第二章钢筋和混凝土材料的力学性能

2.12.22.32.42.1•••σε-“”a’a’aadebbcfycdcdefufyf2.1.1efu“”a0.2%σ0.2fua0.65fua-a-fufy••fu••fu/fy1.25()fu•σ0.2——0.2%•σ0.2=0.85fu0010or5lll−=δδgt(2.5%)••:Dα—•--fyεy1EsyyysfEεεσεεεσ=≤=2.1.2•••2.1.3•••••••HotRolledSteelReinforcingBar•HPB235()HotrolledPlainBarHotrolledRibbedBar•HRB335()•HRB400()•RRB400()RemainedheattreatmentRibbedBar••••37••fy,m-2σ97.73%95%•()HRB400HRB335HPB235RRB400•2.2•••••2.2.1••••••••122.2.2•••1fcufcu150mm20390%280.15~0.3N/mm2/sec••••100mm100150cucuffµ=C50µ=0.95µfcu100=100N/mm2µ0.92fcu,k95%CxxC30fcu,k=30N/mm2145N/mm2C15C20C25C30C35C40C45C50C55C60C65C70C75C80C50fc’•150mm300mmcucff)81.0~79.0(=′fc•h/b=3~4150mm150mm450mm100mm100mm300mm•fc•cuccff1α=C50αc1=0.76ft••0102030405060708090100123456ftfcuGBJ10-8955.0395.0cutff=3/226.0cutff=50015015010016PaP2,2aPfpt⋅=π4/3,19.0cuptff=•fk95%)645.11(ffkfδµ−=•fckfcu,k:kcuccckff,2188.0αα=αc1µfcµfcu≤C50αc1=0.76C80αc1=0.82αc2≤C40αc2=1.0C80αc2=0.870.88•ftkfcu,k:45.055.0,2)645.11(395.088.0fkcuctkffδα−×=N/mm2C15C20C25C30C35fck10.013.416.720.123.4ftk1.271.541.782.012.20C40C45C50C55C60C65C70C75C8026.829.632.435.538.541.544.547.450.22.402.512.652.742.852.933.003.053.10[]fcu=30MPa,δ=0.12,fcu,m=fcu/(1-1.645δ)fc,m=0.76fcu,mfc,k=fc,m(1-1.645δ)0.881.0=0.76fcu0.881.0=20.06MPa2.2.3•-•••--•-•02468102030σ(MPa)ε10-3BACEDAABBCCEDE1σε2-10ε1ε2∆V/V00.511.52σε10-3ABCD-3-2-1f2-13-23-Hognestad-uuccffεεεεεεεσεεεεεεσ≤≤−−−=≤≤−=000020015.010200.0020.0038fc0.15fcσεε0εu00.0010.0020.0030.00410203040506070C80C60C40C20σε-])1(1[0ncccfεεσ−−=0εε≤ccf=σuεεε≤066010)50(0033.010)50(5.0002.0)50(6012−−×−−=×−+=−−=cuucucufffnεε-fcuC50C60C70C80n21.831.671.5ε00.0020.002050.00210.00215εu0.00330.00320.00310.003σεEc=tanα0==σεσddEcσεEc’=tanα’εσ=′cEσεEc’’=tanα’’TangentModulusεσddEc=′′ν(coefficientofelasticity)εεelcE=cEν=εεelv=ElasticModulusSecantModulusν=1~0.5σε0.5fc5~10)N/mm(74.342.21025cucfE+=-σεftεt0••ftfcεt0ε0•ctctcttEfEfEf25.00==′=ε•0.521.27fc•-2.2.4•2.2.4•2.2.4τσ••0.6fc0.6fc•••214σ+′=′ccff•“”2-11••-2.2(b)d=4.76mms=38.1mmd=4.76mms=63.5mm2.2(a)(b)“”fclfcclbcclfAAff==β2.22.2.5Shrinkage••“”εsh=(2~5)10-414d28dtεsh(2~5)10-425%50%•123••2.2••2.2.6Creep•••“”εcr2εcr24t0εelεelεshεcrεel’εel’’εcr’εtσi0.5fcεel=σi/Ec(t0)t04670~80%2~3t0εelεelεshεcrεel’εel’’εcr’εt(t-t0)εc(t,t0)εsh(tt0)εcr(t,t0)=εc(t,t0)-εel-εsh(t,t0)elcrttttεεϕ),(),(00=ϕ(tt0)CreepCoefficientt0εelεelεshεcrεel’εel’’εcr’εtεel'εel''εcr'•(aggregate)•(curing)20~35%1t02(initialstress)σi/fcσi/fc0.5εcrσiϕ=εcr/εel=Ecεcr/σi=σi(0.5~0.8)fcεcrσiεcrσiϕσiσi0.8fc0.8fc••2.3••σs=σs=0••NNσsτσcεsεs=εcNNltltdxσsσcσc+dσcσs-dσsσsσs-dσsτ42dddxdsπστπ⋅=⋅⋅dxddsστ⋅=4••τ00≠⇔≠dxdsστ•NτN12dlF=σsAsF=σsAsτuFd1005d2~3dllτudlAdlFssuπσπτ==τu11τuft22()τu33τuc/dτuc/d“”sds/dτu5544τu2.4NNcAAsσεftεt0fyεyσεNNcrNεs=εc=εεs=εc=εcEσνα=ccssEEσνσ=sssEεσ=cccEεσ′=εsE=ενcE=σsNssccAANσσ+=+=ναρσEccA1+=sEccAAνασNN-σsN-σcνσsσcρ=As/AccEccssEEσνασνσ==sEAνα0+=sEcAAAνασc=ft-σc=ftν=0.501AANcEccσναρσ=+=)/1(0νρασEccANAN+==)(ρανασνασEcEcEsAN+==()ραEctcrAfN21+=()TransformedSection()ραEctcrAfN21+=N=Ncrσc=ftσs=2αEftsσtEfα2=MPa40~20=0=cσ+ρtfρσtsctsfAAf==∆σc=ft0N=σsAsρασttEscrsffAN+==2NNcrσc=0σs=sANσs=fyNu=fyAsft2αEft2αEft+ft/ρfyσsσcNcrNuNσc−Νσs−ΝNcrNuεlεyNρ,Nu=Ncr()ραEctsyAfAf21+=tEytfffαρ2min−=AsαE/νν3.1NcrAs20~40MPaρmin↔Nu=NcrN•••ccssAANσσ+=σc0.5fcelε00,ANc=σ)/1(νραEcAN+=0,0,cEsσνασ=)(ραναEcEAN+=Nt=0elεσs,0σc,0elsβϕεε=∆elcϕεβε)1(−−=∆?0,,=∆+=sstsσσσ?0,,=∆+=cctcσσσNelβϕε(β1)telssssEEβϕεεσ=∆=∆elccccEEϕεβνεσ)1(−−=∆′=∆Ntelϕεσs,0σc,0()νραβE+=110=∆+∆ccssAAσσtsstsσσσ∆+=0,,++=νραϕσ/110,Escctcσσσ∆+=0,,+−=)/1(/10,νρανραϕσEEctφσs,tσc,tρσs=0σc=0σs=0σc=0εshLσs=Esεs()σc=νEcεc()εcLεsLshcsεεε=+cccsssEEεσεσ==sccccsssCTATAC===σσC50