Word Total = 4,259 (words) + (13 figures/tables x 250 words = 3,250 words) = 7,509 words

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1 Susoy, Zaurin, Catbas 1 RELIABILITY OF A MOVABLE BRIDGE BY MEANS OF A FIELD CALIBRATED MODEL by Melih Susoy, Ph.D. Candidate Graduate Research Assistant Civil and Environmental Engineering Department University of Central Florida Engineering II 116 Orlando, FL Phone: (407) Fax: (407) msusoy@gmail.com Ricardo Zaurin, Ph.D. Candidate Graduate Research Assistant Civil and Environmental Engineering Department University of Central Florida Engineering II 116 Orlando, FL Phone: (407) Fax: (407) ricardozaurin@hotmail.com F. Necati Catbas, Ph.D. Assistant Professor Civil and Environmental Engineering Department University of Central Florida Engineering II 413 Orlando, FL Phone: (407) Fax: (407) catbas@mail.ucf.edu Submitted for possible presentation and publication for the Transportation Research Board s 87 th Meeting January 2008 Washington, D.C. 08/01/2007 Word Total = 4,259 (words) + (13 figures/tables x 250 words = 3,250 words) = 7,509 words

2 Susoy, Zaurin, Catbas 2 ABSTRACT Movable bridges are special structures that can change position or configuration according to the needs. They are made of a complex combination of structural, mechanical and electrical systems. Movable bridges are reported as experiencing significantly higher deterioration rates than regular fixed bridges, due to their special operational demands, structural designs and interaction of different systems. Maintenance and management operations pose great challenges, since they require tremendous budget and effort, compared to ordinary bridges. Objective condition evaluation and modeling of these bridges are therefore, essential. The objective of this paper is to present the detailed analyses on a representative movable bridge by using field data from a series of balance tests. System reliability is shown as a promising tool for analyzing the condition of movable bridges, especially when it is based on accurate numerical models. For movable bridges, accurate modeling is crucial, since they have specially adjusted operating mechanisms. Balance condition of the bridge should be precisely represented by the model, and this can be achieved by utilizing field test data. The steps for collecting the data and updating the numerical model are explained in the paper. The writers also investigate a rather common but serious damage scenario involving movable bridges span lock failures. This scenario was analyzed using the field-calibrated numerical model and a system reliability simulation.

3 Susoy, Zaurin, Catbas 3 INTRODUCTION Heavy movable structures groups those kind of structures involving large machinery in which most operational speeds are low and critical forces are large. Large movable structures such as retractable stadium roofs, stands, pitches, navigation locks, dams, flap gates, flood control equipment, movable bridges, and others are some examples that went beyond the conventional civil engineering technology. A movable bridge is a structure which has been designed to have two alternative positions and which can be moved back and forth between those positions in a controlled manner (1). The primary purpose of movable bridges is to allow conflicting flows of traffic to pass through a crossing point or to move traffic across a waterway. A movable bridge may allow access for waterborne, rail, land vehicle or pedestrian traffic. In the majority of the cases, visual inspections and localized testing techniques are conducted to determine the condition of a structure; however, these methods are generally subjective and also require that significant damage must be sustained in order to be perceived. A study conducted by the Federal Highway Administration s NDE Center on the accuracy of bridge visual inspection concluded that at least 56% of the bridges given an average condition rating were done incorrectly (2). Even if the damage is successfully identified, the final problem facing the engineer is accurately assessing its effect on the overall health of the structure. Visual inspection also requires much time and effort, and may overlook locations of limited and/or no accessibility. To objectively evaluate the condition of existing structures and to better design new ones, researchers are exploring novel sensing technologies and analytical methods that can be used to rapidly identify the onset of structural damage (3). Coupled with analytical models, field experimental studies such as structural health monitoring can be employed for the measurement of structural responses under any loading environment to track and evaluate incidents, anomalies, damage and deterioration (4). OBJECTIVES AND SCOPE Movable bridges are reported as experiencing significantly higher deterioration rates than regular fixed bridges, due to their complex structural, mechanical and electrical systems. Maintenance and management operations pose great challenges, since they require tremendous budget and effort, compared to ordinary bridges. The objective of this paper is to present the detailed analyses on a representative movable bridge by using field data from a series of balance tests. System reliability is shown as a promising tool for analyzing the condition of movable bridges, especially when it is based on accurate numerical models. For movable bridges, accurate modeling is crucial, since they have specially adjusted operating mechanisms. Balance condition of the bridge should be precisely represented by the model, and this can be achieved by utilizing field test data. The steps for collecting the data and updating the numerical model are explained in the paper. The writers also investigate a rather common but serious damage scenario involving movable bridges span lock failures. This scenario was analyzed using the field-calibrated numerical model and a system reliability simulation. REPRESENTATIVE MOVABLE BRIDGE Selection of a representative bridge among a group of bridges Florida Department of Transportation (FDOT) is divided into seven geographic districts and one Turnpike district. Each district is responsible for element-level inspections of Florida's 11,100 bridges (6,300 State highway bridges and 4,800 local bridges). FDOT s inventory of 98 movable bridges includes 3 lift type, 94 bascule type, and 1 swing-type bridge. Note that when the 2002 National Bridge Inventory (NBI) is sorted for the years when Florida movable bridge were built, the writers obtained data for 95 bridges (Figure 1).

