Response of idealised composite beam–slab systems under fire conditions

Journal of Constructional Steel Research 56 (2000) 199–224 www.elsevier.com/locate/jcsr

Response of idealised composite beam–slab systems under fire conditions A.Y. Elghazouli *, B.A. Izzuddin Department of Civil and Environmental Engineering, Imperial College of Science, Technology and Medicine, London SW7 2BU, UK Received 10 August 1999; accepted 15 February 2000

Abstract This paper presents a numerical model for beam–slab floor systems in which a single compartment is subjected to fire. The system consists of a composite steel–concrete slab and a bare steel beam. Several idealisations are made in order to illustrate important behavioural patterns which occur under fire conditions. Nonlinear analyses are undertaken using an advanced yet computationally efficient computer program which accounts for the large displacement behaviour at elevated temperatures. The model is shown to capture the main parameters influencing the performance of the system under fire. In particular, the significance of axial restraint and thermal expansion on the overall deformation and capacity of the system is demonstrated. It is indicated that thermal expansion may have beneficial as well as detrimental consequences on the performance, depending on the particular structural configuration under consideration. The paper also closely examines the level of dependency of the response on the sequence of application of loading and elevated temperature as well as the assessment of the overall system response from consideration of the respective responses of individual components. It is shown that such concepts may be effectively employed in undertaking detailed studies for improved quantification of the fire resistance of beam–slab systems with a view to the development of more rational performance-based design procedures.  2000 Elsevier Science Ltd. All rights reserved. Keywords: Fire engineering; Composite beam–slab systems; Nonlinear analysis

* Corresponding author. 0143-974X/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 3 - 9 7 4 X ( 0 0 ) 0 0 0 0 6 - 7

200

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

1. Introduction In recent years, performance-based fire engineering approaches have been introduced in several countries [1–4]. These concepts are being increasingly recognised worldwide due to the considerable benefits offered over conventional prescriptive approaches in terms of cost effectiveness as well as flexibility and rationale of design. Nevertheless, most codified design methods are in effect largely based on the performance of isolated members either through standard fire tests or simple analytical procedures. This methodology fails to recognise the interaction which occurs between various structural elements at elevated temperature. Considerable attention has been directed, in the last few years, towards investigating the performance of structural systems under fire conditions. Following close examination of the behaviour of large steel-framed structures subjected to major fires such as those in the UK in 1990 at Broadgate and in 1991 at Basingstoke [5,6], it was observed that most of these buildings were significantly over-designed and/or over-protected. Consequently, there has been increasing awareness of the benefits of using more rational approaches which are based on true behaviour rather than on idealised representations of isolated elements. Due to the complex interactions which take place between various members in a frame, extensive redistribution of loads occurs during fire. These interactions are being examined through a number of experimental and analytical investigations. In the UK, a large experimental programme has recently been completed on a full-scale eight-storey building at Cardington including six major fire tests [5–7]. In Australia, laboratory tests and analysis were undertaken to assess the performance of a 41 storey building in Melbourne [4]. Other experimental studies on the fire behaviour of complete steel buildings were also reported in other countries [4,5]. In addition to the provision of detailed information for use in further analytical and design studies, these investigations have highlighted the considerable overconservatism of current design approaches. The major fire tests carried out on whole buildings have also been complemented with comparative numerical simulations, in which good correlation between experimental and analytical results has been demonstrated [7–13]. Although difficulties are encountered in faithfully representing the behaviour of concrete and composite slabs at elevated temperatures, a high level of confidence can generally be placed in available analytical tools. However, due to the complexity of the behaviour, it is not usually straightforward to interpret clearly the response and isolate the various effects and parameters influencing the overall performance. There is therefore an essential role for simplified approaches which can be used to assess salient behavioural patterns. Following verification with more detailed representations, the findings may then be used for developing improved design procedures. In this paper, the fire behaviour of a typical composite beam–slab structural system is investigated. In order to illustrate the performance under fire and to gain some insight into fundamental aspects of the behaviour, the loading and structural configuration are idealised in a manner that simplifies the response yet retains the main characteristics of the behaviour. Use is made of an advanced nonlinear analysis pro-

