2010 SCEC Annual Meeting
A statistical analysis of the responses
of tall buildings to recorded and
simulated ground motions
Nirmal Jayaram
Nilesh Shome
Helmut Krawinkler
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
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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
100’
3@20’
140’
3@20’
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Structural model
Column
Rotational
Spring
We use accurate models to
represent element behavior in
response analysis for loss
estimation.
Beam
dc
Panel zone model and shear forcedeformation model at the BeamColumn connection
Engelhardt-E9608-UTDB3-MomentRotation
x 10
Ke = 2250000
M + = 28500
3 yM y = -28500
 = 0.020
p
2  = 0.45
pc
 = 1.5
s
1  = 1.5
c
 = 1.5
a
0  k = 1.3
M c/M y = 1.05
SHEAR FORCE - SHEAR DISTORTION RESPONSE
FOR TYPICAL PANEL ZONE
800
Panel Zone Shear Force (kips)
Moment (k-in)
4
-1
-2
-3
-4
-0.08
-0.06
-0.04
db
Rigid
Element
Moment-rotation models (red)
derived from experimental data (blue)
4
2 Rotational
Springs
-0.02
0
0.02
Chord Rotation (rad)
0.04
0.06
400
0
-400
0.08
-800
-0.02
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-0.01
0
0.01
0.02
Panel Zone Distortion (radians)
0.03
0.04
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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
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Spectrum moments
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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)
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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


1
1
EDP rec  EDP sim   1.96   sˆEDP

nrec nsim




1
1
EDP sim   EDP rec  1.96   sˆEDP

nrec nsim


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







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Story drift ratio: moments
Absolute mean correlation difference = 0.16, One-sided bound = 0.19
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Peak floor acceleration: moments
Absolute mean correlation difference = 0.02, One-sided bound = 0.03
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Residual drift ratio: residual drift ratio
Absolute mean correlation difference = 0.24, One-sided bound = 0.23
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Beam rotation: moments
Absolute mean correlation difference = 0.16, One-sided bound = 0.22
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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*
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OPTIONAL SLIDES
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Story drift ratio: comparison
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Beam moment: moments
Absolute mean correlation difference = 0.17, One-sided bound = 0.22
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Hypothesis testing methodology


1
1
EDP rec  EDP sim   1.96   sˆEDP

nrec nsim




1
1
EDP sim   EDP rec  1.96   sˆEDP

nrec nsim


© 2010 Risk Management Solutions inc.



