fire resistance of reinforced concrete filled steel columns

Second International Workshop « Structures in Fire » – Christchurch – March 2002
FIRE RESISTANCE OF REINFORCED CONCRETE FILLED
STEEL COLUMNS
Kang Hai TAN
Nanyang Technological University, School of Civil and Environmental Engineering,N1-
1c-97, Singapore
ckhtan@ntu.edu.sg
Chu Yang TANG
Nanyang Technological University, School of Civil and Environmental Engineering,N1-
B4-04, Singapore
p141449244@ntu.edu.sg
ABSTRACT
A simple calculation method, the Rankine method, is applied to determine fire resistance of
reinforced concrete filled steel (RCFS) columns. The same method has been applied to steel and
reinforced concrete columns successfully.
RCFS columns in fire can fail under two modes: plastic squashing for stocky columns and
buckling for slender columns. For columns in the intermediate range, these two modes will
interact to each other, causing a reduction in the load capacity of real columns. The Rankine
approach assumes a linear interactive relationship between the two failure modes, which has
been shown to be a lower bound approach. The formulation is presented for both axially- and
eccentrically-loaded columns. The Rankine predictions are compared to four case studies
comprising 61 tested RCFS columns. Good agreement is observed.
KEYWORDS: fire resistance, concrete, column, reinforced concrete, steel, fire test
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Second International Workshop « Structures in Fire » – Christchurch – March 2002
INTRODUCTION
Fire resistance of reinforced concrete filled steel (RCFS) columns, which is traditionally
determined by expensive furnace tests, presents a formidable problem to structural engineers.
1. Steel tube of RCFS columns softens quickly at elevated temperatures and the load is
transferred to the cooler concrete core, which is reinforced by steel reinforcement.
Therefore, the concrete core largely determines the load capacity of RCFS columns, with
only small contribution from the steel tube.
2. The moment capacity of steel tube is also greatly reduced. This phenomenon is particularly
detrimental to columns with steel tubes filled with plain concrete, as the concrete section
cannot resist bending moment by itself. At ambient temperature, such a column can resist
large bending moment by the steel tube. However, when subjected to elevated temperatures,
the moment capacity of the column diminishes quickly as the steel tube softens. This will
likely lead to a loss of ductility and thus a premature failure, as observed by Lie and Stringer
[1]. As a general comment, only design plain concrete filled steel (PCFS) columns to carry
axial loads in fire conditions. Where load eccentricity is anticipated, reinforced concrete
filled steel (RCFS) columns should always be used.
3. The confinement effect to the concrete core will also diminish as a result of the softening of
steel tube.
This paper outlines a simple analytical method, the Rankine method, to determine the fire
resistance of reinforced concrete filled steel (RCFS) columns. The same method has been
applied to steel columns, steel frames, and reinforced concrete columns successfully [2 - 4]. The
Rankine predictions are compared to four case studies comprising of 61 tested RCFS columns
and good agreement is observed.
RANKINE FORMULA
The Rankine formula for columns under fire conditions has the following form:
1 1 1
= +
(1)
P ( t)
u P ( t)
P ( ) t
R
pr
p
e
with P R predicted failure load by the Rankine formula;
u pr reduction factor of the plastic squashing load due to load eccentricity;
P p plastic squashing load;
u pr P p short column capacity;
P e elastic buckling load;
t fire exposure time; t = 0 for ambient conditions.
The theoretical basis of the above formula has been discussed by Tang et al [2]. RCFS columns
in fire can fail under two modes: plastic squashing for stocky columns and buckling for slender
columns. For columns in the intermediate range, these two modes will interact with each other,
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Second International Workshop « Structures in Fire » – Christchurch – March 2002
causing a reduction in the load capacity of real columns. Clearly, the Rankine formula provides
a linear interaction relationship between the plastic squashing load P p and the elastic buckling
load P e . The Rankine load has been shown to be a lower bound approach [2, 3].
FIRE RESISTANCE OF RCFS COLUMNS
Due to the softening of the steel tube at elevated temperatures, the confinement effect to the
concrete core from steel tube diminishes in fire conditions. Furthermore, separation of the
concrete core from the steel tube can also be frequently observed in fire conditions [1], which
suggests a loss of bond at the interface between the concrete core and steel tube. As a result, the
load capacity P of axially-loaded RCFS columns can be simply taken as the sum of the capacity
of concrete core P core and that of the steel tube P tube :
core
tube
P( ) t = P ( t)
+ P ( t)
(2)
where the superscripts “core” and “tube” indicate the contribution from the concrete core and
steel tube, respectively. Both P core and P tube can be determined by the Rankine formula.
CONCRETE CORE CAPACITY
For the concrete core at elevated temperatures:
1 1
1
= +
(3)
core core core
core
P ( t)
u P ( t)
P ( t)
pr
p
e
In Equation (3), the plastic squashing load of the concrete core can be determined from
core
p
P ( t)
= β ( t)
f '(0)
A + β ( t)
f (0)
A
(4)
c
c
c
yr
yr
sr
with f c ′ concrete cylinder strength;
f yr yield strength of steel reinforcement;
A c area of concrete;
area of steel reinforcement.
