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NRC Publications Archive Archives des publications du CNRC Steel Structures Exposed To Fire - A State-Of-The-Art Report Nwosu, D. I.; Kodur, V. K. R. For the publisher’s version, please access the DOI link below./ Pour consulter la version de l’éditeur, utilisez le lien DOI ci-dessous. Publisher’s version / Version de l'éditeur: http://doi.org/10.4224/20337843 Internal Report (National Research Council Canada. Institute for Research in Construction), 1997-12-01 NRC Publications Record / Notice d'Archives des publications de CNRC: http://nparc.cisti-icist.nrc-cnrc.gc.ca/eng/view/object/?id=35f8257c-b5ad-4ea1-b91c-1d055726716a http://nparc.cisti-icist.nrc-cnrc.gc.ca/fra/voir/objet/?id=35f8257c-b5ad-4ea1-b91c-1d055726716a Access and use of this website and the material on it are subject to the Terms and Conditions set forth at http://nparc.cisti-icist.nrc-cnrc.gc.ca/eng/copyright READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE. L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site http://nparc.cisti-icist.nrc-cnrc.gc.ca/fra/droits LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB. Questions? Contact the NRC Publications Archive team at [email protected]. If you wish to email the authors directly, please see the first page of the publication for their contact information. Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez pas à les repérer, communiquez avec nous à [email protected]. Natlonal Research I*# Councll Canada Conseil national de rechelches Canada Steel Structures Exposed ta Fire A State-of=the=ArtReport by D.I. Nwosu and V.K.R. Kodur Internal Report No. 749 Date of issue: December 1997 - STEEL STRUCTURES EXPOSED TO FIRE - A STATE-OF-THE-ART REPORT D.I. Nwosu and V.K.R. Kodur ABSTRACT This report presents a state-of-the-art literature survey on the behaviour of steel structures in fire. The use of steel in building construction. its advantages and disadvantages. its behaviour when exoosed 6 fire and the factors affeciingu this behaviour is presentea. Various rcscarch studies conducted using expcrimcntal and analytical techniques to determine the overall behaviour of steel structures in fire are reviewed. Conclusions derived from these studies are given. Computer programs developed to study the various parameters affecting the overall behaviour of steel structures in fire are presented. STEEL STRUCTURES EXPOSED TO FIRE .A STATE-OF-THE-ART REPORT D.I. Nwosu and V.K.R. Kodur TABLE OF CONTENTS . 1 INTRODUCTION...................................................................................................................... 1 .................................................................................................................................... 1 1.1 GENERAL .......................................................................................................................... 1.1.1 Advantages 2 ........................................................................................... 1.1.2 Disadvantages .................... . 2 1.2 DESIGN CONSIDERATIONS ........................................................................................................... 2 1.3 DESIGN FOR FIRE........................................................................................................................ 3 ................................................................................................................... 3 1.4 CODESOF PRACTICE 1.5 OBJECTIVES AND SCOPE .............................................................................................................. 4 4 2 BEHAVIOUR OF STEEL STRUCTURES IN FIRE ............................................................ 2.1 GENERAL .................................................................................................................................... 4 ................................................................... 4 2.2 TRADITIONAL APPROACHES FORFIREPROTECTION ................................................................................................................ 2.2.1 Insulation Method 4 2.2.2 Capacitive Method ............................................................................................................... 5 2.2.3 Intumescent Coating Method ............................................................................................... 5 2.3 BEHAVIOUR OF STEELSTRUCTURES ........................................................................................... 5 5 ........................................................................ 2.3.1 Single and Continuous Supported Elements 2.3.2 Overall Structural Behaviour .............................................................................................. 6 2.4 FACTORS AFFECTING BEHAVIOUR OF STEEL STRUCTURES IN FIRE............................................. 7 ................................................................................................... 2.4.1 Loading ................. . . 7 2.4.2 Connections ......................................................................................................................... 7 ....................................................................................................................... 2.4.3End Restraint 7 2.4.4 Sprinklers............................................................................................................................. 7 .......................................................................................................... 2.4.5 Structural Interaction 8 8 2.4.6 Compartmentation and Localization of Fire ....................................................................... 8 ................................................................................................. 2.4. 7 Tensile Membrane Action 2.4.8 Temperature Distribution .................................................................................................... 8 ................................................................................................................................... 2.5 SUMMARY 8 3 LITERATURE REVIEW ...................................................................................................... 9 3.1 GENERAL .................................................................................................................................... 9 3.2 EXPERIMENTAL STUDIES ............................................................................................................ 9 3.2.1 United Kingdom................................................................................................................. 10 3.2.2 Australia ........................................................................................................................... 12 3.2.3 Japan ................................................................................................................................. 12 3.3 ANALYTICAL/NUMERICAL STUDIES .......................................................................................... 13 ................................................................................................................. 3.3.1 United Kingdom .14 3.3.2 Japan ................................................................................................................................. 17 3.3.3 Belgium .............................................................................................................................. 18 .................................................................................................................................... 3.3.4 USA 18 . . 3.3.5 The Netherlands................................................................................................................. 19 3.4 SUMMARY ................................................................................................................................. 19 4 COMPUTER PROGRAMS .................................................................................................... 19 4.1 GENERAL .................................................................................................................................. 19 4.2 DEVELOPMENT OF COMPUTER PROGRAMS ............................................................................... 20 4.3 SUMMARY .................................................................................................................................25 5 CONCLUDING REMARKS ..................................................................................................25 6 REFERENCES ......................................................................................................................... 26 . . . - STEEL STRUCTURES EXPOSED TO FIRE A STATE-OF-THE-ART REPORT by D.I. Nwosu and V.K.R. Kodur 1. INTRODUCTION 1.1 General Steel is one of the construction materials which has been in use for a long time. It is a versatile and economical building material whose use is on the increase. The continuing improvement in the quality of fabrication, erection techniques and manufacturing processes in conjunction with the advancements in analytical techniques, made possible by computers, have permitted the use of steel in just about any rational structural system for buildings of any size. Steel frames for building were fist introduced in buildings approximately one hundred years ago, and since then, have made it possible to build different kinds of buildings from those previously in common use. No doubt the kind of buildings that emerged were in response to market requirements of the day. Early buildings with steel frames were generally heavy in dead weight, contained much masonry, were lightly serviced and were generally not of a large span. In some instances, the steel structure was used as a substitute for masonry and timber, and was simply a skeleton around which the building fabric was wrapped. In the early use of steel as a substitute for a building framework, compatibility between the steel frame and the building as a whole was obviously relatively easy to achieve. The requirement was for short spans, heavy cladding and partitioning which substantially stiffened the framework and, in many situations, provided the entire lateral load carrying resistance of the building. Fire protection requirements were not onerous or non-existent. This may be as a direct consequence of the widespread practice of using encasement to protect the steel structure. As a result, the steel frames used in the early buildings were very simple, mainly pin-jointed in design, with simple non-welded connections, which proved quick and simple to erect. Modem steel-framed buildings, by comparison, are of much lighter construction, are often required to have longer spans giving more flexible use, have lightweight partitions incapable of carrying lateral load, are heavily serviced and are liable to alterations in layout and use. With modem construction practice, there are more extensive requirements for fire protection. However, the relatively cheap material costs, fast erection sequences and lighter foundations, achieved by using steel in modem buildings, compare very favourably with those of other building materials. One of the main costs in the use of steel, for the main framework of a building, is the additional protection required to provide adequate safety in the event of a fire. The problem arises because steel softens at high temperatures with significant degradation of strength and stiffness. Current structural fire protective measures concentrate on limiting the rate of temperature rise of the steel framework by a combination of measures which usually include some form of protection to some or all of the exposed surfaces of the members. Despite its problems for use in fire resistant construction, there are advantages in the use of steel for structural members that constitute the primary supporting system of a building. 