Model test and numerical analysis of a special joint for a truss bridge

This paper presents a study on the mechanical behaviours of a special joint between a rigid suspension cable and a truss girder in a rigid suspension stiffened steel truss bridge. Both a model test and a numerical finite element analysis (FEA) have been conducted, and relevant information about the models used, loading procedure and test scheme is presented. The model test shows that the maximum stress in the joint is less than the material allowable stress and the maximal stress induced from the secondary moment accounts for about 30% of the total stress. A three-dimensional finite element model is used in the numerical analysis and the results are in very good agreement with those of the model test. This study shows that the design of the special joint is reasonable and the structure safe. It is also expected that the results presented in this paper would be useful as references for future research and design of rigid suspension stiffened steel truss bridges and joints.     

现有铁路钢桥的评估

对现有铁路钢桥进行一系列的动力试验、加速度测量、评估、有限元模拟和安全指数计算。采用专门列车进行动力试验,并获取动力参数。这些参数还可用于建立桥梁的有限元模型。如果模型能够反映实际工况,就能用于计算每种工况下桥梁结构的安全指数。这些安全指数可用于计算杆件的破坏可能性,因此可采用本模型评估桥梁的可靠性。通过了解现有桥梁结构的实际工况,本研究可为新的货运列车重级荷载研究提供可靠依据。     

Assessment of existing steel railway bridges

A series of dynamic tests, acceleration measurements, evaluation, finite element model simulations and safety index calculations were performed on existing steel railway bridges giving service on railway network. Dynamic tests were fulfilled by using a special test train on these bridges to obtain the dynamic parameters and these parameters were then used to refine the finite element models of the bridges. Once the models have been updated to represent the actual condition, safety indices were calculated for structural components of the bridges for each proposed loading condition. These safety indices were used to calculate failure probabilities of structural members. As the final step, system reliability of the bridges was evaluated based on proposed system models of the bridges. It is believed that this study will provide a reliable background for proposed heavier axle loads resulting from new freight trains by realizing the current condition of bridge structures.     

结构健康监测和可靠性评估

对美国最大跨度桁架桥中的主要桁架构件以及整个结构系统的可靠性进行评估。根据构件和系统的可靠性指标,可以采用随机方法评估大跨桥的安全水平。然而,大多数旧的大跨桥是基于允许应力设计的,其可靠性不可能被保证。本研究的可靠性分析基于对恒荷载、活荷载和风载分布的评估。通过收集大量的输入和响应数据,对大桥进行长期结构健康监测。根据外部荷载影响的模式和大小,长期监测数据清楚揭示了不同结构的性能。案例显示,采用传统的分析方法难以确定由于温度引起的结构响应。为探讨温度对结构的影响以及在可靠性评估中考虑长期监测数据的作用,也对温度引起的响应进行分析。研究显示：温度导致的响应对整个系统的可靠性具有明显的影响。     

大跨度悬索桥颤振可靠度分析的改进响应面法

介绍一种新的计算悬索桥颤振可靠度方法——改进响应面法。该方法利用传统响应面法将极限状态方程近似表达为简单的多项式形式,有效地解决FORM和SORM无法求解隐式极限状态方程的可靠度问题。另外,改进响应面法的使用还能有效地利用现有的确定性颤振分析软件。通过引入有限元方法,改进响应面法可应用于悬索桥颤振可靠度问题。通过使用重要抽样技术,提高改进响应面法的计算效率和计算精度,有效地解决传统响应面法在结构可靠度较大或失效概率较低时出现的迭代不收敛问题。数值算例验证该方法的效率和精度。最后,用该方法计算江阴长江大桥的颤振可靠度,结果表明基于经验公式的改进响应面法会过高地估计大跨度悬索桥的颤振可靠度。实际的悬索桥颤振可靠度应该采用基于有限元法的改进响应面法进行计算。     

