Torsional Stress Concentrations at Rounded Corners of Rectangular Hollow Sections

Abstract

Values are presented for torsional stress concentration factors and stresses at the centre of the outer side of rectangular hollow sections of finite thickness with rounded inner corners. The results were obtained for four different ratios of the corner radius to the thickness of the section, initially for square sections, but in such a way that it was possible to deduce results for all rectangular sections with the same corner radii for which the ratio of wall thickness to breadth of section was less than one eighth. The results for the square sections were obtained by solving the finite difference analogues to Laplace and Poisson equations by the Young-Frankel successive over-relaxation method. The results agree extremely well with such exact analytical results as are available, but a comparison with some previously published results obtained by the Southwell relaxation method shows a serious discrepancy, which is explained.