The OpenSees Community

Hi Frank,

As per your suggestion I used truss elements for the 3 supports that I am using in my problem of 2 equal span structure.

While the case of a structure with I = 3.9e-6 for the beam elements (representing a rigid case) is producing the same period as I have got in other programs, I am not getting the set period for beam I = 1.5969e-9 (representing a flexible case). I should be getting 0.8336s. I know you mentioned about "poorly conditioned system", but in my problem my support stiffnesses and diaphragm properties are calculated to produce the set period. I am also looking at the maximum diaphragm moments.

Can you please suggest how I should fix this problem to get the period of 0.8336s?
**********************
[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 0
node 2 1.0 0
node 3 1.0 5
node 4 1.0 10
node 5 1.0 15
node 6 1.0 20
node 7 1.0 25
node 8 1.0 30
node 9 1.0 35
node 10 1.0 40
node 11 0.0 40
node 12 0.0 20

puts "Node defined"

#Boundary Conditions: #Node no., DX, DY, RZ
fix 1 1 1 1
fix 11 1 1 1
fix 12 1 1 1
fix 2 0 1 0
fix 10 0 1 0
fix 6 0 1 0

puts "Boundary Conditions assigned"

#Nodal mass: #Node no., MX(translational), MY(translational), MZ(rotational)
mass 2 0.0063710499490316 0.0 0.0
mass 3 0.0127420998980632 0.0 0.0
mass 4 0.0127420998980632 0.0 0.0
mass 5 0.0127420998980632 0.0 0.0
mass 6 0.0127420998980632 0.0 0.0
mass 7 0.0127420998980632 0.0 0.0
mass 8 0.0127420998980632 0.0 0.0
mass 9 0.0127420998980632 0.0 0.0
mass 10 0.0063710499490316 0.0 0.0

puts "Nodal Masses defined"

#Specifying material: #Material Tag, Stiffness value
uniaxialMaterial Elastic 1 4.0243
uniaxialMaterial Elastic 2 8.0486

puts "Spring stiffnesses defined"

#Section details: #Section Tag, Material Tag, Axial force deformation (use "P")
section Uniaxial 1 1 P
section Uniaxial 2 2 P

puts "Section forcolumn defined"

#Coordinate Tranformation:
geomTransf Linear 1

#Element details:
#element trussSection $elemTag $Nodei $Nodej $secTag
element trussSection 1 1 2 1

# element elasticBeamColumn $eleTag $iNode $jNode $A $E $Iz $transfTag
element elasticBeamColumn 2 2 3 1.0 2.1e+11 1.5969e-9 1;
element elasticBeamColumn 3 3 4 1.0 2.1e+11 1.5969e-9 1;
element elasticBeamColumn 4 4 5 1.0 2.1e+11 1.5969e-9 1;
element elasticBeamColumn 5 5 6 1.0 2.1e+11 1.5969e-9 1;
element elasticBeamColumn 6 6 7 1.0 2.1e+11 1.5969e-9 1;
element elasticBeamColumn 7 7 8 1.0 2.1e+11 1.5969e-9 1;
element elasticBeamColumn 8 8 9 1.0 2.1e+11 1.5969e-9 1;
element elasticBeamColumn 9 9 10 1.0 2.1e+11 1.5969e-9 1;

element trussSection 10 11 10 1
element trussSection 11 12 6 2

puts "Element details provided"

#Eigen Values: #Displays 4 fundamental periods
set Lambda [eigen -fullGenLapack 8]
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"}}

puts "Done!"

[/code]
****************

Thanks.

Thanks Frank.

I have validated a single span structure (that i was asking questions earlier) and a two span with no pin connection at the mid-span. I have got Opensees, SAP give same results (modal analysis).

The only change in the above problem is the pin connection at the mid-span, and I am not too sure how I should be doing in Opensees. So, with the zerolength element having high rotational stiffness b/w 7 and 16, and the same elements used for earlier problems (that have worked), i should have got correct results. Why am I not getting?

I also vaguely remember you mentioning in an earlier question that a slave node used for equalDOF should not be used as a master node for equalDOF? In my case I am doing:

equalDOF 14 7 1
equalDOF 7 16 1 2

Is this OK?

Does Opensees assume master nodes in equalDOF have boundary conditions as "fix 1 1 1"?

Thanks.

Still no joy

I have also tried with an zerolength element connecting Node 16 (dummy node @mid-span) and 7 (beam node @ mid-span) with a high rotational stiffness. I am getting 0.773s as the period. Below is the code for this case.

