Non-Dimensional Coupled Flexural-Torsional Buckling Analysis of the Thin-Walled Columns with Asymmetric Open Cross-Sections and its Application to the Critical Buckling Load Optimization

Abstract

This study presents coupled flexural-torsional buckling analysis of the thin-walled columns with nonsymmetric open cross-sections in dimensionless and exact man- ner. Transfer matrix method coupled with iterative eigenvalue solution procedure is used to calculate nondimensional buckling loads of the thin-walled columns. For all end conditions considered, closed-form solutions are also presented for the comparison. The related tables show that, to some extent, all results are in good agreement. However, the closed-form solutions available in literature do not completely capture the buckling loads obtained using the transfer matrix method for fixed-fixed, fixed-pinned, and fixed-free end conditions. Therefore, there is a need to find new expressions for buckling parameter to calculate analytically buckling loads. This is carried out by using the Euler’s theory of columns for doubly symmetric cross sections. Through using these expressions, a good matching between the results obtained from the transfer matrix method and closed-form solutions is provided. On the other hand, as a case study, nondimensional solution procedure is applied to the optimization of critical buckling load of the columns. Nondimensionalization is a useful procedure for optimization such that it has led to a naturally scaled optimization model. Three column configurations with different numbers of segments in the longitudinal direction were considered and the maximum dimensionless critical buckling load without constraint violations is attained for the five-segmented column and it is 7.2, which represents 48.0415% gain.