Reliability-Based Assessment of Suspension Bridges: Application to the Innoshima Bridge

Many suspension and cable-stayed bridges were designed and constructed between Honshu Island and Shikoku Island in Japan. All these bridges were designed according to the allowable stress design method. In the allowable stress design method, it is not possible to quantify the reliabilities of both bridge components and the entire bridge system. Therefore, in light of current reliability-based design philosophy, there is an urgent need to assess the safety of suspension bridges from a probabilistic viewpoint. To develop cost-effective design and maintenance strategies, it is necessary to assess the condition of suspension bridges using a reliability-based approach. This is accomplished by a probabilistic finite-element geometrically nonlinear analysis. This study describes an investigation into the reliability assessment of suspension bridges. The combination of reliability analysis and geometrically nonlinear elastic analysis allows the determination of reliabilities of suspension bridges. A probabilistic finite-element geometrically nonlinear elastic code, created by interfacing a system reliability analysis program with a finite-element program, is used for reliability assessment of suspension bridges. An existing suspension bridge in Japan, the Innoshima Bridge, is assessed using the proposed code. The assessment is based on static load effects. Reliabilities of the bridge are obtained by using 2D and 3D geometrically nonlinear models. Furthermore, damage scenarios are considered to assess the effects of failure of various elements on the reliability of undamaged components and on the reliability of the bridge. Finally, sensitivity information is obtained to evaluate the dominant effects on bridge reliability.     

Self-Anchored Suspension Bridges

This paper, summarizing the beginnings, analysis, and future of self-anchored suspension bridges, examines the development of this unique bridge form, its uses over the past century, and its advantages and disadvantages. The Konohana Bridge in Osaka, Japan, illustrates this type and provides a case study to compare conventional suspension bridge theory with the results of a finite-element model. The final portion of the paper evaluates the potential for self-anchored suspension bridge design, and provides recommendations for design engineers. The goal here is to describe the structural behavior of self-anchored bridges in general, and of the Konohana Bridge in particular.     

Theory and Full-Bridge Modeling of Wind Response of Cable-Supported Bridges

As is well known, long, suspended bridge spans require, in the design stage, careful study of their resistance and response to site winds. This has driven, on the one hand, detailed quantitative observation of bridge models in the wind tunnel and, on the other, a steady development and refinement of parallel theory. Currently, both aspects have arrived at good stages of sophistication, although with continued room for improvement. Successes in the extension of bridge spans to record-breaking lengths are mainly due to progress in wind-resistant design, a primary component in the design of long-span bridges. Recently, multimode flutter and buffeting analysis procedures have been developed. These procedures, which were based centrally on frequency-domain methods, take into account the fully coupled aeroelastic and aerodynamic response of long-span bridges to wind excitation. This paper briefly reviews the current state of the art in long-span bridge wind analysis, emphasizing the analytical infrastructure. The focus then turns to exhibit an example of application of the theory to the stability (flutter) and serviceability (buffeting) analyses of a new long-span bridge in North America. This example not only demonstrates the application of the theory to a real structure but also serves to highlight some insights into the versatility that is gained by this analytically based approach. The results demonstrate that the analytical method with appropriate inputs and a complementary full-bridge model agree even for relatively unusual incoming turbulence in the flow caused by the presence of structures upstream of the bridge. This paper seeks to exhibit recent developments in the field to the interested structural∕bridge engineer, outline alternative procedures available for assessment of wind effects on cable-supported bridges, and provide an overview of the basic steps in the process of a typical aerodynamic analysis and design.     

