影響線及其應(yīng)用雙語

第十一章Chapter11影響線及其應(yīng)用Influencelinesandtheirapplication本章主要內(nèi)容Maincontents1、影響線概念Theconceptofinfluence

lines2、靜力法繪制影響線Staticmethod

3、機(jī)動(dòng)法繪制影響線mechanismicmethod

4、影響線應(yīng)用Applicationofinfluencelines（1）利用影響線求固定荷載作用下的內(nèi)力Determineinternalforcesunderfixedloads（2）確定最不利荷載位置

Determinetheunfavorablelocationsofloads（3）簡(jiǎn)支梁的絕對(duì)最大彎矩Determinethemaximumbendingmoment（4）簡(jiǎn)支梁的包絡(luò)圖

Drawenvelopes

§6-1影響線的概念Theconceptofinfluencelines1、移動(dòng)荷載Movingloads移動(dòng)荷載:方向、大小不變，僅作用位置變化的荷載directionandmagnitudedon’tchange,onlypositionschange(movingload)如橋梁上行駛的車輛，工業(yè)廠房中吊車梁上開動(dòng)的行車等,forinstancethemovingcarsonbridges,thecranesinfactories。

結(jié)構(gòu)承受移動(dòng)荷載作用時(shí)，其反力、內(nèi)力以及位移等均隨荷載作用位置的變化而改變。Underthemovingloads,thereactions,internalforcesanddisplacementsofstructureswillchangewiththemovementoftheloads10kNP=10kNP=10kNP=10kN7.5kNP=10kN5kNP=10kN2.5kNP=10kN0kN10kN

為解決千變?nèi)f化的移動(dòng)荷載作用下結(jié)構(gòu)的設(shè)計(jì)問題，基于線彈性結(jié)構(gòu)的疊加原理，如果掌握了單位移動(dòng)荷載下結(jié)構(gòu)的反力、內(nèi)力與位移變化規(guī)律，則任意移動(dòng)荷載下的反力、內(nèi)力與位移可用疊加方法獲得。Forthesolutionofproblemsofdesignofstructures,basedonthesuperpositionprincipleoflinearelasticstructures,ifweknowthevariationlawsofthereactions,internalforcesanddisplacements,thenthereactions,internalforcesanddisplacementsunderanymovingloadscanbedeterminedbysuperpositionprinciple

定義Definition:單位移動(dòng)荷載作用下，結(jié)構(gòu)反力、內(nèi)力或位移等隨荷載位置變化的函數(shù)關(guān)系，分別稱為反力、內(nèi)力、位移的影響系數(shù)方程，對(duì)應(yīng)的函數(shù)圖形分別稱為反力、內(nèi)力、位移的影響線（InfluenceLine縮寫為I.L.）。undertheactionofunitload,thefunctionalrelationsofthereactions,internalforcesanddisplacementsofstructureswiththeunitloadpositionarecalledtheinfluentialcoefficientequation,andthecorrespondingfunctiongraphsarecalledtheInfluenceLineofthereactions,internalforcesanddisplacementsofstructures.為了方便，以下把反力、內(nèi)力和位移均稱為量值或物理量。Fortheconveniencethereactions,internalforcesanddisplacementsofstructurescalledparameters

注意：定義中“單位移動(dòng)荷載”下的量值稱為影響系數(shù)，可以理解為：在單個(gè)移動(dòng)荷載作用下某指定物理量與荷載P的比值，習(xí)慣上以在結(jié)構(gòu)上移動(dòng)的P=1（即量綱一或無量綱）表示“單位移動(dòng)荷載”。因此，物理量影響系數(shù)的量綱是，物理量的量綱和移動(dòng)荷載量綱之比。例如單位移動(dòng)荷載P是集中力，則彎矩、反力偶影響線的量綱為L(zhǎng)(長(zhǎng)度)，剪力、反力影響線的量綱為１(或無量綱)等等。Remark:influentialcoefficients:therationofthepointedquantitytotheunitloads.Thedimensionoftheinfluentialcoefficient

