GATE Mechanical Engineering (ME) 2020 Shift 1 Solved Paper

Question : 34 of 65

Marks: +1, -0

The members carrying zero force (i.e. zero-force members) in the truss shown in the figure, for any load

P>0

with no appreciable deformation of the truss (i.e. with no appreciable change in angles between the members), are

Solution:

Moment at A

(P × 2 ℓ)=\;{R_{E}}/{√{2}} × 4 ℓ

⇒ R_{E}=\;{P}/{√{2}}

Pt. E

F_{1} \sin 45^{∘}+\;{R_{E}}/{√{2}}=0

\;{F_{1}}/{√{2}}+\;{R_{E}}/{√{2}}=0

F_{1}=-R_{E}

F_{1}=-\;{P}/{√{2}}

F_{1} \cos 45+F_{2}+\;{R_{E}}/{√{2}}=0

\;{-P}/{2}+F_{2}+\;{P}/{2}=0

F_{2}=0

Correction option D

{BF}=0

{DH}=0

{GC}=0

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