'V

ÁBACO 23FLEXÃO COMPOSTA

Secções rectangulares

t A'_O~J!SYd-= 3l+e MPa I

1.80

1.60

1.40

1.20

1.00

0.80

0.60

0.40

0.20

o

- 0.20

-0.40

-0.60

-0.80

-1.00

-1.20

Classe do betão

fecl(Mpa)

B15 B20 B25 B30 B35 B40 B45 B50 B55

8,0 10,7 13,3 16,7 20,0 23,3 26,7 30,0 33,3

146

ã/h = O!O~t

a+=

EMRd

.~at=

xh

total de armaduré

NRd

bhfcd

MRd

bh2fcd

As fsydbh . fcd

15/ -.;1.0(, oN

,,, li," 1,\

s'{W," '\ .'" "

,1 '\ .'",) '\ "\ .t>...'?o',} "\

)( ",,-"'

cr./<:, e = MRdINRd

(1=

,I' '\ 'xx-'\. '"I '

N ;'\." '\ As-Árear\ .À \" ,,'j 1\ '" '" "/:.,,(;j As =A +/I., ,,: '('

K\I

1( '\.\ {\ \ '" X V';)( \\ \)< '\ \; \ y< \

..,/ 'V =1'\ \\ A :\ \ Y' \ \ \

\ ....y \ xX \ \ \ 1\ Ye"

\l-\ --J 4 \

-)- --1\ \ j.J. =

-1- f- \-- t-Ct=.6

I A J' 11 I J J e 2.0 W =

1// "/1t 1;;1 j--- If-- ---,

7 ã:O.4-1-:"--;

/ - -+ l- 1-- ICt =.2--I//. // /y / / / /

[5(ZK.I$(/ /O.20/ }'30/ /0.4/'

0.50 0.60 0.70 j.J./ /

,1)\ / /';/

// v/ /,/

!/ >( // y 7') //

/ A // // // //0.,'--

/ / )( /// / -o

/

/ / /\ ///

/ / // / /

'

/. / "ot;'"

/

'V

ÁBACO 24FLEXÃO COMPOSTA

Secções rectangulares~A~QQIfsyq :: 348 MP'i-1

JA:/A::1.ol~/t!~Ô.1Q1

lo:,

0.80

0.60

0.20

0.50 0.60

-0.20

I-0.40

-0.60

-0.80I

-1.00

~MRd

e = NRd

X

(1= 11

As - Área total de armadura

As = A + t::.

0.40

NRd

'V = bhfcd

MRd

1.1= bh2fcd

As fsydW = bh' fcd

0.70 1.1

Ó'

~

-1.20

Classe do betão

roo(Mpa)

B15 B20 B25 B30 B35 B40 B45 B50 B55

8,0 10,7 13,3 16,7 20,0 23,3 26,7 30,0 33,3

147

ÁBACO 25

o

t~~OQ {'f 3488

'V

2,00

1,80

1.60

1,40

1,20

1.00

0,80

0,60

0,40

0,20

148

-- --- - - -- - - - -

---Secções rectangulares.

J/;-l1>ll ./h=O..

2í:'O [W aE =

- h ----+--

A" Es - at:

MRd CL=

-e=-

NRd h"',

As - Área total de ar

0 As=A+A

Ç)'V = NRd'\. ';'

.bhfcdMRd'

0 w o"Ç) \l = bh2fcd"'! 0 ',9",

\\?C\ w = . fsyd/ '\. bh fCd

K0 oó' /}

\ '\ W :\:\."o

\ fx \\\ 0 l'\ ,..o.\\'\ \\\ "'\\\ K\'\

\ \\\ .\\\t\\' \\\ \\\ \-,r 1\ \ \ \ i\f-- --)-- r a =0.6

I ./I I

I1 / I I I ) I II II IIII/ /

/ 11)11 1/1;LII 1/) v11 111;(11a =0,4

/ 0 / / / / /1>%.:00000m00,10 0,20 0,30 0,40 0,50 o.OC

Classe do betão B 15 B20 B25 B30 B35 B40 B45 B50 B55 .

fcd (MPa) 8,0 10,7 13,3 16,7 20,0 23,3 26,7 30,0 33,3 --

'V

ÁBACO 26FLEXÃO COMPOSTA

Secções rectangulares

J A4021~syd = 34f. MP1 ~

1.8

1.6

1.4

1.2

1.00

0.8

0.60

0.40

0.20

o

-0.20

-0.40

-0.60

-0.80

-1.00

-1.20

Classe do betão

foo(MPa)

B15 B20 B25 B30 &35 B40 -B45 B50 B55

8,0 10,7 13,3 16,7 20,0 23,3 26,7 30,0 33,3

]ai'" =~f15f

at=

EMR

-

d

.

