机械设计外文翻译-桥梁使用系统可靠性评估【中文3359字】【PDF+中文WORD】

机械设计外文翻译-桥梁使用系统可靠性评估【中文3359字】【PDF+中文WORD】,中文3359字,PDF+中文WORD,机械设计,外文,翻译,桥梁,使用,系统,可靠性,评估,中文,3359,PDF,WORD 【中文3359字】 桥梁使用系统可靠性评估 摘要:当前桥梁可靠性评估过程描述在AASHTO手册第一版中有说明、评估的内容有，容许应力、载荷系数、负载和阻力系数等。这几个数据可能导致不同的桥面承载能力和桥梁的安全性,确保这几个桥梁参数合格与否是保证桥梁安全性和经济性的必要途径。 本文主要总结研究桥梁建设的改进过程,以提高桥梁结构的可靠性。论文提供了背景，研究计划和总结协调程序的负载测试和分析支持可导致的不可靠因素并提出改进建议。DOI:10.1061 /(土木)be.1943 - 5592.0000171。2011-美国土木工程师学会。 CE数据库主题词：混凝土桥梁;钢筋混凝土;预应力混凝土;负载因素;可靠性;钢材;评估。 作者关键词:桥梁;混凝土(钢筋);混凝土(预应力);状态评估;负载;可靠性;钢;结构工程。 介绍 ： 桥梁评估的AASHTO手册(MBE),第一版(AASHTO 2008)允许桥评估决定通过，传统的容许应力等级(ASR)或负载因素评估(LFR)方法或最近的负载和阻力系数评估(LRFR)方法,它是符合AASHTOLRFD桥梁设计规范(2007)。大桥是否可靠经济,从一个专业工程的观点取决于可靠性评估是否合格。为了解决桥梁不可靠问题 乔治亚理工学院的技术已经进行了多年，研究项目旨在使桥梁在建设当中更加可靠经济。 高级结构工程师,辛普森,Gumpertz,Heger,Inc .41 1Seyon圣,沃尔瑟姆,土木与环境工程学院,乔治亚理工学院。 2亚特兰大,佐治亚州博士,土木与环境工程学院,乔治亚理工学院,30332 - 0355. 3亚特立顿,佐治亚州硕士,土木与环境工程学院,乔治亚理工学院,30332 - 0355. 本文属于《桥梁工程16卷,6号,2011年11月1日。 土木,ISSN 1084 - 0702/2011/6 863 - 871 / $ 25.00。》 框架法来确定实际桥梁评估方法适合那些以AASHTO LRFD桥梁设计规范(AASHTO 2007)而设计的桥梁。 并且此方法已经在美国中部和东部以及其它非地震地区得到了验证。 近期在桥梁评估中实施了LRFD及其LRFR两种评估方法,两者是验证结构可靠性的方法。现有有一种vances,改进的技术评估桥梁方法此种方法会减少不必要的其它因素影响可能性的测量结果。为此,材料优势就可能大大影响标准化或名义假设值在设计和计算评估行为中对桥梁强度增益的影响，一个良好的桥段应在一多年的维护期内没有什么大的修复和裂痕以及其它影响桥梁使用的问题出现,在设计阶段就应该考虑这些问题的造成原因并及时处理。调查桥梁系统的可靠性不是仅仅依靠基于桥梁组件及其本身的评估方法。重要的是适当的考虑这些因素产生的原因并及时避免。 桥梁可靠性额定载荷： 桥的设计问题在AASHTO-LRFD规格(2007),建立了现代的结构可靠性原理分析，要求了现有桥梁的评估过程必须符合规定原则。现有的桥梁之所以存在不安全性是应为，产生差异负载、材料强度特性变换、尺寸改变、自然和人为的危险。以及在设计当中缺乏足够的知识,和人类在建筑设当中犯得一些错误。一个经济可靠的桥梁必须建立在理性的和强大的理论基础以及能够处理一些实践中不确定的影响因素。 极限状态设计和评估桥梁可以定义的一般形式为 G（X）=0 在负载和阻力随机X=（X1，X2，X3，.....Xn），桥梁的基础信息值包括变形、开裂，功能障碍。或者另外一些不合理的因素。 一个桥梁不令人满意的性能定义概率被估算为： =联合密度函数X;Ω=故障域可靠性分析值近视于： 在Φ（）=标准正态分布函数;β=可靠性指标。对表现良好的极限状态,Eq通常是一个常值。可以通过有限元分析对Ep 进一步的分析比对。 在桥梁设计规范的AASHTO LRFD(2007)中建立了在FO可靠性分析,应用于单个梁评估计算，及其计算概率建模的电阻和负载，例如：目标桥梁的可靠性指标β=3.5，那么就说明此桥梁可以使用75年之久。概率估算公式为： 其中D =静负荷不包括重量的磨损面;DA =重量的磨损面(沥青);(L与I)代表活载，Rn =名义电阻。 这个方程是大多数设计师再设计计算式后应用的，同时此方程也是现场检验数据,负荷测试,材料测试,等信息的可靠公式。 另一种概率估算公式为： H代表性能指数,进行检查,并支持现场试验,无论任何目标概率PT,应该依赖于经济学中的合理性在AASHTO-LRFR方法(2007)。H是一个概念上的背离方程式,LRFR介绍一组活负载因素为定值的额定载荷,这取决于现场交通所描述的平均每日车流量，和车载量。 在AASHTO LRFR MBE扩展了极限状态设计实现了一个统一的目标水平对公路大桥安全的评估系统。然而,不确定性模型的负载和阻力嵌入式在LRFR评级格式代表典型值在高山地带和平原地带以及河流地带不懂的地带，不通的环境因素影响，不同的车流量，以及在建桥过程中不同的吨重不同的跨径，不同的材料，相同材料的使用情况的不同都会使得评估的参数值发生改变从而使得被评估大桥的可靠性发生变化。 桥梁评估方法之间存在着一定的区别与联系，根据各种方法得起典型特点，桥梁评估方法大致可以分为基于外观调查的方法，基于规范设计的方法，基于专家经验的方法，有限元法，载荷验证，基于可靠性理论的方法，基于外观调查的方法： 根据我国的《公路养护技术规范》的规定，桥梁技术状况评价等级分为一类，二类，三类，四类，对桥梁整体和桥梁部件均适用。将桥梁划分为15个部件，根据桥梁部件的缺损程度及其标度，缺损对结构使用功能的影响程度以及缺损发展变化情况等，对桥梁各部件分别进行评分，值域为0到5，“0”表示完好状况，“5”表示危险的状况，再根据桥梁部件的评分确定个部件的评鉴等级，桥梁状况的综合评价，此法采用的公式为： 式中：Dr为全桥结构技术状况评分（0-100），评分高表示结构状况好，缺损少，Ri为对桥梁各部件的评分（0-5）,Wi为桥梁个部件权重。 当Dr大于等于88.88>Dr大于等于60.60>Dr大于等于40.40>Dr.这样桥梁的对应级别为一类，二类，三类，四类。 经验系数: 这是依据广泛的的调查研究，确定若干的影响承载力的系数及其取值范围，对桥梁承载能力进行评估的方法。被评估桥梁的承载能力为所有影响之和。 基于设计规范的方法。 桥梁设计规范是指导桥梁设计的标准。这一标准基于工程力学，结构试验和工程经验，切还在不断充实和完善。因此，利用桥规的计算理论来分析该桥梁承载能力的方法，具有坚实的理论基础并得到广泛的应用，然而直接套用桥梁规范于桥梁的话对于准确评估是不准确的，这是设计与评估的差异所致，例如，在评估阶段，可以获得较设计阶段更加坑定的信息按照结构可靠性理论的观点，这意味着评估时载荷和抗力的不定性要比设计时所考虑的要小，于是，在评估时可以适当减小某些安全系数的数值。在譬如设计采用线弹性方法分析破坏极限状态，但用这种方法来分析桥梁的实际承载能力，往往会得到偏于保守的，较为粗糙的结果。 基于桥梁评估方法之专家意见调查方法： 专家意见查看直接收集。分析，归纳专家意见，对某一事件的可能结果做出评估方法，这种方法一直是军事，医学，气象预测，经济，工程等诸多方面的应用了多年。 运用以不确定型层次分析法为基础的综合评估方法进行桥梁状态的综合评估，可分为分解，判断，综合，评估；分解-分解主要是建立桥梁工作状态的递阶层次结构和由判断矩阵求解个指标的权重。把影响结构工作的状态的因素逐级分解为一层一层的，这样可以反映每一层之间的关系，从而得到指标数据。判断-所谓的判断即是确定指标体系中不可再分解的指标的评语，也即指标的状态，在大型桥梁结构的综合评估中，指标评语的确定包含两个问题；一个是评价等级的确定，即对应于机构件的某个状态，我们应该将其划入哪个级别。另外一个是用什么样的方式来量化等级标准，即如何把语言表术转化为数字量。