Optimization of Cable Tensioning in Cable-Stayed Bridges

During the structural analysis of cable-stayed bridges, some specific problems arise that are not common in other types of bridges. One of these problem is the derivation of an optimal sequence for the tensioning of the stay cables. This paper describes a novel solution to this problem, the unit force method. The method takes into account all relevant effects for the design of cable-stayed bridges, including construction sequence, second-order theory, large displacements, cable sag and time-dependent effects, such as creep and shrinkage or relaxation of prestressing tendons. Information about the implementation of this method into a computer program is given, and an example of a practical application of this method concludes this paper. The method is not restricted to the design of cable-stayed bridges and may well be used for other structural applications in the future.     

Stability Analysis of Box-Girder Cable-Stayed Bridges

The objective of this study is to investigate the stability characteristics of box-girder cable-stayed bridges by three-dimensional finite-element methods. Cable-stayed bridges have many design parameters, because they have a lot of redundancies, especially for long-span bridges. Cable-stayed bridges exhibit several nonlinear behaviors concurrently under normal design loads because of large displacements; the interaction among the pylons, the stayed cables, and the bridge deck; the strong axial and lateral forces acting on the bridge deck and pylons; and cable nonlinearity. A typical two-lane, three-span, steel box-girder cable-stayed bridge superstructure was selected for this paper. The numerical results indicate that, if the ratio of the main span length with respect to the total span length, L1∕L, is small, the structure usually has a higher critical load. If the ratio Ip∕Ib increases, the critical load of the bridge decreases, in which Ip is the moment of inertia of the pylon and Ib is the moment of inertia of the bridge deck. When the ratio Ip∕Ib is greater than 10.0, the decrement becomes insignificant. For cable arrangements, bridges supported by a harp-type cable arrangement are the better design than bridges supported by a fan-type cable arrangement on buckling analysis. The numerical results also indicate that use of either A-type or H-type pylons does not significantly affect the critical load of this type of structure. In order to make the numerical results useful, the buckling loads have been nondimensionalized and presented in both tabular and graphical forms.     

Simulation of Construction of Cable-Stayed Bridges

Construction of cable-stayed bridges involves major changes in configuration of the structure with the addition and removal of structural components to the partially constructed structure. At every stage of construction, it is necessary to have sufficient information about the existing partial structure as-built, to verify the requirements called for in the construction guidelines and to investigate the effects of possible modifications in the construction procedures. The final stresses and deformations in the completed structure are strongly dependent on the sequence of events during the construction and the erection procedure used. Therefore, analysis of the actual construction sequence is an important first step in any analysis of the performance of the bridge under external loads. In this paper a general methodology for construction sequence simulation of cable-stayed bridges is presented, and stage-by-stage construction of an actual bridge is simulated. The objective of the simulation is to evaluate short-term and long-term influences of the construction sequence on the structural integrity of the cable-stayed bridge. Comparisons are presented between results from the present analysis, conventional procedures, and the actual field measurements.     

Elastic-Plastic Seismic Behavior of Long Span Cable-Stayed Bridges

This paper investigates the elastic-plastic seismic behavior of long span cable-stayed steel bridges through the plane finite-element model. Both geometric and material nonlinearities are involved in the analysis. The geometric nonlinearities come from the stay cable sag effect, axial force-bending moment interaction, and large displacements. Material nonlinearity arises when the stiffening steel girder yields. The example bridge is a cable-stayed bridge with a central span length of 605 m. The seismic response analyses have been conducted from the deformed equilibrium configuration due to dead loads. Three strong earthquake records of the Great Hanshin earthquake of 1995 in Japan are used in the analysis. These earthquake records are input in the bridge longitudinal direction, vertical direction, and combined longitudinal and vertical directions. To evaluate the residual elastic-plastic seismic response, a new kind of seismic damage index called the maximum equivalent plastic strain ratio is proposed. The results show that the elastic-plastic effect tends to reduce the seismic response of long span cable-stayed steel bridges. The elastic and elastic-plastic seismic response behavior depends highly on the characteristics of input earthquake records. The earthquake record with the largest peak ground acceleration value does not necessarily induce the greatest elastic-plastic seismic damage.     

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.     