Performance-Based Design Approach in Seismic Analysis of Bridges

The seismic design requirements used in the United States are based on the recommendations of the American Association of State Highway and Transportation Officials. These requirements are primarily based on the importance of the structure, the level of deformation imposed on the structure, soil conditions, and the ductility of structural members, especially piers and supports. In the performance-based design approach, the design is primarily focused on meeting a performance objective, which is in line with a desired level of service. Currently, the effort toward implementing the performance-based design approach in buildings is under way in the United States. The seismic performance criteria for buildings have been established and reported by various organizations. It seems that at least three levels of performance, ranging from “fully operational” to “near collapse” can be used to meet the postearthquake conditions, safety, usage, and occupancy for the varous levels of service expected from all types of structures. In this paper a critical evaluation of these performance criteria and their relevance to highway bridge design, in conjunction with the current design practice, is discussed. Various types of designs such as those based on strength, deformation, nonlinear behavior, and energy, which can be used to meet the specified performance levels in seismic design of highway bridges, are also discussed in the paper. Examples of real applications of the method in highway bridges are reviewed. Furthermore, the procedure by which the performance-based method has been implemented in these example cases is described and discussed in the paper.     

Constructability Analysis of the Bridge Superstructure Rotation Construction Method in China

Constructability analysis can provide valuable input to optimizing urban bridge construction in terms of reducing impacts on traffic, safety, and overall project budget and duration. This paper presents a constructability analysis of the superstructure rotation method for bridge construction. The method includes building the bridge parallel to the obstacle being overpassed (a river or a highway) and then rotating the superstructure into place. The method has been used successfully in over one-hundred bridges (mostly in China). The paper documents two case studies of bridges that used this method and provides an analysis of the constructability of the method. This includes identification of the factors influencing the constructability of the methods and lists of design and construction objectives/strategies that support the constructability of bridges using this method.     

Simplified Model for Computer-Aided Analysis of Integral Bridges

This paper presents a computer-aided approach for the design of integral-abutment bridges. An analysis procedure and a simplified structure model are proposed for the design of integral-abutment bridges considering their actual behavior and load distribution among their various components. A computer program, for the analysis of integral-abutment bridges, has been developed using the proposed analysis procedure and structure model. The program is capable of analyzing an integral-abutment bridge for each construction stage and carrying the effects of applied loads on the structure members from a previous construction stage to the next. The proposed analysis methods and structure models are compared with the conventional analysis method and structure model currently used by many structural engineers for the design of integral-abutment bridges. The benefits of using the proposed analysis method and simplified structure model for the design of integral-abutment bridges are discussed. It was concluded that it may be possible to obtain more sound and economical designs for integral-abutment bridges using the proposed analysis method and structure model.     

Dynamic Monitoring of Steel Girder Highway Bridge

Currently there are different monitoring techniques that have been considered for use in the structural evaluation of bridges. These include approaches based on both static and dynamic behavior. The use of dynamic properties has advantages over static properties, since components of the dynamic properties are only marginally influenced by variations in the loading. When dynamic properties are used, field studies have shown that it is not always sufficient to use only natural frequencies and modal displacements. Some research for structural evaluation of bridges indicates that techniques based on use of derivatives of the natural frequencies and the modal displacements may be more effectively used to generate effective diagnostic parameters for structural identification. This paper presents the results of applying one of these methods, the modal flexibility approach, to a field study of a bridge in which the bearings were partially restrained in colder weather. While others have used impact methods with the modal flexibility method, in this study the approach is modified so that excitation is provided by vehicular traffic. The results show that the modified modal flexibility method provides a clear indication that there have been changes in the bridge’s structural behavior.     

Truck Loads and Bridge Capacity Evaluation in China

Over the past 2–3 decades, the economic development in China has natured the establishment of a highway network with a large number of bridges. However, there are still no nationwide specification provisions for assessing their safe load carrying capacity. The research work reported herein focuses on developing reliability based requirements for this purpose. In this study, weigh-in-motion data for more than 7.3 million trucks were gathered from highways in three provinces of China, continuously over 1–16 months in 2006 and 2007. The data were processed and projected to model the live-load spectrum over 3-year and 100-year periods, respectively. The former is the required bridge inspection interval and the latter the bridge design life span, according to current Chinese maintenance and design specifications. The proposed projection method is shown to be more reliable compared with those reported. The resulting load spectra are used to assess the structural reliability of typical Chinese highway bridges at the component level. Based on the accordingly selected target reliability index, the live-load factors for bridge evaluation are developed in this study, proposed to be included in the Chinese national specifications.     

