The perfect pin Jointed frame should satisfy the equation (Where m = number of members and j = number of joints)
- Am = 2j – 4
- Bm = 3j – 3
- Cm = 3j – 2
- Dm = 2j – 3Correct
Solution
Concept
Determinancy equation for pin-jointed frames
Formula
m = 2j - 3
Step-by-step solution
1. A frame structure is considered statically determinate and stable (perfect) if it has just enough members to prevent collapse. 2. For a 2D pin-jointed plane frame, the condition for determinacy is given by m = 2j - 3. 3. If m < 2j - 3 the frame is deficient, and if m > 2j - 3 it is redundant or indeterminate. Answer: D
Explanation
A statically determinate and stable pin-jointed plane frame requires a minimum number of members to maintain its shape under load without being redundant or unstable. This condition is mathematically expressed by the formula m = 2j - 3, where m is the member count and j is the joint count. If m is less than this value, the frame becomes deficient, whereas if m is greater, it becomes redundant.
Why the other options are wrong
A) m = 2j – 4 does not represent a statically determinate 2D pin-jointed truss equation. B) m = 3j – 3 applies to rigid-jointed frames in a plane. C) m = 3j – 2 is not the condition for determinacy of a 2D pin-jointed frame.
Shortcut
Perfect 2D pin-jointed frame equation: m = 2j - 3.
Common mistake
Confusing the 2D plane frame determinacy equation (m = 2j - 3) with space frame formulas or wrong arithmetic constants.
Correct answer: D) m = 2j – 3