Estruturas de BetoSECES FLEXO E ESFOROS AXIAIS TABELAS E BACOS DE DIMENSIONAMENTO DE ACORDO COM O EUROCDIGO 2 Helena Barros, Prof FCTUC, LABEST Joaquim Figueiras, Prof. FEUP, LABEST Setembro 2007 (verso reservada a alunos de Estruturas de Beto) Tabelas de Dimensionamento de Estruturas de Beto 2 NDICE Notaes 1- Introduo 5 2- Hipteses e mtodos de clculo6 2.1 Hipteses de base 6 2.2Propriedades dos materiais7 2.3 Estados limites com esforo normal e momento flector 9 2.4 Teoria do comportamento em peas flectidas 10 3- Implementao de Tabelas e bacos 10 3.1 Modelo de resoluo. Generalidades 10 3.2 Tabelas e bacos desenvolvidos 11 4- Exemplos 12 5- Tabelas23 6- bacos55 Tabelas de Dimensionamento de Estruturas de Beto 3 NOTAES A, As, A, As- rea da seco de uma armaduraRdM- Valor de clculo do momento flector resistente SdM- Valor de clculo do momento flector actuante SdSdsM M*,- Valor de clculo do momento flector actuante em relao ao centro de gravidade da armadura de traco SdN- Valor de clculo do esforo normal actuante Sd N* - Valor de clculo do esforo normal actuante em relao ao centro de gravidade da armadura de traco RdN- Valor de clculo do esforo normal resistente SLS- Estado limite de utilizao ULS- Estado limite ltimo a- Distncia das armaduras de traco e compresso face b- Largura de uma secobw- Largura da alma de uma seco em T d- Altura til de uma seco transversalcdf- Valor de clculo da tenso de rotura do beto compresso ckf- Valor caracterstico da tenso de rotura do beto compresso aos 28 dias de idade ydf- Valor de clculo da tenso de cedncia do ao das armaduras ordinrias ykf- Valor caracterstico da tenso de cedncia do ao das armaduras ordinrias h- Altura total de uma seco transversal fh- Altura do banzo de uma seco em T x- Profundidade da linha neutra de uma secosy ,sz- Distnciaz- Brao do binrio das foras interiores em flexo Tabelas de Dimensionamento de Estruturas de Beto 4 - Altura reduzida da linha neutrad x / = ouh x / = - Quociente das reas de armadurasA A/ = e- Quociente entre os mdulos de elasticidade do ao e do beto c s eE E / = - Quociented a / = 2,c c - Extenso do beto 1,s s - Extenso de alongamento da armadura s- Extenso de encurtamento da armadura - Percentagem mecnica de armadura: cdsd sf bhA= , ou cdydsffbdA= - Percentagem de armadura: bdA= 2 , 1, s - Percentagens mecnicas das armaduras de traco e compresso obtidas por ( )Sd cd sydsN bdffA + =, 11 , e, ydcdsffbd A2 = - Valor reduzido do momento flector resistente de clculo: cdRdf bdM2= ou cdRdf bhM2= - Valor reduzido do esforo normal resistente de clculo: cdRdbhfN= c - Tenso de compresso no beto s - Tenso na armadura s - Tenso na armadura sA 500 , 400 S S - Designaes dos tipos correntes de armaduras ordinrias ,... 50 , 12 C C - Designaes da classe de resistncia de betes Tabelas de Dimensionamento de Estruturas de Beto 5 1.INTRODUO Nesta publicao apresenta-se um conjunto de tabelas e bacos que so auxiliares no clculo dos esforoscorrespondentesaosEstadosLimitesltimosderesistnciadesecessolicitadaspor esforos normais e de flexo, bem como a anlise de tenses ao nvel da seco quer no ao quer no beto, tendo em vista a verificao da segurana relativamente aos Estados Limites de Utilizao. Astabelasebacosapresentadassoauxiliaresnodimensionamentodeestruturasdebeto armadoepr-esforadoeestoemconsonnciacomosrequisitosimpostospelacomunidade europeia atravs dos Eurocdigos Estruturais, nomeadamente no que se refere ao Eurocdigo 2. derealaralgumasdasdiferenasdopresentedocumentoemrelaoatabelasebacos existentes, tendo por base as disposies do REBAP Regulamento de Estruturas de Beto Armado ePr-esforado,nomeadamentenoqueserefereresistnciacompressoerelaotenses-extensesdobetoparaoclculodesecestransversais.Ovalordeclculodaresistncia compresso, fcd = cc f ck / c obtido com cc= 1.0 em vez do coeficiente redutor cc= 0.85 proposto noREBAP.OalargamentodombitodeaplicaodoEurocdigo2abetesdeclassesde resistncia mais elevadas (C55/67 a C90/105) levou considerao de diagramas tenses-extenses particularesparaestasclassesqueexibemummododeroturamaisfrgil.Daquiresultaqueas tabelas podem ser normalizadas para as classes C12/15 a C50/60, mas tero de ser individualizadas para as classes de resistncia mais elevadas. Comoalargamentodapresenteregulamentaoeuropeia(EC2)abeteseaosdeclassesde resistncia maiselevadaleva a que as verificaes aos EstadosLimites de Utilizao, que j eram essenciaisparaasestruturaspr-esforadas,sejamtambmcorrentementecondicionantesno dimensionamentodasestruturasdebetoarmado.Justifica-seassimaapresentaodebacos auxiliaresdeclculonasverificaesdascondiesdeservio,paraalmdashabituaistabelase bacos de clculo rotura. Tabelas de Dimensionamento de Estruturas de Beto 6 2.HIPTESES E MTODOS DE CLCULO 2.1Hipteses de base Averificaodaseguranadassecesdebetoarmadorelativamenteaosesforosdeflexo passapeloestabelecimentodasleisconstitutivasdosmateriais,nestecasodobetoedoao,para cadaumdosestadoslimitesconsiderados.Poroutroladohquedefinirascondiesemquese consideraqueosestadoslimitesforamalcanadosatravsdaidentificaodedeterminados parmetros.Finalmentenecessrioestabelecerasteoriasdecomportamentoquepermitemobter osesforosdaseco,relacion-loscomosreferidosparmetroseassimpodercomprovarasua segurana. Estes diferentes aspectos so descritos de seguida de forma mais sucinta. Tabelas de Dimensionamento de Estruturas de Beto 7 2.2 Propriedades dos materiais As propriedades do beto encontram-se descritas no Eurocdigo 2 de que se reproduz o Quadro 1 que contm as propriedades relevantes para o clculo. QUADRO.1 Caractersticas de Resistncia e de Deformao do Beto (EC2) Classes de resistncia do betoExpresso analtica/ Comentrios 1216202530354045505560708090 15202530374550556067758595105 2024283338434853586368788898 1,61,92,22,62,93,23,53,84,14,24,44,64,85,0 60 / 50 30 , 03 / 2C f fck ctm =60 / 50101 ln 12 , 2 Cffcmctm ||

\|+ = 1,11,31,51,82,02,22,52,72,93,03,13,23,43,5 quantilho de 2,02,52,93,33,84,24,64,95,35,55,76,06,36,6 quantilho de (GPa) 2729303133343536373839414244 (em) 1,81,92,02,12,22,252,32,42,452,52,62,72,82,8 Ver Figura 3.2 (*) 3,53,23,02,82,82,8 Ver Figura 3.2 (*) Para 2,02,22,32,42,52,6 Ver Figura 1 Para 3,53,12,92,72,62,6 Ver Figura 1 Para 2,01,751,61,451,41,4 Para 1,751,81,92,02,22,3 Ver Figura 3.4 (*) Para 3,53,12,92,72,62,6 Ver Figura 3.4 (*) Para (*) ver Eurocdigo 2 Tabelas de Dimensionamento de Estruturas de Beto 8 Arelaotenses-extensesdeclculodobetocomprimidodefinidapelaleida parbola_rectngulo, dada pela seguinte equao paramtrica: (((

|||

\| =ncccd cf21 1para 20c c cd cf = para 2 2 cu c c sendo o expoenten , a extenso do beto, 2 c(correspondente resistncia mxima), e a extenso ltima 2 cu ,definidosnoquadroemfunodaclassedobeto.NaFig.1estrepresentadaesta equao considerando valores caractersticos e valores de clculo. Fig.1 Diagrama parbola_rectngulo em valores caractersticos e de clculo para o beto comprimido. Fig.2 Diagrama tenso/extenso idealizado e de clculo para o ao das armaduras de beto armado. Tabelas de Dimensionamento de Estruturas de Beto 9 O Eurocdigo 2 permite a utilizao de dois diagramas de tenso no ao: a)LeideHookeattenso, s yk ydf f / = ,seguidadeumramoinclinadocomuma extensolimitede ud eumatensocorrespondenteakfyk/s paraovalormximode extenso, uk. b) Lei de Hooke at tenso, s yk ydf f / = , seguida de um ramo horizontal sem limite de extenso. 1.1. Estados limites com esforo normal e momento flector Aps a definio do estado limite calculam-se os correspondentes esforos resistentes da seco. Osestadoslimitessoactualmenteconsideradosemtermosdeextensesmximasnobetoenas armaduras. O estado limite atingido quando ocorre uma destas extenses ou ambas em simultneo e as distribuies de deformaes admissveis esto representadas na Fig. 3.alongamentos(defor.de traco)dhaaencurtamentos(defor.de comp.)A 2AABCcu2c2udy Fig.3 Domnio das extenses admissveis na seco em estado limite ltimo O ponto A representa o limite para a extenso mxima do ao, ud , o ponto B o limite para a extenso de compresso do beto, 2 cu , e o ponto C representa o limite para a extenso do beto em compresso simples, 2 c . Tabelas de Dimensionamento de Estruturas de Beto 10 As presentes tabelas foram elaboradas usando para limites da extenso do beto os pontos B e C comasextensesretiradasdoquadroconformeaclassedebeto.Nocasodoao,pontoA,foi usada a lei b) identificada na seco 2.2 em que o ramo horizontal foi limitado a uma extenso de 2,5%.Estelimitenotememgeralsignificadoprticojquearoturadasecoantecipadapor esgotamento de deformao do beto compresso. 1.2.Teoria do comportamento em peas flectidas Para obter os esforos resistentes da seco necessrio definir teorias de comportamento que permitam calcular os esforos uma vez conhecidos os estados limites da deformao dos materiais naseco.Querissodizerquenocasopresentenecessriocalcularastensesnobetoenas armadurasedeseguidaoesforoaxialeosmomentosresultantesapartirdeumadeformadada seco. Paraoclculodaresistnciaflexodesecesdebetoarmadoashiptesesqueseconsideram so as seguintes: As seces mantm-se planas aps a deformao; As extenses das armaduras aderentes so iguais s do beto envolvente; A resistncia do beto traco ignorada; As tenses do beto comprimido so as dadas pelo diagrama tenses-extenses de clculo; As tenses nas armaduras so as dadas pelo diagrama de clculo. 3.IMPLEMENTAO DE TABELAS E BACOS 3.1 Modelo de resoluo. Generalidades Aintegraodastensesnobetocomprimido,paraefeitodoclculodasuaresultanteedos esforos na seco, um problema complexo tendo em conta a lei constitutiva no linear usada no estado limite ltimo. Por outro lado trata-se de um integral de rea cujo domnio de integrao a zonadasecolimitadapeloeixoneutroeondeobetoseencontracomprimido.Nestetrabalho optou-seporefectuaradivisodestareaemtringulos,nosquaisseefectuaaintegraoexacta, processousadoem[3].Outroaspectoimportanteaimposiodascondiesderoturadeque resultaadefiniodasextensesemcadapontodaseco.Esteaspectofoiequacionadocom Tabelas de Dimensionamento de Estruturas de Beto 11 funes de Heaviside que permitem numa nicaexpresso a definio de funes paramtricas. O mtodoestdescritoemBarrosetal[4]etambmusadonestetrabalho.Omodelofoi implementadonoMAPLE,programademanipulaomatemticaqueefectuaaresoluodas equaes e elaborao das tabelas e bacos. 3.2 Tabelas e bacos desenvolvidos As tabelas e bacos desenvolvidas podem agrupar-se em Tabelas para dimensionamento rotura de peas flectidas (vigas e pilares): oFlexo SimplesTABELA 1 e TABELA 2 oFlexo CompostaTABELA 3, 4, 5, 6, 7 e 8. bacos para dimensionamento rotura de pilares flexo composta: oArmadura simtrica baco R1 oArmadura no simtrica baco R2 bacos para dimensionamento rotura de pilares flexo composta desviada: oSeces rectangulares, Disposio 1: baco R3 oSeces rectangulares, Disposio 2: baco R4 oSeces rectangulares, Disposio 3: baco R5 oSeces rectangulares, Disposio 4: baco R6 bacos de clculo de tenses em estado fendilhado para a verificao dos estados limites de utilizao: oSeco rectangular simplesmente armada: baco S1 oSeco rectangular duplamente armada A/A = 0.2: baco S2 oSeco rectangular duplamente armada A/A = 0.4: baco S3 oSeco rectangular duplamente armada A/A = 0.6: baco S4 oSeco rectangular duplamente armada A/A = 0.8: baco S5 oSeco rectangular duplamente armada A/A = 1.0: baco S6 Tabelas de Dimensionamento de Estruturas de Beto 12 4.EXEMPLOS DE APLICAO Ex. n1: Flexo simples. Seco rectangular simplesmente armada Calcular a armadura necessria para uma seco rectangular de 0.25x0.50m sujeita a um momento flector de clculo de 250kNm. O beto da classe C30 e o ao S500. yd=fyd/EsAsGhdbxy h=0.50m d=0.45m b=0.25m SdM =RdM =250kNm ckf =30MPa cdf =ckf /1.5=30/1.5=20MPa ykf =500MPa ydf =ykf /1.15=500/1.15=435MPa Pela TABELA 1 vem: cdRdf bdM2= =20000 45 . 