SAP2000 to model a pendulum-like structure 1

[Thawkes]

My company has sponsored a capstone project at a local university. They're stumped and I'm hoping to assist them. We are trying to model a pendulum-like structure--a large mass suspended from the roof of a building by 4 vertical cables (like a Jumbotron). The question we're trying to answer is: how will the suspended mass behave during a seismic event? How far could we expect it to move for different input movements? The suspended mass itself doesn't experience inertial forces directly, but only indirectly when the supporting roof structure moves. I've suggested that the students figure out a way to input forced displacement at the 4 support joints. The displacements need to be variable to generate a dynamic response, so we'd like to input horizontal motion of the boundary joints. For simplicity, I suggested a variable motion following a sine curve with an amplitude of, say 12". Is SAP2000 capable of modeling such behavior with forced displacement instead of more conventional loads measured in kips at non-boundary locations?

In case it helps, I received an update from the student team, and it appears they are attempting to use a modal load case, but the inputs don't look like what I have in mind. Using a modal load case, does it sound like they've gone down the wrong path?

Thanks to anyone who takes some time to respond!

 

[Agent666]

So the 4 cables are purely vertical? Or at some angle to the vertical? I think we need to know the geometry better to understand how it might react.

What I'm basically asking is it actually able to swing like a pendulum or is it fixed in space by 4 cables at various angles with a horizontal component. These are completely different answers depending on the situation.

I have no idea what a jumbotron, is which maybe makes it clearer?

Imposing some random deflection in the form of a sine wave is supposed to represent an earthquake how?

 

[r13]

I consider myself an elementary student on dynamic analysis, so don't take too seriously on my comments and questions.

- I don't think you are clear on the objective of this project - what are the students expected to learn, or demonstrate the understanding of this subject?
- What is the forced displacement induced dynamic phenomenon, how the hanging mass is expected to behave?
- Why the use of modal analysis is deemed going the wrong path?

I appreciate your responses and comments.

 

[Blackstar123]

Are modelling the cable and mass system only, that is, without the structure it's hanging from?
If so then I'll suggest to derive the equivalent force function on the mass due to movement of the floor instead of inducing displacement function on your supports.

Idea behind this is the same as what we do for a structure on a shaking ground.
We apply inertia force on the structure to mimic the motion due to ground movement.

I'll refer dynamic analysis by Anil K Chopra for in depth study about the derivations behind solutions of dynamic displacements and most specifically for modal equations.

Sap2000 may not be able to do this, because it determines seismic forces for different modes based on a code specified response spectrum. If you can somehow convert your floor accelerations to a response spectrum than may be you can achieve your goals.

 

[UcfSE]

There are a few questions here. I think what you're missing is a time input, which I see you're trying to answer with a sine function. I expect the students will need help with the frequency of the sine function also as that will have an influence on the analysis results.
1. Yes SAP2000 can load your model with enforced displacement following a sine curve.
2. If you have any time-history data for seismic events, you can check those in SAP2000 also.
3. You can try a response spectrum analysis too. That is generally less computationally burdensome and can still generally provide useful data.

 

[WARose]

I've seen a envelope (i.e. limit) solution to this type of problem. (I.e. figured on paper.) But before I give it.....I have the same type of question the rest have: are we really talking about something suspended (without lateral restraint)?

 

[CivilSigma]

This sounds like the analysis of a structure employing Tuned Mass Dampers.

If they are up to the challenge, I would suggest the software OpenSees. It is specifically designed for dynamic analysis and the design of seismic retrofit.

 

[Thawkes]

Thanks to all who took the time to respond. See here for a short video of the model which may answer some of the previous questions. The 4 cables are vertical (no horizontal component in the at-rest position. There is no lateral restraint. I'll try to state the objective more clearly as some felt it wasn't clear in my original post. We want to know, given the mass and geometry of the suspended system and limited building info, how far we can expect the suspended mass to move horizontally. Building-related inputs I believe we can get for this type of project include the fundamental frequencies/periods of the supporting building structure and the building seismic drift to be expected during a seismic event. This should be a good chance for the students to learn the software and more importantly to get a taste of a real-world dynamics problem. This may be a long shot, but I would love to be able to create a few models and extrapolate from them to determine, without the use of SAP2000 or any other souped-up software, what kind of lateral movement to expect, given a few simple inputs.

