P-u diagram

[aggelos]

I have a simple question..
How can i plot the P-u diagram of a reinforced concrete column, with a horizontal force on the top?

The target should be a displacement value or a force value?

Which recorders are useful?

Is there any example about that?

Thank you.

[silvia]

look at the cantliver column example in the examples manual.
you need to record the support reaction and the node displacement (for a problem like this, i think you can record the reaction at the top node, see what it gives you)

[aggelos]

First of all i need to find and design the moment-curvature diagram.
I try to find the values but i find various problems..

*************************************************************
Here is the model
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# Define model builder
# --------------------
model basic -ndm 2 -ndf 3
# Units KN,m,sec
# Define materials for nonlinear columns
# ------------------------------------------
# CONCRETE tag f'c ec0 f'cu ecu
# Core concrete (confined)
uniaxialMaterial Concrete01 1 -25000 -0.0022 -10000 -0.0033

# Cover concrete (unconfined)
uniaxialMaterial Concrete01 2 -20000 -0.0022 -8000 -0.0034

# STEEL
# Reinforcing steel
set fy 500000; # Yield stress
set E 200000000.0; # Young's modulus
# tag fy E0 b
uniaxialMaterial Steel01 3 $fy $E 0.01

# Define cross-section for nonlinear columns
# ------------------------------------------

# set some paramaters
set colWidth 1.0
set colDepth 1.5

set cover 0.1
set As 0.00000314; # area of no. 7 bars

# some variables derived from the parameters
set y1 [expr $colDepth/2.0]
set z1 [expr $colWidth/2.0]
set d1 0.16

section Fiber 1 {

# Create the concrete core fibers
patch rect 1 15 1 [expr $cover-$y1] [expr $cover-$z1] [expr $y1-$cover] [expr $z1-$cover]

# Create the concrete cover fibers (top, bottom, left, right)
patch rect 2 15 1 [expr -$y1] [expr $z1-$cover] $y1 $z1
patch rect 2 15 1 [expr -$y1] [expr -$z1] $y1 [expr $cover-$z1]
patch rect 2 1 10 [expr -$y1] [expr $cover-$z1] [expr $cover-$y1] [expr $z1-$cover]
patch rect 2 1 10 [expr $y1-$cover] [expr $cover-$z1] $y1 [expr $z1-$cover]

# Create the reinforcing fibers (left, middle, right)
layer straight 3 8 $As [expr $y1-$cover] [expr $z1-$cover] [expr $cover-$y1] [expr $z1-$cover]
layer straight 3 5 $As [expr $y1-$cover] [expr $z1-$cover-$d1] [expr $y1-$cover] [expr $cover+$d1-$z1]
layer straight 3 8 $As [expr $y1-$cover] [expr $cover-$z1] [expr $cover-$y1] [expr $cover-$z1]
layer straight 3 5 $As [expr $cover-$y1] [expr $z1-$cover-$d1] [expr $cover-$y1] [expr $cover+$d1-$z1]

}

# Estimate yield curvature
# (Assuming no axial load and only top and bottom steel)
set d [expr $colDepth-$cover] ;# d -- from cover to rebar
set epsy [expr $fy/$E] ;# steel yield strain
set Ky [expr 39.37*$epsy/(0.7*$d)]

# Print estimate to standard output
puts "Estimated yield curvature: $Ky"

# Set axial load
set P -187.5

set mu 15; # Target ductility for analysis
set numIncr 100; # Number of analysis increments

# Call the section analysis procedure
source metat1.tcl
MomentCurvature 1 $P [expr $Ky*$mu] $numIncr

*************************************************************
Now there is the metat1.tcl file (moment-curvature procedure)
*************************************************************

# 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
#
# 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

proc MomentCurvature {secTag axialLoad maxK {numIncr 100} } {
# Define two nodes at (0,0)
node 1 0.0 0.0
node 2 0.0 0.0

# Fix all degrees of freedom except axial and bending
fix 1 1 1 1
fix 2 0 1 0

# Define element
# tag ndI ndJ secTag
element zeroLengthSection 1 1 2 $secTag

# Create recorder
recorder Node -file section$secTag.out -time -node 2 -dof 3 disp

# Define constant axial load
pattern Plain 1 "Constant" {
load 2 $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 2 "Linear" {
load 2 0.0 0.0 1.0
}

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

# Use displacement control at node 2 for section analysis
integrator DisplacementControl 2 3 $dK 1 $dK $dK

# Do the section analysis
analyze $numIncr
}



*************************************************************

The result is:

Estimated yield curvature: 0.100433673469
WARNING: CTestNormUnbalance::test<>-failed to converge
after 10 iterations
NewtnRaphson::solveCurrentStep<> -the ConvergenceTest object failed in test<>
StaticAnalysis::analyze<> -the Algorithm failed at iteration: 0 with domain at
load factor 0.673815
OpenSees > analyze failed, returned: -3 error flag
-3
OpenSees >


*************************************************************

Any ideas of what i need to change in order to find the correct results?
Why can't i achieve convergence?


Thank you.

[silvia]

do you have the same problem when you run my example? if not, what's different between the two?
likely, your section has reached unreasonably high strain -- look at the results...