$($a$)$ Figure $1$ shows a bridge girder which is constructed to allow vehicle to travel on it$.$ The supports at B and D are pin and roller, respectively. Draw the influence lines for

$[$i$]$ the vertical reactions at supports B and D$,$

$[$ii$]$ the shear force at point $C,$ and

$[$iii$]$ the bending moment at point $C.$

$($b$)$ Determine the maximum values of

$[$i$]$ the vertical reaction forces at supports B and D$,$

$[$ii$]$ the positive shear force at point $C,$ and

$[$iii$]$ the positive bending moment at point $C,$

due to a truck travels from point $E$ to point $A.$