桥底层指标按表述方式的不同可分为；非量化指标和可量化指标。非量化指标主要指暂时无法定量表示的指标，如钢筋腐蚀，混凝土裂纹布置，混凝土保护层的风化等。无论是非量化还是量化指标都有一个由指标值转化为指标评价值得问题。对非量化指标而言，区间数可以在很大程度上描述事务的模糊性和不确定性，比之确定性的数字更能反映实际。同时。对大型桥梁进行评估时，一般有多个专家参与，但个个专家水平所不同，为使评估结果更好地反映桥梁的实际状态，应当对专家的评判采用加权平均。对可量化的指标而言，当实际测量值偏离桥状态时的最优值达到某种程度后，该测点可认为已处于危险状态，其值成为评估时的领结值，这两个值需要通过专家调查确定。综合-大型桥梁的综合评估是个复杂的过程，为了确定评估结果的可靠性，一般需要多为专家的参与，同时应该考虑专家的评判水平。以不确定型层次分析法为基础的综合评估方法，共有两部分的内容需要专家参与，其一是通过专家知识调查的方式构造不确定型两比较判断矩阵，其二是对于人工检测指标的评估。评估-输入实际的检测数值，按照一定的算法进行综合评估，给出相应的桥梁的状态等级，并提出相应的意见。 Bridge Rating Using System Reliability Assessment.II:Improvements to Bridge Rating PracticesNaiyu Wang,M.ASCE1;Bruce R.Ellingwood,Dist.M.ASCE2;and Abdul-Hamid Zureick,M.ASCE3Abstract:The current bridge-rating process described in AASHTO Manual for Bridge Evaluation,First Edition permits ratings to bedetermined by allowable stress,load factor,or load and resistance factor methods.These three rating methods may lead to different ratedcapacities and posting limits for the same bridge,a situation that has serious implications with regard to public safety and the economic well-being of communities that may be affected by bridge postings or closures.This paper is the second of two papers that summarize a researchprogram to developimprovements to the bridge-rating process by using structural reliability methods.The first paper provided background onthe research program and summarized a coordinated program of load testing and analysis to support the reliability assessment leading to therecommended improvements.This second paper presents the reliability basis for the recommended load rating,develops methods that closelycouple the rating process to the results of in situ inspection and evaluation,and recommends specific improvements to current bridge-ratingmethods in a format that is consistent with the load and resistance factor rating(LRFR)option in the AASHTO Manual for Bridge Evalu-ation.DOI:10.1061/(ASCE)BE.1943-5592.0000171.2011 American Society of Civil Engineers.CE Database subject headings:Concrete bridges;Reinforced concrete;Prestressed concrete;Load factors;Reliability;Steel;Ratings.Author keywords:Bridges(rating);Concrete(reinforced);Concrete(prestressed);Condition assessment;Loads(forces);Reliability;Steel;structural engineering.IntroductionThe AASHTO Manual for Bridge Evaluation(MBE),First Edition(AASHTO 2008)allows bridge ratings to be determined throughthe traditional allowable stress rating(ASR)or load factor rating(LFR)methods or by the more recent load and resistance factorrating(LRFR)method,which is consistent with the AASHTOLRFD Bridge Design Specifications(2007).These three ratingmethods may lead to different rated capacities and posted limitsfor the same bridge(NCHRP 2001;Wang et al.2009),a situationthat cannot be justified from a professional engineering viewpointand has implications for the safety and economic well-being ofthose affected by bridge postings or closures.To address this issue,the Georgia Institute of Technology has conducted a multiyearresearch program aimed at making improvements to the processby which the condition of existing bridge structures in Georgiaare assessed.The end product of this research program is set ofrecommended guidelines for the evaluation of existing bridges(Ellingwood et al.2009).These guidelines are established by a co-ordinated program of load testing and advanced finite-elementmodeling,which have been integrated