Nonlinear Finite-Element Analysis of Posttensioned Concrete Bridge Girders

Posttensioning is an effective method for the construction of different types of bridge girders such as those used in segmentally erected bridges. Available nonlinear analysis programs for bridge girders under severe loading conditions are computationally expensive though. In addition, they neglect important phenomena such as bond-slip, friction, and anchorage losses. The objective of the proposed work is to develop a new nonlinear finite-element program for analysis of posttensioned bridge girders. The new model overcomes most of the difficulties associated with existing models. The model is based on the computationally efficient mixed formulation and considers bond, friction, and anchorage loss effects. The mixed formulation is characterized by its fast convergence, usually with very few finite elements and its robustness even under severe loading conditions. The posttensioning operation is accurately simulated using a phased-analysis technique, in which each stage of the posttensioning operation is simulated through a complete nonlinear analysis procedure. Correlation studies of the proposed model with experimental results of posttensioned specimens are conducted. These studies confirmed the accuracy and efficiency of the newly developed software program, which represents an advancement over existing commercial software packages for evaluating posttensioned bridge girders, in particular those subjected to severe loading conditions.     

Recommended Procedures for Simplified Inelastic Design of Steel I-Girder Bridges

This paper presents summary recommendations pertaining to new AASHTO procedures for simplified inelastic design of steel I-girder bridges. First, key developments are summarized that lead to the proposed inelastic design approach. The paper then outlines a set of equations that provide an improved characterization of the inelastic moment-rotation response for a wide range of I-beams and plate girders. Effective plastic moment predictions based on these equations are combined with the recently proposed design method, resulting in greater accuracy and simplicity of the proposed approach. The ease of use of the resulting procedure is illustrated by a design example.     

Reliability-Based Assessment of Suspension Bridges: Application to the Innoshima Bridge

Many suspension and cable-stayed bridges were designed and constructed between Honshu Island and Shikoku Island in Japan. All these bridges were designed according to the allowable stress design method. In the allowable stress design method, it is not possible to quantify the reliabilities of both bridge components and the entire bridge system. Therefore, in light of current reliability-based design philosophy, there is an urgent need to assess the safety of suspension bridges from a probabilistic viewpoint. To develop cost-effective design and maintenance strategies, it is necessary to assess the condition of suspension bridges using a reliability-based approach. This is accomplished by a probabilistic finite-element geometrically nonlinear analysis. This study describes an investigation into the reliability assessment of suspension bridges. The combination of reliability analysis and geometrically nonlinear elastic analysis allows the determination of reliabilities of suspension bridges. A probabilistic finite-element geometrically nonlinear elastic code, created by interfacing a system reliability analysis program with a finite-element program, is used for reliability assessment of suspension bridges. An existing suspension bridge in Japan, the Innoshima Bridge, is assessed using the proposed code. The assessment is based on static load effects. Reliabilities of the bridge are obtained by using 2D and 3D geometrically nonlinear models. Furthermore, damage scenarios are considered to assess the effects of failure of various elements on the reliability of undamaged components and on the reliability of the bridge. Finally, sensitivity information is obtained to evaluate the dominant effects on bridge reliability.     

Ritz-Based Static Analysis Method for Fiber Reinforced Plastic Rib Core Skew Bridge Superstructure

A Ritz-based static analysis procedure is described for fiber-reinforced plastic, skew bridge superstructure, or deck, with a parallel grid core. This is a simplified analysis method based on a transformed plate formulation and the classical Ritz method. The rib core bridge superstructure, or deck, is idealized as a homogeneous, orthotropic skew plate to which the Ritz method is applied to discretize the resultant, equivalent orthotropic skew plate. Three laminated skew plate examples are presented; the results are compared with finite-element solution to verify the validity of the simplified method. A practical demonstration of a rib core skew bridge superstructure is investigated using the simplified method. The procedure provides a useful analysis tool that can be used in the preliminary design stage without the use of finite-element analysis.     

