RESOLUGIO DA LISTA

SOWGIO QUESFAO 1

1)ESFORQ DE Cfi LWLO

Md = ff . MK = 1,4 . 90=126 KN . m = 12.6001W . cm

2)ESTIMATNA DA ALTURA VTIL ( d )

D= h - ( Cnom + 0++0121

D= 50 - (2,5+0,5+1,2) = 46,5 cm3)A' LWLO DOS COEFICIENTES Kc E KS

Kc =bw=d2= 2046,5-2= 3,43 cm2/kNMd 12600

PARA CONCRETO C 20 E Act CA - 50 ( TABELA A - 2)

Kc = 3,4 ⇒ ks= 0,027=D

Id= 0,35 ⇒ DOMINIO 3

Id= 0,35 < 0,45

,LOGO RESPEITA 0 LIMITE DE DUCTIBILIDADE Ok4)POSIQIO Da LINHA NEUTRA

REGIIO COMPRIMIDA

1=0,35{

. x= 16,28 am

d REGIIO TRACIONADA

× = 0,35 . D= 0,35-46,5=16,28 am5)DEFORMAOIO DO CONCRETO E DO Act

DOMIN 103 : CONCRETO ( Gc = 3,5%0 FIXO )

a @ ( 6yd < Eos < 90% . VARIAVEL )

§t=6sd- ×

0,0035 =Gs

-6,28 46,5 - 16,28 Gc= 3,5%0

Gs =

0,0035-(46,5-16,28)=16,286s= 6,5%0

GS = 0,0065 = 6,5%0

6) A' LWLODA AREA DE AGO ( As )

As

=KsgMd_

=

0,027.1-2600=7,32am

'

=D 9010mm ( As ,ef= 7,20am' ) + 1AM

46,5 ↳ TOLERENCIA 5% 6012,5mm ( As ,ef= 7,50mi ) + 1 AM

6,95cm'

4016mm ( As ,ef= 8,0cm'

) 1AM

3020mm ( AS ,ef= 9,45am'

) 1AM

810cm'

MA 'S PRJXIMO DE 7,32am'

2022mm (AS ,ef= 7,60cm'

) 0 NEO COM .

DO OWE 9,45cm'

,LOGO ESWLHO

4016mm

7) ARMADURA MINIMA DE TRAEAO ( As,

min )

AS,

min =L,

min . AC

PARAWNCRETOS ( 20,025 E C 30 : fs,

min = 0,15%

As ,mim= 0,15% . ( bw . h ) =

0,15--20.50= 1,5cm

'

100

8,0cm'

> 1,5 am

'

( Ok )

8) ARMADURA MAXIMA DE TRACEO ( As,

mdx )

As ,mdx= 4% . Ac

AS ,moix=hfj ( bw . h ) =L. ( 20.50 ) = 40cm '

8,0cm'

< 40mi ( Ok )

9) ARMADURA DE PELE ( ASPELE )

AS,

PELE = 0,10% . AC, ALMA

As,

PELE = %kf. ( bwh )= Gq

. (20-50)=1 oni =D 208,0mm

10 ) DETALHAMENTO

h=50 205mm ( PORTA - ESTRBO OU ARMADURA CONSTRUTWA )

⇐- 5mm → 2×2.0 8mm PELE

ESPAEAMENTO VERTICAL DA ARMADURA( nc ) - 4016mm

DE PELE

bw : 20

a > (20£70, 8am

0,5 . OAGREGADO = 0,5 . 1,9cm - -0,95cm

ev = 2am

SOWETO OWESTAT 2

1) ESFORGO DE ofLWLO

Md = ?

2) ESTIMATIVA DA ALTURA JTIL ( d )

D= h - ( Cnomt OH + 0£ )

D= 40 - ( 3+0,5 + !z )

D= 36cm

3) 0 MAXIMO MOMENTO FLETOR SUPORTADO POR ESTA VIGA SERA'

NO

DOMINIO 3,

RESPEITANDO 0 LIMITE DE DUCTIBILIDADE ( Xg= 0,45 )

PARA ONCRETO C25 E CA - 50 OWANDO Id= 0,45 TEMOS :

14=2,2 =D KS = 0,028=D Dominic 3 =D

Id= 0,45

Kc = bw#Md

z

2,2 =

20€Md

Md =2036=2= 11781,82 KN .

am

2,2

Md = ff . MK

MK

=M¥=

1178,1yd= 8415,59 KN . on = 84,15 KN . m

4) POSIQIO DAUNHA NEUTRA ( × )

REGIIO COMPRIMIDA

1=0,45 {. x= 16,2 am

÷- 0,45 . D= 0,45 . 36=16,2 am

REGIIOTRACIONADA

5) DEFORMAEAO DO CONCRETO EDO AGO

DOMINO 3 : CONCRETO ( Gc = 3,5%. FIXO )

A @ ( 6yd < Gs < 10%0 VANAVEL)

§t=±d- x

0*0,35=62 Go . 3,5%036 - 16,2

6s= 0,0035 .

