.

Імовірнісний розрахунок і оцінка ступеня відповідальності елементів сталевих статично невизначених конструкцій: Автореф. дис… канд. техн. наук / О.В

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IIEOAANUeEEE AeA?AEAAIEE OAOI?*IEE OI?AA?NEOAO

?IAI? TH??ss EIIAe?AOTHEA

AI?OUeEI IEAENAIAe? AEAAeENEAAIAE*

OAeE 624.014

?IIA??I?NIEE ?IC?AOOIIE ? IOe?IEA NOOIAIss A?AeIIA?AeAEUeIINO? AEAIAIO?A
NOAEAAEO NOAOE*II IAAECIA*AIEO EIINO?OEOe?E

Niaoe?aeuei?noue 05.23.01 – Aoae?aaeuei? eiino?oeoe??, aoae?ae? oa
nii?oaee

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa oaoi?/ieo iaoe

Iieoaaa – 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia a Iieoaanueeiio aea?aeaaiiio oaoii/iiio oi?aa?neoao?
?iai? TH??y Eiiae?aothea I?i?noa?noaa ina?oe Oe?a?ie

Iaoeiaee ea?iaiee: aeieoi? oaoii/ieo iaoe, i?ioani?

I?/oa?i Na?a?e Oaaei?iae/,

Iieoaanueeee aea?aeaaiee oaoii/iee oi?aa?neoao ?iai? TH??y Eiiae?aothea,
caa?aeoaa/ eaoaae?e eiino?oeoeie ic iaoaeo, aea?aaa ? ieanoian

Ioioeieii iiiiaioe: aeieoi? oaoi?/ieo iaoe, i?ioani?

Oiieoey Eaii?ae Ieeieaeiae/,

Noinueeee aea?aeaaiee aa?a?iee oi?aa?neoao, caa?aeoaa/ eaoaae?e
aoae?aaeueieo eiino?oeoe?e

eaiaeeaeao oaoii/ieo iaoe, aeioeaio

??iae ?aaai Ieoaeeiae/,

Oa?e?anueea aea?aeaaia aeaaeai?y cae?cie/iiai o?ainii?oo, aeioeaio
eaoaae?e aoae?aaeueieo iaoa??ae?a, eiino?oeoe?e oa nii?oae

I?ia?aeia onoaiiaa: AAO “Oe?a?inueeee iaoeiai-aeine?aeiee ?inoeooo
“I?iaeonoaeueeiino?oeoe?y” Aea?aeaaiiai Eii?oaoo Oe?a?ie o ni?aaao
aoae?aieoeoaa, a?o?oaeoo?e ? aeeoeiai? iie?oeee, i. Ee?a

Caoeno aeena?oaoei? aiaeaoaeaoueny “11” o?aaiy 1999 ?ieo i 1300 aiaeeii
ia caniaeaiii niaoeiaeiciaaii? a/aii? ?aaee Ae 25.01.02 i?e
Iieoaanueeiio aea?aeaaiiio oaoii/iiio oiiaa?neoaoi ?iai? TH??y
Eiiae?aothea ca aae?anith: 314601, i. Iieoaaa, Ia?oio?aaiaaee i?iniaeo,
24, aoae. 234.

C aeena?oaoei?th iiaeia iciaeiieoeny a aiaeiioaoei Iieoaanueeiai
aea?aeaaiiai oaoii/iiai oiiaa?neoaoo ?iai? TH??y Eiiae?aothea ca
aae?anith: 314601, i. Iieoaaa, Ia?oio?aaiaaee i?iniaeo, 24.

Aaoi?aoa?ao ?ic?neaiee “9” ea?oiy 1999 ?.

A/aiee nae?aoa? niaoeiaeiciaaii? a/aii? ?aaee

Naiei I.A.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. No/aniee ??aaiue aeiia aei i?iaeooaaiiy aoae?aaeue
oa nii?oae iio?aao? canoinoaaiiy oi?aa?naeueiiai oaoi?/iiai e?eoa??th (
iaae?eiino?. I?ae oei, ?nioth/? iaoiaee i?iaeooaaiiy ia aeathoue
iiaeeeaino? ioe?ieoe iaae?ei?noue nii?oae, cie?aia, noaoe/ii
iaaecia/aieo noaeaaeo eiino?oeoe?e. Aeey oaeiai ?ic?aooieo iio??aii iaoe
iaoiae ioe?iee ?iia??iino? a?aeiiae c iiaeeea?noth a?aooaaiiy
iaea?eueoi? e?eueeino? /eiiee?a, ui iiaeooue aieeiooe ia oeth ioe?ieo.
Aieiaieie ieoaiiyie, ui ia ae??oai? a ?nioth/eo iaoiaeao i?iaeooaaiiy,
ia aeaiee iiiaio ?:

1) aieea ae?enii? ?iaioe noaeaaeo noaoe/ii iaaecia/aieo eiino?oeoe?e;

2) ci?ii?noue ia?aiao??a i?oeiino? ? iaaaioaaeaiiy c /anii, ui a?eueoa
a?aeiia?aea? ?aaeuei?e iiaaae?ioe? oeeo oa?aeoa?enoee;

3) ?iaioa oaeeo eiino?oeoe?e i?ae aaaaoiia?aiao?e/iei ci?iiei
iaaaioaaeaiiyi oa iia’ycaiiy ?ic?aooieo no?eeino? ? i?oeiino?;

4) a?aei?ii?noue aeaiaio?a noaoe/ii iaaecia/aieo noaeaaeo eiino?oeoe?e
ca nooiaiai ?o a?aeiia?aeaeueiino?.

?ic?iaeai? AeAI A.1.2. -… – 96 “Caaaeueii i?eioeeie caaacia/aiiy
iaaeieiinoi i aaciaee aoaeiaaeue, nii?oae, aoaeiaaeueieo eiino?oeoeie oa
iniia”, o yeeo noai?aia caaaeueia iaoiaee/ia iniiaa aeey ia?aoiaeo aei
?ic?aooieo eiino?oeoe?e ii iaae?eiino?. Iinoaea iio?aaa a noai?aii?
eiie?aoieo iaoiae?a ?ic?aooieo ??cieo aeae?a eiino?oeoe?e, cie?aia,
noaeaaeo noaoe/ii iaaecia/aieo, ca e?eoa???i ?iia??iino? a?aeiiae.
Ioaea, aeaia ?iaioa, i?enay/aia ?ic?iaoe? iiaeo iaoiae?a ?ic?aooieo ca
iaae?ei?noth noaeaaeo noaoe/ii iaaecia/aieo eiino?oeoe?e, ? aaaeeeaith ?
aeooaeueiith.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie. Aeaia ?iaioa iia’ycaia c
?ic?iaeith ?iia??i?nieo iaoiae?a ?ic?aooieo noaoe/ii iaaecia/aieo
noaeaaeo eiino?oeoe?e. Aaoi? i?eeiaa o/anoue a iaoeiai-aeine?aeieoeuee?e
?iaio? “?ac?aaioea iaoiaeia ?an/?oa iaae?aeiinoe no?ieoaeueiuo
eiino?oeoeee e ii?ie?iaaiey iaa?ocie ia ieo” (aea?aeathaeaeaoia oaia
?43/96), ui i?iaiaeeeany a Iieoaanueeiio aea?aeaaiiio oaoi?/iiio
oi?aa?neoao? a ia??iae 1996-1997 ??. Eiie?aoiee aianie aaoi?a – ?ic?iaea
?icae?eo “O/?o i?iaeieueiuo nee e iiiaiia?aiao?e/aneiai caa?oaeaiey a
aa?iyoiinoiii iaoiaea i?aaeaeueiiai ?aaiiaaney”.

Iaoa ? caaea/? aeine?aeaeaiiy. Iaoith aeine?aeaeaiue ?iaioe ?
iiaeaeueoee ?icaeoie ?iia??i?niiai ?ic?aooieo noaoe/ii iaaecia/aieo
noaeaaeo eiino?oeoe?e c oe?eeth ooi/iaiiy ioe?iee iaae?eiino?,
?aiaeoaaiiy ?o aeaiaio?a ca nooiaiai a?aeiia?aeaeueiino? oa aee?eooy
?aca?a?a iano/i? caeaoiino?.

Caaea/?, ui aoee iinoaaeai? ia?aae aaoi?ii, noi?ioeueiaai? oaeei /eiii:

?ic?iaeoe iaoiaeeeo ?iia??i?niiai ?ic?aooieo ? ioe?iee iaae?eiino?
noaeaaeo noaoe/ii iaaecia/aieo ?ai c o?aooaaiiyi iicaeiaaeiuei? neee oa
no?eeino?;

?ic?iaeoe aeai?eoi ?iia??i?niiai ?ic?aooieo nenoai c aaaaoiia?aiao?e/iei
(aeaiia?aiao?e/iei) iaaaioaaeaiiyi;

?ic?iaeoe iaoiae ioe?iee nooiaiy aieeao ia iaae?ei?noue iniaeeainoae
ae?enii? ?iaioe noaeaaeo noaoe/ii iaaecia/aieo ?ai;

ooi/ieoe cia/aiiy eiao?oe??ioo noaiii? iaae?eiino? (S oa ioe?ieoe
?aca?ae iano/i? caeaoiino? noaoe/ii iaaecia/aieo noaeaaeo eiino?oeoe?e;

?ic?iaeoe iaoiae ioe?iee nooiaiy a?aeiia?aeaeueiino? ie?aieo aeaiaio?a
noaoe/ii iaaecia/aieo noaeaaeo eiino?oeoe?e, ?o ?aiaeoaaiiy.