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

201

gram, ADAPTIC [14], which accounts for geometric and material nonlinearities and includes temperature-sensitive material models. Typical results from several analyses carried out under ambient and elevated temperatures as well as various boundary conditions are presented, and the main parameters influencing the fire resistance are highlighted. Specific aspects related to the sequence of load application and individual component response, which may have implications on the design process, are presented and discussed. 2. Numerical formulations The advanced nonlinear analysis program ADAPTIC [14] is utilised in this study. The program allows for geometric and material nonlinearities and includes facilities for static and dynamic analysis of 3D steel, reinforced concrete (R/C) and composite steel/concrete frames. The capabilities of the program have been recently extended to model the nonlinear structural response under elevated temperatures [15,16]. The analysis at elevated temperatures may be carried out using the elasto–plastic elements [17] which adopt cubic shape functions or, for enhanced efficiency, quartic elastic elements [15] which are then automatically sub-divided into elasto–plastic cubic elements where and when required on the onset of plasticity. The elasto–plastic formulation of the cubic element is derived in a local Eulerian system where six degrees of freedom are employed. The cubic formulation can model the spread of plasticity within the cross-section and along the length. The element response is assembled from contributions at two Gauss points where the cross-section is discretised into a number of monitoring areas. The formulation utilises a relationship between the direct material stresses and strains and allows various material models to be included. Several material models are incorporated within ADAPTIC which account for the deterioration in the properties of the constituent materials at elevated temperature. A kinematic bilinear model for steel and a multi-linear model for concrete are employed for the steady-state stress–strain relationships, as illustrated in Fig. 1. The variations with temperature of the elastic modulus (E), yield stress (sy) and strainhardening modulus for steel, as well as the compressive strength (sc), compressive strain (ec) and ultimate strain (eu) for concrete, are assumed to follow independent trilinear relationships. For each property, the reduction factors are obtained from a corresponding trilinear curve defined over the temperature domain (Fig. 2(a)). The thermal strain is also assumed to follow a trilinear relationship (Fig. 2(b)). The parameters of the various trilinear curves are user-defined, and may be determined on the basis of available information regarding the reduction factors for the elastic modulus and the effective yield stress, such as those suggested in the Eurocodes [2,3]. Non-uniform temperature distributions may be applied across the section and along the length of a modelled member. The utilised material models have the advantage of computational efficiency, as well as the ability to represent strain reversals and non-monotonic temperature variation. This also allows for the effects of heating and cooling on the response of structural components to be readily modelled, if necessary.

202

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

Fig. 1.

Steady state stress–strain relationships. (a) Steel. (b) Concrete.

3. Structural model 3.1. Member details The idealised beam–slab system shown in Fig. 3 is considered in the current investigation in order to assess the behaviour of a single compartment beam–slab con-

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

203

Fig. 2. Variation of material reduction factors and thermal strain with temperature. (a) Reduction factors. (b) Thermal strain.

figuration. The system represents a compartment of dimensions L×S within a floor of a building. A composite slab of 130 mm depth is assumed, of which the solid part is 75 mm deep and the ribs are 55 mm deep and 300 mm apart. The steel profile is 0.9 mm thick and the solid slab includes a reinforcement mesh of 142 mm2/m in each direction. For the steel beam, the flange and clear web dimensions are 165×10

204

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

Fig. 3.

Idealised composite beam–slab system.

mm2 and 283×6 mm2, respectively. The steel beam has a span (L) of 9.0 m, and the overall span of the slab (S) in the transverse direction to the beam is 6.0 m. These dimensions are selected to represent a typical structural floor unit, similar to that used in recent major fire tests in the UK [5–7]. A few comparative checks are also carried out on systems with other dimensions as described in other parts of this paper. As mentioned before, several idealisations are undertaken in the chosen system in order to highlight the main behavioural patterns. As indicated in Fig. 3, a proportion of the solid part of the slab is assumed to act compositely on top of the steel beam and, in the transverse direction, half the width of the slab is represented as a single member intersecting the centre of the beam. Furthermore, for clarity and simplicity, the load is assumed to be concentrated as a point load at the intersection of the beam and slab members. Although these simplifications cause some quantitative discrepancy with the response of the real system, the main characteristics of the behaviour which are under examination in this study are retained. Furthermore, it can be shown that the idealised system is generally a good lower bound representation of the real system, both in terms of stiffness and capacity. At the same time, it provides a considerably more realistic representation in comparison with current design approaches, which are based on isolated modelling of the composite beam ignoring the interaction with the slab. A finite element model is constructed to represent the structural system described above, as shown in Fig. 4. The steel beam is modelled using 10 beam–column elements. A solid part of the slab, 2 m wide, parallel to and above the steel beam is also represented by 10 R/C beam–column elements of rectangular cross-section, and their nodes are connected to those of the longitudinal steel beam by rigid links, assuming full shear interaction. The middle part of the transverse slab, 4.5 m wide, is idealised into one T-shaped section, and is modelled using 10 R/C beam–column elements along the length. The boundary conditions at the ends of the steel beam and the transverse composite slab (i.e. points A, B, C and D in Fig. 3) are varied depending on the type and purpose of the analysis being carried out, with full rotational restraint assumed at the supports. The two, transverse and longitudinal,

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

Fig. 4.

205

Outline of finite element model.

