The 'slope' at the free end of a cantilever beam of span L, EI, under end point load P is:
Choose the correct answer
θ = PL³/(3EI) (this is the deflection formula)
θ = PL²/(2EI) — slope at free end of cantilever under end point load
θ = PL/(EI)
θ = 2PL²/(EI)
Correct Answer
B. θ = PL²/(2EI) — slope at free end of cantilever under end point load
Why is this the answer?
Cantilever deflection: slope at free end θ = PL²/(2EI); deflection at free end δ = PL³/(3EI). For cantilever under UDL w: θ = wL³/(6EI), δ = wL⁴/(8EI). Mohr''s theorems: (1) change in slope = area of M/EI diagram; (2) deflection = moment of M/EI area about reference. Standard results used in superposition (e.g. propped cantilever analysis).
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