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Vibration characteristics of single-family woodframe buildings Hadj Karim Kharrazi, Mehdi 2001

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Vibration Characteristics of Single-Family Woodframe Buildin by Mehdi Hadj Karim Kharrazi B . S c , Iran University of Science and Technology, 1996 M . S c , Iran University of Science and Technology, 1998 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A P P L I E D S C I E N C E in T H E F A C U L T Y O F G R A D U A T E STUDIES (Department of Civi l Engineering) We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F BRITISH C O L U M B I A August 2001 © Mehdi Hadj Karim Kharrazi, 2001 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Civil Engineering The University of British Columbia Vancouver, Canada Date: August 30, 2001 Abstract The proposed modifications in the forthcoming update of the National Building Code of Canada and insufficient information on the vibration behaviour of Canadian woodframe buildings prompted this investigation of the dynamic behaviour of woodframe houses in Canada. The objectives of this thesis are to gain a better understanding of the dynamic characteristics of single-family woodframe buildings in Canada, to conduct a comprehensive literature study on previous research, to assess whether or not ambient vibration testing can be used effectively for determining the vibration characteristics of woodframe houses and to investigate the use of joint time-frequency technique in the vibration studies of woodframe houses. A variety of full-scale dynamic tests, such as shake table earthquake simulation, ambient and forced vibration tests, were conducted at the University of British Columbia on single-family low-rise woodframe houses with the aim to study the dynamic behaviour of this type of structure. A number of field tests were conducted to collect complementary data for existing timber buildings. The vibration data was analyzed by different analysis methodologies. To study the vibration behaviour of woodframe houses before and after earthquake simulations, time and frequency domain analysis methods, such as frequency domain decomposition and stochastic subspace iteration, were employed. To investigate the behaviour throughout the earthquake simulation, joint time-ii frequency analyses were performed. Among the analyses performed the joint time-frequency analysis is a very powerful tool, which not only provides insight into dynamic characteristics of structures that are not available through frequency domain alone, but also can explain irregular shifts in frequency and verify the results from other analyses. The investigation of vibration characteristics of woodframe houses provided a good understanding of how the natural frequency of the structure changes and how this change is related to the amount of damage observed during each test. The fundamental periods determined from the conducted experiments were in the range of 0.3 to 0.6 seconds and corresponding damping ratios between 3.6 to 16 percent. These periods are significantly longer than the periods suggested by the code formulae. For dynamic testing of buildings the ambient vibration testing method is being recommended, since it is a non-destructive and relatively inexpensive testing method. Frequency results of ambient vibration testing method are found to be typically higher than those obtained from forced vibration testing. Since the latter is considered to be closest to the real frequencies of houses subjected to strong motion, a correlation was done to correct the ambient vibration results. iii Table of Contents ABSTRACT " TABLE OF CONTENTS iv LIST OF FIGURES vii LIST OF TABLES x ACKNOWLEDGEMENT xi Chapter I - Introduction 1.1. Background 1 1.2. Objectives 4 1.3. Scope of Work 5 Chapter II - Current Knowledge and Previous Research 2.1. General 6 2.1.1. Seismic Performance of Low-Rise Light Frame Wood Buildings in Past Earthquakes 10 2.1.2. Importance of Fundamental Period in Earthquake Response 16 2.1.2.1 Application in the Woodframe Construction 18 2.1.3. Current Code Period Formulae 19 2.1.3.1. NBCC 1995 19 2.1.3.2. Uniform Building Code (1997) 20 2.1.3.3. Other Building Codes 22 2.1.3.4. Recent Developments 22 2.1.4. Impact of Upcoming Code Changes on Woodframe Buildings 25 2.1.5. The Need for More Accurate Vibration Characterization of Low-Rise Wood-Frame Buildings .27 2.2. Related Experimental Research 30 2.2.1. Research Performed in the United States 30 iv 2.2.2. Research Performed in Japan 34 2.2.3 Research Performed in Australia 39 2.2.4. Research Performed in Canada 39 2.2.5. Research Performed in Other Countries 40 2.3. Related Analytical Approaches 44 2.4. Summary of Findings 45 Chapter III - Review of Structural Dynamic Testing Concepts and Methods 3.1. Relevant Concepts in Structural Dynamics 48 3.1.1. Review on Time Domain and Frequency Domain Analyses 48 3.1.2. Analysis Tools 62 3.1.2.1. Analysis performed with MathCAD® 63 3.1.2.2. Analysis performed with ARTeMIS® 63 3.2. Applied Dynamic Testing Methods 64 3.2.1. Shake Table Testing 64 3.2.2. Ambient Vibrations Testing 66 3.2.3. Forced Vibration Testing 69 Chapter IV - Experimental Study 4.1. Description of the Earthquake 99 Woodframe House Project 70 4.1.1. Procedure and Methods of Shake Table Tests 73 4.1.2. Description of the Single Story Subsystem 74 4.1.2.1. Input Records for the Subsystem 75 4.1.3. Description of the Two Story System 78 4.1.3.1. Input Records for the Two Storey Test 79 4.1.3. Testing Facility 82 4.1.4. Vibration Data Acquisition System 83 4.1.5. Vibration Analysis Software Programs 89 4.2. Field Test of Full-Scale Light Frame Timber Structures 90 4.2.1. Building Selection for Test Purposes 90 v 4.2.2. Building Description 93 4.2.3. Methodology and Testing Procedure 95 Chapter V - Data Evaluation and Analysis 5.1. Analyses of Subsystem performance, Test Number 5 97 5.1.1. Frequency and Mode Shapes 98 5.1.2. Joint Time - Frequency Analyses 102 5.2. Analyses of Subsystem performance, Test Number 6 112 5.2.1. Frequency and Mode Shapes; 112 5.2.2. Joint Time-Frequency Analyses 112 5.3. Analyses of Two-Storey House performance, Test Number 9 117 5.3.1. Frequency and Mode Shapes 117 5.3.2. Joint Time - Frequency Analyses 117 5.4. Analyses of Field Tests 129 5.4.1. Frequency and Damping 129 5.5. Comparison between the Code and Experimental Fundamental Period 129 5.6. Correlation of Results from Ambient and Forced Vibration Methods 135 Chapter VI - Summary, Conclusions and Recommendations 6.1. Summary 141 6.2. Conclusion 143 6.3. Future Research and Applications 144 Chapter Vll - References 147 Appendix A - Drawings "Earthquake 99 Woodframe House Project" 174 Appendix B - Shake Table Drawings 179 vi List of Figures Fig. 2.1. Modern North American style single-family low-rise woodframe construction with OSB sheathing (courtesy of Dr. H. G. L. Prion)....7 Fig. 2.2. North American style single-family low-rise woodframe construction with board sheathing (courtesy of Dr. H. G. L. Prion)...7 Fig. 2.3. Modern North American style apartment-housing woodframe construction (courtesy of Dr. H. L. G. Prion) 8 Fig. 2.4. Woodframe building in a landslide, Alaska Earthquake 1964 (Courtesy of EERI) 10 Fig. 2.5. Collapsed woodframe in Northridge Earthquake 1994 (Courtesy of EERI) 12 Fig. 2.6. Seismic response factor S for 1995 NBC (NBCC 95) 18 Fig. 2.7. Vancouver "Robust" Uniform Hazard Spectra (9th meeting of CANCEE) 25 Fig. 3.1 Shake table test of Earthquake 99 Woodframe House project at University of British Columbia (courtesy of Dr. Prion) 68 Fig. 4.1. Subsystem timber structure 76 Fig. 4.2. Nahanni earthquake motion record, acceleration, velocity and displacement time history and spectra (5% damping) 77 Fig. 4.3. East elevation view of the two-storey timber structure 79 Fig. 4.4. Plan view of the main floor of the two storey timber structure 80 Fig. 4.5. Northridge earthquake motion record, acceleration, velocity and displacement time history and spectra (5% damping) 81 Fig. 4.6. Sensor layout for the sub-system timber structure 87 Fig. 4.7. Sensor layout for the two-storey timber structure 88 Fig. 4.7. North elevation of one of the timber houses tested in downtown Vancouver 94 Fig. 4.8. Sketch of sensor layout 96 vii Fig. 5.1. Coherence, Frequency Response Function (FRF) and Phase Angle plots before earthquake simulation of test # 5 run 1 99 Fig. 5.2. Frequency Domain Decomposition of Test #5 Data from Ambient Vibration Testing 100 Fig 5.3. First north-south mode shape of the subsystem in test #5 103 Fig 5.4. First east - west mode shape of the subsystem in test #5 104 Fig 5.5. First torsional mode shape of the subsystem in test #5 105 Fig. 5.6. Joint time-frequency plot for test # 5 run 1, Nahanni Earthquake 1985 108 Fig. 5.7. Joint time-frequency plot for test # 5 run 2, Nahanni Earthquake 1985 109 Fig. 5.8. Joint time-frequency plot for test #6 run 1, Nahanni earthquake 1985 115 Fig. 5.9 Joint time-frequency plot for test #6 run 2, Nahanni earthquake 1985 116 Fig. 5.10. 1st North - South Mode shape of the 2-storey in test number 9.. 121 Fig. 5.11.1st East West Mode shape of the 2-storey in test number 9 122 Fig. 5.12.1st Torsional Mode shape of the 2-storey in test number 9 123 Fig. 5.13. 2n d North - South Mode shape of the 2-storey in test number 9.. 124 Fig. 5.14. 2n d East West Mode shape of the 2-storey in test number 9 125 Fig. 5.15. 2nd Torsional Mode shape of the 2-storey in test number 9 126 Fig. 5.16. Joint time-frequency plot for test #9 run 1, Northridge earthquake recorded at Sherman Oak 1994 127 Fig. 5.17. Joint time-frequency plot for test #9 run 2, Northridge earthquake recorded at Sherman Oak 1994 128 Fig. 5.18. Comparison between the natural frequency from NBCC95 formula and experimental results 131 Fig. 5.19. Comparison between the natural frequency from upcoming NBCC and UBC 97 formula and experimental results 133 viii Fig. 5.20. NBCC 95 Normalized design distribution spectrum for peak horizontal ground velocity v=1 m/s for dynamic analysis (NBCC 1995) 134 Fig. 5.21. Correlation between the ambient and forced vibration testing method 136 Fig. 5.22. Hysteresis loop of test number 5 run 1, 1985 Nahanni earthquake 138 Fig. A.1. Two-storey woodframe house elevations view 175 Fig. A.2. Two-storey woodframe house plan view 176 Fig. A.3. Subsystem woodframe house plan view 177 Fig. A.4. Subsystem woodframe house and concrete block, plan view 178 Fig. B.1. Shake table in plan view 180 Fig. B.2. Perspective of the shake table 181 ix List of Tables Table 2.1. Overview of casualties in some recent earthquakes (Rainer and Karacabeyli 2000) 13 Table 2.2. Overview of some research results from Japan (Sugiyama 1984) 37 Table 2.3. Summary of test projects and results 43 Table 4.1. The Earthquake 99 House project, tests performed in summer 2000 72 Table 4.2. Applied earthquake records for Earthquake 99 House project.... 73 Table 4.3. Sensors installed for the shake table 84 Table 4.4. Sensor layout for the subsystem 88 Table 4.5. Sensor layout for the two-storey woodframe house 89 Table 5.1. Values of natural frequencies and damping ratio from test #5 ... 101 Table 5.2. Natural frequencies and damping ratio from test #6 113 Table 5.3. Values of natural frequencies and damping ratio from test #9.... 119 Table 5.4. Natural frequencies and damping ratio from field tests 129 Table 5.5. Seismic design S factor calculated based on fundamental periods obtained from experiment and code formulae 132 Table 5.6. S Spectral acceleration values calculated for Vancouver based on fundamental period obtained from experiment and code formulae 133 Table 6.1. Matrix of proposed future testing programme 146 x Acknowledgments First, I would like to thank my parents Afghani and Youssef Hadj Karim Kharrazi, my wife Benafsha and my brother Hadi who were very understanding and supportive throughout my graduate studies. I gratefully acknowledge the support of my supervisors Drs. Carlos E. Ventura and Helmut L. G. Prion. Their experience in the field of dynamic testing, analysis and timber engineering have been invaluable to my research. Their encouragement toward, and interest in, my academic career is much appreciated. Funding for this study was provided by the Earthquake 99 Woodframe House project and from a Forest Renewal of British Columbia (FRBC) grant awarded to the Department of Civil Engineering. I would like to thank a number of current and former graduate students of the University of British Columbia for their assistance throughout my graduate studies with special thanks to Ms. Tuna Onur, Mr. Jean Francoise Lord and Martin Turek. xi Chapter 1 Introduction The research in this thesis was aimed at determining the dynamic characteristics of light-frame low-rise timber buildings in Canada with a special emphasis on vibration behaviour. This was accomplished by studying the dynamic behaviour of several full-scale low-rise timber house models and by investigating their vibration characteristics. In addition, correlation analysis was conducted between the ambient and forced vibration testing methods. 1.1. Background Structural dynamic characteristics such as fundamental period and damping ratio are essential parameters in determining the structural response due to earthquake motions. The maximum structural response values of velocity, displacement and acceleration corresponding to an earthquake motion can be determined from the earthquake's response spectra by having the natural frequency and damping ratio of a structure. Derived from the above-mentioned principle, the National Building Code of Canada 95 (NBCC 95) recommends formulas for fundamental period of buildings and defines the uniform hazard response spectrum, which are utilized in the design process to calculate the maximum earthquake load of a building. 1 Chapter I - Introduction Proposed modifications in the forthcoming update of the National Building Code have prompted researchers to closely investigate the dynamic characteristics of light-frame low-rise timber buildings in Canada. In the previous code, the fundamental period of this type of structures was essentially estimated by an empirical formula. However this formula was basically developed to predict the fundamental period of steel and concrete structures. In addition, the upcoming code proposes significant changes in the methodology, in which the response factor is calculated, especially in the period range typically represented by woodframe buildings. In the National Building Code of Canada 95, most of the residential timber buildings are considered in a category that does not require an engineered design. This category includes woodframe buildings up to three storeys in height. Additionally, in design procedure, crude estimates of the period and damping are assumed for the woodframe buildings, which are not considered in the above-mentioned category. Thus the need for research on determining the dynamic behaviour and vibration characteristics of both categories is obvious. Determination of the fundamental period of a woodframe building through analytical means is complicated. There are several factors contributing to this complication. These factors include; non-linear behavior, complexity of structure, irregularity of building plan, unknown stiffness of diaphragms and significant contribution of non-structural elements, such as stucco, drywall, etc. A database 2 Chapter I - Introduction of experimental results on natural frequency and damping ratio of full-scale light-frame timber buildings with Canadian construction configuration is not available either. Therefore there is an immediate need for experimental work that would provide a proper estimate of the natural frequency and damping ratio for this type of buildings. To collect a considerable database on vibration behavior of woodframe buildings a non-destructive testing method is required. Ambient vibration test is a non-destructive testing method suitable for measuring the natural frequency of structures. Since this method generates different results especially for timber structures compared to forced vibration test methods such as the sinusoidal sweep test, a proper correlation is considered necessary. Therefore the correlation of the results obtained from sinusoidal sweep and ambient vibration tests and a suitable calibration of the ambient vibration testing technique could be valuable means for conducting ambient vibration tests on timber buildings in future. The collected data could be also helpful in reproducing the sampling space for an artificial intelligence network to simulate the frequency response of the structure and optimize for predicted results in future research. 3 Chapter I - Introduction 1.2. Objectives The main objectives of this thesis are: 1. To gain a better understanding of the vibration characteristics of light-frame low-rise timber buildings. More specifically, the aim is to obtain data for deriving more accurate means of estimating the fundamental period of Canadian light-frame low-rise timber buildings and compare it with the formulae suggested in the National Building Code. 2. To conduct a comprehensive literature study on the previous research in this field in order to have a better idea of what has been done in the past in relation to full-scale testing and dynamic behaviour of woodframe buildings. 3. Assess whether or not ambient vibration testing can be used effectively to determine the vibration characteristics of woodframe houses. This is to be accomplished by evaluating different methods of measuring vibration characteristics of buildings. The thesis also pursues the objective to investigate an appropriate simplified method to test and acquire data for local timber structure with the aim of studying the vibration behaviour. 4 Chapter I - Introduction 4. To investigate the use of joint time-frequency domain techniques to determine the variation of the natural frequencies of a woodframe house during an earthquake. 1.3. Scope of Work Due economic and time limitation only a subset of the data obtained from shake table tests of woodframe houses as a part of the Earthquake 99 Woodframe House project was analyzed in this study. Only three of the sixteen specimens tested during the Earthquake 99 Woodframe House project were included in this study. It is expected that the results and information from this investigation can be readily applied to analysis of the data from the remaining thirteen specimens. Also because of restricted access to existing woodframe houses in Vancouver in the limited time of the study, the permission to only three houses were obtained for non-destructive testing. Thus the field tests specimens were available for ambient vibration testing. 5 Chapter 2 Current Knowledge and Previous Research 2.1. General According to a review of the studied literature on the performance of wood structures in past earthquakes, most one-storey residential buildings of wood-frame platform construction survived earthquake ground motions with peak accelerations of over 0.6 g without loss of life, and many with slight damage. Multi-storey buildings suffered considerable damage and some collapsed, resulting in casualties. The observed failures and collapses in timber structures could be traced essentially to specific instances of lack of lateral bracing, weak first storey, inadequate connection to foundation and the fact that in some cases the observed motions far exceeded the previous versions of design requirements. For single-family and low-rise multi-family dwellings woodframe construction is by far the most common housing type in Canada, the USA, Australia and New Zealand (Fig. 2.1, 2.2 and 2.3). This type of building is also attaining acceptance in other parts of the world, including Japan where it is commonly referred to as 2x4 construction. In the last few decades a large number of woodframe buildings have been subjected to earthquakes; this provides an opportunity to evaluate the general seismic performance of woodframe construction and associate the performance of the this type of construction to quantitative factors of ground 6 Chapter II - Current Knowledge and Previous Research shaking such as peak ground acceleration and response spectra (Rainer and Karacabeyli 2000). Fig. 2.1. Modern North American style single-family low-rise woodframe construction with OSB sheathing (courtesy of Dr. H. L. G. Prion) Fig. 2.2. North American style single-family low-rise woodframe construction with board sheathing (courtesy of Dr. H. L. G. Prion) 7 Chapter II - Current Knowledge and Previous Research Fig. 2.3. Modern North American style apartment-housing woodframe construction (courtesy of Dr. H. L. G. Prion) 8 Chapter II - Current Knowledge and Previous Research To understand the fundamental behaviour of North American style and in particular Canadian style wood-frame construction, the following elements should be explained. A Canadian style modern wood-frame house consists of a concrete foundation or basement (also sometimes concrete block masonry), on top of which a platform is constructed of joists covered with plywood or oriented strand board (OSB) to form the floor of the ground level of the house. This platform is connected directly to the foundation with anchor bolts, or through a short so-called "cripple wall", "pony wall" or "stub wall". This short wall may or may not be connected to the foundation with anchor bolts. On this base, the exterior and interior walls are erected. The walls consist of a horizontal sill plate with 38 x 89 mm (2" by 4") or 38 x 140 mm (2" by 6") vertical timber studs of one storey height at a spacing of typically 30 to 60 cm. A double top plate from 38 mm thick dimension lumber provides the base for the next floor structure. Board or panel sheathing is then nailed to the studs on the outside of the building, while the inside spaces are filled with thermal insulation and then covered with a vapour barrier and gypsum board as the interior finishing. Once the first storey walls are complete, the second storey floor is constructed, which in turn acts as a platform for erection of the second storey walls. This process is continued for all the stories. The roof structure typically consists of prefabricated trusses, which are covered with sheathing and roof tiles (Rainer and Karacabeyli 2000). Further details can be found in Keski (1997). 