The Shear Stress-Strain Diagram ?) 60112 Learning Goal: To determine the modulus

Question

The Shear Stress-Strain Diagram ?) 60112 Learning Goal: To determine the modulus of rigidity of a material from its shear stress-strain diagram Polsson's ratio, and the expanded diamater of a cyl indricall shaft made of the material that is loaded under compression The cylindrical shaft shown balow is made of an al i maloy with a lower yield limit of 20 ks inshear The innal length of the speci en is given by Lo-so in and the i bal diameter is given by d:450 in specimen is then compressed between the two flat metal plates unti' it reaches a new compacted length of L,·49 87 in

Explanation / Answer

Part A

Slope of line=(15-0)/(0.004-0)=3750 ksi

Modulus of rigidity=3750 ksi

Part C

Modulus of elasticity of aluminum=10000 ksi

Let Poisson's ratio be n

3750=10000/(2+2n)

n=0.33

Axial compression=50-49.87=0.13 in

Axial strain=0.13/50=0.0026

Lateral strain=0.0026*0.33=0.000867

Lateral expansion=0.000867*4.5=0.0039 in

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