This paper presents an analytical study on the mechanics response of simply supported beams with stiffness damage by combining the finite element method with the U-transformation method. Firstly

a simply supported beam is divided into

n

substructures

and an equivalent structure with cyclic periodicity is constructed

and the governing equations are established

in which stiffness damage is treated as a loading. Then U-transformation technic is applied to the equations and the analytical expression of nodal deflections of the beam are derived. The influences of damage location and damage degree on these solutions are discussed. Moreover

the natural frequencies of damaged beam are solved.