Abstract
In this paper, a theoretical analysis is presented for estimating the in-plane large displacement elastic-plastic behavior of steel frames having members resting on elastic foundation subjected to either proportional or non- proportional increasing static loads and including shear deformation effect. The analysis adopts the beam- column approach and models the structure’s members as beam-column elements. The formulation of the beam- column element is based on Eulerian approach allowing for the influence of the axial force on bending stiffness. Also, changing in member chord length due to axial deformation, flexural bowing and shear deformation effect are taken into account. The formation of tangent stiffness matrix for the member in local and global coordinates with geometric and material nonlinearly including shear effect have been presented. In a special procedure, the calculation of axial force and plastic moment capacity including shear effect has been explained. New interaction equations between the axial force, shear force and plastic moment capacity for box and I-steel sections are presented in this study. The present search has adopted the linear and nonlinear behaviors of soil and these behaviors have been presented by isolated springs at the nodes. The computational technique utilizes an incremental load approach with a Newton-Raphson iteration to satisfy joint equilibrium equations. In order to verify the efficiency of the present formulation, some case studies reported by previous researches are utilized. The investigation is extended to study the effect of shear deformation on the elastic plastic behavior of structures resting on elastic foundation. As a result of this investigation, several important conclusions are obtained, which assure the necessity of taking into account the shear effect in the analysis of large displacement elastic-plastic behavior of structures resting on elastic foundation.