Analytical Model of Circular CFRP Confined Concrete-Filled Steel Tubular Columns under Axial Compression

This study intends to provide a simplified analytical model of the laterally confined concrete filled steel tube (CCFT) column system which adopts carbon-fiber-reinforced polymer (CFRP) jackets in order to make up for major defects of the traditional concrete filled steel tube (CFT) column system. This CCFT analytical model, by adding one additional parameter for CFRP confinement to the CFT column analytical solution, is greatly simplified and expedites the analytical processes to explain the stress-strain relationship of the CCFT column system. In the study, several types of the CCFT column systems with different parameters are analyzed by the proposed simplified analytical model and its associated numerical program (USC-CFT). To verify the accuracy of the analytical model, this study compares the load-strain relationship calculated by USC-CFT both to the experimental results conducted by the traditional method and to the results calculated by the computer-aided finite element method (FEM) analysis method. This study shows equilibrium conditions, deformation compatibilities, constitutive models, and an analysis procedure used in the proposed simplified analytical solution and presents finite element models and analysis procedure used in FEM analysis.     

Seismic Restrainer Design Methods for Simply Supported Bridges

Existing restrainer design methods recommended by the American Association of State Highway and Transportation Officials (AASHTO) and the California Department of Transportation (Caltrans) to prevent unseating in simply supported bridges subjected to strong earthquakes were evaluated. Three new methods with different levels of complexity were developed: W∕2, modified Caltrans, and the equivalent linear static design for restrainers. The adequacy of different design methods was assessed using a nonlinear response history analysis computer program. Effects of different earthquakes, substructure stiffness, bearing strength, seat width, and skew angle were studied. It was found that in bridges with reinforced concrete pier caps the inherently wide supports help prevent unseating, and simple methods such the AASHTO and W∕2 method are satisfactory. In bridges with steel pier caps that provide narrow bearings the modified Caltrans method is recommended. The relatively involved equivalent linear static design for restrainers method is a more rational design procedure and leads to considerably fewer restrainers than others.     

Modeling Early-Age Bridge Restraint Moments: Creep, Shrinkage, and Temperature Effects

An increasing number of bridges are being designed with continuous spans instead of simple spans. By reducing the number of joints in a bridge, the traveling public receives a better riding surface and corrosion caused by leaking joints can be reduced. Also, redundancy is created when the system is made continuous, producing a tougher structure. However, a continuous system is more complicated to design and secondary restraint moments due to creep, shrinkage, and thermal effects can develop at the connection. This paper presents results from an experimental study done to monitor the early age restraint moments that develop in a two-span continuous system made of full-depth precast concrete bulb tee girders. The restraint moments observed were compared to the predicted restraint moments using the RMCalc program . The observed restraint moments were significantly lower than predicted by the program. Expansion of the deck during curing, which is generally not considered in the predictions, significantly influenced the early age restraint moments. A simplified model to predict the restraint moments considering thermal effects is proposed.     

Time-Dependent Behavior of Concrete-Filled Steel Tubular Arch Bridge

This paper develops a simplified method using a summation procedure and a related computer program to calculate the time-dependent behavior of a concrete filled steel tubular (CFST) arch bridge based on the geometric compatibility principle, a step-by-step time incremental process, and self-equilibrium equations. An experimental test on a scaled (1:5) segmental model of the main arch ribs of the Maocaojie Bridge was used to confirm the effectiveness of the proposed calculation method for evaluating the long-term behavior of CFST arch bridge under sustained load. It is concluded that: (1) the numerical results were in good agreement with the experimental results, demonstrating that the proposed analytical model is capable of predicting long-term effects for CFST arch bridges; (2) the stresses in the steel tubes increased, and the compressive stresses in the concrete decreased due to the effects of concrete creep and shrinkage. The maximum relaxation of the compressive stress in concrete due to concrete creep was 52.7% of the initial concrete stress, and the maximum increase of stress in the steel tubes was 27.3%; and (3) more than 90% of the total creep of the concrete took place in the first year. Subsequent creep of the concrete was limited because of the lack of water exchange between the structure and atmosphere and the reduction of compressive stress in the concrete.     

