機(jī)械設(shè)計(jì)外文翻譯-橋梁使用系統(tǒng)可靠性評(píng)估【中文3359字】【PDF+中文WORD】,中文3359字,PDF+中文WORD,機(jī)械設(shè)計(jì),外文,翻譯,橋梁,使用,系統(tǒng),可靠性,評(píng)估,中文,3359,PDF,WORD 【中文3359字】 橋梁使用系統(tǒng)可靠性評(píng)估 摘要:當(dāng)前橋梁可靠性評(píng)估過(guò)程描述在AASHTO手冊(cè)第一版中有說(shuō)明、評(píng)估的內(nèi)容有，容許應(yīng)力、載荷系數(shù)、負(fù)載和阻力系數(shù)等。這幾個(gè)數(shù)據(jù)可能導(dǎo)致不同的橋面承載能力和橋梁的安全性,確保這幾個(gè)橋梁參數(shù)合格與否是保證橋梁安全性和經(jīng)濟(jì)性的必要途徑。 本文主要總結(jié)研究橋梁建設(shè)的改進(jìn)過(guò)程,以提高橋梁結(jié)構(gòu)的可靠性。論文提供了背景，研究計(jì)劃和總結(jié)協(xié)調(diào)程序的負(fù)載測(cè)試和分析支持可導(dǎo)致的不可靠因素并提出改進(jìn)建議。DOI:10.1061 /(土木)be.1943 - 5592.0000171。2011-美國(guó)土木工程師學(xué)會(huì)。 CE數(shù)據(jù)庫(kù)主題詞：混凝土橋梁;鋼筋混凝土;預(yù)應(yīng)力混凝土;負(fù)載因素;可靠性;鋼材;評(píng)估。 作者關(guān)鍵詞:橋梁;混凝土(鋼筋);混凝土(預(yù)應(yīng)力);狀態(tài)評(píng)估;負(fù)載;可靠性;鋼;結(jié)構(gòu)工程。 介紹 ： 橋梁評(píng)估的AASHTO手冊(cè)(MBE),第一版(AASHTO 2008)允許橋評(píng)估決定通過(guò)，傳統(tǒng)的容許應(yīng)力等級(jí)(ASR)或負(fù)載因素評(píng)估(LFR)方法或最近的負(fù)載和阻力系數(shù)評(píng)估(LRFR)方法,它是符合AASHTOLRFD橋梁設(shè)計(jì)規(guī)范(2007)。大橋是否可靠經(jīng)濟(jì),從一個(gè)專(zhuān)業(yè)工程的觀點(diǎn)取決于可靠性評(píng)估是否合格。為了解決橋梁不可靠問(wèn)題 喬治亞理工學(xué)院的技術(shù)已經(jīng)進(jìn)行了多年，研究項(xiàng)目旨在使橋梁在建設(shè)當(dāng)中更加可靠經(jīng)濟(jì)。 高級(jí)結(jié)構(gòu)工程師,辛普森,Gumpertz,Heger,Inc .41 1Seyon圣,沃爾瑟姆,土木與環(huán)境工程學(xué)院,喬治亞理工學(xué)院。 2亞特蘭大,佐治亞州博士,土木與環(huán)境工程學(xué)院,喬治亞理工學(xué)院,30332 - 0355. 3亞特立頓,佐治亞州碩士,土木與環(huán)境工程學(xué)院,喬治亞理工學(xué)院,30332 - 0355. 本文屬于《橋梁工程16卷,6號(hào),2011年11月1日。 土木,ISSN 1084 - 0702/2011/6 863 - 871 / $ 25.00?！? 框架法來(lái)確定實(shí)際橋梁評(píng)估方法適合那些以AASHTO LRFD橋梁設(shè)計(jì)規(guī)范(AASHTO 2007)而設(shè)計(jì)的橋梁。 并且此方法已經(jīng)在美國(guó)中部和東部以及其它非地震地區(qū)得到了驗(yàn)證。 近期在橋梁評(píng)估中實(shí)施了LRFD及其LRFR兩種評(píng)估方法,兩者是驗(yàn)證結(jié)構(gòu)可靠性的方法?，F(xiàn)有有一種vances,改進(jìn)的技術(shù)評(píng)估橋梁方法此種方法會(huì)減少不必要的其它因素影響可能性的測(cè)量結(jié)果。