Q$2(50$ points$)$: Method of Virtual Works for Frames

For the below loaded frame, take $E=200$GPa,$I=70({10}^6)m{m}^4.$ Note that the frame is fixed at A with roller support provided at $C$ and there is a hinge at point $B.$

Using the Virtual Work Method, you are required to:

$(1)$ The Real Moments $($BMD$)[15$points$].$

$(2)$ The Horizontal Displacement at point B in $mm[25$points$].$

$2\mathrm{.}1.$ The Virtual Moments $($BMD$)[15$points$].$

$2\mathrm{.}2.$ The Horizontal Displacement at point B in mm $[10$points$].$

$(3)$ The slope ${}_A[5$points$].$

$(4)$ The Vertical Displacement at point $C$ in $mm[5$points$].$