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ECOLE POLYTECHNIQUEDETHIES

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PROJE T DE FIND ETUDES .

/\1. ./';

REMERClfMENTS

SOMMAIRE

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TABLE DES MATIERES

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~ ~~'Q/) ~~~\{~. li1~~an.~QIY\J~ ~ td),J:p(;(fh

~ f~~Q/) ~ <tMJ~ 51-it-v'fnVWÙ(f'n ne;vn,eN\)~ ~ f>~x~~vO &>3

~/tr\- e.rvv:vurnY"lQ/yY~~YV~ rk ÀQ/'YYI;~M()~ &1

PARTIE 1

Etude de plansarchitectes

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PARTIE II

Mise en charge

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PARTIE III

Analyse structuraleRéactionsEfforts internesDéforma tions

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2

t -:: ~50 ~ (400» -= A33"3/?>?>·/V~T ~Â 333/'33·10" rrnm4-. A~ .

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4-) COlA ~ ~~~.

c~cL(e- f\À,~cLe.. ~e,(!)bo1. .[eteu.k{ ~ ~on~~ 1 cMA ~~orl.A ~ no~e}~~.

Dm ~ ~@'(e- (4) ~re..o ~ u.u,Lr-B.- ~e.ob~:

.. ~~~ ~ ~~noll J\tvv~n.e._ ~çe- ~ole- ~~~n-olt ~y~.

_ Co-cL{ê,. ~~u *("~uVf.Ad ~-tex-~.• Co...olt'"€.- ~ ·trO\MbueJYftd ~tQ;-('n.e...

. ~ 0Bw.rrtto peK(m{)L~ ( D)

~J-()n. a -= ~ 400~/~'rY/~ -:: 2.4 kN /t'Yn 3

,Il . c.. /.;..,) (,,{M)Vé~Qb ~ yV'J..o (\eN)-p~~ r~~X rouA.~~'Y\,~~)C

lef~tb vi / ~ eJr?>:0/40 " 0,. l.f0 )( 3 /5D ')( 2-4 = .A?>, 4- 4- kN

- .pgr\,0v0 .~ f c>t~)( ((:UA.~~~ y\~ ~

eu:s t€U. ~~;C>1 4 O'X 01 Lr 0 )C 4-( 00 )C ~4 ::: .At:) 1 ~ b kM

- R QkcrrrJo &io f utLt'(e,L) tc~ \JQJf.b~ .:

D,4-0-0,,,(1 -= D1 ot 3 rf"r\

GcuJ.;2('"~ ~~y~

01 ~.~ "'le 0116 --. (6'1 00 - 01 40 ) Y. ~ l; -= 1 (1'?> k1'l

DI <2~ ~ Dl 3D ~ [0100 - OI4D)y.. ~4 -= '3,.. ~1- k:1'ICa,cJ.Ke;> Q)~y~

0, ~~ ~ CJ) ~ îj ~ (3,00 - D,ltO!~ ) y. 2.4 -::: ~ 1 "86 kN01 ~~~ 6)30 ~ (3100-0/40/~) '1. c:?~ -:::: 4-,64- kT'(

~~~ ~)( Y\O~ .db ~PA~~A'3 / 4 lt -+ 1-/'13 -::: ~1/11- kNvtS')-:'6 ~1)-:t~ -:=. ~'3)C)~ kl'-iJ?>, 44 + ~I t:f. -:;: ~ '!, f. J. kNAI5,?-b -t 0;);21- -:=. ~416~ kl'1

L.kO<iY~eb rQM..)O 'V\,O~ ~ ~e..b ~n€A

",f~/44 + ~/x6 := Â1-)?> kNlit~ 1~6 + ~I 36 -= A~ 1 ~ ~ kN

.f3) 44 + 4,b4 -= .A,3 / ù Z k:l'f-15', 3~ + 4, 64 ~ ~O} OD kt1

..ll) fk.r~iA vU-vv\-~O(~ c.k IY /rt'h )~Y"~ ~~

_~G'\,olo cLa!e.e 0].41-)( 6,00)C 2. 4 ::::' 2.4/4 s_Q,~~bw· p\i'At~eJ) 01~~ "" (J, ~ 5" '" ~ 4 -= AI 3 8~~'(~(ù ~QX'"rMM.~~ A,~O~ 6( 00 -= 1,~o

33/6h

°11111 "'8,00-0;10/~)~ ~4 ~ A"'t b?J6,40')(. fJ)30~ 24- '= ~ J~

.A ,?> '" ('3J 00 - "':'0/<2) -== 3, '=11AC) vt g/ ~ ~

~OIOO

~g/~ ~

WTeo ~~~- ~di'tÀP ~

_ PdÎ~ r~e.n

.. Sw('"~~t.-/r~~_v1ANv'fA e.ot.ti{~.A

3? .~MtrJMv-(~V ( L )~~rt~ tOÏJ\- 1::e,y-~ ~,4 k 1'/ IrY'I)'L~~~ p~~~l- 4( g lelY trm 7

SvW6~~ ~'f\À,}~,rrrve (leT'/ Jlm )

~&> iMUX-~

! )4 )( 61 00 -= ,4 ~, 4- 0114,40 ~N/1"rr1 ~.~ ~ F~eD ~ ~<rcl-

4, ~ ')(. 8(0D -::: ~~) '80~)l, 80 \cl'! 1/YYl ~~~ ptrVt.t'(QD~~ ~

~~.,b éX=~.

C~ceA ~~

~ ,L, "'1- ~,85 =- 6, ~4 klY /rrn r~~ -\o-V'r4, 8 '" ~,~ 5" ::: ~"?, i 6 "8 k"l/rrn f(Y\Â/W-eb ~~.-b

;) te-vovr~ ~. (6l,(A))( \J~\ ~ )

. _p~ ~t'\~~~ nU +~ .q / /vvvJr CC)~(QI~FO'"n,~~ r6L~ fÇ~~ r&lt rfiiF~QIrn trt1It-- ~ .A1~0

V ~ ~ ~ l'rn lÀ -=9 1:: 0/30 tePo..(Vd\< \O-Io~ cA. qp\\~ j.

_ P,\~ln\, ~~ ~er-r~ F tt v~p-= q Ce, c~ Cr

Co~~~~ w. r~~()Y\, r&.M.- LJ~ -= 0) s~~~~ ~. r-.c~~CfVV:, ~ Jo/'vJr-= -0)5"

Cp -= ~ 8 - (-0) 5) -:: A, 3 .

J F M I~ M T 3 (~ c 0 1:'1 J)-

.:?, ~, ' r:-: " i\ ), r -15 1b -'Il .2i --1'6 1 '6 14 1 '2.. 1'2..." ,""

,,'::,5;, A( ~ ?- -iu 16, Ji6. .1[, ;J() )~ .;~ )', ~f ~, ·1 ç, /: ,'-,,.,

·1 Cl r.,:l 14 ~ II -"iS ",1 1~. B 2() 1(., ),g ),1 - .\11.J ..... ~,

'.

/c:5~ 15 -1') Ab !, "2. )i 2 ): ~ J,ü. ;W n 'F, A') ·1 (;- '';

\955 ~'-1 14- '\5 13 Il ~ 14 , ..~~ J.o 2'\ )\C, ,.\';' )18,~

); ~,5'; 2.0 -'15 2·1 2.0 /il; '\'t- 2.6 5(~• 2) '\5 ·/x i:.' ~:l5~ ~~ /jG 2'2 2~ 13 ,~9 .Ô: 14 ,:, r :' . 29 31 .\ ç 1(,.'.'i.- . ,

~%~.' . -13 .-\9. ,.14 1\4- 113 -Ir 1)) Ci':-2.~ ;J5 ",ç; ~~, . .) . ,. ,)

~~, ~'J 2.0 "3 .l)e; 1( "Îü 1:2 2~ -{4 c:r ..oiS -14· ;1~... 10

1%1) ~G -1b 15 1.0 l, ?)) 1')

.<~ :23 Q) ~2.4 J\ 2. AS"1 J..

~ :! t:,.1 -1'5 .~~ -12, ~2 JI? 5'.5 ~. 5 9.1 .~, G A -", ),1 f31 ' ,. ' ~

.1,%'2. 11 12. 14- -'iLj 12.. ')0 ":l.-\ 4-0 ~0 ! ..? -I~ 24J'

1%3 2.5 :VJ, n· "IÇ, 11.1 1,5 30 1~ 9.(-\ /:L.1 9 -12.

t}~~ 9 -\'\ 1t) -'I() 9, 1~ -13 1~ J, ç, ~ ~, '3 -"\3

Jor t; -13 10 ~ ~1 .9 ~O )<=- .-10 "'i; 20 .9 -111 .• ~ .....

; ~1

1%C; 1(\ '10 10 9 -10 Ar CI 2'3 1'1- ~? ~ A, -1~• 'co • .J

)1'3~'"~ },2, A4 J\ ?_ .~ ') '\ ;1 -11; 2.(, 22. .Â'i /\ ~ Cl -1 '1,- ...J

J.%~ 'i1 9 9 1D ;: '\ ~2 },3 ~I :, 91 .~ ":'1 J '\ 0.,- -'

)" rCI~O ~ ~1 ~) 'i1 a 20 31 ~2.. -9 -12 13.~ . ., . ...J

1~11J ~4 fi 0 "12 0'1-\ )l'Î -'\~) .-'\ '2.. 9.1; ?') -'\2 -'\1 -'\3

"\911 ), ,I!~ '\'2 },Li /'/ ": ? 2.7. /i~ .J, 'X J:?, )I~ 13, ,

'\~1Î- JIL ~? A, (, .A\~ ),2 ?~ 9, ~5 1~ 14 .9 10

~~~ ~ 9 J,~), /" 1.3 )0 1;'''; AC; VI q. -10 10 ~1

~ .

1'31/! .~ '2.. "13 .lJ3 -'13 -11 10 A~, 1\'=1 -1'?, .9), '12 15

~?l~ ~6 10 l)~ 15 1'1 "\1 -'\3 12 15 '\4 12 11

i ~:~~ j,?, 1'2. 13 ),'2 ~ L1 A,:, ~G 11 1-=l 1G 10 1'7.l ,J

~'3l1 ",', )\~ 11 11 ·12- 14 '!Lj 1S 1~ 10 n 10-

>\9t9, ~1 "'11 10 "\0 ~O ),') "; L\ 15 1; 4 15 11 ~;z

.1,._ 'J

~13l3 ~7. ,\0 ~~ /-5" 23 /1'3 -1'6 1\0 ~ ), )2 ~o 11

"no 11 ~~ ~ q. ~I ~ 7. \0 10 -1(\ ;:J { ~ 'i '11 1:)

~S~1 ~~;lA 11 1() ·1 ') -1e 9.5 ;\1- 14 -\4 10 'Ii·1 l,.'

~99,Z. 1'1- ~o 1~ J\ 7_ 11 9 11 -'15 12, 1'3 12 14

4, A1f/ s I..r

4~/5" -1cÂ~Ag

4~

~ -4,Y'Y\)(.

9t m.t

4 tM.( [~n\--)

p -= 4Ce. t~ cp (K'H )rrn7.)

C0 '30 'f. 0) C1j -" ~ID ". A,?> --:: (l) 1-02f» 3 0 )< .;f,o'Je cp10 ')( .,{'I '3 -= ~ 1- '80)30)C IttO )C~,D '(;.1 /3-=: ~+g0>3 0 ~ Il 14. )C ~f0 1'- Il'1~ -:! 0)~6

_lt-.OHr ~~ <l'!.M J'wJ-- .J)' eot.~~CIV'fÙ-~" tu.vou;l,e,A ( ~~~ ~bv-Uo

F ~ p. ~, ~ -=- ~Y~OlNe. ~~ttoui("e- (rm'l)

~f\;e.A

F ~ p. ~ C'.eN)

F:., -:: D)W~ 1- 6'/00" C~,S; 4-,0 +O,Ji}:: A6, 5-1

F~ -= O):rg x 6,00 'f. C~,l)O+ ~4'1. ) -= vt1-)Â 8Vs -= ~18)( 6,00 f (1/50+01'111) -::= vtt,A 8

1='" -= 0) g6 " b(DO'" Pl;1-.- + A, '20}=.A 6; 66

W"rQ.A o.Dt-kf\.e.b

E-rOvt(A ~ Ckf'i)vi,.ur- ~::-lJ) 10~ l' 1) 00 ~ 3, ~ ~ = 81 ~5

~.~ F"2. =0>1s ~ 3,OD~ 3/61 -= 815"~~~ \='3 ~ ~1-g X ~I oo; 3,6-:1 = 8)~C:1

4~ ~t, -=- 0,-g6 ~ 5{VO '/(. ?J,D4- -::: 7-1 g3.

