A Tool for Learning Mohr's Circle

Abstract

Mastery of the relations among loads on an elastic object and the corresponding stress state as well as the transformed and principal stresses at a point inside the object frequently presents a significant hurdle to Mechanics of Materials students. Mohr's circle is commonly introduced as a tool ostensibly to make transformation and principal information easier to understand and apply. Yet learning Mohr's circle construction and interpretation frequently introduces an additional challenge. A learning tool in the form of a system that gives realtime display of the stress state and its corresponding Mohr's circle at a point in a structure that the student manually loads is introduced. Rather than being a virtual learning environment, a unique synergism among a computer and a physically tangible object is reported. Visual, tactile, and muscular feedback to the learner's attempts to load and deform the object are provided. The results of learning experiments are reported. When the computer program portion of the tool is used alone, it is most effective at improving students' ability to anticipate the way in which stress magnitude varies with transformation angle and for identifying principal stresses on the circle. When the complete tool is used, learners can handle and load the structure and become distinctly more confident of their understanding of Mohr's circle than those who had not. Students who used the complete tool after working related homework problems were more satisfied with the tool man than those who did the opposite. Students who used the complete tool before working homework problems demonstrated a stronger ability to correctly locate Mohr's circle as well as to calculate maximum shear stress.