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CAP1-PAG44.doc 2) Com base no pavimento tipo a seguir: Dimensionar e detalhar todas as armações das lajes do pavimento. Determinar o carregamento das vigas. Dados: Concreto estrutural ( Aço CA50/CA60 Sobrecarga = Revestimento = Considerar alvenaria de tijolos furados sobre todas as vigas (espessura= ) Pé direito estrutural = _1199531936.unknown _1200317858.unknown _1200319732.unknown _1199531969.unknown _1199531905.unknown CAP1-PAG43.doc � ��PAGE � ��PAGE �2� ��NOTAS DE AULA - CONCRETO ARMADO II – 2010 Engº. Renato Martins Grossi Lajes Maciças�� 1) Com base no pavimento tipo a seguir: Dimensionar e detalhar todas as armações das lajes do pavimento. Determinar o carregamento das vigas. Dados: Concreto estrutural ( Aço CA50/CA60 Sobrecarga = Revestimento = Considerar alvenaria de tijolos furados sobre todas as vigas (espessura= ) Pé direito estrutural = � a) Determinação dos carregamentos: b) Verificação das flechas – Determinação da espessura das lajes Laje L2 Conclusão: A espessura de 10cm para as lajes é o suficiente. c) Determinação das reações de apoio e dos momentos fletores: Laje L1 ( Laje armada nas 2,94 x 0,62 = 1,82 7,43 x 0,62 = 4,61 2,68 x 0,62 = 1,66 7,18 x 0,60 = 4,45 2,27 x 1,84 = 4,18 3,32 x 1,84 = 6,11 2,17 x 1,84 = 3,99 3,17 x 1,84 = 5,83 Laje L2 ( Laje armada nas 5,12 x 1,21 = 6,20 10,92 x 1,21 = 13,21 2,19 x 1,21 = 2,65 3,24 x 2,59 = 8,39 4,74 x 2,59 = 12,28 1,83 x 2,59 = 4,74 Laje L3 ( Laje armada nas 4,24 x 0,62 = 2,69 9,65 x 0,62 = 5,98 2,45 x 0,62 = 1,52 7,88 x 0,62 = 4,89 2,73 x 1,84 = 5,02 3,99 x 1,84 = 7,34 2,17 x 1,84 = 3,99 3,17 x 1,84 = 5,83 � Representação das reações de apoio e momentos fletores das lajes Reações de Apoio Momentos Fletores Compensação de momentos Negativos Entre L1-L2 4,61 13,21 8,91 10,57 6,20 0,79 6,99 L3-L1 4,89 4,45 4,67 3,91 1,52 0,07 1,59 L3-L2 5,98 13,21 9,60 10,57 6,20 0,79 6,99 Momentos Fletores (após compensação) Dimensionamento das armaduras Aço CA50 Prescrições de Norma Armação Principal M k e Q A.Contínua A.Alternada Neg 10,57 0,217 5,19 660/15=44 252 193 4,67 0,096 2,12 315/14=23 184 142 Positivos 1,82 - 1,50 * 330/13=25 350 284 1,67 - 1,50 * 315/13=24 365 296 6,99 0,143 3,25 660/15=44 485 392 2,65 - 1,50 * 450/13=35 695 560 2,69 0,055 (1,18) 1,50 * 430/13=33 350 284 1,59 - 1,50 * 315/13=24 465 376 _1200317858.unknown _1329578458.unknown _1329579032.unknown _1329580377.dwg _1329580865.unknown _1329581461.unknown _1329581496.unknown _1329581579.unknown _1329581363.unknown _1329581370.unknown _1329580934.unknown _1329580805.unknown _1329580815.unknown _1329580722.dwg _1329579380.unknown _1329580316.dwg _1329579318/ole-[42, 4D, 52, 1F, 01, 00, 00, 00] _1329578946.unknown _1329578976.unknown _1329579000.unknown _1329578972.unknown _1329578639.unknown _1329578684.unknown _1329578618.unknown _1329578170.unknown _1329578390.unknown _1329578438.unknown _1329578176.unknown _1329578143.unknown _1329578152.unknown _1200318579.unknown _1279662081/ole-[42, 4D, D6, 0D, 00, 00, 00, 00] _1199532241.unknown _1199537434.unknown _1199801965.unknown _1200308155.unknown _1200308174.unknown _1199802528.unknown _1199537618.unknown _1199538019.unknown _1199538052.unknown _1199538122.unknown _1199538136.unknown _1199538032.unknown _1199537714.unknown _1199537469.unknown _1199537479.unknown _1199537455.unknown _1199536577.unknown _1199536718.unknown _1199537411.unknown _1199537420.unknown _1199537396.unknown _1199536588.unknown _1199536631.unknown _1199536586.unknown _1199536587.unknown _1199536578.unknown _1199536585.unknown _1199536362.unknown _1199536489.unknown _1199536576.unknown _1199533182.unknown _1199532424.unknown _1199532055.unknown _1199532072.unknown _1199532171.unknown _1199532082.unknown _1199532064.unknown _1199531936.unknown _1199531969.unknown _1199531905.unknown ExtraLaje2.doc image001.gif PROJCA-PROVA02-LAJEMACICA.pdf PROJCA-PROVA01-LAJEMACICA.pdf Questão 1 – Com base na forma do pavimento tipo a seguir e utilizando a tabela fornecida: a) Determinar os momentos finais (positivos) de todas as lajes ímpares. (11 pontos) b) Determinar o carregamento da viga V8 (07 pontos) c) Verificar a espessura das lajes do PAVTO. (04 pontos) Considerar : • Forma de um PAVTO TIPO da edificação. • Pé direito de 3,05 m. • Concreto � MPaf ck 21= • Aço CA50/CA60 • Revestimento de 2/70,0 mkN • Sobrecarga de 2/55,3 mkN • Alvenaria de tijolos furados sobre todas as vigas. (b =15cm) Lajes Coef. L1 L2 L3 L4 L5 aM 10,47 4,35 5,80 8,45 4,88 aX 12,94 9,77 12,49 18,91 11,42 bM 3,79 2,35 2,23 5,00 3,24 M o m en to s (kN . m /m ) bX 9,15 7,82 9,07 14,72 9,76 Aaq 8,85 7,30 8,11 11,06 7,74 Eaq 12,96 10,71 11,87 16,21 11,31 aq 10,22 5,30 12,10 13,97 6,81 Abq 6,08 5,70 5,69 7,97 6,46 Ebq 8,88 8,32 8,31 11,65 9,43 R ea çõ es (kN /m ) bq 7,00 10,95 10,54 6,73 7,44 α 5,25 4,15 2,67 4,09 3,61 OBSERVAÇÃO É OBRIGATÓRIO MARCAR TODOS OS MOMENTOS ANTES E DEPOIS DA COMPENSAÇÃO NO PRÓPRIO DESENHO h=10cm (todas as lajes) Questão 2 – Dimensionar e detalhar SOMENTE as armações indicadas no desenho de DETALHAMENTO DAS ARMAÇÕES. (11 pontos) Área de aço ( 2cm ) L1 L2 L3 L4 L5 aM 4,37 1,71 2,31 3,45 1,93 bM 1,65 1,65 1,65 1,98 1,35 Área de aço ( 2cm ) L1/L3 L2/L3 L2/L5 L3/L4 L3/L5 X 3,38 4,21 3,45 6,33 2,99 h=10cm (todas as lajes) DETALHAMENTO DA SEGUNDA QUESTÃO FORMULÁRIO Negativo Positivo Compensação de momentos ⋅ ≥ máx médio final X X X 8,0 ( )finalmáx XXM −⋅=∆ 30,0 MMM final ∆+= 2/1 Armação Mínima hbA míns ⋅⋅= %15,0, Peso Específico Carregamentos Espaçamento ⋅ ≤ h cm s 2 20 Concreto 3/25 mkNc =γ Concreto chbpp γ⋅⋅= Diâmetro 8 0.5 hmm ≤≤ φφ Alvenaria 3/13 mkNalv =γ Alvenaria alvhbpp γ⋅⋅= Deformação 3 4)4,0( hE aqgf i ⋅ ⋅⋅+ ⋅= α ifinal ff ⋅= 46,2 ckfE ⋅⋅= 560085,0 300 af adm = Condição de engastamento de uma laje nivelada e parcialmente engastada �Pelo menos 3 2 do lado deve ser engastado para o mesmo ser considerado