Chapitre 10 - Flexion Simple ELU - Sections en T
August 15, 2022 | Author: Anonymous | Category: N/A
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NFK^DWZBSFIWD KBSIFKBL CD^ BWS^ DS HDSIDW^ NABIWD CD SWBZBTQ UTGLIN^ DS GBSIHDKS
VVVVVVVVVVV VVVVVVVVVV V
" DLDHDKS^ CD GDSFK BWHD " Nabpitrd 25= Jldxifk sihpld å l'DLT ^dntifks dk S
(Nfcd NNZ553)
Dksdiokbkt= M. UBÆ^
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
7
^fhhbird
25.
NBLNTL C’TKD ^DNSIFK DK ^DNSIFK DK S B LB JLDQIFK ^IHULD ^IHULD B L’DLT ...................................... L’DLT ...................................... >
25.2.
AYUFSAD^D^ CD NBLNTL ............................................................................... .......................................................................................................... ........................... >
25.2.2. 25.2.7. 25.2.>.
Nblnul cd lb tbgld .............................................. ........................................................................................................... ............................................................. > Dxdhpld cd cétdrhikbtifk cd lbrodur lbrod ur cd tbgld. ............................................................ 3 Nlbssdhdkt cds cijjérdkts nbs cd nblnul - Hfhdkt cd rréjérdknd. éjérdknd. ................................ ................................ 4
25.7.2. 25.7.7.
Aypftaásds cd nblnul .................................................................................................... .................................................................................................... : Dxdrnind cd nfurs= ^dntifk dk S bvdn tbgld pbrtidlldhdkt nfhprihéd ......................... :
25.7.
N B^ FT LB SBGLD SBGLD D^S UBWSID UBWSIDLLDHDKS LLDHDKS NFHUWIHDD NFHUWIHDD .................................................................... ................................................................... :
25.>.
N B^ FT LB SBGLD SBGLD D^S SFSBL SFSBLDHDKS DHDKS NFHUWIHDD ^BK^ BNIDW^ NFHUW NFHUWIHD^ IHD^ ................................ 1
25.>.2.
25.3. 25.4.
Aypftaásds cd nblnul .................................................................................................... .................................................................................................... 1 UFTWNDKSBOD HIKIHTH C BWHBSTWD^ .................................................................................... 9 ’BWHBSTWD^ .....................................................................................
DQDWNIND 2= ^DNSIFK DK S ^BK^ BNIDW^ NFHUWIHD^ ............................................................... 9
25.4.2. 25.4.7. 25.4.>.
Nbrbntéristiquds cds Hbtéribux ..................................................................................... ..................................................................................... 9 Nblnul cd Hgtu............................................................................................................. ............................................................................................................. 25 Nblnul cds brhbturds lfkoitucikblds ........................................................................... 25
25.:.2. 25.:.7.
Nbrbntéristiquds cds Hbtéribux ................................................................................... ................................................................................... 22 Nblnul cd Hgtu............................................................................................................. ............................................................................................................. 22
25.:.
DQDWNIND Kµ7= ^DNSIFK DK S BZDN SBGLD UBWSIDLLDHDKS NFHUWIHDD .......... ................................... ......................... 22
25.:.>. 25.:.3.
25.?. 25.1.
Nblnul cds brhbturds lfkoitucikblds ........................................................................... 27 Zérijinbtifk cu pfurndktbod hikihuh ......................................................................... ......................................................................... 27 CIHDK^IFKKDHDKS B L’DLT BZDN BNIDW^ NFHUWIHD^ ........................................................... 2>
DQDWNIND CD NFTW^= ^DNSIFK DK S BZDN BNIDW^ NFHUWIHD^ ................................................ 2:
25.1.2. 25.1.7. 25.1.>.
Nbrbntéristiquds cds hbtéribux ................................................................................... ................................................................................... 2? Nblnul cd Hgtu............................................................................................................. ............................................................................................................. 2? Nblnul cds brhbturds lfkoitucikblds ........................................................................... 2?
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
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25.Nblnul l’DLT Nblnul c’ukd sdntifk dk S å lb jldxifk sihpld å l’DLT 25.2. Aypftaásds cd nblnul 25.2.2. Nblnul cd lb tbgld Lfrsqu’ukd pfutrd rdntbkoulbird dst sflicbird c’ukd cblld dk Gétfk Brhé qu’dlld suppfrtd, kfus
pfuvfks nfksicérdr qud lb sdntifk résistbktd cd lb pfutrd dst dk jbit nfkstituéd cd lb rdtfhgéd cd lb ndlld-ni (qud l’fk bppdlld « kdrvurd °) dt c’ukd pbrtid cd lb cblld (qud l’fk bppdlld « tbgld °)= Sbgld cd nfhprdssifk Cblld dk G.B.
kdrvurd
L’DN7 (nabpitrd 4.>.7.2) céjikit lb lb lbrodur
pbrtinipbktd cds tbglds cd nfhprdssifk qud l’fk l’fk pdut
prdkcrd dk nfhptd. Ndttd lbrodur djjinbnd cépdkc cd plusidurs pbrbhátrds= Cihdksifks cd l'çhd. Cihdksifks cd lb cblld.
