Torsion is the twisting in a bar when a force is applied to rotate it. A good example is a turning a screwdriver to screw in a screw.
Of course, there are wider applications of Torsion and this post will go into detail on Torsion from a mechanical engineering point of view. This page will be fairly barebones until I figure out a simple and efficient way of linking images to this site.
Torque on a shaft
Any force applied to a shaft that does not intersect with the central line of the shaft (i.e. doesn’t point directly at the centre of the shaft) will create a torque, or turning force, on the shaft. This in turn, creates shearing stresses on faces perpendicular to the axis, that is, on a circular shaft it’d be the circle cross-section.
Consider a very elastic metal shaft (or a very strong person): If the rod is twisted on one end, that end will rotate slightly due to deformation. This rotation is called the shearing strain \(\gamma\) (measured in rad) such that:
Where \(c\) is the radius of the shaft and \(\rho\) is the radial distance of the point from the shaft. I’ll include an illustrated graphic later.
Within the Elastic range
Given Hooke’s law: \(\tau=G\gamma\), the equation for shearing stress is:
The Elastic Tension Formula is:
Where \(J\) is the polar moment of inertia.
The important take-away is how to use the above formulae to calculate the theoretical maximum torque that can be safely applied to a shaft. In the case of a circular shaft:
For a solid circular shaft:
For a hollow circular shaft:
Angle of twist in the elastic range
Simply put, the angle of twist is given by:
Where \(\phi\) is the angle of twist in radians.
Extended for a general shaft subjected to varied torques: