ASSESSMENT OF BRIDGE SERVICE LIFE USING WIRELESS SENSOR NETWORK by A.B.M. Mostafizur Rahman Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science in Engineering in the Civil and Environmental Engineering Program YOUNGSTOWN STATE UNIVERSITY January, 2012   Assessment of Bridge Service Life using Wireless Sensor Network A.B.M. Mostafizur Rahman I hereby release this thesis to the public. I understand that this thesis will be made available from the OhioLINK ETD Center and the Maag Library Circulation Desk for public access. I also authorize the University or other individuals to make copies of this thesis as needed for scholarly research. Signature: A.B.M. Mostafizur Rahman, Student Date Approvals: Dr. AKM Anwarul Islam, Thesis Advisor Date Dr. Javed Alam, Committee Member Date Dr. Frank Li, Committee Member Date Peter J. Kasvinsky, Dean of School of Graduate Studies and Research Date ]]]  ABSTRACT This paper describes a method for estimating remaining service life of a bridge based on real-time responses of the bridge. Real-time responses were recorded using wireless sensor network. With a significant percentage of nation’s bridges being structurally deficient or functionally obsolete and with no quantitative method of health monitoring being used in general practice, it has become the necessity to develop a SHM method, which will provide a quantitative assessment of overall bridge health. This research focuses on estimating overall condition of the bridge analyzing dynamic response rather than focusing on individual damage types, their severity and locations. SHM process in this research uses dynamic responses of a bridge subjected to service loads, collects the response through a system of wireless sensor network, simulates an ideal and practical bridge using finite element model, and then estimates the remaining service life of the bridge based on the modal correlation between the existing and an ideal bridge condition. Results indicate that the bridge under this study has lost approximately 47% of its approximately 50 years of service life in 30 years of service. It was also observed that only higher order modes are more sensitive to damage compared to lower ones. With limited budget available for bridge maintenance and repair, this research can help bridge owners, policy makers, transportation planners or any related professionals or organizations in prioritizing and allocating budgets based on actual bridge condition. ]�  DEDICATION    To my parents, Md. Hussain Ali and Mrs. Ansari Hussain, and my loving wife, Shanzida Alam – without your love, support and patience, this work would never have materialized.   �  ACKNOWLEDGEMENTS This thesis would not have been possible without the guidance and the help of several individuals, who, in one way or another, have contributed and extended their valuable assistance in the preparation and completion of this research. First and foremost, I offer my sincerest gratitude to my supervisor, Dr. Anwarul Islam, who has supported me throughout my thesis with his patience and knowledge while allowing me the room to work in my own way. I would also like to thank him for allowing me the opportunity to work with him in this research. I attribute the level of my Master’s degree to his encouragement and effort, and without him this thesis, too, would not have been completed or written. I am grateful to Dr. Frank Li, who has worked on a major part of this research, developing the wireless sensor network. I owe my deepest gratitude to the Mahoning County Engineer’s Office for their help and support by providing me with the bridge drawings and all other resources including truck and man power for collecting data from the bridge. I would also like to express my cordial appreciation to Dr. Javed Alam, Dr. Scott C. Martin and Dr. Daniel H. Suchora for their help, suggestions and encouragement during the course of this research. I would also like to thank the committee members for serving on my thesis defense committee. Finally, I would like to thank my parents, wife, friends and family members for their support and inspiration.  �]  TABLE OF CONTENTS  ^dZdXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXX]]] /d/KEXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXX]� <EKt>'DEd^XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXX� d>K&KEdEd^XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXX�] >/^dK&&/'hZ^XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXX�]]] >/^dK&d>^XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXX� �X /EdZKhd/KEE>/d 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plan and section (Unit # 2) 20 3.1 SunSPOT hardware developer’s kit 26 3.2 Wireless sensor network configurations 27 3.3 Locations of the sensors along the span 28 3.4 Standard dump truck 29 3.5 Truck axle load distribution with axle distance and track width 30 3.6 Transverse position of the truck on the traffic lane 30 3.7 Location of Hinge Joint # 1 32 3.8 Installation of sensors on the sidewalk of Market Street Bridge 34 3.9 Acceleration of Sensor A 36 3.10 Acceleration of Sensor B 36 3.11 Acceleration of Sensor C 37 3.12 Acceleration of Sensor E 37 3.13 Acceleration of Sensor F 38 4.1 Girder web and flange thickness details 42 4.2 Girder and intermediate cross frames 43 ]�  Figure Caption Page 4.3 FE model showing all elements 44 4.4 Sample time history graphs at (a) 31 ft and (b) 36 ft 46 4.5 Acceleration of node E from Sensor and FEM 48 4.6 Vibration of the bridge while the truck is on the span 49 4.7 Vibration of the bridge after the truck passed the span 49 4.8 Acceleration of Node A 50 4.9 Acceleration of Node B 50 4.10 Acceleration of Node C 51 4.11 Acceleration of Node E 51 4.12 Acceleration of Node F 52 4.13 First mode shape of the damaged bridge 54 4.14 Second mode shape of the damaged bridge 54 4.15 Third mode shape of the damaged bridge 55 4.16 Fourth mode shape of the damaged bridge 55 4.17 Fifth mode shape of the damaged bridge 56 4.18 First mode shape of the undamaged bridge 59 4.19 Second mode shape of the undamaged bridge 59 4.20 Third mode shape of the undamaged bridge 60 4.21 Fourth mode shape of the undamaged bridge 60 4.22 Twelfth mode shape of the undamaged bridge 61 4.23 First similar mode shapes of center girder 67 4.24 Second similar mode shapes of center girder 69 4.25 Third similar mode shapes of center girder 71 4.26 Fourth similar mode shapes of center girder 73 4.27 Fifth similar mode shapes of center girder 75 �  LIST OF TABLES do ��]}v WP �X� Market Street Bridge geometry �� �X� Sample of data collected from Sensor C �� �X� Summary of element properties representing the Damaged Bridge �� �X� Load multipliers for the node at 31 ft and 36 ft �� �X� Change in modulus of elasticity of undamaged and damaged bridge �� �X� Fundamental modal Frequencies of the Damaged Bridge �� �X� Summary of the elements representing the Undamaged Bridge �� �X� Fundamental modal frequencies of the undamaged bridge �� �X� Similarity of mode shapes �� �X� Mode shape values of the undamaged bridge along center girder �� �X� Mode shape values of the damaged bridge along center girder �� �X� Reduction in frequency from undamaged to damaged bridge �� �  Chapter 1 1. INTRODUCTION AND LITERATURE REVIEW--- 1.1 Introduction The main indicator of a nation’s economy is its transportation system; and infrastructure is the major element of a transportation system. For a country like the United States, whose major mode of transportation is a roadway network of 2.7 million miles of paved highways and railways, it is very important to keep this network functional. A recent statistics of the Federal Highway Administrations (FHWA) reveals that out of around 600,000 bridges, more than 25% of them are either structurally deficient or functionally obsolete (National Bridge Inventory, U.S. Department of Transportation, 2011). In the midst of the current global economic crisis, it is necessary to keep the transportation system functional to foster economic growth. But on the other hand, it is not feasible to improve the condition of a significant number of structurally deficient bridges with limited budgets. Therefore, it is necessary to prioritize bridges requiring repair or maintenance based on their current structural conditions. Traditional qualitative methods of structural health monitoring (SHM) of bridges are being used by the state Departments of Transportation (DOT) since early 70s while these methods are quite limited in estimating actual conditions of a bridge. Current practice of bridge health monitoring, �  which is called ‘Condition Rating’, involves visual observation and inspection of each of the bridge components (deck, superstructure, substructure, channel, culverts, approaches, etc.) and assign a single digit numerical value for that component based on the observation. These ratings are entered on the Bridge Inspection Record form, which is later used to update the electronic Bridge Inventory Files that contain a database (Maintenance and operation of the State inventory system, BMS) of all the past ratings of bridges (ODOT Manual of Bridge Inspection, 2010). Statistical analysis is performed using computer software to assess the present health of the bridge based on this database and present condition ratings. Along with the current bridge monitoring practice based on visual observation, the quantitative approach of SHM based on real-time bridge response data appears to be more realistic and effective in monitoring health of bridges. This approach uses advanced information technology to determine current bridge health through its dynamic structural response under vehicular loads. The wireless sensor network (WSN) approach for SHM utilized in this study is a process of assessing the present structural condition of the entire bridge based on its real-time dynamic structural response under standard vehicular loads. The real-time dynamic response of the bridge under moving load is collected via a series of wireless sensor networks deployed on the bridge during the passing of a truck of known weight. The collected data are then processed and compared with a set of computer simulated responses of the same bridge under the same loading condition to estimate its current structural health. The main distinguishing feature of this approach from other ongoing research is that, it does not focus on the damage of any specific elements of the bridge; rather it focuses on �  the overall condition of the bridge based on the combined effects of all individual damages irrespective of their type or extent on the overall behavior of the bridge. 1.2 Literature Review By simple definition, SHM is a process of executing a damage detection, characterization and quantification technique for engineering structures/systems (Dawson, 1976; Farrar and Worden, 2006). For civil engineering structures, damage can be defined as any sort of deviation of the structure’s geometric and/or material properties, boundary conditions, system’s internal and/or external connectivity (bonding of reinforcement, stud connections, construction and expansion joints, shock absorbers, etc.) from its typical design values as a result of which the structure can no longer function at its desired service level (Dawson, 1976; Farrar and Worden, 2006). Presence of damage does not necessarily mean the imminent failure of the structure, but it indicates that the structure is not performing at its optimal performance level. Damage worsens as the structure continues to serve under normal loading conditions and at some time in future, the extent of damage reaches a threshold point where it can no longer be considered as safe operating condition. One of the main goals of SHM is to monitor the system’s performance either continuously or at specified time intervals, and provide its safety and/or reliability status as well as a prognosis of its remaining service life. The history of SHM can be traced back to the beginning of 19th century when railroad wheel-tappers used to use the sound of a hammer striking the train wheel to determine if there was any damage (Farrar and Worden, 2006). Since then, damage identification and �  monitoring have emerged as exciting fields in several branches of engineering and material science. At the earlier stage, the damage assessment was qualitative. But in the last 30 years with the development of modern day tools (high sensitivity sensors, larger computing capacity hard-wares, advanced soft-wares, etc.), SHM has shifted from a qualitative approach to a quantitative approach. Based on several key factors, such as objective, precision level, purpose, method, etc., SHM can be categorized as global or local and stochastic or deterministic. 