~ ,'. '

~ ~~~. ~ ~eA. .'ON\. ~~.A,;~ \,ç<n:.o L~) ~ ~ ~~0l,M;)ln\

rtit ~OVY~.A.v~ ~

t+ L~~~ ')"\n-v r~ ,M..\/'r ~ to\;--~e-

~~ ~

A, ~i)J:) + At \)0 l

'3 l"lY\J€ Ca<A

Â, <26 f) + ()/"-1- ( A 1SC) L 1-.4,5 cr).A, ez 1) D -+- v11 0 fi L + .It, 0 6 ~

~ ~)C ~I'f~~ ~, ~ ~~ ~~ ~

b ~Ol~~ J.Nv~'r/~ ~ f~ 1c~ w'r ~ CA:Ab

~ f~ cMIr~e, & e..t ~~ r'l.Âb ~ L;<YYhfJ'k~(\,Q ee- t4te.-ul ~ ~.~fl-~JYJ-.

Ca,dJçe<)~ CJ.N:~

talu.4 ~ '4~eXIJ:: &rtleP -lJgo-e'u.~~~~ ~-Vy-(?D.

Dm ~tNn~ ~ ~eD~ fov<U~ ~--~y\0l..M--"" ~ --t ("" fYvY'\Aù eJ<-ArJ..,vvXJ .-a..v 0-& ~~rk C:f)~r{lD ~~.: .- Coui~~ ~ti-eL ~~ f~~ lv<YoVU)~

- G~e.- FOlJ~~t8- ~~ ~~~-be/(\(~(.;

- /Axd.;.-€- fOllY~~ .ivvJ.eKn,e. rC-ovn~?-~ ~ &-3- U:u1('~ r~ ~~ ~~~~U: ~ &~_ ~Q; fO'JY"tt~ ~~ ftDvnJ;wv .A -tv- &~L

- CC1---dv'<e. rO\K~ ~~n.e-- r~tfu« A,tK ~e-- LouL'("~ l''ovv"ti.-~ AM:te.x~ 4 ~ ~e.e,.

~ C&'w<~t> Fetc~~~. Ct»LtvOVf~ wv~gC)~~ ("VeN /rrrJ )Goul'tLi> ~~

- PertolD ~ D,A.1- ~ 9.. 4. ~ 4; Dg... ~y-JA~'/'r- If~~ffi\.Ot 'A QIY\k .1\ / '3 0

\..,U ~ 5' 1 ~ 8 k-N/rrnL

bCL~ ='> ~~.:= 6,OD IYY") ~ ~ ~eP. '= ~y.Ê"'!> 'il,.. 6(003 " 3

= ~.A 1 ~ ~ kN//'fY)

R~~ f>~e.. D]~?>)(. 0) ~5 )l- CZ 4 -= A1 ~ 8U~~ ~ ('fY\NVY k I()~~~, 6,0 D

~g/~O

~8, ~o k-N1fY1'1 kAA/'(" \:~ ~ 'POlA-t'YQ,c.

W:=

~ tJJ.tt 9 ~~" -::: ':SI 00 - 0,4 6 -: ~,~6' fYY'

UJ tOL _ 5'13g~ 0;, 8 Ji -=:. 5, wI1 J1 k ty 1fYJ7

~ --3Patolo r Cf),(j""eD (!J, 4 0 ~ 0) 3 D 'Jl ~ 4~l".l.> .Q.I~~~~

07 1, f ')C <! 4 -:::. 4-,0'8A110

'31 ?:> '8 ')eN!lYn7,

51 A-1::: ~J~8

AO,OO.A1, ~ ~

~'1/~~ 'rt:lY /fYYl ~. \,-~t~ ~ fo,'V\.:rle.D 1

C~Q..-O eJ.>(.-tex 't'"\-eo

-~<1\dP ~

.- SMJ'f~~~ re).{rrYlA)\~~

~ S.MK~rtJQ, lL )S..wy-~~'Ct~ vUt'<\À...g~(rrn.e- ().eN/lM)

~T (J1.~ ~J 4 kN Irm2

~~ ~~

~ 1C y..; t~ ~ ~ 'f. ~ ( 4-)' C7OD ~1 6[) 'teJ'!/ f'rn

3 3~QL) ~Q/'(~V,Â)

2)( u.J e~ -= ~,4)(. ~, ~5" -:::: ~ -' ~ 8 kl't 1rm3 3

~ p~~ a-~~ 4, & kti !rrn'l-C<x..dv<"eb~

~, w3~ -= 'i)' 4,&;G,OD -= A~/!10 kN/m.

~w ~~w ~o.. -::: 4( g )( ~l 85 41 fi 6 kN !,TYl.

'3 3

9 L~~'4') ~f1Y) ~ ~ovY~ .

t [\eN /("n)) ~(~~ F«~~L (kN)~) 1GMJY.~~

tl\~~tb rV'C"'~~\)J.D -:: Il, ~ 6 'D (kl'l / rrn )

