Dynamic Stress Analysis of Long Suspension Bridges under Wind, Railway, and Highway Loadings

Computation of the dynamic stress of long suspension bridges under multiloadings is essential for either the strength or fatigue assessment of the bridge. This paper presents a framework for dynamic stress analysis of long suspension bridges under wind, railway, and highway loadings. The bridge, trains, and road vehicles are respectively modeled using the finite-element method (FEM). The connections between the bridge and trains and between the bridge and road vehicles are respectively considered in terms of wheel-rail and tire-road surface contact conditions. The spatial distributions of both buffeting forces and self-excited forces over the bridge deck surface are considered. The Tsing Ma suspension bridge and the field measurement data recorded by a wind and structural health monitoring system (WASHMS) installed in the bridge are utilized as a case study to examine the proposed framework. The information on the concerned loadings measured by the WASHMS is taken as inputs for the computation simulation, and the computed stress responses are compared with the measured ones. The results show that running trains play a predominant role in bridge stress responses compared with running road vehicles and fluctuating wind loading.     

Improved Seismic Response of Multisimple-Span Skewed Bridges Retrofitted with Link Slabs

Results of a recent bridge inventory evaluation indicated that about 50% of Turkish highway bridges have more than 30° of skew angle and can be classified as irregular bridges. During the recent major earthquake in Turkey, multisimple-span bridges with continuous decks and link slabs performed well even though these bridges were in the vicinity of the fault line. This study aims to evaluate the improvements in seismic response of skew bridges in terms of forces and displacements when link slabs are added as a retrofit tool. A series of elastic dynamic analyses and nonlinear time history analyses were conducted to investigate the seismic response of various standard highway bridges with different span lengths and skew angles. A new reinforcement design for edge zones of link slabs is proposed for bridges located in high seismic zones. In practice, link slabs can be implemented easily during a regular redecking of a bridge.     

Bridge Structural Condition Assessment Based on Vibration and Traffic Monitoring

A stochastic model of traffic excitation on bridges is developed assuming that the arrival of vehicles traversing a bridge (modeled as an elastic beam) follows a Poisson process, and that the contact force of a vehicle on the bridge deck can be converted to equivalent dynamic loads at the nodes of the beam elements. The parameters in this model, such as the Poisson arrival rate and the stochastic distribution of vehicle speeds, are obtained by image processing of traffic video data. The model reveals that traffic excitations on bridges are spatially correlated. This important characteristic is usually incorrectly ignored in most output-only methods for the identification of bridge structural properties using traffic-induced vibration measurement data. In this study, the stochastic traffic excitation model with partial traffic information is incorporated in a Bayesian framework, to evaluate the structural properties and update their uncertainty for condition assessment of the bridge superstructure. The vehicle weights are also estimated simultaneously in this procedure. The proposed structural assessment methodology is validated on an instrumented highway bridge.     

Design for Shear in Curved Composite Multiple Steel Box Girder Bridges

Modern highway bridges are often subject to tight geometric restrictions and, in many cases, must be built in curved alignment. These bridges may have a cross section in the form of a multiple steel box girder composite with a concrete deck slab. This type of cross section is one of the most suitable for resisting the torsional, distortional, and warping effects induced by the bridge’s curvature. Current design practice in North America does not specifically deal with shear distribution in horizontally curved composite multiple steel box girder bridges. In this paper an extensive parametric study, using an experimentally calibrated finite-element model, is presented, in which simply supported straight and curved prototype bridges are analyzed to determine their shear distribution characteristics under dead load and under AASHTO live loadings. The parameters considered in this study are span length, number of steel boxes, number of traffic lanes, bridge aspect ratio, degree of curvature, and number and stiffness of cross bracings and of top-chord systems. Results from tests on five box girder bridge models verify the finite-element model. Based on the results from the parametric study simple empirical formulas for maximum shears (reactions) are developed that are suitable for the design office. A comparison is made with AASHTO and CHBDC formulas for straight bridges. An illustrative example of the design is presented.     

Extreme Thermal Loading on Steel Bridges in Tropical Region

In the design of highway bridges, it is important to consider the thermal stresses induced by the nonlinear temperature distribution in the bridge deck irrespective of their spans. To cope with this, design temperature profiles are provided by many bridge design codes, which are normally based on extensive research on the thermal behavior of bridges. This paper presents the results of a comprehensive investigation on the thermal behavior of steel bridges carried out in Hong Kong. A method for predicting bridge temperatures from given meteorological conditions is briefly discussed. The theoretical results have been validated by temperature measurements on experimental models mounted on the roof of a building as well as on an existing steel bridge. Both the theoretical and field results confirm the validity of the one-dimensional heat transfer model on which most design codes are based. Values of design thermal loading for a 50-year return period are determined from the statistics of extremes over 40 years of meteorological information in Hong Kong. The design temperature profiles for various types of steel bridge deck with different thickness of bituminous surfacing are developed.     

