Secondary Response Spectra

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1 Task NA 3.6 Preparatory Course on Seismic Qualification Bristol, January 2011 Secondary Response Spectra Prof. Colin Taylor, University of Bristol Paul Johnston, Atkins

2 Scope Response spectra Modelling and analysis methods Manipulating the output Uncertainties Codes Outline Fundamentals Input Damping Subsystems Analysis Example

3 Fundamentals

4 Fundamentals Dynamic Amplification

5 Fundamentals Response Spectra Response of an infinite series of damped elastic SDOF systems Graphs of the maximum values of acceleration, velocity, and/or displacement maximum response values for several levels of damping plotted against undamped natural frequency or period

6 Fundamentals Response Spectra 0.4 PML Horizontal Response Spectra for 5% damping Acceleration (g) Velocity (cm/s) Displacement (cm) Frequency (Hz) Frequency (Hz)

7 Fundamentals Secondary Response Spectra John Sherstobitoff

8 Fundamentals Why Secondary Response Spectra? Non structural elements difficult to analyse Complex Relatively small Large models required Different design teams/companies

9 Fundamentals Quick View Synthesise time histories Compute motion at point of interest Compute secondary response spectra

10 Input

11 Input Data Input data definition UK Nuclear Areas of high seismicity Time histories Real Artificial

12 Input PML Response Spectra PML Horizontal Response Spectra for 5% damping (vertical is 2/3 of horizontal) Acceleration (g) Hard Site Medium Site Soft Site Frequency (Hz)

13 Input UHS Response Spectra Mean normalized uniform hazard spectra

14 Input Artificial time history for analysis Acceleration 10 to 15 Seconds

15 Input Real Response Spectra Pseudo-acceleration linear response spectra plots, ~ , 1940 El Centro SOOE component, from Chopra (1981)

16 Input Real Time History

17 Damping

18 Damping Damping levels depend on stress levels in structure Level 1 low stress Level 2 high stress Main structural damping ASCE 4, ASCE 43 Equipment damping ASCE 43

19 Damping Effect of Damping Levels

20 Damping Type 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

21 Subsystems

22 Subsystems Subsystems In structure response spectra Acceleration (g) 0.8 7% Response Frequency (Hz)

23 Subsystems Non structural Incorporation in structural model?

24 Subsystems Simple analysis example Simple Mass/spring system K1 = 1000; M1 = 10 K1 M1

25 Subsystems Simple Mass spring system K1 M1 ACCELERATION RESPONSE SPECTRA FREQUENCY (Hz) mass1 mass2 mass3 mass4 mass5 mass6 input

26 Subsystems Simple analysis example Simple Mass/spring system Case 1 K1 = 1000; M1 = 10 K2 = 100; M2 = 1 K1 M1 K2 M2

27 Subsystems Simple Mass spring system K1 M1 K2 M2 ACCELERATION RESPONSE SPECTRA FREQUENCY (Hz) mass1 mass2 mass3 mass4 mass5 mass6 input

28 Subsystems Simple analysis example Simple Mass/spring system Case 2 K1 = 1000; M1 = 10 K2 = 1000; M2 = 10 K1 M1 K2 M2

29 Subsystems Case 2 K1 M1 K2 M2 ACCELERATION RESPONSE SPECTRA FREQUENCY (Hz) mass1 mass2 mass3 mass4 mass5 mass6 in p ut

30 Analysis

31 Analysis Soil Structure Interaction PML Horizontal Response Spectra for 5% damping (vertical is 2/3 of horizontal) Acceleration (g) Hard Site Medium Site Soft Site Frequency (Hz)

32 Analysis Use of FEA Time stepping analysis Step by step Reduced linear (modal) Modal analysis Calculation of mode shapes and mass participation Reduced time history analysis Compute secondary response spectra Manipulate response spectra

33 Analysis Structural Model Structural model 3D Includes mass Stiffness modelling torsion Inclusion of sub-system Increases complexity of the model

34 Analysis Structural Model

35 Analysis Time History Input time history suite Compute artificial time history Adjust real time history using wavelets Use real time histories Rules in the codes

36 Time History Analysis Time histories for each analysis 2 Horizontal 1 Vertical Statistically independent Applied simultaneously More than one set

37 Analysis Calculating Response Spectra Calculation of response of an SDOF Spv ( ξ, ω) = y"( τ )sinω( t τ )exp ξω( t τ ) dτ max Clough & Penzein Calculation by numerical methods

38 Analysis Calculating Response Spectra How many frequencies should be used Frequency Separation on frequencies Always use natural frequencies of the main system (structure)