1.1.1 Advantages Some of the advantages of steel as a structural material are: The high strength of steel per unit weight, results in small cross-sectional sizes and thus minimizes the dead loads of structural members in buildings. The behaviour of structural members made of steel is predictable because of the uniformity of the material (isotropy), unlike other commonly used structural materials. The addition of structural members made of steel to existing buildings can be achieved easily. Since most steel members that make up the primary supporting system of buildings are shop fabricated, high quality control can be easily achieved. The stress-strain characteristic of steel makes it easy to model the response of a structure. Erection of buildings using steel is much faster when compared to other building materials. This can lead to a considerable reduction in construction costs. The ductility property of steel makes it an attractive material for buildings, especially those subjected to seismic loads. I . I. 2 Disadvantages Some of the disadvantages of steel as a structural material are: Steel has a low resistance to corrosion. Consequently, when exposed to a corrosive environment, high maintenance costs may be involved. Steel loses its integrity at high temperatures. Therefore, where a high fire resistance rating is needed, there are additional costs involved in providing fireproofing. Although the low dead load of steel-framed buildings is one of the advantages of using steel, the light weight of a steel frame system can, in certain cases, result in problems with vibration. 1.2 Design Considerations Two design philosophies are currently in use for the design of steel structures: the working stress design and the limit states design. For the working stress design, the structures are designed so that unit stresses computed under the action of working, or service loads, do not exceed predesignated allowable values. In the limit state design philosophy, the structures are designed to satisfy the condition of serviceability limit states (those states concerned with occupancy of the building, such as deflection, vibration, and permanent deformation) and ultimate limit states, which are those concerned with strength, accidental failure due to a fire (fire limit state), buckling, fatigue, fracture, overturning and sliding. The working stress design philosophy has been around for quite some time; however, limit state design is becoming a widely accepted approach. While the limit state design approach has been developed for structural steel design under room temperature, its application for fire resistance design is not fully developed at the present time. Although codes of practice for fire resistant design have recently emerged [I, 21, they are still not fully implemented in Building Regulation Documents. 1.3 Design for Fire Structural design for fire is still in the developing stage in various parts of the world. Traditionally, steel structure designers have not played a part in assessing the structural fire endurance requirements. Instead, the structural design of a steel frame for a building has been independent of any consideration of the thermal effects of a fire. Fire protection is then added on to the completed assembly in accordance with the requirement for fire resistance ratings. With the cost of fireproofing typically representing a significant proportion of the cost of the structural frame for a building, structural engineers are becoming increasingly interested in the proper design of steel structures for fire endurance. Some designs for steel structures to withstand fire have emerged in the recent past. These approaches are based on the fire resistance for individual members. The computation of fire resistance in these design approaches, is based on predicting the behaviour of a structural member were it to be exposed to the heating regime used in fire resistance tests. It does not necessarily imply the capability to predict the performance of that structural member when involved in a fire in a building. Methods for calculating limiting temperature and design temperature are proposed in the British and European Standards for the fire resistance design of steel structures [l, 3,4]. These codes set out a methodology for determining fire resistance, based on fire tests and analytical methods. Methods of fire safety whereby designers can select an appropriate thickness of fire protection or, in many cases demonstrate that no protection is needed, are presented in the British code [I]. In this code, the structural effects of a fire in a building, or part of a building, are considered as a fire limit state. To check the strength and stability of the structure at the fire limit state, the applied loads are multiplied by relevant load factors. The performance criteria used for the final design are: (i) the members should maintain their strength under the factored loads for the required period of fire resistance, and (ii) any specified requirements for the insulation and integrity of compartment walls and floors should be satisfied. 1.4 Codes of Practice Buildings are subjected to regulatory control for health and safety purposes. The safety requirements include provisions for fire protection. In Canada, fire protection requirements in the National Building Code of Canada [5] are given according to the building use and occupancy. In most codes, fire protection is concerned with safeguarding the occupants in the building where the fire may occur, minimizing risk to the adjacent buildings, and thereby avoiding a large and destructive fire. To achieve these aims consideration is given to the planning, layout and construction of the building to control the growth of a fire, prevent it from spreading, safeguard means of escape and prevent collapse of the building. In the codes, provisions are made for subdivision of a building into compartments in order to keep the size of the fire under control. The control of the fire growth and size is concerned with the complete building. However, the code requirements for structural fire resistance at present applies to individual members. The assumption is that if the individual members are satisfactow, at least as well. Moreover, current design the whole structure should specifications in many codes are still based on traditional prescriptive methods of fire protection, where thc structure is designed for the ambient temperature situation and a certain thickness of fire protecrion is specified to achieve the fire resistance requirements. 1.5 Objectives and Scope The main objective of this report is to conduct a comprehensive literature review on the behaviour of steel structures in fire conditions. Attention is focused mainly on structural frames. Both experimental and analyticallnumerical studies relating to the subject are reviewed. In Section 2, the behaviour of steel in fire and the methods currently used for their protection against fire are given. Reviews of previous studies are given in Section 3. Section 4 presents a review of computer programs for analysis of structures exposed to fire. The report is summarized in Section 5. 2. BEHAVIOUR OF STEEL STRUCTURES IN FIRE 2.1 General Steel structures, when exposed to fire, will lose their strength and stiffness. This may cause excessive or permanent deformation that, in some situations, will lead to structural collapse. This situation certainly will violate the serviceabilitv and ultimate strength criteria. Thus, it is common praciice to provide protection to steel framework so that the integrity of the structure can be preserved for a sufficient period to enable safe evacuation of the occupants and to limit property damage. The failure of a structural element under fire would mean that the element is no longer capable of sustaining the applied load on it. However, the failure of some elements in a fire would not necessarily cause the total collapse of the building. Therefore, the behaviour of an isolated structural element in a fire can be significantly different from the behaviour of the same element within a complete structure. 2.2 Traditional Approaches For Fire Protection To achieve a required fire resistance rating, steel structural elements are protected so as to control the rise in temperature when exposed to fire. The most common method of protecting a structural steel member is to encase it in a material which will act as a thermal insulator. Other, less common methods are: the capacitive method, the installation of automatic sprinklers, or the use of intumescent coating. Some of these methods are briefly discussed in the following sections. 2.2. I Insulation Method In this method, materials such as gypsum, perlite, and vermiculite board are used to protect a steel fiame from fire. Other materials which are used include: mineral fibre, ceiling tiles, Portland cement concrete, Portland cement plaster, masonry materials and spray coatings. The insulation may be used as a membrane fire protection, in which a fire resistive barrier is placed between a potential fire source and the steel member to be protected. On the other hand, the insulation may be sprayed directly onto the member to be protected. The latter method is widely used for structural steel frames. 2.2.2 Capacitive Method This method of fire protection is based on using the heat capacity of a material to absorb heat. Using this method, the temperature rise in the element of a building exposed to fire is delayed and its fire resistance increased. Two examples in which the heat capacity of a material is used to gain fire resistance are: (i) water filling in Hollow Structural Section (HSS) columns, where part of the heat is used for heating and evaporation of the water, and (ii) concrete filling in HSS columns, in which the concrete absorbs some of the heat. 2.2.3 Intumescent Coating Method For this method, intumescent coatings are used which foam and form a stable thickness of insulating cover for the steel on application of heat. The method avvears attractive, particularly as the material is appliedto steel in the form of a coat ofpaint. However, the method has its limitations. Materials available, at present, give only a relatively short period of fire resistance and require several on-site applied coats. Moreover, there is a danger of mechanical damage to the coating during the normal use of the structure in which case there would not be a complete cover of insulation available should a fire occur. 2.3 Behaviour of Steel Struetures When a steel structure is exposed to fire, its load carrying capacity is reduced due to the loss in strength and stiffness of the material with increase in temperature. There is a critical temperature at which steel loses a considerable strength such that it can no longer carry the load imposed on it. The time for a structural element to reach this critical temperature depends on many factors such as the applied loads, stress level and the ratio of its surface area exposed to fire to the mass of material per unit length. In a building, various elements are normally linked together and, consequently, the structure responds as a combined or total system to any external loading condition, transmitting stresses and strains to adjoining members. Such interactions also occur under fire conditions and, in general, have a beneficial influence on the behaviour of structures in fire. This is one-of the reasons why, with few exceptions, total structural collapse is not a frequent occurrence in actual buildings when a fire occurs. 