Secondary Response Spectra - SERIES | Seismic … - Secondary Response... · Compute secondary...

Task NA 3.6Preparatory Course on Seismic QualificationBristol, 11-12 January 2011

Secondary Response Spectra

Prof. Colin Taylor, University of Bristol

Paul Johnston, Atkins

SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES

SERIES Training Course - Bristol, Jan 11-12 2011

ScopeResponse spectra

Modelling and analysis methodsManipulating the output

UncertaintiesCodes Outline

FundamentalsInputDampingSubsystemsAnalysisExample



FundamentalsFundamentals



FundamentalsDynamic Amplification



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



PML Horizontal Response Spectra for 5% damping

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0.1 1 10 100

Acc

eler

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n (g

)

0.0

5.0

10.0

15.0

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0.1 1 10 100Frequency (Hz)

Velo

city

(cm

/s)

0.00.51.01.52.02.53.0


Dis

plac

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t (cm

)

FundamentalsResponse Spectra



John Sherstobitoff

FundamentalsSecondary Response Spectra



Non structural elements difficult to analyse▫ Complex▫ Relatively smallLarge models requiredDifferent design teams/companies

FundamentalsWhy Secondary Response Spectra?



FundamentalsQuick View

Synthesise time historiesCompute motion at point of interestCompute secondary response spectra



InputInput



InputInput DataInput data definition▫ UK Nuclear▫ Areas of high seismicity▫ Time histories

Real Artificial



InputPML Response Spectra

PML Horizontal Response Spectra for 5% damping(vertical is 2/3 of horizontal)

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Frequency (Hz)

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Hard SiteMedium SiteSoft Site



Mean normalized uniform hazard spectra

InputUHS Response Spectra



10 to 15 Seconds

Acc

eler

atio

n InputArtificial time history for analysis



Pseudo-acceleration linear response spectra plots, ~ - 0.02, 1940 El Centro SOOE component, from Chopra (1981)

InputReal Response Spectra



InputReal Time History



DampingDamping



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



DampingEffect of Damping Levels



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



SubsystemsSubsystems



SubsystemsIn structure response spectra

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Response Frequency (Hz)

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7%

Subsystems



SubsystemsSubsystemsNon structuralIncorporation in structural model?



Simple Mass/spring system▫ K1 = 1000; M1 = 10

K1 M1

SubsystemsSimple analysis example



SubsystemsSimple Mass spring system

ACCELERATION RESPONSE SPECTRA

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FREQUENCY (Hz)mass1 mass2 mass3 mass4 mass5 mass6 input

K1 M1



SubsystemsSimple analysis exampleSimple Mass/spring systemCase 1▫ K1 = 1000; M1 = 10▫ K2 = 100; M2 = 1

K1 M1 K2 M2



SubsystemsSimple Mass spring system


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FREQUENCY (Hz)mass1 mass2 mass3 mass4 mass5 mass6 input

K1 M1 K2 M2



SubsystemsSimple analysis exampleSimple Mass/spring systemCase 2▫ K1 = 1000; M1 = 10 ▫ K2 = 1000; M2 = 10

K1 M1 K2 M2



SubsystemsCase 2ACC EL ERAT IO N RESPON SE SPEC TR A

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1 .00 0

1 .50 0

2 .00 0

2 .50 0

3 .00 0

3 .50 0

4 .00 0

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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



AnalysisAnalysis



PML Horizontal Response Spectra for 5% damping(vertical is 2/3 of horizontal)

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Frequency (Hz)

Acc

eler

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Hard SiteMedium SiteSoft Site

AnalysisSoil Structure Interaction



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



AnalysisStructural ModelStructural model▫ 3D▫ Includes

mass Stiffnessmodelling torsion

Inclusion of sub-system▫ Increases complexity of the model



AnalysisStructural Model



AnalysisTime HistoryInput time history suite▫ Compute artificial time history▫ Adjust real time history using wavelets▫ Use real time historiesRules in the codes



AnalysisTime History AnalysisTime histories for each analysis

2 Horizontal 1 Vertical

Statistically independentApplied simultaneouslyMore than one set



AnalysisCalculating Response SpectraCalculation of response of an SDOF

Clough & Penzein

Calculation by numerical methods

max)(exp)(sin)("),( ⎥⎦⎤

⎢⎣⎡

⎥⎦⎤

⎢⎣⎡∫ −−−= ττξωτωτωξ dttySpv



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



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



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



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



AnalysisOutput Response Spectra


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FREQUENCY (Hz)

• 2 Mass system• 3 input TH Mass 2

Mass 1

K1

M1

K2

M2



AnalysisACCELERATION RESPONSE SPECTRA

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1.500

2.000

2.500

3.000

0.100 1.000 10.000 100.000FREQUENCY (Hz)

Averaging

K1

M1K2M2


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2.500

0.100 1.000 10.000 100.000

FREQUENCY (Hz)

Averaging results from 3 time histories



AnalysisUncertaintiesUncertainties in the analysis of the main structural analysisUncertainties from▫ Material properties▫ Damping▫ Approximations of modelling▫ SSI

Lower bound Best estimateUpper Bound



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



AnalysisOutput Response SpectraACCELERATION RESPONSE SPECTRA

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2.000

2.500

0.100 1.000 10.000 100.000

FREQUENCY (Hz)



AnalysisEnveloped, broadened spectraBroadened Response Spectra

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2.0

2.5


Acc

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atio

n (g

)



AnalysisEnveloped, broadened spectra



AnalysisAlternative ProcedureSingh method (1975); based on random vibration theoryUses modal amplification factors to modify ground response spectrum



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



AnalysisRules of thumbUK HPGA ~ 0.25gApproximate magnification factor ~ 4 @ 5% dampingAt low damping levels of equipment and structural analysis, high magnifications possible



ExampleExampleStera3D by Dr Taiki SAITO, Building Research Institute, Japanhttp://iisee.kenken.go.jp/net/saito/stera3d/index.html



ExampleExample



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



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



ExampleEl Centro X dirACCELERATION RESPONSE SPECTRA

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ExampleKobe X dirACCELERATION RESPONSE SPECTRA

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ExampleEl Centro Y dirACCELERATION RESPONSE SPECTRA

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ExampleKobe Y dirACCELERATION RESPONSE SPECTRA

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ExampleResponse Spectra for 5% damping

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TH1TH2TH3TH4TH5TH6TH7TH8TH9TH10TH11TH12TH13TH14TH15TH16TH17TH18TH19TH20Env 5%

El Centro/Kobe X Spectra



ExampleEl Centro/Kobe X Spectra - averagedResponse Spectra for 5% damping

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Response Spectra for 5% damping averaged

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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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QuestionsQuestions

Secondary Response Spectra - SERIES | Seismic … - Secondary Response... · Compute secondary...

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