Hi fmk,
Instead of modelling the beam as a continuous system I used the lumped mass model in this below example. The storey stiffnesses and total structure weight have been calculated to give a natural period of 0.5s. I have verified this in SAP, but I am not able to get the same period in Opensees.
Could you please check my below code and correct me if I am doing something wrong?
*****************************
wipe;
model basic -ndm 2 -ndf 3 # Basic 2D model having 3 degrees-of-freedom per node.
#Node details: #Node no., X-coord., Y-coord.
node 1 0 0
node 2 0 0
node 3 0 0
node 4 4 0
node 5 8 0
node 6 12 0
node 7 16 0
node 8 20 0
node 9 24 0
node 10 28 0
node 11 32 0
node 12 36 0
node 13 40 0
node 14 40 0
node 15 40 0
puts "Node defined"
#Boundary Conditions: #Node no., DX, DY, RZ
fix 1 1 1 1
fix 2 1 0 0
fix 3 1 0 0
fix 4 0 0 0
fix 5 0 0 0
fix 6 0 0 0
fix 7 0 0 0
fix 8 0 0 0
fix 9 0 0 0
fix 10 0 0 0
fix 11 0 0 0
fix 12 0 0 0
fix 13 1 0 0
fix 14 1 0 0
fix 15 1 1 1
#Slaving node:
equalDOF 2 3 1 2 3
equalDOF 14 13 1 2 3
puts "Boundary Conditions assigned"
#Nodal mass: #Node no., MX(translational), MY(translational), MZ(rotational)
mass 3 0. 0.00509683995922528 0.
mass 4 0. 0.0101936799184506 0.
mass 5 0. 0.0101936799184506 0.
mass 6 0. 0.0101936799184506 0.
mass 7 0. 0.0101936799184506 0.
mass 8 0. 0.0101936799184506 0.
mass 9 0. 0.0101936799184506 0.
mass 10 0. 0.0101936799184506 0.
mass 11 0. 0.0101936799184506 0.
mass 12 0. 0.0101936799184506 0.
mass 13 0. 0.00509683995922528 0.
puts "Nodal Masses defined"
#Specifying material: #Material Tag, Stiffness value
uniaxialMaterial Elastic 1 8.0486
puts "Spring stiffnesses defined"
#Section details for columns: #Section Tag, Material Tag, Axial force deformation (use "P")
section Uniaxial 1 1 P
puts "Section forcolumn defined"
#Coordinate Tranformation:
geomTransf Linear 1
#Element details: #Element Tag, Nodei, Nodej (both nodes at same coordinate), Section Tag
element zeroLengthSection 1 1 2 1
# connectivity: (make A very large, 10e6 times its actual value)
# element elasticBeamColumn $eleTag $iNode $jNode $A $E $Iz $transfTag
element elasticBeamColumn 2 3 4 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 3 4 5 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 4 5 6 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 5 6 7 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 6 7 8 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 7 8 9 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 8 9 10 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 9 10 11 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 10 11 12 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 11 12 13 37853629000000 2.1e+11 0.00063878 1;
element zeroLengthSection 12 14 15 1
puts "Element details provided"
#Eigen Values: #Displays 4 fundamental periods
set Lambda [eigen -fullGenLapack 4]
puts "Lambda Omega Period"
foreach Lambda $Lambda {
if {$Lambda > 0.0} {
set Omega [expr pow($Lambda,0.5)]
set Period [expr (2*3.14)/$Omega]
puts "$Lambda $Omega $Period"}}
*********************************
Again, as in the other query (distributed-mass model), I have followed the manual and given a very high c/s area for the beam elements.
Regards.
Natural period - Lumped-mass model
Moderators: silvia, selimgunay, Moderators
you have a messed up model .. don't ignore neg eigenvalues, the fact that they are there indicates a problem in your model! .. i can't figure out what you are trying to do so i can't help.
but:
1) if a node totally moves the same as another node remove it whats the point of the equalDOF?
2) you only need to use fix command if the node is constrained
3) you need additional constraints, the zeroLength only handles AXIAL! forces.
but:
1) if a node totally moves the same as another node remove it whats the point of the equalDOF?
2) you only need to use fix command if the node is constrained
3) you need additional constraints, the zeroLength only handles AXIAL! forces.
Hi FMK,
Thanks for your comments.
Sorry for not providing more details. I have also posted another query under subject "Distributed-mass model" with some details about the problem. I am still awaiting your response for that problem
I am modelling a single storey, single bay structure. I have assumed the length of the beam as 40m and divided the beam into 10 elements. I have assumed unit weight, and lumped the mass accordingly at the nodes. I have modelled the columns as springs. I set a target period of 0.5s and worked out the storey stiffnesses (taken in the below codes).
Before trying out complex problems I wanted to confirm if I can get the same 0.5s in Opensees. I have verified this problem and obtained 0.5s in SAP. So, I tried to work on this problem in Opensees:-) Early days for me....
I have made some changes as told by you, but I am unable to figure out again what is going wrong...iam not getting 0.5s. I have below 2 versions ( one with 13 nodes and the other with 15 nodes). Could you please look at them and make comments to make it run in the right way?
********************************************
VERSION 1 (13 nodes)
------------------------------
wipe;
model basic -ndm 2 -ndf 3 # Basic 2D model having 3 degrees-of-freedom per node.
