So your moment frames run in the East to West direction then, with weak axis columns? If so,
1) Add your two moments together for the direction considered.
2) Divide the sum by the distance between footing centroids to get the additional overturning reactions, associated footing bearing pressures, and associated uniform loads exerted by the footings on the strap beamfor this component of the load.
3) Create moment and shear diagrams for the strap including the effects of the concentrated column moments and the uniform footing loads from #3.
4) Add the moments and shears from #3 to the moments and shears that you would have had without the moments applied.
Can you provide:
1) distance between columns?
2) distance between footing centroids?
3) direction of frame shear for case considered?
4) depth of strap beam?
The column shears technically affect strap moments, shears, and axial forces too but that affect should be fairly minor.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.