2.3.1 Single and Continuous Supported Elements The mode of failure in steel elements exposed to fire depends on boundary conditions and the rate of temperature increase. Steel elements can be of flexural or compression type. Those that resist loads primarily through bending, such as beams, are termed flexural elements, while compression elements are those subjected to loads tending to decrease their lengths (e.g., columns). The behaviour of flexural structural elements when exposed to fire is influenced by the continuity of the structural system. The effect of continuity is illustrated in Fig. 1 [6] for a simply supported and a continuous beam subjected to a uniformly distributed load (udl). The beam (Fig. l(a)) is placcd on two simple supports, and the structure is therefore statically determinate, which means that the distribution of forces can be determined from equilibrium. The maximum stresses will occur at the centre of the beam, and as such, the section will yield at this location first when heating is applied. A 'plastic hinge' is formed, which means that, at a certain temperature, the middle section reaches its ultimate strength and will no longer offer resistance to rotation. At this stage, the beam has become unstable and collapses (Fig. l(a)). One hinge is therefore sufficient for a statically determinate flexural member to collapse. In Fig. I(b), a two-span continuous beam subjected to a udl is shown. In this case, the beam is statically indeterminate; the distribution of forces cannot be determined from equilibrium alone, compatibility must be satisfied as well. When exposed to fire, the centre support section reaches its ultimate capacity and the hinge will be formed, so that this section can rotate freely (Hinge 1 in Fig. l(b)). If the span and the loading of the beams in Figs. ](a) and (b) are equal, this hinge will be formed at the same temperature as that in the beam in Fig. l(a). The formation of the hinge at the centre support, however, does not lead to collapse in the beam and the beam can cany further load by transferring the load to other critical sections, namely the span section. Further heating will cause another hinge to be formed in the span region (Hinge 2 in Fig. l(b)). At this instant, the structure will become unstable and collapse occurs. The continuous beam case illustrates the beneficial effect of continuity in structural elements when they are exposed to fire. When one portion of the member reaches its ultimate strength, the moment is then redistributed to other sections of the member that are yet to attain their ultimate capacity, and in so doing, the fire resistance of the element is improved. 2.3.2 Overall Structural Behaviour There is another phenomena which enhances the fire resistance of a continuous beam. This arises in a situation where the beams are either restrained by some means or are active components of a whole structural system where they are restrained by adjacent elements. In these beams, before heating, the mid-span region would be under positive moment, and supports would be under negative moment as shown in Fig. l(c). When the beam is uniformlv heated from the bottom in both svans. the central soan is restrained bv the adjacent e~emkntsfrom deflecting, thereby yen&ating an additionh negative mome; throughout the beam. This reduces the load-induced positive moment at the mid-span and increases the load-induced moment over the support. This has a beneficial effict as the moment capacity (strength) over the support decreases at a lower rate than at midspan, thereby increasing fire resistance. Further heating can lead to formation of a plastic hinge at mid-span. If the restraint provided by the adjacent elements is adequate, the beam can be transformed into two cantilevers, thereby allowing it to resist collapse as long as the moment capacity over the support remains sufficient for the loads. The foregoing situation will usually occur in buildings with a continuous beam system where the internal spans are heated and the surrounding spans are unheated. However, if all the spans are heated or if the heated span is an end the degree of restraint may be considerably reduced. span, P In practice, there is always some interaction between various elements. The simplest form is a beam-column assembly. Frictional resistance at supports and closeness of adjacent elements can develop restraining forces. Fig. 2 [7] shows the effect of heating on the moment distribution in a steel portal frame. This is a typical example of the influence of interaction between a beam and a column element on the behaviour of a steel frame in fire. The figure also illustrates the effect of restraint provided by a column on the moment distribution in the beam and bending moment induced in the column. The restraint provided by the column during heating reduces the moment distribution in the beam thereby enhancing the fire resistance of the frame. In a multi-storey building, a fire is likely to occur in only a part of the structure, particularly where good compartmentation is provided as illustrated in Fig. 3 [S]. This V figure shows the response of a structural building frame subjected to a localized fire. Such a fire has two effects on the exposed niembers of the building. Firstly, the restraint to thermal expansion provided by the surrounding cold members increaseithe axial forces in the heated members which, in the case of columns, can cause instability at lower temperatures than would occur in isolated members. Secondly, additional support is provided by the cooler members around and above the heated area which can divert load paths from the weakened members to the stronger members. 2.4 Factors Affecting Behaviour of Steel Structures in Fire Several factors influence the behaviour of steel structures exposed to fire. Some of these factors are discussed in the following sections. 2.4.1 Loading One of the major factors that influences the behaviour of a structural steel element exposed to fire is the applied load. The limiting temperature and the fire resistance of the element increases if the applied load decreases. Failure will occur when the applied loading is equal to the ultimate strength of the element. Therefore, lowering the applied load on the element will increase its fire resistance. 2.4.2 Connections The beam-to-column connections in modern steel framed buildings are generally designed with shear-resisting connections. The forces are also resisted by vertical bracing or shear walls. When deformations occur in the frame due to fire, moments are transferred to the connections and to the adjacent members, reducing the mid-span moments in the beams. The moment resisted by connections will reduce the effective load ratio to which the beams are subjected, thereby enhancing the fire resistance of the beams. This beneficial effect is more pronounced in large multi-bay steel frames with simple connections, but is smaller in frames designed with moment connections because the effect of continuity is already utilized under normal conditions. 2.4.3 End Restraint The structural response of a steel element under fire conditions can be significantly enhanced by end restraints. For the same loading and fire conditions, a beam with a rotational restraint at its ends would deflect less and survive longer than its simply supported counterpart. The addition of axial restraint to the beam will result in an initial increase in the deflections, due to the lack of axial expansion relief. With further heating, however, the rate of increase in deflection will decrease. 2.4.4 Sprinklers Sprinkler systems are also very important in protecting steel structures in fire. Automatic sprinkler systems are considered to be the most effective and economical way to apply water to suppress a fire [9]. In the event of fire in a building, the temperature rise in the structural elements located in the vicinity of sprinklers is controlled. Therefore, the fire resistance of such elements is enhanced. In addition, fire protection is rarely used for the elements in the area where sprinklers are used. 2.4.5 Structural Interaction In contrast to an isolated element exposed to fire, the way in which a complete structural building frame performs during a fire is influenced to varying degrees by the interaction of the connected structural elements in both the exposed and unexposed portions of the building. This is beneficial to the overall behaviour of the complete frame, because the failure of some of the structural elements may not necessarily endanger its structural stability due to the ability of the remaining interacting elements to develop an alternative load path to bridge over these failed elements. 2.4.6 Compartmentation and Localization of Fire Buildings are usually subjected to fires which remain localized due to compartmentation. This has a two-fold effect on the heated elements. First, the restraint to thermal expansion provided by the surrounding cooler elements increases the axial force in the heated elements which, in the case of columns, can cause more instability at lower temperatures than would occur in isolated elements. However, the cooler area also provides support which can divert load paths from the weakening members increasing the stability of the structure. 2.4.7 Tensile Membrane Action A tensile membrane action is developed by reinforced concrete floor slabs in a steel framed comoosite building. This action occurs when the applied load on the slab is taken by the steefreinforcemes, due to cracking of the entire ddI;th of concrete crosssection. It enhances the fire resistance of a complete framed building by providing an alternative load path after failure of some structural elements has occurred. It also has the potential of providing a means to eliminate fire protection for some steel elements in framed buildings, thereby reducing the cost of fire protection. 2.4.8 Temperature Distribution Depending on the protective insulation and general arrangements of members in a structure. steel members will be subiected to temperature distributions that vary along the length or'over the cross-section. embers subjected to temperature variation across their sections may perform better in fire than those with uniform temperature distribution. This is due to the fact that sections with uniformly distributed temperatures, will attain their load capacity at the same time. However, for sections subjected to non-uniform temperature distribution, some parts will attain the load limit before the others. This will decrease the effect of the fire on the members. 2.5 Summary The following points summaize the information given in this Section: 0 0 When subjected to fire, an unprotected steel structure will lose its stiffness and strength as a result of deterioration in its material properties. The traditional approach to the above problem is to provide insulation to protect the structure's load bearing elements to meet the requirements for fire resistance. The most common and effective method of protecting structural steel is encasing the steel in a material that will act as an insulator. The behaviour of an isolated structural element in fire differs significantly from that of an element within a complex, highly redundant structure. The continuity, elements interaction and restraint to thermal expansion present in a complete structure enhances the fire resistance of the structure. In general, indeterminate structures perform better in fire than determinate structures. The fire resistance of a structure increases with increase in the degree of static indeterminacy. The fire resistance of a complete building may be independent of the failure of some structural elements in the building due to the ability of the remaining elements of the building to develop an alternative load path. The membrane tensile action produced by a reinforced concrete slab can increase the stability of a structural element at large deflection and provide an alternative load path to bridge over failed elements in a framed structure. 