Effect of Ground Motion Frequency on Non-Structural Seismic Damage
by
Han Wu
B.S. Civil & Environmental Engineering
University of California, Los Angeles, 2014
SUBMITTED TO THE DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING IN
PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE DEGREE OF
MASTER OF ENGINEERING
ARCWNES
IN CIVIL AND ENVIRONMENTAL ENGINEERING
MASSACHUSETTS NSTITUTE
OF _fECHNOLOLGY
AT THE
JUL 02 2015
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
LIBRARIES
JUNE 2015
2015 Han Wu.
All Rights Reserved.
The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this theses
document in whole or in part in any medium now known or hereafter created.
Signature of Author:.
Signature redacted
Department of Civil and Environmental Engineering
May 21, 2015
Certified by:
Signature redacted__
' Pierre Ghisbain
Lecturer of Civil and Environmental Engineering
hysis Supervisor
Accep-nted hv:
Signature redacted
7leidi Nepf
f
Donald and Martha Harleman Professor of Civil and Environmental Engineering
Chair, Graduate Program Committee
Effect of Ground Motion Frequency on Non-Structural Seismic Damage
by
Han Wu
Submitted to the Department of Civil and Environmental Engineering on May 21, 2015
in Partial Fulfillment of the Requirements for the Degree of
Master of Engineering in the Field of High Performance Structures
Abstract
The need for economic consideration in structural design triggered the emergence of
performance-based design to minimize material waste while achieving better performance.
The displacement measurements of structures are significant to structural damage evaluation,
and most seismic design methods consider the effect of peak ground acceleration, while the
frequency content of seismic activities remains largely unexplored.
In order to better
understand the impact of low magnitude seismic activities on non-structural damage, we
develop an assessment method for a specific site by comparing structural response with
frequency content analysis on corresponding seismic activities.
A method of analyzing frequency content of seismic activities at San Francisco is presented.
By computing Discrete Fourier Transforms, time history seismic data is transformed from time
domain to frequency domain.
We apply structural response analysis on a representative residential/office/mixed-use building
to evaluate seismic performance. We scale earthquakes with respect to the natural frequency
of the target structure, and structural response simulations are performed based on scaled
We utilize linear analysis in structural response simulations with constant
earthquakes.
damping ratio. The applicability of linear analysis as well as varying damping ratio requires
further justification.
A comparison between frequency content analysis and structural response is presented. The
frequency content analysis provides an amplitude distribution for each seismic activity, and the
magnitude of structural response is influenced by the amplitude distribution for corresponding
seismic activities.
Thesis supervisor: Pierre Ghisbain
Title: Lecturer of Civil and Environmental Engineering
Acknowledgments
The work presented in this thesis would not have been accomplished without the support of my
thesis advisor, Dr. Pierre Ghisbain. His extraordinary knowledge in structural engineering
has inspired and promoted this research. I am grateful for his academic support, as well as
mentorship during my stay at MIT.
The department of Civil and Environmental Engineering at MIT provides me with a great
environment to accomplish this thesis. I am grateful to all my classmates for contributing
countless new ideas on this research. Also, I am particularly grateful to Prof. Jerome Connor
for his advocacy in performance based engineering, with whom discussion of this work has
inspired incredible improvements.
Table of Contents
Table of Contents
Chapter 1. Introduction .................................................................................................................................
1.1
Perform ance-Based Earthquake Engineering ......................................................................
10
10
1.2 Frequency Content Analysis .......................................................................................................
11
1.3 N on-Structural D amage A ssessm ent............................................................................................
12
Chapter 2. Frequency Content Analysis...................................................................................................
2.1
13
Introduction...............................................................................................................................13
2.1.] Site Specification..................................................................................................................13
2.1.2 D ata Selection......................................................................................................................15
2.1.3 Chapter Objectives and Organization..............................................................................
2.2 Proposed M ethod ............................................................................................................................
15
16
2.2.1 Procedure.............................................................................................................................16
2.2.2 FastFourierTransform .......................................................................................................
2.3
18
Seism ic Data Analysis..........................................................................................................
20
2.3.1 Earthquakes and Records ................................................................................................
20
2.3.2 Records Set Filtering............................................................................................................27
2.3.3 Frequency Content ofSeismic Data...............................................................................
30
2.4 Sum m ary.........................................................................................................................................33
Chapter 3. N on-Structural Dam age A ssessm ent .......................................................................................
3.1 Introduction.....................................................................................................................................35
35
Table of Contents
3. L I Sample Structure.................................................................................................................. 35
3.1.2 Chapter Objectives and Organization.................................................................................. 35
3.2 Sam ple Structure D esign ................................................................................................................. 36
3.2.1 D esign Assumptions ............................................................................................................. 36
3.2.2 Simplified Gravity D esign .................................................................................................... 37
3.3 Structural Response ........................................................................................................................ 39
3.3.1 SD OF ................................................................................................................................... 39
3.3.2 Seism ic Data Scaling ........................................................................................................... 40
3.3.3 Finite Element Analysis ....................................................................................................... 43
3.4 Summ ary ......................................................................................................................................... 53
Chapter 4. Conclusions ................................................................................................................................. 55
4.1 Sum mary of Contributions .............................................................................................................. 55
Appendix A ................................................................................................................................................... 60
Appendix B ................................................................................................................................................... 71
Appendix C ................................................................................................................................................... 87
References ..................................................................................................................................................... 88
8
Figures Summary
Figure 1 San Francisco Fault M ap.....................................................................................................14
Figure 2 Recording Station Location................................................................................................
14
Figure 3 NGA W EST-2 User Interface ................................................................................................
17
Figure 4 NGA-W EST 2 Input Interface ..............................................................................................
22
Figure 5 Strike Slip Fault........................................................................................................................24
Figure 6 Selected Time History Acceleration ..................................................................................
26
Figure 7 Selected Discrete Fourier Transforms ...............................................................................
31
Figure 8 Cut off Discrete Fourier Transform ....................................................................................
32
Figure 9 Sample Structure First Dynamic Mode ...............................................................................
40
Figure 10 RSN8617 Acceleration (top) and Displacement (bottom)...............................................
44
Figure 11 RSN 12192 Acceleration (top) and Displacement (bottom)............................................
45
Figure 12 RSN 19427 Acceleration (top) and Displacement (bottom)............................................
46
Figure 13 RSN21418 Acceleration (top) and Displacement (bottom)............................................
47
Figure 14 RSN 12980 Acceleration (top) and Displacement (bottom)............................................
48
Figure 15 Maximum Acceleration .....................................................................................................
52
Figure 16 Rank Comparison ..................................................................................................................
54
Figure 17 Maximum Displacement ..................................................................................................
54
Figure 18 Weight Distribution ...............................................................................................................
57
Figure 19 Maximum Acceleration Based on W eight Distribution ...................................................
58
9
Chapter 1. Introduction
Chapter 1. Introduction
1.1 Performance-Based Earthquake Engineering
Earthquake is one of the most catastrophic natural hazards known to human beings. The
earthquake happens as a result of sudden slip between two chunks of earth lying alongside each
other (Wald 2008). Due to limitations on current technology, earthquake early warning
system is only capable of alarming people after an earthquake has been triggered instead of
forecasting upcoming earthquakes. As most of the populated and urbanized areas are located
in seismically active zones, the threat of seismic activities on built environment increases as
population grows.
Building is the type of structure that provides people with sheltering but unfortunately the
specific structure that is exposed to the most direct damages in seismic activities. As a result
of life threatening situations, focus on quality of design and construction of structures are
increasingly high. In 2008, a catastrophic earthquake with Richter magnitude of 8.0 hit China
and caused tremendous casualties with 69,000 deaths and 18,000 missing (Global Risk
Miyamoto, 2008). This heartbreaking event followed by two other earthquakes in Haiti and
Chile in 2010 emphasize the importance of seismic analysis and design.
Despite the lack of seismic design code requirement in under-developed countries or even in
developing countries, developed countries, such as United States, have established
comprehensive standards regarding seismic design. However, since every earthquake is
different in terms of behavioral characteristics, it is extremely difficult to compare earthquakes
across different regions. Therefore, code specific seismic design tends to be over-generalized,
and as a result, unnecessarily wasting economic resources.
Performance based earthquake engineering is highly appreciated under the situation of
increasing seismic risk.
In performance based earthquake engineering, structures are
designed and analyzed through iterations. The very approach tends to provide better design
in terms of utilizing economic resources and performance under seismic activities. Although
design codes incorporate performance-based features, the pure performance based design
process is different from code based design in terms of evaluation method.
10
Chapter 1. Introduction
1.2 Frequency Content Analysis
Every seismic activity can be decomposed into two major components, namely frequency and
magnitude. Most seismic analysis methods that predict structural responses are focusing on
magnitude of the activity.
Magnitude of seismic activities is typically represented by
measuring ground accelerations. As ground acceleration is the primary measure of seismic
activities, the major analysis focus of seismic activities is on the response of structures with
respect to ground accelerations. On the other hand, earthquake is a cyclic behavior of waves
with different magnitudes, and thus the frequency of seismic activities is represented by
measuring the number of cycles of wave occurring in a specified period of time (Shearer, 2010).
As mentioned in section 1.1, earthquake is a natural behavior due to sliding between two pieces
of earth, and the failure surface between these two pieces of earth is called the fault. Since
faults are developed after earthquakes, the probability of earthquake happening again at faults
is extremely high. Therefore, seismic activities tend to be periodic with decreasing return
periods as magnitude of earthquakes increases. As some urbanized areas are built on faults,
earthquake activities at these specific locations are unavoidable.
While the effect of ground accelerations on structures are drawing great attention, the effect of
frequency content on structural behaviors remains largely unexplored. Also, besides avoiding
resonance, design codes contain very few discussions on frequency behavior while heavily
incorporating peak ground acceleration analysis. As the result of cyclic nature of seismic
activities, low magnitude earthquakes tend to happen more frequently than high magnitude
earthquakes. However, design codes focus primarily on high magnitude earthquakes and their
effects on structural damage. The reason behind is that although most structures experience
limited high magnitude earthquakes during their lifetimes, the damage due to such earthquakes
is catastrophic, while low magnitude earthquakes cause no structural damage or limited
structural damage.
Structures have different natural frequencies due to variations in stiffness and mass. And the
natural frequency of structures affects their responses when experiencing earthquakes with
The frequency of earthquakes experienced by a specific
different frequency contents.
structure changes with the fault type, soil condition between fault and the site and many other
Although comparing different earthquakes across regions is difficult, it is
variables.
reasonable to compare earthquakes at the same location with similar magnitudes.
11
Chapter 1. Introduction
1.3 Non-Structural Damage Assessment
As structures are used for different purposes, non-structural damage begins to draw attention.
The importance of non-structural damage is emphasized after the earthquake with a magnitude
of 6.0 hit Napa Valley, California, in 2014. While causing no casualties, the estimated
economic damage is over $400 million. Although Napa Valley is not a typical representative
of non-structural damage examples due to its high storage value, the very event does
demonstrate the necessity for non-structural damage considerations. (EERI, 2014)
Despite the economic impact of non-structural damages, other non-structural damages may
even cause casualties.
Structures with different purposes have different non-structural
damage after earthquakes. According to FEMA, common types of nonstructural earthquake
damages are separated into three categories, namely Life Safety, Property Loss, and Functional
Loss. These categories include heavy exterior cladding, heavy interior walls, unbraced
masonry parapets or other heavy building appendages, unreinforced masonry chimneys,
suspended lighting, large/heavy ceilings, tall/slender/heavy furniture, heavy unanchored
contents (including televisions, computers, countertop laboratory equipment and microwaves
etc.), glazing, fire protection piping, hazardous materials release, gas water heaters, and other
components, such as elevators (FEMA, 2012).
12
Chapter 2. Frequency Content Analysis
Chapter 2. Frequency Content Analysis
A method to evaluate the frequency content of seismic data is presented in this chapter. The
Fast Fourier Transform method is proposed for the data transformation from time space to
frequency space. All data processed and analyzed are borrowed from the NGA West 2
database at the Pacific Earthquake Engineering Research center.
