機械設計外文翻譯-橋梁使用系統(tǒng)可靠性評估【中文3359字】【PDF+中文WORD】

機械設計外文翻譯-橋梁使用系統(tǒng)可靠性評估【中文3359字】【PDF+中文WORD】,中文3359字,PDF+中文WORD,機械設計,外文,翻譯,橋梁,使用,系統(tǒng),可靠性,評估,中文,3359,PDF,WORD 【中文3359字】 橋梁使用系統(tǒng)可靠性評估摘要:當前橋梁可靠性評估過程描述在AASHTO手冊第一版中有說明、評估的內容有，容許應力、載荷系數、負載和阻力系數等。這幾個數據可能導致不同的橋面承載能力和橋梁的安全性,確保這幾個橋梁參數合格與否是保證橋梁安全性和經濟性的必要途徑。本文主要總結研究橋梁建設的改進過程,以提高橋梁結構的可靠性。論文提供了背景，研究計劃和總結協(xié)調程序的負載測試和分析支持可導致的不可靠因素并提出改進建議。DOI:10.1061 /(土木)be.1943 - 5592.0000171。2011-美國土木工程師學會。CE數據庫主題詞：混凝土橋梁;鋼筋混凝土;預應力混凝土;負載因素;可靠性;鋼材;評估。作者關鍵詞:橋梁;混凝土(鋼筋);混凝土(預應力);狀態(tài)評估;負載;可靠性;鋼;結構工程。介紹 ： 橋梁評估的AASHTO手冊(MBE),第一版(AASHTO 2008)允許橋評估決定通過，傳統(tǒng)的容許應力等級(ASR)或負載因素評估(LFR)方法或最近的負載和阻力系數評估(LRFR)方法,它是符合AASHTOLRFD橋梁設計規(guī)范(2007)。大橋是否可靠經濟,從一個專業(yè)工程的觀點取決于可靠性評估是否合格。為了解決橋梁不可靠問題喬治亞理工學院的技術已經進行了多年，研究項目旨在使橋梁在建設當中更加可靠經濟。高級結構工程師,辛普森,Gumpertz,Heger,Inc .411Seyon圣,沃爾瑟姆,土木與環(huán)境工程學院,喬治亞理工學院。2亞特蘭大,佐治亞州博士,土木與環(huán)境工程學院,喬治亞理工學院,30332 - 0355.3亞特立頓,佐治亞州碩士,土木與環(huán)境工程學院,喬治亞理工學院,30332 - 0355.本文屬于橋梁工程16卷,6號,2011年11月1日。 土木,ISSN 1084 - 0702/2011/6 863 - 871 / $ 25.00。 框架法來確定實際橋梁評估方法適合那些以AASHTO LRFD橋梁設計規(guī)范(AASHTO 2007)而設計的橋梁。 并且此方法已經在美國中部和東部以及其它非地震地區(qū)得到了驗證。 近期在橋梁評估中實施了LRFD及其LRFR兩種評估方法,兩者是驗證結構可靠性的方法?，F(xiàn)有有一種vances,改進的技術評估橋梁方法此種方法會減少不必要的其它因素影響可能性的測量結果。為此,材料優(yōu)勢就可能大大影響標準化或名義假設值在設計和計算評估行為中對橋梁強度增益的影響，一個良好的橋段應在一多年的維護期內沒有什么大的修復和裂痕以及其它影響橋梁使用的問題出現(xiàn),在設計階段就應該考慮這些問題的造成原因并及時處理。調查橋梁系統(tǒng)的可靠性不是僅僅依靠基于橋梁組件及其本身的評估方法。重要的是適當的考慮這些因素產生的原因并及時避免。橋梁可靠性額定載荷：橋的設計問題在AASHTO-LRFD規(guī)格(2007),建立了現(xiàn)代的結構可靠性原理分析，要求了現(xiàn)有橋梁的評估過程必須符合規(guī)定原則。現(xiàn)有的橋梁之所以存在不安全性是應為，產生差異負載、材料強度特性變換、尺寸改變、自然和人為的危險。以及在設計當中缺乏足夠的知識,和人類在建筑設當中犯得一些錯誤。一個經濟可靠的橋梁必須建立在理性的和強大的理論基礎以及能夠處理一些實踐中不確定的影響因素。 極限狀態(tài)設計和評估橋梁可以定義的一般形式為 G（X）=0在負載和阻力隨機X=（X1，X2，X3，.Xn），橋梁的基礎信息值包括變形、開裂，功能障礙?；蛘吡硗庖恍┎缓侠淼囊蛩?。一個橋梁不令人滿意的性能定義概率被估算為： =聯(lián)合密度函數X;=故障域可靠性分析值近視于： 在（）=標準正態(tài)分布函數;=可靠性指標。對表現(xiàn)良好的極限狀態(tài),Eq通常是一個常值。可以通過有限元分析對Ep 進一步的分析比對。在橋梁設計規(guī)范的AASHTO LRFD(2007)中建立了在FO可靠性分析,應用于單個梁評估計算，及其計算概率建模的電阻和負載，例如：目標橋梁的可靠性指標=3.5，那么就說明此橋梁可以使用75年之久。概率估算公式為： 其中D =靜負荷不包括重量的磨損面;DA =重量的磨損面(瀝青);(L與I)代表活載，Rn =名義電阻。這個方程是大多數設計師再設計計算式后應用的，同時此方程也是現(xiàn)場檢驗數據,負荷測試,材料測試,等信息的可靠公式。另一種概率估算公式為： H代表性能指數,進行檢查,并支持現(xiàn)場試驗,無論任何目標概率PT,應該依賴于經濟學中的合理性在AASHTO-LRFR方法(2007)。