Guy, if your distances are correct, then your numbers for spanwise spar cap load are 2X high, so I'd call it: "36,000lb tension in the spar cap", which is reacted as shear in the 4 bolts in each cap. (do a moment balance at the root of the lower spar and you see that the load in the upper spar is 36kip compression, which means it's 36kip compression in the lower, basically, you divided the moment by 4.5", not 9")
Usually you can assume equal STRESS (not load) in all 4 bolts as a starting point in joints like this, so I'll add the area of the 4 bolts: Pi*(.125^2+.219^2)*2 (of each diameter) *2 (double shear) = .79 in^2
36kip/.79in^2=45.5ksi in the bolts, or a
2:1 margin at 6g.
Guy is correct that the aluminum either in tension, compression, or bearing is likely the limiting factor of the joint, but I'd have to have a wing spar or a drawing of it around around to do that.
For fun, IF the spar cap is a piece of 1"x1" bar there, then each Of the 7/16" bolts would have ~6900lb on it, acting on a bearing area of 1" * .4375" = .4375 for a bearing stress of 15,000psi. 2024-T4 (a guess..) has a bearing yield allowable of 64000psi, so over 4:1 factor of safety for causing permanent damage, 5 or 6:1 for actual failure (assuming a 2 D edge distance).
Again, IF the cap is 1x1, then the tensile stress in the cap is 36000lb /1in^2 or 36000 psi, with a yield allowable of 47000 for a 1.3 factor against permamant deformation.
The other issue is that the two 1/4" AN4's in the spar web that were the subject of the SB will in THEORY carry almost all the vertical shear load (assuming they're installed). For that you do:
900lb*6g=5400lb
Area of both bolts: 2 (double shear) * 2 (bolts) * Pi * .125^2 = .2 in^2
Shear stress: 5400/0.2^2 = 27000 psi. I think the shear for AN bolts is 75ksi (75000 psi), so you've got ~3.5 margin, and that's conservative because the other 8 bolts take SOME of the vertical shear.
Of course all that's conservative because the weight of the fuel and wings is outboard of that joint and actually subtracts from most of those stresses.
Just doing the napkin math, and working on dimensions from memory.
Assumptions:
1800 lb gross weight split equally between each wing
6g load
The load on the wings acts 60" out from the joint.
We're now looking at 324,000 in*lb bending moment at the joint.
Assuming the spar is 9" deep:
Each web is supporting ~72,000 lbs of shear force.
How much each of the 4 bolts (in each web) is taking is more than I can tackle off the top of my head. Here are the conditions I see though. They are loaded in double shear and they take a varying amount of load decreasing towards the center. The smaller bolts will deform slightly more, and pass their load off to the main bolts. The designers probably did that to allow stress to flow around the small bolts to the larger bolts efficiently. Ideally the joint is designed such to allow enough elastic (non-permanent) deformation to load all fasteners equally relative to its strength. Often the limiting factor in a joint like this is actually the bearing strength of the aluminum around the joint. It's got to absorb the load of that strong hard steel bolt.
If I get a chance, I'll check my assumptions and dig into the details later.
Guy