The Design, Development, and Implementation of a Structural Dynamic Research Laboratory

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Title:
The Design, Development, and Implementation of a Structural Dynamic Research Laboratory
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english
Creator:
Martinez, Justin
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University of Florida
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Gainesville, Fla.
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Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Civil Engineering, Civil and Coastal Engineering
Committee Chair:
RICE,JENNIFER ANNE
Committee Co-Chair:
CONSOLAZIO,GARY R

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Subjects / Keywords:
dynamics -- excitation -- modal -- models -- structural
Civil and Coastal Engineering -- Dissertations, Academic -- UF
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Civil Engineering thesis, M.S.
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theses   ( marcgt )
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Abstract:
Advancing research in the area of structural dynamics results in safer and more efficient structures. A broad range of approaches to addressing the challenges faced by structures subjected to dynamic loads exist in both analytical and experimental domains. Experimental structural dynamics research enables enhanced understanding of structural and component response to dynamic loading conditions and aids in the creation of accurate structural models. To conduct meaningful and informative structural dynamics research, the appropriate equipment and structural models must be developed and implemented.   The research presented in this thesis is focused on the creation of a comprehensive and versatile structural dynamics laboratory at the University of Florida. This research consists of multiple project phases that include planning, design, and implementation to provide a functional platform to perform structural dynamic experiments. The work is separated into two distinct components that are necessary in a structural dynamic research laboratory: excitation equipment and structural models. Prompt installation of a preassembled uniaxial shake table and long stroke shaker provided experimental potential for small scale research applications. Documentation is also provided for the extensive installation, assembly, and operational process of a larger scale six degree of freedom hydraulic shake table. Structural models included in this work consist of a three dimensional steel truss bridge, a small scale two-dimensional building model, and a larger scale three-dimensional steel building. The development of each of these models had similar project phases, including: design, finite element modeling, fabrication, and dynamic testing to quantify dynamic properties. The final outcome of this research is a laboratory facility with three calibrated structural models representing a number of structural forms with the flexibility for modification to support a variety of experimental investigations and three dynamic excitation instruments with a range of capabilities and configurations to enable testing of many sizes and forms of structural models, components, and sensors.
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In the series University of Florida Digital Collections.
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Includes vita.
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Statement of Responsibility:
by Justin Martinez.
Thesis:
Thesis (M.S.)--University of Florida, 2013.
Local:
Adviser: RICE,JENNIFER ANNE.
Local:
Co-adviser: CONSOLAZIO,GARY R.

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1 THE DESIGN, DEVELOPMENT, AND IMPLEMENTATION OF A STRUCTURAL DYNAMIC RESEARCH LABORATORY By JUSTIN R. MARTINEZ A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMEN TS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2013

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2 2013 Justin R. Martinez

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3 The thesis is dedicated to my parents for their continual love and support throughout my academic career

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4 ACKN OWLEDGMENTS Over the course of this work there were many people who generously devoted their time and hard work to make the completion this project possible so I want to thank everyone who was involved in this project in its entirety. I want to especial ly thank my research advisor Dr. Jennifer Rice for providing me with the opportunity to extend my engineering education while contribut ing to the structural engineering research community at the University of Florida. H er positive guidance and valuable insight throughout the multiple phases of my studies helped me not only succeed in research but also develop as an individual. I also give thanks to Dr. Gary Consolazio for serving as my committee member and for his critical insight on finite element model ing as well as his support to other structural dynamic matters recognize the generous support of two undergraduate research assistants during the course of this work. I give special thanks to Arthriya Sukswan for her critical help with dynamic testing of multiple structural models as well as the assistance with post processing of data sets to expedite result interpretation. Additionally I want to thank Cody Johnson for his support with bridge testing and modifications as well as the co nstruction and assembly of the two dimensional building model. I am truly appreciative of my SIMLab team and their continual feedback on various components of my research. H aving a group of attentive peers to report my research progress provided a valua ble platform to develop my research experience. This work encompassed multiple stages of structural model design and development which required tools and equipment from other lab facilities as well as the

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5 coordination from their respective lab managers. F to thank Dr. Ferarro for introducing me to the Structures Lab and providing me with the proper tools to erect t he steel bridge truss. I am especially grateful for the help from Ryan Makey at the UF Coastal Laboratory with his fabrication an d assembly of the three dimensional building model. I am truly appreciative for the continual support of Scott Bolton at the Powell Structures Laboratory. Scott assisted me in every way possible with the shake table project and made a complex system i nst allation process a n attainable task. Finally, I am so blessed to have such a supportive and loving family who is continually available for encouragement and inspiration. From this emotional support, accomplish ed a variety of life goal s in both academ ic and extracurricular settings the most significant of which is the successful completion of this research

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF FIGURES ................................ ................................ ................................ .......... 9 A BSTRACT ................................ ................................ ................................ ................... 12 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 14 Motivation ................................ ................................ ................................ ............... 15 Content Overv iew ................................ ................................ ................................ ... 18 2 BACKGROUND AND RELATED WORK ................................ ................................ 19 Background ................................ ................................ ................................ ............. 19 Dynamic Fo rces ................................ ................................ ................................ ...... 22 Forced Vibration ................................ ................................ ............................... 2 2 Impact ................................ ................................ ................................ ............... 26 Comparison of Methods ................................ ................................ ................... 27 Structural Models ................................ ................................ ................................ .... 29 Structural Systems ................................ ................................ ........................... 31 Structural Members ................................ ................................ .......................... 32 Full Scale vs. Small Scale ................................ ................................ ................ 32 Similitude ................................ ................................ ................................ .......... 35 Instrumentation ................................ ................................ ................................ 38 Excitation Equipment ................................ ................................ .............................. 41 Specifications and Categories ................................ ................................ .......... 42 Shake Ta bles ................................ ................................ ................................ ... 47 3 EXCITATION EQUIPMENT: MANAGEMENT AND IMPLEMENTATION ............... 53 Small Scale Equipment ................................ ................................ ........................... 53 Large Scale Equipment ................................ ................................ ........................... 57 4 STRUCTURAL MODELS: DESIGN AND TESTING ................................ ............... 66 Bridge Truss ................................ ................................ ................................ ........... 66 Assembly and Modifications ................................ ................................ ............. 68 Finite Element Model ................................ ................................ ........................ 73 Dynamic Testing ................................ ................................ ............................... 76 Test Results ................................ ................................ ................................ ..... 84 2 D Dynamic Building Model ................................ ................................ .................. 97 Design ................................ ................................ ................................ .............. 98

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7 Fabrication ................................ ................................ ................................ ...... 101 Dynamic Testing and Results ................................ ................................ ......... 103 3 D Dynamic Building Model ................................ ................................ ................ 110 Design ................................ ................................ ................................ ............ 111 Finite Element Model ................................ ................................ ...................... 117 Fabrication ................................ ................................ ................................ ...... 121 Dynamic Testing and Results ................................ ................................ ......... 125 5 CONCLUSIONS AND RECCOMMENDATIONS ................................ .................. 139 APPENDIX A DESIGN DRAWINGS ................................ ................................ ........................... 144 B CALCULATIONS ................................ ................................ ................................ .. 145 C USERS MANUALS ................................ ................................ ............................... 146 L IST OF REFERENCES ................................ ................................ ............................. 147 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 151

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8 LIST OF TABLES Table page 2 1 Compared E xcitation Methods ................................ ................................ ............ 27 2 2 Similitude Scale Factors ................................ ................................ ..................... 36 2 3 Sensor Types and Functionality ................................ ................................ ......... 38 2 4 Capability Ranges for Various Shaker Types (De Silva 2007) ........................... 47 2 5 NEES Facilities by Region ................................ ................................ .................. 49 2 6 Largest Shake Table Facilities in the U.S ................................ ........................... 50 2 7 Major Japan Shake Table Facilities ................................ ................................ .... 51 3 1 Highlighted Long Stroke Shaker Spec ifications ................................ .................. 54 3 2 Highlighted Uniaxial Shake Table Specifications ................................ ................ 56 3 3 Highlighted Shake Table Specifications ................................ ............................. 58 4 1 FEM Predicted Natural Frequencies ................................ ................................ ... 75 4 2 FEM vs. Experimental Natural Frequencies ................................ ....................... 95 4 3 Alternate Shaker Systems ................................ ................................ .................. 96 4 4 Predicted Building Natural Frequencies ................................ ........................... 100 4 5 Predicted vs. Experimental Natura l Frequencies ................................ .............. 109 4 6 Predicted, Adjusted and Experimental Frequency Values ................................ 110 4 7 Predicted Natural Frequencies of 3 D Buildin g Model (Weak Axis) .................. 115 4 8 Predicted Natural Frequencies of 3 D Building (Strong Axis) ........................... 116 4 9 6 Story Building Natural Frequen cies ................................ ............................... 131 4 1 0 Predicted vs. Experimental Natural Frequencies ................................ ............. 137

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9 LIST OF FIGURES Figure page 1 1 Building response to earthquake in Chil e ................................ ........................... 16 2 1 Frequency response and corresponding mode shapes ................................ ...... 21 2 2 El Centro Earthquake Time History ................................ ................................ .... 25 2 3 Shaker System ................................ ................................ ................................ ... 28 2 4 Impact Hammer ................................ ................................ ................................ .. 28 2 5 General Structural Model Types ................................ ................................ ......... 30 2 6 Referenced Sensor Layout ................................ ................................ ................. 41 2 7 Perfor mance Curve for Shaker Systems (DeSilva 2007) ................................ .... 43 2 8 Typical Hydraulic Shaker Arrangement ................................ .............................. 44 2 9 Sectional View of Electrodynamic Shaker ................................ ......................... 46 3 1 Long Stroke Shaker ................................ ................................ ............................ 54 3 2 Uniaxial Shake Table ................................ ................................ .......................... 55 3 3 Foundation Construction ................................ ................................ .................... 59 3 4 Shake Table Foundation As Built ................................ ................................ ....... 59 3 5 Shake Table Assembly ................................ ................................ ....................... 60 3 6 Installed Shake Table System ................................ ................................ ............ 61 3 7 Displacement Time History of Input and Output ................................ ................. 63 3 8 Transfer Function of Input and Output ................................ ................................ 63 3 9 Intended Performance Limits (Shore Western Manufacturing, Inc.) ................... 64 4 1 Erected Bridge Model ................................ ................................ ......................... 67 4 2 Bridge Components ................................ ................................ ............................ 68 4 3 Joint Configuration ................................ ................................ .............................. 69 4 4 Bridge Extension ................................ ................................ ................................ 71

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10 4 5 Plan section of the bottom deck of the truss to identify the Modified Connection Blocks ................................ ................................ .............................. 72 4 6 1st & 2nd Horizontal Mode shapes ................................ ................................ ..... 75 4 7 1st & 2nd Vertical Mode shapes ................................ ................................ ......... 75 4 8 Sensor Layout of Short and Long Bridge Compositions ................................ ..... 77 4 9 Horizontal Impact Frequency Response and Mode Shapes ............................... 78 4 10 Band Limited White Noise Frequency Response and Mode Shapes ................. 80 4 11 Sha ker Test Process ................................ ................................ .......................... 81 4 12 APS 113 Performance Curve (APS Dynamics) ................................ .................. 83 4 13 Horizontal Impact Response of Model (1) ................................ .......................... 84 4 14 Horizontal Mode Shape of Model (1) ................................ ................................ .. 85 4 15 Vertical Response from Shaker of Model (1) ................................ ...................... 86 4 16 Vertical Response from Impact of Model (1) ................................ ...................... 86 4 17 Vertical Mode Shape of Model (1) ................................ ................................ ...... 87 4 18 Horizontal Response from Impact of Model (2) ................................ .................. 88 4 19 Estimated Horizontal Modes of Model (2) ................................ ........................... 89 4 20 Vertical Response from Shaker of Model (2) ................................ ...................... 89 4 21 Vertical Response from Impact of Model (2) ................................ ...................... 90 4 22 Estimated Vertical Modes of Model (2) ................................ ............................... 90 4 23 Current Bridge Configuration ................................ ................................ .............. 91 4 24 Horizontal Response from Impact of Model (3) ................................ .................. 92 4 25 Estimated Horizontal Modes of Model (3) ................................ ........................... 92 4 26 Vertical Response from Shaker of Model (3) ................................ ...................... 93 4 27 Vertical Impact Response of Model (3) ................................ ............................... 94 4 28 Estimated Vertical Modes of Model (3) ................................ ............................... 94 4 29 Building Variables ................................ ................................ ............................... 98

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11 4 30 Final 2 D Building Design ................................ ................................ ................. 100 4 31 Erected 2 D Building Model ................................ ................................ .............. 102 4 32 2 D Building Sensor Layout ................................ ................................ .............. 104 4 33 Frequency Response of 2 D Building from Impact ................................ ........... 105 4 34 Frequency Response of 2 D Building ................................ ............................... 107 4 35 Theoretical vs. Experimental Mode Shapes ................................ ..................... 107 4 36 Plan view of Building on Shake Table ................................ .............................. 112 4 37 Final 3 D Building Design ................................ ................................ ................. 116 4 38 Axial Forces and Bending Moments ................................ ................................ 119 4 39 FEM Predicted Modes for the 3 D Building Model ................................ ............ 12 0 4 40 Designed Column ................................ ................................ ............................. 122 4 41 Column Fabric ation Process ................................ ................................ ............. 122 4 42 Joint Interface ................................ ................................ ................................ ... 123 4 43 Erected 3 D Building Model ................................ ................................ .............. 124 4 44 3 D Building Labeling Convention ................................ ................................ .... 126 4 45 3 D Building Sensor Layout ................................ ................................ .............. 127 4 46 Imp act Test Set Up ................................ ................................ ........................... 128 4 47 Weak Axis Frequency Response from Impact ................................ .................. 129 4 48 Strong Axis Frequency Response from Impact ................................ ................ 130 4 49 Torsional Frequency Response from Impact ................................ .................... 131 4 50 Three, Four, and Five Story Building Experimental Results ............................. 132 4 51 Six Story Building Fixed on Shake Table Platform ................................ ........... 134 4 52 X Axis Excitation on 6 Story Building Model ................................ ..................... 135 4 53 Frequency Response of 3 D Building ................................ ............................... 135 4 54 6 Story Building X Axis Mode Shapes ................................ .............................. 136

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12 Abstract of Thesis Presented to the Graduate School of the University of Fl orida in Partial Fulfillment of the Requirements for the Degree of Master of Science THE DESIGN, DEVELOPMENT, AND IMPLEMENTATION OF A STRUCTURAL DYNAMIC RESEARCH LABORATORY By Justin R. Martinez December 2013 Chair: Jennifer Rice Major: Civil Engineering Advancing research in the area of structural dynamics results in safer and more efficient structures. A broad range of approaches to addressing the challenges faced by structures subjected to dynamic loads exist in both analytical and experimental domains. Experimental structural dynamics research enables enhanced understanding of structural and component response to dynamic loading conditions and aids in the creation of accurate structural models. To conduct meaningful and informativ e structural dynamics research, the appropriate equipment and structural models must be developed and implemented. The research presented in this thesis is focused on the creation of a comprehensive and versatile structural dynamics laboratory at the Uni versity of Florida. This research consists of multiple project phases that include planning, design, and implementation to provide a functional platform to perform structural dynamic experiments. The work is separated into two distinct components that ar e necessary in a structural dynamic research laboratory: excitation equipment and structural models. Prompt installation of a preassembled uniaxial shake table and long stroke shaker provided experimental potential for small scale research applications. Documentation is

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13 also provided for the extensive installation, assembly, and operational process of a larger scale six degree of freedom hydraulic shake table. Structural models included in this work consist of a three dimensional steel truss bridge, a sm all scale two dimensional building model, and a larger scale three dimensional steel building. The development of each of these models had similar project phases, including: design, finite element modeling, fabrication, and dynamic testing to quantify dyn amic properties. The final outcome of this research is a laboratory facility with three calibrated structural models representing a number of structural forms with the flexibility for modification to support a variety of experimental investigations and th ree dynamic excitation instruments with a range of capabilities and configurations to enable testing of many sizes and forms of structural models, components, and sensors.

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14 CHAPTER 1 INT RODUCTION Since the early stages of structural design, society has relied heavi ly on an and ultimately assign a safe and dependable design. Over time, increasing demand for taller buildings and longer bridges, while minimizing costs and preserv ing aesthetics, has transformed this valued skill into an essential responsibility. Modern design methods predominantly rely on sophisticated modeling software and advanced analysis techniques, which have been improved through years of experimental testin g and research in many engineering disciplines such as structural dynamics. Structural dynamics can be defined as the behavior of a structure under dynamic fundamental dynamic p roperties. Structures are arbitrarily subjected to dynamic loading as a result of: Pedestrian activity Structural member collapse Oscillating machinery Earthquakes Water impact Wind Explosive blasts Vehicular traffic With progressions in computat ional capabilities and software packages, dynamic analysis methods have shown significant improvement since the 1970s (Tedesco et al. 1999). Despite these advancements, experimental evaluation of structural performance remains a critical area to improve s tructural design and public safety. Research in structural dynamics is growing as new testing capabilities and loading simulations are made available. Although most publicized, earthquake forces are not the only excitations being replicated for dynamic ex periments. Wind engineering

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15 is an a rea in structural dynamics research that has recently improved both its facilities and testing capabilities and studies the s tructural response to wind loading High powered turbines can produce wind loads simulating a h urricane (Shen et al. 2013 & Masters et al. 2008) or tornado (Haan Jr. et al. 2008) event at full scale. Blast or shock load testing is another type of dynamic experiment. With the use of a dynamic drop hammer, the testing facility in Millard et al (201 0) is able to conduct blast simulations and provide appropriate design recommendations of structural members subject to juggernaut type impact. Ongoing research in these fields can help improve the performance of a structure during and after an extreme lo ading condition as well as provide critical information to improve future structural designs. Motivation While loading conditions, the continual revision and expansion of provision s involving design for seismic, wind and other dynamic loads proves there are still many areas of structural design that can be studied and improved. Overstressing and collapse of structures coupled with extensive cracking are both undesirable effects of dynamic loads. Earthquakes in particular, known for unpredictable and forceful behavior, have yielded catastrophic effects to infrastructure across the world such as in Chile and Japan where Richter scale magnitudes reached 9.5 and 9.0, respectively (USGS 2012). Shown in Figure 1 1 is an example of the resulting damage earthquakes can incur.

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16 Figure 1 1 Building response to earthquake in Chil e ( Image taken from: Tweedy, J. (2010, March 1). Chile earthquake: Santiago airport remains closed as tour operators cancel holidays. Mail Online [Photograph]. R etrieved from https://www.dailymail.co.uk Continued research in structural dynamics can lead to new and progressive designs intended to absorb high strain energy levels and ultimately prevent the total collapse of a structure and subsequent loss of life. A structural d ynamic s research facility enables the recreation of multiple types of excitations in a controlled environment and the collection and analysis of resulting structural response data. The complexity of a dynamic research facility can vary sig nificantly as it is directly dependent on a few major factors that will be briefly identified here and discussed in later detail. The most critical component of a structural dynamics research facility is the excitation equipment providing the ability to produce and impose appropriate dynamic loads. This equipment varies in application, system type, and is capable of generating an array of excitations for structural dynamics research. Also of importance in such a research facility are the experimental str uctural models. These full or small scaled structures are valuable in addressing a structural many aspects of structural engineering.

