seismic analysis as a tool for checking the structural system

SEISMIC ANALYSIS AS A TOOL FOR CHECKING THE
STRUCTURAL SYSTEM
Autors:
Doc. Ing. Milan SOKOL, PhD., SLOVAK UNIVERSITY OF TECHNOLOGY,
DEPARTMENT OF STRUCTURAL MECHANICS, Radlinského 11, Bratislava, Slovakia,
e-mail: milan.sokol@stuba.sk
Ing. Katarína TVRDÁ, PhD., SLOVAK UNIVERSITY OF TECHNOLOGY,
DEPARTMENT OF STRUCTURAL MECHANICS, Radlinského 11, Bratislava, Slovakia,
e-mail: katarina.tvrda@stuba.sk
Anotácia
Na železobétonovej rámovej konštrukcii vystavenej vyššej úrovni seizmického zaťaženia boli
počítané seizmické návrhové účinky a posudzované prierezy. Výpočet rotačnej kapacity
prierezov dokázal, že pôvodná voľba triedy poddajnosti „nízka“ bol jedinou vhodnou
alternatívou. Pokiaľ vychádzala odolnosť prierezov nižšia, ako seizmické účinky, návrh
možných konštrukčných opatrení umožňoval len zmenu konštrukčného systému s pridaním
ďalších stien.
Annotation
The frame R/C structure subjected to higher level of seismic effects was analysed. The
analysis of rotation capacity reserves has proved, that initially chosen ductility class “L” was
only choice and for such type of structure there is no possible to use higher ductility class. If
design values were not conservative, it means the resistance of cross section was not
sufficient, the only change of the structural system, e.g. design of additional walls, was an
appropriate solution.
Introduction
A frame building situated in a high vulnerable seismic area is analysed. The seismic effects
are calculated according to Eurocode ENV 1998:1997. The structural system performance is
checked. Rotation capacity of cross sections is discussed.
Description of the building
The layout of the building consists of a ground floor and a first floor with a basement. The
reinforced concrete structure consists of a foundation slab, columns, beams, slab floors and
walls. The unusual structural detail of this structure is a heavy roof slab leading to the high
masses in top level.
The longitudinal section of building is shown on Fig.1 and the transversal section on Fig.2.
Foundation is on a foundation slab. Thickness of this slab is 0,5m. The footprint dimensions
are 29x18 m and the slab is spreaded by 500mm outside the perimeter column axes grid. On
the perimeter of the basement there is a reinforced concrete wall 300mm thick.
Columns are located on a 5.5 x 5.5m grid (i.e. 5x5.5m spans in longitudinal direction and
3x5.5m in transversal direction). The columns are 450x450mm reinforced with 12φ25 bars.
The corner columns are 500x500mm reinforced with 16φ25 bars. The reinforcing bars are
distributed uniformly along the perimeter of the cross-section.
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3125 3200
3250
5500 5500 5500 5500 5500
5500 5500 5500
Fig.1 Longitudinal section
Fig.2 Transversal section
The columns are 450x450mm reinforced with 12φ25 bars. The corner columns are
500x500mm reinforced with 16φ25 bars. The reinforcing bars are distributed uniformly along
the perimeter of the cross-section.
Ground-floor
Thickness of the ground-floor slab is 200mm. The columns are 450x450mm reinforced with
12φ25 bars. The corner columns are 500x500mm reinforced with 16φ25 bars. Beams are
400x650mm (450mm+200mm slab), reinforced by 12φ25 bars uniformly distributed along the
perimeter of the cross-section.
First-floor
Thickness of the first-floor slab is 200mm. The columns are 450x450mm reinforced with
12φ25 bars. The corner columns are 500x500mm reinforced with 16φ25 bars. Beams are
400x650mm (450mm+200mm slab).
Roof
The roof is located over one part of the building, 3x5.5m spans in longitudinal direction and
3x5.5m in transversal direction, with a 1200mm overhang along the perimeter. The thickness
of the roof slab is 200mm. On the roof is an additional 150mm thick concrete covering slab.
Beams are 400x650mm (450mm+200mm slab).
Structural model
The building was modelled as a 3D system consisting of beams, columns, slabs and walls
(Fig.3 and Fig.4). The material concrete C35/45 with characteristic compression strength
35MPa and reinforcing steel S220 are used.
In order to provide sufficient seismic resistance R/C shear walls of 200mm thickness are
arranged in both X and Z horizontal directions (Fig.4).The walls and floors were modelled
with shell elements, the columns and beams as beam elements.
