钢筋混凝土非线性分析第一次大作业

Harbin Institute of Technology

钢筋混凝土结构非线性分

析课程作业

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?哈尔滨工业大学

基于Opensees 钢混柱结构滞回曲线比较分析

一、试验资料

本实验结构如下图所示，柱净高850mm ，截面尺寸为250*250mm mm ，采用40C 混凝土材料，受力纵筋采用335HRB ，箍筋采用235HPB 。柱子采用6根直径为12mm 的335HRB 级钢筋，柱身箍筋采用直径6mm 的235HPB 级钢筋，箍筋间距为50mm 。混凝土保护层厚度为25mm 。竖向施加760KN 荷载，轴压比为0.268。

混凝土强度：

钢筋力学性能：

试验测得的滞回曲线：

二、Opensees建模过程

1、主程序

wipe;

source Units.tcl;

source GeometricParameters.tcl;

source Material.tcl;

source FiberSection.tcl;

source Elements.tcl;

source RecorderRC.tcl;

source PointGravityLoad.tcl;

source Ex4.Portal2D.analyze.Static.Cycle.tcl;

2、定义量纲

set NT 1.0;

set mm 1.0;

set sec 1.0;

set kN [expr 1000.0*$NT];

set MPa [expr 1.0*$NT/pow($mm,2)];

set m [expr 1000.0*$mm];

set mm2 [expr $mm*$mm];

set mm4 [expr $mm*$mm*$mm*$mm];

set cm [expr 10.0*$mm];

set PI [expr 2*asin(1.0)];

set Ubig 1.e10;

set Usmall [expr 1/$Ubig];

puts "|| Units defined completely ||"

3、定义节点

model BasicBuilder -ndm 2 -ndf 3;

node 1 0 0; # node#, X, Y

node 2 0 $Lb;

fix 1 1 1 1;

fix 2 0 0 0; # node DX DY RZ puts "|| Geometric Parameters and Nodal coordinates defined completely ||"

4、定义几何参数

set B [expr 250.*$mm];

set H [expr 250.*$mm];

set Ab [expr $B*$H];

set Izb [expr 1./12.*$B*pow($H,3)];

set Lb [expr 875.*$mm];

set Cover [expr 25.*$mm];

set Bcore [expr ($B-2*$Cover)];

set Hcore [expr ($H-2*$Cover)];

set Acor [expr $Bcore*$Hcore];

set NmBar_12 4;

set Dlbar_12 [expr 12*$mm];

set Albar_12 [expr $PI*pow($Dlbar_12,2)/4.0];

set CAlbar_12 [expr $NmBar_12*$Albar_12];

set CAlbar [expr $CAlbar_12];

set Fy_12 [expr 380.2*$MPa];

set Es_12 [expr 200000.*$MPa];

set Dhbar [expr 6.*$mm];

set Ash [expr $PI*pow($Dhbar,2)/4.0];

set Fyh [expr 588.3*$MPa];

set Esh [expr 210000*$MPa];

set xyt [expr $Fyh/$Esh];

set LDhb [expr 2*($Bcore-$Dhbar)+2*($Hcore-$Dhbar)];

set SV [expr 50*$mm];

set SVc [expr $SV-$Dhbar];

puts "|| Section geometry completely defined ||"

5、定义材料本构关系

set IDsteel_12 1;

set IDcoverC 3;

set IDcoreC 4;

set fc [expr 45.4*$MPa];

set x0 0.002;

set ft [expr $fc/10.];

set Et [expr $ft/0.002];

set fc0 -$fc;

set xc0 -$x0;

set fcu0 [expr 0.2*$fc0];

set xcu0 -0.006;

set lambda 0.10;

uniaxialMaterial Concrete01 $IDcoverC $fc0 $xc0 $fcu0 $xcu0;

set ps [expr $CAlbar/$Ab];

set pcc [expr $CAlbar/$Acor];

set pst [expr $Ash*$LDhb*1.5/($Acor*$SV)];

set lmda [expr $pst*$Fyh/$fc];

set fcc [expr $fc0*(1+0.5*$lmda)];

set xcc [expr $xc0*(1+2.5*$lmda)];

set fcu [expr 0.35*$fcc];

set xcu [expr 20*$xcc];

uniaxialMaterial Concrete01 $IDcoreC $fcc $xcc $fcu $xcu;

set R0 18.5;

set cR1 0.925;

set cR2 0.15;

set haRatio 0.0037;

uniaxialMaterial Steel02 $IDsteel_12 $Fy_12 $Es_12 $haRatio $R0 $cR1 $cR2;

puts "|| Material parameters defined completely ||"

