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Some considerations in the design of unprotected concrete-filled steel tubular columns under fire conditions
J. Construct. Steel Res. Vol. 44, No. 3, pp. 203-223, 1997 © 1998 Building Research Establishment Ltd. Published by Elsevier Science Ltd. Printed in Great Britain PII: S0143-9'74X(97)00(~-6 0143-974X/98 $19.00 + 0.00
ELSEVIER
Some Considerations in the Design of Unprotected Concrete-Filled Steel Tubular Columns Under Fire Conditions Y. C. Wang Structural Design Division, Building Research Establishment, Watford WD2 7JR, UK (Received 21 August 1996; revised version received 16 July 1997; accepted 22 July 1997)
ABSTRACT This paper is concerned with the fire resistant design of centrally loaded unprotected concrete-filled steel tubular columns using Eurocode 4 Part 1.2. It addresses three issues: the column buckling curve to be used for elevated temperature design, the implementation of the calculation method in Eurocode 4 Part 1.2 and the equivalent time of fire exposure. The predicted column fire resistance using the Eurocode 4 Part 1.2 calculation method is compared with the results of tests on 36 concrete-filled circular hollow section columns and seven square hollow section columns conducted at the National Fire Laboratory of Canada. This comparative study indicates that the choice of column buckling curve for elevated temperature design depends on the adopted concrete strength and stiffness-temperature models. If the models in the main text of Eurocode 4 Part 1.2 are used, column bucking curve 'a' seems to give more accurate results. For the standard fire resistant design, this paper proposes a simple method to implement the general calculation method in Eurocode 4 Part 1.2. This proposed method is easy to use and was demonstrated to be quite accurate. Using the parametric time-temperature relationships in Eurocode 1 Part 2.2 to represent the behaviour of realistic fires, this paper studies the equivalent time approach, based on the column resistance. Results from this study show that the equivalent time equation in Eurocode 1 Part 2.2 needs modifying to allow for the inter-dependence between fire load and ventilation factor and this equation is also unsafe. This paper further suggests introducing a multiplication factor in the equivalent time equation to cater for different types of construction element. © 1997 Elsevier Science Ltd.
Present address: The University of Manchester, Manchester M13 9PL, UK. 203
204
Y. C. Wang
NOTATION
Eurocode 1 Part 2.2 symbols Fire compartment floor area Total interior area of fire compartment Area of opening = ~/kpc of compartment lining material Specific heat of lining material Height of opening Thermal conductivity of lining material Conversion factor Opening factor Av~-h/A t Fire load density Equivalent time Ventilation factor = O - I/2AJAt Density of lining material
af
At Av b C
h k kb 0 qf, d te,a
Wf
P
Additional symbols Unreinforced column rigidity at elevated temperature Unreinforced column rigidity at elevated temperature, (E/)r,n o,o reference grades of steel and concrete E h T = 2 0 , R = 0 Unreinforced column rigidity at ambient temperature (EI)T = 2O,R= o,o Unreinforced column rigidity at ambient temperature, reference grades of steel and concrete Colunm Euler load at elevated temperature Ncr, T Column resistance to compression at elevated temperature /V~,r Column squash load at elevated temperature Unreinforced column squash load at elevated temperature Nu,T,R = 0 Unreinforced column squash load at elevated temperature, Nu,T,R = 0 , 0 reference grades of steel and concrete Unreinforced column squash load at ambient temperature Nu,T = 2 0 , R = 0 gu,T = 2 0 , R = 0 , 0 Unreinforced column squash load at ambient temperature, reference grades of steel and concrete Column relative slenderness at elevated temperature /~T Concrete design strength O'cu Reference grade of concrete design strength o-o Column strength reduction coefficient at elevated X~ temperature (EhT, R = 0 =
Considerations in design of unprotected concrete-filled steel tubular columns
205
1 INTRODUCTION The supporting columns to a building play a critical role in its stability under fire conditions. This was clearly demonstrated in a recently completed major research programme on a full-scale eight storey steel-framed building at the Building Research Establishment's Cardington Laboratory [1]. In one of the tests in which the steel H-columns were not fully fire protected, the fire damage extended well beyond the small test area on the floor and over all the storeys above. This strongly suggests the need for fire protecting columns to have sufficient fire resistance. To present the architecturally pleasing feature of exposed steelwork while still maintaining fire safety, unprotected concrete-filled steel tubular columns may be used to rely on their inherently high fire resistance. They also have a number of advantages over either bare steel columns or reinforced concrete columns, including high load carrying capacity, rapid construction and economic use of floor space. There have been a few major research programmes on the fire resistance of concrete-filled columns in Europe [2,3] and Canada [4-8]. The European standard for elevated temperature design Eurocode 4 Part 1.2 [9] is based on the results of the European research programme [2]. While the fundamental approach in Eurocode 4 Part 1.2 [9] is similar to that for ambient temperature design in Eurocode 4 Part 1.1 [10], Eurocode 4 Part 1.2 [9] recommends using column buckling curve 'c' for elevated temperature design and Eurocode 4 Part 1.1 [10] uses column buckling curve 'a' for ambient temperature design. Although the recommendation in Eurocode 4 Part 1.2 [9] is conservative and, therefore, on the safe side, concrete-filled columns should not be unnecessarily put to economic disadvantage. This paper will examine this recommendation using the results of a series of tests [7] undertaken at the National Fire Laboratory in Canada. In the calculation method in Eurocode 4 Part 1.2 [9], only the fundamental principles of heat transfer and structural analysis are given, which become quite complicated in the actual implementation for concrete-filled columns owing to the highly non-uniform temperature distribution in the composite cross-section. While this does not present any problem in the development of numerical tools, engineers with no access to these numerical solutions may be deterred from using this approach. This paper attempts to develop a simple implementation method to promote the use of the calculation method in Eurocode 4 Part 1.2 [9]. Past research studies on concrete-filled columns have only been concerned with the standard fire exposure. Whilst design for standard fire exposure will continue for the foreseeable future, design for realistic fire exposures is gaining acceptance in the context of a performance-based approach. This paper exam-
Y. C. Wang
206
ines the equivalent time concept and assesses whether this applies to concretefilled columns. The objectives of this paper are therefore threefold: (1) to examine the validity of using column buckling curve 'c' for elevated temperature design in Eurocode 4 Part 1.2 [9]; (2) to propose a simple implementation method to use the calculation method in Eurocode 4 Part 1.2 [9]; (3) to assess the applicability of the equivalent time approach in Eurocode 1 Part 2.2 [11] to concrete-filled columns.
2 COLUMN BUCKLING CURVE Eurocode 4 Part 1.2 [9] uses the same approach as in Eurocode 4 Part 1.1 [10] to calculate the column compressive resistance at elevated temperatures. The column resistance Nr is related to the column squash load Nu.r as ArT = X Vu,
(1)
where Xr is the column strength reduction factor and is a function of the relative slenderness of the column Ar which is expressed as
Ar = x/--~-~'"
Ncr,r"
(2)
The relationship between Xr and Ar is represented by a column buckling curve. Eurocode 4 Part 1.1 [10] for ambient temperature design uses four different column buckling curves for different types of column and recommends column buckling curve 'a' for concrete-filled columns. Eurocode 4 Part 1.2 [9] recommends column buckling curve 'c' for elevated temperature design. This curve gives lower values than column buckling curve 'a'; therefore, the column resistance is lower. Whilst this may be considered to be conservative and on the safe side, it may unnecessarily put concrete-filled columns at an economic disadvantage. At elevated temperatures, the strength and stiffness of both steel and concrete decrease. The accuracy of the design method will depend on the adopted model describing the strength and stiffness-temperature relationships. For steel there is good agreement between different models, and the model in Eurocode 4 Part 1.2 [9] is used in this study. For concrete there is a large scatter between the different models, as shown in Fig. 1. This figure compares the model in the main text of Eurocode 4 Part 1.2 [9] and that used by Lie and coworkers [4-6] against some test results in a RILEM report [12]. This
Considerations in design of unprotected concrete-filled steel tubular columns
207
12 + -
+
÷ •
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.
.
