Reliability-Based Life-Cycle Management of Highway Bridges

The objective of bridge management is to allocate and use the limited resources to balance lifetime reliability and life-cycle cost in an optimal manner. As the 20th century has drawn to a close, it is appropriate to reflect on the birth and growth of bridge management systems, to examine where they are today, and to predict their future. In this paper, it is attempted to shed some light on the past, present, and future of life-cycle management of highway bridges. It is shown that current bridge management systems have limitations and that these limitations can be overcome by using a reliability-based approach. It is concluded that additional research is required to develop better life-cycle models and tools to quantify the risks, costs, and benefits associated with highway bridges as well as their interrelationships in highway networks.     

Reliability-Based Modeling of Bridge Deterioration Hazards

This paper presents the results from a study on the deterioration patterns of highway bridges, using estimated sojourn times of bridge components in various deterioration states (condition). With emphasis on the age that the bridge leaves a specified threshold condition state, the uncertainties in the estimated times are best fitted as Weibull probability distribution functions. Using both complete observations’ data and the right-censored data from a 13-year span condition historical data for the bridges, the maximum likelihood estimates are obtained for parameters of the fitted distributions, and reliability analyses are conducted for the various categories of bridges, by the type of roadways carried (interstate, noninterstate, and local roads), and the material type, i.e., cast-in-place concrete decks; prestressed concrete superstructures; steel superstructures, etc. The survival and hazard functions are developed and interpreted, including a combination of the deterioration hazard functions with the hazard functions of the effects of hurricane winds. It was observed that all the bridge categories deteriorated faster with age (nonexponential times), and bridge components located on the interstate roadways are deteriorating faster than similar bridges on noninterstate roadways. Asset worth of bridges are indicated, based on the reliability estimates.     

Preliminary Analysis of Suspension Bridges

This paper reviews the derivation of the fundamental equations of suspension bridge analysis based on the deflection theory. A method is presented for the practical solution of these equations that can be implemented in commercially available mathematical analysis programs or for simpler cases in spreadsheet programs. The method takes advantage of the analogy between a suspended girder and a beam under tension. A table with analytical solutions to the beam-under-tension problem is presented for load cases applicable to suspension bridge analysis. Previous presentations of this method are expanded to address the effects of pylon stiffness and of continuity of the stiffening girder.     

Increasing the Load Capacity of Suspension Bridges

There is a tendency for traffic loads to increase with the passage of time. It is not uncommon, therefore, for bridges to be strengthened and/or widened or sometimes to have lanes or even complete decks added. A few bridges were designed initially with a view to future expansion, such as the George Washington Suspension Bridge, designed to accommodate an extra deck, and the Salazar (now April 25) Bridge, designed to have two train tracks added, but these are exceptions. Suspension bridges behave somewhat differently from other bridge types, and the methods for increasing capacity can also be different. Some ideas are presented of how suspension bridges can be altered to accommodate more load, be it automobile, pedestrian, or even train traffic, and some examples are given. The importance of understanding both structural behavior and structural safety is emphasized.     

Optimum Design of Bridge Abutments under Seismic Conditions: Reliability-Based Approach

The paper focuses on the reliability-based design optimization of gravity wall bridge abutments when subjected to active condition during earthquakes. An analytical study considering the effect of uncertainties in the seismic analysis of bridge abutments is presented. Planar failure surface has been considered in conjunction with the pseudostatic limit equilibrium method for the calculation of the seismic active earth pressure. Analysis is conducted to evaluate the external stability of bridge abutments when subjected to earthquake loads. Reliability analysis is used to estimate the probability of failure in three modes of failure viz. sliding failure of the wall on its base, overturning failure about its toe (or eccentricity failure of the resultant force) and bearing failure of foundation soil below the base of wall. The properties of backfill and foundation soil below the base of abutment are treated as random variables. In addition, the uncertainties associated with characteristics of earthquake ground motions such as horizontal seismic acceleration and shear wave velocity propagating through backfill soil are considered. The optimum proportions of the abutment needed to maintain the stability are obtained against three modes of failure by targeting various component and system reliability indices. Studies have also been made to study the influence of various parameters on the seismic stability.     