9 Chapter II - Current Knowledge and Previous Research 2.1.1. Seismic Performance of Low-Rise Light Frame Wood Buildings in Past Earthquakes Timber structures in general have performed well during previous earthquakes. In the 1964 Alaska earthquake, which measured 8.6 on the Richter scale, timber structures performed exceptionally well. Figure 2.4 demonstrates an example of a building that was displaced by a landslide and the ability of a well-constructed system to sustain extreme deformations. Relatively few failures were observed as a result of inadequate lateral bracing due to either the lack of wall sheathing under the siding or to large openings, particularly near building corners (Rainer and Karacabeyli 2000). Fig. 2.4. Woodframe building in a landslide, Alaska Earthquake 1964 (Courtesy of EERI) 10 Chapter II - Current Knowledge and Previous Research The 1971 San Fernando earthquake (6.6 on the Richter scale), however, did extensive damage to timber structures. Of the 58 deaths and 5,000 injuries, four deaths occurred in wood-frame residences. About 20,500 single-family houses were damaged, of which 730 were demolished or required major rehabilitation. Single-family home damage was reported to be between $58 and $114 million; this dollar loss was larger than that of any other building category in the private sector (Soltis 1986). The primary cause of overall residential damage in the San Fernando earthquake was inadequate lateral support. The lack of racking walls or their non-symmetrical arrangement caused damage or collapse. Most vulnerable were two-storey and split-level homes with a garage on the first floor. Failures in sill plate connections and homes shifting off their foundations were also observed. It was noted that the greatest deficiency of wood-frame construction was its lack of resistance to torsional racking caused by the second storey being stiffer than the first (non-symmetry) (Soltis 1986). The 1994 Northridge earthquake with a magnitude of 6.7 had a significant ground acceleration, both horizontally and vertically, which in some places exceeded gravity acceleration. It caused extensive damage to residential, institutional and commercial buildings (Fig. 2.5.). This represented the most intense ground motion that had so far been recorded in a populated area in North America. The weak first storey in multi-storey wood-frame apartment buildings was found to be 11 Chapter II - Current Knowledge and Previous Research the predominant weakness, which had already been recognized in the 1971 San Fernando earthquake. In this earthquake several building collapses took place, which is not surprising, considering the fact that the combination of the vertical and horizontal ground acceleration exceeded the typical design acceleration of 0.4 g by a factor of 2 and more (Rainer and Karacabeyli 2000). Fig. 2.5. Collapsed woodframe in Northridge Earthquake 1994 (Courtesy of EERI) Besides the above-mentioned earthquakes, the performance of woodframe structures in other earthquakes were assessed and the results are summarized in Table 2.1, which lists the total number of causalities caused by several earthquakes and also reflects the number of deaths in woodframe houses. 12 Chapter II - Current Knowledge and Previous Research Table 2.1. Overview of casualties in some recent earthquakes (Rainer and Karacabeyli 2000) Earthquake M No. of Persons Killed (Approx.) No. of Wood-frame Bldgs. Shaken (Estimated) Total In Wood-frame Buildings Alaska, 1964 8.4 130 <10 N/A San Fernando, 1971 6.7 63 4 100,000 Edgecumbe, 1987 6.3 0 0 7,000 Saguenay, 1988 5.7 0 0 10,000 Lorna Prieta, 1989 7.1 66 0 50,000 Northridge, 1994 6.7 60 16+4 200,000 Hyogo-ken Nanbu (Kobe), 1995 6.8 6,300 0 8,000 Evidently the number of deaths in woodframe houses has been very low, considering the large number of buildings that were severely shaken. But the low number of causalities in woodframe buildings is only one important factor of the woodframe performance in the mentioned earthquakes. Other important factors such as the economic losses and social issues have to be considered. Resources on exact figures for damage or lost of woodframe buildings are not available for all earthquakes mentioned in Table 2.1. Some monetary losses and 13 Chapter II - Current Knowledge and Previous Research social effect for Northridge, Lorna Prieta and San Fernando are mentioned below to reflect the importance of the other factors and thus the importance of this study. In the Northridge earthquake nearly $20 million was recorded in direct property losses, more then half occurred in residential woodframe construction (Hamburger 1994). As mentioned previously, the single family home damage was reported $58 to $114 million for the San Fernando earthquake (Soltis 1986). In the Lorna Prieta earthquake at least 3,700 people were injured and over 12,000 were displaced. Over 18,000 homes were damaged and 963 were destroyed (EQE international Website - (http://www.eqe.com/publications/ lomaprie/lomaprie.htm) 1989). On the basis of observations of the performance of wood-frame buildings in the earthquakes surveyed, the following assessment is made (Rainer and Karacabeyli 2000): • Single-storey wood-frame houses have performed well when subjected to PGA of 0.6 g and even higher, provided some well-known deficiencies such as un-braced stub-walls, and inadequately braced additions like porches and chimneys were absent. The performance of these houses has demonstrated that the life-safety objective inherent in building codes has been satisfied. In fact, for most of the houses the damage sustained from earthquakes was of a minor nature, showing that the objective of damage control has also largely been achieved. 14 Chapter II - Current Knowledge and Previous Research • Some two-storey wood-frame buildings were seriously damaged in areas of 0.6 to 0.8 g PGA in California. In Kobe, on the other hand, they all performed well. In California they largely met the life-safety criterion, whereas in Kobe they met the life-safety criterion with minimal damage. • For three- to four-storey wood-frame structures the life safety objective has largely been achieved for PGA of 0.6 g and larger during the Northridge earthquake except for a few that collapsed and resulted in casualties. These failures were due to a weak first storey and earthquake motions that substantially exceeded the design criteria. The observed behaviour of this type of construction was related to the characteristics of the ground motions and it is concluded that multi-storey wood-frame buildings need to be constructed to greater loading requirements than single-storey houses. This is particularly relevant for multi-storey buildings that are constructed according to prescriptive rules (Rainer and Karacabeyli 2000). The general seismic performance of low-rise light frame timber buildings in past earthquakes was briefly discussed. To investigate the structural response characteristics of this type of structures it is important to discuss the significance of fundamental period in earthquake response, the suggested period formula by different codes, changes in upcoming code, developments of new formula and the need for more accurate vibration characteristics of this type of buildings. 15 Chapter II - Current Knowledge and Previous Research 2.1.2. Importance of Fundamental Period in Earthquake Response The fundamental vibration period of a building is a very important factor that determines the response of the structure to ground motion. It appears in the equation specified in building codes to calculate the design base shear and lateral forces. Because it is in most cases difficult or impractical to compute the period for a structure that is yet to be designed, the National Building Code of Canada (NBCC 95) provides an empirical formula that depends on overall dimensions and material type. Existing building codes require a design earthquake load or base shear based on the building's system characteristics, site location, occupancy, etc. The code specifies simplified formulae to approximate the building's dynamic behaviour. One key parameter that is required to determine how the building will behave during an earthquake is its fundamental period. This is used, for example, to help determine the appropriate seismic base shear coefficient for the design of a structure. The base shear is calculated with the formula: V = (0.6/R).(v.S.I.F.W) (2.1) Where V = the design base shear 16 Chapter II - Current Knowledge and Previous Research R = a force reduction factor based on the building system and its ductility v = the zonal velocity ratio S = the response factor I = the importance factor F = the foundation factor, and W = the building weight, including partial snow load With the empirical formula for the fundamental period or natural frequency of the structure and the acceleration-related seismic zone and velocity-related seismic zone factors the seismic response factor S is calculated. The relationship between fundamental period and seismic response factor is shown in Figure 2.6. This factor is a function of the fundamental period, T, of the structure, and the relative values of the velocity-related and acceleration-related seismic zones, Zv and Za The values, Zv and Za, are reflecting the probability of exceedance of 10% in 50 years of peak horizontal ground acceleration and velocity for a particular geographical location (User's Guide - NBC 1995 / Structural Commentaries of Part 4). The seismic response factor S is obtained on basis of dynamic response studies using a number of representative earthquake records (Heidelbrecht and Lu, 1988). Thus the application of structural response reflects the need of research on structural response of woodframe buildings. 17 Chapter II - Current Knowledge and Previous Research In addition, if the amount for the fundamental period is underestimated the value for the seismic response factor S could be higher than it will be in reality. This could cause a higher value of base shear to be introduced in the design process. Fig. 2.6. Seismic response factor S for 1995 NBC (NBCC 95) 2.1.2.1 Application in the Woodframe Construction NBCC 95 introduces part 9, "Housing and Small Buildings", which applies to buildings of 3 storeys or less in building height, having a building area not exceeding 600 m2 and used for major occupancies classified as Group C, residential occupancies and etc, indicated in section 2.1.3 of the code (NBCC 95). Additional requirements are addressed for this category in section 9.23 of 18 Chapter II - Current Knowledge and Previous Research NBCC 95. All other woodframe buildings not fulfilling the addressed requirements in NBCC 95 section 2.1.3 and 9.23 are required to be designed based on part 4 of NBCC 95, "Structural Design". Thus the fundamental period is required for the calculation of the base shear for the second category of the woodframe buildings. 2.1.3. Current Code Period Formulae Recent research has shown that the current building code period formulae substantially underestimate the building periods for concrete and steel moment-resisting frame buildings, as well as that for concrete shear-wall buildings (Goel and Chopra, 1997, 1998). This might also be the case for wood structures leading to the overall objective of this study to propose a scheme for improvement of the current code period formulae. 2.1.3.1. NBCC 1995 The National Building Code of Canada, like the Australian Standard, has based their period formulae on older versions of the Uniform Building Code (IAEE, 1992). These formulae do not significantly differentiate between building materials or structural systems. The code prescribed natural period is given as T = 0 . 0 9 - ^ or (2.2) 19 Chapter II - Current Knowledge and Previous Research T = 0.1N for moment-resistant space frames. (2.3) T = 0.085(hn) 3/4 for steel moment-resistant space frames. (2.4) T = 0.075(hn) 3/4 for concrete moment-resistant space frames. (2.5) hn = height above the base to the uppermost level in the main portion of the structure. L = the overall building dimension in the direction of the earthquake forces or the length of the wall or braced frame parallel to the applied lateral forces. N = number of stories/levels. 2.1.3.2. Uniform Building Code (1997) The 1997 Uniform Building Code (UBC) prescribes the following period formula (called Method A) for buildings: hn = height, in feet, above the base to the uppermost level in the main portion of the structure. (2.6) 20 Chapter II - Current Knowledge and Previous Research The values of Ct vary according to material and framing characteristics: C t = 0.035 (Steel Moment Resisting Frames) C, = 0.030 (Reinforced Concrete Moment Resisting Frames and Eccentric Braced Frames) c, =0.020 (all other buildings) For Concrete or Masonry Shear Wall Buildings the formula is obtained from additional equations. The UBC also allows for the period to be calculated from structural analysis, but it imposes limits on the maximum periods obtained (see UBC 1997). Another option is to use stiffness information of the building to compute the period with Rayleigh's formula as follows: T = 2TT i=i 1 4 f.6, (2.7) 21 Chapter II - Current Knowledge and Previous Research where: Wi = that portion of the total seismic dead load located at or assigned to level i. 5;= horizontal displacement at level i relative to the base due to applied lateral forces, f. fi = lateral force at level i. g = acceleration due to gravity. n = uppermost level in the main portion of the structure. 2.1.3.3. Other Building Codes Other codes, such as the New Zealand Standard, do not provide a simplified period formula. They prescribe a formula based on Rayleigh's method, similar to "Method B" in the UBC. 2.1.3.4. Recent Developments Alternative period formulae have been presented for reinforced concrete and steel moment-resisting frame buildings and for concrete shear-wall buildings (Goel and Chopra (1997, 1998)). In this study information about the fundamental modes of vibration of a number of buildings was gained by analyzing several recorded motions from various California earthquakes. These records did not cause the structures to experience inelastic deformations, although they were 22 Chapter II - Current Knowledge and Previous Research strongly shaken. These buildings were divided into two categories, depending on the magnitude of the earthquake shaking they experienced, i.e. whether the peak ground acceleration was more or less than 0.15 g. After it was found that the current code formulae substantially underestimated the natural vibration periods for these structures, the theory upon which the code formulae were based was re-evaluated and new formulae were derived by means of a regression analysis. These period formulae resulted in a much better fit, in the least-squares sense, to the measured period data. The final recommended period formulae were derived by observing the trends obtained from the buildings that had experienced peak ground accelerations of 0.15g or greater. This is because at smaller acceleration levels the periods tend to be lower as non-structural components tend to influence the lateral stiffness significantly. Goel and Chopra concluded that Rayleigh's method was adequate to provide a good approximation of the dynamic behaviour of moment resisting frame buildings. Based on this method, the period formula should be of the form T=C(hn)Y. C and y are to be determined from regression analysis, using the relationship ln(T) = ln(C) + y ln(hn). Following this method, there is a 50% probability that the actual period of the building is greater that the period estimated by the regression formula. To be conservative, the formula should provide lower values of the period for determination of design base shear, therefore a lower bound of a standard deviation was chosen from the best-fit line. Also, an upper limit for periods was provided using rational analysis rather than 23 Chapter II - Current Knowledge and Previous Research the code formula. The resulting lower bound period formulae were as follows, with standard error estimates of se = 0.209 for R/C MRF and se = 0.233 for steel MRF: T = 0.016h°90 Reinforced Concrete Moment Frames (2.8) no larger than 1.4 T if using rational analysis T = 0.028h°80 Steel Moment Resisting Frames (2.9) no larger than 1.6 T if using rational analysis where hn = the total building height from base of structure, in feet. Rayleigh's method was not sufficient to give a good estimate for the dynamic characteristics of shear-wall buildings, so various other well established analytical procedures were chosen, such as Dunkerley's method, which combines both flexural and shear deformations of a cantilever. Regression analysis yielded the following formula, with an error of estimate se = 0.143 while the UBC-97 error estimate is se = 0.546: T = o.ooi9hn/-jA7 Concrete Shear Wall (2.10) no larger than 1.4 T if using rational analysis 24 Chapter II - Current Knowledge and Previous Research 2.1.4. Impact of Upcoming Code Changes on Woodframe Buildings Significant changes are being proposed for the NBCC that will significantly affect the design earthquake loads on woodframe buildings. With the proposed changes of the uniform hazard design spectra, the current spectral values that are based on an exceedance probability of 10% in 50 years will be modified to an exceedance probability of 2% in 50 years. This will cause a considerable increase of the spectral acceleration for all period ranges. 0.1 02 OS 1 2 Period (Second) 2%/50 year 50th percentile ... 2%/50 year 84th percentile 10%/50 year 50th percentile . . . 10%/50 year 84th percentile — Cascadia 50th percentile — Cascadia 84th percentile Fig. 2.7. Vancouver "Robust" Uniform Hazard Spectra (9th meeting of CANCEE) 25 Chapter II - Current Knowledge and Previous Research This modification has a profound impact for buildings with lower periods, which is the range for low-rise wood-frame family housing. The modification of the spectral acceleration from current values to higher values will thus produce a higher base shear or a greater earthquake load on the buildings. Considering the past record of building performance, it appears that the current building code already provides a conservative estimate of design forces. It is thus imperative that the period and damping characteristics of low-rise wood-frame buildings be investigated to assure realistic calculation of seismic forces for design (Fig. 2.7). Another proposed modification in the upcoming code is a suggested fundamental period formula for structures, which are not moment frame structures. This formula, which will replace Eq. (2.2), is as follow: 3 T = 0.05(hn)4 (2.11) in where the hn is the height in meter, above the base to the uppermost level in the main portion of the structure. It is very important to have experimental database for the period and damping characteristics of low-rise wood-frame buildings to compare them with the suggested formula shown in Eq. (2.11). 26 Chapter II - Current Knowledge and Previous Research 2.1.5. The Need for More Accurate Vibration Characterization of Low-Rise Wood-Frame Buildings In the past, most research has been done on the dynamic and cyclic characteristics of woodframe subsystems and connections, whereas the full-scale testing of wood shear-wall buildings has hardly been pursued. Considering the fact that over 90% of low-rise residential buildings in Canada are built from wood, it becomes evident that this deficiency emphasizes the importance of this study. The dynamic characteristics of wood-frame buildings as a whole must be better understood in order to establish code requirements for the safe and cost-efficient design of this type of structure. To improve current building practices, several reason are given below to demonstrate needs for and requirements of a study of the dynamic characteristics of wood-frame buildings. 1. Based on the literature study reported herein, no significant information about, study on or records of full-scale testing of light-frame low-rise timber houses are found, especially for Canadian style of construction. This shortage in information may be the causes for inadequate accuracy of the methods to obtain the fundamental period and damping for this type of structures. The only project in Canada that deals with the seismic resistance and dynamic performance of light-frame low-rise timber houses is the "Earthquake 99 Woodframe House Project" at University of British Columbia. 