
governing part (flange or bolt). Whenever the components are characterized
with the bilinear approximation proposed by Jaspart [8.8], the critical failure
mode at ultimate conditions (1, 2 or 3) is indicated. Note that for different
characterization processes, the determinant T-stub for rotation capacity can
change (e.g. joint FS1 and the beam model or the bilinear approximation pro-
318

Ductility of bolted end plate connections
Fig. 8.11 Modelling of the connection and component behaviour (e.g. FS1).
Fig. 8.12 Model loading (e.g. FS1).
319

Monotonic behaviour of beam-to-column bolted end plate connections
Fig. 8.13 NASCon strategy selection and prescribed loading (e.g. FS1).
Table 8.5 Evaluation of initial stiffness (experimental results correspond to
the average results of the two tests).
Sj.ini
Test ID
Average Coeff.
(kNm/mrad) FS1 FS2 FS3 FS4
var.
Experimental 17.52 22.69 22.39 16.67 ⎯ ⎯
Eurocode 3
34.66
(1.98)
46.76
(2.06)
51.76
(2.31)
32.77
(1.97) 2.08 0.08
BM
30.78
(1.76)
45.26
(1.99)
54.78
(2.45) 1.96 1.96 0.18
JBA
34.45
(1.97)
47.65
(2.10)
53.23
(2.38) 2.10 2.10 0.10
Num
30.29
(1.73)
⎯ ⎯ ⎯
⎯ ⎯
Exp
29.51
(1.68)
⎯ ⎯ 42.47
(2.55) 2.12 0.29
Analytical
posed by Jaspart for characterization of the T-stubs – Figs. 8.15a-b).
Table 8.5 summarizes the characteristics of the curves in terms of initial
stiffness. Again, the values in italic correspond to the ratio to the experiments.
320

Ductility of bolted end plate connections
(a) Behaviour of component T-stub top (which determines ultimate conditions).
(b) Behaviour of component T-stub bottom.
Fig. 8.14 Moment-rotation curve (e.g. FS1).
321

Monotonic behaviour of beam-to-column bolted end plate connections
322
Bending moment (kNm)
180
160
140
120
100
80
FS1a
60
FS1b
40
20
0
NASCon prediction (T-stub
top critical - flange)
0 10 20 30 40 50 60 70 80 90 100 110 120
Connection rotation φ (mrad)
(a) Equivalent T-stubs characterized by means of the beam model.
Bending moment (kNm)
180
160
140
120
100
80
FS1a
60
FS1b
40
20
0
NASCon prediction (T-stub
bottom critical - mode 2U)
0 10 20 30 40 50 60 70 80 90 100 110 120
Connection rotation φ (mrad)
(b) Equivalent T-stubs characterized by means of the Jaspart bilinear model.
Bending moment (kNm)
180
160
140
120
100
80
60
FS1a
FS1b
40
20
0
NASCon prediction (T-stub
top critical - flange)
0 10 20 30 40 50 60 70 80 90 100 110 120
Connection rotation φ (mrad)
(c) Equivalent T-stub top characterized numerically (three-dimensional model).
Fig. 8.15 Moment-rotation curve for joint FS1.

Bending moment (kNm)
Ductility of bolted end plate connections
180
160
140
120
100
80
FS1a
60
FS1b
40
20
0
NASCon prediction (T-stub
top critical - flange)
0 10 20 30 40 50 60 70 80 90 100 110 120
Connection rotation φ (mrad)
(d) Equivalent T-stub top characterized experimentally.
Fig. 8.15 Moment-rotation curve for joint FS1 (cont.).
Bending moment (kNm)
240
210
180
150
120
FS2a
90
60
FS2b
30
0
NASCon prediction (T-stub
top critical - flange)
0 10 20 30 40 50 60 70 80 90 100 110 120
Connection rotation φ (mrad)
(a) Equivalent T-stubs characterized by means of the beam model.
Bending moment (kNm)
240
210
180
150
120
FS2a
90
60
FS2b
30
0
NASCon prediction (T-stub
top critical - mode 2U)
0 10 20 30 40 50 60 70 80 90 100 110 120
Connection rotation φ (mrad)
(b) Equivalent T-stubs characterized by means of the Jaspart bilinear model.
Fig. 8.16 Moment-rotation curve for joint FS2.
323

Monotonic behaviour of beam-to-column bolted end plate connections
324
Bending moment (kNm)
400
350
300
250
200
FS3a
150
100
FS3b
50
0
NASCon prediction (T-stub
bottom critical - bolt)
0 10 20 30 40 50 60 70 80 90 100 110 120
Connection rotation φ (mrad)
(a) Equivalent T-stubs characterized by means of the beam model.
Bending moment (kNm)
240
210
180
150
120
FS3a
90
60
FS3b
30
0
NASCon prediction (T-stub
top critical - mode 2U)
0 10 20 30 40 50 60 70 80 90 100 110 120
Connection rotation φ (mrad)
(b) Equivalent T-stubs characterized by means of the Jaspart bilinear model.
Fig. 8.17 Moment-rotation curve for joint FS3.
Bending moment (kNm)
210
180
150
120
90
60
FS4a
FS4b
30
0
NASCon prediction (T-stub
top critical - flange)
0 10 20 30 40 50 60 70 80 90 100 110 120
Connection rotation φ (mrad)
(a) Equivalent T-stubs characterized by means of the beam model.
Fig. 8.18 Moment-rotation curve for joint FS4.

