7968084-Limit-State-Design-of-RCC
May 21, 2018 | Author: Velpandian Mani | Category: N/A
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TATE TATE MA
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t:
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A.DHIRAJLAL,
B .E .E " M . C .
F . E " G RA R A D C .E .E d L EE EE DS DS ) M J S .T .T .E .E .
PRINCIPAL
Thiagarnjar Polytechnic Salem-636005 Tamiln~du.
and .,
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i>;,. .-,.
P.RAM.'ACBANDRAN,
D.E.,
Salem..u3600S';
i}
M.I.S.T.E.,
:~
:i,
T a m i l n a d . ';'; '
:c':
,1
'il "i\;'J
: -. '
.'
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Preface
wa
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wh
he
n d m en en t
nc
nd
Al
'number
"d IS:456~ 1978. ma
me
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he
u de de n
me
em e ly ly , will b e e x r em
ch in in g h e authors i n e n ch
mo
ha 30
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ar
o f P o y te te cchh n ic ic s
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Th
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o f n d a ~S ~ S : a nd n d a d s which IS :456 :456-1 -197 97
1987. IS
56-1 56-1 78 ~ vh v h ic ic h
Ma Ma Bh
ne hw , P
B om om b
Ca
Bh al K an an p
Ch nd ga h, Hy J!
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•
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Preface
wa
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wh
he
n d m en en t
nc
nd
Al
'number
"d IS:456~ 1978. ma
me
With r ic ic h e x pe pe r ie ie n c e fi
he
u de de n
me
em e ly ly , will b e e x r em
ch in in g h e authors i n e n ch
mo
ha 30
."
ar
o f P o y te te cchh n ic ic s
~ .• .• .
~ /;",
Th
au ho
me
g ra ra t
he Bu ~a
mi
o f n d a ~S ~ S : a nd n d a d s which IS :456 :456-1 -197 97
1987. IS
56-1 56-1 78 ~ vh v h ic ic h
Ma Ma Bh
ne hw , P
B om om b
Ca
Bh al K an an p
Ch nd ga h, Hy J!
.•
..
~t
./'
•
'.
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moment M u m ) M om en t
mi
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c om p re s o n m e mb e
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R ~ i ~ ~ rg ~ d ' c o nc ~ e t h a s o d ay ' b e~ 6 ~ ~ '~ i d~ ty 'U ~ ~ i l r i ~ i ~ n J a lm o a l of uc d in g dg wa
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a r td is "e x ~ h s i i 6 J~e~'h{tOristhicti6ri()fl' V o i ~ ' o uh da t o n ~ 'd am s .,
c~nci~'te is very compressio'n:" w ea k n te n o n 'In p ra c i ce , tl the:' snme: ~ tr uc tu ra l m em b ot om on an ns an as h , a in ' o n a n n C> (Q e ~ s~ d ar n d ho ni mb To ~e ~m hi wh is str~ng,in tensi?r is,usedal?ng,,'rith,. c O 9 . e t~ ~ d h i c om b n a o n o f e e a n~ ' c on c e t IS n ow n a s e in fo rc e c O w re te . T h e rn~mr~a~p,n!J; h in d h e he m b n a n , is '1;\
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part. there deflection s h al l g e n er a ll y
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i:!,::r,~~(~'?;~Jjd~Q,~c~i~~~~tie ll lo~~smcludingtheeffects o f e m pe ra tu re , c re e and,shrin5 ,t } P ~ ~ ~ W ~~~? m , t h ~~a~tlevel. (I h e u pp o o f o o o o a n a l o th e h o o n a l n em b~ s~ ~O ld d . , : : . .~ . , t _ , . >'~:_I,.~__~ _ : ; _ ". ' ~ " , . " . .
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a b h e v er ti ca l d ef le ct io n ratios n o greater h a e f e c v e d ep t
ir
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n c u d n g h e ~ffects~( t ~ m p 'e r a tu r ~ , ~ ,~ ~ e p 8 .n ~ application ni he ho no no ma
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'(._
Wh
'.
fckN/mm
'.
