Effects of Pier and Deck Flexibility on the Seismic Response of Isolated Bridges

The seismic response of bridges isolated by elastomeric bearings and the sliding system is investigated under two horizontal components of real earthquake ground motions. The selected bridges consist of multispan continuous deck supported on the piers and abutments. Three different mathematical models of the isolated bridge are considered for the analytical seismic response by considering and ignoring the flexibility of the deck and piers. The mathematical formulation for seismic response analysis of various mathematical models of the bridges isolated by different isolation systems is presented. The accuracy and computational efficiency of various mathematical models of isolated bridges is investigated by comparing their responses under different system parameters and earthquake ground motions. The important parameters selected are the flexibility of deck, piers, and isolation systems. There was significant difference in the computational time required for different models, but it was observed that the seismic response of the bridges obtained from different equivalent mathematical models is quite comparable even for an unsymmetrical bridge. Thus, the earthquake response of a seismically isolated bridge can be effectively obtained by modeling it as a single-degree-of-freedom system (i.e., considering the piers and deck as rigid) supported on an isolation system in two horizontal directions.     

Force-Deformation Behavior of Isolation Bearings

The isolation bearings are widely used in earthquake prone areas to protect the structure from seismic forces. The isolation bearing consists of an isolator to increase the natural period of the structure away from the high-energy periods of the earthquake, and a damper to absorb energy in order to reduce the seismic force. The most common isolation bearings used are lead–rubber bearings. They combine the function of isolation and energy dissipation in a single compact unit, giving structural support, horizontal flexibility, damping, and a centering force in a single unit. The relation between the horizontal force and horizontal displacement of the isolation bearings is nonlinear; to calculate the stiffness and the damping constant, which correspond to effective design displacement, the nonlinear behavior is expressed by bilinear behavior. This technical note presents new relations to calculate yield force, horizontal displacement, and damping.     

Performance Evaluation of Jointless Bridges

A recent trend in bridge design has been toward the elimination of joints and bearings in the bridge superstructure. Joints and bearings are expensive in both initial and maintenance costs and can get filled with debris, freeze up, and fail in their task to allow expansion and contraction of the superstructure. They are also a “weak link” that can allow deicing chemicals to seep down and corrode bearings and support components. Because the behavior is unknown and designs are cumbersome, jointless bridges are not widely used despite their enormous benefits. There are no standardized design procedures for these bridges, only a list of specifications and design recommendations are available. The objective of this research on jointless bridges conducted at the Constructed Facilities Center-West Virginia University is to study the behavior of jointless bridges supported on piles and spread footings and subjected to varying load conditions. In addition, time-dependent material properties have also been incorporated in this study. In this paper, the following items are presented: (1) synthesized analytical data that aids in understanding the performance under varying load combinations; (2) effects of primary versus secondary loads, boundary conditions, and system flexibility on induced stresses at various bridge locations; and (3) field testing and monitoring results of a jointless bridge in the state of West Virginia. Based on analytical and experimental results, conclusions are drawn in terms of design alternations.     

Seismic Design of Lifeline Bridge using Hybrid Seismic Isolation

This paper presents the merits of a hybrid seismic isolation system used for the seismic design of a major bridge. The bridge is analyzed for two different arrangements of seismic isolation systems. The first arrangement consists of friction pendulum bearings at all substructure locations; the other incorporates a hybrid system where laminated elastomeric bearings are used at the abutments and friction pendulum bearings at the piers. Analysis results have demonstrated that the hybrid seismic isolation system provided a structure with a fundamental period long enough to attract smaller seismic forces, while controlling the magnitude of isolation bearings displacements. It also provided a more uniform distribution of seismic forces among substructure elements. As a result, higher seismic forces on the piers were reduced, allowing for a more economical design of substructures. The hybrid seismic isolation system helped to control the wind-induced vibrations and reduced the sizes of the isolation bearings.     

Seismic Fragility of Continuous Steel Highway Bridges in New York State

This paper presents the results of an analytical seismic fragility analysis of a typical steel highway bridge in New York State. The structural type and topological layout of this multispan I-girder bridge have been identified to be most typical of continuous bridges in New York State. The structural details of the bridge are designed as per New York State bridge design guidelines. Uncertainties associated with the estimation of material strength, bridge mass, friction coefficient of expansion bearings, and expansion-joint gap size are considered. To account for the uncertainties related to the bridge structural properties and earthquake characteristics, ten statistical bridge samples are established using the Latin Hypercube sampling and restricted pairing approach, and 100 ground motions are simulated numerically. The uncertainties of capacity and demand are estimated simultaneously by using the ratios of demands to capacities at different limit states to construct seismic fragility curves as a function of peak ground acceleration and fragility surfaces as a function of moment magnitude and epicentral distance for individual components using nonlinear and multivariate regressions. It has been observed that nonlinear and multivariate regressions show better fit to bridge response data than linear regression conventionally used. To account for seismic risk from multiple failure modes, second-order reliability yields narrower bounds than the commonly used first-order reliability method. The fragility curves and surfaces obtained from this analysis demonstrate that bridges in New York State have reasonably low likelihood of collapse during expected earthquakes.     

