Seismic Response of Multiple Span Steel Bridges in Central and Southeastern United States. I: As Built

The seismic response of typical multispan simply supported (MSSS) and multispan continuous steel girder bridges in the central and southeastern United States is evaluated. Nonlinear time history analyses are conducted using synthetic ground motion for three cities for 475 and 2,475-year return period earthquakes (10 and 2% probability of exceedance in 50 years). The results indicate that the seismic response for the 475-year return period earthquake would lead to an essentially linear response in typical bridges. However, the seismic response for a 2,475-year return period earthquake resulted in significant demands on nonductile columns, fixed and expansion bearings, and abutments. In particular, pounding between decks in the MSSS bridge would result in significant damage to steel bearings and would lead to the toppling of rocker bearings, which may result in unseating of the bridge deck.     

Vulnerability Assessment of Cable-Stayed Bridges in Probabilistic Domain

Vulnerability of a structure under terrorist attack can be regarded as the study of its behavior against blast-induced loads. A structure is vulnerable if a small damage can trigger a disproportionately large consequence and lead to a cascade of failure events or even collapse. The performance of structural vulnerability depends upon factors such as external loading condition and structural properties. As many of these factors are random in nature, it is necessary to develop a vulnerability assessment technique in the probabilistic domain. In this study, one such assessment framework is proposed for cable-stayed bridges. The framework consists of two stages of analysis: determining the probability of direct damage due to blast loads and assessing the subsequent probability of collapse due to component damage. In the first stage assessment, damage of the bridge component is defined as the exceedance of a predefined limit state such as displacement or yielding. The damage probability is obtained through a stochastic finite-element analysis and the first-order second-moment reliability method. The second stage assessment further calculates the probability of collapse due to direct damage of some component via an event tree approach. The proposed assessment methods are illustrated on a hypothetical single-tower cable-stayed bridge. It is seen that the proposed methods provide a quantitative tool for analyzing the vulnerability performance of cable-stayed bridges under terrorist attack.     

Bridge Seismic Retrofitting Practices in the Central and Southeastern United States

This paper conducts a detailed review of the seismic hazard, inventory, bridge vulnerability, and bridge retrofit practices in the Central and Southeastern United States (CSUS). Based on the analysis of the bridge inventory in the CSUS, it was found that over 12,927 bridges (12.6%) are exposed to 7% probability of exceedance (PE) in 75-year peak ground acceleration (PGA) of greater than 0.20 g, and nearly 3.5% of bridges in the CSUS have a 7% PE in 75-year PGA of greater than 0.50 g. Since many of the bridges in this region were not designed with explicit consideration of the seismic hazard, many of them are in need of seismic retrofitting to reduce their seismic vulnerability. While several of the states in the CSUS have retrofitted some of their bridges, systematic retrofit programs do not currently exist. The review of retrofit practices in the region indicates that the most common retrofit approaches in the CSUS include the use of restrainer cables, isolation bearings, column jacketing, shear keys, and seat extenders. The paper presents an overview of the common approaches and details used for the aforementioned retrofit measures. This paper serves as a useful tool for bridge engineers in the CSUS as they begin to perform systematic retrofit of vulnerable bridges in the region.     

Kentucky River High Bridge

Cantilever bridge construction can be said to have started with the work of Heinrich Gerber in Germany in 1867. While the principle had been used in many ancient bridges, it was not until Gerber’s work that metal bridges were built using the cantilever principle. The Kentucky High Bridge over the Kentucky River was the first modern cantilever bridge built in the United States. While James Eads had used the cantilever construction method at St. Louis, his bridge acted in service as a series of three arches. The High Bridge, designed by C. Shaler Smith, was one of the most daring and innovative bridges built in the country and carried its load between 1876 and 1912, when it was replaced by Gustave Lindenthal’s three span truss.     

