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Effects of structural continuity on fire resistant design of steel columns in non-sway multi-storey frames
Fire Safety Journal 28 (1997) 101-116 Crown copyright ~) 1997 Published by Elsevier Science Ltd. Printed in Northern Ireland.
0379-7112/97/$17.00 ELSEVIER
PII:
S0379-71
12(96)00083-5
Effects of Structural Continuity on Fire Resistant Design of Steel Columns in Non-sway Multi-storey Frames Y. C. Wang Structural Design Division, Building Research Establishment, Watford, Hertfordshire WD2 7JR, UK (Received 10 July i996: revised version received 25 October 1996: accepted 4 November 1996)
ABSTRACT This paper discusses two aspects of the effect of structural continuity on the .fire resistant design of steel columns in non-sway multi-storey steel frames. One is beneficial and the other is detrimental. The beneficial effect is to enhance the rotational restraint to the column and thus to reduce its effective length and increase its load carrying capacity. The detrimental effect is to increase the column compressive load due to axial restraint to its thermal expansion. This paper attempts to put forward a simple design method to reconcile these two effects. A comprehensive parametric study is performed to evaluate these two effects on the column limiting temperature and its fire protection thickness. It is found from the results of this" parametric study that for buildings with a practical range of axial restraint to columns, these two eff'ects almost cancel each other out. This paper therefore proposes that for the calculation of column limiting temperature, the additional compressive force in the column may be discarded provided the original column slenderness ratio at the cold condition is used for elevated temperature design. The .fire protection thickness of the column may be conservatively obtained by increasing by 20% that calculated using the above limiting temperature. Crown copyright © 1997 Published by Elsevier Science Ltd. NOTATION Kc()
K~(t) K~ L,.
P,, R
C o l u m n axial stiffness at cold condition C o l u m n axial stiffness at e l e v a t e d t e m p e r a t u r e Axial stiffness of spring C o l u m n length Initial axial load in c o l u m n = K~/K~
101
l O2
ALe AP
~mcc A~th
Y. c. Wang
Net increment in column d e f o r m a t i o n I n c r e m e n t in column mechanical d e f o r m a t i o n I n c r e m e n t in column compressive load due to restrained thermal expansion Difference in column mechanical strain at constant stress b e t w e e n two different t e m p e r a t u r e s I n c r e m e n t in column free thermal expansion strain
1 INTRODUCTION
For a building to remain safe under fire conditions, its supporting columns should remain stable. The importance of column stability to building safety was clearly observed in a major p r o g r a m m e of structural fire tests which has been recently completed on the eight-storey steel f r a m e d building in the Building Research Establishment's Cardington Laboratory.' On the one hand, these tests d e m o n s t r a t e d that although m a n y steel beams and connections lost their loading carrying capacities during the fire attack, the reinforced composite floor slabs in the test building had the capacity to bridge over fire d a m a g e d steel beams and connections, and directly transfer the applied loads to the supporting columns via the d e v e l o p m e n t of tensile m e m b r a n e action in the reinforcement. 2 Provided these columns were fire protected and their t e m p e r a t u r e s were below their failure temperatures, the building remained safe and fire damages were restricted to the fire exposed areas. On the other hand, in one test where the columns were not fire protected, fire d a m a g e e x t e n d e d well b e y o n d the small test area on the floor and over all the storeys above. The fire resistance of a steel column has been the subject of m a n y studies) 7 As a result of these studies, the limiting t e m p e r a t u r e of the column can now be predicted with reasonable accuracy. In particular, the m e t h o d proposed in E u r o c o d e 3, Part 1.2 ~ has been validated against a large body of test results. This limiting t e m p e r a t u r e can then be used to calculate the required fire protection thickness for the column under the design fire condition. However, most studies have concentrated on isolated columns with clearly defined b o u n d a r y conditions and loading conditions. It is well recognised that the behaviour of a column in a complete building is different from that of an isolated column because of the effects of structural continuity. O n e effect is beneficial and the other is detrimental.
Fire resistant design of steel columns
103
The beneficial effect is to increase the column load carrying capacity due to improved rotational restraint leading to reduced column effective length ratio. The detrimental effect is the increase in the column compressive load as a result of axial restraint to the column's thermal expansion. Clearly if all columns on the same floor level of a building are heated up to the same temperature in a fire, there will be no increase in the column compressive loads 9 and therefore the net effect of frame continuity is beneficial. Due to the importance of column stability to building safety, this paper addresses the potentially more dangerous scenario where the columns are not heated to the same temperature or fire attack is confined to a part of the building floor area or both. As the cost of fire protection to columns is relatively low, the objective of this paper is to develop a simple and safe method to help designers calculate the required fire protection thickness to the column under this more dangerous fire situation.
2 EFFECTS OF S T R U C T U R A L C O N T I N U I T Y ON C O L U M N BEHAVIOUR
The effects of structural continuity on column behaviour have been studied separately by a number of researchers. 3"9 12 The conclusions of these studies are briefly summarised here.
2.1 R o t a t i o n a l restraint
Under fire conditions, there is a change in the column stiffness relative to that of the surrounding structure. This change in the relative stiffness is due to the different heating and loading rates in the column and the surrounding structure. As the column approaches failure at high temperatures, its bending stiffness is very low due to highly uniform heating and loading. At the same time, there is considerable stiffness in the surrounding beams and columns because of low levels of heating and loading. This leads to a much higher relative rotational restraint to the hot column than at the cold condition. Detailed studies by the author `) and others 1~ indicate that the rotational restraint to the column at failure approaches that of fixed ends. For columns in non-sway frames, a value of 0.6 may be used, although the value of 0.5 is currently recommended in Eurocode 3, Part 1.2. ~
Y. (i Wang
104
a~th'Lc ; °
P AL = o c Kc(t)
+AP
P o Kc °
AP
Kc(t)
AL
AP
C
=ACmec.Lc
T-
+ Kc(t }
A = A e t h . Lc - A L c AP K
where:
s
A / c = Change in column l e n g t h KcCt) = Column s t i f f n e s s at
current temperature
/
/, •
At rest
Final position Fig. 1.
