Текст
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I-[pH pacqeTe TpexcdIOBHbIX YIdIaCTHH H o6oaoqeK c MadIOKeCTKHM 3alIOdIHHTedIeM H TOHKHMH BHeKIHHMH CJIO[MH HeOöXO)LHMO HMeTb B BH)Ly, qTO CH{aTbIe BHeLI/HHe CdIOH npH H3FHöe MOFyT OTpbIßaTbCfl OT 3aIIOJIH|I- TedDt H TepflTb yCTOIqHBOCTb H3OJIHpOBaHHO. 1.4. MATEPHA21bl, HPHMEHIEMblE J121! H3FOTOBEHH! 9EMEHTOB TPEXC21OflHblX KOHCTPYKllHfl COqeTaHH:I MaTepHadIOB HeCylKHX CdIOeB H 3alIOdIHHTedII MOFyT 6bITb fiMbIMH pa3HOOöpaHblMH. Bbi6op cOqeTaHHH oöyCdlOB/IHBaeTC HöHa- qeHHeM KOHCTpyKKHH, yCdlOBHIMH ee pa6OTbI H CrlOCOöaMld H3FOTOBdIeHHI. MaTepHaau HecyIX caoes  3anoaHHTeaa caeyeT no6paTb TaK, aTO6h X CSOfCTSa onoaHa pyr pyra. HaH6oaee UaCTO ScTpeaalo- IRHecI coqeTaHtlfl MaTepHaa'IOB, IIpHMeHfleMblX )a'II H3rOTOBa'IeHHfl Hecy ° umx caoeB n 3anoaHnTeae, npnBeeHI B Ta6a. 1.1. B MamIHOCTpOeHIH HaH6oaee pacnpocTpaHeHbt TpexcaOflHbte KO- CTpyKIJ, HH, HecylRtle CdIOH KOTOpbIX H3FOTOBa-leHbI H3 aa-IIOMHHHeBbIX Ha-IH THTHOBbIX ClTaBOB, Koppo3HOHHO-CTOIKHX Ha-IH zKaponpoqHblx cTaeI, a 3aI1OYIHHTea'Ib )LHCKpeTHbIf'I MeTaYlYIHqeCKHf'I. fHCKpeTHbIe 3aFIOYIHHTea'IH H3 MeTaYlYla IlpHMeH:IIOT B CHYIOBbIX KOHCTpyKIJ, HIX CaMOYleTOB H paKeT, TaK KaK TaKHe 3anoaHHTeIH npoqHb H o6aaalOT XOpOmHM COnpOTHBae- HHeM CZKaTHIO. HaHMeHbmyO MacCy tl BbCOKylO Koppo3HoHHyIO CTOf- KOCTb HMeIOT COTOBbIe 3aIOa'IHHTea'IH H3 aa-IIOMHHHeBO-MaFHHeBbIX CIa'IaBOB. TpexcaoHble KOHCTpyKtHH C TaKHM 3aIOa'IHHTea'I-eM HCIOa'Ib3yIOT Kopnyca CaMOYleTa, (ibIO3ea'l:Ia, neperopooK, CHaOBbX mnaHroyToß, 3aKpKOB, rpyoBbtX Bepef n T. n. TpexcaoHbte KOHCTpyKIHH C Me- 11 
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l.b. THHbl KOHCTPYKll[HI B COOTBeTCTBHH C O6IIHMH Tpe6OBaHHIMH, Ilpe%IBJIIeMbIMH K KOH- CTpyKIIH B eJIOM, TpexcOfiHbIe 9leMeHTbI )LOIHbI y)LOßleTBOpflTb ùCJleylOIHM TpeOBaHHflM: blTb IIpOqHbIMH, KeCTKHMH, TeXHOJIOFHq- HbIMH, HMeTb MHHHMaJIbHyIO M.aCCy H CTOHMOCTb, HMeTb MaKCHMdlbHO BO3MOHOe qHC3-10 yHHqbHILHpoßaHHbIX 9leMeHTOß H MHHHMaIbHOe qHC3-10 coe)LHHeHHfI, )oIIyCKaTb MexaHH3aKHIO TeXHO.rIoFHqeCKOFO npottecca, PHc. 1.9. CxeMbI CTbIKOBKH Kaeenix Tpexcaofinix aa- Helefl n3 HeMeTamlHqecKHx MaTepnaIoß Mem2y co6ofl H C a$IeMeHTMH KpKC oöaa)aTb CTaöHabHblMH IIoKa3aTeJItMH KaqeCTBa BO BpeMeHH npr 3a)aH- HbIX yCaOBHX KCnlyaTalml4. COTOBble naea MOmO coeJIHHtTb cSapKo ecylaX caoes (pHc. 1.8, t3) 14a14 c nOMOimo BKaabmefi pa3al4qbix KOHCTpyKICI: nyCTOTeabIX KOpOöqaTbIX (prlC. 1.8, 6, e); oöpa3oßaHHbIX naacTI4HaMI4 (prlc. 1.8, c) i4,rii4 ynaOTHeHHeM COTOBOrO 3anoaHi4Teat (pHc. 1.8, e), Z-oöpa3Hofi qbOpMbI (pHc. 1.8, ); laH JByTaBpOBO qbOpMbI (pHc. 1.8, a);. CnaOmHbIX (pHc. 1.8, e); cneuHaabHOfi qbOpMbI (pHc. 1.8, U). ]OaTOßOe coeIHeHHe npMeHmT npH HCnOab3OSaHHH eCTKHX c6OpHblX sKaab- me (pc. 1.8, u), cnoco6ux BOClIpHHHMaTb ycae CaTHfl. BO3MOKHO KOMöHHHpOBaHHOe coeee: K oofi nasea sKaa- biml4 npHBapßalOT, a C pyrofi coeHmOT C I1OMOIIbIO 6OaTOB. 3TI coee xopomo pa6OTalOT np CTaTIqeCKIX rI lKaecx a- rpy3ax. 7 | z 3- I-IocaOqHble MeCTa no KOHHqeCKHe BTyJIKH oöpaöaTbBa)T MeXaHHqe- CKH. THnOBbIe BKJIa}bItUH, npHMeHfleMbIe B KJIeeHbIX naHeax c HeCylIHMH CIOIMH H 3II]OJIHHT{JIeM H3FOTOBJIeHHbIMH H3 aJIIOMHHHeBbIX CHJIIBOB, noaaHSl Ha pHC. I.II. Ha6oaee TeXHOJIOrtlqHbI HJIHH2pHqeCKHe Id KOHrtqecKHe BY-dla)LbIII/H. Boabmoe 3HaqeHHe B o6lKefi CHJIOBOI cxeMe arperaTa HMeeT CTblK naneaefi, pa6oTamnx Ha pacTKeHe i OKaTHe. Ha pHc. 1.12 FIOKa3aHBI apHaHTB c6OpKH naHeae c IIOMOIbIO KaeeB H 6OJITOBBIX coe)HHeHHI, a CXeMt 3aJle.ffIKH TOpf[OB rlaHe3]e npHBe}eHbl Ha pHC. 1.13. 16 17 
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Ha pHc 1.14 H 1.1 tloKa3aHbi TttnbI coe)HHeHHH TpeXcaOHHb! naHeefI MeKy CO6Ofi I C pyrIMn 9aeaeHTaMl KOHCTpyKtH- PeKOMeH- )yeMble 3HaqCHfl npaMeTpoß, noKa3aHHblX Ha pHC. 1.14, npHBe)eHbI B Taöa. 1.5. b bz PHC. 1.14. BapHaHTbl COC/I, HtteHHI TpeXC,/IOf'lHbIX riaHe.lefl c MeTfl,/I,/IHqeCKIIMH HecyI.B, HMH C,JIOtMH H COTOBbIM , ,FIO,'rIHHTe'IeM Hcxo)mbIa napaMeTpoM a onpeedleHHH CTpyKTypb] I paaMepa b, coe)HHTeabHoro 3aeMeHTa BaeTC TOamlHa In, KOTOpyiO onpe)eamor Ha ycaoBHa 6eaonacito nepeal Harpy3oK epe3 9$1eMeHT coe}I4HeHHt- PeKOMeH)yeMble pa3MepbI  cTpyKTypa coe)HHHTeabHbX aeMeHTOB, H3FOTOBdICHHbIX H3 CTeK$IOIUI aCTHKa Ha OCHOBe CTeKdIOTKäHH ACTT (6)-O-O, a naoCKHX yaaOB npBeett B Ta6a. 1.6, a ' yraOBbX -- B Ta6a. 1.7. 9 21 
PACqET 3AIIO.rlH HTEJ] ! KOHCTPYKIH fl TPEXCdI01 HBIX 2.1. THIIbl 3AIIOJIHHTEJIEII B KaqecTBe 3anoaHtITelefi Tpexca0fiHblX KOHCTpyKKtIfi nptIMeHOq neaonaacTbI, oöaa;mOltm BblC0KHM ripe;eaoM np0qa0CTtI tI )KeCTK0CTbIO. OHtI npecTaßaoT co6ofi ßyxa3Hble CtICTeMbI, C0CTOIHe tI3 TBep0fi Hall ynpyrosaacTHyHOfi H ra3ooöpa3Hofi qba3m. FIenonaacTo- Bble 3anoaatiTeatI tlMelOT fIqetlCTylO CTpyKTypy. CB0ICTBa 3THX MaTepHaIOB 3aßtICT 0T CB0ICTB noatiMepoß, ti3 KOT0pblX OHtI tI3rOT0- BaeHbI. KpoMe neitonaacToß tlcn0ab3ylOT 3an0aHHTeaH, HpecTaßamolHe co6ofi npocTpatIcTBemtyto KOHCTpyKIUO H3 aeHT, noaoc, aHCTOB CHe- IHaIbnOfI ¢OpMm. TaKHe 3anoamTeaH npHcOeHHmOTC K HecyHM ca0M He no BCefl n0BepXH0CTH, a HcKpeTH0. KOHCTpyKIUH HcKpeTHblX H KOMöHHp0BaHHblX 3anOaHHTeaefI MOryT 6blTb CaMblMH pa3H006pa3HbLMH (pHC. 2.1). B aHTepaType npHBeeo Hx 6oaee TpeXC0T. HaH6oabnlee npHMeHeHHe B TeXHHKe n0ayYHaH C0TOBble 3anOaHH- TezaH H3 pa3aHyHblX MaTepHaaoß. B mecTHrpaHHblX c0TaX MaTepHaa pac- noaomeH laH6oaee SKOHOMHH0, TaK0f 3anoaHHTeab oöaaaeT 6oaee BblC0KHM npeeaoM npOqH0CTH, qeM 3anoaHTeZIH c )pyrofI tOpM0fI tqeeK. a yBeatieHH M0ya ynpyrOCTH cnaOnlHme 3an0aHHTeaH, Ha- npHMep H3 neHonaacTa, apMHpyOT (CM. pHC. 2.1, n). B eax nOßblnleHHS KayecTBa coeHHeH HcKpeTH0r0 3anoaHHTeza c IecyIHMH ca0mvm öaeMeHTbI 3aIIOaHHTeafl )eaaloT c 0T0pTOBKOft (pHC. 2.2, a) nah OöMa- TblBaIOT C'IKa0HHTbIO (9HC. 2.2, 6). as o6ecneeH Hy>KH0fi @0pMm KOHCTpyKaHH  HaCTOlee BpeM pa3pa6oTaHbI rH6He K0p06qaTble 3anoaHtlTeItI ti3 cTaatI, aaK)- HHHeblX cnaao ic apMHp0aHHblX MaTepHaaoß, np0nHTaHHmX CMOa:MH. a n0BblmeHH rIpoqH0CTH H >KeCTK0CTtI 3anoaHHTeefI B MecTaX npHaoeHH C0cpeROTOqeHH0I CHabI Reaecooöpa3Ho yBeaHqHTb Toa- IHuy ero aeHTm, Hall yMeHblLItlTb paaMep fIqeIKtI, tlati TO tI pyroe BpeMeHUO. MOmH0 TaK>Ke BBO;mTb ;onoaHTeabHme aeHTbl Ha (CM. pHC. 2.1, ), yCHaHBaTb aanoaHHTeab B onpe;eaeHHOM HanpaßaeHH coe;HueHHeM ByX COTOBmX CTpyKTyp n0 yra0M (pHc. 2.3). )KeCTKOCTb 3alaOaHHTedI, pa6oTaomero Ha C;AaTHe, yBedIHqHBaIOT layTeM lapHMeHe- IH ropHpoaIX aeT (pHc. 2.4). I-IecMoTp Ha TO, qTO neHo3anoamITeatI tlMelOT fIqeHCTylO CTpyKTypy, cqHT:IOT, qTO 3arioaHHTeab cnaomHofi H o;mopo;mifi. Ero xapaKTeptI- 3ytOT OöblqHblMtI a OHopOHblX MaTeptiaaoß napaMeTpaMH, KOTOpgle onpe;eamOT H3BeCTHblMH MeTOaMH. ,HCKpeTHble 3aII0aHHTedlH B TpeX" 22 
PI4C. 2.2. CIIOCOöbl IIOBblIIIeHHI{ KaqecTBa cOeAHHeHI4i{ /U4cKpeTHOrO 3aIIOIHHTedlfl C He- cym, HMn CaOflMH Pnc. 2.3. Ycnaene COToBoro mecnrpaH- HOFO 3a IIO/IHI4TeIIt PHC. 2.4. TpexcaofiHa KOHCTpyKH C 3a- HOaHHTeeM n3 ropHpOßaHHOfi o3Lrn CJIOBHbIX KOHCTpyKIHIX 06blqHO pacCMaTpHBaIOT KaK HeKOTOpble cnaom- Hble HnH OpTOTpOnHble, o6aamota14e npHBeAeHHbMH xapaKTepHcTH- K flMH. 2.2. I1EHO3AIIOIH HTElH B KaqecTBe neHo3afioaHHTeaef fipHMeHIOT pa3aHqHble fieHOMaTe- pHaabI, CnOCOöb noayqenH KOTOpIIX  HX xapaKTepHCTHKH npHBeAeHuI B pa6oTe [1 ]. HHme npHeenI Aannule [1 ] o aH6oaee pacnpocTpanen- nUlX nenoMaTepHaaax Tna nenonaacTMacc: [IXB-1, [IC-l, YIC-4, [IC-18, [ICB, , K-20, K-40, K-20A-20, [I¥-101, [I[I¥-3, K-40. Fleuon,aacmbt ua ocnoee no,aueunu,ax, aopuOa. 3aBI4CHMOCTH MeXaHH- qeCKHX xapaKTepHCTHK neHonaacTa FIXB-10T naOTHOCTt npH 20°C noKa3aHlol Ha pHc. 2.5. 24 OTHOCIITeJIbHbII -MOAyb CABHra fieHOI]aCTMaCCbl Trlfia YIXB-I MOmHO ofipeAeJIHTb C fiOMOIJ<bIO 9M[IHpHqeCKOfl qbopMybl  = 2800 (b)"s, (2. ) KOßdpHHenT FIyaccona 3xs [IXB-1 paen 0,4. [IpH oxaamenH14 AO TeMnepaTypbI --60 °C hKeCTKOCTb H npeea potIHOCTI eHoaacTa ,2 / ,2  /,2, / o too ma 3ca oao »«G,  foo oo 30o ¢oo ««e/ 1oo zoo JOB #ooff,«z/ Pl4c. .5. 3aBHfiHMOCTb MeXaHHqefiKHX xapaKTepncTK neHonaacTa HXB-I OT naOT- HOCTH HpH 20°C: I-IXB-I Bo3pacTaIOT Ha 20 .J30 oB, a np14arpeBe o TeMnepaTypbl +60 °C CH14IIaIOTCI IIp14MepHO B 2 pa3a no cpaße14m c xapaKTep14CTH- KaMH Hp14 20 M etonlacmbt ml2na ¢19¢19 u ¢19I. [IeHonaacTbl IIJIOTHOCTbIO 50 ... 450 Kr/M a (KayqyKa I0 ... 30 BeCOBblX qacTefl) 14 HJIOTHOCTbIO 450 KF/M s- (KayqyKa 40--50 BeCOBblX qacTef, I) noayqaloT 143 HOBO318qHOfl (lgeHO31bHO- %h0pMaabAel'HAHOfi CMOabl B coqeraH14H c 6yTaAHeH-aKpHaHHTpHabHblM KayqyKOM. Boaee 9JIaCTHqHIe neHonaacTbl coAep>KaT 6oaume KayqyKa. Ha6oaee TepMocToIK14M nS paCCMOTpeHHblX MaTepHaaoß ißaleTcl lleHOllaacT THna  (6e3 KayqyKa). OH Mo)KeT )d-I14TedIbHO pa6oTaTb np14 TeMnepaTypax AO 150 °C, a npH pa6oTe 6e3 KOHTaKTa C KHCJIOpOAOM BsIAepml4BaeT TeMnepaTypy 200 ... 250 °C. OAHaKO OTCyTCTBHe KayqyKa AeaeT fieHonaacT  oqeHb xpynKHM. YIpoqHOCTHble xapaKTepHcT14K14 neHonaacToß , K-20 npHBeAeHbl na pnc. 2.6--2.10. OTnOCHa'ebnbfi oayb caHra neno3anoanHTen THna ¢bK-20 B = 3835 (0) '. . (2.2) Upn oxaaAenH14 npeAea npoqHocTlt 14 MOAyab ynpyrocTH nenonaacTa I-40 nobmmOTCn, a yapnan BI3KOCTb I40THOCHTea-lbHOe nonn:aioTcfl. [IenonaacT K-40 Mono 14CnOabaOßaTb B KaqecTBe aMop- 25 
Trt3attHpoßaHnoro c0 B KOHCTpyKiHX, noßepramHXc sHaKonepe- MeHHblM arpy3KaM, TaK KaK npH [IOJIOAKI4TeJIbHblX TeMnepaTypax to 200 °C OH xopomo racnT Bu6paRum E. 1 / $0 70 0 y «e/ r t PHC. 2.8. 3aBHCHMOCTb Me- XaHHqeCKHX xapaKTepH- CTHK eHoacTa pK-20 OT HOTHOCTn HpH 20°C: a -- npeAe pOqHOCTH CaTHH H paCTeH;   oyb ypyroc o yo $o 70 gg gO y],xe/mr Pnc. 2.9. 3aBHCHMOCTb npeAea IIpoqHOCTI4 npH C}KaTI414 (I) n paCTII>KeHHH (2) neHo- n.acTa PK-20 OT TeMnepaTypb! (a) i naOTnOCTn (6) Jla pa60Tb npn n0BblmeHHblX TeMnepaTypax B KaqecTBe 3ano.rIHH- Te Tpexc3]OfHbX KOHCTpyKtHI zeaecooöpa3Ho npHMeH[Tb neH0: naacTbI K, coep>KanHe MeK0HcnepCHblfi aaZOMHHnfi. 26 3anoIu4TeJIb @K-20A-20 (P3 = I00 ... 500 KrlM ) npn pa6oTe B 3aMKHyTOM o6eMe 6e3 ocTyna KnC0p0)la Bbep>KnßaeT Harpeß o 200 °C ]IJIHTeJ'IbH0, a Harpeß 300 °C -- B TeqeHne HeCKOJIbKHX qaCOB. [IpH TeM- nepaTypax o 100 °C npeea IIp0qHOCTH o2g neHonaacTa ¢K-20A-20 MeIlbttle, qeM \ y neHonacTa @K-20 6e3 aJIIOMI4HI4I, g ). [Ipee npoqocT4 neHon acTa K-0A-0 npz4 pacTl:ä(eHI414 (npz4 paßHbIX I-IJIOTHO- g«2--- CT[X) 3HaqHTeJIbHO Bblme npeeaa npoq- H0CTH npn C>KaTtlI, a M0yab ynpyrocTn npH C>KaTtltI Hne M0ya npn paCTt- eHH. 1-Ip0qHOCTHbm xapaKTepncTnKn neHoaacTa K-20A-20 HpnBeeH Ha pC. 2.11, 2.12. DetonoAugpematbt. MexaHHqecKe xapaKTepncTnKn >KeCTKX neHonzacToß E¥- 101, HH¥-3 np HMepHo COOTBeTCTBymT xapaKTepncTnKaM neHon.acTa K-20. 1-IeH01UIaCTbI H¥-IO1A c 6oabmefi >KeCTK0CTblO, neM y neHonaacTOß YI¥-I01, M0HO mKCnayaTnp0BaT npH TeMnepaTypax o 170 °C. 1-Ipn 6oaee BC0KO TeMnepaType (o 200 °C) M0Ke pa6oTaT neHonaacT ,ù,;.ù 300 p.»«e/  200 JOO 4 .,re/t¢J  zoo ° log ZOO JO0, 9»re/s Ec ,Mfla 20 E, M fla Pike. 2.11. 3aBHCHMOCTb npeeaa poqHOCTH, npeea poopKHoHabHOCTH  MO- 
HY-101T. B ycaonx o,nocToponnero narpea nenonaacT H¥-I01T MOeT paTopeMenno (160 .., 200 c) pa6oTaT npn TeMnepaType ,0 450 ... 550 %. 3aBHCHMOCTH npeteHa HpOqHOCTH npH C)KaTIlH pa3aHqHblX TIIIIOB eCTKtlX I]eHOIlOtlypeTaHOß OT TeMnepaTypbl npBeeHbl Ha pc. 2.13. Fleuon.acmbt na octoee noucmupo.a. Mo)lyab CßHra rleHo3arIoJIHH- Tea THna HC-l MO}KHO paccqI4TaTb nO opMyle Be : 6600 (rS) ''5. (2.3) FIp pacT>KeH MOyab ynpyrOCTH neHonoacTpoaa npMepHO B 1,5 pa3a B,ime, qeM npd4 CI, KaTI414. / CaMue BblCOKHe IIpOqHOCTHbIe xapaKTepHCTHKH H3 BCeX nenonzacToß OHaaOBOfi nZOTnOCT MeeT nenonozcTpoz HC-18 (p = 300 Kr/Ma). HenonnacT HCB MomeT 6UT» nonyea c zm6ofi nnoTnocT»m OT 30 O 600 Kr/ML HeaonzacT HC-4 aMeer nnoTnocrb Ps = 400 ... 800 r/M% 3aBCaMOCT MexaaHecx xaparepcT nenonzaCTO ua ocnoe noncTpoza noKaaanI na pHc. 2.14, 2.15. Kpemnuüopeanuecue nenonacmbt OT31HqaIOTC BblCOKOI TepMO" CTflöHIbHOCTbK), HO M'IOI KoFe3HOHHOI IIpOqHOCTbIO, nOTOMy gX MexanneCKne xapaTepncTn n>Ke MexaHHnecnx xapaKTepncT opraHHnecKnx neHonzacToß (pc. 2.16). o TeMnepaTypbl 200 C Kpe- nfiopranqecKne nenonzacT ycTynmOT nO npoqOCTH opranqecK, OnHaKO upn TeMnepaTypax 200 ... 300 °C npn pa6oTe B yCZOBnaX O- cTyna KHcHOpOa nepBm MeT HeKOTOpm npenMymecTBa- 1-[poqHOCTHble xpKTepHCTHKH KpeMHHIOpFHHqeCKHX IIeHoIuIcTOB MO>KHO HeCKOZbO nOßbmHTb nyTeM BBeeHna B CoCTaB BCneHnBaeMX KOMrIO3HIHh aHIOMHHHeßOfi ny,pi  Bb!COKO.HcrIepcHorO acöecTa [ 1 ], qT O)HOBpeMelIHO nOBbHLIaeT X CTaötlbHOCTb HpH pa6oTe B yCOBHX BbICO- KIx TeMnepaTyp. KpeMilnoprailHqeCKIe neilonaacTi B KOHCTpyKItlH BClaeHeHbI 6blTb He MOFyT, HX BbllayCKaIOT B BHe HCTOB HH noa y?aöp HK flTOB. qbusutecnue ceoücmaa netonaacmo. Tei'IJIOCTOIKOCTb IIeHOrIJIaCTOB THrIa I-[XB Il l-IC CocTaBJIIeT 60 ... 70 °C, npHqeM OHa CHH::aeTcI C yBe- HqeHHeM Coep>KaHH KayqyKa. )KeCTKHe neHOnOHypeTaHbl HMeT TeIIJIOCTOIKOCTb 60 ... I00 °C, a TepMOCTOhKlh neHonolypeTaH yI¥-101T--o 200°C. Hail6oameh TeIIJIOCTOIKOCTbIO 010 250°C) oöJIaaIoT KpeMHHhopraHilqecKHe neHOnJIaCTbl. AJIIOMHHHeBble HafiO- HItTeJIH IlOßblIiIaIOT TeHJIOCTO'fKOCTb HeHOIIJIaCTOB.  / o zoo 2üO =oo .r, KE/  Pic. 2.15. 3aBHClIMOCTb MO)y-  ynpyrOCTH npH C)KaTHH IIe- HOHJIaCTOB Ha OCHOBe HeHOHO- JIHCTIlpoJIa OT I]JIOTHOCTH YIpH 20 °C PHC. 2.16. 3aBI4CHMOCTb IIpe- e3a HpOqHOCTH HpH C}KaTHH opFaHHqeCKHX H KpeMHH[Op- FaHHqeCKHX HeHoHaCTMaCC (p = 200 r/M ) ov TeMnepa- TypI: ! -- nc, nXB;  -- nY, 3 -- K-40 Tenoi3ittecKie xapaKTepHCTIKI neHOnlacTMaCc: TenlonpoBo- HOCTb , TeMlaepaTyporlpOßOl-IOCTb a, y)elbHa TenlOeMKOCTb C, KOgtl- qbilILHel-IT ZIIII-IeIHOFO pacmipeHil . I-[o TerIOilOZlflI2HOl-IHbIM CBOICTBaM rleHoiilaCTbI He ycTyHaIOT Zlyql±IIlM pblXIOBOIOKHtlCTblM H cIIeIHa$1bHblM CTpOHTeHb l-IblM MaTeptla$IaM. HpH yMeHbmeHHH IIJIOTHOCTH neHonJ]aCTOB TeMnepaTyponpoBOHOCTb IlX yBeHHqHBaeTCfl. TenJOI]pOBOHOCTb B OCHOBHOM onpeeHeTc rIJIOTHOCTbIO neHonJ1aCTOB; c yMeHbmeHHeM HIOTHOCTH oHa CHH?AaeTcfl. HailMemne aHaqeHHfl KO3(IxI)IIHeHTa TeII31OIIpOBOHOCTII IlMeIOT neHo- IIaCTbl Ha OCHOBe tIOaHBHHHaX31OpH/a, Hail6obmHe  neHonoail- CTäpO H MHnopa. l-[pIl oxa/eHHH TenonpoBo)IHOCTb yMeHbmaeTcfl, a npIl Harpeße BO3pacTaeT. BBe/eHHe aHOMHHIleBOrO HanoJ]HHTe peaKO yBeJIHqilBaeT TenIOHpOBO)HOCTb. I-[oce OXa)K)eHH B npolecce H3FOTOBdIeHHt BOMO)KHO OTCOeHHe aaoiiTe OT ecymx cHOeB BcIe)CTBHe TeXHOIOrHqeCKHX HecoBep- meHCTB, BbI3BHHblX p3HOCTbIO KO3ttHILHeHTOB IIlHeHoro pacmHpeHm OTejlbHblX CIOeB KOI-ICTpyKILtltI. TO HeoöXO)tlMO yqtlTblßaTb. Ha6oee BhlCoKI4 KO3¢ttlILtlel-IT ilefiIloro pacmHpeIl MeOT KpeMHfiopraIl- ece neonacTbi, aH6oee IlIl3Kfi --neIlonacTl Tna K  qb  FIXB. FIeHoHaaCTMaCCbI oöaaatoT CBOf'ICTBOM noraolaTb Baary npH norpy- meaää B mHnKOCTU. HaMenumIlM BOOnoraolaeaeM Il BICOKOfi nIa- ayqec,u o6aataT neHonaacTb c öaMKHyTOä necTofi c*pyKTypofi 29 
Tna 1-IC  [IXB. C yMenbmenneM HJIOTHOETH Boonoraoenne yBeqn- BaeTc. ]Ilfl yMenbmenn Boonoraomen teaecooöpa3no 3eae a neHon7acToß, conpHKacameeca c BOOfi, nOKpblßaTb n7eHKOfi H7 OKp amnßaTb. HeKoTOpble neHonacTbI BTC CTOIKHMH K tefiCTBnm TOnHB H Mace. 1-IeHOnaCTbI Tnna 1-IC npn HenocpeCTBeHHOM BO3efiCTBHH TOIIJIHB 14 MceJI IIOFJIOIIIOT HX. 1-IeHonacw THna HXB-1 oqeHb c7a6o nomotttaew 6eH3nH: macca nonaßKa H3 HXB-1 3a ro BItep>KKn B 6eH3nHe yBennnacb Ha 1,5 ... 2 %. HHme CWOfiKOCTb neHouacwoß wnna ¢K-20, H¥-101T, d PHC. 2.17. 3aBHCHMOCTb KogbbHIIJ4eHTa 3ByKO- IIOrJIOIH.eHHa IIeHOIIJIaCTOB OT qaCTOTbl 3ByKOBblX KoJleöaHHfi: 1 -- IqXB, c  2,3"10 - M, p  129 Kr/M; 2 FIC-I, c = l0 "I0- M, p 150 Kr/MS; 3- COC- Tbl na6op: npoöKa 2"10 -n M; O/In CO ATHMX 1,5-10 -s M; OytUnbdi npoMeKyOK I0 -s M; FIBXO 10-s . pn  200 Kr/M ", O/IY mnuii npoMeKyZOK 10 -s ra; sa con ATHMX 1,5 "10-s M H-I01: nx Macca yBeJIHqHBaeTCI Ha 1 ... 6 % npH BbepKe B Macae B TeqeHtle 100 ... 200 q. [leHonaacT B3aHM0IeficTByK)T C paCTBOpHTeJIIMH H XI4MHqeCKHMtl peareHTaM TaK I, Ke, KaK HCX02Hble MaTepHaJIbl. tHpbl, X0pp0BaHHbe H apOMaTHqecKHe yraeBOOpob aerKo pa3pymaoT neHonqaCTbl Ha 0CHOBe IIOJItl¢THp0310B. I-IeH0nJIaCTbl rly', (1)K, Il, B C0CTaB KOT0pbIX BX0]IT n0Mepl IIp0CTpaHCTBeHHorO CTpOeHHH, C 0praHHqeCKHMH paCTB0pHTe31fIMH IIpaK" THqeCKH He BaHMo]IeICTByIOT. CToeK K JIeICTBHIO opraHHqecKHx paCTB0" pHTeaefI neHonJ]acT THna HXB. Ha opraHqecKIx pacTBopiTelefl Ha iIeHorl.riacTbl rlpaKTHqeCKII He JIeCTByeT TO.qbKO crIHpT. ]_l]eIOqH H pa • (aB.qeHi-ible KHCJIOTbl rlpaKTHqecKH He BalIMOJIeCTByIOT C IIeHOII.qaCTaMVl, KpeMHH0praHHqeCKHe neHonaCTbl HaöyxaoT B aLeToHe H 6eH3HHe n pa3pymamTcs B TOJIOJIe 5en3one, eTpexxopncTOM yrJ]epoe. HeKoTOpble neHonnacTbL KOHTaKTHpy C MeTannaMH npH noBbImeH" Hx Baa>KHOCTn H TeMnepaType, ycKopImT KoppO3Hm. KaeeBoe coe" HeHHe neHonaCTOB c MeTaJ]aaMn HH npMoe BcneHnBaHHe B TpeXC0" HOI KOHCTpyKILHH rlpeIITCTByeT rIoHa]laHHIO BarH Ha nOBepXH0CT KOHTaKTa, H npH KaqeCTBeHHOM H3r0TOBqeHHH Tpexc.q0f:IH0 KOHCTpyK" IIHH K0pp0a IIpaKTHqeCKH He B03HHKaeT. aLIHTa OT K0ppoaHH np KOHTaKTe C 31106IM I-IeHOII31aCTOM oöecrleqHBaeTCfl aH0]IHpoBaHHeM 14 nJIaKHp0BaHHeM aJIIOMHHHeBblX ecymHx CJIOeB. l-IeH0t-IJIaCTbl I-IC-l, I-IC-2, H3-1, FW-IO1T npaKTHqeCKH He Bbl3blßaIOT Koppoa KaK qepHblX, TaK H IIBeTHbIX MeTaJIJIOß. l-IeHorIJIaCT I-[C-4 c flHOIHpOBflHHbIM H IIJIflKHp0BflHHbIM flJIIOMHHHeM H OKCH]IHp0BflHHbIM MflrHHeBbIMH CnlaßaM He pearHpyeT, no Bbl3blßfleT K0pp03O IIHHKa H ttHHKOBblX nOKpbITHü, l-IeHonlaCT HXB-I BbI3maeT K0ppo3HO, OC0" 6enno npd« |IHI,rlHq¢IH uarpeß_a Ao 60 °C. I]eH0rlJIaCT HY-101 He 3bIßaeT Kopp03Hr! aaOMHHeBblX ClIJIaBOB, oBHaKO BO BaaKHO aTMOCqbepe cnOCOöCTByeT Kopp03Htl OKCHHpOBaHHOrO MarHHeBOrO cfiJlaßa, l-lpH Hen0cpeAcTBeHHOM BcneIHBaHml neHonlacTa l-I-101 B KOHCTpyKILIH C HecyuLHMVl CI0IMH H3 MarHHeBblX c[Ilaß0B K0pp03ml He BO3HHKaeT. l-lpH neptlotlqecKoM Harpeße o TeMnepaTypbl 250 °C BO BJIa:hKHOI aTMOCqbepe KpeMHHfIopraHHqeCKHfl rIeHOtlJIaCT K-40 Bbl3bIßaeT caaöym K0pp03mo OKCH&Hp0BaHH0r0 aIOMHHHeB0r0 Cnlaßa H e3a- IlLeHHOI CTa31H. I-IeH011JIflCTbl 06lflflOT 3HflqHTeJIbHbIM BHyTpeHHHM TpeHHeM HOTOMy x0p0mo riorJioiALalOT 3ByK Ha qaCTOTaX I000 ['Il H 60ee (pHc. 2.17). Ha nnaKX qaCTOTaX K0tHIHeHT 3ByKOrI0rJIOLIeIIHH tleHO- HJIaCTMaCC HeßblCOK. Han6oee BbICOKHI K0tHIIHeHT 3ByK0rI0rJIOLle- Hrtt HMeeT $1acTHqHbII IleHOIUIaCT Ha OCHOBe IIOIHBHHHIXIOpH}Ia FIXBg, Hati6oaee HH3KHft --)KeCTKHI neHo[ioatlCTtlpoa (CM. pHc. 2.17). 2.3. 3AIIOJ1HHTEJ1H JIHCKPETHOB CTPYKTYPbl la  P acqeTa TpexcJI0IHOB KOHCTpyKIIHH C ]IHcKpeTHbIM an0aHHTeJIeM He06X0HM0 3HaTb caeyome HapaMeTpbl: M02yJlH c2ßHra Gxs, Ga, GI2  B IIJIOCKOCTHX xOz, JOz, xOJ C00TBeTCTBeHH0; M0]lyJIH ynpyrocTn Ela, E, Eaa B HarIpaBJIeHHH ocefl K00pHHaT X, ], Z; KO3(HIIHeHTbl l-lyaccoHa vx2, v2aa, la; npeeabl rIp0qH0CTH npH CßHre, CKflTHH H p flCTHKeHHH. K0»qbmHeHTbl l-Iyacc0Ha 3anoiHHTeJl{ 06pa3yIOT KOMneKCbl 1 --- 233322 • 123 - 133V323 . rl13 : A  r21' - A  raa = A ' rlg3 = A ' (2.4) ] --" V215125 lqp tonyenn 06 OTCyTCTBHH c6nKennn cOeB W 1 -----W 2 : W KOMIIJIeKCbl HpHHHMaIOT H3BeCTHbII BH]I rlta-- A ; r13- A ' vla . 1 A ' r223 A r333= 1, re A  I --v3v23. OcTa31bHble rii3 - O. 31 
