AN ANALYSIS OF BEAMS ON NON- HOMOGENEOUS ELASTIC FOUNDATION USING INITIAL VALUE APPROACH

ABSTRACT

The paper presents an analysis of beams on non-homogeneous elastic foundation, where the deformation is partly localized and partly continuous. The soil was modeled to be in layers, in which two layers within the soil strata were considered. The different layers of the soil have their respective sub-grade modulus k, and the entire foundation is resting on a rigid base. The formulation was achieved by imbedding a beam of known bending rigidity within the laygers of the foundation. The deflection in the upper and lower section of the beam due to the pressure resulting from the applied load was correlated using flexural theory of prismatic beams. The solution of the eight order differential equation was solved using initial value approach. Based on the present formulations, numerical cases were examined. The result of the comparative analysis revealed that the supporting medium cannot be said to be homogeneous in nature. The effect of the soil modulus of the underlying soil strata has to be taken into account in the analysis of beams on elastic foundation.  The higher stresses generated was due to continuity in the supporting medium, there providing engineers with a safe design.