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Theory of Structures

Q1:

A simply supported beam which carries a uniformly distributed load has two equal overhangs. To have maximum B.M. produced in the beam least possible, the ratio of the length of the overhang to the total length of the beam, is

A 0.207

B 0.307

C 0.407

D 0.508

ANS:A - 0.207

For overhanging beam on both sides;

If a = length of overhang.
L= length of the overall span.
l = length of span b/w supports = L-2a;
(+ve) Max BM = (-ve) Max BM.
Wl^2/8 - Wa^2/2 = Wa^2/2.
a = l/2*2=0.35 * l.
a = 0.35(L-2a).
a = 0.207L.
Ratio; a/L = 0.207.



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