均布荷载作用下悬臂梁的弹性力学解

Analytical Solution of the Elastic Mechanics for Cantilever Beam under the Even Loads

梁是土木工程中最常见的构件.材料力学基于平衡方程、物理方程和平截面假定的梁的计算分析结果,对浅梁较为精确,对深梁存在较大的误差,难以满足结构设计的要求.为此根据弹性力学平面问题基本理论,采用半逆解法,求出了悬臂梁在均布荷载作用下的应力、形变和位移.可供工程结构设计和弹性力学教学参考.

The beam is the most common component in civil engineering.The results calculated by the method of material mechanics based on the balance equations,the physical equations and the plane crosssection assumption of the beam,are comparatively accurate to shallow beams but have big errors for deep beams,so they can not meet the requirements of the structural design.By means of the basic theory of the plane problem in elastic mechanics and by using the half adverse solving method,the stresses and displacements of the Cantilever beam under the even loads are calculated.They can be used in the teaching of structural designs and elastic mechanics.