A Torsion

1. The act of turning or twisting, or the state of being twisted; the twisting or wrenching of a body by the exertion of a lateral force tending to turn one end or part of it about a longitudinal axis, while the other is held fast or turned in the opposite direction.
2. (mechanics) That force with which a thread, wire, or rod of any material, returns, or tends to return, to a state of rest after it has been twisted; torsibility.
3. (surgery) The stopping of arterial haemorrhage in certain cases, by twisting the cut end of the artery.

Structural Engineering

Torsion (vridning) is the twisting of an object due to an applied force. In structural mechanics, it occurs when a structural element, such as a shaft or a beam, is subjected to a moment that causes it to twist around its longitudinal axis.

Torsion moment (vrimoment or torsjonsmoment), often simply called torque (\(T\)), is the measure of this applied twisting force. It is calculated as the product of the applied force (\(F\)) and the perpendicular lever arm distance (\(d\)) from the axis of rotation to the line of action of the force.

\[T = F \cdot d\]

Mechanics of Materials (Fasthetslære)

When a torsion moment is applied to a solid circular shaft, the element must remain in static equilibrium. The external moment generates two critical internal responses:

1. Shear Stress (\(\tau\)): The twisting action creates internal shear stress that varies linearly across the cross-section. It is zero at the center of the shaft and reaches its maximum at the outer surface.

\[\tau_{max} = \frac{T \cdot r}{I_p}\]

• \(r\): Outer radius of the shaft.
• \(I_p\): Polar moment of inertia (polart arealmoment). For a solid circular cross-section, \(I_p = \frac{\pi \cdot r^4}{2}\).
• \(I_p\): Polar moment of inertia (polart arealmoment). For a solid circular cross-section, \(I_p = \frac{\pi \cdot r^4}{2}\).

2. Angle of Twist (\(\phi\)): This defines the total angular deformation over the length of the shaft.

\[\phi = \frac{T \cdot L}{G \cdot I_p}\]

• \(L\): Length of the shaft.
• \(G\): Shear modulus (skjærmodul) of the material.

Design Note: When modeling rotating mechanical parts like drive axles in 3D CAD software such as PTC Creo, verifying the maximum shear stress (\(\tau_{max}\)) against the material's yield limit prevents torsional failure. If the stress exceeds the limit, the design requires an increased radius or a material with a higher shear modulus.