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Lie Model
•
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•
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0
~
I 1O0
p 200
i ~
I 4[]0
I 500
I 600
, 700
800
900
Temperature [C)
Fig. 1. Comparison between different concrete strength-temperature models. indicates that the model in Eurocode 4 Part 1.2 [9] represents the lower bound to the test results and that of Lie and coworkers [4-6] the upper bound. To assess the influence of the concrete model on the accuracy of the calculation method in Eurocode 4 Part 1.2 [9], both models are used in this paper. The experimental results are taken from Lie and Chabot [7], which consist of 36 tests on circular hollow section (CHS) columns and seven tests on square hollow section (SHS) columns, all undertaken at the National Fire Laboratory of Canada. Comparisons between the calculated column fire resistance and test results are summarised in Table 1, which suggests that if the model of Lie and coworkers [4-6] is used, column buckling curve 'a' gives higher column fire resistance than test results and column buckling curve 'c' appears to be preferable. However, if the concrete model in Eurocode 4 Part 1.2 [9] is used, TABLE 1
Summary of comparisons between predicted fire resistance and test results [7] Concrete model in Eurocode 4 Part 1.2 [9] Column buckling curve 'a' Average pred./test 0.955 Standard deviation 0.256
'c' 0.839 0.234
Concrete model of Lie and coworkers [4-6] Column buckling curve 'a' Average pred./test 1.113 Standard deviation 0.299
'c' 0.954 0.271
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Y. C. Wang
column buckling curve 'a' seems to give more accurate results than column buckling curve 'c'. Although results from this study are not very conclusive, they suggest that because the concrete model in Eurocode 4 Part 1.2 [9] is already a conservative representation of the material test results, as shown in Fig. 1, it may not be necessary to build in an additional margin of safety by using column buckling curve 'c'.
3 IMPLEMENTATION OF THE CALCULATION METHOD IN EUROCODE 4 PART 1.2 To implement the calculation method in Eurocode 4 Part 1.2 [9], the designer is required to solve the fundamental equations of heat transfer to obtain the temperature distributions in the composite cross-section. In addition, because these temperature distributions are highly non-uniform, the user also has to divide the composite cross-section into many fine layers to calculate the column resistance accurately. Designers may be reluctant to adopt this approach because of the complexity and large number of computations involved in this design process. A simple implementation method is therefore needed to reduce this complexity so that designers are encouraged to used the calculation method in Eurocode 4 Part 1.2 [9]. For temperature distributions in the composite crosssection subjected to the standard fire exposure, Lawson and Newman [13] developed a simple tabular method. In their method, two multiplication factors are used to modify the temperature distribution in an infinite concrete slab subjected to the standard fire attack on one side. These two factors account for the different heat conduction in a circular or square section from that in an infinite concrete slab and also the effect of the steel tube acting both as a heat sink and heat shield to the concrete core. The effect of the steel tube in reducing heat flux to the concrete core diminishes at increasing fire exposure time. For the column resistance, eqns (1) and (2) require the values of column squash load and rigidity. Since reinforcements are usually laid at equal distance to the column centre, their contributions to these two values can be obtained in one calculation. This paper presents a simplification to the calculation of squash load and rigidity for the unreinforced concrete-filled section so that the designer does not have to divide the composite section into many fine layers and evaluate each separately. This simplification is developed on the following reasoning. There are only a limited number of steel tubular sections in practical use. In designs for the standard fire resistance, fire resistance ratings are specified in multiples of 30 min. Therefore, the number of fire resistance ratings is also
Considerations in design of unprotected concrete-filled steel tubular columns
209
limited. The general calculation method in Eurocode 4 Part 1.2 [9] may be implemented fully using a numerical method to give the exact squash load and rigidity for all section sizes and fire ratings for one set of reference grades of steel and concrete, the results of which can be used as a design aid table. However, as the grades of steel and concrete are design variables, it is not practical to prepare design aid tables for all combinations of steel and concrete grades. To use the numerically prepared design aid table for the reference grades of steel and concrete, the column squash load and rigidity of any design grades of steel and concrete may be related to those of the reference grades. Using subscript '0' to denote the reference grades, this paper proposes the following relationships: for squash load
NuTR=O Nu,r,R =0,0 •
'
O'cu 0"0
-
+
( Nu,T=20,R=O
O'cul NuTR=O,O
\Nu,r = 20,R = 0,0
O'0 / N u , T = 20,R = 0,0
"
"
(3)
for rigidity (E/)r,R = o
(E/)r = 20,R= 0 m
( E / ) T , R = o,o
(4)
( E / 3 T = 2o,R = o,o
In both equations, T = 20 for ambient temperature and R = 0 for an unreinforced section. Eqn (3) gives the ratio of the column squash load to that with reference grades of steel and concrete at any fire rating. It states that this ratio varies linearly with the change in column squash load for the reference grades of steel and concrete at elevated temperatures. This equation recognises that, after long periods of fire exposure, the steel tube loses its contribution and the column squash load ratio approaches the ratio of concrete design strengths. As an example, Fig. 2 compares the predictions of eqn (3) with those using the exact method in which the cross-section is divided into many layers. The vertical axis gives the ratio of the squash loads at elevated temperature and the horizontal axis gives the ratio of the squash load at elevated temperature to that at ambient temperature for the reference grades of steel and concrete, which were $275 and C30 respectively. Fig. 2 shows that eqn (3) gives very good approximations to the exact values obtained from a full numerical analysis. The same reasoning for squash load may be applied to rigidity. However, since the second moment of inertia is to the fourth power of the distance from the centre of the cross-section, the contribution from the steel tube cannot be ignored even at very high temperatures. Also, there is no change in the modu-
210
Y.C.
Wang
18 16 7,4
i
a.2
1 ~ (1.8
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I
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0.2
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0,6
0.7
0,8
0,9
1
ratk~d ~luaeh load at a~evat~l tmnp, to that a~room ~gttG~, referencegrad4m
Fig. 2. Determination of column squash load for different grades of steel and concrete, CHS 406.4 x I0.
lus of elasticity for different grades of steel and the change in the modulus of elasticity for different grades of concrete is small. Therefore, it is reasonable to assume the ratio of column rigidity at elevated temperature to that at ambient temperature to be independent of the grades of steel and concrete. Fig. 3 shows an example comparing the predictions using eqn (4) and the 1.4
1.2
S
i
1
t
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0.8
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Fig, 3. Determination of column rigidity for different grades of steel and concrete, CHS 406.4 × 10.
Considerations in design of unprotected concrete-filled steel tubular columns
211
exact values from a full numerical analysis. This figure confirms that eqn (4) can be used to calculate the column rigidity with good accuracy.
4 EQUIVALENT TIME OF FIRE EXPOSURE 4.1 Behaviour of real fires
In the current design for fire resistance, the fire exposure is represented by the standard time-temperature curve [14], shown in Fig. 4. However, the behaviour of real fires is significantly different. For example, Fig. 4 compares the standard time-temperature curve with a few measured real fire time-temperature curves. Owing to the complex behaviour of real fires, their time-temperature relationships are very difficult to quantify exactly. Broadly speaking, the timetemperature relationship of a real fire is determined by the size of the opening (which controls the maximum rate of burning), the available combustible materials (which determine the duration of burning) and the interior lining material (which absorbs heat). The ventilation condition is represented by an opening factor O = A,,~/-h/At where Av is the opening area, h the opening height and A t the total interior area of the compartment. The ability of the lining material to absorb heat is represented by the material property b = ~k-pc where k is its conductivity, p its density and c its specific heat. The higher the value of b, the more the lining material absorbs heat and the less severe the fire. The parametric time-temperature relationships originally developed in o
~anda~ tim ex~$um
i0 |
]
0
20
40
60
80
100
120
Fire exposure Uml (minutes)
Fig. 4. Comparison between time-temperature relationships.
~40
160
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Y. C. Wang
Sweden [15] are now widely accepted as providing good approximations to the behaviour of real fires and they have been adopted in Eurocode 1 Part 2.2 [ll]. To design for structural elements against real fire attack, it is no longer possible to specify a single time-temperature curve. Since the standard fire resistance has been used for a long time and a large body of information has been collated on this type of fire exposure, fire safety engineers have attempted to evaluate the effects of real fire exposures in terms of equivalent times of the standard fire exposure [16-18]. This equivalency has been established on the basis of a critical temperature in a structural element, i.e. the equivalent time of a real fire is the time when a structural element is subjected to the standard fire exposure that would give the same critical temperature as the maximum temperature which the structural element will get when subjected to the real fire exposure. This concept is illustrated in Fig. 5. Eurocode 1 Part 2.2 [l l] adopts the equivalent time formula of Pettersson [17] and is expressed as
(5)
kbqf,dW f
re, d =
where kb is a coefficient related to the thermal property b of the lining material, and k b = 0 . 0 4 , 0.055 and 0.07 respectively for b > 2500 J / ( m 2 s 1/2 K ) , b = 720-2500 J/(m 2 s 1/2 K) and b < 720 J/(m 2 s 1/2 K). qf,d is the fire load density defined as the fire load per unit floor area and wf is the ventilation factor related to the opening factor O by
S
Maximum
temperature under real fire exposure
|
Fire eXF.~Ure
time
Fig. 5. Conventional way of determining equivalent time of exposure.
