library.tee.grlibrary.tee.gr/digital/techr/1966/techr_1966_3_682.pdf · 682 ..,......
TRANSCRIPT
682 YnoAoYlolJolt naooaAwv IUmlll
nXVlIII9clJcAl(bocwlt KaTa T~V IJc90bov Courbon
rIpoundwvilia A loyOOiTl bull
To naedv Oxonltw IXel va t XBi crn TIDgt reDnDS VnOAOYU11lOV rwll nQUUaAfoV 86JJe)tw(Jew~ AapJashy01-gt1_ im Ii T nevej chnurrciw TO ~dampPO U H I-d00 6o aih~ gtlexa Xe1aposhyltOtDVpiYTJ te)evTaw~ xal OfPEtAera~ el~ n lv xaB1JYTiJv Co urhon
Bamltal naea60Xai Tii pt06601gt Ia 6n 6 6gteT~r eMrpov ela naOeo al 6T1 01 naaaashy
AO 16eJ~ogtral ~nl iMrpov auew gteal u)eUv anaeap09PwTOV
middotE Uexii ell n) naeovan 6~poalpoundvalV TIOeTIlI al n 90v7ltOOatl Tij ppound0660v gteal yl na pda cia6yw pt066w bull E avgtpoundxeiy itanrvaaeral gtj ymraquo Of- wela Tii 60gtlt 0 inl iAaam w
aTWI~poundw gteal 61 Toli 16clrpovl ual pi (Jaa Tfrv Owela Taamp~ ptTiira gt1 aTaw~a TW evr d Toii tdarpov naaaclAWgt lvd dclpnTOV Opdlo1 E velayovrUl 6 al paOlpangteal axla al emoa vo TO 7ltg6(JA1pa
TiAO TIOerUl Ue lOPlTo aea6etypa vnoAoYlapoii
np6Aoyogt
TO TTpO~Alfia Tiic tmAuCJpoundWe TWV TTaoCJOAWv 8poundfIpoundALWOpoundWe OTTWe Kal TTaV TTpo~A1fIa 6ltjgt0shypWv lJTTOAOyofloV 8poundfIpoundAWOpoundWV poundIva KaTQ TTpWTOV TTpO~AT]fla t6altjgtoflT]xavK~e Kal KaTQ 6tunpov TTpO~A1fI0 rTaTlKjje
EKpoundivo TO OTTOjov TTPUTOVpoundut poundIe ~va TOOGTOV UTTOAOYOfiov poundIva ~ yvWoe TWV 16l0nlTwv TOG tMltjgtoue Kal ~ OUflTTpoundpltjgtopa TOU ~vavTl TWV ltjgtOpTWV To TTAjj80e lIflwe TWV TTapafltshyTpwV (ouv~8we fI~ TTpoo6op0fltvwv tTTaKp~We) TO (mojov UTTpoundotPXHQI poundIe f1Jv OUflTTpoundpltjgtopav TOG tMltjgtoue Ka8OTa TO TTp6~AT]fla tv TTOAAOje 06pOTOV
Kupov fltAT]fla Aomov TWV flpoundApoundTlJTWV 811 TTptTTpound VO ilvQI ~ poundvTa~le Tile OUflTTpoundpltjgtoplie TOG tMltjgtoue poundIe TTopa60xlle ImAoUoTtUTIKae Kal ~ tvapflovoe Tjjc a Kp~dae Tjje oTaTKjje tmAUotWe TTpOe Ta Igttampofltva Tiie tlgtaltjgtofllxavlKjje
Elaaywyi
-H TTapoOoa lgtlfloo(tuOIe OKOTTOV poundXtl va ltjgttPlJ poundIe YVWOIV TOG tlllllVKOO TtXVKOO KOVOO fllav vtav flt801gt0v UTTOAOyofloO TTaOOaAWV atXfljje 6ltjgttlAOfltVT]V poundIe TOV Ka8T]YT]~v
Courbon
H flt801gt0e TTpOUTT08tTpound ~Igtpaolv TWV TTaOOQAWV tTTI tMltjgtoue Ttlldwe OTEPEOO ( ~paxou ) Kal TO TTpoundPl~Qllllov TOV TTQOOaAOV tlgtaltjgtoe IIgt t W Igt t e T6 TpoundAWTQjov oT]flalvt lITi bashyOTOV tlgtaltjgtKov flOPOV UTTOxwptl QvaA6ywe TTpOe ~V 60KoufltvT]v de aino TTUOIV 6vpound~ap-
AITTAwjJQTOUX0C nOAITLICOC MlXOYIKOf EMn ( 1958) ETTlIJCAllTl1i ee(OU MCTao~iou nounxvdou rEshy6pa WTT)IClIlCYOU Ol(upo6tl-laT~ ) Ka6ltTlnlc LXOshywv EB ACpOTTOp(Oi (I MA) r E6pa wnAlolltvou ClKUpo6tIlQTOC) M poundTlt1TT TUX L Q K Q 1 Lno u 6 a Kudo) 1Ja81) P6Twv Oh(olol ETTllJop+wopoundwC ~ITTA Ml1xavLKwv Kushyclot 6IQAt~cwv npOIVTETQlJtvou oKupo6tlJQTOC 616
6ITTAwIJQTOUXOUC MfxavIKouc TTopci TEE Ma9tilJoshyTO Beton Precontrainle tv ro iQ we un6Tpo+oC (AS I EF) AIQT1Jpd rpa+poundiol ITQTl KWV MduWv 6n6 TaU 1958 A A Q P Y Q Ntol KQTQol(tual TOO Beton - Arshyme AIo8lTllu) - ITQTLlCI (Texv 8111-10 1959) ArUi0shyalcuCJ11 30 Adu1tvwv 4al(~apoundwy tTlI TWV laoaTonshyKCJ V +optwv
TJIPI nalmKWY pftlDYlKWY
T1iTW~ T~~ llTTOXWpf)OEW~ TWV ytlTOVIKWV oplwv Ma91]aTlKW~ TOOTO TTapioTaTal w~
t~~~ q = - kr ( 1)
v9a q = ~ aVTlTTitol~ TOG toaou~
f = ~ ~TTOXWPI]OI~ TOG toaou~ k = 0 OtlKTI]~ tMou~
0 C I K T I] ~ to a 0 U ~ ( Betungsziffer Coefficient d elasticile du 501) t~apTiiTal EK ~~ TT0I6T1]TO~ TOO to4gtOU~ Kat T~~ tTTlavtla~ opTIOtw~ TTpOOOlopl~ETal 01 TTClpaaTlKWe tK ~~ CTpf)OCW~ TWV KaBI~ftocWV H TTapaoox~ aOTl] OCI~OIVI] TO TTpWTOV d~ TOV Wink ler (1867) auBalpcroe Kal tv TTo~~ole clva~1]8ije iie oioci Iav 11TT~~v olavo~v TWV TclOCWV ola va tKKIVftOWtv njv oraTlK~V tTTI~UOIV lTTlptPQlOOTQI ot d~ TTo~M~ TTtpITTTWOtle TTmiddotXmiddot 0I0I]poTpoxae OTIJplshy~otvae tTTI TWV OTPWTijpWV -A~~QI TTpOTaOtl~ clKplptortpal (TTX Wieghardt) oUVtTTayovTal TTCplTT~OK~V TOO UTTOshy~oyIOoO Kal Ka8ioTaVTQI OUOXPl]orOI
Ta TTpOKumOVTa tv TTOOU TTCplTTTWOtl ocjgto~aTQ TTptTTCI v IiVTIcrWTTI~wVTQI t KaTiu~I]shy
~OV OUVTCACcrnjV aocjgta~tla~ To k EXtl OIQOTOOtl~ ouvocwe ova ijKO~ tie TOV KOPOV
1lt---+---- - ~ TQ(t~c tampicpou~ Soil tenIon I
I ~~ I
n~ 1I Soli [mLlon
LX I Flg1
H OXtOl~ ( I ) poundivQI aKplp~~ Ola IKpa~ T1ae ~~ cjgtopTlocw~ tvw Ola ICYOAQe TI1ic TO k olv tlval TTMov OTQ9tpov KaB IITI ai TTapaopcjgtwoCI~ au~ovouv ouoava~oywe TTOAU TTpO~ Tae TOOtle 0 Terzaghi TTapaTl]pti IITI ~ oxtole (I) loxutl t njv TTPOUTTOBtOlV OTi ~ tTTt TOO lMcjgtou~ TOOLe otv UTTtppalvtI TO ~IOU Tii~ 6plaK~e aVToxiie TOO tMcjgtoue At TIIat TOO k KualvoVTQI tTa~u 060 Kal 30 kg fern aTTO Ta a~aKWTtpa TTpOe Ta oVBtshyKTlKWTtpa toocjgtl] YTTapxouv o~loTa OlltlOPOI TUTTOI UTTO~OyIOOO TWV TIIwv aUTWV ouvapnjotl ~e TTOIOTI]TOe TOO toacjgtoue no~u tUXPI]OTOe tlVQI 0 TTiva~ TIWV TOO A Relit TOV OTToiov avacjgttptl 0 K lTTupoTToU~Oe de njv TTpayaTdav TOU laquo ETTlppo~ ~e l~aOTIshy
KOTl]TOe TOO toocjgtoue tTTI tKKtVTPWV Bct~lwvraquo Kat TOV OTToiov TTapaBtrotv KaTwTtpw
01 TToooa~OI KdTa njv IBoOov Courbgtn UTTO njv tm)ptlav TWV aVTlopOOtWV TOO TTtplshyPOAAOVTOe lMcjgtoue 9EWPOOVTQI W e a u v EXt 1 e 0 0 K 0 t t TT I t ~ a 0 T 1 K W v OTl]pl~cwv Ka9 O~OV TO fl~KOe Tije OOKOO
H KaTavo~ Tt~oe TOO OUVOAOU TWV KaTaTTovf)otWV TOO 9tt~lou tTTI TWV TTaOOa~WV ~aflPOVtTQI avli~oyoe TTpOe njv TTapaflopcjgtWOIV TWV Ktcjgta~wv TWV TTaooo~wv ETTlXE1shypETTal OI]~aO~ tie T~V I9000v TQUTI]V tflPpuBEortpa Tie ItAtTl] TOU TTPOPXflflaToe aTTOshycjgtEuyOtVI]e ~e ouvf)Bw~ XPI]OlflOTTOIOUtVI]e too a TaT I K ij e I EBoo 0 u
To TTp6p~l]flQ ~e OUVExOOe OOKOG tTTl t~aOTIKwv OTIJpl~twV tfltAtTl]OE TTpWTOe 0 Winkler ( 1867 ) Ola T~V lTTi~uolV TOO TTpop~f)flaToe Tije topOotWe OI0l]POOPOfllKWV ypaflflwv -EKToTt ot TTo~Aol cAtTl]TQI fxouv aoxo~1]9ij 1 TO 8tfla
YTTOpXOUV o~IOTa Ola T~V 9twplav Tije ouvtxoiie t~aOTlK~e aVTlopootwe (k oraB ) Ta olaypoflflaTa Magnelmiddot -w~ KCit 01 TTivaKte TOG KaBI]YI]ToG K navaYWTOUVOKOU Sa TTptTTtl TtAoe v avacjgttp8ij Kat tpyaola TOG KnBl]yl]TOO K Taolou ( 1963 ) laquo naOoamiddot AO 8CflC~WOpoundwe UTTO T~V tTTIOpaov KaTaKopiJ4wv Kat opl~oVTlwv cjgtcpTlwvraquo OTTOU OKPshy
G Magnl StabJllte des constructton$
684 pwS yiVETOI QVQAOYOS tTliAUolS TWV TlOooclAWV SE~EAlWoEWS 6ilETOl It ~ ltITTOIOV TlPOoshytyylolV ltal ~ n~~ TijS ~EyioTlJS (TTlTp(TJO~tVljS 6p~OVTloS )UVQ~EWS tTl TWV TlOooQAWV 6lEU KPlV~O~EV on ~ ~tSo)oS ~ OTloo laquoTSETOI KaTWTpoundpw [axu ~OVOV )l ltOTaKOpushy ~df~KWV ltjgtOUltj TlaaaaAous pnXOVlKWV
n O IOTHI E6Ac1OYL I K kgem
T upltjgtlJ (Aaltjgtpa )) papdo
I(TJTOTQTlJ SOAaaala Q~~OS npoaltjgtaTos (TliXWOlS centunK~ yij nljAOS Aiav uYP6S
raquo cAlyov uyp6S raquo ~ljp6S raquo ~ljp6S Ka aKAljp6s
Xou~ouS ~ a~~ov -ApYAOS ~pound oAlyljv Q~~OV ImTo XQAlKES ~ Q~~OV -A~~oS Aiav aUV(KnK~
raquo apK[T(l raquo raquo oAlyov raquo raquo Alav AEm~
METPO XOAUKES ~ a~~OY Xov)poi xaAu KES ~( oAiyljv a~~ov IKAljpOS ppaxos
06 - shy 12 12 shy 18 15 shy 20 10 shy 15 10 shy 15 20 shy 35 30 shy 60 50 shy 90
100 shy 120 6 - 8 8 - 10
10 - 12 12 - IS 8 - 10 2 - 4 15 - 3
12 shy 15 18 middotshy 24 20 -30
2_ rEVlKi) 9EWpio liOKoii tnl ouvpoundXoult UQOT1Kfjlt 11cicnwlt
0 UTlOAoYla~os )OKO U t)pa~o~vljS tTlI (AOaTlKijS PQaEW~ TlPOOTlOStT T~V yvWOlv TOU vo~ou TlOU au veSt poundIS tKQoTljV StaLY T~V PUSlolV Y TOU lI1ovos Tij~ )OKOU TlpOS niY
ilvnTliEolY q T~V aaKOU~tVljv tTlI TiS liOKoG
bull tbull bull
1
t [I I I I I I-bull bull 2
1 I I I I If
bull bull z
1 i 1 i i 1 i i r i q
L LX 2 Flg2
-EoTW )OKOS aTaSEpCS )laTo~fic tlipa~o~tvlj tTlI TOG tMltjgtouS Eav Y TO PtAOS ~ETpOUshy
~EVOV 9ETLKOV TIpOS Ta QVW )Ex6~(Sa T~V
q= - ky ( 1)
6TloU k 6 )dKTl]S tMltjgtouS ~TOI omSEpa ou~poAi~ouoa TTjV dvrllipoOlV TOG tMltjgtouS ) ~ova)arOV PtAOS
EKKIVO[jVTE~ tK rfis YEV1KiiS t1loWoEWS rfis (AaaTIK0Tl]TOS
1 M dyR=-E J ~ EJ -rx-=- M ( 2)
lilQ 6uo nopoywy~atwv Koro~yofltV tis r~v 68TPn~D
d dEJ--- q = - p (3)0011111WV EJ dx- ~ I - P Yj dx
POXDVIIWV
Q = - EPi - pdx + qdx = - EPi - pdx - k ydx (4)S S middotS S 0 0 ) 0
~ OJ(tmS (3) dva oaltjgtoplK~ ts1owOIS ypaflflK~ 40u pa9flo flpound aro6(pouS ouvrtt shyarasmiddot lHci arrOKtlOnKWS fltflovwfltvo ltjgtopTlo TO O(UTtpOV fltoS Tiis poundsowotws dVQl fllotv ( P = a ) orrOTt ~ OS T~S tsOWOtWS OUVaTQl va Mpu HiS ts~s ytvKaS flopltjgtas
y=e-Yx (Acosyx + Bsinyx)+eY (Ccosyx+D inyx) Yj (5)
Y - A chs yx cos yx I Bshyx cos yx + C chs yx sin yx + D shyx sin yx (5at)
TO A B C D tlvo oTa9(pai unooyl0flpoundval eme TciS opaKas OUV9~KQS Tiis OOKO To y oTa9tpa xapaKTljponK~ r~s OOKO (Ccefficientrelatif) xouoa oaOTOOtiS t I fl~KOS
y=V
kb (6)4EJ
onou k ltI OtlKTljS iMltjgtouS
b TO nMTOS Tiis OOKOU
E TO fl tTpOV taanKOTljTOS T~S OOKO
J ~ pO~ oopavtlas T~S oaTOfl~S T~S OOKOO
1lt] 0 (UPWflpoundV ntv mv T~S ytVK~S t1OWOtWS (] ) nptrrt tis ntv MOIv (5) ~ (Sa) vei npoo9towfitv (va opov oaltjgtopio(wS Tiis ytvK~S i1owo(WS 0 opoS OUTOS tKltjgtpO lETa Oei T~S flpound9600u T~S flETaPlr~s TWV oTa9poundpwv - Quadratures
EiS T~V YpoundVK~V npoundplmwOIv flas OOKOU flt flfjKOlt npoundJTtpaofltvov xwpllofltV T~V oOKev poundIS ~va wPofltvov 6p9floV OooTljflilTwv (arw v Tei apa TWV oaarlflilTwv xapaKTljplmiddot lOVTQl poundiTt orro EVO OUYKtVTpwfltvov ltjgtopTlov dTt (mo flETaPOh~v TOO Oovtfllfltvou ltjgtopshyTIOU
tx l Flg3
Eav omov 6-oKhlpWawfltv T~V (3 ) tiS Ko6( ollloTljfla 90 lXWfl(V va npooolop1awfl(V 4v oro9poundpar
EiS Tei apo TWV TfllflCITWV OuvOfl(9a vei ypaljlwflpoundv on
dyYdx M tlVQl OUV(X~
KO on ~ aouvtx(O T~S QlaouTa flE ntv IETapoh~v TOO ltjgtopTiou poundIs Tei tv h6y~ lltia -EXOfl(V a6poundv 4 (v - I ) t1owotls
Mvaflo OK6fll va ypaljlw poundIs ntv apx~v Ka TO TtOS r~s OOKO on
M = 0
Q = LUYKtVTPWltvov ltjgt0pTlov tis Til 11K po
~TO XW OUVOhKWS 4 (v - I ) + 4 = 4v tsowaltlS 00 rov unooyoflov 4v ara6(pwv
--------
---------
686 3 E+oPlloyrI TIle tv My~ 9eurowploe euroIe T6v unoAoY1I6v 9pound1IeuroAIWOeuroWe tnl EUKollnTwv KOTOKOP+WV naooilAwv
EcrTW (TT) TO aWlla apoundIlpoundAJapoundws KaTaaKpoundulis TlVOS (taKaalltvov) TO OTToiov apoundwmiddot pOuppoundv ws OTpoundPpoundOV aTTapallopcjgtWTOV tTTlKaa~IlpoundVOV tTT KaTaKOpucjgtwV TTaaaaAwv A B A B Au Bo aUlllltTPKWS TOTTOBpoundTTWtVWV WS TTpOS TO tTTITTpound50v T~S poundiK6voS TO 5EPshyXOIlpoundvOV 50 TOU Iltaou TOU TTpound51Aou KaTo T~V lvvoav z ElS TO a~llpoundia A lxollpoundv TTllKTWOV YTToatTOIlEV TOUS TTaaaaAous llolouS Ka tIlTTpoundTT~YlltvouS tVToS TOU tMcjgtouS tiS ~aeoS h ( ftTPOUIlpoundVOV aTTo TOU KaTwTtpou a~jlpoundlou TOU TTpound51Aou )
--- - - -----shy
-II I I Ai
~ Bi
tiT -Iv -_----0 ~ t oj
IS amp
IXmiddot ~ Flg4
------ --------
I
-
lJIIIIIII1mlwv bullnIOIIWV
KaB 6Aov T6 ~aeoS h TO l6lt1cjgtos BpoundwptiTa 0lloypoundvts Ilt 5poundIK~v k OTaBpoundp6v KaTw TOU h Bpoundwpoullpoundv l5acjgtos OTEPpoundOV aTTapa1l6pcjgtWTOV (~paxos) 01 TTaaaaAo oapoundv aUIlTTpoundPcjgttshyPOVTQI WS 50Kol tTTI tAaaTlKlis auvpoundxous ~pl~poundwe
9poundwpoullpoundv WS QPX~V TWV a~6vwv TO ~Ilpoundiov O KtvrpoV ~apoue TWV KpoundejlaAwv Ai 6Awv TWV TToaaaAwv