engastado. Caso contrário o lado será considerado apoiado Espaçamento (cm) x Área da seção cm2/m φ 10 11 12 13 14 15 16 17 18 19 20 5,0 1,96 1,78 1,63 1,51 1,40 1,31 1,23 1,15 1,09 1,03 0,98 6,3 3,12 2,84 2,60 2,40 2,23 2,08 1,95 1,84 1,73 1,64 1,56 8,0 5,03 4,57 4,19 3,87 3,59 3,35 3,14 2,96 2,79 2,65 2,52 10,0 7,85 7,14 6,54 6,04 5,61 5,23 4,91 4,62 4,36 4,13 3,93 12,5 12,27 11,15 10,23 9,44 8,76 8,18 7,67 7,22 6,82 6,46 6,14 Ma Mb Ma Mb Xb Ma Xa Mb Ma Xa Mb Xb Ma Mb Xb qa qb qa qbA qbE qaA qaE qb qaA qaE qbA qbE qa qb Ma Xa Mb Ma Xa Mb Xb Ma Xa Mb Xb Ma Xa Mb Xb qa qb qaA qaE qb qa qbA qbE qa qb COMPENSAÇÃO DE MOMENTOS – PRIMEIRA QUESTÃO Entre 1X 2X médioX máxX⋅8,0 2/1M M∆ fM ARMAÇÕES DAS LAJES – SEGUNDA QUESTÃO Momento sA /c⇔φ Q Comprimento Alternado ou Contínuo N eg at iv o s Po sit iv o s ExtraLaje1.doc EXERICIO UNIBH LAJES.doc Dimensionar e detalhar as lajes do pavimento utilizando lajes maciças. = 20,0 MPa Aço CA50 Sobrecarga = Revestimento = PARA LAJE MACIÇA Fazer o quadro de relação e resumo de aço. GERAL Esboçar o carregamento de todas as vigas todas as vigas. _1307920606.unknown _1322048533.dwg user _1307920614.unknown _1254681446.unknown Exame Especial.doc 1) Calcular e detalhar as armaduras para: os momentos positivos da laje L3; o momento negativo entre as lajes L2 e L3. 2) Fazer os esquemas estáticos (estruturais) das vigas V1 e V6 3) Descrever os passos necessários para determinar a carga do pilar P2 Dados: Pé direito estrutural Observação: Considerar alvenaria de tijolos furados sobre todas as vigas da estrutura Compensação Armação Compr. Alternado � Quadro resumo (momentos fletores – Reações de apoio) Detalhamento das armaduras _1195584528.unknown _1195584589.unknown _1195585425.unknown _1195585518.unknown _1195585606.unknown _1195584667.unknown _1195584682.unknown _1195584636.unknown _1195584561.unknown _1195584574.unknown _1195584538.unknown _1195584215.unknown _1195584251.unknown _1195584281.unknown _1195584306.unknown _1195584237.unknown _1195583820.unknown _1195584083.dwg _1195583784.unknown _1195583627.dwg 01 LAJE MACICA 2015.xls LAJE Dimensões Propriedades Físicas Parametros a = 305.0 cm fck = 20 Mpa dmax = 12.50 mm b = 540.0 cm fc = 1.214 kN/cm2 smin = 10 cm h = 10 cm Ec = * 2,128.7 kN/cm2 Smax = 20 cm d' = 2.5 cm indice = 0.40 Asmin = 1.50 cm2/m kL = 0.295 Carregamento pp = 2.50 kN/m2 qaA = 0.00 0.00 kN/m rev = 0.70 kN/m2 qaE = 0.00 0.00 Extra = 0.00 kN/m2 qa = 3.57 4.03 Sub-total 3.20 kN/m2 qbA = 0.00 0.00 qbE = 0.00 0.00 sc = 0.50 kN/m2 qb = 2.50 2.82 As 0.196 0.312 0.503 0.785 1.227 2.011 3.142 Total = 3.70 kN/m2 k cm2 5.0 6.3 8.0 10.0 12.5 16.0 20.0 Ma = 3.88 1.34 kN.m/m 0.027 1.50 13 20 20 20 20 0 0 Xa = 8.05 2.77 0.057 1.50 - 20 20 20 20 0 0 Tipo 9 Mb = 1.17 0.40 0.008 1.50 13 20 20 20 20 0 0 b/a = 1.75 Xb = 5.72 1.97 0.040 1.50 - 20 20 20 20 0 0 Coef.M = 0.3442 Coef.R = 1.1285 Alfa = 2.81 fi = 0.04 cm 1 ffinal = 0.10 cm 2A fadm = 1.02 cm 2B Status