A floor takeoff that lists joists and subfloor sheets but not hangers leaves out a line the framer has to buy anyway. The wall framing takeoff now counts them for a stairwell opening in the floor.
What is counted. Every joist cut short by the opening becomes a tail joist that hangs from a header, so each tail-joist end at a header gets one single hanger. Each opening has a doubled header at both ends, and each header end meets a doubled trimmer joist, so that is four double hangers per opening. The example 40 x 28 ft floor with a 36 x 100 in stairwell and a beam at 14 ft has 2 cut joist lines with a tail on each side of the opening: 4 single hangers and 4 double ones. The test checks that count by hand, and the budget shows both lines once you type a price for each.
What is not. The hanger model and its load rating, beam hangers, rim ties and nailing are the engineer's call, and the count has not been compared with a real framer's order. The size shown is the joist size you typed.