Considerations in design of unprotected concrete-filled steel tubular columns
Wf = O -
af__
1/2
213
(6)
At
Owing to the non-uniform temperature distribution in the composite section, it is not possible to identify a critical temperature to calculate the equivalent time as illustrated in Fig. 5. In this paper, the equivalent time is established on the basis of the column resistance. This approach is illustrated in Fig. 6. In this paper, the equivalent time is defined as the time under the standard fire exposure which gives the column a resistance equal to the column minimum resistance under the real fire condition. In section 4.2, the results of equivalent time calculated using the approach in Fig. 6 are compared with the predictions from eqn (5) to examine its applicability and accuracy to concrete-filled columns. In this study, the parametric time-temperature relationships in Eurocode 1 Part 2.2 I l l ] are used to represent the behaviour of realistic fires. Using the method in Fig. 6, the equivalent time can be numerically calculated in two steps: first, the temperature distributions in the composite section under both the parametric fire and the standard fire conditions are evaluated; secondly, the minimum column resistance under the parametric fire condition is compared against the decreasing column resistance-time relationship under the standard fire condition to give the equivalent time.
~
/
tandardtim exposure
Realfire
T ~ Minimumcolumn resistance under real fire exposure
I I II /
Equivalent time of standard fire exposure
Fire oxl~eure time
Fig. 6. Determination of equivalent time of exposure in this paper.
Y. C. Wang
214
4.2 Numerical solution for temperature distribution in a composite section
To examine the equivalent time concept, it is necessary to be able to predict accurately the temperature development in a composite cross-section. To this end, a heat transfer finite element analysis computer program has been developed by the author. This program is based on well-developed theories in standard texts such as Zienkiewicz [19] and Bathe [20]. Four types of element may be used: 2-noded 1-dimensional element, 3-noded 1-dimensional element, triangle element and 4-noded 2-dimensional isoparametric element. Owing to symmetry, the temperature distribution in a concrete-filled CHS may be calculated using 1-dimensional elements in the radial direction to reduce computing time. In this method, material thermal properties (thermal conductivity and specific heat) and heat flux to the external surface of the cross-section should be increased in proportion to the radius. This approach may also be applied to a SHS. However, only the average temperature within each layer in the cross-section is calculated. The accuracy of this numerical analysis was examined by checking the predicted temperatures in concrete-filled columns against the test results from Lie and Chabot [7]. Figs 7 and 8 present comparisons for CHS (tests C31 and C32) and SHS (tests SQ01 and SQ02) columns respectively. 2-noded 1dimensional and 4-noded 2-dimensional elements were used for CHS and SHS sections respectively. For both types of section, the results of two tests with identical section size are shown. Lie and Chabot [7] used carbonate concrete for tests C31, C32 and SQ02 and siliceous concrete for test SQ01. In this study, the same concrete thermal 1000 goo
800-
600 8 500 -
,J
1/"
Steel, Prealcted oncre~e, Predicted
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i//
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I
I
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30
40 Fire e x p o s u r e ~
I 50
I 60
i 70
] 80
(mill)
Fig. 7. Comparison between temperatures for tests C31 and C32 [7].
I
90
Considerations in design of unprotected concrete-filled steel tubular columns
215
lOOO 9O0 800
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700 ./'~/./.1
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0
10
20
30
40
50
60
70
80
90
Fire exposure time (min)
Fig. 8. Comparison between temperatures for tests SQ01 and SQ02 [7].
properties in Eurocode 4 Part 1.2 [9] were used for both types of concrete. A moisture content of 10% in concrete was reported by Lie and Chabot [7]. To allow for moisture content, Eurocode 4 Part 1.2 [9] gives higher thermal capacitance at about 100°C at increasing moisture content and its value at 10% was used in the numerical analysis. A convection factor of 25 W/(m 2 °C) and a resultant emissivity of 0.7, as recommended in Eurocode 4 Part 1.2, [9] were also used. Fig. 7 shows that for steel temperatures, the difference between numerical predictions and test results is very small, especially during the important latter stage of the fire exposure. Numerical predictions for concrete temperatures are slightly less accurate. Owing to the uncertainties in the concrete thermal properties, the predicted results are considered to be very satisfactory. Results shown in Fig. 8 for the SHS section follow the same trend.
4.3 Input variables The parametric study was carded out using the following different values for each variable. Column section: CHS 219.6 x 6.3, CHS 219.6 x 20.0, CHS 406.4 x 10.0, CHS 406.4 x 32.0, SHS 200 x 6.3, SHS 200 x 16.0, SHS 400 x 10.0, SHS 400 × 16.0, chosen to cover a range of column dimension and percentage of steel.
216 Column effective length:
Y. C. Wang
2 m , 4 m and 6 m .
Reinforcement area: 0%, 1%, 3% and 5% of the concrete core area. Fire load density:
360 MJ/m 2, 720 MJ/m 2 and 1440 MJ/m 2, representing the lower bound, average and upper bound.
Opening factor:
O = 0.04 m 1/2, 0.1 m 1/2 and 0.2 m 1/2, representing the lower bound, average and upper bound.
Lining material:
b = 720, 1160 and 2500 J/(m 2 s 1/2 K), being the three demarking values in Eurocode 1 Part 2.2 [11].
The reference value for each of the above variables was: column effective length 4 m, reinforcement 3%, fire load density 720 MJ/m 2, opening factor 0.1 m ~/2 and lining material 1160 J/(m 2 s 1/2 K). To facilitate the determination of the parametric fire time-temperature relationships, the compartment was assumed to be 9 m long, 6 m wide and 4 m high. Other input data include steel yield stress 275 N/mm 2, concrete design strength 30 N/mm 2, reinforcement yield stress 450 N/mm 2 and concrete cover to reinforcement 35 mm. Based on the conclusion stated previously, column buckling curve 'a' was used in the calculations of the column resistance to axial compression. Nevertheless, the choice of column buckling curve should only have a very small influence on the equivalent time.
4.4 Results Results obtained for SHS columns were very similar to those for CHS columns and the discussions will be for CHS columns only. Table 2 presents results for unreinforced columns and Tables 3 and 4 give typical results for different levels of reinforcement and column effective lengths. Table 2 indicates that, except for the very high fire load (1440 MJ/m2), the variation in numerically calculated equivalent times using the Fig. 6 approach is reasonably small among different column sizes; Tables 3 and 4 further suggest that the equivalent time is only slightly influenced by different levels of reinforcement and column effective lengths. Since the calculated minimum column resistance subjected to the high fire load of 1440 MJ/m 2 was extremely low (only a few percent of ambient temperature values in many cases), it is
Considerations in design of unprotected concrete-filled steel tubular columns
217
TABLE 2 Comparison between equivalent times of fire exposure for unreinforced columns
Fire load (MJ/m2)
Opening factor 0 (m '~)
eqn (5) time (min)
Predicted equivalent times for different CHSs (min)
219.1 × 6.3 219.1 x 20.0 406.4 x 10.0 406.4 x 32.0 360
0.04 0.10 0.20
23.4 14.8 10.5
47.3 38.3 28.5
52.5 34.3 23.5
50.8 37.0 26.8
53.8 33.3 21.0
720
0.04 0.10 0.20
46.9 29.7 21.0
72.5 53.5 44.8
77.3 62.8 53.8
73.8 53.5 49.8
82.3 68.8 46.8
1440
0.04 0.10 0.20
93.8 59.3 42.0
213.3 136.0 79.0
285.3 257.0 176.5
138.3 96.5 69.8
184.8 158.0 85.3
TABLE 3 Influence of reinforcement on predicted equivalent time
Steel section
CHS CHS CHS CHS
219.1 219.1 406.4 406.4
x x x x
Equivalent time (min) for reinforcement ratio of
6.3 20 10 32
0%
1%
3%
5%
53.5 62.8 53.5 68.8
50.5 62 52.5 68.6
46.4 59.8 51.0 68.6
45.5 57.8 50.9 68.6
TABLE 4 Influence of effective column length on predicted equivalent time
Steel section
CHS CHS CHS CHS
219.1 219.1 406.4 406.4
x x x x
Equivalent time (min) for column effective length of
6.3 20 10 32
2m
4m
6m
49.3 58 54.4 68.7
50.5 62 52.5 68.6
46.0 60.5 50.4 67.6
218
Y. C. Wang
unlikely these columns will be economically used to withstand this high fire load in practical design. Therefore, results in Tables 2-4 seem to suggest that the concept of equivalent time may give consistent results and, therefore, may be applied to concrete-filled columns. Eqn (5) specifies the variation in equivalent time with changes in fire load qf,d, opening factor O and lining material property kb. Sensitivity analyses for these three variables were carried out for all the columns and the results are presented in Fig. 9(a-c). Results in each figure seem to suggest that although the results from eqn (5) agree reasonably well with the median values obtained using a numerical analysis, they indicate a very large scatter. In particular, results in Table 2 indicate that the relationship between the equivalent time and the fire load is strongly influenced by the ventilation factor and vice versa. Generally, the rate of increase in the equivalent time as a function of the fire load reduces at lower ventilation factors. At a high ventilation factor, a fire burns fast and the fire duration is short; thus the effect of the fire on the structural element is mainly controlled by the available fire load. At a lower ventilation factor, the fire duration is longer and the structural behaviour becomes more affected by the peak fire temperature, which is only partly influenced by the fire load. In addition, the rate of reduction in the equivalent time at increasing ventilation factor decreases at higher fire loads. At a low fire load, the fire duration is generally short owing to the limited supply of fuel; thus the structural behaviour is sensitive to the rate of burning, which is controlled by the ventilation factor. At a higher fire load giving a longer fire exposure, the effect of fire on the structural behaviour becomes more affected by the peak temperature, which is also partly controlled by the fire load. Fig. 9(c) shows that discarding the few values for the very high fire load, numerical results are reasonably consistent with predictions using eqn (5) for the effect of lining material on equivalent time. Based on the reasons above, the format in eqn (5) should be modified to reflect the inter-dependence between fire load and ventilation factor. Results in Table 2 also suggest that eqn (5) predicts much lower equivalent times and, therefore, is not safe to use for concrete-filled columns. If the format of this equation is retained, an additional coefficient is required. Using linear regression, a multiplication value of 2.35 was obtained to give better correlations between the results of eqn (5) and the numerically calculated equivalent times, which are compared in Figs 10 and 11 respectively for all unreinforced and reinforced columns.