OK 3 4A 4B 5A 5B 6 Compensação ENTRE X1 X2 XMÉDIO 0,80 XMÁX XFINAL M1/2 ∆M MF 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Limpar Campos Dimensionamento fck = 20.00 Mpa h = 10.00 cm As,min = 1.50 cm2/m Cobrimentos fc = 1.214 kN/cm2 d' = 2.50 cm Smax = 20.0 cm Laje = 2.00 cm fyd = 43.48 kN/cm2 d = 7.50 cm φmax = 12.5 mm Vigas = 2.50 cm NEGATIVOS Mom k As Ferragem Quantitativo Comprimento φ S Comp. Quant. a Cont. Alt. dobra T.Cont. T.Alt 0.000 0.00 0 0 0 0 0 0 0 0.000 0.00 0 0 0 0 0 0 0 0.000 0.00 0 0 0 0 0 0 0 0.000 0.00 0 0 0 0 0 0 0 0.000 0.00 0 0 0 0 0 0 0 0.000 0.00 0 0 0 0 0 0 0 0.000 0.00 0 0 0 0 0 0 0 0.000 0.00 0 0 0 0 0 0 0 0.000 0.00 0 0 0 0 0 0 0 0.000 0.00 0 0 0 0 0 0 0 0.000 0.00 0 0 0 0 0 0 0 0.000 0.00 0 0 0 0 0 0 0 POSITIVO Mom k As Ferragem Quantitativo Comprimento φ S Comp. Quant. Face a Face externa Cont. Alt. 0.000 0.00 0 0 0 0 0.000 0.00 0 0 0 0 0.000 0.00 0 0 0 0 0.000 0.00 0 0 0 0 0.000 0.00 0 0 0 0 0.000 0.00 0 0 0 0 0.000 0.00 0 0 0 0 0.000 0.00 0 0 0 0 0.000 0.00 0 0 0 0 0.000 0.00 0 0 0 0 0.000 0.00 0 0 0 0 0.000 0.00 0 0 0 0 0.000 0.00 0 0 0 0 0.000 0.00 0 0 0 0 0.000 0.00 0 0 0 0 0.000 0.00 0 0 0 0 Limpar Negativos Limpar Positivos TBares LAJE TIPO1 qaA qaE qa qbA qbE qb Ma Xa Mb Xb alfa b/a 0.00 0.00 2.50 0.00 0.00 2.50 4.23 0.00 4.23 0.00 4.76 1.00 0.00 0.00 2.62 0.00 0.00 2.50 4.62 0.00 4.25 0.00 5.26 1.05 0.00 0.00 2.73 0.00 0.00 2.50 5.00 0.00 4.27 0.00 5.74 1.10 0.00 0.00 2.83 0.00 0.00 2.50 5.38 0.00 4.25 0.00 6.20 1.15 0.00 0.00 2.92 0.00 0.00 2.50 5.75 0.00 4.22 0.00 6.64 1.20 0.00 0.00 3.00 0.00 0.00 2.50 6.10 0.00 4.17 0.00 7.08 1.25 0.00 0.00 3.08 0.00 0.00 2.50 6.44 0.00 4.12 0.00 7.49 1.30 0.00 0.00 3.15 0.00 0.00 2.50 6.77 0.00 4.06 0.00 7.90 1.35 0.00 0.00 3.21 0.00 0.00 2.50 7.10 0.00 4.00 0.00 8.29 1.40 0.00 0.00 3.28 0.00 0.00 2.50 7.41 0.00 3.95 0.00 8.67 1.45 0.00 0.00 3.33 0.00 0.00 2.50 7.72 0.00 3.89 0.00 9.03 1.50 0.00 0.00 3.39 0.00 0.00 2.50 7.99 0.00 3.82 0.00 9.39 1.55 0.00 0.00 3.44 0.00 0.00 2.50 8.26 0.00 3.74 0.00 9.71 1.60 0.00 0.00 3.48 0.00 0.00 2.50 8.50 0.00 3.66 0.00 10.04 1.65 0.00 0.00 3.53 0.00 0.00 2.50 8.74 0.00 3.58 0.00 10.34 1.70 0.00 0.00 3.57 0.00 0.00 2.50 8.95 0.00 3.53 0.00 10.62 1.75 0.00 0.00 3.61 0.00 0.00 2.50 9.16 0.00 3.47 0.00 10.91 1.80 0.00 0.00 3.65 0.00 0.00 2.50 9.35 0.00 3.38 0.00 11.16 1.85 0.00 0.00 3.68 0.00 0.00 2.50 9.54 0.00 3.29 0.00 11.41 1.90 0.00 0.00 3.72 0.00 0.00 2.50 9.73 0.00 3.23 0.00 11.65 1.95 0.00 0.00 3.75 0.00 0.00 2.50 9.91 0.00 3.16 0.00 11.89 2.00 0.00 0.00 5.00 0.00 0.00 2.50 12.50 0.00 3.16 0.00 15.63 >2,00 LAJE TIPO2A qaA qaE qa qbA qbE qb Ma Xa Mb Xb alfa b/a 0.00 0.00 1.83 2.75 4.02 0.00 2.91 0.00 3.54 8.40 3.26 1.00 0.00 0.00 1.92 2.80 4.10 0.00 3.26 0.00 3.64 8.79 3.68 1.05 0.00 0.00 2.01 2.85 4.17 0.00 3.61 0.00 3.74 9.18 4.11 1.10 0.00 0.00 2.10 2.88 4.22 0.00 3.98 0.00 3.80 9.53 4.55 1.15 0.00 0.00 2.20 2.91 4.27 0.00 4.35 0.00 3.86 9.88 5.00 1.20 0.00 