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7/23/2019 Clculo de Lajes - Rev. 01.xlsx
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3,5
5m
5,00 m
fck = 20 Mpa
CA = 50
q = 6.5 kN/m
Agressividade = Urbano
! = ".55
# = 5.00
$ ="55
= %.%&5 cm = '.00 cm(0
E =5.00
= ).()".55
*
2).0 5(." '." 0.)%" 0.)%" 0.(66 20.65'
M! =q . +!,
= ".' kN.mm!
M# =q . +!,
= ).5 kN.m
m#
N! =q . +!,
= %.% kN.mn!
-) . q . ! = (.2 kN/m
-2 . q . ! = (.2 kN/m
-" . q . ! = )0.% kN/m
)0"2."
m! m# n! v) v2 v"
)=
2=
"=
q . +!,(
LAJE 1
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cs . $ . 1 "205'6.5
. .
6 = = )0%.")2 K3 = 0."("m!
6 = = 2%0.06" K3 = 0.""0m#
6 = = (&.'6& K3 = 0."&(n!
As =" . M!
= 2.05% cm/m)0 3 d
As =" . M#
= 0.&66 cm/m)0 3 d
As =" . N!
= 5.06% cm/m)0 3 d
)05. bw . d
)05. bw . d
)05. bw . d
46"0mm a cada )5cm
+Asmnimo
, = )20cm/m 7 46"mm a cada 26
4)000mm a cada )5cm
7/23/2019 Clculo de Lajes - Rev. 01.xlsx
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7/49
cm
7/23/2019 Clculo de Lajes - Rev. 01.xlsx
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3,5
5m
5,00 m
fck = 20 Mpa
CA = 50
q = 6.5 kN/m
Agressividade = Urbano
! = ".55
# = 5.00
$ ="55
= %.%&5 cm = '.00 cm(0
E =5.00
= ).()".55
2(.0 5).0 )0.) )2.6 0.")& 0.)%" 0.&)(
M! =q . +!,
= ".( kN.mm!
M# =q . +!,
= ).6 kN.m
m#
N! =q . +!,
= %.) kN.mn!
N# =q . +!,
= 6.5 kN.mn#
-) . q . ! = &." kN/m
-2 . q . ! = (.2 kN/m
-" . q . ! = )6.5 kN/m
m! m# n! n# v) v2 v"
)=
2=
"=
LAJE 2
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-( . q . ! = ".0 kN/m
f = )0"2." = 0.002%"& = 0.2%(cs . $ . 1 "6"'2(.)
6 = = )2".&%5 K3 = 0."(0m!
6 = = 26".0(" K3 = 0.""0m#
6 = = 52.0'" K3 = 0."6'n!
6 = = 6(.'%& K3 = 0."5%n#
As =" . M!
= ).&%5 cm/m)0 3 d
As = " . M# = 0.%)5 cm/m)0 3 d
As =" . N!
= (.60( cm/m)0 3 d
As =" . N#
= ".5%) cm/m)0 3 d
(=
q . +!,(
)05. bw . d
)05. bw . d
)05. bw . d
)05. b* . d
46"0mm a cada )&cm
+Asmnimo
, = )20cm/m 7 46"mm a cada 26
4)000mm a cada )&cm
4)000mm a cada 22cm
7/23/2019 Clculo de Lajes - Rev. 01.xlsx
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*
0.)") 2".(5)
v(
7/23/2019 Clculo de Lajes - Rev. 01.xlsx
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cm
cm
7/23/2019 Clculo de Lajes - Rev. 01.xlsx
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3,5
5m
2,30m
fck = 20 Mpa
CA = 50
q = 6.5 kN/m
Agressividade = Urbano
! = 2."0
# = ".55
$ =2"0
= 5.&50 cm = %.00 cm(0
E =".55
= ).5(2."
2&.6 &5.2 )2.5 )&.5 0.)(( 0."6' 0.25
M! =q . +!,
= ).2 kN.mm!
M# =q . +!,
= 0.5 kN.m
m#
N! =q . +!,
= 2.% kN.mn!
