Journal of Bridge Engineering

A new methodology for concurrent dynamic analysis and structural fatigue prognosis is proposed in this paper. The proposed methodology is on the basis of a novel small time scale formulation of material fatigue crack growth that calculates the incremental crack growth at any arbitrary time within a loading cycle. It defines the fatigue crack kinetics on the basis of the geometric relationship between the crack tip opening displacement and the instantaneous crack growth rate. The proposed crack growth model can be expressed as a set of first-order differential equations. The structural dynamics analysis and fatigue crack growth model can be expressed as a coupled hierarchical state-space model. The dynamic response (structural level) and the fatigue crack growth (material level) can be solved simultaneously. Several numerical problems with single degree-of-freedom and multiple degree-of-freedom cases are used to show the proposed methodology. Model predictions are validated using coupon testing data from open literature. Following this, the methodology is demonstrated using a steel-girder bridge. The proposed methodology shows that the concurrent structural dynamics and material fatigue crack growth analysis can be achieved. The cycle-counting method in the conventional fatigue analysis can be avoided. Comparison with experimental data for structural steels and aluminum alloy shows a satisfactory accuracy using the proposed coupled state-space model.

For the fatigue design of aluminum structures, most applicable international codes specify fatigue-resistance (S-N) curves with slopes that vary, depending on the detail category. This complicates the selection of appropriate damage equivalence factors for use in highway bridge applications. The existing codes also differ in their treatment of high cycle fatigue, with single-slope S-N curves specified in some cases and multislope curves specified in others. In this paper, a recent investigation conducted to examine the fatigue behavior of aluminum welds under in-service highway bridge loading conditions is summarized. Specifically, calculations performed to establish damage equivalence factors for aluminum for use with the AASHTO and Canadian Standards Association (CSA) CAN/CSA-S6 codes are first reviewed. Following this, small-scale fatigue tests of aluminum welds under simulated highway bridge loading conditions are described. A fracture mechanics model is then validated by comparison with the test results and used to perform simulations encompassing a wider range of loading conditions. On the basis of this work, the adequacy of the current design provisions is discussed and possibilities for further extending the employed methodology are identified.

This study evaluates the performance of various methods to prevent and repair fatigue damage in welded connections, a recurring problem that affects a significant number of steel bridges. Experimental tests and analytical simulations were carried out to investigate the fatigue performance of coverplate specimens in which the welded connections were reinforced with carbon-fiber reinforced polymer (CFRP) overlays. Specimens were loaded in three-point bending induced by a cyclic load to evaluate the change in fatigue-crack initiation life of the welded connections caused by the attachment of the CFRP overlays. Test results showed that when bond between the CFRP overlays and the steel was maintained, the reduction in stress demand was sufficient to extend the fatigue life of the welded connections from AASHTO fatigue-design Category E’ in the unreinforced configuration to the infinite fatigue life range. Test results also showed that the fatigue strength of the bond layer was drastically improved by introducing breather-cloth material within the bond layer.

A critical aspect in the design of tubular bridges is the fatigue performance of the structural joints. The estimation of a fatigue crack life using the linear elastic fracture mechanics (LEFM) theory involves the calculation of stress intensity factors (SIF) at a number of discrete crack depths. The most direct way is to carry out modeling by either the finite-element method (FEM) or the boundary-element method (BEM). For tubular joints commonly found in tubular bridges and off-shore structures, due to the complicated geometry resulting from the tube intersections and welding, the construction of the numerical model often becomes a complex process. This paper presents two different model construction techniques that have been developed independently at the Swiss Federal Institute of Technology (EPFL) and the Nanyang Technological University (NTU), Singapore, that are based in the BEM and the FEM, respectively. The SIF values obtained by these two methods are compared. It is found that as long as consistent geometric models are employed, compatible SIF values can be obtained by both approaches. The best and the most consistent values are obtained for the deepest point along the crack front and should be used for fatigue-life computations.