l-IHre npHBeelbl 3aBHCI4MOCTH, cBflSblBat01ie npßeeIHble napa- MeTpbl HCKpeTHOFO 3aiioJiHI4TeJ]fi c FeoMeTpI4eI ftqeeK 3afiOJIHI4TeJDt H CBOfiCTBaMn MaTepnaIa aanoaHnrean (EM, GM,- t,;T, a, c). Comoa,tü uecmuepannbtü 3ano.anume.ab ua .ema..aa (pnc. 2.18). 1-IpnBeeHnIfi MOyab CtBnra aanoznrean B nzococr VOz (203)  = 1,,toT/( V). BqeT H3FH .31eMeHTOB COT B31H[eT H G288 He3HqHTe$1bHO. PHC. 2.18. CIICTeMa KOOphHHaT B COTOBOM 3aIIOJIHHTe$Ie Pnc. 2.19. CxeMa mecTvlrpaH- HOFO 3a rlOJIHIdTe* TM 32 re 2 B = E.¢kt**/(I -- M«.) (k = 2,3); B = 0,5 (B,,« Vg + o,ö«B,); Bu s = Bs  a VBI, +  4ac V +  
CTeHOK COT uanp:aeunfi x[3 n oäa, KOTOpble COOTBeTcTByK)T npeIeJIbttbIM 3naqennM npn CaO;aXHOM nanpxennoM COCTOnHm«. Comoebtü mecmuepamtbtü 3anomumeb u3 twmemaauuectux name- puaoe. [IpnBehennBfi MORyab chBnra 3anoan4Tea B nJOCKOCT4 yOz (203) [22] G,aa-= Gp,tccp(a fl-)" CpeRun TOanInIa CTeHOK COT 1 o,z o, o, 34 TaöaHIa 2.1 COTOIqJIaCT tx, MM fKJI, MM /npn' I-lerlpOIIHTaHHble COTbl Ha OCHOBe 6yMarH THrla A HJIH 6yMarH KpaqbT HenponHTanlable COTbl Hfl O¢HOBe Ka6e.n- HOff H,,rIH 6HTyMHHHHpOBflHHOII 6yMarn I-IpoHHTaHHble COTbl Ha OCHOBe 6yMarH TH- rla A HJIH 6yMarH KpaqbT [IpoIII'ITaHHble COTbl a OCHOBe Ka6eaHOfi H,H 6HTyMHHHHpOBaHHOB 6yMarH 0,08 0,1 0,08 O,1 0,05 0,I 0,2 0,05 0,I 0,2 0,1 -- 1,43 -- 1,62 -- 2,00 -- 1,73 -- 1,93 -- 2,31 0,05 2,82 O, 1 3,93 0,2 6,25 0,3 8,55 0,4 10,88 0,05 3,08 O,1 4,25 0,2 6,25 0,3 8,90 0,4 11,20 ynpyrocT OCHOßbl. YL"IOTttOCTb (od'beMtlat Macca) He[IpOIIHTaHHOrO COTOIIJIaCTa Da  4toc + t 2,59a PMa, tlpoIIHTaHHOFO CO- 4to+ ta + 6tp p,, TOn]acTa Pa = 2,59a re p, = Pne. 2.23. 3aBnCnMOeTu oqb. ka  6tnpn qbmmeTa k» OT paMepa 4toe + t tOT lfeaOpamubtü sanouumeb (prlc. 2.24). 1-IprIße)eHHbIfi Moyab CRBrlra anoannwean Gxs8 = G = GMte,r]a. oq0qbnttnenT 1-Iyaccona 6es necyIanX ezoeß 6an30K K emnntte. oyab nopMaabnofi ynpyrocwn B nanpaßaemm z (3) E8 = 4Este/a. 2* 35 
86 lqpHBe)eI-II-IbII MORyab ynpyrocTn B i-laripaßaei-Irlrl Z (3) 2btc -]- dtcs I-[prlße)ei-ii-iblfl MOyab ynpyrocTn B i-lanpaßlei-Irlrl x (I) Ea = b -J- d co$ t:Z A 1 Ae __ Bx q'- B a [c + (t + t)121 b A q- 2d A cos a c -- (t q- t)/2 ' A x ---- (B x q- B) a q- 2Ba Ic -k- (t + to.)/21 cos a ; 1 1 A = -- (B1 q-- B) a q-- -U B, Ic + (t + t)/21; Et _ (i : 3,4) -- ecrocrn creno 3 n 4. Pneennu oRyau ynpyrocTn  nanpaaennn y (2) B sin  «  + (B + B) ba/(d cos «) 
38 Prm. 2.29. CxeMa-ycnJIeHHoro ILHJHHJpH- qeCKOFO 3aFloa'IHHTea'II 
Pnc. 2.30. 3ano3nITe3b THna KOHHqeCKHX 7]. 1 o6ooqe #   v,' t/ 50 ZOO % 400 Oo 600 NOO 1500 zooozo o«o 50«o Ay3s CHFa 3aOHHT THHfl KOHHqeCX 06030eK OT OTHOmeHH payca 6oumero OCHOBaHH r2 K mary Mey 060OqKaMR  IC. 2.33. 3aBHCHMOCTb aqbqbeKTHBHOFO KOgbbHILHeHTa noroeHna ]» H TOrO KObdpH- KHeHT, OTHeCeHHOFO K MlCCe 1 M 2 IIIHeJIH mi, OT qICTOT.  KOJIeHHf BbIM 3arI0dIHHTedleM He 0631aaloT OIITHMaabIlbIMH 3ByKOH30aHpyloIRHMH CBOICTBaMH. OHaKO tl0 cpaBHeHHIO C Tpexc310flHblMH KOHCTpyKILHIMH TflK0I e H$10THOCTH C FIeH08flIIO$1HHTqeM H$1H C MeTaJ'I$1HqeCKHMH nO)KpenleHHlIMI 0H0CI0fiHbIMI nIaCTIHaMI 0HH HMeOT npeiMye- CTBa (pnc. 2.33). 5O IpnBaa I COOTBeTCTByeT TpexcOHO naHeH c COTOBbIM IJ/eCTHFpaHHbIM 3aIIOHH- TeeM H3 aMHHHeBO ObrH AIT. TOHHa 5aHOHHTe 10 , TOHHfl CTeHKH T 0,04 MM, CTOpOHa aqefiKH 3anOHHTeaa 5 MM. HyHe CaOH H3rOTOBeHbl IöAT TOHHa aecyHx caoeB l I  Il = 0,3 MM. Macca I M  naHeH 2,5 KpBa 2 COOTBeTByeT OHOCOfiHOfl noKpenaeofi naea xa aMHHHR MapKH löAT c TOHHO O6HBKH 1,5 MM. CTpHHrepbl Z-oöpaHofi opl  IöAT pa3MepOM 25X 18XI,5 MM. ar Memy CTpHHrepaM 250 MM. Macca l M i naHeH 4,8 Kr. pHBaa 3 COOTBfiTByeT TpexcoHO naHemi c COBbIM meCTHrpaHHbIM 3a- OtlHTeeM H3 aMHHHeBOfi bFH AIH. TOHHa 3anOHHTea 10 MM, TOHa CTeHKH COT 0,04 MM, cTOpOHa aqefiKH 3anoHHTe.a 5 MM. Hecye caon H3rOTOeHbl Ha CTeKeKCTOHTa KACT-B, TOHa HeCyHX cOeB 1 = t = 0,8 . CCa 1 2 aHeH 3,8 Pe3yabTaTbI öKCnepnMeHTaabHblX nccaeoßaHnfi HCKpeTHblX COTO- BSlX 3anoaTeaefi npßeesI aa pc. 2.34 ... 2.39. Baae MaCCbl gae a aOTOCT 3anoaTeas CKa3blBaeTC He3HaqHbHO (CM. 41 4O 
42 60 0 0 0- 0 20 -0 60 0 PHC. 2.36. 3aBHCHMOCTb HP OtIHOcTH COTOBOrO 3aHO..1HHTe,,qFI HpH HoHepeù- HOM c,aTHH OT HJIOTHOCTH 3aHOIHH- TeJIFI: I  xopomee coeAHHeHHe C HecyHMH C..JIOMH; 2 -- HMemTcH pacCOeHH 12L -- 8O 0 goa 08 tcm  PC. 2.38. 3aBHCHMOCTb HOTHO- CTH IIIeCTHrpaHHOrO COTOBOrO HOnHTen OT pa3Mepa cTopoHM meCTHrpaHHHKa H ToHU O H (obra AMrH, BK-32-200) 2.39. 3aBHCHMOCTb llpeAea HpoqHocTH llpl, l OTpuße mecTHrpaHHoro COTOBOrO paaMepa cTopoHu mecTrpaHHHKa (bora AMrH, 0,05 TeMnepaTypax: 1 -- 20°C; 2 -- 200°C pc. 2.38). C yMeHbmeHeM pa3MepOB flqefi- KI4 (mecTI4rpaHHOfi, KBa21paTHOfl Italt Kpyr- JIOI OpMbI) yBeJII4qI4BaeTCfl iIpe)eJI IIpoq- HOCTH Ha oTpbB HeCymJ4x cOeB OT 3anoJ- HHTeJI, IIpH :TOM iipe)eJI npoqliocTI4 pacTeT 3HaqHTeJIbHO 6bcTpee, qeM IIJIOTHOCTb 3a- IIOJIHI4TeJIfl. C yMeHb]/IeHI4eM, Hanp4Mep, pa3Mepa CTOpOttbI C 0,6 O 3,0 MM mecT4- rpaHHnKa COT Ha a311OMHHHeBOfi Obr c" UF, Mna 31 ° \ ,» ',,,, o o 3 6 g a. 10 M Ta6Ha 2.2 PaaMep CTOpOH IecTHrpaH" TOJIIKHHa TOHHa COTOBO- MM 0,3 !,6 Macca (Kr) 1 M = naHeII lapH 0,3 1,6 0,025 6,0 0,050 0,076 0,025 9,0 0,050 0,076 0,025 12,0 0,050 0,076 BHC-17 I6AT 12 2,75 10,07 25 3,13 10,44 50 3,89 11,22 12 3,13 10,60 25 3,90 11,22 50 5,40 12,73 12 3,50 10,83 25 4,64 11,97 50 6,90 14,24 12 2,62 9,95 25 2,88 10,20 50 3,38 10,70 12 2,88 10,20 25 3,38 10,70 50 4,38 11,76 12 3,13 9,90 25 3,94 11,24 50 5,50 12,83 12 2,56 9,88 25 2,75 10,08 50 3,13 10,45 12 2,74 10,08 25 3,13 10,45 50 3,88 Il,21 12 2,93 10,26 25 3,50 10,39 50 4,64 11,79 27,90 29,07 31,38 29,16 31,46 36,11 30,31 33,79 40,75 27,52 28,30 29,83 28,38 29,93 33,02 29,24 31,64 36,46 27,32 27,90 29,06 27,99 29,16 31,47 28,56 30,29 33,75 8,67 10,99 9,66 10,98 15,62 981 13,30 20,35 7,12 7,90 9,45 7,89 9,44 12,52 8,72 Il,IS 15,96 6,94 7,51 8,67 7,50 8,66 10,98 8,07 9,80 13,26 0,3 1,6 OT4- l 4,44 16,07 5,11 16,74 6,45 18,08 5,15 16,74 6,45 18,08 9,14 20,77 .5,78 17,41 7,80 19,43 ! 1,82 22,96 4,21 15,84 4,66 16,29 5,50 17,18 4,66 16,29 5,58 17,18 7,35 18,98 5,16 18,79 6,55 18,18 9,35 20,97 4,10 15,73 4,44 16,07 5,11 16,74 4,44 16,07 5,11 16,74 6,46 18,08 4,77 16,40 5,77 17,39 7,78 19,40 43 
44 x  Pnc. 3.1. l-IIaCTHHa narpyKena ycnIn- X mmu q, paßrloMeprlo pacnpeJ1ealenHblmi 9 nO npoJIeTy (a), no qaCTH npo.neTa (6), no nacTu npo3era, npumusaloel s onope () 
Hecyuero caos yao. KacaTeabHbIe ianps:emm B ce- qentI naaCTUHbl X : 0 2ql "r13" h--h 1 ' B ceqeHHH X : l 2qll l -- Ii T133-- h2-- hl 4. YLIaCTItHa, ItaFpy»KeHHafl CO- ,Xt Puc. 3.2. I-[IaCTHHa narpyKeHa B cene- nHH X = xl HarpyaKofi, HHTeHCHBHOCTb KOTOpOfi Ha eHuy IHpHHb] paßna Pz 
l l Pnc. 3.3. l-IaacTHna narpyKena pacnpelenennb MOMeHTOM / B ceqennn x : x 1 (a), B cenenna x = 0 (6) 5. YIJIaCTHHa, MOMeHTOM M (pHC. 3.3, a). Hpornöbl IIJ-IaCTHHbl IIpH 0  X  X I wl = -- 61B v (h -- ä) [3x (21 -- xl) -- 21  -- x], npn X 1  X <: I // (x -- xl) 311  31 BTp (h --- bi)  MaKCHMaJIbHble HOpMaJIbHbIe HanpaKeIa B BepXHeM HecyeM coe HflXOflTCfl B ceqeHHH X  (I12max  BTp (h -- h)  21 " HaupnKen B cpeRno IIOBepXHOCTI Bepxnero ecytaero caon B :gTOM ceqeHHH Olp : --Mx/ [It (h., -- hl) ]. KacaTeIbHble HflllpflKeHH B 3fll]OJIHHTeJle B ceqeHHH 0 < X < l rl = --M/Il (h. -- h) I. 6. [IJIaC.THa, narpyKenan pacpe)leaebM n cee x : 0 MOMeHTOM /d, npnJioKeoM na oope (pc 3.3, 6). Hpor5 IIJIaCTl4Hbl Mx w - ölBp (h -- h)  (l -- x) (21 -- x). HaSomfi npor6 HMeeT MeCTO I]pH X =- 0,422651 w : 0,06415 Bp(h -- h) " MaKCHMaJ-IbHbe HopMa3IbHbe HaIIpiKeHI4fl B BepxHeM HeEy[IeM cJIOe axonTCn  ceqennn x = 0: Harpy>KeHHaa pacnpeeeHH»iM B ceqeHI4H x = x t Hanpn>KeHne B cpeHHHOfi noBepXHOCT BepxHero Hecyero B »TOM ceenn eo.cp = M/[t (h -- h) ]. I CJIOfl IacaTeJlbHble HanpflKeHHfl B l]OJIHITeJIe B ceqeHIH 0 < x< l •  = MW1l (hù -- h:) 1. 7. [IaCTHHa, HarpyKeHHafl yCIJII4MH, pacpeeaebMn no 3aKoHy TpeyroJIbmta (pc. 3.4). Flporn6 nJ-I aCTI4Hbl z = «o« Pc. 3.4. Haacnna, nrpyenna ne- paßHOMepHo pacnpe,e,nennofi narpysKofi 49 
B ceqeHgflx x  0, l 2lf 5O rlpn I--2ll < x < I C3 =: C3 -- q 2Bzv (h--ht)  X [ cBp (l-- 2/1)  ] >( Gras 2 ' q l -- 21 C4  C4, -- Bp (h - h)  0 pzx t-- x [ k ( cBrl tx Wl  BTp (h-- bi)  l \---laa -[- 4 x  cB,p 4 )++ cB, p ] baKcuMabHbIe HopMaIbHbIe HanpfiKeHn B BepXHeM HecytReM caoe HaXOtTCfl B ceqeHHH X = Xm: PZ» [j __._)__Xl] / ' O-12max =  2Bp (h --ht) e ( kl 1 -- x B ceqeHHH x = 0 GI max  -- B CeqeHHH X  l Brl3 (be -- h) e 4 ' Pz l -- X 1 Bp(h_h,) " ( -- kl). B BepXHeM tecyeM c2Ioe l -- xt l 51 
52 NlaKCHMaJIbHble HopMaJIbHbIe Hal-lpflKeHgfl HaXOflTC B ceqeHIH V/ 2cBv [ 1 24/ X - 0,3l  + [ + 5 (l6 + 12cBV) B BepxIleM IlecylieM cioe 2 B.rp (___-- h,)./3 ; tB J 3.3. PACqET IIJIACTHH HECI4NIMETPl4qHOFO CTPOEHHfl, HEIOII[HX OH¥ 3AIII[EMJIEHHYlO H OBHY CBOBOJlH¥IO H H3rHBAEMblX IIO lll4JIl4HlPl4qECKOlI IIOBEPXHOCTH 1. l-IacTl4a, arpy>Keas paßrloMeptlo pacnpeeJIeHHbiMl4 aM (pc. 3.9, a}. Hpor6 l-lJIaCTl4ItbI qx { [ CBTp x (2l-- x) ] t_ lex  w ---- 2e, (h-- h,) (2/-- x) + . [ G 12 -- 12  MmcnMa,nbit,Ifi rlporn6 npi x =-l KPOblK¥ yCI4- C31Ofl Pac. 3.9. KocoHo 3apenaeHa nJiacTHHa HarpyKeHa yCH,nHMH q paßHoMepHo pacnpeeaeu no IoßepxHocTI4 (a), rlo tlaCTI4 rIoßepxHOCTI4 53 
Pnc. 3.10. Koneobno saKpenaennaa naacTHna narpyKeHa pacnpeeaeno B ceeu x=l narpyaKofipa Pc. 3.11. KOHCOIIrlO aaKpenaeHnas II$IafiTHHa HarpyKeHa MOMeHTOM pacnpe e,rleHHblM B ceqeHHH X  I 54 Z PHc. 3.12. IOHCOJ]bHO 3aKpenJ]eHHa lJIaCTIII-la HarpyKeHa pacnpeeIeHHofi Harpy3Kofi q = qx (a), q : qo (l -- x) (6) 55 
Pnc. 3.13, KoHcoauo 3aKpenaen- aa naacTna Harpyzxea napofi npoTnBOnOaOZXo anpaaenx ycnaHfi Px, npnaozxenHux B ce- qeHHH X=l 56 3.4. BPOFMBbl H HAIIPfl)KEHMfl IIPH [IOIIEPEqHOM 14 IIPOJ1OJIbHO-IIOIIEPEqHOMt H3FMBE IIJIACTMH C HEC¥111,HMM CJlOflblH H3 PA3JIHqHblX H3OTPOIIHblX MtATEPMAJIOB 57 
n = (1 + v0 aß (0h I -- Tp), 0 =(T--TO/c; Top =Th+Th» FlapaeTp le =  ßoc/ ( 4Gub). Ta6antta 3.1 XapaKTep CocpeoTOqeHHaI HarpyaKa PaBHOMepHo ]pacnpe]eeHHa onHpa (pHc. 3. I4, a) arpyaKa (pc. 3. I4, 6) Eczn onopbI IIJIaCTIIlbl HenORBn¢HbI, TO yCHJIHI C:KaTIfl p, Bbl3BaIIIlbIe arpeßOM, onpeReamoT 3 BblpaKeH Px = Bi. 3aqe KO:¢bHKHeHTOB m n H 1 n CJIeRyeT pa3ealTb a (1-  px/pxp), rae p,-- KpTecKa arpy3Ka, onpene3eMa c no- omuo Bupan¢e, npßee»x B n. 4.2. FIp pacT>Ke npooau- a»I caaM BO Bcex dpopMyaax nepe p 3naK ceRyeT 3MeTb Ha OöpaT»fi. KpOrKH map- npo onepTl 8 ( 12k\. ml= --- 1 --1- ----) , M= 1, m=2, M=8; b ma--l, Ms-- D ' Po:Pz ( 1 48k \. M= 1; m= 1; M----8; b ma 1; Ma   ; Po  qb KpOMKIa aueM - JIeHbI  (1 + 48  m = -- --] M=0; m=--l; M0; mz= 1; Mz=0; Po=Pz 1 48k  ; m, = - (1 + "----U-/ /klt = 0; m = ---g- ; M = 0; m= 1; Ms=0; Po=qb "I ]tttttttl t OopMyab (3.4) ... (3.6) cnpaße)laßui np ycoToß14 c/(t -t-" t) > 3 14 k < 1 npn onpe)leaemm npora6oß 14 k < 10 npa onpeteaerma rmrlp" l-Ip npoßoamo-norlepenHoM 3ri6e rlpoßoabnue ycan orlpeeao I43 yCJIOBH pa6oTb n3]aCTl14b B COCTaBe KOnCTpyKttII C yqeTOM rmrpena. 58 3.5. llPOßOJIbHO-IIOIIEPEqHblil H3FHB IIJIACTHH lqpor6 B uerlTpe rlSlaCmlbi (pIc. 3.15), MKC14Mamlble 14arlpmerm BO BltettIItI, IX CaOIX 14 KacaTeabltble anpe B 3anoJiitl, iTeJie onpe- eJIflIOT HO qbopMyaaM 5 qb    384 D 2 Y Pac. 3.15. FIpolOabHO-nonepeqHUfi e3rH6 II$1aCTHHbl npu JefICTBHH BCeCTOpOHHeff Ha- rpyaKH, pIOKeHHOfi B FI$1OCKOCTH cpeJIIiHHOf noBepXHOCT  panHoMepHo pacnpee- aeHHOfi onepeuHofi Harpya qbopMyab (3.7) cnpaße/taIBU np14 c/(t +' te) > 3 14 k < 1 npi onpe- aezenii 14arIpme14n 14 rlpa k < l0 rlpa orlpeteaerma npora6oß. Ylpn C:hKaTnn TOabKO 140 KOpOTKOI KpoMKe llJIaCTl, Iltbl (npn B  a, Po 0, p, = 0, a rlpa a  b p =/= 0, p = 0) npora6» r nanpmaerms °rlpeRe,nfllOT 14o ¢opMyaaM (3.7). 59 
Ta6aa 3.2 XapaKrep onnpann KoaKRnenT [ Pncyno KpOMKn mapnpo onepT m = c  kc; O, c, m, m, m, m 3.16, a me, m, ma, m 3.16, 6, e KpoMK 1, 2 mapnpno onep- TbI, a 3, 4 3aii,eMJieHbi npn k > 0,5 [ 3,16, c,, ca, mt = ca + kc B cayqae HefiCTBI4fl yCI4aHh pu aHaqenfi KO»I, IRI4eHTOB m, (i =  l-+-. 5) neoöxoArMO pa3AeaTb Ha (l --Pù/Pup), B c.nyqae yc:mfi Px 3Haqenrm KOgdi3di3Ht[HeHTOß m AeflT Ha (l  px/Px p). KpnTr- qecKIe ycnan Px,p  Py,w onpeReafiT na BbIpaeH4fi (4.8). 8.6. TPEXCJIOi;IHAfl IIJIACTHHA CHMMETPHqHOFO CTPOEHHfl, HAFP¥)KEHHAfl COCPEOTOqEHHblM MOMEHTOM, [IpHJIO)KEHHblM K OHOM¥ H3 HEC¥1RHX CJIOEB Flpor6 Harpy:aeoro Hecytttero cao (pc. 3.17) w  a -- (bt herl x -1- !, heil x) cos O, npta k <: 0,5 I 3.16, e m re x---r (k/D,,)°.; r  0- noap»e KOOpAHttaTbI (pnc. 3.17); n p  M e q a ù ù «. 3ùaqeùù ma, onpeea«Moy no pc. 3.16, e, npùnùcnamv her1 x, hei x -- yK KeabBa nepBoro nopKa (eca anax uyc, pacTrHBaHe, TO heb a, hei a -- CyKan Kezna neporo nopuKa nms,ms,«t,«z mz,mù B qKe X = a); b : heq a hei[ a -- her{ X '  I [Ne« / I °,Zl / --hefia)+(hei, aahei[a) +a- her[ X r=a =  COS U, rAe t : l,z -- no-  gg  a)g# ga b/a 0 g4 ga. l,Z l,ö z,o b/a abM .... "- $ Haùpueu CaTU B 3anoaTeae ,   M b o a - Pc. 3.17. Tpexcaoaa naa-  t z31r=a =   o . CTHHa, arpyeaa cpeo-  : HanpeHH  ùecyeM oe ,, qeHHb, M MOMeHTOM B ' (r,)-. : ( (bi her[ a + bu her «)cosO, (o,)-ù = v, (Or,)r=a. ms 03HauaT OAHoKpaTHOe  AByKpaTHOe AùepeHapoßaHne no x. g Cz 8.7. HAHPflEHHO-EOPHPOBAHHOE TOflHHE ACTHH  HTPOHHblMH HECYHMH COflMH H 3AHOHHTEEM B  mz fiPH COHblX CXEMAX HAFPYEHHfl  64 60 $g ,» z,o »/e a g4 a t,z .a e,o »/a PacqeT HanpeHHo-AeopMpoßaHHoro COCTOHH TpexcaofiHbX O z) naHeefi up caoH»x cxeMax HarpyeH (pc. 3.18) npeAcTaßeT Pc. 3.]6. 3aßCHMOCTb KO$HHeHTOß I-'" a, Cl H C20T yeu HacTHHbl 8HaqHTbHble TpyHOfiTH H MOeT 6bITb BbIHHeH TObKO C OMOb napaMeTpa  np nonepenHOM 
t52 ¢ Pnc. 3.18. CxeMbz narpy:eiJn n 3aKpen3eiJn KpoMo nJ]aCTniJ 63 
DBM. a peLueuH 14CI1OJIb3ytOT CI4CTeMy ueaaefiuu Apeaab- bx ypaßaeafi, KOTOpbe pemeab MeToAOM nocaeAoßaTeabx np6a- e. Pemean npecTaßaeab B BHe cTeneabx pAoB eoToporo Maaoro napaMeTpa. B pe3yaTaTe pemen noayqeb rpa (pc. 3.19 ... 3.34) aaBcMOCT 6e3pa3MepHbX napaMeTpoß nporu6a o u Hanpeufi . u u OT 6e3paaMepuoro napaMeTpa arpy3nu Hpu ucnoab3oaHuu sro MeToa onpeeanmT eKOTOpblfi napaMeTp q 0o = 2 ( + T  + Y) ' +0,28 (--+ ' ] k  c/b, X  a/b. Ho napaMpy 0o no rpana onpeReanmT 6epa3epH»In nporn6  eH- Tpe CTHHbI o, 3Hfl KOTOpbI MOmHO HTH MKfiHMbHbI HpoFH np SHHO cxeMe HarpymeHnfl: -- -- (3.8) w.. = woc [ l +  + 2 ). an onpeeaennn acnMaanIX nanpnmennn  necymnx caox cnMeTpnqnon naacTnnx ns rpano (pnc. 3.35 ... 3.50) naxonT no napaMeTpy 00 6eßpaßepHIe napaMeTpI Hanpnmeunn 6x n 6 v, c no- om KOTOp»IX paccqnTbmamT nanpnmennn  uecynx caonx: etc =  0,56«E k2 (1 +  + , ), ev « =  0,50rEck 2 ( l +  + )" afl Hecyero caofl i  1 6epyT 3HK nHyC, afl Hecyero co i = 2  3Ha namc. HHRecI Xo n Yo npn 6epaMepHbiX napaMeTpax HSHpflmeHH 03HqäT, qTO MäKCHMSbHble HSHpflmeHHfl BO3HHKT B ReHTpe HCTHHbI, HHeKfibI XA, B  MKfiHMbHble BO3HnKamT nocepenHe popo naaCTnHbI. Ecan naaCTHa nMeeT HeCnMMeTpnqHym CTpyTypy, TO HeoöxoRno HafiTn paccTofiHne OT HefiTpaabHOñ nOßepXHOCTn npn n3rnöe Ro cpenH" HOff noepxHocTn Hecyero cao 1:zx/2  c/2 ho n uenTpaaHO noepxnocTn necyero caon 2:z/2  c/2 ho, re ho = Bx B-c  x (1 + /2) --BB -xc (1 + /2); B = BI + B + B. oce 3TOFO onpeeaflmT npoFH6bI H Hanpflmemifl B HecyHx cofiX ByX CHMMeTpHqHblX TpeXCOfiHblX HäCTtlH, HMeHX TOT e pa3Mep a b. TOHH8 38HOHHTefl HSCTHHbI I OO3HSqeH8 Z1, HecyHe c0 HMeT napaMeTpbI ll, El, vl. TOHH 3äHOHHTefl BTOpO HCTHHbI, O603HqeHHOñ II, pBH Z, napaMeTpI HecyHX cOeB tu, Eu, v..fi onpeeaeunn nanpnmennfi iqncanmT napaMeTpI 0oi, 0Oli n no rpa" Ka HaxofiT 3pa3MepHbe napaMeTpbI äx i, ii, äv [, ii. afl onpeen 64 / / / i / / II // I//'/  lW// // It'/'/ Ik';, ù II/I I // / 7 •  5t7 1oo tso Pne. 3.19. 3anemoemn 6espasepnoro nportiöa to o, napaerpa qo rpymennn n laKpen.rletittt KpoMoK, IOKaatiHOi tia ptt«. 3.18, a: I --, I; 2 ,= 1,25; ,3--, 1,5; 4  1(o6o:loll I II.  /IP. 65 
/ / ! / PHC. 3.20.3aBHCHMOCTH 6e3pa3MepHoro nporHöa 00T napaMeTpa q0AH cxeM rpyKeHHH H 3aKpeneHHH KpOMOK, nOKa3aHHO Ha pHC. 3.18, 6; OO3HaqeHH Kp HBx CM. Ha pHC. 3.19 5 / '4 ùT l-lpoAoenHe pHC. 3.20 Z 3* 67 
-I II / I I/ I/ t i I/ I, / // I/  A/, / / / ,/ 2 I 0 II, III Ii J 71/ L/I / ///,/ , - 7i'/ ,/ '//I/ / I / / / / I / / / / I / , / / / / / / / g d'O I00 Pnc. 3.21. 3aancnMocTn 6eapasueporo npornöa @00T napaueTpa q0  cxeuu narpy- aenna n 3aKpenJ]elJn Kpouo, noaaalJiJoi na pnc. 3.18, «; o6osnaqelm pna»ix CM. a pnc. 3.19 69 
0 200 00 6o0  PC. 3.99. 3aBCHMOCTH 6e3pa3MepHoro nporHöa @o o napaMeTpa qo ßn cxeMbl Ha rpyKeHH H 3aKpenJ]eHH KpOMOK, riOKa$aHHOI Ha pHc. 3.18, e; OO3HaqeHHl KpHBbl] CM. Ha pHC. 3.19 HpotoaenHe pc. 3.22 
#I II, I/. Iß" I1,'// lllt ' / / I /i/ic /i Ii  / " i/1"./" /I/ l ill " il" 200 00 FIpooa]xemte pHc. 3.24 3 i 600 75 
76 / ! i//. h// / ,/ / / / / / / al =g,6« FlpoAoerme pric. 3.24. ; bt=O,,6b HHff H 3aKpeneHH KpOMOK, nOKa3aHHO Ha pHC. 3.18, c; O)O3HaqeHH KpHBX CM. Ha pHC. 3.19 
78 / I / IL ! / Il/' I///  / // '11/ / ¢1 / /// / 0 / FIpoRozKeHHe pnC. 3.26 ; bt=gg'b ooo -- qo 
_/ i II i/ III, '1// 5- // I// / / / / Hpo;omelne pnc. 3.26 ,,51 /. ,//,, /, / / / 5 Pc. 3.27 3aBrICHMOCTH 6e3pa3Mepuoro nporHöa o OT napaMeTpa q0 a cxeMm uarpy- ea  3aKpeneuH KpouoK, noa3auuo aa pHc. 3.18, u; o6o3uaqeuH KpHBX Ct. na pHC. 3.19 
