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

The effect of multiple vehicles on a bridge’s dynamic amplification is a complex problem. Previously writers have examined multiple vehicle presence by constructing elaborate finite element models or undertaking field tests. Although both these methods give valuable information regarding the magnitude of dynamic amplification, the results tend to be site specific and give limited insight into how large amplifications occur. This paper examines the dynamic amplification factor of a simply supported bridge being crossed by two loads traveling in both the same and opposing directions. Simple numerical point load models are used to determine the critical load velocities and load positions that result in high amplifications. An experimentally validated finite element model is used to examine the applicability of the conclusions to real bridge/vehicle systems.     

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.     

Vehicle Induced Dynamic Behavior of Short-Span Slab Bridges Considering Effect of Approach Slab Condition

In this paper the vehicle induced dynamic bridge responses are calculated by modeling the bridge and vehicle as one coupled system. The dynamic behavior of short slab bridges with different span lengths induced by the AASHTO HS20 truck is investigated. A parametric study is conducted to analyze the effects of different truck speeds and different road surface conditions. Critical truck speeds that result in peaks of dynamic response are found to follow the rule that describes the resonant vibration of bridges due to train loading. The approach slab condition that consists of faulting at the ends and deformation along the span is considered in the analysis. Although the effect of the along-span deformation on the dynamic response of bridges is trivial, the faulting condition of the approach slab is found to cause significantly large dynamic responses in short-span slab bridges. Impact factors obtained from numerical analyses are compared with those values specified in the AASHTO codes.     

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.     

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.     

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.     

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.     

Dynamic Behavior of Deck Slabs of Concrete Road Bridges

This paper treats the dynamic effect of traffic actions on the deck slabs of concrete road bridges using the finite-element method. All the important parameters that influence bridge-vehicle interaction are studied with a systematic approach. An advanced numerical model is described and the results of a parametric study are presented. The results suggest that vehicle speed is less important than vehicle mass and that road roughness is the most important parameter affecting the dynamic behavior of deck slabs. The type of bridge cross section was not found to have a significant influence on deck slab behavior. The dynamic amplification factor varied between 1.0 and 1.55 for the bridges and vehicles studied. These results should be validated by further work.     

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.     

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.     

Evaluation of the Effectiveness of Strengthening Intervention by CFRP on MRWA Bridge No. 3014

Main Roads of Western Australia has a continuing program of bridge upgrading, to refurbish and strengthen bridges to allow for increasing vehicle traffic and increasing axle loads. A 40-year-old, four-span reinforced concrete slab bridge was retrofitted with application of CFRP laminate strips on the top of the deck over the piers, as well as on the deck soffit in the midspan regions, to reduce high moments in both hogging and sagging. The dynamic assessment of the bridge before and after strengthening works provided the opportunity to evaluate the effectiveness of the strengthening intervention through dynamic measurements. A performance evaluation of the repaired structure was carried out through traffic loading application on the updated numerical models of the bridge, before and after retrofit. As a main observation, the addition of CFRP laminate strips led to a significant increase of the structural capacity in flexure. The paper discusses the results obtained from the dynamic-based assessment in terms of effectiveness of the strengthening intervention as well as of efficiency in using such a methodology to evaluate the capacity increase of the retrofitted bridge.     

Role of the Material Constitutive Model in Simulating the Reusable Launch Vehicle Thrust Cell Liner Response

The reusable launch vehicle thrust cell liner, or thrust chamber, is a critical component of the space shuttle main engine. It is designed to operate in some of the most severe conditions seen in engineering practice. These conditions give rise to characteristic deformations of the cooling channel wall exposed to high thermal gradients and a coolant-induced pressure differential, characterized by the wall’s bulging and thinning, which ultimately lead to experimentally observed “dog-house” failure modes. In this paper, these deformations are modeled using the cylindrical version of the higher-order theory for functionally graded materials in conjunction with two inelastic constitutive models for the liner’s constituents, namely Robinson’s unified viscoplasticity theory and the power-law creep model. Comparison of the results based on these two constitutive models under cyclic thermomechanical loading demonstrates that, for the employed constitutive model parameters, the power-law creep model predicts more precisely the experimentally observed deformation leading to the “dog-house” failure mode for multiple short cycles, while also providing much improved computational efficiency. The differences in the two models’ predictions are rooted in the differences in the short-term creep and relaxation responses.     

