1 Structural Model I (parameter definition; nodes; constraints; materials; sections & elements; block & region; geometric transformation) Silvia Mazzoni University of California, Berkeley OpenSees and NEESgrid Simulation Component User Workshop, 2-3 Sept 2004 Sponsored by the National Science Foundation through the Pacific Earthquake Engineering Research Center and the NEESgrid System Integration Project Silvia Mazzoni, UC Berkeley OpenSees User Workshop 2004 2 Example: Reinforced-Concrete Frame ρl col H Ig Ig col beam Hcol beam L beam L col W superstructure
22
Embed
Structural Model I - OpenSees...OpenSees and NEESgrid Simulation Component User Workshop, 2-3 Sept 2004 Sponsored by the National Science Foundation through the Pacific Earthquake
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
Structural Model I (parameter definition; nodes; constraints; materials; sections & elements; block & region; geometric transformation)
Silvia MazzoniUniversity of California, Berkeley
OpenSees and NEESgrid Simulation ComponentUser Workshop, 2-3 Sept 2004
Sponsored by the National Science Foundationthrough the Pacific Earthquake Engineering Research Centerand the NEESgrid System Integration Project
Silvia Mazzoni, UC BerkeleyOpenSees User Workshop 2004 2
Example:Reinforced-Concrete Frame
ρlcol
H
Ig
Igcol
beam
Hcol
beam
Lbeam
Lcol
Wsuperstructure
2
Silvia Mazzoni, UC BerkeleyOpenSees User Workshop 2004 3
ModelBuilder Objects• model Command• node Command• mass Command• Constraints objects• uniaxialMaterial Command• nDMaterial Command• section Command• element Command• block Command• region Command• Geometric Transformation Command• Time Series• pattern Command
Silvia Mazzoni, UC BerkeleyOpenSees User Workshop 2004 4
material tag of the pre-defined UniaxialMaterial object used to represent the stress-strain for the area of the fiber
$matTagarea of fiber$Az coordinate of the fiber in the section (local coordinate system)$zLocy coordinate of the fiber in the section (local coordinate system)$yLoc
cover patch
core patch
steel layer
externalradius
internalradius
9
Silvia Mazzoni, UC BerkeleyOpenSees User Workshop 2004 17
ending angle (optional. default=360.0)$endAngstarting angle (optional. default=0.0)$startAngexternal radius$extRadinternal radius$intRady & z-coordinates of the center of the circle$zCenter$yCenter number of subdivisions (fibers) in the radial direction.$numSubdivRad
number of subdivisions (fibers) in the circumferential direction.
$numSubdivCirc
material integer tag of the previously-defined UniaxialMaterial object used to represent the stress-strain for the area of the fiber
specifies a previously-defined Section object (identified by the argument $sectionTag) to which these UniaxialMaterial objects may be added to recursively define a new Section object
<-section $sectionTag>
Torsion Force-DeformationT
Shear force-deformation along section local z-axisVzMoment-curvature about section local y-axisMyShear force-deformation along section local y-axisVyMoment-curvature about section local z-axisMzAxial force-deformationP
the force-deformation quantities corresponding to each section object. One of the following strings is used:
joint offset values -- absolute offsets specified with respect to the global coordinate system for element-end node j (the number of arguments depends on the dimensions of the current model) (optional)
$dXj $dYj $dZj
joint offset values -- absolute offsets specified with respect to the global coordinate system for element-end node i (the number of arguments depends on the dimensions of the current model) (optional)
$dXi $dYi $dZi
X, Y, and Z components of vecxz, the vector used to define the local x-z plane of the local-coordinate system. The local y-axis is defined by taking the cross product of the x-axis and the vecxz vector. These components are specified in the global-coordinate system X,Y,Z and define a vector that is in a plane parallel to the x-z plane of the local-coordinate system.These items need to be specified for the three-dimensional problem.
$vecxzX $vecxzY $vecxzZ
unique identifier for CrdTransf object$transfTag
Silvia Mazzoni, UC BerkeleyOpenSees User Workshop 2004 22
local coordinate system
Y
Z
X
node j
node i
y
x
z
local xz plane
vecxz (vecxzX, vecxzY, vecxzZ)
vector parallel to vecxz
12
Silvia Mazzoni, UC BerkeleyOpenSees User Workshop 2004 23
element elasticBeamColumn $eleTag $iNode $jNode $A $E $Iz $transfTag
13
Silvia Mazzoni, UC BerkeleyOpenSees User Workshop 2004 25
Nonlinear Beam Column Element
tolerance for satisfaction of element compatibility (optional, default=10-16)
$tol
maximum number of iterations to undertake to satisfy element compatibility (optional, default=1)
$maxIters
element mass density (per unit length), from which a lumped-mass matrix is formed (optional, default=0.0)
$massDens
identifier for previously-defined coordinate-transformation(CrdTransf) object
$transfTagidentifier for previously-defined section object$secTagnumber of integration points along the element.$numIntgrPtsend nodes$jNode$iNode unique element object tag$eleTag
Silvia Mazzoni, UC BerkeleyOpenSees User Workshop 2004 27
region command• label a group of nodes and elements. • This command is also used to assign rayleigh
damping parameters to the nodes and elements in this region.
