problem with ZeroLengthSection Element

[basharfarah]

Hi everyone , i'm working on modeling the cyclic behavior of RC column , so i'm using the combination of (ZeroLengthSection Element +Bond SP01 ) , my problem is with the constraints of the nodes (i,j) how its should be ? this is just a part of my code

node 1 0.0 0.0
node 2 0,0 1.65
node 5005 0.0 0.0

fix 1 1 0 0
fix 5005 1 1 1

element dispBeamColumn 1 1 2 4 1 $transfTag;
element zeroLengthSection 5555 5005 1 1111

i found in the manual command that the node j (in my case no 1) should be restrained horizontally .
I can run my model without ZeroLengthSection Element , but when i include this element , it doesn't works .
so Where is my problem ?? it's correct to model this element like this ???
please any help would be appreciated
thanks .

[mhscott]

How do you define the section that you use in the zero length element?

[basharfarah]

fiber section , this one :
# define the section of zero lenght sectionelement ;
set zerosecttag 1111
section fiberSec $zerosecttag {

# Create the concrete core fibers
patch rect $coreTag 15 15 [expr $cover-$y1] [expr $cover-$z1] [expr $y1-$cover] [expr $z1-$cover]

# Create the concrete cover fibers (top, bottom, left, right)
patch rect $coverTag 15 2 [expr -$y1] [expr $z1-$cover] $y1 $z1
patch rect $coverTag 15 2 [expr -$y1] [expr -$z1] $y1 [expr $cover-$z1]
patch rect $coverTag 2 1 [expr -$y1] [expr $cover-$z1] [expr $cover-$y1] [expr $z1-$cover]
patch rect $coverTag 2 1 [expr $y1-$cover] [expr $cover-$z1] $y1 [expr $z1-$cover]

# Create the reinforcing fibers (left, middle, right)
layer straight $bondtag 4 $Ass [expr $y1-$cover] [expr $z1-$cover] [expr $y1-$cover] [expr $cover-$z1]
layer straight $bondtag 4 $Ass [expr $cover-$y1] [expr $z1-$cover] [expr $cover-$y1] [expr $cover-$z1]
layer straight $bondtag 2 $Ass [expr 0.5*($cover-$y1)] [expr $z1-$cover] [expr 0.5*($cover-$y1)] [expr $cover-$z1]
layer straight $bondtag 2 $Ass [expr -0.5*($cover-$y1)] [expr $z1-$cover] [expr -0.5*($cover-$y1)] [expr $cover-$z1]
}

[basharfarah]

dear professor Michael
do you think the problem is related to the nodes constraints ? or it's related to the section of the zero length element ?
i tried to use the equalDOF command by write
equalDOF 5005 1 1
instead of : fix 1 1 0 0
but i got the same results .
please i really need to solve this problem , otherwise i can't go further in my research .
many thanks

[mhscott]

Try using an elastic section instead of the fiber section. This will tell you if it's a constraints problem or a section problem.

[basharfarah]

Professor Michel , i have tried with an elastic section but i got the same problem ,
when i fix all the DOF of node (1) , it's okay but the ZeroLengthSection Element has no influence on the all behavior . please find below my all code ,
# Wang column c1 -2000 # units KN/m
wipe
# create ModelBuilder (with 2-dimensions and 3 DOF/node)
model BasicBuilder -ndm 2 -ndf 3

# build nodes
node 1 0 0
node 2 0 0.35
node 3 0 0.7
node 4 0 1.05
node 5 0 1.4
node 5005 0 0

fix 5005 1 1 1
equalDOF 5005 1 1

set HCol [expr 1.4]; #column height
set BCol [expr 0.4]; #column diameter
set WCol [expr 0.4]; #column diameter
set clearCover [expr 0.04]; #clear cover of concrete
set ACol [expr $BCol*$WCol]; #area of the column cross-section

#------------------------------------------------------
# Define uniaxial materials
#(the three materails will be defined: one for unconfined concrete cover, one for concrete confined core, and one for reinforcement)
#--------------------------------------------------------

