RC Wall Moment Curvature Analysis

[stuarts]

I am working on running a moment curvature analysis for L shaped walls. I am trying to find the MC response of the wall with an axial load of 0.1 * f'c * Ag.

My code seems to work fine when I have no axial load, but once I add it in the results dont seem to make much sense. Any help would be much appreciated. Thanks.




puts " -------------------------2D Model------------------------"

puts " -------------------------------------------------------------- "

puts " RC Wall Section"

puts " -------------------------------------------------------------- "

# Define model builder
# --------------------
model basic -ndm 2 -ndf 3
set secTag 1

#_______________________________________________________
#_______________________________________________________


# define UNITS ----------------------------------------------------------------------------
set in 1.; # define basic units -- output units
set kip 1.; # define basic units -- output units
set sec 1.; # define basic units -- output units
set LunitTXT "inch"; # define basic-unit text for output
set FunitTXT "kip"; # define basic-unit text for output
set TunitTXT "sec"; # define basic-unit text for output
set ft [expr 12.*$in]; # define engineering units
set ksi [expr $kip/pow($in,2)];
set psi [expr $ksi/1000.];
set lbf [expr $psi*$in*$in]; # pounds force
set pcf [expr $lbf/pow($ft,3)]; # pounds per cubic foot
set psf [expr $lbf/pow($ft,3)]; # pounds per square foot
set in2 [expr $in*$in]; # inch^2
set in4 [expr $in*$in*$in*$in]; # inch^4
set cm [expr $in/2.54]; # centimeter, needed for displacement input in MultipleSupport excitation
set PI [expr 2*asin(1.0)]; # define constants
set g [expr 32.2*$ft/pow($sec,2)]; # gravitational acceleration
set Ubig 1.e10; # a really large number
set Usmall [expr 1/$Ubig]; # a really small number


#_______________________________________________________
#_______________________________________________________

# set up parameters for section and element definition
#--------------------------------------------------
set IDcore 1; # ID tag for core concrete
set IDcover 2; # ID tag for cover concrete
set IDsteel 3; # ID tag for steel

# Define materials for nonlinear section
# ------------------------------------------
#CONCRETE------------------------------------------------------
# Confined concrete: (CORE CONCRETE)
set kfc 1.3; # Ratio between confined and unconfined compressive strength
set fc [expr -6*$ksi]; # CONCRETE Compressive Strength, ksi (+Tension, -Compression)
set Ec [expr 57*$ksi*sqrt(-$fc/$psi)]; # Concrete Elastic Modulus
set fc1C [expr $kfc*$fc]; # CONFINED concrete (mander model), maximum stress
set eps1C [expr 2.*$fc1C/$Ec]; # strain at maximum stress
set fc2C [expr 0.2*$fc]; # ultimate stress
set eps2C [expr 2*$eps1C]; # strain at ultimate stress

uniaxialMaterial Concrete01 $IDcore $fc1C $eps1C $fc2C $eps2C;

# Unconfined concrete: (COVER CONCRETE)
set fc1U $fc; # UNCONFINED concrete (todeschini parabolic model), maximum stress
set eps1U -0.003; # strain at maximum stress
set fc2U [expr 0.1*$fc]; # ultimate stress
set eps2U -0.006; # strain at ultimate stress

uniaxialMaterial Concrete01 $IDcover $fc1U $eps1U $fc2U $eps2U;

# STEEL --------------------------------------------------------------
# Reinforcing steel
set fy [expr 60*$ksi]; # STEEL yield stress
set Es [expr 29000.*$ksi]; # modulus of steel
set Bs 0.01; # strain-hardening ratio
set R0 18; # control the transition from elastic to plastic branches
set cR1 0.925; # control the transition from elastic to plastic branches
set cR2 0.15; # control the transition from elastic to plastic branches

uniaxialMaterial Steel02 $IDsteel $fy $Es $Bs $R0 $cR1 $cR2;