within a structural reliabilityframework to determine practical bridge-rating methods that areconsistent with those used to develop the AASHTO LRFD BridgeDesign Specifications(AASHTO 2007).It is believed that bridgeconstruction and rating practices are similar enough in other non-seismic areas to make the inferences,conclusions,and recommen-dations valid for large regions in the central and eastern UnitedStates(CEUS).The recent implementation of LRFD and its companion ratingmethod,LRFR,both of which have been supported by structuralreliability methods,enable bridge design and condition assessmentto be placed on a more rational basis.Notwithstanding these ad-vances,improved techniques for evaluating the bridge in its in situcondition would minimize the likelihood of unnecessary posting.For example,material strengths in situ may be vastly different fromthe standardized or nominal values assumed in design and currentrating practices attributable to strength gain of concrete on onehand and deterioration attributable to aggressive attack from physi-cal or chemical mechanisms on the other.Satisfactory performanceof a well-maintained bridge over a period of years of service pro-vides additional information not available at the design stage thatmight be taken into account in making decisions regarding postingor upgrading.Investigating bridge system reliability rather thansolely relying on component-based rating methods may also beof significant benefit.Proper consideration of these factors is likelyto contribute to a more realistic capacity rating of existing bridges.This paper is the second of two companion papers that providethe technical bases for proposed improvements to the current LRFRpractice.The first paper(Wang et al.2011)summarized the currentbridge-rating process and practices in the United States,andpresented the results of a coordinated bridge testing and analysisprogram conducted to support revisions to the current rating pro-cedures.This paper describes the reliability analysis frameworkthat provides the basis for recommended improvements to theMBE and recommends specific improvements to the MBE thataddress the preceding factors.1Senior Structural Engineer,Simpson,Gumpertz,and Heger,Inc.,41Seyon St.,Waltham,MA 02453;formerly,Graduate Research Assistant,School of Civil and Environmental Engineering,Georgia Institute ofTechnology.2Professor,School of Civil and Environmental Engineering,Georgia Institute of Technology,790 Atlantic Dr.,Atlanta,GA 30332-0355(corresponding author).E-mail:ellingwoodgatech.edu3Professor,School of Civil and Environmental Engineering,GeorgiaInstitute of Technology,790 Atlantic Dr.,Atlanta,GA 30332-0355.Note.This manuscript was submitted on March 19,2010;approved onAugust 2,2010;published online on October 14,2011.Discussion periodopen until April 1,2012;separate discussions must be submitted for indi-vidual papers.This paper is part of the Journal of Bridge Engineering,Vol.16,No.6,November 1,2011.ASCE,ISSN 1084-0702/2011/6-863871/$25.00.JOURNAL OF BRIDGE ENGINEERING ASCE/NOVEMBER/DECEMBER 2011/863Downloaded 21 Mar 2012 to 180.95.224.53.Redistribution subject to ASCE license or copyright.Visit http:/www.ascelibrary.orgReliability Bases for Bridge Load RatingBridge design,as codified in the AASHTO-LRFD specifications(2007),is established by modern principles of structural reliabilityanalysis.The process by which existing bridges