27 Chapter II - Current Knowledge and Previous Research 2. According to several studies in different countries such as the US, Japan, Australia and New Zealand, the available formulae for the fundamental period have been found inaccurate. These formulae do not specifically deal with low-rise light-frame timber structures at all. 3. In the past, the design of most woodframe buildings was governed by the wind load. The upcoming code rules increase in earthquake forces above the previous governing wind loads. Thus more accurate estimates of earthquake forces are needed. Since these forces are carried out based on fundamental periods, a better understanding of the vibration behaviour is required. 4. Because of the complex behaviour of woodframe structures caused by non-linearity, slackness, friction in connections, non-structural components and etc, the analytical methods of defining the natural frequency for this type of structure is very difficult and not as efficient as field-testing. A number of computer analysis programs have been written to predict the dynamic behaviour of timber structures, but the non-linear behaviour and other complex phenomena such as slackness, friction and yielding in connections of wood frames limit the programs. Full-scale test experimental results are required essentially for the verification of these analysis programs. 28 Chapter II - Current Knowledge and Previous Research 5. For the most part of the accomplished studies in the past, the focus has been on the dynamic and cyclic characteristics of wood subsystems and connection panels, shear wall behaviour and connections. Full-scale studies on testing of wood shear-wall buildings and interaction of components in a system have not been pursued. Therefore a gap exists in the information of the dynamic characteristic of this type of structure as a whole. 6. By testing actual houses, important data could be obtained, which can be helpful in better understanding the dynamic characteristic of existing timber houses and the effect of non-structural components. Also it could help to provide a better scheme for the retrofit of this type of house. The cases, which would be suitable for field-testing, are as follows. 6.1. The change of the dynamic characteristics of old structure due to the aging phenomena. 6.2. The opportunity to study a wide selective range of different lateral load resisting systems, different construction configurations, connection types and workmanship errors. 29 Chapter II - Current Knowledge and Previous Research 6.3.The effects of non-structural elements that are not applied in the simplified modelling of the structures. 2.2. Related Experimental Research To assess the existing knowledge base, a thorough literature study was performed on work done elsewhere to learn from other researchers' experience and to assess whether some of the research data might be relevant to the situation in Canada. Different research projects and studies from different countries are discussed below, the results are compared and important points from various projects are summarized. 2.2.1. Research Performed in the United States The very first full-scale test series of woodframe buildings can be attributed to Rea, Bouwkamp and Clough (1968). In a report to the Department of General Services, State of California, they cited natural frequency values of 5 to 9 Hz and damping ratios of 4 to 6 percent of critical for a one-storey school building of plywood shear walls and glulam roof framing. Yokel et al (1973) evaluated the performance of a conventional two-storey house under simulated wind loads of up to about 1.2 kPa (25 psf.). Walls were constructed with gypsum wallboard on both sides with diagonal 25.4 x 101.2 mm 30 Chapter II - Current Knowledge and Previous Research (1x4 in.) wood braces in the corners. The natural frequency was obtained with a free vibration method by releasing a 8.9 kN (2000 lb) force from the first floor in the vertical direction. The recorded first natural frequency was approximately 9 Hz and damping, computed from plots were within a range of 4 to 9 percent. Loading of the house was performed from the outside by means of an in-house made loading-device, which was attached to heavy-duty vehicles. Yances and Somes (1973) and Tuomi and McCutcheon (1974) evaluated the deformation characteristics of the low-rise light frame timber houses, but paid little attention to the dynamic behaviour. Medearis (1978) surveyed 63 one-and-a-half and two-storey residences of various ages in four states. He found little difference due to age of construction or geographic location. Natural frequencies from 4 to 18 Hz were observed, corresponding to building heights of 40 to 10 feet (frequency is inversely to the proportional height), with an average damping ratio of 5.2%. To obtain the natural frequency of these structures, the ambient vibration method was used. Dowding and Murray (1981) surveyed 23 one, one-and-a-half and two-storey residential timber structures of various ages by recording their dynamic behaviour to blast-induced ground motions. The average overall structural fundamental frequency value was 7 Hz (ranging between 4.8 to 8.0 Hz), with damping ratios ranging from 2 to 23 percent of critical with an average of 4.6 percent. Fundamental frequencies for one-storey wood frame structures averaged 8 Hz, 31 Chapter II - Current Knowledge and Previous Research while one, one-and-a-half and two-story structures averaged 5.8 Hz as a group. In a continuation of the mentioned study, Stagg, Siskind, Stevens and Dowling (1984) confirmed the results in a report to the Bureau of Mines. Falk and Itani (1986) conducted several tests on timber shear walls with different sizes and openings with different dimensions. They reported damping values of 9 to 34 percent of critical and 8 to 29 Hz for the natural frequency. These results were obtained from a partial full-scale woodframe structure. The free vibration and force vibration methods were used to obtain the above values. Polensek and Schimel (1989) determined the natural frequency for a panel connection model (1067mm x 1067mm connection panel with floor, foundation and wall components), within an approximate range of 4 to 9 Hz and 1.5 to 9.7 percent for the damping. An interesting observation in this test was the decrease of the natural frequency as the displacement amplitude increased and a corresponding increase in the damping. Philips and Itani (1993) performed interesting deformation characteristic tests on a 4.88 m (16 ft) wide by 9.75 m (32 ft) long and 2.45 m high timber house. Unfortunately, the results presented in the paper do not include any dynamic behaviour as the test was done quasi-statically. 32 Chapter II - Current Knowledge and Previous Research Camelo et al. (2001) performed Task 1.3.3 of the CUREe Woodframe Project. As part of their task they conducted vibration measurements on a number of different structures with different configurations and heights. The measured frequency for one, two and three storey wood frame buildings were between 4.2 and 7.8 Hz with first mode damping ratios in range of 2.6 to 6.8%. Additionally, regression analysis were performed on obtained natural frequency and building height, which resulted in the following formula: T = 0.032(hn)055 (2.12) Filiatrault, et. al. (2001) as part of Task 1.1.1 of the CUREe Woodframe project tested a full-scale two storey building on a shake table. The structure was tested during 10 phases of construction to determine the performance of the structure with fully sheathed shearwalls, symmetrical and unsymmetrical door and window openings, perforated shearwall construction, conventional construction, and with and without non-structural wall finish materials. The building had plan dimensions of 4.9m x 6.1m and height of 6.1m. They performed four types of shake table tests: quasi-static in-plane floor diaphragm tests, frequency evaluation tests, damping evaluation tests, and seismic tests. For the fully-configured building (wall finish applied, Phase 10 tests), the fundamental transverse frequency was 6.5 Hz (from ambient vibrations), 6.3 Hz (shaking at PGA = 0.05g), 5.8 Hz (shaking at PGA = 0.36g), and 5.5 Hz (shaking at PGA = 0.50g and 0.89g). The equivalent viscous damping ratios were based on log-decrement method and 33 Chapter II - Current Knowledge and Previous Research increased from 3.1% at ambient levels to 12% at PGA = 0.22g shaking, then decreased to about 6% at PGA = 0.5g shaking and beyond (Camelo et al. 2001). 2.2.2. Research Performed in Japan Sugiyama, Kikuchi and Noguchi (1976) performed free vibration testing on a two-storey house with dimensions 7.8 m by 9.55 m in plan and with an average height of 5.10m. The test was conducted by applying a horizontal force to the first and second floor to achieve a certain displacement. Free vibrations were induced by sudden release of the 500 kg loads. The natural frequency was about 7.2 Hz for the natural frequency. The damping ratio was 9 to 11 percent. The same test was conducted by excitation of human power yielding a natural frequency of 7.4 Hz and 7 percent critical damping. Sugiyama (1984) gives a summary of Japanese experience and research on seismic performance of timber buildings (Table 2.2). The test results provide an overview of earlier studies on different woodframe construction types in Japan. As demonstrated in Table 2.2, the range of natural frequency for both, the traditional Japanese and North American woodframe buildings is of 3.13 to 7.14 Hz and the damping ratio is from 3 to 24 percent. Yasumura and Murota (1988) performed forced vibration tests on a full-size woodframe building of three storeys. Each storey had a footprint area of 66 m2 3 4 Chapter II - Current Knowledge and Previous Research with 9.1 m in the longitudinal direction and 7.28m in the transverse direction. The structural system had continuous wall panels with 9.5mm thick Douglas-fir plywood sheathing and 12 mm gypsum boards inside (local system). Forced vibrations were applied through an eccentric weight vibration generator located on the third floor. The response of each floor was measured. The natural frequency range was found to be around 4.8 to 8.8 Hz before the dynamic testing and about 3.1 to 7.2 Hz thereafter. The damping ratio was not identified in this test. Hirashima (1988) analyzed the observed earthquake response of a post and beam wood structure in the same year. The building included two storeys with 105 mm by 105 mm posts. The beams were 105 x 105 mm and 115 x 210mm for the first and second floor, respectively. The building had a footprint area of 26.5 m2 in each floor with 7.28 m in the longitudinal direction and 3.64 m in the transverse direction. The forced vibration test was carried out with an eccentric weight vibration generator of 4kg-cm. The device was bolted down on the second floor of the building. The natural frequency was calculated as 4.0 Hz with a damping ratio of 2.4 percent in the transverse direction and 4.5 Hz with a damping ratio of 1.4 percent in the longitudinal direction. These values were confirmed through a free vibration test. Sakamoto, Ohashi and Fujii (1990) undertook an experimental study on a base isolated two-storey wood frame building. It consisted of two storeys with a 35 Chapter II - Current Knowledge and Previous Research footprint area of about 80 m2 at each floor and with a length of 10.92 m in the longitudinal direction and 7.28 m in the transverse direction. The isolators alone had a natural frequency of 0.5 Hz with 0.15 percent damping. The structure mounted on the isolator was shaken from outside. The natural frequency recorded was 2 to 2.1 Hz for the first mode and 8.5 to 9.7 Hz for the second mode. Arima et al (1990) came up with the idea to use eccentric weight vibration generator for non-destructive testing to shake a number of timber houses. The woodframe buildings were two and three storey family housing structures with different construction methods. The measured natural frequencies were within a range of 3 to 9 Hz. Yasumura (1996) studied different braced frames and moment resisting wood-frames versus shear wall panels with and without gypsum boards. The frequency results were in a range of 0.83 to 3.3 Hz with the moment frames at the low end and the shear walls with the higher values. Kohara and Miyazawa (1998) studied the seismic performance of wooden frame structures based on shake table tests of full-scale duplex houses. These specimens had two storeys with 11.83 m in the longitudinal direction and 7.28 m in the transverse direction for the first storey and 9.10 m in the longitudinal direction and 5.45 m in the transverse direction for the second storey. The 36 Chapter II - Current Knowledge and Previous Research measured natural frequencies were in a range of 6.05 to 6.49 Hz. Their study shows that the recorded natural frequencies by ambient vibration are 1.5 to 2 Hz higher than those obtained by the sine sweep method with forced vibrations. Table 2.2. Overview of some research results from Japan (Sugiyama 1984) Construction type of tested houses No. of Storeys Floor Plan X Dir, Y Dir Researchers Natural Period (s) Natural Frequency (Hz) Damping Ratio Traditional Type (* used house ** built for the test) 1* 5.6mx7.4m Umemura (Short span direction) 0.29 3.45 0.07 2* 5.6mx7.4m 5.6mx7.4m Umemura (Long span direction) 0.29 3.45 0.19 1* 4.55mx7.28m Nakahara Chikazawa Yamashima X: 0.25 4 0.24 Y: 0.25 4 0.20 2** 6.37mx10.41m 4.55mx7.28m Japan Housing and Wood Technology Center X: 0.14-0.15 6.66-7.14 0.03-0.09 Y: 0.16-0.17 5.88-6.25 0.05-0.06 North-American Type (All built for the tests) 2 7.81mx9.29m 7.81mx9.29m Nakahara Sugiyama Y: 0.14 7.14 0.095 2 5.46mx7.28m 5.46mx7.28m Sakamoto Ishiyama X: 0.27-0.29 3.45-3.70 0.035-0.054 Y: 0.25-0.30 3.33-4.00 0.034-0.083 2 5.46mx7.28m 5.46mx5.46m Y: 0.23 4.35 0.028-0.052 3 9.1mx9.22m 10.92mx9.22m 3.64mx9.22m Imaizumi Arima Ishiyama (Building Research Institute) 2 n d fl. X: 0.18-0.19 5.26-5.56 0.032-0.055 3 r d fl. X: 0.17-0.18 5.56-5.88 0.036-0.045 2 n d fl. Y: 0.29-0.31 3.45-3.23 0.029-0.050 3 r t fl. Y: 0.29-0.31 3.45-3.23 0.029-0.053 3 10.46mx11.95m 10.46mx11.95m 10.46mx11.95m 2 n d fl. X: 0.19-0.20 5.00-5.26 0.040-0.077 3 r d fl. X: 0.19-0.20 5.00-5.26 0.045-0.073 2 n d fl. Y: 0.30-0.32 3.13-3.33 0.030-0.047 3* fl. Y: 0.29-0.30 3.33-3.45 0.030-0.057 37 Chapter II - Current Knowledge and Previous Research Ohashi and Sakamoto (1998) subjected a full-scale simple family house, 5.4m by 3.6m in plan and 2.9m high, on a shake table to different ground motions. The was single storey specimen was was designed to be equivalent to the first storey of a two-storey house. As construction method, the conventional Japanese housing configuration was selected. Their study also indicated that the recorded natural frequencies by ambient vibration are higher by 1 to 1.5 Hz compared to results from the sine sweep method. The natural frequencies were calculated as 2.1 to 7 Hz in the transverse direction and 1.5 to 4 Hz in the longitudinal direction with a damping of 1.4 percent. Sato et al (2000) performed several shake table tests to extract the dynamic characteristic values for a three-dimensional full-scale test specimen. The simple house (3.64 by 4.55 m) was constructed with a shear wall system, the configuration of which was changed for each testing set. This was done to capture the effect of the change in the opening ratio in the model versus the natural frequency. The values ranged from 3.28 to 5.85 Hz. The results from ambient vibration were 0.5 to 1.5 Hz higher in the frequency when comparing them with the results of force vibration tests. Sawako et al (2000) evaluated the structural characteristics of 104 wooden residential houses, by ambient vibration testing. Interesting results and correlations were found for a relationship between the age and dimension of the houses with the dynamic characteristics. The natural frequency decreased 3.3 Hz 38 Chapter II - Current Knowledge and Previous Research linearly with increase of 80 years in the age of the timber houses. The natural frequency values ranged from 2.85 to 8.5 Hz. As part of this study, an estimate was done of the damage inflicted on aged houses through past earthquakes. 2.2.3 Research Performed in Australia Foliente et al. (2000) present the details and preliminarily test results of a full-scale one-storey house tested under quasi static loading (CSIRO). No dynamic characteristics results were published in their report. 2.2.4. Research Performed in Canada Rainer et al. (1988) determined the fundamental frequencies of six typical houses in the Brocklehurst area of Kamloops BC and obtained values from 7.0 to 8.9 Hz with an average of 7.8 Hz. Damping ratios for the fundamental mode of the six houses ranged from 3.5 to 7.5 percent of critical with an average of 4.8 percent. Forced vibrations, in this case induced through a passing train, as well as ambient vibrations were used to determine the dynamic characteristics. Frenette et al. (1996) conducted a series of tests on moment resisting wood frame buildings with dowel type connections. The frame was made of parallel stand lumber, had a height of 2.7m and a width of 2.6 m. with a vertical load of 1.7 ton at each storey level. The recorded natural frequency was 3 Hz. 39 Chapter II - Current Knowledge and Previous Research Durham et al. (1999) performed shake table tests on a single shear wall. The frequency results for the single model were 3.3 to 5 Hz. The wooden shear wall was installed and loaded in a steel frame of 3 m length and 2.5 m height. Popovski (2000) performed shake table tests on a two-storey woodframe braced model. The frequencies of the latter woodframe ranged between 3.81 and 8.5 Hz with critical damping ratio between 1.9 and 3.9 percent. Researchers at the University of British Columbia (2000) recently performed a number of earthquake shake table testing under the "Earthquake 99 Woodframe House" project. The objective was to assess the earthquake performance of British Columbia housing stock. The tests were performed in two sets, a single storey subsystem and a full two-storey building. These tests are explained thoroughly in Chapter IV. 2.2.5. Research Performed in Other Countries Gavrilovic and Gramatikov (1990) performed several quasi static and shake table tests in the former Yugoslavia on a truss-frame wooden structure. In their first set, in which the structure was heavily loaded, the obtained natural frequencies were in the range of 3.8 to 4.2 Hz. In the second set, the modelled structures had a frequency range of 6 to 7.2 Hz. The damping ratios were estimated around 3.3 40 Chapter II - Current Knowledge and Previous Research to 8.8 percent. The experimental models were smaller sections of a full-scale structure. The area of the structural specimen was of 6.1 m by 1.1 m. Ceccotti and Vignoli (1991) tested two identical glulam portals with dowelled joints reinforced with internal steel plates in Italy. Their results showed a frequency range of 1.5 to 2 Hz. Touliatos et al. (1991) performed several tests on two storey residential buildings in Greece. The frequency results from their testing were 4.5 to 5.6 Hz. Ellis and Bougard (1998) released a report on dynamic testing and stiffness evaluation of the TF2000 (6 storey) experimental building in the United Kingdom. The six-storey building was 25 m long, 19 m wide and 19.5 m high. The main objective of that report was to determine the characteristics of the fundamental modes of vibration. Two types of tests have been undertaken. The first made use of laser measurements to monitor the ambient response of the structure, which is a type of ambient vibration testing method. The second type of test was a forced vibration test. The ambient vibration test yielded frequency results from 2 to 3.22 Hz with an average of 2.53 Hz, while the forced vibration testing method gave 2 to 4.84 Hz for the fundamental frequencies. Critical damping ranged between 2.44 to 3.30 percent of critical. 41 Chapter II - Current Knowledge and Previous Research Table 2.3 gives a concise summary of all the tests done so far with a brief listing of test characteristics and results. 