fire resistance of reinforced concrete filled steel columns
fire resistance of reinforced concrete filled steel columns
fire resistance of reinforced concrete filled steel columns
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Second International Workshop « Structures in Fire » – Christchurch – March 2002<br />
FIRE RESISTANCE OF REINFORCED CONCRETE FILLED<br />
STEEL COLUMNS<br />
Kang Hai TAN<br />
Nanyang Technological University, School <strong>of</strong> Civil and Environmental Engineering,N1-<br />
1c-97, Singapore<br />
ckhtan@ntu.edu.sg<br />
Chu Yang TANG<br />
Nanyang Technological University, School <strong>of</strong> Civil and Environmental Engineering,N1-<br />
B4-04, Singapore<br />
p141449244@ntu.edu.sg<br />
ABSTRACT<br />
A simple calculation method, the Rankine method, is applied to determine <strong>fire</strong> <strong>resistance</strong> <strong>of</strong><br />
<strong>reinforced</strong> <strong>concrete</strong> <strong>filled</strong> <strong>steel</strong> (RCFS) <strong>columns</strong>. The same method has been applied to <strong>steel</strong> and<br />
<strong>reinforced</strong> <strong>concrete</strong> <strong>columns</strong> successfully.<br />
RCFS <strong>columns</strong> in <strong>fire</strong> can fail under two modes: plastic squashing for stocky <strong>columns</strong> and<br />
buckling for slender <strong>columns</strong>. For <strong>columns</strong> in the intermediate range, these two modes will<br />
interact to each other, causing a reduction in the load capacity <strong>of</strong> real <strong>columns</strong>. The Rankine<br />
approach assumes a linear interactive relationship between the two failure modes, which has<br />
been shown to be a lower bound approach. The formulation is presented for both axially- and<br />
eccentrically-loaded <strong>columns</strong>. The Rankine predictions are compared to four case studies<br />
comprising 61 tested RCFS <strong>columns</strong>. Good agreement is observed.<br />
KEYWORDS: <strong>fire</strong> <strong>resistance</strong>, <strong>concrete</strong>, column, <strong>reinforced</strong> <strong>concrete</strong>, <strong>steel</strong>, <strong>fire</strong> test<br />
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Second International Workshop « Structures in Fire » – Christchurch – March 2002<br />
INTRODUCTION<br />
Fire <strong>resistance</strong> <strong>of</strong> <strong>reinforced</strong> <strong>concrete</strong> <strong>filled</strong> <strong>steel</strong> (RCFS) <strong>columns</strong>, which is traditionally<br />
determined by expensive furnace tests, presents a formidable problem to structural engineers.<br />
1. Steel tube <strong>of</strong> RCFS <strong>columns</strong> s<strong>of</strong>tens quickly at elevated temperatures and the load is<br />
transferred to the cooler <strong>concrete</strong> core, which is <strong>reinforced</strong> by <strong>steel</strong> reinforcement.<br />
Therefore, the <strong>concrete</strong> core largely determines the load capacity <strong>of</strong> RCFS <strong>columns</strong>, with<br />
only small contribution from the <strong>steel</strong> tube.<br />
2. The moment capacity <strong>of</strong> <strong>steel</strong> tube is also greatly reduced. This phenomenon is particularly<br />
detrimental to <strong>columns</strong> with <strong>steel</strong> tubes <strong>filled</strong> with plain <strong>concrete</strong>, as the <strong>concrete</strong> section<br />
cannot resist bending moment by itself. At ambient temperature, such a column can resist<br />
large bending moment by the <strong>steel</strong> tube. However, when subjected to elevated temperatures,<br />
