pro jet de fin d' etudes · 2011-01-20 · dimensionnement des parois extérieures...

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RËPUBLIQUE DU SËNËGAL

ÉCOLE POLVTECHNIQUE DE THIÈS

PRO JET DE FIN D' ET UDES

EN VUE DE L'OBTENTION DU DlPLÔfllE D'INGÉNIEUR DE CONCEPTION

DATE Juin 1986

ANALYSE ET DIMENSIONNEMENT DU MARCHE DE POISSONS

DE SOUBEDIOUME-------------------------------------------------

AUTEUR MAR THIAM

DIRECTEUR Mr Moustapha NDIAYE, Ing. M.Sc.

CO-DIRECTEUR Mr Alain DEBERDT, Ing ..

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LISTE DES FIGURES PAGES

Ferraillage de semelle sous le voile •••••••••••••••••••••••••••• 45

Ferraillage du voile des parois extérieures du sous-sol......... 43

Schéma des poutres 4, 5, 10, 11) ••••• ••• •••••• •••• •••••••••••••• 25

Schéma des poutres 14, 13 •• •••• •••••••••• ••••••••• •••• •••• ••• ••• 26

Schéma de la Console du plancher ht Rez de chaussée ••••••••••••• 29

Schéma de la Console du plancher ht du le étage ••••• •••••••••••• 30

Ferraillage de la semelle de'. poteau 1 ••••• •••••• ••••••••• ••••••• 37

Schéma de la Nervure Nl 21

......dans la cour de service

Vis ••••••••••••••••••••••••••••

Ferraillage et Onf f r age d'un volet de l'escalier central ••••••••

Ferraillage des marches d'escalier à Vis ••••••••••••••••••••••••

Schéma des poutres 3, 6, 9, 12 ••••••••••••••••••••••••••••••••••

Ferraillage du mur de soutenement

Coffrage de s marche s d 'escal ier à

Schéma de s poutre s 1, 2, 8, 7 ••••••••••••••••••••••••••••••••••

Figure 1

Figure 2

Figure 3

Figure q

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure la

Figure 11

Figure 12

Figure 13

Figure 14

LISTE DES TABLEAUX

Tableaux des semelles isolées P 38

Composition

T A BLE f)ES MAT 1ER E' S

Rerner ci ernent s •••••••••••••••••••••••••••••••••••••••••• i

Sommaire ••••••••••••••••••••••••••••••••••••••••••••••• ~ii

Liste des figures •••••••••••••••••••••••••••••••••••••• iii

Table des matières ••••••••••••••••••••••••••••••••••••• iv

11. ELEMENTS INTRODUCTIFS

Introduction ••••••••••••••••••••••••••••••••••••••••••• 1

Options architecturales et fonctionnelles •••••••••••••• 3

II. ANALYSE STRUCIURAl.E::::l

2.1 Structure choisie •••••••••••••••••••••••••••••••••• 5

2.2 Ba se de cal cul ...........' . 6

2.3 Calcul des charges appliquees sur les ouvrages ••••• 8

2.4 Analyse structurale proprement dit ••••••••••••••••• " 14

III. ~ETHODE DE DETERMINATION DES= EFFORTS

3.1 Description du programme •••••••••••••••••••••••••••

3.2 Programme du calcul des efforts ••••••••••••••••••••

3.3 Exemple de fichier d'entrée de données •••••••••••••

3.4 Exemple de fichier de sortie de résultats ••••••••••

:IV. DIMENSIONNEMENT DE =DI:=F=F=:E=RENTS gUVRA~

4.1) Dimensionnernent des poutrelles et poutres ••••••••• 1'8

4.2) Dimensionnement de la dalle pleine ••• ••••••••••••• 27

T A BLE DES MAT l E RES

Dimensionnement des planchers en Console •••••••••••••

Dimensionnement des poteaux ••••••••••••••••••••••••••

Dimensionnement des semelles •••••••••••••••••••••••••

Dimensionnement des parois extérieures du,sous,sol .•••

Dimensionnement de la Semelle filante sous voile •••••

Dimensionnement des murs de soutement dans

la cour de service •••••••••••••••••••••••••••••••••••

~.9) Dimensionnement des escaliers ••••••••••••••••••••••••

4.9.1 Escalier à vis reliant le sous-sol au

rez "de chauss4e •••••••••••••••••••••••••••••••••••••• 51

4.9.2 Escaliers sans limon reliant le R.C au le étage •••••• 54

4.10) Dimensionnement du dallage ••••••••••••••••••••••••••• 56

V CONCLUSION ET RECOMMANDATIONS •••••••••••••••••• 58.

Annexes

1. Calcul des charges ••••••••••••••••••••••••••••••• 60

2. Tableaux des poutres dimensionnées ••••••••••••••• 78

3. Tableaux des pteaux dimensionnées •••••••••••••••• 92

4. Vérification de sections de poutre ••••••••••••••• 97

5. Calcul de dallage ••••••••••••••• •••••••••••••••• 100

TABLE DES MATIERES (suite)

B l B L l ~ G R A PHI E 102

PLA N S DE COFFRAGE

1. du plancher - haut sous - sol

2. du plancher - haut Rez de chaussée

3. du plancher - haut le étage

4. de la toiture

5. de la Fondation

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2-:~) CALcUL 1)(5 CHARGES APPLIQUEECô

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Q~ ·A,O~:3,lJ .Q = 3,o~\IlIl'Y\

Q::3,o!c:NI"",

~) t0ù.hv:> 11 4 - "'0

~ ~e-vJ:,e"G

G ~ 21,5 .lk~\ "'"

Q = 5, 0 ~N 1W1

A) f~ \- eGU.JIX .A 1 :; 1 4 1 6, 1-[ '3, .A D,A 3

,SlJ.JLf(1.,~ Jru'~ul:~ tCVl- r..ttoOA.l

s- 3.~'3,,-J,o;b ~,3.",tl_

.cl~ ~(1N\.~

cLoJL. = )0, <+ ~N

~ 1. -t-~ ~ ~ ~cl J ~ ((\ ',ourC'"nO fOU) '-cU ~~

,.dif~~ J t"'""'- ~ t'~~ ...e f:: O,1-.e.,.

Le~k~~~ (Y\L~e:uJtU) Amk 'UM-e tU~ A ,

AI1\~ =. ~,Aero

"'Mo ~ O,~Sfc.1..3 B T~2. A0'6

.d-.'....:;. Ir" ~-fc: 4cro - :, 4 ~ M Po.- - -1:, Â,AS

d' - ~AA - ~. s s e., &'2- • ~) e,, """ - +"t b AO'tl

~..u.~

o. s s fc. 2.3+

Ob 'IlTll

o,S 5 feu, . 0.8s", '2.0 - A~,t+ t-tP,,-= -ô'l:, ..-\, S"

N. AA -=. ~,~5G ·d,5"Q. -::. .-\,:'5l\A4,~ + /{,5")\ 4,0 ::.- l.S,?> ttJ

~ ~ !(. S 1 ~ ,.. 10" ~ 10 4 -:: Âq,o CNy,t..

1419.~o{;

9 : 3,1IS"y. 'i,Q45" ~L

.. 5,.2. 'li 1-, l o

(,.:. 41,1 ~N

~4~,S1-"0

-14, 9

€;J", cR.n...,.x ~"'l.<>)C...2.0;. 1~ Tl'; vm 'L ~ 1

~..d..L J)t~ 0.2-5 .... 0.1.· -\1:u:,,,, 25 ---'Jo l = - À.G:}~ .... o f'(1-"1.-

~~ ..d-t ~~ .z.o~ ~ 0 --. l = o.3'<o.Z.= t-,o • .(b m~

~ :: o.z.~o.l.;

"\'1.--

t.. 4- ANALy5 l 51 RUc.,.U RA l é PRO PRE MENT 1);1

1)~ {cuen l}~ aiR- 1 lu ;.)()f1ùA1~ kont ,ealeM1eu .0>'1 iUlifi

_k,WYJ: ~ b ll-kuc1wœ tU/t1, mwoLe& &f#tL~ el .&me-aùU- . .La~,cJ.,l'/I'YVMvolt ,d,(1;YW -Et -CM AJ1i ~ r- acl.& /oLe.la.- ~aMCl ,oild mcdf/U'

('(\l~ fuïCA ,~eke;muvt ~~.~ "cl l,a~VL rwru ~~~~

_-fn'~ : '

- W~~Ul- 1M ",vhvrnM 4tJl,~~ . di~~ ÛfY1MJ.JJ..

ffiï.~d.iA '~'~~ ,ClUJ,~~ eX ~~~ ~ ~~

.~ -eX ,ci. .Q,'~ ~ ~cJ;euA.

- S~ ~.J\.E,-~ /0- /dUJ mvn:A.t1eA /oU e.-a.1'wJA tiwd~- so-J:. ,dL ~acl8ll. .s: tWnl ~4M'~~~~ t.Mn- {V"Y\..{)ot&

;œ,du-J; J ~dM ,,~.~ ~ Q..e. ..ca..o ,ck teCL-'O~~~

~ ~·wJlA.·tWA ~.

~ ~'~~ ~ ktte. ~.~ f1\.t.~ 1a.-1l ~~ ~/OJY\.~ ~etuAo.tt ,~a1e.'/ .c f~ ~~. ~ (~ ~~rJi'

&~~ ,du kJC,itÙYYU t 4 IJ-l- /l..ttfrrwâ.cvr'I1 ,C:ieA ~ckvLta /~&l.

Ce.vt. ,~e .-<Ï ~.~ ~ t..-ov.rQ,~,~c,~ r.Qj:~~ ~ ~~'1,i /cl (/1,'dia1t.a~ €d.fL /.UWtTcvvrJ-:

- ~.~ ~/UYw1'~ ~ A-e.e& -ao-cc &M~~/dJ ,cit.aA-cy-m~.