K
= S t i f f n e s s o f column at co s t a r t o f temperature
increment
Restrained column thermal expansion in lire.
2.2 Axial restraint
If the column is h e a t e d up while the remaining frame is kept at lower temperatures, this structural system resembles that of a column being axially restrained against its thermal expansion by a spring, representing the remaining frame. In this case, there is an increase in the compressive force in the column. As schematically illustrated in Fig. 1, this additional compressive force (Ap) may be calculated using the following equation: Ap =
R &.(t) Kc(0/&.,, + R
(AEt,,-- ~E ..... )L~
(1)
This equation was checked against the results of finite element analysis and was found to be accurate. ~° A detailed study is required to evaluate the initial ratio R of the spring stiffness to the column stiffness. However, assuming a typical loading condition and frame geometrical arrangement, an initial restraint stiffness ratio R of about 2% was estimated. ~ Because changes in the n u m b e r of frame storeys and the level of loading would lead to similar changes in both the initial column axial stiffness and the axial stiffness of the spring representing the surrounding structure, the stiffness ratio R would differ from 2% only slightly. In this paper, the range of R is set to be between 0 and 5%.
Fire resistant design of steel columns
105
3 DESIGN METHODS
Three methods may be used to take into consideration the effects of rotational and axial restraints to the column to calculate its limiting temperature and fire protection thickness. 1. The 'complicated' method. In this approach, the column effective length appropriate to the rotational restraint at elevated temperatures is used to evaluate the column load carrying capacity. A lower value of column effective length ratio than that at the cold condition may be used to reflect that the column rotational restraint near failure approaches that of fixed ends under the fire condition. In this paper, the value of 0.6 is used. The axial force in the column includes both the initially applied load and the additional compressive load due to restrained thermal expansion. 2. Inclusion of improved rotational restraint only. The same value of effective column length ratio of 0.6 is taken as in (1). This method is therefore a special case of method (1) with R = 0. This approach is adopted in Eurocode 3, Part 1.2, ~ although the value of effective length ratio is recommended to be 0.5. 3. No structural continuity. In this approach, neither the improved column rotational restraint nor the increased compressive axial load in the column is considered. This method is adopted in the British Standard BS 5950 Part 8.14 The reason for this is because BS 5950 Part 8 '4 was developed on the basis of the results of standard fire resistance tests on individual columns. Method (1) is obviously the most accurate. However, it is also the most time consuming and complicated. The designer has to evaluate the axial restraint stiffness to the column first. Then an iterative process is carried out comparing the variable column axial load at different temperatures against its load carrying capacity to find out the column limiting temperature. Although graphs, which describe the relationships between the column initial axial load and limiting temperatures for different values of axial restraint stiffness and column slenderness, such as those prepared by CTICM ~5 would help, a lengthy design process is still required. The second method would give the column the highest limiting temperature, leading to thinner fire protection. However, it may not be safe. While method (3) is not correct in its treatment of either effect, the column limiting temperature calculated using this method may be quite
106
Y. C. Wang
reasonable. This is because the effects of improved column rotational restraint and increased column compressive force are opposing and therefore may cancel each other out. This m e t h o d is also attractive to designers because it uses the column effective length at the cold condition. Since the assumptions of m e t h o d (3) are implicit in the British Standard BS 5950 Part 8,14 the objective of this paper is to investigate the margin of safety of the BS 5950 Part 8 approach 1~ for the calculation of the column limiting temperature. This will then be used as a basis for the determination of the column fire protection thickness. Having established the column effective length and applied load to be used in various approaches, the column limiting temperature is calculated using the resistance m e t h o d in Eurocode 3, Part 1.2Y Since the column buckling curve 'c' is r e c o m m e n d e d to be used for the design of columns under fire situations, the column axial load resistance, used to calculate the initial axial load ratio, is also determined using the column buckling curve 'c'. The fire protection thickness is also calculated in accordance with the equation given in Eurocode 3, Part 1.2Y A spray fire protection material is assumed. The nominal fire protection material properties are: coefficient of thermal conductivity: 0-17 W/m°C, density: 4 0 0 k g / m 3, specific heat: 1250 J/kg°C. Because of the possible inaccuracy in the Eurocode 3, Part 1.2 equation ~ and different fire protection materials having different thermal properties, the absolute fire protection thickness may be different from that calculated in this study. However, it is reasonable to expect that the degrees of inaccuracy in the predicted fire protection thickness based on the two different design methods (methods 1 and 3) are similar and that the inaccuracy in the fire protection thickness ratio is largely eliminated.
4 PARAMETRIC STUDY The objective of this paper is to develop a simple and safe m e t h o d for the determination of column fire protection thickness, allowing for structural continuity. For the development of such a design method, a comprehensive parametric study is first carried out. In this parametric study, the limiting temperature and necessary fire protection thickness for different standard fire resistance times are calculated using two methods: m e t h o d (1) [the 'complicated' method] and m e t h o d (3) [no consideration of structural continuity] for a large n u m b e r of columns. In the 'complicated' method, the column effective length ratio is taken as 0.6 and the
Fire resistant design of steel columns
107
additional column compressive load is calculated using eqn (1). For each column arrangement, results for different levels of axial restraint to the column [R in eqn (1)] are compared. Detailed input parameters are: • • •
column size: all universal columns, 16 bending about both the major and minor axes; column length: 2.5 m, 5 m, 7.5 m; column effective length ratio at the cold condition: 0.6, 0.7, 0.8, 0.9,
1.0; •
• •
initial axial load ratio: 0.3, 0.5, 0.7. The initial axial load ratio is defined as the ratio of the initial axial load in the column to its load carrying capacity at the cold condition as determined using the column buckling curve 'c'; initial axial stiffness ratio R: 0, 0.5%, 1.0%, 2.0%, 5.0%; standard fire resistance times: 30 min, 120 min.