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17 Finally, without the proper data collection devices such as accelerometers, strain response or structure identification. These sensing and data acquisition capabilities can provide fundamental knowled ge of dynamic structural properties such as natural frequencies, mode shapes, and damping ratios that can be used to understand both linear and nonlinear dynamic behavior. With appropriate post processing of data obtained from dynamic experiments, other st ructural dynamic effects can also be determined. For example, experimental dynamic deflections on a scaled model can be obtained to verify serviceability requirements will be met (De Wilde et al. 2010) The E Defense shake table, discussed in Chapter 2, was used by Ji et al. (2011) to investigate the effects of seismic damage on a specimen representative of a high rise building by imposing vibrations, measuring response data, and applying damage diagnosis methods. System identification, a method applied to examine the inherent properties of a structure, was completed in the dynamic tests conducted by Astroza et al. (2013) using various excitation methods such as ambient, impact, and seismic vibrations. Lastly, w ork done in Rice and Spencer ( 2008 ) showed structural response is not the only area of interest in dynamic testing. A test structure with a known response was used in conjunction with wired a ccelerometers as a baseline measurement to develop a new wireless sensor platform that can collect vibratio n and temperature data for structural health monitoring applications. The objective of this work is to produce a structural dynamics research laboratory capable of performing numerous types of dynamic experiments while maintaining accuracy of measured resu lts by assembling the equipment and models in the facility in

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18 a systematic and calibrated approach. This research includes supporting information and detailed documentation on two critical components necessary in a dynamic research lab: (1) excitation equ ipment and (2) structural models. This work will provide a general guideline for future structural engineering researchers focusing on structural dynamic experiments. Content Overview This section outlines the contents of the research presented in this do cument. Chapter 2 provides a general background on structural dynamics and reviews different cases of related work. Chapter 2 is separated into three discrete sections : dynamic forces, structural models, and excitation equipment. Select ed dynamic researc h facilities are compared and discussed with a focus on their experimental equipment and dynamic testing capabilities. Structural models, small and full scale, are presented outlining their functionality, benefits and limitations, and their importance to understanding dynamic response. Additionally, the capabilities and performance expectations of specific categories of shaker device s are compared. Chapter 3 summarizes the installation process, research potential, and specifications of two types of excit devices that require the basic installation and understanding of controls, and larger, component based systems where distinct installation methods are required Chapter 4 outlines three unique structu ral dynamic research models in detail including the preliminary design and analysis, construction, assembly, and experimental suitability. Concluding remarks summarizing the work is presented in Chapter 5, where future work and recommendations are also di scussed.

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19 CHAPTER 2 BACKGROUND AND RELATED WORK To perform dynamic tests with the confidence that data results are valid and reportable, the design goals of a structural dynamics laboratory must be established and satisfied. The beginning of this chapter will prov ide a general background on structural dynamics as a reference. Subsequently, a discussion on a variety of structural models and their significance in structural dynamic applications as well as a comparison of different types of shaker systems is presente d. Background To describe how the mass of a system significantly influences the dynamic response, the following set of equations ( Equation 2 1 to 2 3) are simplified relationships describing a single degree of freedom dynamic system. The natural circular frequency, of a single degree of freedom (DOF) system, measured in radians/second, is a direct function of two system properties; mass ( ) and stiffness ( ) and can be descri bed by the following equation: ( 2 1 ) Shown in Equation 2 2, the inverse of the natural frequency is the natural period ( ), which is the number of seconds it takes for a system to go through one full oscillation. ( 2 2 ) This parameter can also be manipulated to yield another c ommon quantity, the natural frequency ( ), which is the number of cycles a single DOF system oscillates in one second:

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20 ( 2 3 ) To estimate dynamic response, the infinite DOF of a physical structure can be reduced based on how the majority of the mass is distributed within a system. This generally occurs at each floor level of a build ing. The new number of DOFs, n, can be directly applied to a dynamic analysis, describing a structural system of order n. The linear motion of a multiple DOF structure can then be idealized as a lumped mass model and is described by the following equatio n: ( 2 4 ) where , and represent respectively the mass, damping, and st iffness matrices of size n x n. The variables , and represent respectively the acceleration, velocity, displacement and force vectors of order n. In dynamic experiments, is the time varying external force applied to a structure. In the experimental approach presented in this work, vibration forces are applied to a test structure and subsequent modal analysis is condu cted to obtain unique modal frequency value and a mode shape, both of which are influenced by a number of design factors such as mass, stiffness, damping and boundary condit ions. Mode shapes are specific patterns at which a structure will vibrate when exposed to a natural frequency. R esonant vibration occurs when one or more of the modal, or natural frequencies of a structure are excited resulting in the amplification of deflections, stresses, and strains to a level far beyond those caused by static load ing. Incorporating

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21 determine the natural frequencies of a new structural model. A r esonance search is conducted at lower excitation intensity than main tests to sustain minimal damage potential to a test structure. Detailed modal analysis procedures involving matrix manipulation and linear algebra applications have been thoroughly docu mented (Mota 2011, Rezai 1999, and Schwarz & Richardson 1999); however the general concept is briefly described here. Shown in Figure 2 1 is structural response data plotted in the frequency domain. Figure 2 1 Frequency response and corresponding mode shapes A power spectral density (PSD) function is a Fourier transform function which transforms experimental time history response data into the frequency domain to quantify how m uch, and at what frequency, the applied energy is being distributed throughout a system. By applying a structural dominating peaks fall in the frequency domain plot. Using estimated natural frequency values and analyzing the phase relationship between data collected from selected sensors, the identification of corresponding structural mode shapes can be plotted

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22 ( Figure 2 1 ). For the example shown Figure 2 1 for Mode 1, all sensors are estimated to be in phase with one another and displace in the same direction when excited at a frequency of 3.85Hz. Many other modal analysis methods have been de veloped and are used in structural dynamic research for detailed structural identification applications. Each has their own benefits and limitations depending on the structural model, loading conditions and sensor capabilities. The modal identification p resented in this work mainly relies on the peak picking method. However, other means for system identification are available such as the Eigensystem realization algorithm (Qin et al. 2001). Dynamic Forces mic effects, methodologies for dynamic testing must be developed. Attempts to capture full scale, in service structural response data during a seismic loading event may be achieved, however it is challenging, if not impossible, to predict when this arbitr ary load will occur. Simulation of dynamic loading conditions on a structure within a controlled laboratory setting is a convenient advantage of a dynamic research facility, allowing for complete control of when and how often a test specimen will experien ce a loading event. This ability to generate dynamic loading scenarios can vary depending on the scope of structural dynamic research and the limitations of shaking equipment. Forced V ibration The forced vibration testing methods identified in this sect ion can be applied to a system by use of an excitation device. These versatile pieces of excitation equipment, explained in detail in the last section of this chapter, have multiple modes of operation and have the potential to input energy into a structur al system in a variety of different

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23 ways. Highlighted in this section are three types of signals for which forced vibration can be applied: (1) known harmonic signals intended to excite a discrete frequency, (2) stochastically generated signals where the applied motion is defined by its statistics, and (3) signals representing physical phenomena such as an earthquake. Generated signals where input energy is artificially manipulated to allow for complete control of testing parameters is a common forced vibration testing method for the initial stages of a testing program. Here input excitations can be applied at known energy levels and frequencies as a conservative approach to dynamically characterize a system. The primary motivation for this type of fo rced vibration test is that if loads applied to a test structure are known and the response can be monitored and recorded, then structural dynamic properties are able to be estimated. Simple periodic wave motions such as sine, square, saw tooth and triang le, are implemented and can be modified or amplified accordingly to fit the test application. A well documented and widely used resonance search technique involving a more complex version of a sine generates a periodic sine wave motion at an initial frequency value that increases incrementally to an upper frequency limit and can vary as a function of sweep velocity. This is applied so each natural frequency of a structure in the selected interval wi ll be excited causing resonance and the visual identification of resonant frequencies (Gloth & Sinapius 2004). Shield et al. (2001) applied a sine sweep to identify system characteristics of a large scale single degree of freedom system before submitting t he test structure to seismic simulations.

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24 In randomly generated signals, the only parameters under the control of a testing engineer are the desired statistics of the signal, resulting in an anticipated root mean square of the amplitude of the signal. Thi s type of testing is stochastic and is more representative of practical loading conditions such as vehicular traffic on a bridge, wind forces on a building or other projected service loads. Therefore, this method is proven as an attractive avenue for in s ervice time vibration monitoring of real structures under normal service loads (Salawu and Williams 1993) and allows a test structure to be excited with energy at all levels within a specified frequency range. This interval can be created with a wide rang e of low and high cutoff off frequencies, however applying this signal onto a structure largely depends on the capabilities of the excitation equipment. One or more shakers are used for excitation and are oriented in a variety of ways, both depending on si ze and complexity of a test object and the vibration modes of interest. In earthquake prone regions, a fundamental concern of structural engineers is the behavior of structures exposed to earthquake induced motion. As a result, one of the most important a pplications of structural dynamic studies is analyzing the response of structures to ground shaking caused by an earthquake. In this case, forced vibration is not used for finding the resonant frequencies of a structure; instead they are vital to the appl Earthquake time histories are actual records of past earthquakes that have been recorded using a strong motion accelerograph to capture motion in the x y and z directions. Shown in Figure 2 2 is an acceleration time record of the El Centro earthquake in 1940.

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25 Figure 2 2 El Centro Earthquake Time History Resulting ground accelerations can be incorpo rated to the equation of motion as an applied or external force; shown below: ( 2 5 ) This is the equation of motion of a structure subjected to ground acceleration on independent parameters such as environmental conditions, proximity to fault lines, and seismic wave patterns, each earthquake possesses thumbprint li ke qualities that result in no two records being the same. As such, the comparison of unique earthquake characteristics from multiple time histories has led to substantial findings which classify ground motion into four basic types (Newmark and Rosenbluet h 1971); single shock, moderately long and extremely irregular motion, long ground motion with distinct dominant periods of vibration, and large scale permanent ground deformation. Three earthquake characteristics established from basic ground motion clas sifications and found to significantly influence structural response are identified as peak ground motion, duration of motion, and frequency content. Peak ground motion transformed to peak

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26 ground acceleration (PGA) can be used in dynamic experiments for t he scaling and application of acceleration time histories on structural dynamic models. Impact Impulsive excitation methods can be adopted for dynamic experiments relying solely on free vibration coupled with initial displacement or velocity of a struc ture. The basic concept involves the use of an impact (short duration force) to apply energy to a structure in order to excite the mass and cause the system to accelerate. Accelerations are then measured with accelerometers that are strategically placed at particular degrees of freedom. This can be a quick, simple and low cost approach for finding the modal properties of a test structure, however like most methods, input energy limitations are introduced when larger scale test specimens are of interest. Forces can be generated by an impact hammer either from manual arm motion or a drop hammer apparatus. Hammer size variations depend on the both the type and scale of a test specimen and must provide appropriate impact force to generate measurable vibratio n levels after impact. Lynch (2006) used a modal hammer to impose energy on a full scale bridge to verify the functionality of a new wireless sensor. The hammer size and location of impact yielded reasonably high acceleration responses that were able to be recorded and post processed to compare experimental and known natural frequency data. Although most simple, the impact testing method is highly susceptible to input noise due to the short impact period when force is applied. Also, test procedures must be carefully followed as the human error element is nearly unavoidable. For example, not allowing the impacted structure to come to a rest in between hammer blows could n

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27 requiring a retest. Because of these test flaws, it is essential that a modal hammer is equipped with a load cell at the impact tip; this facilitates direct measurement of imposed force to assist in system post data processing and confirm tests were conducted with minimal error. Comparison of Methods As presented in this section, there are a variety of methods for imposing excitation on a structure. Each method has idea l applications and drawbacks. Compared in Table 2 1 are a few testing characteristics of the two excitation methods discussed in this section. Table 2 1 Compared Excitation Method s Testing Characteristics Excitation Method Forced Vibration Impact Steady State Sine Random Hammer Signal to Noise Ratio Very High Fair Not good Test time Very Long Good Very Good Controlled Frequency Yes Yes No Controlled Amplitude Yes N o No Signal to noise ratio, test time, and the ability to control input frequency and signal amplitude are all factors that must be considered when designing a structural dynamic testing program. With varied differences in testing capabilities, an exper iment can be conducted with the most suitable excitation method. Reynolds and Pavic (2000) compares the functionality of impact hammer and mechanical shaker excitation methods for modal testing of a full scale building floor.

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28 Figure 2 3 and Figure 2 4 5803A) compared in this study. Figure 2 3 Shaker System ( Image taken from: APS Dynamics. n.d. APS 113 Electro seis [Photograph]. Retrieved from http://www.apsdynamics.com October 1,2013. ) Figure 2 4 Impact Hammer (Image taken from: Dytran Instruments, Inc. n.d. Impulse Hammers [Photograph]. Retrieved from http://www.dytran.com October 1, 2013.) Four key factors used for practical comparison of a widely used sh aker system and impact hammer are listed below: 1. Initial equipment cost 2. Time and resources needed to develop the test system 3. Ease of set up and implementation 4. Quality of measured data

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29 Evidence from this comparative study found that the cost of implemen ting a modal test system for examining the vibration behavior of a building floor is ten times greater for a shaker excitation system as compared to hammer impact excitation. This is due to the coupling of the required power amplifier, reaction mass assem bly, digital signal generator and accessories for a shaker system. Furthermore, development time and time demands needed to understand, generate, process, and amplify a give n signal. Conversely, the shaker system proved much more reliable when comparing data quality due to the control of input parameters and ability to strategically manipulate a motion or range of signal frequencies. For research applications where expenses are not always a limiting factor and quality of data prevails as the most critical component to an experiment, it is suggested that a shaker excitation system be used. Specifically, electrodynamic shaker systems are one of three shaker systems covered in the only a quick baseline test of a structure is needed then implementing an impact hammer proves to be the best value of money (Reynolds and Pavic 2000). Structural Models Experimental testing of structural models in a dynamic research facility provides a wealth of information to improve understanding of structural dynamic behavior. There are numerous advantages these models can provide that continually prove their v alue in dynamic research and engineering industry. A few of these benefits include: The validation or improvement of structural design methods, procedures, or new structural systems that can be considered for future governing code revisions or practice te chniques

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30 The accurate correlation between finite element predictions and actual system response The development of new instrumentation devices such as displacement or acceleration sensors With a versatile range of applications, structural models range in s ize, type and system complexity. Considering that dynamic testing facilities have limitations on equipment and power supply options, it is common to find simplified experimental structures using lumped mass models that consist of smaller scales and point mass distributions. These simplifications provide a functional structural model for which to identify dynamic characteristics and preserve the dynamic response of a full scale structure. With the increase in excitation equipment system capacity, structur al models can be designed on a large or even full scale to be geometrically representative of a real structure. Illustrated in Figure 2 5 are three main categories for which structural models can be applied to structural dynamic applications. This section will focus on two of these categories, highlighting previous related applications and significance of both structural systems and structural members. Figure 2 5 General Struct ural Model Types

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31 S tructural S ystems The design and development of an experimental structure that models a parent structural system can be an effective tool in a testing program to predict the response to dynamic loading. In both small and full scale appli cations, these systems can incorporate a collection of beams, columns, slabs, or connection types to collectively represent a real building, bridge or other structural system. For instance, a full scale, light frame wood building was used to measure the r esponse due to a seismic load applied by a shake table (Van de Lindt et al. 2010). This model allowed for the measurement of interstory drift as well as shear wall deformations at multiple excitation levels in order to verify the accuracy of predictions m ade from a SAPWood finite element model. As previously mentioned, decisions on how large or small a test structure is to be constraints. Rather than constructing an entire building model, Dolce et al. (2005) implemented a single building section model to estimate a full system response to dynamic loads. A single 1/3 scale reinforced concrete frame was used in conjunction with a shake table to test the effects of vari ous energy dissipating braces in order to enhance seismic performance. The 1/3 scale was selected to allow for full exploitation of the dimensions and payload capacity of the shake table system. Directly relating to wind loads, a similar sectional approa ch was used in ( Hanson et al. 2000) where a bridge girder section was subject to wind tunnel tests to predict the response of a parent bridge to wind force and direction variances

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32 Structural M embers Rather than studying a global system response of a struc ture, isolated structural members can be subjected to dynamic testing to analyze the behavior of individual beams, columns, or walls. Designing a test program to study the performance of a specific area of a structural system where weaknesses have been kno wn to occur not only isolates a specific test area of interest, but also significantly decreases the material and fabrication cost of a test specimen as well as overall complexity of an experiment. Often, the introduction of a new structural product to the design industry requires research aimed at providing an understanding of how it will respond to specific loading scenarios. By designing a dynamic fatigue test at a simpler structural member level, Zaghi et al. (2012) was able to investigate the increase d ductility potential of a fiber reinforced polymer (FRP) concrete column under dynamic loading conditions. Quicker fabrication time of a structural member, as compared to an entire structural system, can result in prompt recommendations such as the viabi lity of FRP for retrofit applications. Similarly, structural member test specimens can be used to validate or improve design methods and capacities anticipated by code procedures. Testing of an unreinforced retaining wall by Ling et al. (2005), found the lateral load capacities predicted by a conventional design method could be increased. Full Scale vs. Small Scale Structural models are versatile tools used in multiple structural dynamic research areas; however, model size and experimental application s are often limited to the capabilities provided by the laboratory. As a result, determining an appropriate structural model size becomes an obstacle as there are many benefits and drawbacks to having a model at opposite ends of the spectrum.

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33 Full scale models replicate the material and makeup of a real structure or structural member and are as close to their full size and boundary conditions as possible. Kasai et al. (2010) used a full scale, 15.8 meter, five story steel building as a test specimen on the E Defense shake table in Japan. Focusing on structural component development, the performance of four types of dampers were monitored and evaluated by imposing full scale earthquake forces to the structure. Small scale models, idealized structural s ystems on a much smaller scale, can be used in testing environments where full scale testing is not capable. Work done by Wu and Samali (2002) involved a five story steel frame model used as a benchmark structure to allow researchers the ability to test c ontrol algorithms. Standing at a maximum height of three meters, this test specimen offers the flexibility needed to model and test various building configurations. Replaceable beam column connectors allow for connections to be interchanged from pin to f ixed conditions. By adding plates or point masses at pre designated locations, the total mass of the model can range between one and three tons. Additionally, an innovative joint design facilitates floor height modification for each of the five stories. Both small and full scale models have proven their importance to structural dynamic research on many occasions and are evaluated below using similar key points for comparison as Reynolds and Pavic (2000) identified earlier in the chapter. Cost time and re sources. When evaluating small and large scale models, it is apparent that larger models almost always result in increased expenses. Labor costs become a significant factor in a large scale project budget due to an overall increase in fabrication time, p rocesses, and planning in the design and construction of a model.

