The dynamic response of a multi-cracked simply supported girder bridge model under multiple moving load is investigated in this paper. Euler-Bernoulli beam model is used to model the governing equation. The dynamic response of the healthy bridge model under multiple moving loads is first derived based on the Green's function method. Then, the transfer matrix method is used to derive the analytical solution of the forced vibration of the multi-cracked bridge model based on the solution of the healthy bridge case. The effects of crack depth and bridge height-to-span ratio on the natural frequency of the beam are studied by numerical calculations. The effects of different vehicle types, loads, number of vehicles, vehicle spacing, relative crack depth, and location on the transversal displacement of the middle point of the bridge are also investigated. The effects of bridge height-to-span ratio, vehicle speed, load location, relative crack depth and location on the transversal displacement of overall bridge are studied. Parameter analysis for the height-to-span ratio and relative crack depth are studied, and the confidence intervals for the quadratic fit coefficients reach 95%, which indicating that the model fits the data extremely well. The validity of the present solutions is checked by comparison with the results in references.

Multi-cracked beams,Green's function,Simply supported girder bridge,Multiple moving loads,Forced vibration