In the structure shown, the beam is used to support a dead load of $\backslash (0\mathrm{.}6\backslash$mathrm$\{$k$\}/\backslash$mathrm$\{$ft$\}\backslash ),$ a live load of $\backslash (2\backslash$mathrm$\{$k$\}/\backslash$mathrm$\{$ft$\}\backslash )$ and a concentrated live load of $8$ k $.$ Assume the support at A is a pin and B is a roller. Using a moving dimensionless unit load,

a$.$ Draw the influence line diagram for the reaction at point A$.(7\mathrm{.}5$ points$)$

b$.$ Draw the influence line diagram for the shear force just to the right of point A$.(7\mathrm{.}5$ points$)$

c$.$ Draw the influence line diagram for the bending moment at point C $.(7\mathrm{.}5$ points$)$

d$.$ Using the result from part a$,$ determine the maximum positive $($upward$)$ reaction at A $(7\mathrm{.}5$ points$)$

e$.$ Using the result from part b $,$ determine the maximum positive shear just to the right of the support at A $(10$ points$)$

f$.$ Using the result from part c$,$ determine the maximum positive moment at C$.(10$ points$)$