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34 Small scale applications serve as a simplified approach to dynamic testing with very few components included in design. Structural members tend to be symmetrical in shape and dimensioned f or ease of construction which directly reduces the model material and fabrication cost. With the lower cost and prompt fabrication time of these small scale models, sacrificing a test specimen to obtain critical data on a particular limit state can also b e an allowable option and unique advantage. Aside from the models themselves, the excitation equipment needed to reproduce the dynamic loads of interest add to the overall expense of a test setup. Shake table systems for example, require the installation of an adequately sized power supply and a designated facility to contain experiments and protect the functionality of the equipment. With the demands of a full scale experiment, associated costs can grow to hundreds of millions of dollars (Kallinikidou 2 004). As a result, there are only a select few testing facilities around the nation and worldwide capable of performing these types of experiments, most of which have been adopted into the Network for Earthquake Engineering Simulation (NEES) program which is discussed in detail in the next section Quality of measured data The design of any structural model, numerical or experimental, incorporates a number of critical assumptions and appropriate simplifications. Parameters such as boundary conditions, mat erial properties, and applied loads are all areas of uncertainty in the design of these research tools. In full scale models, these assumptions are minimized because of the replicated design and construction of a real structural system or member. Therefo re, full scale models can be a valuable dynamic testing tool when a structural system of interest is complex and if difficulty arises when trying to rely solely on small scale testing or computer models to

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35 predict system response (Salawu and Williams 1993) For example, if a concrete building model is used for dynamic testing, the yield capacity of the steel reinforcement, the compressive strength of concrete, and the construction phases can be practically conserved. By replicating these processes, the da ta obtained from such experiments is expected to closely represent the true response of the real structure. Although it has been proven that reliable conclusions can be drawn from small scale structural model testing (Abrams 1992), data validity is largel y influenced by scaling effects that may alter results or make data interpretation a less direct procedure. Scaling factors can be accepted approach to the design of test s pecimens. Further discussion on the effects of Structural dynamic research interests range in diversity and can include many types of experimental set ups of shake r and structural model combinations. Critical data about a structure can be obtained from both small and full scale systems. Where funding and space limitations are no concern, full scale testing provides the most accurate test conditions. However, the ability to carry out full scale tests is not practical in most cases; and small and large scale structural model variations have been widely accepted in most dynamic testing facilities. Similitude Due to restrictions on space and equipment as well as econ omic constraints most experiments do not utilize full scale models Instead structural members, material, connections, and loads are scaled down to a practical level that can be functional in a laboratory setting. This scaling, or s imilitude is introd uced to structural

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36 dynamic testing as a systematic approach to scale a model and its applied loads to create a test set up that closely resembles a full scale structure. The details of s imilitude theory may be found in literature (eg: Rezai 1999 and Mota 2 011) ; however a general description is briefly provided here The f undamental physical measures most commonly used in engineering applications are mass (M), force (F), length (L), and time (T). These basic quantities are combined to yield more detailed u nits of measure such as acceleration or pressure. Using dimensional analysis techniques (Moncarz & Krawinkler, 1981) relationships between a full scale system and its model can be made and appropriate s caling values assigned. In dynamic similitude, it is common to use length (L), modulus of elasticity (E), and acceleration due to gravity (g) as the fundamental units of measure to derive scaling relationships. In experiments involving reduced scale models in which length is scaled, force and time need t o be scaled as well to simulate an equivalent loading condition on the scaled structure. Some common and established relationships (Krawinkler 1988) used in the design of scaled models are listed in Table 2 2 and explained below: Table 2 2 Similitude Scale Factors Physical Quantity Scale Factor Length 1/L r Time r Frequency r Force 1/L r 2 Scaling factors are typically expressed as ratios and relate a unit of measurement from the full scale (L p ) to the model (L r ). For example, a quarter scale model (L p /L r = ) will

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37 have a length scale factor of L r = 4 and denotes one unit of length of the prototype corresponds to four units of length for the smaller model. To apply an earthqu ake time history to this model, the time scale is scaled by 1 r r the frequency content will be increased, and this is illustrated by the scales presented above. Despite some early critics regardin g the accuracy of these scaling factors, the reliability of experimental results of one half to one third scale models have been generally accepted by many researchers since the 1980 s (Rezai 1999). Applying similitude relationships can vary depending on the experimental data of interest. For instance, if dynamic response of a small scale model was to be measured, then the appropriate mass distribution and boundary conditions must be applied to conserve the dynamic similitude of the full scale parent stru cture. In other cases, model designs can incorporate intricate detail to study localized strength limit states Lu et al. (2008) used a detailed similitude procedure to scale down a 33 story reinforced concrete building to a 1/25 building model. In this i nstance, fine aggregate concrete reinforced with thin steel wires were used in an effort to maintain a legitimate level of material similitude when scaling a reinforced concrete prototype. The fine aggregate, 1.5mm in size, and reinforcement with minimal diameter, were chosen to match dictated similitude requirements as best as possible. Years following, a full scale dynamic test was completed on the in service structure upon its erection using ambient wind loads and the primary excitation method. It was concluded that the previous shake table tests performed at a 1/25 scale were reasonable and similar small scale tests can be used in the future to help meet design practice needs.

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38 In contrast to the work completed by Lu et al. (2008), there are simpler structural models that do not preserve intricate component detail use to study global dynamic response. More idealized systems like a small scale steel test structure representative of a mid rise steel building (Chen & Chen 2002 and Wu & Zamali 2002) can be just as informative with the proper post processing and modal analysis of response data. Instrumentation The general components that make up a dynamic research facility have been identified and include the ability to generate dynamic loads and the impl ementation of test structures. In addition to these components a test facility must have the ability to measure the input excitation and a range of structural model responses by the use of sensing devices. Essential to structural dynamic research, sensor s provide an avenue for researchers to collect and analyze experimental data and gain a thorough understanding of a structural system or material type. Sensor types. Sensing devices can reside in one of two groups, active, where external electrical energy is needed for the device to function or passive, where self contained energy sources are present and no external activation is required (De Silva 2007). Table 2 2 lists some of the sensor types used in structural dynamic applica tions along with their functionality. Table 2 3 Sensor Types and Functionality Sensors Measurement Strain Gauges Material Strain Accelerometers Accelerations Tachometer Velocity LVDT Displacement Str ing Potentiometer Displacement Load Cell Force Barometer Pressure

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39 There are many different types of sensors whose application is directly influenced by the desired data of interest. An instrumentation device passes through two stages while makin g a measurement; first the physical variable being measured is sensed and converted to an analog, then the signal is converted into a form (i.e. digitized) that is suitable for a signal conditioning and processing. In some dynamic experiments, velocity a nd displacement are both determined by directly integrating acceleration response data. In instances where noise may lead to flawed results, it is good practice to use separate sensors to measure velocity and displacement directly and for cleaner data to be obtained. It is not common, however, to differentiate a displacement measurement to determine velocity or acceleration due to the amplification of any noise present in response data. Of the sensor types listed above, two will be briefly identified: ac celerometers and strain gauges. Accelerometers are common sensing devices that measure the acceleration of an object. A variety of sensing mechanisms are utilized in accelerometers, with each suited to specific measurement condition. Some accelerometer s are not capable of measuring very low frequency or DC vibrations, while others possess high sensitivity for measuring very low amplitude vibrations. Trade offs in cost, physical size, measurement bandwidth, sensitivity, and noise levels must be consider ed when selecting the most appropriate sensor for the experimental application. When material strain relationships are an area of focus, strain gauge variations are a widely adopted and an inexpensive sensing device. By measuring strain, engineers are a ble to quantify the magnitude of tension or compression a member is experiencing and resulting studies on material fatigue or deformation can be conducted.

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40 Strain gauge devices function by measuring the change in electrical resistance across the strain ga uges as it undergoes a change in length. Strain gauge selection is based on the material being tested and whether the gauges will be surface mounted or principal stress i nformation. The primary challenges associated with the use of strain gauges are their potential susceptibility to measurement noise and their measurement variability in changing temperatures. These factors must be considered and mitigated before and duri ng testing. Sensor placement. Sensor placement on an experimental model depends on numerous factors including: limitations in the number of available sensors/data acquisition channels, the type of analysis to be conducted (static or dynamic), and the exp ected response of the structure (elastic or inelastic). As a result, strategic sensor placement is required to allow for appropriate data to be collected while making efficient use of sensors devices Figure 2 6 is an example s ensor layout on a section of a small scale steel structure with steel plate shear walls subjected to earthquake vibrations by a shake table (Rezai 1999). A total of five separate sensor types were deployed on the test structure based on expected stress co ncentrations, available data acquisition channels, and nodal locations. Accelerometers were placed at each story level, or nodal location, to measure absolute accelerations with an additional four at the top floor to monitor the torsional response of the structure. In addition to acceleration, string pot displacement transducers were installed at each floor level to capture in plane displacement data. Strain gauge locations were selected where large deformations were expected to occur.

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41 This is illustrat ed by the higher concentration of strain gauges coupled with the additional string pots toward the bottom of the structure where stresses are greatest. Figure 2 6 Referenced Sensor Layout Excitation Equipme nt The significance of vibration testing in structural dynamics is evident as there are numerous benefits and informative conclusions that can be drawn and applied to structural engineering applications. This section describes shaker systems and their fun ctionality in more detail to provide a baseline of information of shaker categories and components as they pertain to structural dynamic research.

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42 Specifications and Categories A variety of shakers are available in multiple areas of engineering with differ ent capabilities and principles of operation. Before developing a testing program, the appropriate selection of shaker device must be made. Shakers can be evaluated by three significant performance specifications; force, power, and stroke ratings. The force rating is the maximum force that could be applied by the shaker to a test object with a mass within the design load of the shaker. Maximum force is usually achieved at higher frequencies in the operating frequency range of the shaker. Similar to fo rce capabilities, the power rating is most useful in the moderate to the high frequency excitations. The stroke rating quantifies the maximum displacement a shaker is capable of moving while exciting an object within the payload limit and is only achieved at very low frequencies. It is important to understand the relationship of these specifications and their limitations. It is not practical to operate a shaker at its maximum stroke and acceleration ratings simultaneously since each of these parameters p eak at different frequency ranges. Figure 2 7 shows a performance curve illustrating a function of this relationship and demonstrates the velocity performance limits as a function of strok e, velocity, and acceleration. Plotted i n the frequency domain, this curve presents the limiting specifica tions of a shaker system and can vary depending on the system specifications. Ideally, a performance curve looks like the diagram in Figure 2 7 and has a linear di splacement amplitude region, a constant velocity amplitude region, and a linear acceleration amplitude region for low, intermediate, and high frequencies, respectively. Additionally, as the mass increases the acceleration and velocity performance decrease s and becomes less able to function at full capacity. It is also

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43 important to realize from this curve that the stroke, velocity, and acceleration ratings cannot be simultaneously achieved. Figure 2 7 Perfo rmance Curve for Shaker Systems (DeSilva 2007) In structural dynamic applications, as well as other engineering disciplines, there are three basic types of shakers widely used: hydraulic, inertial, and electromagnetic systems. In this section the componen ts, processes, and capabilities of each system type are presented. Hydraulic shakers. Hydraulic shaker systems predominantly depend on the flow of hydraulic fluid to facilitate motion. The main system components consist of a piston cylinder actuator, serv o valve, fluid pump, and a driving electric motor or power supply. Figure 2 8 identifies the basic components of a typical hydraulic shaker.

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44 Figure 2 8 Typical Hydraulic Shake r Arrangement ( adapted from De Silva, C. (2007). Vibration, Monitoring, Testing, and Instrumentation. Boca Raton, Florida: Taylor & Fransis Group ) The general process of a hydraulic system involves the pumping of pressurized hydraulic oil (pressure ~ 4000p si) into the cylindrical actuator through a servo valve by means of a pump that is driven by an electric motor (power ~ 150HP). The servo valve regulates the flow rate (~ 100gal/min) of the hydraulic oil entering the actuator which directly controls the r esulting piston motion. A typical servo valve consists of a two stage spool valve which provides adequate pressure differential and a controlled flow to the actuator, which sets it in motion. Hydraulic shakers provide high operation flexibility during th e test and are capable of producing variable force, constant force and wide random input testing. One drawback to hydraulic systems is the inability to reproduce accurate excitations at high frequency levels due to the presence of distortion that are intr oduced in this frequency range. These systems can be applied to heavy load testing with larger scale structural models and can include industrial and civil engineering applications due to their dependable low to intermediate frequency operation potential (DeSilva 2007).

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45 Inertial shakers. In inertial shakers, the force that causes the shaker motion is generated by inertial forces or accelerating masses, a fundamental principle that has been integrated in civil engineering dynamic testing since the 1930s. C omponents consist of two counter rotating masses (rods) and a variable speed electric motor with a connected gear mechanism. The two equal masses rotate at an identical angular speed and along the same radius of motion but in opposite directions. A resul tant sinusoidal force in the direction of symmetry of the two rotating arms is then produced. Each mass has a series of slots where mass can be added and various force magnitudes can be achieved. The masses are driven by an electric motor through a gear mechanism that typically provides several speed ratios that depend on the desired test frequency range. These shaker types are capable of reproducing intermediate excitation forces which are limited by the strength of the carriage frame in which it is emb edded. Excitation motions are exclusively sinusoidal and forces magnitudes are directly proportional to the square of the excitation frequency. Inertial disadvantages include the testing of complex/random excitations and constant force generation along w ith the inability to vary force amplitude. Despite this limitation, this shaker type is quite effective for sine dwell and sine sweep test as it provides a sinusoidal excitation with virtually no distortion and with the addition of a variable speed motor, frequency and amplitude levels can be preset to incrementally vary during a test (DeSilva 2007). Electromagnetic shakers. Figure 2 9 is a schematic of an electromagnetic shaker arrangement with followed by supporting context.

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46 Figure 2 9 Sectional View of Electrodynamic Shaker ( adapted from De Silva, C. (2007). Vibration, Monitoring, Testing, and Instrumentation. Boca Raton, Florida: Taylor & Fransis Group ) capacity of an electric motor and the fundamental forces produced when an electrical excitation signal is passed through a moving coil placed in a magnetic field. There are a variety of com plex components included in an electromagnetic shaker system; as a result these shakers are typically prefabricated by a supplier for immediate use and require minimal set up. The theory on which this shaker type is based is briefly explained. A stationa ry electromagnet consisting of field coils that are wound on a ferromagnetic base generates a steady magnetic field. When the electrical signal is passed through this coil, the shaker head, which is supported on flexure mounts and has its own concentrical ly wound coil, is set in motion. The benefits of this system include high frequency range of operation, flexibi lity of operation and a high lev el of

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47 accuracy of the generated motion. To properly utilize the advantages of an electromagnetic shaker, a ppli cations are typically limited to smaller scale test specimens. Shaker specifications and types are organized in Table 2 4 for a comprehensive review of this section (DeSilva 2007). Table 2 4 Capability Ranges for Various Shaker Types (De Silva 2007) Shaker Type Typical Operational Capabilities Frequency Max. Disp. (Stroke) Max.Vel. Max. Accel. Max Force Hydraulic Low (0.1 500 Hz) High (20 in; 50 cm) Intermediate (50 in/sec; 125 cm/sec) Intermediate (20 g) High (100,000 lbf; 450,000 N) Inertial Intermediate (2 50 Hz) Low (1 in; 2.5 cm) Intermediate (50 in/sec; 125 cm/sec) Intermediate (20 g) Intermediate (1,000 lbf; 4,500 N) Electromagnetic High (2 10,000 Hz) Low (1 in; 2.5 cm) Intermediate (50 in/sec; 125 cm/sec) High (100 g) Low to intermediate (450 lbf; 2,000 N) Shake Tables Shake tables were first used for simulating seismic loads on structures in the 1940s; and after proving to be the most realistic and cos t effective avenue to reproduce ground excitation, their use has been widespread since the 1960s (Williams and Blakeborough 2001). The process of utilizing a shake table for dynamic testing is relatively straightforward: a structural model is positioned o n a stiff platform or table, which is shaken to apply the appropriate base motion to the model. In seismic studies, excitations can be applied to simulate a particular earthquake record. This testing capability is a major advantage of shake table applica tions since the building response is a result of base motion as opposed to an attached loading mechanism, thus providing Assuming ground excitation

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48 can be accurately applied, inertial forces a re then generated throughout the structure and the system response can be monitored. The main components of a shake table system consist of a table or platform to mount a test specimen and the connecting actuators responsible for its excitation. The tabl e must be adequately rigid so that it does not resonate during a test and it transmits the true input motion to the structure with minimal deviation from extraneous energy dissipation. A variety of table platform designs have been implemented. UC San Die go has a 2.2 m shake table consisting of a steel plate surrounded by a torsional stiff shell and internal stiffening honeycomb (Van de Einde 2004). An alternate table design can be found at UC Berkeley where a shake table platform consists of a ribbed, po st tensioned concrete slab (Blakeborough et al. 1986). In order to drive the large mass of the shake table coupled with the test specimen at the required rate, high capacity servo hydraulic equipment is typically implemented. In such a hydraulic system, the velocity content of the earthquake records are usually the governing factor of a simulation since this is directly related to the oil flow rate regulated by the pumping system and servo valves. For standardized table systems hydraulic actuators and t he associated servo valves must fall well within the range of current technological capabilities. In 1999, the National Science Foundation (NSF) launched the George E. Brown, Jr. Network for Earthquake Engineering Simulation (NEES), a program to develop experimental and computational facilities for earthquake engineering research. By establishing this research conglomerate, earthquake engineering studies became a

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49 collaborative effort among the academic community rather than a collection of individual pro jects. The NEES network features 14 laboratories distributed across the nation and as listed in Table 2 5 Table 2 5 NEES Facilities by Region West Coast Central East Coast Universi ty of California, Santa Barbara University of Texas, Austin University at Buffalo, SUNY University of California, Davis University of Minnesota Cornell University University of California, Los Angeles University of Illinois, Urbana Champaign Lehigh Univ ersity University of California, San Diego Rensselaer Polytechnic Institute University of California, Berkeley University of Nevada, Reno Oregon State University With this collective group of researchers, experimental capacities have no t only grown to include large scale shake tables, but tsunami wave basins, geotechnical centrifuges, and field experiments/monitoring as well (NEES 2007). Shake tables systems come in a wide variety of sizes and configurations. In the United States the la rgest shake table systems are at a few select locations; t he University of California at Berkeley (20ft x 20ft 6DOF ), the State University of New York at Buffalo (12ft x 12 ft 5DOF ), and the University of Illinois at Urbana Champaign (12ft x 12ft 1DOF ) A review of these and other U.S. shake tabl e testing facilities is give n in Table 2 6 (Nigbor and Kallinikidou 2004).

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50 Table 2 6 Largest Shake Table Facilities in the U.S Institut ion State Payload (metric ton) Size (mm) DOF Freq. Range (Hz) Max Stroke (m) Max Velocity (m/s) University of California San Diego California 2000 7.612.2 4 0 33 0.75 1.8 EERC, University of California Berkeley California 45.36 6.16.1 6 0 15 0.127 0.7 62 State University of New York at Buffalo New York 50 3.63.6 5 0.1 50 0.15 1.25 University of Nevada at Reno Nevada 45 4.34.5 2 0.1 30 0.3 1 U.S. Army, Civil Engineering Research Lab, Illinois Illinois 45.36 3.63.6 3 0.1 60 0.3 1.3 Wyle Alabama 27 6.16.1 2 0 100 0.152 0.89 University of Illinois at Urbana Champaign Illinois 4.5 3.73.7 1 0.1 50 0.05 0.381 Unique to other shake table facilities, the University California at San Diego recently constructed the first outdoor and largest shake table facility in the U.S. Measuring 25ft x 40ft with a vertical payload of 20 MN, this Large High Performance Outdoor Shake Table (LHPOST) significantly improves the capabilities of the NEES research program. Previously identified limitations of existing shak e table systems are payload, hydraulic power supply, and stroke but also include overhead room to construct and test a tall structural system. The LHPOST is designed to nullify the vertical space constraints and significantly increase payload capacities p roviding a new avenue for full scale model testing (Van Den Einde et al. 2004).

