In this video, Prof. Terje RΓΈlvΓ₯g discusses how you calculate and apply mass and stiffness proportional (Rayleigh) damping to FE models. He also explains why you should be careful with mass proportional damping!!πππ
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Let me close todayβs discussion with a novel suggestion to keep in mind while you are using a convergence algorithm for time history analysis.
From my own perspective, best priorities for analysis parameters are as mentioned below, to achieve appreciable convergence:
1- Changing Solution Algorithm
a) Trying Newton with Initial Tangent
b) Trying Broyden
c) Trying NewtonWithLineSearch
2- Trying reducing the time step by 2: dtanalysisnew=[expr
$DtAnalysis/2]
3- Trying reducing the time step by 10: dtanalysisnew=[expr
$DtAnalysis/10]
4- Trying reducing the time step by 100: dtanalysisnew=[expr
$DtAnalysis/100]
5- Try the previous methods with the smaller timestep:
a) Trying Newton with Initial Tangent
b) Trying Broyden
c) Trying NewtonWithLineSearchπππ
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From my own perspective, best priorities for analysis parameters are as mentioned below, to achieve appreciable convergence:
1- Changing Solution Algorithm
a) Trying Newton with Initial Tangent
b) Trying Broyden
c) Trying NewtonWithLineSearch
2- Trying reducing the time step by 2: dtanalysisnew=[expr
$DtAnalysis/2]
3- Trying reducing the time step by 10: dtanalysisnew=[expr
$DtAnalysis/10]
4- Trying reducing the time step by 100: dtanalysisnew=[expr
$DtAnalysis/100]
5- Try the previous methods with the smaller timestep:
a) Trying Newton with Initial Tangent
b) Trying Broyden
c) Trying NewtonWithLineSearchπππ
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As i mentioned, a little while ago, sometimes we are going to accomplish three-dimensional simulation of a bridge that has a continuous concrete deck with the bents being integral, and the dual-column bent caps for the bridge are supported by reinforced concrete columns.
Following figure indicates the sample of first vertical bending mode shape of mentioned bridge with period of 0.33 sec.πππ
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Following figure indicates the sample of first vertical bending mode shape of mentioned bridge with period of 0.33 sec.πππ
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This figure indicates the sample of first rotational mode shape of mentioned bridge with period of 0.31 sec.πππ
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This figure indicates the sample of first twisting mode shape of mentioned bridge with period of 0.26 sec.πππ
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In this video, Prof. David Garber introduces the Performance-Based Design methodology.πππ
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Professor Stephen William Hawking has passed away. He was an English theoretical physicist, cosmologist, author and Director of Research at the Centre for Theoretical Cosmology within the University of Cambridge. His scientific works included a collaboration with Roger Penrose on gravitational singularity theorems in the framework of general relativity and the theoretical prediction that black holes emit radiation, often called Hawking radiation. Hawking was the first to set out a theory of cosmology explained by a union of the general theory of relativity and quantum mechanics. He was a vigorous supporter of the many-worlds interpretation of quantum mechanics. Hawking was an Honorary Fellow of the Royal Society of Arts (FRSA), a lifetime member of the Pontifical Academy of Sciences, and a recipient of the Presidential Medal of Freedom, the highest civilian award in the United States. In 2002, Hawking was ranked number 25 in the BBC's poll of the 100 Greatest Britons. He was the Lucasian Professor of Mathematicsat the University of Cambridge between 1979 and 2009 and achieved commercial success with works of popular science in which he discusses his own theories and cosmology in general.