PHc. 3.28. 3aBHCBMOCTI[ 6e3pa3MepHoro nporH6a rpyKeHH H CM. Ha pHc. 3.19 0,5 I,U/" i /i'/ .  Il, I/l" UpoozeHne pHC. 3.28 fa'- 82 
B4 • Pc. 8.29. 3acO¢T 6epaeporo npor6a 00T napaeTpa q0  cxe arpy- ea  apeaes poo, oaao a p¢. 3.18, ; o6oaes c. na pc. 3.19 85 
1,8 O,J / ,/,/!i i /,i/" I li l'/" i /,ll'l i Ißi/ / li il I a,= tT,4a ; bt=tT,4b 280 400 Flpooz)KenHe pnc. 3.30 600 87 
FlpoozeHre prc. 3.30 200 'Ii7I ,/ 50 too t5o o" Pac. 3.31. 3aBIICIIMOCTII 6e3paMepHoro nporn6a $o OT napaMeTpa qo z cxeMb! Harpy- ean  3aKpeHenii KpOMOK, HOKa3aIOä Iia pHC. 3.18, H; O603HaqeHHl KpIIBblX cr. na pnc. 3.19 89 
100 1.,"0 FIpoo3meHHe p)Ic. 3.32 91 
zoo Pc. 3.33. 3aBCMOCTI4 6epa3MepHoro npor6a o OT napaMeTpa qo I CXeMI Harpy- • eHn H 3aKpeneHi[ KpOMOK, IIOKaßaHHOI Ha pHC. 3.18, n; O{O3HaqeHI4$1 KpHBblX CM. Ha pnC. 3.19 O3 
2,O ! // ff 1/ I1,'/ III 71 / // ! /i ,/ / // / / // A' 7/ i i I I / I / /// / ,I / / /" / 200 400 FIpo/loaeHe pHc. 3.34 95 
I I I I I I I I I 'i I I I I / ! /, /;/. /// 7// '7 ,/,/ "/i,  I/  3 17 P l, 6 -- ,= 1; 2, 7 -- , = 1,25; 3, 8 -- , = 1,5; 4, 9 -- ,= 2; 5, 10 -- , = 3 4 loßeaen B. H.  ,AP. 97 
98 00 200 FIpoenne pnc. 3.36 
I I I I I I FIpo/lo>eùne pnc. 3.36 100 1ol 
2O (0 7 6 ii / I 5 1 4, ii . i /!J 'i//ii  7 8 I ! 7 103 
I 7 ( I. i I I l-lpojlo)zelllle pc. 3.38 &O 2 i I I /// i •  I  !!',1 # i !! # f 'il # '/ ,i ii, Il,' 'ii/ Ii' Iß' i I I I I I I / / I i / / I i / / HpooKee pc. 3.38 104 105 
5 I I I I I f I i I I / / / I / / I / / / ! .[ / / / / / / ii / i ./ /II  ,I /  // ///. // / ., / / / / / ., / /" / / / 3.39. PYe  saKpen,aex KpOMOK, noKasao a pc. 3.18, 0; oßoaaqe KpBX CM. a pc. 3.35 107 
g I I i I I/ " s /i/ll ' i /' / .,,i i' ?'1  !,,' " "1"1", 4 I / I l i /,, '," , l l ", i I!: , 17,,'//," 200 I-Ipo2toJImen«e p«c. 3.40 108 109 
II0 XO / I / I I I I s/ / / / / / " / / / ,I 8 KpuS»te l- S eoomemcmg/am xpuOue 6-/0 Pc. 3.41. 3aßI4CI41lOCTI 6e3pa3gepHoro rpyeaHa n 3aKpen3enH KpoMo, noa3aHHofi napc. 3.18, c; o6o3naqens pßbx ct. na pc. 3.35 111 
Puc. 3.42. aäpenaeu s KpoMoK, noRaaauofi ua pc. rpya¢euu CM. ua puc. 3.35 1 !ih / / / I I i / / / / / / / / «80 680 l-Ipo/loJKeuue puc. 3.42 113 112 
114 Hpo/oJmenHe pHc. 3.42 5 0 SO 100 150 o Pac. 3.43. 3aBHCHMOCTH 6e3pa3MepHoro-HanpsiKeHHs OT napaMeTpa q«  CXeM Ha- rpyeHH H 3aKpeaeHH KpOMOK, OKa3aHHo Ha pHc. 3.18, u; O603HaqeHHS KpHBMX CM. Ha pHc. 3.35 115 
ZO / / / / X' il/I II I I-IpoomenHe pnc. 3.43 ! //I: LL,ill/ / I / I I / I / / i//i I I / // ! , . // I I I I i I #' ,;'i// i / I I I / I / # i , / / / I i i I /i / I ù/Bi/'// /// # ù, / Pac. 3.44. 3aBI4CI4MOCTI4 6e3pa3Mepnoro"nanpflKenfl OT napaMeTpa q0 Jafl CXeMbI na- rpyKenn n aaKpenaen« KpOMOK, noKa3annofi na p«c. 3.18, r; o6o3naqemifl KpnBX CM. na puc. 3.35 117 
t I / i t iIi  ù/ 158 1,6 119 
I I I I / I i I i II I / I I / i / / / I I I i I ! I I , I I I  I I « I I ,i I I /,,',1 ..1 / , ù .. ,,.',-fl.  i I ,I..li.ßl I i I I I I I Bi I 7 FIpo)o)KenHe pHc. 3.44 ùIl ii.i/ii i 1  ,;',,','i i i 100 150 o Pnc. 3.45. 3aBHCMOCTH 6e3pa3MepHoro HanpmKeHH OT napaeTpa qo a cxeMb! Ha- rpYenH  3aKpeneH gpOMOg, noKa3aHHo Ha pIc. 3.18, a; o6o3Hauemiff KplBX CM. Ha pHc. 3.35 121 
l-Ipoo3en«e p«c. 3.45 122 12,3 
124 5OO l-Ipo,aoz:aeme pnc._3.46 12,5 
126 o 2 i o 0 oo 0»o  Pc. 3.47. 3aBHCnMOCTn 6e3paaMepHoro cM. Ha pnc. 3.35 127 
0 00 I000 1500 2000 a=O,,a ; b=O,,b 0 200 «00 l-[poAoeue pnc. 3.48 128 5 KoöeJe B. H. a /IP- 19-9 
# fll / // I1 // / // dl !1 ù/:71 '///i ICpu»te l-Scoorn«erncrnS.qorn tpt  3 PHc. 3.49. 3aBHCHMOCTH 6e3pa3MepHoro anp¢eH OT napaMeTpa q0  cxeM»i a- rpyKeH H aapene KpOMOK, IIOKa3aHHOI Ha pHC. 3.18 n; oo3HlqeHHI KpHBBIX CM. Ha pc. 3.35 181 
200 « ooo o HpooKeHne pnc. 3.50 133 
HCIHHHblX HIIIpHeHHH B HecyhtiX CJOX TpexcJIOIHOfi IJJIaCTHHbl, HeOöXOHMO nO aKTHqecKoMy npornöy HCTHHbI, HaeHHOMy HO B- pameHn (3.8), BhIqHCaHTb nonpaßoqHhle KOHKHeHTbI PI = 0/0I H PlI  o/II • 3aTeM HaHpeHH B HecyHX COX OHOHHTbHX H8CTHH I H II caeyeT yMHOHTb Ha PI H PlI- HoayqeHHue HaHpsmeHS n necynx osx nepofi naaCTnHbI 6yyT paßHbI HapmeHM B Hecy- eM caoe 1, .a Hanpmenn B HeCyIX gCaOX BTOpOfi] naaCTnHU- HapsmeHSM n HecyeM caoe 2. HaacTnHa, y OTOpOfi X = 3, eopMnpyeTcs np eficTnn Harpy3R nO KnaHpqecKofi nonepxHocTn n MOmeT 6b paccqTaHa no MeTO- Ke, 3OmeHHOfi n pa6oTe [3]. HaHpmeHHfl B 3aHOHHTee TXa a  T2a a  Ta MOHO oHpenTb no BupameHnm (3.7), a »TOrO neoöxonMO paccqnTaTb, KaKOfi paBHO- MepHo pacnpe2eHHofi Harpy3Ke q 6y2eT COOTBeTCTBOBaTb npor6 naa- CTnHU, uarpymennofi fi an nnofi narpy3ofi, OTaquofi OT panHO- MepHo pacHpeeHHOfi HO BCefi oBepXHOCTH. 3aTeM BqHCHT HaHpfl- xeue n 3aonnTeze no ¢OpMyaM (3.7), nOCTanafls n KaqecTne Ha- rpy3Kn 3naqeHne qp. Pe3yabTaTbI pacqeTa aa czyqas HarpymeHnfl TpexcofiHOfi naa- CTHU, 3aeMaenHblfi no KOHTypy, cpanHnaan c napaMeTpaM eop- MtlpOBaHHOFO COCTOHH, oHpeeaeHHUMn no MeTOnKe pacqeTa 6OabmnX nporn6oß npMoyroabHUX TpexcaofiHhlX HaCTHH. Hapnep, aza paofi nzacrn» X = 1 6e3paaep8aa narpyaKa • o = 11,407 (o/c) + 5,2596 (oM  Bespa3epHomy nporn6y o/c = 1,0 COOTeTCTyeT nCTn88a 8arpysxa q = 6,8 MHa. Ho rpasxy (CM. pnC. 3.19, ) npn 6pasepsofi 8arpyse 0 = 60,5 npor6 wo/c 0,72, . e. omn6Ra e npe»maeT 28 %. a naacTH, narpymennblX panoMepno pacnpeeeHHOfi arpy3- ofi no cefi noepxHOCTn, 3nagen npor6o  nanpmefi, gc- enHhe no np6nmennofi MeTOe, nnme 6oaee TOHX 3nae na 15 ... 20 %. 9TO nOTepaeTc scnepMenTaabHO. Om6xa omeT 6bITb oMnencnpoana ynenneM XOSeHTO 3a- naca. 8.8. IIPHBJIH)KEHHOE OflPEF_EHHE flPOFHBOB I HAflPI)KEHHI flOKPEfIIEHHblX fIIACTHH [121 B cnyqae, ec.m TpeXC:IOfiHa IaCTHa C LUapHpo 8aKpenneH- lthIMtl KpOMKaMI4 noKpenena B,ROb ocu x 6aKOft, paclJOOeHHOft a cepetHe nahebei (ptc. 3.51), lt AByMS 5aKaMrI, pacnoO>KeHHUMt Cl4rdMeTpiqHO OTHOCHTeJIbHO OCH (pHc. 3.52), MO)KHO rlpI6aI)KeHHO OpeAedlI4Tb HaI]p)KeHHO-)IeqbopMI4pOßaHHOe COCTOHlte I]J-IaCTHHhI H 135 
[IporH6 nJ]aCTI4HbI O mO6Ofi U3 aUnUfi y = r/2 1.3.5  X        eCTKOCTb np 3r6e TpexcofiHoro naKeTa B KeOM D 12( 1  ++ • (3.14) 136 HapaMeTpbl Tpexcofinofi nJaCTnHKI, noAKpenJeHHofi 6aJKaMn, onpeeJioTc Bbpax4eHMH 1 -L [1 + t2 G3g " Pm -- l -]- 2 DzmZZ " (lm  a] P,n ] 2 . B= 1_ 2c / 2 ' " ' czm : 0,Smb]a; am a = 0,5mb]a,; B, = 0,Smnr/a; ,a = 0,Smnr/a,. HOCTOSHHbXe KO@dpnneHT n nbIpameHHSX (3.9)... (3.12) nMeOT nmI 2 am 1 a 2 I Am = a2 2 eh ami ' Bm = 2 2 eh am ' -- a m O, -- 12 m Cm atham--amtharm . Ere= 1 ' CmlöE6m a2   I  2DPm 
HOBKH 6aio paßHbt HyO H ndlaCTHHa pa36ißaeTcn Ha 2--30Tle3/bHblX  naaCTHbI, nopenaenno onofi 6aaKofi, HanpeHe B Hecy- HX CaORX BO BceX ceqeHX, KpoMe HanpmeHfi no oc x, ceymee: -- =+ 1+ 1 ,  a  a m 1.3,5 1,3,5 i  1,2,   1 cooecye necyey co I,   2  ecymey , cao 2, re L  a 3Fa MoMeHT B ceeH  F m    aKi, nopMabOM ee poobno oC. 1,3,5 Y nacn»i, noßpeenno Yn aa, nanpnen  necy- x cox B ceenx Mey aKaM ceye: 1,3,5 mx si HapseHs B Hecyx COSX 6aKaM  KpoMKaMH HaCTHbI, 1,3,5 L mrty ( Nm9 eh rny "-- F,nGm sh ---m ) -- (I - v) a vi L,,,2 ch o---- -- FùnH m sh sin ' re Lm2    FG;   B  F. 3r6ae MOMeHT B CeqeHHX 6aoK, HOpMabHX K HpoAob- HO OCH, M 4qoa2Efilfi  Em 1,3,5 PaCqeTbI CBHeTebCTByT, qTO HpHBeeHHble pbI CXOTC OCTa- TOqnO 6ZrCTpO. U nnmenepnx pacqeTon OCTaTOqnO n3T» 23 qeHa pua. poFHöbl, onpeeHHbie no pnBeAeHHM BbpaeHnM, OTHqaTC OT 9KcHepHMeHTabHbIX 3naqennfi ne 6oee qeM na 15 %, nanpumennu   na 20 ... 30 %, %  na 50 % n 6oee. F.aaea 4 YCTOlYlq HBOCTb CTEP)KH ElYl 4.1. 5zCTOllqMBOCTb CTEP)KHEII H I-I$IACTH H 138 139 
COOTBeTCTByOIRee eMy xapaKTepHcTHqecKoe ypaßHeltHe MO)KHO CBeCTH K KBaApaTHOMy k×- I z + --T6-- z -- ö- - 0 C eCTBHTebHblMH pa3HblMH KOpHHMH. OOHM KOpHH 2 t  , Z  g. a eope Bea ceye  ' 9 0 +' e X-x KO3HHeHT pHeeHn aHHI. O60Ha lo  lX-, aXOA KpnTnecKy Cnay w  + n/(ö) - ö t + n/(ö)-' EHb 0  meCTKOCTb CTepH pH H3FHöe OTHOCHTeabHO , Fe D  ocn ceneHn; ocpeHenHuI Moya» ynpyrOCTH E onpene H (6.5); 1 b mHPHna CTepH; 0   {C 2 (3 2T8) + 6C (Txtx  T2f2) + + 4(TI @ T2)   [Tl (1 + C)  T2 (2 + C)] 2}  HapaMeTp H3FHHO eCTKOCTH ceqeHHH, 1  0  , OH HMeeT HaHObee 3HaqeHHe HpH cTù o m CTX;     0H  12T1T + T3 (4  3T3) apaMeTp CoöCTBeHHO ]ir6HO meCTKOCTH oeß, 0    0,25, a cTepmHe c aeFKHM anoaHHTeeM T3  0 H   Et+ E2t 12cGa (1 --) 12D b; d  napaMe*p anra,  = _ + 3aC [1/1 @ t +0H 2c (1 + 2)] + 61 2c (H @ C  OTHOmeHHe noepeqHofi CHabI, BOCHpHHHMaeMOfi 3anOaHHTeeM, K HOff oepeqHo cHae, efiCTByDefi B ceqeHHH; N  HOpMaAbHOe yCH" ae B oepeqHblX ceqeHHfiX CTepxHfi npH oceBoM CmaTHH Harpy3KO P' npaomeHHOfi B KOHeBOM ceqeHHH. pH BblqHeHHH KpHTHqeCKOFO yCHaH pp B pa3aHqHblX CyqaX OHpaHH AO3mHO 6blTb H3BeCTHO MHHHMbHOe 3HaqeHHe X. a aHH HC. 4.1) no3yqeHbI c3eyHe 3HaqeHH KOTOpblX cayqae np (P 1 43 (1  0,1k); O  1 + 0,64k  140 pHc. 4.1. Paa3mmble cnocoöbI aaKpen3eHn KOnUOB TpexcJIoIblX cTep)gHefi HnX, KpoMe nnToro (pHc. 4.1, 0), Ha KOHLtaX HecyHe CaIOlt CBaaHbI TOa-lbKO 3arloa-iHHTea-IeM B FIITOM HMeIOTCI aöCOälIOTHO ;eCTKHe Haqb- parMbI. 4.2. PACqET HA Oßll[YIO YCTOBqHBOCTb [IJIACTHH C 3A[IOJIHHTEJIEM CPEJIHEII )KECTKOCTH tt'tttttttttttttttttttt" 1 Z 141 
KpHTHecKHe nanpseHHs B HecynX caonX npn pacqeTe ynpyrofi yCTOftqHBOCTH KOHCTpyKRHH 1  = P  Bt/BI H a I  = Pl B/Bt ( = x, y), BC3IH OHH 6oabme npeeaa i]ponopRHOHadlbHOCTH «1 ha- Idx OI]pe2edlSOT cJIeylOIKHM oöpa3OM: Pc. 4.3. 3aBHCHMOCTb Ro9bbl41LHeHTa p* OT napaueTpa k npu paa3uqHou 3aKpen.qeHHH narpymenHbIX KpOMOK a) ecJ]H lnarpaMMa g -- e MaTepnaJIa He-cylItlX CJIOeB He HMeeT HBHO BblpaeHHOfl IIJIOIKaIKH TeKyqeCTH, TO )ieftCTBHTe]IbHOe KpHTHqecKOe nanpn>KeHne HaXORT no qbopMyaaM HJIH 142 ttlltIIlt Pc. 4.5. MaJlbHblMll ycnJmRMH Px, Pc n Kaca- TeJbm,MH ycJmiMn PXy, eficTsy- IOIIHMH B rIJ]OCKOCTRX, KaCaTe.qbHblX  cpeofi nosepxocTn nacTnma 
CKaTe PX py  PXy "- 0 (pC. 4.6, 6) (pc. 4.6, p* p* Canr xy x Px, Px = P = 0 (pc. 4.6, e) (pHc. 4.6, e) I Cmaxe Px p* H py co cnro Pxu, Pu  0 (pc. 4.7, a pnc. 4.6, HJIH IIO qbopMyae KpoMK 1 map- HHpHo onepv, KpoMK 3, 4 (pnc. 4.8, 6) map- (pnc. 4.8, e) o,s ,o 'a) z,o z,s a/» p$ Pgc. 4.6. 3aBnCnMOCTb KonuneTa p* OT yaean naacT a/b n na- paMeTpa k Pgc. 4.7. CB3b KOgHUHeHTOB p* H PV O \ ù,, 
IO 2 O,B(df=O..:lS) 146 eBCTBylOIIUtMI4 Ha ,/UIHHHble KpOMKH I4 $1e¢3IRI4MH B HJIOCKOCTH PHC. 4.10. HarpyKeße TaCTHbI ._ZI__.__.__I   6eCKOHeqHofi ,[lffInHbl KacaTe.rlbHbI- t ,  lln ycHI4gMn Pxv, /lefiCTBylOn- ' ) ' Mn BOJIB JJIHHHblX KpOMOK n 31e- "I t- KaRnMn BI n,nOCOCTX cpe)IùBBIX //1 / ] /t  nonepxocTefi npn paaanux cno- ..r_ _-_ co6ax 3aKpenae KpOMOI¢ flxg n) OHHpaHHe KpOMOK (IIIp apHnpnoe ne. 4.10, a) alReM.rleHne Pc. 4.10, 6) Px!g npn k 0 I 0.1 0.2 I 0.3 0.4 0.5 I 0,6 0,7 I 0.8 147 
p* =k -1 np k  1. B nocaeHeM cayqae KpHTHqecKoe ycHae onpe)e.qnOT np6JameHHO, TaK KaK C yBedIHqeHHeM k BO3pacTaeT pob H3FHöHOI hecTKoCTH HeCy- tlLHX CJ-IOeB. I-lpH pyFHX cnocoöax orIEpaHHfl 3HaqeHHFI p* rlpHBeßeH B Taöa. 4.4  Ha pHC. 4.15. l-lpH cxeMe OnupaHH, noKaaaHHofi Ha pHC. 4.14, 0, p* = 0,425. 5. eCKOHeqHO )aHHHafl CBO60)HO onepTa IIaCTHHa npu COBMeCT- HOM JeICTBHH CBHralOtKHX H C;KHMalOIIJ, HX yCHEfi, ematEx B cpegH- Hbi 6ecKoHeqHof jlHl, HopMaJIbHblMH yCHJTHflMI4 g. Pnc. 4.12. Harpymee naacT . - ........ bx OßeP" H KCTeJTBHblMH yCHJTHF[MH Pxll ][eHCTByIOIII, HMH B HJTOCKOt--I'14A t.pcZtnr HOCTeI llpH p3JIHqHblX CHOCO6X 3KpelI.qeHHFI KpOMOK 148 p# O  2 3 4 s Px o \\ \ \ \ \ \ 1 2 3 ' /)4 Pnc. 4.13. CBF[3b ely KO9qbII_IeHTaMI p* n P,U npn pa3arlqHOM onnpannn npo- on (c. pnc. 4.12, a n 6) PHc. 4.14. HarpyeHge 6eCKOHeqHO ][,HHHHOB HacTIHbl ycgnn Px, I, eICTByIOIIJ,IMI4  nocgocTn cpe)InHHOfi noepxHocTn Hecyumx coe Omapaaae KporaoK Pc. 4.14, Pc. 4.14, Pc. 4.14, 0 Ta6ana 4.4 p* npn k 0,, [ 0,1 [ 0,2 0,3 4,5 [ 3,3 2,7 4,0 [ 3,2 2,6 0,5 0,8 I 0,9 I 1,0 1,3 I 1,1 I 1,0 0,6 0,7 I 1,7 1,5 I 1,6 1,4 ] 7,0 2,0 149 
Pnc. 4.15. 3aBgCnMOCTb Ko»¢nunenTa P* oT k npn pa3nqHoM ognpannn KpooK (e. pne. 4.14): a--n cyqan 6; 6 --An cyqan e; o -- n cyqan e Eca-IH He oroßopeHo OCO60, TO p* MIHHMH3HpylOT IIo HeKoTOpOMy ReaoMy yHcny, npHHuMaoneMy 3HayeHn l, 2, 3 ... Pc. 4.16. HarpyeHe 6ecroHeqno nnnofi IIJIflCTHHbl yCH,rIHMI4 Pc H KflCflTe,rIbHblMH yCH,rIH- IMH Pc[I, JIeIKflIIJ, HMH B IIJJOCKOCTH cpe}IHHHOI IIOBepXHOCTH HecyIU, HX C,rIoeß Pgc. 4.17. CBI3b MeKJy KOß I" IHHTaMI4 p* H py 150 Ecan KpOMKI onepw RlapHHpHO (pc. 4.18, a), TO 2 l--vl, ( n ) 2 ----]-' [ ,V 2 -- 1,2 na onpeeaneTcn no rpaqbnKy (pc. 4.19). Pnc. 4.18. Harpyenne npMoyrobnofi CTHHbl yCHHMH PX KII],HMH B O- COCTH cpenHno nOBepXOCTn ecy[Knx Coeß Pnc. 4.19• 3aBHCnMOCTb p* OT y3n- nennn naCTnHbl np mapHpnOM 3a- Kpen3ennn TopRoB (CM. pHC. 4.18, a). a --  0,5; 6 -- ECa]14 KOpOTKHe KpOMKH mapHHpHO oHepTBI, a IJIHHHble 3aiReM- eni (pnc. 4.18, 6), TO 151 
5 ×/l+ 2 [ 4n2 n+Cn2+ 1 k_}_(ni_}_ l)k2 L (n+ l)  + n+ 1 Pnc. 4.21. 3amIcHMocTb KO»qbIIHeItTa p* OT y, RJIHIeHI n,rIaCTHHbI npH mapmipHoM 3aKpenaennn rpOUOK aJIoab ocn g n 3aueuaennn aJloab ocn x n acecToponneu ameuae- nun (pnc. 4.18, e): a--, >0, (pn¢. 4.18, el; 6--, <:2,0 (pnc. 4.18,  n el; --, >1,0 (pnc. 4.18, HJIH p* .. { 3 na + 2n" + l '-- (n+ 1)* ' -Jl- L , 16 g 8__  n + 6n + l 2 {2 n + 1 ../-x +6n+l k+----t« , (4.7) -n4 n2-- l j rae [ù = (;: + X) k; [, = [0,75 (n * + ) ;: + x*] ; 152 153 
1-1o 3aaHHOMy 3HaqeHrllO Ol, HOrO yciJIt HaXOtT KprITrlqecKoe 3Haqe- Hne ;pyroro. BeauqHy n : l, 2, 3 ... not6paoT u3 yCOßUa MUnU- MyMa STOrO KpTuqecKoro 8. y)jlrmeHna rlpMoyroJmHa riiacTuHa (a]b))1) HarpyKeHa paßuOMepHO pacnpeeennbIMU C)ßraOtttM ycnJmaM, efiCTByO- !: Pc. 4.22. HarpyKene npaMoyrozbuofi naacTm Hbl yCHJIH$tMH Px r py, eKatttrMr B HJIOCKOCTH cpeHnbx noßepxocxefi ecytttax czoe mM B cpeHHblX naocKocT[X HecytRX caoeB (pc. 4.23). CKOe ycuHe Pxynp -- Pu aB* [(c -t- t*)/21 * b-*" npu k < (1 __,,-)-1, P:u= 1/3 npI4 k>(1 q- -)-- 1-Ipl4 3alIeMIeHI4H KpOMOK (27 +  7-) [  +" (23 +  3-") ] I npn k -.< 0,75 (1 _t_ X-*), 151 155 
11. CBO60,HO onepTa 6eCKOHeqHO J]HHHafl nJIacTHa, cMaeMa yCHJIHtMH, paßHOMepHo pacnpe)eaeHHbM no JIHHHbIM CTOpOHaM Hecy- IIHX CJIOeB H JIehKalIHMH B cpeBHHHIoIX IIJIOCKOCTflX. rC4JIHt ' 2eflCTBylOIIHe a OnH ecymnfi cao, OTJIHqalOTCfl no MO- yao OT ycnanfi, 2efiCTByO[LX Ha pyrofi ecynfi caofi, a HeKOTO- pyO Beannny 2p. TaKHM oöpa3oM, a OH CaOfi 2eICTByeT p -[- Pnc. 4.26. H3acTaa 6ecKoeqofi 3nu, aarpyeHHa ycnan.n pa3- HqHOfi HHTeHCHBHOCTH H eHCTBylO- I/],HMH B OCKOCTH cpeHHHX O- BepXHOCTe HeCyIl]HX coeß 4.4. YCTOflqtlßOCTb TPEXCJIOflHblX nJIACTtlH C /AJIO)KECTKtl/ OPTOTPOnHblNi 3AnOJIHtlTEJIE/ PaCCMOTpUM naaCTHHU CHMMeTpUqUOfi CTpyKTypU El----E2, h  t c uorponubH uecymuMu coflMu, HarnöHa KeCrKOCrb uecymnX coea Maa  ao anHMauue ne npuuHuaeTcfl, c6mKeHue caoea orcy Tcraye (AW =-0). Oc14 CI4MMeTpHI4 3arlOJIHl4TeJI napaaaeabHsI KpoMKaM CTHHbI. FiapaMeTpbI hKeCTKOCTH B I1JIOCKOCTFIX CHMMeTpHH xz = U,D31, IDiC 133 ; ku -= O,5n2B,ca-2Gaä (i = 1, 2). TI 3aBHCHMOCTH cnpaßeAHBbI An npnoyrobHbX TpeXCOHblX nacTmL y opbx Gx/E >0,0001; E/Eh <0,2; c/h  6,0; oayefi Eas, E; k  6omnfi na napaMeTpos k nn ku. 1. HpnMoyronan nacwnHa caTa pasHoMepno pacnpeeeHHu ycnnMn, npnoennMn  ASyM npoTnsOnOOHN poMaM n e- amuMU s nOCOCTnX Hecynx coes (CM. pnc. 4.18). KpnTnecoe ycune pùv p*nZß [(c + h)/21  b -, re p* --o¢¢uueHw, aasucnnfi ov ycosfi aapeneHnn pOMO. pn mapnupnoM onupaHuu scex pOMO p* = (n -1 + n-l)  [1 + 0,5 (1 -- %,)(n-ku + k)] X  1 -- v, ( nz- zku + k) + ku + nZk + xl+ 2 + 1--vL nZ(n_+n_Z)zk.]-. 2 ' n = 1, 2, 3 ... Bb]6npav vaK, gTOöb p* npunnMao MnnUMbnoe anaqeHue. Ecu Aunnbe KpOMKn mapnupHo onepwu, a opovne aaeen, T0 8 Bennny n  1, 2, 3 ... xönpT  ycosnn noyenn NabHoro 3HaqeHH p. Ecn anze pOMR 3aeebz, a OpOTRe mapnpo onepTsL o 2 2   +  -*'.' (0,75 +  + 4-9 2  P* {4n (n  l)-*  [=(n  l)- 2 (n¢6n* l)x 2 
/2 I 36'1 [ 33'3 ] 30'0 I 28'6 / 27'4 [ 26'0 I I I I [ [ 24,6 23,6 22,8 22,3 o -o 0,2 a,« 0,6 o,s e/ö J IIc. 4.27. 3aBHC.MOCTb KobgeTa ]OT yneHgn naacTnH:  -- KpOMKH mapHHpHO ouepT; 6--KpOMKH 3aeMTeHbl 4.5. IIJIACTHHA C )KECTKHM H3OTPOIIHblM 3AnO$1HHTE$1EM PaCCMOTpHM TpeXCJIOflHble npMoyroJIbHble IlYlaCTHHbI CHMMeTpI, Iq- ofI cTpyKTypI (E = El, tt = t) c n3OTpOnHblM aanoJIHnTeeM cpene IKeCTKOCTH. BBeeM OO3HqeHHt Enp - Es" Dn'n=2{B'[(') 2JV 12] k -- Dnc 4b2( NeCocs nac Aoa yAoeopag ycou E,cl(Eh) < 0,2; ßc/(Gl) > 2.  1. I-Ipaoyromaa naCTuaa arpyea ycguau, paoepo aCnpeeHbiMH O ßyM poTHBOnOOHbIM KpoMKaM ecyux coe  eHNH B HOCKOCTH cpHHHbIX nogepxHocTefi. pTeCKOe ycn- e »  0,Sp,D.tb-, re p*  oaae, yuugmgU xa- aTep gKpeNeHHg "KpOMOK PgCCMgTDHBTCN qeTbIpe cyNgfl oo- gzaasx poo. A. Kpou mappo onepgL 159 
5 4 3 2 160 
Pnc. 4.29. I]pMoyroIbaI n,acTI4Ila narpyeua yC-Mn.Px n PV, efiCTBy- IOIII.HMH B IIOCKOCTffX cpeIIHblXùI]Oßepx- OCTe He¢yIIIJ4X ClOeß rCHJIH[ Px H Ph' CBI3aHbl Ko9qbuttHeHT P,j onpe)eauOT H3 Bblp a»KeHH t 1 27  17/   1 (23+13/ )k Pxu 3 1+ 3 npn k  4(1 -- l/k*) ' 3 . 1 npn lk(l+l/k,)'" Pxu  k 3. HpnMoyronan narpyeHa panoMepHo pacnpe- aeaeHHbIMn CHMHMH ycn- HflMH HpHOeHHbH B HO- cKoc, nx cpeanuux noßepxocT necymnX eoeu (pne. 4.20). 38BHCHMOCTb 162 163 
3123 B125 + L   " B13  r#ea- , m-- b ;m :l, 2, 3;n :l, 2, 3 ....  n n - paT 3 OB nOyH MHMbHOFO 3HH pp-  opneTnpoox paceTO oo COOBaT p. BU  - B,+, L , + C Dx . o D + D   ' r = C,C - (D DDù + D«)  + D¢ C; C1 ... C4 OCTONHbIe, onpeeNNT c yNeTOM FpNNNNblX 2 t c  164 
re  =x/a; 1 : Y/b; k = H/( b d); %  qbyHKlrIt nepeMettteHrlfi; 166 Oq 0; aln maplmpHo onepToro Kpan Z =VZ =V - 0 -- Azn eCTKO aeMzeoro Kpan   kV% -- 0X V  0X a = ==0. PemeHne ypanHeH HeTcn B nHe TpHrOHOMeTpHqeCKHX pflOß. HanpMep, zn CXeMU 5 W = 0, X = 0 w=/nslnm»sinùq (p=0; 1; q=0; 1); m n p q X =   fron   n X sin » sin q, (4.11) m n p q re a = (2m  2p 0/2; ù (2n  2q 0/2; , nOCTOflnnbe, noczenmm 3 KOTOpbIX HaxoT 3 {4.9) nocze nocTa- nOnKU n Hero (4.11). Ha cpanHem KOgHKHeHTOB npu OHHaKOBblX npon3eesx «syco ceyeT Ypannenns (4.9) pemamT« MeTOOM Byönona--FaaepKnna, npn TOM ero yMnoamT na 1 1 r=0S=0 B pesybTTe noyqT cc,ey re6pHqecKHx ypßHeHH OTHO- CHbHO n cxeI 5  = 0,  = 0 (seenHe) CHcTey OmnO B BHe tl 1 1 1 pO q:O r=O s= 0  n 1 + kOaÜ { rs2. (4.12) rs ij , re Ü l+ai rs b s a  2 2i+2r--1 2]+2s1 . ail=  t + is; alt = 2 ; is = 2 ' TÜ = b* ar + p; ; (4.13) P 1 1 t 0=0 r0 0 0e BblqHCeHH Terpaa 1 = { 4mi (m  -- P)l[m  -- F + 1)  -- 4ml np gux m + i; 4mQ(m  -- i ) np eeIX m + i. In» BhlqHCNT, 3aMeH m H i Ha n H ]. N nnTH OCTabHblX CXeM YPaaneHfl 6yAyT aHaOrqHblMm 167 
