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RËPUBUOUEDU SËNËGAl
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ÉCOLE POLYTECHNOaUE DE THIÈS'
PRO JET. DE.·F 1 N D' ETUDES. 1
. EN VUE DE L'OBTENTION DU DIPL6'-1E D'INGËNIEUR DE CONCEPTION .'
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T 1 T RE GEOBETONet CONSTRUCTroNS
EN TERRE II ~ ARCHITECTURES'
ET TECHNJOlLJE DE MISE EN ·.Œ UV RE
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Dir<?Cteur :Dr:A LOU DIACK
Génie: Civil
. Dote: Mai 19B?
EVORA
NDIAYE
DIAWSAïD
Auteurs: :-:..N=O=.;EL=--D!:::::._=-=-.=.:..:..:....:.
MOUSSA
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1\ A.5
PARTIE A
Elérllents introductifs·
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I.-INTROQUCTION-
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PARTIE B
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/Prcndro 10 lcmpCraturc t+ - +-Vamblenlo 01 BO " 1- -'CPorlor eur 1111 courbe , /d'humidité roI81''18. '00
,WT,ocer une horizontale 1
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,le tempèeeture du r ,
~fl2 k-::béton.&lC
,Tracer une ventcate ,
••? / 17,V"are te bu jU3QU'/l le
l~vitesse du ""onl.
~y'trecer une horizontale , 1/V ./ver. 18 gouche el lite ."
~V el-apprOJl:imallV'Elmenl la , --~ 1--vitesse d"evaporalion.
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Effet de la température de l'ai'. de l'.humidité relative,de la température du. béton et ~~ la vitesse du ve,nt surte vitesse d'évapora lion supertictelle du béton. (0 apréste bulletin 81 du département de recharche de l'Asso-
r cietion du Ciment Portland)
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PARTIE CConceptioll et réolisotioll
du coffrage.
Exécutioll des coupoles
1- INTROnUCTI'ÜN
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'33
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·PARTIE E
Evaluation économique
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EXF eUT' ON "Dt.S COUPOLES
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VUE EN PLAN DE LA
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252
Valeun de 13 •• k et PI en fonction de III
Etats-limites de service
/l, p, k P, /l, p, k P, /l, p, k P,
0,5222 0,680 1,600 76,80 0.0394 0,770 0,148 5,12 0.0087 0,860 0,048 1.010,4498 0,682 1,382 65,95 0,0381 0,772 0,144 4,93 0.0084 0,862 0,047 0,970,3940 0,684 1.215 57,61 0.0368 0,774 0,140 4,76 0.0081 0,864 0,046 0,940,3498 0,686 1.082 51.00 0,0356 0,776 0,137 4,59 0,0078 0,866 0,D45 0,900,3139 0,688 0.975 45,63 0.0344 0,778 0,133 4,43 0.0075 0,868 0,044 0,87
0,2842 0,690 0,886 41,19 0,0333 Q,780 OJ29 4,27 0.0072 0,870 0,D43 0,830,2591 0,692 0,812 37,45 0.0322 0,782 0,126 4,12 0.0070 0,872 0,042 0,800,2377 0,694 0,746 34,26 0,0312 0,784 0,123 3,98 0,0067 0,874 0,D41 0,770,2193 0,696 0,691 31,51 0.0302 0,786 0,120 3,84 0,0064 0,876 0.039 0,730,2032 0,698 0,642 29,11 0,0292 0,788 0,117 3,70 0,0061 0,878 0.038 0,70
0.1890 0,700 0,600 27.00 0.0282 0,790 0,114 3,58 0.0059 0,880 0.037 0.670,1764 0,702 0,562 25,13 0,0273 0,792 0,111 3,45 0.0057 0,882 0.037 0,650.1652 0,704 0,528 23,47 0.0265 0,194 0,108 3,33 0.0055 0,884 0,036 0,620.1551 0.106 0,498 21,97 0.0256 0,196 0,105 3,22 0,0052 0.886 0.035 0,590,1460 0,708 0,472 20,,63 0.0148 0,198 0,103 3,11 0,0050 0,888 0.034 0,51
0.1378 0,710 0,446 19,41 0.0140 0,800 0,100 3.00 0.0048 ·0,890 0.033 0,540,1303 0,712 0,423 18,30 0,0232 0.802 0.097 2.90 0.0046 0,892 0,032 0,520.1233 0,714 0,403 17,28 0.0225 0,804 oM5 2,80 0.0044 0,894 0.031 0,490,1170 0,716 0,384 16,35 0.0218 0,806 0.093 2,70 0,0042 0,896 0.030 0,470,1112 0,718 0,366 15,49 0.0211 0,808 0,091 2,,61 0,D040 0,898 0.029 0,45
0,1058 0,720 0,350 14,70 0,0204 0.810 0.088 2,52 0.0038 0,900 0.029 0,430,1008 0,722 0,335 13,97 0.0197 0.812 0,086 2,43 0.0034 0,905 0,027 0,380,0962 0,724 0,321 13,29 0.0191 0,814 0.084 2,35 0,0030 0,910 0.025 0,330.0919 0.726 0,308 12,,65 0.0185 0,816 0.082 2,27 0.0026 0,915 0.023 0,290.0878 .0,728 0,296 12.06 0.0179 0,818 0.080 2,19 0.0023 0,920 0.021 0.25
0,0840 0,730 0,284 11,51 0.0173 0,820 0,Q78 2,11 0.0020 0,925 0,019 0,220.0805 0,732 0,273 10,99 0.0168 0,822 0.076 2,04 0,0017 0.930 0.018 0.190,0771 0,734 0,263 10,51 0.0162 0.824 0,Q75 1,97 0.0015 0,935 0,QI6 0.160.0740 0,736 0,254 10,05 0.0157 0,826 0.073 1,90 0.0012 0,940 0,QI5 0.130.0710 0,738 0,245 9,62 0,0152 0,828 0.071 1,83 0.0010 0,945 0.013 0.11
0,0682 0,740 0,236 9.22 0,0147 0.830 0.069 1,77 0.0008 0,950 0.012 0,090.0656 '0,742 0,228 8,84 0,0142 0,832 0,D68 1,71 0,0007 0.955 0.010 0.07
1".0630,0,744 0,221 8,47 0,0137 0.n4 0.066 1.6~ 1 (\.OOOS 1 1),960 0.009 0,05
10.06061 0.746 0,214 8,13 0.0133 0,836\0.065 Il,59 10.0004 0.965 0.008 0,040,/HM,O,74. u,201 7,81 0.0128 0,838 0.063 1,53 0.0003 0.910 U,001 O,OJ
0.0562 0.750 0,200 7,50 0.0124 0,840 0.062 1,48 0.0002 0,975 0.005 0.020,0542 0.7~ 0,194 7,21 0,0120 0,842 0.060 1.42 0,0001 0.980 0.004 0.010,0522 0.1 0,188 6,93 0.0116 0.844 0,059 1.37 0,0000 0,990 0.002 0.000.0504 0,756 0,182 6,,66 0.0112 0,846 0.057 1,320.0486 0,158 0,177 6,41 0.0108 0.848,0.056 1,27
I~~il0.760 0,111 6••7 C,C1Q.; 0.85J 0.0:;5 1,23 1 1
1
0;:5: " ., .. ~.s.; C.ûiûi û.oS2 0.053 1,18
i.... vv
0,D431 0.164 0,161 5,12 0.0097 0.854 0,052 1,140,Q422 0,766 0,.57 5,51 0,0094 0.856 0.051 1.100.0408 0,768 0.1S3 5,31 0,0090 0.858 0.049 1.05
Co\c.u\ do",
Fig, 2. - Dalle uniformémentchaegêe : moments au centre.
0.12-16O.D&I0:7.'>1."
0.71,.'>:(l.n':l~
O,b5S0U.li710O.bS~1
0.(,91R0.1111
n.'j.~41
t.oœ
;,';,,';.:
0,6315(1.l-..l~1
Il '11.~ ~
I).">.l;
Il,li(>1(o(Ull'J'l(lJ\'I.l'ln.'IOS10."_'\(,
0.19.1)0.801-10.&216O,l\.l.'-S;',1\.\0:'
(l,-1 tJ .lli .wcvo0.~105 O,OMi-l
0.5214 0.06120.5-1-:0 O,OM>IU.5(.()~ 0.06500.57~6 0.06:190.5q~9 .. 0,1.162:1
O,llI.l5 0.061r0,6)13 o.!){mOJ~:'I-1 o.O~?6
lI,/,1>:h n.OSSoU,6S1-..l 0,U5j(J
0,1052 0,05660,7244 0,05560,1-138 0.05A6O,1b)5 0.05.\1n.7 ....'-I O.O~~S
(J.I\Ol(, O.OS Il)
(I)i2<"1 O.(I~U'J
o.li~50 0,05000.116(,1 0.Q.,I91O)iq~ (J.n.l,\1
o.,/(l'I~ u f~IH
O.'I.l:'~ 0.(1·1(,.'>li \i;'~;'
]..I! ". ~;
0.'/711 0.0.·':':'11.lO'fl(l O.().MI
G.1~ O.lIb,\.;0,75 0.0621
u.16 O,06Q!I0.11 0,059',0.78 0.05g~
0.79 0.0573O.BO 0.0561
0.81 0.m500.K2 ù,05.1,/os: o.n~~'
o.s., D.O.'> li0,85 U,OS06
0.86 0.04960,81 0.04860.88 0,04160.'19 O.Q.,IM.n,QO O.Q.,IS(,
(1,'/1 O.O·U70.'12 O.l}-.l.\i0.'/.\ o.oox0.94 0.0011'1f)!j.~ n.n·lll!
n.'I(,n.'lio."~
0.'/'11.lIn
d"e. E· \-' -J. e., E.l-- S i:o.~
I~ \loo. JI.., 1"'" ~)
Il,:(\ (I.111l1 1 ll.~.'-I~) 11.11:.'1 U.:.')oi~·l
lJ.J 1 O.IIl;"S ! Il.~~lJiJ (J,II ru lI,."!:.'4
(1.,1.' IllOn [1. .'.~I II) n.IIN". Il. ;(~lfi
Cl,';; Il,IOI,! 1o..'.~()(J n.tux: (un;7
O.':': (j.I{)·:'1 , (J,] seo Il,11)75 U,.1I.\.'-
uy Il.HI\(, o.:'~O() n.lllf,·' n..l:,q
O,4tJ 0.lo!1 0,2500 0.105l 0•.1.11')
D,.n 0,1008 0.2500 0,1OJ~ D,HO?
