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

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FundamentalsFundamentals

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FundamentalsDynamic Amplification

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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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FundamentalsResponse Spectra

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John Sherstobitoff

FundamentalsSecondary Response Spectra

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

FundamentalsWhy Secondary Response Spectra?

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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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Frequency (Hz)

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Hard SiteMedium SiteSoft Site

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Mean normalized uniform hazard spectra

InputUHS Response Spectra

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10 to 15 Seconds

Acc

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

InputReal Response Spectra

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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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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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K1 M1

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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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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

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AnalysisAnalysis

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

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Hard SiteMedium SiteSoft Site

AnalysisSoil Structure Interaction

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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

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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

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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

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AnalysisOutput Response SpectraACCELERATION RESPONSE SPECTRA

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AnalysisEnveloped, broadened spectraBroadened Response Spectra

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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

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ExampleExample

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ExampleExample

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ExampleExample

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ExampleExample

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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

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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

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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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ExampleEl Centro Y dirACCELERATION RESPONSE SPECTRA

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ExampleKobe Y dirACCELERATION RESPONSE SPECTRA

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mass1 mass2 mass3 mass4 mass5 mass6 input

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ExampleResponse Spectra for 5% damping

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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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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