Error During Modelling of 3D Frame Structure

[SUJOY]

While modelling the 3D Frame structure consisting of steel beam and column, I'm getting an error message even after incorporating torsional parameters.


----->>>>>> error message: WARNING - no torsion specified for 3D fiber section, use -GJ or -torsion

My main script----------------------------------------------------------------------------------------------------------------------------------------------------------------------

################################################################################################################################
# --------------------------------------------------------------------------------------------------
# 3D Steel W-section Frame
# nonlinearBeamColumn element, inelastic fiber section
# SET UP ----------------------------------------------------------------------------
wipe; # clear memory of all past model definitions
model BasicBuilder -ndm 3 -ndf 6; # Define the model builder, ndm=#dimension, ndf=#dofs
set dataDir Data; # set up name of data directory -- remove
file mkdir $dataDir; # create data directory
set GMdir "../GMfiles"; # ground-motion file directory
source LibUnits.tcl; # define units
source DisplayPlane.tcl; # procedure for displaying a plane in model
source DisplayModel3D.tcl; # procedure for displaying 3D perspectives of model
source Wsection.tcl; # procedure to define fiber W section

# define GEOMETRY -------------------------------------------------------------
# define structure-geometry paramters
set LCol [expr 12*$ft]; # column height (parallel to Y axis)
set LBeam [expr 20*$ft]; # beam length (parallel to X axis)
set LGird [expr 20*$ft]; # girder length (parallel to Z axis)

# ------ frame configuration
set NStory 3; # number of stories above ground level
set NBay 1; # number of bays in X direction
set NBayZ 1; # number of bays in Z direction
puts "Number of Stories in Y: $NStory; Number of bays in X: $NBay; Number of bays in Z: $NBayZ"

# define NODAL COORDINATES
# calculate locations of beam/column intersections:
set X1 0.;
set X2 [expr $X1 + $LBeam];
set Y1 0.;
set Y2 [expr $Y1 + $LCol];
set Y3 [expr $Y2 + $LCol];
set Y4 [expr $Y3 + $LCol];
set Z1 0.0;
set Z2 [expr $Z1 + $LGird];

node 111 $X1 $Y1 $Z1; # frame 1
node 112 $X2 $Y1 $Z1;
node 121 $X1 $Y2 $Z1;
node 122 $X2 $Y2 $Z1;
node 131 $X1 $Y3 $Z1;
node 132 $X2 $Y3 $Z1;
node 141 $X1 $Y4 $Z1;
node 142 $X2 $Y4 $Z1;
node 211 $X1 $Y1 $Z2; # frame 2
node 212 $X2 $Y1 $Z2;
node 221 $X1 $Y2 $Z2;
node 222 $X2 $Y2 $Z2;
node 231 $X1 $Y3 $Z2;
node 232 $X2 $Y3 $Z2;
node 241 $X1 $Y4 $Z2;
node 242 $X2 $Y4 $Z2;


# define Rigid Floor Diaphragm
set RigidDiaphragm ON ; # options: ON, OFF. specify this before the analysis parameters are set the constraints are handled differently.
set Xa [expr ($X2+$X1)/2]; # mid-span coordinate for rigid diaphragm
set Za [expr ($Z2+$Z1)/2];
# rigid-diaphragm nodes in center of each diaphram
node 1121 $Xa $Y2 $Za; # master nodes for rigid diaphragm -- story 2, bay 1, frame 1-2
node 1131 $Xa $Y3 $Za; # master nodes for rigid diaphragm -- story 3, bay 1, frame 1-2
node 1141 $Xa $Y4 $Za; # master nodes for rigid diaphragm -- story 4, bay 1, frame 1-2
# Constraints for rigid diaphragm master nodes
fix 1121 0 1 0 1 0 1
fix 1131 0 1 0 1 0 1
fix 1141 0 1 0 1 0 1
# ------------------------define Rigid Diaphram, dof 2 is normal to floor
set perpDirn 2;
rigidDiaphragm $perpDirn 1121 121 122 221 222; # level 2
rigidDiaphragm $perpDirn 1131 131 132 231 232; # level 3
rigidDiaphragm $perpDirn 1141 141 142 241 242; # level 4