are rated mustbe consistent with those principles.Uncertainties in the perfor-mance of an existing bridge arise from variations in loads,materialstrength properties,dimensions,natural and artificial hazards,insufficient knowledge,and human errors in design and construc-tion(Ellingwood et al.1982;Galambos et al.1982;Nowak 1999).Probability-based limit states design/evaluation concepts provide arational and powerful theoretical basis for handling these uncertain-ties in bridge evaluation.The limit states for bridge design and evaluation can be definedin the general formGX 01where X X1;X2;X3;Xn=load and resistance randomvariables.On the basis of bridge performance objectives,these limitstates may relate to strength(for public safety)or to excessivedeformation,cracking,wear of the traffic surface,or other sourcesof functional impairment.A state of unsatisfactory performance isdefined,by convention,when GX 0.Thus,the probability offailure can be estimated asPf PGX 0?ZfXxdx2where fXx=joint density function of X;and=failure domain inwhich Gx 0.In modern first-order(FO)reliability analysis(Melchers 1999),Eq.(2)is often approximated byPf?3where =standard normal distribution function;and =reliability index.For well-behaved limit states,Eq.(3)usually isan excellent approximation to Eq.(2),and and Pfcan be usedinterchangeably as reliability measures(Ellingwood 2000).Whenthe failure surface in Eq.(1)is complex or when the reliability of astructural system,in which the structural behavior is modeledthrough finite-element analysis,is of interest,Eq.(2)can be evalu-ated efficiently by Monte Carlo(MC)simulation.The AASHTO LRFD Bridge Design Specifications(2007)areestablished on FO reliability analysis,applied to individual girders(Nowak 1999;Kim and Nowak 1997;Tabsh and Nowak 1991).With the supporting probabilistic modeling of resistance and loadterms(Nowak 1993;Bartlett and McGregor 1996;Moses andVerma 1987),an examination of existing bridge design practicesled to a target reliability index,equal to 3.5 based on a 75-yearservice period(Nowak 1999,Moses 2001).Consistent with suchreliability-based performance objective,the AASHTO-LRFD spec-ifications stipulate that in the design of new bridges1:25D 1:5DA 1:75L I Rn4where D=dead load excluding weight of thewearing surface;DA=weight of the wearing surface(asphalt);(L I)represents live loadincluding impact;Rn=design strength,in which Rn=nominalresistance;and =resistance factor which depends on the particu-lar limit state ofinterest.This equation is familiar to most designers.When the reliability of an existing bridge is considered,allow-ance should be made for the specific knowledge regarding its struc-tural details and past performance.Field inspection data,loadtesting,material tests,or traffic surveys,if available,can be utilizedto modify the probability distributions describing the structuralbehavior and response in Eq.(2).The metric for acceptable perfor-mance is obtained by modifying Eq.(2)to reflect the additionalinformation gatheredPf PGX 0jH?PT5where H represents what is learned from previous successfulperformance,in-service inspection,and supporting in situ testing,if any.The target probability,PT,should depend on the economicsof rehabilitation/repair,consequences of future outages,and thebridge rating sought.In the AASHTO-LRFR method(2007),thetarget for design level checking by using HL-93 load model(at inventory level)is 3.5,which is comparable to the reliabilityfor new bridges,whereas the target for HL-93 operating leveland for legal,and permit loads is reduced to 2.5 owing to thereduced load model and reduced exposure period(5 years)(Moses2001).The presence of H in Eq.