During the life cycle of a bridge, dynamic impacts due to random traffic loads and deteriorated road surface conditions can induce serious fatigue issues for bridge components. It is necessary, and more realistic than the deterministic approach, to use reliability methods and treat the input parameters as random variables for the vehicle-bridge dynamic system. This paper presents a framework of fatigue reliability assessment for existing bridges in lifetime serviceability considering the random effects of vehicle speed and road-roughness condition. Since each truck passage might generate multiple stress ranges, revised equivalent stress-range is introduced to include fatigue damage accumulations for one truck passage. Therefore, the two variables, i.e., the stress-range numbers and equivalent stress ranges per truck passage, are coalesced in the newly defined variable based on equivalent fatigue damage. The revised equivalent stress-range is obtained through a fully-computerized approach toward solving a coupled vehicle-bridge system, including a three-dimensional (3D) suspension vehicle model and a 3D dynamic bridge model. At each truck-pass-bridge analysis, deteriorations of the road-roughness condition are considered, and the vehicle speed and road surface profile are generated randomly. When the stress-range threshold is 3.45 Mpa (0.5 ksi) or below, lognormal distribution is proven a good model to describe the revised equivalent stress-range. In addition to the assumptions of other input random variables being normal or lognormal, fatigue reliability index and fatigue life for a target fatigue reliability index are predicted. The effects of the road surface condition, vehicle speed, and annual traffic increase rate on the fatigue reliability index and fatigue life are also discussed.

An evaluation of concrete reinforcing bar fatigue provisions of AASHTO LRFD Bridge Design Specifications as they pertain to the use of high-strength reinforcing steel is presented. Two large-scale proof tests and a review of available published data demonstrate that presently accepted values for the fatigue or endurance limit for reinforcing steel are applicable, and likely conservative, when applied to higher-strength bars. A minor revision to the AASHTO specification is proposed to eliminate the fatigue penalty resulting from the use of higher-strength reinforcing steel. Finally, it is shown that fatigue considerations will rarely affect the design of typical reinforced-concrete members having a specified yield strength, $f_y\le 690\mathrm{MPa}$.

Resistance (load-carrying capacity) of a bridge girder is a random variable and can be determined by considering the uncertainty in material, fabrication, and professional/analysis properties. Previous calibrations of load and resistance factor design (LRFD) determined the distribution of bridge resistance on the basis of data from more than 30 years ago. This study uses the latest Material properties available in, the literature to update the resistance distribution. The statistical distribution of the resistance was determined through Monte Carlo simulation. The results of the analysis show an increase in bias and a decrease in the coefficient of variation (COV) for all types of bridges in comparison with those used in previous calibration studies. The changes in bias and COV are the result of higher bias and lower COV in material properties owing to better quality control in concrete and steel manufacturing. Steel and concrete bridges saw the greatest change in resistance distribution. Prestressed bridges saw little change because the material properties of prestressing steel, which is the most sensitive parameter in the prestressed bridges, did not change significantly since the previous calibration study. With these resistance distributions, it is expected that the calibration of the load factor in the AASHTO specification will lead to a lower live load factor, thereby possibly reducing the material cost of the bridge. In addition, the ratio of actual to required (design) resistances of representative bridges in Missouri was determined. The analysis showed that almost all representative bridges had a capacity-to-demand ratio greater than 1 according to current AASHTO standards.

A fracture-critical bridge (FCB) is a structure that is expected to collapse after the failure of an essential tension component. In the positive bending moment region, the bottom flanges of a twin steel box-girder bridge are considered to be fracture-critical elements. Bridges with fracture-critical elements are required to undergo stringent hands-on inspections at least every two years. These inspections, which often require lane closures, are labor intensive and costly. There have been multiple cases of FCBs that have experienced a failure in one of their fracture-critical elements without collapsing, which suggests that current provisions may not accurately account for the inherent redundancy that exists in various FCB structural systems. To improve the understanding of how a twin steel box-girder bridge behaves after suffering a full-depth fracture in one of its girders, simplified analytical methods have been developed and are presented in this paper. The proposed methodology has been validated against data from full-scale tests and provides a convenient means for predicting response.

