fiber section

[Olympia]

Dear all,

I have a simple pier (cantilever beam) and when I do eigenvalue analysis considering elastic section, i take the right results. But when I do eigenvalue analysis using fiber section with same dimensions (d=2.0m) and material Ec=32000000 kPa (of course there are also reinforcing bars), I don't take same results as previously, actually my pier is more flexible. Could you please help me (I am a little confused)?
I also include my file (fiber section and elastic section).

Thank you very much,
Olympia

wipe; # clear memory of all past model definitions
model BasicBuilder -ndm 3 -ndf 6; # Define the model builder, ndm=#dimension, ndf=#dofs
set dataDir1 Results1; # set up name of results data directory -- remove
file mkdir modes;
file mkdir $dataDir1

# ==============================================================================
# Define NODES
# ==============================================================================
# nodal coordinates
# NODES of Piers
node 56 24.20 0 4.5;
node 57 24.20 6.86 4.5;

# ==============================================================================
# Define SECTIONS
# ==============================================================================
# ----------------------------------------------------------
# DEFINE PIER Section Properties
# ----------------------------------------------------------
# MATERIAL parameters
set IDconcCorePier 30; # material ID tag -- confined core concrete
set IDconcCoverPier 31; # material ID tag -- unconfined cover concrete
set IDreinfPier 32; # material ID tag -- reinforcement
# nominal concrete compressive strength
set fcPier -38000; # CONCRETE Compressive Strength,(+Tension, -Compression) fcm=30+1.64*5=38 MPA
set EcPier 32000000; # Concrete Elastic Modulus
# confined concrete
set KfcPier 1.3; # ratio of confined to unconfined concrete strength
set fc1CPier [expr $KfcPier*$fcPier]; # CONFINED concrete (mander model), maximum stress
set eps1CPier [expr 2.*$fc1CPier/$EcPier]; # strain at maximum stress
set fc2CPier [expr 0.2*$fc1CPier]; # ultimate stress
set eps2CPier [expr 5*$eps1CPier]; # strain at ultimate stress
# unconfined concrete
set fc1UPier $fcPier; # UNCONFINED concrete (todeschini parabolic model), maximum stress
set eps1UPier -0.002; # strain at maximum strength of unconfined concrete
set fc2UPier [expr 0.2*$fc1UPier]; # ultimate stress
set eps2UPier -0.005; # strain at ultimate stress
set lambdaPier 0.1; # ratio between unloading slope at $eps2 and initial slope $Ec
# tensile-strength properties
set ftCPier [expr -0.14*$fc1CPier]; # tensile strength +tension
set ftUPier [expr -0.14*$fc1UPier]; # tensile strength +tension
set EtsPier [expr $ftUPier/0.002]; # tension softening stiffness
# -----------
set FyPier 550000; # STEEL yield stress
set eyPier 0.00275;
set EsPier [expr $FyPier/$eyPier]; # modulus of steel
set FuPier 660000;
set euPier 0.025;
set bPier [expr ($FuPier-$FyPier)/($euPier-$eyPier)/$FyPier*$eyPier]; # strain-hardening ratio (ratio between post-yield tangent and initial elastic tangent)

#uniaxialMaterial Concrete02 $matTag $fpc $epsc0 $fpcu $epsU $lambda $ft $Ets
uniaxialMaterial Concrete02 $IDconcCorePier $fc1CPier $eps1CPier $fc2CPier $eps2CPier $lambdaPier $ftCPier $EtsPier; # build core concrete (confined)
uniaxialMaterial Concrete02 $IDconcCoverPier $fc1UPier $eps1UPier $fc2UPier $eps2UPier $lambdaPier $ftUPier $EtsPier; # build cover concrete (unconfined)
uniaxialMaterial Steel01 $IDreinfPier $FyPier $EsPier $bPier; # build reinforcement material


