The 'theorem of three moments' (Clapeyron''s equation) is used for:
Choose the correct answer
Analysis of statically determinate trusses only
Analysis of continuous beams — relates bending moments at three consecutive supports to loading and settlement
Design of isolated footings
Column buckling load
Correct Answer
B. Analysis of continuous beams — relates bending moments at three consecutive supports to loading and settlement
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Clapeyron''s three-moment equation: MA×L1/I1 + 2MB(L1/I1+L2/I2) + MC×L2/I2 = −6A1ā1/(I1L1) − 6A2b̄2/(I2L2) + 6EI(δA/L1 − δB(1/L1+1/L2) + δC/L2). Relates moments at three consecutive supports of a continuous beam. One equation per interior support — solve simultaneously. Classic method before computers; now replaced by matrix methods.
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