対称形断面曲げ梁のせん断応力分布とせん断剛性に逆比例するせん断変形

摘要

現在、曲げ梁断面上のせん断応力分布について、「せん断力作用方向に直交する線上で、せん断応力が一様である」と仮定した釣合条件より誘導した式を載せている図書が多い。しかし、せん断応力の水平成分には触れておらず、等方性弾性の長方形断面梁以外の一般断面形では、ひずみ適合にも疑問がある。また、上記一様仮定から導かれたせん断変形の係数も検討を要する。%The purpose of this paper is to describe the theoretical analysis for the shear stress distribution and the shear deformation with warping of orthotropic elastic beams of symmetrical cross sections. Especially, the shear deformations proportional to the shear force and inverse proportional to the shear modulus without minor terms in relation to bending stress in a Poisson'a ratio is analyzed in this paper. For this purpose, introducing in-plane rigidity of the cross section with infinity, a number of degree of freedom of analytical models decrease considerably, and as a result the analysis is became easy. Thus, the general analysis technique about the symmetrical cross section of beams was able to be proposed by using this method. Furthermore, it is proved that assumption of the shear stress uniformly distributed along the horizontal direction of the cross section is equivalent to deal with the beam of G_(zx)= ∞ , the upper and lower bound of the shear deformations are obtained by applying to this model. As the example, the solutions of circular and square rhombic cross sections of beams, which are the shear stress distribution, the warping deformation and coefficients of Timoshenko's berm, are shown.