Seismic Fragility of Continuous Steel Highway Bridges in New York State

This paper presents the results of an analytical seismic fragility analysis of a typical steel highway bridge in New York State. The structural type and topological layout of this multispan I-girder bridge have been identified to be most typical of continuous bridges in New York State. The structural details of the bridge are designed as per New York State bridge design guidelines. Uncertainties associated with the estimation of material strength, bridge mass, friction coefficient of expansion bearings, and expansion-joint gap size are considered. To account for the uncertainties related to the bridge structural properties and earthquake characteristics, ten statistical bridge samples are established using the Latin Hypercube sampling and restricted pairing approach, and 100 ground motions are simulated numerically. The uncertainties of capacity and demand are estimated simultaneously by using the ratios of demands to capacities at different limit states to construct seismic fragility curves as a function of peak ground acceleration and fragility surfaces as a function of moment magnitude and epicentral distance for individual components using nonlinear and multivariate regressions. It has been observed that nonlinear and multivariate regressions show better fit to bridge response data than linear regression conventionally used. To account for seismic risk from multiple failure modes, second-order reliability yields narrower bounds than the commonly used first-order reliability method. The fragility curves and surfaces obtained from this analysis demonstrate that bridges in New York State have reasonably low likelihood of collapse during expected earthquakes.     

Design Method of a Hanger System for Long-Span Suspension Bridge

A parallel wire strand (PWS) rope instead of a strand rope of the center fit rope core type was used as the hanger rope in the world's longest suspension bridge, the Akashi Kaikyo Bridge, one of the Honshu-Shikoku Bridges in Japan. The strand ropes of the center fit rope core type are inconvenient and uneconomical to maintain as 100–200 m-long hanger ropes. This paper presents the design method for the PWS hanger system in long-span suspension bridges. The structural characteristics, structural analysis, stress calculation, and the examination of fatigue against random wind load of the PWS hanger system were also investigated.     

Performance of Bridge Materials by Structural Deficiency Analysis

The diagnostic concept of the structural deficiency of bridges is an essential engineering and management consideration with implications of performance. The structural deficiency analysis reflects the constructed system performance at the serviceability limit states. This paper analyzes trends in the structural deficiency of bridge inventory on the basis of material kind. A multiple-criteria diagnostic approach defines measures for condition, durability, and longevity performances and determines the overall equivalent performance. Thus, the structural performance levels reflect the structural reliability and vulnerability indices for bridge serviceability. The application of the approach analyzes the raw database of the entire bridge inventory in the United States. This comprehensive operational experience provides a national network-level comparative basis. The comparison suggests a relative need for improvements in one or more areas, such as design details or maintenance level, to increase the desirability of bridge construction materials. The results support more objective bridge management and decision making on distribution of funds, updating of policies, perfection of practices, and trade-off analyses for design, construction, maintenance, and replacement.     

Equivalent Wheel Load Approach for Slender Cable-Stayed Bridge Fatigue Assessment under Traffic and Wind: Feasibility Study

In the current AASHTO LRFD specifications, the fatigue design considers only one design truck per bridge with 15% dynamic allowance. While this empirical approach may be practical for regular short and medium span bridges, it may not be rational for long-span bridges (e.g., span length >152.4?m or 500?ft) that may carry many heavy trucks simultaneously. Some existent studies suggested that fatigue may not control the design for many small and medium bridges. However, little research on the fatigue performance of long-span bridges subjected to both wind and traffic has been reported and if fatigue could become a dominant issue for such a long-span bridge design is still not clear. Regardless if the current fatigue design specifications are sufficient or not, a real understanding of the traffic effects on bridge performance including fatigue is desirable since the one truck per bridge for fatigue design does not represent the actual traffic condition. As the first step toward the study of fatigue performance of long-span cable-stayed bridges under both busy traffic and wind, the equivalent dynamic wheel load approach is proposed in the current study to simplify the analysis procedure. Based on full interaction analyses of a single-vehicle–bridge–wind system, the dynamic wheel load of the vehicle acting on the bridge can be obtained for a given vehicle type, wind, and driving condition. As a result, the dimension of the coupled equations is independent of the number of vehicles, through which the analyses can be significantly simplified. Such simplification is the key step toward the future fatigue analysis of long-span bridges under a combined action of wind and actual traffic conditions.     

