calculo de viga 4

8/17/2019 Calculo de Viga 4

1/32

VIGA DE SEÇÃO RETANGULAR SEM ARMADURA DE COMPRESSÃODados MPA

fc 2.00 (KN/cm2) 20

fy 50.00 (KN/cm2) 500 1.0 (adm)

1.15 (adm)fc 1.! (KN/cm2)

fy !." (KN/cm2) 434.7826087

E ### (KN/cm2) 210000

$ 20.00 (cm)% 5.00 (cm)d 2.00 (cm)

M ### (KN.cm)

Mo&'()o L*&*)' S' fcd+,!-5 S' fcd!-5

M ### (KN.cm2) 13708.8 11491.2

L*(%a N'/)a Cac/ado Vao M3 0.42 (adm) 0.4210549717 0.5

4ao da Aa6a(ca 0.83 (adm)

Vao Ad&. Da A&ad/a S' 43+,0-257 S' 430-257 1.00 (adm) 1 2.324415186 1

Cc/o da A&ad/a Diâmetro arra! ec.

A 7.90 (cm2) 20 2.5153933374

A&ad/a M8(*&a Vao M*(. 1 Vao M*(. 2

A 1.35 1.035 1.35

V'*f*ca9o V'*f*ca9o 1.00 (adm) Pa!!o$ o te!te

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Rd1*&

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2/32

VIGA DE SEÇÃO RETANGULAR COM ARMADURA DE COMPRESSÃODados

fc 2.00 (KN/cm2) 20MPA

fy 50.00 (KN/cm2) %A&50A 1.0 (adm)

1.15 (adm)fc 1.! (KN/cm2)

fy !." (KN/cm2)

E 21000.00 (KN/cm2)

$ 15.00 (cm)% 2".00 (cm)d 2!.!= (cm)d> .2? (cm)

M 050.00 (KN.cm)

Mo&'()o L*&*)' S' fcd+,!-5 S' fcd!-5

M 3183.31 (KN.cm2) 3183.3145029 2668.3665686

Mo&'()o R's*s). A>s

M 866.69 (KN.cm2)



Vao Ad&. Da A&. Co&@. S' 43+,0-257 S' 430-257 1.00 (adm) 0.3071193838 1.0749178434 1

Vao Ad&. Da A&. Tac. S' 43+,0-257 S' 430-257 1.00 (adm) 1 1.6905 1

Cc/o da A&ad/a Co&@. D*&')o 4aas ('c.

A 1.04 (cm2) 12.5 0.8497753714

Cc/o da A&ad/a d' Tac. D*&')o 4aas ('c.

A 4.96 20 1.5784880313

A&ad/a M8(*&a Vao M*(. 1 Vao M*(. 2

A 0.63 0.483 0.63

V'*f*ca9o V'*f*ca9o 1.00 (adm) Pa!!o$ o te!te

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Rd1*&

Rd2

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3/32

V'*f*ca9o da D*s@os*9o das A&ad/asDado!

% 2" (cm)d 2!.!= (cm)dB .255 (cm)

$ 15 (cm)

C ! (cm)

0.?! (cm)

d 1.7 (cm)

V'*f*ca9o d' a% ' a6

2

g 2

a 3.74 (cm) Pa!!o$ o te!te

' 2.3 (cm)

' 2 (cm)

a ' 2 (cm)