6、定义纤维截面

set RCSecTag 1;

set b1 20;

set b2 1;

set h1 20;

set h2 1;

set hs1 [expr $Hcore/2-$Dhbar-$Dlbar_12/2];

set bs1 [expr $Bcore/2-$Dhbar-$Dlbar_12/2];

set coverY [expr $H/2];

set coverZ [expr $B/2];

set coreY [expr $Hcore/2];

set coreZ [expr $Bcore/2];

section Fiber $RCSecTag {;

patch quad $IDcoreC $b1 $h1 -$coreY $coreZ -$coreY -$coreZ $coreY -$coreZ $coreY $coreZ;

patch quad $IDcoverC $b1 $h2 -$coverY $coverZ -$coverY -$coverZ -$coreY -$coverZ -$coreY $coverZ;

patch quad $IDcoverC $b1 $h2 $coreY $coverZ $coreY -$coverZ

$coverY -$coverZ $coverY $coverZ;

patch quad $IDcoverC $b2 $h1 -$coreY $coverZ -$coreY $coreZ $coreY $coreZ $coreY $coverZ;

patch quad $IDcoverC $b2 $h1 -$coreY -$coreZ -$coreY -$coverZ

$coreY -$coverZ $coreY -$coreZ;

layer straight $IDsteel_12 3 $Albar_12 $hs1 $bs1 $hs1 -$bs1;

layer straight $IDsteel_12 3 $Albar_12 -$hs1 $bs1 -$hs1 -$bs1;

};

puts "|| Fiber sections defined completely ||"

7、定义单元

set IDColTransf 1;

set IDBeamTransf 2;

geomTransf PDelta $IDColTransf;

geomTransf Linear $IDBeamTransf;

set nP 4;

element nonlinearBeamColumn 1 1 2 $nP $RCSecTag $IDColTransf;

puts "|| Elements defined compoletely ||"

8、定义输出

set dataDir1 EleNode;

file mkdir $dataDir1;

for {set NodeI 1} {$NodeI<=2} {incr NodeI 1} {;

recorder Node -file $dataDir1/Node$NodeI.txt -time -node $NodeI -dof 1

2 3 disp;

};

recorder Node -file $dataDir1/RBase1.txt -time -node 1 -dof 1 2 3

reaction;

puts "|| Recorder defined completely ||"

9、定义荷载

set IDctrlNode 2;

set FN [expr -760*$kN];

pattern Plain 1 Linear {

load $IDctrlNode 0 $FN 0

};

set Tol 1.0e-15; # convergence tolerance for test

constraints Plain; # how it handles boundary conditions numberer Plain;

test system BandGeneral; # how to store and

solve the test NormDispIncr $Tol 6 0;

algorithm Newton;

set NstepGravity 10; # apply gravity in 10 steps

set DGravity [expr 1./$NstepGravity]; # first load increment;

integrator LoadControl $DGravity;

analysis Static;

initialize;

analyze $NstepGravity;

# -------------- maintain constant gravity loads and reset time to

zero------------------------------------------

loadConst -time 0.0

puts "|| Model built completed ||"

10、位移控制分析

variable constraintsTypeStatic Plain; # default;

if { [info exists RigidDiaphragm] == 1} {

if {$RigidDiaphragm=="ON"} {

variable constraintsTypeStatic Lagrange;# for large model, try Transformation

};# if rigid diaphragm is on

};# if rigid diaphragm exists

constraints $constraintsTypeStatic

set numbererTypeStatic RCM

numberer $numbererTypeStatic

set systemTypeStatic BandGeneral; # try UmfPack for large model system $systemTypeStatic

variable TolStatic 1.e-8; # Convergence Test: tolerance

variable maxNumIterStatic 6; # Convergence Test: maximum number of iterations that will be performed before "failure to converge" is returned

variable printFlagStatic 0; # Convergence Test: flag used to print information on convergence (optional) # 1: print information on each step;

variable testTypeStatic EnergyIncr ;# Convergence-test type

test $testTypeStatic $TolStatic $maxNumIterStatic $printFlagStatic;