--, & jwC-tawH /d.e ~~ ~ ,~.~ /~ ,olu/~

~ ~ Ru> ~t~~ ~e.ok·~ ),~. ~ J"::"~ <rr--M.·WM~~~ /ClM- /YYU~'w..- ,oU~ k'}M-~.

~~~ ,~ MN..t. cL..vu.o ,clt ~. f~ (.)MNV- c:.vrch

"4- \"0 ~ ~ <u..l lM.•h~.•_~ b'~ ~.

- -u,'b-V\.

1- ~,"""'" oili~~ ""'" te0~~ ~ k /~~ -dtt.J

. - ~ _MAo.. fcdL~~~ & 1f~ ~unkJ ~ iw 1'cJ,.~

~O-~ ~+ ~& Q.e.o/~ ~ .20.-~ .

_._-_._-----_..--_.-._-----_._-_._---

A5 ':' . .:,-'

._------

___ CHAR 3. _

METHODEDE

DETERMINATIO N

DES EfFOR15

·_--------_. ----.

~ 1~ /Js- /~oy-<'--cSv- (~ CR.~~ yt /CA:Tn.5-'-"- .<ietM<l

leu (cyv~~ ~ ton-~ &aMe- .1'(~u-~. CPa.N\o 1t .cccob« ,tA.; Q

~ ,~ ,~ ~~ Jei-c-ûf:caÂ-r ,au {l\M/ec;JJJ..- (O\M. eo1cu14.t eRAA-ey

~~ ÀQ tkt~ .k~ ~~ r (0J.lt.A-'QWt- <.l ~JluAo~

/ch. ~ fu ek.~ ,~ ~'~~ .J.''1lJYU- ~dWu ~ (ClK'~.-S

~~.e~~ -cU /~cuk ~ ""~ ~ /~Jro-.~ ~~~

./~ -€ew-/~~ mm neo~ L-R'!hu) .

l.~~ .dM.- tw~mL ~~ -€Hl. /~ . ci (;U.e(" !Wr'l- f citur cL./ 1 / /

""~a& ~ 1w ~~<:tlfd ~U.<l /dM 1'\oeu.ol> l ,du>~~ e..t ,.;Lu rma1w.·4W/<1 1 •

~ ,cL:~e-o. ru~ ,aM~ , ~~4 lU' 4-ceJi,,~ ~ lI.ùl'1- ~.~ de

~cJ;, /'fU-l ()'l<ll.YJ (ot-OT"l-W /~ {au r-ut:<fcJ.lc. ~.; (Y"\1TI.lO~ 1 ,...c:Lc.vvI,o .e caCÛLl.

-c!l , ce l:t-~aiQ " I-ft.~ ~ le ,dur,.~~twYl.~ ,dl m.t'O -P"t~ et~.

Ce. F~~ MA-O- Jr-~ /OJ.X-<!- (\).XV ~ok,dL -y.~ Id'~

~ ,clt /y:c.2u;o/:Il /ck~ .

l......c __.:._.. __ ._. __ .

print 11do 100 i=l,nodread *,k,tx<k) ,ty<k)

100 print 12,k,tx<k),ty<k)c

do 90 i=l,nodiresx<i)=Oiresy<i)::O

90 iresr<i)=Oc

print 13do 110 i=l,nnrread *,k,iresK<k) ,iresy<k) ,iresr<k)

110 print 14,k,iresx<k) ,iresy<k) ,iresr<k)cc

DE S ..(:J (,9 RIS, .<"..... . .

CA Le LI L

COORDONNEES DES NOEUDS

RESTREINTES AUX NOEUDS

calcul de l'adresse des diagonales

DONNEES ET CONNECTIVITE DES ELEMENTS

DONNEES CENERALES

print *,' ***************************************'print * **FICHIER DE LECTURE DES DONNEES ? **'print *,' ***************************************!read 99 ,stdonprint *,' ***************************************'print *,' **FICHIER DE LECTURE DES RESULTATS? **'print *,' ***************************************'read 99 ,stratopen <unit=5,file~stdon)

open <unit=6,file=strat)rewind (5)rewind (6)

print 2read *,nel,nod,ndl,nnr,icc,eprint 10,nel,nod,nnr,ic.c,enk=2*ndlnn~ndl*nod

nx=nn+l

c ***********************************************

c ***********************************************c

implicit real*8<a-h,o-z)character*6 stdon stratdimension tx(30),ty<30) ,iresx(30) ,iresy<30.),iresr<30) ,ih(90),

1 j 1 <30 ) , j 2 <30 ) , as <30 ) , a i <30 ) , a 1 <30 ) , i ad <6 ) , ma x a < 1 00 ) , Cl r k <700 ) ,2 a.ma t <6 , 6 ) , w <30 ) , f c <3 0 , 3 , 2 ) , f 1 <6 ) , f 9 <6 ) , v c <9 0 ) , n cc <3 0 ) , r x <3 0 ) ,3ry(30) ,r1;(30)

print 15do 120 i=l,nelread *,k,jl<k),j2<k),as<k),ai<k)al<k)=dsqrt«tx<j2<k»-tx<jl<k»)**2+<ty<j2<k) )-ty<jl<k»)**2)

120 print 16,k,jl<1c),j20:),as<k),ai<k),al<k)cc

123456

1011121314151617181920212223242526272n293031323334353637383940414243444546474849505 15253545556575859606162636465

do 190 i=l,nel

INTRODUCTION DES RESTREINTES

RIGIDITE DES ELEMENTS ET ASSEMBLAGE

icc210 ii = 1

INTRODUCTION DES CHARGES

do 130 i::::l,nnih(i)=O

do 150 i=l,nkif(iad(i>.lt.mi) m i e La d Ci )do 160 i=l,nk"ii=iad(i>iht:::ii-miihi i=ih( i i )if(iht.gt.ihii> ih(ii):::ihtcontinuecontinuema x a ( 1 ) :: 1

maxa(2)=2do 170 i=2,nnma xa ( i + 1) =ma xa ( i ) + i h ( i ) + 1nwk=maxa(nn+l)-lprint *,'nombre d"equations =',nnp r in t 11:, 1 es p ace r e qui 5 pou r gr k =', nwk

do 140 k=l,nelii1=il(k)j j 2 = j 2 ( k )calI adres(iil,ji2,ndl,nk,iad)mi=iad(l)

dol 80 i = 1 , nwkgrk(i)::O.dO

calI tripld (grk,maxa,nn,nwk",nx)

do 200 i=l,nodif(iresx(i) .eq. 1) grk(maxa(3*i-2»=grk(maxa(3*i-2»+1.d20if(iresy(i) .eq.l) grk(maxa(3*i-l»=grk(maxa(3*i-l)~+1.d20if(iresr(i) .eq.l) grk"(maxa(3*i »=grk"(maxa(3*i ) )+1.d20continue

j j 1 = j 1 ( i )

ii2=i2(i)asi=as(i)ai i =a i ( i )a 1 i = ,-,.1 ( i )cs=(tx(ji2)-tx(iil» lali5 n= ( t Y ( j j 2 ) - t Y ( j j 1 ) ) 1 a 1 icalI adres(iil,jj2,ndl,nk, iad)calI rigel(amat,nk",e,asi,aii,ali,cs,sn)calI assemb(iad,ndl,nk,amat,grk,nwk,maxa,nx,nn)continue

do 220 i=l,nelw(i)=O.dOn c c c t j e ü i d ü

do 220 i=l,3do 220 k:::l,2fc(i,j,k)=O.dOdo 230 i :: 1 , nn

160140

666768697071727374757677787980818283848586878889909 19293949596979899

100101102103104105106107108109110Il 1112113114115116117118119120121122123124125126127128129130131

VECTEUR CHARGE

read 11 nelcuif (nelcu .ne.O) print 27if (nelcu .ne. 0) print 28 nelcuif (nelcu .ne. 0) print 29do 250 i:= 1 nelcuread 11 k, w(k)if(nelcu.ne.O) print 12 k, w(lc)continue

print 1print 33,iiread 1I,nnchif(nnch.gt.O) print 23if(n~ch.gt .0) print 25 ,nnchif(nnch.gt.O) print 24do 240 i = 1 nnchread 11 k,vc(lc 1lndl-2) ,vc(lc 1lndl-l) ,vc(k 1lndl)

p r in t 26, k, v c ( k 11 nd 1 - 2) , v c ( k 11 nd 1 - 1 ) , v c ( k 11 nd 1 )

continue

read 11 nelccif (nelcc .ne. 0) print 60 nelccdo 260 i:=l ,nelccread 11 k,ncc(k)ncclc=ncc(lc)do 270 j = 1 , ncckread 11 (fc(k,j,1),1::l,2)if(nelcc.ne.O) print 30 ,k, i, (fc(k,i, 1) ,1=1,2)continuecontinue

localeglobale

:vecteur charge equiv.:vecteur charge equiv

do 300;.- 1,ndliad(j) _ nd1 1l(jjl - 1) + j

iad(j+ndl) = nd1 1l(jj2 - 1) + j

SOLUTION DES EQUATIONS - DEPLACEMENTS

v c ( i )

print 38do 320 i=l,nodprint 35 , i,vc(3 11i-2) ,vc(3 11i-l) ,vc(3 11i)

continue

calI sol(grlc,vc,maxa,nn,nwlc,nx)

do 310 j:= 1 , niev c t iad( j) )=vc( iad( j) )-fl]( j)continue

do 290 i - 1 nela 1 i = a 1 ( i )j j 1 j 1 ( i )ij2:= j2(i)cs = (t x ( j j 2) - t x ( ; ; 1 » 1 al isn := (ty(jj2)-ty(jil» 1 aliwi = wei)calI equiv(fg,fl,nk,wi,fc,cs,sn,i,ali)

270260

cccccc

13213313413513613713813914014114214314414514614714814915015115215315415515615715815916016 1162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197~-. \

1992002012022032042052062072082092102 Il212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263

350340c

c330ccc

CALCUL DES EFFORTS INTERNR~------

print 1print 40

do 330 i=t,nel

j j 1 = j 1 Ci)j j 2 =j 2 Ci)asi=asCi)ai i =~ i ( i )al i =a l ( i )wi=w( i)ncci=ncc(i)cs=(txCjj2)-tx(jjl» talisn= ( t Y C j j 2) - t Y ( j j 1 ) ) ta licalI adresCjjl,jj2,ndl,nk,iad)ca Il ri gel (ama t, n k , e, as i , a i i , a li, cs, sn)calI equivC fg, fI ,nlc,wi, fc,cs,sn, i ,ali)

do 340 k=l,nlcfl(k)=fg(k)fg(k)=O.dOdo 350 j=l,nkfg(Ic)=fg(Ic')+amat(lc,j)*vc(iad(j»fgCk)=fg(k)+fl(lc)

fICl)= fg(1)*cs+fg(2)*snfl(2)=-fg(1)*sn+fg(2)*csf l ( 3 ) = f 9 ( 3 )fl(4)= fg(4)*cs+fg(5)*snfl(5)=-fg(4)*sn+fg(5)*csfl(6)= fg(6)

if(mod(i,2) .eq.O.and.i .gt.2) print 1ifCmod(i ,2) .eq.O.and.i .gt.2) print 40print 61print 17print 35,i,(fl(j),j=1,3)print 18print 35,i,(fl(j),j=4,6)xnl=fl(l)xv 1 =fI (2)xml=fl(3)calI forc(xnl,xvl,xml,wi,fc,ali,i)

continue

CALCUL DES REACTIONS

print 39do 360 i=l,nod

if(iresx(i) .eq.l) go to 144go to 143rx(i)=-vc(3*i-2)*1.d20print 50 , i,rx(i)if(iresy(i) .eq.l) go to 146go to 145ry(i)=-vc(3*i-l)*1.d20print 51 ,i,ry(i)if(iresr(i) .eq.l) go to 147go to 148rz(i)=-vc(3*i )*1.d20print 52 i,rz(i)continue

FORMATS D'ECRITURE

264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329

- --II ITTr e s-i( r) . e q . 1 ) . 0 r . ( ire s y ( i ) . e q . l ) . 0 r . { 1 r e s r \ 1 1 . e q . 1 " 'PO'51 print 4

360 continue210 continueccc1 format('I'2 format(' ',tl0,'DONNEES GENERALES'I' t8,21('*'»4 format(f)10 format(' ',tl0,'nombre d"elements --------:::',t38,i51

l ',tl0,'nombre de noeuds --------':::',t38,i512 " tl0, 'nombre de noeuds restreints:::', t38, i51

3 ',tl0,'nombre de cas de chargement=:',t38,i513 ' , t 1 0 , 'mo d u 1 e d" e 1 as tic i te - - - - - -:::,' , t 3 8 , d 1 0 . 3 )

