Tacoma Narrows Bridge

塔科马大桥朱浩然刘兆锋目录1.背景2.倒塌现象3.原因分析4.解决措施5.建议背景ThebridgewastakenintoserviceinJuly1940,andwaslocatedovertheTacomaNarrowsinthePugetSoundsome60kilometressouthofSeattleintheStateofWashington.Itwasconstructedasa1660metrelongsuspensionbridgewithamainspanof853metres,thethirdlongestsuspensionbridgeintheworld(andUSA)；atthattime.Thebridgedeckwas11.9metrewide,supportedbytwo2.45metredeepplategirders(I-girders).倒塌现象8.am左右，风速大约16-19m/s，加劲梁产生强烈的上下振动（0.9m）振动频率大约0.6Hz.10.am左右，好像什么东西折断（吊杆疲劳断裂），振动形式突然发生了改变，开始出现扭转，成45度不断扭转，振幅从0.9m不断增大到8.5m!10.30am，一块嵌板掉了下来，扭转继续。11.am，整个加劲梁像拉链一样扯裂，然后就是地动山摇...原因分析内因——结构柔度大（未考虑动载效应）；外因——气弹颤振.内因————外因内因——结构柔度大宽跨比：Thebridgeauthoritiesrecommendedthatthewidthofsuspensionbridgesshouldbeatleastaminimumof1/30ofthespanlengthinordertoensureacertainminimumlateralstiffness.TheTacomaBridgehadawidth-to-spanratioofonly1/72(11.9m/853m),buthadbeencheckedagainststaticwindloadingandfoundtobesufficientinbothstiffnessandstrength(withrespecttomaximumallowablelateraldeflectionandstresses).——仅考虑了静载效应。内因——结构柔度大高跨比：Thedepth-to-spanratioforthestiffeninggirderinsuspensionbridges,inthespanrangeof600–900metres,wasrecommendedtobeabove1/90(earlierevenabove1/40),thatis,withadepthofthestiffeninggirderofatleast1/90ofthespanlength.TheTacomaBridge,withits2.45metrehighgirders(seeFig.7.3),hadadepth-to-spanratioofonly1/348.Iftheywouldhavebeentomeetthisrecommendationthenthestiffeninggirderdepthshouldhavebeenatleast9.5metres(i.e.853m/90)!——强缆弱梁.内因——结构柔度大SoitisveryeasytoconcludethattheTacomaBridgehadaveryslenderandflexiblebridgedeck,bothintheverticaldirection(forin-planebending)andinthehorizontal(out-of-plane)lateraldirection.——结构的水平和竖向刚度不够！总之，Tacoma的设计就是太浪了.........外因——气弹颤振Across-sectionsuchastheTacomaBridgedeck–havingasmallwidthinrelationtoitslength,andaveryflexiblestiffeninggirder,consistingofsolidwebplates–isespeciallysensitivetotheformationofvortices(whirlpools)inasteadyairflow,whichappearatregularinterval(i.e.ataconstantfrequency)atthebackofthedeck(ontheleewardside).Thisphenomenoncreatesalternatingsuctioninthetransversedirectiontothewind,perpendiculartothebridgedeck,subjectingittopullingforcesupanddown(intheverticaldirection)atregularfrequency,while,atthesametime,thebridgeispushedhorizontallybythesteadywind.外因——气弹颤振verticaloscillation:TacomaBridgeishavingalight-weightdeck,withaflexiblestiffeninggirder,wherealargeportionoftheload(self-weightandliveload)istakenbythemaincables,thenthereishighpotentialforlargedeflections(notonlysusceptibletowindandtrafficinducedvibrations,butalsosoftanddeformableforliveloads).外因——气弹颤振solution1:Onewayoflimitingthesekindsofvibrationsistolockthecableatmidspan,asthemidpointofthecableismovingbackandforthwhenthecableisstretched(inrelationtothemidpointofthedeckthatis).ThemaincableoftheTacomaBridgewasinfactlockedtothedeckinasimilarway,sothedesignerswereactuallyawareofthisbeneficialeffect.外因——气弹颤振torsionaloscillation:Asthetorsionaldeformationofthedeckwellhasstartedthenthereisalsoatendencyofthewindactingasadrivingforce,asthesurfaceofthedeckisexposed(however,intheoppositedirectionthewindisstabilizing–pushingdowninsteadofpushingup).外因——气弹颤振lateran/torsionalbuckling:Compressionstressesareformedintheendgirderatthewindwardsideandtensionstressesintheotherendgirderattheleewardside,andthecompressionflangecouldbuckletransversetothewindloadingdirection(ifthewindisstrongenoughthatis).——一侧受拉，一侧受压，受压侧可能发生屈曲后失稳。解决措施1.增加扭转加劲，对于Tacoma即添加横向加劲。2.桥面加宽，考虑动载效应。3.改钢板加劲梁为桁架加劲梁。4.提高加劲梁的自重（混凝土结构）新桥采用建议1.任何桥梁建设前必须经过风洞试验测试，以选择最优结构。2.桥梁设计时考虑的经济合理性应建立保证在结构安全的前提下。3.端梁与吊杆的连接细节.（疲劳设计）总之，桥梁的问题总会发生，所以，大家共同努力吧~~谢谢赏脸！