Stiffness Degradation from Takeda Hysteresis Plot

[huffte]

Good advice fakharifar.mostafa. These references should provide valuable guidance for you, adeelfaisal. Whichever route you decide to go for a degraded stiffness parameter, the most important thing is to be explicit in telling your audience how you compute it and why you chose to do it that way.

[adeelfaisal]

Many many thanks huffte & fakharifar.mostafa ! Your recommendations have been very helpful. fakharifar.mostafa, Thanks for

your comprehensive & detailed guidance and references. I've read the references you shared & also some other papers.

1. fakharifar.mostafa, can you please elaborate the sign conventions you feel, are wrong. I couldn't get whether you

referred to sign conventions for forces or to those for displacements or anything else.


2. About extracting strength degradation for dynamic time history analysis, I think Takeda Model does not capture strength

degradation.

Also , the strength degradation for cyclic loading test (as determined in the paper you shared,

"Wang, D., Li, H. N., & Li, G. (2013). Experimental tests on reinforced concrete columns under multi-dimensional dynamic loadings. Construction and Building Materials, 47, 1167-1181. ")

has been calculated to be equal to "Shear force in the third cycle of a displacement level" divided by "maximum shear force

in the three cycles of that displacement level" & it has been stated that maximum shear force is normally recorded for the

first cycle. i.e. Wang calculates the degradation in strength resulting from applying repeated cycles ( three cycles) of a

given displacement level ( and not the degradation resulting from increasing levels of displacements). Such an analogy

doesn't seem to work for the case of dynamic time history analysis where random loading is applied.

I think if a hysteretic model capturing strength degradation is employed, then the strength degradation could also be

plotted against no. of cycles (as you recommended for stiffness degradation).

3. About cumulative damage, I'm reading some more papers (that were referred in the papers you shared) to get a clearer idea

to capture this response parameter. I also plan to capture maximum displacement, residual displacement & maximum

(displacement) ductility as response parameters, to also include the parameters describing peak response in addition to

cumulative damage parameters. (Also, these parameters are straightforward to find)

[fakharifar.mostafa]

1- I guess your stiffness should be:

K= {(Fmax+ve)+(Fmax-ve)}/{(Dmax+ve)+(Dmax-ve)}

2- As long as stiffness degradation, Takeda should work just fine I guess. I recall I recommended using the Sivaselvan and Reinhorn work, as you could explicitly specify the extent of strength degradation, for instance HBD= 0.6 for severe degradation.

http://www.seismosoft.com/forum/topic.asp?TOPIC_ID=1821

However, I also recall that Prof. Pinho somewhere in the forum stated that FB fiber based elements implicitly capture deteriorating behavior to a good extent. I feel that there may not be a unique, conclusive answer to either only using the element only, or element + deteriorating zero length link element and say which one is more accurate. At least, it is beyond my knowledge. More experienced users could help.

I also want to address that, when you introduce a link element like smooth link element to incorporate deterioration, slip, pinching, and degradation you are explicitly specifying for the model that this will happen, which in reality may not always be the case. Keep this in mind, since I have had to deal with it as well.

3- For damage accumulation, it depends what damage measure and type you want to calculate. The response parameters you stated are straightforward. I recommend reading papers that have incorporated Park and Ang damage measure. For start you can read below papers where they used Takeda, which is the one you use, and calculating damage measures.

Park, Y. J., Ang, A. H. S., & Wen, Y. K. (1985). Seismic damage analysis of reinforced concrete buildings. Journal of Structural Engineering, 111(4), 740-757.

Van Cao, V., & Ronagh, H. R. (2014). Correlation between seismic parameters of far-fault motions and damage indices of low-rise reinforced concrete frames. Soil Dynamics and Earthquake Engineering, 66, 102-112.

Cao, V. V., & Ronagh, H. R. (2014). Reducing the potential seismic damage of reinforced concrete frames using plastic hinge relocation by FRP. Composites Part B: Engineering, 60, 688-696.

Van Cao, V., & Ronagh, H. R. (2014). Reducing the seismic damage of reinforced concrete frames using FRP confinement. Composite Structures, 118, 403-415.

[adeelfaisal]

Thank you very much fakharifar.mostafa for your detailed response.

1. Thanks for correcting the stiffness formula. I actually mistakenly put it wrong.

2. About link element to be used for capturing deterioration, I remember you had recommended Sivaselvan & Reinhorn Link

as the best way to capture the deterioration. No doubt, this is the most versatile one but ,as you've pointed out , when we

use a link element, we tell it to behave in a certain way by calibrating it (giving values for various parameters needed to

characterise the link element). Thus the accuracy (in terms of closeness to reality) of the response captured by the link

element is dependent upon the accuracy of its calibrating parameters. Sivaselvan & Reinhorn link elements involve parameters

which have wide ranges & for which finding out the actual values for a given structure seems quite difficult. That's why I

had decided to use Takeda Link, which is relatively simlper & has been widely used in the previous works. So I could find

that majority of researchers are using the default parameters given in this program (S.Struct).

3. About damage measures, Thanks for sharing these valuable papers. I hope that these papers will prove to be of great use

as did the ones you previously shared.

[fakharifar.mostafa]

Best of luck to you adeelfaisal and Merry Christmas.
Don't forget to share your research results in the forum regarding the use of the great SeismoStruct package!