Journal of Bridge Engineering

To evaluate the shear behavior of prestressed concrete (PC) beams with fiber-reinforced polymer (FRP) reinforcements, a total of seven large-scale beams, including one without stirrups, one with steel stirrups, and the remaining five beams with glass FRP (GFRP) stirrups, were tested to failure. Each beam was longitudinally reinforced with posttensioned carbon FRP (CFRP) tendons and nonprestressed GFRP bars. The main test parameters included concrete compressive strength and shear span-to-effective depth ratio (a/d) which varied between 2.0 and 4.0. The shear crack width was measured by using digital image correlation technology. Two shear failure modes, including shear compression and diagonal compression, were observed in the tested beams. All beams exhibited significant reserve strength after the diagonal cracks were fully developed. The ratio of the ultimate shear capacity to the shear load at which the critical shear crack formed ranged from 1.32 to 1.55. The shear capacity of the FRP-PC beams increased with an increase in the concrete compressive strength or reduction in the a/d. It was found that an arching mechanism was developed in the FRP-PC beams with a/d of 3.0 of less. The stirrup strain limit of 0.005 specified in the Canadian recommendation proved to be reasonable for GFRP stirrups, while the stirrup strain limits in American guidelines appeared to be conservative. In addition, a database of shear tests on FRP-PC members was collected to assess the performance of shear strength provisions.

Ballasted tracks are among the most widespread railway track typologies. The ballast possesses multiple functions. Among them, it significantly affects the dynamic interaction between a rail bridge and a moving load in terms of damping and load distribution. These effects entail accurate modeling of the track–ballast–bridge interaction. The paper presents a finite-difference formulation of the governing equations of the track and the bridge, modeled as Euler–Bernoulli (EB) beams, and coupled by a distributed layer of springs representing the ballast. The two equations are solved under a moving load excitation using a Runge–Kutta family algorithm and the finite-difference method for the temporal and spatial discretization, respectively. The authors validated the mathematical model against the displacement response of a rail bridge with a ballasted substructure. In a first step, the modal parameters of the bridge, obtained from ambient vibration measurements, are used to estimate the bending stiffness of an equivalent EB beam representative of the tested bridge. In a second step, the authors estimated the coupling effect of the ballast by assessing the model sensitivity to the modeling parameters and optimizing the agreement with the experimental data. Comparing the bridge’s experimental displacement responses highlights the ballast’s significant effect on the load distribution and damping. The considerable difference between the damping estimated from output-only identification and that determined from the displacement response under moving load proves the dominant role of the ballast in adsorbing the vibrations transmitted to the bridge under the train passage and the different damping sources under high-amplitude excitation. The authors discuss the tradeoff between model accuracy and computational effort for a reliable estimation of ballasted tracks response under moving loads.

Abstract

Wind-resistant rope systems (WRRS) consisting of wind guys (WGs) and ties are widely used in suspension bridges to improve their stability. Shape-finding of WGs is quite problematic due to their three-dimensional (3D) form and differs from that of the main cable. This study analyzed a WRRS with the 3D WG and obliquely intersecting ties. An analytical algorithm for the WG shape-finding in this system was developed and applied to five cases with different sets of known and unknown parameters. The recurrent relations between different parameters, namely, the horizontal force component of the WG, the deflection angle of the vertical plane where the catenary was located, and parameters of the shape equation, were derived based on the static equilibrium between the nodes, reducing the number of unknown quantities. The WG shapes were derived for various cases according to different governing conditions. The feasibility of the proposed algorithm was proved for the particular case study of a pedestrian suspension bridge, and cross-verification was provided for four cases. Besides, the finite-element method was employed to verify the accuracy of the proposed analytical approach. The calculation results revealed the following patterns of the horizontal force components in each catenary segment of the WG: they reached their maximum values at both ends of the WG, gradually decreasing from the ends to the middle and attained their minimum in the middle catenary segment of the WG. All WG nodes were located below the inclined plane passing through the anchor points at both ends and the middle node of the WG.