Seismic Vulnerability and Mitigation during Construction of Cable-Stayed Bridges

The implications of earthquake loading during balanced cantilever construction of a cable-stayed bridge are examined. Finite-element models of a cable-stayed bridge were developed and multiple ground motion time history records were used to study the seismic response at the base of the towers for six stages of balanced cantilever construction. Probabilistic seismic hazard relationships were used to relate ground motions to bridge responses. The results show that there can be a high probability of having seismic responses (forces/moments) in a partially completed bridge that exceed, often by a substantial margin, the 10%/50-year design level (0.21% per annum) for the full bridge. The maximum probability of exceedance per annum was found to be 20%. This occurs because during balanced-cantilever construction the structure is in a particularly precarious and vulnerable state. The efficacy of a seismic mitigation strategy based on the use of tie-down cables intended for aerodynamic stability during construction was investigated. This strategy was successful in reducing some of the seismic vulnerabilities so that probabilities of exceedance during construction dropped to below 1% per annum. Although applied to only one cable-stayed bridge, the same approach can be used for construction-stage vulnerability analysis of other long-span bridges.     

Influence of Deck Material on Response of Cable-Stayed Bridges to Live Loads

During the last three decades, cable-stayed bridges have proven to be first-class structures providing vital transport links. Together with the construction process, erection procedure, and site conditions, the choice of material for the deck is a principal factor in the overall cost of construction. The effects of variable long-span bridge loads on the design of steel, composite, and concrete decks are investigated. Recent American and British long-span bridge loads have been used that are based on direct observations of modern traffic conditions. The three-dimensional finite-element models prepared for the study are based on the geometric and material properties of the Quincy Bayview cable-stayed bridge. Many cable arrangements are considered for the studied concrete, composite, and steel decks. A nonlinear analysis of the cable-stayed bridge models is carried out. The results of the different deck materials are compared. It is shown that the choice of material for the deck can be greatly affected by the distribution of stays and by the intensity of the live load adopted.     

Erection of Cable-Stayed Bridges Having Composite Decks with Precast Concrete Slabs

For the construction of composite steel-concrete decks of cable-stayed bridges, methods of erection and analysis have to be applied that, upon completion of the deck, accurately yield the prescribed dead load configuration of the deck regarding geometry and forces. During deck erection, no unwanted bending moments should be locked into the composite sections when the concrete slab is connected to the steel substructure. Such locked-in moments would bend the deck, cause concrete creep that is difficult to predict, and introduce the risk of deviations from the desired deck alignment and the corresponding distribution of forces. This paper presents a simple and practical method of erection and erection analysis for composite decks with precast concrete slabs. A two-step tensioning procedure of the stay cables is proposed that minimizes the effects of unwanted locked-in moments, making it easy to predict the geometry of the erection stages and to yield the desired dead load configuration of the deck. The method was successfully applied for the erection of the Ting Kau bridge in Hong Kong, a cable-stayed bridge of 1,200 m in length having a composite deck with a precast deck slab.     

Wavelet-Hybrid Feedback Linear Mean Squared Algorithm for Robust Control of Cable-Stayed Bridges

Cable-stayed bridges are flexible structures, and control of their vibrations is an important consideration and a challenging problem. In this paper, the wavelet-hybrid feedback least mean squared algorithm recently developed by the writers is used for vibration control of cable-stayed bridges under various seismic excitations. The effectiveness of the algorithm is investigated through numerical simulation using a benchmark control problem created based on an actual semifan-type cable-stayed bridge design. The performance of the algorithm is compared with that of a sample linear quadratic Gaussian (LQG) controller using three different earthquake records: the El Centro (California, 1940), Mexico City (Mexico, 1985), and Gebze (Turkey, 1999) earthquakes. Simulation results demonstrate that the new algorithm is consistently more effective than the sample LQG controller for all three earthquake records. Additional numerical simulations are performed to evaluate the sensitivity of the new control algorithm. It is concluded that the algorithm is robust against the uncertainties existing in modeling structures.     