Dynamic Analysis of Curved Continuous Multiple-Box Girder Bridges

The use of horizontally curved composite multiple-box girder bridges in modern highway systems is quite suitable in resisting torsional and warping effects induced by highway curvatures. Bridge users react adversely to vibrations of a bridge and especially where torsional modes dominate. In this paper, continuous curved composite multiple-box girder bridges are analyzed, using the finite-element method, to evaluate their natural frequencies and mode shapes. Experimental tests are conducted on two continuous twin-box girder bridge models of different curvatures to verify and substantiate the finite-element model. Empirical expressions are deduced from these results to evaluate the fundamental frequency for such bridges. The parameters considered herein are the span length, number of lanes, number of boxes, span-to-radius of curvature ratio, span-to-depth ratio, end-diaphragm thickness, number of cross bracings, and number of spans.     

Load Distribution for a Highly Skewed Bridge: Testing and Analysis

The American Association of State Highway and Transportation Officials (AASHTO) specifications provide formulas for determining live load distribution factors for bridges. For load distribution factors to be accurate, the behavior of the bridge must be understood. While the behavior of right-angle bridges and bridges with limited skews is relatively well understood, that of highly skewed bridges is not. This paper presents a study aimed at developing a better understanding of the transverse load distribution for highly skewed slab-on-steel girder bridges. The study involved both a diagnostic field test of a recently constructed bridge and an extensive numerical analysis. The bridge tested and analyzed is a two-span, continuous, slab-on-steel composite highway bridge with a skew angle of 60°. The bridge behavior is defined based on the field test data. Finite-element analyses of the bridge were conducted to investigate the influence of model mesh, transverse stiffness, diaphragms, and modeling of the supports. The resulting test and analytical results are compared with AASHTO’s Load and Resistance Factor Design formulas for live load distribution to assess the accuracy of the current empirical formulas.     

Dynamic Behavior of Steel Deck Tension-Tied Arch Bridges to Seismic Excitation

The dynamic responses of steel deck, tension-tied, arch bridges subjected to earthquake excitations were investigated. The 620 ft (189 m) Birmingham Bridge, located in Pittsburgh, was selected as an analytical model for the study. The bridge has a single deck tension-tied arch span and is supported by two bridge piers, which in turn are supported by the pile foundations. Due to the complex configuration of the deck system, two analytical models were considered to represent the bridge deck system. Using the normal mode method, seismic responses were calculated for two bridge models and the results were compared with each other. Three orthogonal records of the El Centro 1940 earthquake were used as input for the seismic response analysis. The modal contributions were also checked in order to obtain a reasonable representation of the response and to minimize computational cost. Displacements and stresses at the panel points of the bridge are calculated and presented in graphical form.     

Impact Factors for Curved Continuous Composite Multiple-Box Girder Bridges

The results from a parametric study on the impact factors for 180 curved continuous composite multiple-box girder bridges are presented. Expressions for the impact factors for tangential flexural stresses, deflection, shear forces and reactions are deduced for AASHTO truck loading. The finite-element method was utilized to model the bridges as three-dimensional structures. The vehicle axle used in the analysis was simulated as a pair of concentrated forces moving along the concrete deck in a circumferential path with a constant speed. The effects of bridge configurations, loading positions, and vehicle speed on the impact factors were examined. Bridge configurations included span length, span-to-radius of curvature ratio, number of lanes, and number of boxes. The effect of the mass of the vehicle on the dynamic response of the bridges is also investigated. The data generated from the parametric study and the deduced expressions for the impact factors would enable bridge engineers to design curved continuous composite multiple-box girder bridges more reliably and economically.     

Flutter of an Arch Bridge via a Fully Nonlinear Continuum Formulation

A fully nonlinear parametric model for wind-excited arch bridges is proposed to carry out the flutter analysis of Ponte della Musica under construction in Rome. Within the context of an exact kinematic formulation, all of the deformation modes are considered (extensional, shear, torsional, in-plane, and out-of-plane bending modes) both in the deck and supporting arches. The nonlinear equations of motion are obtained via a total Lagrangian formulation while linearly elastic constitutive equations are adopted for all structural members. The parametric nonlinear model is employed to investigate the bridge limit states appearing either as a divergence bifurcation (limit point obtained by path following the response under an increasing multiplier of the vertical accidental loads) or as a Hopf bifurcation of a suitable eigenvalue problem (where the bifurcation parameter is the wind speed). The eigenvalue problem ensues from the governing equations of motion linearized about the in-service prestressed bridge configuration under the dead loads and wind-induced forces. The latter are expressed in terms of the aeroelastic derivatives evaluated through wind-tunnel tests conducted on a sectional model of the bridge. The results of the aeroelastic analysis—flutter speed and critical flutter mode shape—show a high sensitivity of the flutter condition with respect to the level of prestress and the bridge structural damping.     