isequaltothedimensionofresponsefunctiondividedbythedimensionoftheunitload.作影響線有兩種基本方法Twobasicmethods：靜力法（staticmethod）,機(jī)動(dòng)法(或者稱虛功法)（mechanismicorvirtualdisplacementmethod）?！?-2用靜力法作單跨靜定梁的影響線Constructing

influencelinesofstaticallydeterminatesinglespanbeamsbystaticmethod靜力法思路theprocedure：利用靜力求解方法（對(duì)靜定結(jié)構(gòu)用平衡條件）求結(jié)構(gòu)在P=1移動(dòng)荷載下所求某物理量與荷載P=1的位置間的函數(shù)關(guān)系式，即影響系數(shù)方程，然后由方程作出影響線。Usingstaticequilibriumequationstodeterminethefunctionsofthedesiredparameterswiththepositionoftheunitloads,thenconstructinfluencelinesbythesefunctions.

1、確定坐標(biāo)系，以坐標(biāo)x表示荷載P=1的位置definethecoordinateoftheunitloadbyx,；2、對(duì)于給定的x，P=1

看成是固定的荷載，確定所求量的值即可得影響系數(shù)方程Forgivenxandunitload,determinethefunctionsofthedesiredparameterswiththepositionoftheunitloadsx,

3、按方程作出影響線并標(biāo)明符號(hào)和控制點(diǎn)的縱坐標(biāo)值constructinfluencelinesbythesefunctions.。注：正確的影響線應(yīng)該具有正確的外形、必要的控制點(diǎn)縱坐標(biāo)值和正負(fù)號(hào)（簡(jiǎn)稱三要素）。內(nèi)力正負(fù)號(hào)規(guī)定與前幾章相同。習(xí)慣上將縱標(biāo)為正的影響線畫于基線上方，但因?yàn)橐獦?biāo)正負(fù)號(hào)，所以這并不是規(guī)定。Particularattentionshouldbepaidtotheform,ordinatesofcontrollingpointsandthesignsoftheI.L.graphs(3elementsofI.L).具體步驟為procedure：