YIpn mapunpuoM 3aKpenerm Bcex RpOMOK abEE ' (, 1 2, 3 .), 1 + 9 k  i)  . (4.14) rae R = [ iZb  + i=) k  ' • mni (4.15 iZbZ Pq ]; Sn  T -- a   (m - i) (-- B aTO ypannenun Sù  0 TObO npu neneTnx m +'i n n + ], nO»TOy cncTea ypannennfl pacnaaeTcn a ony cncTey c neneTnn m + n, pyry  c qeTnH. =n ca- TbIX nzacTun pemenne 6yer qHblM. ' ' . 256b EE', (4.16) p0 0 B  2i + 2r -- 1. (4.17) mij (m - F) npn neqnbx (m + i); li = mi (m  -- i)/[( m -- i  1)  -- 4m] npu qeTnux (m  i); n]/(n  -- ]) npu neqeTnbx n  ]; I]  0 npu qeTUbIX   ]- Hpn OTCyTCTann canraux cu cucTeua (4.16) pacnaaeTcfl nan cxeuu2 =0n  a 1 1 r * v o=o=o (4.18) B ypanennn (4.18) Ri, Ti uqnczmr no +opuyzau (4.18),  KoTopX a =i + 2r l; 1 npn i+p+r=l; I-lpn HeneTnlix ra q- i n n + j «i mni i (ms + i s -- 2) Shn -- (ms _ is ) (n s _ is ) [(mS _ iz + 4)z _ 16mZ], eC XOTfl 6bl ORHO X 3HqeHe qeTHoe, TO Sn  O. Pemenne ynpoaeTcn, pacnaancb na aße ne3aßncnMble CnCTeMbI (KOra CyMMbI m + n TObKO eTHble  TObKO HeeTHble)  Ha ] He- 33BCMbIX CCTeM (npn OTCyTCTB cnnramme cHCTeMbI COCTOHT H3 ßyx HaBHCHMblX CHCTeM OTHOCHTeabHO Iran C qeT- HbIMH HH HeqeTHbIMH 3HaqeHHflMH m. a CXeMb 4  = 0 (mapnupnoe onupanue) 1 1 1 1 pOq,OrO s0  . 2°b re ;,  " , bnUmT no opuyaaM (4.14) ¢opMyae (4.17); ni (n + p -- ) I  (n + p) [(n - p + 4) -- 6n 1 npu neqeTnbx n  1, I =0 npu neTUbX n]. Upu OTCyTCTnn cnrammux cua CUCTeMa (4.19) pacnaaeTc na e ne3aucnMbe CUCTeUU ypanenufi. Hpu eCTOU 3aeMaennu cex KpouoK (cxeMa 1) 1 1  1 1 p:OqOrO s0 re R n T naxoT no opuyaau (4.12) n (4.13), 3aMen a Ha S : mnii (m + i -- 2) (n  + 1 -- 2) (m z  i) (n   ]z) [(m z  i z + 4) z  16mZ][(n z  ]z + 4) z  16nZ] ' eczn m + i n n + j HeqeTHble; Stm, = 0, ecan XOTn 6bi o)lHa I43 nyx ¢yMM tleTHfl. B noc3Ie)HeM c3iyqe CI4CTeM pacna)aeTcfl Ha )ße Ite3ßI4- ¢14Mhle I4H H qeTbIpe He3ßI4CI4MbIe CI4CTeMbI IlpI4 pcy  O. Are6p annecne ypanueunn OTHOCnTeabHO aMrlnTy COCTaBOmnX nporn6a ,tmn coepaT uen3ecTuße Kp4T4necK4e uanpneunn. pa- nennn Rfl nx nbqnceHnfl noyqaIOT na onpe)lenTeafl ¢FI¢TeMbI, npn- PannenHoro K HymO, n3 TnX ypanHennü UOHO HafiTn OHO KpnTnne- CKoe Haflpff)KeHHe npn 3fl]HHbIX OCT3IbHbIX. Upn naannnn cno6oano KpOMn ypaßHeHnn (4.9), (4.10) UOmHO Peb TOqHO na-In npn6anmeuuo. [lyCTb OnH Kpa (l  Z0 CO60leH. 168 169 
170 4.8. '(TOIIqHBOC']'b C)KATblX flJIACTHH C MA$1OB )KECTKOCTbIO IIPH H3FHBE HEC¥11[HX CoqOEB 171 
OTHoC14TeJIbHa norpemHOCTb pacqeTa no bopMyJIaM (4.22) ... (4.26) COCTaßfleT 0,050. YnpoeHHafl ¢OpMya (4.26) fl P,noyneHa 3 TOqO ¢OpMyb (4.22). Ta OpMya np oHOCTOpOHHeM CaTHH 3anucißaeTc B ¢opMe (4.26), napaMeTp KpUTUqecKOfi Harpy3K p* = [/(t0 - )1 I + /( + 10)l. ¢opMya  to 3aBeT OT COOTOmen napaMeTpo k n r: to = Vh  + ¢ + q + ]/ - I/p + q; -- (2/3) (1 -- k) npn ,__ (); «= +_ ,., o= re p- 3r q - 4.9. /ECTHAI VCToBqHBOCTb IIJ1ACTHH 1. CTOBqHBOCTb Hecy14X CIOeß rlaCT14H C COTOBblM 3anoJiH14TeJIeM. I-Iecy[t14e c3ioH Mo)KHO Ilpe)lCTaß14Tb KaK COBOKyI]I-IOCTb ROHIblIeK COT, KOTOpble MOFyT BblI]yq14BaTbCfl Ip14 CLKaT1414 C14JIaM14, JIeH¢al.lL14M14 B cpe- R14I,II,IblX [IOBepXHOCTflX HIeCylR14X CJIOeB. 172 Pi --- 0,91t F " _ viz / 2EiEsti 3 f EiEs 3 / EE 0,4 ]/ 2 z • (1-,) I]p14 cH¢aT1414 IIO OC14 t 14H)eKC X MeHflIOT Ha t. 4.10. PACqET TPEXCJIOBHblX KOHCTPVKIDlfi C PACCJIOEH IIM! KOHCTpyKImfi aHa14314pyeTc  pa6oTax [7, 16]. MeTObI oIeHK14 14pog- HOCT14 coe)14HeH14fl coeß np14 HaJI14q1414 pacc3IoeH14fi 14 HepFeTHqeCK14e Kp14Tep14140TCa14aH14fl 143OmeHtbI B pa6oTax [18, 20, 21 ]. O63op pa6oT nO pacqeTy npoqHOCT14 Kaeebtx coe)114HteH14fi np14eei,i  pa6oTe [14], rRe TaK»Ke BbIßeßeHbI ypaßi,iei,i14fl Rfl onpe)leei,i14 Me»KCOflHIbIX Ha- npTKeH14h B MHOFOCJIOIHbIX no3ior14x OpTOTpOnHblX O6OJIOqKaX,_npflMO- yrOIbHbtX 14 KpyrabtX niacT14Hax. }a nocTpoeH14 Mo)le14 pacqeTa HanpflmeHHO-epopM14poaHHoro COCTOfli,i14fl TpeXCJIOflHOfI KOI,IcTpyKI]1414 C paccJIOeH14flM14 HeOöXO)I14MO K$IaCC14(1)141]14poBaTb pacc3IOeH14fl 14 yCTaHOB14Tb OILeHK14 fi$Ifl 14X napaMe- TpOB. PaccJIOei,i14t B MI-IOFOC3OftI-IblX KOI-ICTpyKI]14flX MO)KHO KJIaCC14(1)141_[14- poßaTb nO c3IeyiOUL14M OCHOBHblM napaMeTpaM. 1. YIo nioa14 i-fi 3OHbI pacc310eH14fl Si 14i14 ee xapaKTepHoMy pa3- epy, ec3m OH OHO3HaqHO onpeeafleT nJloab pacc310eH14fl. CJleyeT Pas14qaTb Mable 3OHbI paccoeH14fl, Kora xapaKTepHblfi pa3Mep pac- CIOeHHfl cpaBHHM C TOJII.I14HOI OTCJIa14BaeMoro cJIOfl; cpeAH14e 3OHbI pac- CIoeun, BepxHas rpaHmta nIoua14 KOTOpblX onpeAeIneTcn noTepefi MeCTHoft yCTOftq14BOCT140TCJia14BaeMoro cioa; 6Oibm14e 3OHI paccJIoeH14n, aaMepBi KOTOpblX cpaBH14MbI C xapaKTepHblM14 pa3MepaM14 KOHCTpyKIL1414. AaIbHefimeM paCCMOTp14M cpeAH14e I4 60IbtU14e 3OHBI paccioeH14a, TaK KaK Bji14flH14e MaJIBIX 3OH pacc3Ioei,i14fl Ha HeCylRylO CllOCOöHOCTb KOHCT- PYKttufi, oqe14AHo, I-ie3Haq14Te3ibI-IO. 173 
174 HHqHblX ycJIOBHfI B KOHeqHblX pa3HOCTflX pemes ypseH, ex nTRrOSb. Tpy, CnOh- BOBa£H MeTOR HpOFOHKH. pH pemeHuu 3aaqH yqHa CHMaeMOCTb 3anOHHTe. aTepHa£bi 3ano£HHTe3fl H HecyHx cOeB 3OTpOnHI. paßHeHHfl paßHOßeCHfl Tpexc0HblX HaCTHH CHMMeTpHqHOFO cTpoeHua (t : t» E : E» v :v) npu RUUHpuqeCKOM u3ruSe HMeT BH: A 5eKTHblX yqaCTKOB D (Fx + ¢),  -- D (F -- ¢), ...xx = q (x); D (Fx -- ),  + 2 (Eaa/c) (F -- ,) = q (x); 2  t -  Eao (1 + ) [D (F, +,), rae D = 0,SEd [(1 + ) -- 0,125]; Dz = 0,5t/2 (1 + i); Da = 0,Sctg-; D = tt/12; an yqaCTO8 C paccoennnun (Ga = 0) O,5D v (F + ),  = q (x); 0,SDr (Fr -- ,), . + 2Eaae - (F -- 1) = q (x); (F + ,),  -- 0,56 ( + ) (F1 -- ),  = 0; (F -- ),  -- 0,56 (1 + ) (F1 + ,),  = 0, 2 rae D v = D [2 + e + 3 (1 + ) (e + 1) -tl -- meeToeTb npn nsrn- 6e paccoennoro naeTa; F, --nponsaobnbe ynnn nnTer- Pnpoaannn, onpeenmne nepeueennn n nanpnmennn  Tpexcofi- nOfi naCTnne; i = 1, 2- nouep necymero con. Honepeqnbe nepeuemennn aepxnero necymero con--w = F, nnmnero necymero con w =. Hpoobnbe nepeuemennn u Hanpnmennn  necymnx conx , =  (F,  -- zF, );  =  (F,  -- zF. ); Enaecbi, x; ,xx; ,xxxx OaHaqanpeuKnpoaanne no x 1, 2 n 4 4 paa. 8pflmeHHfl B 3anOHHTee •  = 0,SEA [(F -- ,),  -- 0,56 (1 175 
I I o Pnc. 4.32. Bannnne cMeeHn eHTpa yqacTKa paccaoeHnn Ha Beanqnny n xa- paKTep n3Menennn npornöa ¢ Tpexcaofi- nofi nacTnn npn UnnnApnqecKoM rnöe narpyaKofi q, pacnpeAeaennofi no qacTnoßepxnocTn (oTnocnTea»nan Ha paccaoeHH -: (lpac/L) 100 : : 13,2 %) pH Ea : 0 Oll = olil07imax H KacaTeJIbHblX Hanpn)eHHfI B 3anoNHHTee ° 0 0 . 0 "I33 max  MaKCHMaJIbHbI[I np  TI33/TI33 max, rAe 0max, G]i max, anpnKen  6e3AeqbeKTHOfi KOHCTpyKKnn Aa]fl Tpexca]oHOfi cMMeTpqHOrO CTpOeHn, a KOTO O AeCTByeT pacnpe)leae_a PY ° L  ceW HaFpy3Ka, npH3]o)eHHa no yqaCTKy floBepxHOCTH )YIHHOH o yqa RHHe npoJ]eTa. IpOMKH naHeJ]H CBO6ORHO onepTbI. 1-IJ]aCTHHa HMeeT CTOK paccoeHH AHHOfi I v (CM. pHC. 4.31). 176 3anOdlHHTe3Ib Tpexc3IOfiHOfi rIJIaCTI4HbI CndlOtnHOfi. jYIHH l-ldIaCTHHbI 910 MM, TOdILIJ, HH HecylaHX CalOe t  tz = 1,5 MM, C  17 MM, MORyalb ynpyrocTn HecyIHX caoen E1 = E,,. = 70 FYIa, KO¢bnneHT Hyac- o o,s , ) PHe. 4.34. I, IseHeHHe Hopa»HUX Ha- Hpuz<eHHü Ha BHemHHx nonepxHocTnx HecymHx coe npH H3rnöe TpexcofiHoü IIoIacTI4HII (Ela = 0, Es : 45 MHa) PHc. 4.36. H3MeHeHHe HopMa$IbHbX Ha- C HpImeHHfi Ha nHyTpeHHIX Zi = W--- n cpeùHHnIx zi = W- ( + + ti ) nO- BepxHoCTflX HecymHx coeß HpH arHöe • pexcaoHofi HaacHHb (Ea  45 MHa) o o,» 1 o .- t,ùe = 13, 2 u I I (3 0 &5 x Puc. 4.37 H3MeHeHHe KaCaTeJIbHblX HaHpflmeHH B 3aHoHHTee npH ll3FIl(e Tpex- C$IOf[HO. H$]aCTHHbI: a -- Eta = O; 6 -- Et a : 45 MYIa COna Hecyiaix cOeB paßeH 0,3, MO)lyb C)IBHFa 3anoJIHHTefl Gl,a = - 15 MYIa. PacneT npoeetI c yneTOM meCTKOCTI 3anoiHITeI n npo- OIOM uanpaIeHmt E  0,45 MVIa H npH onymeHH E  0. 177 
178 
180 181 
v, (1 -- zR') WI, (5.4) -- (1 -- zR l) WI. (5.5) HanpflmeHHfl 13 HeCyl]J, HX CJIOflX = . -I -ly. / __ , -- R [zR 4- 0,5-' (1 + 2? l) vl, (l2e -'« -- [,e-*«)], (5.8) re DT onpe)leamOT no dpOpMyze (3.14); 3ttaK n3]lOC COOTBeTCTByeT i = 2, 3HaK MnHyc--i = 1. Z Pnc. 5.2. Hoay6econenaa Tpexc.uOflHaI RH.UHHpHqecKaI OOJIOqKa narpymena oen- • am Mo, pannoepno pacnpe- eenn»in no opooy ce- qeHH Pc. 5.3. FIoay6ecoxexa qecKa o6oonKa narpyena nonepeq- umi ycnmi Q0, pamomepo pacnpe- aeeaumu no opuomomy ceqeHmo 2. TpexcaofiHan H3]HHRpHnecKan o6o3]onKa HarpyKena panHo- MepHo pacnpeReJIeHHbMn no O)lHOMy H3 TopKoBBIX ceqeHHI nonepeqHbMi KOJIbReßble 02t : 2i (5.9) 188 
rAe i = 1, 2--noMep necymero c3on; np14 i = 1 B B»pae1414nx (5.10), (5.11) 6epyT 3HaK MHnyC, npn i = 2  sna nc. 3. Tpexona npqeca o6ooqa narpyena panoepno pacnpeßeennb no npoeyToqnoY ceqen ycnu p (pc. 5.4). Hporn6 necymnx Oeß w = 0,5 - De @-- ) 3 acna3bnu nporn6 Wx = 0,SpRa[(D¢ ( + 2) 2)- acnMabub MoMenT  ceqenn  = 0 Max  O,SpRa/( + )" P Pnc. 5.4. Knnnpnnec«an Tpexczofinan o6ozona na- rpyena ycnnnun P, pa- nouepno paenpeezennblUn no npouemyToqnouY ceqe- 184 '=0 =0 0 Pnc. 5.5. 3nna KnnnpnnecKan Tpexcofina O60OqKa narpyzena paß- oMepo pacnpeeaeofi no noßepxo- CTn arpy3Kofi; TOpb] O60OqK 3aii{eM- eH 185 
186 Harlpfl:mertrm B Hecyiartx c,rloflx vIeprt,artoHaJIbHbIe  -- fr'lg qRx {  , (I ± 0,5, -) x [ l X 1 [-- I x «=- . «=o Pnc. 5.8. • pexcofinan ooua narpyena paß- noepno pacnpeeennofi narpyofi q; TOpK OOUKH mapunpuo onepTb 
Qo =--0,5p, 5.7. ltAIIPll)KEHHO-EOOPMI4POBAHHOE GOCTOIHI4E OßOlOqKI4, HAFP¥)KEHHOB HA OHH ClOl! B TpeXCaOfiHO KOHCTpyKKHH npe)lcTaßneT nHTepec nepexaqa ycn- on, )xefiCTBymmX C O)XHOfi CTOpOHM O60Oqm TH yCHa-IHH nepexamTc Ha BTOpOfi HecyuH cao 6e3 IIOMOIH, H cneKa,nbHMX COe)IHttHTeglbHblX aoeMeHTOB. B cayqae /IefCTBH MeCTblX arpyaoK no KaCaTeabHOf  HeCytU, HM CaOM gMemT aùaueHùe npoqHOCTb  )KeCTKOCTb Ha CI, BHF aanoaHùTeaù ù ero coeaHùeùHfi c ùecyntmaù CaOùMm Ecaù caßùramntee F PH¢. 5. II. TpexcIOfiHafl 060oqKa rpy¢e«a OCeB0fi CnIofi F, npH3omeofi K OHOMy Hecy- IeMy F 0"21 -- ,.lt 1% [I -- p (1 -- e-r,«)], F 189 
I'Ipn JeBCTBHH Harpy3KH pacCMaTpHBaeMoro THna Han6oee OT- BeTCTBeHIIbIM pacqeTHbM cyqaeM }IBJI}IeTC pacqeT O6OJIOqKH Ha pac- CJIOeHHe. IZ, acaTebHOe HanpeHe Ha rpaHme 3anOHHTeIb--HeCylfi caofl 190 191 
C13 3 o I I I o(=« « 0 lc. 5.16. LHHH)IpHqeCKaH Tpex¢AOflHa o6oaoqKa HarpymeHa cHaofi F qepes teCTKYIO mailC, yCTaHOBeHHyIO B rlpOMe»KyTOqHOM CeqeHHH Ha O)IHOM H3 HeCyilIHX CJIoeB: a --peaabHa cxea HarpyKeHH; 6- pacqeTHa cxeMa 4. Tpexcaoßa uaHH)ipqecKafl O6OJOqKa HarpyKeHa ycan ' }IeICTByIOUU4MH B IIpOH3BOJIbHOM ceqeùù O6OaOqKù (pùc. 5.16). B caY" qae arpy:«emlfl caofl 1 O6OaOqKH B HarpyKeoM CeqeHHH Bo3HHKItYT 192 X (1--e -r«H%) (1 -{- e 2ren%) (1_ er«n%)(1 _{_ e-röH¢Zl) " X O0  . 300  cl2 200  np arpymen cofiF, Hoff K eKofi mafiöe a oo a Hecyx coeß B npOMeyTOHOM eHHH OOKH B 38BHCHMOC OT Be- Hbl CM H MeCTa ee 193 l-lpH paßHbX 3HaqeHHX lapaMeTpOB HecyI,HX C01OeB H 3anOHHTe BepxHefi  HHHefi qacTefi O60OqK peaKTßHaS caa PO = [plE,2«9 (1 -- VI ) Vl -- p2EI,t, (1 -- Vgl) ] (1--e -r'«l) (1 + egr*«") x x [ E2,t ( 1 -- vg) y, + Ent, ( 1 -- Vl ) V21 ( 1 -- e .«ù) ( 1 + e -r'«'). TaKHM o6paoM, 3aßan Bnemnee ycnne pt nah p» nah o6a OnO- BpeMeHo, MOmHO onpeeanTS peaKTnßnSle ycnann B necymnx onx  narpyeHHOM ceeHnn O6OaOKn. 
5.8. PACqET HAI1PDKEHHO-J1EOOPMI4POBAHHOFO COCTOIHI4! OßOJlOqKl4 I1Pl4 I1PO143BOJIbHblX HAFPV3KAX F an onpeeaeHa Hanpa<eo-ae¢opMpoaaoro COCTOaa 060- JIOqKH npn IIpOH3BOJIbHbIX Harpy3Kax HeO6XOIHMO HCIIOJIb3OBaTb IIOJI- Hble ypaßHeHH paBHoBecHn. ]Jlfl OOOqK BeCIMMeTpHqHOrO CTpOeBHS C OpTOTpOrHblMH Hecy- IIHMI4 CJIOIMH I TpexMepHblM OpTOTpOrlBblM 3arlOHHTeM ypaßHeHIa paßHoßecl4fl, BblpameHHble OTHOCITeJIbHO yCl4Jll4l B Hecy[III4X CJIOIX, HMeIOT BHJ 1i" ONli , OS21 -w- 0"I;123 R$'i (Xi O; OQ2i  0T133 ). 3 0 -- N2i - -'--- +  -\3Ti  (5.12) 4"" oi OMi 0T2a 0 (i- 1 2).  c W R3V -- R3 (G* W- 3c) W - ' 194 B MaTpIqHOfI {opMe CICTeMa ypaßHeHIfI (5.12) I4MeeT Btt (5.13), re X y ' Z (5.14) 195 
0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 P,o, 0 0 Plo« 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 --1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Pl0 DlOl 0 0 0 0 0 0 P,0P0 0 0 0 0 0 0 0 0 0 0 0 0 --I 0 0 0 0 0 0 0 0 0 --PI0a PI01 0 0 Pf2« 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0--p,o4 0 0 0 0 --plOl 0 0 01o4ù Pf2« 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 --P,o, 0 0 0 0 0 0 0 0 0 0 0 0 0 0 P4 0 0 0 P224 0 0 0 0 0 0 0 0 P824 P12ß 0 0 0 0 0 0 0 0 P4'« P22« 0 0 0 0 0 0 0 0 P,o, P,o 0 0 P126 0 Pl P324 0 0 0 P224 P426 0 0 0 0 0 P7 0 P724 P72 0 {)101 0 P220 0 0 --D722 0 --P724 P82 0 0 0 0 0 pT 0 0 9'22 0 P'2 0 PI 0 0 P724 0 0 P22 0 P82 Nll N, $2 11 Qll Q Sl Q2 0"13 0"23 "i233 T133 R3Y1 R3Y2 = RZ 0 0 0 0 .196 197 
AEk Alll All« Alm Amt A141 A151 AI A13 A161 A153 A21 A3 A261 TaönRa 5.1 3HaqeHHe KoqbqbHRHerlra 199 
Flpo/10KeHre ra6.. 5.1 3HaqeHHe KOHKHeHTa l-IpotoeHne "ra63. 5.1 3a,aeHHe nodpqbHttHer a ,,-,, (, ) g123 "3 I4 -- glsat21 -- gtaatlI l_ .__2 ia_t_tll__t2i__211 Esr=a  l--g3tzl+ g2tl  +  / tlt I " " E ! Ic srza  + gssRa  + EszrzsslzR  123  142 123  I72 t  1 E23F223  "22 + B2  g123  I42 @ glSSt2I2 G133 E t Gsss I , I 201 200 
3aKOH eopMaLt HeCyIItX C.qOeß OnCblßaeTC OöIIteri3BeCTHblMtt 3aBHCHMOCTfiMH TOHKOCTeHHbIX O OdlOtteK- 3aKo #qbopMattnn 3aIIO3HHTedIfl lpOri3BOeH, I 3aKoHa 3OMaHOt $I TerpabI, OlCblßaIOttte eopMaLtIO rl BXOIKe B ypaßHe- HHfl, npHBeeHbI B TaöJ1. 5.2. T a 6    a 5.2 Ik 161 171 /91 HaqeHHe HHTeFpaa C c 1+0,125F  3 1--0, 95F I c (1+ 0,0012Fx) -- 0,5 c  1 + 3,2F x 48 1--0,25F z 48 X F 1 (1-t-0,15F2) c B 1 -t- 0,15-1 , 30 1 --0,25F  Ik 11 Is Is [9 3HaqeHHe:HnTerpaa] C 6 1 --0,25F 2 1 6 0,5 -- 0,5 c 2 _ 1 + 0,5F --i-g-z  48 X -1 (1_t_0,15F2) c a 1 -t- 0,125 120 1--0,25F i- lk /12 122 12 [62 3HaqeHHe HHTerpaav C 3 c 1--0,125fl, 3 1--0,25F 2 1 C C ä- O,g c 2 1--3,2F  /72 48 1--0,25F 2 Is2 48 X -1 (1+0,15 -2) c 2 1--0,15F t I2 30 1--0,25 Fi 202 KOMIIOI-IeHTbI flll 0 0 0 Z l ( t o +  2 Oz I o " en3opa e¢opMaunn 0 0 0 ao a3e v e33 a2 % a a a« v zR(1 +z/R3) 062 0 0 065 aöe   8133  AU  , 0 2 02 . (5.5) 203 
as   -- R (1 + zlR)' a   R (1 + zll%)' 1 ( tl Oq)l) 0 . a=-- 2 - /-" KacaTe, rIbHble HarlpI:eHHI B 3arloYIHHTeJIe 1 { OUx _1_ OU q)) ..[_ 1 ( Car ¢P CaV Ps) tl 2+z/Ra t 2 + z/Rs s  ] ' -+ 2 l+ms 204 Oz 1 [. 0__ 1 ( +  1 + z/R3 2 az   l+z/Ra F 01 O -- (q)l tl +--; 2 a • B npIßeXeHHblX BblpameHnX KO3qbqbHU, HeHTbl ri  HMelOT BH, (2.4). KOMrlOHeHTbI TeH3opa HarlpieHrifi 3aHOHrITeI 0 0 bs b b bi6 b« × b Ul t/2 U2 0"18 %a "U233 , (5.161 rae bll = E1arll O . Elarll a O bi   E23rsla qgl 0 . E28r21a  O . Ra 1 + z/Ra 013 ' bi4  Ra 1 + z/Ra 013 ' -- L,O   GI I -]- z/R3 1 --  + Eaaraa Oz ' b16 = 0,5 Earns -- U O R  2 -ö + ba I _ E,rl9 a O. Elarlaa 0 bs  _. Fs3rs2a qx 0 . Ra I + z/R oB ' 0,5 Elarxa ,--1.]--1 a  205 
206 Ear r¢ 0 . 34  Ers q 0 F r b  Gm L Oz R (1 -[- z/Ri ' Rm (1 -1 I-- zlR] ; b-- , +--'a b ap , a 0,5t2 az l-- ; bel="'laa'-' -' b°2---Gta3 Oz ' --  - u,ot:--ä: ) - ; b =  % -- 0,5t2 -E" Bbpazxeme (5.16) MO)KHO 3ancaTb B BHe BU =  . (5. ;) Konoez»l eopaun ecyx cOeB 1 IH 2 KHHpqecKo pyroo o6oon 1 Oui. 1 [ Ovl  z R] Y  - Y-- + 2 a oB 1" MepHHO- 207 
1 O . z O e I Ell O) 2 z 0  1 (1  z h«=; Z T--N  0--" MaTpHiia KOMIIOHeHTOB TeH3opa HailplteHI4ft B HecymHX COX dll 0 d 0 dll 0 d 0 du 0 da 0 ds 0 d 0 d4 0 d44 0 dl 0 d 0 d 0 d« 0 d64 0 0 da« 0 ä« 0 "12121 208 ds = Glzl I q'-  '1 "'' z 0 d6 = GI,(I 209 
 +2--+---- [-ö-+w 0--#- -- W-- + 2---6- ] " 210 3HaK tIIOC COOTBeTCTByeT HeCytReMy COO 2, 3HflK MHHyC -- CIOIO 1. B awpHnO OpMe WI4 coonomeni4n Hemw ia x U1 211 
212 213 
214 B cayqae efiCTBH CHMMeTpHqHOfi Itarpy3KH qln (a) COS n (] = X, y, z) Tll : Tln i (a) cos S - Sni (a) sin nl; ui = uùi («) cos n; wi = wùi («) cos nl; u -= X (a) cos nl; "r ---- "r,, (a) sin n[; qyl == qtmi (¢Z) sin n[; FIpH efiCTBI4H attTHCHMMeTpHqttofl Harpy3KH qin (a) sin n B npH- BeAeHHbIX B»IpaKeHlSX qbyHKtHS MeHeTC Ha oöpaTHym (sin Ha cos, a cos Ha sin). 3aaqa pacqeTa TpexeaofiHofi O60OKH CSOAHTCS K onpej{eiemm MaTpmt»-CTOa6ua U CnCTeM» (5.14): U = XA -1. (5.20) Onpeaen U, naxoas 3nauenns KOMnOnenTO nanpsenno-ae¢opMn- poßannoro fiOfiTOH, HCnOb3ys MaTpnqnbIe 3aßfiMOfiTH, npßeen- n»e B STOff raße. 3aaa erKo pemaeTcs na OBM c ncnoab3oßanneM cTanapTn»x nonporpaMM. OMnOnenTbI MaTpbl-CTO6Ra U MOryT 6bITb 3aanbi B Be KOTOpbIX ynK, yOBeTBopmX rpannbIM yCOBSM aßTOMa- THqeCKH (HanpHMep, B BHe pSOB Cypbe). Hp TOM MaTpHbI BTC neßbpoennbM. He pacCMOTpenb cayqan narpyenns Tpexcaofi- HOff nHHpnqeCKOfi O60OqKn. SeMeHTbI MaTp erKo onpeeasTC nyTeM uepenuuposann yHKHfi Ui, Vi, i  nOCTaHOBKOfi saqenfi yHKHfi  X nposso- n»ix. Hp »TOM MaTpuna-cTo6ea U c 3eMeHTaM Ui, Oi, Wl npeo6pa- 3yeTc B MaTpy-CTO6e aMnTyHblX 3HaqeHfi Arena, Brand, Dmni, onpeeaseMblX qcaau m  n. MaTpa-cTo6e Harpy3K MeeT S Ka- qecTse SeMeHTOS KOMnOHeHTbI Harpy3K, onpeeaeHHbm KaR KO3H- HeHTbI yp»e, Tame 3ascsme OT m  n. KOMnOHeHTb[ aMnTy onpeeaSmT noceoaTbHblM nepe6opoM m  n. PacqeT npeKpaamT, Kora OTHOCHTeHa BeanqnHa 6W, n(m) = D,ù(m)/   D,ù(, a HarpyeHHOrO cos oKa3bßaeTc MeHbme 3aAaHHOfi TOqHOfiTH pacqeTa. UpaKTHKa nOKa3bIBaeT, qTO psAbI CXOBSTCS AOCTaTOqHO 6blCTpO. HpH TOqHOCTH pacqeTa 0,01 OCTaTOqHO HCHOb3OBaTb 5 ... 7 qenoB psa. I. HHHpHqecKa Tpexcaofinas O60oqKa narpyena OKabHbIMH CHaMH, HpHoeHHbIMH K OHOMy necyeMy co. pH efiCTBHH na O60OqKy nopMaabnofi paBnoMepno pacnpeaeaennofi narpy3K 215 
