Question

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. (0, 60, -30) kN
• B. (10, 30, -10) kN
• C. (30, -30, 30) kN
• D. (20, 0, 10) kN

Answer 1

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


$\sum F_H=0$
F = 0 ... (i)


$\sum F_V=0$
P = 30 ....(ii)

$\sum F_H=0$
$F_2=F_3$ ....(iii)
$F_2\times 3+30\times 3-F_3\times 1=0$
$F_2\times 3-F_2\times 1+90=0$
2$F_2=-90$
$F_2=-45$
$\Rightarrow$ $F_3=-45$



Q + R = 0...(iv)
$F_3\times 2+R\times 3=0$
-45 $\times 2+R\times 3=0$
R = 30 $\Rightarrow$ Q =-30