Nonlinear Soil–Abutment–Bridge Structure Interaction for Seismic Performance-Based Design

Current seismic design of bridges is based on a displacement performance philosophy using nonlinear static pushover analysis. This type of bridge design necessitates that the geotechnical engineer predict the resistance of the abutment backfill soils, which is inherently nonlinear with respect to the displacement between soil backfill and the bridge structure. This paper employs limit-equilibrium methods using mobilized logarithmic-spiral failure surfaces coupled with a modified hyperbolic soil stress–strain behavior (LSH model) to estimate abutment nonlinear force-displacement capacity as a function of wall displacement and soil backfill properties. The calculated force-displacement capacity is validated against the results from eight field experiments conducted on various typical structure backfills. Using LSH and experimental data, a simple hyperbolic force-displacement (HFD) equation is developed that can provide the same results using only the backfill soil stiffness and ultimate soil capacity. HFD is compatible with current CALTRANS practice in regard to the seismic design of bridge abutments. The LSH and HFD models are powerful and effective tools for practicing engineers to produce realistic bridge response for performance-based bridge design.     

Rating and Reliability of Existing Bridges in a Network

Currently, the load rating is the method used by State DOTs for evaluating the safety and serviceability of existing bridges in the United States. In general, load rating of a bridge is evaluated when a maintenance, improvement work, change in strength of members, or addition of dead load alters the condition or capacity of the structure. The AASHTO LRFD specifications provide code provisions for prescribing an acceptable and uniform safety level for the design of bridge components. Once a bridge is designed and placed in service, the AASHTO Manual for Condition Evaluation of Bridges provides provisions for determination of the safety and serviceability of existing bridge components. Rating for the bridge system is taken as the minimum of the component ratings. If viewed from a broad perspective, methods used in the state-of-the-practice condition evaluation of bridges at discrete time intervals and in the state-of-the-art probability-based life prediction share common goals and principles. This paper briefly describes a study conducted on the rating and system reliability-based lifetime evaluation of a number of existing bridges within a bridge network, including prestressed concrete, reinforced concrete, steel rolled beam, and steel plate girder bridges. The approach is explained using a representative prestressed concrete girder bridge. Emphasis is placed on the interaction between rating and reliability results in order to relate the developed approach to current practice in bridge rating and evaluation. The results presented provide a sound basis for further improvement of bridge management systems based on system performance requirements.     

Revisiting Multimode Coupled Bridge Flutter: Some New Insights

Better understanding of the bimodal coupled bridge flutter involving fundamental vertical bending and torsional modes offers valuable insight into multimode coupled flutter, which has primarily been the major concern in the design of long span bridges. This paper presents a new framework that provides closed-form expressions for estimating modal characteristics of bimodal coupled bridge systems and for estimating the onset of flutter. Though not intended as a replacement for complex eigenvalue analysis, it provides important physical insight into the role of self-excited forces in modifying bridge dynamics and the evolution of intermodal coupling with increasing wind velocity. The accuracy and effectiveness of this framework are demonstrated through flutter analysis of a cable-stayed bridge. Based on this analysis scheme, the role of bridge structural and aerodynamic characteristics on flutter, which helps to better tailor the structural systems and deck sections for superior flutter performance, is emphasized. Accordingly, guidance on the selection of critical structural modes and the role of different force components in multimode coupled flutter are delineated. The potential significance of the consideration of intermodal coupling in predicting torsional flutter is highlighted. Finally, clear insight concerning the role of drag force to bridge flutter is presented.     