These two standard fire resistance times investigate the sensitivity of the proposed exposure conditions. The combinations of all the parameters represent a great majority of columns that practice.
are used in this paper to m e t h o d to different fire above would be able to would be encountered in
5 D I S C U S S I O N ON L I M I T I N G T E M P E R A T U R E S
Figure 2 shows comparisons between the limiting temperatures for the load ratio of 0.5. The three figures (a)-(c) are for the three different values of column effective length ratio at the cold condition, being 0.6, 0.8 and 1, respectively. Figures 3 and 4 are for load ratios of 0.3 and 0.7, respectively, each with an ambient temperature effective length ratio of 0.8. In each of these figures, the comparison is made between the column limiting temperature calculated using the two methods. The temperature in the horizontal axis is calculated using m e t h o d (3) [ambient temperature column effective length ratio, initial load only]. The value on the vertical axis is obtained using m e t h o d (1) [fixed column effective length ratio 0.6, initial axial load plus additional compressive force]. The comparison in each figure is made for different levels of axial restraint. The highest curve as determined from the values on the vertical axis in each figure corresponds to the column limiting temperature that would be obtained
Y. C. Wang
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Fig. 2.
Comparison between different predicted column limiting temperatures, load ratio = 0.5.
Fire resistant design of steel columns
109
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!
oqlk
650
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t
g
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I~ R=O !
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8
i
400 400
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500
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column effective length ratio=0.8, no
Fig. 3.
600
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Comparison between different predicted column limiting temperatures, load ratio = 0.3.
600 55O
:m O
~- 5OO
i"¢= 450 >~
o 400
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column effective length ratio=O.8, no axial restraint
Fig. 4.
Compariosn between different predicted column limiting temperatures, load ratio = 0.7.
110
Y. C. Wang
using method (2) [fixed column effective length ratio 0.6, initial axial load only]. Results in Figs 2(b), 3 and 4 show that for columns with different levels of initial axial load, column limiting temperatures calculated using the two methods are quite close for R = 2%. For the higher value of initial axial load ratio as shown in Fig. 4, the predicted column limiting temperature becomes more conservative using method (3) where frame continuity is ignored. This was also observed for other values of the ambient temperature column effective length ratio. Results in Fig. 2 suggest that over the range of axial restraint considered, the difference in column limiting temperatures calculated using the two different methods is sensitive to the column slenderness ratio. At very low values of the column slenderness ratio, being indicated by the highest limiting temperature values in each figure, the column limiting temperature is not very sensitive to the degree of axial restraint. In these cases, discarding the effect of axial restraint to column but using the effective length of 0.6 would only overestimate the column limiting temperature by about 50°C. If the column effective length at the cold condition is used, the predicted column limiting temperature is very close to that predicted using the 'complicated" method for different values of axial restraint. However, at higher values of the column slenderness ratio, there is a great range of column limiting temperatures for different degrees of axial restraint to the column. The difference in column limiting temperature for the case of no axial restraint (R = 0) and high axial restraint (R = 5%) could be about 200°C. This implies that if the current assumption in Eurocode 3, Part 1.2~ (method 2) is used, the column limiting temperature could be overestimated by 200°C. At the lowest value of ambient temperature column effective length ratio of 0.6, method (3) is identical to method (2) as shown in Fig. 2(a). However, only in a few cases would the column effective length ratio at the cold condition be at such a low level in practical design. For more realistic values of column effective length ratio, the assumptions of discarding both rotational and axial restraints lead to predictions of column limiting temperature which are close to those predicted using the 'complicated' method at the value of axial restraint stiffness ratio R of between 2% and 5%. Since the axial restraint stiffness in realistic buildings would fall in this range, the results of this parametric study suggest that the accuracy of the predicted column limiting temperature obtained by discarding the effects of structural continuity is reasonable. In other words, although BS 5950 Part 8 t4 was not developed to explicitly consider the effects of structural continuity, it gives acceptable results due
Fire resistant design of steel columns
111
to the fact that these two effects almost cancel each other out. Nevertheless, this m e t h o d may lead to an overestimation in the limiting temperature for columns with very low effective length ratios at the cold condition. However, this deficiency may be rectified in the calculation of column fire protection thickness as discussed in the next section.
6 D I S C U S S I O N ON F I R E P R O T E C T I O N T H I C K N E S S In all cases, the column limiting temperature is lower than 650°C. Since temperatures generated in most post-flashover fires will normally induce much higher values of temperature in unprotected steel, this means in a majority of cases, steel columns in buildings should be fire protected to avoid instability. U n d e r this condition, the difference in cost of fire protection to columns is very small with a moderate difference in fire protection thickness. Therefore, provided the proposed design m e t h o d gives a safe column under fire conditions, a moderate overestimation in the column fire protection thickness compared against that calculated using the 'complicated' m e t h o d should be regarded as acceptable. Figure 5 shows comparisons between fire protection thicknesses calculated using the limiting temperatures of Fig. 2 for the standard fire resistance time of 30 min, the initial load ratio being 0.5. In each figure, the horizontal axis represents the fire protection thickness calculated using the limiting temperature of m e t h o d (3) [discarding both effects of structural continuity]. The vertical axis gives the ratio of the fire protection thickness calculated using the limiting temperature from the 'complicated' m e t h o d to the value of fire protection thickness on the horizontal axis. Figure 6 compares the results for the standard fire resistance time of 120 min, other main parameters being a load ratio of 0.5 and ambient temperature column effective length ratio of 0.8. Comparisons between Figs 5(b) and 6 for the two different standard fire resistance times indicate that there is very little difference in results of fire protection thickness ratio for different standard fire resistance times, although the fire protection thicknesses are different. Figures 7 and 8 give results for load ratios of 0.3 and 0.7, respectively, with the standard fire resistance time of 3 0 m i n and the ambient temperature effective length ratio of 0.8. Comparisons between Figs 7, 5(b) and 8 show that the fire protection thickness ratio is only slightly affected by the level of axial load ratio. Discussions will therefore be concentrated on the load ratio of 0.5 with a standard fire resistance time of 30 min whose results are shown in Fig. 5. Figure 5(a) shows that at an ambient temperature column effective
112
Y. C. Wang
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8
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protection thickness (ram), c o l u ~
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(c)
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8
10
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prot~tion thickness (ram), column Bffectlve length ratio=1.01 no a ] i l l restralnt
Fig. 5.
Comparison between different predicted protection thicknesses, load ratio = 0.5, 30 min.
