mrd ,1 s'{w ,) · 2015-08-31 · mrd e = nrd x (1= 11 as-Área total de armadura as = a + t::....
TRANSCRIPT
'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!