Journal of Bridge Engineering

Autoparametric resonance is treated as the reason of arising excessive lateral vibrations in the steel arch bridge (the Solferino Bridge). To explain this phenomenon, a physical model (a double pendulum) is proposed. Its behavior, as a rule, depends on dynamic characteristics of a bridge rather than on its type. The response of a two degree-of-freedom system with quadratic nonlinearities in the presence of two-to-one autoparametric resonance is investigated. The perturbation method of multiple time scales is used to construct first-order nonlinear differential equations and to determine steady state solutions and their stability. Bifurcation analysis is performed to determine a critical (threshold) value in the external load (control) parameter. The autoparametric resonance becomes possible if an excited torsional mode is near a primary resonance and an external load parameter caused by pedestrians is equal or higher than its critical value. When the increasing load parameter passes through the critical value (because a quantity of pedestrians on the bridge is increased), a jump phenomenon (or fast growth) is observed for the lateral mode, the torsional mode is saturated and has much smaller amplitudes. Field tests were held to understand a phenomenon of an excessive lateral movement, and to enforce the Solferino Bridge. Theoretical results of the present paper are compared with those experimental measurements. Swaying of pedestrian bridges can be treated as a two-step process. The first step (achievement of parametric resonance), described in this paper, is the condition for the beginning of the second step—the process of possible synchronization of applied forces and the interactions between them and the lateral and torsional modes of vibration.

In the last several years many cases of large amplitude horizontal vibrations of footbridges have been observed, due to dynamic interaction between the walkers and the footbridge, which may occur when some conditions on the bridge mass, frequency and damping, as well as on the crowd density are met. Such interaction is an intriguing phenomenon, as it is associated with the dynamics of a complex system made of a structure and a number of walkers, the dynamics of the latter being governed by physiology and psychology. Provided this complexity, in this paper a preliminary step is made toward the modeling of the interaction forces exerted by a crowd to a footbridge. The results of an experimental investigation of the lateral forces exerted by one walker to a fixed floor are presented, and used to calibrate a deterministic and stochastic lateral loading models of footbridges, to be used in the case in which no interaction takes place. The results presented are also the background data for more sophisticated dynamic models allowing for bridge-crowd interaction.

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.

Strong earthquakes can result in large longitudinal displacements in multiple-frame bridges. This could lead to excessive displacements/openings at the intermediate joints. Bridges with small seat widths are vulnerable to the unseating of their superstructure. Seismic steel restrainers are currently used to limit the joint openings in bridges. However, past earthquakes have shown that restrainer cables have limitations in regards to preventing unseating in bridges. Other devices have been proposed to limit joint displacements, including metallic dampers, viscoelastic dampers, and shape memory alloys (SMAs), which are known for their ability to recover their original shape after being deformed. A sensitivity study and a case study are conducted using computer simulations to compare the effectiveness of SMA retrofit devices with other devices. The results show that the effectiveness of the devices is a function of the characteristics of the bridge frames and the ground motion characteristics. In all cases, the steel restrainer cables were the least effective in limiting joint displacements. The SMA devices have the additional benefit of significantly limiting the residual joint displacement in bridges.

The paper presents a detailed seismic performance assessment of a complex bridge designed as a reference application of modern codes for the Federal Highway Administration. The assessment utilizes state-of-the-art assessment tools and response metrics. The impact of design assumptions on the capacity estimates and demand predictions of the multispan curved bridge is investigated. The level of attention to detail is significantly higher than can be achieved in a mass parametric study of a population of bridges. The objective of in-depth assessment is achieved through investigation of the bridge using two models. The first represents the bridge as designed (including features assumed in the design process) while the second represents the bridge as built (actual expected characteristics). Three-dimensional detailed dynamic response simulations of the investigated bridge, including soil-structure interaction, are undertaken. The behavior of the as-designed bridge is investigated using two different analytical platforms for elastic and inelastic analysis, for the purposes of verification. A third idealization is adopted to investigate the as-built bridge’s behavior by realistically modeling bridge bearings, structural gaps, and materials. A comprehensive list of local and global, action and deformation performance indicators, including bearing slippage and inter-segment collision, are selected to monitor the response to earthquake ground motion. The comparative study has indicated that the lateral capacity and dynamic characteristics of the as-designed bridge are significantly different from the as-built bridge’s behavior. The potential of pushover analysis in identifying structural deficiencies, estimating capacities, and providing insight into the pertinent limit state criteria is demonstrated. Comparison of seismic demand with available capacity shows that seemingly conservative design assumptions, such as ignoring friction at the bearings, may lead to an erroneous and potentially nonconservative response expectation. The recommendations assist be given to design engineers seeking to achieve realistic predictions of seismic behavior and thus contribute to uncertainty reduction in the ensuing design.