42 Chapter II - Current Knowledge and Previous Research Table 2.3. Summary of test projects and results Reference(s) Natural Frequency (1/Tn) (Hz) Critical Damping Ratio (%) Building type Testing Method Name Year Construction type Number of Story Rea et al. 1968 5.0 to 9.0 4.0 to 6.0 Play wood shear wall North American One-Story Yokel et al. 1973 9.0 4.0 to 9.0 North American Two-Story Free Vibration Medearis 1978 4.0 to 18 5.2 North American Residential (63) One, One and Half and Two -Story Ambient and Frorced Vibration Dowding and Murray 1981 4.8 to 8.0 4.6 North American Residential (23) One, One and Half and Two- Story Ambient Vibration and Force Vibration due to Blast induced Dowrick 1987 1.7 to 10.0 New Zealand residential One- and two-story Polensky and Schimel 1989 4.0 to 9.0 1.5 to 9.7 North American Full-Scale Model Forced and Free Vibration Yasumura and Muroto 1988 3.1 to 8.8 Japanese Three Forced Vibration Hirishima 1988 4.0 to 4.5 1.4 to 2.4 Japanese(Post and Beam) Two Forced and Free Vibration Gavrilovic and Gramatikov 1991 3.8 to 7.2 3.3 to 8.3 truss-frame residential One-story Forced and Free Vibration Sugiyama 1984 3.0 to 7.14 2.8 to 9.5 N. American residential Two- and three-story Forced, Free and Ambient Vibration Test Methods Touliatos et al. 1991 3.45 to 7.14 3.0 to 24 Japanese residential One and Two-Story 4.5 to 5.6 Greece Two-story residential Sakamoto et al. 1990 0.8 to 2.1 0.15 base isolated residential Two-story Forced Vibration Test Kohara et al. 1998 6.05 to 6.49 Japanese residential Two-story Ambient and Forced Vibration Arima et al 1990 3.0 to 9.0 Japanese residential One-, two- and three-story Forced Vibration Nakajima et al. Yasumura et al. 1993-1990 4.7 to 6.2 Japanese residential Three-story Ohashi et al. 1998 1.5 to 7.0 1.4 Japanese residential Sub-system Ambient and Force Vibration Sato et al. 2000 3.28 to 5.85 Japanese residential One Story Ambient and Force Vibration Sawako et al. 2000 2.85 to 8.5 Japanese residential (104) One, Two and Three Story Ambient Vibration Sugiyama et al. 1976 7.2 to 7.4 9 to 11 Japanese residential Two Story Free-Vibration Rainer et al. 1988 7.0 to 8.9 3.5 to 7.5 Canadian Residential (6) Forced and Ambient Vibration Bouwkamp et al. 1994 1.2 to 5.1 comm'l/industrial (plywood roof diaphragm and concrete/masonry walls) One- and two-story Frenette et al. 1996 3.0 Moment resisting frame Two storey Forced Vibration Ellis and Bougard 1996 2.0 to 4.84 2.44 to 3.30 Great Britain Construction Method Six Story Forced and Free Vibration All (Range of Values) 0.80 to 18 0.15 to 24 43 Chapter II - Current Knowledge and Previous Research 2.3. Related Analytical Approaches The currently available analytical models are mostly for static analysis only. Most of the models are also limited to buildings with shear walls and rigid diaphragms. Several researchers like Foschi (1977), Itani and Cheung (1983), Dolan (1989) and Filiatrault (1990), recognized the non-linear behaviour of the fasteners and tried to reduce the problem size by condensation of the fastener elements into one element. Others, such as McCutcheon (1985), used a simple energy approach to find the response of shear walls. Schmidt and Moody (1989) and Yoon and Gupta (1991) extended these static models for three-dimensional analysis of wood structures by assuming rigid floors and connections. Some others, like Kasal (1992), demonstrated the effect of inter-component connections as an important factor. Only limited attempts to perform dynamic analyses on light-frame timber structures have been cited in the literature. Some investigators used a single degree-of-freedom model to obtain the response of a wall. These models are simple but limited to a certain configuration like the work of Stewart, Dean and Carr (1987). Dolan (1989) and Filiatrault 1990 tried to develop a general dynamic model of shear walls by considering the hysteretic behaviour of the fasteners. Good agreement between experimental and analytical results was achieved. Tarabia and Itani (1997) and Ming and Lam (2000) introduced 3D dynamic analytical models for the analysis of light-frame wood buildings and investigated the effect of the structural configurations on the 44 Chapter II - Current Knowledge and Previous Research seismic response of these buildings. This approach seemed to be successful in matching the experimental and analytical results. 2.4. Summary of Findings To investigate the natural frequency of timber structures it is important to understand the hysteretic approximation for this type of structures. Since the stiffness is an essential value for the natural frequency calculation, the hysteretic behaviour can explain to a certain limit the difference in result obtained from the Ambient Vibration Testing Method and Forced Vibration Testing Method. The simplest approximation is to assume that the element is perfectly elastic and sustains no damage. Non-Linear behaviour of structural elements is frequently approximated by the ideal elastoplastic response of timber structures. This response is well established as an approximation to the hysteresis loops produced by concrete and steel structures and is the basis of the world's seismic design codes. But this simplification and approximation is not sufficient to correctly model the load-displacement relationship. However, the elastoplastic approximation is inappropriate for timber elements because there is no facility for modeling pinching of the hysteresis loops. It is observed that a linear elastic model comprising of a mass oscillating between to springs could be used to approximate pinched hysteresis loops of single 45 Chapter II - Current Knowledge and Previous Research degree-of-freedom (SDOF) structures at large displacements. This was developed using the assumption that the first major ground movement during the earthquake would cause the element to yield and slacken but did not account for the residual load at zero displacement observed in test records (Dean et al. 1986). Steward (1987) proposed a hysteretic model incorporating the pinching effect observed in timber elements. This model uses a set of rules to define a tri-linear envelope of the load-displacement response and pinching during repeated loading. Steward's model was developed for plywood shear walls but also represents other structural elements. Dean (1994) proposed a hysteretic model comprising of a rigid bar with a number of nominally bi-linear elastoplastic springs attached to it. This model generates a realistic load-displacement response for timber elements, complete with smooth stiffness transitions. The characteristic of this loop can be modified by altering the characteristics of the springs, with a specified portions of the springs allowed to develop slackness as they are cycled. The model accurately reproduces the behaviour of a range of structural systems but is difficult to match to hysteresis loops, requiring adjustment often generating parameters. Foschi (2000) introduced a similar model with multifaceted behaviour and characteristics. The approach considers the connector as an elasto-plastic beam 46 Chapter II - Current Knowledge and Previous Research in a non-linear medium, which only acts in compression, permitting the formation of gaps between the beam and the medium. The model automatically adapts to any input history, either for force and displacement, and develops pinching as gap is formed. The above-described modelling schemes illustrate the difference between the results from the ambient and forced vibration testing method. Since the ambient vibration testing method does not introduce any extensive artificial forces or displacements to the specimen the obtained frequencies are based on the initial stiffness of the timber structure. Conversely, the forced vibration testing method applies larger displacements than ambient vibration testing method to the structure, which causes the system to adjust to a different stiffness on the hysteresis loop (non-linear behaviour). As a result the decrease of stiffness will shift the natural frequency of the woodframe building to lower values. Several other factors such as slackness, which is generally generated by the existing nailing gaps and decrease in friction force of nailing connections can cause the frequency to shift to lower values in stronger input motions. 47 Chapter 3 Review of Structural Dynamic Testing Concepts and Methods An overview on the theoretical background and the testing methodologies applied in this research for determining the natural frequency of the full-scale woodframe building is presented in this chapter. 3.1. Relevant Concepts in Structural Dynamics In this section, the basic concepts of the time and frequency domain analysis will be reviewed. This information, which is mainly obtained from the dissertation of Felber 1993 and Andersen 1997, will be required to understand basic dynamic testing methods described later. In addition joint time-frequency response analysis will be reviewed. 3.1.1. Review on Time Domain and Frequency Domain Analyses To explain the time domain analysis, the single degree of freedom system (SDOF) is used. The SDOF consists of a mass m, a spring k and a viscous damper c. The equilibrium equation for this system which is subjected to the force P(t) can be written as follow: mx + cx + k-x = P(t) (3.1) 48 Chapter III - Review of Structural Dynamic Testing Concepts and Methods The displacement x(t) of this system can be calculated using the Duhamel integral shown in Eq. (3.2). where h(t) is the impulse response function of the SDOF system and is expressed as: in which £is known as the critical damping ratio, a>n is the undamped natural frequency of the system and cod = ^ co] -£2 . Eq. (3.2) represents the convolution of the forcing function P(t) and the impulse response function h(t) divided by the mass m. Eq. (3.1) is transferred into the frequency domain using Fourier transforms to avoid dealing with convolution in the time domain. Since convolution in the time domain is equivalent to multiplication in the frequency domain, the following equation can be obtained: X(a) = H((o) • P((a) (3.4) (3.2) h{t) = sin{cod • t) (3.3) 49 Chapter III - Review of Structural Dynamic Testing Concepts and Methods co is the circular frequency in radians per second. X(co) is the Fourier transform of the displacement x(t). P(a>) is the Fourier transform of the excitation force p(t). The frequency response function (FRF), H(CD), is the Fourier transform of the impulse response function h(t), divided by the mass m. The FRF H(co) can be obtained from Eq. (3.2). If k, m and c are known, H(co) can be evaluated analytically to give a function based on this parameters. Therefore the inverse can be utilized, where the system's stiffness, mass and damping can be identified by measuring H(a>) (Felber 1993). When doing forced and free vibration testing the input force is known, therefore the above-mentioned concepts are typically used for the analyses. On the other hand ambient vibration analysis differs slightly with the applied conception. Unlike forced vibration testing, the force applied to a structure in ambient vibration testing is not controlled. The structure is assumed to be excited by wind, traffic and human activity and is assumed to be subjected to white noise excitation. The measurements, in our case accelerations, are taken for a long duration to ensure that all the modes of interest are sufficiently excited. Measurements are taken at predetermined locations, which will capture the desired degrees of freedom of the structure. The ambient vibration at any location of a structure can be measured as displacement x(t), velocity x(t), or acceleration x(t). The displacement of the structure can then be expressed as a 50 Chapter III - Review of Structural Dynamic Testing Concepts and Methods linear combination of the mode shapes. In expanded form this equation looks like: MO) = to }y, (0+{cp2 )y2 {<P„ )yn (0 (3.5) For convenient manipulation, this equation can be transferred into frequency domain: {X(co)} = fatff©) + {<P2}Y2(CD) + ... + {<pN}Yn(co) (3.6) where the normalized coordinates are defined as Y^co) are defined as: XJ(co) = HJ(co)-PJ((0) (3.7) Using the fact that X(co) = co1 -X(co), the accelerations of the structure can be expressed in the frequency domain as: {X(a>)} = «2[toJ^1(«)-P1(«) + to2}//2(«)-P2(«) + ... + to„}//n(^)-P„(6>)] (3.8) An individual complex valued acceleration response X^co) can be expressed as: {X(a>)} = co\AXiHx (co) + A2lH2(co) +...+ AniHn(co) • P„(<D)] (3.9) where Ajt =<pJi • P^co). 51 Chapter III - Review of Structural Dynamic Testing Concepts and Methods This indicates that the natural frequencies of a structure can be estimated using the Fourier transform of ambient vibration acceleration records. The acceleration response at the natural frequencies can be estimated using the following: If two acceleration records obtained simultaneously at location a and b are used, one can estimate the modal amplitude ratio of the j t h mode from the two locations using: Then the mode shapes can be determined experimentally using the ratios of the Fourier amplitudes at natural frequencies. However, it is important to keep in mind that this estimate can only be made if the natural frequencies are well separated and lightly damped such that the response at a natural frequency is indeed dominated by the corresponding mode shape (Felber 1993). Also, the modal decomposition of a discrete time system is applied in this study and it is important to present it. This part shows how to modally decompose a p -Xl(<oJ) = <pjra>2HjX<»J)'PJ(a>J) (3.8) XgiPj) „ <Pja •o)2Hj(a)J)-Pj(6)j) = <pJa Xb (<Dj) ~ (pJh • 0)2Hj(co]) • P} (o)j) <pJb (3.8) 52 Chapter III - Review of Structural Dynamic Testing Concepts and Methods variate linear and time - invariant discrete-time system1. This analysis concerns only the free vibration of the system and can be described as follow: x(tk+l) = Ax(tk) (3.9) y(tk) = Cx(tk) (3.10) where matrices A and C describes the structural system and fo is the discrete time sequence. The state vector xffo) and the output vector y(tk) are mx1 and px1 dimensional respectively. The solution of the system is as follow: y(tk) = wk (3.11) where y/ is an mx1 dimensional complex vector and ju is a complex constant. From Eq. (3.11) and Eqs. (3.9 and 3.10) the following will result: ypk* = Ay/ft (3.12) y(tk) = C¥Iuk (3.13) to show that Eq. (3.11) is the only solution then y/ has to be the only solution to the first order eigenvalue problem given below: 1 For information on time discrete systems refer to "Signal and System" Oppenheim and Willsky. 53 Chapter III - Review of Structural Dynamic Testing Concepts and Methods (Ifi-A)i// = 0 (3.14) Eq. (3.14) has non-trivial solutions if the following characteristic polynomial is satisfied: det(Ifi-A) = 0 (3.15) This real-valued polynomial is of mth order. Thus, there will be m roots jUj that are the eigenvalues of A. For each of these eigenvalues there is a non-trivial solution vector y/j which is the corresponding eigenvector. The mode shape 0 ; , which is the apparent part of the eigenvector, is obtained from the observed Eqs. (3.12 and 3.13) as follow: Oj=Cyj, j=1,2,...,m (3.16) By assembling all m eigenvectors, the complex modal matrix T will result in the following: ¥ = [ W 2 . . . ! P J (3.17) where the mxm diagonal matrix n, which contains the m eigenvalues will be: ^"'^ =ju, ju = diag{juJ}J=1,2,...,m (3.18) 54 Chapter III - Review of Structural Dynamic Testing Concepts and Methods by rearranging Eq. (3.18) the modal decomposition of A is defined as follows: A = W JLW'1 (3.19) If the state dimension m divided by the number of output p equals the integral values n and the system is observable, then it is possible to introduce the free vibrations of Eq. (3.9 and 3.10) by an nth order p - variate auto-regressive matrix polynomial as follow: 0 = CA" + AtCA"-] + A2CA"-2 +... + An_xCA + AnC (3.20) from Eq. (3.19) and Eq. (3.20) the following will result: 0 = O F / Z T " 1 + AiCVju"-^-1 + A2C¥ n"-2vi>-' +... + An_xOV^V'' + AnC (3.21) which can be re-written in the following form: 0 = 0¥/u" + 40P//"-' + A20¥ju"-2 +... + An_,CVfi + AnO¥ (3.22) The last equation can be decomposed into m separate relations. Each of these is as follows: 0 - O X + ACVj^r + ACVjUr2 + - + 4,-CVJMJ + AJCYj (3-23) 55 Chapter III - Review of Structural Dynamic Testing Concepts and Methods or 0 = ( / W " + AJU/-1 + A2Mj-2 +... + + An)CWj (3.24) or 0 = (Iy,jMj" + A^;-' + AlM;-< +... + An_xMj + A,)*, , j=1,2,...,m (3.25) while is the eigenvalue problem of the n t h order, for the auto-regressive matrix polynomial, where jUj is the eigenvalue and the mode shape 0 ; the solution vector. To obtain the modal parameter the following transition matrix is given: A = eFT (3.26) where F is the constant intensity matrix (F = vVAx¥~i) and T is a constant sampling interval. To simplify the notation, the complex modal matrix associated with A, is defined as X ¥ A . The following can then be written: VA0>;x=e™*T (3.27) or ^ / / F / 1 = Vexl (3.28) From Eq. (3.28) it is seen that the complex modal matrices ¥ A and ^ a r e equivalent, except for some arbitrary scaling. Since the observation matrix of the 56 Chapter III - Review of Structural Dynamic Testing Concepts and Methods discrete-time system is equal to the observation matrix of the combined continuous - time system and since the mode shapes can be attained as follows: [0,<D2...<DJ = OP (3.29) it also follows, that the mode shapes of the discrete - time system are equivalent to the mode shapes of the continuous - time system, except for an arbitrary scaling factor. Finally, from Eq. (3.28) it is seen that the m eigenvalues of the two systems are related as: Mj•=ex'1 , j=1,2,...,m (3.30) If it is assumed that the system is an under-damped physical system and that the modal frequency is characterized by the angular eigenfrequency a>j or the natural eigenfrequency fj, whereas the modal damping is characterized by the damping ratio ^ , these parameters will be defined as follows: log( u,) AJ=^^J=1,3,..,2s-1 (3.31) a>j = Xj ,j=1,3,..,2s-1 (3.32) 57 Chapter III - Review of Structural Dynamic Testing Concepts and Methods /y=i^,y=ff3,..f2s-f (3.33) Re(AY) A, ,j=1,3,..,2s-1 (3.34) where log is the natural logarithm and s is assumed to be the complex conjugated pairs of eigenvalues which have been identified as the eigenvalues of s under-damped physical modes, among all m eigenvalues (Andersen 1997). For further detail on the above-mentioned method, the reader is referred to the dissertation of Andersen 1997. A brief overview of joint time-frequency domain analysis is presented here. Joint time-frequency analysis involves the analysis of a signal in both time and frequency domain simultaneously. There are two basic approaches to analysis in the joint time-frequency domain. The first approach is to initially cut the signal into slices in time and examine the frequency content. The second approach involves the filtering of discrete time frequency bands, which are in turn, slice into discrete time bands and analyzed for their energy content. The first describes the Short Time Fourier Transform (STFT) and Cohen's Class function, while the latter of the two approaches describes the Wavelet Transform method of analysis. Since Short Time Fourier Transform (STFT) is applied in this study the focus will be on this method. 58 Chapter III - Review of Structural Dynamic Testing Concepts and Methods In using the Short Time Fourier Transform (STFT), the analysis focuses on the signal at a desired time t and suppresses it at all other times. This is accomplished by multiplying the time signal s(t) by a window function w(t), centred at time t. The window function is chosen to leave the signal unaltered at time f and near zero at distant time. The choice depends on the nature or the data and the desired results. To avoid side-lobes2, the Hanning window was chosen for the analysis in this thesis (Black 1998). If the time domain window size is taken to be small, the frequency band of the resulting spectrum will be large and hence is called a wide band spectrum. Conversely, if the window size is taken to a large in time domain, the resulting frequency spectrum is denoted a narrow band spectrum. The STFT of the windowed signal st(r) is given by s, (r) = S{T)W{T -1) and represent the distribution of frequency around time f. Let st(a>) be the STFT of the signal st(r), then (3.35) where w(t) is: (3.36) For further information on side-lobes see Proakis and Manolakis, 1996 59 Chapter III - Review of Structural Dynamic Testing Concepts and Methods The energy density spectrum P(t,a>), or spectrogram, is defined as (Cohen, 1995): in where || is the absolute value of the expression. To obtain the density of one variable in a joint density described by two variables, the other variable is integrated out. The resulting density is known as the marginal density or marginal. The summation of the energy distribution for all frequencies, at a particular time in signal should give you the instantaneous energy, and conversely, the summation over all times, at a particular frequency, should give the energy density spectrum. Therefore, ideally, a joint time-frequency spectrogram should satisfy (Black 1998): i. the instantaneous energy (3.37) (3.38) ii. the energy density spectrum (3.39) 60 Chapter III - Review of Structural Dynamic Testing Concepts and Methods which are referred to as the time and frequency marginal conditions (Cohen, 1995). If the modal characteristics of a structure are thought to be time variant a joint time-frequency analyses can be useful in improving the understanding of the structure's behaviour. These techniques are used to investigate the "softening" phenomena observed during heavy shaking and for the detection of damage during a seismic event. Softening refers to the reduction in stiffness sometimes observed during periods of heavy shaking. Taking the ratio of the output time-frequency spectrogram to the input time-frequency spectrogram approximates a Time-Frequency Response Function (TFRF). The signal used for the input is the recorded acceleration time history at the base of the structure and the output signal is taken to be the acceleration time history at the roof of the structure. As described before the time frequency spectrum is obtained from Eq. (3.37). According to Black (1998), if P(t,co)jn represents the time-frequency spectrogram of the input and P(t,co)out the output time-frequency spectrogram, the TFRF is given by: TFRF\co, t) = (3.40) 61 Chapter III - Review of Structural Dynamic Testing Concepts and Methods The TFRF can be used in much the same way as the Frequency Response Function (FRF) to estimate natural frequency with one exception. To obtain a time-frequency distribution, the STFT of the signal must be squared and thus the phase information is lost. This has the effect of limiting the analysis to estimate natural frequencies from peaks in the TFRFs. For further information on this topic the reader is referred to Cohen 1995 and Black 1998. Equation 3.40 was used in this thesis to perform the time-frequency analysis of the recorded motions of the tested specimens. 