H是一個概念上的背離方程式,LRFR介紹一組活負載因素為定值的額定載荷,這取決于現(xiàn)場交通所描述的平均每日車流量，和車載量。 在AASHTO LRFR MBE擴展了極限狀態(tài)設計實現(xiàn)了一個統(tǒng)一的目標水平對公路大橋安全的評估系統(tǒng)。然而,不確定性模型的負載和阻力嵌入式在LRFR評級格式代表典型值在高山地帶和平原地帶以及河流地帶不懂的地帶，不通的環(huán)境因素影響，不同的車流量，以及在建橋過程中不同的噸重不同的跨徑，不同的材料，相同材料的使用情況的不同都會使得評估的參數值發(fā)生改變從而使得被評估大橋的可靠性發(fā)生變化。 橋梁評估方法之間存在著一定的區(qū)別與聯(lián)系，根據各種方法得起典型特點，橋梁評估方法大致可以分為基于外觀調查的方法，基于規(guī)范設計的方法，基于專家經驗的方法，有限元法，載荷驗證，基于可靠性理論的方法，基于外觀調查的方法：根據我國的公路養(yǎng)護技術規(guī)范的規(guī)定，橋梁技術狀況評價等級分為一類，二類，三類，四類，對橋梁整體和橋梁部件均適用。將橋梁劃分為15個部件，根據橋梁部件的缺損程度及其標度，缺損對結構使用功能的影響程度以及缺損發(fā)展變化情況等，對橋梁各部件分別進行評分，值域為0到5，“0”表示完好狀況，“5”表示危險的狀況，再根據橋梁部件的評分確定個部件的評鑒等級，橋梁狀況的綜合評價，此法采用的公式為： 式中：Dr為全橋結構技術狀況評分（0-100），評分高表示結構狀況好，缺損少，Ri為對橋梁各部件的評分（0-5）,Wi為橋梁個部件權重。當Dr大于等于88.88Dr大于等于60.60Dr大于等于40.40Dr.這樣橋梁的對應級別為一類，二類，三類，四類。經驗系數: 這是依據廣泛的的調查研究，確定若干的影響承載力的系數及其取值范圍，對橋梁承載能力進行評估的方法。被評估橋梁的承載能力為所有影響之和?；谠O計規(guī)范的方法。橋梁設計規(guī)范是指導橋梁設計的標準。這一標準基于工程力學，結構試驗和工程經驗，切還在不斷充實和完善。因此，利用橋規(guī)的計算理論來分析該橋梁承載能力的方法，具有堅實的理論基礎并得到廣泛的應用，然而直接套用橋梁規(guī)范于橋梁的話對于準確評估是不準確的，這是設計與評估的差異所致，例如，在評估階段，可以獲得較設計階段更加坑定的信息按照結構可靠性理論的觀點，這意味著評估時載荷和抗力的不定性要比設計時所考慮的要小，于是，在評估時可以適當減小某些安全系數的數值。在譬如設計采用線彈性方法分析破壞極限狀態(tài)，但用這種方法來分析橋梁的實際承載能力，往往會得到偏于保守的，較為粗糙的結果?；跇蛄涸u估方法之專家意見調查方法： 專家意見查看直接收集。分析，歸納專家意見，對某一事件的可能結果做出評估方法，這種方法一直是軍事，醫(yī)學，氣象預測，經濟，工程等諸多方面的應用了多年。運用以不確定型層次分析法為基礎的綜合評估方法進行橋梁狀態(tài)的綜合評估，可分為分解，判斷，綜合，評估；分解-分解主要是建立橋梁工作狀態(tài)的遞階層次結構和由判斷矩陣求解個指標的權重。把影響結構工作的狀態(tài)的因素逐級分解為一層一層的，這樣可以反映每一層之間的關系，從而得到指標數據。判斷-所謂的判斷即是確定指標體系中不可再分解的指標的評語，也即指標的狀態(tài)，在大型橋梁結構的綜合評估中，指標評語的確定包含兩個問題；一個是評價等級的確定，即對應于機構件的某個狀態(tài)，我們應該將其劃入哪個級別。另外一個是用什么樣的方式來量化等級標準，即如何把語言表術轉化為數字量。橋底層指標按表述方式的不同可分為；非量化指標和可量化指標。非量化指標主要指暫時無法定量表示的指標，如鋼筋腐蝕，混凝土裂紋布置，混凝土保護層的風化等。無論是非量化還是量化指標都有一個由指標值轉化為指標評價值得問題。對非量化指標而言，區(qū)間數可以在很大程度上描述事務的模糊性和不確定性，比之確定性的數字更能反映實際。同時。對大型橋梁進行評估時，一般有多個專家參與，但個個專家水平所不同，為使評估結果更好地反映橋梁的實際狀態(tài)，應當對專家的評判采用加權平均。對可量化的指標而言，當實際測量值偏離橋狀態(tài)時的最優(yōu)值達到某種程度后，該測點可認為已處于危險狀態(tài)，其值成為評估時的領結值，這兩個值需要通過專家調查確定。綜合-大型橋梁的綜合評估是個復雜的過程，為了確定評估結果的可靠性，一般需要多為專家的參與，同時應該考慮專家的評判水平。以不確定型層次分析法為基礎的綜合評估方法，共有兩部分的內容需要專家參與，其一是通過專家知識調查的方式構造不確定型兩比較判斷矩陣，其二是對于人工檢測指標的評估。評估-輸入實際的檢測數值，按照一定的算法進行綜合評估，給出相應的橋梁的狀態(tài)等級，并提出相應的意見。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