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.

 

[ishvaaag]

Please clarify your intent. Some kind of loading need appear (even if through forced displacement from initial shape) to force a notional weightless structure to develop stress.

 

[ishvaaag]

Are you thinking, say, of a lenticular -in section- truss where the bottom chord is pretensioneds, could that be an example?

 

[ishvaaag]

This model is a concrete Warren truss that has prestress modeled as a Tendon Load (no cable element is used). All frame elements are concrete .25x.25m rendered weightless through changes in properties. The tendon runs straight single piece the whole bottom chord, and applies a 20000 kgf of concentrical prestress. Then the truss deflects a bit upwards.

It is easy to make the lenticular example by drawing tendon pieces following equally the segments of the bottom chord.

It seems natural that to impart prestress one uses the tendon element suited to it. You can also use cable elements and for tensile forces following the cable use some equivalent temperature descent. I may also try to apply one of the types of cables that set some amount of tension to the cable to inspection of result; if I find something interesting that way I may post about it.

 

[ishvaaag]

Here an example in with a simple cable has enforced a temperature descent.

 

[ishvaaag]

In latest former example I didn't nullify the weight, what you can do going to properties of the frame element. This obviously forces equilibrium with the non nullified weights.

A third option tension at I end, or at J end, also causes the trusses where the cable is the lower chord yo take stresses in the other members, try yourself.

As indicated, the best control in the stress of what imparts the prestress is through the tendon element.

 

[catenaryworks]

Hi,

Thanks for responding. I am unable to open your Version 15 files in Version 14 that I have. Would you be able to convert the files to this lower version?

To elaborate on my earlier message, I am thinking of cable-strut structures in which the tension members are made of cables (instead of bar elements). The members of this structure will be prestressable. This structure with cables can stand by itself only under prestress.

I want to know how I can create such a 3D cable-strut structure, with no applied loads, no self-weight, but with the 6 constraints that a 3D structure should have. Can SAP find the new equilibrium position(s) such that the structure stands on its own. Of course, the joints will have to move but this is what I am expecting that SAP could automatically do. The analysis results should give me the new joint locations and the prestress forces in the members that make the structure stand in equilibrium.

I will appreciate your help.

 

[ishvaaag]

Hi, catenaryworks,

I in fact tried to convert it to SAP 14 before upload but since I am learning SAP2000 these days, I couldn`t (yet) do. I may however repeat (I hope, since the cable element is changing with every version) in version 14 if I fail to produce the conversion and will do I expect reasonably soon one or another way.

 

[ishvaaag]

This first case may be of scarce interest to you if what you are dealing is just exactly cable elements, but I include it as a preliminar, and because it is one of the ways to impart forces along the lines of what tendons usually are used for.

To make the model simple, it is a Warren truss of 25x24 concrete members. These members are rendered weightless trhough material properties, and, since had rebar impossible to eliminate, I also changed weight property to zero just in case. The tendon runs the bottom chord of the truss, and I have rendered weightless its material. Then I apply a 20 tonnef prestress to the tendon and the truss cambers a bit upwards.

 

[ishvaaag]

Just a "backup" of the concept above, all weightless, again with some tendon at bottom chord.

 

[ishvaaag]

This new one is a net with 4 poles as edges of one central pyramid, that are hinged at both ends. A 100ºC descent of temperature is imposed only in the cables (it shouldn't matter if also on the poles). This is akin to turnbuckle creating tension in the cables to the equivalent of the temperature descent whilst keeping the nodes at position, then relaxing it. SAP2000 is perfectly able to mimick the behaviour.

Tomorrow I will add some sample/s that create stresses in rigid inclusions and against the standing restraints. It may be even more useful if you imagine one case that exemplifies your expected difficulties and we try to produce a model dealing with them.

 

[ishvaaag]

This other has a cube signaled by its edges of 25x25cm concrete elements held in place by 16 cables, everything rendered weightless in the model. We apply a temperature descent of 50ºC to the 8 top cables and of 150ºC to the 8 bottom cables. Upon solution, the equilibrium is found at a higher position of the cube, and all members show either tension or compression at least.

 

[ishvaaag]

I was having some difficulty in producing this model in v.14 and I have made in v.15; this is not to say with more dedication it can't be done in v.14

In this the upper cables originally follow what is the line of lesser tension; the bottom ones follow equilibrium with somewhat higher tension at hanging points and are shorter having less sag. What said, of course, not meaning any tension, just devices provided by SAP2000 to define the shape of the cables.

Then I insterperse a rigid structure of RC 25x25cm frame element members.

All is weightless.

I subject the whole outfit, cable and frame elements to a descent of 100ºC

In this case the shortening results in the 8 members in the outside of the cross plan in compression and the rest in tension. The cables show marginal stress.