Dynamic Response of Three Fiber Reinforced Polymer Composite Bridges

Fiber reinforced polymer (FRP) composite bridge decks are gaining the attention of bridge owners because of their light self-weight, corrosion resistance, and ease of installation. Constructed Facilities Center at West Virginia University working with the Federal Highway Administration and West Virginia Department of Transportation has developed three different FRP decking systems and installed several FRP deck bridges in West Virginia. These FRP bridge decks are lighter in weight than comparable concrete systems and therefore their dynamic performance is equally as important as their static performance. In the current study dynamic tests were performed on three FRP deck bridges, namely, Katy Truss Bridge, Market Street Bridge, and Laurel Lick Bridge, in the state of West Virginia. The dynamic response parameters evaluated for the three bridges include dynamic load allowance (DLA) factors, natural frequencies, damping ratios, and deck accelerations caused by moving test trucks. It was found that the DLA factors for Katy Truss and Market Street bridges are within the AASHTO 1998 LRFD specifications, but the deck accelerations were found to be high for both these bridges. DLA factors for Laurel Lick bridge were found to be as high as 93% against the typical design value of 33%; however absolute deck stress induced by vehicle loads is less than 10% of the deck ultimate stress.     

Life-Cycle Cost of All-Composite Suspension Bridge

This paper reports on the design of two highway suspension bridges made of conventional steel and advanced all-composite carbon fiber reinforced polymer (CFRP), and analyzed their life-cycle costs. The writers assumed that the pultrusion molding method would mainly be used for all composite highway bridges, because of its relatively high quality control performance and mass-production capability. First, the writers obtained the steel and composite highway bridge design in the same dimensional specification. Second, they acquired the future cost of the CFRP pultrusion product through hearing research from a fiber reinforced polymer manufacturer. Third, they calculated the initial costs of the steel bridge and CFRP bridge based on the design specification and the future cost of CFRP. Fourth, they compared the life-cycle cost of the steel and CFRP bridges under several conditions of discount rate, repair cost, and cycle. Finally, they found the critical condition where the CFRP bridge becomes more life-cycle cost-effective than the conventional steel bridge, if they could have expected the drastic cost reduction of the CFRP product.     

Ultimate Capacity Destructive Testing and Finite-Element Analysis of Steel I-Girder Bridges

Current bridge design and rating techniques are based at the component level and thus cannot predict the ultimate capacity of bridges, which is a function of system-level interactions. While advances in computer technology have made it possible to conduct accurate system-level analyses, which can be used to design more efficient bridges and produce more accurate ratings of existing structures, the knowledge base surrounding system-level bridge behavior is still too small for these methods to be widely considered reliable. Thus, to advance system-level design and rating, a 1/5-scale slab-on-steel girder bridge was tested to ultimate capacity and then analytically modeled. The test demonstrated the significant reserve capacity of the steel girders, and the response of the specimen was governed by the degradation of the reinforced-concrete deck. To accurately capture the response of the specimen in an analytical model, the degradation of the deck and other key features of the specimen were modeled by using a dynamic analysis algorithm in a commercially available finite-element analysis program ABAQUS.     

Assessment of Bridge Remaining Fatigue Life through Field Strain Measurement

With the aging of existing steel bridges and the accumulated stress cycles under traffic loads, assessment of remaining fatigue life for continuing service has become more important than ever, especially for decisions on structure replacement, deck replacement, or other major retrofits. Experience from engineering practice indicates that fatigue analysis based on specification loads and distribution factors usually underestimates the remaining fatigue life of existing bridges by overestimating the live load stress ranges. Fatigue evaluation based on field-measured stress range histograms under actual traffic load proves to be a more accurate and efficient method for existing bridges. This paper describes the application of such a method in assessing the remaining fatigue life of bridge structures. Current AASHTO specifications for fatigue evaluation of existing bridges are reviewed and compared. Case studies of three major highway bridges are discussed. Finally, a procedure is proposed for evaluating fatigue life of existing bridges through field strain measurement.     