3.1.2. Analysis Tools To perform the above-mentioned analyses, customized application using two commercial software programs were developed. The commercial software program ARTeMIS® Extractor Version 2.0 (Structural Vibration Solution ApS), was used for the analysis of ambient response testing and modal identification is. Program, MathCAD® Version 2001 Professional (User's Guide with Reference Manual MathSoft Engineering and Education, Inc., 2001), which provided the mathematical environment with digital signal processing applications, was used to write programs and subroutines for the response analyses. Following is a description of the performed analyses within the environment of these commercial packages. 62 Chapter III - Review of Structural Dynamic Testing Concepts and Methods 3.1.2.1. Analysis performed with MathCAD The commercial package MathCAD® has not only significant mathematical solving abilities but also excellent presentation tools to demonstrate the results of numerical analyses. The software includes digital signal processing subroutines, which perform different signal conditionings and filtering. The frequency response function (FRF) was programmed with the help of the available fast Fourier transform (FFT) subroutine and a normalized spectrum for the sine sweep was created. The prepared MathCAD® reports are mostly written for the forced vibration testing. These reports include sinusoidal sweep test and forced vibration test from actual ground motion records. 3.1.2.2. Analysis performed with ARTeMIS® The ARTeMIS® Extractor is an effective tool for modal identification of civil engineering structures such as buildings, bridges, dams and offshore structures. The software allows accurately estimating of natural frequencies of vibration and associated mode shapes and modal damping of a structure from measured responses. The program performs time and frequency domain analyses such as fast Frequency Domain Decomposition (FDD) and Stochastic Subspace Iteration (SSI). Additionally, the matrix between mode shapes obtained from different techniques can be compared by computation of the Modal Assurance Criterion 6 3 Chapter III - Review of Structural Dynamic Testing Concepts and Methods (MAC) option in the program. This was performed for the test data in this project and the results will be shown in detail in the following chapters. 3.2. Applied Dynamic Testing Methods In the past, many research projects dealt exclusively with the deformational characteristics of the building such as stiffness, strength and ductility. To obtain these characteristics, testing methods such as quasi-static testing, pseudo-dynamic testing etc. are sufficient. To obtain the parameters related to the dynamic characteristics of a building, such as the vibrational modes, however, natural frequencies and damping different testing methods and protocols such as dynamic testing methods have to be used. In other words, to capture and collect the realistic dynamic behaviour of a full-scale structure or sub-assembly, several different dynamic testing methods could be used such as ambient, free, forced vibration testing methods etc. Shake table testing, ambient vibration testing and forced vibration testing are dynamic testing methods that have been used for different applications in this study. A detailed explanation of each method is given below. 3.2.1. Shake Table Testing Shake table testing, in terms of loading protocol, most closely resembles the real conditions during an earthquake. A scaled or full-scale model is typically 64 Chapter III - Review of Structural Dynamic Testing Concepts and Methods simplified to a certain degree to ease the testing process. The testing specimen is fixed to the table, which is shaken with a recorded or simulated earthquake motion record. By installing acceleration, displacement and load instrumentation, the important dynamic characteristics of the model can be obtained. To avoid the adverse influence of scaling due to the nonlinear characteristics of the model, shake table specimens should be built as close to full-scale size as possible. The motion of the table in this testing method can be uni-axial, bi-axial ortri-axial, depending on the design of the table. The motion of the shake table can be controlled on the basis of its acceleration, velocity or displacement to achieve the same earthquake motion record, which is selected as an input record for the shake table. Like other methods, this method has its advantages and disadvantages. The advantage of shake table testing is the very realistic approach to simulate an actual motion, and accordingly the results are the closest to reality. Since the loading base or shake table is moved in real time according to the displacement data of an actual recorded or simulated earthquake motion, the generated dynamic response of the structure is more reliable. For reduced-scale systems, some adjustments to the specimen mass and the frequency content of the input record may be necessary. Also the distributed inertia forces can be reproduced correctly and the failure modes linked with three-dimensional response can be observed. In contrast, a few disadvantages of this method are the restraints in shake table size, displacement range and load capacity of the actuators. The 65 Chapter III - Review of Structural Dynamic Testing Concepts and Methods expenses for this sort of test are relatively high, and more expertise and experience is required to interpret the test results. For example, the actual forces involved in this type of test can often only be calculated via the measured acceleration. The understanding of the behavior in terms of forces and displacements and their correlation with the progress of the damage is much more difficult for shake table tests compared to quasi-static test methods. Figure 3.1 shows one of the full-scale shake table tests, conducted at the University of British Columbia. 3.2.2. Ambient Vibrations Testing Another method to define the dynamic characteristic of a structure as far as the natural frequencies and mode shapes are concerned, is ambient vibration testing. As indicated by the term "ambient vibrations", this method uses the excitation from micro vibrations of the surrounding environment on the structure to study its dynamic characteristics. Through very sensitive instrumentation the low amplitude vibration is captured and processed with different analysis tools to extract the frequency content of the structure. Since the data is derived from very small vibrations that are not comparable to realistic earthquake motions, no accurate information on the damping and deformational characteristics of the structure can be obtained. 66 Chapter III - Review of Structural Dynamic Testing Concepts and Methods One of the advantages of this testing method is the fact that it is non destructive and the normal operation of the building is not interrupted. The testing is relatively inexpensive, the preliminarily results are available shortly after each test run and the testing can easily be performed on different sizes and types of structures. The main disadvantage of this testing method is the limited applicability of the results because of the low vibration levels. Several researchers have found that the results from ambient vibration test methods do not correspond very well with forced vibration testing methods in woodframe buildings. Typically, the natural frequency results from forced vibration testing method are lower than results obtained from ambient vibration testing method for woodframe buildings. This can be attributed to factors such as friction in connections, as well as non-linearity and slackness behaviour of woodframe buildings (Dean et al 1986). These factors are not captured with the low level vibrations in ambient vibration testing method. 67 Chapter III - Review of Structural Dynamic Testing Concepts and Methods Fig. 3.1 Shake table test of Earthquake 99 Woodframe House project at University of British Columbia (courtesy Dr. H. Prion) Another method to perform ambient vibration measurements is with laser measurements. The advantage of laser instrumentation is that the measurements can be made remotely, and no equipment needs to be placed on the structure. This is useful for taking measurements during construction or during an experiment that may result in collapse and may cause damage to equipment. 68 Chapter III - Review of Structural Dynamic Testing Concepts and Methods 3.2.3. Forced Vibration Testing Another common testing method is with forced vibrations. In this test the structure is shaken either on the shake table or by a strong vibrator from outside or inside to achieve a considerable amount of movement. This method is not meant to be destructive and is only used to define the dynamic behaviour of the structure. The input motion, which is usually a sinusoidal sweep with determined gradually varying frequency content, is introduced to the structure. In this testing method the structure will experience resonance when the input motion corresponds to the natural frequencies. This can be performed by placing the specimen on the shake table and vibrating with a sinusoidal waveform with increasing frequency starting from close to zero Hertz to a maximum upper-limit, which is depended to the test objectives. In full-scale woodframe house testing where the specimen cannot be placed on the shake table, the sinusoidal sweep can be performed with a mechanical vibrator. The vibrator, which is attached to the structure, vibrates the structure with the desired sine waves. The advantage of this method is that preliminarily results are shortly available shortly after testing. Because of the high level of shaking often experienced at resonance, some damage might occur in the structure, which is a disadvantage of this method. To attach the shaker to the building, it needs to be fastened to the floor or to the frame, which might cause some damage to the woodframe house. The relative expensive costs of forced vibration testing is another disadvantage. 69 Chapter 4 Experimental Study In connection with the Earthquake 99 Woodframe House project several uni-axial shake table tests were conducted at the University of British Columbia. These test were carried out on one-storey subsystems and two-storey light-frame full-scale timber structures. Some of the results of these dynamic tests were used in this research. In addition to the shake table tests, field tests on three actual timber structures were performed from December 2000 to January 2001. These tests are explained in detail in this chapter. 4 .1. Description of the Earthquake 99 Woodframe House Project The Earthquake 99 Woodframe House project had the objective of investigating the performance of the existing housing stock in the Lower Mainland of British Columbia and developing procedures for improvement and retrofit. The testing program consisted of three phases. Phase 1: Quasi-static and dynamic tests conducted on a number of 2.45 x 2.45m (8 x 8 ft) walls with different sheathing configurations (Completed 1999). Phase 2: Shake table testing of a single storey subsystem with different sheathing configurations (Completed 2000). 70 Chapter IV - Experimental Study Phase 3: Shake table testing of a two-storey house with different sheathing configurations. In addition to the above-mentioned testing phases, a pushover test was performed on the two-storey house with stucco and OSB sheathing configurations. The research of this thesis focuses on phase 2 and 3 with an emphasis on determining the dynamic characteristics of the structures. Table 4.1 gives a list of the dynamic tests of phase 2 and 3 during summers of 2000 and 2001. Shake table tests on the two-storey woodframe building conducted during the summer of 2001 are not included in the analyses of this thesis. The earthquake input motion records for the shake table tests were carefully chosen to represent possible events in south-west British Columbia and to have a frequency content that would sufficiently excite the test specimens. The most suitable earthquakes were the 1985 Northwest Territories earthquake motion recorded at Nahanni, the 1994 Northridge, California earthquake motion recorded at Sherman Oaks and Canoga Park, the 1992 Landers, California earthquake recorded at the Joshua Tree Fire Station, the 1995 Kobe, Japan earthquake recorded at Meteorological Research Institute (J.M.A.) and others. Table 4.2 lists the applied earthquake motion records for the project and their properties. 71 Chapter IV - Experimental Study Table 4.1. The Earthquake 99 House project tests schedule Test # Run # Date Conducted earthquake motion record Description of the tested house 1 1 31/3/2000 Sherman Oaks Subsystem woodframe building with OSB wall system and stucco (Engineered). 2 Canoga Park 2 1 4/4/2000 Sherman Oaks Subsystem woodframe building with OSB wall system without stucco (Engineered). 2 Canoga Park 3 1 26/4/2000 Sherman Oaks Subsystem woodframe building with Simpson Strong wall system with stucco (Engineered) 2 Canoga Park 4 1 2/5/2000 Sherman Oaks Subsystem woodframe building with Simpson Strong wall system without stucco (Engineered). 2 Canoga Park 5 1 5/5/2000 Nahanni Subsystem woodframe building with horizontal board sheathing (BC) system without stucco and hold-downs (Non-Engineered). 2 Nahanni 6 1 10/5/2000 Nahanni Subsystem woodframe building with horizontal board sheathing (BC) system without stucco and hold-downs, roof blocking and gypsum board on the center wall. (Non-Engineered) 2 Nahanni 7 1 26/6/2000 UCSD Canoga Park Two Storey woodframe building with Simpson Strong wall system with stucco (Engineered). 8 1 13/7/2000 UCSD Canoga Park Two Storey woodframe building with Simpson Strong wall system without stucco (Engineered). 2 UCSD Canoga Park 9 1 28/7/2000 Sherman Oaks Two Storey woodframe building with OSB panel wall system without stucco (Engineered). 2 Sherman Oaks Two Storey woodframe building with OSB panel wall system without stucco and gypsum wallboards detached from the center walls (Engineered). 10 1 13/6/2001 Nahanni Two Storey woodframe building with OSB panel wall system, hold-downs and stucco. (Engineered) 2 Landers 3 Kobe 11 1 29/6/2001 Nahanni Two Storey woodframe building with OSB panel wall system, rain screen and stucco. (Engineered) 2 Landers 3 Landers 4 Kobe 12 1 17/7/2001 Landers Two Storey woodframe building with OSB panel wall system and without stucco, hold-downs and roof blocking (Non-Engineered). 2 Kobe 13 1 27/7/2001 Kobe Two Storey woodframe building with horizontal board sheathing wall system and without stucco, hold-downs and roof blocking (Non-Engineered). 14 1 3/8/2001 Landers Two Storey woodframe building with OSB panel wall system and without stucco. (Engineered) 2 Kobe 15 1 29/8/2001 Llayllay Two Storey woodframe building with OSB panel wall system and without stucco. (Engineered) 16 1 12/9/2001 Llayllay Two Storey woodframe building with OSB panel wall system and without stucco, hold-downs and roof blocking (Non-Engineered). 72 Chapter IV - Experimental Study Also included in this chapter are the shake table testing procedures, descriptions of the tested subsystems, the two-storey woodframe buildings, and the testing facility for the shake table tests. Part of the project was financed by private companies and the test results are thus of a proprietary nature, which is the reason that only tests 5, 6 and 9 are presented in this thesis. Table 4.2. Applied earthquake records for Earthquake 99 House project Name of the Earthquake record Station Maximum Absolute Peak Values Type Displacement (cm) Velocity (cm/sec) Acceleration (cm2/sec) Nahanni 85 Nahanni 11.70 33.44 315.9 Crustal Northridge 94 Sherman Oaks 13.13 54.90 437.14 Crustal Northridge 94 Canoga Park 12.40 59.84 380.98 Crustal Northridge 94 UCSD modified Canoga Park 14.13 43.90 372.30 Crustal Kobe 95 JMA 19.95 74.32 587.14 Crustal Landers 92 Joshua Tree 15.73 42.71 278.38 Crustal Chile 85 Llayllay 8.40 41.79 345.47 Sub-duction 4.1.1. Procedure and Methods of Shake Table Tests The subsystem and two-storey house specimens were tested with different methods. The testing sequence for the house test consisted of ambient vibration testing, sinusoidal sweep testing, real earthquake motion simulation, sinusoidal sweep and ambient vibration test. The ambient vibration and sinusoidal sweep test were carried out for identification of the natural frequencies of the house. These two were performed before and after each earthquake motion record simulation to identify the frequency change of the structure. This information 73 Chapter IV - Experimental Study helps to evaluate the degradation of the structural stiffness throughout and after earthquake motion tests. From the data collected the natural frequencies and corresponding mode shapes were obtained. The sinusoidal sweep tests were conducted by shaking the specimen for 6 minutes with a sinusoidal wave peak displacement corresponding to 1% of the maximum stroke of the actuator, which is 4.6 mm peak displacement. The shaking frequency was gradually increased from 0.01 to 22Hz in 360 sec. In recording the shake table data no anti-alias analog filter was used and all the data was recorded at a rate of 200 samples per second. The ambient vibration testing was conducted in the UBC Structures Laboratory with insignificant surrounding vibration. The laboratory was quiet and no other activities were allowed throughout the testing. 4.1.2. Description of the Single Storey Subsystem The specimen for tests 5 and 6 was modeled as a subsystem to simulate the first storey of a two-storey timber structure. The single storey subsystem was designed and constructed by TBG Seismic Consultants Ltd. The test specimen was intended to simulate the bottom storey of a two-storey timber house. The mass of the second storey was simulated by an equivalent mass provided by concrete blocks. The specimen was 2.4 m (8') high and had a footprint of 6.0 m (19' 8") wide and 7.52m (24' 8") long (Fig. 4.1). The gravitational load bearing 74 Chapter IV - Experimental Study system consisted of 38 x 89 mm (2" by 4") woodframe construction. The roof system consisted of 38 x 235 mm (2" by 10") joists oriented in the west east direction, perpendicular to the shake direction. These were supported by 38 x 235 mm (2" by 10") rim joists. The joists overlapped in the middle where they were supported on the centre wall. The lateral force resisting system consisted of 20 x 305 mm (1" by 12") board sheathing nailed to the studs. Each board sheath was nailed to the studs with two nails at each stud. The equivalent live and dead load of the second floor was simulated by twelve concrete blocks fastened to the roof sheathing and to each other by steel rods. Each block weighed approximately 14.7 kN (3300 Ib). Window openings were constructed in the east and west walls. The shake table frame constituted the base for the structure. Structural drawings of the sub-system woodframe are provided in Appendix A. In test 5, all internal wall surfaces were covered with gypsum board and the joists were blocked atop the centre wall with 38 x 235 mm (2" by 10") blocks. In test 6 the gypsum boards and the blocking were removed to observe their influence on the structural response of the woodframe house. 4.1.2.1. Input Records for the Subsystem The Nahanni 1985 earthquake motion record was used for tests 5 and 6. The sequence of testing was as follows: First, ambient vibration tests were done, followed by a sinusoidal sweep and the Nahanni displacement input. To estimate 75 Chapter IV - Experimental Study the degradation of the system, a second sinusoidal sweep was performed. To determine the performance of the system during an aftershock the earthquake was simulated again. This was once again followed by a sinusoidal sweep test, to measure the change in the natural frequency and stiffness of the system. To have a comparison for the ambient vibration and the sinusoidal sweep, a last ambient vibration test was performed. The acceleration, velocity and displacement time history and spectra of the earthquake record used in these tests are shown in Fig. 4.2. Fig. 4.1. Subsystem timber structure 76 Chapter IV- Experimental Study Spectral Acceleration (g) 40 20 £ • 0 > "20 a • 10 15 T i m e (s) 1 II f 1 fi I v i AIM Wr 10 15 T i m e (s) 20 25 2 T (sec) Spectral Velocity (cm/s) 1 2 3 T (sec) Spectral Displacement (cm) AA V 10 15 T i m e (s) 25 Fig. 4.2. Nahanni earthquake motion record, acceleration, velocity and displacement time history and spectra (5% damping) The input record, Nahanni earthquake, was provided to the shake table control system at a rate of 200 samples per second. This record has a maximum absolute displacement of 117 mm, maximum absolute velocity of 334.4 mm/sec and maximum absolute acceleration of 0.32 g. 77 Chapter IV - Experimental Study 4.1.3. Description of the Two Storey System The two-storey timber structure was designed and constructed in a similar way as the single storey subsystem. The test specimen represented a two-storey timber house, complete with roof. The first and second storeys were each 2.4 m (8') high with a 0.6m (2') high roof truss at the top. In plan view the model was the same as the one-storey specimen. The construction was similar to the previous specimens, except that in this case thirteen trusses carried the roof weight. The lateral load resisting system in the two-storey configuration consisted of sections of OSB sheathed stud walls (Fig. 4.3). Concrete bricks attached to the floor of the upper floor simulated the equivalent live load. For convenience and speed of construction of the house model the roof load was represented with bricks on the roof. Large openings were constructed in the east and west walls to provide room for windows and doors. Access to the second floor from the first floor was provided by a common stairway (Fig. 4.4). Structural drawings of the two-storey woodframe are provided in Appendix A. In test 9, the interior wall surfaces were covered by gypsum board and joist blocking was provided atop the centre wall as before. In the second test on this specimen, for test 9 run 2, the gypsum boards were disconnected from the studs to determine the effect of dry-walling. 