Enhanced Formula for a Critical Velocity of a Uniformly Moving Load including Shear Contribution

The response of rails to moving loads has been a topic of interest for over a century. A related issue, the critical velocity of moving loads is an important matter related to track design. Analytically, in undamped environment, downward as well as upward displacements tend to infinity when the load is moving over an infinite rail at the critical velocity. However, the classical formula predicts such a critical velocity significantly overestimated than the one experienced in reality, indicating that the formula should be revised. In this contribution the dynamic equilibrium of the soil in the vertical direction is implemented to obtain two frequency dependent parameters incorporating the geometric damping and the soil mass inertia activated by induced vibrations. The new approach is tested on finite and infinite beams. Corrections to the classical formula are proposed.