Fire resistant design of steel columns
113
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0.4
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0 10
20
30
40
50
60
protection thickness (mm), c o l u m n effective length ratio=0.8, no axial r e s t r a i n
Fig. 6.
Comparison between different predicted protection thicknesses, load ratio = 0.5, 120 rain.
length ratio of 0.6, the predicted fire protection thickness from the limiting temperature of method (3) is lower compared to that using method (1). This is the direct result of overestimated limiting temperatures for this effective length ratio using method (3) as shown in Fig. 2(a). Nevertheless, 1.6
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protection thickness (ram), column effective length ratio =0.8, no axial restraint
Fig. 7.
Comparison between different predicted protection thicknesses, load ratio = 0.3, 30 rain.
114
Y. C. Wang 1.2 o
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o • o o Oo o^
o
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Fig. 8.
Comparison between different predicted protection thicknesses, load ratio
0.7,
30 min. the results of the fire protection thickness ratio as represented by the vertical axis are lower than 1.2 for the majority of columns. Values significantly higher than 1.2 (the value of thickness ratio > 1.4) are for long columns (5 m, 7.5 m) of the smallest sections (UC 203 and UC 152 series) bending about the minor axis. Because of the minor role these columns would play in the safety of steel frames in practice, it is proposed that the fire protection thickness to a steel column is obtained by increasing by 20% the fire protection thickness calculated without including the effects of structural continuity. This proposed m e t h o d of determining the column fire protection thickness is quite consistently followed for higher values of ambient temperature column effective length ratio. At these higher values, the calculated fire protection thickness would be greater than that required for all but the most slender columns (7-5 m, UC 152 columns bending about minor axis). Therefore, this proposal leads to stable columns under fire conditions. Although the calculated column fire protection thickness using the proposed m e t h o d may be twice that required, as suggested in Fig. 5(c) for an ambient temperature column effective length ratio of 1.0, i.e. pin-ended column, this gross inaccurate result only applies to columns with very low level of axial restraint ( R < 1-0%). Because the axial restraint stiffness is typically higher than this value and the proposed m e t h o d for fire protection thickness errs on the safe side, it is regarded as satisfactory.
Fire resistant design of steel columns
115
7 CONCLUSIONS AND DESIGN PROPOSALS A comprehensive parametric study was performed in this study to investigate the effects of structural continuity on column limiting temperature and fire protection thickness. Two aspects of the structural continuity are studied: improved column rotational restraint and increased compressive load in column due to axial restraint to column thermal expansion. The results of three different methods are compared. The main conclusions are: 1. If only the effect of improved column rotational restraint is included and a column effective length ratio of 0.6 is used, similar to the recommendation in Eurocode 3, Part 1.2, 8 the column limiting temperature may be overestimated by up to about 200°C for slender columns and more than 100°C in most cases. 2. If neither of the two effects of structural continuity is included, as currently r e c o m m e n d e d in BS 5950 Part 8, ~4 the limiting temperature of a column with light axial restraint (R < 2 % ) would be underestimated. For columns with more realistic axial restraint (2% < R < 5%), the limiting temperature is quite closely predicted. The difference in most cases would be less than 50°C. 3. The column limiting temperature in most cases is less than 650°C. This indicates that steel columns should always be protected to prevent instability since the unprotected steel temperatures induced in post-flashover fires will normally be much higher than this value. Consequently, the following proposals may be made with regard to the fire resistant design of steel columns: 4. The column limiting temperature may be calculated using the effective length ratio and axial load at the cold condition, without explicit consideration of the effects of structural continuity. 5. To compensate for the overestimation in column limiting temperatures in some cases, the column fire protection thickness may be determined by increasing by 20% the fire protection thickness calculated using the limiting temperature in (4). This would err on the safe side for all but a few very slender columns.
REFERENCES 1. Moore, D. B., Full-scale fire tests on complete buildings. In Proceedings of the Second Cardington Conference, Bedford, England, 12-14 March 1996. 2. Wang, Y. C., Tensile membrane action in slabs and its application to the Cardington fire tests. In Proceedings of the Second Cardington Conference, Bedford, England, 12-14 March 1996.
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3. Pettersson, O., Magnusson, S. E. & Thor, J., Fire engineering design of steel structures, Publication 50, Swedish Institute of Steel Construction, Stockholm, Sweden, 1976. 4. Franssen, J. M., Schleich, J. B. & GajoL L. G., A simple model for the fire resistance of axially-loaded members according to Eurocode 3. J. Construct. Steel Res., 35 (1995) 49-69. 5. Burgess, I. W. & Najjar, S. R., A simple approach to the behaviour of steel columns in fire. J. Construct. Steel Res., 31 (1994) 115-134. 6. ECCS-T3, European Recommendations for the Fire S~f'ety of Steel Structures. Elsevier Science, 1983. 7. Janss, J. & Minne, R., Buckling of steel columns in fire conditions. Fire St(f['ty J., 4 (1981) 227-235. 8. CEN, EC3: Design of Steel Structures, Part 1.2: Structural Fire Design, ENV 1993-1-2, CEN, 1995. 9. Franssen, J. M. & Dotreppe, J. C., Fire resistance of columns in steel frames. Fire Safety J., 19 (1992) 159-175. 1(). Wang, Y. C., Lennon, T. & Moore, D. B., The behaviour of steel frames subject to fire. J. Construct. Steel Res., 35 (1995) 291-322. 11. The Steel Construction Institute, The behaviour of steel columns in lire. Report to the Department of the Environment, RT524, The Steel Construction Institute, Ascot, UK, 1996. 12. Ooyanagi, N., Hirota, M., Nakamura, K. & Kawagoe, K., Experimental study of thermal stress within steel frames. In Three Decades of Structural Fire Sqlety, Proceedings of the International seminar held at the Fire Research Station, UK, 1983. 13. Wang, Y. C. & Moore, D. B., The effect of frame continuity on the critical temperature of steel columns. In Proceedings of the 3rd Kerensky Conference on Global Trends in Structural Engineering, Singapore, 20-22 July 1994, pp. 681-686. 14. British Standards Institution, BS 595(1: The structural use of steelwork in buildings, Part 8: Code of practice for fire resistant design. BSI, London, 1990. 15. CTICM, Methode de prevision par lc calcul du comportement au feu des structures en acier. Document Technique Unifie, Construction Metallique, No. 3, 1982. 16. The Steel Construction Institute, Steelwork design guide to BS 5950: Part 1: 1985, Vol. 1: Section properties, member capacities, 2nd edn. The Steel Construction Institute, Ascot, UK, 1987.
