diff --git a/README.md b/README.md index e69de29..2ff1770 100644 --- a/README.md +++ b/README.md @@ -0,0 +1,28 @@ +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.