土木工程英语翻译

翻译6Lateralbucklingofbeams6.1IntroductionInthediscussiongiveninChapter5ofthein-planebehaviourofbeams,itwasassumedthatwhenabeamisloadedinitsstifferprincipalplane,itdeflectsonlyinthatplane.Ifthebeamdoesnothavesufficientlateralstiffnessorlateralsupporttoensurethatthisisso,thenitmaybuckleoutoftheplaneofloading,asshowninFig.6.1.Theloadatwhichthisbucklingoccursmaybesubstantiallylessthanthebeam'sin-planeloadcarryingcapacity,asindicatedinFig.6.2.6.梁的侧面翘曲6.1说明在第五章关于梁的平面内性能的讨论中，假定梁按刚性主平面放置时，梁仅在该平面内倾斜。如果梁没有足够的侧向刚度或侧面支撑，梁会发生平面外屈曲，如图6.1所示。如图6.2所示，当发生平面外屈曲时梁的承载能力会大大减小。Foranidealizedperfectlystraightelasticbeam,therearenoout-of-planedeformationsuntiltheappliedmomentMreachestheelasticbucklingmomentM0b,whenthebeambucklesbydeflectinglaterallyandtwisting,asshowninFig.6.1.Thesetwodeformationsareinterdependent:whenthebeamdeflectslaterally,theappliedmomenthasacomponentwhichexertsatorqueaboutthedeflectedlongitudinalaxiswhichcausesthebeamtotwist.Thisbehaviour,whichisimportantforlongunrestrainedI-beamswhoseresistancestolateralbendingandtorsionarelow,iscalledelasticflexural-torsionalbuckling.作为一个理想的弹性直梁，当施加弯矩达到弹性屈曲弯矩时，梁才会发生侧向弯曲和扭转变形，发生平面外屈曲，如图6.1所示。这两种变形是相互联系的：当梁侧向倾斜时，所承受的弯矩会对侧向梁轴产生扭矩并引起梁扭转。这种特性，对于抵抗侧向弯曲和扭转能力差的无限制I形梁来说很重要，被成为弯扭屈曲。Thefailureofaperfectlystraightslenderbeamisinitiatedwhentheaddi-tionalstressesinducedbyelasticbucklingcausefirstyield.However,aper-fectlystraightbeamofintermediateslendernessmayyieldbeforetheelasticbucklingmomentisreached,becauseofthecombinedeffectsofthein-planebendingstressesandanyresidualstresses,andmaysubsequentlybucklein-elastically,asindicatedinFig.6.2.Forverystockybeams,theinelasticbucklingmomentmaybehigherthanthein-planeplasticcollapsemomentpMinwhichcasethemomentcapacityofthebeamisnotaffectedbylateralbuckling.理想弹性直梁的屈服始于因为因为弹性屈曲产生的附加应力导致的屈服，然而，受平面内弯曲应力和残余应力的影响，理想弹性直梁的中间部位可能在到达屈服弯矩前先行屈服，并发生塑形弯曲，如图6.2所示。对于短梁，其非弹性屈曲弯矩会大于平面内塑形破坏弯矩，受弯承载力不由侧向屈曲控制。Inthischapter,thebehaviouranddesignofbeamswhichfailbylateralbucklingandyieldingarediscussed.Itisassumedthatlocalbucklingofthecompressionflangeoroftheweb(whichisdealtwithinChapter4)doesnotoccur.Thebehaviouranddesignofbeamsbentaboutbothprincipalaxes,andofbeamswithaxialloads,arediscussedinChapter7.在本章，将讲述由侧向屈曲和屈服引起破坏的梁的性能和设计方法。假设第四章中讨论的局部屈曲不会发生。第七章将讨论轴压及压弯构件的性能和设计方法。