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.

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.

Deformation monitoring of long-span railway bridges based on SBAS-InSAR technology

The deformation monitoring of long-span railway bridges is significant to ensure the safety of human life and property.The interferometric synthetic aperture radar(In SAR)technology has the advantage of high accuracy in bridge deformation monitoring.This study monitored the deformation of the Ganjiang Super Bridge based on the small baseline subsets(SBAS)In SAR technology and Sentinel-1A data.We analyzed the deformation results combined with bridge structure,temperature,and riverbed sediment scouring.The results are as follows:(1)The Ganjiang Super Bridge area is stable overall,with deformation rates ranging from-15.6 mm/yr to 10.7 mm/yr(2)The settlement of the Ganjiang Super Bridge deck gradually increases from the bridge tower toward the main span,which conforms to the typical deformation pattern of a cable-stayed bridge.(3)The sediment scouring from the riverbed cause the serious settlement on the bridge’s east side compared with that on the west side.(4)The bridge deformation negatively correlates with temperature,with a faster settlement at a higher temperature and a slow rebound trend at a lower temperature.The study findings can provide scientific data support for the health monitoring of long-span railway bridges.

Safety of the express freight train running over a long-span bridge

Purpose-Express freight transportation is in rapid development currently.Owing to the higher speed of express freight train,the deformation of the bridge deck worsens the railway line condition under the action of wind and train moving load when the train runs over a long-span bridge.Besides,the blunt car body of vehicle has poor aerodynamic characteristics,bringing a greater challenge on the running stability in the crosswind.Design/methodology/approach-In this study,the aerodynamic force coefficients of express freight vehicles on the bridge are measured by scale model wind tunnel test.The dynamic model of the train-long-span steel truss bridge coupling system is established,and the dynamic response as well as the running safety of vehicle are evaluated.Findings-The results show that wind speed has a significant influence on running safety,which is mainly reflected in the over-limitation of wheel unloading rate.The wind speed limit decreases with train speed,and it reduces to 18.83 m/s when the train speed is 160 km/h.Originality/value-This study deepens the theoretical understanding of the interaction between vehicles and bridges and proposes new methods for analyzing similar engineering problems.It also provides a new theoretical basis for the safety assessment of express freight trains.

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.

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.

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.

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.

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.

Theoretical research on structural damage alarming of long-span bridges using wavelet packet analysis

The state equation and observation equation of the structural dynamic systems under various analysis scales are derived based on wavelet packet analysis. The time-frequency properties of structural dynamic response under various scales are further formulated. The theoretical analysis results reveal that the wavelet packet energy spectrum （WPES） obtained from wavelet packet decomposition of structural dynamic response will detect the presence of structural damage. The sensitivity analysis of the WPES to structural damage and measurement noise is also performed. The transfer properties of the structural system matrix and the observation noise under various analysis scales are formulated, which verify the damage alarming reliability using the proposed WPES with preferable damage sensitivity and noise robusticity.

Developments and Prospects of Long-Span High-Speed Railway Bridge Technologies in China

With the rapid developments of the high-speed railway in China, a great number of long-span bridges have been constructed in order to cross rivers and gorges. At present, the longest main span of a constructed high-speed railway bridge is only 630 m. The main span of Hutong Yangtze River Bridge and of Wufengshan Yangtze River Bridge, which are under construction, will be much longer, at 1092 m each. In order to overcome the technical issues that originate from the extremely large dead loading and the relatively small structural stiffness of long-span high-speed railway bridges, many new technologies in bridge construction, design, materials, and so forth have been developed. This paper carefully reviews progress in the construction technologies of multi-function combined bridges in China, including com- bined highway and railway bridges and multi-track railway bridges. Innovations and practices regarding new types of bridge and composite bridge structures, such as bridges with three cable planes and three main trusses, inclined main trusses, slab-truss composite sections, and steel-concrete composite sections, are introduced. In addition, investigations into high-performance materials and integral fabrication and erection techniques for long-span railway bridges are summarized. At the end of the paper, prospects for the future development of long-span high-speed railwav bridges are provided.

Longitudinal force in continuously welded rail on long-span tied arch continuous bridge carrying multiple tracks

Considering arch rib, lateral brace, suspender, girder, pier and track position, the model for the interaction between long-span tied arch continuous bridge and multiple tracks was established by using steel-concrete composite section beam element to simulate concrete-filled steel tube(CFST) arch rib, using the beam element with rigid arm to simulate the prestressed concrete girder and using nonlinear bar element to simulate longitudinal constraint between track and bridge. Taking a(77+3×156.8+77) m tied arch continuous bridge with four tracks on the Harbin-Qiqihar Passenger Dedicated Line as an example, the arrangement of continuously welded rail(CWR) was explored. The longitudinal force in CWR on the tied arch continuous bridge, the pier top horizontal force and torque due to the unbalance load case, were analyzed under the action of temperature, vertical live load, train braking and wind load.Studies show that, it can significantly reduce track displacement to set the track expansion devices at main span arch springing on both sides; the track stress due to arch temperature variation can reach 40.8 MPa; the track stress, pier top horizontal force and torque are related to the number of loaded tracks and train running direction, and the bending force applied to unloaded track is close to the loaded track, while the braking force applied to unloaded track is 1/4 to 1/2 of the loaded track; the longitudinal force of track due to the wind load is up to 12.4 MPa, which should be considered.

