Stability of Slender Webs of Prestressed Concrete Box-Girder Bridges

Long-span, prestressed concrete, box-girder bridges are haunched and have a span-to-depth ratio of 15 to 20 at the piers. This leads to slender webs, particularly for bridges built with high performance concrete. For girders with sloped webs and constant bottom slab width, the web plate is normally warped, which leads to web curvature in the direction of the principal compressive stresses. It is first shown that buckling is not critical as long as the web is uncracked. But, if the webs have shear cracks, the slenderness ratio of the diagonal compression struts can be very high so that the moments and stability of the curved struts need to be studied. It is shown that the tensile forces in the stirrups—determined according to the truss analogy—will counteract the lateral deformations of the slender compression struts. The procedure, which was developed for the design of the Confederation Bridge in Eastern Canada, will be illustrated by applying it to the slender webs of that bridge.     

Literature Review in Analysis of Box-Girder Bridges

The curvilinear nature of box girder bridges along with their complex deformation patterns and stress fields have led designers to adopt approximate and conservative methods for their analyses and design. Recent literature on straight and curved box girder bridges has dealt with analytical formulations to better understand the behavior of these complex structural systems. Few authors have undertaken experimental studies to investigate the accuracy of existing methods. This paper presents highlights of references pertaining to straight and curved box girder bridges in the form of single-cell, multiple-spine, and multicell cross sections. The literature survey presented herein deals with: (1) elastic analysis, and (2) experimental studies on the elastic response of box girder bridges.     

Overlay for Concrete Segmental Box-Girder Bridges

Concrete overlay cracking and delamination were noticed on a concrete segmental box-girder bridge. Analytical investigation and field and laboratory examinations were conducted to identify the major factors causing the defects. The time-dependent stress distribution and its change in the overlay and along the interface between the overlay and the bridge deck were modeled through the finite-element method with the consideration of concrete age, shrinkage, and critical temperature gradients. Appropriate interpretation of the modeling results were verified through field and laboratory examinations. The primary factors causing the defects were identified and discussed. It was concluded that conventional concrete is applicable for a thin bonded overlay construction on concrete segmental box-girder bridges. Removal and replacement were recommended to repair the delaminations through a field test program. Low shrink conventional concrete with a maximum aggregate size of 25.4 mm (1.0 in.) was used without the application of bonding grout. The base deck surface was roughened (by hydroblasting) to a macrotexture of 2.0–2.8 mm (0.08–0.11 in.) on average. The substrata was not presoaked and was surface dry before placing of plastic concrete. Curing consisted of moist curing for 7 days, followed by chemical (curing compound) curing for 21 days. The successful experience gained can be applied to other similar projects.     

Live-Load Distribution Factors for Concrete Box-Girder Bridges

The current American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) Specifications impose fairly strict limits on the use of its live-load distribution factor for design of highway bridges. These limits include requirements for a prismatic cross section, a large span-length-to-width ratio, and a small plan curvature. Refined analyses using 3D models are required for bridges outside of these limits. These limits place severe restrictions on the routine design of bridges in California, as box-girder bridges outside of these limits are frequently constructed. This paper presents the results of a study investigating the live-load distribution characteristics of box-girder bridges and the limits imposed by the LRFD specifications. Distribution factors determined from a set of bridges with parameters outside of the LRFD limits are compared with the distribution factors suggested by the LRFD specifications. For the range of parameters investigated, results indicated that the current LRFD distribution factor formulas generally provide a conservative estimate of the design bending moment and shear force.     

State-of-the-Art in Design of Curved Box-Girder Bridges

The objective of this paper is to provide highlights of the most important references related to the development of current guide specifications for the design of straight and curved box-girder bridges. Subjects discussed in this review include (1) different box-girder bridge configurations; (2) construction issues; (3) deck design; (4) load distribution; (5) deflection and camber; (6) cross-bracing requirements; (7) end diaphragms; (8) thermal effects; (9) vibration characteristics; (10) impact factors; (11) seismic response; (12) ultimate load-carrying capacity; (13) buckling of individual components forming the box cross section; (14) fatigue; and (15) curvature limitations provided by the codes for treating a curved bridge as a straight one. The literature survey presented herein encompasses (1) the construction phase; (2) load distribution; (3) dynamic response; and (4) ultimate load response of box-girder bridges.     

