Fundamentalprinciplesofstructuralbehaviour …

1 Fire Safety Journal 36 (2001) 721 744 Fundamental principles of structural behaviourunder thermal Usmani*, Rotter, S. Lamont, Sanad, M. GillieSchool of Civil and Environmental Engineering, University of Edinburgh, Crew Building,The King s Buildings, Edinburgh EH9 3JN, UKReceived 10 July 2000; received in revised form 15 December 2000; accepted 22 March 2001 AbstractThis paper presents theoretical descriptions of the key phenomena that govern thebehaviour of composite framed structures in fire. These descriptions have been developed inparallel with large scale computational work undertaken as a part of a research project (TheDETR-PIT Project, Behaviour of steel framed structures under fire conditions) to model thefull-scale fire tests on a composite steel framed structure at Cardington (UK). Behaviour ofcomposite structures in fire has long been understood to be dominated by the effects ofstrength loss caused by thermal degradation, and that large deflections and runaway resultingfrom the action of imposed loading on a weakened structure.

2 Thus strength and loads arequite generally believed to be the key factors determining structural response (fundamentallyno different from ambient behaviour). The new understanding produced from theaforementioned project is that, composite framed structures of the type tested at Cardingtonpossess enormous reserves of strength through adopting large displacement , it is the thermally induced forces and displacements, and not materialdegradation that govern the structural response in fire. Degradation (such as steel yielding andbuckling) can even be helpful in developing the large displacement load carrying modes , of course, is only true until just before failure when material degradation and loads beginto dominate the behaviour once again. However, because no clear failures of compositestructures such as the Cardington frame have been seen, it is not clear how far these structuresare from failure in a given fire. This paper attempts to lay down some of the most importantand fundamental principles that govern the behaviour of composite frame structures in fire ina simple and comprehensible manner.

3 This is based upon the analysis of the response of single*Corresponding author. Tel.: +44-131-650-5789; fax: + ( Usmani).0379-7112/01/$ - see front matterr2001 Elsevier Science Ltd. All rights : S 0 3 7 9 -7112(01)00037-6structural elements under a combination of thermal actions and end restraints representing thesurrounding Elsevier Science Ltd. All rights :Composite structures; Thermal expansion; Thermal bowing; Restraint to thermal actions;Non-linear geometrical responses1. IntroductionThis paper is based upon work undertaken as a part of a large multi-organisationproject of modelling the behaviour of steel framed structures in fire [1] (namelythe full-scale tests at Cardington [2]). In executing this project and identifying the keygoverning phenomena it was found necessary to make use of the fundamentalprinciples repeatedly in order to understand the complex interactions of the differentstructural mechanisms taking place. This led to the development of a number ofimportant principles that were found to govern the overall behaviour of thestructure.

4 These principles are very useful in interpreting the results from muchlarger and sophisticated computational models and in helping to develop a coherentpicture of the behaviour. Most of these ideas have already been presented at theINTERFLAM [3] and SiF [4] work was undertaken because the assessment of the adequacy of compositesteel frame structures in fire continues to be based upon the performance of isolatedelements in standard furnace tests. This is despite the widespread acceptanceamongst structural engineers that such an approach is over-conservative and evenmore importantlyunscientific. This view has gained considerable strength in theaftermath of the Broadgate fire [5] and has been reinforced by the Cardington codes such as BS 5950 Part 8 and EC3 (draft) allow designers to takeadvantage of the most recent developments in the field by treating fire-relatedloading as another limit state. The advances in understanding structural behaviour infire achieved in the last few years have been considerable with a large number ofgroups across Europe undertaking extensive research projects and concentrating ona number of different aspects of structural behaviour in fire [6 9].

5 These advancescombined with the findings of the DETR-PIT project [1] make it possible forengineers to treat the design for fire in an integrated manner with the design of astructure for all other types of loading. This can be done by using the numericalmodelling tools that have been instrumental in developing this , the use of such tools, which are indispensable for research, is not practicalin the design office. Exploitation of the new knowledge can only become feasible inpractice if the understanding generated is further developed into simpler analyticalexpressions, enabling consulting engineers and designers to undertake performance-based design of steel frame structures without having to resort to large scalecomputation. The principles presented here constitute a step towards generating theanalytical tools necessary for such analytical expressions developed in this paper have been developed ab initiofrom fundamental structural mechanics. The most fundamental relationship Usmani et al.

