global force and local force

[yfeng]

Hi Vesna,
I observed an interesting result when recording global and local forces.
In a 2D cantilever model, I used one beam column element. Global force and local force are the same since I applied the default orientation of the section that local coordinate coincide with global coordinate.
When I did a moment rotational analysis with zerolengthsection element, recorded global moment is not the same as local moment. And the local force equated to $Hload times global force. $Hload is the lateral load I specified in the load pattern. (Section sill have the default orientation.) It seems that global force recording command is recording the lateral load coefficient.

Do you know why is this happening?

Yuhao Feng

[vesna]

With zerolengthsection element you can only do moment-curvature analysis, not moment rotation analysis.

If you post your example I can take a look.

[yfeng]

Hi Vesna,
Thanks for notifying me this. Is it because the zerolengthsection element doesn't output disp but curvature instead? I tried zerolengthsection since some of the researchers used zerolengthsection element to model Strain penetration effect. It actually makes sense that the a "section" can only do MC analysis. Instead, an "element" can do Moment Rotational analysis.

And here is my script:

# unit is in ksi kips

# SET UP ----------------------------------------------------------------------------
wipe; # clear memory of all past model definitions
model BasicBuilder -ndm 2 -ndf 3; # Define the model builder, ndm=#dimension, ndf=#dofs
set dataDir DataSPspr_st02_US_Test9Rhis_Axialload; # set up name of data directory (can remove this)
file mkdir $dataDir; # create data directory


# define GEOMETRY -------------------------------------------------------------
# define structure-geometry paramters

node 1 0 0
node 2 0 0


print node;


# BOUNDARY CONDITIONS
fix 1 1 1 1;
fix 2 0 1 0; # fix axial first



# Definition of parameters for fiber RC section

# MATERIAL parameters

set matTag 1;
set fc -7.; # CONCRETE Compressive Strength, ksi (+Tension, -Compression)
set Ec [expr 0.14504*5000*sqrt(48.2)]; # Concrete Elastic Modulus,ksi
# confined concrete
set Kfcb 1.29; # ratio of confined to unconfined concrete strength
set Kresb 0.6; # ratio of residual/ultimate to maximum stress
set fc1C [expr $Kfcb*$fc]; # CONFINED concrete (mander model), maximum stress;ksi # CONFINED concrete (mander model), maximum stress;
set eps0 -0.002; # UNCONFINED concrete strain
set fac [expr $fc1C/$fc];
set eps1C [expr $eps0*(1+5*($fac-1))]; # strain at confined concrete strength
set fc2C [expr $Kresb*$fc1C]; # crushing strength;ksi
set eps2C -0.05;
# unconfined concrete---------------------------------------------------------------------------------
set fc1U $fc; # UNCONFINED concrete (todeschini parabolic model), maximum stress
set eps1U $eps0; # strain at maximum strength of unconfined concrete
set fc2U -0.001; # crushing strength;ksi
set eps2U -0.0064; # strain at ultimate stress

set IDconcCore 1;
set IDconcCover 2;

uniaxialMaterial Concrete01 $IDconcCore $fc1C $eps1C $fc2C $eps2C ; # Column core concrete (confined)
uniaxialMaterial Concrete01 100 $fc1C $eps1C $fc2C $eps2C ; # Footing core concrete

uniaxialMaterial Concrete01 $IDconcCover $fc1U $eps1U $fc2U $eps2U; # Column cover concrete (unconfined)
uniaxialMaterial Concrete01 200 $fc1U $eps1U $fc2U $eps2U; # Footing cover concrete (unconfined)

set Fy [expr 0.14504*464.0]; # STEEL yield stress;MPa
set Fu [expr 0.14504*650];

# Strain penetration material-------------------------------------------------------------------------------------

set IDsp01 5;
set sy [expr 1.0*0.447/25.4]; # bar slip at member interface under yield stress (mm)
puts "sy = $sy";
set su [expr 35*$sy]; # bar slip at ultimate stress of rebar (in)
set bsp 0.4; # Initial hardening ratio in the monotonic slip
set rsp 0.8; # pinching factor for cyclic slip

uniaxialMaterial Bond_SP01 $IDsp01 $Fy $sy $Fu $su $bsp $rsp;

#uniaxialMaterial Elastic $matTag $E;

#uniaxialMaterial ReinforcingSteel $IDreinf $Fy $Fu $Es $Esh $esh $eult ;

set Es [expr 0.14504*200000]; # modulus of steel;MPa
set IDreinf 4;
## STEEL rebar
##STEEL02 tag $Fy $E $b $R0 $cR1 $cR2 $a1 $a2 $a3 $a4
uniaxialMaterial Steel02 $IDreinf [expr $Fy/2] $Es 0.01 18.5 0.925 0.15 0.01 0.5 0.05 1.2

set ColSecTag 1;

