Locations of beam-column hinges

[kesavapraba]

Dear Sir/Madam
I would like to model the behavior of the masonry walls attached here as a beam-column element with moment and shear hinges (phenomenological models)in STKO. Boundary conditions: Top-> guided roller, bottom-> fixed. Is that assumption correct? If yes, actually, the wall would undergo double-curvature behavior in the first case i.e., slender wall, in such a case, should we have to assign moment hinges at both top and bottom? or only at the bottom? Because, from the basics of structural analysis, this beam-column would be subjected to the same bending moments at top and bottom (lateral shear x Height/2), so both would reach cracking moments simultaneously. Would it make the model unstable if we have assigned moment hinges at the top and bottom as static-indeterminacy of the beam-column is 1? Thank you

[STKO Team]

Boundary conditions: Top-> guided roller, bottom-> fixed. Is that assumption correct?

It depends on how the experimental set-up has been made. Make sure to model the BC exactly as they are in the experimental set-up. Pay attention to how the vertical displacement is handled. In some experiments, they first apply a vertical load (the wall displace of a certain amount in the Z direction), then they fix the vertical displacement at the current position.

should we have to assign moment hinges at both top and bottom?

Yes, because the rotation is fixed at both ends, so both of them will experience a flexural deformation (it is not a cantilever)

Would it make the model unstable if we have assigned moment hinges at the top and bottom as static-indeterminacy of the beam-column is 1?

I don't understand this one... Why should it be statically-undetermined? It won't be, at least not until one of the 2 hinges completely fails and gives a zero stress.

[kesavapraba]

Dear Sir/Madam
Thanks for your response. It really helps.
"I don't understand this one... Why should it be statically-undetermined? It won't be, at least not until one of the 2 hinges completely fails and gives a zero stress"- I tried to explain it to you by drawing a sketch of the wall idealization. Kindly find the attached figure here.

[STKO Team]

I understand that once the hinges go into softening regime, the analysis becomes unstable, but not yet undetermined. For sure you need to do something to overcome convergence issues.
First you should use a Displacement-Control integrator, as the LoadControl cannot pass the peak.
Here you can find 2 examples (change material parameters as per your experimental test).

• The first one uses the Lumped-Plasticity with Finite-Length-Hinges (i.e. Fiber section at the beam ends, and elastic section in the middle). The fiber section gived a moment-curvature response that is spread along the plastic-hinge length (in this example 150 mm)
• The second one uses the Lumped-Plasticity with Zero-Length-Hinges (i.e. Phenomenological uniaxial models, and elastic section in the middle). The Moment-Rotation is calculated trying to replicate the Moment-Curvature (integrated over the plastic hinge length) of the Fiber section used in the other file

[kesavapraba]

Dear Sir/Madam
Thanks a lot for your quick and helpful response. I greatly appreciate your effort in answering my question. It works perfectly in STKO. I have three more question to ask:
Q1. I read the TCL code of the model, why was the dimension of the model is taken in 3D i.e., -ndm 3 -ndof 6? Can we not perform the same analysis in 2D?

Q2. Why do you assign stiff material in DOFs other than 5? Is it necessary to be assigned or else can we keep it like the below?
# zero_length_elements zeroLength
element zeroLength 2 1 3 -mat 6 -dir 5 -orient 0.0 0.0 1.0 0.0 -1.0 0.0
element zeroLength 3 2 4 -mat 6-dir 5 -orient 0.0 0.0 1.0 0.0 -1.0 0.0

Q3. Suppose I want to plot reaction at bottom vs displacement at the top, how do I achieve it in the post-processing module of STKO?

[STKO Team]

Q1. I read the TCL code of the model, why was the dimension of the model is taken in 3D i.e., -ndm 3 -ndof 6? Can we not perform the same analysis in 2D?

Yes you can, In my example I did it in 3D just to be more general. However you can make the analysis 2D, just by choosing 2D option in the element and material properties, as well as in the boundary conditions.

Q2. Why do you assign stiff material in DOFs other than 5? Is it necessary to be assigned or else can we keep it like the below?

What I wanted to achieve is: plastic hinge about the local Y direction (DOF 5), and continuity in the other DOFs. If you do it like you did (only DOF 5), all the other dofs connecting the external node ad the interior node of the beam will be detached, thus the model will be singular. Then you may ask: Why are you using a stiff material rather then a kinematic constraint like an EqualDOF? well because in OpenSees, multi-point constraints are only available in the global coordinate system. Now immagine your wall is not oriented along the global axes... you would not be able to use kinematic constraints, so you need a stiff material. Now you need to pay attantion: It is always a bad idea to use VERY STIFF materials, as they will make your problem ill-posed. So you can choose the stiffness of your stiff material as beeing just 2 or 3 order of magnitude more than the stiffness of the internal beam... In my case I computed EI for the beam, and then I chose a material which is slightly siffer then that value.

Q3. Suppose I want to plot reaction at bottom vs displacement at the top, how do I achieve it in the post-processing module of STKO?

Use the extract chart data command, there are many example on our webinar web page

[kesavapraba]

Dear Sir/Madam
Thanks a lot for the reply. Yes, your answers clarify the situations very well.