Embed Size (px)
Citation preview
RepUBLIQUE DU SeNeGAL
l:COLE POLYTECHNIQUE DE THI~S
PROJETDE
FIN D'ETUDES
. ,Titre -E LABOR AT r0N-.CWlLERO -.........-.~~~_ CALCU L
-llil..ÉBAc~ E · j EllE. (DE S )
...DES STRUC~D JClli..S
Auteur Ah.d~ GAC.~O~,______ALiouoe _J<ASSE __
Génie CI \L1",-=-L__
Date ..!~3~
-- --.-" ..":':.." ......-
Rejetde-
+~n d'étuJeJ:> ..
Tktw tlQbota1~oo d1un
p-CQ9Wmm~
Q~ calQul ~nttitact~J d'Çlo(lly~e
mQJtlNl<lll~ d<lj /~tvuctUt~~ ~n
/Wux d~m<?rJ~~QnJ;) (tL' Zb)
Auhwt~: ~ bloulo~e ço0ko'. ~LlQUne Ka~~é
Ih.'Ce~Ut :br Jean Robert MU'tat/~ouml''':l\e ..À6' MC1...· )q!3
lïi
.:
A )mon epout>e
~ mee pO'cen\':>
A me':> ami":>
Rbdoulaye GAÇKQ~~<=-~r:,
j 'ni e s r0 r e 1\ rJ
J .' .. """ Ç> ~
OlIM)
J\;O(}~e: ~~:..--
-s>
1
1 .-
1 ~
1
df~~ J 4~ J~Ds.'L'l.nil ~~J"~",
un ....... '+~..Jb~ ..IJi"ltt>Jt n~,fltlllll, lA ~1l~ , (HllQ! {.nbpnb -i'''Jr''~ ~().~"llJ '1' >!\'Yt)/I"U2t JTI'" IIl')\OV
11' I~")J Ill" 'ntt O'tlJa} ) {~'"~ '1" "TlblAll\\.! ~ro.jJTI IATI'f -fZ' Iml~
, {'"o J11.l1"'l~'1.1 (~J
(~f'/'1O itp ;P"i~h)1
S""'ry' ~:uaJ {li P 11"0l~ .J "l''l'p0l'-J -
~r"H:'11"r ~lIr lm ll::lê) ~ '1 "P()~ -,
(~J'CI~,) ~r 1"H"'+-""-Jl:~-
?~,IP'I~,L.1 'f Çn, I Ji "" 11
{-a"J""or {llP lA o.l«'J~ ....' fT "'''j'l1l1/
nl"'?~ blol.l~ &..j.JG~"'O:l l'ml'tr.> -r( Q ')
(0 a ) ~1I1"t<U .. ,l' ,1J"Xf
(~ ~) ~'.J.j. <-.:Q"~ -, " , J..Il>1i
: l ..l.pmb 'P 'Ji ..... 0101 tn:) ~~ "'rh]"... X' il JT\O~ n~"~J,
1. 'jl'\f°11 -
r 'Inpoll
''''Y04~~(Lo1 al ·
,...lh.l
~ t lI</hl
... t<l~ -
I..i l.q"'..al~ ~~1
.. U)flle11
~~ .nn . S'1A~11'\1'\.I.4."'r xmr
~P,/(~~ çllrn1~"~,mb ~?l.\ns ~1
-'
-r:u5le~ rro9ré~ i..;~on+ n~> du +c:ùf. 9u'':
c.ertclI"r)u heu(,,~ > c.fr~"n~
C".U~"'Er'Hn~ ~Uf
au+rts
f>AYE.T
ii
In~roduet,cn
60 u,1Il\l.. rs el
.lu (.(I",~,-q"",t~s Q-t- Je'for"", ..h'o",. S""dnES ra'" lu ... truch.r.ns
CC .... r'b·e~ SOILS l'"""ho .. Je ~rce~ ';>l-..h·'1 .......~ .r4-/ou J~.,a""'·c:f"u.s,
oi l' ~Wl ~'l1'\' ,ru. r lu \·l'\~''"I·oz.u.('J
Vdlw.r ""'d h"" .. ~l~ .
conli'·....... e ... t ra.rh'cu.f.'Ü.. .... .."r1
r"Jr vd"uJe~ .e.I'e~ ,.er"-Senh~J.-)
dt.s stru ~re.~ J u., Eluh" ci',.oq
COWWll"tt r·utu Je u 9Ul' vr....1- J.'.ihe .Id", il n'.2.~1- p~~ 0
F,ou.vc.r 1", l'\(.œ$.,'!-€' Je ~u.,'·r "~c.ol~ Pol~~c.h"'9U.€ J .. TllIlS
J'u~ t(o~(.. W\ ... e Je CQlcul Ce UrQ s.a".. d .....fi Itn r~3ra'"ltJ~
con",h''''", ...., J~l.ul- d'u., 1o,,'} hQ\lc.-! d" r..c.l,lU"d,Q. \lu s.<l11
Gut-u-I- .,n"~I·"1Ut. .{;;:" *1-) 1.. '''l''Oj· ..t 9\0&1' l'lOU.S 4-'1- sou~,'s
c:.o"'~ h h..U· lU' (
1..01 rn>~rQ Ho1 ...... .le
...truetures oV1 ~duJ' Gl" .. I~~~uh'l ,"sa", t
bO' ....9 U ( Jo.- rro~rU"'-"s ro..... r uh"'\>ah'""
frors J,'W\.... s1'o ... s l ,'nl-t't>c1u c),'OI'l d I~"'"", ..,,,h
L..s ~tf'r.."tu 1\oIA)d.u.!..s
Lu.hAn sJ- ,'", ~(Q.J"''o'' J",s d.c. ....~ cl .... /.. stru.c~u.re
e"lcA,d J4.'c..o1f'u·q.l'lh J~ rl1A~n'US Jt' r'·~'J.ite'
Q",\wl d.. l'ordH .Lu ~~~,,''''t ~ J ..s J''''''"''''OIH J,uA"".f.i... .... (i-I,) ...cur ~
.:
, ,_ A~lQ"",~IQ~ .u- '~~(UnO" J~ \.. "" ... /-r,'<,L- ~nen.l.
Jt \'" ,truàu.re..
c.eu dt< ch(l....~""tnh
Cc:olOlI <tH Je'r' .. CR.... €nts
~ttr"""·"'QhO" dQ.s +,-h d"IH IH WI€ ... Lrur~s.
latr ~I Il. tI •
M h'~t1~ ~t'I c.o",~h qUI r~s d(/~rlHll.lùl'U
1'\1..0 ... 4111 t -p t.:J-"51Q. ...~
~/"r~tClh''1\W J,o.r~ da.lI~
t?ur (M'II~rs , 1J tw~nU'..,... .I'
c;f..lW et l'e.n.,rt ~rMCl.1 .u- cw
C'hClpitre ~ : Le ~roblème
Lt. CoI~ Pol'1~«.h"'·9u« Je Th,'e~, "-0. ~~efotu Ie.) a r'"'' VOUlh'ot'l
do( d"Sr~lH Ilthlü~lIe",H'It ~ dl1 rrot\1ouv~( la re.J,e.rche d~t'lS hw/J.u c!oVlilCÙ"'ts A{i(.,~'"~·9I1u \!lU ~'~e(cr l' Q..J"-IIJ«' Je /' ""'gen'·E.ltr.
Lo re.{,~Hc~e Je. n..ll·k.oJc..l ~rQ.~or;(.1 de c.a./eul dv ÜrucJu.ru
~II'IIStrll JQ.h\ o c.o.Jn 1u.o.nd 1::)1'\ stUt,•• la d~ ... ,· ...Q.t;., cieLS1
Q..Ot\*r~•.in~û -tf J~f·Hl'\Qho.,s (Colllhfw 1 S~II) tUAI' d.ouh, l'e.~~(
ICi ~~ I·"'~ortell'lte. d.a.t'\-S I~ e..t)l\.et~~ J f --U.i'I \llu..\lrQ.~'
() qw' t cidt cUw.l tuJ c.n..lhti'u.. lU1f nu'1-O'I v-o.'Q.LI~ du tn>jJ Je
~\l d'il c.(u .f.ll 9lWh'otl , a- !>Q.II~( l'dla.bbnlh'ol'l du ~ro~n:t"''''' t;L' 'l..,b,
OvJu l.t ~ q.w ~L. 'lb c.olld·,/u( \Ali .UW ~~ltr la re.Ju.rcht
dClk} I~ cl.olMclù" J(.) strv..lhArf~, r~ ~rv'ara "" ~t +9Itrr... ~re. d'u YI
Cl.~~()rt l'IlImt'dla~ CUl>C ~dral1~s, E:\1 -ef.{t.r, U' ~b s'qJrm-e Q~ dLS
.duJÙ.lkl> J...our ~1Ja.111-u~"~ J.t~ d:d(l(~ d~ uJcu1~ ~h'~'gul("-r ~'
a.u'<"91.lId\ Jls ont h~'ou.o ûm+ron~~ au cours da.} kocu.l\~ ~~h'~"e.,
dt Sf1ll.J'ucu) ~h, .. Arvl\e' ~1- ~,>S ~tuJ:;h. M~h,",·CfU.f
NO~I\) 9\11, I.>-U ra 110(0.'/-.01'1\ lt froC(jnl""''''1 he ....;uu,Jt t eu 1/:'QtQ~~,
JQ Ht'orl't\ h-o~ ~ou.u(O QAr J SQ I>oU4J sl'",,~I~ d' uhlr's;"h'ol"l ..