01 Q~OVpoundS OX Ka 011 tllejlolvovTo tv T~ ax~lloTl EaTw on TO a uvoAOV TWV 5uvallEWV TWV aaKoujltvwV tK T~e Qvw60IliS tTTI TOU aWIlOTOe BpoundIlpoundAwapoundws 615pound1 Illov KaTOKOshypuejlov auvOTolltvIv V Illov 0pSovTlav auvaTolltv~v H Ka tV Spounduyoe 3
H Il[fOT6TT10le TOU aWIlOTOe BpoundIlpoundAwapoundwc 5UVOTO va opaB~ 60 Tije fpoundTaKv~apoundWe TOU ~Iltlou O
-ECTTW 01 auvcrTwaQl Tf1e IltTOKV~apoundws TdU~e U KaTa TOV lI~ovo x 0 KOTO TOV l~ovo y KO w TTpocjgt~ we TTpOe z H aTpoejl~ apoundWpETTO apoundnK~ KOTO ~v TpyWV0fETPK~V lvvOIov ( QcrTpoundp6crTpOejlOS )
ETTolltvwe ~ KpoundejloA~ Ai TOU Tux6vTOe TToaaaAou AiBi QTTtxouao ToG 0 QTT6crTOOlV Xi ucjgtlcrToTQI Illov 0psovTlov IltTaBpoundOlV ui Illov KOTOK6pucjgtov TOOUTIV 01 KO Illov crTpOshycjgt~v WI
ElvQl 6t ui = u UI == U + Wxi ( 7) WI =r W
E~ oJ 6n 01 TTaaaoAo poundIvo KUKAKlie 5OlOlllie 5OilErPOU D H XOpoKtlPcrTK~ OToB Tij e 50KOO 911 poundIvo
VKD y = 4EJ
TPIIIIO II1ITIIW PllllVIIW
EnpoundllS1) 6 TToaaCLo~ 4gtopTl~poundTQl 1l6vov d~ T1)v Kpound4gta)1)v t1VQl P = 0 887
du Kal ~ (3) ypil4gtual (8)EJ dy + kDu = deg 1) )U0l~ T~~ lSla4gtopIKii~ (~~crwcrpoundwe tlVQl
u (y) = e- yY (A cos yy + Bsinyy) + cYY (C cos yy + D sin yy) (9)
ETTpoundllS1) oi TToaaa)o~ poundIvai KaTei Kavova IlpoundY0)ou Il~KOUe TO yh 6UVTQl TTpaKTlKWe va
epoundwple~ QTTpoundlpOV
Ele T1) ~oa~v B (y = h ) 1) 6p~~ovTla IltTaK[VI)Ol~ u = 0 OetV TO 6t(mpov Ilt)oe Tii~ u ( y ) TTptTTpoundl va tlva~ 1ll61v 6~ oiavli~TTOTpound Tl~1)v TOO y
~TOI C = D = deg KaJ 1) (9) y[VtTal u (y) = e-Y (A cos yy + B sin yy) (9a)
dVQl ~~ = - ye-YY[(A-B)COSyY+(A+B)Sinyy] (10)
~~~ =y2e- Y[(A-B) COSyy +(A+B)sinyy] - ye yY[ -y (A-B) sinyy+y (A +B) COSyy ]
= ye -yy [ - 2 B C08 yy + 2 A in yy ] (11)
~~~ = ye-yY [ 2 (A + B) Con yy + 2 (B - A) sin yy ] (12)
A~ei T1)v djptcr~v TWV A KaJ B eei XPlcr~lloTTo~~awlltv Tei~ cruVe1Ka~ de Tae 6p~aKeie etapoundlC
k I
I Xx oS I I
~
Ix S f~g 5
Earw (gtLei TOV Tux6vTa noaaa)ov AiBi al 6uVOllt~C aJ oaKOUlltVQl tTTI rf~ Kt4gta)~c aUTOU
Ni (KaTaK6pu4gto~)
Qi (6p~~OVTla)
Mi (pO~ KOIl~poundwe) E4gt lIaov TTpO~)tTToVTa~ 1l0VOV KaTa K6pu4gto~ TToaaa)o~ al Q Kai M tlVQl al aUTal 6~ B)ou~
TOUe TTaaao)ou~
Eeiv n 6 eip~elloe TWV TTaaaO)wv poundIvai
n Q = H E Ni = V (13)
n M + ENi Xi = 3
Eeiv F 1) liaToll1) Kal E TO IltTPOV t)aanKOTlToC TOO TTaaao)ou de T1)V ytV~K1)V TTtplTTTWshy
OlV poundIva _ Ni bull h + Ni - No (14)ul- EF 0 C
688 TTPWTO~ OpO~ riVCll ~ KClTOK6puto~ f1poundTOKivI]Ol~ T~~ KpoundcjgtClA~~ TOU TTaoooAou A6y~ tAa-OTlK~~ auTOU napaflopcjgtwapoundwc Tol) KUflaivpoundTCll 030 TToooaAol TPlP~C
090 raquo alXfl~lt
l)poundUTEP0C opoC dVQL KaTaK6pucjgt0C IpoundTa llt ivTjOlC T~lt Kpound+aA~c TOO TTaoOQAou 6y~ ~TTOXWP~OpoundwC TOU i1iQcjgtouC
l X 6 z
N
~UI1S~1J4 T~W 1 FrJtlon di llirllill
I--tshy
u lX 7
Plg6 f ig
Acxof1cVOl IITl 01 naaoaAol t6paloVTQL ltTTl ppoxou ware PU 9l0l~ vo poundIval TTpaKTlKWC 1I]I5EVlKit Kat I5cxolpoundvOl lila Id~ova aacjgtoAtlQv 15 = 100 elval
Ni h UI = Er
El~ N1=- (U +wX i) (15 )
Nib h u+ wXi = Er
A09ivroC OTi apxI) TWV Q~6vwv au ITrimlaquo TTpOe TO k BTWV Kt cjgtoAwv Ai TWV TToaaoAwv clvOt
lXi = 0
ETT0ltvWC V N ( X ) EF EF= 1 1 = U + w 1 - h-= nT (16)
Luv9 ~ Kal dc TO IIplCl
510 Y= 0
( 10) y = o ry= - w =- y( - B) ~ d
I B=u- ~1 dU) ( 11 )EJ - bull = M( dY )= 0
51]Aa51) M = EJ f 213 = - 2y EI ( u - ~ ) ( 11 )
Q = EJy 2 (A + B) = 2EJy (211 - ~) OTTOTpound al t~laWaEllt (13) ypacjgtovTal
H = 2EJ ny ( 2u __1_ w) y
EFV = n - h- u ( I)
- 2 I J ( W) + EF ~ bull =- J1 y~ o 11 - -- w - 1 y h
To OUOTTJlcl (I) IltiS tmTptTTEI va uTToAoyiowlev TO u v OL w
889 TPAPO lollTlIWV pnXOVlKWV
TOUTWV EUPE9tVTWV UTTOAOyiroflEV Tel M Q Ni EK TOU OUltmiflQTO~
M= - 2y EJ (U - ~ )
Q= 2y EJ (2u - ~) ( II )
Nl= E (U+WXI)
nap a T ~ P I) 0 L ~ Al TLfla TWV U u W dvaL TTOAU fllKpai W~ tK TOUTOU BE CITTQIHiTal fIltvaAI) aKpl~EIQ TWV TTpa~EWV KQTa TOV UTTOAOYIOfioV TWV H aKpi~ELa TOO AoyapI9f1LKOU Kav6vo~ BEv poundIvaL ETTapK~~
4 nap66uYila uIToAoYLOlloU
Earw TTpOr lmoAoYLofiov 9EflEAiwOl~ tBpilvou yEcpupa~ H 9EflEAiwOL~ aTTonpoundiTQL eITTo ~va TTtBIAOV iiKaflTTTov tBpar6f1EVOV tTTI OKTW TTaooilAWV KQTQKOpUCPWV BlafiETpou 100 m Ka TOTT09ETT)fltvwv w~ tv TQ OX~flaTI
I
I 0 00
I ~
( jlt~ middotmiddot (11 (
~ t
N I
EilaquoqoO( 2 Soil 2 o o
o 0 ~
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890 EaTW ~ KaTanOVl0u TOU 9tl1poundA(OU pound1lt TO KtVTPOV nilt ~aotwlt 0 ~ KaTW91 KaTaK Mval1llt V = 1400 TJIIIII 6pI~ raquo H = 851 HAm1m poni) S = 1000110
pnXDVlIW Eelgt 6aov TO rrtl5LAov SEwpEiTaL TEAtlWlt QKal1TTTOV ~ AELToupyla aopponlalt TOU npoal5Loshyp(~ETal ( K nilt I1poundTaKLv~atwlt TOU KtVTpOU 0 ( u u W )
H KaTClTT6vlOLlt TOG rraaoaAOU dlt~o A rrap(oTaTal 11pound TOlt (M N Q )
ITOI)(da t6b+ouc
E 15 a cjgt 0 lt I nlAwI5Elt uyp6v TpoundAtiWlt QI1010YEVpoundlt 11pound oraS I5t1KTT)v K = 41 01 1m E 15 a cjgt lt 2 Bpaxw15tlt TEAtlWlt 6vurroxwplTOV
XTOI)(da aaaa~wv
a ) rroloTllt oKupol5[l1aTolt B 160 E = 210000 kg lem TpoundAIKOV I1trpov (AaOTlK6TlTOlt
E = _ E_ 1+ 1
t - lt 0 050 E- 210000 150 000 ~ 1510 timVTOlt TOU poundaoult p = rp - 1 + 050 I
J D _ 314 100 050 10- 1 m~) pom al5pa vtialt b4 - 64
Y ) ~ xapaKTlpIOTlKT) oTa8poundpa -V kD - V 4 10 100 = 033 y - 4El - 4 15 10 050 to I
m
1 y=3OO y = 0110 y=0036
lt ) bull - ~ F D 314 middot100 080 laTol1 1 TOU rraooou bull = 4 = 4 m
EJ = 150 10 050 to-I = 075 10 tm
EF 150 to 080 = 060 10 tm - h- = 2000
pound ) apISl1olt naaaaAwv n = 8 Qrr6aTaollt naooaAwv arro TO KtVTpOV 0 X = 120
IXL = 8 120 = 1150
AI ypoundvIKal t~laWJpoundllt KaTO TO np0lyouI1Eva poundIvai
( I ) 2EJ ny~ ( 2u - ~ ) = H
EFn-h- = V
- 2I1YEJ(U -~) + W EF lXL = EY h
( ) M = - 2yEJ ( 11 -~) )
Q= 2YEJ(2U - ~ )
E1 ( )NI = - h + WXI
EniAuollt oultTrl)I1QTolt ( I )
2 075 10 8 0036 (2u - 3w) = - 85-+
8 middot 060 10 = 1400 -Ishy+shy
- 2 middot 8 middot 011 middot 075 middot 10 (u- 3w) + w 060 10 middot 1150 = - 1000
691 TlInpoRoAmlWY pnXnVIKWY
01 t~awaE~ ypa4gtoVTa 4320 (2u _ 3w) = 85 10-3
1400 U = 48010
-132 (u-3w) +690w= -100010-3
U = - 2904 10- v = - 292 10- W= - 1283 10-
EUpEetvTwV TWV u v W aVTlKaeaTw~Ev TG~ Tl~a~ TWV d~ TO aUCITTwa ( II ~ Kal EXOflEV
M=-2middot 011middot075 middot10 ( 2904+3middot1283) 10-3
Q = 2middot0036 middot 075middot10 (-22904+31263) to-
N = 060middot 10 [ 292 plusmn (-1 283) 120 1 10-
t~ WV TTpoKumEI M = - 1550m Q c - 1060
80 N= + 270
E TT a ~ eE u a I ~ 0) nQ = H 8 middot 1060=85
~) I Mo = - 1000 - 4 270 120 + 480 120 - 8middot 1550 - 1000
napaTraplalli
Ei~ n]v KE4gtaA~v TWV TTaaaaAwv A ~ Taal~ tM4gtou~ Elval
~=-ku = 2904 10-middot 410= 1162 tm ~ 116kgcm
Eav TO Eoa4gto~ ouvaTa v avaap~ n)v TamV Tau~v tTTpoundlO~ Q = 1060 Kal 0 = 100 m 1060
ETTnal on ~ Tpound~vouaa ouva~~ TTapaAa~pavnQj poundi~ paao~ 11 62 = 090 m
5 luYKpau IlE laOaTOTlKrlV IlE901lov KaTG n]v iaOaTQnK~V ~teooov OEv a~~avovTa lJTT o~v at iOI6~T(~ TOO toapou~ 00T( ~ aKa~~(a TWV TTaaaaAwv OTTOT(
85Q= -8- = 1060
001
deg10651=
A M
Ibull
gt--
M= O
1400 1000 305 N = - 8- plusmn 23201202 120= 175 plusmn 130 = 45
F=4 middot080=320m
IX 9 Flg9
laquo Ai TTpoKumouaal olapopai Elval ToaoOTOV ~EyaMT(pal oaov aU~aVEI ~ pOTT~ E raquo
892 BIP)loYPQ+IQ - BibliogrQphy I )nuIVQfj neii~tan cc des )latbriaux 2 Tdatoc e CWpLlL tTtL)6apoundtllt laxi=~lt 6elLampAto30xamp 1tp6TIXOLt vtwv ILlE06Xwv 8 r aato( Comportamcnle di un palo di Fondnziol1c sotta Iaziooc di carichi verUcaH el oriuonlali ( bull Tdqo~ Estimation pratique des tasscmen difCen dull piu pendant un essai d chargnmc nL S EJweonoIlAo E Jlpp(~ n t)a0tLx6MTO~ TOO lMipout in-t txxtvTptlll OpoundIIII)twv ~ IkIUl(a)v ltMtUn blV
I) fiCll(ryu(61WVAo AYTOxi) fW UAlXWII 1 AoICo El~JLUtwO(~c
8 O cnayOJTOVtaXO 01~(w(JtC btl iAlXanxou lBafout
TJIPI nalmKWY pftlDYlKWY
T1iTW~ T~~ llTTOXWpf)OEW~ TWV ytlTOVIKWV oplwv Ma91]aTlKW~ TOOTO TTapioTaTal w~
t~~~ q = - kr ( 1)
v9a q = ~ aVTlTTitol~ TOG toaou~
f = ~ ~TTOXWPI]OI~ TOG toaou~ k = 0 OtlKTI]~ tMou~
0 C I K T I] ~ to a 0 U ~ ( Betungsziffer Coefficient d elasticile du 501) t~apTiiTal EK ~~ TT0I6T1]TO~ TOO to4gtOU~ Kat T~~ tTTlavtla~ opTIOtw~ TTpOOOlopl~ETal 01 TTClpaaTlKWe tK ~~ CTpf)OCW~ TWV KaBI~ftocWV H TTapaoox~ aOTl] OCI~OIVI] TO TTpWTOV d~ TOV Wink ler (1867) auBalpcroe Kal tv TTo~~ole clva~1]8ije iie oioci Iav 11TT~~v olavo~v TWV TclOCWV ola va tKKIVftOWtv njv oraTlK~V tTTI~UOIV lTTlptPQlOOTQI ot d~ TTo~M~ TTtpITTTWOtle TTmiddotXmiddot 0I0I]poTpoxae OTIJplshy~otvae tTTI TWV OTPWTijpWV -A~~QI TTpOTaOtl~ clKplptortpal (TTX Wieghardt) oUVtTTayovTal TTCplTT~OK~V TOO UTTOshy~oyIOoO Kal Ka8ioTaVTQI OUOXPl]orOI
Ta TTpOKumOVTa tv TTOOU TTCplTTTWOtl ocjgto~aTQ TTptTTCI v IiVTIcrWTTI~wVTQI t KaTiu~I]shy
~OV OUVTCACcrnjV aocjgta~tla~ To k EXtl OIQOTOOtl~ ouvocwe ova ijKO~ tie TOV KOPOV
1lt---+---- - ~ TQ(t~c tampicpou~ Soil tenIon I
I ~~ I
n~ 1I Soli [mLlon
LX I Flg1
H OXtOl~ ( I ) poundivQI aKplp~~ Ola IKpa~ T1ae ~~ cjgtopTlocw~ tvw Ola ICYOAQe TI1ic TO k olv tlval TTMov OTQ9tpov KaB IITI ai TTapaopcjgtwoCI~ au~ovouv ouoava~oywe TTOAU TTpO~ Tae TOOtle 0 Terzaghi TTapaTl]pti IITI ~ oxtole (I) loxutl t njv TTPOUTTOBtOlV OTi ~ tTTt TOO lMcjgtou~ TOOLe otv UTTtppalvtI TO ~IOU Tii~ 6plaK~e aVToxiie TOO tMcjgtoue At TIIat TOO k KualvoVTQI tTa~u 060 Kal 30 kg fern aTTO Ta a~aKWTtpa TTpOe Ta oVBtshyKTlKWTtpa toocjgtl] YTTapxouv o~loTa OlltlOPOI TUTTOI UTTO~OyIOOO TWV TIIwv aUTWV ouvapnjotl ~e TTOIOTI]TOe TOO toacjgtoue no~u tUXPI]OTOe tlVQI 0 TTiva~ TIWV TOO A Relit TOV OTToiov avacjgttptl 0 K lTTupoTToU~Oe de njv TTpayaTdav TOU laquo ETTlppo~ ~e l~aOTIshy
KOTl]TOe TOO toocjgtoue tTTI tKKtVTPWV Bct~lwvraquo Kat TOV OTToiov TTapaBtrotv KaTwTtpw
01 TToooa~OI KdTa njv IBoOov Courbgtn UTTO njv tm)ptlav TWV aVTlopOOtWV TOO TTtplshyPOAAOVTOe lMcjgtoue 9EWPOOVTQI W e a u v EXt 1 e 0 0 K 0 t t TT I t ~ a 0 T 1 K W v OTl]pl~cwv Ka9 O~OV TO fl~KOe Tije OOKOO
H KaTavo~ Tt~oe TOO OUVOAOU TWV KaTaTTovf)otWV TOO 9tt~lou tTTI TWV TTaOOa~WV ~aflPOVtTQI avli~oyoe TTpOe njv TTapaflopcjgtWOIV TWV Ktcjgta~wv TWV TTaooo~wv ETTlXE1shypETTal OI]~aO~ tie T~V I9000v TQUTI]V tflPpuBEortpa Tie ItAtTl] TOU TTPOPXflflaToe aTTOshycjgtEuyOtVI]e ~e ouvf)Bw~ XPI]OlflOTTOIOUtVI]e too a TaT I K ij e I EBoo 0 u
To TTp6p~l]flQ ~e OUVExOOe OOKOG tTTl t~aOTIKwv OTIJpl~twV tfltAtTl]OE TTpWTOe 0 Winkler ( 1867 ) Ola T~V lTTi~uolV TOO TTpop~f)flaToe Tije topOotWe OI0l]POOPOfllKWV ypaflflwv -EKToTt ot TTo~Aol cAtTl]TQI fxouv aoxo~1]9ij 1 TO 8tfla
YTTOpXOUV o~IOTa Ola T~V 9twplav Tije ouvtxoiie t~aOTlK~e aVTlopootwe (k oraB ) Ta olaypoflflaTa Magnelmiddot -w~ KCit 01 TTivaKte TOG KaBI]YI]ToG K navaYWTOUVOKOU Sa TTptTTtl TtAoe v avacjgttp8ij Kat tpyaola TOG KnBl]yl]TOO K Taolou ( 1963 ) laquo naOoamiddot AO 8CflC~WOpoundwe UTTO T~V tTTIOpaov KaTaKopiJ4wv Kat opl~oVTlwv cjgtcpTlwvraquo OTTOU OKPshy
G Magnl StabJllte des constructton$
684 pwS yiVETOI QVQAOYOS tTliAUolS TWV TlOooclAWV SE~EAlWoEWS 6ilETOl It ~ ltITTOIOV TlPOoshytyylolV ltal ~ n~~ TijS ~EyioTlJS (TTlTp(TJO~tVljS 6p~OVTloS )UVQ~EWS tTl TWV TlOooQAWV 6lEU KPlV~O~EV on ~ ~tSo)oS ~ OTloo laquoTSETOI KaTWTpoundpw [axu ~OVOV )l ltOTaKOpushy ~df~KWV ltjgtOUltj TlaaaaAous pnXOVlKWV