N# =q . +!,
= 2.0 kN.mn#
-) . q . ! = 2.2 kN/m
-2 . q . ! = 5.5 kN/m
-" . q . ! = ".& kN/m
m! m# n! n# v) v2 v"
)=
2=
"=
LAJE 3
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f =)%).'
= 0.000(65 = 0.0(6
cs . $ . 1 "')((2."
6 = = 2(2.%0' K3 = 0."")m!
6 = = 66).56% K3 = 0."25m#
6 = = )0'.'6% K3 = 0."()n!
6 = = )5".'55 K3 = 0.""5n#
As =" . M!
= 0.&50 cm/m)0 3 d
As =" . M#
= 0.2&0 cm/m
)0 3 d
As =" . N!
= ).&05 cm/m)0 3 d
As =" . N#
= ).)'& cm/m)0 3 d
q . +!,(
)05. bw . d
)05. bw . d
)05. bw . d
)05. b* . d
+Asmnimo
, = )20cm/m 7 46"mm a cada 26
+Asmnimo
, = )20cm/m 7 46"mm a cada 26
46"mm a cada )%cm
+Asmnimo
, = )20cm/m 7 46"mm a cada 26
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*
"5.')5
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cm
cm
cm
cm
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3,5
5m
4,00m
fck = 20 Mpa
CA = 50
q = 6.5 kN/m
Agressividade = Urbano
! = ".55
# = (.00
$ ="55
= %.%&5 cm = '.00 cm(0
E =(.00
= ).)"".55
"5.) ()." )2.& )".6 0.")& 0.)%" 0."(6
M! =q . +!,
= 2." kN.mm!
M# =q . +!,
= 2.0 kN.m
m#
N! =q . +!,
= 6.5 kN.mn!
N# =q . +!,
= 6.0 kN.mn#
-) . q . ! = &." kN/m
-2 . q . ! = (.2 kN/m
-" . q . ! = %.0 kN/m
m! m# n! n# v) v2 v"
)=
2=
"=
LAJE 4
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-( . q . ! = (.6 kN/m
f =)0"2."
= 0.002006 = 0.20)cs . $ . 1 5)(5").)
6 = = )%).0"6 K3 = 0.""(m!
6 = = 2)".0)" K3 = 0."")m#
6 = = 65.50" K3 = 0."5%n!
6 = = &0.)(5 K3 = 0."55n#
As =" . M!
= ).)'' cm/m)0 3 d
As =" . M#
= ).0)0 cm/m)0 3 d
As =" . N!
= ".55" cm/m)0 3 d
As =" . N#
= ".2'0 cm/m)0 3 d
(=
q . +!,(
)05. bw . d
)05. bw . d
)05. bw . d
)05. b* . d
+Asmnimo
, = )20cm/m 7 46"mm a cada 26
+Asmnimo
, = )20cm/m 7 46"mm a cada 26
4)000mm a cada 22cm
4)000mm a cada 2(cm
7/23/2019 Clculo de Lajes - Rev. 01.xlsx
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*
0.2 "".)56
v(
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cm
cm
cm
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3,5
5m
4,30m
fck = 20 Mpa
CA = 50
q = 6.5 kN/m
Agressividade = Urbano
! = ".55
# = (."0
$ ="55
= %.%&5 cm = '.00 cm(0
E =(."0
= ).2)".55
"0.0 ((.0 )).5 )".) 0.")& 0.)%" 0."&
M! =q . +!,
= 2.& kN.mm!
M# =q . +!,
= ).' kN.m
m#
N! =q . +!,
= &.) kN.mn!
N# =q . +!,
= 6." kN.mn#
-) . q . ! = &." kN/m
-2 . q . ! = (.2 kN/m
-" . q . ! = %.5 kN/m
m! m# n! n# v) v2 v"
)=
2=
"=
LAJE 5
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-( . q . ! = (.' kN/m
f =)0"2."
= 0.002")& = 0.2"2cs . $ . 1 ((5(&".%
6 = = )5(.&") K3 = 0.""5m!