2.1 Introduction
This section introduces the approach to seismic data selection and transformation, as well as
its corresponding methodology. This thesis is based on the data and analysis done in this
chapter. Basic methodology and formulae used in this chapter are defined in this section.
2.1.1 Site Specification
As mentioned in Chapter 1, seismic activities are generated due to relative earth movement.
Although most important faults are along the boundaries between continents, many other faults
are located everywhere. These failure surfaces vary dramatically in terms fracture types and
corresponding geotechnical characteristics.
It is not practical comparing and contrasting
different earthquakes across different failure surfaces. Also, the response of a structure to
seismic activities is influenced by the soil conditions and geotechnical characteristics both at
the structure site, and along the route of seismic wave transmission. Active faults within an
area are relatively permanent comparing to the lifetime of structures within that area. A
structure locating in the active seismic zone will experience earthquakes generated by existing
faults within this area. Also, geotechnical conditions at the structure site and along the route
between the site and the fault will vary limitedly in the lifespan of the structure.
Based on the site oriented characteristic, the analysis performed in this thesis is based on a
specific site, and the site chosen for further analysis is San Francisco. All data processed in
this thesis is recorded from the seismic station located at the San Francisco Fire Department,
22 Golden Gate Park. The specific location of the seismic station is labeled in Figure 2.
The advantages for choosing San Francisco are listed below:
M
San Francisco is located in an active seismic zone. U.S. west coast is a seismic active
zone, and therefore seismic data are widely available. Figure 1 shows the seismic
map of San Francisco area with all faults labeled out. Also, non-structural damage
13
Chapter 2. Frequency Content Analysis
is normally caused by low magnitude earthquakes like the Napa Valley Earthquake,
which creates a monetary loss of $400 million.
0
San Francisco is a highly populated area. According to data in 2014, Average
household income in San Francisco is $79,624, which is above national average of
And thus seismic activities will trigger relatively high non-structural
$52,250.
damage cost within this area and more life threatening situations. Running seismic
activities analysis within this area is meaningful (Noss, 2014).
0
All data processed in this thesis is recorded by the San Francisco Fire Department
Data recorded at the very specific site is representative of
seismic station.
characteristics of seismic activities experienced at this site. And thus, we make an
assumption that the data recorded at this site can be used to predict possible seismic
activities in the future at this very site.
Figure 2 Recording Station Location (Google)
Figure
1 San Francisco Fault Map (USGS)
14
Chapter 2. Frequency Content Analysis
2.1.2 Data Selection
Data recorded at the recording station in the San Francisco Fire Department are borrowed
from PEER center, and all data are accessed using NGA West 2. The NGA West 2 provides
readily filtered time history data sets, as well as scaled response spectra.
However,
considering the frequency content focus of this thesis, only time history data are accessed, and
the seismic data are scaled based on the ASCE 7-10 response spectrum at the natural frequency
of the structure analyzed in this thesis. More details about scaling earthquakes are discussed
in section 3.3. Also, detailed data selection procedures and summary of data set are discussed
in section 2.3.2.
2.1.3 Chapter Objectives and Organization
This chapter discusses the implementation of Fast Fourier Transform of seismic data by
converting time history data from time space to frequency space. The objectives of this
chapter are: 1) Evaluating frequency content characteristics of earthquakes of the chosen site;
2) Preparing data set for later structural damage analysis. The results of the analysis in this
chapter are: 1) The summary of the relationship between earthquakes and their corresponding
frequency content; 2) The filtered earthquake records available for structural analysis.
This chapter first demonstrates the proposed method of transforming seismic data, Fast Fourier
Transform in section 2.2. And in section 2.3, detailed data processing procedures along with
analysis results are discussed. Finally, section 2.4 summarizes the findings on frequency
content of earthquake records and provides summary of scaling factors for processed
earthquake records.
15
Chapter 2. Frequency Content Analysis
2.2 Proposed Method
A commonly used procedure to transform data from time space to frequency space is presented
in this section. It is followed by an explanation of the methodology behind Fast Fourier
Transform and its corresponding implementation. Specific terminologies and functions are
presented in this section as well.
2.2.1 Procedure
The proposed frequency content analysis procedure basically includes two parts: 1) Accessing
site specific seismic time history data records from NGA West 2; 2) Applying Fast Fourier
Transform to process desired data. NGA West 2 is a ground motion database operated by the
Pacific Earthquake Engineering Research Center (PEER). Filtering data from the database
requires different input parameters. Figure 3 illustrates the user interface of the database,
illustration of input parameters are listed below:
RSN
record sequence number, each record in the data base is given a unique record
sequence number, it can be used to locate a specific record
Event Name
event name, each earthquake event is given a name, the system will search
for the input string in the event name field of the database
Station Name
station name, the system will search for the input string in the station name
field of the database
Fault type
fault type, selection for fault types including strike slip, normal/oblique,
reverse/oblique, and combinations of these three fault types
Magnitude
magnitude of the earthquake, Richter magnitude is used in the magnitude
field
R_JB (km)
closest distance to the surface projection of the fault plane
R-rup (km)
closest distance to the surface projection of the rupture plane
Vs30 (m/s)
time-averaged shear-wave velocity to 30-meter depth.
D5-95 (sec)
significant duration of normalized acceleration between 5% and 95%
16
Chapter 2. Frequency Content Analysis
Pulse
pulse, selection for types of earthquake including pulse like records, no pulse
like records and any records
New Search
Load Supe Input Values CinpW Vakm
Figure 3 NGA WEST-2 User Interface
17
Chapter 2. Frequency Content Analysis
2.2.2 Fast Fourier Transform
Fast Fourier Transform is an algorithm used to compute the discrete Fourier transform. The
purpose of the Fourier transform is converting a signal from a time domain to frequency domain.
Discrete Fourier transform converts a finite list of functions into a list of finite combination of
complex sinusoids. And these complex sinusoids are combined with coefficients accordingly
to produce the same value as of the original functions. Speaking of that, any wave functions
can be decomposed into a combination of sinusoidal functions, and these functions are arranged
in terms of frequency and corresponding coefficients. Results of the Fourier transform
include frequency content distributions of a specific wave function. The characteristics of the
wave functions of the Fourier transform enable us to performe frequency content analysis on
seismic records. (Heckbert, 1998)
Fast Fourier transform is an ideal method to compute Fourier transforms. This method rapidly
computes coefficients or factors of a discrete Fourier transform matrix with a fixed number of
sinusoidal functions, and by factorizing most of the coefficients to zero, the original function
can be expressed with a product of different sinusoidal functions. The two major benefits of
applying fast Fourier transform to ground motion time history data are listed below:
"
Ground motion activities are represented using wave functions. Ground motion is
the simple shaking behavior of earth in both horizontal and vertical directions.
However, ground motion is complex to compute since it combines different sinusoidal
functions in a single event. Using Fourier transform will effectively decompose the
ground motion into a combination of sinusoidal functions with corresponding
coefficients, and thus frequency content of each ground motion can be determined by
evaluating different combinations of sinusoidal functions.
"
Each ground motion record is numerically intensive. For data recorded in NGA West
2 database, the sampling frequency is 100 Hz. For a ground motion activity lasting
for 100 seconds, there are 10,000 data points recorded.
Therefore, fast Fourier
transform provides a rapid way of computing discrete Fourier transforms.
Also,
ground motion data includes a considerable amount of noise, applying fast Fourier
transform can effectively determine the weight of different sinusoidal functions at
different frequencies, and therefore produces a more intuitive observation of
frequency content of ground motion activities.
Discrete Fourier transform is equivalent to continuous Fourier transform known only at a finite
instants separated by sample times T. The Fourier transform function is expressed as follow:
18
Chapter 2. Frequency Content Analysis
F(o) = ff(t)e-aitdt
where
W
angular frequency, [rad/s]
t
time, [s]
F(a)
Fourier transform of original signal
f (t)
original signal
(2- 1)
The function (2- 1) illustrates the Fourier transform of a continuous signal. However, the
integration of the continuous-time signal over infinite upper and lower bounds is neither
practical nor necessary. For ground motion data processing, signals are processed using
sampled form with a specific time interval, and therefore, we can replace integration by
applying summation over the time interval T, i.e. Discrete Fourier Transform. The discrete
Fourier transform is expressed in equation 2-2 as follows:
N-1
F(OJk) 4 Y
f(t)e-i&ktn,
k = 0,1,2, ... , N
-
1,
(2-2)
n=O
where
Z'iJf(n) f(0)+f(1)+---+f(N-1)
f(tn)
input signal amplitude (real or complex) at time tn [s]
tn
nth sampling instant [s], n an integer
T
sampling interval [s]
F(Ok)
spectrum of x, at frequency Wk
og
kth frequency sample [rad/s]
N
number of time samples
0
As explained at the beginning of this section, fast Fourier transform is the cheapest way of
computing discrete Fourier transform in terms of calculation intensity. Fast Fourier transform
19
Chapter 2. Frequency Content Analysis
is an algorithm introduced by Cooley-Tukey, and it significantly reduces computation intensity.
As equation (2- 2) illustrates, evaluating the definition requires N 2 + N(N - 1) operations:
N 2 operations of complex multiplications and N(N - 1) operations of additions. The fast
Fourier transform algorithm used in this thesis is the Cooley-Tukey algorithm, developed by
J.W. Cooley and J.W. Tukey in 1965. The algorithm divides the transform into two pieces of
size N/2 at each step, and continues the decomposition procedure.
By utilizing the
algorithm, operations required for computing discrete Fourier transform reduce to
(N/ 2 ) log 2 N complex multiplications and (N) log 2 N additions.
The radix-2 Cooley-
Tukey operations are limited to time intervals of power of two sizes. However, in practice,
any other factorization can be applied. In this thesis, sizes of time samples are round up to
the next power of two, and thus we can enjoy the computation efficiency while losing negligible
accuracy by manipulating data sizes. (Smith III, 2007)
2.3 Seismic Data Analysis
A detailed data processing and analysis procedure is discussed in this section. This section
starts out discussing how seismic data used in this thesis are accessed, and follows by an
explanation in data filtering. Then, we apply fast Fourier transform to the data and transform
data from time domain to frequency domain.
2.3.1 Earthquakes and Records
As mentioned in section 2.2, all data accessed and processed in this thesis are obtained from
the NGA-West 2 database operated by Pacific Earthquake Engineering Research Center. The
NGA-West 2 database collects ground motion records from shallow crustal events in active
seismic zone. The database has a set of strong motion records and metadata tables. All
metadata tables were developed by experts within the field of interest, and contain spectrums
for different analysis purposes (PEER NGA WEST). However, in the scope of this thesis, we
will use the strong motion records only, and corresponding spectrums are customized for the
purpose of this thesis only.
There are three basic measurements related to the magnitude of ground motion activities,
namely, ground acceleration, ground velocity and ground displacement.
Ground motion
records in the NGA-West 2 database provide all three different measurements. Since the
focus of this thesis is on the performance of the target structure under seismic activities, we
need to replicate the earthquake events for structural analysis purpose.
Based on this
limitation, we only utilize ground acceleration records for analysis. For each set of ground
acceleration record, there are three subsets of acceleration record indicating ground motion in
three different directions, two horizontal directions plus one vertical direction. For the scope
20
Chapter 2. Frequency Content Analysis
of this thesis, we only take horizontal directions into account, more details about this process
is discussed later in this section.