Iaoeiaa iiaecia ?iaioe:

cai?iiiiiaaii iaoiae o?aooaaiiy eiino?oeoeaii? iii?aaee i?e ?ic?aooieo
iaae?eiino? noaoe/ii iaaecia/aieo noaeaaeo eiino?oeoe?e;

cai?iiiiiaaii ii??aiyeueiee iaoiae ioe?iee ca iaae?ei?noth aieeao
iniaeeainoae ae?enii? ?iaioe noaeaaeo noaoe/ii iaaecia/aieo eiino?oeoe?e
i?e ?ic?aooieo ca ?nioth/eie ii?iaie i?iaeooaaiiy;

cai?iiiiiaaia iaoiaeeea aecia/aiiy ?iia??iino? a?aeiiae noaoe/ii
iaaecia/aieo noaeaaeo eiino?oeoe?e ca ?iia??i?niei iaoiaeii a?aie/ii?
??aiiaaae, a yeiio aaaaeaia noaoe/ia iinoaiiaea caaea/? c o?aooaaiiyi
iicaeiaaeiuei? neee, aeaoi?iiaaii? noaie oa aaaaoiia?aiao?e/iiai
iaaaioaaeaiiy;

aia?oa aeyaeaii caeaaeiino? i?ae nooiaiai a?aeiia?aeaeueiino? aeaiaio?a
noaeaaeo noaoe/ii iaaecia/aieo ?ai oa ?o oa?aeoa?enoeeaie;

ia??oioiaaii ?ic?aooieia? cia/aiiy (S aeey noaeaaeo ?ai ??cieo oei?a;

aeai? ?aeiiaiaeaoe?? ii cieaeaiith iaoaei?iiino? noaeaaeo ?ai aac
nooo?aiai iia??oaiiy iaae?eiino?.

I?aeoe/ia cia/aiiy ?iaioe:

cai?iiiiiaai? iaoiaee ?ic?aooieo aeicaieythoue aeeiiaoe ioe?ieo
iaae?eiino? noaeaaeo noaoe/ii iaaecia/aieo eiino?oeoe?e;

aeei?enoaiiy eiao?oe??ioa noaiii? iaae?eiino? (S oa eiao?oe??ioa
iaaecia/aiino? ?ic?aooieiai? noaie (rd aeicaiey? cieceoe
iaoaeii?noe?noue noaeaaeo noaoe/ii iaaecia/aieo eiino?oeoe?e;

canoinoaaiiy ii??aiyeueiiai iaoiaeo ioe?iee ca iaae?ei?noth aeicaiey?
aecia/eoe ?ic?aooieiao noaio, yea iaea?eueoa a?aeiia?aea? ae?eni?e
?iaio? noaeaaeo noaoe/ii iaaecia/aieo eiino?oeoe?e;

aeei?enoaiiy ?aeiiaiaeaoe?e uiaei ?aia?a aeaiaio?a noaoe/ii iaaecia/aieo
noaeaaeo eiino?oeoe?e aeicaiey? i?iaanoe i?aea?? aeaiaio?a noaeaaeo ?ai,
iaaeeaeath/enue aei ??aiiiaae?eii? nenoaie.

Aoaeoeai?noue oaei? iaoiaeeee iieyaa? a a?eueo iiaiiio o?aooaaii?
?aaeueii? ?iaioe eiino?oeoe?? (ye a noai? i?aoeacaeaoiino?, oae ? a
noaae?? ?oeioaaiiy), i?aaenoaaeaii? ? i?yiiio a?aooaaii? ?iia??i?nii?
i?e?iaee iaaaioaaeaiue oa oa?aeoa?enoee noae?, o?aooaaii? ?oeioaaiiy
a?ae ao?aoe no?eeino?. Aeei?enoaiiy iaoiaeeee aeicaiey? cieceoe
iaoa??aeii?noe?noue oa i?aeaeueoe iaae?ei?noue noaeaaeo noaoe/ii
iaaecia/aieo eiino?oeoe?e.

Ai?iaaaeaeaiiy ?acoeueoao?a ?iaioe aoei i?iaaaeaii i?e ia?aa??i/ieo
?ic?aooieao iano/i? caeaoiino? oa iaae?eiino? iano/eo aoae?aaeueieo
eiino?oeoe?e a?aaee?i? AO “Iieoaaaiiei?iae”. Iaoa??aee aeena?oaoe??
i?eeiyoi aeey a?aooaaiiy i?e ?ic?iaoe? ii?iaoeaieo aeieoiaio?a AAO
“Oe?a?inueeee iaoeiai-aeine?aeiee ?inoeooo “I?iaeonoaeueeiino?oeoe?y”
Aea?aeaaiiai Eii?oaoo Oe?a?ie o ni?aaao aoae?aieoeoaa, a?o?oaeoo?e ?
aeeoeiai? iie?oeee, i. Ee?a.

Iniaenoee aianie caeiaoaa/a. Iniaenoee aianie caeiaoaa/a iieyaa? a oiio,
ui:

?ic?iaeaii iaoiae ioe?iee iaae?eiino? noaeaaeo noaoe/ii iaaecia/aieo
eiino?oeoe?e ia iniia? iaoiaeo a?aie/ii? ??aiiaaae a noaoe/i?e
iinoaiiaoe? c o?aooaaiiyi iicaeiaaeiuei? neee, ui ae?? a iaaacia/ieo
ia?a??cao, oa aeaoi?iiaaii? noaie;

?ic?iaeaii /eneiaee iaoiae ioe?iee iaae?eiino? noaeaaeo noaoe/ii
iaaecia/aieo eiino?oeoe?e c aaaaoiia?aiao?e/iei iaaaioaaeaiiyi;

cai?iiiiiaaii iaoiaeeeo aecia/aiiy ?aiao aeaiaio?a noaeaaeo noaoe/ii
iaaecia/aieo eiino?oeoe?e ca nooiaiai ?o a?aeiia?aeaeueiino?, a oaeiae
?aeiiaiaeaoe?? ii i?iaeooaaiith c o?aooaaiiyi ?aiao;

?ic?iaeaii ii??aiyeueiee iaoiae ioe?iee ca iaae?ei?noth aieeao
iniaeeainoae ae?enii? ?iaioe noaeaaeo noaoe/ii iaaecia/aieo eiino?oeoe?e
i?e ?ic?aooieo ca ?nioth/eie ii?iaie i?iaeooaaiiy, cai?iiiiiaaii
eiie?aoi? cia/aiiy eiao?oe??ioo iaaecia/aiino? ?ic?aooieiai? noaie (rd c
o?aooaaiiyi eiino?oeoeaii? iii?aaee, iiaeai? i?aeoe/i? ?aeiiaiaeaoe?? ii
a?aooaaiith iniaeeainoae ae?enii? ?iaioe eiino?oeoe?e;

ooi/iaii cia/aiiy eiao?oe??ioo noaiii? iaae?eiino? (S;

iiaeai? i?aeoe/i? ?aeiiaiaeaoe?? ii a?aooaaiith ?aiao aeaiaioa i?e
i?iaeooaaii? ? ?ic?aooieo ca iaae?ei?noth noaeaaeo noaoe/ii iaaecia/aieo
eiino?oeoe?e.

Ai?iaaoe?y ?iaioe. Ai?iaaoe?y ?acoeueoao?a aeena?oaoe?? aoea i?iaaaeaia
ia: ?? Oe?a?inuee?e iaoeiai-oaoi?/i?e eiioa?aioe?? c iaoai?ee ??oio?a ?
ooiaeaiaioiaoaeoaaiiy (Iieoaaa, 1995), I?aeia?iaei?e iaoeiai-oaoi?/i?e
eiioa?aioe?? “?ano?niaeiiiii? iaoa??aee, eiino?oeoe??, aoae?ae? oa
nii?oaee” (??aia, 1996), iaoeiai-oaoi?/i?e eiioa?aioe?? aei 100-??//y c
aeiy ia?iaeaeaiiy I.N.Oi?yieea (Iieoaaa, 1997), Ia?o?e Anaoe?a?inuee?e
iaoeiai-i?aeoe/i?e eiioa?aioe?? “I?ia?anneaiua oaoiieiaee e iaoeiu aeey
i?iecaiaenoaa no?ieoaeueiuo iaoa?eaeia, ecaeaeee e eiino?oeoeee”
(Iieoaaa, 1996), i’yo?e i?aeia?iaei?e eiioa?aioe?? “Modern Building
Materials, Structures and Techniques” (A?eueithn, 1997), ia ui??/ieo
iaoeiai-oaoi?/ieo eiioa?aioe?yo Iieoaanueeiai AeOO (1995-1998).

Ioae?eaoe??. Ca iaoa??aeaie aeena?oaoe?? iioae?eiaaii 13 ?ia?o, c ieo 5
o ca??ieeao iaoeiaeo i?aoeue oa 8 o iaoa??aeao ? oacao eiioa?aioe?e, 2
?iaioe iioae?eiaaii aac ni?aaaoi??a.