Assessment of Cable Maintenance Technologies for Honshu-Shikoku Bridges

A dry-air injection system developed as a new anticorrosion method for the suspension bridge cables used in Honshu-Shikoku Bridges has been implemented. In this paper, applicability of this system to existing suspension bridges employing traditional anticorrosion measures, as well as to newly constructed ones, is reported. Along with this development, several suspenders in a suspension bridge, which had been in service for 17 years, were opened up for inspection. A characteristic pattern of corrosion was observed in this investigation. Also, nondestructive inspections of bridge suspenders based on principles of magnetism were carried out on-site and indoors. Effectiveness of this nondestructive inspection method is discussed in this paper, referring to comparisons between the results of the exposed inspection of suspenders and those of nondestructive inspection.     

In-Service Evaluation of Cable-Stayed Bridges, Overview of Available Methods and Findings

This paper discusses advances in evaluation and health monitoring of cable-stayed bridges and available methods. Bridge engineers and highway administrators in the United States are gradually becoming more comfortable with cable-stayed bridges, and the past few years have seen a significant increase in construction of these elegant bridges in many parts of this great nation. In the last decade, several investigations have been directed to condition assessment of cable-stayed bridges and contributed extensively to advances in construction, design, and health monitoring of this type of structures. Results of these investigations have helped toward formation of a unified approach for in-service evaluation and problem solving of these aesthetic structures. This paper describes this approach with reference to sources for more detailed information. Additionally, discussed in this paper are a series of methods developed or tailored for evaluation of these unique structures. The paper also reviews the typical problems observed in the course of field evaluations for in-service cable-stayed bridges.     

Orthogonal Effects in Seismic Analysis of Skewed Bridges

In seismic analysis of bridges, the designer chooses the direction of the applied earthquake forces arbitrarily. This paper investigates the effects of seismic force direction on the responses of slab-girder skewed bridges in response spectrum and time history linear dynamic analyses. The combination rules for orthogonal earthquake effects, such as the 100/30, 100/40?percentage rules and the SRSS method are also examined. It is concluded that either the SRSS or the 100/40?percentage rule in the skew direction should be used in the response spectrum analysis of skewed bridges. For time history analysis none of the combination rules provide conservative results. In this case, the application of paired acceleration time histories in several angular directions is recommended.     

Full-Scale Tests of Seismic Cable Restrainer Retrofits for Simply Supported Bridges

Many parts of the central and southeastern United States have recently begun initiating seismic retrofit programs for bridges on major interstate highways. One of the most common retrofit strategies is to provide cable restrainers at the intermediate hinges and abutments in order to reduce the likelihood of collapse due to unseating. To evaluate the force-displacement behavior of the cable restrainer retrofits, a full-scale bridge setup was constructed based on an existing multispan, simply supported steel girder bridge in Tennessee, that has been considered for seismic retrofit using cable restrainers. Seismic cable restrainers were connected to the bridge pier using steel bent plates, angles, and undercut anchors embedded in the concrete as specified by typical bridge retrofit plans. The full-scale bridge model was subjected to monotonic loading to test the capacity of the cable restrainer system and to determine the modes of failure. The results showed that the primary modes of failure are in the connection elements of the pier and girders, and they occur at force levels much lower than the strength of the cable. Modifications to the connection elements were designed and tested. The new connections resulted in a higher strength and deformation capacity of the cable restrainer assembly.     

Research on Cable Anchorage Systems for Self-Anchored Suspension Bridges with Steel Box Girders

A new type of steel-concrete composite cable anchorage system is conceived and investigated preliminarily for self-anchored suspension bridges with steel box girders to optimize the mechanical behavior of the conventional cable anchorage systems. Model tests and 3D elaborate finite-element analysis (FEA) of the pure steel and steel-concrete composite cable anchorage systems are carried out for the Qingdao Bay Bridge Project, which is under construction in China. For the pure steel anchorage system, a complex stress distribution with obvious stress concentration is observed in the test. The FEA results of the stress distribution correlate well with the experimental measurements. The pure steel anchorage system adopted in the final design of the Qingdao Bay Bridge Project is reliable with a sufficient safety margin. In the contrast test of the composite anchorage system, owing to the composite effect between the steel and concrete, the stress level is reduced significantly and the stress distribution becomes more uniform in comparison with the pure steel anchorage system. The measured stress reduction rate of the composite anchorage averages approximately 40%, which is slightly smaller than the FEA results, and indicates the partial composite effect between the steel and concrete. The proposed composite anchorage system can effectively reduce the thickness and consumption of the steel plates, improve the mechanical behavior of the anchorage system, and simplify the fabrication and construction procedures.     

