Link Element (Takeda) use for Hysteretic Behavior

[anantparghi]

Hi Adeel,
Thank you very much for your reply. I performed the pushover analysis, and when the reinforcement is yielding at that time the yield force is 97kN, but how do we find the initial stiffness ? Initial stiffness = initial force/ initial deformation ?
But, I dont know how do we find the initial stiffness?

Pushover
https://drive.google.com/file/d/0B3tbcU ... sp=sharing

Cyclic
https://drive.google.com/file/d/0B3tbcU ... sp=sharing

Anyway, I changed the Takeda Properties according to Pushover analysis, but I dont see there is any force in link element? If you cold help, I would greatly appreciate you.
Thanks
Anant

quote:Originally posted by adeelfaisal

Dear Anantparghi
I've checked your model.I'm not very sure about why link is not

behaving in the expected way but i would suggest you to check if

you have correctly calibrated the link element. Fy =500 kN for the

Takeda Link is the default value used by the program. You need to

find out the actual parameters for your column by performing

static pushover analysis for your column to get the capacity curve

for your column and converting the capacity curve to idealized

bilinear curve.

Best of Luck-- Anant

quote:Originally posted by anantparghi

Hi Adeel,
Thank you very much for your reply. I am running static time history analysis.I restrained the second node of the link which is the first node of column. The first node of the link was restrained only y+rx+rz. The load I applied to the top of the column with axial mass, and lateral cyclic load.


quote:Originally posted by adeelfaisal

Are you applying the load to the restrained end and is the second node of the link the first node of your column? I tried to download your model but access was denied.

quote:Originally posted by anantparghi

I am analyzing a RC circular concrete column for static time history analysis. For the stiffness degradation I used Takeda Link element for the static time history analysis.
I am getting base shear and displacement, but not getting force in the Link element.
As per the previous discussion on forum, I restrain the first node and unrestained the second node, then not I was not getting any force. After that I restrain the second node, the base shear and displacement is good, but no force in the link element.
Anybody, could please check the mode.
https://docs.google.com/file/d/0B3tbcUu ... pIZDA/edit

https://drive.google.com/open?id=0B3tbc ... authuser=0
Thanks
Anant

[adeelfaisal]

The yield force you obtain from the actual capacity curve(97.9kN)

is indeed its actual value but Takeda link calibration needs an

idealized yield point to be obtained from bilinearly idealized

capacity curve. I refer you to the topic Post-Yield Stiffness from

Capacity Curve in the same forum.Keep the starting and ending

point of the actual curve fixed and change the position of yield

point around its actual position till the area under the bilinear

curve becomes equal to that under the actual curve. an example

using autocad is available here https://drive.google.com/file/d/0B1zFr_ ... sp=sharing

Initial Stiffness is the slope of the line joining origin and the

bilinearly-idealized yield point.

I guess that you should include FRP confinement for static

pushover analysis also (as you do in the Static time History

Analysis)

Best of luck -- Anantparghi

quote:Originally posted by anantparghi

Hi Adeel,
Thank you very much for your reply. I performed the pushover analysis, and when the reinforcement is yielding at that time the yield force is 97kN, but how do we find the initial stiffness ? Initial stiffness = initial force/ initial deformation ?
But, I dont know how do we find the initial stiffness?

Pushover
https://drive.google.com/file/d/0B3tbcU ... sp=sharing

Cyclic
https://drive.google.com/file/d/0B3tbcU ... sp=sharing

Anyway, I changed the Takeda Properties according to Pushover analysis, but I dont see there is any force in link element? If you cold help, I would greatly appreciate you.
Thanks
Anant

quote:Originally posted by adeelfaisal

Dear Anantparghi
I've checked your model.I'm not very sure about why link is not

behaving in the expected way but i would suggest you to check if

you have correctly calibrated the link element. Fy =500 kN for the

Takeda Link is the default value used by the program. You need to

find out the actual parameters for your column by performing

static pushover analysis for your column to get the capacity curve

for your column and converting the capacity curve to idealized

bilinear curve.