Considerations in design of unprotected concrete-filled steel tubular columns
219
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1
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J
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Fig. 9. Comparison of the influence of (a) fire load, (b) opening factor and (c) lining material on equivalent time. 5 CONCLUSIONS This paper considered three issues in the design of concrete-filled columns under fire conditions. They are: the column buckling curve to be used in Eurocode 4 Part 1.2 [9], the implementation of the calculation method in Eurocode 4 Part 1.2 [9] and column design under real fire conditions. From these studies, the following conclusions may be drawn.
220
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Wang
~
3
2.5
high fire load
2
i
1.5
J
1
05 ( ~
high fire load
0 0.5
1.5 Unchanged Eurocode 1 Part 2,2 equation
(c)
Fig. 9. Continued. 300
250
200 .E E 150
i
$
! 50
-
4
•
v
J o 0
50
100
150
200
i 250
300
Modified Eurocode 1 Part 2.2 equation, minutes
Fig. 10. Comparison between equivalent times for unreinforced columns.
(1) Using the calculation method in Eurocode 4 Part 1.2 [9], the choice of column buckling curve is dependent on the adopted concrete strength and stiffness-temperature model. Using the model in the main text of Eurocode 4 Part 1.2 [9], a comparison between calculations and 43 Canadian fire tests suggests using column buckling curve 'a' may give more accurate results than using column buckling curve 'c'. (2) For design under the standard fire condition, the general calculation
Considerations in design of unprotected concrete-filled steel tubular columns
221
300
250
i
200
i
150 i
! E w"
$
Z
$ i i
50
100
150
200
250
300
Modified Eurocode 1 Part Z.2 equation, minutes
Fig. 11. Comparison between equivalent times for reinforced columns.
method in Eurocode 4 Part 1.2 [9] may be implemented in a simplified manner using some design aids which may consist of the temperature distribution calculation method of Lawson and Newman [13], a numerically generated table giving the exact squash load and rigidity for all tubular sections under different standard fire resistance times and eqns (3) and (4) in this paper. (3) The equivalent time concept seems to be applicable to concrete-filled columns. However, the format of the equation in Eurocode 1 Part 2.2 [11] should be modified to reflect the inter-dependence between fire load and ventilation factor. This equation also produces much lower equivalent times and, therefore, may be unsafe to use. (4) If the format of the equivalent time equation in Eurocode 1 Part 2.2 [11] is retained, a multiplication factor should be introduced to cater for different types of construction element. For concrete-filled columns, this multiplication factor may be 2.35.
REFERENCES 1. Building Research Establishment, Fire, static, dynamic tests at the large building test facility. Proc. Second Cardington Conf., 12-14 March, Building Research Establishment, UK, 1996. 2. ECCS-TC3, Calculation of the Fire Resistance of Centrally Loaded Composite
222
3. 4. 5.
6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
18.
Y. C. Wang Steel-Concrete Columns Exposed to the Standard Fire. Technical Note No. 55, European Convention for Constructional Steelwork, first edition, 1988. Rudolph, K., Richter, E., Hass, H. and Quast, U., Principles for calculation of load-bearing and deformation behaviour of composite structural elements under fire action. Proc. First Int. Symp. on Fire Safety Science, 1985, pp. 301-310. Lie, T. T. and Chabot, M., A method to predict the fire resistance of circular concrete filled hollow steel columns. J. Fire Protection Eng., 1990, 2(4), 111126. Lie, T. T., Chabot, M. and Irwin, R.J., Fire Resistance of Circular Hollow Steel Sections Filled with Bar-Reinforced Concrete. Internal Report No. 636, Institute for Research in Construction, National Research Council of Canada, Ottawa, 1992. Lie, T. T. and Irwin, R. J., Fire Resistance of Rectangular Hollow Steel Sections Filled With Bar-Reinforced Concrete. Internal report No. 631, Institute for Research in Construction, National Research Council of Canada, Ottawa, 1992. Lie, T. T. and Chabot, M., Experimental Studies on the Fire Resistance of Hollow Steel Columns Filled with Plain Concrete. Internal Report No. 611, Institute for Research in Construction, National Research Council of Canada, Ottawa, 1992. Kodur, V. K. R. and Lie, T. T., Fire resistance of circular steel columns filled with fibre-reinforced concrete. J. Struct. Eng. ASCE, 1996, 122(7), 776-782. European Committee for Standardization, Eurocode No. 4: Design of Composite Steel and Concrete Structures, Part 1.2: Structural Fire Design, ENV 1994-1-2. British Standards Institution, UK, 1994. European Committee for Standardization, Eurocode No. 4: Design of Composite Steel and Concrete Structures, Part 1.1: General Rules and Rules for Buildings, DD ENV 1994-1-1. British Standards Institution, UK, 1992. European Committee for Standardization, Eurocode 1: Basis of Design and Actions on Structures, Part 2.2: Actions on Structures Exposed to Fire, ENV 1991-2-2. British Standards Institution, UK, 1994. RILEM, Properties of Materials at High Temperatures: Concrete, ed. U. Schneider. Department of Civil Engineering, University of Kassel, 1985 Lawson, R. M. and Newman, G. M., Structural Fire Design to EC3 and EC4, and Comparison with BS 5950. Technical Report, SCI publication 159, The Steel Construction Institute, UK, 1996. British Standards Institution, BS476: Fire Tests on Building Materials and Structures, Part 20: Methods for Determination of the Fire Resistance of Elements of Construction (General Principles). British Standards Institution, UK, 1987. Pettersson, O., Magnusson, S. E. and Thor, J., Fire Engineering Design of Steel Structures. Publication 50, Swedish Institute of Steel Construction, Sweden, 1976. Law, M., A Relationship between Fire Grading and Building Design and Contents. JFRO Internal Note No. 374, Fire Research Station, UK, 1970. Pettersson, O., The Connection Between a Real Fire Exposure and the Heating Conditions According to Standard Fire Resistance Tests--with Special Application to Steel Structures. CECM-III-74-2E, Chapter II, European Convention for Constructional Steelwork, 1974. Harmathy, T. Z., Fire severity: basis of fire safety design. In Fire Safety of Concrete Structures, ed. M. S. Abrams. Publication SP-80, American Concrete Institute, Detroit, 1980, pp. 115-141.
Considerations in design of unprotected concrete-filled steel tubular columns
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19. Zienkiewicz, O. C., The Finite Element Method, 3rd edition. McGraw-Hill, UK, 1977. 20. Bathe, K. J., Finite Element Procedure in Engineering Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1982.