As a result of construction problems with curved I-girders, increased tub girder research, and improved fabrication techniques, twin steel tub girder superstructures are increasingly more common for curved highway ramps. Historically, however, choosing a twin tub girder bridge instead of a bridge composed of three or four I-girders has resulted in a nonredundant or “fracture critical” designation for the bridge. This paper presents results from an analytic investigation of the redundancy of twin steel tub girder bridges. Parametric nonlinear finite-element analyses are used to determine the role of different bridge components in developing load transfer from a damaged girder to an undamaged girder. The key parameters of span length, bridge continuity, curvature, location of girder damage, and type and spacing of external bracing are investigated. The results of this study indicate that twin steel tub girder bridges can be classified as redundant if the bridge is designed in accordance with the AASHTO Load and Resistance Factor Design (LRFD) design code and additional design and proportioning criteria are incorporated. Minimum design criteria are proposed to allow for a redundant classification, thus reducing fabrication and maintenance/inspection costs for this increasingly popular bridge type.

Historical data show that terrorist attacks against transportation assets have increased in recent years and that the vast majority of these attacks have been bombings. As such, there is growing interest in protecting highway infrastructure from blast loads. To address this concern, the National Cooperative Highway Research Program (NCHRP) sponsored a project to investigate the performance of highway bridges subjected to the nearby detonation of an explosive, and this paper presents research that advances the understanding of blast loads acting on bridge columns. Unlike large wall panels for which much of the existing knowledge about blast effects against structures has been established, the research presented in this paper focuses on slender structural components in which the effects of cross-sectional geometry, engulfment of blast pressures, and clearing effects strongly influence loading history. Based on the findings obtained from this study, a simplified procedure for predicting blast loads acting against bridge columns is proposed.

Hangers in arch bridges and other long vertical bars in truss bridges are typically slender members and often adopt an aerodynamically unfavorable H-section due to the conveniences in manufacture, construction, and maintenance. In contrast to the very narrow range of wind attack angles of horizontal members, hangers may suffer wider wind attack angles, possibly from 0° to 360°, and are therefore more prone to wind-induced vibrations. In August 2006, large torsional vibration with severe damage was observed on the 13 longest hangers of the Dongping arch bridge in China during a strong wind. While vibrations of hangers were usually caused by galloping, and vortex shedding excitation, the present case was likely to be a kind of torsional flutter instability. Therefore an in-depth investigation on the hangers’ aerodynamic performances in forms of flutter, galloping, and vortex shedding has been conducted through a series of wind tunnel tests. First, with section model and aeroelastic models tests of the longest hanger in the bridge, the observed field vibration is confirmed as torsional flutter under large attack angles from 15° to 25°, and the experimental onset velocity coincides well with the field observation; the flutter derivative $A_2^{*}$ becomes positive at a low reduced wind velocity, which further implies that the H-section is prone to flutter instability. Then, the influences of web perforation on flutter, galloping, and vortex shedding are studied with four section models having different web perforation ratios but the same depth-to-width ratio $D/B=0.416$ (flange depth $D$ to web width $B$). It is found that the web perforation may increase the galloping critical velocity to some extent but have no obvious effects on flutter instability and the Strouhal numbers, at least for the shallow H-section with $D/B=0.416$. Next, a total of 16 H-section models with different $D/B$ ratios, web perforation ratios, and flange perforation ratios are tested to investigate their effects on aerodynamic behaviors of hangers. A comparison of the experimental results with previous work is made, which may explain why the flutter instability of H-shaped hangers under large attack angles was not treated by earlier investigators.