(5)is a conceptual departure fromEqs.(2)and(3),which provide the basis for LRFD.For example,traffic demands on bridges located in different places in the high-way system may be different.To take this situation into account,LRFR introduces a set of live-load factors for the legal load rating,which depend on the in situ traffic described by the average dailytruck traffic(ADTT).Furthermore,the component nominal resis-tance in LRFR is factored by a system factor sand a membercondition factor cin addition to the basic resistance factor for a particular component limit state.The system factor dependson the perceived redundancy level of a given bridge in its rating,whereas the condition factor is to account for the bridges site-specific deterioration condition,and purports to include the addi-tional uncertainty because of any deterioration that may be present.The basis for the LRFR tabulated values for cwill be furtherexamined later in this paper.The LRFR option in the AASHTO MBE extends the limit statedesign philosophy to the bridge evaluation process in an attempt toachieve a uniform target level of safety for existing highway bridgesystems.However,the uncertainty models of load and resistanceembedded in the LRFR rating format represent typical values fora large population of bridges involving different materials,con-struction practices,and site-specific traffic conditions.Althoughthe LRFR live-load model has been modified for some of the spe-cific cases as discussed previously,the bridge resistance modelshould also be“customized”for an individual bridge by incorpo-rating available site-specific knowledge to reflect the fact that eachbridge is unique in its as-built condition.A rating procedure thatdoes not incorporate in situ data properly may result in inaccurateratings(and consequent unnecessary rehabilitationor postingcosts)for otherwise well-maintained bridges,as indicated by many loadtests(Nowak and Tharmabala 1988;Bakht and Jaeger 1990;Moseset al.1994;Fu and Tang 1995;Faber et al.2000;Barker 2001;Bhattacharya et al.2005).Improvements in practical guidancewould permit the bridge engineer to include more site-specificknowledge in the bridge-rating process to achieve realistic evalu-ations of the bridge performance.This guidance must have a struc-tural reliability basis.Improvements in Bridge Rating by UsingReliability-Based MethodsIn this section,the bridge ratings in light of the reliability-based updating of in-service strength described in the previoussection are examined.The possibilities of incorporating availablesite-specific data obtained from material tests,load tests,advanced864/JOURNAL OF BRIDGE ENGINEERING ASCE/NOVEMBER/DECEMBER 2011Downloaded 21 Mar 2012 to 180.95.224.53.Redistribution subject to ASCE license or copyright.Visit http:/www.ascelibrary.orgstructural analysis,and successful service performance to make fur-ther recommendations for improving rating analysis are explored.Incorporation of In Situ Material TestingThe companion paper summarized the load test of Bridge ID129-0045,a reinforced concrete T-beam bridge that was designedaccording to the AASHTO 1953 design specification