Relabel the figure as:
From the equilibrium condition:
The vertical equilibrium:
The varying load given is divided into a rectangle and a triangular load.
w1L + (1/2)(w2 - w1)L = P + 2P
w1L + (1/2)w2L - (1/2)w1L = 3P
(1/2)w1 + (1/2)w2L = 3P/L
w1 + w2 = 6P/L
Considering the moment at B:
w1L + (1/2)L + (1/2)(w2 - w1)L + (1/3)L = P(2/3)L + 2P(1/3)L
w1L2/2 + w2L2/6 - w1L2/6 = 4PL/3
2w1 + w2 = 8P/L
If P = 500 lb and L = 12 ft., what are the magnitudes of w1, w2 ?
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