I explain my proposed method and algorithm to generate the P-M interaction diagram for the RC members under the axial loading and monoaxial bending moment or even biaxial bending moment. I proposed a nonlinear approach, you may apply a simplified linear method as well. First for finding the moment for an imposed P a nonlinear numerical simulation should be applied in each point on the curve of P-M interaction. In my proposed simulation algorithm, the shearwall is decomposed into two macro-element (ME) positioned between the inflection point (zero moment) and critical sections (maxim moments). Then the nonlinear behavior of ME are analyzed. In fact a Macro-Element acts as fixed bottom-free top half-column under monoaxial or biaxial bending moment (i.e. lateral force in the applied horizontal force direction) with axial load. Finally, the two connected MEs are assembled to determine the global behavior of the shearwall.

To find the status of the entire shearwall, the applied loads and also the secondary moments, due to P-∆ effect, may be considered in the simulation of the shearwall.

In the proposed algorithm, for each concrete and reinforcement element and uniaxial behavior is considered and their strain distributions are assumed to form a plane which remains a plane during deformation (Kinematics Navier’s hypothesis). The stresses of concrete and steel are expressed as nonlinear functions of strains (ε) in each (i, j) concrete and (k) steel elements. For compressive confined and unconfined concrete elements my proposed stress-strain model and for reinforcements, the expression proposed by Park and Kent based on the Ramberg-Osgood cyclic model have been used in the proposed simulation algorithm. The concrete tensile stress is assumed to be linear up to the concrete tensile strength. To determine the maximum compression strain value of unconfined concrete, Equation given by CEB Code can be used. This equation is particularly applicable where there is a loss of concrete cover outside the stirrups.

To determine the failure of confined concrete situated inside the stirrups, in the proposed simulation, Equation proposed by Sheikh can be used:

The basic equilibrium is justified over a critical hypothetical cross-section assuming the Navier law with an average curvature. The method used qualifies as a “Strain Plane Control Process” that requires the resolution of a quasi-static simultaneous equations system using a triple iteration process over the strains. The calculations are based on the non-linear stress-strain relationships for concrete and reinforcement FE. In order to reach equilibrium, three main strain parameters (the strains in the extreme compressive point), (the strains in the extreme tensile point) and (the strains in the point M located at another corner of the section) are used as three main variables.

For nonlinear numerical simulation you need to define the equilibrium equations, strain plane on the section, stress-strain relationship for any disretized concrete and steel elements, and apply a convergence method to approach to the solution. For more information you may study my publications in nonlinear simulation of RC members or similar papers.

I hope it is useful for you.

I wish you the best of luck.

Excellent question

Did you try the Lamina method?

Another easy way is to use section designer in SAP2000, it will give you p-m directly.

I would encourage you to try out https://www.engissol.com/cross-section-analysis-design.html software, which can produce interaction curves of R/C automatically, considering non-linearities.

Have a look at a related example here: https://www.engissol.com/interaction-diagram-composite-column-cross-section-analysis-design-software-application.html