What is the torsional deflection of a steel shaft with a diameter of 130mm and a length of 1,295mm which is subjected to a twisting moment of 5*10^6Nmm (take G=85,000Nmm^2?

 What is the torsional deflection of a steel shaft with a diameter of 130mm and a length of 1,295mm which is subjected to a twisting moment of 5*10^6Nmm (take G=85,000Nmm^2?

Solution

Assuming that this is a solid shaft, θ = TL/KG where T is the torsional moment, L is the shaft length, K is the torsional area moment, which for a solid shaft is K = ½πr^4. Also, G = 85,000N/mm^2 not 85,000Nmm^2.

Then, θ = 5*10^6Nmm * 1295mm / 0.5(3.1416)65^4mm^4 * 85000N/mm^2

θ = 6475*10^6 / 2.3834*10^12 = 2.717*10^-3 radians

which is 0.156° Answer