Equivalent vertical stiffness of an elastic half-space interacting with a beam, including the shear stresses at the beam - half-space interface

The equivalent vertical stiffness of an elastic half-space interacting with a beam with finite width is derived. Both vertical and shear stresses are taken into account at the interface of the beam and the half-space. A comparison is made with the case of the equivalent stiffness of a smooth contact. It is shown that the differences are small if the phase velocities of the waves in the beam are smaller than the Rayleigh wave velocity in the half-space. For phase velocities larger than R-wave velocity the differences can be substantial. The analysis shows that the shear stresses at the interface have to be taken into account, if a load moving along the beam can generate waves with phase velocities larger than the Rayleigh wave velocity.