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.     

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.     

Dynamic Monitoring of Steel Girder Highway Bridge

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

Vibration Performance of a Large Cantilever Grandstand during an International Football Match

Vibration problems in stadia are becoming more common due to increased structural slenderness and more lively dynamic crowd excitation. Unfortunately, there is very little guidance available to design engineers dealing with the assessment and design of stadia structures. This paper presents unique data from a program of modal testing and in-service monitoring of a large contemporary cantilever grandstand in the United Kingdom. The in-service monitoring was carried out during an international football match, during which the stadium was full to capacity. Modal properties obtained from the testing on the empty structure are presented and the results from in-service monitoring are described. It is found that crowd occupation can significantly alter the modal properties of a stadium, and that the changes can vary according to the crowd configuration. Additionally, previously proposed methods for assessment of vibration serviceability have been applied and it has been shown that they can lead to inconsistent results, which is a result of their sensitivity to the data acquisition and analysis techniques used. It is concluded that it is very important that consistent methods of data acquisition, analysis, and vibration serviceability assessment are utilized by future researchers and practitioners. Also, further research is required to define vibration serviceability limits using the state-of-the-art vibration dose approach.     

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.     

Control of Seismically Excited Cable-Stayed Bridge Using Resetting Semiactive Stiffness Dampers

Cable-stayed bridges are prone to exhibit large amplitude oscillations because of their large flexibility, small mass, and small inherent damping. Hence, the reduction of seismic or wind-induced vibration of cable-stayed bridges is vital for their safety and serviceability. In this paper, a resetting semiactive stiffness damper (RSASD) is used to control the peak dynamic response of a recently developed benchmark problem on a cable-stayed bridge subject to earthquakes. The model of the benchmark cable-stayed bridge is based on the actual cable-stayed bridge that is under construction on Cape Girardeau, Mo. The prime aim of this study is to investigate the application of protective devices, such as semiactive and passive dampers, in reducing the displacement of the deck as well as base shear and moments at the base of the towers. In this research, the applications of the RSASD as well as passive viscous and fluid dampers to the benchmark bridge problem have been investigated. Numerical simulations are conducted by installing RSASD devices as well as passive viscous and friction dampers between the pier and the deck of the bridge. Numerical results clearly indicate that the displacement of the deck, and shear and moments at the base of the towers, are reduced substantially by installing these protective devices. In particular, energy dissipating capabilities and performance of the RSASD are quite remarkable. It is shown that the RSASD is quite effective in reducing peak response quantities of the bridge to a level similar to that of the sample active controller. A further reduction in response quantities can be achieved by using the RSASD in a combination of passive viscous dampers.     

Interactive 3D CAD for Effective Derrick Crane Operation in a Cable-Stayed Bridge Construction

The high expectation of esthetic and functional quality in modern civil infrastructure has resulted in the increased demand for long span bridges. In advanced or developing countries, long span bridges such as cable-stayed and suspension bridges are considered even as landmarks that symbolize the prosperity or culture of the region. These long span bridges require higher level of design and construction technologies than other types of bridges. In particular, the construction of cable-stayed bridges involves precise and sophisticated operation of construction equipment such as derrick cranes. However, it is not easy to plan the operations of a derrick crane before the actual construction process takes place. Unexpected spatial constraints in the construction site may hinder the smooth operation of a derrick crane, which leads to lower than expected productivity and safety. This study applies interactive three-dimensional (3D) computer aided design (CAD) to the derrick crane operation for the purpose of identifying potential problems. Construction managers can have the two way process with the 3D CAD system to interactively test their construction plans and scenarios. The case study shows that the interactive 3D CAD system significantly improves the constructability of the cable-stayed bridge construction.     