# define material tags
set coreTag 1
set coverTag 2
set steelTag 3

#define longitudinal reinforcement
set barArea [expr 0.00030172]; #area of longitudinal bar #5
set db [expr 0.0196]; #longitudinal bar diameter
set numBars 12; #number of longitudinal bars
set fy [expr 497000]; #yield strength of longitudinal bars
set fu [expr 592000]; #ultimate strength of longitudinal bars
set Es [expr 200000000]; #modulus of elasticity of steel
set Esh [expr $Es*0.018]; # tangent at initial strain hardening (calibrated from the coupon test)
set esh 0.0095 ; #strian at initial hardening
set eult 0.0669 ; # strian at maximum stress
set lsr 6.25 ; # slendress ratio

#define transverse reinforcement
set dh [expr 0.00635]; #diameter of the spiral #12
set NoHoops 2; #number of hoops in the bundle
set Asp1 [expr 0.00003166]; #area of transverse reinforcement bar
set stran [expr 0.05]; #the centerline distance between spirals along the height of the column
set fyh [expr 459000]; #yield strenght of the hoop
set fyhu [expr 576000]; #ultimate strenght of the hoop
#------------------------------------------
# define steel model
#------------------------------------------

uniaxialMaterial Steel02 [expr $steelTag+1] $fy $Es 0.018 18.0 0.925 0.15; # Menegotto-Pinto uniaxial steel model (coefficients by Terzic, 2010)
uniaxialMaterial MinMax $steelTag [expr $steelTag+1] -min -0.080 -max 0.080

# defind bond slip material
uniaxialMaterial Bond_SP01 200 74 0.022 90 0.66 0.4 0.6 ; # stress in KSI slip in inche

#-------------------------------
#define concrete model
#-------------------------------

# Plain (unconfined concrete)

#compression
set fc [expr 24940]; # compressive strenght of plain concrete on the day of the test (data from the concrete cylinder tests)
set eps0 0.002; #strain that corresponds to fc' (Caltrans SDC)
set epss 0.005; #ultimate strain for unconfined concrete (Caltrans SDC)
set Ec [expr 149600.*sqrt($fc)]; # the formula from ACI building code

#Confined concrete

#compression
# Mander's equations for calculating confined concrete compressive strength and corresponding strain (Mander, 1988)

set ds [expr $BCol-2.0*$clearCover-$dh]; #diameter of spirals between spiral bar centers (diameter of the confined core)
set Asp [expr $Asp1*$NoHoops]; #total area of transverse reinforcement in the bundle

set As [expr $barArea*$numBars]; #total area of the longitudinal steel in the section
set Ac [expr $ds*$ds]; #area of core of section
set rho_cc [expr $As/$Ac]; #ratio of area of longitudinal reinf. to area of core of section
set rho_t [expr $Asp/$ds/$stran]; # ratio of transverse reinforcement
set fcc 29178; #confined concrete compressive strength
set epscc [expr $eps0*(1.0+5.0*($fcc/$fc-1.0))]; #strain that corresponds to fcc'

# ultimate stress and strain
set ecr [expr $Ec/($Ec-$fcc/$epscc)]; #r factor (Eq. 6 in Mander, 1988)
set epscu [expr 0.004+0.14*$fyh/$fc*$rho_t]; #ultimate strain (by Dawn Lehman,1998, PEER 1998/01)
set fcu [expr $fcc*$epscu/$epscc*$ecr/($ecr-1.0+pow($epscu/$epscc,$ecr))]; #strength that corresponds to ultimate strain (Mander, 1988)

uniaxialMaterial Concrete02 $coverTag -$fc [expr -2.0*$fc/$Ec] 0.0 -$epss 0.1 [expr 0.1*$fc] [expr 0.1*$fc/(2.0*$fc/$Ec)] ; # plain concrete
uniaxialMaterial Concrete02 $coreTag -$fcc [expr -2.0*$fcc/$Ec] -$fcu -$epscu 0.1 [expr 0.1*$fcc] [expr 0.1*$fcc/(2.0*$fcc/$Ec)]; # confined concrete