Fy,N/mm
-,
250
415
500 2.00
20
2.97
2.07'.' ~~ 2.76
25
3.71
15
30 ~ercentagc
3.32 4.13
4.46
>=-"
ofs'teeB for limiting sectlon (%
m om om e The percentage
2.65
~f wsistance will
3.98
st mi
ge
nf
m en en t
n.
mp
(Tu)
mp
Total tensile
Stress
.:::0.87 Ast. fckb. X u m a
Ar 0.87 fy
.b st -.
m)
15
--.;.~---------.;.~------------------0.87
:-
-
4\'.38
.:
As
..
~~~- -. ------~ ---.- --~------------------------::::: -------------~-------------~0.87 0.87 fyO: fyO:S7 S7
: ::::-------------:
-
-
-
-
-
-
-
-
-
K, 1;
As
41:3 41:3
X~(max)..,
fc
= = - .;.; .- -~- ~ . ;.; . ~ -,- , ;~ : '.1;
'd
41.38x15xO.531,ii 250
1.316
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i"
Download And Print Valu Values es
f%
=415 N/mm
-250N/mm
0.566
1.757
0.955
0.755
.2.1Y7
1.194
O~943.
2.637
1.433
1(132
.;
.'
d ,r,r cH cH h E l g '
1 I1 I1 !1 !1 0m 0m e o l co-efficient
Qu !-
Con-
Steel grade
crete
grade
,' ~: :'
Charac-teristic .strength (fy)
:M15
0.531
(mild:
N/ffim2 0.479·-
2.23, tHil
'bd
0.531
(mild
,'·'M20
F eA t
_(
'.
Unde Unde
~t
1.318%
.""-"
L757%
r=r=t==: N/rrun2J 415
0.479
2.76
N/mm
0.955%
..
!'d:2=tC_
Il'e Il'ein info forc rced ed sect sectio ion: n:
When'the percentage steel h a h a in th baj~~b~(~tiridlt!6~,itiMn~utr~lllbti~'m o ~ e s of compres compressi sion on force of'tension.: J,J, wa ha he !l·;i.~i,f} 1;:'.1,'(,'1/"-1 steells ls strai strained ned beyond.theyield point . " H e t i i l d e r i i 1 c r e a s i n g bending m o m e n t , ' steel attains (0.87 rYilfs);+ 0.002' or he nc m a x m u m p er er m i b l v a u e of strain. ie.;iOi0035
Henc~ thef'~lure
widb~due' t~ i h ~ ;l.iliJie ~ f ~ t e e l . " S t i c t 1ifJiIUf~ i fJiIUf~ i 'd i ltl t e d '
co cret cretee- ai s, th stra strain in in steel will be grea greate te than (0.87 fy Es) Wil be es er m i n g n eu eu t a l a x Xu(max).ax '.;' ;:. ":~"':l -:':'" ':'"
r. ."
::r:~l,!;~l~j.iwmwM-'$W=kmt*_~:m';~~~*?I¢AA.*'*.*?
" 0 " '
'iH:
0.002
c n i o u { f i iii i lll l lrl r e '-' - H c r e ;:; : J l le l e hh e the value. of actu actual al neutral
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0.0035
fy Es
SECTION
0.002
DIAGRAM
TRAI
fo will b e e s
h a nX u fm a x] ,
Tlledcsignstr6ss
0. ,
~
Moment
an
of he
on
= T e ns i
o rc e
= 'A s 0 .
fy d -0 .
st 0 .8 7 y . st
O.87fy
----------------
S u bs ti tu ti n g v a lu e
u.36 c k b .
:.
an Xu
1 1 , : , 0 .4 2 - - - -
.l,·
in h e
0.42 As
0.87 fy
d)
As
------------------------
0.36 f ck . b .d .
