## 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.