The elastic foundation stiffness (EFS), defined as the pressure producing a unit normal
deflection of the foundation, is considered. The elastic foundation capability is assumed for
foundation slab (EFS=50MPa/m) as well as for walls under the ground level
(EFS=25MPa/m).
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Fig.3 Structural 3D model
Fig.4 R/C shear walls
Static Loads
Basement
Dead load Self-weight of foundation slab 500 mm 12.5 kN/m 2
Self-weight of concrete wall 300mm
19.5 kN/m
Ground-floor
Dead load Self-weight of slab 200 mm 5 kN/m 2
Additional self-weight 2.5 kN/m 2
Self-weight of masonry partition walls 5.6 kN/m 2
First-floor
Dead load Self-weight of slab 200 mm 5 kN/m 2
Additional self-weight 2.5 kN/m 2
Self-weight of masonry partition walls 4.9 kN/m 2
Roof
Dead load Self-weight of slab 200 mm 5 kN/m 2
Additional self-weight of concrete cover 3.75 kN/m 2
Seismic load
The site ground acceleration is quite high reaching the value of a g =3.2ms -2 . The soil
parameters are similar to the soil class B (ENV1998). It is assumed a „Low“-ductile structure
and then the calculation of behaviour factor is taken according to (ENV 1998-1-3). Choice of
a „Low“-ductile structure is due to the fact, that the cross-sectional reinforcement does not
allow adequate rotational capacity.
q 0 =5 for R/C frame structure,
k D =0.5 - ductility class factor (DC „L“),
k R =0.8 - structural irregularity factor,
q=q 0 k D k R =2.
Because ductility class “L” was chosen, the masonry walls (thickness 400mm) are not taken
into account as structural elements. In spite of this, the masonry walls should be furnished
with a provision to protect them against falling out of the R/C frame during seismic design
situation. The inelastic (q=2) design response spectrum, shown on Fig.5, is assumed.
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Fig.5 Inelastic design response spectrum (q=2)
Seismic effects
Seismic effects are calculated on the 3D model. Accidental eccentricity
e a =0.05L =1.375m
is assumed in such a way, that the centre of gravity of distributed masses of all loads on the
deck is shifted in –x direction by the value e a . The seismic effects are calculated in
combination with dead load. The effects in all three directions are combined together using all
combinations of the following loads: dead load + seismic effects in one direction with
magnitude 100% and seismic effects in another two directions with magnitude 30%. Finally
the envelope of all these combinations is considered.
First eigenfrequencies are shown in Fig.6. It is seen that the structure is irregular and the
torsion and bending modes are coupled, so the 3D modelling is necessary.
Seismic displacements are shown on Fig.7.
Fig.6 Eigenfrequencies [Hz]
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z
x
ux [mm]
uz [mm]
Fig.7 Seismic displacements
Beam bending moments especially in reinforcing beams of the slabs are shown on Fig8.
Basement Ground floor 1 st floor
y 0 z 0
M y0
[Nm]
M z0
[Nm]
N [N]
Fig.8 Bending moments in reinforcing beams of the slabs
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Column bending moments and normal forces are shown on Fig.9. All values are in local
coordinate system.
x 0
y 0
Bending moments m x0 [kNm/m]
Bending moments m y0 [kNm/m]
-234
-183
y 0
z 0
173
224
Mz 0 [kNm]
-194
-151
151
194
-1710
-1490
71
294
My 0 [kNm]
N [kN]
Fig.9 Column bending moments and normal forces, corner’s columns 500x500mm
Membrane forces and beam bending moment on shear walls 200mms are shown on Fig.10.
Stresses on shear walls 200mm are on Fig.11.
y 0
x 0
Membrane forces t x0 [kN/m]
Membrane forces t y0 [kN/m]
Fig.10 Beam bending moments and membrane forces
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z
y
x
Stresses σ x [MPa] Stresses σ y [MPa] Stresses τ xy [MPa]
Fig.11 Stresses on shear walls
Cross-section rotation capacity
The prescribed minimum rotation capacity (CCDF) for column - ductile class „L“ is μ 5.