A sr
The terms β c (t) and β yr (t) are the respective strength reduction factors accounting for the
deterioration of concrete and steel reinforcement under fire conditions.
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Second International Workshop « Structures in Fire » – Christchurch – March 2002
∫ fc
'( t)
dAc
β
c
( t)
=
(5)
f '(0) A
c
yr
c
f
yr
( ) t Asr
β yr ( t)
=
∑
(6)
f (0) A
sr
Similarly, the elastic buckling load of the concrete core can be determined from:
P
core
e
2
π [ β
( t)
=
Ec
( t)
⋅ 0.2E
(0) I + β
c
L
c
2
e
Esr
( t)
⋅ E (0) I ]
sr
sr
(7)
with E c elastic modulus for concrete;
I c second moment of area of concrete;
E sr elastic modulus of steel reinforcement;
I sr second moment of area of steel reinforcement;
column effective length taking note of different support conditions
L e
The terms β Ec (t) and β Esr (t) are the respective stability reduction factors accounting for the
deterioration of concrete and steel reinforcement under fire conditions.
∫ Ec
( t)
dI
c
β
Ec
( t)
=
(8)
E (0) I
c
yr
c
Esr
( t)
I
sr
β yr ( t)
=
∑
(9)
E (0) I
sr
The material reduction factors β c (t), β yr (t), β Ec (t) and β Esr (t) can be determined either
experimentally or by finite element analysis. Based on their previous study of RC columns in
fire conditions [4], the authors proposed to adopte the following material models. They are
modified from Dotreppe et al. [5]:
γ ( te)
β
c(
t)
=
(10a)
− 0.25
−0.5
A
1+
(0.3A
t ) c
c
e
0.9te
β
yr
( t)
= γ ( te
) ⋅ (1 −
) ≥ 0
(10b)
0.046c
+ 0.11
Ec
0.15
c
te
β ( t)
= (1.1A
) ⋅ β ( t)
(10c)
2
yr
c
β ( t)
= 0.8β
( t)
+ 0.2β
( t)
(10d)
Esr
yr
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Second International Workshop « Structures in Fire » – Christchurch – March 2002
with c concrete cover;
γ ( t e
) an empirical factor to account for the effect of concrete spalling; γ ( t e
) = 1.0 for
RCFS columns as they are protected from spalling by the steel tube;
Here, the equivalent time t e in terms of fire severity can be estimated by
te
α
aggα
ISOt
= (13)
where
α agg = 1.0 for siliceous aggregate and α agg = 0.9 for carbonate aggregate;
α ISO = 1.0 for ISO 834 fire and α ISO = 0.85 for ASTM-E119 fire.
STEEL TUBE CAPACITY
The steel tube capacity can be determined from:
1
=
P ( t)
u
+
tube tube tube
pr
Pp
( t)
1
P
1
tube
e
( t)
where
tube
p
P ( t)
= k ( t)
⋅ f (0)
A
(14)
P
tube
e
y
y
s
2
e
s
2
π E (0) I
s
( t)
= kE
( t)
⋅
(15)
L
with f y yield strength of the steel tube;
A s
E s
I s
area of the steel tube;
elastic modulus for steel tube;
second moment of area of steel tube.
The factors k y (t) and k E (t) are the respective material reduction factors to yield strength and
elastic modulus of structural steel at elevated temperatures. Table 1 shows the values of k y (t)
and k E (t) at different fire temperatures for ISO 834 [6] and ASTM E119 [7] fires obtained from
the finite element program SAFIR [8], by adopting the Eurocode 3 structural steel material
model [9].
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Second International Workshop « Structures in Fire » – Christchurch – March 2002
Reduction factor k y (t) Reduction factor k E (t)
Time t (hour) ISO 834 ASTM
E119
ISO 834 ASTM
E119
0 1.000 1.000 1.000 1.000
0.5 0.371 0.362 0.242 0.235
1.0 0.065 0.073 0.073 0.077
1.5 0.050 0.055 0.051 0.057
2.0 0.034 0.042 0.039 0.047
2.5 0.027 0.037 0.030 0.041
3.0 0.020 0.032 0.023 0.036
3.5 0.015 0.028 0.017 0.031
4.0 0.011 0.023 0.012 0.026
Table 1 : strength reduction factors k y (t) and k E (t) of steel tube
EFFECT OF LOAD ECCENTRICITY
The effect of load eccentricity e on concrete core is to lower the short column capacity
u core pr P core core
core
p . For axially-loaded columns, u pr is unity. The magnitude of u pr for
eccentrically-loaded columns can be determined from the conventional axial-load-bendingmoment
interaction diagram, as shown in Figure 1 [10]. From computing the short column
capacity u core pr P core p , the value to u core pr can be readily determined.
