A Review of the Key Points in the Design of Small-Radius Curved Ramp Bridges

This article explores the fundamentals of small-radius curved ramp bridges.It covers the selection of box girder spans,support methods,and forms,along with design optimization techniques for this type of bridge structure.The purpose of this paper is to provide robust support for enhancing the design quality of these bridges and ensuring their efficacy in real-world applications.

Seismic fragility analysis of three-tower cable-stayed bridges with different connection configurations

Seismic fragility analysis of three-tower cable-stayed bridges with three different structural systems,including rigid system(RS),floating system(FS),and passive energy dissipation system(PEDS),is conducted to study the effects of connection configurations on seismic responses and fragilities.Finite element models of bridges are established using OpenSees.A new ground motion screening method based on the statistical characteristic of the predominant period is proposed to avoid irregular behavior in the selection process of ground motions,and incremental dynamic analysis(IDA)is performed to develop components and systems fragility curves.The effects of damper failure on calculated results for PEDS are examined in terms of seismic response and fragility analysis.The results show that the bridge tower is the most affected component by different structural systems.For RS,the fragility of the middle tower is significantly higher than other components,and the bridge failure starts from the middle tower,exhibiting a characteristic of local failure.For FS and PEDS,the fragility of the edge tower is higher than the middle tower.The system fragility of RS is higher than FS and PEDS.Taking the failure of dampers into account is necessary to obtain reliable seismic capacity of cable-stayed bridges.

Regularity classification and corresponding analysis method requirements of horizontally curved bridges with unequal pier heights

The seismic behavior of horizontally curved bridges,particularly with unequal height piers,is more complicated than that of straight bridges due to their geometric properties.In this study,the seismic responses of several horizontally curved single-column-bent viaducts with various degrees of curvature and different pier heights have been investigated,employing three different analysis approaches:namely,modal pushover analysis,uniform load method,and nonlinear time history analysis.Considering the investigated bridge configurations and utilizing the most common regularity indices,the results indicate that viaducts with 45-degree and 90-degree deck subtended angles can be categorized as regular and moderately irregular,respectively,while the bridges with 180-degree deck subtended angle are found to be highly irregular.Furthermore,the viaducts whose pier heights are asymmetric may be considered as irregular for almost all ranges of the deck subtended angles.The effects of higher transverse and longitudinal modes are discussed and the minimum analysis requirements are identified to assess the seismic response of such bridge configurations for design purposes.Although the Regularity Indices used here are useful tools to distinguish between regular and irregular bridges,further studies are needed to improve their reliability.

Dynamic Characteristics of a Curved Cable-stayed Bridge:Operational Modal Testing and FE Modeling

This paper summarizes the analytical and experimental dynamic analyses carried out to assess the actual dynamic behaviour of a curved cable-stayed bridge,recently erected in the commercial harbour of Porto Marghera ( Venice,Italy). Ambient vibration tests were carried out to determine the dynamic characteristics of the bridge and more than 20 modes were identified in the frequency range 0～10Hz. In the theoretical study,a 3D FE model of the bridge was developed using an integrated CAD-FEA approach; subsequently,the information obtained from the field tests,combined with simple manual tuning,provided a linear elastic model,accurately fitting the modal parameters of the bridge in its present condition.

Recent Construction Technology Innovations and Practices for Large-Span Arch Bridges in China