0.4S 0,0994 0,23000 0.1026 0,34910.49__ __o,0980-- -- --0.23000 - D,lOI] 0.3580
o.so 0,0966 0,1$00 0,1000 0,3671-
D,51 0,0951 0,1500 0.0987 0,)758
0,52 D,IfJJ7 0.2500 0,0914
1
O.J8SJD,S] O.D9n 0,2500 0.0961 0.3949
0.>1 0.0908 O.lSOO 0.09411 0,,;050
0,55 0,0894 0.2500 0,0936 O,.t150
o.."'" O.llSRO , o..'~oo o.oo: }1
O.~~.'-l
1
0,57 1 O.OS()~ 1 U.2:>02 U,U'7IV V."~~ ,1
0.581
0,0351 1 o,2!uJ O,OS9/ 0,4-16210.59 C'.':'~)~ ".!"' O.O811~ 0,4565
0.60 0,0822 O.29~8 0.0810 0.4612
0.61 0.0808 0,3015 0.0851 0.4181
0,62 O,019~ 0.3205 0.084~ 0,4891
0,63 0.0119 0,)338 0,08JI o.sco-0.<» 0,0165 0,3412 0,OB[9 0.5111
0,65 0,0151 0,3613 0,0805 0.5235
O.M 0,07)7 0.315) 0.0192 0.5351
0,61 0,O72~ 0.)395 0.0180 0.5~6')
0,68 0,0710 0,403-1 0.07tJ1 0.~584
0.69 o.oe» 0,4181 0,0155 O,510~
0::00 O.06S-l 0,H20 0.0143 0,58 Il
0,11 0,0611 0,.w11 0,0731 0,59,W
u,u o.osss 0,462-1
1
U.O~ !'>' i o},~..:;.;;:
0.7.\ 0.lIh4t, O,41RO :J.Oias 0.6;lill
0.4 ~ a
Il,·fI· I , :Il,. ~1.
M.M.
'rn .o)~ e ""\"" : 0.0 C '''''''~
~~1
':'"
'.
ldol~ ~'.' 1.. '.,_ ....,/. di ,1.1,.,"" d .. I\~~,r'''''': ~, ,: .. , l, ... ~", ;',,',1.,. (:, /. III l. 1. ",. 1'",,1':.,'.-•• J'JI ", l'",,',Il.'1'1111,'1;111 0'111"';1' ;'1;/,0'1111l:."r'l Off,,'l I~"I J' 1"'''''·,Ir'· 19h!> (0"''''''.''''0 ;'ft"""" " ~,~ ~(,u
f."n 1 T 1\ 1 p. 1 ~ [""., 1"'" (J,. ,,,,:,1,, .,,,,n J fi '.;lJ\I.~lH
if . .Dimensionne ment-'li. i Chor-qes de caleu.1
a/ if>.a.iA4.wA. ..dA. .fa. ~Cl.a.1R.t
PDU/l ..t.U'IR Ao1RR. ~ni:. .A.uft. ~cJJw....cMU ln\ ~t
~ ..une ~1>a"44.t(AJI.. ..cum~ ~ 1. .d .1. ..dA -la.~r li-O '105
~étl ~ .d..t. ~ .JoPlL (1),216 CC])
!ba. F ~k~ ..uJ:. ...wu. ~..cevvt..U ,CI.R. '1;0", x ~,S'm
10\'el'lt -1. :: 4-5"00 :: ""2,5 m," A.t ~z. ~ 11-5"00 .. -100mm •.,. "0 r
or '+fi
.fvu-o ...GW'17'r\4 ~ ...u.I'le .Jiri<>UU'L ,ck. 42.0 mm .A.t~ k
1l~ ..d'..urU.~1"f\i.J:i ?t0'1..ul~~ .Lr"·44UI.Il j>vwt. .ieu·
~ ~~ ,d.o.U.u.
b} C~ .d!~~to:tùm.
..:Q.Mo..44.A ..i"oCCll.U,'·e,& -1 kN lm?
c) ~~ ema.ne1l.t.u .-a.ufu~ ~ ~cL ~rof-re.
.' "'" J[f11.I..4 t'e.ncmA -une ~~ .k 0,015' m ~cL'4QÙ'4R.U"- ;..
22.00 ~/m3 .
c:: ",015' iii 2.2.00 " 9,g1 .10- 3:: O,32.'f lc.N Iml.
d.) PlTik 'P~~re ..tk ~ ~cl.~
f~ù!.rt.t î : .2*, S kN/m3 .J- lr:: 0,12. '"
'YI = 0,12. li 21#0,5' =
A .(.,J,t:af -fim..d:e ..ultime
t ., ",35(7 .,.1,~G= -1,35 (2.,'If~ o,32.4-)+",~lCf" 5,91kHfm:2.
A .f...'-<.t-cd -€imite. .ole A.vw-t:c.e
1" G+ Q = J.,~1f + O,32.1f'" 1. c '+,1.Glf ~ '+,3 iN/mL
PARTIE 0Dimerlsionnement dela dalle en béton Clrllîé
--'-.
Tf. '2. Colcul dtis moments (if- dqJ armafures
a) .:Dalle i
~,s-- "3,550,99
t4 .J.o.Jb. f>vr~ ..clAr'\/) .eu,~ ...u.n4 .J- rn .cCY'I4J.:d.lre ~'..J1.,
.ut AJit.'cu.11.e.. A.Wt 4Cn. .CDTlét1Wt.. ..4.U.r cp-tah. K1ff«C1.4 AJ.·mpfu . [10]
le.el<
'"0(" '.99
t.lo.O. (v" 0 ) p... :: 0,0316
EL. S. (v.. 0,2.) Pli c: 0/ Olf-4-~
..
'.p'j" O,9l1-1.
P:1 .. Oj984l
~~ ..une {,Qnck ..Je 1. m ...da ~~~,.. -4u..L·V'Q.l'\.t "X.~ }l'
E"LU 1 J>" 5,~1 klolJrflL l( i m '= S/91 /c.N/nt
E" l S : p = 4, 3 le N l"l' Il 1 '"
~ ~' EL.V. ("'''0)
"
Mil "t ' lPli/> 'II " 0,0316 ... 5',91 'lI (S,S) " 2,12' le,.,.",
fI:J Mil ,. 2,12.lC 9.,,'111:- 2,66 kI'J·m
50
~ of' E. L. .5. (~= 0,2)
2 1= jJllpi. = O,OI+~9 .. 1+,3)1 (~,5) ,. l,3i JcN.W)
Ca./eul de ('armo.+Ure.
tu; <trmCLfurtU .hl'tdu.u ,.cL'..une .42.ete:rm .JUe.to.n.r'~iNz. ~rrt.W ~
...un lncrrt'lerd:" M ~tX.n.t 1/-re ..J.J.tVtf'fÛ.ne'e.J t'cv eu~ .A.U.ivan-
4= _
d.'~ Cl, (3, sooo ~. ; U; .-.
. .
(b= ..f,S" p4-?l[6J. . .~.
M en N.,., 1 b e.t d en cm , Ob et OJ Ln MPa...--, A en c,;,l
<Ti .ut ~Q.. _t:Am.trai ....ti ..d.v.. ~hn ..k..u -la 'Fe ,c.om.~~.xlOKllA.·
ft. ,C(tA -d'..wu ...4.u::t;m. -'U.c.tCU\'(t" 'at"'U
~ = 0.'5 f u .• :: .H, 3 HP"
q>0\UI. ~d...o ~..d..R. S,.,m -4i:..un ~t'lrobCl.~ ciA.. 1:)mm
d:: -120 - .., 5 - 2.,5' oc -102., S mm.,. -10, 2.~ c.nl
~ ~'E:L.o. (~..o)
Mx . :: 2, 12. 1dJ•.".,
.'
..
51
= 0,023
ta..Aa.~ l'\'.f.bt clcnc ..<Vt.m~~ ~
~ ( 0; = 11-52. MPct )
~:. O} 9US p. 11-(;2. [c;]
? 32 C'J
J>a..r du a,.mct'twt.u tk
0,59 cm1.2120
0, 'JUs. iD, 2. S Il '+52
M"A :. =__----"'..;..;;;;; ::
-f02.,5" _ 5"+5" :.1.
fl-= 2"0 0,02. 5' ~ ~~ O).5B:f5='H,a " -100" (9,=J-S')l
A= 2'60 0,61t
:. C/Il
0, 9B'Tf> Il ',fS' >l »s:
" .. M,x :: 2., 3~ kN.",
c:Lu ,arrno:t..tr"f.S ,te'lcf.u.u .R.l- &. ~_
Uj .. 15'0 MPa p. 2f.:f. [,]
t: 251 Lc l
~ e' t.L.S. ( V-... 0,2.)
~o. ..4..eC.t:m ,.,e CAmt er tA -"fMII.
It.a.t.'vrt .ut ~di.c..La.b& .
f1!Ji - ----r bJ t 63
~I = 0,9~S k .. D,oie; f.," 0, ie; p. 2.5'2. [,]
6'i ::: k ~ .... 0,01' Jt 15'0 e J,If MPa.
