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.

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