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 - 11. -::11111111-11-1- CL CL 0e U, ........... 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U, 00 CL CL w ii u .. .. .............. . i IIII~Nf .......... / I i tz Appendix C Appendix C U Side View of Target Structure 87 References References EERI. (2014). EERI Special Earthquake Report - M6.0 South Napa Earthquake of August 24, 2014. Oakland: EERI. FEMA. (2012). Common Types of Nonstructural Earthquake Damage. In FEMA, FEMA E-74 Reducing Risks of Nonstructural Earthquake Damage-A Practical Guide (pp. 2-22-2-28). Jessup: FEMA. Global Risk Miyamoto. (2008). 2008 M8 Sichuan, China Earthquake Field Investigation. Lafayette: Global Risk Miyamoto. Heckbert, P. (1998). Fourier Transforms and the Fast Fourier Transform (FFT) Algorithm. Pittsburgh: Carnegie Mellon University. Nevada Seismological Lab. (2015, 3 28). Living with Earthquakes in Nevada: A Nevadan's guide to preparing for, surviving and recovering from an earthquake. Retrieved from University of Nevada, Reno: http://crack.seismo.unr.edu/ep/nvguide/sbgl.html Noss, A. (2014). Household Income: 2013. 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