(pnc. 5.18) H HarpymeHnn MOMeHTOM, eICTByIOIB, HM BOYlb o6pa3ymtRe, nepeMetReHH m uI,    Amnt,c°s  COs " 1, = XXDmnl2sin. mna cosn.  0 3T nblpameHn COOTeTcTymT nepeMeeHM TpeXCOfiHOfi 060- OqKH, KOTOpa n TopaoblX ceneHnx MeeT aöCOmTHO mecTKe =0 =0 pc. 5.18. nznnpnqecKaa nOBepXHOeTH Hyero coa KOHKeBble 9eMeHTbl H CBO6OBHO OHHpaeTCH 3THMH 3eMeHTaMH ycTa- noaean»IM  cpennofi noepxnocT, na meCTe onop»l. PemeHe CcTeMbl (5.14)  npnT»IX ¢ynufi nepeMeen «oTca K pe- eHH CHCTeMM aFeöpaHqecKHx ypaßHeHH OTHOCHTebHO MaKCBMb" HblX MHHTyx KOMHOHeHTbl Harpy3KH Zx, 20T Bo3eCTBH yCHH qz, pBHOMepH0 pacnpeßezeHHOfi no qacT noBepXHOCT, MemT B [8] mh mn« (5.21) 8 Zmnh2- g n (n 1, 2, 3...; m 1, 2, 3...). Ecz arpy3na pnzomena  cepene npoze,a,  4B q sin mz (n=0; m=1,3,5..-); (5.22) (n= 1, 2, 3...; m= 1, 3, 5...). 216 B cyqae )IeCTBH cocpe)IOTOqeHHOfl CHälbI F B l'oqKe (21 = 0,51 0 H [  0, KOMIIOHeHTbl Harpy3KH HMelOT BH m--I Zrnn, -- (-- I) 2 2F (n = 0, 1, 2, 3. • m = 1, 3, 5..). R3Zo! ,2 Hpn HarpyKeHHH O60OqKH MOMenTOM, paBnoMepno pacnpeaeen- HblM nO qaCTH oKpyKHOeTn H efiCTByOnmM B npoxoa]bHOM nanpaßaeHnH Z . 2h, PHC. 5.19. IJdtBltHJtplttleCKarl O6OßOtlKa «arpyme«a MOMeHTOM, JeficTBylOlrlM B/IO$Ib o6- pasyDefi no yqacTKy noßepxnocTH (n=1,2,3...; m=1,3,5...). 217 
218 KOMIIOHeHTbl psa HOpMabHOI COCTaBYIBIOIReI Harpy3KH MO:hKHO npe- CTaBHTb B caeaymiReM BHae: B caynae HarpyKeHH O60OqKH H(HKOCTblO II$IOTHOCTblO [Oa¢ 8pRa (COSo sin n[o -- n cos nj5 o sin o) Zrnn ,* --- mnn (n s -- 1) Pnc. 5.21. LHHHpHqecKa O60OqKa HarpymeHa no qaCTH noBepXHOCTH aBeHHeM, nOCTOHHHM nO Hne n nepeMenniM no nepnMeTpy O6OaOqKn 219 
TaKItM 06pa3OM, pacqeT TpexcIOfiHOfi KHHHpHqeCKOfi O60$IOqKI4 S onncannblX Tpex cayqasx nposOflT nO caeymtaefi cxeMe: onpeeasmT MaTpHUy-CTOa6eI (5.20) Kag CyMMy MaTpHU npn pa3- jIHqHbIX IT/ H n. B KaqeCTBe IIpaßofi qaCTH HCllOa-lb3ylOT Bblpa7:eHHfl (5.21) ... (5.27); onpeeOT KOMrlOHeHTbI TeH3opa Haiip:eHHfi Hecynx cJIOeB nO Bbtpa,'eiiHm (5.18) DU - R,1,2 ii DXA -= R,; HaXO)IT KOMIIOHeHTbI eHsopa HaiipsKeHn saiioan'eas IIo b- paKeHHm (ö. 17) BaU , aH BaXA - ; npH HeoöXOHMOCTH onpeesmT KOMIIOHeHTbl eqbopMattH HeCy- mnx caoes (5.17)  aanoHTea (5.15) An. cXA -  e. c; AaXA - - BbIqHCJIfllOT ycHdlHe H MOMeHTbI B HecytttHX C$1OflX IIO Bblpa:eHrl/O (5.19) MXA -1 --- T. LIHcdIO qleHOß papa B KaKOfi MaTpHle paßHO qHCdIy qleHOß papa s uazpHue U. 220 HaI TO.rIIIHHa aanoHHTeIfl c/2t2 »_. 2,5. I-IpHHHMaIOT, qTO 3aIIO$1HHTeII He BOCIIpHHHMaeT yCH.rIHI B cpeHHHOI IIOBepXHOCTH, Kora O60IOqKH, npHMeHeMble B KOHCTpyKKHX leTaTeIbHbIX annapaToB, HMeIOT napaMeTpbi, yoBeTBOpoHe yKa3aHHbIM orpaHnqeiiniM. I/]ciibl - TaHHI HX KpynHoraöapHTHbIX MOee Ha yCTOIqHBOCTb IIpH efiCTBlln pa3nqHblX BHeIIIHHX CHI CBHeTeIbCTByIOT, qTO TeOpHI, nocTpOeHHa Ha nepeqHcleHHbiX onyeHnX, oöeciieqHBaeT jOCTflTOqI-lylO TOqHOCTb p aCqeTOß. I-lepeMeeHH 3aIIOIHHTeJI B cpeHHHOI IIOBepXHOCTH aßfllOT B BHj napa6o»l nn npMOfi. PacqeTbt nOKa3bIBaOT, qTO paaHnaa MeKy KpHTHqeCKHMH IIarpy3KaMn npH aTHX onyeHnX IIeBeanKa (o 5 oB), Hiiora IIpHHHMflIOT rHnoTe3y npMOfi HOpMaH .rII Bcex CIOeB, pacqeTiibte 3iiaqeiiH KpHTHqeCKHX Harpy3OK IIpH TOM 6oabme KCIIepH MeHTa.qbH blX. 3ecb IIpHBeßeHbl H3BeCTHble ypaBHeHH, qbopMyIbl dI onpeeaeiin KpHTHqeCKHX yCHH HaH rpaqbuKH AaS oteiiKH BHSIIHS IIapaMeTpOB O60OqeK IIa KpHTHqecKHe IIarpy3Ku, OIIH IIO3BOaflOT BbIIIOaiitlTb IIe- oöxoßnM»ie B»IqnCaeiiHS, pe3ybTab pacqeTa yoBaeTBOpHTeabiiO CXO- lflTCfl C aKCIIepHMeiiTOM. KCiiepHMeiiTabiiafl oneiiKa pe3y.rlbTaTOB aiia no pa6oTaM aBTOpOB, TaK KaK B ny6HKaaHsX IIpH OIIncaiiHH pe3yabTa- TOB aKCiiepHMeiiTabii»X HccJeAosaiin yCTOIqHBOCTH aH60 IIpnBO- /mTCS ycJmBii»e IIapaMeTpb! KpHTnqeCKO IIarpy3Kn 6e3 HX o6ciie- IIun, aH60 yKa3bIBaOTCfl pe3ybTaTbl eHiiHqiiblX I4CiibITalml. OTI¢Oiie- nHS pacqeTii»IX 3iiaqeiiH KpHTHqeCKHX IIarpy3oK OT aKCiiepHMeiiTaab- II»X B IIeiieii»x pemeiiHsx IIe IIpeB»maT 24 %. B IIpHBeeiiii»X 3ec HIIeII»X pemeiiHsx IIpu OCeBOM CaTtlH pacqeTiibe 3iiaqeiiH B»ue OiibITiibIX IIa 40 ... 70 %, a IIpH BiiemiieM aBaeiinH OnH MOryT 6blTb MeHblIle OIIblTHblX. Tpexcaoiible o6oog TepST yCTOSOCTb, Tag me KSK OHO- CIOHble, C pe3KrIM XJIOIIKOM H oöpaosaHrIeM SbliiyqrIH TOll me qbOpMbl. Cssb MeKy CIOIMH coxpaHseTcs XO xonga, IIoce KOTOpOrO TObKO H HeKOTOpOI qacTrI IIoBepxHOCTrI HaödlloXaeTcs paccdlOeHHe. Y'pSBHeHHI yCTOqHBOCTH lqOdIyqeHbI H80CHOBe IIpIHttHiia BOSMOH(- HblX IIepeMeliLeHl4; rI BaprIaKHOHHOrO ypaßHeHrIS 9 = 0, (6.1) 221 
222 (6.5) (6.6) o. k**, kur, k v _ napaMewpi KpHBH3HbI; qù; q. = ÖF' THCHBHOCTH KOMHOHeHTOB IIOBepXHOCTHblX KCaTeJIBHbIX. (6.7) qv -- Og HH- CHa7 -- HOpMadlbHblX H 223 
FpanHnnbIe yCJIOBI4I Ral qbyHKLtI414 nanpKenfi    nepeMeenfi  cpennnofi noßepxnocTn 3anncbßaTcfl, Ta e a n  onoon- nux oaoqeK, B Be npon3Beenfi COBeTCTByX yCa Ha ne- peeenfl. HanpnMep, np neorpanqennblX na pax nepeMeennflx • + 0; V ( +¢) =0- Fpannqnble yOß fl ynKfi 7   aaßncflT OT nOCnTebnblX nepeMeenn necynx Oeß. Hpn mapnnpnoM onpan Kpaeß H CBO60nOM OTHOCHTabHOM nepeMeen necynx Oeß (O CBfl3anbl TbKO aanOHTeeM) eyeT npnn ceßyne qeTblpe yOßn: ö ö  0;  I [ O  0x0 _)0. Ecaù nocùTeabnBIe cueenù oeß neßoauonBI (où 3anbI ecTM bKOM), fl eCTKO 38eaHHBIX Kpaeß, eù necyùe 0ù CBfl3aHBI 3aHHTeeM, 1 -- V  X = E nece co CBfi3aHBI eCTKM KObKOM  Ha CBOHOM  OOp Kpae, re necye Kpa CBfl3aß Mey COO TObKO 3anoHHTeeM, HMeeM 0 0  0; Ox Ha o6nx ypaßnen (6.3) nyqenbI neapaoßannue ypaßnen T  D(I --V)Vx + - Tù  ( 1 H" V   0 924 4 rpam4qHble ycaoß4fl CBO6ORHOrO onpaHHS 060X TopRoB (9  V(9  X  VX  VX  0. BBeeM neKoTopy ynKRH XI, TaK, qTOöbl VX=X; Rä Ox« I --  V  X  . Tora ypanennfl (7.15) CaOflTCfl K OnOMy ypanenn  V  ) VaX +   V  D ( 1 --  Rä Ox «  +r,,+ 0  ( -vv) V,l- 0. FpannqnbIe yons CBOoro onpanfl o6ox gpae npMyT BnR X1  V*  VX  VX  0. Hp OCeBOM CaT caaM, panoepno pacnpeßeaennbiM no py, e opTqecoe COCTOSHe naraTb 3MOMeHTHbIM, T 1  P; T = T = 0  pemene npnflTb B . mx   X0 sm  sin ,  gpTqecoro nanpen noayqM @opMyay +  ' }, (6.8) . C C  rRe k : dR' #HO ' an nannRpnqecKnx ooqeK c opTponnblMn CaOSMH aBTOpOM npeRomenbI neannenble ypanennn y¢TOqHBOCTH, noayqenHble sHep- F@THq@CKHM M@TOOM, og--O; 0; 0, a KOTOpbI ceye K,+KI , I+B ( 1 ) P:--  (n¢-- 4*)n +«+ (1 --nW) + +G +«(;+), + [ù +,« ,+1«+ , + + + 2 (G + ERG1) (1 -- u) ] + 2 [4 + (P + Pu)a x x( c+h c+th(1_) mc+h  . 8 Koöeae B. H. n p. 225 
226 + r) L 2t261  bt _ « +  +', +,)]. X (1- vz)« - 2«214 +(F. ' k 'l- Fpanenùe (6.11) nnanecn ypanenne nnnnpnecno nonepx- noc,n c aRanno @opo (6.10) saan npne, eane na STO noepxnoc,n (pnc. 6.1). Toa nepecee- nn npnx--pemenne ypnenn yC*O- qHBOCTH, opeeflee 8HqeHHe eTpa npnTnecnoro nnpmennn n ne- noopo @op»i nepù yc,onnocTn. 3a pceTnoe nenne napep pn- Tùecnoro nnpnmennn n ncex ero enn, nyennx npn nix @op nopn ycTonOCn, I6ùpT BHqHH, COOTBTCTBy HHM@Hb@My Pùe. 6.1. K pacey a ye- ypoBH HepFHH pBHOBeCHO COCTOflHHfl TOqHBOCTb o6ooe np onpeeneMoMy ypaBHeHHeM oceaoM cmaT =K2+K1 1+  2 «2a2(  1 )  (n  - 4,)  (--n,)g+«na [( +) (g+8,)+ + (K + K,D) ng + (ù + vD) «ng + 2 ( + Etl) ( -- ) x {+) +(2«+tl+tO4oa¢ [«(+)+ nl-*«(+9- (') pae (6.8) ... (6.12) a onpeee p* pem a B  ce- 1) ac no nyo o oöpaae m no ypaem (6.11) onpeem ecepnym 8" 
H hKeCTKOCTH npH HarHöe IecyHx C$10eB '=20+Ö ---z'i+ l-)' Roc, aoqHo 6mxgo conaJlaIoman c peyma, aMH HCnU*aIH. 228 6.3. ¥CTOBqHBOCTb IHJ1HHJIPHqECKHX OBOJIOqEK llPH BHEIIHEM JABJ1EHHH HpH paBHOMepHOM pacnpeheaeHHH jaBIeHHS no 6OKOBOfi noBepx- HOCTH CBOHO onepTofi OOqKH e 3OTpOHIMH HecyHMH KpHTHqecKoe aeHHe qp [9] HaxoflT H3 HefiHOrO ypaßHeHH D (1-- H V ' s EH H V),+  )V%l+ R ax a (1 d 0 +«( + ),o, pemenne oporo  1= oslncos aeT 5e3pa3MepHoe KpHTHqeCKOe aßeHHe q, [ + k ( + n)] ( + n ) V  n  [ + k ( + n)] + n  ( + n)  " Hpn O3HaneHnnX k, , , , BBeReHHbIX B n. 6.3, KpnTnqecKoe Rae- nne naxoam no opMye q* E HO HHHMbHOe 3HaqeHHe q* HaXORT pH BapbpOßaHHH n. Hpn nnemneM pannoMepno aaennn nennefinoe pemenne, npe- OeHHOe aBTOpOM, X RHHHpHqeCKHX 060oqeK CO mnaHrOyTaMH yqTbIßaeT X ncKpeTHOe pacnoomenne n conTcn K TpeM ypan- HeHHM: r + 2  B (1 + ra) (1 - n*) +  + 01  + ¢ n ,-  + r r + ¢  (1 -- ,) sin   + 9  ¢ sin   + % i=0 .  mnxi __ a  __ sin; (6.13) xsm + 18(1 )sin 3mnxi -- 2(1-- 2,)-- 2, + 2B1 [(l +ra)(l 229 
-- 2---ä(l -- 1))] + "q--F(1 --'q)+O+ 2% äl sm -- - =0 
r  [ 9a  1 2 mxi 3mxi ù a  !  x sm  +.6   cos  +  4  n -  n - 4)]x cos +2«  sù,+ (l - 2)sin x [9 3m.xi ] mzx, «' .  x,}; (6.19) X sin l 2 sin t 2sm t M  + M  + M  + Ma + M» = O, (6.20)  COS2 l ' r M = 4   cos , 6aa   162a  3mnxi 72a« mx +  g @ 8 +  aaa ; sin 7 aza- sin  X 3mxz 16a  -  mxi • a2 l ' 2 2 2 42 2  2--4 2 1 2( )2 -- -- 2 a  2 g  + F 162 , mxi 3mgxi 2a2  2 •  mnx  sm  sin 1 XSlfl + ff3 18a4 9a--- 2si n mgxi 3mgxi 1 2 X  aa  sin l 4 sm  +4Xsm  mxa. l ' 232 233 
1  sm   + q& c  ; sin   + O6oanaqen14 re Ke, qTO B ypaa14e1414x (6.13)... (6.15). 03 [' e s P«c. 6.5. Ba«Hn«eyAanHen« Oö¢MIOqKH Ha OTHOCHTe$IbHyiO Be- $IHqHFIy KpHTHqecKoro AaB$1eHHgl IpH t:epaßHOMepnOM narpy>KeHHn iipH   l, ht  12,  = 2,5 X X 10-a: 1 --a  1,4"10-; 2 -- a  3,3 X XIO-; 3 -- s  6,0-1ff - i PHC. 6.6. BIHHHe OTHOIIIeHHH TO$IIIHHbI 3aIIOIHHTedla Ha OTHOCHT$IbHylO qHHy KpHTHqeCKOFO JaB3IeHHff IIpH panoMepoM Harpymennn npH  = I, = 4, 6 = 2,5.10-a: 1 --a= 1,4"10-; 2 a= 8, 3"10-; 3  ' = 6,0"10 - YpaßHeH14 (6.18) ... (6.20) pemmoT TaK Hie, KaK ypaß14e1414a (6.9) .., (6.11), HO npla u14cae noayBoaI BOab o6paßyomefi m = I. XapaTep BJIH;IH14fl napaMewpoß 050aoqvm Ha p14T14qecIoe xaßJiel-I14e TaKOfi Hie, KaK np14 paBHOMepHOM pacpeeaemm aBJeH14fl riO nO- BepXHOCT14, HO Kp14T14qeCKOe Aaß$IeH14e H14Hie. OTHOIIIeH14e Kp14T14qeCK14X 14arpyaoK 0ö = qö/q* yMe14bmaeTc c pOCTOM meCTOCT14 06OZOqKm 3aß14C14MOCT14 Oö OT ya14He1414fl 060aOqK14 k = I/R, OT14OC14Teab140B TOJIUL141-1bI 3flHOJII-I14TeIff hg  c/[2 140THOIIIeHHff TO$1IH,1414 14eCy14X COeB t np14BeenbI Ha p14c. 6.5 ... 6.7. IIInaHrOyT B cpeHeM ceqeH1414 yBeI14q14BaeT Kp14T14qecKoe aßleH14e, CKOfi Harpy3K14 tlp14 BO3paCTaH14H KODqb14KI4eHTa HieCTKOCT14 ql .I C14MMeTp14qHblX 060IOqeK Ra - 200 MM C HecylR14M14 COflM14 143 16A'i TOZttmnO I = 0,5 MM, noApenzennbx OH14M mnanroyToM B cpene ceqen1414, noKaaano na p14c. 6.8. Idaenen14e HieCTKOCT14 mnanroyTa co- npoßoxtaerc CMeHO dpOpM noTep14 yCTOq14BOCT14, np14 »TOM MenVTC BJI14/H14e HepaBHOMepHOCT14 pacnpeAeeH14 BHemHero AaBeH14 B KO$1bKeBOM HaripaBleH1414 pacCMOTpeHO H. I-I. CeMeHIOKOM. I-IoKa3aHO, 234 qTO np14 HarpymeH HepaBHOMepHblM BHemHHM aBaeH14eM pemeH14e AOmHO ytI14TblBaTb MOMeHTHOCTb OKp14TriqecKoro COCTOSH14S. paBHeH14fl yCTOIqHBOCTH C14MMeTp14qHOI IL145114H2p14qeCKOI 060- IOqK14 C OpTOTpOHblM14 C0M140THOC14TeabHO qbyHKIm 140pMab14oro 1 --= 1,4-10-; 2 ---, = 3,3.10-a; 3 --s = 6,0-10-* Pi4c. 6.8. B.rIHffHHe >KeCTKOCTH mnaHroyTa Ha KpHTHqeCKOe ,aß$1eHHe 235 
S 1 -- (l)/1-q-c A_t,(.2.) t2"{-c _L 2 D(.3) • t2 -F C 1 AO - co C11C22 -- C C66 (i, ] = 1, 2, 6); C. ).. _- ](k)h:ù, "-',lY)('k') = -10ti(k)hk," hl  tl; h, = t,; h3  c. BHemHan cuaa 3aaeTcfl  BHe aßeHHfl, flTOflHHOFO Bb 06pa3ymefi u u3Menammeroca B KobeBOM nanpaßenuu no 3aKony q=qo(l +ecosn0). an pennn ypaßnenn (6.21) neo6xoRnMo naT RopnTnecne naaennn BnyTpennnx cna. x naxoRnT n annefinsIX ypanennfi pa- HOBCH oo Oo o + s2  ) -- o = O; O*Wo O'Wo  02o (1 W 2e cos n0) = 0; O'o  2 O'¢o - O'¢o . o*o (6.22) Fpana»e youa o 0, o0" ¢o 0, ¢0, Wo  O,   M ycOBgnM yRoeTopn w =  (a + c cos n0) cos fr0   (cn + bcos n0) sin k 236 w --- F, F, A,,,,, cos Cm« COS nO; I-IpIMeHIOT MeTO By6HoßaFaaepKUHa, uorop»IU npuBORHT K CUCTeMe UHefiH»IX areSpauecuux ypaßHeHUfi OTHUTebHO B ¢yHKUU nporu: uAI--  AI [«o (i, ], m) mq -- Po (i, j, m) mq] --  AI_ù X m X[a/ù(i, ], --n, m)mq--lù(i , 1, --n, m)mq]--  A=I,ù x m x (i, /,  2n, m) m=q -- O, (6.23) x (« + ,?) 237 
238  .to  o  e 2.  Pc. 6.9. BaHe cTeneH HepaBHoMepHo- CT pacnpeAeaeHHu BHemHero AaßaeHH no nonepeqHoMy ceqeHH o6oaoä Ha KpHTH- qecäoe aeHHe HaFpy3Ky BospacTaeT, yBeIHqHBaeTc H HeoöxO)HMOe qHC2IO qIeHOB paJa. [],zI.q KOpOTKHX OOZIOqeK MOH4:HO oFpaHHqHTbC O[[HHM qZIeHOM 6.4. ¥CTOBqHBOCTb I[HJIHHAPHqECKHX OßOJIOqEK, HAFPY)KEH H blX ¥CH$IHIMH, JIEflCTB¥IOIIIHMH BJO$1b OCH OBO$1OqKH, H BHEIIIHHM }IAB$1EHHEM CTaHOB$IeHO, qTO KpHTHqeCKHe Harpy3KH rpH OBHOBpeMeHHOM CTBHH BHemHero )laBaeHHS H CH{HMaIOIILHX OCeBblX ycHaHfi He MOryT onpeAeaTbCn d-IHHeIHbIMH COOTHOmeHHMH BHAa p*/pö + q*/qö = 1. I-[oFpeRIHOCTB OK3bIBeTCfl 3HqHTe3"IbHOII npH He6OdlßIOM BHelIIHeM /taßaeHHH, KOTOpOe xapaKTepHo AaS npaKTHKH. B HeKoTOpblX caytlax CBfl3b )leI'CTByIOIReFO BJ(MIb OCH HaHpHeHHa H KpHTHqeCKOFO MO»KeT 6blTb peAcTaßeHa OMaHO IHHHefi. Ha ypaßHeHHS (6.1))laa KpHTHeCKHX HarpyaoK noay,eHt [19] ABe qbopMyaBI Aas BBIqHCIeHH OBHOrO BeCTHOM ApyroM. EcaH ycuaHe, AeficßyolRee B)lOab OCH, COCTaBIIeT 3HaqHTe3bHyO AOHO KpHTHqeCKOFO yCHHfl HpH OCeBOM CmaTHH, TO pacqeT cIeßyeT BeCTH 0 ypaßHeHHO -L 239 
YIpH MaJIbIX 3HaqeHI4flX ycHaHfi, /lefICTByIO1RI4X B/lOJIb OC14, 14 npeo6a- /lammefi pou/laßaeHHa ce/lyeT 14HOJIb3OßaTb ypaßHeHue » n P*+(n--l) s[+e(mu+nZ]+ x 8ma 4  (mn   n )  ( + ) - HapaMeTps p*  q* CBfl3flHbI C yCHHflMH, efiCTBymM BOb OC Pp, P*  Et (c + t) HapaMeTps o6oaoq Z, s, e, g npaeeu a n. 6.2. yqmy CXOHMOCTb C KcnepMeHTOM, oco6eo npn cpaanTeabo MaBIX BeHHX oöe¢eqßaeT peeHe TKHX ypßHeH: i=0 I r X sin  T    (1 ) sin mnx T 9   sin 3mnxi -  q . ca xi 18« a .. Xi . 3Xi ]- , I (6.24) --q -£1; E (-  « 2sin mnxi n 4---4 -w- x 1 a-p« B I (1 - Fa) 52 +  01 - (6.25) (6.26) 240 r X 162q - -- 324] 2 2 Sii12 l 361  sm  × X . 3mxi 72a 4 mxi 3maxi c¢ 2 s,n n t- aaa (5¢x -{- ]) l  sin  sirl l F  X ,2 x («-- ) « + - M2 : 4tx2 1 2 2 a "--  4 a a I- 2c¢2 ,, 2 / 2 ] 4 + h-aù ( «- n)± 1 • YpaßHeHl4I (6.24)... (6.26) pemaioT B nopse, 143aOeHHOM  n. 6.3. 9HeprH eopMau BSIqT no ypaßHeH (6.16), K OTOpOMy npnöaßa ypaßHeHne, onpeReamee pa6oTy CMa- mefi Harpy3KH Ap = p*a (2+ 2¢2). O603HaqeHfl COBCTByT npBeAeHHIM K ypaßHeHflM (6.9)... (6.11). PeH ypaßneHfi (6.24) . . . (6.26) ha oSoaone c napaMeTpaMn, xapaKTepHbIM S peaanux KOH¢TpyKRfi, npßeenu Ha pc. 6.10, 6.Il. Npn MaablX RaßaeHfix (q  0,5qp) Kpßble MemT fißHO upa- eHHbIh HHefiHbIfi xapaKTep, np 6oabmnx AaßeHX 3aBCHMOCTb ey p*  q* 6naa K HHeHO. TO yoßeTBOpHTebHO cora- CyeTc C 9KcnepnMeHTOM. 241 
eoro mo Aae p oc- qe « pa3qo ;e«TOCTb]O =0,09, = Puc. 6. 1 I. CBab MeKy KpHTHqeCKHMH narpya- KaMII p* H q* )Ifl HeCHMMeTpHqHbIX o6oaoqeK IIpH %' -- 0,73 H . = 4 E [-l (1 2 mgxi « -- 21¢ ) sin  + r + 91 -, sin  sin + fr2  q (1  -- 4,) [-1 • 3maxi - a . maxl -[ max, + en  ¢ sm  +  (1 -- 2n¢ ) + sn j sin  + 'Wsn' --  qö: (6.27) « l 1 [ -- -- p; =  * + * --  --n(-n,)+ *+n *+4(« +n,)_ XCOS 2 2rruxi I9 . 3tmXi c (]--2l,)sin ra ] 9sin l  Zsin +2 $sin  xi « ..    -- qo, (6.28) ocaeanee ypasnenne n ero osnUnenTm eonaaa e ypane- (6.20). AaropnTM pemennn ypaunenn TOT e, qTO n aa ypane- yCTORqnOeTn npn OCeOM emaTnn. Dneprnm ReopMaRnn mnnc- no ypasnennm (6.17),  mopoy npneoeannnmT ypanenne aas pa6oTbI enMamme cnam AS» = 4 -- ¢)- 243 
Pe3y»TaTI pemenHn ypaßneHfi (6.27)... (6.29) npn BOSMOZXSlX coqeTanx napaMeTpoß o6ooqeK npecTaßebI a pc. 6.12. FIone. ene KpHBbX p*÷qö TaIOe x<e, gag B cynae oceßoro cX<aT  paBO. PnC. 6.12. Cs3 eKy KpHTHqeCKHMH arpy3KaH p* H qö np arpyKeHH oceßofi CHIO H lepaßHoleplbil meuilHl 2aßieHHel o6oioqeK: a -- caaeTpnbx (v  0,09,   4); 6 -- ecaaeTpnnbx (v  0,73,   4) Mepnoro Bemnero 2aßaenu. IoJzHqecTBenoe pa3Jmque oöycJzoßJzeno CnUKenHeM gpTqecKoro aBzen BCJIeCTBHe nepaßnoMepnoro ero pacnpeezenHn no IIOBepXHOCTH. 6.5. ¥CTOBqHBOCTb IHJIHH)IPHqECKHX OßOJIOqEK rlPH H3FHBE H KPYqEHHH FIp6eoe pemene saaqH yCTOIqHBOCTH IIHdlHHApHqecIOfi O6OaaOq npu usru6e, a Taime npu Haru6e  OCeBO CmaTUH npußeAeHo B pa6oTe [19], re ypaßHeHHe (6.8) paßHoßecun ImUHpqecio o60- oqiH cueTpuqoro cTpoeun c aaeriUM aanoaaHTee npearaeTca pacnpocTpaHUTb Ha O60OqIU HeCUeTpqHOrO CTpOeHHfl aaeHofi Io»qbOputmeHTOß x<eCTIOCTm Tora ypaßHeHUe (6.8) npHMeT BU (I-- Boc V2)[ (l--vö)B* 0aw + DoVSw -- V' k [  öw tt- + öw T +2Ow T, ) ] : 0, (6.30) 1 1 rAe D* = Dx + Dz +  B (c + t -- 2a)  +  ßz (c + tz + 2a)  + + +B« + B; Do = D, + D + (B, + B) [ " 4» +  (B + B)] + + B1 BB 244 W = sin -V t¢ cos-u y" o FIoce rlo)cTaHoßI¢rt pn)Ia B ypaßnenne (6.28) noynaeTcn 6ecionennan eneTeMa nnenxx ypaßnenn OTnOenTeno aMnnTy) rapMonHI eoeTaßnmtttnx npornöa fn. Onpe)enTea» eneTeMx F0 -- 1 0 ............ --2 F --1 ............ 0 --1 F ............ 1 0 ........... --1 Fn_x --1 ........... 0 -- 1 F p*]. 245 
///% Pc. 6.13. 3asncnocTb texIy OCeBblMH yCHJIHIMH H HarHöam- IRHM MOMeHTOM npH paanqnoü )KeCTKOCTH Hpi OHOBpeMeHHOM narpyKennn OCeBOfi cHMamiefi Harpy3Kofi H 3- FHöaHM MOMeHTOM pemeHue ypaBne- uu (6.30) npeacTaßeT co6ofi Hy 3flBHCHMOCTb m* OT p* (CM. pUC. 6.13), T. e. pacq MOnO BeCTH nO ypaßeHU m*/m ö + p*/pö -- I. (6.32) rae mö, pö 6e3pa3Mepnie ce aaea r6amero moMenTa H HaupeHHfl CaTHfl, uoyqeHHbI npH pa3ebHOM HarpymeHHH. Pacq no ypaBHeHm (6.32) ony" CTHMO yHpOCTHTb, yqHTbIßfl yCTH0- BeHHym np pemeH Bblp ameHHfl (6.31) HeHaqTebHym paHy B Be- = p, TO  (6.32) ceyeT m* + + p* = pö. ; TaKHM oöpa3oM, pHTHqecoe COCTOflHHe npn n3rH6e MOMeHTOM, a TaKKe np OHOBpeMeHHOM HarpymeHH OCeßOfi narpysgofi  M0- MeHTOM onpeencn MaKcHMa£bHbIM HanpmeHHeM cmaTH, nOTBepmaeTc pe3y£bTaTaMH »cnepHMeHTa. CmHMaman HopMabHa cHa H H3rHöamHfi MOMeHT B ceqeHsX o6ooqH MoryT BO3HHKflTb npn HepaBHoMepHoM pacnpeezenH oce- BOfi CH£bI nO TopKaM O60£oqKH. B oKpHTHqeCKOM COCTOHHH MepHHO" HabHOe ycze, pacpeAeaeHHoe B oepeqHOM ceqeH o6ozoqK, T = --- P @  cos , (6.33) re P 3uaueuHe OCeBIX cHMamHx yCHHfi, efiCTBymHX B TOp" aOBOM ceeuHu oSoouu;  = Pa  uaruSammufi MOMeHT, pacnpe- eeuuifi B TopOBOM ceueH, a a KceTpHCTeT npuoenHn cui, I. e. paccTonuue OT UUUU paßoeüCTBymefi o ocu 246 247 
Pc. 6.14. BnHne yaHeH n OTHOCnTebHOß TOHHU O60- aOqK Ha KpTqecKoe ene npn Kpyqen MeTpa KpHTHqecI<oro i<acaTenbHoro HanpnKeHnn CBO)HTCfl K peLue- HIO Tpex aireöpalqecKHx ypaßHeH OTHOCHTeJIbHO T, A1, A: ;- 2A,(__I) (A+n  B s[l+l(A+n)] 2c - , A2 _{_ n2 2 [ +(n+-)l (6.36) A = me A, A--napaMeTpbI BOJIHOOöpa3OBaHHn; m, n--qHcna BOJIH, m=l, 2, 3..., n----2, 3, 4... 248 l'Io HaHMeHblIIeMy 3HaqeHHtO re* onpeaeaflr I<pHTHqecI<oe 3HaqeHHe pyTmero MOMeHTa mp = aninEt c + t V-  " 3Haenne ¢, riaxonT I43 (6.36) rlocTarIoßIOh B nero pasnmIrIix eoeTann nena BOnn. 249 
250 251 