# determine support nodes where ground motions are input, for multiple-support excitation
set iSupportNode "111 112 211 212"

# BOUNDARY CONDITIONS
fixY 0.0 1 1 1 0 1 0; # pin all Y=0.0 nodes

# calculated MODEL PARAMETERS, particular to this model
# Set up parameters that are particular to the model for displacement control
set IDctrlNode 141; # node where displacement is read for displacement control
set IDctrlDOF 1; # degree of freedom of displacement read for displacement control
set LBuilding [expr $Y4]; # total building height

# Define SECTIONS -------------------------------------------------------------
set SectionType FiberSection; # options: Elastic FiberSection

# define section tags:
set ColSecTag 1
set BeamSecTag 2
set GirdSecTag 3
set ColSecTagFiber 4
set BeamSecTagFiber 5
set GirdSecTagFiber 6
set SecTagTorsion 70

if {$SectionType == "Elastic"} {

# material properties:
set Es [expr 29000*$ksi]; # Steel Young's Modulus
set nu 0.3; # Poisson's ratio
set Gs [expr $Es/2./[expr 1+$nu]]; # Torsional stiffness Modulus
#set J $Ubig; # set large torsional stiffness for opensees version 2.5.0
set G 8e+7; # G = Shear Modulus
# set J [expr $pi/32 * ((pow($Dia,4)))]; # J = Polar moment of Inertia
set J [expr 4249.*pow($in,4)];
set GJ [expr $G * $J] # G*J= Torsion Rigidity


# column sections: W27x114
set AgCol [expr 33.5*pow($in,2)]; # cross-sectional area
set IzCol [expr 4090.*pow($in,4)]; # moment of Inertia
set IyCol [expr 159.*pow($in,4)]; # moment of Inertia
# beam sections: W24x94
set AgBeam [expr 27.7*pow($in,2)]; # cross-sectional area
set IzBeam [expr 2700.*pow($in,4)]; # moment of Inertia
set IyBeam [expr 109.*pow($in,4)]; # moment of Inertia
# girder sections: W24x94
set AgGird [expr 27.7*pow($in,2)]; # cross-sectional area
set IzGird [expr 2700.*pow($in,4)]; # moment of Inertia
set IyGird [expr 109.*pow($in,4)]; # moment of Inertia

section Elastic $ColSecTag $Es $AgCol $IzCol $IyCol $Gs $J
section Elastic $BeamSecTag $Es $AgBeam $IzBeam $IyBeam $Gs $J
section Elastic $GirdSecTag $Es $AgGird $IzGird $IyGird $Gs $J

set matIDhard 1; # material numbers for recorder
## (stress-strain recorder will be blank, as this is an elastic section)

} elseif {$SectionType == "FiberSection"} {
# define MATERIAL properties
set Fy [expr 60.0*$ksi]
set Es [expr 29000*$ksi]; # Steel Young's Modulus
set nu 0.3;
set Gs [expr $Es/2./[expr 1+$nu]]; # Torsional stiffness Modulus
set Hiso 0
set Hkin 1000
set matIDhard 1
uniaxialMaterial Hardening $matIDhard $Es $Fy $Hiso $Hkin

# ELEMENT properties
# Structural-Steel W-section properties
# column sections: W27x114
set d [expr 27.29*$in]; # depth
set bf [expr 10.07*$in]; # flange width
set tf [expr 0.93*$in]; # flange thickness
set tw [expr 0.57*$in]; # web thickness
set nfdw 16; # number of fibers along dw
set nftw 2; # number of fibers along tw
set nfbf 16; # number of fibers along bf
set nftf 4; # number of fibers along tf
Wsection $ColSecTagFiber $matIDhard $d $bf $tf $tw $nfdw $nftw $nfbf $nftf

# beam sections: W24x94
set d [expr 24.31*$in]; # depth
set bf [expr 9.065*$in]; # flange width
set tf [expr 0.875*$in]; # flange thickness
set tw [expr 0.515*$in]; # web thickness
set nfdw 16; # number of fibers along dw
set nftw 2; # number of fibers along tw
set nfbf 16; # number of fibers along bf
set nftf 4; # number of fibers along tf

Wsection $BeamSecTagFiber $matIDhard $d $bf $tf $tw $nfdw $nftw $nfbf $nftf
# girder sections: W24x94
set d [expr 24.31*$in]; # depth
set bf [expr 9.065*$in]; # flange width
set tf [expr 0.875*$in]; # flange thickness
set tw [expr 0.515*$in]; # web thickness
set nfdw 16; # number of fibers along dw
set nftw 2; # number of fibers along tw
set nfbf 16; # number of fibers along bf
set nftf 4; # number of fibers along tf
Wsection $GirdSecTagFiber $matIDhard $d $bf $tf $tw $nfdw $nftw $nfbf $nftf

# assign torsional Stiffness for 3D Model
# section fiberSec $SecTag -GJ $GJ { # Define the fiber section
# patch circ $matTag $numSubdivCirc $numSubdivRad .....
#}
# New Method 1
uniaxialMaterial $SecTagTorsion $GJ ;# Doesn't have to be elastic
section Aggregator $ColSecTag $SecTagTorsion T -section $ColSecTagFiber
section Aggregator $BeamSecTag $SecTagTorsion T -section $BeamSecTagFiber
section Aggregator $GirdSecTag $SecTagTorsion T -section $GirdSecTagFiber
# section Fiber 1 -torsion 5 {
patch ...
layer ...}

# Method 2 (same as before)
#section Fiber 1 -GJ $GJ {
# patch ...
# layer ...
#}
#uniaxialMaterial Elastic $SecTagTorsion $Ubig
#section Aggregator $ColSecTag $SecTagTorsion T -section $ColSecTagFiber
#section Aggregator $BeamSecTag $SecTagTorsion T -section $BeamSecTagFiber
#section Aggregator $GirdSecTag $SecTagTorsion T -section $GirdSecTagFiber

} else {
puts "No section has been defined"
return -1
}

set QdlCol [expr 114*$lbf/$ft]; # W-section weight per length
set QBeam [expr 94*$lbf/$ft]; # W-section weight per length
set QGird [expr 94*$lbf/$ft]; # W-section weight per length

# 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
set IDBeamTransf 2; # all beams
set IDGirdTransf 3; # all girders
set ColTransfType Linear ; # options, Linear PDelta Corotational
geomTransf $ColTransfType $IDColTransf 0 0 1 ; # only columns can have PDelta effects (gravity effects)
geomTransf Linear $IDBeamTransf 0 0 1
geomTransf Linear $IDGirdTransf 1 0 0

# Define Beam-Column Elements
set np 5; # number of Gauss integration points for nonlinear curvature distribution

# Frame 1
# columns
element nonlinearBeamColumn 1111 111 121 $np $ColSecTag $IDColTransf; # level 1-2
element nonlinearBeamColumn 1112 112 122 $np $ColSecTag $IDColTransf
element nonlinearBeamColumn 1121 121 131 $np $ColSecTag $IDColTransf; # level 2-3
element nonlinearBeamColumn 1122 122 132 $np $ColSecTag $IDColTransf
element nonlinearBeamColumn 1131 131 141 $np $ColSecTag $IDColTransf; # level 3-4
element nonlinearBeamColumn 1132 132 142 $np $ColSecTag $IDColTransf
# beams
element nonlinearBeamColumn 1221 121 122 $np $BeamSecTag $IDBeamTransf; # level 2
element nonlinearBeamColumn 1231 131 132 $np $BeamSecTag $IDBeamTransf; # level 3
element nonlinearBeamColumn 1241 141 142 $np $BeamSecTag $IDBeamTransf; # level 4

