Civil Engineering MCQAE Level Civil Engineering
For a fixed-fixed beam of span L and plastic moment capacity M_p, the plastic collapse load for a central concentrated load is:
Structural AnalysisFixed-Fixed Collapse LoadMEDIUM
Choose the correct answer
A
4M_p/L
B
6M_p/L
C
8M_p/L
D
12M_p/L
Correct Answer
C. 8M_p/L
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Three hinges form at collapse: both fixed ends and midspan. Virtual work: W × L/4 × θ = M_p(θ + 2θ + θ) = 4M_pθ. Hence W = 8M_p/L... wait, let me redo: W × (Lθ/4) = M_p × 4θ → W = 16M_p/L? No. With central load, δ = L/2 × θ (if θ is end rotation): W × Lθ/2 = M_p × (θ + 2θ + θ) = 4M_p×θ → W = 8M_p/L. ✓
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