Closed-form design solutions for parallelogram hollow structural sections under bending scenarios

Abstract

Parallelogram shaped sections are compelling candidates for structural boundary members to accommodate transitions at corners and to cater for architectural aesthetics. Generally, parallelogram shaped sections possess no axis of symmetry and therefore require careful design considerations in engineering practice. However, there is limited information on this topic in the literature. This paper examined the behaviour of parallelogram shaped hollow structural sections subjected to bending moments. Closed-form solutions were derived for two types of parallelogram shaped sections (i.e., parallelogram sections and parallelogram hollow structural sections), including equations of moment inertia, general flexure equations, and equations of neutral axis. Toward practical applications, two common loading conditions were discussed, and design equations for the yield moment and plastic moments were formulated. Furthermore, the stresses at the vertices of the parallelogram were rewritten in a straightforward form as the product of a stress factor and the stress of a rectangular section. Finite element (FE) models verified by test results in the literature were developed to enable a parametric study, and the correlation among test results, FE data, and predictions by equations justified the adequacy of the proposed theoretical model and the corresponding closed-form solutions. The findings in this work show that the aspect ratio and inclination angle have a major influence on the section properties and stress distribution of parallelogram sections, whereas parallelogram hollow structural sections are further affected by an additional factor known as the shape constant. Parallelogram shaped sections may produce much greater stresses than rectangular sections under the same moments.