#Node details: #Node no., X-coord., Y-coord.
node 1 0 0
node 2 0 0
node 3 4 0
node 4 8 0
node 5 12 0
node 6 16 0
node 7 20 0
node 8 24 0
node 9 28 0
node 10 32 0
node 11 36 0
node 12 40 0
node 13 40 0
puts "Node defined"
#Boundary Conditions: #Node no., DX, DY, RZ
fix 1 1 1 1
fix 2 1 0 1
fix 12 1 0 1
fix 13 1 1 1
puts "Boundary Conditions assigned"
#Nodal mass: #Node no., MX(translational), MY(translational), MZ(rotational)
mass 2 0. 0.00509683995922528 0.
mass 3 0. 0.0101936799184506 0.
mass 4 0. 0.0101936799184506 0.
mass 5 0. 0.0101936799184506 0.
mass 6 0. 0.0101936799184506 0.
mass 7 0. 0.0101936799184506 0.
mass 8 0. 0.0101936799184506 0.
mass 9 0. 0.0101936799184506 0.
mass 10 0. 0.0101936799184506 0.
mass 11 0. 0.0101936799184506 0.
mass 12 0. 0.00509683995922528 0.
puts "Nodal Masses defined"
#Specifying material: #Material Tag, Stiffness value
uniaxialMaterial Elastic 1 8.0486
puts "Spring stiffnesses defined"
#Section details: #Section Tag, Material Tag, Axial force deformation (use "P")
section Uniaxial 1 1 P
puts "Section forcolumn defined"
#Coordinate Tranformation:
geomTransf Linear 1
#Element details: #Element Tag, Nodei, Nodej (both nodes at same coordinate), Section Tag
element zeroLengthSection 1 1 2 1
# connectivity: (make A very large, 10e6 times its actual value)
# element elasticBeamColumn $eleTag $iNode $jNode $A $E $Iz $transfTag
element elasticBeamColumn 2 2 3 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 3 3 4 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 4 4 5 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 5 5 6 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 6 6 7 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 7 7 8 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 8 8 9 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 9 9 10 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 10 10 11 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 11 11 12 37853629000000 2.1e+11 0.00063878 1;
element zeroLengthSection 12 12 13 1
puts "Element details provided"
#Eigen Values: #Displays 4 fundamental periods
set Lambda [eigen -fullGenLapack 4]
puts "Lambda Omega Period"
foreach Lambda $Lambda {
if {$Lambda > 0.0} {
set Omega [expr pow($Lambda,0.5)]
set Period [expr (2*3.14)/$Omega]
puts "$Lambda $Omega $Period"}}
********************************************
VERSION 2 (15 nodes)
-----------------------------
wipe;
model basic -ndm 2 -ndf 3 # Basic 2D model having 3 degrees-of-freedom per node.
#Node details: #Node no., X-coord., Y-coord.
node 1 0 0
node 2 0 0
node 3 0 0
node 4 4 0
node 5 8 0
node 6 12 0
node 7 16 0
node 8 20 0
node 9 24 0
node 10 28 0
node 11 32 0
node 12 36 0
node 13 40 0
node 14 40 0
node 15 40 0
puts "Node defined"
#Boundary Conditions: #Node no., DX, DY, RZ
fix 1 1 1 1
fix 2 1 0 1
fix 3 1 0 0
fix 13 1 0 0
fix 14 1 0 1
fix 15 1 1 1
#Slaving node: #Master node no., Slave node no., dofs to be coupled
equalDOF 2 3 2
equalDOF 14 13 2
puts "Boundary Conditions assigned"
#Nodal mass: #Node no., MX(translational), MY(translational), MZ(rotational)
mass 2 0. 0.00509683995922528 0.
mass 4 0. 0.0101936799184506 0.
mass 5 0. 0.0101936799184506 0.
mass 6 0. 0.0101936799184506 0.
mass 7 0. 0.0101936799184506 0.
mass 8 0. 0.0101936799184506 0.
mass 9 0. 0.0101936799184506 0.
mass 10 0. 0.0101936799184506 0.
mass 11 0. 0.0101936799184506 0.
mass 12 0. 0.0101936799184506 0.
mass 14 0. 0.00509683995922528 0.
puts "Nodal Masses defined"
#Specifying material: #Material Tag, Stiffness value
uniaxialMaterial Elastic 1 8.0486
puts "Spring stiffnesses defined"
#Section details: #Section Tag, Material Tag, Axial force deformation (use "P")
section Uniaxial 1 1 P
puts "Section forcolumn defined"
#Coordinate Tranformation:
geomTransf Linear 1
#Element details: #Element Tag, Nodei, Nodej (both nodes at same coordinate), Section Tag
element zeroLengthSection 1 1 2 1
# connectivity: (make A very large, 10e6 times its actual value)
# element elasticBeamColumn $eleTag $iNode $jNode $A $E $Iz $transfTag
element elasticBeamColumn 2 3 4 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 3 4 5 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 4 5 6 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 5 6 7 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 6 7 8 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 7 8 9 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 8 9 10 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 9 10 11 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 10 11 12 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 11 12 13 37853629000000 2.1e+11 0.00063878 1;
element zeroLengthSection 12 14 15 1
puts "Element details provided"
#Eigen Values: #Displays 4 fundamental periods
set Lambda [eigen -fullGenLapack 4]
puts "Lambda Omega Period"
foreach Lambda $Lambda {
if {$Lambda > 0.0} {
set Omega [expr pow($Lambda,0.5)]
set Period [expr (2*3.14)/$Omega]
puts "$Lambda $Omega $Period"}}
*******************************************
Please tell me which one is the right approach and what is going wrong?
Thanks for your help.
Thanks for your comments.