R/C members are assumed to be rigidly connected at their intersection above the centre of the steel beam. 3.2. Material properties The models depicted previously in Fig. 2 are used in conjunction with suitable material properties. For steel, the elastic modulus (E) is 210×103 N/mm2 at ambient temperature, which drops after 100°C in a piecewise linear manner to 210×102 N/mm2 at 1000°C and to 0 N/mm2 at 1200°C. The yield stress (sy) at ambient temperature is 310 N/mm2, reducing after 400°C to 34.1 N/mm2 at 800°C and to 0 N/mm2 at 1200°C; moreover, for simplicity, no strain hardening is considered (i.e. m=0). As for thermal strain, it is assumed to increase linearly to 0.01 at 750°C, thereafter remaining constant up to 850°C, afterwards increasing linearly to 0.015 at 1200°C. Similarly, for concrete, the compressive strength (sc) is 45 N/mm2 which reduces after 300°C to 1.8 N/mm2 at 1100°C and to 0 N/mm2 at 1200°C. The compressive strain (ec) is 0.0025 at ambient temperature, which increases to 0.0125 at 600°C and to 0.015 at 900°C, remaining constant thereafter. The ultimate strain (eu) is 0.02 at ambient temperature, increasing linearly to 0.05 at 1200°C. Finally, the thermal strain (eth) increases linearly to 0.0096 at 1200°C. 4. Response characteristics The structural model, discussed in the previous section, consists of two structural sub-systems in parallel, namely the composite beam and the transverse slab, each

206

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

making a contribution towards resisting the applied central load. The focus of the following study is to investigate and gain an insight into the influence of axial restraint and thermal expansion on the response characteristics of the individual subsystems as well as of the overall system under idealised fire loading conditions. Furthermore, consideration is given to whether the deformation states of the subsystems and the overall system for a specific level of loading and temperature distribution are dependent on the sequence of application of loading and elevated temperature. It is envisaged that independency in the aforementioned context could have considerable positive implications towards the possibility of developing simplified design-related procedures for improved quantification of the fire resistance of composite beam–slab systems. The adopted idealisation of transient fire loading is based on a linear variation with time (t) of temperatures and gradients in the various system components. At (t=100 min), the steel beam is subjected to a centroidal temperature of 1000°C and a gradient of 300°C/m, and both the compositely acting concrete and the transverse slab are subjected to a centroidal temperature of 500°C with a gradient of 5000°C/m. It should be noted that all the graphical results presented below are given in terms of the reference temperature, which is considered to be the centroidal temperature of the steel beam. In the following sections, the response characteristics of the composite beam, the transverse slab and of the overall system are considered in detail. 4.1. Composite beam As mentioned before, and shown in Fig. 4, the 9.0 m long composite beam is modelled by 10 beam column elements representing the steel beam, connected by rigid links to 10 reinforced concrete elements with rectangular cross-section. The isolated composite beam has an ambient load carrying capacity of around 350 kN, which is approximately twice that of the bare steel beam. If axial restraint is also provided at both ends, tensile membrane action would dominate the response following the attainment of the plastic flexural capacity. The fire resistance of the same composite beam is assessed by subjecting the beam to the previously described temperature history, and several aspects of the behaviour are discussed below. 4.1.1. Influence of axial restraint The level of axial restraint provided to the beam depends on the position of the beam within the structural floor and the stiffness of the surrounding structure. An internal compartment may be assumed as effectively restrained, whereas an edge compartment may in some cases approach that of unrestrained conditions. To illustrate the effect of axial restraint on the response, the composite beam is subjected to the linear temperature history described before, and the results are presented in Fig. 5(a). In this case, a vertical concentrated load of 250 kN is applied at the centre, representing approximately 60% of the ambient capacity of the composite beam. Fig. 5(a) depicts the variation of vertical deflection with time at the midspan of the beam for the cases of axially restrained beam with and without accounting for

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

207

Fig. 5. Influence of axial restraint on the response of composite beam. (a) Load ratio of 0.6. (b) Load ratio of 0.4.

208

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

thermal expansion (Res.(Exp) and Res.(No Exp)) and for the case of an axially unrestrained beam (Unres.). For the unrestrained case, the beam reaches its capacity at a reference temperature of about 550°C, and the displacement increases rapidly thereafter. On the other hand, for the restrained beam, thermal expansion causes an early buckling of the system due to compressive action leading to a rapid increase in deformation. The responses of the two restrained cases (including and excluding thermal expansion) are similar after around 750°C, where the tensile membrane action prevails due to large displacements and loss of bending stiffness. At lower temperatures, it is evident that the displacement response ignoring thermal expansion is always smaller than that accounting for it. Similar trends are observed in Fig. 5(b), where the beam is subjected to a load of 140 kN, representing 40% of ambient capacity, but with a relative enhancement in fire resistance as expected. It is also noteworthy that for the composite beam, uniform temperature distribution in the steel and concrete sections, based on the respective centroidal temperatures, would lead to very similar results. The above discussion generally implies that buckling in the beam due to thermal expansion can have adverse effects on the mechanical strains in the slab reinforcement, which in a real situation would be at relatively low temperatures. On the other hand, thermal expansion can have beneficial effects in terms of introducing precompression and hence reducing the tensile forces in the beam connections to the surrounding structure. Moreover, the occurrence of thermal buckling within an effectively restrained compartment would reduce the thermal expansion forces on adjacent parts of the structure, and hence would decrease the likelihood of undesirable modes of failure such as in partitions and walls. Therefore, the merits of thermal expansion depend on the particular structural configuration, and cannot be determined in isolation of restrictions on the connection resistance and the allowable material mechanical strains. If such restrictions are not violated prior to the attainment of tensile membrane action, thermal buckling can then be considered to be a transient phenomenon which does not influence the structural response at elevated temperature. For such situations, the presence of axial restraint, regardless of whether it initiates thermal buckling, becomes the main determinant of the actual fire resistance of the composite beam–slab system. 4.1.2. Steady-state response It is useful at this stage to examine the steady-state load–displacement response of the composite beam at various reference temperatures. For the axially unrestrained beam, the ultimate load is reached with the attainment of the plastic capacity which reduces with the increase in temperature as depicted in Fig. 6(a). On the other hand, Fig. 6(b) shows the response of the axially restrained system for various temperatures, excluding thermal expansion. This case is presented to illustrate the effect of tensile membrane action which dominates the response at relatively large displacement. It may also represent a possible situation in which the surrounding structure does not provide an effective axial restraint against thermal expansion, whilst sufficient support is available for the development of tensile membrane action. The characteristic relative increase in capacity at low temperatures, and at small displace-