<rb"' :: 0,' feu =- 0,' Il 20 a -1'2. MP~
(peu d~lTllQ.htre1 do co", pres
siol'l )
23;0
0, 9~5 IC -10,2.S Il 15'0
A =__..=..:~__
fi = q001b
23JO
0,9:325" 1l. 9,1-5" -ISO
A ::. __---=~:.....___
'JC. ::J
1"' 0,0316 0. ~111
1"'\ ( \ul •...,) 2,1-2. 2.,""
P~<:u.lq.' 0, o2.~ 0, 02. 5
~DJ 9885 O,9S"f5"
A (cm2.) 0(59 O,b11
53
· EL5 ( t .. 0,2.)
x. ~
p O,04-q9. 0,98'11-
M (le!'!.",) 11 '?Il- 1,3~
Pl 0,00-1 S 0,OO1G
~I °19~5 0,9315
A( cm") -1)'5 1,1-1
4-,4t 0 Q- .. ,J'J4-,5
=} e; ..J...iRR. ~u. 4alUl ..d..a..u.x .-cLvw:.
...te:CT7\A
. ELÙ (~.. 0)
'lC. '<f
P o,0~16 6,~"H1
M (k.~'"') '+,1./-0 '+,3 0
1-' c:0.1 euJé' O.Oll':J- 0,0'+&
~0) 9% 15 0/ ~SO
/\ (~'tflz.) O,9:f ,-1,0 ,
. E'lS (~=OI2.)
.f
~ ~
p 0,0 1.f.lf-3 0,98'4-".1
M (kN.m). 3,82 :',16
p~ 0,002.&1- °100:l6
(3. O)'3'f~ 0/9..,5
A (c:m2 ) <,ft .2, Cl'1
55
~I = O,9U le.:: 0,02.2.
cr" = k q; c 0,021 li. -ISO:: 3,3 MPQ
Ob -1 cO,, .fCU
:: 0,' lit 20 • i2. MPt2
U; r 3,3 MP", < ~-I., 12 MP., (1)tUl c:L'Q,.m~ ~~VTn~)
-f,II-- :'+,5
0, '31 c 0,11-
~ ~ .dan.. .4ur~ .e4.hr~ "10
Mo:: p eIl '1.. = 5", ~H 1< ( -f, II-) 'l.= -f, li-~ ""'."",
8 8
Merm.erLt AUr ".<l~AAi B
M MQ :: - o,~ 11 -f,Yf c: - O,f25 ktJ.,."l.
~LS I1q :: - o, s ... 1f,3 ... ('1,.,.):: _o,~21-k.N.W/
g
Momenf AU.r~ A ~rove"Q,nt c1J. -la c:l.a1& 2.
~l MG. - O,If 1'1,. :: - 0,1/ lit "",40 .. - -1,~, IcH.m
ELSIM(1 :: - 0, If Mlit :: - 0, f.I. " 3, Ir2: " - -f, ~3 le.~. ""
... ) MomeP'\.t~.vt frCWf!e de. iD.. da1lR lA
ELU Mt'" -1, »s: IeN. l'Y)
ELS Mt = '1,OStI- IcN.1"I)
t:"LU- N.m ...) r: 0,0'1'
-I~'SO
0,994- "</ 10,2.5" Il 11-52.
S6
::
· EL5 :
le. = Of 01
oiOS,,"
0,95"5 l' ofO,1'" -15"0=
cl Ar,.,.,aiWu..4.wI. 0f'1?"i A
ELU: l'1 .. H~o N.".. 8Qrre.\ HA .:!:Jfe 1
J:: 120 - 15' - 3 D ",02, ml\')
p = M 1'HO O,01r c) ~= 0,992.5= =Ira. b dt 1-1,3 • -100 _ (-10,2)1
A" f"/ -iT'O 0,5 c.rnz
= ={3d trJ 0,9925" 40,2. 11 3lf~
(iL 5 1
M" -i5''l-O N. PlI
0,000(;"
oi 5",30
""00,, (-10,2.)'1" :l'f0Pl =----:.....- :: ----...:....---
~of = 0/J5::fr Je:. 0 ( 00!JS'
Q"'b = k.~ :: O,oo~5" JI: 21f0 .. 2.,28 .:. <Tb-' c -f2MPQ
,,",S'30
o,9Sffi ~ -10, Z " ~lfo
51
,;.',...,.
E (yI®
@ c ® .:D
J' ..,5
. J)~ 3
1-
t,,:: 2,25"
..:I
2.95
'le "'cJ
~ O,O?i '+ O,~5&+-5
M ( k.M.ln) -1,'15 "", -t0
M !oc: = O,~5 M j .. O,8!Elr. '1,"'0 ~ O/~~S I.../'J. ""
M Ei F " Ml! ,. ..f,15' kN.".,
Ml!l : _ 0,3 MI' .. - 0, 3 Il ..j,oiS" = _ 0/311-5 kN.1'I)
Mc. co - 0/5 M" e - 0/5" ~ "",-'Il) e. - 0,5+5 kN.OI
S8
ns ct: 0,2.)
L ~
t" 0,04-131 °113, 94-
M (k.~'''') 0,~9 0)9'
Mk. '" O,%~ M~ c 0,'5 x 0,9' .. O,M' kJ.l. 'ni
M~F e M'ji .. o,~~ lN.rn
Me " - 0,3 l'1 J.. _ 0, 3 .,. 0) 99 .. - 0,291 k/ll. ft)
M, = - 0,5" M~ " - 0, S 11 0,9' .. - 0, lf~ 5 Ic.N. Pt)
~l/ = 2,25 m
au (-J-c> 0)
2, '2. 5',,-=2., ifS
0,92.
'le.. ~
p 0, O&l-!1- 0,82. 51
M (""'.1'1\) i, ~1 1,0 i
0,1-5" M~ .. o)~ 'It -f,or .,Mit" -f, ~1 Id/.t'/')
q, 81 le"'. ""
Mc .. - 0,5 M,I a - O,S" -f, M. .. - O,6S!i Jc.tJ.""
Mb .. -O,SM1/, ... -'O,GSS IeN.""
5"9
ns (te: 0,'1)
1(.~
t-' c.osos 0) if'39
M (ktl.m) 1,H OJ~1-
MC.D ., 0,15 M~ = 01lS"" 019l c °lf2Hi ':l: 01l3 k,.,. II'!
MGH = Mit" 1/11 lN.m
Mc. c: - 0,5 Mit :-O,S • ..f,.f1 .. - 0155'5 ~ - 015"6 /c.N. '"
Ml)" -l1 5 M" .. _ 0,5" /c.N. '"
=) Cl(. ~It .. 2,95' =' OJ <;6f:t lI-,50
X- l
fi 0,0~3; 0,3153
M(bJ..... ) 3~1'3- "'142.
M~J'': M le a 31 1- j "N. "rYl
Ml(z = M:J = -f,.4t2.Ic.N.lII
M K" Mb .. - OIS l'1lt = - 1.,90 i». '"
60
le: 'A
P 0,0'1 9 2 0,5351
M (1tN.....) 2,96 1)59
Mn = Ml!' " .2,,'6. k tI. '""
M \(.1: ; M~ " -1,59 klll.'f't'\
Mil :: - o,'=> H~ .. - -f, '+8 kN..,.,
Mil. "-o,SM
lt_ - '1,48 kN."""
ÂarrtQnfo,
I!t'Vl.~ -4ln ,eGn'lF .tUlh-~A-•
ELU (1) .. 0) ELS (V., (),2.)
.l>aU.t @ -/, "'S Ic.~. ri') 0,99 k.N.....
.Dcaffe ® --1,31 lN0h'l 1,H "".m1)o.eR& ® 3,H /c.N. lrl 2,96 1c.H. 'I9l
ecJ)
1(
M éLu (lc.N. \'fi)
- 0, 'HS - 0,521-
-O,Sb
- 1, 4~
- -1, L+g
(d_ = -«0, zs cm)
E"L.lJ, Ml- D -4,-15 k.N,rn p-= 0,003=1 ~= O}9952.
ill Mf: D 0,99 Ic.N'JTj Pi =O}OOO' ~... = O,9S1-5
As = O,2.5 cm'l.
As:: O} 61- ,,,,l
DcJla if
eU) Mt : -4, ~1 1c..N. ft! 1-''' 0,0'11 ~=' 0,991105 As:: 0,4 g ,,,,2.
El':> Mt " ~,H kN. rr, f, ... 0,000 'f (31" 0, 95'5 As = O,7K. lAfIL-
E'L.I,) :
tLS 1-M4: " 3) 1-~ lr.~. tI't
Mt .. 2,96 Ic.N.M
r-= 0,032 (?> = 0)99-4-:
t'of" O,Oc>1~ ~1 = 0)521
As:: 0) 83<:"'"''
As :: 2,08 c",'
A~ ec:u(e~ HA 1:'iP4.f FE''fO 4> ro mm d= 10,2. CIr)
US " 3&ffl MPa. ~ ... .2If0 MPa
~:
~L.I,) : MQ :: • OJH5 Ic.III.JTj pc O,OoG (3= o,99'f As .. O,2.0 un1.
EL S : Mq = _ 0,52.1 "N.1'Il Pi:: 0,0002- ~i" O,9'fS As:: o,2Z cmt
A~ e:
ELlJ MQ .. - 0,6' "N.", fJ .. 0,00' r; :: o,99'f As ... q19 cm2.
f'LS Mq =- 0,5' lt.tl.", Pi'" 0,0002. f.I,:: o,91;S; As .. O}2.'3 cmt
A~ 1).e.t l<
ELU MQ " -1 )90 Ic.A1m p ... 0,016
{;L S,Ma = -",1+ 8 kN.." Pi" O,OOOf,
~ = O}991
~1 ... 0,9515'
As = 0, 54C1111.
4s = 0 / 63 cm2.
~.oo ....
L
s.
Q CDe
CD M ®K
of.. = -f,So tri
ELU ("=0)
..e., '" 2,2.0 m
'2, '20 ...
