Seismosoft | Earthquake Engineering Solutions

I've obtained Hysteresis Plot using Takeda Link.

I've to find stiffness degradation resulted from Dynamic Time History Load. How can i find the stiffness degradation from the hysteresis plot. I guess that the slope of the final loading branch should be considered as the degraded stiffness and compared with the initial stiffness, Sy. Is it the right approach ? Comment plz

Seismostruct model https://drive.google.com/folderview?id= ... sp=sharing

Excel Sheet containing the plot https://drive.google.com/file/d/0B1zFr_ ... sp=sharing

Dear adeelfaisal,

The way you have described is correct.

Thank you very much z.gronti. I appreciate your response. It has solved one of the big problems i was facing in my work. Thanks again.

Dear z.gronti,

When i check the stiffnesses of last loading branches, I find that the stiffness of the last negative loading branch and that of last positive loading branch differ by about 1000 kN/m (e.g in one case, Stiffness of last negative loading branch is about 5100 kN/m whereas that of last positive loading branch is about 6100 kN/m).Can you please say something about Which

value i should use ?

Dear adeelfaisal,

I can see that the diagram is not symmetric. You may compute the stiffness degradation by comparing the stiffness of the first positive loading branch with the stiffness of the last positive loading branch, however i think that this is an issue that should be discussed with your supervisor.

Thank you very much z.gronti. Unfortunately my supervisor is not expert in the topic he assigned me (This is really unfortunate but i've got to do it). I was thinking if averaging the slopes of last positive & negative loadings could be the

solution.

Other members are requested to please share their valuable comments. fakharifar.mostafa , huffte & others. please.

I wonder if it might reveal a pattern if you plot number of cycles on the x-axis versus absolute value of stiffness on the y-axis to help in deciding what value for degraded stiffness would be appropriate.

Best of luck, adeeldaisal.

Thanks huffte for your valuable comment. Can you please explain absolute value of stiffness for each cycle ? I guess it is

equal to the (sum of absolute values of maximum drifts on positive & negative sides in a cycle )/(sum of absolute values of

maximum forces on positive & negative sides in that cycle). Please see the picture in the ppt file available from the link

https://drive.google.com/file/d/0B1zFr_ ... sp=sharing for clarification.

Did I rightly get it?

Dear adeelfaisal,

Huffte's recommendation is perfect. I have an additional comment, stiffness degradation is often reported as an average value at constant drift limits, for static cyclic column, joint, member tests.

For clarity of what I mean, look at Figs. 10 & 11 of the below paper:

Esmaeeli, E., Barros, J.A.O., Sena-Cruz, J., Fasan, L., Prizzi, F.R.L., Melo, J., Varum, H., Retrofitting of Interior RC Beam-Column Joints Using CFRP Strengthened SHCC: Cast-in-Place Solution, Composite Structures (2014), doi: http://dx.doi.org/10.1016 j.compstruct.2014.12.012

Stiffness degradation is often reported at constant drifts and as you guess it should be decremental. For column cyclic tests, constant drifts are applied (e.g. 0.25%, 0.5% up to 6% for instance). And since usually at each drift ratio, 2 to 3 cycles are applied, in order to report the stiffness degradation, they average the stiffnesses at corresponding drift ratios.
I am not so sure about my understanding of what you're exactly doing, however, similar procedure should work for you, but instead of drift, you can use cycles on x-axis, as recommended by Huffte. From a dynamic time history analysis you get a hysteresis behavior, similar to Fig. 7 of the abovesaid paper. Your hysteresis curve is smilar, except it is not symmetrical.

And regarding the positive and negative, YES, you should consider the average on both positive and negative, even if your link element hysteresis is unsymmetrical (you apply ground motion, not predefined drift ratios!). Your illustration seems ok, except sign conventions that I feel are wrong.
And I DO recommend you reading the below paper, on how to extract strength degradation and cumulative damage. What you are referring to (stiffness degradation) is a form of damage accumulation (providing hysteresis capacity):
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.

Hope this helps and good luck on your work.

PS: one non-related additional comment: introduction of a very small value for strain hardening of the reinforcing bar, usually dramatically helps the numerical convergency of highly nonlinear models under dynamic time history analysis. I learned it in the hard way.