Application of Suspension Bridges Stiffened by Prestressed Concrete Slabs in China

Four suspension bridges stiffened by prestressed concrete slabs were designed and constructed on highways in southwestern mountainous areas of China. These bridges are the first applications of its kind in China. This paper discusses the site condition, adaptability, and design and construction features of these bridges. These bridges have single suspension spans between 278 and 388?m and deck width between 14.4 and 15.0?m. The longitudinal distance between hangers is only 5?m, which is relatively small for this bridge type, and there are only two lanes. The dual direction prestressed concrete slabs are 0.6?m deep, and its wind blocking area is relatively small. Dynamic analysis and wind tunnel tests verify that the wind resistance requirements are easily satisfied.     

Assessment of Variable Uncertainties for Reliability-Based Design of Foundations

LRFD shows promise as a viable alternative to the present working stress design (WSD) approach to shallow foundation design. The key improvements of LRFD over the traditional WSD are the ability to provide a more consistent level of reliability and the possibility of accounting for load and resistance uncertainties separately. For LRFD to gain acceptance in geotechnical engineering, a framework for the objective assessment of resistance factors is needed. Such a framework, based on reliability analysis, is proposed in this paper. Probability density functions (PDFs), representing design variable uncertainties, are required for analysis. A systematic approach to the selection of PDFs is presented. A procedure such as that proposed provides a rational probabilistic basis for the development of LRFD methods in geotechnical engineering.     

Control of Suspension Bridge Nonlinear Vibrations due to Moving Loads

The flexibility and low damping of the long-span suspended cables in the suspension bridges make them prone to vibrations due to wind and moving loads, which affect the dynamic response of the suspended cables and the bridge deck. This paper shows the design of two control schemes to control the nonlinear vibrations in the suspended cable and the bridge deck due to a vertical load moving on the bridge deck with a constant speed. The first control scheme is an optimal state feedback controller. The second control scheme is a robust state feedback controller, whose design is based on the design of optimal controllers. The proposed controllers, whose design is based on Lyapunov theory, guarantee the asymptotic stability of the system. A vertical cable between the bridge deck and the suspended cable is used to install a hydraulic actuator able to generate the active control force on the bridge deck. The MATLAB software is used to simulate the performance of the system with the designed controllers. The simulation results indicate that the proposed controllers are capable of significantly reducing the nonlinear oscillations of the system. In addition, the performance of the system with the proposed controllers is compared to the performance of the system controlled with a velocity feedback controller. It is found that the system with the proposed controllers can provide better performance than the system with the velocity feedback controller.     

Life-Cycle Cost of All-Composite Suspension Bridge

This paper reports on the design of two highway suspension bridges made of conventional steel and advanced all-composite carbon fiber reinforced polymer (CFRP), and analyzed their life-cycle costs. The writers assumed that the pultrusion molding method would mainly be used for all composite highway bridges, because of its relatively high quality control performance and mass-production capability. First, the writers obtained the steel and composite highway bridge design in the same dimensional specification. Second, they acquired the future cost of the CFRP pultrusion product through hearing research from a fiber reinforced polymer manufacturer. Third, they calculated the initial costs of the steel bridge and CFRP bridge based on the design specification and the future cost of CFRP. Fourth, they compared the life-cycle cost of the steel and CFRP bridges under several conditions of discount rate, repair cost, and cycle. Finally, they found the critical condition where the CFRP bridge becomes more life-cycle cost-effective than the conventional steel bridge, if they could have expected the drastic cost reduction of the CFRP product.     

Effect of Hanger Flexibility on Dynamic Response of Suspension Bridges

Linearized continuum models of a suspended span with unloaded backstays and of a symmetric three-span suspension bridge are used to study the effects of the flexibility of the hangers on the vertical vibrations of suspension bridges. The models include elastic parabolic cables, flexible distributed hangers with variable length, and a stiffening girder represented by an elastic beam. It is shown that the free vibrations of a suspended span with unloaded backstays are controlled by five dimensionless parameters, while six dimensionless parameters control the response of a symmetric three-span suspension bridge. The results indicate that the flexibility of the hangers has a significant effect on the natural frequencies of the higher modes only when the relative stiffness of the girder is very high. The effects of hanger flexibility on the response of a suspension bridge to localized impulsive loads are also found to be small. These findings confirm the traditional, albeit previously untested, assumption of inextensible hangers. Finally, the threshold amplitudes of free vibrations that would result in the incipient slackening of the hangers are determined.     