As discussed at the beginning of this section, we use the NGA-West 2 database to access
earthquake records. Since the database has a tremendous volume of ground motion data for
San Francisco area, we only consider the data recorded by the San Francisco Fire Department
ground-motion recording station. The input parameters of the NGA-West 2 interface for
target data are listed below:
RSN
N/A1 ; since we are finding multiple data sets instead of a specific data set,
this section is left blank
Event Name
N/A; since there are multiple faults within the area and the purpose of
sourcing data is finding all possible earthquake events happened in the
previous, this section is left blank
Station Name
22 Golden; since we are looking for ground motion records from the San
Francisco Fire Department ground motion recording station only, the station
needs to be specified in the input section. "22 Golden" is the first chunk of
characters in the station's name string
Fault type
N/A; since we are interested in frequency content of seismic data at a specific
site, the fault type does not need to be specified. And therefore, this section
is left blank
Magnitude
N/A; since all earthquakes will be scaled to produce equivalent results, this
section is left blank for all possible past events
RJB (km)
N/A; No specific fault is chosen
R-rup (km)
N/A; No specific fault is chosen
Vs30 (m/s)
N/A; No specific earthquake magnitude is chosen
D5-95 (sec)
N/A; No specific earthquake magnitude is chosen
1
N/A used in this section represents blank in the NGA-West 2 interface
21
Chapter 2. Frequency Content Analysis
N/A; No specific earthquake type is chosen
Pulse
NGA-West 2 database provides a suite of spectrum analysis when searching for ground motion
records. Since we are not using the spectrum provided by NGA-West 2, the input parameters
for the suite section are randomly chosen. Figure 4 shows the interface of NGA-West 2 with
input parameters listed above.
New Search
Load
~
Ak Sm np VLus rG1!vnp auws
Figure 4 NGA-WEST 2 Input Interface
22
Chapter 2. Frequency Content Analysis
Based on the searching with input parameters above, we are able to locate total of 25 ground
motion data sets recorded by the San Francisco Fire Department recording station dated from
2003 to 2008, and each record represents a unique event. Out of 25 ground motion records,
22 of them are generated by the strike slip fault type. Strike slip faults are vertical or nearly
vertical fractures (as shown in Figure 5) where two pieces of earth next to each other move
horizontally or nearly horizontally.
Strike slip is the most common fracture plane in
California, and therefore the ground motion data obtained from NGA-West 2 is representative.
Table 1 below summarizes the records obtained from NGA-West 2 with earthquake mechanism
specified.
Record Name
Magnitude
Time
Mechanism
RSN12192_40199209
RSN12980_40146204
RSN19427_40138528
RSN19457_40139437
RSN19488_40139808
RSN19537_40145275
RSN19640_40152518
RSN19703_40154733
RSN19813_40182619
RSN19863_40183725
RSN19898 40187964
RSN19978_40193843
RSN20372_51128377
RSN20421_51132363
RSN20478_51136961
RSN20509_51147365
RSN20541_51151992
RSN20710_51156428
RSN20891_51169283
RSN20947_51171759
RSN21064_51177644
RSN21381_51203888
RSN21418_51207740
RSN21504_51177103
RSN8617 40204628
4.2
4.0
3.9
3.6
4.3
4.0
3.6
4.3
3.6
3.7
4.5
3.4
4.1
3.5
3.7
3.7
3.7
4.2
3.7
4.3
3.7
3.5
4.1
3.6
5.5
2007
2003
2002
2002
2003
2003
2004
2004
2006
2006
2006
2007
2003
2003
2004
2004
2004
2005
2006
2006
2007
2008
2008
2006
2007
strike slip
strike slip
strike slip
normal
strike slip
strike slip
normal
strike slip
strike slip
strike slip
strike slip
strike slip
strike slip
strike slip
reverse
strike slip
strike slip
strike slip
strike slip
strike slip
strike slip
strike slip
strike slip
strike slip
strike slip
Table 1 Ground Motion Data Summary
23
Chapter 2. Frequency Content Analysis
Strike-Slip Faults
right lateral
left lateral
Artwork by Dale Glasgow
Figure 5 Strike Slip Fault (Nevada Seismological Lab)
As discussed earlier in this section, ground acceleration data is the only measurement we take
into account. Also, we ignore vertical ground acceleration for the scope of this thesis. Sincehorizontal ground acceleration is measured in two directions, North-South and West-East, it is
practical to aggregate two measurements into a single acceleration record. In order to merge
two acceleration records, we apply Square Root of Sum of Square (SRSS) method to compute
the single acceleration record. The theory behind aggregating acceleration file and its
advantages are listed below:
"
Ground motion acceleration records are measured at a fixed point, i.e. a specified
recording station.
The directions of the acceleration records depend on the
orientation of the recording station as well as the orientation of the recording
instruments.
In order to produce analysis results that can be applied without
restrictions on structure orientation, acceleration records in two directions need to be
combined into one acceleration record. And then, the combined acceleration record
can be applied from both directions of the structure in later structural analysis part in
chapter 3.
"
Response spectrum of the structure requires single sided record data. By aggregating
acceleration records, we ultimately create the single sided acceleration record that can
be applied later in the structural analysis part.
24
Chapter 2. Frequency Content Analysis
SRSS is a rapid and efficient way of combining records. It takes the sum of square of two
parameters, and the positive result of the square root of the sum is the target value. In our
case, we take the sum of square of ground acceleration records from both directions at each
time step, and the square root of the sum is the aggregated acceleration record. The sampling
frequency of NGA-West 2 database is 100 Hz, meaning the time step is 0.01 sec. The time
interval of each record lasts from 200 seconds up to 360 seconds depending on the event. And
therefore, each data record contains a considerable amount of sampling points, ranging from
20,000 points to 36,000 points. Computation efficiency is significant, and thus SRSS is ideal
for the scope of our analysis for its high performance cost ratio. By applying SRSS, the total
operations for both data processing and structural analysis are cut in half. The SRSS function
and its parameters are defined in equation 2-3 as follows:
iiagg
where
iagg
NS
UWE
N
E
(2-3)
aggregate acceleration [ft/s 2]
2
acceleration in North-South direction [ft/s
2
acceleration in West-East direction [ft/s
In order to obtain a more intuitive understanding of the ground motion activities, we utilize
Matlab to plot time history diagrams from the aggregated acceleration. As discussed before,
computational efficiency is significant in our analysis, and Matlab is ideal for analyzing data
with intensive sampling data points. Also, Matlab is the most suitable solution for repetitive
computations, which is the case for plotting time history diagrams for different data sets. In
addition, by applying a plot feature of Matlab, we are able to filter out noise and aftershock
portions of the data. Selected time history diagrams for ground acceleration are shown below
in Figure 6, and the remaining are shown in Appendix A. The unit for measuring ground
acceleration in NGA-West 2 database is in percentage of gravitational acceleration, meaning
the Y-axis of time history diagrams shows the magnitude of acceleration in percentage of
gravitational acceleration, while X-axis shows the time [s].
25
Chapter 2. Frequency Content Analysis
Single Sided Acceleration Diagram
0.14
Single Sided Acceleration Diagram
0012
RSN20541
RS#4e17
0-12
0.01
0.1
0.008
0.08
0.006
8
8006
0,004
I
0.04
0002
0.02
nL-J
0
50
100
008v
150
200
Time (s)
250
350
300
~~LJL
00
400
100
50
150
200
250
350
300
400
Time (s)
Single Sided Acceleration Diagram
Single Sided Acceleration Diagram
015r
RSN12teO
0.07
006
01
005
004
0.02
001
0
a 10-3
8
L
005k
50
100
150
o
250
200
-
0
20
L
40
L
60
80
Time (s)
Single Sided Acceleration Diagram
100
120
Time (s)
160
140
180
200
Single Sided Acceleration Diagram
10-3
--
-
003
R8N16537
--
RI2I5J
2.5
6
2
4
8
3
I
8
<1
2j.
05
200
250
0
50
100
Time (s)
150
200
Trpm (S)
250
300
350
40
0
Figure 6 Selected Time History Acceleration
26
Chapter 2. Frequency Content Analysis
2.3.2 Records Set Filtering
Time history data plots in the precious section provided an intuitive view of the ground motion
activities. Keep in mind, the ground acceleration records plotted above are single sided as a
result of aggregating accelerations in both directions. Also, single sided acceleration records
have no impact on the performance of structures. And therefore, single sided acceleration
records are valid to be utilized within the scope of this thesis. Ground acceleration time
history records plotted above are summarized as three categories as follow:
E
Pulse like wave function. This type of earthquake has one major pulse in the ground
motion acceleration plot. And the magnitude of the pulse is significantly larger than
the rest ups and downs of the wave function. Pulse like ground motion is the most
typical ground motion activity, which produces one significant shake with a bunch of
small vibrations.
0
Two-pulse wave function. This type of earthquake has two major pulses follow each
other in the ground motion acceleration plot. And the difference in magnitude
between these two pulses is relatively small compares to the difference with the rest
ups and downs of the wave function. Two-pulse ground motion is similar to a pulse
like ground motion follows by another pulse like ground motion within a short time
interval.
N
Multi-pulse wave function. This type of earthquake has multiple major pulses follow
each other in the ground motion acceleration plot. Each pulse is accompanied by a
series of smaller vibrations. Multi-pulse like ground motion is not a typical wave
function in our analysis.
In Table 2 ground acceleration records are summarized in terms of shape of wave function,
also, corresponding fault types are listed as well for later analysis and comparison. According
to our summary, out of 25 ground acceleration records, 15 are pulse like ground motion
activities, 8 are two pike pulse like ground motion activities, and the other 2 are multi-pulse
ground motion activities. For our scope of analysis, in order to limit the variables other than
frequency related parameters, we eliminate multi-pules ground motion in later analysis. As
for two pulse ground motion activities, we tend to eliminate noise manually as much as possible,
and the same ideology applies to pulse like ground motion activities as well. Also, the lengthy
recording time results in delays in structural analysis computation time. For the consideration
of computation efficiency, tails of acceleration records with negligible magnitudes are deleted
manually.
27
Chapter 2. Frequency Content Analysis
Record Name
Wave Function
Time
Mechanism
RSN12192
Pulse
2007
strike slip
RSN12980
Pulse
2003
strike slip
RSN19427
Pulse
2002
strike slip
RSN19457
Pulse
2002
normal
RSN19488
Two-Pikes
2003
strike slip
RSN19537
Two-Pikes
2003
strike slip
RSN19640
Pulse
2004
normal
RSN19703
Two-Pikes
2004
strike slip
RSN19813
Two-Pikes
2006
strike slip
RSN19863
Multi Pikes
2006
strike slip
RSN19898
Pulse
2006
strike slip
RSN19978
Two-Pikes
2007
strike slip
RSN20372
Two-Pikes
2003
strike slip
RSN20421
Pulse
2003
strike slip
RSN20478
Pulse
2004
reverse
RSN20509
MultiPikes
2004
strike slip
RSN20541
Two-Pikes
2004
RSN20710
Two-Pikes
2005
strike slip
strike slip
RSN20891
Pulse
2006
strike slip
RSN20947
Pulse
2006
strike slip
RSN21064
Pulse
2007
strike slip
RSN21381
Pulse
2008
strike slip
RSN21418
Pulse
2008
strike slip
RSN21504
Pulse
2006
strike slip
RSN8617
Pulse
2007
strike slip
Table 2 Time History Data Category
28
Chapter 2. Frequency Content Analysis
Record Name
(Data Points)
Wave Function
Mechanism
RSN12192
RSN12980
RSN19427
RSN19457
RSN19488
RSN19537
RSN19640
RSN19703
RSN19813
RSN19898
RSN19978
1600-6000
2000-6000
2000-6000
1600-6000
5000-10000
5000-10000
5000-10000
5000-10000
5000-10000
5000-10000
5000-10000
Pulse
Pulse
Pulse
Pulse
strike slip
strike slip
strike slip
normal
Two-Pikes
Two-Pikes
Pulse
strike slip
strike slip
normal
Two-Pikes
Two-Pikes
Pulse
strike slip
strike slip
strike slip
Two-Pikes
strike slip
RSN20541
1-6000
Two-Pikes
strike slip
RSN20710
RSN20891
RSN20947
RSN21064
RSN21381
RSN21418
RSN21504
RSN8617
1000-6000
1-5000
2000-6000
2000-5000
1-4000
1-5000
1-5000
1000-6000
Two-Pikes
Pulse
Pulse
Pulse
Pulse
Pulse
Pulse
Pulse
strike
strike
strike
strike
strike
strike
strike
strike
slip
slip
slip
slip
slip
slip
slip
slip
Table 3 Cut off Range
Table 3 summarizes the cut off range of data points for the ground motion acceleration data
records plotted above. There are total of 25 data sets accessed from NGA-West 2 database,
and they can be combined into 3 different wave function categories as mentioned above.
