Journal of Bridge Engineering

The frictional resistance between main cable and saddle of a long-span, multispan suspension bridge is significant for the safety of the bridge. Typically, the main cable of a long-span, multispan suspension bridge has hundreds of strands. It is essential to understand the frictional resistance between the main cable and saddle for the design and evaluation of the bridge. In order to understand the fundamental mechanism of formation of frictional resistance, this paper studies the frictional resistance between single strand and saddle through finite element analysis. A simple yet effective and efficient model is delivered as a tool for analyzing the frictional resistance between single strand and saddle. The model is validated against model test results, and then used to investigate the distribution of strand force, nominal coefficient of friction, and the friction components at the saddle's side and bottom surfaces. The strand tension distributions are nonuniform along the strand and in the radial direction of the saddle. The friction components at the saddle's side and bottom surfaces follow opposite trends as the relative slip between the strand and saddle increases.

The capability to accurately evaluate the frictional resistance between the main cable and saddle is essential for the design and evaluation of suspension bridges. In this paper, an analytical model is developed to predict the frictional resistance between the main cable and saddle based on slipping compatibility conditions and is validated against model test data. The relative slip between adjacent strands is considered. The development process of the frictional resistance is analyzed. The development process of the total frictional resistance between the main cable and saddle can be divided into three stages: (1) the nearly linear growing stage, (2) the slow growing stage, and (3) the steady ultimate stage. Incorporating vertical frictional plates into the saddle trough increases the frictional resistance between the main cable and saddle but aggravates the unevenness of the distribution of the single strand frictional resistance.

This paper introduces field tests of the first continuous multispan slab-on-girder bridge with hybrid glass fiber-reinforced-polymer (GFRP)–steel reinforcement in Canada. The bridge was constructed in 2012 on Chemin Dunant overpassing the extension of Highway 410 in Sherbrooke (Quebec). The bridge consists of three spans with a maximum span of 44.6 m and is a typical slab-on-girder bridge with three traffic lanes. The bridge cross section consists of five steel girders, 1.9-m depth, covered with a 200-mm-thick concrete slab. The deck slab was reinforced with hybrid GFRP–steel reinforcement with a top mat of GFRP bars and a bottom mat of galvanized-steel bars. The Ministry of Transportation of Quebec recommends using galvanized-steel bars instead of black-steel bars because the former has higher corrosion resistance. The amount of reinforcement was determined using the empirical design method based on a steel reinforcement ratio of 1.0% according to existing design codes . The bridge was examined under live-load field testing involving seven load cases of truck locations. The steel-girder deflection was measured, and the strains in the GFRP and steel bars over an intermediate bridge pier were recorded. The field test showed very low strains in the GFRP and steel bars. The visual field inspection over approximately 6.5 years revealed that the bridge performed well under normal traffic conditions, confirming the applicability of using hybrid reinforcement in continuous bridges. An analytical parametric study was conducted examining the effects of changing the top reinforcement bar diameter, top and bottom reinforcement spacing, the hybrid- or GFRP-reinforced deck slab, and the dimensions of the steel-girder cross section (noncompact). The study revealed that the empirical method is conservative and calls for an unreasonable amount of reinforcement. Accordingly, the flexural design method (sectional analysis) should be used for the negative moment section.

Slab splitting, resulting from the dispersion of a number of intermediate loads arranged in a line, is a common problem in such engineering structures as steel–concrete composite girders and pylon anchorages of cable-stayed bridges. Previous studies on intermediate anchorages have two major limitations: improper adoption of results obtained from studies on end anchorages and neglecting to account for the beneficial effect from lateral stress overlapping. Through load path modeling, finite-element modeling, and experimental testing, this study provides new insight into this common problem. For the single-load case, a load path model is established to capture the flow of forces in the intermediate anchorage zone, from which an explicit equation for the distribution of transverse stresses is derived. For the multiple-load case, an analytical method is proposed to evaluate the splitting effects in slabs with different load spacings. The analytical method is applied to predict slab splitting in prefabricated composite beams. Four prefabricated composite box girders with different spacings of stud clusters were tested and used to verify the proposed analytical method. Furthermore, the analytical method was applied to predict the splitting effect in pylon anchorages of cable-stayed bridges, and the results compared with results of finite-element analysis using shell elements. It is found that the splitting force equation for the end anchorage zone would significantly overestimate the splitting effect in slabs with closely spaced intermediate loads. In composite girders with precast concrete deck, only the front halves of transverse rebars in intervals between shear pockets are effective to protect the slab from longitudinal splitting failure.

