Instability occurs in a pin-jointed plane frame when________________?
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Answer: A. (m + r)<2j
Explanation
A pin-jointed plane frame requires a minimum number of members and supports to maintain geometric stability. When the combined count of members and reactions falls below twice the number of joints, internal mechanisms form. Therefore, the mathematical condition (m + r) < 2j correctly identifies a structurally unstable pin-jointed plane frame. Stability criteria for planar trusses ensure that rigid bodies are fully constrained against rigid-body translations and rotations. The variable m represents total framework members, r represents support reactions, and j denotes total pin joints. A deficiency in members or reactions creates unconstrained degrees of freedom leading to collapse under load.
The condition m + r equals 2j defines a stable and statically determinate pin-jointed plane frame system. When (m + r) exceeds 2j, the pin-jointed plane frame is classified as stable and statically indeterminate. Selecting none of the above is wrong because the instability condition formula is explicitly provided in option A.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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