Statistical Modeling of Coupled Shear-Moment Resistance for RC Bridge Girders

Many reinforced concrete bridges are posted or restricted to traffic, and repair or replacement decisions for these bridges involves both economical and safety considerations. To avoid the high costs of unnecessary replacement or repair, safety evaluation should be done with the most accurate methods available. Due to variability in material properties, geometrical properties, and methods of analysis, load carrying capacity evaluation may lead to uncertain outcomes. This paper presents a statistical model for combined shear-moment resistance of conventionally reinforced concrete bridge girders with common vintage design details and properties. New statistical data on stirrup spacing variability were developed from field measurements on in-service deck-girder bridges and these were combined with available data in the literature to model resistance uncertainty. The model offers bias factor and coefficient of variation for combined moment and shear carrying capacity per modified compression field theory. AASHTO-LRFD and ACI-318 were utilized to calculate capacity of the selected sections and strength reduction factors in AASHTO-LRFD and ACI-318 were compared using the obtained statistical parameters.     

In-Situ Evaluation of Two Concrete Slab Systems. II: Evaluation Criteria and Outcomes

The primary objective of in-situ load testing is to evaluate the safety and serviceability of an existing structural system with respect to a particular load condition and effect. In light of technological advances in construction methods, analytical tools and monitoring instrumentation, new different evaluation criteria are being proposed in addition to different in-situ load test methods. Some criteria may be more appropriate than others based on the expected damage and failure mechanisms of the structure being considered. The companion paper describes the rationale and application of both a consolidated and an alternative approach to the determination of load level, loading procedure and instrumentation requirements for two case studies. This paper discusses in detail the evaluation criteria and outcomes of these two field projects consisting of a posttensioned concrete slab with structural deficiencies due to tendon and mild reinforcement misplacement and a floor bay of a two-way reinforced concrete slab showing cracking at the positive and negative moment regions. After discussing the relative merits of the evaluation methodologies and the significance of their respective acceptance thresholds, concepts for the development of a new global criterion are discussed.     

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

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

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.     

Bayesian Model Updating Using Hybrid Monte Carlo Simulation with Application to Structural Dynamic Models with Many Uncertain Parameters

In recent years, Bayesian model updating techniques based on measured data have been applied to system identification of structures and to structural health monitoring. A fully probabilistic Bayesian model updating approach provides a robust and rigorous framework for these applications due to its ability to characterize modeling uncertainties associated with the underlying structural system and to its exclusive foundation on the probability axioms. The plausibility of each structural model within a set of possible models, given the measured data, is quantified by the joint posterior probability density function of the model parameters. This Bayesian approach requires the evaluation of multidimensional integrals, and this usually cannot be done analytically. Recently, some Markov chain Monte Carlo simulation methods have been developed to solve the Bayesian model updating problem. However, in general, the efficiency of these proposed approaches is adversely affected by the dimension of the model parameter space. In this paper, the Hybrid Monte Carlo method is investigated (also known as Hamiltonian Markov chain method), and we show how it can be used to solve higher-dimensional Bayesian model updating problems. Practical issues for the feasibility of the Hybrid Monte Carlo method to such problems are addressed, and improvements are proposed to make it more effective and efficient for solving such model updating problems. New formulae for Markov chain convergence assessment are derived. The effectiveness of the proposed approach for Bayesian model updating of structural dynamic models with many uncertain parameters is illustrated with a simulated data example involving a ten-story building that has 31 model parameters to be updated.     

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.     

Reliability-Based Load and Resistance Factor Rating Using In-Service Data

Traditional bridge evaluation techniques are based on design-based deterministic equations that use limited site-specific data. They do not necessarily conform to a quantifiable standard of safety and are often quite conservative. The newly emerging load and resistance factor rating (LRFR) method addresses some of these shortcomings and allows bridge rating in a manner consistent with load and resistance factor design (LRFD) but is not based on site-specific information. This paper presents a probability-based methodology for load-rating bridges by using site-specific in-service structural response data in an LRFR format. The use of a site-specific structural response allows the elimination of a substantial portion of modeling uncertainty in live load characterization (involving dynamic impact and girder distribution), which leads to more accurate bridge ratings. Rating at two different limit states, yield and plastic collapse, is proposed for specified service lives and target reliabilities. We consider a conditional Poisson occurrence of identically distributed and statistically independent (i.i.d.) loads, uncertainties in field measurement, modeling uncertainties, and Bayesian updating of the empirical distribution function to obtain an extreme-value distribution of the time-dependent maximum live load. An illustrative example uses in-service peak-strain data from ambient traffic collected on a high-volume bridge. Serial independence of the collected peak strains and of the counting process, as well as the asymptotic behavior of the extreme peak-strain values, are investigated. A set of in-service load and resistance factor rating (ISLRFR) equations optimized for a suite of bridges is developed. Results from the proposed methodology are compared with ratings derived from more traditional methods.     