Dynamic Response of Suspension Bridge to High Wind and Running Train

A framework is presented for predicting the dynamic response of long suspension bridges to high winds and running trains. A three-dimensional finite-element model is used to represent a suspension bridge. Wind forces acting on the bridge, including both buffeting and self-excited forces, are generated in the time domain using a fast spectral representation method and measured aerodynamic coefficients and flutter derivatives. Each 4-axle vehicle in a train is modeled by a 27-degrees-of-freedom dynamic system. The dynamic interaction between the bridge and train is realized through the contact forces between the wheels and track. By applying a mode superposition technique to the bridge only and taking the measured track irregularities as known quantities, the number of degrees of freedom of the bridge-train system is significantly reduced and the coupled equations of motion are efficiently solved. The proposed formulation is then applied to a real wind-excited long suspension bridge carrying a railway inside the bridge deck of a closed cross section. The results show that the formulation presented in this paper can predict the dynamic response of the coupled bridge-train systems under fluctuating winds. The extent of interaction between the bridge and train depends on wind speed and train speed.     

Response Spectrum Analysis of Suspension Bridges for Random Ground Motion

The response spectrum method of analysis for suspension bridges subjected to multicomponent, partially correlated stationary ground motion is presented. The analysis is based on the relationship between the power spectral density function and the response spectrum of the input ground motion and fundamentals of the frequency domain spectral analysis. The analysis duly takes into account the spatial correlation of ground motions between the supports, the quasi-static component of the response, and the modal correlation between different modes of vibration. A suspension bridge is analyzed under a set of important parametric variations in order to (1) compare between the responses obtained by the response spectrum method of analysis and the frequency domain spectral analysis; and (2) investigate the behavior of suspension bridges under seismic excitation. The parameters include the spatial correlation of ground motion, the angle of incidence of the earthquake, the ratio between the three components of ground motion, the number and nature of modes considered in the analysis, and the nature of the power spectral density function of ground motion. It is shown that the response spectrum method of analysis provides a fair estimate of responses under parametric variations considered in the study.     

悬索管桥的构造设计

以某大跨度悬索管桥的设计为例,综述了悬索管桥关键部位的构造设计。通过几年的使用验证构造设计的参数是安全、经济、可靠的。     

Cracking and Fracture of Suspension Bridge Wire

When water enters a suspension bridge cable, the wires that make up the cable start to deteriorate. The protective zinc coating is the first element that is damaged, followed by corrosion of the steel itself. The wires are subjected to high axial tensile stresses from the bridge loading, bending stresses caused by straightening the curved wires inside the cable, and residual stresses introduced in their manufacture. These stresses, along with the corrosive environment, can lead to stress corrosion cracking or hydrogen-assisted cracking, two processes that lead to eventual failure of the wires. A fracture analysis indicates that the wires in the cable may be subjected to slightly different forces than a wire tested in the laboratory, but that the results of laboratory tests will give conservative values of cable strength.     

Vibration Studies of Tsing Ma Suspension Bridge

A three-dimensional dynamic finite element model is established for the Tsing Ma long suspension Bridge in Hong Kong. The two bridge towers made up of reinforced concrete are modeled by three-dimensional Timoshenko beam elements with rigid arms at the connections between columns and beams. The cables and suspenders are modeled by cable elements accounting for geometric nonlinearity due to cable tension. The hybrid steel deck is represented by a single beam with equivalent cross-sectional properties determined by detailed finite element analyses of sectional models. The modal analysis is then performed to determine natural frequencies and mode shapes of lateral, vertical, torsional, longitudinal, and coupled vibrations of the bridge. The results show that the natural frequencies of the bridge are very closely spaced; the first 40 natural frequencies range from 0.068 to 0.616 Hz only. The computed normal modes indicate interactions between the main span and side span, and between the deck, cables, and towers. Significant coupling between torsional and lateral modes is also observed. The numerical results are in excellent agreement with the measured first 18 natural frequencies and mode shapes. The established dynamic model and computed dynamic characteristics can serve further studies on a long-term monitoring system and aerodynamic analysis of the bridge.     