Bending moment (kNm)
210
180
150
120
90
60
Ductility of bolted end plate connections
FS4a
FS4b
30
0
NASCon prediction (T-stub
top critical - mode 1U)
0 10 20 30 40 50 60 70 80 90 100 110 120
Connection rotation φ (mrad)
(b) Equivalent T-stubs characterized by means of the Jaspart bilinear model.
Bending moment (kNm)
210
180
150
120
90
60
FS4a
FS4b
30
0
NASCon prediction (T-stub
top critical - flange and bolt)
0 10 20 30 40 50 60 70 80 90 100 110 120
Connection rotation φ (mrad)
(c) Equivalent T-stub top characterized experimentally and T-stub bottom
characterized by means of the beam model.
Fig. 8.18 Moment-rotation curve for joint FS4 (cont.).
In general, the analytical predictions overestimate the initial stiffness in comparison
with the experiments, Sj.ini, (e.g. specimen FS1 – Sj.ini.Exp = 17.52
kNm/mrad, Sj.ini.BM = 30.78 kNm/mrad = 1.76 Sj.ini.Exp). This is quite straightforward
from the statistical analysis of the ratios to the experiments also presented
in Table 8.5 in italic.
The examination of the curves also shows that the analytical predictions for
resistance can also be slightly overestimated for some specimens, particularly
in the plastic domain (e.g. FS3, Fig. 8.17) though for thinner end plates the predictions
are good (e.g. FS1, FS4, Figs. 8.15 and 8.18).
The rotation capacity is clearly underestimated by the analytical methods,
even for the cases of FS1 and FS4 with the experimental component characterization.
Table 8.6 sets out the rotation predictions (experimental and analytical;
values in italic represent the ratio to the experimental values). Experimen-
325

Monotonic behaviour of beam-to-column bolted end plate connections
tally, two rotation values were evaluated: the rotation corresponding to maximum
load level, Φ M , and the rotation capacity, ΦCd (see also Table 7.8).
max
Analytically, the rotation capacity is attained when the first component reaches
failure. The experimental values in Table 8.6 are the averaged values between
the tests for each configuration, except for FS1 and FS3 for which the value of
tests “b” are adopted. This table also indicates the critical component for each
methodology (EPX: cracking at the extension of the end plate; BNSo+i: bolt
nut stripping of the outer and inner bolt; BNSi: bolt nut stripping of the inner
bolt; BTi: inner bolt in tension; Tt-fl: T-stub top, flange; Tb-b: T-stub bottom,
bolt; Tt-fl+b: T-stub top, flange and bolt; 1U: mode 1 critical at ultimate conditions;
2U: mode 2 critical at ultimate conditions).
The statistical investigation of the results shows that the application of the
beam model for the characterization of the individual T-stubs provides an average
ratio to the experiments of 0.40 with a coefficient of variation of 0.58. The
predictions obtained from application of Jaspart’s approximation [8.8] yield a
lower value for the average ratio but also a lower coefficient of variation. Nevertheless,
when both approaches are compared in terms of failure predictions, the
beam model gives a better agreement with the experimental observations.
The joint ductility properties are further analysed in the following sections.
Table 8.6 Comparison of the predictions of rotation capacity of the various
joints and failure modes.
φCd
Test ID
Average Coeff.
(mrad) FS1 FS2 FS3 FS4
var.
Experimental
111.22
EPX
71.89
BNSo+i
48.74
BNSi
62.97
BTi
⎯ ⎯
29.20 28.80 35.00 13.50
BM (0.26) (0.40) (0.72) (0.21) 0.40 0.58
Tt-fl Tt-fl Tb-b Tt-fl
20.96 19.44 13.52 14.56
JBA (0.19) (0.27) (0.28) (0.23) 0.24 0.17
2U 2U 2U 1U
39.84 ⎯ ⎯ ⎯ ⎯ ⎯
Num (0.36)
Tt-fl
29.52 ⎯ ⎯ 36.80
Exp (0.27)
(0.58) 0.43 0.52
Tt-fl Tt-fl+b
Analytical
8.3.3 Evaluation of the rotation capacity according to other authors
Having discussed the results obtained from the author’s methodology in terms
326

