In this paper

the nonlinear analysis of steel frame in fire is carried out by adopting a new constitutive relationship which takes account of the temperature-stress path. The aim of this study is to put forward a new and more reasonable method for analyzing plane steel frames in fire. According to the experimental data

the constitutive relation of steel Q235 is obtained through regression analysis under three kinds of stress-strain paths

that is

heating and constant-load

heating and loading

heating and unloading. Then the incremental expressions of stress-strain relations for different stress-temperature paths are obtained. Based on the principle of virtual work

the non-elastic thermal elemental stiffness equations of plane steel frames for finite element analysis under different stress-temperature paths are derived. Moreover

the incremental iteration method is modified and a criterion is proposed for selection of one of the three kinds of stress-strain-paths. This study will provide a theoretical basis for the whole process analysis of steel frame in fire.