附加偏心距和偏心距增大系数

8.3附加偏心距和偏心距增大系数8.3Additionaleccentricityandeccentricitymagnifyingcoefficient附加偏心距和偏心距增大系数Accidentaleccentricityea（附加偏心距）e0+eaiscalledinitialeccentricityei（初始偏心距）areconsideredinthecalculation.aieee+=01、Accidentaleccentricity附加偏心距参考以往工程经验和国外规范，附加偏心距取ea=20mmorh/30两者中的较大值，此处h是指偏心方向的截面尺寸。8.3附加偏心距和偏心距增大系数8.3附加偏心距和偏心距增大系数由于施工误差、计算偏差及材料的不均匀等原因，实际工程中不存在理想的轴心受压构件。为考虑这些因素的不利影响，引入附加偏心距ea(accidentaleccentricity)，即在正截面压弯承载力计算中，偏心距取计算偏心距e0=M/N与附加偏心距ea之和，称为初始偏心距ei(initialeccentricity)，aieee+=0参考以往工程经验和国外规范，附加偏心距ea取20mm与h/30两者中的较大值，此处h是指偏心方向的截面尺寸。一、附加偏心距二、eccentricitymagnifyingcoefficient◆◆second-ordereffectwillappearduetolateraldeflection，thencausetheadditionalmoment◆◆Ifthecolumnisslender,theadditionalmomentcannotbeneglected.◆◆ThelateraldeflectionofmiddleThelateraldeflectionofmiddleshowedinFig.showedinFig.isisf.◆◆Forthesectioninmiddle,theForthesectioninmiddle,theeccentricityofaxialloadiseccentricityofaxialloadisei+f，andthemomentisM=N(ei+f).elxfyπsin⋅=fyxeieiNNNeiN(ei+f)le8.3附加偏心距和偏心距增大系数二、偏心距增大系数◆◆由于侧向挠曲变形，轴向力将产生二阶效应(second-ordereffect)，引起附加弯矩◆◆对于长细比较大的构件，二阶效应引起附加弯矩不能忽略。◆◆图示典型偏心受压柱，跨中侧向挠度为f.◆◆对跨中截面，轴力N的偏心距为ei+f，即跨中截面的弯矩为M=N(ei+f).elxfyπsin⋅=fyxeieiNNNeiN(ei+f)le8.3附加偏心距和偏心距增大系数二、◆◆IfthesectionandtheIfthesectionandtheinitialeccentricityaretheinitialeccentricityarethesame,buttheslendernesssame,buttheslendernessl0/handthelateraldeformationaredifferent,theinfluenceofsecondsecond--ordereffectordereffectisdifferentisdifferentandwillcausedifferentfailure.elxfyπsin⋅=fyxeieiNNNeiN(ei+f)le8.3附加偏心距和偏心距增大系数Eccentricitymagnificationfactor二、Eccentricitymagnificationfactor偏心距增大系数◆◆在截面和初始偏心距相同的情况下，柱的长细比l0/h(slenderness)不同，侧向挠度f的大小不同，二阶效应的影响程度会有很大差别，将产生不同的破坏类型。elxfyπsin⋅=fyxeieiNNNeiN(ei+f)le8.3附加偏心距和偏心距增大系数MNN0M0NusNuseiNumNumeiNumfmNulNuleiNulflFortheslendernessofshortFortheslendernessofshortcolumncolumnl0/h≤5◆◆LateraldeformationLateraldeformationfcomparewithinitialcomparewithinitialeccentricityeccentricityeiisverysmall.isverysmall.◆◆ThemomentinthemiddleThemomentinthemiddleM=N(ei+f)isincreasingwiththeincreaseoftheN8.3附加偏心距和偏心距增大系数◆◆UntilthesectionreachesultimatelimitstatesandUntilthesectionreachesultimatelimitstatesandoccursoccursfailure.failure.◆◆Forashortcolumn,thedeformationForashortcolumn,thedeformationfisnegligible.MNN0M0NusNuseiNumNumeiNumfmNulNuleiNulfl对于长细比l0/h≤5的短柱◆◆侧向挠度f与初始偏心距ei相比很小,◆◆柱跨中弯矩M=N(ei+f)随轴力N的增加基本呈线性增长，◆◆直至达到截面承载力极限状态产生破坏。◆◆对短柱可忽略挠度f影响。8.3附加偏心距和偏心距增大系数MNN0M0NusNuseiNumNumeiNumfmNulNuleiNulflFortheslendernessFortheslendernessl0/hofthemiddleslendercolumnis5~30◆◆fcannotbeneglectedcannotbeneglectedcomparingcomparingwithwithei.