Beam Foundation

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Subgrade reaction theory based on discrete spring model

The analysis of the foundation beam is based on the solution of the differential equation

where k=k_s×B, EI=Flexural rigidity of foundation beam,

k_s=Modulus of subgrade reaction, B=width of foundation beam. The foundation base is assumed to be smooth and the soil pressure is assumed uniform across the width. The solution of this differential equation is complicated and cumbersome except for very simple problems. For practical problems where the loads are in the form of several concentrated loads, moments and UD loads it becomes necessary to resort to numerical solutions. The software module uses finite element solution of the problem using the exact displacement function and therefore gives exact solution to the problem.

Elastic half-space model

In this approach the subsoil is modelled by a homogeneous, isotropic elastic half-space characterised by an elastic modulus and a Poisson ratio. This model has the merit of accounting for the continuous nature of the soil medium. The discrete spring bed model does not account for the soil continuity. The solution is based on the vertical displacement due to a distributed surface loading on an elastic half-space (given by “Boussinesq”). Again numerical solution of the problem is essential for tackling practical problems as no analytical solution is available for finite beams. The software module for Elastic half-space model is based on finite element formulation assuming a smooth base and uniform soil pressure across the width.