#Define Section
#-----------------------
# set some paramaters
set colWidth $WCol
set colDepth $BCol
set cover $clearCover
set Ass $barArea ; # area of 19.6 bars
set secTag 1

# some variables derived from the parameters
set y1 [expr $colDepth/2.0]
set z1 [expr $colWidth/2.0]
set secnTag 1
section fiberSec $secTag {

# Create the concrete core fibers
patch rect $coreTag 15 15 [expr $cover-$y1] [expr $cover-$z1] [expr $y1-$cover] [expr $z1-$cover]

# Create the concrete cover fibers (top, bottom, left, right)
patch rect $coverTag 15 2 [expr -$y1] [expr $z1-$cover] $y1 $z1
patch rect $coverTag 15 2 [expr -$y1] [expr -$z1] $y1 [expr $cover-$z1]
patch rect $coverTag 2 1 [expr -$y1] [expr $cover-$z1] [expr $cover-$y1] [expr $z1-$cover]
patch rect $coverTag 2 1 [expr $y1-$cover] [expr $cover-$z1] $y1 [expr $z1-$cover]

# Create the reinforcing fibers (left, middle, right)
layer straight $steelTag 4 $Ass [expr $y1-$cover] [expr $z1-$cover] [expr $y1-$cover] [expr $cover-$z1]
layer straight $steelTag 4 $Ass [expr $cover-$y1] [expr $z1-$cover] [expr $cover-$y1] [expr $cover-$z1]
layer straight $steelTag 2 $Ass [expr 0.5*($cover-$y1)] [expr $z1-$cover] [expr 0.5*($cover-$y1)] [expr $cover-$z1]
layer straight $steelTag 2 $Ass [expr -0.5*($cover-$y1)] [expr $z1-$cover] [expr -0.5*($cover-$y1)] [expr $cover-$z1]
}

# define the section of ZeroLengthSection Element :bond slip material NO 200
section fiberSec 1111 {
# Create the concrete core fibers
patch rect $coreTag 15 15 [expr $cover-$y1] [expr $cover-$z1] [expr $y1-$cover] [expr $z1-$cover]

# Create the concrete cover fibers (top, bottom, left, right)
patch rect $coverTag 15 2 [expr -$y1] [expr $z1-$cover] $y1 $z1
patch rect $coverTag 15 2 [expr -$y1] [expr -$z1] $y1 [expr $cover-$z1]
patch rect $coverTag 2 1 [expr -$y1] [expr $cover-$z1] [expr $cover-$y1] [expr $z1-$cover]
patch rect $coverTag 2 1 [expr $y1-$cover] [expr $cover-$z1] $y1 [expr $z1-$cover]

# Create the reinforcing fibers (left, middle, right)
layer straight 200 4 $Ass [expr $y1-$cover] [expr $z1-$cover] [expr $y1-$cover] [expr $cover-$z1]
layer straight 200 4 $Ass [expr $cover-$y1] [expr $z1-$cover] [expr $cover-$y1] [expr $cover-$z1]
layer straight 200 2 $Ass [expr 0.5*($cover-$y1)] [expr $z1-$cover] [expr 0.5*($cover-$y1)] [expr $cover-$z1]
layer straight 200 2 $Ass [expr -0.5*($cover-$y1)] [expr $z1-$cover] [expr -0.5*($cover-$y1)] [expr $cover-$z1]
}
# define elements prop
# Define coordinate transformation #
set transfTag 1
# geomTransf Linear $transfTag
geomTransf PDelta $transfTag
# geomTransf Corotational $transfTag

set numIntgrPts 4

# set eleType forceBeamColumn
set eleType dispBeamColumn

element $eleType 1 1 2 $numIntgrPts $secTag $transfTag;
element $eleType 2 2 3 $numIntgrPts $secTag $transfTag;
element $eleType 3 3 4 $numIntgrPts $secTag $transfTag;
element $eleType 4 4 5 $numIntgrPts $secTag $transfTag;

element zeroLengthSection 5555 5005 1 1111
#------------------------------------------------------
# Define Gravity Load
#---------------------------------------------------------
set IDctrlNode 5
set IDctrlDOF 1