An aerodynamic describing function (ADF)-based model for simulating the nonlinear self-excited forces on bridge decks is developed, where the ADFs can be conveniently identified using the experimentally or numerically obtained free or forced vibration data. An efficient calculation procedure based on the ADFs is accordingly established to predict the nonlinear flutter state and/or postflutter limit cycle oscillations (LCOs). Two numerical examples are utilized to demonstrate the simulation accuracy and efficiency of nonlinear bridge flutter with the proposed ADF-based model. The capabilities of the ADF-based model in capturing typical features of nonlinear postflutter vibration such as LCO and a hysteresis phenomenon are demonstrated. A nondimensional postflutter index is designed to quantitatively assess the postflutter performance of bridge decks. Finally, the effects of structural dynamics and aerodynamic properties (e.g., structural damping ratios, natural frequencies, and aerodynamic derivatives) on the postflutter behavior of a bridge deck are examined in terms of the wind speed extension after the critical state with acceptable postcritical vibrations and the proposed postflutter index.

The Stockbridge damper (SD) has been used for vibration mitigation of suspender cables subjected to vortex-induced and other types of resonant vibrations. This paper studies its effectiveness and robustness, as well as a simplified design method, by using full-scale suspender experiments. The experiments were conducted on a 36 m prototype suspender cable of a bottom-through arch bridge, and two SDs were designed to control, respectively, the first- and second-mode cable vibrations. The damping effects were tested by placing the damper at different locations, and the robustness of the damper was investigated by varying the cable tension force and hence the cable frequency, to produce deviations from the frequency tuning condition. Furthermore, combined effects of the two SDs were studied. The experimental results are discussed and compared with theoretical results based on complex modal analysis of a taut cable equipped with a linear tuned mass damper. The properties of the SD vibrating with small amplitude were used in the theoretical analysis. The experimental results show that the SD is effective and robust for suspender cable vibration control. The comparison indicates that the analytical analysis generally gives conservative predictions of the damping ratios as long as the damper is installed close to an antinode of the mode shape of the target mode. This suggests that the theoretical analysis can be used for practical design of SDs.

Corrosion increases the nominal stress of reinforcing bars and accelerates the fatigue crack propagation. The stress redistribution induced by bond degradation between concrete and rebars makes the fatigue life prediction of reinforced concrete (RC) structures more complicated. This paper proposes a crack propagation-based fatigue life prediction method for corroded RC beams incorporating fatigue damage of concrete, fatigue bond degradation, and pitting corrosion. The fatigue damage of concrete is modeled based on plastic strain analysis. For the fatigue-worsened bond degradation between concrete and corroded rebars, a novel strain-incompatibility analysis method is developed to quantify the slip of reinforcements in concrete. The fatigue crack propagation parameters of rebars and the corrosion pit-induced stress concentration are experimentally obtained. The stress intensity for the fatigue crack at the corrosion pit root is calculated by an asymptotic interpolation method. Then, the fatigue failure analysis of corroded RC beams is performed, where the reinforcement fracture, concrete crush, and bond degradation-induced anchorage failure at beam ends are checked. The proposed method is verified by the test data. The effects of bond degradation and concrete damage on the fatigue life prediction are analyzed and discussed. The proposed method for fatigue life prediction gives a reasonable estimate of the service life of corroded RC beams.