Nbs cd cd nabrod. Ufrtéd lb pfutrd. Nfkcitifks c'bppuis. Brhbturds trbksvdrsblds.
Bvbkt tfutd t futd nafsd, il nfkvidkt cd nfksicérdr ld snaéhb snaé hb suivbkt qui cfkkd lds cistbknd l5 dktrd pfikts cd hfhdkt kul =
BSSDKSIFK, lb pfrtéd L> cd lb nfksfld kd cfit pbs cépbssdr lb hfitié cd lb trbvéd bcmbndktd. Cd plus, ld rbppfrt cds pfrtéds cd cdux trbvéds bcmbndktds cfit ítrd nfhpris dktrd 7/> dt 2,4.
L'DN7 ikciqud éobldhdkt qud cbks lds nbs nfurbkts (pfutrds nfktikuds cd gçtihdkt), il pdut ítrd nfksicéré ukd lbrodur cd tbgld nfkstbktd sur tfutd lb lfkoudur cd lb pfutrd dk bcfptbkt blfrs lb vbldur dk trbvéd. Ld snaéhb prénécdkt sd résuhd cfkn å trfis vbldurs = L58 5.14L dk trbvéd cd rivd. L58 5.?5L dk trbvéd iktdrhécibird. L58 L dk nfksfld.
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
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Cbks ld nbs c’ukd pfutrd isfstbtiqud, lb lfkoudur L5 nfrrdspfkc å lb pfrtéd dktrd -bxds.
Ufur lds pfutrds dk S fu dk L, lb lbrodur djjinbnd gdjj cd lb tbgld pdut-ítrd nblnuléd å pbrtir cd lb jfrhuld suivbktd= gdjj gdjj i gw g ,
Bvdn
gdjj ,i
5.7g i 5.2 l 5 5.7l 5
Sfut dk vérijibkt
gdjj i gi ,
Lds cijjérdktds kftbtifks sfkt dxpliquéds cbks lb jiourd ni-cdssfus=
25.2.7.
Dxdhpld cd cétdrhikbtifk cd lbrodur cd tbgld.
Urdkfks pbr dxdhpld lb pfutrd suivbktd =
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
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Fk nadrnad å cétdrhikdr lds lbrodurs cds tbglds cd nfhprdssifk cd lb jild G. Lds pfrtéds cfivdkt ítrd nfksicéréds dktrd-bxd, cfkn = Srbvéd 2 (trbvéd cd rivd)8; L28 4.15 h 8; L58 5.14*4.18 5.14*4.18 3.9> h Srbvéd 7 (trbvéd iktdrhécibird)8; L78 :.25 h 8; 8; L58 5.?5*:.28 3.7? h Srbvéd > (trbvéd cd rivd)8; L>8 4.15 h 8; L58 5.14*4.18 5.14*4.18 3.9> h
Lbrodur tbgld „ Srbvéd 2 gw8 5.>5h
g287 h dt g78 7.45 h dt g8 3.15 h 5.7*L58 5.91: h
gdjj ,2
5.7g2 5.2l 5
gdjj ,7
5.7g7
gdjj gdjj ,2 gdjj ,7 gw 5.19> 5.91: 5.>5 7.2?9h g
5.2l 5
5. 7 * 7 5.2* 3.9> 5.19>h
5.7 * 7.4 5.2* 3.9> 5.99>h 8; fk rdtidkt gdjj ,7 5.91:h
Lbrodur tbgld „ Srbvéd 7 gw8 5.>5h g287 h dt g78 7.45 h dt g8 3.15 h 5.7*L58 5.143 h
gdjj ,2
5.7g2 5.2l 5
5. 7 * 7 5.2* 3.7? 5.17?h
gdjj , 7 5.7g7 5.2l 5 5 .7 * 7.4 5.2* 3.7? 5.97? 97?h 8; fk rdtidkt gdjj , 7 5.143h gdjj gdjj ,2 gdjj , 7 gw 5.17? 5.14 143 3 5.>5 2.912h g
25.2.>. Nlbssdhdkt cds cijjérdkts nbs cd nblnul - Hfhdkt cd réjérdknd. L’bkblysd c’ukd sdntifk dk S å l’DLT nfkcuit å nblnuldr cbks uk prdhidr tdhps lb pfsitifk cd l’bxd
kdutrd. Dk djjdt 7 nbs cd jiourds sfkt pfssiglds = 2- Lb tbgld dst pbrtidlldhdkt nfhprihéd = gdjj
j nncc
δn x u
5,1.x u
aj c δs
gw
Cbks nd nbs fk b = 5,1. xu a j fu xu 2 ,74a j Ld ciborbhhd rdntbkold dst ukiqudhdkt situé cbks lb tbgld, lb pfutrd jfkntifkkd cfkn nfhhd ukd pfutrd rdntbkoulbird cd lbrodur gdjj . Dk djjdt, cbks nd nbs, lb kdrvurd cd lbrodur g w dst dk zfkd cd trbntifk dt sb résistbknd dst kéolioéd (fk kéoliod lb résistbknd cu gétfk tdkcu).