Reliability Analysis of Suspension Bridges against Fatigue Failure from the Gusting of Wind

A fatigue reliability analysis of suspension bridges due to the gustiness of the wind velocity is presented by combining overall concepts of bridge aerodynamics, fatigue analysis, and reliability analysis. For this purpose, the fluctuating response of the bridge deck is obtained for buffeting force using a finite-element method and a spectral analysis in frequency domain. Annual cumulative fatigue damage is calculated using Palmgren–Miner’s rule, stress-fatigue curve approach and different forms of distribution for stress range. In order to evaluate the reliability, both first-order second-moment (FOSM) method and full distribution procedure (assuming Weibull distribution for fatigue life) are used to evaluate the fatigue reliability. Probabilities of fatigue failure of the Thomas Bridge and the Golden Gate Bridge for a number of important parametric variations are obtained in order to make some general observations on the fatigue reliability of suspension bridges. The results of the study show that the FOSM method predicts a higher value of the probability of fatigue failure as compared to the full distribution method. Further, the distribution of stress range used in the analysis has a significant effect on the calculated probability of fatigue failure in suspension bridges.     

Analytical and Field Investigation of Roma Suspension Bridge

The Roma–Ciudad Miguel Aleman International Suspension Bridge is an historic unstiffened suspension bridge with a 192 m (630 ft) main suspended span, originally constructed in 1928. In 1997 the bridge was inspected and a full-scale nondestructive load test was conducted. The resulting experimental data are evaluated and compared to the results of analyses by finite-element method modeling. The history of the bridge is reviewed, with an emphasis on modifications and retrofits to the structure. The unique behavior and attributes of unstiffened suspension bridges are discussed in the specific context of this particular bridge.     

Structural Characteristics and Applicability of Four-Span Suspension Bridge

A four-span suspension bridge which has two main 2,000 m spans is investigated with respect to the deformation characteristics. Generally, deformation behavior of the four-span suspension bridge is mainly influenced by rigidity of the center tower. This study is focused on properties such as bending and torsional rigidity of the girder, sag ratio, and dead load. The result of this investigation clarified that the lower rigidity under live load than the three-span bridge is caused by the smaller cable spring coefficient of the main span, which is 1/6 of the side span. Nevertheless, the tendency is stable and can be assisted by stiffened rigidity of the center tower. Live load deflection of the girder can be reduced to less than 1/200 of the main span length, which is useful and economical, by stiffening the bending coefficient of the center tower. Moreover, relatively lower rigidity of the center tower is sufficient for the 2,000 m span suspension bridge than for the 1,000 m span case, keeping the same deflection ratio. Three-dimensional sag geometry of the main cable is effective in limiting the torsional deformation, which is an especially important issue for the four-span suspension bridge caused by twist of the center tower.     

Roebling Suspension Bridge. II: Ambient Testing and Live-Load Response

This is the second part of a two-part paper on the evaluation of the historic Roebling suspension bridge using dynamic-analysis techniques. Dynamic properties are determined using ambient field testing under natural excitation. The finite-element (FE) model described in the first part of this two-part paper is modified to more accurately represent current bridge properties. Modifications of the model are based on correlating the FE model frequencies with ambient test frequencies by adjusting the FE model stiffness parameters. The updated 3D FE model is subsequently subjected to an extreme live-load condition to evaluate static safety margins. In addition, cable areas are reduced by 10 to 40% to simulate further deterioration and corrosion. The safety margin of the main cables is demonstrated to be good even when assuming a very conservative 40% cable area reduction, and truss member forces remain within the maximum load-carrying capacity even when the cable areas are reduced by 40%.