All design specifications for steel reinforced concrete structures provide guidelines for the thickness of minimum concrete cover over the reinforcing steel. The thickness of the concrete cover is a function of many considerations such as cracking, migration of deleterious substances that can cause corrosion of steel, or constructability concerns. This paper examines the current state of practice for concrete covers for buried steel reinforced concrete structures from the perspective of chloride-induced corrosion. The evaluation is performed using the fully probabilistic fib model for chloride-induced corrosion. Results of parametric analysis based on the Monte Carlo simulation procedure are presented. Correlation is made with a reliability index to permit an evaluation of the current codes based on reliability principles.

This paper experimentally investigates a vibration-based scour monitoring approach applicable to bridges with multiple simply supported spans on shallow foundations. A monitoring strategy based on the relative changes in pier-mode shape amplitudes due to scour is postulated. The first global mode shape of a bridge structure with multiple spans is extracted from acceleration measurements using an output-only approach, frequency domain decomposition (FDD). The relative changes of the pier-mode shape amplitudes under scour are then tracked. Here, each pier-mode shape value is compared with the mean values of the remaining piers in a process that creates a mean-normalized mode shape (MNMS). The approach is demonstrated on a scaled model of a bridge with four spans, supported on sprung foundations, where scour is simulated by the replacement of springs, with springs of lower stiffness corresponding to a reduction in foundation stiffness. It is shown that at a given “scoured” pier, significant increases in the MNMS value occur, suggesting that the location of the scour can be identified. The magnitude of the MNMS at a given pier also increases with an increase in stiffness loss due to scour. In practice, the approach would work best by carrying out a visual inspection of the bridge to establish the initial health condition at the time of sensor installation. After this initial process, the bridge can be monitored remotely for scour on an ongoing basis.

In a hurricane event, bridges that span rivers near coasts are at risk of experiencing water rise and increased wave loads. Such riverine bridges often allow barges to pass underneath them on a daily basis, introducing the risk of barge collision. Considering that a barge collision can occur at any time prior to or during a hurricane, there are situations that a bridge pier damaged by a barge is not repaired when a hurricane occurs. This can be due to an inadequate assessment of pier damage, unavailability of resources for repair activities, or shortage of reaction time between the barge collision and the hurricane event. Such a multihazard risk, in which residual damage due to barge collision(s) increases the vulnerability of bridge piers to hurricane-induced wave loads, was largely unexplored in the literature. This motivated the current study to investigate a set of representative bridge piers under various barge collision and hurricane event scenarios. For this purpose, rigorous finite-element simulations are conducted to capture and compare the structural response of both intact and damaged bridge piers. With an in-depth understanding of deformation patterns and failure modes, the cumulative consequences of these two extreme events are determined in various combinations. This leads to the quantification of how hurricane-induced damage is magnified, making a bridge pier vulnerable to failure, as the extent of residual damage due to barge collision increases. The outcome of this systematic assessment is expected to help ensure the safety and functionality of the bridge structures that serve the coastal communities separated by rivers, especially during hurricane events.

An outdoor test was conducted on a prefabricated column–pile cap–pile system at a cohesive soil site. The half-scale test unit consisted of a precast bridge column, a precast pile cap, and eight steel piles. The components were connected utilizing socket connections that were preformed in the pile cap with corrugated steel pipes. To evaluate the system performance and the behavior of various connections, the test unit was subjected to combined vertical and lateral loads at service conditions as well as at conditions representing extreme events. The test unit remained undamaged under the loads representing the service conditions, and a plastic hinge was formed in the column under loading conditions representing a seismic event. The column connection and pile connections exhibited excellent behavior as they maintained fixity with the formation of a column plastic hinge. The outdoor test demonstrated that up to 40% of column top displacement was produced by foundation flexibility at the service conditions. The description of the outdoor test and key results are included in this paper.