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
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7- Lb tbgld dt lb kdrvurd sfkt nfhprihéds gdjj
δgn x u
a5 c δst
g5
Cbks nd nbs fk b = fu xu 2 ,74a j Ufur nfkkbëtrd cbks qudl nbs lb sdntifk sd trfuvd, il sujjit cd nblnuldr ld hfhdkt résistbkt cd lb tbgld H gtu qud l’fk bppdl « hfhdkt cd réjérdknd °.
H gtu gdjj a j c
a j
. j nc 7
^i HDc ≣ Hgtu 8; lb tbgld dst cfkn pbrtidlldhdkt nfhprihéd, kfus sfhhds cbks ld prdhidr nbs
si HDc ; Hgtu 8; lb tbgld dt lb kdrvurd sfkt nfhprihéds, kfus sfhhds cbks ld cduxiáhd nbs
25.7. Nbs fù lb tbgld dst pbrtidlldhdkt pbrtidlldhdkt nfhprihéd nfhprihéd 25.7.2. Aypftaásds cd nblnul
Kfus sfhhds cbks ld nbs fù Hu ≣ Hgtu Lb sdntifk dk S dst nfksicéréd nfhhd ukd sdntifk rdntbkoulbird cd lbrodur g djj dt cd abutdur utild c. Lds équbtifks cu nabpitrd 9 sdrfkt utiliséds (jldxifk sihpld DLT sur lds sdntifks rdntbkoulbirds). Zfir dxdrnind ni-bprás 25.7.7. Dxdrnind cd nfurs= ^dntifk dk S bvdn tbgld pbrtidlldhdkt nfhprihéd
Urdkfks lb pfutrd suivbktd = 225 27 44
75
^fllinitbtifks = HDc8 775 @K.h f Hsdr8 23:,? @K.h f Hbtéribux = Gétfk= N74/>5 f Bnidr= ^355G f Dkrfgbod cds brhbturds = >nh Nlbssd c’dkvirfkkdhdkt = Q5 Abutdur utild = c85,44 h
Lfi cd nfhpfrtdhdkt cd l’bnidr bvdn pblidr afrizfktbl. Fk sd prfpfsd cd cétdrhikdr lds brhbturds lfkoitucikblds å l’DLT
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
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N brbntéris brbntéris tiquds tiquds cds Hbté Hbtéribux ribux
Gétfk N74/>5 8; j nc
j nth
7/>
5.>5 j n`
Bnidr ^355 = j yc
j n`
74
n
7/ >
5 .>5 74
j y`
s
2:,:? Hpb
2,4
355 2,24
7.4: Hp Hpb b
>3?.1> Hpb
N blnul blnul cd Hgtu
Cbks uk 2dr tdhps, il kfus jbut cétdrhikdr ld hfhdkt qud pdux équiligrdr lb tbgld sduld = a j H gtu gdjj a j c . j nc
7
Fk b cfkn =
H gtu
5,27 2,25 5,27 5,44 2:.:? 2,51 HK .h 7
Cbks kftrd nbs, kfus bvfks HDc < Hgtu 8; lb tbgld dst cfkn pbrtidlldhdkt nfhprihéd, dt il kfus jbut jbird uk nblnul dk nfksicérbkt ukd sdntifk rdntbkoulbird cd cihdksifk g8225nh dt c844nh
H Dc
5,775
nu
Nblnul cd
Nblnul cu grbs cd ldvidr zg = z n
gw.c ·. j nc u
=
u
2,25 5,44· 2:,:?
2,74 2 (2 7 ) nu
5,535
2,74 2 (2 7 5,535)
5,542
5,3 ) 5.44 ( 2 5,3 5,542) 5,4>9h c (2
Nblnul cd lb sdntifk c’brhbturds =
Bu
f
H Dc z n . j yc
5,775
5,4>9 >3?,1>
3
22,?>.25 h· 22,?>nh·
Kfus nafisissfks ukd sdntifk cd = 7AB74 + 2 AB 2: sfit 22,1> nh7
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
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25.>. Nbs fù fù lb tbgld dst tftbldhdkt tftbldhdkt nfhprihéd sbks bnidrs nfhprihés 25.>.2. Aypftaásds cd nblnul
Kfus sfhhds cbks ld nbs fù Hu ; Hgtu Ld nblnul c’ukd sdntifk dk S nfksistd dk lb cétdrhikbtifk cds bnidrs sur cdux sdntifks jintivds =
Tkd 2árd sdntifk jintivd nfrrdspfkcbkt å l’çhd cd lb pfutrd dt c’ukd sdntifk c’bnidrs
ikjéridurs Ndttdnfhpfséd 2 sdntifk cfit équiligrdr ld hfhdkt HDc2. Tkd 7áhd kftéd sdntifkB2. jintivd cds bilds cd lb tbgld cd nfhprdssifk dt c’ukd sdnti fk áhd c’bnidrs ikjéridur s kftéd B7. Ndttd 7 sdntifk cfit équiligrdr ld hfhdkt HDc7.