為此,材料優(yōu)勢(shì)就可能大大影響標(biāo)準(zhǔn)化或名義假設(shè)值在設(shè)計(jì)和計(jì)算評(píng)估行為中對(duì)橋梁強(qiáng)度增益的影響，一個(gè)良好的橋段應(yīng)在一多年的維護(hù)期內(nèi)沒(méi)有什么大的修復(fù)和裂痕以及其它影響橋梁使用的問(wèn)題出現(xiàn),在設(shè)計(jì)階段就應(yīng)該考慮這些問(wèn)題的造成原因并及時(shí)處理。調(diào)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(píng)估方法。重要的是適當(dāng)?shù)目紤]這些因素產(chǎn)生的原因并及時(shí)避免。 橋梁可靠性額定載荷： 橋的設(shè)計(jì)問(wèn)題在AASHTO-LRFD規(guī)格(2007),建立了現(xiàn)代的結(jié)構(gòu)可靠性原理分析，要求了現(xiàn)有橋梁的評(píng)估過(guò)程必須符合規(guī)定原則?，F(xiàn)有的橋梁之所以存在不安全性是應(yīng)為，產(chǎn)生差異負(fù)載、材料強(qiáng)度特性變換、尺寸改變、自然和人為的危險(xiǎn)。以及在設(shè)計(jì)當(dāng)中缺乏足夠的知識(shí),和人類(lèi)在建筑設(shè)當(dāng)中犯得一些錯(cuò)誤。一個(gè)經(jīng)濟(jì)可靠的橋梁必須建立在理性的和強(qiáng)大的理論基礎(chǔ)以及能夠處理一些實(shí)踐中不確定的影響因素。 極限狀態(tài)設(shè)計(jì)和評(píng)估橋梁可以定義的一般形式為 G（X）=0 在負(fù)載和阻力隨機(jī)X=（X1，X2，X3，.....Xn），橋梁的基礎(chǔ)信息值包括變形、開(kāi)裂，功能障礙。或者另外一些不合理的因素。 一個(gè)橋梁不令人滿(mǎn)意的性能定義概率被估算為： =聯(lián)合密度函數(shù)X;Ω=故障域可靠性分析值近視于： 在Φ（）=標(biāo)準(zhǔn)正態(tài)分布函數(shù);β=可靠性指標(biāo)。對(duì)表現(xiàn)良好的極限狀態(tài),Eq通常是一個(gè)常值。可以通過(guò)有限元分析對(duì)Ep 進(jìn)一步的分析比對(duì)。 在橋梁設(shè)計(jì)規(guī)范的AASHTO LRFD(2007)中建立了在FO可靠性分析,應(yīng)用于單個(gè)梁評(píng)估計(jì)算，及其計(jì)算概率建模的電阻和負(fù)載，例如：目標(biāo)橋梁的可靠性指標(biāo)β=3.5，那么就說(shuō)明此橋梁可以使用75年之久。概率估算公式為： 其中D =靜負(fù)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(gè)方程是大多數(shù)設(shè)計(jì)師再設(shè)計(jì)計(jì)算式后應(yīng)用的，同時(shí)此方程也是現(xiàn)場(chǎng)檢驗(yàn)數(shù)據(jù),負(fù)荷測(cè)試,材料測(cè)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(shù),進(jìn)行檢查,并支持現(xiàn)場(chǎng)試驗(yàn),無(wú)論任何目標(biāo)概率PT,應(yīng)該依賴(lài)于經(jīng)濟(jì)學(xué)中的合理性在AASHTO-LRFR方法(2007)。H是一個(gè)概念上的背離方程式,LRFR介紹一組活負(fù)載因素為定值的額定載荷,這取決于現(xiàn)場(chǎng)交通所描述的平均每日車(chē)流量，和車(chē)載量。 在AASHTO LRFR MBE擴(kuò)展了極限狀態(tài)設(shè)計(jì)實(shí)現(xiàn)了一個(gè)統(tǒng)一的目標(biāo)水平對(duì)公路大橋安全的評(píng)估系統(tǒng)。