"'
= 0, <;~
"IC.. j
t' O,ol-iO 0,4-034-
M ( k.tlT'I\) 0,94- O,'3S
MPIC. = 0, 'Cf N)l '::. o,,{ Il 0)'34- ..- 0, so 1&.,.)'1'1)
1'1 Mill li Mj = °1 3'6 Ic.AI.m
MM = - OIS Ml! :: - O,5"lC 0,9"1 .. - 0, (H· lN.",
Mp .... - «s t1)l = _ o,f " 0J'Lf ... - O,l/-f "N.m
63
ELS (~CO,2.)
'lC. 'c!-
P 0,0'«;":1- o.S5SY.
M(lc.N......) °1~1f- 0,1.1-2.
MPJc.c 0lcr.r M'Il = 0l~( lt O.T~ ... o(Go kN.~
MM"' M~ :: °1 '4- 2- hl. .....
,.., l'\ c - o,S Ml! c - o,~ 'J. O,~ .. -0,3~ lr.~. n'l
Hp -o,S' M'Il ~
0. 'Til- - O,~T It". ri): = - o.) ., "
°1 y,~
"l<. :t
P 0, o5"2.~ O/G~"~
t1 ("~''") 0, ':l-O O,4-G
Mol<. cr MJ == 0. ':la lc.tJ .....
MIJ'\ ... M~ 2 0, '4-' IctJ.....
MM = -o,S 1"'\" = - 0.5' 11, 0.1-0 ... - OI~5 ktJ.""
6é..
FL.s (v= 0,2.)
':t. ~
P 0,05"'6 0,1518
M(kNrn) 0)58 0,4-3
MOK '" Ml ;. 0,58 J..~.I'I'I
T1 LM ~ M~ = 0,43 lcJ.J.rn
MM = - 0,5 M. =- 0,5 " 0,58" :: - 0,29 . kMm
~x = 2., so '"
élU (~~o)
c') 0( .. .el! = 2.,~ ..~'J s.o
x. ':J
1'" O,059b 0) SilIf
t1 (IcN.",,) -1,8' -f,o1
M PS :" M 1/ ~ 1, i' k.~.""
MQR, '" M, 0 -1,01 ld/.m
M p .. -O/~ Ml' ., -O,S~ "",B' " -0,93 lc.tI1.rn
65
Ets (~" 0,2. )
1t 11
t-' 0,0 GG i 01 G+'10
M( /tN.rn) ~,5 ~IO
: -1,0 hl. rtl
f
i
APPUiS
1'1
r
ELU (kN.m)
o 't01
E" L. 0 (k.l\I. "')
- 0 1 41-
- 0,93
66
Els (lUI.",)
°1 63
~,s
E"L ~ CIt~.m)
- 0,31-
])a1A G
ELU: Mt " 0, BO ic.N.h) P: D,oo'f ~= O/~9b5' As :' O,11cm~
éLS : Mt .. 0,63 k.N..", Pi " O,OOO't- ~i" 0,9'S AS " O,42.cml.-
f'LU: Mt" 0,:'.0 kN.1'rI
E"LS, Mt" 0,5g k.Nm
f-' .. o.cee
p, = O,OOOIf
~" o,99=F As;: o,'1Scm1.
~-t" 0, 9GS' As =0,39 cml
J)a1.lR 8
~l..lJ : Mt :. -f,~b kN."., P':1 0,01' f3 = 0,992, Ai " O,'4-0crr,t
Mt "- "',5" /cN 'lfI fJ-t " 0,0009S' ~1 " O,'lfb_1
ELS. As = "1,03cm
~ BGVVU..4 #-lA i~ 1 Ff:LfO cf> b",m cl" "o,l. Cm
O"S .. 3Lf~ MPtA. ~ = 2.1K> MPQ
Appul M
E'LlJ ,
ELS 1
1-'= 0/0011
p, " 0,00015
~ ... O,99'll As:: 0,"'9 cm1
p., "0)91015 A.s= O,-15c",~
~;>
éLU: Mq .. - o,9!> kll/. "1 fJ" O,OO! ~t= 0,996 A.s;: O,2.' onl.
ei:S , MC! " - 0,=15" It.~.", P, :: 0,0003 ~, =0,910 As :: o,'M Cil
SQe~ d/ a.et:er mt:n.l'malQS·
- do.'f\Jj ~ cL. 't'ec.ti.ml .e1As ~ fI> b ~o = 0,OOQ6)C ",00)C .,2. = 0, T2 cm 2
_ <La l'\.G ~Q. ci..Vt.t.etitm f 1-
As ~ ;~o( fo
bl,o co O,H. (b~ol) cm'&.
Re:CD.W=h. DotiG-,geA /~ .A 'QcieJ'L- .44Yli: d..cnrt~eb pcvt ...uJli.t~1 ..k fhr~
J)d1L 1'10. 0( A, ~ +r~ (crr1') As -en lntuée (crnt.)
Suilh:lll.t .el A..Wva.nf fy.
..4 0)99 -f,{,5 "',=11
2. 0)99 21 :f.1 2) S1
~A 0,31 0,51- 0,1-2.
3 0,9' 0,13 °rl2.
If. 0,92. D, "f6 0,1-2-
5 0,"6 l,OB ",15
, 0,68 o,S'l 0/12.
f °183 0,18 0,12."
ff o/H· -1,03 0,12.
A(>pw's
~ao At.e.~ ,.d.' <lel,'4!h .et ~ 7lo-rnbl12. de. ~~~ ..cltm.",-4,
-pa.r- W'Ù bi da eqrF"r
4pJXAi 1'\0, A (c",Z.) NOMbre de OaN"flS
A 0,'5 3
8 0,2.'2. .of
C 0,2.3 -1
l> 0,63 :3
K 0, G3 :3
M 0,-15 -1
P 0,31 2
F€lfo
1'0
<l 6 mm
~O"T\3'tUu r ..dR.D -cA.a.pecu.t.'j( AU,r _~ (p. z:~'+ C(,J )
'/:,... eu.,~ -c4.0 -~~ ~ 1>~ k. '?t« du~ ..RAt ..a.u "1'n (1(1\.4 e'r :
- ~ ~ ~ ~ ~ -r-nd.v~ ..du -<fw.'I. .iraW.., .eJlc.a.~
.el~ ~J.l;.ti -4 f..i f.r-f _J.I-u..tl -a..~i. n '~ena.nJ:. ~
à .u.n.e :b-~fl eU 'l..\..'lX"
/ ._.;. i .k ~ ~ /'ra.n.d..e 1>t1f"tte .k ~'/. .i:n::u..-ell" ..el1cQ.~aI'l.t
'f .
.t1tJjfu ~d.id M" ..dMf ..wt~ --r1>~I'I.cud: .( -«J\~ -rrcw/t
4.R ~"
i 'II 2./3 "l =- 01 S':/t" '30
If0,6",
K -1- "5
1,0111
...
:f.eb .e. JQ?l..n:cf1 8.~. 5 d..u. cLcx:.u.meflt ..feeC..AAr ..u..ru'.
~~ (;b.T.O.)[HJ, ~ ,........t ~a.J.m.dbu, ~/.i.f Yll.ut~fcu.ifl~~'
~ ..J.t .ca1~ ~ ~e-Fv.., 1~ k A~ ~Q."~.
~ -~ -4Wl. -leuJ1.J ~a.fre _eetiJ 1 4i -t.w .e.vneb'him.6
.4.uè:~ -44'J1.t JtL~Jfu
..j, " Mt:- ~ ---e. 20 Mit
A 2.-~-bd fit
Ml! "1rIfrm.uJ 7Yltt'(l'I'I'I.t>1 ~I\ ~~ tttr ban.k .da..f.ar~ .u.ni.t'J
dcuy &. Mn.O f.... 1 -&...~ ~ .d..o1L..ut AAA.t~e. 'u.~
.fi~t A.Wl. .&.U _~ (M" > Mj )
Mt: mumen.t -Ut tra...u.u 'Qr ba. ....d..e cie. .f.a.r~r .....LniJ:l, ...d.a.FUl -ta. o4..U\4
.f" 1 -Cvrrt~ .te.ru.c. .du ~...d'enc44.-bwm.r.ril. Itl.i. .J.,. ~CJm-t&' ~
TUI..i:ht (Mt ~ o):çS- Mit )
A: ~e:tùm..ko .,CV'tI't'let1WUA .:h.n.c:l.u.u l'.-.r ~a.Yle& ck -&.~ b
( b c -reo cm)
j'.-ie A(a.~rc ·tte,"Cf/.UQ"~ ..cl..e .=J.c.J...u.. .eu jllc.?u.o" on ..u:tA:~ -&.0
frr~ 4W.Y-o."-fu
ilr :----
&t: -(p.Ju.. 'h1dKLmah AmU -eltClr:JC!.(l k F.6t.. ktU .J..'~'ca..
~
'v: p.:c~ 'tF!a/lc,ÙncJa /Ul"lU~ .-ek.ecm~..tkuW._J.'~·c«i:ûn
I+j =----=--- I o
. l ~ "WlO'J"e.n.t ..d.'.Â'''VI.:tÜI f4c:q.I o ?>'IO'I"l'\QI\l d' LIU/l.t.R .J.t. .ea 4I'~ ~,.Ju.ncL.u ~o~-
1\1. a.oec 1'1= 15 1 1>CIr r~P""'t ~ {Jo.xe ta.44lU\.t tClr.e. CV'l
~ ~k ~ii ck ,c4I.-th. 4t~) 71 = E4t:I'td'
EfH!l.c,,.
1\,: 0,05 ff.2.8
(2+ôh)jb
Âlr
= 0,0'2. fu,'i
(2.+3h)!b
jJ=-1 _ ",iS f t u
1+ fUS ... ft,ulm t rertcl p= 0
J .
