Beams and Moments
If we have a beam resting on two supports, an example of which is shown below, it will be held up by the reactions A and B at the two supports. We can resolve vertically to get an equation for A and B but this is not sufficient to find A and B. To find A and B we need to find another equation. We can do this by taking moments about a point. If the beam is uniform the weight will act through the centre of the rod. This is shown below as the 70N force, which will act at a point 1.5m from either end, or 1m from A.
Resolving vertically gives us the equation(1)
Taking moments about A gives
Then from (1)
It is important to note that the following assumptions have been made:
The beam is uniform so the weight acts at the midpoint.
The beam is rigid and does not bend so all the distances are horizontal and add in a natural way.