Multi Modal Response Spectrum Analysis Implemented in OpenSees
1. Budapest University of Technology and Economics
Department of Structural Engineering
Multi modal response spectrum analysis implemented in OpenSEES
OpenSeesDays Portugal
July03-04, 2014, Porto
József Simon
László Gergely Vigh
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TDK konferencia 2011
2014.07.04.
OpenSeesDays-Porto
Introduction
Research project:
Seismic analysis of bridges in moderate seismic regions
Database of existing bridges
Pre-Eurocode era –lack of seismic design
Seismic behavior is not known
Thousands of structures
Parametric study to recognize vulnerable configurations
Fast analysis method is needed
Multi modal response spectrum analysis
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풑푖 = 풎 휱푖
휱푖
푇풎 휾
휱푖
푇풎 휱푖
푆푑 푇푖
Theoretical background
Response spectrum analysis:
• Based on modal analysis (eigenvectors and eigenvalues)
• Importance of a mode characterized by the modal mass:
푚푖
∗ =
휱푖
푇풎 휾 2
휱푖
푇풎 휱푖
• Load vector for each mode:
• Quasi-static loading, static analysis
• Combination of the responses from each mode:
퐸퐴퐵푆푆푈푀 = 퐸푖 , 퐸푆푅푆푆 = 퐸푖 ퟐ , 퐸퐶푄퐶 = 퐸푖 휌푖푗 퐸푗
풊 풋
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OpenSeesDays-Porto
RSA modul in OpenSees
proc RSA{agsoiltype eqtype ξ q qdsumtype elelist nodelist}
WritteninTCL
3Danalysisofanystructure
agpeakgroundacceleration[m/s2]
soiltype(A,B,C,DorE)
eqtype(1or2)
ξdampingratio
qbehaviorfactor
qdneededtocalculatedisplacements
sumtype(ABSSUM,SRSS,CQC)comb.method
elelist
nodelist
Defines the shape of the standard spectrum
Only results of listed nodes and elements are stored and combined
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OpenSeesDays-Porto
RSA modul in OpenSees
Modalanalysis>eigencommand(Φi)
Massmatrixcompilation>nodeMasscommand(m)
Note: mass has to be defined in nodes!
Modalmasscalculation(m* i)
Necessarynumberofmodes(e.g.90%rule)
Loadvectorcompilation(pi)
Staticanalyses
Storingresponses(nodelistandeleslist)
Note: only eleResponse$e_num forces!
Combinationofresponses(sumtype)
Combinedresponses>globalvariables
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RSA modul in OpenSees
Output:
Globalvariables
Globalcoordinatesystem!!(displacementsandforcesaswell)
3·3=9globallistvariablesfordisplacements
3·2·6=36globallistvariablesforelementinternalforces
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OpenSeesDays-Porto
Ex.1 -Equivalent linear analysis of girder bridges with seismic isolators
ThreedimensionalnumericalmodelinOpenSees
No energy dissipation is expected in the piers!!
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Ex.1 -Equivalent linear analysis of girder bridges with seismic isolators
In TCL (automatic iteration) with RSA
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Ex.1 -Equivalent linear analysis of girder bridges with seismic isolators
Threecontinousgirderbridges(concrete,composite,steel)
Onlyonefixed/isolationbearing!
Twosoiltypes(C,E),twopeakgroundacc.(1.0and1.4m/s2)
C
ag=1.4 m/s2
Compared to NLTHA:
The accuracy of the internal forces (pier moments, isolator forces) is ±25%
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Ex.2 - Seismic assessment of M0 Highway bridge at Háros, Hungary
0
50
100
150
200
250
300
350
P2 P3 P4 P5 P6 P7 P8 P9
Mx longitudinal moments [MNm]
Pier number
RSA
THA
Comparison of RSA and LTHA
results
Upper-limit for the responses!
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OpenSeesDays-Porto
Ex.3 –Parametric seismic analysis of multi-girder bridges
Number of supports:2-5
Spans: 4-8-12-16-20-24 m
Outer/inner span ratio: 0.75-1.00
Pier height:2-6-10-14 m
Pier cap cross-section:1.20x1.00 m
Pier:0.60x0.90 m
Abutment:1.00x2.00 m (14 m wide)
Number of piers in the lateral direction:4 (distributed in every 3 m)
Piles:D=80 cm 1x5 (abutment) –2x5 (piers)
Fixed parameters:
Nearly half of the higher level road bridges!!!
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Superstructure: ElasticBeamColoumn
Pier: ElasticBeamColoumn
Abutments: ElasticBeamColoumn
Rigid links
Rigid links
Foundation and backfill: linear springs
Ex.3 –Parametric seismic analysis of multi-girder bridges
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Concluding remarks
RSA should be implemented in the soure code:
Massmatrixcanbeconstructedevenwithdiscontinuous, unlumpedmasses
Duringthecombinationoftheresponses,theelementtypecanberecognizedandspecificresponsescanbequeried, stored
Anystructurecanbeanalyzedin2Dor3Daswell
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Thank you for your attention!
Acknowledgement :
This presentationwas supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.