13
(1,) ])~ 1
.ell ': e;j .. 3,5117
"'" 0, 12."C') - ..e; 3,5
fa::: -12. C"I Mt 0 Ml(
l= 0, 0 3 <. .. 0,052.0
",'l.f,1\J. du .om~ 'Yl!il;cvd 1'a.b vJrt.f'.e , on tr-oddA. e:t.ù cde.tJ.l
.J.,.€Cl~
ol.-:: ., 1. 0 0
2'.0,0'+'+9.,. 3,~ Il (a,s) .... i,al ~tJ,"",
0, 0 "''+9)l 1 • (3,S) 1. e 0,~5 kN.",
-too Un
..
I .. :. -tOO'i.(ll)! + 400 J' -12. Il (6,09 - '/+ ~5")I, .fIT1 1l (,*O,Z5' - ',o9i'11.
A1=- =bd
0,933
lrs ::1M 2~2.0 411-2. MPq= =
(3, cl A 0, 9~~ li ""O,lS" Je "",1<>
pc -1 - -f,l! .fUI", - A,1{111 ... .. _ 0,13'=
~!Üs + fuS 'h 0, 001l " ,,~z. - ",a
=) f'eo d'~ I t ., 1 0
~eo &uu-~ ~rmo.ru."""t.o G ~tAfl.t J:>ar d.LrnA.~ ..<k. et:m~
~ ~t fu _&tar~ -el'~~toL.m Q .-ek -ecu.rt.e.~ ) fa.
~~ .:to:t.alP 4.VL1l
1:11 ..
E;. =L
'131-00 Il (20) 3 Il 10. 014-5 MH~.
.:f pur
~. 1/3 '1 'lbOSMp,~l. :: "1000 'Il. (~,,,) ..
t. t lf,'Ir Mt e -t,':l-B lC (3,S) • '10
0,1' (.'"'" = :::
:J E". r, 'x-100'l! li -14 rss
=O,~lI (3,5)2.· -10:'
9 lCH~05 10 ""'H55
t~ c .e .. 0,002. e. e q ooz.x3S0 .. 0):1-0 c."". Ok!50-0
b) ])cdfa 2- ~,." 4145", Mt .. M. 0( .. -1,0
A 0,12.e 0, O~~ <
..,'" 0, OS'- =
.f. ~,lf5 20
se Go.ut .cD.eCII00." .(ID. ~~
r1 GK1- 2193 t.tJWI
" 0, 0 "'If~ lC 3,?> )l (,+,~~) ::
M Q .,. ~ 0/O!fli-9 " '1 )C ( II-/f.;) ~ '" 0/89 k/lJrn
100 c.""
~ ..d.e~·U
~ ho..prnt ~ ,t'œtlh~
100 x "2.' + -I5)l 2,81 Il -fO, ~b _. 6,14 Cfrl
.fOOlC~2. + .f~lC 2,81
I o .:1 15135 cm'
j c.~ .. 2,81 :: O,OO2.T ..) f., ~ 0,21 ~I = O,91JS"bd "100" iO,2.5'
382·0
o,':HJ5" If -IO,2.!:" 2,81
M
~, dAos '" -......;...=----
-1 .f, loS"' Il -1, .. 0r~ ---------if Il 0,002.1 ,,14-5 -+ -f,3
= O,06~
~i :: O,o! f t 1•
sf::
0,05' II ... ,
5" '" O,OO"l..=1
!
-fS135 -IOG10 c'"~"
~S13S
.., + 2,'1 le 0,"'-11-
J.-(+>-.. p
I t ll " ----='-- '= ------_ c
l t0,8! Il (1I-,4-s) • -lO
S Il H'o!)"" -10(i;10
Mt el.j EU' Il,,.
M,-tl.
j E"( I.f.j
0,1'2.' II ~,3ll (1,'1-)2.=
O,12.~ " -f " (1,4) t = o 2.'-1 f 1c.N•.",
1A~ = O.9lc",
100 (.m
~~ .la. ~t:':' : f411. J'L~ ~ ~'.:vû.tt. 4O.pAf"Ùlu.re
-l00. -12. • b .j. 15'. o,~~ 1<-40, 2S .. ~, of CI'Q
il" -100 + AS''' 0, ~=I
0,09= 0,00030, si100" iO,25'
f=-~-
-1055"
0,95' l< -to, 2.5" " 0,91<r;=--_....:..:.=~--~
.f,=t5 lt .f,g
if .. 0,000.9 'Il 4'12 + -t18
J f ,ot.t If c 10
0,81, (l.lf)l. 10;::
'" eoous; '".6'0
e, :: 2,25", ~~:: 2,30",
~- ..€.
0,12. :: 0,05'32,2.5"
> ..i200
:z o,Or
A O.l~ 1;-12.40. 4 2. 2- 3, 'i~ . -(o~J-'" = < - .. -- ::
bd -roo" 10.ZS fa 62.0
t;~ uér~r:~ ..ck. fA !&~ l'l'ut- fGt4 ~3o..tniu.
e) Pa..ek LI
-R.1I " .2,25'm ~1= 2.,4~",
G>, 0 S3 :> --i.. 0, 05'2.0
A- :> -.-.;;..--
I>d2._ ,.52.0
~ O,/l.s 0,014- 1 O,or cm co.1.CJ.A.b e: ~~ch~- . <.- .. -">
e. L,'fS 2.0
MG1-
2 ) 21- J..tJ. '",. O,oH2 '.t 3,3 ... (2.><35) ..JI
Ma..l.. 0,0192 li -f,O 1l (l, ~s) .. O,'~ 1c.AJ. rtI
Af'" - .. -~....;....-:: 0,002.0bd
=) .f,'" 0,20 ~t- ~,= 0/12.g
crs « lqGo 3 -f~ MP~0, '37.8 __ -10,Z!.. 2.0'
p.. A -1...;.:I~~.;..,;",.}I._.f;.:..'V,--_.. _ O,of < 0
M, (,l.2. T 1. f
~=Mtil J./J.fll(2.'I5') .10 O,b9" (2..'5") . 10
+ ::. -+, ~V'ro ~€~ r o 9" ,/OOlff. "''+-9'0 , ... .n'OS'" .(y.~S'o
ft = 0, -1 S" + 0, O~ .. 0, -1 S <: o.ooz: ,. 2.,5 = O,!iS cm olc.!
3)' J)o.UL ,
ek .. -1, 5"0 '" ~ .. .2,20 Il)
.l, .. ~ .. O,Ogf. .4,::)
0(=0,68 Mf:::'O,BSM ll
~ . Ht:. O. fiS'.. O,OH(<0 Nil ~o
.!... 2. ::: 3, iS'. -10· 3
Ge. 52.0
-l. ::: ~,5'o ."
.ft 0,-(2,- ..~J «,«
> i ... o.os.20
A O,:U-::rbq -100 .. ~o:t'!)
2-- ..~fI.
.2.- "52.0
gO
€. = 2,~Om -i~ " 3,0 ... 0(", o;n 1'1-1: " My
..p, 0, -il. O,on > .f .0, of- " :- - ".e.. 2/~O 20
A _ A.03 ---10- 3 2. 2- 5 -3- - :: <: -::- :- 3,& .40
bel -foc:>.,. -tO,2.!" ~ 52.0
~ ut J:~ ...:"hi~nt/ ..du. F.,} .dR 1rtA.Q LUI
'Yll1mL~ 1 ..cf.l.u.~ .tu Yl"/Q.-tirtèv.t..x dù~~ AW"l .&. ~rI.'"tM..
rharIÂ ~~ / .eu ---r-~<a:h ..e.a.:Wni.t.·'fAlI.() / af.rten.1Ul far ..C'U,'-
-uo.? -d: -,.w.~rd J.t:i .i.1l·rru·r'I~ ~ A.t &. ~ca:tPm _du
rrFt'I~ 1 1bu.en1. ..4UA.+6ew .4./:Jre ..ut:.~ ..daAo &. mi&n?
..dL .(,iftm.
l1 rtJl .uL·f.t4a"LAm i0d..ic..L~ _eU -CQ4 -ra..ru-t1.a1., ..Lrai.t A.Q.I'I..6-&
.urw ..ck ..e,/-e:eundY'tLt }(e~cM. til/ut ..a.ù'I.4.i -F -du~ ont J:ti
'mQ~ r« l.f:~ .a """d.&r'I~ ~mtdt~ cL'~ ...uJUl ~ne
1 • L '2~Çlt'ICe Q. lf Jqurs.
"Cl. ..um~ ..c:l.u ~~ ..u. ioitAn~~ A.WlC
-&ifnu .1n.a.d1b:cmYUiA.
-Io~~ Mtbti.:t..:~ .v.i,.·~~·4{4 ~t.JA _~ ~ r -€4~
'" (~) ~.fL ~e ..2 ('"'OW'"). i>~ -bn.l.rBeD Ta.~~. __ L. L.hJt~~tJJ'lf.'L..
AoO'TU- ""T-~ oUI ..a.t1"eke
hl)d.o.~ _d.v. .f>éfm
_~ce~
f~ -dt. ~~euJ. : 20 MPa
<J"~t:: .2.0" -1,1 S' :li 2 3 f1r~ r163 C12.J
~'uunerd::
Ol" c~ ...UJ\ .+"4d Rm etti -k 10 <:.JI'l
PrellDtU ..UJ\ .d.c4a?
~ - "') 81·~ -
-Ul -Cl:men.t ~ !SD kal m3
~. -195 [11]
E= c- ::1,H
a5"o a -I,f, 2. ~ -II::;' ~/rrl31,n..
Svit .un. -Mf:#.tt.. h .2'1- l..JJ1ln J
f = J.lI-~O .. -tll-If',:) ~ .2}fCf:f kal")!S,H
:t~ me'Btt'l? ..ut .QXf'r'-'mefli:aP. .R.t- D"n ;ren.d. -tu~ ..w.i~
Setbl.e 30 %
'flQ.n..t..tJ4i ~ ., 1 ?>5 %
..eyt~.d. ~e. 2. t ~ 5 01.
-'1910 X 0,3 ...
