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The effects of structural continuity on the fire resistance of concrete filled columns in non-sway frames
Journal of Constructional Steel Research 50 (1999) 177–197
The effects of structural continuity on the fire resistance of concrete filled columns in nonsway frames Y.C. Wang Manchester School of Engineering, University of Manchester, Manchester M13 9PL, UK Received 14 August 1997; received in revised form 21 September 1998; accepted 20 October 1998
Abstract This paper presents the results of a series of theoretical studies on the effects of structural continuity on the fire resistance of composite columns of concrete filled steel tubes. In particular, these theoretical studies concern the changes in column effective lengths, axial loads and bending moments under fire conditions and the effects of these changes on column fire resistance. These studies are carried out to confirm (or otherwise) the recommendation on column effective length in Eurocode 4 Part 1.2 and to put forward additional suggestions on column axial loads and bending moments at the fire limit state. Finite element analysis is used to evaluate the non-uniform temperature distributions in composite cross-sections and to analyse the structural response at elevated temperatures. The results of these studies have validated the recommendation in Eurocode 4 Part 1.2 that the boundary conditions for continuous columns may be assumed to be built-in. They also suggest that at the fire limit state, additional axial loads in columns due to restrained thermal expansions are very small and that column bending moments become much lower than those at ambient temperature. For calculating its fire resistance, a column may be assumed to be under pure axial load equal to its ambient temperature value, the result of which may only slightly overestimate the exact column fire resistance. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Composite columns; Fire resistance; Structural continuity; Interaction; Design method; Bending moment
Notation Lb Lc Le
beam span column height column effective length
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1. Introduction Composite columns made of steel and concrete have many advantages over bare steel or reinforced concrete columns, being able to give increased strength with reduced cross-sectional size and possessing inherently high fire resistance. Many different types of composite columns have been developed, including the more commonly used concrete encased steel H sections and concrete filled steel tubes as shown in Fig. 1. The subject of this paper is concrete filled circular/square steel tubes. Columns of this type offer speedy construction, good impact resistance and the possibility of using exposed steelwork without compromising fire safety. The traditional method of evaluating the fire resistance of a structural element is by performing the standard fire resistance test [1], which is time consuming and expensive. Recently, calculating the fire resistance of individual loadbearing members is becoming more acceptable and for composite columns, the calculating procedures are now well established [2]. In Europe, Eurocode 4 Part 1.2 [2] may be used for such purposes. This code has been developed as a result of many experimental and analytical studies carried out in Europe [3–7]. The fire resistance of concrete filled columns has also been extensively investigated elsewhere, especially in Canada [8–12] and Japan [13]. However, most of the investigations reported in the more widely available literature sources have focused on the fire resistance of individual columns whose boundary and loading conditions are well defined and remain unchanged during the fire exposure. When a composite column interacts with other structural members in a frame under fire conditions, both its boundary conditions and loading conditions change. It is therefore necessary to accurately determine their values to allow the column fire resistance to be correctly evaluated. Both aspects of structural continuity have been addressed for steel columns by a number of investigators [14–16], using numerical methods. It has been generally concluded that at the fire limit state, built-in boundary conditions may be assumed for continuous steel columns. Eurocode 4 Part 1.2 [2] adopts this conclusion and recommends that for a composite column continuous at both ends, its effective length ratio may be taken as 0.5
Fig. 1.
Typical examples of steel–concrete composite sections.
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and for a column continuous at one end only, an effective length ratio of 0.7 may be used. For a steel column, uniform temperature distribution over the cross-section is usually assumed, so that when the column approaches failure at the fire limit state its stiffness has almost diminished, thus giving very high restraint stiffness relative to that of the column and validating the assumption of built-in boundary conditions. For concrete filled columns, because the inner concrete core is cooler and therefore may still retain some stiffness at the fire limit state, it is necessary to check the assumption of infinite restraint stiffness relative to the column. Eurocode 4 Part 1.2 [2] does not give specific guidance on the determination of the axial load and bending moments in a composite column as part of a frame. Thus for practical designs, the values of these forces may be assumed to be unchanged and equal to those at ambient temperature. However, Kimura et al. [13] tested a series of frames comprised of concrete filled square tubular members and observed that column bending moments became very small at the fire limit state, and the columns could be assumed to be axially loaded only. This observation is a result of very low column bending stiffness attracting very small bending moments, and is therefore consistent with the conclusion of the builtin boundary conditions for continuous columns. It is also a very important observation for concrete filled columns. Under pure axial loads, many fire tests [11] have demonstrated that unreinforced concrete filled columns have very high inherent fire resistance. However, when subjected to bending, their fire resistance rapidly decreases due to the loss of the steel tube and the inability of the remaining unreinforced concrete core to resist bending, thus limiting the applicability of this type of column. However, if the observation of Kimura et al. [13] can be extended more generally to columns in other configurations, it may not be necessary to design unreinforced concrete filled columns for bending under fire conditions, thereby fully utilising their high fire resistance under pure axial loads. The objectives of this paper are therefore two-fold: (1) to evaluate the effective lengths of composite columns in frames under fire conditions to validate (or otherwise) the assumption adopted in Eurocode 4 Part 1.2 [2]; (2) to study the variations in column axial loads and bending moments, in particular to check the assumption that composite columns many be assumed to be under pure axial loads at the fire limit state.
2. Methodology of analysis At the fire limit state, the effects of structural continuity on fire exposed columns are expected to provide built-in boundary conditions, and also to reduce column bending moments to a negligible level, both being results of very low column bending stiffness at elevated temperatures. While this can be easily envisaged for a steel column whose cross-section is usually under uniform temperature, and therefore its stiffness diminishes uniformly and becomes very small under load at the fire limit state, a concrete filled column may still retain some stiffness due to the cooler con-
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crete core and reinforcement. Hence the effects of structural continuity on a composite column may not be sufficient to allow the assumptions of the built-in boundary condition and negligible bending moments. To evaluate the exact boundary conditions to a composite column and its bending moments at the fire limit state, it is necessary to accurately calculate the non-uniform temperature distributions in the composite cross-section, and to evaluate the structural interaction between the composite column and other members. 2.1. Numerical calculation for temperature distributions in composite crosssections A finite element analysis computer program has been developed by the author to evaluate temperature distributions in two-dimensional continuous media. This analysis is based on well developed numerical methods for heat transfer in a textbook by Bathe [17]. In the program, either one-dimensional line elements or two-dimensional elements may be used. Due to symmetry when a concrete filled circular/square column is exposed to a uniform temperature field, the one-dimensional two-noded line elements may be used with each element representing a circular/square slice of the cross-section. The varying circumference of each slice may be accounted for by multiplying the thermal capacitance of each element by the circumferential length. 2.2. Validation of the temperature calculation method Fig. 2 is used to indicate the accuracy of the computer program, where the calculated steel and concrete temperatures are compared with those measured during a
Fig. 2. Comparison between calculated and measured temperatures, Test C17 [11].
