Path A-D-K Length and Net Area
Since thickness is not constant along the path, it is easier to look at this problem in different manner than you would if you had a constant thickness along the path.
The logical approach is to look at things in terms of AREA. In this approach you add and subtract area from the member gross area.
Net Area = Gross area - Cross Sectional Area of Holes + Additional Area Due to Stagger
For this problem, all the holes are on the web. The area reduction for a hole on the web equals the effective diameter of the hole times the thickness of the web.
EFFECTIVE HOLE DIAMETER = bolt dia. + 1/16" for std hole + 1/16" damage allowance
WEB HOLE AREA = (effective hole diameter) * tw
WEB HOLE AREA = (.875" + .125") * (0.415") = 0.415 in2
There are two staggers on this path. Both staggers have 3" gage and 3" pitch and are located on the web. The stagger areas then, are each:
STAGGER AREA = tw * s2/4g = 0.415 * (3 in)2/(4*3") = 0.311 in2
The net area then, in this case, equals the gross area less three hole areas plus two stagger areas.
Net Area = Ag - 3 hole areas + 2 stagger areas
Net Area = 20.0 in2 - 3*(0.415 in2) + 2*(0.311 in2) = 19.38 in2