árd
^dntifk jintivd 7 = Fk énrit l’équiligrd cd lb sdntifk 7 =
Djjfrt cd nfhprdssifk rdpris cbks ld gétfk = J n 7
Grbs cd ldvidr pbr rbppfrt bux bnidrs tdkcus B7 = z n 7 c
Hfhdkt rdpris pbr ndttd sdntifk = H Dc 7 (gdjj gw ).a j . j nc c
(gdjj gw ).a j . j nc
a j 7
a j
7
Nfkkbissbkt ld hfhdkt cd jldxifk å rdprdkcrd, fk pdut dk cécuird lb sdntifk c’bnidr kéndssbird = H Dc 7 B7 a j
c
yc 7 . J
^dntifk jintivd 2 =
Lb sdntifk jintivd 2 nfrrdspfkc å uk cihdksifkkdhdkt nlbssiqud cd sdntifk sdntifk rdntbkoulbird =
Dc Fk cfit équiligrdr ld hfhdkt H Dc 2 H H Dc 7
H Dc 2
nu
u
z n2 c ( 2 5,3 u )
gw .c ·. J nc
2
B
2,74 2
(2 7 )
nu
H Dc 2
z n2. J yc
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
9
25.3. Ufurndktbod hikihuh c’brhbturds c’brhbturds Ld pfurndktbod hikihuh å hdttrd dk plbnd dst ld híhd qud pfur lds sdntifks rdntbkoulbirds = Ld pfurndktbod hikihuh c’ukd pfutrd dk jldxifk sihpld dst céjiki pbr (§9.7.2.2 cd l’DN7) =
B s ,hik
j nt djj
j nt ,djj .gw .c 5.7: Hbx j y` 5.552>.g .c w
Bvdn
,
j nth si lb hbitrisd cd lb jissurbtifk dst rdquisd.
a 2.: . j nth j nt ,djj j nth, jl Hbx cbks lds butrds nbs. 2555 j nth
a = abutdur cd lb sdntifk dxprihéd dk hh.
25.4. Dxdrnind 2= 2= ^dntifk dk S sbks bnidrs nfhprihés Urdkfks l’dxdhpld suivbkt =
^fllinitbtifks = f HDc8 995 @K.h Hsdr8 ?55 @K.h f Hbtéribux = Gétfk= N74/>5 f f Bnidr= ^455G Dkrfgbod cds brhbturds = >nh Nlbssd c’dxpfsitifk Q5 Cdksité cu gétfk = 74@K/h> Abutdur utild = c85,34 h dt c’85,53h Lfi cd nfhpfrtdhdkt cd l’bnidr bvdn pblidr afrizfktbl.
Fk sd prfpfsd cd cétdrhikdr lds brhbturds lfkoitucikblds å l’D LT 25.4.2. Nbrbntéristiquds cds Hbtéribux
Gétfk N74/>5 8; j nc
j nth
7/ >
5.>5 j n`
Bnidr ^455 = j yc
74
n
2,4
7/>
5 .>5 74
j y`
j n`
s
2:,:? Hpb
7.4: Hp Hpb b
455 2,24 3>3.?1 Hpb
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
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25.4.7. Nblnul cd Hgtu
Cbks uk 2dr tdhps, il kfus jbut cétdrhikdr ld hfhdkt qud pdux équiligrdr lb tbgld sduld = a j H gtu gdjj a j c . j nc
7
Fk b cfkn =
5,24 2:,:? 5,9>1 HK .h 2,55 5,24 5,34
H gtu
pdut céjikir si lb tbgld dst dktiárdhdkt nfhprihéd. Dk nfhpbrbkt Hgtu dt ld hfhdkt H Dc7, fk Cbks kftrd nbs, kfus bvfks H Dc ; Hgtu 8; lb tbgld dst cfkn dktiárdhdkt nfhprihéd, dt il kfus jbut jbird uk nblnul dk nfksicérbkt ukd sdntifk dk S.
25.4.>. Nblnul cds brhbturds lfkoitucikblds
^dntifk jintivd 7 = Ld hfhdkt rdpris pbr ndttd sdntifk vbut =
H Dc 7 (gdjj gw ).a j . j nc c
a j
5,24 (2 5.75 ) 5,24 2:,:? 5.?45 HK .h 5,34 7 7
B pbrtir cd nd hfhdkt, fk dk cécuit lb sdntifk c’bnidr ==
H Dc 7
B7
a j c . J yc 7
5.?45
5.24 3>3.?1 5.34 7
3:.253 h· 3:nh·
^dntifk jintivd 2 = Lb sdntifk jintivd 2 nfrrdspfkc å uk cihdksifkkdhdkt nlbssiqud cd sdntifk sdntifk rdntbkoulbird =
5.?45 5.735 HK .h H Dc 2 H Dc H Dc 7 5.995
nu
H Dc 2 gw .c ·. J nc
5.735
5.75 5.34· 2:.:?
5.>44
Ufur uk ^455G, bvdn ukd nlbssd c’dxpfsitifk QN5, fk b nfhprihés
nu lu 5,>?7 8; pbs c’bnidrs
Fk réblisd cfkn uk cihdksifkkdhdkt sbks brhbturds nfhprihés =
2,74 2 (2 7 )
2. 74 2
2
7 5.>44 5.4??
z n2 c (2 5,3 u ) 5.34 (2 5.35 5.4??) 5.>3:h
B2
u
nu
5.735 H Dc 2 24.94.25 3 h· 24.94nh· z n2. j yc 5.>3: 3>3.?1
^dntifk tftbld Il jbut cfkn plbndr bu tftbl B2 + B7 sfit :2,94 nh· Fk vfit qudsbndttd pfutrd k’dst pbs lds trás gidk cihdksifkkéd dt qu’il sdrbit sfuabitbgld c’buohdktdr abutdur bjik cd récuird sdntifks c’bnidrs taéfriquds. taéfriquds.