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test on a concrete filled circular hollow section column (Test C17), conducted by Lie and Chabot [11]. In the calculations, a resultant emissivity of 0.7 and a heat transfer coefficient for convection of 25 W/m°K were used. The thermal properties of both steel and concrete were assumed to be those in Eurocode 4 Part 1.2 [2]. An increased concrete specific heat was used to account for concrete moisture, but the steel/concrete interface effect was not addressed because the composite cross-section was treated as a continuous medium with varying thermal properties. Fig. 2 shows that the steel temperatures were very accurately predicted. Differences between the calculated and measured concrete temperatures are slightly higher; however, considering the uncertainties associated with concrete thermal properties and heat transfer characteristics of the test furnace, the calculated temperatures were not fine-turned to agree with the test results exactly. Nevertheless, the calculated temperatures were regarded to be acceptable for the purpose of the studies in this paper in which the results of the same temperature analysis were used to facilitate structural analysis of the same composite column in different structural configurations. 2.3. Finite element analysis for structural response and its validation This analysis uses a finite element analysis computer program developed by the author for steel and composite frames under fire conditions [18]. This computer program has been extensively calibrated against the results of a large number of fire tests on steel and composite beams, steel columns, concrete columns and steel frames. In this paper, some additional examples are provided to demonstrate the capacity of this computer program to analyse the behaviour of composite columns both at ambient temperature and under fire conditions. Fig. 3 compares the load versus major and minor axis deflection relationships for a slender, concrete filled rectangular hollow section steel column, tested under axial load and biaxial bending moments [19]. Results in this figure indicate that the computer program is capable of simulating quite accurately the behaviour of composite columns up to the maximum applied load. Fig. 4 compares the axial shortening versus fire exposure time for a concrete filled circular steel column (Test C17) exposed to the standard heating condition, tested by Lie and Chabot [11]. This figure shows that the finite element analysis program may be used to predict both the column deflection history and its fire resistance time with reasonable accuracy. Since the computer program has the capacity to analyse the response of steel frames, it may be considered to be acceptable for studying structural interaction between composite columns and other members in frames.
3. Parametric studies Three parametric studies were carried out to evaluate effective lengths, bending moments and additional axial loads for composite columns of concrete filled Circular
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Fig. 3.
Load–deflection curves, Test 3 [19].
Hollow Section (CHS) steel tubes in subframes (to be referred to as subframe columns) at the fire limit state. Because of the similarity in the final results of these parametric studies between CHS columns and columns with square sections, only CHS columns are discussed in this paper. In all calculations, the standard heating regime [1] was assumed. For heat transfer calculations, the thermal properties of steel and concrete in Eurocode 4 Part 1.2 [2] were used. For structural response analysis, steel was assumed to be grade S275 having a yield stress of 275 N/mm2 and Young’s modulus of 205 000 N/mm2, and concrete grade C25/30 with a compressive strength of 30 N/mm2 and modulus of elasticity of 30 500 N/mm2. The stress–strain relationships of both steel and concrete followed those in Eurocode 4 Part 1.2 [2].
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Fig. 4.
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Comparison between test and calculated column behaviour, C17 [11].
3.1. Column effective length The effective length of a subframe column was evaluated by first computing the subframe column failure time. The column was then analysed individually as a simply supported column under the same axial load but with different lengths. Different failure times of the simply supported column with different lengths were calculated and compared with that of the subframe column. The column failure time was used for all comparisons for two reasons: firstly, it is one of the principal values which may be used to indicate the column behaviour under fire conditions; secondly, it was difficult to select one temperature value to represent the non-uniform temperature distribution in a composite cross-section. The subframes in Fig. 5(a) and (b) were used to evaluate the effective lengths for columns continuous at both ends and for columns continuous at one end respectively. These subframes were adopted to simulate columns in simple construction. If a subframe column is restrained by adjacent beams, the subframes in Fig. 5(a) and (b) will give the least favourable column effective length. Three key parameters were investigated, being column length, column cross-section size and the applied load ratio. The column lengths were 2.5 m, 5 m and 7.5 m. Four cross-section sizes were selected and they were: CHS 273 ⫻ 6.3, CHS 273 ⫻ 25, CHS 457 ⫻ 10 and CHS 457 ⫻ 40. Both unreinforced and reinforced concrete filled columns were studied. As will be seen from the results, structural continuity has the greatest effect on slender columns. Therefore, reinforcement was provided to columns of the smallest cross-section of CHS 273 ⫻ 6.3. Reinforcement was in the form of a smaller steel circular hollow section, being CHS 139.7 ⫻ 5.0, CHS 114.3 ⫻ 6.3 or CHS 114.3 ⫻ 3.6, giving ratios of the reinforcement area to the concrete area of 4.1%, 4.2% and 2.4% respectively, and concrete covers of 60 mm, 73 mm and 73 mm respectively.
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Fig. 5.
Subframes used for studies on column effective length.
