Effective mode shapes of multi-storey frames subjected to moving train loads

This paper deals with the effect of the mode shapes on the dynamic response of a multi-storey frame subjected to moving train loads which are modelled as loads of constant intervals with constant velocity using the finite element method. The multi-storey frame is modelled as a number of Bernoulli-Euler beam elements. First, the first few modes of the multi-storey frame are determined. Then, the effects of force span length to beam length ratio and velocity on dynamic magnification factor (DMF) are evaluate via 3D velocity-force span length to beam length ratio-DMF graphics and its 2D projections. By using 3D and 2D graphics, the directions of critical speeds that force the structure under resonance conditions are determined. Last, the mode shapes related to these directions are determined by the time history and frequency response graphs. This study has been limited by the vibration of the frame in the vertical direction.