Non-linear finite element analysis of steel frames in fire conditions
The present work is concerned with the development of a finite element approach and its subsequent use for behavioural studies on steel frames in fire conditions. The nonlinear structural analysis is based on a tangent stiffness formulation using large deformation theory. Deterioration in material strength and stiffness at increasing temperature is represented by a set of nonlinear stress-straintemperature relationships using a Ramberg-Osgood equation in which creep effects are implicitly included. The clearly nonlinear form of steel material properties at elevated temperatures is better represented as a set of continuous stressstrain relationship than in a bilinear form although provision is made for any form of relationship to be included. Structures subject to increasing loads or temperatures are analysed using an incremental Newton-Raphson iterative procedure. The analysis permits collapse load or critical temperature to be calculated at a specified temperature or load level respectively, and provides a complete load-deformation and temperature-deformation history for two-dimensional multistorey steel frames. A nonlinear method of frame analysis, based on largedeformation theory, has been used which includes the effect of geometric nonlinearity, temperature-dependent nonlinear material behaviour and variation in temperature distribution both along and across the section. The effects of thermal strains, residual stresses and thermal bowing are also included and different values of the elastic stiffnesses of the support conditions can be considered. A beam element with two nodes and three degrees of freedom at each node is used in the analysis. Gradual penetration of yielding through the cross-section is accounted for using the transformed area approach. The validity of this method is tested by comparing with experimental and analytical data covering as wide a range of problem parameters as possible. The comparisons show good agreement with this data. The method has been used to study a number of aspects of frame behaviour in fire. The influence of slenderness ratio, stress-strain representation and material models, various forms of protection, magnitude of residual stress and thermal gradient along and across the section of a frame are investigated. An approximate curve based on statistical analysis of the derived results is suggested as a simple means of predicting the critical temperature or collapse load of a uniformly heated steel frame. Further examples are presented which illustrate the special form of moment redistribution that occurs at elevated temperatures for frames that contain partially heated elements. Finally, general conclusions and recommendations for future work are presented.