78 Chapter IV - Experimental Study Fig. 4.3. East elevation view of the two-storey timber structure 4.1.3.1. Input Records for the Two Storey Test The Sherman Oaks record was used for the tests on the two-storey specimen. As for the one storey specimen, ambient vibration tests were conducted first, followed by a sinusoidal sweep and the Sherman Oaks earthquake simulation. To estimate the degradation of the system, a second sinusoidal sweep was performed. To investigate the response of the system during an aftershock, a second test was conducted with the Sherman Oaks record. The input record was 79 Chapter IV - Experimental Study provided for the shake table control system at the rate of 200 samples per second. This record has a maximum absolute displacement of 131 mm, maximum absolute velocity of 549 mm/sec and maximum absolute acceleration of 0.45 g. 25'-lY P L A N - MAIN F L O O R Fig. 4.4. Plan view of the main floor of the two-storey timber structure 80 Chapter IV - Experimental Study Following the earthquake simulation a second sinusoidal sweep was performed to measure the change in the natural frequency and stiffness of the system. To have a comparison for the ambient vibration and the sinusoidal sweep tests, a last ambient vibration test was performed. The acceleration, velocity and displacement time history and spectra of the earthquake record used in these tests are shown in Fig. 4.5. The entire test routine was repeated on the same specimen with the gypsum wallboard detached. -500 100 E 50 •3 0 20 30 40 Time (s) 20 30 Time (s) 30 Time (s) 40 15 S 0.5 < 1 JiiiJL 150 E 100 •5 50 > 60 1 \ fi u V V V ~ 20 3 u "S. 10 tn a Spectral Acceleration (g) 1 2 3 T (sec) Spectral Velocity (cnv's) 1 2 3 T (sec) Spectral Displacement (cm) 60 2 T (sec) A A — ^ /v V y \ / A r \ /r"^ [*J V Fig. 4.5. Northridge earthquake motion record, acceleration, velocity and displacement time history and spectra (5% damping) 81 Chapter IV - Experimental Study 4.1.3. Testing Facility The Department of Civil Engineering at the University of British Colombia possesses two shake tables. One of the shake tables, which was employed for the Earthquake 99 Woodframe House project tests, consists of a horizontal frame made of HSS 203 x 203 x 6.4 mm (8"x 8"x1/4") sections with HSS 127 x 127 x 9.5 mm (5"x5 x3/16") sections as diagonal braces. The usable load area of the shake table is 7.53 m (24' 81/2") long and 6.01 m (19' 81/2") wide. The shaking table has a maximum load capacity of approximately 310 kN (77 kips). It is supported on eight 152.5 mm (6") wheels, which move in the north-south direction on four steel guides. The drawings are available in Appendix B. The maximum shake table stroke is ±450 mm in the north-south direction. The maximum pushing force capacity of the actuator is about 260 kN and a maximum velocity about 450 mm/sec. The actuator, powered by a hydraulic pump, has a maximum loading capacity of 0.53m3/min @ 20 MPa but this capacity is not used at all times. The hydraulic pump is driven by a 200 Hp electrical motor, which requires 575 Volts, three phase electrical power. The electrical motor is capable of producing a maximum rotational velocity of 1800 rpm. The maximum capacity of the servo valve is 0.53m3/min but the average used is 0.35 m3/min. The shaking table is controlled by a signal generator, which sends an analog signal to the hydraulic jack and receives the feedback from a Linear Variable Differential Transformer (LVDT) attached to the actuator. The LVDT has a stroke range 920 82 Chapter IV - Experimental Study mm long. The shake table is controlled by the displacement feedback. The input command and feedback of the actuator is recorded to evaluate the performance of the shake table after each test. Four channels capture the displacement due to bending of the shake table in the vertical direction. Three accelerometers measure the acceleration in the N-S direction and one in the E-W direction. Two displacement transducers measure the displacement for the table in the N-S direction (Table 4.3). The clearance height of the structure laboratory is approximately 7 meters which allows the two-storey full-scale timber structure be mounted on the shake table. 4.1.4. Vibration Data Acquisition System Two vibration data acquisition systems were employed to record the forced vibration testing and only one to record the ambient vibration testing. Since the focus of the research is on the natural frequency of the houses, the characteristics of the sensors responsible for capturing the data for the ambient and forced vibration are represented here. The components of the vibration measurement hardware utilized are as follows (Ventura and Turek 2001): 83 Chapter IV - Experimental Study Table 4.3. Sensors installed for the shake table Instrument type Measurement Direction Location Displacement Transducer PT 101-0150-Cellesco Shake Table Horizontal Displacement North - South West side of the shake table East side of the shake table LVDT Transducer (Duncan Electronics 606) Shake Table Vertical Displacement Up - Down North - east corner of the shake table North - west corner of the shake table South - east corner of the shake table South - west corner of the shake table LVDT Sensor MTS LPRCVU03601 Shake Table Horizontal Displacement North - South Center of the shake table attached to the actuator Load Cell MTS-Model 661.22 Capacity 100 kips Introduced load from actuator to shake table horizontal Load North - South Center of the shake table attached to the actuator IC Sensor 3028 Accelerometer Shake Table Horizontal Acceleration North - South West side of the shake table East side of the shake table Center of the shake table IC Sensor 3028 Accelerometer Shake Table Horizontal Acceleration East - West West side of the shake table Sensors and Cables: Sensors convert the physical excitation into electrical signals. The current hardware measurement system has sensor connections capable of measuring up to sixteen plus thirty-two different signals from sixteen plus thirty-two different sensor locations or directions. Some of the sensors (force-balanced accelerometers, Kinemetrics, Model FBA-11) are capable of measuring accelerations of up to ±0.5g with a resolution of 0.2ug. Other sensors such as the EpiSensor (FBA ES-T) provide full-scale recording ranges of ±0.25 to 84 Chapter IV - Experimental Study ±4g (user selectable). A bandwidth of DC to 200 Hz allows the user to study motions at higher frequencies while maintaining the DC response that allows simple field calibration and reduces post-processing confusion. Four types of outputs can be field-selected by the user: ±2.5V single-ended output for use with traditional Kinemetrics earthquake recording instruments; ±10V single-ended or ±20V differential output for use with 24-bit digital recorders currently on the market. Key features of the EpiSensor include: low noise, dynamic range: 155 dB+, bandwidth: DC to 200 Hz. Full-scale range: user selectable ranges are ±0.25g, ±0.5g, ±1g, ±2g or ±4g. Outputs: user selectable ranges are ±2.5V single-ended, ±0V single-ended, ±5V differential, and ±20V differential. Linearity: less than 1000 ug/g2. Cross-axis: less than 1% (including misalignment). Thermal sensitivity: zero point <500ug/°C. Operating temperature: -20° to 70°C (0° to 160°F). For the tests conducted on the timber house 2 triaxial and 4 uni-axial EpiSensors with ±0.5g range setting and a resolution of 0.2|jg were employed in each test setup and case. Cables are used to transmit the electronic signals from sensors to the signal conditioner. Signal Conditioner: No signal conditioner unit is used for improving the quality of the signals. Data Acquisition: For data acquisition a Kinemetrics VSS3000 unit acquisition system was used. The VSS300 is fully portable and designed 85 Chapter IV - Experimental Study for ambient and forced-vibration field measurements. The system consists of a laptop computer, a 16-bit Analog-to-Digital Converter and an interface panel for connecting up to 16 transducers, all-in-one housing. The system provides programmable software gains and digital filters for all channels. Data acquisition is controlled by Windows-based software with extensive configuration, importation, analysis, graphing, and reporting capabilities. It features a graphical programing language that accommodates a wide variety of user requirements. Key Features: Connect up to 16 transducers; Software-programmable gain; Digital filters; Laptop-based system; Window-based software; Programmable gains of 1, 10, 100, and 1000; combination with AID gains; maximum voltage range: 0 to +10, ±5V; 16 bits resolution; software programmable gain of 1, 2, 4, 8; digital filters with low pass, high pass and bandpass filters; A/D speed of 100 kHz; sampling rate up to 1000 sps for all channels. For the sinusoidal sweep and ambient vibration tests conducted on the three timber houses considered in this study, each dataset was collected for 6 to 15 minutes respectively at a sampling rate of 2000 samples per second and decimated to 200 sps, for storage purposes. Data Acquisition Computer: Signals converted to digital form are stored on the hard disk of the data acquisition computer in ASCII form. The data can then be transferred to a data analysis computer where numerical analysis of measured data can be done independently of the data 86 Chapter IV - Experimental Study acquisition processes. In this way, preliminary on-site data analysis can be carried out concurrently with data acquisition. The accelerometers for the ambient vibration test were typically taken in the east-west and north-south direction of the structure. Figures 4.6 and 4.7 show typical accelerometer layout of the frames. The layout for both the subsystem and the two-storey house are indicated in Tables 4.4 and 4.5 respectively. 10 W 4 , 5 , 6 Fig. 4.6. Sensor layout for the subsystem timber structure 87 Chapter IV - Experimental Study Fig. 4.7. Sensor layout for the two-storey timber structure Table 4.4. Sensor layout for the sub-system Channel number Sensor Type Direction Location 1 FBA ES-T # 1 North-South Centre of the Shake Table 2 FBA ES-T # 2 East-West 3 FBA ES-T # 3 Up-Down 4 FBA ES-T # 4 North-South Laboratory floor close to actuator 5 FBA ES-T # 5 East-West 6 FBA ES-T # 6 Up-Down 7 FBA ES-T #7 North-South Roof Floor, West Wall 8 FBA ES-T # 8 North-South Roof Floor, South Wall 9 FBA ES-T # 9 East-West Roof Floor, East Wall 10 FBA ES-T #10 East-West Roof Floor, North Wall 88 Chapter IV - Experimental Study Table 4.5. Sensor layout for the two-storey woodframe house Channel number Sensor Type Direction Location 1 FBA II #1 North-South Roof Floor, West Wall 2 FBA II #2 East-West Roof Floor, South Wall 3 FBA II #3 North-South Roof Floor, East Wall 4 FBA II #4 East-West Roof Floor, North Wall 5 FBA II #5 East-West Second Floor, North Wall 6 FBA II #6 East-West Second Floor, South Wall 7 FBA ES-T # 7 North-South Second Floor, East Wall 8 FBA ES-T #8 North-South Second Floor, West Wall 9 FBA ES-T #9 North-South Shake Table, East Wall 10 FBA ES-T # 10 East-West Shake Table, North Wall 11 FBA ES-T # 1 North-South Shake Table, South-West Corner 12 FBA ES-T # 2 East-West 13 FBA ES-T # 3 Up-Down 14 FBA ES-T # 4 North-South Laboratory floor close to actuator 15 FBA ES-T # 5 East-West 16 FBA ES-T # 6 Up-Down 4.1.5. Vibration Analysis Software Programs Three different data acquisition packages were used to record the forced vibrations of the frame. These software packages are LabView™ Version VI (LabView™ Data Acquisition Basic Manual (VI), National Instrument, 1998), Earthquake Simulator Software® version 1.0 (User's Guide, Filiatrault, 1993) and 89 Chapter IV - Experimental Study DASYLab® Version 5.01.10 (DASYLab® User's Guide, lOtech, 1998), where only DASYLab® was used to record the ambient vibration of the frame. 4.2. Field Test of Full-Scale Light Frame Timber Structures As discussed in Chapter 2, some crucial information are needed to be gathered on the dynamic characteristics and behaviour of Canadian style light-frame low-rise woodframe buildings. To achieve this goal, additional tests were performed on existing timber structures. Before embarking on an extensive testing program, it was imperative to consider all the issues involving testing methods and building selection to assure a complete and useful data set. The following will discuss some of these issues such as testing methodology and other related parameters. 4.2.1. Building Selection for Test Purposes A number of different methods are available for performing the vibration tests. Although the Laboratories at the University of British Columbia have the facilities to conduct full scale shake table tests, this method is not always feasible for full-scale testing because of the associated cost and limitation on size and scope of different building configurations. The most suitable testing method for observing the dynamic behaviour of existing buildings are forced, free and ambient vibration testing. Besides the issue of expense, the most important point to consider is the suitability of the testing method to achieve the desired data. 90 Chapter IV - Experimental Study The ambient vibration method is by far the most convenient, cost effective and non-destructive testing method available to determine the fundamental period of structures. It has one definite disadvantage in that the vibrations created by ambient disturbances are very small and thus not quite comparable to the motion experienced in an earthquake. As mentioned in Chapter 2, the results obtained by different researchers by ambient testing method and forced vibration testing had a discrepancy of 0.5 to 2.5 Hz with the former yielding higher frequencies. Forced vibrations induced by a shaker would overcome the shortcoming of the ambient vibration method. The method is very intrusive, however, and a certain amount of damage to the building might occur where the shaker is attached to the floor. The same would be the case for a free vibration test, where a force needs to be introduced to the building to apply the initial displacement. With the possibility of doing both ambient and forced vibration tests on the Earthquake 99 Woodframe House project, the opportunity presented itself to correlate results from these two methods. This correlation was then applied to data sets where only ambient vibration tests could be done. Ambient vibration testing, in comparison with the forced vibration and free vibration testing methods, is very inexpensive, fast and least intrusive. Access to buildings for these tests is rather uncomplicated as compared to other methods. 91 Chapter IV - Experimental Study Therefore', despite the difference in results thus obtained, it is very efficient and practical for testing existing buildings. To obtain a representative sample of results from the entire housing stock, it was important to carefully select the building types to be tested. The most important issues related to building selection, which needed to be considered to interpret appropriate results for correlating the dynamic characteristics to the building property, are addressed as below. • The stiffness, ductility and dynamic behaviour of timber houses are strongly related to the structural construction configuration. Therefore construction configuration is one of the most important factors. The different configurations to be considered include platform frame construction (with panel and board sheathing), post and beam construction and post and beam construction combined with woodframe construction. • The structural dimension and footprint area are important in determining the relationship between the dynamic characteristics and the building geometry. The degree of symmetry of the building is another factor to be considered. 92 Chapter IV - Experimental Study • The structural age and overall condition are important to demonstrate the effect of aging and deterioration on the stiffness and natural frequency. (Sawako 2000) • The effective shear wall area is another important feature. Since the lateral resisting capacity of the structure depends on this feature, it can be defined as an important parameter in assessing the dynamic characteristics of a structure. These issues had to be considered before, through and after testing so that the collected data could be evaluated correctly. 4.2.2. Building Description In the process of restoring a group of timber structures in downtown Vancouver (Mole Hill) by City of Vancouver, three of these structures were accessed by the UBC earthquake engineering research group to conduct ambient vibration testing for defining the fundamental periods of those houses. The single-family timber structures were typical Victorian type of construction having three storeys having the longitudinal direction in the north-south direction (Fig. 4.7). They were built about eighty to ninety years ago. The typical structural system of these timber buildings is mainly post beam construction with a combination of stud walls sheathed by narrow boards. The lateral resisting system is basically board 93 Chapter IV - Experimental Study sheathing to the stud walls in the outside perimeter. The structure is constructed on top of concrete foundation perimeter walls. The attic is roofed with trusses mainly positioned in the north south direction. The gross footprint area of the tested structures was approximately from 355 m2 to 440 m2 for 3 floors and their basement. The total height of the buildings was 12.5 m (41') on average. The buildings were about 20m (66') long in the longitudinal direction and 9m (29') wide in the transverse direction. The height of each floor was in the range of 2.74 m to 3.05 m (9'to 10'). Fig. 4.7. North elevation of one of the timber houses tested in downtown Vancouver 94 Chapter IV - Experimental Study The floor deck consisted of joists with wooden deck sheathing. The first floor was connected through a stairwell to the second floor and to the artic. Large window opening were constructed mainly in the front side and backside of the building, which is the north and south view of the structure. Therefore the larger lateral resisting members were identified in the two east and west sides of the building. 4.2.3. Methodology and Testing Procedure The ambient vibration testing method was applied to capture the modal behavior of the buildings and to perform non-destructive vibration tests. The aim here was to capture the fundamental period of the structure. Two setups were selected for the sensor layout of the building. These setups covered all floors essentially by placing two sensors in the transverse direction and one in longitudinal direction, which can be used to identify the torsional modes (Fig. 4.8). 95 Chapter IV - Experimental Study 3rd Floor 1st Floor R Reference Sensors | [2nd Setup North Fig. 4.8. Sketch of sensor layout To collect data, the same acquisition data system as explained in 4.1.4 was used. Data were recorded for 15 min with 2000 samples per second and decimated to 200 samples per second for recording purposes. No analog anti-alias filter was applied. The gain of the system was set to ±25 mV. To check the results from ambient vibration with impact (forced) vibration, additional impact tests were applied. These were performed by using human force to introduce impact force on one of the main posts in the first and second floor. The data were recorded with the same instrumentation and setup. The tests were conducted in December 2000 and January 2001. Throughout the ambient vibration testing, the surrounding environment was windy with adjacent working construction labor. 96 Chapter 5 Data Evaluation and Analysis The results of analyses performed on acquired data from the woodframe house tests are presented in this chapter. The vibration characteristics, such as natural frequency and critical damping ratio of woodframe houses in test 5, 6 and 9 were identified from ambient and forced vibration data collected before and after each earthquake simulation. The frequency change throughout the earthquake simulation was studied using a joint time-frequency analysis. Later in this chapter, the identified fundamental periods are compared with fundamental periods calculated by different formulae suggested by building codes, and a correlation between the ambient and forced vibration methods is carried out. 5.1. Analyses of Subsystem Performed, Test Number 5 To determine natural frequency of the house before, throughout and after the simulation different analyses were performed. The time and frequency domain analysis were conducted to determine the natural frequency of the woodframe house before and after the earthquake simulations. To determine the frequency change throughout the earthquake simulation, joint time-frequency analyses were conducted using the methods described in Chapter 3. 