# SECTION GEOMETRY -------------------------------------------------------------
set PierSecTag 1; # set tag for symmetric section
set DSecPier 2.0; # Column Diameter (m)
set coverSecPier 0.0695; # Column cover to reinforcing steel NA (0.0695=cover of the 1st layer of bar reinforcement)
set numBarsSecPier 65; # number of uniformly-distributed longitudinal-reinforcement bars
set barAreaSecPier 0.00049087; # area of longitudinal-reinforcement bars (Ö25)

# Generate a circular reinforced concrete section
# with TWO layers of steel evenly distributed around the perimeter and a confined core.
# confined core.
# by: Michael H. Scott, 2003
# Notes
# The center of the reinforcing bars are placed at the inner radius
# The core concrete ends at the inner radius (same as reinforcing bars)
# The reinforcing bars are all the same size
# The center of the section is at (0,0) in the local axis system
# Zero degrees is along section y-axis
#
set riPier 0.0; # inner radius of the section, only for hollow sections
set roPier [expr $DSecPier/2]; # overall (outer) radius of the section
set nfCoreRPier 10; # number of radial divisions in the core (number of "rings")
set nfCoreTPier 10; # number of theta divisions in the core (number of "wedges")
set nfCoverRPier 10; # number of radial divisions in the cover
set nfCoverTPier 10; # number of theta divisions in the cover

# Define the fiber section
section fiberSec $PierSecTag {
set rcPier [expr $roPier-$coverSecPier]; # Core radius
patch circ $IDconcCorePier $nfCoreTPier $nfCoreRPier 0 0 $riPier $rcPier 0 360; # Define the core patch
patch circ $IDconcCoverPier $nfCoverTPier $nfCoverRPier 0 0 $rcPier $roPier 0 360; # Define the cover patch
set thetaPier [expr 360.0/$numBarsSecPier]; # Determine angle increment between bars
layer circ $IDreinfPier $numBarsSecPier $barAreaSecPier 0 0 $rcPier $thetaPier 360; # Define the reinforcing layer
layer circ $IDreinfPier $numBarsSecPier $barAreaSecPier 0 0 0.8405 $thetaPier 360; # 2nd layer: d-cover=1.0-0.1595=0.8405m
}

# assign torsional Stiffness for 3D Model
set SecTagTorsionPier 200; # ID tag for torsional section behavior
set SecTag3DPier 201; # ID tag for combined behavior for 3D model
set UbigPier 1.e10; # a really large number
uniaxialMaterial Elastic $SecTagTorsionPier $UbigPier; # define elastic torsional stiffness
section Aggregator $SecTag3DPier $SecTagTorsionPier T -section $PierSecTag; # combine section properties


# ==============================================================================
# Define SECTIONS (ELASTIC RESPONSE)
# ==============================================================================
# define section tags:
#set PierSecTag 2

# material properties:
#set fc 38; # concrete C30/37 compressivev strength (fm=fck+1.64*s=38)
#set Ec 32000000; # concrete Young's Modulus C30/37
#set nu 0.2; # Poisson's ratio
#set Gc [expr $Ec/2./[expr 1+$nu]]; # Shear Modulus
# ----------------------------------------------------------
# DEFINE DECK Section Properties
# ----------------------------------------------------------
# PIER section properties:
#set AgCol 3.146; # Circular-Column cross-sectional area
#set IzCol 0.785; # about-local-z Circular-Column gross moment of inertia
#set IyCol 0.785; # about-local-z Circular-Column gross moment of inertia
#set Jc 1.571; # Torsional constant

#section Elastic $PierSecTag $Ec $AgCol $IzCol $IyCol $Gc $Jc



# ==============================================================================
# Define ELEMENTS
# ==============================================================================
# set up geometric transformations of element
# separate columns and beams, in case of P-Delta analysis for columns
# in 3D model, assign vector vecxz
set IDColTransf 1; # all columns (piers) will have the same transformation

