In the figure below, $a,b,$ and $c$ are hinges, which is a three$-$hinge collinear

structure, and point b bears a load $P.$

$E,$I, and A are the elastic modulus, moment of inertia, and cross$-$sectional

area of the component respectively. Assuming that the rotation of point a

and c are extremely small, the small deformation theory still applies. Try

to find the vertical displacement of point $b.($Tip: After point $b$ performs

displacement, the three hinges are no longer collinear$)$