I-Iocdle BBeeHrtfl HOBOB nepeMermofi x, TaKOfi, qTO ypaßnenne COBMeCTOCT eopMaKu unTerpupyc OTAebO MOo  Hanoßnna, OCTabnbm ypaßnenn na (6.37)COBMeCTnO Byöuoßa. Bn pemenn B6npamT B ¢opMe wfX--sin x n . ln r .  cos sn « ' r' x cos Y • (6.39) X  Z n'x sln  sn a Bxpaennn (6.37) yaozeTopnmr ceM rpannqnIM yczonnu; Bbx6npamT ns ycoßnn MHnnMyMa gpnTnqecKoro aßennn, Rn gOTo- poro n3 xapaKTepncTecgoro ypaßnennn noyena opMya 4B [1--' D] q'='roOatg« [ tg« (D+D)+Da+ O«J' (6.40) rae D = n (n -- 1) (m a + me) + 2  (2n -- 1) sin a ) ma -- 8za; +z Ba m+n--4 2B(2n+l) ; Da = Fadxo + Fdn + Fadx + Fadxa; D4 = 2 (c -- ) A  -- caeA; c 2GcaA ; D = (c -- cc«) A  -- 3necb m =  (p + 4n/ ) (i = 1, 2 ..... 8); px = 2(n t-l); p = 2; Pa = 2nx + l; p =2ha--l; 6Pim i z, (+ l/) (i 1, 2, 3, 4); 2, 3, 4); n  n I B, = 2 (ù,--,ln«) ; Du = (4t2/2 -r t21 -]- nl) ( --16n2/¢2)- 11 (2n I --1)UXl/ . (+ 1ù1y ' 252 t/ (2n I -- 1) (El 2 -- 16ng21 2) q- 4nlt/ (4t21 2 ---nl  -]- n,) ,1 . Ba = (Z + 16n/t)  ' a a -- e--n, __ e--(kt+k+n) ; k 3 a =  -- « + ,; a =  - 2,« + ,; al0 = e -n -- e-- (2k+nO ; f12o --- e"& -- e--k'; /21 = [e " -- e- (k-ù,) ] (I -- 253 
1 c2 = 0,25 ([1 -- [2) [3D; c3 = 2D; c« = ( + ,) D; / 1 = ö; c = , - ) D; c = , +  + ) D; c t . t . B=, 2=, = ; D=  ; t' ù(--) .= sin 2  sin   2 2 n2 1  n  +S [16.(n-- 2) -- l(nx -- 2) z +4 , +, ]; A2= n sin « m2 • PeeHne »TO 3aaqn 3KeHepMeHTbHO He npoßepeHo, Ho coo- erazenne e peyz»TaTaMn neniTannfi mapnnpno onepTiX o6ozoe HO3BO HOFTb qTO KpTeKoe ßeHe» BbIqeHHOe opMyze (6.38), ne ime oniTnoro. CneTeMa ypanenn (6.4)azn eepnaeeofi o6ozoan [10] noepea- eTOM npeoöpaoannfi e noMom»m nponoz»nofi rapMonnaecofi ¢ynann eOanTCn  ayM ypaHennnM, nnTerpnpyeMiM [191: V  1--V  . Pemee neporo ypae (6.a9) my  e VXl =--, 2D  d + H  2EH re o6osnaaennn coorercryr npneaennu  ypanenn (6.4). o peeHHe KCepHMeHbHO He poßepeHO. n noororo CBO60HO oneproro no Konrypy cepnqecKoro cer- enra pnrnaecoe azenne omno narn anazornano. Hapaerp Z  sro czyaae naxoar ns xapaRrepncrnaecoro ypanennn In (Xt) = O, re In (Xt)--ynunn Beccezn nepnoro poa n-to nopna; n  qnco BOH, o6pasynxcn no oKpymHOCTH B OCKOCTn, noh ocnoßann; r panyc OCHOBaHHa. 254 XaparepHcTHqecgoe ypaBHeHHe (6.40) MOIKeT 6bITb ncnob3oßai4o  npi4-pyri4x Kpaesbix yC3OBI4nX, ec314 oci4oßi4an BMTI414a I4e 3axBaTb- BaeT secb cerMei4T, qeMy COOTSeTCTByeT Mni414Ma3bi4oe 314aqei414e qup p nepBoM Kopi4e ypaßi4ei414 (6.40). 11.7. ¥CTOBqHBOCTb KPHBO.,qI4HEflHblX HAHESIEfl Kpi4Ti4qeci4e I4arpy3i4 pyroo nai4eai4 npi4 pa3aii4qi4ix cyqanx Harpyei414n I4 oni4pai414n MOKI40 noyqrT I43 ypaßi4ei414n (6.4), cai414oro ooceo y nepeeme , ao, qo npor6 oepTOM pae HMemT 02Xl 041 08X1 06onaqennn CM.  ypasnennnM (6.4)... (6.7). 1. PaßHoMepHoe oceßoe caTne H aßeHne no BHemHe noßepxHo- eT CBO60HO onepTofi naheen. Ony n» narpyao npn »aannn pyrofi MOHO HflTH H3 ypaBHeHHfl : 1 + k (n  + mlZ ) (n2 + m2/2)2 + l n  .  12b a (1 -- T) zn n3ocofi co6ono onepofi nzacnnbi, cmaofi no opon po- KaM, D [ I +  (nz + mz/t)] (n + m/) Pv   [I   (n + m/)] mz/ 2. CBO60HO onepTan nane narpyena npoobHIMH CHMa- nn ycnnnn, panoepni aßeHHeM H KacaTebHIMH cHaMH O KOHTypy. Paannle KOM6HHaRHH KpHTHqecKHx yCHH pp, Bp MOHO HafiTH H3 6econenofi CHCTeMbl HHefiHblX areöpanecnx pannennfi b z (m, n, i, ] 1, 2, 3 .... ). 255 
I3 »THX ypaßHeHHfi MOHHO HoJIyqHTb BbIpa:KeHHe  napaMeTpa Ka- CaTeJIbHbIX yCHI HI:I T* = 3262T]Or4D,). (6.41) f]31I HeqeTHbIX CyMM T* = /AAAA.2/A., r)le 6x = 0 npH m =/: 1, 6mx - 1 np m = 1. HpH pa3)ieabOM HarpyeHI4H no (6.41) BbltIHCJ]IIIOT JIH60 Pp, 3H160 qv" 3n n3ocgofi nacTni,ibi npH ygaSaHHOM onHpaHHH KpOMOK KpIITHIqeCKOe aHaqeHHe OCeBblX yCHIJIHfl, HpHIJIOKeHHbIX K KOpOTKHM aameMeni,ibiM KpoMKaM, onpeenmT no dpopMye Pip tD [1_ q-_0k [n +. (m Z- " 1)/ l [n_-]- (m -- 1)z/2lZ l1 ---  [ 1 -}- k In  -- (m -- l)Z/] 2 (m  -- 1)1  x" --- ml) --- q__ 1 q- 0k (n  -- (m -- 1)/ ) (n  -- (m -- 1)/)  ] l.q-k(n.q-(m.q - 1)z/) 2---- ])-ß.  J " 4. l-laHeJIb, eCTKO 3a],eMJei,ii,ia no npnMoJHHefiHbIM KpoMKaM H CO60I,IO onepTa no KpHBO£HHefiHbIM, Harpyei,ia C:KHIMaOm, HM yCHIJHIMH H BHemHHM 2IaBaeHHeM. KpHTHqeCKHe 3HaqeHIH CmHMaOmX 256 6.8. ¥CTOBqHBOCTb IIHJIHHIPHqECKHX OBOJIOqEK C PACCJIOEHHIIMH I-IpHIHflTO, qTO pacc1oeHHe HMeeT MeCTO IIO BCefi rIOBepXHOCTH 060- OqXH Ha rpaHHnle c OHIH Ha HecyHX CJCeB. PaccJmeHHy TpexcJmfiHym n:HIHHIXpqecxy O60oqxy r OKHO Hpe2CTaBHTb KaK /IByXCJOfiHy, O2HIH HIa CJOeB KOTOpOfi HMeeT napa- MeTpbl OTCJOHBmeroc Hecymero cJo, a pyrofi- napaeTpbl Tpex- CJOfiHOrO naKeTa, y KOTOpOrO O,HIH HI3 HecyuIHX CJIOeB OTCyTCTByeT, r. e. ero rapaMeTpbl paßi,ib HyJHO. CJIOH TaKOfl ßyXCJ]OfIHOfl O6OJIOqKH t}KBHI,HCTflHTHbl, HO aasopa Mexy COMH HeT. KacaTebHbm yCHIHI C OAOrO CO a pyro nepeaßaTbca e MoryT. 9 Koöee B. H.  p. 257 
258 Hecymero HecylRero 9* 259 
F.aaea 7 flPOEKTHPOBAHHE TPEXCIOFIHblX fl,rlACTHH H OBOJIOqEK 7.1. OBII[HE HPHHI1Hflbl flPOEKTHPOBAHHJt I-IpoeKTHpOBtttHK BcerAa cTpeMHTC CO3)IaTb OI]THMad]bHyIO KOH- CTpyKI/HIO, HOgTOMy I'IpOeKTHpOBaHHe B KaKOffI-TO CTeI'IeHH IBJIIeTct OI]THMabHbIM. {HaKO B pnAe cd]yqaeß TeXHOd]orHqecKHe H BbIqHCJ-Itt- TeJIbHbIe BO3MOH¢HOCTH oFpaHHqHBaIOT npHMeHeHHe MerO)IOß OnTHMrt3a- UHH. HanpHMep, npH flpoeKTHpOBaHHH KOHCTpyKIIHI H3 Tpa)IHILHOHHblX MaTepHaJoß rIpoeKTrtpOßlHK BapbHpyeT TOJIbKO reoMe'rpHqecKHe i]apa- MeTpI KOHCTpyKIHH, a xapaKTeprtCTHKH MaTepHasla, KaK npamo, IqpHHHMaeT 3aAaHHbIMH. B 6OJIblIII, IHCTBe cJyqaeB CO3)IaIOTCfl KOHCTpyKILHH, y)IOBJeTBOpIO- IIHe orpaHHqeHHflM nO Hecym, efI C[IOC06HOCTH, npH :gTOM npoßepIOT COOTBeTCTBHe 3aflaCOB flpoqHOCTH, yCTOflqHBOCTH HJIH HHbIX xapaKTepH- CTHK HeKOTOpOI BbI6paHHOI KOHCTpyKILHH 3fl,flHHbIM Tpe6OBaHHIM. ECJIH TH Tpe6OBaHH He BbIFIOHIIOTCI, TO nepexoAT  pacqeTy HOBOrO BapHaHTa KOHCTpyKt[HH. HHbIMH CJIOBaMH, OCHOBHbIM opyAHeM THpOBI.U, HKfl C£yKaT HHTyHILHI H O[IbIT, fl He t[eeHaflpaßJleHHbil [IOHCK. /eTOAbl O[ITHMH3flI][HH [I03BOJIIIOT flJIFOpHTMH3HpOBflTb npoIeCc THpOBflHHI, KOHOMHTb MflTepHflJI H ,OöHBflTbCI CO3,flHHI KOHCTpyK- I][HH MHHHMflJIbHOI MaCCbl, flOßbILtla ee :9geKTHBHOCTb, »ICflJlyaTa- IIHOHHbIe H TeXHOJIOFHqecKHe xflpflKTepHCTHKH. Pfl3BHTHe H flpHMeHeHHe MeTO)IOB OIqTHMH3flItHH E nepByo oqepe)Ib 06ycJIOB]eHO yCJIOKHeHHeM 3flI, flq H LIIHpOKHM BHeI, peHHeM JIeKTpOHHO-BbIqHCJIHTeJIbHOfI TeXHHKH )VIn HX peLueHlm. B pa6oTe [3] npviBe)eH aIropHTM onepaImfi npn npoeKTHpoßauml Tpexc,rIOHbIX I]J-IflCTHHOK H o6o,rIoqeK c 3flflO,rIHHTe3]eM pfl3HqHbIX TH- HOB, KOTOpbIfI BKJIIOqfleT: 1) onpe)ieeHHe npHBe)leHHIX KeCTKOCTHbIX, IIpOqHOCTHblX H MflC- COBIX xapaTeplCTl sanommTeJm; 2) onpe)ieaeHle KpHTHqecmx HarpysoI H npoßepKy oöIItefI yCTO,- qHBOCTH; 3) onpe/teJIeHle HanpXeHHO-)IedpoprHpoßaHHOrO COCTOHHn CTIrI (lal 06OJOqm 0 I npoßepIy ee iaa npoqrmcT; 4) pflcqeT MeCTHOI yCTOflqHBOCTH 9JIeMeHTOB [IJIflCTHH HJIH O6OJIOtIKH I l]poßepKy BblrlO¢lHeHHI yCJIOBHfI coxpaHeHrl HecyntefI CnOCOöHOCTrI flpH floTepe MeCTHOITI yCTOIIqHBOCTH :gJIeMeHTflMH Tpe:XCd]OIHO KOH- CTpyKI/HH; ) yAOBJeTBOpeHHe KpHTepmo npOqHOCTH aanOJIHHTeJ rl CBarI c HeCyIII, HMH CJIOIMH; ö) onpeeIeHHe napareTpoß TpexcJmflHIX nIaCTHH H 060IOeK, yAOBJIeTBOpoIItHX yCJIOBHIM 1... 5. AHaJII43 rlpI4BeAeHHoro aJIrOpHTMa CBI4IeTeJIbCTByeT, qTO 3aaqa BbI6opa OnTHMaabHblX napaMeTpoß Tpexc.nofHbIX naCTHH H o6oaoqe 260 261 
l-lpH O1]THMH3aILHH napaMeTpoß TpexcJOfiHblX nJ]aCTHH H o6ooqeK Ha qba3OBble H ynpaßme nepeMeHHble HaKJlabIßa3T orpaHl4qeH THrla paBeHCTB H HepaBeHCTB. I'HMH orpaHHqeHHMH npH CTaTHqeCHOM HarpyKen MoryT 6bITb ceye yCJIOBHfl: orpaHqeHH Ha yC gag np o6efi, Tag H npH MeCTHO nOTepe yCTOqHBOCTH, T. e. orpaHHeHn BHa p HepaBeHCTBa  MagCMabHO BO3MOHbIX anpmeHfi B Hy. x caox, T. e. orpaHeHH Ha npebHle 3naeHs HanpeHHfi B MaTepHaax, H3 gOTOpIX H3rOTOBeHI Hecyme con, c yqeTOM Te. nepaTyp HarpeBa: Fe «[n i gKBHBfleHTHOe HanpmeHHe B i-M HecyeM coe, onpe. eeHHOe no KflKOfi-H60 TeOpHH HpOqHOCTH: OFpflHHqeHH Hfl MflKCHMflbHO oHyCTHMy eOpMflTHBHOCTb CTHH HH OoOqKH HH ee eMeHTOB: i  i non,   i non, Vi  i non; HepaBeHCTBa, CB3hIB MKCMbHO BO3MOHbI Hanpe- H B 3anoHTee c eCTByM  9KBBaeHTHbIM, T. e. 0rpa- HHqeHH Ha peAbHble 3HaqeHH HapfleHH B MaTepHaax, H3 KOTOphIX H3FOTOBeH 3flHOHHTeb: TeXHOOFHqecKHe OFpflHHqeHH, o6yCOBeHHble BO3MOHOCTb H3FO- TOBeHHfl TeX HH HHbIX aeMeHTOB TpeXCOfiHO HflCTHHKH HH O0- OqKH. TH yCOBHfl MOFyT 6bITb HfloeHbl KflK Hfl THHbl HeCyHx COeB H 3anoHHTefl, Tag H Ha reoMeTpHqecKHe pa3Mepbl naCTHH OooqKH B OM; KCHyaTaHOHHble opaHHqeHHfl TpexcoHblX HaCTHH H o6o- oqeK; orpaHHqeHHfl o6ycoBeHHMe pa3HqHMMH cneHaZbHMMH Tpe60- BaHHMB. OCHOHble ypaBnenHn cBflablßamT ¢aaoale epeMenHble c ypaas, BMH yHKHflMH H BHemHHMH Bo3eCTBHflMH H pacqnofi MOam, B MaTeMaTHqKO OpMyzHpoBKe aaaqa OnTU' I [; /(h, u)0; g(h, u)0; RRo; flflo; ppo; ...}; L (h) u = q, re p =p(h, u); R = R(h, u); xapaTepsye Hecyy CnOCOöHOCTb Tpexc£oHofi pTep aqecTa npoeKTpoau; oFpaHHqeHH THna paBeHCTB H HepaBeHCTB, HaK£abIBaeMbIX Ha ynpaß- Onpeene ypaaeu MeT, uanpMep, Ba (5.14)  OryT 6IT sanca»I B onepaTopuofi opMe, re pc. 7.1. Cxea pacneTa Ha »BM napaMeTpoß onTaabofi TpeXC.rIOfiHOfi naaCTHHKH HH 060- OqKH: H -- 6oK nauaoro p6nmen; B -- 6OK Oopunpoßan rpanenTa ynpaßmefl Bu, v, w --6oK pemennfl aaaqH opeeeHfl paueTpoa nanpmenno-e0opunpoaannoro Hfl TpeXCOHO HaCTHH HH OOOqKH;  -- 6OK cpaanenn eICTByIOtIIJX Ha BeKTop 0a3OBblX nepeMeIleHHfi u. B psAe 3aAaq, O[IHCbIBflIOIKHX OrITHMH3aILHIO qflCTOT C06CTBeHHbIX KoeöaHHfi H KpHTHqecKHx HaFpy3oK, noTep yCT0fiB0CT, onpeIeIme ypaBHeHH, IBJIflIOTCfl ypaBHeHHMH, OI]HCIIBflIOIIHMH 3fl,flqH Hfl COCTBeH- Hble 3HflqeHHI M (h) u = XN (h) u, UK+t ùn ,ux.vx,. x WK+ [ - , u«,t, vx÷t, wx,t honm, Ußnm, Vnm, rAe M, N -- AdpdpepeHaaabHie onepaTopi; k -- C06CTBeHHoe nHCaTO, xapaTepHayee naeToTy eoöeTBennix oeöaHH Hn pHTnnecy narpyay noTepH yeTOnBOeTn. A. ECH  =  (X), rAe x  opaHnaTI Tone cpeaHnno noBepx- HOCTH TpexCOHO HCTHHbI H O60OqKH B ROM HH OTebHbIX cOeB, a Ke3eBa yHKRHfl HMeeT BHA HHTerpa3a I wo pemaea aaaqa onTaanu c pacnpezeeaHi napaMpaMm B. Ecau ynpanaflmne nepeMeHHble npecTaßflmT co6ofi OnTMn- aupyeue napaMp  e aaßneflT oT KoopnnaT ToqeK cpennnofi noßepxHocT nacTnHbl  06OqKn, a efian CyKn napaMpoß I  • (h), o paecMavpnaae aaaqa napaMeTpuqeeKo onTnMnaauun. B. Ee3n yaaefl aanneaT aaßnenMOeVU, eaamamue aaqeHn = p (h), fl = fl ), R = R (h), o aaaa onnMnaaunu naauaaete aaaqefi e oequMn eßflaMm 3s nuc3enoro pemen aaaq A, B, B npnMemv paanqe MeTObI, OCHoBaHHbIe Ha BapHaHoHHOM HCqHceHHH H MaMaTHqeCKOM nporpaMMupoßaum 3 pemeu aaaaq A n B ncno3baymT MeTOa noc3eaoßaTenbofi OnTnMUaauu [5, 6]. AropUTMbI pemeu aag3mqamTc B noc3eoßaTe3bnbix npu63umeHuX  OnTUMa3bnoMy pemeuum n OCHOßabI Ha MabIX aapuauux ynpaB3mmefi ¢yuun h  MnorogpaTnOM pemeuun aaaqn onpee3eHu nanpenno-e¢opMu- poBaoro COCTOUH npu ¢UcupoBauofi ¢yuUU 3 aaqeHx napaMeTpa h. OBIMn qaCTMn a3ropuTMa pemeu (puc. 7.1) SB3mTC 30ga Bui onpeenenn nanpmenno-opMupoßannoro COCTOUH 263 
265 
KpHTHqecKall Harpy3Ka pp Ha eHHHILy ILIHpHHbl rlaHe$1H B npes. IIoIoXeHHH ynpyrofi pa6OTbl KOHCTpyKIkHH (4.1) Pp =  P*, (7.3) rRe i  1, 2 --uouep uecymero co. HH HO rpaHKaM, pHBeeHHbIM Bn. 4.2. eCTBHTebHy KpHTHqeCKy Harpyay c yqeTO paSoT MaTe- pHaa BHemHHX COeB 3a npeoM npoopHoHabHOCTH H peHx yCOBH paSOT aHH HaXOT yTeM epecqeTa o ypaßHeHH (7.3). nn STOrO onpeemT pTHqecKe HapueHHU BO BHemHHX COX aCTHHbl, HCXO H3 HeaH3HpOBaHHbIX yCOBH paSOT B ypy- ro 3OHe: BPe BPe ECH HecyHe CO BbIOHeHbI H3 MflTepHsOB, He HMeHX HOKH TeKyqecTH, efiCTBHTebHOe KpHTHqecKoe HflHpfleHHe ope- z o opMyM (7.4) +, rae  = /«, q  0,8... 1,0, ou aaaHCHT OT aecTaa nactHuL Ec.H Hecye C.OH H3FOTOBeHbI H3 MaTepHa, HMeero qeTKO BblpameHHy nOKy TeKyqeCTH, TO eCTBHbHOe KpHTHqecKoe uanpmeHe onpeaemT Ha ipameHü o HaeHHbIM 8HflqeHHM tk, l BbIqHT KpHTHqeCKHe yCH- Hfl Ha eaHHHy mHpHHm HacTHHm HO OpMyaM Ha hByX 3naqenHfi Ph BblöHpamT Menbmee, KOpOe pHHHMamT aa efiCTBHTebHym KpHTHqecKym narpyaKy. TaKHM oöpaaoM, orpaHHqeHH 0 KpHTHqeCKOfi Harpy3Ke noTep yCfiHBOCTH Mem BHa (7.3) H (7.4), re BBOHTC C yqeTOM 3aaHHOfi TeMnepaTypbI. OFpaHHqeHH HO MeCTHO ycqHBOCTH HecyHx caoeB 1,82t  EG np c/ti > d; P = # W (7.5) re "-0,<,o+,); =0,4 V , i- 1, 2- HOMep CJIOt, ,- KO»qb(pllILl4eHT, yqHTblßaIOnLllI CrlOCO6 aa- KpenzeuHn KpoMoK nzacTHm,i (, -- 1 npH CBO60HO onepTblX KpoMKax, B- 2 npH aanLeMdleHHblX KpoMKaX). ¥CdIOBHe IIpOqHOCTH H yCTOIqHBOCTH COT HMeeT BH 5,44Pkl - tcTa -1 (c + ti) I -I < O'p. %v nn  min ([(ù]c,, %T); (7.6) (7.7) Fe W0h -- 3aaHHble 3HaqeHH HaqabHO HOFH6H; ffuU. CT, ffB. CT -- upeAenI ffpoHopHOHbHOCTH H HpOqHOCTH Mapna COT; «c : _ 1,73E  (t/a)k, k  O¢uueT (puc. 2.20). 3aqa CBOHTC K HaxomAeHn BeKTopa ypaßamHX epeMeH- ix, MUUMnaupymUX enym ¢yKum (7.2)  yonneTnopnmmym nIpameunM (7.6), (7.7). 3aaqa HeHHeHOFO porpaMMpOßaHnn MeeT  () =  + ,54 (1 - ) . ,e7 l 1 pk p ycnonn « 2VV2 lo '  1 { 5,17.10   npn d>d; 5,17.10/ np d<da, rae  = s,9v[m ( - vt)/t; «, = ( - m)/(m); a = 0,9v;°'*; Bt  t/(c + 2t);  = (c  h)/lo;  = tc/a; l  l, 2 -- otep coa. TaK KaK paccMaTpBaeTc aaaqa onTma acTHHbI CHM- MeTpHOfi cTpyKTypI, MOmO pemaT» aaaqy np 6OM aHaqeHHH l. 3. OTHMHaaH TpexcoHbIX OCKHX pMOyrObHbIX c erKHM aanoTeem npH HrHöe paBoepHo pacnpeaeeofi a- rpyao q  cmaT CHO p, aectBye B nOCOCtH cpenofi nOBepXOCT (C. pHC. 3.15). aactHa eeT CHeTpHUy ctpytypy, t.e. tt = t = t. pHHffTO, qTO fl,  C. B naCTHHe HCOb3yeTCff CHOmHO aano- HHTb, HpoqHOCTHbIe H eCTKOCTHIe xapaKTepHCTHKH KopoFo CBff- aHI C HOTHOCTb 3flBHCHMOCTMH BHAa • où = , (7.8) 0¢  p, (7.9) 
re ¢, n, 0, p --BeJIHqHHBI. 3aBHelft{ne OT CBOfICTB 3anoIHTeJn (cM. r. 2). H ycnonn oöecneeHnn peöyeo nponocn necynx oen TpexcaofiHofi naacTnnBi («  Oon) OnTnMbHa anHa 3ano. HHT H HecyHx OeB -(  ,  «_l,  qb    q»m (7.10) P8 o.r 2 Co " Ha yczon oöecneeHn conneHn Tpeöyeofi npeaezofi c- Mae CHbI Pr CO 3HaqeHHeM KpHTHqecKo HaFpy3KH  HaCTHH czeyet «o, =  /,- - (7.11) A pl'  (7.12) Pzonr = 2 (Aconr/4 -- A) ' re A p zE»h,  .  b  , 1, m2, i, , R3  KO$HHeHTbI Kopble 3BHCT OT cxeMb Hrpy- e  3aKpeneH KpOMOK nacr  COOTHOmeH pa3Mepoß cropon: mapHHpHO onHpaHHg Kpobl0K mx m ms    s  s  I, B cy- qae aameena poIoa ma  I/5, ms  2/3,   4, ù  I, s  4. aa aecyx coe OnTHMabHO 6yeT HaHMeHbmag TOHHa, onycKaela Ha yCOBH meCTKOCTH  npoqHOCTH pH eflCTBH CTa- TqeCKHX H HHaMHqeCKHX cocpeoToqeHHblX yCHHfi, bleCTHOfl yCTOfl- nBOCrn  TexoornqecKnx oalomocrefl naToea nacrn. Reeaa yung ee Bn m = 2pt + Psc, rne mä --lacca BcecTe e6onmoro £nanaaoa oaIomx aHaaenfl nnozHo- CTe 3aoHHT BO3MOHOCTH co3aHH OnTHMabHblX orpaHebL OnbT npoezrpoßa  KcnyaraR nozaabßaeT, q qacTo HHa HecyHX cOeB onpeec H3 TexHoorHqecKHX CooöpaeHHfi, a He Ha yCOBHfi upoqHOCTH H yCTOfiqHBOCTH, H UpHHHMaeT MHHHMbHble 3HflqeHH T. e. BbIXOHT Hfl orpflHHqeHHe CHH3y HO - HHe. Ha yCOBH oöecneqeHHn TpeöyeMofi poqHOCTH Tpexc.ofiOfi na- CTHbl BbI6Op HHbl 3anoHHTe 3aBHCHT OT BeHqHHbl a:  =  Cx pH n » I; C v = Cml n pH n  l; npH  = l eKTHBHOCTb TpexcoBHOß FIJIaCTHHbl He 3aBHCHT OT TOJIIII, HHbl 3aHOJIHHTefl. aecb C -- naH6oJee BbIFOHafl BeßlHqHHa TOJIIII, HHbI 3aFIOJIHHTeJIfI £max H Cmin --MaKCHMaJIbHafl H MHHHMaJIbHafl JoHyCTHMbIe TOIII.HHBI 8aFIo- HHTe,,qefI, onpeeJeMbie TeXHOJIOrHqeCKHMH BO3MOH(HOCTfIMH H3rOTOB,,qe- HHfl. I/Icxo)t H3 yCJIOBHt oöecneqeHHn TpeöyeMofI FKeCTKOCTH (W  OrITHMabHylO TOJIIII, HHy 3aIlOJIHHTeJIfl onpej{eJIIOT npH p  e Ha BBI- a:KeHHfl Co.r -- R (p -- e) ' I3 c.ayqae CBO6OJIHOrO ollrlpaHrl TrlHHbIX KpOMOK H$IaCTHH 2  I. ECIH p  8 -- 1, TO TOTIIHHa 3aIOTHHTeJIt tBTteTCt HaHBbIFO)- HeIttleI. ;C3OBHe coßna)eHHn TpeöyeMol CXHMaoIefI Harpy3KH pr C KpH- THqeCKHM 3HaqeHHeM Ph BbII7OJTHIeTCI npH HCIIOJTb3OBaHHH Bblpaxe- ù (7.0)... (7.2). FIzoTnOCTb 3anoznITezn, oöecnemmalomylo m,mozneme yCZOBHn TpeöyeMo npOqHOCTH rlpH tl,-----t,Zon, m,IqHC.rImOT no qbopMyze (7.  0). EcTrl pacqeTHoe 3HaqeHrle OFITHMad-lbHOI FIOTHOCTH BbIXOHT 3a pee,i BO3MOFKHbIX C TOqKH 3peHrl TexHoorrlrl, TO FIOTHOCTb FIpH- HHMaIOT paßHOI )3mln, eC$IH )301a'r  )3mln, HdlH )3rnax, ecqH )3oia'r  ' )3max- B 9TOM czyqae TOIIHHa 3al/OIHHTeqt onpeezneTc cey- lOtqrlMrl Bblp axeHrlMrl: ) oöeceqeHH TpeöyeMofI npoqHOCTrl (r i < rzon ) C  qbmi/(8rzot); )Tn oöecneqeHHn TpeöyeMofI FKeCTKOCTH c > ¢öm/(2,o); )T CoBna/IeHH TpeöyeMofI CXHMaiOtqefI Harpy3KH p C KpHTHqe- >_ 1 //[ A + c  +  A } rlClOTb3ylOT lprlße/eHHble BblpaxeHrlt COBMeCTHO C dpOpMyOfI « > ml + 1/ m + 4m , m 768 E, tiWno u Bt = 1 J cJyqa CBO60,/J, HOFO onHpaHH JIHHHblX KpoMoK H,,rlaCTHHbI. 269 
tlö CBO60HOe pae KpOMOK npx y = b/2 l >b l <b 1,0 1,I 1,2 1,3 1,4 1,5 1,6 1,7 0,0214 0,0228 0,0243 0,0255 0,0262 0,0270 0,0276 0,0280 0,0214 0,0276 0,0349 0,0425 0,0504 0,0582 0,0658 0,0730 0,0138 0,0165 0,0191 0,0210 0,0227 0,0241 0,0251 0,0260 0,0433 0,0530 0,0616 0,0697 0,0770 0,0643 0,0906 0,0964 1,8 0,0282 1,9 0,0283 2,0 0,0284 3,0 0,0284 4,0 0,0284 5,0 0,0284 0,0284 0,0799 0,0863 0,0987 0,1276 0,1389 0,1412 0,1422 0,0267 0,0272 0,0276 0,0279 0,0282 0,0284 0,0284 0,I017 0,1064 0,1204 0,1336 0,1400 0,1416 0,1422 270 T.e. 6,2 < o.1,» B »TOM cyqae OFI'FHMI/IbtlOe 311lqeHlle TOrlII/,HHbI 3auO H HTe Con r : lkRq I/ö, rae ko : 0,422  ; " I+1 /  : a,/a; B, B2 KOgHHeHTBI 3anaca, oöeceqname Ha- PHc. 7.2. PacneTa cxeMa Tpexonopofi Tpexcaofi- o naacTnbI, n3r6aeMofi no nanHpnecKo nosep- OCTH MOMHTOM , paß- noepno pacnpeeaeHHU Ha npaßofi onope Moyb CABra 3anoTe, COOTBeTCTByfi OTMbHOfi TO- nHe, onpe X [//(1 + l [  ]s R3 -« (2»]1 + El]2) (['1/'n2 + Ol' t) ($O11//) 2 0,5 ] " n NOTHOCTb 3aOHnTe 5. OnTnMn3a] MaCCbI Hepa3pe3Hofi RByxnpoeTHOfi naCTnHbI CnlMeTpnqHOfi cTpyKTypbt, n3rnöaeMofi no anznpnecofi nonepx- OCTn (pnC. 7.2). NaacTna arpyea panoMepo pacnpeezesM no npanofi onope [71 ] MOMeHTOM, HTeHCHBHOCTb OTOpOrO a ennuy mnpns[ pana M. 3aas[ M, mnpna naCTItbI b, zna poeTOß l I  /It, TOHa 3öHOHT C, UOCTOHHö HO HH HaCTHHKH MaTpHabI HeCy- nX coeB n 3anOHnTe, RonyCTnMbIe yrzI nOßOpOTa HefiTpabHOfi nOBepXHOCTn naCTnHbI 02 a npaßofi onope nah MaKCnMabHbIfi nporn6 paßoro npoeTa max2. Tozny necynx czoen ns[6npam re nHnn rpannua onpeezneTcn rexnozornefi n3rOTOßeHn n rpe- 6onaHnnMn »cnzyaTaunn, a sepxnn BO3MOHOCTb ncnozb3o- sann Teopnn TpexcoHblX naCTnH, re npnHTO tl {v)/C (( 1. nnHRpnqecKa eCTKOCTb npoeTOß naCTnH OHa yoßeTBO- pTb orpanuennM   < B  t   e, KOTOpbIe COOTBeTCTByT t  t {} OflTBOCTb (ynpyran nHTerpabHa eCTKOCTb) naCTnHbI A -- Ml{i (4/i + 3l[i)/112 (ll +/h)]  M0 = Mn/hWx» (7.13) re l. ,-  2li;Etbc«ttt (j  I, II). 271 