97 Chapter V - Data Evaluation and Analysis 5.1.1. Frequency and Mode Shapes To determine the natural frequencies and damping ratios from sinusoidal sweep tests, the frequency response function (FRF), coherence function and phase angle of the input and output data were calculated. In addition, to verify the results a stochastic subspace iteration (SSI) analysis was performed. As an illustration of the work performed Figure 5.1 shows the FRF, coherence and phase angle obtained from sinusoidal sweep test for the woodframe house before the earthquake simulation of test 5 run 1. To obtain the system's dynamic parameters from data recorded by the ambient vibration testing method, frequency domain decomposition (FDD) and stochastic subspace iteration (SSI) analysis were performed. The plotted average of the normalized singular values of the spectral density matrices for the test number 5 before the first earthquake simulation is shown in Figure 5.2. For the analysis the data was decimated by a factor of 4 and the frequency resolution was set to 1024 frequency lines. In Figure 5.2 the horizontal and vertical axes are the frequency (Hz) and Spectral Density Magnitude, respectively. 98 Chapter V - Data Evaluation and Analysis Coherence Amplitude \fVy Amplitude - 2 0 0 3.5 FRF _ x ..(..., ji... , A 3.5 Phase 3 3.5 4 Frequency (Hz) Fig. 5.1. Coherence, Frequency Response Function (FRF) and Phase Angle plots before earthquake simulation of test # 5 run 1 It is known that not all of the peaks in an average of the normalized singular values of the spectral density matrices plot necessarily correspond to a natural frequency (Bendat and Piersol, 1993). To confirm whether or not a peak of the plot is associated with a natural frequency additional tools are needed, such as the SSI analysis. For example, more than 15 peaks In Figure 5.2 can be picked which could be possible modes under 20 Hz but are not necessarily a real mode shape. 99 Chapter V - Data Evaluation and Analysis The natural frequencies identified for the wood frame house test 5 are listed in Table 5.1, which also includes damping ratios calculated by the half-power bandwidth method1 for each test. The first column in Table 5.1 shows the type of the test performed on the woodframe house. In Table 5.1, it can be seen that the frequency results from the ambient vibration methods are up to 1.18 Hz higher than the results attained from the sinusoidal sweep method. l-requency Domain Decomposition - Peak Picking Average ot the Normalized Singular Values of Spectral Density Matrices of all Data Sets. ARTeMIS Extractor, Enterprise License, ARTX-0300E-190601 PA Project: EQ99 )^9_2.axp Frequency [Hz] Fig. 5.2. Average of normalized singular values of spectral density matrices for sinusoidal sweep test before test 5 run 1 1 For more information refer to "Dynamic of Structures, Theory and Applications to Earthquake 100 Chapter V - Data Evaluation and Analysis Table 5.1. Natural frequencies and damping ratios identified from test #5 Test Type Frequency (Hz) Damping ratio (%) of 1st mode in the N/S Direction 1st mode in the North South Direction 1st mode in the East West Direction 1st mode of Torsion AVT 3.91 3.30 5.52 2.57 Sine Sweep before earthquake simulation 3.08 3.05 4.85 4.20 Sine Sweep between earthquake simulations 1.05 2.77 3.61 Not possible to determine Sine Sweep after earthquake simulation 0.88 2.71 3.60 5.20 AVT 2.06 3.03 4.65 2.90 The detected mode shapes of the subsystem are shown in Figure 5.3 to 5.5. In Figure 5.3 to 5.5 the top-left figure shows the mode shape from top view. The top-right and bottom-left shapes display the east and north elevation, respectively. Finally, the perspective view of the house is shown in the bottom right corner. The mode shapes in Figure 5.3 to 5.5 are presented in sequential order to match Table 5.1. The subsystem woodframe building was built to model the bottom storey of a two-storey house and therefore only the first mode shape was identified. Engineering", Chopra A. K., Page 78. 101 Chapter V - Data Evaluation and Analysis 5.1.2. Joint Time - Frequency Analyses Each of the two earthquake simulations was analyzed using the short time Fourier transform (STFT) to a yield joint Time-Frequency Response Function (TFRF). The time-frequency information is displayed in joint frequency plots (Fig. 5.6), in which the input and output time signals, the standard frequency response function (FRF) and the time-frequency response function (TFRF) are displayed. The TFRF is shown in Figure 5.6 and 5.7 as a contour plot in the lower-right corner of the figures, where the horizontal and vertical axes are frequency (Hz) and time (sec), respectively. The left figures display the input and output signal, where the horizontal and vertical axes are acceleration (g's) and time (sec), respectively. In the top-right corner of Figures 5.6 and 5.7 the FRF is displayed, where the horizontal and vertical axes are frequency (Hz) and FRF magnitude, respectively. For the generation of the the TFRF plots a 256-point window was used, thus at a sampling rate of 200 samples per second, the window length corresponds to 1.28 seconds, which is longer than the fundamental period of the structure. 102 Chapter V - Data Evaluation and Analysis Fig 5.3. First north-south mode shape of the subsystem in test #5 103 Chapter V - Data Evaluation and Analysis 104 Chapter V - Data Evaluation and Analysis Fig 5.5. First torsional mode shape of the subsystem in test #5 105 Chapter V - Data Evaluation and Analysis The following should be noted in viewing time-frequency plots. The TFRF of strong motion consists of a series of peaks, since the frequency content of the acceleration of the simulated earthquakes is not constant. If the input is continuous in frequency and time, the peak values are displayed in form of a ridge. The ridge will be present at a particular frequency, for all time values. For the sake of clarity in the contour plots, the time-frequency response function (TFRF) is shown only at the contour levels higher than 50% of the maximum peak of TFRT. Note that the amplitude of the TFRF does not represent the strength of shaking. It indicates, which frequency components are present at a certain time and their relative strengths. The information contained in the TFRF is fundamentally different than the FRF. The FRF averages the frequency content over the entire time of the record. More specifically, it is the ratio of the total energy that is contained in the output, at a particular frequency to the total energy in the input. The TFRF conveys information on the relative energy level at a particular frequency during a small window of time. When the magnitude of shaking at the roof level, for a given time and frequency is greater than that at the shake table, a peak will be shown. Hence a large peak may be present during free decay of the vibration when the input is very small. 106 Chapter V - Data Evaluation and Analysis Each time-frequency plot contains a vast amount of information on the response of the structure to earthquake excitation. The scope of this thesis does not include a comprehensive study conducted for every time-frequency plot. Instead, a discussion of the important features with respect to the frequency response of the building is presented for each test. Thus the general characteristics of the time-frequency response function of tests 5, 6 and 9 are described to be able to discuss information contained in the TFRF. Figures 5.6 and 5.7 show the time frequency response plots for the 1985 Nahanni earthquake in the north-south direction for test number 5. The figure caption states the test number and sequence of each plot. The TFRFs show unstable frequencies for both earthquakes. This is expected as the frequency domain analysis shows considerable variation in the calculated frequencies. The input and output signals used for the FRF and TFRF are from accelerometers attached to the shake table and south-centre of the roof level respectively. Same accelerometer type was utilized for the roof level and shake table, where the accelerometer type is indicated in Table 4.3. 107 Chapter V - Data Evaluation and Analysis Fig. 5.6. Joint time-frequency plot for test # 5 run 1, Nahanni Earthquake 1985 108 Chapter V - Data Evaluation and Analysis Fig. 5.7. Joint time-frequency plot for test # 5 run 2, Nahanni Earthquake 1985 109 Chapter V - Data Evaluation and Analysis One interesting feature of the TFRF is its ability to provide insight into the behaviour of the FRF. For example, in Figure 5.6 the frequency fluctuations observed in the TFRFs around the first natural frequency shifts to a lower value during the heavy shaking. The magnitude of the peaks during the free vibration is considerable. In the case of a steady-state forced input, a structure will vibrate at the same frequency as the driving force. However, an earthquake is transient and steady state motion may not be achieved in general. For this reason there will be some modal response of the building during heavy shaking. The low level of modal response seen in the TFRF does not necessary mean that the building does not vibrate in its modes during heavy shaking. It just means that the magnitude of the response, at a particular frequency, is eclipsed by the magnitude of the input since the duration of shaking is assumed to be short (Black 1998). Figures 5.6 shows a shift in the frequency in the north-south direction throughout the earthquakes. In the beginning of the TFRF the peaks are concentrated close to 3 Hz, which is in the vicinity of the natural frequency of the house before the test. This shifts to 1.5 Hz and finally, the peaks shift gradually to 1.0 Hz toward the end of the excitation. The frequency shift agrees with the natural frequencies determined before and after the test. This indicates considerable structural damage in the woodframe house, which was confirmed upon inspection of the 110 Chapter V - Data Evaluation and Analysis house after the test. The structural damage observed consisted mainly of pulled out nails in sheathing connections and crack in sheathings. The frequency shift happens gradually throughout the record. This means that the stiffness was decreased about 88.6 % in the first earthquake simulation. For the second earthquake simulation the house already had low initial natural frequencies (Table 5.1). As seen in Figure 5.7, the fundamental natural frequency shifts from 1.0 Hz to 0.8 Hz. This is in agreement with the natural frequencies of the house determined by the frequency and time domain analysis (Table 5.1). The frequency shift occurs gradually till the 20th second of the record. Since the structure had a relatively low stiffness, the natural frequency of the structure more closely matched the frequency of the input record (Fig. 4.2). The frequency domain analysis identified a decrease of the natural frequency from 3.08 to 1.04 Hz in the north-south mode. For test number 5 it can be concluded that the stiffness of the structure decreased by 88.6% due to an earthquake with a peak acceleration of 0.32g. The reason for this shift is not decipherable from the frequency domain analysis alone. A joint time-frequency analysis shows that the shift in test number 5 run 1 occurs during the first 10 seconds of shaking and that the natural frequency of the house decreased about 65.9 % during this part of the shaking. In test number 5 run 2 the stiffness of the structure had already been decreased considerable and the decrease due to the 111 Chapter V - Data Evaluation and Analysis second excitation occurs mainly during the free vibration when the input excitation is small. The structural stiffness reduction was about 36% of the remaining stiffness and the natural frequency decreases about 16.2%. 5.2. Analyses of Subsystem Performed, Test Number 6 The analyses performed on the data from test number 5 were repeated for the acquired data from test number 6. These include frequency and time domain analyses to obtain the natural frequency before, throughout and after earthquake simulation. Joint time-frequency analyses were conducted to investigate the frequency behaviour of the woodframe throughout the earthquake simulation. 5.2.1. Frequency and Mode Shapes The natural frequencies and damping ratios analysed from acquired data for the woodframe house test number 6 are displayed in Table 5.2. The difference in results from ambient and forced vibration data is as high as 1.17 Hz. Mode shapes were similar in appearance and sequence to test number 5 (Figures 5.3 to 5.5). 5.2.2. Joint Time-Frequency Analyses Since the structure in test number 6 had a similar construction configuration as in test number 5, the responses are expected to be similar. Figures 5.8 and 5.9 112 Chapter V - Data Evaluation and Analysis display time frequency response plots of test 6 for the Nahanni 1985 earthquake in the north-south direction. The figure caption states the test number and sequence of each plot. The TFRFs show shift in the frequency for both earthquake simulations. This is as expected from the frequency domain analysis, which showed difference in the calculated frequencies before and after the test (Table 5.2). Table 5.2. Natural frequencies and damping ratio from test #6. Test Type Frequency(Hz) Damping Ratio (%) of 1st mode in the N/S Direction 1SI mode in the North South Direction 1" mode in the East West Direction 1st mode of Torsion AVT 2.32 2.99 4.31 1.93 Sine Sweep before earthquake simulation 1.66 2.78 4.11 7.60 Sine Sweep between earthquake simulations 0.80 2.67 3.97 8.82 Sine Sweep after earthquake simulation 0.76 1.98 3.52 8.92 AVT 1.93 2.91 4.27 2.57 Figures 5.8 shows a shift in the frequency in the north-south direction. In the beginning of the TFRF the contour lines are clustered around 1.6 Hz, which is in the vicinity of the natural frequency of the house before the test (Fig. 5.7). This value shifts to 1.2 Hz in the first 10 seconds of the earthquake record and it is close to 0.8 Hz around the 20th second of the record. The frequency shifts agree with the natural frequencies determined before and after the test. This indicates considerable structural damage in the woodframe house, which was confirmed 113 Chapter V - Data Evaluation and Analysis upon inspection of the house after the test. The structural damage consisted of cracks in the studs and connection failure in board sheathing such as nail pulled out. For the second earthquake simulation the house already had low initial natural frequencies and as seen in Figure 5.9 this amount does not shift considerably. This is in agreement with the natural frequencies of the house after the simulation test (Table 5.2). The structural stiffness reduction was measured as 9.7% of the remaining stiffness. The frequency domain analysis identified a decrease of the natural frequency from 1.66 to 0.8 Hz in the north-south mode. For test 6 it can be concluded that the stiffness of structure decreased by 76.8% due to an earthquake with a peak acceleration of 0.32g. The reason for this shift cannot be resolved from the frequency domain analysis alone. A joint time-frequency analysis shows that the shift in test number 6 run 1 occurs during the first 15 seconds of shaking and that the natural frequency of the house decreased about 52 % during this part of the shaking. In test 6 run 2 the stiffness of the structure had already been decreased considerably and the decrease due to the second excitation occurs mainly during the free vibration when the excitation was relatively small (t > 10 sec). The reduction in the natural frequency for the second simulation was observed about 5%. 114 Chapter V - Data Evaluation and Analysis Fig. 5.8. Joint time-frequency plot for test #6 run 1, Nahanni earthquake 1985. 115 Chapter V - Data Evaluation and Analysis 20 15 E i— 10 0 Output, X J -0.1 0 0.1 Accle (g's) <S 1 FRF E E 0.5 in I Input, X 2 3 Frequency (Hz) -0.5 0 0.5 Accel (g's) 1 2 3 Frequency (Hz) Fig. 5.9 Joint time-frequency plot for test #6 run 2, Nahanni earthquake 1985. 116 Chapter V - Data Evaluation and Analysis 5.3. Analyses of Two-Storey House Performed, Test Number 9 Analyses similar to those for tests number 5 and 6 were repeated for the data from test number 9. Joint time-frequency analyses were conducted to investigate the frequency behaviour of the woodframe throughout the earthquake simulation. 5.3.1. Frequency and Mode Shapes The natural frequencies and damping ratios obtained from the data acquired are, displayed in Table 5.3. The difference in frequencies obtained from ambient and forced vibration tests is as high as 2.21 Hz. The second torsional mode was only identified by the ambient vibration method because the frequency of this mode was higher than the frequency range of the sinusoidal sweep test2. Mode shapes obtained from test number 9 are displayed in Figures 5.10 to 5.15. These mode shapes are presented in the same order as the modes listed in Table 5.3. 5.3.2. Joint Time-Frequency Analyses Each of the two earthquake simulations was analysed using a short time Fourier transform (STFT) analysis. The time-frequency information is displayed in joint-frequency plots, which illustrate the input and output time signals, the standard frequency response function (FRF) and the time-frequency response function. The TFRF is shown in Figures 5.16 and 5.17. At a sampling rate of 200 samples 2 See Chapter 4 for details on sinusoidal sweep test 117 Chapter V - Data Evaluation and Analysis per second, the 256 point window corresponds to 1.28 seconds, which is longer than the fundamental period of the structure. Figures 5.16 and 5.17 show the time frequency response plots for the 1994 Northridge earthquake recorded at Sherman Oaks for test number 9 in the north-south direction. The figure captions state the test number and sequence of each plot. The TFRFs show insignificant shift in the frequency of both earthquakes simulation. This was expected since the frequency domain analysis showed small variation in the calculated frequencies. Figures 5.16 and 5.17 indicate small shift in the frequency in the north-south direction between the two earthquakes. In the beginning of the TFRF the peaks are concentrated close to 3.4 Hz, which is in the vicinity of the natural frequency of the house before the test. This shifts to 3 Hz in the first 15 seconds of the earthquake record and remains at that level till the end of the excitation. The frequency shifts agree with the natural frequencies determined before and after the test. This indicates slight damage in the woodframe house, which was confirmed upon inspection of the house after the test. 118 Chapter V - Data Evaluation and Analysis Table 5.3. Values of natural frequencies and damping ratio from test #9. Frequency (Hz) Damping Ratio in Test Type 1s t mode in the North South Direction 1 s t mode in the East West Direction 1s t mode of Torsion 2 n d mode in the North South Direction 2 n d mode in the East West Direction 2n d mode of Torsion percent (%) 1 s t mode in the N/S Direction AVT 4.79 5.51 9.85 15.43 18.50 23.34 2.85 Sine Sweep 1 3.33 4.84 6.78 11.07 16.81 N/A 8.90 Sine Sweep II 3.05 4.81 6.06 11.02 16.61 N/A 7.31 Sine Sweep III 2.94 4.81 6.00 11.00 16.39 N/A 14.89 Sine Sweep IV 2.11 4.72 5.92 10.80 16.48 N/A 18.62 AVT 4.31 4.91 7.47 12.40 16.04 21.94 3.50 Figure 5.16 shows that the natural frequency shifts from 3.3 Hz to 2.8 Hz. This is in agreement with the natural frequencies of the house before the test and close to results obtained after the simulation (Table 5.3). The disjoint seen in Figure 5.16 around the 12th second is because of decrease in TFRF's magnitude to lower values than the preset contour threshold. With other words the TFRF's peak exist in that range but is not shown. The frequency domain analysis identified decrease of the natural frequency from 2.94 to 2.11 Hz in the first north-south mode. For test number 9, runs 1 and 2, it can be concluded that the stiffness of the structure decreased by 16.1% of the original stiffness and 28% of the remaining stiffness, respectively, during earthquake simulations with a peak acceleration of 0.45g (Fig. 4.5). The reason 119 Chapter V - Data Evaluation and Analysis for this shift cannot be resolved from the frequency domain analysis alone. A joint time-frequency analysis shows that a slight shift occurs in test number 9 run 1, which resulted in a frequency decrease about 14.4%. In test number 9 run 2 the stiffness of the structure decreased considerably and this occurred in the first 10 second of strong shaking of the record. The natural frequency decreased about 28.2%. 120 Chapter V - Data Evaluation and Analysis 121 Chapter V - Data Evaluation and Analysis 122 Chapter V - Data Evaluation and Analysis 123 Chapter V - Data Evaluation and Analysis 124 Chapter V - Data Evaluation and Analysis 125 Chapter V - Data Evaluation and Analysis 126 Chapter V - Data Evaluation and Analysis Input, X -2 0 Accel (g's) 20 15 10 Input, X s 0.1 FRF E 0.05 j i ... V V 0 1 2 3 4 5 6 7 Frequency (Hz) 20-5 10-| i --2 0 2 Accel (g's) 0 1 2 3 4 5 6 7 Frequency (Hz) Fig. 5.16. Joint time-frequency plot for test #9 run 1, Northridge earthquake recorded at Sherman Oaks 1994. 