Let n represent the number of members and y the number of joints; for a statically determinate frame, what is the relation n =________________?
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Answer: C. 2/-3
Explanation
A statically determinate pin-jointed plane frame satisfies the strict equilibrium condition between members and joints. The fundamental algebraic formula relating members and joints in such structures is given by two j minus three. Any planar framework adhering to this specific equation can be solved using equations of static equilibrium alone. Structural determinacy ensures that all internal forces can be determined using static equilibrium equations exclusively. Pin joints transmit only forces and are assumed to be frictionless hinges allowing free rotation. Trusses are common engineering examples of frameworks designed to be statically determinate.
Civil engineers verify structural determinacy before analyzing roof trusses and bridge frameworks. Structures with fewer members than required by this formula are unstable and prone to collapse. Redundant structures exceeding this formula require compatibility equations for complete structural analysis. Option A underestimates the required number of structural members needed to ensure planar stability. Option B represents an incorrect algebraic ratio that does not satisfy standard planar truss equilibrium. others
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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