1.2.1 Modal Frequency and Mode Shape Equation of motion for any dynamic system having multi-degree of freedom (MDOF) can be described by Eq. 1.1 (Clough, 1993). > y ?< � 7= E > o ?< � 6= E > w ?< � = L<�= (1.1) Here, [M] = mass matrix, [C] = damping matrix, [K] = stiffness matrix, {f} = nodal force vector, < � = = nodal displacement vector, < � 6= = nodal velocity vector and < � 7= = nodal acceleration vector.It is necessary to determine the modal frequencies and mode shapes in order to solve this equation. Modal frequencies and mode shapes are determined by solving Eq. 1.2 for � � and<� % � = : B > w ? F� � � > y ? C<� % � = L< �= (1.2) Here, � � = modal frequency for i th mode shape, and < � % � = L < � � = L<�=� � � = i th mode shape. �  1.2.2 Deterministic and Stochastic SHM Based on the type of method used to analyze structural health, SHM process falls mainly into two categories, deterministic approach and stochastic (probabilistic) approach. Deterministic SHM follows the deterministic mathematical model for processing and analyzing the collected real-time data to assess health. In this approach, all data points and variables are uniquely determined from structures or finite element models at current and earlier states. Since there is no random variable or probabilistic distribution in deterministic model, results obtained in this approach are more accurate and reliable but because of complex relationships between variables; it is not popular for applications where three or more sets of variables are involved. Yet deterministic approach of SHM has been widely used during the early days of health monitoring research despite complexity in numerical solutions. Numerous researchers (Loland and Dodds, 1976; Begg, et al., 1976; West, 1984; Yuen, 1985; Srinivasan and Kot, 1992; Salawu and Williams, 1994, 1995) have developed in the past various methods of health assessment based on the deterministic model. Stochastic SHM process is developed based on the stochastic mathematical model where all variables and data sets do not have any unique values determined from the system, in fact, some or all of them are obtained from randomness or probability distributions. Since randomness is present, results of stochastic process have less accuracies and reliability compared to deterministic process. In recent years, stochastic approach of SHM has become more popular among researchers because of its capability of handling multiple variable and data sets with complex or undefined inter-relationships among variables. Farrar and Worden (2006) in an article divided stochastic model development process for �  SHM into three categories: supervised learning, unsupervised learning and outlier or novelty detection. The authors also cited the four steps of SHM defined by Farrar, et al. (2001) as steps of “statistical pattern recognition paradigm”. These steps are also equally applicable with little or no modification for deterministic SHM approach. The steps are: “operational evaluation, data acquisition, normalization and cleansing, feature selection and information condensation, and statistical model development for feature discrimination”. Although stochastic approach is one of the promising approaches of SHM in solving large scale civil engineering structures with complex inter-relationship among environmental, geometric and material properties, existing technical available literature is not as advanced as the deterministic approach, therefore, needs more attention from researchers. 1.2.3 Global and Local SHM Based on the objective and purpose of health monitoring, it can be categorized as global SHM or local SHM. In global SHM, overall structural condition of the structure is assessed based on real-time responses (dynamic or static) and results are interpreted in quantitative format in terms of a single or multiple numerical parameters. These quantitative results may be in either of the following terms: structural health index, percent of remaining design service life, remaining service life based on design life, etc. Global SHM does not identify and/or quantify each of the individual damage present in the structure, rather it emphasizes on the combined effect of all present damages on the �  overall performance of the structure. Global SHM, if developed to a level of practical use, can be very useful for transportation officials in prioritizing structurally deficient bridges for maintenance and repair. Local SHM tries to identify all the damages present in a structure, such as damage types, locations and extents of damage. This type of SHM received the most attention from researchers since the evolution of modern SHM. Doebling, et al. (1996) summarized past significant works on local SHM and in the same article, they cited Rytter (1993) who classified SHM into four levels. These levels are: Level 1: Determination that damage is present in the structure Level 2: Determination of the geometric location of the damage Level 3: Quantification of the severity of the damage Level 4: Prediction of the remaining service life of the structure Researchers have been trying different approaches and various methods using characteristic dynamic or static parameters for damage identification, localization and quantification. Some of these are effect of damage on modal frequencies and mode shapes or strain mode shapes, damage identification using changes in dynamically measured flexibility matrix or measured stiffness matrix, damage identification and localization by unity check in between mode shapes, damage detection by repeated update of structural property matrices (mass, stiffness and damping) to match measured static or dynamic responses, damage localization by locating structural nonlinearity, damage detection using fuzzy logic and neural network, etc. (Doebling, et al. 1996). �  Since, this research methodology uses frequency and mode shape changes for assessing structural health using a unity check method called Modal Assurance Criterion (MAC), some of the previous works using similar methods cited by Doebling, et al. (1996) are summarized in this section of literature review. Mode shape was used in damage identification and localization for the first time by West (1984). He tested a structure before and after damage occurred and determined the level of co-relation between the mode-shapes using modal assurance criteria (MAC). The change in MAC value is used to locate and quantify the structural damage. Yuen (1985) developed two parameters to compare the changes in mode shape and mode-shape-slopes of damaged and undamaged structures. These parameters are shown in Eqs. 1.3 and 1.4. < � � = � L [� � _ � � � F < � � = � � � (1.3) < � � = � � L [� � _ � � � � F < � � = � � � � (1.4) Where, < � � = � = i th mode shape of damaged structure, < � � = � = i th mode shape of undamaged structure, � � � = frequency of i th mode at damaged condition, � � � = frequency of i th mode at undamaged condition. Simulation was done with reducing stiffness to observe the change in these parameters and thereby to identify the damaged location from predicted values. He also suggested that the mode shapes need to be ortho-normalized in order to use higher mode shapes. Ortho-normalized mode shape is a form of orthogonal shape where �  the resulting vectors are all unit vectors. Mass ortho-normalization of a mode shape can be done using Eqs. 1.5 and 1.6. 0 � � L � � � � � � L � � � � � � � - : �; � � � � � � � � : �; � � � � � � � � � (1.5) Where, 0 � = N th mode shape, 0 � � = ortho-normalized N th mode shape, T � 5 : �; = displacement along DOF 1 of N th mode shape, and = � � LI 5 :T � 5 : � ; ; 6 EI 6 :T � 6 : � ; ; 6 E� EI � :T � � : � ; ; 6 L � I � :T � � : � ; ; 6 � � @ 5 (1.6) Here, I � = lumped mass associated with i th DOF. Fox (1992) proposed “Node Line MAC” instead of global MAC since the latter is less sensitive to damage. He also suggested that graphical comparison of relative mode shapes are the best way to detect damage if only mode shapes and resonant frequencies are analyzed. He also suggested a method to enhance the relative changes in order to better identify the damage location. Srinivasan and Kot (1992) suggested that mode shape is more sensitive to damage than resonant frequencies, and the changes in mode shape is well quantified by MAC values of damaged and undamaged structures. Ko, et al. (1994) to detect damage in steel framed structures described a method, which uses a combination of MAC, COMAC and sensitivity analysis. Sensitivity analysis is performed to determine the most relevant DOF, and then the MAC values between damaged and undamaged structures are analyzed to determine the most sensitive mode ��  shape. With this pre-determined DOF and mode shape, COMAC is calculated to identify damage in a structure. They found that only particular mode shapes can indicate damage in structures. Salawu and Williams (1994, 1995) demonstrated that the most important task in SHM is to select the mode shape, which is the most sensitive to damage. They compared results of mode shape relative change and mode shape curvature change to detect damage, and suggested that the MAC values can be used to identify the most sensitive mode to damage. 1.2.4 Use of MAC in SHM Modal assurance criterion (MAC) is a tool for orthogonality check between two modal vectors (Allemang, 2003). This tool is used to determine the degree of correlation between two mode shapes. In this research, MAC is used to compare the similar mode shapes of damaged and undamaged structure. MAC value ranges from 0 to 1 with 1 indicating full correlation and 0 indicating no correlation at all. Mathematical derivation of MAC is shown in Eqn. 1.7 (Burns, 2004). /#% L  < � � = � � < � � = �  . < � � = � � � < � � = � � < � � = � � � < � � = � (1.7) Where, < 0 � = � = mode shape of model A, < 0 � = � � = transpose of mode shape of model A, < 0 � = � = mode shape of model B, < 0 � = � � = transpose of mode shape of model B. ��  There are various other techniques used by researchers for determining the degree of correlation between analytical and experimental modal model. Some of these methods are: Modal Correlation Coefficient (MCC), Partial Modal Assurance Criterion (PMAC), Coordinate Modal Assurance Criterion (COMAC), Enhanced Coordinate Modal Assurance Criterion (ECOMAC), Weighted Modal Assurance Criterion (WMAC), Scaled Modal Assurance Criterion (SMAC), Cross Orthogonality and Pseudo- orthogonality check (COC and POC), Coordinate Orthogonality Check (CORTHOG), Modal Assurance Criterion Square Root (MACSR), Modulus Difference Method, Frequency Response Assurance Criterion (FRAC), Frequency Domain Assurance Criterion (FDAC) and Inverse Modal Assurance Criterion (IMAC) (Allemang, 2003; Avitabile, 1998). These methods usually fall into two categories, vector based methods and DOF based methods (Avitabile, 1998). Most of these techniques mentioned earlier are an extension, subset, or partial variation of MAC or another technique. MCC and IMAC are used instead of MAC in cases where higher sensitivity is desired because of small changes in magnitudes of modal vectors. PMAC was developed to investigate a particular set of DOFs of a system, which provides location specific correlation information. Further refined versions of this method are COMAC, ECOMAC and Modulus Difference, providing correlation between each individual pair of DOFs. WMAC, SMAC, MACSR, COC, POC and CORTHOG are correlation techniques based on normalized