D')'&*(a9o da A)/a )*

' 2.8

' 1 K

( g As Ca&ada a6 y Asy

d 23.37 (cm) 1 2 3.1 1 2 1 3.1416

d 23.37 (cm) 2 2 3.1 1 2 1 3.1416Passo/ (o )'s)' 3 0 2 &2 0

4 0 2 &2 0

5 0 2 &2 0

6 0 2 &2 0

7 0 2 &2 08 0 2 &2 0

om

t

ma*

+

,

-

ca+c

adt


4/32

9 0 2 &2 0gg 6.3 gg 6.2832

D')'&*(a9o d' d>

' 0.625

( g As Ca&ada a6 y Asy

d 4.255 (cm) 1 1.25 1.2 1 2 0.625 0.76699

d 4.255 (cm) 2 1.25 1.2 1 2 0.625 0.76699Passo/ (o )'s)' 3 0 2 &2 0

4 0 2 &2 0

5 0 2 &2 0

6 0 2 &2 0

7 0 2 &2 08 0 2 &2 0

9 0 2 &2 0gg 2.5 gg 1.53398

ca+c

adt


5/32

'39o S*&@'s F A&ad/a Ta(s6'saDados

fc 2.50 (KN/cm2) 25

fy 50.00 (KN/cm2) %A&50A 1.0 (adm)

1.15 (adm)fc 1.=7 (KN/cm2)

fy !.== (KN/cm2)

E 21000.00 (KN/cm2)

$ 15.00 (cm)% 2".00 (cm)d 2!.!= (cm)d> .2? (cm)

V 5?.=0 (KN)

g 0.?! (cm)! 17 (cm)

Vd2 0.9

V 152.11!??0= (KN)

Vd!

f 1.28 (MPA) 0.128248196 (KN/cm2)

V 26.97 (KN)

%a+c$+ado Ma*

f 43.48 (KN/cm2) 43.47826087 43.5

V 30.01 (KN)

V 56.98 (KN)

V'*f*ca9o do 'f'*)o co)a()'

56.70 KN

152.1136607 (KN) Pa!!o$ o te!te

56.98 (KN) Pa!!o$ o te!te

V'*f*ca9o do co'f*c*'()' d' A&ad/a

18.89881575 MPA

Ma*

500 MPA 500 500

g 0.789703992 0.0075595263Pa!!o$ o te!te

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Sd

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62

Rd2

c)d

c

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s;

Rd!

!d

d2

d3

ctm

!


6/32

Ad'(c*a '()' co(c')o ' ao.Dados

fc 2.50 (KN/cm2)

fy 50.00 (KN/cm2) 1.0 (adm)

1.15 (adm)fc 1.=7 (KN/cm2)

fy !.== (KN/cm2)

E 21000.00 (KN/cm2)L 500.00 (cm)

$ 20.00 (cm)% ?0.00 (cm)d 5. (cm)d> 5.5? (cm)

V ".00 (KN)g 1.25 (cm)

! 17 (cm)g 1 2.25 (adm)g 2 1 (adm)g 3 1 (adm)

Cc/o d' f$d

0.288558 (KN/cm2) 8.54988

Co&@*&'()o d' A(coaH'&+ 47.40158 (cm)

Mo&'()o R's*s)'()'g 1.25 (cm)

2 ( arra!)

A 2.454375 (cm2)

g 0.967498 (a+a-aca)

M 5658.297 (KN.cm)

D*aHa&as* Mrd

0 0

47.40158 &5658.297

452.60 &5658.297

500.00 0

:

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c

s

d

d

s

;

Sd

d

!

d1

0 100 200 300 400 500 600

&3000

&2000

&1000

0 0 0


7/32

A@o*os '3)&os d' 6*Hasa + 54.44 (cm) deca+aem do diarama

, 20 (cm)

c 3 (cm)

+ 17 (cm)

A !e 6.14 (cm2)

Cc/o d' $ M*imo!

:+

om

ma*

&6000

&5000

&4000

&5658.2966458958 &5658.2966458958


8/32

+ 1."15"= (cm) 14.81587 1.184082 12.5 10

Pa!!o$ o te!te (;' +ma*)

+ 17 cm

Cc/o d' As-('c

A 1.919123

Co&@aa9o '()' $ ' As'f

+ 17 (cm)

A 5.351144 (cm2) ($ti+iado a eo +ec)

ec

!ec

!e


9/32


10/32


11/32


12/32

La's Mac*as

Para +a?e! em o etre a maior e a meor dime!>o or !$:erior a 2 ca+c$+e como -ia

V8(c/os

CaHas A)/a()'s (as a's%ara! Permaete!