for H-15loading and was constructed in 1957.The specified 28-day com-pression strength of the concrete was 17.2 MPa(2,500 psi),whereas the yield strength of the reinforcement was 276 MPa(40 ksi).The scheduled demolition of this bridge provided an op-portunity to secure drilled cores to determine the statistical proper-ties of the in situ strength of the 51-year old concrete in the bridge.Four-inch diameter drilled cores were taken from the slab of thebridge before its demolition.Seven cores were taken from the slabat seven different locations along both the length and width of thebridge.Cores also were taken from three of the girders that were ingood condition after demolition;these were cut into 203 mm(8-in.)lengths and the jagged ends were smoothed and capped,resultingin a total of 14 girder test cylinders.Tests of these 102 203 mm(4 8 in.)cylinders conformed to ASTM Standard C42(ASTM1995)and the results are presented in Table 1.An analysis of thesedata indicated no statistically significant difference in the concretecompression strength in the girders and slab,and the data weretherefore combined for further analysis.The mean(average)com-pression strength of the concrete is 33 MPa(4,820 psi)and thecoefficient of variation(COV)is 12%,which is representative ofgood-quality concrete(Bartlett and MacGregor 1996).The meanstrength is 1.93 times the specified compressionstrength of the con-crete.This increase in compression strength over a period of morethan 50 years is typical of the increases found for good-quality con-crete by other investigators(Washa and Wendt 1975).If these results are typical of well-maintained older concretebridges,the in situ concrete strength is likely to be substantiallygreater than the 28-day strength that is customarily specified forbridge design or condition evaluation.Accordingly,the bridge en-gineer should be provided incentives in the rating criteria to rate abridge by using the best possible information from in situ materialstrength testing whenever feasible(Ellingwood et al.2009).It iscustomary to base the specified compression strength of concreteon the 10th percentile of a normal distribution of cylinder strengths(Standard 318-05;ACI 2005).A suitable estimate for this 10th per-centile based on a small sample of data is provided byfc?X1?kV6where?X=sample mean;V=sample coefficient of variation;andk p%lower confidence interval on the 10th percentile compres-sion strength.By using the 21 tests from Bridge ID 129-0045 withp%75%as an example,k=1.520(Montgomery 1996)and fccan be expressed as fc 11:520 0:12 4;820 3;941 psi(27.17 MPa),a value that is 58%higher than the 17.2 MPa(2,500 psi)that otherwise would be used in the rating calculations.In the FE modeling of this bridge that preceded these strengthtests,the concrete compression strength was set at 17.2 MPa(2,500 psi),which was the only information available before thematerial test.To determine the impact of using the actual concretestrength in an older bridge on the rating process,the finite-elementmodel was revised to account for the increased concrete compres-sion strength(and the corresponding increase in stiffness)into theanalysis of the bridge.Only a modest enhancement in the estimatedbridge capacity in flexure was obtained,but a 34%increase wasachieved in the shear capacity ratings for the girders by using theresults of Table 1.Bridge System Reliability Assessment