Nonlinear Analysis of Steel Space Structures

Abstract

A second‐order nonlinear analysis of steel space structures has been presented. Of the two types of nonlinearities, material and geometric, only geometric nonlinearity has been considered. The material of the structure steel has been assumed to be linearly elastic. In geometric nonlinearity, the effects of instability produced by axial forces, the bowing of the deformed members, and finite deflections have all been included. For this purpose, the secant stiffness matrix in the deformed state and the modified kinematic matrices along with the geometric matrix necessary for formulating the tangent stiffness matrix, have been developed. These matrices are used in the analysis, which is carried out by the displacement method through an iterative‐incremental procedure based on Newton‐Raphson technique. The iterations that take into account the latest geometry are repeated until the unbalanced loads become negligible and equilibrium is obtained. The equilibrium equations are solved by Cholesky's method. Results of an illustrative example and conclusion based on them are also given.