0379-7112/97/$17.00 ELSEVIER
PII:
S0379-71
12(96)00083-5
Effects of Structural Continuity on Fire Resistant Design of Steel Columns in Non-sway Multi-storey Frames Y. C. Wang Structural Design Division, Building Research Establishment, Watford, Hertfordshire WD2 7JR, UK (Received 10 July i996: revised version received 25 October 1996: accepted 4 November 1996)
ABSTRACT This paper discusses two aspects of the effect of structural continuity on the .fire resistant design of steel columns in non-sway multi-storey steel frames. One is beneficial and the other is detrimental. The beneficial effect is to enhance the rotational restraint to the column and thus to reduce its effective length and increase its load carrying capacity. The detrimental effect is to increase the column compressive load due to axial restraint to its thermal expansion. This paper attempts to put forward a simple design method to reconcile these two effects. A comprehensive parametric study is performed to evaluate these two effects on the column limiting temperature and its fire protection thickness. It is found from the results of this" parametric study that for buildings with a practical range of axial restraint to columns, these two eff'ects almost cancel each other out. This paper therefore proposes that for the calculation of column limiting temperature, the additional compressive force in the column may be discarded provided the original column slenderness ratio at the cold condition is used for elevated temperature design. The .fire protection thickness of the column may be conservatively obtained by increasing by 20% that calculated using the above limiting temperature. Crown copyright © 1997 Published by Elsevier Science Ltd. NOTATION Kc()
K~(t) K~ L,.
P,, R
C o l u m n axial stiffness at cold condition C o l u m n axial stiffness at e l e v a t e d t e m p e r a t u r e Axial stiffness of spring C o l u m n length Initial axial load in c o l u m n = K~/K~
101
l O2
ALe AP
~mcc A~th
Y. c. Wang
Net increment in column d e f o r m a t i o n I n c r e m e n t in column mechanical d e f o r m a t i o n I n c r e m e n t in column compressive load due to restrained thermal expansion Difference in column mechanical strain at constant stress b e t w e e n two different t e m p e r a t u r e s I n c r e m e n t in column free thermal expansion strain
1 INTRODUCTION
For a building to remain safe under fire conditions, its supporting columns should remain stable. The importance of column stability to building safety was clearly observed in a major p r o g r a m m e of structural fire tests which has been recently completed on the eight-storey steel f r a m e d building in the Building Research Establishment's Cardington Laboratory.' On the one hand, these tests d e m o n s t r a t e d that although m a n y steel beams and connections lost their loading carrying capacities during the fire attack, the reinforced composite floor slabs in the test building had the capacity to bridge over fire d a m a g e d steel beams and connections, and directly transfer the applied loads to the supporting columns via the d e v e l o p m e n t of tensile m e m b r a n e action in the reinforcement. 2 Provided these columns were fire protected and their t e m p e r a t u r e s were below their failure temperatures, the building remained safe and fire damages were restricted to the fire exposed areas. On the other hand, in one test where the columns were not fire protected, fire d a m a g e e x t e n d e d well b e y o n d the small test area on the floor and over all the storeys above. The fire resistance of a steel column has been the subject of m a n y studies) 7 As a result of these studies, the limiting t e m p e r a t u r e of the column can now be predicted with reasonable accuracy. In particular, the m e t h o d proposed in E u r o c o d e 3, Part 1.2 ~ has been validated against a large body of test results. This limiting t e m p e r a t u r e can then be used to calculate the required fire protection thickness for the column under the design fire condition. However, most studies have concentrated on isolated columns with clearly defined b o u n d a r y conditions and loading conditions. It is well recognised that the behaviour of a column in a complete building is different from that of an isolated column because of the effects of structural continuity. O n e effect is beneficial and the other is detrimental.
Fire resistant design of steel columns
103
The beneficial effect is to increase the column load carrying capacity due to improved rotational restraint leading to reduced column effective length ratio. The detrimental effect is the increase in the column compressive load as a result of axial restraint to the column's thermal expansion. Clearly if all columns on the same floor level of a building are heated up to the same temperature in a fire, there will be no increase in the column compressive loads 9 and therefore the net effect of frame continuity is beneficial. Due to the importance of column stability to building safety, this paper addresses the potentially more dangerous scenario where the columns are not heated to the same temperature or fire attack is confined to a part of the building floor area or both. As the cost of fire protection to columns is relatively low, the objective of this paper is to develop a simple and safe method to help designers calculate the required fire protection thickness to the column under this more dangerous fire situation.
2 EFFECTS OF S T R U C T U R A L C O N T I N U I T Y ON C O L U M N BEHAVIOUR
The effects of structural continuity on column behaviour have been studied separately by a number of researchers. 3"9 12 The conclusions of these studies are briefly summarised here.
2.1 R o t a t i o n a l restraint
Under fire conditions, there is a change in the column stiffness relative to that of the surrounding structure. This change in the relative stiffness is due to the different heating and loading rates in the column and the surrounding structure. As the column approaches failure at high temperatures, its bending stiffness is very low due to highly uniform heating and loading. At the same time, there is considerable stiffness in the surrounding beams and columns because of low levels of heating and loading. This leads to a much higher relative rotational restraint to the hot column than at the cold condition. Detailed studies by the author `) and others 1~ indicate that the rotational restraint to the column at failure approaches that of fixed ends. For columns in non-sway frames, a value of 0.6 may be used, although the value of 0.5 is currently recommended in Eurocode 3, Part 1.2. ~
Y. (i Wang
104
a~th'Lc ; °
P AL = o c Kc(t)
+AP
P o Kc °
AP
Kc(t)
AL
AP
C
=ACmec.Lc
T-
+ Kc(t }
A = A e t h . Lc - A L c AP K
where:
s
A / c = Change in column l e n g t h KcCt) = Column s t i f f n e s s at
current temperature
/
/, •
At rest
Final position Fig. 1.