# Define rebar diameter & area per bar size

set db3 [expr 0.375*$in]
set db4 [expr 0.5*$in]
set db5 [expr 0.625*$in]
set db6 [expr 0.75*$in]
set db7 [expr 0.875*$in]
set db8 [expr 1.0*$in]
set db9 [expr 1.128*$in]
set db10 [expr 1.27*$in]
set db11 [expr 1.41*$in]

set Ab3 [expr 0.11*$in2]
set Ab4 [expr 0.2*$in2]
set Ab5 [expr 0.31*$in2]
set Ab6 [expr 0.44*$in2]
set Ab7 [expr 0.6*$in2]
set Ab8 [expr 0.79*$in2]
set Ab9 [expr 1.0*$in2]
set Ab10 [expr 1.27*$in2]
set Ab11 [expr 1.56*$in2]

# Define cross-section geometry for section
# ------------------------------------------

puts "Section Dimensions"
# set some paramaters
set bf [expr 210*$in]; # flange width
set h [expr 138*$in]; # nominal depth
set bw [expr 30*$in]; # web thickness
set tf [expr 24*$in]; # flange thickness
set bbf [expr 74*$in]; # width of boundary element 1 into flange
set tbe1 [expr 50*$in]; # depth of boundary element 1 in to flange end of web
set tbe2 [expr 32*$in]; # depth of boundary element 2 into far end of web
set cover [expr 2$in]; # Clear concrete cover over rebar

puts "bf = $bf in"
puts "h = $h in"
puts "bw = $bw in"
puts "tf = $tf in"

# some variables derived from the parameters
set y1 [expr $tbe1-$tf]
set y2 [expr $h-$tf]
set y3 [expr $y2-$tbe2]
set z1 [expr $bf-$bw]
set z2 [expr $bbf-$bw]

puts "y1 = $y1 in"
puts "y2 = $y2 in"
puts "y3 = $y2 in"
puts "z1 = $z1 in"
puts "z2 = $z2 in"

#Gross area of the section
set Ag [expr $z1*$tf+$h*$bw]
puts "Ag = $Ag in^2"

#------------------------------------------------------
#Boundary Element definitions
# __________
# | 1________|
# | |a
# | |
# | | 1 is location of boundary element 1 (1a is in web section, 1b is in flange section)
# | | 2 is location of boundary element 2
# | |
# |2|
# |_| a is the location of the origin (0,0) to define for wall patches (inside corner of web and flange)
#
# y
# |
# |
# z____|

#Define Steel in Boundary Element 1a (web section)

#set rho1a 0.01; # steel ratio in boundary element 1 (in flange/web)
#set As1a [expr $rho1a*$bw*$tbe1]; # Area of steel in BE given rho for the BE

# 2 rows of bars with (13) #10 bars per row
set nb1a 13; # Number of bars per row (y direction)

#Define Steel in Boundary Element 1b (flange section)

#set rho1b 0.01; # steel ratio in boundary element 1 (in flange/web)
#set As1b [expr $rho1b*$z2*$tf]; # Area of steel in BE given rho for the BE

# 2 rows of bars with (5) #10 bars per row
set nb1b 5; # Number of bars per row (z direction)

#Define Steel in Boundary Element 2 (in web end)

#set rho2 0.01; # steel ratio in boundary element 2 (web end)
#set As2 [expr $rho2*$bw*$tbe2]; # Area of steel in BE given rho for the BE

# 2 rows of bar with (6) #10 bars per row
set nb2 6; # Number of bars per row (y direction)

#-----------------------------------------------------------------
#Section model set up and discritization

#Define discritization size of concrete patches
set nfdb 20; # number of fibers along boundary element depth
set nftb 20; # number of fibers along boundary element thickness
set nfbf 20; # number of fibers along flange/web width
set nftf 20; # number of fibers along flange/web thickness