~u 10 tl(ltuff d.tr troJ~~ 1 a' Sia.VOI( a..~,.'I·ULt~ çf"'l~Ie du ca./eu.I t>\llnft,ftl
l , \
(Mtf-kodl lU} cAt~lo.\J"'«"~\ J ) W CUlS ...· 10 Ca~a..uh· +ri.! 1'·t\Ild·~~ cL.
~.ÔJ taltul dl l' r:: c..ol,) 1'~IJ'l\ot""~ cL..'~i ..tUt /a t"uhe.. !douro cu,t\I'i ... u rni~s) MAlU-1 .vuclr·e.ron> tulle..t\Ill ...t I~ S+tvcluns r'atlu
.3
•G ' , \ 'Ji _ ene~ i~e~
L~~ rfl'l'1('\'P"'> d~ 6c:U~ Je \0 WI€tk.od" ~<\tr,'u'tll~ S~,,+
.fol'\J~.. .......r- 1" CJ<> .... "'''rt- J'l.:lat.......""t (chsc~h~Clho.,) dG.l ..+nlLhru
c.o",,\>I.Q)l't') .e..~ l.l" ur\u.·" "'0"" Ln JIl U:>m~OSQl'\h. ~o..,t chCltu ro
des LAro.J"e'... fsh'9U€S s~h4U.e.s .cl- ~V\ll~""U.U Rxrrt'm:e.s 1-ev,)ry mc VI1Atn'o'e"e - Ll1.s VI1Atr(e.ts c.o""tCl.3...,t€-5 c...orrQs~o"Jo."t
CWlt d.i~e"ho il:\')\ 4>1t! J" 1Col ":>tn.o.J ••n -rw~ t ct....oI', ..~.h-e
~ If.i"~I"~'"
a.t~."d. a r
cl Il> blocs
bLI"Qj)scJOtl JfZ.S ria1u
,>hlll.h.ln.tiu clv, ,
~sht"'R rul.. 0" nJu..} cl..n..," u., f'n:>L/..tw.t,
e.oV'\~lt)(fZ,,, -t-l'1 UM Sllfl'€ dll t...-ol/ll~"';II} ~CUL...,"t tlJ.s ~' ..+'oLe::;: cV\cr:h'>Clho.., .,1" 1.. Sh'tA,Ltu'f'1I rr"'fl-h'Q UJ1 .. a"QI~~
rr PI/.Mtl.n' cl':~\tQ.h'ol1.s c;l1?'~n'9\(V h",\.\IJ.r,.,,~s
Il "st ~lA.t~~ a k.<1-kr ek'fer.....llho., dl/.lc;,
,>~J-ur' cV~crf'kH~ dLuna. >'\Me..<", cerl",.,k. 10.
.:
1.. _ .I;,\-... ~"~ ~ ~\In_,Nou.~ d".ASh'l'\~lM'I\~ W U) .d..~.s c;\ s.w\'ft t",ur +ruJ:i(
U.tH ~tn.lLhHt cl' l'a....d. da.. le> \o\.lIl'{..k"dC!..
GI_ D,';;ç,ri-!'"I'Saho" Ji ~stru.t.h... r!.
1\ ~'a~,l .I.e ')u,b d-ù)\''>.er 1Gl OS tl1.A.t.h.tf".l1. .l2.n ...", urhu'", ""nitr(
,e.a.ra.J'~If'l'sh''111l5 ~lU""'9lA((; .Lu t\oIo'/,e.- t'd'/...lli/.
r:')(e",~I{: Pour IQ s+ruc!'Ur() .12.1'\ .fert\olo cl" CAJns ~"'l ~'"
clI'mt"s,'ol'l) ) 01"1 u hl.'~€ des ~Ie'rne...h 1..ll'\,:d"Wltl'1!"O" ""h .
b. c..~ 01)..
1?ouf cha9u~ ~Jt/r'\'lQl'\t, ot'\ Ch.""SI'~ I~
c - Calcul de..s J';~"'ll\qho,,}_d" qmtrw'..hs
II ~ ~J rctr dAftt'r.t... uaho"l G\ Fr h'r J.f.S Jll'~I,ue...,.t."ts
cl _ Matrl'CR. cl" na,dll"/ .Ill lJ~le'Il\Il"~
e'~t 11~1u~€. I~ r11.U IM~o,.-h;(I\~{ .et \'" ~lt.u J..'ft,u'l~ ~.R"l..C1"-~
la ~IIL~ C.fI'~'·9U.ll.. I?ov.y ,>" (..o ... ~tn.o<,ho,,) IlYl lIh-ll~ ~lu.h'w.1'"J
~~'~k.oJu ,k,t ull~ dll C:euh~I''al1o
Il - A-S,HM~IQ.f. d.r<... ~~~~ ...b
L~') 11AQ.~n'u.s Jll..~ chWC!l'Ih ~e'~Il"~J dQ la shuch.,.-, s,-f"\t, ,e:uJ{i'Vlbl~ ru.r U'U-( lUI" l'"I'I.a.frl'CI ~";"-al.e .. L' e:t.S.JR~tlaf
.es~ ~' J>,uf l.t.p 'f-A'; ch aCfW noeud~ Qiï JIlS ~"'Q",b
C)~~ Jtt11'~, \0 \ro./w.r J.t., J~'rIClU'I1.4~"'~ ~t- 1.........;IM' t 9u.r hn.J /11,,1
:J~/~~\A.~5 cl Cl ~lI.UJ ..
f - SO\lIh'o ... dll} :9lLo..h·ol1.) ~'I\M.IIh:.Y111~,
811,1 ~ ce fù('o rr tkhw.o .....Jl..i,..odQ.S ~t- QI/~
dt ckol~s~.. Il ~ M-01if 'toUR la. "'.aJ...o ~ n'r<ll'~/\ ' , 1 1 1
~r ~Q.nQ.fGl ~~IH\~ ~"" .. tn·1\u ~ t>-c:l .... d.«I.
~ -, c.a.! e.u.J.1 XI ~~/.c/I\4( K.ku're.~
la ~luh-C)h JIl~ SI.'rlLa.h-ol1~ l-I-QUJ J..n.,lt4' I~~ d(I'~laul\4(a\.h q~'
Servi('l)kt cr ~ IlI.if I~~ J;~(I""'Qh'o"s ~ co.......nv·..hs, /
h _ Int~rr"-eJ~h'o'" J~ r"UtllhJ.- ,(i'\ l' 1 J - ' JI . - LI -/I.!l::'QUr" "~~t1I·.wr/ .\'a~~ J'e.voll.lt-r UII' ""'IHu,U~ ~ -
lu r~ulh.b d' OrclÙ\ll~ULr.> a..~ .. JJ1 ju.fr t:Lt. Je.~n/ Jo ~"-~U-'SI"'''
Il-~ ~r c.oh~~UQ.,t Ù la f-G\L"I,~~' dl) :>0.... ""'--oJilc ..