Ianya oa no?oeoo?a ?iaioe. Aeena?oaoe?y neeaaea?oueny c anooio, i’yoe
?icae?e?a, caaaeueieo aeniiae?a, nieneo aeei?enoaieo aeaea?ae c 189
iaeiaioaaiue oa 4 aeiaeaoe?a. Caaaeueiee ia’?i ?iaioe 240 noi??iie
iaoeiiieno, c ieo 120 noi??iie iniiaiiai oaenoo, 38 ?enoie?a oa 22
oaaeeoe?.

INIIAIEE CI?NO

O anooi? ia??oioiaaia aeooaeuei?noue i?iaeaie, aeeeaaeai? iaoa ? caaea/?
aeine?aeaeaiue, iaoeiaa iiaecia oa i?aeoe/ia oe?ii?noue ?iaioe, iiaeaia
?? caaaeueia oa?aeoa?enoeea.

A ia?oiio ?icae?e? i?iaiae?ciaaii no/aniee noai oai??? ?iia??i?niiai
?ic?aooieo aoae?aaeueieo eiino?oeoe?e acaaae? oa, cie?aia, noaeaaeo
noaoe/ii iaaecia/aieo eiino?oeoe?e. I?iaaaeaii iaeyae iaoeiaeo
aeine?aeaeaiue ii ioe?ioe? iano/i? caeaoiino? oa iaae?eiino? noaeaaeo
noaoe/ii iaaecia/aieo nenoai ca noaiii a?aie/ii? ??aiiaaae.

Aeine?aeaeaiiyie iano/i? caeaoiino? noaeaaeo eiino?oeoe?e a noai?
ieanoe/iino? oa a?aie/ii? ??aiiaaae caeiaeeny I.A.Aeyaae?i,
A.A.Aaicae?a, A.A.Aaia?e?ia, I.Ae.AEoae?i, A.I.Eoci?oeia, E.E.Iaeaiaio,
A.I.Ia?iyeia, A.I.I?ioeaiei A.A.O?io?iiae/, I.E.*a?iia, A.A.*??an,
A.N.Oaaai?i, I.I?ac?e, I.Oeaeioae, I.Oioa/ae, A.O.Eieoa?, A.A.I?e,
O.A.Oiaeae oa ?i.

Noaoe/ii iaaecia/ai? noaeaa? eiino?oeoe?? aeoaea iioe?ai? a i?aeoeoe?
aoae?aieoeoaa ? iathoue iaai? ia?aaaae ia?aae noaoe/ii aecia/aieie.
Iaei??th c iniiaieo ia?aaaa ? iiaeeea?noue i?aeaeuaiiy ?o iano/i?
caeaoiino? ca ?aooiie aeei?enoaiiy ieanoe/ii? noaae?? ?iaioe aei
aeinyaiaiiy eiino?oeoe??th a?aie/iiai noaio. I?e ioe?ioe? iaae?eiino?
oaeiai aeaeo eiino?oeoe?e aaaeeeai a?aoiaoaaoe iniaeeaino? ?o ?oeioaaiiy
— iine?aeiaio a?aeiiao iaaacia/ieo ia?a??c?a oeyoii ooai?aiiy oa?i???a
ieeiiino?. Ii oai?aoe/iei ioe?ieai aeayeeo aaoi??a, iiaeeeai ca?eueoeoe
iaaaioaaeaiiy ia ?aio ia 10-30% ii??aiyii ?c cae/aeiei ?ic?aooieii.

Iniiae oai??? iaae?eiino? aoae?aaeueieo eiino?oeoe?e caeeaee
I.N.No?aeaoeueeee, I.?.?aeai?oeei, A.A.Aieio?i. Iaae?ei?noth
aoae?aaeueieo eiino?oeoe?e a oaeiae ?iia??i?niei i?aaenoaaeaiiyi
iaaaioaaeaiue caeiaeeny oae? a/ai?, ye A.ss.Aa?aoeeia, ?.A.Ai?ioia,
I.?.Eacaeaae/, A.I.Ei?ieueia, A.I.Eoaec?n, A.O.Iouaiia,
A.A.Iaoeinueeee, A.A.Ia?aeueiooa?, N.O.I?/oa?i, A.Ae.?aeca?,
I.I.Neeaaei?a, N.A.Oeiaoaa, A.I.Oeiaiianueeee, A.Aoaono?, A.Aa?aooa,
I.Ae?oeaanai, O.Eao?ao?, N.A.Ei?iae, A.?.I?o/ae, O.Iican, Ae.O?aiaiiie,
I.Iae?a oa ?i.

Aiae?c noaio ieoaiiy aeyaea, ui aeaye? iiiaioe, iia’ycai? c ooi/iaiiyi
ioe?iee iaae?eiino? eiino?oeoe?e, iio?aaothoue ?ica’ycaiiy. Aei oaeeo
ieoaiue iaeaaeaoue o?aooaaiiy iicaeiaaeiuei? neee oa aeaoi?iiaaii?
noaie, ui a aeayeeo aeiaaeeao ia? nooo?aa cia/aiiy. Oaeiae ?iia??i?nia
iiaeaeue eiino?oeoe?? iio?aao? a?eueo aeineiiaei? iiaeae? ciai?oi?o
aieea?a, iniaeeai oeo, ui ?aae?cothoue aaaaoiia?aiao?e/ia iaaaioaaeaiiy.

A ?icae?e? iaaaaeai? iniiai? iieiaeaiiy ?iia??i?niiai ?ic?aooieo
aoae?aaeueieo eiino?oeoe?e oa ?ic?aooieo noaoe/ii iaaecia/aieo nenoai ca
a?aie/ieie noaiaie.

Inoaii?i /anii iaei oaaae i?eae?ey?oueny aea/aiith ae?enii? ?iaioe
noaeaaeo noaoe/ii iaaecia/aieo eiino?oeoe?e. Oea iia’ycaii, ia?aaeon?i,
c iio?aaith a aeineoue eiooiaieo aenia?eiaioao. Aea ?iiae? ianooaae
aoae?aieoeoaa aeicaieythoue i?iaaaeaiiy oaeeo aeine?aeaeaiue, ?, ye
?acoeueoao, iiaeeeaa aeineoue cia/ia aeiiii?y iaoa??aeo. Oaeiae oe?eaaei
iai?yieii aeine?aeaeaiue ? neeaaeia iaoaiaoe/ia iiaeaethaaiiy noi?nii?
?iaioe eiino?oeoe?e, yea noaei iiaeeeaei inoaii? 10-15 ?ie?a ? aeicaiey?
nooo?ai cieceoe iaoa??aeii?noe?noue caaaeyee o?aooaaiith ia?a?iciiae?eo
coneeue a nenoai?. O ca’yceo c ?icaeoeii ?iia??i?niiai ?ic?aooieo
noaeaaeo eiino?oeoe?e noa? iaiao?aeiith ?ic?iaea iaoiaeeee o?aooaaiiy
ae?enii? ? noi?nii? ?iaioe eiino?oeoe?e i?e ioe?ioe? ?o iaae?eiino?.

Aeine?aeaeaiiy a iaeano? oai?aoe/ii? oa ae?enii? ?iaioe noaeaaeo ?ai
i?iaiaeeee ?.?.Aaeaiy, I.I.Aa?aee/aanueeee, A.I.Aaeue, E.N.Aaneeue?aa,
I.E.A?c??, ?.Ae.A?oae?a, ?.I.??iae, A.ss.?naee?i, A.N.Eaca?iianueeee,
I.A.E?aeianueeee, A.I.Eoci?oeia, TH.N.Ia?oeiia, A.A.?ainueeee,
I.A.Naiei, TH.I.No?oaaoeueeee, A.I.*e/oe?i, A.A.Oai??i, ?.N.Oaia,
Ae.No?aainii, A.N.Aia, O.O.Ia, ?.I.Aaiiao, I.Ee?iai?eea?, E.Oa?aaoo,
I.E.Ae?aie oa ?i.

A ?icae?e? iaaaaeaii iaeyae iaoeiaeo ?ia?o oa iniiai? canaaee ii
o?aooaaiith ae?enii? ?iaioe noaoe/ii iaaecia/aieo noaeaaeo eiino?oeoe?e.

A e?ioe? ?icae?eo i?aaenoaaeai? iniiai? caaea/? ?iaioe.

Ae?oaee ?icae?e i?enay/aii o?aooaaiith ae?enii? ?iaioe noaeaaeo
eiino?oeoe?e i?e ?ic?aooieo iaae?eiino?. O iueiio i?iiiio?oueny
iaoiaeeea ioe?iee a?aeiia?aeiino? ?ic?aooieiai? noaie ?aaeuei?e
eiino?oeoe??.

Aeey o?aooaaiiy eiino?oeoeaii? iii?aaee ca i?oei?noth i?e ?ic?aooieo
?iia??iino? a?aeiiae aeaiaioa aai an??? eiino?oeoe?? aeei?enoa?ii
ni?aa?aeiioaiiy:

\AIAAe?EOUe Equation.2 , (1)

– aeiaaeeiaa iaaaioaaeaiiy, yea ni?eeia? aeaiaio eiino?oeoe??;

( – eiao?oe??io ia?aoiaeo a?ae ciai?oiueiai iaaaioaaeaiiy aei
iai?oaeaiiy a aeaiaio?;

– aeiaaeeiaa iai?oaeaiiy a aeaiaio? a?ae aeiaaeeiaiai iaaaioaaeaiiy;

– aeiaaeeiaa eiino?oeoeaia iii?aaea ca iai?oaeaiiyi, ?iciiae?eaiiy
yei? iaea?aeo?oueny oeyoii aenia?eiaioaeueieo aeine?aeaeaiue
eiino?oeoe??.

