Dynamic Interaction of Railway Train and Bridges

An analytical method for obtaining the dymanic responses of a train of locomotives moving on bridges is presented. The ratio of dynamic response to maximum static response is called the amplification factor, and its maximum absolute value minus one is called the impact. Each four-axle locomotive is modelled as a rigid body with three degrees of freedom: bounce, pitch and roll, and with a suspension system consisting of springs mounted on wheels. The locomotives are assumed to be connected by frictionless joints to form the train. The bridge is modelled as a three dimensional structure, with the masses lumped at the truss joints. All joints, including the floor beam connections, are assumed to be rigid, except those for the bracing members, which are assumed to be hinged. Vertical displacements are considered as the only dynamic degree of freedom. The mathematical formulation is described briefly, and a numerical example is given. Locomotive and truss member properties, together with stresses in some typical members, are given in the tables. The amplification factors of the responses in some typical bridge members are shown in the figures.