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The presence of a crack in a structural member introduces a local flexibility that affects its dynamic
behavior. In this paper the effect of the crack on the deformation of a beam is considered similar to that of
an elastic hinge.
The exact shape functions of the cracked beam element are derived from the differential equations of the
Timoshenko beam theory.
Four different shape functions were adopted for two segments separated by the crack. The exact shape
functions are needed for the derivation of the exact equivalent nodal loads in static analysis, for the
derivation of the consistent mass matrix in vibration analysis and for the derivation of the geometric
stiffness matrix in the stability analysis.
The stiffness matrix and the consistent translational and rotatory inertia mass matrices of the cracked
beam element will reduce to the corresponding matrices of Timoshenko uncracked beam finite element
when the crack effect is eliminated.