PEDRO HENRIQUE SALES CAVALCANTE
CÁLCULO E DETALHAMENTO ESTRUTURAL ESTRUTURAL DE LAJES L AJES E VIGAS
Trabalho solicitado pela disciplina de Concreto Armado II, na Universidade Federal do Piauí-UFPI, do curso de Engenharia Civil, sendo solicitado como requisito
parcial
de
aprovação
na
disciplina. Prof. Msc. Eunice Silva Santos
TERESINA, JANEIRO DE 2017
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Sumário 1.0 CONSIDERAÇÕES INICIAIS ................................................................................. 4 2.0 ESFORÇOS SOLICITANTES E CONSIDERAÇÕES DE CÁLCULO DOS PILARES PILARES ................ ................................. ................................. ................................. .................................. ................................. ................................. ................... .. 5 3.0 CÁLCULO DE ARMADURA DOS DOS PILARES .......... ................... ................... ................... ................... ................... ........... 6 5.0 DETALHAMENTO DETALHAMENTO E DISPOSIÇÕES CONSTRUTIVAS CONSTRUTIVAS .................... ........... ................... .................. ........ 29 6.0 REFERÊNCIAS BIBLIOGRÁFICAS ..................................................................... 30 7.0 ANEXOS ANEXOS ............... ................................ .................................. .................................. ................................. ................................. ............................ ........... 31
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1.0 CONSIDERAÇÕES INICIAIS
Para o presente dimensionamento dimensionamento foram adotadas as seguintes considerações: considerações: ●
●
●
Classe de agressividade agressividade II: ○
Agressividade: Agressividade: moderada
○
Tipo de ambiente para efeito de projeto: urbano urbano
○
Risco de deterioração deterioraçã o da estrutura: estrutur a: pequeno
Qualidade do concreto - concreto armado: ○
fck: 30 MPa
○
Relação água/cimento água/cimento em em massa: máxima de 0,6
Aço: CA50 ○
●
●
fyk = 500 MPa
Cobrimento nominal: ○
Laje: 30 mm
○
Viga/Pilar: Viga/Pilar : 25 mm
Peso específico dos materiais de construção: ○
Concreto armado: 25 KN/m²
Revestimento:
○
o
Reboco inferior (argamassa de cal, cimento e areia com 1,5 cm de espessura): 19 KN/m³
o
Forro de gesso (3 cm cm de espessura): 12,5 KN/m³
o
Camada de regularização regularizaçã o (cimento e areia com 3,5 cm de espessura): 21 KN/m³
●
o
Acabamento (granito com 1 cm de espessura): 28 KN/m³
o
Parede (tijolos furados): 13 KN/m³
Valores das cargas verticais (edifício residencial); ○
Dormitórios, salas, copa, cozinha, banheiros: 1,5 KN/m²
○
Despensa, área de serviço, lavanderia: lavanderia: 2,0 2,0 KN/m² KN/m²
○
Fosso sem acesso a pessoas: 0,5 KN/m²
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2.0 ESFORÇOS SOLICITANTES E CONSIDERAÇÕES DE CÁLCULO DOS PILARES PIL ARES Para o cálculo do dimensionamento dos pilares foram encontradas as reações das vigas em cada pilar e a essas reações foram somados o peso próprio dos pilares. Os momentos iniciais de primeira ordem de cálculo para os pilares de extremidade e de canto foram obtidos por meio de um modelo estrutural simplificado que é prescrito pela norma vigente. Todos os elementos da estrutura deste projeto foram considerados elementos de nós fixos (pilares contraventados) e sem cargas horizontais atuantes.
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3.0 PROCEDIMENTO DE VERIFICAÇÃO DA NECESSIDADE DE CONSIDERAÇÃO DOS EFEITOS LOCAIS DE SEGUNDA ORDEM E CÁLCULO DE ARMADURA DOS PILARES 1. Esforço normal característico:
= × ×
= força normal característica do pilar; = coeficiente de majoração da força normal em função da menor dimensão
do pilar;
= coeficiente de ponderação das ações no ELU (definido na Tabela 11.1 da
NBR 6118).