_ ' -- -- ~ -~ - -
II
OVER REINlFonCW:O SECTION:
'1'1
Whe he nw nt he ~0Wn
nt ge
mo
he mp
that
nc nc mw
nd
he
ma he
ii
ie
called a s o ve r r e n fo rc e
mo
ec on
Print document 21
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Whe value
he actual n eu tr a a xi s
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is m o
w i Download And h a Print he ha he
fy
s)
O .O O a n
he ' .. '
.:
0,B7 :Es.
0.002
SECTION
Th
ve
nf m m en d
nf
ha ma
will
Here
o n .isundesirable n c h e h' ho ak a l tomoment ha
mp gn an
Xufrnax).
(01a~~)\J';.:
Qu.b.d
. '
d ep t
l_'!
, ,
ngly re nfor
;_
,'):
se io
Stt~ No.2 D e Xu
m in e
he
0.87 fy.Ast fck.b.d
-j
f ", _ .
:~. .
o fl ir n it in g neutra axis.for ~imiting,secti9n.
--;---~------......
;moves' ailure is
ri..~-------~----~--;. .. b.d~
, J , - - - -- - - ~ - -. ; -
~~(>
Types
wi ho warning. Th n i E in c
';
u(
Mu(lim)
o n a i u r is d d H ow e no nc h e limiting
~c ai n~ -:«, ..
a l 'axis
ti
i,
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. .. .. .
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~u=0,87zy.ABt.d
b)
Xu
Xu ma
Mu
m)
Qu.b.d
0.36 fc 'c
If
/d
"b
he
we
he
No
.
mi
sectio
m om e
'j
taken equal
::
To filldAst fff~ give
!~ ..
he
Mu
Mu(lim)
Type
'[
-:~-~~~!--0.4~ - ~ u ; ~ , ~ ~ ' { l
Xu(max)
ne
he
l--:::k'
u n And de r Print r ei n o rc ed . Download
0.42
~~~=J
and Bendi~
b,d
Momen,t.
Mu
Xu m a
Mu m)
1100 0.87 fy Qu.b.d Xu(max) =0.36 f c - -- -- -- -- -
.....
~-~::21b.
E q ~ : ~ u( : ~: :,: : ~ :~ t~ ! ~ ~ ~ _ , ~ c l t i o n Mu
Mu
From the: a bo v )0
H en c
Mu gn
m) he
he
nd
fok.b.d e qu a ti on , A s m a determined,
m)
i·
Print document
23
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gn
n f@ R " o r g av e : H Download And Print
D im B t n g s n g
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Step No.l~:~in factored m om en t M u Ste~N().l:
' . s c e p N ~ . ~. .
Xu ma ~ ~ ua t
Mu
':~ ,~ .'
~everarm.
Mu m)
,_.;
to
ma
(max)
'0
0.36 fc
-'d--
- -- -- -- -. i- - : . . il
Assuming
Step No.4:
n d A s by e qu a i n ,3
0'
value o f
mi
Carl'
an
o ta l c om p re s i v
o un d
o ta l
ns
o rc e
ck.b X u m a 0.36 fck.b.Xu .(max)
st
'.
(max) x:..... _~_;~~~~-~'~._ 0.87 fy.
~~----------------------------------------~----------------------~-mp
mi
mo
used .. A l
mi
he
mi
m m wide'X fe 4 1 ' S
am nt
:. ..
'Mu(Iiilti·~'Q~.b.d2::.,.
';'j;;.,.
; : ' . : t : ~ < , ~: ::~ ~ . ' ; · : : : " ~ : ~ ' : : · ! - : -
·;
tl~!~'--'
!:
,:,.i:=~.0
st for l im i ti n g s ec ti o
nf
singly
'f
0.716% 500
·107 rrun
ProVid~4'bats'l2{Y#" ofr~sistance ()ra singly reinforced simply supported RCbe~m;360;' numbers nc r"
r'
:1,'
(,.'1
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'-
'-
fck.b.d (max)
b)
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Solution
lS.andFe
dforM
415
ie, t h
Xu ma
Since
0.36
"::::i
15
600
'600
0.479
s ec ti o
is u nd e
_ _
0. x415
e in fo r e d
_ M
942.48
_ ~ "..;,.~I:u'''''''''''': '~
(max)
s.s.
terr..
fo
Fe
1 _ _
c)
.,
.,
c)
of s in g ly ' r ei n o rc e s im p l s up po rt e :Calcuiate the m om en t o f e s a n effective is r ei n o rc e w i t n um b o f2 0m m Fe 4 1 ee
~~
b)
5-16
:~:l!
