Library Articles

The shear stress in beam due to torque can be derived with three principals:
Geometry, Hooke's Law, and Equilibrium.

Circular Members

 
Geometry:

g = shear strain
f = angle of twist
q = angle of twist / unit length




Hooke's Law:




Equilibrium:









Relationship between Torque and Shear:
  T = G · q · J
Polar Moment of Area for Circular Shapes:
 
Angle of Twist:
 

Circular Shaft:
Hollow Shaft:
Thin Walled Tube: J = 2pr3t