Question

A simply supported rectangular beam of span L and depth 'd' carries a central load W. The ratio of maximum deflection to maximum bending stress is

• A. $\frac{L^2}{6Ed}$
• B. $\frac{L^2}{8Ed}$
• C. $\frac{L^2}{48Ed}$
• D. $\frac{L^2}{12Ed}$

Answer 1

The correct option is A $\frac{L^2}{6Ed}$

$Maximumbendingmoment,M=\frac{WL}{4}$

$Maximumdeflection,\delta =\frac{W{L}^3}{48EI}$

$Maximumbendingstress,f=\frac{M}{Z}$

$\therefore \frac{\delta }{f}=\frac{L^{2}Z}{12EI}=\frac{L^2}{6Ed}(as\frac{I}{Z}=\frac{d}{2})$