modal vector weighted by mass and stiffness matrices. FRAC and FDAC are similar tools which are suitable for frequency domain analysis. Choice of the suitable technique for a particular case is made based on the nature and objective of the study. Since this research is solely focused on the overall assessment of the bridge health and ��  not individual damage location, methods providing spatial correlation information are not used; rather degree of correlation of the entire modal vector is determined using MAC. SHM can be further classified as smart structures with wired or wireless sensors embedded into the structure during construction or sensors installed later on old structures for continuous health monitoring and intermittent health monitoring at specified interval, etc. 1.2.5 Research Methodology This research method uses dynamic response data (acceleration) collected via a system of wireless sensor network installed during data collection process from a real-life bridge, which is in service for past 30 years and from a finite element model (FEM) simulation. All data points used in analyses are actual measured data; none of them are obtained from randomness or statistical probability distribution. Therefore, this research falls into the category of deterministic model. The collected and simulated acceleration data were then used to determine mode shapes of the bridge at both damaged and undamaged states, comparison of which using mode shape correlation gives an overall quantitative assessment of the structural condition of the bridge. Since this research does not determine type, location and severity of any individual damage, but only gives an overall assessment of current health and estimation of remaining serving life of the bridge, therefore, it is a global SHM process. ��  Chapter 2 2. PROBLEM STATEMENT AND METHODOLOGY--- 2.1 Problem Statement This study focuses on quantitative assessment of structural health of a specific bridge in service, based on real-time dynamic response of the structure. This involves the following tasks and the flow diagram shown in Fig. 2.1. � Development of wireless sensor networks in order to collect, transmit and store the dynamic response of the bridge subjected to moving loads. � Estimation of the present equivalent stiffness of the entire bridge cross-section based on recorded dynamic response. � Determination of the fundamental modal frequencies and mode shapes of the bridge in current condition using the estimated reduced stiffness. � Development of a Finite Element (FE) model of the bridge from the original construction drawings in order to determine the fundamental modal frequencies and mode shapes, which will represent the condition of the bridge without any damage or loss of stiffness. ��  � Comparative study between these two stages, which are the existing bridge and the FE model bridge to replicate the original condition, and assess the present health of the structure based on their correlation. Figure 2.1: Flow Diagram of SHM. Bridge Selection FEM Development Data Collection Damaged Stiffness Calculation Damaged Mode Shape Undamaged Mode Shape Comparative Analysis Assessed Present Health Sensor Network Development ��  2.1.1 Bridge Selection The structure selected for the health monitoring study is a bridge on Market Street over the Mahoning River and CSX Railroads near City Hall in downtown Youngstown, Ohio, commonly known as the ‘Market Street Bridge’. The formal name of the bridge is ‘Vietnam Veterans Memorial Bridge’. It is owned and maintained by Mahoning County Engineer’s Office. The Bridge No. is MAH-62-17.75 and was designed by Glaus, Pyle, Schomer, Burns & De Haven, Inc. in 1978. It was opened to traffic in 1983 and has been in service since then. The reasons for selecting this bridge for health monitoring are: (1) it is on one of the major roads connecting downtown Youngstown with Boardman and Southside of Youngstown; (2) traffic volume is relatively high; (3) this bridge is old enough to have a potential need for health assessment; and (4) it is conveniently located near YSU campus, as shown in Fig. 2.2. Figure 2.2: Location of the bridge selected for SHM study. Image source: Google Maps, 2011 ��  Figure 2.3: Aerial view of the selected bridge. 2.1.2 Bridge Description The selected bridge, an aerial view of which is shown in Fig. 2.3, is a four-lane steel plate girder bridge with concrete deck. It consists of thirteen spans supported by twelve concrete piers. The deck is 9.25 in. thick reinforced concrete slab spanning over seven equally spaced 5 ft deep steel plate girders. Transverse angle bracings are provided at a spacing of 14 ft on center for lateral stability of the girders. The vertical alignment of the bridge has a downward slope of 3.85% from southwest to northeast end of the bridge, as shown in Figs. 2.4 and 2.5. The entire bridge is divided into four units to allow for the thermal expansion and contraction. Units are joined together by three hinge joints occurring at Span No. 4, 8 and 11. The bridge has variable span lengths ranging from 78 ft 2 in. to 210 ft. Width of the bridge also varies along the length of the bridge. Table 2.1 provides a summary of the bridge geometry. Image source: Bing Maps, 2011 ��  Table 2.1 – Market Street Bridge geometry Span No. Unit No. Length (ft) Left support Right support Deck Width 1 1 191 Abutment # 1 Pier # 1 82 ft to 67 ft 10 in. 2 1 210 Pier # 1 Pier # 2 67 ft 10 in. 3 1 168 Pier # 2 Pier # 3 67 ft 10 in. 4 2 99.33 Pier # 3 Pier # 4 67 ft 10 in. 5 2 111 Pier # 4 Pier # 5 67 ft 10 in. 6 2 111 Pier # 5 Pier # 6 67 ft 10 in. 7 2 111 Pier # 6 Pier # 7 67 ft 10 in. 8 3 116 Pier # 7 Pier # 8 67 ft 10 in. to 79 ft 6 in. 9 3 116 Pier # 8 Pier # 9 10 3 93 Pier # 9 Pier # 10 79 ft 6 in. 11 4 85 Pier # 10 Pier # 11 79 ft 6 in. 12 4 85 Pier # 11 Pier # 12 79 ft 6 in. 13 4 78.2 Pier # 12 Abutment # 2 79 ft 6 in. This bridge has four lanes of traffic (two lanes of traffic in each direction) of 12 ft width each and sidewalks on both sides. Width of each side walk is 5 ft and is separated from the traffic lanes by a continuous concrete barrier. Another continuous concrete railing is provided on the exterior edge of each side walk. The horizontal alignment of the bridge is straight. ��  Figure 2.4: View of Market Street Bridge from downtown Youngstown. Figure 2.5: Market Street Bridge (looking towards downtown Youngstown). Image source: Rdcatman, City-Data.com, 2007 Image source: Daysleeper47, Wikimedia Commons, 2006 ��  2.1.3 Original Construction Drawings Original construction drawings of the bridge were collected from the office of Mahoning County Engineer in order to develop an FE model of the bridge representing the undamaged state. The undamaged state herein refers to the new bridge immediately after construction while the damaged state refers to the existing bridge. Figs. 2.5, 2.6 and 2.7 show some images of the original construction drawings of the bridge. Figure 2.6: General plan (partial). ��  Figure 2.7: Girder details (Unit # 2). Figure 2.8: Slab plan and section (Unit # 2). ��  2.1.4 Span Selection for SHM Because of resource and time limitation, it was not practically feasible to perform the health monitoring of the entire bridge. For such constraints, a representative specific span of the bridge was chosen for health assessment, which would indicate the overall current structural condition of the bridge. Considering all the factors, Span No. 6 of Unit No. 2 (Table 2.1), spanning between Piers5 and 6, was selected to be appropriate for this purpose. The main reasons for selecting this span are listed below: • It has uniform roadway width and girder spacing throughout the entire span. • Adjacent spans on both sides have the same span length, roadway width and other geometric properties. • There are no hinge joints on the adjacent spans, therefore, the span can be considered continuous. • The span is on the middle part of the bridge. • During the data collection, the test truck will get enough distance to attain constant speed; also the sensor network operator will get enough time for data collection during the truck passes the hinge joint # 1. 2.2 Methodology The current structural condition of the bridge under investigation is evaluated using the dynamic responses of the bridge. Basic structural properties (stiffness, mass, damping) of any structure are directly reflected on its dynamic responses, such as acceleration, ��  vibration frequency, vibration amplitude, mode shape, etc. Total mass of a structure or the mass of its structural component does not change substantially over time resulting into any significant effect on its structural functionality. Which means, mass is not a parameter or variable in SHM. Also, there is no precise method to measure the actual damping of any structure at any point of time. Damping is only estimated as a ratio of its critical damping and it has certain values based on the type of material. Therefore, damping is also assumed as a constant throughout the life span of the structure. The only parameter that plays significant role in health monitoring of a structure is the stiffness, which is a function of material properties (modulus of elasticity, poisons ratio, etc.), cross-sectional properties (effective depth, crack location and extent of crack, reinforcement, etc.), length of the member and boundary conditions. Damage, as it is defined in SHM as changes in material or geometric property or any support conditions (Farrar and Worden, 2007); this study is limited to damages caused by changes only in material or geometric properties, i.e., change in stiffness of the structure. In this study, acceleration and mode shape are used as the basis of health monitoring. At least two data points are needed for the analysis. First one is the undamaged state of the bridge and the second one being the current response of the bridge. For the first set of data, needed were acceleration and mode shape responses of the bridge from the undamaged state, which are the responses of the bridge after construction. Since no data have been collected at that time (almost 30 years ago), FE model (FEM) of the bridge has been developed to simulate the undamaged state of the bridge. FE model of the bridge is developed and analyzed using computer software named “Autodesk Simulation Multiphysics,” formerly known as “Algor”. One representative span of the bridge is ��  modeled in this software using geometric and material properties from actual construction drawings. Some assumptions and simplifications were made in modeling, which are stated later, in order to increase the reliability of the model. A modal analysis of the resulting FEM was performed to get the first five fundamental modal frequencies and respective mode shapes. This is the response of the undamaged bridge representing the basic structural properties without any influence of external loads. Next, the computer model has been simulated for an equivalent truck load moving at a constant speed of 35 mph over the entire span. The response of the bridge in terms of vibration amplitude and acceleration were recorded. The second set of data was obtained from the field response of the actual bridge representing the current damaged state. Several sets of data were collected through a series of wireless sensor network. A loaded truck was run over the bridge at a constant speed of 35 mph, and the acceleration of the bridge was collected and transmitted to a server via the wireless sensor network. Only the acceleration response was recorded in this process because there is no practical means of determining the fundamental mode shapes of any structure through any sensor or physical measurement. The mode shapes of the damaged structure were thus determined using a reduced stiffness computer model. In order to simulate the mode shapes of the damaged structure, the stiffness of the FE model bridge was modified to match the stiffness of the damaged bridge since it was assumed that irrespective of the type, extent and location of damage, mode shapes will be directly affected by the stiffness of the bridge. Based on this assumption, the stiffness of each element (concrete deck and steel girders) of the model bridge was reduced by certain percentage so that it produces the same acceleration as the existing bridge would ��  do. This reduced stiffness is then used for modal analysis to obtain the damaged mode shape. The structural health is assessed from the correlation analysis of the similar mode shapes of the two structures. The correlation method used in this study is Modal Assurance Criteria (MAC) developed based on the orthogonality property of the mode shape. The deviation of the MAC values from the unity indicates the deterioration of the structural health. 