Arch bridges provide significant technical and economic benefits under suitable conditions.In particular,concrete-filled steel tubular(CFST)arch bridges and steel-reinforced concrete(SRC)arch bridges are two types of arch bridges that have gained great economic competitiveness and span growth potential due to advancements in construction technology,engineering materials,and construction equipment over the past 30 years.Under the leadership of the author,two record-breaking arch bridges—that is,the Pingnan Third Bridge(a CFST arch bridge),with a span of 560 m,and the Tian’e Longtan Bridge(an SRC arch bridge),with a span of 600 m—have been built in the past five years,embodying great technological breakthroughs in the construction of these two types of arch bridges.This paper takes these two arch bridges as examples to systematically summarize the latest technological innovations and practices in the construction of CFST arch bridges and SRC arch bridges in China.The technological innovations of CFST arch bridges include cable-stayed fastening-hanging cantilevered assembly methods,new in-tube concrete materials,in-tube concrete pouring techniques,a novel thrust abutment foundation for nonrocky terrain,and measures to reduce the quantity of temporary facilities.The technological innovations of SRC arch bridges involve arch skeleton stiffness selection,the development of encasing concrete materials,encasing concrete pouring,arch rib stress mitigation,and longitudinal reinforcement optimization.To conclude,future research focuses and development directions for these two types of arch bridges are proposed.

Data-driven methods for predicting the representative temperature of bridge cable based on limited measured data

Cable-stayed bridges have been widely used in high-speed railway infrastructure.The accurate determination of cable’s representative temperatures is vital during the intricate processes of design,construction,and maintenance of cable-stayed bridges.However,the representative temperatures of stayed cables are not specified in the existing design codes.To address this issue,this study investigates the distribution of the cable temperature and determinates its representative temperature.First,an experimental investigation,spanning over a period of one year,was carried out near the bridge site to obtain the temperature data.According to the statistical analysis of the measured data,it reveals that the temperature distribution is generally uniform along the cable cross-section without significant temperature gradient.Then,based on the limited data,the Monte Carlo,the gradient boosted regression trees(GBRT),and univariate linear regression(ULR)methods are employed to predict the cable’s representative temperature throughout the service life.These methods effectively overcome the limitations of insufficient monitoring data and accurately predict the representative temperature of the cables.However,each method has its own advantages and limitations in terms of applicability and accuracy.A comprehensive evaluation of the performance of these methods is conducted,and practical recommendations are provided for their application.The proposed methods and representative temperatures provide a good basis for the operation and maintenance of in-service long-span cable-stayed bridges.

Seismic Performance of Prefabricated Continuous Girder Bridge

Bearings are the weak link in the seismic design of bridges.Using a continuous girder bridge as an example,it is demonstrated that bearing damage should be considered under large earthquake conditions.The bearing,acting as a fuse-type unit,can be designed to be preferentially damaged to effectively control the displacement of the beam and the response at the base of the pier during an earthquake.

Dynamic Response of Sea-Crossing Rail-cum-Road Cable-Stayed Bridge Influenced by Random Wind–Wave–Undercurrent Coupling

Sea-crossing bridges are affected by random wind–wave–undercurrent coupling loads, due to the complex marine environment. The dynamic response of long-span Rail-cum-Road cable-stayed bridges is particularly severe under their influence, potentially leading to safety problems. In this paper, a fluid–structure separation solution method is implemented using Ansys–Midas co-simulation, in order to solve the above issues effectively while using less computational resources. The feasibility of the method is verified by comparing the tower top displacement response with relevant experimental data. From time and frequency domain perspectives, the displacement and acceleration responses of the sea-crossing Rail-cum-Road cable-stayed bridge influenced by wave-only, wind–wave, and wind–wave–undercurrent coupling are comparatively studied. The results indicate that the displacement and acceleration of the front bearing platform top are more significant than those of the rear bearing platform. The dominant frequency under wind–wave–undercurrent coupling is close to the natural vibration frequencies of several bridge modes,such that wind–wave–undercurrent coupling is more likely to cause a resonance effect in the bridge. Compared with the wave-only and wind–wave coupling, wind–wave–undercurrent coupling can excite bridges to produce larger displacement and acceleration responses: at the middle of the main girder span, compared with the wave-only case, the maximum displacement in the transverse bridge direction increases by 23.58% and 46.95% in the wind–wave and wind–wave–undercurrent coupling cases, respectively;at the tower top, the variation in the amplitude of the displacement and acceleration responses of wind–wave and wind–wave–undercurrent coupling are larger than those in the wave-only case, where the acceleration change amplitude of the tower top is from-0.93 to 0.86 m/s^(2) in the waveonly case, from-2.2 to 2.1 m/s^(2) under wind–wave coupling effect, and from-2.6 to 2.65 m/s^(2) under wind–wave–undercurrent coupling effect, indicating that the tower top is mainly affected by wind loads, but wave and undercurrent loads cannot be neglected.

