A simple CAD method for constructing sand-heap formations as an analogous means of determining the fully plastic torque capacity of various structural sections

A brief review is presented of the sand-heap analogy as a means of determining the ultimate plastic torque capacity of a ductile metallic prismatic bar of known cross-section. A novel method using an industry-standard computer-aided design (CAD) tool is then described for determining the shape and corresponding sand-heap volume for a general cross-section that can include the presence of keyways, fillets, rebates, and holes. Existing solutions for simple regular cross-section shapes are used as a benchmark for the solutions from the new method, and perfect agreement is found. Subsequent examples are presented which demonstrate the ease with which sand-heap formations and their corresponding volumes can be found for more general cross-sections that are more representative of those used in practical engineering applications.