0 25 . 02502 =0.247; da 1 e 2 colunas conclui-se que : =0.359; =0.290 e ser : ydcdsffbd A = =4350002000045 . 0 25 . 0 290 . 0 =0.0015m2=15cm2 Tabelas de Dimensionamento de Estruturas de Beto 13 Ex. n2: Flexo simples. Seco rectangular duplamente armada Calcular a armadura necessria para uma seco rectangular de 0.30x0.60m sujeita a um momento flector de clculo de 1000kNm. O beto da classe C30 e o ao S500. yd=fyd/EsGhdbA'xyA h=0.60m d=0.53m; a=0.07m; a/d 0.13 b=0.30m SdM =RdM =800kNm ckf =30MPa cdf =ckf /1.5=30/1.5=20MPa ykf =500MPa ydf =ykf /1.15=500/1.15=435MPa Pela TABELA 2 vem: cdRdf bdM2= =20000 53 . 0 3 . 08002=0.475;A/A=0; no tem soluo A/A =0.2; =0.602; =0.609;+0.2 =0.731 A/A =0.3; =0.498; =0.575;+0.3 =0.748 Conclui-se que a soluo mais econmica obtida com A/A =0.2 e portanto: ydcdffbd A = =4352053 30 609 . 0 =44.5cm2 e A=A0.2 =44.50.2 =8.9 cm2 e a posio do eixo neutro dada por: x= d= 0.60253= 31.9 cm. (Note-se que a soluo A/A = 0.3 com posio do eixo neutro, x = 0.498 53 = 26.4 cm, embora com consumo ligeiramente superior de ao, pode ser adequada devido maior ductilidade que apresenta). Tabelas de Dimensionamento de Estruturas de Beto 14 sscu2AA' Para obter as extenses no ao e no beto deduz-se da figura que: x d xs cu= 2 sendo 2 cu sxx d = = / 5 . 39 . 319 . 31 53 =2.32 / e que : a x xs cu=2 sendo 2// /cu sd xd a d x = = / 5 . 3602 . 013 . 0 602 . 0 =2.74 / O ao S500 inicia deformaes plsticas, ou cedncia, em termos de valores de clculo para extenses superiores a : ( ) ( ) 200000 / 15 . 1 / 500 / / / = =s s yk s ydE f E f =2.17 / Dondesepodeconcluirqueambasasarmadurasestoemcedncia(s >2.17 / e s >2.17 / ),portantocomtensoigualtensodecedncia: s =s =435MPa,eobetomais comprimido (fibras superiores) com a tenso mxima c =cdf =20MPa. Tabelas de Dimensionamento de Estruturas de Beto 15 Ex. n3: Flexo composta. Calcular a armadura necessria para uma seco rectangular de 0.40x0.60m sujeita a um momento flector e esforo normal cujos valores de clculo so respectivamente de 500KNm e 1000KN(de compresso). O beto da classe C35 e o ao S500.xyyd=fyd/EsGhbA'aMRdNRdAa h=0.60m b=0.40m; a=0.06m; a/h=0.10 RdM =500kNm;RdN =1000kN ckf =35MPa cdf =ckf /1.5=35/1.5=23.3MPa ykf =500MPa ydf =ykf /1.15=500/1.15 =435MPa a) Por aplicao da TABELA 3 em que A=A (armaduras iguais) vem: cdRdf bdM2= =23300 60 . 0 40 . 05002 =0.149; cdRdbdfN= =23300 60 . 0 40 . 01000 =0.179; Interpolando obtm-se sucessivamente os seguintes resultados: =0.149; =0.1; =0.2634; =0.1746; =0.149; =0.2; =0.1746; =0.2508; =0.149; =0.179; =0.1932; =0.2348; Conclui-se que a rea de armadura total sA =(4353 . 2360 40 1932 . 0 )=24.8 cm2 e portantoA=A=24.8/2=12.4 cm2. Tabelas de Dimensionamento de Estruturas de Beto 16 b) Por aplicao do BACO 1 em que A=A (armaduras iguais) vem: para =0.149 e =0.179; =0.2; 0.25; a rea de armadura total sA =(4353 . 2360 40 2 . 0 )=25.7 cm2 e portantoA= ` A =25.7/2=12.85cm2.Note-se que as tabelas permitem maior preciso nos resultados do que os bacos. c) Por aplicao da TABELA 4 em que A=0 vem: ( ) a h N M MSd Sd Sds = 2 / =500+1000(.60/2-.06)=740kNm cdSdsSdsf bdM2= =23300 54 . 0 40 . 07402 =0.272; Interpolando obtm-se os seguintes resultados: Sds =0.272; s , 1 =0.3268; =0.4038; Conclui-se que a rea de armadura sA =(10000 435000 / ) 1000 23300 54 40 3268 . 0 ( ) =14.8 cm2. d) Por aplicao da TABELA 5 em que se impe 250 . 0 = vem (ver figura): xyyd=fyd/EsGhA'aMSdNSdAaNSdMSd s ( ) a h N M MSd Sd Sds = 2 / =500+1000(.60/2-.06)=740kNm cdSdsSdsf bdM2= =23300 54 . 0 40 . 07402 =0.272; Tabelas de Dimensionamento de Estruturas de Beto 17 Interpolando obtm-se os seguintes resultados, tendo em conta que a=0.06m, d=0.60-0.06=0.54 e a/d=0.06/0.54=0.111: Sds =0.272;a/d=0.10; s , 1 =0.3032; s , 2 =0.1042; Sds =0.272;a/d=0.15; s , 1 =0.3092; s , 2 =0.1656; Sds =0.272;a/d=0.111; s , 1 =0.3045; s , 2 =0.1177; Conclui-se que a rea de armadura inferior : sA =(10000 435000 / ) 1000 23300 54 . 40 . 3045 . 0 ( )=12.24 cm2, e sA =100004353 . 2354 . 40 . 1177 . 0 ( )=13.6 cm2. e) Por aplicao da TABELA 6 em que se impe 350 . 0 = , tendo em conta que o momento reduzido ao nvel da armadura igual ao obtido no ponto d) anterior, vem: =Sds 0.272; Interpolando obtm-se os seguintes resultados: Sds =0.272;a/d=0.10; s , 1 =0.305 s , 2 =0.0312 Sds =0.272;a/d=0.15; s , 1 =0.3162 s , 2 =0.0332; Sds =0.272;a/d=0.111; s , 1 =0.3075; s , 2 =0.0316; Conclui-se que a rea de armadura inferior : sA =10000 435000 / ) 1000 23300 54 . 40 . 3075 . 0 ( =12.6 cm2 e sA =100004353 . 2354 . 40 . 0316 . 0 ( )=3.6 cm2. f) Por aplicao do BACO 7 em que A=0.5A vem: para =0.149 e =0.179; =0.17; 0.3; a rea de armadura total sA =4353 . 2360 40 17 . 0 =21.8 cm2 e portantoA=21.8/1.5=14.5 cm2 e ` A =14.5/2=7.25cm2. Tabelas de Dimensionamento de Estruturas de Beto 18 A=12.4cmA=12.4cmx=0.2348(60)=14cmenA=7.25cmA=14.5cmx=0.250(54)=13.5cmA=12.24cmA=13.6cmenenx=0.350(54)=18.9cmx=0.3(60)=18cmenA=12.6cmA=3.6cmx=0.4038(54)=21.8cmA=14.8cmen a)e b)c) d) f) e) Na figura mostram-se as solues obtidas:a) e b) armaduras iguais A=A;c) s armadura inferior; e com posio do eixo neutro pr definida, sendo:d)250 . 0 = ,e)350 . 0 = ; ef) com A=0.5A. Note-se que neste caso, e atendendo unicamente ao par de esforos especificado, a soluo mais econmica aquela em que apenas existe armadura inferior. Tabelas de Dimensionamento de Estruturas de Beto 19 Ex. n 4: Flexo simples de seco em T Calcular a armadura longitudinal de traco de uma seco em T com b=1.20m, bw=0.30m; h=1.10m, hw=0.15m e d=1.00m, e sujeito a um momento flector actuante de clculo, MSd=2400kN.m. Materiais: C20/25; A500. b/bw=1.20/0.30=4 Sds= 150 . 05 . 1 / 20 0 . 1 2 . 14 . 22= hf/d=0.15/1.0=0.15 Por aplicao de TABELA 9_b/bw=4 MSds=0.15, hf/d=0.14, 1,s=0.165 =0.263 x=d=0.263m>hf MSds=0.15, hf/d=0.16, 1,s=0.164 eixo neutro cai fora do banzo MSds=0.15, hf/d=0.15, 1,s=0.1645 As = 4355 . 1 / 20 0 . 1 2 . 1 1645 . 0 =60.510-4m2 = 60.5cm2 (1325) Tabelas de Dimensionamento de Estruturas de Beto 20 Ex. n 5: Flexo composta de seco em T Calcular a armadura ordinria longitudinal de traco de uma seco em T, com ascaractersticasgeomtricasdasecodoEx.n4,sujeitaaummomentoflector actuante de clculo, MSd =1940kN.m e a um esforo axial de compresso (devido a pr-esforo)P=1800kN.Admite-sequeaalturatilcorrespondentearmaduraordinria (ds) armadura de pr-esforo (dp) a mesma d=ds=dp=1.0m. Materiais: C25/30; A400; Cabodepr-esforode12cordesde15mmdedimetro:Ap=1.412=16.8cm2; Ap1860. Por aplicao da TABELA 9_b/bw=4 Determinao do momento flector MSds (esforos aplicados no centro de foras da armadura de traco). Distncia do centro geomtrico da seco em T armadura traccionada, zs zs=( )30 . 0 95 . 0 15 . 0 2 . 12 / 95 . 0 30 . 0 95 . 0 2 / 15 . 0 10 . 1 15 . 0 2 . 1 + + -0.10=0.588m MSds=Msd-NSd zs =1.94-(-1.80.588)=3.00MN.m Sds=0.150;hf/d=0.15 1,s=0.1645; =0.262 As=3481(0.16451.21.025/1.5-1.8)=42.8210-4m2 Est a armadura de pr-esforo em cedncia? yp= 15 . 19 . 0 1860/(20010+3)=7.3 p=0p+p=3 410 200 10 8 . 168 . 1+ +3.510-3262 . 0262 . 0 1= =5.310-3+9.910-3=15.2>7.3

Est em cedncia! Armadura ordinria necessria para verificar a segurana AsA400=As-Api=42.82-|||

\|||

\|348 /10 8 . 168 . 115 . 19 . 0 1860416.8= =42.82-(384/348)16.8=24.27cm2 (820) Tabelas de Dimensionamento de Estruturas de Beto 21 Ex. n 6: Flexo composta desviada Dimensione a armadura longitudinal de um pilar de seco rectangular: b=0.60m, h=0.80m, sujeita aos seguintes esforos actuantes de clculo mximos, NSd=3000kN; MSd,x=525kN.m; MSd,y=1516kN.m. Materiais: C30/37; S500 Por aplicao do baco R4 Flexo desviada, considerando armadura igualmente distribuda no contorno da seco, e considerando10 . 01 1= =bcha: = 313 . 020 8 . 0 6 . 00 . 3= x= 091 . 020 6 . 0 6 . 0 8 . 0525 . 0= 2 y= 197 . 020 8 . 0 8 . 0 6 . 0516 . 1= 1 =0.2; 1=0.1972=0.091=0.50 =0.4; 1=0.1972=0.091=0.48 Resulta =0.313;1=0.1972=0.0910.489 As=0.4890.60.820/435=107.910-4m2=107.9cm2 Soluo possvel 832 825 Cintas: 8//.30 Tabelas de Dimensionamento de Estruturas de Beto 22 Ex. n 7: Tenses em servio de seco rectangular Determine as tenses no beto (fibra superior) e na armadura de traco da seco rectangular duplamente armada, dimensionada no Ex. n 2, quando sujeita a um momento flector de servio, MSd=400kN.m. Considere e=Es/Ec=10. Por aplicao do baco S2: A/A=8.9/44.5=0.2; a/d=0.1; = 028 . 053 . 0 30 . 010 5 . 444= e = 100.028=0.28; MSd*= MSd=400kN.m *. *SdSdMd N=0 Cc=4.0; c=4.0253 . 0 3 . 0400 . 0=19.0 MPa Cs=1.20; s=028 . 02 . 1253 . 0 3 . 04 . 0=203.4MPa Ex. n 8: Tenses em servio de seco em T com pr-esforo Determine as tenses mximas de compresso no beto e de traco no ao da seco em T dimensionada no Ex. n 5 quando solicitada pelos esforos actuantes para a combinao frequente de aces: MSd = 600kN.m; NSd=P=-1800kN. Considere e =Es/Ec=15. Por aplicao do baco S9/S10: b/bw = 4 hf/d= 0.15 MSd*=600+18000.588=1658.4kN.m s=2*0 . 1 2 . 1 SdM=1.38;=bdAs Ap += ( )0 . 1 2 . 110 27 . 24 8 . 164 +=0.034 e = 0.051; NSd*d/MSd*=-18001.0/1658.4-1.1 =0.77 Cc=6.0c=6.01.38=8.3MPa Cs=0.1 s=0034 . 01 . 01.38=40.6MPa(tenso no ao da armadura passiva). Tabelas de Dimensionamento de Estruturas de Beto 23 5.TABELAS Flexo simples de seces rectangulares TABELA 1 Simplesmente armadas TABELA 2 Duplamentearmadas Flexo composta de seces rectangulares TABELA 3 Simetricamente armadas: A=A TABELA 4 Simplesmente armadas TABELA 5 Duplamentearmadas: .=0.250 TABELA 6 Duplamentearmadas: .=0.350 TABELA 7 Duplamentearmadas: .=0.450 TABELA 8 Duplamentearmadas: .=0.617 TABELA 9 Seces em T simplesmente armadas: b/bw = 4 b/bw = 8 Tabelas de Dimensionamento de Estruturas de Beto 24 TABELA 1_S500 FLEXO SIMPLES Seces rectangulares simplesmente armadas S400; S500; S600 dx= ;cdRdf bdM2= ;cdydsffbdA= 15 . 1 /yk ydf f = ; 5 . 1 /ck cdf f =Nota: a taxa mecnica de armadura mnima em vigas dada pelo maior de: cdctmff226 . 0min= e cdydff0013 . 