(ASAP)problem about the MK-bilin——why it is still elastic

[yuqing]

I am a senior student from Tongji University China, nowadays I met some problems when applying MK (bilin material) model. I am so sincerely expected u could give me some advice.
My target is to monitor a cantilever column under cyclic loading and then get the relationship between moment and curvature. Under such load, there would appear plastic hinge near the bottom of the column. I apply the MK (bilin) to define my material and then use that material to simulate the hinge, and the other region of column is still elastic. So I separate the column into 2 parts. The upper part of column I use elasticBeamColumn and towards the hinge I use forceBasedColumn with material I defined.
The measurement is that I output the rotation of the top of hinge θ and moment of the base point. Use θ/ Lh（length of hinge I measured by experiments）,I would get the curvature, then I would get the Moment-curvature figure.
However, when I apply the MK model, the output shows that the column still in elastic which contrary to my experiment results. My problem is what is the range of lamda_S lamda_A and so on, what how to calculate them. Hope u could see my tcl file and find why it would be. Or could u provide me a example.tcl for MK (bilin) model.

here is my input

# Units: mm kg s N
wipe
model BasicBuilder -ndm 2 -ndf 3;
if { [file exists output] == 0 } { # create the data directory

file mkdir output;
}


# define node；
set Lh 112.85 ;
node 1 0.0 0.0 ;
node 2 0.0 $Lh ;
node 3 0.0 1500 ;

# define constraints
fix 1 1 1 1 ;

# define material
uniaxialMaterial Bilin 2 2.43e11 1.0 1.0 300182999 -300182999 30 30 30 30 1 1 1 1 0.0116 0.0116 0.047 0.047 0.4 0.4 0.06 0.06 1 1;
uniaxialMaterial Elastic 3 1526749548.05 ; # 3 E*A
section Aggregator 1 3 P 2 Mz ;

geomTransf Linear 1 ;

# define element
# No. nodei nodej Trans Gauss-Lobatto intege section1 integrate point
element forceBeamColumn 1 1 2 1 Lobatto 1 5;
# No. nodei nodej Area E Iz Trans
element elasticBeamColumn 2 2 3 7596 2.01e5 136371279 1;


recorder Node -file output/disp_2.out -time -node 2 -dof 3 disp;
recorder Node -file output/reaction_1.out -time -node 1 -dof 3 reaction;


# define gravity
pattern Plain 1 Linear {
load 3 0 -1000 0
}

# define parameters of gravity
constraints Plain
numberer Plain
system BandGeneral
test NormDispIncr 10e-8 6 2
algorithm Newton
integrator LoadControl 0.1
analysis Static
analyze 10
puts "Analysis of gravity is completed..."


# -------- Analysis of lateral force: displacement control------------------------
loadConst -time 0.0
pattern Plain 2 Linear {
load 3 1 0.0 0.0;
}

# 1st loading 0.5Δe=2.5mm
integrator DisplacementControl 3 1 0.25;
analyze 10;
integrator DisplacementControl 3 1 -0.25;
analyze 20;

# 2nd loading 0.75Δe=3.75mm
integrator DisplacementControl 3 1 0.25;
analyze 25;
integrator DisplacementControl 3 1 -0.25;
analyze 30;

# 3rd loading Δe=5mm 3 rounds
integrator DisplacementControl 3 1 0.25;
analyze 35;
integrator DisplacementControl 3 1 -0.25;
analyze 40;

integrator DisplacementControl 3 1 0.25;
analyze 40;
integrator DisplacementControl 3 1 -0.25;
analyze 40;

integrator DisplacementControl 3 1 0.25;
analyze 40;
integrator DisplacementControl 3 1 -0.25;
analyze 40;

# 4th loading Δe=10mm 3 rounds
integrator DisplacementControl 3 1 0.25;
analyze 60;
integrator DisplacementControl 3 1 -0.25;
analyze 80;

integrator DisplacementControl 3 1 0.25;
analyze 80;
integrator DisplacementControl 3 1 -0.25;
analyze 80;

integrator DisplacementControl 3 1 0.25;
analyze 80;
integrator DisplacementControl 3 1 -0.25;
analyze 80;

# 5th loading Δe=15mm 3 rounds
integrator DisplacementControl 3 1 0.25;
analyze 100;
integrator DisplacementControl 3 1 -0.25;
analyze 120;

integrator DisplacementControl 3 1 0.25;
analyze 120;
integrator DisplacementControl 3 1 -0.25;
analyze 120;

integrator DisplacementControl 3 1 0.25;
analyze 120;
integrator DisplacementControl 3 1 -0.25;
analyze 120;

# 6th loading Δe=20mm 3 rounds
integrator DisplacementControl 3 1 0.5;
analyze 70;
integrator DisplacementControl 3 1 -0.5;
analyze 80;

integrator DisplacementControl 3 1 0.5;
analyze 80;
integrator DisplacementControl 3 1 -0.5;
analyze 80;

integrator DisplacementControl 3 1 0.5;
analyze 80;
integrator DisplacementControl 3 1 -0.5;
analyze 80;

# 7th loading Δe=25mm 3 rounds
integrator DisplacementControl 3 1 0.5;
analyze 90;
integrator DisplacementControl 3 1 -0.5;
analyze 100;

integrator DisplacementControl 3 1 0.5;
analyze 100;
integrator DisplacementControl 3 1 -0.5;
analyze 100;

integrator DisplacementControl 3 1 0.5;
analyze 100;
integrator DisplacementControl 3 1 -0.5;
analyze 100;

