Torsion

Torsion

In solid mechanics, torsion is the twisting of an object due to an applied torque. In sections perpendicular to the torque ax is, the resultant shear stress in this section is perpendicular to the radius.

For solid shafts of uniform circular cross-section or hollow circular shaf ts with constant wall thickness, the torsion relations are:

where:

·        R is the outer radius of the shaft i.e. m, ft.

·        t is the maximum shear stress at the outer surface.

·        f is the angle of twist in radians.

·        T is the torque (N·m or ft·lbf).

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

·        G is the shear modulus or more commonly the modulus of rigidity and is usually given

in gigapascals (GPa), lb f/in² (psi), or lbf/ft².

·        J is the torsion constant for the section. It is identical to the polar moment of inertia for a round shaft or concentric tube only. For other shapes J must be determined by other means. For solid shafts the membrane analogy is useful, and for thin walled tubes of arbitrary shape the she ar flow approximation is fairly good, if t he section is not re-entrant. For thick walle d tubes of arbitrary shape there is no simp le solution, and finite element analysis (FEA) may be the best method.

·        The product GJ is calle d the torsional rigidity.