The pin-jointed 2-D truss is loaded with a horizontal force

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The pin-jointed 2-D truss is loaded with a horizontal force of 15 kN at joint S and another 15kN vertical force at joint U, as shown. Find the force in member RS (in kN) and report your answer taking tension as positive and compression as negative.

1. 0
2. 1
3. 3
4. 2

Correct Option: A

∑ M_T = 0
⇒ R_v × 8 – 15 × 4 + 15 × 4 = 0
∴ R_v = 0
Take moment about V, MV = 0
⇒ R_H × 4 = 0
∴ R_H = 0
We know that if two members meet at a joint which are not col-linear and also there is no external forces acting on that joint then both members will carry zero forces.
∴ F_QV = F_QR = 0
Now, consider joint R
∑ F_y = 0

⇒ F_RU sin 45º = 0
⇒ F_RU = 0
Now, 0 ∑ F_x = ⇒ F_RS + F_RU cos 45º = 0
⇒ F_RS + F_RU cos 45º = 0
∴ F_RS = 0
So, force is member is “RS” will be zero.