1、簡(jiǎn)支梁的影響線I.L.forsimplebeam（1）支座反力影響線

TheI.L.forreactionsP=1ABlRARB1I.L.RA1I.L.RBUsingequilibriumequationstodeterminethereactionforcefunctionswiththeunitloadpositionx,thenconstructILbythesefunctions.（2）內(nèi)力力影響響線I.L.forinternalforcesABlCabP=1RARBI.L.MC㈠I.L.QCCharacteristics特點(diǎn)：：BendingmomentandshearingforceILsABlCabP=1RA1I.L.RA1I.L.RBI.L.MC㈠I.L.QCRB2.懸臂梁梁的影影響線線I.L.forcantileverbeamsP=1CABlab㈠bI.L.MC1I.L.QC3、伸臂臂梁的的影響響線I.L.foroverhangingbeamsll1l2aba1b1ABCDEK1K2P=1RARB11I.L.MCI.L.QCI.L.RAI.L.RBll1l2aba1b1ABCDEK1K2P=1RARB○－○－○－I.L.MK1a1b111I.L.MK2I.L.QK1I.L.QK2§6-3間接荷載作作用下的影影響線I.L.forforgirderswithfloorsystems主梁Girder橫梁Floorbeam縱梁stringerP設(shè)：縱梁簡(jiǎn)簡(jiǎn)支在橫梁梁上，橫梁梁簡(jiǎn)支在主主梁上。Ifstringerslieonfloorbeam,andfloorbeamslieongirder,主梁只在橫橫梁處（結(jié)結(jié)點(diǎn)處）受受集中力作作用。荷載loads縱梁stringer橫梁floorbeams主梁Girder對(duì)主梁而言言，這種荷荷載稱為間接荷載或結(jié)點(diǎn)荷載panelloads。PanelpointsThetransformationoftheloads間接荷載作作用下主梁梁某量值的的影響線的的繪制TheI.L.ForonedesiredquantityforgirderduetopanelloadsP=1以D截面彎矩MD為例taketheI.L.forMDonthesectionD：1、當(dāng)P=1位于橫梁（（結(jié)點(diǎn)）處處時(shí)，與直直接荷載相相同，既間間接荷載作作用下的影影響線在結(jié)結(jié)點(diǎn)處的值值與直接荷荷載作用下下的影響線線在結(jié)點(diǎn)處處的值相同同。WhenP=1locatesatpanelpoints,theordinatesofI.L.isidenticaltothatofI.L.whenP=1isapplieddirectlytothegirder.DP=1P=1直接荷載下下影響線間接影響線線值與直接接影響線值值相同2、當(dāng)P=1在橫梁（結(jié)結(jié)點(diǎn)）之間間時(shí)whenP=1islocatedwithinstringercontainingthelocationoftheresponsefunction：DP=1DP=1xdAB直接荷載下下影響線yAyBI.L.MD間接荷載作作用下AB段影響線結(jié)點(diǎn)（橫梁梁）間影響響線為直線線，且在兩兩端與直接接影響線值值相同。Theordinatesbetweenpointsareconnectedbystraightlines,andtheordinatesat2endsareidenticaltothatoftheI.L.undertheactionofloadsapplieddirectlyongirder.I.L.MD間接荷載作作用下影響響線繪制過過程procedureforconstructingI.L.duetopanel-pointloads：（1）作出直接接荷載作用用下的影響響線ConstructI.L.whenP=1isapplieddirectlytothegirder；（2）取各結(jié)點(diǎn)點(diǎn)出的豎標(biāo)標(biāo)，并在各各豎標(biāo)間連連直線Connectalltheordinatesatpanelpointsbystraightlines?！?-4用機(jī)動(dòng)法作作單跨靜定定梁的影響響線MechanismicmethodforconstructingI.L.forstaticallydeterminatesingle-spanbeams(Muller-Breslaumethod)思路：利用用虛位移原原理將靜力力學(xué)問題轉(zhuǎn)轉(zhuǎn)化為幾何何作圖問題題UsingvirtualdisplacementmethodtheproblemofconstructionofI.L.istransformedintogeometricproblem以簡(jiǎn)支梁支支座A的反力RA影響線為例例TaketheconstructionofI.L.forreactionRAatsupportAasanexample.ABP=1ABP=1RAAP虛位移圖由虛功原理理：P為P=1作用點(diǎn)沿P=1方向的虛位位移。由于于P=1是移動(dòng)的，，因此各點(diǎn)點(diǎn)的P連線構(gòu)成圖圖形，稱為為（豎向））虛位移圖圖。