Pinned connection

openc · Post by **openc** » Mon Apr 26, 2010 1:53 am

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?

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[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

openc · Post by **openc** » Mon Apr 26, 2010 4:45 pm

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

Post by **fmk** » Tue Apr 27, 2010 3:59 pm

as i told you before you need to fix this model .. it's obviously messed up, e.g. node 1 is totally fixed and not connected to anything, element 11 connected to 14 and 15 in dirn 2 which is fixed at both nodes. i am not going to waste time trying to figure out what you are trying to do. the opensees results for the eigenvalues are correct for the model you input. if they differ from another program it is because the models are different or numerical problems exist due to nearly singular matrices.

openc · Post by **openc** » Tue Apr 27, 2010 4:19 pm

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.

Post by **fmk** » Tue Apr 27, 2010 4:30 pm

what is node 16 for? don't see it connected using any element.

openc · Post by **openc** » Tue Apr 27, 2010 4:37 pm

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.

openc · Post by **openc** » Wed Apr 28, 2010 12:15 am

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

openc · Post by **openc** » Thu Apr 29, 2010 1:03 am

Still no joy

Post by **fmk** » Thu Apr 29, 2010 11:33 am

you put an element for the rotation at 16 .. you take it out .. without the rotational spring for node 16 the system is singular (the system matrix has a zero on the diag because the rotational dof has no element proving a stiffness term for it!) .. the terms you put in for the beam column element 2.1e11 1.5e-9 make the system when it is present poorly conditioned and are of such proportions one would wonder why you are not just using truss elements .. one has to ask if you know what you are doing????

openc · Post by **openc** » Thu Apr 29, 2010 2:00 pm

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.