Aeroelastic Analysis of Bridges: Effects of Turbulence and Aerodynamic Nonlinearities

Current linear aeroelastic analysis approaches are not suited for capturing the emerging concerns in bridge aerodynamics introduced by aerodynamic nonlinearities and turbulence effects. These issues may become critical for bridges with increasing spans and/or with aerodynamic characteristics sensitive to the effective angle of incidence. This paper presents a nonlinear aerodynamic force model and associated time domain analysis framework for predicting the aeroelastic response of bridges under turbulent winds. The nonlinear force model separates the aerodynamic force into low- and high-frequency components according to the effective angle of incidence. The low-frequency force component is modeled utilizing quasi-steady theory. The high-frequency force component is based on the frequency dependent unsteady aerodynamic characteristics, which are similar to the traditional force model but vary in space and time following the low-frequency effective angle of incidence. The proposed framework provides an effective analysis tool to study the influence of structural and aerodynamic nonlinearities and turbulence on the bridge aeroelastic response. The effectiveness of this approach is demonstrated by utilizing an example of a long span suspension bridge with aerodynamic characteristics sensitive to the angle of incidence. The influence of mean wind angle of incidence on the aeroelastic modal properties and the associated aeroelastic response and the sensitivity of bridge response to nonlinear aerodynamics and low-frequency turbulence are examined.     

Effects of Random Material Properties on Buckling of Composite Plates

Composites exhibit a considerable amount of variation in their material properties because their fabrication∕manufacturing process involves a large number of parameters that cannot be controlled effectively. In the present study, the material properties have been modeled as random variables for better prediction of the system behavior. The classical laminate theory and first-order and higher-order shear deformation theories have been employed in deriving the governing equations for buckling of laminated rectangular plates. A mean-centered first-order perturbation technique has been used to find the second-order statistics of the buckling load. The approach has been validated by comparison with results of Monte Carlo simulation. Typical results have been presented for a plate with all edges simply supported. The effectiveness of the theories in predicting the buckling load dispersions has been examined. The sensitivity of buckling loads to change in the standard deviation of random material properties and to system parameters—side-to-thickness ratio and aspect ratio—has been examined for cross-ply symmetric and antisymmetric laminates.     

Stochastic Model for Multilane Traffic Effects on Bridges

In modern approaches, the target and design values for traffic effects on bridges are obtained through suitable stochastic traffic models processing recorded traffic data. To this aim, several theoretical and numerical stochastic models have recently been proposed. Despite their elegance, theoretical models often have limited fields of application, while numerical models, particularly efficient when single-lane traffic flow is considered, turn out to be unsatisfactory when traffic in several lanes, or a combination of traffic actions with those from other sources must be dealt with. This paper presents a more general theoretical stochastic traffic model, which is able, not only to reproduce actual traffic, but to account for such traffic interactions as well. The model, based on an equilibrium renewal process of vehicle arrivals, can be used in all cases where sophisticated evaluation of real traffic effects is required, such as calibration of conventional load models in bridge codes, assessment of existing bridges, as well as the design and analysis of bridges with less traditional schemes or subjected to particular traffic conditions. The efficiency of the model is illustrated through meaningful applications.     

Aerodynamic Coupling Effects on Flutter and Buffeting of Bridges

The effects of aerodynamic coupling among modes of vibration on the flutter and buffeting response of long-span bridges are investigated. By introducing the unsteady, self-excited aerodynamic forces in terms of rational function approximations, the equations of motion in generalized modal coordinates are transformed into a frequency-independent state-space format. The frequencies, damping ratios, and complex mode shapes at a prescribed wind velocity, and the critical flutter conditions, are identified by solving a complex eigenvalue problem. A significant feature of this approach is that an iterative solution for determining the flutter conditions is not necessary, because the equations of motion are independent of frequency. The energy increase in each flutter motion cycle is examined using the work done by the generalized aerodynamic forces or by the self-excited forces along the bridge axis. Accordingly, their contribution to the aerodynamic damping can be clearly identified. The multimode flutter generation mechanism and the roles of flutter derivatives are investigated. Finally, the coupling effects on the buffeting response due to self-excited forces are also discussed.     

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.