◆◆fisincreasingastheincreaseofaxialload,thespeedofthemomentinthemiddleofcolumnspanM=N(ei+f)isbiggerthanthatofN.◆◆MisincreasingquicklyastheincreaseofNandappearsnonlinear◆◆AlthoughitwillreachtheultimatelimitstatesthatthecarryiAlthoughitwillreachtheultimatelimitstatesthatthecarryingngcapacityislowerthantheshortcolumncapacityislowerthantheshortcolumn..◆◆Forslendercolumn,wemustconsidertheadditionalForslendercolumn,wemustconsidertheadditionaldeformationindesign.deformationindesign.8.3附加偏心距和偏心距增大系数MNN0M0NusNuseiNumNumeiNumfmNulNuleiNulfl长细比l0/h=5~30的中长柱◆◆f与ei相比已不能忽略。◆◆f随轴力增大而增大，柱跨中弯矩M=N(ei+f)的增长速度大于轴力N的增长速度，◆◆即M随N的增加呈明显的非线性增长◆◆虽然昀终在M和N的共同作用下达到截面承载力极限状态，但轴向承载力明显低于同样截面和初始偏心距情况下的短柱。◆◆因此，对于中长柱，在设计中应考虑附加挠度f对弯矩增大的影响。8.3附加偏心距和偏心距增大系数MNN0M0NusNuseiNumNumeiNumfmNulNuleiNulfl8.3附加偏心距和偏心距增大系数FortheslendernessoftheslenderFortheslendernessoftheslendercolumncolumnl0/h30◆◆TheinfluenceoflateralTheinfluenceoflateraldeformationdeformationfisbig.isbig.◆◆LateraldeformationLateraldeformationfisisinstablebeforeitreachestheinstablebeforeitreachestheultimatelimitstates.ultimatelimitstates.◆◆TheaxialloadisappearedTheaxialloadisappearedbeforetheinteractionlinebeforetheinteractionlineNu-Mu◆◆Thisfailureisinstablefailure,Thisfailureisinstablefailure,andweshoulddesignitandweshoulddesignitspecialty.specialty.MNN0M0NusNuseiNumNumeiNumfmNulNuleiNulfl8.3附加偏心距和偏心距增大系数长细比l0/h30的长柱◆◆侧向挠度f的影响已很大◆◆在未达到截面承载力极限状态之前，侧向挠度f已呈不稳定发展◆◆即柱的轴向荷载昀大值发生在荷载增长曲线与截面承载力Nu-Mu相关曲线相交之前◆◆这种破坏为失稳破坏，应进行专门计算偏心距增大系数iiiefefe+=+=1ηφ⋅=1020lf0hscεεφ+=，21200141911ζζη⎟⎠⎞⎜⎝⎛+=hlhei取h=1.1h08.3附加偏心距和偏心距增大系数elxfyπsin⋅=fyxeieiNNlel02/022lxdxyd=−=φ202lfπ=2010lf≈0017.025.10033.00hb+×=φ017.1711h⋅=hl0201.015.1−=ζNAfc/5.01=ζ偏心距增大系数iiiefefe+=+=1η2/022lxdxyd=−=φφ⋅=1020lf0017.025.10033.00hb+×=φ0.17.22.01ie+=ζ0hscεεφ+=，hl0201.015.1−=ζ，8.3附加偏心距和偏心距增大系数elxfyπsin⋅=fyxeieiNNlel0202lfπ=2010lf≈017.1711h⋅=21200141911ζζη⎟⎠⎞⎜⎝⎛+=hlhei取h=1.1h08.3附加偏心距和偏心距增大系数Effectivelengthforanon-swaycolumn8.3附加偏心距和偏心距增大系数Effectivelengthforaswaycolumn8.3附加偏心距和偏心距增大系数Effectivelengthinanon-swayandswayframe8.3附加偏心距和偏心距增大系数表8-4框架结构各层柱段的计算长度楼盖类型柱的类别计算长度底层柱1.0H现浇楼盖其余各层柱1.25H底层柱1.25H装配式楼盖其余各层柱1.5H注：表中H对底层柱为从基础顶面到一层楼盖顶面的高度；对其余各层柱为上、下两层楼盖顶面之间的高度；8.3附加偏心距和偏心距增大系数按有侧移考虑的框架结构，当竖向荷载较小，水平荷载较大，或竖向荷载大部分作用在框架节点及其附近时，柱的计算长度可取，⎩⎨⎧+++=HHllu)2.02()](15.01[minmin0ψψψ∑∑=)/()/(bbcclEIlEIψ),min(minluψψψ=8.3附加偏心距和偏心距增大系数Δ3Δ2Δ1有侧移框架结构的二阶效应★★Ifthemethodaboveisused,theexpressionIfthemethodaboveisused,theexpressionηeiinequationinequationshou