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
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25.:. Dxdrnind kµ7= ^dntifk dk S bvdn tbgld tbgld pbrtidlldhdkt pbrtidlldhdkt nfhprihéd Urdkfks lb pfutrd suivbktd = 275 24 ?4
74
^fllinitbtifks = HDc8 >45 @K.h f Hsdr8 294 @K.h f Hbtéribux = Gétfk= N>5/>? f Bnidr= ^455G f Dkrfgbod cds brhbturds = >nh Nlbssd c’dxpfsitifk Q5 Hbitrisd cd lb jissurbtifk rdquisd. Abutdur utild = c85,:1 h Cdksité cu gétfk = 74@K/h> Lfi cd nfhpfrtdhdkt cd l’bnidr bvdn pblidr iknliké.
Fk sd prfpfsd cd cétdrhikdr lds brhbturds lfkoitucikblds å l’DLT 25.:.2. Nbrbntéristiquds cds Hbtéribux
Gétfk N>5/>? 8; j nc
j nth
7/>
5.>5 j n`
j n`
n
>5 2,4
7/>
5 .>5 >5
Bnidr ^455G = j yc
j y` s
75 Hpb
7.95 Hp Hpb b
455 3>3.?1 Hpb 2,24
25.:.7. Nblnul cd Hgtu
Cbks uk 2dr tdhps, fk cétdrhikd ld hfhdkt qud pdux équiligrdr lb tbgld sduld = a j H gtu gdjj a j c . j nc
7
Nd qui kfus cfkkd =
H gtu
5,24 2,75 5,24 5,:1 75 7,21 HK .h 7
Cbks kftrd nbs, ld hfhdkt cd jldxifk bppliqué H Dc dst ikjéridur å H gtu . Lb tbgld dst cfkn pbrtidlldhdkt nfhprihéd, dt il kfus jbut jbird uk nblnul dk nfksicérbkt ukd sdntifk rdntbkoulbird cd cihdksifk gw gdjj 275nh dt c8:1nh.
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
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25.:.>. Nblnul cds brhbturds lfkoitucikblds
Nblnul dk jldxifk sihpld sur ukd sdntifk rdntbkoulbird = 5,>45 H Dc nu 5,5>2 gw .c ·. j nc 2,75.5,:1·.75
2,74 2 (2 7 nu )
2,74 2 (2 7 5,5>2)
u
z n
Nblnul cd l’bllfkodhdkt cds bnidrs tdkcus =
5,3 u ) c (2
5,5>9
5,:1 (2 5,3 5,5>9) 5,:?h 2 su
u
.
nu 7
u
Ufur uk gétfk cd cd résistbknd résistbknd ikjéridurd ikjéridurd å 45 Hpb, fk b
f
su
f
2 u u
. nu 7
2 5.5>9
5.5>9
>.4 1:.73 ‵
Nblnul cd lb nfktrbiktd cbks lds bnidrs tdkcus = Ufur uk bnidr ^455G = su 3>7,?2 ?7? ,7?. su f
su
f
nu 7 >.4 ‵.
3:: 3:: Hp Hpb b.
3>7,?2 ?7?,7? 5. 51:73 394.3> Hpb 3:: Hpb 8;
^dntifk c’brhbturds tdkcuds = Bu
H Dc z n
su
su
3:: Hp Hpb b.
5,>45 22,72nh· 5,:? 3::
Kfus nafisissfks ukd sdntifk cd = 7AB74 + 2 AB 75 sfit 27,9: nh7. Wdhbrqud =
Kfus rdhbrqufks, cbks ndt dxdrnind dt cbks ndlui cu nfurs, qud l'fk dst systéhbtiqudhdkt bu pivft B. Cbks ld nbs c'ukd sdntifk dk S cfkt lb tbgld cd nfhprdssifk dst pbrtidlldhdkt nfhprihéd, nd sdrb systéhbtiqudhdkt ld nbs, nbr lfrsqud Hu 4 cd rbnnfurnissdhdkt. 25.:.3. Zérijinbtifk cu pfurndktbod hikihuh Ld pfurndktbod hikihuh c’ukd pfutrd dk jldxifk sihpld dst céjiki pbr (§9.7.2.2 cd l’DN7) =
B s ,hik
j nt djj
5.7: j nt ,djj .gw .c Hbx j y` 5.552>.g .c w
Bvdn
,
j nth nbr lb hbitrisd cd lb jissurbtifk dst rdquisd (vfir ékfkné).
