no obvious pinching in fiber section model?

[achengtw]

Dear Silvia,

I am simulating the SDOF frame (two rigid coulmn and one beam with two hinges at the ends ). I applied fiber section made of concrete02 and steel02 to the hinge part. However, there is no obvious pinching observed even the cyclic drift up to 6%. Its reinf. ratio is only 1.25% and it should heavily pinched according to test data. Could you help me to figure out what wrong it is?

ps. I modified from your example4 and on the result page, there is no obvious pinching either.

Thanks a lot in advance:)

-------------------------------------

# --------------------------------------------------------------------------------------------------
# SDOF RC Frame-- Build Model
# nonlinearBeamColumn element, inelastic fiber section
#
# ^Y
# |
# 3_________(3)______________ 4 ___
# | | |
# | | |
# | | |
# (1) (2) LCol
# | | |
# | | |
# | | |
# =1= =2= _|_ -------->X
# |----------LBeam------------|
#

# SET UP ----------------------------------------------------------------------------
wipe; # clear memory of all past model definitions
model BasicBuilder -ndm 2 -ndf 3; # Define the model builder, ndm=#dimension, ndf=#dofs
set dataDir Data; # set up name of data directory
file mkdir $dataDir; # create data directory
set GMdir "GMfiles"; # ground-motion file directory
source LibUnits.tcl; # define basic and system units

# define GEOMETRY -------------------------------------------------------------
set LCol [expr 12*$ft]; # column length
set LBeam [expr 24*$ft]; # beam length
set Weight [expr 2000.*$kip]; # superstructure weight
# define section geometry
set HCol [expr 14.*$in]; # Column Depth
set BCol [expr 14.*$in]; # Column Width
set HBeam [expr 14.*$in]; # Beam Depth
set BBeam [expr 6.*$in]; # Beam Width

# calculated parameters
set PCol [expr $Weight/2]; # nodal dead-load weight per column
set Mass [expr $PCol/$g]; # nodal mass
set MCol [expr 1./12.*($Weight/$LBeam)*pow($LBeam,2)]; # beam-end moment due to distributed load.
# calculated geometry parameters
set ACol [expr $BCol*$HCol]; # cross-sectional area
set ABeam [expr $BBeam*$HBeam];
set IzCol [expr 1./12.*$BCol*pow($HCol,3)]; # Column moment of inertia
set IzBeam [expr 1./12.*$BBeam*pow($HBeam,3)]; # Beam moment of inertia

# nodal coordinates:
node 1 0 0; # node#, X, Y
node 2 $LBeam 0
node 3 0 $LCol
node 4 $LBeam $LCol

# Single point constraints -- Boundary Conditions
fix 1 1 1 0; # node DX DY RZ
fix 2 1 1 0; # node DX DY RZ
fix 3 0 0 0
fix 4 0 0 0

# nodal masses:
mass 3 $Mass 0. 0.; # node#, Mx My Mz, Mass=Weight/g, neglect rotational inertia at nodes
mass 4 $Mass 0. 0.

# Define ELEMENTS & SECTIONS -------------------------------------------------------------
set ColSecTag 1; # assign a tag number to the column section
set BeamSecTag 2; # assign a tag number to the beam section
# define section geometry
set coverCol1 [expr 2.2*$in]; # Column cover to reinforcing steel NA.
set coverCol2 [expr 1.3*$in];
set numBarsCol 2; # number of longitudinal-reinforcement bars in each side of column section. (symmetric top & bot)
set barAreaCol [expr 0.2*$in2]; # area of longitudinal-reinforcement bars