?- Car-O-t,h.'n'sh"p&u JC/. \'~r~w~ l:QuJn, ,
Un I2.re~.(I.\~ t0u..tn d'ul'l~ shU,th.t.f€ t /a l1 .f ~~r}/-..t~ll~
(Jt WIll lam drc,'h d C1 IOl'\~t.\.(r L, J€ HM>d.u1A1 d.'e.1aJht.lh'~)
JCI S~t.ho'" b"1>va,..sal~ A) JQ lo\M>lM4l.f. d'I'ou,rh·, 1...
u.~ I\IIQ'Io.1 tla.,UM orl'~'ùH
Ja~) I-'! S~I'1~
J~ la shu..t.hMt so ... ~ lr\·h..t~ cku.u
Ch(;o.9u~ b<urt .es]- CDJcu.h'n·s~ fc"«f-n'"",,·f-q' j (h "J') ..eJ 01- ort"Q.,fà
~u, ch 0. 9\.H> b.a.rTL d" stru.ctu", co... Jc/f·","1- u",1
~!>~iMJl d'c:uo> ioe..a..u ... CL) ln' ",- uJ ~'..e/J.\o\Jll1t .IlJ Vl'\ tl-I...LI,l
5a rM.ltr"o d" rftt'J,t/ \<:l c..a 1.1 [Ic.'J.. <91'\ +rnh.lofvrl\o.l
.e.:,,~w'h aH.I_ u· ta' UhJl ""otn'(.t d" roh..h'o... L~J J.~ ....Cl.. 'Ù'
~ 1'Q)(~n'""H tar mrrrt 0- u... ~sl-il'\v ~I-ob2 CG) lit' "",
la sh.uJu..rt; ()\', obhe"'~ (;\Ior} la ~Clt'l'U ~lQbQ'Jl [k] Jo(
l' hli~H\~'
C9h r~ J~ /"0 c..ol1.5+rUÙt I~ l-\A.Gt~r"Cl' d~ ro~'d...t+/
~~(oIJl [G1 d(> \.. ~trt.ll~Uff 1:x;tt'" ~H.. "'" bl"'~J .Lllb J."{f~
twGl\~'~ lk) l 'CQ.lt.u..I.H I~ 1'1\l.Ql<l\l.l.L\ C)'I'IJl~«tll:fU.c,> (4Ialtll.At....~)
.cl- I~ 4rr~.-. J..a.u, 1"1 1"'~1\II€ cl '(;\>('<> 'J-tobcu..>e.. PC>l.t.(' .ç.,..c.·h'tp,..l' "l\h(~,~kI~ vtu n~IhJ:;,( 'Ç-h.bl.J~lHIAJ J..~ dAa.J~I4o""" J..~
0tt(\t, J1M\.~tw ... ) b ~v~o.",b .Q} (\iI.Nv~ ..p':t.~I'~)'H'\b )
CWJC -u' !)-pl t ~ \.1. r 1'\ ') t \'l Co< )('/l...) 1., uu.t.oc •
~ ck<l'l'h~ U~II t.ol\v~..,ho~ U.hl'C;l.I~ dl;> 'in~ ... r.rh-u..tl!.4 1.tS ~(Cllod.u..u.} du ~~ ~ru JJ- d""r/.. CJ.lI.AR ....~.
4 - A~Wv}.hoh li UM strucfu(, r~~b&'1\1J cJ,a.r~'~
Jam tlh t'ail
l.t.l Jd~'Q.u w€ .. h Ho dClAM ~t- A..,.. ~ 1 e tif lü ~ r<J)· fwc:la.l~s ~oub.,
F" F'1'~~ .
lv JCûS'S (.I.8,sso"t- -R." +l""lLl!e~ ~o,,+ n.,.,~Ia.~ ra.r Jo ~r~ hodQ.(.t..5
r
stAh"9U'l'IItn t- ~u"vClI GMI~t.),
sol"'(.\·hc 91.l ' li Sil>
[l( u",,~lt: Ba", ~~I'>0rl".,,~ u." ~~ .....~ U.""~,,,,".i ... ,., l-r
rt ~Ilrh't
,,~--,-,--=~,,-Iw..;.;..he, u ~ lit eft ~ "Cf lU Va, tn~
jununnnnsu 'II
~ L J
r)'\oJQ.IA>( ,'nhr(cz.u.r~
~ .. :
,~ "~"'UU1l-."~
./1.1- Jas J;~''''t&'''.,,~
,cl, n't"dd.' ca.rR.J(r"~Q"~
"Q.~ ~":k",,,,&,,t lu VlLJ.u.r.rs
.J- d' un, ~'llù.(rf «II ClIo.)" , .ùI J) 01'1 F~ .Lttl'r, r' C~IIC:f'U
~rrr).LW! IIHhi dl ICI tflQt~ rrtt- c1;~IA<I"""'" ~&J= [kH~j
l. \lm" troLl!"", ch",
J, ç,l (;1 ~1tI bclt",
tCh~~,"tce.- a: f.1~l'l'len~s cI,QISI'S tA- ChC:H"je ... e.nts
..f - ksCfl}bR.tI
Il Q ~h' rfUIIHs 4 ~~u ~Ie''''en~.s 01 5<:l""';r
•
j
,Bc;tff, b,·o rohclc.G
J
0 0
h J
Px.rff e:t.r h'U1' ~~ Q.I, h .. ~ .ell(.u~rt'f ... J0 ~h J
';a rrt .Ill'\C c:uh'Gt .,,,, 1.., (If e:t.rh·w'~ hJ'
~I----Q
h
IOs.sQ~rrs, ht,-l"s
Sm.L~Ufl' t la •u ,
a r'k(.•,tI.~ 1 ~ - ••
~ 1-'- r s nrt "'1"1.>
'1 W ' t.O"shhu,,+'
c~<U'~:.. da'U
..t h ~ ",:..., I.e,
1....,· f' ........
J I '
1- M~~f1'c' .If rit''',H lU" .JII~."~ Il'' c:ue-.} 10C4A.ts
2..-"" GS:,,'....HU1
A~rl,) • ICl r~(/."4 fi d..o..vc\( Gl.t's(.Hh)a' s hvcJu.r, ~'Ct~t ~Cl,·"tr~ ....f-)
J~b rl\<,'lur 1.0 MAllf ..·u ) df r"'â"d"~"~ J" '1'scu ~Jl"", .. 1-s-LQ J~r"""· ..,,h·o .. d f olle ke .. h ..u t- f s.. f...;r, èt l'r;o.,'c1.. J~ FI.v~........
tQr... ,' 1.t}cf'lllllu Oh twl-- ob,.:
M~H...Jf J f Co.sh5/·"~o
Solu.h·o ... d'J''1''Qh(l~s c/"tr~hFO"tJ
111
1
ij1i
1
\
1
1
1
E, L, A, 1.
tA.t,
Me~ücu [k'] du c1.4~('&I\h btf't, d'''/Ql'llc..b
&- Q}( ~o~r lb C41cu1 s r\lf 1Cl! ~r"'''_
.L. htl"" ~ , Q.a.r crut- 141' 1", bOrT,
Aa, ~91
rA~,
f.F~
.)1Ft
Mot.: Now 11.0\1.) ~o(,t\aro~s
1\",,"0\'1 dll 1.. "-cok\.lU [k']
o,»",t.. rt la ~) ~'n:r.J ...
.~~
.l)l\l~rs"on dt la t"tIClh'ol'\ tom. JCl'~'eu.tM'''~.
~Cll\S 1« <:rIA... Je (Il ~roje.t-) I~ ecJtu1.s su·~"t ~s Cf 1'~'J.
1c:l41Q ~d-l..od.Q ~tQ.~~"CjIol~ dll CcU't.'8t,Q.t\o) t«....v9,d.iwant
la ~IIU -f- ...... I..a, i0\t(' "CU"YÏt ..k.e.ou.cou ,. \..lt-~x..'t d.CllU f..
Q..rlc:lu dJs CAeH> J, ShuchuQ.) .
~s ~ la ..,Q.h,'u dl l"\·~d..·tall -'!." \lulv d.u -f.k..r;M~ d~
~~) ~t ~M;~t"'i""
2-b
1
- ~~Ie:u.t1AA.&Uk lu,,'l.ùr, J. 41..=' , lu a.uJrb .d.a..f-Jua1.
~~IdnJw _ dw ::. 0
~ - d.f:A
I~---------
'3 GAo,''(c
~( Ç,,) t( FI)
f l Ll !.L 4~ ?
F,L i.L Ae.l a..
JI.O : ~d =C> FI :: kil: 9-~Hï e.4 l-
c:I\JJ Fa. L~ +faL\.
=0 .:::t> l=~L l=s- ::: - - - ~ ::0d{:t. ~ 2.~ 3 t..
Ju) I=z, L" F, L=b
F.. L~i-':::1 - -+ :Q ~ '::Q
d~!> ~ 61 l-
( .i )
(Z. .\ )
Fs tl1-t' s.. 1HIl1 ..... ,. d.<:il. ..., (.0 .Lt 0., CIl :
F"L 1=1. L:= Q Ct "rw
.3 4 )9~R l.t ~~ Oll 1=1.::' '" 1>0'" ~~.: C>
G}rl>~~UU Q~" ~or~') no~I.t.è:tu".cJ- 01'\
'1rr:w Q.C.l'l( ..&'''Iu ...h.....} d'A."Iw·\,'bl'••
"5~J·~: 0 ~ F, .. J=4 :'0 "=t> 1;. .. - g.,l..
r MC!>:.;o =t> F6 =0
1: t1t :0 ~ Fs = 0
t=; w: "-II = ~'-F2. :: k - ..
loI -
F!, :; k\\ :;,
~= "-41a
~ - -l.I=s= k.SI ::. ...