Influence of Inelastic Tower Links on Cable-Supported Bridge Response

A new concept for bridge tower designs in seismic zones incorporates sacrificial link schemes that enable the tower shafts to remain elastic under large seismic excitation. In order to study the influence of inelastic tower links on the seismic response of cable-supported bridges, global seismic time history analyses were performed on models of the new San Francisco-Oakland Bay Bridge East Span self-anchored suspension bridge (SASB) and a cable-stayed bridge (CSB) alternative. The addition of inelastic links to the signature tower improved the behavior of both structures. The tower and overall bridge demands were reduced, including the tower drift and moments as well as the suspension cable, cable stay, and superstructure drifts and axial loads. The inelastic tower links protected the SASB and CSB tower shafts from nonlinear behavior under the 1,500-year Safety Evaluation Earthquake (SEE) event as well as a 2,500-year event. When the inelastic tower links were removed, the SASB tower shafts yielded under the SEE. It was shown that the inelastic tower links could be used to tune the dynamic response of bridge towers in regions of high seismicity.     

Sliding Mode Control of Cable-Stayed Bridge Subjected to Seismic Excitation

The working group on bridge control within the ASCE Committee on Structural Control recently initiated a first-generation benchmark problem addressing the control of a cable-stayed bridge subjected to seismic excitation. Previous research examined the applicability of a LQG-based semiactive control system using magnetorheological (MR) dampers to reduce the structural response of the benchmark bridge and confirmed the capability of the MR damper-based system for seismic response reduction. In this paper, sliding mode control (SMC) is applied in lieu of the LQG formulation to the benchmark bridge problem. The performance and robustness of the SMC-based semiactive control system using MR dampers (SMC/MR) is investigated through a series of numerical simulations, and it is confirmed that SMC/MR can be very effectively applied to the benchmark cable-stayed bridge, subjected to a wide range of seismic loading conditions.     

Niagara Cantilever

The first modern metal cantilever bridge in the United States, using erection methods that were to be utilized in most future cantilever bridges, was by C. C. Schneider across the Niagara Gorge in 1883. The Niagara, saw in order, John Roebling’s Railroad Suspension Bridge, Samuel Keefer’s Honeymoon Suspension Bridge, Edward Serrell’s Lewiston-Queenston Suspension Bridge, Schneider’s cantilever, Leffert Buck’s arch bridge at the falls as well as Buck’s arch built under Roebling’s suspension bridge. Schneider’s bridge had a useful life of over 40 years during a period when rolling stock on the railroads was increasing rapidly. The speed of erection of a new style bridge coupled with its performance makes it one of the most innovative and significant bridges built in the world at the time.     

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.     

Wave Passage and Ground Motion Incoherency Effects on Seismic Response of an Extended Bridge

This paper investigates the implications of ground motion spatial variability on the seismic response of an extended highway bridge. An existing 59-span, 2,164-meter bridge with several bearing types and irregularity features was selected as a reference structure. The bridge is located in the New Madrid Seismic Zone and supported on thick layers of soil deposits. Site-specific bedrock input ground motions were selected based on a refined probabilistic seismic hazard analysis of the bridge site. Wave passage and ground motion incoherency effects were accounted for after propagating the bedrock records to the ground surface. The results obtained from inelastic response-history analyses confirm the significant impact of wave passage and ground motion incoherency on the seismic behavior of the bridge. The amplification in seismic demands exceeds 150%, whereas the maximum suppression of these demands is less than 50%. The irregular and unpredictable changes in structural response owing to asynchronous earthquake records necessitate in-depth seismic assessment of major highway bridges with advanced modeling techniques to realistically capture their complex seismic response.     