3. LITERATURE REVIEW 3.1 General A large amount of research into the behaviour of structures exposed to a fire has been concerned with the structural performance of single structural elements, and the development of analytical techniques. In recent years, various studies have been undertaken on the overall behaviour of structures when subjected to fire. A number of experimental and numerical studies for protected and unprotected steel framed buildings have been conducted or are in progress [lo-181. The following section presents a review of these studies. The review, presented below, is divided into the separate countries where they were conducted. 3.2 Experimental Studies Due to the very high cost of providing facilities for fire tests, coupled with the difficulty of preparing the tests to investigate the true response of a complete structure, experimental studies on the overall behaviour of steel structures in fire are progressing at a very slow rate. There is a limited amount of research being carried out at this time [l 1, 15, 16, 17, 191. Objectives of the experimental studies included: (i) observing and monitoring structural and non-structural elements within a real compartment subjected to a real fire, (ii) assessing the overall behaviour of the structure under actions that correspond, as closely as possible, to the impact of real fires, and (iii) providing data over a range of fire scenarios so that the computer models can be verified. Other studies have used scale models to study the overall behaviour under fire conditions. In the United Kingdom 120,211, fire tests have been conducted on a full-scale eight-storey composite frame at the British Research Establishment Large Building Test Facility (LBTF) at its Cardington Laboratory (see the results obtained from some of the tests in the table below). In Australia [17, 191 a fire test on a 41-storey prototype structure was conducted to investigate the likely effect of fire in the building: (i) if the existing automatic sprinkler system complying with the requirements of extra light hazard is left in the building, and (ii) if the previously protected parts of the building are left unprotected. The experimental study was also aimed at providing data for a risk assessment on fire safety in the prototype building. In Japan [22], fire tests on the behaviour of multi-storey steel frame buildings were conducted to investigate the impact of using fire-resistance (FR) steel for structural elements for buildings. The features of the above experimental studies and the observations and conclusions derived from them are highlighted in the following tables. 3.2.1 United Kingdom Study Detail and Objectives Place [Ref] BSC and DOE Compartment Fire Test [II ] The research describes a fire test on Timber cribs: a. . Full scale. loaded, 2-D mainly steel frame consisting o f . . Fire and Structural Characteristics fire load of 25 kdmi 118 ventilation ofwalls in companment a) unprotected steel beam spanning test companment at ceiling height b) two biock-in steel columns I Obtain data for the preparationof design guidelines and developmest o f analytical techniques to simulate the structural stability o f steelwork in natural fires. To relate the observed deflection behaviour o f the frame with a simplified theory. . I I I The research examines a number of features from the collaborative test program initiated jointly by Sweden (BSC) and the UK (FRS). Fire test on: Steel columns in various locations in a campanment Steel frames . Objective: To highlight situations where unprotected steelwork had adequate inherent firc resistance. The observed survival time was greater than that expected from the individual beam, which indicates the potential benefit from continuity. Attainment o f a 30 min fire resistance for the frame nleans lhal ru;h a connru;lion cuuld me21 the prtn ~sionsundcr lhe IJu~ld#ng Kcguiallons fur ground and upper storeys in office, shop and factorv assenihlv and storane ~~~ Objectives: BSCIFRS Fire Tests [ I 51 ConclusionslObse~ations ~ I cnnncctiunr provided 30 mil! tire rrr~sloncvuilhoul the ncud fur addili.,nui fire proleution Wood and woodlplastic fuels burned undcr different ventilation I conditions and thermal oro~ertics. . . Iil~lbcr.'rihtirr. .oad Ill. I S dnd 2,. .g m' ~ ~ ( 1n2.g1,1 anJ I X ~ e n l i l a l i mdt one uall l a w fire loads and laree I jmlilauun openmy .eleclcd kt rcprt3cnl o;;upanuiz, >u;h as s;h~n,lj and nlulti-~h,rr.) t117ict ~ ~ I The woodlplastic fire had little effect on the maximum steel temperature attained. I i l l c lcmpcralur: rire ot',Ie~l n i~nctiuno f both lhr. reclion lazl%,r (lire cxpn>r.dpcrnrnevr di, idcd h) cross sectional area) and position. I lernpcralure gradlent. i!crors lhc paniall) built ,crtioll D/MIIUIIIIIS lnlo lhc dc,uhle-lcafexlcmal uailr reached 400°C and resulted in substantial thermal bowing. Changing compartment lining affected the combustion eas vmpcralure. inrli;aling thc ncud tu a;ioun~ t j r lhcrmdl pn,pcnies o i enclosure in any analytical approach. . I - BRE Fire Tests E20.21 I Tens were Performed at the Large Building Test Facility (LBTF) at Cardington Experimental Building: Steel-frame structure: . Eight storeys with 5-bay long by 3-bay wide (approx. 945 mi rectangular area) with composite (Concrete-Steel) floors. Two wmer tests representative of a comer office and one Large Compartment test which is representative of a large open plan office. In the comer tests, unprotected steel beams within compartment were tested to investigate shedding and bridging mechanisms between beams and slabs. Fire Load: Timber cribs with fire load of40 kgim' . . Objectives: To examine the behaviour of multi-storey, steel-framed buildings subjected to real fires. To use data from tests to validate computer models for structural analysis at elevated temperatures. To assess the tire pans ofthe forthcoming Eurocodes. BST Fire Test Program 1231 Building tested was an eight-storey steel framed structure. Four tests were planned (first three Test was performed at the tests were completed). Large Building ~~~t ~ ~ ~ ati l i Test t ~ 1: One dimensional Restrained Beam. Cardington. Test 2: Two-dimensional plane frame. Test 3: Three-dimensional comer tests. Objectives: Test I: To check the effect of expansion of heated members on the movement in the frame. Test 2: To examine the behaviour of the frame around the connections. Test 3: To determine the extent of membrane action provided by the composite metal deck floor system. Preliminary results obtained fmm the wmer fire test indicated that: The maximum temperature of 903°C was recorded after 114 min at the middle section on the bottom flange of the unprotected beam 8 2 of Fig. 4. A maximum temperature of 690°C was obtained after 114 min for the edge beam which was totally covered by the fire. The slab maximum deflection at its centre which was 266.9 mm after 130 min was found to have reduced to 159.7 mm once the cooling occurred. The primaly beam on the west end boundmy ofthe compartment remained straight throughout the test. This was attributed to the restraint provided by the secondary beam framing into its web and partly due to the position of the partitions relative to the underside of the lower flange of the beams. The integrity of the structures was demonstrated by restriction of all damages to the areas within the compartment. Contributing to the enhancement of the structure's performance was the membrane action provided by the wmposite floor slab. . Fire Load: Test I : Heatins was done in a gasfired furnace. Test 2: Heating was done in a gasfire furnace nearly 5 times longer than the typical floor fumace BS 467 (IS0 834) [241 fire resistance tests on floor beams. Test 3: Heating was provided by wood cribs with a fire load of 45 kg/m1. . . The beneficial effect of continuity provided by surrounding structure was shown in Test I , where a steel temperature of up to 900°C was achieved, Test showed [hat, in real structures, steel members can a very large deformation without structural collapse. The derived from membrane action provided by the floor slab when one or more members lose stiffness and strength was also shown when the steel temperature attained in Test 3 was approximately 1000°C. There was a wnservative correlation behveen the measured time temperalure response in Test 3 and the parametric equation of Eurowde 1. Thermal expansion of members can be constrained by the surrounding structure resulting in a negligible movement ofthe building's external facade. . 12 3.2.2 Australia Place [Ref] Fire Load and Structural Characteristics ObjectivesIStudy Details Fire test in 4 i-storey prototype structure. Fire Tests of Omce Building at BHP ResearchMelbourne Laboratories [17, 191 Building tested Represents a segment ofone typical storey of prototype building with two parts: a) purpose part; and b) existing part . . Objectives: To observe the nature, duration and severity of fire generated by the and Of offices typical of those in the prototype building. To investigate and evaluate the influence of fire on the unprotected composite slab and steel framing. To investigate the effectiveness of an extra light hazard sprinkler system. To generate data to be used for risk assessment study. Fire load: Conciusions/Observations The structure ofthe test building remain undamaged during the test. Open area: Work stations and ~h~ required load was sustained bookcases containing large without excessive deflection. amounts of combustible materials ,Steel members and composite including drawings, books, floor slab suffered no permanent magazines and plastic coated deflection. folders. Extra light hazard sprinkler Small Office: Fitted out as a system was effective in representative office with the controlling developing and wellcontents including a desk, developed fires in both small and bookcases and chairs. open pian office areas. For refurbished building Wood Equivalent~i~ ~ ~ ~ d adequate : performance of unprotected floor (slab and beams) Test I: In small office, 52 kglm2. in fire conditions was established. Test 2: In open plan area, 53.5 kglm'. Test 3: In open plan area, 53.9 kg/m2, and in smali office, 52.1 kdm2. Test 4: In small ofice, 67.5 kglm', and in open plan area, 64.3 kglm'. . . 3.2.3 Japan ObjectiveslStudy Details Place [Ref.] Nippon Steel Corporation and Chiba University, Tokyo [22] . . Stage I: Test on steel columns made of fire-resistant (FR) steel. Stage 2 (Anaiyticai-design): Fire-safe design of Yokohama Sogo warehouse where FR steel was used for its interior columns and beams. Fire-safe design of Tobihata building where FR steel was used for its external frames Objectives: To confirm experimentally that protection thickness could be reduced. To show that the strength of building elements at high temperatures could be retained. . ConclusionslObservations Fire Load and Structural Characteristics Fire load: Standard time-temperaturc Curve according to JIS 1304 [251. • The results From the test showed that FR steel columns will not fail until the steel temperature exceeds 600'C. The deformation behaviour of FR steel agreed with other forms of steei, although the tire resistance time differs with protection thickness. The protection thicknesses that satisfied the required fire resistance (in hours) were 10 mm and20mminl handzh, respectively; while those with conventional steei were 20 mm and 30 mm in I hand 2 h, respectively. . . 