-~at=

vx

h

total de armadura

NRdbh fcd

MRd

bhzfcd

As fsydbh . fcd

149

I IA ;; 1..Oor\

1

,, ::J

"{[J,, . 'l,, . \,,1\ Ir\\ .X,,1\\[ r\\ v'\ R .t' e = MRd'0 c' a=

\ 'r\ , r\\ ";': NRd

/

\ "1\ \f\?\\ 1\\A Ç)'t>/

As - Área\ ,\ K . !\'XX'/ \ As = A+A

('i Iv I\\iX\\ \ "Ç)':>

',\ l;Z'

I\J \ \\ \ V'<'

..) 'V=I I\X \ \ \\ )( f\\

" 'V \ \\ X \\ \ 1\ _n h , ,$I

\ -\--\ -\- --\ I\ C\ /'1' 1.1=

I Y 1 } } Wn } úJ =I/!/: -j--, j; 1/ -j- 1- rJ-1a 1 2,0/ - '"'

I .i-A 7 Vh /J j / VI '/

D(\ o/ 1/20/ /o.o I0.40 0.50 0.60 0.70 1.1

V\VIri /j '/ 11:Q,,([,

V, K; '/ 1//71/V)'j 1// /j I;'"',.\7

1/ I/) '///V/ VI 0 i/V/ VI 'X \,..V/ VI '-"\

q

V/V

V

ÁBACO 25FLEXÃO COMPOSTA

Secções rectangulares

-

I ~t.OO Ifsyd_= ~~a (

nai M:=riilC>I'V

o

2,00

1,80

1,60

1,40

1,20

1.00

0.80

0,60

0,40

0,20

148

. 1A.:/A..=1.

::{W aE"-. -- Es - at:

MRd a=e:-NRd h"-.1

t As- Área total de armaa..r-!

As = A +

C)

'V='\. ;-.

0 0 'Jbh fcd

MRd

w ',C)J.1.= bh2fcd0 '<9"

*: W = As. fsyd/ I\. bh fCd()

6' /

\ \\\:\."o\\\ X C\\W \.rt o'

\\\ \\\ \\\ \ \ \\\\ .\\\ .\\\ \\\ \\\ \\\ \\\::r \i \\ \ \ "\

\-a=0.6

/ ./ J J II J J ) ) ) J J J J J J J

I lI; l11, V1; t11 1/; '11 1; 111a=O,4

V 0 / /v //0000077W;o

0.10 0,20 0,30 0,40 0,50 :'.iL

Classe do betão B 15 B20 B25 B 30 B 35 B40 B45 B 50 B 55

fcd (MPa) O 17 13 17 20 23 27 30 33

\)

ÁBACO 26FLEXÃO COMPOSTA

Secções rectangularesLA~ If~~34~ M~~~

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.41

0.20

o

-0.20

-0.40

-0.60

-0.80

-1.00

-1.20

Classe do betão

fcd(Mpa)

B15 B20 B25 B30 B35 B40 .B45 B50 B55

8,0 10,7 13,3 16,7 20,0 23,3 26,7 30,0 33,3

)~=~151

a~

EMR

.

d

..~a:t=

xh

total de armadura

NRdbh fcd

. MRd

bh2fcd

As fsydbh . fcd

149

li. lIA-:?}f,Qo\.I

\.1

I\.l .'\ <v

" {W\.J\ ,\\\. ,\\ \

I

,1\'\/ \.\\

1,J\ \[ \.\ '/\' <t' e= MRd'0 reiNRd

Cl=

\ '\' \ 1\\..;:/

\'y\ \ \\ )\ <:>'P

/As - Área

{\'K " \X.X\/ \ As=A+ A

\"i \l \y/\\\ \ ..,(;)':>

1\ X\ Kq IV \ \\ \ y'<'

! \) =;I\.X \ \ ,\ )( \\'X/V \ \\ X \\ \ 1\ _0.60.....".0 =

\ +-' -\- -\ I\ C\/

;: I Y J J J t1 n J w =11//. /-7j; 1; -/-1- V-1a=f:-4'l..0- ti

! l0 /; -1-A /-;í7 :;//.V;bj ZI j / /1 '/

l>?\ :o//20/ /o.o I0.40 0.50 0.60 0.70

.V\ (I r tG/j / VQ"

/ >v '/ II 1'j // /x '/ II /j li'-"-"o

/ /) Y /1// Ii ['XI/ // 'X \

// //';'; \,- q

///

/laoiI!