1910 'lit 0J~ .-
1910 Il O,?>5" ..
S=f~ ~
ccs,s k~
"i,S It.ca
Clmen.:t 350 ~ C,rnrw1a:t 41P~ of. : "f,S~
E'"eu.t. 111 ~ Grqru.J.of ~e 2 l '~t,5k8
SQ.f,~ Sf?> Ic~
83-
l)-ofume d' 1.1." mnJe (4 "" 1 5'0 7'fIffl, ~,. 300 mm) ,. S,3 /.
:Pour .Lln'.> QcieI{U <k 3 'n'\~ U1"l a -W\ ~lTle V
V ... 'B 11 5",~ " -t,OS' .. -1')'95 as .ff l
C:men.t ~5"O 'll 0,011- = 5"/ 95 ~
5e:a..&& 513 '1' 0,011 "- 91 =1-lt "1€"Q.U.. 1n ~ 0, off .. 3,1 s k~
G,ott~a.t ~e -i ccs.s y °/01':f .. HJ~~ ~
Gnuu.J.a:t ~e. 2. b68,5 1C O,01:t- .. HJ~~ k~
fou -r~ah, )l'él:a.d 1>CUl y"Jm~ ) .i.e a ~.IU~~
~ .J'qCUJ. .d. .da. .-cimen..t tour~ .{'~~.
~e.b.lfU~ ~rtD1u -4An.t ~ ..4U.iV"Q1\.fu
'8(nHZl1.t ..,2./4 9 Ir.~
Eo..u. b/6r ~S~ 9/l'l ~Grtt~.1:'Jfe 1 11) '3G k~ (Y/us = -HI S%)
Grttn..u1o.:t ..t:tfe Z. -t")~' k3 (wm : -1?>, ?> 70 )
~~u J'JtaJA ~o.At AU".n CUl 1re'rnoui~aae (~d~QU.
", ... ,~, 'll (q-t-tS + O/"'~~) = 1,li'2 k~
Eo..u *C4ce: c, bf - 2, sz .. 51 SU; k~
R.~t ecua.f ciment r.riJ. :. 3,8(; ., 0,3:1"'t,~9
61 .2 41 -e.uai
~4 m«me TI1~~..ut -uii t;uo aoec ..LUt t"affurt ,'n.i.h'4f.
~ '= 4)':fo, cP,. &el1..t ..fu, ep-ta.~ ..4UA.'l)CLtl.ThA -ru-r 1 ".,3 rk
~~ ~t €Il jNimcu.ieJ.an:t. fu~~6.·F'
c.c:men.t ~ 35'0 ~
l:ew. 2.0' Ic.~
.s~ 5~1,"!>~ ( ~o·1. )
GnvuJcd: :l:~ -:L 5'-1-, 3 ~ ( ~o·l. )
GrGt~t ~ 2- f5' ,'1- L.3 ( /fO·t. )
;;gQ -1cie~ .u1: ~ ~ tu 'f-UcU'.:tiiU -4M.i va.PI.~
Cl'm~,J; 5", ~5 k~
E'a..u. ~.5 ka5a.b& ~,~~ k~
G~ .t'tP~ J. , 9,'4- kaGrQ~ ~ 2- -12, i' '"
S.,.:i- UIl r~ ~(Ul 1o:men.t
eC
... 0,5"9
gs
Re',,.siances ell COrrl[>f'eu"on
1~" <!~$4i
EchQ"ti lions " Fr (kM) O'""Cr-1PQ)
4lj""'I"' -tl5 ~,9
"'" 4 l,lolLn -rH <\0.12Q U iOll" 23' "3,&4-3
Ec.~~"ti liens F", ("N) üCr-1P",)
..j " :fj."" .(2~ 1-.0
l4"" jours
-t-U ',l
3 À 2.& JO"'"-'t%S -to,,Ç
c; n1.Ûnr~Q~ .,4'.e,.t +e.t:u.1 ~ ~ 'o.c:r daN ~ ~b.'rm..o cie.
cho.tti:ü.r.. 11 üf- d.rnc cli~c:J.,. .k .u tn"'6)leer .extU!Î"em4ni:...4.Ur
~ fUat:tt J.u Ufnt YncuA.iD. ~bJU4IZ ~~ ..k Jtt4J'U:a.i4
o&tel'l.UA fut. 4Al7t4~ ._(-Vle. CU4.fre~ .
86
8.2. .f~ ~
i,~ 'mé~~ ~ ~ -au kn.b Jl.t nl77l ...ck
mGvuue ~u.e . ~ Afr(I.f ..ck. ~ 'lYLid:f. ,c.'A.!d -et -cWu. ~ -b.
.fa. b",.P;t.,. .ut -oa"uu.tf. A.WlC -<f1~1( .f.a:t~tÙ1J,114 • i>~ ~
lancu .Lf'I -C#Yrl~ ~~ -a.cx.c ..LC.n .4C~.it-u ~
-&.tRn.
Pan:trl'laff-e..s cle me.Lu.re.
i<r;;t -'U~U an ce CUl e~ -en rc.t:m, dt. oC
Wtt f'~'ll'lee JU'\ _e.n-n.~ rh~lol-e
l.VMiI'l: l'~s(~ tn.'lce ..a.n~ nu.h~:m.a.k
mJ.Ja"fje 110.1 20 ~ClbJ.e. t ~D eù'n-4lttt + i ~o.1.:tL 40 .3 iJrrvl.u.R.cd
~~·b.·1(Ml (~) + 2 ~ru.Ja1 f?a.&'ri6..'1u e. ~
R.~ Il 35, '31f, s-t , uo , 32. =) I<.c ::r 3Y-,C+
R.d. C«ori':Ji .. 3D =) \.\J.,. 2: Z~/G MPQ ~t- vJfrtj'n" "i-.~ MPq
mJla.n~e no. 2 :;fO SQ.b/e + 't,5" Q'r'lent + 5 b& t b ~~
t'..fe'n:Q1u.e. ~ /1. ~ru.c1A.t -ecc1érr:.U1v..é F
-R.~ .. 3~
W" :' .22.,1 MPQ
Rot CArI'O",~, : 29
w",,',. -:: -'lb/O HP.,
89 ..
te ..dto...~ke 6'aÛ: .e'~ _cL'..une ltLe,o-n,mèV1.
da.~ ta.J'lil~·Qn.. Po"ur dJl feus arrt.~ .A."n.fnmo...t.:.mo J A.t
~~ eut c.Ra..r:trQ. k Jucemma.n.d.a.t.i..an..o~~ ia ,'1.1A
à ei.4.AIQ k ~t
88
1. l ~cl;:--. ,
J)~~~",k.~~~Pt c.a~'P cb.
~ck ~~~Ct-4~.1L~~
~~~J~~~~~~r-~~~ktU-~ ~~~/I-L~
~~~.~.
C--.-f'i~ k P -r:~~~t~ l I
EP"-~~~ ,dJ"",- W A~ ,A.-u-..
~~~)4()v..~~~~~
~ ~; cj}~~~~~.rZti.~
~~~:
- ..G. L.tvt 4~~~~ e~-o.C-o
A~("'N,~~ ~.bY~.
- .Ro.~ /th-~A..&k~ ..e--~
~~.d~~Â~~fJ
~j'~~..f/~~.
-~~'~~~6J:1~~~~F .~.~d'A-~~L~~~_.
~o
ïï .~ 4 u~t Af:A;)}j 4 ~iovAAt.:
Ir. -1 : Be1b,..,.."ek. ~tz .,J; & Iv..,do. t.....1
L,. ~~'&I'''-~ rliL i:~.LI( :: ~x "!I ,~- .;f) QQ'" 01'1S + ~ s» + 0) 90'" Et" o),,~ +~ 60 + -1) 80 +(~IO)1S)
;:. 5"6) &5"""
L.t.= (lx ..H/"o) -+ Lt-JSO+ 0liS-l-~30+ 3,004-~.!c+O)30+3)5"O-t(t)(3)o0
;:. 5 1) ~ S )'w\
L .... ,· L.., + LJ...
~ 5"1S)' s+ ST; ,~- ~ L~ ..-1..14-1 6~
V8P ~ ~~-<k~JA.~.
Vap::: 0 1:J.Q l( 0) 40" L
-:. 0).2.0 )t 0,40 ~ "'1"It-J 6
~ V&p.: 3} 1.63 '1"tl3
Ir.. .t... : ~*- ,~~ -c..Jv\~ :
~,
V", ..~.........~ ~~~~.fa. &""' d.4~.n..:.~c1.Ai~~
e: '" r èoQe~~~ "elJ,u.:n, d'rri-ni:blo.lll..l"~d)...-&U\-~ ....... ~-e.:~
L-=. n.e. +(t)T-1.)~
~ h - L-..t.. .- -;-;r=.......,~), - 04-0 _ ~., .2. 6 6
Scn:..e.-t. : Op3 + o} ~ 0
V-s"" ~~~~~
Vt H " ~t"'\L rd..tod-~~~ .V-Sc.= ~~ ~k~~~dL~-~.
":rV: V'\. [e. "(.b h) If ..lJ
v~v:: ..t 66 [0)03. Cc2.x O} .... S") x 0,.2..0]: 0,4-1'8g'rV\3
V:rl-\ =. L Il e ... h
:. ,f~4-)' )( O)O~ Il O)J./:J 'Co o} 68,6 ~
V-:rc = V~" -\0 VOS H
=- 0)4rBZ -+- ,,>68~6 --4> V~c. =' ..1) -1664,.,..3
~ J.,.~ ': n-i--1.