Several data sets are eliminated randomly to minimize the volume of necessary data sets.
Also, cut-off points for data sets are determined intuitively for the purpose of eliminating blank
values or negligible values. Filtered time history plots for ground motion acceleration are
plotted with Fourier transform diagrams in section 2.3.3.
29
Chapter 2. Frequency Content Analysis
2.3.3 Frequency Content of Seismic Data
As mentioned in section 2.2, fast Fourier transform is used in our analysis to transfer ground
acceleration records from time space to frequency space. Considering the large amount of
sampling points in our data sets, we have to use numerical tools computing Fourier transforms.
Also,
Matlab has a built-in function that computes fast Fourier transform automatically.
Matlab is efficient in terms of plotting and handling large volume of data, and thus, we use
Matlab to compute fast Fourier transform.
Matlab's built-in fast Fourier transform function uses Cooley-Tuckey method computing
discrete Fourier transform. The function and its implementation are listed below in equation
2-4:
Y = ff t(X, n)
where
Y
n-point Discrete Fourier Transform
n
size of X
X
matrix of original data in time space
ff t(X, n)
Fast Fourier Transform operation command
(2-4)
As mentioned in section 2.2, Cooley-Tuckey method's computation efficiency is limited by the
power of two size of sampling points. Meaning, the count of data points must be power of
two. In order to take advantage of the computation efficiency, we deliberately make n, size
of X, the next power of two. And we will only plot the discrete Fourier transform up to the
signal length at the end. Selected filtered time-history ground acceleration diagrams are
The
plotted in Figure 7, along with corresponding discrete Fourier transform diagram.
remaining filtered time-history ground acceleration diagrams with corresponding discrete
Fourier transform diagrams are attached in Appendix A.
30
Chapter 2. Frequency Content Analysis
Single Sided Acceleration Diagram
0 15
Single Sided Acceleration Diagram
10-3
RSN20710
RSN0) 17-
0.1-
S
4-
0105
02
0
5
15
10
2D
25
30
35
40
45
50
Time (s)
Single-Sided Amplitude Spectrum of y(t)
0.02
0_
0
5
15
10
20
25
30
35
40
50
45
Time (s)
Sngle-Sided Amplitude Spectrum of y(t)
1.,t5 10-3
RSW17
11
0 01
0.006
0
0
5
10
20
15
25
30
35
40
45
50
0
0
5
10
20
15
Frequency (Hz)
25
30
35
40
45
-.
50
Frequency (Hz)
Single Sided Awceleration Diagram
0 03
Single Sided Aceleration Diagram
RSNI2192
0 06
002
001
0 02
0
35
20
25
30
Time (s)
Single-Sided Amplitude Spectrum of y(t)
10
5
10-3
15
---
40
0
45
e
1
10
15
25
20
30
35
40
45
Time (s)
Single-Sided Amplitude Spectrum of y(t)
10-3
,
RSN121921
5
15
4
1
2
05
0
O
5
10
15
20
25
30
35
40
45
50
0
5
10
15
Frequency (Hz)
i
~RSNr2lO4j~4
0)
0. 013
25
30
4A
35
45
so
Frequency (Hz)
Single Sided Aoceleratlon Diagram
0 D8
20
Single Sided Acceleration Diagram
0 08
--
0 04
0
2004
0 02
0.02
RSN2 1418
WI
01
0
5
10-3
40
30
35
25
Time (s)
Single-Sided Amplitude Spectrum of y(t)
10
15
20
-
45
50
0
5
10
15
20
25
30
35
40
45
50
Time (s)
Single-Sided Amplitude Spectrum of y(t)
-in'
-RS5~i418
RSN21504
4
2
2
0
5
10
15
30
25
20
Frequency (Hz)
35
40
45
50
0
5
10
15
20
25
30
35
40
45
50
Frequency (Hz)
Figure 7 Selected Discrete Fourier Transforms
31
Chapter 2. Frequency Content Analysis
The Discrete Fourier transforms illustrated above include different types of ground motion
acceleration data records. The maximum acceleration for all ground acceleration records
happens at 0 Hz, and the acceleration drops dramatically after that. After dropping to its
average level, the acceleration gradually dies out. The variation of acceleration after initial
high points tend to differentiate one data record from another. Although the difference in
accelerations at different frequencies is relatively small, the trend of variation between high
frequency accelerations and low frequency accelerations can be observed. Therefore, discrete
Fourier transforms are analyzed without initial high points in acceleration. Figure 8 shows
the discrete Fourier transforms of ground motion acceleration data for selected ground motion
records without initial high points.
Single Sided Acceleration Diagram
Single Sided Acceleration Diagram
8 1o4
1
015
IRSaN20710
0
S2
0.05
0
5
10
20
30
25
45
40
35
0
50
5
10
15
30
25
20
35
40
45
50
Time (s)
Time (s)
Single-Sided Akude Spectrum of y(t) cut-off
1-3
1-5
15
ude Specu
A
dd
10
1
cut-off
-- R20710
->-
Rdf6lJ7
05
0.5
5
0
10
15
25
20
35
30
40
45
50
0.
5
0
10
15
Single Sided Acceleration Diagram
35
20
25
30
Frequency (Hz)
Frequency (Hz)
40
45
50
Single Sided Acceleration Diagram
11'RSNIa451
RSN1I2192
-M
002
004
S0
0 01
02
5
0
8
15
10
35
30
25
20
40
Time (s)
cit-off
Single-Sided Amplitude Spectrum of y(t)
- RSN12a2
10-1
S
5
0
45
15
20
30
25
40
35
45
Time (s)
Single-Sided Amplitude Spectrum of y(t) cut-off
10
j
10
RSN1B45
3
-4
2
0
5
10
15
20
25
30
35
40
45
50
0
5
10
15
20
25
30
35
40
45
50
Frequency (Hz)
Frequency (Hz)
Figure 8 Cut off Discrete Fourier Transform
32
Chapter 2. Frequency Content Analysis
The plots above with cut-off discrete Fourier transforms clearly show the acceleration trends
in terms of frequency, and the plots for rest of ground motion data sets are listed in Appendix
By excluding initial high points, acceleration variations with frequency are clear.
A.
Although cut-off discrete Fourier transforms have a considerable amount of noise due to
complexities in the nature of ground motion activities, relative trend within the diagram is
obvious. According to the data analyzed above, most ground accelerations are peaked at two
different frequency ranges, namely, 1-3 Hz and 7 Hz. However, as observed in the diagrams
above, frequencies other than the two ranges mentioned before are having significant impact
on the behavior of ground acceleration.
2.4 Summary
This chapter completes the frequency content analysis. We use ground motion acceleration
data obtained from NGA-West 2 database to perform frequency content analysis using fast
Fourier transform. The data accessed are site specific, all data are recorded by San Francisco
Fire Department Recording Station. In order to accomplish the analysis task as well as
maintaining consistency and applicability of our analysis results, accelerations in two
horizontal directions are aggregated into one acceleration that can be applied later in the
structural response analysis. And time history diagrams for acceleration are plotted in
As mentioned in section 2.3, we cut-off negligible acceleration values to promote computation
efficiency. Discrete Fourier transforms are computed based on filtered data. However, as
we can see from Figure 7, initial high points of acceleration values skewed the Fourier
By eliminating initial high points, we are able to produce relatively clear
transforms.
The accelerations in frequency domain can be
acceleration trend based on frequency.
summarized of having frequency concentration range of 1-3 Hz and 5-7 Hz.
The reasons why discrete Fourier transforms display the very phenomenon are as follow:
*
Initial high points at low frequency contents are visualized due to complexity in the
nature of seismic data. Discrete Fourier transform establishes a frequency domain
for time history functions, and it decomposes time domain functions into a
combination of predetermined sinusoidal functions with corresponding coefficients.
However, since seismic activities are extremely complex, discrete Fourier transforms
The practical way of computing Fourier
of seismic data are hard to compute.
transforms is setting high initial values and modifying it with numerous functions.
*
As we can observe from the cut-off spectrum diagrams, the variation between
Meaning, sinusoidal functions with different
frequencies are clear but small.
frequency characteristics affect the overall behavior of the ground motion. However,
33
Chapter 2. Frequency Content Analysis
some sinusoidal functions with frequency ranges from 1-3 Hz or 5-7 Hz are weighted
more in terms of frequency content than that of other sinusoidal functions
34
Chapter 3. Non-Structural Damage Assessment
Chapter 3. Non-Structural Damage Assessment
A method to determine structural response is presented in this chapter and followed by a
discussion of evaluating non-structural damage of a target building. Finite element analysis
method is utilized to determine structural response criteria including accelerations and
displacements of the target structure.
3.1 Introduction
The section introduces the target structure to be analyzed and the approach used to evaluate
non-structural damage. All ground motion acceleration data used in this section are obtained
from the results in chapter 2. The data applied in this chapter include filtered ground motion
acceleration records, which are produced at the end of chapter 2. Also, the ASCE 7-10
response spectrum is used to scale ground motion acceleration records.
3.1.1 Sample Structure
A sample structure is designed in section 3.2 to be analyzed for performance under ground
motion activities. Since this thesis focuses on site specific structural response, the site chosen
for analysis is San Francisco, Bay Area. All data accessed in this thesis are obtained from
NGA-West 2 database, and the recording station is San Francisco Fire Department recording
station. The recording station is located in 22 Golden Gate Park as shown in Figure 2, and as
we can see, the recording station is located in a highly populated area near downtown San
Francisco. According to the picture, the typical building type in San Francisco is low rise
residential, mixed-use and office buildings. Considering the fact that this thesis is performed
to evaluate non-structural damage induced by seismic activities, which is applicable to the
majority of residents in San Francisco, we decide to design a typical office/residential/mixed
use low rise building for later use. Therefore, the sample structure is determined to be a 5
story 70 ft tall building with 5 bays by 6 bays in plan. The side view of the building is shown
in Appendix C, more details about the design process are carried out in section 3.2.
3.1.2 Chapter Objectives and Organization
This chapter discusses the finite element analysis of the structural performance under seismic
activities. Then the results obtained from the structural analysis are utilized in determining
non-structural damage assessment. The objectives of this chapter are: 1) Design a target
structure which is representative of residential/office/mixed-use structures in San Francisco; 2)
Evaluating structural response under seismic activities summarized in Chapter 2.
35
Chapter 3. Non-Structural Damage Assessment
This chapter first illustrates the design procedures of the target structures as well as sizing
procedures in section 3.2. And in section 3.3, detailed ground motion records scaling process
and structural response analysis are discussed in detail. Finally, section 3.4 talks about the
structural response results and demonstrates the non-structural damage assessment based on
the results.
3.2 Sample Structure Design
As mentioned in section 3.1.1, the target structure is set to be a 5 story 70 ft height building
with 5 bays by 6 bays in plan. The structure is selected based on the consideration of
representativeness of typical residential/office/mixed use buildings in San Francisco Area.
This section provides basic assumptions for the structural design as well as detailed gravity
design procedures. The reason for gravity design only is discussed in this section as well.
3.2.1 Design Assumptions
The target structure is selected to represent typical residential/office/mixed-use structures in
San Francisco Area. Several assumptions for the structure in terms of location and design are
listed below:
"
The proposed location for the structure is at 22 Golden Gate Park, which is the location
for the recording station where all data used in this thesis are recorded. Since this
thesis focuses on the seismic induced structural impact on a site specific basis,
analyzing a target structure at the specific site where data are recorded is ideal for
minimizing non-controllable effects of our analysis. Also, the 22 Golden Gate Park
is located close to downtown San Francisco, which is a representative location for
typical residential/office/mixed-use buildings.
"
The structural design of this building follows ASCE 7-10 building code. However,
safety factors for load determination and capacity determination are ignored. This
thesis focuses on comparison analysis between ground motion activities with different
frequency content, and therefore we are only using relative results instead of absolute
results. Based on this consideration, minimum design criteria is sufficient for the
design process
*
The structural design only considers gravity design. Meaning, no lateral system is
specifically designed for the structure.