YIoaTaIIBOCTb yoßIeTBOpleT oFpaHHqeHHIM .  A  Ä, re A  A3HaqeH nOaTBOCT, opeeeMble 3 (7.13) p B ßl(2)e I(2) l Bl(2)p ßl(2)e B(2). OaTHBOCTb RoHa oöecneqnBaTb eopMaunm, He npeBbima- mym onyCTnMy (Wmaxa n 0a). Macca naCTHHI na eHHHUy mHpHHbl OHTHMabHafl eCTKOCTb HaCTHHbI oöecHeqHBafl MHHHMab- ym MacCy, caeyma. HpH l/ln  1/2 naaCTHna OntHMaabnOfi CTpygTypu ne HMeev nepnoro npoaeta, T.e. B z),eù = 0; B 2)ùpùù = M2lll/3C. B. 2)= 0. HpH li/lù  1/2 Bl(2) npaB H Bl(2) aeù onpeeanmT taK e, a n caynae A. EcaH Bt 2),ù  B 2), TO npH lI/lIl  1/2 noaomnB B (2),eù   2) H pemH OTnOCHTeabuO  ypaBHeHHe nafieM Bl(2) npan H3 nbtpaenHn (7.14) np noaynennoM B. HoaaraeM B (2) npaB = 1 (2) H onpeeaneM Bl,2en H3 (7.15) HpH 3HaqeHHH  oHpeeeHHOM H3 BblpaeHHfl . OHTMbHbIe nO e¢TKO¢T TpeXc.oHbIe Ha¢THbL H- Rpnqecgan e¢TKOCTb HaaCTHbI paana Dar, re Da =  t2)c2/4. Haacnna onepTa no gonypy F, orpannqnameMy oöaaCTb B naococTn xOy. O6eM Mapnaaa necynx caoea V npenoaaraeTcn 3flflHHbIM: Toamnna 3anoanHtean CHTaetcn nocnno no naom fl, . e. c = const. O6CTb  CHMMeTpHqHa OTHOCHTbHO Hq KoopHHaT,  Ha- rpy3Ka B BHe cocpeoToqeHHo CHbI npHoeHa B Haqe oopHHaT, T. e. q = p6 (x, 9), rae 6 --CnMSOa aeabra-ynKnn. 3aaa OntHMHaUHH 3agaaeen a OtucganHH ynguHH t, yoaae- Taopnme H3onepHMetpHeCgOMy yOaH (7.16) H aoctaaanmefi MnnHMyM BeaHHne nporHöa naacTHnS w (0, 0) a nae KOOpaHnat. 272 Heo6×OHMble I4 OCTaTOqHble yca'IOßl4t OHTHMaJIbHOCTH HMelOT BHI, U:= 2 2 2 wxx -[- wyy -[- 2v ¢2)Wx, Wvu -q- 2 ( 1 -- v (2)) w, = , rAe z __ MHO:KHTea'Ib Y[arpaH:aa. BeTOAHKa pemeHn OnTMa.nbHOfi 3aAann H3aoeHa n pa6oTe [6]. }1an pyrofi TpexofiHOfi nnaCTmKX CHMMeTpnHOrO CTpOeHn (t =  t : t) paAyca r0 pemeHe npooaa'cn  noanpnsx :oopAHaTax (r, q). OnTHMaaboe pacnpeAeeHe TOIIS ecymHx caoe BaeTCI 3aBHCHMOCTbIO t : -- (4V/rö) In (r/ro), 
9. l-lpH IpoeKTHpOBaHHH eTaTe'IbHbIX annapatoß paaMep OTCe. KOB (arperatoB) Kopnycon H qbioaexe, HX qbopMa u MawepHa MOryT o,0/ r / üß5 onpeeTbC a3naqenHeM annapaTa. Torna CHH3HTb MaCcy HeCHMMe- TpnqOfl 0603OqKH MOYAO r3annbM oöpa3OM 3a cqeT pallHoabnoro BbI6opa OTnOCHTebbX TO31Htt c3OeB, nanpHMep  ---- tlRs, t = tzlt=, h = clt. 274 qaCTO Iecyma CHOCOöHOCTb O60oqeK opeeeTc HX meCTKO- CTb, a oöeceqeHH KOpO Tpeöye yBeHqeHHe MaCC KOH- CTpyKHH, OgMy 3aqa MaccoBo OHTHMH3aHH M0meT pemaTbc KaK oöpaTHa 3aAaqa yCTOqHBOCTH. OrpaHHqeHHMH B heft np paa- HqHblX BHeHHX cHax 6yyt ypaBHeHH BHa (6.10), (6.11), (6.14), (6.15), (6.18)... (6.20). OyHKH e3H HMeet BH Hble MHOBTeB arpaHma; o6oHaeu ocabHIX Be COOTBeTCTByT BpBBeeHHMM K ypaBHeHBM (6.1), (6.16), (6.17). paBHeHH (7.17) 
rlO 3aKOHy q = q0 COS q, rAe 0 <  < , noKa3alto tla pllc. 7.4, a B3aHMOCBI3b HX npH oceBoM C:aTHI4 Ha pHC. 7.5. 1-IpH pacqeTe OHTHMaJIbHblX apaMeTpon CXOAT 3 yCJOnH KeJmcTù CBI3H Me2,y HeCym, HMH CaOM H 3afloaHHTeaeM. ä)KcepHMeltTaablfO yCTaHOBJIeHO, qTO rlpH 6o.nbmofi OTHOCHTeJIBHOIt ToJnluiHe 3allOJIHltTeJI}I (h t  50) BO3MOÄeH ero OTpmn OT ecymHx C.IOeB. B aTOM cayùae )a 8 28 / 1 Z cr  / z  R«. Pc. 7.4. aBCMOCTb OTMaabHX apaMeTpo OT pa3MepoB o6oaoqn npn BHeIMHeM aBeHHH PHC. 7.5. CB3b Mey OHTHMflabHMH napaMeTpaMn npH oceBOM cFKaTHH n0BblmeHHi HaeHOCTH pacqeTa OnTHMaabHbIX napaMeTpoB ueaeco- oöpa3o BmnHCaTb nanpeH B aanoaTeae Hall Kaeesmx mBax rlp KpTHneCKOfl arpy3Ke. 7.8. CPABHEHHE MACCOBOB t)@@EKTHBHOCTH TPEXCIOBHb[X r[IACTHH H OBOIOqEK H PFFHX THOB TOHKTEHHblX KOHCTPFKH  OeHKH eecooöpaßHOCTH HCOb3OBHH TpeXOHbIX KOH- ctpyKH aec npyrHx THnOB nactH  O60OUeK B pne pa6ot noyuem aaHtHecHe aaBCHMOCtH, OBOHe COpypOBa yCaOBH, npH KOTOpIX TaKan aaMena aeKTHBHa. KpHTepHeM • OCT  6oabcTne caynaes saeTC MaCCa ocpyu, xo  pe caynaes CnOab3yT CMOCme noa3aam oeM panuoueo 3aMem a6opmx  ropposamx ltlaHH2:pHqecKorO H3rHöa IBaIeTCI BbIllOHeHHe (9) 4 aon (c + t ()  W*; (c -F tl (2)) z tl (2)  2 (1 -F k)  I*; COOTHO- re ffäon --AonycKaeMble HarlpXeHH MaTepHaaa, H3 KOTOporo H3ro- TOßleHa a6opa HH roppHpoßaHHal KOHCTpyKIIHI; W* = bt/(2h) -- o I ) PHc. 7.6. fI, Hana3oH rIpHMeHeHl4 TpexcJIOflHbIX o6oJIoqeK: l -- pH ]I, eIC.TBHH OC.eBOi cMamnle/i c;  -- np ]I,eiC.TBHH BHemltel'O H3hITONHOI'O 
Ban cJyqan narpy)KeHH oceBoI CHJIOI p KO¢p¢pHItHeHT, FIOKa3/I- BaIOIIHI (IXp(KTHBHOCTb rlpHMeHeHHI TOFO HJIH HHOFO THE[a O6OJIOqKH 0,303 (2 + 0,950Neß), re O = 93/91 (2), Nv : 4J«T l (2)R3 2 EI(2)pKp Fp - 4Etp*. Pnc. 7.7. 3aBHCHMOCTb napaMeTpoß NF n Nq OT KpI4THqeCKOfi Harpy3Kn:] a- BHHKe pagnyca O6OJIOqK  Ha NFI 6- BHHHe yHHeHHn OBOJIOqKH sa Nq npH qIp ;> 0,2 /M.Ha; - BnHHe yaHHenn O60.qOqKH Ha Nq npn 2 ,MFIa > qp < 0,2 ,MFIa; e  .qkIHHe ykIHeHH O60#IoqKlt Ka Nq np qIp < 0,2 MI'Ia a cyqaa HarpymeHHn paBHOMepHb]M BHeI_LIHHM laBJeHHeM 2 qu 0,71Nq «ù = 0,545 (1 + 0,71Nq) °,6 ' p* H q* --napaMeTpu KpHTHqeCKOfi HarpyagH. 3aBHCHMOCTb apaeTpo NF H Nq OT COOTHOmeHH paaepo OSO- oqKH C HecyHMH COflMH H3 aMHHHeßx CaßOß OKa3aHa Ha pHC, 7,7, 278 Ha pHC. 7. pHBeeHu aaBHCHM0CTH MaKCHMaYlbHbIX Hapfl)KeHH a paaJHqHoro THrla opennenix  tpexcnoix rIJIaCTHH OT rlapaMeTpa P/l. OHH rIo3BoJIIIOT rlpH6HmeHHO orlpeeJIHTb OöJIaCTH IIpHMeHeHHn pa3IHqHbIX KOHCTpyKRHfi [23]. 7.4. HEKOTOPblE PEKOMEH)AIHH rlO FIPHBJIH)KEHHOM¥ OflTHMAIbHOM¥ FIPOEKTHPOBAHHIO 
280 7.5. BJIHflHHE J1EOEKTOB THIIA PACCJIOEHH$I HA IIAPAMETPbl TPEXCJIOfiHblX HJIACTHH l-lpl« poeKTrlpOBaHHH TpexcOiHhlX nJIaCTI4H H 060OqeK ceRyeT yqHTblßaTb BO3MOH{HOCTb BO3HHKHOBeHHI )Ie(I3eKTOB THHa pacc.rlOeHrm B poaecce H3rOTOB3IeHHt OHCTpyKn  pn ee acnayaTaRH. I-IaaHqHe aTHX )eqbeKTOß HeOXOHMO yqHTblßaTb pH COCTaBdleHHH 3aaqH OnYHMa,qbHOrO npOeKTHpOBaHH, KaK OFpaHHqeHHe. AHIJIH3 HanpI:I-KeHHO-eqbOpMHpOBaHHOFO COCTOIHHI TpexcJIOHHOH n$1aCTHHbI CHMMeTpHqHOI cTpyKTypbI, HaxoRIILeICl no)I 2:eICTBHeM pacnpeeaeHHOfi no yqaCTKy noBepXHOCTH HarpyaKH H HMemtttefi CBO- 60)HO onepTlie KpOMKH, lqOKa3blßaeT, qTO lqapaMeTpbI HalqpI:I-KeHHO- etlOpMHpOßaHHOrO COCTOIHHI TaKOI n$1aCTHHbI IlpH HaJIHqHH paccoe- HHI cytKeCTBeHHO OTJIHqaIOTCI OT apaMeTpoß 6e3eqbeKTHO HJIaCTHHbI. YIpHqeM OTMeqaeTcl H KOJIHqeCTBeHHOe H KaqeCTBeHHOe OTJIHqHe OCO- 6eHHO B cayùae, eC,H MeCTO )eteKTa He COBna)aeT c MeCTOM npHaoxe- HHit rlarpy3KrI. ECH paccOeHH CBHHyTbI OTHOCHTeJIbHO HaFDy3KH, )eflCTByOtttefi Ha epxnIfl uecyuft cofi  aeHTpe npoeTa, TO KprlBa nporI6O CTaHOBHTCt HeCIIMMeTpIlqHOI Il MaKCHMa31bHbII nporI5 Bo3pacTaeT no cpaBHeHHIO C 6e3)IeeKTHblMH KOHCTpyKKHflMH (CM. pHC. 4.32). IpoMe TOTO, poHcXOJlrlT cMenleHHe MaKCHMyMa npornSa a CTOpOHy 3OHbI pac- c,rIOeHH. I-[o,qomeHlle MaKCHMaJIbHOFO porHa opeeafleTc pa3Me- paMn pacc,OeHH. FIpn onpe)eaeHHOfi BeannHe 3OHrI paccaoeHn MaKCHMyM npor«6a coßa)aeT c 5a«amefi  arpyaKe rpamtefi 3OHbI paccaoeHH. HanpxeHn B HecytttnX CaOX TpexcaofiHO-"naacTHrI CHMMe- Tp«qOrO CTpOemI panHbI rto aöCOalOTHOfI neHqHHe, ecaH 3artoaHH- TeJIb JIerKHI H Hec:I-KHMaeM B lqOlqepeqHOM HalqpaB3IeHHH. C:I-KHMaeMOCTh 3alIOJIHHTeJII prl JIOKaJIbHblX Harpy3Kax IIpHBO)IHT K yBeTHqeHH: nanpmeHHfl B HecyttteM caoe, K KOTOpOMy npHaomeHa narpyaKa, 20... 25 % no cpane«K) c anpKe«MH )pyroro cao (CM. pnc. 4.33). FIpn aTOM paaHntta B HanpxeHnX npH y)aaeHnn OT MeCT npH,qoTKeHH $1OKaJIbHOl Harpy3KH 6blCTpO yMeHbmaeTc H Ha paCCTO Hnn, 50IbtueM 3t, (1 + ,), npaKTnqecKH panHa nyam Ha 5ea)e qbeKTHbIX yqaCTKaX H B O$1aCTH 3OHbI pacc,qoeHH, re IIpOHCXOH" 3HaqHTe$1bHOe H3MeHeHHe HalqpI:IeHHOFO COCTOIHHI HecyIKHX C,rlOeß HanpTKeHH Ha BHemHHX nOBepXHOCTX HecyIHX C$1OeB pH t (2) X ( 1 4-.  (2)/2) H --tl (2)0 +  (2)!2) 3HaqHTedlbHO BO3paCTalOT B o6a CTH 3OHbI paccoeHH, 6HKaflttle K MecTynpHOKeHH Harpy3KH, Ha IIpOTHBOnOJIO ]'KHOII FpaHHRe'Y MeHbmal°Tc; npI 60,bmHX BeJIHqHHa: 3OH'pacc,oeHfi OHn MOryT-nOMeHTb 3HaK (CM. pHC. 4.34--4.35). O'blCHleTCl pe3KHMH3rH60 M HecyIKHX C,rlOeß Ha rpaHHILax 3OH pac C$1OeHHI. I-IoTOMy apxeHH Ha nHyTpeHHHX noBepxHOCTX ecy IRHX C$1OeB (rx 1 (2)/ H3MeHIOTC"'npOTHBOnO,qO»KHblM oöpa3oM: Ha Kafimefi K Harpy3Ke rpaHHRe 3OHb! pacc,qoenH yMeHbKIaIOTCfl, a H npOTIißOrIOJIOKnO --BO3pacTaOT. HanpmeHH B cpeHHHblX noBepx HOCTIX HecylRHX C,rIOeB O'xl.2c p B 3oHe pacc,aoeHH OCTaIOTCI rlpaKTI qecKrl nOCTOIHHbIMH no ),rlHHe (CM. prlc. 4.36). 
KacaTeäbHe HanpgKeHHg B 3a- nOHHTeä]e xz pe3KO Bo3pacTaOT Ha rparIHtax 3OHbl pacc3oeHH CO cToporlbl 6e3eeKTHIX yqaCTKOB  pana y3m B 3OHe paccoeHn (CM. pHC. 4.37, 4.38). BoapacTanHe xapaKTepHCTHK Ha- rlp xeHH0-e¢op MHp OßaHHOrO COCTO- HHI SaBHCHT B nepBym oqepeb OT paaMepoß 3OHbI paccaoerH. Ha pHC. 7.9 . . . 7.11 npHBeaeHbI SaBHCHMOCTH OTHOCHTebHbX MaKcH- MabHbIX NpOFH6OB  = maxpac/max 0, HanpneHHfi B Hecyx Pc. 7.10. 3aBHCHMOCTb OTHOCHb- PHC. 7.11. OTHOCHTebHIe Kaca- HUX HanpmeHnfi a Hecnx cnox TebHbIe HanpeHH B 3anoHH- Tpexcofinofi 6aKn npn narnöe OT wee npn paanqnbx paaMepax pa3Mepa paccoenn n Moy ynpy- paccoenn Spae n Moyx yn- ron MaTepnaa 3anonnTe pOCTn COX G x Gxl (2) max pac/Gxl (2) max 0 H 3aHOHH T  T133 max pac/T133 max 0 OT OTHOCHSbHbIX pa3MepOß 3OHbI paccoeuHm HaHpeHH Bo3pa- CTaT HpH yBe3HqeHHH paccoeHH HO HHeHOMy 3aKoHy. CTHHb BO3pacTaHH HaHpeHHfi CHbHO 3aBHCHT OT MORyg yHpyrocTH 3a- HOHH H fl flCOTHO FKHX 3aHOHHTe OHa 6yeT ropa3o BbIme, qeM Rfl 3aHonHefi, y KoTopbIX MORyb HMeeT Koneqnoe 3HaqeHHe. ECH OTc.aHBaTC oßa HecyHx CO, TO ,  H  BO3- pactamt B 6obme cTenenn, qeM Kora otcaoen OaHn necymHfi caoü. qeT CHMaeMOCtH aanonHTen npaKTHqecKH ne n3Mennet aanHCH- MOCtefi W H • OW pa3Mep0B aon paccaoenHn H necobo yMenbmaeT , TaK KaK B aTOM yqae MaKCHMbHbIe HaHpgeH B 6e3eeKTHOfi KOnCTpyHn 6yyw 6obme. 282 AHaJIH3 pe3ybTaTOß pacqeToß TpexcoIHblX KOHCTpyKRI4fi IpyrHX napaMeTpax arpyxeH H 3aKpeneHn e BbIIBHJI KaqecTBen- nbix OTaHqHfi  xapaKTepe uapxeHo-edpopMHpoBanoro COCOH IIO cpaßHeHHIO C paCCMOTpeHHbIM. To xe caMoe MOTKHO CKa3aTb H B OT- OmeHHH OHCTpyanfi pyrHX THnOB (HaHHpHeCHe H cqbepHqeCKHe O60oqKH), XOT KOHqecTBeHHe 3aBHCHMOCTH 6yIyT HHbIMH. 7.6. I]POEKTHPOBAHHE TPEXCJIOflHb[X KOHCTPYK[[Hfl C YqETOM PACCJIOEHH 1-ipH oUeHKe BJIHHH paccoeHHn Ha HanpnxeHrlo-eqbopMHpoBaH- HOe COCTOHHe TpexcofiHbIX KOHCTpyKRH BaKHO ne TObKO 3HaTb xapaKTep H3MeHeHH napaMeTpoB 9TOTO COCHH, HO H onpeeHTb KpHTHqeCKHe pa3Mepbi 3OH paccoenHfi, KOTOpble He HpHBOT K pa3- pymeHm KOHCTpyKHH HH K BbiXOy 3a onycTHMbie npeebl napa- MeTpOB HaHpeHHO-eOpMHpOBaHHOrO COCHH, T. e. OeHHTb cyym CHOCOHOCTb HH CTOKOCTb KOHCTpyKHH K paCCOeHHM.  KaqeCTBe OCHOBHOFO napaMeTpa, HO3BOmero OeHHTb BHHHe paCC.OeHH Ha HeCyym CHOCOHOCTb Tpexc.OHO HaCTHHbl HH OOOqKH HpHMeHmT OTHOCHTebHy HoaRb 3OHbl pacOeHH pHTHqeCKHe HH oHyCTHMble OTHOCHTebHble pa3Mepb 3onbi paccoe- HH, HpH KOpbIX KOHCTpyKH yoßeTBOpeT yCOBHM eCTKOCTH, HpOqHOCTH H MeCTHO yCTOqHBOCTH HH B o6eM cyqae yCOBHM coxpanenHn necefi CnOCOönOCTH, 3anHcbIßamT  ceymeM ahne:   %/k, (7.18) re  aKTOp, onpeenmHfi nanpnenno-eopMHpoßannoe CO- CTOHHe B oKpeCTHOCTH paCCMaTpHBaeMOfi TOqKH; 0n  3HaqeHHe aTopa, COOTBeTCTnymee nacTynenHm npeRebnoro COCTOnnH; k -- KOSHRHeT 3aaca. HpeoOHM, qTO yCOBH (7.18)  6e3eeTuUX KOUcTpyKHfi H  KOHCTpyKHfi C paccOeHHflMH HMeT OHH H TOT e mpac pa3HbIe. 3aHHeM yCOBHfl ZebHIe 3HaqeHHfl aKTOpOB on H Ton (7.18) Z 6eazeenbix OCyKUH, CqHa pac 0 ö  v0 = []:  []/ko; an KOHCTpyKuHfi C pacc.OeHHnMH vPC []/kpa c. COBHe coxpanenHn Hecye CHOCOöHOCTH B OTHOCH3bHOM R KOHCTpyKRH C pacc.oeHHMH  = pù¢/o = ko/kpa, (7.19 rRe ko, kvae --KO@@HHeHTbl aanaca Ran 6e3Re@eKTHOfi paccoennofi KOHCTpyKHH, pHqeM I  kpac  0" EC.H kpac To npn onpeReenHX yCOBHX Maefiman 3ona paccaoenHn MOe7 BbI3BaTb napymenHe yCOBH (7.19). ByeM CqHTaTb pac = [- B OTO cyae KOHCTpyKRH yRoßeTBopneT Tpe6oBaHHM coxpanenHn cyefi COCOöHOCTH 6e Hmnero aanaca. 28 
OKorlqaTeJ/brlO yCZOBHe (7.19) npHMer BH)   ko. KOg@gageHT 3anaca k o = [ ]/@ onpeeeTc OTOmeue onycKaeMoFo 3Hqe- HUa aropa I]  ero pacewHoy zHaeHum o za 6ezeerHo OH crpyauu. HoTep pa6OTOCnOCO6HOCT KOHCTpyKa BCeCTBe Haq pac- coe MOeT npo30T: np paspymeu a nacTqeCKOM eopMposan ecymx cOeB np efiCTB nopMabnbX nanpenfi, Bo3pacTaX OT paccaoenfi  KOHCTpyKRX; npn pa3pymen 3anouT OT nanpnenfi cßra, TaKte Bo3pacTamx np uan paccoeufi B KOUCTpyKnX, pa3pyme- uue 3anouTe OT CaT B nonepenuoM uanpaBeu np pacneT- HOM uarpyeu npaKTeCK He 3aBCT OT Hafi paccoeuuU; np 3uanTebUOM paccaoen KOUCTpyKR, Kora 3a ceT pa3- pymenn coeAnTbnoro caon npocxoAT porpeccpymmee yBe- anene nanaa»nofi 3OHbI paccaoenn, KOTOpafi fißfieTCfi KaK 6bi naaTOpOM 9TOrO npoecca, s KonennoM Tore ysnene 3on paccoenn npsoA K nanTeabnoMy cnenm eCTKOCTn On- CTpyKa  papymenm necymnx czoe  anoanTezn; B peyzbTaTe MeCTnOfi noTepn yCTOfiBOCTn necyero con B one pacczoenn, nTO MOeT npecT K smynsanm necymero caos, ero papymenm z OTpmy OT 3anoznTean; B pe3yabTaTe nanTea»noro cnen eCTKOCT KOnCTpyKaI ee nepeMemenn CTaHOBfiTCfi BbIme npeAeabno onycTMblX, oöycoß- aenn»IX ynKaOnabnbM nananeneM Aannofi KOnCTpyKa. TaKM o6paoM, yCZOn coxpanenn pa6OTOCnOCO6nOCT pacnaAamT- cn na nTb OTbnbX ycoßfi, KaoMy 3 KOTOpbX COOTBeTByeT qnpeAezenfi Kp Tepfi p a6oTocnoco6nocT TpexcofinbX KOnCTp yKanfi. Zn Tpexcaofinofi nzacTn c necymnM CZOnM  naacTnnx MaTepnaoß, KOTOpan naxoATCn B ycoßnx anpnecKoro n3- r6a, c cnoz»osaneM TpeTbero KpTepn nponnocT yose npon- OCT, COOTBCTByee nepBoMy 3 yKa3abX Bbe caynaeß noTep pa6OTOCnOCO6nOCT, MeeT B 6  ko, (7.20) rne 6x = a./a. -- OTnOCTeZbnoe MacMaabnoe nanpnene, onpeAezneMoe OTnOmenHeM MaKcMaz»noro nanpnenn s OnCTpyK- K C pacczoeneM K MaKCMaZbnOMy nanpnenm s 6eeeKTnOfi KOnCTpyKan np TOfi e narpy3Ke; ko= [a]/a.  KOgaenT 3anaca, KOTOpfi onpeneaneTcs OTnO- meneM onycKaeMbX nanpnenfi  pacneTnbM S 6e3AeeKTnOfi KOn- crpynn. 3aaß KOgaenT anaca, MOHO C nOMOb 3aBI4CMOCT ä I  = f (S) onpeAezTb onycKaeMe OTnOCTeZbne paMep 3on pac- coeHfi. Bzn anoznT np anZnApneCKOM r6e TpexczofinOfi na- CTnU yczose nponnocT so STOpOM czynae noTep pa6oTocnocoöno- CT MeeT B xsZ  kot, (7.21) 284 0 rAe k0x= l331/33-- KO»I4[[tteHT 3anaca, onpeezfleMbfi OTHO- eneM onycKaeMbX KaCaTebbX anpemtü  3anotTe K pacqeTHblM KaCaTebHblM HanpetlltM B 6e3eeKTHOfi KOHCTpyK- HH. 3HaS kot, c nOMObm 3aBCMOCTeU Z = [ (S) onpeAemT Aony- CKeMble OTHOCHTebHbe p3MepbI 30HbI pccoeHlI nO KCTebHblM HanpmeHHfiM.  coenwe»noro con npn nann  OncWpyK paccoe- nn ycoe nponnocw, coowewcwymee ycom neo3pacwan HaqabHblX 3OH paccoenn, onpeenewc na OCHOBe yCOB npon- HOCT, yqTblßaero BO3MOHOCTb pa3pymen sworo co 50 ow KaCaTebHbIX HanpneHfi ZlSS, nSo OT HOpMabHbIX HanpmeHfi Ho OT HX COBMeCTHOFO eCTBHH: 0 1 - (,/,) - 0,5 (/) t + g ()  0, Fe T133° 6o33  pacqeTHbIe KacaTebHbIe H HOpMabHbIe Hanpnme- HHH 0 3anenn onycKaeMIX nanpmennfi [zss]  [ass]  KOnKpe» HblX TnOB coeHTebHblX cOeB (pa3qHble BnbI KeeßblX nanblX coenenfi  T. .) onpenmw SKcnepMenTa»no  pac- qeTOM. TaK KaK nanpnenn a npaKTqeCKH ne 3aBCT OT pacc30enfi, swo ycoße MOmHO nepencawb B ceymeM Bne: n 5e3eeKwnOfi KOnCWpyK n KOCWpyKn C pacc30ennM Pa3e3 sw Bblpamen pyr na pyra c yqeTOM TOTO, qTO X npaßble qacw paßHbI, noyqM 0 0 k* (7.22) T133 pac/T1330  133  T133 pac/T133 0 = ox. Cpanan ipamene (7.21) c (7.22) MOnO, ceawb mo, wo yCOB npOqHOCT  3anOHTe  COeHHHTebHOFO COH OH- HaKOßbe  onpeenmTcn KacaTe3bblM HanpneHnMn. Bo3pacTaHne KacaTebHbX nanpnenfi B coeHHHTebHOM coe npn nann pac- coeHfi MOeT npBeCTH K yBeqeH CXOHO noaH 30H pac- coenn, ec 5yew napymeno ycone (7.22). 3aa 3 onpeen k; c nOMO»m 3acMocwefi z  [ (S), nocwpoennblX 3n .HblX coeB, onpeeT onyCTMble OTHOCHTebHble pa3MepbI 3OHb paccoenn 3 yCOB npOqHOCT coeHHHTbHOFO COH. Paccoenn bi3bmamw ne WO3bKO cnene npeea KOncwpyK, no Moryw bI3aw»  Mecwnym nowepm ycwofinocw 285 
Hecyiero cJo B 3OHe paccJoeHu. rCJIOBHe MeCTHOB yCTOBqHBOCT!! ;I cJIyqa I[HJIHH,pHqeCKOFO H3FHöa I-IJIaCTHtl P < Pp/kov, (7.23) rAe pup -- KpI4TI4qecKat Harpy3Ra MeCTnOfi noTepH yCTOfiqI4BOCTH; KOSppuenx 3anaca. C nOMOlbO .TOFO yC:IOBH MOnO onpee2iTb RpTqeCRe pa3- ep 30n paccoenn no yCTOqHBOCTH. oceHHM H3 yKa3aHHblX cyqaeß noTep pa6OTOCnOCOöHOCTH KOHCTpyKHH 9B9eTC9 3HqHTebHOe CHHeHHe ee eCTKOCTH pll HaHqHH paccoeH. CnOb3y B KqeCTBe OCHOBHO xapaKTep- CTHKH eCTKOCTH KOHCTpyKHH ne3nny Hw = l/w, yczonne pa6oo- cnoco6noc 3anmeM n ne o  kot, re ko = [w]/wo- KO9- UenT 3anaca, paßHblfi onomenm onycKaeMoro MaKcMaz»noro npor6a K pacneTnoMy. onycKaeMblfi MaKcMaabHblfi npor6 onpee3neTCn yHKaoazb- HblM H3HqeHHeM KOHCTpyKHH. HOFHqHO 3HHCblBC9 ycoße fl KOHCTpyKHH  paccOeHeM: pHH9B kpa c w  1, noyqaeM  : wacWo  kot. (7.24) C noMo» sancocvefi  = [ ), noynennix n paccMavpnae- MblX cyqaeß, onpeAT onycKaeMble OTHOCTebHble pa3MepI pac- c3oenfi. Cnb3y yCOBH novep pa6ovocnocoönocv BceACTBHe pacoena (7.20)... (7.24), omao onpeAev» AonycKaeMblX OTHOCTebHbX paaMepoß so paccoenfi, KOTOpble CTBeTCTByT naT paCCMOTpeHHblM cyqaaM novepn pa6ovocnoco6- nocTn. Onacnofi  KpTqecKofi aOHOfi paccoena 6yAe HaMeHb- aff H3 HHX. Conoynnocv» aancocvefi xapavepacv nanpaenno-Aeop- MupoBaHHOrO COCVOaHa OV napaMevpoß paccoenfi Aa pasnnqnUlX Kocpyafi ono npeAcvanv» n nAe noorpa (c. pnc. 7.12). C HX HOMOb onpeAeaT cTeneHb yBeqeHa xapaKTepCTK Ha- npeHHO-AeopMpOßaHHOrO COCTOaHn (MaKCnMabHbIX KacaTeb- UlX  nopa»nIX nanpaenfi, npor6on) n 3aBHCHMOCTH OT paaepon paccnoen Aa onpeno oncpyKa 6o Aonycaeie paa- MepuI paccoenfi np aaAannofi cvenen BO3MOHOFO nanpaenfi  npor6on npn nan Aeevon. Ta a saAana pe- maecn n 3unefinofi nocanonKe, MOnO npaeafi n oncvpya npn nann paccnoenfi nponopanonaa»no cnenn paapymax narpyso. 3naa paapymae arpya 3a 6eaeevno OncpyKa, OnO onpeAev» coovnevcye HaFpy3KH Aa KOHCTpyKHH C paccoeHHaMH: C nOMOb HOMOrpaMM naxoa% no CKO»O paa ynenc» aanpaena,  no cvo»o e paa yMen»mav Aonycaeie narpys A3a 6eaAe{enofi oncpya. 286 nepeceqemm OrlyCTHTb nepneHAHKyJp Ha OCb a6cICC H onpeAeaTb CTeneHb CHHeHH pa6OTOCHOCOöHOCTH naCTHHbI BceACTBHe HflHqH paccaoeHH. HoorpaMI MOnO nOCTpOHTb Hmb A KOHCTpyKKH, y KOTOpblX oHyCTHMO npHHTb Et : 0. B aqecwne npepa na pnc. 7.12 npneAenuI noorpauI 3a o[lpeAeaen yBeaqen AeopMaufi, nanpefi B necyx caoax H KaCaTebHblX nanpen B 3anoHHTee np 3aAaHHblX pa3Mepax paccaoeuü B TpexcOUHbX naacTHax c OHOU 3OHOU paccoeus pa3MepOM  npu 3aaHHblX W, aO, ZXa npu uUHpqeCKOM 3r6e. HOMOrpaMMa  onpeAeeHs KacaTeabHbIX uanpseufi B 3anoaH- Teae (pc. 7.12, e) p Ha paccoeHü nocTpoeHa  UeKOTOpblX 287 
