# EXCEL BASED SETTLEMENT OF BEAMS ON ELASTIC FOUNDATIONS WITH FREE-ENDS AND ARBITRARY LOADING

### AMIR W. AL-KHAFAJI, ROBERT JACOBS

The deflection of long footings placed on homogeneous and isotropic soils involves soil-structure differential equations models whose solution may not be possible for most practical problems. The analytical solution of beams on elastic foundation problem involves soil modulus of subgrade reaction and simplifying assumptions relative to applied loading. The exact solutions are available in relatively simple cases of loading, uniform cross sectional properties of the footing and constant soil modulus of subgrade reaction. Therefore, the Finite Difference Method (FDM) or Finite Element Method (FEM), are typically used to compute the deformation of beams with variable loading and geometry resting on elastic foundations with variable modulus of subgrade reaction. The finite differences method was used to solve this problem for long beams with arbitrary loading and constant cross-sections using an Excel Workbook to compute beam deflections providing both numerical and graphical output. The foundation is modeled as a long beam with free ends and a constant modulus of subgrade reaction. The proposed solution presents an efficient method involving a complex ordinary differential equation model for beams on elastic foundations encountered in engineering practice.

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