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.