4 Susoy, Zaurin, Catbas 4 Figure 1 Distribution of Florida Movable Bridges by Span Length and Age (NBI, 2002) The majority of the movable bridges in Florida have main spans between 20m and 40m (~65 to 135ft), and those with less than 20m or more than 60m are very rare. The average span length is about 37m (120ft). Almost half of this bridge population is 40 to 50 years old, with the average of 42.5 years. Properties of the Representative Movable Bridge As given before, bascule bridges constitute by far the majority of movable bridge types. Based on this analysis and interaction with FDOT structures and maintenance engineers, bascule type is selected for detailed investigation, and the movable bridge over the road SR-3, known as Christa McAuliffe Bridge, was selected as the representative bridge considering its type, span length, age, opening frequency, type of traffic and accessibility (Figure 2). The selected representative movable span is the south-bound span of two parallel spans on SR-3, crossing the Barge Canal in Merritt Island, FL. This span was constructed in 1961, and underwent extensive rehabilitation twice, first in and second in It has double bascule leaves, each 70-ft (20m) long, and 40-ft (12m) wide, carrying two traffic lanes. The representative bridge opens about 6-7 times a day. Figure 2 Case Study: Bascule Bridge in Merritt Island, FL The movable bridge has concrete infrastructure for its piers and approach spans. The movable main span consists of a steel framework of welded plate girders (Figure 3). Two main girders, at both sides form the main frame together with the floor beams and transverse beams that carry the steel deck. Main girders also support the counterweight, which provides a balancing weight against the leaf. The sections shown in Figure 3 indicate the main transverse girder locations. The counterweight is constructed of cast-in-place reinforced concrete and has slots for adjusting the balance condition with additional

5 Susoy, Zaurin, Catbas 5 weight blocks. The counterweight is below the reinforced concrete approach span. Each leaf is about 50-ft (15m) long, and they are locked at each other by span locks at the tips when in closed position. The deck is made of a steel open grid, to provide maximum strength with minimum weight. The deck section between the live load shoe and the counterweight is also filled with concrete. The open grid is produced by welding steel plates as a tight square grid. Figure 3 Movable Bridge Main Girder Each leaf rotates around steel drums, called trunnions, to provide an opening angle of up to 85 degrees. The rotating torque is produced by electrical motors and transmitted to the main girder by means of a reducer and assembly of gears and shafts. The final gear on the assembly is called the pinion, and it engages with the rack assembly on the girder directly below the trunnion. When the leaf is in closed position, the main girders rest on a steel pedestal, called the live load shoe (LLS). The LLS acts as a roller support, and ensures that the traffic loads are not received by the mechanical parts. Movable Bridge Balance Tests Movable bridge operation is based on the balance of the span weight and the counterweight. When the weights of the leaf and counterweight are in equilibrium about the pivot point (trunnion), this state is called balanced condition. However, this is not the desired configuration. Weights of the leaf and counterweight should be distributed in such a way that the leaf can be closed manually without too much effort in the event of a power failure. There are no accepted standards for this weight distribution, however, maintenance engineers agree that this condition should make the leaf drift slowly downward without power during most of the closing operation. At the same time, the motor should make the minimum torque to overcome the static friction. Florida Department of Transportation is using Bascule Bridge Balance Tests (5) for evaluating the balance state and verify the functioning of the shaft-gear-trunnion system. A test team of engineers from FDOT State and Materials Office in Gainesville conducts these tests by visiting the bridges with approximately an annual schedule, or whenever there is a rehabilitation or alteration on the bridge which should change its balance condition. The test is performed by mounting strain sensors on the main drive shafts to obtain the torsional shear strain (Figure 4). Torsion creates pure shear strain on the surface of circular shafts, which can be measured by two strain gages placed along principle axes, perpendicular to each other. Strain data is sent with an amplifier to the data acquisition software on a laptop to be converted into torque values while the bridge is in operation.