ELSEVIER
Some Considerations in the Design of Unprotected Concrete-Filled Steel Tubular Columns Under Fire Conditions Y. C. Wang Structural Design Division, Building Research Establishment, Watford WD2 7JR, UK (Received 21 August 1996; revised version received 16 July 1997; accepted 22 July 1997)
ABSTRACT This paper is concerned with the fire resistant design of centrally loaded unprotected concrete-filled steel tubular columns using Eurocode 4 Part 1.2. It addresses three issues: the column buckling curve to be used for elevated temperature design, the implementation of the calculation method in Eurocode 4 Part 1.2 and the equivalent time of fire exposure. The predicted column fire resistance using the Eurocode 4 Part 1.2 calculation method is compared with the results of tests on 36 concrete-filled circular hollow section columns and seven square hollow section columns conducted at the National Fire Laboratory of Canada. This comparative study indicates that the choice of column buckling curve for elevated temperature design depends on the adopted concrete strength and stiffness-temperature models. If the models in the main text of Eurocode 4 Part 1.2 are used, column bucking curve 'a' seems to give more accurate results. For the standard fire resistant design, this paper proposes a simple method to implement the general calculation method in Eurocode 4 Part 1.2. This proposed method is easy to use and was demonstrated to be quite accurate. Using the parametric time-temperature relationships in Eurocode 1 Part 2.2 to represent the behaviour of realistic fires, this paper studies the equivalent time approach, based on the column resistance. Results from this study show that the equivalent time equation in Eurocode 1 Part 2.2 needs modifying to allow for the inter-dependence between fire load and ventilation factor and this equation is also unsafe. This paper further suggests introducing a multiplication factor in the equivalent time equation to cater for different types of construction element. © 1997 Elsevier Science Ltd.
Present address: The University of Manchester, Manchester M13 9PL, UK. 203
204
Y. C. Wang
NOTATION
Eurocode 1 Part 2.2 symbols Fire compartment floor area Total interior area of fire compartment Area of opening = ~/kpc of compartment lining material Specific heat of lining material Height of opening Thermal conductivity of lining material Conversion factor Opening factor Av~-h/A t Fire load density Equivalent time Ventilation factor = O - I/2AJAt Density of lining material
af
At Av b C
h k kb 0 qf, d te,a
Wf
P
Additional symbols Unreinforced column rigidity at elevated temperature Unreinforced column rigidity at elevated temperature, (E/)r,n o,o reference grades of steel and concrete E h T = 2 0 , R = 0 Unreinforced column rigidity at ambient temperature (EI)T = 2O,R= o,o Unreinforced column rigidity at ambient temperature, reference grades of steel and concrete Colunm Euler load at elevated temperature Ncr, T Column resistance to compression at elevated temperature /V~,r Column squash load at elevated temperature Unreinforced column squash load at elevated temperature Nu,T,R = 0 Unreinforced column squash load at elevated temperature, Nu,T,R = 0 , 0 reference grades of steel and concrete Unreinforced column squash load at ambient temperature Nu,T = 2 0 , R = 0 gu,T = 2 0 , R = 0 , 0 Unreinforced column squash load at ambient temperature, reference grades of steel and concrete Column relative slenderness at elevated temperature /~T Concrete design strength O'cu Reference grade of concrete design strength o-o Column strength reduction coefficient at elevated X~ temperature (EhT, R = 0 =
Considerations in design of unprotected concrete-filled steel tubular columns
205
1 INTRODUCTION The supporting columns to a building play a critical role in its stability under fire conditions. This was clearly demonstrated in a recently completed major research programme on a full-scale eight storey steel-framed building at the Building Research Establishment's Cardington Laboratory [1]. In one of the tests in which the steel H-columns were not fully fire protected, the fire damage extended well beyond the small test area on the floor and over all the storeys above. This strongly suggests the need for fire protecting columns to have sufficient fire resistance. To present the architecturally pleasing feature of exposed steelwork while still maintaining fire safety, unprotected concrete-filled steel tubular columns may be used to rely on their inherently high fire resistance. They also have a number of advantages over either bare steel columns or reinforced concrete columns, including high load carrying capacity, rapid construction and economic use of floor space. There have been a few major research programmes on the fire resistance of concrete-filled columns in Europe [2,3] and Canada [4-8]. The European standard for elevated temperature design Eurocode 4 Part 1.2 [9] is based on the results of the European research programme [2]. While the fundamental approach in Eurocode 4 Part 1.2 [9] is similar to that for ambient temperature design in Eurocode 4 Part 1.1 [10], Eurocode 4 Part 1.2 [9] recommends using column buckling curve 'c' for elevated temperature design and Eurocode 4 Part 1.1 [10] uses column buckling curve 'a' for ambient temperature design. Although the recommendation in Eurocode 4 Part 1.2 [9] is conservative and, therefore, on the safe side, concrete-filled columns should not be unnecessarily put to economic disadvantage. This paper will examine this recommendation using the results of a series of tests [7] undertaken at the National Fire Laboratory in Canada. In the calculation method in Eurocode 4 Part 1.2 [9], only the fundamental principles of heat transfer and structural analysis are given, which become quite complicated in the actual implementation for concrete-filled columns owing to the highly non-uniform temperature distribution in the composite cross-section. While this does not present any problem in the development of numerical tools, engineers with no access to these numerical solutions may be deterred from using this approach. This paper attempts to develop a simple implementation method to promote the use of the calculation method in Eurocode 4 Part 1.2 [9]. Past research studies on concrete-filled columns have only been concerned with the standard fire exposure. Whilst design for standard fire exposure will continue for the foreseeable future, design for realistic fire exposures is gaining acceptance in the context of a performance-based approach. This paper exam-
Y. C. Wang
206
ines the equivalent time concept and assesses whether this applies to concretefilled columns. The objectives of this paper are therefore threefold: (1) to examine the validity of using column buckling curve 'c' for elevated temperature design in Eurocode 4 Part 1.2 [9]; (2) to propose a simple implementation method to use the calculation method in Eurocode 4 Part 1.2 [9]; (3) to assess the applicability of the equivalent time approach in Eurocode 1 Part 2.2 [11] to concrete-filled columns.
2 COLUMN BUCKLING CURVE Eurocode 4 Part 1.2 [9] uses the same approach as in Eurocode 4 Part 1.1 [10] to calculate the column compressive resistance at elevated temperatures. The column resistance Nr is related to the column squash load Nu.r as ArT = X Vu,
(1)
where Xr is the column strength reduction factor and is a function of the relative slenderness of the column Ar which is expressed as
Ar = x/--~-~'"
Ncr,r"
(2)
The relationship between Xr and Ar is represented by a column buckling curve. Eurocode 4 Part 1.1 [10] for ambient temperature design uses four different column buckling curves for different types of column and recommends column buckling curve 'a' for concrete-filled columns. Eurocode 4 Part 1.2 [9] recommends column buckling curve 'c' for elevated temperature design. This curve gives lower values than column buckling curve 'a'; therefore, the column resistance is lower. Whilst this may be considered to be conservative and on the safe side, it may unnecessarily put concrete-filled columns at an economic disadvantage. At elevated temperatures, the strength and stiffness of both steel and concrete decrease. The accuracy of the design method will depend on the adopted model describing the strength and stiffness-temperature relationships. For steel there is good agreement between different models, and the model in Eurocode 4 Part 1.2 [9] is used in this study. For concrete there is a large scatter between the different models, as shown in Fig. 1. This figure compares the model in the main text of Eurocode 4 Part 1.2 [9] and that used by Lie and coworkers [4-6] against some test results in a RILEM report [12]. This
Considerations in design of unprotected concrete-filled steel tubular columns
207
12 + -
+
÷ •
0.8
|
.
.
0.6
~ 0.4 ~
Lie Model
•
+
-
•
0.2
0
~
I 1O0
p 200
i ~
I 4[]0
I 500
I 600
, 700
800
900
Temperature [C)
Fig. 1. Comparison between different concrete strength-temperature models. indicates that the model in Eurocode 4 Part 1.2 [9] represents the lower bound to the test results and that of Lie and coworkers [4-6] the upper bound. To assess the influence of the concrete model on the accuracy of the calculation method in Eurocode 4 Part 1.2 [9], both models are used in this paper. The experimental results are taken from Lie and Chabot [7], which consist of 36 tests on circular hollow section (CHS) columns and seven tests on square hollow section (SHS) columns, all undertaken at the National Fire Laboratory of Canada. Comparisons between the calculated column fire resistance and test results are summarised in Table 1, which suggests that if the model of Lie and coworkers [4-6] is used, column buckling curve 'a' gives higher column fire resistance than test results and column buckling curve 'c' appears to be preferable. However, if the concrete model in Eurocode 4 Part 1.2 [9] is used, TABLE 1
Summary of comparisons between predicted fire resistance and test results [7] Concrete model in Eurocode 4 Part 1.2 [9] Column buckling curve 'a' Average pred./test 0.955 Standard deviation 0.256
'c' 0.839 0.234
Concrete model of Lie and coworkers [4-6] Column buckling curve 'a' Average pred./test 1.113 Standard deviation 0.299
'c' 0.954 0.271
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Y. C. Wang
column buckling curve 'a' seems to give more accurate results than column buckling curve 'c'. Although results from this study are not very conclusive, they suggest that because the concrete model in Eurocode 4 Part 1.2 [9] is already a conservative representation of the material test results, as shown in Fig. 1, it may not be necessary to build in an additional margin of safety by using column buckling curve 'c'.
