5 The beam to be is supported by a roller and pin support as

5. The beam to be is supported by a roller and pin support as shown The moment at B is replaced by couple acting at points A and C. What is the magnitude of the Forces that constitute the force couple 100 N 150 N/m 3 Nm 0.2m o.8m 0.3m 0.5m

Solution

A couple consists of two parallel forces that are equal in magnitude, opposite in sense and do not share a line of action.  The resultant force of a couple is zero. BUT, the resultant of a couple is not zero; it is a pure moment.

Let F be the force that acts on the force couple

The moment at B is replaced by the force acting on A and C

Moment at B= Moment at A+Moment at C

3Nm=-100N*[0.2+0.8]m +F*[0.3+0.5]m

3Nm=-100Nm+F*0.8 m

103Nm= F*0.8 m

F=103/0.8=128.75N

The magnitude of the force that constitute the force couple is 128.75N