Q$1$ A hinged beam structure is given in Figure $1.$

Figure $1$ Indeterminate Beam with an Internal Hinge $H$

Find the influence lines for:

$($a$)$ The vertical support reaction at $B$

$($b$)$ The shear force at $D$

$($c$)$ The bending moment at $D$

$($d$)$ The most unfavourable position of the uniformly distributed load $q$ for the above

$($e$)$ The corresponding extreme values of the quantities for this distributed load.