3 IMPLEMENTATION OF THE CALCULATION METHOD IN EUROCODE 4 PART 1.2 To implement the calculation method in Eurocode 4 Part 1.2 [9], the designer is required to solve the fundamental equations of heat transfer to obtain the temperature distributions in the composite cross-section. In addition, because these temperature distributions are highly non-uniform, the user also has to divide the composite cross-section into many fine layers to calculate the column resistance accurately. Designers may be reluctant to adopt this approach because of the complexity and large number of computations involved in this design process. A simple implementation method is therefore needed to reduce this complexity so that designers are encouraged to used the calculation method in Eurocode 4 Part 1.2 [9]. For temperature distributions in the composite crosssection subjected to the standard fire exposure, Lawson and Newman [13] developed a simple tabular method. In their method, two multiplication factors are used to modify the temperature distribution in an infinite concrete slab subjected to the standard fire attack on one side. These two factors account for the different heat conduction in a circular or square section from that in an infinite concrete slab and also the effect of the steel tube acting both as a heat sink and heat shield to the concrete core. The effect of the steel tube in reducing heat flux to the concrete core diminishes at increasing fire exposure time. For the column resistance, eqns (1) and (2) require the values of column squash load and rigidity. Since reinforcements are usually laid at equal distance to the column centre, their contributions to these two values can be obtained in one calculation. This paper presents a simplification to the calculation of squash load and rigidity for the unreinforced concrete-filled section so that the designer does not have to divide the composite section into many fine layers and evaluate each separately. This simplification is developed on the following reasoning. There are only a limited number of steel tubular sections in practical use. In designs for the standard fire resistance, fire resistance ratings are specified in multiples of 30 min. Therefore, the number of fire resistance ratings is also
Considerations in design of unprotected concrete-filled steel tubular columns
209
limited. The general calculation method in Eurocode 4 Part 1.2 [9] may be implemented fully using a numerical method to give the exact squash load and rigidity for all section sizes and fire ratings for one set of reference grades of steel and concrete, the results of which can be used as a design aid table. However, as the grades of steel and concrete are design variables, it is not practical to prepare design aid tables for all combinations of steel and concrete grades. To use the numerically prepared design aid table for the reference grades of steel and concrete, the column squash load and rigidity of any design grades of steel and concrete may be related to those of the reference grades. Using subscript '0' to denote the reference grades, this paper proposes the following relationships: for squash load
NuTR=O Nu,r,R =0,0 •
'
O'cu 0"0
-
+
( Nu,T=20,R=O
O'cul NuTR=O,O
\Nu,r = 20,R = 0,0
O'0 / N u , T = 20,R = 0,0
"
"
(3)
for rigidity (E/)r,R = o
(E/)r = 20,R= 0 m
( E / ) T , R = o,o
(4)
( E / 3 T = 2o,R = o,o
In both equations, T = 20 for ambient temperature and R = 0 for an unreinforced section. Eqn (3) gives the ratio of the column squash load to that with reference grades of steel and concrete at any fire rating. It states that this ratio varies linearly with the change in column squash load for the reference grades of steel and concrete at elevated temperatures. This equation recognises that, after long periods of fire exposure, the steel tube loses its contribution and the column squash load ratio approaches the ratio of concrete design strengths. As an example, Fig. 2 compares the predictions of eqn (3) with those using the exact method in which the cross-section is divided into many layers. The vertical axis gives the ratio of the squash loads at elevated temperature and the horizontal axis gives the ratio of the squash load at elevated temperature to that at ambient temperature for the reference grades of steel and concrete, which were $275 and C30 respectively. Fig. 2 shows that eqn (3) gives very good approximations to the exact values obtained from a full numerical analysis. The same reasoning for squash load may be applied to rigidity. However, since the second moment of inertia is to the fourth power of the distance from the centre of the cross-section, the contribution from the steel tube cannot be ignored even at very high temperatures. Also, there is no change in the modu-
210
Y.C.
Wang
18 16 7,4
i
a.2
1 ~ (1.8
|
"6 O.6
I
(1,4 0.2 0 0.1
0.2
0.3
0.4
06.
0,6
0.7
0,8
0,9
1
ratk~d ~luaeh load at a~evat~l tmnp, to that a~room ~gttG~, referencegrad4m
Fig. 2. Determination of column squash load for different grades of steel and concrete, CHS 406.4 x I0.
lus of elasticity for different grades of steel and the change in the modulus of elasticity for different grades of concrete is small. Therefore, it is reasonable to assume the ratio of column rigidity at elevated temperature to that at ambient temperature to be independent of the grades of steel and concrete. Fig. 3 shows an example comparing the predictions using eqn (4) and the 1.4
1.2
S
i
1
t
O,B
t.
" ~
~EquatdOn (4)
"
C~meteitnmff~60
II
.g '~ 04
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0.1
0.2
0.3
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0.6
0.7
rltfO Of dllldlly I t l¢lIetltN tllml~ to Ulal at morn I~ltp, ~ n c e
0.8
0,9
1
grlCkm
Fig, 3. Determination of column rigidity for different grades of steel and concrete, CHS 406.4 × 10.
Considerations in design of unprotected concrete-filled steel tubular columns
211
exact values from a full numerical analysis. This figure confirms that eqn (4) can be used to calculate the column rigidity with good accuracy.
4 EQUIVALENT TIME OF FIRE EXPOSURE 4.1 Behaviour of real fires
In the current design for fire resistance, the fire exposure is represented by the standard time-temperature curve [14], shown in Fig. 4. However, the behaviour of real fires is significantly different. For example, Fig. 4 compares the standard time-temperature curve with a few measured real fire time-temperature curves. Owing to the complex behaviour of real fires, their time-temperature relationships are very difficult to quantify exactly. Broadly speaking, the timetemperature relationship of a real fire is determined by the size of the opening (which controls the maximum rate of burning), the available combustible materials (which determine the duration of burning) and the interior lining material (which absorbs heat). The ventilation condition is represented by an opening factor O = A,,~/-h/At where Av is the opening area, h the opening height and A t the total interior area of the compartment. The ability of the lining material to absorb heat is represented by the material property b = ~k-pc where k is its conductivity, p its density and c its specific heat. The higher the value of b, the more the lining material absorbs heat and the less severe the fire. The parametric time-temperature relationships originally developed in o
~anda~ tim ex~$um
i0 |
]
0
20
40
60
80
100
120
Fire exposure Uml (minutes)
Fig. 4. Comparison between time-temperature relationships.
~40
160
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Y. C. Wang
Sweden [15] are now widely accepted as providing good approximations to the behaviour of real fires and they have been adopted in Eurocode 1 Part 2.2 [ll]. To design for structural elements against real fire attack, it is no longer possible to specify a single time-temperature curve. Since the standard fire resistance has been used for a long time and a large body of information has been collated on this type of fire exposure, fire safety engineers have attempted to evaluate the effects of real fire exposures in terms of equivalent times of the standard fire exposure [16-18]. This equivalency has been established on the basis of a critical temperature in a structural element, i.e. the equivalent time of a real fire is the time when a structural element is subjected to the standard fire exposure that would give the same critical temperature as the maximum temperature which the structural element will get when subjected to the real fire exposure. This concept is illustrated in Fig. 5. Eurocode 1 Part 2.2 [l l] adopts the equivalent time formula of Pettersson [17] and is expressed as
(5)
kbqf,dW f
re, d =
where kb is a coefficient related to the thermal property b of the lining material, and k b = 0 . 0 4 , 0.055 and 0.07 respectively for b > 2500 J / ( m 2 s 1/2 K ) , b = 720-2500 J/(m 2 s 1/2 K) and b < 720 J/(m 2 s 1/2 K). qf,d is the fire load density defined as the fire load per unit floor area and wf is the ventilation factor related to the opening factor O by
S
Maximum
temperature under real fire exposure
|
Fire eXF.~Ure
time
Fig. 5. Conventional way of determining equivalent time of exposure.