Process Monitoring and Terminal Verification of Cable-Stayed Bridges with Corrugated Steel Webs under Contruction

In this paper,the construction process of a cable-stayed bridge with corrugated steel webs was monitored.Moreover,the end performance of the bridge was verified by load test.Owing to the consideration of the bridge structure safety,it is necessary to monitor the main girder deflection,stress,construction error and safety state during construction.Furthermore,to verify whether the bridge can meet the design requirements,the static and dynamic load tests are carried out after the completion of the bridge.The results of construction monitoring show that the stress state of the structure during construction is basically consistent with the theoretical calculation and design requirements,and both meet the design and specification requirements.The final measured stress state of the structure is within the allowable range of the cable-stayed bridge,and the stress state of the structure is normal and meets the specification requirements.The results of load tests show that the measured deflection values of the mid-span section of the main girder are less than the theoretical calculation values.The maximum deflection of the girder is−20.90 mm,which is less than−22.00 mm of the theoretical value,indicating that the girder has sufficient structural stiffness.The maximum impact coefficient under dynamic load test is 1.08,which is greater than 1.05 of theoretical value,indicating that the impact effect of heavy-duty truck on this type of bridge is larger.This study can provide important reference value for construction and maintenance of similar corrugated steel web cable-stayed bridges.

Fragility curves of concrete bridges retrofitted by column jacketing

The Northridge earthquake inflicted various levels of damage upon a large number of Caltrans' bridges not retrofitted by column jacketing.In this respect,this study represents results of fragility curve development for two (2) sample bridges typical in southern California,strengthened for seismic retrofit by means of steel jacketing of bridge columns.Monte Carlo simulation is performed to study nonlinear dynamic responses of the bridges before and after column retrofit.Fragility curves in this study are represented by lognormal distribution functions with two parameters and developed as a function of PGA.The sixty (60) ground acceleration time histories for the Los Angeles area developed for the Federal Emergency Management Agency (FEMA) SAC (SEAOC-ATC CUREe) steel project are used for the dynamic analysis of the bridges. The improvement in the fragility with steel jacketing is quantified by comparing fragility curves of the bridge before and after column retrofit.In this first attempt to formulate the problem of fragility enhancement,the quantification is made by comparing the median values of the fragility curves before and after the retrofit.Under the hypothesis that this quantification also applies to empirical fragility curves developed on the basis of Northridge earthquake damage,the enhanced version of the empirical curves is developed for the ensuing analysis to determine the enhancement of transportation network performance due to the retrofit.

Simplified Method and Influence Factors of Vibration Characteristics of Isolated Curved Girder Bridge

The isolated curved girder bridge's vibration characteristics play a major part in the seismic responses of structures and anti-seismic properties.A clear analytic relationship between design parameters and the system's vibration characteristics could be established by its simplified dynamic analysis model,making it convenient for providing a reference to the optimization of design and safety analysis.A double-mass six-degree-of-freedom model for curved girder bridges with isolation bearings installed at the top of the bridge piers is built and a simplified analysis method for the vibration characteristics of the system is provided.Combined with the Matlab programming,the influences of radius of curvature,central angle,bridge deck width and damping ratio of the isolation layer and circular frequency of the isolation layer of isolated curved girder bridges on the pseudo-undamped natural circular frequency(called pseudo-frequency for short)and system damping ratio are systematically analyzed,and the sensitivity of vibration characteristics of isolated curved girder bridges is studied.The results show that the vibration characteristics of isolated curved girder bridges can be reflected well with this simplified model and calculation method.The pseudo-frequency of curved girder and system damping ratios increases with the increase of the isolation layer.The third-order vibration characteristic is more sensitive to the parameters of a curved girder,and the first-order vibration characteristic is sensitive to both central angle and radius of curvature to some extent while insensitive to the width of the bridge deck.Furthermore,the second-order vibration characteristic is not sensitive to the parameters of a curved girder.