the moment capacity <strong>of</strong> the column diminishes quickly as the <strong>steel</strong> tube s<strong>of</strong>tens. This will<br />
likely lead to a loss <strong>of</strong> ductility and thus a premature failure, as observed by Lie and Stringer<br />
[1]. As a general comment, only design plain <strong>concrete</strong> <strong>filled</strong> <strong>steel</strong> (PCFS) <strong>columns</strong> to carry<br />
axial loads in <strong>fire</strong> conditions. Where load eccentricity is anticipated, <strong>reinforced</strong> <strong>concrete</strong><br />
<strong>filled</strong> <strong>steel</strong> (RCFS) <strong>columns</strong> should always be used.<br />
3. The confinement effect to the <strong>concrete</strong> core will also diminish as a result <strong>of</strong> the s<strong>of</strong>tening <strong>of</strong><br />
<strong>steel</strong> tube.<br />
This paper outlines a simple analytical method, the Rankine method, to determine the <strong>fire</strong><br />
<strong>resistance</strong> <strong>of</strong> <strong>reinforced</strong> <strong>concrete</strong> <strong>filled</strong> <strong>steel</strong> (RCFS) <strong>columns</strong>. The same method has been<br />
applied to <strong>steel</strong> <strong>columns</strong>, <strong>steel</strong> frames, and <strong>reinforced</strong> <strong>concrete</strong> <strong>columns</strong> successfully [2 - 4]. The<br />
Rankine predictions are compared to four case studies comprising <strong>of</strong> 61 tested RCFS <strong>columns</strong><br />
and good agreement is observed.<br />
RANKINE FORMULA<br />
The Rankine formula for <strong>columns</strong> under <strong>fire</strong> conditions has the following form:<br />
1 1 1<br />
= +<br />
(1)<br />
P ( t)<br />
u P ( t)<br />
P ( ) t<br />
R<br />
pr<br />
p<br />
e<br />
with P R predicted failure load by the Rankine formula;<br />
u pr reduction factor <strong>of</strong> the plastic squashing load due to load eccentricity;<br />
P p plastic squashing load;<br />
u pr P p short column capacity;<br />
P e elastic buckling load;<br />
t <strong>fire</strong> exposure time; t = 0 for ambient conditions.<br />
The theoretical basis <strong>of</strong> the above formula has been discussed by Tang et al [2]. RCFS <strong>columns</strong><br />
in <strong>fire</strong> can fail under two modes: plastic squashing for stocky <strong>columns</strong> and buckling for slender<br />
<strong>columns</strong>. For <strong>columns</strong> in the intermediate range, these two modes will interact with each other,<br />
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Second International Workshop « Structures in Fire » – Christchurch – March 2002<br />
causing a reduction in the load capacity <strong>of</strong> real <strong>columns</strong>. Clearly, the Rankine formula provides<br />
a linear interaction relationship between the plastic squashing load P p and the elastic buckling<br />
load P e . The Rankine load has been shown to be a lower bound approach [2, 3].<br />
FIRE RESISTANCE OF RCFS COLUMNS<br />
Due to the s<strong>of</strong>tening <strong>of</strong> the <strong>steel</strong> tube at elevated temperatures, the confinement effect to the<br />
<strong>concrete</strong> core from <strong>steel</strong> tube diminishes in <strong>fire</strong> conditions. Furthermore, separation <strong>of</strong> the<br />
<strong>concrete</strong> core from the <strong>steel</strong> tube can also be frequently observed in <strong>fire</strong> conditions [1], which<br />
suggests a loss <strong>of</strong> bond at the interface between the <strong>concrete</strong> core and <strong>steel</strong> tube. As a result, the<br />
load capacity P <strong>of</strong> axially-loaded RCFS <strong>columns</strong> can be simply taken as the sum <strong>of</strong> the capacity<br />