6 = = 226.'"' K3 = 0."")m#
6 = = 5'.")( K3 = 0."6"n!
6 = = 6&.566 K3 = 0."5%n#
As =" . M!
= ).(0& cm/m)0 3 d
As =" . M#
= 0.'(% cm/m)0 3 d
As =" . N!
= ".'&% cm/m)0 3 d
As =" . N#
= ".((( cm/m)0 3 d
(=
q . +!,(
)05. bw . d
)05. bw . d
)05. bw . d
)05. b* . d
46"0mm a cada 22cm
+Asmnimo
, = )20cm/m 7 46"mm a cada 26
4)000mm a cada 20cm
4)000mm a cada 2"cm
7/23/2019 Clculo de Lajes - Rev. 01.xlsx
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*
0.2)( 2%.&06
v(
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cm
cm
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3,5
5m
2,20m
fck = 20 Mpa
CA = 50
q = 6.5 kN/m
Agressividade = Urbano
! = 2.20
# = ".55
$ =220
= 5.500 cm = %.00 cm(0
E =".55
= ).6)2.2
20.' 55.0 '.2 )2." 0.")& 0.)%" 0.("6
M! =q . +!,
= ).5 kN.mm!
M# =q . +!,
= 0.6 kN.m
m#
N! =q . +!,
= ".( kN.mn!
N# =q . +!,
= 2.6 kN.mn#
-) . q . ! = (.5 kN/m
-2 . q . ! = 2.6 kN/m
-" . q . ! = 6.2 kN/m
m! m# n! n# v) v2 v"
)=
2=
"=
LAJE 6
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-( . q . ! = ".6 kN/m
f = )52." = 0.0006&% = 0.06%cs . $ . 1 22(&(0.)
6 = = 200.'62 K3 = 0."""m!
6 = = 52%.%(6 K3 = 0."26m#
6 = = %%.(62 K3 = 0."(&n!
6 = = ))%.26' K3 = 0."(0n#
As =" . M!
= 0.')) cm/m)0 3 d
As = " . M# = 0.""' cm/m)0 3 d
As =" . N!
= 2.)5& cm/m)0 3 d
As =" . N#
= ).5%) cm/m)0 3 d
(=
q . +!,(
)05. bw . d
)05. bw . d
)05. bw . d
)05. b* . d
+Asmnimo
, = )20cm/m 7 46"mm a cada 26
+Asmnimo
, = )20cm/m 7 46"mm a cada 26
46"0mm a cada )(cm
46"0mm a cada )'cm
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*
0.252 20.62
v(
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cm
cm
cm
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4,7
5m
5,00m
fck = 20 Mpa
CA = 50
q = 6.5 kN/m
Agressividade = Urbano
! = (.&5
# = 5.00
$ =(&5
= )).%&5 cm = )2.00 cm(0
E =5.00
= ).05(.&5
*
2'." ().2 )).' 0.)%" 0.(02 0.2"2 2'.'(
M! =q . +!,
= 5.0 kN.mm!
M# =q . +!,
= ".6 kN.m
m#
N! =q . +!,
= )2." kN.mn!
-) . q . ! = 5.& kN/m
-2 . q . ! = )2.( kN/m
-" . q . ! = &.2 kN/m
""0%.'
m! m# n! v) v2 v"
)=
2=
"=
q . +!,(
LAJE 7
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cs . $ . 1 ))0)""0.0
. .
6 = = )%0."0% K3 = 0.""(m!
6 = = 25".5"% K3 = 0.""0m#
6 = = &".2") K3 = 0."5"n!
As = " . M! = ).&60 cm/m)0 3 d
As =" . M#
= ).2"6 cm/m)0 3 d
As =" . N!
= (.5&' cm/m)0 3 d
)05. bw . d
)05. bw . d
)05. bw . d
46"0mm a cada )&cm
46"0mm a cada 25cm
4)000mm a cada )&cm
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4,7
5m
3,00m
fck = 20 Mpa
CA = 50
q = 6.5 kN/m
Agressividade = Urbano
! = ".00
# = (.&5
$ ="00
= &.500 cm = %.00 cm(0
E =(.&5
= ).5%"
20.' 55.0 '.2 )2." 0.")& 0.)%" 0.("6
M! =q . +!,
= 2.% kN.mm!
