混凝土結(jié)構(gòu)理論 英文版重點

－PAGE1－《混凝土結(jié)構(gòu)理論》課程重點內(nèi)容總結(jié)-版本2015.12.30華南理工大學(xué)混凝土結(jié)構(gòu)課程組版本2015年12月30日星期三(初稿，此處指明的是重點，需根據(jù)新規(guī)范逐步調(diào)整，最終版會根據(jù)大家的整理重新上傳）(如此文件與課本有沖突，以課本說法為準）第一章緒論建筑結(jié)構(gòu)名詞:結(jié)構(gòu)，構(gòu)件，構(gòu)造分類:按材料混凝土、砌體、木、鋼、組合按受力磚混、單層廠房、框架、框剪、剪力墻、筒體、巨型、懸掛、大跨度。鋼筋混凝土結(jié)構(gòu)優(yōu)點:耐久性好、耐火性好、可模性好、整體性好、就地取材、節(jié)約鋼材缺點:自重大、工期長、抗裂性差混凝土結(jié)構(gòu)的發(fā)展參見課本[chapter1,2羅晗吳志浩]Chapter1Introduction1.Thegeneralconceptofconcretestructures(1)Classification.①Plainconcretestructure:Withoutsteelbarsorreinforcement.②Reinforcementconcretestructure(R.C.S)—It’sakindofstructurethatreinforcementconcreteismainload-bearingskeleton.(ReinforcedConcreteisakindofmaterialsofconstructionthatconcreteandsteelarecombinedincertainmethodforconcertedaction.)③Prestressedconcretestructure—It’sakindofstructurethatreinforcementconcreteequipswithpre-stressbyallocatingpre-stressedsteelbarsmethodandtensilemethodetc.④Steelreinforcedconcretestructure(Encasedconcretestructure)⑤Concretefilledtubestructure⑥Compositestructure(Hybridstructure)(2)Theroleandrequirementsofreinforcement.①Role:(a)ImprovingtheloadcapacityofRCmembers.(Beamcanworkhealthilywithcracks.)(b)ImprovingthedeflectioncapacityofRCmembers.(Beambecomeductile,haveobviousfailureomenfromcrackingtocollapse.)②Requirement:(a)Reinforcementandconcretecanworktogether—Thereissufficientlystrongbondbetweenreinforcementandconcrete.(Reason:i.Thethermalexpansioncoefficientofthebarsandtheconcreteisnearlythesame.ii.Theconcretecovercanpreventthesteelbarsinsidefrombucklingundercompressionanrusting.)(b)Theallocationandnumberofreinforcementshouldbedeterminedbycalculationanddetailingrequirements.(3)Mainadvantagesanddisadvantagesofconcretestructure①Advantages(a)Locallyavailableresources.(b)Durabilityandfireresistance.(c)Thevariousformscanbedeposited.(d)highstiffness.②Disadvantages(a)Largedeadmass:density25kN/m3(b)Easilycracked:inherentweakness.(c)Longcuringperiod.2.Thedevelopmentandapplicationofconcretestructure(1)Development.①Firststage:1850tothelatenineties(a)ApplicationofR.Ccomponent.(b)Capacityiscalculation:i.elasticanalysismethodii.allowablestressdesignprincipal.②Secondstage:theearlytwentiestothesecondworldwar(a)Spacestructureandpre-stressedconcrete,thinshellsstructure.(b)Capacitycalculation:i.plasticanalysismethod,ii.failurestatedesignprinciple③Thirdstage:thesecondworldwartonow(a)industrializationconstructionmethod.(b)limitstatedesignprinciplebasedonprobabilitytheory.(c)Materials:highstrengthconcreteandreinforcement.(d)Structure:high-riseandoff-shorestructure.(2)Theapplicationandprospectsincivilengineeringapplication:①Industrialandcivilbuildings.②Transportfacilities.③Waterconservancyandhydro-powerconstructions.④Foundationworks.etc.Prospects:①Lunarsurfaceengineering.②Largespanbuilding.③High-risebuilding.etc.第二章材料的力學(xué)性能混凝土 1．基本概念:抗壓好，抗拉差； 2．組成:水泥凝膠+砂+石；3．強度:3.1單軸強度a．立方體抗壓強度150mm×150mm×150mm的試件，在20±3℃的溫度下，和90％以上的濕度中，按標準試驗方法測得。C15，20，25，30，35，40，45，50，55，60，65，70，75，80，其中C50及C50以上是高強混凝土。一般結(jié)構(gòu)中，要求C20以上，預(yù)應(yīng)力中需要C30或者C40注意點:套箍效應(yīng)b．