T-shaped wall

[Jfoyian]

Hello all,

I am modeling a T-shaped wall using fiber section. In order to make sure that the section is properly working, I applied moment-curvature analysis and checked it with my hand calculations and other programs. When I divide the T-shape wall into two to get 2 rectangular walls, I obtain perfectly matching moment-curvature analysis results for both walls separately. However, when I combine the two rectangular walls and analyze the entire T-shape, curvature results are as expected, whereas the moment capacity is significantly different. Is there any particular reason for this? Do I need to do something different for T or L shaped walls?

Thanks in advance.

[vesna]

how did you model 2 rectangular walls? What were their nodal coordinates?

Why don't you model it with one wall and assign fiber T section to it?

[Jfoyian]

Vesna, thanks for your reply. Yes, this is what I did. I have one 2-D wall with fiber T section assigned to it. However, since it didn't seem to be properly working, I removed the flange portion to check whether it works well as a rectangular wall only. Basically, I managed to get perfect result when I analyzed the flange or the web separately. However, I wasn't able to get good results when I combined both in order to create a single T-section wall. So I would appreciate if you could help me with that.

[vesna]

There are two things that you have to be careful about:

1. Make sure that you define coordinates of your T section relative to the centroid of the section.
2. Make sure your local y and z axis have the right orientation. When in 2D, local x and y axes are in the X-Y plane, where X and Y are global axes. Local x axis is the axis connecting the two element nodes, and local y and z axes follow the right-hand rule (e.g., if the element is aligned with the positive Y axis, the local y axis is aligned with the positive X axis, and if the element is aligned with the positive X axis, the local y axis is aligned with the positive Y axis).

[Jfoyian]

Vesna,

Thank you for the suggestions. I double-checked my model considering these; however, changing the location of the reference point does not change my results. I figured that the T-section actually works pretty well without applied axial load. I believe the problem is with the location of the applied load. I would assume that when the coordinates are defined relative to the geometric centroid of the section, the axial load is applied at that point as well; which would give different moment capacity results than the case when the coordinates are defined relative to another point (e.g. corner of the section). Do I need to specify something else to define the location of the applied axial load?

Here is how I apply the load in the Moment-Curvature analysis file:

#MomentCurvatureZ {secTag axialLoad maxK {numIncr 100}
MomentCurvatureZ $WallSecTagFiber $Pgrav [expr $Ky*$mu] $numIncr

Inside the MomentCurvatureZ.tcl file:

# Define two nodes at (0,0)
node 1001 0.0 0.0
node 1002 0.0 0.0
# Fix all degrees of freedom except axial and bending
fix 1001 1 1 1
fix 1002 0 1 0
# Define element tag ndI ndJ secTag
element zeroLengthSection 2001 1001 1002 $secTag
# Define constant axial load
pattern Plain 3001 "Constant" {
load 1002 $axialLoad 0.0 0.0;
}
# Define analysis parameters
integrator LoadControl 0.0
system SparseGeneral -piv; # Overkill, but may need the pivoting!
test NormUnbalance 1.0e-9 10
numberer Plain
constraints Plain
algorithm Newton
analysis Static
# Do one analysis for constant axial load
analyze 1
# Define reference moment
pattern Plain 3002 "Linear" {
load 1002 0.0 0.0 1.0
}
# Compute curvature increment
set dK [expr $maxK/$numIncr]
# Use displacement control at node 2 for section analysis, dof 3
integrator DisplacementControl 1002 3 $dK 1 $dK $dK

Thanks!

[vesna]

Yes, the load is applied at coordinate (0,0) of the local coordinate system.

[Jfoyian]

Vesna,

If the load is applied at the origin of the local coordinate system, the moment capacity should be changing when I change the origin, right? However, no matter which point I choose as a reference point of the cross-section, I obtain the same result. I was hoping that you might find an explanation to this..

Thanks for your help!

[Jfoyian]

Dear Vesna,

To be more clear, can you please explain how OpenSees creates the element? Does it automatically locate the element node at the geometric centroid of the cross-section no matter how the cross-section is defined? It seems to be that way because I am getting the same results when I define the origin of the local coordinate system at the edge of the wall, at the geometric centroid, or at an arbitrary point. I would expect the axial load remain the same for these three cases but the moment capacity be totally different. I am very confused. Thanks for your help.

[jgeis]

Dear Vesna,

I am running into the same problem as Jfoyian. When I set up a simple BeamColumn element with a fiber section, I get the same results whether I define the origin of the local coordinate system at the geometric centroid of the section or the corner of the section. I am also confused as to why this is. Shown below is the OpenSees code for both cases. Only the coordinates of the fiber section are altered.

Thanks 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

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

# Creates Section (square with sides = 0.1023949ft = 1.2287388in)
set TopChordSectTag 1
section Fiber $TopChordSectTag {
patch rect $TopChordMatTag 5 5 -0.05119745 -0.05119745 0.05119745 0.05119745
}

# 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;

# 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 1;

# 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
____________________________________________________________________

# 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 (square w/ sides=0.1023949ft=1.2287388in)
set TopChordSectTag 1
section Fiber $TopChordSectTag {
patch rect $TopChordMatTag 5 5 0.0 0.0 0.1023949 0.1023949
}

# 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;

# 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 1;

# 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
______________________________________________________________