Torsion of shafts

Torsion is twisting about the long axis. Shafts that drive pumps, curved bridge girders, edge beams that support slabs on one side and the spandrels of buildings all carry torque. For a solid or hollow circular shaft the theory is simple because plane sections stay plane and radii stay straight, so shear strain grows linearly from zero at the centre to a maximum at the surface.

The torsion equation T / J = τ / r = G θ / L links torque T, polar moment J, shear stress τ at radius r, shear modulus G and angle of twist θ over length L. A hollow shaft is more efficient than a solid one, since the material near the centre carries little stress. Power transmitted by a shaft is P = 2π N T / 60 with N in rpm.

Non-circular sections warp and need other methods. A thin-walled closed tube carries torque by a constant shear flow q = T / (2 A₀), with A₀ the area enclosed by the wall's centre line, which is why box girders are so torsionally stiff. Open sections such as I-beams and channels have very small St Venant (uniform) torsional stiffness; where warping is restrained, for example at a fixed end, warping resistance adds considerably to their torsional capacity. In reinforced concrete, torsion is resisted by closed stirrups plus extra longitudinal bars, combined with shear and bending in design.