How to Determine Depth of Neutral Axis of Circular, Tied Concrete Column

[csways_]

Hi,

I am working on an interaction diagram for a circular, tied concrete column in accordance with CRSI's Design Guide for Reinforced Concrete Columns. For pure bending, CRSI states that there is no closed-form solution to determine the depth of the neutral axis and that a trial-and-error approach must be used. However, they do not go over the approach.

Is anyone able to help here?

Thanks!

 

[KootK]

I'd think it the same as with rectangular columns:

1) Assume a NA location.
2) Work out P & M for that.
3) Adjust a NA location.
4) Construct a PM diagram.

 

[KootK]

Just clued in that you're looking for the pure moment case. Pretty much the same though:

1) Assume NA location.
2) Calculate P & M for that.
3) If P isn't zero, move the NA around until it is.

From an algorithmic perspective, you could use your starter NA as the depth it would be if it were a rectangular section of the same width and shift downwards from there. Somewhat less brute force-ish.

 

[WARose]

The procedure is like a rectangular section. (And it is a trial and error procedure.)

Figuring the area of the compression zone (and it's centroid) is a challenge by itself. In Wang & Salmon's Reinforced Concrete design text (p. 504-505 in the 6th edition), they've got a some design aides to that end.

 

[BridgeSmith]

Should be able to plug the calculations into an Excel sheet and do a goal seek to find the correct neutral axis depth.

 

[csways_]

Got it. Thanks!

 

[IDS]

My RC Design Functions spreadsheet has a function for elastic analysis of a circular section, with or without axial load:

https://newtonexcelbach.com/2019/04/30/rc-design-functions-8_03/

For strength analysis it is actually easier because you only have to equalise the internal and applied forces, but I haven't got round to doing a function for a circular section yet.

You can use my Beam Design Functions spreadsheet, but you need to enter the concrete as a series of trapezoidal layers, and enter the depth from the top for each pair of reinforcing bars:

https://newtonexcelbach.com/2011/09/07/using-beam-design-functions/

The spreadsheets include an iterative solver function that is much faster than using Excel goal-seek, and is easy to automate with VBA.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[IDS]

I have now added a ULS function for circular columns to the RC Design Functions spreadsheet, which has much more convenient input than the Beam Design Functions spreadsheet. Download from:

https://newtonexcelbach.com/2019/06/09/uls-design-of-circular-reinforced-concrete-columns/

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/