Plank Resting on Two Supports
A plank resting on two supports, as below, will experience reaction forces
and
at each support.
Resolving vertically, (upwards forces equal downwards forces), gives
(1)
Since we have two unknownsand
assuming W is known, besides the equation above, we need one other equation to findand
We can obtain this equation by taking moments, either aboutorTaking moments aboutgives
and 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 aboutgives
and from this we obtain
Substituting this into (2) gives