<strong>of</strong> <strong>concrete</strong> core P core and that <strong>of</strong> the <strong>steel</strong> tube P tube :<br />
core<br />
tube<br />
P( ) t = P ( t)<br />
+ P ( t)<br />
(2)<br />
where the superscripts “core” and “tube” indicate the contribution from the <strong>concrete</strong> core and<br />
<strong>steel</strong> tube, respectively. Both P core and P tube can be determined by the Rankine formula.<br />
CONCRETE CORE CAPACITY<br />
For the <strong>concrete</strong> core at elevated temperatures:<br />
1 1<br />
1<br />
= +<br />
(3)<br />
core core core<br />
core<br />
P ( t)<br />
u P ( t)<br />
P ( t)<br />
pr<br />
p<br />
e<br />
In Equation (3), the plastic squashing load <strong>of</strong> the <strong>concrete</strong> core can be determined from<br />
core<br />
p<br />
P ( t)<br />
= β ( t)<br />
f '(0)<br />
A + β ( t)<br />
f (0)<br />
A<br />
(4)<br />
c<br />
c<br />
c<br />
yr<br />
yr<br />
sr<br />
with f c ′ <strong>concrete</strong> cylinder strength;<br />
f yr yield strength <strong>of</strong> <strong>steel</strong> reinforcement;<br />
A c area <strong>of</strong> <strong>concrete</strong>;<br />
area <strong>of</strong> <strong>steel</strong> reinforcement.<br />
A sr<br />
The terms β c (t) and β yr (t) are the respective strength reduction factors accounting for the<br />
deterioration <strong>of</strong> <strong>concrete</strong> and <strong>steel</strong> reinforcement under <strong>fire</strong> conditions.<br />
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Second International Workshop « Structures in Fire » – Christchurch – March 2002<br />
∫ fc<br />
'( t)<br />
dAc<br />
β<br />
c<br />
( t)<br />
=<br />
(5)<br />
f '(0) A<br />
c<br />
yr<br />
c<br />
f<br />
yr<br />
( ) t Asr<br />
β yr ( t)<br />
=<br />
∑<br />
(6)<br />
f (0) A<br />
sr<br />
Similarly, the elastic buckling load <strong>of</strong> the <strong>concrete</strong> core can be determined from:<br />
P<br />
core<br />
e<br />
2<br />
π [ β<br />
( t)<br />
=<br />
Ec<br />
( t)<br />
⋅ 0.2E<br />
(0) I + β<br />
c<br />
L<br />
c<br />
2<br />
e<br />
Esr<br />
( t)<br />
⋅ E (0) I ]<br />
sr<br />
sr<br />
(7)<br />
with E c elastic modulus for <strong>concrete</strong>;<br />
I c second moment <strong>of</strong> area <strong>of</strong> <strong>concrete</strong>;<br />
E sr elastic modulus <strong>of</strong> <strong>steel</strong> reinforcement;<br />
I sr second moment <strong>of</strong> area <strong>of</strong> <strong>steel</strong> reinforcement;<br />
column effective length taking note <strong>of</strong> different support conditions<br />
L e<br />
The terms β Ec (t) and β Esr (t) are the respective stability reduction factors accounting for the<br />
deterioration <strong>of</strong> <strong>concrete</strong> and <strong>steel</strong> reinforcement under <strong>fire</strong> conditions.<br />
∫ Ec<br />
( t)<br />
dI<br />
c<br />
β<br />
Ec<br />
( t)<br />
=<br />
(8)<br />
E (0) I<br />
c<br />
yr<br />
c<br />
Esr<br />
( t)<br />
I<br />
sr<br />
β yr ( t)<br />
=<br />
∑<br />
(9)<br />
E (0) I<br />
sr<br />
The material reduction factors β c (t), β yr (t), β Ec (t) and β Esr (t) can be determined either<br />
experimentally or by finite element analysis. Based on their previous study <strong>of</strong> RC <strong>columns</strong> in<br />
<strong>fire</strong> conditions [4], the authors proposed to adopte the following material models. They are<br />
modified from Dotreppe et al. [5]:<br />
γ ( te)<br />
β<br />
c(<br />
t)<br />
=<br />
(10a)<br />
− 0.25<br />
−0.5<br />
A<br />
1+<br />
(0.3A<br />
t ) c<br />
c<br />
e<br />
0.9te<br />
β<br />
yr<br />
( t)<br />