K
= S t i f f n e s s o f column at co s t a r t o f temperature
increment
Restrained column thermal expansion in lire.
2.2 Axial restraint
If the column is h e a t e d up while the remaining frame is kept at lower temperatures, this structural system resembles that of a column being axially restrained against its thermal expansion by a spring, representing the remaining frame. In this case, there is an increase in the compressive force in the column. As schematically illustrated in Fig. 1, this additional compressive force (Ap) may be calculated using the following equation: Ap =
R &.(t) Kc(0/&.,, + R
(AEt,,-- ~E ..... )L~
(1)
This equation was checked against the results of finite element analysis and was found to be accurate. ~° A detailed study is required to evaluate the initial ratio R of the spring stiffness to the column stiffness. However, assuming a typical loading condition and frame geometrical arrangement, an initial restraint stiffness ratio R of about 2% was estimated. ~ Because changes in the n u m b e r of frame storeys and the level of loading would lead to similar changes in both the initial column axial stiffness and the axial stiffness of the spring representing the surrounding structure, the stiffness ratio R would differ from 2% only slightly. In this paper, the range of R is set to be between 0 and 5%.
Fire resistant design of steel columns
105
3 DESIGN METHODS
Three methods may be used to take into consideration the effects of rotational and axial restraints to the column to calculate its limiting temperature and fire protection thickness. 1. The 'complicated' method. In this approach, the column effective length appropriate to the rotational restraint at elevated temperatures is used to evaluate the column load carrying capacity. A lower value of column effective length ratio than that at the cold condition may be used to reflect that the column rotational restraint near failure approaches that of fixed ends under the fire condition. In this paper, the value of 0.6 is used. The axial force in the column includes both the initially applied load and the additional compressive load due to restrained thermal expansion. 2. Inclusion of improved rotational restraint only. The same value of effective column length ratio of 0.6 is taken as in (1). This method is therefore a special case of method (1) with R = 0. This approach is adopted in Eurocode 3, Part 1.2, ~ although the value of effective length ratio is recommended to be 0.5. 3. No structural continuity. In this approach, neither the improved column rotational restraint nor the increased compressive axial load in the column is considered. This method is adopted in the British Standard BS 5950 Part 8.14 The reason for this is because BS 5950 Part 8 '4 was developed on the basis of the results of standard fire resistance tests on individual columns. Method (1) is obviously the most accurate. However, it is also the most time consuming and complicated. The designer has to evaluate the axial restraint stiffness to the column first. Then an iterative process is carried out comparing the variable column axial load at different temperatures against its load carrying capacity to find out the column limiting temperature. Although graphs, which describe the relationships between the column initial axial load and limiting temperatures for different values of axial restraint stiffness and column slenderness, such as those prepared by CTICM ~5 would help, a lengthy design process is still required. The second method would give the column the highest limiting temperature, leading to thinner fire protection. However, it may not be safe. While method (3) is not correct in its treatment of either effect, the column limiting temperature calculated using this method may be quite
106
Y. C. Wang
reasonable. This is because the effects of improved column rotational restraint and increased column compressive force are opposing and therefore may cancel each other out. This m e t h o d is also attractive to designers because it uses the column effective length at the cold condition. Since the assumptions of m e t h o d (3) are implicit in the British Standard BS 5950 Part 8,14 the objective of this paper is to investigate the margin of safety of the BS 5950 Part 8 approach 1~ for the calculation of the column limiting temperature. This will then be used as a basis for the determination of the column fire protection thickness. Having established the column effective length and applied load to be used in various approaches, the column limiting temperature is calculated using the resistance m e t h o d in Eurocode 3, Part 1.2Y Since the column buckling curve 'c' is r e c o m m e n d e d to be used for the design of columns under fire situations, the column axial load resistance, used to calculate the initial axial load ratio, is also determined using the column buckling curve 'c'. The fire protection thickness is also calculated in accordance with the equation given in Eurocode 3, Part 1.2Y A spray fire protection material is assumed. The nominal fire protection material properties are: coefficient of thermal conductivity: 0-17 W/m°C, density: 4 0 0 k g / m 3, specific heat: 1250 J/kg°C. Because of the possible inaccuracy in the Eurocode 3, Part 1.2 equation ~ and different fire protection materials having different thermal properties, the absolute fire protection thickness may be different from that calculated in this study. However, it is reasonable to expect that the degrees of inaccuracy in the predicted fire protection thickness based on the two different design methods (methods 1 and 3) are similar and that the inaccuracy in the fire protection thickness ratio is largely eliminated.
4 PARAMETRIC STUDY The objective of this paper is to develop a simple and safe m e t h o d for the determination of column fire protection thickness, allowing for structural continuity. For the development of such a design method, a comprehensive parametric study is first carried out. In this parametric study, the limiting temperature and necessary fire protection thickness for different standard fire resistance times are calculated using two methods: m e t h o d (1) [the 'complicated' method] and m e t h o d (3) [no consideration of structural continuity] for a large n u m b e r of columns. In the 'complicated' method, the column effective length ratio is taken as 0.6 and the
Fire resistant design of steel columns
107
additional column compressive load is calculated using eqn (1). For each column arrangement, results for different levels of axial restraint to the column [R in eqn (1)] are compared. Detailed input parameters are: • • •
column size: all universal columns, 16 bending about both the major and minor axes; column length: 2.5 m, 5 m, 7.5 m; column effective length ratio at the cold condition: 0.6, 0.7, 0.8, 0.9,
1.0; •
• •
initial axial load ratio: 0.3, 0.5, 0.7. The initial axial load ratio is defined as the ratio of the initial axial load in the column to its load carrying capacity at the cold condition as determined using the column buckling curve 'c'; initial axial stiffness ratio R: 0, 0.5%, 1.0%, 2.0%, 5.0%; standard fire resistance times: 30 min, 120 min.