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

209

Fig. 6. Steady-state response of composite beam at various temperatures. (a) Axially unrestrained beam. (b) Axially restrained beam without thermal expansion. (c) Axially restrained beam (with thermal expansion).

210

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

Fig. 6. (continued)

ment, is caused by compressive membrane action effected by the different tensile and compressive response characteristics of concrete. For the axially restrained system, the results are shown in Fig. 6(c). Additional curves at 50, 100 and 150°C are included to highlight the characteristics of the behaviour at low temperatures. It is important to note in this case that the load is applied to a configuration which is allowed to buckle under elevated temperatures only. For this purpose, an initial imperfection of 1/2000 of the beam length is assumed. As shown in the load–displacement plots, the initial application of temperature causes transverse displacement in the beam at a zero load. This displacement increases with increasing temperature as expected, which corresponds to the thermal buckling of the composite beam. With the gradual application of load thereafter, the displacement increases accordingly, and the response becomes increasingly dominated by tensile membrane action in a manner similar to the restrained case without thermal expansion (Fig. 6(b)). 4.1.3. Effect of load sequence The influence of the loading sequence is illustrated for the axially restrained beam in Fig. 7(a) and (b) for load ratios of 0.6 and 0.4, respectively. Fig. 7 also shows a curve representing the response in the restrained case without any applied load (Exp(T)) to highlight the effect of pure thermal buckling. Using the results obtained

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

Fig. 7.

211

Effect of loading sequence on composite beam. (a) Load ratio of 0.6. (b) Load ratio of 0.4.

212

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

from the steady state plots, given in Fig. 6, it is shown that good approximation of the deformation state, for both cases with and without thermal expansion, can be obtained by applying the central load after the elevated temperatures (T→L), in comparison to the more realistic simulation where the elevated temperatures are applied after the loading (L→T). As expected, the above approximation gives accurate results for the unrestrained case which, for clarity, is not shown in Fig. 7. This approximation is also accurate for the restrained case without thermal expansion (i.e. (NoExp.(T→L)) as depicted in Fig. 7. It also provides reasonable results for the restrained case including thermal expansion (i.e. (Exp.(T→L), where the slight inaccuracies are attributed to initial compressive plasticity caused by restraint to expansion and thermal buckling. As shown in Fig. 7, for the restrained case, the displacement obtained from the steadystate response given in Fig. 6(c) is accurate at low temperatures, up to about 400°C after which plasticity due to restraint to thermal expansion causes a discrepancy in displacement which reaches a maximum of about 10% at 600°C. At higher temperatures, in excess of 600°C, the displacement is again well represented by the steadystate response, where tensile membrane action dominates the response. In order to achieve such a favourable approximation in the restrained case, it is important that the load is applied to a configuration which is allowed to buckle under initial elevated temperatures as discussed in the previous section. 4.2. Transverse slab 4.2.1. Steady-state response As in the case of the composite beam, the steady-state response of the composite slab is examined at various reference temperatures for the three cases of axial restraint with and without thermal expansion. In Fig. 8(a), the load–displacement response of the axially unrestrained slab indicates an ambient capacity of about 180 kN. For comparison purposes, Fig. 8(b) shows the response for of the axially restrained system excluding thermal expansion. This, as mentioned before, may exist in some situations. For example, a slab in an edge compartment may not be provided by sufficient restraint to thermal expansion, but the development of a compressive ring in the slab coupled with adequate reinforcement anchorage allow the development of tensile membrane action. As shown in Fig. 8(b), the influence of compressive membrane action at small displacements and the domination of tensile membrane action at higher displacements are evident, with the effect of compressive membrane action gradually reducing with the increase in temperature. The steady-state response for the axially restrained composite slab, accounting for thermal expansion, is shown in Fig. 8(c). Additional curves are shown for reference temperatures of 50, 100 and 150°C to illustrate the behaviour at lower temperatures. The response is obtained by applying the temperature as an initial condition followed by a gradual application of loading. For temperatures lower than 200°C, compressive membrane action at small displacements is followed by tensile membrane action at larger displacements. At temperatures in excess of 200°C, initial deformations are caused by thermal buckling, due to the application of the temperature, effectively

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

213

Fig. 8. Steady-state response of transverse slab at various reference temperatures. (a) Axially unrestrained slab. (b) Axially restrained slab without thermal expansion. (c) Axially restrained slab (with thermal expansion).