軸心抗壓強度(較接近于實際構(gòu)件）150mm×150mm×300mm 3.2雙軸受力:要點(雙向應(yīng)力狀態(tài)下混凝土的破壞包絡(luò)圖）結(jié)論:1）雙向受拉強度與單向受拉接近；2）一向受拉，一向受壓時，受壓或受拉強度均降低；3）雙向受壓時抗壓強度比單向受壓強度高(在雙向應(yīng)力比值為0.5～0.7時可以達到最大）【要點】:需要明白這個雙向受力圖怎么畫出來的 3.3三向受力:近似公式: 4．變形 4.1受力變形4.1.1短期一次加載(單軸）a）應(yīng)力應(yīng)變曲線:是一種非線性材料，彈塑性材料，有上升和下降段，應(yīng)力圖由拋物線段和直線段組成。0.002，0.0033；b）泊松比:μ=0.2；c）模量:混凝土的模量是一個變值，分原點模量(彈性模量）、切線，割線模量(割線模量或彈塑性模量）。4.1.2長期荷載(徐變）:概念見書，分線性徐變和非線性徐變。需要了解影響徐變的因素:內(nèi)在因素；環(huán)境因素；應(yīng)力因素。 4.1.3重復(fù)荷載:疲勞破壞:特征是裂縫小而變形大疲勞強度與重復(fù)作用時應(yīng)力變化的幅度關(guān)系很大，變化幅度越小，疲勞強度越高 4.2體積變形(溫度變形，收縮變形）非荷載變形 收縮:混凝土在空氣中凝結(jié)硬化時，水分析出引起了混凝土的收縮。 影響因素:水泥，骨料，養(yǎng)護條件，制作方法，使用環(huán)境等。影響:引起混凝土開裂；使預(yù)應(yīng)力構(gòu)件產(chǎn)生預(yù)應(yīng)力損失鋼筋分類勁性鋼筋(角鋼，槽鋼，工字形鋼）柔性鋼筋(普通鋼筋，鋼絲束）鋼絲束+普通鋼筋【包括光面鋼筋HPB235+變形鋼筋HRB335(II級），HRB400(III級），RRB400(余熱處理III級）】要求記住普通鋼筋的強度品種:【2.1碳素鋼:低、中、高碳鋼。隨碳增加，強度大塑性小】；【低合金鋼錳硅釩鈦】強度屈服強度，極限強度變形(畫變形圖）0.0015，0.01，塑性指標:伸長率和冷彎性能加工性能(冷拉(抗拉強度提高、抗壓強度降低），冷拔(同時提高抗拉強度和抗壓強度））鋼筋與混凝土的粘結(jié)粘結(jié)的重要意義:粘結(jié)是鋼筋和混凝土這兩種性質(zhì)不同的材料能形成整體，共同工作的基礎(chǔ)。粘結(jié)應(yīng)力的產(chǎn)生:粘結(jié)應(yīng)力與梁的剪力變化規(guī)律一致粘結(jié)的分類:a錨固粘結(jié)和延伸粘結(jié)b裂縫附近的局部粘結(jié)粘結(jié)的機理:【光面鋼筋:膠接力，摩阻力】；【變形鋼筋(主要是機械咬合力）:膠接力(化學(xué)，較?。?，摩阻力(混凝土收縮引起），咬合力(表面的凹凸）】影響粘結(jié)的因素:見書各種措施:錨固長度:；;還有第四章的las，及搭接長度[chapter1,2羅晗吳志浩]Chapter2thephysicalandmechanicalpropertiesofconcretestructurematerialsI.ReinforcementTheclassificationstructuralsteel(Angles,channels,I-sectionsteel)flexiblereinforcement(ordinarysteelbar,roundwires,strandedcable)VarietiesCarbonsteelLowcarbonsteel,medium-carbonsteel,highcarbonsteel.Thestrengthincreaseswhiletheplasticdecreasewiththeincreasingofcarbon.lowalloysteel:manganese,silicon,vanadium,titaniumStrength:fy—yieldstrength(designstrength)fsu—ultimatestrengthYieldratio:fy/fsu,fy/fsu≤0.8Forthehardsteelthathasnoobviousyieldpoint,theyieldstrengthisspecified.DeformationInChineseCode,thestress-straincurveissimplifiedtobilinearcurves.[0.0015，0.01]Plasticityindex:elongationandthecoldbendingperformanceColdworkingColdstretched(冷拉）--Timeeffectofcoldstretching(冷作硬化效應(yīng))Cold-stretchedsteelcannotbewelded.Tensilestrengthofcold-stretchedsteelisincreased.Thecompressivestrengthcannotbeincreased.Theelongationofthatisobviouslydecreased.Colddrawn(冷拔）:Bothtensilestrengthandcompressivestrengthofcold-drawnsteelisincreased.Thereinforcementrequirementsforconcretestructures①Strength②Ductility③Mechanism(weldability可焊性,processing施工性)④BondwithconcreteⅡ.ConcreteBasicconcept:Goodcompressivestrength,whilerelativeweaktensionstrengthComposition:cementgel+sand+gravelStrengthuniaxialstrengthCubiccompressivestrength:Cubicconcretespecimens(150mm×150mm×150mm)curedat20+-3°Candrelative90％humidityfor28days,usingstandardtestmethods.Thereare14concretegrades.(C15，20，25，30，35，40，45，50，55，60，65，70，75，80)，C50andabovearecalledashigh-strengthconcrete.C20oraboveisappliedincommonstructure,whileC30orC40isappliedinprestressedconcretestructure.