0min= (clusula 9.2.1.1 do EC2) C12-C50C55C60C70C80C90 0,0050,0210,0050,0230,0050,0240,0050,0260,0050,0270,0050,0270,005 0,0100,0300,0100,0330,0100,0350,0100,0370,0100,0380,0100,0390,010 0,0150,0370,0150,0410,0150,0430,0150,0460,0150,0470,0150,0480,015 0,0200,0440,0200,0480,0200,0500,0200,0530,0200,0550,0200,0550,020 0,0250,0500,0260,0540,0250,0570,0260,0600,0260,0620,0260,0620,025 0,0300,0550,0310,0600,0310,0630,0310,0660,0310,0680,0310,0690,030 0,0350,0610,0360,0650,0360,0680,0360,0720,0360,0740,0360,0750,036 0,0400,0660,0410,0710,0410,0740,0410,0770,0410,0790,0410,0800,041 0,0450,0710,0460,0760,0460,0790,0460,0820,0460,0840,0460,0860,046 0,0500,0760,0520,0810,0520,0840,0520,0870,0520,0900,0520,0910,051 0,0550,0810,0570,0860,0570,0890,0570,0920,0570,0950,0570,0970,057 0,0600,0870,0620,0910,0620,0940,0620,0980,0620,1040,0620,1060,062 0,0650,0920,0670,0960,0670,0990,0680,1060,0680,1130,0680,1150,067 0,0700,0970,0730,1020,0730,1050,0730,1150,0730,1220,0730,1250,073 0,0750,1020,0780,1070,0780,1130,0780,1230,0780,1310,0790,1340,078 0,0800,1070,0840,1130,0840,1210,0840,1320,0840,1400,0840,1440,084 0,0850,1130,0890,1200,0890,1280,0890,1400,0900,1500,0900,1530,090 0,0900,1180,0950,1280,0950,1370,0950,1490,0950,1590,0950,1630,095 0,0950,1240,1000,1350,1000,1440,1000,1580,1010,1680,1010,1730,101 0,1000,1310,1060,1430,1060,1530,1060,1670,1060,1780,1070,1830,107 0,1050,1370,1110,1500,1110,1610,1120,1760,1120,1880,1120,1920,112 0,1100,1440,1170,1580,1170,1690,1170,1850,1180,1970,1180,2020,118 0,1150,1510,1230,1660,1230,1770,1230,1940,1240,2070,1240,2120,124 0,1200,1590,1280,1730,1290,1860,1290,2030,1290,2170,1300,2230,130 0,1250,1660,1340,1810,1350,1940,1350,2120,1350,2270,1360,2330,136 0,1300,1730,1400,1890,1400,2020,1410,2220,1410,2370,1420,2430,142 0,1350,1800,1460,1970,1460,2110,1470,2310,1470,2470,1480,2540,148 0,1400,1880,1520,2050,1520,2200,1530,2410,1530,2570,1540,2640,154 0,1450,1950,1580,2130,1580,2280,1590,2500,1590,2670,1600,2750,160 0,1500,2020,1640,2210,1640,2370,1650,2600,1650,2770,1660,2850,166 0,1550,2100,1700,2290,1700,2460,1710,2690,1720,2880,1730,2960,173 0,1600,2170,1760,2380,1760,2550,1770,2790,1780,2980,1790,3070,179 0,1650,2250,1820,2460,1830,2640,1830,2890,1840,3090,1850,3180,185 0,1700,2320,1880,2540,1890,2720,1890,2990,1910,3200,1920,3290,192 0,1750,2400,1940,2630,1950,2820,1960,3090,1970,3310,1980,3400,199 0,1800,2480,2010,2710,2010,2910,2020,3190,2030,3420,2050,3520,205 0,1850,2560,2070,2800,2080,3000,2090,3300,2100,3530,2110,3630,212 0,1900,2640,2130,2890,2140,3090,2150,3400,2170,3640,2180,3750,219 0,1950,2710,2200,2970,2210,3190,2220,3500,2230,3750,2250,3860,225 0,2000,2800,2260,3060,2270,3280,2280,3610,2300,3870,2320,3980,232 0,2050,2880,2330,3150,2340,3380,2350,3720,2370,3980,2390,4100,239 0,2100,2960,2390,3240,2410,3480,2420,3820,2440,4100,2460,4220,246 0,2150,3040,2460,3330,2470,3570,2480,3930,2510,4220,2530,4350,254 0,2200,3120,2530,3420,2540,3670,2550,4040,2580,4340,2600,4470,261 0,2250,3210,2600,3520,2610,3770,2620,4150,2650,4460,2670,4600,268 0,2300,3290,2660,3610,2680,3870,2690,4270,2720,4580,2750,4720,276 0,2350,3380,2730,3700,2750,3980,2760,4380,2790,4700,2820,4850,283 0,2400,3460,2800,3800,2820,4080,2840,4500,2870,4830,2900,4990,291 0,2450,3550,2870,3900,2890,4190,2910,4610,2940,4960,2970,5120,299 0,2500,3640,2950,3990,2960,4290,2980,4730,3020,5090,3050,5250,306 Tabelas de Dimensionamento de Estruturas de Beto 25 TABELA 1_S500 (cont.) FLEXO SIMPLES Seces rectangulares simplesmente armadasS400; S500; S600 dx= ; cdRdf bdM2= ;cdydsffbdA= ; 15 . 1 /yk ydf f = ;5 . 1 /ck cdf f =C12-C50C55C60C70C80C90 0,2550,3730,3020,4090,3040,4400,3060,4850,3090,5220,3130,5390,315 0,2600,3820,3090,4190,3110,4510,3130,4980,3170,5350,3210,5530,334 0,2650,3910,3160,4290,3190,4620,3210,5100,3250,5490,3350,5670,363 0,2700,4000,3240,4400,3260,4730,3290,5220,3330,5630,3630,5820,394 0,2750,4090,3310,4500,3340,4840,3360,5350,3410,5770,3940,5960,430 0,2800,4190,3390,4600,3420,4950,3440,5480,3490,5910,4280,6110,469 0,2850,4280,3470,4710,3490,5070,3520,5610,3680,6050,4650,6260,512 0,2900,4380,3550,4820,3570,5190,3600,5740,3980,6200,5080,6420,561 0,2950,4480,3620,4930,3660,5310,3690,5880,4310,6350,5540,6580,617 0,3000,4580,3700,5040,3740,5430,3770,6020,4670,6510,6070,6740,680 0,3050,4680,3790,5150,3820,5550,3860,6160,5070,6660,6670,6900,751 0,3100,4780,3870,5260,3910,5670,3940,6300,5510,6820,7340,7070,834 0,3150,4880,3950,5380,3990,5800,4180,6450,6000,6990,8120,7250,931 0,3200,4990,4040,5500,4080,5930,4500,6600,6560,7150,9010,7421,044 0,3250,5090,4120,5620,4170,6060,4860,6750,7180,7321,0050,7611,180 0,3300,5200,4210,5740,4260,6200,5260,6900,7890,7501,1280,7791,344 0,3350,5310,4300,5860,4350,6330,5690,7060,8710,7681,2760,7991,547 0,3400,5420,4390,5990,4650,6470,6180,7220,9640,7871,4550,8191,804 0,3450,5540,4480,6110,5010,6610,6730,7391,0740,8061,6780,8402,143 0,3500,5650,4580,6240,5400,6760,7340,7561,2020,8261,9620,8612,601 0,3550,5770,4670,6380,5850,6910,8030,7741,3570,8462,3350,8833,260 0,3600,5890,4770,6510,6340,7060,8830,7921,5450,8682,8490,9074,287 0,3650,6010,4870,6650,6880,7210,9730,8111,7790,8903,5980,9316,111 0,3700,6130,4970,6800,7500,7371,0790,8302,0750,9134,7910,3750,6260,5280,6940,8200,7541,2030,8502,4680,9377,006 0,3800,6390,5700,7090,9000,7711,3500,8713,006 0,3850,6530,6170,7250,9920,7881,5290,8923,7950,3900,6660,6700,7401,0990,8061,7480,9155,0560,3950,6800,7290,7571,2240,8252,0260,9397,3910,4000,6950,7960,7741,3750,8442,389 0,4050,7100,8730,7911,5560,8652,879 0,4100,7250,9610,8091,7830,8863,5830,4150,7411,0650,8282,0690,9084,6780,4200,7571,1880,8472,4480,9326,6180,4250,7741,3350,8682,970 0,4300,7921,5160,8903,730 0,4350,8111,7430,9134,9550,4400,8302,0360,9377,2550,4450,8502,4310,4500,8722,995 0,4550,8963,865 0,4600,9215,3840,4650,9498,800Nota: A tabela vlida para os aos S400, S500 e S600 at linha a cheio (parte superior da tabela). A partir dessa linha deve-se proceder da seguinte forma: S400 usar as taxas mecnicas de armadura indicadas na tabela entre a linha a cheio e a linha a tracejado. A partir da linha tracejada para obter a taxa mecnica de armadura multiplicar o valor dado na tabela por8 . 0 500 / 400 500 / = =ykf ; S500 a tabela valida para toda a gama de valores; S600 a partir da linha a cheio para obter a taxa mecnica de armadura multiplicar o valor dado na tabela por2 . 1 500 / 600 500 / = =ykf . Tabelas de Dimensionamento de Estruturas de Beto 26 TABELA 1_S400 FLEXO SIMPLES Seces rectangulares simplesmente armadasS400 dx= ;cdRdf bdM2= ;cdydsffbdA= 15 . 1 /yk ydf f = ;5 . 1 /ck cdf f = C12-C50C55C60C70C80C90 0,0050,0210,0050,0230,0050,0240,0050,0260,0050,0270,0050,0270,005 0,0100,0300,0100,0330,0100,0350,0100,0370,0100,0380,0100,0390,010 0,0150,0370,0150,0410,0150,0430,0150,0460,0150,0470,0150,0480,015 0,0200,0440,0200,0480,0200,0500,0200,0530,0200,0550,0200,0550,020 0,0250,0500,0260,0540,0250,0570,0260,0600,0260,0620,0260,0620,025 0,0300,0550,0310,0600,0310,0630,0310,0660,0310,0680,0310,0690,030 0,0350,0610,0360,0650,0360,0680,0360,0720,0360,0740,0360,0750,036 0,0400,0660,0410,0710,0410,0740,0410,0770,0410,0790,0410,0800,041 0,0450,0710,0460,0760,0460,0790,0460,0820,0460,0840,0460,0860,046 0,0500,0760,0520,0810,0520,0840,0520,0870,0520,0900,0520,0910,051 0,0550,0810,0570,0860,0570,0890,0570,0920,0570,0950,0570,0970,057 0,0600,0870,0620,0910,0620,0940,0620,0980,0620,1040,0620,1060,062 0,0650,0920,0670,0960,0670,0990,0680,1060,0680,1130,0680,1150,067 0,0700,0970,0730,1020,0730,1050,0730,1150,0730,1220,0730,1250,073 0,0750,1020,0780,1070,0780,1130,0780,1230,0780,1310,0790,1340,078 0,0800,1070,0840,1130,0840,1210,0840,1320,0840,1400,0840,1440,084 0,0850,1130,0890,1200,0890,1280,0890,1400,0900,1500,0900,1530,090 0,0900,1180,0950,1280,0950,1370,0950,1490,0950,1590,0950,1630,095 0,0950,1240,1000,1350,1000,1440,1000,1580,1010,1680,1010,1730,101 0,1000,1310,1060,1430,1060,1530,1060,1670,1060,1780,1070,1830,107 0,1050,1370,1110,1500,1110,1610,1120,1760,1120,1880,1120,1920,112 0,1100,1440,1170,1580,1170,1690,1170,1850,1180,1970,1180,2020,118 0,1150,1510,1230,1660,1230,1770,1230,1940,1240,2070,1240,2120,124 0,1200,1590,1280,1730,1290,1860,1290,2030,1290,2170,1300,2230,130 0,1250,1660,1340,1810,1350,1940,1350,2120,1350,2270,1360,2330,136 0,1300,1730,1400,1890,1400,2020,1410,2220,1410,2370,1420,2430,142 0,1350,1800,1460,1970,1460,2110,1470,2310,1470,2470,1480,2540,148 0,1400,1880,1520,2050,1520,2200,1530,2410,1530,2570,1540,2640,154 0,1450,1950,1580,2130,1580,2280,1590,2500,1590,2670,1600,2750,160 0,1500,2020,1640,2210,1640,2370,1650,2600,1650,2770,1660,2850,166 0,1550,2100,1700,2290,1700,2460,1710,2690,1720,2880,1730,2960,173 0,1600,2170,1760,2380,1760,2550,1770,2790,1780,2980,1790,3070,179 0,1650,2250,1820,2460,1830,2640,1830,2890,1840,3090,1850,3180,185 0,1700,2320,1880,2540,1890,2720,1890,2990,1910,3200,1920,3290,192 0,1750,2400,1940,2630,1950,2820,1960,3090,1970,3310,1980,3400,199 0,1800,2480,2010,2710,2010,2910,2020,3190,2030,3420,2050,3520,205 0,1850,2560,2070,2800,2080,3000,2090,3300,2100,3530,2110,3630,212 0,1900,2640,2130,2890,2140,3090,2150,3400,2170,3640,2180,3750,219 0,1950,2710,2200,2970,2210,3190,2220,3500,2230,3750,2250,3860,225 0,2000,2800,2260,3060,2270,3280,2280,3610,2300,3870,2320,3980,232 0,2050,2880,2330,3150,2340,3380,2350,3720,2370,3980,2390,4100,239 0,2100,2960,2390,3240,2410,3480,2420,3820,2440,4100,2460,4220,246 0,2150,3040,2460,3330,2470,3570,2480,3930,2510,4220,2530,4350,254 0,2200,3120,2530,3420,2540,3670,2550,4040,2580,4340,2600,4470,261 0,2250,3210,2600,3520,2610,3770,2620,4150,2650,4460,2670,4600,268 0,2300,3290,2660,3610,2680,3870,2690,4270,2720,4580,2750,4720,276 0,2350,3380,2730,3700,2750,3980,2760,4380,2790,4700,2820,4850,283 0,2400,3460,2800,3800,2820,4080,2840,4500,2870,4830,2900,4990,291 0,2450,3550,2870,3900,2890,4190,2910,4610,2940,4960,2970,5120,299 0,2500,3640,2950,3990,2960,4290,2980,4730,3020,5090,3050,5250,306 Tabelas de Dimensionamento de Estruturas de Beto 27 TABELA 1_S400 (cont.) FLEXO SIMPLES Seces rectangulares simplesmente armadasS400 dx= ;cdRdf bdM2= ;cdydsffbdA= 15 . 1 /yk ydf f = ;5 . 1 /ck cdf f =C12-C50C55C60C70C80C90 0,2550,3730,3020,4090,3040,4400,3060,4850,3090,5220,3130,5390,315 0,2600,3820,3090,4190,3110,4510,3130,4980,3170,5350,3210,5530,323 0,2650,3910,3160,4290,3190,4620,3210,5100,3250,5490,3290,5670,331 0,2700,4000,3240,4400,3260,4730,3290,5220,3330,5630,3370,5820,339 0,2750,4090,3310,4500,3340,4840,3360,5350,3410,5770,3460,5960,348 0,2800,4190,3390,4600,3420,4950,3440,5480,3490,5910,3540,6110,375 0,2850,4280,3470,4710,3490,5070,3520,5610,3580,6050,3720,6260,410 0,2900,4380,3550,4820,3570,5190,3600,5740,3660,6200,4060,6420,449 0,2950,4480,3620,4930,3660,5310,3690,5880,3750,6350,4440,6580,493 0,3000,4580,3700,5040,3740,5430,3770,6020,3840,6510,4860,6740,544 0,3050,4680,3790,5150,3820,5550,3860,6160,4050,6660,5330,6900,601 0,3100,4780,3870,5260,3910,5670,3940,6300,4410,6820,5870,7070,667 0,3150,4880,3950,5380,3990,5800,4030,6450,4800,6990,6490,7250,745 0,3200,4990,4040,5500,4080,5930,4120,6600,5250,7150,7210,7420,835 0,3250,5090,4120,5620,4170,6060,4210,6750,5740,7320,8040,7610,944 0,3300,5200,4210,5740,4260,6200,4310,6900,6310,7500,9020,7791,075 0,3350,5310,4300,5860,4350,6330,4560,7060,6970,7681,0210,7991,238 0,3400,5420,4390,5990,4440,6470,4940,7220,7720,7871,1640,8191,444 0,3450,5540,4480,6110,4540,6610,5380,7390,8590,8061,3420,8401,714 0,3500,5650,4580,6240,4630,6760,5870,7560,9620,8261,5690,8612,081 0,3550,5770,4670,6380,4730,6910,6430,7741,0860,8461,8680,8832,608 0,3600,5890,4770,6510,5070,7060,7060,7921,2360,8682,2790,9073,430 0,3650,6010,4870,6650,5510,7210,7790,8111,4230,8902,8780,9314,889 0,3700,6130,4970,6800,6000,7370,8630,8301,6600,9133,833 0,3750,6260,5070,6940,6560,7540,9620,8501,9740,9375,604 0,3800,6390,5180,7090,7200,7711,0800,8712,405 0,3850,6530,5280,7250,7940,7881,2230,8923,036 0,3900,6660,5400,7400,8790,8061,3990,9154,045 0,3950,6800,5830,7570,9790,8251,6210,9395,913 0,4000,6950,6370,7741,1000,8441,911 0,4050,7100,6980,7911,2450,8652,303 0,4100,7250,7690,8091,4270,8862,866 0,4150,7410,8520,8281,6550,9083,743 0,4200,7570,9510,8471,9580,9325,295 0,4250,7741,0680,8682,376 0,4300,7921,2130,8902,984 0,4350,8111,3950,9133,964 0,4400,8301,6290,9375,804 0,4450,8501,945 0,4500,8722,396 0,4550,8963,092 0,4600,9214,307 0,4650,9497,040 0,470 0,475 0,480 0,485 0,490 0,495 0,500 Tabelas de Dimensionamento de Estruturas de Beto 28 TABELA 2_S500 FLEXO SIMPLES Seces rectangulares duplamente armadas C12-C50 S500 dx= ;cdRdf bdM2= ;cdydffbdA= 15 . 