Nd qui kfus cfkkd =
B s , hik
7,95 5.7: 5,74 5,:1 7.4:nh· Hbx 7.4:nh· 455 5.552> 5.74 5.:1 7.72nh·
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
2>
25.?. Cihdksifkkdhdkt å l’DLT bvdn bvdn bnidrs nfhprihés nfhprihés Kfus bvfks vu bu nabpitrd 9 (jldxifk sihpld sur lds sdntifks rdntbkoulbirds) qud lfrsqud ld hfhdkt récuit dst supéridur å ukd vbldur lihitd, fk cfit hdttrd dk plbnd cds bnidrs nfhprihés. Cbks ld nbs cds sdntifks dk S, nd nbs dst rbrd dt siokijid uk hbuvbis cihdksifkkdhdkt cd lb sdntifk cd gétfk. Fk préjárdrb cfkn rdcihdksifkkdr lb sdntifk cd gétfk plutót qud cd hdttrd dk plbnd cds bnidrs nfhprihés. Cbks ld nbs fù Hu ; Hgtu, lb tbgld dst cfkn dktiárdhdkt nfhprihéd, il jbut cfkn prfnécdr å uk nblnul dk cénfhpfsbkt lds sdntifks jintivds tdl qud kfus l’bvfks dxpfsé dk 25.>. Cfkn, cbks ld nbs fù lb 7d sdntifk jintivd cfkkd uk cds bnidrs nfhprihés.
nu lun il
dst kéndssbird cd hdttrd dk plbnd
Cbks ld nbs cd lb kéndssité c’bnidrs nfhprihés, il jbut cénfhpfsdr lb pfutrd cd lb jbïfk suivbktd = Tkd 2árd sdntifk jintivd nfrrdspfkcbkt å l’çhd cd lb pfutrd dt nfhpfséd c’ukd sdntifk c’bnidrs
ikjéridurs kftéd B2. Ndttd 2 árd sdntifk pdut équiligrdr ld hfhdkt H Dc 2 . Tkd 7áhd sdntifk jintivd nfhpfséd cds bil ds cd lb tbgld cd nfhprdssifk dt c’ukd sdntifk áhd c’bnidrs ikjéridurs kftéd B7. Ndttd 7 sdntifk cfit équiligrdr ld hfhdkt H Dc 7 . Tkd >áhd sdntifk jintivd nfrrdspfkcbkt å lb sdntifk c’bnidrs nfhprihés kftéd B’ bvdn ukd áhd sdntifk c’bnidr tdkcu B> qui pdrhdt c’bvfir l’équiligrd cd lb sdntifk. Ndttd > sdntifk jintivd pdut équiligrdr ld hfhdkt H Dc > .
^fit dk tdrhds cd céjfrhbtifk dt c’djjfrts =
Fk cfit bvfir évicdhhdkt H Dc
H Dc 2 H Dc 7
H Dc > .
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
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Dquiligrd cd lb sdntifk 2 = hdhgrurd ukiqudhdkt Ufur cihdksifkkdr lb sdntifk jintivd 2, il kfus jbut cétdrhikdr ld hfhdkt récuit cd lb sdntifk dt ld nfhpbrdr bu hfhdkt récuit lihitd. Ndttd nfhpbrbisfk kfus pdrhdttrd cd cétdrhikdr lb kéndssité fu kfk cd hdttrd dk plbnd cds bnidrs nfhprihés. Il kfus jbut cfkn cétdrhikdr ld hfhdkt qud cfit rdprdkcrd lb hdhgrurd sduld dk cécuisbkt cu hfhdkt tftbl ld hfhdkt rdpris pbr lds bilds cd lb tbgld cd nfhprdssifk (hfhdkt rdpris pbr lb sdntifk 7).
Lds bilds cd lb tbgld rdprdkkdkt ld hfhdkt H Dc 7 (gdjj gw )a j J nc c
a j
.
7
Ld hfhdkt rdstbkt å rdprdkcrd r dprdkcrd pbr lb hdhgrurd (bvdn nds bnidrs nfhprihés) vbut cfkn = H Dc H Dc 7 . Ld hfhdkt récuit nfrrdspfkcbkt dst =
nu
H Dc
H Dc 7
gwc · J nc
Il kfus jbut dksuitd cétdrhikdr ld hfhdkt récuit lihitd
lun nfkjfrhéhdkt
bu §9.: cu nabpitrd 9. Il y b
présdknd c’bnidrs nfhprihés fk b nu lun . Cbks ld nbs c’bnidrs nfhprihés, ld hfhdkt H Dc H Dc 7 vb sd cistrigudr dktrd lb sdntifk jintivd 2 qui
nfrrdspfkc å lb hdhgrurd sbks bnidr nfhprihé dt lb sdntifk jintivd > bvdn bnidrs nfhprihés. Lb sdntifk jintivd 2 nfrrdspfkc å uk cihdksifkkdhdkt nlbssiqud cd sdntifk rdntbkoulbird rdntbkoulbird qui trbvbilld bu hfhdkt récuit lihitd (n'dst-å- cird mustd bvbkt lb hisd dk plbnd c’bnidrs nfhprihés) = H Dc 2 g c · J lun w nc
2,74 2
lu
z n c (2
B2
(2 7 lun )
5,3 ul )
H Dc 2
z n J yc Lds bnidrs nfhprihés sdrfkt nblnulés lfrs cd l’équiligrd cd lb sdntifk jintivd >.
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
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Dquiligrd cd lb sdntifk 7 = bilds cd lb tbgld cd nfhprdssifk. Cbks ld nbs c’ukd sdntifk dk S bvdn bnidrs nfhprihés, nds brhbturds sdrfkt plbnéds ukiqudhdkt sur lb lbrodur cd l’çhd cd lb pfutrd. Ubr nfkséqudkt, nds bnidrs nfhprihés k’iktdrvidkkdkt pbs cbks ld
nblnul cd lb sdntifk jintivd 7. L’équiligrd cd lb sdntifk 7 sd jbit cfkn sbks bnidr nfhprihé.
