Look up torsion in Wiktionary, the free dictionary.

Wikibooks has a book on the topic of

Solid Mechanics

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. Wikipedia does not have an article with this exact name. ... Wiktionary is a Wikimedia Foundation project intended to be a free wiki dictionary (hence: Wiktionary) (including thesaurus and lexicon) in every language. ... Image File history File links Wikibooks-logo-en. ... Wikibooks logo Wikibooks, previously called Wikimedia Free Textbook Project and Wikimedia-Textbooks, is part of the Wikimedia Foundation. ... Solid mechanics is the branch of physics and mathematics that concern the behavior of solid matter under external actions (e. ... In physics, torque can be thought of informally as rotational force. The SI units for Torque are newton meters although centinewton meters (cN·m), foot-pounds force (ft·lbf), inch pounds (lbf·in) and inch ounces (ozf·in) are also frequently used expressions of torque. ... Shear stress is a stress state where the shape of a material tends to change (usually by sliding forces -- torque by transversely-acting forces) without particular volume change. ...

The shear stress at a point on a shaft is:

T is the applied torque, r is the distance from the center of rotation, and J is the polar moment of inertia. Polar moment of inertia is a measure of an objects ability to resist torsion. ...

The angle of twist can be found by using:

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

The radian is a unit of plane angle. ... The newton (symbol: N) is the SI unit of force. ... The metre, or meter (US), is a measure of length. ... A foot (plural: feet) is any of several old units of distance or length, measuring around a quarter to a third of a meter. ... A pound-force (abbreviations: lbf or lbf) is a unit of force. ... In materials science, shear modulus S, sometimes referred to as the modulus of rigidity, is defined as the ratio of shear stress to the shear strain: S = shear stress/shear strain = (F/A)/Φ. Another commonly accepted symbol is G. Shear modulus is usually measured in ksi (kips per square inch... The gigapascal, symbol GPa is an SI unit of pressure. ... Polar moment of inertia is a measure of an objects ability to resist torsion. ...

Polar moment of inertia

Main article: Polar moment of inertia

The polar moment of inertia for a solid shaft is: Polar moment of inertia is a measure of an objects ability to resist torsion. ...

Where r is the radius of the object.

The polar moment of inertia for a pipe is:

Where the o and i subscripts stand for the outer and inner radius of the pipe. In classical geometry, a radius of a circle or sphere is any line segment from its center to its boundary. ...

See also

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