Three Bimoments Equation of V.I. Slivker’s Semi-Shear Theory for the Calculation of Multi-Span Thin-Walled Beams
Abstract
This article discusses the method of static calculation of multi-span thin-walled beams with bending torsion in the framework of the semi-shear theory of V.I.Slivker. The main advantage of the semi-shear theory is that it is suitable for rods of both open and closed (as well as open-closed and multi-contour) profiles due to the similarity of differential equations according to the theories of V.I. Slivker and A.A. Umansky, and also increases the accuracy of the calculation due to taking into account part of the shear deformation. The analytical solution of the problem is obtained based on three bimoments equations system of, including values of correlating functions for cases of application of torsional loads in the span and on the cantilever of thin-walled multi-span continuous beams. Bimoment func-tions for a number of simple beams are obtained within the framework of the semi-shear theory. It is shown that the values of the parameter of the influence of the shape of the cross-section of the semi-shear theory ranges from 1.000086 to 1.0014 for channel profiles, while the presence of shelf bends (C-profile) in comparison with the channel profile reduces the value of this parameter by 10%, which indicates a lower contribution of part of the shear deformations to the stress strain state at the torsion of the C-profile. It is shown that, despite the convergence of the calculation results by the proposed method, due to the proximity of the values of the shape influence parameter to 1.0 with the similar one according to the theory of V.Z. Vlasov, the area of application of the proposed method are significant-ly wider (both open and closed profiles).