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

$$\eqalign{ & {\text{Deflection max }}\left( {\text{A}} \right) = \frac{{{\text{P}}{{\text{L}}^3}}}{{48{\text{E}}I}} \cr & {\text{Deflection max }}\left( {\text{B}} \right) = \frac{{5{\text{w}}{{\text{L}}^4}}}{{384{\text{E}}I}};\,\,\,\left( {{\text{w}} = \frac{{\text{P}}}{{\text{L}}}} \right) \cr & = \frac{{5{\text{P}}{{\text{L}}^3}}}{{384{\text{E}}I}} \cr & {\text{Ratio}} = \frac{{{\text{P}}{{\text{L}}^3}}}{{48{\text{E}}I}} \times \frac{{384{\text{E}}I}}{{5{\text{P}}{{\text{L}}^3}}} = \frac{8}{5} \cr} $$