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51 Despite the local significa nce and payload capacities, domestic shake tables identified in Table 2 6 are still considered medium siz ed tables compared to those overseas, with the exception of the recently constructed LHPOST. Typically, specimen size limitations for smaller sized shake tables can be viewed as a disadvantage due to problems associated with scaling of nonlinear dynamic r esponses. The exception is in Japan where some very large and expensive facilities have been constructed and dynamic testing can be conducted on full scale structures. In particular is the E Defense shake table which has three translational and three ro tational degrees of freedom in the X Y and Z axis and measures 20m x 15m in size. With a total of 24 actuators (five units in the X and Y axis), this table system is the largest and most complex system in the world. Recent ex periments conducted include a long period seismic response of a large scale high rise building (Chung et al. 2010) and earthquake effects on a full scale, six story, light frame wood building (van de Lindt 2010). Shown in Table 2 7 are some of the shake table facilities located in Japan identifying their size and capacities. Table 2 7 Major Japan Shake Table Facilities Institution Payload (ton) Size (mm) DOF Freq. R ange (Hz) Max Stroke (m) Max Velocity (m/s) NIED E Defense 1200 2015 6 0 50 1 2 National Research Institute for Earth Science and Disaster Prevention 1088 2015 3 0 15 1 2 Nuclear Power Engineering Corp 1000 1515 1 horz& vert 0 30 0.2 0.75 NRC for Dis aster Prevention, Tsukuba 500 1515 1 horz& vert 0 50 0.03 0.37 Public Works Research Institute 272.11 88 1 horz& vert 0 50 0.6 2

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52 Although electromagnetic shakers have established their value in selected engineering applications (Reynolds and Pavic 2000) and inertial shakers gave rise to structural dynamic testing in the early 1930s, hydraulic systems are becoming the most prevalent for shake table systems in structural engineering research. Specific actuator placement, overall motion versatility, and co llectively large payload capacity has made this system type rise above others as the most practical and effective method for shake table testing. It is evident by comparing shake table capabilities in the U.S ( Table 2 6 ) and Japa n ( Table 2 7 ) that large to full shake table testing is a high priority overseas. Despite this contrast, collaborative research can continue to be done with existing facilities to strengthen the structural enginee ring field.

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53 CHAPTER 3 EXCITATION EQUIPMENT: MANAGEMENT AND IMPLEMENTATION The selection and implementation of appropriate excitation equipment is necessary for their essential ability to input energy into a structural model or system. Chapter 2 highlighted the capabilities and performance criteria for three types of excitation equipment, two of which are adopted in the dynamic testing laboratory presented in this work: hydraulic and electro magnetic systems. This chapter will identify three different excitation instruments incorporated into the testing facilities: (1) a uniaxial shake table, (2) a long stroke shaker, and (3) a six degree of freedom shake table. Small Scale Equipment With the broad application of dynamic testing and research in both industry and academia, excitation equipment packages are widely marketed and made available for a number of test applications. These packages, which often provide the necessary hardware and control software, provide an expedited approach to populating a laboratory wit h testing equipment that may be easily assembled and rapidly integrated into a testing program. This section will identify two small scale excitation systems adopted in this manner: a long stroke shaker and a uniaxial shake table. Performance specificati ons, research applications, and an overall review of each piece of equipment will be presented to illustrate how the integration of such systems assists in creating a versatile structural dynamics research laboratory. Long Stroke Shaker An APS 113 elec trodynamic long stroke shaker has been incorporated into the laboratory facility for a range of test applications. The shaker operates in conjunction with a power amplifier that provides the motion signal to the

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54 shaker. When used with an appropriate func tion generator (such as LabView and an NI analog output module), this versatile system can be used to generate an array of motion types including a general sine wave or sine sweep variation, random white noise, or re allows for large displacements at low frequency vibrations. Figure 3 1 shows the long stroke shaker installed on the ground floor of the laboratory followed by Table 3 1 which presents some highlighte d performance specifications for the long stroke shaker system Figure 3 1 Long Stroke Shaker Table 3 1 Highlighted Long Stroke Shaker Specifications Long St roke Shaker Specifications DOF 1 Force (lb f ) 30 Stroke (in) 6.25 Velocity (in/sec) 39 Freq. Range (Hz) 0 200 Operation Horizontal or vertical For the tests discussed in detail in Chapter 4, this system is configured to apply a band limited white noise excitation to a structural bridge model for experimental modal analysis. Bolted to the floor of the lab, the shaker has a fixed base and is attached to

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55 an isolated bottom node of the bridge ( Figure 3 1 ). Using the signal a mplifier, generated signals can be adjusted to the appropriate magnitude for the particular testing application. With the unique ability to operate in both the horizontal and vertical modes along with the long stroke capacity, this instrument has the pote ntial to be a useful tool in the laboratory for current and future research interests. Uniaxial Shake Table In contrast to the long stroke shaker, which is configured to impart a single point vertical excitation force to a structural model, the laborator y also includes a bench scale uniaxial Quanser shake table, suitable for providing horizontal base excitation to structural models. Isolated on a rigid concrete table, this mechanical shake table has the ability to impose excitation to a 17 pound mass at a maximum by researchers and educators worldwide for structural dynamics demonstrations and small scale testing. Displayed in Figure 3 2 is the uniaxial shake table as it is installed in the lab and Table 3 2 highlights additional performance specifications of the shake table system. Figure 3 2 Uniaxial Shake Table

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56 Table 3 2 Highlighted Uniaxial Shake Table Specifications Uniaxial Shake Table Specifications DOF 1 Table Size (ft) 1.5 x 1.5 Payload (lb) 17.1 Force (lb) 159.3 Stroke (in) 3 Velocity (in/sec) 26.18 Acceleration (g) 2.5 The control system of the shake table utilizes an accelerometer to measure the generated shake table motion to provide the fe edback for the control loop. Figure 3 2 illustrates the use of an external LVDT sensor to measure reference displacement data of any imposed vibration during a test. This system has been applied to numerous types of structural dy namic research applications including both random vibration and harmonic motion testing of a small scale structural building model which enables an array of post processing system identification methods to be implemented. Both excitation devices presented in this section are small scale models which have been implemented in the lab for early stage sensor development for structural health monitoring research and can be used further for structural dynamic experiments. The specifications of each are clearly listed with critical performance limits identified to highlight the importance of understanding the capabilities of a system. In both cases this excitation equipment required minimal assembly and allowed for prompt application to research experiments afte r a thorough review through the users manuals of each. When a new piece of excitation equipment is included in a lab, it is good practice to

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57 use. Following the develo pment of the appropriate guides, the combination of these two compact pieces of excitation equipment have provided the tools needed for a versatile structural dynamic research laboratory. Large Scale Equipment The required size and complexity of ex citation equipment must match the models and components to be tested; larger experiments require larger testing equipment. To expand the dynamic testing capabilities of the laboratory identified in this work, a larger scale excitation system was implement ed. This section will provide a detailed outline of all project phases from the system selection through the installation process. Additional information on system performance and experimental applications will also be included to emphasize the significa nce of incorporating such a system to a testing program. Shake Table A six degree of freedom (6DOF) shake table was the largest and most complex addition to the laboratory facilities developed in this research. Unlike the previous excitation devices pre sented in this chapter, this excitation system did not come ready to use and required detailed assembly and installation to be properly calibrated and experimentally functional. Intended to be housed in the University of Florida Powell Structures Laborato ry, this shake table provides seismic research capabilities in addition to the existing tornado, hurricane, and blast experimental capabilities at the lab. During the design phases of an expansion to Powell Lab, it was decided that the new shake table sys tem would be purchased and included in this newly constructed building. Purchased from a servo hydraulic test equipment manufacturer (Shore Western

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58 able platform on which to attach experimental models, six hydraulic actuators used to drive the table into motion, and a hydraulic service manifold used to regulate hydraulic fluid values from low to high pressure operations. Identified in Table 3 3 are highlighted shake table specifications. Table 3 3 Highlighted Shake Table Specifications Large Shake Table Specifications DOF 6 Table Size (ft) 4 x 4 Payload (lb) 2,200 Stroke (i n) Z 3 in X & Y 6 in Velocity (in/sec) 20 (X,Y,Z) Acceleration (g) Z 2.0 g X & Y 4.0 g Freq. Range (Hz) 0 200 One unique feature of this shake table system is the ability to apply both translational and rotational motion in the X Y and Z axi s, resulting in the six available degrees of freedom identified in Table 3 3 To accommodate potential seismic accelerations up to designed wi th a mass 50 to 100 times the table and payload mass, is to approximate a rigid support condition and ensure that vibration is not transferred to the surrounding structure. Figure 3 3 shows the initial and completed construction phase of the isolated mass concrete foundation for which the newly integrated shake ta ble system would be installed.

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59 A. B. Figure 3 3 Foundation Construction This heavily reinforced concrete foundation was dimensioned and designed to withstand increased lateral forces in addition to the vertically applied forces coupled with the the horizontal actuators will be bolted. Displayed in Figure 3 4 is an as built schematic of the shake table pit a week after construction. Figure 3 4 Shake Table Foundation As Built

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60 oriented actuato each actuator to be equally leveled and is fastened by an additional (4) anchors bolts above to resist any uplift forces during full scale operation. Following the delivery of the sh ake table system from the manufacturer, the assembly was initiated. The unique shape of hydraulic actuators coupled with their 200 lbself weight made their transportation from the packaged crate to the concrete pit an installation challenge. Careful proj ect planning during this installation process was essential to effectively install this system while maintaining a superior level of safety. Figure 3 5 shows the actuator shape and the gantry crane used to lift and transport the set of actuators and the shake table platform. A. B. Figure 3 5 Shake Table Assembly Shoring was designed and constructed to place the horizontal and vertical actuators in the appropriate position and wer e collectively used as temporary support for the shake table platform. Actuators were then bolted to a torque of 150lb in to predrilled holes on the shake table perimeter and leveled to ensure installation accuracy. This torque spec

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61 was then applied to a ll actuator bolted connection to the surrounding supports. After all major components of the system were properly connected and leveled, hydraulic hoses were connected from the hydraulic manifold system to each actuator according to the specified hose con nection layout provided by the manufacturer. To generate hydraulic fluid pressure, the shake table system is powered by 125 HP hydraulic power supply with a maximum pressure output of 3000psi. This power supply system was designed and manuf actured by an external company to meet the specific operational requirements of the shake table. As a final assembly step, the temporary shoring beneath the table was removed to allow for the system calibration phase of the project to begin. Shown below in Figure 3 6 is the final assembly of the shake table system as it is currently in the lab. Figure 3 6 Installed Shake Table System In addition to the hardware components of the system, a cent ral processing unit with a preloaded control interface was delivered to function as the main control system of the table. The control system enables multiple variations of motion to be manipulated and with the integration of an LVDT and accelerometer sens or at each actuator, both displacement and acceleration controlled excitation can be applied.

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62 The shake table manufacturer provided personal technical support for one week. This support enabled an initial professional calibration of the shake table syste m as well as thorough education on system performance and control program interface. Following the on site commissioning, a Shake Table Instruction Manual (Appendix 1) was composed. This document provides a detailed description on the multiple phases of operation pertaining to the intended structural dynamic research experiments of the facility. With the multiple excitation degrees of freedom provided by this machine, there is a wide range of experimental application possibilities. Upcoming experimental tests utilizing the shake table include random white noise base excitation on a steel building model to characterize structural dynamic properties, as discussed in Chapter 4. Additional forced vibration can be applied by this system such as uni and mult i axis seismic acceleration time histories or harmonic vibration variations. It must be noted that there is an elaborate convergence process associated with any new excitation record applied to the shake table system in order to align the desired input mo tion with the resulting response of the table. Once an input signal and output motion of the table is converged, this motion can be stored and immediately applied to experiments in future applications. This summarized convergence process is detailed in t he Shake Table included in the Appendix C section of this document. An effective method to ensure the appropriate alignment of an input signal and output response is the plotting of a transfer function between each. Plotting this relationsh ip provides a frequency domain visual to determine if the signals are equal in content. For example if two signals are truly identical with one another, the transfer function ratio plot should be

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63 a constant line with a magnitude of 1. Figure 3 7 presents a time history displacement record of two representative white noise signals with frequency content ranging from 0 2.5 Hz. Following is a transfer function plot between the two sources in Figure 3 8 Figure 3 7 Displacement Time History of Input and Output Figure 3 8 Transfer Function of Input and Output

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64 In the time domain, it can be difficult to observe the subtle differences when comparing two signals. Plotting the transfer function provides a visual ratio in the frequency domain that can be a more effective platform to observe signal inconsistencies. The visual presented in Figure 3 8 illustrates a reasonably successful convergence as indicated by the relatively constant graph from the 0 2.5 Hz frequency range of the input and output signals. As a future recommendation, a system performance characterization program should be developed to quantify the true limit states of the system. Figure 3 9 plots the intended performance curve of the shake table system under a fully loaded condition (added 1 ton mass) according to the system design and power suppl y specifications. Figure 3 9 Intended Performance Limits (Shore Western Manufacturing, Inc.) The stroke, velocity, and acceleration specifications identified earlier in this section in Table 3 3 originate from this performance curve which was created by a computer

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65 model (Shore Western Manufacturing, Inc.) to predict system capabilities. To provide a contextual interpretation of the information presented in Figure 3 9 a brief explanation of each limit referring to the X axis will be presented here. A translational stroke limit of six inches can only be obtained at a low frequency range from 0 2Hz. After which, in the intermediate frequency range of 2 12Hz a maximum velocity limit of 30 in/sec is the controlling factor of motion. Frequencies higher than approximately 12Hz can be controlling factors, a six inch stroke, is the only limit conserved when comparing theoretical capabilities based on system design ( Figure 3 9 ) to the specified limits of the system ( Table 3 3 ). As a conservative measure, the specified X axis vel ocity and capabilities from Figure 3 9 above. With unique variability in any hydraulic system, the value of these parameters may change. As a result it is important to incorporate a performance characterization test program for the shake table unit to compose a SIMLab specific performance curve and ensure true performance meets the specified limits. A uniaxial shake table, long stroke shaker, and 6D OF shake table have all been identified as valuable pieces excitation equipment integrated into the research facility presented in this work. With the proper operational instruction and background knowledge of these systems, there exists a matrix of exper imental possibilities for which these machines can be applied.

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66 CHAPTER 4 STRUCTURAL MODELS: DESIGN AND TESTING A key aspect of the development of the structural dynamics laboratory undertaken in this research is the creation of a number of structural models with a range of design, construction, and dynamic performance characteristics. This chapter present s three different s tru ctural models designed and implemented for dynamic testing, including a steel truss bridge, a small scale two dimensional building, and a th ree dimensional steel building model. The design, assembly/construction, and experimental applications of each model are identified fo llowed by further discussion on improvements and future experiments Bridge Truss In this section, a laboratory scale, st eel truss bridge is presented for use in dynamic experiments. The bridge, u sed in previous academic applications, was ori ginally designed and built for structural health monitoring research and damage identification applications at Texas Tech University The truss was modified as part of the work presented in this thesis in an effort to improve its applicability for a range of dynamic tests. A detailed and comprehensive description of the original truss bridge design is presented in Hernandez (2011 ); how ever, a general overview is briefly provided here. The bridge model was designed as a 1/6 th scale model of an existing steel bridge located in the North West Texas panhandl e, maintaining general material and boundary conditions of the original bridge Th e model size and design is a reflection of geometric similitude relationships aimed at closely matching the dynamic characteristics of the model with those measured on the real bridge A s ubsequent iterative design

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67 procedure, coupled with finite element m odel predictions of dynamic characteristics was the basis for member cross sectional dimensions In addition to achieving the desired dynamic characteristics, the bridge was also designed with specific functionality to make it useful in testing damage detection interchanging original truss elements with elements possessing smaller cross sectional dimensions. To achieve this element interchangeability, specially designed conn ection blocks were fabricated, as discussed later in detail. The resulting model was a simply supported, steel bridge truss spanning 10f t with rigid connections at each nodal location as shown in Figure 4 1 Figure 4 1 Erected Bridge Model The bridge had a width measuring 2ft and had a top and bottom deck separated by a height of 1.25ft. Observed in Figure 4 1 the bottom deck is divided into four 2ft x 2.5ft rectangular bays. Because this structure was designed, fabricated and originally properties were inherited by the dynamic research facility presented in this work There fore, this

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68 structure provided a rapid and prefabricated approach to begin to populate the facility with new structural dynamic models. The objective of this portion of the bridge work is to present the systematic assembly and experimental testing of the br idge and to quantify dynamic characteristics. This process illustrates key issues in practica l dynamic testing on structural models in addition to providing known fundamental parameters of the bridge model for future use. The t esting techniques includin g instrumentation methods and data processing procedures are discussed to provide a foundation for future experiments on str uctural models. Assembly and Modifications The assembly of a structural model used in dynamic testing requires a level of consi stency and precision to ensure the accuracy and legitimacy of experimental results and conclusions This section outlines a general assembly process and identifies the equipment used to ensure the integrity of the fully assembled model The disassembled bridge model was shipped to UF in groups of like components Figure 4 2 shows the various bridge components, consisting of steel truss members, screw/bolt fasteners, and nodal connection blocks. Figure 4 2 Bridge Components

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69 With the erector set like composition of the model precise construction methods were required to preserve dimensional accuracy and overall symmetry of the system dictated in the design drawings Each no dal block is designed to connect adjacent steel members in to a semi rigid connection which provid es a continuous chord (two for both top and bottom levels) of hollow steel members spanning the length between supports. This is made possible by the combina tion of steel screws bolts, and nuts, connecting the connection block to the steel truss member. An example of a member to connection block assembly is shown in Figure 4 3 Figure 4 3 Joint Configuration This member connection is applied throughout the entire structure. The bottom level bridge deck was erected first, followed by the connection of individual vertical truss members to each node. The top deck level was then used as the final component to unite the system components. A ccuracy to the thousandth of an inch was maintained with the utilization of a large 32 inch caliper to verify that the center to center dimensions of each truss element in the physical model were c onsis tent with the design specifications

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70 While all of the components of the original truss were sent from Texas Tech, the truss supports had to be fabricated at UF to elevate the truss off the ground. The truss support design required the supports to have a high stiffness relative to the truss to ensure that any vibration imparted results in primarily truss vibration and not motion in the supports. T he construction of the rigid steel supports shown in Figure 4 1 used a combination of a horizontal band saw and MIG welder After model erection, t o confirm each supported end of the model shared the same elevation, a Dewalt rotary laser level was used as a reference for each end and appropriate adjustments were made to match the height s of each support end. ensured equal mass distribution throughout the model and aimed to minimize discrepancy in dynamic response. In previous work (Hernandez 2011), dynamic experiment s i dentified high vertical stiffness of the model in comparison to the full scale structure on which this model is based This discrepancy is likely due to the mass from the wooden decking and cross members of the full scale bridge that were not accounted for in the finite element model. Th e result was a decreased mass to stiffness ratio and subsequent lower frequencies ( Eq. 2 1 ) in the modeled full scale structure At UF, i n an effort to reduce the vertical stiffness of the model the bridge was extended one extra bay length of 2.5ft to cr eate a total span of 12 .5 ft. The goal of lengthening the bridge was to decrease its natural frequencies of the vertical direction and provide a larger bridge model with increased nodal variety to be exposed to dynamic experiments. A visual comparison of the bridge extension is illustrated in Figure 4 4.

