Linear analysis of two-dimensional semi-rigid frames

Abstract

It is usual to assume that a displacement caused at any point in a structure is linearly dependent on the magnitude of the loads applied. This paper focuses on the linear analysis of 2-D frames with flexural connected beam-column members considering shear displacements. A computer program was written in MATLAB for this purpose. To achieve the above purpose, first, the element stiffness matrix with linear flexural springs at its ends has been obtained by using relevant differential equations, considering shear deformations. In the analysis of the stiffness methods, it has been observed that the loading vector can be obtained by means of the loads applied between the joint points. It is found that the presents of an axial load in a member affect the values of the fixed-end forces, and these are the subject of another paper. For linear cases, the semi-rigid end forces have been obtained for a uniformly distributed load, an unsymmetrical point load, a linearly distributed load, an unsymmetrical trapezoidal distributed load, and an unsymmetrical triangular distributed load. To prove the validity of the computer program, some problems in the literature have been solved differently. There was a good agreement between the relevant results.