Il format(II' ',t8,22('*')/' ',tl0,'DONNEES DES NOEUDS'/' ',t81,22( '*' )11' ',t8, 'noeud' ,7K, 'coordx' ,10x, 'coordy')

12 format(' ',5K,i5,2(5x,fl0.3»13 format(III' ',t8,25('*')/tl0,'RESTREINTES AUX NOEUDS'I'

1 t8,25( '*')1 t16, 'noeud' ,12K,' iresK' ,12K,' iresy' ,12x,' iresr'14 format(' ',4(i2K,i5»15 format<lll' ',t8,24('*')/tl0,'DONNEES DES ELEMENTS'/'

1 t8,24('*' )11' ',t8, 'elmt' ,tI8, 'noeudl' ,t28, 'noeud2',2 t42, 'aire' ,t57,' inertie' ,t74,' longueur')

16 forma t (' ',3 ( 5 x, i 5) ,3 ( 7 x, dl 0 . 3) )17 format(/" ,t8, 'elmt' ,t23, 'ng' ,t40, 'vg' ,t57, 'mg'18 format(' t23, 'nd' ,t40, 'vd' ,t57, 'md')23 format(/" ,t20,22( '*'),' ',t22, 'charges aux noeuds',/' ',t20,

122('*')1)

24 format(" ,t8, 'noeud' ,t26,' fx' ,t46,' fy' ,t64, 'moment'25 format(' ',t8,'nombre de noeuds charges :::',i5/)

26 format(" ,5x,i5,3(10x,dl0.3»27 format(/" ,t20, '*lllcharge en travee*lll' l' ',t20,20( '*' )/)28 format(" ,tl0, 'nombre d' 'elements avec charge uniforme :::' ,i5/)

29 format(" ,tl0, 'elmt' ,t22, 'W')30 forma t (' " t 1 0 , i 3 , i 7 ,5 x, 2 d 1 0 . 3 )33 forma t (' " t 13 , 25 ( , 'IIr ' ) 1 t 10, 'CAS DE CHARGEMENT NO. ' , t 31 , i 5 /

It9,25(''IIr'»35 format(" ,5x,i5,6(5x,dI2.4»36 format<III", tl0, 'nombre d' 'equations' ,t31, i5/)

37 format(' ',tl0,'espace requis par grk',t31,i5/)38 format(/" ,t8,15(''IIr' )/' ',tl0, 'DEPLACEMENTS'/' ',t8,15(''IIr')1

II' • ,tB, 'noeud' ,t24, 'dx' ,t40, 'dy' ,t56, 'rot.')39 format(/,' ',tI2,13(''IIr')/' ',tI4,'REACTIONS'I' ',tI2,13('lll')/)40 format(/" ,t8,19('lll' )/' ',tl0, 'EFFORTS INTERNES' 1 ',t8,19( ''IIr'41 format(/' ',5x,i5,6(5x,d12.4»50 format(" ,tl0, 'noeud' ,tI6,i2,tI9, 'rx:::' ,fI2.4)51 format(" ,tl0, 'noeud' ,t16,i2,tI9, 'ry:::' ,fI2.4)52 format(" ,tl0, 'noeud' ,tI6,i2,tI9, 'rz:::' ,fI2.4)59 format(" ,i5)60 format</" ,tl0, 'nombre d"elements avec charges c o n c a n t r e e s e ' ,i5

111' ',tl0,'elmt',3x,'no. ch.',5x,'fy',8x,' x')61 format<II' ',t20,''IIr'llren bouts de membrure'llr'llr'/' ',t20,24(''IIr'»

,9'9 f o r ma t t a ë )

cclose(unit:::5)close(unit=6)

cstopend

csubroutine adres(jjl,jj2,ndl,n,iad)

cdimension iad(n)do 1 i:::l,ndliad(i):::ndl'llr(jjl-1)+i

331332333 c334335 c336337338 c339340341 1342 c343344345346347348 c349350351352353354 c355356357358359360361362363364365366367368369370371372373374375376 c377378379 2380381382 c383384 c385386387 c3883893903913923J13394395 2

lad( l+ndl l=ndl"( J J~-ll+lreturnend

subroutine rigel(sm,n,e,asi,aii,ali,cs,sn)

implicit real*8(a-h,0-z)dimension sm(n,n)

do 1 i=l,ndo 1 j=l,nsm(i,'j)=O.dO

cax=e*asi/alial=4.dO*e*aii/alia2=2.dO*e*aii/alia3=6.dO*e*aii/(ali**2)a4=12.dO*e*aii/(ali**3)

dl=cox*(cs**2)+a4*(sn**2)d2=(cax-a4)*cs*snd3=cax*(sn**2)+a4*(cs**2)d4=-a3*snd5:::a3*cs

sm ( 4 , 1 ) = - dlsm ( 1 , 1 ) = dlsm(4,4)= dlsm ( 2 , 1 ) = d 2sm(4,2)=-d2sm(5,l)=-d2sm(5,4)= d2sm(2,2)= d3sm(5,2)=-d3sm(5,5)= d3sm(3,l)= d4sm(4,3)=-d4sm ( 6 , 1 ) = d 4sm(6,4)=-d4sm(3,2)= d5sm(5,3)=-d5sm(6,2)= d5sm(6,5)=-d5sm(3,3)::: alsm(6,6)= alsm(6,3)= a2

do 2 i==l,ndo 2 j=i,nsm ( i , j ) == sm ( j , i )returnend

subroutine assemb(iad,ndl,nk,ptK,grK,nwK,maxa,nx,nn)

implicit real*8(a-h,o-z)dimension iad(nk) ,ptk(nk,nk) ,grk(nwk) ,maxa(nx)

do 3 i==l,nkii=iad(i)do 2 j=l,nkjj=iad(j)if(jj.lt.ii) go to 2k=maxa(jj)+jj-iigrk(k)=grk(k)+ptk(i,'j)continue

subroutine tripld (a,maxa,nn,nwK,nnm)

implicit real*8(a-h,o-z)dimension a(nwk),maxa(nnm)

continuereturnend

localglobal

syts.syts.

:charges suiv.:charges suiv.

CHARGES EQUIVALENTES AUX NOEUDSSYSTEME GLOBAL

f 1 ( 1 ) = O.dOf 1 ( 2 ) _. -wc * cl / 2.dOf 1 ( 3 ) = -wc * cl**2 / 12 . dOf 1 ( 4 ) - O.dOf 1 ( 5 ) = -wc * cl / 2.dOf 1 ( 6 ) = -f1(3)

do 1 j = 1 3p = fc(k,j,l)

implicit real*8(a-h,o-z)dimension fl(6) ,fg(6),fc(30,3,2)

do 140 n=l,nnkn=maxa(n)kl:::kn+lku=maxa(n+l)-lkh=ku-lclif(kh) 110,90,50k=n-kh

-, ic=Oklt=kudo 80 j=l,khic=ic+lklt=klt-lki=maxa(k)nd=maxa(k+l)-ki-lif(nd) 80,80,60kk=min(ic,nd)c=O.dOdo 70 l=l,kkc=c+a(ki+I)*a(klt+l)a(kIU=a(klt)-ck=k+lk=nb=O.dOdo 100 kk=kl,kuk=k-lki=maxa(k)c=a(kk)/a(ki)b=b+c*a(kk)a(kk)=ca t k n r e aï k n ï c-b

if(a(kn» 120,120,140print 1000,nstopf o r ma t t 'matrice singuliere rangee', is :continuereturnendsu br 0 u tin e e qui v (f g , fi, n k , wc , f c , cs, sn, Il: , cl)

396 3397398399 c400401 c402403404 c40540640740840941041 1 50412413414415416417418419420 60421422423 70424425 80426 90427428429430431432433 100434435 110436 120437438 1000439 140440441442443 . c444 c445 c446 c447 c448 c449 c450451452 c453454455456457458459 c460461

substitution a rebours

print 56

subroutine sol(a,v,maxa,nn,nwk,nnm)

subroutine forc (xnl,xvl,xml,wi,fc,al"i,le)

P08- ek)**2

:matrice decomposee:vecteur chargement

a ( k )

eJe - t c l Je , ) , ~ } Cl

f 1 ( 2 ) - f 1 ( 2 ) - P 11 (l.dO + 2.dO * ek) * ( 1 . dOf 1 ( 3 ) - f 1 ( 3 ) - P * ek * cl * (l.dO - ek)**2f 1 ( 5 ) f 1 ( 5 ) - P * ek**2 * ( 3 . dO - 2.dO * ek)f 1 ( 6 ) - fI ( 6 ) + p * ek**2 * cl * ( 1 . dO - ek)

continue

f g ( 1 ) f 1 ( 1 ) * cs - f 1 ( 2 ) * snf 9 ( 2 ) = f 1 ( 1 ) * sn + f 1 ( 2 ) lie csfg(3) - f 1 ( 3 )f 9 ( 4 ) = f 1 ( 4 ) * cs - f 1 ( 5 ) * snf g (5 ) = f 1 ( 4 ) * sn + f 1 ( 5 ) * csf 9 ( 6 ) = f 1 ( 6 )

returnend

implicit real*8(a-h,o-z)dimension a t nwk ) ,maxa(nnm) ,v(nn)

RESOLUTION POUR LARGEUR DE BANDE VARIABLE

implicit real*8(a-h,o-z)dimension fc(30,3,2)

do 200 n = 1le = maxa(n)v(n) ::: v(n)n = nndo 230 1 = 2 , nnk 1 ::: ma x a ( n ) + 1ku ::: maxa(n + 1) - 1

do 180 n = 1 , nnk 1 = ma x a ( n ) + 1ku = maxa(n + 1) - 1kukl=ku-Ielif(leulel) 180, 160 160k = nc = O".dOdo 170 kk ::: kl leuk = le - 1c = c + a(kk) *" v(k)v t n ) ::: v t n ) - ccontinue

Ieukl=ku-klif(leulel) 230 210 210k = ndo 220 kk = kl kule = k - 1v(k) = v(k) - a(kk) * v(n)n = n - 1returnend

220230

46346446546646746846947047147247347447547647747847948048148248348448548648748848949049149249349449549649749849950050150250350450550650750850951051 1512513514515516517518519520521522523524525526527

529530531532533534535 c536537 c538539540 10541 c542543544545 11546 c547548549550551 c552 12553554555 c556 100557558559560561 20562 53563 56564565566

pl~~U.C10

p2=plp3=P2xl=fc<!<:,1,2)x2=fc<lc,2,2)x3=fc<!<:,3,2)x=O.dO

do 20 i=l,ll

if<x.gt.xl) go to 10go to 100continue

if<x.gt.x2.and.x2.gt.xl) go to 11pl=fc<k,l,l)go to 100continue

if<x.gt.x3.and.x3.gt.x2) go to 12pl=fc<k,l,l)p2"-:fc<!<:,2,l)go to 100

pl=fc<!<:,l,l)p2=fc<k,2,l)p3=fc<k,3,l)

an=-xnlav=-xvl-pl-p2-p3-wi*xam=-av*x-xml-wi*x**2/2.dO-pl*xl-p2*x2-p3*x3print 53,x,an,av,amx=x+.ldO*alicontinueformat<' ',5x,f7.2,3<5x, f12.3»format < / t20,' **aux 10-eme de portee**'

1/t20,24<'*')/tl0,' X',t26,'N',t43,'V',t60,'M')returnend

-------------------.....EXE'M PlE.J)E ~1C.UltR DE DONIfEElJI---------j .. 3)

.,'@ Li. 'l4 ç

~ li :. 3 3 -1.

..., o. ~. ,.;

-<. lt,'lljf ,J.'r

.3 lj. 'l4Ç O.

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0.0 c. D

(J. 0 4 I·Bd-'t

A e C-<l..ll

~ '0. -'B,o O.

.t O. - ~'" 1f.0 O.

4 O. - '3+.0 Q.

-.----- .... ---_...._..-----..---..---------1It~) 1),mens \ o-n'n em. e1\l des ~ou.t'l,eUtQ

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-to*- ~~~e-vJ: ~ et~

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~~~ ,tt~ ,olu~ .et~ -CW1 i!uut/~VYY1-&nt ~ fcÙt /uwva;rÛ 1!e~ rc1'Ll~ iOJYV(\ ea.e 'l.

~--------------------- __J

3"/1 .'., ..,.... ,E)( E M, EbE U. FleHl ER li R ~ 5 UL"~ i 5

\ l l r "

li::J(~ TRAVE.r 2, ,. z1-

7 Avr 09:35 1986 pte05 Page 2

*****************~*******

CAS DE CHARGEMENT NO.*************************

**charges aux noeuds************************

nombre de noeuds charges = 3

noeud1