Multiflood and Multilayer Method for Scour Rate Prediction at Bridge Piers

The SRICOS method was proposed in 1999 to predict the scour depth versus time curve at a cylindrical bridge pier for a constant velocity flow, a uniform soil, and a deep-water condition. In this article, the method is extended to include a random velocity-time history and a multilayer soil stratigraphy; it is called the Extended-SRICOS or E-SRICOS. The algorithms to accumulate the effects of different velocities and to sequence through a series of soil layers are described. The procedure followed by the computer program to step into time is outlined. A simplified version of E-SRICOS called S-SRICOS is also presented; calculations for the S-SRICOS method can easily be done by hand. Eight bridges in Texas are used as case histories to compare predictions by the two new methods (E-SRICOS and S-SRICOS) with measurements at the bridge sites.     

Simplified Method for Calculating Lateral Distribution Factors for Live Load Shear

The simplified equal distribution factor (EDF) method for live load shear presented in this study originates from Henry’s method, a method that has been used in Tennessee for nearly forty years. Henry’s method allows for equal distribution of live load effects in all beams. This study focused on a careful examination and modification of Henry’s method by comparing shear distribution factors obtained from Henry’s method with those from finite element analysis and other code-specified methods for actual bridges. Twenty-four Tennessee bridges with six different types of superstructures were used in the study. The effects of structural parameters on the shear distribution factors were also studied. Modification factors to Henry’s method were proposed based on the comparison study. The proposed modification factors include structure type factors that are applied to different types of superstructures and a skew correction factor that is used to account for the effects of skew angle for skewed bridges. With proper modifications, the simplified EDF method can produce very reasonable and reliable distribution factors for live load shear.     

Nonlinear Flexural Behavior of Prestressed Concrete Girder Bridges

This paper presents a procedure to improve the accuracy of the classical grillage method for the nonlinear analysis of concrete girder bridges. The procedure uses equivalent element plastic hinge lengths that account for the actual mesh size instead of using a mesh-independent global plastic hinge length. A thorough review of the results of tests conducted on two 1∕3-model prestressed concrete girders and a 1∕3-model prestressed concrete girder bridge is undertaken in order to model the nonlinear properties of prestressed concrete girder bridges. The purpose of this review is to study the extent of plastification and plastic hinge length development as well as the evaluation of the validity of the grillage method for the nonlinear analysis of girder bridges. An Lp transfer model is used to calculate the plastic hinge length for every beam element of the grillage based on the results from the experiments and other empirical models. The Lp transfer model allows the use of empirical data obtained from tests on individual girders to model the response of a variety of bridge configurations subjected to different loading conditions. The equivalent grillage element plastic hinge length Lgp is calculated as a function of the grillage mesh size. A number of examples are presented to demonstrate the validity of the proposed method by comparing the analytical results of grillage analysis using the Lp transfer model with those of laboratory and in situ tests on full-scale and model-scale prestressed concrete bridges. The proposed approach has a high potential for use in engineering practice because of the simple input requirement and improved accuracy.     

Design Optimization Procedures for Fiber Reinforced Plastic Bridges

A simplified optimization procedure is described for a novel fiber reinforced plastic bridge system. The bridge system is modeled using a transformed anisotropic plate that is discretized using the Ritz method. This provides a structural model that is incorporated into a stiffness-based optimization algorithm using the optimality criteria method. The resulting procedure provides a useful design tool that can be used to produce a minimum weight design without resorting to finite-element analysis, which is only used to check the strength of the final design. A two-lane highway bridge serves as a demonstration problem.     

Simplified Method of Lateral Distribution of Live Load Moment

This paper introduces a simplified method, known as Henry’s method, for the calculation of distribution factors of the live load moment. Using the simplified method, the live load effects are equally distributed in all beams, including interior and exterior beams. This method has been used in Tennessee for nearly four decades. It offers advantages in simplicity of calculation and flexibility in application. To carefully examine the simplified method, 24 actual bridges of six different types of superstructures were selected for the study. The distribution factors of actual bridges using Henry’s method were compared with the ones from the AASHTO LRFD, the AASHTO standard, and finite-element analysis. In the comparison study, the effects of bridge superstructure types and key parameters that significantly affected the calculation of distribution factors are discussed. Based on the results of the comparison and evaluation, a modified Henry’s method was proposed by introducing modification factors to Henry’s method. With proper modification, the simplified method can be used to determine reasonable and reliable distribution factors of the live load moment.     

