(Solved):         1 of 8 Learning Goal: To determine the modulus of rigidity of ...

 

 

 

 

1 of 8 Learning Goal: To determine the modulus of rigidity of a material from its shear stress-strain diagram, Poisson's ratio, and the expanded diameter of a cylindrical shaft made of the material that is loaded under compression. The cylindrical shaft shown below is made of an aluminum alloy with a lower yield limit of \( 20 \mathrm{ksi} \) in shear. The initial length of the specimen is given by \( L_{0}=50 \) in and the initial diameter is given by \( d_{0}=3.50 \mathrm{in} \). The specimen is then compressed between the two flat metal plates until it reaches a new compacted length of \( L_{f}=49.92 \mathrm{in} \mathrm{in} \). \( \nabla \quad \) Part A - Using a shear stress-strain diagram to determine the modulus of rigidity Using the shear stress-strain diagram provided below, determine the slope of the curve (modulus of rigidity) of the material up to the proportional limit. Express your answer in kilopounds per square inch to three significant figures. View Available Hint(s) \( G \) \( = \) Part B Complete previous part(s) Part C - Lateral expansion of the cylindrical shaft due to the axially applied force Part C - Lateral expansion of the cylindrical shaft due to the axially applied force The cylindrical shaft experienced a lateral expansion due to the compressive force applied to it. Determine this lateral expansion, \( \delta^{\prime} \), of the radius of the cylindrical shaft. Express your answer to three significant figures and include appropriate units. View Available Hint(s)