# Discretize the section with layers and patches
section Fiber $secTag {

# Define boundary elements (confined)
# ID, nfIJ, nfJK, yI, zI, yJ, zJ, yK, zK, yL, zL
patch quad $IDcore $nftb $nfdb -$y2 $bw -$y2 0 -$y3 0 -$y3 $bw; #BE 2
patch quad $IDcore $nftb $nfdb -$y1 $bw -$y1 0 $tf 0 $tf $bw; #BE 1a
patch quad $IDcore $nftb $nfdb 0 0 0 -$z2 $tf -$z2 $tf 0; #BE 1b
patch quad $IDcore $nftb $nfdb 0 0 0 -$z2 $tf -$z2 $tf 0; #BE 1b

# Define web/flange elements (unconfined)
patch quad $IDcover $nfbf $nftf -$y3 $bw -$y3 0 -$y1 0 -$y1 $bw
patch quad $IDcover $nfbf $nftf 0 -$z2 0 -$z1 $tf -$z1 $tf -$z2


# Define Bottom boundary element reinforcement
# ID, #bars, Abars, y start, z start, y end, z end
layer straight $IDsteel $nb1a $Ab10 [expr $tf-$cover] $cover -$y1 $cover; #BE 1a Row 1
layer straight $IDsteel $nb1a $Ab10 [expr $tf-$cover] [expr $bw-$cover] -$y1 [expr $bw-$cover]; #BE 1a Row 2
layer straight $IDsteel $nb1b $Ab10 $cover 0 $cover -$z2; #BE 1b row 1
layer straight $IDsteel $nb1b $Ab10 [expr $tf-$cover] 0 [expr $tf-$cover] -$z2; #BE 1b row 2
layer straight $IDsteel $nb2 $Ab10 -$y3 [expr $bw-$cover] [expr -$y2+$cover] [expr $bw-$cover]; #BE 2 row 1
layer straight $IDsteel $nb2 $Ab10 -$y3 $cover [expr -$y2+$cover] $cover; #BE 2 row 2
}



#_______________________________________________________
#_______________________________________________________


# set AXIAL LOAD --------------------------------------------------------
set P [expr 0.1*$fc*$Ag*$kip]; # + Tension, - Compression (NOTE: $f'c is negitive, as previously defined)
puts "Axial Load on Section = $P kip"

# set Maximum Curvature:
set Ku [expr 0.001/$in];
set numIncr 100; # Number of analysis increments to maximum curvature (default=100)
puts "Number of analysis increments: $numIncr
"

#_______________________________________________________
#_______________________________________________________


# ANALYSIS of section --------------------------------------------------

# 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 -orient 1 0 0 0 1 0

# Create Moment Curvature recorder ----> output moment (col 1) & curvature (col 2)
recorder Node -xml Mphi.out -time -node 1002 -dof 3 disp;

#Create Stress-Strain recorder ---> col1 = Moment (k-in), col2 = stress (ksi), col3 = strain (in/in)
recorder Element -xml SSFlangeSteel1.out -time -ele 2001 section fiber $tf $cover $IDsteel stressStrain; # Top steel recorder 1
recorder Element -xml SSFlangeSteel2.out -time -ele 2001 section fiber $tf -$z1 $IDsteel stressStrain; # Top steel recorder 2
recorder Element -xml SSFlangeConc1.out -time -ele 2001 section fiber $tf $cover $IDcore stressStrain; # Top concrete recorder 1
recorder Element -xml SSFlangeConc2.out -time -ele 2001 section fiber $tf -$z1 $IDcore stressStrain; # Top concrete recorder 2
recorder Element -xml SSWebSteel.out -time -ele 2001 section fiber -$y2 $cover $IDsteel stressStrain; # bottom steel recorder
recorder Element -xml SSWebConc.out -time -ele 2001 section fiber -$y2 $cover $IDcore stressStrain; # bottom concrete recorder

# Define constant axial load
pattern Plain 3001 Constant {
load 1002 $P 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-1 100
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 $Ku/$numIncr]