Peramete! ()

%om: g , @ota+

%ara! Acidetai! :: 25 0.12 3

cotra:i!o 21 0.01 0.21

taco 0.65

!!o 12.5 0.01 0.125

@ota+ 3.985

Acidetai! (:) 2

6.5

d 9.1

D')'&*(a9o dos 'sfoos JC


13/32

Para $ti+iar a! Brm$+a! de armad$ra C10

T*@o 1

.00 (m)

5.00 (m)

@ 7.1 (KN/m2) 1.25

m* m m* m

15.9 9.157233 6.5 0 0

22.4 (KN.m/m) (KN.m/m) (KN.m/m) (KN.m/m) 0

0

14.3

T*@o 2

.00 (m)

5.00 (m)

@ 7.1 (KN/m) 1.25

m* m m* m

20.2 7.207921 6.169492 0 14.85714

23.6 (KN.m/m) (KN.m/m) (KN.m/m) (KN.m/m)

0

9.8

18.7

T*@o 3

.00 (m)

5.00 (m)

@ 7.1 (KN/m) 1.25

m* m m* m

21.4 6.803738 4.136364 14.707071 0


9.9

0

23.8

T*@o 4

.00 (m)

5.00 (m)

*

*

*

a

*

*

*

a

*

*

*

a

*


14/32

@ 7.1 (KN/m) 1.25

m* m m* m

26.2 5.557252 5.578544 0 13.11712


0

11.1

24.5

T*@o 5

.00 (m)

5.00 (m)

@ 7.1 (KN/m) 1.25

m* m m* m

26.4 5.515152 3.020747 11.464567 0 48.2 (KN.m/m) (KN.m/m) (KN.m/m) (KN.m/m)

12.7

0

37.9

T*@o 6

.00 (m)

5.00 (m)

@ 7.1 (KN/m)

1.25m* m m* m

24.9 5.84739 4.232558 13.117117 11.28682


11.1

12.9

28.2

T*@o 7

.00 (m)

5.00 (m)@ 7.1 (KN/m)

1.25

m* m m* m

29.5 4.935593 3.052411 10.785185 8.32


13.5

17.5

42.5

T*@o 8 .00 (m)

*

*

a

*

*

*

a

*

*

*

a

*

*

*

a

*


15/32

5.00 (m)

@ 7.1 (KN/m) 1.25

m* m m* m

29.8 4.885906 4.033241 11.464567 10.78519


12.7

13.5

33.8

T*@o 9

.00 (m)

5.00 (m)

@ 7.1 (KN/m) 19.7 1.25

m* m m* m 33.4 4.359281 2.883168 9.7718121 8.225989


14.9

17.7

47.6

A&ad/a d' f'39o @i:o

Dados MPA &3 5.515152

fc 2.50 (KN/cm2) 25 &y 3.020747

fy ?0.00 (KN/cm2) 600 &$3 11.46457

1.0 (adm) &$y 0

1.15 (adm)

fc 1.=7 (KN/cm2)

fy 52.1= (KN/cm2) 521.7391

E 21000.00 (KN/cm2) 210000

$ 100.00 (cm)

% 12.00 (cm)

1.00

1.00 (cm)c 2.50 (cm)

.00 (m)

5.00 (m)

d ".00 (cm)

M 25?.00 (KN.cm/m)

Mo&'()o L*&*)' ' fcd+,!- S' fcd!-5

M 3108.57 (KN.cm/m) 3108.571 2605.7143


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16/32


Vao Ad&. Da A&ad/a ' 43+,0-25 ' 430-257 1.00 (adm) 1 40.785748

Cc/o da A&ad/a 4aas ('c.