# It is absolutely necessary to define the transformation of the local to the global
# axes properly in order to translate the correct local stiffness of the elements
# (which also use local Z-Y axes)
geomTransf Linear $IDColTransf 0 0 1;

# Define Beam-Column Elements
set np 5; # number of Gauss integration points for nonlinear curvature distribution
# PIERS
element nonlinearBeamColumn 55 56 57 $np $PierSecTag $IDColTransf; # Element 55

# ==============================================================================
# Define MASSES at NODES
# ==============================================================================
set mpier [expr 20];

mass 57 $mpier $mpier $mpier 1e-9 1e-9 1e-9;

fix 56 1 1 1 1 1 1;

# PROCEDURE TO VISUALISE THE MODEL BEFORE RUNNING THE ANALYSIS
source DisplayPlane.tcl;
source DisplayModel3D.tcl;


# procedure for displaying 3D perspectives of model
# Define DISPLAY -------------------------------------------------------------
set xPixels 1000; # height of graphical window in pixels
set yPixels 500; # height of graphical window in pixels
set xLoc1 300; # horizontal location of graphical window (0=upper left-most corner)
set yLoc1 400; # vertical location of graphical window (0=upper left-most corner)
set dAmp 10; # scaling factor for viewing deformed shape, it depends on the dimensions of the model
DisplayModel3D NodeNumbers $dAmp $xLoc1 $yLoc1 $xPixels $yPixels
DisplayPlane NodeNumbers $dAmp XY

set numModes 3;

# Define RECORDERS -------------------------------------------------------------
for { set k 1 } { $k <= $numModes } { incr k } {
recorder Node -file [format "modes/mode%i.out" $k] -nodeRange 58 61 -dof 1 2 3 4 5 6 "eigen $k"
}

# perform eigen analysis
#-----------------------------
set lambda [eigen $numModes];

# calculate frequencies and periods of the structure
#---------------------------------------------------
set omega {}
set f {}
set T {}
set pi 3.141593

foreach lam $lambda {
lappend omega [expr sqrt($lam)]
lappend f [expr sqrt($lam)/(2*$pi)]
lappend T [expr (2*$pi)/sqrt($lam)]
}

puts "periods are $T"

# write the output file cosisting of periods
#--------------------------------------------
set period "modes/Periods.txt"
set Periods [open $period "w"]
foreach t $T {
puts $Periods " $t"
}
close $Periods



DisplayModel3D ModeShape $dAmp 300 10 800 500 1


integrator LoadControl 0 1 0 0
test EnergyIncr 1.0e-10 100 0
algorithm Newton
numberer RCM
constraints Transformation
system ProfileSPD
analysis Static

analyze 1

[fmk]

i think this problem was fixed .. can you try with version 2.3.0 of the code.

[jgeis]

Dear fmk,

I am having a similar problem to that mentioned by Olympia. I am modeling a L2x2x1/8 angle as a simple BeamColumn with a 100 lb point load acting in the vertical direction at the midpoint. The angle section is rotated such that it opens downward. In other words, the angle at 0 degrees from the vertical looks like " L ". When rotated 135 degrees clockwise, it looks like " ^ ".

If I model the element as a fiber section with the same material and section properties, I get deflections that are about 1.5 times smaller than the deflections from an elasticBeamColumn element. I have tried using the newest version (2.3.0) of the code and am getting the same results.