wt.. ~ A" 1) 0 L (kN Irm J

~ ~",wc\;i.,tM.-v ~ ~t~ J)e- MIltv-.ùxv\--~{v\A;Y'\A ~~ VYVV\"-\'u:n~~~\f~:

- ~~~v f'0l'~~ f\YY\-~U;~ k~ ~t-("O\N~f~ ~~~L r~cUrr~ ~Ft\.e- ca, ~b~ ~)(l -t'(0Vù~ fO'VtJV" rfJ.JU~dvY ~ rfY\,ON"\- V'YV\-- / .

~o~ f'fY'\-Ov'~JvrMjVN'"\' ~~ ~Q, 6.. ~{;U)U ~~r~~~ ~~a. E~ ; .

- Ltv(}VY<à'Q. .r:~~ ~(Jh-clt.f.c~ ~\~ ~

\t""cWw ~ ~~ .~<~~Q;. f(JY\-dA/<-û ~~Y'~~ ~~)C -t"(-oW~ ~~ ~ O'\AIY tfM)~ te, rrno~

~8 ~ ~rrÔ~\-A ~ cE{fF'

PARTIE IV

ûimensionnement deséléments structuraux

Dalles avec poutresCisaillement poutresTorsion poutres

. PoteauxSemelles isolées

D.A,rMIV~nY\,i"'~i-- ~~~ ravJYw

J:!~~c)~e.n :tcAfk: ..~ 1 -= ~o /lit pO\. j~ -,: 400 VIA Po.,

c .t ::= b000 rYY\'fY\

~CfU.\-< 4Lb :

~ '26V'{.· 400et>t..tet( rve. ~ 00 )C 4- 00

.pot~)C

4-C)O~ 400

tto-~Qp. :

~) Er.~QM)'( ~ t& ~.

~ - G000 - ~"l( ~ 5() - 51- li 0,." ~)C - ~ -

~ /)'l ~~)O -= '51- 5V (YYlY'n

Ù& ~"c(Q.é

~~v1.E.f~~ rf'Y\LM~o

~ . _ t" (MO +i'6'/A,l»)IY\MI'\ - - .

~ .. . 36 000 + '5 DOO; (A +ft»~ -= 4 00 M pO\. ( o 400 J --)~A -== .{ ~. =:. 5150 cOD + (~/~ -=4'3'3 '331-> ·lYWn 36{!)OO+5'OOO~..f;l\(4+-1) /

~ . - A36 t'O\m~~ - ,

26

Ef>oW:>Âewy-- (YY\,(JvlQA/'MMxn ~

~ ""'0.;0 = -Lm ('f?DD + ~'tJ1A,>; )<36 VOl)

t """"'" = 5+50 ( gO0 + 400/l/i) -:::: J1-01

·tr3' ooo

~ fYl't~>" -= vi. 1-0 tYY\ ()\

ù~ rr~d ~~~'1-V fYr\<n

trov\AAQM)Y' ~~~.~ . _. ("" [() 00 + ~ ~~//1_1 _5)_---

""i"""" - 3G000 + '5OD/')ftCc,'l '"- Di" (~ -;B~)(-1 +~ ))

\J~~,,", ~ ~~ =

- ~oWy~ rd.e.- rvl,u~

~ -=: 400 fY'(\ m

b--:: ~~D fVY'~

~ ~ .{-1- () rmM

'iS(/~ -= 4001 IL1-0 -::: ~(~5 ~ ~,lr

b/~ -=. 300/41-0 -= wlC 16 Z ~, ~

-rcJlo ~ 1 --";> S-:; AJ3

~ -= ~ODCJ + 300 -= '3A 5() rmm~

<Q4-= e

Ed) ?C ~~[~J:S E'b ~ ~$Ces e t1 j .

3

~.., -= i~~Oo (~135) -.. A'-~ ~ A/6{

6l v1 -== ~ ')4 '=. A J b -1 '7 C>1 (3 e>k

2.5 r-------------r------r--......,---r--r--~~~

-,b

b+(o-h) 6b+4h ..,

L9

1.8~-----+---------t-JL--~r-t_r_-J;;:::--r_

2.0

2.\

f

1.0 1.5 2 3 4 5 6 7 8 9 10a/h

ru RIGIDITE RELATIVE DE POUTRES DE RIVE

2.8

108 96 753 4

e/h

21.5

1.7

1.1

1.2

1.9

1.0

1.8

1.3

1.5

2.0 t-------t----F

2.6-

2.7

2.2 t------t---------+f-+++--------f-~-_+----=~~_+-__+_-___\

2.1

2.4

2.5

2.3

f

[I] R1GIDITE RELATIVE DE POUTRES INTERIE JBESr.:

- .p<nAJ~~ jvy\ite~'.,.\)~AÂ/r.eA

rot -= 4-00 f'Y"'\V"Yl

6 -::: ~ 50 fh1, l'Y)

~ z .{1- 0 fmv'Y\

'!5( t~ -:= ViOC) III10 :::: Ojt ?J5 ~ \J)l 'tb/-bt ~ ~501).10 -= /i101 ~ Al ~

. lo(jb~ 2 ~ -::; .4 ,51

~ -=- 6oro rtYt~

~~. ~~ "f ~l~rJ E~1 7- ~~t?

cQ., -= ~ 1) 0 .,.. ( ~/?; ~)3Je tA 15t -:: 0; e5~ 6000

~z -=- ~3 -= ~B -::: ~(.. -= ()l g5 '7 0) g 0k

ô1 ryY) -:: ~I 0) 3>

~ -::::. 1i:1- 25 ('800 -+ q,OOIA,5)'4 3G DOC) + 5'0001" 1x[A/~3-0,5 (A-O},)(1+ f)]~~~4 -

i"-"'l = A/)5 mvm

3D

- PO'\lYî-~ ~ rvt..Ve.D ('~ u3te:o J S 2 0\ S'3L'nt -= 6.000 - ~ ~ ~...I)O/~ -= 5';j 5<D rm~

t lYl S -:: bOOO - ~oo/~ - <!5v/~ ~ 6':f't'i.:J fYY1rfh

J ==- ~,.,., f -z: 515V -= vi, (J 0 . j), t: ':S>c 60tJ() -=. a15e~~ 5+~f1 /(-J 4--"f.6000 )

~1't\1 ~ C~1 + ~ 7- + ~8 + ~ ~) / 4 -= (1) 61. + ?J )< 01 g5")/4~ . -=- vi, 04- 5+5 f) ( 800 + ,-!-OD/4,'5 )

~i. -~" OClÇ) +5000"+[-1P4 -015~ [A - D/t~)(1+ :d.)\\-= J 53 1 1) --1/)0 'J

tt -== A 5'5 /Î"Yl1YYl1\fi1AMAe-

-PO\lY\~ ~~ ::'4-. ~fY\J~ ~ 6000 - 2.)C CP"ÇJ 01~ :=. 515 0 /YY\/YYl -::; em..s

):::: J:!.= 5+50 :=. vd '/J. -= Lt x: tOM -= vi~ 61- 5"D 1 J 4)C. btJlJOms

~'m:= (~~+~3 + ~ig + ~(,) /4 -= (01 85')( ~JI4-= tJ> &5n _ _ 5ifjO[gOO+400 / A,5)t1~e, -

?b ooo -t 5CJOO>o1 >ClC)/8 5-O/~ (-4 -~)(J1 +:f)]-= A IJs, 4 ('fV\lVn

~MI~..e -= A 5 fi ()'nlh'\

pefvt/Y~ ~ fWYI-Y\t~)c (IJ"\,\. ~)~ """,,, <:: <t.. "'"1l,"""""{' < 1, ""....

(()M, f\-Q/yvd ~ -= Ab0 fYY\tYh.

~. Mo~ ~ ~~~~C:)\("\Xl)~·

_ è~~~JY"("\AW\J\-'

~cri~ r,0 ~-'e. ~ t& (tLGlt~

olA 60 ~ 24 )< -1, 'è fi = 4-,?:>O k: f'l11Y'rJ '"L

Su(A;,(~~ r-vrrmo\;~vt 13D )C ~/l ~ 6 -:::.-1l

b:' · k 1'1 1fYY) "-

WcJ.~ :=. 6'1 4'2, kN INn 'L

$<Mk~Q.b.J- ~~ \"~~:T CJ-lk- : ~ 1 4- )C. -1// 5' -;:. '31 G(J tc l'{I~ 1- -= VJifw8 ~ vJ.lg -+ w!g -:::: 6/4?' -+ '3 , GO

w~ -=- ~O (03 kN (rm 1..

l'~tk ~~; 4- 1 8 '1- .,115' -= "1/~O kN!rm~",w~

wr= VJ.l.~ + w~ -= b! 43 + 7, '2{)

\}.id -::. ,,1/3J;?:, i,e;1'{((YYI2.

- W~ ~ (YnOyy\-vY\Àr:~M~~~ r&le-. ~tuJ., ~e,v~ C~ o 1\11) ( fA?> (;)

v~+~ rrJ.RJ> t'VV>~Yv0~ lfV-~~~~"'fY\Jù\rrvOC(;~ eX- ~ ~~~

(~~3 C:, -1 ~ A?> (, viD)

f~::; ~{

Tot\ \B _.(J,.A6 ~~4-+A,3 \ - ~,v14 7 ~(O

1- Ci - ~, 4- -

~eh J.Lu A-Olf,fCJ<\- ttk ~ ~~~ ~ J:>-lA;Y-~~ n-~~~(J/~e;w.

p~~J<~ - (!)-16 )(. ~ 4 + vil 3 =- vi 1 01 <:: G

t1)

l''''-~ - 4-, ~

OIY\ llJlm,\. ~VY" ~ ~~ ~ t'V9Jpfd1\.c!v~ ~~MMk /.AMJY~~.,

- Mo·mhVV~.A tfJJ.J'v'rC:b~ 0"~~~.

T~ VJJ -= AfJ) Os !el'! j(rY) ..,flIt

o~ Cwg. 10 - 3) ti e~

8~z- -== bo0 (J) rfY\ f'YY'\

~h-e lfJ ~ B~"" -== Goa 0 - 300/2 - ~C;CJ/ 2 -== Iii- ~5

= ~~~~~~ .Mo -= AJo[O'3· tD~3 .. G000 ,,(H ~5) ~ -= ~4.G,b .t0-6

~ N~

~Vv-eB .v\- c.~In=- 600V - ~)( ~5()/~ -= 5'f-IJO /YYl1YY)

=: 51 5"'0 tYY\ l'l"Y\ . ~

140= .AJJ;03 '-40-~1' 6000~l515'D 2 _~ ~4~( f-.(rf

.~ N-/YnM

e'l.::: fOOO- <<:- i

Î

- - - -1- -'--- ~ 1 -1

1

1

7'

-t1

'300

-~fr~ ~ (7Yt~ ~~ck 'f'6~'>C / ~~ LD ..WYL~~ eA--.

, <$lI\ÀJ'lC r-orvSY"QA .

C -==- ~ ( vi - CJ1 6 ?:> 3. ) ?v:~'à-. 3 .~

C -= C'vi - () ~ 3 y 3()f)) (30CJ)~400) 400;c 3

-f CII- (JI Ù'3 '1: A6D ) ~ &,60)~~ ~LrO2?4D 3

C -==. ~ 1 6 gg . AD Cb !h1()Yl 4-

r _ t1 ~ 3> _ b(J()O Y' {t60 )3>> - vt2 - A ~

JS

-:: ~ 1 éJ48 ·/iO ~ fYY)NYl4-

~ _ ~b C r: é-/: t - ~E ~ cch ~ ~.$

cs 1~k - ~ JO'2?~ 'AO~

I-Jb - ~)< ~ ,O/rrg,JlO ~

Jt = o.s«70 M-o~QM/b f~éA ~~ rok f el1arY' N

IVwJel &.' ~<Q/YY\Àté ~3~ UJbn.e- ~

.t?-/~ := h00o/r;1'25 = A-t osd,vt::: Di ~5 -==> ~-'t 4!z,(~ Z é? es)(~l 0,=- t1 t'9

~oo-- ~tWr~(~~~~ ~nh)

ToJ.,~ ~ e:z-/e/l-::;A161J~A,O

~01 ~Z /e~ /31: %o V ADO

(JI ~~ m/~1 X ?~ tI1}O ~ ~/5 115

0)5'1,- 0 =: X - ..{Oo =/ X -:;; CJ) f.{ (_ '25) + AaO~/5""- 0 1lJ- .ioo ~ 5'

x -= ÛJI;" ~ ;{

v1 ()V\À r01lé (rMOrNXY\-- fO~~ )

~zlt~ ~ AIV

%60

?X.

16~2~-O )(- '0 A8~

1 ::: ~ X -::: ':,1 _ (.A 1j ) -t 6o..1/0 - 0 15'-h0 vtt 0 .

x-= 13/ ~5%

S:-Mfr<9 ,,\~~ (f'Mom,wvJ..-~~~~)

TaIb~ J tZjeA:=/11 0 => X-== "11;2

- f--_. --.----.---~----.- ---~ ------ _ .. _.------- - - -- -- ---_.- ._---- -_._----+-- .-.. ---------- --- ------- --

Design Moments lor Column Strlps, Middle Strlps and Beams

-- -

DESIGN MOMENTS FOR COLUMN STRIPS

Percentage 01 interlor Negative Design Moment

--.-1[2/ r, 0.5 1.0 2.0

_.

[ï] ('" [2/[') = 0 75 75 75

(It, [2/[') ~ 1.0 90 75 45f---

Percentage of Exterlor Negallve Design Moment

[2/ t, 0.5 1.0 20

(It 1[2/ [ .l = 0 /3, ".0 100 100 100

m /3. ~ 2.5 75 75 75----~

~:~~2/f , ) ~ 1.0/3, = 0 100 100

~13, ~ 25 90 75

-- Percentage 01 Posillve Design Momen.t - --

~~J~[?/ [,

---~r rITJ (0, r2/ E,) = 0

('" [2IE,) ~ 1.0

DESIGN MOMENTS FOR BEAMS 1

[TIPercentage 01 Column Strlp Moment

(0, [2/ [,) = 0.0 0-- --

(0IE21f,)~ 1.0 85~--

Nolee: That portion al the design moment nol resisted by the column strip will be assigned la middle stries.

t.mear interpolation shall be made for in-belween values.

% MOMENTS' PONDERES DE BANDES . POTEAUX,DE BAf'IDES MEDIANES ETDES POUT RES

1 .

T"ew~ .NY\It0v~ ~N2- wt~~ ~

~z /t:= be)()CJ/5"HO =::: ~I 04- .

cR1 z: ~.g;; =7 "1-1 Jq. /(, -= eJ) '85"" -11 04 :::: 0 g.9

TC("b~ovu..)('

'3 ~ ~ ~ltu ---==> '1-3/ 35" i:~ ~-tA )C J:M.A"pr-é)Jl~ :-y '1~ %

T,()L,V~ ~~~

Mo~)..-~~ ~~~ ~ AOO - ~ 4-, ~ ~ 5'( ~'/ J1 % (~/5q7 rOVV- {'(n~Wx).

lko~F'~t-J- : AOO -,,1-3/ 35 -=- '2?',65~ G1 G'5 Z (vit '3/33 %fevv- NnO'V-\Avr)

/tAo~~~~.' (/WO - '1-,'7 ,z: ~6~5 % (Jt ~15'k ~ (rnAr~ti.M).

TI(lXN~ ~~

titD~ ~~~: viOO - '1-T; -= ~Jo. ~1? % (J

/lLto~ ~~.: Â C) 0;.. i3 J ?ç :::: '?2 67

65~6, 66 %

ZMo~ ~ bO\lvv~ ~ ~C>~)c7 ~)<IfCiW~ . -t~QQ, 4

9~ eZ/eA %f!) ()

o, gC!J x ?.,11 0 85

()l 8Oj- 0 ::: X- 0 "7 'X -== -=~ &C!J >< g5~I 0 - o gç- 0 /l, 0

X -:=. 7-~/ 66

aw:a &&::& <i==&:.

40

CDo

~ '1-l-

41

1

li) \..r) ~ 0 Ji-........ ~ - ~J '-" ~

........cd)

~rn <r -....l) ~

e "' '" ~F 1 + ) + \

('(\

i ;~ CJ ~ csJ .~ eN..... ...... ......

"'" en~ -

~--Q~i ~

\-~

~

~. + ( + ~

j ~ '\:)Q

i ......\f1

r<l€) CSV l4- 00 [<)cL L \ '-.0....... . -)"i en...... -....

~0 ai> ~'" '"'

'-D-t ~

i ~) + ~

Ji..~

~ . Ld) ,

1~~ ~csV csV

~~:0 ......... ":..0 --"- éI' CJ - 0~ ev ~ aV

~tl,

~ ) ~.+ ;- l

.~?t ~ l~ '~ ~\,... Aè j~0

~ ~e

\; 0 <L :3 ~.

~Ja,

'~ et% 'ê ~J:r"' ..;,- ___..rr/

fh"rrrv~u ~r~i.eÂ..{/(~ fCMJ'{ /Vtfô~e- ~rThO m<W\;V-j)YVQ~~p

.c:l-= ~ - tVvwob. - f$'# 2-D

-:: .,160 - ~O - .A~/5 -= 4"201 5

d:= A W f'N\ 'f'n

-i ('(Y\. dL tow-~cIMK ~~ => b-;; .{,OVOIYY\rY\

le ~~ ~ ecf! S\.1 - D cA8\\ 1=='72 hcF '6 L l.f11~J~

_ /lit-.- LD " ~ e" ~ ,&I)~ ~ 00 [ J - f iJ;Zq -.4,00 J=>ILOOD)CL.4;'0) 'l. ~ ,10x:G)6rJx. ~ 0 .

~Ob~ /4Ilq. := '34 Of [v1-A616'1e] -=->~

5bibl 61 f - 3~O f + {)i(JG§ tAA~ ~ 0

M" ~ ~N'm

@, ~/OC)04~~40 3~v10 ~ 300 300(JIOD~

1-11- 6;. V016~4D 3tfvtO~~OO 3006>,00~

43/-1 (JÎ~vt.-1 -102.16 1- ((j>~l; ~A4(')O A4tO

40)4 ~D~8 cAJl1-b 6 çSA~=>-1 ~VO .A10

4f+.,

1-r/J.{~~>4400 .A40

+rp~O --===-'/ 1-00 4/~O691

f-=~ ='> 14>:= tbd = ~'< vtOOO~ A-40

() I4G

-::: ."tA o000eM.?, (+) e4 emM t1 lA~ (rmm

L

) t4~['1Y1m)fJ>OO~

(J 1O.;t~

O2D06

fif.3: _~ I"YY\.O~~ ~'f\~b (<è)ek fi.. ~ovx ~ (OV("~("Q.A~ ~ ~\- rilè~~ te to{)~ (w'=..A01D3/LNlryn1).

PcfVlJy ~ f~~Cw -:=. A11 6':; \.eN!;m"l ), rfM- pWJ:>ll.fr0l>.flN ~ '6li"~-(j!,A ~t.io r-:': ~lYiJ J>6't\

~..(NWQh apf'(Ox~WYY\.~.

. - '1C1W\ ~ ~ ceL 'ât JCMiÎ-- ~ù,~~~M.- CO~ 'f\...e. 17Y0'VV\4ûe,f{~cd ~ eJ)~ ~\'€.a,{,tYe ~)c

~~ ~ lllr 4- J- b tLi~vJJa.}.A 8~-<<1n~ ~~.MM-VOlNL\-- Q,a. ~n.e (~ V\.€- ~O'Y\w-tuou"1\cŒ B.

_A-<-rnvothN''feb ~ p~b (Q(JYl~k&ih~)

e~,==~ -=.~Lr = 0-(0035 f = Ot046à~ uoo fW\~~

~) tf'\: _ _ • ,y l::WVV\.~.

~ t.~ -=: <A60 fYYIrtYl P~eô t.:= 400!lY)rrt1

J.:= ~- 40- ~~o- ~1=r?~/~ := 400 -hV-d1-2'~~)2cl =5~6 /l'Yl rt'Yl .

lVJ -= -'l60/?'3 6 -= DI 4- 'B >- 0;>0)0 ~ e.g/d -= 0:> ~