• The region is specified by either elements or nodes, not both. If elements are defined, the region includes these elements and the all connected nodes. If nodes are specified, the region includes these nodes and all elements whose external nodes are prescribed
4. set eps1C [expr 2.*$fc1C/$Ec]; # strain at maximum stress
5. set fc2C $fc; # ultimate stress
6. set eps2C [expr 5*$eps1C]; # strain at ultimate stress
7. set fc1U $fc; # UNCONFINED concrete maximum stress
8. set eps1U -0.003; # strain at maximum stress
9. set fc2U [expr 0.1*$fc]; # ultimate stress
10. set eps2U -0.006; # strain at ultimate stress
11. set Fy [expr 68.*$ksi]; # STEEL yield stress
12. set Es [expr 29000.*$ksi]; # modulus of steel
13. set epsY [expr $Fy/$Es]; # steel yield strain
14. set Fy1 [expr 89.8*$ksi]; # steel stress post-yield
15. set epsY1 0.06; # steel strain post-yield
16. set Fu [expr 95.2*$ksi]; # ultimate stress of steel
17. set epsU 0.1; # ultimate strain of steel
18. set Bs [expr ($Fu-$Fy)/($epsU-$epsY)/$Es]; # post-yield stiffness ratio of steel
MATERIAL PROPERTIES
concrete
steel
20
Silvia Mazzoni, UC BerkeleyOpenSees User Workshop 2004 39
parameters.tcl
1. set pinchX 1.0; # pinching parameter for hysteretic model 2. set pinchY 1.0; # pinching parameter for hysteretic model 3. set damage1 0.0; # damage parameter for hysteretic model 4. set damage2 0.0; # damage parameter for hysteretic model
5. set betaMUsteel 0.0; # degraded unloading stiffness based on MU^(-beta)
6. set betaMUjoint 0.0; # degraded unloading stiffness based on MU^(-beta)7. set betaMUph 0.0; # degraded unloading stiffness based on MU^(-beta)8. set G $U; # Torsional stiffness Modulus9. set J 1.; # Torsional stiffness of section10. set GJ [expr $G*$J]; # Torsional stiffness
HYSTERETIC MODEL
Silvia Mazzoni, UC BerkeleyOpenSees User Workshop 2004 40
parameters.tcl
1. # define COLUMN REINFORCEMENT parameters2. set NbCol 20; # number of column longitudinal-reinf. bars3. set AsCol [expr $GrhoCol*$Acol]; # total steel area in column section4. set AbCol [expr $AsCol/$NbCol]; # bar area of column longitudinal reinforcement
5. # set up parameters for column section and element definition6. set np 5; # Number of integration points7. set riCol 0.0; # inner radius of column section8. set roCol $Rcol; # outer radius of column section
9. set IDcore 1; # ID tag for core concrete10. set IDcover 2; # ID tag for cover concrete11. set IDsteel 3; # ID tag for steel
12. set nfCoreR 8; # number of radial fibers in core13. set nfCoreT 16; # number of tangential fibers in core14. set nfCoverR 2; # number of radial fibers in cover15. set nfCoverT 16; # number of tangential fibers in cover
16. set IDcolFlex 2; # ID tag for column section in flexure, before aggreg. torsion17. set IDcolTors 10; # ID tag for column section in torsion18. set IDcolSec 1; # ID tag for column section
19. set IDcolTrans 1; # ID tag for column transformation, defining element normal20. set IDbeamTrans 2; # ID tag for beam transformation, defining element normal
Column&beam-model properties
21
Silvia Mazzoni, UC BerkeleyOpenSees User Workshop 2004 41
parameters.tcl
1. set Pdl [expr $Weight/2]; # gravity axial load per column
2. set Wbeam [expr $Weight/$Lbeam]; # distributed gravity dead load
3. set Mdl [expr $Wbeam*pow($Lbeam,2)/12]; # nodal moment
4. set Mass [expr $Weight/$g]; # mass of superstructure
5. set Mnode [expr $Mass/2]; # nodal mass for each column
GRAVITY
Silvia Mazzoni, UC BerkeleyOpenSees User Workshop 2004 42
parameters.tcl
1. # define DAMPING parameters from $xDamp --SDOF system, use stiffness proportional damping only
2. set xDamp 0.02; # modal damping ratio
3. set lambda [eigen 1]; # eigenvalue analysis4. set omega [expr sqrt($lambda)]; # natural frequency (rad/sec)5. set Tperiod [expr 2*$PI/$omega]; # period (sec.)
6. set alphaM 0; # mass-prop. RAYLEIGH damping parameter; D = alphaM*M7. set betaK 0; # stiffness proportional damping; +beatK*KCurrent8. set betaKcomm [expr 2*$xDamp/$omega]; # +betaKcomm*KlastCommitt9. set betaKinit 0; # +beatKinit*Kini
DAMPING
NOTE: you actually have to move these commands to after the model has been set up, as you cannot perform an eigenvalue analysis at this point, yet
22
Silvia Mazzoni, UC BerkeleyOpenSees User Workshop 2004 43
parameters.tcl
1. set DxPush [expr 0.1*$in]; # Displacement increment for pushover analysis
2. set DmaxPush [expr 20*$in]; # maximum displamcement for pushover analysis
3. set DtAnalysis [expr 0.005*$sec]; # time-step Dt for lateral analysis
4. set DtGround [expr 0.02*$sec]; # time-step Dt for input grond motion
5. set TmaxGround [expr 50 *$sec]; # maximum duration of ground-motion analysis
6. set gamma 0.5; # gamma value for newmark integration
7. set beta 0.25; # beta value for newmark integration