Considerations in design of unprotected concrete-filled steel tubular columns
Wf = O -
af__
1/2
213
(6)
At
Owing to the non-uniform temperature distribution in the composite section, it is not possible to identify a critical temperature to calculate the equivalent time as illustrated in Fig. 5. In this paper, the equivalent time is established on the basis of the column resistance. This approach is illustrated in Fig. 6. In this paper, the equivalent time is defined as the time under the standard fire exposure which gives the column a resistance equal to the column minimum resistance under the real fire condition. In section 4.2, the results of equivalent time calculated using the approach in Fig. 6 are compared with the predictions from eqn (5) to examine its applicability and accuracy to concrete-filled columns. In this study, the parametric time-temperature relationships in Eurocode 1 Part 2.2 I l l ] are used to represent the behaviour of realistic fires. Using the method in Fig. 6, the equivalent time can be numerically calculated in two steps: first, the temperature distributions in the composite section under both the parametric fire and the standard fire conditions are evaluated; secondly, the minimum column resistance under the parametric fire condition is compared against the decreasing column resistance-time relationship under the standard fire condition to give the equivalent time.
~
/
tandardtim exposure
Realfire
T ~ Minimumcolumn resistance under real fire exposure
I I II /
Equivalent time of standard fire exposure
Fire oxl~eure time
Fig. 6. Determination of equivalent time of exposure in this paper.
Y. C. Wang
214
4.2 Numerical solution for temperature distribution in a composite section
To examine the equivalent time concept, it is necessary to be able to predict accurately the temperature development in a composite cross-section. To this end, a heat transfer finite element analysis computer program has been developed by the author. This program is based on well-developed theories in standard texts such as Zienkiewicz [19] and Bathe [20]. Four types of element may be used: 2-noded 1-dimensional element, 3-noded 1-dimensional element, triangle element and 4-noded 2-dimensional isoparametric element. Owing to symmetry, the temperature distribution in a concrete-filled CHS may be calculated using 1-dimensional elements in the radial direction to reduce computing time. In this method, material thermal properties (thermal conductivity and specific heat) and heat flux to the external surface of the cross-section should be increased in proportion to the radius. This approach may also be applied to a SHS. However, only the average temperature within each layer in the cross-section is calculated. The accuracy of this numerical analysis was examined by checking the predicted temperatures in concrete-filled columns against the test results from Lie and Chabot [7]. Figs 7 and 8 present comparisons for CHS (tests C31 and C32) and SHS (tests SQ01 and SQ02) columns respectively. 2-noded 1dimensional and 4-noded 2-dimensional elements were used for CHS and SHS sections respectively. For both types of section, the results of two tests with identical section size are shown. Lie and Chabot [7] used carbonate concrete for tests C31, C32 and SQ02 and siliceous concrete for test SQ01. In this study, the same concrete thermal 1000 goo
800-
600 8 500 -
,J
1/"
Steel, Prealcted oncre~e, Predicted
/.// •
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loo. 0 0
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./~,
i//
~,,~, I
I
I
I
I0
20
30
40 Fire e x p o s u r e ~
I 50
I 60
i 70
] 80
(mill)
Fig. 7. Comparison between temperatures for tests C31 and C32 [7].
I
90
Considerations in design of unprotected concrete-filled steel tubular columns
215
lOOO 9O0 800
Z: S'Z,
I ~.~.~/"
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700 ./'~/./.1
Steel Test SQ01
600
:/ i,~
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/
~/ /
." i
~
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0
10
20
30
40
50
60
70
80
90
Fire exposure time (min)
Fig. 8. Comparison between temperatures for tests SQ01 and SQ02 [7].
properties in Eurocode 4 Part 1.2 [9] were used for both types of concrete. A moisture content of 10% in concrete was reported by Lie and Chabot [7]. To allow for moisture content, Eurocode 4 Part 1.2 [9] gives higher thermal capacitance at about 100°C at increasing moisture content and its value at 10% was used in the numerical analysis. A convection factor of 25 W/(m 2 °C) and a resultant emissivity of 0.7, as recommended in Eurocode 4 Part 1.2, [9] were also used. Fig. 7 shows that for steel temperatures, the difference between numerical predictions and test results is very small, especially during the important latter stage of the fire exposure. Numerical predictions for concrete temperatures are slightly less accurate. Owing to the uncertainties in the concrete thermal properties, the predicted results are considered to be very satisfactory. Results shown in Fig. 8 for the SHS section follow the same trend.
4.3 Input variables The parametric study was carded out using the following different values for each variable. Column section: CHS 219.6 x 6.3, CHS 219.6 x 20.0, CHS 406.4 x 10.0, CHS 406.4 x 32.0, SHS 200 x 6.3, SHS 200 x 16.0, SHS 400 x 10.0, SHS 400 × 16.0, chosen to cover a range of column dimension and percentage of steel.
216 Column effective length:
Y. C. Wang
2 m , 4 m and 6 m .
Reinforcement area: 0%, 1%, 3% and 5% of the concrete core area. Fire load density:
360 MJ/m 2, 720 MJ/m 2 and 1440 MJ/m 2, representing the lower bound, average and upper bound.
Opening factor:
O = 0.04 m 1/2, 0.1 m 1/2 and 0.2 m 1/2, representing the lower bound, average and upper bound.
Lining material:
b = 720, 1160 and 2500 J/(m 2 s 1/2 K), being the three demarking values in Eurocode 1 Part 2.2 [11].
The reference value for each of the above variables was: column effective length 4 m, reinforcement 3%, fire load density 720 MJ/m 2, opening factor 0.1 m ~/2 and lining material 1160 J/(m 2 s 1/2 K). To facilitate the determination of the parametric fire time-temperature relationships, the compartment was assumed to be 9 m long, 6 m wide and 4 m high. Other input data include steel yield stress 275 N/mm 2, concrete design strength 30 N/mm 2, reinforcement yield stress 450 N/mm 2 and concrete cover to reinforcement 35 mm. Based on the conclusion stated previously, column buckling curve 'a' was used in the calculations of the column resistance to axial compression. Nevertheless, the choice of column buckling curve should only have a very small influence on the equivalent time.
4.4 Results Results obtained for SHS columns were very similar to those for CHS columns and the discussions will be for CHS columns only. Table 2 presents results for unreinforced columns and Tables 3 and 4 give typical results for different levels of reinforcement and column effective lengths. Table 2 indicates that, except for the very high fire load (1440 MJ/m2), the variation in numerically calculated equivalent times using the Fig. 6 approach is reasonably small among different column sizes; Tables 3 and 4 further suggest that the equivalent time is only slightly influenced by different levels of reinforcement and column effective lengths. Since the calculated minimum column resistance subjected to the high fire load of 1440 MJ/m 2 was extremely low (only a few percent of ambient temperature values in many cases), it is
Considerations in design of unprotected concrete-filled steel tubular columns
217
TABLE 2 Comparison between equivalent times of fire exposure for unreinforced columns
Fire load (MJ/m2)
Opening factor 0 (m '~)
eqn (5) time (min)
Predicted equivalent times for different CHSs (min)
219.1 × 6.3 219.1 x 20.0 406.4 x 10.0 406.4 x 32.0 360
0.04 0.10 0.20
23.4 14.8 10.5
47.3 38.3 28.5
52.5 34.3 23.5
50.8 37.0 26.8
53.8 33.3 21.0
720
0.04 0.10 0.20
46.9 29.7 21.0
72.5 53.5 44.8
77.3 62.8 53.8
73.8 53.5 49.8
82.3 68.8 46.8
1440
0.04 0.10 0.20
93.8 59.3 42.0
213.3 136.0 79.0
285.3 257.0 176.5
138.3 96.5 69.8
184.8 158.0 85.3
TABLE 3 Influence of reinforcement on predicted equivalent time
Steel section
CHS CHS CHS CHS
219.1 219.1 406.4 406.4
x x x x
Equivalent time (min) for reinforcement ratio of
6.3 20 10 32
0%
1%
3%
5%
53.5 62.8 53.5 68.8
50.5 62 52.5 68.6
46.4 59.8 51.0 68.6
45.5 57.8 50.9 68.6
TABLE 4 Influence of effective column length on predicted equivalent time
Steel section
CHS CHS CHS CHS
219.1 219.1 406.4 406.4
x x x x
Equivalent time (min) for column effective length of
6.3 20 10 32
2m
4m
6m
49.3 58 54.4 68.7
50.5 62 52.5 68.6
46.0 60.5 50.4 67.6
218
Y. C. Wang
unlikely these columns will be economically used to withstand this high fire load in practical design. Therefore, results in Tables 2-4 seem to suggest that the concept of equivalent time may give consistent results and, therefore, may be applied to concrete-filled columns. Eqn (5) specifies the variation in equivalent time with changes in fire load qf,d, opening factor O and lining material property kb. Sensitivity analyses for these three variables were carried out for all the columns and the results are presented in Fig. 9(a-c). Results in each figure seem to suggest that although the results from eqn (5) agree reasonably well with the median values obtained using a numerical analysis, they indicate a very large scatter. In particular, results in Table 2 indicate that the relationship between the equivalent time and the fire load is strongly influenced by the ventilation factor and vice versa. Generally, the rate of increase in the equivalent time as a function of the fire load reduces at lower ventilation factors. At a high ventilation factor, a fire burns fast and the fire duration is short; thus the effect of the fire on the structural element is mainly controlled by the available fire load. At a lower ventilation factor, the fire duration is longer and the structural behaviour becomes more affected by the peak fire temperature, which is only partly influenced by the fire load. In addition, the rate of reduction in the equivalent time at increasing ventilation factor decreases at higher fire loads. At a low fire load, the fire duration is generally short owing to the limited supply of fuel; thus the structural behaviour is sensitive to the rate of burning, which is controlled by the ventilation factor. At a higher fire load giving a longer fire exposure, the effect of fire on the structural behaviour becomes more affected by the peak temperature, which is also partly controlled by the fire load. Fig. 9(c) shows that discarding the few values for the very high fire load, numerical results are reasonably consistent with predictions using eqn (5) for the effect of lining material on equivalent time. Based on the reasons above, the format in eqn (5) should be modified to reflect the inter-dependence between fire load and ventilation factor. Results in Table 2 also suggest that eqn (5) predicts much lower equivalent times and, therefore, is not safe to use for concrete-filled columns. If the format of this equation is retained, an additional coefficient is required. Using linear regression, a multiplication value of 2.35 was obtained to give better correlations between the results of eqn (5) and the numerically calculated equivalent times, which are compared in Figs 10 and 11 respectively for all unreinforced and reinforced columns.