2.2.1 Assumptions Following assumptions were made for this study to simplify the SHM process: � The effects of temperature and lateral wind force were neglected during the data collection process. � Deck reinforcement was assumed to have less contribution towards the overall cross-sectional stiffness of the entire bridge. � Concrete barriers were not included in the FE model for simpler analyses. � Vibrations induced due to surface roughness of the deck and vehicle suspension system were ignored. � The boundary conditions at both ends of the span were taken as fixed. � It was assumed that the bearing pads supporting the girders have minimal effects on its vibration characteristics. ��  Chapter 3 3. DATA COLLECTION--- 3.1 Wireless Sensors The actual process of structural health monitoring begins with the field data collection. Acceleration response of the selected representative span of the Market Street Bridge was recorded using a series of wireless sensor network while a truck with pre-defined load was passing over the bridge at a specific speed. The truck used in this experiment was a standard 20,000 lb dump truck with an axle distance of 13 ft 6 in. Sensors used for data collection were SunSPOT (Sun Small Programmable Object Technology), as shown in Fig. 3.1, which is a Java based small programmable wireless sensor network (WSN), developed by Sun Microsystems, currently owned by Oracle. These sensors consist of three directional acceleration sensors operable within a scale of 2g to 6g with temperature, humidity and light sensors. The maximum supported sampling rate is 1 kHz. The main feature of SunSPOT is that it does not run under any conventional operating system (OS), rather it runs on squawk Java Virtual Machine (JVM), which acts both as an OS and as a software application platform. Another key  feature is it has a built-in using a universal serial b and one base station, whi Figur �� program controlled rechargeable battery, whic us (USB) port. Each development kit comes w ich collects data from sensors wirelessly. e 3.1: SunSPOT hardware developer’s kit. Image source: Oracle h can be charged ith two sensors Corporation, 2011 ��  3.2 Sensor Networks In this study, eight sensors with two base stations were used to build two wireless sensor networks. Each base station was connected to 4 sensors in a series network. Two laptops were connected to each of the base stations to store collected data. Two independent wireless networks were configured with each of them consisting of four sensors, one base station and a laptop, as shown in Fig. 3.2. In each of these networks, the sensor farthest from the base station transmits data to the nearest sensor and eventually to the base station, which transmits data to the laptop connected via a USB port. For example, in Sensor Network 1, Sensor A transmits data to Sensor B, sensor B transmits its own and data collected from Sensor A to sensor C, and so on. Consequently, Sensor D transmits all data to the base station, which then stores all collected data into the attached laptop. Figure 3.2: Wireless sensor network configurations. Customized programs were written to operate the sensors for this project using a standard Java Integrated Development Environment (IDE), such as NetBeans. All the sensors and ��  base stations were tested and calibrated before installing them in their designated critical locations on the bridge. Sensor Network 1 was deployed to collect data at a sampling rate of 1 kHz and Sensor Network 2 was set to collect data at a sampling rate of 10 Hz, and the scale for all the sensors was set to 2g. An additional extended battery pack was connected to each of the sensors via USB ports as a backup in case of primary battery failure leading to interruption in collecting data for an extended period of time. The sensors were then deployed on the bridge deck using tape. One sensor was placed at the center of the span under investigation, and others were placed on both sides of the center line at 5 ft spacing. The longitudinal distributions of sensors are shown in Fig. 3.3. Figure 3.3: Locations of the sensors along the span. 3.3 System Configurations The truck used in the data collection process was a dump truck, as shown in Fig. 3.4, owned by Mahoning County Engineer’s Office. The truck was a standard dump truck 111' 36' 40' A 56' 55' Sensors Bridge Pier # 5 Bridge Pier # 6 B C DEFG H 7 @ 5' =35' ��  having an axle distance of 13 ft 6 in. between rear and front axles and a track width of 6 ft, as shown in Fig. 3.5. A schematic diagram of transverse position of the truck during driving over the bridge is shown in Fig. 3.6. Prior to running the experiment, the truck was loaded to a total weight of 20,000 lb so that the front axle carries 4,000 lb and the rear axle carries 16,000 lb. The truck was driven along the rightmost northeast bound lane closer to the sidewalk, where the sensor networks were placed for data collection. Figure 3.4: Standard dump truck used in this study. Image source: Country Fare, Inc., 2011 ��  Figure 3.5: Truck axle load distribution with axle distance and track width. Figure 3.6: Transverse position of the truck on the traffic lane. 13'-6" 4k 16k Elevation Plan 6' 12' 12' 12' 12' 10'-4" 10'-4" 10'-4" 10'-4" 10'-4" 10'-4" Sensors 5' 5" 2' TRUCK LOAD Steel Girder Concrete Deck Traffic Lane 1' 9 1 4 " Barriers ��  Since the sensors were very sensitive and the accuracy of health monitoring process is solely dependent on the quality of the bridge response data, the bridge was closed down for all traffic before running the truck so that the acceleration measured by the sensors are the response of the bridge due to the moving truck only. Thus, the accelerations recorded through the sensors are free of noise caused by vibration of other moving vehicles. The truck was run on the bridge three times at three different speeds of 15 mph, 25 mph and 35 mph. As the truck had to turn around after each pass and come back to the southwest side of the bridge for the next pass, the bridge was opened to traffic for a short period of time in between each pass to avoid long queue of vehicles and traffic jam. The data were collected using two independent sensor networks each consisted of four sensors, one base station and one laptop used as a server, as stated earlier. Since two sets of sensor network were totally independent of each other, both sensor network and the truck timing were synchronized manually by visual observation. For manual synchronization, a point on the bridge was selected as a reference point so that when the truck was observed to pass that point, both sensor networks were activated for data collection. The criterion for choosing a reference point was to ensure visibility from both laptops locations, so that the person operating the laptop can turn on the sensors at the same time the truck hits the reference point. In this case, the Hinge Joint No. 1, as shown in Fig. 3.7, was selected as the reference point, which is located on Span No. 4 in between Piers 3 and 4. The distance of this joint from the span under investigation is approximately 200 ft, which will take four seconds at a speed of 35 mph (approximately 50 ft/sec) for the truck to reach the span after passing the reference point. In the FEM, the analysis starts when the front axle of the truck hits the span, which creates a four-second ��  time lag between the data collected from the actual bridge and the data obtained from the FEM analysis. This time lag was incorporated in the comparative analysis of the collected data. Figure 3.7: Location of Hinge Joint # 1. 3.4 Data Acquisition Process As stated earlier, the truck was run at three constant speeds of 15mph (22ft per sec), 25mph (37 ft per sec), and 35 mph (50 ft per sec). The truck started from the southwest side of the bridge and achieved the required constant speed before reaching the reference point and continued until the end of the bridge. As soon as the front axle hit the reference point (Hinge Joint 1), an observer standing there signaled the laptop operators to start data collection. Data collected at each speed were stored using Microsoft Excel ‘csv’ file format. Table 3.1 shows the sample data from one of the sensors (full data set is attached in Appendix A). ��  Table 3.1 – Sample of data collected from Sensor C IP Address Time, (msec) Sample no. Acceleration, (g) X Y Z 0014.4F01.0000.7B3C 0 0 0.1875 -0.03125 1.296875 0014.4F01.0000.7B3C 4 1 0.15625 -0.04688 1.3125 0014.4F01.0000.7B3C 9 2 0.15625 -0.04688 1.3125 0014.4F01.0000.7B3C 13 3 0.171875 -0.03125 1.296875 0014.4F01.0000.7B3C 18 4 0.1875 -0.03125 1.3125 0014.4F01.0000.7B3C 22 5 0.1875 -0.03125 1.3125 0014.4F01.0000.7B3C 27 6 0.171875 -0.04688 1.296875 0014.4F01.0000.7B3C 31 7 0.171875 -0.04688 1.296875 0014.4F01.0000.7B3C 36 8 0.171875 -0.03125 1.296875 0014.4F01.0000.7B3C 46 9 0.203125 -0.03125 1.3125 0014.4F01.0000.7B3C 49 10 0.203125 -0.03125 1.3125 0014.4F01.0000.7B3C 54 11 0.1875 -0.03125 1.296875 0014.4F01.0000.7B3C 58 12 0.1875 -0.01563 1.296875 0014.4F01.0000.7B3C 63 13 0.171875 -0.01563 1.296875 0014.4F01.0000.7B3C 67 14 0.1875 -0.0625 1.3125 0014.4F01.0000.7B3C 72 15 0.1875 -0.0625 1.3125 0014.4F01.0000.7B3C 77 16 0.171875 -0.01563 1.328125 0014.4F01.0000.7B3C 86 17 0.1875 -0.03125 1.296875 0014.4F01.0000.7B3C 90 18 0.1875 -0.03125 1.296875 0014.4F01.0000.7B3C 94 19 0.1875 -0.04688 1.296875 0014.4F01.0000.7B3C 99 20 0.1875 -0.04688 1.296875 0014.4F01.0000.7B3C 103 21 0.1875 -0.04688 1.296875 0014.4F01.0000.7B3C 108 22 0.1875 -0.04688 1.296875 0014.4F01.0000.7B3C 112 23 0.1875 -0.04688 1.296875 0014.4F01.0000.7B3C 117 24 0.203125 -0.04688 1.328125 0014.4F01.0000.7B3C 126 25 0.171875 -0.03125 1.3125 0014.4F01.0000.7B3C 130 26 0.171875 -0.03125 1.3125 0014.4F01.0000.7B3C 135 27 0.203125 -0.04688 1.296875 0014.4F01.0000.7B3C 139 28 0.203125 -0.04688 1.296875 0014.4F01.0000.7B3C 144 29 0.1875 -0.03125 1.3125 0014.4F01.0000.7B3C 148 30 0.171875 -0.03125 1.328125 0014.4F01.0000.7B3C 153 31 0.171875 -0.03125 1.328125 0014.4F01.0000.7B3C 164 32 0.203125 -0.03125 1.328125 ...……………………. …. … ………. ………… ………. ...