Ductility of bolted end plate connections
of predictions of rotation capacity, the proposals from other researchers are
now analysed. The verifications on ductility requirements for these specimens
according to Eurocode 3 have already been carried out in Chapter 7. The main
conclusions are summarized in Table 8.7.
Three alternative procedures for evaluation of the rotation capacity are illustrated.
These procedures were proposed by Adegoke and Kemp [8.5], for
thin end plates, Beg et al. [8.3] and Zoetemeijer [8.9]. This latter method is restricted
to those cases where type-2 plastic failure mode is critical and consequently
it is only validated by specimen FS3, for which the plastic failure mode
of both equivalent T-stubs is of type-2. The three methodologies have been described
in Chapter 1, §1.6.2. Table 8.8 sets out the main results for the above
procedures. In general, the rotation capacity is underestimated.
The application of the methodology proposed by Adegoke and Kemp [8.5]
requires the definition of the location of the neutral axis of the connection at
plastic and ultimate conditions (cf. §1.6.2 and references [8.5,8.10]). This location
was defined from the results obtained through application of the UC mechanical
model. This method reflects the tendency observed in the experiments:
the rotation capacity decreases with the plate thickness, for identical
plate steel grades. For the specimen with steel S690, the rotation capacity is
overestimated. However, the scope of the method is restricted to current steel
grades and consequently the latter results are just illustrative. The method proposed
by these authors yields an average ratio to the experiments of 0.53 with a
Table 8.7 Verification of the recommendations for rotation capacity according
to Eurocode 3 (values in [mm]).
Test
Maximum Critical component governing Verification?
ID
tp
tp
the joint resistance
FS1 10.40 11.80 End plate in bending Yes.
FS2 15.01 11.75 End plate in bending No.
FS3 20.02 11.76 End plate in bending No.
FS4 10.06 8.25 End plate in bending No.
Table 8.8 Analytical evaluation of the rotation capacity according to other
authors.
φCd
Test ID
Average Coeff.
(mrad) FS1 FS2 FS3 FS4
var.
Experimental 111.22 71.89 48.74 62.97 ⎯ ⎯
Adegoke and 31.66 22.71 17.47 72.88
Kemp (0.28) (0.32) (0.36) (1.16) 0.53 0.79
Beg et al. 48.40 47.88 105.40 49.34
(0.44) (0.67) (2.16) (0.78) 1.01 0.77
Zoetemeijer ⎯ ⎯ 17.53
(0.36)
⎯ ⎯ ⎯
327

Monotonic behaviour of beam-to-column bolted end plate connections
(rather high) coefficient of variation of 0.79.
Beg and co-authors’ proposals [8.3] do not reproduce well the actual behaviour.
In fact, for specimen FS3 that employs a thicker end plate, the predictions
are the highest. Though the averaged ratio in this case is unitary, the high coefficient
of variation indicates that the methodology is not sufficiently accurate.
Finally, the predictions for FS3 by applying the Zoetemeijer’s proposals
[8.9] underestimate the experimental results.
8.3.4 Characterization of the joint ductility
A joint ductility index has been proposed in Chapter 1 and it has been defined
as follows:
ΦCd
ϑ j = (8.1)
ΦM
Rd
Essentially, it relates the rotation value at ultimate conditions with a rotation
value attained in a plastic situation. In Eq. (8.1), the values of ΦCd and Φ M Rd
were adopted. However, in this work other distinct values of rotation have been
defined: ΦXd, corresponding to the rotation at which the moment first reaches
Mj.Rd, and φ M , the rotation value at maximum load (see Figs. 1.28 and 7.7).
max
Tables 8.9 and 8.10 evaluate the experimental joint ductility indexes and explore
the above differences. In these examples, the joint rotation and the connection
rotation are equal and so the latter values are indicated. As expected, if
the index is related to φ (ϑj.Rd), usually lower than φXd, its value is greater
328
M Rd
than if related to φXd (ϑj.Xd). The differences between the two indexes vary be-
tween 47% in FS4a and 68% in FS1b. Two possibilities are considered in terms
φ (at Mmax). The
of the rotation at ultimate conditions: φCd (failure) and M max
ductility indexes are naturally bigger in the first case, with deviations that vary
between 31% in FS1b and 50% in FS2a. Again, in these comparisons, the test
results corresponding to specimens FS1a and FS3a should be excluded.
Another relevant aspect that warrants some attention relates to the indexes
values within the same test series. This aspect is restricted to series FS2 and
FS4. The differences between the two tests can diverge 8% for ϑj.Xd (at failure)
and 33% for the same index, for specimens FS4 and FS2, respectively. These
differences, however, are not consistent for the alternative definitions and
within the same test series.
Analytically, the joint ductility indexes are also evaluated. Table 8.6 sets
out the analytical predictions for rotation capacity. From the analytical point of
view, these are also the values at Mmax except when the experimental charac-
terization of the T-stub top is input (e.g. Fig. 8.15 for specimens FS1). These
values are again repeated in Table 8.11 along with the rotation values for φ .
M Rd

