Mechanical Characterization of Beams on Tensionless Foundation Materials

The deformation and internal forces of beams on tensionless foundation materials were studied. The reaction force between the beam the foundation was fitted as a cubic polynomial about the deflection based on the experimental data, and the corresponding control equations of beams were derived by the finite difference method. Results show there are significant differences between tensionless and tensional foundation materials for the deformation and internal forces of beams. The difference is varying with the length of beams. Both the relative errors of the maximum of deflection and slope can be over 20%, and the relative errors of the maximum of shearing force and bending moment are smaller comparatively, so the tensionless effect of foundation materials can not be neglected for the stiffness verification and the strength verification of beams.

A Novel Technique for Dynamic Analysis of Beam-Like Structures on Tensionless Elastic Foundations Subjected to Moving Loads

In this paper, a novel method is proposed to address the non-linear dynamic response of a beam-like structure supported by a tensionless foundation due to moving loads. A lattice spring model (LSM) is developed to describe the structure as a discrete assembly of particles interacting via shear and rotational springs while the tensionless foundation is simulated using a chain of one-way normal springs connecting the particles to the ground. The total time for the travelling load to traverse the beam is divided into a number of steps and the generalised explicit matrix equation can be solved for each time step to obtain the time-history response of the structure. An iterative procedure is adopted to obtain the correct sign of lateral displacement for all particles at each time step, which determines the lift-off regions throughout the beam.