The structure is designed with gravity
members only, and all members are sized with gravitational force considerations only.
36
Chapter 3. Non-Structural Damage Assessment
Two way slabs are designed to transfer load to beams, and beams are designed based
on tributary area method. Also, columns are designed using tributary area method
as well. Columns are assumed to be rigid and fixed at the ground support. The
overall structural system of the building is assumed to be a frame system. The frame
system, however, is not specifically designed to satisfy any lateral design criteria.
0
The building utilizes steel beams and columns with typical concrete floor slabs.
Steel structure is chosen based on two considerations: 1) steel structures have high
ductility, and thus steel structural behaviors are more predictable under low magnitude
earthquake events; 2) steel structures are easier to implement in finite element analysis
model, and using steel structures will promote computation efficiency.
3.2.2 Simplified Gravity Design
The simplified gravity design for the target structure is illustrated in this section. The design
procedure is decomposed into two parts, namely, load determination and member sizing.
Also, for each part, the computation is separated into parts in terms of member types. The
Design procedure is detailed once only for each type of structural member for illustration, and
other members are designed the same way.
Member
Size
Beam
W44X335
W8X31
Column
W8X48
Table 4 Member Sizing
37
Chapter 3. Non-Structural Damage Assessment
The parameters used in the load determination process are defined below:
a
distributed load demand [psf]
WL
line load [k/f]
AT
tributary area [ft2 ]
PD
demand load [kip]
Pc
member capacity [kip]
L
length [ft]
w
width [ft]
MN
nominal moment [kip -ft]
MD
moment demand [kip - ft]
0
reduction factor
Typical Beam:
a = 200 psf 2
ft 2
CO = 22 ft x 200 psf = 4.4 kf
WL x
=266.2 kip ' ft
MD
8
AT = 22 ft x 22 ft = 484
0MN > MD3
Select W44 x 335 from AISC Steel Manual
2
Distributed load is set to be 200 psf arbitrarily to match typical distributed load for residential/office/mixed-use
buildings
As mentioned in Section 3.1, we ignore factor of safety in the design procedure, and therefore the reduction factor 0 is
set to 1.
3
38
Chapter 3. Non-Structural Damage Assessment
Typical Column:
w = 200 psf
AT =
22 ft x 22 ft = 484 ft
PD=
x AT =
2
96.8 kips
Check for Buckling
12 x E x I
Pcr
where
(KL)
2
Pcr
critical load to induce buckling [kip]
E
Young's modulus [ksi]
I
moment of inertia [in']
KL
effective length [f t]
Select W 8 x 31 from AISC Steel Manual
There are two member sizes used for columns. The first column size is W 8 x 31, which is
applicable to columns above first floor. The second column size is W 8 x 48, which is
applicable to columns between ground floor and first floor.
3.3 Structural Response
This section performs structural analysis on the target structure, and the response under ground
motion activities are determined using data prepared in chapter 2. This section first develops
a virtual Single Degree of Freedom structure with natural frequency equivalent to first failure
mode frequency of the target structure. And the ground motion records are scaled with respect
to ASCE 7-10 response spectrum at the period corresponding to the first failure mode frequency.
After obtaining scaled seismic records, we use the finite element analysis model to determine
corresponding displacements and acceleration parameters.
3.3.1 SDOF
A virtual SDOF model equivalent to the first dynamic mode of the target structure is developed
in this section for the purpose of scaling ground motion acceleration records. In order to
obtain the frequency for the first dynamic mode of the target structure, we used the finite
element analysis model before conducting structural response analysis under seismic activities.
And therefore, we borrowed dynamic analysis results in terms of modal analysis. More detail
39
Chapter 3. Non-Structural Damage Assessment
about finite element model implementations and performing analysis are discussed in section
3.3.3
As determined from the finite element analysis model, frequency for the first failure mode of
the sample structure is 0.2716 Hz, and the corresponding period is 3.682 sec. The dynamic
mode is shown in Figure 9. With the first dynamic mode frequency known, we are able to
scale acceleration records with respect to the ASCE 7-10 spectrum.
SCAe 1 47.7
Woleto ScaleI1W 5 7
ll~gtigted
Ccaeo Modes
Cocoteo Eleoet
DeforowaOm resofcto 5000
Cane A I Oyoos MOdelI
mode 1
Freqoeocy 0.2716m,Pered 3 6V s
A
Figure 9 Sample Structure First Dynamic Mode
3.3.2 Seismic Data Scaling
As mentioned in section 2.1, we are using unscaled time history ground motion data from
NGA-West 2 database although the scaled response spectrum are provided. The reason for
using unscaled data is due to the consideration of the site-specific feature of our analysis. The
scaled response spectrum provided by NGA-West 2 minimizes the differences between target
spectrum and scaled spectrum over a range of periods. This method is ideal for analyzing the
response of structures under multiple dynamic modes, and it will provide more reliable results.
However, the scaling method utilized by NGA-West 2 is very computationally expensive, and
it will not provide us with a desired result under the scope of our analysis.
Since we are analyzing non-structural damage under seismic activities for the target building,
no permanent structural damage will be considered. For most structures, the number of
dynamic modes to be analyzed very much depends on the type of analysis to be performed.
The most typical dynamic modes analysis utilizes are the first three modes, while the first mode
40
Chapter 3. Non-Structural Damage Assessment
is the most common case. Our case analyzes performance of structures before reaching any
dynamic mode, which means the traditional scaling method provided by NGA-West 2 is too
cumbersome and costs an unnecessary amount of computations. Based on the finite element
analysis model, the first dynamic mode has a frequency of 0.2716 Hz with primary motion axis
on the weak axis of the structure. Therefore, the results obtained from the dynamic mode
analysis is reasonable, and indeed, we will use this frequency as a target frequency to scale
ground accelerations.
According to ASCE 7-10, the spectral acceleration at a frequency of 0.2716 Hz, or period of
3.682 sec, is 5.8 ft/s2 , and thus 5.8 ft/s 2 is the target spectral acceleration. Instead of
scaling spectral acceleration with respect to multiple periods, we are scaling spectral
acceleration with respect to one specific point only. The advantages of scaling seismic data
at a specific point are listed below:
*
Considering the fact that our analysis considers a considerable amount of ground
acceleration data records, by scaling seismic activities using one reference point only,
we are able to significantly reduce computation time. Since we used convolution
integral computing the response spectrum, evaluating response at a specified point
promotes computation efficiency significantly as well.
"
As mentioned at the beginning of this section, we are focused on non-structural
damage only, and thus structural responses beyond first dynamic modes are not related
to the analysis. By matching the first dynamic mode response only, we are able to
And therefore, more reliable
produce an exact match for spectral accelerations.
results with less noise and bias are computed using this approach.
The spectral acceleration at the very period is computed and the corresponding scaling factor
is determined by comparing with spectral acceleration of 5.8 ft/s 2. The function used to
determine the scaling factor is shown in equation 3-1. Table 5 summarizes all data records
used in structural analysis with corresponding scale factors.
ST2 + (Y X SA)2
where
a
variance
ST
target spectral acceleration [ft/s 2]
SA
data spectral acceleration [ft/s2 ]
y
scaling factor
(3-1)
41
Chapter 3. Non-Structural Damage Assessment
By evaluating scaling factor at one reference point, we are able to reduce the variance to 0.
Record Name
Scale Factor
RSN12192
RSN12980
RSN19427
RSN19457
RSN19488
RSN19537
RSN19640
RSN19703
RSN19813
RSN19898
RSN19978
RSN20541
RSN20710
RSN20891
RSN20947
RSN21064
RSN21381
RSN21418
RSN21504
RSN8617
100.0569289
56.16726223
769.3328028
312.7190381
1222.081753
1005.199307
1062.076543
1504.929943
1805.166511
79.12147875
79.12147875
1137.701059
1556.21143
548.2041588
258.1219404
513.3651974
544.65208
106.3751742
158.1674393
70.90811287
Table 5 Scale Factor Summary
42
Chapter 3. Non-Structural Damage Assessment
3.3.3 Finite Element Analysis
This section discusses the implementation and operation of the finite element analysis model.
The software used for finite element analysis modelling in this thesis is GSA. GSA is an
efficient tool in modelling structural behaviors.
The modelling tool is easy to use and
provides various analysis results including displacements, velocities and accelerations for each
node, as well as member forces and stresses for each element. This section is decomposed
into two parts, model set up and model analysis. For the first part, detailed procedure is
provided for setting up the model. As for the second part, results obtained from structural
analysis are illustrated.
Part One: Model Set-Up
Step 1: Model typology is imported from SAP 2000, and the 3-D model is built in GSA.
model is layered into different planes.
The
Step 2: Members of the model are identified with corresponding cross-sections and materials.
All elements used in this model are built-in in the GSA database. The floor slab is identified
as typical concrete floor slabs.
Step 3: Self-weight loadings, namely, concrete weight, steel weight and live load are identified
in this model.
Step 4: The ASCE 7-10 response spectrum is loaded in the model. Since the GSA database
has the built-in ASCE 7-10 spectrum, we do not need to manually input the spectrum but set it
up in the GSA model.
Step 5: All data records are uploaded into the load curve section under dynamic analysis part.
Each data record is scaled with the scaling factor obtained in the previous section.
Step 6: Modal analysis task, as well as all time history analysis tasks are set up in the model
with output step time of 0.02 sec.
Part Two: Modal Analysis
Structural response results with maximum spectral acceleration and maximum displacements
for selected ground motion data records are summarized from Figure 10 to Figure 14 (Rest are
shown in Appendix B). Further discussion and analysis of these results are illustrated at the
end of this section. Also, maximum displacements and accelerations for all data records with
corresponding node number and ground motion records sequence numbers are summarized in
Table 6.
43
Chapter 3. Non-Structural Damage Assessment
I
RSN8617
Strike Slip
Scale 14757
'1 di
11-
I F
I I I I IH
I I I
I
Li-' m
~
PC
N
A,
QAPW
lee
1-4
A.%_R. -00-1S.A
.01
RevokAed
0,77508W.2
0.7500 W2
0o 72M ftw.
kk
SEP
Ir
DR
aCrOWn W4 1250 fftt128W
r1:5
K
0,600081.
057508.2
047580
0 32508f8/s2
8.
4500 1n
042508
OIWO
4
0.400081W2
0.375081.
0.30081
0325008
0,3000
82
Cn*e CI* Caobkion case I
SagWO mo.058. vaw,
of env
Scam, 4A7
IWonvuli SCOW 11582 7
tloIpedHd
C Ortcdam Nde
K
Resolved Tramuledem W 580 mlfpx cim
*
'A
)1
K,
LI_
p
2400 in
Z3100 in
92000 i
I;;V
19 00 4n
1200Gm
Case. CI CoaMabon cuea I
SWag
" Von65of61
etO
Figure 10 RSN8617 Acceleration (top) and Displacement (bottom)
The ground motion record set RSN8617 refers to an earthquake with strike slip mechanism.
Acceleration and displacements contour plots are shown in Figure 10 RSN8617 Acceleration
(top) and Displacement. Refer to the frequency content Fourier diagram of this ground motion
record in chapter 2, two peaks at frequency of 2 Hz and 4 Hz are observed. The maximum
acceleration for this set of data record, 0.79 ft/s 2 happens at the middle section of the top
floor.
