Torsion is the twisting of a beam under the action of a torque (twisting moment). It is systematically applied to screws, nuts, axles, drive shafts etc, and is also generated more randomly under service conditions in car bodies, boat hulls, aircraft fuselages, bridges, springs and many other structures and components. A torque, T , has the same units (N m) as a bending moment, M . Both are the product of a force and a distance. In the case of a torque, the force is tangential and the distance is the radial distance between this tangent and the axis of rotation.

All torsion problems can be solved using the following formula:

T/J = shear stress/ r = (G * angle)/ L

where:

T = torque or twisting moment, [N×m, lb×in]
J = polar moment of inertia or polar second moment of area about shaft axis, [m4, in4]
τ = shear stress at outer fibre, [Pa, psi]
r = radius of the shaft, [m, in]
G = modulus of rigidity (PanGlobal and Reed’s) or shear modulus (everybody else), [Pa, psi]
θ = angle of twist, [rad]
L = length of the shaft, [m, in]