An analysis model of cracked Timoshenko beam was proposed and the closed form solution of the deflection is obtained in the paper.Firstly

in the framework of the consistent beam theory

the Dirac δ function was adopted to simulate the local flexibility caused by the crack.The differential governing equation of the cracked Timoshenko beam was built by using of the generalized functions

and then the deflection was deduced in a closed form.Secondly

according to the linearly elastic fracture mechanics

the model parameters of the cracked Timoshenko beam were derived from the relationship between the crack depth and the sudden changes in the deflection and slope.Finally

the effects of crack depth on the deflection

slop and curvature were analyzed

and the damage sensitivity of the structural responses was studied.Meanwhile

the numerical simulation was carried out by introducing the singular crack element into the FE analysis.The numerical simulations were compared with the analysis solution to validate the proposed approach for cracked Timoshenko beam.The results demonstrate that the proposed model and solutions are accurate and efficient

which has promising feasibility in structural model updating and damage identification.