MecMovies 4.0 : M6.2: Torsion Theory for Circular Sections

A small area d A is located at a radial distance rho from the axis of the shaft. A torque T acts on the shaft. A shear stress tau acts on the surface d A. Moment about shaft axis, d M = rho time tau d

We must determine the relationship between the torque

T

transmitted by the shaft and the shear stress

τ

that is developed internally in the shaft material.

Suppose we consider a very small portion of the cross-sectional surface. This area $dA$ is located at a radial distance $ρ$ from the axis of the shaft.

In response to applied torque $T$ , shear stresses $τ$ are developed on the cross-sectional surfaces.

Stress is defined as force per unit area. The resultant shear force acting on the small element is simply the product of $τ$ and $dA$ .

Moment is the product of a force and a distance. For the small area that we are considering, the resultant shear force $τ dA$ acting at a radial distance $ρ$ creates a moment $dM$ about the shaft axis.