# Frame 2
# columns
element nonlinearBeamColumn 2111 211 221 $np $ColSecTag $IDColTransf; # level 1-2
element nonlinearBeamColumn 2112 212 222 $np $ColSecTag $IDColTransf
element nonlinearBeamColumn 2121 221 231 $np $ColSecTag $IDColTransf; # level 2-3
element nonlinearBeamColumn 2122 222 232 $np $ColSecTag $IDColTransf
element nonlinearBeamColumn 2131 231 241 $np $ColSecTag $IDColTransf; # level 3-4
element nonlinearBeamColumn 2132 232 242 $np $ColSecTag $IDColTransf
# beams
element nonlinearBeamColumn 2221 221 222 $np $BeamSecTag $IDBeamTransf; # level 2
element nonlinearBeamColumn 2231 231 232 $np $BeamSecTag $IDBeamTransf; # level 3
element nonlinearBeamColumn 2241 241 242 $np $BeamSecTag $IDBeamTransf; # level 4

# girders connecting frames
# Frame 1-2
element nonlinearBeamColumn 1321 121 221 $np $GirdSecTag $IDGirdTransf; # level 2
element nonlinearBeamColumn 1322 122 222 $np $GirdSecTag $IDGirdTransf;
element nonlinearBeamColumn 1331 131 231 $np $GirdSecTag $IDGirdTransf; # level 3
element nonlinearBeamColumn 1332 132 232 $np $GirdSecTag $IDGirdTransf;
element nonlinearBeamColumn 1341 141 241 $np $GirdSecTag $IDGirdTransf; # level 4
element nonlinearBeamColumn 1342 142 242 $np $GirdSecTag $IDGirdTransf;


# --------------------------------------------------------------------------------------------------------------------------------
# Define GRAVITY LOADS, weight and masses
# calculate dead load of frame, assume this to be an internal frame (do LL in a similar manner)
# calculate distributed weight along the beam length
set GammaConcrete [expr 150*$pcf]; # Reinforced-Concrete weight density (weight per volume)
set Tslab [expr 6*$in]; # 6-inch slab
set Lslab [expr $LGird/2]; # slab extends a distance of $LGird/2 in/out of plane
set DLfactor 1.0; # scale dead load up a little
set Qslab [expr $GammaConcrete*$Tslab*$Lslab*$DLfactor];
set QdlBeam [expr $Qslab + $QBeam]; # dead load distributed along beam (one-way slab)
set QdlGird $QGird; # dead load distributed along girder
set WeightCol [expr $QdlCol*$LCol]; # total Column weight
set WeightBeam [expr $QdlBeam*$LBeam]; # total Beam weight
set WeightGird [expr $QdlGird*$LGird]; # total Beam weight

# assign masses to the nodes that the columns are connected to
# each connection takes the mass of 1/2 of each element framing into it (mass=weight/$g)
set Mmid [expr ($WeightCol/2 + $WeightCol/2 +$WeightBeam/2+$WeightGird/2)/$g];
set Mtop [expr ($WeightCol/2 + $WeightBeam/2+$WeightGird/2)/$g];

# frame 1
mass 121 $Mmid 0 $Mmid 0. 0. 0.; # level 2
mass 122 $Mmid 0 $Mmid 0. 0. 0.;
mass 131 $Mmid 0 $Mmid 0. 0. 0.; # level 3
mass 132 $Mmid 0 $Mmid 0. 0. 0.;
mass 141 $Mtop 0 $Mtop 0. 0. 0.; # level 4
mass 142 $Mtop 0 $Mtop 0. 0. 0.;

