Corrosion and Embrittlement in High-Strength Wires of Suspension Bridge Cables

An in-depth analysis of the deterioration mechanisms in high-strength wires of suspension bridge cables is presented. Accelerated cyclic corrosion tests were conducted to assess the relative effect of corrosion on galvanized and ungalvanized wires. Samples were corroded under various levels of sustained loads in a cabinet that cyclically applied an acidic salt spray, dry conditions, and 100% relative humidity at elevated temperature, and mass loss, hydrogen concentration, ultimate load, and elongation at failure were measured. Elongation measurements indicated a significant embrittlement of the wires that could not be explained solely by the presence of absorbed hydrogen (hydrogen embrittlement). The main cause of reduction of wire elongation was found to be the surface irregularities induced by the corrosion process. The experimental results were validated through a numerical analysis using a finite-element method model of the corroded steel wire and through a series of scanning electron microscope analyses of the fracture surfaces.     

Field Static Load Test on Kao-Ping-Hsi Cable-Stayed Bridge

Field load testing is an effective method for understanding the behavior and fundamental characteristics of a cable-stayed bridge. This paper presents the results of field static load tests on the Kao-Ping-Hsi cable-stayed bridge, the longest cable-stayed bridge in Taiwan, before it was open to traffic. A total of 40 loading cases, including the unit and distributed bending and torsion loading effects, were conducted to investigate the bridge behavior. The atmospheric temperature effect on the variations of the main girder deflections was also monitored. The results of static load testing include the main girder deflections, the flexural strains of the prestressed concrete girder, and the variations of the cable forces. A three-dimensional finite-element model was developed. The results show that the bridge under the planned load test conditions has linear superposition characteristics and the analytical model shows a very good agreement with the bridge responses. Further discussion of deflection and cable forces of the design specifications for a cable-stayed bridge is also presented.     

Probabilistic Strength Estimates and Reliability of Damaged Parallel Wire Cables

Cable reliability analysis involves the combined evaluation of cable capacity and cable load in a probabilistic manner. Assessment of cable capacity is only possible through visual inspections of the wires, field sampling, laboratory analysis of the degraded wire populations, and analytical techniques. In addition to a brief presentation of cable mechanics and deterministic models that approximate cable strength, this paper discusses inspection methodologies and statistical methods of estimation of the sizes of the degraded wire populations, and wire properties, leading to cable capacities. These capacities are described by probability distributions. The paper also discusses fundamentals of reliability analysis as they apply to bridge cables. Load criteria of present standard specifications (such as AASHTO or other international codes) are not applicable to long-span suspension bridges. The paper discusses criteria of bridge loading and reliability indices for bridge cables. More work is needed in the evaluation of loading for long-span bridges.     

Field Load Tests and Numerical Analysis of Qingzhou Cable-Stayed Bridge

A field load test is an essential way to understand the behavior and fundamental characteristics of newly constructed bridges before they are allowed to go into service. The results of field static load tests and numerical analyses on the Qingzhou cable-stayed bridge (605?m central span length) over the Ming River, in Fuzhou, China are presented in the paper. The general test plan, tasks, and the responses measured are described. The level of test loading is about 80–95% of the code-specified serviceability load. The measured results include the deck profile, deck and tower displacements, and stresses of steel-concrete composite deck. A full three-dimensional finite-element model is developed and calibrated to match the measured elevations of the bridge deck. A good agreement is achieved between the experimental and analytical results. It is demonstrated that the initial equilibrium configuration of the bridge plays an important role in the finite-element calculations. Both experimental and analytical results have shown that the bridge is in the elastic state under the planned test loads, which indicates that the bridge has an adequate load-carrying capacity. The calibrated finite-element model that reflects the as-built conditions can be used as a baseline for health monitoring and future maintenance of the bridge.     