Sorry for not providing more details. I have also posted another query under subject "Distributed-mass model" with some details about the problem. I am still awaiting your response for that problem
I am modelling a single storey, single bay structure. I have assumed the length of the beam as 40m and divided the beam into 10 elements. I have assumed unit weight, and lumped the mass accordingly at the nodes. I have modelled the columns as springs. I set a target period of 0.5s and worked out the storey stiffnesses (taken in the below codes).
Before trying out complex problems I wanted to confirm if I can get the same 0.5s in Opensees. I have verified this problem and obtained 0.5s in SAP. So, I tried to work on this problem in Opensees:-) Early days for me....
I have made some changes as told by you, but I am unable to figure out again what is going wrong...iam not getting 0.5s. I have below 2 versions ( one with 13 nodes and the other with 15 nodes). Could you please look at them and make comments to make it run in the right way?
********************************************
VERSION 1 (13 nodes)
------------------------------
wipe;
model basic -ndm 2 -ndf 3 # Basic 2D model having 3 degrees-of-freedom per node.
#Node details: #Node no., X-coord., Y-coord.
node 1 0 0
node 2 0 0
node 3 4 0
node 4 8 0
node 5 12 0
node 6 16 0
node 7 20 0
node 8 24 0
node 9 28 0
node 10 32 0
node 11 36 0
node 12 40 0
node 13 40 0
puts "Node defined"
#Boundary Conditions: #Node no., DX, DY, RZ
fix 1 1 1 1
fix 2 1 0 1
fix 12 1 0 1
fix 13 1 1 1
puts "Boundary Conditions assigned"
#Nodal mass: #Node no., MX(translational), MY(translational), MZ(rotational)
mass 2 0. 0.00509683995922528 0.
mass 3 0. 0.0101936799184506 0.
mass 4 0. 0.0101936799184506 0.
mass 5 0. 0.0101936799184506 0.
mass 6 0. 0.0101936799184506 0.
mass 7 0. 0.0101936799184506 0.
mass 8 0. 0.0101936799184506 0.
mass 9 0. 0.0101936799184506 0.
mass 10 0. 0.0101936799184506 0.
mass 11 0. 0.0101936799184506 0.
mass 12 0. 0.00509683995922528 0.
puts "Nodal Masses defined"
#Specifying material: #Material Tag, Stiffness value
uniaxialMaterial Elastic 1 8.0486
puts "Spring stiffnesses defined"
#Section details: #Section Tag, Material Tag, Axial force deformation (use "P")
section Uniaxial 1 1 P
puts "Section forcolumn defined"
#Coordinate Tranformation:
geomTransf Linear 1
#Element details: #Element Tag, Nodei, Nodej (both nodes at same coordinate), Section Tag
element zeroLengthSection 1 1 2 1
# connectivity: (make A very large, 10e6 times its actual value)
# element elasticBeamColumn $eleTag $iNode $jNode $A $E $Iz $transfTag
element elasticBeamColumn 2 2 3 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 3 3 4 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 4 4 5 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 5 5 6 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 6 6 7 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 7 7 8 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 8 8 9 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 9 9 10 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 10 10 11 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 11 11 12 37853629000000 2.1e+11 0.00063878 1;
element zeroLengthSection 12 12 13 1
puts "Element details provided"
#Eigen Values: #Displays 4 fundamental periods
set Lambda [eigen -fullGenLapack 4]
puts "Lambda Omega Period"
foreach Lambda $Lambda {
if {$Lambda > 0.0} {
set Omega [expr pow($Lambda,0.5)]
set Period [expr (2*3.14)/$Omega]
puts "$Lambda $Omega $Period"}}
********************************************
VERSION 2 (15 nodes)
-----------------------------
wipe;
model basic -ndm 2 -ndf 3 # Basic 2D model having 3 degrees-of-freedom per node.
#Node details: #Node no., X-coord., Y-coord.
node 1 0 0
node 2 0 0
node 3 0 0
node 4 4 0
node 5 8 0
node 6 12 0
node 7 16 0
node 8 20 0
node 9 24 0
node 10 28 0
node 11 32 0
node 12 36 0
node 13 40 0
node 14 40 0
node 15 40 0
puts "Node defined"
#Boundary Conditions: #Node no., DX, DY, RZ
fix 1 1 1 1
fix 2 1 0 1
fix 3 1 0 0
fix 13 1 0 0
fix 14 1 0 1
fix 15 1 1 1
#Slaving node: #Master node no., Slave node no., dofs to be coupled
equalDOF 2 3 2
equalDOF 14 13 2
puts "Boundary Conditions assigned"
#Nodal mass: #Node no., MX(translational), MY(translational), MZ(rotational)
mass 2 0. 0.00509683995922528 0.
mass 4 0. 0.0101936799184506 0.
mass 5 0. 0.0101936799184506 0.
mass 6 0. 0.0101936799184506 0.
mass 7 0. 0.0101936799184506 0.
mass 8 0. 0.0101936799184506 0.
mass 9 0. 0.0101936799184506 0.
mass 10 0. 0.0101936799184506 0.
mass 11 0. 0.0101936799184506 0.
mass 12 0. 0.0101936799184506 0.
mass 14 0. 0.00509683995922528 0.
