Find the diameter of a solid steel shaft to transmit 20 kW at 200 r.p.m. The ultimate shear stress for the steel may be taken as 360 MPa and a factor of safety as 8.If a hollow shaft is to be used in place of the solid shaft, find the inside and outside diameter when the ratio of inside to outside diameters is 0.5 .

Explanation

The diameter of the solid steel shaft can be calculated using the formula for the torque capacity of a solid shaft: d = sqrt((64 \* P \* N) / (π \* τ_u \* n)), where d is the diameter of the shaft, P is the power transmitted, N is the speed of rotation, τ_u is the ultimate shear stress, and n is the factor of safety. Substituting the given values, we get the diameter of the shaft as 47 mm. For a hollow shaft with a ratio of inside to outside diameters of 0.5, the inside diameter is given by d_i = 0.5 \* d_o and the outside diameter is given by d_o = 47 mm.

Explanation

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