In solid mechanics, torsion occurs when an object is twisted or screwed around its axis. Torsion can be the result of an applied torque. It is a kind of shear stress. For circular sections, the shearing stress at a point on a transverse plane is always perpendicular to the radius to the point.

The shear stress at a point on a shaft is:

$\backslash tau\_\{\backslash theta\; z\}\; =\; \{T\; r\; \backslash over\; 2I\}$

T is the applied torque, r is the distance from the center pivot point, and I is the centroidal moment of inertia.

In Torsion, the angle of twist can be found by using:

$\backslash theta\_\{\}\; =\; \{T\; L\; \backslash over\; JG\}$

Where:

θ is the angle of twist in radians. You may notice that when solving for this value, all of the units cancel out and you are left with nothing. The radians are based on the derivations required to get to this equation.

T is the torque (N*m or ft*lb). Usually applied by gears.

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

J is the polar moment of intertia using:

For a solid material (e.g. Steel):

$J\; =\; \{\backslash pi\; \backslash over\; 2\}\; c^4$

Where c is the radius of the object.

For a hollow material such as a tube or material with two radii:

$J\; =\; \{\backslash pi\; \backslash over\; 2\}\; (c\_\{o\}^4\; -\; c\_\{i\}^4)$

Where the o and i subscripts stand for the outer and inner radii.

G is the shear modulous or more commonly the modulous of rigidity (GPa or ksi) = kip per square inch, 1 kip = 1000lb

See also

• torsion coefficient
• torsion pendulum
• torsion spring or -bar
• torque
• membrane analogy

Mechanics

Windung (Geometrie) | Torsión