Reliability-based strength limit state for steel railway bridges

Railway bridges require special attention to provide safe and economical service. To assess the reliability of a structure, all critical parameters need to be specified. Load and resistance are random in nature; hence, the probabilistic approach is the best method for accurate evaluation of the performance of a bridge. In this study, identification of critical parameters was conducted on a typical through-plate girder, riveted, open deck railway bridge. This type of structure is a weakest link system. In such a system, the failure of one component can lead to failure of the entire structural system. This research involved identification of the basic load and resistance parameters and the development of analytical procedures for modelling the structural behaviour. The finite element method (FEM) was used to investigate the structural performance characteristics of the evaluated bridge. A three-dimensional structural model was developed to determine stress distribution in the members and connections. Based on the results of FEM analysis, the reliability indices were calculated for critical components.     

稳定型悬索桥与普通悬索桥固有振动对比研究

用含索组合有限元模型模拟稳定型悬索桥和普通悬索桥,考虑结构几何非线性特征,导出了系统广义特征方程,计算了两桥型前十阶特征对,对比分析了稳定型悬索桥及普通悬索桥垂直—扭转耦合固有振动。结果表明．稳定型悬索桥具有良好时自振特性。     

Evaluating rating factor for prestressed concrete girder bridges by nonlinear finite element analysis

This study provides a new approach to evaluate the load carrying capacity in rating factor (RF) of prestressed concrete I type girder bridges utilising nonlinear finite element (FE) analysis. RF has been conventionally calculated either by ultimate strength design (USD) or allowable stress design methods in terms of live load effects. This study introduces nonlinear FE analysis as a new approach to estimate the RF. In general, nonlinear FE analysis is considered as one of the most efficient methods to simulate structural behaviour. This method can also simulate a live load effect, which is very important for the load carrying capacity of structures. To apply nonlinear FE analysis, an FE live load constant was conceptually suggested to estimate the RF. On comparing the RF obtained via the conventional method of USD, it was found that the RF estimated by nonlinear FE analysis approach has almost the same value. Hence, the nonlinear finite element method-based RF methodology can be efficiently used to estimate the load carrying capacity of bridges.     

Life-cycle reliability assessment of reinforced concrete bridges under multiple hazards

This paper proposes a novel probabilistic methodology for estimating the life-cycle reliability of existing reinforced concrete (RC) bridges under multiple hazards. The life-cycle reliability of an RC bridge pier under seismic and airborne chloride hazards is compared to that of a bridge girder under traffic and airborne chloride hazards. When conducting a life-cycle reliability assessment of existing RC bridges, observational data from inspections can provide the corrosion level in reinforcement steel. Random variables related with the prediction of time-variant steel weight loss can be updated based on the inspection results using Sequential Monte Carlo Simulation (SMCS). This paper presents a novel procedure for identifying the hazards that most threaten the structural safety of existing RC bridges, as well as the structural components with the lowest reliability when these bridges are exposed to multiple hazards. The proposed approach, using inspection results associated with steel weight loss, provides a rational reliability assessment framework that allows comparison between the life-cycle reliabilities of bridge components under multiple hazards, helping the prioritisation of maintenance actions. The effect of the number of inspection locations on the updated reliability is considered by incorporating the spatial steel corrosion distribution. An illustrative example is provided of applying the proposed life-cyle reliability assessment to a hypothetical RC bridge under multiple hazards.     

Reliability-based condition assessment of deteriorating concrete bridges considering load redistribution

A wide variety of models have been proposed for estimating the reliability of highway bridges. For reinforced concrete bridges subjected to environmental attack, time-variant reliability methods have to be used. In this study, the condition of reinforced concrete girder bridges is assessed using a time-variant system reliability approach in which both load and resistance are time-variant quantities. Several system models are considered, including failure of any girder (series system) and failure of a specified number of adjacent girders (series-parallel system). Adaptive importance sampling is used to determine the cumulative-time system failure probability. An existing reinforced concrete T-beam bridge located near Pueblo, Colorado, is investigated. The influence of resistance degradation and post-failure load redistribution is included. A comparison of reliability estimates for several system models is given, including the influence of correlation among initial girder strengths. The results can be used as a guide for the selection of system models for bridge reliability analysis, identification of critical girders in a bridge system, and for the development of optimal reliability-based maintenance strategies for reinforced concrete highway bridges.     