45'

t,ild =- el 4K/' é>; OJO" --'7 f>crw\t<€D ~ T

~<Mh<~ ~~ bu..) 'z: ~ bD fYY"ItYn

b~ 2" ~~)) t::: Ô)l2 '5 ~ 60CJ() -=- 41;00 IYY\~~j L. ~ ~ 6~ + bw ~ A,~y J1bO + ~ 50 -::; ~0W rrY\fYY)

b} ~ 4 b~ -:: 4)C ~ 50 -::: /L,OCJO rrorrv-,'oS";:; _tOodrrt\/Yn ="7 bUw- 41 0

PcrvJ'C~ ~ bw :::: '500 (YY\fY'h

b! ~ ~1A ~ := GCO(!)O/v1l2 '"::: 500 f"YY) fYYl

b~ L 6 Brt + bw -:= 6~460+~O(') -= ~CJJ-60 rmrrn6J ~ 5'00 ('fY\fYn ~ bJ/kw-=~66(~~lO)

*14~ .A<('(V\,o.t.,v<<?b ,. '2 -c; M '; ~ J "Z.Mil. ~ Il.t bd .~o -~ ~.~ ~ 'l. ·10 ~().

f ~ i4> /brl ~') b4~ -:: ~bdlu

1

, P~€Â A/V\X~/"J,..e.0v~ (~~O 7C qDO) b": ~hO 'tV\Yn

1" 01,~.~ p~~€;~ cl-=: ~3 b rw"l t"'N\

M'2 -:: ~Il ~ Il '2. e 0' rtç,w%-11.14 ~~ 4-0 J1, ~~ A04~ 3f!/; ~5

1

~ '..0 -+ C!)O/6g 3/~ °/~~ g23 ~ fP ~5C) b-~ r- -.46~44- GIf} 11/ ~~ J16~3 ~30eJ4~'eO-c:

V\

+ 1'1,1'3 ~/g o.es'-....,

144- ~ cp Cf6.-(- '-'~ \--r- - ~~ AG f}/3-6 '302- ~erp..(5"fi.o /-u )

~ .+-Mi5'D 4/ () 1, ~4- .AOir <i 3 C7J4':r- l-V'.........

- ~4~,35~ 1-- 1-1 6 ~/4,f; '2066 3(j30<:Il-s/'.. -+40D 3b" .1,08 M1- ~q5t5 'c

6 \- /<l:

kN'rn fi/\. Oyy\'~J) ~~\ct\.A 0. y\'~(L ?CL''< p~~{O-n'\.e.1

46'.....~;C7

.....~-....

T-BeamsRelnforcement Ratio p. (%) Baud on Web Wldth, for Resistance Factors Kr(MPa)Relnforcement fr = 400 MPa Concrele f; == 20 MPa

h/d 0.10 0.15 0.20

~ 2.0 3.0 4.0 5.0 6.0 2.0 2.5 3.0 4.0 5.0 1.5 2.0 3.0 4.0 5.0Kr

1.2 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.37 0.36 0.36 0.36 0.361.4 0.43 0.42 0.42 0.42 0.42 0.43 0.42 0.42 0.42 0.42 0.43 0.43 0.42 0.42 0.421.6 0.49 0.48 0.48 0.48 0.48 0.49 0.49 0.48 0.48 0.48 0.50 0.49 0.48 0.48 0.481.8 0.56 0.55 0.54 0.54 0.54 0.56 0.55 0.55 0.54 0.54 0.56 0.56 0.55 0.54 0.54

2.0 0.62 0.61 0.60 0.60 0.60 0.62 0.61 0.61 0.60 0.60 0.63 0.62 0.61 0.60 0.602.2 0.69 0.67 0.67 0.66 0.66 0.69 0.68 0.S7 -O.S7-- 0.66= ~-:~?-o==O;59=-·. t\ "''7 t\ 1>'7 0.66v.v, V.VI

2.4 0.76 0.74 0.73 0.72 0.72 0.75 0.74 0.74 0.73 0.72 0.77 0.75 0.74 0.73 0.722.6 0.83 0.80 0.79 - 0.79 0.78 0.82 0.81 0.80 0.79 0.79 0.84 0.82 0.80 0.79 0.792.8 0.90 0.87 0.85 0.85 0.84 0.89 0.87 0.87 0.85 0.85 0':92 '0.89 0.87 0.85 0.85

3.0 0.97 0.93 0.92 0.91 0.91 0.96 0.94 0.93 0.92 0.91 0.99 0.96 0.93 0.92 0.913.2 1.05 1.00 0.98 0.97 0.97 1.03 1.01 1.00 0.98 0.97 1.07 1.03 1.00 0.98 0.973.4 1.13 1.07 1.05 1.04 1.03 1.11 1.08 1.06 1.05 1.04 1.15 1.10 1.06 1.05 1.043.6 1.21 1.14 1.11 1.10 1.09 1.18 1.15 1.13 1.11 1.10 1.23 1.17 1.13 1.11 1.103.8 1.30 1.21 1.18 1.16 1.15 1.26 1.22 1.20 1.18 1.16 1.32 1.25 1.20 1.18 1.16

4.0 1.39 1.28 1.24 1.23 1.22 1.34 1.29 1.27 1.24 1.23 1.41 1.32 1.27 1.24 1.234.2 1.48 1.36 1.31 1.29 1.28 1.43 1.37 1.33 1.31 1.29 1.51 1.40 1.33 1.31 1.294.4 1.58 1.44 1.38 1.36 1.34 1.52 1.44 1.40 1.37 1.36 1.61 1.48 1.40 1.37 1.364.6 1.69 1.53 1.45 1.42 1.41 1.61 1.52 1.48 1.44 1.42 1.72 1.57 1.47 1.44 1.424.8 1.80 1.61 1.52 1.49 1.47 1.71 1.61 1.55 1.51 1.49 1.66 1.54 1.51 1.49

5.0 1.70 1.60 1.55 1.54 1.81 1.69 -Üi:3"-- .- ~ i .55 - (75 1.62 1.57 1.551:57

5.2 1.80 1.67 1.62 1.60 1.93 1.79 1.70 1.64 1.62 1.85 1.69 1.64 1.625.4 1.90 1.76 1.69 1.67 1.88 1.79 1.71 1.68 1.95 1.76 1.71 1.685.6 2.01 1.84 1.76 1.73 1.98 1.87 1.78 1.75 2.06 1.83 1.78 1.755.8 2.12 1.93 1.83 1.80 2.09 1.96 1.85 1.82 1.91 1.85 1.82

6.0 2.02 1.91 1.86 2.05 - 11 nn !_... on- - Î.;; (L92:: 1.88

6.2 2.11 1.99 1.93 2.15 ~:991 ~:g; - 2.07 1.99 1.956.4 2.22 2.07 2.00 2.26 2.07-. -2~ 2.15 2.06 2.026.6 2.32 2.15 2.07 2.37 2.15 2.09 2.24 2.13 2.0~

6.8 2.24 2.14 2.23 2.15 2.33 2.20 2.15

7.0 2.33 2.22 2.32 2.22 2.43 2.27 2.227.2 2.43 2.30 2.40 2.29 2.53 2.35 2.297.4 2.53 2.38 2.50 2.36 2.64 2.42 2.367.6 2.64 2.47 2.59 2.44 12.?_Q) 2.437.8 2.55 2.70 2.51 2.57 2.50

8.0 2.65 2.81 2.59 2.65 2.578.2 2.75 2.67 2.74 2.648.4 2.85 2.76 2.83 2.728.6 2.96 2.85 2.92 2.798.8 2.94 3.01 2.86

9.0 3.04 3.12 2.939.2 3.14 3.22 3.019.4 - 3.25 3.089.6 3.169.8 3.24

Values below solidline indicate T-beam behavior(a> n, shown at left)

L 1- b, • 1 0.85<IJcf~--.i- A. M, == Krbd2 10-6p., == b.,d

~~L=L~'. -

,.

[ p.,<IJ. f, ~JASOVE

AXIS rA. . K, == p.,<IJ.f, 1 - 1.7<IJcf~ b,SOUDUNET == p.,b.,d<IJ.f, r- ..

1.. b -1 ~ b, h, h, a a 0SHOW---_ .. --_.

., .K, == .0.85 <lJcf~ 2<. 1-n,;,--- l)-d(l -=-2d.l-+-d(l =-2d)-' ~~~D..,

POUTRES EN T-47·--·

j

f>O"\Vf<'ll/.> eM;te~~l"QA (~OO~ 4- 00,) b-:: ~OOtmlY)et~ '336....",,,,

M~ =:Mt- .}f.~ f% ~ /J5_ 1)1;.) 65" .J[/6 °l4~ 4<!> . ~ fi;~o

"'t

.'t) ~

+4-6, ~3 ~c/J~Oç;) t- ~I i.t 0/43 43?,\. 1--

~~ '5...... - 3f., r;'2. ~/6 0/8'2- ~~6\.J'"---."1 h

- 3~/~g .l\/~ 8)36 363 2fP45t-r@"

-4~ 00 () (5' ()/35";~~ 35"3 . 2 r(J45~~ ~ /'-J\ (- -+4-~ 5~ A,E Ollti '6lr ~ fP~V--.... 4 .\.. -

-~1-) ~9 ~)g o,g9 8Q);t ~ rp30QI

~.H

C r +44,6'& .{J3 0,4 0 403 . f2f/J 20es-e,

7 ~ -= t'~-M~€-' ~~~e-Tl t r~_

~ <{}..,)Jet-' . . ~,y~

{CD ~etk f.CJU..).Je.-~ fC!"W" ~ f'ovvlrc~

~O'h cyJu.olt-n~ f QA.AA)'~IY\\ ~'( € rvet.,Y\.AAA f Ol/l,v

b ~-~~ -tx~l)Q)YD~ ,

1 N"\C\ .' / tr\ k! "Z.v ",\'" W g -:: .A,;()1o ?, N ty)-)

-, 3 0VJ -::. Ji 0, 0 3 . ! 0 '1= ~150 .AD -== ~ r J , g

VJ:::' 2.:f, 60 kN

p~~ ~ UJJ -::: J1~1 G~ kN!rm'1.

\I~ -::. A'?> J, s .to-r,;" 215{)' W:' -::: 31-1 4 ~

Vg ~ ?:J 1-1 50 kl'l

V7 -= e, ~ A ~ VF: la J

v7. ~ D, ~ ~.-110 )C()/6fJ ~ V~O )C A()OO'f:~~6 '/0-3

-= 6f.(O~

V~~ 61)viOIcH'

V~ '7 y~ ~ ~ ~)G ~ UXA.

\J;VYY\JV~~~·~·~~ f:o'Vv~~ ~teNÀ.e-LNYeb ,

-.!:!'Ôr-0~~

~~. 600(j)C 6000lC.A60t ~ 'W WlP.x- 8'6 ~ 400 Mf""

~50~4DO

- ~

-------~

. -------

~

1

v

~ [J1 -e

1O[

1C)I..;ri

i

1 300-_.--,--

{---A"--v

'i1

---- -i'

,NleJ~M, JMrv-np~~

.A)~j10-(\-- rele- eAAO\À-~r-.

vf"''''v r-.

{)~ovyyvm,e, ~~ _~__! v{r _~~O'&-A ty(tvY~.&'\(ÀX\'y- 400 ~ J_2.4,~~_/C-----I-t,-f------

V (kN) ,~1b r-t

Vt e&.. t'o\.,'tJ€-- ~ fO\~)c

Vf ~ J -:: '?i~G l'MM ~ ~ 80l-U ~ fe>h,e\AA')CV~ -= D leN cGL ?,0 OC) <"'N"'~

'336 -+- 400 .::: 5"~ 0 rmN\ ~ ?>OOO - i)';6 t: ~ 46 4 ~fY'r)ot.

..YL ~ ~4 6 4 ~ Vf) 7; o, t ~ VI C~1'l)V1 ~000 (\ tN\AX\.)O

;0; Vi ·10 '3>_:= YS' lO~ -= Ô) O~-1 ~O6' V~ (JV\ P~)j b 0\ ~6'D~?>~ b <t

w

Ab 4- 1 (S3

.A~tl{1

Â J b1

~3~)\b1

A6~/f6?>

.A,Q>4

2) W~ ~ âfr~ f~ ~ .~KlbQ~\-ot,nut oLu.- \o~t-P'h

v;-= ()/~~ ~m:::: fJ)"l"'(J-1107'0160~Y'2.0~ -= o, fi 4- M pO\- ~/2 ::: 0) <21 M Pt\.

Vj. '> iJ';,/~ lQ;\y~..c ~o.Ax-eb

etl("~~ ~'fTe. N tI.ttJ ~ f(!){'~ ~- ut tf)J..}J"et

b-o~r ~ A'S5°

------+------------

~ cP. A., 'rS ..... b. (v,- Vc )

s~ d/4

s~300 mm

~ cP. A., frs ..... b. (v, - vc )

s~ d/2

s~ 600 mm

closely spacedstirrupsrequired

·""I..A' 1(:-'/.I:L r-- - t:5

normal stirrupsrequired

- --

2.5

V,

(MPa)

[tSJ 2.0

s ~ A., f/(0.35 b.)

s~d/2

s~ 600 mmminimum stirrupsrequired0.5

1·°L-__---------:~~1

no stirrups requlred

40353025

OL.- ---L ...... --lL-- ....J

)~

f~ (MPa)

Stlrrup DesIgn Requlrements of Clause 11.3for Non-Prestressed Beams wlth VerticalStlrrups, Zero Axial Load and Zero Torsion.Values are tor normal denslty concrete.

ru ETRIERS PRES DES SUPPORTS

~_ CMP~)vg - l/e (MPo)

>f. 05 )llv~~bw (v~-~)

2 g0 rryvY)') .J1 C!J 4- ~IY\"\

SLd/~-= '33b/~ Ç~cJ14 ~"33-6/4= A6gfn\ trn' ;:: ;84 rt'f\ l'YY\

S~ 000 fYV\f\'v1 :ç ~ ?>OO rm IW\

c;c::.A6~ ~=-go

'3) Wc.vd ~ ~~cA ~y; ~I'(~ ~ti.QArtl.e ~ ~ty~ .

W éX~...o ~tYW\r ~<JU;'("e, F'v-uAVf '7 V'?t -= ~&1ltI~ -= c9-, '-1 tAIt POL

g té. l -= 3'3G -:: J b -g lm (YYl ~r~~0l)&""'ffiM.VY"\ .

2 ~ J...:= bl.\J(~-\fc.):::2t)() (u .. vo{.)5 r/Js IJ v ~'t 68000 S

\- 4::, o, 00361 b( ~~-trl,)

~/I 1 ,_-1=\f~ _ "1~ta 1 --

. . -..T>r--1--··~--. - . -1-· --,' -:::-------------,.....r ........--------

o r;i~,}-l----J_·-·,--.1... \1(, .----- c' ,. !'-"~~..~~-+~-0__ ----7q ')_/ 1 -:'0'):) J,') :;1):): 3()'JO -'.,.Dr) ,/:)..., 1 ./(1./,,1.

. .:'__ ., -~~---{-----------------------------/.

"

No. 20 ;1153,OOO!

1

1 1 1., 1-y-n.'1

No. 15

136,000

102,000

1

No. 10

51,000

Values of q,. A.,f, for U stirrups

., 68,000

1 1 1

400

300

" (MPa)

14 s, ~I

Superimpose the 1/s curve on diagram.Read stirrup spacing where curve crosses heavyvertical Iines. Number of required stirrups equalsnumber of verticallines intersected.

Uae of Dlagram:

1

1 1 1 1 1 1 1 1 1 1 1 1 l '" 2040001

l ,f 1

1

1

~ t !1,"'j

t !1 (v, - vc ) b. _ 15 q,. A., f, - 5

. _. . . . . , , 1

3. If v,> 0.6 Àq,c ,jf[then s ~ dJ4and s~ 31)0 mm

4. s ~ A.,f,J(O.35 b.)

Il

_ ,

'!"~'-':' ,~"''')''''-''

.... r' .._". l "'.. 1 ......... 1 1

75 mm spacing

Notea:

1. If v,E;;; Àq,c JT[2. 8";; dJ2

El: 600 mm

-.- - ............

(V, - vc ) b. 141. A., r, =9"

, ''TJTTTl T0006., , , . .. r-,r'{,1 1 1 ;25

lm

l

0'010'_f:;'J,~..;.~,.\,. ~l"-"~i:'1,f.~~..':;:['.~'~]f!·j~' ~.J1..'?I''<.:' ?~>I·;·:I·':··I·'··II Il il,-': '~:: ,~. ~:; ;~~ [~ Ô~~ ;:: t t i :~!':~ ~~ .. . .:i'1· . '» .~. ; .: ,:,. "'-r C'" ~~ ,', ~' ";;'. , • 100 mm spacmç

...' -: ~ ,', ~:: ~:~ ~: :; t~·· ;:;~. ~~: :;.:: '... 1 1 1 1 1 1 l '.' " .: ,.J ..:1 ~I ~. ~ ~, ~. :~; "'" ,. .... ... ri

i·. _ ,;;;1 0..::", .- _ ;,;, ,"" __,... . .• ..,

0.014 r. 1 1 1 Iii 1 1 Iii ,1 1 1 l " 1 1 1 1 1 1 1 1 1 Iii i i il Iii 1 i 1

0.012

OI?')~1,

0006 ---' "

.• )"1. 1

1 1 1 1

1:DCDDE.~

CDQ.

~ Il~~~

C"0(1)"0IIInS-eclit

CTOC

0iiiclitCD......w

6

1

5

····1· '..'. 1~." '<:, '1~""'i.·~I·~~~>~' ~~~. .~~, ~ . 'l'--'':~'~ .~::~ ..;:_~~~:::~:~. ,S"'~

43

Required stirrup distance ln metres = SI

r"oo'?ji,~ri.·.~~I~k'5Wf:':~J1f:::·,~i0~;~~~~?~%~·[;;i:P:';*"~'I:';<,i't~~~:?·~1r;',::::\, .:~ ......,:.~,,~t:' ;''~'~"'"","~ .."I ".,' ", .• c , (:f ......<" ,~ ......<>;...:-.~I ......~], .... : ....~ •.-: .~'.:-'.' , ..........

~' 1'2iF'';,...., ,'~jJb,.,.,f f

500 mm spaclJ 'l'" <" .J.mp,. 4.1

, ' ['.. 1 l"

•1

",'H6

0" "'L'.' ,,' 1 > 1 1 1 J 1 1

o

0.002 f~.r?:-~~'fr\\

[1J ETRIERS AUX AUTRES PART fES DE LA POUTRE

:-5 ~_It"J~ -= .~:oO."Ao 0 :;<!.44lm IYY'\

-~~5bw ~~5')o~bO

ç~ (J)~A\f~~ ~_~w.ClJS-\f(;)_ ~l)D(tJ~-V'e.j)

- hw [lJ&-lF~J ç - q t4vS~ - C1~Ç ~ ~"oDYJ 4-00

.i -= CO' Vg-\J(.

~ 21~

A 14D()/005r.1.

u1~ 86

~

11

