Vibration Control of Railway Bridges under High-Speed Trains Using Multiple Tuned Mass Dampers

In this paper, multiple tuned mass dampers (MTMDs) are considered for suppressing the vibration of railway bridges under high-speed trains. The interaction equations of motion between the vehicle and the bridge with MTMDs have been developed. The effectiveness of MTMDs on suppressing resonant vibration of railway bridges is examined and the optimum parameters of MTMDs for suppressing the resonant vibration are proposed. The results indicate that the use of the MTMD with the optimum parameters reduces the displacement and acceleration responses of railway bridges significantly.     

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.     

Dynamic Response of Plates on Elastic Foundation to Moving Loads

A procedure incorporating the finite strip method and a spring system has been developed and applied to treat the dynamic response of plate structure resting on an elastic foundation to moving loads. The response to a single moving concentrated load is first investigated and then the effects of velocity, elastic foundation stiffness, moving path, and distance between multiple moving loads are studied. The response under a moving harmonic load with constant velocity is finally treated and the effect of the load frequency is investigated. Results indicate that the foundation stiffness and the velocity and frequency of the moving load have significant effects on the dynamic response of the plate and on resonant velocities. Some of these findings might find use in practical applications.     

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.     

Dynamic Characteristics of Infinite and Finite Railways to Moving Loads

Some fundamental dynamic characteristics of a railway subjected to a harmonic or constant moving load are established and presented in this paper. The railway is modeled as an infinite or finite Timoshenko beam on viscoelastic foundation. The dynamic-stiffness matrices characterized by the complex wave numbers are employed to deal with this problem. The relationship between the forced frequency and the resonant velocity of the moving load, and the resonant frequency of the railway are especially emphasized and intensively discussed. The fundamental dynamic characteristics of a railway modeled as a Bernoulli-Euler Beam on viscoelastic foundation are also included for comparison.     

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.     

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.     

Dynamic Response of Suspension Bridge to High Wind and Running Train

A framework is presented for predicting the dynamic response of long suspension bridges to high winds and running trains. A three-dimensional finite-element model is used to represent a suspension bridge. Wind forces acting on the bridge, including both buffeting and self-excited forces, are generated in the time domain using a fast spectral representation method and measured aerodynamic coefficients and flutter derivatives. Each 4-axle vehicle in a train is modeled by a 27-degrees-of-freedom dynamic system. The dynamic interaction between the bridge and train is realized through the contact forces between the wheels and track. By applying a mode superposition technique to the bridge only and taking the measured track irregularities as known quantities, the number of degrees of freedom of the bridge-train system is significantly reduced and the coupled equations of motion are efficiently solved. The proposed formulation is then applied to a real wind-excited long suspension bridge carrying a railway inside the bridge deck of a closed cross section. The results show that the formulation presented in this paper can predict the dynamic response of the coupled bridge-train systems under fluctuating winds. The extent of interaction between the bridge and train depends on wind speed and train speed.     

Equivalent Wheel Load Approach for Slender Cable-Stayed Bridge Fatigue Assessment under Traffic and Wind: Feasibility Study

In the current AASHTO LRFD specifications, the fatigue design considers only one design truck per bridge with 15% dynamic allowance. While this empirical approach may be practical for regular short and medium span bridges, it may not be rational for long-span bridges (e.g., span length >152.4?m or 500?ft) that may carry many heavy trucks simultaneously. Some existent studies suggested that fatigue may not control the design for many small and medium bridges. However, little research on the fatigue performance of long-span bridges subjected to both wind and traffic has been reported and if fatigue could become a dominant issue for such a long-span bridge design is still not clear. Regardless if the current fatigue design specifications are sufficient or not, a real understanding of the traffic effects on bridge performance including fatigue is desirable since the one truck per bridge for fatigue design does not represent the actual traffic condition. As the first step toward the study of fatigue performance of long-span cable-stayed bridges under both busy traffic and wind, the equivalent dynamic wheel load approach is proposed in the current study to simplify the analysis procedure. Based on full interaction analyses of a single-vehicle–bridge–wind system, the dynamic wheel load of the vehicle acting on the bridge can be obtained for a given vehicle type, wind, and driving condition. As a result, the dimension of the coupled equations is independent of the number of vehicles, through which the analyses can be significantly simplified. Such simplification is the key step toward the future fatigue analysis of long-span bridges under a combined action of wind and actual traffic conditions.     