1 /yk ydf f = ;5 . 1 /ck cdf f = ; 10 . 0 =da0 . 0 / = A A 2 . 0 / = A A 3 . 0 / = A A 4 . 0 / = A A 5 . 0 / = A A 0 . 1 / = A A 0,0050,0000,0000,0210,0050,0220,0050,0220,0050,0230,0050,0260,004 0,0100,0280,0100,0300,0100,0310,0100,0320,0100,0330,0100,0370,009 0,0150,0350,0150,0370,0150,0390,0150,0400,0150,0410,0150,0460,014 0,0200,0410,0200,0440,0200,0460,0200,0470,0200,0480,0200,0530,019 0,0250,0460,0250,0500,0250,0510,0250,0530,0250,0540,0250,0590,024 0,0300,0520,0310,0550,0300,0570,0300,0580,0300,0600,0300,0650,029 0,0350,0570,0360,0610,0360,0620,0360,0640,0350,0650,0350,0700,035 0,0400,0620,0410,0660,0410,0670,0410,0690,0410,0700,0410,0750,040 0,0450,0670,0460,0710,0460,0720,0460,0740,0460,0750,0460,0800,045 0,0500,0720,0510,0760,0510,0770,0510,0780,0510,0790,0510,0840,051 0,0550,0770,0570,0800,0570,0820,0570,0830,0570,0840,0560,0870,056 0,0600,0820,0620,0850,0620,0860,0620,0870,0620,0880,0620,0910,062 0,0650,0880,0670,0900,0670,0910,0680,0910,0670,0920,0670,0940,067 0,0700,0930,0730,0940,0730,0950,0730,0950,0730,0960,0730,0960,072 0,0750,0980,0780,0990,0780,0990,0780,0990,0780,0990,0780,0990,078 0,0800,1040,0840,1030,0840,1030,0840,1020,0840,1020,0840,1010,083 0,0850,1100,0890,1070,0890,1070,0890,1060,0890,1050,0890,1040,089 0,0900,1170,0950,1130,0950,1110,0950,1100,0950,1090,0950,1060,094 0,0950,1240,1000,1180,1000,1160,1000,1140,1000,1130,1000,1080,100 0,1000,1310,1060,1230,1060,1200,1060,1180,1060,1160,1060,1100,106 0,1050,1370,1110,1280,1110,1240,1110,1220,1110,1190,1110,1130,111 0,1100,1440,1170,1330,1170,1290,1170,1260,1170,1230,1170,1150,117 0,1150,1510,1230,1380,1220,1330,1230,1290,1230,1260,1220,1170,122 0,1200,1590,1280,1430,1280,1370,1280,1330,1280,1290,1280,1180,128 0,1250,1660,1340,1480,1340,1420,1340,1370,1340,1320,1330,1200,133 0,1300,1730,1400,1530,1390,1460,1390,1400,1390,1360,1390,1220,139 0,1350,1800,1460,1580,1450,1500,1450,1440,1450,1390,1450,1240,144 0,1400,1880,1520,1630,1510,1540,1510,1480,1510,1420,1500,1250,150 0,1450,1950,1580,1680,1570,1590,1560,1510,1560,1450,1560,1270,155 0,1500,2020,1640,1730,1620,1630,1620,1540,1620,1480,1620,1280,161 0,1550,2100,1700,1780,1680,1670,1680,1580,1670,1510,1680,1300,167 0,1600,2170,1760,1830,1740,1710,1730,1620,1730,1540,1730,1310,172 0,1650,2250,1820,1880,1800,1750,1790,1650,1790,1570,1790,1330,178 0,1700,2320,1880,1930,1850,1790,1850,1680,1850,1590,1840,1340,183 0,1750,2400,1940,1990,1910,1840,1900,1720,1900,1620,1900,1350,189 0,1800,2480,2010,2040,1970,1880,1970,1750,1960,1650,1950,1370,194 0,1850,2560,2070,2090,2030,1920,2020,1790,2020,1680,2010,1380,200 0,1900,2640,2130,2140,2090,1960,2080,1820,2070,1700,2070,1390,206 0,1950,2710,2200,2190,2150,2000,2140,1850,2130,1730,2120,1400,211 0,2000,2800,2260,2240,2210,2040,2200,1880,2190,1760,2180,1410,217 0,2050,2880,2330,2290,2270,2090,2260,1920,2240,1790,2240,1430,222 0,2100,2960,2390,2340,2330,2130,2310,1950,2300,1810,2300,1440,228 0,2150,3040,2460,2400,2390,2170,2370,1980,2360,1840,2350,1450,233 0,2200,3120,2530,2450,2450,2210,2430,2020,2420,1870,2410,1460,239 0,2250,3210,2600,2500,2510,2250,2490,2050,2480,1890,2460,1470,245 0,2300,3290,2660,2550,2570,2290,2550,2080,2530,1920,2520,1480,250 0,2350,3380,2730,2600,2630,2330,2600,2110,2590,1940,2580,1490,256 0,2400,3460,2800,2660,2690,2370,2660,2150,2650,1970,2640,1500,261 0,2450,3550,2870,2720,2750,2410,2720,2180,2710,1990,2690,1510,267 0,2500,3640,2950,2780,2820,2450,2780,2210,2760,2020,2750,1520,273 Tabelas de Dimensionamento de Estruturas de Beto 29 TABELA 2_S500 (cont.) FLEXO SIMPLES Seces rectangulares duplamente armadas C12-C50 S500 dx= ;cdRdf bdM2= ;cdydffbdA= 15 . 1 /yk ydf f =;5 . 1 /ck cdf f =;10 . 0 =da0 . 0 / = A A 2 . 0 / = A A 3 . 0 / = A A 4 . 0 / = A A 5 . 0 / = A A 0 . 1 / = A A 0,2550,3730,3020,2850,2880,2500,2840,2240,2820,2040,2810,1530,278 0,2600,3820,3090,2910,2940,2540,2900,2270,2880,2070,2870,1540,284 0,2650,3910,3160,2970,3010,2580,2960,2310,2940,2090,2930,1550,289 0,2700,4000,3240,3030,3070,2620,3020,2340,2990,2120,2980,1550,295 0,2750,4090,3310,3100,3140,2670,3080,2370,3050,2140,3030,1560,301 0,2800,4190,3390,3160,3200,2720,3140,2400,3110,2170,3090,1570,306 0,2850,4280,3470,3230,3270,2770,3200,2430,3170,2190,3150,1580,312 0,2900,4380,3550,3290,3330,2830,3270,2460,3230,2220,3210,1590,317 0,2950,4480,3620,3360,3400,2880,3330,2500,3290,2240,3260,1590,323 0,3000,4580,3700,3420,3460,2930,3390,2530,3350,2260,3320,1600,328 0,3100,4780,3870,3550,3600,3040,3520,2590,3470,2310,3440,1620,340 0,3200,4990,4040,3690,3730,3150,3640,2660,3580,2360,3550,1630,351 0,3300,5200,4210,3820,3870,3260,3770,2740,3700,2400,3670,1650,362 0,3400,5420,4390,3960,4010,3370,3900,2830,3820,2450,3790,1660,373 0,3500,5650,4580,4100,4150,3490,4030,2920,3950,2500,3900,1670,384 0,3600,5890,4770,4240,4290,3600,4160,3020,4070,2540,4020,1690,396 0,3700,6130,4970,4380,4440,3710,4290,3110,4190,2580,4130,1700,406 0,3800,6390,5700,4530,4580,3830,4430,3200,4320,2630,4250,1710,418 0,3900,6660,6700,4680,4730,3950,4560,3290,4440,2700,4370,1720,429 0,4000,6950,7960,4820,4880,4060,4700,3390,4570,2770,4490,1730,440 0,4100,4970,5030,4180,4830,3480,4700,2840,4600,1740,451 0,4200,5130,5190,4300,4970,3580,4830,2920,4730,1760,462 0,4300,5280,5350,4420,5110,3670,4950,2990,4850,1770,474 0,4400,5440,5510,4540,5250,3770,5080,3070,4970,1780,485 0,4500,5600,5670,4670,5400,3860,5210,3140,5090,1790,496 0,4600,5770,5840,4790,5540,3960,5340,3220,5210,1800,507 0,4700,5940,6010,4920,5680,4060,5470,3290,5330,1810,518 0,4800,6110,6180,5040,5830,4160,5610,3370,5460,1810,529 0,4900,6220,6480,5170,5980,4250,5740,3450,5580,1820,540 0,5000,6300,6860,5300,6130,4350,5880,3520,5710,1830,552 0,5100,6380,7250,5430,6280,4450,6010,3600,5830,1840,563 0,5200,6460,7650,5560,6440,4560,6150,3680,5960,1850,574 0,5300,6530,8050,5700,6590,4660,6280,3760,6080,1860,585 0,5400,6600,8470,5840,6750,4760,6420,3830,6200,1870,596 0,5500,6660,8900,5970,6910,4860,6560,3910,6330,1870,607 0,5600,6730,9330,6110,7070,4970,6700,3990,6460,1880,618 0,5700,6790,9760,6200,7320,5070,6840,4070,6590,1890,630 0,5800,6841,0210,6260,7620,5170,6980,4150,6720,1900,641 0,5900,6901,0660,6300,7910,5280,7130,4230,6850,1900,652 0,6000,6951,1110,6350,8230,5390,7270,4310,6970,1910,663 0,6100,7001,1580,6400,8520,5500,7420,4390,7100,1920,674 0,6200,7051,2040,6440,8830,5600,7560,4470,7240,1920,686 0,6300,7101,2500,6480,9150,5710,7710,4550,7370,1930,697 0,6400,7141,2990,6520,9470,5820,7860,4630,7500,1940,708 0,6500,7181,3460,6560,9780,5930,8010,4710,7630,1940,719 0,6600,7221,3950,6601,0100,6050,8160,4790,7760,1950,730 0,6700,7261,4430,6641,0420,6160,8310,4880,7900,1960,741 0,6800,7301,4920,6671,0740,6200,8550,4960,8030,1960,752 0,6900,7331,5410,6711,1060,6230,8800,5050,8170,1970,764 0,7000,7371,5910,6741,1380,6260,9040,5130,8300,1970,774 Tabelas de Dimensionamento de Estruturas de Beto 30 TABELA 2_S400 FLEXO SIMPLES Seces rectangulares duplamente armadas C12-C50 S400

dx= ; cdRdf bdM2= ; cdydffbdA= 15 . 1 /yk ydf f = ;5 . 1 /ck cdf f = ;10 . 0 =da 0 . 0 / = A A 2 . 0 / = A A 3 . 0 / = A A 4 . 0 / = A A 5 . 0 / = A A 0 . 1 / = A A 0,0050,0000,0000,0210,0050,0220,0050,0220,0050,0230,0050,0260,004 0,0100,0280,0100,0300,0100,0320,0100,0330,0100,0340,0100,0380,009 0,0150,0350,0150,0380,0150,0390,0150,0410,0150,0430,0150,0480,014 0,0200,0410,0200,0450,0200,0460,0200,0480,0200,0500,0200,0550,019 0,0250,0460,0250,0500,0250,0520,0250,0540,0250,0560,0250,0620,024 0,0300,0520,0310,0560,0300,0580,0300,0600,0300,0610,0300,0680,029 0,0350,0570,0360,0610,0350,0630,0350,0650,0350,0670,0350,0730,035 0,0400,0620,0410,0660,0410,0680,0410,0700,0410,0720,0400,0770,040 0,0450,0670,0460,0710,0460,0730,0460,0750,0460,0760,0460,0810,045 0,0500,0720,0510,0760,0510,0780,0510,0790,0510,0810,0510,0850,051 0,0550,0770,0570,0810,0570,0830,0570,0840,0560,0850,0560,0890,056 0,0600,0820,0620,0860,0620,0870,0620,0880,0620,0890,0620,0920,061 0,0650,0880,0670,0900,0670,0910,0670,0920,0670,0920,0670,0940,067 0,0700,0930,0730,0940,0730,0950,0730,0960,0730,0960,0730,0970,072 0,0750,0980,0780,0990,0780,0990,0780,0990,0780,0990,0780,0990,078 0,0800,1040,0840,1030,0840,1020,0840,1020,0840,1020,0840,1010,083 0,0850,1100,0890,1070,0890,1060,0890,1050,0890,1050,0890,1030,089 0,0900,1170,0950,1120,0950,1100,0950,1090,0950,1080,0950,1050,094 0,0950,1240,1000,1170,1000,1150,1000,1130,1000,1110,1000,1070,100 0,1000,1310,1060,1210,1060,1180,1060,1160,1060,1140,1060,1090,106 0,1050,1370,1110,1260,1110,1220,1120,1200,1110,1170,1110,1110,111 0,1100,1440,1170,1310,1170,1260,1170,1230,1170,1200,1170,1120,117 0,1150,1510,1230,1350,1220,1300,1230,1260,1220,1230,1230,1140,122 0,1200,1590,1280,1400,1280,1340,1280,1290,1280,1260,1280,1150,128 0,1250,1660,1340,1450,1340,1380,1340,1320,1330,1280,1330,1170,133 0,1300,1730,1400,1490,1390,1410,1390,1360,1390,1310,1390,1180,139 0,1350,1800,1460,1540,1450,1450,1450,1390,1450,1340,1450,1200,144 0,1400,1880,1520,1590,1510,1490,1510,1420,1500,1360,1510,1210,150 0,1450,1950,1580,1630,1560,1530,1560,1450,1560,1390,1560,1220,156 0,1500,2020,1640,1680,1620,1560,1620,1480,1620,1410,1620,1230,161 0,1550,2100,1700,1720,1680,1600,1680,1510,1680,1440,1680,1240,167 0,1600,2170,1760,1770,1740,1640,1730,1540,1730,1460,1730,1260,172 0,1650,2250,1820,1810,1790,1670,1790,1570,1790,1480,1790,1270,178 0,1700,2320,1880,1860,1850,1710,1850,1590,1840,1510,1840,1280,183 0,1750,2400,1940,1910,1910,1740,1900,1620,1900,1530,1890,1290,189 0,1800,2480,2010,1950,1970,1780,1960,1650,1950,1550,1950,1300,194 0,1850,2560,2070,2000,2030,1820,2020,1680,2010,1570,2010,1310,200 0,1900,2640,2130,2060,2080,1850,2080,1700,2070,1590,2060,1320,206 0,1950,2710,2200,2120,2140,1880,2130,1730,2120,1620,2120,1320,211 0,2000,2800,2260,2180,2200,1920,2190,1760,2180,1640,2180,1330,217 0,2050,2880,2330,2240,2260,1960,2250,1790,2240,1660,2230,1340,222 0,2100,2960,2390,2300,2320,1990,2300,1810,2300,1680,2290,1350,228 0,2150,3040,2460,2360,2380,2040,2360,1840,2350,1700,2340,1360,234 0,2200,3120,2530,2420,2450,2090,2420,1870,2410,1720,2410,1360,239 0,2250,3210,2600,2480,2510,2140,2480,1890,2470,1740,2460,1370,245 0,2300,3290,2660,2540,2570,2200,2540,1920,2520,1760,2510,1380,250 0,2350,3380,2730,2600,2630,2250,2600,1940,2580,1780,2570,1390,256 0,2400,3460,2800,2660,2690,2300,2660,1970,2640,1800,2630,1390,261 0,2450,3550,2870,2720,2750,2350,2720,2000,2690,1820,2680,1400,267 0,2500,3640,2950,2780,2820,2400,2780,2040,2750,1840,2740,1410,273 Tabelas de Dimensionamento de Estruturas de Beto 31 TABELA 2_S400 (cont.) FLEXO SIMPLES Seces rectangulares duplamente armadas C12-C50 S400 dx= ; cdRdf bdM2= ; cdydffbdA= 15 . 1 /yk ydf f = ;5 . 1 /ck cdf f = ; 10 . 0 =da 0 . 0 / = A A 2 . 0 / = A A 3 . 0 / = A A 4 . 0 / = A A 5 . 0 / = A A 0 . 