A 0.62 (cm2) 10 0.7914886

A&. N'Ha)*6a M8(*&a

A 1.44

A&. Pos*)*6a P*(c*@a M8(*&a

A 0.94

A&. Pos*)*6a S'c. M8(*&a M3*&o '()'0.2875

A 0.90 0.9 0.7392857

Es@aa&'()o P*(c*@a

s 7 (cm)

s 20.00 (cm)

Es@aa&'()o S'c/(d*a

s 10.00 (cm)

s 33.00 (cm)

V'*f*ca9o V'*f*ca9o

1.00 (adm) Pa!!o$ o te!te

U(*fo&*


17/32

Co&@*&'()o das $aas Armad$ra Po!iti-a

C 5.34 (m)

$ 20 (cm)

$ 20 (cm)C 4.34 (m)

$ 20 (cm)

$ 20 (cm)

Armad$ra Neati-a

4 (m)

C 2 (m)

Ea?e! em a+a=o

3 (m)

3 (m)

C 6 (m)

R'a's d' A@o*o

*

1

2

*

*1

*2

*

*

a+

4

3


18/32

1 45 () P0 0 0

2 30 () P1 4 0

3 30 () P2 4 5

4 45 () P3 0 5

4 (m) P4 1.4641016 1.464102

5 (m) P5 1.4641016 3.535898

A 1 2.92820323 (m2)

A 2 8.966679 (m2)

A 3 2.92820323 (m2)

A 4 5.17691454 (m2)

6.66166235 (KN/m)

16.3193558 (KN/m)

6.66166235 (KN/m)

9.42198446 (KN/m)

*

-1

-2

-3

-4

2

1

A1

A2 A4


19/32


20/32


21/32


22/32

1 2 3

4 5 6

7 8 9


23/32


24/32

%+c$+o de A1

P0 0 0 1.071797

P4 1.464102 1.464102 1.856406

P1 4 0 0

P0 0 0 2.72"20!%+c$+o de A2


25/32

P2 4 0 &1.856406

P4 1.464102 1.464102 0

P5 1.464102 3.535898 10.82309

P3 4 5 ".7???=7

%+c$+o de A3

P3 0 5 20

P2 4 5 &10.82309

P5 1.464102 3.535898 &6.248711

P3 0 5 2.72"20!

%+c$+o de A4

P0 0 0 0

P3 0 5 6.248711

P5 1.464102 3.535898 0

P4 1.464102 1.464102 &1.071797P0 0 0 5.1=?715


26/32

P*a'sDados

fc 2.50 (KN/cm2)

fy 50.00 (KN/cm2) 1.0 (adm) 1.15 (adm)

fc 1.=7 (KN/cm2)

fy !.== (KN/cm2)

E 21000.00 (KN/cm2)

E 2"00.00 (KN/cm2)

E 2!"0.00 (KN/cm2)( 1 .00 (adare!)( 2 !.00 (:r$mada!)

1200.00 (cm)P*a's$ 20 (a dire=>o do carreameto)% 0 (a dire=>o do carreameto)

V*Has$ 20 (a dire=>o do carreameto)% 50 (a dire=>o do carreameto)Ca'Ha&'()os

< 15 (KN/m)

< 20 (KN/m)

< 5 (KN/m)

Pa&')o d' I(s)a$**dad'(F!ar Gtoo+)

NK' 750 KN d' =-2 &&(aa+i!ar !em a a=>o do -eto) (aa+i!ar !em a! a=He! ormai!)