(36-16,2)=0,0042= 4,2%

. 6s= 4,2%0-16,2

6) A' LWLO DA AREA DE AGO ( As )

AS = KS . Md = 0,028 . 11781,82 = 9,16 am

'

=D 7012,5mm ( As ,ef= 8,75cm'

) + 1AM-d 36 ↳ TOLERANCIA 5% 5016mm ( As ,ef= 10mi ) + 1AM

8,70mi 3020mm ( As ,ef= 9,45mi ) 1 AM

2025mm ( As ,ef= 9,45cm'

) ON Com .

LOGO ESCOLHO 3020mm ( AS,

ef = 9,45 am

'

)

7) ARMADURA MINIMA DE TRAEAO ( As,

min )

As,

min = I,

min . AC

PARA WNCRETOS C 20,025 E C 30 : fs,

min = 0,15%

As,

min = 0,15% . ( bw . h ) =

0,15--20.40

=

1,2cm'

100

9,45 am

'>

1,2cm'

( Ok )

8) ARMADURA MAXIMA DE TRACEO ( AS,

mdx )

As ,mdx= 4% . Ac

As,

moix = ⇒ ( bw . h ) = ¥.

(20-40)=32cni

9,45 am

'< 32 cmi ( Ok )

9) DETALHAMENTO

205mm ( PORTA - ESTRIBO OU ARMADURA CONSTRUTIVA )

⇐-5mm h= 40

( k ) -

3020mmbw= 20

SOWETO OWESTAJ 3

1) ESFOR .WS DE A' LWLO

Md = ff . MK = 1,4 . 55=77 KN . m = 77001W . cm

2) ESTIMATNA DA ALTURA VTIL

D= ?

3) of LWLO DO'

d'

PARA 0 DOMINIO 3 RESPEITANDO 0 UMITE DEDUCTIBILIDADE( 1=0,45)d

PARA CONCRETO C25 E AGO A -50

Kc= 2,2 ; ks= 0,028 ; DOMINO 3 ; Id= 0,45

Kc = bw . d2Td

2,2=12127700

D= way = 37,57cm.

4) A' LWLODA UNHA NEUTRA ( × )

X = 0,45- REGIIO COMPRIMIDA

d {. x= 16,90 cm

X = 0,45 . D= 0,45 . 37,57=16,90 am

REGIEOTRACIONADA

5) of LWLO DADEFORMAEAO DO CONCRETO E DO A ,O

DOMINI 03 : CONCRETO ( Gc = 3,5%. FIXO )

A @ ( 6yd < Gs < 10%0 VARIAVEL)

E×=±d- x

0,0035 = GS- -

16,90 37,57 - 16,90

Eos = 0,0035 . (

37,57- 16,90 ) Gc= 3,5%0

16,9065-0,0042=4,2%o 65-4,2%0

6) A' LWLO DA AREA DE AGO ( As )

As=KsgMd_= 0,028.7700 = 5,74cm

'

=D 7010mm ( As ,ef= 5,60cm' ) team

-37,57↳ TOLERANCIA 5% 5012,5mm ( AS ,ef= 6,25mi ) + 1AM

5,45 am

'

3016mm ( As ,ef= 6,0cm'

) + 1AM

2020mm ( As ,ef= 6,30am'

) + 1AM

ESWLHO 3016mm Pas As = 6,0cm'

E'

Mais PRJXIMO DE 5,74 an'

PORTANTOTEREMOS 2 GMADAS a = {¥[j|a%mp€%Yj%Yqmm=9,5mm

7) A' LWLO DO'

h' ↳ 0,95cm

ev= 2cm

FORMULA DO'

d'

PARA DUAS CAMADAS

d=h - ( cnom + Ott Ol +eg )37,57

= h - (2,5+0,5+1,6+22)h=

37,57+5,6=43,17

I 45cm

8) ARMADURA MINIMA DE TRAAIO ( AS,

min )

AS ,mim= I. min .Ac

AS ,min= 0,15% . ( bwh )

