Mechanics of Materials: Torsion

Vital Cocolot José Artemio

Torsional Deformation

In the field of solid mechanics, torsion is the twisting of an object due to an applied torque. Torsion is expressed in either the Pascal (Pa), an SI unit for newtons per square metre, or in pounds per square inch (psi) while torque is expressed in newton metres (N·m) or foot-pound force (ft·lbf). In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius.

In non-circular cross-sections, twisting is accompanied by a distortion called warping, in which transverse sections do not remain plane. For shafts of uniform cross-section unrestrained against warping, the torsion is:

where:

 T: is the applied torque or moment of torsion in Nm.

 t: (tau) is the maximum shear stress at the outer surface

J_T : is the torsion constant for the section. 

r: is the perpendicular distance between the rotational axis and the farthest point in the section (at the outer surface).

 ℓ: is the length of the object to or over which the torque is being applied.

φ:(phi) is the angle of twist in radians.

G: is the shear modulus.

Fig.1 Torque applied to a steel bar.

Torque is a moment that twists a structure. Unlike axial loads which produce a uniform, or average, stress over the cross section of the object, a torque creates a distribution of stress over the cross section. To keep things simple, we're going to focus on structures with a circular cross section, often called rods or shafts. When a torque is applied to the structure, it will twist along the long axis of the rod, and its cross section remains circular.

Fig.2 The angle lets us determine the shear strain at any point along the cross section.

Bibliographic

[1]	Douglas P. Holmes, «Mechanics of Materials: Torsion,» [En línea]. Available: https://www.bu.edu/moss/mechanics-of-materials-torsion/. [Último acceso: 15 Agosto 2021].