(payattentiontoconfiningeffects.)Axialcompressivestrength(moresimilartotheactualstructuremember）150mm×150mm×300mmBiaxialstrength:StrengthofconcreteinbiaxialstressstateUnderbi-axialtension,thetensilestrengthisessentiallythesameasuniaxialstrength.Whenthespecimenisundertensioninonedirectionandcompressionintheotherdirection,boththetensileandcompressivestrengtharelowerthanthatinuniaxialloadsUnderbi-axialcompression,asshowninthefirstquadrant,themaximumcompressivestrengthoccurswhentheratiois2or0.5andthestrengthisabout27%higherthantheuniaxialcompressivestrength.[Note]:shouldneedtounderstandhowthisdiagramisobtainedTriaxialstressstate:DeformationLoadingdeformationShort-termmonotonicloading(uniaxial)Stress-straincurve:Concreteisanonlinearmaterial,plasticmaterials.Thecurvehaveascendinganddescendingbranches.InChineseCode,thiscurveissimplifiedtoapowerexponentsegmentandlinesegment.[KeyNumber]0.002,0.0033Poissonratio:μ=0.2Modulus::Therearethreemethodstoexpressthemodulusofconcrete.1)Initialmodulusofelasticity2)Secantmodulus3)Tangentmodulus.Long-termload(creep)Whenastressorloadisappliedtoaconcretespecimenandkeptconstant,thespecimenshowsanimmediatestrain(elasticstrain)followedbyafurtherdeformationwhichmaybecomeseveraltimestheoriginalimmediatestrainandisreferredtoasthecreepstrain.Orsimply,creepisincreasedinstrainwithtimeduetoasustainedload.Twokinds:Linearandnonlinearcreep.Causes(a)Plasticflowingofcementgel;(b)Internalmicro-fissuresdevelop.Thefactorsaffectingcreepconcreteformation:theamountofcement,watercementratio(水灰比)More→↑themixproportionbetter→↓concreteage(加載齡期)longer→↓curingcondition:temperature↑,humidity↓→↑stresscondition:larger→↑Repeatedloading:Fatiguefailure:Cracksaresmallwhiledeformationislarge.Themagnitudeoftherepeatedloadhaslargeeffectonthefatiguestrength.Thesmallertheamplitudeis,thehigherthefatiguestrengthis.Non-loadingdeformation(temperaturedeformation,shrinkagedeformation)Shrinkage:Theshrinkageofconcreteisthoughttobeduemainlytothelossofabsorbedwaterinthegel.Influencefactors:cement,aggregate,maintenancecondition,productionmethods,theenvironment,etc.a).Barsaresubjectedtocompressivestress,whileconcretegainstensilestress.b).tocauselossofprestressing.c).tocausesecondaryinternalforcesinthestaticallyindeterminatestructuresⅢ.Bondofconcreteandreinforcement(1)Thedefinitionandimportanceofbinder.①Definitionofbond:Thebondstressisshearstressthatthesurfaceofreinforcementandconcreteproduces,inordertoresistdifferentofdeformation.②Theimportantmeaningofthebond:Forreinforcedconcretetobehaveasintended,itisessentialthatbondforcesbedevelopedontheinterfacebetweenconcreteandsteel.Itisthebondforcewhichensuresthesetwokindsofdifferentmaterialstoformawholeandworktogether.(2)Theclassificationofbond ①anchoragebond ②localbondnearthecracks(3)Formationofbondaction①Adhesionaction—Chemicaladhesionactionbetweencementgelandbars’surface.②Frictionaleffect—Derivedfromgrippingeffect,whichisresultedfromthedryingshrinkageofthesurroundingconcrete.③Interlockingeffect:Resultingfromthebarsurfacedeformationorribsandconcrete.ForHPB300gradebars:①②;Fordeformedbars:①②③(5)Thefactorsaffectingbondstrengthτu5)Thediameterandsurfaceshapeofbars→τuofplainbarissmaller.Ifthediameterofbarislarger,therelativesuperficialarea(相對表面積)oftheribissmallerbecausetheparametersofribsarenotincreasedlinearlywithdiameter,sotheτuissmaller.Iftheepoxyresin(環(huán)氧樹脂[e?p?ksi?rez?n])isusedtopreventrustingofbars,τuissmallerbecausethesurfaceissmoother.