Calibration of column (fiber element) for flexure

kaustavsengupta · Post by **kaustavsengupta** » Thu Aug 30, 2018 1:57 am

Dear Members,

I have been trying to calibrate a column model from PEER SPD (Ang et al. 1981 unit no. 4) but the strength of the model is coming higher than that of the experimental values in the plot (base shear vs top displacement). I am using modified kent and park model (concrete02) along withh confinement factor (Ke) as per Mander et al 1988. The steel used is steel02 as per Giuffré-Menegotto-Pinto Model. The column is a cantilever column. The plastic hinge length is of same value as the depth of section (400 mm). It is dispbeamcolumn uniaxial material near the joint till the plastic hinge length. The rest of the column is elastic element with effective stiffness(Ec*I), Ec is effective young's modulus of concrete and I is the moment of inertia of the square section. The loading is displacement controlled and hysteretic in nature.

Kindly share some knowledge about why I am getting high values of strength at all points. I ma sharing part of my code which I think is critical for the abrupt variation.

# SET UP ----------------------------------------------------------------------------
# units: kip, inch, sec
wipe; # clear memory of all past model definitions
file mkdir Data; # create data directory
model BasicBuilder -ndm 2 -ndf 3; # Define the model builder, ndm=#dimension, ndf=#dofs

# define GEOMETRY -------------------------------------------------------------
set LCol 63; # column length=1600 mm 1 inch=25.4 mm
set Weight 187.5 ; # superstructure weight 1 kip = 4.448 kN
# define section geometry
set HCol 15.75; # Column Depth in inches
set BCol 15.75; # Column Width in inches

# calculated parameters
set PCol $Weight; # nodal dead-load weight per column
set g 386.4; # g.
set Mass [expr $PCol/$g]; # nodal mass
# calculated geometry parameters
set ACol [expr $BCol*$HCol]; # cross-sectional area
set IzCol [expr 1./12.*$BCol*pow($HCol,3)]; # Column moment of inertia

#Element :-
# 2
# |
# 3
# |
# 1
#;-----

# nodal coordinates:
node 1 0 0; # node#, X, Y
node 2 0 $LCol;
node 3 0 $BCol; #(from jeon dissertation)
#node 3 0 0; # for spring bottom
#node 4 0 $LCol; # for spring top

# Multi point constraints -- Boundary Conditions # node DX DY RZ
fix 1 1 1 1;
fix 2 0 1 0; #CANTILEVER COLUMN GIVEN IN THE DATABASE, SO FREE AT NODE 2
fix 3 0 0 0;
#fix 3 1 1 1;
#fix 4 1 1 1;

# nodal masses:
mass 2 $Mass 1e-9 $Mass; # node#, Mx My Mz, Mass=Weight/g, neglect rotational inertia at nodes

# Define ELEMENTS & SECTIONS -------------------------------------------------------------
set ColSecTag 1; # assign a tag number to the beamcolumn section
#set eleID 1;

# MATERIAL parameters -------------------------------------------------------------------
set IDconcU 1; # material ID tag -- unconfined cover concrete
set IDconcC 2; # material ID tag -- confined cover concrete
set IDreinf 3; # material ID tag -- reinforcement

# nominal concrete compressive strength
set fc -3.63; # CONCRETE Compressive Strength (+Tension, -Compression) in ksi. 1 ksi=6.895 MPa
set Ec [expr ((57000*sqrt(-$fc*1000))/1000)*0.41]; # Concrete Elastic Modulus in ksi the term in sqr root needs to be in MPa, modified due to effective stiffness by 0.41 factor(jeon dissertation)
# confined concrete
set rhos 0.022; # rhosy=ratio of volume of hoop steel to the volume of concrete core measured to the outside of hoops.
set Fyt 40.6; # transverse steel yield stress value in ksi, 1 ksi=6.895 MPa
set Kfc 1.15; # ratio of confined to unconfined concrete strength (by Mander et al 1988)
set fc1C [expr -$Kfc*$fc]; # CONFINED concrete (modified kent and park model), maximum stress fpc=fc1C
set eps1C [expr $Kfc*0.0025]; # strain at maximum stress eps1C=epsc0
set fc2C [expr 0.2*$fc1C]; # ultimate stress
set eps50wC [expr ((3+(0.29*(-$fc)*6.895))/((145*(-$fc)*6.895)-1000))]; # fc is converted to MPa for calculation 1 ksi=6.895 MPa, eps50w is calculated with values in MPa
set sh 90; # center-to-center spacing of hoop steel in mm
set eps50kC [expr (0.75*$rhos*sqrt($BCol*25.4*0.86/$sh))];
#set zwC [expr 14.596/6.895]; #1 ksi=6.895 MPa
set zwC [expr (0.5/($eps50wC+$eps50kC+$Kfc*0.0025))/6.895]; # slope of the descending branch in modified kent and park model
set eps2C [expr (($fc1C-$fc2C)/$zwC)+$eps1C]; # strain at ultimate stress