Without the element b/w Nodes 16 and 7 I am getting 1.036s. The target period that I should be getting is 0.8336s. Quite frustrated as not able to fix the problem. Any help please.
*****************************
[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 5
node 5 0 10
node 6 0 15
node 7 0 20
node 8 0 25
node 9 0 30
node 10 0 35
node 11 0 40
node 12 0 40
node 13 0 40
node 14 0 20
node 15 0 20
node 16 0 20

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 11 0 1 0
fix 12 0 1 1
fix 13 1 1 1
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 12 11 1
equalDOF 14 7 1
equalDOF 7 16 1 2


puts "Boundary Conditions assigned"

#Nodal mass: #Node no., MX(translational), MY(translational), MZ(rotational)
mass 2 0.0063710499490316 0.0 0.0
mass 4 0.0127420998980632 0.0 0.0
mass 5 0.0127420998980632 0.0 0.0
mass 6 0.0127420998980632 0.0 0.0
mass 14 0.0127420998980632 0.0 0.0
mass 8 0.0127420998980632 0.0 0.0
mass 9 0.0127420998980632 0.0 0.0
mass 10 0.0127420998980632 0.0 0.0
mass 12 0.0063710499490316 0.0 0.0


puts "Nodal Masses defined"

#Specifying material: #Material Tag, Stiffness value
uniaxialMaterial Elastic 1 4.0243
uniaxialMaterial Elastic 2 8.0486

uniaxialMaterial Elastic 3 100000000.00

puts "Spring stiffnesses defined"

#Section details: #Section Tag, Material Tag, Axial force deformation (use "P")
section Uniaxial 1 1 P
section Uniaxial 2 2 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

# element elasticBeamColumn $eleTag $iNode $jNode $A $E $Iz $transfTag
element elasticBeamColumn 2 3 4 1 2.1e+11 1.5969e-009 1;
element elasticBeamColumn 3 4 5 1 2.1e+11 1.5969e-009 1;
element elasticBeamColumn 4 5 6 1 2.1e+11 1.5969e-009 1;
element elasticBeamColumn 5 6 7 1 2.1e+11 1.5969e-009 1;
element elasticBeamColumn 6 7 8 1 2.1e+11 1.5969e-009 1;
element elasticBeamColumn 7 8 9 1 2.1e+11 1.5969e-009 1;
element elasticBeamColumn 8 9 10 1 2.1e+11 1.5969e-009 1;
element elasticBeamColumn 9 10 11 1 2.1e+11 1.5969e-009 1;
element zeroLengthSection 10 12 13 1
element zeroLengthSection 11 15 14 2
element zeroLength 12 7 16 -mat 3 -dir 6

puts "Element details provided"

#Eigen Values: #Displays 4 fundamental periods
set Lambda [eigen -fullGenLapack 8]
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"}}

puts "Done!"

[/code]
******************************
Thanks

Thanks Frank.

Node 16 is the dummy node at the mid-span. Node 7 is the mid-span node on the beam. I saw in some of the forum questions, and the suggestion was to have this dummy node (Node 16).

Node 14 and 15 define the zero length element section for the central spring at the same mid-span.

P.S- Node 15 is fixed and not 14 as mentioned in my last message.

Thanks Frank, and I am sorry to keep bugging you with stupid questions.

The node 1 is fixed and is connected to node 2 by Element 1, as above.

Element 11 (for central spring) is connecting nodes 14 (fixed) and 15, defined by section tag 2.

*******
I have 2 equal spans, with end supports modelled as springs (zero length element section). The central support (also modelled as a spring) has twice the end-support stiffness.

I need to have a pinned connection at the central support. This should give same support displacement in the 1st mode. So, could you please tell me how my connection (where the 2 beams and the spring meet) be defined? What should I be doing?

Thanks so much.

Can I get some help for the above please? Thanks.

Hello Frank;

I am having some trouble getting the below code to run properly. The example below is a 2 span single storey structure having supports modelled by springs. I want to have a pinned connection at the centre (defined by Node 7). I was hoping the below code was correct, but it looks like there is somehting wrong. I have verified the same problem in SAP and another software, and I get fundamental period of 0.8336s in both the softwares. Could anyone please suggest what I need to correct?

