GATE ME 2014 Set 2 — Question 17
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Engineering Mechanics → Statics → Trusses (Joints & Sections)
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Question
A two member truss is shown in the figure. The force (in kN) transmitted in member is
Correct answer
18 to 22
Solution
To find the force in member , we analyze the equilibrium of joint .
1.Geometry of the Truss:
- Member is horizontal with length .
- Member is vertical with length .
- Let be the angle member makes with the horizontal member .
- From the geometry, .
- A vertical downward load of is applied at joint .
- Let be the force in member and be the force in member .
- Summing forces in the vertical () direction:
- Summing forces in the horizontal () direction:
3.Calculating the Force in AB:
- From Eq. 1, .
- Substitute into Eq. 2:
- Since , then .
4.Conclusion:
- The negative sign indicates that the member is in compression.
- The magnitude of the force transmitted in member is .
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