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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