6 Susoy, Zaurin, Catbas 6 Figure 4 Strain Gage Assembly for Torsional Strain on the Main Shaft Angle of rotation of the bascule leaf is measured with tiltmeters, using the same data acquisition system. Tiltmeters are resistance-based and pendulum type, and they are attached on the main girder via their magnetic bases. The balance test is performed during a consecutive opening and closing operation. Test data is recorded as torque (T) versus the angle of rotation (θ). Typical plots of average torque (AVT), which is the average of opening and closing torques, with respect to the opening angle θ, are given in Figure 5. The average torque changes with the horizontal distance between the trunnion and center of gravity, thus, it is a cosine curve. The positive region of this plot is unbalance towards the leaf side, and the negative region corresponds to unbalance towards the counter-weight (heel) side. Trunnion Center of Gravity Trunnion Center of Gravity Figure 5 Different Cases of Average Torque during Opening and Closing AVT is affected by environmental conditions, such as wind, ice or snow, and the friction in the system, which acts in the opposite direction of the movement. The friction is obtained from the difference between the opening and closing torques, as per the equation below;

7 Susoy, Zaurin, Catbas 7 T f To Tc = (1) 2 where T f is the friction torque, T o is the opening torque and T c is the closing torque. The friction number is indicative of lubrication on the trunnion, rack and gears, as well as any mechanical problem. Although there are no quantitative limits, maintenance is required when the friction number is calculated to be relatively high, in comparison with the previous values. The writers and FDOT personnel conducted bridge balance tests on two different movable bridges. The bridges were instrumented as described before and shown in Figure 6(a). The raw data were provided by FDOT to the writers for analysis. In addition, the writers obtained data from past studies to track the bridge balance characteristics. Average torque and friction torque were calculated and plotted against the rotation angle for the three different tests (Figure 6(b, c, d)). Comparison of results of the three tests performed on different dates shows that, although the average torque curves have similar shapes, their magnitudes change significantly. Difference between opening and closing curves indicates the friction torque, which is always acting against the direction of movement. Figure 6(e) and Figure 6(f) show the average torque and friction torque comparisons of the three most recent balance tests on Christa McAuliffe Bridge. A decreasing trend of average torque, as observed for consecutive tests, can be mainly because of different balance conditions, due to changes in dead loads or reconfigurations. The difference in average torques are relatively low. However, the friction changes are very significant from one test to the other. Friction torque is known to decrease by proper maintenance and lubrication of the mechanical parts, mainly, the trunnion. Also, rehabilitation efforts on this bridge have improved the mechanical operation, leading to lower friction torque values.

8 Susoy, Zaurin, Catbas 8 Figure 6 Comparison of Results for the Three Balance Tests (a) Data Collection, (b) Balance Test on 02/11/2003, (c) Balance Test on 05/06/2003, (d) Balance Test on 02/21/2006, (e) Comparison of Average Torques, (f) Comparison of Friction Torques

9 Susoy, Zaurin, Catbas 9 Balance and friction results are affected by all rehabilitation, alteration and maintenance works, as well as deterioration effects. Although reduction of the total imbalance and friction can be associated with the overall rehabilitation work, the root reasons of the change in imbalance and friction numbers need further exploration. In the current practice, the change in friction with respect to baseline is considered and some rules of thumb in terms of bridge balance are employed based on the engineers experience. To track the bridge balance and imbalance and their interaction with other phenomena such as environmental effects, it is clear that the bridge balance should be monitored for long term, and performed real-time for each bridge operation, in order to track the balance condition dependably and identify the interaction of deterioration and maintenance actions. Also, accurate numerical models of movable bridges should possess the same balance condition with the actual bridge. Incorrect balance condition will lead to different support reactions and internal stresses for the numerical model, and a fundamentally different behavior. Therefore, the balance test is crucial for modeling movable bridges. FINITE ELEMENT MODELING AND CALIBRATION WITH EXPERIMENTAL DATA As mentioned in previous sections, critical structural elements were identified as the deck, girder and transverse beams from the inspection reports. Development of a finite element model (FEM) helped determine the locations and types of extreme stresses over these members by performing load simulations and reliability analysis. The bridge is formed by two variable-depth bascule girders, connected in the transverse direction by W beams which at the same time support six W16 36 responsible for holding the deck and transferring the loads to the W and bascule girders (Figure 7). Figure 7 Finite Element Model Development for the Movable Bridge (deck not shown) The structural model for this bridge could be simplified as consisting of two simply supported beams with a hinge connection at the center. Main girders of the bridge were modeled with shell elements, having six degrees of freedom at each node. Frame elements were used for transverse beams and floor beams. The deck was made up of steel grating in order to provide rigidity while being light weight. It was first modeled as a grid of frame elements, and then, an equivalent deck model was used exhibiting the same behavior as the first deck model, but using shell elements with constant thickness, which proved to be more efficient in terms of computation time. The model was formed of different types of finite elements, and in order to accurately represent the connectivity between these, rigid link elements were used at necessary locations. They were used for connecting the web and flange sections of the main girder, which was made of shell elements, for

