# Shear Stress Analysis Example for College Students

A 400 kg mass is supported by a frictionless pulley with a radius of 0.50 m. The pulley is attached to pin-connected frame members

The length of the 5.80 mm diameter cable ( E = 124 GPa) is 7.50 m. The diameter of the pins is 28.40 mm. The pins are in double shear.

Requirements:

1] Elongation of the cable material

2] Shearing stress of the pin at A

The tension force in the cable is determined to be equal to the weight of the supported object. That is

Then applying the concept of elongation, where P = the axial force in the material, L = the initial length of the material, A = the cross-sectional area of the material, and E = the modulus of elasticity of the material, we have

Therefore,

The total shear will be the resultant reaction at the hinge support

Using

summation moments at D are in

Next, the summation vertical forces are in

Then,

The shearing stress

Note that the resisting area will be twice the cross-section of the pin because the pin is in double shear. Therefore,

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