All Problems

Elastic deformations

Problem 1.305

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

Reveal Answer
(a) φ=(l/2πr3ΔrG)N\varphi=\left(l / 2 \pi r^{3} \Delta r G\right) \cdot N (b) φ=(2l/πr4G)N\varphi=\left(2 l / \pi r^{4} G\right) \cdot N.