Practical Applications

Pedestrian suspension bridges are in a stage of rapid development and usually have relatively narrow decks with lower stiffness, which may cause a decrease in the wind-resistant performance especially when these bridges are located in valleys with high wind speeds. In this situation, the application of wind-resistant rope systems may be a great potential approach to increase the overall stiffness and improve the wind-resistant performance of the bridge. In addition, wind-resistant rope systems will be a highly feasible reinforcement measure for old suspension bridges with cumulatively fatigue damaged cables or poor performance under wind load. However, no matter how the wind-resistant rope systems are applied as the part of the structures, it is inseparable from refined shape-finding analysis of the wind-resistant rope system.

The incorporation of corrugated steel webs in prestressed concrete bridges has improved their structural performance. However, the low axial stiffness of the shear deformable corrugated steel webs affects the shear distribution in the section and its potential shear failure mode. Design engineers often assume that the corrugated steel webs resist all the shear force; however, there is the risk of shear failure in the concrete flanges near the diaphragms and point loads due to the interaction between the local flexure of the concrete flanges and the shear deformation of corrugated steel webs. However, there is limited research on the shear failure of concrete flanges. The shear distribution in the composite section and the shear failure in the concrete flanges were studied experimentally and numerically in this study. Tests showed that local shear failure could occur in the concrete flanges. A formula is proposed to estimate the shear capacity of the composite section considering a potential shear failure in the concrete flanges together with some design recommendations.

The deflection of a bridge under a dominant load, called key deflection is an important parameter that reflects the load-bearing capacity of in-service bridges. The impact vibration test is a good candidate for obtaining structural flexibility as well as deflection. However, traditional impact tests require accelerometers to be installed on the full bridge, which makes the test work very complicated. To address this issue, mobile impact testing with optimized substructures was proposed in this paper for rapid estimation of bridge key deflection. Using the basis that the deterioration of an in-service bridge is suitable for structural perturbation theory, the key deflection of an in-service bridge can be approximately expressed in the form of the weighted superposition of several main eigenvectors, which are calculated from the flexibility matrix of the structural finite element model. An optimized substructural impact test and virtual loading method were proposed to determine the weighting coefficients corresponding to the main eigenvectors and to obtain bridge key deflection. A numerical simulation illustrates that the proposed method can estimate bridge key deflection under different structural damage conditions and dominant loads. To verify the effectiveness of the proposed method in practice, the impact testing data of a continuous girder bridge are analyzed. The same key deflection estimation quality can be obtained from both the full bridge impact test and the proposed test method with a limited substructural area, which indicates that the proposed optimized substructural testing method greatly improves the test efficiency while ensuring the estimation accuracy.

This paper presents the formulation of a comprehensive risk-targeted performance-based seismic design (PBSD) framework involving the seismic design of bridge piers for California Ordinary Standard Bridges (OSBs), facilitating risk-informed design and decision making in the face of uncertainty. A full-fledged implementation of this all-inclusive design method formulated by retaining the inherent rigor of the underlying seismic performance assessment methodology might impose a seemingly prohibitive computational cost for the available resources in the current scenario of seismic bridge design practice. For reasons of practicability, the findings of the full-fledged design framework are inventively utilized to distill out a simplified and computationally more economical PBSD procedure. Its efficacy is validated using four already-built California testbed OSBs as cases in point. The proposed simplified design methodology is able to (1) find a design point in the primary design parameter space of a bridge to be designed for multiple risk-targeted performance objectives; and (2) delineate an approximate, yet sufficiently accurate, feasible design domain and identify the limit states controlling its boundary in the primary design parameter space of the bridge, at a computational cost significantly lower than that of the original method.

The preliminary design and comparisons of major technical and economic indicators between a steel-ultrahigh-performance fiber-reinforced concrete (UHPFRC) composite truss (SUCT) arch bridge and a concrete-filled steel tubular (CFST) arch bridge with both spans of 375 m are carried out in this study. Compared with the CFST arch bridge, the SUCT arch bridge can improve the durability of the bridge and has advantages in terms of steel consumption, self-weight, carbon emission, and other indicators due to the use of UHPFRC with high compressive strength as the arch ribs to bear the large axial forces. Adoption of the cyclic construction method for the SUCT arch bridge with two closure processes results in a total cost basically equivalent to that of the CFST arch bridge. For the K-joints in the connection area of the UHPFRC arch ribs and steel web members, a new hybrid connection form of “perforated shear connectors (PBL) + headed studs” is proposed. Loading tests in three directions in plane, pull-out tests, and parameter analysis are carried out. The experimental results show that the new hybrid connector is reasonable for the K-joints, which has advantages of large stiffness, short force transmission path, and high efficiency, and can ensure the continuity of steel fibers. Moreover, the new hybrid connector displays good shear performance, pull-out performance, and high bearing capacity. Based on the results of parameter analysis, the sensitivity of the pull-out bearing capacity to the three variables is compressive stress in the arch rib, followed by the tensile and compressive strengths of UHPFRC.