I would prefer to apply forced displacement to the supporting nodes at the top of the cables, because that is what will truly happen in the real world, but that is not the direction he students are currently taking. I am concerned that what they have modeled does not consider the dynamic properties of any real-world building structure, so the accelerations they have applied are an arbitrary guess, but maybe I am wrong. Maybe applying lateral accelerations is more appropriate. Thoughts? What kind of acceleration is reasonable, and how would we determine that with very limited information about the supporting building?

There is no reason to have modeled the 4-column frame around the suspended mass in my opinion, but I don't think it hurts. The exterior frame appears to be relatively rigid in the model the students are working with.

Final thought: Some of you out there recognize that this boils down to a fairly simple dynamics problem. It could probably be solved by hand as easily as it could be solved with costly dynamic analysis software. It's been quite a few years since I took a dynamics course...

Thanks again!

 

[ThomasH]

Hello

First, I don't use SAP200 so I can't really add anything redarding how to model in that software. But since it is a school assignment I assume that the important part is understanding the problem.

You have a (rigid) box hanging in four vertical cables connected to a frame and you move the frame sideways. The box has no or very little horisontal support meaning three modes with zero or near zero frequency. Some software don't like that situation, I don't know about SAP.

Now, if you move the fram sideways instantaneously the box will first remain at the original position, in theory. That is due to mass inertia, if you have something in zero gravity it will not move without applying a force. But you have applied a small force, because you inclined the cables, and created a small horisontal force component that depends on the inclination if the cables.

If you just move the frame to a new position the box will follow but will act as a perpendulum until it becomes stationary at the new position. It will move back and forth and the driving force will vary with the inclination until a new state of equilibrium with vertical cables is reached. The start position will be the max amplitude fot the perpendulum. If it is a seismic situation it becomes more complicated since the target position is not stationary.
Ant the force from a perpendulum is usually described as a sine-function.

Assuming I understood the question correct .

Thomas

 

[r13]

I think a study on damping effect can be interesting.

 

[Guest262653]

You need to perform a non-linear time-history analysis. I would forget modal analysis as it is inherently linear and it can't capture the cable behaviour appropriately.
CSI's wiki page has the description of a Newton craddle problem analysed with SAP2000 that may be a nice reference for your problem:
Link

 

[WARose]

Final thought: Some of you out there recognize that this boils down to a fairly simple dynamics problem. It could probably be solved by hand as easily as it could be solved with costly dynamic analysis software. It's been quite a few years since I took a dynamics course...

The people you are working with on this project.....chances are, a course of dynamics is a bit more recent for them.

In any case, this problem has 2 parts, #1: figuring how much the supporting frame accelerates......then #2: figuring how much the supported mass rises/swings.

For #1: In the programs I have used (and I cannot remember if SAP has this or not), it is possible (for a given response curve) to get the program to give you the max. accelerations, displacements, velocities, etc for a location on a frame during a seismic event. If you have one, you can typically get the other with a variety of methods in any structural dynamics text.

For #2: The max. height the mass can rise can be reduced to a simple conservation of work/kinetic energy problem. Using a dynamics text I have and applying these principals, I came up with the following:

W(L-LcosΘ)=0.5(m)(v[sup]2[/sup])

Where:
W=the weight of the suspended mass
L=suspended height (i.e. cable length)
Θ=angle of cable (measured off the vertical) at the max. height it rises to [in degrees]
m=mass of suspended weight
v=max. velocity of supporting frame

The (L-LcosΘ) term is the rise height. You would solve for Θ in this case.

I checked by doing a problem and it checked out. (By the answer in the back of the book. The problem was a mass suspended from a massless rod, with the rod hanging from a rolling cart on a track. It was asked to determine the cart velocity required to get the mass to rise 30[sup]0[/sup] in the event of a sudden stop at that velocity.)

Certainly there are numerous approaches......but I think conservation of energy is in order.

Hope this helps.