Consider a reinforced concrete section subjected to both axial and bending. We can develop N-M interaction curve for such section, and determine whether it is adequate to resist the combination of design axial force and bending moment.

First, we need to define the material properties. The characteristics strength of concrete and rebar needs to be adjusted with partial factor of safety, to obtain their design strength. There are also some limits to the strain that can be developed in concrete and rebar.

Next, we should define the column dimension, concrete cover, rebar and the reinforcement configuration. The exact position of each rebar needs to be determined at this point.

After all the parameters are decided, we can start the trial and error process for the development of N-M interaction curve. Each of these trials start with the selection of neutral axis depth, x. For example, we can use x equals to zero for the first trial. Any part of concrete located above the neutral axis is considered under compression, and the remaining part is considered subjected to tension.

For each rebar, we need to determine the strain developed using similar triangle approach. Then, from strain we can calculate the resisting force developed in each of them. As for concrete, the resistance equals to the multiplication of design concrete strength and area of concrete section under compression. By summing all the resistances from these components, we can obtain the axial resistance of the section for the first trial case.

The moment resistance from each force component on the other hand, is the product of resisting forces and their lever arms from the centroidal axis of section. By summing all them up, we get the total moment resistance of the section.

After we obtain a pair of axial and moment resistances, we can proceed with another trial by setting different depth to neutral axis. By plotting all the data pairs on N-M axes and joining them together, we eventually produce a N-M interaction curve for the section.

In this worked example, we need to develop an interaction curve for a 300x300 square column. The characteristics concrete strength is taken as 30MPa, while that for rebar is 500MPa. The concrete cover is 30mm. The column section consists of 8H12 longitudinal reinforcement and H10-125 as link.

First, we determine the factored material properties which we will adopt during the design stage. For our case, the design strength of concrete and steel are 17MPa and 435MPa respectively. Moreover, we define the maximum strain in both concrete and rebar based on provisions of the design code.

Then, we set the convention for the analysis process. The origin of trial neutral axis is at the top of column section. During the iterative process, region above the neutral axis is deemed under compression and those below the axis is considered under tension.

Up next, we derive correlations between resistance force and moment develop in both concrete and rebar, with the position of neutral axis, x.

Once the correlations are defined, we can proceed with the iterative process. In our example, the following x positions are used: 0, 50mm, 100mm, 150mm, 200mm, 250mm and beyond the concrete section.

The output from this iterative process is N-M (axial-moment) data pairs. These point should be plotted on axial versus bending axes, and by joining them we can obtain an interaction curve.