Flutter reliability analysis of suspension bridges

A reliability analysis method is proposed in this paper through a combination of the advantages of the response surface method (RSM), finite element method (FEM), first-order reliability method (FORM) and the importance sampling updating method. The method is especially applicable for the reliability evaluation of complex structures of which the limit state surfaces are not known explicitly. After the accuracy and efficiency of the method are demonstrated through numerical examples, the method is used to estimate the flutter reliability of a suspension bridge. The uncertainties such as material properties, geometric parameters, structural damping ratio, flutter derivatives and extreme wind velocity at the bridge site are considered. The example suspension bridge is the Jiang Yin Bridge with a main span length of 1385 m built in China. The results show that the proposed method based on an empirical formula in which the limit state function is explicitly represented as a function of variables overestimates the flutter reliability of suspension bridges. The actual flutter reliability should be more accurately analyzed using the proposed method based on the deterministic finite element method in which the limit state function is implicitly represented as a function of variables. Finally, the most influential random variables on flutter reliability of suspension bridges are identified by using a sensitivity analysis.     

Reliability-based optimization of steel truss arch bridges

A reliability-based optimization approach is developed and applied to minimize the weight of steel truss arch bridges subject to probabilistic (the overall probability failure of the structure) and deterministic (stress and deflection) constraints. The method intelligently integrates the genetic algorithm (GA), the finite element method and the first order reliability method. A real-coded/integer-coded method is used to realistically represent the values of the design variables. Three GA operators consisting of constraint aggregate selection procedure, arithmetic crossover, and non-uniform mutation are proposed. The finite element method (FEM) and the first order reliability method are used to compute the value of the probabilistic and deterministic constraint functions. A numerical example involving a detailed computational model of a long span steel arch bridge with a main span of 550 m is presented to demonstrate the applicability and merits of the present method. Finally, several important parameters in the present method are discussed.     

用于悬索桥非线性分析的鞍座-索单元

悬索桥是跨越能力最大的一种桥型,鞍座是使主缆转向的一个重要构件,直接约束着主缆的变形。然而,鞍座及其顶推的模拟一直是悬索桥非线性分析时的一个难点,现有方法存在一定的不足之处。为此,本文提出了一种基于弹性悬索精确解的二节点新单元———鞍座-索单元,这种单元隐含了主缆与鞍座相切及主缆无应力长度保持不变这两个重要条件,同时将鞍座及其顶推的模拟融为一体,提出了基于NewtonRaphson法的状态求解方法,并推导了其切线刚度矩阵和等效节点力。计算表明,状态求解方法精确而有效,切线刚度矩阵推导正确。采用这种单元,既可使悬索桥非线性分析的计算模型更接近实际结构,也能显著提高计算精度和计算速度,并且具有很好的通用性。     

Fatigue reliability model for steel railway bridges

Railway bridges are exposed to repetitive high stress due to the live load which may lead to failure even when the stress level is lower than the allowable stress. Therefore, components and connections need to be analysed for possible damage caused by fatigue. The basic approach for estimating the remaining fatigue life of a structure element is to use S–N curves. However, those laboratory specimens tested with a constant-amplitude stress range show a wide range variability in the results. This means that fatigue resistance has to be considered as a random variable. If load and resistance parameters are random variables, structural performance should be measured in terms of reliability. The objective of this study is to present a reliability model for the fatigue limit states demonstrated on a typical steel railway bridge. The results from the reliability analysis for the fatigue limit state are presented for various time periods from 10 to 100 years and three cases of operating conditions. In each considered case of load, the lowest reliability indices were obtained for the riveted angle in the stringer-to-floor-beam connection which means that this member has the highest probability of fatigue crack development in the entire bridge.     

