1. Nirmal Jayaram Nilesh Shome Helmut Krawinkler 2010 SCEC Annual Meeting A statistical analysis of the responses of tall buildings to recorded and simulated ground motions

2. Objectives We are interested in performing statistical analysis to evaluate the level of similarity between the responses of tall buildings to recorded and simulated ground motions In this study, we analyze the structural response of a 40 story steel moment frame (SMF) building designed based on the 2006 IBC We consider structural response parameters (aka engineering demand parameters) such as story drift ratio (SDR), peak floor acceleration (PFA), residual drift ratio (ResDR) and beam plastic rotation Recorded ground motions are selected from the NGA database, and simulated ground motions are selected from the Puente Hills simulations © 2010 Risk Management Solutions inc. 2

3. Structural model We use a 40 story steel moment frame buildings (SMF) designed by Professor Helmut Krawinkler based on the 2006 IBC code as a representative SMF tall building in CA It has 3-bay perimeter frames on each side, as commonly done for SMF frames The fundamental period of the structure equals 6.4s. The 2 nd and 3 rd mode periods are 2.4s and 1.4s respectively © 2010 Risk Management Solutions inc. 3

4. Structural model We use accurate models to represent element behavior in response analysis for loss estimation. © 2010 Risk Management Solutions inc. 4 Moment-rotation models (red) derived from experimental data (blue) Panel zone model and shear force- deformation model at the Beam- Column connection

5. Ground motion selection We selected recorded and simulated ground motion sets with the following properties: Both sets have 40 ground motions each The ground motions are chosen so that their spectra have a target conditional mean spectrum (CMS) mean and variance, for a target scenario earthquake of magnitude 6.5, distance 5km, epsilon 1. This is based on deaggregation of seismic hazard at Civic Center, Los Angeles for a 2,475 return period Sa(5s) For each recorded ground motion, we select a simulated ground motion so that the response spectra of both ground motions match © 2010 Risk Management Solutions inc. 5

6. Spectrum moments © 2010 Risk Management Solutions inc. 6 The ground motions are selected based on an algorithm developed by Jayaram et al. (2011)

7. Engineering demand parameters (EDP) of interest Story drift ratio: The absolute maximum (over time) ratio of the relative displacement between two adjacent stories to the story height (∆/h) Peak floor acceleration: The absolute maximum (over time) acceleration at the floor level Residual drift ratio: The story drift ratio at the end of the excitation Beam plastic rotation: The absolute maximum (over time) plastic rotation of the beam (γ) © 2010 Risk Management Solutions inc. 7

8. Hypothesis testing methodology In this study, the EDPs are estimated for the selected recorded and simulated ground motions. We are interested in testing whether there are systematic differences between the EDPs in these two cases, using hypothesis testing Hypothesis testing is used to identify whether differences in the EDPs are due to the randomness associated with finite sample sizes or are inherent/ systematic Suppose we are interested in testing whether mean(EDP rec ) differs from mean(EDP sim )  Null hypothesis mean(EDP rec ) - mean(EDP sim ) = 0  Alternate hypothesis mean(EDP rec ) - mean(EDP sim ) ≠ 0 Reject null hypothesis if © 2010 Risk Management Solutions inc. 8

9. Story drift ratio: moments Absolute mean correlation difference = 0.16, One-sided bound = 0.19 © 2010 Risk Management Solutions inc. 9

10. Peak floor acceleration: moments Absolute mean correlation difference = 0.02, One-sided bound = 0.03 © 2010 Risk Management Solutions inc. 10

11. Residual drift ratio: residual drift ratio Absolute mean correlation difference = 0.24, One-sided bound = 0.23 © 2010 Risk Management Solutions inc. 11

12. Beam rotation: moments Absolute mean correlation difference = 0.16, One-sided bound = 0.22 © 2010 Risk Management Solutions inc. 12

13. Summary We compared the structural responses of tall buildings under sets of recorded and simulated ground motions, and observed some differences Further investigation is required to identify the reasons for these differences EDPSignificance of deviation in MedianDispersionCorrelation SDRInsignificant except at lower stories InsignificantInsignificant* PFASignificantInsignificant ResDRInsignificant except at lower stories InsignificantSignificant RotationInsignificant*InsignificantInsignificant* © 2010 Risk Management Solutions inc. 13

14. OPTIONAL SLIDES © 2010 Risk Management Solutions inc. 14

15. Story drift ratio: comparison © 2010 Risk Management Solutions inc. 15

16. Beam moment: moments Absolute mean correlation difference = 0.17, One-sided bound = 0.22 © 2010 Risk Management Solutions inc. 16

17. Hypothesis testing methodology © 2010 Risk Management Solutions inc. 17

18. PFA mismatch © 2010 Risk Management Solutions inc. 18

19. Residual drift ratio: comparison © 2010 Risk Management Solutions inc. 19

20. Beam moment: comparison © 2010 Risk Management Solutions inc. 20

21. Beam rotation: comparison © 2010 Risk Management Solutions inc. 21

22. Dominant spectral periods: PEER TBI set StorySDRPFAStorySDRPFA 10.550.05210.440.23 20.640.05220.440.23 30.650.43230.440.23 40.650.42240.440.38 56.090.42250.440.21 66.090.23260.070.21 760.23270.070.21 85.960.5280.070.05 95.960.5290.075.96 105.530.5300.070.05 110.210.54310.070.38 120.370.5320.070.05 130.380.5332.010.05 140.380.5342.015.47 150.380.233520.4 160.380.23361.990.38 170.380.23371.990.38 185.720.23382.920.38 190.440.23392.960.38 200.440.23400.530.64 © 2010 Risk Management Solutions inc. 22

23. Dominant spectral periods: CMS-based set StorySDRPFAStorySDRPFA 16.50216.50 2 0226.50 3 0236.50 4 0246.50 5 0256.50 6 0266.50 7 0276.50 8 0286.50 9 0296.50 106.50306.50 116.50316.50 126.50326.50 136.50332.50 146.50342.50 1570352.50 1670362.50 1770372.50 186.503830 196.503930 206.504060 © 2010 Risk Management Solutions inc. 23

24. Dominant period: PFA and SDR © 2010 Risk Management Solutions inc. 24

25. 15 recorded and 15 simulated ground motions were selected for the PEER TBI (OVE level) The mean and the standard deviation of the recorded and the simulated response spectra show some mismatches even at long periods © 2010 Risk Management Solutions inc. 25

26. Story drift ratio: moments Absolute mean correlation difference = 0.2 © 2010 Risk Management Solutions inc. 26

27. Peak floor acceleration: moments Absolute mean correlation difference = 0.15 © 2010 Risk Management Solutions inc. 27

28. Residual drift ratio: moments Absolute mean correlation difference =0.3 © 2010 Risk Management Solutions inc. 28

29. Beam moment: moments Absolute mean correlation difference = 0.27 © 2010 Risk Management Solutions inc. 29

30. Beam rotation: moments Absolute mean correlation difference = 0.28 © 2010 Risk Management Solutions inc. 30

31. PEER building: Concrete core wall, EW component © 2010 Risk Management Solutions inc. 31

32. PEER building: Concrete core wall, NS component © 2010 Risk Management Solutions inc. 32

33. PEER building: Dual system, EW component © 2010 Risk Management Solutions inc. 33

34. PEER building: Dual system, NS component © 2010 Risk Management Solutions inc. 34

35. PEER building: Braced frame, EW component © 2010 Risk Management Solutions inc. 35

36. PEER building: Braced frame, NS component © 2010 Risk Management Solutions inc. 36