Ine?eueee ?iciiae?eaiiy eiino?oeoeaii? iii?aaee oa i?oeiino? noae?
aeia?a a?aeiia?aea? caeiio Aaona, oi aeey ni?iuaiiy a ?ic?aooieao
iiaeeeaa aeei?enoaiiy noi?niiai ?iciiae?eaiiy eiino?oeoeaii? iii?aaee oa
i?oeiino? iaoa??aeo, yea oaeiae ? ii?iaeueiei. Ia iniia? eiino?oeoeaii?
iii?aaee ca iai?oaeaiiyie ciaoiaeeoueny eiao?oe??io iaaecia/aiino?
?ic?aooieiai? noaie (rd, ca aeiiiiiaith yeiai aac iia??oaiiy ii?iaoeaii?
iaae?eiino? ciaioo?oueny iaoa??aeii?noe?noue eiino?oeoe?? (yeui
caieaeaia oai?aoe/ia ioe?iea iano/i? caeaoiino? aeaiaioa), aai
i?aeaeuo?oueny iaae?ei?noue (yeui ioe?iea caieaeaia). Cie?aia, ia/eneaii
(rd (oaae. 1) aeey a?aooaaiiy ae?enii? ?iaioe noaeaaeo oa?i (?en. 1) i?e
noi?ni?e ?iaio? ?c cae?ciaaoiiieie ieeoaie iie?eooy. Aeai? oaaeeoe? 1
iieacothoue iiaeeea?noue cieaeaiiy iane aeaiaio?a i?e (rd1. Aeey oeueiai aeaaaeai? oi?ioee
aeiaooeo u?eueiinoae ?iciiae?eaiue eiino?oeoeaii? iii?aaee oa i?oeiino?,
eiino?oeoeaii? iii?aaee oa iaea?eueo aaeeaaieo ooieoe?e ?iciiae?eaiue
ciai?oi?o iaaaioaaeaiue.

?en. 1. Oa?ia, ae?enia ?iaioa yei? aiae?coaaeany.

Iicia/aiiy aeine?aeaeoaaieo ?ic?aooieiaeo noai: oa?i??ia cae??ieaiiy
?eaaey (a), ?aiia noaia (a) oa aei?noea cauaieaiiy ?eaaey (a).

?ic?iaeaii ii??aiyeueiee iaoiae ioe?iee iniaeeainoae ae?enii? ?iaioe
noaeaaeo noaoe/ii iaaecia/aieo eiino?oeoe?e c caaaeueiii?eeiyoeie
?ic?aooieiaeie noaiaie c oi/ee ci?o ?o aieeao ia iaae?ei?noue
eiino?oeoe?e. Ioe?iea ?ic?aooieiai? noaie aaco?oueny ia aecia/aii?
?iia??iino? aeoiaeo iaaacia/iiai ia?a??co eiino?oeoe?? ca a?aie/iee
noai, aecia/aiee ii?iaie, c aeei?enoaiiyi iiaeaeae noioanoe/ieo
?iciiae?eaiue iaaaioaaeaiue. Ii??aiyiiy aeeiio?oueny i?ae ?acoeueoaoaie
oai?aoe/ieo aeaieo ??cieo ?ic?aooieiaeo noai oa ?acoeueoaoaie
aenia?eiaioo ca iaeiaaacia/i?oei ia?a??cii. I?iaaaeaia ?iia??i?nia
ii??aiyeueia ioe?iea ?ic?aooieiaeo noai iiia?a/ieo ?ai ca aeaieie
aenia?eiaioaeueieo aeine?aeaeaiue ?.?.Aaeai? oa aecia/aia ?ic?aooieiaa
noaia, yea e?aua a?aeiia?aea? ae?eni?e ?iaio? ?ai.

Oaaeeoey 1 – Eiao?oe??io (rd, ui o?aoiao? ae?enio ?iaioo aeaiaio?a
noaeaai? oa?ie (?en. 1)

Aeaiaio Oa?i??. nie?aiiy C o?aooaaiiyi noi?nii? ?iaioe c ieeoaie
iie?eooy Iaen.

eiino?oeoe?? aac ieeo

iie?eooy Oa?i. nie?. ?aiia eiino?. AEi?noea cauaie. cia/.

(rd

aeaoa?i?i?noe/ia eiino?oeoeaia iii?aaea

aa?oi?e iiyn 1,0 0,54 0,54 0,60 0,60

ieaei?e iiyn 1,0 0,96 1,02 0,86 1,02

iii?iee ?ice?n 1,0 0,97 0,98 0,93 0,98

noioanoe/ia eiino?oeoeaia iii?aaea (VK=0,11)

aa?oi?e iiyn 1,0 0,63 0,63 0,70 0,70

ieaei?e iiyn 1,0 1,12 1,19 1,01 1,19

iii?iee ?ice?n 1,0 1,14 1,15 1,09 1,15

A o?aoueiio ?icae?e? ?ic?iaeaii ?iia??i?niee iaoiae a?aie/ii? ??aiiaaae
a noaoe/i?e iinoaiiaoe? c o?aooaaiiyi iicaeiaaeiuei? neee.

Ine?eueee a aeoaea iioe?aiiio e?iaiaoe/iiio niinia? caaaeaiiy a?aie/ieo
oiia aaeueie aaaeei caaeaoe aeiaeaoeiaa aioo??oi? coneeey, oi a iniiao
aeaiiai ?iia??i?niiai iaoiaeo a?aie/ii? ??aiiaaae iieeaaeaii noaoe/iee
niin?a c o?aooaaiiyi iicaeiaaeiuei? neee ca I.I.I?ioeaiei:

, (2)

– iicaeiaaeiy neea oa iiiaio a ?-io ia?a??c? a?ae ciai?oiueiai
iaaaioaaeaiiy F;

;

– a?aie/i? iicaeiaaeiy neea oa iiiaio a ?-io ia?a??c?.

?icaeyaeathoueny iniaeeaino? oi?ioaaiiy ii/aoeiaeo oiia, aiae?cothoueny
i?ii?aei? ??oaiiy, iiaeeea? iaoai?cie ?oeioaaiiy eiino?oeoe?e. Oeyoii
ae??oaiiy iao?eoe? e?i?eieo oiia a?aie/iiai noaio aecia/aii eiao?oe??io
aa??aoe?? ?iciiae?eaiiy iano/i? caeaoiino? noaoe/ii iaaecia/aii?
noaeaai? eiino?oeoe?? oa ?iia??iino? ?? ?oeioaaiiy. I?ioean ?ic?aooieo
iio?aao? aeiaeaoeiaiai aiae?co iao?eoe? oiia, ine?eueee iaea?aeaiee a
?acoeueoao? ?ic?aooieo iaoai?ci ?oeioaaiiy iiaea iaoe iaaeeeoeiaee aai
/anoeiaee oa?aeoa?.

Aaaaeaii o?aooaaiiy aeaoi?iiaaii? noaie ca aeiiiiiaith cai?iiiiiaaii?
?iia??i?nii? ?ioa?i?aoaoe?? oi?ioee Ia?/aioa-?aie?ia:

, (3)

– noioanoe/i? aaee/eie ia?aiao??a a?aie/iiai iaaaioaaeaiiy ia
eiino?oeoe?th c o?aooaaiiyi aeaoi?iiaaii? noaie oa ieanoe/iiai
a?aie/iiai iaaaioaaeaiiy, ui caeaaeaoue a?ae aeiaaeeiai? aaee/eie iii?o
iaoa??aeo;

Rcr – ia?aiao? a?aie/ii? iano/i? caeaoiino? noaoe/ii iaaecia/aii?
eiino?oeoe?? c e?i?eii-i?oaeiiai iaoa??aeo.

Ine?eueee ca noioanoe/i? oa?aeoa?enoeee i?e ?ic?aooieo i?eeiathoueny
o?eueee i?oei?noue noae? oa ciai?oi? iaaaioaaeaiiy, oi ia?aiao?
no?eeino? Rcr, ye oaeee, ui caeaaeeoue a?ae aaiiao?e/ieo oa?aeoa?enoee
eiino?oeoe?? oa ia?a??c?a, i?iiiio?oueny i?eeiaoe ye aeaoa?i?iiaaiee.

Aeey ooi/iaiiy ioe?iee iaae?eiino? noaoe/ii iaaecia/aii? noaeaai?
eiino?oeoe?? a ieanoe/i?e noaae?? c o?aooaaiiyi ae?enii? ?iaioe
i?iiiio?oueny aeei?enoaiiy eiino?oeoeaii? iii?aaee o aeaeyae?
eiao?oe??io?a, ui ei?aaothoue iano/o caeaoi?noue ie?aieo ia?a??c?a oa
ci?iththoue eiao?oe??ioe aa??aoe?? i?oeiino? oeeo ia?a??c?a, aieeaath/e
ia ioe?ieo iaae?eiino? eiino?oeoe?? a oe?eiio.

Aeey a?eueo ?aaeueiiai iiaeaethaaiiy i?ioeano aenieoaoaoe?? noaoe/ii
iaaecia/aieo noaeaaeo eiino?oeoe?e ?ic?iaeaii /eneiaee iaoiae ?ic?aooieo
?iia??iino? a?aeiiae ca aaaaoiia?aiao?e/iith iiaeaeeth iaaaioaaeaiiy oa
aeai?eoi ?ic?aooieo iaae?eiino? i?e aeaiia?aiao?e/iiio iaaaioaaeaii?.