Whilst not illogical in general, displacements when looked at thigh amplification (calculated nonlinear large deformation) show some kinks improper of cable behaviour, but this may as well be a defect of my model as a device of the solving routines; I am not expert to say what.

 

[ishvaaag]

I also whilst doing these and other models have become aware of the necessity whilst modeling cable things of not producing mechanisms or extremely high stresses in the cables with forces transversal to taut members. At the least and specially for those like me wanting to use SAP2000 to solve cable matters, extreme care is required and familiarization with the program against examples in texts, that I may eventually undergo whenever in my knowledge of the program seems proper, that may be not yet, since I have (as always) such a lot of things to do, SAP and not.

 

[ishvaaag]

Let's examine for a moment the mechanism thing. Consider a catenary cable and then we put it in a weightless environment. As soon that happens, the catenary becomes only ONE of the possible solutions to the directrix of the cable without any stiffness in a weightless environment: any path of the same length -even with kinks- is a solution to the cable position.

For a cable with some stiffness, a initial position, and a set of excitations and environment, the actual position can only then be derived from the laws of the mechanics. In absence of such data and process, every line of equal length is a solution.

What means:

That the solution -we are not to forget it is a solution got by SAP2000 v.15- of my entry 5 Aug 12:05 is but, if something, in spite of its apparent beauty, at most, just one of many possible solutions, because whatever the predominance of the tightening produced by the cables of the top of bottom set, the other has ample deformation ability to soak the required movement without problem; hence the sets of solutions really are all those that require the cinematics (as related to the measure of the cables with some holgure) of the problem. The "solution" found by SAP2000 must then, more than anything a device of its inner workings, since nothing really impels the outfit to the final shape shown in the image other than the relaxation worked by the program, and it is patent that there are many other positions that also satisfy the necessary requirements of relative positions between the parts after the descent of temperature.

Hence, for non-taut cables, the weightless environment becomes a severe requirement from the viewpoint of structural analysis since it widens the scope of the satisfactory solutions. A such cable is a mechanism able to take every shape compatible with its length, even with kinks (like chain links of the length of the elements, as, I remark, is the case, since the deformed shape shows such unnatural kinks ... because there is not a gravity forcing to take some catenary shape, or stiffness present to force some constant angle at a node.

 

[catenaryworks]

Hi ishvaag,

I will try to see if I can open your files on a university computer. I have attached an image of what I would like to know about. If all the tensile members shown are elastic, and all the 12 members were prestressable.....I would like to model this such that the structure finds an equilibrium configuration with a certain level of prestress in all the members. To start assume that the top triangle and the bottom triangle are parallel. This is not an equilibrium configuration. Only at a particular angle of twist between the top and bottom triangle, will this structure come to equilibrium. I understand from your last message that there can be several different equilibrium configurations, which will depend on the level of prestress in the members. Hope this can be a fundamental learning model from which I can do more complicated structures. Thanks again for answering so thoroughly and taking the effort to help.

 

[catenaryworks]

Ishvaag,

Can you NOT use temperature, and instead use elongation and prestress to analyze the above image I sent.

 

[ishvaaag]

My introduction to the case started by showing tendons because precisely are other kind of cables that are set apart by their prestress and may be needed to attain proper description of some situations.

In any case, you can get equilibrium for your problem only for some final configurations and stresses and even with the help of tendon elements SAP2000 might only be able to prove equilibrium more than find it. The main difficulty is that the initial dimensions prior to relaxation of the tendons and taking loads of the strut may need be so close to the final dimension (and to the proper side of length and force) that even if in a case with the rotated symmetry your problem has, we with difficulty can get the same for one arbitrary geometry, and so will render the process unworthy for general application.

I will be addressing your problem soon, first in Mathcad for inspection of the required inner workings of the thing, then we'll try to make the use we can in SAP2000 to see what we can make.

 

[ishvaaag]

Well, I have it analyzed in Mathcad; see it for yourself...

For a given input data you get infinite feasible solutions (within the realm of the acceptable stresses) that can satisfy equilibrium. Under such circumstances, it is quite likely that whatever SAP2000 may find be just a verification of a well set case, or just a device of its inner workings, since obviously 1 solution won't advert of the infinite others to the inadverted. Anyway we can give it a try later.

 

[ishvaaag]

I have managed to produce one model different from the setup above (the initial rotation angle of one triangle respect the other is 15 deg), all weightless, and as you can see at least shows rational movement. It neither goes mandatorily to the 30 deg setup, what critizices my study above as being one set of solutions for this kind of collection of structural outfits, but not the complete set. The SAP2000 model shows significant movement at low stresses.

I tried first with tendons with force in the retentors, established in several ways, then the structure didn't show any response; in the end I returned to load the retentors through a temperature descent forcing their shortening, and this is the model I am uploading.

For the particular case SAP2000 since showing what more or less one could expect might be right in this structure.