Analytical solutions for Euler–Bernoulli beam on visco‐elastic foundation subjected to moving load

TLDR

Dynamic beam responses depend on system damping and the velocity of the moving load. The study develops analytical steady‑state solutions for an infinite beam on a visco‑elastic foundation under a moving load and derives dynamic amplification curves for beam deflection. Foundation resistance is modeled with compressive (kₛ) and shear (tₛ) parameters, enabling calculation of deflection, bending moment, shear force, and contact pressure. These solutions yield beam responses closer to reality than Winkler‑spring models and provide amplification curves for deflection, bending moment, shear force, and contact pressure useful for design. © 2012 John Wiley & Sons, Ltd.

Abstract

SUMMARY Analytical solutions for the steady‐state response of an infinite beam resting on a visco‐elastic foundation and subjected to a concentrated load moving with a constant velocity are developed in this paper. The beam responses investigated are deflection, bending moment, shear force and contact pressure. The mechanical resistance of the foundation is modeled using two parameters k s and t s — k s accounts for soil resistance due to compressive strains in the soil and t s accounts for the resistance due to shear strains. Since this model represents the ground behavior more accurately than the Winkler spring model, the developed solutions produce beam responses that are closer to reality than those obtained using the existing solutions for Winkler model. The dynamic beam responses depend on the damping present in the system and on the velocity of the moving load. Based on the study, dynamic amplification curves are developed for beam deflection. Such amplification curves for deflection, bending moment, shear force and contact pressure can be developed for any beam‐foundation system and can be used in design. Copyright © 2012 John Wiley & Sons, Ltd.