fx.000d+00.000d+00.000d+00

**charge en travee**********************

-0.970d+02-0.234d+03-O.970d+02

moment,OOOd+OO.000d+00.000d+00

nombre d'elements avec charge uniforme - 2

elmt12

-37.000-37.000

DEPLACEMENTS*lt.*************

noeud12

dx-0.3056d-33-0.2518d-110.6164d-33

-0.3009d-33

dy-0.1657d-17-0.1908d+05-0.4625d-17-0.1657d-17

rot.-O,4718d+06

O,4080d-09-0.1965d-09

0.4718d+06

7 Avr 09:35 1986 pte05 Page 3

EFFORTS INTERNES*******************

**en bouts de membrure**************************

el m t1

ng0.3056d-13

nd-0.3056d-13

vg0.6871d+02

vd0.1143d+03

mg-0.1421d-13

md-0.1126d+03

**aUK 10-eme de portee**************************

X N V M

.00 0.000 -68.707 0.000

.49 0.000 -50.410 29.452

.99 0.000 -32.114 49.8561 . 48 0.000 -13.817 61.2121 . 98 0.000 4 . 479 ~2. q? 0.000 22.776 56.7822.97 o .000 41.072 40.9953.46 0.000 59.369 16.1613.96 0.000 77.665 -17.7214 .45 0.000 95.962

~4.95 0.000 114.258 -1 .627

ng-0.3056d-13

nd0.3056d-13

vg0.1143d+03

vd0.6871d+02

mg.0.1126d+03

md.0000d+00

x.00.49.99

1.481 . 982 . 472.973 .463.964 .454.95

**aUK 10-eme de portee**************************

N0.0000.0000.0000.000o . 0000.0000.0000.0000.0000.0000.000

**en bouts de membrure**

M-112.627-60.650-17.721

16.16140.99556.78263.52161.21249.85629.452

7 Avr 09:35 1986 pte05 Page 4

************************

ng0.4625d+03

nd-0.4625d+03

vg0.6111d-13

vd- a .61 1 1 d - 1 3

mg0.9914d-13

md0.1694d-14

**aUH 10-eme de portee**************************

X N V M.00 -462.517 a . aaa a . aaa.17 -462.517 0.000 0.000.33 -462.517 a . aaa 0.000.50 -462.517 a . aaa 0.000.66 -462.517 0.000 0.000.83 -462.517 a . aaa 0.000.99 -462.517 0.000 0.000

1 . 16 -462.517 a . aaa 0.0001.32 -462.517 0.000 0.0001.49 -462.517 0.000 0.0001.65 -462.517 0.000 0.000

*************REACTIONS

*************

(noeud 1 rH= 0.0000noeud 1 ry= 165.7065

noeud 3 rH= 0.0000noeud 3 ry= 462.5169

noeud 4 rH= 0.0000noeud 4 ry= 165.7065

7 Avr 09:35 1986· pte05 Page 5

*************************CAS DE CHARGEMENT NO. 2

*************************

**charge en travee**********************

elmt12

-14.800-14.800

lIr***lIr****lIr*****DEPLACEMENTS

*lIr**lIr**lIrllrllrllr*lIrllr*

noeud12

dx-0.1157d-33-0.9539d-12

0.2309d-33-0.1204d-33

dy-0.2746d-18-0.3772d+04-0.9145d-18-0.2746d-18

rot.-0.1876d+06

0.1638d-09-O. 8367d-l 0

0.1876d+06

7 Avr 09:35 1986 pte05 Page 6

*******************EFFORTS INTERNES

*******************

*~en bouts de membrure**************************

ng0.1157d-13

nd-0.1157d-13

vg0.2746d+02

vd0.4572d+02

mg.0000d+00

md-0.4515d+02

**aux 10~eme de portee**************************

X N V M

.00 0.000 -27.463 .000

.49 0.000 -20.145 11.771

.99 o . 000 -12.826 19.9231 . 48 0.000 -5.508 24.4561.98 0.000 1 . 8 1 1 25.3702.47 0.000 9 . 130 22.6652.97 0.000 16.448 16.3413 . 46 0.000 23.767 6.3983.96 0.000 31.085 -7.1644.45 o ; 000 ~ -24.3454.95 0.000 45.723 -45.146

ng-0.1157d-13

nd0.1157d-13

vg0.4572d+02

vd0.2746d+02

mg0.4515d+02

md.0000d+00

**aux 10-eme de portee**************************

X N V M

.00 o .000 -45.723 -45.146

.49 o .000 -38.404 -24.345

.99 o .000 -31.085 -7.1641 . 48 0.000 -23.767 6.3981.98 0.000 -16.448 1 6 . 3412.47 0.000 -9.130 22.6652.97 0.000 -1.811 25.3703 .46 0.000 5.508 24.4563.96 0.000 12.826 19.9234 . 45 o .000 20.145 11.7714 .95 o .000 27.463 o .000

7 Avr 09:35 1986 pte05 Page 7

************************

R. 0 ~

**auK 10-eme de portee**************************

x.00. 1 7.33.50.66.83.99

1 . 1 61.321.491.65

ng0.9145d+02

nd-0.91'l5d+02

-91.445-91.445-91.445-91.445-91.445-91.445-91.445-91.445-91.445-91.445-91.445

vg0.2315d-13

vd-0.2315d-13

v0.0000.0000.0000.0000.0000.000o .0000.0000.0000.000o . 000

mg0.3905d-13

md-0.8510d-15

M0.0000.0000.0000.0000.0000.000o .0000.0000.0000.0000.000

*************REACTIONS

*****lIt*******

·noeud 1 rx= 0.0000noeud 1 ry= 27.4635

noeud 3 rx= 0.0000noeud 3 ry= 91.4451

noeud 4 rK= 0.0000noeud· 4 ry= 27.4635

7 Avr 09:35 1986 pte05 Page 8

R. ,tO

CAS DE CHARGEMENT NO. 3*************************

**charge en travee**********************

e lm t1

'W-14.800

DEPLACEMENTS***************

noeud12

dx-0.6830d-19-0.5629d+03

0.1366d-18-0.6830d-19

dy-0.2975d-18-0.1886d+OQ-.0 . 457 Zd - 1 8

0.2286d":19

rot.-0.2338d+06

o . 935 4 d.+ 0 5-0.4626d+05-0.4620d+05

7 Avr 09:35 1986 pte05 Page 9

*******************EFFORTS INTERNES

*******************

ng0.6830d+Ol

nd-0.6830d+Ol

vg0.2975d+02

- v d0.4344d+02

mg-0.3908d-13

md-0.3384d+02

**aux 10-eme de portee**************************

X N V M.00 -6.830 -29.749 0.000.49 -6.830 -22.431 12.902.99 -6.830 -15.112 22.184

1 . 48 -6.830 -7.794 27.8471.98 -6.830 - . 475 29.8922 .47 -6.830 6.844 28.3172.97 -6.830 14.162 23 1243. 46 -6.830 21.481 14.3113.96 -6.830

~1.879

4.45 -6.830 -14.1724.95 -6.830 43.437 -33.842

**en bouts de membrure****.**********************

ng-0.6830d+Ol

nd0.6830d+Ol

0.2286d+Olvd

-0.2286d+Ol

mg0.1130d+02

md-0.1776d-14

**auK 10-eme de portee**************************

X N V M.00 6.830 -2.286 -11.304.49 6.830 -2.286 -10.173.99 6 . 830 -2.286 -9.043

1.48 6 .830 -2.286 -7.9131.98 6.830 -2.286 -6.7822 .47 6.830 -2.286 -5.6522.97 6.830 -2.286 -4.5223.46 6 .830 -2.286 -3.3913.96 6 . 830 -2.286 -2.2614 . 45 6.830 -2.286 -1.1304.95 6.830 -2.286 0.000

7 Avr 09:35 1986 pte05 Page 10

************************

ng0.4572d+02

nd-0.4572d+02

vgo .1366d+02

vd-0.1366d+02

mg0.2254d+02

md-0 ..3553d-14

**aux 10-eme de portee**************************

x.00. 17.33.50.66.83.99

1 . 1 61 . 321.491.65

N-45.723-45.723-45.723-45.723-45.723-45.723-45.723-45.723-45.723-45.723-45.723

-13.659-13.659-13.659-13.659-13.659-13.659-13.659-13.659-13.659-13.659-13.659

M-22.538-20.284-18.030-15.777-13.523-11.269-9.015-6.761-4.508-2.254

.,*************

REACTIONS*************

noeud 1 rH= 6.8297noeud 1 ry= 29.7494

noeud 3 rH= -13.6594noeud 3 ry= 45.7225

noeud 4 rH= 6.8297noeud 4 ry= -2.2859

· TIIMEN5IONNEMENT

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f' y 1f. ~ : Â 4"""l;> -tc~ ~ et~ ~.y~ 1-:; 1. r"'" ' ('Y"O~

i~~ -a, O\6~5 1c 'l8 ~C}+1.) -: 0lbg5'~ ZS.-t.<t'2. = Ç(2 .

'il '..;

. _ '2. ~

HI~ 1- 1-,0 . " ~ 0

/[0' Aoll'lo. ~4nb

• f\Ja.2wr". kt.,dL ,tck (A-rt: ~ b. S. 2-)

f~~&. ~ -~:

.e... ~~ ~...t f-t < O,Goa. ~

.Qo.. fe.Jl.... l"".t4 ~ .( O,S'-"'"1" 0,001.. 12.

- th' .Q.G\. '?" '\Xu e ,( s .......

~ t.. r-tu -e ~ 5 l'Y'

~~ ('<M)ToV-l .e:: -1-.0 l'YI 0,5+ =1-00

<"1000

b" 110 0 Wv\ 1 d -:c 'Z. '2 •J <-w- -CL .,........ d.n\.vu. As: 1.\ \ 05"""'1. J n'\-

. ---- ..-._-_._-_._---- --------.._-_..._---------'

4,.~.A) ~$1>&.du ~~ -Reud: Bc~ ~~ .e-R~e

~ CÀ ,Co"'tV:>~ (}.V\.o. ~ ,clc:JL~ e, ,a.--c:. MlLtl.:~ ~c:l' 'UNI. ,c..ml:"'U.r clr.>

.d.i l'Y\~ ~~~~ -R- ,(:.('/'~ ()UI\, ~ rtaM.~ ~J-L"

• d<Y'W1U/l

..e = ~ 5 0 Vw\ J ~ e E 40 t~ -i. f c 2 'à ~ 2.. S 11 P Q

• t'pCU''iPW"o.. ·ch ~ cl~ -R t ;; ~5 0 : -1~,s -7..g::- -lqc.v., -? d:: .-\3,S-~·.1~

•~~~ ~ p~ -e n cl ,Q-OT\. ('(VI -Q 0/1.~ ..eU b C1.oY1 dL '0 ~ .., 0-0 0YY\.

Colu,& ,~ ,cR.aJI..~

~'J..o Tfo pH'.

t r VI'I e, dt. f < ,,* e,

~o~ e, c~ ~ d""", c.h eA·~-<.

C; "=. 5", q S 'N rW\ 2

C(( CV\-~ r l/VYncU2kr1 f c . due . .au 1'0.".cU -~

G~:: .25,.. -it05")(.O,-i~ :: 3,6 -iNI""

Co.1c.J. .~ ~~

M (" '::. SI qS- 'f,. .1,S L -r- 3, 0 ..,. A.s =- .1\ 1, ?<. {N. m ! (Y"l

Na. '::. ?>,o~A,SL + -I,01<.AS:= l.j/r)-~N.mJMe

M.u"=' ....\A,':l.)<,,':>5 ~ i..(,T-r)'.A,S"'<. ~<It; ~N.""\m;

2.:1.,4 )< AD _ .-\ ,2..3

1001' 41 , ) 1.-

..J..T.-\o (g-;...\4iX>l)

------".> 1\.1. -:::; 4 0/0

u -::> As::. ~)< 10 0)<, 1',.J _ '5, 1( Cffi1-

a- 0101>0