AS ,min= 0,1 . ( 12.45 ) = 0,81cm'

100

6,070,81 ( OK )

9) ARMADURA MAXIMA DE TRAETO ( As ,moix )

AS ,mdx= 4% . Ac

As ,mdx= 4- . ( bw . h )100

As,

mix = 1 . 12.45 = 21,6 cni100

6,0<21,6 ( ON

10 ) DETALHAMENTO

205mm ( PORTA - ESTRIBO OU ARMADURA CONSTRUTIVA )

⇐-5mm h= 45

- ( 2C ) - 1016mmev= 2cm -

( nc ) -2016mmbw= 12

Soweto OWESTEO 4

1) ESFORGO DE A' LWLO

Md = ff . Mk = 1,4 . C- 91 ) = - 127,4 KN . m = - 12740 KN . am ( MOMENTO NEGATIVE)

2) ESTIMATNA DA ALTURA JTIL ( d )

D= h - ( Cnom + Ot +

OFGPESTIMO10mm = 1 am

D= 30 - ( 2,5cm + 0,5 + 12 )

D= 26,5cm

3) A' LWLO DO KC E KS

Kc =

bing.gl =

20=26,52--1,10→ PARA CONCRETO C 20 E A .W A -50

12740 ↳ DOMINIO 4 → REDIMENSIONAR A PEEA

4) A' LWLO DO NOVO'

d'

PARA 0 DOMINO 3 RESPEITANDO 0 UMITE DE

DUCTIBIUDADE ( Id= 0,45 )

PARA dI= 0,45 E CONCRETO C 20 E AQ A - 50 TEMOS :

Kc = 2,8 ; KS = 0,028 ; DOMINIO 3 ; ×g= 0,45

Kc = bw#Md

2,8=20 . d2-12740

D= feta20

D= 42,23 am

5) A' LWLO DA Posiofo DA UNHA NEUTRA ( × )

REGIIO TRACIONADA

1=0,45 . x= 19,0 am

:= 0,45 . 42,23 = 19 am

{ % REGIO COMPRIMIDA

6)of LWLO DADEFORMAEAO DO CONCRETO E DO AGO

DOMINI 03 : CONCRETO ( Gc = 3,5%. FIXO )

A @ ( 6yd < Gs < 10%0 VARIAVEL)

§t=±d- x

0,0035 = Gs Gs = 4,2% .⇒ 2,23 - 19

Gs = 0,0035 ( 42,23 - 19 ) = 0,0042 = 4,2%0 Gc= 3,5%0.9

7)A' LWLO DA AREA DE AGO ( As )

As=KsdMd_

= 0,028 . 12740 = 8,45cm'

=D 7012,5mm ( AS, ef= 8,75cm

'

) + 1AM

-42,23 ↳ TOLERANCIA 5% 5016mm ( As, ef : 10mi ) + 1AM

8,02cm'

3020mm ( As, ef = 9,45mi )

2025mm ( As ,ef= 9,80cm'

) NE COM.

ESWLHO 3020mm

8)of LWLO DO

'

h'

UMAFORMULA DO

'

d'

PARA

#AtCAMADAS

d=h - ( cnom+0++012)

42,23 = h -(2,5+0,5+2-2)h = 42,23+4=46,23 = 50 cm9)ARMADURA MINIMA DE TRAAIO ( AS,

min )

AS ,mim= I. min .Ac

AS ,min= 0,15% . ( bwh )

AS ,min= 0,15 .

(20-50)=1,5cm

'

TOO9,45 >

1,5( Ok )

10 ) ARMADURA MAXIMA DE TRAETO ( As ,moix )

AS ,mdx= 4% . Ac

As ,mdx= 4- . ( bw . h )100

AS ,mdx =

1.(20-50)=40,0

cni100

9,45<40,0( ON

10 ) ARMADURA DE PELE ( ASPELE )

AS,

PELE = 0,10% . AC, ALMA

As,

PELE = %kf. ( bwh )= Gq

. (20-50)=1 oni =D 208,0mm

11 ) DETALHAMENTO

h=5O ( 1C )-3020mm⇐- 5mm → 2×2.0 8mm PELE

ESPAEAMENTO VERTICAL DA ARMADURA205mm

DE PELE( PORTA - ESTRIBO )

bw : 20

a > (20£70, 8am

0,5 . OAGREGADO = 0,5 . 1,9cm - -0,95cm

ev = 2amA VIGA FOI REDIMENSIONADA

DE (20×30) PARA (20×50)