2. Índice de esbeltez esbeltez para seção retangular:
= 3,46× ℎ
= comprimento equivalente de flambagem; ℎ = altura em relação ao eixo de flexão.
3. Momento fletor mínimo mínimo de de primeira primeira ordem: ordem:
,í = ×(1,5+0,03×ℎ)
= força normal de projeto do pilar; ℎ = altura em relação ao eixo de flexão (mesma direção de ); 4. Esbeltez limite:
25+12,5× = ℎ 35 ≤ ≤ 90
= excentricidade inicial de primeira ordem; ℎ = altura em relação ao eixo de flexão (mesma direção de );
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5. Caso a comparação comparação da esbeltez com a esbeltez limite, demonstre demonstre que é necessário considerar os efeitos locais de segunda ordem, este pode ser calculado com base na metodologia do pilar-padrão com curvatura aproximada:
= × 10 × [ℎ × 0,005 (+0,5) +0,5)]
0,005 = 1 [ℎ × 0,005 ≤ ] (+0,5) +0,5) ℎ ×
= comprimento equivalente de flambagem; = força normal de projeto do pilar; ℎ = altura em relação ao eixo de flexão (mesma direção de ); = coeficiente adimensional relativo a força normal de projeto. 6. De posse do momento total (momento inicial mais momento de segunda ordem), juntamente com os coeficientes adimensionais adimensionais calculados, entrase no ábaco de flexão reta ou flexão oblíqua para se determinar a taxa de armadura:
= × × Parâmetros de entrada nos ábacos:
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Pilar 1 Eixo X (Canto) –
Pilar 1 Eixo Y (Canto) –
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Pilar 8 Eixo X (Extremidade) –
Pilar 12 Eixo X (Extremidade) (Extremidade) –
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Pilar 19 Eixo X (Canto) –
Pilar 19 Eixo Y (Canto) –
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Pilar 20 Eixo Y (Extremidade) (Extremidade) –
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3.0 MEMÓRIA DE CÁLCULO
Para cada um dos pavimentos foi executado o dimensionamento da armadura conforme os procedimentos explicados em 3.0. Os resultados encontrados foram obtidos com auxílio do programa Excel e encontram-se abaixo:
3.1 PAVIMENTO TÉRREO 1. Esforço normal característico: PIL Esforço Esforço Peso Próprio por AR 1 (KN) 2 (KN) Pavimento (KN)
N° Esforço Pavime característico ntos Nk (KN)
P1
20,74
17,79
2,6845
4
P8
36,95
33,59
2,6845
4
P1 5
55,11
47,81
2,6845
4
PIL Esforço Esforço Peso Próprio por
Ỵ
n 1, 2 164,858 5 1, 2 292,898 5 1, 2 422,418 5
N° Esforço Pavime característico
Ỵ
Esforço de Ỵ cálculo Nd f (KN) 1 , 4 288,5015 1 , 4 512,5715 1 , 4 739,2315
Esforço de Ỵ cálculo Nd
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P19 P20
295 295
14 14
26 26
39,258 39,258
72,907 PILAR MEDIO 72,907 PILAR MEDIO
3. Momento fletor mínimo mínimo de de primeira primeira ordem:
PILAR Esforço de cálculo Nd (KN) b h M1d,min,x M1d,min,y e1x, min e1y, min P1 288,5015 14 26 657,78342 553,92288 2,28 1,92 P8 512,5715 14 26 984,13728 1168,66302 1,92 2,28 P15 739,2315 14 26 1419,32448 1685,44782 1,92 2,28
PILAR Esforço de cálculo Nd (KN) b h M1d,min,x M1d,min,y e1x, min e1y, min P12 547,5715 14 26 1248,46302 1051,33728 2,28 1,92 P19 235,3015 14 26 536,48742 451,77888 2,28 1,92 P20 543,1615 14 26 1238,40822 1042,87008 2,28 1,92