20, 1??Ic 7623826.66666667

(i*ar a +ar$ra e admitir a a+t$ra)

(atJ atiir o me!mo de!+ocameto)

gg 0.24397 * 0.6 Es)/)/a d' (s f*3os

:

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c

s

d

d

s

c*

cs

)o)

co

ti:o

-eto

72mm


27/32

I&@'f'*'s Go$a*sFD'sa@/&o 12 (m)g 1 0.00288675

1

g 0.005

g 0.0025

Passo/ (o )'s)'

g 0.00235702

I&@'f'*'s Loca*sFD'sa@/&o d' 1 a(c'

i 3g 1 0.0057735

0

g 0.005

g 0.00333333

N9o Passo/ (o )'s)'

Mo&'()o &8(*&o d' 1 Od'&FCo(s*d'a's das I&@'f'*'s Loca*s

% 0. (m) (e=>o tra!-. do :i+ar)

' 0.027 (m)ea/ 0.01118034

0

e 0.0025

e 0.0017

N9o Passo/ (o )'s)'

Ce >o :a!!ar o te!te $ti+iar o -a+or !$:erior

ea/ 0.025ea 0.01 (m)

a+or da e*cetridade 1L rdem

ea c 0.027 (m)

A(*s' d' 's)/)/as d' (s f*3os

!

i

a

!

i

1mi

a!

ai

Na! e!tr$t$ra! de B! i*o! o c+c$+o :ode !er rea+iado co!iderado cada e+emeto i!o+adametecomo arra! -ic$+ada! a! e*trmidade! ao! demai! e+emeto!.


28/32

A(*s' d' ''&'()os *soados% 0. (m)

% 0.2 (m)

% 0.? (m) 0 5 (m) 5 (m)

5 (m)

5 (m)

86.5 (adm)

28.8333333 (adm)

D*s@'(sa d' a(*s' d' 'f'*)os d' 2 od'& '& ''&'()os *soados

N 12"7 (KN)

M 1500 (KN.cm)M 1000 (KN.cm)

M 2=0?.7 (KN.cm)

M 2500 (KN.cm)

M 1500 (KN.cm)

M 25!.= (KN.cm)

a1) a2)

) c)

*

*

*

d

1A*

1*

1d*mi

1A

1

1dmi


29/32


30/32

Caso a2K

Cc/o d' afa J3-yKM1a M1d-&*( M1aM1d- afa$

1 1500 2706.9 a+a'1 1

1 2500 4253.7 a+a'1 1

Cc/o d' ' J3-yK

' 1.16369279 (cm)

' 1.93948798 (cm)Cc/o da 's$')'< 1 J3-yK a&$*da !5 +70 C%'ca

!5 %o!iderar 2L rdem 25.72731 ;35 ;90 Gora da Gai*a

!5 Di!:e!ar 2L ordem 25.40406 ;35 ;90 Gora da Gai*a

D')'&*(a9o dos 'f'*)os d' 2 Od'&.

MQ)odo a@o3. 1 F P*a @adao co& c/6a)/a a@o3*&ada JEs$.+70 a@'(asK

A 1200 (cm2) 0.60153333 (adm)

1 0.00025 (adm)

1 8.333&005 (adm)

M 2706.9

M 4253.7

M 10763.15 (KN.cm)

M 6939.11667 (KN.cm)

' 8.35 (cm)

' 0 (cm)

MQ)odo a@o3*&ado 2 F P*a @ad9o co& *H*d'< : a@o3*&ada.

$ &7597.3794 (adm)

c &13956776 (adm)

M 9126.61801 (KN.cm)

$ 7865.47352 (adm)

c &65796232 (adm)

M 5081.8431 (KN.cm)

' 7.08038635 (cm)

' 0 (cm)

*

1*

1

1*

1

c

*

1d*a

1da

d*tota+

dtota+

*

*

*

d*tot

dtot

*tot

tot


31/32

D*&'(s*o(a&'()o d' P*a'sF ELU

Cc/o da A&ad/a M8(*(a

A !mi 4.8 (cm2)

Cc/o da A&ad/a M3*&a

A !ma* 96 (cm2)

D')'&*(a9o dos co'f*c*'()'s

0.60153333

' 7.08038635

' 1.93948798

0.21295442

0.01944444 0.2 (aco)

A 20.5620288

*

*

!


32/32

calculo de viga 4

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