(6)ThebasicdetailrequirementstoensurereliableadhesionIftheanchoragelengthislarger,thetotalbondstressislarger.→Inapull-outtest,iftherearenotstirrupsandlateralforces,whentheanchoragelengthislargeenoughtomakethebarreachingyield.Itiscalledthebasedanchoragelength——lab.→Mechanicalanchorageeffectoftheendsofbarsthroughdevelopmentlength,splicing(疊接),hooks(彎鉤),andcrossbars.τuismuchlarger.(CH.P33.F.2-28)Thebasedanchoragelength——(inbook,page32)Theanchoragelength——(inbook,page3)Thelaplength——ll=ξlla(inbook,page107)Theanchoragelength——las(inbook,page102)第三章:受彎構(gòu)件的正截面受彎承載力引言主要受彎構(gòu)件:梁板；四種基本受力形式:壓(拉）彎剪扭；受彎構(gòu)件三種截面:單筋，雙筋，T形配筋率:保護層厚度的定義和作用；受彎構(gòu)件正截面三種破壞形式:少筋破壞、適筋破壞、超筋破壞；受彎構(gòu)件正截面三個受力階段:I(包括Ia）、II、III(包括IIIa）受力全過程受力階段現(xiàn)象特點IM-f圖呈直線彎矩小,應(yīng)變小，鋼筋:彈性階段；混凝土:彈性階段，受拉區(qū)略顯塑性拉力受鋼筋和混凝土共同承擔Ia混凝土即將開裂，轉(zhuǎn)折點1混凝土達到受拉應(yīng)變ct，是嚴格不允許出現(xiàn)裂縫構(gòu)件的設(shè)計依據(jù)，可作為受彎構(gòu)件抗裂度的計算依據(jù)。IIM-f呈曲線，裂縫出現(xiàn)并開展鋼筋:彈性階段；混凝土:壓區(qū)出現(xiàn)塑性，拉區(qū)逐漸退出工作拉力主要由鋼筋承擔，是使用階段的裂縫開展與寬度計算的依據(jù)。IIa鋼筋即將屈服，轉(zhuǎn)折點2鋼筋達到屈服應(yīng)變σy；IIIM-f呈曲線，裂縫寬度發(fā)展較快鋼筋:屈服階段；混凝土:塑性、壓區(qū)應(yīng)力圖形更加飽滿中性軸一直上升IIIa混凝土壓碎，破壞極限承載力的設(shè)計依據(jù)，混凝土達到極限壓應(yīng)變cu承載力計算原理3.1四個基本假定平截面假定；不考慮混凝土的抗拉強度混凝土受壓的應(yīng)力應(yīng)變關(guān)系，為一個曲線段加一個直線段【需知道關(guān)鍵點，當混凝土強度小于C50的時候，這個曲線段是一個二次拋物線】縱向受拉鋼筋的極限拉應(yīng)變?nèi)?.01，鋼筋的應(yīng)力應(yīng)變關(guān)系，為兩個直線段【需知道關(guān)鍵點】3.2適筋梁公式的推導(dǎo)過程:要求看書理解【難點】3.3力的平衡方程:見書注:其中的h0的取法:h0=截面高度－保護層厚度－0.5縱筋直徑，一般梁可取h0=h-as=h-35(單排鋼筋）；h0=h-50~60(雙排鋼筋）；板可取h0=h-as=h-20，一般考試會直接給出as?？荚嚨臅r候，只要是受彎或者壓彎計算，一般都要驗算兩個適用條件，配筋率和界限受壓高度，沒有做的會扣分。當為適筋梁時，有兩種情況，【難點】1.Mu已知，求As，x——(截面設(shè)計）2.As已知，求Mu，x——(截面復(fù)核）3.4問題的擴展幾個相關(guān)的問題:a．防止超筋破壞:控制x<=ξbh0，在適筋梁范圍內(nèi)，隨配筋率減小，構(gòu)件的變形能力增強，延性增大。b.防止少筋破壞:規(guī)定最小配筋率:min＝min{45ft/fy％,0.2％}c.關(guān)于簡化公式:α，ξ，γ；一般考試會給出后兩者與α的關(guān)系式。3.5雙筋梁的計算:【難點】1概念:一般用鋼筋受壓不是非常經(jīng)濟，只在如下情況用:1）受壓區(qū)太大，在截面和強度都受到限制的情況下用；2）有異號彎矩的作用。注意點:雙筋梁和雙排鋼筋梁的概念是不同的2計算公式:見書P62。注意點:公式中的受壓鋼筋達到屈服應(yīng)變，這一點要求受壓區(qū)不能太小，要x>=2as’，其受壓區(qū)高度仍應(yīng)該小于界限高度(適筋范圍）3計算方法:1．直接求解方程法:1）假設(shè)As’已經(jīng)知道；2）假設(shè)x=；3）根據(jù)As+As’為最小作為優(yōu)化的約束條件2.疊加法(用于已知受壓鋼筋面積的情況，需在理解的基礎(chǔ)上掌握）注意點:(1）若求得的x<2as’，則表明受壓鋼筋不能屈服，需重新計算，(2）若用雙筋梁計算出來的橫截面積還比按單筋梁截面計算的橫截面積大時，可以按照單筋梁的計算結(jié)果作為設(shè)計面積。適用條件:(1）x(2）x2as’一般來說:鋼筋最小配筋率是自然滿足的，所以不需要驗算。3.6T型截面和異型截面的抗彎設(shè)計【難點】概念:受拉區(qū)混凝土有很大部分的混凝土不起作用，將這部分的混凝土去掉之后可以節(jié)省材料，于是產(chǎn)生T型梁，工字型梁，箱型梁等等。計算原理:五個基本假定仍然成立，力平衡方程仍然成立。注意點:分清楚受壓區(qū)和受拉區(qū)。判別受壓區(qū)的范圍(在腹板區(qū)還是在翼緣區(qū)），判別方法:假設(shè)法或者界限點法以T型梁為例作分析:T型梁的分類:第一類，中和軸在翼緣內(nèi)；第二類:中和軸在腹板內(nèi)計算公式:第一類T型梁，計算公式同普通單筋截面梁，不過梁寬b變?yōu)閎f。第二類T型梁，具體見書如何判別第一或第二類T型梁1）假定法；2）直接判斷法適用條件:(1）x(2）拓展內(nèi)容:假如是矩形梁挖孔怎么作？假如是梯形梁挖圓孔怎么辦？