On the out-of-plane deviation of the bending deformation states of moderately thick bars of asymmetric cross-sections

Abstract

A characteristic feature of the six-parameter theories of bars is a coupled form of the constitutive equations; in particular the equations linking transverse forces with transverse shear deformations cannot be, in general, decoupled, keeping a separated form of the remaining constitutive equations. The mentioned feature of the constitutive equations implies that within the six-parameter theories of straight elastic prismatic bars there do not exist, in general, plane states of bend-ing/shearing deformations. Thus, any vertical load causes lateral deflections, the only exception being the pure bending problem. The present paper delivers analytical solutions: the closed formulae for shape functions, i.e. deformation states associated with kinematic loads at the ends, and solutions to selected static problems corresponding to the transverse span load. Although elementary, the presented solutions seem to be derived for the first time. In particular, the hitherto published shape functions concerned the theories of moderately thick bars in which all the constitutive equations are decoupled.