PrepresentsthedisplacementofthepointofapplicationofP=1.Thetrackofdisplacementordinatesconstitutevirtualdisplacementgraph令A(yù)=1，則Ra=P，此時(shí)虛位位移圖P便代表Ra的影響線。。1+I.L.RA沿RA方向單位位位移引起沿沿P=1方向的虛位位移圖機(jī)動(dòng)法：1.將與量值X相應(yīng)的聯(lián)系系拆除，并并代之以相相應(yīng)的力X，得到釋放放約束結(jié)構(gòu)構(gòu)1.FromagivenstructurereleasetherestraintcorrespondingtotheresponsefunctionwhoseI.L.isdesired,andimposeacorrespondingforcesXtoobtainthereleasedstructure.2.ApplyaunitdisplacementinthedirectionX,constructdeflectedshapediagramofthereleasedstructurethatisconsistentwiththesupportandcontinuityconditionsofthereleasedtoobtainthegeneralshapeoftheinfluenceline.2.使體系沿X正方向產(chǎn)生生單位位移移所得荷載載作用點(diǎn)的的豎向位移移圖即代表表X的影響線。。注意：位移移是單位力力作用點(diǎn)處處的位移Attention:Thedisplacementisthedisplacementofthepointwheretheunitloadisappliedto.機(jī)動(dòng)法作影影響線I.L.bymechanismicmethod§6-5多跨靜定梁梁的影響線線Influencelinesofstaticallydeterminatemulti-spanbeams求Mk，QB左，及RF當(dāng)F=1在量值本身身所在段時(shí)時(shí)等同于單單跨梁；當(dāng)F=1在對(duì)于量值值本身所在在段來講為為基本部分分時(shí)量值為為零；當(dāng)F=1在對(duì)于量值值本身所在在段來講為為附屬部分分時(shí)量值影影響線為直直線。根據(jù)據(jù)在鉸處量量值已知及及支座處為為零定出影影響線。利用機(jī)動(dòng)法法求Mk,QB左,RF影響線.機(jī)動(dòng)法作影影響線I.L.bymechanismicmethod試作圖示多多跨梁的影響線。機(jī)動(dòng)法作影影響線I.L.bymechanismicmethod試作圖示結(jié)結(jié)點(diǎn)傳荷主主梁的影響線?！?-6桁架的影響響線I.L.fortrusses只討論單跨跨梁式桁架架的影響線線HereonlyI.L.forsinglespangirdertrussesarediscussed.梁式單跨桁桁架的支座座反力計(jì)算算與相應(yīng)單單跨梁的反反力計(jì)算相相同，故兩兩者反力影影響線相同同。Themethodfordeterminationofreactionsofsinglespangirdertrussesisidenticaltothemethodofthereactionsforsinglespanbeams,thereforetheI.Lforthese2typesofstructuresareidentical.主要討論桁桁架桿件內(nèi)內(nèi)力影響線線HerewewillmainlydiscusstheI.Lforthemembersoftrusses.桁架承受的的是結(jié)點(diǎn)荷荷載—間接荷載Theloadsareappliedonthejointsoftruss,theycanbetreatedaspanelpointloads.桁架桿內(nèi)力力影響線與與間接荷載載作用下的的影響線特特征相同—在各結(jié)間為為直線段。。ThecharacteristicsoftheI.L.formembersoftrussisidenticaltothatofI.L.forpanelpointloads-theordinatesatallthepointsareconnectedbystraightlines.將P=1作用于各結(jié)結(jié)點(diǎn)上，求求出內(nèi)力值值，得結(jié)點(diǎn)點(diǎn)處影響線線值，再連連以直線，，即得所求求內(nèi)力影響響線。Determinetheordinatesatjoints,andthenconnecttheordinatesatthepoints,weobtaintheI.L.注意attentions：1、區(qū)分P=1在上弦或下下弦移動(dòng)ItisnecessarytoidentifytheI.L.forunitloadappliedontopchordsandonbottomchords.2、對(duì)斜桿，，可繪出內(nèi)內(nèi)力的水平平或豎向分分力影響線線forinclinedmemberswemayconstructtheI.L.forverticalorhorizontalcomponentsoftheinternalforces.3、對(duì)于求內(nèi)內(nèi)力截開的的區(qū)間應(yīng)該該給予特別別的關(guān)注,截開節(jié)間兩兩端的豎標(biāo)標(biāo)需要連直直線。