P
P p
core
A
u pr core P p
core
e
1
Balanced
point B
u pr core P p core e
C
M p
core
M
FIGURE 1 : Determination of u pr
core
For steel tubes, the term u pr tube can be readily determined from [2]:
u
tube
pr
1
= (16)
1 + eA / S
s
s
with S s plastic modulus of the steel tube.
48

Second International Workshop « Structures in Fire » – Christchurch – March 2002
CASE STUDIES
Four case studies comprising a total of 61 RCFS columns tested under standard fire ISO 34 and
ASTM E119 are analysed to verify the Rankine formula. The test conditions of these case
studies are summarized in Table 1.
Case
Study
Ref No Section Size
(mm)
1 [11],
22 Square 200×200;
UTI/CTICM
225×225;
2 [11],
CSTB
3 [12, 13],
Technical
University of
Braunschweig
10 square;
circular
21 square;
circular
4 [14], CNRC 8 square;
circular
260×260;
300×300
140×140;
160×160;
225×225;
∅219.1
200×200;
260×260;
300×300;
∅273
203.2×203.2;
254×254;
304.8×304.8;
∅273.1
Table 2 : test conditions of the four case studies
Length
(m)
End
support
3.6 pinnedfixed;
fixedfixed
3.7,
4.2, or
5.2
3.6 fixedfixed
pinnedfixed
3.81 fixedfixed
Eccentricity
(mm)
Fire
curve
Aggregate
Type
0 to 100; ISO 834 Siliceous
aggregate
0 ISO 834 Siliceous
aggregate
0 or 100 ISO 834 Siliceous
aggregate
0 ASTM
E119
Carbonate
aggregate
The comparisons of the Rankine prediction with the test results for the four case studies are
shown in Figure 2.
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Second International Workshop « Structures in Fire » – Christchurch – March 2002
Predicted load capacity (kN)
3000
2000
1000
0
UTI/CTICM
Mean 0.70
SD 0.185
COV 0.263
0 1000 2000 3000
Applied load (kN)
Predicted load capacity (kN)
1200
800
400
0
CSTB
Mean 0.68
SD 0.139
COV 0.205
0 400 800 1200
Applied load (kN)
Predicted load capacity (kN)
1600
1200
800
400
0
Braunschweig
Mean 0.99
SD 0.267
COV 0.270
0 400 800 1200 1600
Applied load (kN)
Predicted load capacity (kN)
4000
3000
2000
1000
0
CNRC
Mean 0.63
SD 0.177
COV 0.280
0 1000 2000 3000 4000
Applied load (kN)
FIGURE 2 : Comparison with test results
For all the four case studies, the Rankine predictions give consistent predictions with coefficient
of variations around 25%, which are reasonably good for RCFS columns under fire conditions.
Furthermore, for most of the columns, the Rankine predictions are on the conservative side, since
the method ignores the confinement effect of steel tube on concrete core.
CONCLUSIONS
The Rankine approach for RCFS columns in fire conditions is presented in the current paper. A
theoretical model is derived for both axially- and eccentrically-loaded columns. Four case
studies including 61 RCFS columns are analyzed to verify the approach. The experimental
results show that the Rankine approach is not only accurate and consistent, but also conservative.
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Second International Workshop « Structures in Fire » – Christchurch – March 2002
REFERENCES
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1994.
[2] Tang, C. Y., Tan, K. H. and Ting, S. K., Basis and Application of a Simple Interaction
Formula for Steel Columns under Fire Conditions, J. Struct. Engrg., ASCE, October, Vol.
127, No. 10, pp 1206-1213, 2001.
[3] Tang, C. Y. and Tan, K. H., Basis and Application of a Simple Interaction Formula for
Steel Frames under Fire Conditions, J. Struct. Engrg., ASCE, October, Vol. 127, No. 10,
pp 1214-1220, 2001.
[4] Tang, C. Y., An Interactive Formula for Fire Resistance of Columns, M.Eng. Thesis,
School of Civil and Environmental Engineering, Nanyang Technological University,
Singapore, 2002.
[5] Dotreppe, J.C., Franssen, J.M., Vanderzeypen, Y., Calculation Method for Design of
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[6] ISO 834, Fire Resistance Teats-Elements of Building Construction, International
Standards Organisation, 1975.
[7] ASTM-E119, Standard Methods of Fire Tests of Building Construction and Materials,
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[9] Eurocode 3, Design of Steel Structure. Part 1.2: General Rules – Structural Fire Design,
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[12] Kordina, K., and Klingsch, W., Fire Resistance of Composite Columns of Concrete Filled
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SA/108, Studiengesellschaft P. 35, 1983.
[13] Hass, R., Practical Rules for the Design of Reinforced Concrete and Composite Columns
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Council Canada, 1992.
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Second International Workshop « Structures in Fire » – Christchurch – March 2002