Streamlined box girders are widely used when designing long-span bridges owing to their aerodynamic and aerostatic stability. However, the flutter performance of this type of girder requires improvement when they are employed in extreme wind load conditions. Based on wind tunnel tests and coupled flutter analysis, in this study, we attempted to improve the flutter performance of streamlined box girders by configuring them with an upper central stabilizer (UCS), which was then applied to a long-span suspension bridge being constructed in southern China with a main span of 1,666 m connecting Shenzhen and Zhongshan. Initially, aerostatic wind tunnel tests and free vibration tests were conducted in a wind tunnel. The results show that the girder configured with the UCS could have higher drag coefficients and could also reach a higher critical flutter speed than the ones without UCS, indicating that a higher UCS is not suitable for aerostatics, but the girder’s flutter performance was aerodynamically enhanced. Then, to investigate the dynamic mechanism behind this enhancement, flutter derivatives of the girder with UCS were extracted from forced vibration wind tunnel tests and used in flutter analysis. The calculated results agreed well with the test results. Finally, a series of parametric tests were conducted to analyze the dynamic mechanism of enhancement, including evaluation of the aerodynamic damping ratio, phase lag, amplitude ratio of vertical to torsional motion, and energy participation levels of the two types of motion. The analytical results revealed that the enhanced flutter performance of the box girders can be mainly attributed to an increase in the uncoupled aerodynamic damping ratio which is directly related to the flutter derivative, and changes in the phase lag, amplitude ratio, and energy participation level can be described as a unified result of the variation in the UCS height.

A series of seismic centrifuge tests were performed on an RC girder-type bridge with a 3 × 3 pile-group foundation embedded in dry sand to investigate the seismic behavior under various scour conditions. Based on the equivalent primary period and mass, the bridge plate was reduced to a lumped iron block supported by a single pier. The laminar shear box was excited in three earthquake events and one white noise event. The test results show that the bending moment at the pile head and the acceleration at the pile cap both increase significantly with increasing scour depth, which is a potential failure mode in practice. The maximum bending moment, which generally occurs under the soil surface at a distance of approximately 1.9–2.2 times the outer diameter of the pile, is the largest in the corner pile and the smallest in the inner pile. The results show that the maximum bending moment is augmented 63.5% at most by scour. The acceleration response and dominant frequency of the model were noticeably influenced by soil nonlinearity. However, the damping that soil in the far field provided to the bridge system considering soil–structure interaction (SSI) was negligible and has little influence on the system frequency. These observations suggested that measures should be taken to meet the bending moment demand of the pile increased by scour and provided some guidelines for the aseismic design of the bridge and a benchmark for further theory analysis.

Durability damage of reinforced concrete bridges in an offshore environment often occurs in varying degrees with the extension of service life. Meanwhile, statistical data on earthquake damage show that most of the main earthquakes are accompanied by strong aftershocks, and the seismic response of bridges under the main shock and main aftershock is different. To analyze the effects of the main aftershock sequence and durability damage on the seismic performance of concrete bridges, this study establishes a nonlinear dynamic analysis model of an offshore bridge with a continuous rigid-frame girder based on the OpenSEES platform. Moreover, this work constructs the main aftershock sequence considering the degradation of the mechanical properties of materials after durability damage repair under normal maintenance conditions and the time-varying seismic effect of shortening the subsequent service period, and investigates the time-varying seismic fragility of offshore bridges under the main aftershock sequence. Results show that the seismic response of bridge structures considering the main aftershock sequence is significantly larger than that considering the main shock only. Material deterioration will lead to the increase in the seismic response of bridge components under earthquake. The seismic time-varying fragility of offshore bridges considering material deterioration and seismic time-varying effects is analyzed based on time-varying seismic action in the entire life cycle. The influences of the two factors should be considered comprehensively when evaluating the seismic performance of bridges throughout their entire life.

This paper focuses on energy harvesting from low-frequency vibrations in bridges via an electromagnetic device. Two pre-stressed concrete highway bridges are considered as case studies. In situ vibration measurements are reported and analyzed. An electromagnetic vibration energy harvester (VEH) with a low resonant frequency (tunable around 4 Hz) has been designed. The VEH is of the cantilever type, with 12 magnets mounted on a beam and acting as an inertial mass. By electromagnetic induction, the moving magnets produce an electric current in a surrounding conductive coil. A single-degree-of-freedom model of the VEH is presented with the main purpose of estimating the electrical power generated under various operating conditions. A procedure for identifying the model parameters from simple measurements is described. Optimizing the coil geometry so as to maximize the electromechanical coupling is crucial to maximize the output power. That issue does not seem to have been addressed in the literature and is discussed in detail in this paper. The coil that has been fabricated approximates that optimal geometry. For harmonic excitation with normalized amplitude, the designed VEH achieves the best power density to date among experimentally validated low-frequency electromagnetic VEHs. During a field test on a highway bridge, the harvester produced an average power of 112 μW through a load resistance of 3.3 kΩ. We present a simple formula for estimating the output power of electromagnetic VEHs in terms of traffic intensity. That formula could be useful in future studies related to vibration energy harvesting in bridges.

