Therefore it is important for us to know how to analyse the stresses on such structures due to torque loadings. The theory presented in this section is based on the assumption that:

1. the cross-sections are closed (no open-ends), and
2. thin enough such that the shear stress is even throughout the thickness.

We’ll be looking at the shear stress and angle of twist due to the torque loading.

Average shear stress

The average shear stress for torque-loaded thin-walled tubes can be calculated using:

Note:

• T is the torque applied (units: Nm)
• t is the thickness of the point where we are calculating τ_avg (units: m or mm)
• A_m is the mean area enclosed within the boundary of the cross-section, measured along the centreline of the thickness (units: m² or mm²)

An example of the A_m calculation is shown below:

Angle of twist

The angle of twist for torque-loaded thin-walled tubes can be calculated using:

Note:

• G is the shear modulus (units: GPa)
• L is the length of the beam. Often, questions ask for the angle of twist per unit length, in which you can shift L to get Φ/L
• ∮ ds is the perimeter of the enclosed area. For ∮ ds/t, each length of the perimeter is to be divided by its respective thickness (we’ll show you this in the example).

Let’s look at an example now.