# 8th loading Δe=30mm 3 rounds
integrator DisplacementControl 3 1 0.5;
analyze 110;
integrator DisplacementControl 3 1 -0.5;
analyze 120;

integrator DisplacementControl 3 1 0.5;
analyze 120;
integrator DisplacementControl 3 1 -0.5;
analyze 120;

integrator DisplacementControl 3 1 0.5;
analyze 120;
integrator DisplacementControl 3 1 -0.5;
analyze 120;

# 9th loading Δe=35mm 3 rounds
integrator DisplacementControl 3 1 0.5;
analyze 130;
integrator DisplacementControl 3 1 -0.5;
analyze 140;

integrator DisplacementControl 3 1 0.5;
analyze 140;
integrator DisplacementControl 3 1 -0.5;
analyze 140;

integrator DisplacementControl 3 1 0.5;
analyze 140;
integrator DisplacementControl 3 1 -0.5;
analyze 140;

# 10th loading Δe=40mm 3 rounds
integrator DisplacementControl 3 1 0.5;
analyze 150;
integrator DisplacementControl 3 1 -0.5;
analyze 160;

integrator DisplacementControl 3 1 0.5;
analyze 160;
integrator DisplacementControl 3 1 -0.5;
analyze 160;

integrator DisplacementControl 3 1 0.5;
analyze 80;

puts "Analysis of pushover is completed..."


Thanks please help me ASAP

[f.ribeiro]

The Bilin material and the parameters proposed by Lignos and Krawinkler (2011) were thought to define a Moment-Rotation relationship. Thus, it is appropriate to be assigned to concentrated plasticity elements. However, if you want to implement it in a distributed plasticity element, you should be aware of the relationship between Moment-Rotation and Moment-Curvature. Please see Scott and Ryan (2013).
My personal suggestion is to use the Beam-With-Hinges element and define the hinge section flexural behavior using the Bilin Material according to Scott and Ryan (2013) and Ribeiro et al. (2014).

M.H. Scott, K. Ryan. "Moment-rotation behavior of force-based plastic hinge elements". Earthquake Spectra, 2013; 29:(2)597-607.

F.L.A. Ribeiro, A.R. Barbosa, M.H. Scott, and L.C. Neves. "Deterioration Modeling of Steel Moment Resisting Frame Using Finite-Length Plastic Hinge Force-Based Beam-Column Elements." Journal of Structural Engineering, In press, Accepted February 2014.

[yuqing]

So Thanks!!!!!
After few days I have learned such problem, and now I could get the right result.
Your reply could give me detailed info about this model which is quite useful.
Thank you all the time ^ _ ^

[Tas]

f.ribeiro wrote:
> The Bilin material and the parameters proposed by Lignos and Krawinkler
> (2011) were thought to define a Moment-Rotation relationship. Thus, it is
> appropriate to be assigned to concentrated plasticity elements. However, if
> you want to implement it in a distributed plasticity element, you should be
> aware of the relationship between Moment-Rotation and Moment-Curvature.
> Please see Scott and Ryan (2013).
> My personal suggestion is to use the Beam-With-Hinges element and define
> the hinge section flexural behavior using the Bilin Material according to
> Scott and Ryan (2013) and Ribeiro et al. (2014).
>
> M.H. Scott, K. Ryan. "Moment-rotation behavior of force-based plastic
> hinge elements". Earthquake Spectra, 2013; 29:(2)597-607.
>
> F.L.A. Ribeiro, A.R. Barbosa, M.H. Scott, and L.C. Neves.
> "Deterioration Modeling of Steel Moment Resisting Frame Using
> Finite-Length Plastic Hinge Force-Based Beam-Column Elements." Journal
> of Structural Engineering, In press, Accepted February 2014.


When the desired moment-rotation behavior is not hardening (as it is described in the article "M.H. Scott, K. Ryan. "Moment-rotation behavior of force-based plastic
> hinge elements". Earthquake Spectra, 2013; 29:(2)597-607") but softening, can we use a similar calibration and which is this?

[f.ribeiro]

The paper by Scott and Ryan (2013) only addresses the case of elasto-plastic material with hardening. In the case you have a softening region, the second paper proposes a calibration procedure for force-based beam column elements. Hope it helps.

[Tas]

f.ribeiro wrote:
> The paper by Scott and Ryan (2013) only addresses the case of
> elasto-plastic material with hardening. In the case you have a softening
> region, the second paper proposes a calibration procedure for force-based
> beam column elements. Hope it helps.

I will try to find and read your paper,
Thank you.

[yuqing]

f.ribeiro wrote:
> The paper by Scott and Ryan (2013) only addresses the case of
> elasto-plastic material with hardening. In the case you have a softening
> region, the second paper proposes a calibration procedure for force-based
> beam column elements. Hope it helps.

Excuse me, are there any commands that could output the hinge section moment and rotation in distributed plastic hinge model? would u give me a example THX!

[f.ribeiro]

You can record the moment at the element ends, where the plastic hinges will form. The rotation is obtained by integrating the curvature along a defined length so there is no rotation associated with the hinge section. What you can do is to record the curvature at your hinge section (using the element - deformation recorder) and then multiply it by the plastic hinge length. This will give your the rotation of the plastic hinge.

[yuqing]

f.ribeiro wrote:
> You can record the moment at the element ends, where the plastic hinges
> will form. The rotation is obtained by integrating the curvature along a
> defined length so there is no rotation associated with the hinge section.
> What you can do is to record the curvature at your hinge section (using the
> element - deformation recorder) and then multiply it by the plastic hinge
> length. This will give your the rotation of the plastic hinge.

Cool. I would have a try. Thank you for your reply!