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.     

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.     

Refined Stick Model for Dynamic Analysis of Skew Highway Bridges

Stick models are widely employed in the dynamic analysis of bridges when only approximate results are desired or when detailed models are difficult or time-consuming to construct. Although the use of stick models for regular bridges has been validated by various researchers, the application of such models to skew highway bridges continues to present challenges. The conventional single-beam stick model used to represent the bridge deck often fails to capture certain predominant vibration modes that are important in obtaining the true dynamic response of the bridge. In this paper, a refined stick model is proposed for the preliminary dynamic analysis of skew bridges. The model utilizes a dual-beam stick representation of the bridge deck. The validity of the model is established by comparing results obtained from the proposed model with numerical solutions obtained for skew plates and a skew bridge. It is shown that this dual-beam stick model is superior to the conventional single-beam model in estimating the natural vibration frequencies and in predicting the predominant vibration modes of the bridge. Because of its simplicity and relative accuracy, this model is recommended for the preliminary dynamic analysis of skew highway bridges.     

Experimental Study on the Stability of Railroad Silt Subgrade with Increasing Train Speed

The comfort and safety of a moving train is largely determined by the dynamic response of the railway track and its foundation (i.e., subgrade). To study the dynamic stability of a silt subgrade subjected to train traffic loading with increasing speed, cyclic triaxial tests were conducted for compacted silt specimens with varying dry density, water content, dynamic stress, and load frequency. The laboratory test results and field measurements of the subgrade dynamic stress under train loading indicate that with increasing train speed, an increase in dynamic stress and load frequency does not impair the stability of the silt subgrade, provided the subgrade is in sound physical condition (i.e., its natural water content approximates the optimal water content) and the relative compaction is at least 90%. However, if the relative compaction is 85%, the subgrade is stable only at a dynamic stress level that is below 70 kPa, and the subgrade may suffer shear failure at a higher dynamic stress level. The elastic deformation of the subgrade linearly increases with an increase in train speed. However, if the degree of saturation of the silt subgrade increases, the thresholds of both the dynamic stress and resilient modulus decrease markedly, accompanied by sharp increases in elastic deformation and cumulative deformation and can even result in the shear failure of the subgrade. These conditions are unfavorable for the high speeds and stability needed for trains; therefore, train speeds should be limited in wet conditions to reduce subgrade dynamic stress and load frequency.     

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.     

Full-Scale Test and Analysis of a Curved Steel-Box Girder Bridge

Since the first edition of the AASHTO Guide Specifications for Horizontally Curved Steel Girder Highway Bridges was published in 1980, there have been two more editions including many revisions to the specifications. Some changes were based on valid research results and others were based on limited or uncertain research results and information. The current edition of the specifications contains provisions that may result in unreasonably conservative load capacity ratings. In this paper, the results of field tests and analyses conducted on the Veterans’ Memorial curved steel-box girder bridge are discussed. Test and analytical results show: (1) current AASHTO guide specifications regarding the first transverse stiffener spacing at the simple end support of a curved girder may be too conservative for bridge load capacity ratings; (2) current AASHTO guide specifications may greatly overestimate the dynamic loadings of curved box girder bridges with long span lengths; and (3) a plane grid finite-element model of about 20 elements per span in the longitudinal direction can be used to analyze curved multigirder bridges with external bracings located only over supports. The research results are instructive and applicable to bridge design and bridge load-rating activities.     

