The Effects of Shear Deformation in Rectangular and Wide Flange Sections

Abstract

Shear deformations are, generally, not considered in structural analysis of beams and frames. But shear deformations in members with low clear span-to-member depth ratio will be higher than normally expected, thus adversely affecting the stiffness of these members. Inclusion of shear deformation in analysis requires the values of shear modulus (modulus of rigidity, G) and the shear area of the member. The shear area of the member is a cross-sectional property and is defined as the area of the section which is effective in resisting shear deformation. This value is always less than the gross area of the section and is also referred to as the form factor. The form factor is the ratio of the gross area of the section to its shear area. There are a number of expressions available in the literature for the form factors of rectangular and wide flange sections. However, preliminary analysis revealed a high variation in the values given by them. The variation was attributed to the different assumptions made, regarding the stress distribution and section behavior. This necessitated the use of three-dimensional finite element analysis of rectangular and wide flange sections to resolve the issue.

The purpose of finite element analysis was to determine which, if any, of the expressions in the literature provided correct answers. A new method of finite element analysis based on the principle of virtual work is used for analyzing rectangular and wide flange sections. The validity of the new method was established by analyzing rectangular sections for which closed form solutions for form factor were available. The form factors of various wide flange sections in the AISC database were calculated from finite element analysis and an empirical relationship was formulated for easy calculation of the form factor. It was also found that an empirical formula provided good results for form factors of wide flange sections.

Beam-column joint sub-assemblies were modeled and analyzed to understand the contribution of various components to the total drift. This was not very successful since the values obtained from the finite element analysis did not match the values calculated using virtual work. This discrepancy points to inaccuracies in modeling and, possibly, analysis of beam-column joints. This issue needs to be resolved before proceeding further with the analysis.