Beam axial force during pushover

[greser]

I have a question regarding the implementation of pushover analysis in RC structures and the consequent inelastic behavior of beam elements.

If we consider a 2D frame subject to pushover analysis, when the horizontal force is imposed at one end of the structure, the gradual increase of the force results in an increase of the beam axial loading. This beam axial force increase is fictitious (in my opinion), since during the realistic earthquake loading (that the pushover is trying to reproduce in some aspects), the horizontal loading is distributed at the slab and not imposed directly in one end of the frame.

In concentrated plasticity models, this beam axial force is not important during the analysis, since the beam section inelastic behavior is predefined from a sectional analysis, usually taking into consideration zero axial force (no axial force - bending moment interaction).
In seismostruct on the other hand, this (nonrealistic) increased axial loading value may participate in the determination of the beams inelastic response, since it results in modification of the loading of the individual fibers. In other words, I am afraid that Seismostruct considers the interaction between axial force and bending moment even in beams, which is not desirable during the pushover analysis specifically, where beam axial loading is not realistic.

Using a diaphragm-type constraint in a 2d frame (2 bays) doesn't seem to resolve the issue, since a strict rule on the relative displacement of the beam ends seems to result in a further increase of the developing axial force.

Are those suspicions correct, or is it something that I am missing?

[huffte]

I believe, in my non-expert opinion,that your point is to be well taken, but is not a shortcoming of SeismoStruct. It is more of a shortcoming of the nature of 2D force-based pushover analysis. The axial loads in beams during strong ground shaking are probably not as large as might be indicated from a 2D pushover analysis, but nor are they zero as as in your alternate scenario.

In fact, I took about 5 minutes to create a very simple 3-storey model. I first applied a 2D pushover, for which axial loads in ground floor beams were about -1400. I then performed a dynamic time history analysis on the exact same model subjected to the Chi-Chi accelerogram t(factored up by two) provided with SeismoStrucy, for which the axial loads in ground floor beams was about -1200. Maybe you could do something similar to see if you get a like result.

Certainly, the excellence of SeismoStruct in predicting response to time history loads is proven.

Note, as well, that this issue could very well be also related to the previous interesting post you began on the forum:

http://www.seismosoft.com/forum/topic.asp?TOPIC_ID=1250

Good question greser.

[greser]

Dear huffte,

Thanks once again for your valuable contribution. I am not suggesting that this a Seismostruct fault, I am just skeptical regarding the accuracy of combining pushover analysis with fiber based sectional behavior in general, without taking any precautions/limitations to the extent of the accepted beam axial force.

I am not suggesting that the actual beam axial force is zero, I am just saying that its value is not significant, so that it is generally accepted correct to calculate the beam's strength without considering axial force in common structural systems.

Just to make my case, consider any pushover analysis at a structure with more than one bays (e.g. the 3D structure appearing in the 1st tutorial, manual page 53, with 3 bays in X direction). If you check the axial forces diagram, you will notice that the axial force at the first beam in the x-direction is considerably larger than the axial force of the second beam, which in turn is almost double the value of the third beam. This is expected in this analysis type, since a part of the axial loading of the first beam is "transferred" as shear loading of the in-between column.
The beam axial values themselves in this example may not be unrealistic, something that happens in my 2d frame, yet it is definitely not an accurate reproduction of the expected response where all beams should have similar axial force. My point is that when this inaccurate beam axial force values interfere with the calculation of the sectional inelastic behavior, it is expected to produce erroneous results.

I will try an example similar to yours, yet I have to ask if you checked the consistency of the beam axial force value at successive beams in the pushover analysis compared to the time-history analysis. Do both analyses yield the same results at the last bays of the frame you modeled?

A trick that could improve the beam axial forces situation in a multi-bay frame, would be to apply the pushover load evenly distributed in all beam-column joints of a floor. The results would be probably more realistic but still tampered and the theoretical question remains the same.

[huffte]

Yes. I see your point. My initial first simple test was s single bay so I didn't compare beams in a line on a given floor level. And I also had the same idea as you about applying the forces uniformly to all nodes at a given level, but surprisingly, this had very little effect on the results for my simple test anyway. Perhaps it could have a more significant impact on multi-bay models.

Sounds like a good research project greser. Best of luck with this interesting problem.

[TUC]

Certainly this issue is quite important and obviously it's no a matter of Seismostruct but it concerns the principles of proper modeling generally.

