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# Multi Modal Response Spectrum Analysis Implemented in OpenSees

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Presentation @ University of Porto during the OpenSees Days Portugal 2014 workshop

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### Multi Modal Response Spectrum Analysis Implemented in OpenSees

1. 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
2. 2. 2 7/11/2014 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
3. 3. 3 7/11/2014 TDK konferencia 2011 2014.07.04. OpenSeesDays-Porto Introduction Response spectrum analysis: Mostwidelyused Well-known Relativelyfast(comparedtoothermethods) Suitableforparametricstudyorsensitivityanalysis Linearmethod,but Canbeusedwithnon-linearelements(effectivestiffnessanditerativesolution) Overestimates(generally)theinternalforces Thus,givesanupperlimitfortheresponses
4. 4. 27/01114/2.0071.404. OTpDeKn kSoenefseDreanysci-a P2o0r1t1o 4 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
5. 5. 5 7/11/2014 TDK konferencia 2011 2014.07.04. 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
6. 6. 6 7/11/2014 TDK konferencia 2011 2014.07.04. 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
7. 7. 7 7/11/2014 TDK konferencia 2011 2014.07.04. OpenSeesDays-Porto RSA modul in OpenSees Output: Globalvariables Globalcoordinatesystem!!(displacementsandforcesaswell) 3·3=9globallistvariablesfordisplacements 3·2·6=36globallistvariablesforelementinternalforces
8. 8. 8 7/11/2014 TDK konferencia 2011 2014.07.04. OpenSeesDays-Porto Ex.1 -Equivalent linear analysis of girder bridges with seismic isolators EC8-2Section7 1.Non-linearbehaviorapproximatedbybi-linearcharacteristic. NLTHA 2.Equivalentlinearstiffnessandeffectivedamping. LRSA ITERATION NEEDED!! ξ = ?? •EC -AASHTO •JPWRI •CALTRANS 94 •CALTRANS 96 Fivestandard methods: Continousgirderbridges Withisolationbearinginthelongitudinaldirection Comparisonoftwoanalysismethods(non-linearelements!)
9. 9. 9 7/11/2014 TDK konferencia 2011 2014.07.04. OpenSeesDays-Porto Ex.1 -Equivalent linear analysis of girder bridges with seismic isolators ThreedimensionalnumericalmodelinOpenSees No energy dissipation is expected in the piers!!
10. 10. 10 7/11/2014 TDK konferencia 2011 2014.07.04. OpenSeesDays-Porto Ex.1 -Equivalent linear analysis of girder bridges with seismic isolators In TCL (automatic iteration) with RSA
11. 11. 11 7/11/2014 TDK konferencia 2011 2014.07.04. OpenSeesDays-Porto 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%
12. 12. 27/01114/2.0071.404. OTpDeKn kSoenefseDreanysci-a P2o0r1t1o 12 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!
13. 13. 13 7/11/2014 TDK konferencia 2011 2014.07.04. 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!!!
14. 14. 14 7/11/2014 TDK konferencia 2011 2014.07.04. OpenSeesDays-Porto Superstructure: ElasticBeamColoumn Pier: ElasticBeamColoumn Abutments: ElasticBeamColoumn Rigid links Rigid links Foundation and backfill: linear springs Ex.3 –Parametric seismic analysis of multi-girder bridges
15. 15. 27/01114/2.0071.404. OTpDeKn kSoenefseDreanysci-a P2o0r1t1o 15 Ex.3 – Parametric seismic analysis of multi-girder bridges Superstructure Abutments Backfill soil Superstructure-abutment Superstructure-pier joints Piers Pier foundations Hp (m) 4 8 12 16 20 24 2 0.56 1.13 1.77 2.11 3.04 3.73 6 0.47 0.85 1.27 1.75 2.27 2.98 10 0.64 0.94 1.26 1.63 2.10 2.68 14 1.31 1.60 1.80 2.15 2.62 3.05 Támaszköz méterben Critical components at longer bridges Components found to be adequate Spans (m) D/C ratio for piers (4 span bridges)
16. 16. 16 7/11/2014 TDK konferencia 2011 2014.07.04. OpenSeesDays-Porto Concluding remarks Response spectrum analysis: Linearmethod,but Canbeusedwithnon-linearelements(Ex.1) Overestimates(generally)theinternalforces Thus,givesanupperlimitfortheresponses(Ex.2) Relativelyquick, Suitableforparametricstudyorsensitivityanalysis(Ex.3) Alsoitprovidessolidbasefor: detailedseismicassessment retrofitplanning developmentofdesignconceptsfornewbridges
17. 17. 17 7/11/2014 TDK konferencia 2011 2014.07.04. OpenSeesDays-Porto Concluding remarks RSA should be implemented in the soure code: Massmatrixcanbeconstructedevenwithdiscontinuous, unlumpedmasses Duringthecombinationoftheresponses,theelementtypecanberecognizedandspecificresponsescanbequeried, stored Anystructurecanbeanalyzedin2Dor3Daswell
18. 18. 18 7/11/2014 TDK konferencia 2011 Thank you for your attention! Acknowledgement : This presentationwas supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.