I do not know what your particular application is, but in my experience anchor bolts are not designed to work in bending, normaly only axial forces and maybe some shear.
In any case biaxial bending could be studied as single bending, just work on the axis created by adding the vectors Mx and My
If you want to resist moment with single bolt then it is not possible .............. Theorotically single bolt means pin connection and it will not resist moment.
If you want to design group of bolts for bi axial design then you have to go by trial and error method to find neutral axis and do the design
In wood structures, particularly in connecting the wood sill plate to the concrete foundation, the primary application of the anchor bolts, or sill plate anchors, is to resist shear. Any tension loads are taken by holdowns.
Similarly in any ledger connection to a concrete wall (except the holddowns).
I also agree however, that (moment)"resistance is futile" when dealing with a single anchor bolt.
Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask
Check out Hilti's anchor catalog, section 4. They have procedures for designing anchor bolts for bending. You typically have this when the bolts have a standoff distance from the concrete in which they are embedded. I've found them to be in reasonable agreement with other equations I've used and have been satisfied with Hilti's explanation of the derivations of those equations.
I've contacted Hilti about this, too. I had a different experience. I know they have had the equation listed in there technical guide for a long time, but that was the only explanation I got from them. I still have no idea where it came from.
I actually choose to ignore this when designing anchors, and if I use Profis, I will go through their printout and readjust the values (if I need to to get them to work). The reason is that App. D makes you use a reduction factor of (I think it's) 0.8 on the steel shear value if you have a grout bed (e.g. a standoff distance). I wouldn't use this for a 3" grout bed, but a 3/4" or 1" is fine IMO. If you use a 1" standoff distance in Profis the steel gets something like a ludicrous 70% reduction in capacity. Only 30% of the steel shear capacity is good for a 1" standoff? I don't agree with that, and there's nothing in App. D to make me think differently. I've also never found any article regarding this (though, I admittedly haven't looked too hard).
If you are designing the bolt for Mx and My then you should resolve the components into M being sqrt(Mx^2+My^2) and then calculate the bending capacity of the bolt (I doubt you will get much capacity out of one).
I think what you are referring to is an anchor bolt group with loading from a baseplate which is subject to Mx, My, V and N. In which case you should calculate the actions induced on the anchors for each action separately and superimpose the actions contributing the the bolt pull-out (Mx, My and N) to give a total pull-out for the particular bolt under consideration. This is then to be designed in combination with V.