Effect of secondary elements on bridge structural system reliability considering moment capacity

Secondary elements such as barriers, sidewalks, and diaphragms may increase the load carrying capacity of girder bridges. This in turn affects reliability. The objective of this study is to evaluate the potential benefit of secondary elements on the system reliability of girder bridges, if these elements are designed with the structural system to participate resisting vehicular live loads. Simple span, two lane structures are considered, with composite steel girders supporting a reinforced concrete deck. For structural analysis, a finite element procedure is developed that combines a grillage model of the bridge deck with solid elements for edge-stiffening effects. Random variables considered are composite girder, barrier, and sidewalk flexural strengths (each in turn composed of many random variables), load magnitude (dead load and truck traffic live load), and live load position. System resistance parameters are estimated with a point integration method. System resistance is evaluated in terms of maximum load carried at ultimate capacity. It was found that the interaction of typical secondary element combinations has a varying effect on system reliability, depending on element stiffness, bridge span, and girder spacing.     

既有铁路钢筋混凝土梁桥动态可靠性评估

介绍了既有桥梁结构的动态可靠性分析方法,提出了桥梁的恒载概率模型、活载概率模型及抗力概率模型,并对可靠度计算方法中的验算点法进行了介绍。以一座既有铁路钢筋混凝土梁桥为工程背景,计算了该桥的活载效应统计参数、恒载效应统计参数及抗力统计参数等,利用验算点法计算了桥梁结构构件的可靠度指标,又采用PNET方法分析了整个桥梁体系的可靠性,最后给出了桥梁的可靠性评估结果。结果显示动态可靠性评估应用于铁路钢筋混凝土梁桥可以得到较好的评估结果。     

大跨度斜拉桥几何非线性静力计算分析

以斜拉桥作为研究对象,对斜拉桥的几何非线性问题进行了详细的介绍,并讨论了斜拉桥非线性分析的几种基本方法,编制相应的计算程序对几座典型的实桥进行了计算分析.计算结果表明,斜拉桥这种柔性结构在恒载作用下是高度非线性的,跨径越大,几何非线性表现得越突出,结构分析与设计中考虑几何非线性的影响就显得十分必要.     

Time-variant reliability profiles for steel girder bridges

Evaluation of existing steel bridges becomes more important due to natural aging, increasing load spectra, deterioration caused by corrosion, and other problems. In the result, bridge structures exposed to aggressive environmental conditions are subjected to time-variant changes of resistance. Therefore, there is a need for evaluation procedures for an accurate prediction of the load carrying capacity and reliability of bridge structures, in order to make rational decisions about repair, rehabilitation, and expected life-cycle costs. The objective of this paper is to develop time-variant reliability models for steel girder bridges. Traditional methods based on deterministic analysis do not reveal the actual load carrying capacity of the structure. The proposed approach is based on reliability analysis of components and structural systems. The study involves the selection of representative structures, formulation of limit state functions, development of load models, development of resistance models for corroded steel girders, development of the reliability analysis method, reliability analysis of selected bridges, and development of the time-dependant reliability profiles including deterioration due to corrosion. The results of the study can be used for a better prediction of the service life of deteriorating steel girder bridges, and development of optimal reliability-based maintenance strategies.     

Seismic system reliability analysis of bridges using the multiplicative dimensional reduction method

Abstract

A combined method of finite element reliability analysis and multiplicative dimensional reduction method (M-DRM) is proposed for systems reliability analysis of practical bridge structures. The probability distribution function of a structural response is derived based on the maximum entropy principle. To illustrate the accuracy and efficiency of the proposed approach, a simply supported bridge structure is adopted and the failure probability obtained are compared with the Monte Carlo simulation method. The validated method is then applied for the system reliability analysis for a practical high-pier rigid frame railway bridge located at the seismic-prone region. The finite element model of the bridge is developed using OpenSees and the M-DRM method is used to analyse the structural system reliability under earthquake loading.