Structural health monitoring of bridges based on train-induced vibrations has attracted extensive attention and takes advantage of the high-magnitude and regularly spaced features of trainloads. However, the monitoring process is restricted because the relationship between bridge characteristics and the dynamic features of train-induced vibration responses is not well represented. In this study, train-induced acceleration characteristics of a bridge are investigated, and the relationship between the train speed and spectral amplitude of the bridge acceleration at a frequency equal to the ratio of the speed to carriage length is revealed. Based on the phenomenon that the speed–amplitude correlation trend is consistent with the structural frequency response function (FRF), a dynamic index called the equivalent frequency response function (EFRF) is proposed. The evolution rules of the EFRF curve with varying natural frequencies and train loads are distinguished, and the structural performance variation can be determined according to the relationship between the structural stiffness, natural frequencies, and EFRF. Because the speed–amplitude points are scattered due to the train configuration parameters and measurement noise, the EFRF curve should be fitted first. In addition, the normal fluctuation in the speed–amplitude points is limited using the local Shewhart control chart, considering the heteroscedasticity of the speed–amplitude points. Then, speed–amplitude points that exceed the control limits are used to identify abnormal train-induced vibrations. Finally, the monitoring data for a railway bridge with multiple lanes are considered to verify the proposed method. The results show that the abnormal train-induced vibration warning based on speed–amplitude points have a similar performance to that based on the speed–acceleration correlation, but the causes of the abnormal vibration can be identified explicitly only with the speed–amplitude correlation.

Full-scale laboratory tests were conducted to assess the fatigue performance of a new rib-to-floor beam (RFB) connection with a stress relieving slit for orthotropic steel decks (OSDs) in highway bridges. The slit rib-to-floor beam (S-RFB) connection combines aspects of the previously used fitted RFB connection and extended cut-out RFB connection. Different loading configurations were used to study the in-plane fatigue stress response and out-of-plane fatigue stress response of the S-RFB connection. Both static and cyclic fatigue loading tests were conducted. The test results indicate that the S-RFB connection provides good fatigue performance and that the AASHTO specifications for fatigue design of OSDs are applicable to the design of the S-RFB connection.

A bridge scour identification method was developed based on a time-frequency analysis that was combined with trend change detection. The basic concept behind this method is to probabilistically consider the interference-induced random variations in the natural frequencies to reveal their scour-induced change trends. First, the natural frequencies were instantaneously analyzed based on the bridge structural health monitoring (BSHM) data by time-frequency analysis. The probability distribution of the frequencies is obtained by kernel density estimation (KDE) and normalized by the probability integral transform theory. Then, based on the normal fluctuation in the frequencies that were defined by the control limits, an anomaly diagnosis for the frequencies is conducted using the control chart method. Continuously diagnosed anomalies are further regarded as a detected trend change in the frequencies, which is the key indicator to warn of scour in terms of the probability (P). Finally, the Jintang Bay Bridge, Zhoushan, Zhejiang Province, China, which is a 1,210-m-long cable-stayed bridge, was selected as a case study to comprehensively illustrate the application of this method using numerical simulations. The long-term BSHM field data from the Anqing Yangtze River Bridge, Anqing, Anhui Province, China, which is a 1,038.5-m-long cable-stayed bridge, were used as another case study to effectively prove the validity of this method in practice. These applications showed that the proposed bridge scour identification method that was based on time-frequency analysis and probabilistic trend change detection is effective. The developed methodology does not require any underwater devices and operations and could be conveniently integrated into a routine BSHM system.

