The $12$ foot long steel beam weighs $97$ lb$.$ft $($Hint: this corresponds to a distributed load located at the center of the beam of $97*12=1164$ lb$).$ In addition to its own weight, the beam carries a $40$ kip load at the point shown. Two bearing pads that are $11$ in by $8$ in and $0\mathrm{.}5$ in thick are placed between the beam on the concrete beneath it $($Hint: area needed to obtain compressive strength is $11*8$ in$*$in$).$ These pads serve to distribute the force more evenly. The bearings have an elastic modulus of $3000$ psi.

$1)$ Estimate the deflection $($elongation$)$ of the beam at each pad assuming each pad deforms uniformly. Clearly identify its sign.

$2)$ With the deflection computed in part $1,$ estimate the angle at which the beam tilts.