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.

Effects of fundamental factors on coupled vibration of wind-rail vehicle-bridge system for long-span cable-stayed bridge

In a wind-vehicle-bridge(WVB) system,there are various interactions among wind,vehicle and bridge.The mechanism for coupling vibration of wind-vehicle-bridge systems is explored to demonstrate the effects of fundamental factors,such as mean wind,fluctuating wind,buffeting,rail irregularities,light rail vehicle vibration and bridge stiffness.A long cable-stayed bridge which carries light rail traffic is regarded as a numerical example.Firstly,a finite element model is built for the long cable-stayed bridge.The deck can generally be idealized as three-dimensional spine beam while cables are modeled as truss elements.Vehicles are modeled as mass-spring-damper systems.Rail irregularities and wind fluctuation are simulated in time domain by spectrum representation method.Then,aerodynamic loads on vehicle and bridge deck are measured by section model wind tunnel tests.Eight vertical and torsional flutter derivatives of bridge deck are identified by weighting ensemble least-square method.Finally,dynamic responses of the WVB system are analyzed in a series of cases.The results show that the accelerations of the vehicle are excited by the fluctuating wind and the track irregularity to a great extent.The transverse forces of wheel axles mainly depend on the track irregularity.The displacements of the bridge are predominantly determined by the mean wind and restricted by its stiffness.And the accelerations of the bridge are enlarged after adding the fluctuating wind.

Structural health monitoring of long-span suspension bridges using wavelet packet analysis

During the service life of civil engineering structures such as long-span bridges, local damage at key positions may continually accumulate, and may finally result in their sudden failure. One core issue of global vibration-based health monitoring methods is to seek some damage indices that are sensitive to structural damage, This paper proposes an online structural health monitoring method for long-span suspension bridges using wavelet packet transform （WPT）. The WPT- based method is based on the energy variations of structural ambient vibration responses decomposed using wavelet packet analysis. The main feature of this method is that the proposed wavelet packet energy spectrum （WPES） has the ability to detect structural damage from ambient vibration tests of a long-span suspension bridge. As an example application, the WPES-based health monitoring system is used on the Runyang Suspension Bridge under daily environmental conditions. The analysis reveals that changes in environmental temperature have a long-term influence on the WPES, while the effect of traffic loadings on the measured WPES of the bridge presents instantaneous changes because of the nonstationary properties of the loadings. The condition indication indices VD reflect the influences of environmental temperature on the dynamic properties of the Runyang Suspension Bridge. The field tests demonstrate that the proposed WPES-based condition indication index VD is a good candidate index for health monitoring of long-span suspension bridges under ambient excitations.

Seismic spatial effects on long-span bridge response in nonstationary inhomogeneous random fields

The long-span bridge response to nonstationary multiple seismic random excitations is investigated using the PEM (pseudo excitation method). This method transforms the nonstationary random response analysis into ordinary direct dynamic analysis, and therefore, the analysis can be solved conveniently using the Newmark, Wilson-9 schemes or the precise integration method. Numerical results of the seismic response for an actual long-span bridge using the proposed PEM are given and compared with the results based on the conventional stationary analysis. From the numerical comparisons, it was found that both the seismic spatial effect and the nonstationary effect are quite important, and that both stationary and nonstationary seismic analysis should pay special attention to the wave passage effect.

Seismic spatial effects on dynamic response of long-span bridges in stationary inhomogeneous random fields

The seismic analysis of long-span bridges subjected to multiple ground excitations is an important problem. The conventional response spectrum method neglects the spatial effects of ground motion,and therefore may result in questionable conclusions.The random vibration approach has been regarded as more reliable.Unfortunately,so far, computational difficulties have not yet been satisfactorily resolved.In this paper,an accurate and efficient random vibration approach—pseudo excitation method (PEM),by which the above difficulties are overcome,is presented.It has been successfully used in the three dimensional seismic analysis of a number of long-span bridges with thousands of degrees of freedom and dozens of supports.The numerical results of a typical bridge show that the seismic spatial effects~ particularly the wave passage effect,are sometimes quite important in evaluating the safety of long-span bridges.