When using the FBE or DBE approach in conjunction with Fiber sections the issue of considering unrealistic axial forces should be carefully taken into account because axial forces contribute to the inelastic response of the member indeed. The first thing that someone should keep in mind is that it is wrong (or at least it should be treated very carefully) to constrain the translational d.o.f at the ends of beams by using full diaphragmatic action or, in case of 2D frames, by imposing equal translational displacements, because in such cases some unwanted and unrealistic axial forces are developing due to the shift of the neutral axis after cracking (this happens in case of using Fiber sections) that may result in estimating wrong moment capacity of beam's section. In the first 2 or 3 messages of another post in this forum this issue is also discussed: http://www.seismosoft.com/forum/topic.asp?TOPIC_ID=1049

Alternatively, I have proposed another way of modeling FBE or DBE without using fiber section (if you are interested, see here: http://www.seismosoft.com/forum/topic.asp?TOPIC_ID=1091)

In case of analyzing 2D frames through push over analysis, in order to simulate seismic analysis, obviously it is not a proper way to impose lateral loads in only one side of the frame (this is not realistic anyway, the lateral forces should be applied to the nodes that carry the lumped masses of the structure so these masses aren't only in one side...) but these loads should be distributed at the ends of members. This way axial forces would be zero (if the lateral loads at the ends are equally distributed).

Regards.

[greser]

Dear TUC,

Thank you for your very useful comments. I agree with all your considerations regarding the co-existence of fiber modeling and rigid diaphragms, I believe there is a also a related warning in the Seismostruct manual.

During pushover analysis, application of forces only in one side of the frame is common, since in most programs the beam section's inelasticity is modeled using a pre-defined behavior law that is not affected by the level of the developing axial force. Therefore, even in the case of rigid diaphragms where axial force may obtain artificially much larger values, there are no worries concerning the behavior of the beam section at the inelastic range.

This is clearly not the case when the fiber approach is employed, as you've also suggested, since axial forces affect directly the sectional inelastic behavior. Your proposal for predefined constitutive law at beam sections could be quite useful in those cases. Application of lateral loads distributed at all member ends seems to be the only effective solution for now.
Perhaps a revision of the 1st tutorial appearing in Seismostruct manual (page 53) should be considered as well. I am not sure if I should also post those thoughts in the "04-Unexpected behaviour/errors" section to receive proper attention by Seismostruct developers.

[ruipinho]

Hi greser,

We all seem to agree that what you are saying makes sense, and, as everybody also has noted already, this is something that is not necessarily a limitation of SeismoStruct per se, and that the Help System/User Manual of the program does caution users about this issue.

With regards to your suggestion for the Tutorial in SeismoStruct to be updated, my own opinion would be:

- in practical applications, where 3D models are typically employed, one does indeed tend not to apply the pushover loads on one side of the structure only, but rather computes the nominal load vector at each beam-column node of the building, typically by making use of the modal shape vector(s), as recommended by seismic codes and regulations

- given, however, the difficulties that many engineers, still relatively novice to the issue of nonlinear analysis of structures subjected to seismic action, seem to continue to have when faced with the task of running pushover analyses (a review of the posts in the 'Getting Started' section of this Forum does render this evident), I still think that a simple tutorial where loads are applied on one side of the structure only may be useful

- I do agree, however, that such simple application example may perhaps then be complemented by another one, where instead it is shown how the loads may/should be applied to all the beam-column nodes


Finally, no, I do not think that you need to repeat your post in the 'Unexpected behaviour/errors' section of this Forum, in order to "receive proper attention by SeismoStruct developers", since one can readily see posts from 'seismosoft' on all different sections of this Forum, which demonstrates that the Seismosoft Support team does reads all posts that appear in this Forum - they may not respond to all, but that is simply due to lack of time, and I am sure that they are very grateful to those experienced users who try hard to help others (thus giving more time for Seismosoft developers to continue to develop great tools that are provided for free to tens of thousands of users).

Best,

Rui

[greser]

Dear Rui,

I am sure that Seismostruct developers are checking the posts in all forum sections. I was just referring to the tutorial issue, that is just a detail of this discussion and could easily be overlooked.
I agree with the need of simplicity in the beginners examples, therefore, along with the existing tutorial example, a mere suggestion to the user to apply distributed pushover loading at all nodes with a brief explanation of the emerging issues should be enough (similar comments already exist in the manual in the form of NOTE or IMPORTANT and require only few text lines). No need for additional application example.

Thanks for your contribution in this discussion. It is nice to have this forum to exchange our ideas.

[seismosoft]

Hi Greser and thank you for your input,
In the upcoming v7 release (a preview is already available in the SeismoSoft facebook page and YouTube channel) the new Building Modeller, which will be the main tool for the derivation of real building models, creates incremental forces in all the beam-column joint, where there is mass.

SeismoSoft Support