= γ ( te<br />
) ⋅ (1 −<br />
) ≥ 0<br />
(10b)<br />
0.046c<br />
+ 0.11<br />
Ec<br />
0.15<br />
c<br />
te<br />
β ( t)<br />
= (1.1A<br />
) ⋅ β ( t)<br />
(10c)<br />
2<br />
yr<br />
c<br />
β ( t)<br />
= 0.8β<br />
( t)<br />
+ 0.2β<br />
( t)<br />
(10d)<br />
Esr<br />
yr<br />
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Second International Workshop « Structures in Fire » – Christchurch – March 2002<br />
with c <strong>concrete</strong> cover;<br />
γ ( t e<br />
) an empirical factor to account for the effect <strong>of</strong> <strong>concrete</strong> spalling; γ ( t e<br />
) = 1.0 for<br />
RCFS <strong>columns</strong> as they are protected from spalling by the <strong>steel</strong> tube;<br />
Here, the equivalent time t e in terms <strong>of</strong> <strong>fire</strong> severity can be estimated by<br />
te<br />
α<br />
aggα<br />
ISOt<br />
= (13)<br />
where<br />
α agg = 1.0 for siliceous aggregate and α agg = 0.9 for carbonate aggregate;<br />
α ISO = 1.0 for ISO 834 <strong>fire</strong> and α ISO = 0.85 for ASTM-E119 <strong>fire</strong>.<br />
STEEL TUBE CAPACITY<br />
The <strong>steel</strong> tube capacity can be determined from:<br />
1<br />
=<br />
P ( t)<br />
u<br />
+<br />
tube tube tube<br />
pr<br />
Pp<br />
( t)<br />
1<br />
P<br />
1<br />
tube<br />
e<br />
( t)<br />
where<br />
tube<br />
p<br />
P ( t)<br />
= k ( t)<br />
⋅ f (0)<br />
A<br />
(14)<br />
P<br />
tube<br />
e<br />
y<br />
y<br />
s<br />
2<br />
e<br />
s<br />
2<br />
π E (0) I<br />
s<br />
( t)<br />
= kE<br />
( t)<br />
⋅<br />
(15)<br />
L<br />
with f y yield strength <strong>of</strong> the <strong>steel</strong> tube;<br />
A s<br />
E s<br />
I s<br />
area <strong>of</strong> the <strong>steel</strong> tube;<br />
elastic modulus for <strong>steel</strong> tube;<br />
second moment <strong>of</strong> area <strong>of</strong> <strong>steel</strong> tube.<br />
The factors k y (t) and k E (t) are the respective material reduction factors to yield strength and<br />
elastic modulus <strong>of</strong> structural <strong>steel</strong> at elevated temperatures. Table 1 shows the values <strong>of</strong> k y (t)<br />
and k E (t) at different <strong>fire</strong> temperatures for ISO 834 [6] and ASTM E119 [7] <strong>fire</strong>s obtained from<br />
the finite element program SAFIR [8], by adopting the Eurocode 3 structural <strong>steel</strong> material<br />
model [9].<br />
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Second International Workshop « Structures in Fire » – Christchurch – March 2002<br />
Reduction factor k y (t) Reduction factor k E (t)<br />
Time t (hour) ISO 834 ASTM<br />
E119<br />
ISO 834 ASTM<br />
E119<br />
0 1.000 1.000 1.000 1.000<br />
0.5 0.371 0.362 0.242 0.235<br />
1.0 0.065 0.073 0.073 0.077<br />
1.5 0.050 0.055 0.051 0.057<br />
2.0 0.034 0.042 0.039 0.047<br />
2.5 0.027 0.037 0.030 0.041<br />
3.0 0.020 0.032 0.023 0.036<br />
3.5 0.015 0.028 0.017 0.031<br />
4.0 0.011 0.023 0.012 0.026<br />
Table 1 : strength reduction factors k y (t) and k E (t) <strong>of</strong> <strong>steel</strong> tube<br />
EFFECT OF LOAD ECCENTRICITY<br />
The effect <strong>of</strong> load eccentricity e on <strong>concrete</strong> core is to lower the short column capacity<br />
u core pr P core core<br />
core<br />
p . For axially-loaded <strong>columns</strong>, u pr is unity. The magnitude <strong>of</strong> u pr for<br />
eccentrically-loaded <strong>columns</strong> can be determined from the conventional axial-load-bendingmoment<br />
interaction diagram, as shown in Figure 1 [10]. From computing the short column<br />
capacity u core pr P core p , the value to u core pr can be readily determined.<br />
P<br />
P p<br />
