J is the number of joints, B the number of members and R the number of reactions. If B = 4, R = 3 and J = 4, the truss is:
Try it first: pick an option, then read the explanation.
Correct answer: D. Unstable
Asked in SSC JE 22/01/2018 (Morning)
Detailed Explanation
Compare the number of unknowns (B + R) with the number of equations (2J).
\[ B + R = 4 + 3 = 7 \quad < \quad 2J = 8 \]
Equivalently, \(B_{req} = 2J - 3 = 5 > 4\).
Why “Unstable” Is Correct
There are fewer unknowns than equations, so the truss is deficient — a mechanism, i.e. unstable. A four-joint truss with four members is a quadrilateral with no diagonal, which can collapse sideways.
| Truss | Condition (j joints, m members, 3 reactions) | Behaviour |
|---|---|---|
| Perfect (determinate) | m = 2j − 3 | Stable; solvable by statics |
| Deficient | m < 2j − 3 | Unstable (a mechanism) |
| Redundant | m > 2j − 3 | Stable but statically indeterminate |
Why the Other Options Are Wrong
- A. Statically determinate: Determinate needs B + R = 2J (8); here it is 7.
- B. Statically indeterminate and stable: Indeterminate needs B + R > 2J.
- C. Stable: With too few members it cannot be stable.
Key Point
B + R < 2J → unstable; = 2J → determinate; > 2J → indeterminate.
Key Concepts for Students
- Adding one diagonal makes the quadrilateral a perfect truss.
- Counting is necessary but not sufficient for stability.
- Degree of indeterminacy = (B + R) − 2J.
Practice more: this is question 20 in Beams and Trusses MCQs – Part 2. Try the whole set and check every answer instantly.