VA:""" (\'\-\- -1) (Jo Je .e... )( ..t):::. (~6~+4.) (O).20J<.OJ.-fSXO}4-0) ----... VA,":. 3J.2..04M
S
n:.?i ;-ft~Uhrr.~~~:V'1=- lA3)bS-+;,l,gS)k 0)"4 It~JgO- O,AIf. (-t,1'1-1)S04~}.tl(o)~a+Ojl'Od'I"Ii-)
+O}A~(?»SOll:~l\. ~}IW- 01~ll-:1.)A.t) ... 'lJ'14.5'1 ""J
V1.'=- 0)1.'+ [415lt3x.P)80 -4.)5011 1.)1.sJ : SjOS4=J ,.,,3
V3 =~Ol i>O+O)ED)X089 - a} 8 lf o, tr}o,JO + '-)80)t C330l = o} 5.2. ~t m}
V,+ = 0) 30 [-1)BS")l..t} ~o - -il 5h O} IDJ ~ o} -f.4-[-t'1/h2}80 - -1} ~~(~~ -f"~) - O)lx ~9B
- 0)"'+ l-1)'h -1,"0-8,3'11.2.,80 +O}95'C.l130+.t,O~+C?'1-.rlt.-i)~ =1)36Z3~
Vs =. 0) -14-[S"165~ .l)c!O- 1.,30 x ..lI00] ... 0) 30)< .t,go L.t) ~5' +..1 JI ~)toJ
-t 0) 30 ( - o)zo( -1) '3.3 + 1..) ~5")) =- -10)B136.f
V, = ''l'!'+[~)80 (It) 35">1 L ;. J.)t -i}f!») -(DI g9 ~ -ij 1S -+- 0)'·:bt-d."t y. 4-0.>~ Il "1) ~s)J4 4-) 05'"x 0)3 0 )< ~~.3 .. 1) o.z.K9~
V-r'=- ~TT (O/1-1._OIlj..t.)jl"O)30 + (..t)(-:t}80)<~30t+ 4)"'8)tOJ"'~1I1.}SO):: -"-;g1.3~.t
S~ "T :~ ~1"'L );~ ,JJ~~ .et J.,..~ ..dLU~
"'T'-= Y;, + V~ + Vl + V", + Vs ~ V6 + '1/;
::= g)~4-5"1 + 5) 0 s-4 ~ + 0) 5.2.:38 + "1)36 i 3 +A O)8rj~+Tj0.28.HdJfl38
~ VT = '+ ':f,~O'f ......1
~ io.~~~~ el.... -1.).2,1))( .2)36 rn.l.~
~ JI ?) 5 ~~ e-.. flaUb:,.,. .:k.~_ ..2~)( -tlf.x -:i 1. e,...,3~
Âr-u-~ ck 16%d,~~ .cX.J~%.,Je.~~
9:1
rvJ."....rt'\JI .
5~ Vs :> ruJ.--.-.~ k ~ &0.. ak'Ut-..Vt.= ~kW~~~.4U.,;;t,.
=- OJ~')l 4 ~ ":16 0 e,
VI- :. 0) 2..1.1-" YT
=~.,l.IJ.l<lf1-J~60CJ. ~ VL..=- -1.-1.?'+6J.S~3
II:-4: "P~)~ erpgbo'4_.eN\.U~~,
~,
5~: ~~~~ ck k-J."JA~,"~
~ =~~ th-..&~ .e... r-ts
~:o~ ct k tkJJ,. ~ '""5"1:' 4-JSr ~ '+,"" 9 = Ag) 44 t3
51, =- 0) l.j.-L >< 3, B -= -1.,55'3'
$) == 015J..(3"~·'-OJ4S) = -1.)1-368
54 =6/H' )( 43J t.! - ~UJ 881+1.+
Ss == l.f-,o-1 )( 3.J8 4 'Co -1.-1.,3881.1-
S, := 5j60 le 0)50 ::. ~J 1000
S=1= .lJ~8)< ~J8.2 :::. ~'+036
~ = .~ S...:..4.=4
0'\,. y../ ~ Se>I" J..eJ
:: -1.L'1/-f 0 8 ,1 )t 0 J "1... ~ \t.I= --1.4,S33)-r13
~.~~~kd.t~
J) -=~~ "cl~ rteo.M--lp .if Vp r .to......t~ J ~--... .t~ d4,~ 40'«'.
Vp~ n [~\~pJ
';:. i LTt 1'.4;"5''- x O)3~ ~ Vi =O!D4-.l.41'V)~~,
S~ ~ bd ~ d..:.--J..!AL~ d.a la.~bw =' ~~,f.:~ tb k~Ve ~~~ tiL1..&~--le, = ~".b e:~
Vc ; f [!>e~t - 1)~ ] ) le.
= Jr. [4-) &~ - (I.~) 65" - o)th J.)~] le 0 .t 1.Û \/.3
_:> vc.= 0)"1-0.2 6 fVI
lI_S: '~f!4et~~;
'Ùc= ~,cLe~da-.ok~~.
Vp c = ~rd.t.~~~I'~k~~.
\f~~)~~~:
V= ±1l Ri• .t [-1~J'3
V6C,~ ~rr [(.iJ·H+O)4.-iJZ."(-i)1'O-+Or~:~) - .2.)Hl..,. -1.)'t-j ---i> VG>C::,Sj4-g':JO~
Vpc :::. ~1Trr -i135+0)H)'l..~(Dr·O+-O)H) - ..-:1,352xO/~.OJ ~ Vpc =0 1"'lf'flr(
Yp ::: ~~ ~ ~~...rAl-o ....k k peJ;:ti. e-.p.&
Vp ,;; 4[1'>< -1)5" ... -1.,:s(J)8S~ ~Lj.o)j _ V,,,, ..-d.)6313M3
If. _ r;, ~ p"rti.honS
1!d~k~~~~I~/~ .J!)~. . ~
i~ .1.0.~~ ,.A~ ~e.t ~.-d.a-k ~ d cJj
Ab. .f 1~,,~ ..&~ fU~~ r---- ,fp..F~ ~.
p""" ~ ~~ 1
Vf" = t Ti" [( .l)11+~H+oJ0"1)'1.... (1.)g'1~OJO~) - (JITHO)"1.1.~ (-:1J81 )]
_:> Y!!1 = 0) 38 1 j m3
?"-.1h~~:fr ,'L 2, Il
V{J. " f Tf~-1-)3S"-tO)H+C?01;i' Co)g1.-\-o)o~ - r'1,3Sto)1.1.Jll. (O)8<1.)J
_;:> Vf.1 =- 0) 0., 50 ......s
~M~'L ''1.. ~ 1'Jf!,"; L~~S - (3JZS- 2...XOJLJ. 6 ) + ;1J60 >r -1.),2..0J >ro)Ol.
~ .!fJ ::::: O)~066 ,",,3
Vf4 e, OJ 0 2. [ ~ 00'1.. - 1\", .Pit0 t..]
_ 34= = 0) 0655,..,.3
svJ V>:' 11 ~..l.~ e&-~A p-~~~
kh~·LI
VF ::- ?:- Vp.:.......:-4, 't.
'D1Tl
lII.- T~~:
_W!.~ e.c:v"-' l-........ Fr. s-J,& ~ Trnt,dJt b TltU rk-8 ~IQ fltbf.-- 1r: 12 s,~
I~("'rt) (Y"\?> ) (1"",3) (J"'I3) C"",3) f"") (1-) S~ (--&.~)
~J.,.~ 600)~o .2.) 0 z, a J) t~ S-)~6 0 0 0 0 ô
~ -J.r. CÙ<I~ 11g/~ lf 0) ~~ 0 D/lr 0 0 0 0 0 .)
hdfx' ~-~e;.J .Allg) l't 0}T1 0 314 0 0 0 'D Q 0
~V\-~ 45 r?f lt "0 3 '3 0 0 61.;'U, 0 0 0 0 Ci
~JR~ 441f1j,ll? .2)52 0 ~)3. S- A 't) '+~ 0 0 0 0 0
.~ '::SD~5.L 3) 0 b ~46 G)O~ 1+).210 4l!l,H A1.t)'3K ,11.',000 :?> .too.ch-o
~ ,fo1)~;~ 0,'15 O)~" o)3~ 0 "3 "3J =1'~ 6~,!t3 0 2p S' A 'r0So' !;,,'""." .
'""" ",J
,p~ 6/14 0,01 0J 0 .z. °ID3 0 AO) l 2- 331-60 0 OS' 0J
~~ 691)37 -1..}<"1 0 94~ 8)g,. 0 0 0 0 0,
.~~ ~18)~8 0) .t1 0 o,O~ . A)5".L 0 0 0 D 0
~.c.n..~(o ).p5JSS o,3f. 0 o)ti -Z-) 64 0 0 0 'V '0
;:::,_:t"":'_A .._.t-:..PP.... J.3315~ oJ.2.4- 0 f)Jf!ô 0 0 0 0 '0 0
'.:/
>:..
N.~~ k bd:'r>'\~; Cu
l q"Q..J;$ T..t.oA. ~~ ~~(~.e.-FP<) (~. C,"A)
~""'i-,.J; J. "g Sc::LG4 .f, ., 5"0 4-6 fi> }-oo
~ A ~ Y"'>~ .2-00 3. fo'"oo
.~ 3~ -1o.&-frQ ?lo.ooo
~ J.J)~ -1000 .2JJ.ooo
..~ 3 1-60 ?-b.tJDO4 00 .,....
~ dR ~ti 6"\1"- u5~ Soo 40.00 0
A~ ek cLA~ tl'lll'Wl ,,~~ ;f?;'OO .23.400
~1i4 ~ - - -1.tj 000
RQ~f- 6~ roo 4~o
~ 4d,.6~ <!J,00 33l?oo
~rkr - - .-12.~ooo
~<4. J .l~ ,,/65.000 330.000. ~~.