puts "Nodal Masses defined"
#Specifying material: #Material Tag, Stiffness value
uniaxialMaterial Elastic 1 8.0486
puts "Spring stiffnesses defined"
#Section details: #Section Tag, Material Tag, Axial force deformation (use "P")
section Uniaxial 1 1 P
puts "Section forcolumn defined"
#Coordinate Tranformation:
geomTransf Linear 1
#Element details: #Element Tag, Nodei, Nodej (both nodes at same coordinate), Section Tag
element zeroLengthSection 1 1 2 1
# connectivity: (make A very large, 10e6 times its actual value)
# element elasticBeamColumn $eleTag $iNode $jNode $A $E $Iz $transfTag
element elasticBeamColumn 2 3 4 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 3 4 5 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 4 5 6 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 5 6 7 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 6 7 8 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 7 8 9 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 8 9 10 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 9 10 11 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 10 11 12 37853629000000 2.1e+11 0.00063878 1;
element elasticBeamColumn 11 12 13 37853629000000 2.1e+11 0.00063878 1;
element zeroLengthSection 12 14 15 1
puts "Element details provided"
#Eigen Values: #Displays 4 fundamental periods
set Lambda [eigen -fullGenLapack 4]
puts "Lambda Omega Period"
foreach Lambda $Lambda {
if {$Lambda > 0.0} {
set Omega [expr pow($Lambda,0.5)]
set Period [expr (2*3.14)/$Omega]
puts "$Lambda $Omega $Period"}}
*******************************************
Please tell me which one is the right approach and what is going wrong?
Thanks for your help.
you need to fix your model:
1) the zero length needs to act in the 2 direction and not 1(x) direction., use a zeroLength with a uniaxial material acting in the 2 dirn.
2) your choice of arguments A,E,I and the spring are such that when you do figure out your spring, you will find that you still have a singular system! .. i.e. the beam terms are of order e8, are numerically far greater the spring term 8.0, so numerically it's as if the spring is not there. matlab reports a condition number of e20.
1) the zero length needs to act in the 2 direction and not 1(x) direction., use a zeroLength with a uniaxial material acting in the 2 dirn.
2) your choice of arguments A,E,I and the spring are such that when you do figure out your spring, you will find that you still have a singular system! .. i.e. the beam terms are of order e8, are numerically far greater the spring term 8.0, so numerically it's as if the spring is not there. matlab reports a condition number of e20.
Hi Frank,
Thanks for your reply. I have modified my code by defining the beam in Y direction and the spring in X direction. The below code gave me 0.5s as fundamental period.
I am trying to do dynamic time-history analysis and I have couple of questions. Could you please answer these for me:
1. Does the ground motion input file need to start with a zero value?
2. I am needing the maximum force in the spring and the maximum bending moment at the centre of the beam.
When I ask for element envelope for a element; I am getting 3 rows by 12 columns of values. (a) What are these values representing in case of global forces and local forces?
When I ask for element results for the same element I am getting 7 columns of values. I know the 1st column is time-step. (b) what are the other columns representing?
As mentioned above, I am also wanting maximum force in the spring. But, the element recorder for spring element considering "global" gives just one column of time-step values. Whereas the "local" gives 2 columns of results. (c) What does the second column represent? (d) Can we obtain the envelope results too?
I am confused (and may have confused you too - sorry about it). Could you please have a look at my below example and suggest? I am also putting the ground motion input (from file "latha.eqf") at the end.
*********************************
[code]
wipe;
model basic -ndm 2 -ndf 3 # Basic 2D model having 3 degrees-of-freedom per node.
#Node details: #Node no., X-coord., Y-coord.
node 1 0 0
node 2 0 0
node 3 0 0
node 4 0 4
node 5 0 8
node 6 0 12
node 7 0 16
node 8 0 20
node 9 0 24
node 10 0 28
node 11 0 32
node 12 0 36
node 13 0 40
node 14 0 40
node 15 0 40
puts "Node defined"
#Boundary Conditions: #Node no., DX, DY, RZ
fix 1 1 1 1
fix 2 0 1 1
fix 3 0 1 0
fix 13 0 1 0
fix 14 0 1 1
fix 15 1 1 1
#Slaving node: #Master node no., Slave node no., dofs to be coupled
equalDOF 2 3 1
equalDOF 14 13 1
puts "Boundary Conditions assigned"
#Nodal mass: #Node no., MX(translational), MY(translational), MZ(rotational)
mass 2 0.00509683995922528 0. 0.
mass 4 0.0101936799184506 0. 0.
mass 5 0.0101936799184506 0. 0.
mass 6 0.0101936799184506 0. 0.
mass 7 0.0101936799184506 0. 0.
mass 8 0.0101936799184506 0. 0.
mass 9 0.0101936799184506 0. 0.
mass 10 0.0101936799184506 0. 0.
mass 11 0.0101936799184506 0. 0.
mass 12 0.0101936799184506 0. 0.
mass 14 0.00509683995922528 0. 0.