The present study is designed to determine the effect of major parameters on maximum total bending moments of curved girders, establish the relationship between key parameters and girder distribution factors (GDFs), and develop new approximate distribution factor equations. A level of analysis study using three numerical models was performed to establish an appropriate numerical modeling method on the basis of field test results. A total of 81 two-traffic lane curved bridges were analyzed under HL-93 loading. Two approximate GDF equations were developed based on the data obtained in this study: (1) a single GDF based on total girder normal stress; and (2) a combined GDF treating bending and warping normal stress separately. The two equations were developed based on both an averaged coefficient method and regression analysis. A goodness-of-fit test revealed that the combined GDF model developed by regression analysis best predicted GDFs. The present study demonstrated that radius, span length, cross frame spacing and girder spacing most significantly affect GDFs. The proposed GDF equations are expected to provide a more refined live load analysis for preliminary design.

This paper studies a Kansas Department of Transportation welded plate girder bridge that developed fatigue cracks at small web gaps close to the girder top flange. Repair had been previously performed by softening the connection plate end with a slot retrofit, but cracks were recently found to have reinitiated at some of the repaired details and are again propagating. A comprehensive finite-element method study was performed to investigate the cracking behavior observed in the bridge and to recommend appropriate measures for future bridge retrofit. The analytical results show that stresses developed at the top flange web gaps could exceed yielding under the loading of an HS15 fatigue truck. The current slot repair used in the bridge was found to have introduced higher magnitude fatigue stresses in the web gap. To achieve a permanent repair of the bridge, it is recommended that a welded connection plate to flange attachment be used during future bridge retrofit. The web gap details should be able to withstand unlimited number of load cycles once this additional repair is performed.

This paper presents an analysis of the data collected in the ambient vibration test of the International Guadiana cable-stayed Bridge, which links Portugal and Spain, based on different output-only identification techniques: peak-picking, frequency domain decomposition, covariance-driven stochastic subspace identification, and data-driven stochastic subspace identification. The purpose of the analysis is to compare the performance of the four techniques and evaluate their efficiency in dealing with specific challenges involved in the modal identification of the tested cable-stayed bridge, namely the existence of closely spaced modes, the perturbation produced by the local vibration of stay-cables, and the variation of modal damping coefficients with wind velocity. The identified natural frequencies and mode shapes are compared with the corresponding modal parameters provided by a previously developed numerical model. Additionally, the variability of some modal damping coefficients is related with the variation of the wind characteristics and associated with a component of aerodynamic damping.

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 $>152.4\mathrm{m}$ or $500\mathrm{ft}$ ) 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.

This paper presents a comparison between the live load distribution factors of simple span slab-on-girders concrete bridges based on the current AASHTO-LRFD and finite-element analysis. In this comparison, the range of applicability limits specified by the current AASHTO-LRFD is fully covered and investigated in terms of span length, slab thickness, girder spacing and longitudinal stiffness. All the AASHTO-PCI concrete girders (Types I–VI) are considered to cover the complete range of longitudinal stiffness specified in the AASHTO-LRFD. Several finite-elements linear elastic models were investigated to obtain the most accurate method to represent the bridge superstructure. The bridge deck was modeled as four-node quadrilateral shell elements, whereas the girders were modeled using two-node space frame elements. The live load used in the analysis is the vehicular load plus the standard lane load as specified by AASHTO-LRFD. The live load is positioned at the longitudinal location that produced the extreme effect, and then it is moved transversely across the bridge width in order to investigate all possibilities of one-lane, two-lane and three-lane design loads. A total of 886 bridge superstructure models were built and analyzed using the computer program SAP2000 to perform this comparison. The results of this study are presented in terms of figures to be practically useful to bridge engineers. This study showed that the AASHTO-LRFD may significantly overestimate the live load distribution factors compared to the finite-element analysis.

