CONCRETO ARMADO - Instabilidade

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CONCRETO ARMADO - Instabilidade

Text of CONCRETO ARMADO - Instabilidade

  • Parmetro de instabilidade

    Determinao da rigidez equivalente da estrutura

    CURSO ABCIC - ROBERTO CHUST CARVALHO*

  • M1,tot,d: momento de tombamento, ou seja, a soma de todos os momentos de todas as foras horizontais da combinao considerada, com seus valores de clculo, em relao base da estrutura;Mtot,d: a soma dos produtos de todas as foras verticais atuantes na estrutura, na combinao considerada, com seus valores de clculo, pelos deslocamentos horizontais de seus respectivos pontos de aplicao, obtida da anlise de 1 ordem.Em geral as lajes formam septos e portanto os deslocamentos horizontais dos andares so os mesmos para todas as cargas verticais no mesmo pavimento.

    CURSO ABCIC - ROBERTO CHUST CARVALHO*

  • CURSO ABCIC - ROBERTO CHUST CARVALHO*

  • CURSO ABCIC - ROBERTO CHUST CARVALHO*

  • CURSO ABCIC - ROBERTO CHUST CARVALHO*

  • *O processo geral, analogamente ao processo , um mtodo iterativo que consiste da considerao da no-linearidade fsica e geomtrica da estrutura, considerando, a cada iterao, a posio deformada da estrutura. Este processo tende a simular o que realmente ocorre na estrutura quando da atuao das foras horizontais.

    CURSO ABCIC - ROBERTO CHUST CARVALHO*

  • A NBR6118:2003 prescreve que, para a anlise dos esforos globais de 2 ordem em estruturas reticuladas com no mnimo 4 andares, a no linearidade fsica pode ser considerada de maneira aproximada, tomando-se como rigidez dos elementos estruturais os seguintes:

    CURSO ABCIC - ROBERTO CHUST CARVALHO*

  • *Em elementos em que h atuao com o normal

    Considerao melhor Relaes N, M e 1/R para determinar EI do pilarPara vigas fissuradas ou elementos sem normal:

    Grf1

    000

    0.83924805851.076950066716.584854288

    6.07619965536.697194675118.7243272684

    8.25260310688.8703203789

    9.944259151810.6164203989

    11.496907895512.2403214396

    12.983894025213.8070576666

    14.429050316115.3377771328

    15.841555710916.5850000443

    17.224821573416.8408178358

    17.442002160217.8043231822

    17.56047665217.9426002723

    17.660026780318.059343612

    17.744585270118.1596410671

    17.817004102418.2429999882

    17.879266159318.2470048553

    17.932852445918.3239207813

    17.978858554418.3921950448

    18.01809581718.4531550497

    18.051272394718.5078529066

    18.079453737818.5569688076

    18.103608407118.6011286377

    18.124473231118.6407672433

    18.1426486318.6762112587

    18.158569516718.7077020586

    18.172606367918.7355955259

    18.185051599818.7604550711

    18.196142649518.7827556722

    18.23040843718.8028801971

    18.215006028818.8211401865

    18.223072271118.8800381564

    18.230384362118.8530452903

    18.237036355418.8670783856

    18.243107930918.8800387204

    18.243339716818.8897193439

    18.8901650605

    N = 100,00 kN

    0,85 . f cd

    1,10 . f cd

    Reta Secante

    q

    M (kNm)

    MxNxC

    DIAGRAMA MOMENTO FLETOR x ESFORO NORMAL x CURVATURAEsforo Normal Mximo kNReta Secante10.0CA-252171.040

    q12.5CA-504352.070

    Dados do ConcretoDados do Ao0.0000.00016.0CA-605222.480

    Seo TransversalTipo1,103.3751,389.09016.5853.41420.0

    0.851.10b [mm]h [mm]Cobrimento [mm]18.7243.85522.0

    40.0000.0240.031200.000200.00030.000CA-504.3502.070210.00022.5

    25.0

    Taxa de Armadura32.0

    10 mm25 mm40.0

    10.02157.08035.00010.02157.080165.0000.79%

    160.0003,200.000

    Dados das Curvas Obtidas com

    qq

    18.24316.02016.5853.414971.494

    qx [mm]N [kN]zg [mm]M [kN.m]Rcc aRcc bRcc cRcc dzg azg bzg czg d

    0.0000.000

    0.0500.124494.90193.4870.1153.7930.0822.721100.00091.7680.839145.639-10,548.57793.487-10,600.729165.835-1,904.46991.768-1,893.631