10 Susoy, Zaurin, Catbas 10 connecting the transverse beams, which were made up of frame elements, to the main girder, and for linking the deck elements to the girders (Figure 8). Also, because different frame elements, like W and W16 36 have non-coinciding centers of gravity, in those connections between them, a rigid link was necessary to ensure a robust model. Figure 8 Rigid Links Used for Building the Main Girder and the Trunnion Region The trunnion is a critical component of a movable bridge, providing a pin support about which the weight of the whole span rotates during opening and closing of the movable bridge. The trunnions are built to be very rigid and strong, and to allow rotation with minimum friction during rotation. A pin support connected to the girder with rigid links simulates the trunnion region in the FEM, reproducing the rotational displacement freedom and the rigidity of the trunnion/hub/girder assembly. Figure 9 FEM calibration with Balance Test Data To achieve the same balance condition with the actual bridge, the model was calibrated using the balance test data from the most recent test. The initial average torque for that test was 106 kip-ft. The initial torque was adjusted in the model by releasing the live load shoe, and assigning a moment reaction at the trunnion (Figure 9). This effectively represents the initial condition of the leaf prior to opening, and the moment reaction at the trunnion represents the unbalanced moment, or the initial average torque value. Therefore, only a single leaf of the bridge model was analyzed, fixing at the trunnion and removing the live load shoe support. The weight of the counterweight was adjusted by iteration to match the calculated imbalance moment. The final obtained weight was used in the original model that will provide the same balance state. This calibrated model was then used for evaluating the bridge behavior and running analyses to calculate the load rating and bridge system reliability with different load conditions. RELIABILITY SIMULATION OF THE MOVABLE BRIDGE Reliability Reliability of a bridge is the ultimate probability of meeting the specified performance levels over a given time, which is the design life. Reliability method involves probabilistic analysis of all resistance and demand parameters of a structure. Failure probability is evaluated by defining failure limit states, denoted

11 Susoy, Zaurin, Catbas 11 g, and estimating the joint probability distributions of these limit state functions. Limit states define the failure criteria according to a selected failure mode. The curve or surface defined by g = 0 is the failure surface dividing failure and survival spaces. Engineers aim is always making g greater than zero, but how close to zero it may approach is related with the balance between risk and cost (6-8). Reliability index is a unit of failure probability, which is the area under the limit state surface. For a linear limit state function, which is used in this study, First-Order Reliability Method (FORM) can be used for calculating the reliability index. The limit state function is shown in Eq. (2). g ( M u,m DL,M LL ) M u M DL M LL = (2) M u, M DL, M LL : random variables representing the moment capacity, dead load moment and live load moment, respectively. Evaluation of the reliability index, β, according to the FORM is given in Eq (3). µ M µ u M µ DL M LL β = (3) ( σ ) + ( σ ) 2 + ( σ ) 2 M u 2 M DL M LL where µ represents the mean values and σ represents the standard deviations of the random variables. Component reliabilities can be generated with the sensor-based degradation models for time functions of reliability. System reliability and component reliabilities can be monitored in real-time, and different alert levels can be triggered when a value below a critical reliability index is calculated. System Reliability System reliability is a major concept in reliability analysis, because individual limit state functions are assembled together in a system model. The failure conditions are determined by the system model, since failure of one or two members may not be important due to redundancy. On the other hand, there may be critical components (fracture-critical) which have to stay intact for the structural integrity of the whole system. System reliability can be modeled with certain assumptions, which is assembling the failure limit states as parallel or series links after determining the failure modes. Evaluation of a system model is performed by reducing first the parallel components. System failure probability of parallel systems are solved by; n ( P f ) = ( Pf ) i k = 1 k, n: # of parallel members (4) Therefore, the model is reduced to only serially connected members. Failure of each component means failure, so all the components should survive for structural integrity. So, the resulting series system can be solved by the following; m ( P f ) = 1 ( P ) system [ f ] i 1, m: # of series components (5) i= 1 Parallel and series models of the movable bridge structural components were constructed according to the most general structural failure mechanisms. The main components of the system were the main girder bending failure state, main girder shear failure state, and the moment failure of the transverse beams. The main girder failure states were assumed as the failure condition at any of the monitored sections. These sections, however, are not completely independent, therefore cannot be modeled as acting in series.

