Effect of Vehicle Velocity on the Dynamic Amplification of a Vehicle Crossing a Simply Supported Bridge

Many writers, using both experimental tests and complex numerical models, have examined the effect of vehicle velocity on a highway bridge’s dynamic amplification. Although these tests and models give valuable quantitative information on dynamic amplification, they give little insight into how amplification is affected by individual vehicle/bridge parameters. This paper uses relatively simple numerical models to investigate the effect of vehicle velocity on a bridge’s dynamic amplification. A single vehicle crossing a simply supported bridge is modeled as a constant point force. A set of critical velocities are determined associated with peaks of dynamic amplification for all beams. The reasons for these large amplifications are discussed. A more complex finite element model, validated with field tests, is used to test the applicability of the conclusions obtained from the simple models to a realistic bridge/vehicle system.     

Overview of a Modal-Based Condition Assessment Procedure

Condition assessment is a term that is used to describe the process of characterizing the physical condition of constructed systems. This paper summarizes a condition assessment (CA) procedure based on a complete system of field-testing, finite element (FE) modeling, and load rating. Experimental techniques, including both modal testing and truckload testing, are used to collect measurements of the constructed systems. The basic mechanism and procedure of the FE modeling and calibration are presented. Different physical parameters of FE models are adjusted during the calibration process using both static and dynamic responses as criteria to achieve convergence between experimental measurements and analytical results using carefully developed objective functions. Finally, a bridge load rating is completed on the basis of the calibrated model. These developments are described and illustrated using a representative bridge as an example.     

Shear Live-Load Distribution Factors for I-Girder Bridges

A full scale, single lane test bridge was used to evaluate a typical slab-on-girder bridge’s response to shear. The results of the shear load test provided the means to evaluate the level of detail for a finite element model that is required to accurately replicate the behavior of bridges subject to shear loads. This finite element modeling scheme was then used to evaluate more than 200 finite element bridge models. The bridge models investigated the effects of girder spacing, span length, overhang distance and skew angle on the shear live-load distribution factor. The finite element shear distribution factors were compared with those calculated according to the American Association of State Highway and Transportation Officials load and resistance factor design (AASHTO LRFD) specifications. It was found that the AASHTO LRFD procedure accurately predicted the shear distribution factor for changes in girder spacing and span length. However, the LRFD shear distribution factor for the exterior girder was found to be unconservative for certain overhang distances and overly conservative for the interior girder for higher skew angles. Alternative equations are provided for the single and multilane exterior girder correction factor.     

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.     

Dynamic Response of a Highway Bridge Subjected to Moving Vehicles

Several full-scale load tests were performed on a selected Florida highway bridge. The bridge was dynamically excited by two fully loaded trucks, and the strain, acceleration, and displacement at selected points were recorded for the investigation of the bridge’s dynamic response. Experimental data were compared with simplified vehicle and bridge finite-element models. The vehicle was represented as a three-dimensional mass–spring–damper system with 11?degrees of freedom, and the bridge was modeled as a combination of plate and beam elements that characterize the slab and girders, respectively. The equations of motion were formulated with physical components for the vehicle and modal components for the bridge. The coupled equations were solved using a central difference method. It was found that the numerical analysis matched well with the experimental data and was used to successfully explain critical dynamic phenomena observed during the testing. Impact factors for this tested bridge were thoroughly investigated by using these models.     

Finite‐Element Calculations on Alliant FX/80

The finite‐element method has proven to be an invaluable tool for analysis and design of complex, high‐performance systems, such as those typically encountered in the aerospace or automotive industries. However, as the size of the finite‐element models of such systems increases, analysis computation time using conventional computers can become prohibitively high. Parallel processing computers provide the means to overcome these computation‐time limits, provided the algorithms used in the analysis can take advantage of multiple processors. The writers have examined several algorithms for linear and nonlinear static analysis, as well as dynamic finite‐element analysis. The performance of these algorithms on an Alliant FX/80 parallel supercomputer has been investigated. For single load‐case linear static analysis, the optimal solution algorithm is strongly problem dependent. For multiple load cases or nonlinear static analysis through a modified Newton‐Raphson method, decomposition algorithms are shown to have a decided advantage over element‐by‐element preconditioned conjugate gradient algorithms. For eigenvalue/eigenvector analysis, the subspace iteration algorithm with a parallel decomposition is shown to achieve a relatively high parallel efficiency.     

Experimental Evaluation of Dynamic Effects for a Selected Highway Bridge

The paper presents an experimental study of the actual dynamic effects for a preselected typical highway bridge. Knowledge of the dynamic impact factors is important for accurate determination of the ultimate load capacity and performance assessment of constructed bridges. Static and dynamic field tests were performed on a two-lane concrete highway bridge built in 1999 on U.S. 90 in northwest Florida. During the tests, one or two fully loaded trucks crossed over the bridge, which was instrumented with strain gauges, accelerometers, and displacement transducers. A wooden plank was placed across the lanes for some runs to trigger extensive dynamic vibration and to simulate poor road surface conditions. Data collected from the tests were used for comprehensive assessment of the bridge under dynamic loading. Impact factors obtained from the tests with higher speeds were found larger than corresponding values recommended by bridge codes. Analysis revealed that stiff vehicle suspension, road surface imperfection, and “bouncing” of the truck loading contributed to the high impact factors. Experimental data were also used for validation of the finite-element models developed for the vehicle–bridge system.     

