Task NA 3.6Preparatory Course on Seismic QualificationBristol, 11-12 January 2011
Secondary Response Spectra
Prof. Colin Taylor, University of Bristol
Paul Johnston, Atkins
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ScopeResponse spectra
Modelling and analysis methodsManipulating the output
UncertaintiesCodes Outline
FundamentalsInputDampingSubsystemsAnalysisExample
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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FundamentalsFundamentals
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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FundamentalsDynamic Amplification
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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Response of an infinite series of damped elastic SDOF systemsGraphs of the maximum values of▫ acceleration, ▫ velocity, and/or ▫ displacementmaximum response values for several levels of dampingplotted against undamped natural frequency or period
FundamentalsResponse Spectra
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PML Horizontal Response Spectra for 5% damping
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0.1 1 10 100
Acc
eler
atio
n (g
)
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20.0
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Velo
city
(cm
/s)
0.00.51.01.52.02.53.0
0.1 1 10 100Frequency (Hz)
Dis
plac
emen
t (cm
)
FundamentalsResponse Spectra
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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John Sherstobitoff
FundamentalsSecondary Response Spectra
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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Non structural elements difficult to analyse▫ Complex▫ Relatively smallLarge models requiredDifferent design teams/companies
FundamentalsWhy Secondary Response Spectra?
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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FundamentalsQuick View
Synthesise time historiesCompute motion at point of interestCompute secondary response spectra
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InputInput
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InputInput DataInput data definition▫ UK Nuclear▫ Areas of high seismicity▫ Time histories
Real Artificial
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InputPML Response Spectra
PML Horizontal Response Spectra for 5% damping(vertical is 2/3 of horizontal)
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0.3
0.4
0.1 1 10 100
Frequency (Hz)
Acc
eler
atio
n (g
)
Hard SiteMedium SiteSoft Site
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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Mean normalized uniform hazard spectra
InputUHS Response Spectra
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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10 to 15 Seconds
Acc
eler
atio
n InputArtificial time history for analysis
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
SERIES Training Course - Bristol, Jan 11-12 2011
Pseudo-acceleration linear response spectra plots, ~ - 0.02, 1940 El Centro SOOE component, from Chopra (1981)
InputReal Response Spectra
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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InputReal Time History
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DampingDamping
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DampingDampingDamping levels depend on stress levels in structure▫ Level 1 – low stress▫ Level 2 – high stressMain structural damping▫ ASCE 4, ASCE 43Equipment damping▫ ASCE 43
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DampingEffect of Damping Levels
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DampingDampingType of Component Level 1 Level 2
Reinforced concrete structures 4 7
Electrical cabinets and other equipment
3 4
Piping 5 5
Massive low stressed mechanical components
2 3
Cable trays 5 10
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SubsystemsSubsystems
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SubsystemsIn structure response spectra
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Response Frequency (Hz)
Acc
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7%
Subsystems
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SubsystemsSubsystemsNon structuralIncorporation in structural model?
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Simple Mass/spring system▫ K1 = 1000; M1 = 10
K1 M1
SubsystemsSimple analysis example
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SubsystemsSimple Mass spring system
ACCELERATION RESPONSE SPECTRA
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FREQUENCY (Hz)mass1 mass2 mass3 mass4 mass5 mass6 input
K1 M1
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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SubsystemsSimple analysis exampleSimple Mass/spring systemCase 1▫ K1 = 1000; M1 = 10▫ K2 = 100; M2 = 1
K1 M1 K2 M2
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SubsystemsSimple Mass spring system
ACCELERATION RESPONSE SPECTRA
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FREQUENCY (Hz)mass1 mass2 mass3 mass4 mass5 mass6 input
K1 M1 K2 M2
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SubsystemsSimple analysis exampleSimple Mass/spring systemCase 2▫ K1 = 1000; M1 = 10 ▫ K2 = 1000; M2 = 10
K1 M1 K2 M2
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SubsystemsCase 2ACC EL ERAT IO N RESPON SE SPEC TR A
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F R EQ U EN C Y (H z)m ass1 m ass2 m a ss3 m ass4 m ass5 m a ss6 inp ut
K1 M1 K2 M2
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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AnalysisAnalysis
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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PML Horizontal Response Spectra for 5% damping(vertical is 2/3 of horizontal)
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0.1 1 10 100
Frequency (Hz)
Acc
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atio
n (g
)
Hard SiteMedium SiteSoft Site
AnalysisSoil Structure Interaction
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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AnalysisUse of FEATime stepping analysis▫ Step by step▫ Reduced linear (modal)
Modal analysisCalculation of mode shapes and mass participationReduced time history analysis
Compute secondary response spectraManipulate response spectra
Analysis
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AnalysisStructural ModelStructural model▫ 3D▫ Includes
mass Stiffnessmodelling torsion
Inclusion of sub-system▫ Increases complexity of the model
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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AnalysisStructural Model
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AnalysisTime HistoryInput time history suite▫ Compute artificial time history▫ Adjust real time history using wavelets▫ Use real time historiesRules in the codes
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AnalysisTime History AnalysisTime histories for each analysis