puts "Nodal Masses defined"
#Specifying material: #Material Tag, Stiffness value
uniaxialMaterial Elastic 1 8.049
puts "Spring stiffnesses defined"
#Section details: #Section Tag, Material Tag, Axial force deformation (use "P")
section Uniaxial 1 1 P
puts "Section forcolumn defined"
#Coordinate Tranformation:
geomTransf Linear 1
#Element details: #Element Tag, Nodei, Nodej (both nodes at same coordinate), Section Tag
element zeroLengthSection 1 1 2 1
# connectivity: (make A very large, 10e6 times its actual value)
# element elasticBeamColumn $eleTag $iNode $jNode $A $E $Iz $transfTag
element elasticBeamColumn 2 3 4 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 3 4 5 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 4 5 6 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 5 6 7 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 6 7 8 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 7 8 9 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 8 9 10 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 9 10 11 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 10 11 12 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 11 12 13 1 2.1e+11 0.0006388 1;
element zeroLengthSection 12 14 15 1
puts "Element details provided"
#Eigen Values: #Displays 4 fundamental periods
set Lambda [eigen -fullGenLapack 10]
puts "Lambda Omega Period"
foreach Lambda $Lambda {
if {$Lambda > 0.0} {
set Omega [expr pow($Lambda,0.5)]
set Period [expr (2*3.14)/$Omega]
puts "$Lambda $Omega $Period"}}
recorder Node -file Noddisp.txt -time -node 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -dof 1 disp
recorder EnvelopeNode -file EnvNoddisp.txt -node 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -dof 1 disp
recorder Element -file DiaGLOB_max.txt -time -ele 7 globalForce
recorder Element -file DiaLOC_max.txt -time -ele 7 localForce
recorder EnvelopeElement -file DiaGLOB_env.txt -time -ele 7 globalForce
recorder EnvelopeElement -file DiaLOC_env.txt -time -ele 7 localForce
recorder Element -file SpringForceLOC_max.txt -time -ele 1 localForce
recorder Element -file SpringForceGLOB_max.txt -time -ele 1 globalForce
set xDamp 0.05; # 2% damping ratio
set nEigenI 1; # mode 1
set nEigenJ 10; # mode 3
set lambdaN [eigen [expr $nEigenJ]]; # eigenvalue analysis for nEigenJ modes
set lambdaI [lindex $lambdaN [expr $nEigenI-1]]; # eigenvalue mode i
set lambdaJ [lindex $lambdaN [expr $nEigenJ-1]]; # eigenvalue mode j
set omegaI [expr pow($lambdaI,0.5)];
set omegaJ [expr pow($lambdaJ,0.5)];
set alphaM [expr $xDamp*((2.*$omegaI*$omegaJ)/($omegaI+$omegaJ))]; # K-prop. damping parameter; +betaKcomm*KlastCommitt
set betaK [expr 2.*$xDamp/($omegaI+$omegaJ)]; # K-prop. damping parameter; +betaKcomm*KlastCommitt
puts "alphaM = $alphaM"
puts "betaK = $betaK"
# DYNAMIC ground-motion analysis -------------------------------------------------------------
# create load pattern
set accelSeries "Series -dt 0.02 -filePath latha.eqf -factor 0.01"; # define acceleration vector from file (dt=0.01 is associated with the input file gm)
pattern UniformExcitation 2 1 -accel $accelSeries; # define where and how (pattern tag, dof) acceleration is applied
rayleigh $alphaM 0. $betaK 0.; # set damping based on first eigen mode
# create the analysis
wipeAnalysis; # clear previously-define analysis parameters
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 1.0e-8 30; # 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
integrator Newmark 0.5 0.25 ; # determine the next time step for an analysis
analysis Transient; # define type of analysis: time-dependent
analyze 15000 0.001; # apply 1000 0.001-sec time steps in analysis
puts "Done!"
*********************************
[Ground motion input in cm/sec/sec]
0
-0.92392
-1.4775
-5.2594
-20.215
-43.705
-38.304
36.794
67.573
61.588
-24.736
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76.595
124.09
125.72
2.8275
-204.4
-183.28
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72.633
144.86
116.02
37.666
-42.59
-94.343
30.5
115.78
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12.537
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120.3
97.989
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-76.865
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-226.85
19.572
122.76
53.302
46.99
169.47
275.57
182.78
88.979
8.0709
134.81
100.02
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-80.783
94.115
-11.646
-37.958
49.868
32.54
32.946
83.683
19.45
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119.58
62.148
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1.1398
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120.79
148.84
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35.18
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92.592
224.82
269.52
108.15
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25.182
157.05
268.16
299.64
396.28
449.49
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450.21
403.02
346.99
422.91
442.37
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388.06
309.91
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207.33
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74.232