然而,不確定性模型的負(fù)載和阻力嵌入式在LRFR評(píng)級(jí)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(chē)流量，以及在建橋過(guò)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(huì)使得評(píng)估的參數(shù)值發(fā)生改變從而使得被評(píng)估大橋的可靠性發(fā)生變化。 橋梁評(píng)估方法之間存在著一定的區(qū)別與聯(lián)系，根據(jù)各種方法得起典型特點(diǎn)，橋梁評(píng)估方法大致可以分為基于外觀調(diào)查的方法，基于規(guī)范設(shè)計(jì)的方法，基于專(zhuān)家經(jīng)驗(yàn)的方法，有限元法，載荷驗(yàn)證，基于可靠性理論的方法，基于外觀調(diào)查的方法： 根據(jù)我國(guó)的《公路養(yǎng)護(hù)技術(shù)規(guī)范》的規(guī)定，橋梁技術(shù)狀況評(píng)價(jià)等級(jí)分為一類(lèi)，二類(lèi)，三類(lèi)，四類(lèi)，對(duì)橋梁整體和橋梁部件均適用。將橋梁劃分為15個(gè)部件，根據(jù)橋梁部件的缺損程度及其標(biāo)度，缺損對(duì)結(jié)構(gòu)使用功能的影響程度以及缺損發(fā)展變化情況等，對(duì)橋梁各部件分別進(jìn)行評(píng)分，值域?yàn)?到5，“0”表示完好狀況，“5”表示危險(xiǎn)的狀況，再根據(jù)橋梁部件的評(píng)分確定個(gè)部件的評(píng)鑒等級(jí)，橋梁狀況的綜合評(píng)價(jià)，此法采用的公式為： 式中：Dr為全橋結(jié)構(gòu)技術(shù)狀況評(píng)分（0-100），評(píng)分高表示結(jié)構(gòu)狀況好，缺損少，Ri為對(duì)橋梁各部件的評(píng)分（0-5）,Wi為橋梁個(gè)部件權(quán)重。 當(dāng)Dr大于等于88.88>Dr大于等于60.60>Dr大于等于40.40>Dr.這樣橋梁的對(duì)應(yīng)級(jí)別為一類(lèi)，二類(lèi)，三類(lèi)，四類(lèi)。 經(jīng)驗(yàn)系數(shù): 這是依據(jù)廣泛的的調(diào)查研究，確定若干的影響承載力的系數(shù)及其取值范圍，對(duì)橋梁承載能力進(jìn)行評(píng)估的方法。被評(píng)估橋梁的承載能力為所有影響之和。 基于設(shè)計(jì)規(guī)范的方法。 橋梁設(shè)計(jì)規(guī)范是指導(dǎo)橋梁設(shè)計(jì)的標(biāo)準(zhǔn)。這一標(biāo)準(zhǔn)基于工程力學(xué)，結(jié)構(gòu)試驗(yàn)和工程經(jīng)驗(yàn)，切還在不斷充實(shí)和完善。因此，利用橋規(guī)的計(jì)算理論來(lái)分析該橋梁承載能力的方法，具有堅(jiān)實(shí)的理論基礎(chǔ)并得到廣泛的應(yīng)用，然而直接套用橋梁規(guī)范于橋梁的話(huà)對(duì)于準(zhǔn)確評(píng)估是不準(zhǔn)確的，這是設(shè)計(jì)與評(píng)估的差異所致，例如，在評(píng)估階段，可以獲得較設(shè)計(jì)階段更加坑定的信息按照結(jié)構(gòu)可靠性理論的觀點(diǎn)，這意味著評(píng)估時(shí)載荷和抗力的不定性要比設(shè)計(jì)時(shí)所考慮的要小，于是，在評(píng)估時(shí)可以適當(dāng)減小某些安全系數(shù)的數(shù)值。在譬如設(shè)計(jì)采用線彈性方法分析破壞極限狀態(tài)，但用這種方法來(lái)分析橋梁的實(shí)際承載能力，往往會(huì)得到偏于保守的，較為粗糙的結(jié)果。 基于橋梁評(píng)估方法之專(zhuān)家意見(jiàn)調(diào)查方法： 專(zhuān)家意見(jiàn)查看直接收集。