~~~

-h----------,-------4-.1

h 1

. .J'l000---- . /_. _ _.-.1. 1 _ 1

._. ,~~ 50e } 1/,};

.- "

i __"'. ~-

P~~n.~\.- IQJY\.-~ co:um ~-f~'(eJ> ~ f\.Û)~ (~i..Vt~:~ )/

( TC)r~ role- UYYn-~Q/~)

H'-àf-~eA:

~~ fOOD y. 6000 )( '~bOà~ = ~O b1A~a. g~-= 400 Mf,,-

Pd\A,r<~ ~'f'~ 300")< 400

-1','.',"

:.~O•

'---r--

--~ rr -r- ir1 1

l '--->1 1

1 \ 1.-t-t-r---.1 1 ~ III-li ;1 111

1 Il

1

1 1 1

i"'~L- - - ---=---------ft, - - - -----r -.- -----.r- - - -

~ ;- 4 0 0 :111 \ t i

1i . ~1-1-0--"------'-----'-;---------l..,. ~r

A

AOO

y /lltO"MWIJ'r ~ -fu,~ h~.

- ct,ovr~A_~CfY\~~C1CCl0 ~ : ~4 x ~)A 6() -= 3/-8 4- lGNI/)'J'12.~~t- p-0fl)na,~ Â-, ~ 0 ~~/ffY)

\.,Vol ~ G"I A4 kNI/'«)

\JJ,Lg =: vi, ~iJ ~ brv! 4 -::: ~ '+ '3 JeJ'I!rrn'L

-k-~r k c.1-ow-~ f()'Yl~WTaù, we~ -:: A,l) 'F- ~,4- = 3, 60 kN(tm ~

vvr= UJJg+ Wtr:::. 6/ 4 ?:, + ~, {, 0 -'- .A O/)'-?> /eN1/YI?"1

~~: we~ -:;. -1.,'i~ 4,8-=: '4(~O kN/mL

lJJ~ -=: Wd~ + U.Jq ";;; (;,4?:' + '"4, '20 -:::: A'\ b' '3 k..N//n1

iii' -

1

1

Il1

\q <6- &~ ttU ~ voto-nne-

? 1- 3 := '300fJ - tJ =)1 X ~ '3 4- ~ ( ~ 800 )x- 3 »sco-o ?:JOOO

X -=. lJ -=- ? ~ )1-?, le1'1 ' /)')')

~ MOYYt(Wli~ ~ ~\;)I,r(H.e- ~ ~~<::~~ ·ecL r-~e, ~~ ([CL ~vVVf~

~

1;" == ~" ~4 A~ VJ~~v ~ 30() y; 4 00 ~ vi ~o ()rJ() rrn rm ?

Pc ~ ~ C30D +400) -=- /lit o0 cmlY'n

~y := .&1 ~0 000)z " 0)4 'l''~) 0 ,,0;60)C '(2 () .4,0-.. v1400 ·

T - A~ 0)· kl't· fYY)Ct" - vL J '-r

~ ~1ôl:r::: 2 i 1b /el'!. fYYl

(JI 61- ~'y' ::: :1) 4 0 kH '/)'Yl

1j ? ~~ri1:y ~) Om ~1MùK wmfY~~ ~J-.A\ rh ~6\.. 1:0 r.~ .

Dm ~~ ~~ ~eD (OV\cYt\;~~ h t-O(~.

T~ ~~'F ~ 0;61 ~'f.

V i)JJrn..~~VVVt- ~ Q.o.- -fo \~( AIt~~ d,e, A\JYY1-r~~ )

p~:: ~ (3 4~ -k ~i, ~ )

p~ -= vLvt ~ b ('1"(\ fYYl

~e -:= D;6S~ )C ~vt?J611~ -.=. '1r:;G CYY) (YY'\ '2.

b) ~ ('rrnctb.,vy-e ~ ~~Gon .

M~ -::; .~.~ ~ k ~~ ~ ~ wb~~fY\ -= 6/00 - Dt 4D:=: fi 1 GO f't'AiYY'

)cn;~ : w -; ~O l O~ )c 6,00 ::: 20106 k:N Itm. "2.3vu. Q-::: ~D)()6 ~ (~) 6 ) :::: 60

1ÜJ-1 (te:N -rtY) .

() AD~~~ : L,U::: v1 ~I b'3 )G S(Oo -::: 0;';::( ~ b \cH/t1'n

"l- "3M~ oz '2+ ,DG )Ols/,) -:::. ~5",4 00) LcN'nn

v'LO

$ --=. Mt")-' t,O ~ '"::: o m $ l vi - e t$~ ~ J~ bel 'l- G 't'~ O~ A,1~ ~~

la -==- '?JOb é'tY\~ ; cl -:: ~":? 6 m'\0'Yl

60

0, 0"'30 M'l. -= ?>40 e- 'i666, 61- ("='-;>

5'/66,61- (- '34 0 e+ I>t D30 b1('1- c:=. o .

t1 r-z, oz vvts lieN~) f 14 s t~m~)

0~/l!)-i ()/001 ~ q?~.'Î =-'? Aj)OQ

851 ft ot> 010 oC!J ~ cp 0;~ -7? .AJJOO

c) l4 (~(e.. ~ ÛAo4,~~ tY~U~~etR

l::: Jlr4lJ W~rY1 .a. ~ ~0t-1.Je ~ ex l-ob~T01): '1"= A (45 k ~02Q;", ?,~::= 64-, GO \cH

~

HM.t,Ju.'(~ ~-::.-l{-lI1" ~1, ~~ lJ,b := Zf/1g kW

~cM,~<?Nv\-- ~ Q.e, ~V't -;. DI ~ ~ ~ VF" bolc Ol,

=0) ~ ~4,0 lC 01 6D V2o , 300 'le ?>'36 -!0- ~

\Il- -= 5' 4 lcN v;/~ ::: ~ f \GN

v~ / v; /2 ~7 ~ ~ii\tyvUur~ ACfY\.~ ~otV'ltAf CfUK ~r~r1\~ ~ ~O\.À-~).-

~'ff\A,V(y) lA v -z: D) 35 b ::: 0)35 ')( '300 -= é), ~b '3 rM fY\ 7. .

oS ~~. 400 ~

J) 14(~e 'I"\U~~ 1c>'~/Q.cL ~~JvlrV\ J ~ Ù.L\ ~ ~. '

Ehm-J> 8~~ b~~ WV{OV) 4. -= vlOO f'YY\~'2 ~v:: 200 fYY\rrY\'a..

~ ,el(.ooCoY\-o.iu,<e, ~~vt'e.