# frame 2
mass 221 $Mmid 0 $Mmid 0. 0. 0.; # level 2
mass 222 $Mmid 0 $Mmid 0. 0. 0.;
mass 231 $Mmid 0 $Mmid 0. 0. 0.; # level 3
mass 232 $Mmid 0 $Mmid 0. 0. 0.;
mass 241 $Mtop 0 $Mtop 0. 0. 0.; # level 4
mass 242 $Mtop 0 $Mtop 0. 0. 0.;

set FloorWeight2 [expr 4*$WeightCol + 2*$WeightGird + 2*$WeightBeam]
set FloorWeight3 [expr 4*$WeightCol + 2*$WeightGird + 2*$WeightBeam]
set FloorWeight4 [expr 2*$WeightCol + 2*$WeightGird + 2*$WeightBeam]
set WeightTotal [expr $FloorWeight2+$FloorWeight3+$FloorWeight4]; # total building weight
set MassTotal [expr $WeightTotal/$g]; # total building mass

# --------------------------------------------------------------------------------------------------------------------------------
# LATERAL-LOAD distribution for static pushover analysis
# calculate distribution of lateral load based on mass/weight distributions along building height
# Fj = WjHj/sum(WiHi) * Weight at each floor j
set sumWiHi [expr $FloorWeight2*$Y2+$FloorWeight3*$Y3+$FloorWeight4*$Y4]; # sum of storey weight times height, for lateral-load distribution
set WiHi2 [expr $FloorWeight2*$Y2]; # storey weight times height, for lateral-load distribution
set WiHi3 [expr $FloorWeight3*$Y3]; # storey weight times height, for lateral-load distribution
set WiHi4 [expr $FloorWeight4*$Y4]; # storey weight times height, for lateral-load distribution
set F2 [expr $WiHi2/$sumWiHi*$WeightTotal]; # lateral load at level
set F3 [expr $WiHi3/$sumWiHi*$WeightTotal]; # lateral load at level
set F4 [expr $WiHi4/$sumWiHi*$WeightTotal]; # lateral load at level


# Define RECORDERS -------------------------------------------------------------
recorder Node -file $dataDir/DFree.out -time -node 141 -dof 1 2 3 disp; # displacements of free node
recorder Node -file $dataDir/DBase.out -time -node 111 112 211 212 -dof 1 2 3 disp; # displacements of support nodes
recorder Node -file $dataDir/RBase.out -time -node 111 112 211 212 -dof 1 2 3 reaction; # support reaction
recorder Drift -file $dataDir/DrNode.out -time -iNode 111 -jNode 141 -dof 1 -perpDirn 2; # lateral drift
recorder Element -file $dataDir/Fel1.out -time -ele 1111 localForce; # element forces in local coordinates
recorder Element -xml $dataDir/PlasticRotation1.out -time -ele 1111 plasticRotation; # element forces in local coordinates
recorder Element -file $dataDir/ForceEle1sec1.out -time -ele 1111 section 1 force; # section forces, axial and moment, node i
recorder Element -file $dataDir/DefoEle1sec1.out -time -ele 11111 section 1 deformation; # section deformations, axial and curvature, node i
recorder Element -file $dataDir/ForceEle1sec$np.out -time -ele 111 section $np force; # section forces, axial and moment, node j
recorder Element -file $dataDir/DefoEle1sec$np.out -time -ele 1111 section $np deformation; # section deformations, axial and curvature, node j
set yFiber [expr 0.]; # fiber location for stress-strain recorder, local coords
set zFiber [expr 0.]; # fiber location for stress-strain recorder, local coords
recorder Element -file $dataDir/SSreinfEle1sec1.out -time -ele 1111 section $np fiber $yFiber $zFiber stressStrain; # steel fiber stress-strain, node i

# Define DISPLAY -------------------------------------------------------------
set xPixels 1200; # height of graphical window in pixels
set yPixels 800; # height of graphical window in pixels
set xLoc1 10; # horizontal location of graphical window (0=upper left-most corner)
set yLoc1 10; # vertical location of graphical window (0=upper left-most corner)
set dAmp 2; # scaling factor for viewing deformed shape, it depends on the dimensions of the model
DisplayModel3D NodeNumbers $dAmp $xLoc1 $yLoc1 $xPixels $yPixels