A~kr.J :L~ -1 5'. 6/llf. 31.2.~g
.~cJ...~ .- -- ,2.14 o~-o
-1.535. 678"'
-? eTe. = 4.535.;618 F' CFA
ft..~..d)~~ rb~~~ drJ~7 rJJ.~ r<J1.tev:..Pflf. ..e-. Dv\..Y\-~e A.5
V:: ~~.J:r...e.,~ a ~u-v'>Q ~; 1!:!:.!:!.l
"2:. -1 , Rc:.-", cI.R.~ tJ. J;1~ r:k J"l.W -~ dt
~ d.t .-1. Y"'\.~ c:Jk~ :
J>~PE;NSES e-n l:.C~A
};~~ ~~ Pe1cli~ + s.e..~e.nJz~
d~ .AOT5.2.~ -2';) 14-3 .-f3'55
e,a...o. 61. L .2l.l-.t ,;114
/~d.t~ 60W 4S0 .14-0
~ :2.-4.(,00 1) 0
b~~ lU> 0000 0 0
~ 31.~J. 1.1-4-1- 31.63/'
A~ 0::&~ ,,..,,,.,, 3~.2. 43 0 0
~ dJ. t ....,... cL. .1.'•• .ft /}.2,..t 4-1) 0 0--Ldi:'s souk .42.3000 0 0
f-lJ.Lf-- .2..100 c 0
S~ "'-'.F""" ~SOQo ..-165"00 -1..1000
~~ .-115.l71IO 0 0
ToTA.L 6 B7. s s. e FcFA 53+ 16 Fc~ s g 4"f.:t FCFA.
31G3 F
·..n·
3160'"
.-1.11.} 108.2..
5 (.:p.r F
~~C.,.f)
~'l.FM~
coJLcJ~ 1'+t .e.r..~~~r~ ..&~
".J.'.............. oLo1ft -e-. id»: ~.~ p r CL -r-ef-t.P ""- 561 +, - 1 ( 3 16 0 + 3 -i 6 3) :: 0, ~ 4-/ 567171
p:. 4-ft. %
y..~:~ k e.-Û,el.,....~;/J
~.~~~~:
~ -rrr« --ru- -ft. /p Ab~~)~ (~IJ)Q.
~~_~~:~k~~~.
k /J4M-f-u tet-R.t. et (~ 5 T .e..'t o. •
Sr= SJ+ .2j80lt~~o-+l~>oo+OI80)1..~3;so(.3)so+.l>r04-0 )
'= -111.)-10 8 .2. + 7-)g4- +.-14)1+4- .. -15)05L
----;;. S T = /f 58) 4- '+ r'YI
ceû.±k&~: Cc.
Ce. :: 3 -1. G0 Ir -1 58) 4- q.
= 500670 FI C~A-
'3~ ~~ 2... ~t ek ~ ~~ ~ p-Ut-v...).A1ft/~.du- ~-~. 4 ~~~ ;~'C~.O)
r -"
.s, ~y. -dJ.~ .i:~ )~~) ci.k>~~dJ
.-eo.~~ e-.~~.
i..,./~ .J1..~,-~ Î~ Â- c-a.o.cv ~ d....-~'I..
r<h~ 4d.CI~~~ Ch'-~:
c.en..t ks 8~~ 80 -:1 0 ~ c.FA-
~t r::k .i:~~ 53~15~.cF'A
'.S.-i-/: CH e- ~t .-tM rb is.. ~y~'CM "" 4. 5 3567 P, - 8010 - 53H',f - 6 8:;'S-~'3 - 5311 0 6 -.26Jf':1-.t.
~ ~ -::: r OJ.:J"j."6 . ~
S-:l Cc o "~~ J.M d.....1ai2.........,J~ dt. C81A..~
Cc 0 ::: Cl-\ + Cc.
= 103 '3 i- 6+ $0061'0
:2:.3:E~ k- e.e-ar.k~~A~l~
~t--...e....... ~ ,n-a-.be. - e:..~ A:-~~MN dJ/r.: C8A•
5XL. ~ k~ ~~ AJ~,:1,2.0 ....... A.J-~ ~ ~~
-1J~X -dL .2)8D"'" ds:~~~.
S'~~~~.~~~~~~
"tk AS~ ~~.-0> V= 0 AS"· [..2..!VO J- A~ )-~80] ~ 5.>ro6,.."J~: _A~~~ j&!~~~.RJdJ'
~~~ ~t-ek A ~.d;Al-&. Krte°4<x.
-~~~ /Ch AO% ~ -fi ~t A!Â~
~~À.~~ ~~~...c..Ii\-~
c.ewd ..b.~~~F .J.. aI-~~ ~ ~
~ ~~.e- ~ th- ~~~. [1]
T~~~~~Al;lLt,~~;a.r~
~·liz~~~~rL~·
~~.di~~{~)~)··iip~p =- 5) '7 or:... 8010+ 63'j:tS
d, O/f.2.1f, +IJ)~'U
z: /i-1*.:rJt1- I::qlt
~~lo..~~~: R-,r
fhT = PeP +- AI -10 (Vr - V)". ~VT )
... t+"'1q..'11{'f + "'/10, (q:ry~60,,"-§~O~ le 1039'9-{1{. T-I 16011-
= .-1.:1 S6 605 F CFA
6rQt rh k.~ U\..~~" Cc:
Cc.: :56?-'+ - /fô~) 4-1t :;::. 8' '461+ P C/:A
-- c&A- = PnT + Cc..
~ CaA.:.2. 05'6 06'3 P CFA
A.00
"7.4: Ca1~~~:
~L..~ArN!~~~~~~~-bt.-+-~ ~ ~ML~~ J:&;t-~~A.L~ ~yY"\.l ·J.>..atz~ ~,-cf.,. ,.~ j roL--t~~t~~~/Or~-~+4.i&!~~
~e-u-><J ~~ (OVI-~.
~: t.. ~ H-t~~ k~rt"'-~~.f>~::-Ht~~~~J'
~t~·FU~· .PA;' CeA- - C TB ,...-1 0 0
C&A-s: <':056 .060- -1S3~69-8 .. A 00
.J.Os6.06!3
P,2 =1
J( /(00
PARTIE FConclusions
~~~rvva..~:
4 1\L~ ~rkt~ .e: ~/.-c/.Lrd~ ~~ lt.v1.~- ~~J A.K~-~~
.flJ'U- ree€Qa~ti~~~~~?a&,-rJÂ~r~~~~~~J~~k~.
~~~J s.~ -dl~ A:1u- ~u.:- d.uL~~~hd.e4~d-~~~"k4
~~~~~Â~~io-
~~)k..J2aJ:i4 ~.
1;Jl-~ k~ A ~ .e-.- ~c-U~ c1.DiJ:
~JZ'o-fi~ ~!-unL~~~~~~
~~~~~)(~~~~~~.
ck,~~ ~~~~~1~i"1
Â~~~,& ~).2~~~!tfk.
cli-J:i"k ~ d..eJ.a. .J-~ k ~~~ch~. .
~~~~d~~.A.Hit~.9~ 1.z l'U-~ k ~) J. if~y~,o.jvl.i;-J/~4~~~~~~~
~~~~~At-~.
- ~ ~~~ tust~~ ~~~~.
~~.AiL~ABS.
k~~.i~~ ~4J~~J~..&..~~..Jk~ rN- ~~~di~.
~A/~~4h ~p~+:-,t~~~ ..J> .J/~ eL. 4--1.% .et.c: ~ervt~ s: J/E~
o
/~ d ~ fcl:e..v..~~ f'e- /~~ k~~~~~~ih'~~
/~~~~e.-r~'1-~)~r
~ Re.. ~c...w ",dt.~~ .&~.
c;1;c..~ ~.t- ~t ~~ et-/~~
~~~~~4~.PI' '-',L. / ' ./ ;.JJ•• _ ,r fi
Jd..-....~~/~/J~-(~~ ---.Vw.t:-~rothJ/~_~~.&..~,r~
~~~~~~~.~~).-1'~~ ~k~~ ..e~~Lbd-
~~.J:b.~'p-)~·/~~)rif1Ac1L
~ AJz. ~v-J; ,-0.. ~ 1F~t~..Q)~
~~~~~~~d~4
._~~.-cJ.~~~~~~~N.
~U-4.L~~~,J/~~··
~.d-~~~~.
PARTIE G
Références
A1:~~kk~,
~t"~fA:W
~k~~k~r--~~~u...eo-C.eo..~~oÛ.; ~ L:~ Ak rL:.~ 4)SJlfJ GM
"J t:L-.t Lo ... --!) ..,0 "" •
~ .-f.-..t.. Jr~"'~ J..,. i: ..d..o.lA
5.,=~u-~
a. ~ T- 4 s;~e.cr-··.1a/~L
w",.~~k~ F ~ olo1t.~ &-l:r.h-.
w~,,~~~~~~~A~~
~~~~~~.
J.~ ..~~~~~:: ~~k~ ~~J..w.J.:d,~
~I.r.= ~~ oLu. ~f:o..,...
'd',~ ~ ~~1(AL ~~
5~:I 1. c:a~..t
"=- 1" 4)5 .. 0) -4..2. = 0.z T M-~
WA ': ~be'S~
-:. .l5"O).l.'1 ': 6)'rSiN/m
W,z. ':. ~. 5,t, '" ~. ~ • .fl.
':. -2-.f), -1)1 0) -1u -= -l}'4 Iz N ,..,..-1-
'Il -: -1.) 3,. (W'l ~ 'NoL) + -d.) 5 LL
LL"~~
~-r--~~n-v~ LL.,. 4./..N.m~
-+ W,.. -1., a.s;.( 6,75 + .l} ,~) + ~)5 a( --! Il 4;l0)~ Wc .-16)1j.~ -i N. mot
CÂOe..l k ~dJ.~-'~da.ia.~.H........
:!u'fe~~ ...k~~ ~~~:
M....-.~ wL~ r. YJ1,t ~
... "'~J If 6 ,. ~," 0.A~
@~~Ut-.~:
c9~~\ l'1~:~~~~~kJx.~
(fI.' cKff~"d..c.~
f~" ~k~~e--~~olg~
ci : ~..c.c..t:t. -ck~ ~•.J-....~:~.J,.~~4~~.
A·.~A~
....u..... M....-.Go •.t.... JI.
~-:: -1.)5~..& ~~...p
~.., 0) es f::'lfb
= 0) 85 Il.LO "=' .-1-1.) .3 MF:...A.1 5
Il -1,66. -10 3-. ....,... '" - .r.
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-135
