To calculate torque on a supported beam

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gnits
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Homework Statement
To calculate torque on a supported beam
Relevant Equations
equate forces and torques
Could I please ask for help with the last part of the following question?

Text problem on a non-uniform rigid beam AB of length 3a and weight nW resting on supports P and Q, with AP = PQ = QB = a, including the final part asking to show L = (1/3)(n + 1)Wa.


I have the first two parts done, answers are:

Distance of COG from A = a(1+n)/n

and W1 = W(1+n)/3

I can't see how to go about the last part. Here's my diagram for the system prior to the torque L being added:

Free-body diagram of a horizontal beam from A to B with supports P and Q, weights W at A, nW at x from P, and W1 at B, with forces F1 and F2 upward at the supports and spacing a, a, a and d = a - x labelled.

In this situation we have (are told) F1 = F2 = F say, and so W1 + W + nW = 2F and so as we know W1 in terms of W and n we have F = 2W(n+1)/3 and we are told that after torque L is applied then this increases by 1.5 times, so now F1 = W(n+1) and so F2 = W(n+1)/3. As F1 has increased then we know that L is counter-clockwise.

Can't see though what equation to set up to calculate the L which would lead to this value for F1.

Thanks for any help,
Mitch.
 
Of all the forces acting on the beam after L is applied, which is the one that you neither know nor care about? What axis can you take moments about to avoid involving that force?
 
haruspex said:
Of all the forces acting on the beam after L is applied, which is the one that you neither know nor care about? What axis can you take moments about to avoid involving that force?

Thanks very much. That helped me to see it. Moments about Q.

Mitch.