Nonlinear analysis of beams on elastic foundation with consideration of horizontal resistance

Considering the interface resistance between beam and foundation soil, the longitudinal and transversal coupling-deformation and the nonlinear characteristics of the deformation of the beam, a deformation control differential equation is established based on the Winkler elastic foundation model. The corresponding analytical solutions for the deformation, rotation angle, shear force and moment of the finite-length under symmetric loads are presented using the Galerkin method. In addition, the influences of the load, flexural rigidity, interface resistance and vertical coefficient of subgrade on the behaviors of foundation beams are investigated. The analytic results illustrate that the horizontal resistance has no effect on the change tends of the internal force and deformation of the foundation beams, but has a great effect on the values of them. The larger the horizontal resistance is, the greater the effect of resistance acting on the foundation beam is. Moreover, when the flexural rigidity of the foundation beams is larger, the effects of the horizontal resistance on the behaviors of the foundation beams are smaller.