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71 Figure 4 4 Bridge Extension The results of dynamic experiments and the modification effects of the extension are section of this chapter. One effective characteristic that can be incorporated in the design of a structural dynamic model is the level of experimental adaptability ; an extreme case is identified in Chapter 2 (Wu & Samali 2002) where the mass, boundary conditions, and story height can be manipulated to model a range of structural behavior To apply a similar approach to the model bridge lateral cross bracing on the bottom deck was installed This increased the model versatility to not only include an extension, but to also incorporate a lateral bracing dimension to study the dynamic effects of different bridge augmentations Due to 45 degree face angle of the nodal connection blocks combined with the rectangular shape of the bottom level bays (2.5ft x 2ft) this design modification

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72 required a n adjustment to the connection blocks the lateral cross bracing was to be connected to. Figure 4 5 shows a plan view section cut of the bridge and helps clarify the geometric limits of the se components and the need for connection block alteration. Figure 4 5 Plan section of the bottom deck of the truss to identify the Modified Connection Blocks After the connection block modifications were c omplete, a total of three phases of the bridge model were tested; these models include a shorter span without lateral bracing, shorter span with lateral bracing, and longer span with lateral bracing. The dynamic experiments of each bridge configuration ar e conducted and described later in the section. In appropriate instances, models in this section may also be referred to as (1) for short without lateral bracing, (2) for short with lateral bracing, and (3) for long with lateral bracing.

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73 Finite Element M odel Finite element (FE) modeling of a structural dynamic model enables the prediction of its dynamic response and strength capacity and is a critical stage in the design process Upon fabrication of the final model design the anticipated response values can be compared to data obtained through experiments and appropriate adjustments to either the computer model or the test specimen can be made. A general finite element software package (ADINA 8.8) was used to create a finite element model for each confi guration of the bridge to be assessed. All of the bridge FE models, similar to experimental models, contained the same material properties, element cross section properties, and boundary conditions, with the only changes between the configurations being th e span dimension and the addition of lateral diagonal members between nodes. To accurately model the existing experimental bridge parameters the dimensions, nodal locations and mass were all preserved when transitioning from the real to computer model Due to the three d imensional configuration of the bridge, all six degrees of freedom were left active for the entire model and support conditions we re modeled to represent a traditional simple support, with fixity resembling pinned and roller ends. To m odel these particular boundary conditions the pin nodes were restrained from translation in the X, Y and Z direction and the roller nodes were restrained from translation in only the Y and Z direction. B eam pipe element s w ere implemented to represent ste el truss members rather than truss element to allow for all degrees of freedom to be active and both horizontal and vertical natural frequencies could be quantified simultaneously.

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74 The material makeup of the structure contains three types of components a ll made up of the same steel material. Material properties and dimensions were consistent with the real model and are listed below: E = 30,000ksi Pipe area = 0.07 in 2 Mass Density = 0.00029k/in^3/g Span 1 = 10ft Span 2 = 12.5ft Width = 2ft Height = 1.2 5ft The natural frequencies calculated from experimental results provide the primary basis for comparing the model with the FE analysis results The mass of the bridge is an essential parameter for the accurate modeling of a structure for dynamic compa rison. The density listed above is only applied to the pipe beam members so only the mass of those elements are accounted for in the FE model. Contained in the lab model are steel connection blocks located at each node that also contribute to the overall mass of the structure. To account for this collective 35 pounds of dead load, a representative point mass of 1.5 pounds was added to each nodal location in the FE model. Experimental m odal analysis is not influenced by loading conditions with the result s being a function of the geometric and boundary condition parameters As a result, element discretization capabilities typically applied to a finite element model around boundary constraints or load concentrations was not required Figure 4 6 illustrates the first and second horizontal bending modes of the bridge which. Following Figure 4 6 is Figure 4 7 which also i dentif ies the first and second mode bu t in the vertical direction. These renderings are a result of a finite element

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75 Eigen analysis providing a visual interpretation of the global mode shapes of the structure. A. B. Figure 4 6 1st & 2nd Ho rizontal Mode shapes A. B. Figure 4 7 1st & 2nd Vertical Mode shapes This analysis was applied to all model configurations to provide a general dynamic response estimate of each. Table 4 1 lists FE model predict ions for the first three horizontal and vertical modal frequency values for the models (1), (2), and (3) Table 4 1 FEM Predicted Natural Frequencies Mode Shape Frequency (Hz ) Original (1) Short Braced (2) Long Braced (3) Horizontal 1st 5.9 93.76 90.70 2nd 13.0 197.9 194.3 3rd 20.7 204.8 200.1 Vertical 1st 60.1 60.9 41.1 2nd 107.0 93.5 92.3 3rd 204.0 202.4 196.7

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76 The first three natural frequencies in each di rection for each bridge configuration presented in Table 4 1 were determined by plotting the mode shapes in the finite element program and recording the corresponding frequency of vibration Evaluating these FEM results it can b e seen that the horizontal bracing included in model (2) and (3) add s significant stiffness in the horizontal plane resulting in an increase in horizontal natural freq uencies. The functional result of the bracing on the bottom plane is representative of a n extremely stiff bridge deck coupled with a moderately flexible beam system above which more closely resembles a full scale bridge. By implementing a n FE bridge model, dynamic response predictions can be recorded, used as a reference, and may assist in the interpretation of experimental response data in the future Dynamic Testing To obtain fundamental dynamic characteristics for each of the model configurations a series of structural dynamic tests were conducted Structural dynamic testing consists of an experimental phase where data is acquired from a vibration test followed by an analysis phase where the data is processed to extract modal parameters such as natural frequencies, modal damping ratios and mode shapes of the structure of interest Th is section details the experimental setup providing detail on the applied excitation methods as well as the instrumentation devices used. Instrumentation. To monitor r espo nse during vibration tests the models were instrumented with high sens itivity uniaxial accelerometers (PCB Piezotronic ICP) specifically designed for modal analysis and structural testing applications. These sensors were used on all structural models presented in this work. The data acquisition system (National Instruments CompactDAQ) to which the accelerometers were connected, provides 20 channels of 24 bit resolution acceleration

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77 measurement. Each of the accelerometers was connected at selected nodes depend ing on the length of the bridge. Sensor placement on the origina l and extended models is shown in Figure 4 8 Figure 4 8 Sensor Layout of Short and Long Bridge Compositions To enable vertical and lateral acceleration measurement, two sensors were placed at each identified node using the installed magnetic mounts This instrumentation plan resulted in a total of ten different nodal locations to be monitored each collecting horizontal and vertical response data T he extended bridge model incre ased the number of nodal locations by from 24 to 30 T o capture the general response of the extended structure, the accelerometers were relocated to alternate locations as shown in Figure 4 8 The installation of lateral cross b racing is not shown in Figure 4 8 as it did not influence sensor placement. Impact test There are several methods for conducting vibra tion tests and as discussed in Chapter 2 the use of an impact hammer to impose vibrations t o a test specimen is a quick and common approach. The purpose of the impact tests on the bridge was to obtain initial dynamic parameters of the system in a timely manner. F or the most accurate and ideal system identification techniques an impact hammer

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78 equipped with a tip load cell tip may be used to document a known input energy level. For impact test s of the bridge models, a mallet hammer without load cell instrumentation was used to impart forces to excite the structures Due to the multi dimensiona l response of the model, modes in the horizontal, vertical, and torsional directions were anticipated. As a result a series of impact tests were applied both horizontally and vertically, allowing for the dominating mode shapes to be present for the direc tion in which the structure was impacted. For example, in a horizontal impact test, the dominating response data will be derived from node accelerations in the horizontal direction; therefore, subsequent modal analysis should contain higher energy at thes e horizontal frequencies Shown below in Figure 4 9 is an example of frequency domain response data after being subjected to a horizontal impact test. Figure 4 9 Horizontal Impac t Frequency Response and Mode Shapes Using the ies of a structure it is shown that the first three horizontal natural frequencies are 2.32 Hz, 5 00 Hz, and 8.44H z. By following the steps below, the mode shapes illustrated in Figure 4 9 were able to be obtained:

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79 1. Select a reference node. This is typically a node of impact. 2. Calculate the cross power spectral density (PSD) function (a frequency domain representation) between each measurement node and the reference node. 3. Identify peaks in the frequency response (PSD) that are believed to represent a natural frequency. 4. Determine the amplitude of the PSD at each natural frequency 5. Analyze the phase angle value of the cross PSD at th e selected frequencies to 6. Construct the mode shapes by plotting the value of the PSD amplitude measured at each nodal location for a particular identified natural frequency, normalized by th e maximum amplitude. Values are positive if they are in phase with the reference and negative if they are out of phase. The mode s hapes in Figure 4 9 correspond to lateral ly displaced shapes and are best visualized from a plan vi ew (i e. looking down on the bridge). The selection of the impact node location is determined by the anticipated bridge mode shapes. As shown in the second mode shape plot (corresponding to a natural frequency of 5 Hz) in Figure 4 9 the mid span node remains stationary while the quarter span modes have equal and opposite magnitudes. It is important to note that i f impact was applied at the mid span location, minimal energy would be contributed to the second modal frequency and result in negligible response for that mode Impact nodes of interest changed between horizontal and vertical impact tests. S uccessive experiments were conducted on the different test specimens to study the dynamic effects of both an extended and lateral ly cross brac ed variations of the model with e xperimental results compared in a later Experimental Result s Ambient vibration test. A secondary excitation approach was also applied as forced vibration method with the use of the long stro ke shaker For these model s the purpose of forced vibration testing was to provide energy input in a specific frequency

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80 range in the vertical direction where the impact test was unable to provide adequate excitation T hese tests were conducted by fixing a long stroke shaker (APS 113 Electro seis) to a bottom connection block, N ode 8 to apply a vertical random excitation A band limited white noise signal was created with the use of a Lab View interface enabling the alteration of various signal paramete rs such as white noise amplitude a nd bandwidth cutoff frequencies controlling upper and lower frequency content. Figure 4 10 displays example frequency response data of the vertical motion of the bridge when expo sed to a band limited white noise signal between 20 and 1 2 0 Hz. Figure 4 10 Band Limited White Noise Frequency Response and Mode Shapes Due to the high levels of stiffness in the vertical direction it was difficult to impose a dequate energy into the structure to excite higher energy modes and as a result limited the level of response vibration As a result the frequency response data shown in Figure 4 10 has a low signal to noise ratio in comparison to horizontal impact response data ( Figure 4 9 ). Even when plotted in a logarithmic scale, where frequency peaks are more easily identified differences in peaks are difficult to distinguish. The cause of t he

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81 challenges associated with distinguishing clear peaks in the response were investigated and further explained later in the chapter. Due to configuration and space limitations, there was no practical method to utilize the long stroke shaker for horizon tal excitation; the excitation in the horizontal direction was strictly limited to the use of a n i mpact hammer. This constraint clearly illustrates how the experimental limitations of a dynamic research laboratory are derived from many factors such as eq uipment capabilities and space constraints . In contrast to an impact test where only a hammer is used to generate excitation, a forced vibration test by use of shaker equipment contains many steps in the process of signal generation and application Figure 4 11 breaks down the ambient vibration test set up into a simplified process as it pertains to this facility and identifies each component in the order in which it applies. Figure 4 11 Shaker Test Process

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82 In a forced vibration test the signal is generated through the control system such as a LabView interface Input parameters are manipulated according to the type of excitation the test specimen is to be subject to. Th e signal is then sent to the data acquisition system (DAQ) where it is converted from a digital to analog signal to be sent to the amplifier and shaker. The amplifier (APS Amp lifier 12 5 ) is used to scale the signal to the desired magnitude. M anual adjust ments are used to modify the proportional gain and voltage of the incoming signal which is then sent to the vertical shaker to impose vibration to the test structure. Magnetically mounted accelerometers located at discrete degrees of freedom collect vibra tion data that is then sent back to the DAQ for signal conversion back to the control system. D igital data is then stored to be used for data post processing and modal analysis This basic dynamic testing process is similar in most structural dynamic res earch facilities, and although the stages have been shown at distinct phases and grouped as they relate to the facility in this work, it should be noted that these processes can be incorporated in as little a single device (Salawu and Williams 1993). It m ust be noted that vertically applied motion to the structure resulted in frequency response peaks that were difficult to identify and associate with resonant frequencies. This is due to the overall high stiffness of the bridge models in the vertical and h orizontally braced directions. In the case of forced vibration, the origin of this matter is a combination of the shakers capabilities and inherent bridge stiffness. In a band limited white noise signal, equal energy is provided for all frequencies in th e specified bandwidth range therefore a very wide range of frequencies will result in lower energy input. The velocity, power, and stroke limits of a shaker pose a challenge to

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83 provide sufficient energy to significantly excite a mode at a higher frequency value with a large enough force to capture vibration response. This is the case in the vertical direction of the bridge. Nodal amplitudes of vibration are limited due the inability for the shaker to apply enough force at a high frequency range in which the vertical frequencies of the bridge reside As a result a low signal to noise ratio makes it difficult for clear peaks to be detected in the frequency domain. Figure 4 12 is a graphical representation of the shaker capabiliti es. This illustrates the maximum force envelope for a fixed body of the APS 113 shaker is 133N (30lbf) which is only attainable from 0 ~ 25 Hz, after which an apparent decrease in force potential develops. Figure 4 12 APS 113 Performance Curve (APS Dynamics) A static analysis revealed a maximum displacement of 0.004 inches when a 30lb force was applied to the structure, a displacement too small to obtain the clear dynamic characteristics desired from an ex periment. The intended functionality of the APS 113 Shaker is for dynamic experiments but at a relatively low frequency range. For the

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84 bridge models, it can be concluded that is not a suitable excitation technique for vertical vibration applications. T est Result s This section will present response data from the dynamic experiments conducted with both hammer impact and ambient vibration applied by a vertical shaker, followed by a comprehensive summary of experimental result s In i nstances where the bri dge stiffness levels were of high magnitude, it was difficult to identify clear peaks to be associated with modal frequencies in the frequency respon se data In these cases, the predicted natural frequencies from the finite element model were used as a po int of reference to identify candidate peaks allowing for a guided estimate of dynamic response. Model (1) Horizontal The original bridge orientation had a span of ten feet without lateral bracing. As a baseline measure of the unmodified model horizonta l impact tests were conducted and response vibration was monitored. Horizontal n atural frequencies of the model (1) were determined using a PS D function and plotted in the frequency domain (log scale) shown in Fig ure 4 13 Fig ure 4 13 Horizontal Impact Response of Model (1)

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85 Figure 4 14 Horizontal Mode Shape of Model (1) The dominant peaks at 2.3 4 Hz, 5. 13 Hz and 9.3 Hz are linked to the first, second and third horizontal resonant frequencies of the bridge specimen, respectively. This unmodified version of the bridge model provided a responsive structure for which to conduct structural dynamic experiments and straight forwardly appl y the peak picking technique to obtain modal identities The finite element model predicted the first three horizontal frequencies to occur at 5 9 13 0 20.7 Hz. It is observed that the FEM values are an average of 2.5 times greater than those presented in the data in Fig ure 4 13 indicating either a lack of mass representation or excessive stiffness representation in the finite element model With the hig h confidence level in the experimental horizontal response, this FE to ex perimental model relationship can be recorded and potentially applied to help characterize the bridge response in other modifications. Model (1) Vertical. To isolate response in the vertical direction, random vibration was applied using the electromagnetic shaker. The p rojected frequencies from the finite element model resulted in a first vertical mode at 60.1 Hz, so a white noise signal with bandwidth rang ing from 20 100Hz was used to target the first vertical natural frequency

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86 of the bridge Shown in Figure 4 15 is the vertical frequency response data from a vertically applied ambient vibration from the long stroke vertical shaker. Figure 4 15 Vertical Response from Shaker o f Mo del (1) In an attempt to improve the low signal to noise ratio of bridge response shown in Figure 4 15 hammer impact was applied downward on the model (1) with the intention of providing sufficient energy to excite a vertical mod e Figure 4 16 shows the bridge response plotted in the frequency domain as a result of vertica l i mpact on the bridge. Figure 4 16 V ertical Response from Impact of Model (1)

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87 F igure 4 17 Vertical Mode Shape of Model (1) A persistent low signal to noise ratio due to the lack of energy applied to the structure makes it difficult to confidently identify the frequency peak associated w ith a particular mode. The most evident peak appears at 57.9 Hz and can be concluded to be the first bending modal frequency in the vertical directio n. As previously identified, FEM predictions indicated the first vertical frequency to occur at 60.1Hz w hich is relatively close to first natural frequency of 57.9Hz. A new FE to experimental model relationship was then developed to assist in the interpretation of noisy vertical response data. Subsequently, a 2 nd and 3 rd vertical mode could be chosen, howe ver t he irregular shape of mode 2 illustrated in Figure 4 16 is a reminder that the 2 nd and 3 rd natural frequencies are strictly estimated values. The experimental results from model (1) in both the horizontal and vertical direc tions, proved to be critical information to compare with the finite element model predictions Using the FE predictions as a reference and understanding how those

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88 predictions relate to the experimental model, r easonable estimat es can be applied to future response data sets to identify modal parameters of additional bridge models Model ( 2 ) Horizontal The inherited configuration of the bridge was experimentally proven to be overly flexible in the horizontal direction as compared to a typical full scale b ridge As an initial modification, lateral bracing was added to the bottom bridge deck of the structure preserving the ten foot span but adding lateral force resistance to the system. Figure 4 18 display s response from horizonta l impact tests Figure 4 18 Horizontal Response from Impact of Model (2) Various peaks occur throughout the frequency response plot and it is difficult to attribute on e specific peak to a horizontal mode. FEM predictions of the first three horizontal modes for model (2) are 93.8, 197.9, and 204.8Hz. Using the previously established horizontal relationship between the experimental and FE model frequency values an estimated approach to determining the hor izontal frequencies of model (2) can be applied. Figure 4 19 is the mode shape plot from the frequency response data found in Figure 4 18

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89 Figure 4 19 Estimated Horizontal Modes of Model (2) As a result the first three estimated horizontal frequencies of model (2) are 49.3, 108, and 118Hz, respectively. In instances where numerous peaks occur in a frequency response such as the data shown for model (2) the use of a FE model can be a useful tool in estimating dynamic response. Model ( 2 ) Vertical Vertical response is plotted in Figure 4 20 and Figure 4 21 as a result of vertical shaker and hammer impa ct tests, respectively. Figure 4 20 Vertical Response from Shaker of Model (2)

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90 Figure 4 21 Vertical Response from Impact of Model (2) Figure 4 22 Estimated Vertical Modes of Model (2) As in model (1) verti cal data, model (2) response data is filled with peaks at many frequency ranges at similar amplitudes In model (1) peaks were difficult to identify and now with the addition of lateral cross bracing, more members are included in the system and present an even noisier data set. Selection of peak values for this test set was based on previous vertical test results since the addition of horizontal lateral bracing

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91 should have minimal effect on the vertical response of the system. As a result mode shape plots in Figure 4 21 mimic typical shapes for mode 1, 2, and 3. Model ( 3 ) Horizontal A final modification was the extension of t he braced bridge model (2) This extension added an extra 2.5 foot bay extending the total span to 12 .5 feet and preserved the lateral bracing components Figure 4 23 shows model (3), the current composition of the bridge with v ertical shaker attached Figure 4 23 Current Bridge Configuration A fter evaluation the FE model predictions ( Table 4 1 ), it was determined that lengthening the bridge model would n ot affect the horizontal flexibility of the bridge as much as it would the vertical direction. The first v ertical mode is expected to drop by roughly 20 Hz from m odel (2) to m odel (3) The dynamic response from the braced extension is illustrated in the figures below.