Equivalent Wheel Load Approach for Slender Cable-Stayed Bridge Fatigue Assessment under Traffic and Wind: Feasibility Study

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?m or 500?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.     

Torsional Design of Hybrid Concrete Box Girders

Hybrid concrete box-girder bridges that include prestressed slabs and corrugated steel webs provide a major improvement over traditional prestressed concrete box-girder bridges. To reduce the self-weight, high strength concrete is used for the top and bottom slabs and corrugated steel webs are employed for the webs. Because the weight of the girders has been reduced, the span length can be increased for more cost-effective design. A series of systematic tests on hybrid concrete box girders subjected to torsion has been performed. According to the test results, an analytical model was developed. Using the developed analytical model, a step-by-step procedure for torsional design of such bridges is presented in this article. Based on the design procedure proposed, a girder is designed by the analytical model and checked to satisfy structural codes.     

Transverse Analysis of Strutted Box Girder Bridges

The computer program STRUTBOX is presented for the transverse analysis of strutted box girder bridges, and particularly for bridges designed and constructed using the strutted box widening method. The program allows the deck prestressing and other reinforcing to be proportioned for transverse flexure, and the web stirrups and slab reinforcing to be proportioned for longitudinal shear and torsion. The program also gives an indication as to the severity of shear lag effects. The program is based on the folded plate method and is no more difficult to use than a plane frame computer program. The paper also demonstrates how the results given by a folded plate analysis can be approximated by using some simple membrane force equations in conjunction with a plane frame analysis. What is particularly interesting is that there is danger in using a plane frame analysis alone to approximate the results of a folded plate analysis for strutted box girder bridges (as well as other box girder bridges) because there are significant differences in the axial force diagrams given by the two methods.     

Behavior of Split Timber Stringers Reinforced with External GFRP Sheets

A large number of timber bridges are at the end of their service life in North America and the prohibitive costs of replacement make owners face the challenge of developing efficient rehabilitation techniques. This paper presents the results from an experimental program of testing old full scale timber stringers with longitudinal splits. Stringers were reinforced for shear and bending using glass fiber-reinforced polymer (GFRP) sheets. A total of nine full-scale Douglas-fir beams were tested in three-point bending after strengthening for flexure and shear with GFRP sheets. Horizontal shear forces in shear reinforcement were calculated using a simplified model. Beams that failed by debonding of shear reinforcement, failed at horizontal shear forces within the range of 150–266?kN. Design charts were constructed on the basis of these calculated forces to simplify the design of shear reinforcement for different sizes and locations of splits.     

Simplified Inelastic Design of Steel Girder Bridges

Inelastic design of steel girder bridges can result in beneficial material and fabrication cost savings and reduce the susceptibility of steel girder bridges to fatigue. The ability to redistribute large negative region moments, coupled with section capacities exceeding the yield moment, results in an efficient structure used to its limit-state capacity. Proposed LRFD inelastic design provisions are presented that allow compact or noncompact pier sections resulting in consistent bridge design across the steel girder bridge inventory. This paper illustrates the simplified inelastic design provisions, presents an example design of a two-span composite bridge comprising noncompact sections at the pier, and summarizes the experimental verification of the example design. The proposed inelastic design procedures are simple to apply, removing the cumbersome continuity and iterative requirements of past inelastic design practice.     

Anchorage of External Tendons in End Diaphragms

External posttensioning tendons in concrete box girder bridges are usually anchored in very massive end diaphragms. Several incidences of distress of such diaphragms have been reported in the literature. This paper presents the results of an analytical and experimental research program on design and behavior of end diaphragms when used for the anchorage of external tendons. Finite-element analysis results, strut-and-tie models, and results of a physical test series of half-scale specimens are included. The strut-and-tie model approach is shown to be an effective method to describe the flow of forces in the structure and for design. Ultimate strength predictions based on simple strut-and-tie models were safe but quite conservative. Refined strut-and-tie models based on finite-element analysis results were required to arrive at satisfactory reinforcement arrangements for crack control.