cálculo de lajes - rev. 01.xlsx

7/23/2019 Clculo de Lajes - Rev. 01.xlsx

1/49


2/49


3/49


4/49

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


5/49

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


6/49


7/49

cm


8/49

3,5

5m

5,00 m

fck = 20 Mpa

CA = 50

q = 6.5 kN/m


! = ".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


9/49

-( . 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


10/49

*

0.)") 2".(5)

v(


11/49

cm

cm


12/49

3,5

5m

2,30m

fck = 20 Mpa

CA = 50

q = 6.5 kN/m


! = 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


13/49

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


14/49

*

"5.')5


15/49

cm

cm

cm

cm


16/49

3,5

5m

4,00m

fck = 20 Mpa

CA = 50

q = 6.5 kN/m


! = ".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


17/49

-( . 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


18/49

*

0.2 "".)56

v(


19/49

cm

cm

cm


20/49

3,5

5m

4,30m

fck = 20 Mpa

CA = 50

q = 6.5 kN/m


! = ".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


21/49

-( . 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


22/49

*

0.2)( 2%.&06

v(


23/49

cm

cm


24/49

3,5

5m

2,20m

fck = 20 Mpa

CA = 50

q = 6.5 kN/m


! = 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


25/49

-( . 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


26/49

*

0.252 20.62

v(


27/49

cm

cm

cm


28/49

4,7

5m

5,00m

fck = 20 Mpa

CA = 50

q = 6.5 kN/m


! = (.&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


29/49

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


30/49


31/49


32/49

4,7

5m

3,00m

fck = 20 Mpa

CA = 50

q = 6.5 kN/m


! = ".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


33/49

-( . 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


34/49

*

0.252 20.62

v(


35/49

cm

cm


36/49

4,7

5m

3,30m

fck = 20 Mpa

CA = 50

q = 6.5 kN/m


! = "."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


37/49

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


38/49

*

"&.)%&


39/49

cm

cm


40/49

4,7

5m

5,00m

fck = 20 Mpa

CA = 50

q = 6.5 kN/m


! = (.&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


41/49

-( . 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


42/49

*

0.)%" "'.6%"

v(


43/49

cm


44/49

4,7

5m

1,50m

fck = 20 Mpa

CA = 50

q = 6.5 kN/m


! = ).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


45/49

cm

cm


46/49

4,7

5m

5,00m

fck = 20 Mpa

CA = 50

q = 6.5 kN/m


! = (.&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


47/49

-( . 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


48/49

*

0.)%" "'.6%"

v(


49/49

cm

cálculo de lajes - rev. 01.xlsx

Documents