F& ::. IL"l ':. ...
JIU _--dF,
--- -11 ~
4""'f~I'r ~G-
f<.~ ..) f(F~)
Ft.L1.-~L ~-2.G! !o
f~L ::iL -1- l-ei
dW FIL-t> Ft :0- ':: ----.; = 0
eif, ea
d\.IJ f:~L~ Ft. L1. ':. 1 ( .i ):: - ...dF" ~e:1 2..&1
JUI F1. L" Ft. L (U)- = - ... - ::. 0cH:3 '2..~ El
~ ( li ) F~ .:- F1- L- z,
(..\) ~'\.Ll ~1. LS F (i_i.): El-i' - - :tl --...~ 4~
'2. ~ AI, L3
r- Il..él )( L ~EIr~ : _ __
2.~' L"1.
Le: c;U.&..SoJooo' 1~ r I.I;-w.~ ~'I~ ..I~c>"'I'loI.CU~ r~os. ...t.è:tu.,.Jo l-C.J
~UQ.~"K) (J',''1w '''' Lr, S'''H~1'",r t-ov.r r~G"IIcI"Q ~, rr. F6
'l..F... :: ~ ::z$> ~4 -::. 0
~':.-Q -=) ti-= 1t.e:1--L.~"ffi1~ ::.- 0 ="'1 ~= -~
L'L-
\
JU!.-d~
Jw fi = 0- =-0 ~JF;
dU) ~ L~ F L"L...1:.- -+ .-!.- -::"0
dF", ~El 2..E1
c!W oF1-L1. F\L =-,-- --+dt:~ 2.E:I E::\
l "2.1)
hi. l.i) i'\.o vs c:Ll·d.u....so"'s ~v.J' ~~ = ~~
oz.Ft. L 1-('2.,' ) =t> F1. L 2. -
2.€:1 3 El
J=l.. l ~)o= ElF1.':: - 6e:1
~ -6 L"L L"L
~ ~(O Lli \AH'
d.r.. ~u..-lt"Ln .> '0'"
I:F-..:;.o -='1)
".
"s"~'""""''''lv.r Jl-t- V.h"I'"SOl"lt I~) e"'(uAh"ol\'>
N'1!l: 0 \"1 .t.-o CJI·JQrr>I.\°t- d., 1..1
proJ\A..I'h ,;; Il C1\.\.h. lUC:hQ ~,·tQ'
""'o.tn°cùtl1e :
1
~.u.r IC$ JQ plc:u..r;"M\!s
Clt 10 r'} , SClU..) f.. ,.~ ~
K' -1"
EAT
o
o
o
o
o
_ GE.l
Li"
o
_ 6EIL2.
o
o
Gel-Llo
le.aL
o
o
E4-L
o
o
o
_ILEIL\
ElEf-L'L.
o
11. el
--cr-
o
l.EI-J..
o
GEl
L'Z.
4EIL
•~p.e 1.
suIVQ.I'I t- lo
tAL
o
o
o
o
o
o
o
o
_E.A-L..
o
o
o
o
o
o
o
o
• r"lP'! 15"EA
0 Cl_EA 0 0T l-
3EI _~EI -~0 ïJ" 0 0 Li \...1.
0 0 0 0 0
K~:_liA
0 0EA- 0L. L
0 -~ 0 0~EI 3EI- L2.L\ L..'
0_ ~E.'
0~EI ;~J- 0 - -U· l-1. L
•T~"e 4
EÂ _U- 0 0 0L. l-
3E\ _36\0 -~ 00 - -~ Lt. LJ
0 _3EI ~E\0
~E10- -Llo t, L.1.
k'4 ::
_e:A0 0
lla 0-L l-
_3E\ ?lei 3e:10 - Ll- O ~ 0
L.~ L~
o o o o o
s, J)~terminQh'on de. ICI MettrIe, d" rolzlhon [À]2ol.U"" IQ Ja-.., Yl\I'''llh'on d li lÀ] On raA d'un ~)('C2.ft'I 1>10(
sl'WI~I~ d1unf ~rt.el. F
y
XF.,
SOl'\t le.>,
cr~Q,UJf ( G)X,V c.oordo nnus ~ QXa.s
tu rloceu.uc ( L)1.1~ sent Coo rJo \'\l'1Ii.U 41\ QlCt.~
b(.: a,,~lf VItre Gtl(e,s 10 c.cw..c .u- <:\Xe..s ~Io I.cw.x
Lu <;.oSII\\lS .l.'rww.n de. 'L oUI n.1Q.h'of\ ~ X Col- '1 sont Coso(
2<V"" trQ.r\1~rl'l'\"hol'l tl"\'~l\o,"ik'\''t"t) On \1nt~I(~·.
1=.... ::. J=)( CoS 0( ... I=y ~'" el
F~ :: _Fx S1'" li( 1- J=y cosIII
~t ~\l} ~rmo M"t""Cl'e.II€:
Fl.
Id'
Fy
-~'"o( lcosl( )
1oc",rec.
A;:. Cos 'lg( + s .." 'l g( =,, l
(-1) CoslC (-4)1 Sin III
0" toh~t"~t 'lUt
et1r+!. \)~ r1Cllt,
• bdiarJWIino,,~ n\Q.I·l\t<L"~"t L~J ~oltr \,.ln ~{rl1Qn+- J( 6' cl<L8~ clQ.ll·b~r~/
L....-----__-+x1:." S.tl b...hU.t ~,.. 1'~_~lt / '.1
~ncG. en" "" Q :, ,; 6.,1[~,.At., :: At, CoS li( .... A!i
lSol'" Il( ~'nl( 0j '4\,
:. - /),'1., SoI'n cl 4- A'~l Coso( ::;. A~I :: - ~fnll(~ ,
~, cos 0( 1:1 X 4~1
9, : e' G, 0 0 1 9',,
On Q 1A,L.\ = t).,))(' Â1(;}
~ ~lJ= lÀ t1X' At G3
..,f:" ~rQ~~OS<l"t 01'1 obh'~l'\t :
/ •6-'1 C.o~a( 'f1'lQ( 0 0 0 0 61,
A~I _51'rllI/ c.o~ 0(. 0 0 0 0 6'!II
9. 0 0 ~ 0 0 0 &'': X 1
Att. 0 0 0 CQS~ l'\'nt( 0 A'"l.
6.;" 0 0 0 _~1'no( c.œl( 0 A'~1o
&l. 0 0 0 0 0 -4 e~
, .-iùr JCl~r~ cl ~ '.'LlIr!-e'0" a dol'lt. ) ~O\tr un ClQMlIl'lf- Q
eoS'~ 11'1\0( 0 0 0 0
_.&1 ho( CbJ0( 0 0 0 0
~]0 0 A () 0 0--
Co.i1< S1',u(0 0 0 0
0 0 0 _J.1'Ila( ~ 0
0 0 0 0 0 -4
G-I{lll\d Oh n~Q.rt df la n.lah·ol'l ~= 1<6 01\ q
~ ~L.):: l KL]x{ Â L}
~ FI>-~:: l\<ç] li , A(;.} = LÀ] \ ~ I=L!~a.r O\dlw.rs oPl'\ ~ ~AL1: L)..])(i t1 crJbr o~ ~ r:(T1:: L).)\ l Kl.1)( ~ 6 J = L~)t')( [Kd le [À1)( [6ç]
KG-: K . K - k 1) '--
(?.CA ~...c..ih' (4r K) ) I\..OIL~
[K} = l>.j \ U~/Jl( [).J ) ex 9...·,
Cbd:i..t ~1'I\C\iiol'\ ""lU "ut~n"u., [K) J ..s
Jlun IPrd-lnCl~eu.t Je ~Il.h"h"
a- IQ ""''Y'I' It ~rl)JWr,~nJI.\À~ dOlic.
~ l'tl ......~e A'"chfla.~ ll.I\ts kt I>&~ dr~:rlI(l."'ts .)
dl! r-ï~" .1.'''''' 't'obCllI ef,
clotu""l'llt,'ott ""li CM
4-' Mat-r,·cll.s
~l"I_ç cru lOI
1Cl. ~rrrlltit [k]:: LÀ)t)( L\(')x LÀ).