The load ratio is the ratio of the applied load in a column under fire condition to the column’s strength at ambient temperature. For a fully designed column, this value is usually 0.5–0.6. In this study, two values were used, 0.4 and 0.7, representing the lower and upper bounds on the load ratio. Column strengths at ambient temperature were calculated using Eurocode 4 Part 1.1 [20], assuming an effective length ratio of 1.0. 3.2. Variations in column bending moments Fig. 6(a) and (b) were used to study variations in column bending moments for columns continuous at both ends and at one end respectively. For columns continuous at both ends, applied loads on beams in Fig. 6(a) were arranged to induce single curvature bending in the column. Beam ends were assumed to be simply supported and beam–column connections were assumed to be rigid. Both reinforced and unreinforced columns were analysed. 3.2.1. Unreinforced columns Column length was 2.5 m, 5 m or 7.5 m. To ensure that bending moments had the greatest influence, the smallest column cross-section size of CHS 273 ⫻ 6.3 was used. Beams were chosen to have a 356 ⫻ 171 ⫻ 67UB steel section, their length being either 6 m or 9 m. The larger applied load on the beam was determined to give a bending moment in the centre of a simply supported beam of 60% of its plastic moment capacity. For a beam length of 6 m, this beam load was 133.1 kN. Assuming a typical frame spacing of 6 m, this load represented a uniformly distrib-
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Fig. 6.
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Subframes used for studies on moment transfer and additional axial load.
uted floor load of 7.5 kN/m2, simulating a typical dead load of 2.5 kN/m2 and imposed load of 5 kN/m2. The smaller load was 1/3 of the larger load, thus representing the dead load only. For different beam lengths, column bending moments were about 10–40% of the column plastic moment capacities at ambient temperature. The additional axial loads of 30% of the column compressive strength were applied, giving total load ratios between 0.4 and 0.7. 3.2.2. Reinforced columns Columns of CHS 273 ⫻ 6.3 were analysed. The same three levels of reinforcement as in Section 3.1 were assumed. Only the 7.5 m columns were studied. However, an additional column load case was included in the analysis, applying a total axial load in each column of 60% of the unreinforced column’s compressive strength. 3.3. Additional axial loads in columns The subframe in Fig. 6(b) was used to study additional axial loads in columns due to restrained thermal expansion. Previous studies on steel columns [15] suggest greater effects of additional axial loads on more slender columns. The smallest column cross-section size of CHS 273 ⫻ 6.3 was therefore used for this study. Other parameters were the same as in Section 3.2 for unreinforced columns.
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The amount of the additional axial load in a column whose thermal expansion is restrained is a function of the restraint stiffness. To account for the influence of additional storeys in real buildings above a column, the Young’s modulus of steel for beams in Fig. 6(b) was multiplied by a factor of 10. At this modulus of elasticity, the maximum restraint stiffness was 1%, 2% and 3% of the axial stiffness of the 2.5 m, 5 m and 7.5 m column respectively.
4. Results and discussions
4.1. Column effective length 4.1.1. Unreinforced columns The results are given in Fig. 7 and Fig. 8 for unreinforced concrete filled columns continuous at both ends and at one end respectively. They show the comparisons between failure times of subframe columns and those of simply supported columns. Effective length ratios of 0.5 and 0.7 were used for the simply supported columns whose results are given in Figs. 7 and 8 respectively. Results in Figs. 7 and 8 indicate that for all column lengths, cross-section sizes and load ratios, there is a very close agreement between the failure times of subframe columns and those of simply supported columns with appropriately reduced effective lengths recommended in Eurocode 4 Part 1.2 [2]. Therefore, these results confirm the recommendation in Eurocode 4 Part 1.2 [2] that for columns continuous at both ends, an effective length ratio of 0.5 may be used and for columns continuous at one end, an effective length ratio of 0.7 may be used. This conclusion suggests although concrete filled columns had cooler concrete cores, their influence on column
Fig. 7.
Comparison for columns continuous at both ends, unreinforced.
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Fig. 8.
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Comparison for columns continuous at one end, unreinforced.
effective lengths was small due to their small size and their low stiffness at highly increased stresses, as a result of the loss of the steel tube and the outer concrete. Although Figs. 7 and 8 show that in a few cases, using built-in boundary conditions gave columns higher fire resistance, the differences between these fire resistance times and those of subframe columns were very small. Fig. 5(a) and (b) represent the two minimum restraint situations to a subframe column and they have provided the column with the maximum rotational restraint. Therefore, if a subframe is provided with additional rotational restraint from adjacent beams, it is still valid to adopt the assumption of built-in boundary conditions for the subframe column at the fire limit state. 4.1.2. Reinforced columns For short columns, failure is generally due to the applied load exceeding the squash resistance and hence the effect of different boundary conditions on column failure times is small. In contrast, slender columns fail by buckling and therefore their fire resistance times are more sensitive to changes in the boundary conditions. These general trends were followed by the results of studies on unreinforced concrete filled columns. Therefore, columns with the smallest cross-section of CHS 273 ⫻ 6.3 was reinforced to three different levels to study the influence of reinforcement on column boundary conditions at the fire limit state. The results for all columns are shown in Fig. 9. The differences between failure times of subframe columns and the simply supported columns with the appropriately reduced effective lengths are larger than those shown in Figs. 7 and 8 for unreinforced columns, with the failure times of simply supported columns being higher. This suggests that the residual stiffness of the reinforcement had some effect on the column effective length at the fire limit state. However, results in Fig. 9 indicate that at the three different reinforcement
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Fig. 9.
Comparison for all reinforced columns, axial load.
ratios, the agreement between the failure times of the subframe columns and those of the simply supported columns of reduced effective lengths is still quite good. Therefore, the effect of reinforcement on column effective length may be regarded as small, and for reinforced columns, the assumption of built-in boundary conditions at the fire limit state may still be used as for unreinforced columns. 4.2. Variation in column bending moment 4.2.1. Unreinforced columns Figs 10 and 11 show the variations in bending moments at the column top and centre respectively for columns continuous at the top, obtained using the structural subframe in Fig. 6(b). The horizontal axis gives the ratio of the bending moment in the column to the column’s plastic moment capacity at ambient temperature. Both figures suggest that column bending moments started to decrease rapidly after a few minutes of fire exposure, as a result of rapid reduction in the column flexural bending stiffness. This tendency was continued for short columns. However, for more slender columns, their response was affected by the P–⌬ effect as the column lateral deflections increased. Under this condition, Fig. 11 shows that the bending moment in the column centre increased after early reduction and Fig. 10 suggests a reversal in the sign of the column top bending moment, which created a very complicated double curvature bending mode in the column. Similar behaviour was also observed for columns continuous at both ends, simulated using the subframe in Fig. 6(a). Fig. 12 shows variations in column bending moments at top, centre and bottom for the 7.5 m long subframe column and Fig. 13 compares the bending moment diagrams of the column at ambient temperature, at 30 minutes and at failure. Fig. 13 clearly illustrates the variation in column effective
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Fig. 10.