This study presents a crack propagation stochastic process model for orthotropic steel deck (OSD) based on the structural health monitoring (SHM) data. An inhomogeneous compound Poisson process model, which is integrated into four types of Poisson models, is proposed to describe the daily random traffic flow. The transient analysis was performed by the finite element model (FEM) to turn the vehicle load model into fatigue stress model. The OSD strain measured data and calculated data by the FEM were compared to verify the computational result. Then, the crack propagation model was deduced by combining the stress model and fracture mechanics. Furthermore, the fatigue crack growth rate under different vehicles load sequence and overload vehicles is discussed. The results show that the loading sequence, which is the higher vehicle load in the front of the row, causes more fatigue damage than do the other loading sequences. The crack propagation slowed down under the overloading vehicle, and an overload correction factor is proposed, with value as 0.804 for engineering applications in this study.

The vibration serviceability assessment of footbridges under pedestrian traffic requires a probabilistic approach considering the uncertainty in the dynamic behavior of the structure and the variability of multiple load parameters, such as the pedestrians’ arrival time and step frequency. In view of engineering applications, a major challenge lies in the development, verification, and validation of efficient prediction models. With this challenge in mind, this paper uses a spectral approach to predict the dynamic response induced by unrestricted pedestrian traffic. A spectral load model available in the literature is extended to account for multiple harmonics of the vertical walking load and for application to arbitrary mode shapes. Furthermore, a closed-form expression is proposed to estimate the variance of the multimode structural response taking into account both resonant and nonresonant contributions. The performance of the proposed approach is evaluated for a simply supported beam as well as a real footbridge where multiple modes considerably contribute to the overall structural response. The results show that the proposed approach allows a good and mildly conservative estimate of the structural response to be obtained.

Pretensioned concrete girders—especially those having large prestress forces—are susceptible to flexural cracking at their top flanges near the girder end as a result of prestress transfer. One effective method to reduce such extreme-fiber stresses is to partially debond some of the strands. The 2017 edition of AASHTO LRFD Bridge Design Specifications provides limits on the number of strands that can be debonded at a given location and in each row of strands. The limits are attributed to an experimental study in which the test specimens were designed under the previous AASHTO Standard Specifications. Some states have allowed the AASHTO limits to be exceeded, while others have adhered to the limits. National Cooperative Highway Research Program Project 12-91 Strand Debonding for Pretensioned Girders was initiated to develop a unified approach to the design of partially debonded strand details in prestressed concrete bridge girders. Detailed design case studies and synthesis of experimental data suggest that the debonding ratio is not a sufficient metric by itself to gauge the performance and capacity of prestressed concrete girders. Despite having a greater extent of debonding than the 2017 AASHTO limits, girders meeting the requirements for shear and longitudinal reinforcement in end regions are expected to perform adequately in terms of strength, deformability, stiffness, crack widths, and modes of failure.

The sequence of loading during construction of simply supported skewed bridges influences the magnitude of stresses developed in the girders and is usually not explicitly addressed in design codes. Many designers and contractors use ad hoc methods to analyze the structural behavior during different construction phases of skewed bridges. Although bridge design permits unshored and shored construction, design guidelines to estimate the accumulation of skew girder stresses due to different load conditions (1) before the concrete hardening, and (2) after placing the asphalt layer and the barrier wall are as yet unavailable. In this paper, a three-dimensional finite element modeling was conducted to determine the moment and shear distribution factors of simply supported skewed composite I-girders under dead load conditions by considering different parameters, including skew angles, girder stiffness, cross-bracing layout, span length, and number of design lanes. Finally, the results signify the importance of considering the effect of moment and shear magnification factors for rational prediction of girder dead load stresses and support reactions, and to develop more realistic design guidelines for shored and unshored sequences of construction.