Cai?iiiiiaaiee o?ae ?ic?aooieo iieyaa? a aecia/aii? nii/aoeo
aeaoa?i?i?noe/ii?, a iio?i ? noioanoe/ii? iaae? n-aei??ii? iaeano?
iiaeeeaeo noai?a eiino?oeoe?? a i?inoi?? n iacaeaaeieo noioanoe/ieo
ciai?oi?o coneeue ca ?iia??i?niei iaoiaeii a?aie/ii? ??aiiaaae. Iio?i
aeeiio?oueny i?inoi?iaa /eneiaa aaeaioeaia ?ioaa?oaaiiy ca caaaeueiith
oi?ioeith oiiaieo ooieoe?e iaae?eiino? I.?.?aeai?oeeia:

, (4)

– ooieoe?? u?eueiino? ?iciiae?eaiiy ciai?oiueiai iaaaioaaeaiiy oa
?ioaa?aeueia ooieoe?y ?iciiae?eaiiy iano/i? caeaoiino? noaoe/ii
iaaecia/aii? noaeaai? eiino?oeoe??.

c eii?aeeiaoaie oeaio?o F1 oa F2 aei??aith?:

, (5)

aea p(F) – i?aeeiaoa u?eueiino? ?iciiae?eaiiy iaaaioaaeaiiy a oi/oe? F.

?en. 2. Aei ?ic?aooieo noaoe/ii iaaecia/aieo noaeaaeo eiino?oeoe?e ca
aeaiia?aiao?e/iei caaaioaaeaiiyi.

.

?iia??i?noue iiae?? ?oeioaaiiy eiino?oeoe?? a ?-o?e eieaeuei?e cii?:

. (6)

Noia ?iia??iinoae ?oeioaaiue a on?o eieaeueieo ciiao aei??aith?
?iia??iino? ?oeioaaiiy eiino?oeoe??:

. (7)

Ca aeeeaaeaiith ?ic?iaeaiith iaoiaeeeith aeeiiai? ?ic?aooiee noaoe/ii
iaaecia/aieo noaeaaeo ?ai c o?aooaaiiyi iicaeiaaeiuei? neee,
aeaoi?iiaaii? noaie, aeaiia?aiao?e/iiai iaaaioaaeaiiy oa ae?enii?
?iaioe.

A /aoaa?oiio ?icae?e? aeeeaaeaii ?acoeueoaoe aeeiiaiiai /eneiaiai
aenia?eiaioo ii ia/eneaiith iaae?eiino? 105 noaeaaeo noaoe/ii
iaaecia/aieo ?ai, aecia/aiith nooiaiy a?aeiia?aeaeueiino? ?o aeaiaio?a
oa ioe?ioe? ?aca?a?a iano/i? caeaoiino?.

On? ?aie aoee cai?iaeoiaai? ca?aeii ae?th/eo ii?i i?iaeooaaiiy c
noaiaea?oieo aeaioaa??a c oe?ieiaaeeaaieo ia?ie noae?. Eiio?ao?aoe??
?ai, ui aeei?enoiaoaaeeny i?e i?iaaaeaii? iaoaiaoe/iiai aenia?eiaioo,
iiaeai? a oaae.2.

Iaoaiaoe/iee aenia?eiaio aeyaea, ui ?iia??i?niee iaoiae a?aie/ii?
??aiiaaae a noaoe/i?e iinoaiiaoe? aea? ioe?ieo iaae?eiino? aeaui ieae/o
i?ae iaoiae eiia?iiaaieo iaoai?ci?a, aea, caaaeath/e ia ooi/iaiiy
?iciiae?eaiiy aioo??oi?o coneeue oa niin?a caaaeaiiy a?aie/ieo oiia,
ne?ae aaaaeaoe noaoe/io ioe?ieo a?eueo aeecueeith aei ?aaeueii?, yea
?aeiiaiaeo?oueny aeey iiaeaeueoiai aeei?enoaiiy o i?aeoe/ieo
?ic?aooieao.

Aeey i?enei?aiiy ?ic?aooie?a iaoiaeeeo ia/eneaiiy ?iia??i?nieo
iieaciee?a eiino?oeoe?e ?aae?ciaaii a aeaeyae? eiiieaeno i?ia?ai
“FORTUNA” aeey IAII oeio IBM PC, ui aeicaiey? aaoiiaoeciaaii aeeiioaaoe
an? o?oaeii?noe? ?ic?aooiee.

Oaaeeoey 2. – Eiio?ao?aoe?? ?ai, ui aeei?enoiaoaaeeny i?e i?iaaaeaii?
iaoaiaoe/iiai aenia?eiaioo

Aoee iaea?aeai? aeai? ii ?iia??iino? a?aeiiae noaoe/ii iaaecia/aieo
noaeaaeo ?ai ca iaeiiia?aiao?e/iei iaaaioaaeaiiyi c o?aooaaiiyi
iicaeiaaeiuei? neee oa aeaoi?iiaaii? noaie oa ca aeaiia?aiao?e/iei
iaaaioaaeaiiyi. O?aooaaiiy iicaeiaaeiuei? neee oa aeaoi?iiaaii? noaie
aeaui cieaeo? ioe?ieo iaae?eiino? (ia 2-4 ii?yaeee), a aeaiia?aiao?e/ia
iiaeaeue iaaaioaaeaiiy aea? iiaeeea?noue aeaui i?aeaeueoe oeth ioe?ieo
caaaeyee o?aooaaiith iacaeaaeiino? ae?? ciai?oi?o iaaaioaaeaiue.

A i’yoiio ?icae?e? aeeeaaeaii iaoiae ioe?iee nooiaiy a?aeiia?aeaeueiino?
aeaiaio?a noaeaaeo noaoe/ii iaaecia/aieo eiino?oeoe?e ca
eia?ei-?iia??i?niei iaoiaeii, ?iia??i?niei iaoiaeii a?aie/ii? ??aiiaaae
c o?aooaaiiyi iane aeaiaioa.

Cai?iiiiiaaii iaoiae ioe?iee nooiaiy a?aeiia?aeaeueiino? aeaiaio?a
noaeaaeo noaoe/ii iaaecia/aieo eiino?oeoe?e oa ?o ?aiaeoaaiiy ia aac?
?iia??i?niiai iaoiaeo a?aie/ii? ??aiiaaae a noaoe/i?e iinoaiiaoe?. Aeey
oeueiai aeei?enoaiee oaeee iieaciee, ye ieoiiee aianie:

, (8)

aea Qc0(i), Qc – a?aeiia?aeii ?iia??i?noue a?aeiiae eiino?oeoe?? i?e
aaniethoi?e a?aeiia? ?-ai aeaiaioa oa ?iia??i?noue a?aeiiae iniiaii?
eiino?oeoe??.

I?eioeei ?ic?aooieo iieyaa? a ioe?ioe? iaae?eiino? ca ?iia??i?niei
iaoiaeii a?aie/ii? ??aiiaaae iniiaii? eiino?oeoe?? oa eiino?oeoe?? c
cia/ii ineaaeaiei aeine?aeaeoaaiei aeaiaioii. Iai?eeeaae, aeey
aeaiiiaa?oiai? noaeaai? noaoe/ii iaaecia/aii? ?aie (?en. 3,a) nooiai?
a?aeiia?aeaeueiinoae aeaiaio?a eiino?oeoe?? ?iciiae?eai? oae, ye ia ?en
3,a. A?aeiia?aeii aei nooiai?a a?aeiia?aeaeueiino? ?aia ieaeiueiai
?eaaey aeyaeany iaea?eueoei, a ?aia noiye?a iaeiaioei.

Iaaaaeaii ?acoeueoaoe iaoaiaoe/iiai aenia?eiaioo ii ?aiaeoaaiith
aeaiaio?a noaoe/ii iaaecia/aieo noaeaaeo ?ai. Aeai? ca ?acoeueoaoaie
iaoaiaoe/iiai aenia?eiaioo ia aeicaieythoue iaeiicia/ii noaa?aeaeoaaoe a
aoaeue-yeiio aeiaaeeo ia?aaaao iaeiiai eiino?oeoeaiiai aeaiaioa iaae
?ioei, aea a a?eueoino? aeiaaee?a niinoa??aa?oueny oaiaeaioe?y aei
ia?aaaaeaiiy nooiaiy a?aeiia?aeaeueiino? ?eaaey iaae eieiiith a iecueeeo
?aiao c cia/iei aa?oeeaeueiei iaaaioaaeaiiyi oa a?eueo?e
a?aeiia?aeaeueiino? eieiie a aenieeo ai?eciioaeueii caaaioaaeaieo ?aiao.
Iaaaaeaii i?eeeaaee ae?aa?ai a?aeiia?aeaeueiino? aeaiaio?a aeayeeo
aeae?a ?ai.

