Solving Beam Deflection Problems using a Tradition Approach

This paper presents a new approach to solving beam deflection problems. The approach involves the direct application of derived force-deformation formulas, a procedure commonly used with axial and torsion bar problems. This direct application of derived force-deformation formulas, referred to by the authors as Method of Segments, is extended to beam deflection analysis in order to provide a solution procedure for beams that is consistent in philosophy and application with that presented in most mechanics of materials textbooks for axially loaded bars and torsionally loaded shafts. The beam force-deformation formulas, involving slope and displacement, are derived by double integration for a beam of uniform cross-section, material and distributed loading with end shear forces and couples. Application of the formulas is direct and requires no integration or continuity equations. Furthermore, by identifying segments of uniform geometry, material and distributed loading, this approach can easily be applied to beams of discontinuous geometry and material that supports both concentrated and distributed loading.