Vehicle Collision with Bridge Piers

Inelastic transient finite element simulations are used to investigate the demands generated during collisions between vehicles and bridge piers. Such collisions have occurred in the past, sometimes with catastrophic consequences. Two different types of trucks and two different bridge/pier systems are used in the simulations. The approach speeds for the trucks range from 55 to 135 kph. Various quantities of interest are extracted from the finite element results and used to develop a better understanding of the vehicle/pier crash process and to critique current specifications addressing such events. Although physical vehicle–pier impact tests were not carried out as part of this research, a variety of exercises are conducted to provide confidence in the analysis results. The simulations show that current collision design provisions could be unconservative and that there may be a population of bridge piers that are vulnerable to accidental or malicious impact by heavy trucks.     

Response of Timber Bridge to Traffic Loading

This paper summarizes results from an analytical and experimental study of the response to traffic loading of a glued-laminated timber bridge. A numerical model to simulate the passage of a vehicle over a bridge was developed. Calculated modal characteristics of an existing bridge were compared with results of ambient vibration and hammer impact testing. The analysis was used to simulate passages over the bridge of a three-axle vehicle, an empty logging truck, and results were compared with experimental data for such loading. The numerical model was then used to simulate the bridge response to a fully loaded logging truck. Results of these simulations were used to study dynamic amplification factors and to assess dynamic provisions of the new Canadian Highway Bridge Design Code.     

Innovative Bridge Condition Assessment from Dynamic Response of a Passing Vehicle

An innovative approach for damage assessment of a bridge deck is proposed with the measured dynamic response of a vehicle moving on top of a structure. The simply supported bridge deck is modeled as a Euler–Bernoulli beam. The moving vehicle serves as a smart sensor and force transducer in the structural system. The damage is defined as the flexural stiffness reduction in the beam finite element. The identification algorithm is based on dynamic response sensitivity analysis, and it is realized with a regularization technique from the measured vehicle acceleration measurement. Measurement noise, road surface roughness, and model errors are included in the simulations, and the results indicate that the proposed algorithm is computationally stable and efficient, and the identified results are acceptable and not sensitive to the different parameters studied.     

Slip between Glue-Laminated Beams in Stress-Laminated Timber Bridges: Finite-Element Model and Full-Scale Destructive Test

Stress-laminated timber bridge decks consist of several sawn timber beams or glue-laminated (glulam) beams held together with prestressed steel bars. Frictional shear stresses between the beams transfer loads between individual beams. Because the vertical (transverse) shear stress component has been extensively discussed, this paper considers the horizontal shear stress. A full-scale test and corresponding finite element simulations for a specific load case confirmed that horizontal slip occurred between beams. Using an elastic-plastic material model, the finite element model handled both vertical and horizontal frictional slip. The results showed that the finite element model gives reliable results and that slip in general leads to permanent deformations, which may increase with load cycling. Horizontal slip between beams over a large area of the bridge deck begins at a low load, resulting in a redistribution of load between beams, but does not lead to immediate failure. Vertical slip between beams starts at a high load close to the load application point and leads to failure.     

Long-Term Structural Health Monitoring of the San Ysidro Bridge

As part of the Lifecycle Innovative Financing Evaluation initiative, the San Ysidro Bridge along U.S. Route 550 will be monitored throughout a 10?year warranty period to determine changes in deflection, stiffness, and load-carrying capacity. This paper discusses an initial live-load test on the San Ysidro Bridge as well as a subsequent load test on a full-scale single lane test bridge. The two load tests in conjunction with finite element modeling were used to determine the load rating for both shear and moment of the San Ysidro Bridge. This load rating was then compared with the load rating using the distribution factors from the American Association of State Highway and Transportation Officials (AASHTO) Standard and Load and Resistance Factor Design Specifications. According to both AASHTO specifications, the interior girder shear controlled the load rating of the San Ysidro Bridge. Using the finite element modeling scheme of frame and shell elements the interior girder moment was found to control the design. This load rating will be used as a baseline for comparison with future load ratings throughout the warranty period.     

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.     

Analysis of Traffic-Induced Vibrations in a Cable-Stayed Bridge. Part II: Numerical Modeling and Stochastic Simulation

This paper describes the development of a numerical model to simulate the dynamic response of the bridge–vehicle system of Salgueiro Maia cable-stayed bridge, using the results from an extensive experimental investigation to calibrate this model. Further, a set of stochastic Monte Carlo simulations of the bridge–vehicle dynamic response is also presented, with the purpose of evaluating dynamic amplification factors, taking into account the randomness of different factors associated to characteristics of the pavement, of the vehicles and of the traffic flow.     

