GATE Civil Engineering (CE) 2019 Shift 1 Solved Paper

Question : 35 of 65

Marks: +1, -0

Consider the pin-jointed plane truss shown in the figure (not drawn to scale). Let

{R}_{ {P}}, {R}_{ {Q}}

, and RR 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

Solution:

Σ F_{M}=0

F_{1}=0

.....(i)

Σ F_{v}=0

{p}=30

....(ii)

Σ F_{H}=0

{F}_{2}= {F}_{3} . . .

(iii)

{F}_{2} × 3+30 × 3- {F}_{3} × 1=0

{F}_{2} × 3- {F}_{2} × 1+90=0

2 {F}_{2}=-90

{F}_{2}=-45

⇒ {F}_{3}=-45

{Q}+ {R}=0 . . . \;\text " (iv) "\;

{F}_{3} × 2+ {R} × 3=0

\;\; -45 × 2+ {R} × 3=0

{R}=30 ⇒ {Q}=-30

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