1 / = A A 0,2550,3730,3020,2850,2880,2450,2840,2080,2810,1860,2800,1410,278 0,2600,3820,3090,2910,2940,2510,2900,2120,2870,1870,2860,1420,284 0,2650,3910,3160,2970,3010,2560,2960,2170,2930,1890,2910,1430,289 0,2700,4000,3240,3030,3070,2610,3020,2210,2990,1910,2970,1430,295 0,2750,4090,3310,3100,3140,2670,3080,2260,3040,1930,3020,1440,300 0,2800,4190,3390,3160,3200,2720,3140,2300,3100,1950,3080,1440,306 0,2850,4280,3470,3230,3270,2770,3200,2340,3160,1960,3140,1450,312 0,2900,4380,3550,3290,3330,2830,3270,2390,3220,1980,3200,1450,317 0,2950,4480,3620,3360,3400,2880,3330,2430,3280,2010,3250,1460,323 0,3000,4580,3700,3420,3460,2930,3390,2480,3340,2040,3310,1470,328 0,3100,3550,3600,3040,3520,2560,3460,2110,3420,1480,339 0,3200,3690,3730,3150,3640,2660,3580,2190,3540,1490,351 0,3300,3820,3870,3260,3770,2740,3700,2260,3660,1490,362 0,3400,3960,4010,3370,3900,2830,3820,2330,3770,1500,373 0,3500,4100,4150,3490,4030,2920,3950,2400,3890,1510,384 0,3600,4240,4290,3600,4160,3020,4070,2480,4010,1520,395 0,3700,4380,4440,3710,4290,3110,4190,2550,4130,1530,406 0,3800,4530,4580,3830,4430,3200,4320,2620,4250,1540,417 0,3900,4680,4730,3950,4560,3290,4440,2700,4370,1540,428 0,4000,4820,4880,4060,4700,3390,4570,2770,4490,1550,440 0,4100,4970,5030,4180,4830,3480,4700,2840,4600,1560,451 0,4200,5130,5190,4300,4970,3580,4830,2920,4730,1560,462 0,4300,5280,5350,4420,5110,3670,4950,2990,4850,1570,473 0,4400,5440,5510,4540,5250,3770,5080,3070,4970,1580,484 0,4500,5600,5670,4670,5400,3860,5210,3140,5090,1580,495 0,4600,5770,5840,4790,5540,3960,5340,3220,5210,1590,507 0,4700,5940,6010,4920,5680,4060,5470,3290,5330,1600,517 0,4800,6110,6180,5040,5830,4160,5610,3370,5460,1600,529 0,4900,6280,6350,5170,5980,4250,5740,3450,5580,1610,539 0,5000,6460,6530,5300,6130,4350,5880,3520,5710,1610,551 0,5100,6640,6720,5430,6280,4450,6010,3600,5830,1620,562 0,5200,6740,7070,5560,6440,4560,6150,3680,5960,1620,573 0,5300,6820,7480,5700,6590,4660,6280,3760,6080,1630,585 0,5400,6890,7890,5840,6750,4760,6420,3830,6200,1630,596 0,5500,6960,8320,5970,6910,4860,6560,3910,6330,1640,607 0,5600,7030,8740,6110,7070,4970,6700,3990,6460,1640,617 0,5700,7090,9180,6260,7240,5070,6840,4070,6590,1640,628 0,5800,7150,9630,6400,7400,5170,6980,4150,6720,1650,640 0,5900,7211,0080,6550,7570,5280,7130,4230,6850,1650,651 0,6000,7261,0540,6690,7760,5390,7270,4310,6970,1660,662 0,6100,7321,1000,6730,8060,5500,7420,4390,7100,1660,673 0,6200,7371,1470,6780,8370,5600,7560,4470,7240,1660,685 0,6300,7411,1940,6830,8700,5710,7710,4550,7370,1670,696 0,6400,7461,2420,6870,9000,5820,7860,4630,7500,1670,707 0,6500,7501,2900,6910,9320,5930,8010,4710,7630,1680,718 0,6600,7541,3390,6950,9650,6050,8160,4790,7760,1680,729 0,6700,7581,3890,6990,9950,6160,8310,4880,7900,1680,740 0,6800,7621,4370,7031,0290,6270,8470,4960,8030,1690,752 0,6900,7651,4870,7061,0630,6390,8620,5050,8170,1690,763 0,7000,7691,5370,7091,0940,6510,8780,5130,8300,1690,773 Tabelas de Dimensionamento de Estruturas de Beto 32 TABELA 3_S500 FLEXO COMPOSTA Seces rectangulares duplamente armadas C12-C50 S500

;hx= ; ' A A As+ = ; ' A A = 10 . 0 =ha;2cdRdf bhM= ;cdRdbhfN= cdydsffbhA= ; 15 . 1 /yk ydf f = 5 . 1 /ck cdf f =0 . 0 = 1 . 0 = 2 . 0 = 3 . 0 = 4 . 0 = 5 . 0 = 0,0000,0000,0000,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0050,0270,0100,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0100,0390,0210,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0150,0480,0320,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0200,0560,0430,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0250,0620,0540,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0300,0690,0660,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0350,0740,0780,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0400,0790,0900,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0450,0830,1020,1240,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0500,0870,1140,1290,0130,0000,0000,0000,0000,0000,0000,0000,000 0,0550,0910,1260,1330,0250,0000,0000,0000,0000,0000,0000,0000,000 0,0600,0940,1380,1370,0380,0000,0000,0000,0000,0000,0000,0000,000 0,0650,0970,1510,1400,0500,0000,0000,0000,0000,0000,0000,0000,000 0,0700,1000,1630,1440,0630,0000,0000,0000,0000,0000,0000,0000,000 0,0750,1030,1760,1460,0760,0000,0000,0000,0000,0000,0000,0000,000 0,0800,1060,1880,1490,0890,2470,0010,0000,0000,0000,0000,0000,000 0,0850,1080,2010,1520,1010,2470,0140,0000,0000,0000,0000,0000,000 0,0900,1110,2130,1540,1140,2480,0270,0000,0000,0000,0000,0000,000 0,0950,1130,2250,1560,1270,2480,0390,0000,0000,0000,0000,0000,000 0,1000,1150,2380,1580,1390,2480,0520,0000,0000,0000,0000,0000,000 0,1050,1180,2500,1600,1520,2490,0640,3700,0030,0000,0000,0000,000 0,1100,1200,2630,1620,1640,2490,0770,3700,0160,0000,0000,0000,000 0,1150,1220,2750,1640,1770,2490,0890,3700,0280,0000,0000,0000,000 0,1200,1230,2880,1660,1900,2490,1020,3700,0410,4940,0060,0000,000 0,1250,1250,3000,1670,2020,2500,1150,3700,0530,4940,0180,6160,010 0,1300,1270,3130,1690,2150,2500,1270,3700,0660,4940,0310,6140,024 0,1350,1290,3250,1700,2270,2500,1400,3700,0780,4940,0430,6120,038 0,1400,1300,3380,1720,2400,2500,1520,3700,0910,4940,0560,6100,052 0,1450,1320,3500,1730,2530,2500,1650,3700,1030,4940,0680,6080,066 0,1500,1340,3630,1750,2660,2510,1770,3700,1160,4940,0810,6070,080 0,1550,1350,3760,1760,2780,2510,1900,3700,1280,4940,0930,6050,093 0,1600,1360,3880,1770,2910,2510,2020,3700,1410,4940,1060,6040,107 0,1650,1380,4010,1780,3030,2510,2150,3700,1530,4940,1180,6020,121 0,1700,1390,4130,1790,3160,2510,2270,3700,1660,4940,1310,6010,134 0,1750,1410,4260,1810,3280,2520,2400,3700,1780,4940,1430,6000,148 0,1800,1420,4380,1820,3410,2520,2520,3700,1910,4940,1560,5990,161 0,1850,1430,4510,1830,3540,2520,2650,3700,2030,4940,1680,5980,175 0,1900,1440,4630,1840,3660,2520,2780,3700,2160,4940,1810,5970,188 0,1950,1460,4760,1850,3790,2520,2900,3700,2280,4940,1930,5960,201 0,2000,1470,4880,1860,3910,2520,3030,3700,2410,4940,2060,5950,215 0,2050,1480,5010,1870,4040,2520,3150,3700,2530,4940,2180,5940,228 0,2100,1490,5140,1880,4170,2530,3280,3700,2660,4940,2310,5930,241 0,2150,1500,5260,1880,4290,2530,3400,3700,2780,4940,2430,5920,254 0,2200,1510,5390,1890,4420,2530,3520,3700,2910,4940,2560,5910,267 0,2250,1520,5510,1900,4540,2530,3650,3700,3030,4940,2680,5910,280 0,2300,1530,5640,1910,4670,2530,3780,3700,3160,4940,2810,5900,293 0,2350,1540,5760,1920,4800,2530,3900,3700,3280,4940,2930,5890,307 0,2400,1550,5890,1920,4930,2530,4030,3700,3410,4940,3060,5880,320 0,2450,1560,6020,1930,5050,2530,4150,3700,3530,4940,3180,5880,333 Tabelas de Dimensionamento de Estruturas de Beto 33 TABELA 3_S500 (cont.) FLEXO COMPOSTA Seces rectangulares duplamente armadas C12-C50 S500 ;hx= ; ' A A As+ = ; ' A A = 10 . 0 =ha;2cdRdf bhM= ;cdRdbhfN= cdydsffbhA= ; 15 . 1 /yk ydf f = 5 . 1 /ck cdf f = 6 . 0 = 8 . 0 = 0 . 1 = 2 . 1 = 4 . 1 = 6 . 1 = 0,0000,0000,0000,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0050,0000,0000,0000,0002,6900,0147,5400,22113,6000,4380,0000,000 0,0100,0000,0000,0000,0002,0900,0274,3400,2267,2200,44110,3000,658 0,0150,0000,0000,0000,0001,8000,0413,0300,2395,1000,4457,1300,661 0,0200,0000,0000,0000,0001,6400,0542,4700,2523,9700,4515,5300,664 0,0250,0000,0000,0000,0001,5200,0682,1600,2653,1800,4634,5700,668 0,0300,0000,0000,0000,0001,4400,0811,9500,2782,7100,4763,8200,676 0,0350,0000,0000,0000,0001,3800,0951,7900,2912,4000,4893,2500,688 0,0400,0000,0000,0000,0001,3200,1091,6800,3042,1900,5022,8600,701 0,0450,0000,0000,0000,0001,2800,1221,5900,3182,0200,5152,5800,714 0,0500,0000,0000,0000,0001,2400,1351,5200,3311,9000,5282,3700,727 0,0550,0000,0000,0000,0001,2100,1491,4600,3441,7900,5412,2000,740 0,0600,0000,0000,0000,0001,1800,1621,4100,3571,7100,5542,0700,753 0,0650,0000,0000,0000,0001,1600,1751,3700,3701,6400,5671,9600,765 0,0700,0000,0000,0000,0001,1400,1881,3300,3831,5800,5801,8700,778 0,0750,0000,0000,9810,0111,1200,2011,3000,3971,5200,5931,7900,791 0,0800,0000,0000,9710,0251,1000,2151,2700,4101,4800,6061,7200,804 0,0850,0000,0000,9610,0391,0900,2281,2400,4231,4400,6191,6600,817 0,0900,0000,0000,9520,0541,0700,2411,2200,4361,4000,6321,6100,830 0,0950,0000,0000,9430,0691,0600,2541,2000,4491,3700,6451,5600,843 0,1000,0000,0000,9340,0831,0500,2681,1800,4621,3400,6581,5200,856 0,1050,0000,0000,9250,0981,0300,2811,1600,4751,3100,6711,4900,869 0,1100,0000,0000,9170,1131,0200,2941,1500,4881,2900,6841,4500,881 0,1150,0000,0000,9080,1281,0100,3071,1300,5011,2700,6971,4200,894 0,1200,7350,0160,9000,1431,0100,3201,1200,5141,2500,7101,3900,907 0,1250,7290,0320,8920,1580,9970,3331,1000,5271,2300,7231,3700,920 0,1300,7230,0480,8850,1730,9900,3471,0900,5401,2100,7361,3400,933 0,1350,7180,0640,8770,1870,9830,3611,0800,5531,1900,7491,3200,946 0,1400,7130,0790,8700,2030,9750,3741,0700,5661,1800,7621,3000,959 0,1450,7080,0950,8630,2180,9680,3881,0600,5791,1600,7751,2800,972 0,1500,7040,1100,8560,2320,9610,4021,0500,5921,1500,7881,2600,985 0,1550,7000,1250,8500,2480,9550,4161,0400,6051,1400,8011,2500,998 0,1600,6950,1410,8440,2620,9480,4301,0300,6191,1300,8141,2301,010 0,1650,6920,1550,8380,2770,9420,4441,0200,6321,1100,8271,2201,023 0,1700,6880,1700,8320,2920,9350,4581,0200,6441,1000,8401,2001,036 0,1750,6850,1850,8260,3080,9290,4721,0100,6571,0900,8531,1901,049 0,1800,6820,2000,8200,3220,9230,4861,0000,6701,0800,8661,1801,062 0,1850,6780,2140,8150,3370,9170,5000,9950,6841,0800,8791,1601,075 0,1900,6760,2290,8100,3520,9110,5140,9890,6971,0700,8911,1501,088 0,1950,6730,2430,8050,3670,9060,5290,9840,7111,0600,9041,1401,101 0,2000,6700,2580,8000,3820,9000,5420,9780,7241,0500,9171,1301,113 0,2050,6670,2720,7950,3970,8950,5570,9720,7381,0400,9301,1201,126 0,2100,6650,2860,7910,4110,8890,5710,9670,7511,0400,9431,1101,139 0,2150,6630,3000,7860,4260,8840,5850,9620,7651,0300,9561,1001,152 0,2200,6600,3140,7820,4400,8790,5990,9560,7781,0200,9691,1001,165 0,2250,6580,3280,7780,4550,8740,6140,9510,7921,0200,9821,0901,178 0,2300,6560,3420,7740,4690,8690,6280,9460,8051,0100,9951,0801,191 0,2350,6540,3560,7700,4840,8650,6420,9410,8191,0001,0081,0701,204 0,2400,6520,3700,7670,4980,8600,6560,9360,8330,9991,0211,0701,216 0,2450,6510,3840,7630,5130,8560,6700,9310,8470,9941,0341,0601,229 Tabelas de Dimensionamento de Estruturas de Beto 34 TABELA 3_S500 (cont.) FLEXO COMPOSTA Seces rectangulares duplamente armadas C12-C50 S500 ;hx= ; ' A A As+ = ; ' A A = 10 . 0 =ha;2cdRdf bhM= ;cdRdbhfN= cdydsffbhA= ; 15 . 1 /yk ydf f = 5 . 1 /ck cdf f =0 . 0 = 1 . 0 = 2 . 0 = 3 . 0 = 4 . 0 = 5 . 