# for improved-convergence procedure:

variable maxNumIterConvergeStatic 2000;

variable printFlagConvergeStatic 0;

variable algorithmTypeStatic Newton

algorithm $algorithmTypeStatic;

integrator DisplacementControl$IDctrlNode $IDctrlDOF $Dincr set analysisTypeStatic Static

analysis $analysisTypeStatic

set IDctrlNode 2; # node where displacement is read for displacement control

set IDctrlDOF 1; # degree of freedom of displacement read for displacement contro

# characteristics of cyclic analysis

set iDmax " 2 3 10 15 20 22 30 35"; # vector of displacement-cycle peaks, in terms of storey drift ratio

set Dincr [expr 0.05]; # displacement increment for pushover. you want this to be very small, but not too small to slow down the analysis

set Fact 1; # scale drift ratio by storey height for displacement cycles

set CycleType Full; # you can do Full / Push / Half cycles with the proc

set Ncycles 2; # specify the number of cycles at each peak # create load pattern for lateral pushover load

set Hload [expr $FN]; # 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 foreach PushNode $iPushNode {

load $PushNode $Hload 0.0 0.0}

}

# ----------- set up analysis parameters

source LibAnalysisStaticParameters.tcl;#

constraintsHandler,DOFnumberer,system-ofequations,convergenceTest, solutionAlgorithm,integrator

# --------------------------------- perform Static Cyclic Displacements Analysis

source LibGeneratePeaks.tcl

set fmt1 "%s Cyclic analysis: CtrlNode %.3i, dof %.1i, Disp=%.4f %s";

# format for screen/file output of DONE/PROBLEM analysis foreach Dmax $iDmax {

set iDstep [GeneratePeaks $Dmax $Dincr $CycleType $Fact];# this proc is defined above

for {set i 1} {$i <= $Ncycles} {incr i 1} {

set zeroD 0

set D0 0.0

foreach Dstep $iDstep {

set D1 $Dstep

set Dincr [expr $D1 - $D0]

integrator DisplacementControl$IDctrlNode $IDctrlDOF $Dincr

analysis Static

# ----------------------------------------------first analyze command------------------------

set ok [analyze 1]

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

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

if {$ok != 0} {

puts "Trying Newton with Initial Tangent .."

test NormDispIncr$Tol 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} {

set putout [format $fmt1 "PROBLEM" $IDctrlNode $IDctrlDOF [nodeDisp $IDctrlNode $IDctrlDOF] $LunitTXT]

puts $putout

return -1

}; # end if

}; # end if

#

---------------------------------------------------------------------------------------------

--------

set D0 $D1; # move to next step

}; # end Dstep

}; # end i

};# end of iDmaxCycl

#

---------------------------------------------------------------------------------------------

-------

set LunitTXT "mm";

if {$ok != 0 } {

puts [format $fmt1 "PROBLEM" $IDctrlNode $IDctrlDOF [nodeDisp $IDctrlNode $IDctrlDOF] $LunitTXT]

} else {

puts [format $fmt1 "DONE" $IDctrlNode $IDctrlDOF [nodeDisp $IDctrlNode $IDctrlDOF] $LunitTXT]

}

11、绘制滞回曲线

三、比较分析

试验测得的数据和Opensees计算所得数据偏差比较大，可能是因为实验数据不准确引起的，或者试验中给定的参数与实际实验参数的误差引起的，因此试验时的参数测量一定要准确，这样才能精确的反映材料的变形关系，不然会对计算结果有很大的影响。

四、设计总结

通过本次设计，我初步掌握了Opensees在非线性分析中的应用，对于搞研究有很大的帮助，可以帮助我们抽象的设计分析问题。

Opensees提供的设计平台具有很好的精准度，可以帮助我们来验证试验结果的可靠性。