12 Susoy, Zaurin, Catbas 12 Accounting for the correlation of the failure probabilities at these sections, two limit cases were considered. The first case is assuming no correlation between the failure of monitored sections, which can be modeled as a series system in this case, and the second case is modeling them as fully correlated limit states, so the failure of the main girder system depends on the section with the highest probability of failure. The system model is shown in Figure 10(a), which illustrates the lower bounding case and Figure 10(b), which illustrates the upper bound case. (a) (b) Figure 10 Movable Bridge System Reliability Model with Parallel/Series Assembly (a) Lower Bound, (b) Upper Bound SIMULATIONS AND ANALYSIS RESULTS Movable Bridge System Reliability The system reliability was first calculated according to dead load and AASHTO standard live load with distributed lane loading and an HL-93 truck load placed on one lane at the midspan. Results of the finite element analysis were used to generate the input variables, and the reliability was calculated by using the statistical parameters of the random variables. The system reliability index was obtained as 4.11 for the lower bound, and 4.14 for the upper bound case.

13 Susoy, Zaurin, Catbas 13 Span lock, which is the locking bar between the tips of the two opposite leaves ensures distribution of the live load to both sides and an equal response. Span locks of Christa McAuliffe Bridge are operated by hydraulic units that drive the locking bar into the receptor with the bridge operator s control. These parts are extremely vulnerable to damage, and frequent failures are reported by bridge owners. Failure can occur by malfunction or breaking of the locking bar. If the span lock failure occurs in closed position, the bridge balance and alignment becomes disrupted. One side of the leaf may experience increased deflection and stresses, while the deflection and stresses on the other side may reduce. Therefore, system reliability can capture the effect of this failure scenario. The system reliability analysis was repeated with one of the span locks intact and one failed. The system reliability was re-calculated, and the results show a significant drop of the index to 2.82 (lower) and 2.93 (upper). System reliability indices for the two cases are shown in Table 1. Table 1 Reliability Analysis Results β system Location Upper Bound Lower Bound Main Girder (Initial) Main Girder (Span-Lock Failure) System (Initial) System (Span-Lock Failure) Reliability analysis was performed also for a moving load case, where a single standard truck is simulated crossing the bridge. The aim of this simulation is to observe the effect of a moving load if the applied moment is monitored with strain gages on the girders and used for calculating the reliability. Moving Load Simulation with Damage Scenario Safety indices based on component or system reliability can be evaluated with much higher accuracy and confidence over long term throughout the monitoring process. Component-based monitoring data should be assessed to produce reliability of each monitored structural component, and deterioration with time. Components to be instrumented should be carefully selected, as well as the parameters to monitor. Using SHM techniques makes it possible to retrieve information about the status of individual elements of a bridge. Since every component requires unique maintenance work, maintenance operations can be scheduled more specifically and efficiently. Also, once individual deterioration and maintenance models are available for each critical node, a network reliability analysis can be conducted within the bridge components, in order to determine the most critical ones (parallel/series reliability). Structural condition state and reliability are to be determined from component data. Reliability of the structural system depends on reliability of its components, so if there is no redundancy, weakest link will determine the overall reliability. Presence of redundant members makes it necessary to perform a system reliability analysis, modeling the structure as parallel and/or series combinations of the components (9, 10).

