Application of the direct iteration method for non-linear analysis of steel frames in fire

Abstract

Based on finite element method, a direct iteration method capable of predicting the non-linear behavior of steel frames at elevated temperatures is proposed, in which the second-order effects of large deflections, the progressive softening of materials with temperature rise, gradual penetration of inelastic zone both over the section and along the member, non-uniform distribution of temperature within steel members are all taken into consideration. The secant stiffness matrix that relates the total element displacements to the corresponding total forces is used in deriving the basic finite element equations. Different from the commonly used Newton–Raphson method in which the deformations are calculated incrementally, the direct iteration method used in this paper allows the calculation of the total structural responses corresponding to a specified load level and temperature distribution by a straight iteration process. During this process, strains are used to check whether a point on a section is in the elastic domain or not. A computer program was developed to apply this method for analyzing steel frames in fire. To examine the validity of the method and the program, comparisons are made between the program predictions and test results available for steel frames both at room temperature and under fire conditions, in most cases, a satisfactory agreement is obtained.