分析，歸納專(zhuān)家意見(jiàn)，對(duì)某一事件的可能結(jié)果做出評(píng)估方法，這種方法一直是軍事，醫(yī)學(xué)，氣象預(yù)測(cè)，經(jīng)濟(jì)，工程等諸多方面的應(yīng)用了多年。 運(yùn)用以不確定型層次分析法為基礎(chǔ)的綜合評(píng)估方法進(jìn)行橋梁狀態(tài)的綜合評(píng)估，可分為分解，判斷，綜合，評(píng)估；分解-分解主要是建立橋梁工作狀態(tài)的遞階層次結(jié)構(gòu)和由判斷矩陣求解個(gè)指標(biāo)的權(quán)重。把影響結(jié)構(gòu)工作的狀態(tài)的因素逐級(jí)分解為一層一層的，這樣可以反映每一層之間的關(guān)系，從而得到指標(biāo)數(shù)據(jù)。判斷-所謂的判斷即是確定指標(biāo)體系中不可再分解的指標(biāo)的評(píng)語(yǔ)，也即指標(biāo)的狀態(tài)，在大型橋梁結(jié)構(gòu)的綜合評(píng)估中，指標(biāo)評(píng)語(yǔ)的確定包含兩個(gè)問(wèn)題；一個(gè)是評(píng)價(jià)等級(jí)的確定，即對(duì)應(yīng)于機(jī)構(gòu)件的某個(gè)狀態(tài)，我們應(yīng)該將其劃入哪個(gè)級(jí)別。另外一個(gè)是用什么樣的方式來(lái)量化等級(jí)標(biāo)準(zhǔn)，即如何把語(yǔ)言表術(shù)轉(zhuǎn)化為數(shù)字量。橋底層指標(biāo)按表述方式的不同可分為；非量化指標(biāo)和可量化指標(biāo)。非量化指標(biāo)主要指暫時(shí)無(wú)法定量表示的指標(biāo)，如鋼筋腐蝕，混凝土裂紋布置，混凝土保護(hù)層的風(fēng)化等。無(wú)論是非量化還是量化指標(biāo)都有一個(gè)由指標(biāo)值轉(zhuǎn)化為指標(biāo)評(píng)價(jià)值得問(wèn)題。對(duì)非量化指標(biāo)而言，區(qū)間數(shù)可以在很大程度上描述事務(wù)的模糊性和不確定性，比之確定性的數(shù)字更能反映實(shí)際。同時(shí)。對(duì)大型橋梁進(jìn)行評(píng)估時(shí)，一般有多個(gè)專(zhuān)家參與，但個(gè)個(gè)專(zhuān)家水平所不同，為使評(píng)估結(jié)果更好地反映橋梁的實(shí)際狀態(tài)，應(yīng)當(dāng)對(duì)專(zhuān)家的評(píng)判采用加權(quán)平均。對(duì)可量化的指標(biāo)而言，當(dāng)實(shí)際測(cè)量值偏離橋狀態(tài)時(shí)的最優(yōu)值達(dá)到某種程度后，該測(cè)點(diǎn)可認(rèn)為已處于危險(xiǎn)狀態(tài)，其值成為評(píng)估時(shí)的領(lǐng)結(jié)值，這兩個(gè)值需要通過(guò)專(zhuān)家調(diào)查確定。綜合-大型橋梁的綜合評(píng)估是個(gè)復(fù)雜的過(guò)程，為了確定評(píng)估結(jié)果的可靠性，一般需要多為專(zhuān)家的參與，同時(shí)應(yīng)該考慮專(zhuān)家的評(píng)判水平。以不確定型層次分析法為基礎(chǔ)的綜合評(píng)估方法，共有兩部分的內(nèi)容需要專(zhuān)家參與，其一是通過(guò)專(zhuān)家知識(shí)調(diào)查的方式構(gòu)造不確定型兩比較判斷矩陣，其二是對(duì)于人工檢測(cè)指標(biāo)的評(píng)估。評(píng)估-輸入實(shí)際的檢測(cè)數(shù)值，按照一定的算法進(jìn)行綜合評(píng)估，給出相應(yīng)的橋梁的狀態(tài)等級(jí)，并提出相應(yīng)的意見(jiàn)。 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