Load Distribution for a Highly Skewed Bridge: Testing and Analysis

The American Association of State Highway and Transportation Officials (AASHTO) specifications provide formulas for determining live load distribution factors for bridges. For load distribution factors to be accurate, the behavior of the bridge must be understood. While the behavior of right-angle bridges and bridges with limited skews is relatively well understood, that of highly skewed bridges is not. This paper presents a study aimed at developing a better understanding of the transverse load distribution for highly skewed slab-on-steel girder bridges. The study involved both a diagnostic field test of a recently constructed bridge and an extensive numerical analysis. The bridge tested and analyzed is a two-span, continuous, slab-on-steel composite highway bridge with a skew angle of 60°. The bridge behavior is defined based on the field test data. Finite-element analyses of the bridge were conducted to investigate the influence of model mesh, transverse stiffness, diaphragms, and modeling of the supports. The resulting test and analytical results are compared with AASHTO’s Load and Resistance Factor Design formulas for live load distribution to assess the accuracy of the current empirical formulas.     

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.     

Design of Looping Cable Anchorage System for New San Francisco–Oakland Bay Bridge Main Suspension Span

Located at the rocky edge of the Yerba Buena Island, the west anchorage of the San Francisco–Oakland Bay Bridge suspension span serves as the anchor for this single tower self-anchored suspension bridge. With extensive comparative studies on numerous alternatives, the new looping cable anchorage system is recommended for the final design of the west anchorage of the self-anchored suspension span. The looping cable anchorage system essentially consists of a prestressed concrete portal frame, a looping anchorage cable, deviation saddles, a jacking saddle, independent tie-down systems, and gravity reinforced-concrete foundations. This anchorage system is chosen for its structural efficiency and dimensional compactness. This paper describes major design issues, design philosophy, concept development, and key structural elements and details of this innovative suspension cable anchorage system.     

Suspension Cable Design of the New San Francisco–Oakland Bay Bridge

Various factors contribute to the difficulty in designing the main suspension cable for the new San Francisco–Oakland Bay Bridge Self-Anchored Suspension Span (or East Bay Bridge Suspension Span). The key factors are bridge design life, cable geometry, cable anchorage layout, cable construction method, and cable corrosion protection system. This paper describes the unique main suspension cable geometry layout for the East Bay Bridge Suspension Span, reviews the available technologies for each of the aforementioned design considerations, and presents the final cable design recommendations.     

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.     

Analytical Load Rating of an Open-Spandrel Arch Bridge: Case Study

The live load structural capacity of open-spandrel arch bridge structures is difficult to quantify. In addition to live and dead loads, geometric nonlinear effects, temperature effects, and material behavior play key roles in the design and load rating of such a structure. This paper is a case study that illustrates the effect these variables have on load rating a two-span shallow concrete arch bridge. Presented are load ratings of the structure’s arch ribs using a three-dimensional finite-element model with American Association of State Highway and Transportation Officials publications. As a result of this study, a refined analysis is recommended for load rating arch bridges.     

Higher Level Evaluation of a Reinforced Concrete Slab Bridge

In New Mexico, many reinforced concrete slab (RCS) bridges provide service on interstates I-10, I-25, and I-40. The load rating for this type of bridge largely depends on the live-load moment in the slab. Consequently, the objective of this study was to determine a more accurate value for the equivalent strip width using higher level evaluation techniques. A continuous RCS bridge was evaluated starting with an AASHTO load and resistance factor rating analysis. A diagnostic test was then conducted to measure live-load strains which showed that the slab stiffness fit within cracked and gross section behavior. Furthermore, slab moments from finite element analysis agreed reasonably well with experimental moments derived using the average of the cracked and gross section modulus. From refined analysis, the equivalent strip widths for positive moment were 26.1 and 22.1% greater than those calculated by the AASHTO approximate method for the exterior and interior spans, respectively. The refined widths for negative moment were greater than AASHTO by 13.1 and 11.1%. This increase in the equivalent strip width reduced the live-load effects, which proportionally increased the rating factors.     