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Column top moment–time relationships.
length, as indicated by the distance between the two inflection points in the column moment diagram, as the fire exposure time increases. At the column failure time, Fig. 13 shows that the column effective length is half the column length. The complicated bending behaviour, shown in Figs. 10, 11 and 13, did not affect the subframe column failure times. When the subframe columns were analysed as simply supported columns with reduced effective lengths corresponding to built-in boundary conditions, and with no bending moment, their failure times were very close to those of the subframe columns. The fire resistance results are shown in Fig. 14, which suggests although different levels of column bending moments had some effect on column failure times, this effect was small. In contrast, if the failure times of the subframe columns were calculated using the simply supported columns, with the reduced column effective lengths but subject to the ambient temperature bending moments, much lower column failure times were obtained. Fig. 15 compares the subframe failure times with those from simply supported columns whose bending moments were equal to those in the subframe col-
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Fig. 11.
Column centre moment–time relationships.
umns at ambient temperature. It can be seen that applying the ambient temperature subframe frame bending moments to the simply supported columns resulted in much lower column failure times. This strongly indicates that the column fire resistance calculations should take into account the observation that the subframe bending moments were substantially reduced at the failure time. The reduction in column bending moments is clearly illustrated in Fig. 12 for short columns. For more slender columns, although Fig. 12 still shows some bending moments at the failure times, these bending moments were due to the P–⌬ effect. However, they were much lower than those induced by the P–⌬ effect in simply supported columns that were subject to initial bending moments equal to those in the subframe column at ambient temperature. An example is shown in Fig. 16.
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Fig. 12.
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Moment–time relationships, Lb ⫽ 9 m, Lc ⫽ 7.5 m.
4.2.2. Reinforced columns The combined effects of bending moments and reinforcement on column fire resistance were also studied and the results are plotted in Fig. 17. This figure shows quite close agreement between the failure times of subframe columns and those of the simply supported columns with reduced effective lengths but not subject to any bending moment. The results in Fig. 17 are also very similar to those in Fig. 9 for reinforced columns without bending moments. This suggests that for reinforced subframe columns with bending moments, their fire resistance times may still be calculated on the basis that column boundary conditions are built-in and bending moments are very small.
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Fig. 13.
Fig. 14.
Column moment diagrams at different fire exposure times.
Comparison for all columns with bending moments, unreinforced.
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Fig. 15.
Comparison between subframes and simple columns with moments, unreinforced.
Fig. 16.
Moment–time relationships, Lb ⫽ 9 m, Lc ⫽ 7.5 m.
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Fig. 17. Comparison for all columns with bending moments, reinforced.
4.3. Additional axial load in column Fig. 18 shows the variations in additional axial loads for subframe columns with three different column lengths and two different beam lengths. The results are for beams with a modulus of elasticity of 10 times the steel Young’s modulus to simulate additional floors above the column. Additional axial loads in subframe columns with normal steel Young’s modulus were very small. Fig. 18 indicates that as expected, initial increases in the column axial loads were in proportional to the restraint stiffness relative to the column axial stiffness. The more slender the column, the higher the restraint stiffness relative to the column and therefore the higher the additional axial load. The additional axial load decreased at longer fire exposure as a result of the following three reasons: 앫 the column stiffness was reduced and therefore attracted less load; 앫 the additional axial load due to the restrained thermal expansion became smaller at reducing column stiffness, the extreme case being a column of zero stiffness giving no additional axial load; 앫 increased column deflection under load in the opposite direction to thermal expansion acted as a counter effect to thermal expansion, and this effect was much more pronounced at higher temperatures when the column deflection accelerated. Consequently, when columns approached failure at the fire limit state, the additional axial loads were substantially lower than their peak values and the total axial loads were approximately the same as the initial values at ambient temperature. The fire resistance of simply supported columns with appropriately reduced effective lengths and under the initial axial loads were calculated. The results of these calculations are included in Fig. 14. The fact that increasing the beam stiffness ten-
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Fig. 18. Column axial load–time relationships.
fold made a negligible difference in the overall agreement suggests that any additional column axial load due to the restrained thermal expansion would have small effect on the column fire resistance.
5. Conclusions This paper presents the results of three parametric studies on the effects of structural continuity on the fire resistance of concrete filled tubular columns. Both reinforced and unreinforced columns under both axial loads and bending moments were analysed. For unreinforced columns under pure axial loads, a range of column cross-section sizes, column heights and load ratios were studied. For columns under both axial loads and bending moments and for reinforced columns, the more slender columns were examined, as their fire resistance times were more sensitive to variations in bending moments and reinforcement. The following conclusions may be drawn: 1. The Eurocode 4 Part 1.2 [2] recommendation on column effective length at the
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fire limit state was validated. Specifically, for non-sway frames, the effective length ratio for a column continuous at both ends may be taken as 0.5 and that for a column continuous at one end may be taken as 0.7. This assumption gives very accurate results of fire resistance for unreinforced subframe columns. The fire resistance of reinforced subframe columns were slightly over estimated, but differences were small. 2. Primary column bending moments in continuous frames diminished at increasing temperatures. For short columns, secondary moments due to large column deflections were also small, thus columns may be assumed to resist axial loads only at the fire limit state. For longer columns, the secondary bending moments became higher. However, these secondary bending moments induced a complicated double curvature bending mode, and the column fire resistance times did not seem to be reduced by these double curvature bending moments. Therefore, slender columns may also be assumed to resist pure axial loads. In contrast, when the bending moments in the subframe columns at ambient temperature were applied to the simply supported columns, much lower column failure times were obtained. Both reinforced and unreinforced columns behaved very similarly. 3. Some additional axial loads were generated in columns due to restraint to their thermal expansions. However, as the column temperatures increased, these additional axial loads decreased and the total column axial loads returned to their ambient temperature values.
