A New Approach To Solve Beam Deflection Problems Using The Method Of Segments

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. Introduction The great majority of undergraduate mechanics of materials textbooks 1-50 directly apply previously derived force-deformation formulas to problems involving the straight bar subjected to centric axial loading and the straight circular cross-section bar (shaft) subjected to twisting couples. In both cases, the bars are uniform in cross-section and material, and the concentrated loads are applied at the ends and distributed loads are continuous along the full length. The force-deformation formulas are shown in Figures 1 and 2 for bars subjected to centric axial loading and twisting couples, respectively. These formulas, referred to as Material Law Formulas by the authors, are commonly found in mechanics of materials textbooks 1-50 .