n O IOTHI E6Ac1OYL I K kgem
T upltjgtlJ (Aaltjgtpa )) papdo
I(TJTOTQTlJ SOAaaala Q~~OS npoaltjgtaTos (TliXWOlS centunK~ yij nljAOS Aiav uYP6S
raquo cAlyov uyp6S raquo ~ljp6S raquo ~ljp6S Ka aKAljp6s
Xou~ouS ~ a~~ov -ApYAOS ~pound oAlyljv Q~~OV ImTo XQAlKES ~ Q~~OV -A~~oS Aiav aUV(KnK~
raquo apK[T(l raquo raquo oAlyov raquo raquo Alav AEm~
METPO XOAUKES ~ a~~OY Xov)poi xaAu KES ~( oAiyljv a~~ov IKAljpOS ppaxos
06 - shy 12 12 shy 18 15 shy 20 10 shy 15 10 shy 15 20 shy 35 30 shy 60 50 shy 90
100 shy 120 6 - 8 8 - 10
10 - 12 12 - IS 8 - 10 2 - 4 15 - 3
12 shy 15 18 middotshy 24 20 -30
2_ rEVlKi) 9EWpio liOKoii tnl ouvpoundXoult UQOT1Kfjlt 11cicnwlt
0 UTlOAoYla~os )OKO U t)pa~o~vljS tTlI (AOaTlKijS PQaEW~ TlPOOTlOStT T~V yvWOlv TOU vo~ou TlOU au veSt poundIS tKQoTljV StaLY T~V PUSlolV Y TOU lI1ovos Tij~ )OKOU TlpOS niY
ilvnTliEolY q T~V aaKOU~tVljv tTlI TiS liOKoG
bull tbull bull
1
t [I I I I I I-bull bull 2
1 I I I I If
bull bull z
1 i 1 i i 1 i i r i q
L LX 2 Flg2
-EoTW )OKOS aTaSEpCS )laTo~fic tlipa~o~tvlj tTlI TOG tMltjgtouS Eav Y TO PtAOS ~ETpOUshy
~EVOV 9ETLKOV TIpOS Ta QVW )Ex6~(Sa T~V
q= - ky ( 1)
6TloU k 6 )dKTl]S tMltjgtouS ~TOI omSEpa ou~poAi~ouoa TTjV dvrllipoOlV TOG tMltjgtouS ) ~ova)arOV PtAOS
EKKIVO[jVTE~ tK rfis YEV1KiiS t1loWoEWS rfis (AaaTIK0Tl]TOS
1 M dyR=-E J ~ EJ -rx-=- M ( 2)
lilQ 6uo nopoywy~atwv Koro~yofltV tis r~v 68TPn~D
d dEJ--- q = - p (3)0011111WV EJ dx- ~ I - P Yj dx
POXDVIIWV
Q = - EPi - pdx + qdx = - EPi - pdx - k ydx (4)S S middotS S 0 0 ) 0
~ OJ(tmS (3) dva oaltjgtoplK~ ts1owOIS ypaflflK~ 40u pa9flo flpound aro6(pouS ouvrtt shyarasmiddot lHci arrOKtlOnKWS fltflovwfltvo ltjgtopTlo TO O(UTtpOV fltoS Tiis poundsowotws dVQl fllotv ( P = a ) orrOTt ~ OS T~S tsOWOtWS OUVaTQl va Mpu HiS ts~s ytvKaS flopltjgtas
y=e-Yx (Acosyx + Bsinyx)+eY (Ccosyx+D inyx) Yj (5)
Y - A chs yx cos yx I Bshyx cos yx + C chs yx sin yx + D shyx sin yx (5at)
TO A B C D tlvo oTa9(pai unooyl0flpoundval eme TciS opaKas OUV9~KQS Tiis OOKO To y oTa9tpa xapaKTljponK~ r~s OOKO (Ccefficientrelatif) xouoa oaOTOOtiS t I fl~KOS
y=V
kb (6)4EJ
onou k ltI OtlKTljS iMltjgtouS
b TO nMTOS Tiis OOKOU
E TO fl tTpOV taanKOTljTOS T~S OOKO
J ~ pO~ oopavtlas T~S oaTOfl~S T~S OOKOO
1lt] 0 (UPWflpoundV ntv mv T~S ytVK~S t1OWOtWS (] ) nptrrt tis ntv MOIv (5) ~ (Sa) vei npoo9towfitv (va opov oaltjgtopio(wS Tiis ytvK~S i1owo(WS 0 opoS OUTOS tKltjgtpO lETa Oei T~S flpound9600u T~S flETaPlr~s TWV oTa9poundpwv - Quadratures
EiS T~V YpoundVK~V npoundplmwOIv flas OOKOU flt flfjKOlt npoundJTtpaofltvov xwpllofltV T~V oOKev poundIS ~va wPofltvov 6p9floV OooTljflilTwv (arw v Tei apa TWV oaarlflilTwv xapaKTljplmiddot lOVTQl poundiTt orro EVO OUYKtVTpwfltvov ltjgtopTlov dTt (mo flETaPOh~v TOO Oovtfllfltvou ltjgtopshyTIOU
tx l Flg3
Eav omov 6-oKhlpWawfltv T~V (3 ) tiS Ko6( ollloTljfla 90 lXWfl(V va npooolop1awfl(V 4v oro9poundpar
EiS Tei apo TWV TfllflCITWV OuvOfl(9a vei ypaljlwflpoundv on
dyYdx M tlVQl OUV(X~
KO on ~ aouvtx(O T~S QlaouTa flE ntv IETapoh~v TOO ltjgtopTiou poundIs Tei tv h6y~ lltia -EXOfl(V a6poundv 4 (v - I ) t1owotls
Mvaflo OK6fll va ypaljlw poundIs ntv apx~v Ka TO TtOS r~s OOKO on
M = 0
Q = LUYKtVTPWltvov ltjgt0pTlov tis Til 11K po
~TO XW OUVOhKWS 4 (v - I ) + 4 = 4v tsowaltlS 00 rov unooyoflov 4v ara6(pwv
--------
---------
686 3 E+oPlloyrI TIle tv My~ 9eurowploe euroIe T6v unoAoY1I6v 9pound1IeuroAIWOeuroWe tnl EUKollnTwv KOTOKOP+WV naooilAwv
EcrTW (TT) TO aWlla apoundIlpoundAJapoundws KaTaaKpoundulis TlVOS (taKaalltvov) TO OTToiov apoundwmiddot pOuppoundv ws OTpoundPpoundOV aTTapallopcjgtWTOV tTTlKaa~IlpoundVOV tTT KaTaKOpucjgtwV TTaaaaAwv A B A B Au Bo aUlllltTPKWS TOTTOBpoundTTWtVWV WS TTpOS TO tTTITTpound50v T~S poundiK6voS TO 5EPshyXOIlpoundvOV 50 TOU Iltaou TOU TTpound51Aou KaTo T~V lvvoav z ElS TO a~llpoundia A lxollpoundv TTllKTWOV YTToatTOIlEV TOUS TTaaaaAous llolouS Ka tIlTTpoundTT~YlltvouS tVToS TOU tMcjgtouS tiS ~aeoS h ( ftTPOUIlpoundVOV aTTo TOU KaTwTtpou a~jlpoundlou TOU TTpound51Aou )
--- - - -----shy
-II I I Ai
~ Bi
tiT -Iv -_----0 ~ t oj
IS amp
IXmiddot ~ Flg4
------ --------
I
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lJIIIIIII1mlwv bullnIOIIWV
KaB 6Aov T6 ~aeoS h TO l6lt1cjgtos BpoundwptiTa 0lloypoundvts Ilt 5poundIK~v k OTaBpoundp6v KaTw TOU h Bpoundwpoullpoundv l5acjgtos OTEPpoundOV aTTapa1l6pcjgtWTOV (~paxos) 01 TTaaaaAo oapoundv aUIlTTpoundPcjgttshyPOVTQI WS 50Kol tTTI tAaaTlKlis auvpoundxous ~pl~poundwe
9poundwpoullpoundv WS QPX~V TWV a~6vwv TO ~Ilpoundiov O KtvrpoV ~apoue TWV KpoundejlaAwv Ai 6Awv TWV TToaaaAwv
01 Q~OVpoundS OX Ka 011 tllejlolvovTo tv T~ ax~lloTl EaTw on TO a uvoAOV TWV 5uvallEWV TWV aaKoujltvwV tK T~e Qvw60IliS tTTI TOU aWIlOTOe BpoundIlpoundAwapoundws 615pound1 Illov KaTOKOshypuejlov auvOTolltvIv V Illov 0pSovTlav auvaTolltv~v H Ka tV Spounduyoe 3
H Il[fOT6TT10le TOU aWIlOTOe BpoundIlpoundAwapoundwc 5UVOTO va opaB~ 60 Tije fpoundTaKv~apoundWe TOU ~Iltlou O
-ECTTW 01 auvcrTwaQl Tf1e IltTOKV~apoundws TdU~e U KaTa TOV lI~ovo x 0 KOTO TOV l~ovo y KO w TTpocjgt~ we TTpOe z H aTpoejl~ apoundWpETTO apoundnK~ KOTO ~v TpyWV0fETPK~V lvvOIov ( QcrTpoundp6crTpOejlOS )
ETTolltvwe ~ KpoundejloA~ Ai TOU Tux6vTOe TToaaaAou AiBi QTTtxouao ToG 0 QTT6crTOOlV Xi ucjgtlcrToTQI Illov 0psovTlov IltTaBpoundOlV ui Illov KOTOK6pucjgtov TOOUTIV 01 KO Illov crTpOshycjgt~v WI
ElvQl 6t ui = u UI == U + Wxi ( 7) WI =r W
E~ oJ 6n 01 TTaaaoAo poundIvo KUKAKlie 5OlOlllie 5OilErPOU D H XOpoKtlPcrTK~ OToB Tij e 50KOO 911 poundIvo
VKD y = 4EJ
TPIIIIO II1ITIIW PllllVIIW
EnpoundllS1) 6 TToaaCLo~ 4gtopTl~poundTQl 1l6vov d~ T1)v Kpound4gta)1)v t1VQl P = 0 887
du Kal ~ (3) ypil4gtual (8)EJ dy + kDu = deg 1) )U0l~ T~~ lSla4gtopIKii~ (~~crwcrpoundwe tlVQl
u (y) = e- yY (A cos yy + Bsinyy) + cYY (C cos yy + D sin yy) (9)
ETTpoundllS1) oi TToaaa)o~ poundIvai KaTei Kavova IlpoundY0)ou Il~KOUe TO yh 6UVTQl TTpaKTlKWe va
epoundwple~ QTTpoundlpOV
Ele T1) ~oa~v B (y = h ) 1) 6p~~ovTla IltTaK[VI)Ol~ u = 0 OetV TO 6t(mpov Ilt)oe Tii~ u ( y ) TTptTTpoundl va tlva~ 1ll61v 6~ oiavli~TTOTpound Tl~1)v TOO y
~TOI C = D = deg KaJ 1) (9) y[VtTal u (y) = e-Y (A cos yy + B sin yy) (9a)
dVQl ~~ = - ye-YY[(A-B)COSyY+(A+B)Sinyy] (10)
~~~ =y2e- Y[(A-B) COSyy +(A+B)sinyy] - ye yY[ -y (A-B) sinyy+y (A +B) COSyy ]
= ye -yy [ - 2 B C08 yy + 2 A in yy ] (11)
~~~ = ye-yY [ 2 (A + B) Con yy + 2 (B - A) sin yy ] (12)
A~ei T1)v djptcr~v TWV A KaJ B eei XPlcr~lloTTo~~awlltv Tei~ cruVe1Ka~ de Tae 6p~aKeie etapoundlC
k I
I Xx oS I I
~
Ix S f~g 5
Earw (gtLei TOV Tux6vTa noaaa)ov AiBi al 6uVOllt~C aJ oaKOUlltVQl tTTI rf~ Kt4gta)~c aUTOU
Ni (KaTaK6pu4gto~)
Qi (6p~~OVTla)
Mi (pO~ KOIl~poundwe) E4gt lIaov TTpO~)tTToVTa~ 1l0VOV KaTa K6pu4gto~ TToaaa)o~ al Q Kai M tlVQl al aUTal 6~ B)ou~
TOUe TTaaao)ou~
Eeiv n 6 eip~elloe TWV TTaaaO)wv poundIvai
n Q = H E Ni = V (13)
n M + ENi Xi = 3
Eeiv F 1) liaToll1) Kal E TO IltTPOV t)aanKOTlToC TOO TTaaao)ou de T1)V ytV~K1)V TTtplTTTWshy
OlV poundIva _ Ni bull h + Ni - No (14)ul- EF 0 C
688 TTPWTO~ OpO~ riVCll ~ KClTOK6puto~ f1poundTOKivI]Ol~ T~~ KpoundcjgtClA~~ TOU TTaoooAou A6y~ tAa-OTlK~~ auTOU napaflopcjgtwapoundwc Tol) KUflaivpoundTCll 030 TToooaAol TPlP~C
090 raquo alXfl~lt
l)poundUTEP0C opoC dVQL KaTaK6pucjgt0C IpoundTa llt ivTjOlC T~lt Kpound+aA~c TOO TTaoOQAou 6y~ ~TTOXWP~OpoundwC TOU i1iQcjgtouC
l X 6 z
N
~UI1S~1J4 T~W 1 FrJtlon di llirllill
I--tshy
u lX 7
Plg6 f ig
Acxof1cVOl IITl 01 naaoaAol t6paloVTQL ltTTl ppoxou ware PU 9l0l~ vo poundIval TTpaKTlKWC 1I]I5EVlKit Kat I5cxolpoundvOl lila Id~ova aacjgtoAtlQv 15 = 100 elval
Ni h UI = Er
El~ N1=- (U +wX i) (15 )
Nib h u+ wXi = Er
A09ivroC OTi apxI) TWV Q~6vwv au ITrimlaquo TTpOe TO k BTWV Kt cjgtoAwv Ai TWV TToaaoAwv clvOt
lXi = 0
ETT0ltvWC V N ( X ) EF EF= 1 1 = U + w 1 - h-= nT (16)
Luv9 ~ Kal dc TO IIplCl
510 Y= 0
( 10) y = o ry= - w =- y( - B) ~ d
I B=u- ~1 dU) ( 11 )EJ - bull = M( dY )= 0
51]Aa51) M = EJ f 213 = - 2y EI ( u - ~ ) ( 11 )
Q = EJy 2 (A + B) = 2EJy (211 - ~) OTTOTpound al t~laWaEllt (13) ypacjgtovTal
H = 2EJ ny ( 2u __1_ w) y
EFV = n - h- u ( I)
- 2 I J ( W) + EF ~ bull =- J1 y~ o 11 - -- w - 1 y h
To OUOTTJlcl (I) IltiS tmTptTTEI va uTToAoyiowlev TO u v OL w
889 TPAPO lollTlIWV pnXOVlKWV
TOUTWV EUPE9tVTWV UTTOAOyiroflEV Tel M Q Ni EK TOU OUltmiflQTO~
M= - 2y EJ (U - ~ )
Q= 2y EJ (2u - ~) ( II )
Nl= E (U+WXI)
nap a T ~ P I) 0 L ~ Al TLfla TWV U u W dvaL TTOAU fllKpai W~ tK TOUTOU BE CITTQIHiTal fIltvaAI) aKpl~EIQ TWV TTpa~EWV KQTa TOV UTTOAOYIOfioV TWV H aKpi~ELa TOO AoyapI9f1LKOU Kav6vo~ BEv poundIvaL ETTapK~~
4 nap66uYila uIToAoYLOlloU
Earw TTpOr lmoAoYLofiov 9EflEAiwOl~ tBpilvou yEcpupa~ H 9EflEAiwOL~ aTTonpoundiTQL eITTo ~va TTtBIAOV iiKaflTTTov tBpar6f1EVOV tTTI OKTW TTaooilAWV KQTQKOpUCPWV BlafiETpou 100 m Ka TOTT09ETT)fltvwv w~ tv TQ OX~flaTI
I
I 0 00
I ~
( jlt~ middotmiddot (11 (
~ t
N I
EilaquoqoO( 2 Soil 2 o o
o 0 ~
Ix a Flg8
890 EaTW ~ KaTanOVl0u TOU 9tl1poundA(OU pound1lt TO KtVTPOV nilt ~aotwlt 0 ~ KaTW91 KaTaK Mval1llt V = 1400 TJIIIII 6pI~ raquo H = 851 HAm1m poni) S = 1000110
pnXDVlIW Eelgt 6aov TO rrtl5LAov SEwpEiTaL TEAtlWlt QKal1TTTOV ~ AELToupyla aopponlalt TOU npoal5Loshyp(~ETal ( K nilt I1poundTaKLv~atwlt TOU KtVTpOU 0 ( u u W )
H KaTClTT6vlOLlt TOG rraaoaAOU dlt~o A rrap(oTaTal 11pound TOlt (M N Q )
ITOI)(da t6b+ouc
E 15 a cjgt 0 lt I nlAwI5Elt uyp6v TpoundAtiWlt QI1010YEVpoundlt 11pound oraS I5t1KTT)v K = 41 01 1m E 15 a cjgt lt 2 Bpaxw15tlt TEAtlWlt 6vurroxwplTOV
XTOI)(da aaaa~wv
a ) rroloTllt oKupol5[l1aTolt B 160 E = 210000 kg lem TpoundAIKOV I1trpov (AaOTlK6TlTOlt
E = _ E_ 1+ 1
t - lt 0 050 E- 210000 150 000 ~ 1510 timVTOlt TOU poundaoult p = rp - 1 + 050 I
J D _ 314 100 050 10- 1 m~) pom al5pa vtialt b4 - 64
Y ) ~ xapaKTlpIOTlKT) oTa8poundpa -V kD - V 4 10 100 = 033 y - 4El - 4 15 10 050 to I
m
1 y=3OO y = 0110 y=0036
lt ) bull - ~ F D 314 middot100 080 laTol1 1 TOU rraooou bull = 4 = 4 m
EJ = 150 10 050 to-I = 075 10 tm
EF 150 to 080 = 060 10 tm - h- = 2000
pound ) apISl1olt naaaaAwv n = 8 Qrr6aTaollt naooaAwv arro TO KtVTpOV 0 X = 120
IXL = 8 120 = 1150
AI ypoundvIKal t~laWJpoundllt KaTO TO np0lyouI1Eva poundIvai
( I ) 2EJ ny~ ( 2u - ~ ) = H
EFn-h- = V
- 2I1YEJ(U -~) + W EF lXL = EY h
( ) M = - 2yEJ ( 11 -~) )
Q= 2YEJ(2U - ~ )
E1 ( )NI = - h + WXI
EniAuollt oultTrl)I1QTolt ( I )
2 075 10 8 0036 (2u - 3w) = - 85-+
8 middot 060 10 = 1400 -Ishy+shy
- 2 middot 8 middot 011 middot 075 middot 10 (u- 3w) + w 060 10 middot 1150 = - 1000
691 TlInpoRoAmlWY pnXnVIKWY
01 t~awaE~ ypa4gtoVTa 4320 (2u _ 3w) = 85 10-3
1400 U = 48010
-132 (u-3w) +690w= -100010-3
U = - 2904 10- v = - 292 10- W= - 1283 10-
EUpEetvTwV TWV u v W aVTlKaeaTw~Ev TG~ Tl~a~ TWV d~ TO aUCITTwa ( II ~ Kal EXOflEV
M=-2middot 011middot075 middot10 ( 2904+3middot1283) 10-3
Q = 2middot0036 middot 075middot10 (-22904+31263) to-
N = 060middot 10 [ 292 plusmn (-1 283) 120 1 10-
t~ WV TTpoKumEI M = - 1550m Q c - 1060
80 N= + 270
E TT a ~ eE u a I ~ 0) nQ = H 8 middot 1060=85
~) I Mo = - 1000 - 4 270 120 + 480 120 - 8middot 1550 - 1000
napaTraplalli