core<br />
A<br />
u pr core P p<br />
core<br />
e<br />
1<br />
Balanced<br />
point B<br />
u pr core P p core e<br />
C<br />
M p<br />
core<br />
M<br />
FIGURE 1 : Determination <strong>of</strong> u pr<br />
core<br />
For <strong>steel</strong> tubes, the term u pr tube can be readily determined from [2]:<br />
u<br />
tube<br />
pr<br />
1<br />
= (16)<br />
1 + eA / S<br />
s<br />
s<br />
with S s plastic modulus <strong>of</strong> the <strong>steel</strong> tube.<br />
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Second International Workshop « Structures in Fire » – Christchurch – March 2002<br />
CASE STUDIES<br />
Four case studies comprising a total <strong>of</strong> 61 RCFS <strong>columns</strong> tested under standard <strong>fire</strong> ISO 34 and<br />
ASTM E119 are analysed to verify the Rankine formula. The test conditions <strong>of</strong> these case<br />
studies are summarized in Table 1.<br />
Case<br />
Study<br />
Ref No Section Size<br />
(mm)<br />
1 [11],<br />
22 Square 200×200;<br />
UTI/CTICM<br />
225×225;<br />
2 [11],<br />
CSTB<br />
3 [12, 13],<br />
Technical<br />
University <strong>of</strong><br />
Braunschweig<br />
10 square;<br />
circular<br />
21 square;<br />
circular<br />
4 [14], CNRC 8 square;<br />
circular<br />
260×260;<br />
300×300<br />
140×140;<br />
160×160;<br />
225×225;<br />
∅219.1<br />
200×200;<br />
260×260;<br />
300×300;<br />
∅273<br />
203.2×203.2;<br />
254×254;<br />
304.8×304.8;<br />
∅273.1<br />
Table 2 : test conditions <strong>of</strong> the four case studies<br />
Length<br />
(m)<br />
End<br />
support<br />
3.6 pinnedfixed;<br />
fixedfixed<br />
3.7,<br />
4.2, or<br />
5.2<br />
3.6 fixedfixed<br />
pinnedfixed<br />
3.81 fixedfixed<br />
Eccentricity<br />
(mm)<br />
Fire<br />
curve<br />
Aggregate<br />
Type<br />
0 to 100; ISO 834 Siliceous<br />
aggregate<br />
0 ISO 834 Siliceous<br />
aggregate<br />
0 or 100 ISO 834 Siliceous<br />
aggregate<br />
0 ASTM<br />
E119<br />
Carbonate<br />
aggregate<br />
The comparisons <strong>of</strong> the Rankine prediction with the test results for the four case studies are<br />
shown in Figure 2.<br />
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Second International Workshop « Structures in Fire » – Christchurch – March 2002<br />
Predicted load capacity (kN)<br />
3000<br />
2000<br />
1000<br />
0<br />
UTI/CTICM<br />
Mean 0.70<br />
SD 0.185<br />
COV 0.263<br />
0 1000 2000 3000<br />
Applied load (kN)<br />
Predicted load capacity (kN)<br />
1200<br />
800<br />
400<br />
0<br />
CSTB<br />
Mean 0.68<br />
SD 0.139<br />
COV 0.205<br />
0 400 800 1200<br />
Applied load (kN)<br />
Predicted load capacity (kN)<br />
1600<br />
1200<br />
800<br />
400<br />
0<br />
Braunschweig<br />
Mean 0.99<br />
SD 0.267<br />
COV 0.270<br />
0 400 800 1200 1600<br />
Applied load (kN)<br />
Predicted load capacity (kN)<br />
4000<br />
3000<br />
2000<br />
1000<br />
0<br />
CNRC<br />
Mean 0.63<br />
SD 0.177<br />
COV 0.280<br />
0 1000 2000 3000 4000<br />
Applied load (kN)<br />
FIGURE 2 : Comparison with test results<br />
For all the four case studies, the Rankine predictions give consistent predictions with coefficient<br />
<strong>of</strong> variations around 25%, which are reasonably good for RCFS <strong>columns</strong> under <strong>fire</strong> conditions.<br />
Furthermore, for most <strong>of</strong> the <strong>columns</strong>, the Rankine predictions are on the conservative side, since<br />
the method ignores the confinement effect <strong>of</strong> <strong>steel</strong> tube on <strong>concrete</strong> core.<br />
CONCLUSIONS<br />
The Rankine approach for RCFS <strong>columns</strong> in <strong>fire</strong> conditions is presented in the current paper. A<br />
