P delta transformation

[BrownTrout_NZ]

Hi STKO team

I have a question regarding the p-delta transformation. I checked with and without p - delta transformation but the push over Q-D curve was identical and does not appear to be working.

I assigned entire building weight divided by 4 (for now to see the maximum effect)for the corner posts to model PD leaning columns as below(axial load).

pdelta.PNG (710.87 KiB) Viewed 2919 times

below is stko parameter.

pdelta4.PNG (29.51 KiB) Viewed 2919 times

Below snip shows local axis. local blue > z is orientating global x +. and TCL appears to be correct.
Not sure why STKO input -0.0 for z, however.

pdelta2.PNG (426.67 KiB) Viewed 2919 times

pdelta5.PNG (46.87 KiB) Viewed 2919 times

question

• why can we not specify the local axis in stko?

• I would expect QD curve will drop slightly with PD columns

Can you please advise what I am doing wrong ? Your input would be appreciated.

[STKO Team]

I have a question regarding the p-delta transformation. I checked with and without p - delta transformation but the push over Q-D curve was identical and does not appear to be working.

Probably, the load is small and does not induce noticeable P-Delta effects. Try with a larger load to see if the difference appears

Not sure why STKO input -0.0 for z, however.

Not important, the Z axis is computed as cross(X,Y).

Can you please advise what I am doing wrong ? Your input would be appreciated.

If you refer to the error in the last image, there's an error in how you input the points in the backbone (see the error message)

[BrownTrout_NZ]

Hi

Sorry, last snip was accidentally posted & irrelevant. I increased the p -delta leaning column load x 10 times and started to see the difference. Below is what I got.

I would expect corotation & p-delta should go below the linear. Up to certain displacement is as expected but beyond around 5 inches the p -delta & corotation go above the linear, which is unusual to me.

Do you know what is causing this ? This is purely changing the beam-col element transformation, from Linear > p -delta > corotation.

pd.PNG (20.69 KiB) Viewed 2895 times

[STKO Team]

Can you share your model? it's difficult to tell.
It seems like some elements with nonlinear kinematics are going in tension (stineffened due to large displacement)

[BrownTrout_NZ]

Hi STKO team

Further to my previous query, I still find something funny in my model. I checked p-delta, linear and corotational for, normal conditions and x10 exaggerated to see the p-delta sensitivity as previous.

1. I still have p-delta effect initially smaller than not considering it but in the end ramping up significantly. I have increased column load by 10.

roofqd.PNG (40.02 KiB) Viewed 2731 times

2. I am aware that p delta leaning columns are squashed significantly. My understanding is that these are connected with rigid diaphragms in x and y direction but free to move z directions. Will the p-delta transformation effect be effective from the deflected shape under gravity loading in OpenSees ? In my exaggerated x10 load condition, the column is squashed 2m at the top. I can easily specify larger section, but have been avoiding it try not to attract moment between rigid diaphragms. I am pushing to 20 inches at roof COM, which is only 3.3 % and the column axial load is still under compression.

colaxial.PNG (932.19 KiB) Viewed 2731 times

3. Ideally I want to have these p-delta columns pin connected, but whatever way I tried to pin them via below(high lighted in yellow), the model does not appear to run. I have been modifying the flexural stiffness modifier to really small number so that significant moment will not be attracted. Is there a clean way of having full pin connection to the diaphragm ?

pdcol_prop.PNG (21.7 KiB) Viewed 2731 times

The model can be downloaded from below.

BASE_TEST_PO_IMPERIAL-PD-CHECK-71.zip

(178.94 KiB) Downloaded 112 times

Your input would be much appreciated.

[STKO Team]

Regarding the issue of making leaning columns fully released in rotation about local y and z axes
If you release rotational degrees of freedom (DOFs) at both the I and J nodes, the shared node between two elements will exhibit a singularity in its rotational DOFs.
To address this:

• Ensure all columns have a consistent local X-axis direction (e.g., all pointing along +Z). This ensures that the I-node is always at the bottom and the J-node at the top of each column.
• Release only Ry and Rz at the I-node. This prevents moment transfer between adjacent columns while avoiding singularities, since the node between two columns derives stiffness only from the J-node of the lower element.
• Fix the global Ry and Rx rotations at the base node of the first column (as this node has no supporting element beneath it and would otherwise cause a singularity).

Anyway, this won't solve the issue of the curve going up.
I suspect the issue might be due to using corotational kinematics for the columns, but not for the walls (unfortunately, MVLEM_3D does not support nonlinear kinematics).
Can you try modeling the shear walls with shell elements (e.g., ASDShellQ4) that also use corotational kinematics?

Hint:
A strange thing you can notice in your current model is an increasing FX reaction in the leaning columns in the opposite direction of the walls' reactions. And they are zero when using Linear kinematics

[BrownTrout_NZ]

Hi STKO team

Thanks for the heads up.. I really need to use SFI-MVLEM for my research this time, not the easiest model to deal with.. that is for sure.

I will investigate the model further and be back.

[BrownTrout_NZ]

Hi STKO team

I checked with a simple model with PD leaning column and I get similar results as below.

I am aware that the displacement level and PD force I have here are huge trying to get QD descending curve that we often see in textbooks, but I could not get it with P-delta transformation.

I know many researchers include p-delta transformation for mainly moment frame structures, not sure if it is really working for wall structures. Within realistic drift level, p delta effect is not significant but when assessing the collapse, it becomes really important. I do not fully understand this but it is not true large deformation problems where node coordinates are updated at each load step ?

The example wall is 72 inch high and up to around 6% drift, the p - delta is indeed lower than not considering it. Majority of wall will collapse before that anyway.

I am interested if someone can demonstrate QD- descending curve with p-delta transformation with shear wall model in OpenSees.

SINGLE WALL.PNG (57.08 KiB) Viewed 2694 times

SINGLE WALL QD.PNG (117.5 KiB) Viewed 2694 times

[STKO Team]

Maybe the pdelta effect is not very visible within reasonable force-drift values in your example.
The only way you have to validate your approach is to either find some benchmark or experimental result in literature, or model everything with a corotational approach (p-delta is a subset of corotational) and check the results