Particularattentionshouldbepaidtothecutpanel，theordinatesattheendsofpanelshouldbeconnectedbystraightline.桁架內(nèi)力計(jì)計(jì)算—結(jié)點(diǎn)法、截截面法(力矩法、投投影法)I.L.byjointmethodandsectionmethodP=1abcdABRARB11ⅠⅠⅡⅡACDACFEDEF求F12、F45、F15、F25的影響線（1）F12的影響線用I-I面截開結(jié)構(gòu)構(gòu)，以5為矩心列平衡方程程即得F12的表達(dá)式式（2）F45的影響線線用I-I面截開結(jié)結(jié)構(gòu)，以以1為矩心列平衡方方程即得得F45的表達(dá)式式（3）F15的影響線線用I-I面截開結(jié)結(jié)構(gòu)，以以o為矩心列平衡方方程即得得F15的表達(dá)式式（5）F4A的影響線線以結(jié)點(diǎn)A為隔離體體，列平平衡方程程即得F4A的表達(dá)式式（4）F25的影響線線用II-II面截開結(jié)結(jié)構(gòu)，列列豎向平平衡方程程即得F25的表達(dá)式式單位荷載載作用于于上下弦弦所引起起的指定定量值影影響線是是不同的的whentheunitvalueloadactsonupperandbottomchordstheILofthedesiredquantityaredifferent.1.利用結(jié)點(diǎn)點(diǎn)K求出2個(gè)斜桿桿內(nèi)力的的關(guān)系。。2.然后利用用截面I-I截開結(jié)構(gòu)構(gòu)，利用用豎向平平衡方程程求出b桿的內(nèi)力力。3.c桿內(nèi)力類類似求出出。4.最后利用用結(jié)點(diǎn)3’的平衡來來求a桿的內(nèi)力力。§6-7利用影響響線求量量值DeterminequantitiesbyI.L.本節(jié)解決決的問題題是Theproblemtobesolved：當(dāng)若干個(gè)個(gè)集中荷荷載或分分布荷載載作用于于已知位位置時(shí)，，利用影影響線來來求某一一量值。。Whenthepositionsofseveralconcentratedordistributedloadsaregiven,determinethedesiredquantitiesbyI.L.1、集中荷荷載作用用Forconcentratedforces當(dāng)荷載處處于影響響線為直直線段時(shí)時(shí)loadswithinstraightsegmentoftheI.L.2、均布荷荷載作用用foruniformlydistributedloadsω-ω+§6-8最不利荷荷載位置置Themostunfavorablelocationoftheloads本節(jié)要點(diǎn)點(diǎn)：為了了進(jìn)行設(shè)設(shè)計(jì)，必必須確定定某量值值的最大大（最小小）值。。為此，，必須先先確定使使該量值值發(fā)生最最大（最最小）值值時(shí)的荷荷載位置置。位置置一確定定，就可可用上節(jié)節(jié)的方法法求出最最大（最最?。┲抵?。Forthepurposeofdesign,itisnecessarytodeterminethemaximumofthedesiredquantity.Forthisendwemustdeterminetheloadlocationsinducingthemaximumofthequantity.Oncethemostunfavorablelocationsaredetermined,wecanusethemethodsinthepreviousparagraphtodeterminemaximumandminimum.定義：稱稱使某量量值為最最大（最最?。┲抵档暮奢d載位置為為該量值值的最不不利荷載載位置。。Definition:thecriticalpositionsonwhichthevaluesofthedesiredquantityofastructurewillreachtomaximumvalues(positiveornegative)arecalledthemostunfavorablepositions.本節(jié)就是是討論如如何利用用影響線線來確定定最不利利荷載位位置InthissectionwewilluseI.L.todeterminethemostunfavorablepositions。1、單個(gè)集集中荷載載singleconcentratedforce將單位載放在在影響線最大豎標(biāo)處產(chǎn)生最最大量值。PlacetheloadatthelocationofthemaximumpositiveordinateofI.L.todevelopmaximumpositivevalue將單位載放在在影響線最小豎標(biāo)處產(chǎn)生最最小量值PlacetheloadatthelocationofthenegativemaximumordinateofI.L.todevelopmaximumnegativevalue。