Ei~ n]v KE4gtaA~v TWV TTaaaaAwv A ~ Taal~ tM4gtou~ Elval
~=-ku = 2904 10-middot 410= 1162 tm ~ 116kgcm
Eav TO Eoa4gto~ ouvaTa v avaap~ n)v TamV Tau~v tTTpoundlO~ Q = 1060 Kal 0 = 100 m 1060
ETTnal on ~ Tpound~vouaa ouva~~ TTapaAa~pavnQj poundi~ paao~ 11 62 = 090 m
5 luYKpau IlE laOaTOTlKrlV IlE901lov KaTG n]v iaOaTQnK~V ~teooov OEv a~~avovTa lJTT o~v at iOI6~T(~ TOO toapou~ 00T( ~ aKa~~(a TWV TTaaaaAwv OTTOT(
85Q= -8- = 1060
001
deg10651=
A M
Ibull
gt--
M= O
1400 1000 305 N = - 8- plusmn 23201202 120= 175 plusmn 130 = 45
F=4 middot080=320m
IX 9 Flg9
laquo Ai TTpoKumouaal olapopai Elval ToaoOTOV ~EyaMT(pal oaov aU~aVEI ~ pOTT~ E raquo
892 BIP)loYPQ+IQ - BibliogrQphy I )nuIVQfj neii~tan cc des )latbriaux 2 Tdatoc e CWpLlL tTtL)6apoundtllt laxi=~lt 6elLampAto30xamp 1tp6TIXOLt vtwv ILlE06Xwv 8 r aato( Comportamcnle di un palo di Fondnziol1c sotta Iaziooc di carichi verUcaH el oriuonlali ( bull Tdqo~ Estimation pratique des tasscmen difCen dull piu pendant un essai d chargnmc nL S EJweonoIlAo E Jlpp(~ n t)a0tLx6MTO~ TOO lMipout in-t txxtvTptlll OpoundIIII)twv ~ IkIUl(a)v ltMtUn blV
I) fiCll(ryu(61WVAo AYTOxi) fW UAlXWII 1 AoICo El~JLUtwO(~c
8 O cnayOJTOVtaXO 01~(w(JtC btl iAlXanxou lBafout
684 pwS yiVETOI QVQAOYOS tTliAUolS TWV TlOooclAWV SE~EAlWoEWS 6ilETOl It ~ ltITTOIOV TlPOoshytyylolV ltal ~ n~~ TijS ~EyioTlJS (TTlTp(TJO~tVljS 6p~OVTloS )UVQ~EWS tTl TWV TlOooQAWV 6lEU KPlV~O~EV on ~ ~tSo)oS ~ OTloo laquoTSETOI KaTWTpoundpw [axu ~OVOV )l ltOTaKOpushy ~df~KWV ltjgtOUltj TlaaaaAous pnXOVlKWV
n O IOTHI E6Ac1OYL I K kgem
T upltjgtlJ (Aaltjgtpa )) papdo
I(TJTOTQTlJ SOAaaala Q~~OS npoaltjgtaTos (TliXWOlS centunK~ yij nljAOS Aiav uYP6S
raquo cAlyov uyp6S raquo ~ljp6S raquo ~ljp6S Ka aKAljp6s
Xou~ouS ~ a~~ov -ApYAOS ~pound oAlyljv Q~~OV ImTo XQAlKES ~ Q~~OV -A~~oS Aiav aUV(KnK~
raquo apK[T(l raquo raquo oAlyov raquo raquo Alav AEm~
METPO XOAUKES ~ a~~OY Xov)poi xaAu KES ~( oAiyljv a~~ov IKAljpOS ppaxos
06 - shy 12 12 shy 18 15 shy 20 10 shy 15 10 shy 15 20 shy 35 30 shy 60 50 shy 90
100 shy 120 6 - 8 8 - 10
10 - 12 12 - IS 8 - 10 2 - 4 15 - 3
12 shy 15 18 middotshy 24 20 -30
2_ rEVlKi) 9EWpio liOKoii tnl ouvpoundXoult UQOT1Kfjlt 11cicnwlt
0 UTlOAoYla~os )OKO U t)pa~o~vljS tTlI (AOaTlKijS PQaEW~ TlPOOTlOStT T~V yvWOlv TOU vo~ou TlOU au veSt poundIS tKQoTljV StaLY T~V PUSlolV Y TOU lI1ovos Tij~ )OKOU TlpOS niY
ilvnTliEolY q T~V aaKOU~tVljv tTlI TiS liOKoG
bull tbull bull
1
t [I I I I I I-bull bull 2
1 I I I I If
bull bull z
1 i 1 i i 1 i i r i q
L LX 2 Flg2
-EoTW )OKOS aTaSEpCS )laTo~fic tlipa~o~tvlj tTlI TOG tMltjgtouS Eav Y TO PtAOS ~ETpOUshy
~EVOV 9ETLKOV TIpOS Ta QVW )Ex6~(Sa T~V
q= - ky ( 1)
6TloU k 6 )dKTl]S tMltjgtouS ~TOI omSEpa ou~poAi~ouoa TTjV dvrllipoOlV TOG tMltjgtouS ) ~ova)arOV PtAOS
EKKIVO[jVTE~ tK rfis YEV1KiiS t1loWoEWS rfis (AaaTIK0Tl]TOS
1 M dyR=-E J ~ EJ -rx-=- M ( 2)
lilQ 6uo nopoywy~atwv Koro~yofltV tis r~v 68TPn~D
d dEJ--- q = - p (3)0011111WV EJ dx- ~ I - P Yj dx
POXDVIIWV
Q = - EPi - pdx + qdx = - EPi - pdx - k ydx (4)S S middotS S 0 0 ) 0
~ OJ(tmS (3) dva oaltjgtoplK~ ts1owOIS ypaflflK~ 40u pa9flo flpound aro6(pouS ouvrtt shyarasmiddot lHci arrOKtlOnKWS fltflovwfltvo ltjgtopTlo TO O(UTtpOV fltoS Tiis poundsowotws dVQl fllotv ( P = a ) orrOTt ~ OS T~S tsOWOtWS OUVaTQl va Mpu HiS ts~s ytvKaS flopltjgtas
y=e-Yx (Acosyx + Bsinyx)+eY (Ccosyx+D inyx) Yj (5)
Y - A chs yx cos yx I Bshyx cos yx + C chs yx sin yx + D shyx sin yx (5at)
TO A B C D tlvo oTa9(pai unooyl0flpoundval eme TciS opaKas OUV9~KQS Tiis OOKO To y oTa9tpa xapaKTljponK~ r~s OOKO (Ccefficientrelatif) xouoa oaOTOOtiS t I fl~KOS
y=V
kb (6)4EJ
onou k ltI OtlKTljS iMltjgtouS
b TO nMTOS Tiis OOKOU
E TO fl tTpOV taanKOTljTOS T~S OOKO
J ~ pO~ oopavtlas T~S oaTOfl~S T~S OOKOO
1lt] 0 (UPWflpoundV ntv mv T~S ytVK~S t1OWOtWS (] ) nptrrt tis ntv MOIv (5) ~ (Sa) vei npoo9towfitv (va opov oaltjgtopio(wS Tiis ytvK~S i1owo(WS 0 opoS OUTOS tKltjgtpO lETa Oei T~S flpound9600u T~S flETaPlr~s TWV oTa9poundpwv - Quadratures
EiS T~V YpoundVK~V npoundplmwOIv flas OOKOU flt flfjKOlt npoundJTtpaofltvov xwpllofltV T~V oOKev poundIS ~va wPofltvov 6p9floV OooTljflilTwv (arw v Tei apa TWV oaarlflilTwv xapaKTljplmiddot lOVTQl poundiTt orro EVO OUYKtVTpwfltvov ltjgtopTlov dTt (mo flETaPOh~v TOO Oovtfllfltvou ltjgtopshyTIOU
tx l Flg3
Eav omov 6-oKhlpWawfltv T~V (3 ) tiS Ko6( ollloTljfla 90 lXWfl(V va npooolop1awfl(V 4v oro9poundpar
EiS Tei apo TWV TfllflCITWV OuvOfl(9a vei ypaljlwflpoundv on
dyYdx M tlVQl OUV(X~
KO on ~ aouvtx(O T~S QlaouTa flE ntv IETapoh~v TOO ltjgtopTiou poundIs Tei tv h6y~ lltia -EXOfl(V a6poundv 4 (v - I ) t1owotls
Mvaflo OK6fll va ypaljlw poundIs ntv apx~v Ka TO TtOS r~s OOKO on
M = 0
Q = LUYKtVTPWltvov ltjgt0pTlov tis Til 11K po
~TO XW OUVOhKWS 4 (v - I ) + 4 = 4v tsowaltlS 00 rov unooyoflov 4v ara6(pwv
--------
---------
686 3 E+oPlloyrI TIle tv My~ 9eurowploe euroIe T6v unoAoY1I6v 9pound1IeuroAIWOeuroWe tnl EUKollnTwv KOTOKOP+WV naooilAwv
EcrTW (TT) TO aWlla apoundIlpoundAJapoundws KaTaaKpoundulis TlVOS (taKaalltvov) TO OTToiov apoundwmiddot pOuppoundv ws OTpoundPpoundOV aTTapallopcjgtWTOV tTTlKaa~IlpoundVOV tTT KaTaKOpucjgtwV TTaaaaAwv A B A B Au Bo aUlllltTPKWS TOTTOBpoundTTWtVWV WS TTpOS TO tTTITTpound50v T~S poundiK6voS TO 5EPshyXOIlpoundvOV 50 TOU Iltaou TOU TTpound51Aou KaTo T~V lvvoav z ElS TO a~llpoundia A lxollpoundv TTllKTWOV YTToatTOIlEV TOUS TTaaaaAous llolouS Ka tIlTTpoundTT~YlltvouS tVToS TOU tMcjgtouS tiS ~aeoS h ( ftTPOUIlpoundVOV aTTo TOU KaTwTtpou a~jlpoundlou TOU TTpound51Aou )
--- - - -----shy
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~ Bi
tiT -Iv -_----0 ~ t oj
IS amp
IXmiddot ~ Flg4
------ --------
I
-
lJIIIIIII1mlwv bullnIOIIWV
KaB 6Aov T6 ~aeoS h TO l6lt1cjgtos BpoundwptiTa 0lloypoundvts Ilt 5poundIK~v k OTaBpoundp6v KaTw TOU h Bpoundwpoullpoundv l5acjgtos OTEPpoundOV aTTapa1l6pcjgtWTOV (~paxos) 01 TTaaaaAo oapoundv aUIlTTpoundPcjgttshyPOVTQI WS 50Kol tTTI tAaaTlKlis auvpoundxous ~pl~poundwe
9poundwpoullpoundv WS QPX~V TWV a~6vwv TO ~Ilpoundiov O KtvrpoV ~apoue TWV KpoundejlaAwv Ai 6Awv TWV TToaaaAwv
01 Q~OVpoundS OX Ka 011 tllejlolvovTo tv T~ ax~lloTl EaTw on TO a uvoAOV TWV 5uvallEWV TWV aaKoujltvwV tK T~e Qvw60IliS tTTI TOU aWIlOTOe BpoundIlpoundAwapoundws 615pound1 Illov KaTOKOshypuejlov auvOTolltvIv V Illov 0pSovTlav auvaTolltv~v H Ka tV Spounduyoe 3
H Il[fOT6TT10le TOU aWIlOTOe BpoundIlpoundAwapoundwc 5UVOTO va opaB~ 60 Tije fpoundTaKv~apoundWe TOU ~Iltlou O
-ECTTW 01 auvcrTwaQl Tf1e IltTOKV~apoundws TdU~e U KaTa TOV lI~ovo x 0 KOTO TOV l~ovo y KO w TTpocjgt~ we TTpOe z H aTpoejl~ apoundWpETTO apoundnK~ KOTO ~v TpyWV0fETPK~V lvvOIov ( QcrTpoundp6crTpOejlOS )
ETTolltvwe ~ KpoundejloA~ Ai TOU Tux6vTOe TToaaaAou AiBi QTTtxouao ToG 0 QTT6crTOOlV Xi ucjgtlcrToTQI Illov 0psovTlov IltTaBpoundOlV ui Illov KOTOK6pucjgtov TOOUTIV 01 KO Illov crTpOshycjgt~v WI
ElvQl 6t ui = u UI == U + Wxi ( 7) WI =r W
E~ oJ 6n 01 TTaaaoAo poundIvo KUKAKlie 5OlOlllie 5OilErPOU D H XOpoKtlPcrTK~ OToB Tij e 50KOO 911 poundIvo
VKD y = 4EJ
TPIIIIO II1ITIIW PllllVIIW
EnpoundllS1) 6 TToaaCLo~ 4gtopTl~poundTQl 1l6vov d~ T1)v Kpound4gta)1)v t1VQl P = 0 887
du Kal ~ (3) ypil4gtual (8)EJ dy + kDu = deg 1) )U0l~ T~~ lSla4gtopIKii~ (~~crwcrpoundwe tlVQl
u (y) = e- yY (A cos yy + Bsinyy) + cYY (C cos yy + D sin yy) (9)
ETTpoundllS1) oi TToaaa)o~ poundIvai KaTei Kavova IlpoundY0)ou Il~KOUe TO yh 6UVTQl TTpaKTlKWe va
epoundwple~ QTTpoundlpOV
Ele T1) ~oa~v B (y = h ) 1) 6p~~ovTla IltTaK[VI)Ol~ u = 0 OetV TO 6t(mpov Ilt)oe Tii~ u ( y ) TTptTTpoundl va tlva~ 1ll61v 6~ oiavli~TTOTpound Tl~1)v TOO y
~TOI C = D = deg KaJ 1) (9) y[VtTal u (y) = e-Y (A cos yy + B sin yy) (9a)
dVQl ~~ = - ye-YY[(A-B)COSyY+(A+B)Sinyy] (10)
~~~ =y2e- Y[(A-B) COSyy +(A+B)sinyy] - ye yY[ -y (A-B) sinyy+y (A +B) COSyy ]
= ye -yy [ - 2 B C08 yy + 2 A in yy ] (11)
~~~ = ye-yY [ 2 (A + B) Con yy + 2 (B - A) sin yy ] (12)
A~ei T1)v djptcr~v TWV A KaJ B eei XPlcr~lloTTo~~awlltv Tei~ cruVe1Ka~ de Tae 6p~aKeie etapoundlC
k I
I Xx oS I I
~
Ix S f~g 5
Earw (gtLei TOV Tux6vTa noaaa)ov AiBi al 6uVOllt~C aJ oaKOUlltVQl tTTI rf~ Kt4gta)~c aUTOU
Ni (KaTaK6pu4gto~)
Qi (6p~~OVTla)
Mi (pO~ KOIl~poundwe) E4gt lIaov TTpO~)tTToVTa~ 1l0VOV KaTa K6pu4gto~ TToaaa)o~ al Q Kai M tlVQl al aUTal 6~ B)ou~
TOUe TTaaao)ou~
Eeiv n 6 eip~elloe TWV TTaaaO)wv poundIvai
n Q = H E Ni = V (13)
n M + ENi Xi = 3
Eeiv F 1) liaToll1) Kal E TO IltTPOV t)aanKOTlToC TOO TTaaao)ou de T1)V ytV~K1)V TTtplTTTWshy
OlV poundIva _ Ni bull h + Ni - No (14)ul- EF 0 C
688 TTPWTO~ OpO~ riVCll ~ KClTOK6puto~ f1poundTOKivI]Ol~ T~~ KpoundcjgtClA~~ TOU TTaoooAou A6y~ tAa-OTlK~~ auTOU napaflopcjgtwapoundwc Tol) KUflaivpoundTCll 030 TToooaAol TPlP~C
090 raquo alXfl~lt
l)poundUTEP0C opoC dVQL KaTaK6pucjgt0C IpoundTa llt ivTjOlC T~lt Kpound+aA~c TOO TTaoOQAou 6y~ ~TTOXWP~OpoundwC TOU i1iQcjgtouC
l X 6 z
N
~UI1S~1J4 T~W 1 FrJtlon di llirllill
I--tshy
u lX 7
Plg6 f ig
Acxof1cVOl IITl 01 naaoaAol t6paloVTQL ltTTl ppoxou ware PU 9l0l~ vo poundIval TTpaKTlKWC 1I]I5EVlKit Kat I5cxolpoundvOl lila Id~ova aacjgtoAtlQv 15 = 100 elval
Ni h UI = Er
El~ N1=- (U +wX i) (15 )
Nib h u+ wXi = Er
A09ivroC OTi apxI) TWV Q~6vwv au ITrimlaquo TTpOe TO k BTWV Kt cjgtoAwv Ai TWV TToaaoAwv clvOt
lXi = 0
ETT0ltvWC V N ( X ) EF EF= 1 1 = U + w 1 - h-= nT (16)
Luv9 ~ Kal dc TO IIplCl
510 Y= 0
( 10) y = o ry= - w =- y( - B) ~ d
I B=u- ~1 dU) ( 11 )EJ - bull = M( dY )= 0
51]Aa51) M = EJ f 213 = - 2y EI ( u - ~ ) ( 11 )
Q = EJy 2 (A + B) = 2EJy (211 - ~) OTTOTpound al t~laWaEllt (13) ypacjgtovTal
H = 2EJ ny ( 2u __1_ w) y
EFV = n - h- u ( I)
- 2 I J ( W) + EF ~ bull =- J1 y~ o 11 - -- w - 1 y h
To OUOTTJlcl (I) IltiS tmTptTTEI va uTToAoyiowlev TO u v OL w
889 TPAPO lollTlIWV pnXOVlKWV
TOUTWV EUPE9tVTWV UTTOAOyiroflEV Tel M Q Ni EK TOU OUltmiflQTO~
M= - 2y EJ (U - ~ )
Q= 2y EJ (2u - ~) ( II )
Nl= E (U+WXI)
nap a T ~ P I) 0 L ~ Al TLfla TWV U u W dvaL TTOAU fllKpai W~ tK TOUTOU BE CITTQIHiTal fIltvaAI) aKpl~EIQ TWV TTpa~EWV KQTa TOV UTTOAOYIOfioV TWV H aKpi~ELa TOO AoyapI9f1LKOU Kav6vo~ BEv poundIvaL ETTapK~~
4 nap66uYila uIToAoYLOlloU
Earw TTpOr lmoAoYLofiov 9EflEAiwOl~ tBpilvou yEcpupa~ H 9EflEAiwOL~ aTTonpoundiTQL eITTo ~va TTtBIAOV iiKaflTTTov tBpar6f1EVOV tTTI OKTW TTaooilAWV KQTQKOpUCPWV BlafiETpou 100 m Ka TOTT09ETT)fltvwv w~ tv TQ OX~flaTI
I
I 0 00
I ~
( jlt~ middotmiddot (11 (
~ t
N I
EilaquoqoO( 2 Soil 2 o o
o 0 ~
Ix a Flg8
890 EaTW ~ KaTanOVl0u TOU 9tl1poundA(OU pound1lt TO KtVTPOV nilt ~aotwlt 0 ~ KaTW91 KaTaK Mval1llt V = 1400 TJIIIII 6pI~ raquo H = 851 HAm1m poni) S = 1000110
pnXDVlIW Eelgt 6aov TO rrtl5LAov SEwpEiTaL TEAtlWlt QKal1TTTOV ~ AELToupyla aopponlalt TOU npoal5Loshyp(~ETal ( K nilt I1poundTaKLv~atwlt TOU KtVTpOU 0 ( u u W )
H KaTClTT6vlOLlt TOG rraaoaAOU dlt~o A rrap(oTaTal 11pound TOlt (M N Q )
ITOI)(da t6b+ouc
E 15 a cjgt 0 lt I nlAwI5Elt uyp6v TpoundAtiWlt QI1010YEVpoundlt 11pound oraS I5t1KTT)v K = 41 01 1m E 15 a cjgt lt 2 Bpaxw15tlt TEAtlWlt 6vurroxwplTOV
XTOI)(da aaaa~wv
a ) rroloTllt oKupol5[l1aTolt B 160 E = 210000 kg lem TpoundAIKOV I1trpov (AaOTlK6TlTOlt
E = _ E_ 1+ 1