Ductility of bolted end plate connections
Table 8.9 Experimental evaluation of the joint ductility indexes at φ M .
Rd
Test ID Rotation values at the KR [mrad] Ductility indexes at Mmax
φKR.inf
φ φKR.sup
M Rd
φ ϑj.inf ϑj.Rd ϑj.sup
M max
FS1a 3.0 5.8 17.5 61.6 20.53 10.62 3.52
FS1b 4.2 6.5 25.0 77.1 18.36 11.86 3.08
FS2a 6.5 7.1 20.0 41.7 6.42 5.87 2.09
FS2b 6.3 7.7 20.5 40.3 6.40 5.23 1.97
FS3a 5.5 7.5 15.0 25.0 4.55 3.33 1.67
FS3b 5.5 8.9 18.0 30.0 5.45 3.37 1.67
FS4a 6.9 10.2 21.0 37.7 5.46 3.70 1.80
FS4b 6.9 9.5 21.6 43.8 6.35 4.61 2.03
Test ID Rotation values at the KR [mrad] Ductility indexes at failure
φKR.inf
φ φKR.sup φCd ϑj.inf ϑj.Rd ϑj.sup
M Rd
FS1a 3.0 5.8 17.5 68.9 22.97 11.88 3.94
FS1b 4.2 6.5 25.0 111.2 26.48 17.11 4.45
FS2a 6.5 7.1 20.0 82.9 12.75 11.68 4.15
FS2b 6.3 7.7 20.5 60.9 9.67 7.91 2.97
FS3a 5.5 7.5 15.0 42.8 7.78 5.71 2.85
FS3b 5.5 8.9 18.0 48.7 8.85 5.47 2.71
FS4a 6.9 10.2 21.0 61.7 8.94 6.05 2.94
FS4b 6.9 9.5 21.6 64.2 9.30 6.76 2.97
Table 8.10 Experimental evaluation of the joint ductility indexes at φXd.
Test ID Rotation values at the KR [mrad] Ductility indexes at Mmax
φKR.inf φXd φKR.sup
φ ϑj.inf ϑj.Xd ϑj.sup
M max
FS1a 3.0 18.2 17.5 61.6 20.53 3.38 3.52
FS1b 4.2 20.0 25.0 77.1 18.36 3.86 3.08
FS2a 6.5 17.5 20.0 41.7 6.42 2.38 2.09
FS2b 6.3 19.2 20.5 40.3 6.40 2.10 1.97
FS3a 5.5 13.8 15.0 25.0 4.55 1.81 1.67
FS3b 5.5 18.2 18.0 30.0 5.45 1.65 1.67
FS4a 6.9 19.2 21.0 37.7 5.46 1.96 1.80
FS4b 6.9 18.3 21.6 43.8 6.35 2.39 2.03
Test ID Rotation values at the KR [mrad] Ductility indexes at failure
φKR.inf φXd φKR.sup φCd ϑj.inf ϑj.Xd ϑj.sup
FS1a 3.0 18.2 17.5 68.9 22.97 3.79 3.94
FS1b 4.2 20.0 25.0 111.2 26.48 5.56 4.45
FS2a 6.5 17.5 20.0 82.9 12.75 4.74 4.15
FS2b 6.3 19.2 20.5 60.9 9.67 3.17 2.97
FS3a 5.5 13.8 15.0 42.8 7.78 3.10 2.85
FS3b 5.5 18.2 18.0 48.7 8.85 2.68 2.71
FS4a 6.9 19.2 21.0 61.7 8.94 3.21 2.94
FS4b 6.9 18.3 21.6 64.2 9.30 3.51 2.97
329

Monotonic behaviour of beam-to-column bolted end plate connections
For further comparisons, this is the relevant rotation at plastic conditions. Table
8.12 evaluates the joint ductility index for the various joints (cf. rotation values
in Table 8.11). For the analytical procedures, the ductility index was evaluated
at the analytical value for rotation capacity but with respect to the analytical
and experimental values of
330
φ (ϑj.Rd.anl and ϑj.Rd.exp, respectively), as shown
M Rd
in Table 8.12 (cf. rotation values in Tables 8.9 and 8.11). For the various processes
the index ϑj.Rd.anl is bigger than ϑj.Rd.exp.
The analytical predictions of the ductility index are quite severe, particularly
for the thinner end plate specimens, FS1 and FS4 (2 nd -4 th columns, Table
8.12 and 7 th column on Table 8.9). This situation also results from the underestimation
of the T-stub component ductility itself (e.g. FS4, Fig. 8.10 and Table
8.3). The analytical predictions for deformation capacity of the individual Tstubs
are rather conservative, as seen above. Consequently, the rotation capacity
of the overall joint, which is calculated from the individual components
contribution, is also underestimated. On the contrary, for specimen FS3 that
uses a 20 mm thick end plate, the ductility index is overestimated (2 nd on Table
8.12 and 7 th column on Table 8.9).
Table 8.11 Analytical predictions of rotation of the various joints (in [mrad]).
Test
ID
Analytical predictions
BM JA Num Exp
φ M φCd φ Rd
M φCd φ Rd
M φCd φ Rd
M φCd
Rd
FS1 3.0 29.2 2.4 21.0 4.6 39.8 3.3 29.5
FS2 3.4 28.8 3.0 19.4 ⎯ ⎯ ⎯ ⎯
FS3 4.4 35.0 3.4 13.5 ⎯ ⎯ ⎯ ⎯
FS4 5.0 13.5 4.0 14.6 ⎯ ⎯ 4.4 36.8
Table 8.12 Analytical evaluation of the joint ductility indexes.
Test
Analytical predictions
ID BM JA Num Exp
ϑj.Rd.anl ϑj.Rd.exp ϑj.Rd.anl ϑj.Rd.exp ϑj.Rd.anl ϑj.Rd.exp ϑj.Rd.anl ϑj.Rd.exp FS1 9.73 4.49 8.75 3.23 8.65 6.12 8.94 4.54
FS2 8.47 3.89 6.47 2.62 ⎯ ⎯ ⎯ ⎯
FS3 7.95 3.93 3.97 1.52 ⎯ ⎯ ⎯ ⎯
FS4 2.70 1.36 3.65 1.47 ⎯ ⎯ 8.36 3.72
8.4 DISCUSSION
The rotational behaviour of bolted extended end plate beam-to-column connections
was evaluated in the context of the component method. The methodology

