Stress in a Solid Shaft

    ➤➤ A solid steel shaft in a rolling mill transmits 20 KW at 2 Hz. Determine the diameter of the shaft if the shearing stress in not to exceed 40 MPa.

Solution:

Given,

          Power, P = 20 KW = 20 x 10³ KJ/sec

          Frequency, f = 2 Hz

          Shearing Stress, τ = 40 MPa = 40 x 10⁶ N/m²

          Diameter, d=?

We Know that,

                        Torque, T = P/ 2πf

                                         = 20 x 10³ / (2π x 2)

                                         = 1590 N.m

 

We also know that,

                       Torsion formula, 

                                                τ = 16T/ πd³

                              =>  40 x 10⁶ = (16 x 1590)/ πd³

                                          => d = 58.71 mm

So, the diameter of the Shaft = 58.71 mm.