Torsion (mechanics) Totally Explained

Everything about Torsion Mechanics totally explained

In solid mechanics, torsion is the twisting of an object due to an applied torque. In circular sections, the resultant shearing stress is perpendicular to the radius.
For solid or hollow shafts of uniform circular cross-section and constant wall thickness, the torsion relations are: ť

frac^4)

Where the o and i subscripts stand for the outer and inner radius of the pipe.
For a thin cylinder ť J = 2π R³ t

Where R is the average of the outer and inner radius and t is the wall thickness.

Failure mode

The shear stress in the shaft may be resolved into principal stresses via Mohr's circle. If the shaft is loaded only in torsion then one of the principal stresses will be in tension and the other in compression. These stresses are oriented at a 45 degree helical angle around the shaft. If the shaft is made of brittle material then the shaft will fail by a crack initiating at the surface and propagating through to the core of the shaft fracturing in a 45 degree angle helical shape. This is often demonstrated by twisting a piece of blackboard chalk between one's fingers.

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