Ductility of bolted end plate connections
was restricted to joints whose behaviour was governed by the end plate modelled
as equivalent T-stubs in tension. It has been shown that the overall M-Φ
response can be modelled fairly accurately provided that the T-stub component
F-∆ behaviour is well characterized. Because ductility is such an important
characteristic in connection performance, the evaluation of the joint rotation
capacity, i.e. the available joint rotation, was addressed with greater depth. In
order to meet the ductility requirements, the required joint rotation, Φj.req must
be less or equal to the available joint rotation, Φj.avail:
Φ ≤Φ (8.2)
jreq . javail .
It is generally accepted that a minimum of 40-50 mrad ensures “sufficient rotation
capacity” of a bolted joint in a partial strength scenario [8.11]. Tables 8.9
and 8.10 show that joints FS2 and FS4 also guarantee this condition at maximum
load. Therefore, the Eurocode 3 current provisions seem too conservative
as far as rotational capacity is concerned (Table 8.7). This study affords some
basis for the proposal of some additional criteria on this topic.
From the analysis of the ductility indexes in Table 8.9 (top half of the table),
computed at maximum load, a minimum joint ductility index of 4.0 seems
appropriate in order to ensure “sufficient rotation capacity”. This limitation
should be set in conjunction with an absolute minimum value of 40 mrad and is
valid for steel grade S355. For steel grade S690 similar criteria might be established.
However, the T-stub component in isolation has to be further explored
for higher steel grades because of the inherent specificities. In addition, the
analytical procedure has to be calibrated with other joint specimens since the
joint ductility indexes are not yet accurate enough (cf. Tables 8.9 and 8.12).
Naturally, as the above mentioned joints were designed to confine failure to
the end plate and bolts, the deformation behaviour is exclusively dependent on
these two components that form an equivalent T-stub. Therefore, the conclusions
are only valid if the T-stub determines collapse. In this case it would be
preferable to set a criterion in terms of the component ductility index, rather
than the joint ductility index. However, it is found out that the information contained
in Table 8.4 is not sufficient and can even be contradictory. For instance,
take specimen FS3 as an example. In terms of joint ductility index (Tables 8.9
and 8.12), it is quite lower than the remaining cases. As for the single T-stub,
the ductility index is higher than for specimen FS2 or FS4. This situation may
arise in the definition of the equivalent T-stub itself. For specimens FS1 or
FS4, corresponding to thin end plates, the predictions for rotation capacity are
underestimating but the ratio to the experiments is consistent (see Table 8.6
and the BM characterization). In both specimens, where the equivalent T-stubs
are governed by a type-1 plastic mode, the whole yield line pattern is likely to
develop. For the other two cases, type-2 “plastic” failure mode is also present
and therefore the complete pattern may not develop fully. This means that the
actual T-stub effective width may be different from beff in Table 8.2. Consequently,
the T-stub response for assessment of the joint rotational behaviour
would also be different.
331