EAL.. )
e _s 0 0 0 0 .. Q 0 _t 0 0
S e 0 0 Il 0 0 0 0 0 0 0
0 0 ~ 0 0 0 0 0 0 0 0 0
1.. 1<',:: x0 0 0 C -} 0 _t. 0 0 1. 0 0
0 1:) 0 s e 0 0 0 0 0 0 0,
0 0 Cl 0 0 ~ 0 0 0 0 0 0
e1l 0 0 _ et. 0 0
St. 0 0 _ 'it. 0 0
0 0 0 0 0 0
_et. 0 0 e.t 0 0
_St. 0 0 Al. 0 0
0 0 0 0 0 C>
e.:t. 0 0 _Ct. 0 0 <!. ..& 0 0 0 0
At. 0 0 -~.. e 0 _A e 0 0 0 0
t ') 0 0 0 0 tl 0 0 0 ~ 0 0 0[\(,,11:~ J( ~I x). = )(
_e.t 0 0 e.t. 0 0 0 0 0 e, ~ 0
_ Al. 0 0 Al. a 0 0 0 0 -~ e 0
0 0 1) 0 0 1) 0 e 0 0 0 ~
e,'L ... eSt. a _ c1. t _ est. 0
es t. \ '\.t. 0 _CSt _ Sl .. 0
[K t) =0 0 a 0 0 0
_ et... _Ut. 0 e.'\.t,. e.s l- a
_eH _':."'.... 0 C-s... ~'Io l- a
0 0 0 o o 0
• T'3~t.-4
tY\ troœ.bl" d(l 1CIA -
~.. u.t If ~,.. 2. ) 01\ oLh'lI"~en"'... "'c "" Q.n ,"c t't 9u.c~O\""+ ~ 12.61 6E1 2.~-- .... L.' :'t L.'Z. ... '}L - ) -- Il) l--
c2.J. + 5t.~1
,_ tt.1.'Il"'s\~): _ e.J tl-ft) : S}1 es (l-!I) $)-1
S'"...... t.\ 1 \. '" lies ('l-'3) 1 -~ _ es tt-'6) 1 _ (s ~ oH ~ , _t.)1, ,
[KI) =S'r , - tff 11l _ s~
1 eâ- , \t1 1
_ (t'"1.+ S"!I) , es ("'-'1-) _S} e1.~'t' s'L~,
es ('A.-~ ),
1 1 _S}1 ,
1_ c.s (l.-~) 1 _ (s\.... c..\})'
~ es (1.-'4') 1 st'l + c'"~,
C}1 . 1 1 11 1 ,
1s~ _ e} 1 \1. _ S} , C} 1.4. 1 ,.
•'!'tt-Q ! : posons ~= .... ~El _ ~ . 3~::1} • 3El ::uL. > L:"- ) U- J ~
C\+S\.11 es(t-II) 0 ' - (c.\.H"U) : es (u-r) S}
C.S(l-U) st).+ c1.u 0 es (U-1) , _ (c;. ... 51.1.) _C}1 1
0 e 0 0 1 0 1 0K~] " _ (ct..+<0'1.1/ ) 1
1c.1.'(. + s'"u 1 ,
es (Il-"l) , 0 C.S(l-U)1 - S!'1 1
c.s(u-l.) _ (sl.... c\.u): ~s (x-u),
st-«. ... C1.q 10 , e..~
1,
S} _ C} 1 0 _ s} , e}~1 1
• 1t
---+---..X'Ill
•l1tt~ 4 : POlO" S El:: 11.1 3~I ='1 ~EI '= } , ~EI - u- -- L L2. > L-'-
1 1 , ,c.\. S'"Il 1 C.S('l.-u) s~ 1 _ (e'"Jl+ 51.,,) , _eS(l-q) 1 0
1 1, 1
CS (x.-U) S1.11 + c1.q _C}, _ull.-\.Il , _lS\.+t'-q)I 01
1
[K41=S~ 1 _ e} 't' _Sir c.} , 0
_(t'.... s1.U) ,1
_s~f 1_ CSlI.-l() 1 ~'I.l.+ S~ CoS (l-U) 0,_ ((\.u + ç\... ):
, , r_cs('l-ul 1 e.~1 Cs( "-'1) ~'I.'(.'t e'"u 1 0,
11 ,
0 1 0 1 01 o , 0 ()1 , 1 ,
5. ~)C~,",~Ie. J~ calœll de Mlltrl'U.. 1<
50(~ 1" sh-ttclura SlotlW'Cl"t-e :
'te 10l&N
~
C
E. l , 4 \ L:: 2.00 Gfl", ; \: S'O 0 ,., ; A: ID W\...
'-"CC I;S" ", '1
· b~( NlI'I\Qh'o" ch ll.4B
l(.C4):o. '((,\)::0)
)( (1.) :: 4 i '( (t) :: 3
T~~• .l·~~lWItn~: T~~f"
4-::. 0.11S
': ': O· (;
E"A'l( - - - - _
- l- - ::. 40000
~= ~-=Gx 111" s-Io-"
~ 140L'\.. S'"
~- U:: te:'t::. b 1.lb
t" ~lo-6'
400- ....L ~
A~r~ cèl CALI ~ Cl" obt\~.,t :
2.S'6 ~4' c ,qIB·q 144 _ 2.S"6$4·<; _ IQlsi· q 144
A'tln·q 14461'4 _ICH, _llIln.q -144'" 4 _IClL
lKMl:-'44 _lllt io\) -144 1cU. 4~o
_ ,ql n.q _144 'J..5'~~4· , _'44-1..H.\4., -1't,J"&·q
_Iql n·q _'44(,1·4 Iqr. -IClIl"a.q 144"'4 1Il 2-
144 _Iqt. 4~o _144 IH foo
2.c>ooo 0 0 - Z.OOO 0 0 0
0 2-4 _ 1Zoo 1;) _'2.4 _\1.0
0 _12.0 fOo 0 \ 1.0 400
L~BLl = _ 2.0000 0 0 'ta e e 0 0 0
0 _ '2..4 11.0 0 1.~ 1'2.0
0 _ 12.0 400 0 12.0 fOv
6 - t.x ~w ~I.t dQ c:a.I cul ~ c..e~ ruter\J,r:( ct 1\ IHl( Q B t~\l.r 'Q.~ 1'11 e lVt ~ l'l1t~ ~ ""-rlit
( A-lral\"ll("~ MQl..c.lrLLf' A.~ ~ M~l\.A l, \.lrf J
MtlU.~l"\.l.rt lt. :; Mtw~tt.lrt 2..
1-10~t J,,' 01\ V2.U.J falCp U".f ~C1k"" CO"" ~Qrn,"~"oh (l'th,
(t.\ h-fI1.<H /'" lu(l.~·"'CJ dQ r~(,...(, c"'( CM(/' "t r<;J. r.: O"<l,-~,
"" ().A'" tJ au", cd c.J1~ CU< Col<-~" Dr, :.P ~J~ ....... rt '~t. '.(r
c:..J ~ts - ).. 1.... "10 t"'-r k J"o 0œux '" w.. Cet...r
(0'> .1. uJc...J 1<.<", ... lA~1 o~ "" J1)C' r'T""~' E- ~ .. kP" ,R."t~~ cl cJuJ e:t.<- Col-- ~(,.. t. '" 21q- Pxt'r,·..... ù Q, Pc.,
A~r~ <::UI"1'Ir trc:>u.ut' /.u l'l'Iatnus dQ rl'~dl'I-v', l':krr ~'VClt\t(
Jo.t\S "cU1l111.fH (S~ d. CoII~I'J~rQ.r Iv chargf.S S;.u.r /0 struL!-urCl'
1\ ~t ~!It~ CooMl'l<o.lQ 1"'1I"'l'o l ll ""t 'l t JQ ~Q"'Q( I(!~ c111~} ~
\'tQw.ls .At lu c~o.r~ w-r ICI} M~",LnlfU se'FrèlViCllI1- La ll:V~o'"
~t CJW liL} C~(l(~ CU),>(" ~ds RA- (4.} eka..r~ ku' II/.} ""tM brur~l ,
"",t trw'hll~ da c.L'He(Qrt~~ l'l'Ill''''UIl.l:
L~} dQ.r~ GU.\.>< IUlWcls s",t rrihu tG'.Lr ~'a.\RI0111.,l-
l'rn~icAl'at ota "-51 U~ ~( dq clC1-f'f ") h\Q.A'S l,> c~CLr~ ~r
I-Cb "".eMb'1A.rQ~ ~t- ~H~~ .2t1 c.oMrl-e .e.., calULICl.Ut- 1(/) r~h'olU
9\A1.i1\.Q} t..-oJ.w:it",r c;\..U,J( l'\..&Wds. eu r~o",s I:..tu.VQ"~ .e~~-n
l'hQ trn",s~r~ll.>.R.W\ ck(L(~ ~'9\4.\·"",I~""~Q..s II..odGlICl..S.Q}
, 1 /Coh4I,.,·"QU cu,.el- le s c-f\.Cl.r~ d,'ruh"'CltIt ""rrl,~\..t(4.,) ~
~~.