14 Susoy, Zaurin, Catbas 14 Figure 11 Moving Truck Load The results for each position of the truck (Figure 11) were obtained from the finite element simulation and processed by the component and system reliability algorithms developed in MATLAB. The horizontal axis is the truck position, which can also be regarded as time. The vertical axis shows the reliability index, which changes according to the position of the truck. The minimum reliability index was calculated as 4.42 when the middle axle of the truck arrives at the midspan (Figure 12). The calculated reliability is relatively high, since the simulation uses a single truck crossing the bridge without lane loads or additional load cases. This analysis only indicates the real-time changes for a moving load for making a comparison. Figure 12 Effect of Span-lock Failure on System Reliability The dashed line on Figure 12 shows the same analysis with a span lock failure. The minimum system reliability is seen when the middle axle of the truck is at the midspan, which yield an index of

15 Susoy, Zaurin, Catbas This shows that the reliability index changes more than 1.0 for the span lock failure case, which can be obtained if strain gage measurements are available for a truck crossing. The comparison of the peak strains, or minimum reliability index points with this system reliability model indicates damage has occurred. CONCLUSIONS AND RECOMMENDATIONS Movable bridges undergo similar degrading effects as their fixed counterparts, while they are much more susceptible to damage due to their complex movable mechanisms and slender structural elements, and suffer much faster deterioration than fixed bridges. They require constant and extensive maintenance work to keep up satisfactory performance, which requires major funding compared with those for fixed bridges, and still frequent malfunctions cause unexpected interruptions to either waterborne or land traffic, or both with corresponding negative economical effects. The studied movable bridge was found to be representative of the majority of movable bridges in the state of Florida. This bridge was modeled with a finite element software, which was calibrated with data collected from the bridge. The data, obtained from balance tests, provided the actual balance condition of the movable bridge. The resulting numerical model possesses the same balance state with the actual bridge, therefore, it is accurate enough to perform condition estimations with different load and damage scenarios. System reliability index of the bridge was evaluated with the calibrated finite element model using upper and lower bounds for the system reliability. Span lock failure scenario is also simulated, for which case the system reliability index drops to considerably, however the reliability value for this damage simulation is still higher than 2.5 which is considered by AASHTO LRFR (11) for condition assessment of existing bridges. It was also discussed that changes in system reliability could be observed in real-time if strain data is available for the movable bridge. ACKNOWLEDGMENTS The research project described in this paper is supported by the State of Florida Department of Transportation. The authors would like to thank Mr. Marcus Ansley, the Head of Structures Research for this support and guidance throughout the project. Mr. Ron Meade from District 5 helped greatly in providing the authors with inspection data, movable bridge operation and field support. Messrs. Lee Smith and Duane Robertson coordinated and conducted field tests with the writers, and also provided the writers with legacy data. The writers also greatly appreciate the valuable feedback provided by Messrs. Angel Rodriguez and Alberto Sardinas, who have shared their experience and expertise. Their support is greatly recognized and appreciated. The opinions, findings, and conclusions expressed in this publication are those of the authors and not necessarily those of the State of Florida Department of Transportation. REFERENCES 1. T. L. Koglin. Movable Bridge Engineering. John Wiley and Sons, Turner-Fairbanks Highway Research Center. Bridge Study Analyzes Accuracy of Visual Inspections S. C. Liu and M. Tomizuka. Vision and Strategy for Sensors and Smart Structures Technology Research. Proceedings of the 4 th International Workshop on Structural Health Monitoring, September 15-17, 2003, Stanford, CA, pp A. E. Aktan, M. Pervizpour, F. N. Catbas, R. A. Barrish, K. A. Grimmelsman, X. Qin, E. Kulcu, S. K. Ciloglu, J. Curtis and G. V. Haza-Radlitz. Integrated Field, Theoretical and Laboratory Research for Solving Large System Identification Problems. Advances in Structural Dynamics, 2000, Hong Kong. 5. L. E. Malvern, S. Y. Lu and D. A. Jenkins. Handbook of Bascule Bridge Balance Procedures. Report submitted to Florida Department of Transportation, 1982.

16 Susoy, Zaurin, Catbas O. Ditlevsen and H. O. Madsen. Structural reliability methods. Wiley, Chichester ; New York, R. E. Melchers. Structural Reliability Analysis and Prediction. John Wiley & Sons, A. S. Nowak and K. R. Collins. Reliability of Structures. McGraw-Hill, M. Susoy, F. N. Catbas and D. M. Frangopol. Implementation of Structural Reliability Concepts for Structural Health Monitoring. Proceedings of the 4 th World Conference on Structural Control and Monitoring, July 11-13, 2006, San Diego, CA. 10. M. Susoy, F. N. Catbas and D. M. Frangopol. Reliability-Based SHM of a Long-Span Bridge. Journal of Engineering Structures, Elsevier (submitted), AASHTO. Guide Manual for Condition Evaluation and Load and Resistance Factor Rating (LRFR) of Highway Bridges, 1st Edition