A simply$-$supported beam $AB$ is under two concentrated loads of magnitude $P$ as

shown in the figure below. The equations of the elastic curve and the slope found

using the double integration method are shown below.

For coordinate $x_1,$

$EI\frac{d^2{v}_1}{d{x}_1^2}-P{x}_1$

$EI\frac{d{v}_1}{d{x}_1}-\frac{P}{2}{x}_1^2+C_1$

$EI{v}_1=\frac{P}{6}{x}_1^3+C_1{x}_1+C_2$

For coordinate $x_2,$

$EI\frac{d^2{v}_2}{d{x}_2^2}=Pa$

$EI\frac{d{v}_2}{d{x}_2}=Pa{x}_2+C_3$

$EI{v}_2=\frac{Pa}{2}{x}_2^2+C_3{x}_2+C_4$

The maximum deflection will occur at the center of the beam due to symmetry

considerations. Use appropriate symmetry, boundary and continuity conditions to

find the values for integration constants $C_1$ and $C_3.$ Select the correct values from

the options given below. To get full points you need to justify vour answer.