Ia aac? i?iaaaeaiiai iaoaiaoe/iiai aenia?eiaioo oa oeyoii ?iia??i?niiai
aiae?co cia/aiiy eiao?oe??ioo noaiii? iaae?eiino? (S aeey aei?noeeo
noaeaaeo noaoe/ii iaaecia/aieo ?ai ca oi?ioeith:

, (9)

aea (R – ii?iaoeaia a?aeoeeaiiy ?ic?aooieiaiai cia/aiiy a?ae
iaoaiaoe/iiai i/?eoaaiiy i?oeiino? noae?;

VR, VS – a?aeiia?aeii, eiao?oe??ioe aa??aoe?? iano/i? caeaoiino?
ie?aiiai ia?a??co oa on??? eiino?oeoe??;

RR, RS – ??aiicaaacia/ai? a?aeiini? ?ic?aooieia? ia?aiao?e iano/i?
caeaoiino? eiino?oeoe?? a?aeiia?aeii i?e ooai?aii? ia?oiai oa?i??o
ieanoe/iino? oa a noai? a?aie/ii? ??aiiaaae.

a)

a)

?en. 3. Aeaiiiaa?oiaa noaeaaa ?aia (a)

oa nooiai? a?aeiia?aeaeueiino? ?? aeaiaio?a (a).

Ia ?en. 4 cia?aaeaii caeaaei?noue eiao?oe??ioo noaiii? iaae?eiino? (S
aeey noaeaaeo noaoe/ii iaaecia/aieo ?ai a?ae nooiaiy noaoe/ii?
iaaecia/aiino? n ca aeaiei iaoaiaoe/iiai aenia?eiaioo. Eiaeia oi/ea
a?aeiia?aea? eiie?aoi?e ?ai?, e?eaa a?aeoai?th? iaeneiaeueii iiaeeea?
(i?e oiia? ??aiiiaae?eiino? aeaiaio?a) cia/aiiy (S, ?ic?aoiaai? ca
oi?ioeith:

. (10)

Aiae?c a?ao?eo caeaaeiino? cia/aiiy (S aeey ?ai (aeea. ?en. 4) a?ae
iaeneiaeueii iiaeeeai? e?eueeino? oa?i???a ieeiiino? (nooi?iue noaoe/ii?
iaaecia/aiino? n+1) aea? ciiao c?iaeoe aeniiaie, ui an? ?aie
ciaoiaeyoueny a iaeano?, iaiaaeai?e a?aieoeath iaeneiaeueieo cia/aiue ?
ia?aaaaeath/a a?eueo?noue ?ai oyae?? aei iaeneiaeueieo cia/aiue
eiao?oe??ioo (S, ui aiai?eoue i?i a?aeiia?aei?noue oai?aoe/ieo canaae oa
?acoeueoao?a iaoaiaoe/iiai aenia?eiaioo.

Iio??aii a?aei?oeoe, ui i?e iaaeeaeaii? iaoai?cio ?oeioaaiiy aei
aaei/iiai eiao?oe??io (S ciaioo?oueny, a i?e cnoaiiio ( ca?eueoo?oueny.
Iaeneiaeuei? cia/aiiy (S aoee io?eiai? aeey iiaiiai iaoai?cio
?oeioaaiiy, a /anoeiaee iaoai?ci i?ecaiaeeoue aei ciaioaiiy
eiao?oe??ioa. Aiae?c iaoai?ci?a ?oeioaaiiy aeyaea, ui aeaye? ia?a??ce a
a?aie/iiio noai? ia i?eeiathoue o/ano? a e?iaiaoe/iiio iaoai?ci?, aea ?o
iio??aii o?aoiaoaaoe i?e ioe?ioe? iaae?eiino? oa aecia/aii? eiao?oe??ioa
(S.

?en. 4. Caeaaei?noue eiao?oe??ioo noaiii? iaae?eiino? (S aeey noaeaaeo
noaoe/ii iaaecia/aieo ?ai a?ae nooiaiy noaoe/ii? iaaecia/aiino? n.

.

Ia iniia? noaoenoe/ieo aeaieo i?iaaaeaiiai iaoaiaoe/iiai aenia?eiaioo
aoee iaea?aeai? ?ic?aooieia? cia/aiiy (S aeey aeei?enoaiiy a
i?iaeooaaii? (aeea. oaae. 3).

Oaaeeoey 3. – ?ic?aooieia? cia/aiiy eiao?oe??ioo noaiii? iaae?eiino?
aeey noaoe/ii iaaecia/aieo noaeaaeo ?ai (oaae. 2)

1 iiaa?o 2 iiaa?oe 3 iiaa?oe

1 i?iaii 1,18 1,21 1,21

2 i?iaiie 1,19 1,26(1,27

3 i?iaiie 1,24

Eiao?oe??io noaiii? iaae?eiino? (S i?ecia/aiee aeey aeei?enoaiiy a
oi?ioe? ae?th/eo ii?i aeey ?ic?aooieo iano/i? caeaoiino? ia?a??c?a
noaoe/ii iaaecia/aieo noaeaaeo eiino?oeoe?e c o?aooaaiiyi ieeiii?
noaae?? ?iaioe:

. (11)

AENIIAEE

?ic?iaeaiee ?iia??i?niee iaoiae a?aie/ii? ??aiiaaae a noaoe/i?e
iinoaiiaoe? c o?aooaaiiyi iicaeiaaeiuei? neee ca aeaiia?aiao?e/iei
(aaaaoiia?aiao?e/iei) iaaaioaaeaiiyi oa c o?aooaaiiyi aeaoi?iiaaii?
noaie, yeee aeicaiey? ooi/ieoe ?iia??i?noue a?aeiiae caaaeyee
iaaeeaeaiith aei ?aaeueieo oiia ?iaioe eiino?oeoe?? ? ?aeiiaiaeo?oueny
aeey aeei?enoaiiy.

?iia??iino? a?aeiiae noaeaaeo noaoe/ii iaaecia/aieo ?ai, aecia/ai? ca
?ic?iaeaiei ?iia??i?niei iaoiaeii a?aie/ii? ??aiiaaae c o?aooaaiiyi
iicaeiaaei?o nee ca?eueoothoueny ia 1(3 ii?yaeee ii??aiyii c aiaeia?/iei
?ic?aooieii c o?aooaaiiyi o?eueee caeiath/eo iiiaio?a; o?aooaaiiy
aeaoi?iiaaii? noaie oaeiae aea? ca?eueoaiiy ?iia??iino? a?aeiiae ?ai ia
1(4 ii?yaeee. O aeiaaeeo aeaiia?aiao?e/iiai iaaaioaaeaiiy ?iia??i?noue
a?aeiiae ?ai ciaioo?oueny ia 2(3 ii?yaeee.

Aecia/ai? caeiie noi?niiai ?iciiae?eaiiy eiino?oeoeaii? iii?aaee oa
ciai?oi?o iaaaioaaeaiue aeicaieythoue ioe?ithaaoe iaae?ei?noue noaoe/ii
iaaecia/aieo eiino?oeoe?e c o?aooaaiiyi ae?enii? ?iaioe. Cai?iiiiiaai?
cia/aiiy eiao?oe??ioa (rd aeathoue iiaeeea?noue ciaioaiiy iane aeayeeo
aeaiaio?a noaeaaeo e?ieayieo oa?i aac nooo?aiai iia??oaiiy iaae?eiino?.
?ic?iaeaiee ii??aiyeueiee iaoiae ioe?iee aieeao ia iaae?ei?noue
iniaeeainoae ae?enii? ?iaioe noaeaaeo noaoe/ii iaaecia/aieo eiino?oeoe?e
aeicaiey? ye?nii aecia/eoe ?ic?aooieiao noaio, yea e?aua a?aeiia?aea?
ae?eni?e ?iaio? nenoaie.

Cai?iiiiiaaii iaoiaeeeo ?aiaeoaaiiy aeaiaio?a noaeaaeo noaoe/ii
iaaecia/aieo ?ai, yea aea? iiaeeea?noue aoaeoeaii aieeaaoe ia ?o
iaae?ei?noue oa iaoa??aeii?noe?noue i?e i?iaeooaaii?. ?acoeueoaoe
iaoaiaoe/iiai aenia?eiaioo aeicaieythoue noaa?aeaeoaaoe, ui aeey
iecueeeo ?ai c cia/iei aa?oeeaeueiei iaaaioaaeaiiyi i?e i?iaeooaaii?
a?eueoa oaaae iio??aii iaaeaaaoe ?eaaeth, a aeey aenieeo ?ai c
ia?aaaaeaiiyi ai?eciioaeueii? neeaaeiai? iaaaioaaeaiiy iio??aii
ca?eueooaaoe iaae?ei?noue no?eie.

Ooi/iaiiy eiao?oe??ioo noaiii? iaae?eiino? (S aeicaieeei iaa?oiooaaoe
eiai cia/aiiy aeey i?aeoe/iiai ?ic?aooieo noaeaaeo ?ai c e?euee?noth
iiaa?o?a oa i?iaii?a a?ae iaeiiai aei o?ueio a ?ioa?aae? (S=1,18(1,27.

?ic?iaeai? i?aeoiaee, iaoiaeeee oa i?aeoe/i? ?aeiiaiaeaoe??
aeicaieythoue nooo?ai ciaioeoe iaoaeii?noe?noue noaeaaeo noaoe/ii
iaaecia/aieo eiino?oeoe?e.

NIENIE IIOAE?EIAAIEO I?AOeUe CA OAIITH AeENA?OAOe??

Noaoo? o iaoeiaeo aeaeaiiyo

Ai?oueei I.A. ?ic?aooiie iaae?eiino? noaeaaeo noaoe/ii iaaecia/aieo
eiino?oeoe?e// Ca??iee iaoeiaeo i?aoeue (aaeocaaa iaoeiiaoaeoaaiiy,
aoae?aieoeoai) Iieo. aea?ae. oaoi. oi-o ?i. TH??y Eiiae?aothea, aeione
1. – Iieoaaa: IAeOO ?i. TH??y Eiiae?aothea, 1998. – N.79-86.