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PFA mismatch
0
10
40
35
30
a
Story
S (T) (g)
25
20
15
-1
10
10
5
0
1
10
10
T (s)
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0
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
SDR
18
Residual drift ratio: comparison
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Beam moment: comparison
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Beam rotation: comparison
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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
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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
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Dominant period: PFA and SDR
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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
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Story drift ratio: moments
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Absolute mean correlation difference = 0.2
26
Peak floor acceleration: moments
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Absolute mean correlation difference = 0.15
27
Residual drift ratio: moments
Absolute mean correlation difference =0.3
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Beam moment: moments
Absolute mean correlation difference = 0.27
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Beam rotation: moments
Absolute mean correlation difference = 0.28
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PEER building: Concrete core wall, EW component
50
50
Recorded
Simulated
40
40
35
35
30
30
25
25
20
20
15
15
10
10
5
5
0
0
0.005
0.01
0.015
0.02
0.025
Median SDR
0.03
0.035
0.04
Recorded
Simulated
45
Story
Story
45
0
0.045
0
0.05
0.1
0.15
0.2
0.25
0.3
Dispersion of SDR
0.35
0.4
0.45
50
Recorded
Simulated
45
50
Recorded
Simulated
45
40
40
35
35
30
25
Story
Story
30
20
25
20
15
15
10
10
5
0
0.2
5
0.4
0.6
0.8
1
Median PFA
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1.2
1.4
1.6
0
0
0.05
0.1
0.15
0.2
0.25
Dispersion of PFA
0.3
0.35
0.4
31
PEER building: Concrete core wall, NS component
50
50
Recorded
Simulated
40
40
35
35
30
30
25
20
15
15
10
10
5
5
0
0.005
0.01
0.015
Median SDR
0.02
0.025
0
0.03
50
0.05
0.1
0.15
0.2
0.25
0.3
Dispersion of SDR
0.35
0.4
0.45
Recorded
Simulated
45
40
40
35
35
30
30
Story
25
20
25
20
15
15
10
10
5
0
0.2
0
50
Recorded
Simulated
45
Story
25
20
0
Recorded
Simulated
45
Story
Story
45
5
0.3
0.4
0.5
0.6
0.7
0.8
Median PFA
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0.9
1
1.1
1.2
0
0
0.05
0.1
0.15
0.2
0.25
0.3
Dispersion of PFA
0.35
0.4
0.45
32
PEER building: Dual system, EW component
50
50
Recorded
Simulated
40
40
35
35
30
30
25
25
20
20
15
15
10
10
5
5
0
0
0.005
0.01
0.015
Median SDR
0.02
0.025
0
0.03
50
0.1
0.15
0.2
0.25
0.3
Dispersion of SDR
0.35
0.4
0.45
0.5
Recorded
Simulated
40
35
35
30
30
25
Story
Story
0.05
45
40
20
25
20
15
15
10
10
5
0
0
50
Recorded
Simulated
45
Recorded
Simulated
45
Story
Story
45
5
0
0.2
0.4
0.6
0.8
Median PFA
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1.2
1.4
1.6
0
0
0.2
0.4
0.6
0.8
Dispersion of PFA
1
1.2
1.4
33
PEER building: Dual system, NS component
50
50
Recorded
Simulated
40
40
35
35
30
30
25
25
20
20
15
15
10
10
5
5
0
0
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018
Median SDR
0
0.02
50
0
0.1
0.15
0.2
0.25
0.3
Dispersion of SDR
0.35
0.4
0.45
35
35
30
30
Story
40
25
25
20
20
15
15
10
10
5
5
0
0.2
0.4
© 2010 Risk Management Solutions inc.
0.6
0.8
Dispersion of PFA
1
1.2
Recorded
Simulated
45
40
0
0.05
50
Recorded
Simulated
45
Story
Recorded
Simulated
45
Story
Story
45
1.4
0
0
0.5
1
1.5
Median PFA
34
PEER building: Braced frame, EW component
40
Recorded
Simulated
35
40
Recorded
Simulated
35
30
30
25
20
Story
Story
25
15
20
15
10
10
5
5
0
0
0.005
0.01
0.015
Median SDR
0.02
0.025
0
40
0.2
0.3
0.4
Dispersion of SDR
0.5
0.6
0.7
30
30
25
25
20
20
15
15
10
10
5
5
0.4
0.5
0.6
0.7
Median PFA
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0.8
0.9
Recorded
Simulated
35
Story
Story
0.1
40
Recorded
Simulated
35
0
0
1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
Dispersion of PFA
0.35
0.4
0.45
0.5
35
PEER building: Braced frame, NS component
40
40
Recorded
Simulated
30
30
25
25
20
15
10
10
5
5
0
0.005
0.01
0.015
Median SDR
0.02
0.025
0
0.03
40
0.1
0.2
0.3
0.4
Dispersion of SDR
0.5
0.6
0.7
Recorded
Simulated
35
30
30
25
25
Story
20
15
20
15
10
10
5
0
0.25
0
40
Recorded
Simulated
35
Story
20
15
0
Recorded
Simulated
35
Story
Story
35
5
0.3
0.35
0.4
0.45
0.5
0.55
Median PFA
© 2010 Risk Management Solutions inc.
0.6
0.65
0.7
0.75
0
0
0.05
0.1
0.15
0.2
0.25
0.3
Dispersion of PFA
0.35
0.4
0.45
36