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.

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.

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.

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.

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.

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.

Dynamic finite element model updating of prestressed concrete continuous box-girder bridge

The dynamic finite element model （FEM） of a prestressed concrete continuous box-girder bridge, called the Tongyang Canal Bridge, is built and updated based on the results of ambient vibration testing （AVT） using a real-coded accelerating genetic algorithm （RAGA）. The objective functions are defined based on natural frequency and modal assurance criterion （MAC） metrics to evaluate the updated FEM. Two objective functions are defined to fully account for the relative errors and standard deviations of the natural frequencies and MAC between the AVT results and the updated FEM predictions. The dynamically updated FEM of the bridge can better represent its structural dynamics and serve as a baseline in long-term health monitoring, condition assessment and damage identification over the service life of the bridge .

Free Vibration Analysis of RC Box-Girder Bridges Using FEM

The free vibration analysis of simply supported box-girder bridges is carried out using the finite element method.The fundamental frequency is determined in straight,skew,curved and skew-curved box-girder bridges.It is important to analyse the combined effect of skewness and curvature because skew-curved box-girder bridge behaviour cannot be predicted by simply adding the individual effects of skewness and curvature.At first,an existing model is considered to validate the present approach.A convergence study is carried out to decide the mesh size in the finite element method.An exhaustive parametric study is conducted to determine the fundamental frequency of box-girder bridges with varying skew angle,curve angle,span,span-depth ratio and cell number.The skew angle is varied from 0°to 60°,curve angle is varied from 0°to 60°,span is changed from 25 to 50 m,span-depth ratio is varied from 10 to 16,and single cell&double cell are used in the present study.A total of 420 bridge models are used for parametric study in the investigation.Mode shapes of the skew-curved bridge are also presented.The fundamental frequency of the skew-curved box-girder bridge is found to be more than the straight bridge,so,the skew-curved box-girder bridge is preferable.The present study may be useful in the design of box-girder bridges.

Simulation of Temperature Field in Original Segment of Concrete Box-Girder Bridge

Temperature field and its variation with time are necessary for analyzing the thermo-mechanical performance of mass concrete structures at their early ages. This paper carries out a temperature field simulation analysis for an original segment of a real box girder bridge with the finite element software ANSYS. Two representative exothermic rate models are used to describe the heat- releasing process caused by the cement hydration in concrete. The exothermic rate model that conforms to reality more closely is recognized by comparing the simulation results with the data gathered from the optical fiber temperature sensors pre-embedded in the original segment. The air temperature and wind velocity that constitute thermal boundary conditions are determined in the light of the local meteorological department and correlative research achievements of recent years. Moreover, the consideration for the steel formwork acting as a barrier to heat loss is also proved to be beneficial to improve the simulation effect.

Seismic fragility analysis of highway bridges considering multi-dimensional performance limit state

Fragility analysis for highway bridges has become increasingly important in the risk assessment of highway transportation networks exposed to seismic hazards. This study introduces a methodology to calculate fragility that considers multi-dimensional performance limit state parameters and makes a first attempt to develop fragility curves for a multi-span continuous (MSC) concrete girder bridge considering two performance limit state parameters: column ductility and transverse deformation in the abutments. The main purpose of this paper is to show that the performance limit states, which are compared with the seismic response parameters in the calculation of fragility, should be properly modeled as randomly interdependent variables instead of deterministic quantities. The sensitivity of fragility curves is also investigated when the dependency between the limit states is different. The results indicate that the proposed method can be used to describe the vulnerable behavior of bridges which are sensitive to multiple response parameters and that the fragility information generated by this method will be more reliable and likely to be implemented into transportation network loss estimation.

Effect of seismic retrofit of bridges on transportation networks

The objective of this research is to determine the effect earthquakes have on the performance of transportation network systems.To do this,bridge fragility curves,expressed as a function of peak ground acceleration(PGA)and peak ground velocity(PGV),were developed.Network damage was evaluated under the 1994 Northridge earthquake and scenario earthquakes.A probabilistic model was developed to determine the effect of repair of bridge damage on the improvement of the network performance as days passed after the event.As an example,the system performance degradation measured in terms of an index,'Drivers Delay,'is calculated for the Los Angeles area transportation system,and losses due to Drivers Delay with and without retrofit were estimated.