Vehicle Condition Surveillance on Continuous Bridges Based on Response Sensitivity

This paper presents the parameter identification of a vehicle moving on a multispan continuous bridge deck modeled as a continuous beam based on dynamic response sensitivity analysis. This technique is for the monitoring of “road-friendliness” of vehicles using the highway pavement. The moving vehicle is modeled as a single degree-of-freedom system comprising three parameters, a two degrees-of-freedom system comprising five parameters, or a four degrees-of-freedom system comprising 12 parameters. The modified beam functions are used to calculate the response of the continuous bridge. Starting with an initial guess on the unknown parameters, the identification can be realized based on least-squares method and regularization technique from measured strain, velocity, or acceleration measurement from as few as a single sensor. Simulation studies and experimental results indicate that the identified results are acceptable, and the responses reconstructed from the identified parameters agree well with the measured responses.     

Evaluation of In-Service Performance of Tom’s Creek Bridge Fiber-Reinforced Polymer Superstructure

The Tom’s Creek Bridge is a small-scale demonstration project involving the use of fiber-reinforced polymer (FRP) composite girders as the main load-carrying members. The project is intended to serve two purposes. First, by calculating bridge design parameters such as the dynamic load allowance, transverse wheel load distribution, and deflections under service loading, the Tom’s Creek Bridge aids in modifying current American Association of State Highway and Transportation Officials bridge design standards for use with FRP composite materials. Second, by evaluating the FRP girders after exposure to service conditions, the project begins to answer questions about the long-term performance of these advanced composite material beams when used in bridge design. This paper details the in-service analysis of the Tom’s Creek Bridge. Five load tests, at 6-month intervals, were conducted on the bridge. Using midspan strain and deflection data gathered from the FRP composite girders during these tests, the aforementioned bridge design parameters have been determined. The Tom’s Creek Bridge was determined to have a maximum dynamic load allowance, IM, of 0.90, a transverse wheel load distribution factor, g, of 0.101, and a maximum deflection of L/490. Two bridge girders were removed from the Tom’s Creek Bridge after 15 months of service loading. These FRP composite girders were tested at the Structures and Materials Research Laboratory at Virginia Tech for stiffness and ultimate strength and compared to preservice values for the same beams. These measurements indicate that, after 15 months of service, the FRP composite girders have not significantly changed in stiffness or ultimate moment capacity.     

Dynamic Simulation of the Maglev Vehicle/Guideway System

A numerical model has been developed to investigate the dynamic characteristics of the Maglev system. Modeling of the guideway with the surface irregularity and modeling of the Maglev vehicle are described. Numerical simulations are performed in Simulink to solve the coupled problem. Based on this model a study focused on the dynamic characteristics of the guideway and the vehicle/guideway interaction has been made. The effects of various approaches to model the Maglev vehicle at different levels of accuracy are also investigated. The numerical results are compared with the corresponding values given by MSB-AG-Fahrweg. The conclusions derived by the research are presented in the end of this article.     

Operational Requirements for Long-Span Bridges under Strong Wind Events

In the absence of intensive wind tunnel tests, this study provides an effective and accurate approach to estimate the operational driving speed limit on bridges subjected to different road conditions and wind intensities, through a convenient continuous simulation technique (CSP). A fast and vigorous simulation tool, vehicle performance simulation, is developed to effectively model the performance of vehicles traveling on bridges by considering the interactions between wind, vehicles, and the bridge. The CSP, on the other hand, dramatically reduces the data generation time and makes a reliability analysis of vehicles possible. The application of the proposed method on the Confederation Bridge in Canada is presented as a numerical example. The simulation result overrides the general impression that only high-sided vehicles are sensitive to wind attacks, and this work demonstrates that light-weighted vehicles are also likely to suffer from instability problems on bridges under relatively low wind velocity. In addition, different types of vehicle can undergo different instability mechanisms under the same wind condition and these vehicle instability mechanisms vary with wind velocity.     