# MATERIAL parameters -------------------------------------------------------------------
set IDconcU 1; # material ID tag -- unconfined cover concrete
set IDreinf 2; # material ID tag -- reinforcement
set IDconcC 3; # material ID tag -- confined cover concrete
# nominal concrete compressive strength
set fc [expr -5.7*$ksi]; # CONCRETE Compressive Strength, ksi (+Tension, -Compression)
set Ec [expr 57*$ksi*sqrt(-$fc/$psi)]; # Concrete Elastic Modulus
# confined concrete
set Kfc 1.3; # ratio of confined to unconfined concrete strength
set Kres 0.2; # ratio of residual/ultimate to maximum stress
set fc1C [expr $Kfc*$fc]; # CONFINED concrete (mander model), maximum stress
set eps1C [expr 2.*$fc1C/$Ec]; # strain at maximum stress
set fc2C [expr $Kres*$fc1C]; # ultimate stress
set eps2C [expr 20*$eps1C]; # strain at ultimate stress
set lambda 0.1; # ratio between unloading slope at $eps2 and initial slope $Ec
# unconfined concrete
set fc1U $fc; # UNCONFINED concrete (todeschini parabolic model), maximum stress
set eps1U -0.003; # strain at maximum strength of unconfined concrete
set fc2U [expr 0.2*$fc1U]; # ultimate stress
set eps2U -0.05; # strain at ultimate stress
set lambda 0.1; # ratio between unloading slope at $eps2 and initial slope $Ec
# tensile-strength properties
set ftC [expr -0.14*$fc1C]; # tensile strength +tension
set ftU [expr -0.14*$fc1U]; # tensile strength +tension
set Ets [expr $ftU/0.002]; # tension softening stiffness
# -----------
set Fy [expr 67.*$ksi]; # STEEL yield stress
set Es [expr 29000.*$ksi]; # modulus of steel
set Bs 0.01; # strain-hardening ratio
set R0 18; # 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 $IDconcU $fc1U $eps1U $fc2U $eps2U $lambda $ftU $Ets; # build cover concrete (unconfined)
uniaxialMaterial Concrete02 $IDconcC $fc1C $eps1C $fc2C $eps2C $lambda $ftC $Ets; # Core concrete (confined)
uniaxialMaterial Steel02 $IDreinf $Fy $Es $Bs $R0 $cR1 $cR2; # build reinforcement material

# FIBER SECTION properties -------------------------------------------------------------
# symmetric section
# y
# ^
# |
# --------------------- -- --
# | o o | | -- cover
# | | |
# | | |
# z <--- | + | H
# | | |
# | | |
# | o o | | -- cover
# --------------------- -- --
# |-------- B --------|
#
# RC section:
set coverY [expr $HBeam/2.0]; # The distance from the section z-axis to the edge of the cover concrete -- outer edge of cover concrete
set coverZ [expr $BBeam/2.0]; # The distance from the section y-axis to the edge of the cover concrete -- outer edge of cover concrete
set coreY [expr $coverY-$coverCol1]
set coreZ [expr $coverZ-$coverCol2]
set nfY 16; # number of fibers for concrete in y-direction
set nfZ 4; # number of fibers for concrete in z-direction
section fiberSec $BeamSecTag { # Define the fiber section
patch quadr $IDconcC $nfZ $nfY -$coreY $coreZ -$coreY -$coreZ $coreY -$coreZ $coreY $coreZ;
patch quadr $IDconcU 2 $nfY -$coverY $coverZ -$coreY $coreZ $coreY $coreZ $coverY $coverZ;
patch quadr $IDconcU 2 $nfY -$coreY -$coreZ -$coverY -$coverZ $coverY -$coverZ $coreY -$coreZ;
patch quadr $IDconcU $nfZ 2 -$coverY $coverZ -$coverY -$coverZ -$coreY -$coreZ -$coreY $coreZ;
patch quadr $IDconcU $nfZ 2 $coreY $coreZ $coreY -$coreZ $coverY -$coverZ $coverY $coverZ; # Define the concrete patch
layer straight $IDreinf $numBarsCol $barAreaCol -$coreY $coreZ -$coreY -$coreZ; # top layer reinfocement
layer straight $IDreinf $numBarsCol $barAreaCol $coreY $coreZ $coreY -$coreZ; # bottom layer reinforcement
}; # end of fibersection definition

# Column section:
section Elastic $ColSecTag 1.e6 1.e6 1.e6; # elastic column section

# 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
set BeamTransfTag 2; # associate a tag to beam transformation (good practice to keep col and beam separate)
set ColTransfType Linear ; # options, Linear PDelta Corotational
geomTransf $ColTransfType $ColTransfTag ; # only columns can have PDelta effects (gravity effects)
geomTransf Linear $BeamTransfTag ;

