Plank Resting on Two Supports

A plank resting on two supports, as below, will experience reaction forcesandat each support.

Resolving vertically, (upwards forces equal downwards forces), gives(1)

Since we have two unknownsandassuming W is known, besides the equation above, we need one other equation to findandWe can obtain this equation by taking moments, either aboutorTaking moments aboutgivesand from this we obtain

Substituting this into (1) gives

Suppose now that someone stands on the plank. The weight of the person is twice the weight of the plank, and they stand betweenand1m from

Resolving vertically now gives(2)

Talking moments aboutgivesand from this we obtain

Substituting this into (2) gives