SAP 2000: Cable-Strut structures under self-stress 1

[catenaryworks]

Hello,

I would like to know how to model 3D cable-strut structures in SAP 2000. There will be no externally applied loads and self-weight will not be taken into account. Which means, on analysis, the structure should find a new equilibrium position resulting in internal forces (prestress forces) in the members. If you have experience with this, and have examples to share, I will appreciate you taking the time to help.

 

[catenaryworks]

ishvaaag,

Your MathCad solution is very instructive. Thank you again. I understand that you use temperature change for changing the tendon lengths to eventually achieve the equilibrium configuration. The analytical solution, like your MathCad results, gives alpha=30. From your message on "6 Aug 11 13:30", do you mean that SAP will not be able to do what MathCad has done for you, with regard to finding the equilibrium configuration?

I get the attached error message when I try to open your SAP files. Do you know how I can escape this? See attached error message.

So, exactly, what element type, what load cases/combinations, and other specifications did you use in SAP? Also, I think I have access to MathCad at college. Would you mind sharing your file, so I can see how it works? Do you think it is more powerful than SAP for finding equilibrium configurations?

 

[ishvaaag]

On my entry at 13:30, we must first investigate what differentiates the Mathcad model from the SAP2000 model.

In the Mathcad worksheet model we assume as a simplification inextensible rods and cables that out of the geometry, and then we find that for every geometry that takes the shape of the solution in which one triangle is rotated 30 deg from the one that keeps its position we can have infinite sets of grouped tensile and compressive stresses in the members that satisfy equilibrium as long as they meet some precise proportions that depend on the dimensions of the base and length of the strut (or overall height of the outfit, if you want).

SAP2000 on the contrary is an advanced analysis program, and, partly at least, mechanical solver, and simply, as long you go within the basic understandings of the program and make a good model it is accepted by most of its users provides a reliable answer to equilibrium and other useful structural stuff. From this description and knowing that it admits property modifiers, we must expect that SAP2000 will (or at least can, with a proper model) resolve for solutions that take the final shape of the kind found through Mathcad.

But to produce such model we first than anything need make the axial rigidity of the members very big. Imagine we have rigidity enough to mimick the infinite axial rigidity of the Mathcad model to tolerance, then we can for go the obvious solution when producing the model of just using one of the geometries of the found solution, then if I set some force on, say, the retentors, wil relax it to take the values proportional that we may established through mathcad for the same geometry and that would be all. I suspect the overall high stiffness may do worrying things numerically but this is just a suspicion and we may defer it to further proof. Even so, then you may believe that the forces found are the "solution" to the structural case (within the named parameters), yet you may eventually by inspection discover what we did through the Mathcad study, that other forces, just proportional, also would be, and even if you have found "THE" one that correspond to its derivation from the unrelaxed force applied to the retentors, you might be forfeiting the other proportional answers that may also be of your interest.

This is no surprise, since we all solve everyday for just a set of hypotheses and forfeit every other understandings of the problem and secondary ways of structural response that would burden our structural design tasks.

We maybe need not to adjust ourselves just to the tight geometry of the answer, and maybe with SAP2000 we can set the case of the cables at the triangles hanging somewhat loose, whereas the retentors (to be loaded) and struts have the straight geometry. We should expect that as long the slackened cables at the triangles have the final length, and axial rigidity brings the solution of a final shape of the kind found in Mathcad, it also will find the solution, something that we also can bring to test.

Yet SAP2000 potentially at least has shown us that it needs not to abide within the hypothesis of perfect rigidity and found shapes of the Mathcad study, since it can derive solutions according to the laws of structural analysis not within these limits.


Respect the kind of error you refer to I found it when I tried to convert v15 to v14 yet since I am not SAP2000 expert, but novice, I have not found solution if it exists and maybe someone may help us in the task whilst we learn how.


Whilst you get the model working, I didn't manage to get any response till I used for all elements other than the struts the cable element; i.e., the tendon element -in whatever definition I put where the retentors are- failed to produce meaningful response, maybe because they are thought to be applied on some beam or struts or whatever other reason that for now escapes me. I inmovilized the vertices of the upper triangle in an horizontal plane (whilst allowing it to vary in position in such plane and forfeiting the lack of enough constraints that might bring the outfit in movement and so, analysis error), i.e., one node inmovilized XYZ, other YZ, and other just Z.