t - lt 0 050 E- 210000 150 000 ~ 1510 timVTOlt TOU poundaoult p = rp - 1 + 050 I
J D _ 314 100 050 10- 1 m~) pom al5pa vtialt b4 - 64
Y ) ~ xapaKTlpIOTlKT) oTa8poundpa -V kD - V 4 10 100 = 033 y - 4El - 4 15 10 050 to I
m
1 y=3OO y = 0110 y=0036
lt ) bull - ~ F D 314 middot100 080 laTol1 1 TOU rraooou bull = 4 = 4 m
EJ = 150 10 050 to-I = 075 10 tm
EF 150 to 080 = 060 10 tm - h- = 2000
pound ) apISl1olt naaaaAwv n = 8 Qrr6aTaollt naooaAwv arro TO KtVTpOV 0 X = 120
IXL = 8 120 = 1150
AI ypoundvIKal t~laWJpoundllt KaTO TO np0lyouI1Eva poundIvai
( I ) 2EJ ny~ ( 2u - ~ ) = H
EFn-h- = V
- 2I1YEJ(U -~) + W EF lXL = EY h
( ) M = - 2yEJ ( 11 -~) )
Q= 2YEJ(2U - ~ )
E1 ( )NI = - h + WXI
EniAuollt oultTrl)I1QTolt ( I )
2 075 10 8 0036 (2u - 3w) = - 85-+
8 middot 060 10 = 1400 -Ishy+shy
- 2 middot 8 middot 011 middot 075 middot 10 (u- 3w) + w 060 10 middot 1150 = - 1000
691 TlInpoRoAmlWY pnXnVIKWY
01 t~awaE~ ypa4gtoVTa 4320 (2u _ 3w) = 85 10-3
1400 U = 48010
-132 (u-3w) +690w= -100010-3
U = - 2904 10- v = - 292 10- W= - 1283 10-
EUpEetvTwV TWV u v W aVTlKaeaTw~Ev TG~ Tl~a~ TWV d~ TO aUCITTwa ( II ~ Kal EXOflEV
M=-2middot 011middot075 middot10 ( 2904+3middot1283) 10-3
Q = 2middot0036 middot 075middot10 (-22904+31263) to-
N = 060middot 10 [ 292 plusmn (-1 283) 120 1 10-
t~ WV TTpoKumEI M = - 1550m Q c - 1060
80 N= + 270
E TT a ~ eE u a I ~ 0) nQ = H 8 middot 1060=85
~) I Mo = - 1000 - 4 270 120 + 480 120 - 8middot 1550 - 1000
napaTraplalli
Ei~ n]v KE4gtaA~v TWV TTaaaaAwv A ~ Taal~ tM4gtou~ Elval
~=-ku = 2904 10-middot 410= 1162 tm ~ 116kgcm
Eav TO Eoa4gto~ ouvaTa v avaap~ n)v TamV Tau~v tTTpoundlO~ Q = 1060 Kal 0 = 100 m 1060
ETTnal on ~ Tpound~vouaa ouva~~ TTapaAa~pavnQj poundi~ paao~ 11 62 = 090 m
5 luYKpau IlE laOaTOTlKrlV IlE901lov KaTG n]v iaOaTQnK~V ~teooov OEv a~~avovTa lJTT o~v at iOI6~T(~ TOO toapou~ 00T( ~ aKa~~(a TWV TTaaaaAwv OTTOT(
85Q= -8- = 1060
001
deg10651=
A M
Ibull
gt--
M= O
1400 1000 305 N = - 8- plusmn 23201202 120= 175 plusmn 130 = 45
F=4 middot080=320m
IX 9 Flg9
laquo Ai TTpoKumouaal olapopai Elval ToaoOTOV ~EyaMT(pal oaov aU~aVEI ~ pOTT~ E raquo
892 BIP)loYPQ+IQ - BibliogrQphy I )nuIVQfj neii~tan cc des )latbriaux 2 Tdatoc e CWpLlL tTtL)6apoundtllt laxi=~lt 6elLampAto30xamp 1tp6TIXOLt vtwv ILlE06Xwv 8 r aato( Comportamcnle di un palo di Fondnziol1c sotta Iaziooc di carichi verUcaH el oriuonlali ( bull Tdqo~ Estimation pratique des tasscmen difCen dull piu pendant un essai d chargnmc nL S EJweonoIlAo E Jlpp(~ n t)a0tLx6MTO~ TOO lMipout in-t txxtvTptlll OpoundIIII)twv ~ IkIUl(a)v ltMtUn blV
I) fiCll(ryu(61WVAo AYTOxi) fW UAlXWII 1 AoICo El~JLUtwO(~c
8 O cnayOJTOVtaXO 01~(w(JtC btl iAlXanxou lBafout
lilQ 6uo nopoywy~atwv Koro~yofltV tis r~v 68TPn~D
d dEJ--- q = - p (3)0011111WV EJ dx- ~ I - P Yj dx
POXDVIIWV
Q = - EPi - pdx + qdx = - EPi - pdx - k ydx (4)S S middotS S 0 0 ) 0
~ OJ(tmS (3) dva oaltjgtoplK~ ts1owOIS ypaflflK~ 40u pa9flo flpound aro6(pouS ouvrtt shyarasmiddot lHci arrOKtlOnKWS fltflovwfltvo ltjgtopTlo TO O(UTtpOV fltoS Tiis poundsowotws dVQl fllotv ( P = a ) orrOTt ~ OS T~S tsOWOtWS OUVaTQl va Mpu HiS ts~s ytvKaS flopltjgtas
y=e-Yx (Acosyx + Bsinyx)+eY (Ccosyx+D inyx) Yj (5)
Y - A chs yx cos yx I Bshyx cos yx + C chs yx sin yx + D shyx sin yx (5at)
TO A B C D tlvo oTa9(pai unooyl0flpoundval eme TciS opaKas OUV9~KQS Tiis OOKO To y oTa9tpa xapaKTljponK~ r~s OOKO (Ccefficientrelatif) xouoa oaOTOOtiS t I fl~KOS
y=V
kb (6)4EJ
onou k ltI OtlKTljS iMltjgtouS
b TO nMTOS Tiis OOKOU
E TO fl tTpOV taanKOTljTOS T~S OOKO
J ~ pO~ oopavtlas T~S oaTOfl~S T~S OOKOO
1lt] 0 (UPWflpoundV ntv mv T~S ytVK~S t1OWOtWS (] ) nptrrt tis ntv MOIv (5) ~ (Sa) vei npoo9towfitv (va opov oaltjgtopio(wS Tiis ytvK~S i1owo(WS 0 opoS OUTOS tKltjgtpO lETa Oei T~S flpound9600u T~S flETaPlr~s TWV oTa9poundpwv - Quadratures
EiS T~V YpoundVK~V npoundplmwOIv flas OOKOU flt flfjKOlt npoundJTtpaofltvov xwpllofltV T~V oOKev poundIS ~va wPofltvov 6p9floV OooTljflilTwv (arw v Tei apa TWV oaarlflilTwv xapaKTljplmiddot lOVTQl poundiTt orro EVO OUYKtVTpwfltvov ltjgtopTlov dTt (mo flETaPOh~v TOO Oovtfllfltvou ltjgtopshyTIOU
tx l Flg3
Eav omov 6-oKhlpWawfltv T~V (3 ) tiS Ko6( ollloTljfla 90 lXWfl(V va npooolop1awfl(V 4v oro9poundpar
EiS Tei apo TWV TfllflCITWV OuvOfl(9a vei ypaljlwflpoundv on
dyYdx M tlVQl OUV(X~
KO on ~ aouvtx(O T~S QlaouTa flE ntv IETapoh~v TOO ltjgtopTiou poundIs Tei tv h6y~ lltia -EXOfl(V a6poundv 4 (v - I ) t1owotls
Mvaflo OK6fll va ypaljlw poundIs ntv apx~v Ka TO TtOS r~s OOKO on
M = 0
Q = LUYKtVTPWltvov ltjgt0pTlov tis Til 11K po
~TO XW OUVOhKWS 4 (v - I ) + 4 = 4v tsowaltlS 00 rov unooyoflov 4v ara6(pwv
--------
---------
686 3 E+oPlloyrI TIle tv My~ 9eurowploe euroIe T6v unoAoY1I6v 9pound1IeuroAIWOeuroWe tnl EUKollnTwv KOTOKOP+WV naooilAwv
EcrTW (TT) TO aWlla apoundIlpoundAJapoundws KaTaaKpoundulis TlVOS (taKaalltvov) TO OTToiov apoundwmiddot pOuppoundv ws OTpoundPpoundOV aTTapallopcjgtWTOV tTTlKaa~IlpoundVOV tTT KaTaKOpucjgtwV TTaaaaAwv A B A B Au Bo aUlllltTPKWS TOTTOBpoundTTWtVWV WS TTpOS TO tTTITTpound50v T~S poundiK6voS TO 5EPshyXOIlpoundvOV 50 TOU Iltaou TOU TTpound51Aou KaTo T~V lvvoav z ElS TO a~llpoundia A lxollpoundv TTllKTWOV YTToatTOIlEV TOUS TTaaaaAous llolouS Ka tIlTTpoundTT~YlltvouS tVToS TOU tMcjgtouS tiS ~aeoS h ( ftTPOUIlpoundVOV aTTo TOU KaTwTtpou a~jlpoundlou TOU TTpound51Aou )
--- - - -----shy
-II I I Ai
~ Bi
tiT -Iv -_----0 ~ t oj
IS amp
IXmiddot ~ Flg4
------ --------
I
-
lJIIIIIII1mlwv bullnIOIIWV
KaB 6Aov T6 ~aeoS h TO l6lt1cjgtos BpoundwptiTa 0lloypoundvts Ilt 5poundIK~v k OTaBpoundp6v KaTw TOU h Bpoundwpoullpoundv l5acjgtos OTEPpoundOV aTTapa1l6pcjgtWTOV (~paxos) 01 TTaaaaAo oapoundv aUIlTTpoundPcjgttshyPOVTQI WS 50Kol tTTI tAaaTlKlis auvpoundxous ~pl~poundwe
9poundwpoullpoundv WS QPX~V TWV a~6vwv TO ~Ilpoundiov O KtvrpoV ~apoue TWV KpoundejlaAwv Ai 6Awv TWV TToaaaAwv
01 Q~OVpoundS OX Ka 011 tllejlolvovTo tv T~ ax~lloTl EaTw on TO a uvoAOV TWV 5uvallEWV TWV aaKoujltvwV tK T~e Qvw60IliS tTTI TOU aWIlOTOe BpoundIlpoundAwapoundws 615pound1 Illov KaTOKOshypuejlov auvOTolltvIv V Illov 0pSovTlav auvaTolltv~v H Ka tV Spounduyoe 3
H Il[fOT6TT10le TOU aWIlOTOe BpoundIlpoundAwapoundwc 5UVOTO va opaB~ 60 Tije fpoundTaKv~apoundWe TOU ~Iltlou O
-ECTTW 01 auvcrTwaQl Tf1e IltTOKV~apoundws TdU~e U KaTa TOV lI~ovo x 0 KOTO TOV l~ovo y KO w TTpocjgt~ we TTpOe z H aTpoejl~ apoundWpETTO apoundnK~ KOTO ~v TpyWV0fETPK~V lvvOIov ( QcrTpoundp6crTpOejlOS )
ETTolltvwe ~ KpoundejloA~ Ai TOU Tux6vTOe TToaaaAou AiBi QTTtxouao ToG 0 QTT6crTOOlV Xi ucjgtlcrToTQI Illov 0psovTlov IltTaBpoundOlV ui Illov KOTOK6pucjgtov TOOUTIV 01 KO Illov crTpOshycjgt~v WI
ElvQl 6t ui = u UI == U + Wxi ( 7) WI =r W
E~ oJ 6n 01 TTaaaoAo poundIvo KUKAKlie 5OlOlllie 5OilErPOU D H XOpoKtlPcrTK~ OToB Tij e 50KOO 911 poundIvo
VKD y = 4EJ
TPIIIIO II1ITIIW PllllVIIW
EnpoundllS1) 6 TToaaCLo~ 4gtopTl~poundTQl 1l6vov d~ T1)v Kpound4gta)1)v t1VQl P = 0 887
du Kal ~ (3) ypil4gtual (8)EJ dy + kDu = deg 1) )U0l~ T~~ lSla4gtopIKii~ (~~crwcrpoundwe tlVQl
u (y) = e- yY (A cos yy + Bsinyy) + cYY (C cos yy + D sin yy) (9)
ETTpoundllS1) oi TToaaa)o~ poundIvai KaTei Kavova IlpoundY0)ou Il~KOUe TO yh 6UVTQl TTpaKTlKWe va
epoundwple~ QTTpoundlpOV
Ele T1) ~oa~v B (y = h ) 1) 6p~~ovTla IltTaK[VI)Ol~ u = 0 OetV TO 6t(mpov Ilt)oe Tii~ u ( y ) TTptTTpoundl va tlva~ 1ll61v 6~ oiavli~TTOTpound Tl~1)v TOO y
~TOI C = D = deg KaJ 1) (9) y[VtTal u (y) = e-Y (A cos yy + B sin yy) (9a)
dVQl ~~ = - ye-YY[(A-B)COSyY+(A+B)Sinyy] (10)
~~~ =y2e- Y[(A-B) COSyy +(A+B)sinyy] - ye yY[ -y (A-B) sinyy+y (A +B) COSyy ]
= ye -yy [ - 2 B C08 yy + 2 A in yy ] (11)
~~~ = ye-yY [ 2 (A + B) Con yy + 2 (B - A) sin yy ] (12)
A~ei T1)v djptcr~v TWV A KaJ B eei XPlcr~lloTTo~~awlltv Tei~ cruVe1Ka~ de Tae 6p~aKeie etapoundlC
k I
I Xx oS I I
~
Ix S f~g 5
Earw (gtLei TOV Tux6vTa noaaa)ov AiBi al 6uVOllt~C aJ oaKOUlltVQl tTTI rf~ Kt4gta)~c aUTOU
Ni (KaTaK6pu4gto~)
Qi (6p~~OVTla)
Mi (pO~ KOIl~poundwe) E4gt lIaov TTpO~)tTToVTa~ 1l0VOV KaTa K6pu4gto~ TToaaa)o~ al Q Kai M tlVQl al aUTal 6~ B)ou~
TOUe TTaaao)ou~
Eeiv n 6 eip~elloe TWV TTaaaO)wv poundIvai
n Q = H E Ni = V (13)
n M + ENi Xi = 3
Eeiv F 1) liaToll1) Kal E TO IltTPOV t)aanKOTlToC TOO TTaaao)ou de T1)V ytV~K1)V TTtplTTTWshy
OlV poundIva _ Ni bull h + Ni - No (14)ul- EF 0 C
688 TTPWTO~ OpO~ riVCll ~ KClTOK6puto~ f1poundTOKivI]Ol~ T~~ KpoundcjgtClA~~ TOU TTaoooAou A6y~ tAa-OTlK~~ auTOU napaflopcjgtwapoundwc Tol) KUflaivpoundTCll 030 TToooaAol TPlP~C
090 raquo alXfl~lt
l)poundUTEP0C opoC dVQL KaTaK6pucjgt0C IpoundTa llt ivTjOlC T~lt Kpound+aA~c TOO TTaoOQAou 6y~ ~TTOXWP~OpoundwC TOU i1iQcjgtouC
l X 6 z
N
~UI1S~1J4 T~W 1 FrJtlon di llirllill
I--tshy
u lX 7
Plg6 f ig
Acxof1cVOl IITl 01 naaoaAol t6paloVTQL ltTTl ppoxou ware PU 9l0l~ vo poundIval TTpaKTlKWC 1I]I5EVlKit Kat I5cxolpoundvOl lila Id~ova aacjgtoAtlQv 15 = 100 elval
Ni h UI = Er
El~ N1=- (U +wX i) (15 )
Nib h u+ wXi = Er
A09ivroC OTi apxI) TWV Q~6vwv au ITrimlaquo TTpOe TO k BTWV Kt cjgtoAwv Ai TWV TToaaoAwv clvOt
lXi = 0
ETT0ltvWC V N ( X ) EF EF= 1 1 = U + w 1 - h-= nT (16)
Luv9 ~ Kal dc TO IIplCl
510 Y= 0
( 10) y = o ry= - w =- y( - B) ~ d
I B=u- ~1 dU) ( 11 )EJ - bull = M( dY )= 0
51]Aa51) M = EJ f 213 = - 2y EI ( u - ~ ) ( 11 )
Q = EJy 2 (A + B) = 2EJy (211 - ~) OTTOTpound al t~laWaEllt (13) ypacjgtovTal
H = 2EJ ny ( 2u __1_ w) y
EFV = n - h- u ( I)
- 2 I J ( W) + EF ~ bull =- J1 y~ o 11 - -- w - 1 y h
To OUOTTJlcl (I) IltiS tmTptTTEI va uTToAoyiowlev TO u v OL w
889 TPAPO lollTlIWV pnXOVlKWV
TOUTWV EUPE9tVTWV UTTOAOyiroflEV Tel M Q Ni EK TOU OUltmiflQTO~
M= - 2y EJ (U - ~ )
Q= 2y EJ (2u - ~) ( II )
Nl= E (U+WXI)
nap a T ~ P I) 0 L ~ Al TLfla TWV U u W dvaL TTOAU fllKpai W~ tK TOUTOU BE CITTQIHiTal fIltvaAI) aKpl~EIQ TWV TTpa~EWV KQTa TOV UTTOAOYIOfioV TWV H aKpi~ELa TOO AoyapI9f1LKOU Kav6vo~ BEv poundIvaL ETTapK~~
4 nap66uYila uIToAoYLOlloU
Earw TTpOr lmoAoYLofiov 9EflEAiwOl~ tBpilvou yEcpupa~ H 9EflEAiwOL~ aTTonpoundiTQL eITTo ~va TTtBIAOV iiKaflTTTov tBpar6f1EVOV tTTI OKTW TTaooilAWV KQTQKOpUCPWV BlafiETpou 100 m Ka TOTT09ETT)fltvwv w~ tv TQ OX~flaTI
I
I 0 00
I ~
( jlt~ middotmiddot (11 (
~ t
N I
EilaquoqoO( 2 Soil 2 o o
o 0 ~
Ix a Flg8
890 EaTW ~ KaTanOVl0u TOU 9tl1poundA(OU pound1lt TO KtVTPOV nilt ~aotwlt 0 ~ KaTW91 KaTaK Mval1llt V = 1400 TJIIIII 6pI~ raquo H = 851 HAm1m poni) S = 1000110
pnXDVlIW Eelgt 6aov TO rrtl5LAov SEwpEiTaL TEAtlWlt QKal1TTTOV ~ AELToupyla aopponlalt TOU npoal5Loshyp(~ETal ( K nilt I1poundTaKLv~atwlt TOU KtVTpOU 0 ( u u W )
H KaTClTT6vlOLlt TOG rraaoaAOU dlt~o A rrap(oTaTal 11pound TOlt (M N Q )
ITOI)(da t6b+ouc
E 15 a cjgt 0 lt I nlAwI5Elt uyp6v TpoundAtiWlt QI1010YEVpoundlt 11pound oraS I5t1KTT)v K = 41 01 1m E 15 a cjgt lt 2 Bpaxw15tlt TEAtlWlt 6vurroxwplTOV
XTOI)(da aaaa~wv
a ) rroloTllt oKupol5[l1aTolt B 160 E = 210000 kg lem TpoundAIKOV I1trpov (AaOTlK6TlTOlt
E = _ E_ 1+ 1
t - lt 0 050 E- 210000 150 000 ~ 1510 timVTOlt TOU poundaoult p = rp - 1 + 050 I
J D _ 314 100 050 10- 1 m~) pom al5pa vtialt b4 - 64
Y ) ~ xapaKTlpIOTlKT) oTa8poundpa -V kD - V 4 10 100 = 033 y - 4El - 4 15 10 050 to I