3.3 AnalyticaVNumerical Studies A number of analytical/numerical studies have been conducted on the overall behaviour of steel structures in fire [3,4, 14, 18,26,27]. The main objectives of these studies were to demonstrate the inherent fire resistance of unprotected steel structures or to show that the amount of fire protection required can be reduced by investigating the overall response of a complete frame exposed to fire. Most of these studies concentrated on the development of models, which were generally based on the finite element method (FEM) with a few models developed using the finite difference method (FDM) to determine the temperature distribution across a section (thermal analysis). In the U.K., at the University of Sheffield, University of Nottingham, Loughborough University of Technology and British Research Establishment (BRE), considerable research on the development of numerical models to study the overall behaviour of steel structures in fire is being carried out. Similar studies have been conducted in Japan, Belgium, the United States and the Netherlands [8, 12, 13,281. Some of the models deal with two-dimensional steel frames (composite and noncomposite) [27,29] and others with three-dimensional steel frames (composite and noncomposite) [26,30]. These models have been used to study the effects of parameters such as continuity, end restraint and continuous floor slabs, which influence the behaviour of the heated steel frame. With the exception of a few recent studies [6, 18,291, most of the models that deal with the concept of composite action have included the effect of the floor slab by representing the beams as composite elements based on the effective width concept. The models, however, did not include any membrane or bridging action of the slab, which may be a major influence on the structural response. Also, most of the models have only been used to assess the effectiveness of using various types of sub-assembly (subframes) in predicting the structural behaviour in fire. This approach has been employed in order to reduce the amount of computation and computer memory required. The research studies carried out on the overall structural response of steel structures when exposed to fire are outlined in the following - tables with the observations and conclusions reached by various studies. 3.3.1 United Kingdom Place [Ref.] Conclusions Observations p University of Sheftieid and University of Nottingham 1271 The study presented the development of a numerical program on the behaviour of a steel frame under fire conditions Structures studied: 2-Dsingle- and two-bay singlestorey steel frame Obiectives: . . . ~S~ ~ To develop a finite element formulation that permits full loadtemperature history of steel frames. To validate results from the approach with known experimental data from tire tests. To investigate the effects of various forms of partial protection on the collapse temperature of sway frames. University of Sheftield [261 The study formulated and developed a computer program for nonlinear analysis of 3-D steel frames in fire (3DFIRE) Structure analyzed: Multi-storey frame. ,simple column subframe in a three-storey framed structure with fire in a ground-floor compartment. . . Objectives: To analyze multi-storey column subfmmes in various tire conditions. To provide analytical and numerical formulations for conducting parametric on 3-D column subframes from multi-storey frame construction. Analysis Technique: Finite Element Method (FEM) . . . . . Formulation : ~~~~d~~ previous FE program fNSTAF PI1 Element type truss and beam elements. - Capabilities: Allows for materiai and geometric nonlinearities. Variation oftemperature across and along each member is possible with the program. Allows for different material models. Thermal strains, residual stresses and thermal bowing can be considered. Analysis Technique: FEM Formulation: . ~~~~d~~ the program ~NSTAF . . . . PI]. All basic principles of INSTAF were retained. but 3-D formulation of element stifiess and elevated temperature characteristics were included. Element type -twonode I-D beam elements. Capabilities: Allows for material and geometric nonlinearities. Allows for materiai variation as temperature increases. Capable of analysis to high deformation levels at ambient and elevated temperatures. . . Comparisons between analysis and test data for columns and frame indicated that in all cases satisfactoly agreement was obtained. Results from the analysls of2-D two-bay single-storey steel frame to demonstrate the potentials of the formulation show that: a) A critical temperature of 450PC was attained when all members In the frame were unprotected. b) Protection of the beam only raised the critical temperature to 436°C. c) Insulation of one beam and one column provided a21% increase in critical temperature. d, Ofeither three columns or one complete ring frame increased critical temperatures to 64S°C and 634°C. respectively. . . Comparison with full fire frame analysis of previous studies exhibits an excellent agreement. Comparison with large-deflection elastic solutions showed an excellent correlation through the linear and nonlinear ranges. at a lower load using the formulation. NO explanation was given for this observation. BRE 130,321 Structure Analyzed: An eight storey 3 by 5 bay building with steel columns and composite beams was used in the experimental study. . Objectives: carry out a comprehensive parametric study of steei frame behaviour in fire conditions. To examine the applicability of using subframe to predict behaviour of structures in fire. To compare the behaviour of complete multi-storey framed building with associated subframes. TO . Loughborough University of Technology and University of shefield 1331, Analysis Technique: . FEM - Element type two-node beam element. Fuii composite action between beams and exists, Uniform and non-uniform temperature distributions for columns beams, respectjveiy, The fire is confined to a compartment of one bay in one storey only. . . Conditions of Analysis Frame was analyzed as a whole with fire in each C o m p ~ e n t . Subframes with different boundary condition combinations were analyzed. Subframe was formed by extending heated compartment by one bay (let? and right) and one storey (top and bottom). A series of analytical studies was presented on the behaviour of composite building frames in fire Analysis Technique: Structure analyzed: . ,unprotected plain composite steel-concrete frame (see frame and fire location in Fig. 5 -this is a section through the Cardington frame). Both rigid and semi-rigid beam-column connections were investigated. Both full frame and subframe analysis were performed. . Objectives: To assess the effectiveness of using different 2-D subassemblies in predicting the behaviour in fire of afuil plain composite frame. FEM Formulation: All analysis based on previous finite element (FE) program NARR2 [I (1. Element type - Beam and plate elements. Composite action: The beams were treated as fully composite, with an effective concrete flange width equal to a quarter of the span. ,~h~ method developed is oftaking into account strain reversal. It is therefore, possible to assess the residual stress effects on the frame elements after a iocal fire was extinguished, and the frame was returned to ambient temperature. . . For steel frames subjected to vertical loads, subframes may be used for elevated temperature analysis. Connected beam in a frame may be designed as pinned support from coiumns for fire safety if the wlumn is designed to reach its limiting temperature in fire (bending moment in the column is neglected). Built-in support conditions may be assumed when calculating the load-bearing capacity of columns in a rigidly connected steei frame under fire conditions. The influence of thermal restraint is much more important in columns than in beams. Extrapolation of values from the code to constructions where stability is the governing factor may result in overestimation of limiting temperatures. . . . . The study suggested that steel frames in a fire can be adequately represented by appropriate subframes similar to those used in conventional structural design. Subframes Ohosen were capab1e Of representing the behaviour of the beams and columns in the area of interest without introducing unrealistic conditions or restraint. Only when it is obvious that the beam or the wiumn behaviour dominates, were individual elements considered in isolation to quantify the behaviour ofthe whole frame. Overall results ofthis study showed that failure in most cases was precipitated by the columns. Indicative study for frames with protected columns demonstrated a contrast behaviour to the above observation, therefore, it was highly recommended to cover all possibilities in the choice of subframes. Boundary conditions that caused artificial restraint to axial thermal expansion were avoided. Subframe models were consistent and reliable in predicting failure temperature. However, they were less reliable in predicting internal forces in beams. . . British Research Establishment 1341. This study described a finite element computer program for studying the structural behaviour o f steel frames at elevated temperatures. Structures Analyzed: 2-D one-bay sway at ambient temperature [35]. 3-D column assemblage with beam-column connections tests at ambient temperature [36]. Three portal frames tested at elevated temperature [I61. A nonsway ponai frame tested at Cardington Laboratory 1371. . Steel Construction Institute and University of Shefield [38] Developmento f a computer program for both 2-D and 3-D analysis o f framed buildings under tire conditions is presented in this study. . Structures analyzed: Simply supported composite beams from hvo tests conducted in 1982 1391. 