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.

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.

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.

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.

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.

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.

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.

考虑加载历史的小半径曲线桥梁梁轨相互作用分析

目前,大部分考虑加载历史的梁轨相互作用研究都集中在直线桥梁上,针对曲线桥梁,尤其是小半径曲线桥梁,梁轨相互作用的研究相对较少。采用理想弹塑性滞回阻力模型模拟扣件纵向阻力,运用有限元软件,建立以城东特大桥为研究对象的钢轨-桥梁-墩台三维有限元空间力学计算模型,研究曲线半径对于梁轨相互作用的影响,探究了多荷载耦合作用、往复荷载作用以及循环荷载作用下考虑加载历史效应的曲线桥梁梁轨相互作用情况,并提出“拉力百分比”以及“压力百分比”的概念以便分析曲线半径对传统线性叠加法误差的影响。结果表明,曲线桥梁中梁轨纵、横向相互作用分别与曲线半径成正、反比,相关数据改变幅度与曲线半径成反比且当曲线半径超过800 m时基本收敛,此时可采用“以直代曲”的简化算法;曲线半径对于横向梁轨相互作用影响程度大于纵向,相较于挠曲、制动工况,伸缩工况受曲线半径影响更加显著;多荷载耦合作用下,采用传统线性叠加法相较于考虑加载历史更为保守且温度荷载起主要贡献;考虑加载历史时钢轨在往复荷载作用下会产生不可忽视的残余内力,且在循环荷载作用下将会产生收敛于第1次往复荷载下的残余内力,这是扣件纵向阻力的弹塑性滞回特性决定的;线性叠加法误差与曲线半径具有相关性,相较于挠曲、制动工况,伸缩工况下对其更为敏感。研究结果可为考虑加载历史下曲线桥梁结构设计提供参考。

不同地震激励方向下隔震曲线梁桥易损性分析

为进一步评估隔震曲线梁桥在地震激励下的抗震性能,从地震易损性角度出发并兼顾考虑地震激励方向对其易损性的影响。利用APDL建立采用板式橡胶支座的隔震曲线梁桥有限元模型,从PEER中选取同一地震事件中的近断层地震动,按规范规定比例输入水平双向地震动进行非线性动力时程分析,结合地震响应与损伤指标计算得到各构件地震易损性曲线;考虑地震激励方向的变化,通过MATLAB编程绘制得到桥梁结构构件(桥墩与支座)以及整体系统的地震易损性曲面,分析探讨地震激励方向对隔震曲线梁桥易损性的影响。结果表明:不同极限状态下各桥墩切向损伤条件概率明显大于其径向,各支座的切向与径向易损性相差不大,但仍是各支座的切向易损性略大于径向易损性;桥梁各构件(桥墩与支座)切向易损性对地震激励方向均表现出很强依赖性,而径向易损性对其的依赖性相对较弱,且伴随损伤等级的提高,构件易损性对地震激励方向更加敏感;桥梁整体系统易损性对地震激励方向的变化不太敏感,且因各构件响应之间的相关性较高,其系统易损性更接近于易损性最大的构件——易损性下限;当进行隔震曲线梁桥抗震性能评估时,应考虑不同地震激励方向对其地震易损性的影响,从而使得易损性分析结果更加合理,能够更加真实地反映隔震曲线梁桥的实际损伤状态。

装配式混凝土梁桥预应力摩阻损失研究

装配式预应力混凝土梁桥以其施工效率高、构件质量好等优势应运而生,混凝土构件在工厂可以标准化生产确保质量,而预应力损失却难以把控。现行规范中对于弯曲孔道预应力摩阻损失的计算在接触压力、弯曲夹角等方面存在不适用性。基于弹性接触理论,揭示该公式在推导过程中的缺陷,对某线路装配式混凝土梁桥进行预应力沿程损失试验,验证预应力混凝土梁桥的有效预应力不足来源于计算公式缺陷。

车辆荷载作用下钢-混凝土组合梁疲劳应力分析

【目的】随着桥梁服役期延长和车辆荷载增加等多种因素的影响,结构承载力会变得越来越弱,疲劳寿命不断降低,最终可能导致低应力疲劳破坏。因此有必要对车辆荷载下拱桥钢混组合梁的疲劳细节应力进行研究。【方法】采用数值模拟的方法,利用Midas FEA NX软件建立3个标准长度的三维实体精细有限元模型,分析钢混组合梁易损疲劳关键点的位置,并研究车辆荷载横向最不利加载位置和纵向加载下的疲劳细节应力变化规律。【结果】结果表明,组合梁次横梁与中纵梁交点处有三处疲劳关键点;靠近桥梁中线位置是车辆荷载下钢梁疲劳最不利的横向加载位置;四种不同标准的纵向车辆加载时,三个疲劳关键点均出现两次应力峰值,且最大应力幅值均低于常幅疲劳强度的极限值。【结论】研究成果可为钢-混凝土组合梁试验和相关研究提供参考。

重载与中强地震联合作用下的曲线独柱墩桥梁倾覆性分析

为探讨移动车辆和中强地震联合作用对曲线梁桥的抗倾覆影响,建立车-桥-地震分析模型,提出考虑地震作用的曲线梁桥车-桥耦合振动分析方法。以多跨曲线连续梁桥为研究对象,对比分析中强地震和重载车辆偏载组合作用下的支座反力和主梁倾覆时整体转角大小。研究地震动类型、峰值、车辆关键参数等因素对曲线梁桥倾覆稳定性的影响。结果表明:不同车辆和地震荷载组合会改变桥梁的受力情况,纵向间隔2 m的3辆100 t车辆以3 m/s速度行驶时,三跨曲线梁桥的倾覆最明显;综合考虑重载及地震联合作用,对抗倾覆性规范中的稳定系数计算公式进行了修正;分析了五跨曲线梁桥中墩支座偏心距对抗倾覆稳定系数的影响,计算结果表明中墩两相邻支座设置偏心时曲线桥最大抗倾覆系数为1.55。