    0.5000.322128.75995.2570.2347.732-0.091-2.989100.00043.5286.07695.257-669.83963.528-701.56843.528-197.864-22.848-180.937

    1.0000.47795.311101.5470.3029.947-0.348-11.494100.00032.4568.253101.547-184.680-43.146-329.37332.456-135.902479.643-3.363

    1.5000.61281.664109.0720.35011.545-0.625-20.617100.00027.9959.944109.072-35.091-183.717-327.88127.995-277.025241.280114.858

    2.0000.74274.158117.0490.39212.917-0.908-29.966100.00025.59111.497117.04936.385-348.210-428.87425.591152.071205.008160.532

    2.5000.86869.440125.2020.43014.201-1.195-39.403100.00024.12512.984125.20278.231-533.018-579.99024.12552.204190.442173.185

    3.0000.99466.248133.4000.46915.462-1.481-48.862100.00023.17914.429133.400105.905-736.199-763.69423.17933.550182.677175.496

    3.5001.12063.996141.5680.50716.738-1.768-58.307100.00022.55615.842141.568125.802-956.403-972.16922.55626.958177.916174.826

    4.0001.24762.368149.6540.54718.056-2.053-67.710100.00022.15317.225149.654141.026-1,192.515-1,201.14322.15324.084174.744173.421

    4.5001.33859.463150.1260.55018.156-2.375-68.283100.00021.24317.442150.126144.905-1,497.875-1,503.09621.24322.274170.822170.203

    5.0001.42456.949150.1820.54918.100-2.701-68.283100.00020.45917.560150.182147.083-1,832.811-1,835.91020.45921.012167.937167.644

    5.5001.50854.825150.2990.54517.984-3.030-68.283100.00019.80817.660150.299148.542-2,193.845-2,195.60219.80820.095165.802165.666

    6.0001.59053.008150.4610.54017.821-3.360-68.283100.00019.26217.745150.461149.533-2,580.693-2,581.62219.26219.403164.175164.115

    6.5001.67251.440150.6580.53417.625-3.691-68.283100.00018.80217.817150.658150.217-2,993.061-2,993.50218.80218.865162.906162.882

    7.0001.75350.075150.8780.52817.404-4.022-68.283100.00018.41317.879150.878150.703-3,430.656-3,430.83118.41318.437161.898161.890

    7.5001.83348.879151.1140.52017.168-4.355-68.283100.00018.08517.933151.114151.064-3,893.157-3,893.20818.08518.091161.087161.085

    8.0001.91347.827151.3570.51316.925-4.687-68.283100.00017.80817.979151.357151.351-4,380.221-4,380.22817.80817.809160.425160.425

    8.5001.99346.898151.6020.50616.681-5.019-68.283100.00017.57718.018151.602151.602-4,891.467-4,891.46717.57717.577159.882159.882

    9.0002.07346.076151.8410.49816.442-5.352-68.283100.00017.38618.051151.837151.841-5,426.529-5,426.52617.38617.386159.432159.432

    9.5002.15445.344152.0740.49116.208-5.684-68.283100.00017.22818.079152.043152.074-5,985.292-5,985.26117.23117.228159.056159.056

    10.0002.23444.689152.3010.48415.981-6.016-68.283100.00017.09518.104152.197152.301-6,567.724-6,567.62017.10617.095158.739158.741

    10.5002.31544.100152.5230.47815.760-6.347-68.283100.00016.98518.124152.281152.523-7,173.800-7,173.55917.00916.985158.470158.475

    11.0002.39643.567152.7390.47115.544-6.679-68.283100.00016.89118.143152.281152.739-7,803.488-7,803.03016.93716.891158.241158.250

