$10\mathrm{.}4-36$ The continuous frame $\backslash ($ A B C $\backslash )$ has a pinned support at $\backslash ($ A $\backslash ),$ a sliding support at $\backslash ($ C $\backslash ),$ and a rigid corner connection at $\backslash ($ B $\backslash )($see figure$).$ Members $\backslash ($ A B $\backslash )$ and $\backslash ($ B C $\backslash )$ each have length $\backslash ($ L $\backslash )$ and flexural rigidity $\backslash ($ E I $\backslash ).$ A horizontal force $\backslash ($ P $\backslash )$ acts at mid$-$height of member $\backslash ($ A B $\backslash ).$

$($a$)$ Find all reactions of the frame.

$($b$)$ What is the largest bending moment $\backslash ($ M$\_\{\backslash$text $\{$max $\}\}\backslash )$ in the frame? Note: Disregard axial deformations in members $\backslash ($ A B $\backslash )$ and $\backslash ($ B C $\backslash )$ and consider only the effects of bending.

PROBLEM $10\mathrm{.}4-36$