M# =q . +!,
= ).) kN.m
m#
N! =q . +!,
= 6.( kN.mn!
N# =q . +!,
= (.% kN.mn#
-) . q . ! = 6.2 kN/m
-2 . q . ! = ".6 kN/m
-" . q . ! = %.5 kN/m
m! m# n! n# v) v2 v"
)=
2=
"=
LAJE 8
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-( . q . ! = (.' kN/m
f =526.5
= 0.002"(" = 0.2"(cs . $ . 1 22(&(0.)
6 = = )0%.0&" K3 = 0."("m!
6 = = 2%(.(02 K3 = 0.""0m#
6 = = (&.5&" K3 = 0."&6n!
6 = = 6".60" K3 = 0."5'n#
As =" . M!
= ).&(6 cm/m)0 3 d
As =" . M#
= 0.6"% cm/m)0 3 d
As =" . N!
= (."(& cm/m)0 3 d
As =" . N#
= ".)0( cm/m)0 3 d
(=
q . +!,(
)05. bw . d
)05. bw . d
)05. bw . d
)05. b* . d
46"0mm a cada )%cm
+Asmnimo
, = )20cm/m 7 46"mm a cada 26
4)000mm a cada )%cm
4%00mm a cada )6cm
7/23/2019 Clculo de Lajes - Rev. 01.xlsx
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*
0.252 20.62
v(
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cm
cm
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4,7
5m
3,30m
fck = 20 Mpa
CA = 50
q = 6.5 kN/m
Agressividade = Urbano
! = "."0
# = (.&5
$ =""0
= %.250 cm = '.00 cm(0
E =(.&5
= ).(("."
2'.0 &).' )2.% )&.5 0.)(( 0."5' 0.25
M! =q . +!,
= 2.( kN.mm!
M# =q . +!,
= ).0 kN.m
m#
N! =q . +!,
= 5.5 kN.mn!
N# =q . +!,
= (.0 kN.mn#
-) . q . ! = ".) kN/m
-2 . q . ! = &.& kN/m
-" . q . ! = 5.( kN/m
m! m# n! n# v) v2 v"
)=
2=
"=
LAJE 9
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f =&&0.%
= 0.00)""6 = 0.)"(
cs . $ . 1 5&&0%6.)
6 = = )&".0'5 K3 = 0.""(m!
6 = = (2'.)55 K3 = 0."2&m#
6 = = &6.(00 K3 = 0."52n!
6 = = )0(.(5( K3 = 0."("n#
As =" . M!
= ).25( cm/m)0 3 d
As =" . M#
= 0.('5 cm/m
)0 3 d
As =" . N!
= 2.''5 cm/m)0 3 d
As =" . N#
= 2.)"( cm/m)0 3 d
q . +!,(
)05. bw . d
)05. bw . d
)05. bw . d
)05. b* . d
46"0mm a cada 25cm
+Asmnimo
, = )20cm/m 7 46"mm a cada 26
4%00mm a cada )6cm
4%00mm a cada 2"cm
7/23/2019 Clculo de Lajes - Rev. 01.xlsx
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*
"&.)%&
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cm
cm
7/23/2019 Clculo de Lajes - Rev. 01.xlsx
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4,7
5m
5,00m
fck = 20 Mpa
CA = 50
q = 6.5 kN/m
Agressividade = Urbano
! = (.&5
# = 5.00
$ =(&5
= )).%&5 cm = )2.00 cm(0
E =5.00
= ).05(.&5
(0.2 (0.2 )(." )(." 0.")& 0.)%" 0.")&
M! =q . +!,
= ".6 kN.mm!
M# =q . +!,
= ".6 kN.m
m#
N! =q . +!,
= )0." kN.mn!