005 184.13kNm'"
is
b'
f;
0.37
Ast.fy
0.87 fy.Ast.d
wide
~3bo'24'
=?
O.6
I)
15 concrete
g)
~_
0.36.x 0.479
(max) I~ h e e c o n is o v e r e in f or c ed , The o ve r r ei n o rc e S in c X u s in c e f a il ur e u dd e w i h ou t w ar n n g . The mm nd ha am m om e ov nf a m Mu resistance of i m i i n gs ec ti o
Qu.b.d
2.
beam mm ar n d h e m om en t h e effective 0 mm , re used,
nc nd
he mp
0,87IY,A~lf,
I)
.H
603.19
0,36 fck.b.d
0.36
0 x 5
sectionisundesirable h ou l be redesigned,
Nm
m.Ef an load, €oncrete
~-------~------~- --------------------------- =' 0:40
Soh. Ass
O m. F in d h e a f w o n g g ra d F c4 1
b)
c) d)
I;
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_ _ _ _ _ _ _ _ _ _ _ _ _Cancel _ _ _ _ _ _ _ Download And Print 0479 1100
xu}
I
Xu (max)
•t
~
.
_
. "
,
; .
section is underreinforced.
,~
. . _
='
, .
·i ·' '"
i,e',
,.,i
41
=..o.~7"x415
~'rm
Fd ., --------
.
.
:
.'
29.0
'~
Su
~l
1'9.33
Wo
I.
----------
KNIM
-i-.
.5
.5 mp
29.0 kN/m
ad
!n
kNm'
\:,~
Example: bending m o m e n t Ii ~i
me C on c e t g ra d MiS
ar
E f c t e ; dept~"d rg
5~)(Jmm
Solu~ion:
Assuming 20n:undia It
nd
beam, 300ri1ln g ra d Fe 41
(20/2)
a)Nlu(l\n~)';j_Q~1.b.d2:::
2.07 .x 3()nx4$.:;7,,7.1~4.28 k N 1 1 1
b) ~ en d n g m om e
KN
:.,~_>::
~ - , l . . . : :;,.;cr.d~,,::;,;': .
-::!
••
[0.5
I~
'j.~pt!~~'lO:f 4~starcc bC~Yfee~po~n,~sofz~ro.n iome~tswit~ 'I
-
,
,
~,
-
j.
, ,
' :
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:ll,
iti::Cas :lWhen
!~\Hcl'e h e r e :\"",
neutral Axis lies
'i
:'
Download And Print Xu:.
Mu
0.36
- -- -- -- -- 1 ' ; .
Tota
w) Df
O.~46 fck
'~,'"
Mu
Total tensile
Moanr.ni
I'esistnn~~
ar ih section,
0.87
Ast>
Xu
(lim when balanced'
Wh
Xu ma
."
Equa
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"MlJQim)
+::,
i.'
"~
M o m e n t of resistanc
h e section, Mu w h
i':';':
ov
nf
d.
o ve r r ei n o rc ed , resistance me
ma resistance section
~
de~i~~ble the limitingsection,
:
m om e l'
Dr 0.2d)
2b)D ri
'" ~
C:we 0.36 FCI(,Xubl . . C:rc
D .4 4E iF CK ,W C b
'" <
-0
.~
Ii
DN
.i
..
..
1,'.
.