Overweight vehicles require permits to cross the highway bridges, which are designed for “design load vehicles” (prescribed in the national standards). A new, fast, and robust method is presented for the verification of bridges, which requires minimal input only: the axle loads, axle spacing, the bridge span(s), and the superstructure type. The bridge can be a single or a multispan girder, an arch bridge, a frame structure, or a box girder. The overweight vehicle may operate within regular traffic or it may cross the bridge at a given lane position while other traffic is prohibited on the bridge. The method is illustrated by numerical examples for deck-girder bridges and for a box girder.

A model that applies to initial bridge load ratings based on allowable stress, load factor, and load and resistance factor design is presented. The prognostic component calculates bridge load ratings probabilistically considering random variables representative of load and resistance effects. The diagnostic component helps to point out the sensitivity rankings of these input parameters. Monte Carlo simulation and Bayesian networks are the tools employed in this bidirectional model. The model is applied to a beam in a prestressed concrete bridge at the beginning of its service life to demonstrate conclusions related to its applicability as a tool in areas related to bridge design and load rating.

This paper presents findings of a research study conducted by the writers for the Arkansas State Highway and Transportation Department. The study investigated precast nonprestressed concrete channel beam sections cast without shear reinforcement used in short, multispan bridges. The original objective of the study was to establish a correlation for inspection purposes between the beam’s visual deteriorated state and its corresponding approximate structural capacity. However, during four-point load testing of 33 beams, it was found that beam strength was more a function of a beam’s concrete compression strength rather than deterioration state. A national survey of state transportation departments within the contiguous states was conducted by the authors and found that 13 states currently use precast channel beam bridges. The particular section considered in this paper is a $5.79\mathrm{m}$ $\left(19\mathrm{ft}\right)$ precast channel beam section used to cross small streams and depressions; however constructed without shear reinforcing steel. Bridges using these sections were constructed in the 1950s through to the early 1970s and were designed for H15 loading. Thirty-three formally in-service beams, in various states of deterioration, were load tested. The writers found that the majority of the beams exhibited load capacity greater than the initially required H15 design strength. Second, member strength was a function of concrete compressive strength. Of the 33 beams load tested, 28 beams showed ductile behavior; conversely, the other five beams failed without exhibiting a yield plateau.

A bridge approach slab serves as a structural slab between the bridge structure and the approach embankment. The primary causes of approach slab failures are undermining, settlement and cracking. Undermining and settlement of the slab can be treated by either mud jacking or by pumping grout material to fill the voids beneath the slab. Transverse and longitudinal cracking leads to distress of the slab and reduces its life expectancy. The objective of this technical note is to numerically study the extent and location of cracks by performing a nonlinear finite-element analysis of the slab. The factors affecting the cracks such as the thickness of the slab and the contact conditions with the soil underneath have been parametrically studied. This technical note brings out the issues and advantages related to the usage of finite-element analysis for approach slabs. The tension stiffening component, has been calibrated before being used for the approach slab model. A thicker approach slab could be a more viable solution as compared to the expensive soil treatment.

Although AASHTO LRFD specifications provide moment capacity equations as an approximate design method and recommend an orthotropic plate model as the refined method for the analysis of filled grid decks, no guidelines are provided for the determination of the flexural rigidities associated with the plate analysis. This technical note briefly reviews orthotropic thin plate theory, discusses the determination of the flexural rigidities using Huber’s assumption, and applies the theory to concrete-filled steel grid decks. The accuracy of the orthotropic plate analysis is assessed by comparing it to results of an earlier finite-element analysis.