In this study, seven one-third-scale bridge column specimens are tested via a quasi-static cyclic test to understand seismic performance differences between cast-in-place (CIP) and precast bridge columns with various shear span-to-depth ratios and connection design details. The columns are designed based on practical engineering application, which aims to provide design reference for the seismic behavior of real-world bridge structures with varying column heights, such as bridge ramps. Based on the test results, it was found that column height exceeding the plastic hinge region is of combined bending and shear failure and that the full development of the plastic hinge region of these columns yields the same damage progression. However, short columns that are lower than the height of the plastic hinge are subjected to pure shear failure, and they are also of the same level of seismic performance except for displacement-related indices. Though the strengthening effect of the grouted splice sleeve connections is observed and damage is more concentrated at the joint for precast bridge columns, the difference of overall seismic performance between CIP and precast bridge columns is less than 5% in terms of ductility and energy dissipation. The addition of shear keys or change of bond material help improve the structural integrity, while the increase of seismic performance is still limited.

Abstract

To overcome nonconvergence in the two-dimensional–three degrees of freedom (2D–3DOF) method, the practical modal-driven flutter analysis method (PMDFA) was proposed for the coupled flutter in long span bridges that used a genetic algorithm (GA). First, formulas in the 2D–3DOF method were updated when the assumed initial displacement was expressed as an exponential form for the frequency and damping. Then, the calculation results from the modified formulas proved to be identical to the exact solution that was calculated by the complex eigenvalue analysis (CEVA). However, due to the inherent defects in the iterative equations, the original fixed-point method (FPM) failed to converge when the frequencies of heaving and torsion were close. To overcome the convergence limitations in the FPM, a powerful GA without the restrictions of the iterative equation properties was introduced into the revised 2D–3DOF method. Then, the flutter analysis of suspension bridges with a main span from 1,000 to 5,000 m was carried out, and the numerical calculation showed that the FPM failed to complete the flutter calculation in most cases; however, the GA performed the analysis. In addition, a study on a suspension bridge showed that the numerical results obtained by the PMDFA were in reasonable agreement with the experimental results. Therefore, the proposed GA-based method has advantages of high accuracy and strong robustness and has wider application prospects in the flutter analysis of super long span bridges.

Practical Applications

Flutter instability can cause a large amplitude vibration and destroy a structure completely and it must be avoided during the service life of a structure. With an increase in the span, flutter performance has become an important index in the wind resistance design of long span bridges. The 2D–3DOF method can evaluate the flutter performance of structures effectively and establish a deep understanding between aerodynamic parameters and aerodynamic performance. Therefore, it plays an important role in the analysis of the flutter mechanism. However, due to the defect in the original convergence algorithm, sometimes it cannot calculate U_craccurately in practical engineering applications. Therefore, to overcome this problem, a GA was introduced into this paper to calculate convergence. The case study showed that the proposed GA-based method has the advantages of high accuracy and strong robustness, and could deal with the problem perfectly. In addition, the iteration problem of nonconvergence might occur in the other methods, such as the CEVA or the multimodal flutter analysis and the solution idea in this paper might have a certain reference value for the convergence calculation.

Fire is an accidental, severe hazard for bridges during their lifetime. Hangers in suspension bridges are among the most vulnerable components with respect to the hanger fatigue effect, and fatigue performance after fire exposure is vital to bridge safety. Therefore, a comprehensive assessment of the postfire hanger fatigue property is necessary. In this study, fatigue tests were conducted on steel wires after various elevated temperatures, and a multiparameter Weibull model was adopted to describe the fatigue data. Based on the fatigue life distribution of steel wires and the corresponding parallel systems, the hanger fatigue life was evaluated using the Monte Carlo simulation and order statistics approach, and the S–N curves were obtained. The results demonstrated that the fatigue life of the hanger was significantly lower than the mean life of the individual wires, and degraded as the exposure temperature increased. In addition, two small cables consisting of 19 parallel steel wires were tested for verification, and the results were consistent with those of the analytical model. The results of this study can be applied to quantify the extent of damage caused by fire and to assess the remaining hanger service life.