1 '
~} t'Ca. c1\o"" ~ cJ...a.? J .Q..I'\ +ra..v~ Un>\1- J.ili r ...... '"cl s,rar IR.~ lu": H..odll\ h-r.d..'·""014 kAU.J d.e c.Je.u..1 C.·u.:H...,dA d CI 0uh~lltI-
Lw t"''' «'Qw~I.) 4 ~t , dlMo!ol u.~ r-1HA.U:t.( mw.r} ~~l')l.wu
d~ ~ ~~tiLW k.cJ (L). kiGW ~k> ~ Ill.,} ~~""lM.Lr
Jow I~ ~~~i .......... ~I.okl CG-) .. .Q- " II.
&- ChQr3(l.n"len~st-J ..~ odl~ ~'IV I.c.'\o ecu d~ cla..rc~,u••~t'\t.J' le:. ~un c..eu.ra..,h
• Casl
, Llti ll!! Il! "L
ltr~ t Fe;Ft ' Fr
L L J
)
dv ~h"~I'Qk.o Q.,M(;
- ,1.. JIl~'" u""c..~s bI l =0
Fr Jo' ~c; rr 1........f-koJ(/ ,"",~L.·.,It.
la CO'\< J...tw,;, .1" ~It«-Ij ~'~M'" :Jr~ Jw;:: dw,::.-o
dJ=s- d.fr.'
..eT to~ ~1oW'f;,
k.ll)\I.~ e:tlClIltÙJ "">
'['4~o >
c:w..e r~ 1f.cJ.
Ft.::: wlz,
I='!l =wll.--It
Fs ': wL-z
~wl"- -'1
L ~= .. ru.r ~u.var Ji Jo çJ
t4....ill'l:ll\.n :
Ft. =
• Q.o.s z.
F, = ,:~t [It Ol\.L ~ Co\' ( J- ~Q)J
f~- F,4-
L
Fs - tuCQ I:i; - J:J- - ~
L LFI ~p () r:,• Q~s 3 t}
cH' L=L&LCI ..L. ~ JtF~ , 1=".(
MêlM' tri> uJG' 4U.~ j;-O\A.t 1" Ccl~ ...
F(; : .p",'1.bF :- P«L 1.
1-1. ) ~ L1.
ft z: f> b'ÜQ+L) . ~ _P c:.'1. (iL+a )
L\ > S - L~
Ch.. ~ae~ 4: M~h,ce Gén~r",le
.Ac. Trn~ortlln(Q de la "",,rM~rolu.h"ol'l dD~ IUWd.J clans le;
C()n~th"o"" dll la h1Atrl"tt inCl'ml,
•
10 rro 'Zita ""... <-t...,'
cl rl.ll'l k..eutl : d.o ...{.;- ~CU< kl'~
~~al. Cr r~~J.' S'atlc:r"hr
1: lùlW1e'r~ 1Ilta 1 ~ JJI
La IYlAtrltf dQ. n'~"d'U de la
de ~w ft} é.le~enb tar n:t~rort,
11 lfa dwX' ~ /'L> dll 4IlMuo-h-hol1:
- Ullf k.lll"l:ro\"'~ local, COtT/lS ~",J~Ht if "~III:"'I1"+ (cie A'" \ ~,. 011
(li ~ c(,'â'~ GU L'l..rh' (dell) I--r k1lWc/)
- Uh' k.uM:n:>~ ~~QI.t CorT~.1po.,..I.-.t Gt 1.. shuc..n..r•. 0",
a..fftl, d' do~UJP JolI dll "~I; ...... ~ u., vet-l:ntr d'",Jr..w qw'ut .s-C'-l,lùlh"eh
,V(1) : \Je..lk..U( c:l'Cldr~J,t d..u cM 1 l . 1W~C.n>~!.a , du UI
\JO.) '= ~(H--..l) + 1
V(l+b)=- ô(J-')+l
, ,a.u lu.eutl -« cl" l' ~fQ.~.Q.,.f-
r
CUI '"wel:r d" l'cle''''lIk 1
, Il
~l------~--"to1,r 111
. Nu.~~roho.hon ~~b.J~
\lU):. ~ Cl-' h\ :. 4
Vb.):: S
V(!l) ~ (,
V tHI):: 10
VU+1.h Il
'J Uu) ",-12
cl.. 1.. lloIa.h-ù:.. ..1.. r't,'Jd/
ScI.... ~'\I:" ce .... ~h
Au 1'\,'" ll.CW d '\.Ln 1\0 eu ~
c.o",~,.,·W,"o,u cl", t,~(lt.U"
Itlle,.. ~Q.CfIl' '''~PlI
~"'~ la ~a.tr"v G
ca.\ CLl.l 1 1:> l'\
l' 1
k J, 1Qle~I"~
9U l LL I'l JJI 4!~~ l:.lo tt lA", ' .'" tI..ot'l,
0\1 ~ rU1to"trel'lt flLu,'wr> ~/''''ft\h 1 It.~,
JI.Q.UJC 11'lI~ tu",ul~u
A~r~ u
ca10 b<4l~
'.lA. few-
t\.ttl Utl.. I\IH\(~ro""'h'o... "l'It«lh%,,,~,) f.e~ i(rIMU de! f.. "' ... ~nu G
~t f?I; ~~roJ,~ d.. 1.. ol"c\~.,Q,'e tr""l.oI·~",I~ u 01'\ o~k('"~
CU'lUi 1.&1'111 mCol trl'CI bo"Je~
~Clntr I\fu'",'II"l,'l,u 1" lev~( ..Ill (,.q",de, (\ {a«.t ~"':n>'të.r de
~~"t ~crtR e:p.v la clJt~(e"CI "'(lJ('I''''/tI, 1u-- J 1 s~' ... ''''''l'I''f'I1l'S(l~
CO'l'\ Cl la. r 7'U-( cl, ~C"IJ,: N,:: (1 loi-JI +.4)-'C' ijbL......GUI« !-JbL: l\o~Lr, J, clt'lr~ Jp ~'I.tr~" r""r kMuJ: 3 ..l~f\J
NI ': ~ ( H+-:I\ + 1)-t=-)( 012 WI el~:s
r r------, .G
x
1.. ; 4 ~ 6' lO1of cr,ÙI' (x),
)( X "~~(n;e!,,1i S!l .1.11
'IC 'IC X,'~~-Nl .- ,
<, ,
'JC ''IC • X ''JC<,
''JC 'JC x" • 'JC 'l(.<,
X 'le X 'IC
,)( 'le )(.
~
1 PT 77",4
.A 2. ?> 4
)( x x x
)( x y. 'le: X
X ')( X 'le )( X
x x 'le: )C )( '1(<,
,')( 'l( ')( }( x
)( )C ')( X
Ntlu) "o~n.~ 9utI
14. Jo!! ~ Q'W''\ ~If
~(en\'Q.fo jUU~I~(O~
, 11-- J 1~o.x '= 3
1.. 1CL(~(" ..le !-O\d. e.l~ "",'111'110/11. ~"lL"
dt 1W~:feho" ~I'\ a.tfe.t te"" 1..
11+ -J' II\.A.~)C ::: 2. .a.t- t0u.r \... J w.'Ct~~ ..
L~ cAA'""~~,'",, .,If \... M ...~n·a ut N)t NbL le NI
ou Nu~ I~ k..olULr. d. k.~,h dll.lQ ~f-rtt~rf~ "''1.:' N... ""ilL II.,~ 1. no,,".r. d 'f~ILa.""'o.. S
E?ol.lr 10 ~rocaro.MMAAO") c ..~~ Lu",... 9'W d. sh.c.hr ~ UC'''I'S
~'" 1W.1.s ~~Ilr dQk. ol'Q.~oncll~ ~rinl.lrR.11I. ..e.o te"4"\- c.o ....~~ Je
la ~""itr;' dl? I~ ~QJ'ÙA G
2..- Mf\Q JI" rn'moln
La "",~,',,~ d~"~ Q .... di~~o~
( l.P"M S100 ) s l'b cke 14 'l'la.hl"œs
- l ,.c'/Ut- dÀ. r,\'VIeu\ ,'Rr, f""curt ~
Ir'a"f r'..... Il''8,,e ) ~c;u.) d '1.(11'
,Sou r LUit .s.w.1.t h:l.....~ ee
~t ....1:Jt
MCltrÙ::I fi !i f-o c.lcQ... :
,IIdo "-of.r. ~"üat) r S"ut.Ls c:lQCOllo 110\'1 d Q
aNolU trof,t-e' dv }ur 9U.I 1.. lM...tr,'u Cc;.JdQ
bClPld:a (~t. u..,.. bOll 1'\0 l\.u"'~rCl""'ho"l).RI-
La CohU'~I.t"I\CW ~~ CfIU f'~rQ.{g noe'Moto.", fUJ\.U're
r'~CfUl 1'01'1 l'If sl-och 914' '~~("'H t\4\'I
J~ la oVto ao ,,,tU tr'l'l4.u·~O\'.f (ou CUA JQ.jje>I.I))
1 •rMU~olrCl > k.o\L\
la sfruJ-v.rll lU~
~ tot.t'fn''fl.l€ _
.e5~ ~IIU ~~h'~
Mth au J.eutu.s
0
\ ,\
\ '.• \\\ \\ ).J,
~11-
\\
\\ \
\ \/
s.~~"1t : L·'t".. , L.~".( 1- ul"' 3
1· J- ,. [.N, "', NI
NI: lar~r J, ~"Jt nl.f>t-tLo1\,) - 1f .
