Two Experiments To Teach Modulus Of Elasticity And Modulus Of Rigidity

The relationship between loads and deformation in a structure is a difficult concept mechanics students often must master with little prior exposure to materials science concepts such as Hooke’s law for elastic modulus. Two hands on experiments have been designed to help demonstrate for mechanics students in an introductory strength of materials course the concept of structural stiffness and to help differentiate between the structural stiffness and the modulus of elasticity for a material under applied axial load and the modulus of rigidity for a material under applied shear loading. In the first experiment two different size wires of the same material are loaded in tension. As the applied load is increased the students record the load and the corresponding deflection of the wires. Using elementary mechanics the students can compute the stiffness of each system from a plot of load versus elongation. Then by applying the fundamental definitions of both stress and strain the data can be recast in the form of a stress-strain diagram for the material and the students can compute the modulus of elasticity for the material of the two wires. The second experiment looks at the relationship between applied torque and angular displacement. Using a simple apparatus to load both a solid circular rod and a hollow circular rod, the students can record the applied torque and the corresponding angle of twist. Plotting this data the students can compute the torsional stiffness of each system. By manipulating the torqueangular displacement relationship the students can compute the modulus of rigidity for the material of both systems. In both experiments the students will observe that while the structural stiffness varies with the geometry of the structural element, both the modulus of elasticity and the modulus of rigidity are independent of geometry and thus material properties. The apparati and application of each of these experiments will be described in detail in this paper.