The 'fixed end moment' (FEM) for a fixed-fixed beam under UDL w is wL²/12 because:
Choose the correct answer
From simple beam formula wL²/8
From slope-deflection with zero end rotations: moment needed to prevent rotation at fixed ends under UDL
Experimentally derived constant
Only valid for point loads
Correct Answer
B. From slope-deflection with zero end rotations: moment needed to prevent rotation at fixed ends under UDL
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Fixed-fixed beam under UDL w: slope-deflection equations with θA=θB=0 (no rotation) and Δ=0 (no sway). FEM = ±wL²/12 at each end (hogging at supports). The value wL²/12 comes from integrating the moment-area or slope-deflection: EI×θ = (area of M/EI diagram) = 0 at fixed ends. Midspan moment = wL²/24 (vs wL²/8 for SS beam). Total of support + midspan = wL²/8.
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