214

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

Fig. 8. (continued)

replacing the phenomenon of compressive membrane action occurring at higher loads for lower temperatures. Thereafter, the response becomes largely dominated by tensile membrane action. 4.2.2. Transient response Similar to the composite beam, the transient response of the transverse slab to elevated temperature may be obtained using the previously described temperature time history. The slab is subjected to a central load representing about 60% of the ambient capacity, and is considered axially restrained with and without thermal expansion as well as axially unrestrained. For the axially restrained cases, limit points due to compressive membrane action prevent a conventional static elevated temperature analysis to be undertaken, where the temperature is applied after the loading. While this can be remedied by the use of the dynamic analysis capabilities of ADAPTIC [14], the approach investigated for the composite beam is used instead, where the loading is applied after elevated temperature (T→L) on a thermally buckled configuration (Exp.(T)). The axially unrestrained case does not present such numerical problems, hence the corresponding response is determined using the conventional simulation of loading after elevated temperature (L→T), as shown in Fig. 9. As in the case of the composite beam, the presence of axial restraint mobilises tensile membrane action at large displacements, which is responsible for an improvement in the fire resistance beyond the reference temperature of 700°C achieved for

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

Fig. 9.

215

Transient response of transverse slab.

the unrestrained case. However, it is evident that axial restraint is responsible for the rather violent thermal buckling at a temperature of around 200°C, which occurs due to the sudden release of the initial compression in the slab. However, again thermal buckling for the isolated slab may be considered as a transient phenomenon if the dynamics associated with it and the restrictions on mechanical strains in the reinforcement are not exceeded before the attainment of the tensile membrane action. 4.3. Beam–slab system 4.3.1. Influence of axial restraint The ambient load carrying capacity of the overall beam–slab system is estimated as 530 kN, compared to 350 kN for the composite beam. A vertical concentrated load of 210 kN is applied at the centre, so that comparison can be made with the response of the composite beam. This force represents a load ratio of 0.6 for the beam (i.e. ratio of applied load to beam ambient capacity), but only about 0.4 for the system (i.e. ratio of applied load to system ambient capacity). The previously described transient temperature time history is also considered. The central vertical displacement is shown in Fig. 10 for four different cases: (i) full axial restraint, (ii) axially unrestrained, (iii) axially unrestrained beam only, and (iv) axially unrestrained slab only, all of which include thermal expansion effects. As shown in Fig. 10, whereas the axial restraint causes a relative increase in deformation at an early stage due to buckling effects, it is again evident that the overall fire resistance of the restrained system is increased as compared to the unrestrained system. It is also clear that the role of the slab axial restraint in reducing the overall response comes at an earlier stage (around 700°C) than that of the composite beam (around 900°C). In general, as expected, the above results indicate that the fire resistance of the

216

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

Fig. 10.

Effect of axial restraint on the system response with a load of 210 kN.

system is improved compared to that of the isolated composite beam for the same central load. This applies for both restrained and unrestrained cases, with the slab restraint having a more significant influence on the behaviour. In restrained slab cases, a relatively sudden thermal buckling of the slab occurs at low temperatures in comparison with a more gradual response in the restrained beam situation. 4.3.2. Steady-state response In order to compare the behaviour with that of the restrained beam and slab components, the steady-state response of the restrained system is examined as shown in Fig. 11. The response of the axially unrestrained system is not shown herein, but may be clearly assessed by integrating the response of the unrestrained beam and slab at any specific level of displacement. As observed from Fig. 11, the steadystate response of the restrained system may also be obtained by combining the loads from the constituent composite beam and slab components in Fig. 6(c) and Fig. 8(c), respectively. In other words, by careful examination of Fig. 6(c) and Fig. 8(c), the contribution of the beam and slab to the steady-state response of the overall restrained system at various displacement and temperature levels may be evaluated, leading to a close match to the results depicted in Fig. 11. 4.3.3. Effect of load ratio The initial load applied on the system may have a significant influence on the response. For an axially unrestrained system, the fire resistance reduces with the increase in load, following similar displacement response to that described previously for a load of 210 kN. In this case, relatively small displacements are maintained until a point is reached when the attainment of a plastic mechanism is accompanied by an abrupt increase in deformations. For a system with axially restrained boundary conditions, the variation of central

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

Fig. 11.