on the Basisof Static Push-Down AnalysisAlthough component-based design of a new bridge provides ad-equate safety at reasonable cost,component-based evaluation ofan existing bridge for rating purposes may be overly conservativeand result in unnecessary repair or posting costs.It is preferable toperform load rating regarding bridge posting or road closurethrough a system-level analysis.A properly conducted proof loadtest can be an effective way to learn the bridges structural perfor-mance as a system and to update the bridge load capacity assess-ment in situations in which the analytical approach produces lowratings,or structural analysis is difficult to perform because ofdeterioration or lack of documentation(Saraf and Nowak 1998).However,a proof load test represents a significant investment incapital,time,and personnel,and the trade-off between the informa-tion gain and the riskof damaging the bridge during the test mustbeconsidered.Proof tests are rarely conducted by the state DOTs(Wang et al.2009)for rating purposes.One of the key conclusions from the companion paper(Wanget al.2011),in which bridge response measurements obtained fromthe load tests of the four bridges were compared with the results offinite-element analyses of those bridges with ABAQUS(2006),was that the finite-element modeling procedure was sufficientfor conducting virtual load tests of similar bridges.These virtualload tests can provide the basis for developing recommendationsfor improving guidelines for bridge ratings by using structural reli-ability principles.As noted in the introductory section,such guide-lines require the bridge to be modeled as a structural system toproperly identify the performance limit states on which such guide-lines are to be based.To identify such performance limit states and to gain a realisticappraisal of the conservatism inherent in current bridge design andcondition rating procedures,a series of static push-down analysesof the four bridges was performed.These analyses are aimed atdetermining the actual structural behavior of typical bridges whenloaded well beyond their design limit;as a sidelight,they provideadditional information to support rational evaluation of permit loadapplications(section 6A.4.5 in the Manual of Bridge Evaluation).In a push-down analysis,two rating vehicles are placed side-by-side on the bridge in a position that maximizes the response quan-tity of interest in the evaluation(e.g.,maximum moment,shear,anddeflection).The loads are then scaled upward statically and the per-formance of the bridge system is monitored.The dead weight of thebridge structure is included in the analysis.The response is initiallyelastic.As the static load increases,however,elements of the bridgestructure begin to yield,crack,or buckle,and the generalized load-deflection behavior becomes nonlinear.If the bridge structure isredundant and the structural element behaviors are ductile,substan-tial load redistribution may occur.At some point,however,a smallincrement in static load leads to a large increment in displacement.At that point,the bridge has reached its practical load-carryinglimit,and is at a state of incipient collapse.Table 1.Compression Tests of 4 8 in:Cores Drilled from RC ConcreteBridge(ID 129-0045)SourceNumberAverage(psi)Standarddeviation(psi)Coefficient ofvariationGirder144,8806030.12Slab74,6985730.12Overall214,8205860.12Note:1 psi 6:9 Pa.JOU