Ld hfhdkt rdpris pbr lds bilds cd lb tbgld cd nfhprdssifk =
c a H Dc 7 (gdjj gw ).a j . J nc 7 j
Lds brhbturds kéndssbirds pfur équiligrdr nd hfhdkt sfkt céjikids pbr = H Dc 7 B7 a j c J yc
7
Dquiligrd cd lb sdntifk > Lb sdntifk > dst nfhpléhdktbird å l’équiligrd cd lb sdntifk 2.
Lb sdntifk > cfit équiligrdr ld hfhdkt rdstbkt, sfit H Dc > H Dc H Dc 2 H Dc 7 . B pbrtir cd nd hfhdkt, fk cihdksifkkd ukd sdntifk c’bnidrs nfhprihés nfhhd kfus l’bvfks vu cbks
ld nbs cds sdntifks rdntbkoulbirds = B'
H Dc >
(c
c ' ) sn
Fk cétdrhikd sn bvdn lb jfrhuld cds tribkolds sdhglbglds (céhbrnad icdktiqud bu nblnul sur lds sdntifks rdntbkoulbirds - nabpitrd 9) =
sn
>,4
2555 l c
( l c c ' ) dt
sn
sn
D s
Lb vbldur jikbld cd lb nfktrbiktd sur lds bnidrs nfhprihés cépdkc cfkn cd lb lfi cd nfhpfrtdhdkt utiliséd, å pblidr afrizfktbld fu å pblidr iknliké. Cbks lds 7 nbs, si
sn
yc sn 755555. sn (vfir §9.:.2 pfur lb céjikitifk cd
yc ).
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
^i
sn
yc
2:
, il jbut nfksicérdr cdux nbs cd jiourd =
Ciborbhhd å pblidr afrizfktbl =
Ciborbhhd å pblidr iknliké = ^355 B sn >3:,4> ?3? ,::. sn f
sn
j yc .
>:> HU HUb b
^355 G sn
>3:,4> ,41. sn >?>HU HUb b 4?:
^355 N sn
>3:,4> ?27 ,2?. sn >94HU HUb b
f
f
^455 B sn ^455 G sn f
^455 N sn
f
f
HUb b 343 HU 3:: HU HUb b
3>7,?2 947 ,>1. sn 3>7,?2 ?7? ?7 ? ,7?. sn
3>7 3>7,?2 194 ,47. sn
39> 39> HU HUb b
Uuis fk nblnul ukd sdntifk c’brhbturds tdkcuds B> qui cfit équiligrdr lb sdntifk c’bnidrs nfhprihés
B’ = B> B'
sn
j yc
^dntifk tftbld å hdttrd dk Şuvrd pfur B 8 B2 + B7 + B> Ld nbs c'ukd sdntifk dk S bvdn bnidrs nfhprihés dst trás rbrd. Dk djjdt, dk ráold oékérbld, ld jbit cd prdkcrd dk nfhptd lb tbgld cd nfhprdssifk cbks ld cihdksifkkdhdkt b pfur fgmdntij c'évitdr cd hdttrd dk plbnd cds bnidrs nfhprihés dk jbisbkt trbvbilldr bu hidux lb tbgld cd nfhprdssifk. ^i fk brrivd bu nbs c'ukd sdntifk dk S bvdn bnidrs nfhprihés, fk préjárdrb rdcihdksifkkdr lb sdntifk cd gétfk pfur évitdr nd nbs cd jiourd.
25.1. Dxdrnind cd nfurs= nfurs= ^dntifk dk dk S bvdn bnidrs bnidrs nfhprihés nfhprihés Urdkfks l’dxdhpld suivbkt =
^fllinitbtifks = HDc8 :>5 @K.h f Hsdr8 334 @K.h f Hbtéribux = Gétfk= N74/>5 f Bnidr= ^355G f Dkrfgbod cds brhbturds = >nh Nlbssd c’dxpfsitifk = QC Cdksité cu gétfk = 74@K/h> Abutdur utild = c85,34 h dt c’85,5>h Lfi cd nfhpfrtdhdkt cd l’bnidr bvdn pblidr afrizfktbl. Nfdjjinidkt c’équivbldknd = d
24
Fk sd prfpfsd =
Cd cétdrhikdr lds brhbturds lfkoitucikblds å l’DLT Cd vérijidr ld pfurndktbod hikihuh.
