Recording hysteretic behaviour

[Rana]

Dear friends
Let us assume a cantelever pier modeled as (a) a single element and (b) discretized in 4 elements. Mass is lumped at the top and the pier is subjected to base excitation. I would like to plot the overall hysteretic response of the pier.

We have two options: (i) Global response Parameters / Hysteretic Curves; (ii) Element Action Effects/ Frame Hysteretic Curves.

My simple expectation is that for system with single element (case a), area of the hysteresis curves obtained from both alternatives shall be identical.

For case b, to get hysteretic response element-wise, I should take output from (ii) and for the entire pier from (i). Sum of the areas for each element obtained for (ii) should be equal to that I get for (i).

This is, however, not the case. Area of the hysteretic curve from Global response is more than that from Element Action Effects. How to then get the true hysteretic response for elements and for systems?

Please guide
Kind regards
Rana

[huffte]

This is an interesting question Rana. I will attempt an answer.

I assume that your elements have some mass? Or did you zero out the density of the elements? Let us suppose that during some instant of time during the analysis, the lumped mass is in its original position while the intermediate nodes are deflected from their original positions. There would be potentially many instants when this is true. This might explain why the element summation of hysteresis energies is greater than the global hysteresis. This is just a guess, but it does make some sense, I believe. For example, if I had a series of light, very soft springs supporting a large mass subjected to a high frequency ground motion, then the large mass might remain virtually motionless while the spring nodes experience a lot of motion due to higher mode effects.

It would seem that the hysteresis of primary interest would be the global hysteresis at the lumped mass node. But I guess it also depends upon what you are trying to study.

Best of luck Rana.

[Rana]

Thank you for your interesting explanation. I would like to elaborate little.
I model a pier with a mass at top and zero material density. I use infirmFB and do not take geometric nonlinearity. In case (a) I take one element for entire pier and (b) 4 elements for pier.

For (a), area of moment-rotation curve obtained from Frame Hysteretic Response under Element Action is lesser than the area of the Hysteretic area obtained from Global Response menu. This difference vanishes when I consider zero damping.

For (b), sum of the areas of moment-rotation for each element obtained from Frame Hysteretic Response under Element Action is also lesser than the area of the Hysteretic area obtained from Global Response menu. The difference continues to exist even when damping is set to zero.

How can I get the hysteretic energy dissipation? I would like to rely on Element Action output. I could not, however, explain the reason.

Please guide.

Kind regards
Rana

[seismosoft]

Hi Rana,
There are several reasons for the differences that you get:
1) damping imposes external forces on the structure (this is how damping works in all programs) and the global response is the sum of the element+damping reponse
2) the global response refers to the global axis system, while the element response refers to the local damping system (since you do not consider geometrical nonlinearity however, this should not make any difference in your case)
3) If you do not apply a force-based convergence criterion (this is the default of the program), in the highly inelastic range there will be differences between the element and the global behaviour. This gets more important with the increase of the number of elements, i.e. in your case (b) with of the 4 elements.

Best Regards,
Seismosoft Support