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Assessment of Structural Performance of Steel Academic Year 3―1 Ho Thu Hien Building on Shake Table Using Multi-Input 2010 Multi-Output Models Master’ ster ’s Thesis Academic Year Year 2010 2010 Keio University Graduate School of Science and Technology School of Science for Open and Environmental Systems Systems As we know, earthquakes have caused many serious damages; that is why it is needed to study the health of buildings after these earthquakes. After a large earthquake, evaluation of damage of structures is an important task for health assessment. Vibrations of buildings give us valuable information on it. Changes in the modal properties like natural frequencies, modal shapes and modal damping are very important to assess the structures.

Among the representative structural characteristics, natural frequencies provide the global information. However they are relatively simple, accurate to measure and easy to obtain. Besides, the changes in frequencies must be considered to assess the health of structure. When the frequency shifts give the general health assessment, the mode shape changes can be categorized up to the higher level of damage identification – determination of the geometric location of the damage.

This study will consider the frequencies shifts and their mode shapes with various levels of seismic excitations. The excitations are represented by different intensity levels of the 1995 Hyogoken Nanbu Earthquake that are obtained in JR – Takatori Station. The acceleration data of E–defense tests on full scale 4-story steel building will be analyzed. Five sets of acceleration data were measured at center and 4 corners on shake table and 4 stories of the full-scale model were considered as inputs and outputs signals of many types of multi-input multi-output (MIMO) models.

From the defined models, some first mode natural frequencies of structure will be obtained and compared to each other. By analyzing the two first mode natural frequencies of X and Y directions, the capacity of structure will be assessed with its performance. The aim of this research is to assess the capacity of a steel building after a seismic activity using real-size shake table tests. Course No Sub school: Fundamental Science and Technology Mathematics Physics Molecular Chemistry Applied Physics and Physico-Informatics Chemical Biology Biosciences and Informatics Sub school: Integrated Design Engineering Multidisciplinary and Design Science System Integration Engineering Smart Device and System Engineering Photonics and Image Information Engineering Science and Technology for Designing Functions Sub school: Science for Open and Environmental Systems Space and Environment Design Engineering Science of Environment, Resources and Energy Applied and Computational Mechanics Computer Science Smart Media Communication Engineering Open Systems Management ABSTRACT As we know, earthquakes have caused many serious damages; that is why it is needed to study the health of buildings after these earthquakes.

After a large earthquake, evaluation of damage of structures is an important task for health assessment. Vibrations of buildings give us valuable information on it. Changes in the modal properties like natural frequencies, modal shapes and modal damping are very important to assess the structures. Among the representative structural characteristics, natural frequencies provide the global information.

However they are relatively simple, accurate to measure and easy to obtain. Besides, the changes in frequencies must be considered to assess the health of structure. When the frequency shifts give the general health assessment, the mode shape changes can be categorized up to the higher level of damage identification – determination of the geometric location of the damage. This study will consider the frequencies shifts and their mode shapes with various levels of seismic excitations.

The excitations are represented by different intensity levels of the 1995 Hyogoken Nanbu Earthquake that are obtained in JR – Takatori Station. The acceleration data of E–defense tests on full scale 4-story steel building will be analyzed. Five sets of acceleration data were measured at center and 4 corners i on shake table and 4 stories of the full-scale model were considered as inputs and outputs signals of many types of multi-input multi-output (MIMO) models. From the defined models, some first mode natural frequencies of structure will be obtained and compared to each other.

By analyzing the two first mode natural frequencies of X and Y directions, the capacity of structure will be assessed with its performance. The aim of this research is to assess the capacity of a steel building after a seismic activity using real-size shake table tests. ii DEDICATION To my lovely and happy family, THEUHF! iii ACKNOWLEDGEMENTS First of all, I would like to express my sincere gratitude and thanks to my advisor Professor Akira Mita for his kind advices, valuable suggestions, invaluable guidance, moral support and effective encouragement throughout the course of this study. My special gratitude is due to all my dear friends: Ms Kondo, Ms Take, Ms Hasegawa, Mr Okamoto, Mr Oshihara, Mr Kosakai, Ms Nakamura, Ms Maho, Ms Goshima, Ms Ishikawa, Mr Mutara, Mr Sato, Mr Ichimura and others, especially, international students (Mr Xing, Ms Soroka, Ms Chua and Mr Kelpal) for making my time spent at Keio University an unforgettable memory as well as for what they helped for me to overcome lot of difficulties in foreign environment.

