Analysis of a 3D Tall RC Building with Core Walls

[OmerOdabasi]

Hello all,

I wish to consult with you expert Opensees users about a particular problem I have. I am first putting up a general description of my model and then I will explain the type of problem I am encountering. Finally, I will share some observations that might trigger a light-bulb moment for the reader. Before I start however, I'd like to point out that the model does run both gravity and eigenvalue analysis. These results seem to agree with basic hand calculations. The challenge is to run a successful dynamic analysis.

Plan view: https://drive.google.com/open?id=1SdLXT ... Scw22cy0jO
3D view of the first story (OS model): https://drive.google.com/open?id=1K_YK- ... a6B-70KnRJ

Note: I am willing to share the full model with those who think that they can help.

As the title suggests, I have a 3D model of an RC tall building in Opensees. To summarize the critical properties of my model:

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MATERIALS
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Steel: Steel02, nothing crazy. Concrete: Concrete01
<E.g., uniaxialMaterial Steel02 100 462000 2E+08 0.01 18.5 0.925 0.15;>


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ELEMENTS
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Beams/Columns:
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'beamWithHinges' element with standard modified Gauss-Radau plastic hinge integration method. E.g.,
<< Nothing special is going on here. I have the elastic properties of my frame section assigned at the interior. At the hinge IPs, 'Aggregator' sections with linear torsional and shear force-deformation relationships are assigned>>

Shear Walls:
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1) 'forceBeamColumn' elements with five integration points. The elements inherit 'Aggregator' sections similar to the beam/column members. Linear uniaxial materials are used to mimic tors. and shear F-D relationships.
2) Here comes the tricky part. Each planar wall segment is modeled by a 'forceBeamColumn' plus twoNodeLink elements stretching across the two ends of the cross section (like a fishbone) to be able to simulate the actual geometry of the shear walls. This way I connect my beams by respecting the acutal geometry.
3) The twoNode link elements are assigned with linear elastic force-deformation relationships that have large stiffness values (3e+8 in all DOFs. Units: kN-m, so it is a large stiffness value in all DOFs)
<E.g., element twoNodeLink 675 439 402 -mat 2 2 2 2 2 2 -dir 1 2 3 4 5 6 -orient 0 0 1 -mass 0; >

Ficticious Columns:
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These are simple twoNodeLink elements that level the entire building height with the coordinates (plan coord, i.e., x,y) of the centre of mass at each storey. These are essentially truss-like elements that are quite stiff in only the axial DOF. Seismic mass are assigned (two translational and one rotational around the vertical axis) at the top node of these elements. The reason I am using twoNodeLink element instead of a truss element is that, as far as I am aware, they don't participate in formation of the damping matrix so they won't cause any spurious damping forces.
<E.g., element twoNodeLink 2222 1323 1349 -mat 2 3 3 3 3 3 -dir 1 2 3 4 5 6 -orient 1 0 0 -mass 0;>
<where 2: stiff elastic uniaxial mat. & 3: flexible elastic uniaxial mat.>

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MASS ASSIGNMENTS - CONNECTIVITY - DIAPHRAGMS
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1) Nodes at each story are slaved to a master node, i.e., the top node of the fictitious column of the respective story. Constraints are created by the 'rigidDiaphragm' command.
2) The mass is lumped at each story to this slave node as two terms in translational DOFs and one in rotational.
<E.g. rigidDiaphragm 3 1 2 3 4 . . . 403 407;

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DAMPING
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Applying modal damping for all (15) modes calculated.
modalDamping 0.015;

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ANALYSIS SETUP
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The following are the start-up settings for dynamic analysis. Obviously I do switch between different algorithms and test schemes and play around with the number of iterations and the tolerance. It is also worth noting that I am using the analysis time step as the time step of the ground motion. Along the way, upon non-cnvergence, I do try to run using a smaller time step.

numberer Plain;
system UmfPack;
constraints Transformation;
test NormDispIncr 1e-3 100 2
algorithm KrylovNewton
integrator Newmark 0.5 0.25;
analysis Transient;

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O B S E R V A T I O N S
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1) The elements are loaded successfully in the end of gravity analysis.
2) Eigenvalue analysis runs fine and the plotted modes/mode shapes look reasonable.
3) There is a tedious problem caused by the use of rigid diaphragm together with RC fiber beams. Elements develop significant axial forces due to the constraints. This is caused by the shift of neutral axis in bending leading to excess axial strains at the section level, and consequently, at the element level. Since the element is not allowed to shorten/elongate, it causes axial forces to develop. This behaviour was resulting in significant (~0.5*fc*A) axial forces to develop in my coupling beams ultimately transfer very large moments/shears to the walls rendering the analyses very difficult to converge after a point. As a temporary solution, I reduced the area assignment of the beamWithHinges interior IPs to a thousandth of its original value. This doesn't lead to any significant change in behaviour other than allowing for the strains to develop at the element interior, getting rid of the excess axial forces.
4) Upon performing dynamic analysis on the model, I can barely make it get through the first 3 seconds at best. This point corresponds to an acceleration value of 0.01g. The structure does a full swing to one side, starts coming back and right before it reaches back to zero top displacement it hits a non-convergence point. I did try different ground motions, and I did scale them down quite a lot to see if it will be any good. But none of it worked.
5) Both pushover and dynamic analyses do run fine for the same model with only the core-walls+coupling beams modelled and the frames excluded. I am getting reasonable results in the end of these analyses. The core wall configuration is a pretty standard one. It is more or less symmetric in Y-Y plan dimension. The Left hand side mirror counterpart looks like the letter 'E'.

Any kind or form of comment or feedback is appreciated! I hope that I am committing a terribly obvious mistake that can be picked up from these lines. Otherwise I'd be happy to exchange e-mails with anyone willing to help. My e-mail address: omer.odabasi@iusspavia.it

Many thanks,
Ömer

[selimgunay]

From waht you have described and non-convergence starting at the very beginning, I think the two-node link elements may be the problem. Probably they are not stable.

[OmerOdabasi]

Thank you very much for the prompt reply! I had the same doubt for a long while untill I ran the same analysis using only the core-wall configuration where the same elements still exist. And it runs just fine.

I am wondering if it's the diaphragm causing problems together with the gravity beams across plan (which are modelled as beamWithHinges elements as I mentioned). Because some of them connect to another beam instead of a column joint. I put up the following visuals for clarity, please check them out.

Plan view: https://drive.google.com/open?id=1SdLXT ... Scw22cy0jO
3D view of the first story (OS model): https://drive.google.com/open?id=1K_YK- ... a6B-70KnRJ