……………………. …. … ………. ………… ………. ��  Deployment and location of sensors over the bridge sidewalk are shown in Fig. 3.8. The locations were critical for the span under consideration, and were carefully chosen to produce and collect maximum possible dynamic structural response. Figure 3.8: Installation of sensors on the sidewalk of Market Street Bridge. ��  3.5 Data Processing Only acceleration in the vertical direction was needed for mode shape analysis. The orientation of the sensors was maintained in such a way that their z-axes coincide with the vertical axis. As the high pass filter of the sensors was turned off during the data collection process, the three dimensional accelerometers were indicating the device’s orientation. As a result, the acceleration due to gravity was always present in the z- direction, which was later normalized to get the actual acceleration. This was done by taking the average of the values, and then subtracting this average value from each of the acceleration. The resulting column is the acceleration of the bridge in vertical direction in terms of g caused by the moving truck only. This was multiplied by the value of g =386.4 in./sec 2 for converting the responses into in./sec 2 . Due to some frequency interference problems, Sensor D of Network No. 1 and Sensors G and H of Network No. 2 did not transmit any of their own acceleration data. Graphical plots of the acceleration against time of the remaining sensors are shown in Figs. 3.9 to 3.13. ��  Figure 3.9: Acceleration of Sensor A. Figure 3.10: Acceleration of Sensor B. r�� r�� r�� r�� r� � � �� �� �� �� ���� ���� ���� ���� ���� ���� ���� ���� ���� o� �]}vU ]vl � � d]uUu� o��]}v}(^v�}� r� r� r� r� � � � � � ���� ���� ���� ���� ���� ���� ���� ���� ���� o� �]}vU ]vl � � d]uUu� o��]}v}(^v�}� ��  Figure 3.11: Acceleration of Sensor C. Figure 3.12: Acceleration of Sensor E. r�� r�� r� � � �� �� �� ���� ���� ���� ���� ���� ���� ���� ���� ���� o� �]}vU ]vl � � d]uUu� o��]}v}(^v�}� r�� r�� r�� r� � � �� �� �� ���� ���� ���� ���� ���� ���� ���� ���� ���� o� �]}vU ]vl � � d]uUu� o��]}v}(^v�}� ��  Figure 3.13: Acceleration of Sensor F. r�� r�� r� � � �� �� ���� ���� ���� ���� ���� ���� ���� ���� ���� o� �]}vU ]vl � � d]uUu� o��]}v}(^v�}�& ��  Chapter 4 4. MODELING, SIMULATION AND MAC ANALYSIS--- 4.1 Finite Element Model Analysis Three different types of finite element model (FEM) analyses were performed in this study. First one is a transient stress analysis (direct integration method) of the damaged bridge model, second one is a modal analysis of the damaged state of the bridge, and the third one is also a modal analysis of the undamaged state of the bridge. The software used for FEM analysis is Autodesk Simulation Multiphysics 2012 developed by Autodesk, Inc. (Autodesk, Inc., 2011), which was previously known as Algor. 4.1.1 Transient Stress Analysis by FEM Transient stress analysis was performed in order to estimate the present equivalent stiffness of the entire cross-section of the damaged bridge by simulating the moving load in a similar manner as it was during the field data collection. This process can be divided into three phases: model development, moving load generation, and analysis and post- processing. ��  4.1.1.1 Model Development Model development is the first step of any FE transient stress analysis. The success of the FE analysis is largely dependent on how the model is developed because one needs to select among the best suitable options, and make the best assumptions and simplifications depending on the nature, scope and type of analysis. Therefore, choice of best options is very critical for the accuracy and success of the FEM. For example, the finer the mesh will be, the more accurate the result will be; but on the other hand, finer mesh will complicate the model, which will require high performance computing hardware and will take more time to run. Therefore, the user has to decide the mesh size depending on the type of analysis, available resources and the level of accuracy desired. As stated earlier, because of the practical limitations, it was not possible to perform SHM on the entire bridge, but only on a selected span. Following information were obtained from the original bridge drawings to incorporate into the FEM: • Deck Type: Reinforced Concrete • Deck width: 67 ft 10 in. • Deck thickness: 9.25 in. • Overhang: 3 ft 1 in. • No. of girders: 7 • C/C spacing of girders: 10 ft 4 in. • Girder type: Built-up steel plate girder • Girder depth: 5 ft • Flange width: 1 ft 4 in. ��  • Web thickness: 5/16 in. • Flange thickness: 7/8 in. (at the mid-span of the girder), 1¾ in. (near both ends of the span) • Steel cross frame members: L 5 X 5 X 5/16 • Cross frame spacing: 14 ft Initially, the entire span along with all four barriers was modeled with brick elements, and the slab reinforcement was incorporated as embedded beam elements. Due to repeated crashing of the program while running, it became necessary to simplify the model by eliminating the barriers and by using plate elements instead of brick elements for the deck and girders. Also, deck reinforcement was replaced with equivalent thick slab under the assumption that the slab has developed cracks because of repeated traffic loads and being in service for long time. The moment of inertia of a reinforced cracked section was calculated. The equivalent slab thickness is the thickness of a pure concrete slab, which will produce the same moment of inertia as the reinforced cracked slab will. This thickness was calculated to be 5 in. (calculation is attached in Appendix B) since the slab thickness was reduced from 9.25 to 5 in., the software will only consider the mass of a 5 in. thick slab. Therefore, to account for the mass lost due to reduction in thickness, a pseudo-slab was modeled on top of this slab with a thickness of 4.25 in. having a concrete modulus of elasticity (E c ) equal to zero so that only the mass of the slab is accounted for in the analysis without increasing the stiffness of the entire deck slab. ��  Figure 4.1: Girder web and flange thickness details. The deck and the web of the girders, as shown in Fig. 4.1, were meshed with maximum mesh size of 1 ft X 1 ft. Because of the geometric limitation of the flange, it was not possible to keep the aspect ratio of the mesh as 1:1; therefore, it was meshed as 8 in X 1 ft. Intermediate cross frames at every 14 ft interval along the span were modeled as beam elements. Since the span was actually a continuous span, to make the FEM span behave as continuous, boundary conditions for all the end nodes of the girder and the deck were made as pin support. That way, each group of the end nodes will act as a support having stiffness in between a fixed support and a continuous span. The entire span was modeled as 6 different parts. The attributes of all the parts are summarized in Table 4.1. 111' Bridge Pier # 5 Bridge Pier # 6 31'-6" tf=1 3/4 " 49' tf=7/8" 30'-6" tf=1 3/4" 5' Web Thickness, tw= 5 16 " ��  Table 4.1 – Summary of element properties representing the Damaged Bridge Part No. Part Name Element Type Thickness/ Area Material Max Mesh Size 1 Web Plate 0.3125 in. Steel 1 ft X 1 ft 2 Flange 1 Plate 1.75 in. Steel 8 in. X 1 ft 3 Deck Plate 5 in. Concrete 1 ft X 1 ft 4 Flange 2 Plate .875 in. Steel 8 in. X 1 ft 5 X Bracing Truss 3 in. 2 Steel N/A 6 Pseudo-Deck Plate 4.25 in. Concrete 1 ft X 1 ft Fig. 4.2 shows the girders with cross frames and supports while Fig. 4.3 shows the entire FE model of the bridge span including girders, cross frames and the deck slab. Figure 4.2: Girder and intermediate cross frames. ��  Figure 4.3: FE model showing all elements. 4.1.1.2 Moving Load Generation Autodesk Simulation Multiphysics does not have any built-in function for simulating moving load, therefore, the moving truck load was simulated by developing a series of time-history graphs equivalent to similar loading conditions during field data collection. The model was analyzed for the truck moving at a speed of 35 mph, which is equivalent to approximately 50 ft/sec. To make the model simple, the truck load was applied on nodes at 5 ft intervals, which will require 0.1 sec for the truck to reach the adjacent node. Therefore, a total of 22 time history graphs were developed for each 0.1 sec interval and applied to corresponding 44 nodes where the truck wheel is supposed to be at that time instance. A static 1 kip load was applied on each of these 44 nodes and this was converted into time synchronized truck wheel loads of magnitude 2 kip and 8 kip by ��  multiplying the nodal loads with load multipliers, which are the y-axis values of the time history graphs developed. Table 4.2 shows samples of load multiplier (all 22 time history data is attached in Appendix C) for nodes at a distance of 31 ft and 36 ft. Each time history graph was developed by calculating the time required for the front and rear wheel to reach the corresponding node from the starting end of the span and then assigning the corresponding load multiplier values, as 2 for front wheel and 8 for rear wheel. Figs. 4.4 (a) and (b) show the time history graphs for these nodes. Table 4.2 – Load multipliers for the node at 31 ft and 36 ft Node @ 31 ft Node @ 36 ft Time, (sec) Load Multiplier Time, (sec) Load Multiplier 0 0 � � 0.51 0 �X�� � 0.61 2 �X�� � 0.71 0 �X�� � 0.78 0 �X�� � 0.88 8 �X�� � 0.98 0 �X�� � ��  (a) (b) Figure 4.4: Sample time history graphs at (a) 31 ft and (b) 36 ft. � � � � � � � � � � � �X� �X� �X� �X� � �X� >} D �o�]�o]� d]uU� d]uZ]��}��(}�v}���(� � � � � � � � � � � � �X� �X� �X� �X� � �X� >} D �o�]�o]� d]uU� d]uZ]��}��(}�v}���(� ��  4.1.1.3 Analysis and Post-Processing Linear transient stress analysis by direct integration method was performed on the developed model of the damaged bridge. Damping coefficient alpha (. ) and beta ( ) were assumed to be zero for this analysis. Other analysis parameters are listed below: Number of time steps: 400 Time step size: 0.01 sec Output interval: 1 Objective of this analysis was to find the stiffness of the damaged bridge by parametric iterations, which will produce the same acceleration as it was on the actual bridge. The parametric iterations were done by comparing the field accelerations obtained from sensors (Figs. 3.9 to 3.13) with the FE model accelerations (Figs 4.8 to 4.12) of the respective node. Fig. 4.5 shows a comparative graph of acceleration at node E obtained from sensor and FEM. The model acceleration of a particular node in the FEM was changed to match the field acceleration of the same node by gradually reducing the moduli of elasticity of the girder steel (E s ) and deck concrete (E c ) starting from their original values of 29,000 ksi and 3,000 ksi respectively. After several trial runs, it was determined that by setting E s = 14,500 ksi and E c = 1,400 ksi, both the field sensor and the FEM give the same maximum acceleration at a specific time. The reduced moduli of elasticity determined here from FEM simulation represent the equivalent stiffness of the bridge at current damaged condition. Table 4.3 shows the changes in modulus of elasticity for steel and concrete from undamaged to damaged condition as simulated in ��  FE model. Figs. 4.6 and 4.7 show the deflected shapes of the bridge while the truck is on the span and after the truck passes the span, respectively. Figure 4.5: Acceleration of node E from Sensor and FEM. Table 4.3 – Change in modulus of elasticity of undamaged and damaged bridge Modulus of Elasticity Undamaged Bridge (Standard value) (ksi) Damaged Bridge (FEM simulation) (ksi) Percent Reduction (%) Steel Girder (E s ) 29,000 14,500 ksi 50.00 Concrete Deck (E c ) 3,000 1,400 ksi 53.33 r�� r�� r�� r� � � �� �� �� � ��� ���� ���� ���� ���� ���� ���� ���� o� �]}vU ]vl � � d]uU� o��]}v}(v}(�}u^v�}�v&D X&�}u&D X&�}u�]P^v�}� ��  Figure 4.6: Vibration of the bridge while the truck is on the span. Figure 4.7: Vibration of the bridge after the truck passed the span. Acceleration data were collected from this analysis at the points where the sensors were located on the field. Since the analysis was performed for a total time period of 4 sec ��  (first 2.38 sec when both or either of the truck axles was on the bridge), all the results were generated only for 4 sec time period. Following graphs in Figs. 4.8 to 4.12 show the acceleration responses from the FEM at all sensor points under consideration. Figure 4.8: Acceleration of Node A. Figure 4.9: Acceleration of Node B. r� r� r� r� � � � � � �� �� ��X���X���X���X�� o� �]}vU ]vl � � d]uU� o��]}v}(E}(�}u&D r� r� r� � � � � � �� �� ��X���X���X���X�� o� �]}vU ]vl � � d]uU� o��]}v}(E}(�}u&D ��  Figure 4.10: Acceleration of Node C. Figure 4.11: Acceleration of Node E. r� r� r� � � � � � �� ��X���X���X���X�� o� �]}vU ]vl � � d]uU� o��]}v}(E}(�}u&D r� r� r� � � � � � �� �� � �X� � �X� � �X� � �X� � o� �]}vU ]vl � � d]uU� o��]}v}(E}(�}u&D ��  Figure 4.12: Acceleration of Node F. 4.1.2 Modal Analysis of Damaged Bridge Modal analysis was done on the same FEM with the reduced stiffness determined in previous analysis. Modal frequencies and mode shapes obtained from this FEM represented the current damaged mode shape of the bridge. Mode shape of a vibrating body is the pattern of its deflected shape after subjected to excitation, in which all parts of the system is in phase and vibrates at same frequency. The frequencies of the natural mode shapes are called natural frequencies. Since the pattern of the displaced shape is the main feature of mode shape, the magnitude or sign of displacement is not significant; rather the relative displacements of the nodes are of more importance. In this study, only vertical mode shape was considered for analysis and it was represented mathematically as the vertical displacements of the nodes. r� r� r� � � � � � �� �� � �X� � �X� � �X� � �X� � o� �]}vU ]vl � � d]uU� o��]}v}(E}&(�}u&D ��  4.1.2.1 Model development Development of the FEM is the same as the previous one. All geometric properties remained the same except the material properties were changed. Modulus of elasticity of the girder steel was set to E s = 14,500 ksi, and that for the deck concrete was set to E c = 1,400 ksi. 4.1.2.2 Analysis and Post-Processing Analysis parameters for modal analysis: Number of frequencies/ modes to calculate: 5 Lower cut-off frequencies: 0 cycle/sec. Upper cut-off frequencies: 0 cycle/sec. This FE model was analyzed for only first five natural mode shapes and their respective frequencies. Table 4.4 below shows the fundamental modal frequencies and Figs 4.13 to 4.17 show the mode shapes of the damaged bridge obtained from modal analysis, Table 4.4 – Fundamental modal Frequencies of the Damaged Bridge Mode Shape Frequency, (cycle/sec) 1 3.54316 2 3.65891 3 5.96377 4 8.28727 5 8.3565 ��  Figure 4.13: First mode shape of the damaged bridge. Figure 4.14: Second mode shape of the damaged bridge. ��  Figure 4.15: Third mode shape of the damaged bridge. Figure 4.16: Fourth mode shape of the damaged bridge. ��  Figure 4.17: Fifth mode shape of the damaged bridge. 