Wrong Results in Dynamic Analysis

[Paolo]

Hi!
I’m checking the results of dynamic analysis on a Three-Dimensional Elastic Frame.
The model consists of four stories and one bay in each direction with elasticBeamColumn elements for pillars and beams (beams have very big values of E G J Iy Iz).
I can’t find a maximum displacement similar to the elastic response spectra.
The record I’ve adopted is I-ELC180 (in x direction). For the period of the first mode (0.489 s) the elastic displacement spectra (obtained with Seismosignal) is 4.46cm , while dynamic analysis gives a maximum displacement of 5.4 cm.
The script I’m using is:




# Units: Kg, cm, s
model BasicBuilder -ndm 3 -ndf 6
set h 300.0
set by 500.0
set bx 500.0
node 1 [expr -$bx/2] [expr $by/2] 0
node 2 [expr $bx/2] [expr $by/2] 0
node 3 [expr $bx/2] [expr -$by/2] 0
node 4 [expr -$bx/2] [expr -$by/2] 0
node 5 [expr -$bx/2] [expr $by/2] $h
node 6 [expr $bx/2] [expr $by/2] $h
node 7 [expr $bx/2] [expr -$by/2] $h
node 8 [expr -$bx/2] [expr -$by/2] $h
node 10 [expr -$bx/2] [expr $by/2] [expr 2*$h]
node 11 [expr $bx/2] [expr $by/2] [expr 2*$h]
node 12 [expr $bx/2] [expr -$by/2] [expr 2*$h]
node 13 [expr -$bx/2] [expr -$by/2] [expr 2*$h]
node 15 [expr -$bx/2] [expr $by/2] [expr 3*$h]
node 16 [expr $bx/2] [expr $by/2] [expr 3*$h]
node 17 [expr $bx/2] [expr -$by/2] [expr 3*$h]
node 18 [expr -$bx/2] [expr -$by/2] [expr 3*$h]
node 20 [expr -$bx/2] [expr $by/2] [expr 4*$h]
node 21 [expr $bx/2] [expr $by/2] [expr 4*$h]
node 22 [expr $bx/2] [expr -$by/2] [expr 4*$h]
node 23 [expr -$bx/2] [expr -$by/2] [expr 4*$h]
node 9 0 0 $h
node 14 0 0 [expr 2*$h]
node 19 0 0 [expr 3*$h]
node 24 0 0 [expr 4*$h]
fix 1 1 1 1 1 1 1
fix 2 1 1 1 1 1 1
fix 3 1 1 1 1 1 1
fix 4 1 1 1 1 1 1
rigidDiaphragm 3 9 5 6 7 8
rigidDiaphragm 3 14 10 11 12 13
rigidDiaphragm 3 19 15 16 17 18
rigidDiaphragm 3 24 20 21 22 23
fix 9 0 0 1 1 1 0
fix 14 0 0 1 1 1 0
fix 19 0 0 1 1 1 0
fix 24 0 0 1 1 1 0
geomTransf PDelta 1 0 1 0
element elasticBeamColumn 1 1 5 900 290000 126087 114210 67500 67500 1
element elasticBeamColumn 2 2 6 900 290000 126087 114210 67500 67500 1
element elasticBeamColumn 3 3 7 900 290000 126087 114210 67500 67500 1
element elasticBeamColumn 4 4 8 900 290000 126087 114210 67500 67500 1
element elasticBeamColumn 5 5 10 900 290000 126087 114210 67500 67500 1
element elasticBeamColumn 6 6 11 900 290000 126087 114210 67500 67500 1
element elasticBeamColumn 7 7 12 900 290000 126087 114210 67500 67500 1
element elasticBeamColumn 8 8 13 900 290000 126087 114210 67500 67500 1
element elasticBeamColumn 9 10 15 900 290000 126087 114210 67500 67500 1
element elasticBeamColumn 10 11 16 900 290000 126087 114210 67500 67500 1
element elasticBeamColumn 11 12 17 900 290000 126087 114210 67500 67500 1
element elasticBeamColumn 12 13 18 900 290000 126087 114210 67500 67500 1
element elasticBeamColumn 13 15 20 900 290000 126087 114210 67500 67500 1
element elasticBeamColumn 14 16 21 900 290000 126087 114210 67500 67500 1
element elasticBeamColumn 15 17 22 900 290000 126087 114210 67500 67500 1
element elasticBeamColumn 16 18 23 900 290000 126087 114210 67500 67500 1
geomTransf PDelta 500 0 0 1
element elasticBeamColumn 17 5 6 900 999999999 999999999 999999999 999999999 999999999 500
element elasticBeamColumn 18 6 7 900 999999999 999999999 999999999 999999999 999999999 500
element elasticBeamColumn 19 7 8 900 999999999 999999999 999999999 999999999 999999999 500
element elasticBeamColumn 20 8 5 900 999999999 999999999 999999999 999999999 999999999 500
element elasticBeamColumn 21 10 11 900 999999999 999999999 999999999 999999999 999999999 500
element elasticBeamColumn 22 11 12 900 999999999 999999999 999999999 999999999 999999999 500
element elasticBeamColumn 23 12 13 900 999999999 999999999 999999999 999999999 999999999 500
element elasticBeamColumn 24 13 10 900 999999999 999999999 999999999 999999999 999999999 500
element elasticBeamColumn 25 15 16 900 999999999 999999999 999999999 999999999 999999999 500
element elasticBeamColumn 26 16 17 900 999999999 999999999 999999999 999999999 999999999 500
element elasticBeamColumn 27 17 18 900 999999999 999999999 999999999 999999999 999999999 500