Response of Prestressed Concrete I-Girder Bridges to Live Load

Design and evaluation of prestressed concrete I-girder bridges is in large part dependent on the transverse load distribution characteristics and the dynamic load amplification, as well as service level, live load, and tensile stresses induced in the girders. This study presents the results of field tests conducted on three prestressed concrete I-girder bridges to obtain dynamic load allowance statistics, girder distribution factors (GDF), and service level stress statistics. The field-based data are also compared to approximate and numerical model results. Bridge response was measured at each girder for the passage of test trucks and normal truck traffic. The dynamic amplification is observed to be a strong function of peak static stress and a weak function of vehicle speed and is independent of span length, number of axles, and configuration. GDFs for one- and two-lanes are less than code specified GDFs. Results from the numerical grillage models agree closely with experimentally derived results for transverse distribution.     

Development of an Efficient Connector System for Fiber Reinforced Polymer Bridge Decks to Steel Girders

This paper discusses the development of an innovative and efficient connector to be used with fiber reinforced polymer (FRP) decks supported by steel girders. A summary is provided detailing various proprietary connectors currently employed by FRP deck manufacturers. The paper then describes the development and experimental testing of a clamped shear stud-type connector. Experimental testing was conducted in two phases. The first phase consisted of individual connector testing. In this phase, several variations of the connector are tested and evaluated for strength, damage development, and overall performance. Results of this phase of testing are used to select a final connection design to be used in the second phase of testing, which consisted of testing a scale model bridge that incorporates several of the proposed connectors. The bridge is subjected to static load tests and the resulting reactions and deflections from these tests are compared with comprehensive finite element models of the system.     

Nonlinear Finite Element Analysis of a FRP-Strengthened Reinforced Concrete Bridge

Three-dimensional nonlinear finite element (FE) models are developed to examine the structural behavior of the Horsetail Creek Bridge strengthened by fiber-reinforced polymers (FRPs). A sensitivity study is performed varying bridge geometry, precracking load, strength of concrete, and stiffness of the soil foundation to establish a FE model that best represents the actual bridge. Truck loadings are applied to the FE bridge model at different locations, as in an actual bridge test. Comparisons between FE model predictions and field data are made in terms of strains in the beams for various truck load locations. It is found that all the parameters examined can potentially influence the bridge response and are needed for selection of the optimal model which predicts the magnitudes and trends in the strains accurately. Then, using the optimal model, performance evaluation of the bridge based on scaled truck and mass-proportional loadings is conducted. Each loading type is gradually increased until failure occurs. Structural responses are compared for strengthened and unstrengthened bridge models to evaluate the FRP retrofit. The models predict a significant improvement in structural performance due to the FRP retrofit.     

Fatigue Damage of Steel Bridges Due to Dynamic Vehicle Loads

This paper focuses on the fatigue damage caused in steel bridge girders by the dynamic tire forces that occur during the crossing of heavy transport vehicles. This work quantifies the difference in fatigue life of a short-span and a medium-span bridge due to successive passages of either a steel-sprung or an air-sprung vehicle. The bridges are modeled as beams to obtain their modal properties, and air-sprung and nonlinear steel-sprung vehicle models are used. Bridge responses are predicted using a convolution method by combining bridge modal properties with vehicle wheel forces. A linear elastic fracture mechanics model is employed to predict crack growth. For the short-span bridge, the steel-sprung vehicle caused fatigue failure up to 6.5 times faster than the air-sprung vehicle. For the medium-span bridge, the steel-sprung vehicle caused fatigue failure up to 277 times faster than the air-sprung vehicle.     

Sensitivity of Live Load Distribution Factors to Vehicle Spacing

Two slab-on-girder bridge superstructures are analyzed using grillage models. Different live load placement configurations are investigated to determine the sensitivity of live load shear and moment to vehicle spacing. Results from both bridges show that the distribution factors are relatively insensitive to vehicle spacing. Therefore significant computational speedups are available when applying vehicle loads on an influence surface with a fixed spacing.     

Vibration Studies of Tsing Ma Suspension Bridge

A three-dimensional dynamic finite element model is established for the Tsing Ma long suspension Bridge in Hong Kong. The two bridge towers made up of reinforced concrete are modeled by three-dimensional Timoshenko beam elements with rigid arms at the connections between columns and beams. The cables and suspenders are modeled by cable elements accounting for geometric nonlinearity due to cable tension. The hybrid steel deck is represented by a single beam with equivalent cross-sectional properties determined by detailed finite element analyses of sectional models. The modal analysis is then performed to determine natural frequencies and mode shapes of lateral, vertical, torsional, longitudinal, and coupled vibrations of the bridge. The results show that the natural frequencies of the bridge are very closely spaced; the first 40 natural frequencies range from 0.068 to 0.616 Hz only. The computed normal modes indicate interactions between the main span and side span, and between the deck, cables, and towers. Significant coupling between torsional and lateral modes is also observed. The numerical results are in excellent agreement with the measured first 18 natural frequencies and mode shapes. The established dynamic model and computed dynamic characteristics can serve further studies on a long-term monitoring system and aerodynamic analysis of the bridge.