Concrete Column Reinforcement as Annulus

[KootK]

Concrete column design charts are sometimes constructed by analyzing columns where the reinforcement is approximated as an annulus of steel (HSS essentially) within the column. I'm trying to do something similar in a MathCAD spreadsheet.

The trouble that I'm having is in programmatically figuring out the moment capacity contribution of the annulus for various depths and angles of the neutral axis. Depending on the situation, the annulus may be fully elastic, fully plastic, or -- most likely -- partially plastic.

I can probably work out some kind of algorithm looking at the lines individually. It seems to me, however, that there should be some relatively simple way of performing these calculations. I thought that was the whole point of using the annular shape after all. Does anybody know of a simple method that I could use to solve this problem or any papers that might shed some light on the procedure?

I have a second, related question as well. When this "annular ring" method is described in Park & Paulay, they state that the steel area is proportioned equally to the four sides of the column. Why is that? I would have though it more reasonable to apportion an area of steel to each side of the column in proportion to the length of that side. Any ideas?

Thanks,

KK

 

[cntw1953]

Method/procedure to construct interaction diagrams for reinforced concrete column has been long established, and is a given in most elemtary reinforced concrete design textbooks. It is rather simple once you have developed a spreadsheet, or use MathCad. Also, I love the program developed by PCA - PCACOL, why use the approximate method? I couldn't see the advantage and the merit.

 

[KootK]

cntw1953,

I want to develop a program for handling biaxial bending which is not so straight forward. As a pre-procesing routine, I want to use the annulus method to estimate the optimal size of a column loaded biaxially given a certain maxium reinforcement ratio and specified dimension limits.

I do have PCA Column and agree that it is an excellent program. However, I like to develop my own solutions to important technical problems that I occur frequently in practice. I don't want to be beholded to PCA for all of my column designs.

I also tackle some problems simply because I find them technically interesting. This os one of those problems.

KK

 

[cntw1953]

You can construct interaction diagram/envelop for biaxial bending using basic theories as well, just a little bit lengthy and complicate.

But as you have other technical issue, I shall stop here, just wish luck in piecing the puzzle.