Vibration of highway bridges, although often ignored, is a serviceability issue that may contribute to concrete deck cracking and delamination. A recently constructed prestressed concrete bridge in the Dallas–Fort metroplex experienced extensive transverse deck cracks, potholes, and excessive vibration. The bridge was load-rated employing a novel and combined Nondestructive Evaluation (NDE) and load test method. Ground Penetrating Radar scans showed satisfactory concrete cover for the top reinforcement in the deck, indicating negligible surface wearing and construction error. Impact Echo scans of the top of the deck revealed severe concrete delamination at the top of the girders with fully cast-in-place (CIP) concrete and also at the interface of the precast deck panels and the CIP topping. The calculated neutral axis depths of the composite girders using an initial and follow-up load test after about a year were found to be in the web, indicating only 59% partially composite action. It was concluded that the excessive vibration was due to the deck delamination and the partial-composite action that reduced the stiffness of the superstructure. Both the deck and the composite girders can safely carry HS-20 live loading as required by the Texas Department of Transportation. However, the long-term bridge serviceability and durability could be compromised due to the concrete degradation and loss of stiffness.

This paper experimentally and numerically evaluates the participation of bridge rail in carrying live load through (1) performing field testing on steel and prestressed concrete girder bridges; (2) developing validated finite-element numerical models; and (3) performing parametric numerical investigations. The focus is on composite, steel and prestressed concrete multigirder bridges with an intact reinforced concrete rail that is integral to the deck. Measured data indicate that rails participate in carrying the live load, that gaps in rail in the positive moment region increase the strain in exterior girders, and that composite behavior is not fully developed near abutments. The parametric study on two- and three-span continuous steel and prestressed concrete girder bridges indicated the effect of different rail sections on behavior, that a discontinuity in rail at piers has negligible impact on positive moment behavior, and that a skew (up to 30°) also has negligible impact on positive moment behavior. This paper culminates in recommendations to evaluate girder bridges considering rail participation.

This paper presents the evaluation of three methods for manually estimating the elastic lateral-torsional buckling (LTB) resistance of general doubly and singly symmetric I-section members having any combination of transitions (steps) in the cross-section plate dimensions along the unbraced length. The study focuses on common unbraced lengths having idealized torsionally simply supported (fork) end conditions. Method 1 is a simple procedure specified in the AASHTO LRFD Specifications. Method 2 is a recently published procedure that seeks to estimate the LTB resistance via a length-weighted average cross-section approach. Method 3 is an extension of an approach that has been shown to be accurate and efficient for doubly and singly symmetric prismatic I-section members. Method 3 addresses a wide range of nonprismatic I-section member geometries and is recommended in AISC-MBMA Design Guide 25 2nd edition. Results from all three methods are evaluated by an extensive parametric study of I-girder unbraced lengths having various single or multiple cross-section transitions. On average, Method 2 provides the best predictions for single-curvature bending cases; however, certain cases are shown to exhibit undesirable unconservative errors. Method 3 provides the best predictions of the three methods for reverse-curvature bending cases, although the predictions tend to be highly conservative. This method gives slightly more conservative results than Method 2 for single-curvature bending cases, and it limits the worst-case unconservative errors to 7%.

Abstract

Load-posted bridges have potential effects on traffic, commerce, and emergency egress due to detours in routes between origins and destinations. Posted bridges can also be problematic for state departments of transportation from a management standpoint because they may call for more frequent maintenance, monitoring, and inspection. For these reasons, it is beneficial for states to minimize the number of load-posted bridges. This study investigates a continuous steel plate girder bridge superstructure and proposes a methodology for exploring the refined load rating of this bridge type in a safe manner through refined modeling and load testing. Load test results were used to examine live load distribution factors, and finite-element models were developed to refine load ratings. It was determined that the refined load-rating factors for the bridge are significantly higher than the currently posted limits, and therefore, the posting could be removed. The methodology presented in this paper can potentially be used to increase the load-rating factors for similar continuous steel girder bridges.

Practical Applications

The results of this case study suggest that some continuous steel girder bridges that were designed as noncomposite without shear studs may have unaccounted reserve capacity that can increase their load ratings. For a specific bridge or a group of the same type of load-posted bridges, refined analysis methods can be used to improve the load rating or potentially even remove the posting. Live load distribution factors may be determined through refined analysis to provide a more accurate estimate of the load distribution among girders. In addition, for certain bridges that are designed as noncomposite, the level of partial composite action can be determined through nondestructive load testing. Naturally, these refined analysis methods require more time and effort than a basic load rating analysis. However, the results could create a more manageable inventory for bridge owners and allow more trucks to use bridges currently posted for load, providing economic benefits.