~ _ AOOO +- ~ -= .t000 r i q --=- .1'3':1~ rm fYYl '2t;~- ct ~

'3 ep OZ b "="/ l4S :;; A400 ~ (y'h'-

'fjWx elr<Ol;("~'<e ~~4ù-éÀe.A.Ny'

14 _ M MS _ "1bb M~ -/0'>""'( - ~ - O)Ug - - ~ -o)~ li"3b~4DO

~

$1'\'\- Mâ -= G9 1~ -1 !eN -l'Y' ='1 145 ""1 :::: - AC!lÇl) /?I6 Tf1 Tf1

l

~~k M~ -= ilbtlt ~k:N-m=7 Ills","'l -:::' - --:s~ ~ mm"

~ cp .{0 -=-7 A~ -:= 2.0 (') /'rf\ -rn*l- ~n'(ff\AAXY)'.

AtJ0vt~}D 'v1~O

DJJm~(1Y\(\,~· ~~ ~e>~xJVY\Jt&-~'v2

~~ =30 M Po.. ~~ -:= 400 M Pa.

P6~'>t: ~c.~-h-~À~)C ~,)( ~wm;J~k~ O/~

.j)e-\ Q-CUAx s: eJA.<rY\ (l'Y)yYl) li~~ e-fPte,~ 3!;0 x'3~ 0 '?, t

û06~ sGDx; ':$iiO ~~

lê~tQ.OU;' 4 00 ~ 400 .J1~~{Q~ 4QOy400 R-CF~~ 40~~4VO ~.ç

~'f~WY\J'y- FiO rco rrr:O-« ~.'pr6~(L M~... é /iOO ~/7'!'~ ~~ ~ rJtuOUA-X

.A) EQ()VY\ ()CùYY\ \Q;V$\-- _

le-:= O)~ n,.~ 0)3~

e<M ~

3'sOO ?JbD'~500 40C)4000 400

63

Q::;- 0;60~~ 0)65.'( -;: 0) 60

jI] \11Vto e~ f~>C

t11 /M? ~ ()/5

'\fCfV\P ~ f'ô~ ~ ~n-eJ:>:êI7n'y~CC>~Y\.,~ CdVVik-l.

OfY1 4~Q- ~ 1 e&t\r cll~yt~.~) 'rA(~l~ ~ rot~)G'

1dv~~_ 1&-::- :s1;0 fYY\{YY\

~ -::: 2t 0 () (m fYn

~l(YY\rm) 400 400 4-00 3J?D 36Dp~;: ~ ·~1{)1 N ~6"3~ ~ooCQ. A2+-61 ~23 ':)g6

i\ /A~ A1),~ A ~-I S' ~)-1 1/ r; 3/~

f1Il '2- / !fl0rJ~ Jl,t?6 A,CJ6 111 q6 2,5'3 ~/33

r 0; é>-4 Ji 67D1 O?ûJ!. (J/O.!J. °IOA~

~ ~irOO AbOO 11600 K~~~ Jl,~15s

8rp~O gc/JJlr) 8 cjJ4 6 grfA6 gr/JA~

~fO-L~~ w.d (e. . c1.1 0~ L- :Il G d "'M(Q.

ç f:: .4 9 ep#AO

s~ ~.

64 .-

--------_ -----------_.__ . - --"-"-'-----'

r rValue.8 01 Gamma 'or Colu";n" .

h Longitudinal Bar Sizemm 1 -15 -120 1 251 30- 1-- 35-. +·45 - 1--65

40 mm cover to No. lOties

Note: Gamma, y, is the ratio of the centre to centre distancebetween the outermost reinforcing bars (measured perpendicularto the axis 01 bending) to the column size.

0.470.550.60

0.650.680.71

0.740.760.77

0:790.800.81

0.820.840.86

0.870.88

0.510.580.63

0.670.710.73

0.760.770.79

0.80"0,82

0.83

0.840.850.87

0.880.89

I-_--~~__~~~J- --_-~ ~i~ -~~-;:~l -- .;064 0.63 0.60~€e- ~~ O;~- -~-~.~---=:-;;;;;-_.=_-~'-=--= . - ::

0.71 0.69 0.67

0.73 0.72 0.700.75 0.74 0.720.77 0.76 0.74

0.79 0.78 0.760.80 0.79 0.770.81 0.80 0.79

0.82 0.81 0.800.84 0.83 0.820.85· 0.85 0.84

0.87 0.86 0.850.88 0.87 0.86n.. -- . - .. ...A.~!===_= _="= "."

.. '

300 0.53 0.52 0.501

0.48350 0.60 0.59 057

10.56

400 0.65 064 062 \ 0.61--450 0.69 0.68 ~'-~~ - -~.~-500- O~72 0.71 V;"'"V--- -V;VQ

550 0.74 0.74 0.73 0.72

600 0.77 0.76 0.75 0.74650 0.78 0.78 0.77 0.76700 0.80 0.79 0.79 0.78

750 0.81 0.81 0.80 0.79800 0.82 0.82 0.81 0.81850 . 0.83 0.83 0.82 0.82

900 0.84 0.84 0.83 0.831000 0.86 0.86 0.85 0.851100 0.87 0.87 0.86 0.86

1200 0.88 0.88 0.87 0.871300 0.89 0.89 0.88 0.881400 0;90 -0;90' 0:89 -z: I={he~

200 0.41 0.391

0.36250 0.53 0.51 0.49 0.47 0.45

300 0.60 0.59 057 0.56 0.54350 0.66 0.65 0.63 0.62 0.60400 0.70 0.69 0.68

10.67 0.65

450 0.74 0.73 0.72 0.71 0.69.500 0.76 0.76 0.74 0.74 0.72550 0.78 0.78 0.77 0.76 0.75

600 0.80 0.80 0.79 0.78 0.77650 0.82 0.81 0.80 0.80 0.79700 0.83 0.83 0.82 0.81 0.80

750 0.84 0.84 0.83 0.82 0.82800 0.85 0.85 0.84 0.83 0.83850 0.86 0.86 0.85 0.84 0.84

900 0.87 0.86 0.86 0.85 0.851000 0.88 0.88 0.87 0.87 0.861100 0.89 0.89 0.88 0.88 0.87

1200 0.90 0.90 0.89 0.89 0.881300 0.91 0.91 0.90 0.90 0.891400 0.92 0.91 - 0.91 .. -0:91 -. - 0.90

50 mm cover !ONOJQ·ILlC's_-

TABLE 1 VALEURS OÊ '6

Interection-Dlagrams·forAxlal·boad and Moment··Reslstanc.for RectangularColumn wlth an Equal Number of·Bars on ail Four Faces. . .

1_.-- - -- cA· .... ----- ..... . .. r-; _ . r-, - . - .. -_.. ~. E:"r:l''g ..... .......... <, f~c30MPa.... ...... ...... <,

....... a .- ~ i"-.... ')',,0.60 • ! •.\JIIU r'" ......... i"-.... .. ~ ..

.......... ........... 1'-...f y. 400MPa ~J-t.~ 1fl IQR n 'l? .... ....... ........ V

1'0.... ......... VEQUAL RE INF'a CEMENT........... "- v ./' " J'

.J /0 U. JI ...... \'" 1)<' ..... /~ ON F'OLIR SIDESi""'o.... ......~"=» /' v - '......... ~ ""'- v .....~

1 .... "1 ~ 1--" 1\............ /' "'"

,....,"~ 'il, "-- ....... ~

""'".....~1"'..

---- "- ~~ "- -i--~~ -..... -.-- ~ ---- \

""~-~- \. \. '\.-EI,2 = 571 bh 3 r- , , \. '\-

1\ \--Eln - kbhJ/(1+~d)

\ \ \..1 \ \. "" \. -,

- v ,1

./, / 1

~ ./ / j

~ ~ ./ / .~ ~ ~ ./

~ ~~

~ ~ ./

25

20

...... OlCLI<t:

10

5

oo 1 2 3

Mr------~~

A_h' MPa..~.. - .. -

4 5

Interaction Dlagrams for Axial Load and Moment Rellisiance ior Rectangular Column wlth 8n Equal'Number ofBars on ail Four Faces. .

654J

MPa2 ~3~

rAh'9

1o

- -

,- - ,. ......" <, <,

E· •t . 0

'...... .... '(,; .0 'T r--.... . <, f~=30MPa • 0

.......... ,. <; • 1 0._, _... ........ ..... ........../ ')'=0.65 · ! 0, •UI-' ......""- ...... ./ <, .. ......."""- ...... V

f y=400MPa ktt-i 1'",1 lnD 1'00.. " ,/ ~ /......... r '" t>

EQUAL REINF' a CEMENT........ 10... .~ .. V l"- v)~ oU ..... L 1 •

"""" ( o~ ~ ./ ON F'OUR SIDES1"'. ~ ..... ~ (~."

,.,""l' ~" "- V' lX (' o~i> -~ '" .-.-r--...

'fJ + '" / ~ ..... ~ n .~~ i-""'" -- "'"~ .." ~i:r-""" -lC'",,' f) ~1--- " '".. ---" -- .~-- <, -.

+ ~~1-"'1( l' " r-, '\'--

EI12 = 571 bh3 '- \.. " "r--~ !'\.

t \ Ill. \.. II\. '\.~

Eln = kbhJ/(1+~d), 1 • , 1\- ., 1 J J

~ 1 Il, '1

~, , J,., ./ ./ f 1

~ ./ ~ ..,.; 1/ .., , V L/

-o

20

25

5

oa..:E 15

...0'

a...... I<t: i\2

10~}!l

~}r;

FIGURE 2 DIAGRAMMES D INTERACTION

tlYY\-~n~~ rtLe.- lU~eik

.Àfto~ .

~~r.Cl1~~C.âO'nt'\..QI::)

CA. = Coz. -= 400 fYV'\ 'N'

~~ -= 2. 0 M rD\.-~ == 400 MP~

~1(Y\.~g~~ ~o ?UPe<.

~ ~ 400 MPOL~~C1h .

.p~clo ~piW~ct~ «l.:::: ct 4 kN 11h13

ÇoeCo..-r~ fe9~\OVY\-"k ~ ,bot ~ I).rrn ~ ~-'«:(JOY\-oUu..vv~ -= ~()O kN ((YY\9..

PavJvo~ :pr~M~ ~ f3jt;!)~3

O.Ç ~ tA G kN /1YYl

S~~~'tA ~eK~eN\;teo A, 3 kN /,rm"2-~~~tbp~DUf\.~ l Q;\r~ e ~ (4- k 71 ! 'YY1 '2. t\-<i\~ )

Pt{)L;n-~ ~«\~ 4( 8 kN /rm 2

· 4) LttaA.;'C~eA ~ nA,J e.otM- ~ ~~~

"* S Q.,'(Y\.-~ i.b6teéA Jv.Ntvv~ l F 4 )- LfAov<-~QA feK~~.t~ Fk'(\.~ bOOO v: 6000 )C .4,1-lJ JM»Y'" 1) MV~)c:

~ 1;)( 0) A1 )<. G, 00)(.6,00)( Cl. 4 -:::.. 734-,401<1'1~<~ovv-~~ r~I"YY\..Ol~~ .), '3 ,~JY !'rrnz-='"7 5"?< b100 ~ 61 () i) .c A (~ == 2'3 4- 1 00 k N

Rek()'YY\.1o w ~ O''LA.\'""-CeA

~ 4 )( 5 ')(. ( o1 40 - 01 A1- ) ~ fi, bOY. 0, 2f) ~ ~ 4 -= .4 ç4- 1 Ç6 k '"Poteavv')C 4- 00 )c 4 00 ")( '3 500 1 ~ LM-nA,t~

~> 3 'f'. 01 4 0 ~ 0) 4- D )( '3/ ~ 0 )( ~ 4 :::. 4- 0 , 3~ leN

PoC(2,()(,AN)c 400 ~ 400 ~ 4000 1 ~ vlAJ~

~ 2 -:o, 40 'f ~4D 'f- 4,OQx ~~ -:= 301-=t~ kN

PL) -::: '134/40 + <t '34',00 +.A Z; 2r1 56 + 40l '3 ~ +?>0I':1~

~.D ::: Av1 ~ tr, DD kAY

- SvU/y ~ovv<l\~.P~OL'(\,-~ /é}..~~ Jr Re:s ~ ~û 4, g k1'l!m,'2SvLAr\~OV~ ~ ~~~e -= b100 ""P 6,00 -= '36 1 Or!) rra 2

~ 4 rvUJ~)G ~ 4)< 36,00 := 444 /Y)"\2

B:= .Jl44-,00 (l'Y) '"2 /' eo ryn'2.

ç:'~ ~~ & J:VvVY~~eAD(5D + 'f2o lA 44 -=- (J, "8 f-

=-'7 4,8 ')( CJ1 g-; == 4-1 CZO k-,y/rm2.