44
Chapter 3. Non-Structural Damage Assessment
M RSN12192
Strike Slip
Scale. 1 47
Isoeic Scale 1:582 7
I:07750
COlcSOlen Nodes
CoecNnt Eleaents
Resolved Acceleratin .4 ON000
Output aa: glbl
ft/s2/ptc
W1a
s2
0.7250 ft2
0 7000 W12
0.7500
0,6750 W1,2
06250 W1s2
06000 W
057500 W2
0 5500012
*0.52501) R
*05000ft/12
0 4750 V12
0.4500 012
0 4250 W2
0,4000 W92
0 3750 ,2
3500
2ftI2
0,3250 f1s2
03000 0S2
CwCl .Coolbelaten Case 1
Sooed absolute value afenv
L
Scale: 1 475.7
leomslc Scale: 15827
Conieet Nodes
Colcithet Elements
Resolved Translation,
Output axm global
U 5
000 i/poc.cm
3.000 in
2,700 i
2-600 i
12c00
2 50
2400
in
i
2.300 m
o
in
2.200 in
2,000 in
in
1.800 in
1.900
r
1,500 in
1.400 in
1.700
1 300 in
1.200 in
1100
L_
i
1'000 W1
Case
lCmiialncs
1
Figure 11 RSN 12192 Acceleration (top) and Displacement (bottom)
The ground motion record set RSN 12192 refers to an earthquake with strike slip mechanism
as well. As shown in Figure 11 RSN12192 Acceleration (top) and Displacement, the maximum
deflection for this data set is 2.7 in happens at the corner of the top floor, while the maximum
acceleration of 0.72 ft/s2 happens at the middle of the top floor as well. The frequency
content of the Fourier transform for this data shows two peaks at 2 Hz and 4 Hz.
45
Chapter 3. Non-Structural Damage Assessment
E
RSN19427
Strike Slip
Scale 1:475.7
Wometnc Scale
Hlghlgoted
1 582
7
CouctmtNudes
Coincident Elenot
Resolved Accelearben
Output axis global
1000
A 1 250 ft/a2JIc
fRis2
0$0001 W12
0 7000 11/S2
0 6000 ft/%2
005000 f9/s2
0400011112
0 4000 /a2
0 3000 fV/%2
Case: C1 CoftabtO case
Signed absolu vaise of env
Scale: 1 475.7
waomwhic Scale
A
>4
)
IA
1
52 7
Cmcdent Nodes
Coicx*Mn Eletnienta
Resolved Translabon, .
Output axe global
5
000 eVpMcm
2 400 o
2300m
2.200 im
2 100
in
2000in
1.900
1800 in
1.700 m
1600 in
1500
in
1400 m
)
1 300 m
1200 m
1 100 in
1.000 in
0 9000 o
0,7000 in
0.50DO in
CI . Coe*ubiPoon case 1
Soned absolute vale of eov
Case
Figure 12 RSN 19427 Acceleration (top) and Displacement (bottom)
The ground motion record set RSN 19427 refers to an earthquake with strike slip mechanism
as well. Acceleration and displacement contour plots are shown in Figure 12 RSN19427
Acceleration (top) and Displacement.
The maximum deflection for this data set is 2.2 in
happens at the corner of the top floor, while the maximum acceleration of 1 ft/s2 happens at
the side of the top floor. The frequency content of the Fourier transform for this data shows
two peaks at 3 Hz and 6 Hz.
46
Chapter 3. Non-Structural Damage Assessment
U
RSN21418 Strike Slip
Scaw 1 475.7
boffatmi Scale 1 582 7
Coalctf No0des
80401,44 Acceteatas
WA2.500 81s2/pt
1250 W.
I20M81.2
I1008812
1.050 W4.2
1.000 fV62
015008/,2
0,900081,S2
0.7500 W32
0.7000881S2
086500812
08000 W1a
0.550081
0.50008/12
0.4500881s2
0400088W
0,350W1
02500881
Caw: CI COombr Case I
Soled aee~81 YaW Of 40v
)
Scale, 1:4757
f0404081 Scat. I 582 7
ii
K4
H-I-4 Ai
Coocater Entn8
Resolved Tranialln1550DOO
I
I
iWQ7Wu ;
-:!q- zt - I u1
picm~Y
3,500 i
IILZ
'A
r'
K,
K
II-
Figure 13 RSN21418 Acceleration (top) and Displacement (bottom)
The ground motion record set RSN 21418 refers to an earthquake with strike slip mechanism
as well. Acceleration and displacement contour plots are shown in Figure 13 RSN21418
Acceleration (top) and Displacement. The maximum deflection for this data set is 3.5 in
2
happens at the corner of the top floor, while the maximum acceleration of 1.1 ft/s happens
at the middle of the top floor as well. The frequency content of the Fourier transform for this
data shows a declining frequency after the initial high points until 5 Hz, and a gradual bouncing
back from 5 Hz to 9 Hz.
47
Chapter 3. Non-Structural Damage Assessment
MRSN12980
Strike Slip
Scalb 1 475.7
*ono*c Scab I 5827
C
2acam
00M
0100
ia
L
0
a
020 Ws2
4Rf9A1ean(pads92e(to
0igu0
SAlM 1
e75s
0900 W
S.00
fdroaa5
OAaHz
0,300
V
W
00 9Hz.
W
~ Seid
~~~~Cage
C1Ceaubncg
f
abkt te
Acclertio (op)andDislaemet. hemaxmumdefecionforthsodat
trwisn
1
251 in pmc
back rom 5Hz to9MHz
48
Chapter 3. Non-Structural Damage Assessment
Maximum Displacements and Maximum Acceleration Summary
Results Summary
Record Number
Node
Max. Dis. (in)
Node
Max. Acc. (ft/s^2)
254
2. 366
181
0. 7939
7
252
1.096
2.318
107
252
36
2.408
254
2.662
143
143
0.7924
0.7562
0.7948
0.7178
Strike
36
2. 724
221
0.7123
Slip
252
36
253
2.629
2. 724
2. 431
0.6846
0.7184
Strike
Slip
36
252
25
144
145
36
Mechanism
Strike
Slip
RN12192
RSN12980--
RSN19427
RSN19457
RSN19488
RSN19537
Strike
Slip
-
2.509
-2.425
-
N
136
147
36
2.509
254
2.218143
36
252
2.263
2.174
110
253
2.264
2.847
36
252
36
182
252
0.8726
142
143
0. 7315
2. 934
2.826
2.934
258
25
0.7209
0. 6961
144
0. 7318
253
2.641
181
0.7813
36
252
1
182
0.78
1
252
36
2.702
2.602
2. 702
0.7428
0. 7828
254
2. 703
181
Strike
36
2. 762
182
Slip
252
36
2.657
2.762
252
179
Normal
Strike
Slip
Table 6 Structural Response Summary
142
Chapter 3. Non-Structural Damage Assessment
N
Maximum Displacements and Maximum Acceleration Summary
Results Summary
Record Number
Node
Max. Dis. (in)
Node
Max. Acc. (ft/s^2)
253
36
2. 034
2.097
143
258
0. 6833
252
36
2.019
2. 097
253
2. 347
252
145
143
0.6548
0. 6854
0. 788
108
252
2.405
2. 329
145
25
0.79
0. 7574
36
253
2.421
2. 546
145
143
Strike
108
2.604
258
0.79
0. 859
0.8469
Slip
252
36
253
2.516
2.616
1.985
252
144
143
221
252
2.021
1.951
221
252
110
253
2.03
1.769
142
181
0.6497
Strike
36
1.807
254
0.8818
Slip
252
110
1.739
1.809
252
143
0. 8479
0.8919
241
2. 29
143
0. 724
36
252
2. 768
2.663
258
252
0. 7147
0.6905
36
2. 768
144
0. 7246
254
1. 965
143
0. 5956
Strike
221
1.994
182
0.5949
Slip
252
36
1.927
2. 003
252
144
0. 5677
0. 596
Mechanism
RSN19640
Normal
RSN19703
Strike
Slip
RSN19898
RSN20891
Strike
Slip
Strike
Slip
Table 7 Structural Response Summary
0.6773
0. 8182
0.8593
0. 6497
0.6426
0.6171
0.8907
Chapter 3. Non-Structural Damage Assessment
E
Maximum Displacements and Maximum Acceleration Summary
Results Summary
Record Number
RSN21381
RSN21418
RN19978
RSN20710
RSN21064
Node
Max. Dis. (in)
Node
Max. Acc. (ft/s'2)
253
2.924
143
0.7239
73
252
3.008
2.895
258
252
0.7165
0.6926
36
253
3.009
3. 006
145
0.7256
36
3.092
35
252
2 33
36
2.975
0 61
3.092
252
1440
253
1.985
143
0.6497
Strike
221
2.021
221
0.6426
Slip
252
110
1.951
2.03
252
142
254
1.949
181
0.6171
0.6497
0.8183
7
0. 9055
258
0. 809
252
36
1.922
1.992
252
144
0.782
0.8192
253
2.666
143
221
252
2.744
2.657
258
252
36
2.753
144
253
2. 143
143
Strike
36
2.203
258
Slip
252
36
2. 124
2.203
252
144
Mechanism
Strike
Slip
Strike
Slip
Strike
Slip
Strike
Slip
Table 8 Structural Response Summary
180
I
08X77
Chapter 3. Non-Structural Damage Assessment
The summary table above shows the results of maximum accelerations and maximum
displacements of the structure with corresponding nodes for each ground motion data record
performed. This thesis focuses on the non-structural damage of the structure under seismic
activities, and therefore acceleration is the major concern of our analysis. As we can see from
the maximum acceleration column of the chart, it varies from 0.5 to over 1 ft/s 2 , which is a
wide range. Since all earthquake records applied in this analysis are scaled with respect to
ASCE 7-10 response spectrum, the variance in acceleration of the building should not be
effected by the scaling factors. Therefore, we are more concerned about the acceleration of
the structure to determine the non-structural effect of seismic activities.
,
.
In the summary table above, the acceleration summary part shows a cutoff point at 0.9 f t/s 2
Accelerations of the structure indicates a continuous trend from 0.6 ft/s 2 to 0.9 ft/s 2 , and
there is a gap existing between at 0.9 ft/s 2 . After 0.9 ft/s 2 , the trend continues to rise to
1.1 ft/s 2 . This observation illustrates a discontinuity between 0.8 ft/s 2 and 0.9 ft/s 2
and thus all accelerations above 0.9 ft/s 2 are highlighted in red in the maximum acceleration
column. Note that there are 4 maximum accelerations for each ground motion record with
small differences between them. The reason behind is that GSA provides acceleration nodal
results with a range of maximums. Therefore, the four maximum accelerations for each
ground motion record is the maximum range of accelerations. In order to make more intuitive
comparison, the average value of the four maximum accelerations is computed to illustrate a
mean maximum acceleration for each data record. Figure 15 shows the trend of declining
maximum acceleration with corresponding data record.
Maximum Acceleration Summary
1.2
z
1.2
1
z
EN011
C-4
zq
C)
CC
00
Z) Z
U1n
z
~
cc
V
-'
ED
CO
:
r
r.
'0
00~,
-
:Z
'q
z
z
00
-.4
*-
0
r-4
-
0.8
coca
) r
f
0.6
CU
u~ 0.4
U
0
0.2
0
0
5
10
15
20
25
Ground Motion Record
Figure 15 Maximum Acceleration
52
Chapter 3. Non-Structural Damage Assessment
3.4 Summary
This chapter completes the structural analysis of the target structure. We use the gravity
design part of the ASCE 7-10 as a guideline to design a typical residential/office/mixed-use
structure, and the structure is used as a target structure in later analysis. The earthquake
records obtained from NGA-West 2 are scaled with respect to ASCE 7-10 response spectrum.
However, as opposed to traditional scaling method where ground motion records are scaled
with respect to every point of the target spectrum (i.e. ASCE 7-10 response spectrum), we scale
the ground motion records with respect to the response spectrum at the first dynamic mode
frequency of the target structure. By doing so, we significantly reduce the computation time
and obtain a specifically-scaled ground motion records. Scaled ground motion records are
implemented in GSA as load curves to evaluate the structural response of the target structure.
Maximum accelerations and displacements of the structure under each data record are
Also, selected
evaluated and summarized in Table 8 Structural Response Summary.
Figure 10
from
shown
are
plots
contour
displacements
maximum
maximum accelerations and
to Figure 14. However, since the focus of this analysis is on non-structural damage of the
Therefore, maximum
building, we are more concerned about the acceleration results.
accelerations for all ground motion records are plotted in Figure 15 with corresponding record
2
sequence number. The plot clearly shows two declining trends, one above 0.9 ft/s and
another one below 0.9 ft/s2 . The result indicates that frequency content of earthquakes has
an impact on the structural response of the target structure.
