混凝土結(jié)構(gòu)理論英文crack

Whyshouldweensuretheextentofcrackingandthedeflectionatserviceloadliewithintheacceptablemagnitude?Howmuchistheallowablevalueofdeflection?Howmuchistheallowablevalueofcrackwidth?Whydoweusuallydonotcheckthecrackwidth?Limitstatesofthethecrackwidth

of

notexceedthespecifiedlimitslimitstateControlbymainlybyCanmeetthelimitstateControlbymainlyby 5Mlf 384 48Controlof(1)Definitionof 5Mlf Forelasticsimply-support 384 48Thevalue5/48changesindifferentloadtypes.Inspecializedloadtypes,itisaconstant.Forelasticmaterial,qandfislinear.ButforRCmember,itisdifferent,therigiditywillchange.Threestages:Aftercrackofconcrete,rigiditydecreases,plasticAftersteelbaryielded,rigiditydecreasesmoreControlof(2)CalculationofThecalculationoftheshort-termrigidityBsaftercracking.Strainfeature:1)theaveragecurvatureinpuremomentThetensilestrainofsteelandcompressivestrainofconcreteisuneven,maximumincrackposition,andchangingbetween2.ControlofThedepthoftheneutralaxisisthenfluctuatingaroundanaveragevaluePlanesectionassumptionisstilleffectiveinoverallControlofStrainofsteelandconcreteincrackingInthisstage,therelationshipbetweenthestressandthemomentcanbecalculatedthroughforcebalanceequation(similartothebalanceequationsinultimatestatus,exceptthattheconcretestrainshapeisdifferent,sothepreviousformularcan’tbedirectlyused)A0B A0 E 2ControlofRelationbetweenaveragestrainofwholememberandstrainbetweencracksNon-uniformcoefficientA0B A0 E cx h[bh(b' (b' Ms f EABs 6 ffEA 0

E E0.87

EAh2EA EABs 6 ffEA 0

E E0.87

EAh2EA E

EEA E

1 Es/EcAs/ (

EAh2('E 1 EAh2(')E Mh0EAhh

()E Mxsc s s x 0.87；1.10.65ftk，在0.4～1.0

6 ；te 0.2 ff

13.5

EAB 6 ff2.Controlof 1.10.65 ;Between0.4~M

E

6E

0.87hA;te

Bs

2EsAs0EsA ffb(df)LongLongtermandshortterm①Differentkindofload:Deadloadandlive②"quasi-permanentvalue"ofthevariableloadisusedtoevaluateitslong-termeffectonthestructure(ψq),ψqisdeterminedbythedegreeofpermanencyofavariableloadagainsttheexpectedlifespanofthestructureanddiffersindifferentvariableloads.Forinstance,thevalueforlifeloadonfloorslabsinofficeorresidencebuildingsis0.4.①Longtermload:Deadload+quasi‐permanentlive→quasi-permanent②Shorttermload:Deadload+characteristiclive1)BM(M1) 2.00.4Thisformulaisforshort-termrigidity，Sincethedeflectionofconcretetendstoincreasewithtimeundersustainedloadcausedcreepandshrinkage,thelong‐termsectionrigidityBshouldbereducedwithtime.1)BM(M1) 2.00.4Ml M)l Mlf q

kB1)BM(M1) 2.00.4TheprincipleofleastForasimplificationforthecalculationofthedeflectionofthebeamswithvariablesectionrigidity,theCodespecifiesthatforasegmentofthemember,therigiditycalculatedforthesectionundertheabsolutemaximummomentinthatsegment(whichisalsotheminimumrigiditysection)istakenastheuniformrigidityofthatsegment.Whenthereexistoppositesignmoment,choosetheleastrigidityin|Mmax|positiontocalculatethe2.ControlofSeveralproblemstoberigidityisrelatedwithsteelratioisrelatedtoCapacityanddeflection:sometimesthesteelbarsareaaredeterminedbythedeflectionrequirement.FlangewillincreaseThegradeofconcretehavenotmucheffectonTheeffectivedepthofsectionhasthemaximumeffectontheincreaseofrigidity.2.ControlofSpan-depthratiohasalargeeffecttoFornormalload,crackcheckingmaybeignoredwhenthespan-depthratioisbetween10and20.Thereasonfordeflectiondailynon-structuralmemberbadcausesomeotherbadSomereasonsforwhyshouldwecontrolthedeflectionorcrackHaveinfluenceonfunctionofBridgeprecise

