Two cantilever beams, sharing the same cross$-$sectional geometry and Young's modulus $(E),$ are built$-$in as illustrated in Fig. P$2($a$)$ and subjected to an end load $P,$ as shown in Fig. P$2($b$).$ It is assumed that the two beams remain in contact at $x=0$ and $x=L$ during the deflection of the beam.

$[25$ pts$]$

$($a$)$ Derive the equation of the elastic curve using the integration method. $[15$ pts$]$

$($b$)$ Determine the maximum deflection and the maximum slope of the beam. $[10$ pts$]$

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Fig. P$2$