pattern Plain 1 Linear {
load $IDctrlNode 0. -450 0.;# node#, FX FY MZ
}
constraints Plain; # how it handles boundary conditions
numberer Plain; # renumber dof's to minimize band-width (optimization), if you want to
system BandGeneral; # how to store and solve the system of equations in the analysis
test NormDispIncr 1.0e-8 6 ; # determine if convergence has been achieved at the end of an iteration step
algorithm Newton; # use Newton's solution algorithm: updates tangent stiffness at every iteration
integrator LoadControl 0.1; # determine the next time step for an analysis, # apply gravity in 10 steps
analysis Static # define type of analysis
analyze 10; # perform gravity analysis
# Print out the state of nodes 2
print node 5
# Print out the state of element 1
print ele 1
puts "Gravity Analysis Completed"
# Set the gravity loads to be constant & reset the time in the domain
loadConst -time 0.0
#---------------------------------------------------------
# Cyclic load pattern
#--------------------------------
set dt 0.02

# define time series
timeSeries Path 2 -dt $dt -filePath wang-displac.txt

# define load pattern
pattern Plain 2 2 {
sp $IDctrlNode $IDctrlDOF 1.0
}

# define recorders for displacement and force
recorder Node -file Disp-meter.out -time -node 5 -dof 1 disp; #records displacement at the top node (TN)
recorder Node -file Force-kelonweton.out -time -node 1 -dof 1 reaction; #records displacement at the top node (TN)

# cyclic analysis objects
constraints Penalty 1.0e14 1.0e14
integrator LoadControl $dt
numberer Plain
system BandGeneral
test NormDispIncr 1.0e-7 10 0
algorithm Newton
analysis Static
analyze 1200

