OK, worked on the wing tip molds and the cabin air mixer box, and got to a stopping point, then came back in a looked at this again.
Assuming the wing and fuselage are solidly mounted to each other at the fuselage walls, the wing shear is dropped into the fuselage at the walls, while bending moment passes through the fuselage to the other wing. In a symmetric pull with equal shear and bending from each wing, the problem is simple - the carry-through sees only bending. The bending can resolve to simple tensile and compressive loads if the web is omitted from the spar, but additional bending is present. The curvature of the spar just outside of mount can be expected to carry through the center section as well. This curvature = M/(EI) just outboard and will result in bending stresses in each cap, and must be superimposed upon the tensile/compressive stresses. Tension is fairly straightforward, but compression will require that buckling be precluded using curved column theory. I do not know about the Aero structural texts, but us Mechanical Engineers use Roark's for this sort of thing.
Go through FAR Part 23, and you will see that we also have to cover a certain amount of asymmetric lift. The shear through the fuselage will be the difference in lift between the two wings. The moment imposed upon the root section will not be constant, but will increase from the low lift wing toward the high lift wing. The moment at the high lift wing will be greater than the low lift by the amount of the shear in through the fuselage times the width between fuselage walls. Then we carry wing curvature from just outside the fuselage through the fuselage.
So, for the spar through the fuselage, starting with asymmetric lift, you need to calculate the shear and bending moment diagrams, Through the fuselage, the shear is the difference between the lift of the two wings, and highest moment is highest moment in the high lift wing. The spar devolves into two elements, one with tension, one with compression. Load summary:
- Magnitude of axial loads is Max moment divided by distance between cap centroids;
- The shear difference between the wings must be carried by the set, but since shear sharing may be difficult to compute, I suggest that each element should be designed to carry all of the shear;
- The wing curvature at the root will be carried through the axial elements through the fuselage, with the resultant stresses being superimposed upon the axial stresses.
- Spar fuselage elements will also be subject to curved column failure and must be precluded.
Ends up being a tad more complicated than might have been hoped. Maybe a spar curved around the duct will be more compact...
Billski