m
1 y=3OO y = 0110 y=0036
lt ) bull - ~ F D 314 middot100 080 laTol1 1 TOU rraooou bull = 4 = 4 m
EJ = 150 10 050 to-I = 075 10 tm
EF 150 to 080 = 060 10 tm - h- = 2000
pound ) apISl1olt naaaaAwv n = 8 Qrr6aTaollt naooaAwv arro TO KtVTpOV 0 X = 120
IXL = 8 120 = 1150
AI ypoundvIKal t~laWJpoundllt KaTO TO np0lyouI1Eva poundIvai
( I ) 2EJ ny~ ( 2u - ~ ) = H
EFn-h- = V
- 2I1YEJ(U -~) + W EF lXL = EY h
( ) M = - 2yEJ ( 11 -~) )
Q= 2YEJ(2U - ~ )
E1 ( )NI = - h + WXI
EniAuollt oultTrl)I1QTolt ( I )
2 075 10 8 0036 (2u - 3w) = - 85-+
8 middot 060 10 = 1400 -Ishy+shy
- 2 middot 8 middot 011 middot 075 middot 10 (u- 3w) + w 060 10 middot 1150 = - 1000
691 TlInpoRoAmlWY pnXnVIKWY
01 t~awaE~ ypa4gtoVTa 4320 (2u _ 3w) = 85 10-3
1400 U = 48010
-132 (u-3w) +690w= -100010-3
U = - 2904 10- v = - 292 10- W= - 1283 10-
EUpEetvTwV TWV u v W aVTlKaeaTw~Ev TG~ Tl~a~ TWV d~ TO aUCITTwa ( II ~ Kal EXOflEV
M=-2middot 011middot075 middot10 ( 2904+3middot1283) 10-3
Q = 2middot0036 middot 075middot10 (-22904+31263) to-
N = 060middot 10 [ 292 plusmn (-1 283) 120 1 10-
t~ WV TTpoKumEI M = - 1550m Q c - 1060
80 N= + 270
E TT a ~ eE u a I ~ 0) nQ = H 8 middot 1060=85
~) I Mo = - 1000 - 4 270 120 + 480 120 - 8middot 1550 - 1000
napaTraplalli
Ei~ n]v KE4gtaA~v TWV TTaaaaAwv A ~ Taal~ tM4gtou~ Elval
~=-ku = 2904 10-middot 410= 1162 tm ~ 116kgcm
Eav TO Eoa4gto~ ouvaTa v avaap~ n)v TamV Tau~v tTTpoundlO~ Q = 1060 Kal 0 = 100 m 1060
ETTnal on ~ Tpound~vouaa ouva~~ TTapaAa~pavnQj poundi~ paao~ 11 62 = 090 m
5 luYKpau IlE laOaTOTlKrlV IlE901lov KaTG n]v iaOaTQnK~V ~teooov OEv a~~avovTa lJTT o~v at iOI6~T(~ TOO toapou~ 00T( ~ aKa~~(a TWV TTaaaaAwv OTTOT(
85Q= -8- = 1060
001
deg10651=
A M
Ibull
gt--
M= O
1400 1000 305 N = - 8- plusmn 23201202 120= 175 plusmn 130 = 45
F=4 middot080=320m
IX 9 Flg9
laquo Ai TTpoKumouaal olapopai Elval ToaoOTOV ~EyaMT(pal oaov aU~aVEI ~ pOTT~ E raquo
892 BIP)loYPQ+IQ - BibliogrQphy I )nuIVQfj neii~tan cc des )latbriaux 2 Tdatoc e CWpLlL tTtL)6apoundtllt laxi=~lt 6elLampAto30xamp 1tp6TIXOLt vtwv ILlE06Xwv 8 r aato( Comportamcnle di un palo di Fondnziol1c sotta Iaziooc di carichi verUcaH el oriuonlali ( bull Tdqo~ Estimation pratique des tasscmen difCen dull piu pendant un essai d chargnmc nL S EJweonoIlAo E Jlpp(~ n t)a0tLx6MTO~ TOO lMipout in-t txxtvTptlll OpoundIIII)twv ~ IkIUl(a)v ltMtUn blV
I) fiCll(ryu(61WVAo AYTOxi) fW UAlXWII 1 AoICo El~JLUtwO(~c
8 O cnayOJTOVtaXO 01~(w(JtC btl iAlXanxou lBafout
--------
---------
686 3 E+oPlloyrI TIle tv My~ 9eurowploe euroIe T6v unoAoY1I6v 9pound1IeuroAIWOeuroWe tnl EUKollnTwv KOTOKOP+WV naooilAwv
EcrTW (TT) TO aWlla apoundIlpoundAJapoundws KaTaaKpoundulis TlVOS (taKaalltvov) TO OTToiov apoundwmiddot pOuppoundv ws OTpoundPpoundOV aTTapallopcjgtWTOV tTTlKaa~IlpoundVOV tTT KaTaKOpucjgtwV TTaaaaAwv A B A B Au Bo aUlllltTPKWS TOTTOBpoundTTWtVWV WS TTpOS TO tTTITTpound50v T~S poundiK6voS TO 5EPshyXOIlpoundvOV 50 TOU Iltaou TOU TTpound51Aou KaTo T~V lvvoav z ElS TO a~llpoundia A lxollpoundv TTllKTWOV YTToatTOIlEV TOUS TTaaaaAous llolouS Ka tIlTTpoundTT~YlltvouS tVToS TOU tMcjgtouS tiS ~aeoS h ( ftTPOUIlpoundVOV aTTo TOU KaTwTtpou a~jlpoundlou TOU TTpound51Aou )
--- - - -----shy
-II I I Ai
~ Bi
tiT -Iv -_----0 ~ t oj
IS amp
IXmiddot ~ Flg4
------ --------
I
-
lJIIIIIII1mlwv bullnIOIIWV
KaB 6Aov T6 ~aeoS h TO l6lt1cjgtos BpoundwptiTa 0lloypoundvts Ilt 5poundIK~v k OTaBpoundp6v KaTw TOU h Bpoundwpoullpoundv l5acjgtos OTEPpoundOV aTTapa1l6pcjgtWTOV (~paxos) 01 TTaaaaAo oapoundv aUIlTTpoundPcjgttshyPOVTQI WS 50Kol tTTI tAaaTlKlis auvpoundxous ~pl~poundwe
9poundwpoullpoundv WS QPX~V TWV a~6vwv TO ~Ilpoundiov O KtvrpoV ~apoue TWV KpoundejlaAwv Ai 6Awv TWV TToaaaAwv
01 Q~OVpoundS OX Ka 011 tllejlolvovTo tv T~ ax~lloTl EaTw on TO a uvoAOV TWV 5uvallEWV TWV aaKoujltvwV tK T~e Qvw60IliS tTTI TOU aWIlOTOe BpoundIlpoundAwapoundws 615pound1 Illov KaTOKOshypuejlov auvOTolltvIv V Illov 0pSovTlav auvaTolltv~v H Ka tV Spounduyoe 3
H Il[fOT6TT10le TOU aWIlOTOe BpoundIlpoundAwapoundwc 5UVOTO va opaB~ 60 Tije fpoundTaKv~apoundWe TOU ~Iltlou O
-ECTTW 01 auvcrTwaQl Tf1e IltTOKV~apoundws TdU~e U KaTa TOV lI~ovo x 0 KOTO TOV l~ovo y KO w TTpocjgt~ we TTpOe z H aTpoejl~ apoundWpETTO apoundnK~ KOTO ~v TpyWV0fETPK~V lvvOIov ( QcrTpoundp6crTpOejlOS )
ETTolltvwe ~ KpoundejloA~ Ai TOU Tux6vTOe TToaaaAou AiBi QTTtxouao ToG 0 QTT6crTOOlV Xi ucjgtlcrToTQI Illov 0psovTlov IltTaBpoundOlV ui Illov KOTOK6pucjgtov TOOUTIV 01 KO Illov crTpOshycjgt~v WI
ElvQl 6t ui = u UI == U + Wxi ( 7) WI =r W
E~ oJ 6n 01 TTaaaoAo poundIvo KUKAKlie 5OlOlllie 5OilErPOU D H XOpoKtlPcrTK~ OToB Tij e 50KOO 911 poundIvo
VKD y = 4EJ
TPIIIIO II1ITIIW PllllVIIW
EnpoundllS1) 6 TToaaCLo~ 4gtopTl~poundTQl 1l6vov d~ T1)v Kpound4gta)1)v t1VQl P = 0 887
du Kal ~ (3) ypil4gtual (8)EJ dy + kDu = deg 1) )U0l~ T~~ lSla4gtopIKii~ (~~crwcrpoundwe tlVQl
u (y) = e- yY (A cos yy + Bsinyy) + cYY (C cos yy + D sin yy) (9)
ETTpoundllS1) oi TToaaa)o~ poundIvai KaTei Kavova IlpoundY0)ou Il~KOUe TO yh 6UVTQl TTpaKTlKWe va
epoundwple~ QTTpoundlpOV
Ele T1) ~oa~v B (y = h ) 1) 6p~~ovTla IltTaK[VI)Ol~ u = 0 OetV TO 6t(mpov Ilt)oe Tii~ u ( y ) TTptTTpoundl va tlva~ 1ll61v 6~ oiavli~TTOTpound Tl~1)v TOO y
~TOI C = D = deg KaJ 1) (9) y[VtTal u (y) = e-Y (A cos yy + B sin yy) (9a)
dVQl ~~ = - ye-YY[(A-B)COSyY+(A+B)Sinyy] (10)
~~~ =y2e- Y[(A-B) COSyy +(A+B)sinyy] - ye yY[ -y (A-B) sinyy+y (A +B) COSyy ]
= ye -yy [ - 2 B C08 yy + 2 A in yy ] (11)
~~~ = ye-yY [ 2 (A + B) Con yy + 2 (B - A) sin yy ] (12)
A~ei T1)v djptcr~v TWV A KaJ B eei XPlcr~lloTTo~~awlltv Tei~ cruVe1Ka~ de Tae 6p~aKeie etapoundlC
k I
I Xx oS I I
~
Ix S f~g 5
Earw (gtLei TOV Tux6vTa noaaa)ov AiBi al 6uVOllt~C aJ oaKOUlltVQl tTTI rf~ Kt4gta)~c aUTOU
Ni (KaTaK6pu4gto~)
Qi (6p~~OVTla)
Mi (pO~ KOIl~poundwe) E4gt lIaov TTpO~)tTToVTa~ 1l0VOV KaTa K6pu4gto~ TToaaa)o~ al Q Kai M tlVQl al aUTal 6~ B)ou~
TOUe TTaaao)ou~
Eeiv n 6 eip~elloe TWV TTaaaO)wv poundIvai
n Q = H E Ni = V (13)
n M + ENi Xi = 3
Eeiv F 1) liaToll1) Kal E TO IltTPOV t)aanKOTlToC TOO TTaaao)ou de T1)V ytV~K1)V TTtplTTTWshy
OlV poundIva _ Ni bull h + Ni - No (14)ul- EF 0 C
688 TTPWTO~ OpO~ riVCll ~ KClTOK6puto~ f1poundTOKivI]Ol~ T~~ KpoundcjgtClA~~ TOU TTaoooAou A6y~ tAa-OTlK~~ auTOU napaflopcjgtwapoundwc Tol) KUflaivpoundTCll 030 TToooaAol TPlP~C
090 raquo alXfl~lt
l)poundUTEP0C opoC dVQL KaTaK6pucjgt0C IpoundTa llt ivTjOlC T~lt Kpound+aA~c TOO TTaoOQAou 6y~ ~TTOXWP~OpoundwC TOU i1iQcjgtouC
l X 6 z
N
~UI1S~1J4 T~W 1 FrJtlon di llirllill
I--tshy
u lX 7
Plg6 f ig
Acxof1cVOl IITl 01 naaoaAol t6paloVTQL ltTTl ppoxou ware PU 9l0l~ vo poundIval TTpaKTlKWC 1I]I5EVlKit Kat I5cxolpoundvOl lila Id~ova aacjgtoAtlQv 15 = 100 elval
Ni h UI = Er
El~ N1=- (U +wX i) (15 )
Nib h u+ wXi = Er
A09ivroC OTi apxI) TWV Q~6vwv au ITrimlaquo TTpOe TO k BTWV Kt cjgtoAwv Ai TWV TToaaoAwv clvOt
lXi = 0
ETT0ltvWC V N ( X ) EF EF= 1 1 = U + w 1 - h-= nT (16)
Luv9 ~ Kal dc TO IIplCl
510 Y= 0
( 10) y = o ry= - w =- y( - B) ~ d
I B=u- ~1 dU) ( 11 )EJ - bull = M( dY )= 0
51]Aa51) M = EJ f 213 = - 2y EI ( u - ~ ) ( 11 )
Q = EJy 2 (A + B) = 2EJy (211 - ~) OTTOTpound al t~laWaEllt (13) ypacjgtovTal
H = 2EJ ny ( 2u __1_ w) y
EFV = n - h- u ( I)
- 2 I J ( W) + EF ~ bull =- J1 y~ o 11 - -- w - 1 y h
To OUOTTJlcl (I) IltiS tmTptTTEI va uTToAoyiowlev TO u v OL w
889 TPAPO lollTlIWV pnXOVlKWV
TOUTWV EUPE9tVTWV UTTOAOyiroflEV Tel M Q Ni EK TOU OUltmiflQTO~
M= - 2y EJ (U - ~ )
Q= 2y EJ (2u - ~) ( II )
Nl= E (U+WXI)
nap a T ~ P I) 0 L ~ Al TLfla TWV U u W dvaL TTOAU fllKpai W~ tK TOUTOU BE CITTQIHiTal fIltvaAI) aKpl~EIQ TWV TTpa~EWV KQTa TOV UTTOAOYIOfioV TWV H aKpi~ELa TOO AoyapI9f1LKOU Kav6vo~ BEv poundIvaL ETTapK~~
4 nap66uYila uIToAoYLOlloU
Earw TTpOr lmoAoYLofiov 9EflEAiwOl~ tBpilvou yEcpupa~ H 9EflEAiwOL~ aTTonpoundiTQL eITTo ~va TTtBIAOV iiKaflTTTov tBpar6f1EVOV tTTI OKTW TTaooilAWV KQTQKOpUCPWV BlafiETpou 100 m Ka TOTT09ETT)fltvwv w~ tv TQ OX~flaTI
I
I 0 00
I ~
( jlt~ middotmiddot (11 (
~ t
N I
EilaquoqoO( 2 Soil 2 o o
o 0 ~
Ix a Flg8
890 EaTW ~ KaTanOVl0u TOU 9tl1poundA(OU pound1lt TO KtVTPOV nilt ~aotwlt 0 ~ KaTW91 KaTaK Mval1llt V = 1400 TJIIIII 6pI~ raquo H = 851 HAm1m poni) S = 1000110
pnXDVlIW Eelgt 6aov TO rrtl5LAov SEwpEiTaL TEAtlWlt QKal1TTTOV ~ AELToupyla aopponlalt TOU npoal5Loshyp(~ETal ( K nilt I1poundTaKLv~atwlt TOU KtVTpOU 0 ( u u W )
H KaTClTT6vlOLlt TOG rraaoaAOU dlt~o A rrap(oTaTal 11pound TOlt (M N Q )
ITOI)(da t6b+ouc
E 15 a cjgt 0 lt I nlAwI5Elt uyp6v TpoundAtiWlt QI1010YEVpoundlt 11pound oraS I5t1KTT)v K = 41 01 1m E 15 a cjgt lt 2 Bpaxw15tlt TEAtlWlt 6vurroxwplTOV
XTOI)(da aaaa~wv
a ) rroloTllt oKupol5[l1aTolt B 160 E = 210000 kg lem TpoundAIKOV I1trpov (AaOTlK6TlTOlt
E = _ E_ 1+ 1
t - lt 0 050 E- 210000 150 000 ~ 1510 timVTOlt TOU poundaoult p = rp - 1 + 050 I
J D _ 314 100 050 10- 1 m~) pom al5pa vtialt b4 - 64
Y ) ~ xapaKTlpIOTlKT) oTa8poundpa -V kD - V 4 10 100 = 033 y - 4El - 4 15 10 050 to I
m
1 y=3OO y = 0110 y=0036
lt ) bull - ~ F D 314 middot100 080 laTol1 1 TOU rraooou bull = 4 = 4 m
EJ = 150 10 050 to-I = 075 10 tm
EF 150 to 080 = 060 10 tm - h- = 2000
pound ) apISl1olt naaaaAwv n = 8 Qrr6aTaollt naooaAwv arro TO KtVTpOV 0 X = 120
IXL = 8 120 = 1150
AI ypoundvIKal t~laWJpoundllt KaTO TO np0lyouI1Eva poundIvai
( I ) 2EJ ny~ ( 2u - ~ ) = H
EFn-h- = V
- 2I1YEJ(U -~) + W EF lXL = EY h
( ) M = - 2yEJ ( 11 -~) )
Q= 2YEJ(2U - ~ )
E1 ( )NI = - h + WXI
EniAuollt oultTrl)I1QTolt ( I )
2 075 10 8 0036 (2u - 3w) = - 85-+
8 middot 060 10 = 1400 -Ishy+shy
- 2 middot 8 middot 011 middot 075 middot 10 (u- 3w) + w 060 10 middot 1150 = - 1000
691 TlInpoRoAmlWY pnXnVIKWY
01 t~awaE~ ypa4gtoVTa 4320 (2u _ 3w) = 85 10-3
1400 U = 48010
-132 (u-3w) +690w= -100010-3
U = - 2904 10- v = - 292 10- W= - 1283 10-
EUpEetvTwV TWV u v W aVTlKaeaTw~Ev TG~ Tl~a~ TWV d~ TO aUCITTwa ( II ~ Kal EXOflEV
M=-2middot 011middot075 middot10 ( 2904+3middot1283) 10-3
Q = 2middot0036 middot 075middot10 (-22904+31263) to-
N = 060middot 10 [ 292 plusmn (-1 283) 120 1 10-
t~ WV TTpoKumEI M = - 1550m Q c - 1060
80 N= + 270
E TT a ~ eE u a I ~ 0) nQ = H 8 middot 1060=85
~) I Mo = - 1000 - 4 270 120 + 480 120 - 8middot 1550 - 1000
napaTraplalli
Ei~ n]v KE4gtaA~v TWV TTaaaaAwv A ~ Taal~ tM4gtou~ Elval
~=-ku = 2904 10-middot 410= 1162 tm ~ 116kgcm
Eav TO Eoa4gto~ ouvaTa v avaap~ n)v TamV Tau~v tTTpoundlO~ Q = 1060 Kal 0 = 100 m 1060
ETTnal on ~ Tpound~vouaa ouva~~ TTapaAa~pavnQj poundi~ paao~ 11 62 = 090 m
5 luYKpau IlE laOaTOTlKrlV IlE901lov KaTG n]v iaOaTQnK~V ~teooov OEv a~~avovTa lJTT o~v at iOI6~T(~ TOO toapou~ 00T( ~ aKa~~(a TWV TTaaaaAwv OTTOT(
85Q= -8- = 1060
001
deg10651=
A M
Ibull
gt--
M= O
1400 1000 305 N = - 8- plusmn 23201202 120= 175 plusmn 130 = 45
F=4 middot080=320m
IX 9 Flg9
laquo Ai TTpoKumouaal olapopai Elval ToaoOTOV ~EyaMT(pal oaov aU~aVEI ~ pOTT~ E raquo
892 BIP)loYPQ+IQ - BibliogrQphy I )nuIVQfj neii~tan cc des )latbriaux 2 Tdatoc e CWpLlL tTtL)6apoundtllt laxi=~lt 6elLampAto30xamp 1tp6TIXOLt vtwv ILlE06Xwv 8 r aato( Comportamcnle di un palo di Fondnziol1c sotta Iaziooc di carichi verUcaH el oriuonlali ( bull Tdqo~ Estimation pratique des tasscmen difCen dull piu pendant un essai d chargnmc nL S EJweonoIlAo E Jlpp(~ n t)a0tLx6MTO~ TOO lMipout in-t txxtvTptlll OpoundIIII)twv ~ IkIUl(a)v ltMtUn blV