4.1.3 Modal Analysis of Undamaged Bridge Modal analysis of the undamaged bridge was done in order to determine the mode shape of the bridge when there was no damage present. As there were no data collected after the construction of the bridge, assumption was made that the bridge had the full stiffness according to its design from the archived bridge plans. 4.1.3.1 Model Development Finite element model was developed in the same procedure as the previous one, except certain changes that were made in the deck elements and material properties. From the calculations according to the American Association of State Highway and Transportation ��  Officials (AASHTO) Bridge Design Specifications, 4 th ed. [A4.6.2], it was determined that for the worst case scenario, the cracking moment of a slab strip is less than the actual moment for a HS-20 truck load, for which the bridge was designed in 1979 (calculation is attached in Appendix D). This indicates the slab did not crack initially under the design truck load. Therefore, the deck thickness was taken as 9.25 in. and there was no need for modeling a pseudo-deck, as no correction for mass was needed. Since this model represents undamaged state of the bridge, modulus of elasticity for steel was taken as E s = 29,000 ksi and that for concrete was taken as E c = 3,000 ksi, with compared to the damaged bridge where these were reduced to 14,500 ksi and 1,400 ksi respectively. Table 4.5 shows the summary of the FE model properties representing the Undamaged Bridge and their comparison with the Damaged Bridge. Table 4.5 – Summary of the elements representing the Undamaged Bridge Part No. Part Name Element Type Thickness/ Area Material Max Mesh Size Undamaged Bridge Damaged Bridge 1 Web Plate 0.3125 in. 0.3125 in. Steel 1 ft x 1 ft 2 Flange 1 Plate 1.75 in. 1.75 in. Steel 8 in. x 1 ft 3 Deck Plate 9.25 in. 5 in. Concrete 1 ft x 1 ft 4 Flange 2 Plate .875 in. .875 in. Steel 8 in. x 1 ft 5 X Bracing Truss 3 in. 2 3 in. 2 Steel N/A 6 Pseudo-Deck Plate none 4.25 in. Steel 1 ft x 1 ft ��  4.1.3.2 Analysis and Post-Processing Analysis parameters in this case were same as they were for the damaged bridge except, this time it was analyzed for up to 13 th mode shape to find the mode shapes similar to the damaged mode shape. Table 4.6 below shows the natural modal frequencies of undamaged bridge obtained from modal analysis of the FE model. Table 4.6 – Fundamental modal frequencies of the undamaged bridge Mode Shape Frequency, (cycle/sec) 1 5.00141 2 5.21542 3 7.41937 4 11.5915 5 11.7539 6 11.9157 7 11.9299 8 11.9388 9 11.941 10 11.942 11 11.9492 12 12.0445 13 12.3868 It was observed that there were some unwanted mode shapes occurred due to the local buckling of the girder webs and flanges. Only mode shapes exhibiting vertical deflections and similar to the mode shapes found in the damaged bridge were considered for health monitoring purposes. These mode shapes are shown in Figs. 4.18 to 4.22. ��  Figure 4.18: First mode shape of the undamaged bridge. Figure 4.19: Second mode shape of the undamaged bridge. ��  Figure 4.20: Third mode shape of the undamaged bridge. Figure 4.21: Fourth mode shape of the undamaged bridge. ��  Figure 4.22: Twelfth mode shape of the undamaged bridge. 4.2 MAC Analysis Correlation analyses of the similar mode shapes between undamaged and damaged bridge were carried out to determine the current structural condition of the bridge. Theory of MAC was applied in this process. MAC requires mode shape data from two similar modes of the structure under consideration. From the modal analysis of both structures, it was observed that similar mode shapes do not occur in the same order in the undamaged structure as in the damaged structure. In this case, the first four mode shapes of damaged bridge is similar to the first four mode shapes of undamaged bridge but the fifth mode of damaged bridge is similar to the twelfth mode of undamaged bridge. Modes fifth to eleventh of the undamaged bridge occurred due to local buckling and lateral displacement, which are excluded from this study since it is beyond the scope of this research. Similarity between mode shapes is shown in Table 4.7. ��  Table 4.7 – Similarity between mode shapes Undamaged Bridge Damaged Bridge Mode # 1 Mode # 1 Mode # 2 Mode # 2 Mode # 3 Mode # 3 Mode # 4 Mode # 4 Mode # 12 Mode # 5 Also, because of the large size of the finite element models in terms of their number of nodes, it was not practically possible to include mode shapes of all the nodes into the analysis. Therefore, 22 nodes along the top flange of the center girder at an interval of 5 ft were chosen as the representative mode shapes. The mode shape values (vertical displacements) of these nodes are shown in Tables 4.8 and 4.9. ��  Table 4.8 – Mode shape values of the undamaged bridge along center girder Nodal distance along x axis, (in.) Mode Shape of Undamaged Bridge Mode 1 Mode 2 Mode 3 Mode 4 Mode 12 12 -0.00025 -6.3E-16 0.00029 0.00091 2.46E-12 72 -0.00207 -5.4E-15 0.002396 0.006543 1.19E-11 132 -0.0049 -1.3E-14 0.00557 0.013606 1.34E-11 192 -0.00847 -2.3E-14 0.009521 0.020898 8.7E-12 252 -0.0125 -3.4E-14 0.013935 0.027318 5.96E-14 312 -0.01674 -4.6E-14 0.018516 0.032004 -1.1E-11 372 -0.02096 -5.8E-14 0.023065 0.034264 -2.4E-11 432 -0.02489 -7E-14 0.027276 0.033276 -3.6E-11 492 -0.02824 -8E-14 0.030817 0.028594 -4.6E-11 552 -0.03076 -8.9E-14 0.033493 0.020634 -5.6E-11 612 -0.03229 -9.4E-14 0.035126 0.010327 -5.6E-11 672 -0.03275 -9.6E-14 0.035615 -0.00117 -4.5E-11 732 -0.03207 -9.5E-14 0.03489 -0.01252 -3.1E-11 792 -0.03033 -9.1E-14 0.033038 -0.02245 -2.2E-11 852 -0.02763 -8.3E-14 0.030169 -0.02982 -2.1E-11 912 -0.02415 -7.3E-14 0.026476 -0.03377 -2.5E-11 972 -0.02013 -6.1E-14 0.022173 -0.03404 -2.4E-11 1032 -0.01589 -4.8E-14 0.017592 -0.03124 -2.1E-11 1092 -0.01167 -3.6E-14 0.013028 -0.02615 -1.8E-11 1152 -0.00771 -2.4E-14 0.008686 -0.01948 -1.2E-11 1212 -0.00427 -1.3E-14 0.004862 -0.01214 -5.5E-12 1272 -0.00162 -5E-15 0.001876 -0.00526 -4.8E-13 ��  Table 4.9 – Mode shape values of the damaged bridge along center girder Nodal distance along x axis, (in.) Mode Shape of Damaged Bridge Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 12 -0.00013 1.27E-15 0.000155 0.000433 2.48E-12 72 -0.00152 1.46E-14 0.001788 0.003937 2.02E-11 132 -0.00405 3.88E-14 0.004664 0.00917 2.01E-11 192 -0.00741 7.09E-14 0.008432 0.015015 3.01E-11 252 -0.01133 1.08E-13 0.012746 0.020478 3.42E-11 312 -0.01553 1.48E-13 0.017329 0.02472 -3.9E-11 372 -0.01976 1.88E-13 0.021926 0.027153 -1.7E-10 432 -0.02374 2.26E-13 0.026224 0.026897 -3.2E-10 492 -0.02715 2.58E-13 0.029924 0.023386 -4.2E-10 552 -0.02973 2.83E-13 0.032638 0.017018 -4.3E-10 612 -0.0313 2.97E-13 0.034326 0.00856 -3.3E-10 672 -0.03178 3.01E-13 0.034979 -0.00097 -1.5E-10 732 -0.03108 2.94E-13 0.034081 -0.01038 3.27E-11 792 -0.02929 2.77E-13 0.032167 -0.01849 2.07E-10 852 -0.02653 2.51E-13 0.029254 -0.02434 3.54E-10 912 -0.02298 2.17E-13 0.025404 -0.02721 4.37E-10 972 -0.01893 1.79E-13 0.021021 -0.02685 4.22E-10 1032 -0.01468 1.39E-13 0.016403 -0.024 3.66E-10 1092 -0.01051 9.93E-14 0.011853 -0.01946 2.92E-10 1152 -0.00669 6.31E-14 0.007627 -0.01385 1.86E-10 1212 -0.00347 3.27E-14 0.004009 -0.00804 8.35E-11 1272 -0.00114 1.08E-14 0.001347 -0.00306 2.75E-11 ��  Pairs of similar mode shapes of the center girder at both undamaged and damaged conditions are presented in Figs. 4.23 to 4.27. These graphs were developed by plotting the vertical mode shape displacements of each node along the top of the center girder against their respective x-coordinate values. It was observed that each of the first four pairs of mode shapes is almost identical in shape (as shown in Figs. 4.23 to 4.26), which also reflected in their MAC values. Significant deviations have been observed between the mode shapes of the last pair (Fig. 4.27), therefore, the MAC value of the corresponding pair also deviates significantly from unity. For the matrix operations of the mode shape matrices and MAC value calculations, MathCAD 14.0 (Parametric Technology Corporation, 2007) has been used. Following notations have been used in the MAC analysis: Un = Undamaged mode shape matrix of the n th similar mode Dn = Damaged mode shape matrix of the n th similar mode Un T = Transpose of the mode shape matrix Un MACn = MAC value for the n th similar mode shapes For example, first mode shape matrix of the undamaged condition is denoted as U1 in MathCAD and formed as a column matrix using the values of first column of Table 4.8, similarly, same matrix of damaged condition is denoted as D1 and formed using the values from first column of Table 4.9. Transpose of these two matrices is denoted as U1 T and D1 T and transpose operation is performed using MathCAD built-in transpose command. MAC value for each set is calculated in MathCAD using Eq. 4.1. ��  /#%J L : � � � � � � � ; . : � � � � � � ; �: � � � � � �; (4.1) Formulation of the mode shape matrices, their transpose matrices and MAC calculation using Eq. 4.1 for all five cases are shown in MathCAD format in subsequent sections following the mode shape graphs of each case. ��  4.2.1 MAC Value of First Similar Mode Shapes (a) At undamaged condition (b) At damaged condition Figure 4.23: First similar mode shapes of center girder. r�X��� r�X�� r�X��� r�X�� r�X��� r�X�� r�X��� � � ��� ��� ��� ��� ��� ��� ��� ��� ��� ���� ���� ���� ���� ���� ]��v~]vX ]�o�ouv��}u�}vv�~]vX~u}� r�X��� r�X�� r�X��� r�X�� r�X��� r�X�� r�X��� � � ��� ��� ��� ��� ��� ��� ��� ��� ��� ���� ���� ���� ���� ���� ]��v~]vX ]�o�ouv��}u�}vv�~]vX~u}� ��  MAC value calculation using MathCAD for first similar mode shapes: U1 0.000246393− 0.00206899− 0.00490081− 0.00846656− 0.012498− 0.0167446− 0.0209645− 0.0248928− 0.0282385− 0.0307563− 0.0322907− 0.0327451− 0.0320685− 0.0303264− 0.0276291− 0.0241452− 0.0201338− 0.0158899− 0.0116665− 0.00770766− 0.00426696− 0.00161522− � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � := D1 0.000131662− 0.00151984− 0.00405037− 0.00741336− 0.0113283− 0.0155291− 0.0197623− 0.0237431− 0.0271543− 0.0297305− 0.0313049− 0.0317766− 0.0310768− 0.02929− 0.0265319− 0.0229833− 0.0189253− 0.0146785− 0.010514− 0.00668768− 0.00346855− 0.00113933− � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � := U1 T            = D1 T            = MAC1 U1 T D1⋅ () 2 U1 T U1⋅ () D1 T D1⋅ () ⋅ := MAC1 1= ��  4.2.2 MAC Value of Second Similar Mode Shapes (a) At undamaged condition (b) At damaged condition Figure 4.24: Second similar mode shapes of center