Introduction to Elasticity/Torsion of circular cylinders
Torsion of Circular Cylinders 
About the problem: 
- Circular Cylinder.
- Centroidal axis thru the center of each cross section (c.s.)
- Length , Outer radius .
- Applied torque .
- Angle of twist .
- Each c.s. remains plane and undistorted.
- Each c.s. rotates through the same angle.
- No warping or change in shape.
- Amount of displacement of each c.s. is proportional to distance from end.
- Shear strains in the cylinder ().
- Shear stress in the cylinder ().
- Relation between torque () and angle of twist ().
- Relation between torque () and shear stress ().
If is small, then
If the material is linearly elastic,
The torque on each c.s. is given by
where is the polar moment of inertia of the c.s.