No. of Steel
bars
Steel bar area
Young'
modulus Steel Concrete
Design bending
moment
ohybova pruzna
unosnost po
odpadnuti krycej
vrstvy
5 C35/45
H B d1 (cover) Φs As Es fyk fck Msd Mu q
[mm] [mm] [mm] [mm] [mm2] [MPa] [MPa] [MPa] [kNm] [kNm]
500 500 25 25 2454,4 200000 220 35 454,0 227,0 2
1 / r
=
d [mm] 462,5 vyska od horneho okraja po os vystuze
xlim [mm] 351,90 Hranica pruzneho pretvorenia Medzny moment zo seizmického výpo
ξsy 0,7609 pre hodnotu q= 2
εsy,k 0,0011
Ns [N] 539961
xcu' [mm] 34,283 vyska tlaceneho betonu po odpadnuti krytia d0[mm]= 420 rameno vnutornych sil po odpadnuti kryt
xcu [mm] 59,283 suradnica neutralnej osi po odpadnuti krytia
ξcu 0,1282
ε
εcu 0,0035 cu( 1−ξsy)
= 5,94 concrete failure
Tecenie vystuze
Nsd [N] 1079922
xsu'd [mm] 68,567 vyska tlaceneho beton μ1/r= min = 5,01
xsu [mm] 93,567 suradnica neutralnej o
ξsu 0,2023
ε su ,k (1 − ξ sy )
εsu,k 0,0201
ε sy ,k (1 − ξ cu )
= 5,01 steet failure
ε
sy,
k
ξ
cu
ξ cu =(x cu +d 1 )/d
ξ sy =x lim /d
σ b
ε cu =-0,0035
concrete
Tear off cover
ε c
d
d 1
H
B
steel
x
ε su,k
x lim
d 1
x cu ‘
ε sy,k =f yk /E s
σ s
x cu
ε s
Fig. 12 Cross section 500x500mm rotation capacity analysis
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The rotation capacity CCDF is calculated assuming, that f y,k is not greater than 220MPa and
concrete C35/45 is used. Although many parameters of cross section were changed, e.g.
concrete material characteristics, cross section geometry, steel reinforcement parameters, the
rotation capacity does not increase significantly over the value 5. So the reasonable
characteristics for this analysis were taken into account finally (Fig. 12).
The analysis of rotation capacity reserves has proved, that initially chosen ductility class “L”
was only choice and for such type of structure there is no possible to use higher ductility
class. If design values were not conservative, it means the resistance of cross section was not
sufficient, only change of the structural system, e.g. design of additional walls, is necessary.
CONCLUSIONS
Due to the fact that the considered site ground acceleration is quite high a g =3.2ms -2 and the
building has a large mass from an additional concrete layer situated on the roof, it was
necessary to make some changes to the original design of the building. These changes can be
summarised in the following:
• The material was changed to concrete C35/45 and reinforcing steel S220.
• The cross-section of 400x400mm columns was changed to 450x450mm.
• The reinforcement of the members was strengthened. The columns 450x450mm were
reinforced with 12φ25 bars, the columns 500x500mm with 16φ25 bars, the beams
400x650mm with 12φ25, all bars are uniformly distributed along the perimeter of the
cross-section.
• Reinforcing seismic resistance R/C shear walls of 200mm thickness were arranged in
both transversal and longitudinal directions.
In spite of this, the following results were obtained:
• The beams in the ground-floor do not fulfil the design criteria for the moment
resistance and the rotation capacity at the same time. When the reinforcement would
be enlarged, then the rotation capacity will be lower than 5 for DC”L” and the
behaviour factor q=2 can not be used. It means, that larger design spectrum values
should be used, up to a value q=1, which means a 100% increase of seismic load.
• The columns have no reserve for the bending in both directions.
Therefore a change of the structural system to a wall system or to a combined frame-wall
system was proposed.
ACKNOWLEDGEMENT
We kindly acknowledge the research program nr. 1/0573/08 granted by the Scientific Grant
Agency of the Slovak Ministry of Education.
REFERENCES:
[1] ENV 1998. Design Provisions for Earthquake Resistance of Structures, Brussels, 1995.
[2] FLESCH, R. & SOKOL, M.: Earthquake-resistant-design of high-rise-buildings using
different structural models and methods. In: 11 th WCEE, Acapulco 1996. Paper 640
(CD).
[3] KOHNKE, P.C: Ansys, Eng. System, Theoret. Manual, Swanson Analysis System. 1989.
[4] MESKOURIS. K. et al.: Seismic motion damage potential for R/C wall stiffened
buildings. In Fajfar, P. & Krawinkler, H., Nonlinear Seismic Analysis and Design of RC
Buildings; Proc. int. Conf., Bled, July 1992. London-Elsevier. 125-136. 1992.
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