4. Esbeltez limite:
αbx αby PILAR MbX MaX MbY MaY MbX/MaX Mby/MaY P1 678,44 341,215 213,045 106,6975 1,988306493 1,996719698 0,4 1
PILAR Mb
Ma
Mb/Ma
αbx αby
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PILAR Esforço de cálculo Nd (KN) e1x e1y ƛlimX ƛlimY P1 288,5015 2,3516 0,738454 65,3264418 35 PILAR Esforço de cálculo Nd (KN) e1x e1y P8 512,5715 0,789012
ƛlimX
PILAR Esforço de cálculo Nd (KN) e1x P15 739,2315
ƛlimX
e1y
35
0
PILAR Esforço de cálculo Nd (KN) e1x e1y P12 547,5715 1,742581 P20 543,1615 0,397741
ƛlimY
35 ƛlimY
35
ƛlimX
35
ƛlimY
35 35
35 35
PILAR Esforço de cálculo Nd (KN) e1x e1y ƛlimX ƛlimY P19 235,3015 3,293073 0,283806 66,4580203 35
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5. Caso a comparação da esbeltez com a esbeltez limite demonstre que é necessário considerar os efeitos locais de segunda ordem, este pode ser calculado com base na metodologia do pilar-padrão com curvatura aproximada:
PILAR P1 P8 P15
Esforço de cálculo Nd Área do (KN) pilar 288,5015 364 512,5715 364 739,2315 364
PILAR P12 P19 P20
Esforço de cálculo Nd Área do (KN) pilar V 547,5715 364 0,702014744 235,3015 364 0,30166859 543,1615 364 0,696360897
V 0,369873718 0,657142949 0,947732692
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PILA Area do R pilar P1 P8 P15
Md, tot Md, tot x y 1450,58 364 678,44 9 2360,88 1909,98 364 2 7 3006,32 2539,98 364 9 9
PILA Area do R pilar P12 P19 P20
Md, tot Md, tot x y 2010,84 2467,18 364 3 7 1183,09 364 774,865 8 1998,22 2453,95 364 3 4
µx 0,03345 4 0,21619 8 0,27530 5
µx 0,09915 4 0,03820 8 0,09853 2
µy 0,13283 8 0,09418 1 0,12524 6
d/h em x 0,14423 1 0,26785 7 0,26785 7
d/h em y ωx ωy ω 0,26785 7 0 0 0 0,14423 0,7 0,1 0,7 1 2 5 2 0,14423 1,2 1,2 1 5 0,5 5
µy 0,22593 3 0,10834 2 0,22472 1
d/h em x 0,14423 1 0,14423 1 0,14423 1
d/h em y ωx ωy Ω 0,26785 0,1 0,8 0,8 7 8 5 5 0,26785 7 0 0 0 0,26785 0,1 0,8 0,8 7 8 5 5
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3.2 1° PAVIMENTO 1. Esforço normal característico: Esforço Esforço Peso Próprio por N° PILAR 1 (KN) 2 (KN) Pavimento (KN) Pavimentos P1 20,74 17,79 2,6845 3 P8 36,95 33,59 2,6845 3 P15 55,11 47,81 2,6845 3
Esforço característico Nk (KN) 123,6435 219,6735 316,8135
Esforço de cálculo Nd (KN) Ỵn Ỵf 1,25 1,4 216,3761 1,25 1,4 384,4286 1,25 1,4 554,4236
Esforço Esforço de Esforço Esforço Peso Próprio por N° característico cálculo Nd PILAR 1 (KN) 2 (KN) Pavimento (KN) Pavimentos Nk (KN) (KN) Ỵn Ỵf P12 44,76 30,78 2,6845 3 234,6735 1,25 1,4 410,6786
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PILAR P12 P19 P20
Esforço de cálculo Nd (KN) b 410,6786 176,4761 407,3711
h 14 14 14
M1d,min,x M1d,min,y e1x, min e1y, min 26 936,3473 788,503 2,28 1,92 26 402,3656 338,8342 2,28 1,92 26 928,8062 782,1526 2,28 1,92
4. Esbeltez limite: PILAR P1
MbX MaX MbY MaY MbX/MaX Mby/MaY αbx 1003,391 1003,391 317,3275 317,3275 1 1
PILAR P8
Mb Ma Mb/Ma 604,2575 604,2575 1
αbx
PILAR P15
Mb
αbx
Ma 0
Mb/Ma 0
0
αby
0,4
1 αby
1
1 αby
1
1
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PILAR P19
Esforço de cálculo Nd (KN) e1x e1y ƛlimX ƛlimY 176,4761 6,50027 0,566125 70,31282 35
