Chapter 3, Problem 52P

The thin-walled open cross-section shown is transmitting torque T. The angle of twist per unit length of each leg can be determined separately using Eq. (3-47) and is given by

${\theta }_1=\frac{3T_i}{G{L}_i{c}_i^3}$

where for this case, i = 1, 2, 3, and T_i represents the torque in leg i. Assuming that the angle of twist per unit length for each leg is the same, show that

$T=\frac{G{\theta }_1}{3}{\displaystyle \underset{i=1}{\overset{3}{\sum }}{L}_i{c}_i^3}$ and τ_max = Gθ₁c_max

Problem 3-52