#if Concrete02 is used then the following standard parameter values are required (Opensees days 2008)
set lambdaC 0.1;
set ftUC [expr 0.14*$fc1C];
set EtsC [expr $ftUC/0.0025];

# unconfined concrete
set fc1U [expr -$fc]; # CONFINED concrete (modified kent and park model), maximum stress fpc=fc1C
set eps1U 0.0025; # strain at maximum stress eps1C=epsc0
set fc2U [expr -0.2*$fc]; # ultimate stress
set eps50wU [expr (3+(0.29*(-$fc)*6.895))/((145*(-$fc)*6.895)-1000)]; # fc is converted to MPa for calculation, eps50w is calculated with values in MPa
set eps50kU 0; #rhos for unconfined concrete is zero
#set zwU [expr 14.596/6.895]; #1 ksi=6.895 MPa
set zwU [expr (0.5/($eps50wU+$eps50kU+$eps1U))/6.895]; # slope of the descending branch in modified kent and park model
set eps2U [expr (0.8*(-$fc)/$zwU)+$eps1U]; # strain at ultimate stress

#if Concrete02 is used then the following standard parameter values are required (Opensees days 2008)
set lambdaU 0.1;
set ftUU [expr -0.14*$fc];
set EtsU [expr $ftUU/0.0025];

# steel
# -----------
set Fy 61.93; # STEEL yield stress in ksi (longitudinal steeel yield stress)
set Es 29000; # modulus of steel
set Bs 0.001; # strain-hardening ratio
set R0 20; # control the transition from elastic to plastic branches
set cR1 0.925; # control the transition from elastic to plastic branches
set cR2 0.15; # control the transition from elastic to plastic branches

uniaxialMaterial Concrete02 $IDconcC -$fc1C -$eps1C -$fc2C -$eps2C $lambdaC $ftUC $EtsC; # build core concrete (confined)
uniaxialMaterial Concrete02 $IDconcU -$fc1U -$eps1U -$fc2U -$eps2U $lambdaU $ftUU $EtsU; # build cover concrete (unconfined)
uniaxialMaterial Steel02 $IDreinf $Fy $Es $Bs $R0 $cR1 $cR2; # build reinforcement material

## section GEOMETRY -------------------------------------------------------------
set HSec $HCol; # Column Depth
set BSec $BCol; # Column Width
set coverH 1.08; # Column cover to reinforcing steel NA, parallel to H = 22.5+5 = 27.5 MM
set coverB 1.08; # Column cover to reinforcing steel NA, parallel to B = 22.5+5 = 27.5 MM
set numBarsTop 4; # number of longitudinal-reinforcement bars in steel layer. -- top
set numBarsBot 4; # number of longitudinal-reinforcement bars in steel layer. -- bot
set barAreaTop 0.311; # area of indivitual longitudinal-reinforcement bar -- top #
set barAreaBot 0.311; # area of indivitual longitudinal-reinforcement bar -- bot #
set barAreaInt 0.311; # area of indivitual longitudinal-reinforcement bar -- intermediate skin reinf #

