Many products and components are subjected to torsional forces during their operation. Products such as switches, fasteners, and automotive steering columns are just a few devices subject to such torsional stresses. By testing these products in torsion, manufacturers are able to simulate real life service conditions, check product quality, verify designs, and ensure proper manufacturing techniques.
For torsional shear, the specimen is loaded into a machine and fixture that has a fixed end and a rotating end. The rotating end of the fixture allows torque to be applied to the specimen.
When a bar is loaded in torsion, a relative angle of rotation Φ is produced between any two cross sections of the bar. This relative angle of rotation is
determined by measuring the relative tangential displacement δ observed at radius R of the angular displacement gauge: Φ = δ/ R
The twist of the bar, defined as the relative angle of rotation per unit length, is given by (Φ/L)= (δ /RL) where L is axial distance between the cross sections.
In the laboratory, L is the gauge length of the angular displacement gauge.
If the bar is of uniform circular cross section, then the shear strain Y everywhere in the bar is proportional to the radial distance from the bar axis.
The maximum value of Y is found at the surface of the bar and has the value
Y max =r Φ /L where r is the radius of the bar.
Note that this eqns. are based only on the geometry of deformation, and are therefore independent of material behaviour.