Dynamic Analysis of Steel Curved Box Girder Bridges

The impact of seven three-span continuous single box girder bridges, with overall span lengths ranging from 76.2 to 213.36 m (250–700 ft), due to vehicles moving across rough bridge decks is analyzed. The box girder is divided into a number of thin-walled beam elements. Both warping torsion and distortion are considered in the study. The analytical vehicle is the HS20-44 truck included in the American Association of State Highway and Transportation Officials specifications and simulated as a nonlinear vehicle model with 11 degrees of freedom. Truck parameters include the body, suspensions, and tires. The bridge deck surface is assumed to be good and was simulated using a stochastic process (power spectral density function). The analytical results show that the impact factors of torque and distortional torque for the curved single box girder bridges could be very high, while those of the other responses are generally less than that of corresponding straight box girder bridges. The proposed impact equations can be used in the design of continuous curved single box girder bridges.     

Experimental Verification of Smart Cable Damping

Stay cables, such as are used in cable-stayed bridges, are prone to vibration due to their low inherent damping characteristics. Transversely attached passive viscous dampers have been implemented in many bridges to dampen such vibration. However, only minimal damping can be added if the attachment point is close to the bridge deck. For longer bridge cables, the relative attachment point becomes increasingly smaller, and passive damping may become insufficient. A recent analytical study by the authors demonstrated that “smart” semiactive damping can provide increased supplemental damping. This paper experimentally verifies a smart damping control strategy employing H2/linear quadratic Gaussian (LQG) clipped optimal control using only force and displacement measurements at the damper for an inclined flat-sag cable. A shear mode magnetorheological fluid damper is attached to a 12.65?m inclined flat-sag steel cable to reduce cable vibration. Cable response is seen to be substantially reduced by the smart damper.     

Damage Analysis of Hanshin Expressway Viaducts during 1995 Kobe Earthquake. III: Three-Span Continuous Girder Bridges

Almost all the single reinforced concrete (RC) piers from P35 to P350 received consistently severe damage, considering the large residual inclination of piers included in earthquake-induced severe damage. However, some of the piers in the section from P35 to P350 remained lightly damaged, and this phenomenon is observed especially in many piers under fixed bearings in continuous girder bridges. In this study, using experimentally based models for metal bearings and installing them to an existing FEM code, a nonlinear dynamic response analysis of a continuous girder bridge system is conducted. It is shown that the results depend on the ground motion, but the fuse effect of the breaking of the bearings could have been a reason for the phenomenon.     

Distribution of Wheel Loads on Continuous Steel Spread-Box Girder Bridges

Composite concrete-steel spread (multispine) box girder bridges remain one of the most common types constructed. Current design practices in North America recommend few analytical methods for the design of such bridges in simply supported construction. However, the effects of continuous construction have not been dealt with fully. In designing a continuous bridge, it is important to determine the maximum negative and positive stresses, maximum reactions, and shears in the bridge subjected to various loadings. This paper presents an extensive parametric study using a finite-element model in which 60 continuous bridge prototypes of various geometries, each subjected to various loading conditions, are analyzed for the distribution of flexural stresses, deflection, shears, and reactions. The parameters considered in the study are span length, number of spread boxes, and number of lanes. Distribution factors for maximum flexural stresses, deflection, shears, and reactions, suitable for design, are deduced for AASHTO truck loading. Results from tests on five box girder bridge models verify the finite-element model. A design example is presented to illustrate the use of the deduced formulas for the distribution factors.     

Seismic Performance Assessment of Simply Supported and Continuous Multispan Concrete Girder Highway Bridges

Seismic evaluations of typical concrete girder bridges are conducted for both a multispan simply supported and a multispan continuous girder bridge common to the Central and Southeastern United States. These evaluations are performed for an approximate hazard level of 2% in 50?years by performing nonlinear time history analyses on three-dimensional analytical models. The results show significant vulnerabilities in the reinforced concrete columns, the abutments, and also in unseating of the girders. In general, the longitudinal loading of the bridges results in larger demands than the transverse loading. However, the simply supported bridge sustains bearing deformations in the transverse direction which are on the same order as their longitudinal response. These results suggest that both longitudinal and transverse loading are significant and should be considered when performing seismic hazard analyses of these bridges.     

Three-Dimensional Finite-Element Analysis of High Damping Rubber Bearings

A three-dimensional finite element modeling of high damping rubber bearings is studied. At first, the constitutive model of high damping rubber materials proposed by the writers is formulated in order to derive the constitutive tensor, which is required in the application of the finite element method. Second, a mixed finite-element method consistent with the proposed constitutive model is described. In this method, slightly compressible materials with rate form constitutive models are applied. Then, using the constitutive model and the finite-element method, a three-dimensional finite element model of high damping rubber bearings is constructed. The simulations by the model are found to be in good agreement with the experimental results of the bearing. Finally, complex deformation such as torsional or rotational deformation of the bearing are simulated by the finite-element model, and the design equations for these deformation are proposed on the basis of the simulations or experimental results.     