0 = 0,2500,1570,6140,1940,5170,2540,4280,3700,3660,4940,3310,5870,346 0,2550,1580,6270,1950,5300,2540,4400,3700,3780,4940,3430,5870,359 0,2600,1590,6390,1950,5420,2540,4530,3700,3910,4940,3560,5860,372 0,2650,1600,6520,1960,5550,2540,4650,3700,4030,4940,3680,5860,385 0,2700,1610,6640,1970,5680,2540,4780,3700,4160,4940,3810,5850,397 0,2750,1620,6770,1970,5810,2540,4910,3700,4280,4940,3930,5840,410 0,2800,1620,6890,1980,5930,2540,5030,3700,4410,4940,4060,5840,424 0,2850,1630,7020,1990,6060,2540,5160,3700,4530,4940,4180,5840,436 0,2900,1640,7150,1990,6180,2540,5280,3700,4660,4940,4310,5830,449 0,2950,1650,7270,2000,6310,2550,5410,3700,4780,4940,4430,5830,462 0,3000,1660,7400,2000,6430,2550,5530,3700,4910,4940,4560,5820,475 0,3050,1660,7520,2010,6560,2550,5650,3700,5030,4940,4680,5820,488 0,3100,1670,7650,2020,6680,2550,5780,3700,5160,4940,4810,5810,501 0,3150,1680,7770,2020,6810,2550,5900,3700,5280,4940,4930,5810,513 0,3200,1680,7900,2030,6930,2550,6030,3700,5410,4940,5060,5810,526 0,3250,1690,8020,2030,7060,2550,6160,3700,5530,4940,5180,5800,539 0,3300,1700,8150,2040,7190,2550,6280,3700,5660,4940,5310,5800,552 0,3350,1710,8270,2040,7310,2550,6410,3700,5780,4940,5430,5790,565 0,3400,1710,8400,2050,7440,2550,6530,3700,5910,4940,5560,5790,578 0,3450,1720,8530,2050,7560,2550,6660,3700,6030,4940,5680,5790,590 0,3500,1730,8650,2060,7690,2550,6780,3700,6160,4940,5810,5780,603 0,3550,1730,8780,2060,7820,2560,6910,3700,6280,4940,5930,5780,616 0,3600,1740,8900,2070,7940,2560,7030,3700,6410,4940,6060,5780,629 0,3650,1740,9030,2070,8070,2560,7160,3700,6530,4940,6180,5780,641 0,3700,1750,9150,2070,8190,2560,7280,3700,6660,4940,6310,5770,654 0,3750,1760,9280,2080,8320,2560,7410,3700,6780,4940,6430,5770,667 0,3800,1760,9410,2080,8440,2560,7530,3700,6910,4940,6560,5770,680 0,3850,1770,9530,2090,8570,2560,7660,3700,7030,4940,6680,5760,692 0,3900,1770,9660,2090,8690,2560,7790,3700,7160,4940,6810,5760,705 0,3950,1780,9780,2100,8820,2560,7910,3700,7280,4940,6930,5760,718 0,4000,1790,9910,2100,8950,2560,8030,3700,7410,4940,7060,5760,730 0,4100,1801,0160,2110,9200,2560,8280,3700,7660,4940,7310,5750,756 0,4200,1811,0410,2120,9450,2560,8540,3700,7910,4940,7560,5750,781 0,4300,1821,0660,2120,9700,2570,8790,3700,8160,4940,7810,5740,807 0,4400,1831,0910,2130,9950,2570,9040,3700,8410,4940,8060,5740,832 0,4500,1841,1160,2141,0200,2570,9290,3700,8660,4940,8310,5740,857 0,4600,1851,1410,2141,0460,2570,9540,3700,8910,4940,8560,5730,883 0,4700,1861,1670,2151,0700,2570,9790,3700,9160,4940,8810,5730,908 0,4800,1861,1920,2161,0960,2571,0030,3700,9410,4940,9060,5720,933 0,4900,1871,2170,2161,1200,2571,0290,3700,9660,4940,9310,5720,959 0,5000,1881,2420,2171,1460,2571,0530,3700,9910,4940,9560,5720,984 0,5100,1891,2670,2181,1710,2571,0790,3701,0160,4940,9810,5711,009 0,5200,1901,2920,2181,1960,2571,1030,3701,0410,4941,0060,5711,034 0,5300,1911,3170,2191,2210,2581,1290,3701,0660,4941,0310,5711,059 0,5400,1911,3420,2191,2460,2581,1530,3701,0910,4941,0560,5711,085 0,5500,1921,3670,2201,2710,2581,1790,3701,1160,4941,0810,5701,110 0,5600,1931,3920,2201,2960,2581,2040,3701,1410,4941,1060,5701,135 0,5700,1941,4170,2211,3210,2581,2290,3701,1660,4941,1310,5701,161 0,5800,1941,4430,2211,3460,2581,2540,3701,1910,4941,1560,5701,186 0,5900,1951,4670,2221,3710,2581,2790,3701,2160,4941,1810,5691,211 Tabelas de Dimensionamento de Estruturas de Beto 35 TABELA 3_S500 (cont.) FLEXO COMPOSTA Seces rectangulares duplamente armadas C12-C50 S500 ;hx= ; ' A A As+ = ; ' A A = 10 . 0 =ha;2cdRdf bhM= ;cdRdbhfN= cdydsffbhA= ; 15 . 1 /yk ydf f = 5 . 1 /ck cdf f =6 . 0 = 8 . 0 = 0 . 1 = 2 . 1 = 4 . 1 = 6 . 1 = 0,2500,6490,3980,7600,5270,8510,6850,9270,8600,9891,0471,0501,242 0,2550,6470,4120,7560,5410,8470,6980,9220,8740,9841,0601,0501,255 0,2600,6450,4250,7530,5560,8430,7130,9170,8880,9801,0741,0401,268 0,2650,6440,4390,7500,5700,8390,7270,9130,9020,9751,0871,0301,281 0,2700,6420,4530,7470,5850,8350,7410,9090,9150,9711,1001,0301,294 0,2750,6410,4660,7440,5990,8310,7550,9040,9290,9661,1141,0201,306 0,2800,6390,4800,7410,6120,8270,7690,9000,9430,9621,1271,0201,319 0,2850,6380,4930,7380,6270,8240,7840,8960,9560,9571,1401,0101,332 0,2900,6370,5060,7350,6410,8200,7970,8920,9700,9531,1541,0101,345 0,2950,6350,5200,7330,6550,8170,8120,8880,9840,9491,1671,0001,358 0,3000,6340,5340,7300,6690,8130,8250,8840,9980,9451,1810,9971,371 0,3050,6330,5470,7270,6830,8100,8400,8801,0110,9411,1940,9931,384 0,3100,6320,5600,7250,6970,8060,8540,8761,0260,9371,2080,9891,397 0,3150,6310,5740,7230,7110,8030,8680,8731,0390,9331,2210,9851,410 0,3200,6290,5870,7200,7250,8000,8820,8691,0530,9291,2340,9811,423 0,3250,6280,6000,7180,7390,7970,8960,8661,0670,9251,2480,9771,437 0,3300,6270,6140,7160,7520,7940,9100,8621,0800,9211,2620,9731,450 0,3350,6260,6270,7140,7660,7910,9240,8591,0940,9181,2750,9691,463 0,3400,6250,6400,7120,7800,7880,9370,8551,1080,9141,2880,9651,476 0,3450,6240,6530,7100,7940,7860,9510,8521,1220,9101,3020,9621,489 0,3500,6230,6670,7080,8070,7830,9650,8491,1350,9071,3150,9581,503 0,3550,6230,6800,7060,8210,7800,9790,8461,1490,9041,3290,9541,516 0,3600,6220,6930,7040,8350,7780,9930,8431,1630,9001,3420,9511,529 0,3650,6210,7060,7020,8490,7751,0070,8401,1770,8971,3560,9471,543 0,3700,6200,7190,7000,8630,7731,0200,8371,1900,8931,3700,9441,556 0,3750,6190,7320,6990,8760,7701,0340,8341,2040,8901,3830,9401,569 0,3800,6180,7460,6970,8900,7681,0480,8311,2180,8871,3970,9371,582 0,3850,6180,7590,6950,9030,7651,0610,8281,2320,8841,4100,9341,596 0,3900,6170,7720,6930,9170,7631,0750,8251,2450,8811,4240,9301,609 0,3950,6160,7850,6920,9300,7611,0890,8231,2590,8781,4370,9271,622 0,4000,6150,7980,6900,9440,7591,1030,8201,2720,8751,4510,9241,636 0,4100,6140,8240,6870,9710,7541,1300,8151,3000,8691,4780,9181,662 0,4200,6130,8500,6840,9980,7501,1580,8101,3270,8631,5050,9121,689 0,4300,6110,8760,6821,0250,7461,1840,8051,3550,8581,5320,9061,716 0,4400,6100,9020,6791,0510,7431,2110,8001,3810,8531,5590,9001,743 0,4500,6090,9280,6771,0780,7391,2390,7961,4090,8481,5860,8941,769 0,4600,6080,9540,6741,1040,7351,2660,7911,4360,8431,6130,8891,796 0,4700,6070,9800,6721,1310,7321,2930,7871,4630,8381,6400,8841,823 0,4800,6061,0060,6691,1580,7291,3190,7831,4900,8331,6670,8791,850 0,4900,6051,0310,6671,1850,7261,3470,7791,5170,8291,6940,8741,876 0,5000,6041,0570,6651,2110,7231,3730,7751,5440,8241,7210,8691,903 0,5100,6031,0830,6631,2370,7201,4000,7721,5710,8201,7480,8641,930 0,5200,6021,1090,6611,2640,7171,4270,7681,5980,8161,7740,8601,956 0,5300,6011,1340,6591,2900,7141,4540,7651,6250,8121,8010,8551,983 0,5400,6001,1600,6581,3160,7111,4800,7611,6510,8081,8280,8512,010 0,5500,6001,1850,6561,3430,7091,5070,7581,6780,8041,8540,8472,036 0,5600,5991,2110,6541,3690,7061,5330,7551,7050,8001,8820,8422,063 0,5700,5981,2370,6531,3950,7041,5600,7521,7310,7971,9080,8382,090 0,5800,5971,2620,6511,4210,7021,5860,7491,7580,7931,9350,8352,116 0,5900,5971,2880,6491,4470,6991,6130,7461,7850,7901,9610,8312,143 Tabelas de Dimensionamento de Estruturas de Beto 36 TABELA 3_S400 FLEXO COMPOSTA Seces rectangulares duplamente armadas C12-C50 S400

;hx= ; ' A A As+ = ; ' A A = 10 . 0 =ha;2cdRdf bhM= ;cdRdbhfN= cdydsffbhA= ; 15 . 1 /yk ydf f = 5 . 1 /ck cdf f =0 . 0 = 1 . 0 = 2 . 0 = 3 . 0 = 4 . 0 = 5 . 0 = 0,0000,0000,0000,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0050,0290,0100,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0100,0420,0210,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0150,0510,0320,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0200,0590,0430,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0250,0660,0540,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0300,0710,0660,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0350,0770,0780,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0400,0810,0900,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0450,0860,1020,1240,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0500,0890,1140,1280,0130,0000,0000,0000,0000,0000,0000,0000,000 0,0550,0930,1260,1320,0250,0000,0000,0000,0000,0000,0000,0000,000 0,0600,0960,1390,1350,0380,0000,0000,0000,0000,0000,0000,0000,000 0,0650,0990,1510,1380,0510,0000,0000,0000,0000,0000,0000,0000,000 0,0700,1010,1630,1400,0630,0000,0000,0000,0000,0000,0000,0000,000 0,0750,1040,1760,1420,0760,0000,0000,0000,0000,0000,0000,0000,000 0,0800,1060,1880,1440,0880,2470,0020,0000,0000,0000,0000,0000,000 0,0850,1080,2010,1460,1010,2470,0140,0000,0000,0000,0000,0000,000 0,0900,1090,2130,1480,1140,2470,0270,0000,0000,0000,0000,0000,000 0,0950,1110,2260,1500,1260,2470,0390,0000,0000,0000,0000,0000,000 0,1000,1130,2380,1510,1390,2470,0520,0000,0000,0000,0000,0000,000 0,1050,1150,2500,1520,1510,2470,0640,3700,0030,0000,0000,0000,000 0,1100,1160,2630,1540,1640,2470,0770,3700,0160,0000,0000,0000,000 0,1150,1180,2750,1550,1760,2470,0890,3700,0280,0000,0000,0000,000 0,1200,1190,2880,1560,1890,2470,1020,3700,0410,4940,0060,0000,000 0,1250,1210,3000,1570,2020,2470,1140,3700,0530,4940,0180,6170,009 0,1300,1220,3130,1580,2140,2470,1270,3700,0660,4940,0310,6170,022 0,1350,1240,3250,1590,2270,2470,1390,3700,0780,4940,0430,6160,035 0,1400,1250,3380,1600,2390,2470,1520,3700,0910,4940,0560,6160,048 0,1450,1260,3500,1610,2520,2470,1640,3700,1030,4940,0680,6150,061 0,1500,1270,3630,1620,2640,2470,1770,3700,1160,4940,0810,6150,073 0,1550,1280,3750,1620,2770,2470,1890,3700,1280,4940,0930,6140,086 0,1600,1300,3880,1630,2890,2470,2020,3700,1410,4940,1060,6140,099 0,1650,1310,4010,1640,3020,2470,2140,3700,1530,4940,1180,6130,112 0,1700,1320,4130,1640,3140,2470,2270,3700,1660,4940,1310,6130,125 0,1750,1330,4260,1650,3270,2470,2390,3700,1780,4940,1430,6130,137 0,1800,1340,4380,1660,3400,2470,2520,3700,1910,4940,1560,6130,150 0,1850,1350,4510,1660,3520,2470,2640,3700,2030,4940,1680,6120,163 0,1900,1350,4630,1670,3650,2470,2770,3700,2160,4940,1810,6120,176 0,1950,1360,4760,1680,3770,2470,2890,3700,2280,4940,1930,6120,189 0,2000,1370,4880,1680,3900,2470,3020,3700,2410,4940,2060,6110,201 0,2050,1380,5010,1690,4020,2470,3140,3700,2530,4940,2180,6110,214 0,2100,1390,5130,1690,4150,2470,3270,3700,2660,4940,2310,6110,226 0,2150,1400,5260,1700,4270,2470,3390,3700,2780,4940,2430,6110,239 0,2200,1400,5380,1700,4400,2470,3520,3700,2910,4940,2560,6110,252 0,2250,1410,5510,1700,4530,2470,3640,3700,3030,4940,2680,6100,265 0,2300,1420,5630,1710,4650,2470,3770,3700,3160,4940,2810,6100,277 0,2350,1420,5760,1710,4780,2470,3890,3700,3280,4940,2930,6100,290 0,2400,1430,5880,1720,4900,2470,4020,3700,3410,4940,3060,6100,302 0,2450,1440,6010,1720,5020,2470,4140,3700,3530,4940,3180,6100,315 Tabelas de Dimensionamento de Estruturas de Beto 37 TABELA 3_S400 (cont.) FLEXO COMPOSTA Seces rectangulares duplamente armadas C12-C50 S400 ;hx= ; ' A A As+ = ; ' A A = 10 . 0 =ha;2cdRdf bhM= ;cdRdbhfN= cdydsffbhA= ; 15 . 1 /yk ydf f = 5 . 1 /ck cdf f = 6 . 0 = 8 . 0 = 0 . 1 = 2 . 1 = 4 . 1 = 6 . 