Engineering the Tower and Main Span Construction of Stonecutters Bridge

Stonecutters Bridge is the second longest cable-stayed bridge in the world and the first major bridge with a twin-box girder superstructure. It has a number of innovative structural features which made the construction of the bridge a significant challenge. This paper describes the fabrication and erection procedures for the bridge towers and the main span superstructure. These were developed in close interaction between the contractor and his construction engineering consultant to ensure a safe and effective construction. A stage-by-stage analysis was set up to model every step of the main span erection. The results were first used in the verification analyses to establish the adequacy of the permanent works throughout construction. In parallel, extensive wind tunnel testing as well as numerical analyses were performed to ascertain the effects of typhoon wind loads on the structure. The structural deformations predicted by the erection analysis were incorporated into a comprehensive geometric control procedure. This paper describes the construction methodologies developed and the related engineering input. It outlines studies undertaken to achieve an effective construction, ensure structural adequacy of all erection stages, ascertain an acceptable aerodynamic performance of the bridge, and exercise full control over the bridge geometry throughout erection.     

Applicability of 4D CAD in Civil Engineering Construction: Case Study of a Cable-Stayed Bridge Project

Four-dimensional (4D) computer-aided design (CAD) has been credited with improving construction planning procedures. The integration of three-dimensional CAD with schedule information has enabled the effective detection of design and planning flaws in many construction projects. However, the benefit of 4D CAD has been centered on architectural constructions, as other areas such as civil infrastructure have seldom been the target of 4D CAD application. This paper presents a case study in which a cable-stayed bridge construction was analyzed and modeled using the 4D graphic simulation approach. The cable-stayed bridge was chosen for the case study because it suitably represents the complex nature of modern civil infrastructure. 4D CAD models were developed at three different levels of detail: activity, discrete operation, and continuous operation. The clear definitions of the three levels of detail of 4D CAD and their application results for the cable-stayed bridge are presented herein.     

Probabilistic Seismic Demand Models and Fragility Estimates for Reinforced Concrete Highway Bridges with One Single-Column Bent

In performance-based seismic design, general and practical seismic demand models of structures are essential. This paper proposes a general methodology to construct probabilistic demand models for reinforced concrete (RC) highway bridges with one single-column bent. The developed probabilistic models consider the dependence of the seismic demands on the ground motion characteristics and the prevailing uncertainties, including uncertainties in the structural properties, statistical uncertainties, and model errors. Probabilistic models for seismic deformation, shear, and bivariate deformation-shear demands are developed by adding correction terms to deterministic demand models currently used in practice. The correction terms remove the bias and improve the accuracy of the deterministic models, complement the deterministic models with ground motion intensity measures that are critical for determining the seismic demands, and preserve the simplicity of the deterministic models to facilitate the practical application of the proposed probabilistic models. The demand data used for developing the models are obtained from 60 representative configurations of finite-element models of RC bridges with one single-column bent subjected to a large number of representative seismic ground motions. The ground motions include near-field and ordinary records, and the soil amplification due to different soil characteristics is considered. A Bayesian updating approach and an all possible subset model selection are used to assess the unknown model parameters and select the correction terms. Combined with previously developed capacity models, the proposed seismic demand models can be used to estimate the seismic fragility of RC bridges with one single-column bent. Seismic fragility is defined as the conditional probability that the demand quantity of interest attains or exceeds a specified capacity level for given values of the earthquake intensity measures. As an application, the univariate deformation and shear fragilities and the bivariate deformation-shear fragility are assessed for an example bridge.     

Safety Analysis of Moving Road Vehicles on a Long Bridge under Crosswind

This paper presents a safety analysis of high-sided road vehicles running on a long span cable-stayed bridge when the road vehicle enters a sharp-edged crosswind gust while the bridge is oscillating under fluctuating winds. Road vehicle accidents, including overturning, excessive sideslip, and exaggerated rotation, are defined first. The mathematical model and the equation of motion of coupled road vehicle–bridge systems under crosswind are then established, which include road surface roughness, vehicle suspension, and the sideslip of the vehicle tire relative to the bridge deck in the lateral direction. A case study using a real long cable-stayed bridge and a high-sided road vehicle is finally conducted, and an extensive computational work is performed to obtain a series of accident vehicle speed against mean crosswind speed, by which the decision on the threshold of mean wind speed above which the bridge should be closed to the road vehicle can be made. The obtained accident vehicle speeds are also compared with those for the same vehicles running on the ground. It is shown that the oscillation of the cable-stayed bridge will lower the accident vehicle speed when wind speed reaches a certain level.     

