What is the condition for stability of truss with b number of bars, r number of external support reactions with j number of joints ?
- Ab + r = 2jCorrect
- Bb + r > 2j
- Cb + r < 2j
- Db + r < j
Solution
Concept
Static determinacy and stability of a plane truss
Formula
b + r = 2j (stable and statically determinate)
Step-by-step solution
1. A stable and statically determinate plane truss satisfies b + r = 2j. 2. If b + r < 2j the truss is unstable; if b + r > 2j it is indeterminate.
Explanation
The number of equilibrium equations at the joints (2j) equals the number of unknown bar forces and reactions (b + r) for a determinate truss.
Why the other options are wrong
b + r < 2j (c) means unstable. b + r > 2j (b) is a statically indeterminate (but also stable) truss. b + r < j (d) is much less than needed.
Shortcut
b + r = 2j: determinate; < 2j: unstable; > 2j: indeterminate.
Common mistake
Choosing the indeterminate case.
Correct answer: A) b + r = 2j