2 Horizontal 1 Vertical
Statistically independentApplied simultaneouslyMore than one set
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AnalysisCalculating Response SpectraCalculation of response of an SDOF
Clough & Penzein
Calculation by numerical methods
max)(exp)(sin)("),( ⎥⎦⎤
⎢⎣⎡
⎥⎦⎤
⎢⎣⎡∫ −−−= ττξωτωτωξ dttySpv
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AnalysisCalculating Response SpectraHow many frequencies should be used
Always use natural frequencies of the main system (structure)
Frequency Separation on frequencies
0.5 - 3.0 0.1
3.0 - 3.6 0.1
3.6 - 5.0 0.2
5.0 - 8.0 0.25
8 - 15 0.5
15 - 18 1.0
8 - 22 2.0
22 - 34 3.0
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AnalysisTime History AnalysisData handling▫ 3 directions▫ 3 input time histories per direction▫ 10 locations of interest for equipment ▫ 90 output time histories▫ 3 damping levels of interest▫ 270 response spectraSimplify by▫ Averaging▫ enveloping
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AnalysisOutputData from:▫ 3 directions H1, H2, V▫ One or more analyses -1, -2 etc▫ A number of locations, A, B etcH1-1 A; H2-1 A; V-1 AH1-2 A; H2-2 A; V-2 A
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AnalysisOutput Response SpectraData for 3 directions (H1, H2, V) remain and are treated separately initiallyData from analyses (1,2,3 etc) - averagedData from different locations (A, B, C, etc) – enveloped
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AnalysisOutput Response Spectra
ACCELERATION RESPONSE SPECTRA
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• 2 Mass system• 3 input TH Mass 2
Mass 1
K1
M1
K2
M2
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AnalysisACCELERATION RESPONSE SPECTRA
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Averaging
K1
M1K2M2
ACCELERATION RESPONSE SPECTRA
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Averaging results from 3 time histories
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AnalysisUncertaintiesUncertainties in the analysis of the main structural analysisUncertainties from▫ Material properties▫ Damping▫ Approximations of modelling▫ SSI
Lower bound Best estimateUpper Bound
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AnalysisUncertaintiesPeak broadening▫ Applying +-15% fi (in lieu of detailed analysis) ▫ Use best estimate SSI analysis onlyPeak lopping▫ Reduce peak spectral response by 15% in lieu of more detailed assessment▫Peak shifting▫ A number of analyses using different spectra either side of the calculated
response spectra▫ Mode by mode analysis▫ Less conservative potentially
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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AnalysisOutput Response SpectraACCELERATION RESPONSE SPECTRA
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FREQUENCY (Hz)
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AnalysisEnveloped, broadened spectraBroadened Response Spectra
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Acc
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)
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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AnalysisEnveloped, broadened spectra
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AnalysisAlternative ProcedureSingh method (1975); based on random vibration theoryUses modal amplification factors to modify ground response spectrum
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AnalysisCodesASCE 4-98 Seismic analysis of safety related nuclear structuresASCE/SEI 43-05 Seismic Design Criteria for Structures, Systems and Components in Nuclear FacilitiesASME III Appendix N Dynamic Analysis
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AnalysisRules of thumbUK HPGA ~ 0.25gApproximate magnification factor ~ 4 @ 5% dampingAt low damping levels of equipment and structural analysis, high magnifications possible
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ExampleExampleStera3D by Dr Taiki SAITO, Building Research Institute, Japanhttp://iisee.kenken.go.jp/net/saito/stera3d/index.html
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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ExampleExample
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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ExampleExample
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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ExampleExample
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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ExampleExample
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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ExampleExample
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ExampleEl Centro X ACCELERATIONS
-8.00E+02
-6.00E+02
-4.00E+02
-2.00E+02
0.00E+00
2.00E+02
4.00E+02
6.00E+02
8.00E+02
0 2 4 6 8 10 12 14
TIME (s)
mass1 mass2 mass3 mass4 mass5 mass6 input
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ExampleKobe X ACCELERATIONS
-1.00E+03
-5.00E+02
0.00E+00
5.00E+02
1.00E+03
1.50E+03
0 5 10 15 20 25TIME (s)
mass1 mass2 mass3 mass4 mass5 mass6
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ExampleEl Centro X dirACCELERATION RESPONSE SPECTRA
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mass1 mass2 mass3 mass4 mass5 mass6 input
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ExampleKobe X dirACCELERATION RESPONSE SPECTRA
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mass1 mass2 mass3 mass4 mass5 mass6 input
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ExampleEl Centro Y dirACCELERATION RESPONSE SPECTRA
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mass1 mass2 mass3 mass4 mass5 mass6 input
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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ExampleKobe Y dirACCELERATION RESPONSE SPECTRA
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mass1 mass2 mass3 mass4 mass5 mass6 input
SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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ExampleResponse Spectra for 5% damping
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TH1TH2TH3TH4TH5TH6TH7TH8TH9TH10TH11TH12TH13TH14TH15TH16TH17TH18TH19TH20Env 5%
El Centro/Kobe X Spectra
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ExampleEl Centro/Kobe X Spectra - averagedResponse Spectra for 5% damping
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Response Spectra for 5% damping averaged
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TH1TH2TH3TH4TH5TH6TH7TH8TH9TH10TH11TH12TH13TH14TH15TH16TH17TH18TH19TH20Env 7%
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ExampleEnvelope results 1&2 3&4 5&7 floorsEnveloped Response Spectra
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ExampleBroadened Spectra – Top floor 5% Response Spectra
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ExampleBroadened Spectra – 3 levels Broadened Response Spectra
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SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES
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QuestionsQuestions