Two thin-walled circular tubes, one having a seamless section, the other a split section (see attachment), are subjected to the action of identical twisting moments. Both tubes have equal outer diameter "Do", inner diameter "Di", and thickness "t".
Determine the ration of their angles of twist.
What we have here is two tubes with equal radius and thickness. The ratio of the angle of twist for the tube with the closed section over the tube with the open section is 3(R^2/t^2). (In words this is 3 times R squared divided by t squared.) How is this determined to be so? The formula for angle of twist is TL/GJ where T = the internal torque in the shaft, L = the length of shaft being "twisted", ...
This solution is provided in 298 words. It discusses stress and strain in relation to angle of twist.