اصول اساسی رفتار سازه تحت اثرات حرارتی

This paper presents theoretical descriptions of the key phenomena that govern the behaviour of composite framed structures in fire. These descriptions have been developed in parallel with large scale computational work undertaken as a part of a research project (The DETR-PIT Project, Behaviour of steel framed structures under fire conditions) to model the full-scale fire tests on a composite steel framed structure at Cardington (UK). Behaviour of composite structures in fire has long been understood to be dominated by the effects of strength loss caused by thermal degradation, and that large deflections and runaway resulting from the action of imposed loading on a ‘weakened’ structure. Thus ‘strength’ and ‘loads’ are quite generally believed to be the key factors determining structural response (fundamentally no different from ambient behaviour). The new understanding produced from the aforementioned project is that, composite framed structures of the type tested at Cardington possess enormous reserves of strength through adopting large displacement configurations. Furthermore, it is the thermally induced forces and displacements, and not material degradation that govern the structural response in fire. Degradation (such as steel yielding and buckling) can even be helpful in developing the large displacement load carrying modes safely. This, of course, is only true until just before failure when material degradation and loads begin to dominate the behaviour once again. However, because no clear failures of composite structures such as the Cardington frame have been seen, it is not clear how far these structures are from failure in a given fire. This paper attempts to lay down some of the most important and fundamental principles that govern the behaviour of composite frame structures in fire in a simple and comprehensible manner. This is based upon the analysis of the response of single structural elements under a combination of thermal actions and end restraints representing the surrounding structure.

This paper is based upon work undertaken as a part of a large multi-organisation project of modelling the behaviour of steel framed structures in fire [1] (namely the full-scale tests at Cardington [2]). In executing this project and identifying the key governing phenomena it was found necessary to make use of the fundamental principles repeatedly in order to understand the complex interactions of the different structural mechanisms taking place. This led to the development of a number of important principles that were found to govern the overall behaviour of the structure. These principles are very useful in interpreting the results from much larger and sophisticated computational models and in helping to develop a coherent picture of the behaviour. Most of these ideas have already been presented at the INTERFLAM [3] and SiF [4] conferences. This work was undertaken because the assessment of the adequacy of composite steel frame structures in fire continues to be based upon the performance of isolated elements in standard furnace tests. This is despite the widespread acceptance amongst structural engineers that such an approach is over-conservative and even more importantly unscientific. This view has gained considerable strength in the aftermath of the Broadgate fire [5] and has been reinforced by the Cardington tests. Current codes such as BS 5950 Part 8 and EC3 (draft) allow designers to take advantage of the most recent developments in the field by treating fire-related loading as another limit state. The advances in understanding structural behaviour in fire achieved in the last few years have been considerable with a large number of groups across Europe undertaking extensive research projects and concentrating on a number of different aspects of structural behaviour in fire [6], [7], [8] and [9]. These advances combined with the findings of the DETR-PIT project [1] make it possible for engineers to treat the design for fire in an integrated manner with the design of a structure for all other types of loading. This can be done by using the numerical modelling tools that have been instrumental in developing this understanding. However, the use of such tools, which are indispensable for research, is not practical in the design office. Exploitation of the new knowledge can only become feasible in practice if the understanding generated is further developed into simpler analytical expressions, enabling consulting engineers and designers to undertake performance-based design of steel frame structures without having to resort to large scale computation. The principles presented here constitute a step towards generating the analytical tools necessary for such use. All analytical expressions developed in this paper have been developed ab initio from fundamental structural mechanics. The most fundamental relationship that governs the behaviour of structures when subjected to thermal effects is with equation(1) The total strains govern the deformed shape of the structure δ through kinematic or compatibility considerations. By contrast, the stress state in the structure σ (elastic or plastic) depends only on the mechanical strains. Where the thermal strains are free to develop in an unrestricted manner, there are no external loads, axial expansion or thermal bowing results from equation(2) By contrast, where the thermal strains are fully restrained without external loads, thermal stresses and plastification result from equation(3) The single most important factor that determines a real structure response to heating is the manner in which it responds to the unavoidable thermal strains induced in its members through heating. These strains take the form of thermal expansion to an increased length (under an average centroidal temperature rise) and curvature (induced by a temperature gradient through the section depth). If the structure has an insufficient end translational restraint to thermal expansion, the considerable strains are taken up in expansive displacements, producing a displacement-dominated response. Thermal gradients induce curvature leading to bowing of a member whose ends are free to rotate, again producing large displacements (deflections). Members whose ends are restrained against translation produce opposing mechanical strains to thermal expansion strains and therefore large compressive stresses (see Eq. (1)). Curvature strains induced by the thermal gradient in members whose ends are rotationally restrained can lead to large hogging (negative) bending moments throughout the length of the member without deflection. The effect of induced curvature in members whose ends are rotationally unrestrained, but translationally restrained, is to produce tension. Therefore, for the same deflection in a structural member, a large variety of stress states can exist, large compressions where restrained thermal expansion is dominant and very low stresses where the expansion and bowing effects balance each other; in the cases where thermal bowing dominates, tension occurs in laterally restrained and rotationally unrestrained members, while large hogging moments occur in rotationally restrained members. The variety of responses can indeed exist in real structures if one imagines the different types of fire a structure may be subjected to. A fast burning fire that reaches flashover and high temperatures quickly and then dies off can produce high thermal gradients (hot steel and relatively cold concrete) but lower mean temperatures. By contrast, a slow fire that reaches only modest temperatures but burns for a long time could produce considerably higher mean temperature and lower thermal gradients. Most situations in real structures under fire have a complex mix of mechanical strains due to applied loading and mechanical strains due to restrained thermal expansion. These lead to combined mechanical strains which often far exceed the yield values, resulting in extensive plastification. The deflections of the structure, by contrast, depend only on the total strains, so these may be quite small where high restraint exists, but they are associated with extensive plastic straining. Alternatively, where less restraint exists, larger deflections may develop, but with a lesser demand for plastic straining and hence a lesser destruction of the stiffness properties of the materials. These relationships, which indicate that larger deflections may reduce material damage and correspond to higher stiffnesses, or that restraint may lead to smaller deflections with lower stiffnesses, can produce structural situations which appear to be quite counter-intuitive if viewed from a conventional (ambient) structural engineering perspective. The ideas presented above will be more formally explored in the following sections in the context of simple structural configurations and analytical expressions will be developed for many cases of fundamental importance.

It is now well recognised that contrary to popular belief, composite steel framed structures possess a much larger inherent fire resistance than that apparent from testing single steel members in fire furnaces. It is also accepted that the current prescriptive approaches of designing such structures are overly conservative and not based on rational principles. It is therefore possible to construct these strcutures much more economically, without any loss of fire resistance, by removing or drastically reducing the fire protection of steel members. However, to fully exploit the considerable reserves of strength, it is imperitive that the mechanics of whole steel frame structure behaviour in fire is understood well. The ideas presented in this paper are a step in this direction. The fundamental principles presented in this paper provide a means of estimating forces and displacements in real structures with appropriate idealisations. Such estimates can be of considerable use in assessing the results from more rigorous numerical analyses or they can be used in design calculations. There are, however, a considerable number of very important issues that remain to be investigated as mentioned in the previous section. Considerable effort is required to address these issues to satisfaction before a complete set of principles can be developed. Ref. [12] describes an early attempt at using these principles to model a real fire test with encouraging results and demonstrates the potential of such analyses. Further work is being carried out to put the ideas presented here to more rigorous testing.