GATE ME 2020 Set 1 — Question 15
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Engineering Mechanics → Statics → Trusses (Joints & Sections)
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Question
The members carrying zero force (i.e. zero-force members) in the truss shown in the figure, for any load with no appreciable deformation of the truss (i.e. with no appreciable change in angles between the members), are
Correct answer
(C) BF, DH, GC, CD and DE only
Solution
Step-by-step identification of zero-force members:
1.Joint B: Members AB and BC are collinear, and BF is the third member. Since there is no external load or support at B, .
2.Joint G: Members FG and GH are collinear, and GC is the third member. With no external load at G, .
3.Joint E: The support is a roller on a incline. The reaction force is perpendicular to the incline (at to the vertical). Member HE is also at a angle (1m height, 1m width). Since and are collinear, summing forces perpendicular to this line at joint E gives , so .
4.Joint D: Since , we are left with members CD and DH. These two members are not collinear and there is no external load at D, so both must be zero-force members: and .
Combining these, the zero-force members are BF, DH, GC, CD, and DE.Continue learning with Success Tracker
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