Haveanadverseeffectonthestructuralmember.Suchaschangingthesupportconditions,producingunstable,crackorvibrationproblems

ThechangingofsupportwillEndangerthesafetyofthewall

Crackingofbrick FallingoffoftheCrushingofbrick FeelingPa），混凝土保護(hù)層厚度20mm，Example8-1】Thefigureshowsacantileverslabofanentranceunderuniformlydistributedloads.Characteristicvalueofliveloadanddeadloadonfloorpk=0.5kN/mandgk=8kN/m,respectively(coefficientofquasi-permanentψq=1.0).ThelongitudinalreinforcementsareofgradeHRB335withadiameterof16mmandaspacingof200mm(Es=2×105MPa).TheconcreteisofgradeC30(ftk=2.01MPa,Ec=3×104MPa),thicknessofconcretecoverc=20mm.Find:whetherthemaximumdeflectionofslabcanmeettherequirementofcode. 1gpl2180.53238.25kN 1gpl2181.00.532 由題知As1005mm2b1000mm,h020020162

0.51000

【Solution1mstripofFindthecharacteristicvalueof 1gpl2180.53238.25kN Longterm Findnon-uniformlydistributedstraincoefficientoflongitudinaltensilereinforcementψgivenAs1005mm2,b1000mm,h02002016/2

0.51000

Mq0.87h

0.87172

1.10.65

1.1 0.652.010.01005254.34

＝0589E

2s s

EA

B s

0.26E 2105 5.35210N1.150.5890.266.67 B M(-1)

38.251062-1 5.3522.6761012Nmm2Mlf k

38.25106 4

Fidlong-termrigidity B M(-1)

38.251062-1 5.3522.6761012Nmm2FindthemaximumdeflectionfofMlf k

38.25106 4

Can’tmeetDiscuss:Thekeytocheckthedeformationofmembersunderflexureistofindlong-termrigidityB.EIinthedeflectionformulainmechanicsofmaterialsshallbereplacedbyBindeformationcalculationofmembers.Whenamemberisloadedtoitscrackingload,atthemomentwhencrackisimpending,theconcretetensilestresswillbeftk.Thenfirstcrackmayappearstochasticallyonaweaksection.Themomentthatcrackappears,thetensilestressintheconcretewillbereleasedatthecrackedsection,andthesteelstressatthecrackedsectionwillbesuddenlyincreased.However,tensilestressoftheconcreteincreasesfromthecrackedsection,becausetensionistransferredfromthesteeltotheconcretebybond.WhenthetensilestressincreasesuptothevalueofthetensilestrengthofconcreteatsectionB.anewcrackwillappear.3.Crackwidthσc＝ft，σs＝σs1＝Ncr/As；Ncrσs2As＝ftAte＝lminτmπdlmin＝ftAte/(τmπd)＝dft/(4ρteτm)；其中根據(jù)裂縫間距的統(tǒng)計(jì)值界乎l和2l之間，取beforecracking，nearthecrackingaxisσc＝ft，aftercracking，ifweselectthecrackingpositionandtheno-crackingsectionforstudy,respectivelyσs1＝Ncr/As；Ncr－σs2As＝ftAte＝lminτmπd＝ftAte/(τmπd)＝dftinwhichThecrackspaceisbetweenland2l,sodefineft/τm接近一個常數(shù)，再根據(jù)試驗(yàn)結(jié)論，對原假定進(jìn)行k1，k2ft/τmisclosetoaconstant，then,combinedwiththetestconclusion，theformulacanbewroteas:νrelatedtothesteeltypes：plainroundork1，k2isAssumingthecrackwidthnearsteelpositionisequaltothewidthonsurface,theequationisasfollow:ωm＝(εsm－εcm)lm＝εsm(1-εcm/εsm)lm=φσs/Esαclmm (1.9c0.08dm sk sk(1.9c0.08dE Es

EsE

1.10.65ft/teCrackwidthm (1.9c0.08dmAndconsideringτl(amplifyingcoefficientduetolongtermloadeffect)×τs(amplifyingcoefficientofthemaximumcrackwidthtotheaveragecrackwidth) sk sk(1.9c0.08dE Es

E Es

1.10.65ft/te

sqisthestressoflongitudinalreinforcementincrackingsectionofconcretemembercalculatedbyquasi-permanentcombinations.

0.87h Axia