Deflection Part I: An Alternative Mechanics of Materials Approach Using Foundational Theory and Modern Engineering Tools

Here we present an alternative approach to solving beam deflection by applying energy methods to the moment curvature equation and integrating numerically.The approach capitalizes on fundamentals augmented by Castigliano's Second Theorem and the Heaviside step function, together with a modern equation solver.By carefully writing correct governing equations and then using a modern equation solver, the analyst can save time on calculations and spend additional time contemplating the meaning and usefulness of the results.By way of examples, we demonstrate this straight-forward, five-step approach using simple and challenging beam deflection problems found in classical publications.In this paper, we solve beams of uniform cross-section, non-uniform cross-section and statically indeterminate loadings using the alternative approach.We believe this alternative approach could be successfully introduced and mastered at the undergraduate Mechanics of Materials level as one of several methods available for deflection determination.