Elasticity matrix in bending rods with allowance for transverse shear
Journal Title: Вісник Одеської державної академії будівництва та архітектури - Year 2016, Vol 1, Issue 65
Abstract
Consideration is given to the procedure of accounting for the effect of transverse shear on deflections in linearly bent rods under static loading. The question of determining their deflections from the transverse load is not trivial. Thus, in the paper [1] the curvature of the elastic line of deflection ( ) was shown not to be exactly proportional to the bending moment. In addition, S.P. Timoshenko [2] proposed to introduce in beams, in addition to the deflection caused by bending, a value of deflection which is a consequence of transverse shear caused by transverse force . Justification of the need to clarify the value of such deflection, according to him, involved many factors the problem of whose influence on structural reliability for construction practice has not been solved yet. He solved many problems of accounting for the influence on the structural material strength of, e.g, local stresses caused by holes, notches, recesses, abrupt changes in cross-sections, etc. [3]. The approach of a separate determination of bending deflection and of beam transverse shear proposed by him revealed a significant effect of shear depending on their cross section depth. Prof. B.N. Zhemochkin also pointed to a similar effect in his textbook on the theory of elasticity [4]. In his calculation of freely supported and distributed load wall beam, at a beam height to length ratio of 1: 2 normal stresses from transverse shear exceeded similar stresses caused by bending by 6.7%. Thus, for the purposes of using similar dependencies in the finite element method in matrix form, the need arose for a more justifiable obtaining of elasticity matrix that would take into account the effect of the bending moment and lateral force on deflections. The methodology considers the conditions of the force factors equilibrium in an inclined section and the conditions of elasticity matrix symmetry when using the FEM.
Authors and Affiliations
V. S. , Kukunaev
Keywords
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