6 / Fire Safety Journal 36 (2001) 721 744722governs the behaviour of structures when subjected to thermal effects isetotal ethermal emechanicalwithemechanical-sandetotal-d: 1 The total strains govern the deformed shape of the structuredthrough kinematic orcompatibility considerations. By contrast, the stress state in the structures(elastic orplastic) depends only on the mechanical strains. Where the thermal strains are free todevelop in an unrestricted manner, there are no external loads, axial expansion orthermal bowing results frometotal ethermalandetotal-d: 2 By contrast, where the thermal strains are fully restrained without external loads,thermal stresses and plastification result from0 ethermal emechanicalwithemechanical-s: 3 The single most important factor that determines a real structure response to heatingis the manner in which it responds to the unavoidable thermal strains induced in itsmembers through heating. These strains take the form of thermal expansion to anincreased length (under an average centroidal temperature rise) and curvature(induced by a temperature gradient through the section depth).

7 If the structure hasan insufficient end translational restraint to thermal expansion, the considerablestrains are taken up in expansive displacements, producing a displacement-dominated response. Thermal gradients induce curvature leading to bowing of amember whose ends are free to rotate, again producing large displacements(deflections).Members whose ends are restrained against translation produce opposingmechanical strains to thermal expansion strains and therefore large compressivestresses (see Eq. (1)). Curvature strains induced by the thermal gradient in memberswhose ends are rotationally restrained can lead to large hogging (negative) bendingmoments throughout the length of the member without deflection. The effect ofinduced curvature in members whose ends are rotationally unrestrained, buttranslationally restrained, is to produce , for the same deflection in a structural member, a large variety of stressstates can exist, large compressions where restrained thermal expansion is dominantand very low stresses where the expansion and bowing effects balance each other;in the cases where thermal bowing dominates, tension occurs in laterally restrainedand rotationally unrestrained members, while large hogging moments occur inrotationally restrained members.

8 The variety of responses can indeed exist in realstructures if one imagines the different types of fire a structure may be subjected to. Afast burning fire that reaches flashover and high temperatures quickly and then diesoff can produce high thermal gradients (hot steel and relatively cold concrete) butlower mean temperatures. By contrast, a slow fire that reaches only modesttemperatures but burns for a long time could produce considerably higher meantemperature and lower thermal Usmani et al. / Fire Safety Journal 36 (2001) 721 744723 Most situations in real structures under fire have a complex mix of mechanicalstrains due to applied loading and mechanical strains due to restrained thermalexpansion. These lead to combined mechanical strains which often far exceed theyield values, resulting in extensive plastification. The deflections of the structure, bycontrast, depend only on the total strains, so these may be quite small where highrestraint exists, but they are associated with extensive plastic straining.

9 Alternatively,where less restraint exists, larger deflections may develop, but with a lesser demandfor plastic straining and hence a lesser destruction of the stiffness properties of thematerials. These relationships, which indicate that larger deflections may reducematerial damage and correspond to higher stiffnesses, or that restraint may lead tosmaller deflections with lower stiffnesses, can produce structural situations whichappear to be quite counter-intuitive if viewed from a conventional (ambient)structural engineering ideas presented above will be more formally explored in the following sectionsin the context of simple structural configurations and analytical expressions will bedeveloped for many cases of fundamental Thermal expansionHeating induces thermal expansion strains (sayeT) in most structural are given byeT aDT: 4 If a uniform temperature rise,DT;is applied to a simply supported beam withoutaxial restraint, the result will simply be an expansion or increase in length oflaDTasshown in Fig.

10 1. Therefore the total strain (sayet) is equal to the thermal strain andthere is no mechanical strain (sayem) which means that no stresses develop in Thermal expansion against rigid lateral restraintsClearly, beams in real structure do not have the freedom to elongate in the mannerdescribed above. Therefore, a more realistic case is to consider an axially restrainedbeam subjected to a uniform temperature rise,DT(as shown in Fig. 2). It is clear tosee that in this case the total strainetis zero (no displacements). This is because theFig. 1. Uniform heating of a simply supported Usmani et al. / Fire Safety Journal 36 (2001) 721 744724thermal expansion is cancelled out by equal and opposite contraction caused by therestraining forceP( eT em 0 thereforeeT em). There now exists auniform axial stresssin the beam equal toEem:The magnitude of the restrainingforcePis,P EAem EAeT EAaDT:If the temperature is allowed to rise indefinitely, then there will be two basicresponses, depending upon the slenderness of the beam:1.