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5.0686
5.9267
6.5142
6.1559
8.5175
10.458
5.3896
2.2236
4.2645
2.5139
2.9358
3.1649
3.6246
0.27627
0.3375
2.3909
-3.2222
-3.4838
-5.1566
-0.71886
0.13312
-2.7392
-0.53464
-4.6504
-3.0981
-3.7475
3.7059
0.34923
-1.8499
3.7917
2.3916
0.56373
1.3886
3.8281
0.60574
0.53733
-1.0641
-4.8148
-4.315
0.38516
4.4668
9.1334
2.1785
-5.6529
-5.6897
-7.7272
-5.2938
-1.9482
-6.7179
-5.3016
-6.2883
-3.9094
-3.8476
0.15026
1.185
0.94066
3.2966
-2.5446
1.4911
0.29267
-1.6754
-5.1175
-4.7873
-11.553
-3.5268
3.2371
2.0744
3.2414
-7.3032
-7.107
-4.2497
1.7552
2.1191
2.9403
0.72925
-3.3986
1.0085
3.8428
-0.88049
1.2786
1.7728
-4.6533
3.6291
11.238
4.8459
1.1397
5.6077
1.0418
-3.5367
4.3201
5.4727
-1.7605
0.2414
1.8177
-0.47496
6.5638
7.8594
1.3412
-8.5595
-8.1239
-4.1968
-3.9227
0.77817
1.8113
1.5361
0.97977
3.3781
4.2688
6.9083
6.9707
4.5439
3.2264
4.5008
6.1737
6.2549
3.7568
-5.4495
-1.5182
4.1641
5.7551
3.0852
-2.9128
-5.459
-5.3925
-5.8564
-7.0963
-4.1191
-4.1993
-3.9587
4.4875
1.2051
-3.1487
-3.0445
0.46744
0.1796
-1.9683
-3.1642
-3.2024
-3.5281
-3.2099
1.2876
-4.4168
-1.9954
-2.233
1.52
3.0397
4.1212
1.8033
-2.1439
0.29005
-0.35236
5.5018
3.4922
5.104
2.8323
-0.30562
5.387
-3.1255
-3.8434
-3.7205
-0.99106
3.7201
5.0948
5.5217
3.3672
5.738
5.217
7.0027
6.9786
3.3561
4.1835
5.8935
0.3899
9.7687
16.985
-6.846
-21.993
-9.7736
2.9433
-4.4792
-10.505
-12.74
-10.162
-7.4734
2.13
23.702
47.59
39.618
3.6359
0.25174
-11.629
-32.666
-26.764
-7.019
6.5764
10.416
7.7679
-9.1611
-12.025
-2.6432
-10.91
-15.794
4.3501
8.4559
-3.2538
17.257
18.275
-3.1056
-4.5886
0.79195
3.138
9.6361
3.6612
-17.726
-15.654
-1.6945
-5.6963
2.9907
5.133
13.612
17.06
-1.7776
0.6579
1.7828
-0.53988
-12.345
-13.234
2.1883
13.89
-10.682
-15.37
5.5159
-5.1785
-15.014
-2.6681
13.25
-0.76403
2.6518
2.6391
-7.02
-3.749
-0.77173
2.3397
3.9979
3.691
-10.949
-11.801
1.0379
2.6807
-4.3305
5.7297
8.7355
-0.98961
-4.0715
-2.4899
-5.9642
-8.1468
-3.0089
1.7074
7.4634
7.1996
6.8008
4.5862
-1.3528
1.7566
0.56279
-5.6368
-8.6903
-6.5818
4.5375
4.2596
1.3751
1.6862
7.1619
10.814
8.266
10.25
1.5124
-12.481
-17.138
-9.566
-10.525
-11.481
1.0206
2.4522
6.5889
11.002
14.313
2.2578
-2.8412
0.94247
-9.9301
-4.846
-0.87003
-7.8884
-14.452
-1.3416
2.674
1.2646
6.1606
-0.27988
2.7474
7.7269
3.4753
-6.8661
-10.392
-5.7973
-8.2902
5.2946
13.718
8.7698
9.4324
-0.30024
-3.0896
-4.7929
-4.6531
-6.1071
1.5984
-0.43481
-1.8117
5.0293
3.1655
3.9732
1.8009
1.3836
-4.8321
-2.9955
-10.434
-8.6732
-7.3847
-7.4397
0.65754
2.8392
3.9239
5.2413
5.1408
2.7252
4.2874
5.8724
8.0653
-0.37774
-0.72246
1.4658
0.57552
-3.7834
-1.4489
0.31721
-7.8589
-8.4713
-0.58443
6.4904
6.536
7.4684
4.8421
2.7985
-5.5279
-6.5045
1.9153
1.0997
-1.9661
2.6891
6.3752
**********************
Thank you for your time.
Thanks for your reply. I have modified my code by defining the beam in Y direction and the spring in X direction. The below code gave me 0.5s as fundamental period.
I am trying to do dynamic time-history analysis and I have couple of questions. Could you please answer these for me:
1. Does the ground motion input file need to start with a zero value?
2. I am needing the maximum force in the spring and the maximum bending moment at the centre of the beam.
When I ask for element envelope for a element; I am getting 3 rows by 12 columns of values. (a) What are these values representing in case of global forces and local forces?
When I ask for element results for the same element I am getting 7 columns of values. I know the 1st column is time-step. (b) what are the other columns representing?
As mentioned above, I am also wanting maximum force in the spring. But, the element recorder for spring element considering "global" gives just one column of time-step values. Whereas the "local" gives 2 columns of results. (c) What does the second column represent? (d) Can we obtain the envelope results too?
I am confused (and may have confused you too - sorry about it). Could you please have a look at my below example and suggest? I am also putting the ground motion input (from file "latha.eqf") at the end.
*********************************
[code]
wipe;
model basic -ndm 2 -ndf 3 # Basic 2D model having 3 degrees-of-freedom per node.
#Node details: #Node no., X-coord., Y-coord.
node 1 0 0
node 2 0 0
node 3 0 0
node 4 0 4
node 5 0 8
node 6 0 12
node 7 0 16
node 8 0 20
node 9 0 24
node 10 0 28
node 11 0 32
node 12 0 36
node 13 0 40
node 14 0 40
node 15 0 40
puts "Node defined"
#Boundary Conditions: #Node no., DX, DY, RZ
fix 1 1 1 1
fix 2 0 1 1
fix 3 0 1 0
fix 13 0 1 0
fix 14 0 1 1
fix 15 1 1 1
#Slaving node: #Master node no., Slave node no., dofs to be coupled
equalDOF 2 3 1
equalDOF 14 13 1
puts "Boundary Conditions assigned"
#Nodal mass: #Node no., MX(translational), MY(translational), MZ(rotational)
mass 2 0.00509683995922528 0. 0.
mass 4 0.0101936799184506 0. 0.
mass 5 0.0101936799184506 0. 0.
mass 6 0.0101936799184506 0. 0.
mass 7 0.0101936799184506 0. 0.
mass 8 0.0101936799184506 0. 0.
mass 9 0.0101936799184506 0. 0.
mass 10 0.0101936799184506 0. 0.
mass 11 0.0101936799184506 0. 0.
mass 12 0.0101936799184506 0. 0.
mass 14 0.00509683995922528 0. 0.