I) fiCll(ryu(61WVAo AYTOxi) fW UAlXWII 1 AoICo El~JLUtwO(~c
8 O cnayOJTOVtaXO 01~(w(JtC btl iAlXanxou lBafout
TPIIIIO II1ITIIW PllllVIIW
EnpoundllS1) 6 TToaaCLo~ 4gtopTl~poundTQl 1l6vov d~ T1)v Kpound4gta)1)v t1VQl P = 0 887
du Kal ~ (3) ypil4gtual (8)EJ dy + kDu = deg 1) )U0l~ T~~ lSla4gtopIKii~ (~~crwcrpoundwe tlVQl
u (y) = e- yY (A cos yy + Bsinyy) + cYY (C cos yy + D sin yy) (9)
ETTpoundllS1) oi TToaaa)o~ poundIvai KaTei Kavova IlpoundY0)ou Il~KOUe TO yh 6UVTQl TTpaKTlKWe va
epoundwple~ QTTpoundlpOV
Ele T1) ~oa~v B (y = h ) 1) 6p~~ovTla IltTaK[VI)Ol~ u = 0 OetV TO 6t(mpov Ilt)oe Tii~ u ( y ) TTptTTpoundl va tlva~ 1ll61v 6~ oiavli~TTOTpound Tl~1)v TOO y
~TOI C = D = deg KaJ 1) (9) y[VtTal u (y) = e-Y (A cos yy + B sin yy) (9a)
dVQl ~~ = - ye-YY[(A-B)COSyY+(A+B)Sinyy] (10)
~~~ =y2e- Y[(A-B) COSyy +(A+B)sinyy] - ye yY[ -y (A-B) sinyy+y (A +B) COSyy ]
= ye -yy [ - 2 B C08 yy + 2 A in yy ] (11)
~~~ = ye-yY [ 2 (A + B) Con yy + 2 (B - A) sin yy ] (12)
A~ei T1)v djptcr~v TWV A KaJ B eei XPlcr~lloTTo~~awlltv Tei~ cruVe1Ka~ de Tae 6p~aKeie etapoundlC
k I
I Xx oS I I
~
Ix S f~g 5
Earw (gtLei TOV Tux6vTa noaaa)ov AiBi al 6uVOllt~C aJ oaKOUlltVQl tTTI rf~ Kt4gta)~c aUTOU
Ni (KaTaK6pu4gto~)
Qi (6p~~OVTla)
Mi (pO~ KOIl~poundwe) E4gt lIaov TTpO~)tTToVTa~ 1l0VOV KaTa K6pu4gto~ TToaaa)o~ al Q Kai M tlVQl al aUTal 6~ B)ou~
TOUe TTaaao)ou~
Eeiv n 6 eip~elloe TWV TTaaaO)wv poundIvai
n Q = H E Ni = V (13)
n M + ENi Xi = 3
Eeiv F 1) liaToll1) Kal E TO IltTPOV t)aanKOTlToC TOO TTaaao)ou de T1)V ytV~K1)V TTtplTTTWshy
OlV poundIva _ Ni bull h + Ni - No (14)ul- EF 0 C
688 TTPWTO~ OpO~ riVCll ~ KClTOK6puto~ f1poundTOKivI]Ol~ T~~ KpoundcjgtClA~~ TOU TTaoooAou A6y~ tAa-OTlK~~ auTOU napaflopcjgtwapoundwc Tol) KUflaivpoundTCll 030 TToooaAol TPlP~C
090 raquo alXfl~lt
l)poundUTEP0C opoC dVQL KaTaK6pucjgt0C IpoundTa llt ivTjOlC T~lt Kpound+aA~c TOO TTaoOQAou 6y~ ~TTOXWP~OpoundwC TOU i1iQcjgtouC
l X 6 z
N
~UI1S~1J4 T~W 1 FrJtlon di llirllill
I--tshy
u lX 7
Plg6 f ig
Acxof1cVOl IITl 01 naaoaAol t6paloVTQL ltTTl ppoxou ware PU 9l0l~ vo poundIval TTpaKTlKWC 1I]I5EVlKit Kat I5cxolpoundvOl lila Id~ova aacjgtoAtlQv 15 = 100 elval
Ni h UI = Er
El~ N1=- (U +wX i) (15 )
Nib h u+ wXi = Er
A09ivroC OTi apxI) TWV Q~6vwv au ITrimlaquo TTpOe TO k BTWV Kt cjgtoAwv Ai TWV TToaaoAwv clvOt
lXi = 0
ETT0ltvWC V N ( X ) EF EF= 1 1 = U + w 1 - h-= nT (16)
Luv9 ~ Kal dc TO IIplCl
510 Y= 0
( 10) y = o ry= - w =- y( - B) ~ d
I B=u- ~1 dU) ( 11 )EJ - bull = M( dY )= 0
51]Aa51) M = EJ f 213 = - 2y EI ( u - ~ ) ( 11 )
Q = EJy 2 (A + B) = 2EJy (211 - ~) OTTOTpound al t~laWaEllt (13) ypacjgtovTal
H = 2EJ ny ( 2u __1_ w) y
EFV = n - h- u ( I)
- 2 I J ( W) + EF ~ bull =- J1 y~ o 11 - -- w - 1 y h
To OUOTTJlcl (I) IltiS tmTptTTEI va uTToAoyiowlev TO u v OL w
889 TPAPO lollTlIWV pnXOVlKWV
TOUTWV EUPE9tVTWV UTTOAOyiroflEV Tel M Q Ni EK TOU OUltmiflQTO~
M= - 2y EJ (U - ~ )
Q= 2y EJ (2u - ~) ( II )
Nl= E (U+WXI)
nap a T ~ P I) 0 L ~ Al TLfla TWV U u W dvaL TTOAU fllKpai W~ tK TOUTOU BE CITTQIHiTal fIltvaAI) aKpl~EIQ TWV TTpa~EWV KQTa TOV UTTOAOYIOfioV TWV H aKpi~ELa TOO AoyapI9f1LKOU Kav6vo~ BEv poundIvaL ETTapK~~
4 nap66uYila uIToAoYLOlloU
Earw TTpOr lmoAoYLofiov 9EflEAiwOl~ tBpilvou yEcpupa~ H 9EflEAiwOL~ aTTonpoundiTQL eITTo ~va TTtBIAOV iiKaflTTTov tBpar6f1EVOV tTTI OKTW TTaooilAWV KQTQKOpUCPWV BlafiETpou 100 m Ka TOTT09ETT)fltvwv w~ tv TQ OX~flaTI
I
I 0 00
I ~
( jlt~ middotmiddot (11 (
~ t
N I
EilaquoqoO( 2 Soil 2 o o
o 0 ~
Ix a Flg8
890 EaTW ~ KaTanOVl0u TOU 9tl1poundA(OU pound1lt TO KtVTPOV nilt ~aotwlt 0 ~ KaTW91 KaTaK Mval1llt V = 1400 TJIIIII 6pI~ raquo H = 851 HAm1m poni) S = 1000110
pnXDVlIW Eelgt 6aov TO rrtl5LAov SEwpEiTaL TEAtlWlt QKal1TTTOV ~ AELToupyla aopponlalt TOU npoal5Loshyp(~ETal ( K nilt I1poundTaKLv~atwlt TOU KtVTpOU 0 ( u u W )
H KaTClTT6vlOLlt TOG rraaoaAOU dlt~o A rrap(oTaTal 11pound TOlt (M N Q )
ITOI)(da t6b+ouc
E 15 a cjgt 0 lt I nlAwI5Elt uyp6v TpoundAtiWlt QI1010YEVpoundlt 11pound oraS I5t1KTT)v K = 41 01 1m E 15 a cjgt lt 2 Bpaxw15tlt TEAtlWlt 6vurroxwplTOV
XTOI)(da aaaa~wv
a ) rroloTllt oKupol5[l1aTolt B 160 E = 210000 kg lem TpoundAIKOV I1trpov (AaOTlK6TlTOlt
E = _ E_ 1+ 1
t - lt 0 050 E- 210000 150 000 ~ 1510 timVTOlt TOU poundaoult p = rp - 1 + 050 I
J D _ 314 100 050 10- 1 m~) pom al5pa vtialt b4 - 64
Y ) ~ xapaKTlpIOTlKT) oTa8poundpa -V kD - V 4 10 100 = 033 y - 4El - 4 15 10 050 to I
m
1 y=3OO y = 0110 y=0036
lt ) bull - ~ F D 314 middot100 080 laTol1 1 TOU rraooou bull = 4 = 4 m
EJ = 150 10 050 to-I = 075 10 tm
EF 150 to 080 = 060 10 tm - h- = 2000
pound ) apISl1olt naaaaAwv n = 8 Qrr6aTaollt naooaAwv arro TO KtVTpOV 0 X = 120
IXL = 8 120 = 1150
AI ypoundvIKal t~laWJpoundllt KaTO TO np0lyouI1Eva poundIvai
( I ) 2EJ ny~ ( 2u - ~ ) = H
EFn-h- = V
- 2I1YEJ(U -~) + W EF lXL = EY h
( ) M = - 2yEJ ( 11 -~) )
Q= 2YEJ(2U - ~ )
E1 ( )NI = - h + WXI
EniAuollt oultTrl)I1QTolt ( I )
2 075 10 8 0036 (2u - 3w) = - 85-+
8 middot 060 10 = 1400 -Ishy+shy
- 2 middot 8 middot 011 middot 075 middot 10 (u- 3w) + w 060 10 middot 1150 = - 1000
691 TlInpoRoAmlWY pnXnVIKWY
01 t~awaE~ ypa4gtoVTa 4320 (2u _ 3w) = 85 10-3
1400 U = 48010
-132 (u-3w) +690w= -100010-3
U = - 2904 10- v = - 292 10- W= - 1283 10-
EUpEetvTwV TWV u v W aVTlKaeaTw~Ev TG~ Tl~a~ TWV d~ TO aUCITTwa ( II ~ Kal EXOflEV
M=-2middot 011middot075 middot10 ( 2904+3middot1283) 10-3
Q = 2middot0036 middot 075middot10 (-22904+31263) to-
N = 060middot 10 [ 292 plusmn (-1 283) 120 1 10-
t~ WV TTpoKumEI M = - 1550m Q c - 1060
80 N= + 270
E TT a ~ eE u a I ~ 0) nQ = H 8 middot 1060=85
~) I Mo = - 1000 - 4 270 120 + 480 120 - 8middot 1550 - 1000
napaTraplalli
Ei~ n]v KE4gtaA~v TWV TTaaaaAwv A ~ Taal~ tM4gtou~ Elval
~=-ku = 2904 10-middot 410= 1162 tm ~ 116kgcm
Eav TO Eoa4gto~ ouvaTa v avaap~ n)v TamV Tau~v tTTpoundlO~ Q = 1060 Kal 0 = 100 m 1060
ETTnal on ~ Tpound~vouaa ouva~~ TTapaAa~pavnQj poundi~ paao~ 11 62 = 090 m
5 luYKpau IlE laOaTOTlKrlV IlE901lov KaTG n]v iaOaTQnK~V ~teooov OEv a~~avovTa lJTT o~v at iOI6~T(~ TOO toapou~ 00T( ~ aKa~~(a TWV TTaaaaAwv OTTOT(
85Q= -8- = 1060
001
deg10651=
A M
Ibull
gt--
M= O
1400 1000 305 N = - 8- plusmn 23201202 120= 175 plusmn 130 = 45
F=4 middot080=320m
IX 9 Flg9
laquo Ai TTpoKumouaal olapopai Elval ToaoOTOV ~EyaMT(pal oaov aU~aVEI ~ pOTT~ E raquo
892 BIP)loYPQ+IQ - BibliogrQphy I )nuIVQfj neii~tan cc des )latbriaux 2 Tdatoc e CWpLlL tTtL)6apoundtllt laxi=~lt 6elLampAto30xamp 1tp6TIXOLt vtwv ILlE06Xwv 8 r aato( Comportamcnle di un palo di Fondnziol1c sotta Iaziooc di carichi verUcaH el oriuonlali ( bull Tdqo~ Estimation pratique des tasscmen difCen dull piu pendant un essai d chargnmc nL S EJweonoIlAo E Jlpp(~ n t)a0tLx6MTO~ TOO lMipout in-t txxtvTptlll OpoundIIII)twv ~ IkIUl(a)v ltMtUn blV
I) fiCll(ryu(61WVAo AYTOxi) fW UAlXWII 1 AoICo El~JLUtwO(~c
8 O cnayOJTOVtaXO 01~(w(JtC btl iAlXanxou lBafout
688 TTPWTO~ OpO~ riVCll ~ KClTOK6puto~ f1poundTOKivI]Ol~ T~~ KpoundcjgtClA~~ TOU TTaoooAou A6y~ tAa-OTlK~~ auTOU napaflopcjgtwapoundwc Tol) KUflaivpoundTCll 030 TToooaAol TPlP~C
090 raquo alXfl~lt
l)poundUTEP0C opoC dVQL KaTaK6pucjgt0C IpoundTa llt ivTjOlC T~lt Kpound+aA~c TOO TTaoOQAou 6y~ ~TTOXWP~OpoundwC TOU i1iQcjgtouC
l X 6 z
N
~UI1S~1J4 T~W 1 FrJtlon di llirllill
I--tshy
u lX 7
Plg6 f ig
Acxof1cVOl IITl 01 naaoaAol t6paloVTQL ltTTl ppoxou ware PU 9l0l~ vo poundIval TTpaKTlKWC 1I]I5EVlKit Kat I5cxolpoundvOl lila Id~ova aacjgtoAtlQv 15 = 100 elval
Ni h UI = Er
El~ N1=- (U +wX i) (15 )
Nib h u+ wXi = Er
A09ivroC OTi apxI) TWV Q~6vwv au ITrimlaquo TTpOe TO k BTWV Kt cjgtoAwv Ai TWV TToaaoAwv clvOt
lXi = 0
ETT0ltvWC V N ( X ) EF EF= 1 1 = U + w 1 - h-= nT (16)
Luv9 ~ Kal dc TO IIplCl
510 Y= 0
( 10) y = o ry= - w =- y( - B) ~ d
I B=u- ~1 dU) ( 11 )EJ - bull = M( dY )= 0
51]Aa51) M = EJ f 213 = - 2y EI ( u - ~ ) ( 11 )
Q = EJy 2 (A + B) = 2EJy (211 - ~) OTTOTpound al t~laWaEllt (13) ypacjgtovTal
H = 2EJ ny ( 2u __1_ w) y
EFV = n - h- u ( I)
- 2 I J ( W) + EF ~ bull =- J1 y~ o 11 - -- w - 1 y h
To OUOTTJlcl (I) IltiS tmTptTTEI va uTToAoyiowlev TO u v OL w
889 TPAPO lollTlIWV pnXOVlKWV
TOUTWV EUPE9tVTWV UTTOAOyiroflEV Tel M Q Ni EK TOU OUltmiflQTO~
M= - 2y EJ (U - ~ )
Q= 2y EJ (2u - ~) ( II )
Nl= E (U+WXI)
nap a T ~ P I) 0 L ~ Al TLfla TWV U u W dvaL TTOAU fllKpai W~ tK TOUTOU BE CITTQIHiTal fIltvaAI) aKpl~EIQ TWV TTpa~EWV KQTa TOV UTTOAOYIOfioV TWV H aKpi~ELa TOO AoyapI9f1LKOU Kav6vo~ BEv poundIvaL ETTapK~~
4 nap66uYila uIToAoYLOlloU
Earw TTpOr lmoAoYLofiov 9EflEAiwOl~ tBpilvou yEcpupa~ H 9EflEAiwOL~ aTTonpoundiTQL eITTo ~va TTtBIAOV iiKaflTTTov tBpar6f1EVOV tTTI OKTW TTaooilAWV KQTQKOpUCPWV BlafiETpou 100 m Ka TOTT09ETT)fltvwv w~ tv TQ OX~flaTI
I
I 0 00
I ~
( jlt~ middotmiddot (11 (
~ t
N I
EilaquoqoO( 2 Soil 2 o o
o 0 ~
Ix a Flg8
890 EaTW ~ KaTanOVl0u TOU 9tl1poundA(OU pound1lt TO KtVTPOV nilt ~aotwlt 0 ~ KaTW91 KaTaK Mval1llt V = 1400 TJIIIII 6pI~ raquo H = 851 HAm1m poni) S = 1000110
pnXDVlIW Eelgt 6aov TO rrtl5LAov SEwpEiTaL TEAtlWlt QKal1TTTOV ~ AELToupyla aopponlalt TOU npoal5Loshyp(~ETal ( K nilt I1poundTaKLv~atwlt TOU KtVTpOU 0 ( u u W )
H KaTClTT6vlOLlt TOG rraaoaAOU dlt~o A rrap(oTaTal 11pound TOlt (M N Q )
ITOI)(da t6b+ouc
E 15 a cjgt 0 lt I nlAwI5Elt uyp6v TpoundAtiWlt QI1010YEVpoundlt 11pound oraS I5t1KTT)v K = 41 01 1m E 15 a cjgt lt 2 Bpaxw15tlt TEAtlWlt 6vurroxwplTOV
XTOI)(da aaaa~wv
a ) rroloTllt oKupol5[l1aTolt B 160 E = 210000 kg lem TpoundAIKOV I1trpov (AaOTlK6TlTOlt
E = _ E_ 1+ 1
t - lt 0 050 E- 210000 150 000 ~ 1510 timVTOlt TOU poundaoult p = rp - 1 + 050 I
J D _ 314 100 050 10- 1 m~) pom al5pa vtialt b4 - 64
Y ) ~ xapaKTlpIOTlKT) oTa8poundpa -V kD - V 4 10 100 = 033 y - 4El - 4 15 10 050 to I
m
1 y=3OO y = 0110 y=0036
lt ) bull - ~ F D 314 middot100 080 laTol1 1 TOU rraooou bull = 4 = 4 m
EJ = 150 10 050 to-I = 075 10 tm
EF 150 to 080 = 060 10 tm - h- = 2000
pound ) apISl1olt naaaaAwv n = 8 Qrr6aTaollt naooaAwv arro TO KtVTpOV 0 X = 120
IXL = 8 120 = 1150
AI ypoundvIKal t~laWJpoundllt KaTO TO np0lyouI1Eva poundIvai
( I ) 2EJ ny~ ( 2u - ~ ) = H
EFn-h- = V
- 2I1YEJ(U -~) + W EF lXL = EY h
( ) M = - 2yEJ ( 11 -~) )
Q= 2YEJ(2U - ~ )
E1 ( )NI = - h + WXI
EniAuollt oultTrl)I1QTolt ( I )
2 075 10 8 0036 (2u - 3w) = - 85-+
8 middot 060 10 = 1400 -Ishy+shy
- 2 middot 8 middot 011 middot 075 middot 10 (u- 3w) + w 060 10 middot 1150 = - 1000
691 TlInpoRoAmlWY pnXnVIKWY
01 t~awaE~ ypa4gtoVTa 4320 (2u _ 3w) = 85 10-3
1400 U = 48010
-132 (u-3w) +690w= -100010-3
U = - 2904 10- v = - 292 10- W= - 1283 10-
EUpEetvTwV TWV u v W aVTlKaeaTw~Ev TG~ Tl~a~ TWV d~ TO aUCITTwa ( II ~ Kal EXOflEV
M=-2middot 011middot075 middot10 ( 2904+3middot1283) 10-3
Q = 2middot0036 middot 075middot10 (-22904+31263) to-
N = 060middot 10 [ 292 plusmn (-1 283) 120 1 10-
t~ WV TTpoKumEI M = - 1550m Q c - 1060
80 N= + 270
E TT a ~ eE u a I ~ 0) nQ = H 8 middot 1060=85
~) I Mo = - 1000 - 4 270 120 + 480 120 - 8middot 1550 - 1000