~~~a.~ f.n.,~~cJJ cr

c.x-rt\n'V. ~ e.u,;. cl<> r -e,r~~

l, s~,

1~~r=:t=jF~~~~~~

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A,:!..--

'-------------------

1 = ~ 1 ~ 0 YYl --"1 {\ t? ~ ::- \g Vm -"') c\ ~ \ b 1 2. CA(V\-1).,

~~ ~UO ("'-l <'~~ tCl.OctL,.....~ r-m ctKI e-""r e,

roieto r'0 P"<" ~ '.3 j( 0 ( -i li

r m e ~ f"->1re.

-r-0he.t;., of 4GUY1 e&.u.'u

~i colo ln" 1:> r r .... .L. ..Q (<u'VI.Ote"u.

. Sv.A~~ J'~~

Q -= 3, 0 ~rJ \ m1..

Q,,:: ..1,0 «!'lI m

Calw-R.~ ~ .. d-t.~

Me,.,:: ("i-)t~,?L + .3,o:><'l.,30 -= 2.4,{,-4N,'r"r)lrYl2-

2..l--\ Q ~ 3,0.,.. ~~ + -1, 0 " 2.1 1, -.A. t> 1 2 .v... 1\). l'Y) 1 WI

VI)J.. ~ )(..,s~ v .... ,' + l,S,.; lO,L. - l-l1l1S" ~~iyv, \ 'r"r)

. CcJ.cul .dt .Q.a.. r.u.~ -c\..' Ia.n.../YY\,.~ .eu-,.,~'ti.t dvv.cJu

X ::. ~<i\5" -{oo 0 - --1, ~ <4

.-10" " 16, 't '2.

(9", c.R.n~ oJ..n" AT.o\ b C~ -:. -l s CAon]

A ,,,,10<>.16,'2._'1 t~ = b /1 0 0 0 -") A,5:- _ ,1bd /loao

. c:.cSu-J.! ,olt.<,~ JA""",~~

V)J,6 ~ ',t ... 2·3 -1 ~, 0 _ ;18 14 ~ N1V'(1

V.lJ,~ ':: 3,0 ~l,'l:. { A,l) =- t-. q -&.tJ\r<\

VAl...":: .A1~S)l .{~14t1,S'fo.':f,Gj ":.. 3",i- ~rvlm

C; ..... ::. \I.v.:: ~b,t- )</;3,:: 0,1..1' """Pa -< 0,05 fqg ': l,tsI1P"bd A,u.o.//,1.-

.d..M.c ""'" &un.~ /~/Q~ --d..L 'tt..\f'GVÛA.'1"i.U-n AT 'il (e ~ 'W ........, J2.:;0"" 2. '1>u ""

'--'--'----,--4'---":"-.., Oô

I"'-'t-------'f-----I;2.5 e-

l -t.~ 10__.. _, .,. , .. __ ..__ ..,_~, ... -J

A,,~) "D,-menelO1'\'T\e.me 1'\ t deô ~oteew.,)t

1; etu.dL ~ 10..- ldet~~ ,d~ ~OlWt.eA ~cr-'tA.t~o.1.,

cY\eCL?acÙnL ~~ ~ ~~'e..t' xh f6YVYYLe ~ /JJZ. fa.-Vu .DwAJa4:

-& /l"Y1ffoU ~ck ~~e-n1l'deJ to fe~:

a) Si ~ rteau- .RAt~ -o: /UI1U /~reA4~~ ~.

