This is the jog that John Holtz referred to I believe. I did the following in Inventor LT.
What I noticed and not sure if there is an option for this is the vertical line in the bottom plate where the section line jogs. Personally I do not believe there should be a line here as there is no change in material type or dimensions at the jog, but I am not an expert in the field.
The above was done in Inventor. I had to jog the section line in order to get the geometry. I then had to add a "sketch" to the drawing. This is where I clicked on individual lines and turned their visibility off (section jog lines). I also had to turn off the automatic hatch in Section F-F.
I then drew in the boundary lines for the rib. I then projected the required section lines into the sketch. Once all the lines were in place I did a manual hatch of the area.
I did a similar thing for section E-E. I had to project the right side line work and manually hatch. The hatch scale did not match so I had to adjust the hatch scale so it would match.
Your hand sketch of the cross section AA (from original drawing) or HH (Inventor drawing) is technically wrong. The cross section is taken through the rib, but the rib is not hatched. However, the hand sketch is somewhat common to ignore the hatching in the rib. I doubt apps have the intelligence to ignore accurate cuts and show "common" techniques.
To get the cross section shown in the hand sketch, the section "line" needs to have jog around the rib. It would be in the centerline on the left side, then jog to be outside the rib for the right side of the part.