# section GEOMETRY -------------------------------------------------------------
set pi 3.1416;
set DSec 24; # Column Diameter
set Across [expr (3.14/4)*pow($DSec,2)];
set coverSec [expr 31.75/25.4]; # Column cover to reinforcing steel NA.
set numBarsSec 16; # number of longitudinal-reinforcement bars in column
set barAreaSec [expr 284.9/pow(25.4,2)]; # area of longitudinal-reinforcement bars
set ColSecTag 1; # set tag for symmetric section
set dbar [expr 19.05/25.4] ; # bar diameter

# Generate a circular reinforced concrete section
# with one layer of steel evenly distributed around the perimeter and a confined core.
# confined core.
#
#
# Notes
# The center of the reinforcing bars are placed at the inner radius
# The core concrete ends at the inner radius (same as reinforcing bars)
# The reinforcing bars are all the same size
# The center of the section is at (0,0) in the local axis system
# Zero degrees is along section y-axis
#
set ri 0.0; # inner radius of the section, only for hollow sections
set ro [expr $DSec/2]; # overall (outer) radius of the section
set nfCoreR 8; # number of radial divisions in the core (number of "rings")
set nfCoreT 24; # number of theta divisions in the core (number of "wedges")
set nfCoverR 2; # number of radial divisions in the cover
set nfCoverT 24; # number of theta divisions in the cover

set ZerSecTag 1;
source RCcircSection.tcl;
RCcircSection $ZerSecTag $ri $ro $coverSec 100 200 $IDreinf $numBarsSec $barAreaSec $nfCoreR $nfCoreT $nfCoverR $nfCoverT

set IDColTransf 1; # all columns
set ColTransfType Linear ; # options: Linear, PDelta, Corotational
# set ColTransfType PDelta ; # options: Linear, PDelta, Corotational
geomTransf $ColTransfType $IDColTransf; # only columns can have PDelta effects (gravity effects)

# Duplicate the spring in our tiger model
# tag ndI ndJ secID
element zeroLengthSection 1 1 2 $ZerSecTag

print element;

recorder Node -file $dataDir/disp.xls -node 2 -dof 3 disp; # check input dipl
recorder Element -file $dataDir/eleglobal_1.xls -time -ele 1 globalForce;
recorder Node -file $dataDir/sectionforce.xls -node 1 -dof 3 reaction;
#recorder Element -file $dataDir/eleSection_1.xls -time -ele 1 section 1 force;
recorder Element -file $dataDir/elelocal_1.out -time -ele 1 localForce ;

set IDloadTag 100; # load tag

set PCol [expr 0.000225*-756200]; # Axial load
# define GRAVITY -------------------------------------------------------------
pattern Plain 1 Linear {
load 2 $PCol 0 0
};

# Gravity-analysis parameters -- load-controlled static analysis

set Tol 1.0e-8; # convergence tolerance for test
constraints Plain; # how it handles boundary conditions
numberer Plain; # 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
test NormDispIncr $Tol 1000 ; # determine if convergence has been achieved at the end of an iteration step
algorithm Newton; # use Newton's solution algorithm: updates tangent stiffness at every iteration
set NstepGravity 10; # apply gravity in 10 steps
set DGravity [expr 1./$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

puts "Model Built"

loadConst -time 0.0

# -------------define computational parameters for cyclic test---------
source LibAnalysisStaticParameters2.tcl;

source Test9Rhis.tcl; # displacement history for test

# create load pattern for monotonic load

set Hload 100; # define the lateral load as a proportion of the weight so that the pseudo time equals the lateral-load coefficient when using linear load pattern
set iPushNode 2; # define nodes where lateral load is applied in static lateral analysis
pattern Plain 200 Linear { ; # define load pattern -- generalized
load $iPushNode 0.0 0.0 $Hload
};

# Set up parameters that are particular to the model for displacement control

set IDctrlNode 2; # node where displacement is read for displacement control
set IDctrlDOF 3; # degree of freedom of displacement read for displacement control

set Dpre 0;
set Dincr 0.0001;

foreach Dmax $iDmax {
set Ddiff [expr $Dmax-$Dpre];
set Nsteps [expr int(abs($Ddiff)/$Dincr)];
if {$Ddiff<0} {; # avoid the divide by zero
set dx [expr -1*$Dincr];
} else {
set dx $Dincr;
}
integrator DisplacementControl $IDctrlNode $IDctrlDOF $dx;
analyze $Nsteps;
set Dpre $Dmax;
}; # end of iDmaxCycl

puts "Spring Simulation Done";


vesna wrote:
> With zerolengthsection element you can only do moment-curvature analysis,
> not moment rotation analysis.
>
> If you post your example I can take a look.

[vesna]

I could not run your code as I do not have all source files you are using in the script. However I tested your recorder commands on one of the fiber sections given in Example 9 of example manual and it worked fine. Local and global recorder were giving me the same bending moment.

I would suggest you to look at the example manual and to build your code based on it.

[amir70007]

Hi...
What is the difference between global, local and basic forces?

[vesna]

Global forces follow global coordinate system sign convention and local forces follow local coordinate system sign convention. Basic forces are reduced set of forces for an element and include only axial force and bending moments at the element ends.