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92 Figure 4 24 Horizontal Response from Impact of Model (3) FEM predictions of the first three horizontal modes for model (3) are 90.7, 194.0, and 197.1Hz. Preserving the established horizon tal relationship originally developed with model (1) an estimated approach can be applied once more to estimate the horizontal frequencies of model (2). Horizontal mode shapes and their associated frequency values are shown in Figure 4 25 Figure 4 25 Estimated Horizontal Modes of Model (3)

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93 The first three estimated horizontal frequencies of model ( 3 ) are 29.8, 39.0 and 83.0H z, respectively. Although the addition of new horizon tal elements creates a more c omplex structure the use of a FE model to estimate experimental response can be adopted as a reasonable approach to estimate dynamic characteristics. Model ( 3 ) Vertical The v ertical frequency response is plotted in Figure 4 20 and Figure 4 21 as a result of vertical shaker and hammer impact tests, respectively. Figure 4 26 Vertical Response from Shaker of Model (3) Fre quency response data of the extended and horizontally braced bridge model is illustrated in Figure 4 26 This band limited white noise signal was generated with frequency content ranging from 20 100Hz and explain s f energy at the 20Hz mark. Similar to past shaker applications on the bridge, there is very little energy differential and separation between peaks. A relatively noticeable peak is apparent in the interval of 20 40Hz however i t is impossible by visual in spection to determine what this peak represents. Vertical impact applied at Node 21 is shown below in Figure 4 27 but has similar signal to noise ratio issues.

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94 Figure 4 27 Vertica l Impact Response of Model (3) Figure 4 28 Estimated Vertical Modes of Model (3) By applying a vertical impact to the test structure only a percentage of the frequency range for which this structure respo nds is excited. Both horizontal and vertical

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95 directions are braced in their respective planes and cause an overall increase in system stiffness and subsequent natural frequencies. Predicted vs. Experimental Table 4 2 presents estimated experimental natural frequency values of all models along with their predicted FE values for a global comparison. Table 4 2 FEM vs. Experimental Natural Frequencies Mode Shape Frequency (Hz) Origi nal Short Braced Long Braced FEM Experiment FEM Experiment FEM Experiment Horizontal 1st 5.9 2.3 4 93.76 4 9 3 90.70 29.8 2nd 13.0 5.13 197.9 108.0 194.3 39.0 3rd 20.7 9.3 204.8 1 18.0 200.1 83.0 Vertical 1st 60.1 57.9 60.9 55.3 41.1 42.4 2nd 10 7.0 90.1 93.5 92.6 92.3 88.2 3rd 204.0 181.0 202.4 183.0 196.7 212 Although the FE model predictions were used as a guideline to select candidate peaks in the frequency domain, the discrepancy of the FEM vs. experimental results needs to be addressed. As mentioned, the horizontal predictions for the FE model were 2.5 times higher than the resulting experimental horizontal response. In the vertical direction the relationship established showed a very close comparison between the FE model and experiment al structure. In any creation of a computer based model there are a number of assumptions that are made on member connectivity and boundary conditions. This difference in the FE model can be attributed to an overestimation o f rotational stiffness at supp orts or at nodal locations. As a future recommendation model updating is an encouraged path for future work with the FE model to create a

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96 model that can accurately predict the response of the structure in both the horizontal and vertical directions. The data analysis challenges presented in this section corresponding to bridge stiffness and excitation equipment limitations are important factors that must be considered when selecting both a new structural model and excitation equipment for a dynamic resea rch lab. The combination of high bridge stiffness in the vertical direction and the inability for the vertical shaker to impose appropriate force at the high frequency range of the structure made it extremely difficult to confidently characterize the dyna mic response of all bridge models I t is recommended that if future work is to be conducted with this model where natural frequencies in all directions need to be accurately quantified, then alternate excitation methods must be explored. Table 4 3 provides a list of shakers that can be implemented in future testing applications. Table 4 3 Alternate Shaker Systems Shaker Type Freq. Max Max Max Bridge Range Force Force Disp. Stress (Hz) (kN) (lbf) (in) (ksi) APS 113 0 200 0.133 30 0.004 0.76 Modal Exciter 2 5000 1 225 0.028 5.73 Low force 0 4000 5.12 1150 0.15 29.28 Medium force 0 3500 9.8 2200 0.28 56.02 Medium force 0 3000 22.2 5000 0.63 127.32 The current shaker model is listed above as APS 113 and has a capacity of producing a maximum of displacement of 0.004in on the current bridge model (3). With the selection of an alternate shaking device larger displacements can be generated and subsequent modal analysis performed. The applied bridge stress column to the far right of the table is also included to the resulting stress applied to the bridge at this forces is known and a yielding failure mode is not encountered.

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97 Although natural frequencies ranges are relatively high compared to practical applications, this bridge specimen can still be used for damage detection applications by replacing truss members with other members possessing a decreased cross sectional area as described by Hernandez 2011. If a newly adopted shake r cannot be purchased due to cost limitations, this structure can be modified to induce a decrease in overall system stiffness. This goal could be accomplished by applying a permanently distributed mass to the structure or additional modification to the c onnection blocks to influence the vertically oriented diagonal truss members. Manipulating the angle s of these members in a manner to reduce the total number of members resisting vertical forces will lead to a decrease in vertical stiffness. After these modifications, this bridge model will be a multi purpose test tool and will add to the inventory of structures presented further in this work. 2 D Dynamic Building Model Structural models integrated in a dynamic research facility are done so to contribute to a variety of testing applications. The structural bridge model presented in the previous section is a useful tool but for very specific testing situations To extend the capabilities of the laboratory identified in this work, a seven story two dimens ional structural dynamic building model was designed and fabricated. This section provides a detailed explanation on the design construct ion and testing of the building model The purpose of t his structure was to introduce a building test model that is responsive to low energy excitation that possesses clearly identifiable, well separated natural frequencies Such a model can be used as a bench mark structure and a ppl y to a number of current and future research projects

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98 Desig n This section will explai n the rationale behind the final building design and review the dynamic analysi s With no particular parent stru cture on which to base the design physical facility constraints were u sed to provide initial design bounds for overall model dimensions, appli ed mass, and boundary conditions Figure 4 29 identifies width (W), height (H), mass ( M), fixity (k) and material /cross section (EI) as critical variables included in the building design process that influence the models dynamic response Figure 4 29 Building Variables Model variables (H) and ( W ) were influenced by physical dimensions of both the lab facili t y and of the excitation equipment planned to be used for dynamic experi ment s The platform dimens ion of the uniaxial shake table was used as a starting point for the width (W) of each floo r of t he building model and limited values to be no more than 18 inches. The shake table was mounted on strong table support allowing for 5 f eet of clearance between the shake table elevation and an accessible height for sensor installation Using the dimensional constraints provided by the laboratory and shake table, a width of 12 inches was selected and after concluding on a total of seven s tory levels, an inter story height of 8 inches was chosen. These parameters resulted in a

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99 width two thirds the maximum limit W ith even ly distributed dimension s of 8 inches per story a total height resulted in 56 inches half a foot under the maximum al lowable height. Material /cross section geometry (EI) and fixity (k) selection were based on the possible materials and connection configurations The purpose of this structure is to provide a responsive model where dynamic characteristics are intended to be easily obtained. After investig ating past experimental building models applied f or structural dynamic researc h, a common column material used was spring steel allowing for a more flexible structural model. PVC was chosen as the floor material where ma ss would be affixed With PVC material used at each floor level, spring steel was fastened by a tight bolted connection and similar to practical connection types rotational restraint would fall It was determined that the desired range of frequencies for the building would be representative of a commonly constructed multi story light frame structures, 0 20Hz In this design the bulk of the mass (M) would be concentrated at each floor, or each degree of freedom (DOF) With a total of seven stories, th is system was modeled as a 7 th order multi DOF flexible shear building frame and a preliminary modal analysis (Appendix A ) based on MDOF equation of motion principles (Eq. 2 4 ) was implemented f or design Listed below are the concluded design parameters corresponding to the variables identified in Figure 4 29 : E = 30 ,000ksi I = 0.000031250 in 4 H = 8 in W = 12 in k factor = 12 (assumed rigid) M = 4.2 lbf

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100 By adjus ting the applied mass h olding dimensions, material, and boundary conditions constant and solving the equation of motion, frequencies could be predicted and targeted to the desired range prior to model construction/testing. The preliminary predictions of the system natural frequencies are shown on Table 4 4 Table 4 4 Predicted Building Natural Frequencies Mode Frequency (Hz) 1 2.1 2 6.3 3 10.1 4 13.5 5 16.4 6 18.5 7 19.8 The c alculated frequencies obtained from the dynamic analysis explained above are compared to experimental frequencies later in this section. Figure 4 30 identifies the design parameters of the final building design to be used for the f abrication phase. Figure 4 30 Final 2 D Building Design Two of the seven floors of the building system are illustrated above. The s mall size of the building model members and components made in house fabrication a cost effective

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101 and manageable option The following section will outline both the fabrication and assembly process to construct a dependable model reflective of design parameters. Fabrication In this section, the fabricat ion metho ds of the two dimensional building model are identified in detail Maintaining accurate fabrication and assembly technique is critical during the construction of any structural model and allows for more confidence in experimental findings. Similar to the bridge assembly, individual tools used as well as precision methods will be presented as a reference for any future researcher wishing to construct a similar model. Both column and floor plate material was ordered in bulk and trimmed to the appropriate dimensi ons noted in the design drawing s (Appendix A ). Columns and floor girders were cut from a 0.05 inch thick sheet of multi purpose spring steel 10 95 and a 0.5 inch thick clear PVC sheet, respectively. This was performed with a band saw mach ine PVC oo Both machines were provided by the University of Florida Structures and Coastal laboratories and when combined with preliminary dimension marks resulted in a quick, economic, and accurate method to mass producing the 14 columns and eight floor plates illustrated in Figure 4 30 Steel plates were used to provide the isolated masses located at each story level. Using a horizontal band saw and noting a steel density o f 0.282 lb/in 3 a sheet of steel was ordered and cut into seven 8 inch 4.2 lb. segments to meet the design guidelines. The f astener layout called for inch b olt holes located at the top and bottom of all metal column s to be ce ntered and separated by 1 inch ( Figure 4 30 ). through holes were needed at the center of each PVC floor beam and steel plate to fix

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102 each mass at the floor level. All bolt holes were performed using a drill press ma chine with appropriate drill bit coupled with center punch device to assure proper hole placement Once all components were cut and drilled to correct dimensions the erection phase required minimal forecasting. 20 fasteners tightened into predrilled h oles connected PVC beams to the top and bottom of each steel column. This member orientation was preserved for seven stories; after which mass was applied to each level and fastened with a bolt. Figure 4 31 shows the erected s tructural model after the final stages of assembly. Figure 4 31 Erected 2 D Building Model

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103 With the proper fabrication and assembly methods, this two dimensional building model will prove to be a valuable structural dynamic research tool to be used in numerous experime nts and academic applications. Dynamic Testing and Results Although the closely matched design requirements, physical fabrication of structural me mbers and various assumptions in analysis can introduce discrepancies between the actual and predicted response. As a result, with any new structural model, dynamic experiments must be conducted in order to characterize inherent dynamic properties and qua ntify its response to dynamic loading. Similar to the bridge model discussed earlier in this work a series of hammer impact and forced vibration experiments were used to input energy to the system and collect structural response data to obtain natural fr equencies and mode shapes of the building model. This section identifies the sen s or instrumentation and dynamic testing details of both impact and random ground excitation methods. Instrumentation. To capture building response to dynamic excitation, the u niaxial accelerometers (PCB Piezotronic ICP) joined with the 20 channel data acquisition system (National Instruments CompactDAQ) previously imp lemented on bridge tests were applied. Seven degrees of freedom combined with a two dimensional building orien tation resulted in a total of seven accelerometers installed ; one at each floor level of the building The magnetic feature of the sensors allowed for easy attachment to the exterior of each column. Figure 4 32 is a schematic of the sensor layout for the building model.

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104 Figure 4 32 2 D Building Sensor Layout In contrast to the bridge model, this building model only had one orientation with no additional modifications; therefore the manipulation in sensor layout was not needed and could be preserved for both impact and random vibration tests Because the s tiffness differential between rigid floor beams and slender columns is significantly high, only one chord of the system is ne eded to me monitored to accurately capture system response. As shown above, the string of nodes included on the left chord was chosen. During both impact and random vibration testing, the bottom PVC floor plate was fixed to the base floor to establish a rigid connection. It is common practice during a dynamic test to capture input energy being applied to the system so an eighth sensor was fixed

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105 to the shake table platform during the shake table ground excitation tests. By capturing input vibration, futu re structural identification methods can be completed to obtain full dynamic characteristics of the structure. Impact Test. Applying energy by use of an impact hammer was the initial excitation method used on the model and was a quick and effective testing method to verify m odel design goals To perform this pretesting phase a mallet hammer was used to provide impact to the test specimen I n plane impact was the only applicable force direction due to the two dimensional configuration of the model Build ing frequency response data as a result of hammer impact at the top floor is displayed in Figure 4 33 Figure 4 33 Frequency Response of 2 D Building from Impact Plotted in the frequency domain, the seven fundamental frequenc ies can be clearly identified. S election of nodal impact location for this structure was conducted in a similar fashion to previous bridge impact tests and relied on the expected mode shapes

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106 of the structur e. For example, maximum displacement in a Mode 1 dominating response occurs at the top floor level When deciding on a floor of impact, if Mode 1 is the modal response of interest then impact should be applied to the t op floor If Mode 2 is the modal re sponse of interest then impact should be applied the floor with the largest anticipated displacement for Mode 2 which is at the quarter points. It is important to note that if Mode 2 was the response mode of interest and impact was applied to the middle s pan of the structure, then minimal energy would be applied to Mode 2 because the node of impact has no theoretical vibration response. Ambient v ibration t est. After exposing the building model to impact dynamic testing and obtaining resonant frequencies, t he next step in the dynamic testing program was to apply forced ground excitation by means of the uniaxial shake table. This test method is used as a secondary measure to confirm structural dynamic findings previously obtained from the less complex impa ct tests detailed earlier. Subjected to a band limited white noise vibration, this structure was monitored in a similar fashion as impact tests conserving the same sensor type and orientation with the addition of a sensor at the base of the shake table plat form. A large benefit to the impact pretesting previously described, is not only the identification of fundamental modes, but the confidence in the selection of frequency range for a random vibration test. As discussed earlier, a band limited white noise vibration signal requires a range of frequency content for which the random signal is to be generated. If dynamic characteristics of this test structure were unknown, an estimated frequency range would need to be chosen and then refined for future shake table tests. After obtaining the seven modal frequencies from the pretesting procedure, a frequency range of 0 20Hz

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107 was selected and applied to generate a random input signal. Shown in Figure 4 34 is frequency response data coll ected as a result of ambient vibration. Figure 4 34 Frequency Response of 2 D Building Figure 4 35 Theoretical vs. Experimental Mode Shapes

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108 Confirming the dynamic characterization found from impulse tests, the shake table vibration tests proved to be another dynamic testing method to obtain critical information on the structural system. Illustrated on each mode shape plot are the corresponding calculate d theoretical mode shapes based on the design parameters Using calculated eigenvectors with a reference node located at the shake table platform, these shapes are able to be compared to experimental mode shapes obtained from frequency response data. It is clear the theoretical behavior anticipated by applying the equation of motion is an accurate analysis method to predict system response for this test structure. It is also found that the peak picking technique is a dependable method for determining mod al frequencies due to the well separated, high amplitude peaks in the frequency response of the model. In some instances, the frequency response peaks can be associated with bending modes of different directions or even torsional modes as was the case wit h the bridge. By designing one layer of structural members intending to only resist load in one direction, the presence of other bending or torsional components are eliminated, providing a dependable structural model with clear data that can be confidentl y quantified. Predicted vs. Experimental Although mode shapes illustrated in Figure 4 35 share similar deflection orientations, numerical magnitudes of natural frequencies differ slightly between design and experimental natural frequencies. Table 4 5 compares the calculated natural frequencies from Table 4 4 to the experimental frequencies obtained from both testing methods.

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109 Table 4 5 Predicted vs. Experimental Natural Frequencies Mode Frequency (Hz) Predicted Experimental 1 2.1 1.5 2 6.3 4.7 3 10.1 7.3 4 13.5 10.8 5 16.4 13.0 6 18.5 15.2 7 19.8 16.8 I nput variables applied to the dynamic analysis method include ma ss (m), material properties (EI), building dimensions (H) and fixity (k). While the transition from design to fabrication can alter some of these parameters, the only variable not strictly regulated is the fixity between beam and column interface An ass umption in the preliminary analysis was a rigid connection with column stiffness calculated as ( 4 1 ) where (H), (E) and (I) correspond to column height, m odulus and inertia respectively. A coefficient of 12 was the support coefficient used to calculate the stiffness of a c olumn with fixed ends which prevent s rotation. In a case where top and bottom column supports possessed pinned ends, a coefficient of 3 would be applied C onnection types like the bolted connections located at each floor of the model building would have a realistic coefficient between the two extremes however this is nearly impossible to predict After c omparing experimental to theoretic al frequency values which were a true column support coefficient of 6. 25 was determined to be the most accurate estimation to parallel the first three modes of each model.