Analytic Model of Long-Span Self-Shored Arch Bridge

An innovative self-shoring staged construction method was developed to build the world’s longest reinforced composite concrete arch bridge across the Yangtze River at Wanxian, in Chongqing, China. The method uses a steel tube truss frame constructed by the conventional cantilever launching technique. This steel frame with concrete-filled tubes performs the dual role of arch falsework and arch main reinforcement for the final reinforced concrete arch bridge. An optimized schedule for concrete placement was proposed to control the stresses, deflections, and stability of the arch rib during construction. The time dependent effects of concrete, the nonlinear stress-strain relationship of steel and concrete, as well as the geometric nonlinearility were considered. Control information at various stages of construction can be provided using the model developed. A program was developed to conduct parametric studies for selection of the final construction scheme and to direct the construction progress by monitoring and comparing actual and predicted stress and deflection.     

Feasibility of a 1,400 m Span Steel Cable-Stayed Bridge

This paper describes the feasibility of 1,400 m steel cable-stayed bridges from both structural and economic viewpoints. Because the weight of a steel girder strongly affects the total cost of the bridge, the writers present a procedure to obtain a minimum weight for a girder that ensures safety against static and dynamic instabilities. For static instability, elastoplastic, finite-displacement analysis under in-plane load and elastic, finite-displacement analysis under displacement-dependent wind load are conducted; for dynamic instability, multimodal flutter analysis is carried out. It is shown that static critical wind velocity of lateral torsional buckling governs the dimension of the girder. Finally, the writers briefly compare a cable-stayed bridge with suspension bridge alternatives.     

Probabilistic Seismic Demand Models and Fragility Estimates for Reinforced Concrete Bridges with Two-Column Bents

Probabilistic models are developed to predict the deformation and shear demands due to seismic excitation on reinforced concrete (RC) columns in bridges with two-column bents. A Bayesian methodology is used to develop the models. The models are unbiased and properly account for the predominant uncertainties, including model errors, arising from a potentially inaccurate model form or missing variables, measurement errors, and statistical uncertainty. The probabilistic models developed are akin to deterministic demand models and procedures commonly used in practice, but they have additional correction terms that explicitly describe the inherent systematic and random errors. Through the use of a set of “explanatory” functions, terms that correct the bias in the existing deterministic demand models are identified. These explanatory functions provide insight into the underlying behavioral phenomena and provide a means to select ground motion parameters that are most relevant to the seismic demands. The approach takes into account information gained from scientific/engineering laws, observational data from laboratory experiments, and simulated data from numerical dynamic responses. The demand models are combined with previously developed probabilistic capacity models for RC bridge columns to objectively estimate the seismic vulnerability of bridge components and systems. The vulnerability is expressed in terms of the conditional probability (or fragility) that a demand quantity (deformation or shear) will be greater than or equal to the corresponding capacity. Fragility estimates are developed for an example RC bridge with two-column bents, designed based on the current specifications for California. Fragility estimates are computed at the individual column, bent, and bridge system levels, as a function of the spectral acceleration and the ratio between the peak ground velocity and the peak ground acceleration.     

Reliability-Based Optimum Design of Glulam Cable-Stayed Footbridges

This work presents a procedure for finding the reliability-based optimum design of cable-stayed bridges. The minimization problem is stated as the minimization of stresses, displacements, reliability, and bridge cost. A finite-element approach is used for structural analysis. It includes a direct analytic sensitivity analysis module, which provides the structural behavior responses to changes in the design variables. An equivalent multicriteria approach is used to solve the nondifferential, nonlinear optimization problem, turning the original problem into sequential minimization of unconstrained convex scalar functions, from which a Pareto optimum is obtained. Examples are given illustrating the procedure.