【難點】【注意:梁中空心的開方孔或者圓孔的箱形梁書上沒有講，其原理和工字型梁一樣】本章小結(jié):附加，適筋梁的Mmax＝[chapter3王卓煒吳梓楠彭出]chapter3Flexuralmembers1.IntroductionTypicalmemberswithflexure:beams,slabsetc；Fourbasicformstobearloadings:compression(tension）,flexure,shear,torsion；Threetypicaltypesofmemberswithflexure:singlyreinforcedrectangularbeam，doublyreinforcedrectangularbeam，Tsectionbeamthesteelratio:thedefinitionofconcretecover:Concretecover,inreinforcedconcrete,istheleastdistancebetweenthesurfaceofembeddedreinforcementandtheoutersurfaceoftheconcrete；thefunctionsofconcretecover:(1)anti-rust(2)anti-fire(3)completebondbetweenconcreteandsteelbarsThreefailuremodesofnormalsectionofflexuralmember:scarce-reinforcement,under-reinforcement,over-reinforcement；Threestagesintestforflexuralbeam:I(includeIa）、II、III(includeIIIa）stageBehaviorcharacteristicIM-φislinearlowbendingmoment,smallstrain;reinforcementandconcretesharethebearingforce.reinforcement:elastic;concreteincompressivezone:elastic;concreteintensionzone:slightlyplasticityIaconcreteisnearlytobecracked,turningpoint1concretetensionalstrainreachesεct.εct≈200με,σs≈40MPaAbeamwithoutcracksaredesignedonthebasisofstageIa.IItherelationshipbetweenMandφisNon-linear,crackingisvisiblethestageaftertheconcretehasbeencrackedandthesteelbarstakeupalmostallthetensionforcebuthasnotyetyielded.Non-linearitybeginstoshowintherelationshipbetweenloadanddeflection.Stressdistributionintheconcretecompressivezonealsoshowsnonlinearity.Butitisfoundfromexperimentsthatplane-sectionsremainasplanes.Abeaminserviceisusuallyinthisstage.IIaSteelstrainreachestheyieldturningpoint2steelstrainreachestheyield,ForHPB335steel,εy≈1500με,σs=300MPaIIItherelationshipbetweenMandφiscurvilinear,thewidthofcracksincreaserapidly.thestiffnessofthebeamismuchfurtherweakened.Considerableshiftintheneutralaxispositionoccurs.Load-deflectionrelationshipbecomesmorenon-linearIIIaConcretecrushedandfailedextensivedevelopmentsofcracksandcrushingoftheconcreteinthecompressionzoneleadtotheultimatecollapseofthebeam.ConcretecompressivestrainreachesεcuIII.Principleofthebearingcapacitycalculation3.1Fourbasicassumptions:1)Planesectionremainsplaneafterbending.2)Thetensilestrengthinconcretecanbeneglected. 3)Strain-stresscurveofconcreteconsistsofastraightlineandacurvedline.(WhenconcreteislessthanC50,strain-stresscurveisaquadraticparabola.)4)Theultimatetensilestrainofreinforcementintensionmustbe0.01.Strain-stresscurveofsteelconsistsoftwostraightlines.3.2Theprocessofbearingcapacitycalculationformulaofunder-reinforced-beama.SelectingIIIaforstudy,inthiskeystatus,steelbarshaveyielded(maybejustyieldedoryieldedforatime),concretejustcrushed.b.AccordingtothePlanesectionassumption,thestressofsteelisdefinedasfy,thelimitstrainofconcreteisεcu,theedgestressofconcreteisfc.Supposethepositionoftheneutralaxis,thestrainfromtheneutralaxistocompressionzoneislinear,thenthecurveofstresscanbedrawn.c.Atbalancestatus,totaltensileforceinsteelbars=totalcompressivestressinconcrete;steelandconcreteformamoment=externalmoment.Ifthevalueofexternalmomentisgiven,theneutralaxiscanbesolvedaccordingtothesetwoequations.d.Simplifythecalculationprocess:usinganequivalentrectanglestressblocktoreplacetheactualstressdistribution.WhentheconcretegradeislessthanC50,heightoftheequivalentrectangleis0.8timesastheoriginandwidthoftheequivalentrectangleisequal.3.3Balanceequationα1fcbx-σsAs=0Mu=α1fcbx(h0-0.5x)=σsAs(h0-0.5x)Methodtogeth0:h0=h–c–0.5dc:thicknessofconcretecoverd:diameteroflongitudinalreinforcementForbeam:h0=h-as=h-35(single-rowsteel)h0=h-50~60(double-rowsteel)Forslab:h0=h-as=h-20Under-reinforcedbeams:1.Muisgiven,calculateAs,x(sectiondesign).2.Asisgiven,calculateMu,x(sectioncheck).3.4ExpansionSomerelevantquestionsa.Topreventover-reinforcedfailuremode,weneedtocontrolx<=ξbh0,forunder-reinforcedbeams,ifthereinforcementratiobecomessmaller,thedeformationabilityofthebeamwillincrease,andtheductileabilitywillincrease.b.Topreventscarce-reinforcedfailuremode,thesmallestreinforcementratioρmin＝min{45ft/fy%,0.2%}c.Aboutthesimplifiedequation:therelationamongα，ξ，γwillbegivenintest.3.5Calculationofdoublereinforcedbeam:1Concept:It’snoteconomictousereinforcementforcompression;reinforcementisusedforcompressiononlyinthefollowingcircumstances:1)Thecompressionzoneistoolarge,andthesizeofthecrosssectionandstrengthofconcretearelimited;2)Differentsignsofmomentactonthestructure.2Formulas:Thespecificcontentsareatpage62ofourChinesetextbook(page49ofEnglishtextbooks).Caution:inordertomakethereinforcementincompressionzonesyield,thecompressionzonecan’tbetoosmall,sox>=2as’,thecompressionzoneisstillsmallerthantheboundarycompressionzoneheight.3Calculationmethods:Solvetheequationdirectly.Superpositionmethod(itcanbeusedonlywhentheareaofthecompressionzoneisknown)Caution:(1)Aftercalculation,ifx<2as’,thenthereinforcementincompressionzonewon’tyield,weneedtorecalculate.Ifthecrosssectionareacalculatedbydoublereinforcedbeamislargerthantheareacalculatedbysinglereinforcedbeams,wecanusetheresultcalculatedbysinglereinforcedbeams.Applicability:(1）xξbh0(2）x2as’Normally,wedon’tneedtochecktheleastreinforcementratiobecauseitwillsatisfyautomatically.3.6FlexuraldesignofT-sectionandnoncircularsectionConcept:Theconcreteintensioncontributeslittletotheflexurebearingcapacity.Removepartofconcreteintensionwon’treducethebearingcapacityofRCbeam.Furthermore,itcansavematerialandreduceself-weight.[T-section,I-section,box-sectionbeam]Calculationassumption:Fourbasicassumptionsandtheforcebalanceequationisstilleffective.Note:Determinetheneutralaxisisinflangeorinweb.Determinedmethod:AssumptionmethodCriticalmethodT-sectionBeam:TypesofT-sectionbeam:NeutralaxisinflangeNeutralaxisinwebFormula:Neutralaxisinflange:α1fcbf’x-fyAs=0Mu=α1fcbf’x(h0-0.5x)=fyAs(h0-0.5x)Neutralaxisinweb:α1fcbx-α1fc(bf’–b)hf’-fyAs=0Mu=α1fcbx(h0-0.5x)+α1fc(bf’–b)hf’(h0-0.5hf’)DeterminetypeofT-sectionbeam:HypothesismethodDirectlymethod

Note:xξbh0Expand:HowtoworkouttheproblemwhenrectangularbeamorT-sectionbeamwithholes?Summary:Mmax＝(Under-reinforcedbeam)第四章:斜截面承載力計算概述(實例和較簡單理論） 1．內(nèi)力:要求掌握:應(yīng)力跡線圖;剪應(yīng)力的分布:對矩形截面，中性軸位置處最大，上下截面處為0。2．裂縫的產(chǎn)生:裂縫特征及其產(chǎn)生的原因和位置:1）腹剪斜裂縫;2）彎剪斜裂縫3．鋼筋配置:實際中首選箍筋，不用彎筋，箍筋最好的角度是什么？為什么不這么做？原因:1）由于裂縫方向的不定性；2）彎起鋼筋傳力過于集中；3）彎筋數(shù)量有限，無法形成骨架。4．斜截面承載力分類:斜截面承載力理論主要是斜截面抗剪，也有斜截面抗彎問題存在。受彎構(gòu)件斜截面的受力特點和破壞形態(tài)。1.受力特點:受彎矩，剪力的共同作用，采用剪跨比考慮這種相互關(guān)系。引入剪跨比的概念:廣義剪跨比:，狹義剪跨比剪跨比不同，導(dǎo)致破壞形態(tài)也不相同。2.破壞形態(tài):具體見書，包括斜壓破壞；斜拉破壞；剪壓破壞。相比之下，剪壓破壞是比較好的，箍筋可以得到充分發(fā)揮，必須利用它。但應(yīng)注意，三種情況都屬于脆性破壞，只是脆性程度不同。要避免斜壓破壞和斜拉破壞。后面會提到，用限制截面尺寸來避免斜壓破壞，用最小配箍率和最小箍筋直徑和間距來限制斜拉破壞。