Dynamic Influence Lines of Beams and Frames

A general method for the calculation of the response of beams and frames, with a lumped mass distribution, traversed by a vertical force is presented. The process of modal analysis is applied to a system with a finite number of degrees of freedom. The resulting differential equations are integrated by the Laplace transform method. An expression in closed form is found for the dynamic influence lines of the deflections of the structure. Static influence lines are also calculated by modal super-position. The method is applied to a wide class of structures, and some general conclusions, related to the order of magnitude of the dynamic effects of a moving force, are presented.