Model Validation for Bridge-Road-Vehicle Dynamic Interaction System

The dynamic response of highway bridges subjected to moving truckloads has been observed to be dependent on (1) dynamic characteristics of the bridge; (2) truck configuration, speed, and lane position on the bridge; and (3) road surface roughness profile of the bridge and its approach. Historically, truckloads were measured to determine the load spectra for girder bridges. However, truckload measurements are either made for a short period of time [for example, weigh-in-motion (WIM) data] or are statistically biased (for example, weigh stations) and cost prohibitive. The objective of this paper is to present results of a 3D computer-based model for the simulation of multiple trucks on girder bridges. The model is based on the grillage approach and is applied to four steel girder bridges tested under normal truck traffic. Actual truckload data collected using a discrete bridge WIM system are used in the model. The data include axle loads, truck gross weight, axle configuration, and statistical data on multiple presence (side by side or following). The results are presented as a function of the static and dynamic stresses in each girder and compared with code provisions for dynamic load factor. The study provides an alternate method for the development of live-load models for bridge design and evaluation.     

Assessment of Highway Bridge Upgrading by Dynamic Testing and Finite-Element Model Updating

The Land Transport Authority of Singapore has a continuing program of highway bridge upgrading for refurbishing and strengthening bridges to allow for increasing vehicle traffic and increasing axle loads. One subject of this program has been a short-span bridge taking a busy main road across a coastal inlet near a major port facility. Experiment-based structural assessments of the bridge were conducted before and after upgrading works including strengthening. Each assessment exercise comprised three separate components: (1) a strain and acceleration monitoring exercise lasting approximately one month; (2) a full-scale dynamic test carried out in a single day without closing the bridge; and (3) a finite-element model updating exercise to identify structural parameters and mechanisms. This paper presents the dynamic testing and the modal analysis used to identify the vibration properties and the quantification of the effectiveness of the upgrading through the subsequent model updating. Before and after upgrade, similar sets of vibration modes were identified, resembling those of an orthotropic plate with relatively weak transverse bending stiffness. Conversion of bearings from nominal simple supports to nominal full fixity was shown via model updating to be the principal cause of natural frequency increases of up to 50%. The utility of the combined experimental and analytical process in direct identification of structural properties has been proven, and the procedure can be applied to other structures and their capacity assessments.     

Dynamic and Impact Behavior of Half-Through Arch Bridges

The objective of this paper is to present the results of an investigation of the dynamic and impact characteristics of half-through arch bridges with rough decks caused by vehicles moving across them. Seven arch bridges modeled as three-dimensional structures with overall span lengths ranging from 20?to?200?m (65.5?to?656.2?ft) are analyzed. The American Association of State Highway and Transportation Officials Specifications HS20-44 truck is the applied vehicle loading used in the analysis and is simulated as a three-dimensional, nonlinear vehicle model with 11 degrees of freedom. Truck components include the body, suspension, and tires. The bridge deck surface is assumed to have a “good” surface roughness and is simulated using a stochastic process (power spectral density function). The effect on impact factors of span length, rise-to-span ratio, and vehicle speed is discussed. The results of the analyses show that the impact factors of bending moment and axial force will not exceed 0.4 and 0.25, respectively. The proposed impact equations are simple and conservative and can be used in the design of half-through arch bridges.     

Dynamic Performance Simulation of Long-Span Bridge under Combined Loads of Stochastic Traffic and Wind

Slender long-span bridges exhibit unique features which are not present in short and medium-span bridges such as higher traffic volume, simultaneous presence of multiple vehicles, and sensitivity to wind load. For typical buffeting studies of long-span bridges under wind turbulence, no traffic load was typically considered simultaneously with wind. Recent bridge/vehicle/wind interaction studies highlighted the importance of predicting the bridge dynamic behavior by considering the bridge, the actual traffic load, and wind as a whole coupled system. Existent studies of bridge/vehicle/wind interaction analysis, however, considered only one or several vehicles distributed in an assumed (usually uniform) pattern on the bridge. For long-span bridges which have a high probability of the presence of multiple vehicles including several heavy trucks at a time, such an assumption differs significantly from reality. A new “semideterministic” bridge dynamic analytical model is proposed which considers dynamic interactions between the bridge, wind, and stochastic “real” traffic by integrating the equivalent dynamic wheel load (EDWL) approach and the cellular automaton (CA) traffic flow simulation. As a result of adopting the new analytical model, the long-span bridge dynamic behavior can be statistically predicted with a more realistic and adaptive consideration of combined loads of traffic and wind. A prototype slender cable-stayed bridge is numerically studied with the proposed model. In addition to slender long-span bridges which are sensitive to wind, the proposed model also offers a general approach for other conventional long-span bridges as well as roadway pavements to achieve a more realistic understanding of the structural performance under probabilistic traffic and dynamic interactions.