base shear

[ssami]

Hi all
I have a mass spring model,I performed a dynamic analysis under earthquake for this model,I want to record base shear of this model,
I tried to record of base shear with writing "node1 reaction",that node1 is the base, is this true? if "node 1 reaction" records base shear,what means another nodes reaction
node 2 reaction,node3 reaction,...(except node1) ?

script:

wipe

model basic -ndm 1 -ndf 1
set dts 0.01
node 1 0.
node 2 0.
node 3 0.
node 4 0.
node 5 0.
node 6 0.

fix 1 1


uniaxialMaterial Elastic 1 1247714919
uniaxialMaterial Elastic 2 1166713619
uniaxialMaterial Elastic 3 1166713619
uniaxialMaterial Elastic 4 501758956.3
uniaxialMaterial Elastic 5 501758956.3


element zeroLength 1 1 2 -mat 1 -dir 1 -doRayleigh 1
element zeroLength 2 2 3 -mat 2 -dir 1 -doRayleigh 1
element zeroLength 3 3 4 -mat 3 -dir 1 -doRayleigh 1
element zeroLength 4 4 5 -mat 4 -dir 1 -doRayleigh 1
element zeroLength 5 5 6 -mat 5 -dir 1 -doRayleigh 1

mass 2 519580.0911
mass 3 518619.2511
mass 4 513488.9117
mass 5 508358.5723
mass 6 438901.7862



# ------------ define & apply damping
# RAYLEIGH damping parameters, Where to put M/K-prop damping,
set xDamp 0.05
set nEigenI 1
set nEigenJ 3
set lambdaN [eigen [expr $nEigenJ]]
set lambdaI [lindex $lambdaN [expr $nEigenI-1]]
set lambdaJ [lindex $lambdaN [expr $nEigenJ-1]]
set omegaI [expr pow($lambdaI,0.5)]
set omegaJ [expr pow($lambdaJ,0.5)]
set alphaM [expr $xDamp*(2*$omegaI*$omegaJ)/($omegaI+$omegaJ)]
set betaKcomm [expr 2.*$xDamp/($omegaI+$omegaJ)]


rayleigh $alphaM 0.0 0.0 $betaKcomm

set accel "Series -dt 0.01 -filePath AR.txt -factor [expr 1]"

pattern UniformExcitation 3 1 -accel $accel

recorder Node -file node1reac(linear).out -time -node 1 -dof 1 reaction
recorder Node -file node2reac(linear).out -time -node 2 -dof 1 reaction
recorder Node -file node3reac(linear).out -time -node 3 -dof 1 reaction
recorder Node -file node4reac(linear).out -time -node 4 -dof 1 reaction
recorder Node -file node5reac(linear).out -time -node 5 -dof 1 reaction
recorder Node -file node6reac(linear).out -time -node 6 -dof 1 reaction

constraints Plain
numberer Plain
system BandGeneral
test NormDispIncr 1.0e-6 10
algorithm ModifiedNewton
integrator Newmark 0.5 0.25
analysis Transient
analyze [expr int(30/$dts)] $dts


Thanks so much.

[fmk]

the reaction recorders will record the nodal force unbalance at a node (node forces - element forces), the nodal reaction!

in a transient analysis the other recorders will not be 0 as the inertia forces and damping forces are not included. in a static analysis recorders recording anything not fixed should be nearly 0.0.

[cxc08]

fmk wrote:
> the reaction recorders will record the nodal force unbalance at a node
> (node forces - element forces), the nodal reaction!
>
> in a transient analysis the other recorders will not be 0 as the inertia
> forces and damping forces are not included. in a static analysis recorders
> recording anything not fixed should be nearly 0.0.

Dear frank,
I am testing a very simple twoNodeLink element. The nodal reaction recorder equaled to the inertia force but did not include the damping force. Following is my scripts.

*********************************************************************************
wipe
model BasicBuilder -ndm 2 -ndf 3
set A1 1.0
set E [expr 10./3.]
set mass1 0.2533
set H 1.0
set I1 1.0
set pi 3.14
set k [expr 3.*$I1*$E/$H**3]
node 1 0.0 0.0
node 2 0.0 $H -mass $mass1 0.0 0.0

fix 1 1 1 1
fix 2 0 1 1

geomTransf Linear 10
uniaxialMaterial Elastic 1 $k
element twoNodeLink 1 1 2 -mat 1 -dir 2

set G 386.
timeSeries Path 2 -dt 0.02 -filePath ElCentroLevel2.y -factor $G
pattern UniformExcitation 2 1 -accel 2

recorder Node -file point_2_disp.out -time -node 2 -dof 1 disp
recorder Node -file point_2_vel.out -time -node 2 -dof 1 vel
recorder Node -file point_2_acce.out -time -node 2 -dof 1 accel
recorder Node -file point_2_DampingForce.out -time -node 2 -dof 1 rayleighForces
recorder Node -file point_2_ResistingForce.out -time -node 2 -dof 1 reaction
recorder Element -file point_2_EleForce.out -time -ele 1 force

set lambda [eigen -fullGenLapack 1]
set T [expr (2*$pi)/sqrt($lambda)]
puts "T = $T"
set freq [expr sqrt($lambda)]
set dampRatio 0.05
rayleigh [expr 2.*$dampRatio*$freq] 0. 0. 0.

integrator Newmark 0.5 0.25
test EnergyIncr 1.0e-10 20 4
algorithm Linear
numberer Plain
constraints Plain
system BandGeneral

analysis Transient
analyze 3000 0.02

print -node 2
*********************************************************************************

Moreover, I found that the unbalance force is quite large in each analysis step.
Here the unbalance force means "mass*accel+c*vel+k*disp+mass*Sa".
"accel", "vel", and "disp" are relative acceleration, velocity and displacement of node 2 in dof 1.
Sa is the ground motion acceleration.
Value of "mass*accel+c*vel+k*disp" was always lags compared with "-mass*Sa".
Test type seems not influence the results.

Because of the unbalanced force, the difference between input energy and absorbed energy (kinetic energy+damping energy+strain energy) is also quite large.

Could you explain why the difference exists and how to reduce?

PS, I want to use energy as a term to evaluate my model. Do you have any suggestions about how to obtain each energy variables?

Looking forward for your reply.
I will deeply appreciate for your help.

chen

[cxc08]

Oh I have just found the reason. I made a mistake when calculate the earthquake input energy. The first acceleration in the input ground motion file corresponds to time "0.0 sec". I took it as "0.02 sec". That caused all the differences. Sorry for the confusing problems in the last post.
But the reaction force still doesn't include the damping force. Could anyone explain why?

[fmk]

the effect of the damping is just to reduce the displacements and thus typically the reaction forces. in effect it is already taken into account.

however if you wish to see them instead of recation, try this undocumented feature:
reactionIncInertia