2、可任意斷續(xù)續(xù)分布的均布布荷載Arbitraryuniformlydistributedloads荷載布滿影響響線所有正面面積部分產(chǎn)生生最大量值Theloaddistributingoverallthesectionswithpositiveordinatewilldevelopmaximumpositivevalue；荷載布滿影響響線所有負(fù)面面積部分產(chǎn)生生最小量值Theloaddistributingoverallthesectionswithnegativeordinatewilldevelopmaximumnegativevalue；3、一系列間距距不變的移動(dòng)動(dòng)荷載組（行行列荷載）Aseriesofmovingconcentratedloadswithfixeddistancesbetweenthem或or（1）、當(dāng)S為極大時(shí)，whenSismaximumthenΔS<0，則Δx<0（荷載左移whenloadsmoveslightlytotheleft）Δx>0（荷載左移whenloadsmoveslightlytotheright）（2）、當(dāng)S為極小時(shí)whenSisminimumthen,ΔS>0,則Δx<0（荷載左移whenloadsmoveslightlytotheleft）Δx>0（荷載左移whenloadsmoveslightlytotheright）即，當(dāng)荷載左左、右移動(dòng)微微小距離時(shí)，，Ritgαi必須變號(hào)，ＳＳ才能是極值值．I.e.whenloadsmoveslightlytotheleftandright,Ritgαichangesitssign,thenSreachesitsextremevalues.若荷載從左向向右移動(dòng)，Ritgαi由正變負(fù)，ＳＳ取極大。Ritgαi由負(fù)變正，ＳＳ取極小。Whenloadsmovefromlefttoright,Ritgαichangesitssignfromnegativetopositive.Ｓhasitsminimumvalue條件conditions：tgαi為常數(shù)，故只只有Ri變化，Ritgαi才有可能變號(hào)號(hào)。tgαiisconstant,OnlywhenthevalueofoneoftheresultantsRichangesitsmagnitudethathasthepossibilitytomakethesunRitgαichangeitssign.只有當(dāng)某一集集中荷載恰好好位于影響線線的某一頂點(diǎn)點(diǎn)時(shí)，才有可可能。ThisispossiblewhenoneoftheseriesofloadslocatesatthevertexpointoftheI.L.最不利荷載位位置的大致估估計(jì)Theapproximateidentificationofthemostunfavorableposition：（1）、荷載中數(shù)數(shù)值較大且較較密集的部分分置于影響線線的最大豎標(biāo)標(biāo)附近；thepartofloadswithgreatermagnitudesanddensityshouldbeplacedonthevicinityofpositionwithmaximumordinates（2).同符號(hào)的影響響線范圍內(nèi)的的荷載應(yīng)盡可可能多ThediapasonofI.L.withthesamesignshouldbeplacedasmoreloadsaspossible。通過試算，來來確定最不利利荷載位置Bytrialstodeterminethemostunfavorablepositions當(dāng)某荷載位于于影響線某頂頂點(diǎn)時(shí)，使Ritgαi變號(hào)，稱該荷荷載為臨界荷荷載，此時(shí)的的荷載位置稱稱為臨界位置置。TheloadwhichmakesthesumRitgαichangeitssignwhenitmovestotheleftortotherightofthepositionofvertexoftheI.L.istermedascriticalpositionoftheloads.當(dāng)影響線為三三角形時(shí)，臨臨界荷載Pcr滿足WhentheI.L.hastheTriangularshape,criticalloadPcrsatisfiesthefollowingcondition：（極大值）均布荷載作用用時(shí)foruniformlydistributedloads：DeterminethemostunfavorablelocationoftheloadsandabsolutemaximumvalueofZExampleICExampleII因?yàn)橛袩o窮大大斜率，需要要試算§6-9簡(jiǎn)支梁的絕對(duì)對(duì)最大彎矩Theabsolutemaximummoment定義：各截面的最最大彎矩中的最大大值稱為絕對(duì)最大大彎矩。Themaximummomentamongthemaximummomentsateverysectionsistermedastheabsolutemaximummoment.對(duì)一般的移動(dòng)荷載載，理論上應(yīng)將各各截面的最大彎矩矩求出，來獲得絕絕對(duì)最大彎矩。Theoreticallyforgeneralmovingloadsweshouldatfirstdeterminethemaximummomentsateverysectionsinordertodeterminetheabsolutemoment.實(shí)際中，截面無窮窮多，不可能這樣樣作，因此可取有有限個(gè)截面，來近近似計(jì)算。