All Problems

Elastic deformations

Problem 1.305

Determine the relationship between the torque \(N\) and the torsion angle \(\varphi\) for (a) the tube whose wall thickness \(\Delta r\) is considerably less than the tube radius; (b) for the solid rod of circular cross-section. Their length \(l, \mathrm{ra}-\) dius \(r,\) and shear modulus \(G\) are supposed to be known.

Reveal Answer
(a) \(\varphi=\left(l / 2 \pi r^{3} \Delta r G\right) \cdot N\) (b) \(\varphi=\left(2 l / \pi r^{4} G\right) \cdot N\).