Using Inclinometers to Measure Bridge Deflection

Deflection of a bridge span under designed loads is an important parameter for bridge safety evaluation. However, it is inconvenient to obtain the bridge deflections directly. For bridges over rivers, railways, or highways, a direct measurement method is impractical. A promising bridge deflection measurement method (inclinometer method) is presented in this paper. It offers a simple, practical and inexpensive method of measuring static and dynamic deflections of bridge spans under loads, even for bridge spans that traverse great heights. Hundreds of experiments and practical tests on simple and continuous bridges, utilizing dynamic and static loads, under various vehicle speeds, show that the method has very high precision, which provides an authentic basis for new-built bridge acceptance and old bridge safety evaluation. The method does not need fixed observation positions as other deflection measurement methods because the inclinometers are installed on the bridge directly, which increases measurement efficiency greatly. These features indicate that as a potential method of measuring bridge deflection, inclinometers have significant engineering application value and a promising future.     

Natural Frequency of Railway Girder Bridges under Vehicle Loads

To investigate the natural frequency of a railway girder bridge under vehicle loads, two methods are presented. First, the natural frequency of a railway girder bridge under vehicle loads is obtained by solution of the eigenvalue of the vehicle-bridge interaction equation at each step of the numerical integration. Second, based on the vehicle-bridge interaction equation, an approximate formula is developed. The results show that the natural frequency of a railway girder bridge under vehicle loads varies periodically as the vehicles pass over the bridge. The results obtained with the two methods are then compared, showing that a good agreement is achieved. From parametric studies, the effects of the unsprung mass, the sprung mass, and the stiffness of the vehicle suspension are discussed.     

3D Unsteady RANS Modeling of Complex Hydraulic Engineering Flows. II: Model Validation and Flow Physics

A chimera overset grid flow solver is developed for solving the unsteady Reynolds-averaged Navier-Stokes (RANS) equations in arbitrarily complex, multiconnected domains. The details of the numerical method were presented in Part I of this paper. In this work, the method is validated and applied to investigate the physics of flow past a real-life bridge foundation mounted on a fixed flat bed. It is shown that the numerical model can reproduce large-scale unsteady vortices that contain a significant portion of the total turbulence kinetic energy. These coherent motions cannot be captured in previous steady three-dimensional (3D) models. To validate the importance of the unsteady motions, experiments are conducted in the Georgia Institute of Technology scour flume facility. The measured mean velocity and turbulence kinetic energy profiles are compared with the numerical simulation results and are shown to be in good agreement with the numerical simulations. A series of numerical tests is carried out to examine the sensitivity of the solutions to grid refinement and investigate the effect of inflow and far-field boundary conditions. As further validation of the numerical results, the sensitivity of the turbulence kinetic energy profiles on either side of the complex pier bent to a slight asymmetry of the approach flow observed in the experiments is reproduced by the numerical model. In addition, the computed flat-bed flow characteristics are analyzed in comparison with the scour patterns observed in the laboratory to identify key flow features responsible for the initiation of scour. Regions of maximum shear velocity are shown to correspond to maximum scour depths in the shear zone to either side of the upstream pier, but numerical values of vertical velocity are found to be very important in explaining scour and deposition patterns immediately upstream and downstream of the pier bent.     

The effect of inertia on tensile ductility

One-dimensional numerical simulations of dynamic tensile tests have been carried out over a wide range of test velocities for materials having aHollomon-type constitutive law with power-law strain-rate sensitivity. A variety of values of the strain-hardening exponent and strain-rate-sensitivity index have been used to analyze the effect of inertia on tensile ductility. Results show that the total elongation of the specimen is enhanced by inertia at high test velocities. This inertial effect varies with the strain-hardening exponent and strain-rate-sensitivity index and can be scaled with the normalized material density and the test velocity. Based on these results, the critical test velocity for the onset of the inertial effect as a function of material parameters has been numerically determined. To account for the effect of inertia on the enhancement of tensile ductility, a simple phenomenological explanation has been proposed.