Best of Luck-- Anant

quote:Originally posted by anantparghi

Hi Adeel,
Thank you very much for your reply. I am running static time history analysis.I restrained the second node of the link which is the first node of column. The first node of the link was restrained only y+rx+rz. The load I applied to the top of the column with axial mass, and lateral cyclic load.


quote:Originally posted by adeelfaisal

Are you applying the load to the restrained end and is the second node of the link the first node of your column? I tried to download your model but access was denied.

quote:Originally posted by anantparghi

I am analyzing a RC circular concrete column for static time history analysis. For the stiffness degradation I used Takeda Link element for the static time history analysis.
I am getting base shear and displacement, but not getting force in the Link element.
As per the previous discussion on forum, I restrain the first node and unrestained the second node, then not I was not getting any force. After that I restrain the second node, the base shear and displacement is good, but no force in the link element.
Anybody, could please check the mode.
https://docs.google.com/file/d/0B3tbcUu ... pIZDA/edit

https://drive.google.com/open?id=0B3tbc ... authuser=0
Thanks
Anant

[anantparghi]

Hi Adeel,
Thank you very much for your help, please see the excel sheet for the capacity curve.
In Takeda link elemen, I should provide the Yielding force- 97kN, and the Initial stiffness should be form Idealized bi-linear capacity curve post yield stiffness, is it right?

https://drive.google.com/file/d/0B3tbcU ... sp=sharing

So, by this idealized curve post yield stiffness would be higher that the yield stiffness right?

quote:Originally posted by adeelfaisal

The yield force you obtain from the actual capacity curve(97.9kN)

is indeed its actual value but Takeda link calibration needs an

idealized yield point to be obtained from bilinearly idealized

capacity curve. I refer you to the topic Post-Yield Stiffness from

Capacity Curve in the same forum.Keep the starting and ending

point of the actual curve fixed and change the position of yield

point around its actual position till the area under the bilinear

curve becomes equal to that under the actual curve. an example

using autocad is available here https://drive.google.com/file/d/0B1zFr_ ... sp=sharing

Initial Stiffness is the slope of the line joining origin and the

bilinearly-idealized yield point.

I guess that you should include FRP confinement for static

pushover analysis also (as you do in the Static time History

Analysis)

Best of luck -- Anantparghi

quote:Originally posted by anantparghi

Hi Adeel,
Thank you very much for your reply. I performed the pushover analysis, and when the reinforcement is yielding at that time the yield force is 97kN, but how do we find the initial stiffness ? Initial stiffness = initial force/ initial deformation ?
But, I dont know how do we find the initial stiffness?

Pushover
https://drive.google.com/file/d/0B3tbcU ... sp=sharing

Cyclic
https://drive.google.com/file/d/0B3tbcU ... sp=sharing

Anyway, I changed the Takeda Properties according to Pushover analysis, but I dont see there is any force in link element? If you cold help, I would greatly appreciate you.
Thanks
Anant

quote:Originally posted by adeelfaisal

Dear Anantparghi
I've checked your model.I'm not very sure about why link is not

behaving in the expected way but i would suggest you to check if

you have correctly calibrated the link element. Fy =500 kN for the

Takeda Link is the default value used by the program. You need to

find out the actual parameters for your column by performing

static pushover analysis for your column to get the capacity curve

for your column and converting the capacity curve to idealized

bilinear curve.

Best of Luck-- Anant

quote:Originally posted by anantparghi

Hi Adeel,
Thank you very much for your reply. I am running static time history analysis.I restrained the second node of the link which is the first node of column. The first node of the link was restrained only y+rx+rz. The load I applied to the top of the column with axial mass, and lateral cyclic load.


quote:Originally posted by adeelfaisal

Are you applying the load to the restrained end and is the second node of the link the first node of your column? I tried to download your model but access was denied.

quote:Originally posted by anantparghi

I am analyzing a RC circular concrete column for static time history analysis. For the stiffness degradation I used Takeda Link element for the static time history analysis.
I am getting base shear and displacement, but not getting force in the Link element.
As per the previous discussion on forum, I restrain the first node and unrestained the second node, then not I was not getting any force. After that I restrain the second node, the base shear and displacement is good, but no force in the link element.
Anybody, could please check the mode.
https://docs.google.com/file/d/0B3tbcUu ... pIZDA/edit

https://drive.google.com/open?id=0B3tbc ... authuser=0
Thanks
Anant

[adeelfaisal]