Since October 2007, the Federal Highway Administration (FHWA) has required the implementation of LRFD methods in all new bridge designs, including pile design. The resistance factors provided nationally for LRFD of driven piles are relatively conservative. Therefore, the Iowa Department of Transportation and Iowa State University collaborated and established regional resistance factors that are more efficient than those provided in the AASHTO Specifications, which are complemented with improved construction control methods. Iowa's LRFD guidelines for piles have been used in enough completed projects since 2012, allowing an assessment of the accuracy of the regional resistance factors and construction control methods. The piles used in these projects included both end-bearing piles in rock and friction piles. The friction piles were installed in cohesive, noncohesive, and mixed soil sites. The evaluation for the different pile categories and soil types found that the regional LRFD resistance factors developed were successfully applied in Iowa's driven pile design and effectively reduced the piles' contract lengths, resulting in cost–benefit over AASHTO's recommended resistance factors.

This paper presents a control strategy that simultaneously reduces vertical and lateral buffeting responses during the construction of China's Pingtang Bridge, a multiple-span, composite, cable-stayed bridge with supertall concrete towers. The buffeting performance of the bridge and its suppression under the most extended double-cantilever state were investigated via a wind-tunnel test of a 1:225 scale aeroelastic model. The model's modal properties were checked before testing. The vertical and lateral displacements at the cantilever end of the longest double-cantilever state were measured; buffeting responses of the bridge deck reached the maximal values in the yaw-wind case at some mean wind speeds. The inclined wind-resistant cables (WRCs) on both sides of the cantilevered spans were designed considering the pretension and inclination degree. The combination of vertical WRCs and lateral tuned mass dampers was also considered as an alternative measure. Results show that both measures can effectively control both vertical and lateral deck buffeting, especially for the inclined WRCs, and the reduction ratio is larger at a low wind speed than that at a high wind speed due to the aerodynamic damping effect.

Long-span continuous reinforced-concrete rigid-frame bridges are sensitive to the shrinkage and creep of concrete and the relaxation of prestressing tendons and have experienced problems related to serviceability loss because of excessive multidecade deflections. Moreover, the large negative bending moment and shear force in the box girder near the piers may lead to cracks in the top slabs and webs. To improve the structural performance and mitigate the long-term deflection of bridges, a novel type of open-web continuous reinforced-concrete rigid-frame bridge was developed during the design of the Beipan River Bridge with a 290-m main span. In this paper, the design and construction techniques of the novel bridge type are summarized first. Then, a structural analysis of the Beipan River Bridge is conducted. The results are compared with conventional rigid-frame bridges. Moreover, the long-term girder deflections are checked through the combined application of monitoring data and finite-element analysis. The results show that the bridge alignment is quite stable during the first 5 years in service and that the open-web design philosophy can effectively mitigate the long-term girder deflections.

The Luiz I Bridge is a century-old double-deck truss metallic structure over the Douro River in Porto, which was built to serve as a road and pedestrian link between the cities of Porto and Vila Nova de Gaia. For many years, this bridge has been submitted to high lateral vibration levels induced by pedestrians during the festivities of the St. John holiday that occurs every year in June, which arise from a phenomenon of pedestrian–structure interaction known as Lock-in. More recently, this structure has also been used during the athletic races that occur along the banks of the Douro River, some of which cross the lower deck of the bridge inducing high levels of vertical vibration. In order to measure these phenomena, the structure was instrumented with continuous dynamic monitoring systems in the context of the dynamic tests performed by the Faculty of Engineering of the University of Porto in the past few years. Within this scope, the main objective of this paper is to characterize the lateral and vertical vibration levels of both decks of the bridge measured since 2014 and to evaluate these vibration levels in terms of human comfort, by turning to the most recent guidelines in this area. The results of this investigation corroborate the adverse comments expressed by many people that use this structure.