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110 Table 4 6 compares the experimental frequencies values with those calculated using the adjusted support coefficient of 6.25 Table 4 6 Predicted Adjusted and Experimental Frequency Values Mode Frequency (Hz) Predicted Adj usted Experimental 1 2.1 1.5 1.5 2 6.3 4.5 4.7 3 10.1 7.3 7.3 4 13.5 9.8 10.8 5 16.4 11.8 13.0 6 18.5 13.3 15.2 7 19.8 14.3 16.8 Adjusting this interstory stiffness and comparing frequency data to experimental response provides an even more a ccurate numerical model of the physical structural system. The o bjective of this work was to design, build, and dynamically identify a small scale structural building model that can be used as a dependable structure with an identifiable behavioral respons e. It is illustrated by clear frequency response data obtained from multiple dynamic tests that this building model can effectively contribute to structural dynamic tests and be utilized as a baseline structure for future research applications. 3 D Dyna mic Building Model Previous work involving the design and construction of the two dimensional building not only provided the facility with a new structural model but also laid a solid foundation for the design and analysis process of any future building to be integrated into the laboratory. Additionally, by significantly e xpanding the force generating capabilities of the facility by adding the six degree of freedom shake table lar ger test structures are able to be introduced t o the dynamic testing progr am, in particular a

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111 larger scale 3 D building model. Incorporating such a model would not only fully utilize s hake table dimensions force cap acities, and multiple degrees of freedom but provide current and future researchers an opportunity to expand re search interests to larger model applications Similar to the two dimensional building, a primary objective of this portion of work is to produce a responsive structural model however an additional goal is to incorporate model versatility allowing for mu ltiple types of experimental set ups to be implemented Design This section details the decision process and provides explanation behind the various design parameters selected such as dimensions, distributed masses, and model adaptability. In some structu ral dynamic experimental applications, the design of a test model design will be targeted to resemble an existing structure so tests can be applied and direct conclusio ns can be made relating to that structure. As a general approach, t h e building model pr esented in this section was designed to model not a specific structure, but a typical mid rise steel building by preserving dynamic similitude. This left many design variables to be determined which are mainly based on laboratory space constraints where t he structure w ill be contained the excitation equipment projected to be used during testing, and overall project expenses for materials and fabrication. Using past building model design experiences as a guideline model width (W), height (H), mass (M), f ixity (k) and material /cross section geometry (EI) needed to be selected so the dynamic response of the structure could be predicted. To do this, capabilities of the newly installed shake table were used as a starting point to determine the initial direct ion of design.

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112 Multi DOF motion capabilities influenced the general model design to include three dimensional member orientation which enabled response motion to occur in both a strong and weak axis. P roviding a multi directional response model would be a progressive step forward from the previous structure which was strictly based on planar motion Floor pates, supported by multiple rows of columns, were sized based on the 4ft x 4ft shake table platform having a length and width of x Figure 4 36 illustrates the proposed building and shake table dimensions. Figure 4 36 Plan view of Building on Shake Table The p late thickness was determined later as it was influenc ed by a number of factors that were finalized later in the design process. With more than twenty feet of clear space available i n the facility where the model would be housed vertical space constraints were not applicable. Investigation

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113 on similar work performed with a steel structural mo del to be u sed in shake table applications ( Wierschem et al. 2012) helped to narrow this design parameter. Selecting a n intersto r y height of ten inches in combination with a total of six floor levels yielded a total he ight of approximately 60 inches (with the final dimension s depending on plate thickness ) The dimensions chosen provided a workable model for instrumentation, as well as preserving a height to width ratio from previous model designs where successful exper imental applications were established. Aiming for experimental longevity and model durability, structural steel was selected as the primary material With the project budget being a nother factor for s tructur al design fabrication costs were expected to remain lowest if mater ial continuity was maintained. All steel with the exception of the column components was A36 grade and a s a preventive measure, columns were designed with high strength steel having a n increased yield stress of 100ksi Increasing th e column strength would help prevent the structure from encountering inelastic failure modes and facilitate a wider range of base excitation forces to be generated. intentions to what is actually installed on a structure can alter the structural response predicted by preliminary analysis methods To create a column to floor interface to most accurately resemble a assembly of three steel components wher e a main column element is inserted and welded to a steel flange at each column end would be implemented. This design was based on a previous welded connection detail ( Wierschem et al. 2013 ) where a rigid support condition was intended

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114 and achieved. Weld ing design and fabrication methods are later explained in the section of this chapter. Similar to the previous building specimen this model would also contain distributed masses at each floor resulting in a shear building model. Not only was the magnitude of individual masses adjusted to resemble a typical mid rise steel structure with natural frequencies from 0 20Hz, but the collective mass of the system was also taken into consideration to confirm the shake table maximum payload of 2,200 lbs was not exceeded. As a c onservative approach, mass constraints were not to exceed 75% of payload capacity, resulting in an upper bound of 1650lbs. The referenced building design incorporated the attachment of additional masses at each story ; however due to the steel material of the plates, the option to have the floor plates themselves act as the main mass of the system proved most practical. Using an iterative dynamic analysis procedure (Appendix A ) described previously, design variables from the 6 th order shear building model were applied to target the desired mid rise steel structure frequency range while remaining under the experimentally conservative payload limit Input parameters were : E = 29,000ksi H = 9.5 in. w = .5 in. t=.25in k factor = 12 (assumed rigid) M = 4.2 lbf where (E) is steel modulus of elasticity, (h) is intersto r y height, (w) & (t) is the width and thickness of supporting rectangular columns at each floor, (k factor) is the support coefficient of a rigid connection, and (M) is the mass of each plate. A dynamic analysis w as conducted for both strong and weak bending possibilities and provid ed frequency

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115 response estimations ; however the weak axis bending was used first to finalize building design parameters that satisfied the intentions of the model. While (E), (H), and (k) variables remained constant in the analysis, mass (M) and column cross section (w and t) progressed through a series of adjustments in order to achieve desired expected natural frequency values. Becaus e these three parameters provided an array of design possibilities this process became a matter of project practicality including factors from both material expenses and size availability. For example, s teel plates proved most economical when ordered in increments. This coupled with a prescribed payload limit of 1650 lbs. provided a starting point for the selection of distributed masses. By p reserving perimeter plate dimensions which was based on shake table platform size a varying p late thickness of yielded a total building weight of 1026lb, 1368lb, and 2052lb res p ectively weighing 195 p ounds each. Locking this design vari able, and using an iterative approach for column dimension inputs, a column width resulted in the targeted natural frequencies which are displayed in Table 4 7 Preserving these design variables, a second dynamic analysis was performed on the strong axis with increased natural frequency predictions identified below in Table 4 8 Table 4 7 Predicted Natural Frequencies of 3 D Bui lding Model (Weak Axis) Mode Frequency (Hz) 1 2.1 8 2 6. 43 3 10. 29 4 13. 56 5 16. 04 6 17.59

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116 Table 4 8 Predicted Natural Frequencies of 3 D Building (Strong Axis) Mode Frequency (Hz) 1 4.37 2 12.85 3 20 59 4 27.13 5 32.09 6 35.19 The increase in modal frequencies between Table 4 7 a nd Table 4 8 is directly influenced by resonant frequencies can be compared to experimental results to verify design assumptions and provide a range of frequencies for which the structural mo del will dramatically respond. The final design is illustrated in Figure 4 37 Figure 4 37 Final 3 D Building Design

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1 17 An additive design component involving interstory cross bracing was implemented as a stability measure during building transportation. Because the targeted freque ncies are obtained without these members applied to the structure, anticipated dynamic tests will not include these members since they will significantly add to the lateral stiffness of the model and augment resonant frequency values to an impractical rang e. Singular cross bracing components however, can be added to test the effects of stiffness discon tinuity in a structure. After all fundamental design checks were complete and confidence in model design was established, shop drawings included in Appendi x 1 were created and delivered to the UF Coastal Laboratory where the proper manufacturing equipment is available to fabricate the structure as precise to th e design drawings as possible. Finite Element Model After design parameters were determined, a fi nite element model was developed using a general finite element software package (ADINA 8.8). This model was created to not only confirm calculated dynamic characteristics of the test structure, but to identify critical limit states of the model prior to real testing applications. To most accurately represent the parent building model two separate element types were i mplemented As a result of being subject to both axial compression from gravity and bending moment due to ground motion, columns were repre sented in the finite element model by beam elements A series of four node shell element s were used to model each steel floor plate It is important to note that plate bending was not anticipated in the 1 inch thick steel plates in comparison to the slim columns so nine node shell element s w ere not adopted for this modeling application

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118 The steel material and member dimensions were represented using a standard modulus of 30,000ksi and column and plate dimens respectively. Similar to the previous bridge model, a steel density of 0.00029k/in 3 /g was used to account for the total mass of the system. Global boundary conditions were released allowing for the full three dimensional response of the model To simula te a fixed connection to the shake table, the bottom nodes were restrained from both translation and rotation in the X, Y, and Z axes Relative to plate and building sizes, the selected column cross section seemed quite small with potential stability con cerns. To ensure this structure would not buckle under its own self weight, bucking calculations (Appendix 1) were performed and compared to the FE predictions proving that despite the proportionally small column thickness, each bottom column would only b e loaded to 15% of the critical buckling load. This limiting state was quantified using an appropriate rigid fixity assumption based on the welded joint connection. This structural model is intended to remain a long lasting structural dynamic research t ool in the lab. To limit any permanent deformation during testing static defle ction checks were also performed on the FE model to determine the maximum distance the structure can displace. Due to the bolted connections fixing the base plate of the model to the shake table, inertial lateral forces generated from either ground motion or impact excitation will cause the structure to respond similar to a cantilever beam. As a result, highest stress will occur in the base columns where translation and rotati on are both restrained for bottom nodes. Figure 4 38 present s a visual of the FE

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119 model subject to a n 830 pound static load corresponding to an effective yielding stress of the bottom columns. A. B. Axial Forces Bending Momen ts Figure 4 38 Axial Forces and Bending Moments Incorporating both axial force and bending stress components effective stresses were calculated for critical elements T op story displacement of 3 in result ed in base columns reaching their 100 ksi yielding stress. Using this max imum displacement value as a limiting constraint for dynamic testing, preventive measures will be instilled to ensure generated forces will not invoke a top level displacement of thi s magnitude. Using the modal analysis feature of the finite element program, previous natural frequency calculations listed in Table 4 7 and Table 4 8 were confidently verified. Illustrated in Figure 4 39 are the six mode shapes in the limiting weak axis of motion

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120 Mode Shape 1 Mode Shape 2 Mode Shape 3 Mode Shape 4 Mode Shape 5 Mode Shape 6 Figure 4 39 FEM Predic ted Modes for the 3 D Building Model The development of a finite element model is a valuable component to the structural dynamic research done in this lab. With a working and accurate computer model, potential experiments can be simulated and preliminary results can be anticipated and compared. This will prevent any misuse of the structural model and shake table combination

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121 FE model, fabrication, detailed in the next section, was t he subsequent phase in the development of this structural model. Fabrication In the previous structural models identified in this work, such as the two dimensional building model, fabrication by the structural designers was possible due to the m inimal costs associate d with material and the smaller scale of the project. In the case of the three dimensional building model, where the scale and level of detail is increased it was decided to seek a third party fabricator to ensure quality and precis ion of the various components required in the model design. After a cost analysis of different fabrication avenues, the University of Florida Coastal Engineering Laboratory had the capabilities, personnel, and availability to perform a project of this mag nitude As a result this section will provide a general outline of the fabrication phases with detailed plan sets and photos included in Appendix A With multiple steel components in the building design a total of four different steel sizes were deliver ed for assembly. Floor plates were shipped in the design accuracy tolerance of +/ the fastener holes in the proper location, a vertical drill and mag drill was used to cut the face through hol es and edge holes, respectively. Cross bracing, delivered in precut holes to fasten to the edge of each floor. Although floor plates weight approximately 200 pounds each the columns posed to be the most challenging fabrication component in the structure. To preserve a rigid connection, the column flange interface was designed as a welded joint; Figure 4 40 provides a sketch of the designed col umn.

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122 Figure 4 40 Designed Column strength steel Organized in Figure 4 41 are photos correspondin g to the genera l process of the column assembly. Figure 4 41 Column Fabrication Process

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123 The process illu strated Figure 4 41 is explained here. The ends of each column fac e plates acting as the top and bottom column flanges. These plates not only provide an element for column connection, but also are large enough to provide bolted con nection points to fix the assembled column to floors above and below The three component set is then fit into a steel frame to allow for accurate alignment while welding. The full penetration weld la yers (full details in Appendix A ) are applied until th e void is eliminated and the final column assembly is then smoothed for a final product. Figure 4 42 shows an assembled column floor plate interface with cross bracing attached. Figure 4 42 Joint Interface Using bolted connections to connect the welded column flanges to the floor plates, each node closely resembles a rigid connection. Subsequent d y namic experiments are used to verify this connectivity assumption. Figure 4 43 shows the erected building model after the final stages of assembly.

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124 Figure 4 43 Erected 3 D Building Model By using the appropriate fabrication methods and equipment, this three dim ensional building model will not only be used in various structural dynamic experiment applications but should prove to be a valuable research tool for future research projects

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125 Dynamic Testing and Results After the construction of a building model the ne xt step is to apply the test specimen to dynamic experiments to quantify its dynamic response Similar to the previous building, test results can be used to verify or rectify a design assumption such as a boundary condition or joint stiffness to accuratel y represent physical experimental model. As shown in Figure 4 43 the steel structure is separated by individual components consisting of a plate at each floor and six connecting columns above and below the intermediate stories. B y utilizing this configuration type multiple structures could be tested ranging from a three to a fully erected six story building. Using previous dynamic testing procedure s from past structural models as a basis both impact and forced vibration excitat ion methods were applied to the various model s with subsequent modal analysis to characterize each structure and compare to previous calculations. Although this test specimen provides the ability to test multiple building models with altered heights this section will elaborate on the instrumentation and testing methods of the six story model followed by the supporting results from other building compositions. Instrumentation. The building has the potential to respond in each of the strong, weak, and t orsional axes In p rior building instrumentation o nly one chord of sensors was needed to monitor the planer response motion of the model. The three dimensional response of the steel building in combination with the limited number of sensors available in the laboratory presented a more detailed instrumentation process than the previous applications explained in this work

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126 Figure 4 44 3 D Building Labeling Convention Figure 4 44 ill ustrates the select ed labeling configuration of each floor plate Based on the supporting column orientations, the X and Y axes identified in Figure 4 44 are associated with the strong and weak axes respectively. To monitor vib ration response of the structure, the same uniaxial accelerometers are used as in previous testing applications. This required each corner to have two possible sensor positions to capture dominant vibrations in either the X or Y axis. When selecting sens or positions it is most common to select locations associated with anticipated maximum limit states or vibration amplitudes For example, accelerometer s are used to capture vibrational response and should be placed in areas that experience maximum relativ e displacement ( corners of each plate) If member strength is a concern strain transducers should be placed where maximum stresses are anticipated to occur (bottom floor columns) In the case of the building, corner nodes are the area of interest due to the larger difference in vibration between the intermediate stories. Figure 4 45 identifies the sensor layout of the 3 D building model.

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127 Figure 4 45 3 D Building Sensor Layout Sh own above in Figure 4 45 with reference to the labeling convention in Figure 4 44 sensors were placed on the A, C and D column ends at each floor level. This sensor arrangement provided the most efficie nt use of the 20 channels available by the d ata acquisition system. By applying sensors on the A and C columns in particular, weak axis bending response can be recorded. Additionally, the single line of sensors at chord D captures strong axis vibrations. Torsional modes are quantified by comparing the difference in phase between the A and C columns If these sensor groups are out of phase from one another, torsion is considered to be the dominating mode and can then

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128 be quantified accordingly. Thus, usi ng this sensor distribution layout provides the most effective orientation to monitor the g lobal response of the structure and provide sufficient data to perform modal analysis calculations Impact testing. To quantify dynamic response, impact tests by use of an impact hammer were performed first as a fast and effective dynamic testing method. Tests were conducted during the building assembly process allowing for impact testing and dynamic characterization of a three, four, and five story building model To monitor v ibrational response of a ll three dimensions multiple impact locations were needed Figure 4 46 identif ies the location and direction of impact for each of the four building models. A. B. Weak Axis Test Strong Axis Test C. Torsion Test Figure 4 46 Impac t Test Set Up

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129 Impact to the top plate of each building was applied at Node B to isolate weak axis response and quantify associate modal frequencies in this direc tion. Plotted in Figure 4 47 is the frequency response of sensors columns A from impact to Node B at the top floor of the fully erected six story building model. Figure 4 47 Weak Axis Frequency Response from Impact Visually clean peaks of energy are associated with dominating weak axis vibration response. As a result confident weak axis frequency values are selected for each of the six modal frequencies as 2.18, 6 .43, 10.29, 13.56, 16.04, and 17.59 Hz, respectively. A similar approach was preserved for a second round of tests where impact was applied to Node E with the intention of the strong axis to be the dominating bending mode. A similar trend of results is il lustrated in the frequency domain for strong axis response of sensors at Node D as a result of impact tests ; this is displayed Figure 4 48

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130 Figure 4 48 Strong Axis Frequency Respon se from Impact When comparing weak and strong axis response, there is an expected increase in frequency values as a result of the increase in stiffness along the strong axis. After further review of frequency response data in Figure 4 47 and Figure 4 48 smaller peaks can be observed between the larger energy peaks. This is due to a portion of the input energy distributed to torsion response modes of vibration In the case of this 3 D building where torsi on components may dominate the response of applied excitation, it is important to first identify torsion frequency peaks, This allows for a subsequent selection of both s trong and weak frequency peaks. To isolate torsion response, impact was applied to a nonconcentric nodal locatio n ; Node G This forced a combin ed response of the strong and weak axis and allowed for the calculation of torsion modes by analyzing the phase of sensors location at A and C. Plotted in Figure 4 49 is the frequency response data of the 6 story building with data configured to separate a torsion al mode from a bending mode.

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131 Figure 4 49 Torsional Frequency Response from Impact By isolating the sensors located on area A and C of each floor and analyzing the phase data between each, the torsion frequencies can be both visualized and quantified In Figure 4 49 high energy peaks are associated with torsion modes and low energy peaks are identified as strong or weak bending modes of vibration. Resulting natural frequency values are collected in Table 4 9 for the six story bu ilding configuration after the impact tests were applied to all dimensions of the structure. Table 4 9 6 Story Building Natural Frequencies Mode Frequency (Hz) Weak Axis Strong Axis Torsion 1 2.18 3.72 3. 9 2 6.43 11.35 11.54 3 10.29 18.85 18.62 4 13.56 23.99 24.41 5 16.04 28.63 29.17 6 17.59 31.68 31.86 Preliminary design parameters for the structural model were selected so natural frequency ranged from 0 20Hz. As shown in Table 4 9 the intended dynamic response was achieved in the actual experimental model. As mentioned previously, this model

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132 presented an opportunity to conduct impact tests on multiple buildings each with different hei ghts and t he dynamic testing procedure implemented on the fully erected structure was preserved from these previous tests. Presented in Figure 4 50 are the combined natural frequency results from the three, four, and five story building models. 3 Story Building Mode Frequency (Hz) Weak Strong Torsion 1 3.85 7.02 7.45 2 11.1 20.08 21.12 3 16 28.99 30.46 4 Story Building Mode Frequency (Hz) Weak Strong Torsion 1 2.91 5.43 5.74 2 8.39 16.05 16.54 3 12.85 24.72 25.39 4 15.77 30.33 31.37 5 Story Building Mode Frequency (Hz) Weak Strong Torsion 1 2.89 4.46 4.64 2 7.4 13.37 13.61 3 11.7 21.3 21.73 4 15 27.34 27.77 5 17.2 31.19 31.68 Figure 4 50 Three, Four, and Five Story Building Experimental Results

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133 As the number of stories increase from three to five it can be seen that natural frequency values decrease in magnitude. F or example, weak axis mode 1 frequency values steadily decline from to 3.85, 2.91, and 2.89Hz for the three, four, and five story buildings respectively. Similar trends can be found in the strong and torsion frequency values of each mode shape This can be attributed to the increase in overall mass of the structure which has a direct influence on the inherent f requency. Ambient vibration testing. Past excitation equipment and model combinations consisted of the uniaxial shake table for the 2 D building model and the long stroke vertical shaker for the steel bridge truss. Following the natural progression of past dynamic testing procedures, the 6 DOF shake table could now be implemented as the excitation source for random vibration of the building. As mentioned in the shake table section of this work, the table payload capacity is 2,200lbs. Although the fully erected building model is roughly 1,500lbs, a conservative approach was taken for the first round o f tests of this new structure. Because this was the first structure to be subject to motion by the shake table, it was decided that initially testing half of the model was a safe and logical test strategy when integrating new excitation equipment into the lab. After three story building shake table tests were complete and confidence was gained in testing proced ure and system demand, the same ground exc itation was applied to the fully erected six story structure. Figure 4 51 shows the building and shake table combination just before applying base excitation via the newly installed shake table system

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134 Figure 4 51 Six Story Building Fixed on Shake Table Platform Eight were used to fasten the building model to the shake table platform. This provided a fixed connection to the table and ensured minimal damping effects from the ground to floor plate interface. Internal LVDT sensors in each actuator were used to collect reference ground motion displacements. With known input energy and collected response vibrations a full system identification can be made available for futu re work with the structure. Referring to p revious impact test results a range of physical frequencies for which the building will response could be drawn from to set a n upper and lower frequency limit on a n excitation signal A band limited white noise s ignal with frequency range from 0 20Hz was applied as a ground ex citation in the X axis to isolate weak axis vibration response. Figure 4 52 shows the applied displacement time history record of for the ambient vibration test.