Dear Anant,

Once you have converted the capacity curve to a bilinear curve, forget about the actual curve. Yield point , Initial Stiffness and post-yield stiffness .... all will be calculated from bilinear curve. Dear Anant, Post-Yield Stiffness is always lesser than initial stiffness. and their ratio is called alpha.

quote:Originally posted by anantparghi

Hi Adeel,
Thank you very much for your help, please see the excel sheet for the capacity curve.
In Takeda link elemen, I should provide the Yielding force- 97kN, and the Initial stiffness should be form Idealized bi-linear capacity curve post yield stiffness, is it right?

https://drive.google.com/file/d/0B3tbcU ... sp=sharing

So, by this idealized curve post yield stiffness would be higher that the yield stiffness right?

quote:Originally posted by adeelfaisal

The yield force you obtain from the actual capacity curve(97.9kN)

is indeed its actual value but Takeda link calibration needs an

idealized yield point to be obtained from bilinearly idealized

capacity curve. I refer you to the topic Post-Yield Stiffness from

Capacity Curve in the same forum.Keep the starting and ending

point of the actual curve fixed and change the position of yield

point around its actual position till the area under the bilinear

curve becomes equal to that under the actual curve. an example

using autocad is available here https://drive.google.com/file/d/0B1zFr_ ... sp=sharing

Initial Stiffness is the slope of the line joining origin and the

bilinearly-idealized yield point.

I guess that you should include FRP confinement for static

pushover analysis also (as you do in the Static time History

Analysis)

Best of luck -- Anantparghi

quote:Originally posted by anantparghi

Hi Adeel,
Thank you very much for your reply. I performed the pushover analysis, and when the reinforcement is yielding at that time the yield force is 97kN, but how do we find the initial stiffness ? Initial stiffness = initial force/ initial deformation ?
But, I dont know how do we find the initial stiffness?

Pushover
https://drive.google.com/file/d/0B3tbcU ... sp=sharing

Cyclic
https://drive.google.com/file/d/0B3tbcU ... sp=sharing

Anyway, I changed the Takeda Properties according to Pushover analysis, but I dont see there is any force in link element? If you cold help, I would greatly appreciate you.
Thanks
Anant

quote:Originally posted by adeelfaisal

Dear Anantparghi
I've checked your model.I'm not very sure about why link is not

behaving in the expected way but i would suggest you to check if

you have correctly calibrated the link element. Fy =500 kN for the

Takeda Link is the default value used by the program. You need to

find out the actual parameters for your column by performing

static pushover analysis for your column to get the capacity curve

for your column and converting the capacity curve to idealized

bilinear curve.

Best of Luck-- Anant

quote:Originally posted by anantparghi

Hi Adeel,
Thank you very much for your reply. I am running static time history analysis.I restrained the second node of the link which is the first node of column. The first node of the link was restrained only y+rx+rz. The load I applied to the top of the column with axial mass, and lateral cyclic load.


quote:Originally posted by adeelfaisal

Are you applying the load to the restrained end and is the second node of the link the first node of your column? I tried to download your model but access was denied.

quote:Originally posted by anantparghi

I am analyzing a RC circular concrete column for static time history analysis. For the stiffness degradation I used Takeda Link element for the static time history analysis.
I am getting base shear and displacement, but not getting force in the Link element.
As per the previous discussion on forum, I restrain the first node and unrestained the second node, then not I was not getting any force. After that I restrain the second node, the base shear and displacement is good, but no force in the link element.
Anybody, could please check the mode.
https://docs.google.com/file/d/0B3tbcUu ... pIZDA/edit

https://drive.google.com/open?id=0B3tbc ... authuser=0
Thanks
Anant

[adeelfaisal]

Dear Anant,
see section 3.3.3.2.4 of FEMA 356. FEMA 356 can be obtained from
https://drive.google.com/file/d/0B1zFr_ ... sp=sharing

Look at fig 3-1 and try to find out which case is yours (a) or (b).

