Column 3D Interaction Surface vs Code Biaxial Formulae

[Trenno]

What are the major benefits to defining the 3D interaction/failure surface over using codified bi-axial bending column clauses?

I assume with the exponents in the unity equation they result in generally conservative capacities? Whereas you may be able to squeeze more capacity from full 3D interaction surfaces?

 

[rapt]

Trenno,

I will qualify the Eurocode comment slightly. Just looked at a square column at 45 degrees under Eurocode and it still shows Mx combined with My using the code combination formulae gives a very different result to Mxy at 45 degrees. The Mxycapacity at 45 degrees is significantly less than the capacity at Mx and My individually. But the applied M*xy moment is much higher if equal M*x and M*y moments in both directions.

Just that you do not have to try to fudge (guess) a phi capacity reduction factor like you have to with ACI and AS codes. The relative contributions and their individual capacity factors from the different materials is handled automatically by the different material factors.

Where are you now that you are designing to Eurocode? I thought you were in Brisbane.

 

[IDS]

With a little C# coding, you can get a nice surface with 0.5 degree increments with a click of a button!

Or even a little VBA coding:

https://newtonexcelbach.com/2014/08/10/faster-biaxial-bending/

The download file has now been updated for AS 3600-2018 and also works for Eurocode 2 (rectangular stress block only) and ACI 318.

There will be a new blog post in a few days comparing the bi-axial analysis with the simplified methods in AS 3600 and Eurocode 2.

Also a cross-check with the example in the Enercalc paper (with near exact agreement).

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[IDS]

I have now posted on results of comparisons with AS 3600 and Eurocode 2 simplified methods. In summary conclusions were:

1) For biaxial moments with axial loads below the balance load Eurocode 2 was highly conservative and AS 3600 even more so.
2) For axial loads above the balance load Eurocode 2 moves closer to the detailed analysis, and AS 3600 becomes unconservative.
3) For very high axial loads, such that the rectangular stress block limit is outside the section, the detailed analysis shows a large reduction in capacity under biaxial loads, which is not reflected in either code.
4) The detailed analysis used a rectangular stress block. Use of a parabolic-linear stress block would show a further significant reduction in capacity when the concrete compression zone was triangular.

[URL unfurl="true"]https://newtonexcelbach.com/2019/11/21/biaxial-bending-update/[/url]

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[rapt]

IDS,

Remember that until AS3600-2018, phi was not defined as .65, it was the phi calculated at each at Mx and My. Depending on the column dimensions and reinforcing pattern and the location of the point on the interaction curve, it could have been anywhere up to .85.

 

[Trenno]

4) The detailed analysis used a rectangular stress block. Use of a parabolic-linear stress block would show a further significant reduction in capacity when the concrete compression zone was triangular.

Though I understand the parabolic-linear stress block is a more accurate representation of true concrete behaviour?

 

[Agent666]

Yeah basically. Rather than looking at it as a reduction in capacity, its more correct to think about it in terms of the other old school ways are significantly over estimating the capacity in certain scenarios.

 

[Trenno]

Thanks for the clarification, Agent666. I thought that was the case.

Ps - you should check your emails from your engineer v sheep blog.

 

[IDS]

On the stress block:
By "capacity" I mean the code "design capacity", and yes using a concrete stress-strain curve that is close to the actual behaviour of the concrete will give a result that is closer to the actual behaviour of the concrete than using a crude approximation. The reason for not including the parabolic-linear curve in the comparison is that I don't have the code to do it for biaxial bending at the moment, but I'm working on it.

On the reduction factors:
For axial loads below the balance load the AS 3600 alpha value is very close to the Eurocode 2 value, so the biaxial lines to AS 3600-2009 would be a little more conservative than the Eurocode lines in my plots (which are already conservative), because the base phi value is 0.8 rather than 0.85.
Comparing the AS 3600-2018 results with the 2009 values:
- Low axial loads, which were already conservative, are now more conservative.
- High axial loads, which were already unconservative, are now more unconservative because phi has gone from 0.6 to 0.65.
which doesn't seem to make any sense.

Also the phi factor in Eqn 10.6.4 is always 0.65, without the requirement that Q/G is >= 0.25, which doesn't seem to make sense either.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Celt83]

IDS, I'm a bit embarrassed to ask this question but you can expand on this statement from you blog post, "After adjusting the Enercalc moments to the centroid of the uncracked concrete section, the results are in near exact agreement."

Looks like the plastic center falls at (10,15.229) and geometric center would be (10,15), not clear to me how you are getting an adjustment to the My component since the plastic center and geometric center fall at the same X coord. I understand the need to get the capacities about the geometric axis because that is how the column is modeled and reactions reported as a bar element.

Edit: Nevermind was reading your screencap incorrectly the adjusted column is the values from the Enercalc PDF adjusted by Pu*(G.C. - P.C.), for some reason thought you were adjusting the items in your Phi Mu column.

Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

 

[IDS]

Celt83 - Correct.

[URL unfurl="true"]https://www.youtube.com/watch?v=2xZEJvDlOlg[/url]

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Ingenuity]

https://www.youtube.com/watch?v=2xZEJvDlOlg

bigsmile

Hehe. That was a great series too.

 

[Trenno]

Check out Agent666's blog series on the topic

So when do we get the next installment of the blog? Have you set up a Github and/or open sourcing this side project?

 

[Agent666]

So when do we get the next installment of the blog? Have you set up a Github and/or open sourcing this side project?

Trenno, planning on spending some quality time with it over the xmas break, life (mainly work) kind of got in the way over the last few months... hang in there!

Once its in a more usable/finalised state and I've finished the documentation/verification side of things i'll publish it to my github page.

 

[Celt83]

sorry to bump an older thread but I worked out the general formulas for the compression block force and moments assuming the stress-strain relationship of the concrete is defined in a linear piece-wise manor and thought I would share because I've never seen this published anywhere.

I used Green's Theorem and parametric formulations for the start and end point coordinates and stresses. The formulas assume coordinates are in counter clockwise order, clockwise points would produce (-) values so can be used for voids.

My analysis process is now find the plastic centroid and translate so it is at 0,0 (pc used for convenience) assume a neutral axis angle and depth and rotate the cross section so the neutral axis is the new x-axis. The rotation makes it so that strain now only varies with y which makes the next steps a little simpler. Now starting with any coordinate move in counter-clockwise order and inject new points at each y associated with the piece-wise strain definitions, after all the needed point are injected run the P, Mx, and My formulas for each coordinate pair and sum the results and that gets you the compression block forces.

Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

 

[Trenno]

Bumping this thread. Agent - have you had a chance to progress your 3D interaction tool? Very curious to see where it leads.