Bending Shear Stress for Solid Beams of Arbitrary Non-Symmetrical Cross-Section

Abstract

The aim of this work is to develop a new numerical calculation program to calculate the shear stress subjected to a shear force for the general case of deflected bending, and to develop in this context a new numerical computational program for the calculation of the shear stress distribution in an arbitrary complex cross-section, in light to determine the position, and the value of the maximum stress, and consequently the determination of the shape factor seen in their practical importance. The calculation is valid for any axis and not necessary for the two principal axis of inertia. The calculation of the geometric characteristics of the section is necessary in this case. The formulae is done by the calculation of the static moment of the cutoff portion of section, where the calculation is made by an evaluation of an integral of complex function. View the obtained of a complex function, the calculation is given numerically by the use of the high order Gauss-Legendre formulae. The validation of the results is made by the convergence of the numerical accurate results to those for a chosen section like the arbitrary triangle which the exact result can be calculated analytically by the use of the new formulae. In this case, the solution is seen when the relative error given by the quadrature approaches to zero. The application will be for unsymmetrical section, views their practical interests in engineering.

Strain energy form coefficients for bending of short beams having full and thin-walled arbitrary cross section with application for FEM and Airfoils

“…For an arbitrary section and under the shear force effect T y applied along the central axis Gy oriented arbitrarily, the following result can be written according to 14 …”