Everything rendered weightless one way or another.

Then I just applied a descent of temperature to the retentors, and then the solution adopted the kind of predominantly rotational displacement that we see to be consistent with the nature of the outfit. You can dump all this in just one hypotheses, even dead load case, since the members have no weight.

Respect sharing the Mathcad worksheet, I have already made in my post of 6 Aug 11 13:30. It is the wholly operative file with extension .mcd

The file is for Mathcad 2000, but, since the mathematics are simple, any of the later Mathcad 11, 12, 13, 14 or 15 should open it without any problem in the automatical conversion.

 

[catenaryworks]

Ishvaaag -- Thanks so much for your thorough responses. I will try to figure out how I can open your SAP files and work with your messages.

 

[catenaryworks]

Ishvaaag,

Can you post your .s2k files instead of your .sdb for all the above that you sent.

.s2k can be opened in older versions.

 

[ishvaaag]

I have tried to open the ones of v15 in v14 and it doesn'work but of course I will post them (I hope in some hours) once I have rounded them in a zip file.

 

[ishvaaag]

Well, here goes the .s2k package. Some come from 15 and others 14.2.4, I think.

I am still a bit puzzled by the fact of Mathcad going definitely for the alpha=30 deg solution (I have ranged the limits for alpha by ten sexagesimal degrees, then the following, without finding other solution) and SAP2000 finding final configurations of equilibrium of other angles ... at the moment I can't see how it can be (other than the forces in the retentors and struts become both zero at the rotated angle -then obliging so as well in the triangle cables since the strut and retentor not exerting any action- and then equilibrium is feasible for other rotation angles; I have not examined the values in the 15 deg rotation case to see if such is the case to some program tolerance); in any case, when the rotation is set to 30 deg and you relax the imparted forces, the deformation occurrs quite homotetically, as is expected from the Mathcad result, whereas at the 15 deg case some rotation becomes quite apparent.

 

[catenaryworks]

Ishvaaag -- Open the .SDB file in Wordpad. Within the Wordpad file, search for PROGRAM CONTROL where the version number will be written. Change the version number from 15.X.X to 14.X.X. Go to your version 14, then to FILE, then Import the saved Wordpad file. It should open now.

I could open your model in v14 and I looked through the member type, loading, etc. I see that you have given a temperature decrement to all the cables, not just the vertical cables. Any particular reason for that?

Also how do you determine the various equilibrium configurations? How do you know the angle of rotation between the top and bottom triangles? I ask this because when you run the analysis, it displaces to a particular configuration, not several.

Any reason why you put the supports at the top?

I note that there are support reactions at all the constraints. Shouldn't they come out as ZERO?

I see the point you are making about MathCad giving a precise 30 deg. angle at which equilibrium is achieved, whereas SAP may not.

 

[ishvaaag]

Well, the whole thing as how the Mathcad insight relates to the SAP2000 answers remains open, I myself not being an specialist nor in SAP2000 nor in the kind of structural outfit. By the way I have found today it belongs to some kind of structures dealt with in a book, that I haven't even started to read, but I list

Free Standing Tension Structures
From tensegrity systems to tension-strut systems
Wang Bin Bing
SPON Press
London 2004

Our already familiar 30º between triangles outfit and plan is extant at p. 24 in such book.

Respect the model, I think in the model starting at 15º I only affected the retentors to the descent of temperature, whereas in the 30º case, I subjected everything to the descent. My idea when doing this in the second case was that whatever the input desequilibrium (non relaxed temperature descents) if it has to come to forces in the members at some particular proportion it wouldn't matter what members are prestressed or not.

Respect why I retained the kind of support provided XYZ, YZ and Z atop, since not under weight, it wouldn't matter that was the bottom plane the one holding the restraints. It is just a device to provide rotational stability to the outfit, enabling for answer from the program, and a plane of reference to where look for relative deformation. Respect why I elected the 3 supports in one triangle plane, it was because from the Mathcad study I expected it remaining plane and then I was not restraining relative movement within the plane, whilst as well, for non-zero stresses in the members, the restrained joints keeping as well relative restraint between the joints given the expected tensile stresses in the triangle cables.