S, 2.>C Il OM ,",If lMaJr"U, ,
ba....J:~ d"0'" Q rr \.4111 f ? "'11r'1l1 (.
<x.tn. Q'~"'IUt d'o,..Jr, ':J ..Ai- de IlU~r b .Ill" .... 0" c.c.h·!.tlf
ulf cû~r-~~ .La.,.... 'Ci ~ro~rQ ... "".. ho" ) a.u '''w d.Q ",,/-oe..&tlr
ctxq:: 81 krlM.B la ~QC.a.,·"t hln sh>(.b 91.t~ ~lî
s ~)(,I/W~'o(. dl! c:~.Icu' maillAi!
~'#- 1Cl stru.l1ltn dt la ~Q.'à" g 1 ( clClp. ~)
,..------- ~J ~.,
, .Nll"'Ho~
-, V<.~) =f
V(t) =z.
V l'>);:~ ~
v(2.H) = S
" (~H) =.ro.
k("~r dQ ba."o:\(l: NI;:: ~ (..I ...A) =- .ç;,
Au c(~~'·.·n 3 ot\ ct.v-cui- 02hLtt' ~ u,uJ'r'l'~ k. Je~ l4.\alI4~l"lA.rtJ
~ At ~
f ' " 1LC' t.ua.trru d.e ,..,.C§,·cL·ft ~"fl"1lr.l dl!. 'Q ~~nutl&rl da,,1- {e.
co",tr,LlI.tio'" ,."d,·v'·doall.( dol! c~Q.~u" ~J~Q""" 0"" 'f'A~
G ': 11::, -+ ~'\.. t0l.tr ""ll I\I.tIMo:"or....h'o",
~to\ 0.
r: ,t. , 4 s c ~ Cf
11
lt6?( Iq'r& \4.4 -~6~ -IqIH 14.41 0,
'~In 1 1446' -Iqz. -'qlr~ _III v61 _Iqt._---1
144 _1'11. 1 1(00 -11111 l'Il. ÂgU1
1",G]: -~(6s( -Ilf If3 _'"'' 1
4f6Jt -Iqln -'''II -'1.0000 0 01
I-,q'h lCft 1'''''1'1_1111161 _'''In, 'Tt. 0 -14 _11.0
1144 -Iqt 400 _I~v H 1 1600 0 , 2.0 401>
---1
_ t ..oo o 0 0 1 loC/o 0 0 0
0 0 -41 ue 0 2.4 Ito'--
1_Ita 400 0 \1.0 1
8000 1-- ~
4 - ~)C(/M~'~ ch ca1eu.\ ~"'-,.. o,..Jr'ng.I14'"
VII1'( q not~e. 8
1".>,
f.J ok : M....I lA'~ t.'U" b-..lWs J~ G ca.! C4(." ..-le;: !.4.<Q..I'.. f<'r Joo... .-r-r r&~( ~ Cc>w~rt1",
CC> ... ~tu t::. JI'"e.- e.u.vo ceJ c.u1JJ :tl(.o Ceif
~r-~'I lIA. ~p" ~ et.. c..Jt.J """'... lu....1 J<.t .2" ~~
~s cl.. cJC4! ct.. ~t"i:.u
ChoihcS': Risoluhol'\ du s~sl-ëm€,NIJIlh'on1- ~ethacle d~ o~o'uk •
1- R~~()lllhon d'u!') systeme dr:~",h'otl> 1,'Yl~'({A'r~)
Qe. rfo~I(- rYlQ r€IJ~~ UtlN
1'·"ÙI.I·re>. v.... :>""'" 91.1"
l·l'I'l~Qrf,:.nu dQ.l\.~ \f~h.t"lt des ~!>~t"'(J
~~ru.Ju(. k.. elcu·r. 11 F-ù ~ t-e-n h..h"~
cru u+ f~<L rI' ""' ~1~ll'l111 J"
na~ ~ It-~ '" 1"11\.0 h'lUt\ huJw·'>a. ... t
(~Q'+loJ" AA ~'~'ClV""t"'h) :
,11 ~\JC'\hol1.s l''I->e'w'rcs ~l:P-
1'.e9'IL,·ld...... des k...eu.~
ah 1(, .,. q,~ 1(.1-+ '" T Gl1n
lin -::: b,
Cl 1.1 l, 't q 11. ~ t -4 •• -+ '" z.n 1l1'\ = b'\.
CI,,,
...
<:4 ......
=
1"
[A): rI1a~n'U' du e...e.ff"L(.eH~j
\B3 veJ:iu.r slôl..o>."l ~l/..,,"~r.
\)(} v.tJ:W.{ des ,'''to''I1.UU
•Jk,. ... \ 1.1 co-J(•
~1l~"Cffn+) {r}~QM ~9 v- ~~}
cl, ",-oh, rt-oJ·e.I'- 1 [GJ.lf.ra. 10. ......1,..,·\..1 dt.J
rI1Q.~"'·v .JQ.~ {-on" nt('e./~",+.l' IR. ~r ~!
.,.. ..f,.,·v JQ.~ J~rlau .... e ...h s.t-~ 1.t ~(Jl/..~ I""~"""'r~.33
ru~ ; . ~.'! ,. ;',,, ::\' ':.; Sr" ift.t ,,.;re ~J
l'... Vf. ...s e [Gr· c:l~ s<>rt. CJlt (
L", Soluhol'\ du ~~te-..... ~ d·~4U.Q.,h·o"'>
ÙWl1rHol'I chn.th de la l'I-tClh";'(L JQ S
'ln. lIt~r) ~. It..s YI
10 l\ICA.f".u [GJ rI't.~~
(;tdhoe~ dii lor.s UI1(
~yq ~ t~H
~.ff"u·e~t$ [ GJ
[Gl~{~J
[Gr~ {FJ
[Gri [<;J~ ~1
~ hJ:La Sollth·.,1'1 dIA t"' li..; >\A ( .u
df 1''''''Vf.rSïo''l c:lll 1" l\Aa.h ..v JI? n'l"clt'h' ~ci
~l'·cc.hoYl ta,. /, Vel1t.u( ,~nu'
Noh ..) 9 u ·J ~Cl rlu.~\·w.">
.Ü C)t1 <Ac1o~~a.r" /0 ~~H'+k.oJl' cl..
lM " QM)( au c.a.1 cul-.
t- MdbJlI dl' C-hol~sky-, 1
Cl - G-e.", e'"" 1.'h3
CJ;lrrù [A] cl" J"..... GI't) '0" (l'\~ Il) ~J Rh, t\4,'V,
t~ Jwt J' li. ~.t k. llh·,. CI t ""a"~ l 't.A'(f ("~ l'l"w.,,
~pfrl'" +rl",,,,~ ... lcur, ~f-t'","E.u(.,g [CJ. L}'SI't\4'''~5 dlOld'01\ Q.U'(' ""'UI'II Jg.~
.... (~.·fn>.A·ru ..2." ~"Illl\t d<ntL :;h.
Avnl" )
r
q" Cl''L . . . q,'l b" 0 0 ... 0 JI Yt " C!1'l
CI t, ~lt ~ tl-, b" 11 t
o ... ~ 0 A .. ~h
:: "1'0
Cl" 1 "1 .. "CI ""
bn , bli.· . k~ .. 0 0 - A
E" .llfrJ.vO.,t 1.. ""'I.dh~"c",h·o .... ,,+ ".... l'J,,,,h·ta.,t- CtUQ.1. 1..
VI-! C1~no or"l,,,tll( [A.l 0... soo.d· J~tr"""'hLr 14-> ~I":",,",~j JQ.)
l'M~h,u.s frt·G4"~lllo.ùo j.~
~'-I
a-.() _ [ b,.,. <.e " - r;'1 ",' <::J-AJ bù '
e. ...... ::: .4
ni~ lors (Ar' - ( [B)[c1)-~ - [cJ-'. [BJ -1- -
[bJ dt' le tlAQh,' o tn·Cl"'~I.lIC\.i... ""~;,·wr. v~1
a.cro·I/Q .. 1-
A~r;> lIoLllh'r'l"C4lh'ol'l <f
IL~ fo o·" L> cl" 1.. ...... ..J.,ü
..cl .... ". ~c...h"o ... ,01'1 oL h-, ..~ FkQI" ....".. ~Lb] t«r I~> nl.. h'o ...>.
