moment – curvature analysis 3D

[hrodrigues]

I need to perform a moment – curvature analysis 3D.
I’m using the example: Example 9. Moment-Curvature Analysis of Section (3D model)
However I need to impose a biaxial curvature a curvature in the xx direction and a curvature in the zz direction.

What should I change??

Only the reference moment ??
# Define reference moment
pattern Plain 3002 "Linear" {
load 1002 0.0 0.0 0.0 0.0 0.0 1.0
}
And how can I plot the moment-curvature relationships in both directions ?
Thanks for your help.

Extract of the procedure:
proc MomentCurvature3D { secTag axialLoad maxK {numIncr 100} } {

# Define two nodes at (0,0)
node 1001 0.0 0.0 0.0
node 1002 0.0 0.0 0.0

# Fix all degrees of freedom except axial and bending
fix 1001 1 1 1 1 1 1
fix 1002 0 1 1 1 1 0

# Define element
# tag ndI ndJ secTag
element zeroLengthSection 2001 1001 1002 $secTag

# Create recorder
recorder Node -file data/Mphi.out -time -node 1002 -dof 6 disp; # output moment (col 1) & curvature (col 2)

# Define constant axial load
pattern Plain 3001 "Constant" {
load 1002 $axialLoad 0.0 0.0 0.0 0.0 0.0
}

# Define analysis parameters
integrator LoadControl 0 1 0 0
system SparseGeneral -piv; # Overkill, but may need the pivoting!
test EnergyIncr 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 0.0 0.0 0.0 1.0
}

# Compute curvature increment
set dK [expr $maxK/$numIncr]

# Use displacement control at node 1002 for section analysis, dof 6
integrator DisplacementControl 1002 6 $dK 1 $dK $dK

# Do the section analysis
set ok [analyze $numIncr]

# ----------------------------------------------if convergence failure-------------------------
….

[silvia]

it depends on how you want to control the curvatures in the two directions.
i'd create two curvature histories and use the sp command for each direction, in two load patterns....

[hrodrigues]

Thanks for your help Silvia.
I would like to impose a linear curvature history in each direction.
So I create a SP command to impose the curvatures but it’s not working.
Should I release more DOF ??

proc MomentCurvature3D { secTag axialLoad maxK {numIncr 100} } {
##################################################
# A procedure for performing section analysis (only does
# moment-curvature, but can be easily modified to do any mode
# of section reponse.)
#
# MHS
# October 2000
# modified to improve convergence by Silvia Mazzoni, 2006
#
# Arguments
# secTag -- tag identifying section to be analyzed
# axialLoad -- axial load applied to section (negative is compression)
# maxK -- maximum curvature reached during analysis
# numIncr -- number of increments used to reach maxK (default 100)
#
# Sets up a recorder which writes moment-curvature results to file
# section$secTag.out ... the moment is in column 1, and curvature in column 2

# Define two nodes at (0,0)
node 1001 0.0 0.0 0.0
node 1002 0.0 0.0 0.0

# Fix all degrees of freedom except axial and bending
fix 1001 1 1 1 1 1 1
fix 1002 0 1 1 1 1 0

# Define element
# tag ndI ndJ secTag
element zeroLengthSection 2001 1001 1002 $secTag

# Create recorder
recorder Node -file data/Mphi.out -time -node 1002 -dof 6 disp; # output moment (col 1) & curvature (col 2)

# Define constant axial load
pattern Plain 3001 "Constant" {
load 1002 $axialLoad 0.0 0.0 0.0 0.0 0.0
}

# Define analysis parameters
integrator LoadControl 0 1 0 0
system SparseGeneral -piv; # Overkill, but may need the pivoting!
test EnergyIncr 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" {
# sp $node $DOF $Reference
sp 1002 6 1
}

pattern Plain 3003 "Linear" {
sp 1002 5 1
}

# Compute curvature increment
set dK [expr $maxK/$numIncr]

# Use displacement control at node 1002 for section analysis, dof 6
integrator DisplacementControl 1002 6 $dK 1 $dK $dK

# Do the section analysis
set ok [analyze $numIncr]

# ----------------------------------------------if convergence failure-------------------------

[silvia]

you might want to release dof 5, but that's a moot point, i think.
play around with an elastic material and see where it takes you.

[hrodrigues]

Thanks once again. I think i have my problem almost solve.
One last question.
To record the M-C results in the example you have:
# Create recorder
recorder Node -file data/Mphi.out -time -node 1002 -dof 6 disp; # output moment (col 1) & curvature (col 2)

these should record the moment and curvature relation for the 6 DOF
however if I put
recorder Node -file data/Mphi.out -time -node 1002 -dof 5 disp; # output moment (col 1) & curvature (col 2)
to record at the same time the M-C relation for the 5 DOF the curvature in fact in the curvature for the 5 DOF however the moment is associated with the moment of 6 DOF, these is related I think with the “time”
how can I record the moment – curvature in the DOF 5 ?

[silvia]

i would use the element recorder for the zero-length element at the section. ask for force on one and deformation on another, don't use time.

[hrodrigues]

Silvia,
Once again thank you for your help.
To get the results I use the following records:
recorder Element -file Defo$klei.txt -ele 1 deformation; # section deformations, axial and curvature, node j
recorder Element -file Force$klei.txt -ele 1 force ; # section forces, axial and moment, node j
there is any possibility of getting only the My and Mx from the Force record ?
thanks once again.
Hugo

[silvia]

if you go down to the section you can break it down into just axial and moments....

[dinochen1983]

I think make a program to control OpenSEES analysis is the way to solve the moment-rotation curve 3D problem. The programe is just like Xtract!