Maximum displacements are summarized using the same method applied to maximum
accelerations record. Figure l7shows the maximum displacements of each data record with
corresponding record sequence number. The maximum displacements of the target structure
also shows a declining trend, however, the trend is separated into basically three step functions.
The trend is continuous above 2.6 in, in between 2 in to 2.6 in and below 2 in. Note that the
ground motion record RSN21418 produces the maximum displacements among all other
ground motion records, while RSN21504 produces the maximum accelerations. The rank for
maximum displacements is totally different from the rank for maximum accelerations as shown
in Figure 16.
53
Chapter 3. Non-Structural Damage Assessment
Acceleration Rank vs. Displacement Rank
0Strcutral Response
1.2
C:
*
0
0
*
1
0.8
0%
0@
2 0.6
0)
0.4
S0.2
0
E
E
2
1.5
2.5
3.5
3
Maximum Displacement (in)
Figure 16 Rank Comparison
CIC
4
(n
'-4
ZN
(N
tA Z
CC
C L
W,
00
r,
00
-4
-4
(An(
Cn
0
'4Jr
1.D
M
0
rN
-4
-4
ZZL
(Ac(
3
00
Ch
-4
(A
r-
Nmn
-
4.5
Maximum Displacements Summary
N
In
fN
Z
Zo
Oc
0
00
N
(N
(
CO
CA
0C
0)
-Z
0A
Co
2.5
2
.5
1.5
Z
(A
Co
0
E
u
0
-4
-4
..
-4
N
z
0n z
cc
-40L
(A
acZ
0
0.5
0
0
5
10
15
20
25
Ground Motion Record
Figure 17 Maximum Displacement
54
Chapter 4. Conclusions
Chapter 4. Conclusions
This chapter summarizes the frequency content analysis in chapter 2, frequency content
analysis, and the structural response analysis in chapter 3, non-structural damage assessment.
The relationship between frequency content of the ground motion records and the structural
response of the target structure is determined. Since the purpose of this analysis is based on
non-structural damage of the target structure, the maximum accelerations of the structure is the
major focus of this chapter. Limitations and possible future research are stated in this chapter
as well.
4.1 Summary of Contributions
At the end of chapter 3, maximum accelerations and maximum displacements of the target
structure with corresponding ground motion records are shown in Figure 15 and Figure 17.
According to the results, there is a clear decreasing trend in maximum accelerations, as well as
for maximum displacements. Recall from chapter 2, where frequency contents of the seismic
records are analyzed, the Fourier transforms of the ground motion records illustrate different
distributions of peaks. Therefore, based on these two sets of results, the frequency content of
seismic activities have an impact on the structural response of the target structure.
The focus of this thesis is on non-structural damage induced by ground motion activities.
According to the parameters discussed in chapter 1, non-structural damage of a building refers
to movement of non-structural components within the target structure, and thus in the following
discussion, we focus on the acceleration parameters. The reasons for applying acceleration
parameters as measurements are listed below:
*
Acceleration parameters are more directly related to the measurement of nonstructural damage. The movement non-structural components within the building is
due to impulse forces applied to them. Displacement parameters provided by the
GSA model refer to the movement of the whole floor. Since these displacement
parameters are more of macro level, they do not measure the relative motion in
Impulse force triggers the movement of non-structural
between each floor.
components. Each non-structural component has a mass, and the momentum stored
in the component during seismic activities is directly relate to the relative velocity
between components. Considering the fact that relative velocity depends on the
acceleration, the larger the acceleration, the more momentum will be stored in
components. Therefore, acceleration is more applicable to non-structural damage
assessment, while displacement is an apt measurement for structural damage.
55
Chapter 4. Conclusions
E
For structural analysis before first dynamic mode in our case, the acceleration
parameters are more precise. According to Section 3.1, we scaled the ground motion
records with respect to the ASCE 7-10 response spectrum. However, instead of the
traditional scaling method, which scales the ground motion record with respect to the
continuous target spectrum at various frequencies or periods, we scale the records with
respect to the target spectrum at the natural frequency of the target structure. As the
results shown in chapter 2, our displacement results are way below the first dynamic
mode of the structure. Therefore applying acceleration parameters as measurements
is more suitable in this thesis.
As illustrated in Figure 15, the maximum acceleration for ground motion data records
performed decreases from 1.1 ft/s 2 to 0.6 ft/s 2 . Also, in chapter 2, the distribution of
Fourier transforms of each ground motion record is different. Since seismic activities are
scaled in the exactly same way and all scaled data are simulated on the same structure, the
impact of frequency content of seismic activities on its corresponding structural response is
obvious. From Fourier transforms obtained in chapter 2, the following observations are made:
"
"
The Fourier transforms can be categorized into three categories:
1.
Discrete Fourier transforms show a gradual decrease in peaks' distribution
approximately from 0 Hz to 4 Hz. Small bouncing backs to no bouncing backs
are observed after 4 Hz.
2.
Discrete Fourier transforms show two clear chunks of peak distributions with
similar magnitudes. Magnitudes at other frequencies are significantly smaller
than those within the peak frequency range.
3.
Discrete Fourier transforms show approximately uniform distribution of peaks.
Meaning the magnitudes of peaks in the Fourier transform diagram are similar,
no obvious ups and downs are observed.
Recall that the frequency for the first dynamic mode of the structure is 0.28 Hz. The
weight of distributions from 0 Hz to 0.28 Hz is different from one ground motion
record to another.
Based on the observations above, the impact of frequency content of seismic activities on its
corresponding structural response can be related to the weight of distribution below the natural
frequency of the target structure. The weight of distribution for Fourier transforms is
computed using equation 4-1 as shown below:
56
Chapter 4. Conclusions
Z=Offj x A
W
rL
W
where
(4- 1)
==
g 0 (f2 x A)
weight of distribution for frequency at fi
fi
fi
target frequency
A
frequency step
n
number of steps
In Table 9 Weight Distribution, the weight of distribution at the natural frequency of the target
structure is computed for each ground motion record with corresponding maximum
acceleration. Also, in Figure 18, the weight distribution at the natural frequency is plotted for
each ground motion record. And in Figure 19, maximum acceleration for each ground motion
record is plotted based on the rank of weight distribution value.
Spectrum Weight of Fourier Transform at Natural Frequency
0.012
0.01
C
00
0Y)
rN -4
00~
t
I -q
(
0i
Z
rWj sr
0
4
V)
r4
F
(A
6A
I~ n
ZA
Lnz
0.004
Zr-.0) 0 0
8
Z- 9-
4
8
~O~0
0
z
002
A
z
0.002
2
*
4.
Z
CA 0
S-4
00
4r4012
a
1
(
'-4
0.008
ZI
6
1
Figure 18 Weight Distribution
57
Chapter 4. Conclusions
Maximum acceleration based on Fourier Transform
weight spectrum
1.2
CO
1
00.
0.8
2 0.6
0
n.....
.
Z~~~~
r4 z
U)
(A
Ln
00
.
0
W
***o00 -4....
rN4
00
a
1-4
M
-1
(N
Z
V)
N
rU)
'U0.4
00 ......
9-
9
~0000
0
00
V)
z
V)
Ln-
N
U)
0
tt
n
Z
~
(
1-1
L
W
ZU
X0
0.2
0
Figure 19 Maximum Acceleration Based on Weight Distribution
Record Name
Acc. (ft/s^2)
Weight
RSN12980
RSN20541
RSN21418
RSN21064
RSN21504
RSN19537
RSN12192
RSN21381
RSN20947
RSN19813
RSN19898
RSN19978
RSN19457
RSN19640
RSN19488
RSN8617
RSN20891
0.92135
0.878075
1.04125
0.916825
1.06825
0.9589
0.708275
0.71465
0.58855
0.84585
0.639775
0.639775
0.720075
0.6752
0.771725
0.784325
0. 71345
0.010641
0.009566
0.009453
0.009315
0.008976
0.008547
0.007781
0.007699
0.007436
7.01E-03
0.0067
0.0067
0.006459
6.01E-03
0.005979
0.004121
0. 004022
Table 9 Weight Distribution
0
~z
00
Chapter 4. Conclusions
Comparing the results in Table 9 and Figure 19, a clear decreasing trend in acceleration is
observed. Even though the data points in Figure 19 does not match exactly with the data
points in Figure 19, the fitted trend line still shows a decrease in magnitude of maximum
acceleration. Therefore, it can be concluded that the frequency content of seismic activities
has an amplification impact on the maximum acceleration of the target structure at natural
frequency. Meaning higher the weight of the frequency distribution at natural frequency of
the target structure, larger the maximum acceleration will occur in structural response.
However, the quantitative magnification parameter is not determined. Possible applications
of the analysis results are listed below:
E
For prospect structures, the analysis method can be applied in design process if
earthquake records are available, especially for structures with high net worth, such as
structures used as storage for luxury items, or structures with strict restrictions on
movements of non-structural components, such as medical facilities. By analyzing
the frequency content of earthquake events, the frequency range with the largest
weight of distributions can be avoided, thus minimizes non-structural damage.
0
For existing structures, the analysis method can be applied to retrofit, thus avoid future
damages.
Note that both applications require knowledge about ground motion records, meaning that the
method is only applicable with predictions on future earthquake events. Therefore, the results
can be applied in both design process and analysis process if and only if past earthquake events
can be used as predictions for possible future ground motion activities. Also, instead of using
traditional scaling method, this thesis scales time-history acceleration records with respect to
the target response spectrum at a single point, which is the natural frequency point. Future
research on the scaling effect of this scaling method is required to further verify its reliability
below the first dynamic mode frequency. At the end, earthquake records are scaled and
analyzed with 5% constant damping ratio, and further research is necessary for analyzing
various damping ratios.
59
Appendix A
Appendix A
*
Time History Acceleration
Shigle Sided Acceleraion Diagram
0 15
Single
0.014
RSN12980
Sided Acceleration Diagram
-R5ft19427
-
il
0012
001
011-
ODD8
0 0006 III
005
0004
0002
0
0
20
40
60
80
100
120
140
160
180
0
200
100
20
7
1
120
160
140
180
200
Time (s)
Time (s)
Single Sided Acceleration Diagram
--
8 ,10
3
Skngle Sided Acceleraion Diagram
7
RSNI94SSI
6
--
R519537
6I
I
4-
4
3
3
2
0
50
100
150
200
0
250
50
100
Time (s)
Single Sided Acceleraon Diagram
0.01
150
200
250
Time (s)
Single
10
Sided Acceleration Diagram
RSN184O
0.009
RSN197031
5'
0,008
0.007
4
0006~
0 005k
0.004
0.003
L
0.002
0.001
0
50
L
100
150
Time (s)
1
200
250
3
0
50
100
150
200
250
300
350
400
Time (s)
60
Appendix A
Single Sided Acceleration Diagram
1- -
14
RSN19813
45
4
Single Sided Acceleration Diagram
5
4
4
35S
35)
3
5 251
25
1
20
1.5
14
15
05
0
0
0
50
100
150
200
Time (s)
250
350
300
400
100
150
200
250
350
300
400
Time (s)
Single Sided Acceleration Diagram
14
50
0
Single Sided Acceleration Diagram
0 14
RSN1 998
RSN19898
3 12
0 12
0
01
1
008
0 08
0,06-
S006
0
0,04
04
0 02
0
50
L100
002
150
200
250
300
350
0
400
50
100
150
0.14
----
200
250
350
300
400
Time (s)
Time (s)
Single Sided Acceleration Diagram
Single Sided Acceleration Diagram
0. 14
-7 RSN20421
I-RSN20372
0
0 121-
12
0.1
0.1
~008k
0 08
I
006
0,06k
0,04
0.04
0 02
002
0
50
100
150
200
Time (s)
250
300
350
400
0
50
100
150
200
250
300
350
400
Time (s)
61
Appendix A
Single Sided Acceleration Diagram
Single Sided Acceleration Diagram
0-014
0012
01
S0 a 0
-2
80006
I
005
0004
0002
20
0
40
60
80
100 120
Time (s)
140
160
180
200
80
100
120
180
160
140
200
Time (s)
Single Sided Acceleration Diagram
103
60
40
20
0
8
Single Sided Acceleration Diagram
10-?