Theoretical Studies of the XY-FP Seismic Isolation Bearing for Bridges

The XY-friction pendulum (XY-FP) bearing is a modified friction pendulum that consists of two perpendicular steel rails with opposing concave surfaces and a connector. The connector resists tensile forces, allows independent sliding in the two orthogonal directions and enables small relative rotation of the rails about a vertical axis. Theoretical analyses were undertaken to study applications of XY-FP bearings to bridges. Two of the key features of the XY-FP bearing for the seismic isolation of bridges are: (1) resistance to tensile axial loads and (2) opportunity to provide a different period of isolation in each principal direction of the isolated structure. Numerical analyses on an XY-FP isolated bridge with different isolation periods in the principal directions subjected to near-field ground motions demonstrated the effectiveness of XY-FP bearings. Furthermore, numerical analyses that investigated the sensitivity of XY-FP isolation system response to differences in the coefficients of friction of the bearings demonstrated that bounding analysis using upper and lower estimates of the coefficients of friction will generally provide conservative estimates of displacements and shear forces for isolation systems with nonuniform isolator properties.     

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.     

Seismic Response of Multiple Span Steel Bridges in Central and Southeastern United States. II: Retrofitted

Part I of this two-part paper evaluated the seismic response of typical multispan simply supported (MSSS) and multispan continuous steel girder bridges in the central and southeastern United States. The results showed that the bridges were vulnerable to damage resulting from impact between decks, and large ductility demands on nonductile columns. Furthermore, fixed and expansion bearings were likely to fail during strong ground motion. In this paper, several retrofit measures to improve the seismic performance of typical multispan simply supported and multispan continuous steel girder bridges are evaluated, including the use of elastomeric bearings, lead-rubber bearings, and restrainer cables. It is determined that lead-rubber bearings are the most effective retrofit measure for reducing the seismic vulnerability of typical bridges. While isolation provided by elastomeric bearings limits the forces into the columns, the added flexibility results in pounding between decks in the MSSS steel girder bridges. Restrainer cables, which are becoming a common retrofit measure, are effective in reducing the hinge opening in MSSS bridges with steel bearings. However, when used with elastomeric bearings, the restrainer cables negate the isolation effect of the bearings.     

Effect of Hanger Flexibility on Dynamic Response of Suspension Bridges

Linearized continuum models of a suspended span with unloaded backstays and of a symmetric three-span suspension bridge are used to study the effects of the flexibility of the hangers on the vertical vibrations of suspension bridges. The models include elastic parabolic cables, flexible distributed hangers with variable length, and a stiffening girder represented by an elastic beam. It is shown that the free vibrations of a suspended span with unloaded backstays are controlled by five dimensionless parameters, while six dimensionless parameters control the response of a symmetric three-span suspension bridge. The results indicate that the flexibility of the hangers has a significant effect on the natural frequencies of the higher modes only when the relative stiffness of the girder is very high. The effects of hanger flexibility on the response of a suspension bridge to localized impulsive loads are also found to be small. These findings confirm the traditional, albeit previously untested, assumption of inextensible hangers. Finally, the threshold amplitudes of free vibrations that would result in the incipient slackening of the hangers are determined.     

Seismic Response of Multiple Span Steel Bridges in Central and Southeastern United States. I: As Built

The seismic response of typical multispan simply supported (MSSS) and multispan continuous steel girder bridges in the central and southeastern United States is evaluated. Nonlinear time history analyses are conducted using synthetic ground motion for three cities for 475 and 2,475-year return period earthquakes (10 and 2% probability of exceedance in 50 years). The results indicate that the seismic response for the 475-year return period earthquake would lead to an essentially linear response in typical bridges. However, the seismic response for a 2,475-year return period earthquake resulted in significant demands on nonductile columns, fixed and expansion bearings, and abutments. In particular, pounding between decks in the MSSS bridge would result in significant damage to steel bearings and would lead to the toppling of rocker bearings, which may result in unseating of the bridge deck.     

采用不同支座的桥梁地震反应对比分析

在E2地震作用下,分别对采用高阻尼橡胶支座与普通支座的桥梁结构进行时程反应分析,对结构的自振周期及桥墩墩底内力进行对比分析,结果表明,采用高阻尼橡胶支座能使结构自振周期延长,增加耗能时间,减震效果明显。     

Train-Induced Vibration Control of High-Speed Railway Bridges Equipped with Multiple Tuned Mass Dampers

This paper deals with the applicability of multiple tuned mass dampers (MTMDs) to suppress train-induced vibration on bridges. A railway bridge is modeled as an Euler-Bernoulli beam and a train is simulated as a series of moving forces, moving masses, or moving suspension masses. According to the train load frequency analysis, resonant effects will occur as the modal frequencies of a bridge are close to the multiple of the impact frequency of the train load to the bridge. An MTMD system is then designed to alter the bridge dynamic characteristics to avoid excessive vibrations. Numerical results from simply supported bridges of the Taiwan High-Speed Railway (THSR) under real trains show that the proposed MTMD is more effective and reliable than a single TMD in reducing dynamic responses during resonant speeds, as the train axle arrangement is regular. It is also found that the inner space of a bridge box-girder of the THSR is wide and deep enough for installation and movement of MTMDs.     

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.