Consideration of shear deformation in the calculation of bent structural elements

Abstract

The article studies the effect of experimental stresses on the deformation of structural elements subject to bending. It is known that the bending element of the structure is a beam, the main problem is to check their uniformity, for this it is necessary to determine the displacements caused by external forces, this task is carried out on the basis of integrating the main differential equation of the bent axis of the beam. But in general, the bending of the beam is significantly affected by tensile stresses arising on the surfaces of its cross section. Shear deformation caused by these stresses can in some cases significantly affect the deformation of the beam, that is, its composure. It is known that when deriving the main differential equation of the bent axis of the beam, only the effect of the bending moment is taken into account. In this case, the axis of the beam is curved, there is a stretching of the longitudinal layers from the neutral on one side and compression on the other. It is based on the hypothesis that the cross sections of the beam are straight, and the straight sections remain perpendicular to its bent axis. The article derives a differential equation for a curved beam axis taking into account the influence of shear deformation.