A truss containing j joints and m members will be a simple (perfect) truss if:
Try it first: pick an option, then read the explanation.
Correct answer: B. m = 2j − 3
Asked in SSC JE 03/03/2017 (Evening); SSC JE 04/03/2017 (Evening)
Detailed Explanation
A simple truss starts as a triangle (3 joints, 3 members). Each new joint is added with 2 new members.
Start: \(m = 3,\ j = 3\). Each step adds 1 joint and 2 members, so
\[ m - 3 = 2(j - 3) \;\Rightarrow\; m = 2j - 3 \]
Why “m = 2j − 3” Is Correct
This is also the count that makes the number of unknowns (m + 3 reactions) equal to the number of joint equations (2j). So a perfect plane truss satisfies m = 2j − 3.
| 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. j = 2m − 3: m and j are swapped.
- C. m = 3j − 2: 3j − 2 does not come from adding two members per joint.
- D. j = 3m − 2: Swapped and wrong coefficients.
Key Point
Perfect plane truss: m = 2j − 3. Space truss: m = 3j − 6.
Key Concepts for Students
- A single triangle: 3 = 2(3) − 3.
- Deficient: m < 2j − 3; redundant: m > 2j − 3.
- Space truss joints give 3 equations each.
Practice more: this is question 24 in Beams and Trusses MCQs – Part 2. Try the whole set and check every answer instantly.