In the mine winder system (see adjoining figure), the 5 m diameter winding drum

Question

In the mine winder system (see adjoining figure), the 5 m diameter winding drum is connected to an electric motor by a solid A-36 steel shaft 360 mm in diameter and 1.2 m long. The motor is used as a brake to prevent further rotation at the end of the shaft. When the cage of mass 6000 kg is lowered into the mine, there is a 200 m of A-36 steel wire rope, having an effective cross-sectional area of 3000 mm2, between the cage and the drum. If material with a mass of 9000 kg is then loaded into the cage, determine - by how much the cage is displaced downwards; the resulting maximum shear stress in the shaft.

Explanation / Answer

tau = (T*p) / Ip where tau = shear stress (Mpa)
T = torque (Nm)
p = radius of cross-
section at which
youwant to know
tau
Ip = Polar moment of
inertia (mm^4)

With a round shaft subjected to a given torque, the highest shear stress (tau) will occur at the maximum radius of the cross-section, so

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