The torsional-flexural behaviour of thin-walled prismatic members

Abstract

A study is made of the behaviour of thin-walled prismatic members of doubly symmetric open cross-section in which the second moment of area about the major principal axis is very much greater than that about the minor principal axis. The member carries an axial thrust and terminal major axis moments, which can be either equal or unequal in magnitude. These forces are considered constant. An investigation is made of their effects in causing reductions of minor axis bending resistance and of the torsional resistance of the section. It is assumed that deflexions of the member due to major axis bending are negligible. The governing equations for the member are derived and a general solution is obtained. This is compared with an independent numerical solution. The end conditions considered are deflexion and rotation in the minor axis bending plane and twist and rate of twist about the centroidal axis. Associated with these end conditions are the minor axis moments and shears and the torque and bimoments about the centroidal axis. Thus a complete set of force-deflexion equations can be derived with which single members or sets of members forming complete frameworks can be analysed.