217

Steady-state response of the restrained system at various temperatures.

vertical deflections against reference temperature is shown in Fig. 12 for different load ratios. It should be noted that the values indicated refer to the load ratios against the capacity of the overall system. Therefore, system load ratios of 0.25 and 0.4 represent composite beam load ratios of about 0.4 and 0.6, respectively, whereas a system ratio of 0.7 exceeds a beam ratio of unity. As shown in Fig. 12, the response at low system load ratios is not significantly different from that due to thermal expansion only (i.e. load ratio of zero). At load ratios greater than 0.4, the system shows signs of deterioration at temperatures in excess of 700°C. At a load ratio of 0.7, the abrupt increase in displacement at 140°C is caused by thermal buckling. At load ratios higher than 0.7, limit points due to compressive membrane action prevent a conventional static elevated temperature analysis to be undertaken. It is important to note here that in accordance with current design approaches, the design load would be based on a proportion of the ambient capacity of the isolated composite beam, typically in the range of 40% to 60%. In most design cases, the composite beam would also be assumed to be simply supported which may not be a realistic assumption particularly at elevated temperatures. This is due to the likely influence of compressive axial loads and temperature differential between the steel beam and connection on increasing the effective rotational stiffness. Consequently, in a realistic restrained system situation, the actual system load ratio may be significantly low, typically between 10% and 20%. In such a situation, the response of the restrained system would be almost totally dominated by the effects of thermal expansion as discussed above, and would not be sensitive to slight variations in the applied

218

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

Fig. 12.

Response of axially restrained system under various load ratios.

load. This situation would directly resemble that of the first major fire test carried out by British Steel on the Cardington Frame [5–7]. It is also of interest to investigate the axial forces at the supports for both the steel beam and the slab within the restrained system, as this may have implications for further design studies considering appropriate failure criteria. Fig. 13(a) depicts the axial force at the end of the steel beam (i.e. in the beam-to-column connection) for the restrained system under various load ratios. Noting that positive force values indicate compression whilst negative values indicate tension, it is evident that regardless of the load level, tension is developed in the connection at a central vertical displacement of about 0.5 m. At this deformation, which is marginally larger than 1/20 of the beam span, the pre-compression effect of thermal expansion is replaced by tension due to the gradual domination of tensile membrane action. Similarly, Fig. 13(b) depicts the relationship between the central vertical displacement of the system and the tension at the support of the slab for various load levels. It is indicated that tensile forces are developed at the end of the slab at displacement levels between 0.3 and 0.4 m which is also not significantly influenced by the load level for this particular situation. 4.3.4. Effect of load sequence As with the composite beam, consideration is given to the influence of the sequence of loading on the predicted deformation state of the overall system. This could be carried out by predicting the transient displacement response from the steady-state response of the system or, more importantly in this case, from integration of the steady-state behaviour of the constituent members. In order to examine this, the transient system displacement of the axially restrained case given in Fig. 10 (for

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

219

Fig. 13. Axial forces at supports for restrained system under various load ratios. (a) Axial forces at support of steel beam. (b) Axial forces at support of composite slab.

220

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

a load of 210 kN, representing a system load ratio of 0.4) is reproduced in Fig. 14 (Exp.(L→T), and the integrated steady-state response obtained from the members is superimposed (Exp.(T→L). The response of the restrained system without load (Exp.(T)) is also shown. It should be noted that the steady-state response of the system can be readily obtained by combining any of the beam plots given in Fig. 6 with any of the slab plots given in Fig. 8, depending on the reference temperature and the restraint conditions for each component. For example, the displacement response of the system with unrestrained beam and restrained slab is predicted by combining the response from Fig. 6(a) with that from Fig. 8(c). For a given temperature, the displacement at which the total load carried by the beam and the slab equals the applied load would indicate the corresponding displacement of the system. Similarly, the steadystate response of the fully restrained system is obtained from Fig. 6(c) and Fig. 8(c), which directly corresponds to the combined system response given in Fig. 11. For compactness, only the fully restrained case is depicted in Fig. 14 as it demonstrates the maximum discrepancy of the load sequence approximation. As discussed before for the composite beam, prediction of the system response is most accurate in the unrestrained case as well as for the axially restrained case without thermal expansion. The approximations for the case of unrestrained slab, and the case of unrestrained beam, lie between the fully unrestrained case and the fully restrained case, as expected. In general, it is evident from Fig. 14 that good approximation of the transient response of the restrained system is obtained by applying the loading after the elevated temperatures. The response is well predicted at relatively low and relatively high reference temperatures. The highest discrepancy in displacement of about 6% occurs at intermediate temperatures, between 400 and 800°C, due to plasticity effects

Fig. 14.

Effect of load sequence on the restrained system response for a system load ratio of 0.4.