Correction of Errors in Simplified Transverse Bending Analysis of Concrete Box-Girder Bridges

In design practice, the transverse bending analysis of box-girder bridges is commonly done by modeling the cross section as a frame of unit width with imaginary supports at the web locations. The transverse bending moments obtained from simple frame analysis (SFA) is sometimes increased by a small percentage to accommodate the errors in modeling. In this paper, a large number of simply supported box-girder bridges have been analyzed by both SFA and three-dimensional finite element analysis for different load conditions and wheel contact areas, and the errors in SFA have been studied and quantified. The error is found to vary widely at the web-top flange junction as well as under the load (maximum sagging moment), depending on the eccentricity of loading, the wheel contact dimensions and the web-flange thickness ratio. Accordingly, a set of correction factors to the results of SFA have been proposed, which is expected to be of significant use in design practice. The use of the correction factors is demonstrated by means of two illustrative examples. The scope of the study is limited to the simplest case of a single-cell concrete box-girder bridge (simply supported with end diaphragms) without overhanging flanges.     

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.     

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.     

Distribution Factors for Curved Continuous Composite Box-Girder Bridges

The use of horizontally curved composite box-girder bridges in modern highway systems has become increasingly popular for economic as well as for aesthetic considerations. Based on a recent literature review on the design of box-girder bridges, it was observed that a simple design method for curved bridges, based on load distribution factors for stresses and shears, is as yet unavailable. This paper presents the results of an extensive parametric study, using a finite element method, in which the structural responses of 240 two-equal-span continuous curved box-girder bridges of various geometries were investigated. The parameters considered in this study included span-to-radius of curvature ratio, span length, number of lanes, number of boxes, web slope, number of bracings, and truck loading type. Based on the data generated from this study, empirical formulas for load distribution factors for maximum longitudinal flexural stresses and maximum deflection due to dead load as well as AASHTO live loading were deduced. An illustrative design example is presented.     

Estimation of Collapse Load of Single-Cell Concrete Box-Girder Bridges

The simplified equations available at present to predict the collapse loads of single-cell concrete box-girder bridges with simply supported ends are based on either space truss analogy or collapse mechanisms. Experimental studies carried out by various researchers revealed that, of the two formulations available to predict the collapse load, the one based on collapse mechanisms is found to be more versatile and better suited to box sections. Under a pure bending collapse mechanism, the existing formulation is found to predict collapse load with high accuracy. However, in the presence of cross-sectional distortion, there are significant errors in the existing theoretical formulation. This paper attempts to resolve this problem, by proposing a modification to the existing theory, incorporating an empirical expression to assess the extent of corner plastic hinge formation, under distortion–bending collapse mechanism. The modified theoretical formulations are compared with the experimental results available in the literature. New sets of experiments are also conducted to validate the proposed modified theory to estimate the collapse load. In all cases, it is seen that the modified theory to predict the collapse load match very closely with the experimental results.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Preliminary Assessment and Rating of Stream Channel Stability near Bridges

The primary cause of bridge failure in the United States is scour and channel instability around the bridge foundations. The ability to assess channel stability in the vicinity of bridges is needed to alert engineers to possible unstable conditions at the bridge foundations, to design stable road crossings, and to mitigate against erosion at those structures. This information is valuable for stream stabilization projects as well, particularly for cases where the reach to be restored includes a bridge. However, a systematic methodology for rapidly assessing channel stability that is applicable at bridges located in the various regions of the country does not currently exist. In this study, an assessment method for the preliminary documentation and rating of channel stability near bridges was developed, based on prior stability assessment methods as well as observations at bridges in 13 physiographic regions of the continental United States. This method provides an assessment of channel stability conditions as they affect bridge foundations. It is intended for a quick assessment of conditions for the purpose of documenting conditions at bridges and for judging whether more extensive geomorphic studies or complete hydraulic and sediment transport analyses are needed to assess the potential for adverse conditions developing at a particular bridge in the future.     

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.