Answer:
F(F) = 15037 lb
F(E) = 24481.5 lb
F(D) = 24481.5 lb
Step-by-step explanation:
(The diagram of the figure and Free Body Diagram is attached)
Data given:
W(A) = 50,000 lb
W(B) = 8000 lb
W(C) = 6000 lb
∑F = 0
F(F) + F(E) + F(D) - W(A) - W(B) - W(C) = 0
F(F) + F(E) + F(D) = W(A) + W(B) + W(C)
F(F) + F(E) + F(D) = 50000 + 8000 + 6000
F(F) + F(E) + F(D) = 64000 lb
∑M(o)
∑M(o) = M(F) + M(E) + M(D) + M(A) + M(B) + M(C)
Where
M(F) = 27i × F(F)k = -27F(F)j
M(E) = 14j × F(E)k = 14F(E)i
M(D) = -14j × F(D)k = -14F(D)i
M(A) = 7i × -50000k = 350,000j
M(B) = (4i - 6j) × -8000k = 48000i + 32000j
M(C) = (4i + 8j) × -6000k = -48000i + 24000j
∑M(x) = ∑M(i) = 0
∑M(i) = 14F(E) - 14F(D) = 0
F(E) = F(D)
∑M(y) = ∑M(j) = 0
∑M(j) = -27F(F) + 350,000 + 32,000 + 24,000 = 0
27F(F) = 406,000
F(F) = 15037 lb
F(F) + F(E) + F(D) = 64000 lb
F(E) = F(D)
F(F) + 2F(E) = 64000
2F(E) = 64000 - 15037
2F(E) = 48963
F(E) = 24481.5 lb
F(D) = 24481.5 lb