In a simply supported beam of span L subjected to central concentrated load, the central deflection is 24
mm. Then the slope at supports is:
-
A.
(48/L) radians
-
B.
(36/L) radians
-
C.
(24/L) radians
-
D.
(72/L) radians
Correct Answer:
D. (72/L) radians
Explanation:
For a simply supported beam of length L with a central point load P, the formula for maximum central deflection (δ) is PL^3 / 48EI, and the formula for the slope at the supports (θ) is PL^2 / 16EI.
By rearranging the deflection formula to solve for the term (P / EI), we get:
(P / EI) = 48δ / L^3
Substituting this into the slope formula:
θ = (48δ / L^3) \* (L^2 / 16)
θ = 3δ / L
Given that the central deflection (δ) is 24 mm:
θ = 3 \* (24) / L
θ = 72 / L radians
Therefore, the slope at the supports is (72 / L) radians, which corresponds to option D.
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