0.00 2.29 2.94 4.30 0.00 4.72 0.00 3.89 10.16 5.44 1.25 0.00 0.00 2.38 2.95 4.32 0.00 5.09 0.00 3.92 10.41 5.88 1.30 0.00 0.00 2.47 2.96 4.33 0.00 5.44 0.00 3.93 10.64 6.32 1.35 0.00 0.00 2.56 2.96 4.33 0.00 5.79 0.00 3.94 10.86 6.74 1.40 0.00 0.00 2.64 2.96 4.33 0.00 6.12 0.00 3.91 11.05 7.15 1.45 0.00 0.00 2.72 2.96 4.33 0.00 6.45 0.00 3.88 11.23 7.55 1.50 0.00 0.00 2.80 2.96 4.33 0.00 6.76 0.00 3.85 11.39 7.95 1.55 0.00 0.00 2.87 2.96 4.33 0.00 7.07 0.00 3.81 11.55 8.32 1.60 0.00 0.00 2.93 2.96 4.33 0.00 7.28 0.00 3.78 11.67 8.68 1.65 0.00 0.00 2.99 2.96 4.33 0.00 7.49 0.00 3.74 11.79 9.03 1.70 0.00 0.00 3.05 2.96 4.33 0.00 7.53 0.00 3.69 11.88 9.36 1.75 0.00 0.00 3.10 2.96 4.33 0.00 7.56 0.00 3.63 11.96 9.69 1.80 0.00 0.00 3.15 2.96 4.33 0.00 8.10 0.00 3.58 12.05 10.00 1.85 0.00 0.00 3.20 2.96 4.33 0.00 8.63 0.00 3.53 12.14 10.29 1.90 0.00 0.00 3.25 2.96 4.33 0.00 8.86 0.00 3.45 12.17 10.58 1.95 0.00 0.00 3.29 2.96 4.33 0.00 9.08 0.00 3.36 12.20 10.87 2.00 0.00 0.00 5.00 2.96 4.33 0.00 12.50 0.00 3.36 12.20 15.63 >2,00 LAJE TIPO2B qaA qaE qa qbA qbE qb Ma Xa Mb Xb alfa b/a 2.75 4.02 0.00 0.00 0.00 1.83 3.54 8.40 2.91 0.00 3.26 1.00 2.82 4.13 0.00 0.00 0.00 1.83 3.77 8.79 2.84 0.00 3.48 1.05 2.89 4.23 0.00 0.00 0.00 1.83 3.99 9.17 2.76 0.00 3.70 1.10 2.95 4.32 0.00 0.00 0.00 1.83 4.19 9.49 2.68 0.00 3.89 1.15 3.01 4.41 0.00 0.00 0.00 1.83 4.38 9.80 2.59 0.00 4.09 1.20 3.06 4.48 0.00 0.00 0.00 1.83 4.55 10.06 2.51 0.00 4.26 1.25 3.11 4.55 0.00 0.00 0.00 1.83 4.71 10.32 2.42 0.00 4.43 1.30 3.16 4.62 0.00 0.00 0.00 1.83 4.86 10.54 2.34 0.00 4.58 1.35 3.20 4.68 0.00 0.00 0.00 1.83 5.00 10.75 2.25 0.00 4.73 1.40 3.24 4.74 0.00 0.00 0.00 1.83 5.12 10.92 2.19 0.00 4.87 1.45 3.27 4.79 0.00 0.00 0.00 1.83 5.24 11.09 2.12 0.00 5.01 1.50 3.31 4.84 0.00 0.00 0.00 1.83 5.34 11.23 2.04 0.00 5.09 1.55 3.34 4.89 0.00 0.00 0.00 1.83 5.44 11.36 1.95 0.00 5.18 1.60 3.37 4.93 0.00 0.00 0.00 1.83 5.53 11.48 1.87 0.00 5.22 1.65 3.40 4.97 0.00 0.00 0.00 1.83 5.61 11.60 1.79 0.00 5.26 1.70 3.42 5.01 0.00 0.00 0.00 1.83 5.68 11.72 1.74 0.00 5.36 1.75 3.45 5.05 0.00 0.00 0.00 1.83 5.75 11.84 1.68 0.00 5.46 1.80 3.47 5.09 0.00 0.00 0.00 1.83 5.81 11.94 1.67 0.00 5.53 1.85 3.50 5.12 0.00 0.00 0.00 1.83 5.86 12.03 1.59 0.00 5.60 1.90 3.52 5.15 0.00 0.00 0.00 1.83 5.90 12.08 1.54 0.00 5.68 1.95 3.54 5.18 0.00 0.00 0.00 1.83 5.94 12.13 1.48 0.00 5.76 2.00 4.38 6.25 0.00 0.00 0.00 1.83 7.03 12.50 1.48 0.00 6.50 >2,00 LAJE TIPO3 qaA qaE qa qbA qbE qb Ma Xa Mb Xb alfa b/a 2.17 3.17 0.00 2.17 3.17 0.00 2.69 6.99 2.69 6.99 2.46 1.00 2.27 3.32 0.00 2.17 3.17 0.00 2.94 7.43 2.68 7.18 2.72 1.05 2.36 3.46 0.00 2.17 3.17 0.00 3.19 7.87 2.67 7.36 2.96 1.10 2.45 3.58 0.00 2.17 3.17 0.00 3.42 8.28 2.65 7.50 3.18 1.15 2.53 3.70 0.00 2.17 3.17 0.00 3.65 8.69 2.62 7.63 3.40 1.20 2.60 3.80 0.00 2.17 3.17 0.00 3.86 9.03 2.56 7.72 3.61 1.25 2.63 3.90 0.00 2.17 3.17 0.00 4.06 9.37 2.50 7.81 3.80 1.30 2.73 3.99 0.00 2.17 3.17 0.00 4.24 