These two standard fire resistance times investigate the sensitivity of the proposed exposure conditions. The combinations of all the parameters represent a great majority of columns that practice.
are used in this paper to m e t h o d to different fire above would be able to would be encountered in
5 D I S C U S S I O N ON L I M I T I N G T E M P E R A T U R E S
Figure 2 shows comparisons between the limiting temperatures for the load ratio of 0.5. The three figures (a)-(c) are for the three different values of column effective length ratio at the cold condition, being 0.6, 0.8 and 1, respectively. Figures 3 and 4 are for load ratios of 0.3 and 0.7, respectively, each with an ambient temperature effective length ratio of 0.8. In each of these figures, the comparison is made between the column limiting temperature calculated using the two methods. The temperature in the horizontal axis is calculated using m e t h o d (3) [ambient temperature column effective length ratio, initial load only]. The value on the vertical axis is obtained using m e t h o d (1) [fixed column effective length ratio 0.6, initial axial load plus additional compressive force]. The comparison in each figure is made for different levels of axial restraint. The highest curve as determined from the values on the vertical axis in each figure corresponds to the column limiting temperature that would be obtained
Y. C. Wang
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Fig. 2.
Comparison between different predicted column limiting temperatures, load ratio = 0.5.
Fire resistant design of steel columns
109
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Fig. 3.
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Comparison between different predicted column limiting temperatures, load ratio = 0.3.
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Fig. 4.
Compariosn between different predicted column limiting temperatures, load ratio = 0.7.
110
Y. C. Wang
using method (2) [fixed column effective length ratio 0.6, initial axial load only]. Results in Figs 2(b), 3 and 4 show that for columns with different levels of initial axial load, column limiting temperatures calculated using the two methods are quite close for R = 2%. For the higher value of initial axial load ratio as shown in Fig. 4, the predicted column limiting temperature becomes more conservative using method (3) where frame continuity is ignored. This was also observed for other values of the ambient temperature column effective length ratio. Results in Fig. 2 suggest that over the range of axial restraint considered, the difference in column limiting temperatures calculated using the two different methods is sensitive to the column slenderness ratio. At very low values of the column slenderness ratio, being indicated by the highest limiting temperature values in each figure, the column limiting temperature is not very sensitive to the degree of axial restraint. In these cases, discarding the effect of axial restraint to column but using the effective length of 0.6 would only overestimate the column limiting temperature by about 50°C. If the column effective length at the cold condition is used, the predicted column limiting temperature is very close to that predicted using the 'complicated" method for different values of axial restraint. However, at higher values of the column slenderness ratio, there is a great range of column limiting temperatures for different degrees of axial restraint to the column. The difference in column limiting temperature for the case of no axial restraint (R = 0) and high axial restraint (R = 5%) could be about 200°C. This implies that if the current assumption in Eurocode 3, Part 1.2~ (method 2) is used, the column limiting temperature could be overestimated by 200°C. At the lowest value of ambient temperature column effective length ratio of 0.6, method (3) is identical to method (2) as shown in Fig. 2(a). However, only in a few cases would the column effective length ratio at the cold condition be at such a low level in practical design. For more realistic values of column effective length ratio, the assumptions of discarding both rotational and axial restraints lead to predictions of column limiting temperature which are close to those predicted using the 'complicated' method at the value of axial restraint stiffness ratio R of between 2% and 5%. Since the axial restraint stiffness in realistic buildings would fall in this range, the results of this parametric study suggest that the accuracy of the predicted column limiting temperature obtained by discarding the effects of structural continuity is reasonable. In other words, although BS 5950 Part 8 t4 was not developed to explicitly consider the effects of structural continuity, it gives acceptable results due
Fire resistant design of steel columns
111
to the fact that these two effects almost cancel each other out. Nevertheless, this m e t h o d may lead to an overestimation in the limiting temperature for columns with very low effective length ratios at the cold condition. However, this deficiency may be rectified in the calculation of column fire protection thickness as discussed in the next section.
6 D I S C U S S I O N ON F I R E P R O T E C T I O N T H I C K N E S S In all cases, the column limiting temperature is lower than 650°C. Since temperatures generated in most post-flashover fires will normally induce much higher values of temperature in unprotected steel, this means in a majority of cases, steel columns in buildings should be fire protected to avoid instability. U n d e r this condition, the difference in cost of fire protection to columns is very small with a moderate difference in fire protection thickness. Therefore, provided the proposed design m e t h o d gives a safe column under fire conditions, a moderate overestimation in the column fire protection thickness compared against that calculated using the 'complicated' m e t h o d should be regarded as acceptable. Figure 5 shows comparisons between fire protection thicknesses calculated using the limiting temperatures of Fig. 2 for the standard fire resistance time of 30 min, the initial load ratio being 0.5. In each figure, the horizontal axis represents the fire protection thickness calculated using the limiting temperature of m e t h o d (3) [discarding both effects of structural continuity]. The vertical axis gives the ratio of the fire protection thickness calculated using the limiting temperature from the 'complicated' m e t h o d to the value of fire protection thickness on the horizontal axis. Figure 6 compares the results for the standard fire resistance time of 120 min, other main parameters being a load ratio of 0.5 and ambient temperature column effective length ratio of 0.8. Comparisons between Figs 5(b) and 6 for the two different standard fire resistance times indicate that there is very little difference in results of fire protection thickness ratio for different standard fire resistance times, although the fire protection thicknesses are different. Figures 7 and 8 give results for load ratios of 0.3 and 0.7, respectively, with the standard fire resistance time of 3 0 m i n and the ambient temperature effective length ratio of 0.8. Comparisons between Figs 7, 5(b) and 8 show that the fire protection thickness ratio is only slightly affected by the level of axial load ratio. Discussions will therefore be concentrated on the load ratio of 0.5 with a standard fire resistance time of 30 min whose results are shown in Fig. 5. Figure 5(a) shows that at an ambient temperature column effective
112
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Comparison between different predicted protection thicknesses, load ratio = 0.5, 30 min.
Fire resistant design of steel columns
113
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40
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protection thickness (mm), c o l u m n effective length ratio=0.8, no axial r e s t r a i n
Fig. 6.