~ M1'\- (YY1$oU. dt -cRmz.~~~ rtlNU ~~<~~,

b) St' -t 1~crtea.(t ~ /~cuv~ l'cie far u~ etz,~

4 'eW /~ a ~~~ /~ k ~de ,dl ~o.rc.~_

~ (YY\.~ ~ rwn.t~,~e. .eu /dWl'u ~~ q-cu .fa.

~ o« F /dC1lV'ltÏ~ ~ ,olv..vx' -d.vt.e~ .

'DCVVV3 tU ,CM ,cU ~eluIlLJ ~q-w ('(U)W) IOJJ~ "ci,~~ ) fu

('rY"U:rrY\-emM ~ Wn4~bii' ~ /~ lV<ÛwM lai~ .et. m.L ~ t-'cw-f1\'S ~ I~k l ,~' (TU'Ml~ ~ IC-aO ,ete r+eci.u reFte..

_~ 1-:.', l.:J/,JV\Nl..JL .

..k4) ?r\'n~ /d.u.. I~ùn~~ ,c;;lQ w rrea.wacScn.t , N.u. ~,1~ ~O..Q 1'IJ.l;tivYU'.

- ~ \' : 5 e c:.li.fi,.. ~ b~ ru.d.u..l.h. ,dt A t.w\ ,d-f ~ "'~ l ~~~ .

~~ JlLJ.-~~~ f? r-:: (6 -~) [~ -1..) (Am~)

_ AoS .QG\. /X.~ "cl.. "o.Û'u ~~tu.d..ltn..~

_ 0".>:= ...\, ~s

., 0( ~Co-4f'~ ~),.a!~'~e... .d...t Q,(M(~'~ etc;1..L.d

4ft ,dM 2.~ (Yl~

)Pd\Al::;(~ :

N LI.. < p( ( Br fc.z..\i +- A5

fe \- >1t~S "ts )

l . .... .__...-....._--...-

O,S'SYI' ) $ 5 a

LO,bO l5"~O)

~ , Qa tmiJ;\t ,etu (~~/~~ ~ ~ r t eau ~

~ {~ .ev-r0JYl1 q 0~ ) 2a.~ t'o-ro oK - oU -dun~ li taA..11, '1..0 .

Î\ \4>.-e-~ -e'~~ -d'~

Az: ~ ~ ~ 'r . ~w -d'~

'b ~~ ,d.!-&.tm

"V{?VJl. (\)J\'\..l ~ o-u, l\..Vn to* e a.r.L - dL M~ Jt.I2. cl eun '}Mi~

~ :::. ; 1 4 c., fi au. ) = ?J, 't b .f.:f. ~~"ta. dvu.~ t:I...t.~ b

.R~' (YWWJ ~-kY\O. ,ck F~VL- 2t ,co1euf (ddadie) d.M-jx'fea..JJ/K

"du ~~ da.~ .

PGIA- .ta~ ~ pf e ~Vt.bl'\/.l là1rWJ ~~ .tolMltUl\.e -lM~

r recuvx. "dM(~ ~ea.u....-x~ ..2t. "'~U1"\"I-'Y\.~e,.yJ; -:l.<. fa.-J-fdoW...lJ'~ k yY1~ ~~ .(~ ,GVf\"t\~ ~J

l ._._._-. -...

rlit ~.l)1) VvY\,~eNY"\-~ des t0\-eCl..UlK

4.4.2.~) })~OA~~~~ rreC\..l..VX.- A,?:>, 4, b,1-, '3, ~D,..I!'

A::. 314(,""~ :: 33 '-..(~ ~~Zo

cA 0.85 - 0.1-1-::. . C?>y--"\-t o. z: 3 S

NM .:::; ~ Lç,< ~C'tl1~ kl "t s,:: A, ~5 , f e ~ lt.", 1\ P ...~ ,..~

D.~ -b\:, OsD'\, ::. ~,'i f. -= 20 H l'aC tg

N..u <Sr ~etl',

+- A i' <----;>01., D./\ ~b Ifs

~ '7/is

[ N~AJ ~r feUIl--':> te: -O."l Yb

-1 A ';>/A,1s [ '3,S.~o _

!.tou O.1-'l..

&n c..R.n' &~ 1-1 l' c

..Hl" '2.0 Jne ~ oJi

D. ':l • ~,s-

eX ..Q' ..v1:-c:>At~ extl ,~~ ~

7 Avr 09:35 1986 pte05 Page

DONNEES GENERALES*********************

nombre d'elements --------~

nombrè de noeuds --------=nombre de noeuds restreints~

nombre de cas de chargement=module d'elasticite ------~

DONNEES DES NOEUDS**********************

O.100d+Ol

noeud1234

coordK.000

4.9454.9459.890

coordy1 . 6501.650

.0001.650

RESTREINTES AUX NOEUDS*************************

noeud13

DONNEES DES ELEMENTS************************

iresK iresy111

iresrooo

nombre d'equations =espace requis pour grk =

noeudl122

noeud22

aireO.600d-Ol0.600d-010.400d-Ol

inertie0.200d-030.200d-030.133d-03

longueur0.495d+Ol0.495d+Ol0.165d+Ol

"." -.

~ -{' = .A, ~ 0 -'l,.\ -= 33 -"> 0( -::. O.:t1.

La. n.<-~~~~ tY\ €. CL-t:> <:V.IU o<A..GI.

A > '155/-+e [~0/ .

...e~ ":. ..I,qo "1"\

[." ~d;~ ,J.. 1ra.l\.-"'-~

p( ;;; o. 'f Z-

li T , _ c;v..r«

45 -t) lnhodLlchoY'

C-vvvvn<. ~, r\-(l.cl.U/lL ~~~ I~ ,1\Arvv.J ~.Jd~..~,~~À:

k ,~~~e..m.eMt. s: f1"1'V"1~ ~ :

? . ~~.à: t...~e.liAR .a..u~

~~ : .Q.,..ccv..4~.o ~'i-=-o..PA ~ ~ (cL ...(i~MWt0-· -r }'-.

/(Â <.t.g ",{..INV\.~ ,du. r -\- e Q.U.

o.' e.! '01 /cli'Y'0~.~ ~ ~J1. ~ ç.;,..~

a 1 v; \:,')<. \\s.-.J( ~

\,'-10do. ~

p ,c;W{c.

d b~ L.Cl I

~ /OJ\IVI'\.~ Aa, to.AaJJ.J.v:J .(UJ. ,~ a' ,eu.vusn.t d&vtc. ~"~

Aa.'::' Pi a/- al

~ S :l) ~ , c:lt. ,coJ-uJ,

fe.E.4 0 ~ -1. =, ~s::2.l.Ior\PQ

1?" \- e<UI- 1-

Pc;.." 352.,'2.~N 0" b:: :lO,><Lo.

~ E.~...l -~.. ......w.~

H... :;~,~5d)S2.'2. +-~,Sl<~Yllq -:: (;Cf:t,3-2.tJ

~l.:3. Aooo __ 11 4(,2", rtI.".... :: -1 ~,t'2. wn"

J:! :: A,S0.

1 b'a ~ ~.

cl b >/ ,;j 30 - .3 0 -:: 2'5, ~ -'" d b -:: 31 ""'"

li()Y\~ /'1-'-'-'- il'~ ,o...c ~'&1Y v".-t lh. fYY\~ --') do. = db - ~'-' = l-4 """"

~ 4~ ~'tR. ~ û~ z: ::54~~Pa.

, - 69 l:l>o"l'(.130 0 - :l o o ) _ '\..." - lcf.dq C-vyj

8 "-310 y.. ~ t+ g

b'tl;oo~ ('6';0 -Zoo)?>" __~oo 1<;\ 1-1 Il

Ab' -::: 5' 0 01 e 0 l' (-toOtJ - 300 )

8 ." 310 '" l '-{ o

1\0.' _ S'DO -100 ~ ( Ça - t-oo)

Sl)< 300 't- 2.. "" D

x 4iro -=- 50ewv.2, g

f~~b'~~

---------

r-------!

I~==:::::=========::=~- ---__.11

.-_._---ij1 ,~ i...-.-- . _o. ~:

l -----.--.-.._--..-.

'.~ TABLEAU)/. DE? SEMELLE? U;olES

~o~ea.u.1)( r SeYY1e~

(Y\~ s~~(Y'~

61 Ab' fltr mJ~~ ct' t", a.' It-rmo. hb)l~

- h..'''J

"';1. C-I'V1 e-m'l. ~ OmL Cvvt

2- 40x 20 .s~1

-1~0 -1 21<6 <3T~4 '30 6,5 6T~~ 4-10

3 ~OI'-2.o 531

OS '3,00 ~T.-\l ~ 0, 6',t ."T11. 40,

Y 30" 20 SI; 14-0 '3,51- STn 1 95 6,1- 3 671:L 40-----t-

5 40" ?<J 55 "\55 9,,~ s 'T1L-\ i 'Do 4,93 ST1Z- 40

9 1 t;)ox:w S6 2,40 ~~,U (,T201

'je;; '1,:>4 5THI1

--l----"'J >0.,,7.0 sï- -12.5 't,!l-~ 1-Tü '3S 5,30 i-T-fO 3S

-10 ~o xU> Sg 1~5 '3.,r3 bTHt '30, 6,c'oo 4T ~4 ?,c;

-t~ s-"xw 5'3 2.-t5 1\6,0 ~TI1, go f,5"L " T-'I.t 5?

1 go 5,05 1-T10 40-12- 40 "f.7.,0 S~o ,fbO q,~.3 i T l"-t4

-13,ZS 1'}TIl''~l~----------

'Il.! i 4ù)'.1.v .s ~ l' .-\'35 b,5't 6T-t:L 1;t51 ..