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

221

caused by restraint to thermal expansion, and before the prevalence of tensile membrane action. It is also noteworthy that for higher load ratios, up to 0.7, it can be shown that the discrepancy at intermediate temperatures for restrained systems is still well below 10%. This can be carried out by detailed examination of Fig. 6(c) and Fig. 8(c), or alternatively Fig. 11, in conjunction with Fig. 12. The above-described approximation of the transient response by using the steadystate response of the components may be utilised to interpret the behaviour of the system at various temperature levels, depending on the applied load. For example, for the fully restrained system, the contribution of the components may be illustrated by examining Fig. 6(c) and Fig. 8(c) in conjunction with Fig. 14. At reference temperatures below 200°C where the displacement is less than 0.1 m, gradual thermal buckling in the beam is accompanied by an increase in the load contribution of the slab due to compressive membrane action. Thereafter, thermal buckling of the slab occurs, and the beam carries a significant share of the load. At a reference temperature of 400°C, corresponding to a displacement of about 0.25 m, the load is almost totally carried by the composite beam. At a reference temperature of 800°C, corresponding to a displacement of about 0.4 m, most of the load is carried by the slab, which is at lower actual temperature compared to the beam, and which is shown to have developed considerable tensile membrane action at this stage. At the higher reference temperature of 1000°C, the beam gradually makes a modest contribution to the response through its own tensile membrane action. Similar observations regarding the contribution of the constituent components to the behaviour of the system under various restraint conditions or load ratios may be undertaken using the approaches discussed above. These concepts, namely “sequence of load application” and “integration of component response”, are of considerable benefit in understanding the complex behaviour of structural systems under fire conditions. Furthermore, with further verification and design studies, these methods could have considerable implications towards the possibility of developing more rational and cost-effective design-related guidelines.

4.3.5. Influence of compartment size The investigations described above have been undertaken, as mentioned before, for a typical beam–slab system with dimensions, L×S in Fig. 3, of 9×6 m2. For verification purposes, further comparative studies have also been carried out on other systems with compartment sizes of 6×4.8 m2 and 12×7.2 m2, respectively, representing possible practical ranges. The details of the slab have been retained, and the size of the steel beam has been varied to provide comparable ambient capacity for the systems. As expected, buckling deformations due to restraint to thermal expansion become more pronounced with the increase in compartment dimensions. It is also noteworthy that, for restrained systems, the development of tensile forces at the supports of the steel beam and composite slab appear to be related to the respective beam and slab spans, slightly exceeding 1/20 of the length. For brevity, the full results are not presented herein but, as anticipated, the same conclusions in terms of the observed behavioural patterns and applicability of concepts dealing with

222

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

loading sequence and integration of constituent member response can clearly be drawn.

5. Conclusions The behaviour of an idealised composite beam–slab system under fire conditions is investigated in this paper. The load-carrying capacity of a typical configuration is estimated under ambient temperature, followed by an assessment of the fire resistance of the isolated components as well as the overall system. The loading and structural configuration are idealised in a manner that simplifies the response yet retains the main characteristics of the behaviour. Using this approach and employing an advanced nonlinear analysis program, salient parameters influencing the performance of the system are identified and examined. Several aspects of overdesign are illustrated through detailed examination of the system considered. In accordance with current design approaches, the design load for the fire situation would be based on a proportion of the ambient capacity of the isolated composite beam, typically in the range of 40% to 60%. In most design cases, the composite beam would also be assumed to be simply supported which may not be a realistic assumption particularly at elevated temperatures. Due to the difference in temperature between the steel beam and the connection as well as the occurrence of compressive forces due to restraint to thermal expansion, connections may provide relatively high rotational stiffness. Moreover, estimating the load ratio on the basis of the isolated composite beam without due account of the contribution of the transverse slab can be considerably conservative. Consequently, in a realistic situation, particularly for restrained systems, the actual system load ratio may be significantly low, typically between 10% and 20%. In such a case, the response of the restrained system would be dominated by the effects of thermal expansion, and would not be sensitive to variations in the applied load. The results of this study also clearly demonstrate the significant influence of the level of axial restraint on the attained fire resistance. This is illustrated both in the response of the individual components as well as that of the overall system. Comparison of the behaviour for variations of axially unrestrained as well as axially restrained boundary conditions is presented in detail. Whereas axial restraint causes a relative increase in deformation at an early stage due to buckling effects, the overall fire resistance of the restrained system usually increases as compared to the unrestrained system, with the slab restraint having a more significant influence on the behaviour. It is also indicated that thermal expansion may have beneficial as well as detrimental consequences on the performance of axially restrained systems, depending on the particular structural configuration under consideration as well as the adopted failure criteria. In restrained systems, buckling in the beam due to thermal expansion can have adverse effects on the mechanical strains in the slab reinforcement, which in a real situation would be at relatively low temperatures. On the other hand, thermal expansion can have beneficial effects in terms of introducing pre-compression and hence reducing the tensile forces in the beam connections to the surrounding struc-