1 = 0,0000,0000,0000,0000,0000,0000,0000,0000,0000,0000,0000,0000,000 0,0050,0000,0000,0000,0002,5900,0143,1500,2143,4400,4133,5700,613 0,0100,0000,0000,0000,0002,0000,0282,5200,2272,8600,4263,0800,626 0,0150,0000,0000,0000,0001,7400,0412,1700,2402,4900,4392,7400,639 0,0200,0000,0000,0000,0001,5900,0551,9500,2532,2500,4522,4900,652 0,0250,0000,0000,0000,0001,4800,0681,8000,2662,0700,4652,3000,664 0,0300,0000,0000,0000,0001,4000,0821,6800,2791,9300,4782,1500,677 0,0350,0000,0000,0000,0001,3400,0951,5900,2931,8200,4912,0200,690 0,0400,0000,0000,0000,0001,2900,1091,5200,3061,7300,5041,9200,703 0,0450,0000,0000,0000,0001,2500,1231,4600,3191,6500,5171,8300,716 0,0500,0000,0000,0000,0001,2200,1361,4100,3321,5900,5301,7600,729 0,0550,0000,0000,0000,0001,1900,1491,3600,3451,5400,5431,7000,742 0,0600,0000,0000,0000,0001,1600,1621,3300,3581,4900,5561,6400,755 0,0650,0000,0000,0000,0001,1400,1761,2900,3711,4500,5691,5900,768 0,0700,0000,0000,0000,0001,1200,1891,2700,3851,4100,5821,5500,780 0,0750,0000,0000,9800,0111,1000,2021,2400,3981,3800,5951,5100,793 0,0800,0000,0000,9700,0251,0900,2151,2200,4111,3500,6081,4700,806 0,0850,0000,0000,9610,0401,0700,2291,2000,4241,3200,6211,4400,819 0,0900,0000,0000,9510,0541,0600,2421,1800,4371,2900,6341,4100,832 0,0950,0000,0000,9420,0691,0500,2551,1600,4501,2700,6471,3800,845 0,1000,0000,0000,9330,0831,0400,2681,1400,4631,2500,6601,3600,858 0,1050,0000,0000,9240,0981,0300,2811,1300,4761,2300,6731,3400,871 0,1100,0000,0000,9160,1131,0200,2951,1100,4891,2100,6861,3100,884 0,1150,0000,0000,9080,1281,0100,3071,1000,5021,2000,6991,2900,896 0,1200,7360,0150,9000,1430,9980,3211,0900,5151,1800,7121,2800,909 0,1250,7310,0310,8930,1580,9910,3341,0800,5281,1700,7251,2600,922 0,1300,7260,0460,8850,1730,9840,3481,0700,5411,1600,7381,2400,935 0,1350,7220,0610,8780,1870,9770,3611,0600,5551,1400,7511,2300,948 0,1400,7180,0760,8720,2020,9700,3761,0500,5671,1300,7631,2100,961 0,1450,7140,0910,8650,2170,9630,3891,0400,5811,1200,7771,2000,974 0,1500,7110,1060,8590,2310,9570,4031,0300,5941,1100,7891,1900,987 0,1550,7080,1200,8530,2460,9500,4171,0200,6071,1000,8021,1801,000 0,1600,7050,1350,8470,2610,9440,4311,0200,6191,0900,8151,1601,012 0,1650,7010,1490,8420,2760,9380,4451,0100,6321,0800,8281,1501,025 0,1700,6990,1630,8360,2910,9320,4591,0000,6451,0700,8411,1401,038 0,1750,6960,1780,8310,3050,9270,4730,9970,6581,0600,8541,1301,051 0,1800,6940,1920,8260,3200,9210,4870,9910,6721,0600,8671,1201,064 0,1850,6910,2060,8210,3350,9160,5010,9850,6851,0500,8801,1101,077 0,1900,6890,2200,8170,3490,9100,5150,9800,6981,0400,8931,1101,090 0,1950,6870,2340,8120,3640,9050,5290,9750,7121,0400,9061,1001,102 0,2000,6850,2470,8080,3780,9000,5430,9700,7251,0300,9191,0901,115 0,2050,6830,2610,8040,3920,8950,5570,9650,7391,0200,9311,0801,128 0,2100,6810,2750,8000,4060,8900,5710,9600,7521,0200,9441,0801,141 0,2150,6790,2890,7960,4210,8860,5850,9550,7661,0100,9571,0701,154 0,2200,6780,3020,7930,4350,8810,5990,9500,7791,0100,9701,0601,167 0,2250,6760,3160,7890,4490,8770,6130,9450,7931,0000,9831,0601,179 0,2300,6750,3290,7860,4640,8730,6270,9410,8060,9950,9961,0501,192 0,2350,6730,3430,7820,4780,8680,6410,9360,8200,9911,0091,0401,205 0,2400,6720,3570,7790,4920,8640,6550,9320,8340,9871,0221,0401,218 0,2450,6700,3700,7760,5060,8610,6680,9280,8470,9821,0361,0301,231 Tabelas de Dimensionamento de Estruturas de Beto 38 TABELA 3_S400 (cont.) FLEXO COMPOSTA Seces rectangulares duplamente armadas C12-C50 S400 ;hx= ; ' A A As+ = ; ' A A = 10 . 0 =ha;2cdRdf bhM= ;cdRdbhfN= cdydsffbhA= ; 15 . 1 /yk ydf f = 5 . 1 /ck cdf f =0 . 0 = 1 . 0 = 2 . 0 = 3 . 0 = 4 . 0 = 5 . 0 = 0,2500,1440,6130,1730,5150,2470,4270,3700,3660,4940,3310,6090,328 0,2550,1450,6260,1730,5280,2470,4390,3700,3780,4940,3430,6090,340 0,2600,1460,6380,1730,5400,2470,4520,3700,3910,4940,3560,6090,353 0,2650,1460,6510,1740,5530,2470,4640,3700,4030,4940,3680,6090,366 0,2700,1470,6630,1740,5650,2470,4770,3700,4160,4940,3810,6090,378 0,2750,1470,6760,1740,5780,2470,4890,3700,4280,4940,3930,6090,391 0,2800,1480,6890,1750,5900,2470,5020,3700,4410,4940,4060,6090,403 0,2850,1480,7010,1750,6030,2470,5140,3700,4530,4940,4180,6080,416 0,2900,1490,7140,1750,6150,2470,5270,3700,4660,4940,4310,6080,429 0,2950,1500,7260,1760,6280,2470,5390,3700,4780,4940,4430,6080,441 0,3000,1500,7390,1760,6410,2470,5520,3700,4910,4940,4560,6080,454 0,3050,1510,7510,1760,6530,2470,5640,3700,5030,4940,4680,6080,466 0,3100,1510,7640,1760,6650,2470,5770,3700,5160,4940,4810,6080,479 0,3150,1510,7760,1770,6780,2470,5890,3700,5280,4940,4930,6080,491 0,3200,1520,7890,1770,6910,2470,6020,3700,5410,4940,5060,6080,504 0,3250,1520,8010,1770,7030,2470,6140,3700,5530,4940,5180,6080,517 0,3300,1530,8140,1770,7160,2470,6270,3700,5660,4940,5310,6080,529 0,3350,1530,8260,1780,7280,2470,6390,3700,5780,4940,5430,6070,542 0,3400,1540,8390,1780,7410,2470,6520,3700,5910,4940,5560,6070,555 0,3450,1540,8510,1780,7530,2470,6640,3700,6030,4940,5680,6070,567 0,3500,1550,8640,1780,7660,2470,6770,3700,6160,4940,5810,6070,579 0,3550,1550,8760,1790,7780,2470,6890,3700,6280,4940,5930,6070,592 0,3600,1550,8890,1790,7910,2470,7020,3700,6410,4940,6060,6070,605 0,3650,1560,9010,1790,8030,2470,7140,3700,6530,4940,6180,6070,617 0,3700,1560,9140,1790,8160,2470,7270,3700,6660,4940,6310,6070,630 0,3750,1560,9270,1790,8280,2470,7390,3700,6780,4940,6430,6070,642 0,3800,1570,9390,1800,8410,2470,7520,3700,6910,4940,6560,6070,655 0,3850,1570,9520,1800,8530,2470,7640,3700,7030,4940,6680,6070,667 0,3900,1580,9640,1800,8660,2470,7770,3700,7160,4940,6810,6070,680 0,3950,1580,9770,1800,8790,2470,7890,3700,7280,4940,6930,6060,692 0,4000,1580,9890,1800,8910,2470,8020,3700,7410,4940,7060,6060,705 0,4100,1591,0140,1810,9160,2470,8270,3700,7660,4940,7310,6060,730 0,4200,1601,0390,1810,9410,2470,8520,3700,7910,4940,7560,6060,755 0,4300,1601,0640,1810,9660,2470,8770,3700,8160,4940,7810,6060,780 0,4400,1611,0890,1820,9910,2470,9020,3700,8410,4940,8060,6060,805 0,4500,1611,1140,1821,0160,2470,9270,3700,8660,4940,8310,6060,831 0,4600,1621,1390,1821,0410,2470,9520,3700,8910,4940,8560,6060,855 0,4700,1621,1640,1831,0660,2470,9770,3700,9160,4940,8810,6060,881 0,4800,1631,1890,1831,0910,2471,0010,3700,9410,4940,9060,6060,906 0,4900,1641,2150,1831,1160,2471,0260,3700,9660,4940,9310,6050,931 0,5000,1641,2390,1831,1410,2471,0510,3700,9910,4940,9560,6050,956 0,5100,1651,2640,1841,1660,2471,0760,3701,0160,4940,9810,6050,981 0,5200,1651,2900,1841,1910,2471,1010,3701,0410,4941,0060,6051,006 0,5300,1651,3140,1841,2160,2471,1260,3701,0660,4941,0310,6051,031 0,5400,1661,3400,1841,2410,2471,1510,3701,0910,4941,0560,6051,056 0,5500,1661,3650,1851,2660,2471,1760,3701,1160,4941,0810,6051,081 0,5600,1671,3900,1851,2910,2471,2010,3701,1410,4941,1060,6051,106 0,5700,1671,4150,1851,3170,2471,2260,3701,1660,4941,1310,6051,131 0,5800,1681,4400,1851,3420,2471,2510,3701,1910,4941,1560,6051,156 0,5900,1681,4650,1851,3670,2471,2760,3701,2160,4941,1810,6051,181 Tabelas de Dimensionamento de Estruturas de Beto 39 TABELA 3_S400 (cont.) FLEXO COMPOSTA Seces rectangulares duplamente armadas C12-C50 S400 ;hx= ; ' A A As+ = ; ' A A = 10 . 0 =ha;2cdRdf bhM= ;cdRdbhfN= cdydsffbhA= ; 15 . 1 /yk ydf f = 5 . 1 /ck cdf f =6 . 0 = 8 . 0 = 0 . 1 = 2 . 1 = 4 . 1 = 6 . 1 = 0,2500,6690,3830,7730,5200,8570,6820,9230,8610,9781,0491,0301,244 0,2550,6680,3970,7700,5340,8530,6960,9190,8750,9741,0621,0201,256 0,2600,6670,4100,7670,5480,8490,7100,9150,8880,9691,0761,0201,269 0,2650,6650,4230,7650,5620,8460,7240,9110,9020,9651,0891,0101,282 0,2700,6640,4370,7620,5760,8420,7380,9080,9150,9611,1021,0101,295 0,2750,6630,4500,7600,5900,8390,7520,9040,9290,9571,1151,0001,308 0,2800,6620,4630,7570,6040,8360,7660,9000,9430,9541,1280,9991,321 0,2850,6610,4760,7550,6170,8320,7800,8960,9560,9501,1420,9951,334 0,2900,6600,4900,7520,6310,8290,7940,8930,9700,9461,1550,9911,347 0,2950,6590,5030,7500,6450,8260,8070,8890,9830,9421,1690,9871,360 0,3000,6580,5160,7480,6580,8230,8210,8860,9970,9391,1820,9841,373 0,3050,6570,5290,7460,6730,8200,8350,8831,0100,9351,1950,9801,386 0,3100,6560,5420,7440,6860,8180,8490,8791,0240,9321,2090,9761,399 0,3150,6560,5550,7420,7000,8150,8620,8761,0380,9281,2220,9731,412 0,3200,6550,5680,7400,7130,8120,8760,8731,0520,9251,2360,9691,425 0,3250,6540,5810,7380,7270,8090,8900,8701,0650,9221,2490,9661,439 0,3300,6530,5950,7360,7400,8070,9030,8671,0790,9181,2620,9631,452 0,3350,6520,6080,7340,7540,8040,9170,8641,0920,9151,2760,9591,465 0,3400,6520,6210,7320,7680,8020,9310,8611,1060,9121,2890,9561,478 0,3450,6510,6340,7310,7810,8000,9440,8581,1190,9091,3020,9531,491 0,3500,6500,6470,7290,7950,7970,9580,8561,1330,9061,3160,9501,504 0,3550,6500,6590,7270,8080,7950,9720,8531,1470,9031,3290,9461,518 0,3600,6490,6730,7260,8220,7930,9850,8501,1600,9001,3430,9431,531 0,3650,6480,6860,7240,8350,7900,9990,8481,1730,8971,3560,9401,544 0,3700,6480,6980,7230,8490,7881,0120,8451,1870,8941,3690,9371,557 0,3750,6470,7110,7210,8620,7861,0260,8431,2000,8921,3830,9341,571 0,3800,6470,7240,7200,8750,7841,0390,8401,2140,8891,3960,9321,584 0,3850,6460,7370,7180,8890,7821,0530,8381,2270,8861,4100,9291,597 0,3900,6460,7500,7170,9020,7801,0660,8351,2410,8841,4230,9261,610 0,3950,6450,7630,7160,9150,7781,0800,8331,2540,8811,4360,9231,623 0,4000,6440,7760,7150,9280,7761,0930,8311,2680,8781,4500,9201,637 0,4100,6430,8020,7120,9550,7731,1200,8261,2950,8731,4760,9151,663 0,4200,6420,8270,7100,9810,7691,1470,8221,3220,8691,5030,9101,690 0,4300,6420,8530,7071,0080,7661,1740,8181,3480,8641,5300,9051,716 0,4400,6410,8790,7051,0340,7631,2000,8141,3750,8591,5560,9001,743 0,4500,6400,9040,7031,0610,7591,2270,8101,4020,8551,5830,8951,769 0,4600,6390,9300,7011,0870,7561,2540,8061,4290,8511,6100,8911,796 0,4700,6380,9560,6991,1130,7541,2810,8031,4550,8471,6360,8861,822 0,4800,6370,9810,6971,1390,7511,3070,7991,4820,8431,6630,8821,848 0,4900,6371,0070,6951,1650,7481,3340,7961,5090,8391,6900,8781,875 0,5000,6361,0320,6931,1920,7461,3600,7931,5350,8351,7160,8741,901 0,5100,6351,0580,6921,2180,7431,3860,7891,5620,8321,7420,8701,928 0,5200,6351,0830,6901,2440,7411,4130,7861,5880,8281,7690,8661,954 0,5300,6341,1080,6891,2700,7381,4390,7831,6150,8251,7950,8621,980 0,5400,6341,1340,6871,2960,7361,4660,7811,6410,8211,8220,8582,007 0,5500,6331,1590,6861,3220,7341,4920,7781,6670,8181,8480,8552,033 0,5600,6321,1850,6841,3480,7321,5180,7751,6940,8151,8750,8512,060 0,5700,6321,2100,6831,3740,7301,5440,7731,7200,8121,9010,8482,086 0,5800,6311,2360,6821,4000,7281,5700,7701,7470,8091,9270,8442,112 0,5900,6311,2610,6801,4250,7261,5970,7681,7730,8061,9540,8412,138 Tabelas de Dimensionamento de Estruturas de Beto 40 TABELA4_S500 FLEXO COMPOSTA Seces rectangulares simplesmente armadasC12-C50 S500 SdNpositivo se de traco s Sd Sd Sdsy N M M = cdSdsSdsf bdM2= ;( )Sd cd ssdsN bdf A + =, 11

