a. 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 138 MPa in shear. The initial length of the specimen is given by L0 = 50 cm and the initial diameter is given by d0 = 4.75 cm The specimen is then compressed between the two flat metal plates until it reaches a new compacted length of Lf = 49.98 cm. (Figure 1).

i. Using the shear stress-strain diagram provided below (Figure 2), determine the slope of the curve (modulus of rigidity) of the material up to the proportional limit.

ii. Using the modulus of rigidity from Part A and the modulus of elasticity of E=69.6GPa, determine the value of Poisson's ratio for the aluminum alloy.

iii. The cylindrical shaft experienced a lateral expansion due to the compressive force applied to it. Determine this lateral expansion, ??, of the cylindrical shaft.

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