The displacement-based seismic-design (DSD) methods, owing to their simplicity and efficiency, have been more and more recognized in structural seismic-research communities during the past few years. However, the dynamic $P\mathrm{\text{-}}\Delta$ effect, as has long been well realized to be a key issue in structure earthquake engineering that could amplify the structure’s seismic responses or even trigger the structure’s instability, is still not well solved practically because of the complicated nonlinear mechanism. Therefore, in aim to achieve a practical and general purpose solution to consider the $P\mathrm{\text{-}}\Delta$ effects in various DSD methods for single-degree-of-freedom (SDOF) systems, first, the existing approaches of considering $P\mathrm{\text{-}}\Delta$ effects in current seismic analysis and design were evaluated by carrying out a large set of nonlinear time-history analyses, and then new design formulas and recommendations on threshold of neglecting $P\mathrm{\text{-}}\Delta$ effects and the allowable design thresholds were promoted on the basis of the statistics data. At last, the proposed procedure was illustrated by a seismic-design example.

Movement of industrial freight infrequently requires special overload vehicles weighing 5 to 6 times the normal legal truck weights. The gross vehicle weight of the vehicles frequently exceeds 1800 kN whereas, the normal interstate legal limit in the United States is 356 kN. Because of the unusual configuration of the vehicles, it is difficult to analyze the effect of these loads on highway bridges by using current simplified analysis methods. This report aims to provide modified moment and shear load distribution factor equations for the vehicles to quickly determine their effects on multigirder bridges. Finite element analyses of 118 multigirder bridges and 16 load cases of overload vehicles for each multigirder bridge were performed, and the load distribution factor equations for the multigirder bridges were proposed on the basis of the analysis results. Various configurations of the vehicles, number of bridge spans, skew angles of the bridge and diaphragms were considered in developing the equations. The developed equations were found to be capable of replacing a time-consuming 3D finite element analysis rationally and conservatively.

This paper describes the results of numerical simulations performed to investigate the spalling mechanism observed in several partial-depth precast prestressed concrete (PPC) bridge decks. Corrosion-induced cracking of prestressed steel reinforcement and panel butting were modeled using 2D finite element analysis to examine the nature of crack propagation that triggers the spalling effect observed. A parametric study was carried out on the basis of field observations from several bridges. FEM results showed that spalling is sensitive to side and bottom cover, and spacing of reinforcement attributable to bridging cracks. Findings indicate that the spalling mechanism is triggered by the presence of a critical bridging crack.

Temporary shoring supports are used in construction of horizontally curved bridges to help ensure that the final constructed geometry is maintained by mitigating excessive girder deformations. Limited guidance currently exists in available design specifications and guidelines with respect to optimal placement of shoring towers because the number and locations of these supports are often site specific. However, if preliminary information could be provided to bridge designers and constructors with respect to shoring tower placement as a function of global curved bridge parameters, such as number of spans and radius of curvature, the amount of time required to specifically locate and proportion the towers could be reduced. This research aimed to examine the effects of shoring tower positioning on curved bridge behavior at different stages of construction. Sequential analyses of multiple idealized double-span curved bridges with varying radii were conducted using nonlinear finite-element models and vertical deformations and rotations of the girders, and shoring tower reactions were compared for different shoring support locations and different erection sequences. On the basis of the results, optimal shoring locations were obtained for the curved girders at different construction stages.

Current AASHTO specifications provide engineers with a temperature gradient across the depth of the cross section to predict the vertical thermal behavior of bridges. This gradient is based on one-dimensional heat flow and does not account for change in the cross section, as found in prestressed concrete girders, nor does it account for thermal effects on the sides of the girder. Furthermore, the current specifications do not provide the transverse temperature gradient that is needed to predict the lateral thermal behavior of the girders, especially during construction, before the placement of the bridge decks. To determine the transverse and vertical temperature gradients in prestressed concrete girders, experimental and analytical studies were conducted on a prestressed BT-63 concrete girder segment. The analytical results were found to be in good agreement with experimental measurements. The analytical model was then used to determine the seasonal temperature gradients in four standard PCI girder sections at selected cities in the United States. On the basis of these findings, vertical and transverse temperature gradients were developed to aid engineers in predicting the thermal behavior of prestressed girders during construction.