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.     

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.     

Stochastic Finite-Element Analysis for Elastic Buckling of Stiffened Panels

The variability of the random buckling loads of beams and plates with stochastically varying material and geometric properties is studied in this paper using the concept of the variability response function. The elastic modulus, moment of inertia, and thickness are assumed to be described by homogeneous stochastic fields. The variance of the buckling load is expressed as the integral of the auto- and cross-spectral density functions characterizing the stochastic fields multiplied by the deterministic variability response functions. Using this expression spectral-distribution-free upper bounds of the buckling load variability are established. Further, the buckling load variability for prescribed forms of the spectral density functions is calculated. Using a local average approach, the commercial finite-element package ABAQUS is incorporated into the analysis of these random buckling loads. The technique is applied to study variability of the critical buckling load of a stiffened steel plate used in experiments to model a barge deck.     

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

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

Control of Suspension Bridge Nonlinear Vibrations due to Moving Loads

The flexibility and low damping of the long-span suspended cables in the suspension bridges make them prone to vibrations due to wind and moving loads, which affect the dynamic response of the suspended cables and the bridge deck. This paper shows the design of two control schemes to control the nonlinear vibrations in the suspended cable and the bridge deck due to a vertical load moving on the bridge deck with a constant speed. The first control scheme is an optimal state feedback controller. The second control scheme is a robust state feedback controller, whose design is based on the design of optimal controllers. The proposed controllers, whose design is based on Lyapunov theory, guarantee the asymptotic stability of the system. A vertical cable between the bridge deck and the suspended cable is used to install a hydraulic actuator able to generate the active control force on the bridge deck. The MATLAB software is used to simulate the performance of the system with the designed controllers. The simulation results indicate that the proposed controllers are capable of significantly reducing the nonlinear oscillations of the system. In addition, the performance of the system with the proposed controllers is compared to the performance of the system controlled with a velocity feedback controller. It is found that the system with the proposed controllers can provide better performance than the system with the velocity feedback controller.     

The beta-adrenomimetic effect of human and animal blood serum

The conventional analysis and design of highway bridges ignore the contribution of sidewalks and∕or railings in a bridge deck when calculating the flexural strength of superstructures. The presence of sidewalks and railings or parapets acting integrally with the bridge deck have the effect of stiffening the outside girders and attracting more load while reducing the load effects in the interior girders. This paper presents the results of a parametric study showing the influence of typical sidewalks and railings on wheel load distribution as well as on the load-carrying capacity of highway bridges. A typical one-span, two-lane, simply supported, composite steel girder bridge was selected in order to investigate the influence of various parameters such as: span length, girder spacing, sidewalks, and railings. A total of 120 bridges were analyzed using three-dimensional finite-element analysis. American Association of State Highway and Transportation Officials (AASHTO) HS20 design trucks were positioned in both lanes to produce the maximum moments. The finite-element analysis results were also compared with AASHTO wheel load distribution factors. The AASHTO load and resistance factor design (LRFD) wheel load distribution formula correlated conservatively with the finite-element results and all were less than the typical empirical formula (S∕5.5). The presence of sidewalks and railings were shown to increase the load-carrying capacity by as much as 30% if they were included in the strength evaluation of highway bridges.     

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.     

Simply Supported Curved Cellular Bridges: Simplified Design Method

The use of curved composite bridges in interchanges of modern highway systems has become increasingly popular for economic and aesthetic considerations. Bridges with a concrete deck composite with a steel multicell section can adequately resist torsional and warping effects induced by high curvature. Although current design practices in North America recommend few analytical methods for the design of curved multicell box girder bridges, economical requirements in the design process point to a need for a simplified design method. This paper summarizes the results from an extensive parametric study, using the finite-element method, in which simply supported curved composite multicell bridge prototypes are analyzed to evaluate the moment and deflection distributions between girders, as well as the axial forces expected in the bracing system, due to truck loading as well as dead load. Results from tests on four, 1∕12 linear-scale, simply supported curved composite concrete deck-steel multicell bridge models are used to substantiate and verify the analytical modeling. The parameters considered in the study are cross-bracing system, aspect ratio, number of lanes, number of cells, and degree of curvature. Based on the data generated from the parametric study, expressions for moment and deflection distribution factors are deduced. Expressions for the maximum axial force in bracing members are also derived. An illustrative design example is presented.     