PL -::: 4)( 36,00 .,.: tr, 20 -::: 604-,8

".. '.:\

_ L~ t.o 'f\.(f"r\ 'fr/Y'clvt~P-:: P

n+ PL. -::; v1JL 0)4-( DO + 600.,~D -::. .A~ 'j '8., go ~iY

.... ~~~ ff/noltrt-wP~ ~ ..t,2--6 '\,+v1,'1Pl- -:;:.;f1~0yMC!)4/0D..(-.A~1îi)C.60h,~D

~& -= ~3f!:JC1j/ 10 kN.

Âiù'YY'&·

}4 -= fS -::::.Ji1~ V?I gO -:::: ~ ~ <b 4q.> ~oo /

V1 = ~100 rvv-; 1.

s~ette ~ceé ~ lA ~ b"2-~ 6--=ff =V~/)O -= 3/0fJrrn.

~~r~w«~fU~~ ~ k fQt/YY'~.rct -:=:.!1 -:= n ~~, t 0 = ~ be,.0. kN(,rn '2.

g,J Aj <J:){ 00

1. -::: ~061 G'S "(zN/rrn P1

gJ_~~\.- ~~~W\Y\&..

otb

-:: ~& - ~:::: ?>DOf)- h 00 '":: .A?J00~ .~

rotb -; A300 'YYIv'n , ~t~o r'rY\ •

4-:: C( b ( - ~ .J ') cf)(»e.c:

9sg + o, ot cl rf>c~g~ '" A000

~' .. ':.~"

-----1r--ab

11 ~ P,1

~<..~ D~-l.

~/

d /

b = 1 /

1- ___ .!L.. ---

ab - d 1 d ~ttÎttÎtt1

Q.,(kN/m2 )

Plan Elevation

Values ot effective depth d in mm

q., ab (m)

(kN/m 2) 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 d/ab100 150 150 150 150 157 188 219 251 282 314 345 376 408 439 471 157150 150 150 150 174 218 262 305 349 393 436 480 524 567 611 655 218200 150 150 162 217 271 325 380 434 488 542 597 651 705 760 814 271250 150 150 190 254 317 381 444 508 572 635 699 762 826 889 953 317300 150 150 215 286 358 430 501 573 645 717 788 860 932 1003 1075 358

350 150 157 236 315 394 473 552 631 710 789 868 947 1026 1105 1184 394400 150 170 256 341 427 512 597 683 768 854 939 1024 1110 1195 1281 427450 150 182 273 364 456 547 638 729 820 912 1003 1094 1185 1277 1368 456500 150 192 289 385 482 578 675 771 B6!3 =. 86-1. 1061 1157 1254 1350 1446 482550 150 202 303 404 506 607 708 809 911 1012 1113 1214 1315 1417 1518 506

.600 150 211 316 422 527 633 739 844 950 1055 1161 1266 1372 1478 1583 527650 150 219 328 438 547 657 766 876 985 1095 1205 1314 1424 1533 1643 547700 150 226 339 ·452 566 679 792 905 1018 1132 1245 1358 1471 1584 1698 566750 150 233 349 466 582 699 816 932 1049 1165 1282 1398 1515 1632 1748 582800 150 239 . 359 478 598 718 837 957 1077 1197 1316 1436 1556 1675 1795 598

1

850 150 245 367 490 612 735 858 980 1103 1225 .. 1348 1471. 1593 1716 1838 612._900 150 250 375 501 626 751 877 1002 1127 1252 1378 1503 1628 1754 1879 626950 150 255 383 511 639 766 894 1022 1150 1278 1405 1533 1661 1789 1917 639

1000 150 260 390 520 650 780 911 1041 1171 1301 1431 1561 1691 1822 1952 6501100 150 268 403 537 672 806 940 1075 1209 1344 1478 1613 1747 1881 2016 672

1200 150 276 414 552 690 829 967 1105 1243 1381 1520 1658 1796 1934 2072 6901300 150 283 424 566 707 849 990 1132 1274 1415 1557 1698 1840 1981 2123 7071400 150 289 433 578 722 867 1012 1156 1301 1445 1590 1734 1879 2024 2168 7221500 150 294 441 589 736 883 1031 1178 1325 1473 1620 1767 1914 2062 2209 736

Note:Capacity reduction factor"'c = 0.60 has been included in table values.Minimum effective depths have been determined according to:1) one way shear requirements (CSA Standard A23.3. Clauses 11.2.5.2. 11.1 0.1.1. 15.5.2)2) minimum depth requirements (CSA Standard A23.3. Clause 15.7)

CISAILLEMENT UNIDIME NT 1DNNE L

~ = co~WcLVV\iÎr W ~~\owwe ~ ~Q\ OY\ ~ z: 0)60

À == GO~~ f<TVV'·~ ùNYt r-~ elu. ~(YY\ ~(!JY~CfU,'(' ~ !toh)r-lYY\- ~ ~~\:e,' If\-O(~~

À 7 A (OD cl

~ d.-= -, (-d--+-.A.-~~-;-V-~'--)l~~ 6c

J1-:: ~ ~OO (. ~66i 1> 3 ) =4 3 ~~b6/63 +Â 20V§;o

<el-=: 4~~ ~\'"n,

k U~I( ~ d.. fUJvY~ aJfy-e tYmMJrd !Cter~ rele ~ \-~~ 1

- wCAiet~\-- \~~.~

J _-(~ q~s +fYY1) +Vrm Z -1- 4Lq~J--Wm )(V18!I'IJqs~e:: - '2. Lq&t rvn ')

<6lAJ <U. r{Y\::: 4 x AOOD \C 6) 4 -« ). >c rficVS~ tt ::: c -= 4~~~~ ~ ~Ji n.Oé~ 1YYl:::: <z)t~\lJ:

rYY'l =- ÛJ60VW -::: 4- ~~31 ~5m ~ 4 ~<f)3/~b_~-------:---~--------jt}.

d _-(~)C U6/63+4~~::3/ o;;)+'{(L~~ fb'=3/ ~q)'l. +4[~b6~6 3 -t-42Cb"3 /211)--400 ~(~66/63+4~~~/ ~'J)

-::: 1,145"Il

.' 1 rd-:; 5'3 ~ rYn JY) _

f~ =20 MPa

A, = area of footing, m2

Ac = area of column, m 2

For clrcular, polygonal, or rectangular columns with aspect ratios not exceeding 2.0, use h = VA:.

P,... square

~J''' ~columny

•h-----... ~

d

t,_ ••• 0 00 .~

t t++ t +t tttttql' = P,IA,

Values of footing to column area ratio, A,IAc

ql'd/h

(kN/m2 ) 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

100 34 43 53 65 77 89 103 118 133 150 167 185 204 224 244 266150 23 30 36 44 52 61 70 80 90 101 113 125 138 152 166 180200 18 23 28 34 40 46 53 61 69 77 86 96 105 116 126 137250 15 19 23 27 32 38 44 50 56 63 70 78 86 94 103 112300 12 16 19 23 28 32 37 42 48 53 59 66 72 79 87 94

350 11 14 17 20 24 28 32 37 41 46 52 57 63 69 75 82400 10 12 15 18 21 25 29 33 37 41 46 51 56 61 67 73450 9 11 14 16 19 23 26 30 33 37 42 46 51 55 60 66500 8 la 13 15 18 21 24 27 30 34 38 42 46 . 51 55 60550 8 10 12 14 16 . 19 22 25 28 31 . 35 39 43 47 51 55

600 7 9 11 13 15 18 20 23 26 29 33 36 40 43 47 51650 7 8 10 12 14 17 19 22 25 27 31 34 37 41 44 48700 6 8 10 12 14 16 18 21 23 26 29 32 35 38 42 45750 6 8 9 11 ;3 15 i7 19 2~ 24 27 30 33 36 39 43800 6 7 9 10 12 . 14 16 19 21 23 26 29 31 34 37 41

850 6 7 8 10 12 14 16 18 20 22 25 27 30 33 36 39900 5 7 8 10 11 13 15 17 19 21 24 26 29 31 34 37950 5 6 8 9 11 13 14 16 18 20 23 25 28 30 33 36

1000 5 6 7 9 10 12 14 16 18 20 22 24 26 29 32 341100 5 6 7 8 10 11 13 15 16 18 20 22 25 27 29 32

1200 4 5 7 8 9 11 12 14 15 17 19 21 23 25 28 301300 4 5 6 7 9 10 12 13 15 16 18 20 22 24 26 281400 4 5 6 7 8 10 11 12 14 16 17 19 21 23 25 271500 4 5 6 7 8 9 11 12 13 15 16 18 20 22 24 26

Nole:Capacity reduction tactor e, = 0.60 has been included in table values. Columns with aspect ratios greater than 2.0 must be ccnslcered on anindividual basis.Also minimum depth requirements 01Clause 15.7 must be checked.

[2] CISAILLEMENT:> BIDIMENTIONNEL

Le c.AA~~ wJr· ~CÜK·~ nd. ~.O'\MJeA ~

rJ -= 5 3 g r(Y\ YY'I .

4) il) ~ lYnolJLu;.re ~nÀ-'(Y\M,N1 ~. t.r\ft0\À)~wv\r .F~ ek- UAOlÀ,~~ ~ & fùVYY\.&b.-

PCT\. Tl (..O'Yl, '(\.l(1)yy\)IlNv\r

VJ ~ et~~ ( Io? - Cc- +0( J'}

:::: ~ 66(iJ '3 (l'6OCJO)'2 - ( 400 + 538)'l- ) -:1.D-'

Vg -= ~A 65 k"l

Vc -= ( A +1:- )< o, ~ ~ cp, € ~o d

le -= 3 0 0 0 -::: ~ b0 -:: 4- ( c + d) ':: 4- (t,00 +?;3 S)'?>OO 0 6

0-= '3 '15 ~ l'YY\ ~Y'L

v, --::; (.-1 + ~ ))C G) ~ fC..{ 1 OO)G 0)60 y: y2- 0 )C ?> i ;-~ )C~"'j, '0-1

\ (

Vv -= '3 ~ 4- ~; ~ 4 k1y

V(; '7 Or 4 ~ 1Je Yfl 60 d == ~ lr~A,00~ CJ1 60 xVfo y:

?J+ ~~ )C 53s ./o-~Vc -::: '3 ~ '4 Cj) ~ 4 k:N >2 A661 ~6 Ve i't .o"e..

'1-3

V1~·~ ~~v- rO\A rfN'Av\fOU()l ~ ~e_ ~\t<--v ('N'vC1L ~...AJYY\ÂÂJ'(Y"'j ~k otJ\ ("~

.d. b ~GJ-~ -= Ji ~ 1 0) 4 V'{()(b - 0)016Jl/K

-=- A ~, 0)4 (.If/?) -O)D1iJ) '(~o -= 30/ 'ig

M., -:: 30 î'Y\YY) .b V"(\. Cl )0

~ b C 30 t'nty)

2f!A b()t/\'\QA rtl[VlA.A l ~ <YY\ rfi G"\;Y vUt'Cv-eMex~ U~if(~Q ~ .e~~ ~ <6L~ùV(ü-- f~ ~e,f~ 1-(~ i\MJl·~ ~~ N° »o Ldb=2C1j-,~mfr»)

_kY\~ ~ JJ~~r-,

~(JYY\.F-( ~G'Y1

t6~ -= DI2 4 dl. ~'a 1VJ~

10CA(1'.>.> w JbL...."",) e~ rl'MYY1)/lJ;,OlztJJb~~

~l) 2r;/~ J)4D "> 445 Ole

~ V A0)/5 4- 20 ? ~ 4 ~ ok.

Jt5 tA b ?; 45 '> ~ ~ 0 Ol-c

AD V<A) 3 '246 / ~ov Ok.-.

\Jcr\,y' ~ ~~~

~~ cet\~ ~ ~ ~~Q601 <: of -= q:-s g ~ 5 t, tJ fY'nJ"l') . Oh.

_~r~'UA/V ,euYn~. J~_::::- ~l?1 ~ (b()(/fre "10

'2~)

PA -=. et -+ olbw>~ UW1Wr . -= li4 D -r 2- fi + '1 6tt::: 64 tJ rn'\ YY"\ •

c-, r('-vY\d..

~'\ == .6 50 rfY\ 'VY) Jy-. cl::: 6S" 0 frr\ 1'Y\

.- ·Z(JY\.~y ~~oM~Û..

~,J. -= l '0;c ) - 1 fi -= ;<100; l,OlJ - "1>; ~ ...t"2M

~cl -=- A~ ~ ~ ('n-)()'Y)

Ce,Me. t,!YY'~ ~\-- ~~~ frJW{ f<()'YlI\):)~e;r f~~(o\'\'ltYY\~V- ~ CAIY\ttyoVv~ k er ~e;y- ùV(~ 4

k{Vln1 .