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135 Figure 4 52 X Axis Excitation on 6 Story Building Model With displacement RMS amplitude of 0.25 inches this excitation was applied for 100 second duration and p rovide d equal energy content at all frequency values in specified range with the intention to supply adequate energy for each of six modal frequencies of the building to be excited Figure 4 53 illustrates the building frequency response when subject to ground motion along t he X axis. Figure 4 53 Frequenc y Response of 3 D Building

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136 After appropriate post processing of data and applying modal analysis, calculated natural frequencies were consistent with those found fr om impact tests. Figure 4 54 shows resulting mode shapes in the X direction from the building response data when exposed to shake table vibration as it compares to the calculated mode shapes from preliminary analysis. Figure 4 54 6 Story Building X Axis Mode Shapes Falling between the intended 0 20Hz frequency range, the calculated mode shapes are plotted against the experimental modes shapes to illustrate the minimal dynamic variation betw een the design and fabrication phases. Predicted vs. Experimental. After the final tests were conducted and accurate system identification was obtained, the calculated natural frequency values from the lumped mass modal analysis were compared to experime ntal finding s Presented in Table 4 10 are compared natural frequency values in both the strong and weak dimensions.

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137 Table 4 10 Predicted vs. Experimental Natural Frequencies Mode F requency (Hz) Weak Axis Strong Axis Predicted Experimental Predicted Experimental 1 2.18 2.0 8 4.37 3.72 2 6.43 6.23 12.85 11.35 3 10.29 9.95 20.59 18.85 4 13.56 13. 00 27.13 23.99 5 16.04 15.5 0 32.09 2 8.63 6 17.59 17. 50 36.19 31. 68 After a naly zing predicted versus experimental natural frequency data design assumptions are confidently confirmed. There is larger frequency differential for the strong axis results when compared to the weak axis. This may be attributed to a few variables that can arise in any fabrication process of a structural model in particular the column flange connections. The welded joint connection on the top and bottom of each column detailed earlier in this section may have minor internal inconsistencies as the human el ement is introduced After initially characterizing the structure by quantifying natural frequencies it would be most appropriate to pursue other system identification techniques to validate current test results and to also quantify other inherent dynamic properties of the structure. A damping ratio of 0.05 was used in preliminary design and analysis however with input and output response data now available, a natural damping ratio can be calculated for use in future structural dynamic applications. Pres ented in this chapter were three individual structural models that each had a unique component and particular scope of work and each subject to multiple phases

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138 including assembly, design, fabrication and construction. In depth documentation and explanatio n of these project phases have developed this work into a valuable resource for any future researcher looking to pursue a similar area of structural dynamic r esearch.

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139 CHAPTER 5 CONCLUSIONS AND RECCOMMENDATIONS The overall goal of this research was to plan, design, and implement a fully functional research laboratory that provides a broad array of structural dynamic testing capabilities. The final outcome is a laboratory facility with three calibrated structural models representing a number of structural forms with the flexibility for modification to support a variety of experimental campaigns. Additionally, this research resulted in three dynamic excitation instruments with a range of capabilities and configurations to enable testing of many sizes and forms of str uctural models, components, and sensors. The scope of work presented in this document involves a variety of projects, all aimed to contribute to this overall goal. The main components of this research have been separated into two distinct chapters accordi ng to their functional role in the operation of the laboratory. Each project is thoroughly explained to provide a body of reference for both the design basis and research intentions of the facility. The excitation equipment employed in the laboratory co nsists of three instruments that are identified as either small or larger scale. Due to minimal installation and setup demand, the small scale devices served as an expedited approach to apply excitation for initial research interests such as sensor develo pment. As identified in Chapter 3, these devices consist of a uniaxial shake table and a long stroke shaker. On a larger scale, a 6 DOF shake table was integrated into the facility to increase the structural dynamic experimental potential and address ne w research interests. Not only was this piece of equipment implemented on a larger geometric scale than previous models, but it involved a multi dimensional project management component due to a variety of project phases. As a requirement of this work, e xplanation on the

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140 assembly, installation, and operation of the shake table system is documented, indicating the necessary planning and installation required for the successful completion of a project of this magnitude. Upon completion of these project pha ses, a calibrated and functional shake table system is available for appropriate research applications, including an operational procedure documented in a comprehensive, laboratory specific specified performance values is applied by the table, it is recommended that a full shake table characterization be performed. This characterization will allow for true performance limits to be recorded since these limits may differ slightly from the spec ified values due to the variability in the hydraulic system. As structural models were added to the laboratory inventory, all three pieces of excitation equipment presented in this research were used in multiple instances to apply energy into these structu res. These dynamic experiments enabled modal identification of each of the structural models. While the design and application intention of all of the excitation equipment is to be a useful tool for general dynamic research, the newly installed shake tabl e system also enables experimental work specific to the field of earthquake engineering. The structural models introduced in this research each have a unique purpose and research intention but all provide a valuable tool directed toward the overall field o f structural dynamic research. The prefabricated, predesigned three dimensional bridge model was promptly adopted into the facility with an initial project phase of construction and assembly. With the proper means and precision assembly methods outlined i n this work, a workable

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141 bridge model was integrated into the laboratory testing program within a few months. When compared to the dynamic response of a full scale bridge, the assembled structure possessed an overly low horizontal stiffness and an overly h igh vertical stiffness. As a result, two modifications were made to the original bridge structure. To address the overly flexible horizontal component, horizontal cross bracing along the bottom bridge deck was added to provide lateral force resistance. As illustrated by experimental modal analysis, this bracing significantly increased horizontal frequencies creating a stiff bridge deck with a more flexible top layer beam system which is a closer representation of an actual bridge. Extending the original bridge span by 2.5ft (one extra bay) the originally high vertical stiffness was reduced but is still demonstrating high vertical frequency response. One critical component to the bridge portion of this work was the creation of finite element (FE) bridge m odel. Using predicted modal frequencies as a reference, a functional relationship was established with experimental results in both the horizontal and vertical directions. These relationships were implemented to estimate ranges of frequency response asso ciated with a modal frequency. By witnessing the benefits this research tool, a new procedure to include a FE model for future structural model testing was suggested and implemented. One challenge encountered during the various stages of bridge testing wa s the inability to impose adequate energy to excite the higher frequency modes of the bridge. This was the case particularly for the vertical motion component. As discussed, the long stroke shaker applied to the bridge for vertical excitation cannot impo se adequate energy at the high range of frequencies in the vertical direction. It is suggested that

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142 future work conducted with this bridge model utilize an alternate shaker system with adequate high frequency energy generating capabilities to ensure relia ble diagnosis of the vertical dynamic response. The two dimensional, seven story building model included in the testing program encompassed project stages associated with design, construction, and structural dynamic testing. The purpose of this small sc ale model was to introduce a responsive structure for which structural dynamic response can be easily and confidently attained. The design methods, testing procedure and subsequent modal analysis pertaining to this structure was to serve as a reference fo r the three dimensional building model intended to be used in combination with the newly installed 6 DOF shake table. After applying both impact and random white noise base excitation, the structural dynamic characteristics were obtained, recorded and com pared to preliminary analysis to confirm the calculations were properly performed. This model can be adopted in many future research applications as a benchmark structure with quantified dynamic response and can also be applied for general education on st ructural dynamics. The three dimensional, six story building model implemented for this facility had similar project stages as the two dimensional building involving design, assistance in construction, and dynamic testing to quantify dynamic response. T he multiple project phases of this model drew from the various experiences with previous models. An FE approach was adopted from the previous bridge project after observing the benefit of a incorporating a working FE model to a project. Additionally, bas ic building design principl e s were taken from the previous design from the two dimensional building. Both static and modal analyses were applied to the FE model to quantify various limit states

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143 and verify preliminary design prior to the construction of th e building. After fabrication of beam and column elements and construction of the building model system, strong, weak, and torsional impact tests were conducted to obtain the global dynamic response in all dimensions. The 6 DOF shake table was then used to impose a random white noise base excitation to the six story model and verify the impact test results. Future work with this structure can include a variety of testing applications. Model versatility allows for the ability to interchange elements that can vary in cross section or material type, add concentric or non concentric masses at each floor, or to apply cross bracing on selective sides of the building. Additional experimental possibilities can be developed with the excitation capabilities of th e shake table and can include motions on a multi axial plane as well as seismic simulations. A future recommendation for this model involves the application of alternate system identification methods in an effort to provide a confidence level to a given m ode shape or to quantify other dynamic parameters such as inherent damping ratios. All three models developed in this work were created to obtain structural dynamic characteristics to be used in future research applications. The development of these model s followed by the testing procedures highlighted in this work provided the components necessary to accomplish this research goal. By incorporating three different excitation instruments and structural dynamic models into a testing program, the facility di scussed in this work has the appropriate resources to provide current and future researchers a platform to conduct a wide variety of structural dynamic research experiments.

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144 APPENDIX A DESIGN DRAWINGS Design drawings can be found in the University of Flor ida Institutional Repository at: http://ufdc.ufl.edu/IR00003553/00001

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145 APPENDIX B CALCULATIONS Calculations can be found in the University of Florida Institutional Repository at: http://ufdc.ufl.edu/IR00003553/00001

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146 APPENDIX C USERS MANUALS Users Manuals can be found in the University of Florida Institutional Repository at: http://ufdc.ufl.ed u/IR00003553/00001

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147 LIST OF REFERENCES APS Dynamics. n.d. APS 113 Electro seis [Photograph]. Retrieved from http://www.apsdynamics.com/ October 1,2013. Astroza, R., Conte, J., Restrepo, J., Ebrahimian, H., & Hutchinson, T. (2013) Shake Table Testing of a Full Scale Five Story Building: System Identification of the Five Story Test Structure Structures Congress 2013 pp. 1472 1484. Pittsburgh, PA. Billing, J. R. (1984). Dynamic L oading and T esting of B ridges in Ontario. Canadian Journal of Civil Engineering Vol. 11 Issue 4, pp. 833 843. Axis Shaking Proc. 8 th Eur. Conf. on Earthquake Engineering, Lisbon, Vol. 4, pp. 97 100. Lisbon. cale Three orey Structural Control and Health Monitoring Vol. 11, Issue 4, pp. 239 257. Chung, Y. L., Nagae, T., Hitaka, T., & Nakashima, M. (2010). Seismic Resistance Capacity o f High Rise Buildin gs Subjected t o Long Period Ground Motions: E Defense Shaking Table Test. Journal of Structural Engineering Vol. 136 Issue 6, pp. 637 644. De Silva, C. (2007). Vibration, Monitoring, Testing, and Instrumentation. Boca Raton, Florida: Taylor & Fransis Gr oup. Shaking Table Tests o n Reinforced Concrete Frames w ithout a nd w ith Passive Control Systems Earthquake Engineering & Structural Dynamics, Vol. 34, Issue 14, pp. 1687 1717. Dytran Instruments, Inc. n.d. Impulse Hammers [Photograph]. Retrieved from http://www.dytran.com October 1, 2013. Sine Runs During Modal Mechanical Systems and Signal Processing Vol. 18, Issue 6, pp. 1421 1441. Engineering Structures Vol. 30, pp. 1146 1159. Hanson, H., Throft Christensen, P., Mendes, P ., & Branco, F. (2000) Tunnel Tests of a Bridge Model with Active Vibration Control Structural Engineering International, Vol 4, pp. 249 253.

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148 Scale Truss Bridge for Structural Health Monitoring Ji, X., Fenves, G., Kajiwara, K., & Nakashima, M. (2011) a Full J. Struct. Eng ., Vol. 137 Issue 1, pp. 14 21. Kasai, K., Ito, H., Ooki, Scale Shake Table Tests of 5 In Proc., 7th Intern. Conf. on Urban Earthquake Engin. & 5th Intern. Conf. on Earthquake Engin Tokyo, Japan. Kr awinkler, H. (1988 ). Scale Effects i n Static a nd Dynamic Model Testing o f Structures. 9th World Conference on Earthquake Engineering Vol. 8, pp. 865 876 Tokyo Kyoto, Japan Ling, H. I., Mohri, Y., Leshchinsky, D., Burke, C., Matsushima, K., & Liu, H. ( 2005). Scale Shaking Table Tests on Modular Block Reinforced Soil Retaining Journal of Geotechnical and Geoenvironmental Engineering Vol. 131, Issue 4, pp. 465 476. Lu, X., Fu, G., Shi, W., & Lu, W. (2008). Shake Table Model Testing a nd i t s Application. The Structural Design of Tall and Special Buildings Vol. 17 Issue 1, pp. 181 201. Phil. Trans. R. Soc. A Vol. 365, pp. 345 372. Masters, F. J., K. R. Gurley, & D. O. Prevatt. (2008). "Full scale simulation of turbulent wind driven rain effects on fenestration and wall systems." 3rd international symposium on wind effects on buildings and urban environment 2008. Millard, S. G., Molyneaux, T. C. K ., Barnett, S. J., & Gao, X. (2010). Dynamic Enhancement of Blast Resistant Ultra High Performance Fibre Reinforced Concrete Under Flexural a nd Shear Loading. International Journal of Impact Engineering, Vol. 37 Issue 4, pp. 405 413. Mills, R. S. (1979) Model Tests on Earthquake Simulators: Development and implementation of experimental procedures. Moncar z, P. D., Krawinkler, H. (1981) eport No. 50, Stanford University, California Mota, M. A. C. A. (2011). Shake table acceleration tracking performance impact on dynamic similitude.

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149 NEES (2007). the George E. Brown, Jr. Network for Ear thquake Engineering Simulation: A Vision for an Integrated Community Davis, CA. Evaluation o f Large Scale Seismic Testing Method s f or Electrical Substation Systems PEER 410 Final Report University of Souther n California Qin, Q., Li, H.B., Qian, L.Z., & Lau, C. K. (2001). Modal Identification of Tsing Ma Bridge Journal of Sound and Vibration Vol. 247, Issue 2, pp. 325 341. Reynolds, P,. and Pavic, A. (200 Experimental Techniques, Vol. 24, Issue 3, pp. 39 44. Rezai, M. (1999). Seismic Behaviour o f Steel Plate Shear Walls b y Shake Table Testing. lumbia. Proc. SPIE Smart Structures/NDE 2008, Vol. 6932, San Diego, CA. Scale Dynamic Testing of Bridge 121. CSI Reliability Week: Paper 28, pp.1 12. Orlando, FL. ( http://vibetech.com/assets/papers/ ) Shen, S. Y., Masters, F. J., & II, H. U. (2013). A New Simulator to Recreate Extreme Dynamic Loads on Large Scale Building Component and Cladding Systems. Advances in Hurricane Engineering pp. 1090 1097 Shi Effective Force Testing Method for Seismic Simulation of Large Scale Phil. Trans. R. Soc. Lond. A Vol. 359, Issue 1786, pp. 1911 1929. Tedesco, J. W., McDougal, W. G., & Ross, C. A. (1999). Structural dynamics: Theory and applications Menlo Park, Calif: Addison Wesley Longman. Tweedy, J. (2010, March 1). Chile earthquake: Santiago airport remains closed as tour operators cancel holidays. Mail Online [Photograph]. Retrieved from https://www.dailymail.co.uk < http://earthquake.usgs.gov/earthquakes/world/10_largest_world.php > (Oct. 14, 2013)

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150 van de Lindt, J. W., Pei, S., Liu, Dimensional Seismic Response of a Full Scale Light Journal of Structural Engineering Vol. 136, Issue 1, pp. 56 65. Van Den Einde, L., Restrepo, J., Conte, J. P., Luco, E., Seibl e, F., Filiatrault, A. & Thoen, B. (2004). Development o f t he George E. Brown Jr. Network f or Earthquake Engineering Simulation (NEES) Large High Performance Outdoor Shake Table a t t he University o f California, San Diego. Proceedings of the 13th World C onference on Earthquake Engineering Vancouver, B.C. Canada. Wierschem, N. E., Luo, J., Al Shudeifat, M. A., Hubbard, S. A., Ott, R. J., Fahnestock, L. A., ... & Bergman, L. A. (2012). Simulation and Testing of a 6 Story Structure Incorporating a C ouple d T wo Mass Nonlinear Energy Sink. Proceedings of the ASME 2012 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference Chicago, IL. Wierschem, N. E., Luo, J., Hubbard, S., Fahnestock, L. A., Spencer J r, B. F., Vakakis, A. F., & Bergman, L. A. Experimental T esting of a L arge 9 S tory S tructure E quipped with M ultiple N onlinear E nergy S inks S ubjected to an I mpulsive L oading. Structures Congress, pp. 2241 2252. Williams, M. S., & Blakeborough, A. (2001). Laboratory Testing o f Structures Under Dynamic Loads: An Introductory Review. Phil. Trans. R. Soc. Lon. A: Mathematical, Physical and Engineering Sciences Vol. 359 Issue 1786, pp. 1651 1669. Engineering Structures Vol 24, Issue 9, pp. 1203 1215. Zaghi, A. E., Saiidi, M. S., & Mirmiran, A. (2012). Shake Table Response a nd Analysis o f a Concrete Filled FRP Tube Bridge Column. Composite Structures Vol. 94, Issue 5, pp. 1564 1574.

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151 BIOGRAPHICAL SKETCH Justin Roger Martinez was born in Norwich, Connecticut in November of 1988 and was raised in San Antonio, Texas where he developed a passion for the sport of baseball. To prolong his baseball career Justin attended La redo Community College where he received an Associate of Science degree This was followed by two more years as a student athlete at the University of Texas at San Antonio where he obtained a Bachelor of Science in Civil Engineering. With a graduate rese arch assistantship opportunity available, Justin pursued his interest in the structural engineering discipline and obtained a Master of Sci ence in Civil Engineering from the University of Florida