I have been fumbling around this for a while now, say a couple of years off and on. I have played with different ideas and approaches. Read some stuff, read some other stuff, re-read the original stuff. Talked with people about how it works. Doodled endlessly and wrote pages of notes. All to discover that it was right in front of me the whole time and it really is fairly straight forward.

P-M interaction diagrams determine the capacity envelope of a reinforced concrete member with a combination of axial force and moment applied at a section of the member.

The maximum usable concrete strain is given from experimentation as 0.003. Then it is a matter of iterating over a range of curvature values or neutral axis locations, either one works because they are related by a single equation. The strain in the steel is determined based on distance from the neutral axis. The stress in the steel is then calculated based on the strain in the steel and modulus of elasticity. Alternatively, a value directly from the stress-strain diagram could be use. Also depending on the material model it could be elastic-perfectly plastic or a more exact model. Finally, the forces and moments on the cross-section are summed. For each iteration a corresponding P-M pair are added to the array.

The one thing I am still unsure about is how a cracked section analysis plays into the development of P-M interaction diagrams. The answer to this is that the cracked section is taken care of by the stress-strain diagram of the concrete. Instead of using a Whitney stress block one can find the actual strain at discrete points, calculate the stress based on the strain and the stress-strain diagram, multiply the stress by the assumed area the discrete point represents to get a force for use in the force and moment equilibrium.