you can model this kind of joints in SAP2000 by using the "end-relese" of the element, from the "assign" menu. In particular in your case you should release the Moments in both the initial and end nodes of the ties. see the attached sketch. Hope this could help. Best regards

With all respect to Dr. Stefano ,  As I understand, this is not the case.

I understand that the cable is fixed in one end of the horizontal arm and goes above the vertical strut to the other end of the horizontal arm and then stressed from that point. It means that tension force is equal in both parts of cables and will always be equal under any loading condition because it is one inverted V shape element. ( of coarse if we assumed that the top of the strut is totally smooth).

So, the challenge is to model the joint at the top of the strut to maintain the tension in both parts of he cable equal regardless the loading condition.

It is really and interesting modeling problem, but I want to ask 2 questions,

1st, Is the connection at the mid of the horizontal arm (between 2 modules) hinged or rigid ?

2nd, What is the purpose of that structure?how will you load it ( in what direction) ?

regards

Dear Ahmed, your comment is not in contrast with what I wrote. I only spoke about A WAY of modeling the joints in SAP2000. Once made that one could apply initial strain or initial stress conditions to the ties, involving the geometric stiffness contribution of the elements and to obtain the wanted self-stress state. In general, as in Suspension Bridges, the self-stress state needs to be calibrated with respect to the other load conditions. I was not going into deep details on how to obtain that. Your very good and detailed explanation of the joint between cables and the strut, involve to model a contact behavior that is not easy in SAP2000 software. If one wants to use SAP2000 some parts of the structure should be modeled in a simplified way. 

Best Regards 

Dear Dr. Stefano,

I really appreciate your fast response, I agree with you that SAP2000 may not be able to accurately simulate the behavior of that joint and we have to simplify it. So, I tested some alternative in the attached model. the idea is to check the axial force in both part of cable after applying horizontal force on the top of the vertical strut, if both tension forces are equal then the modeling is successful. 

I started with your proposal ( at the left) and ended with final model ( at the right). the final one shows excellent results. it shows that tension in cables reminds constant after applying horizontal force which is logic because the cable will slip on the smooth top of rod. Hence, the only effect of that cable is to apply per-compression force on the vertical strut and it have no effect on the stiffness of the structure. it can be replaced by per-compression force on the vertical strut.

best regards

the model

Dear Dr. Ahmed, many thanks for your great effort in providing the CORRECT models. The analysis you provided do not account for the 2nd order effect in the stiffness, that needs to be considered if you have pre-tensioned cables in a structure. This only means that you should account for it into the analysis. One can do that by considering in SAP2000 (for example) the P-Delta contribution. If you do that, you will have a more realistic behavior of the tied model and you could see that there is no practical differences between the first (left) and last (right) models (See the attached screenshots) This means that the modeling choices are equivalent "in practice". 

Best Regards

Thanks a lot Dr. Stefano and Dr. Ahmed for your help. i think your answers entirely solved my problem.

Regarding Dr. Ahmed's questions, this structure (cable-strut structure) is one particular example of a general type of structures called "deployable/retractable structures". They are flexible structures that has the ability to fold and deploy. The figure below shows three stages of the deployment process of the flat grid whose figure attached to the question. The flat grid cable-strut structures are composed of many modules and the final grid shape depends on the configuration of the modules. There is algorithm that helps generating new modules. these structures are always compared to the conventional space truss that's composed of only struts. The most common criteria are the self weight, deformation and max stresses of the members. They're often lighter and more rigid than the conventional space truss due to using active cables that prestress the structure before loading it. Also, there are "passive cables" that terminate the deployment process at a predefined configuration; they're often used in the horizontal planes. 

This structure is used as a covering roof for large span spaces. It's often covered by membrane elements. After being deployed, the structure are lifted to be supported upon columns to cover the predetermined space.

It could be tested under gravity loads like live and snow loads. Also, it could be tested under lateral loads such as wind and earthquake loads. 

All the connections between the modules are hinged to facilitate the deployment and retraction of the structure.

i have additional question, if i model the cables as cable element, how can i release the moments at its ends?

Dear Dr. Stefano, your comment is quite right an I appreciate. 

and Dear Abdelrahman, I think id you use very small inertia modifier (0.01) you will release the end moments, and good luck in your research.

It was an interesting and useful discussion, I really enjoyed it, thanks for both of you

best regards