spiral staircase for loft

ill toss a pic of the stairs up shortly
but it is basically a metal channel, welded across from the center pipe to the railing, and with a few hole drilled in to run bolts trough

the loft is really more of a closet top, so more then likely 2X4 framing
i figure there are also 2x4s running along the 8 1/2 foot (long red line)
thats where i wanted to lagbolt/ deckscrew another 2x4 to
then on the small red lines, i was hoping to catch the studs, and attach a 2x4 to that
those 3 2x4s, plus one mounted to the stairs, would be the frame work of the added section

im not a carpenter like @Cope so thats the best i could come up with