ACI Concrete Column Design not able to validate Robot's Results

[DonBAE]

I'm looking at a simple short column with biaxial moment creating a resultant moment at 45 degrees. I have several questions. 16"x24" column, 10ft tall, (6)#8 vertical (3 bars on the long side), f'c = 6 ks

 

1. what is U?

2. what is phi*Sn?

3. On the 3D interaction surface and on the 2nd interaction plot right clicking and selecting governing case appears to do nothing.

4. Clicking on help withing the column design tool produces the index page, it appears no help documentation for this module exists???

5. How does Robot determine the capacity, is it based on a vector projection from the load point out to the capacity curve?

6. When viewing the My-Mz interaction plot how do we set N to be at the applied load, again right clicking and selecting governing case appears to do nothing?

7. What stress block does Robot use, whitney block, PCA Parabolic, something else?

Possible major error in Robot:

Reported Capacity:

 

Robot produced P-M Curve: Note on the Curve displayed it is not possible to be at Phi*Mn=265.85 ft-kips while also obtaining a Phi-Pn = 1153.81 kips. something seems very off here. 

Excel Verification of the same column and loading with matching unit vector approach:
Yields phi-Pn = 841.27 kips and phi-Mnx=phi-Mny=189.29 ft-kips = phi-Mn = 267.69 ft-kips [Whitney Stress Block]

The excel verification has also been confirmed using two other commercially available software packages.

[DonBAE]

@gwizdzm Thank you very much for the continued explanations and conversation.

My spreadsheet approach and your algorithm description are very similar and we get good agreement on the P-M curve and load point locations. The "Factor" approach you outlined makes sense to me and I understand how that relates to the slenderness effects better now thank you for the illustration.

I'm still a bit a loss on the actual calculations being done for U and phi-Sn, going back to my original post:

Here U=0.19, what is 0.19? I assume U=0.19= min[...some bracket function..]

Again phi-Sn = 0.57, what is 0.57? again I assume phi-Sn=0.57 = min[....some bracket function..]

Looking further now at the model where I increased the design loads by the "Factor" such that the load point now lies on  or very very near to the P-M curve

Here U=phi-Sn=0.57, what is 0.57? This is the most confusing one as the load point lies on the P-M curve so I would have expected U=phi-Sn=1.0 for this case, so I ask again how is the 0.57 being computed?

[szymon.duzyk · Accepted solution]

All parameters and values should be in calculation note but here are needed equations:

Kn = valN / phi / A / Fck;                                       // Kn = Pn / (fc' * A) = Pu / (phi * fc' * A)

Rny = Kn * Muy / valN / getDimH;                      // Rny = Kn * (ez/h), ez = Muy / Pu

Rnz = Kn * Muz / valN / getDimB;                      // Rnz = Kn * (ey/b), ey = Muz / Pu

U_factored = squerroot(Kn * Kn + Rny * Rny + Rnz * Rnz);

U_strength = U_factored * _SftyMrgn;

where:

_SftyMrgn           2.9582601337903767   

U_factored         0.19062732740283736 

U_strength         0.56392522306681958 

Kn          0.18682375298904733 

valN       1245502.0522729398   

phi         0.65000000000000002 

Rny        0.021017672211267827             

Muy       85416.530744878211   

Rnz        0.031526508316901736             

Muz       85416.530744878211   

[DonBAE]

@szymon.duzyk excellent thank you!

"All parameters and values should be in calculation note but here are needed equations:"

actually none of the information you just provided appears in the calculation note, at least not under ACI 318 design provisions. As I noted before I am new to Robot so perhaps there is a more detailed calculation note that I don't know how to view, would you be able to show where this information can be found in the calculation note?

[szymon.duzyk]

I mean that you can find all these parameters in a note, but there aren't any detailed equations which I posted. 

[szymon.duzyk]

Sorry, all values are in metric units, i apologize. Please set metric units in preferences and view note.

[DonBAE]

@szymon.duzyk understood thank you.

One final question phi-Pn how is this being computed, in the original problem phi-Pn was reported as 1153.81 kip

then in the model where the applied load was increased by _SftyMargin phi-Pn was reported as 847.61 kips

Since these values are not consistent I can see that they are not related to phi*F'c*A nor to ACI 318-14 eq. 22.4.2.2. They also do not appear to coincide with the F.sec vector from @gwizdzm posts.

[szymon.duzyk]

I have to discussed it with with @gwizdzm on Monday.

[gwizdzm · Accepted solution]

I'll try to explain what is in the calculation note under variables: Mu, phi-Mn, phi-Pn.

Drawing will be the best I think. To have nice drawing I've took your original example:

and I've multiply force by 2.5:

I hope that drawing is clear in this moment
phi-Mn - maximum capacity for moment when acting axial load is fix
phi-Pu - maximum capacity for axial force when acting moment is fix.

Of course it is true for each case but in your original file phi-Pu is equal maximum phi-Pu (acting moment is relatively small) in the case where forces are multiplied by 2.95, distance between Pn and phi-Pu is too small to show it on the drawing.

[DonBAE]

@gwizdzm 

ah thank you, I had a feeling that's where those results where coming from. Was able to reproduce Phi-Mn at the consistent axial M-M slice. Will double check phi-Pn know that I know the reference.

@gwizdzm @szymon.duzyk Thank you both for providing the very helpful information on this topic it is much appreciated. I have much more confidence in the results being presented now.

@okapawal Thank you for your assistance and getting the others involved to provide further insight.

One final suggestion for future Robot Releases it would be wonderful if the information provided here was included in the official documentation.