puts "Nodal Masses defined"
#Specifying material: #Material Tag, Stiffness value
uniaxialMaterial Elastic 1 8.049
puts "Spring stiffnesses defined"
#Section details: #Section Tag, Material Tag, Axial force deformation (use "P")
section Uniaxial 1 1 P
puts "Section forcolumn defined"
#Coordinate Tranformation:
geomTransf Linear 1
#Element details: #Element Tag, Nodei, Nodej (both nodes at same coordinate), Section Tag
element zeroLengthSection 1 1 2 1
# connectivity: (make A very large, 10e6 times its actual value)
# element elasticBeamColumn $eleTag $iNode $jNode $A $E $Iz $transfTag
element elasticBeamColumn 2 3 4 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 3 4 5 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 4 5 6 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 5 6 7 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 6 7 8 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 7 8 9 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 8 9 10 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 9 10 11 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 10 11 12 1 2.1e+11 0.0006388 1;
element elasticBeamColumn 11 12 13 1 2.1e+11 0.0006388 1;
element zeroLengthSection 12 14 15 1
puts "Element details provided"
#Eigen Values: #Displays 4 fundamental periods
set Lambda [eigen -fullGenLapack 10]
puts "Lambda Omega Period"
foreach Lambda $Lambda {
if {$Lambda > 0.0} {
set Omega [expr pow($Lambda,0.5)]
set Period [expr (2*3.14)/$Omega]
puts "$Lambda $Omega $Period"}}
recorder Node -file Noddisp.txt -time -node 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -dof 1 disp
recorder EnvelopeNode -file EnvNoddisp.txt -node 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -dof 1 disp
recorder Element -file DiaGLOB_max.txt -time -ele 7 globalForce
recorder Element -file DiaLOC_max.txt -time -ele 7 localForce
recorder EnvelopeElement -file DiaGLOB_env.txt -time -ele 7 globalForce
recorder EnvelopeElement -file DiaLOC_env.txt -time -ele 7 localForce
recorder Element -file SpringForceLOC_max.txt -time -ele 1 localForce
recorder Element -file SpringForceGLOB_max.txt -time -ele 1 globalForce
set xDamp 0.05; # 2% damping ratio
set nEigenI 1; # mode 1
set nEigenJ 10; # mode 3
set lambdaN [eigen [expr $nEigenJ]]; # eigenvalue analysis for nEigenJ modes
set lambdaI [lindex $lambdaN [expr $nEigenI-1]]; # eigenvalue mode i
set lambdaJ [lindex $lambdaN [expr $nEigenJ-1]]; # eigenvalue mode j
set omegaI [expr pow($lambdaI,0.5)];
set omegaJ [expr pow($lambdaJ,0.5)];
set alphaM [expr $xDamp*((2.*$omegaI*$omegaJ)/($omegaI+$omegaJ))]; # K-prop. damping parameter; +betaKcomm*KlastCommitt
set betaK [expr 2.*$xDamp/($omegaI+$omegaJ)]; # K-prop. damping parameter; +betaKcomm*KlastCommitt
puts "alphaM = $alphaM"
puts "betaK = $betaK"
# DYNAMIC ground-motion analysis -------------------------------------------------------------
# create load pattern
set accelSeries "Series -dt 0.02 -filePath latha.eqf -factor 0.01"; # define acceleration vector from file (dt=0.01 is associated with the input file gm)
pattern UniformExcitation 2 1 -accel $accelSeries; # define where and how (pattern tag, dof) acceleration is applied
rayleigh $alphaM 0. $betaK 0.; # set damping based on first eigen mode
# create the analysis
wipeAnalysis; # clear previously-define analysis parameters
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 1.0e-8 30; # 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
integrator Newmark 0.5 0.25 ; # determine the next time step for an analysis
analysis Transient; # define type of analysis: time-dependent
analyze 15000 0.001; # apply 1000 0.001-sec time steps in analysis
puts "Done!"
*********************************
[Ground motion input in cm/sec/sec]
0
-0.92392
-1.4775
-5.2594
-20.215
-43.705
-38.304
36.794
67.573
61.588
-24.736
-153.69
-222.63
-179.5
76.595
124.09
125.72
2.8275
-204.4
-183.28
-73.988
72.633
144.86
116.02
37.666
-42.59
-94.343
30.5
115.78
-104.45
-98.441
12.537
-138.07
-58.57
120.3
97.989
-196.55
-216.88
-78.038
-120.89
-74.814
-76.865
-138.07
-226.85
19.572
122.76
53.302
46.99
169.47
275.57
182.78
88.979
8.0709
134.81
100.02
-104.9
-80.783
94.115
-11.646
-37.958
49.868
32.54
32.946
83.683
19.45
-359.13
-329.9
-158.82
-212.07
-157.63
119.58
62.148
-84.892
-49.13
-13.969
1.1398
51.199
155.05
81.515
120.79
148.84
135.34
35.18
-64.024
92.592
224.82
269.52
108.15
-234.87