*****************************
[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 5
node 5 0 10
node 6 0 15
node 7 0 20
node 8 0 25
node 9 0 30
node 10 0 35
node 11 0 40
node 12 0 40
node 13 0 40
node 14 0 20
node 15 0 20
node 16 0 20

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 11 0 1 0
fix 12 0 1 1
fix 13 1 1 1
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 12 11 1
equalDOF 14 7 1
equalDOF 7 16 1 2

puts "Boundary Conditions assigned"

#Nodal mass: #Node no., MX(translational), MY(translational), MZ(rotational)
mass 2 0.0063710499490316 0. 0.
mass 4 0.0127420998980632 0. 0.
mass 5 0.0127420998980632 0. 0.
mass 6 0.0127420998980632 0. 0.
mass 14 0.0127420998980632 0. 0.
mass 8 0.0127420998980632 0. 0.
mass 9 0.0127420998980632 0. 0.
mass 10 0.0127420998980632 0. 0.
mass 12 0.0063710499490316 0. 0.


puts "Nodal Masses defined"

#Specifying material: #Material Tag, Stiffness value
uniaxialMaterial Elastic 1 4.0243
uniaxialMaterial Elastic 2 8.0486
puts "Spring stiffnesses defined"

#Section details: #Section Tag, Material Tag, Axial force deformation (use "P")
section Uniaxial 1 1 P
section Uniaxial 2 2 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 1.5969e-009 1;
element elasticBeamColumn 3 4 5 1 2.1e+11 1.5969e-009 1;
element elasticBeamColumn 4 5 6 1 2.1e+11 1.5969e-009 1;
element elasticBeamColumn 5 6 7 1 2.1e+11 1.5969e-009 1;
element elasticBeamColumn 6 7 8 1 2.1e+11 1.5969e-009 1;
element elasticBeamColumn 7 8 9 1 2.1e+11 1.5969e-009 1;
element elasticBeamColumn 8 9 10 1 2.1e+11 1.5969e-009 1;
element elasticBeamColumn 9 10 11 1 2.1e+11 1.5969e-009 1;
element zeroLengthSection 10 12 13 1
element zeroLengthSection 11 15 14 2

puts "Element details provided"

#Eigen Values: #Displays 4 fundamental periods
set Lambda [eigen -fullGenLapack 8]
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"}}

puts "Done!"
***********************************

Thanks

Thanks Frank. I have answered my questions myself - was really tired and a night's sleep helped me the next morning



I have used Rayleigh damping, but is there an option for providing constant damping for all the modes?

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
-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
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**********************

Thank you for your time.

Can somebody help with the above please?

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.

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.

Hi fmk,

I am working on a 1 storey high problem where I am modelling columns as springs and the diaphragm as a beam. I have assumed mass and storey stiffness values to get a fundamental period of 0.5s. I checked this in SAP too and I am getting 0.5s.

I am trying the same example in Opensees and not quite getting the same 0.5s. I may be doing something wrong. Could you please correct me? The code is as below -

*****************************
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"

#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"

#Section details for beam:
section Elastic 2 2.1e+11 37853629000000 0.00063878
puts "Beam sections defined"

#Coordinate Tranformation:
geomTransf Linear 1

#Element details: #Element Tag, Nodei, Nodej, no. of iteration points, Section tag, Coordinate transformation tag, -mass (mass/unit length)
#Element details: #Element Tag, Nodei, Nodej (both nodes at same coordinate), Section Tag
element zeroLengthSection 1 1 2 1
element forceBeamColumn 2 3 4 8 2 1 -mass 0.00254841997961264
element forceBeamColumn 3 4 5 8 2 1 -mass 0.00254841997961264
element forceBeamColumn 4 5 6 8 2 1 -mass 0.00254841997961264
element forceBeamColumn 5 6 7 8 2 1 -mass 0.00254841997961264
element forceBeamColumn 6 7 8 8 2 1 -mass 0.00254841997961264
element forceBeamColumn 7 8 9 8 2 1 -mass 0.00254841997961264
element forceBeamColumn 8 9 10 8 2 1 -mass 0.00254841997961264
element forceBeamColumn 9 10 11 8 2 1 -mass 0.00254841997961264
element forceBeamColumn 10 11 12 8 2 1 -mass 0.00254841997961264
element forceBeamColumn 11 12 13 8 2 1 -mass 0.00254841997961264
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 note that:
(1) The results are senstive to the value of $numIntrgrPts (used for beam element). This may be one reason? What should be the right value please?
(2) Following the manual example, I have given a very high value for the beam c/s area. Is this OK?

Thanks for your time.

Thanks fmk. I have posted the same query in the other forum (feedback/suggestions) to remind you..