May peace be on him and condolences to his dear family, colleagues and the scientifics community at large for this loss.πππ
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May peace be on him and condolences to his dear family, colleagues and the scientifics community at large for this loss.πππ
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Self Centering Viscoelastic Dampers (SCVDs) devised by (Karavasilis, Blakeborough et al. 2011). SCVDs are attained from series combination of viscoelastic (VE) dampers and self-centering (SC) device. The behavior of VE part is represented by generalized Maxwell which is combination of springs and dashpots. SC part consists of a pretensioning elastic tendon and a friction-based part. Under small amplitudes of deformation the SC part is inactive and SCVDs acts as a VE damper. Under large amplitudes of deformation the SC part is activated and SCVDs behaves as a hysteretic damper. Indeed, the VE part acts as an energy dissipating device and the SC part eliminates the residual drifts and inelastic deformations. Following figure indicates the SCVDs model.πππ
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Which types of content do you prefer to study in this channel? Your votes help admins to growth of the channel Contents.
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Professional Tcl Language examples about different structures β 46
πππππππ 53%
New algorithms to develop professional Code-Writing β 25
ππππ 29%
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Professional Tcl Language examples about different structures β 46
πππππππ 53%
New algorithms to develop professional Code-Writing β 25
ππππ 29%
Video cources about earthquake engineering concepts β 12
ππ 14%
Discussing about users big wrongs in programming β 4
π 5%
π₯ 87 people voted so far. Poll closed.
As i accounted for some details about Self Centering Viscoelastic Dampers (SCVDs) devised by (Karavasilis, Blakeborough et al. 2011) a little while ago, take example 5 for instance:πππ
(Part 1);
wipe ;
# Units: Kips, Inch, Sec ;
model BasicBuilder -ndm 2 -ndf 3; # Define the model builder, ndm = # dimension, ndf = # dofs ;
source DisplayModel2D.tcl; # procedure for displaying a
2D perspective of model
source DisplayPlane.tcl; # procedure for displaying a
plane in a model
####################################
# Define Building Geometry, Nodes, and Constraints
####################################
# define structure-geometry parameters
set NStories 5; # number of stories
set NBays 3; # number of frame bays
set WBay 158; # bay width in Inch
set HStory1 197; # 1st story height in Inch
set HStoryTyp 158; # story height of other stories in Inch
set HBuilding [expr $HStory1 + ($NStories-1)*$HStoryTyp]; # height of building ;
# calculate nodal masses -- lump floor masses at frame nodes
set g 386; # acceleration due to gravity
set Floor2Weight 900; # weight of Floor 2 in Kips
set Floor3Weight 900; # weight of Floor 3 in Kips
set Floor4Weight 900; # weight of Floor 4 in Kips
set Floor5Weight 900; # weight of Floor 5 in Kips
set Floor6Weight 700; # weight of Floor 6 in Kips
set WBuilding [expr $Floor2Weight + $Floor3Weight + $Floor4Weight + $Floor5Weight + $Floor6Weight];# total building weight ;
set NodalMass2 [expr ($Floor2Weight/$g) / (4.0)]; # mass at each node on Floor 2 ;
set NodalMass3 [expr ($Floor3Weight/$g) / (4.0)]; # mass at each node on Floor 3 ;
set NodalMass4 [expr ($Floor4Weight/$g) / (4.0)]; # mass at each node on Floor 4 ;
set NodalMass5 [expr ($Floor5Weight/$g) / (4.0)]; # mass at each node on Floor 5 ;
set NodalMass6 [expr ($Floor6Weight/$g) / (4.0)]; # mass at each node on Floor 6 ;
set Negligible 1e-9; # a very smnumber to avoid problems with zero ;
# define nodes and assign masses to beam-column intersections of frame
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(Part 1);