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The effects of structural continuity on the fire resistance of concrete filled columns in nonsway frames Y.C. Wang Manchester School of Engineering, University of Manchester, Manchester M13 9PL, UK Received 14 August 1997; received in revised form 21 September 1998; accepted 20 October 1998
Abstract This paper presents the results of a series of theoretical studies on the effects of structural continuity on the fire resistance of composite columns of concrete filled steel tubes. In particular, these theoretical studies concern the changes in column effective lengths, axial loads and bending moments under fire conditions and the effects of these changes on column fire resistance. These studies are carried out to confirm (or otherwise) the recommendation on column effective length in Eurocode 4 Part 1.2 and to put forward additional suggestions on column axial loads and bending moments at the fire limit state. Finite element analysis is used to evaluate the non-uniform temperature distributions in composite cross-sections and to analyse the structural response at elevated temperatures. The results of these studies have validated the recommendation in Eurocode 4 Part 1.2 that the boundary conditions for continuous columns may be assumed to be built-in. They also suggest that at the fire limit state, additional axial loads in columns due to restrained thermal expansions are very small and that column bending moments become much lower than those at ambient temperature. For calculating its fire resistance, a column may be assumed to be under pure axial load equal to its ambient temperature value, the result of which may only slightly overestimate the exact column fire resistance. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Composite columns; Fire resistance; Structural continuity; Interaction; Design method; Bending moment
Notation Lb Lc Le
beam span column height column effective length
0143-974X/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 3 - 9 7 4 X ( 9 8 ) 0 0 2 4 5 - 4
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1. Introduction Composite columns made of steel and concrete have many advantages over bare steel or reinforced concrete columns, being able to give increased strength with reduced cross-sectional size and possessing inherently high fire resistance. Many different types of composite columns have been developed, including the more commonly used concrete encased steel H sections and concrete filled steel tubes as shown in Fig. 1. The subject of this paper is concrete filled circular/square steel tubes. Columns of this type offer speedy construction, good impact resistance and the possibility of using exposed steelwork without compromising fire safety. The traditional method of evaluating the fire resistance of a structural element is by performing the standard fire resistance test [1], which is time consuming and expensive. Recently, calculating the fire resistance of individual loadbearing members is becoming more acceptable and for composite columns, the calculating procedures are now well established [2]. In Europe, Eurocode 4 Part 1.2 [2] may be used for such purposes. This code has been developed as a result of many experimental and analytical studies carried out in Europe [3–7]. The fire resistance of concrete filled columns has also been extensively investigated elsewhere, especially in Canada [8–12] and Japan [13]. However, most of the investigations reported in the more widely available literature sources have focused on the fire resistance of individual columns whose boundary and loading conditions are well defined and remain unchanged during the fire exposure. When a composite column interacts with other structural members in a frame under fire conditions, both its boundary conditions and loading conditions change. It is therefore necessary to accurately determine their values to allow the column fire resistance to be correctly evaluated. Both aspects of structural continuity have been addressed for steel columns by a number of investigators [14–16], using numerical methods. It has been generally concluded that at the fire limit state, built-in boundary conditions may be assumed for continuous steel columns. Eurocode 4 Part 1.2 [2] adopts this conclusion and recommends that for a composite column continuous at both ends, its effective length ratio may be taken as 0.5
Fig. 1.
Typical examples of steel–concrete composite sections.
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and for a column continuous at one end only, an effective length ratio of 0.7 may be used. For a steel column, uniform temperature distribution over the cross-section is usually assumed, so that when the column approaches failure at the fire limit state its stiffness has almost diminished, thus giving very high restraint stiffness relative to that of the column and validating the assumption of built-in boundary conditions. For concrete filled columns, because the inner concrete core is cooler and therefore may still retain some stiffness at the fire limit state, it is necessary to check the assumption of infinite restraint stiffness relative to the column. Eurocode 4 Part 1.2 [2] does not give specific guidance on the determination of the axial load and bending moments in a composite column as part of a frame. Thus for practical designs, the values of these forces may be assumed to be unchanged and equal to those at ambient temperature. However, Kimura et al. [13] tested a series of frames comprised of concrete filled square tubular members and observed that column bending moments became very small at the fire limit state, and the columns could be assumed to be axially loaded only. This observation is a result of very low column bending stiffness attracting very small bending moments, and is therefore consistent with the conclusion of the builtin boundary conditions for continuous columns. It is also a very important observation for concrete filled columns. Under pure axial loads, many fire tests [11] have demonstrated that unreinforced concrete filled columns have very high inherent fire resistance. However, when subjected to bending, their fire resistance rapidly decreases due to the loss of the steel tube and the inability of the remaining unreinforced concrete core to resist bending, thus limiting the applicability of this type of column. However, if the observation of Kimura et al. [13] can be extended more generally to columns in other configurations, it may not be necessary to design unreinforced concrete filled columns for bending under fire conditions, thereby fully utilising their high fire resistance under pure axial loads. The objectives of this paper are therefore two-fold: (1) to evaluate the effective lengths of composite columns in frames under fire conditions to validate (or otherwise) the assumption adopted in Eurocode 4 Part 1.2 [2]; (2) to study the variations in column axial loads and bending moments, in particular to check the assumption that composite columns many be assumed to be under pure axial loads at the fire limit state.
2. Methodology of analysis At the fire limit state, the effects of structural continuity on fire exposed columns are expected to provide built-in boundary conditions, and also to reduce column bending moments to a negligible level, both being results of very low column bending stiffness at elevated temperatures. While this can be easily envisaged for a steel column whose cross-section is usually under uniform temperature, and therefore its stiffness diminishes uniformly and becomes very small under load at the fire limit state, a concrete filled column may still retain some stiffness due to the cooler con-
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crete core and reinforcement. Hence the effects of structural continuity on a composite column may not be sufficient to allow the assumptions of the built-in boundary condition and negligible bending moments. To evaluate the exact boundary conditions to a composite column and its bending moments at the fire limit state, it is necessary to accurately calculate the non-uniform temperature distributions in the composite cross-section, and to evaluate the structural interaction between the composite column and other members. 2.1. Numerical calculation for temperature distributions in composite crosssections A finite element analysis computer program has been developed by the author to evaluate temperature distributions in two-dimensional continuous media. This analysis is based on well developed numerical methods for heat transfer in a textbook by Bathe [17]. In the program, either one-dimensional line elements or two-dimensional elements may be used. Due to symmetry when a concrete filled circular/square column is exposed to a uniform temperature field, the one-dimensional two-noded line elements may be used with each element representing a circular/square slice of the cross-section. The varying circumference of each slice may be accounted for by multiplying the thermal capacitance of each element by the circumferential length. 2.2. Validation of the temperature calculation method Fig. 2 is used to indicate the accuracy of the computer program, where the calculated steel and concrete temperatures are compared with those measured during a
Fig. 2. Comparison between calculated and measured temperatures, Test C17 [11].