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
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25.1.2. Nbrbntéristiquds cds hbtéribux
Lds nbrbntéristiquds cds hbtéribux sfkt lds suivbktds = j n` 74 Gétfk N74/>5 8; j nc 2:,:? Hpb 2,4 n
j nth
7/ >
5.>5 j n`
7/>
5 .>5 74
j y`
Bnidr ^355 = j
yc
s
355 2,24
7.4: Hp Hpb b
>3?.1> Hpb
25.1.7. Nblnul cd Hgtu
Cbks uk 2dr tdhps, il kfus jbut cétdrhikdr ld hfhdkt qud pdux équiligrdr lb tbgld sduld = a j H gtu gdjj a j c . j nc
7
Fk b cfkn =
5,25 5,14 5,25 5,34 2:,:? 5,4:? HK .h 7
H gtu
Dk nfhpbrbkt Hgtu dt ld hfhdkt H Dc, fk pdut céjikir si lb tbgld dst dktiárdhdkt nfhprihéd. Cbks kftrd dt nbs, kfusjbut bvfks H Dcnblnul 8 5.:>5 ; Hgtu lb tbgld dst cfkn dktiárdhdkt nfhprihéd, il kfus jbird uk dk HK.h nfksicérbkt ukd8; sdntifk dk S.
25.1.>. Nblnul cds brhbturds lfkoitucikblds
25.1.>.2. Dquiligrd cd lb sdntifk 2 - hdhgrurd sduld sduld Kfus bllfks cbks uk 2dr tdhps cétdrhikdr lb kéndssité cd hdttrd dk plbnd cds bnidrs nfhprihés = a j Hfhdkt rdpris pbr lds bilds cd lb tbgld = H Dc 7 (gdjj gw )a j J nc c 7
H Dc 7 (5,14 5,74).5,25.2: ,:? 5,34
f
H Dc
Hfhdkt récuit cd lb hdhgrurd =
f
nu
5,:>5 5,355
nu
5,74.5,34·.2:,:?
5,25
5,355 HK .h
7
H Dc 7
gwc · J nc
5,7?7
Cbks ld nbs c’ukd nlbssd c’dxpfsitifk QC, fk cétdrhikd ld hfhdkt récuit lihitd å pbrtir cds jfrhulds cu nabpitrd 9 - §9.:.3, dk nfksicérbkt ukd lfi cd nfhpfrtdhdkt cd l’bnidr å pblidr afrizfktbl dt ukd kubknd c’bnidr ^355G.
Fk b cfkn =
lun
j n` (3.:9 2.?5 ) j n` (249.95 ?:.75 )
H Dc
5.:>5
H sdr
5.334
2.37
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
lun
21
74 (3.:9 2.?5 2.37) 74 (249.95 ?:.75 2.37)
Cbks kftrd nbs, fk b
nu lun ,
5.7>5
il kfus jbut cfkn hdttrd dk plbnd cds bnidrs nfhprihés.
Lb sdntifk jintivd 2 cfit ítrd cihdksifkkéd pfur rdprdkcrd ld hfhdkt récuit lihitd = H 5.34· 2:.:? 5.293 HK .h g c · J 5.7>5 5.74
Dc 2
lu
z n
B2
lun
w
nc
2,74 2 (2 7 lun )
2, 74 2 (2 7 5.7>5
2 5.3 5.>>2 5,3 ul ) 5.34 c (2
H Dc 2 z n J yc
5.>>2
5. >95h
5.293 23.>5nh· 5.>95 >3?.1>
25.1.>.7. Dquiligrd cd lb sdntifk 7 - Bilds cd lb tbgld Lb sdntifk 7 cfit rdprdkcrd ld hfhdkt H Dc 7 qud kfus bvfks nblnulé prénécdhhdkt =
H Dc 7
B7
5,355 HK .h
H Dc 7 5.355 71.?4nh· 5.25 a j c J yc 5.34 .>3?.1>
7
7
nfhprihés 25.1.>.>. Dquiligrd cd lb sdntifk > - Bnidrs nfhprihés Lb sdntifk > cfit équiligrdr ld hfhdkt rdstbkt, sfit H Dc > H Dc H Dc 2
H Dc >
5.:>5
5.293 5.355
H Dc 7 =
5.5>: HK .h
B pbrtir cd nd hfhdkt, fk cihdksifkkd ukd sdntifk c’bnidrs nfhprihés nfhhd kfus l’bv fks vu cbks
ld nbs cds sdntifks rdntbkoulbirds = H
B'
Dc >
(c
c ' ) sn
Fk cétdrhikd sn bvdn lb jfrhuld cds tribkolds sdhglbglds = >.4 >,4 sn 5.>>2 5.34 5.5> 5.557?9 ( c c ' ) l 2555 5.>>2 5.34 2555 l c
Ufur uk bnidr ^355 8;
Ublidr afrizfktbl 8;
yc
sn
yc 5.552?>9 8; sn
j yc
Hpb b >3?.1> Hp
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NKBH NNZ553 „ Dléhdkts cd Gétfk Brhé
Nd qui kfus cfkkd= B'
H Dc >
(c c ' ) sn
29
5.5>:
5.34
5.5> >3?.1>
7.3:nh· .
Lb sdntifk c’bnidrs tdkcus qui équiligrd lds bnidrs nfhprihés vbut =
B>
B'
sn
j yc
7.3:
>3?.1>
>3?.1>
7.3:nh·
25.1.>.3. ^dntifks tftblds å hdttrd dk Şuvrd. Lds sdntifks tftblds å hdttrd dk Şuvrd sfkt cfkn = Bnidrs tdkcus = B8 B2 + B7 + B>8 23.>5 + 71.?4 + 7.3:8 34.42 nh· Bnidrs nfhprihés= B’8 7.3: nh· 7.3: nh·
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