9.65 2.45 7.88 3.99 1.35 2.78 4.08 0.00 2.17 3.17 0.00 4.42 9.93 2.39 7.94 4.15 1.40 2.84 4.15 0.00 2.17 3.17 0.00 4.58 10.17 2.32 8.00 4.31 1.45 2.89 4.23 0.00 2.17 3.17 0.00 4.73 10.41 2.25 8.06 4.46 1.50 2.93 4.29 0.00 2.17 3.17 0.00 4.86 10.62 2.16 8.09 4.61 1.55 2.98 4.36 0.00 2.17 3.17 0.00 4.99 10.82 2.07 8.12 4.73 1.60 3.02 4.42 0.00 2.17 3.17 0.00 5.10 10.99 1.99 8.14 4.86 1.65 3.06 4.48 0.00 2.17 3.17 0.00 5.21 11.16 1.91 8.15 4.97 1.70 3.09 4.53 0.00 2.17 3.17 0.00 5.31 11.30 1.85 8.16 5.06 1.75 3.13 4.58 0.00 2.17 3.17 0.00 5.40 11.43 1.78 8.17 5.16 1.80 3.16 4.63 0.00 2.17 3.17 0.00 5.48 11.55 1.72 8.17 5.25 1.85 3.19 4.67 0.00 2.17 3.17 0.00 5.56 11.67 1.66 8.18 5.33 1.90 3.22 4.71 0.00 2.17 3.17 0.00 5.63 11.78 1.63 8.19 5.41 1.95 3.25 4.75 0.00 2.17 3.17 0.00 5.70 11.89 1.60 8.20 5.49 2.00 4.38 6.25 0.00 2.17 3.17 0.00 7.03 12.50 1.60 8.20 6.50 >2,00 LAJE TIPO4A qaA qaE qa qbA qbE qb Ma Xa Mb Xb alfa b/a 0.00 0.00 1.44 0.00 0.00 3.56 2.01 0.00 3.09 6.99 2.25 1.00 0.00 0.00 1.52 0.00 0.00 3.66 2.32 0.00 3.23 7.43 2.60 1.05 0.00 0.00 1.59 0.00 0.00 3.75 2.63 0.00 3.36 7.87 2.97 1.10 0.00 0.00 1.66 0.00 0.00 3.84 2.93 0.00 3.46 8.26 3.35 1.15 0.00 0.00 1.73 0.00 0.00 3.92 3.22 0.00 3.56 8.65 3.74 1.20 0.00 0.00 1.80 0.00 0.00 3.99 3.63 0.00 3.64 9.03 4.14 1.25 0.00 0.00 1.88 0.00 0.00 4.06 3.99 0.00 3.72 9.33 4.56 1.30 0.00 0.00 1.95 0.00 0.00 4.12 4.34 0.00 3.77 9.69 5.01 1.35 0.00 0.00 2.02 0.00 0.00 4.17 4.69 0.00 3.82 10.00 5.41 1.40 0.00 0.00 2.09 0.00 0.00 4.22 5.03 0.00 3.86 10.25 5.83 1.45 0.00 0.00 2.17 0.00 0.00 4.25 5.37 0.00 3.90 10.49 6.25 1.50 0.00 0.00 2.24 0.00 0.00 4.28 5.70 0.00 3.90 10.70 6.66 1.55 0.00 0.00 2.31 0.00 0.00 4.30 6.03 0.00 3.89 10.91 7.06 1.60 0.00 0.00 2.38 0.00 0.00 4.32 6.35 0.00 3.85 11.08 7.46 1.65 0.00 0.00 2.45 0.00 0.00 4.33 6.67 0.00 3.81 11.24 7.84 1.70 0.00 0.00 2.53 0.00 0.00 4.33 6.97 0.00 3.79 11.39 8.21 1.75 0.00 0.00 2.59 0.00 0.00 4.33 7.27 0.00 3.76 11.53 8.58 1.80 0.00 0.00 2.63 0.00 0.00 4.33 7.55 0.00 3.72 11.65 8.93 1.85 0.00 0.00 2.72 0.00 0.00 4.33 7.82 0.00 3.67 11.77 9.25 1.90 0.00 0.00 2.78 0.00 0.00 4.33 8.09 0.00 3.60 11.83 9.58 1.95 0.00 0.00 2.83 0.00 0.00 4.33 8.35 0.00 3.52 11.88 9.90 2.00 0.00 0.00 5.00 0.00 0.00 4.33 12.50 0.00 3.52 11.88 15.63 >2,00 LAJE TIPO4B qaA qaE qa qbA qbE qb Ma Xa Mb Xb alfa b/a 0.00 0.00 3.56 0.00 0.00 1.44 3.09 6.99 2.01 0.00 2.25 1.00 0.00 0.00 3.63 0.00 0.00 1.44 3.22 7.20 1.92 0.00 2.35 1.05 0.00 0.00 3.69 0.00 0.00 1.44 3.35 7.41 1.83 0.00 2.45 1.10 0.00 0.00 3.74 0.00 0.00 1.44 3.46 7.56 1.73 0.00 2.53 1.15 0.00 0.00 3.80 0.00 0.00 1.44 3.57 7.70 1.63 0.00 2.61 1.20 0.00 0.00 3.85 0.00 0.00 1.44 3.66 7.82 1.56 0.00 2.68 1.25 0.00 0.00 3.89 0.00 0.00 1.44 3.74 7.93 1.49 0.00 2.74 1.30 0.00 0.00 3.93 0.00 0.00 1.44 3.80 8.02 1.41 0.00 2.77 1.35 0.00 0.00 3.97 0.00 0.00 1.44 3.86 8.11 1.33 0.00 2.80 1.40 0.00 0.00 4.00 0.00 0.00 1.44 3.91 8.13 1.26 0.00 2.85 1.45 0.00 0.00 4.04 