Problem $2$

$(30$ points$)$

Draw the following influence lines of the beam in Figure $2$ by any method:

$(1)$ vertical force at support $\backslash (\backslash$boldsymbol$\{$B$\}\backslash ),(2)$ vertical force at support $\backslash (\backslash$boldsymbol$\{$F$\}\backslash ),(3)$ bending moment at support $\backslash (\backslash$boldsymbol$\{$F$\}\backslash ),$

$(4)$ shear force at point $\backslash (\backslash$boldsymbol$\{$C$\}\backslash ),$ and $(5)$ bending moment at point $\backslash (\backslash$boldsymbol$\{$E$\}\backslash ).$ Provide the numeric values at $\backslash (\backslash$boldsymbol$\{$A$\},\backslash$boldsymbol$\{$B$\}\backslash ),$

$\backslash ($ C$,$ D$,$ E $\backslash ),$ and $\backslash ($ E $\backslash ).$