Ai?oueei I.A. Ii??aiyeueiee iaoiae aiae?co aieeao ae?enii? ?iaioe ia
iaae?ei?noue noaeaaeo eiino?oeoe?e// Ca??iee iaoeiaeo i?aoeue (aaeocaaa
iaoeiiaoaeoaaiiy, aoae?aieoeoai), Iieo. aea?ae. oaoi. oi-o ?i. TH??y
Eiiae?aothea, aeione 3. – Iieoaaa: IAeOO ?i. TH??y Eiiae?aothea, 1998. –
N.139-143.

I?/oa?i N.O., Ai?oueei I.A. ?iia??i?niee iaoiae a?aie/ii? ??aiiaaae a
noaoe/i?e iinoaiiaoe?// Aeooaeuei? i?iaeaie aiaeiiai ainiiaea?noaa. Ca.
iaoe. no. O.3. Oe?a?inueea aea?aeaaia aeaaeai?y aiaeiiai ainiiaea?noaa.
??aia, 1997. – N.91-94.

I?/oa?i N.O., Ai?oueei I.A. Ioe?iea iaae?eiino? noaoe/ii iaaecia/aieo
eiino?oeoe?e// I?iaeaie oai??? ? i?aeoeee cae?ciaaoiio: Ca. iaoe. no. –
Iieoaaa, 1997. – N.393-396.

I?/oa?i N.O., Ai?oueei I.A. Aeine?aeaeaiiy aieeao ae?enii? ?iaioe
nenoaie “oa?ia – ieeoe iie?eooy” ia iaae?ei?noue// Ca. iaoe. no.
“Noaeacae?ciaaoiii? eiino?oeoe??: i?iaeooaaiiy, aoae?aieoeoai,
aenieoaoaoe?y”, – E?eaee ??a, 1998. – N.151-154.

Iaoa??aee oa oace eiioa?aioe?e

Ie/oaei N.O., Aieoueei A.A. ?acaeoea aa?iyoiinoiiai iaoiaea
i?aaeaeueiiai ?aaiiaaney// Proceedings of 5th International Conference
“Modern Building Materials, Structures and Techniques”, Vol. III.
Vilnius, 1997. pp.88-93.

I?/oa?i N.O., Ai?oueei I.A. Aeine?aeaeaiiy ieanoe/iiai ?oeioaaiiy
noaoe/ii iaaecia/aieo noaeaaeo ?ai iaoiaeii a?aie/ii? ??aiiaaae//
Iaoa??aee ??? I?aeia?. neiiic?oio “Iaoai?ea ? o?ceea ?oeioaaiiy
aoae?aaeueieo iaoa??ae?a oa eiino?oeoe?e”. – Euea?a: Eaiaiy?, 1998. –
N.181-186.

I?/oa?i N.O., Ai?oueei I.A. Aiae?c a?aeiia?aeaeueiino? aeaiaio?a nenoaie
“aoae?aey-ooiaeaiaio”// I?aoe? ?? Oe?a?inueei? iaoeiai-oaoi?/ii?
eiioa?aioe?? c iaoai?ee a?oio?a ? ooiaeaiaioiaoaeoaaiiy. *.3.
Iieoaanueeee oaoi?/iee oi?aa?neoao. Iieoaaa, 1996. – N.92-93.

I?/oa?i N.O., Ai?oueei I.A., Iauaiei A.I. ?icaeoie ?iia??i?niiai
?ic?aooieo ye can?a i?aeaeuaiiy aeiiii?/iino? eiino?oeoe?e//
?ano?niaeiiiii? iaoa??aee, eiino?oeoe??, aoae?ae? oa nii?oaee. Iao.
I?aeia?. iaoe.-oao. eiio. *.1. Oe?a?inueea aea?aeaaia aeaaeai?y aiaeiiai
ainiiaea?noaa. ??aia, 1996. – N.114.

I?/oa?i N.O., Ai?oueei I.A. Ioe?iea aaaeeeaino? aeaiaio?a aoae?aaeueieo
eiino?oeoe?e// Oace aeiiia. 47 iaoe. eiio. i?ioani??a, aeeeaaea/?a,
iaoeiaeo i?aoe?aiee?a, ani??aio?a oa nooaeaio?a oi?aa?neoaoo. *.3.
Iieoaanueeee oaoi?/iee oi?aa?neoao. Iieoaaa, 1995. – N.37.

I?/oa?i N.O., *?/oe?i A.I., Ai?oueei I.A. Ia’?aeiaiee i?aeo?ae aei
ioe?iee iaae?eiino? noaoe/ii iaaecia/aieo eiino?oeoe?e// Oace aeiiia. 48
iaoe. eiio. i?ioani??a, aeeeaaea/?a, iaoeiaeo i?aoe?aiee?a, ani??aio?a
oa nooaeaio?a oi?aa?neoaoo. *.3. Iieoaanueeee oaoi?/iee oi?aa?neoao.
Iieoaaa, 1996. – N.30.

I?/oa?i N.O., Ai?oueei I.A. Aeei?enoaiiy oa?aeoa?enoee iaae?eiino? i?e
ioe?ioe? aaaeeeaino? aeaiaio?a aoae?aaeueieo eiino?oeoe?e// Oace aeiiia.
48 iaoe. eiio. i?ioani??a, aeeeaaea/?a, iaoeiaeo i?aoe?aiee?a,
ani??aio?a oa nooaeaio?a oi?aa?neoaoo. *.3. Iieoaanueeee oaoi?/iee
oi?aa?neoao. Iieoaaa, 1996. – N.31.

I?/oa?i N.O., Ai?oueei I.A. I?i aeaye? i?aeoiaee aei ioe?iee iaae?eiino?
aoae?aaeueieo iaoei oa onoaoeoaaiiy// I?ia?anneaiua oaoiieiaee e iaoeiu
aeey i?iecaiaenoaa no?ieoaeueiuo iaoa?eaeia, ecaeaeee e eiino?oeoeee.
Oac. aeiee. Ia?aie Anaoe?aei. iao/i.-i?aeoe/. eiio. – Iieoaaa, 1996. –
N.123-124.

AIIOAOe??

Ai?oueei I.A. ?iia??i?niee ?ic?aooiie ? ioe?iea nooiaiy
a?aeiia?aeaeueiino? aeaiaio?a noaeaaeo noaoe/ii iaaecia/aieo
eiino?oeoe?e. — ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe
ca niaoe?aeuei?noth 05.23.01 – aoae?aaeuei? eiino?oeoe??, aoae?ae? oa
nii?oaee. – Iieoaanueeee aea?aeaaiee oaoi?/iee oi?aa?neoao ?iai? TH??y
Eiiae?aothea, Iieoaaa, 1999.

Aeena?oaoe?th i?enay/aii ieoaiiyi ioe?iee iaae?eiino? noaoe/ii
iaaecia/aieo noaeaaeo eiino?oeoe?e ca iano/ith caeaoi?noth oa
?aiaeoaaiith ?o aeaiaio?a ca nooiaiai a?aeiia?aeaeueiino?. A
aeena?oaoe?? ?ic?iaeaii ?iia??i?niee iaoiae a?aie/ii? ??aiiaaae a
noaoe/i?e iinoaiiaoe? c o?aooaaiiyi iicaeiaaeiuei? neee, aeaoi?iiaaii?
noaie, aaaaoiia?aiao?e/iiai iaaaioaaeaiiy oa ae?enii? ?iaioe. I?iaaaeaii
ia’?iiee iaoaiaoe/iee aenia?eiaio ii ia?aooaaiith iaae?eiino? noaeaaeo
noaoe/ii iaaecia/aieo eiino?oeoe?e ca iaeiiia?aiao?e/iei oa
aeaiia?aiao?e/iei iaaaioaaeaiiyi, a oaeiae c o?aooaaiiyi aeaoi?iiaaii?
noaie, oa aeeiiaii ioe?ieo ?o aeaiaio?a ca nooiaiai a?aeiia?aeaeueiino?.
Ooi/iaii eiao?oe??io noaiii? iaae?eiino? oa cai?iiiiiaaii iaoiaeeeo
o?aooaaiiy ae?enii? ?iaioe, ui aeicaieeoue ciaioeoe iaoaeii?noe?noue
iano/eo eiino?oeoe?e.

Eeth/ia? neiaa: noaeaa? noaoe/ii iaaecia/ai? eiino?oeoe??, ?iia??i?niee
?ic?aooiie, aeaoi?iiaaia noaia, iaae?ei?noue, ae?enia ?iaioa, iaoiae
a?aie/ii? ??aiiaaae, iano/a caeaoi?noue, aaaaoiia?aiao?e/ia
iaaaioaaeaiiy.

Aieoueei A.A. Aa?iyoiinoiue ?an/ao e ioeaiea noaiaie ioaaonoaaiiinoe
yeaiaioia noaeueiuo noaoe/anee iaii?aaeaeeiuo eiino?oeoeee. — ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa oaoie/aneeo iaoe
ii niaoeeaeueiinoe 05.23.01 – no?ieoaeueiua eiino?oeoeee, caeaiey e
nii?oaeaiey. – Iieoaaneee ainoaea?noaaiiue oaoie/aneee oieaa?neoao eiaie
TH?ey Eiiae?aothea, Iieoaaa, 1999.

