A secant stiffness approach to the fire analysis of steel beams

Abstract At elevated temperatures the stress-strain characteristics of structural steels become non-linear and deteriorate rapidly. A secant-stiffness method suitable for analysis of flexural structures in fire is presented. A mathematical model based on a modification of the Ramberg-Osgood equation is used to represent the moment—curvature—temperature relationship. An iterative procedure is used to converge on the correct curvature profile which satisfies equilibrium, compatibility and material criteria. As this converges regardless of the initial values assumed the structure can be analysed over a range of temperatures by moving across the moment—curvature curves. The method has been used to analyse both statically determinate and indeterminate beams under fire conditions in which temperature distribution over the cross-section remains uniform. A comparison with an incremental tangent—stiffness approach has shown its efficiency in terms of speed and accuracy.