~. 'I
NEUTRAL
~.":
~I
h e nD fi s g i ~a te rt ha n str~ss~istHbuti?n. in ofthe ~tre~s.J,)l~ck IS taken
a c t u a l ' Neutral
2d
h e curvilinear
~ange
P . ~ r t, i : \ n?tH~~fprrp'Jhie~,ip~~ ~ 3 p t : n . ~th~~! d t,h~~~ptt~of~~,st,~~!5u_l,ar
is Factor
c om p re s v e
::
o rc e in
nc
+'0.440' fc (bj-bw where Yf
~i
,;
(.Tu)
Equating the 0,87 f)
0446 Ick
~ - - - ~ - - - - - - O ~ 3 6 - f ~c ik- b- - ~- - - - - - - - - - * - - - : .. ~ . ,
web) t1all~
'I
Df
Total t en s il e o rc e in ~ ei n o rc em en t i n e n i o Xu
i'
"i"
Tot~l comprrHi'.
nc
comes into the flange also. Hence
he
0,87 fy Ast.
1,;;1:,:;.;.",1
;
•
i1,.. f.,'
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r:
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fy
under reinforced ,-M:u
mp
'.
,:.~f:,::·','·!/,yf"
~1 1"
(d
:.
Xu)
'.':':i'P(lfi:;:)'~:Y:':w>
~-
vr 1-
! 'o ta l
en il
force
leve~
~O~42XU)~
M~ment or:~esistnnc
T h m om en t
re is anc
o f thesection
'I
ma mu
.,
'I
Xu ma
Xll(nl~x)
Then:Mu.(Ii~)
0,]6 -~----------- 1- 0.42
------J
OA46 ':
'.
where Yf=
TypeLj
g n
Xu(max)
l a
h e m om en t
(Mu)
nr 'I
' , I '
I,
1100
0.
llxil;
Assume
neutral
y)
e)
Factor
ax
he
If',
a ng e
st
Dr of typeU.
mp
correct, p ro ce e
u r h er . If h e
mp
wr ng
follow h e p ro ce du r
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, , ~ ) k; " e r , ulld~r re
forc
Xu(max)
or ba anCancel
Download And Print d , h e e c o n is u n d e r e n f or ce d
h e s ec ti o
is o ve r r ei n fo rc e
d, th
I) M o m en t o f resistance
fo limiting
ov
Ii)' ¥ om e n
of re
a nc e
o r u nd e
ec on
xu(max)l'
-----d----
..•r>Mlim)
r e n fo r e d
d--
0.42
e i _ fo rc e e c o n
fy Ast
- -- -- -- -- -- -
Type ..
)' in L.N.
Factor -,
-.
--------~-~,--~---------------------~ 1100
t.,_
~;
.::.
0.87 fy,
".i
...
ill
,i
Ii'i~ldA.N.t\. Facto]:
A s s u ' f8 ~ l , ~ 1h e n eu tr a axis lies 'with in
th
flange.
..
OH11)lcAst ..
~ ," 7
a.;;
_-",.'
" :" '
: I I (
. .. -- . .. .. .. . . .. -
2 ' _ •
II'Xu >DF,liI(: a~;\lIq,lpljnn is \\>Tong Then, assume to.4]lXu' (or) rositjl,Hl,~)r!fc~J!.r,,' (I:\i~' ,\hl'i1 Dr
with in th Df
"'._",
c) O-.'H, Uud~,~ n'il,ruJ'C('cj or ,Ihesl'criohi!rundcr If
J;: x~ (m ax) ',d,'~ :Xu(max)
.lre
'.
f~ -
reinforced,
reinforced
the sect on
balanced
0;43 Xu
,1
th
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at i)
en of
Xu>
Download And Print
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ec
ei
ce
L,
.. ~ I
Mu
Xu 0.36 ~-------
,
d
,I ~~----~~---" d
's
0.2
also
Mu
ck
~ _ ~ ~ -~ -
when Df> 0.43;U
ii)
Xutmax)
Mu(lim)
0.42
xu{max>l
----------------
0.36 ----------
n+
0.446 fcLb
(or)
-:~:-~~~:~~--1
0.3~ ~u~~:~x)
Mu(I,im)
fck
b.,) Yf
(ori 0.2
ma
when
65
(or) 0.2
-____,,.......---..;._,.-------_._-------:----------~h'('11
m om e Fi~t1 th
Mu
position ;.d~neutral axis b)
i) 'Assume
hi
B.t\:l
he 11
1',
'''1>:
If,
bJ..