wipe ;
# Units: Kips, Inch, Sec ;
model BasicBuilder -ndm 2 -ndf 3; # Define the model builder, ndm = # dimension, ndf = # dofs ;
source DisplayModel2D.tcl; # procedure for displaying a
2D perspective of model
source DisplayPlane.tcl; # procedure for displaying a
plane in a model
####################################
# Define Building Geometry, Nodes, and Constraints
####################################
# define structure-geometry parameters
set NStories 5; # number of stories
set NBays 3; # number of frame bays
set WBay 158; # bay width in Inch
set HStory1 197; # 1st story height in Inch
set HStoryTyp 158; # story height of other stories in Inch
set HBuilding [expr $HStory1 + ($NStories-1)*$HStoryTyp]; # height of building ;
# calculate nodal masses -- lump floor masses at frame nodes
set g 386; # acceleration due to gravity
set Floor2Weight 900; # weight of Floor 2 in Kips
set Floor3Weight 900; # weight of Floor 3 in Kips
set Floor4Weight 900; # weight of Floor 4 in Kips
set Floor5Weight 900; # weight of Floor 5 in Kips
set Floor6Weight 700; # weight of Floor 6 in Kips
set WBuilding [expr $Floor2Weight + $Floor3Weight + $Floor4Weight + $Floor5Weight + $Floor6Weight];# total building weight ;
set NodalMass2 [expr ($Floor2Weight/$g) / (4.0)]; # mass at each node on Floor 2 ;
set NodalMass3 [expr ($Floor3Weight/$g) / (4.0)]; # mass at each node on Floor 3 ;
set NodalMass4 [expr ($Floor4Weight/$g) / (4.0)]; # mass at each node on Floor 4 ;
set NodalMass5 [expr ($Floor5Weight/$g) / (4.0)]; # mass at each node on Floor 5 ;
set NodalMass6 [expr ($Floor6Weight/$g) / (4.0)]; # mass at each node on Floor 6 ;
set Negligible 1e-9; # a very smnumber to avoid problems with zero ;
# define nodes and assign masses to beam-column intersections of frame
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Self Centering Viscoelastic Dampers (SCVDs), (Part 2);
# command: node nodeID xcoord ycoord -mass mass_dof1 mass_dof2 mass_dof3
# nodeID convention#
node 11 0 0;
node 21 160 0;
node 31 320 0;
node 41 480 0;
node 12 0 200 -mass $NodalMass2 $Negligible $Negligible;
node 22 160 200 -mass $NodalMass2 $Negligible $Negligible;
node 32 320 200 -mass $NodalMass2 $Negligible $Negligible;
node 42 480 200 -mass $NodalMass2 $Negligible $Negligible;
node 201 240 200;
node 202 240 200;
.
.
.
.
node 16 0 840 -mass $NodalMass6 $Negligible $Negligible;
node 26 160 840 -mass $NodalMass6 $Negligible $Negligible;
node 36 320 840 -mass $NodalMass6 $Negligible $Negligible;
node 46 480 840 -mass $NodalMass6 $Negligible $Negligible;
node 601 240 840;
node 602 240 840;
# constrain beam-column joints in a floor to have the same lateral displacement using the "equalDOF" command
# command: equalDOF $MasterNodeID $SlaveNodeID $dof1 $dof2...
set dof1 1; # constrain movement in dof 1 (x-direction)
equalDOF 12 22 $dof1; # Floor 2: Pier 1 to Pier 2
equalDOF 12 32 $dof1; # Floor 2: Pier 1 to Pier 3
equalDOF 12 42 $dof1; # Floor 2: Pier 1 to Pier 4
.
.
.
equalDOF 16 26 $dof1; # Floor 6: Pier 1 to Pier 2
equalDOF 16 36 $dof1; # Floor 6: Pier 1 to Pier 3
equalDOF 16 46 $dof1; # Floor 6: Pier 1 to Pier 4
# assign boundary condidtions
# command: fix nodeID dxFixity dyFixity rzFixity
# fixity values: 1 = constrained; 0 = unconstrained
# fix the base of the building;
fix 11 1 1 1;
fix 21 1 1 1;
fix 31 1 1 1;
fix 41 1 1 1;
##################
# Define Section Properties and Elements
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# command: node nodeID xcoord ycoord -mass mass_dof1 mass_dof2 mass_dof3
# nodeID convention#
node 11 0 0;
node 21 160 0;
node 31 320 0;
node 41 480 0;
node 12 0 200 -mass $NodalMass2 $Negligible $Negligible;
node 22 160 200 -mass $NodalMass2 $Negligible $Negligible;
node 32 320 200 -mass $NodalMass2 $Negligible $Negligible;
node 42 480 200 -mass $NodalMass2 $Negligible $Negligible;
node 201 240 200;
node 202 240 200;
.