# element connectivity:
set numIntgrPts 5; # number of integration points for force-based element
element nonlinearBeamColumn 1 1 3 $numIntgrPts $ColSecTag $ColTransfTag; # self-explanatory when using variables
element nonlinearBeamColumn 2 2 4 $numIntgrPts $ColSecTag $ColTransfTag;
element beamWithHinges 3 3 4 $BeamSecTag 10.5 $BeamSecTag 10.5 $Ec $ABeam $IzBeam $BeamTransfTag;

# Define RECORDERS -------------------------------------------------------------
recorder Node -file $dataDir/DFree.out -time -node 3 4 -dof 1 2 3 disp; # displacements of free nodes
recorder Node -file $dataDir/DBase.out -time -node 1 2 -dof 1 2 3 disp; # displacements of support nodes
recorder Node -file $dataDir/RBase.out -time -node 1 2 -dof 1 2 3 reaction; # support reaction
recorder Drift -file $dataDir/Drift.out -time -iNode 1 2 -jNode 3 4 -dof 1 -perpDirn 2 ; # lateral drift
recorder Element -file $dataDir/FCol.out -time -ele 1 2 globalForce; # element forces -- column
recorder Element -file $dataDir/FBeam.out -time -ele 3 globalForce; # element forces -- beam
recorder Element -file $dataDir/ForceColSec1.out -time -ele 1 2 section 1 force; # Column section forces, axial and moment, node i
recorder Element -file $dataDir/DefoColSec1.out -time -ele 1 2 section 1 deformation; # section deformations, axial and curvature, node i
recorder Element -file $dataDir/ForceColSec$numIntgrPts.out -time -ele 1 2 section $numIntgrPts force; # section forces, axial and moment, node j
recorder Element -file $dataDir/DefoColSec$numIntgrPts.out -time -ele 1 2 section $numIntgrPts deformation; # section deformations, axial and curvature, node j
recorder Element -file $dataDir/ForceBeamSec1.out -time -ele 3 section 1 force; # Beam section forces, axial and moment, node i
recorder Element -file $dataDir/DefoBeamSec1.out -time -ele 3 section 1 deformation; # section deformations, axial and curvature, node i
recorder Element -file $dataDir/ForceBeamSec$numIntgrPts.out -time -ele 3 section $numIntgrPts force; # section forces, axial and moment, node j
recorder Element -file $dataDir/DefoBeamSec$numIntgrPts.out -time -ele 3 section $numIntgrPts deformation; # section deformations, axial and curvature, node j


# Gravity-analysis parameters -- load-controlled static analysis
set Tol 1.0e-8; # convergence tolerance for test
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 $Tol 6 ; # determine if convergence has been achieved at the end of an iteration step
algorithm Newton; # use Newton's solution algorithm: updates tangent stiffness at every iteration
set NstepGravity 10; # apply gravity in 10 steps
set DGravity [expr 1./$NstepGravity]; # first load increment;
integrator LoadControl $DGravity; # determine the next time step for an analysis
analysis Static; # define type of analysis static or transient
analyze $NstepGravity; # apply gravity
# ------------------------------------------------- maintain constant gravity loads and reset time to zero
loadConst -time 0.0

puts "Model Built"

[silvia]

play with the material properties.
otherwise, you could try hysteretic material for steel.

[achengtw]

Thank you very much for your instant reply:)

I tried to lower f'c but the results did not change much. The whole hysteretic loop just looked like steel one.

I am wondering that since fiber section default assuming perfectly bonded so that the hysteretic loop will keep full before reaching its max strain even concrete only have little stength. That is, it may just like two flanges at the top and bottom with strain compatibility.

Could you please give me one example of fiber section made of steel and concrete material showing obvious pinching so that I can quickly change my parameters to fit the test result.

Thank you very much for your help and time:)

[silvia]

don't have you, just play with a moment-curvature analysis.
think about what properties will give you pinching.