Thin-walled beam with open cross-sections as a Timoshenko bar

The principal aim of the present paper is to analyse influence of shear stress on deformation of thin-walled beams with open cross-sections. In particular, the text presents critical remarks on the hitherto existing attempts to consider the shear effect by substituting function defining warping of a beam within Vlasov's theory with a new function $\theta(x)$. The paper is also aimed at a quantitative analysis of influence of shear-force on the displacement field which fulfils Bernoulli's assumptions. Contrary to solid bars, where the quantitative analysis shows that the influence of the shear forces on the deformation is negligible, this influence can be significant in thin-walled beams.