# Use displacement control at node 1002 for section analysis, dof 3
integrator DisplacementControl 1002 3 $dK 1 $dK $dK

# Do the section analysis
set ok [analyze $numIncr]
puts "Analysis Run"

# ----------------------------------------------if convergence failure-------------------------
set IDctrlNode 1002
set IDctrlDOF 3
set Dmax $Ku
set Dincr $dK
set TolStatic 1.e-2;
set testTypeStatic EnergyIncr
set maxNumIterStatic 6
set algorithmTypeStatic Newton
set fmt1 "%s Pushover analysis: CtrlNode %.3i, dof %.1i, Curv=%.4f /%s"; # format for screen/file output of DONE/PROBLEM analysis

if {$ok != 0} {
# if analysis fails, we try some other stuff, performance is slower inside this loop
set Dstep 0.0;
set ok 0
while {$Dstep <= 1.0 && $ok == 0} {
set controlDisp [nodeDisp $IDctrlNode $IDctrlDOF ]
set Dstep [expr $controlDisp/$Dmax]
set ok [analyze 1]; # this will return zero if no convergence problems were encountered
if {$ok != 0} {; # reduce step size if still fails to converge
set Nk 4; # reduce step size
set DincrReduced [expr $Dincr/$Nk];
integrator DisplacementControl $IDctrlNode $IDctrlDOF $DincrReduced
for {set ik 1} {$ik <=$Nk} {incr ik 1} {
set ok [analyze 1]; # this will return zero if no convergence problems were encountered
if {$ok != 0} {
# if analysis fails, we try some other stuff
# performance is slower inside this loop global maxNumIterStatic; # max no. of iterations performed before "failure to converge" is ret'd
puts "Trying Newton with Initial Tangent .."
test NormDispIncr $TolStatic 2000 0
algorithm Newton -initial
set ok [analyze 1]
test $testTypeStatic $TolStatic $maxNumIterStatic 0
algorithm $algorithmTypeStatic
}
if {$ok != 0} {
puts "Trying Broyden .."
algorithm Broyden 8
set ok [analyze 1 ]
algorithm $algorithmTypeStatic
}
if {$ok != 0} {
puts "Trying NewtonWithLineSearch .."
algorithm NewtonLineSearch 0.8
set ok [analyze 1]
algorithm $algorithmTypeStatic
}
if {$ok != 0} {; # stop if still fails to converge
puts [format $fmt1 "PROBLEM" $IDctrlNode $IDctrlDOF [nodeDisp $IDctrlNode $IDctrlDOF] $LunitTXT]
return -1
}; # end if
}; # end for
integrator DisplacementControl $IDctrlNode $IDctrlDOF $Dincr; # bring back to original increment
}; # end if
}; # end while loop
}; # end if ok !0
# -----------------------------------------------------------------------------------------------------
global LunitTXT; # load time-unit text
if { [info exists LunitTXT] != 1} {set LunitTXT "Length"}; # set blank if it has not been defined previously.
if {$ok != 0 } {
puts [format $fmt1 "PROBLEM" $IDctrlNode $IDctrlDOF [nodeDisp $IDctrlNode $IDctrlDOF] $LunitTXT]
} else {
puts [format $fmt1 "DONE" $IDctrlNode $IDctrlDOF [nodeDisp $IDctrlNode $IDctrlDOF] $LunitTXT]
}

puts "Analysis Finished"
puts " -------------------------------------------------------------- "

[silvia]

you need to set the gravity load constant after the axial-load analysis.

[stuarts]

Wouldn't adding a gravity load analysis just increase the axial load on the wall section? Or does it do something else?

When I have the axial load at 0.1f'cAg the moment to reach a specific curvature is about 1% of the moment at the same curvature when there is no axial load, which makes no real sense. Is this purely because I don't have a gravity analysis?

Should I be using the "analyze $GravSteps" command?

[silvia]

you do have a gravity analysis in the script

[stuarts]

Where?

I am pretty new to OpenSees so I have been modifying the M-C script from the examples online. I know what most of the commands are doing except in the actual analysis section of the code, I am still trying to figure out exactly what everything does, which makes troubleshooting a little harder!

[silvia]

the analysis is performed using previously-defined model and analysis parameters whenever the command "analyze" is invoked.
look for it in the script.