Problem $1$: $(45$ points$)$

The steel truss ABC shown in the figure below is held by a hinge support at A $,$ a horizontal roller support at B$,$ and a vertical roller support at C$.$ The structure is stable and statically indeterminate to the $\backslash (1^\{\backslash$text $\{$st $\}\}\backslash )$ degree $($one support was added to the truss previously analyzed in "Learning assessment activity $\backslash$#I"$).$ All members have a constant axial rigidity $\backslash ($ E A$=30,000\backslash$mathrm$\{$kN$\}\backslash ).$

The truss is not subjected to any external forces, but member BC was fabricated $3$ cm too long, as shown.

Answer the following questions. Show all your work!!

Important Note: you can use several results already obtained in the solution of "Learning assessment activity $\backslash$#$1-$ Problem $1."$ If you do$,$ document them clearly.

$[$A$]$ Use the force method with the horizontal reaction at B as redundant

to calculate the internal forces in all the members of the truss.

$[$B$]$ Use a method of your choice to calculate the horizontal displacement

$\backslash ($ u$\_\{$C$\}\backslash )$ of node C $.$