Monotonic behaviour of beam-to-column bolted end plate connections
Finally, although it has been shown that deemed-to-satisfy criteria for sufficient
rotation capacity stated in Eurocode 3 are overconservative, the establishment
of more accurate criteria still requires further work.
8.6 REFERENCES
[8.1] Kuhlmann U, Kühnemund F. Ductility of semi-rigid steel joints. In: Proceedings
of the International Colloquium on Stability and Ductility of Steel
Structures (SDSS 2002) (Ed.: M. Ivanyi), Budapest, Hungary; 363-370,
2002.
[8.2] Faella C, Piluso V, Rizzano G. Structural Semi-Rigid Connections –
Theory, Design and Software. CRC Press, USA, 2000.
[8.3] Beg D, Zupančič E, Vayas I. On the rotation capacity of moment connections.
Journal of Constructional Steel Research; 60:601-620, 2004.
[8.4] Zandonini R, Zanon P. Experimental analysis of end plate connections.
In: Proceedings of the First International Workshop on Connections in Steel
Structures, Behaviour, Strength and Design (Eds.: R. Bjorhovde, J.
Brozzetti and A. Colson), Cachan, France; 40-51, 1988.
[8.5] Adegoke IO, Kemp AR. Moment-rotation relationships of thin end plate
connections in steel beams. In: Proceedings of the International Conference
on Advances in Structures, ASSCCA’03 (Eds.: G.J. Hancock, M.A.
Bradford, T.J. Wilkinson, B. Uy and K.J.R. Rasmussen), Sydney, Australia;
119-124, 2003.
[8.6] European Committee for Standardization (CEN). prEN 1993-1-8:2003,
Part 1.8: Design of joints, Eurocode 3: Design of steel structures. Stage
49 draft, May 2003, Brussels, 2003.
[8.7] Borges LAC. Probabilistic evaluation of the rotation capacity of steel
joints. MsC thesis. University of Coimbra, Coimbra, Portugal, 2003.
[8.8] Jaspart JP. Study of the semi-rigid behaviour of beam-to-column joints
and of its influence on the stability and strength of steel building frames.
PhD thesis (in French). University of Liège, Liège, Belgium, 1991.
[8.9] Zoetemeijer P. Summary of the research on bolted beam-to-column
connections. Report 25-6-90-2. Faculty of Civil Engineering, Stevin
Laboratory – Steel Structures, Delft University of Technology, 1990.
[8.10] Kemp AR, Nethercot DA. Required and available rotations in continuous
composite beams with semi-rigid connections. Journal of Constructional
Steel Research; 57:375-400, 2001.
[8.11] Grecea D, Statan A, Ciutina A, Dubina D. Rotation capacity of MR
beam-to-column joints under cyclic loading. In: Proceedings of the Fifth
International ECCS/AISC Workshop on Connections in Steel Structures,
Innovative steel connections, Amsterdam, The Netherlands; 2004 (to be
published).
332

9 CONCLUSIONS AND RECOMMENDATIONS
9.1 CONCLUSIONS
The primary goal of this dissertation was to develop a methodology for the
characterization of the full nonlinear rotational behaviour of bolted end plate
beam-to-column steel connections based on the component method. Because of
the emphasis recently placed on the design of joints within the partial
strength/semi-rigid approach, special attention was addressed to the characterization
of the ductility of this joint type. The scope of the research was restricted
to end plate connections for which the collapse was governed by the
tension zone idealized by means of T-stubs.
This goal was achieved by firstly conducting a comprehensive experimental
test programme of thirty-two individual T-stubs that were supplemented by robust
FE analyses. The research on T-stubs constitutes a reliable database for
validation of a simplified analytical (beam) model for characterization of the F-
∆ behaviour of T-stub connections. This investigation drew particular attention
to the assemblies made up of welded plates that model the end plate behaviour
in the context of the T-stub idealization. Additionally, eight monotonic fullscale
tests on end plate connections were conducted to analyse the ultimate response
of this joint type and assess their behaviour from a ductility point of
view. The tests showed that end plate connections can achieve rotation capacity
provided that the end plate is a “weak link” relative to the bolts.
There are some original contributions in this research work:
1. A detailed review on the state-of-art of the characterization of the M-Φ behaviour
of bolted end plate beam-to-column steel connections which highlighted
the current methodologies and Eurocode 3 provisions [9.1];
2. A comprehensive test programme on WP-T-stub connections that constitutes
a database of experimental results on this simple connection. Previous research
work on this assembly type is not documented in technical literature. Piluso et
al. [9.2] refer a single test on a WP-T-stub to validate an analytical methodology.
This test programme provided insight into the actual behaviour of this
simple connection, failure modes and deformation capacity. The main parameters
affecting the deformation response of WP-T-stubs were identified and their
influence on the overall behaviour of the connection was qualitatively and
quantitatively assessed. The role of the welding and the presence of transverse
stiffeners were also tackled. Additionally, the behaviour of WP-T-stubs and
HR-T-stubs was confronted in order to clarify the main differences between
both assembly-types;
3. Documentation of the problems with the welding consumables and the pro-
333