39 Time History Analysis Data 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 spectra Simplify by Averaging enveloping

40 Analysis Output Data from: 3 directions H1, H2, V One or more analyses -1, -2 etc A number of locations, A, B etc H1-1 A; H2-1 A; V-1 A H1-2 A; H2-2 A; V-2 A

41 Analysis Output Response Spectra Data for 3 directions (H1, H2, V) remain and are treated separately initially Data from analyses (1,2,3 etc) - averaged Data from different locations (A, B, C, etc) enveloped

42 Analysis Output Response Spectra 2 Mass system ACCELERATION RESPONSE SPECTRA 3 input TH Mass M2 K Mass 1 M K FREQUENCY (Hz)

43 Analysis Averaging Averaging results from 3 time histories M2 K2 M1 K1 ACCELERATION RESPONSE SPECTRA ACCELERATION RESPONSE SPECTRA FREQUENCY (Hz) FREQUENCY (Hz)

44 Analysis Uncertainties Uncertainties in the analysis of the main structural analysis Uncertainties from Material properties Damping Approximations of modelling SSI Lower bound Best estimate Upper Bound

45 Analysis Uncertainties Peak broadening Applying +-15% f i (in lieu of detailed analysis) Use best estimate SSI analysis only Peak 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

46 Analysis Output Response Spectra ACCELERATION RESPONSE SPECTRA FREQUENCY (Hz)

47 Analysis Enveloped, broadened spectra Broadened Response Spectra Acceleration (g) Frequency (Hz)

48 Analysis Enveloped, broadened spectra

49 Analysis Alternative Procedure Singh method (1975); based on random vibration theory Uses modal amplification factors to modify ground response spectrum

50 Analysis Codes ASCE 4-98 Seismic analysis of safety related nuclear structures ASCE/SEI Seismic Design Criteria for Structures, Systems and Components in Nuclear Facilities ASME III Appendix N Dynamic Analysis

51 Analysis Rules of thumb UK HPGA ~ 0.25g Approximate magnification factor ~ 5% damping At low damping levels of equipment and structural analysis, high magnifications possible

52 Example Stera3D by Dr Taiki SAITO, Building Research Institute, Japan

53 Example

54 Example

55 Example

56 Example

57 Example

58 Example El Centro X ACCELERATIONS 8.00E E E E E E E E E TIME (s) mass1 mass2 mass3 mass4 mass5 mass6 input

59 Example Kobe X ACCELERATIONS 1.50E E E E E E TIME (s) mass1 mass2 mass3 mass4 mass5 mass6

60 Example El Centro X dir ACCELERATION RESPONSE SPECTRA FREQUENCY (Hz) mass1 mass2 mass3 mass4 mass5 mass6 input

61 Example Kobe X dir ACCELERATION RESPONSE SPECTRA FREQUENCY (Hz) mass1 mass2 mass3 mass4 mass5 mass6 input

62 Example El Centro Y dir ACCELERATION RESPONSE SPECTRA FREQUENCY (Hz) mass1 mass2 mass3 mass4 mass5 mass6 input

63 Example Kobe Y dir ACCELERATION RESPONSE SPECTRA FREQUENCY (Hz) mass1 mass2 mass3 mass4 mass5 mass6 input

64 Example El Centro/Kobe X Spectra Response Spectra for 5% damping 450 Acceleration Frequency (Hz) TH1 TH2 TH3 TH4 TH5 TH6 TH7 TH8 TH9 TH10 TH11 TH12 TH13 TH14 TH15 TH16 TH17 TH18 TH19 TH20 Env 5%

65 Example El Centro/Kobe X Spectra - averaged Response Spectra for 5% damping 450 Acceleration TH1 TH2 TH3 TH4 TH5 TH6 TH7 TH8 TH9 TH10 TH11 TH12 TH13 TH14 TH15 TH16 TH17 TH TH19 TH20 Env 5% 400 Response Spectra for 5% damping averaged Frequency (Hz) Acceleration TH1 TH2 TH3 TH4 TH5 TH6 TH7 TH8 TH9 TH10 TH11 TH12 TH13 TH14 TH15 TH16 TH17 TH18 TH19 TH20 Env 7% SERIES Training Frequency Course (Hz) - Bristol, Jan

66 Example Envelope results 1&2 3&4 5&7 floors Enveloped Response Spectra Acceleration (g) Frequency (Hz)

67 Example Broadened Spectra Top floor 5% Response Spectra Acceleration Frequency (Hz)

68 Example Broadened Spectra 3 levels Broadened Response Spectra Acceleration Frequency (Hz)

69 Questions

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