Interesting Bill, inrested in the formula to calculate this, to knock up a spreadsheet with. Any chance of the basics please?

Several analytical tools are needed to do it.

Lift distribution - I just used a spanwise elliptical for the diagram I showed. That is usually pretty darned good, but you have to do something to add in aileron effect before you are ready for the next step. Folks love the extension of it called Schrenck's Approximation. There is a whole set of arguments over which one to use...

Then we build up the shear diagram using numerical integration to sum loads outboard of any spot along the entire semi-span. This is rigorously correct for cantilever wings as is. We usually stop accumulating lift from the wing at the fuselage. Externally braced wings will have loads from the bracing "drop in" at their connection points, and so are handled by any of several approaches. I like the two pass method that I will go through below.

Then we build up the bending moment diagram again using numerical integration to sum moments starting at the tip and working inboard. This is rigorously correct for cantilever wings as is. Externally braced wings require another pass through the math, which follows.

Since the wing in question is externally braced, the root connection is usually a single pin or bolt connecting each spar to the fuselage. No moment can be reacted from the wing to the fuselage at the root. Instead, the entire wing moment is carried by the external brace.

Take the moment about the root connection point and divide the moment by the lateral distance from root connection to strut mounting. This is the vertical force dropped in at the strut connection.

Make a new shear diagram - the shear from tip to strut mount is taken from before. The shear diagram from the strut mount on the wing to the root connections is the original shear minus the vertical component of the strut load.

To get the new moment diagram, you repeat the numerical integration like you used above, but now numerically integrate the adjusted shear diagram. The moment curve then has a cusp at the strut mount and should be zero at the root mount. You can numerically integrate starting at the root end towards the strut mount, with moment at the root equal to zero - Moment at the strut mount should be same working from top to the mount and working root to the mount.

The external brace can not carry much moment at all, and is most appropriately analyzed as a pin connected joint. As such, it can only carry load along its length. We know the vertical component (calculated from wing moment) and its angle to the fuselage end mount is determined, then simple trig gives us the horizontal component of the load and the load along its length. The horizontal component of the brace load shows up as compression in a high wing under positive g. Add that to the spar's load case. Under negative g or bracing from above, the sense of these loads is reversed.

Where loads are tensile, a simple calculation will show many struts and even some spars appear to be over built. I urge thoroughness here - we are supposed to design airplanes for negative g flight as well. I have had loose navigational materials fly about the cabin on a couple occasions and am glad the airplane stayed together through them. Anyway, any time the flight loads put compression loads on structures, the designer must also consider buckling in its many forms (Euler, Johnson, crippling, and wrinkling being the major ones).

While I specified numerical integration to proceed from lift distribution to shear and them moment diagrams, this can also be done using integral calculus. If one enjoys integral calculus, knock yourself out. It does get kind of interesting when the lift is elliptically distributed, using Schrenk's approximation, and when adding in effects of a deflected aileron.

My reference for shear and bending analysis is

__Mechanics of Materials__ by Timoshenko and Gere, chapters 4-6, there are other texts that cover this just fine. Buckling using Euler and Johnson methods is in all versions of Shigley, while crippling/wrinkling/etc you go to Bruhn or other aircraft structures texts.

Billski