8-storey composite frame building from the Cardington tests on unprotected secondary beam at the seventh floor level ofthe building. . . . Objectives: To study the ways in which different boundary conditions to the 3-D subframe affect structural response predictions. To make Comparisonbetween the overall behaviour ofbuildings and single elements in tire. To develop the model to ensure that the software can be run on personal computer hardware, even for fairly large structures. Validation and Convergence Studies: . Convergence studies against classical theoretical solutions were carried out to test the bending and membrane characteristics o f shell elements included in the program (see next column). Validation ofthe program and convergence studies [29] on composite beams were conducted. . Analysis Technique: FEM Formulation: - Element type 2-node beam element with six degrees of freedom per node. Capabilities: Material and geometric nonlinearity were considered. Allowed for uniform and nonuniform temperature distributions across and dong elements cmsssection and length, respectively. • The inclusion o f the semi-rigid, beam-column connections were possible. Analysis Technique: . The average ratio o f predicted temperatures ofthe analysis to the test results of the portal frame of Ref. 1 161was 0.94 and the coeficient o f variation was 0.07. This, suggested by the authors, can be accepted as satisfactoty agreement. Comparison with the Cardington frame test, shows that the fire resistance ofthe rigid frame was about 12% lower than the test result. No explanation was given for the difference. The differences in the steel temperatures between the cardington test and the analysis were much smaller, because the steel temperatures in the later stage ofthe fire test increased slowly with time. . . . Comparison behveen overall structure behaviour and isolated FEM member behaviour indicated that the development of design metbods for tire safety o f structures ~ ltypes. ~ two.node~ beam ~ ~ tneeds to be redirected from its traditional emphasis on element and four-node shell isoiated member behaviour to element Ihe effect of conQePtsbasedOn local and concrete slab including membrane overall behaviour of the structure. Validation and convergence study Capabilities: on composite beams indicated that even very small numbers o f shell ~ l l o w for s the positioning ofthe elements produced accurate reference axis and location of solutions with the program. beam at Point The tests and the computer model on or outside the beam crossresults was that the structure Section, surrounding a tire zone had a Aliows the inclusion of non-iinear mBjor influence on the spring elements to represent semiperformance of the directly heated rigid connectioncharacteristics. elements. I ~ c ofI sheo u elements ~ ~ ~ that ~ The effect of slabs was the behaviour o f the floor slab particularly important in providing be re!Jresented (i.e., continuity in its own plane and membrane action of the supported againstdeflection. slab be The continuity effect offered by the slabs not only provided support and reduced deflections but also caused considerable restraint to axial thermal expansion, which increased deflections. . . . . . 17 3.3.2 Japan Tokyo Institute of Technology, Yokohama 1131 Developed a general computer program for the analysis of large displacement elastoplastic thermal creep deformation in a fire compartment Structures analyzed: H cross-section steel beams with simple, hinged and built-in ends. Two steel frames: (i) Single-bay portal frame, fixed at base with loaded beam ( T Y P1). ~ (ii) Multt-storey rectangular frames -computation time reduced by assuming column ends hinged and free to displace longitudinally at the points 0.5 and 0.7 column length from the heated beam (Type 2). . Nagoya University and Sumitomo Heavy Industry, ~~k~~ [lo] Analysis Features ObjectivesIStudy Details Place [Ref.] Analysis Technique: . FEM . . Formulation: - Element type linear element (both I- and 2-D elements) Allows for material and geometric nonlinearities. . This study presented the evaluation ofthe strength of unprotected steel structures during and after fire. Analysis Technique: . • Structure analyzed: Formulation: . 2-D plane frame. . Objectives: To study the progress of deformation and reduction of strength of steel framed structure during fire. To study how the strength ofthe frame members are recovered after fire. To determine the length of strengthening plates, necessary for recovery ofthe initial strength aRer fire. . FEM The temperature distribution in the section of the steel frame members was by 2-D FEM Standard temperature-timecurve specification was according to fire resistance test [241. Heat transfer source to members were given by radiation and con~ection. Three-node seven degrees of freedom beam elements was adopted for the structural analysis potiion. . . Conclusions/Obse~ations Large difference in the vetiical midspan deflection between elastic-plastic and elastic-plasticcreep analyses of beams at 80 to 90 min offire exposure (approximately 450°C). For frame Type I, deformation of beam with small flexural rigidity follows that of the columns. because the columns which have large flexural rigidity deflect towards the inside of the fire wmparlment, inclusion of creep at fire temperatures exceeding 4509C is crucial especially for the beam cases. The strength of the frame structure during the fire decreases according to the increase in fire duration. This reaches only 43% ofthe pre-fire strength in the case of fire duration of 30 min. The structure can recover full initial strength (pie-fire) only when the duration of fire is less than 10 min. ,For a 30 fire duration, the reduction of post-fire strength compared to the pie-fire strength was up to 79%, By increasing the cross-sectional area of the centre part of the horizontal element (beam) of the frame structure the strength of the post-fire structure can be enhanced. . I8 3.3.3 Belgium Place [Ref ] ObjectivesIStudy Details University of Liege. Belgium, ERE and BST, US [I21 The study presented the results of a number of numerical simulations of the Cardington fire test on a full-size loaded mainly unprotected steel frame [i I]. Analysis Techniques: Objectives: Formulation: To show how the rewmmendations presented within the Eurocode [3,4] context can be applied in anumedcal model Ofthe frame behaviOur;and how the results provided by the numerical model compare with the fire test results [I I]. Analysis Features Finite difference method (FDM) for thermal analysis. FEM for structural analysis. Element type for structural two.node beam element. . Effect oflarge displacements were taken into account, stress.strain relationships and thermal strains of materials can be wnsidered. Conciusions/Obse~ations The numerical model simulated with reasonable agreement the thermal and structural behaviour of the steel frame tested at Cardington. With the exception of the local buckling of the beam that occurred at the moment of failure which could not be modelled using a beam element, the frame behaviour was accurately predicted up to the failure point. The yield strength at ambient temperature has a great influence on the fire resistance of the structure The behaviour of an isolated column and bean1 during tire is different from the behaviour of the frame as a whole. . . 3.3.4 USA American Iron and Steel institute [a, 141 Washington, DC Analysis Features ObjectivesIStudy Details Place [Ref,] . Structures analyzed: . Composite (steel and concrete) floor beams. Two-storey structural steel frame with concrete and steel deck floor slab. Portion of 42storey offlce building located on the West coast of the United States. . Objectives: * To predict fhe performance of structural steel framed floor systems underexposure to high temperature. To develop a design concept for structural fire endurance using wmputer models FIRES-T3 and FASBUS iI for thermal and structural analyses, respectiveiy. Analysis Technique: FEM . Fornulation: element type - elements to represent the frame, and triangular plate bending element to represent the slab were . . Capabilities: Geometric and material nonlinearities can be modelled. Temperature distribution across elements can be either uniform or nonuniform Effect ofthermal restraint by the slab on the elements can be modelled, Conciusions/Obse~ations The application of the model to an actual building has demonstrated its capability as a design tool. 19 3.3.5 The Netherlands Place [Ref,] ObjectivesIStudy Details Netherlands Organization for Applied Scientific ~~~~~~~hRIO [18,281 A theoretical analysis on the stability o f tire exposed steel frames is presented. Analysis technique: Structures analyzed: Formulation: steel beams, braced and unbraced steel frames Analysis Features FEM - Beam elements. Capabilities: Can handle nonlinearity for both geometry and material. 3.4 ConclusionsIObservations Theoretically determined critical temperatures in all cases were lower than the critical temperatures resulting fmm the experiments. The maximum deviation was IOO°C and the minimum was 25°C. In the case ofthe unbraced frames, the extent o f initial inclination ofthe frame had a significant effect on the critical temperature. I t was suggested by the authors that both theoretical and experimental analysis should be performed on the stability ofan unbraced frame loaded by additional horizontal forces. Summary Based on the literature survey presented, this section can be summarized as follows: The traditional approach of using standard fire tests on isolated members in rating buildings vrovides limited information on the actual verformance of a building durine exposure io fires. Full-scale fire testing is expensive and time consuming, however, it provides data over a range of fire scenarios in a real structure so that analytical/numerical models can - -- he - - tested. .-- -- -. Numerical modelling of steel behaviour in fire allows the effect of parameters such as continuity, restraint, and the membrane characteristics of a floor slab to be easily investigated. The overall behaviour of a structure in fire is significantlv different from that of a single element subjected to the same fire expos;re. - 4. COMPUTER PROGRAMS 4.1 General w Evaluation of structural fire resistance based on the overall structural behaviour of steel framed buildings has become a practical reality with advancements in computer technology. Initially, the fire resistance of a structure was determined based on a standard fire test of a single element in a furnace. These test procedures have several shortcomings including the size of the element, available loading capacities, and the restraint characteristics. These problems can be solved by conducting full-scale tests on complete frames. However, such tests are expensive, time consuming and difficult to perform, especially on complete structures. Considerable progress has been made in the development of simple analytical models for the evaluation of fire resistance of elements, and fire resistance can now be estimated using these simplified calculation models. However, these models do not apply to all cases and have severe limitations when more parameters have to be taken into consideration in order to simulate real situations. During the last decade or so, there has been considerable progress in the development of computer programs to predict the overall response of structures in fire [8, 14, 18,28, 33,401. These new models are now making it possible to analyze different kinds of structures under realistic fire exposure conditions. Unlike the traditional fire test methods and empirically derived calculation solutions, the numerical models are now providing solutions considerably closer to reality. 4.2 Development of Computer Programs There have been a number of computer programs developed in recent years aimed at modelling the behaviour of frame structures in fire. The most ceneral and vcrsatilc approach isbased on the finite element method (thermal and stru&ral analysis). Using this method, various factors affecting the behaviour of structures in fire have been modelled (for example, nonlinear material behaviour, geometrical nonlinearity, nonuniform temperature distributions and thermal strains). The main advantage of the method is that it enables the behaviour of complicated structures to be studied. There are a few computer programs with thermal analysis formulations based on the finite difference method. The majority of these programs model two-dimensional behaviour. Recently, computer programs capable of full three-dimensional analysis of frames, which can take into account composite action, the effects of slabs and other panels and rotational stiffness of connections, have been developed. Some of these computer programs and their salient features are presented in the table below. Salient Features Name and Reference CEFlCOSS (computergngineering of the ~i~ resistance f o r ~ m p o s i t e and Steel Structures) Schleich, J.B. ABED, Luxembourg 1411 . Type of Analysis: Thermal and Structural Analysis Formulations: Thermal analysis by finite difference method (FDM). Stmctural analysis by FEM Element type - two-node beam elements. . Types of structures that can be analyzed: Single element - columns and beams (steel or concrete) with or without protection. 