Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let RP, RQ, and RR denote the vertical reactions (upward positive) applied by the supports at P, Q, and R, respectively

Q. Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let R_P, R_Q, and R_R denote the vertical reactions (upward positive) applied by the supports at P, Q, and R, respectively, on the truss. The correct combination of (R_P, R_Q, R_R) is represented by

(A) (30, –30, 30) kN

(B) (20, 0, 10) kN

(C) (10, 30, -10) kN

(D) (0, 60, -30) kN

Ans: (30, -30, 30) kN

Solution:

The correct option is C (30, -30, 30) kN

∑FH=0
F = 0 … (i)

∑FV=0
P = 30 ….(ii)

∑FH=0
F2=F3 ….(iii)
F2×3+30×3−F3×1=0
F2×3−F2×1+90=0
2F2=−90
F2=−45
⇒ F3=−45

Q + R = 0…(iv)
F3×2+R×3=0
-45 ×2+R×3=0
R = 30 ⇒ Q =-30