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

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

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

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 2nd and 3rd mode periods are 2.4s and 1.4s respectively


3@20’

140’

3@2

0’

100’

Structural model

We use accurate models to represent element behavior in response analysis for loss estimation.


-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08-4

-3

-2

-1

0

1

2

3

4x 10

4

Ke = 2250000

My+ = 28500

My- = -28500

p = 0.020

pc = 0.45

s = 1.5

c = 1.5

a = 1.5

k = 1.3

Mc/M

y = 1.05

Chord Rotation (rad)

Mo

men

t (k

-in

)

Engelhardt-E9608-UTDB3-MomentRotation

Moment-rotation models (red) derived from experimental data (blue)

Beam

Column2 Rotational

SpringsRotationalSpring

db

dc

RigidElement

SHEAR FORCE - SHEAR DISTORTION RESPONSEFOR TYPICAL PANEL ZONE

-800

-400

0

400

800

-0.02 -0.01 0 0.01 0.02 0.03 0.04

Panel Zone Distortion (radians)

Pan

el Z

one

Sh

ear

For

ce (

kip

s)

Panel zone model and shear force-deformation model at the Beam-Column connection

Ground motion selectionWe 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


Spectrum moments


The ground motions are selected based on an algorithm developed by Jayaram et al. (2011)

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)


simrecEDPrecsim

simrecEDPsimrec

nnsEDPEDP

nnsEDPEDP

11ˆ96.1

11ˆ96.1

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(EDPrec) differs from

mean(EDPsim) Null hypothesis

mean(EDPrec) - mean(EDPsim) = 0 Alternate hypothesis

mean(EDPrec) - mean(EDPsim) ≠ 0

• Reject null hypothesis if


Story drift ratio: moments

Absolute mean correlation difference = 0.16, One-sided bound = 0.19© 2010 Risk Management Solutions inc.

9

Peak floor acceleration: moments

Absolute mean correlation difference = 0.02, One-sided bound = 0.03


Residual drift ratio: residual drift ratio



Beam rotation: moments



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

EDP Significance of deviation in

Median Dispersion Correlation

SDR Insignificant except at lower stories

Insignificant Insignificant*

PFA Significant Insignificant Insignificant

ResDR Insignificant except at lower stories

Insignificant Significant

Rotation Insignificant* Insignificant Insignificant*


OPTIONAL SLIDES


Story drift ratio: comparison


Beam moment: moments



simrecEDPrecsim

simrecEDPsimrec

nnsEDPEDP

nnsEDPEDP

11ˆ96.1

11ˆ96.1

Hypothesis testing methodology


PFA mismatch

100

101

10-1

100

T (s)

Sa(T

) (g

)

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.60

5

10

15

20

25

30

35

40

SDR

Sto

ry


Residual drift ratio: comparison


Beam moment: comparison


Beam rotation: comparison


Dominant spectral periods: PEER TBI set

Story SDR PFA Story SDR PFA

1 0.55 0.05 21 0.44 0.23

2 0.64 0.05 22 0.44 0.23

3 0.65 0.43 23 0.44 0.23

4 0.65 0.42 24 0.44 0.38

5 6.09 0.42 25 0.44 0.21

6 6.09 0.23 26 0.07 0.21

7 6 0.23 27 0.07 0.21

8 5.96 0.5 28 0.07 0.05

9 5.96 0.5 29 0.07 5.96

10 5.53 0.5 30 0.07 0.05

11 0.21 0.54 31 0.07 0.38

12 0.37 0.5 32 0.07 0.05

13 0.38 0.5 33 2.01 0.05

14 0.38 0.5 34 2.01 5.47

15 0.38 0.23 35 2 0.4

16 0.38 0.23 36 1.99 0.38

17 0.38 0.23 37 1.99 0.38

18 5.72 0.23 38 2.92 0.38

19 0.44 0.23 39 2.96 0.38

20 0.44 0.23 40 0.53 0.64


Dominant spectral periods: CMS-based set

Story SDR PFA Story SDR PFA

1 6.5 0 21 6.5 0

2 6.5 0 22 6.5 0

3 6.5 0 23 6.5 0

4 6.5 0 24 6.5 0

5 6.5 0 25 6.5 0

6 6.5 0 26 6.5 0

7 6.5 0 27 6.5 0

8 6.5 0 28 6.5 0

9 6.5 0 29 6.5 0

10 6.5 0 30 6.5 0

11 6.5 0 31 6.5 0

12 6.5 0 32 6.5 0

13 6.5 0 33 2.5 0

14 6.5 0 34 2.5 0

15 7 0 35 2.5 0

16 7 0 36 2.5 0

17 7 0 37 2.5 0

18 6.5 0 38 3 0

19 6.5 0 39 3 0

20 6.5 0 40 6 0


Dominant period: PFA and SDR


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


Story drift ratio: moments

Absolute mean correlation difference = 0.2© 2010 Risk Management Solutions inc.