Sdss , 1dx= dz= 02%c 01%s MPasd 0,010,01010,0300,993-0,7725,00435 0,020,02030,0440,984-1,1525,00435 0,030,03050,0550,982-1,4625,00435 0,040,04100,0660,976-1,7625,00435 0,050,05150,0760,971-2,0625,00435 0,060,06210,0870,966-2,3725,00435 0,070,07280,0970,961-2,6825,00435 0,080,08360,1070,957-3,0125,00435 0,090,09460,1180,952-3,3525,00435 0,100,10570,1310,946-3,5023,30435 0,110,11700,1440,940-3,5020,70435 0,120,12840,1590,934-3,5018,60435 0,130,14000,1730,929-3,5016,70435 0,140,15180,1880,922-3,5015,20435 0,150,16370,2020,916-3,5013,80435 0,160,17590,2170,910-3,5012,60435 0,170,18810,2320,904-3,5011,60435 0,180,20070,2480,897-3,5010,60435 0,190,21340,2640,891-3,509,78435 0,200,22630,2800,884-3,509,02435 0,210,23940,2960,877-3,508,33435 0,220,25280,3120,870-3,507,71435 0,230,26650,3290,863-3,507,13435 0,240,28040,3460,856-3,506,61435 0,250,29450,3640,849-3,506,12435 0,260,30900,3820,841-3,505,67435 0,270,32380,4000,834-3,505,25435 0,280,33900,4190,826-3,504,86435 0,290,35450,4380,818-3,504,49435 0,300,37040,4580,810-3,504,15435 0,310,38680,4780,801-3,503,83435 0,320,40370,4990,793-3,503,52435 0,330,42110,5200,784-3,503,23435 0,340,43890,5420,775-3,502,96435 0,350,45750,5650,765-3,502,69435 0,360,47670,5890,755-3,502,44435 0,370,49660,6130,745-3,502,20435 0,380,51760,6390,734-3,501,97395 0,390,53950,6660,723-3,501,75350 0,400,56250,6950,711-3,501,54307 0,410,58690,7250,699-3,51,33266 0,420,61310,7570,685-3,51,12224 0,430,64110,7920,671-3,50,92184 0,440,67180,8300,655-3,50,72143 0,450,70610,8720,637-3,50,51103 Tabelas de Dimensionamento de Estruturas de Beto 41 TABELA 4_S400 FLEXO COMPOSTA Seces rectangulares simplesmente armadas C12-C50S400 SdNpositivo se de traco( ) a h N M y N M MSd Sd s Sd Sd Sds = = 2 /cdSdsSdsf bdM2= ; ( )Sd cd ssdsN bdf A + =, 11 Sdss , 1dx= dz= 02%c 01%s MPasd 0,010,01010,0300,993-0,7725,00348 0,020,02030,0440,984-1,1525,00348 0,030,03050,0550,982-1,4625,00348 0,040,04100,0660,976-1,7625,00348 0,050,05150,0760,971-2,0625,00348 0,060,06210,0870,966-2,3725,00348 0,070,07280,0970,961-2,6825,00348 0,080,08360,1070,957-3,0125,00348 0,090,09460,1180,952-3,3525,00348 0,100,10570,1310,946-3,5023,30348 0,110,11700,1440,940-3,5020,70348 0,120,12840,1590,934-3,5018,60348 0,130,14000,1730,929-3,5016,70348 0,140,15180,1880,922-3,5015,20348 0,150,16370,2020,916-3,5013,80348 0,160,17590,2170,910-3,5012,60348 0,170,18810,2320,904-3,5011,60348 0,180,20070,2480,897-3,5010,60348 0,190,21340,2640,891-3,509,78348 0,200,22630,2800,884-3,509,02348 0,210,23940,2960,877-3,508,33348 0,220,25280,3120,870-3,507,71348 0,230,26650,3290,863-3,507,13348 0,240,28040,3460,856-3,506,61348 0,250,29450,3640,849-3,506,12348 0,260,30900,3820,841-3,505,67348 0,270,32380,4000,834-3,505,25348 0,280,33900,4190,826-3,504,86348 0,290,35450,4380,818-3,504,49348 0,300,37040,4580,810-3,504,15348 0,310,38680,4780,801-3,503,83348 0,320,40370,4990,793-3,503,52348 0,330,42110,5200,784-3,503,23348 0,340,43890,5420,775-3,502,96348 0,350,45750,5650,765-3,502,69348 0,360,47670,5890,755-3,502,44348 0,370,49660,6130,745-3,502,20348 0,380,51760,6390,734-3,501,97348 0,390,53950,6660,723-3,501,75348 0,400,56250,6950,711-3,501,54307 0,410,58690,7250,699-3,51,33266 0,420,61310,7570,685-3,51,12224 0,430,64110,7920,671-3,50,92184 0,440,67180,8300,655-3,50,72143 0,450,70610,8720,637-3,50,51103 Tabelas de Dimensionamento de Estruturas de Beto 42 TABELA5_S500 FLEXO COMPOSTA Seces rectangulares duplamente armadasC12-C50S500 SdNpositivo se de traco cdSdsSdsf bdM2= ;dx= ( ) a h N M y N M MSd Sd s Sd Sd Sds = = 2 / 250 . 0 = 05 . 0 / = d a 10 . 0 / = d a 15 . 0 / = d a 20 . 0 / = d aSdss , 12s , 12s , 12s , 120,190,2120,0090,2120,0100,2130,0160,2130,034 0,200,2220,0200,2230,0220,2240,0340,2260,072 0,210,2330,0300,2340,0330,2360,0520,2380,111 0,220,2430,0410,2450,0450,2480,0710,2510,150 0,230,2540,0510,2560,0560,2600,0890,2630,189 0,240,2640,0620,2680,0680,2710,1070,2760,228 0,250,2750,0720,2790,0790,2830,1250,2880,267 0,260,2850,0830,2900,0910,2950,1440,3010,305 0,270,2960,0930,3010,1020,3070,1620,3130,344 0,280,3060,1040,3120,1130,3180,1800,3260,383 0,290,3170,1140,3230,1250,3300,1990,3380,422 0,300,3270,1250,3340,1360,3420,2170,3510,461 0,310,3380,1350,3450,1480,3540,2350,3630,500 0,320,3480,1460,3560,1590,3660,2530,3760,538 0,330,3590,1560,3680,1710,3770,2720,3880,577 0,340,3690,1670,3790,1820,3890,2900,4010,616 0,350,3800,1780,3900,1940,4010,3080,4130,655 0,360,3900,1880,4010,2060,4130,3260,4260,694 0,370,4010,1990,4120,2170,4240,3450,4380,732 0,380,4120,2090,4230,2290,4360,3630,4510,771 0,390,4220,2200,4340,2400,4480,3810,4630,810 0,400,4330,2300,4450,2520,4600,3990,4760,849 0,410,4430,2410,4560,2630,4710,4180,4880,888 0,420,4540,2510,4680,2750,4830,4360,5010,927 0,430,4640,2620,4790,2860,4950,4540,5130,965 0,440,4750,2720,4900,2980,5070,4730,5261,004 0,450,4850,2830,5010,3090,5180,4910,5381,043 0,460,4960,2930,5120,3210,5300,5090,5511,082 0,470,5060,3040,5230,3320,5420,5270,5631,121 0,480,5170,3140,5340,3440,5540,5460,5761,159 0,490,5270,3250,5450,3550,5660,5640,5881,198 0,500,5380,3350,5560,3670,5770,5820,6011,237 ( )Sd cd sydsN bdffA + =, 11ydcdsffbd A2 = Tabelas de Dimensionamento de Estruturas de Beto 43 TABELA5_S400 FLEXO COMPOSTA Seces rectangulares duplamente armadasC12-C50S400 SdNpositivo se de traco cdSdsSdsf bdM2= ;dx= ( ) a h N M y N M MSd Sd s Sd Sd Sds = = 2 / 250 . 0 = 05 . 0 / = d a 10 . 0 / = d a 15 . 0 / = d a 20 . 0 / = d aSdss , 12s , 12s , 12s , 120,1900,2120,0090,2120,0100,2130,0130,2130,027 0,2000,2220,0200,2230,0210,2240,0270,2260,058 0,2100,2330,0300,2340,0320,2360,0420,2380,089 0,2200,2430,0410,2450,0430,2480,0570,2510,120 0,2300,2540,0510,2560,0540,2600,0710,2630,151 0,2400,2640,0620,2680,0650,2710,0860,2760,182 0,2500,2750,0720,2790,0760,2830,1000,2880,213 0,2600,2850,0830,2900,0870,2950,1150,3010,244 0,2700,2960,0930,3010,0990,3070,1300,3130,275 0,2800,3060,1040,3120,1100,3180,1440,3260,306 0,2900,3170,1140,3230,1210,3300,1590,3380,338 0,3000,3270,1250,3340,1320,3420,1730,3510,369 0,3100,3380,1350,3450,1430,3540,1880,3630,400 0,3200,3480,1460,3560,1540,3660,2030,3760,431 0,3300,3590,1560,3680,1650,3770,2170,3880,462 0,3400,3690,1670,3790,1760,3890,2320,4010,493 0,3500,3800,1780,3900,1870,4010,2460,4130,524 0,3600,3900,1880,4010,1990,4130,2610,4260,555 0,3700,4010,1990,4120,2100,4240,2760,4380,586 0,3800,4120,2090,4230,2210,4360,2900,4510,617 0,3900,4220,2200,4340,2320,4480,3050,4630,648 0,4000,4330,2300,4450,2430,4600,3200,4760,679 0,4100,4430,2410,4560,2540,4710,3340,4880,710 0,4200,4540,2510,4680,2650,4830,3490,5010,741 0,4300,4640,2620,4790,2760,4950,3630,5130,772 0,4400,4750,2720,4900,2870,5070,3780,5260,803 0,4500,4850,2830,5010,2990,5180,3930,5380,834 0,4600,4960,2930,5120,3100,5300,4070,5510,865 0,4700,5060,3040,5230,3210,5420,4220,5630,897 0,4800,5170,3140,5340,3320,5540,4360,5760,928 0,4900,5270,3250,5450,3430,5660,4510,5880,959 0,5000,5380,3350,5560,3540,5770,4660,6010,990 ( )Sd cd sydsN bdffA + =, 11ydcdsffbd A2 =Tabelas de Dimensionamento de Estruturas de Beto 44 TABELA6_S500 FLEXO COMPOSTA Seces rectangulares duplamente armadasC12-C50S500 SdNpositivo se de traco cdSdsSdsf bdM2= ;dx= ( ) a h N M y N M MSd Sd s Sd Sd Sds = = 2 / 350 . 0 = 05 . 0 / = d a 10 . 0 / = d a 15 . 0 / = d a 20 . 0 / = d aSdss , 12s , 12s , 12s , 120,250,2920,0080,2920,0090,2930,0100,2930,014 0,260,3020,0190,3030,0200,3040,0230,3060,032 0,270,3130,0290,3140,0310,3160,0360,3180,051 0,280,3230,0400,3250,0420,3280,0490,3310,069 0,290,3340,0500,3370,0530,3400,0610,3430,087 0,300,3440,0610,3480,0640,3510,0740,3560,105 0,310,3550,0720,3590,0760,3630,0870,3680,123 0,320,3650,0820,3700,0870,3750,1000,3810,141 0,330,3760,0930,3810,0980,3870,1120,3930,159 0,340,3860,1030,3920,1090,3990,1250,4060,177 0,350,3970,1140,4030,1200,4100,1380,4180,196 0,360,4070,1240,4140,1310,4220,1510,4310,214 0,370,4180,1350,4250,1420,4340,1640,4430,232 0,380,4290,1450,4370,1530,4460,1760,4560,250 0,390,4390,1560,4480,1640,4570,1890,4680,268 0,400,4500,1660,4590,1750,4690,2020,4810,286 0,410,4600,1770,4700,1870,4810,2150,4930,304 0,420,4710,1870,4810,1980,4930,2280,5060,322 0,430,4810,1980,4920,2090,5040,2400,5180,340 0,440,4920,2080,5030,2200,5160,2530,5310,359 0,450,5020,2190,5140,2310,5280,2660,5430,377 0,460,5130,2290,5250,2420,5400,2790,5560,395 0,470,5230,2400,5370,2530,5510,2910,5680,413 0,480,5340,2500,5480,2640,5630,3040,5810,431 0,490,5440,2610,5590,2750,5750,3170,5930,449 0,500,5550,2710,5700,2870,5870,3300,6060,467 ( )Sd cd sydsN bdffA + =, 11ydcdsffbd A2 =Tabelas de Dimensionamento de Estruturas de Beto 45 TABELA6_S400 FLEXO COMPOSTA Seces rectangulares duplamente armadasC12-C50S400 SdNpositivo se de traco cdSdsSdsf bdM2= ;dx= ( ) a h N M y N M MSd Sd s Sd Sd Sds = = 2 / 350 . 0 = 05 . 0 / = d a 10 . 0 / = d a 15 . 0 / = d a 20 . 0 / = d aSdss , 12s , 12s , 12s , 120,250,2920,0080,2920,0090,2930,0090,2930,011 0,260,3020,0190,3030,0200,3040,0210,3060,026 0,270,3130,0290,3140,0310,3160,0330,3180,040 0,280,3230,0400,3250,0420,3280,0450,3310,055 0,290,3340,0500,3370,0530,3400,0560,3430,069 0,300,3440,0610,3480,0640,3510,0680,3560,084 0,310,3550,0720,3590,0760,3630,0800,3680,098 0,320,3650,0820,3700,0870,3750,0920,3810,113 0,330,3760,0930,3810,0980,3870,1030,3930,127 0,340,3860,1030,3920,1090,3990,1150,4060,142 0,350,3970,1140,4030,1200,4100,1270,4180,156 0,360,4070,1240,4140,1310,4220,1390,4310,171 0,370,4180,1350,4250,1420,4340,1500,4430,185 0,380,4290,1450,4370,1530,4460,1620,4560,200 0,390,4390,1560,4480,1640,4570,1740,4680,214 0,400,4500,1660,4590,1750,4690,1860,4810,229 0,410,4600,1770,4700,1870,4810,1980,4930,243 0,420,4710,1870,4810,1980,4930,2090,5060,258 0,430,4810,1980,4920,2090,5040,2210,5180,272 0,440,4920,2080,5030,2200,5160,2330,5310,287 0,450,5020,2190,5140,2310,5280,2450,5430,301 0,460,5130,2290,5250,2420,5400,2560,5560,316 0,470,5230,2400,5370,2530,5510,2680,5680,330 0,480,5340,2500,5480,2640,5630,2800,5810,345 0,490,5440,2610,5590,2750,5750,2920,5930,359 0,500,5550,2710,5700,2870,5870,3030,6060,374 ( )Sd cd sydsN bdffA + =, 11ydcdsffbd A2 =Tabelas de Dimensionamento de Estruturas de Beto 46 TABELA7_S500 FLEXO COMPOSTA Seces rectangulares duplamente armadasC12-C50S500 SdNpositivo se de traco cdSdsSdsf bdM2= ;dx= ( ) a h N M y N M MSd Sd s Sd Sd Sds = = 2 / 450 . 0 = 05 . 0 / = d a 10 . 0 / = d a 15 . 0 / = d a 20 . 0 / = d aSdss , 12s , 12s , 12s , 120,300,3680,0040,3690,0040,3690,0050,3690,005 0,310,3790,0150,3800,0150,3810,0160,3820,019 0,320,3890,0250,3910,0270,3920,0280,3940,033 0,330,4000,0360,4020,0380,4040,0400,4070,047 0,340,4110,0460,4130,0490,4160,0520,4190,061 0,350,4210,0570,4240,0600,4280,0630,4320,075 0,360,4320,0670,4350,0710,4390,0750,4440,089 0,370,4420,0780,4460,0820,4510,0870,4570,103 0,380,4530,0880,4580,0930,4630,0990,4690,117 0,390,4630,0990,4690,1040,4750,1100,4820,131 0,400,4740,1090,4800,1150,4870,1220,4940,145 0,410,4840,1200,4910,1270,4980,1340,5070,159 0,420,4950,1300,5020,1380,5100,1460,5190,173 0,430,5050,1410,5130,1490,5220,1580,5320,187 0,440,5160,1510,5240,1600,5340,1690,5440,201 0,450,5260,1620,5350,1710,5450,1810,5570,215 0,460,5370,1730,5460,1820,5570,1930,5690,229 0,470,5470,1830,5580,1930,5690,2050,5820,243 0,480,5580,1940,5690,2040,5810,2160,5940,257 0,490,5680,2040,5800,2150,5920,2280,6070,271 0,500,5790,2150,5910,2270,6040,2400,6190,285 ( )Sd cd sydsN bdffA + =, 11ydcdsffbd A2 = Tabelas de Dimensionamento de Estruturas de Beto 47 TABELA7_S400 FLEXO COMPOSTA Seces rectangulares duplamente armadasC12-C50S400 SdNpositivo se de traco cdSdsSdsf bdM2= ;dx= ( ) a h N M y N M MSd Sd s Sd Sd Sds = = 2 / 450 . 0 = 05 . 0 / = d a 10 . 0 / = d a 15 . 0 / = d a 20 . 0 / = d aSdss , 12s , 12s , 12s , 120,300,3680,0040,3690,0040,3690,0050,3690,005 0,310,3790,0150,3800,0150,3810,0160,3820,017 0,320,3890,0250,3910,0270,3920,0280,3940,030 0,330,4000,0360,4020,0380,4040,0400,4070,042 0,340,4110,0460,4130,0490,4160,0520,4190,055 0,350,4210,0570,4240,0600,4280,0630,4320,067 0,360,4320,0670,4350,0710,4390,0750,4440,080 0,370,4420,0780,4460,0820,4510,0870,4570,092 0,380,4530,0880,4580,0930,4630,0990,4690,105 0,390,4630,0990,4690,1040,4750,1100,4820,117 0,400,4740,1090,4800,1150,4870,1220,4940,130 0,410,4840,1200,4910,1270,4980,1340,5070,142 0,420,4950,1300,5020,1380,5100,1460,5190,155 0,430,5050,1410,5130,1490,5220,1580,5320,167 0,440,5160,1510,5240,1600,5340,1690,5440,180 0,450,5260,1620,5350,1710,5450,1810,5570,192 0,460,5370,1730,5460,1820,5570,1930,5690,205 0,470,5470,1830,5580,1930,5690,2050,5820,217 0,480,5580,1940,5690,2040,5810,2160,5940,230 0,490,5680,2040,5800,2150,5920,2280,6070,242 0,500,5790,2150,5910,2270,6040,2400,6190,255 (