N# =q . +!,
= )0." kN.mn#
-) . q . ! = '.% kN/m
-2 . q . ! = 5.& kN/m
-" . q . ! = '.% kN/m
m! m# n! n# v) v2 v"
)=
2=
"=
LAJE 10
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-( . q . ! = 5.& kN/m
f =""0%.'
= 0.00226& = 0.22&cs . $ . 1 )(5'&22.)
6 = = 2(&."%5 K3 = 0.""0m!
6 = = 2(&."%5 K3 = 0.""0m#
6 = = %%.000 K3 = 0."(&n!
6 = = %%.000 K3 = 0."(&n#
As =" . M!
= ).26& cm/m)0 3 d
As =" . M#
= ).26& cm/m)0 3 d
As =" . N!
= ".&(6 cm/m)0 3 d
As =" . N#
= ".&(6 cm/m)0 3 d
(=
q . +!,(
)05. bw . d
)05. bw . d
)05. bw . d
)05. b* . d
46"0mm a cada 2(cm
46"0mm a cada 2(cm
4)000mm a cada 2)cm
4)000mm a cada 2)cm
7/23/2019 Clculo de Lajes - Rev. 01.xlsx
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*
0.)%" "'.6%"
v(
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cm
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4,7
5m
1,50m
fck = 20 Mpa
CA = 50
q = 6.5 kN/m
Agressividade = Urbano
! = ).50
# = (.&5
$ =)50
= ".&50 cm = %.00 cm(0
E =(.&5
= ".)&).5
M =q . +!,
= ).0 kN.m)(.22
N =q . +!,
= 7).% kN.m%
6 = = 2'(.)2" K3 = 0."2'M
6 = = )65.(&0 K3 = 0.""5N
As =" . M
= 0.6)5 cm/m)0 3 d
Espaamento mnimo = 2 x h ou 20cm = (6,3mm a cada 16cm - 1,96cm/m
As = " . N = ).))" cm/m)0 3 d
)05. bw . d
)05. bw . d
+Asmnimo
, = )20cm/m 7 46"mm a cada 26
+Asmnimo
, = )20cm/m 7 46"mm a cada 26
!s"
= 0,2 x 1,96 = 0,392 ou 0,90cm/m (o meno# = !s"
= 0,392 ($,0mm a cada 30cm
LAJE 11
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cm
cm
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4,7
5m
5,00m
fck = 20 Mpa
CA = 50
q = 6.5 kN/m
Agressividade = Urbano
! = (.&5
# = 5.00
$ =(&5
= )).%&5 cm = )2.00 cm(0
E =5.00
= ).05(.&5
(0.2 (0.2 )(." )(." 0.")& 0.)%" 0.")&
M! =q . +!,
= ".6 kN.mm!
M# =q . +!,
= ".6 kN.m
m#
N! =q . +!,
= )0." kN.mn!
N# =q . +!,
= )0." kN.mn#
-) . q . ! = '.% kN/m
-2 . q . ! = 5.& kN/m
-" . q . ! = '.% kN/m
m! m# n! n# v) v2 v"
)=
2=
"=
LAJE 12
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-( . q . ! = 5.& kN/m
f = ""0%.' = 0.00226& = 0.22&cs . $ . 1 )(5'&22.)
6 = = 2(&."%5 K3 = 0.""0m!
6 = = 2(&."%5 K3 = 0.""0m#
6 = = %%.000 K3 = 0."(&n!
6 = = %%.000 K3 = 0."(&n#
As =" . M!
= ).26& cm/m)0 3 d
As = " . M# = ).26& cm/m)0 3 d
As =" . N!
= ".&(6 cm/m)0 3 d
As =" . N#
= ".&(6 cm/m)0 3 d
(=
q . +!,(
)05. bw . d
)05. bw . d
)05. bw . d
)05. b* . d
46"0mm a cada 2(cm
46"0mm a cada 2(cm
4)000mm a cada 2)cm
4)000mm a cada 2)cm
7/23/2019 Clculo de Lajes - Rev. 01.xlsx
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*
0.)%" "'.6%"
v(
7/23/2019 Clculo de Lajes - Rev. 01.xlsx
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cm