Point B is hinge.

$11\mathrm{.}2-8$ The figure shows an idealized structure con$-$ sisting of bars $AB$ and $BC$ that are connected using a hinge at $B$ and linearly elastic springs at A and $B.$ Rotational stiffness is denoted ${}_R$ and translational stiffness is denoted $.$

$($a$)$ Determine the critical load $P_{cr}$ for the structure from the figure part a$.$

$($a$)$ Find $P_{cr}$ if an elastic connection is now used to connect bar segments $AB$ and $BC$ from the figure part $b.$