-277.86
-172.33
-106.47
9.3812
25.182
157.05
268.16
299.64
396.28
449.49
447.85
450.21
403.02
346.99
422.91
442.37
392.37
388.06
309.91
169.61
147.36
41.86
91.854
209.09
207.33
49.066
-165.53
-286.45
-682.88
-360.38
-49.907
-402.68
-353.04
-435.8
-588.54
-545.52
-410.61
-189.7
-36.911
-91.571
-356.24
-165.82
-50.424
-269.92
-412.99
-290.65
-496.82
-653.35
-220.08
294.03
831.74
967.61
229.44
-484.96
-539.26
-546.98
-20.252
351.64
163.81
-163.51
-469.9
-612.82
-467.74
44.979
356.66
374.39
428.44
441.28
555.49
468.41
-44.125
-28.649
44.216
-271.9
-339.47
-368.01
-459.68
-688.7
-621.08
-45.75
400.02
610.9
663.89
741.02
690.62
356.45
51.793
-23.957
26.163
167.95
-4.331
-347.96
-105.71
225.87
215.28
72.505
-85.489
-161.35
-163.55
-41.189
219.62
362.27
372.77
267.65
-177.14
-526.99
-555.52
-605.12
-472.21
185.82
454.42
459.12
587.8
631.11
564.87
49.248
-521.46
-833.21
-753.31
-469.14
-162.44
16.439
-28.648
152.11
424.74
465.2
85.151
-428.37
-573.44
-629.64
-490.6
-162.08
55.925
254.96
496.49
567.18
424.59
93.487
-324.54
-205.1
20.159
30.165
-35.143
49.328
302.68
377.14
513.06
603.19
541.15
153.09
-424.07
-538.26
-308.14
-105.2
39.407
140.06
105.15
-41.599
-198.45
-327.43
-275.99
-186.24
-190.3
56.264
296.84
107.28
-148.54
-212.73
-6.8067
228.86
269.61
198.98
-46.758
-94.809
-92.646
-205.65
-185.98
-199.73
-236.44
-305.53
-332.65
-233.8
-113.35
-75.109
-88.643
-29.55
-0.42437
9.0014
105.45
125.27
61.158
13.372
-68.751
-80.808
40.828
2.6806
-12.53
74.232
77.598
140.45
180.98
196.18
269.56
349.34
387.37
347.21
299.86
275.01
226.79
240.81
150.23
-46.632
-254.66
-492.83
-554.42
-377.11
-103.8
129.02
160.15
-196.94
-650
-704.65
-617.18
-355.96
372.32
627.29
547.53
546.35
304.71
103.72
199.25
244.42
10.479
-192
-260.62
-284.74
-182.38
57.719
100.76
30.606
-63.262
-160.35
-47.746
95.093
-17.34
-194.11
-250.06
-272.96
-127.02
193.98
268.5
279.96
269.69
210.99
253.52
202.34
38.144
-60.739
-95.513
-118.45
-102.46
-94.733
-141.47
-177.33
-107.94
32.504
190.29
212.49
68.897
-77.291
-172.58
-163.14
-5.6322
111.36
121.75
83.092
73.258
19.199
-3.7116
98.26
147.42
96.312
-22.811
-84.232
-49.024
13.265
-33.68
-150.64
-159.22
-110.79
-73.995
40.281
85.469
16.661
-28.72
2.2302
40.988
32.376
48.264
17.299
-38.533
-11.343
11.644
-38.944
-54.359
-76.235
-134.02
-203.53
-208.62
-248.55
-181.3
16.109
62.204
45.665
29.748
48.027
105.93
169.19
221.31
234.86
175.58
147.78
162.01
130.95
56.653
13.291
24.814
21.908
0.56138
-58.527
-133.54
-192.54
-209.68
-147.77
-138.37
-140.09
-77.495
-25.102
-44.107
-54.244
5.1774
50.86
73.003
125.36
175.98
147.86
126.8
158.13
127.91
27.659
-18.85
-18.081
16.075
64.417
81.52
65.107
28.671
41.726
47.056
-43.214
-142.82
-214.59
-252.25
-205.4
-136.29
-84.004
-68.174
-57.905
-98.591
-90.652
1.125
-19.222
-10.151
18.843
61.772
112.88
100.02
91.167
115.93
78.315
4.6011
-18.523
17.516
78
88.581
87.003
97.104
132.15
136.41
76.904
41.334
69.973
86.943
77.254
7.2407
-72.425
-133.81
-185.98
-125.38
-71.88
-100.12
-131.84
-154.27
-171.11
-148.67
-137.03
-120.97
-110.16
-62.109
32.282
70.612
68.976
62.931
75.571
83.154
130.71
163.04
129.92
35.498
33.601
63.963
53.585
44.845
36.458
45.999
38.781
52.102
38.523
-39.485
-97.155
-51.208
-29.598
-50.909
-40.989
-37.409
-38.677
18.655
33.381
-5.9298
-26.832
-72.623
-80.112
-25.145
-2.6926
-13.952
13.009
-4.447
-77.547
-84.342
-77.463
-41.838
-4.3951
26.663
74.167
44.724
44.778
101.73
112.93
26.827
2.5378
25.165
-20.823
-5.9531
13.646
-5.6243
19.035
55.149
55.151
16.87
16.853
64.864
58.019
-35.867
-59.747
-22.993
15.776
32.546
16.836
9.4494
-19.081
-31.276
-26.029
-7.8279
14.197
-10.983
-52.768
-87.567
-82.681
-67.428
-101.89
-100.4
-76.272
-21.733
19.665
1.6723
10.042
29.262
33.309
33.884
34.632
40.958
14.396
4.0008
27.157
29.703
-11.866
-52.755
14.449
93.998
76.621
13.145
-11.48
17.277
14.798
-16.165
-30.992
-30.796
-32.646
-37.89
-23.279
-1.1208
2.8977
0.2736
0.94395
-20.044
-27.331
15.276
51.683
48.663
28.8
18.072
6.8469
-4.6245
10.284
27.317
14.072
32.872
53.472
29.015
-7.9224
-35.273
-50.729
-53.721
-48.578
-39.883
-44.507
-35.91
-7.5391
5.5077
-4.4159
1.9757
22.68
2.0577
-0.25803
11.937
24.483
10.156
-25.811
-13.269
9.529
21.991
-9.4583
-41.923
6.7168
28.566
35.27
38.205
21.181
9.4377
9.1267
25.252
19.614
23.4
35.687
45.572
28.19
18.367
37.023
25.921
23.151
-1.0677
-10.201
24.208
29.989
14.933
-11.979
-31.474
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