Lateral-Torsional Buckling of Stepped Beams with Continuous Bracing

Continuous span multibeam steel bridges are common along the state and interstate highways. The top flange of the beams is typically braced against lateral movement by the deck slab, and in many bridges the cross section is stepped at discrete points along the span. Design equations for lateral–torsional buckling (LTB) resistance in the American Association of State Highway and Transportation Officials “Load and resistance factor design bridge design specifications” are for prismatic beams and ignore the lateral restraint provided by the bridge deck. A new design equation is proposed that can be applied to I-shaped stepped beams with continuous top flange lateral bracing. By including the effects of the change in cross section size and the continuous top flange bracing, the calculated LTB resistance is significantly increased. Critical bending moment values from the proposed equation are compared to values from finite element method buckling analyses. The new equation is sufficiently accurate for use in design and in the evaluation of existing bridges.     

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.     

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.     

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.     

Design and Evaluation of Experimental Bridges in Tennessee

This paper describes the design and evaluates the adequacy of the moment connection of an experimental two-span highway bridge designed by the Tennessee Department of Transportation. The Massman Drive Bridge is an experimental design that unifies the construction economy of simple span bridges and the structural economy of continuous span bridges. The experimental connection, consisting of cover plates and kicker wedge plates, is used to connect the two adjoining girders over the center pier. As a result, the bridge is designed to function as a continuous bridge during the deck pour and behave compositely with the reinforced concrete deck under the live load. After completing a moment comparison analysis, it is concluded that the Massman Drive Bridge indeed acts as continuous over the pier as it was designed.     

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.     

Laboratory and Field Testing of Composite Bridge Superstructure

Bridge rehabilitation utilizing a hybrid fiber-reinforced polymeric composite has recently been completed in Blacksburg, Va. This project involved replacing the superstructure in the Tom's Creek Bridge, a rural short-span traffic bridge with a timber deck and corroded steel girders, with a glue-laminated timber deck on composite girders. To verify the bridge design and to address construction issues prior to the rehabilitation, a full-scale mock-up of the bridge was built and tested in the laboratory. This setup utilized the actual composite beams, glue-laminated timber deck panels, and the skewed geometry implemented in the rehabilitation. Following rehabilitation, the bridge was field tested under controlled conditions (vehicle load and position). Both tests examined service load deflections, girder strains, load distribution, degree of composite action, interpanel deck deflections, and impact factor. The field test results indicate a service load deflection of L∕400 under moving loads and a high factor of safety in the composite members against material failure. The data from the field test serve as a baseline reference for future field durability assessments as part of a long-term performance and durability study.     

Approximate Series Solution for Analysis of FRP Composite Highway Bridges

The design of a deck-and-stringer bridge system is usually reduced to the analysis of a T-beam section, loaded by concentrated loads corresponding to an equivalent fraction of the applied truck load. This equivalent load is defined by wheel load–distribution factors, which approximate the overall behavior of the bridge superstructure. In this paper, a one-term approximation of a macroflexibility series solution including deformations for fiber-reinforced polymer (FRP) deck-and-stringer orthotropic bridge systems, is used to develop explicit expressions for symmetric and asymmetric load distribution factors. It is significant that the equations presented herein include important parameters that represent, as accurately as possible, the response characteristics of the super structure, such as the geometry and material properties of the FRP deck and stringers, bridge aspect ratio, and number and spacing of stringers. As an illustration in actual design applications, the formulation presented in this paper is used to develop an analytical method for FRP deck-and-stringer bridge systems, and the method is verified by predicting the response of an all FRP model bridge in the lab and an FRP deck on steel stringers in the field. The results of the present formulation compare well with experimental lab and field results. The simplified analysis presented in this paper can be used with sufficient accuracy for the design of composite FRP deck on stringers 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.     

Locality of Truck Loads and Adequacy of Bridge Design Load

United States highway bridge design has advanced into the era of risk-based practice, milestoned by the American Association of State Highway and Transportation Officials Load and Resistance Factor Design Bridge Design Specifications. On the other hand, national and state design codes cannot specifically account for localized risk for each bridge site, which may have significantly different loading conditions from the national average. This issue is focused on here, as related to the adequacy of current bridge design loads for sites in the state of Michigan. The structural reliability indices are calculated for a randomly selected sample of new bridges from the Michigan inventory, including four major girder bridge types. Weigh-in-motion truck load data collected in Michigan are used to statistically characterize the truck load effect in the bridges’ primary members for moment and shear at critical cross sections. The reliability indices are found to vary significantly among the bridge sites and types investigated. Many of them indicate inadequate design load for the Detroit area.