A load $P=30kN$ is applied to the below bearn as shown. The beam is simply supported

Where the reaction at the left support is $2\frac{P}{3}$ and ot the rieht support it is equal to $\frac{P}{3}.$

Consider a modulus of flexure stiffess Ele $2521\mathrm{.}9la.$

Consider the moment equation of the beam given as $M=\frac{2}{3}x-P,$ then apply

Macaulay's integration method to answer the following.

A$)$ Derive the equation of the slope and the deflection as function of integration

constants A and B$,[6$ marks$]$

B$)$ Solve for the integration of constants A and $B$ and determine their values and uni:

$[6$ marks$]$

C$)$ Express the condition that allows to determine the maximum deflection. At$.$

location in the beam the maximum deflection happens. $[5$ marks$]$