By kern, I assume you mean the farthest location from the centroid of the section for application of axial compressive load that will NOT put tension in the section.
Is this what you are looking for?
This distance will vary depending on the axis about thich the moment is aplied. I would just do a strain analysis of the section (with zero strain at one side and 0.003 at the opposite side). From there, get the strains in the steel. This will give you the stresses and forces in the steel. With the strain diagram and stress/force diagram, you can get the axial load and moment. The moment divided by the axial load will give you the eccentricity. This will be your kern distance.
This is a common point to get when constructing an interaction diagram for a column.
You may have 2 kerns depending on how thin the L is. Develop it the same way as for a rectangle and get the diamond shape, where this intersects your actual section is where your kern is.
The diamond will be centred on the centroid of the section.
I am thinking that you will get 4 different values for the kern. One in each direction for each axis. If you consider eccentricities that don't lie on an axis, then they will also be different.
For example, if you consider an L bent about its x-axis, there will be a different eccentricity that causes 0 strain in the top fiber than the eccentricity that causes 0 strain in the bottom fiber.
you are correct in my thinking. I didn't know there was a way to outline the kern on the cross section for that type of section. How would you do that? I could get the locations for the four points that I noted.... would you just connect those with straight lines and call it a day?
What about finding the moment of inertia of the transformed section and dividing that by the product of the transformed area of the section and the c distance? I tried going this route but it's the c distance that is throwing me since this is an L shaped column and not a plain old rectangular column.
I'm not sure what that quotient would give you, but I would follow the suggestions outlined above. It will take a bit of time, but will give you what you're looking for.
Ok but why would the strain diagram be 0 at one end and 0.003 at the other? Would it not resemble a typical strain diagram with 0.003 at the top and fy/Es at the bottom?
No, because the definition of the "kern" is the area in which an axial compressive force can be applied and not cause any tension in the section.
Therefore, you need to define this boundary in your section, i.e. ultimate compressive strain at one end and 0 strain at the other - this is right on the cusp of allowing tension in the section, but there isn't any yet.
Once you define this in your section, just use the strains to determine the net axial force and net moment.
This will give you the combination of axial load and moment that will define the edge of your kern. Now that you have an axial load, P, and a moment, M, you can determine the eccentricity of the axial load without the moment (M=Pe, or e=M/P). This eccentricity is the maximum eccentricity that can be applied to your section without causing tension in the section. That is the definition of the kern.
Thanks for your help, StrEIT. Concrete is one of my weaker subjects and I'm trying to get a handle on it. I'm having difficulty visualizing this problem as a column and not as a beam. The fact that it has 3 layers of reinforcing (looking at it in section) is throwing me off track.
If you've ever generated an interaction diagram by hand, this is one of the points you will usually generate. As I mentioned earlier, however, you will have different kern dimensions for each direction on each axis due to the lack of symmetry.