引出一句話:強柱弱梁，強剪弱彎。形式特點破壞過程箍筋備注斜壓破壞無腹筋梁:剪跨比較小(）時，有腹筋梁:剪跨比很小或者剪跨比較大，但腹筋配置過多同時腹板較薄時，先在梁腹出現(xiàn)數(shù)條由集中力指向支座的斜裂縫，其將砼分割為數(shù)個傾斜受壓柱體，最后小柱體壓壞，箍筋未屈服。有點類似超筋破壞。脆性破壞。斜拉破壞無腹筋梁在剪跨比較大(），有腹筋梁在(）同時腹筋很少時斜裂縫一旦出現(xiàn)，很快形成一條主斜裂縫而破壞。箍筋立即屈服，有點類似少筋破壞危險性非常大。脆性破壞。剪壓破壞無腹筋梁在剪跨比適當(），有腹筋梁:剪跨比不論，但是截面尺寸適當，且腹筋配置適當時，荷載增加，首先在受拉邊緣出現(xiàn)一些豎向裂縫，在沿豎向延伸一小段之后就斜向延伸成斜裂縫，數(shù)條裂縫中，最終有一條發(fā)展為破壞裂縫，稱為臨界斜裂縫，隨荷載增大，斜裂縫不斷向上延伸，【而后與臨界斜裂縫相交的箍筋達到屈服】，剪壓區(qū)混凝土在剪力和壓力的共同作用下達到極限強度破壞，箍筋先于混凝土破壞達到屈服變形能力較差，仍為脆性破壞影響斜截面受剪承載力的主要因素。(敘述各個因素）混凝土強度；2）配箍率和箍筋強度3）剪跨比:斜壓破壞的強度是最高，(由于抗壓能力比抗拉強），4）縱筋配筋率:縱筋起的作用是銷栓作用，但是影響比較小。5）加載方式:直接加載和間接加載(附圖），間接加載導(dǎo)致受剪承載力的降低。6）截面形式:翼緣的存在對于有腹筋梁適當提高，但不是很明顯，一般可以忽略不計。梁斜截面承載力的計算公式。受剪機理:具體見書。1）帶拉桿的梳形拱模型:適用于無腹筋梁；2）拱形桁架模型，適合于有腹筋梁；3）桁架模型:適合于有腹筋梁計算方法對于無腹筋梁:在均布荷載作用下，在集中荷載作用下；注意點:1）Vc和Vs不是獨立的，他們共同作用；2）未考慮縱筋的銷栓作用3）需要考慮部分箍筋可能達不到屈服強度4）理解剪跨比λ的取值方式，剪跨比只有在集中力作用明顯的情況下才考慮計算公式:有無彎起鋼筋時:見書。對于公式的一些解釋鋼筋的作用是有限的，當截面過小而剪力過大的時候，會發(fā)生斜壓破壞，在薄腹梁中更容易產(chǎn)生這個問題，因此限制更加嚴格，因此必須限制截面。對于厚腹()梁:；對于薄腹()梁:注意截面的腹板高度在不同截面形式中的范圍。箍筋的最小配箍率集中力占主要作用的情況下，的取值要求限制在1.5～3之間。厚板的問題，，，當h0<800時取1。連續(xù)梁的問題，比較復(fù)雜。斜截面承載力的計算方法和步驟。(計算和復(fù)核）要點:截面的選取，計算步驟見書。需特別注意的，必須掌握書課后4.7及4.8這種彎剪綜合的題目。縱向鋼筋的彎起、截斷和錨固。斜截面受彎問題:為什么a0.5h0，需要知道原理，什么是斜截面的受彎問題鋼筋彎起的問題名詞:抵抗彎矩圖，充分利用點，不需要點。一些原則:1）抵抗彎矩圖需包住整個外力彎矩圖。2）彎筋和軸線的交點應(yīng)該在該鋼筋的不需要點之外，彎起點必須在充分利用點的0.5h0之外。鋼筋截斷的問題名詞:錨固長度；支座錨固長度；抗震錨固長度；搭接長度；抗震搭接長度具體作法:L1L2≥1.2la≥20d≥1.2la+h0≥Max{20d，h0}截斷點處于負彎矩區(qū)≥1.2la+1.7h0≥Max{20d，1.3h0}構(gòu)造要求:見書[Chapter4劉子彥楊凱越顏博]Chapter4UltimateBearingCapacityofDiagonalSectionforFlexuralMembersI.Introduction(samplesandbasictheories)Internalforce:theprincipalstresstrajectoriesdiagraminthebeam;thedistributionoftheshearstressinthesection:forrectanglesection,themaximumstresslocatesattheneutralaxis,andzerostressatbothtopandbottomofthesection.Theoccurrenceofcracks:thecharacteristics,reasonsandlocationsofcracks:1)Web-shearcracks;2)Flexural-shearcracksClassificationofthereinforcement:webreinforcementincludesstirrups(transverseties)andbent-upbars,andskeletonofsteelincludeslongitudinalreinforcement,webreinforcementandsomeotherdetailingbars.Reinforcedconcretebeamswithoutwebreinforcementstillhavelongitudinalreinforcement.Distributionofthereinforcement:Thereasonsthatstirrupswouldbethefirstchoiceswhilebent-upbarsarenotusedingeneral,arethat1)theuncertaintyofthedirectionsofthecracks;2)theundueconcentrationofforcetransmittedbybent-upbars;3)thefinitenumberofthebent-upbarsfailingtoformskeletonofsteelinabeam.Theclassificationofthediagonalsectioncapacity:1)shearingresistanceinthediagonalsection;2)bendingresistanceinthediagonalsection.II.TheStressFeaturesandFailureModesofDiagonalBendingSection1.Stressfeature:Giventhecombinedactionsofthemomentandshearforce,weintroducetheconceptofshearspanratio:Generalizedshearspanratio:,calculatedshearspanratio:Differentshearspanratiowouldresultindiversefailuremodes.2.FailuremodePleaserefertothetextbook(ForEnglishP67,ChineseP79)orPPT.FailuremodesIncludesshearcompressionfailure,diagonalcompressionfailureanddiagonalsplittingfailure,andbestofwhichisshearcompressionfailureasitcanmakefulladvantageofthestirrups.Thoughthebrittlenessisdifferent,allthreeshearfailuresbelongtobrittlefailure,whichmeansdiagonalcompressionfailureanddiagonalsplittingfailureshouldbeavoided.Toassuretheshearcompressionfailure,thelimitationonsectionalsizeisintroducedtopreventdiagonalcompressionfailure,andminimumstirrupratio,diameterandspacingtoavoiddiagonalsplittingfailure.Aconceptispresented:strongcolumnandweakbeam,andstrongshearandweakbending.ModeCharacteristicsofreinforcedconcretebeamswithoutwebreinforcementCharacteristicsofreinforcedconcretebeamswithwebreinforcementFailureprocessStirrupNotesDiagonalcompressionfailureShearspanratiocanbeeitherquitesmallorbig.Webreinforcementisundueoritisthin-webbeam(TorIsectionbeam)Severaldiagonalcracksfromactingpointoftheconcentratedforcetothesupport,separatetheconcreteintodiagonalcompressioncylinders.Finally,thetinycylindersarecrushedunderthepressureThestirrupsdonotyield,similartoover-reinforcedbeamBrittlefailure.DiagonalsplittingfailureandsimultaneouslytheamountofwebreinforcementislowOncethediagonalcrackoccurs,anditwouldextendrapidlyupwardandsplitthememberintotwo.Thestirrupsyieldimmediatelyafterthecrack,similartoscare-reinforcedbeamVerydangerous.BrittlefailureShearcompressionfailureThewebreinforcementisproperlyset，orandthewebreinforcementisnotlessFirstly,verticalcracksoccurintensilezone,andformacriticaldiagonalcracklater.Withconcreteshearcompressivezonegettingsmaller,theconcreteiscrushedunderincreasingnormalstressandshearstress.ThestirrupsyieldbeforetheconcreteiscrushedTheabilityoftransformationisbad.Brittlefailure3.FactorsAffectingtheStrengthofDiagonalSectionStrengthofConcrete;StirrupsRatioandtheStrengthofStirrupShearSpanRatioλ:theshearresistanceofdiagonalcompressionfailureisthehighestduetothestrongercompressionresistanceofconcrete;LongitudinalSteelRatio:Affecttheextendingofdiagonalcracksinthecompressionzoneowingtothedowelactionforce,butindirectly.LoadingWay:Indirectloading;Directloading,whichresultsinthedeclineoftheshearcapacitySectionForm:Flangeslightlyincreasethestrength,butcanbeignored.4.StrengthCalculationMethodsofMembersUnderShearMechanismCombarchmodewithtierod:usedforbeamswithoutwebreinforcement.Arch-trussmode:usedforbeamswithwebreinforcement.Trussmode:usedforbeamswithwebreinforcement.CalculationFormembersunderuniformloads,forbeamsunderbothconcentratedloadsanddistributedloads,whentheshearforceproducedbyconcentratedloadsatthesupportisequaltoormorethan75%ofthetotalforce.:Vc,Vsisnotindependent;rather,theyinfluenceeachother.Thedowelactionsuppliedbylongitudinalbarsisnottakenintoconsideration.It’snotingthatpartofthestirrupsmaynotreachtheiryieldstrength.Asλ<1.5,letλ=1.5;asλ>3,letλ=3.Andλisonlytakenwhenconcentratedloadsdominate.,Thefunctionofreinforcementisnotunlimited.Diagonalcompressionfailurewillhappenwhenthesectionistoosmallwhiletheshearforcetobetoolarge,especiallyinsmall-depth-of-webbeams.Andthusaminimumsizeonthedimensionsofsection(upperboundofshearresistance)isset.Thishelptorestrictthewidthofthediagonalcracksandtopreventfromdiagonalcompressionfailure.For,;for,.Noticewhath0standsforindifferentsituation.Lowerboundofshearstrengthiscontr