Abstract: Based on the mechanics of continuous damage, equations governing static and dynamical behaviors of linear elastic beams with damage are derived, in which the effect of shearing deformation is taken into account. For static plane problems, the equations are decoupled. Differential equations of deflection, rotation angle and damage, together with their general solutions, are presented. Analytic expressions of deflection, rotation angle, and damage are obtained under different boundary conditions. As numerical examples, curves of deflection, rotation angle and damage under a uniform load are given. The influence of damage on the mechanical property of the beam is investigated.

Key words: analytical solution, shearing deformation effect, static response, elastic solid with damage