Question

A simply supported beam 'A' carries a point load at its mid span. Another identical beam 'B' carries the same magnitude of load but it is uniformly distributed over the entire span. The ratio of the maximum deflections of beams 'A' and 'B' will be

• A. 8/3
• B. 2/3
• C. 3/5
• D. 8/5

Answer 1

The correct option is D 8/5

At the centre of simply supported beam,
(i) deflection due to point load is ${\delta }_A=\frac{W{L}^3}{48EI}$

(ii) Deflection due to UDL is ${\delta }_B=\frac{5}{384}\times \frac{w{L}^4}{EI}$

where wL = W

$\therefore {\delta }_B=\frac{5}{384}\times \frac{W{L}^3}{EI}$

$Hence,\frac{{\delta }_A}{{\delta }_B}=\frac{8}{5}$