Nonlinear analysis of steel frameworks through direct modification of member stiffness properties

This paper presents a computer-based method for nonlinear analysis of planar steel frameworks under monotonic loading that is directly based on the matrix displacement method of analysis. Stiffness degradation factors progressively deteriorate the post-elastic bending, shearing and axial stiffness properties of framework members over an incremental load history until failure of part or all of the structure occurs. The analytical procedure is based on Timoshenko beam theory to allow for the analysis of frameworks for which effects of shear deformation on elastic behavior may be significant, and employs transcendental stability functions to model the effect of axial force on the bending stiffness of members. Also accounted for is the influence of residual stresses on the initial-yield and full-yield capacities of members, and the effect of both combined moment plus axial force and combined moment plus shear force on the post-elastic behavior of members. The nonlinear analysis method is applied for two benchmark planar steel structures, and it is shown to give results comparable to both experimental and analytical results previously published in the literature. The method is readily implemented on a computer using conventional matrix structural analysis techniques, and is directly applicable for the efficient nonlinear analysis of frameworks of any scale or complexity.