Comparison between different predicted protection thicknesses, load ratio = 0.5, 120 rain.
length ratio of 0.6, the predicted fire protection thickness from the limiting temperature of method (3) is lower compared to that using method (1). This is the direct result of overestimated limiting temperatures for this effective length ratio using method (3) as shown in Fig. 2(a). Nevertheless, 1.6
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Fig. 7.
Comparison between different predicted protection thicknesses, load ratio = 0.3, 30 rain.
114
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Comparison between different predicted protection thicknesses, load ratio
0.7,
30 min. the results of the fire protection thickness ratio as represented by the vertical axis are lower than 1.2 for the majority of columns. Values significantly higher than 1.2 (the value of thickness ratio > 1.4) are for long columns (5 m, 7.5 m) of the smallest sections (UC 203 and UC 152 series) bending about the minor axis. Because of the minor role these columns would play in the safety of steel frames in practice, it is proposed that the fire protection thickness to a steel column is obtained by increasing by 20% the fire protection thickness calculated without including the effects of structural continuity. This proposed m e t h o d of determining the column fire protection thickness is quite consistently followed for higher values of ambient temperature column effective length ratio. At these higher values, the calculated fire protection thickness would be greater than that required for all but the most slender columns (7-5 m, UC 152 columns bending about minor axis). Therefore, this proposal leads to stable columns under fire conditions. Although the calculated column fire protection thickness using the proposed m e t h o d may be twice that required, as suggested in Fig. 5(c) for an ambient temperature column effective length ratio of 1.0, i.e. pin-ended column, this gross inaccurate result only applies to columns with very low level of axial restraint ( R < 1-0%). Because the axial restraint stiffness is typically higher than this value and the proposed m e t h o d for fire protection thickness errs on the safe side, it is regarded as satisfactory.
Fire resistant design of steel columns
115
7 CONCLUSIONS AND DESIGN PROPOSALS A comprehensive parametric study was performed in this study to investigate the effects of structural continuity on column limiting temperature and fire protection thickness. Two aspects of the structural continuity are studied: improved column rotational restraint and increased compressive load in column due to axial restraint to column thermal expansion. The results of three different methods are compared. The main conclusions are: 1. If only the effect of improved column rotational restraint is included and a column effective length ratio of 0.6 is used, similar to the recommendation in Eurocode 3, Part 1.2, 8 the column limiting temperature may be overestimated by up to about 200°C for slender columns and more than 100°C in most cases. 2. If neither of the two effects of structural continuity is included, as currently r e c o m m e n d e d in BS 5950 Part 8, ~4 the limiting temperature of a column with light axial restraint (R < 2 % ) would be underestimated. For columns with more realistic axial restraint (2% < R < 5%), the limiting temperature is quite closely predicted. The difference in most cases would be less than 50°C. 3. The column limiting temperature in most cases is less than 650°C. This indicates that steel columns should always be protected to prevent instability since the unprotected steel temperatures induced in post-flashover fires will normally be much higher than this value. Consequently, the following proposals may be made with regard to the fire resistant design of steel columns: 4. The column limiting temperature may be calculated using the effective length ratio and axial load at the cold condition, without explicit consideration of the effects of structural continuity. 5. To compensate for the overestimation in column limiting temperatures in some cases, the column fire protection thickness may be determined by increasing by 20% the fire protection thickness calculated using the limiting temperature in (4). This would err on the safe side for all but a few very slender columns.
REFERENCES 1. Moore, D. B., Full-scale fire tests on complete buildings. In Proceedings of the Second Cardington Conference, Bedford, England, 12-14 March 1996. 2. Wang, Y. C., Tensile membrane action in slabs and its application to the Cardington fire tests. In Proceedings of the Second Cardington Conference, Bedford, England, 12-14 March 1996.
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3. Pettersson, O., Magnusson, S. E. & Thor, J., Fire engineering design of steel structures, Publication 50, Swedish Institute of Steel Construction, Stockholm, Sweden, 1976. 4. Franssen, J. M., Schleich, J. B. & GajoL L. G., A simple model for the fire resistance of axially-loaded members according to Eurocode 3. J. Construct. Steel Res., 35 (1995) 49-69. 5. Burgess, I. W. & Najjar, S. R., A simple approach to the behaviour of steel columns in fire. J. Construct. Steel Res., 31 (1994) 115-134. 6. ECCS-T3, European Recommendations for the Fire S~f'ety of Steel Structures. Elsevier Science, 1983. 7. Janss, J. & Minne, R., Buckling of steel columns in fire conditions. Fire St(f['ty J., 4 (1981) 227-235. 8. CEN, EC3: Design of Steel Structures, Part 1.2: Structural Fire Design, ENV 1993-1-2, CEN, 1995. 9. Franssen, J. M. & Dotreppe, J. C., Fire resistance of columns in steel frames. Fire Safety J., 19 (1992) 159-175. 1(). Wang, Y. C., Lennon, T. & Moore, D. B., The behaviour of steel frames subject to fire. J. Construct. Steel Res., 35 (1995) 291-322. 11. The Steel Construction Institute, The behaviour of steel columns in lire. Report to the Department of the Environment, RT524, The Steel Construction Institute, Ascot, UK, 1996. 12. Ooyanagi, N., Hirota, M., Nakamura, K. & Kawagoe, K., Experimental study of thermal stress within steel frames. In Three Decades of Structural Fire Sqlety, Proceedings of the International seminar held at the Fire Research Station, UK, 1983. 13. Wang, Y. C. & Moore, D. B., The effect of frame continuity on the critical temperature of steel columns. In Proceedings of the 3rd Kerensky Conference on Global Trends in Structural Engineering, Singapore, 20-22 July 1994, pp. 681-686. 14. British Standards Institution, BS 595(1: The structural use of steelwork in buildings, Part 8: Code of practice for fire resistant design. BSI, London, 1990. 15. CTICM, Methode de prevision par lc calcul du comportement au feu des structures en acier. Document Technique Unifie, Construction Metallique, No. 3, 1982. 16. The Steel Construction Institute, Steelwork design guide to BS 5950: Part 1: 1985, Vol. 1: Section properties, member capacities, 2nd edn. The Steel Construction Institute, Ascot, UK, 1987.