2- and 3-D composite or nonwmposite frames. . . Capabilities: Allows for geometric and material nonlinearities. Allows for strain hardening effect to be included. Evaporation of moisture in wncrete can be accounted for. Cooling effect alongside structural elements as well as real end conditions can be simulated. Can be used on personal computers (PC) and workstations. . Limitations: Creep cannot be considered implicitly. No graphics and post processing capabilities. Applications For columns, beams and frames of any of the following: a) Bare steel profiles b) Steel sections protected by any type of insulation; and C) Any type ofcomposite stee,.concrete cross. section TWOframe tests results were sirnulaled using the program. TASEF-2 (Temperature Analysis of SlructuresExposed t o l r e 2-D Version) - - Wickstrom U. Lund Institute of Technology. Sweden [42] Type ofAnalysis: Only thermal analysis Formulations: FEM Element type four-node rectangular element - Validation: TASEF-2 used to analyze square plates subjected to heat transfer from surrounding gas and compared to analytical solutions. Steel beams embedded i n concrete. Wide flange I-beam. Steel box-girder embedded in concrete. Types of structures that can be analyzed: Steel, concrete or composite (steel and concrete) structures .. . Capabilities: Allows for nonlinear boundary conditions. Dependency o f material properties on temperature considered. Heat transfer by convection and radiation hetween enclosed surfaces in structures with voids can be considered. Material propertics including thermal conductivity Has mesh generation capability. Can he used an I'Cs and workstations Can also accept I-and 3-D elements. Has the capability o f mesh generation. . . . . Limitations: Good accuracy was not possible for concrete temperature because the influence of mass transfer o f water is not considered. No graphics and post-processing capabilities. FIREST3 @re Esponse o f - Structures Thermal -2 Dimensional Version) Iding. R.. Bresler, B. and Nizamuddin. Z. University o f California, Berkeley. USA [43] Type ofAnalysis: Only thermal analysis Formulations: FEM Element types Four-node hexahedron and six-node (degenerated hexahedron) 3-D elements. I-and 2-D elements can also be handled. - Types o f structures that can be analyzed: Steel, concrete or composite (steel and concrete) structures. Capabilities: Allows for nonlinear characteristics of thermal properties ofmaterial. Allows for heat transfer fmm the fire to the environment. Allows for any form offire exposure curve (i.e., constant temperature, linear change, ASTM E l 19 or natural burning) Can be used on PCs and mainframes. . . . Limitations: Cannot model heat transfer through cavities i n an assembly. Contains no post-processing and graphic capabilities. . Program has been validated against a variety o f structural problems i n lire . Predictio~~s have been made of heat transfer through steel beams with direct applied fire protection material using the program. SAFlR Franssen. J.M. University o f Liegc. Belgium 1441 Type ofAnalysis: Heat transfer and structural analysis Formulations: Present application: Protected or unprotected steel structures. Commercial/industriaI applications: . FEM Element types: triangular and quadrilateral elements for plane sections, solid elements with 6 or 8 nodes for 3-D structures Types o f structures that can be analyzed: Plane sections and 3 - 0 structures. . . Capabilities: Allows for variable materials. Properties and evaporation o f moisture allowed. Allows for material and geometric nonlinearitics. Effect ofthermal strains can be considered. Allows for loading reversal. Allows for prescribed displacenient. Allows for skewed external supports. Residual stresses can be included. Prestressed structures can be analyzed Automatic adaptation o f time step is possible. Calculation can proceed until failure. Can be adapted to give results in a format compatible with commercial software such as IDEAS, etc. Automatic mesh generation capabilities. .. . Fire resistance of T steel profiles protected by intumescent insulation Tliermal protection of sandwich steel wall. Concrete under temperature variation Fire resistance o f steel frames. . Current developments: . Introduction o f shell elements. Introduction o f plane stress and 3-D plasticity material. European Community sponsored Research (SAFIR used): . . Buckling curves o f hot rolled H sections. Design rules for steel structures in natural fires in closed car parks. Design rules for steel structures In natural fires in large compartments. Steel buildings through tire safety concept. Limitations: No post-processingand graphic capabilities. FASBUS I 1 (Fire Analysis o f -Steel @ildingSystems) Chiapetta. R.. Iding. R.H. and Bresler. B.. Illinois fnstitute o f Technology and American Iron and Steel Institute. USA [45] Type o f Analysis: Structural analysis only . FEM Element types beam and triangular plate bending elements for frame and slab. respectively. - Types ofstructures that can be analyzed: Steel frame floor system. Skeletal and composite steel frames. . . Capabilities: Geometty and arrangement of structural elements. Allows for changes in material properties. Allows for application o f loads and restraining conditions. Allows for temperature profile and distribution in the structural membea as a result o f the fire exposure. Can be run on PCs. .. Limitations: N o graphic or post-processing capabilities Can only handle problems with 99 nodes, 180 elements (beam and slab) and 150 time steps. FASBUS was validated against a test conducted by the National institute of Standards and Technology (formerly the National Bureau o f Standards) and the American Steel lnstitute [46] on two-storey four-bay structural steel frame with a concrete and steel deck floor slab. Structural steel beams with concrete slabs formed over steel deck (composite and noncomposite design). STABRA (Sl'Anil voor BRAnd: STANlL for fire) Kerstma. J.. Biilaard. F.S.K. and Twill. I...Institute TNO fbr Building Materials and Building Structures. Delft. The Netllerlands (401 Type o f Analysis: Thermal and structural analysis Formulations: . Validation: With the help o f STANST 1281. a comparison was made between theoretical analysis and the experiments presented i n Ref. [18]. FEM Element type Beam element - . Types o f structures that can he analyzed: 2-D frame structures Capabilities: Allows for material and geometric nonlinearities. Creep included in stressstrain relationship, Allows for nonuniform distribution o f temperatures. Can be run on PCs. . - Limitation: 3DFIRE N a ~ aS.R r and Burgess I.W. University ofShefiield.. UK 1261 Influence o f thermal expansion not taken into account . Type of Analysis: The program was validated against a range of previous analyses including: Thermal and structural analysis Formulations: FEM Element type two-node I - D element. - Types o f structures that can be analyzed: 2- and 3-D frames. Capabilities: Allows for geometric and material nanlinearities, including changes in material properties with change In temperature Temperature distribution across members can he uniform or nonuniform Can be used on PCs. Limitations: No graphics or post-processing capabilities. Cannot model effect o f composite action. Large-deflection elastic, inelastic analyses (ambient temperature). Full fire analysis of2-D frame structures. Local analysis o f mufti-storey column subframes in various fire scenarios. ALGOR Type o f Analysis: ALGOR, INC. Pittsburgh. PA, USA [47] Thennal and structural analysis (call also handle nonstruclural problena). The program was for a variety o f small and large structural temperatures, problems under ambient and Note: This is a general purpose cammercial program. Formulations: - FEM Element types: I-.2- and 3-D elements with linear nodes along each side. Types of structures that can be analyzed: I-.2- and 3-D structures, including frame (plane and space). shell, plane stress and plane strain structures. Capabilities: Allows for steady and transient heat transfer analyses. Geometric and material noniinearities can be modelled. Ambient and elevated temperature problems (structural and nonstructural) can he handled Allows for residual stress. Can be run on PCs or workstations. Can be run interactively or in a batch mode. Has graphics and post-processing capabilities Has automatic mesh generation capability . ARAQlJS Hihbit. Karlsson & Sorensen, Inc.. USA [48] . . 'Type o f Analysis: Thermal and structural prohlems, including nonstructural problems. Formulations: FEM Element types: I-.2- and 3-D elements. including axisymmetric elements. All the elements are available in linear, quadratic and cubic formuiations. . Types ofstructures that can be analyzed: I-.2- and 3-D structures. including frame (plane and space). shell. plane stress and plane strain structures. Capabilities: Geometric and material nonlinearity . s Material can vary from one element to another. Prescribed displacements. Isotropic, onhotropic or fully anisotropic conductivity. Latent heat for hear rransfer prohlrrns involving phase change. Specific heat far transient heat transfer analysis Can be run interactively or i n a batch mode. Excellent post-processing and graphics capabilities. Contains subroutines for different applications which can be modified by experienced users for some specific problems. . .. Program was validated on a large number of problems which include: . Structures (concrete and steel) at ambient and elevated temperatures. . Limitations: No CAD capability for mesh generation. Program requires an input file to accomplish this. Can only be run on mainframes. Research and development work continues in different sectors in making better utilization of computer generated solutions with the aim of eventually providing the structural design engineer with solutions based on sound scientific and engineering practice to handle the design of structures for fire. 4.3 Summary The use of computer programs to evaluate the behaviour of structural steel in fire is now becoming popular among structural design engineers. Information on the computer programs that deal with this subject is presented in this section. Based on this information, the following can be derived: The overall structural behaviour of structures when exposed to fire is now a practical reality with computer programs. The influence of many parameters that affect the fire resistance of steel structures, such as membrane or bridging action of the floor slab, continuity of support, connection types, etc. can now be modelled with ease using computer programs. Computer programs based on the finite element method are the most versatile techniques to model complicated problems such as those encountered in the study of the overall behaviour of unprotected and protected steel frames exposed to fire. 5. CONCLUDING REMARKS The introduction of steel as an important building material, the behaviour of steel structures in fire and a literature survey on research activities on the behaviour of steel structures in fire are presented in this report. The literature survey focused mainly on overall structures rather than single element behaviour in fire. Both an experimental and theoretical literature survey were presented. Based on the information presented in this report, the following concluding remarks can be made: 1. 