Included below are the elastic and fiber section files, respectively. Thank you for your insight.
__________________________________________________________________________________________________
# Create ModelBuilder with 3 dimensions and 6 DOF/node
model basic -ndm 3 -ndf 6

# Nodal Coordinates (ft)
node 1 0.0 0.0 0.0
node 2 2.75 0.0 0.0
node 3 5.5 0.0 0.0

# Define Boundary Conditions (pin and roller)
fix 1 1 1 1 0 0 0
fix 3 0 1 1 0 0 0

# Define Geometric Transformation
set IDTopChordTransf 1
geomTransf Linear $IDTopChordTransf 0 -0.7071 -0.7071;

# Connectivity
element elasticBeamColumn 1 1 2 3.364000e-003 4.176000e+009 1.606154e+009 1.413000e-007 9.16077000e-006 9.16077000e-006 $IDTopChordTransf
element elasticBeamColumn 2 2 3 3.364000e-003 4.176000e+009 1.606154e+009 1.413000e-007 9.16077000e-006 9.16077000e-006 $IDTopChordTransf

# Applied Loads (100 lb in vertical directino at middle node)
pattern Plain 1 Linear {
load 2 0.0 0.0 -100.0 0.0 0.0 0.0
}

puts "model built"

# Output
recorder Node -file Node2.out -node 2 -dof 1 2 3 4 5 6 disp;

puts "recorders specified"

constraints Transformation
numberer RCM
system BandGeneral
test NormDispIncr 1.0e-6 6
algorithm Newton
integrator LoadControl 0.1
analysis Static

puts "analysis set up"

analyze 10
puts "done with analysis"
loadConst -time 0.0
______________________________________________________________________________
# Create ModelBuilder with 3 dimensions and 6 DOF/node
model basic -ndm 3 -ndf 6

# Nodal Coordinates (ft)
node 1 0.0 0.0 0.0
node 2 2.75 0.0 0.0
node 3 5.5 0.0 0.0

# Define Boundary Conditions (pin and roller)
fix 1 1 1 1 0 0 0
fix 3 0 1 1 0 0 0

# Creates UniaxialMaterial (E = 4.176000e+009 lb/ft^2)
set TopChordMatTag 1
uniaxialMaterial Elastic $TopChordMatTag 4.176000e+009

# Creates Section (Angle = L2x2x1/8)
set TopChordSectTag 1
section Fiber $TopChordSectTag {
patch rect $TopChordMatTag 1 5 -0.04553 -0.03511 -0.03511 0.121136
patch rect $TopChordMatTag 5 1 -0.04553 -0.04553 0.121136 -0.03511
}

# Assign torsional stiffness for 3D model
set TopChordTorsionMat 2; #ID tag for torsional section behavior
set Utorsion 1.413000e-007; # torsional stiffness (J = 1.413000e-007 ft^4)
uniaxialMaterial Elastic $TopChordTorsionMat $Utorsion; # define elastic torsional stiffness

# Creates Section Aggregator to Include Torsion
set SecTag3D 3; #ID tag for combined behavior for 3D model
section Aggregator $SecTag3D $TopChordTorsionMat T -section $TopChordSectTag;

# Define Geometric Transformation
set IDTopChordTransf 1
geomTransf Linear $IDTopChordTransf 0 -0.7071 -0.7071;

# Connectivity
set numIntgrPts 5; # number of Gauss integration points for nonlinear curvature distribution
element nonlinearBeamColumn 1 1 2 $numIntgrPts $SecTag3D $IDTopChordTransf
element nonlinearBeamColumn 2 2 3 $numIntgrPts $SecTag3D $IDTopChordTransf

# Applied Loads (100 lb in vertical direction at middle node)
pattern Plain 1 Linear {
load 2 0.0 0.0 -100.0 0.0 0.0 0.0
}

puts "model built"

# Output
recorder Node -file Node2.out -node 2 -dof 1 2 3 4 5 6 disp;

puts "recorders specified"

constraints Transformation
numberer RCM
system BandGeneral
test NormDispIncr 1.0e-6 6
algorithm Newton
integrator LoadControl 0.1
analysis Static

puts "analysis set up"

analyze 10
puts "done with analysis"
loadConst -time 0.0
__________________________________________________________________________________

[toggi007]

I´m having similar problems with my model, have you found out whats wrong?
however why are you adding torsion to a model where your rotation dof are not restrained..