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test on a concrete filled circular hollow section column (Test C17), conducted by Lie and Chabot [11]. In the calculations, a resultant emissivity of 0.7 and a heat transfer coefficient for convection of 25 W/m°K were used. The thermal properties of both steel and concrete were assumed to be those in Eurocode 4 Part 1.2 [2]. An increased concrete specific heat was used to account for concrete moisture, but the steel/concrete interface effect was not addressed because the composite cross-section was treated as a continuous medium with varying thermal properties. Fig. 2 shows that the steel temperatures were very accurately predicted. Differences between the calculated and measured concrete temperatures are slightly higher; however, considering the uncertainties associated with concrete thermal properties and heat transfer characteristics of the test furnace, the calculated temperatures were not fine-turned to agree with the test results exactly. Nevertheless, the calculated temperatures were regarded to be acceptable for the purpose of the studies in this paper in which the results of the same temperature analysis were used to facilitate structural analysis of the same composite column in different structural configurations. 2.3. Finite element analysis for structural response and its validation This analysis uses a finite element analysis computer program developed by the author for steel and composite frames under fire conditions [18]. This computer program has been extensively calibrated against the results of a large number of fire tests on steel and composite beams, steel columns, concrete columns and steel frames. In this paper, some additional examples are provided to demonstrate the capacity of this computer program to analyse the behaviour of composite columns both at ambient temperature and under fire conditions. Fig. 3 compares the load versus major and minor axis deflection relationships for a slender, concrete filled rectangular hollow section steel column, tested under axial load and biaxial bending moments [19]. Results in this figure indicate that the computer program is capable of simulating quite accurately the behaviour of composite columns up to the maximum applied load. Fig. 4 compares the axial shortening versus fire exposure time for a concrete filled circular steel column (Test C17) exposed to the standard heating condition, tested by Lie and Chabot [11]. This figure shows that the finite element analysis program may be used to predict both the column deflection history and its fire resistance time with reasonable accuracy. Since the computer program has the capacity to analyse the response of steel frames, it may be considered to be acceptable for studying structural interaction between composite columns and other members in frames.
3. Parametric studies Three parametric studies were carried out to evaluate effective lengths, bending moments and additional axial loads for composite columns of concrete filled Circular
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Fig. 3.
Load–deflection curves, Test 3 [19].
Hollow Section (CHS) steel tubes in subframes (to be referred to as subframe columns) at the fire limit state. Because of the similarity in the final results of these parametric studies between CHS columns and columns with square sections, only CHS columns are discussed in this paper. In all calculations, the standard heating regime [1] was assumed. For heat transfer calculations, the thermal properties of steel and concrete in Eurocode 4 Part 1.2 [2] were used. For structural response analysis, steel was assumed to be grade S275 having a yield stress of 275 N/mm2 and Young’s modulus of 205 000 N/mm2, and concrete grade C25/30 with a compressive strength of 30 N/mm2 and modulus of elasticity of 30 500 N/mm2. The stress–strain relationships of both steel and concrete followed those in Eurocode 4 Part 1.2 [2].
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Fig. 4.
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Comparison between test and calculated column behaviour, C17 [11].
3.1. Column effective length The effective length of a subframe column was evaluated by first computing the subframe column failure time. The column was then analysed individually as a simply supported column under the same axial load but with different lengths. Different failure times of the simply supported column with different lengths were calculated and compared with that of the subframe column. The column failure time was used for all comparisons for two reasons: firstly, it is one of the principal values which may be used to indicate the column behaviour under fire conditions; secondly, it was difficult to select one temperature value to represent the non-uniform temperature distribution in a composite cross-section. The subframes in Fig. 5(a) and (b) were used to evaluate the effective lengths for columns continuous at both ends and for columns continuous at one end respectively. These subframes were adopted to simulate columns in simple construction. If a subframe column is restrained by adjacent beams, the subframes in Fig. 5(a) and (b) will give the least favourable column effective length. Three key parameters were investigated, being column length, column cross-section size and the applied load ratio. The column lengths were 2.5 m, 5 m and 7.5 m. Four cross-section sizes were selected and they were: CHS 273 ⫻ 6.3, CHS 273 ⫻ 25, CHS 457 ⫻ 10 and CHS 457 ⫻ 40. Both unreinforced and reinforced concrete filled columns were studied. As will be seen from the results, structural continuity has the greatest effect on slender columns. Therefore, reinforcement was provided to columns of the smallest cross-section of CHS 273 ⫻ 6.3. Reinforcement was in the form of a smaller steel circular hollow section, being CHS 139.7 ⫻ 5.0, CHS 114.3 ⫻ 6.3 or CHS 114.3 ⫻ 3.6, giving ratios of the reinforcement area to the concrete area of 4.1%, 4.2% and 2.4% respectively, and concrete covers of 60 mm, 73 mm and 73 mm respectively.
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Fig. 5.
Subframes used for studies on column effective length.