Impact of Commercial Vehicle Weight Change on Highway Bridge Infrastructure

Heavy trucks represent a major load to highway bridges in the transportation infrastructure system. These loads are directly related to the truck weight limits of the jurisdiction, and largely determine the standard loads for bridge design and evaluation. Thus, truck weight limit is one of the major factors affecting bridge deterioration and expenditure for maintenance, repair, and/or replacement. Truck weight in this paper not only refers to the truck gross weight but also to the axle weights and spacings that affect load effects. This paper presents the concepts of a new methodology for estimating cost effects of truck weight limit changes on bridges in a transportation infrastructure network. The methodology can serve as a tool for studying impacts of such changes. The resulting knowledge is needed when examining new truck weight limits, several of which have been and are still being debated at both the state and federal levels in the United States. The development of this estimation method has considered maximizing the use of available data (such as the bridge inventory) at the state infrastructure system level. In application examples completed (but not reported herein), the costs for relatively inadequate strength of existing bridges and for increased design requirement for new bridges were found dominant in the total impact cost.     

Extreme Thermal Loading on Steel Bridges in Tropical Region

In the design of highway bridges, it is important to consider the thermal stresses induced by the nonlinear temperature distribution in the bridge deck irrespective of their spans. To cope with this, design temperature profiles are provided by many bridge design codes, which are normally based on extensive research on the thermal behavior of bridges. This paper presents the results of a comprehensive investigation on the thermal behavior of steel bridges carried out in Hong Kong. A method for predicting bridge temperatures from given meteorological conditions is briefly discussed. The theoretical results have been validated by temperature measurements on experimental models mounted on the roof of a building as well as on an existing steel bridge. Both the theoretical and field results confirm the validity of the one-dimensional heat transfer model on which most design codes are based. Values of design thermal loading for a 50-year return period are determined from the statistics of extremes over 40 years of meteorological information in Hong Kong. The design temperature profiles for various types of steel bridge deck with different thickness of bituminous surfacing are developed.     

Number of Cable Effects on Buckling Analysis of Cable-Stayed Bridges

Cables instead of interval piers support cable-stayed bridges, and the bridge deck is subjected to strong axial forces due to the horizontal components of cable reactions. The structural behavior of a bridge deck becomes nonlinear because of the axial forces, large deflection, and nonlinear behavior of the cables and the large deformation of the pylons as well as their interactions. The locations and amplitude of axial forces acting on the bridge deck may depend on the number of cables. Agrawal indicated that the maximum cable tension decreases rapidly with the increase in the number of cables. This paper investigates the stability analysis of cable-stayed bridges and considers cable-stayed bridges with geometry similar to those proposed in Agrawal's paper. A digital computer and numerical analysis are used to examine 2D finite element models of these bridges. The eigen buckling analysis has been applied to find the minimum critical loads of the cable-stayed bridges. The numerical results indicate that the total cumulative axial forces acting on the bridge girder increase as the number of cables increases, yet because the bridge deck is subjected to strong axial forces, the critical load of the bridges decreases. Increasing the number of cables may not increase the critical load on buckling analysis of this type of bridge. The fundamental critical loads increase if the ratio of Ip∕Ib increases until the ratio reaches the optimum ratio. If the ratio of Ip∕Ib is greater than the optimum ratio, depending on the geometry of an individual bridge, the fundamental critical load decreases for all the types of bridges considered in this paper. In order to make the results useful, they have been normalized and represented in graphical form.     

Case-Based Reasoning for Converting Working Stress Design-Based Bridge Ratings to Load Factor Design-Based Ratings

In 1995, the Federal Highway Administration (FHWA) required that all bridges, regardless of the design method used for the original design, be based on the load factor design (LFD) method. In order to comply with the FHWA requirements, state departments of transportation have converted to the LFD method for all new bridge ratings. Further, all existing bridges previously rated using the working stress design (WSD) method must be converted to the LFD method. Consequently, thousands of bridges must be rerated using the LFD method. Steel bridges rated by the WSD method have critical data missing to make the proper conversion to the LFD method. This paper presents a methodology and an intelligent decision support system to help bridge engineers convert a WSD-based bridge rating to the LFD-based rating with little human effort using the artificial intelligence approach of case-base reasoning. The proposed methodology can help bridge engineers create the missing LFD-based data efficiently and quickly with a minimum amount of work. This research demonstrates how bridge engineers can use a novel computing paradigm and modern computer tool to convert an antiquated database to current design.