I think you need to perform, additionally to the code provisions, a biaxial design of the wall cross section, only if the thickness of the wall is relatively large, a fact that could cause the neutral axis to rotate so that it is not perpendicular to the wall length. So you have to verify the adequacy of the reinforcment bars under the out-of-plane laods as well. This won't be that difficult if you use any software for analyzing cross section. As for code reference, I am afraid that I cannot suggest anything, as this matter might not be covered by a concrete regulation. But anyone else could contribute, since there are many experienced engineers in this forum.
Regards.
Analysis and Design of arbitrary cross sections Reinforcement design to all major codes
Moment Curvature analysis
Design as a slab for out of plane loading. Depending on the code an average shear stress of 0.6N/mm^2 should work without shear reinforcement. Flexural reo as per slab design and deflections as per slab design.
The presence of axial load makes it a little different from a concrete slab. Check out section 14.4 of ACI 318 (Walls designed as compression members) and 14.8 (alternative design of slender walls).
For short, squat walls the axial force shouldn't be a major consideration. But, you should at least do a calculation to demonstrate that fact.
out of plane forces are supposed to be taken by the return walls/perpendicular walls or the box action of any c or l shaped walls.
there is a software that deals with out of plane loadings...you can check s-concrete