theoretical model is derived for both axially- and eccentrically-loaded <strong>columns</strong>. Four case<br />
studies including 61 RCFS <strong>columns</strong> are analyzed to verify the approach. The experimental<br />
results show that the Rankine approach is not only accurate and consistent, but also conservative.<br />
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Second International Workshop « Structures in Fire » – Christchurch – March 2002<br />
REFERENCES<br />
[1] Lie, T. T. and Stringer, D. C., Calculation <strong>of</strong> the Fire Resistance <strong>of</strong> Steel Hollow<br />
Structural Section Columns Filled with Plain Concrete, Can. J. Civ. Eng., 21, 382-385,<br />
1994.<br />
[2] Tang, C. Y., Tan, K. H. and Ting, S. K., Basis and Application <strong>of</strong> a Simple Interaction<br />
Formula for Steel Columns under Fire Conditions, J. Struct. Engrg., ASCE, October, Vol.<br />
127, No. 10, pp 1206-1213, 2001.<br />
[3] Tang, C. Y. and Tan, K. H., Basis and Application <strong>of</strong> a Simple Interaction Formula for<br />
Steel Frames under Fire Conditions, J. Struct. Engrg., ASCE, October, Vol. 127, No. 10,<br />
pp 1214-1220, 2001.<br />
[4] Tang, C. Y., An Interactive Formula for Fire Resistance <strong>of</strong> Columns, M.Eng. Thesis,<br />
School <strong>of</strong> Civil and Environmental Engineering, Nanyang Technological University,<br />
Singapore, 2002.<br />
[5] Dotreppe, J.C., Franssen, J.M., Vanderzeypen, Y., Calculation Method for Design <strong>of</strong><br />
Reinforced Concrete Columns under Fire Conditions, ACI Structural Journal, V. 96, No.<br />
1, 9-18, 1999.<br />
[6] ISO 834, Fire Resistance Teats-Elements <strong>of</strong> Building Construction, International<br />
Standards Organisation, 1975.<br />
[7] ASTM-E119, Standard Methods <strong>of</strong> Fire Tests <strong>of</strong> Building Construction and Materials,<br />
American Society for Testing and Materials, Philadelphia, PA, USA, 1995,<br />
[8] Franssen, J.M., Cooke, G.M.E., and Latham, D.J., Numerical Simulation <strong>of</strong> a Full Scale<br />
Fire Test on a Loaded Steel Framework, J. <strong>of</strong> Constructional Steel Research, 35: 377-<br />
408, 1995.<br />
[9] Eurocode 3, Design <strong>of</strong> Steel Structure. Part 1.2: General Rules – Structural Fire Design,<br />
ENV 1993-1-2, European Committee for Standardization, 1995.<br />
[10] Nilson, A.H. and Winter, G., Design <strong>of</strong> Concrete Structures, 11 th Ed., New York:<br />
McGraw-Hill, 1991, 1991.<br />
[11] Grandjean, G., Grimault, J.P., and Petit, L., Determination de la durée au feu des pr<strong>of</strong>ils<br />
creux remplis de béton, Rapport Final. Commission des Communautés Européennes,<br />
Recherche Technique acier. Luxembourg (in French), 1981.<br />
[12] Kordina, K., and Klingsch, W., Fire Resistance <strong>of</strong> Composite Columns <strong>of</strong> Concrete Filled<br />
Hollow Sections – Research report, CIDECT 15 C1/C2-83/27 (part <strong>of</strong> C.E.C. 7210-<br />
SA/108, Studiengesellschaft P. 35, 1983.<br />
[13] Hass, R., Practical Rules for the Design <strong>of</strong> Reinforced Concrete and Composite Columns<br />
Submitted to Fire, Technical Report No. 69, Institute für Baust<strong>of</strong>fe, Massivbau und<br />
Brandschutz der Technischen Universitä Braunschweig (in German), 1986 ().<br />
[14] Chabot, M. and Lie, T.T., Experimental Studies on the Fire Resistance <strong>of</strong> Hollow Steel<br />
<strong>columns</strong> Filled with Bar-Reinforced Concrete, Internal report No. 628, National Research<br />
Council Canada, 1992.<br />
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