I would like to thank to the Ministry of Education, Science and Culture of Japan (Monbukagakusho) for the full financial support and the research facilities they provided during my study. Finally, but not the least, I would like to thank and dediacte my mother, my husband and my son, for all the trust, support that they gave me. Without their love, encouragement, inspiration and sacrifice, this work could hardly be completed. iv TABLE OF CONTENTS Page ABSTRACT i DEDICATION iii ACKNOWLEDGMENTS iv TABLE OF CONTENTS v LIST OF FIGURES vii LIST OF TABLES x 1 INTRODUCTION 1 1.4 Organization of this Thesis 9 2 EXPERIMENTAL DATA 10 2.3 Full-scale 4-story steel building 12 v 2.5 Results of experiments 16 SYSTEM IDENTIFICATION FOR STRCUTURAL HEALTH 3 19 MONITORING 3.4 Experimental verification 34 4 MULTI-INPUT MULTI-OUTPUT MODELS 43 4.2 MIMO identification method 45 4.3 Application of MIMO models 46 4.1 Type of models 46 4.2 Application 48 5 CONCLUSION 59 REFERENCES 61 vi LIST OF FIGURES Page Figure 2.1 Shake table set in position 12 Figure 2.2 Full-scale 4-story steel building 13 Figure 2.3 Position of accelerometers on 5 floors of building 14 Figure 2.4 Vibration Periods at Each Shaking 17 Figure 2.5 Collapse of specimen after test by Takatori 100 % 18 Figure 3.1 A dynamic system with input u(t), output y(t) and disturbance e(t) 25 Figure 3.2 General-Linear Model Structure 29 Figure 3.3 AR Model Structure 30 Figure 3.4 ARX Model Structure 31 Figure 3.5 ARMAX Model Structure 32 Figure 3.6 Time history of JR-Takatori earthquake record 35 Figure 3.7 Steel building acceleration responses under JR-Takatori 36 vii Figure 3.8 Acceleration responses of steel building (m/s2) under JR-Takatori 38 5% Figure 3.9 Transfer functions, PSD and coherence 39 Figure 3.10 1st mode Natural Frequency 41 Figure 3.11 Accuracy Fitting between models and measused data 41 Figure 3.12 2nd mode Natural Frequency 42 Figure 4.1 Two SISO models in X and Y directions (Input at E-Defense, output 46 at roof) Figure 4.2 “2 in 2 out” model (Inputs at E-Defense, outputs at roof) 47 Figure 4.3 “4 in 4 out A” model (Inputs at E-Defense, outputs at roof) 47 Figure 4.4 “4 in 4 out B” model (Inputs at E-Defense, outputs at roof) 48 Figure 4.5 1st mode Natural Frequency.

Left: X direction, right: Y direction 49 Figure 4.6 1st mode Natural Frequency 50 Figure 4.7 1st mode Natural Frequency 50 Figure 4.8 2nd mode Natural Frequency 51 Figure 4.9 2nd mode Natural Frequency 51 Figure 4.10 Decrease Natural Frequency-1st mode 52 Figure 4.11 Decrease Natural Frequency-2nd mode 52 Figure 4.12 The 1st mode shape of “2 in 8 out” models 54 viii Figure 4.13 The 1st mode shape of “4 in 16 out A” models 55 Figure 4.14 The 1st mode shape of “4 in 16 out B” models 56 Figure 4.15 Imaginary part of 1st mode shapes 57 Figure 4.16 Damping ratio of 1st mode 57 ix LIST OF TABLES Page Table 2.1 Specification of Shaking System 12 Table 2.2 Three dimensional loading of JR-Takatori 100% 15 Table 2.3 Schedule of experiments 15 Table 2.4 Summary of Response 17 Table 2.5 Damage to the internal non-structural components 18 Table 4.1 1st natural frequency in X and Y directions 49 Table 4.2 1st mode shape in X and Y directions 58 x Chapter 1 Introduction Chapter 1 Introduction 1. Overviews Earthquakes, as the major threat to the human life and economy, have caused many serious damages. That is why it is needed to study the health of buildings after these earthquakes. The structural health monitoring has become a major research focus in the area of structural dynamics.

The interest in the ability to monitor a structure and detect damage at the earliest possible stage is pervasive throughout the civil, mechanical and aerospace engineering communities. Damage or fault detection, as determined by changes in the dynamic properties or response of structures, is a subject that has received considerable attention in the literature. The basic idea is that modal parameters (notably frequencies, mode shapes and modal damping) are functions of the physical properties of the structure (mass, damping and 1 Chapter 1 Introduction stiffness). Therefore, changes in the physical properties will cause changes in the modal properties.

Ideally, a method that can successfully detect damage must be able to address the following criteria: 1. Assess that structural damage has occurred 2. Determine the location of the damage 3. Quantify the severity of the damage 4.

Predict the remaining service life of the damaged structure At present structural damage detection is still in its infancy. In spite of the multitude of techniques that have been developed, not many techniques are able to address all the criteria for a successful damage detection technique. To date, existing damage detection techniques can be categorized into two main areas of study, as follows: 1. Damage detection techniques based on experimental data 2.

Damage detection techniques based on modal data and finite element data Early damage detection techniques involved determining frequency shifts of resonant frequencies of a structure. It was found that changes in the stiffness of a structure often indicated the presence of damage. It was also found that a change in the stiffness of a structure was also linked to changes in natural frequencies of the same structure. One set of natural frequency was measured before the structure was put into service, subsequent natural frequency measurements could be used to determine whether the structure was still sound by comparing the measured frequency with the original natural frequency.

Furthermore, by measuring the natural frequencies of a structure at 2 Chapter 1 Introduction difference stages of its life, it is possible to observe the frequency shifts as the damage propagates through the structure [4]. A similar damage detection technique based on frequency used statistical methods to predict the most likely damage location. It was assumed that sets of frequencies were measured before the structure was put into service, which represented the undamaged structure. From these, frequencies shifts of the first several modes for all possible damage scenarios were calculated mathematically.

Measurements of natural frequencies of the structure at different stages of its life would then be fitted against the postulated damage scenarios. The quality of the fit to each postulated damage scenario indicated the existence of damage. The method proposed by researchers [4] did not give any indication with regards to the accuracy of their predictions. Their method would still locate damage from slight changes in the natural frequencies due to temperature effects or measurement noise, even though no damage actually exists.

Hassiotis developed a method for the estimation of structural damage using measured changes in the natural frequencies [27]. This method proved successful in identifying both the location and the severity of the damage. However, light damage was not identified well because the change in the eigenvalues due to damage was sometimes less than the change due to noise.