cedures is made. During the experiments on WP-T-stubs, some of the specimens
showed early damage of the plate material near the weld toe due to the
effect of the welding consumable that induced premature cracking and reduced
the overall deformation capacity. A solution to this problem was given by setting
requirements to the weld metal to be used;
4. Advanced FE modelling was conducted on HR-T-stubs and WP-T-stubs. A
robust three-dimensional model that encompasses material and geometrical
nonlinearities and contact friction phenomenon was developed. The model
provided qualitative and quantitative understanding about the T-stub behaviour.
It may also be used as a benchmark for FE modelling of bolted end plate
steel connections;
5. Although no new models were developed in this work, some problems with
existing models were identified and some modifications were tested (e.g. the
modification on the definition of the distance m for WP-T-stubs on Chapter 6);
6. The completion and documentation of monotonic tests on bolted end plate
connections in bending, up to failure;
7. Tests on bolted connection employing high-strength steel grade S690 were
carried out. There is growing demand for high-strength steels in construction
and insufficient knowledge on these steel grades. In this work some results on
bolted connections that use S690 are given to provide additional information
on this subject;
8. A methodology for characterization of the rotational response of a joint
based on the component method was implemented and calibrated against experimental
results. The methodology was restricted to joints whose behaviour
was governed by the end plate modelled as equivalent T-stubs in tension. The
results of this particular study along with the conclusions drawn from the
analysis of individual T-stubs afforded some basis for the proposal of some criteria
for the verification of sufficient rotation capacity. The proposal was made
in terms of a non-dimensional parameter, the joint ductility index. Naturally,
this limitation was set in conjunction with an absolute minimum value of 40
mrad. This proposal was restricted to S355 as it was recognized the data were
insufficient for higher steel grades.
Several conclusions are drawn from this research work:
1. The prediction of failure should be based upon a deformation-based criterion
rather than a resistance-based parameter. However, for consistency with Eurocode
3 that uses the β-ratio at design conditions to predict the critical “plastic”
collapse mode, in this work a similar ratio βu (at ultimate conditions) was
brought in, to identify the potential fracture mode. Naturally, this brings some
inconsistencies with the observed and the predicted failure type;
2. The experimental-numerical work on the T-stub behaviour (both assembly
types) identifies the major contributions of the overall T-stub deformation: the
flange flexural deformation and the tension bolt elongation. Usually, a higher
deformation capacity of the T-stub is expected if the flange cracking governs
the collapse instead of bolt fracture. The cracking associated to the flange
mechanism, in the case of the welded plates assembly, also depends on struc-
334

Conclusions and recommendations
tural constraint conditions and modifications in the mechanical properties in
the HAZ, particularly those linked to the presence of residual stresses;
3. During the experiments, the importance of the correct selection of electrodes
and welding procedures in the case of the testing of WP-T-stubs was highlighted.
It has been shown that the use of evenmatch soft low hydrogen electrodes
ensures a ductile behaviour;
4. In general, bolts fail in tension before stripping. The stripping of the bolt
threads and/or nut is not likely to occur in most cases. In the full-scale tests, the
nut stripping phenomenon occurred in four tests. In the experimental investigation
on individual T-stubs the same problem was observed in one test. In fact,
this phenomenon is rather frequent in practice. Research indicates that when
the nut hardness is below a certain level (89 Rockwell B or 180 Brinell) there
is a risk of stripping. This phenomenon limits the ductility performance of the
whole joint and therefore it should be avoided. A solution to this problem can
be given by setting requirements to the hardness and strength properties of the
nut;
5. A two-dimensional beam model for assessment of the T-stub behaviour was
developed. It retains all the relevant behavioural characteristics. To obtain the
F-∆ curve, a numerical incremental procedure is required and, consequently, the
model is not suitable for hand calculations. However, it clearly simplifies the process
of behaviour characterization when compared to the three-dimensional FE approach
or the experimental technique. The applicability of the model was well
demonstrated within the range of examples shown in the text. The behaviour
predicted by this model is rather good in terms of resistance. With respect to
ductility, it reflects an overestimation of test results that is within an acceptable
error. These differences may derive from a great sensitivity of the model to
strain hardening parameters and bolt ductility. Additionally, the model encompasses
a major simplification regarding the T-stub width, which is kept constant
with the course of loading. It is well known that as the load increases, the flange
width tributary to load transmission also increases. The implementation of such a
variation is not straightforward. Ideally, the T-stub breadth should vary with the
loading and this variation should be dependent on the failure mode as well;
6. Concerning the evaluation of the F-∆ response of T-stubs by means of other
simplified methodologies, the bilinear approximation proposed by Jaspart [9.3] is
accurate in terms of curve mimicry. However, the prediction of the potential failure
mode is sometimes incorrect;
7. The T-stub idealization of end plate behaviour is reliable in the elasticyielding
domain. When strain hardening is present such idealization should be
re-evaluated, especially in terms of effective width that is clearly different from
the initial elastic behaviour;
8. The methodology developed for the evaluation of the M-Φ curve of joints
and its ductility, in particular, mainly depends on the T-stub idealization of end
plate behaviour as the joints were designed to confine failure to the end plate
and bolts. As a result, the conclusions drawn in Chapter 8 are only valid if the
335