Identification of a Distribution of Stiffness Reduction in Reinforced Concrete Slab Bridges Subjected to Moving Loads

The method for identifying arbitrary stiffness reduction in damaged reinforced concrete slab bridges under moving loads is proposed and dynamic signals measured at several points are used as response data to reflect the properties of the moving loads sensitivity. In particular, the change in stiffness in each element before and after damage, based on the system identification method, is described and discussed by using a modified bivariate Gaussian distribution function. The proposed method in this work is more feasible than the conventional element-based damage detection method from the computational efficiency because the procedure of finite-element analysis coupled with microgenetic algorithm using six unknown parameters irrespective of the number of elements are considered. The validity of the technique is numerically verified using a set of dynamic data obtained from a simulation of the actual bridge modeled with a three-dimensional solid element. The numerical calculations show that the proposed technique is a feasible and practical method that can prove the exact location of a damaged region as well as inspect the complex distribution of deteriorated stiffness, although there is a modeling error between actual bridge results and numerical model results as well as a measurement error like uncertain noise in the response data.     

Increasing the Load Capacity of Suspension Bridges

There is a tendency for traffic loads to increase with the passage of time. It is not uncommon, therefore, for bridges to be strengthened and/or widened or sometimes to have lanes or even complete decks added. A few bridges were designed initially with a view to future expansion, such as the George Washington Suspension Bridge, designed to accommodate an extra deck, and the Salazar (now April 25) Bridge, designed to have two train tracks added, but these are exceptions. Suspension bridges behave somewhat differently from other bridge types, and the methods for increasing capacity can also be different. Some ideas are presented of how suspension bridges can be altered to accommodate more load, be it automobile, pedestrian, or even train traffic, and some examples are given. The importance of understanding both structural behavior and structural safety is emphasized.     

Dynamic Load Allowance for Through-Truss Bridges

The objective of the present study was to experimentally evaluate the statistics of dynamically induced stress levels in steel through-truss bridges as a function of bridge component type, component peak static stress, vehicle type, and vehicle speed. Better understanding of critical bridge rating parameters will enable more accurate bridge evaluations of this type of structure. Three 60-year-old, steel through-truss bridges with similar characteristics were investigated in the present study. Several bridge components on each of the three bridges were instrumented (truss members, stringers, and floor beams), and dynamic strain data were collected under controlled and normal traffic conditions. The dynamic strain histories were processed to obtain bridge component peak static response and peak dynamic response, resulting in the determination of the dynamic load allowance (DLA) for each of the instrumented bridge components for each of several truck crossings. The calculated DLA value are plotted as a function of member peak static stress for each bridge member instrumented. The DLA data are examined as a function of component type, component location, truck type, number of axles, truck speed, and truck direction. This study has demonstrated that the DLA is dependent on truck location, component location, component type, and component peak static stress but appears to be nearly independent of vehicle speed.     

Effect of Construction Loads and Vibrations on New Concrete Bridge Decks

This paper presents an investigation on the effects of construction loads and vibrations on typical newly poured reinforced concrete bridge decks. The main objective of this paper was to perform dynamic finite-element analyses of concrete bridge decks under construction loads and vibrations. Two types of bridges were modeled by effectively simulating the loads encountered during construction. Separate analyses were performed to simulate one truck as well as two side-by-side trucks. Additional analyses were performed to simulate the loads during construction and pouring sequence. The loads imposed by concrete mixer trucks, including the full concrete load and the load imposed by a trailer unit carrying the pump, were taken into consideration during the modeling of the bridges. The results obtained consisted of vibration modes and frequencies for each structure in addition to top and bottom stresses in each principal direction. A separate analysis was performed that took into account the sequence of pour to determine the effect of moving loads from adjacent traffic and construction loads on fresh concrete. The time history and dynamic analysis indicated that the sequence of pour has a significant effect on the deformation of the concrete at early ages. As a result, the first three mode shapes obtained by the finite-element analysis will be used to optimize sensor locations for future dynamic field testing.     

Dynamic Analysis of Metallic Arch Railway Bridge

This work describes some of the most interesting aspects of the experimental and numerical dynamic analyses of the Luiz I Bridge, an old arch double-deck iron bridge, when subjected to the moving loads of the new light metro of Porto. Presented are the methodology and computational tools developed, as well as some of the most significant results obtained from numerical simulations conducted on the basis of an experimentally calibrated finite-element model, both in terms of structural safety and of the comfort of pedestrians and train passengers.