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Updated README.md with my understanding of how to compute the PM inte…
…raction diagram.
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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. | ||
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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. | ||
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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. | ||
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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. |