0.00 0.00 1.44 3.96 8.15 1.19 0.00 2.89 1.50 0.00 0.00 4.07 0.00 0.00 1.44 4.00 8.20 1.14 0.00 2.91 1.55 0.00 0.00 4.10 0.00 0.00 1.44 4.04 8.25 1.08 0.00 2.92 1.60 0.00 0.00 4.13 0.00 0.00 1.44 4.07 8.28 1.03 0.00 2.92 1.65 0.00 0.00 4.15 0.00 0.00 1.44 4.10 8.30 0.98 0.00 2.93 1.70 0.00 0.00 4.18 0.00 0.00 1.44 4.12 8.31 0.95 0.00 2.93 1.75 0.00 0.00 4.20 0.00 0.00 1.44 4.14 8.32 0.91 0.00 2.94 1.80 0.00 0.00 4.22 0.00 0.00 1.44 4.15 8.33 0.87 0.00 2.94 1.85 0.00 0.00 4.24 0.00 0.00 1.44 4.16 8.33 0.83 0.00 2.95 1.90 0.00 0.00 4.26 0.00 0.00 1.44 4.16 8.33 0.80 0.00 2.95 1.95 0.00 0.00 4.28 0.00 0.00 1.44 4.17 8.33 0.76 0.00 2.96 2.00 0.00 0.00 5.00 0.00 0.00 1.44 4.17 8.33 0.76 0.00 3.13 >2,00 LAJE TIPO5A qaA qaE qa qbA qbE qb Ma Xa Mb Xb alfa b/a 1.71 2.50 0.00 0.00 0.00 3.03 2.02 5.46 2.52 6.17 1.84 1.00 1.79 2.63 0.00 0.00 0.00 3.08 2.27 5.98 2.56 6.46 2.08 1.05 1.88 2.75 0.00 0.00 0.00 3.11 2.52 6.50 2.60 6.75 2.31 1.10 1.96 2.88 0.00 0.00 0.00 3.14 2.76 7.11 2.63 6.97 2.54 1.15 2.05 3.00 0.00 0.00 0.00 3.16 3.00 7.72 2.65 7.19 2.77 1.20 2.13 3.13 0.00 0.00 0.00 3.17 3.23 8.81 2.64 7.36 3.00 1.25 2.22 3.25 0.00 0.00 0.00 3.17 3.45 8.59 2.61 7.51 3.22 1.30 2.30 3.36 0.00 0.00 0.00 3.17 3.66 8.74 2.57 7.63 3.42 1.35 2.37 3.47 0.00 0.00 0.00 3.17 3.86 8.88 2.53 7.74 3.62 1.40 2.44 3.57 0.00 0.00 0.00 3.17 4.05 9.16 2.48 7.83 3.80 1.45 2.50 3.66 0.00 0.00 0.00 3.17 4.23 9.44 2.43 7.91 3.98 1.50 2.56 3.75 0.00 0.00 0.00 3.17 4.39 9.68 2.39 7.98 4.14 1.55 2.61 3.83 0.00 0.00 0.00 3.17 4.55 9.91 2.34 8.02 4.30 1.60 2.67 3.90 0.00 0.00 0.00 3.17 4.70 10.13 2.28 8.03 4.45 1.65 2.72 3.98 0.00 0.00 0.00 3.17 4.84 10.34 2.22 8.10 4.59 1.70 2.76 4.04 0.00 0.00 0.00 3.17 4.97 10.53 2.15 8.13 4.71 1.75 2.80 4.11 0.00 0.00 0.00 3.17 5.10 10.71 2.08 8.17 4.84 1.80 2.85 4.17 0.00 0.00 0.00 3.17 5.20 10.88 2.02 8.16 4.96 1.85 2.89 4.22 0.00 0.00 0.00 3.17 5.30 11.04 1.96 8.14 5.07 1.90 2.92 4.28 0.00 0.00 0.00 3.17 5.40 11.20 1.88 8.13 5.17 1.95 2.96 4.33 0.00 0.00 0.00 3.17 5.50 11.35 1.80 8.12 5.28 2.00 4.38 6.25 0.00 0.00 0.00 3.17 7.03 12.50 1.80 8.12 6.50 >2,00 LAJE TIPO5B qaA qaE qa qbA qbE qb Ma Xa Mb Xb alfa b/a 0.00 0.00 3.03 1.71 2.50 0.00 2.52 6.17 2.02 5.46 1.84 1.00 0.00 0.00 3.12 1.71 2.50 0.00 2.70 6.47 1.97 5.56 1.96 1.05 0.00 0.00 3.21 1.71 2.50 0.00 2.87 6.76 1.91 5.65 2.08 1.10 0.00 0.00 3.29 1.71 2.50 0.00 3.02 6.99 1.84 5.70 2.18 1.15 0.00 0.00 3.36 1.71 2.50 0.00 3.16 7.22 1.77 5.75 2.28 1.20 0.00 0.00 3.42 1.71 2.50 0.00 3.28 7.40 1.70 5.75 2.37 1.25 0.00 0.00 3.48 1.71 2.50 0.00 3.40 7.57 1.62 5.76 2.46 1.30 0.00 0.00 3.54 1.71 2.50 0.00 3.50 7.70 1.55 5.75 2.53 1.35 0.00 0.00 3.59 1.71 2.50 0.00 3.59 7.82 1.47 5.74 2.61 1.40 0.00 0.00 3.64 1.71 2.50 0.00 3.67 7.91 1.41 5.73 2.67 1.45 0.00 0.00 3.69 1.71 2.50 0.00 3.74 8.00 1.35 5.72 2.73 1.50 0.00 0.00 3.73 1.71 2.50 0.00 3.80 8.07 1.29 5.69 2.78 1.55 0.00 0.00 3.77 1.71 2.50 0.00 3.86 8.14 1.23 5.66 2.82 1.60 0.00 0.00 