    11.5002.47743.084152.9500.46515.333-7.010-68.283100.00016.81218.159152.184152.950-8,456.768-8,456.00216.88616.812158.044158.058

    12.0002.55942.643153.1550.45915.127-7.341-68.283100.00016.74518.173151.980153.155-9,133.613-9,132.43816.85616.745157.874157.894

    12.5002.64042.240153.3560.45214.926-7.673-68.283100.00016.68818.185151.658153.356-9,834.002-9,832.30516.84616.688157.726157.753

    13.0002.72241.870153.5520.44714.730-8.003-68.283100.00016.63918.196151.213153.552-10,557.912-10,555.57316.85316.639157.598157.632

    15.0003.04940.655154.2920.42413.990-9.326-68.283100.00016.50518.230148.061154.292-13,688.316-13,682.08417.05216.505157.225157.295

    14.0002.88541.215153.9310.43514.352-8.665-68.283100.00016.56118.215149.922153.931-12,076.214-12,072.20516.92016.561157.388157.439

    14.5002.96740.925154.1130.43014.169-8.995-68.283100.00016.53118.223149.065154.113-12,870.568-12,865.51916.97816.531157.301157.362

    15.0003.04940.655154.2920.42413.990-9.326-68.283100.00016.50518.230148.060154.292-13,688.365-13,682.13317.05216.505157.225157.295

    15.5003.13140.404154.4670.41913.816-9.656-68.283100.00016.48318.237146.905154.467-14,529.590-14,522.02717.14316.483157.158157.238

    16.0003.21440.171154.6380.41413.645-9.986-68.283100.00016.46418.243145.593154.638-15,394.225-15,385.18017.25116.464157.099157.189

    16.0203.21740.162154.6450.41313.638-10.000-68.283100.00016.46318.243145.538154.645-15,429.297-15,420.19017.25616.463157.097157.187

    qx [mm]zg [mm]M [kN.m]Rcc aRcc bRcc cRcc dzg azg bzg czg d

    0.0000.000

    0.0500.102408.15394.9180.0933.0770.0612.005100.00089.3881.077128.666-14,196.36994.918-14,230.117136.640-1,916.40289.388-1,911.218

    0.5000.286114.23597.6530.1986.534-0.127-4.186100.00038.5546.69797.653-958.14237.793-1,018.00138.554-192.844-172.266-171.411

    1.0000.42484.799105.0140.2498.214-0.401-13.228100.00028.8048.870105.014-305.073-123.555-533.64228.804-115.840276.0243.353

    1.5000.54672.772113.4730.2839.345-0.692-22.817100.00024.86410.616113.473-101.308-328.759-543.54024.864-130.618205.359105.056

    2.0000.66166.142122.3370.31110.273-0.989-32.610100.00022.73012.240122.337-3.296-566.429-692.06222.730-2,119.410186.505146.573

    2.5000.77561.964131.3670.33711.118-1.288-42.485100.00021.42013.807131.36754.251-832.442-909.55921.42086.708177.883160.723

    3.0000.88759.127140.4480.36211.938-1.588-52.386100.00020.56415.338140.44892.289-1,124.605-1,172.76420.56440.975173.027165.159

    3.4140.98057.413147.9640.38312.621-1.837-60.586100.00020.07216.585147.964115.415-1,385.410-1,417.95920.07229.945170.407166.152

    3.5000.99957.112149.5150.38712.765-1.888-62.280100.00019.98916.841149.515119.535-1,441.405-1,471.38619.98928.587169.969166.214

    4.0001.09954.966155.1110.39913.172-2.201-68.283100.00019.34917.804155.111135.974-1,806.304-1,825.44019.34923.657167.294165.422

    4.5001.17752.292155.4480.38912.834-2.536-68.283100.00018.49417.943155.448142.451-2,241.938-2,254.93618.49421.016164.627163.625

    5.0001.25250.065155.8590.37712.424-2.873-68.283100.00017.78818.059155.859147.077-2,713.929-2,722.71117.78819.297162.696162.147

    5.5001.32548.180156.3260.36211.956-3.213-68.283100.00017.19818.16