Theory of Torsion:

Torsion

If moment is applied in a plane perpendicular to the longitudinal axis of the beam or shaft. It will be subjected to torsion. 

Example:

Shaft transmitting torque or power.

L beam

Portio Beam

Cuved beams

Closed colied springs

Torsion Formula:

T / J = Cθ  / I = fs /  R 

where T - Torque applied 

fs Maximum shear stress due to torsion

R - radius of shaft

L - length of shaft 

J - polar moment of inertia = πD^4 / 32 a For solid circlar shaft.

= π ( D1^4 - D2^4 ) / 32

Theory of Torsion Assumptions:

Plane normal sections of shaft remain plane after twisting.

Torsion is uniform along the shaft.

Material of the shaft is homogeneous, and isotropic.

Stress is proportional to strain i.e... all the stress are with in elestic limit.