3.81 1.71 2.50 0.00 3.91 8.20 1.18 5.62 2.83 1.65 0.00 0.00 3.84 1.71 2.50 0.00 3.95 8.25 1.13 5.58 2.84 1.70 0.00 0.00 3.87 1.71 2.50 0.00 3.99 8.30 1.07 5.56 2.86 1.75 0.00 0.00 3.90 1.71 2.50 0.00 4.02 8.34 1.00 5.54 2.88 1.80 0.00 0.00 3.93 1.71 2.50 0.00 4.05 8.38 0.97 5.55 2.90 1.85 0.00 0.00 3.96 1.71 2.50 0.00 4.08 8.42 0.94 5.56 2.92 1.90 0.00 0.00 3.99 1.71 2.50 0.00 4.10 8.45 0.91 5.60 2.94 1.95 0.00 0.00 4.01 1.71 2.50 0.00 4.12 8.47 0.88 5.64 2.96 2.00 0.00 0.00 5.00 1.71 2.50 0.00 4.17 8.33 0.88 5.64 3.13 >2,00 LAJE TIPO6 qaA qaE qa qbA qbE qb Ma Xa Mb Xb alfa b/a 0.00 0.00 2.50 0.00 0.00 2.50 2.02 5.15 2.02 5.15 1.49 1.00 0.00 0.00 2.62 0.00 0.00 2.50 2.22 5.50 2.00 5.29 1.63 1.05 0.00 0.00 2.73 0.00 0.00 2.50 2.42 5.85 1.98 5.43 1.77 1.10 0.00 0.00 2.83 0.00 0.00 2.50 2.65 6.14 1.94 5.51 1.90 1.15 0.00 0.00 2.92 0.00 0.00 2.50 2.87 6.43 1.89 5.59 2.02 1.20 0.00 0.00 3.00 0.00 0.00 2.50 2.97 6.67 1.83 5.64 2.14 1.25 0.00 0.00 3.08 0.00 0.00 2.50 3.06 6.90 1.77 5.68 2.24 1.30 0.00 0.00 3.15 0.00 0.00 2.50 3.19 7.09 1.71 5.69 2.34 1.35 0.00 0.00 3.21 0.00 0.00 2.50 3.32 7.28 1.65 5.70 2.41 1.40 0.00 0.00 3.28 0.00 0.00 2.50 3.43 7.43 1.57 5.71 2.49 1.45 0.00 0.00 3.33 0.00 0.00 2.50 3.53 7.57 1.49 5.72 2.56 1.50 0.00 0.00 3.39 0.00 0.00 2.50 3.61 7.68 1.43 5.72 2.62 1.55 0.00 0.00 3.44 0.00 0.00 2.50 3.69 7.79 1.36 5.72 2.68 1.60 0.00 0.00 3.48 0.00 0.00 2.50 3.76 7.88 1.29 5.72 2.73 1.65 0.00 0.00 3.53 0.00 0.00 2.50 3.83 7.97 1.21 5.72 2.77 1.70 0.00 0.00 3.57 0.00 0.00 2.50 3.88 8.05 1.17 5.72 2.81 1.75 0.00 0.00 3.61 0.00 0.00 2.50 3.92 8.12 1.13 5.72 2.85 1.80 0.00 0.00 3.65 0.00 0.00 2.50 3.96 8.18 1.07 5.72 2.88 1.85 0.00 0.00 3.68 0.00 0.00 2.50 3.99 8.24 1.01 5.72 2.90 1.90 0.00 0.00 3.72 0.00 0.00 2.50 4.02 8.29 0.99 5.72 2.93 1.95 0.00 0.00 3.75 0.00 0.00 2.50 4.05 8.33 0.96 5.72 2.96 2.00 0.00 0.00 5.00 0.00 0.00 2.50 4.17 8.33 0.96 5.72 3.13 >2,00 image004.jpg PROJCA-PROVA03-LAJEMACICA.pdf PROJCA-PROVA04-LAJEMACICA.pdf EXAME2007.doc EXAME ESPECIAL – CONCRETO ARMADO Professor: Renato Martins Grossi Dimensionar as armaduras positivas da Laje L1 Dimensionar as armaduras negativas entre as lajes L1 e L3 Determinar o carregamento da Viga V2 Verificar a espessura das lajes do PAVTO. Considerar : Pé direito de 2,95 m. Concreto ( Aço CA50 Momentos e Reações L1 L2 L3 6,58 4,65 8,29 13,65 11,48 17,66 2,22 3,89 6,83 9,68 10,74 17,84 8,62 6,68 9,51 12,61 9,80 13,92 7,49 6,15 9,14 11,07 8,98 13,11 7,49 5,69 7,12 4,68 5,18 7,77 5,22 2,96 5,44 Alvenaria de tijolos furados sobre todas as vigas. (base alvenaria =15cm) BOA SORTE� MOMENTOS E REAÇÕES DETALHAMENTO _1227563142.unknown _1227563197.unknown _1227563318.unknown _1259012445.unknown _1259012622.unknown _1227563315.unknown _1227563317.unknown _1227563225.unknown _1227563148.unknown _1227563193.unknown _1227563104.unknown _1227563128.unknown _1183315309.dwg _1181650998.dwg
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