Before going through work done by couple, make sure to check torque and couple meaning from here.

Consider a wheel of radius ‘r’ rotating about an axis through a center due to the application of a couple of magnitude ‘F’ at points A and B.

Let’s consider a wheel covers angular displacement ‘‘ such that the wheel moves from A to A^{‘} as shown in the figure.

Work done in displacing from A to A^{‘} is given by: =

=

Similarly, Work done in displacing from B to B^{‘} is given by:

=

The total work done by a couple can be calculated by adding work done by both forces.

Where is the torque due to a couple which is calculated by the product of either force with the distance between them.