The load ratio is the ratio of the applied load in a column under fire condition to the column’s strength at ambient temperature. For a fully designed column, this value is usually 0.5–0.6. In this study, two values were used, 0.4 and 0.7, representing the lower and upper bounds on the load ratio. Column strengths at ambient temperature were calculated using Eurocode 4 Part 1.1 [20], assuming an effective length ratio of 1.0. 3.2. Variations in column bending moments Fig. 6(a) and (b) were used to study variations in column bending moments for columns continuous at both ends and at one end respectively. For columns continuous at both ends, applied loads on beams in Fig. 6(a) were arranged to induce single curvature bending in the column. Beam ends were assumed to be simply supported and beam–column connections were assumed to be rigid. Both reinforced and unreinforced columns were analysed. 3.2.1. Unreinforced columns Column length was 2.5 m, 5 m or 7.5 m. To ensure that bending moments had the greatest influence, the smallest column cross-section size of CHS 273 ⫻ 6.3 was used. Beams were chosen to have a 356 ⫻ 171 ⫻ 67UB steel section, their length being either 6 m or 9 m. The larger applied load on the beam was determined to give a bending moment in the centre of a simply supported beam of 60% of its plastic moment capacity. For a beam length of 6 m, this beam load was 133.1 kN. Assuming a typical frame spacing of 6 m, this load represented a uniformly distrib-
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Fig. 6.
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Subframes used for studies on moment transfer and additional axial load.
uted floor load of 7.5 kN/m2, simulating a typical dead load of 2.5 kN/m2 and imposed load of 5 kN/m2. The smaller load was 1/3 of the larger load, thus representing the dead load only. For different beam lengths, column bending moments were about 10–40% of the column plastic moment capacities at ambient temperature. The additional axial loads of 30% of the column compressive strength were applied, giving total load ratios between 0.4 and 0.7. 3.2.2. Reinforced columns Columns of CHS 273 ⫻ 6.3 were analysed. The same three levels of reinforcement as in Section 3.1 were assumed. Only the 7.5 m columns were studied. However, an additional column load case was included in the analysis, applying a total axial load in each column of 60% of the unreinforced column’s compressive strength. 3.3. Additional axial loads in columns The subframe in Fig. 6(b) was used to study additional axial loads in columns due to restrained thermal expansion. Previous studies on steel columns [15] suggest greater effects of additional axial loads on more slender columns. The smallest column cross-section size of CHS 273 ⫻ 6.3 was therefore used for this study. Other parameters were the same as in Section 3.2 for unreinforced columns.
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The amount of the additional axial load in a column whose thermal expansion is restrained is a function of the restraint stiffness. To account for the influence of additional storeys in real buildings above a column, the Young’s modulus of steel for beams in Fig. 6(b) was multiplied by a factor of 10. At this modulus of elasticity, the maximum restraint stiffness was 1%, 2% and 3% of the axial stiffness of the 2.5 m, 5 m and 7.5 m column respectively.
4. Results and discussions
4.1. Column effective length 4.1.1. Unreinforced columns The results are given in Fig. 7 and Fig. 8 for unreinforced concrete filled columns continuous at both ends and at one end respectively. They show the comparisons between failure times of subframe columns and those of simply supported columns. Effective length ratios of 0.5 and 0.7 were used for the simply supported columns whose results are given in Figs. 7 and 8 respectively. Results in Figs. 7 and 8 indicate that for all column lengths, cross-section sizes and load ratios, there is a very close agreement between the failure times of subframe columns and those of simply supported columns with appropriately reduced effective lengths recommended in Eurocode 4 Part 1.2 [2]. Therefore, these results confirm the recommendation in Eurocode 4 Part 1.2 [2] that for columns continuous at both ends, an effective length ratio of 0.5 may be used and for columns continuous at one end, an effective length ratio of 0.7 may be used. This conclusion suggests although concrete filled columns had cooler concrete cores, their influence on column
Fig. 7.
Comparison for columns continuous at both ends, unreinforced.
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Fig. 8.
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Comparison for columns continuous at one end, unreinforced.
effective lengths was small due to their small size and their low stiffness at highly increased stresses, as a result of the loss of the steel tube and the outer concrete. Although Figs. 7 and 8 show that in a few cases, using built-in boundary conditions gave columns higher fire resistance, the differences between these fire resistance times and those of subframe columns were very small. Fig. 5(a) and (b) represent the two minimum restraint situations to a subframe column and they have provided the column with the maximum rotational restraint. Therefore, if a subframe is provided with additional rotational restraint from adjacent beams, it is still valid to adopt the assumption of built-in boundary conditions for the subframe column at the fire limit state. 4.1.2. Reinforced columns For short columns, failure is generally due to the applied load exceeding the squash resistance and hence the effect of different boundary conditions on column failure times is small. In contrast, slender columns fail by buckling and therefore their fire resistance times are more sensitive to changes in the boundary conditions. These general trends were followed by the results of studies on unreinforced concrete filled columns. Therefore, columns with the smallest cross-section of CHS 273 ⫻ 6.3 was reinforced to three different levels to study the influence of reinforcement on column boundary conditions at the fire limit state. The results for all columns are shown in Fig. 9. The differences between failure times of subframe columns and the simply supported columns with the appropriately reduced effective lengths are larger than those shown in Figs. 7 and 8 for unreinforced columns, with the failure times of simply supported columns being higher. This suggests that the residual stiffness of the reinforcement had some effect on the column effective length at the fire limit state. However, results in Fig. 9 indicate that at the three different reinforcement
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Fig. 9.
Comparison for all reinforced columns, axial load.
ratios, the agreement between the failure times of the subframe columns and those of the simply supported columns of reduced effective lengths is still quite good. Therefore, the effect of reinforcement on column effective length may be regarded as small, and for reinforced columns, the assumption of built-in boundary conditions at the fire limit state may still be used as for unreinforced columns. 4.2. Variation in column bending moment 4.2.1. Unreinforced columns Figs 10 and 11 show the variations in bending moments at the column top and centre respectively for columns continuous at the top, obtained using the structural subframe in Fig. 6(b). The horizontal axis gives the ratio of the bending moment in the column to the column’s plastic moment capacity at ambient temperature. Both figures suggest that column bending moments started to decrease rapidly after a few minutes of fire exposure, as a result of rapid reduction in the column flexural bending stiffness. This tendency was continued for short columns. However, for more slender columns, their response was affected by the P–⌬ effect as the column lateral deflections increased. Under this condition, Fig. 11 shows that the bending moment in the column centre increased after early reduction and Fig. 10 suggests a reversal in the sign of the column top bending moment, which created a very complicated double curvature bending mode in the column. Similar behaviour was also observed for columns continuous at both ends, simulated using the subframe in Fig. 6(a). Fig. 12 shows variations in column bending moments at top, centre and bottom for the 7.5 m long subframe column and Fig. 13 compares the bending moment diagrams of the column at ambient temperature, at 30 minutes and at failure. Fig. 13 clearly illustrates the variation in column effective
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Fig. 10.
