Provas de concreto armado

Esta é uma pré-visualização de arquivo. Entre para ver o arquivo original

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 = 
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CAP1-PAG43.doc
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��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
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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.
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user
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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
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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