collapse is determined by the T-stub component. The characterization of the Tstub
behaviour and failure modes is therefore crucial. Two simplified methodologies
were implemented for that purpose: (i) the proposed beam model and
(ii) the bilinear approximation proposed by Jaspart. The outcomes were quite
good, in general. However, the prediction of the failure modes was more accurate
in the first case, as already explained;
9. This methodology provided satisfactory results in terms of joint ductility,
perhaps too conservative. However, a correcting factor can be defined to improve
the results. This work does not permit the establishment of such a correction
due to lack of data. Furthermore, the conclusions for series FS2 and FS3
are quite limiting as the governing failure mode was the nut stripping of the inner
bolts. This phenomenon should be avoided as explained and thus further
investigation on the behaviour of these specimens is required;
10. As already mentioned above, a minimum joint ductility index of 4.0 was
proposed in order to ensure “sufficient rotation capacity”. Additionally, an absolute
minimum rotation value of 40 mrad should also be guaranteed. It would
have been preferable to set a criterion in terms of the T-stub component ductility
index, rather than the joint ductility index. However, there was not enough
data to make such a proposal;
11. For steel grade S690, similar criteria for rotation capacity should be established.
However, the T-stub component in isolation has to be further explored
for higher steel grades because of the inherent specificities;
12. With reference to the end plate behaviour modelled as equivalent T-stubs
(Chapter 8), the results for specimens FS2 and FS3 could be further improved
if the effective width of the T-stub bottom was reduced. The suggestion for this
reduction is based on experimental observations of the yielded portions of the
end plate below the tension beam flange. If the following T-stub breadth:
beff. red. bot = mep + eep + 0.5dh+
m2
(9.1)
( FS 2)
is implemented, then for the above specimens, b = mm and
336
eff . red. bot 122.37
( FS 3)
b eff . red. bot = 124.07 mm (0.60 and 0.61 times the original value obtained from
Eurocode 3, respectively – cf. Table 8.2). If the equivalent T-stub response is
re-evaluated with these changes (beam model characterization), the corresponding
joints M-Φ curves will fit the experiments better, as shown in Figs.
9.1 and 9.2. From a resistance point of view, the results are clearly improved.
Also, the failure mode is compliant with experimental evidence. In terms of
ductility, the results do not vary significantly, though. This problem is probably
linked to the T-stub idealization itself and so additional research should be carried
out.
9.2 FUTURE RESEARCH
Some relevant issues were exposed during this investigation that warrant fur-

Bending moment (kNm)
240
210
180
Conclusions and recommendations
150
FS2a
120
90
FS2b
60
30
0
NASCon original prediction (Tstub
top critical - flange)
NASCon prediction (T-stub
bottom critical - bolt)
0 10 20 30 40 50 60 70 80 90 100 110 120
Connection rotation φ (mrad)
Fig. 9.1 Moment-rotation curve for joint FS2 (T-stub characterization by means
of the beam model and reduced effective length of the T-stub bottom).
Bending moment (kNm)
400
350
300
250
200
150
100
50
FS3a
FS3b
0
0 10 20 30 40 50 60 70 80 90 100 110 120
Connection rotation φ (mrad)
NASCon original prediction
(T-stub bottom critical - bolt)
NASCon prediction (T-stubs
top - flange & bottom critical
- bolt)
Fig. 9.2 Moment-rotation curve for joint FS3 (T-stub characterization by means
of the beam model and reduced effective length of the T-stub bottom).
ther consideration. They are listed below and are proposed as future research:
1. The bolt force-elongation curve that was proposed in Chapter 6 for the bolt
response simplified modelling requires further investigation as far as fullthreaded
bolts are concerned. This curve was derived for short-threaded bolts.
This work clearly shows that for full-threaded bolts the predictions of bolt fracture
overestimate the overall results. The formula for evaluation of the bolt
fracture should include explicitly the ratio between the bolt shank and threaded
lengths. Additionally, there should be a resistance limitation as it was observed
that the bolt force at fracture could be as high as 1.30Bu, whereby Bu is the bolt
tensile strength, evaluated in engineering stresses;
2. A clarification of the definition of the distance m is needed. Chapters 3-5
337

gave experimental and numerical results for the stress and strain results on WP-
T-stubs and showed that the yield lines near the flange-to-web connection
would potentially develop at the end of the fillet weld. This would change the
expression for computation of the distance m. According to Eurocode 3, m in
these cases is defined as follows:
m = d − 0.8 2aw (9.2)
Chapter 6 compared the beam model results obtained when this distance was
employed with those obtained from:
m = d − 2aw (9.3)
which are further improved. The latter definition is more compliant with the
observations and should be regarded as a possible modification. Additional
work on this subject is essential;
3. Further research on the T-stub idealization of the end plate behaviour is required.
Three-dimensional FE analysis may be helpful for investigating this
specific topic. The numerical results presented in this research work can be
used as benchmarks for validation of the global joint model. Naturally, the experimental
results are also essential for the calibration procedures. The establishment
of more appropriate rules for the definition of the effective equivalent
T-stub width, particularly in the post-limit regime, are fundamental. The experiments
can not provide enough results for this analysis. Advanced FE modelling
provides all the necessary data and will be carried out by the author as a
follow up study to this investigation.
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