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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
:
:
c
s
d
d
s
;
Sd
Rd1*&
3
<
s
s
s&*(
s
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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)
L*(%a N'/)a Cac/ado Vao M3 0.50 (adm) 0.5 0.5
4ao da Aa6a(ca 0.80 (adm)
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
:
:
c
s
d
d
s
;
Sd
Rd1*&
Rd2
3
<
>s
s
>s
s
s&*(
s
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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
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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
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'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
:
:
c
s
d
d
s
;
Sd
+
62
Rd2
c)d
c
y;d
s;
Rd!
!d
d2
d3
ctm
!
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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
:
:
c
s
d
d
s
;
Sd
d
!
d1
0 100 200 300 400 500 600
&3000
&2000
&1000
0 0 0
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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
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+ 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) ($ti+iado a eo +ec)
ec
!ec
!e
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La's Mac*as
Para +a?e! em o etre a maior e a meor dime!>o or !$: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
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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
35.2 (KN.m/m) (KN.m/m) (KN.m/m) (KN.m/m)
9.9
0
23.8
T*@o 4
.00 (m)
5.00 (m)
*
*
*
a
*
*
*
a
*
*
*
a
*
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@ 7.1 (KN/m) 1.25
m* m m* m
26.2 5.557252 5.578544 0 13.11712
26.1 (KN.m/m) (KN.m/m) (KN.m/m) (KN.m/m)
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
34.4 (KN.m/m) (KN.m/m) (KN.m/m) (KN.m/m)
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
47.7 (KN.m/m) (KN.m/m) (KN.m/m) (KN.m/m)
13.5
17.5
42.5
T*@o 8 .00 (m)
*
*
a
*
*
*
a
*
*
*
a
*
*
*
a
*
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5.00 (m)
@ 7.1 (KN/m) 1.25
m* m m* m
29.8 4.885906 4.033241 11.464567 10.78519
36.1 (KN.m/m) (KN.m/m) (KN.m/m) (KN.m/m)
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
50.5 (KN.m/m) (KN.m/m) (KN.m/m) (KN.m/m)
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
L*(%a N'/)a Cac/ado Vao M3 0.03 (adm) 0.033387 0.5
*
*
a
*
*
*
a
c
!
d
d
!
+ma*
+
om
*
d
Rd1*&
3
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4ao da Aa6a(ca 0.99 (adm)
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&*
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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$ra Neati-a
4 (m)
C 2 (m)
Ea?e! em a+a=o
3 (m)
3 (m)
C 6 (m)
R'a's d' A@o*o
*
1
2
*
*1
*2
*
*
a+
4
3
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1 45 () P0 0 0
2 30 () P1 4 0
3 30 () P2 4 5
4 45 () P3 0 5
4 (m) P4 1.4641016 1.464102
5 (m) P5 1.4641016 3.535898
A 1 2.92820323 (m2)
A 2 8.966679 (m2)
A 3 2.92820323 (m2)
A 4 5.17691454 (m2)
6.66166235 (KN/m)
16.3193558 (KN/m)
6.66166235 (KN/m)
9.42198446 (KN/m)
*
-1
-2
-3
-4
2
1
A1
A2 A4
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1 2 3
4 5 6
7 8 9
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%+c$+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$+o de A2
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P2 4 0 &1.856406
P4 1.464102 1.464102 0
P5 1.464102 3.535898 10.82309
P3 4 5 ".7???=7
%+c$+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$+o de A4
P0 0 0 0
P3 0 5 6.248711
P5 1.464102 3.535898 0
P4 1.464102 1.464102 &1.071797P0 0 0 5.1=?715
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P*a'sDados
fc 2.50 (KN/cm2)
fy 50.00 (KN/cm2) 1.0 (adm) 1.15 (adm)
fc 1.=7 (KN/cm2)
fy !.== (KN/cm2)
E 21000.00 (KN/cm2)
E 2"00.00 (KN/cm2)
E 2!"0.00 (KN/cm2)( 1 .00 (adare!)( 2 !.00 (:r$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$ra)
(atJ atiir o me!mo de!+ocameto)
gg 0.24397 * 0.6 Es)/)/a d' (s f*3os
:
:
c
s
d
d
s
c*
cs
)o)
co
ti:o
-eto
72mm
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I&@'f'*'s Go$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!.
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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
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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
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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
*
*
!
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