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