127 Chapter V - Data Evaluation and Analysis 20 15 1 io a> E Output, X — r ~ -4 0 Accel (g's) 20 15 10 0 Input, X t J. 1 - r - 2 - 1 0 1 Accel (g's) S 1 a) £ 0.5 20. OJ E FRF I . 1 > 1 1 \ t 2 4 6 Frequency (Hz) T Frequency (Hz) Fig. 5.17. Joint time-frequency plot for test #9 run 2, Northridge earthquake recorded at Sherman Oaks 1994. 128 Chapter V - Data Evaluation and Analysis 5.4. Analyses of Field Tests Analyses were performed on the data acquired from the field house tests. These include frequency and time domain analyses to obtain natural frequencies. 5.4.1. Frequency and Damping The natural frequencies and damping ratios analysed from the acquired data are presented in Table 5.4. The maximum difference between the results from ambient and forced vibration tests is 0.42 Hz. Table 5.4. Natural frequencies and damping ratio from field tests. House No. Height (m) Length (m) Width (m) Number of Storey First detected natural frequency (x dir) AVT FVT 1 12.72 12.67 8.96 4 2.22 2.00 4 11.90 12.32 8.00 4 2.59 N/A 5 11.97 12.90 8.02 4 2.48 2.02 5.5. Comparison between the Code Formula and Experimental Results of Fundamental Period In this section, the results obtained from analyses discussed previously are compared with the suggested formulae in the National Building Code of Canada (NBCC) 95, Uniform Building Code (UBC) 97 and the upcoming NBCC. The comparison of the results from suggested code formulae with the experimental 129 Chapter V - Data Evaluation and Analysis outcomes were done not only to assess the accuracy of the suggested formula but also to determine the effect on the seismic design factors such as the NBCC 95's S response factors and the upcoming NBCC's uniform hazard spectral accelerations. The experimental periods from test 5, 6 and 9 utilized in this comparison are those determined from the sinusoidal tests performed before the first earthquake simulation, when the structure was still undamaged. The suggested formula in NBCC 95 (Eq. (2.2)) is plotted as a function of height in Figure 5.18. The shearwall length considered is 4.5 m, representing the approximate shearwall length in tests number 5, 6 and 9, and 9 m for the field house test. Figure 5.18 illustrates that the fundamental periods from test number 6 is significantly longer than the suggested value in NBCC 95, whereas the result from tests number 5, 9 and the field house tests are close to the suggested NBCC 95 value. The suggested formula in UBC 97 (Eq. (2.6)) and the upcoming NBCC (Eq. (3.11)) is plotted as a function of building height in Figure 5.19. It is evident that the fundamental periods obtained from experimental data are significantly longer than the suggested empirical formulae. 130 Chapter V - Data Evaluation and Analysis Table 5.5 displays values of the NBCC 95's seismic response factor S for Vancouver, which are carried out based on fundamental period values of the experimental study and the suggested code formulae. The results from experimental periods are lower than those attained based on the code formulae (Table 5.5). 0.7 0.6 0.5 8 9 Height (m) 10 11 12 13 + Test #5 • Field House Tests Test #6 NBCC (4.5m) X Test #9 NBCC (9m) Fig. 5.18. Comparison between the natural frequency from NBCC95 formula and experimental results. The values of the design spectral acceleration from NBCC 95 (Fig. 5.20) and upcoming NBCC's uniform hazard spectra (Fig. 2.7) were calculated for Vancouver based on the fundamental period from the experimental study and the suggested code formulae. Table 5.6 compares the spectral acceleration values of the upcoming NBCC's uniform hazard spectra for Vancouver, with the design spectral acceleration given by NBCC 95. The percentage differences for 131 Chapter V - Data Evaluation and Analysis the S factor are also illustrated in Table 5.6. Percentage differences in Tables 5.5 and 5.6 are referred to differences with respect to results from experimental periods. It is evident that the empirical formulae suggested in the codes do not accurately represent the actual fundamental periods of woodframe buildings. The inaccuracy can result in an increase of the seismic design factor values for the tested specimens. Table 5.5 displays the maximum percentage difference of the S design factor with respect to the results from experimental tests is 58% higher. It can be seen that the difference in some cases is significant. Table 5.5. Seismic design S factor calculated based on fundamental periods obtained from experiment and code formulae. T Period (sec) S Factor Test Name Experimental NBCC 95 Experimental NBCC Formula Percentage Difference (%) EQ 99 Test # 5 0.32 0.24 2.65 3.0 +13 EQ 99 Test # 6 0.60 0.24 1.9 3.0 +58 EQ 99 Test #9 0.30 0.24 2.75 3.0 +9 Field test house # 1 0.50 0.38 2.1 2.6 +24 Field test house # 3 0.39 0.36 2.5 2.65 +6 Field test house # 4 0.39 0.36 2.5 2.65 +6 132 Chapter V - Data Evaluation and Analysis 0.7 . 0 6 0 5 0 4 m • Period (se 0.3 -0.2 -— f t W 0.1 -0 -i 5 6 7 8 9 Height (m) 10 11 12 13 » Test #5 • Test #6 —H—Test #9 « Field House Tests UBC 97 upcoming NBCC Fig. 5.19. Comparison between the natural frequency from upcoming NBCC and UBC 97 formula and experimental results. Table 5.6. Spectral acceleration values calculated for Vancouver based on fundamental period obtained from experiment and code formulae. T Period (sec) Spectral Acceleration (g's) NBCC 95 Spectral Acceleration (g's) upcoming NBCC Test Name Experimental NBCC 95 Upcoming NBCC Experimental NBCC Formula Percentage Difference {%) Experimental Upcoming NBCC Formula Percentage Difference (%) EQ 99 Test #5 0.32 0.24 0.19 0.63 0.63 0 0.80 1 +25 EQ 99 Test #6 0.60 0.24 0.19 0.42 0.63 +32 0.57 1 +75 EQ 99 Test #9 0.30 0.24 0.19 0.63 0.63 0 0.85 1 +18 Field test house # 1 0.50 0.38 0.34 0.5 0.63 +30 0.66 0.75 +14 Field test house #3 0.39 0.36 0.32 0.63 0.63 0 0.70 0.80 +14 Field test house #4 0.39 0.36 0.32 0.63 0.63 0 0.70 0.80 +14 133 Chapter V - Data Evaluation and Analysis In Table 5.6 the maximum percentage difference was calculated about 75 % for the design spectral acceleration of NBCC 95 (Fig. 5.20) and upcoming NBCC's uniform hazard spectra. According to upcoming formulae, the design is for much higher values which may lead to conservative design. Because of the complexity of woodframe construction it is not deemed appropriate to express the fundamental period of this type of construction as a function of height only. To come up with a more accurate formula a large database of experimental natural frequencies and damping ratios is required to perform a regression analysis. 0.02 0.040.060.08 0.01 0.1 Period, T, s Fig. 5.20. NBCC 95 Normalized design distribution spectrum for peak horizontal ground velocity v=1 m/s for dynamic analysis (NBCC 1995). 134 Chapter V - Data Evaluation and Analysis 5.6 Correlation of Results from Ambient and Forced Vibration Methods In the analyses conducted on the results of tests number 5, 6 and 9, some differences between the frequencies determined from ambient and forced vibration testing methods were observed. This difference varied from 1.16 to 2.21 Hz. The ambient vibration method is a relatively inexpensive and non-destructive testing method and is therefore the preferable method to identify the natural frequencies of wood frame houses. It is therefore important to calibrate this method with respect to the forced vibration results for future usage. Ambient and forced vibration results from Tables 5.1, 5.2 and 5.3 are correlated in this section. The correlation factors for frequencies obtained before and after the earthquake simulation were 0.998 and 0.987, respectively. Figure 5.21 shows the correlation, where the vertical and horizontal axes are the results obtained from ambient and forced vibration tests, respectively. If the results were perfectly matched, they would have been on the 45-degree line. Also, the correlated trend-lines for ambient and forced vibration results are displayed in Figure 5.21. 135 Chapter V - Data Evaluation and Analysis Fig. 5.21. Correlation between the ambient and forced vibration testing method. The natural frequency obtained by the ambient vibration method can be modified to better represent the actual natural frequency of the structure with the help of Figure 5.21. For example, if the measured frequency by ambient vibration method is 5 Hz, the actual frequency of the structure before sever shaking is about 4.5 Hz (by using the dashed line in Fig. 5.21). For a similar analysis after sever shaking, the dotted line should be used in Figure 5.21. 136 Chapter V - Data Evaluation and Analysis The observed difference in frequency results obtained from ambient and forced vibration testing method can be explained based on the stiffness behaviour of the structure throughout the earthquake simulation. To demonstrate the stiffness change, hysteresis diagrams of the earthquake simulation are utilized. Figure 5.22 is the hysteresis loop of test number 5 run 1 for 1985 Nahanni earthquake simulation. The horizontal and vertical axes are the relative displacement of the roof with respect to the shake table (mm) and the actuator load (kN), respectively. The dashed curve shows the hysteresis of the test from the start to the end of the simulation. Curve A in Figure 5.22 shows the hysteresis curve at the very beginning of the test, where the house is assumed to have its original stiffness. Curve B in the same figure demonstrates the hysteresis curve close to the end of the earthquake simulation with decayed stiffness. The tangent lines are plotted to demonstrate the stiffness of the house at times during the earthquake simulation. The tangent lines of curve A are marked with numbers land 2, while those of curve B are marked with 3 and 4. 137 Chapter V - Data Evaluation and Analysis Center Wall Fig. 5.22. Hysteresis loop of test number 5 run 1, 1985 Nahanni earthquake 1 3 8 Chapter V - Data Evaluation and Analysis The stiffness decay for the undamaged and damaged house can be demonstrated with the tangent lines 1, 3 and 4. From this figure, it can be observed clearly that the stiffness in a damaged house decreases as the number of loading cycles increases. To explain the difference between the results obtained from ambient vibration and forced vibration testing methods, in Fig. 5.22 can be seen that the stiffness for minute displacements such as up to 1mm (tangent line 1) is about 40 x 103 kN/m which is higher than the stiffness 25 x 103 kN/m estimated for small displacement such as 5 mm (tangent line 2). This results in a stiffness change of 37%. With regards to the displacement nature of the ambient and forced vibration tests, the stiffness values will be different for the displacement values introduced by each method3. Thus the difference in resulting frequencies from the two testing methods can be interpreted based on the stiffness shift due to displacement seen in Fig. 5.22. Many factors contribute to the stiffness shift due to minute and small displacements, where the kinematics friction resistance existing in the structural system, such as friction in the connections, can be one of the factors. The stiffness for tangent line 3 and 4 are about 6 x 103 kN/m and 2 x 103 kN/m, respectively, which results in about 67% stiffness decrease. 3 For information on performed ambient vibration and sine sweep tests refer to Chapter 3 and 4 139 Chapter V - Data Evaluation and Analysis The correlated trend-line plotted in Figure 5.21 for results obtained after shake table testing is much lower than the trend-line plotted for the results obtained before the shake table testing. In this case, the difference can be referred to as stiffness decay of the structure. As seen in Figure 5.22 the tangent lines 1 and 2 of curve A define the stiffness of the structure for minute and small displacements, respectively before the test. The difference between the tangent lines 3 and 4, which represent the stiffness due to minute and small displacements, respectively, is much more pronounced since considerable damage has been introduced to the structure and the stiffness decays faster. Therefore the difference between ambient and forced vibration test results is more pronounced for previously damaged buildings. 1 4 0 Chapter 6 Summary, Conclusions and Recommendations The research in this thesis was aimed to investigate the vibration behaviour of single-family woodframe buildings, to compare experimental findings with suggested code formulae and to assess methods of measuring vibration parameters. To this end, several tests with different methodologies were performed to determine the vibration characteristics of timber structures before, throughout and after earthquake excitations and to assess the suitability of the different methods. 6.1. Summary The objectives of this study were achieved through the following research activities: • Conducting a comprehensive literature study on accomplished research of dynamic behaviour and full-scale testing of woodframe buildings. • Conducting several earthquake motion simulation tests on the shake table for full-scale light-frame timber buildings to investigate the structural response of different construction types. 141 Chapter VI - Conclusions and Recommendations • Performing ambient and forced vibration tests such as sinusoidal sweep tests, before and after each earthquake simulation to identify the natural frequency of the building system studied and investigate its changes through out the simulation tests. • Performing field-tests on a group of existing woodframe low-rise buildings to determine their vibration characteristics. • Performing time and frequency domain analyses on data recorded from full-scale timber building models to obtain their natural frequencies and mode shapes. • Performing joint time-frequency response analyses to study vibration characteristics of the woodframe house throughout earthquake simulation. • Evaluating correlation between the results obtained from ambient and forced vibration testing. From the analyses of vibration data, the natural frequencies obtained from the tested specimens were in the range of 1.66 to 3.33 Hz with damping ratios between 3.6 and 16 percent. These results are in reasonable agreement with earlier research on woodframe buildings discussed in Chapter 2. The fundamental periods obtained from experimental data were in general longer than the suggested formulae in building codes. 142 Chapter VI - Conclusions and Recommendations Consistent differences were found when comparing the results from ambient and forced vibration tests. Therefore, a correlation of the results from the ambient and forced vibration testing methods was performed. The correlation diagram in Figure 5.21 will be useful to correlate ambient to forced vibration results for future non-destructive testing performed on woodframe buildings. 6.2. Conclusion The conducted comprehensive literature study on previous accomplished research provided a better idea of what has been done in the past in relation to full-scale testing and dynamic behavior of woodframe buildings. Based on the literature study the fundamental period identified by different researchers for single-family low-rise woodframe houses were extremely scattered in the range of 0.06 to 1.25 second and corresponding critical damping ratio about 0.15 to 24 percent. The investigation of vibration characteristics of woodframe houses provided a good understanding of how the natural frequency of the structure changes and how this change is related to the amount of damage observed during each test. Among the analyses performed the joint time-frequency analysis is a very powerful tool, which not only provides insight into dynamic characteristics of structures that are not available through frequency domain alone, but also can explain irregular shifts in frequency and verify the results from other analyses. 143 Chapter VI - Conclusions and Recommendations Based on results from this study, the suggested code formulae are not accurate and are just gross approximation of the actual fundamental period of woodframe buildings. To study the result of the above-mentioned inaccuracy, the NBCC's seismic design factors such as spectral acceleration and the S factor were calculated based on periods obtained from the experimental study and the suggested code formula. The spectral acceleration and the S factor obtained from periods extracted of the codes formula can be as high as 75% and 58% respectively, than those carried out based on the experimental studies. The ambient vibration testing method can be effectively used as a non-destructive and relative inexpensive technique for estimating the fundamental period of wood frame houses. The study showed that house periods at the ambient vibration level are generally shorter than the actual periods during strong ground shaking. A correlation study between results of forced and ambient vibration tests were conducted in order to develop a simple technique for correcting the period of the house obtained from ambient vibration tests. 6.3. Future Research and Applications One of the future applications of this research is the development of an empirical formula for the fundamental period of the Canadian light-frame low-rise timber buildings. This thesis is a reference for further studies in this field. 144 Chapter VI - Conclusions and Recommendations One of the weaknesses in the study on the vibration behavior is that the fundamental period of woodframe buildings measured after a strong excitation is not a sufficient parameter by itself for evaluating the frequency shift of the woodframe house due to strong motion excitation. An initial fundamental period for woodframe buildings is required as benchmark. In Chapter 5, it was demonstrated that the suggested code formulae are inaccurate for this purpose. Therefore, a comprehensive natural frequency database of woodframe houses, which have not experienced strong motion excitation, is required. This database can provide a proper benchmark for the vibration studies of the woodframe houses in future. As mentioned above a database of natural frequencies for woodframe buildings with different configurations needs to be compiled. Table 6.1 outlines a suggested categorization of future house testing. The classification of the timber buildings in Table 6.1 is based on existing interest from the industry, importance and prevalence of each construction type. The arrangement is basically taking into account the height, footprint area, construction type and age of timber houses. The reason for considering the age of these buildings was discussed in Chapter 2. For further information on Table 6.1 see Kharrazi et al. 2000 The collected data will also be helpful in reproducing the sampling space for an artificial intelligence network to simulate the frequency response of the structure and optimize for predicted results. 145 Chapter VI - Conclusions and Recommendations Table 6.1. Matrix of proposed future testing programme (Kharrazi et al. 2000) No Interest Less Interest More Interest Main Interest AVT = Ambient Vibration Test FVT = Forced Vibration Test FRVT = Free Vibration Test 146 Chapter 7 References 1. 1995, "Structural Design", P. 137-160, 4, National Research Council Canada, 2. 1999, "Minutes of the Ninth Meeting of the Canadian National Committee on Earthquake Engineering (CANCEE)", P. 1-54, National Research Council Canada, Vancouver, BC Canada. 3. Ad Hoc and (Structural Engineering Associations of California), 1989, "Reflections on the Lorna Prieta Earthquake", P.67-72, Structural Engineering Associations of California, California, USA. 4. Adeli H and Mohammadi J, 1984, "Fundamental Period of Vibrations of Structures", P.320-323, ASCE Mech. Division Proceedings, ASCE, 5. Andereasson S, 1999, "Three-Dimensional Interaction in Stabilization of Multi-Storey Timber Frame Buildings", 12p CIB W18/32-15-1, Austria. 6. 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Yasumura M, 1996, "Evaluation of Seismic Performance of Timber Structural", P.45-52, Vol. 1, International Wood Engineering Conference, 168. Yasumura M, Murota T, Nishiyama H, and Yamaguchi Y, 1988, "Experiments on a Three-Storied Wooden Frame Building Subjected 172 Chapter Vll - References to Horizontal Load", P.262-275, Vol. 2, Proceedings of the 1988 International Conference on Timber Engineering, Seattle, Washington. 169. Yeh CT, Hartz BJ, and Brown CB, 1971, "Damping Sources in Wood Structures", P.411-419, Journal of Sound and Vibration, Vol. 19, No.4, 170. Yokel FY, Hsi G, and Somes NF, 1973, "Full Scale Test on a Two-Story House Subjected to Lateral Load", 26p, No. 72-600301 / Coden: BSSNBV, National Bureau of Standards Building Science Series (No.44), Washington DC, USA. 173 Appendix A Drawings The following are drawings of the Earthquake 99 Woodframe House project provided by T B G Seismic Consultant Ltd. These drawings include elevation and plan views of the subsystem and two-storey house test specimens. 174 Appendix A Drawings The following are drawings of the Earthquake 99 Woodframe House project provided by TBG Seismic Consultant Ltd. These drawings include elevation and plan views of the subsystem and two-storey house test specimens. 174 Appendix A Appendix A a'-io 1/4' 1-1—- i—I— r Fig . A . 2 . Two-storey woodframe house plan view 176 Appendix A Appendix A F i g . A . 4 . Subsystem woodframe house and concrete block, plan view 178 Appendix B Shake Table Drawings 179 Appendix B Fig. B.1. Shake table In plan view 180 181 381-moav nws g xipuaddv g xjpuaddv P21 g xjpueddv g xipuaddv 

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