########### and this's the displacement history (wang-displac.txt file) #############
0
0.00035
7.00E-04
0.00105
0.0014
0.00175
0.0021
0.00245
0.0028
0.00315
0.0035
0.00385
0.0042
0.00455
0.0049
0.00525
0.0056
0.00595
0.0063
0.00665
0.007
0.0063
0.0056
0.0049
0.0042
0.0035
0.0028
0.0021
0.0014
0.0007
-9.55E-18
-0.0007
-0.0014
-0.0021
-0.0028
-0.0035
-0.0042
-0.0049
-0.0056
-0.0063
-0.007
-0.0063
-0.0056
-0.0049
-0.0042
-0.0035
-0.0028
-0.0021
-0.0014
-0.0007
-1.21E-17
0.0007
0.0014
0.0021
0.0028
0.0035
0.0042
0.0049
0.0056
0.0063
0.007
0.0063
0.0056
0.0049
0.0042
0.0035
0.0028
0.0021
0.0014
0.0007
6.24E-17
-0.0007
-0.0014
-0.0021
-0.0028
-0.0035
-0.0042
-0.0049
-0.0056
-0.0063
-0.007
-0.00595
-0.0049
-0.00385
-0.0028
-0.00175
-0.0007
0.00035
0.0014
0.00245
0.0035
0.00455
0.0056
0.00665
0.0077
0.00875
0.0098
0.01085
0.0119
0.01295
0.014
0.0126
0.0112
0.0098
0.0084
0.007
0.0056
0.0042
0.0028
0.0014
3.23E-16
-0.0014
-0.0028
-0.0042
-0.0056
-0.007
-0.0084
-0.0098
-0.0112
-0.0126
-0.014
-0.0126
-0.0112
-0.0098
-0.0084
-0.007
-0.0056
-0.0042
-0.0028
-0.0014
-4.23E-16
0.0014
0.0028
0.0042
0.0056
0.007
0.0084
0.0098
0.0112
0.0126
0.014
0.0126
0.0112
0.0098
0.0084
0.007
0.0056
0.0042
0.0028
0.0014
5.22E-16
-0.0014
-0.0028
-0.0042
-0.0056
-0.007
-0.0084
-0.0098
-0.0112
-0.0126
-0.014
-0.01225
-0.0105
-0.00875
-0.007
-0.00525
-0.0035
-0.00175
-5.46E-16
0.00175
0.0035
0.00525
0.007
0.00875
0.0105
0.01225
0.014
0.01575
0.0175
0.01925
0.021
0.0189
0.0168
0.0147
0.0126
0.0105
0.0084
0.0063
0.0042
0.0021
0
-0.0021
-0.0042
-0.0063
-0.0084
-0.0105
-0.0126
-0.0147
-0.0168
-0.0189
-0.021
-0.0189
-0.0168
-0.0147
-0.0126
-0.0105
-0.0084
-0.0063
-0.0042
-0.0021
5.97E-16
0.0021
0.0042
0.0063
0.0084
0.0105
0.0126
0.0147
0.0168
0.0189
0.021
0.0189
0.0168
0.0147
0.0126
0.0105
0.0084
0.0063
0.0042
0.0021
-1.19E-15
-0.0021
-0.0042
-0.0063
-0.0084
-0.0105
-0.0126
-0.0147
-0.0168
-0.0189
-0.021
-0.01855
-0.0161
-0.01365
-0.0112
-0.00875
-0.0063
-0.00385
-0.0014
0.00105
0.0035
0.00595
0.0084
0.01085
0.0133
0.01575
0.0182
0.02065
0.0231
0.02555
0.028
0.0252
0.0224
0.0196
0.0168
0.014
0.0112
0.0084
0.0056
0.0028
-3.19E-15
-0.0028
-0.0056
-0.0084
-0.0112
-0.014
-0.0168
-0.0196
-0.0224
-0.0252
-0.028
-0.0252
-0.0224
-0.0196
-0.0168
-0.014
-0.0112
-0.0084
-0.0056
-0.0028
3.98E-15
0.0028
0.0056
0.0084
0.0112
0.014
0.0168
0.0196
0.0224
0.0252
0.028
0.0252
0.0224
0.0196
0.0168
0.014
0.0112
0.0084
0.0056
0.0028
-4.77E-15
-0.0028
-0.0056
-0.0084
-0.0112
-0.014
-0.0168
-0.0196
-0.0224
-0.0252
-0.028
-0.02485
-0.0217
-0.01855
-0.0154
-0.01225
-0.0091
-0.00595
-0.0028
0.00035
0.0035
0.00665
0.0098
0.01295
0.0161
0.01925
0.0224
0.02555
0.0287
0.03185
0.035
0.0315
0.028
0.0245
0.021
0.0175
0.014
0.0105
0.007
0.0035
-7.96E-15
-0.0035
-0.007
-0.0105
-0.014
-0.0175
-0.021
-0.0245
-0.028
-0.0315
-0.035
-0.0315
-0.028
-0.0245
-0.021
-0.0175
-0.014
-0.0105
-0.007
-0.0035
8.95E-15
0.0035
0.007
0.0105
0.014
0.0175
0.021
0.0245
0.028
0.0315
0.035
0.0315
0.028
0.0245
0.021
0.0175
0.014
0.0105
0.007
0.0035
-9.95E-15
-0.0035
-0.007
-0.0105
-0.014
-0.0175
-0.021
-0.0245
-0.028
-0.0315
-0.035
-0.03115
-0.0273
-0.02345
-0.0196
-0.01575
-0.0119
-0.00805
-0.0042
-0.00035
0.0035
0.00735
0.0112
0.01505
0.0189
0.02275
0.0266
0.03045
0.0343
0.03815
0.042
0.0378
0.0336
0.0294
0.0252
0.021
0.0168
0.0126
0.0084
0.0042
-1.43E-14
-0.0042
-0.0084
-0.0126
-0.0168
-0.021
-0.0252
-0.0294
-0.0336
-0.0378
-0.042
-0.0378
-0.0336
-0.0294
-0.0252
-0.021
-0.0168
-0.0126
-0.0084
-0.0042
1.55E-14
0.0042
0.0084
0.0126
0.0168
0.021
0.0252
0.0294
0.0336
0.0378
0.042
0.0378
0.0336
0.0294
0.0252
0.021
0.0168
0.0126
0.0084
0.0042
-1.67E-14
-0.0042
-0.0084
-0.0126
-0.0168
-0.021
-0.0252
-0.0294
-0.0336
-0.0378
-0.042
-0.03745
-0.0329
-0.02835
-0.0238
-0.01925
-0.0147
-0.01015
-0.0056
-0.00105
0.0035
0.00805
0.0126
0.01715
0.0217
0.02625
0.0308
0.03535
0.0399
0.04445
0.049
0.0441
0.0392
0.0343
0.0294
0.0245
0.0196
0.0147
0.0098
0.0049
-2.23E-14
-0.0049
-0.0098
-0.0147
-0.0196
-0.0245
-0.0294
-0.0343
-0.0392
-0.0441
-0.049
-0.0441
-0.0392
-0.0343
-0.0294
-0.0245
-0.0196
-0.0147
-0.0098
-0.0049
2.37E-14
0.0049
0.0098
0.0147
0.0196
0.0245
0.0294
0.0343
0.0392
0.0441
0.049
0.0441
0.0392
0.0343
0.0294
0.0245
0.0196
0.0147
0.0098
0.0049
-2.51E-14
-0.0049
-0.0098
-0.0147
-0.0196
-0.0245
-0.0294
-0.0343
-0.0392
-0.0441
-0.049
-0.04375
-0.0385
-0.03325
-0.028
-0.02275
-0.0175
-0.01225
-0.007
-0.00175
0.0035
0.00875
0.014
0.01925
0.0245
0.02975
0.035
0.04025
0.0455
0.05075
0.056
0.0504
0.0448
0.0392
0.0336
0.028
0.0224
0.0168
0.0112
0.0056
-3.18E-14
-0.0056
-0.0112
-0.0168
-0.0224
-0.028
-0.0336
-0.0392
-0.0448
-0.0504
-0.056
-0.0504
-0.0448
-0.0392
-0.0336
-0.028
-0.0224
-0.0168
-0.0112
-0.0056
3.34E-14
0.0056
0.0112
0.0168
0.0224
0.028
0.0336
0.0392
0.0448
0.0504
0.056
0.0504
0.0448
0.0392
0.0336
0.028
0.0224
0.0168
0.0112
0.0056
-3.50E-14
-0.0056
-0.0112
-0.0168
-0.0224
-0.028
-0.0336
-0.0392
-0.0448
-0.0504
-0.056
-0.05005
-0.0441
-0.03815
-0.0322
-0.02625
-0.0203
-0.01435
-0.0084
-0.00245
0.0035
0.00945
0.0154
0.02135
0.0273
0.03325
0.0392
0.04515
0.0511
0.05705
0.063
0.0567
0.0504
0.0441
0.0378
0.0315
0.0252
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[wuhaoshrek]

