Problem 302: Torsion

Problem 302:

                    What is the minimum diameter of a solid steel shaft that will not twist through more than 3° in a 6-m length when subjected to a torque of 12 kN·m? What maximum shearing stress is developed? Use G = 83 GPa.

Solution:

Given,

           Length, L = 6 m

           Torque, T = 12 KN.m

           Angle of twist, θ = 3°

           G = 83 GPa.

           Minimum diameter, d =?

           Maximum shearing stress, τ_max =?

We know that , Angle of twist,

 

So, Minimum diameter = 113.98 mm

 

We also know that, maximum shearing stress,

So, Maximum shearing stress = 41.27 MPa