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Column top moment–time relationships.
length, as indicated by the distance between the two inflection points in the column moment diagram, as the fire exposure time increases. At the column failure time, Fig. 13 shows that the column effective length is half the column length. The complicated bending behaviour, shown in Figs. 10, 11 and 13, did not affect the subframe column failure times. When the subframe columns were analysed as simply supported columns with reduced effective lengths corresponding to built-in boundary conditions, and with no bending moment, their failure times were very close to those of the subframe columns. The fire resistance results are shown in Fig. 14, which suggests although different levels of column bending moments had some effect on column failure times, this effect was small. In contrast, if the failure times of the subframe columns were calculated using the simply supported columns, with the reduced column effective lengths but subject to the ambient temperature bending moments, much lower column failure times were obtained. Fig. 15 compares the subframe failure times with those from simply supported columns whose bending moments were equal to those in the subframe col-
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Fig. 11.
Column centre moment–time relationships.
umns at ambient temperature. It can be seen that applying the ambient temperature subframe frame bending moments to the simply supported columns resulted in much lower column failure times. This strongly indicates that the column fire resistance calculations should take into account the observation that the subframe bending moments were substantially reduced at the failure time. The reduction in column bending moments is clearly illustrated in Fig. 12 for short columns. For more slender columns, although Fig. 12 still shows some bending moments at the failure times, these bending moments were due to the P–⌬ effect. However, they were much lower than those induced by the P–⌬ effect in simply supported columns that were subject to initial bending moments equal to those in the subframe column at ambient temperature. An example is shown in Fig. 16.
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Fig. 12.
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Moment–time relationships, Lb ⫽ 9 m, Lc ⫽ 7.5 m.
4.2.2. Reinforced columns The combined effects of bending moments and reinforcement on column fire resistance were also studied and the results are plotted in Fig. 17. This figure shows quite close agreement between the failure times of subframe columns and those of the simply supported columns with reduced effective lengths but not subject to any bending moment. The results in Fig. 17 are also very similar to those in Fig. 9 for reinforced columns without bending moments. This suggests that for reinforced subframe columns with bending moments, their fire resistance times may still be calculated on the basis that column boundary conditions are built-in and bending moments are very small.
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Fig. 13.
Fig. 14.
Column moment diagrams at different fire exposure times.
Comparison for all columns with bending moments, unreinforced.
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Fig. 15.
Comparison between subframes and simple columns with moments, unreinforced.
Fig. 16.
Moment–time relationships, Lb ⫽ 9 m, Lc ⫽ 7.5 m.
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Fig. 17. Comparison for all columns with bending moments, reinforced.
4.3. Additional axial load in column Fig. 18 shows the variations in additional axial loads for subframe columns with three different column lengths and two different beam lengths. The results are for beams with a modulus of elasticity of 10 times the steel Young’s modulus to simulate additional floors above the column. Additional axial loads in subframe columns with normal steel Young’s modulus were very small. Fig. 18 indicates that as expected, initial increases in the column axial loads were in proportional to the restraint stiffness relative to the column axial stiffness. The more slender the column, the higher the restraint stiffness relative to the column and therefore the higher the additional axial load. The additional axial load decreased at longer fire exposure as a result of the following three reasons: 앫 the column stiffness was reduced and therefore attracted less load; 앫 the additional axial load due to the restrained thermal expansion became smaller at reducing column stiffness, the extreme case being a column of zero stiffness giving no additional axial load; 앫 increased column deflection under load in the opposite direction to thermal expansion acted as a counter effect to thermal expansion, and this effect was much more pronounced at higher temperatures when the column deflection accelerated. Consequently, when columns approached failure at the fire limit state, the additional axial loads were substantially lower than their peak values and the total axial loads were approximately the same as the initial values at ambient temperature. The fire resistance of simply supported columns with appropriately reduced effective lengths and under the initial axial loads were calculated. The results of these calculations are included in Fig. 14. The fact that increasing the beam stiffness ten-
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Fig. 18. Column axial load–time relationships.
fold made a negligible difference in the overall agreement suggests that any additional column axial load due to the restrained thermal expansion would have small effect on the column fire resistance.
5. Conclusions This paper presents the results of three parametric studies on the effects of structural continuity on the fire resistance of concrete filled tubular columns. Both reinforced and unreinforced columns under both axial loads and bending moments were analysed. For unreinforced columns under pure axial loads, a range of column cross-section sizes, column heights and load ratios were studied. For columns under both axial loads and bending moments and for reinforced columns, the more slender columns were examined, as their fire resistance times were more sensitive to variations in bending moments and reinforcement. The following conclusions may be drawn: 1. The Eurocode 4 Part 1.2 [2] recommendation on column effective length at the
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fire limit state was validated. Specifically, for non-sway frames, the effective length ratio for a column continuous at both ends may be taken as 0.5 and that for a column continuous at one end may be taken as 0.7. This assumption gives very accurate results of fire resistance for unreinforced subframe columns. The fire resistance of reinforced subframe columns were slightly over estimated, but differences were small. 2. Primary column bending moments in continuous frames diminished at increasing temperatures. For short columns, secondary moments due to large column deflections were also small, thus columns may be assumed to resist axial loads only at the fire limit state. For longer columns, the secondary bending moments became higher. However, these secondary bending moments induced a complicated double curvature bending mode, and the column fire resistance times did not seem to be reduced by these double curvature bending moments. Therefore, slender columns may also be assumed to resist pure axial loads. In contrast, when the bending moments in the subframe columns at ambient temperature were applied to the simply supported columns, much lower column failure times were obtained. Both reinforced and unreinforced columns behaved very similarly. 3. Some additional axial loads were generated in columns due to restraint to their thermal expansions. However, as the column temperatures increased, these additional axial loads decreased and the total column axial loads returned to their ambient temperature values.
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