This is basically a solution convergence issue. Are you sure the element modelling and connectivity are done properly? Does the analysis run properly under monotonic loads?

In addition to the first answer, I would add that it is normal to restrain the point where you want to apply your displacement loading. It is the case in every numerical code.

Do your model step by step with elastic properties and simple loading like suggested above and complete it once this simple model works.

Interesting question, following the answers.

Dear Rohan Bhasker and Damien Decret ,

Thank you for your reply. I have tried run the model under monotonic loads, however, the analysis was not complete. The analysis run until half way only. Is that mean there is something wrong with my connectivity or the restraint issue? Is there any suggestion on reference of step-by-step procedure on how to conduct cyclic/monotonic loading using SAP2000 so that I can do checking on my model?

I guess the boundary conditions are: nodes at the bottom totally blocked and you apply the cyclic loading to the nodes at the top.

Since you use elastic properties for your frame, you can compare the results you get until the analysis stops with analytical solution.

As for tutorials, you can find some on internet like this one: https://www.csiamerica.com/products/sap2000/watch-and-learn

Dear Tze Che Van,

Before you get into dynamic analysis, it is critical to ensure that the structural model works fine. First, you could try applying gravity loads on the beams and checking whether the internal forces/support reactions (in all members) are reasonable values (against hand calculations). Any issue with connectivity/restraints can be detected this way. If the connectivity is fine, but you still encounter erroneous values, check the material property assignment. My suggestion in a nutshell, would be to start with linear static analysis of the structure and then to slowly proceed to nonlinear dynamic analysis in a step by step fashion. When you start nonlinear dynamic analysis in SAP or any other software, there are many more variables that need to be defined related to the constitutive laws, hysterisis behavior, solution algorithm, convergence criteria, load/displacement control etc. Try getting the model rectified first. I'll be happy to give my input if you face any difficulty along the way.

Regards

Rohan

Dear Damien Decret ,

You are totally right on the boundary conditions. I have tried to re-model the frame and finally the analysis managed to run and complete. I think it must be my careless mistake in modelling and caused overlapping of element. However, I am still not understand and not sure what is the most appropriate value for viscous proportional damping for cyclic loading. Can you please give me some advice on this matter?

Dear Rohan Bhasker ,

I have rectified the model and managed to carry out the analysis successfully. However, I am not sure which value should be the input for the viscous proportional damping for cyclic loading. Do you have any suggestion on the input for this part?

Dear Catherine Van Tze Che ,

That's good news. What can kind of test are you doing now? The viscous damping is for dynamic only. With a cyclic test you assign the displacement U so your model as to determine K(U).U only and the viscous damping is not needed.

In dynamic, you assign indirectly a external force. Then the viscous damping is one of the parameters to determine the displacement U. It depends on the kind of material you have for your frame. The common value is 5% but you can find 10%.

Dear Tze Che Van,

Glad to know that the model works fine now. I agree with the above comment by Damien Decret. If you are using Rayleigh damping model instead of assigning a constant value for the damping coefficient, you will need to additionally specify whether the damping is based on initial or tangent stiffness. I would recommend giving Priestley and Grant (2005) a read when you have time.

Regards

Dear Rohan Bhasker and Damien Decret ,

Thank you for the guidance provided by both you. It really helped a lot in my previous work. I have successfully run the cyclic analysis using SAP2000. Now I am working on incremental dynamic analysis on a simple 5-storey building but not sure how to define the critical damping ratio of 5%. I tried to compare analysis result using modal damping which enables constant damping ratio to all modes and Rayleigh damping for only 1st and 2nd natural period. Both results are very different from each other. Model using modal damping is unable to converge while model using Rayleigh damping can for the same time histories. For your information, I am using direct integration method Can anyone explain what is the rational behind this behaviour?

Regards

Dear Catherine Van Tze Che ,

Glad to know you were able to go forward with our help. For the Rayleigh damping, if you note C=a.M+b.K, the damping at a given mode i depends on a and b and the modal frequency fi. In order to have good appreciation of the two constants a and b, usually, we take two nodes far from each other (one low frequency and one high frequency). That may explain the two very different results. I suggest you to keep the first mode and try with the 2nd mode, the 3rd mode, etc until you see that a and b converge to a given value.

Did you try to make your test with a null damping, with a very small damping, with a very high damping?

Regards,

Damien

Dear Damien Decret ,

I am not sure on how to determine the 'given value' that you stated in your previous reply. Could you explain more?

Dear Catherine Van Tze Che ,

I meant that by making the iteration by always keeping the first mode and taking a second mode that is always getting higher (2nd mode, 3rd mode, 4th mode, etc), you will see that the constants a and b will change of value in the first iteration until they have almost always the same value. What I called "given value" is the value of convergence of the two parameters.

I hope I explained well.

Always do modal analysis of the structure and check frequency of building as well as animation, most of the times its an individual member which causes these null steps

https://www.youtube.com/watch?v=DVyu2hCQMvU this video is very useful and shows step by step how to apply a displacement in sap2000