$(0)$ Problem $3(20$ points$).$ For the given beam with constant $EI,$ answer the questions using Conjugate Beam Method:

$($a$)[10$ points$]$ Construct the conjugate beam for the given structure and loading. Answer:

$Ay=12kN$

$Cy=0,$ Moretat $A,{\displaystyle \underset{?}{\overset{?}{}}}MA=0,MA+12(3)=0,MA=-36kN-n,1*P=-36+12(3)=0$

$($b$)$ points$]$ Determine the deflection at point $C,{}_C,$ using conjugate beam method.

Answer: ${}_C=$

$-10$