Comparative Modeling Study of Reinforced Beam on Elastic Foundation

Abstract

In this paper, governing ordinary differential equations are derived for a reinforced Timoshenko beam on an elastic foundation. An analytical solution is obtained for a point load on an infinite Timoshenko beam on elastic foundation. Special attention is drawn to the location, tension, and shear stiffness of reinforcement and its influence on settlement/deflection of the beam and reinforcement tension force. A finite element (FE) model is established for the same infinite beam problem. Results from the TB model (Timoshenko beam on elastic foundation) are compared with results from the FE model and from the PB model (the Winkler model, based on the pure bending beam theory). It is found that results from the proposed TB model are, in general, in good agreement with results from the FE model as compared with results from the PB model. The TB model is better than the PB model in considering the shear deformation of the beam. This TB model is particularly useful in modeling a reinforced beam with or without considering the reinforcement shear stiffness. The TB model has practical applications in modeling geosynthetics/fiber-glass reinforcement of foundation soils or pavement.