2. 3. 4. 5. 6. Steel compares favourably with other building materials because of the cheap material costs, fast erection sequences and lighter foundation requirements. Steel structures will lose their stiffnesses and strengths when exposed to fire due to deterioration in the material property. The problem of rapid increase of temperature in steel when exposed to fire is usually solved by providing protection to steel structures with an insulating material, thus delaying the temperature increase in the steel. The fire resistance of a complete structure is entirely different from the fire resistance of a single structural element. The failure of some structural steel elements in a fire will not endanger the safety of a complete steel framed building, if the rest of the structure can develop an alternative load path to bridge the failed elements. Membrane action from the reinforced concrete slab in steel framed composite structures is the primary mechanism that accounts for the stability of structural 7. 8. 9. 10. 1I . 12. elements at large deflections and for providing an alternative load path after the failure of some structural elements. The behaviour of three-dimensional steel frames in fire can be investigated by using two-dimensional subframes if the frame is subjected to vertical loads. The subframes chosen for investigation, however, must reflect the behaviour of beams and columns in the area of interest without introducing unrealistic conditions or restraints. Isolated elements can be used to quantify the behaviour of a whole frame in fire when it is obvious that the condition of the beam or column in the frame dominates. Various factors affecting the behaviour of structures in fire conditions that proved difficult and complex to investigate using experimental techniques, can now be investigated using computer programs. The finite element method is the most general and versatile numerical method for investigating various factors (e.g. non-linear material behaviour, geometric nonlinearity, nonuniform temperature distributions and thermal strains) affecting the behaviour of structures in fire conditions. Structures surrounding a fire zone have a major influence on the performance of the directly heated elements. Factors such as continuity, element interactions, types of connections, sprinklers, load ratio, restraint condition and temperature distribution will affect the performance of a structure in fire. Finally, the application of computer models to overall behaviour of steel structures in fire have demonstrated their value as sound engineering tools. Continued development in this direction will make it possible to use the models to identify and evaluate different parameters. The most significant of the parameters will then be used to develop an optimum design of structures for fire. It is, therefore, anticipated that the design of a structure to withstand fire will eventually become a routine part of structural design of building frames. 6. REFERENCES 1. BS5950: Part 8, "Structural Use of Steelwork in Building", Part 8. Code of Practice for Fire Resistant Design, British Standards Institution, London 1990. 2. Lawson, R.M. and Newman, G.M. "Fire-resistant Design of Steel Structures" - A Handbook to BS5950: Part 8, Steel Construction Institute, Ascot, UK, 1990. 3. Eurocode 3, "Design of Steel Structures", Part 10: Structural Fire Design (Draft) Commission of the European Communities, 1990. 4. Eurocode 4, "Design of Composite Structures", Part 10: Structural Fire Design (Draft) Commission of the European Communities, 1990. 5. National Building Code of Canada, "Supplement to the National Building Code of Canada", Association Committee on the National Building Code, National Research Council of Canada, 1990. 6. Witteveen, J., "Some Aspects with regards to the Behaviour and the Calculation of Steel in Fire", Proceedings of Symposium held at the Fire Research Station, Paper No. 6, 1967, pp. 66-75. 7. Malhotra, H.L. "Design - of Fire-Resistance Structures", Surrey University Press, 1982. 8. Jeanes, D.C. "Developing Design Concepts for Structural Fire Endurance Using Computer Models", Design of Structures Against Fire, Edited by R.D. Anchor, H.L. Malhotra and J.A. Purkiss, 1986, pp. 127-154 9. Fleming, R.P. "Automatic Sprinkler System Calculation", SFPE Handbook of Fire Protection Engineering, Section 4, Chapter 3, NFPA Publication, Quincy, MA, 1995. ~ - 11. Cooke, G.M.E. and Latham, D.J., "The Inherent Fire Resistance of a Loaded Steel Framework", Steel Construction Today, Vol. I, 1987, pp. 49-58. 12. Franssen, J.M., Cooke, G.M.E. and Latham, D.J. "Numerical Simulation of Full Scale Fire Test on a Loaded Steel Framework", Journal of Constructional Steel Research, Vol. 35, No. 3, 1995, pp. 377-408. 13. Fununura, F. and Shinohara, Y. "Inelastic Behaviour of Protected Steel Beams and Frames in Fire", Report of the Research Laboratory of Engineering Materials, No. 3, Tokyo, 1978. 14. Jeanes, D.C. "Application of the Computer in Modelling Fire Endurance of Structural Steel Floor System", Fire Safety Journal, Vol. 9, 1985, pp. 119-135. 15. Latham, D.J., Kirby, B.R. and Thomas, G. "The Temperatures Attained by Unprotected Structural Steelwork in Experimental Natural Fires", Fire Safety Journal, Vol. 12, No. 2, 1987, pp. 139-152. 16. Rubert, A. and Schaumann, P. "Structural Steel and Plane Frame Assemblies Under Fire Action", Fire Safety Journal, Vol. 10, No. 3, 1986, pp. 173-184. 17. Thomas, I.R., Bennetts, I.D., Dayamansa, P., Proe, D.J. and Lewins, R.R., "Fire Tests of the 140 William Street Office Building", Report No. BHPR/ENGl92/043lSG2C, Australia, Feb. 1992. 18. Witteveen, J., Twilt, L. and Foss, G., Orientational Small-scale Model Tests on the Stability of Braced and Unbraced Frames at Elevated Temperatures", TNO-IBBC, Report BI-74-26105.3.14.6.21, 1974. 19. Thomas, I.R., Bennetts, I.D., Poon, S.L. and Sims, J.A.., "The Effect of Fire in Building at 140 William Street - A Risk Assessment", Report No. BHPR/ENG/9210441SG2C, Australia, Feb. 1992. 20. Lennon, T. "Large Compartment Fire Tests", Second Cardington Conference, UK, 1996. .. . .. 21. Moore, D.B. "Full-scale Fire Tests on Complete Building", Second Natural Fire Tests, Cardington Conference, UK, 1996. 22. Sakumoto, Y. and Saito, H. "Fire-safe Design of Modem Steel Buildings in Japan", Journal of Constructional Steel Research, Vol. 33, 1995, up. 101-123. 23. Kirby, B.R. "British Steel Technical ~ u r o ~ e aire n ~ e sProgram t - Design, Construction and Results", Second Cardington Conference, UK, 1996. 24. BS467: "Fire Tests on Building Materials and Structures", British Standards Institution, London 1972. 25. Japanese Standard Association, "Method of Fire Resistance Tests for Structural Parts of Buildings", Japanese Industrial Handbook, JIS A 1304, 1975, pp. 335-339. 26. Najjar, S.R. and Burgess, I.W. "A Nonlinear Analysis for Three-dimensional Steel Frames in Fire Conditions". Engineering Structures, Vol. 18. No. 1. 1996. vv. 77-89. n ~ ~ r a m ~el;avio& e ~nder'~ire 27. Saab, H.A. and Nethercot, i ) . ~ ? ~ o d e f l i Steel Conditions", Engineering Structures, Vol. 13, No. 4, 1991, pp. 371-382. 28. Witteveen, J., van Douwen, A.A., Twilt, L. and Biljaard, F.S.K., "On the Stability of Fire Exposed Steel Frames", TNO-IBBC, Report BI-76-7125.3.3 13320, 1976. 29. Bailey, C.G. , Burgess, I.W. and Plank, R.J., "The Behaviour of Steel Framed Structures Subjected to Local Conditions", Proc. Nordic Steel Construction 95.-Malmo. Sweden. 1995. Sweden Institute of Steel Construction. Conference - .. . .. .. . '~ , Publication 150, Vol. 1 1 , ' ~693-700. ~. ' 30. Wang, Y.C., Lennon, T. and Moore, D.B., "The Behaviour of Steel Frames Subjected to Fire", Journal of Constructional Steel Research, Vol. 35, No. 3, 1995, pp. 391-322. 3 1. El-Zanaty, M. and Murray, D.W. "Nonlinear Analysis of Steel Frame", ASCE Journal of Structural Division, Vol. 109, No. ST2, 1983, pp. 353-368 32. Wang, Y.C. and Lennon, T., "Computer Program for Structural Analysis at Elevated Temperatures", Building Research Establishment, Client Report 77/92. -- - ~ 32. Wang, Y.C. and Lennon, T., "Computer Program for Structural Analysis at Elevated Temperatures", Building Research Establishment, Client Report 77/92. 33. El-Rimawi, J.A., "NARR2: A Program for the Structural Analysis of 2-D Frames at Elevated Temperatures", Research Report, University of Sheffield, Department of Civil Engineering. Jan. 1993 34. Wang, YC : . and koore, D.B. "Steel Frames in Fire: Analysis", Engineering Structures, Vol. 17, No. 6, 1995, pp. 462-472 35. Arnold, P., Adams, P. and Lu, Le-Wu, "Strength and Behaviour of an Elastic Hybrid Frame", ASCE, Journal of Structural Division, Vol. 94, No. STl, 1968, pp. 243-266. 36. Gibbons, C. "The Strength of Biaxially Loaded Beam-column in Flexibly Connected Steel Frames", Ph. D. Thesis, Department of Civil Engineering, University of Sheffield, UK, 1990. 37. Latham, D.J., Thomson, G., Kirby, B.R. and Wainman, D.E. "Second Natural Fire Test on a Steel Loaded Steel Frame at Cardington, RS/RSC/7281/12186/E, Swindon Laboratories, British Steel Corporation, UK, 1986. 38. Bailey, C.G:, Burgess, I.W. and Plank, R.J., "Computer Simulation of a Full-scale Structural Fire Test", The Structural Engineer, Vol. 74, No. 6, 1996, pp. 93-100. 39. Wainrnan, D.E. and Kirby, B.R., "Compendium of UK Standard Fire Test Data on Unprotected Structural Steel", Vol. 1, Ref. No. RSIRSCIS10328/1/87/B and Vol. 2. Ref. No. RS/R/S11199/88/B, British Steel Corporation, Swindon Laboratories, UK, 1987 and 1988. 40. Kerstma, J., Bijlaard, F.S.K. and Twilt, L. "A Computer Program for the Analysis of the Fire Exposed Steel Structures", Report No. BI-77-72105.3.3 1320, TNO, Netherlands. ~ ~ ~ 1976. ~ ~ ~ ~ ~ ~ , 41. Schleich, J.B., "CEFICOSS - Computer Engineering of the Fire Resistance for Composite and Steel Structures", Repon No. EUR10828, ABED, I.u?tembourg, ~ 19x5 A,--. 42. Wickstrom, U., "TASEF-2 - A Computer Program for Temperature Analysis of Structures Exposed to Fire", Report No. 79-2, Lund Institute of Technology, Lund, Sweden, 1979. 43. Iding, R., Bresler, B. and Nizamuddin, Z., "FIRES-T3 - A Computer Program for the Fire Response of Structures - Thermal - Three-Dimensional Version", Report No. UBC FRG 77-15, University of California, Berkeley, USA, 1977. 44. Franssen, J.M., "SAFIR Version 1.3", University of Liege, Belgium, 1996. 45. Chiapetta, R.L., Iding, R. and Bresler, B., "FASBUS I1 -Fire Analysis of Steel Building Systems", Report IITRI, Project 58095, Chicago, IL, USA, 1972. 46. Jeanes, D.C, "Predicting Fire Endurance of Steel Structures", Preprint 82-033, American Society of Civil Engineers, ASCE Convention, 1982. 47. Algor Inc., "Algor User Manual and Release Notes", Pittsburgh, PA, USA, 1993. 48. Hibbitt, Karlson and Sorensen Inc., "ABAQUS User Manual", Version 5.4, Pawtucket, Rl,USA, 1994. (a) Simply Supported beam [6] (b) Continuous beam [6] L~.fan fln (c) Effect of fire on moment distribution in restrained beams [7] FIG. 1. Behaviour of Beams in Fire FIG. 2. Moment Distribution in a Steel Frame Exposed to Fire [7] FIG. 3. Response of Structural Building Frame to Fire [8] - FIG. 4. Plan of 2nd 3rd Floor of Eight-Storey Building at the Cardington Large Building Test Facility (LBTF) [21] m 0) C w In UQ171a1UB 61~h101U8 I U) D i #-O 1 ' I R Fixed bases 7x3000mm FIG.5. Section Through the Cardington Frame including Fire Compartments Studied [33]