If a structure has 10 joints, at how many joints (at minimum) must the equilibrium equations be satisfied for stability?
Try it first: pick an option, then read the explanation.
Asked in SSC JE 27/01/2018 (Evening)
Detailed Explanation
A structure is in equilibrium only if every part of it is in equilibrium. In a pin-jointed truss, each joint is a ‘part’ where forces meet.
Why “10” Is Correct
If even one joint were not in equilibrium, that joint would move and the structure would not be at rest. So the equilibrium equations must hold at all 10 joints — option (d).
Note: the commission cancelled this question in its revised key, probably because the wording (‘minimum number … for stability’) is unclear. The principle is that all joints must be in equilibrium.
Why the Other Options Are Wrong
- A. 7: Three joints would be left unbalanced.
- B. 8: Two joints would be left unbalanced.
- C. 9: One joint would be left unbalanced.
Key Point
Equilibrium of a structure = equilibrium of every joint and member.
Key Concepts for Students
- 2j equations are available for a plane truss with j joints.
- Three of these are used up by overall equilibrium (reactions).
- Method of joints uses ΣFx = 0 and ΣFy = 0 at each joint.
Practice more: this is question 7 in Beams and Trusses MCQs – Part 1. Try the whole set and check every answer instantly.