Aeenna?oaoeey iinayuaia aii?inai ioeaiee iaaeaaeiinoe noaoe/anee
iaii?aaeaeeiuo noaeueiuo eiino?oeoeee ii ianouae niiniaiinoe e
?aiaee?iaaieth eo yeaiaioia ii noaiaie ioaaonoaaiiinoe.

A ia?aii ?acaeaea i?iaaaeai iaci? e aiaeec iaoiaeia ?an/?oa noaoe/anee
iaii?aaeaeeiuo noaeueiuo eiino?oeoeee ii iaae?aeiinoe. Ioia/aiu
i?aeiouanoaa e iaaeinoaoee iaeioi?uo niiniaia ioeaiee aa?iyoiinoe ioeaca
eiino?oeoeee yoiai aeaea a i?aaeaeueiii ninoiyiee. Naeaeai iaci?
ioa/anoaaiiie e ca?oaaaeiie eeoa?aoo?u ii aii?inai ?an/?oa eiino?oeoeee
ii i?aaeaeueiiio ?aaiiaaneth, iaae?aeiinoe, aeaenoaeoaeueiie ?aaioa.
Eceiaeaiu iniiaiua caaea/e enneaaeiaaiee.

Ai aoi?ii ?acaeaea i?aaeeiaeaia iaoiaeeea o/aoa aeaenoaeoaeueiie ?aaiou
a aa?iyoiinoiii ?an/aoa noaoe/anee iaii?aaeaeeiuo noaeueiuo eiino?oeoeee
n iiiiuueth eiyooeoeeaioa iaii?aaeaeaiiinoe ?an/aoiie noaiu, eioi?ue
iicaieeo o/eouaaoue niaianoioth ?aaioo yeaiaioia, iaaeinoaoee ?an/?oiuo
noai e aieaa yooaeoeaii eniieueciaaoue ianouoth niiniaiinoue
eiino?oeoeee.

Iieo/aiu eiie?aoiua cia/aiey eiyooeoeeaioa iaii?aaeaeaiiinoe ?an/aoiie
noaiu aeey eaaeeo oa?i, iicaieythuea iieo/eoue iuooeiue yeiiiie/aneee
yooaeo aac nieaeaiey iaae?aeiinoe eiino?oeoeee.

I?aaeeiaeai n?aaieoaeueiue iaoiae ioeaiee niioaaonoaey ?an/?oiie noaiu
aeaenoaeoaeueiie ?aaioa noaeueiuo eiino?oeoeee, iicaieythuee auae?aoue
iaeaieaa yooaeoeaiua iiaeaee aeey i?iaeoe?iaaiey nii?oaeaiee.

A o?aoueai ?acaeaea ?ac?aaioai aa?iyoiinoiue iaoiae i?aaeaeueiiai
?aaiiaaney a noaoe/aneie iinoaiiaea n o/aoii i?iaeieueiie neeu,
aeaoi?ie?iaaiiie noaiu, iiiaiia?aiao?e/aneiai caa?oaeaiey e
aeaenoaeoaeueiie ?aaiou.

Iaoiae iniiaai ia noaoe/aneie oi?ioee?iaea caaea/e i?aaeaeueiiai
?aaiiaaney n eniieueciaaieai a oneiaeyo ieanoe/iinoe iianiuo na/aiee ia
oieueei i?aaeaeueiiai ieanoe/aneiai iiiaioa, ii e i?aaeaeueiie
i?iaeieueiie neeu.

O/?o aeaoi?ie?iaaiiie noaiu i?iecaiaeeony n iiiiuueth iiaeeoeoee?iaaiiie
oi?ioeu Ia?/aioa-?aieeia, aaeaioe?iaaiiie aeey aa?iyoiinoiiai ?an/?oa.

O/?o aeaenoaeoaeueiie ?aaiou naycai n aaaaeaieai a oneiaey ieanoe/iinoe
e aa?iyoiinoiua ia?aiao?u eiyooeoeeaioia iaii?aaeae?iiinoe ?an/?oiie
noaiu e eiyooeoeeaioia aa?eaoeee i?i/iinoe ioaeaeueiuo na/aiee.

?aoaiea caaea/e iiiaiia?aiao?e/aneiai iiaeaee?iaaiey caa?oaeaiey
au?aaeaii a /eneaiiii aeaea e iicaieyao o/eouaaoue ?aaeueiua
?ani?aaeaeaiey aiaoieo iaa?ocie.

A /aoa??oii ?acaeaea i?aaenoaaeaiu iniiaiua ?acoeueoaou i?iaaaeaiiiai
iaoaiaoe/aneiai yenia?eiaioa ii ?an/aoo iaaeaaeiinoe noaeueiuo
noaoe/anee iaii?aaeaeeiuo ?ai ii iaeiiia?aiao?e/aneiio e
aeaooia?aiao?e/aneiio caa?oaeaieth, a oaeaea n o/aoii aeaoi?ie?iaaiiie
noaiu, iaeaeaiu eiyooeoeeaiou noaiiie iaae?aeiinoe e auiieiaia ioeaiea
eo yeaiaioia ii noaiaie ioaaonoaaiiinoe.

A iyoii ?acaeaea i?aaenoaaeaiu iaoiaeu aiaeeca noaiaie ioaaonoaaiiinoe
yeaiaioia noaoe/anee iaii?aaeaeeiuo noaeueiuo eiino?oeoeee.

Iieacai oiae ?aoaiey eiaeei-aa?iyoiinoiui iaoiaeii, aa?iyoiinoiui
iaoiaeii i?aaeaeueiiai ?aaiiaaney n o/?oii aana yeaiaioa e ii e?eoa?eth
oaeaeueiiai aeeaaea. I?iaiaeece?iaaiu caaeneiinoe iaaeaeo niioiioaieyie
i?i/iinoe noiae e ?eaaey, auniou e i?ie?oa, aa?oeeaeueiie e
ai?eciioaeueiie iaa?ocie a neo/aa i?iaeoe?iaaiey ?aaiiiaae?aeiie
i?inoaeoae noaoe/anee iaii?aaeaeeiie ?aiu.

Ooi/iai eiyooeoeeaio noaiiie iaaeaaeiinoe aeey noaoe/anee iaii?aaeaeeiuo
noaeueiuo ?ai. I?aaeeiaeai iaoiae ii?aaeaeaiey ?an/?oiiai cia/aiey
eiyooeoeeaioa noaiiie iaae?aeiinoe enoiaey ec aai noioanoe/aneie
i?e?iaeu. Iniiauaaynue ia aeaiiuo iaoaiaoe/aneiai yenia?eiaioa,
i?aaeeaaaaony ?yae eiyooeoeeaioia noaiiie iaae?aeiinoe aeey noaoe/anee
iaii?aaeaeeiuo noaeueiuo ?ai.

A ea/anoaa auaiaeia aeaiu ?aeiiaiaeaoeee ii eniieueciaaieth,
eiyooeoeeaioia noaiiie iaae?aeiinoe e iaii?aaeae?iiinoe ?an/?oiie noaiu,
iaoiaeia ioeaiee iaae?aeiinoe noaoe/anee iaii?aaeaeeiuo noaeueiuo
eiino?oeoeee, ?aiaee?iaaieth yeaiaioia aeey yooaeoeaiiai nieaeaiey aana
nii?oaeaiee eee iiauoaiey eo iaae?aeiinoe.

Eeth/aaua neiaa: noaeueiua noaoe/anee iaii?aaeaeeiua eiino?oeoeee,
aa?iyoiinoiue ?an/ao, aeaoi?ie?iaaiiay noaia, iaaeaaeiinoue,
aeaenoaeoaeueiay ?aaioa, iaoiae i?aaeaeueiiai ?aaiiaaney, ianouay
niiniaiinoue, iiiaiia?aiao?e/aneia caa?oaeaiea.

Gnitko A.V. Estimation of Reliability and Degree of Significance of
Elements Redundant Steel Structures. – Manuscript.

Dissertation for degree of Candidate of Technical Sciences on Speciality
05.23.01 – Building Structures, Buildings and Edifices. Poltava State
Technical University named in honour of Yuriy Kondratyuk, Poltava, 1999.

Dissertation is devoted to the problems of estimation of redundant steel
structures through carrying capacity and ranging of the elements by
degree of significance. Probabilistic method of limit state in statical
mode with the account of longitudinal force, deformed mode,
multi-parameter loading and real behaviour was worked out. Large scale
mathematic experiment for calculation of reliability of redundant steel
structures by single-, two-parameter loading and with account of
deformed mode was performed. The estimation of elements by degree of
significance had been done. The coefficient of structural reliability
had been defined more precisely. Method which accounts the real
behaviour and permits to reduce metal capacity of carrying structures
had been suggested.

Keywords: redundant steel structures, probability estimation, deformed
mode, real behaviour, reliability, limit state method, carrying
capacity, multi-parameter loading.

_______________

(I?aeien aaoi?a)

I?aeienaii aei ae?oeo 8.04.99 ?.

Oe?aae 100 i?. Oiia. ae?oe. a?e. 1.0.

Caiiaeaiiy ? 176. Oi?iao 60(84 1/16

Aeaeaaieoeoai Iieoaanueeiai aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo

?iai? TH??y Eiiae?aothea

PAGE 6

!30

3,0

6.0

3,0

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F2

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