napaTraplalli
Ei~ n]v KE4gtaA~v TWV TTaaaaAwv A ~ Taal~ tM4gtou~ Elval
~=-ku = 2904 10-middot 410= 1162 tm ~ 116kgcm
Eav TO Eoa4gto~ ouvaTa v avaap~ n)v TamV Tau~v tTTpoundlO~ Q = 1060 Kal 0 = 100 m 1060
ETTnal on ~ Tpound~vouaa ouva~~ TTapaAa~pavnQj poundi~ paao~ 11 62 = 090 m
5 luYKpau IlE laOaTOTlKrlV IlE901lov KaTG n]v iaOaTQnK~V ~teooov OEv a~~avovTa lJTT o~v at iOI6~T(~ TOO toapou~ 00T( ~ aKa~~(a TWV TTaaaaAwv OTTOT(
85Q= -8- = 1060
001
deg10651=
A M
Ibull
gt--
M= O
1400 1000 305 N = - 8- plusmn 23201202 120= 175 plusmn 130 = 45
F=4 middot080=320m
IX 9 Flg9
laquo Ai TTpoKumouaal olapopai Elval ToaoOTOV ~EyaMT(pal oaov aU~aVEI ~ pOTT~ E raquo
892 BIP)loYPQ+IQ - BibliogrQphy I )nuIVQfj neii~tan cc des )latbriaux 2 Tdatoc e CWpLlL tTtL)6apoundtllt laxi=~lt 6elLampAto30xamp 1tp6TIXOLt vtwv ILlE06Xwv 8 r aato( Comportamcnle di un palo di Fondnziol1c sotta Iaziooc di carichi verUcaH el oriuonlali ( bull Tdqo~ Estimation pratique des tasscmen difCen dull piu pendant un essai d chargnmc nL S EJweonoIlAo E Jlpp(~ n t)a0tLx6MTO~ TOO lMipout in-t txxtvTptlll OpoundIIII)twv ~ IkIUl(a)v ltMtUn blV
I) fiCll(ryu(61WVAo AYTOxi) fW UAlXWII 1 AoICo El~JLUtwO(~c
8 O cnayOJTOVtaXO 01~(w(JtC btl iAlXanxou lBafout
889 TPAPO lollTlIWV pnXOVlKWV
TOUTWV EUPE9tVTWV UTTOAOyiroflEV Tel M Q Ni EK TOU OUltmiflQTO~
M= - 2y EJ (U - ~ )
Q= 2y EJ (2u - ~) ( II )
Nl= E (U+WXI)
nap a T ~ P I) 0 L ~ Al TLfla TWV U u W dvaL TTOAU fllKpai W~ tK TOUTOU BE CITTQIHiTal fIltvaAI) aKpl~EIQ TWV TTpa~EWV KQTa TOV UTTOAOYIOfioV TWV H aKpi~ELa TOO AoyapI9f1LKOU Kav6vo~ BEv poundIvaL ETTapK~~
4 nap66uYila uIToAoYLOlloU
Earw TTpOr lmoAoYLofiov 9EflEAiwOl~ tBpilvou yEcpupa~ H 9EflEAiwOL~ aTTonpoundiTQL eITTo ~va TTtBIAOV iiKaflTTTov tBpar6f1EVOV tTTI OKTW TTaooilAWV KQTQKOpUCPWV BlafiETpou 100 m Ka TOTT09ETT)fltvwv w~ tv TQ OX~flaTI
I
I 0 00
I ~
( jlt~ middotmiddot (11 (
~ t
N I
EilaquoqoO( 2 Soil 2 o o
o 0 ~
Ix a Flg8
890 EaTW ~ KaTanOVl0u TOU 9tl1poundA(OU pound1lt TO KtVTPOV nilt ~aotwlt 0 ~ KaTW91 KaTaK Mval1llt V = 1400 TJIIIII 6pI~ raquo H = 851 HAm1m poni) S = 1000110
pnXDVlIW Eelgt 6aov TO rrtl5LAov SEwpEiTaL TEAtlWlt QKal1TTTOV ~ AELToupyla aopponlalt TOU npoal5Loshyp(~ETal ( K nilt I1poundTaKLv~atwlt TOU KtVTpOU 0 ( u u W )
H KaTClTT6vlOLlt TOG rraaoaAOU dlt~o A rrap(oTaTal 11pound TOlt (M N Q )
ITOI)(da t6b+ouc
E 15 a cjgt 0 lt I nlAwI5Elt uyp6v TpoundAtiWlt QI1010YEVpoundlt 11pound oraS I5t1KTT)v K = 41 01 1m E 15 a cjgt lt 2 Bpaxw15tlt TEAtlWlt 6vurroxwplTOV
XTOI)(da aaaa~wv
a ) rroloTllt oKupol5[l1aTolt B 160 E = 210000 kg lem TpoundAIKOV I1trpov (AaOTlK6TlTOlt
E = _ E_ 1+ 1
t - lt 0 050 E- 210000 150 000 ~ 1510 timVTOlt TOU poundaoult p = rp - 1 + 050 I
J D _ 314 100 050 10- 1 m~) pom al5pa vtialt b4 - 64
Y ) ~ xapaKTlpIOTlKT) oTa8poundpa -V kD - V 4 10 100 = 033 y - 4El - 4 15 10 050 to I
m
1 y=3OO y = 0110 y=0036
lt ) bull - ~ F D 314 middot100 080 laTol1 1 TOU rraooou bull = 4 = 4 m
EJ = 150 10 050 to-I = 075 10 tm
EF 150 to 080 = 060 10 tm - h- = 2000
pound ) apISl1olt naaaaAwv n = 8 Qrr6aTaollt naooaAwv arro TO KtVTpOV 0 X = 120
IXL = 8 120 = 1150
AI ypoundvIKal t~laWJpoundllt KaTO TO np0lyouI1Eva poundIvai
( I ) 2EJ ny~ ( 2u - ~ ) = H
EFn-h- = V
- 2I1YEJ(U -~) + W EF lXL = EY h
( ) M = - 2yEJ ( 11 -~) )
Q= 2YEJ(2U - ~ )
E1 ( )NI = - h + WXI
EniAuollt oultTrl)I1QTolt ( I )
2 075 10 8 0036 (2u - 3w) = - 85-+
8 middot 060 10 = 1400 -Ishy+shy
- 2 middot 8 middot 011 middot 075 middot 10 (u- 3w) + w 060 10 middot 1150 = - 1000
691 TlInpoRoAmlWY pnXnVIKWY
01 t~awaE~ ypa4gtoVTa 4320 (2u _ 3w) = 85 10-3
1400 U = 48010
-132 (u-3w) +690w= -100010-3
U = - 2904 10- v = - 292 10- W= - 1283 10-
EUpEetvTwV TWV u v W aVTlKaeaTw~Ev TG~ Tl~a~ TWV d~ TO aUCITTwa ( II ~ Kal EXOflEV
M=-2middot 011middot075 middot10 ( 2904+3middot1283) 10-3
Q = 2middot0036 middot 075middot10 (-22904+31263) to-
N = 060middot 10 [ 292 plusmn (-1 283) 120 1 10-
t~ WV TTpoKumEI M = - 1550m Q c - 1060
80 N= + 270
E TT a ~ eE u a I ~ 0) nQ = H 8 middot 1060=85
~) I Mo = - 1000 - 4 270 120 + 480 120 - 8middot 1550 - 1000
napaTraplalli
Ei~ n]v KE4gtaA~v TWV TTaaaaAwv A ~ Taal~ tM4gtou~ Elval
~=-ku = 2904 10-middot 410= 1162 tm ~ 116kgcm
Eav TO Eoa4gto~ ouvaTa v avaap~ n)v TamV Tau~v tTTpoundlO~ Q = 1060 Kal 0 = 100 m 1060
ETTnal on ~ Tpound~vouaa ouva~~ TTapaAa~pavnQj poundi~ paao~ 11 62 = 090 m
5 luYKpau IlE laOaTOTlKrlV IlE901lov KaTG n]v iaOaTQnK~V ~teooov OEv a~~avovTa lJTT o~v at iOI6~T(~ TOO toapou~ 00T( ~ aKa~~(a TWV TTaaaaAwv OTTOT(
85Q= -8- = 1060
001
deg10651=
A M
Ibull
gt--
M= O
1400 1000 305 N = - 8- plusmn 23201202 120= 175 plusmn 130 = 45
F=4 middot080=320m
IX 9 Flg9
laquo Ai TTpoKumouaal olapopai Elval ToaoOTOV ~EyaMT(pal oaov aU~aVEI ~ pOTT~ E raquo
892 BIP)loYPQ+IQ - BibliogrQphy I )nuIVQfj neii~tan cc des )latbriaux 2 Tdatoc e CWpLlL tTtL)6apoundtllt laxi=~lt 6elLampAto30xamp 1tp6TIXOLt vtwv ILlE06Xwv 8 r aato( Comportamcnle di un palo di Fondnziol1c sotta Iaziooc di carichi verUcaH el oriuonlali ( bull Tdqo~ Estimation pratique des tasscmen difCen dull piu pendant un essai d chargnmc nL S EJweonoIlAo E Jlpp(~ n t)a0tLx6MTO~ TOO lMipout in-t txxtvTptlll OpoundIIII)twv ~ IkIUl(a)v ltMtUn blV
I) fiCll(ryu(61WVAo AYTOxi) fW UAlXWII 1 AoICo El~JLUtwO(~c
8 O cnayOJTOVtaXO 01~(w(JtC btl iAlXanxou lBafout
890 EaTW ~ KaTanOVl0u TOU 9tl1poundA(OU pound1lt TO KtVTPOV nilt ~aotwlt 0 ~ KaTW91 KaTaK Mval1llt V = 1400 TJIIIII 6pI~ raquo H = 851 HAm1m poni) S = 1000110
pnXDVlIW Eelgt 6aov TO rrtl5LAov SEwpEiTaL TEAtlWlt QKal1TTTOV ~ AELToupyla aopponlalt TOU npoal5Loshyp(~ETal ( K nilt I1poundTaKLv~atwlt TOU KtVTpOU 0 ( u u W )
H KaTClTT6vlOLlt TOG rraaoaAOU dlt~o A rrap(oTaTal 11pound TOlt (M N Q )
ITOI)(da t6b+ouc
E 15 a cjgt 0 lt I nlAwI5Elt uyp6v TpoundAtiWlt QI1010YEVpoundlt 11pound oraS I5t1KTT)v K = 41 01 1m E 15 a cjgt lt 2 Bpaxw15tlt TEAtlWlt 6vurroxwplTOV
XTOI)(da aaaa~wv
a ) rroloTllt oKupol5[l1aTolt B 160 E = 210000 kg lem TpoundAIKOV I1trpov (AaOTlK6TlTOlt
E = _ E_ 1+ 1
t - lt 0 050 E- 210000 150 000 ~ 1510 timVTOlt TOU poundaoult p = rp - 1 + 050 I
J D _ 314 100 050 10- 1 m~) pom al5pa vtialt b4 - 64
Y ) ~ xapaKTlpIOTlKT) oTa8poundpa -V kD - V 4 10 100 = 033 y - 4El - 4 15 10 050 to I
m
1 y=3OO y = 0110 y=0036
lt ) bull - ~ F D 314 middot100 080 laTol1 1 TOU rraooou bull = 4 = 4 m
EJ = 150 10 050 to-I = 075 10 tm
EF 150 to 080 = 060 10 tm - h- = 2000
pound ) apISl1olt naaaaAwv n = 8 Qrr6aTaollt naooaAwv arro TO KtVTpOV 0 X = 120
IXL = 8 120 = 1150
AI ypoundvIKal t~laWJpoundllt KaTO TO np0lyouI1Eva poundIvai
( I ) 2EJ ny~ ( 2u - ~ ) = H
EFn-h- = V
- 2I1YEJ(U -~) + W EF lXL = EY h
( ) M = - 2yEJ ( 11 -~) )
Q= 2YEJ(2U - ~ )
E1 ( )NI = - h + WXI
EniAuollt oultTrl)I1QTolt ( I )
2 075 10 8 0036 (2u - 3w) = - 85-+
8 middot 060 10 = 1400 -Ishy+shy
- 2 middot 8 middot 011 middot 075 middot 10 (u- 3w) + w 060 10 middot 1150 = - 1000
691 TlInpoRoAmlWY pnXnVIKWY
01 t~awaE~ ypa4gtoVTa 4320 (2u _ 3w) = 85 10-3
1400 U = 48010
-132 (u-3w) +690w= -100010-3
U = - 2904 10- v = - 292 10- W= - 1283 10-
EUpEetvTwV TWV u v W aVTlKaeaTw~Ev TG~ Tl~a~ TWV d~ TO aUCITTwa ( II ~ Kal EXOflEV
M=-2middot 011middot075 middot10 ( 2904+3middot1283) 10-3
Q = 2middot0036 middot 075middot10 (-22904+31263) to-
N = 060middot 10 [ 292 plusmn (-1 283) 120 1 10-
t~ WV TTpoKumEI M = - 1550m Q c - 1060
80 N= + 270
E TT a ~ eE u a I ~ 0) nQ = H 8 middot 1060=85
~) I Mo = - 1000 - 4 270 120 + 480 120 - 8middot 1550 - 1000
napaTraplalli
Ei~ n]v KE4gtaA~v TWV TTaaaaAwv A ~ Taal~ tM4gtou~ Elval
~=-ku = 2904 10-middot 410= 1162 tm ~ 116kgcm
Eav TO Eoa4gto~ ouvaTa v avaap~ n)v TamV Tau~v tTTpoundlO~ Q = 1060 Kal 0 = 100 m 1060
ETTnal on ~ Tpound~vouaa ouva~~ TTapaAa~pavnQj poundi~ paao~ 11 62 = 090 m
5 luYKpau IlE laOaTOTlKrlV IlE901lov KaTG n]v iaOaTQnK~V ~teooov OEv a~~avovTa lJTT o~v at iOI6~T(~ TOO toapou~ 00T( ~ aKa~~(a TWV TTaaaaAwv OTTOT(
85Q= -8- = 1060
001
deg10651=
A M
Ibull
gt--
M= O
1400 1000 305 N = - 8- plusmn 23201202 120= 175 plusmn 130 = 45
F=4 middot080=320m
IX 9 Flg9
laquo Ai TTpoKumouaal olapopai Elval ToaoOTOV ~EyaMT(pal oaov aU~aVEI ~ pOTT~ E raquo
892 BIP)loYPQ+IQ - BibliogrQphy I )nuIVQfj neii~tan cc des )latbriaux 2 Tdatoc e CWpLlL tTtL)6apoundtllt laxi=~lt 6elLampAto30xamp 1tp6TIXOLt vtwv ILlE06Xwv 8 r aato( Comportamcnle di un palo di Fondnziol1c sotta Iaziooc di carichi verUcaH el oriuonlali ( bull Tdqo~ Estimation pratique des tasscmen difCen dull piu pendant un essai d chargnmc nL S EJweonoIlAo E Jlpp(~ n t)a0tLx6MTO~ TOO lMipout in-t txxtvTptlll OpoundIIII)twv ~ IkIUl(a)v ltMtUn blV
I) fiCll(ryu(61WVAo AYTOxi) fW UAlXWII 1 AoICo El~JLUtwO(~c
8 O cnayOJTOVtaXO 01~(w(JtC btl iAlXanxou lBafout
691 TlInpoRoAmlWY pnXnVIKWY
01 t~awaE~ ypa4gtoVTa 4320 (2u _ 3w) = 85 10-3
1400 U = 48010
-132 (u-3w) +690w= -100010-3
U = - 2904 10- v = - 292 10- W= - 1283 10-
EUpEetvTwV TWV u v W aVTlKaeaTw~Ev TG~ Tl~a~ TWV d~ TO aUCITTwa ( II ~ Kal EXOflEV
M=-2middot 011middot075 middot10 ( 2904+3middot1283) 10-3
Q = 2middot0036 middot 075middot10 (-22904+31263) to-
N = 060middot 10 [ 292 plusmn (-1 283) 120 1 10-
t~ WV TTpoKumEI M = - 1550m Q c - 1060
80 N= + 270
E TT a ~ eE u a I ~ 0) nQ = H 8 middot 1060=85
~) I Mo = - 1000 - 4 270 120 + 480 120 - 8middot 1550 - 1000
napaTraplalli
Ei~ n]v KE4gtaA~v TWV TTaaaaAwv A ~ Taal~ tM4gtou~ Elval
~=-ku = 2904 10-middot 410= 1162 tm ~ 116kgcm
Eav TO Eoa4gto~ ouvaTa v avaap~ n)v TamV Tau~v tTTpoundlO~ Q = 1060 Kal 0 = 100 m 1060
ETTnal on ~ Tpound~vouaa ouva~~ TTapaAa~pavnQj poundi~ paao~ 11 62 = 090 m
5 luYKpau IlE laOaTOTlKrlV IlE901lov KaTG n]v iaOaTQnK~V ~teooov OEv a~~avovTa lJTT o~v at iOI6~T(~ TOO toapou~ 00T( ~ aKa~~(a TWV TTaaaaAwv OTTOT(
85Q= -8- = 1060
001
deg10651=
A M
Ibull
gt--
M= O
1400 1000 305 N = - 8- plusmn 23201202 120= 175 plusmn 130 = 45
F=4 middot080=320m
IX 9 Flg9
laquo Ai TTpoKumouaal olapopai Elval ToaoOTOV ~EyaMT(pal oaov aU~aVEI ~ pOTT~ E raquo
892 BIP)loYPQ+IQ - BibliogrQphy I )nuIVQfj neii~tan cc des )latbriaux 2 Tdatoc e CWpLlL tTtL)6apoundtllt laxi=~lt 6elLampAto30xamp 1tp6TIXOLt vtwv ILlE06Xwv 8 r aato( Comportamcnle di un palo di Fondnziol1c sotta Iaziooc di carichi verUcaH el oriuonlali ( bull Tdqo~ Estimation pratique des tasscmen difCen dull piu pendant un essai d chargnmc nL S EJweonoIlAo E Jlpp(~ n t)a0tLx6MTO~ TOO lMipout in-t txxtvTptlll OpoundIIII)twv ~ IkIUl(a)v ltMtUn blV
I) fiCll(ryu(61WVAo AYTOxi) fW UAlXWII 1 AoICo El~JLUtwO(~c
8 O cnayOJTOVtaXO 01~(w(JtC btl iAlXanxou lBafout
892 BIP)loYPQ+IQ - BibliogrQphy I )nuIVQfj neii~tan cc des )latbriaux 2 Tdatoc e CWpLlL tTtL)6apoundtllt laxi=~lt 6elLampAto30xamp 1tp6TIXOLt vtwv ILlE06Xwv 8 r aato( Comportamcnle di un palo di Fondnziol1c sotta Iaziooc di carichi verUcaH el oriuonlali ( bull Tdqo~ Estimation pratique des tasscmen difCen dull piu pendant un essai d chargnmc nL S EJweonoIlAo E Jlpp(~ n t)a0tLx6MTO~ TOO lMipout in-t txxtvTptlll OpoundIIII)twv ~ IkIUl(a)v ltMtUn blV
I) fiCll(ryu(61WVAo AYTOxi) fW UAlXWII 1 AoICo El~JLUtwO(~c
8 O cnayOJTOVtaXO 01~(w(JtC btl iAlXanxou lBafout