111 0 A'W ! S 41l,

1 «30 6, 'L 45-is --t'Be> -1 'l, ...( , llT14 9T101

1 51'3L-

-ta,n 14011- 40)<1,0 11-0 1-T14 85 5,52- 5 TI 2-

S 14- 111,:61

6.' ~ 1-,,~ '-1 D ... l.o JI '1-5 iPT1'{, go 'TH. 4;5

1~ /.tox'lo SAS -110 -11,2. "-' " T1 (, 2S ss« " in. 40

La 4lJ "'20 s~" , ,11 '30 .J12,~0 1 1-T-1b 1 '30 ,6;55 "Tt z. ·4-15" i

'THl '30,

(0,2.':) :452-\ l.i 0 ~ 2v SA:J 1\15 I1 A,-H 1 (,T-12

2,o'l<'W 5 -\~ SD A/2.Cj 5T 6 ! 50 AI'?> ':l ST'- ,20

l.t(; 30)< '/,0 5 -iq~~ ;0," GY<" '35 6,'10 1-T 1z 40

,+0 :>, olt 4Tlo Q.s41- 2o}.w 52-0 '10 '2,~1- hT10

,-"- -

Hf{ '2o"z,v SZ1 ~o 41A~ 4T-12 "no 4-,-::'.2. li fI:L ~5

--------- --- - --- -~ -- - -- - --- - -

4C1 2v~'ùJ 522. 1-~ 3,4-3 5110 '1-5 ~/61 S'A 1' 0 2:.5

-----_._--.__ ...--_.. -._--~.-_._-_.._-~-, -

Po~e~ S-e.rn~

m~ S<>Jü.,... tY\': 6' Alb ~ lT'O!ul~ a' Aa' A,mcJU/! VIb,,~ ,,<-0

C-w\'l.. ~t.CJm'L ~ GwI Cm .

50 2.Jy..'W S.2..3 ~o_+ d, 'L1 3Tb ~O d, '2-1- 3T6 loS

5-1 MJ'W S'V.4 40 01- '2. loi!'- 40 °,'19 HIG {5i 1

'52 :S-o)\~O SQ.S ..no ! 'n, ~'\ 3TA,t ~s 5,5'2> 5TH.. 35

ç, 201<10 52' c 601 60 2--, O~ ST8i ,.1,90 s 'r 'il 2..0

5""Lj son.., sn Q, 30 i AO,"b2. '3T" (, <30 6, 50 G;,T..f.2.. 55

~5 ~o ~ 1.0.7 CS z..Sî' 1'<-.5 -! 1-, 60 'fT ~2.- ~S 5,3S 5T~.2.. ~5

311 2,36 , T~ 20'5

~O • ~o S2~ ~S 1 ;',0<:1 S'TA 0 60

3.t ~o 1<30 ':>30 ~~o :+,05 ~T",o ~O 4,St 1- Ua 301 -

~O l.t,\!S q. HO20~ 30 S3~ ~20 t,DL 'j TtfO 30

--/-------1--. -- --

~ 4 Zodo S32 .1125 '1,~q s r ~ li <Bs 5",~ 0 S T-12.1

35---'

35 2N~!Jo S 331

qo 1 3,43 5" T /( D 60 2,\{ o GTS 2S1

5 T'la 1.2542- 20A~O 534 ~O.~5 T-/~ 'tG 3/~o

~ ~,~r<. ~

~ ~i~ 1---- .>5b ~: 20 sg l<p~S~ç, 4Tb tp=-50 0,61 ~Tb 20

I~-1---'1 .

L____.__ - ___0

.._-_.__._._----_ .._.._-- .._- .... --

-+ ':; 0, b 5" Cl~:: D, (; /-1 (la.

1) MUIL ,,L. "ou.t~

Q::: Ar::, ~'t:: 1C"81'0,21.-.,, ~~ ::. H,2 ~N'l 2.-

Q,\"::. A tv.JQ. ~: 0,1..1-"'1- s "3,0 ~ ~,05.e..~

MG = ~~2. ::. ~ll1"ISI8l'.~,ll)C. 2.2.. = ~.2,.c~N.1'Yl:J, ~

1'1 Gl ::. (5IA, ! :: 4, 0 s , I,s::: lé,.-1 ~ N. m"l.-

M)..( = 1,3 ç t-t,6- + \,5' Na.': ~,3 5' ~ ~ 2, 6 + ~, S')' 6, A ~ 26, 2 ~ N·. l'Y)

fa.. ~ c:.k ,J..' (e:tJVvY\.~ .e.,.,."'~~ 'l\ e: CCo'>':l~

\JoU.-=. A,~S'l- -1'1,':t + ~1J50 .'4,05 '::. 3Q..,l tN-3

G,u.-::. 3~,1"AD -:O,A9.1-MP" <0,05.0 ::A,.l.sKVo..iC'2,g

-1. D, Al:.

~<. ,CL c...:....... ~~~....Q.~ Cfc:L<l 'N~ e::u--u.. ~ ~ ('r"'l'I.(.(A- ,J.. r.:>....le.",u.!.

l__. ..._.... .-..-..-.__.. . ....._

k /CÂa-t.'JI<> r cJM db ~.&,

- U)\,(J t:.4u.- la. /Le 4 ~

,fCl- ~. Jit.eur~ ~ --F-u.t1t ~~ 1

/a~ .e.t la '~Q/l..'.Y N..revvW. rw

,C~cu.D ,d2 !UTG d VIa

MT _ ,{4 4, {, 4 33 '2..+ + 2.'8'1,ç + ? 3,2, 'l- + -1 'bD, 0& _.---------------------

';?!.l,b tfAA;t·+.Â3l-.5 -t--i-4;{,+t"S-o"

I1,Q4',,2. ,.a.,CH")<L

" ,CCI l CLLl

Met:::.. 0 1 ~ 5 l' A 5 6, 3.. ~ - 244 l '>1 ..(?, (I). ,m

s~ -.. D, 2.. Cs. "t" -+ ~, 5 ~ 3 ,0") -=. .."', b S ,.,...

A- t "::. lv'\ \: -:. '2..l.l Lh g )',~o- 3 "Â D 4 -=

-l f<'/"I5

1,{,s"aS2

l --------.-_ •...__....._.. -_ ..._- .. --_ ....--

-1 5" ID ,~ )( l.; ,g,() _ 3 =+. t..N2.-

M..\nUl r~~ r.>t<.J. ..e' 1fe1 .du. rrn..wt dt 'k-v..J;C/J'n e-rd ,c;Lt..m.Q.ht cU .œ« ,GUIA-t1

A~ ~ ~,3 ~'I., m .c:lt. .QOJ\~ ~ /\1,1.0 Ce. ,:-\s""""1

A f N") a..\Mw. k-vv~cJt"

5.e..J. .R- 1>~ ~&v:"- ~. 'à'C- ..b~~ eu- ~O-Ad .-cu.v1<. ~w.U.o

('Y\)l\N>r~ ~ _al<LNV> ~..... f~ s '"'1.,-e",,:e.wt.e.. :- Ar m~. -Go'\ k.v.u. _ '1..l.NI..l-

~~ A.t:: l.;,:l.{ CN>'\L (G 1 ~O) .: 1J.c<-UA. rw--v ~ ~~ ~t. 5 D, -15 e,

~~ Q... tcuvt.tL -\N1te-v.:e.MAL - A r rn~ 'o..U/X~ - """""" ~ iWl\.L lUe..&"

AfA..:: ..t I H Gv>1t C~T,{o) ci 1-Ja,(!4.'t.. p.wt. ~euA- Jz a f:. 0,.10 -e" , ~ :Lî-Ao(e=lo)

~ '& tn<-~ .

Au tAA ,~ Ç{"8\"~.~

• ~~ etv.>. ait.,: 0"1'\. -rXo.. C<. A Tb Ce = 2.0 t.v».) ,~QG>. A,oovJ.,..(. ~ ah

- ~ OI4>YYI -Lt ~11-0 l'Y\ - ,~ ~ fo..AA7l

_ .M.~'IW\-Ook. : ,..... tJc:>-e..t. .d.~ ~A.- fa-u <W ~ ,oUt~ AT ~ (f! "- ~'>Coo>'\)

~oU ~ ~ ~ .Q,OJIJIJI.A ,J." T -1 0 et \ b ~ ~ t rm.ÛYne. ~.

1l .. . ._._.. ..__..__._.... ...._

l ---------------------"40

A~ f.,.f lto ~-i.

Wfr = sc 'il ~N 1 >'Y'l

Gv, ""-e-n 0. <IAML,.~ e1tc. /e:U 2,"",-~ \" = A l'YI

k. r~ ~ ,~.oI..atcel!/ r~e .-rre,.~v..,....w-.

;j 1 CcJuJ {@IX f1~ 1vnui-f!.4 'uft: ff1 (.

CJV1 ~'>l- /t.0t.L .€f~UIA ,k ~d& ~ ~ J.'~~,.dt~ ~'da

1«~aJ,t. ~. ~~ (\i.N\.(. .e..ra.i.o~ -e, ~ .{ s- Gwt cR: b'::- 50 v,...,.,

(VJG -: -a, I~ -t 2-'5 'j. 0,..\&1'-0,50 :: C3 0, .rL .2..N. V'I"

NJG- -= 'Z.-b,A .lb..N\>'Y'l

c,J J /..u f..". /.)<~ "f'&{~

A -a, pC ~'- bj _ "01\0"" (300 -2-<>0) -= 2.~ l "'" ",1. -::. 2., ~ e.v-: 1.. =l sTg 1wJ..gç{' crs g"''l..5)< 34&

-e, z,g HAl", --es ::. C!J of.e :: 0, i '" <j 0-0 z:

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.ANNEXES

~ de Calcul Ik~

-'v0UlJ l'ef!d ci'um: C~L urruf~

JGefarLtU

~-_ ..-.-._-_...__.__ .._--------'------'

\," f " ,

GROS ŒUVRE 34 , .

..• -_.~ -"'--.

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.- -~. --_... .~_. -- --.. - - 1/1------- _., ._- --- - ~ .. .. .. .- •.. ..- . - ."

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~~ ... .. ..-... - .. " -

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... -'-'" - - cltR_._-.. .. -_.~ --- -- --'--. .. '---- .- .. .. .- -. -'

JO 1,0 ~O W 'ID 8090100

0" /II"-//(/ ('II \'0111/11(- l'il/<I;('/: lIIillillWI CI1R1I/1'sm,1 sur /11 1"""1',

Si un exprime les pl'I:,sillllS Cil bar cl les longueurlCil 1:111: r ~-. U.7.