girder. r�X�r�� r�r�� r�r�� r�r�� r�r�� r�r�� � � ��� ��� ��� ��� ��� ��� ��� ��� ��� ���� ���� ���� ���� ���� ]��v~]vX ]�o�ouv��}u�}vv�~]vX~u}� � �r�� �r�� �X�r�� �r�� �X�r�� �r�� �X�r�� � ��� ��� ��� ��� ��� ��� ��� ��� ��� ���� ���� ���� ���� ���� ]��v~]vX ]�o�ouv��}u�}vv�~]vX~u}� ��  MAC value calculation using MathCAD for second similar mode shapes: U2 6.3253E-16− 5.39737E-15− 1.29126E-14− 2.25515E-14− 3.37527E-14− 4.57159E-14− 5.79431E-14− 6.97901E-14− 8.032E-14− 8.85444E-14− 9.39624E-14− 9.63693E-14− 9.50163E-14− 9.05378E-14− 8.31055E-14− 7.29662E-14− 6.111E-14− 4.84277E-14− 3.56972E-14− 2.36821E-14− 1.31776E-14− 5.02025E-15− � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � := D2 1.26989E-15 1.45978E-14 3.88069E-14 7.0912E-14 1.08204E-13 1.48167E-13 1.88376E-13 2.26121E-13 2.58389E-13 2.82556E-13 2.97167E-13 3.01441E-13 2.94401E-13 2.77242E-13 2.50999E-13 2.17279E-13 1.7885E-13 1.38661E-13 9.93001E-14 6.31465E-14 3.27453E-14 1.07532E-14 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � := U2 T           = D2 T            = MAC2 U2 T D2⋅ () 2 U2 T U2⋅ () D2 T D2⋅ () ⋅ := MAC2 0.999= ��  4.2.3 MAC Value of Third Similar Mode Shapes (a) At undamaged condition (b) At damaged condition Figure 4.25: Third similar mode shapes of center girder. � �X��� �X�� �X��� �X�� �X��� �X�� �X��� �X�� � ��� ��� ��� ��� ��� ��� ��� ��� ��� ���� ���� ���� ���� ���� ]��v~]vX ]�o�ouv��}u�}vv�~]vX~u}� r�X�� r�X��� r�X�� r�X��� r�X�� r�X��� r�X�� r�X��� � � ��� ��� ��� ��� ��� ��� ��� ��� ��� ���� ���� ���� ���� ���� ]��v~]vX ]�o�ouv��}u�}vv�~]vX~u}� ��  MAC value calculation using MathCAD for third similar mode shapes: U3 0.000290274 0.0023955 0.00556964 0.00952134 0.013935 0.0185156 0.0230645 0.0272756 0.030817 0.0334934 0.0351257 0.0356147 0.0348899 0.0330377 0.0301686 0.0264763 0.0221726 0.017592 0.0130281 0.00868569 0.00486211 0.0018762 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � := D3 0.000154883 0.00178843 0.00466425 0.0084323 0.0127464 0.0173291 0.0219264 0.026224 0.0299235 0.0326381 0.0343256 0.0349789 0.0340813 0.0321669 0.029254 0.0254039 0.0210214 0.0164026 0.0118525 0.0076271 0.00400902 0.00134652 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � := U3 T            = D3 T            = MAC3 U3 T D3⋅ () 2 U3 T U3⋅ () D3 T D3⋅ () ⋅ := MAC3 0.999= ��  4.2.4 MAC Value of Fourth Similar Mode Shapes (a) At undamaged condition (b) At damaged condition Figure 4.26: Fourth similar mode shapes of center girder. r�X�� r�X�� r�X�� r�X�� � �X�� �X�� �X�� �X�� � ��� ��� ��� ��� ��� ��� ��� ��� ��� ���� ���� ���� ���� ���� ]��v~]vX ]�o�ouv��}u�}vv�~]vX~u}� r�X�� r�X�� r�X�� � �X�� �X�� �X�� � ��� ��� ��� ��� ��� ��� ��� ��� ��� ���� ���� ���� ���� ���� ]��v~]vX ]�o�ouv��}u�}vv�~]vX~u}� ��  MAC value calculation using MathCAD for fourth similar mode shapes: U4 0.000910117 0.00654276 0.0136064 0.0208982 0.0273181 0.0320038 0.0342638 0.0332755 0.0285944 0.0206338 0.0103266 0.00116705− 0.0125247− 0.0224462− 0.0298177− 0.0337732− 0.0340375− 0.0312428− 0.0261485− 0.0194766− 0.0121383− 0.00526403− � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � := D4 0.000432669 0.00393707 0.0091698 0.0150146 0.0204783 0.0247204 0.0271532 0.0268965 0.0233863 0.0170181 0.00855996 0.000967776− 0.0103756− 0.0184898− 0.0243356− 0.0272096− 0.0268504− 0.0239984− 0.0194601− 0.0138472− 0.00803987− 0.00305718− � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � := U4 T          = D4 T           = MAC4 U4 T D4⋅ () 2 U4 T U4⋅ () D4 T D4⋅ () ⋅ := MAC4 0.998= ��  4.2.5 MAC Value of Fifth Similar Mode Shapes (a) At undamaged condition (b) At damaged condition Figure 4.27: Fifth similar mode shapes of center girder. r�r�� r�r�� r�r�� r�r�� r�r�� r�r�� r�r�� � �r�� �r�� � ��� ��� ��� ��� ��� ��� ��� ��� ��� ���� ���� ���� ���� ���� ]��v~]vX ]�o�ouv��}u�}vv�~]vX~u}�� r�r�� r�r�� r�r�� r�r�� r�r�� � �r�� �r�� �r�� �r�� �r�� � ��� ��� ��� ��� ��� ��� ��� ��� ��� ���� ���� ���� ���� ���� ]��v~]vX ]�o�ouv��}u�}vv�~]vX~u}� ��  MAC value calculation using MathCAD for fifth similar mode shapes: U5 2.46182E-12 1.19035E-11 1.34347E-11 8.69827E-12 5.9638E-14 1.10972E-11− 2.35865E-11− 3.59704E-11− 4.58563E-11− 5.5685E-11− 5.6341E-11− 4.45272E-11− 3.14162E-11− 2.23334E-11− 2.0806E-11− 2.48866E-11− 2.38913E-11− 2.05009E-11− 1.77792E-11− 1.16013E-11− 5.47314E-12− 4.83006E-13− � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � := D5 2.47768E-12 2.01557E-11 2.01342E-11 3.01267E-11 3.41823E-11 3.92054E-11− 1.70281E-10− 3.21883E-10− 4.21237E-10− 4.28503E-10− 3.29566E-10− 1.48945E-10− 3.27475E-11 2.07009E-10 3.54203E-10 4.37185E-10 4.21702E-10 3.65798E-10 2.92077E-10 1.85702E-10 8.35252E-11 2.7497E-11 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � := U5 T            = D5 T            = MAC5 U5 T D5⋅ () 2 U5 T U5⋅ () D5 T D5⋅ () ⋅ := MAC5 0.054= ��  Chapter 5 5. RESULTS AND DISCUSSIONS--- 5.1 Results It is clear from the FEM results that there are distinct differences in the behavior of the two models. Acceleration graphs from the damaged model of the bridge show that the acceleration is the maximum at the instant when the truck reaches that corresponding node, which is desirable from practical standpoint. After the truck passes the span, the acceleration started diminishing out. This behavior is also expected, which explains the effectiveness of the FEM. Comparison of the natural frequencies of the structure at the damaged and undamaged conditions shows that the frequencies of the damaged structure is around 30% less than that of the undamaged structure for majority of the mode shapes. Table 5.1 below summarizes the frequencies of mode shapes for both conditions and also shows the percent reduction between undamaged and damaged condition for each mode shape. ��  Table 5.1 – Reduction in frequency from undamaged to damaged bridge Similar Mode Shape Undamaged frequency, (cycle/sec) Damaged frequency, (cycle/sec) % Reduction in frequency, (%) 1 5.00141 3.54316 29.16 2 5.21542 3.65891 29.84 3 7.41937 5.96377 19.62 4 11.5915 8.28727 28.51 5 12.0445 8.3565 30.62 It is known from structural dynamics that natural frequency is directly proportional to square root of stiffness and inversely proportional to square root of mass. Since mass was constant for both cases, therefore, frequency decrease indicates a reduction in stiffness, which means that stiffness of the bridge has been reduced due to the presence of some type of damage in the bridge. Identification of type, nature, intensity and location of damages is beyond the scope of this research. The MAC values of the first four similar mode shapes are 1 or almost close to 1 but the MAC value for the fifth similar mode shape is 0.054. According to theory of MAC, if the mode shapes are unique, the MAC value should be ideally 1, and it reduces down to 0 with reducing degree of correlation, 1 indicating full correlation and 0 indicating no correlation at all. Based on this theory, it can be concluded that first four mode shapes are not sensitive to damage; whereas fifth one is a very good indication of the presence and extent of damage. ��  This MAC value can be used to quantify the present structural condition of the bridge by normalizing the effect of stiffness reduction corresponding to this value. The bridges were usually designed to last around 50 years in service. Therefore, the reduction in service life of girders and deck can be estimated by the product of MAC deviation and percentage of reduction in member stiffness. Sample calculations are shown below. MAC value L r�rwv Deviation in MAC L : s Fr�rwv ; L r�{vx Calculations of structural service life of girders: Reduction in equivalent stiffness in girder of damaged structure L : 6 = 4 4 4 ? 5 8 9 4 4; 6 = 4 4 4 � srr L wr� Normalized reduction in equivalent stiffness of girder L : r�{vx �wr� ; L vy�u� Reduction in estimated structural service life of 50 years L : vy�u� ; �wrUA=NO L tu�yUA=NO Remaining structural service life of the girder L wr Ftu�y L tx�uUA=NO N txUA=NO Theoretically, for an average design service life of 50 years, remaining structural service life is 20 years after 30 years of construction. Calculations of structural service life of deck: Reduction in equivalent stiffness in deck of damaged structure L : 7 4 4 4 ? 5 8 4 4; 7 4 4 4 � srr L wu�uu� ��  Normalized reduction in equivalent stiffness of deck L : r�{vx �wu�uu� ; L wr�vw� Reduction in estimated structural service life of 50 years L : wr�vw� ; �wrUA=NO L tw�tUA=NO Remaining structural service life of the deck L wr Ftw�t L tv�zUA=NO N tvUA=NO Theoretically, for an average design service life of 50 years, remaining structural service life is 20 years after 30 years of construction. 5.2 Discussions The main objective of this health monitoring research was to express the current overall structural condition of the bridge analyzing real-time dynamic response data. From the data collected and analysis performed, it can be suggested that this bridge has lost approximately 47% of its service life since it was built 30 years ago. This conclusion is based on certain facts, assumptions and simplifications. This appears to be very practical and reasonable because of the fact that those bridges were usually designed and built to last around 50 years. After 30 years in service, the bridge has lost almost half of its service life. Therefore, the effectiveness and applicability of the FEM have been validated to some extent during the various stages of this structural health monitoring process. ��  The acceleration recorded through the sensors show that the amplitude does not diminish over time as it does in case of acceleration measured from FEM. One of the possible reasons is because the acceleration recorded in the sensors are not only the vibration caused by the horizontal movement of the truck over the span, but also due to the vibration induced by the surface roughness of the deck and the vehicle suspension system, which is a continuous source of vibration. On the other hand, the acceleration given by the FEM is only due to the horizontal motion of the truck at a constant speed, however, it does not account for the surface roughness and vehicle suspension. Srinivasan and Kot (1992) suggested based on their study that changes in mode shapes are more sensitive to damage than change in resonant frequencies. This study also shows that frequencies change only 30% whereas the damage is almost 50%. Ko, et al. (1994), Salawu and Williams (1994) and Lam, et al. (1995) observed in their individual studies that not all mode shapes are sensitive to damage and higher order mode shapes are likely to be more sensitive of damage. Same behavior also observed in this study. First four mode shapes were found to be insensitive to damage but the fifth similar mode (which is actually the twelfth mode in the undamaged bridge and fifth mode in the damaged bridge) shows significant changes in MAC values. ��  Chapter 6 6. CONCLUSIONS AND RECOMMENDATIONS--- 6.1 Conclusions Health monitoring is one of the most researched topics in the field of civil, mechanical and materials engineering. In bridge engineering, the aspects of health monitoring are very wide, considering the fact that percentage of structurally deficient bridges in the nation is very high. The method described in this study provides a more realistic quantitative health assessment of the bridge based on real-time structural response compared to traditional theoretical load rating and visual qualitative inspection. The first step of this process is to record the dynamic responses of the bridge when subjected to a standard truck load. Second step is to simulate the same loading on a finite element model of the bridge in order to determine the equivalent stiffness of the bridge cross- section, which will produce the same dynamic responses as in the real bridge. Third step is to determine the fundamental modal frequencies and mode shapes of the bridge with reduced stiffness determined in the previous step. This represented the mode shape of the bridge at damaged state. Fourth step is to determine the fundamental modal frequencies and mode shapes of the bridge with full stiffness, which represented mode shapes