RPNI 8537
6
6
4
-
4
3
213.
21.
OL0
0
50
100
150
200
50
0
250
Time (s)
Single Sided Acceleration Disgrarn
~,
0.01
250
200
150
100
Time (s)
Single Sided Acceleration Diagram
6
0 009
4
-
0 008
0007
0-006
3
0.005
0004
2
0003
0.002
i
0001
0-0
50
100
150
Time (s)
200
20
250
0
11i
50
100
150
200
250
300
350
400
Time (s)
62
Appendix A
Single Sided Acceleration Diagram
014
Single Sided Acceleration Diagram
10,3
7
0
12
1
25
01
-
2
0.08
1.5
82.0
1
0.04
05
00.02_
50
0
100
150
200
250
350
300
0
400
50
100
150
Single Sided Acceleration Diagram
0012
200
250
300
350
400
350
400
Time (s)
Time (s)
10-1
7,
_7
Rr
Single Sided Acceleration Diagram
5I
0.01
5
0008-
3
0004
2
0 002
0
kLJL
50
0
100
150
200
250
300
350
0
400
50
100
150
0_15
Single Sided Acceleration Diagram
-------
200
250
300
Tim (s)
Time (s)
-
Single Sided Acceleration Diagram
0 045
-
-- RS
SNM
RSN20947
-
0 035
0 03
0 01
0025002
0015
< .oosj-
001
0005
EL&
0
0
50
100
150
200
Time (s)
250
300
350
400
0
50
100
150
200
250
300
350
400
Time (s)
63
Appendix A
015
-
_
Single Sided Acceleration Diagram
Single Sided Acceleration Diagram
0014
RSN19427
0012
001
01
0008
0006
0.0
0004
0 002
0
20
40
60
80
100
120
140
160
180
200
0
20
40
60
80
Time (s)
Single Sided Acceleration Diagram
Single
10
-
7 -
100
120
140
160
180
200
Time (s)
Sided Acceleration Diagram
7~L7
RSN19488
6
6
Ii
5f
4
3
3
2
2
0
0
50
100
150
200
250
0
50
150
200
250
Time (s)
Single Sided Acceleration Diagram
0.01
10
3
Single Sided Acceleration Diagram
I
0 009
--
RSN19O40
5
4
0 008
0.007
0 006
0 004
100
Time (s)
r
3
4
RSN18703
2
0003
0.002
*
1
0.001
L .A.
0
50
AM&
100
150
Time (s)
200
250
0
0
50
100
150
200
Time (s)
250
300
350
400
64
Appendix A
Single Sided Acceleration Diagram
Single Sided Acceleration Diagram
0 014
.
0 .018
1-
RSN210641
0.016.
2 *I
0.012
0014
001
0,012
0012
00
0.0052
0.006
0004
0,004
0002
0002
Gt
0
50
100
150
200
250
300
350
0
400
50
100
150
Single Sided Acceleration Diagram
0 07.-
200
250
300
350
400
Time (s)
Time (s)
Single Sided Acceleration Diagram
0.07
5-RSN21504
0.06
0 06
0 05
005
0,04
4
004
-
0 03
0,02
0.02
001
0f01
0
50
100
150
200
Time (s)
250
300
350
400
0
L
50
100
150
200
250
300
350
400
Time (s)
65
Appendix A
Filtered Time History Acceleration and Fourier Fast Transforms
0
Single Sided Acceleration Diagram
015
Single Sided Acceleration Diagram
01.5
o'fl
-RS
S04
002
5
0
Is
10
20
25
35
30
40
45
S103
5
0
so
Time (s)
Single-Sided Anplitude Spectrum of y(t) cut-off
10
15
20
25
35
30
40
45
Time (s)
Single-Sided Amplitude Spectrum of y(t) cut-off
104
4
2
05
0
5
10
20
15
30
25
0
35
45
0
50
5
10
15
Frequency (Hz)
Single Sided Acceleration Diagram
10
RRSNN194-48
-
0,02
20
25
30
Frequency (Hz)
35
40
45
50
40
45
50
45
50
Single Sided Acceleration Diagram
3
1
01
0.01
0
4
5
10
20
15
25
30
35
Time (s)
Single-Sided Amplitude Spectrurn of y(t)
10,
40
45
0
cut-off
5
15
20
25
30
35
Time (a)
Single-Sided Amplitude Spectrum of y(t) cut-off
1
3
10
L
1
05
0
0
0
5
10
15
20
25
30
35
40
45
50
0
5
10
15
Frequency (Hz)
20
25
30
35
40
Frequency (Hz)
Single Sided Acceleration Diagram
Single Sided Acceleration Diagram
100
.iII.
RSN194&0
10
S0,005~
2
0
0
0
5
10
15
20
25
30
35
Time (s)
Single-Sided Amplitude Spectrm of y(t)
1
6
40
45
50
cut-off
4
2
10
15
20
25
30
Frequency (Hz)
35
40
10
15
20
25
30
Time (s)
Single-Sided Ampitude Spectrum
10s
2
5
5
35
40
45
50
45
50
of y(t) cut-off
1RSN974
-
4
00
0
0
45
50
0
5
10
15
20
25
30
35
40
Frequency (Hz)
66
Appendix A
Single Sided Acceleration Diagram
1
Single Sided Acceleration Diagram
0
RSN10813-
RSN19St8
0
4
0.05
2
0
1
5
0
1
15
Single-Sided
6,10-5
2N
25
3w
40
35
45
0
5
0
50
Time (s)
Amplitude Spectrum of y(t) cut-off
10
15
20
26
30
40
35
45
5D
Time (s)
Single-Sided Amplitude Spectrum of y(t) cuta-ff
100
RSNINNe
4
60.5
2
0
0
0
5
10
15
20
25
30
40
35
45
50
0
5
10
20
15
Single Sided Acceleration Diagram
01 5
30
25
35
40
45
50
Frequency (Hz)
Frequency (Hz)
Single Sided Acceleration Diagram
0015r-
C0 01
0
0.005
S05
0
5
1
10
15
20
25
30
35
40
45
0
50
Time (s)
Single-Sided Ampliude Spectrum of y(t) cut-off
-
60
Time (s)
Single-Sided Amplitude Spectrum of y(t) cut-off
10.s
--
50
40
30
20
10
S1997
RSN20541j
--
-4
0.5
5
0
10
15
20
25
30
40
35
45
5
0
50
10
15
Single Sided Acceleration Diagram
102
8
20
30
25
40
35
45
50
Frequency (Hz)
Frequency (Hz)
Single Sided Acceleration Diagram
0 () 1
RSN20OU1
---
:-:---
0 005
2
0
5
0
10
15
20
25
30
35
40
45
F
10 -
5
0
50
Time (s)
cut-off
Single-Sided Amplitude Spectrum of y(t)
E1.5
15
20
30
25
35
40
~
45
50
45
50
Time (s)
Single-Sided Amplitude Spectrum of y(t) cut-off
104
N
10
0RSN2MIJ
7
0 5
5
10
15
20
25
30
Frequency (Hz)
35
40
45
si
0
5
10
15
20
25
30
35
40
Frequency Hz)
(
0
67
Appendix A
Single Sided Acceleration Diagram
0.1sr
R
~
S0e17
C0.1
Single Sided Acceleration Diagram
0, 08
0.0e
RSN12192
0
O0.04
0.05
5
0
20
15
10
0.02
25
30
45
40
35
0
50
5
Tire (s)
Single-Sided AmItude Spectrum of y(t) cut-off
i
40
35
30
25
20
15
RSN212
RS
---
45
Time (S)
Single-Sided Amplitude Speum of y(t) CIt-Off
0
1
10
14
05
0
0
....
10
5
0
20
15
25
30
35
40
45
50
5
0
10
15
Single Sided Acceleration Diagram
003
20
25
30
35
40
45
50
40
45
50
45
5(0
Frequency (Hz)
Frequency (Hz)
RSN194S7
Single Sided Acceleration Diagram
10-3
8
-
oa-R69e
002
4
0.01
-
u
5
0
10
15
40
35
30
25
20
Tirme (S)
au-off
of
y(t)
Single-Sided Amplitude Spectrum
10
5
0
45
1
5,
0
Snt
10-
10
15
10
20
30
25
Time (s)
Ampiude
-ded
35
Spectrum of
y(t)
cul-off
2RSNI48B
3
2
05
0
1
0.5
0
10
15
20
25
30
35
40
45
0
50
5
10
15
Single Sided Acceleration Diagram
0.01
20
25
30
40
35
Frequency (Hz)
Frequency (Hz)
Single Sided Acceleration Diagram
10-3
F-
-- RSNBO4O
RSN93
S0.005
5
0
10
15
20
25
30
35
40
45
50
10-5
5
0
Time (s)
Single-Sided Amplitude Spectrum of y(t) CUt-on
0
45
35
40
25
30
15
20
10
Tire (s)
Single-Sided Amplitude Spectrum of y(t) cut-off
50
- RSN1S7S3
8RSN09*48
6
6
S4
4
2
2
0
5
10
15
20
25
30
Frequency (Hz)
35
R5194
45
40
_
__
50
0
5
10
15
20
25
30
35
40
45
50
Frequency (Hz)
68
Appendix A
0 04
0.
0 02
00
10
5
0
20
15
Time (s)
Single-Sided Amplitude Spectrum of y(t) cut-off
10
,
Single Sided Acceleration Diagram
-
,
-
-
-
-
-
-
-
-
,
-
-
-
5
5
0
40
35
30
25
-
-
0.015 e
Single Sided Acceleration Diagram
0,06
Time (s)
Single-Sided Amplitude Spectrum of y(t) cut-Off
104
1.5
40
35
30
25
20
15
10
E
RSN20947
RSN2I3I
3
..
2
II
3-
---ioos
0
15
10
5
20
25
45
40
35
30
0
50
20
15
10
5
0
Single Sided Acceleration Diagram
a 1
0.01
0,05
0
5
20
15
10
50
27
c9
RSN129o
5
45
40
35
30
Time (s)
Single-Sided Amplitude Spectrum of y(t) cut-off
20
15
10
5
0
40
35
30
25
Single Sided Acceleration Diagram
0.015F
15
0
25
Frequency (Hz)
Frequency (Hz)
40
35
30
25
Time (s)
Single-Sided Amplitude Spectrum of y(t) cut-off
10
RSN14
RSN129e
05
0.5
5
0
10
15
20
25
30
35
45
40
0
50
5
10
30
25
20
Frequency (Hz)
15
Frequency (Hz)
40
45
50M
40
45
so
Single Sided Acceleration Diagram
Single Sided Acceleration Diagram
103
35
RSN21S4
RSN195371
0.01
C
0
2
10
15
Sngle-Sided
w,
20
25
30
35
40
45
1
30
25
20
15
10
5
0
50
Time (s)
Amplitude Spectrum of y(t) cut-off
Time (s)
Single-Sided Amplitude Spectrum of y(t)
cut-off
-
5
0
RSN21064
05
05
05
0
5
10
15
30
25
20
Frequency (Hz)
35
40
45
50
0
5
10
15
20
25
30
35
40
45
50
Frequency (Hz)
69
Appendix A
Single Sided Acceleration Diagram
0.087
Single Sided Acceleration Diagram
008
006
RS2110006
0.04
0.04
3 0O2
002
o0
0
0
5
10
15
20
25
30
35
40
45
50
Time (s)
Single-Sided Amplitude Spectrum of y(t) cut-
10
10
15
20
25
30
35
Time (s)
Single-Sided Ampktude Spectrum of y(t)
-4
40
45
50
45
50
cut-off
,
6 46
10 -4
5
E-
RSW21 41 8R
-4
0
-0
5
10
15
20
25
30
Frequency (Hz)
35
-
-4
40
45
50
0-0
5
10
15
20
25
30
35
40
Frequency (Hz)
70
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Appendix C
Appendix C
U
Side View of Target Structure
87
References
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