A rigid-jointed plane frame comprising 14 joints, 15 members, and 3 reaction components possesses a static indeterminacy degree of__________________?
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Answer: C. 6
Explanation
Degree of static indeterminacy for a rigid plane frame is calculated using the formula 3m plus r minus 3j. Substituting fifteen members, three reaction components, and fourteen joints yields 3 times 15 plus 3 minus 3 times 14. Evaluating this arithmetic expression results in forty-five plus three minus forty-two, giving a final degree of six. Static indeterminacy measures the number of unknown forces exceeding the available equations of static equilibrium. Each member adds three internal force unknowns, each reaction adds one, and each rigid joint provides three equations. Rigid-jointed plane frames transmit axial, shear, and bending forces across every continuous structural member connection.
An indeterminacy degree of two underestimates the structural redundancy resulting from the given joint and member counts. An indeterminacy degree of three fails to account for the actual number of independent joint equilibrium equations. An indeterminacy degree of eight overestimates the redundant unknowns based on correct formula substitution.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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