mhscott wrote:
> Try using an elastic section instead of the fiber section. This will tell
> you if it's a constraints problem or a section problem.

Hi,
can you explain the note on the zero-length section element:

The section force-deformation response represented by section string P acts along the element local x-axis, and the response for code Vy along the local y-axis. The other modes of section response follow from this orientation.

I didn't see any string used in the example, how should we assign the section orientation for the element? thanks

[basharfarah]

hi , actually i got the same results with and without using the orientation , any way you can read the description of the orientation in the manual "Geometric Transformation Command and the zero length element command " . you should read both of these commands .

[wuhaoshrek]

basharfarah wrote:
> hi , actually i got the same results with and without using the
> orientation , any way you can read the description of the orientation in
> the manual "Geometric Transformation Command and the zero length
> element command " . you should read both of these commands .

yes you can have the same results if the local orientation is coincidentally the same with the global orientation. as what said in
the note of the zerolength element command.

[basharfarah]

Exactly , but i still have problem with applying the (ZeroLengthSection Element +Bond SP01 ), Did you try it before ,
i will be grateful if you can provide any help ,

[wuhaoshrek]

basharfarah wrote:
> Exactly , but i still have problem with applying the (ZeroLengthSection
> Element +Bond SP01 ), Did you try it before ,
> i will be grateful if you can provide any help ,

yeah, it works, but i haven't verified it yet, and in fact I haven't come up with how I should verify it.