Part A

Determine the position $\backslash ($ a $\backslash )$ of roller support $\backslash ($ B $\backslash )$ in terms of $\backslash ($ L $\backslash )$ so that deflection at end $\backslash ($ C $\backslash )$ is the same as the maximum deflection of region $\backslash ($ A B $\backslash )$ of the simply supported overhang beam. $\backslash ($ E I $\backslash )$ is constant. $($Figure $1)$

Express your answer in terms of $\backslash ($ L $\backslash ).$

$\backslash [$

a$=$

$\backslash ]$