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.     

Evaluation of Viscous Dampers for Stay-Cable Vibration Mitigation

Many cable-stayed bridges around the world have displayed excessive and unanticipated vibrations of the main stays, often associated with the simultaneous occurrence of wind and rain, and mitigation of these vibrations has become a significant concern in cable-stayed bridge design and retrofit. Much of the previous research on this problem has been conducted using wind tunnels, and there have been relatively few opportunities to measure the vibrations at full-scale. This paper presents results from long-term field measurements of cable vibrations on a cable-stayed bridge in the United States. Characteristics of different types of measured vibrations are summarized, and the effectiveness of passive linear dampers in vibration suppression is evaluated by comparing response statistics from two stays before and after installation of dampers and by investigating in detail the damper performance in a few selected records corresponding to different types of excitation. The dampers are observed to be quite effective, but a fundamental limitation of mode-dependence in linear damper performance is emphasized, and some potential advantages offered by a nonlinear damper are discussed.     

In-Situ Evaluation of Two Concrete Slab Systems. I: Load Determination and Loading Procedure

The primary objective of in-situ load testing is to assess the safety and serviceability of an existing structural system with respect to a particular load effect. At this time, the most appropriate loading level and procedure, as well as the associated evaluation criteria are being reconsidered in light of technological advances in construction methods, analytical tools, and monitoring instrumentation. The in-situ load test method for reinforced concrete systems described in the ACI Building Code Requirements for Structural Concrete, namely the 24–h load test method and its evaluation criteria, has been in use for several decades, but may no longer serve the needs of contemporary construction and engineering practices. As a result, other load test methodologies and associated evaluation criteria are under development. This paper and a companion paper describe the rationale and application of an alternative approach to the determination of load level, loading procedure, instrumentation requirements, evaluation criteria and outcomes for two field projects. The first case study is relative to a posttensioned concrete slab where many areas were characterized by tendon and reinforcement misplacement, resulting in inadequate flexural strength and inadequate shear/flexure transfer at column/slab intersections. The second case study is the structural evaluation of a typical floor bay of a two-way reinforced concrete slab system, presenting distributed cracking at the positive and negative moment regions. Finite-element-method models were created for both structures to aid the load test design. The numerical models validated the field observations.     

In-Service Diagnostics of a Highway Bridge from a Progressive Damage Case Study

Development of diagnostic and prognostic routines for application to in-service measurements from highway bridges necessitates analysis of experimental measurements from in-service highway bridges under natural or prescribed induced damage. This is generally limited to the unique opportunity of investigating end-of-service life bridges prior to reconstruction and consequently only a limited library of such case studies exist. This paper documents a field test of an end-of-service bridge span with prescribed progressive damage to a bearing as well as several diaphragm connections. Thirty dual-axis accelerometers were distributed across the bridge span with data acquisition and transmission facilitated by a real-time lossless wireless sensor network. A highway department service truck applied traffic excitation to the structure through routine passes on a consistent lane of traffic. Output-only system identification was applied to the baseline time history response to develop a state-space model of the bridge dynamics used for forward prediction in the form of a Kalman filter. Simple statistical evaluation of the prediction error in the model demonstrates the variance can be used to localize and generally quantify the degree of damage in the structure. The case study additionally illustrates the potential importance of monitoring lateral acceleration along the girders to permit identification of damage to elements, such as the diaphragms, that contributing primarily to the lateral and torsional response of primary structural members.     

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.