As I was giving insight in my previous entry, it may turn that, effectively, all non-zero stresses mean the 30º deg final status, whatever the initial unrelaxed forces, i.e., all other shapes not having the 30 deg rotation by inception would relax totally to zero if have to get to equilibrium (to, then, a different than 30º angle); this is as of now conjecture. All equilibrium situations for rotated angles different than zero would be showing zero stresses in all members. There would be a match between the initial loading and shape and final angle, yet the forces for all with non 30º rotation will have become zero, something that hints to a somewhat unstable equilibrium that must be not, since it has relaxed what have been actual and maybe significant forces to gain such zero stress state. The puzzling nature of the zero stress is patent since it seems easy to throw such system easily from such equilibrium ... to once suppressed the cause immediately returning to (maybe another, if dependant on the loading ... or maybe not, if depending on just the available geometry)... doesn't sound as unstable equilibrium if the shape is restored after disturbance.

As of now, I have not entered in detailed examination of the results nor the implications of the same. By the above suggested hypotheses, some forces should be zero, where the members may be showing some stress. I expect to give a look at that.

But when performing non-linear analyses, I have seen, even in examples in the watch and learn by CSI for cable elements, that the cables that should show zero stress, show not. It must be a device of the tolerance convergence and impossibiliy of getting a wholly accurate result numerically by the program, whatever the tolerances extant within. I don't know even where to look as of now to see where the tolerances are set (I have not even managed to read the ample documentation of SAP2000) nor what that would mean for a case like ours. But that zeros can have 0.02 or small values in SAP2000 I have seen with my eyes.

Thanks as well for your explanation on opening files of one version in other that I expect to try soon.

 

[ishvaaag]

errata: 3d line of 6th paragraph, should read

All equilibrium situations for rotated angles different than 30º would be showing ...

 

[ishvaaag]

I have also discovered an interesting feature in SAP2000. One of the ways of establishing the initial shape of one cable is by setting the initial tension in the cable. So you go and define this way a sagging cable, and see it so in the screen. You then proceed and set property modifiers, weight reduced to zero, nongravity environment ... you look the cable in the screen, and what was before a sagged shape is now a straight shape, since in gravity zero even a small tension puts the cable straight. So, when defining the shape of the cable these ways, SAP2000 follows the standing gravity.

Everything seen points to SAP2000 being able to approximate anything that does not become a mechanism, and maybe even mechanisms should be representable as long as appropriate definition of the initial states and hinge behaviour is entered with some dynamic hypothesis; this however is an unlikely model most of us can be able to produce, particularly if not an specialist in the problem and how SAP2000 deals with things like the axial compressive stiffness of the cables and things like that. I mean, some particular inabilities of SAP2000 purportedly shown by the models I have made and -posted here and non posted- may well derive from being bad set models, particularly in not being dynamic analyses along time.

 

[catenaryworks]

According to BBWang's book page 28, such prisms are geometrically flexible and contain infinitesimal mechanisms. There is a mention about dumb elements used to make the structures geometrically rigid. We can then use the stiffness-method for analysis.

SAP must be using Stiffness Method. Which means, the analysis will blow up because of the mechanism. Am I right?

 

[catenaryworks]

Ishvaaag -- This was posted by Osquro to my question about opening files in other versions. His explanation is more elaborate and clear. Here it is .......

osquro (Structural) 15 Aug 11 9:57

Try using .s2k (or .$2k) file.

Lets say that version 14.2.4 file was created in the computer A and the computer B has SAP v14.1.0 installed.

- Make sure computer B has the same regional configuration (decimal separator) of computer A. If it is not possible to check, take a look to the file created in computed B and identify decimal separator. Then you have two options a) Change regional configuration in computer B according to computer A. b) Change decimal separator in .s2k file according to computer B (find and replace). If you select the last option, make sure that the string containing version is period-separated and the string containing units is comma-separated, regardless decimal separator, as shown bellow:

TABLE: "PROGRAM CONTROL"
ProgramName=SAP2000 Version=14.2.4 CurrUnits="KN, m, C" ...

- Change the string contatining version to the desired release. In this case:

TABLE: "PROGRAM CONTROL"
ProgramName=SAP2000 Version=14.1.0 CurrUnits="KN, m, C" ...

- Make sure desired default units for the model are selected in SAP2000 graphic user interface (bottom-right).
- Try to import the model.
- Let us know any trouble.

 

[ishvaaag]

I have (by error) added a further comment at thread

http://www.eng-tips.com/viewthread.cfm?qid=304487&page=1

Please read there.