26

Peak floor acceleration: moments

Absolute mean correlation difference = 0.15© 2010 Risk Management Solutions inc.

27

Residual drift ratio: moments

Absolute mean correlation difference =0.3


Beam moment: moments

Absolute mean correlation difference = 0.27


Beam rotation: moments

Absolute mean correlation difference = 0.28


PEER building: Concrete core wall, EW component


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

5

10

15

20

25

30

35

40

45

50

Dispersion of PFA

Sto

ry

Recorded

Simulated

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

5

10

15

20

25

30

35

40

45

50

Dispersion of SDR

Sto

ry

Recorded

Simulated

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.0450

5

10

15

20

25

30

35

40

45

50

Median SDR

Sto

ry

Recorded

Simulated

0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

5

10

15

20

25

30

35

40

45

50

Median PFA

Sto

ry

Recorded

Simulated

PEER building: Concrete core wall, NS component


0 0.005 0.01 0.015 0.02 0.025 0.030

5

10

15

20

25

30

35

40

45

50

Median SDR

Sto

ry

Recorded

Simulated

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

5

10

15

20

25

30

35

40

45

50

Dispersion of SDR

Sto

ry

Recorded

Simulated

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

5

10

15

20

25

30

35

40

45

50

Dispersion of PFA

Sto

ry

Recorded

Simulated

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.20

5

10

15

20

25

30

35

40

45

50

Median PFA

Sto

ry

Recorded

Simulated

PEER building: Dual system, EW component


0 0.2 0.4 0.6 0.8 1 1.2 1.40

5

10

15

20

25

30

35

40

45

50

Dispersion of PFA

Sto

ry

Recorded

Simulated

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

5

10

15

20

25

30

35

40

45

50

Median PFA

Sto

ry

Recorded

Simulated

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15

20

25

30

35

40

45

50

Dispersion of SDR

Sto

ry

Recorded

Simulated

0 0.005 0.01 0.015 0.02 0.025 0.030

5

10

15

20

25

30

35

40

45

50

Median SDR

Sto

ry

Recorded

Simulated

PEER building: Dual system, NS component


0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.020

5

10

15

20

25

30

35

40

45

50

Median SDR

Sto

ry

Recorded

Simulated

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

5

10

15

20

25

30

35

40

45

50

Dispersion of SDR

Sto

ry

Recorded

Simulated

0 0.2 0.4 0.6 0.8 1 1.2 1.40

5

10

15

20

25

30

35

40

45

50

Dispersion of PFA

Sto

ry

Recorded

Simulated

0 0.5 1 1.50

5

10

15

20

25

30

35

40

45

50

Median PFA

Sto

ry

Recorded

Simulated

PEER building: Braced frame, EW component


0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

5

10

15

20

25

30

35

40

Dispersion of PFA

Sto

ry

Recorded

Simulated

0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

40

Median PFA

Sto

ry

Recorded

Simulated

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

5

10

15

20

25

30

35

40

Dispersion of SDR

Sto

ry

Recorded

Simulated

0 0.005 0.01 0.015 0.02 0.0250

5

10

15

20

25

30

35

40

Median SDR

Sto

ry

Recorded

Simulated

PEER building: Braced frame, NS component


0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

5

10

15

20

25

30

35

40

Dispersion of SDR

Sto

ry

Recorded

Simulated

0 0.005 0.01 0.015 0.02 0.025 0.030

5

10

15

20

25

30

35

40

Median SDR

Sto

ry

Recorded

Simulated

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

5

10

15

20

25

30

35

40

Dispersion of PFA

Sto

ry

Recorded

Simulated

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.750

5

10

15

20

25

30

35

40

Median PFA

Sto

ry

Recorded

Simulated

Documents

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