Wheel Load Distribution in Simply Supported Concrete Slab Bridges

This paper presents the results of a parametric study related to the wheel load distribution in one-span, simply supported, multilane, reinforced concrete slab bridges. The finite-element method was used to investigate the effect of span length, slab width with and without shoulders, and wheel load conditions on typical bridges. A total of 112 highway bridge case studies were analyzed. It was assumed that the bridges were stand-alone structures carrying one-way traffic. The finite-element analysis (FEA) results of one-, two-, three-, and four-lane bridges are presented in combination with four typical span lengths. Bridges were loaded with highway design truck HS20 placed at critical locations in the longitudinal direction of each lane. Two possible transverse truck positions were considered: (1) Centered loading condition where design trucks are assumed to be traveling in the center of each lane; and (2) edge loading condition where the design trucks are placed close to one edge of the slab with the absolute minimum spacing between adjacent trucks. FEA results for bridges subjected to edge loading showed that the AASHTO standard specifications procedure overestimates the bending moment by 30% for one lane and a span length less than 7.5 m (25 ft) but agrees with FEA bending moments for longer spans. The AASHTO bending moment gave results similar to those of the FEA when considering two or more lanes and a span length less than 10.5 m (35 ft). However, as the span length increases, AASHTO underestimates the FEA bending moment by 15 to 30%. It was shown that the presence of shoulders on both sides of the bridge increases the load-carrying capacity of the bridge due to the increase in slab width. An extreme loading scenario was created by introducing a disabled truck near the edge in addition to design trucks in other lanes placed as close as possible to the disabled truck. For this extreme loading condition, AASHTO procedure gave similar results to the FEA longitudinal bending moments for spans up to 7.5 m (25 ft) and underestimated the FEA (20 to 40%) for spans between 9 and 16.5 m (30 and 55 ft), regardless of the number of lanes. The new AASHTO load and resistance factor design (LRFD) bridge design specifications overestimate the bending moments for normal traffic on bridges. However, LRFD procedure gives results similar to those of the FEA edge+truck loading condition. Furthermore, the FEA results showed that edge beams must be considered in multilane slab bridges with a span length ranging between 6 and 16.5 m (20 and 55 ft). This paper will assist bridge engineers in performing realistic designs of simply supported, multilane, reinforced concrete slab bridges as well as evaluating the load-carrying capacity of existing highway bridges.     

Roebling Suspension Bridge. I: Finite-Element Model and Free Vibration Response

This first part of a two-part paper on the John A. Roebling suspension bridge (1867) across the Ohio River is an analytical investigation, whereas Part II focuses on the experimental investigation of the bridge. The primary objectives of the investigation are to assess the bridge’s load-carrying capacity and compare this capacity with current standards of safety. Dynamics-based evaluation is used, which requires combining finite-element bridge analysis and field testing. A 3D finite-element model is developed to represent the bridge and to establish its deformed equilibrium configuration due to dead loading. Starting from the deformed configuration, a modal analysis is performed to provide the frequencies and mode shapes. Transverse vibration modes dominate the low-frequency response. It is demonstrated that cable stress stiffening plays an important role in both the static and dynamic responses of the bridge. Inclusion of large deflection behavior is shown to have a limited effect on the member forces and bridge deflections. Parametric studies are performed using the developed finite-element model. The outcome of the investigation is to provide structural information that will assist in the preservation of the historic John A. Roebling suspension bridge, though the developed methodology could be applied to a wide range of cable-supported bridges.     

Evaluation of Load Distribution Factor by Series Solution for Orthotropic Bridge Decks

In bridge engineering, the three-dimensional behavior of a bridge system is usually reduced to the analysis of a T-beam section, loaded by an equivalent fraction of the applied live load, which is called the live load distribution factor (LDF). The LDF is defined in the both the AASHTO Standard Specifications and the LRFD Specifications primarily for concrete slabs and has inherent applicable limitations. This paper provides explicit formulas using series solutions for LDF of orthotropic bridge decks, applicable to various materials but intended for fiber-reinforced polymer (FRP) decks. The present formulation considers important parameters that represent the response characteristics of the structure that are often omitted or limited in the AASHTO Specifications. A one-term series solution is proposed based on the macroflexibility approach, in which the bridge system is simplified into two major components, deck and stringers. The governing equations for the two components are obtained separately, and the deflections and interaction forces are solved by ensuring displacement compatibility at stringer lines. The LDF is calculated as the ratio of the single stringer interaction force to the summation of total stringer interaction forces. To verify this solution, a finite-element (FE) parametric study is conducted on 66 simply supported concrete slab-on-steel girder bridges. The results from the series solution correlates well with the FE results. It is also illustrated that the series solution can be applied to predict LDF for FRP deck-on-steel girder bridges, by favorable comparisons among the analytical, FE, and testing results for a one-third-scale bridge model. The scale test specimen consists of an FRP sandwich deck attached to steel stringers by a mechanical connector. The series solution is further used to obtain multiple regression functions for the LDF in terms of nondimensional variables, which can be used for simplified design purposes.     