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

223

ture. Moreover, the occurrence of thermal buckling within an effectively restrained compartment would reduce the thermal expansion forces on adjacent parts of the structure hence decrease the likelihood of undesirable modes such as failures to partitions and walls. Therefore, the merits of accounting for thermal expansion depend on the particular structural configuration, and cannot be determined in isolation of restrictions on the connection resistance and the allowable material mechanical strains. If such restrictions are not violated prior to the attainment of tensile membrane action, thermal buckling can then be considered to be a transient phenomenon which does not influence the structural response at elevated temperature. For such situations, the presence of axial restraint, regardless of whether it initiates thermal buckling, becomes the main determinant of the actual fire resistance of the composite beam–slab system. The results of this investigation also suggest that a good approximation of the deformation state can be obtained by applying the load after the elevated temperatures, in comparison with the more realistic simulation where the elevated temperatures are applied after the loading. This approximation provides accurate predictions for unrestrained cases, and for restrained cases when ignoring thermal expansion buckling effects. For the restrained cases including thermal expansion effects, the results are accurate at relatively low and relatively high temperatures. At intermediate temperatures, typically between 400 and 800°C, slight inaccuracies in displacement predictions, shown to be less than 10%, are attributed to initial compressive plasticity during thermal buckling. At higher temperatures, typically in excess of 800°C, the displacement is well represented by the steady-state approximation, where tensile membrane action is dominant. It is also illustrated in this study that an insight into the system behaviour may be obtained through appropriate consideration of the respective responses of individual components. Important behavioural phenomena such as thermal buckling, compressive and tensile membrane actions, and the degree of load sharing between constituent components of the system at various temperatures, may be assessed using this approach. More importantly, using idealised loading conditions, it is shown that the response of the system may be readily predicted by integrating the steady-state responses of the constituent components taking appropriate consideration of the existing boundary conditions at the ends of each member. With the application of suitable loading idealisation procedures, this methodology may be generalised for use in other structural configurations and loading scenarios. This would lead to considerable simplification of the analysis requirements, and would allow the introduction of hand calculations and/or graphical representations based on constituent members in a given system. The concepts examined in this paper, namely “sequence of load application” and “integration of component response”, are shown to be of considerable benefit in understanding the complex behaviour of structural systems under fire conditions. In conjunction with appropriate consideration of possible failure criteria, such as those related to material strain limits and connection performance, these concepts may be used for undertaking detailed design-related studies. With further verification and parametric studies, the application of these approaches could have considerable

224

A.Y. Elghazouli, B.A. Izzuddin / Journal of Constructional Steel Research 56 (2000) 199–224

implications towards improved quantification of the fire resistance of beam–slab systems, with a view to the development of more rational design procedures.

References [1] British Standards Institution: BS5950, The Structural Use of Steelwork in Buildings, Part 8: Code of Practice for Fire Resistant Design, 1990. [2] ENV 1993-1-2: Eurocode 3, Design of Steel Structures, Part 1–2: General Rules, Structural Fire Design. Commission of the European Communities, 1995. [3] ENV 1994-1-2: Eurocode 4, Design of Composite Steel and Concrete Structures, Part 1–2: General Rules, Structural Fire Design. Commission of the European Communities, 1995. [4] Johnson PF. International developments in fire engineering of steel structures. Journal of Constructional Steel Research 1998;46(1–3): Paper no. 415 [on CD-ROM]. [5] The behaviour of multi-storey steel framed buildings in fire. British Steel Report, Swinden Technology Centre, 1999. [6] Robinson J. Fire—A technical challenge and a market opportunity. Journal of Constructional Steel Research 1998;46(1–3): Paper no. 179 [on CD-ROM]. [7] O’Connor MA, Martin DM. Behaviour of a multi-storey steel framed building subjected to fire attack. Journal of Constructional Steel Research 1998;46(1–3): Paper no. 169 [on CD-ROM]. [8] Wang YC, Lennon T, Moore DB. The behaviour of steel frames subject to fire. Journal of Constructional Steel Research 1995;35:291–322. [9] Bailey CG. Development of a computer software to simulate the structural behaviour of steel framed buildings in fire. Computers and Structures 1998;67(6):421–38. [10] Bailey CG, Lennon T, Moore DB. The behaviour of full-scale steel framed buildings subjected to compartment fires. The Structural Engineer 1999;77(8):15–21. [11] Huang ZH, Burgess IW, Plank RJ. Nonlinear analysis of reinforced concrete slabs subjected to fire. American Concrete Institute, Structural Journal 1999;96(1):127–35. [12] Rose PS, Bailey CG, Burgess IW, Plank RJ. The influence of floor slabs on the structural performance of the Cardington frame in fire. Journal of Constructional Steel Research 1998;46(1–3): Paper no. 181 [on CD-ROM]. [13] Izzuddin BA, Song L, Elnashai AS, Dowling PJ. An integrated adaptive environment for fire and explosion analysis of steel frames—Part II: Verification and application. Journal of Constructional Steel Research 2000;53:87–111. [14] Izzuddin, B.A., Nonlinear dynamic analysis of framed structures. PhD Thesis, Imperial College, University of London, 1991. [15] Izzuddin BA. Quartic formulation for elastic beam–columns subject to thermal effects. Journal of Engineering Mechanics, ASCE 1997;122(9):861–71. [16] Song L, Izzuddin BA, Elnashai AS, Dowling PJ. An integrated adaptive environment for fire and explosion analysis of steel frames—Part I: Analytical models. Journal of Constructional Steel Research 2000;53:63–85. [17] Izzuddin BA, Elnashai AS. Adaptive space frame analysis—Part II: A distributed plasticity approach. Structures and Buildings Journal, Proceedings of the Institution of Civil Engineers 1993;99(3):317–26.