The effect of different intensity measures and earthquake directions on the seismic assessment of skewed highway bridges

In this study the probable seismic behavior of skewed bridges with continuous decks under earthquake excitations from different directions is investigated. A 45° skewed bridge is studied. A suite of 20 records is used to perform an Incremental Dynamic Analysis （IDA） for fragility curves. Four different earthquake directions have been considered： -45°, 0°, 22.5, 45°. A sensitivity analysis on different spectral intensity measures is presented; efficiency and practicality of different intensity measures have been studied. The fragility curves obtained indicate that the critical direction for skewed bridges is the skew direction as well as the longitudinal direction. The study shows the importance of finding the most critical earthquake in understanding and predicting the behavior of skewed bridges.

Experimental verification of bridge seismic damage states quantified by calibrating analytical models with empirical field data

Bridges are one of the most vulnerable components of a highway transportation network system subjected to earthquake ground motions. Prediction of resilience and sustainability of bridge performance in a probabilistic manner provides valuable information for pre-event system upgrading and post-event functional recovery of the network. The current study integrates bridge seismic damageability information obtained through empirical, analytical and experimental procedures and quantifies threshold limits of bridge damage states consistent with the physical damage description given in HAZUS. Experimental data from a large-scale shaking table test are utilized for this purpose. This experiment was conducted at the University of Nevada, Reno, where a research team from the University of California, Irvine, participated. Observed experimental damage data are processed to identify and quantify bridge damage states in terms of rotational ductility at bridge column ends. In parallel, a mechanistic model for fragility curves is developed in such a way that the model can be calibrated against empirical fragility curves that have been constructed from damage data obtained during the 1994 Northridge earthquake. This calibration quantifies threshold values of bridge damage states and makes the analytical study consistent with damage data observed in past earthquakes. The mechanistic model is transportable and applicable to most types and sizes of bridges. Finally, calibrated damage state definitions are compared with that obtained using experimental findings. Comparison shows excellent consistency among results from analytical, empirical and experimental observations.

Performance-based system seismic assessment for long-span suspension bridges under two-level seismic hazard

Since there are few studies on the performance-based seismic evaluation of the long-span suspension bridge system under two-level earthquake hazard in Chinese code,the developed procedure of this study can be regarded as a general program to assess the seismic performance of the overall system for long-span suspension bridges.In the procedure,the probabilistic seismic demand models of multiple bridge components were developed by nonlinear time-history analyses incorporating the related uncertainties,and the component-level fragility curves were calculated by the reasonable definition of limit states of the corresponding components in combination with seismic hazard analysis.The bridge repair cost ratios used to evaluate the system seismic performance were derived through the performance-based methodology and the damage probability of critical components.Furthermore,the repair cost ratios of the overall bridge system that was retrofitted with fluid viscous dampers for the main bridge and changed restraint systems for the approach bridges were compared.The results show that peak ground velocity and peak ground acceleration can be selected as the optimal intensity measurements of long-span suspension bridges using the TOPSIS(technique for order preference by similarity to an ideal solution).The bridge repair cost ratios can serve as accurate evaluation indicators to provide an efficient evaluation of retrofit measures.The seismic evaluation of long-span bridges is misled when ignoring the interaction of adjacent structures.However,the repair cost ratios of a bridge system that has optimum seismic performance are less sensitive to the relative importance of adjacent structures.

Scour effect on a sea-crossing bridge under combined action of service and extreme seismic loads

Foundation scour is an important cause for structural failure of sea-crossing bridges. Usually, the sea-crossing bridges operate under the harsh natural environment in which service wind, wave and vehicle loads are stronger and extreme loads such as earthquake, hurricane, and ship collision, are more frequent. As a result of the foundation scour,the dynamic behavior of bridge under different combined action of service and extreme loads may be further escalated.In particular, this work has investigated the scour effect on a sea-crossing bridge under service wind, wave and vehicle loads as well as extreme seismic loads. The dynamic coupled earthquake-wind-wave-vehicle-bridge(EWWVB) system is established by considering the interactions within the system, and the p-y curve method is used to calculate the loaddisplacement relation of the pile and soil under various levels of foundation scour. After that, a case study has been performed on a cable-stayed bridge with foundation scour. The results indicate that the dynamic characteristics of bridge structure will change after considering bridge scour, and the dynamic responses of bridge and vehicle will be affected to different degrees under service and seismic loads considering bridge scour.