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

shear stress analysis

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

shear stress analysis example

Therefore,

mechanics internal stress

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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