.
.
.
node 16 0 840 -mass $NodalMass6 $Negligible $Negligible;
node 26 160 840 -mass $NodalMass6 $Negligible $Negligible;
node 36 320 840 -mass $NodalMass6 $Negligible $Negligible;
node 46 480 840 -mass $NodalMass6 $Negligible $Negligible;
node 601 240 840;
node 602 240 840;
# constrain beam-column joints in a floor to have the same lateral displacement using the "equalDOF" command
# command: equalDOF $MasterNodeID $SlaveNodeID $dof1 $dof2...
set dof1 1; # constrain movement in dof 1 (x-direction)
equalDOF 12 22 $dof1; # Floor 2: Pier 1 to Pier 2
equalDOF 12 32 $dof1; # Floor 2: Pier 1 to Pier 3
equalDOF 12 42 $dof1; # Floor 2: Pier 1 to Pier 4
.
.
.
equalDOF 16 26 $dof1; # Floor 6: Pier 1 to Pier 2
equalDOF 16 36 $dof1; # Floor 6: Pier 1 to Pier 3
equalDOF 16 46 $dof1; # Floor 6: Pier 1 to Pier 4
# assign boundary condidtions
# command: fix nodeID dxFixity dyFixity rzFixity
# fixity values: 1 = constrained; 0 = unconstrained
# fix the base of the building;
fix 11 1 1 1;
fix 21 1 1 1;
fix 31 1 1 1;
fix 41 1 1 1;
##################
# Define Section Properties and Elements
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Self Centering Viscoelastic Dampers (SCVDs), (Part 3);
###### Material for Beams&Columns Elements ;
uniaxialMaterial Steel02 77 42.06 29e3 0.020
uniaxialMaterial Elastic 78 5.8e3 0.2
# Columns Story 1&2&3 , W14 x 145
section Fiber 21 {
.
.
}
# Columns Story 4&5 , W14 x 74
section Fiber 22 {
.
.
}
# Beams Story 1 , W21 x 83
section Fiber 23 {
.
.
}
# Beams Story 2&3 , W21 x 73
section Fiber 24 {
.
.
}
# Beams Story 4 , W18 x 60
section Fiber 25 {
.
.
}
# Beams Story 5 , W18 x 50
section Fiber 26 {
.
.
}
# however, it is done here simply for illustrative purposes.
# set up geometric transformations of element
geomTransf Corotational 1; # Corotational transformation
geomTransf PDelta 2; # PDelta transformation
# define nonlinear column elements using "element" command
# command: element nonlinearBeamColumn $eleID $iNode $jNode $numintgrpts
$Sectag $transfTag
# Columns Story 1
element nonlinearBeamColumn 101 11 12 5 21 2;
element nonlinearBeamColumn 102 21 22 5 21 2;
element nonlinearBeamColumn 103 31 32 5 21 2;
element nonlinearBeamColumn 104 41 42 5 21 2;
.
.
# Columns Story 5
element nonlinearBeamColumn 501 15 16 5 22 2;
element nonlinearBeamColumn 502 25 26 5 22 2;
element nonlinearBeamColumn 503 35 36 5 22 2;
element nonlinearBeamColumn 504 45 46 5 22 2;
# define nonlinear beam elements
# Beams Story 1
element nonlinearBeamColumn 1001 12 22 5 23 2;
element nonlinearBeamColumn 1002 22 201 5 23 2;
element zeroLength 1003 201 202 -mat 78 -dir 1;
element nonlinearBeamColumn 1004 202 32 5 23 2;
element nonlinearBeamColumn 1005 32 42 5 23 2;
.
