A 'propped cantilever' of span L under UDL w has propping reaction R at the free end equal to:
Choose the correct answer
R = wL/2
R = 3wL/8 — found by compatibility (zero deflection at prop) using superposition of cantilever and prop
R = wL/4
R = wL (full span load on prop)
Correct Answer
B. R = 3wL/8 — found by compatibility (zero deflection at prop) using superposition of cantilever and prop
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Propped cantilever: fixed at A, prop at B. Deflection at B = 0. Superpose: cantilever deflection under w = wL⁴/(8EI); upward prop deflection = RL³/(3EI). Setting sum = 0: R = 3wL/8. Fixed end reaction at A = 5wL/8 (vertical). Fixed moment at A = wL²/8. Maximum sagging BM under UDL occurs at x = 5L/8 from fixed end.
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