Problem 301: Torsion

Problem 301:

                    A steel shaft 3 ft long that has a diameter of 4 in is subjected to a torque of 15 Kip.ft. Determine the maximum shearing stress and the angle of twist. Use G = 12 × 10⁶ psi.

Solution:

Given,

           Length, L= 3 ft = 3 x 12 in

           Diameter, D = 4 in

           Torque, T = 15 kip.ft = 15000 x 12 = 180000 psi.in

                        G = 12 × 10⁶ psi.

           Maximum Shearing stress, τ_max  = ?

           Angle of twist, θ = ?

We know that, maximum shearing stress,

So, the maximum shearing stress = 14.32 ksi

We also know that, angle of twist,

So, the angle of twist = 1.23^o