Mathematical idealization of a crane has three bars with

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Mathematical idealization of a crane has three bars with their vertices arranged as shown in the figure with a load of 80 kN hanging vertically. The coordinates of the vertices are given in the parentheses. The force in the member QR, F_QR will be

1. 30 kN Compressive
2. 30 kN Tensile
3. 50 kN Compressive
4. 50 kN Tensile

Correct Option: A

Take moment about R
∑ M_R = 0
80 × 3 = VQ × 2
∴ V_a = 120 kN
Consider Joint Q

∠ PQR = 104.03°
∴ Q = 104.03° – 90 = 14.03°
Resolve vertically,
∑ F_v = 0
F_QP .cos + V_Q = 0

∴ F_QP =	120
	cos14.03°

Resolve horizontally,
∑ F_H = 0
F_QP sin θ = F_QR

	120	× sin14.03° = F_QR
	cos14.03°

∴ F_QR = 120 × tan 14.03° = 30 kN_M