Inelastic large deflection analysis of space steel frames using an equivalent accumulated element

This paper presents a new model to perform inelastic large deflection analysis of space steel frames depending on the spread of plasticity method. A stiffness matrix of a beam-column element with only two nodes and six degrees of freedom for each node is derived to represent the space frame member. The proposed matrix includes the effect of section yielding along the member as well as the effect of large deflection. Stiffness degradation at the cross-section due to yielded parts is calculated using a formula for the tangent modulus which is affected by the sectional internal forces. The proposed technique of accumulation of rigidity factors is submitted as a first step to get exact first order stiffness factors for a member with variable cross sections. The effect of large deflection is included by considering the axial force while deriving the stiffness factors. Both cubic and higher order shape functions are tried to produce an element that can represent the member without discretization. A finite element program based on stiffness matrix method is developed to predict the inelastic large deflection behavior of steel space frames using the derived stiffness matrix. The proposed finite element technique exhibits good correlation when compared with the conventional spread of plasticity model results. Verification by solving benchmarked steel structures is carried out. The analysis results indicate that the new model is accurate with simple equations and it achieves a significant improvement to the run time.