A Method for Elastic Shear Buckling Calculation of Curved Bridge Webs

Curved composite bridges and curved steel bridges have already been constructed around the world;however, the calculation for shear buckling of curved bridge webs generally uses the equations for straight bridge webs or just introduces a modification factor for bridge design. In this paper, the curved bridge web is equivalent to an isotropic cylindrical flat shell, and the double triangular series satisfying four-edge simply supported boundaries are used as the displacement function of the shell. Then by means of the Galerkin method, the analytical formula for elastic shear buckling stress of curved bridge webs is deduced. The parameter studies show that the shear buckling coefficient kc of curved bridge webs is positively correlated with the parameter h2 / (Rt), and negatively correlated with the length-height ratio l/ h. This implies that the elastic shear buckling stress of a curved bridge web is larger than that of an equivalent straight bridge web. For a curved bridge with the parameter h2 / (Rt) less than 2, the amount of increase is less than 4.5%. The elastic shear buckling stress of curved bridge webs can be estimated conservatively as the webs in straight bridges. While for a curved bridge with larger h2 / (Rt), using the equations for straight girders to calculate the elastic shear buckling stress is too conservative. The proposed formulas provide a more accurate estimation for shear buckling stress of curved bridge webs.

Mechanical response of continuously reinforced concrete pavement on foam concrete interlayer for two-way curved arch bridge

In order to research the mechanical response of continuously reinforced concrete pavement on foam concrete interlayer for a two-way curved arch bridge, the elliptical vehicle load is translated into the rectangular load based on the equivalence method. Then, a three-dimensional finite element model of the whole bridge is established. The reliability of the model is verified. Additionally, the mechanical response of continuously reinforced concrete pavement under vehicle loading is analyzed. Finally, the most unfavorable loading conditions of tensile stress, shear stress and vertical displacement are determined. The results show that the most unfavorable loading condition of tensile stress, which is at the bottom of continuously reinforced concrete pavement on the two-way curved arch bridge, is changed compared with that on homogeneous foundation. The most unfavorable loading condition of shear stress at the top is also changed. However, the most unfavorable loading condition of vertical displacement remains unchanged. The tensile stress at the bottom of about 1/4 span of the longitudinal joint, the shear stress at the top of intersection of transverse and longitudinal joint, together with the vertical displacement at the central part of longitudinal joint, are taken as design indices during the structural design of continuously reinforced concrete pavement on the two-way curved arch bridge. The results are helpful for the design of continuously reinforced concrete pavement on unequal- thickness base for the two-way curved arch bridge.

Coupled Vibration of Long-Span Railway Curved Girder Bridges and Vehicles

The structure of a long curved girder bridge is represented with a three-dimensional curved finite element model. Each 4-axle ~vehicle is modeled by a dynamic system of 35 degrees of freedom. The random irregularities of the track are generated from a power spectral density function under the given track condition. The dynamic interaction between the bridge and train is realized through the contact forces between the wheels and track. Then based on these models, the coupled equations of motion are solved by applying the time-integration and iteration techniques to the coupled system. The proposed formulation and the associated computer program are then applied to a real curved girder bridge. The dynamic responses of the bridge-vehicle system and the derailments and offload factors related to the riding and running safeties of vehicles are computed. The results show that the formulation presented in this paper can well predict dynamic behaviors of both bridge and train with reasonable computation efforts.

