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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
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
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