A pin-jointed truss has 9 joints and 17 members. It is supported by a hinge and a roller. What is the degree of indeterminacy?
- A0
- B1
- C2Correct
- D3
Solution
Concept
Static indeterminacy of pin-jointed planar truss
Formula
Ds = m + r - 2·j
Step-by-step solution
1. Total degree of static indeterminacy for a 2D pin-jointed truss is Ds = m + r - 2·j. 2. Given number of members m = 17, number of joints j = 9. 3. Support reactions r: hinge provides 2 reactions, roller provides 1 reaction; total r = 2 + 1 = 3. 4. Ds = 17 + 3 - 2·(9) = 20 - 18 = 2. Answer: C
Explanation
For a planar pin-jointed truss, total static indeterminacy is given by Ds = m + r - 2j. With 17 members, 3 support reactions from a hinge and roller, and 9 joints, Ds evaluates to 17 + 3 - 2(9) = 2.
Why the other options are wrong
A) 0 represents a statically determinate truss. B) 1 accounts for only one redundant member. D) 3 would require 18 members or 4 reactions.
Shortcut
Ds = m + r - 2·j = 17 + 3 - 18 = 2.
Common mistake
Forgetting to include external reaction components or using 3j instead of 2j for pin joints.
Correct answer: C) 2