Determination of Optimal Cross-Section Dimensions of Rectangular Hollow Sections Under Oblique Bending: Analytical and Numerical Study.

An insignificant number of rigorous studies have been devoted to the development of analytical procedures that determine the optimal cross-section dimensions of rectangular hollow section (RHS) members subjected to oblique bending, albeit their ubiquity in numerous application fields. In response to this, an analytical procedure has been developed based on the concept of minimizing maximum effective stress in the RHS caused by an applied oblique bending moment, in order to reduce material costs without compromising strength requirements. The RHS members addressed in this study have been assumed to be produced by hollowing out rectangular solid sections at different cross-section area extraction ratios; therefore, only the wall thicknesses of the RHS members have been taken into consideration as design variables. The minimization of maximum effective stress has been achieved by establishing a functional correlation between the cross-section design variables. The proposed procedure allows specifying the optimal cross-sectional dimensions for given different cross-section area extraction ratios and bringing cost-effective use of materials. After the subtle mathematical calculations, the derived analytical expressions have been made available to practical engineering in simple math forms for use in real design applications. The analytical procedure has been validated against numerical results which have been extracted from finite element analyses carried out in Abaqus engineering software.