Effect of Skewness on the Distribution of Live Load Reaction at Piers of Skewed Continuous Bridges

This paper presents a study of the skewness effect on live load reactions at the piers of continuous bridges. Two prestressed concrete I-beam bridges and one steel I-girder bridge were selected for the study. To evaluate the skew effect, the skew angle of the bridges was varied from 0 to 60°. Live load reaction at support and shear at the beam ends of the selected bridges were determined using finite-element analysis. The comparison of the distribution factors of live load reactions and shear revealed that the distribution factor of reaction at piers was higher than that of shear at beam ends near the same support. The increase in the reaction distribution factor was more significant than that in the shear distribution factor in the interior beam line when the skew angle was greater than 30°. The LRFD shear equations and the Lever rule method could conservatively predict live load reaction distribution for piers in exterior beam lines but underestimate live load reaction distribution in interior beam lines. It is recommended that more research be performed for the distribution factor of live load reaction to quantify the responses.     

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%.     

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.     

Performance of a Tied-Arch Reinforced Concrete Railway Bridge: Rating, Safety Assessment, and Bond Length Evaluation

This study presents investigations regarding visual inspection, dynamic testing, and finite-element modeling of an approximately 80-year old reinforced concrete tied-arch railway bridge that is still in service in Turkey. Investigations were conducted as part of a systematic periodic inspection along Ankara-Zonguldak railway line. The bridge is subject to heavy freight trains with increasing axle loads. Field tests such as material tests and dynamic tests were used to calibrate the finite-element model of the bridge. Detailed information regarding testing and model updating procedure is given. Based on test results, computer model was refined. The calibrated model of the bridge structure was then used for structural assessment and evaluation. Despite sufficient overall safety, local details were found to be problematic. Due to insufficient bond length in hanger-to-arch connection, a strengthening scheme using steel channel sections was proposed.     

Live Load Radial Moment Distribution for Horizontally Curved Bridges

The present study is designed to determine the effect of major parameters on maximum total bending moments of curved girders, establish the relationship between key parameters and girder distribution factors (GDFs), and develop new approximate distribution factor equations. A level of analysis study using three numerical models was performed to establish an appropriate numerical modeling method on the basis of field test results. A total of 81 two-traffic lane curved bridges were analyzed under HL-93 loading. Two approximate GDF equations were developed based on the data obtained in this study: (1) a single GDF based on total girder normal stress; and (2) a combined GDF treating bending and warping normal stress separately. The two equations were developed based on both an averaged coefficient method and regression analysis. A goodness-of-fit test revealed that the combined GDF model developed by regression analysis best predicted GDFs. The present study demonstrated that radius, span length, cross frame spacing and girder spacing most significantly affect GDFs. The proposed GDF equations are expected to provide a more refined live load analysis for preliminary design.     

Lateral Load Distribution in Curved Steel I-Girder Bridges

The purpose of this paper is to develop new formulas for live load distribution in horizontally curved steel I-girder bridges. The formulas are developed by utilizing computer model results for a number of different horizontally curved steel I-girder bridges. The bridges used in this study are modeled as generalized grillage beam systems composed of horizontally curved beam elements for steel girders and substructure elements for lateral wind bracing and cross frames which consist of truss elements. Warping torsion is taken into consideration in the analysis. The effect of numerous parameters, including radius of curvature, girder spacing, overhang, etc., on the load distribution are studied. Key parameters affecting live load distribution are identified and simplified formulas are developed to predict positive moment, negative moment, and shear distribution for one-lane and multiple-lane loading. Comparisons of the formulas with finite element method and grillage analysis show that the proposed formulas have more accurate results than the various available American Association of State Highway and Transportation Officials specifications. The formulas developed in this study will assist bridge engineers and researchers in predicting the actual live load distribution in horizontally curved steel I-girder bridges.