PILAR P1 P8 P15
Considerar efeitos de 2 ordem em x não sim sim
Considerar efeitos de 2 ordem em y Sim Sim Sim
PILAR P12 P20 P19
Considerar efeitos de 2 ordem em x não sim não
Considerar efeitos de 2 ordem em y Sim Sim Sim
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P12 P19 P20
PILAR P1 P8 P15
PILAR P12 P19 P20
0,000187 0,000348 desconsiderar 0,000265 0,000492 desconsiderar 0,000188 0,000349 0,000188 Area do pilar
Area do pilar
0,000347919 desconsiderar 3,027766 1412,618 2031,942 0,00035714 desconsiderar 3,108011 1147,143 887,3239 0,000349362 1,637098 3,040326 1595,713 2020,693
Md, tot x 364 1003,391 364 1932,911 364 2487,659
Md, tot y 1087,942 1519,868 2030,406
µx 0,049477 0,177007 0,227808
µy 0,099628 0,074944 0,100119
d/h em x 0,144231 0,267857 0,267857
d/h em y ωx 0,267857 0,144231 0,144231
Md, tot x 364 1412,618 364 1147,143 364 1595,713
Md, tot y 2031,942 887,3239 2020,693
µx 0,069656 0,056565 0,078684
µy 0,186075 0,081257 0,185045
d/h em x 0,144231 0,144231 0,144231
d/h em y ωx 0,267857 0,267857 0,267857
ωy
0 0,4 0,7
ω
0,02 0 0,18
ωy
0 0 0
0,02 0,4 0,7
ω
0,5 0 0,5
0,5 0 0,5
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21
3.3 2° PAVIMENTO 1. Esforço normal característico: Esforço Esforço Peso Próprio por N° PILAR 1 (KN) 2 (KN) Pavimento (KN) Pavimentos P1 20,74 17,79 2,6845 2 P8 36,95 33,59 2,6845 2 P15 55,11 47,81 2,6845 2
Esforço característico Nk (KN) 82,429 146,449 211,209
Esforço de cálculo Nd (KN) Ỵn Ỵf 1,25 1,4 144,2508 1,25 1,4 256,2858 1,25 1,4 369,6158
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PILAR P1 P8 P15
Esforço de cálculo Nd (KN) b 144,2508 256,2858 369,6158
PILAR
Esforço de cálculo Nd (KN)
b
h
M1d,min,x M1d,min,y e1x, min e1y, min 26 328,8917 276,9614 2,28 1,92 26 492,0686 584,3315 1,92 2,28 26 709,6622 842,7239 1,92 2,28
h
M1d,min,x M1d,min,y e1x, min e1y, min
14 14 14
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PILAR P12 P20
Esforço de cálculo Nd (KN) e1x e1y 273,7858 5,159573 271,5808 1,189002
PILAR P19
Esforço de cálculo Nd (KN) e1x e1y ƛlimX ƛlimY 117,6508 9,750405 0,849187 74,21924 35
ƛlimX
68,70141 35
ƛlimY
35 35
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P15
0,000367 0,000197
0,000357
≤0,005/h em
PILAR P12 P19 P20
0,000192
3,108011 1,673578 1858,432 1461,305
≤0,005/h
1/r em x 1/r em y x em y e2x 0,000226 0,00042 0,0004 2 desconsiderar 0,000357 desconsiderar 0,000295 0,000549 desconsiderar 0,000357 desconsiderar 0,000227 0,000421 0,000192 0,000357 1,673578
e2y 3,108011 3,108011 3,108011
Md, tot x 1412,618 1147,143 1073,716
Md, tot y 1376,598 591,5492 1365,511
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26
3. Momento fletor mínimo mínimo de de primeira primeira ordem:
Esforço de cálculo Nd
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5. Caso a comparação da esbeltez com a esbeltez limite, demonstre que é
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682,755 0,01592 0,06252 0,14423 0,26785
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Paulista
(UNESP),
fev/2015,
78p.
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