.
# Beams Story 5
element nonlinearBeamColumn 5001 16 26 5 26 2;
element nonlinearBeamColumn 5002 26 601 5 26 2;
element zeroLength 5003 601 602 -mat 78 -dir 1;
element nonlinearBeamColumn 5004 602 36 5 26 2;
element nonlinearBeamColumn 5005 36 46 5 26 2;
element corotTruss 901 21 201 30 77;
element corotTruss 902 31 202 30 77;
element corotTruss 903 22 301 30 77;
element corotTruss 904 32 302 30 77;
element corotTruss 905 23 401 30 77;
element corotTruss 906 33 402 30 77;
element corotTruss 907 24 501 30 77;
element corotTruss 908 34 502 30 77;
element corotTruss 909 25 601 30 77;
element corotTruss 910 35 602 30 77;
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###### Material for Beams&Columns Elements ;
uniaxialMaterial Steel02 77 42.06 29e3 0.020
uniaxialMaterial Elastic 78 5.8e3 0.2
# Columns Story 1&2&3 , W14 x 145
section Fiber 21 {
.
.
}
# Columns Story 4&5 , W14 x 74
section Fiber 22 {
.
.
}
# Beams Story 1 , W21 x 83
section Fiber 23 {
.
.
}
# Beams Story 2&3 , W21 x 73
section Fiber 24 {
.
.
}
# Beams Story 4 , W18 x 60
section Fiber 25 {
.
.
}
# Beams Story 5 , W18 x 50
section Fiber 26 {
.
.
}
# however, it is done here simply for illustrative purposes.
# set up geometric transformations of element
geomTransf Corotational 1; # Corotational transformation
geomTransf PDelta 2; # PDelta transformation
# define nonlinear column elements using "element" command
# command: element nonlinearBeamColumn $eleID $iNode $jNode $numintgrpts
$Sectag $transfTag
# Columns Story 1
element nonlinearBeamColumn 101 11 12 5 21 2;
element nonlinearBeamColumn 102 21 22 5 21 2;
element nonlinearBeamColumn 103 31 32 5 21 2;
element nonlinearBeamColumn 104 41 42 5 21 2;
.
.
# Columns Story 5
element nonlinearBeamColumn 501 15 16 5 22 2;
element nonlinearBeamColumn 502 25 26 5 22 2;
element nonlinearBeamColumn 503 35 36 5 22 2;
element nonlinearBeamColumn 504 45 46 5 22 2;
# define nonlinear beam elements
# Beams Story 1
element nonlinearBeamColumn 1001 12 22 5 23 2;
element nonlinearBeamColumn 1002 22 201 5 23 2;
element zeroLength 1003 201 202 -mat 78 -dir 1;
element nonlinearBeamColumn 1004 202 32 5 23 2;
element nonlinearBeamColumn 1005 32 42 5 23 2;
.
.
# Beams Story 5
element nonlinearBeamColumn 5001 16 26 5 26 2;
element nonlinearBeamColumn 5002 26 601 5 26 2;
element zeroLength 5003 601 602 -mat 78 -dir 1;
element nonlinearBeamColumn 5004 602 36 5 26 2;
element nonlinearBeamColumn 5005 36 46 5 26 2;
element corotTruss 901 21 201 30 77;
element corotTruss 902 31 202 30 77;
element corotTruss 903 22 301 30 77;
element corotTruss 904 32 302 30 77;
element corotTruss 905 23 401 30 77;
element corotTruss 906 33 402 30 77;
element corotTruss 907 24 501 30 77;
element corotTruss 908 34 502 30 77;
element corotTruss 909 25 601 30 77;
element corotTruss 910 35 602 30 77;
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