Preliminary Estimation of Torsion of Curved Bridges Subjected to Earthquake Loading

This paper focuses on the seismic response of the curved and post-tensioned concrete box girder bridges. More specifically, it investigates how the curvature influences the response of a bridge subjected to earthquake. Parametric analysis of different radius of curvature is performed and the internal forces, torsion moment, axial and shear along the bridge are calculated. Two types of connections are investigated, the monolithic connection and deck connection with bents and abutments with rubber bearing. The response spectrum seismic analysis was performed. The models were designed, according to the provisions of EC8-part 2, EC2 and the Greek regulations E39/99. Diagrams relating the curvature with the torsion moment have been obtained from the results of parametric analysis. These diagrams could be used by engineers for preliminary design of such kind of bridges.

Behaviour and Analysis of Horizontally Curved Steel Box-Girder Bridges

Various theories and analytical formulations were implemented and exploited in the 1980s and 1990s for the design of bridge beams or decks curved in the horizontal plane and subjected to out-of-plane loads. Nowadays, the Finite Element Method (FEM) is a valid tool for the analysis of structures with complex geometries and, therefore, the development of sophisticated analytical formulations is not needed anymore. However, they are still useful for the validation of FE models. This paper presents the case study of an existing viaduct built in North Italy, aiming to compare analytical approaches and numerical modelling. The bridge is characterized by an axis curved in two directions and a rectilinear segment. The global analysis of the viaduct is carried out with special attention to the attributes that cause torque action and bending moment. The theoretical developments focus on a deeper understanding of the torsional response under different constraint and loading conditions and aspire to raise awareness of the mutual interaction of flexural and torsional behaviour, that are always present in these complex curved systems. The examination of the case study is also obtained by comparing the response of isostatic and hyperstatic curvilinear steel box-girders.

Probability evaluation method for cable safety of long-span cable-stayed bridges

A method of cable safety analysis is proposed for safety evaluation of long-span cable-stayed bridges. The Daniels＇ effect and the probability of broken wires in the cable are introduced to develop the cable strength model and the reliability assessment technique for long-span cable-stayed bridges based on the safety factors analysis of stay cables in service. As an application of the proposed model, the cable safety reliability of the cable No. 25 of Zhaobaoshan cable-stayed bridge in China is calculated. The effects of various parameters on the estimated cable safety reliability are investigated. The results indicate that the proposed method can be used to assess the safety level of stay cables in cable-stayed bridges effectively. The Daniels＇ effect should be taken into account for assessment, and the probability of broken wires can be used to simulate the deterioration of stay cables in service.

Mechanical performance evaluation of a new type of cable-stayed beam-arch combination bridge based on field tests

In order to study the mechanical performance of a new type of cable-stayed beam-arch combination bridge, the results of field static and dynamic load tests are comparatively analyzed with numerical results based on the Jingyi bridge straddling the Daxi River in Yixing. First, the test scheme, tasks, the corresponding measure method, as well as the relevant codes are described. Secondly, two sets of three- dimensional finite element models are established. One is Ansys which uses the solid element and the other is Midas which adopts the beam element. Finally, the experimental and analytical results are comparatively analyzed, and they show an agreement with each other. The results show that the bridge possesses adequate load-carrying capacity under all static load cases, but the capacity of dissipating external input energy is insufficient due to the relatively smaller damping ratio. The study results can provide a reference for further study and optimization of this type of bridge. Calibrated finite-element models that reflect the real conditions can be used as a baseline for future maintenance of the bridge.

Application of uncertain type of AHP to condition assessment of cable-stayed bridges

In order to guarantee the safety service and life-span of long-span cable-stayed bridges, the uncertain type of analytic hierarchy process （AHP） method is adopted to access the bridge condition. The correlative theory and applied objects of uncertain type of AHP are introduced, and then the optimal transitive matrix method is chosen to calculate the interval number judgment matrix, which makes the weights of indices more reliable and accurate. Finally, with Harbin Songhua River Cable-Stayed Bridge as an example, an index system and an assessment model are proposed for the condition assessment of this bridge, and by using uncertain type of AHP, the weights of assessment indices are fixed and the final assessment results of the bridge are calculated, which proves the feasibility and practicability of this method. The application of this assessment method can provide the scientific basis for maintenance and management of long-span cable-stayed bridges.