[anantparghi]

Hi Adeel,
As you suggested, I read all the documents, and draw bi-linear idealized capacity curve.
I found the all the properties for Takeda element as follows.
Yield force = 114.15 kN
Initial stiffness (sy) = 15230.42 kN/m
Post yielding to initial stiffness ration = 0.05
Outer loop stiffness degradation factor =0.4
Inner loop stiffness degradation factor = 0.9

After running time history analysis, I got the force in the link element, But the Global response Parameters-Hysteresis curve results is not matching with the experimental work. I guess, Takeda link is governed but the experimental and SeismoStruc results are not matching.
You can see the seismostruct file and Excel sheet for Takeda, Please have a look, I am doing right? Please help me to get the right results.

https://drive.google.com/file/d/0B3tbcU ... sp=sharing

https://drive.google.com/file/d/0B3tbcU ... sp=sharing
Thanks
Anant

[adeelfaisal]

Hi Anant,

I've checked your model and excel sheet. Yes you did it right now except the second parameter. I think it should be the slope of the line joining origin & the idealized yield point (Fy =114.18 kN) .i.e second parameter should be 8986 kN/m .

About the mismatch between experimental & S.struct results, more expert members of the forum may please look into it. I don't have any probable reason in mind for the mismatch.

Anant, do you have any idea about how can we obtain stiffness degradation from Takeda Hysteretic Plot resulting from time history analysis ? I've got stuck

[anantparghi]

Hi Adeel,
Thank you very much for your reply. I appreciate you for this help.
Yeah, you are right about the initial stiffness that would be 8986 kN/m should be the initial stiffness I should use for the Takeda link, initial stiffness (sy).
Still, I am not sure because, We are using this stiffness for Pushover capacity curve. The stiffness using should be kN/m. However, most of the researchers are using moment curvature/rotation analysis to get the Takeda link parameter, such as rotation spring parameter. For the moment curvature/rotation analysis the unit will be different.
So, I dont which parameter we should use and what would be the Unit of the stiffness here in Seismostruct. Logically it should be the kN/m.

About your question, stiffness degradation, as I know for Static time-history analysis, we may find the stiffness for each cycle by average of K+ (Positive stiffness) and K- (negative stiffness). I.e ((K+) + (K-)/2) for each and every cycle. Now, we could have stiffness of each cycle, so how much reduction in stiffness that we should plot by graphically and compare it. If, I will come across any other solution for to determined the stiffness degradation, I will let you know.
Thanks
Anant
Thanks
Anant

[adeelfaisal]

Hi Anant,

I was also initially confused regarding whether to use Force Vs Drift Relation or Moment Curvature/Rotation Relation. But i think it all depends on what type of relation we are interested in. I think that Takeda Link is not specific to Moment-Rotation Relation. If we are interested in obtaining hysteretic behavior in terms of moment-rotation relation, we should use the same for Takeda (i.e stiffness will then be in kN-m / radian). But if we are interested in lateral stiffness of a pier, we can model the hysteresis behavior using Base Shear Vs Drift Relation (and accordingly Stiffness in kN/m).

This seems logical from Takeda original paper (1970) available here

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

The term "Load Deflection" curve is being used in the paper (Look at Fig.3 and also note the term "yield load" is being used. The term load can be a force or a moment. and perhaps for the same reason, Seismostruct doesn't display any units for the parameters used to calibrate Takeda Link.

About response to my query about Stiffness Degradation, thanks Anant for your response. I think the method averaging K+ and K- for each cycle will be used when you're applying incremental cyclic lateral load at the tip and getting hysteresis response directly from the global response Hysteretic Curve and not from link element hysteretic curve.

But for earthquake load (accelerogram used as input loading curve), The load is varying in a random way (i.e we do not have well-defined cycles of loading).

Z.gronti has replied to my query which i posted in a separate topic "Stiffness Degradation from Takeda Hysteresis Plot ". He has agreed to the method i described in the query.