Task $2$: Supporting structure in R$^2$

$(10$P$)$

Given:

According to Fig. $2\mathrm{.}1,$ there is a three$-$part supporting structure consisting of a frame beam $($part $1),$ a rectangular plate $($part $22)$ and an inclined pendulum support $($part $3).$ This supporting structure is rigidly clamped at point A and firmly $($articulated$)$ at point I. At point I there is a two$-$value moment joint and at point H there is a two$-$value shear force joint. The load on the structure is carried out by a horizontal individual force $3$F $($with F$=2*$q$*$b at point D$,$ by a constant load $($q$)$ and by two triangular loads $($with maximum value q$).$ The load quantities shown and the geometric quantity $($b$)$ are known $.$ The dead weights of the structural parts can be neglected.

Wanted: The programming task must be solved in Wolfram Mathematica $($version $7)!$

$($a$)$ Check whether the mathematical condition for static determinacy is fulfilled!$(1$P$)$

$($b$)$ Determine the support reactions at points A and I as well as the connection reactions at points E and H using the intersection principle! Use the coordinate system shown for your calculation!