01·· A= -•• b· .
'"...·.1
J .' " l 1. J .: - -AJ LoO ,r rJA.
r:,
JA~ = 0
3E>
.6~ U"II h'!Ah"u trl'Q"'â"'~r' ,'" ~~"~r'
bt-I.. ""'~ ...( r'I"\(U'112!:R) l' ""V.trJ( L~] .le? 1... """"hl'(.( tro'C\"~..u;
-~ ou 'ali""t.. ~s c:I~ le:
hr~~> d~ 1",d'i:l.~""c.I( \6r1'.. u~ .. f.( Il..1,.,fk.t. ..Jro 'tA [ E.) rA. ~ le?}
./L,'-olJ -
-, ~ 100 J 1", n.~ ~n'u [4]-1 SI2 cal tt.tlt ~ar Iq nl",hot')
[A1-1
- [t.] lb]
CA] .ut kjM;fr",lu
o ... F ~ k1 ,rff,.., [ 4J s ll'\A.)
t-rfa."s-' CÙr. ~~n'f.U(I [H-]
+n'c:..,~u'a.irf
[ ~]
d 'I.U1I
trQ4-11a...~ 0\.1 la
r'" H.Llok~ JJ.) )
tor YVI 2 cL.. tro etuJ.pttr UIH l'M~~,,'V
\c. trolU ~c>~~: cl e
Lt!. ~'Q~fl1h de! la I\'IClhlv [M]::o [14)-1 So"'~ J~fI";""'~
COI tlM.-\.f de! la nJe:tt~ ~\",\.h-\'Lnl~ [1I)[tfJ-'= LN) C~] ~l
U 9\l.A' l..O ..dlÙ~ ",-:
1\'1 .. ~
"J-I
- L L ~ t' rYI 'rh.is r:.,· J '
o
(uj)
lA] -1 := ( (H) t l~Jtl-,
- [HY'([H]tr'-
- ([H]-') ([Hl1)t-
~+,
r~t n·,. C:etl culu
i~) : velhu.r d4-} J l1'~Ia.I.II>t~ "'~>
~ ~J : Vute.u.(" dCl.> fo ......·s01'1 ClI : l G] ~b1:: ~fJ
Or 01'\ ~~ ..R.trrr, 1 VII 91.11' [ G] .h~ ~ ....itn ·9l14
[ G1:: (HJt-[~) OIA [H] ~. UIlI IhQ~n'u
hra"'à'U I«...-r t1
w~arfW('
bOlot l ~J t [ ij) ~ t>! e ~ F:)
L~)\[)1 =~I.Ü ,Oh 0\ ~rQn
l~Jt~ul;~~J
o~ rw.!- alor>
ro~r ~ ~l
1
.Rot r....r Iq rol.U1-, re\~I1.~ r,
U... = F, 114"U'I..:: l Ft. - \+,1. U,) / Kz. t
,ruou~ ~Qr
1>... ", U,,/"....Il'I-I '=- (U"_,- H"_I.D,,) /»-.._., "_.
'"~.l :=. (U" - L " ,'r br) / "Ii
f"; ,.,
c- Pn'~",,""M~
4~ u.tti ~'t, \~ ~lttJ!hl r"nd,'ttl U JG.-ldo> ',,".1.>
~O,.n~.1Y OlW~"
W\t ~'QU '·M~od(J,,~v. ~l'\ Vlfa" ~ f~<ku> J.,'I/ ... t- ih-# 12" t.o"W"'-
d.lh',l,l GlA>Lt CU\>l J~f"'- f-lC"'·sh..,t- cl..,,> l'i "",,~,,"t. ~~#~.. I~ J~
1C) stru.,Jv. r1 ..eJ- J C) lA,.> /, +"""'.... lM, .. t- cl t,) J, cu~. •
Uh~ cuhl\l cV tro~I1:I""",IAtt..-:, Ll"lA'Sf~ ~It\ IQ rQ.l~.,..c~ç J. le;
rkeLtrla (~) l'jl.tlq J. ICI cV'U)l\I\ r~d•..; ~.. 'fUD Iv ~("'H dJl (..
.1'«%",,01, ~ ... u·~"I( h>\t- J..n."'~.1 ,h,v> le ~n..'
-e .tt' 0 AIl,o'A' I~.s forl\ùJJ> Jo... "'CI.. t k> Cl.c...,heJ ·h/.C' ...o~
J~lo holthltl [If» (.U.\J( clu vW~r .."bp...,/d,·...;" ~U}.J- c.w, ...
.Lu va.Jw.r w.li kr"" l. c; •
dJl~lo.Vh"'Hh ~!! 101It- hujouC') Q.(.( d"l~h"·"A~4.U"
A.VO-l l' Cl>ht<.( 9\'" LlQI.L) uttll'J'~\, Jl l'\D kol.LJ
cl _ ~,. dli c.a.' cul cl ".1 J "}' a.t/lM .nh,
( Mo t f-I...o J" t\i 0 I!&!dl! J CI clw1(1) I~.,)
[ ,1
'2.
Cl :
G
h :~ :: ~Il ~II
hl L = s, th,,::z.)
~ - q /h -I?, - d'Il \1-
h _(" - M.v ~t\î =lt- ~)/hu ~u - d'u L
h~'l:: ~
'li .f/rI. -1/r...br -011 :
H: ft 3-~
~
LG] ~bJ ~ ~rJ
[1J]t [U]~bl ~ ~I=J
PoJOl1l [If] ~~} :: {uJ
,,~ {;1 : '.<h..r d.4r3'~ ••f
Jl.: ofI~
-,
l, _d Ok \)\. 1'; t
l-r/,~ f,e - ~)t4""~'.1 df aa/wl cw Co~~~(
lJ&.a~itre. ~: i=ore..es dOlns lu iJimenb
UM foiS 9U.' 10 "'Cltrlt~ de n~I"Jl'h' ~~n~ra/( G!- * c..ons+Tui~€ Q/-qu.€
1'01"1 t> d~,b,rrnl": l.t Ue-lfwr fbL
Jfi} ~rœs cw..<' ~n ClU~n."'Q"h )
01\ e)~ ltn "'UILe. d, calcul,r k~ d~~Ia.U!,,"enh ~ ""'ndroi~ J,n
Jo~r~ JCI k1.lI'"h' t Clr let rtl/:tr~
~ h~: [G] -1 ~ çJ
b' ~t\ = {\ - fbJ
•
~ ~r") r~II~.lf llL rl(l.(..hon>
e(~kJClI4~, (J qui t\<>\ol.l l'I'1f-eru.lt) c'fJf dCl ho u.vu' lô {:c ..~ F~"")
~lJ.r lQ ~huttu.(I ou ~luh;~ ~r ~ tt1.woLruu 'lu,t' U>""''''oJ...n~ tJl~
shuJu.u. Pour un. lI\~m~n.&.fI J.,...,,~, COMn/l'(~Cl..t I,u JI/.~o.."'''''''''b
~II SI,) ~tn't>\"f~ .cJ- ~ Ccl.(a.~·rrst"'jU4) c:ID n''ij',.:kfD' J CI œlU ,-"LI'l«'CI}
fi .tl.ra ~).·11. cl" c.Jtu(u 'oU ~rh as.sov"; 0' S4> d:~I"lIho",h
~f QCWJ~ ~~Clr lA.} d,llr1~ ~~n'lWr4,) (~l-)1
~,., c.I'<:tufn,} 'hr"",u) '4> cJ,arrJ h.,,... \co CGtWCI Jo.s ~J,1 ,
Clh d(,~ oVQ",;( "R'lwfd"l" cs CfW' ~(",.Ifl('i cl 'l.tt",
oÎi ~fM~: veJ-w ( r, tDrlL> ~ l'\~J~.Lk): ~a.hru Je ""'S,·dd.' d/J /.......C ... L......ft C-t>nl.f.rnl.:
1>-cn.c. 1'0\.<.( JyOIl.\I'u ~ tlfforh t-""/l Ja..u 14~ ~c",,~ru.rL} "'tp.. J~
t°\.lV~( +ro.ur lu dr"1t't1llol~u d''4(-orh HAT"'-CW." J '4forh -franJ,a",I-J
.cl".b kAOho'kh ''''P J.ü{f.'1"G cl 'l4tt:LIr 1" ""/lIT/' u J~ r:J--'ddl' [kJ .1 ..cl" fA» ~L"" k n . 41