element elasticBeamColumn 28 18 15 900 999999999 999999999 999999999 999999999 999999999 500
element elasticBeamColumn 29 20 21 900 999999999 999999999 999999999 999999999 999999999 500
element elasticBeamColumn 30 21 22 900 999999999 999999999 999999999 999999999 999999999 500
element elasticBeamColumn 31 22 23 900 999999999 999999999 999999999 999999999 999999999 500
element elasticBeamColumn 32 23 20 900 999999999 999999999 999999999 999999999 999999999 500
set g 981
set m1 [expr 24000/$g]
set m2 [expr 24000/$g]
set m3 [expr 24000/$g]
set m4 [expr 24000/$g]
# Rotary inertia of floor about master node
set i1 [expr $m1*($bx*$bx+$by*$by)/12.0]
set i2 [expr $m2*($bx*$bx+$by*$by)/12.0]
set i3 [expr $m3*($bx*$bx+$by*$by)/12.0]
set i4 [expr $m4*($bx*$bx+$by*$by)/12.0]
# Set mass at the master nodes
mass 9 $m1 $m1 0 0 0 $i1
mass 14 $m2 $m2 0 0 0 $i2
mass 19 $m3 $m3 0 0 0 $i3
mass 24 $m4 $m4 0 0 0 $i4
# Define gravity loads
set P 6000
pattern Plain 1 "Linear" {
foreach node {5 6 7 8 10 11 12 13 15 16 17 18 20 21 22 23 } {
load $node 0.0 0.0 -$P 0.0 0.0 0.0
}
}
system BandGeneral
constraints Transformation
numberer RCM
test NormDispIncr 1.0e-12 10 3
algorithm Newton
integrator LoadControl 0.01
analysis Static
initialize
analyze 100
puts “Gravity load analysis completed”
loadConst -time 0.0
# Define earthquake excitation
set dt 0.01
set outFile I-ELC180.g3
set accelSeries "Path -filePath $outFile -dt $dt -factor $g"
source ReadSMDFile.tcl
ReadSMDFile I-ELC180.at2 $outFile dt
pattern UniformExcitation 2 1 -accel $accelSeries
set csi 0.05
set pi 3.141592654
set aa [eigen 2]
set w12 [lindex $aa 0]
set w22 [lindex $aa 1]
set w1 [expr pow($w12,0.5)]
set w2 [expr pow($w22,0.5)]
set T1 [expr 2*$pi/$w1]
set T2 [expr 2*$pi/$w2]
puts "Periodo I modo: $T1"
puts "Periodo II modo: $T2"
set beta [expr 2*$csi/($w1+$w2)]
set alpha [expr 2*$csi*$w1-$beta*$w12]
puts "alpha: $alpha beta: $beta"
rayleigh $alpha 0.0 $beta 0.0
# End of model generation
# -----------------------
# Start of analysis generation
# Create the convergence test
# tol maxIter printFlag
test EnergyIncr 1.0e-8 20 3
algorithm Newton
# Create the system of equation storage and solver
system SparseGeneral -piv
# Create the constraint handler
constraints Transformation
integrator Newmark 0.5 0.25
numberer RCM
analysis Transient
# End of analysis generation
# --------------------------
# Start of recorder generation
# ----------------------------
recorder Node -file node24DxDfi.out -time -node 24 -dof 1 2 6 disp
# End of recorder generation
# --------------------------
# Perform the analysis
puts "eigen values at start of transient: [eigen 6]"
set tFinal [expr 4000 * 0.01]
set tCurrent [getTime]
set ok 0
while {$ok == 0 && $tCurrent < $tFinal} {
set ok [analyze 1 .01]
if {$ok != 0} {
puts "regular newton failed .. lets try an initail stiffness for this step"
test NormDispIncr 1.0e-12 100 0
algorithm ModifiedNewton -initial
set ok [analyze 1 .01]
if {$ok == 0} {puts "that worked .. back to regular newton"}
test NormDispIncr 1.0e-12 10
algorithm Newton
}
set tCurrent [getTime]
}
if {$ok == 0} {
puts "Transient analysis completed SUCCESSFULLY";
} else {
puts "Transient analysis completed FAILED";
}

I’m working on this structure, but I’ve tryied other simple examples (with only one mode, wihout Rayleigh...) and I didn’t find good results. Have you got any ideas?
Thank you very much and sorry for the length of all this!
Best regards.
Paolo

[silvia]

please show me the simple model that does not work.
i guess you are comparing to zero damping, right?
what dof are you comparing? at what period? wouldn't you need some equivalent displacement for sdof?
what about the PDelta, does this affect your results, since you have it turned on.
i think showing me the simple model will help better.

[ekalkan]

If you are comparing the elastic response from your 3D model with the one from SDOF aproximation (i.e., from elastic spectra of records) then you should not expect to see a good match. It can only happen if your structure behaves in pure first mode only. Otherwise discrepancy is evident.