An Efficient Approach to Approximate the Deflection Curve of an Arbitrarily Supported Beam Subject to External Loads

In this paper, an approximate method is developed that can be used to efficiently obtain the deflection curve of any prismatic or non-prismatic, statically determinate or indeterminate beam under various loading conditions. This allows for a quick validation of the exact deflection curve, which is especially useful at the undergraduate level. This proposed method approximates the deflection curve as the weighted sum of the eigenfunctions of the dynamic uniform beam. The weights of each eigenfunction are obtained by solving a set of linear algebraic equations. The mathematics needed to apply this method is relatively simple, and can be easily taught at the undergraduate level. The proposed method is validated against the exact deflection curve for multiple examples, and excellent agreements are shown between the approximate and exact deflection curves.