Problem $2(40$ points$).$ For the given beam with constant $EI,$ answer the questions using Moment$-$Area Methoa:

$($a$)[10$ points$]$ Draw the curvature diagram of the frame.

$($b$)[20$ points$]$ Moment$-$Area Method: Draw the elastic curve and show the geometric relations to find the slope angle at point $C,{}_C,$ and the horizontal displacement at point $B,{}_B.$

$($c$)[10$ points$]$ Moment$-$Area Method: Calculate ${}_B.$

Answers:

$($b$)$ Geometric relationship

$($c$){}_B=19\mathrm{.}1177(mm)$