6.2Elasticbeams6.2.1BUCKLINGOFSTRAIGHTBEAMS6.2.1.1SimplysupportedbeamswithequalendmomentsAperfectlystraightelasticbeamwhichisloadedbyequalandoppositeendmomentsisshowninFig.6.3.Thebeamissimplysupportedatitsendssothatlateraldeflectionandtwistrotationareprevented,whiletheflangeendsarefreetorotateinhorizontalplanessothatthebeamendsarefreetowarp(seesection10.8.3).ThebeamwillbuckleatamomentA/0bwhenadeflectedandtwistedequilibriumposition,suchasthatshowninFig.6.3,ispossible.Itisshowninsection6.10.1.1thatthispositionisgivenbywhereistheundeterminedmagnitudeofthecentraldeflection,andthattheelasticbucklingmomentisgivenby,yzobMM（6.2）WherewhereEIyistheminoraxisflexuralrigidity,GJthetorsionalrigidity,andE/wthewarpingrigidityofthebeam.Equation6.3showsthattheresistancetobucklingdependsonthegeometricmeanoftheflexuralresistance)/(22LEIyandthetorsionalresistance)/(22LEIGJW.6.2.弹性梁6.2.1直梁的屈曲6.2.1.1端弯矩相等的简支梁如图6.3所示，一个承受相等梁端弯矩的理想弹性直梁。梁端简支侧向弯曲和扭转不会发生，因为端部可以在平面内自由转动从而不限制梁端转角。当侧移和扭转达到平衡时，在obM作用下梁会弯曲，如图6.3所示。这种情况在6.10.1.1中给出公式：为梁跨中挠度，大小未知，弹性屈曲弯矩计算公式为：,yzobMM（6.2）yEI为侧向弯曲刚度，GJ为扭转刚度，WEI为翘曲刚度。公式6.3表示梁的抗屈曲能力取决于临界弯矩)/(22LEIy以及临界扭矩)/(22LEIGJW。Equation6.3ignorestheeffectsofthemajoraxiscurvatureXobEIMdzvd22andproducesconservativeestimatesoftheelasticbucklingmomentequaltoXWXyEILEIGJEIEI2/1/122timesthetruevalue.Thiscorrectionfactor,whichisjustlessthanunityformostbeamsectionsbutmaybesignificantlylessthanunityforcolumnsections,isusuallyneglectedindesign.Nevertheless,itsvalueapproacheszeroasIyapproachesIxsothatthetrueelasticbucklingmomentapproachesinfinity.ThusanI-beaminuniformbendingaboutitsweakaxisdoesnotbuckle,whichisintuitivelyobvious.Research[1]hasindicatedthatinsomeothercasesthecorrection.factormaybeclosetounity,andthatitisprudenttoignoretheeffectofmajoraxiscurvature.公式6.3忽略了强轴曲率XobEIMdzvd22，并且保守估计梁的屈曲弯矩等于真实弯矩乘以XWXyEILEIGJEIEI2/1/122。这种修正，在大多数梁截面设计中是可以忽略的，柱的设计中则不然。它把梁的yI和XI当作零处理，使得梁的弹性屈曲弯矩接近无穷大。很明显，I型钢梁不会绕弱轴屈曲。研究【1】表明在其他情形下修正值接近真实值，忽略强轴曲率是可以的。6.2.1.2BeamswithunequalendmomentsAsimplysupportedbeamwithunequalmajoraxisendmomentsMandasshowninFig.6.4a.Itisshowninsection6.10.1.2thatthevalueoftheendJimomentMabatelasticflexural-torsionalbucklingcanbeexpressedinthe.-formofyzmobMM（6.4）inwhichthemomentmodificationfactormwhichaccountsfortheeffectofthenon-uniformdistributionofthemajoraxisbendingmomentcanbecloselyapproximatedbyorby6.2.1.2端弯矩不等的简支梁如图6.4.a所示，一简支梁承受端弯矩M和M，6.10.1.2所示，弯扭屈曲梁端弯矩公式为：yzmobMM（6.4）表明强轴弯矩不均匀分配作用影响的修正系数m近似表示为：或者Theseapproximationsformthebasisofaverysimplemethodofpredictingthebucklingofthesegmentsofabeamwhichisloadedonlybyconcentrated.loadsappliedthroughtransversememberspreventinglocallateraldeflectionandtwistrotation.Inthiscase,eachsegmentbetweenloadpointsmaybetreatedasabeamwithunequalendm