Les ehlll'l!l.:s SUlU cxpritucvs duns le premier COI enMN ("" IUO Il cl duns 1.: second CliS en daN (ew 1 kg),

I)cs précuutions doivent être .prises pour que Ilplaque uppuie SUI' toute 511 surfllce, avunt de proœderIl l'cssal (intcrposirion de sable l'in par exemple),

1>11115 les l::IS Uli l'Ill! cunnuit l'imllcc porlont c'ail·Iornicn CIIIC un l'cUI ~c paSSCI' de "culIl b ID ploqucen '1lliiisUllI le di:II!I':II11IllC de cUI...cspondance 'de laügure 17,

4 5 6 7 89 10 lS 20o 0,

100 10

K : mudulc· de réaction du sul (ou Illoduk,h: Wès\cl'gilDrtl). .

Cc mcdalc CSI d~le'l'n,in~ nu moyen I,h,: 1\:ssili sUlI"üll"\lde Wcslel'8nnrtl ~Lli .censure b mesurer l'cnfouccmcn:" d'une plnquc d'odel' .de 25 mm d'épaisseur Cl de;1 cm de dilll1lèlN ·.IOLIS lilW ehul'jlC de io kN dcl'~"

ioppunt sur le sol une.centrnintc moycùnc c pur 1;,L' 1 . •

[ormulc K r=. -,:.(1 .'

" c1~pcnd du ~y';îci;nc d'unilés choisi..' . ~ l ;, 1', '! • -1,&' .

Si on cxpnme.Ic~ p"~s.~io"s en MPII el les longueurs,'11111: ".=O,O7'(~: ." ,

, " ": f' , .'1 ~.

.f'lu, 17.- Relation entre le module K

.,~I)'lry(.I,~.e cnn,CJ,l, VERIFICATION I)U DALLAGE SOUS

L'EFFFET D'UNE CHARGE UNIFORMEMENTREPAlnlE

PAR BANDE DE LONGUEUR INFINI!

" :! ;~~ '.,,< ";. ("

. .r..:~ . ,\

C,l,ll. Vérlflcollun des eonlralnle.

A t1~ruut ch: cnkul plus précls, on peUl utlll.c!" lestubleaux .ulvunlS donnum l'enveloppe de. contraintesen 'dlxlèmc de MPo, soit ton bDr, don. un dalla80 pour\1l\C' cl\l1l10 \1I\lrorml: do 10 kN/m' li I/m') n!parlledt: flll;O'1 DI~IIIOIn:, rcpollllli »ur un .ou...ol homol~ne.

Le. tableaux ci-après donnent la conlralnle maximaleen bar (enveloppe de. conlrDinle.) de traction parr1exlon pour une charge r~parllc .ur une bando partiellede largeur variable, d'un dalluge de largeur totale Lentre jolnl'. en lonction de l'épaisseur Il du COtpl dedallage el du module de rëacricn du sol K <expriméen bor/cm ou MPn/rn).

1., -,

~ (.~ ~ . 'J " ( : .

l' ,. u

, ,,:~, ,;,'" , ~I .

.v ' ...

K module de réaction du sul, (ULI 1110llukclc \V~sterg:l:ml),

Cc module eSI délel'lniné' au 11101'él1 dé l'éSS,\j Sl:ll1d:\\dde Wcstcrguard qui consiste il mesurer l'Cl1fUI1CClllC:,[(' dunc plaque 'u'acier de 25 111111 d'~'p:lissélll CI dL';'j l'Ill dl' dinmcu'c SOliS une l'h:II't~L' dl' jl) kN d~'\'L"

loppcllH sur lé sol 1\l1e, , coruruintc l11ul'eùllL' " Il:11' 1,1

formule K = --=:_, ..a

c dépel1d dll système dunités choisi,

S; 11n exprime lés pres,si.o,lis Cil M\':1 Cl ks longucur«en Ill: C,= 0,01,

,--,-"--,----------------

GROS ŒUVRE 34

Si 1111 cxprim,: ks 11I'l",illI1.' ,II Il:11' l'I les longueursl'Il ,III : l' ;c', O.7 ,

Les cl1aq,es SUI1I e:-:pril1\éL'S dalls le premier cas' Cili'l'lN (=ce 100 1) L'I dan s le second cas Cil daN ("",1 kg),

Dcs prccuutious duÎI'Cl11 ct re prises pour que laplaque appuie sur roure ,:1 "urfacc, avant de procéderil l'essai (irncrposition de sable [in par exemple),

!):l11S les C;lS ou 1'1111 conn.rit lindicc portant caiil'Ul'tliéll l'Ille UI1 pClIl sc p.isscr de l'essai il la plaquel'lllllilis:1111 ,le (li:lgrallll11e (le correspondance 'de lafigure 17,

()II fll,(,\/({ t'II (,(}lIlfllt' l'iudic« millimul CHR1I/1'Sl/l'l; SI/I' 1(/ [onuv,

,Fig, 17" -' Relation cn t rc le moclute K"Cl' l'ilH\lce CBH,

5 578910 15 20 J0 1,0 sa 6~ '10 8090 100

...''"c·l,".

. ,' ...

C.3.3, VERIFICATION DU DALLAGE SOUSL'EFFFET D'UNE CHARGE UNIFORMEMENT

REPARTIEPAR BANDE DE LONGUEUR INFINIE

C.3,3I, Vérificuriun des conrruinrcs

A déluu: de culcul plus nrécls. 011 peu: utiliser- les'tublcaux suivants d0I1IH11l1 l'enveloppe des contraintesen 'dixième de MPu, soit en bar. dons un dallage pourune: charge uniforme de 10 kN/m l (1 t/m l ) "répartied\:,:ru~'ol1 uléurolrc, rcposnnt sur lIll sous-sol homogène:

Les tableaux ci-après donnent la contrainte maximaleen bar (enveloppe des contraintes) de traction parflexion' pour une charge répartie sur une bande partiellede largeur variable,d'uil dallage de largeur totale Lentre joints, Cil fonction de l'épaisseur Il du corps dedallage ct du module de réuct ion du sol K (expriméen bar/cm ou MPa/Ill),

, .....

N' 424 MAI 1984 ~

r:. = 12000 MPa (120000 hMS) E " .'~ oon MPa (380000 bars)

. î',~

• sou du SlHIS'Slll SUI)IJUI'! de 1<1 forme. sur une profondeur de 1./2 sous réserve que K augmente avec1;1 pl'O(ondL'ur,

K ... IH

: K .. Iilit)

, ·c-------...-.':(L'Ill) 1 8 10 I~ 1 IH

r- - - - , - - - - ...:'-' -:.:.l:..:,(~C.:.:'l.:..:l)_·__· ..._:----:::::.1 ------,--

lit' 1

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Les valeurs; dc",',K il prendre en COl11ptC dans CL'Stableaux correspondent [lUX plus [aib lcs vulcurs dl"modules de 'ré~i'l:lions normnlisés. obtenues pur cssai :

• soit delu [cimc 'ei,'surf,n;c :

C,)j:!, Evaluilli~li. 'dcstùsSCI1lCIlIS d ifféreut icls. " '...':'

Les iasscmcuts dir'f0i::dnlicls eurre les .IlICS de stOCk:tgL'clics zones dc-circulutiou doivent èrrc l'v;r1ul's ;1 p'lrtir,iL's pnrnmètrcs sulvnnts; .

• résùÙlllsde' I~" n:COlln;!iSSIII1CL' géOIL'chl1iquc :• 'hélér~géliéiit'dl'l~is51'.:• rép:lr1 iiio'n ~id~;~i;D~ges : . . ,• dislalH;c:cnlrC~)lxc,s;des bandes chllrgc~~ :

é1"11 isscur clc:'fil:,' ~ôticll\;eo1i1 press ible,Le I;ISscl'~cnlcsL ,.~siil11é ;1 pun ir des essais de

corn press ibi1i lé,

;1) Cns d'un sol homogèuc soumis il des charges légères

J\ dél'aut de justifiL';lliullS plliS précises el lorsqueonl'CUI ;Idlllcllrc «lIL' 1:1 ré'alïioll du sol est uniforme. uneestimation approchée du i asscmcn: différcntiel imoycn~ (, en t l'L' les bords cl il' milicll de /<1 zone chargée delurgcur 1\ est clonné; 1';11'

avec l' churuc lIl1iforllll'mcl1l répartie sur 10 largeurIl :

K module de réaction du sol.

.r:1.1;"

BIBL10GRAPHI E

Pierre CHARON

1, CcJ~ ,cl~ 01W2-a~ -&n. Umv &2.me

SAWU~ M ne~ B. A.E.L ~O ~~. ~~_

~ . Gue tri '1Î et LAVA UR

z. T'L~ ,ili ..Ge!..tM.-~é T"{: gen~(~ - ~~ b UM-<rd -

2. - -II - -II •••, - _, _ T:t: CcJ.cu1.d.u\'.v:.m J:wm~ - 'ln~rt\L cdAh..u.r

k -" -l' - ." - 'J 3: lu rJ.~ . "'em.< <! dJ.:lEur

5 -,'- -.'- -1' - Tl-j:

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n. fa .JYW.~~ _~ ~.

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e-t .&wak~ e.M. \j~ ~ ~ev.-t.t Q0- tVY\.et4lt-o- c4 "dM

é.b:Jb ~iwt~,

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} ea 'Y\ Le. Co \l e.c.

AO M!"ffl(.'f\to ,d'~ l'o..u.. ~.A.f".\..-.'Z>~ <t re~~"'VH..'l'ltrCI.'('Y'\l:'j(<.o

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A n n o..Q.v. ..cl es 1.1. 'è-:T.p.

~~~ COb.

-{ (; lL. Ç{ <: 1'\ aM cl "Te~~ .d-u.- .t~ ~ -QeWV'U," 1

L..2-~ FoU c.u EP-.

... _--_ _ -.- _---_ _ _. __._--------

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