)A.: •. Factor Assume tha(A.N.t\ lies
h e a ng e
~:
250
1256.65
~---------------- -~--------------..;-~-----~------0,06
k b
Xu
0.06
,S nc Xu c) Over unde
'Since d) ~Mom
6 X
465
Of as um
0 X
' '
28.00
on
o un d
tof resistan
As!
th
section
u n de r r e n fo rc ed ;
ofT-beam
!:-~~~--: 5X
Nmm
123. kN
II
o·
Qk ,) 411'
OQ:-.,
reinforced or balanced. Xu max)
,.
1:
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\.
T-
of flange 100mm thick, 1000 rn
id
an ri
:w ~~ 9<
0~
ha
erall"dept fo
ia
tw
55
....
Solution 'oj:
'i
~
:
.4
~1~'f:1
.";-::~~,~l~_:;~:.!:j
r:
(m
j:
! '. ." " " "
225,13mm ,1
';:1
,-
:.t'
Assume fy
X4
314:
-----= ------.------~-- ----------------------------
0.32
0.32
t--I'~ -
~--'-
500 h: .160
Sinc Xu
.:::.
,asstlrn tion
ou
no
rr ct
Plte
rieiDtraln-tis.
i)
- -- -- ~ -
.;
(hf-
-------~.::.:-t-,~-.;,------------------------------------_~
0,
300
. O
23
'0
Chcd, 04 th
ahuve
o un d c or re c
'I
wl\~n
0,43
orbalanced.
rnm;
Xutniax),
th
sectio
is unde reinforced
'.
'·~~~~'_'L_J:t~:t~,~
Print document ;,51
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W ) ,D f d ,
~ :~ ): : '),2
i,:
i;
+,;;, ~'
0.446
) 1
484.68
10 Nmm
48 .6
:~
kN
i~
..
T-
m on o nn ri depth of mm. Ar from m. M2 Fe415
mm hi ha ng wi 1100mm. mm providedin tension is 3041 atan cffeotive\::d~er bf70rilm used. Determine h e m o in en t o f e s a nc e of ti
S o lu t o n L .N .
F ac to r
Fo M2
415,
u (m a
0.479, Xufrnax)
600 ";'287Amni
0 .4 7
b) A.N.A Factor Assume that A.N.A
st j,0.23
:-----, ~--~------------= = - - - -- - - -- - - -- - - -- - - -- -
0.36 c k b f
0.36
20
1100
..
('
138mm nc Xu
Dr he
mp
nd ~wi
i)
0.87 -- ==
fc
';',l
Df
-----------r-------------------------------~0.36
20
126 m m
u> D f h e
_.:~_.;,!~ 0.2"1
......
~c
mp
f'
nd
i~
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Check,
nr
;~t:
~"-'l'Y;;
120
-----=-::----'= 0.95> 0 .4 3 , T ~ e a b ov e a ss um p ti o
ii) Assume
(Dfl
D f Xu
~o
is
0.43 fy
_
~
'where
0.65 D f
"Substituting the valu ofYfin th
abov equation 20(1100-450)(0.1
------,
Xu
0.65
120)
-----------.;-----------':'-------------------------------------------------------0.26 .3
~x~==,is?
mrn; andD
,"He~c~, th
Xu
120/157
neutral Jxis lies w i
r, under
450
600
0.76
he
0.43
Xu.>
when
rc
Xu(max)
0.479;
0.26 ./!
S in c
--'-~-------- h e e c o n
~-
u nd e
e in fo rc ed .
TXu
0.446
" "
;,J
I",
vr
(0:'15
D1
101.55
M~'"
3\~
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