Considerations in design of unprotected concrete-filled steel tubular columns
219
,, S ]
]| '
J
E
z
2 f
1
J
l
I
J
J
J
J
I
J
0 0
0.5
1
1.5
2
2.5
3
3.5
4
Unchanged Eurocode t Part 2.2 equation
(a) 4
i
v
! 3.5
I
3
2.5
I~ l z
2
J
1.5
0.5
0 (b)
0.5
1
1.5
2
2.5
Unchanged Euro©ode 1 Part 2.2 equation
Fig. 9. Comparison of the influence of (a) fire load, (b) opening factor and (c) lining material on equivalent time. 5 CONCLUSIONS This paper considered three issues in the design of concrete-filled columns under fire conditions. They are: the column buckling curve to be used in Eurocode 4 Part 1.2 [9], the implementation of the calculation method in Eurocode 4 Part 1.2 [9] and column design under real fire conditions. From these studies, the following conclusions may be drawn.
220
Y. C.
Wang
~
3
2.5
high fire load
2
i
1.5
J
1
05 ( ~
high fire load
0 0.5
1.5 Unchanged Eurocode 1 Part 2,2 equation
(c)
Fig. 9. Continued. 300
250
200 .E E 150
i
$
! 50
-
4
•
v
J o 0
50
100
150
200
i 250
300
Modified Eurocode 1 Part 2.2 equation, minutes
Fig. 10. Comparison between equivalent times for unreinforced columns.
(1) Using the calculation method in Eurocode 4 Part 1.2 [9], the choice of column buckling curve is dependent on the adopted concrete strength and stiffness-temperature model. Using the model in the main text of Eurocode 4 Part 1.2 [9], a comparison between calculations and 43 Canadian fire tests suggests using column buckling curve 'a' may give more accurate results than using column buckling curve 'c'. (2) For design under the standard fire condition, the general calculation
Considerations in design of unprotected concrete-filled steel tubular columns
221
300
250
i
200
i
150 i
! E w"
$
Z
$ i i
50
100
150
200
250
300
Modified Eurocode 1 Part Z.2 equation, minutes
Fig. 11. Comparison between equivalent times for reinforced columns.
method in Eurocode 4 Part 1.2 [9] may be implemented in a simplified manner using some design aids which may consist of the temperature distribution calculation method of Lawson and Newman [13], a numerically generated table giving the exact squash load and rigidity for all tubular sections under different standard fire resistance times and eqns (3) and (4) in this paper. (3) The equivalent time concept seems to be applicable to concrete-filled columns. However, the format of the equation in Eurocode 1 Part 2.2 [11] should be modified to reflect the inter-dependence between fire load and ventilation factor. This equation also produces much lower equivalent times and, therefore, may be unsafe to use. (4) If the format of the equivalent time equation in Eurocode 1 Part 2.2 [11] is retained, a multiplication factor should be introduced to cater for different types of construction element. For concrete-filled columns, this multiplication factor may be 2.35.
REFERENCES 1. Building Research Establishment, Fire, static, dynamic tests at the large building test facility. Proc. Second Cardington Conf., 12-14 March, Building Research Establishment, UK, 1996. 2. ECCS-TC3, Calculation of the Fire Resistance of Centrally Loaded Composite
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3. 4. 5.
6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
18.
Y. C. Wang Steel-Concrete Columns Exposed to the Standard Fire. Technical Note No. 55, European Convention for Constructional Steelwork, first edition, 1988. Rudolph, K., Richter, E., Hass, H. and Quast, U., Principles for calculation of load-bearing and deformation behaviour of composite structural elements under fire action. Proc. First Int. Symp. on Fire Safety Science, 1985, pp. 301-310. Lie, T. T. and Chabot, M., A method to predict the fire resistance of circular concrete filled hollow steel columns. J. Fire Protection Eng., 1990, 2(4), 111126. Lie, T. T., Chabot, M. and Irwin, R.J., Fire Resistance of Circular Hollow Steel Sections Filled with Bar-Reinforced Concrete. Internal Report No. 636, Institute for Research in Construction, National Research Council of Canada, Ottawa, 1992. Lie, T. T. and Irwin, R. J., Fire Resistance of Rectangular Hollow Steel Sections Filled With Bar-Reinforced Concrete. Internal report No. 631, Institute for Research in Construction, National Research Council of Canada, Ottawa, 1992. Lie, T. T. and Chabot, M., Experimental Studies on the Fire Resistance of Hollow Steel Columns Filled with Plain Concrete. Internal Report No. 611, Institute for Research in Construction, National Research Council of Canada, Ottawa, 1992. Kodur, V. K. R. and Lie, T. T., Fire resistance of circular steel columns filled with fibre-reinforced concrete. J. Struct. Eng. ASCE, 1996, 122(7), 776-782. European Committee for Standardization, Eurocode No. 4: Design of Composite Steel and Concrete Structures, Part 1.2: Structural Fire Design, ENV 1994-1-2. British Standards Institution, UK, 1994. European Committee for Standardization, Eurocode No. 4: Design of Composite Steel and Concrete Structures, Part 1.1: General Rules and Rules for Buildings, DD ENV 1994-1-1. British Standards Institution, UK, 1992. European Committee for Standardization, Eurocode 1: Basis of Design and Actions on Structures, Part 2.2: Actions on Structures Exposed to Fire, ENV 1991-2-2. British Standards Institution, UK, 1994. RILEM, Properties of Materials at High Temperatures: Concrete, ed. U. Schneider. Department of Civil Engineering, University of Kassel, 1985 Lawson, R. M. and Newman, G. M., Structural Fire Design to EC3 and EC4, and Comparison with BS 5950. Technical Report, SCI publication 159, The Steel Construction Institute, UK, 1996. British Standards Institution, BS476: Fire Tests on Building Materials and Structures, Part 20: Methods for Determination of the Fire Resistance of Elements of Construction (General Principles). British Standards Institution, UK, 1987. Pettersson, O., Magnusson, S. E. and Thor, J., Fire Engineering Design of Steel Structures. Publication 50, Swedish Institute of Steel Construction, Sweden, 1976. Law, M., A Relationship between Fire Grading and Building Design and Contents. JFRO Internal Note No. 374, Fire Research Station, UK, 1970. Pettersson, O., The Connection Between a Real Fire Exposure and the Heating Conditions According to Standard Fire Resistance Tests--with Special Application to Steel Structures. CECM-III-74-2E, Chapter II, European Convention for Constructional Steelwork, 1974. Harmathy, T. Z., Fire severity: basis of fire safety design. In Fire Safety of Concrete Structures, ed. M. S. Abrams. Publication SP-80, American Concrete Institute, Detroit, 1980, pp. 115-141.
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19. Zienkiewicz, O. C., The Finite Element Method, 3rd edition. McGraw-Hill, UK, 1977. 20. Bathe, K. J., Finite Element Procedure in Engineering Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1982.