# define GRAVITY -------------------------------------------------------------
# GRAVITY LOADS # define gravity load applied to beams and columns -- eleLoad applies loads in local coordinate axis
pattern Plain 101 Linear {
# Frame 1
# columns
eleLoad -ele 1111 -type -beamUniform 0. 0. -$QdlCol; # level 1-2
eleLoad -ele 1112 -type -beamUniform 0. 0. -$QdlCol
eleLoad -ele 1121 -type -beamUniform 0. 0. -$QdlCol; # level 2-3
eleLoad -ele 1122 -type -beamUniform 0. 0. -$QdlCol
eleLoad -ele 1131 -type -beamUniform 0. 0. -$QdlCol; # level 3-4
eleLoad -ele 1132 -type -beamUniform 0. 0. -$QdlCol
# beams
eleLoad -ele 1221 -type -beamUniform -$QdlBeam 0.; # level 2
eleLoad -ele 1231 -type -beamUniform -$QdlBeam 0.; # level 3
eleLoad -ele 1241 -type -beamUniform -$QdlBeam 0.; # level 4

# Frame 2
# columns
eleLoad -ele 2111 -type -beamUniform 0. 0. -$QdlCol; # level 1-2
eleLoad -ele 2112 -type -beamUniform 0. 0. -$QdlCol
eleLoad -ele 2121 -type -beamUniform 0. 0. -$QdlCol; # level 2-3
eleLoad -ele 2122 -type -beamUniform 0. 0. -$QdlCol
eleLoad -ele 2131 -type -beamUniform 0. 0. -$QdlCol; # level 3-4
eleLoad -ele 2132 -type -beamUniform 0. 0. -$QdlCol
# beams
eleLoad -ele 2221 -type -beamUniform -$QdlBeam 0.; # level 2
eleLoad -ele 2231 -type -beamUniform -$QdlBeam 0.; # level 3
eleLoad -ele 2241 -type -beamUniform -$QdlBeam 0.; # level 4

# girders connecting frames
# Frame 1-2
eleLoad -ele 1321 -type -beamUniform -$QdlGird 0.; # level 2
eleLoad -ele 1322 -type -beamUniform -$QdlGird 0.;
eleLoad -ele 1331 -type -beamUniform -$QdlGird 0.; # level 3
eleLoad -ele 1332 -type -beamUniform -$QdlGird 0.;
eleLoad -ele 1341 -type -beamUniform -$QdlGird 0.; # level 4
eleLoad -ele 1342 -type -beamUniform -$QdlGird 0.;
}
# Gravity-analysis parameters -- load-controlled static analysis
set Tol 1.0e-8; # convergence tolerance for test
variable constraintsTypeGravity Plain; # default;
if { [info exists RigidDiaphragm] == 1} {
if {$RigidDiaphragm=="ON"} {
variable constraintsTypeGravity Lagrange; # large model: try Transformation
}; # if rigid diaphragm is on
}; # if rigid diaphragm exists
constraints $constraintsTypeGravity ; # how it handles boundary conditions
numberer RCM; # 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 (large model: try UmfPack)
test EnergyIncr $Tol 6 ; # determine if convergence has been achieved at the end of an iteration step
algorithm Newton; # use Newton's solution algorithm: updates tangent stiffness at every iteration
set NstepGravity 10; # apply gravity in 10 steps
set DGravity [expr 1./$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
set Tol 1.0e-6; # reduce tolerance after gravity loads
puts "Model Built"

[mhscott]

This is most likely the problem: https://wp.me/pbejzW-9X

[selimgunay]

It looks like you should use Method 2 that you commented out.

[AmirMix]

uniaxialMaterial Elastic 5 $GJ ;# Doesn't have to be elastic
section Aggregator 1 5 T -section 3

# Method 2
section Fiber 1 -GJ $GJ {
patch ...
layer ...
}