Torsiuneelastic

Torsiuneelastic refers to the elastic component of a material’s or structure’s response when subjected to torsional loading. In this regime deformations are reversible and the shear stress–strain relationship is linear, so the material follows Hooke’s law for shear. The key quantity is the shear modulus G, which governs the stiffness to torsion.

For a solid circular shaft of radius R and length L carrying a constant torque T, the standard relations are: the angle of twist φ over the length satisfies φ = T L /(G J), where J is the polar moment of inertia, J = π R^4 / 2 for a solid circle. The shear strain at a radius r is γ(r) = r dφ/dx, and the corresponding shear stress is τ(r) = G γ(r). The maximum shear stress occurs at the outer surface (r = R) and is τmax = G R dφ/dx. If T is constant along the shaft, dφ/dx = T /(G J) and φ = TL/(GJ).

For non-circular cross-sections, torsion involves warping and the relation between T and φ' is expressed through a torsion constant Jt, which depends on the cross-section shape. The general idea remains: within the elastic limit, τ is proportional to γ and total twist is proportional to the applied torque.

Torsiuneelastic is distinct from viscoelastic and plastic torsion. In the elastic regime, unloading recovers the original dimensions and geometry. It is a fundamental consideration in the design of shafts, couplings, and other torsion-loaded components, where the yield shear strength sets the allowable torque.