G) Ç't~tD""l.V'i~ p.VYn~ ~DeM / ~ ('(Y\f)rn~ FoY\~r

{'(nCÂy-~rJ.R ~\ wt~ ~ t Ol ~eu.-e. ~ fÇ)~'>G

~ ,«{ eth -== ~ 661 6~7< ( A.-1 '3) ':::; 4 60/ bD l?N

r.}

• tA y rrt'\..OLtux-e ~ ~ 0etr'rYliQ~

t> Q"Vt/'("" ~ rve ~~ eMJ't W. J fY"Y\ 4 }:)~~

Ill>::: A/it a- V[A,~t Jl - 4Le l ~ ~: l q~ ct~ )

~.>:: At']x ~O)C 65'0 - LAIt; ~ so xJi,o)'-- 4-4A 'Q-,c O)D~ 4'i())60

~~ ~ ~/O"'l~+AOO)~ ~x(t;60..f-~OO)/? A?>Ob rmm?lnn.

Vl~ <:::: s, 1-b Jij ~ ~ ~ D)1- b 'i x ~ 0 -c 'i 60. c::. g 4- .Ar, /Y)1 rn 2- (rm

,~ = 20 MPa

'1 = 400 MPaMax. db = 27.4 Jab - 0.075

:5 43.1 (ab - 0.075)

PI

~ ...f-(~)-4 ~AI

------------ --.j I--e-- 75 mm

1.~m~~ 75 mm 1 lEl~_.! - - - - - ~ - --t UUUUAI..ALU AUU•.U1A

11111111 Il Il Il , Il Il Il Ilq,l= P,lA; (kN/m 2 )

Plan Elevation

c ~

Values of A. (mm2) required in a 1 m width of footi~

q., ab2 d (mm)

(kN) 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525

50 520 550 600 650 700 750 800 850 900 950 1000 1050 1100 1150 1200 125060 632 550 600 . 650 700 750 800 850 900 950 1000 1050 1100 1150 1200 125070 748 625 600 650 700 750 800 850 900 950 1000 1050 1100 1150 1200 125080 868 721 620 650 700 750 800 850 900 950 1000 1050 1100 1150 1200 125090 991 820 702 650 700 750 800 850 900 950 1000 1050 1100 1150 1200 1250

100 1119 921 786 688 700 750 800 850 900 950 1000 1050 1100 1150 1200 1250120 1391 1130 959 836 742 750 800 850 900 950 1000 1050 1100 1150 1200 1250140 1689 1350 1137 987 874 786 800 850 900 950 1000 1050 1100 1150 1200 1250160 2023 1583 "'-322 1142 1009 905 821 850 900 950 1000 1050 1100 1150 .icoo. ~125!L "~

180 -- 1832 1514 1302 1146 1026 930 851 900 950 1000 1050 1100 1150 1200 1250

200 2101 1716 1466 1286 1149 1040 951 900 950 1000 1050 1100 1150 1200 1250250 -- 2266 1902 1652 1467 1322 1205 1109 1027 1000 1050 1100 1150 1200 1250300 2913 2380 2043 1800 1615 1468 1346 1245 1158 1084 1100 1150 1200 1250350 -- 2918 2463 2152 1920 1738 1591 1468 1364 1274 1196 1150 1200 1250400 -- 2922 2525 2239 2019 1842 1696 1573 1468 1377 1297 1226

(~:~~J450 3432 2925 2574 2309 2101 1930 1787 1666 1560 1468 1387500 -- 3356 2927 2612 2367 2170 2006 1866 1747 1642 1550 1469600 -- 3703 3260 2929 2669 2457 2280 2128 1997 1882 1781700 -- 3979 3537 3200 2931 2710 2523 2363 2223 2101

800 4803 4202 3768 3432 3159 2933 2740 2573 2428900 -- 4947 4383 3963 3631 3359 3130 2934 2763

1000 -- 5059 4532 4128 3804 3534 3305 31071200 -- 5826 5221 4761 4392 4086 3826-- --1400 5837 5332 4927 45901600 -- 6383 5844 54111800 -- 6865 63032000 -- 7289--

Note:Steel areas shawn are based on Ilexurai and minimum reinlorcement (Clause 7.8.1) requirements. Where numerical values are not shown.required steel area is in excess 01 that specilied in Clause 10.3.3 and ellective depth d must be increased.

Continued

ARMATU~E.S DE FLEXION

·16

POUR 1M DE 5EMELL E

f~ = 20 MPa. fy = 400 MPra=---=--:=-=Max. db = 27.4 Jab - 0.075

~ 43.1 (ab - 0.075)

---------""-'---1.~m~-.1 _

Plan

.. .lAA.t.tII."'.!!! 1 l.tlili

1 1 1 1 1 1 1 l " 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Q.,= P,IA, (kN/m2)

Elevation

Values of A. (mm2) required in a 1 m width of footing

d (mm)

400500600700800

90010001200

_.10:101)

1600

18002000220024002600·

28003000350040004500

500055006000

650070007500

550

13001396169119922299

26132934360143055051

585067137661

575

13501350160918942184

24802782340540584744

5471624670797987

600

14001400153618062081

23602645323138414479

51485854660374068274

625

14501450146917261987

22532522307536494245

48675518620269267698

85279431

650 675 700

1500 1550 16001500 1550 16001500 1550 16001653 1587 16001902 1825 1754

2155 2066 19842411 2310 22182936 2809 26933477 3322 31824038 3852 3684

4619 4399 42025225 4966 47355857 5555 52876520 . 6168· 58597218 6809 6454

7959 7483 70748751 8194 7722

10189 9503

725 750

1650 17001650 17001650 17001650 17001688 1700

1909 18402133 20542588 24903054 29363532 3393

4023 38604528 43405048 48335585 53396141 5861

6717 64007315 69588935 8449

10790 10118

775

17501750175017501750

17751982240128283265

37124169463751175610

61186641,80279553

11271

800 825 850 900 950 1000

1800 1850 1900 2000 2100 22001800 1850 1900 2000 2100 22001800 1850 1900 2000 2100 22001800 1850 1900 2000 2100 22001800 1850 1900 2000 2100 2200

1800 1850 1900 2000 2100 22001914 1851 1900 2000 2100 22002317 2240 2168 2037 2100 22002728 2636 2549 2393 2256 22003147 3038

oc-293T-2755'" =Zsfis ~ 2453-

3575 3449 3332 3121 2937 27754012 3867 3733 3494 3285 31014458 4294 4142 3872 3637 34314915 4730 4560 4257 ·3995 .. 376553ô3 .. 5Î iô· 4Sô5··- -4{;4~~~--435e"· "·:41 C4

5863 5632 5420 5047 4726 44476356 609951:165- 54:>~5iüû .. 47957654 7322 7022 6502 6063 56869065 8637 8257 7608 7068 6611

10623 10070 9588 8781 8124 7574--11659 11041 10035 9237 8580--- 12657 11389 10418 9636

----- 12873 11683 10750--

13050 11932-- 13197

14566

Note:Steel areas shown are basee on flexural and minimum reinforcemenl (Clause 7.8.1) requiremenls. Where numerical values are nol shown,required steel area is in excess of thal specified in Clause 10.3.3 and effective depth d must 'be increased.

Œ (SU1TE)

'1 .. ..••__ -'..:.__ ._-......"-'-._..n--'-__- .. _ .• ~ - •

Dm ~(~'r F O~~i~ ta.. \)~ ~ tf1~ tQ- rwiliK(€lu. ~o'v\o ~a.A..L 3

~~ tev<-~tuJ( b~ '?» 00 NYl.

~ A> -:: 3/00 )C 4~OO

~~ (~S-/,~) eoo~o [vt~J 6) ~OO

JU') (A 6,0 ) ~()0

~ 4000

vi?> 3 Q)C>O

20 40DO

b-+~ - Jb/tN

f!) N\. f4~\-- f 0 -(kx.A~ r$ ~O

20 elvt5~.

'('vQ\'(~ uk~ ~e -:= ~ Cè- S tnî 'fY"\ CfVt,

e rz: /l, Lf CJ rrn l'Y' ~ ~ottAAA

1)T~~~ ~ Vl1YV\-1~ ,a,~~<~~

~ C-{)"Nr ovJr.

_ R.~\-0Jn ve" rtf\.A.- C-{)'YV\ yOv\J'(l,Le" ~e- <iL, ~'ou

~~~e, k V()'Y\J\-ouJr ~ ~ ~.(2/Yn&,

~. ~ -:::. f'!- :::. 23,~~,1 0 -::. .A 4 ~ Ç?) 8 , A? '5 k P", '""'- -1,5' . 1tJ'"A~ (t)40) l kPOt.-

~b :;: .A 5 VU PO\.,.

~ -::: ()) 'g 6" cp ~ l \ rr;;;;4db eMm (;~e- ~. <rr:«

yfL, /l'lz. -:: V?J,O%I Ab-"1 -:=. 1(1)"":? ~ ~Vi4-1/;-}7-- 2

~_•.o == ~ 85 r- D1607< ~O ~ 2.. -:::. 20/ 4: vu rOt-bC9-(1rn

~ _. J -:: ~o1 4: M rOt '7 ~ -::; v1 Ci vu Pa~rot.-(}rr. b

~k:.

p~ -:: ~?> '!J Cl) 1 1- D 'veN

Dl 8~ c1J, ~ ~ ~v -::: D-? '815 >c ())60 ~ 20 ~ (0,40)-. io''=- A 6 '?, ~ kN ce: PJ "=- O)'3Sb~ 140 kH

~ ~sOj~(10 - ÂG3~ -:;. 161/40kzHb4 rn'("\.cLluJçe- f\1VV'<' ~ ~.'1~ ~ t1%l?<~

1'\; -::: '1 ('1, 1. r:J .10 3 -::. 1b'/. ,10 .{0 3 -:::. Z258' l'l'\'\ /YI"l-

rps ~ ~ DIeJi Y.. 4- 0 0

- 0-'

'2.>00

CONCLUSION

r (' , Q0r ~à M. V'\C ~ 1"~ ct:lVL rf'n<7\"rv,

0()"rnp~~ ~ ~ôj...lmeY'\ cF· %\ ~cW\' ~ uQ

k ~'Q)\etb~ i?/YYV'QIYV\-- ~ ptQ{;f)V) (G{/,f ek.:tute.o A~b cele-· r~C0YV:> ~ loê;f(l'r\ ~/{~ (co~rCA-~e-

{l.;\ ~~,«(~CLtQ ), .

,~lU> f twvv> :Jjz. leâ,t(,YY) rt(){~ t>~~ "-1À- (V(Jr(~em .~ e-oLw c~·~ ~ ~.~()'Yl~Q/YY\. ..QIY\,\-<t~ G% 'L.tArâ~u.Arù> ~e;vv'r/.l vt>t'JA.-ltu, r 0vIA\c .

r~'f~ te.e" f~ _JI/YY\ro~tJ' •.-sUc ~ cJ:A rYtRmir-,2 ~~ rc1\A. t'(OCLY »e. f<1lA.(J:M.M.--V:"-e... ekJ)/~cL'\e.. rà cd ',-e:t.JvG-t-'(eD ~~~ c()'YYI tnQ..J

~ Jl.o~~t..D ) te- Yl-rnoCUA.- &\rc. ta 1CivÏftc.e- ~..e aD ()QjYV)\QUJY 1 ~ rfY\ItA,.{J:) ~ g(tYL~O'"YU../

~ ~cJ1CJ-- ~Q.h , lUh ',' , .~OCy /0\è -tvOvVcU1., c er->t vlAf\.~ Q}:l~e... de.. .pco ~dM(e ~ ,ClYY\.ce- rt:m. { GcLtUN,e.. eA-~~~ %1 20t-l~· }~ f' QM.ir Qh"f'(' (G!fYY\.e-âà (@Y ~\!cf1A

PQ/,< ~~~t- oYI n e-,'< •

BIBIOGRAPHIE

_ G0cle.- N ako '0vcJ.X ~ 8> GlhYn- Q/YV~ . r<1u.Ca-~cLoc A~ '65

Frw fOll"f ~. cQr('(v~.t~' ~o vCé~ cocle..nfuof'ctJ ,dM. b~Qrrv~ / êt 0~~ ncib:c>·~ctJ~

~ (\;~~ CctYVLL~ otlOvWOt.

_ Calcul ~ (JVU.J'iOv~~ VY\ beJcrn ~b~~~f~éfQ,({~ pe<"y t ~~O cA:~~ c.CLn.(Â~~e

~ ('().o (r(YlC{.~a.kQ'Y) .e..,y ~pr oVtAJ~ f qj'\ ~[W\f::>Ùe c.Dl (\.ocolA0Y\..- ~ f\ 0 ( ('f'(\..e.D .

" C~c. vJ,e. D~", \i1 e::vnd bCièlk ,/k Q cfJJ2JJ'ù tA--~()'Y) LDl h C\..,d..M?rn Y"\-e d..e.

tl'fY\-e/n.\r po ~~ ~OVYLol (tLi ccp1LPG A)

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