# Torsional Stiffness

on . Posted in Classical Mechanics

Torsional stiffness, abbreviated as $$k$$, is a material's or a structure's resistance to twisting or torsional deformation when subjected to a torque or rotational force.  It is a measure of how much a material or structure resists being twisted or rotated around its longitudinal axis.  Torsional stiffness is an important mechanical property in various engineering applications, especially in the design of components and structures that experience torsional loads.

Torsional stiffness is determined by the material properties, cross-sectional geometry, and the length of the component or structure.  Materials with a higher shear modulus are stiffer in torsion and can withstand larger torsional loads without excessive deformation.

Torsional stiffness is crucial in various engineering applications, including the design of shafts, drive systems, vehicle suspensions, and mechanical components that transmit rotational forces.  Engineers and designers calculate torsional stiffness to ensure that a structure or component can handle the expected torsional loads without excessive twisting or deformation, which could lead to failure or reduced performance.

### Torsional Stiffness FORMULA

$$k = G \; J \;/\; l$$     (Torsional Stiffness)

$$G = k \; l \;/\; J$$

$$J = k \; l \;/\; G$$

$$l = G \; J \;/\; k$$

Symbol English Metric
$$k$$ = torsional stiffness  $$lbf-ft\;/\;deg$$ $$N-m\;/\;rad$$
$$G$$ = shear modulus $$lbf\;/\;in^2$$ $$Pa$$
$$J$$ = torsion constant (polar momentum of inertia) $$in^4$$ $$mm^4$$
$$l$$ = length $$in$$ $$mm$$