Torsion (mechanics)

From Wikipedia, the free encyclopedia

In solid mechanics, torsion is the twisting of an object due to an applied torque. In circular sections, the resultant shearing stress is perpendicular to the radius.

The shear stress at a point on a shaft is:

<math> \tau_{\theta_{z}} = {T r \over J} </math>

T is the applied torque, r is the distance from the center of rotation, and J is the polar moment of inertia.

The angle of twist can be found by using:

<math> \theta_{} = {T L \over JG} </math>

Where:

• θ is the angle of twist in radians.
• T is the torque (N*m or ft*lb_f).
• 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).
• J is the polar moment of inertia

[edit] Polar moment of inertia

Main article: Polar moment of inertia

The polar moment of inertia for a solid shaft is:

<math> J = {\pi \over 2} r^4 </math>

Where r is the radius of the object.

The polar moment of inertia for a pipe is:

<math> J = {\pi \over 2} (r_{o}^4 - r_{i}^4) </math>

Where the o and i subscripts stand for the outer and inner radius of the pipe.

[edit] See also

• torsion coefficient
• torsion pendulum
• torsion spring or -bar
• torque
• membrane analogyde:Windung (Geometrie)

es:Torsión (ingeniería) he:מאמץ פיתול it:Torsione

For a thin cylinder

J = 2π R³ t

Where R is the average of the outer and inner radius and t is the wall thickness