of the ��  bridge at a state without any damage. Final step of this method is to compare the similar mode shapes of two conditions and correlate them using a popular mode shape correlation algorithm known as Modal Assurance Criteria (MAC). Resulting MAC values are the indicator of the current structural condition of the bridge. It was observed that only higher order modes are sensitive to damage. Therefore, in this case, MAC value of fifth similar mode pair has been used to interpret the result in terms of remaining structural service life. Final results show that girders and deck of the selected bridge span under study have an estimated remaining service life of approximately 26 years and 24 years, respectively. Main functional feature of this method is that it does not focus on any individual discrete defect in the bridge; rather it gives an overall assessment of the remaining service life of the bridge by taking into account the effects of any type of damage present. Further refinement and justification of this method may be necessary before incorporating it into real life application due to the assumptions undertaken at the beginning of the process and due to the hardware, resources and technical limitations faced in several stages of this study. Despite all the limitations, it can be concluded that this process of SHM can be a useful source of information regarding structural service life and health data in every aspect of bridge maintenance, repair and rehabilitation, including budget allocation, strategic planning, etc. ��  6.2 Recommendations Based on the experience, challenges faced and technical difficulties, following recommendations were made for further investigations, studies and extension of this research: � Effects of temperature and transverse wind may be considered during the data collection. � Vibrations induced from the surface roughness and vehicle suspension system should be considered while performing finite element analysis. � Traffic railing barriers should be included to represent actual condition with greater stiffness. � Deck reinforcement may be included in the FEM. � Boundary conditions at the end of the span can be modified as elastic support with stiffness equivalent to the adjoining elements in order to more accurately represent the continuous span. � The effect of bearing pads at the base of the girders should be included. � Bridge can be simulated with truck running on interior lane or on multiple traffic lanes. � The effect of structural damage on lateral mode shapes or higher order mode shapes should be investigated. ��  REFERENCES 1. American Association of State Highway and Transportation Officials (AASHTO). (2007). AASHTO LRFD Bridge design specifications SI units (4 th ed.). Washington, DC: AASHTO. 2. American Concrete Institute (ACI). (2008). Building code requirements for structural concrete and commentary. Farmington Hills, MI: ACI 3. Allemang, Randall J. (2002). The modal assurance criterion – twenty years of use and abuse. 4. Autodesk, Inc. (2012). Autodesk simulation multiphysics (version 2012) [software]. San Rafael, CA. 5. Autodesk, Inc. (2011). AutoCAD (version 2011) [software]. San Rafael, CA. 6. Avitabile, Peter. (1998). Overview of analytical and experimental modal model correlation techniques. 7. Barker, Richard M., & Pucket, Jay A. (2007). Design of highway bridges (2 nd ed.). Hoboken, NJ: John Wiley & Sons, Inc. 8. Begg, R.D., A.C. Mackenzie, C.J. Dodds, and O. Loland. (1976). Structural Integrity Monitoring Using Digital Processing of Vibration Signals. in Proc. 8th Annual Offshore Technology Conference, Houston, TX, 305–311. 9. Bing Maps. (2011). [Market Street bridge, Youngstown, OH] [Bird’s eye view]. Retrieved from http://www.bing.com/maps/?v=2&cp=qvg95188c0ct&lvl=18.7&dir=277.03&sty=b &form=LMLTCC 10. Burns, Lawrence V. (2004). MAC evaluations utilized in FEA analysis for mode identification. IMAC-XXII: Conference & Exposition on Structural Dynamics. 11. Clough, Ray W., & Penzien, Joseph (1993). Dynamics of structures (2 nd ed.). New York, NY: McGraw-Hill, Inc. 12. Country Fare, Inc. (2011). [Single Axle Dump Truck] [Digital Image]. Retrieved October 24, 2011 from Countryfareinc.com: http://www.countryfareinc.com/images/pictures/equipment/SingleAxleDumpTruck 810cy_l.jpg 13. Dawson, Brian (1976). Vibration condition monitoring techniques for rotating machinery. The Shock and Vibration Digest (London: SpingerLink) 8(12):3 14. Daysleeper47. (2006). Wikimedia Commons. [Market Street Bridge (looking towards downtown Youngstown] [Digital image]. Retrieved October 24, 2011 from Wikimedia Commons: http://commons.wikimedia.org/wiki/File:DowntownYoungstownLookingNorth.jpg 15. Doebling, S. W., Farrar, C. R., Prime, M. B. & Shevitz D. W. (1996). Damage identification and health monitoring of structural and mechanical systems from ��  changes in their vibration characteristics: a literature review. Los Alamos National Laboratory report LA-13070-MS. 16. Farrar, C. R., Doebling, S. W. & Nix, D. A. (2001) Vibration-based structural damage identification. Phil. Trans. R. Soc. A 359, 131–149. (doi:10.1098/rsta.2000.0717) 17. Farrar, Charles R., & Worden, Keith (2006). An introduction to structural health monitoring. Phil. Trans. R. Soc. A 2007 365, 303-315. (doi:10.1098/rsta.2006.1928) 18. Fox, C.H.J. (1992). The Location of Defects in Structures: A Comparison of the Use of Natural Frequency and Mode Shape Data. in Roc. of the 70th International Modal Analysis Conference, 522-528. 19. Google Maps. (2011). [Market Street bridge, Youngstown, OH] [Street map]. Retrieved from http://maps.google.com/maps?saddr=Market+St&daddr=Market+St&hl=en&ll=41. 095492,-80.641451&spn=0.018661,0.042272&sll=41.096979,- 80.648918&sspn=0.018661,0.042272&geocode=FRQXcwIddFox- w%3BFd4LcwId-lEx-w&vpsrc=6&mra=dme&mrsp=1&sz=15&t=m&z=15 20. KO, J. M., C. W. Wong, and H. F. Lam (1994). Damage Detection in Steel Framed Structures by Vibration Measurement Approach. in Proc. of 12th lnternational Modal Analysis Conference, 280-286. 21. Lam, H.F., J.M. KO, and C.W. Wong (1995). Detection of Damage Location Based on Sensitivity Analysis. in Proc. of the 13th International Modal Analysis Conference, 1499-1 505. 22. Loland, O. and J.C. Dodds. (1976). Experience in Developing and Operating Integrity Monitoring System in North Sea. in Proc. of the 8th Annual Offshore Technology Conference, 313–319. 23. McCormac, Jack C., & Brown, Russell H. (2009). Design of reinforced concrete (8 th ed.). Hoboken, NJ: John Wiley & Sons, Inc. 24. Ohio Department of Transportation (2010), Bridge Inspection Manual (Part 1). (orc 5501.47). Retrieved January 28, 2012 from: http://www.dot.state.oh.us/Divisions/Engineering/Structures/News%20Document/ Manual%20of%20Bridge%20Inspection_2010.pdf 25. Oracle Corporation. (2011). Sun SPOT World. [Sun SPOT hardware developer’s kit] [Digital image]. Retrieved October 25, 2011 from sunspotworld.com: http://www.sunspotworld.com/images/SPOTKit.png 26. Parametric Technology Corporation (2007). MathCAD 14.0 [software]. Needham, MA. 27. Rdcatman. (2011). City-Data.com. [Market Street bridge, view from downtown Youngstown] [Digital image]. Retrieved October 25, 2011 from City-Data.com: http://www.city-data.com/picfilesc/picc37108.php ��  28. Rytter, A. (1993). Vibration Based Inspection of Civil Engineering Structures. P h. D. Dissertation. Department of Building Technology and Structural Engineering. Aalborg University, Denmark. 29. Salawu, O.S. and C. Williams (1994). Damage Location Using Vibration Mode Shapes. in Proc. of 12th lnternational Modal Analysis Conference, 933-939. 30. Salawu, O.S. (1995). Nondestructive Assessment of Structures Using the Integrity Index Method Applied to a Concrete Highway Bridge. Insight, 37(1l) 8, 75 -878. 31. Srinivasan, M.G. and C.A. Kot (1992). Effects of Damage on the Modal Parameters of a Cylindrical Shell. in Pa. of the 70th International Modal Analysis Conference, 529-535. 32. U.S. Department of Transportation (2010), Federal Highway Administration (FHWA). National Bridge Inventory (NBI). Retrieved from http://www.fhwa.dot.gov/bridge/nbi/defbr10.cfm#c 33. West, W.M. (1984). Illustration of the Use of Modal Assurance Criterion to Detect Structural Changes in an Orbiter Test Specimen. in Proc. Air Force Conference on Aircraft Structural Integrity, 1-6. 34. Yuen, M.M.F. (1985). A Numerical Study of the Eigenparameters of a Damaged Cantilever. Journal of Sound and Vibration, 103, 301-31 0.  ��  APPENDICES APPENDIX A Acceleration data of Sensors A, B and C Sensor A Sensor B Sensor C Time, msec Acceleration Time, msec Acceleration Time, msec Acceleration From Sensor, g Normalized, in/sec^2 From Sensor, g Normalized, in/sec^2 From Sensor, g Normalized, in/sec^2 ����  �X���� �X�������� ���� r�X�� r�X������� ���� �X���� r�X�������  ���� �X���� �X�������� ���� r�X�� r�X������� ���� �X���� �X���� ���� ���� �X���� �X�������� ���� r�X��� r�X������ ���� �X���� �X���� ���� ���� �X���� r��X������ ���� r�X��� r�X������ ���� �X���� �X���� ���� ���� �X���� r��X������ ���� r�X��� r�X������ ���� �X���� �X���� ���� ���� �X�� r�X������� ���� r�X��� r�X������ ���� �X���� r�X����� �� ���� �X�� r�X������� ���� r�X�� r�X������� ���� �X���� r�X����� �� ���� �X���� �X�������� ���� r�X��� r�X������ ���� �X���� r�X��� ���� ���� �X���� �X�������� ���� r�X��� r�X������ ���� �X���� r�X��� ���� ���� �X���� r��X������ ���� r�X�� r�X������� ���� �X���� 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���� �X������ r��X������� ���� �X������ r�X�������� ���� �X������ r�X�������� ���� �X������ r�X�������� ���� � ��X�������� ���� �X������ r�X�������� ���  ���� �X������ �X��������� ���� �X������ r�X������ ���� �X������ �X��������� ���� �X������ r�X������ ���� �X������ �X��������� ���� �X������ �X��������� ���� �X������ �X��������� ���� �X������ r�X������ ���� �X������ r�X�������� ���� �X������ r�X������ ���� �X������ �X��������� ���� �X������ �X���������  �X������   �X������  ���  APPENDIX B Calculation of equivalent deck width: Deck reinforcement: #6 @ 8” o.c. = 0.66 in. 2 /ft f c ’ = 4,000 psi, n = 8 For equilibrium: st �U � U t Lz�r�xx� : y�yw FU ; 6 By solving, y = 2.21 in. Cracked moment of inertia of 1 ft width deck strip, + � � L st �t�ts 7 u Ez�r�xx� : y�yw Ft�ts ; 6 + � � L trw�tuEJ� 8 Say, thickness of equivalent deck is, h e >D � 7 st L trw�tu D � L w�{EJ� N wEJ� (it is rounded down to be on conservative side). 1' 9 1 4 " 1 1 2 " y 0.66 in^2 ���  APPENDIX C Time history data: d]u ,]�}�� /v� d]uU � >} D�o�]�o]� d]u ,]�}�� /v� d]uU � >} D�o�]�o]� � � � � � � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � � � � � � � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � � � � � � � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � � � � �� � � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � � � � �� � � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � � � � �� � � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � ���  d]u ,]�}�� /v� d]uU � >} D�o�]�o]� d]u ,]�}�� /v� d]uU � >} D�o�]�o]� �� � � �� � � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �� � � �� � � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �� � � �� � � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �� � � �� � � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �� � � �� � � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � �X�� � ���  APPENDIX D Calculations of cracking moment and actual moment on AASHTO design slab strip width: Design slab strip width for positive moment (AASHTO [A4.6.2] eqn. 6.16a-US): M + : 59 > Ltx�r Ex�x5 here, SW + = design slab strip width, in. S = girder centre to centre distance in ft 59 > L tx�r Ex�x� sr�uu L {v�szEJ� L y�zwBP Cracking moment, M cr : B � Ly�w � B � � Ly�w� vrrr L vyv�uvLOE + � L st � {�tw 7 st L y{s�vwEJ� 8 / � � L � � � � � � L 8 ; 8� 7 8� ; = 5� 8 9 5� . 1 . � 5 5 6 4 4 4 �y�zw L wu�s k-ft Assuming the worst case scenario that the slab strip will act as a simple support, actual maximum moment on slab due to single wheel load could be: / � L � � 8 L <� 5 4� 7 7 8 Ltr�xx k-ft Therefore, M cr > M a ; Deck was not initially cracked. 10'-4" 8 k 5'-2" 5'-2"