Application of modern engineering tools in the analysis of the stepped shaft: Teaching a structured problem-solving approach using energy techniques

The importance of analysis and design of shafts is well-described in most Machine Design textbooks. Shafts are subjected to both combined and variable loading, resulting in fatigue-mode stress and deflection; to further complicate the calculations, many shafts are of a stepped or tapered cross-sectional area. A thorough review of the textbooks available and the wider body of mechanical engineering literature revealed a paucity of strategies for either teaching or conducting the analysis required for proper design. In this paper we describe a structured problem-solving approach which uses the students' understanding of free-body-diagrams, shear and moment equations, and energy methods. With the development of note-taking handouts supplied to the students, the structured analysis is lead by the instructor using Castigliano's theory of internal energy. The problem formulation is kept general until the last step. The numerical integration can be performed software of the students' choice. We have found that using this approach accomplishes a richer, deeper understanding of design among our students and increases their confidence as indicated by our pre- and post-activity assessment.