Butinrealitywecannotdosobecauseoftheinfinityofthesectionsinstructures.Thereforewemaytakeseveralsectionstodoapproximatecalculation確定絕對(duì)最大彎矩矩要解決以下兩個(gè)個(gè)問題2problemsneedtobesolved：（1）絕對(duì)最大彎矩發(fā)發(fā)生在哪一截面；；Identifythesectionatwhichtheabsolutemaximummomentisreached（2）此截面發(fā)生最大大彎矩時(shí)的荷載位位置Thepositionsonwhichtheabsolutemaximummomentisreached.對(duì)由集中荷載組成成的移動(dòng)荷載，問問題可以簡(jiǎn)化,因?yàn)閺澗氐淖畲笾抵迭c(diǎn)必定是某個(gè)集集中載的作用點(diǎn)：：Foraseriesofmovingconcentratedloadstheproblemmaybesimplified,becausethesectionwithmaximumbendingmomentisoneoftheapplicationpointsofloadsFK作用點(diǎn)處的彎矩Mx為ThemomentatthesectionofapplicationofFKis式中MK表示FK以左梁上荷載對(duì)于于FK點(diǎn)處的力矩總和WhereMKisthesumofmomentsinducedbyalltheloadsintheleftofFKabouttheapplicationpointofFK支座反力為ThereactionatsupportAis極值條件為theconditionforextremevalueis即當(dāng)FK與合力FR的位置對(duì)稱于梁的的中點(diǎn)時(shí)FK之下截面的彎矩達(dá)達(dá)到最大值I.e.whenFKandFRaresymmetricalwithrespecttothemiddlepointofthebeamthemomentattheapplicationsectionofFKreachesitsmaximumvalue當(dāng)FR位于FK的左邊時(shí)WhenFRislocatedattheleftofFKwehave在荷載多時(shí)，上述述方法非常煩雜。。Whentherearemanyloads,thepreviousmethodisverycomplicated.可以利用這樣的事事實(shí)：通常簡(jiǎn)支粱粱的絕對(duì)最大彎矩矩發(fā)生在粱的中點(diǎn)點(diǎn)附近。Butwecanusethefollowingfact:generallythemaximumbendingmomentarisesatthemiddleofthebeam.使粱中點(diǎn)截面發(fā)生生最大彎矩的臨界界荷載通常也是發(fā)發(fā)生最大彎矩的荷荷載。利用這一事事實(shí)可得下列簡(jiǎn)化化方法。Thecriticalloadsthatinducemaximumbendingmomentatthemiddleofbeamareloadsthatresultinmaximumbendingmoment.Usingthisfactwecanobtainthefollowingsimplifiedmethod.計(jì)算最大彎矩的基基本方法(basicmethodfordeterminationofmaximumbendingmoment1、首先確定使粱的的中點(diǎn)發(fā)生最大彎彎矩的臨界荷載3、計(jì)算作作用處的彎彎矩，即為絕對(duì)最最大彎矩。2、計(jì)算合力，，把把與與對(duì)對(duì)稱于梁梁的中點(diǎn)布置，這這時(shí)要注意是否有有力移出粱跨。如如果有力移出粱跨跨，需要重新計(jì)算算合力，重復(fù)上述述步驟.Atfirstdeterminetheloadthatinducesthemaximummomentatthemiddleofthebeam,andcalculatetheCalculateFR,andplaceFRandFksymmetricallywithrespecttothemiddleofthebeam,inthiscaseneedpayattentiontowhetherthereareloadsoutsidethespan,ifthereare,thencalculateFRagain,andrepeattheabovementionedprocedureCalculatethemomentatthepositionofweobtainthemaximumbendingmoment并計(jì)算此時(shí)粱中點(diǎn)點(diǎn)的最大彎矩DeterminetheabsolutemaximumbendingmomentofthesimplebeamunderthegivenloadsandcompareitwiththemaximumbendingmomentatthemiddleofthebeamDeterminethemaximumbendingmomentatthemiddleofthebeamDeterminetheabsolutemaximumbendingmoment§6-10簡(jiǎn)支梁的內(nèi)力包絡(luò)絡(luò)圖Theenvelopesofinternalforces