Question

A beam having a length of 20 metres is pivoted at its mid-point. A 200 N load is located at a point 5 m from the right hand end of the beam. A 300 N load is located at a point 8 m from the right hand end. In order for the beam to be in equilibrium, what load is required at the extreme left end of the beam

Answer 1

Take moments about the mid-point (pivot).

Distances from the pivot:
- 200 N is 5 m to the right,
- 300 N is 2 m to the right,
- the left end is 10 m to the left.

Sum of moments of the right-side loads = 200×5 + 300×2 = 1000 + 600 = 1600 N·m.

To balance, the moment from the left-end load W (at 10 m) must equal 1600 N·m:
W × 10 = 1600 ⇒ W = 160 N.

So a 160 N downward load at the extreme left end is required for equilibrium.