# FIBER SECTION properties -------------------------------------------------------------
#
# y
# ^
# |
# --------------------- -- --
# | o o o o | | -- coverH
# | | |
# | o o | |
# z <--- | + | Hsec
# | o o | |
# | | |
# | o o o o | | -- coverH
# --------------------- -- --
# |-------Bsec------|
# |---| coverB |---|
#
# y
# ^
# |
# ---------------------
# |\ cover /|
# | \------Top------/ |
# |c| |c|
# |o| |o|
# z <-----|v| core |v| Hsec
# |e| |e|
# |r| |r|
# | /-------Bot-----\ |
# |/ cover \|
# ---------------------
# Bsec
#
# Notes
# The core concrete ends at the NA of the reinforcement
# The center of the section is at (0,0) in the local axis system

set coverY [expr $HSec/2.0]; # The distance from the section z-axis to the edge of the cover concrete -- outer edge of cover concrete
set coverZ [expr $BSec/2.0]; # The distance from the section y-axis to the edge of the cover concrete -- outer edge of cover concrete
set coreY [expr $coverY-$coverH]; # The distance from the section z-axis to the edge of the core concrete -- edge of the core concrete/inner edge of cover concrete
set coreZ [expr $coverZ-$coverB]; # The distance from the section y-axis to the edge of the core concrete -- edge of the core concrete/inner edge of cover concreteset nfY 16;# number of fibers for concrete in y-direction
set nfY 16; # number of fibers for concrete in y-direction
set nfZ 16; # number of fibers for concrete in z-direction
set numBarsInt1 2; # number of intermediate bars per side
set numBarsInt2 2; # number of intermediate bars per side
set coreYint1 1.48; #for intermediate bars above (0,0)
set coreYint2 -1.48; #for intermediate bars below (0,0)

section fiberSec $ColSecTag {; # Define the fiber section
fiber 0.0 0.0 184 $IDconcC; #HCol=15.75 in, BCol=15.75 in, coverH=coverB=(0.89+0.19)=1.08 in, c/c of stirrup distance = 13.59 in
fiber 0.0 6.8 15.843 $IDconcU;
fiber 0.0 -6.8 15.843 $IDconcU;
fiber 6.8 0.0 15.843 $IDconcU;
fiber -6.8 0.0 15.843 $IDconcU;
patch quadr $IDconcC $nfZ $nfY -$coreY $coreZ -$coreY -$coreZ $coreY -$coreZ $coreY $coreZ; # Define the core patch
patch quadr $IDconcU $nfZ 1 -$coverY $coverZ -$coreY $coreZ $coreY $coreZ $coverY $coverZ; # Define the four cover patches
patch quadr $IDconcU $nfZ 1 -$coreY -$coreZ -$coverY -$coverZ $coverY -$coverZ $coreY -$coreZ
patch quadr $IDconcU 1 $nfY -$coverY $coverZ -$coverY -$coverZ -$coreY -$coreZ -$coreY $coreZ
patch quadr $IDconcU 1 $nfY $coreY $coreZ $coreY -$coreZ $coverY -$coverZ $coverY $coverZ
layer straight $IDreinf $numBarsInt1 $barAreaInt $coreYint1 $coreZ $coreYint2 $coreZ; # intermediate skin reinf. +z
layer straight $IDreinf $numBarsInt2 $barAreaInt $coreYint1 -$coreZ $coreYint2 -$coreZ; # intermediate skin reinf. -z
layer straight $IDreinf $numBarsTop $barAreaTop $coreY $coreZ $coreY -$coreZ; # top layer reinfocement
layer straight $IDreinf $numBarsBot $barAreaBot -$coreY $coreZ -$coreY -$coreZ; # bottom layer reinforcement
}; # end of fibersection definition

# --------------------------------------------------------

# define geometric transformation: performs a linear geometric transformation of beam stiffness and resisting force from the basic system to the global-coordinate system
set ColTransfTag 1; # associate a tag to column transformation
geomTransf Corotational $ColTransfTag ;

#Element :-
# 2
# |
# 3
# |
# 1
#;-----

# element connectivity:
set numIntgrPts 5;
#element elasticBeamColumn $eleTag $iNode $jNode $A $E $Iz $transfTag <-mass $massDens> <-cMass>
element elasticBeamColumn 1 3 2 $ACol $Ec $IzCol $ColTransfTag $Mass;
#element dispBeamColumn $eleTag $iNode $jNode $numIntgrPts $secTag $transfTag
element dispBeamColumn 2 1 3 $numIntgrPts $ColSecTag $ColTransfTag Radau;
#each using section 1, and the element uses geometric transformation 1