The structure in Figure $1$ is statically determinate and has two sections $(AB$ and $BC.$

Determine the influence lines for the following quantities, showing all important values:

$($i$)$ Reaction force at $A$

$($ii$)$ Shear force at $B$

$($iii$)$ Shear force at $C$

$($iv$)$ Moment at midspan between $B$ and $C$

The beam is subjected to a live concentrated load of $50kN$ and a dead load of $5k\frac{N}{m}.$ Determine the

worst hogging moment at midspan between B and C$.$