Taöa i.a 7.2 £, MM 5 lO 15 20 25 30 35 40 45 Ea  10 0,961 0,959 0,9681 0,980 0,990 0,997 0,603 0,610 0,713 0,844 0,982 0,524 0,758 0,357 0,232 0,463 0,254 0,168 0,2641 0,1961 O,131 0,159 0,160 0,468 0,550 0,655 0,711 0,723 0,756 0,365 0,463 0,538 0,305 0,409 0,519 0,391 0,396 0,429 0,259 0,314 0,395 0,226 0,316 0,418 0,212 0,213 0,234 I 0,201 0,245 0,311 0,180 0,257 0,350 0,124 0,125 0,137 0,164 0,200 0,256 0,108 0,149 0,217 0,301 0,750 0,817 0,791 0,824 0,656 0,777 0,519 0,690 0,473 0,521 0,4911 0,595 0,516 0,597 0,263 0,295 0,392 0,481 0,444 0,527 0,156 0,177 0,326 0,403 0,390 0,471 E13  5 MHa 0,98( 0,05 0,491 0,30 0,88 0,10 0,501 0,20 0,701 0,15 0,36[ 0,14 0,49C 0,20 0,28 O, ll5 0,329 0,25 0,237 0,094 0,979, 0,950 0,931 0,930 0,938 I 0,939 0,959 0,05 0,78410,551 0,499 0,530 0,604 I 0,699 0,804 , 0,37810,349 0,399 0,480 0,57210,657 0,727 0,880 , 0,726 0,630 0,600 0,610, 0,639 0,673 0,10 0,510 , 0,340 0,320 0,316 0,364,0,450 0,522 0,22010,222 0,262 0,314 0,402 I 0,500 0,570 0,415 0,151 0,189 0,236 0,308 0,390 0,470 i 0,483  0,238 0,165 0,147 0,148  0,160 0,176 0,113 0,118 0,143 0,188 0,250 0,324 0,399 0,-5 i 0,324 10,142 0,096 0,084 0,085 / 0,091 0,101 0,233,0,143 0,125 0,135 0,160 10,195 0,238 9,093 10.097 0,117 0,156 0,211 10,277 0,347 288 0,854 0,880 0,852 0,876 0,895 0,746 0,786 0,538 0,613 0,701 0,806 0,662 0,710 0,329 3,363 0,575 3,670 0,595 3,648 0,199 ),223 0,487 ),572 O,54O ),595 0,969i 0,977 0,910 0,781 0,821 0,706 0,757 0,593 0,682 0,641 0,697 0,370 0,403 0,439 0,513 0,543 0,605 0,195 0,216 0,348 0,410 0,471 0,535 0,114 0,125 0,288 0,342 0,410 0,479 Taöatiua 7.3 £, MM 5 10 15 20 25 30 35 40 45 0,956 0,933 0,948 0,968 0,983 0,993 0,999 0,50 0,544 0,521 0,688 0,895 0,329 0,470 0,652 0,778 0,850 0,889 0,912 0,926 0,938 0,972 0,939 0,931 0,941 0,955 0,968 0,979 0,989 0,996 0,75 0,669 0,500 0,525 0,628 0,761 0,901 0,322 0,396 0,474 0,597 0,703 0,779 0,831 0,880 0,910 0,979 0,950 0,931 0,930 0,938 0,949 0,959 0,969 0,979 1,00 0,784 0,551 0,499 0,530 0,604 0,699 0,804 0,378 0,349 0,399 0,480 0,572 0,657 0,727 0,983 0,950 0,938 0,928 0,929 0,936 0,945 1,25 0,883 0,619 0,523 0,506 0,536 0,593 0,667 0,361 0,354 0,377 0,424 0,489 0,561 0,630 0,985 0,964 0,944 0,931 0,926 0,928 0,935 1,50 0,967 0,689 0,565 0,518 0,516 0,544 0,591 0,386 0,371 0,377 0,403 0,446 0,500 0,558 0,986 0,968 0,949 0,935 0,927 0,926 0,928 1,75 l,O00 0,757 0,614 0,546 0,521 0,527 0,553 0,412 0,391 0,388 0,400 0,427 0,465 0,51 l 0,987 0,970 0,953 0,939 0,930 0,925 0,925 2,00 l,O00 0,821 0,667 0,583 0,542 0,530 0,539 0,436 0,413 0,403 0,407 0,423 0,449 0,483 0,987 0,972 0,957 0,943 0,933 0,927 0,925 2,25 l,O00 0,883 0,721 0,625 0,571 0,546 0,941 0,459 0,434 0,421 0,419 0,427 0,444 0,469 Ta6aa 7.4 0,967 0,972 0,992 0,50 0,954 0,701 0,966 0,357 0,570 0,757 0,853 0,898 0,920 0,938 0,950 0,958 0,975 0,960 0,970 0,985 0,997 0,75 0,689 0,592 0,706 0,882 0,332 0,422 0,574 0,709 0,853 0,980 0,961 0,959 0,968 0,980 0,990 0,997 i,00 0,495 0,603 0,610 0,712 0,844 0,982 0,302 0,254 0,463 0,550 0,655 0,750 0,817 0,854 0,880 I 0,983 0,964 I 0,955 0,958 0,967 0,976 0,984 0,998 1,25 0,889 0,651 [ 0,598 0,636 0,721 0,826 0,960 0,364 0,371 0,470 0,500 0,589 0,671 0,766 0,856 0,946 289 
[IpojoienHe TaßI. 7.4 C, MM 0,985 0,967 0,955 0,553 0,958 0,966 0,990 1,50 0,970 0,710 0,617 0,612 0,657 0,731 0,850 0,388 0,381 0,406 0,458 0,526 0,599 0,670 0,722 0,810 0,986 0,970 0,957 0,951 0,952 0,957 0,964 0,988 1,75 0,771 0,652 0,616 0,631 0,677 0,734 0,832 0,980 0,413 0,398 0,408 0,440 0,490 0,548 0,614 0,686 0,768 0,987 0,972 0,959 0,951 0,949 0,952 0,960 0,980 2,00 0,932 0,696 0,637 0,628 0,642 0,668 0,704 0,752 0,437 0,418 0,418 0,437 0,471 0,540 0,642 0,768 0,920 0,987 0,973 0,960 0,951 0,947 0,946 0,978 0,950 0,974 2,25 0,891 0,743 0,668 0,641 0,622 0,620 0,634 0,674 0,459 0,438 0,432 0,441 0,465 0,495 0,528 0,562 0,600 Ta6Ina 7.5 C, MM 0,733 0,587 0,609 0,668 0,724 0,771 0,808 0,858 0,910 0,50 0,317 0,302 0,420 0,582 0,755 0,923 0,197 0,307 0,483 0,637 0,739 0,801 0,838 0,880 0,908 0,831 0,654 0,592 0,604 0,643 0,685 0,725 0,766 0,806 0,75 0,405 0,288 0,304 0,575 0,474 0,587 0,704 0,818 0,926 0,192 0,226 0,310 0,426 0,542 0,638 0,711 0,769 0,810 0,880 0,726 0,630 0,600 0,611 0,639 0,673 0,720 0,778 1,00 0,492 0,322 0,287 0,307 0,357 0,426 0,506 0,594 0,688 0,203 0,211 0,250 0,316 0,401 0,490 0,571 0,650 0,734 0,906 0,780 0,679 0,625 0,611 0,621 0,644 0,682 0,730 1,25 0,572 0,368 0,302 0,291 0,310 0,349 0,401 0,478 0,560 0,220 0,215 0,232 0,269 0,324 0,390 0,460 0,526 0,586 0,922 0,817 0,723 0,660 0,629 0,623 0,634 0,666 0,720 1,50 0,642 0,417 0,329 0,297 0,289 0,315 0,347 0,406 0,478 0,239 0,227 0,232 0,232 0,252 0,333 0,387 0,490 0,630 0,932 0,843 0,758 0,693 0,654 0,637 0,636 0,642 0,662 1,75 0,706 0,467 0,363 0,316 0,299 0,303 0,320 0,338 0,374 0,260 0,243 0,240 0,250 0,272 0,303 0,343 0,410 0,490 0,939 0,861 0,785 0,723 0,680 0,655 0,646 0,650 0,665 2,00 0,762 0,516 0,399 0,340 0,312 0,304 0,310 0,338 0,400 0,279 0,260 0,253 0,256 0,268 0,289 0,318 0,360 0,420 0,943 0,875 0,808 0,749 0,705 I 0,676 0,661 0,652 0,656 2,25 0,813 0,563 0,437 0,368 0,331 I 0,324 O,311 0,312 0,318 0,298 0,277 0,267 0,265 0,272 0,286 0,306 0,338 0,376 29O 7.7. OCHOBHblE II$'TH CHH)KEHHI BHIHHI PACCJIOEHHI;I HA IIPOqHOCTb TPEXCOBHblX KOHCTP$'KIHII  KaXofi opeofi ocpyia e paccoefi OIa- qeCTBeHHO OeHHBaOT napaMeTpaMH i, paBHblMH OTHOILIeHHO COOTBeT- CTByOnX xapaKTepCTK HanpnKeHHo-edpopMpOßaHHOrO COCTOmt 6e3edpeKTHOfi KOHCTpyKI K aHaa]orqHblM xapaKTepICTKaM KOH- cTpyKI C paccaloeHnM. Eca] 3aaHa onpeeennan 3OHa paccoe- mm, TO yBea]qeHe napaMeTpoß i FoBopHT O I]OBbIIIeHHH qyBCTBHTeJIb- nOCT KOCTpyK K paccaloennnM. YIp5ee napaMeTpoß  K eHHHe CBHeTeJIbCTByeT O CHH'KeHHH qyBCTBHTeJIbHOCTH K paccoe- nnM. B ciynae pi ---- 1 KOHCTpyKn He 3MeHneT cBoero HanpnKenno- eqbopMpoßannoro cocTonnn np nanqn paccaoenfi. TaKM oSpa3oM, nOHnTe yBCTBTea]bHOCT K paccaoeHnM, xapaK- Tep13yeMoe napaMeTpaM p,, FIO3BOa]IeT cpaBHBaTb pa3JlqHble KOH- CTpyKln C OqK 3pen Bnnn pacc30enn na paSOTOCnOCOSHOCTb, onpeea]nTb OCHOBHble FIyTH CHH»KeHHI qyBCTBHTeJIbHOCTH K paccaloeHIM  HaxoJIITb TaKte coqeTaHn reoMeTpqecKx  ynpyrx xapaKTept- CTK necytanx ca]oeß i 3arOalHTea], np KoTopblX 3HaqlTea]bHO aeTcI 14JIl rloßbiiLlaeTci qyBCTBHTeJIbHOCTb K paccJIoemlM. Bonpoc cnenn Bnnn paccaloen oen pemaT»c B KOM- neKce c npo6neMaM MaCCOBO  qbynKona»nofi SqbdpeKTaBOCTn KOnCTpyKfi. I/I3Mennn ynpyre  reoMeTpecKe xapaKTepcTK KOnCTpyKfi, nWO6I yMen»mT» X yBCTBTe»nOCT» K paccoennM, 291 
np14 onpeAeJIe1414blX yCJOBHaX 14arpy)KeH14a. OqeB14AHO, T14 ycJOB14t TaK- iKe BJI14HIOT Ha qyBCTB14TeJIbHOCTb KOHCTpyKR14I K paccJIOeH14IM 14 143Me- HHIOT KOJI14qeCTBeHHO ee 3aB14CHMOCTb OT reOMeTp14qecKHX H ynpyrx xapaKTepHCTHK. OHaKO KaqeCTBeHHO BJI14FIHHe He 143MeHeTC. a a l'Pz Pnc. 7.14. CxeMa IlarpyKeHHI TpexcJIOfiHOfi I7.rlaCTHHbI yCHJII4- E IIl:z::::lll tlllIltll:: ùMH joz, pacrpee.'IeI]I-IblMH BCe- b L/2 b qeHHI4 X : L/2. OTc.rIoettbt o6a HeCyIRHX CIOI Ha yqaCTKaX « L b--b 292 I25 """"- 1,00 $P.C=8, 8 PHC. 7.15. 3aBHCHMOCTb lapaMeTp0B qyBCTBH- TeJIbHOCTH w (cnJiomHble JIHHI4H) H , (mTpl4- XOBble) OT MOAy,.'It ynpyroCTH HeCytRrlX Cdloeß npn E  0 (a) n E : 45 MFIa (6) 0 7 10 1516 20 iKeH140-AeqbopM14pOBaHHOe COCTOIH14e 6e3AeqbeKTHOft KOHCTpyKR1414 rlpaK- B. Baa1414e MoAyaa ynpyrocT14 14ecyH14x caoeß. Ha p14c. 7.15 E, = 45/Villa. B nepBOM cayyae C yBeJ]14qeH14eM MoAyJ]I yrlpyFocTH HecyH14X CJ]oeB qyBCTB14TeJ]bHOCTb K paccJOeH14qM H14IKaeTc, OHaKO IapaMeTpb] qyBCTB14TeJIbHOCTH OCTtIOTCI 60Jbme, qeM BO BTOpOM cJyqae, KoFAa C qyBCTB14TeJIbHOCTb K paCCJIOeHHIM CHaqJIa Bo3paCTaeT,  3aTeM MeA- JIe14110 CH14I, KaeTcI. TaK14M oöpa3oM, xapaKTep 143MeHeH14H qyBCTB14TeJ/b- HOCT14 3t]B14C14T OT OTHOItleH14I E,z/E,, = lz. KorAa 9TO OTHO14IeH14e MeHbtIIe  l0 -4, qyBCTB14TeJIbHOCTb K pflcceIH14IM CH14IKfleTCI C BO3- pacTa1414eM MoAyaa ynpyrocT14 14ecyH14x caoeß. KorAa Exz 6oJmme -- 10 -a, rlpO14CXOA14T Bo3paCTaH14e qyBCTB14TeJIbHOCT14. Ha146OJibIee 3Haqe14He napaMeTpa w 14  np141414MaT np14 Ez  10 -a. 293 
FIpH tlClqOJIb3OBaHHH COßpeMeHHblX MaTepHaJ/oß H yBeJIHqeHtltl MO)ya] ynpyrocTH Hecy[RHX ca]oeß qyBCTBHTeJIbHOCTb K paccJIOeHHIM nOßbIHaeTcfl. O,HaKO yBea/HqeHHe napaMeTpoß w H o He3HaqHTeJIbHo, a HCI-IOJ/b3OBaHHe 6OJIee :bKeCTKHX Hecy[RHX CJ/OeB I-IpHBO)HT K CylIeCTBeH- nOMy Bo3pacTa14m eCTKOCT14 Bcefi KOnCTpyKu14m B. BzHnn14e MO)yan cn14ra 3anozn14Tean Gxaa. Ha pc. 7.16 noKa- 3alibi 3aB14CHMOCT14 Iw, Io OT GlZ z np14 Ex = 0 r E = 45 MI]a n pa33HqHblX pa3Mepoß 3OH paccaoeHnfi. C yBe14eH14eM MO)yn c)ß14ra Smc : 8,8 Pc. 7.|6. 3aBtlCHMOCTb llapaMeTpoß '-IyBCTBtlTeJIbHOCTtl q?w (cnaomHbie II1414) 14 ¢0 (ItlTpXOBble) OT MOJly,rI ra 3arioIHHTeIfl npn Ea = 0 (a) n El:   = 45 MHa (6) lZ 20 2 » , a 10 20 Gn, Pll7a 3a140JIHHTeJI 14apaMeTpb! qyBCTB14Te,bHOCT14 Bo3pacTaB3T B o6o14x cay- nanx. FIp TOM nySCTS14Tea»nOCT» K pacczoenHnM no KeCTKOCT yse- JIq14BaeTc oqenb ne3HaqTeIbno 14 npaKTqeCK ee MOnO CqTaTb He3aßHcfie OT MOyfi CBHFa 3anOHHTefi. yBCTBHTbHOCTb K pac- caoennM no UopMaa»nUM nanpsenunM TaKte Bo3pacTaeT ue3Ha- Ten»no. TaK, np yBeaen MoyS cAßra B 2 pa3a (OT 16 AO 32 MHa, CM. pc. 7.16, a) napaMeTp o Bo3pacTamT ne 6oaee eM na 13 %. B  me BpeMn nopMabnIe npor6I 6e3e¢eKTnUlX naneae yMen»- mamTcn na 25 %, a Hanpseufi --ua 15 %. F. B,nnne TOaMHbI 3aHOHnTefl C. ßeqeHHe TOMHbI 3a- HOHHTe 3HaqnTebHO HOßbmaeT eCTKOCTb KOHCTpyKKn, qTO HpH- BOMT HpH TeX e arpy3Kax K yMenbmenum MaKCUMaabnbX nporn- 6os o  nanpnmennfi o (puc. 7.17, a). OAnaKo B aTOM cayqae, ecn CqTaTb 3aHOHTeb a6CTHO erKHM (Exa 0), 3HaqbHO noßimaeTcs yBCTBZbnOCT» KOHCTpyKaH K pacc¢toeHM. TO O6cneTc oenb MaOfi 3rSno eCTKOCTb paccoennoro HaKeTa no cpaßnenm c eCTKOCTb 6e3eeKTHOfi KOHCTpyKKm H3rSna eCTKOCTb paccoeHHoro HKeT onpeeaeTc TObKO COöCTBeHHbIMH eCTKOCTHMH necymx cOeB. OTHOmeHHe H3rHöHblX eCTKOCTe pac- caoennIX  6e3AeeTnIX acTefi TpexcaOfiHOfi KOHCTpyKaH 294 Bo3paCTaHH14 TOJIH],14Hbl 3arlOJHHTeJt yMeHbHaeTcI, T. e. yBeJI14qHBaeTCl qyBCTB14TeJ]bHOCTb KOHCTpyKIL1414 K paccaoeHSM. EcJI14 3f114OJIH14TeIb 14e IBd/IeTCI flöCO/IOTHO /eFK14M, TO )JII pacc3oem HOFO FlaKeTa Heoxo)HMO yqHTblßaTb ero H3F14HyIO IKeCTKOCTb, 3aB14- cHMOCTb I]apaMeTpoß qyBCTBHTeJIbHOCTH OT TOdlHI, HHbI 3a14OJIH14TedIFI / 2 PHC. 7.17. 3aBHClIMOCTb napa- MeTpOB qyBCTBwrebHOCTIt w (mTpHXOßble) OT TOamHHbl IIOdlHItTe3Dt C 1t apaMeTpa  npn E = 0 (a) n E= = 45 MFIa (6) n qbnKcnpoan- I-iO ., = 13,2 % npn pz3nblX E (e) 6y)eT 14HOB. Bo3pacTaH14e qyBCTB14TedlbHOCT14 K paccdloeHHM 14poHc- XO)T TOabKO )O o14pe)eaeHHO TOJm14HbI 3a14oJm14Tean (CM. p14c. 7.17, 6), noce nero 14apaMeTpi nyBCTB14Tea»nOCT14 yMen»mamTc n np146an- IKaIOTCI K e)HHHILe 14p14 yBedI14qeI-IHH TOdIIHHbI 3aFIO31H14Te31FI. /aKCH- MyMbI KpHBblX w I4 (, np14 KOTOpblX KOHCTpyKI[rII o6a)aeT Ha146OJIb- mefi qyBCTB14TedlbHOCTbIO K paccJoeHHnM, B 6OJIbmOl cTeneH14 3aB14C:IT OT Moydll ynpyrocT14 3arlOdlHHTeII. C BO3paCTaH14eM EI MaKcHMyMBI yMeHbItlalOTCH FIO BedI14qHHe H CBHFaIOTCI B CTOpOHy MeHbH14X TOdlI14H aanoJmTean (CM. p14C. 7.17, e). 295 
TaKHM oöpa3oM, rlplt BbI6Ope TOJIIII, ItHbI 3arlOIHHTe3]R, qTOöbI cye- CTBeItItO yMeItbUIHTb qyBCTBHTe3]btIOCTb KOtICTpyKII3tlt K paccoennM, neoöxoAuMO A3I KaZKAOrO KOHKpeTHOrO cyqan paccMaTpßaTb 3aB- CttMOCTH w tt {G OT C tt I (2}. JI. Bzunne roamnu necyuux caoes h t. Ha pHc. 7.18 I]OKa3atia 3aBttCttMOCTb napaMeTpoß OT TOULmm necymnx coe. UßeJIqemie TOJIIil, ttHbI necynx cOeB AI TpexcOfiHbX KOnCTpyKaufi C aöCOJIOTHO !,5 Prlc. 7.18. 3aBHCltMOCTb rlapaMeTpoß qyBCTBI,ITe,rlbrlOCTI4 w (mTpHXOßbIe ,rlHrl!4rl) t,1 « (cnaomsble) OT TOairmI secyirtx caoeß rl napaMeTpa  nprl E  0 (a) H E : = 45 M[Ia (6) 296 0 20 40 60 H,  o 0,02 o,v, 0,06 / 7.8. PACqET KPHTHqECKHX IIAPAMETPOB PACCJ1OEHHI TPEXCJIOBHbiX IIJ1ACTHH H OEOJ1OqEK Pa3pymeHHe TpexcJOfHblX rlJIaCTHH H O60IOqeK npH pacc,noeHHH MO:FKeT 6blTb KoFe3HOHHOFO H aFe3HOHHOFO THHa. I-IpH KoFe3HOHHOM pa3pylIIeHHH rlpOHCXOAHT HapylMeHHe ILedlOCTHOCTH OAHOpOAHOFO MaTe- pHaJa, T. e. JIH60 paccJoetlHe HecylRel'o CJlOl, JiH60 paccJioeHHe CrlJOIM- HOFO 3aHOJIHHTeJII. LlalI],e rlpOHCXO)IHT KoFe3HOHHOe pa3pylMeHHe 3a o HOJIHHTeJIeI THrla rleHOrlJIaCTOB. l-IpH aFe3HOHHOM pa3pyl_HeHHH HpoHcxo):I, HT paccJIOeHHe H0 FpaHHRe CJIOeB pa3HopO)HblX MaTepHaJIOB. TOT BH,Il pa3pylJleHHR HaH6oJIee xapaKTepeH )Jll TpexcJIOftHblX KOHCTpyKILHI. TeopHs paccJIOeHHI TpexcJIOflHblX KOHCTpyKRHfl HoKa He pa3pa- 6OTaHa, HOTOMy ,Jll OII, eHKH yCJIOBHI pacrlpOCTpaHeHHl paccJIOeHHI HCrlOJIb3ylOT rlpHöJIHHeHHble 3aBHCHMOCTH. [IpHHHMaeTcI, qTO pa3pylLieHHe rlpOHCXO,HT rlO rlpOMeHyTOqHOMy THrly Me»Ky aFe3HOHHblM H KoFe3HOHHblM. Ec]H HeCylLI, He CJIOH OqeHb :FKeCTKHe, a 3arlOJIHHTeJlb -- MaJIOrlpoqHbIl, TO paccJiOeHHe rlpHöJIH- KaeTcI K aAre3HOHHOMy THrly; ecJIH IlapaMeTpbI KeCTKOCTH Hecyl/LHX CJIOeB H 3arlOJIHHTeJIR 6JIH3KH, TO paccJIOeHHe 6JIH3KO K KoFe3HOH- HoMy. 297 
IpHTHgecKHe 3HageHHs HanpsKeHHü, np KOTOpbIX BO3HHKaT paccoenu aAre3Honnoro THHa, ceAyHe: aa yqaa paccoeHua OTAHpOM (7.2) fl cyqa paccoeH CBHFOM " 2 G1aII la B OCKOCTH xOz; (7.26) hp 133  2 B OCKOCTH 0X, (7.27) GII aa re a  nooßna Ann nemerocn AeKTa Tna paccnoena; Ha- n3OTOCT» noepxaocTaofi snepr paspymean np OTApe; H Oa-- nnOTnT» noepxocTaofi sneprn paapymennn np cre. TeopeTqecaa n3OTnOCT» noepxnocTnofi saeprn paapymenn H H =    + 71 u ::  ), (7.28) 4 4  a  a (7.29) I  KcHepHMeHTabHO HoyqeHHble HaqeHH HOTHOCTH HepFHH pa- pymeHH a TpexcoHblX KOHCTpyKH C aHOHHTeeM H neHO- HacTa AOCTaTOqHO xopoo COBHaAaT C opeTHqeCKHMH HaqeHHMH, onpeeeIn no opyaaM (7.28), (7.29). EcH HaqeHH KpHTHqecKHX HaHpeHH paccoeHH, onpeAeeH- ix no nipaennM (7.25) n (7.26)  (7.27), 6o»me npeAeon npoq- HOCTH np paCTfleHHH HH CBHFe, pacCqHTaHHblX nO pMyaM F. 2 HH onpeeHHhIX KCnepHMeHTabHO, TO paccoeHHe CTByHX B aHOHHTee HaHpeHHX 3 H i3m 6yeT HMeTb MeCTO. Ecan coöaeno ycone «  «u,  o  *ii, wo np pacqe» ix napaewpax nanpameno-Aeopponannoro cocwoanna  paa- epax Meerocn paccoena npoecc paccoenn ne 6ye paan- BaTbC. Hp an nanan»nIX npor6on  eficwnyefi n nOCOCTn cpennofi nonepxoc CHMae narpya P, niabmamefi npflmeHH CaTH 1 (2), KpHTHqecKoe HanpeHHe paBHTH paccoe- HH 2 EH o (7.30) ffp re Hw 0 = 0,5T 0e,  0  o/p  OTHOCHbHbI HaqabHbI nporH6; anp  HOOBHHa mara peryapnoro nporSa. 3HaqeHHe ffpwo HeOöXOHMO CpaBHHTb C npeeoM flpoqHOCTH 3a- flOHHTe Ha OTpblß zaa. ECH BblflOHfieTCfi yCOBHe up TO paccoeHe 5yeT, ecn ffp wo  «za, TO paccoeHn He npo3ofiAeT. 298 CII HCOK $1HTEPATYPbl 1. Aaecaupon A. t., Bopouu H. t., IIa«aon B. B. KOHCTpyKILHH C sanoa- HHTeaHMH H3 HeHoHaaCTOB. M.: MamHHOCTpOeHHe, 1972. 211 c. 2. Aaecanpoß A. ., Bpmgep . 3., Kypman . M. PacqeT TpexcOHblX naeae. M.: O6opor3, 1960. 270 c. 3. Aaecanpoa A. ., pman B KH.: poqHOCTb, yCTOfiqHBOCTb, KoaHHH. .: MamocTpoee, 1968, T. 2, C. 243326. 4. AaeKnpoB A. ., HayMoBa M. H. OnTMahnble napameTpbl TpexcaofiHhlX HflCTHH H O60OqeK C COTOBbIM 3aHHHTeeM HpH CaTHH H Harpeße.  B KH.: TeopHn oaoqeK  aaCTHH. Tp. VIII Bcecom3ofi Ko¢epeKa no TeopHH o60aoe a naac- CTH. M.: HayKa, 1971, 1973, c. 200204. 5. ApMaH . . pHoeHHH TeopHH OTHMabHOrO ypaßeHH CHCTeMaM. M.: Mp, 1977, 144 C. 6. Bauuq H. B. OnTMaa opm ynpyrx Te. M.: HayKa, 1980, 256 c. 7. Byraon H. H. PaTa pa»pyme CaOCTIX CTeKOHCTHKOB HO noepx- HOCT pa3zea.  po6ebt npOqHOCT, 1978, N 4, C. 4951. 8. Bafinöepr . B. CnpaBOqHHK nO HpOqHTH, yCTOqHBOCTH H KoeöaHHaM nacT. KeB: ByßehaK, 1973, C. 487. 9. Bonpocm pacqeTa 3eMeHTOB BHaKHOHHbIX KOHCTpyKKHfI. PacqeT TpeXOHblX naefi a O60oqeK. M.: Oporas, 1959. 305 c. 10. Fpaam . H., qyao H. H. VCTOfiqOCTb  KeöaHa TpexcaofiHX O60OqeK. M.: MamHocTpoeHe, 1973. 170 c. 11. aoa H. B., apcaä H. B. O60Tamabofi ropapoKe emx cOeB TpexcoHOfI HaCTHHKH.  B KH.: CTTHK H HHMHK ooqeK. KaHb: 1979, abtu. 12, c. 172179. 12. 3aahöepaa A. C., Koöeae B. H. onepeqHblfi sr6TpexcaofiHblX oepTblX acTa, noaKpeebtx 6aaKama. .: KHHHTC, 1975, btn. 144. 128 c. 13. Komnoaaqaonnme maTepaaabI  OCTpyKaaX aeTaTeabmx anapaTom C6OpHK CTaTefl. M.: MamHocTpoeHe, 1975, 272 c. 14. Kpmcan B. H. oce eeble KOCTpyK B MOaeTocTpoem M.: MamocTpe, 1980. 1 c. _ 15. aaan B. T., amaTpoeae, 1976. 408 c. 16. Maamee A. B. AH CP. Mexau Tneporo wa, 1978,  6, c. 101--105. 17. flparep B. Ocoß TeOpuu OnTaoro npoeTpoßaa ocpyK. M.: Mp, 1977. 112 c. 18. flpoxopon B. ., epmmen B. B. ecymym CnO6HOCTb Tpexcaofimx gOHCTpyKRfl.--Texnora cyazpoeua, 1981, N I0, c. 25--. 19. Pacqee aeMen aBHaRHOHHb OCTpyRfi. Tpexofibe na  OSO- aOqKm M.: Mamopoee, 1965, sbm. 3, 4. 415 c. 20. CeMeum H. H. O5 yqeTe econepmeoro KOTaKTa caoes n asyxcofibx - apIueCKX o50oax.- Hpzana MexaKa, 1981, N l, c. 58--63. 21. Yczauonaeuue KpTepeß paspymen BX coeenfl np KOMSnpO- BaaOM arpyen/. Monsun, M. XacTo, H. MäCT  p.- TeopqecKne OCOB neepbx pacqeTOß. M.: Mnp, 1978, N I, C. 29--36. 22. yurcufi B. E. CTpOHTebHble KOncTpyKRHH C COTOmbMH 3anOHHTemMH. .: CTpofinaaT. 1977. I12 C. 23. r- Xepcab T0tiEcTeablC KOCTpyKR. M-: MamatlOCTpOee. 1965. 526 c. 
I]PEMETH bi  cmcKa ,nnTepTyp,I. CC,I.nK/a K TeKCTy iHbl H CTpaHHU, bl cIIpiBORHHKi. AJIaBI4THOe Beapa3MepHoe Hapeae 64, 97 Be3paMepHufi npor6 64, 65 heCTKOCTb O60OKH 264 aCTHb 141, 264 cTepHn 140 HcKpeTHbfl 5, 31 ueK 40 eCTKfl 9 KDpaTHbI 35 KpaTbfl yCeHHfl 36 KOHCTpyKHH , 3, 4 erHfi 9 34. 35 CnOHOfl 5 TH yHHeHHIX COT 3, 38 HpqecKHfl 38 pqecKfl ycefi 38, 39 eCTHFpaHHfi yCHenHbfi 36 Ke 13, 14, 15 KOcTpyK Keeue 16 KOM6ponannue 16, 19 ocnonue Tnu 16, 17. 19. 20 cnapm 16 Ko»e npepunccT 5 KoaenT Hyaccoa 32, 33, 35, 40 KpTep Kaqecea 261 pHTHqeCKHe napaeTp paccoeH 297 Macca naeaefl 43 Maepu aanoTe 11, 12, 22, 24 uecyx coen 11, 12, 14 MecTua fioTep ycToflunocTu necFux caoen 40 oAy cnura 40 ynpyrocT 34--37 Hcye COH 8 Hpee npoocT TpexcoflHofl o* cTpyHH 41 nra anoHTe 32, 34--40 npyrocTH 33, 39 pHBeeHHaR nOTHOgTb 8aoHHTeR Hpno 15 Pa0oRfl o0eM SanOHHTeR 5 FKA3ATEb Cnoße »eMeHT 10, 11 CpeHEfl MOyb CBHra 3aHOHllTeI 34 CyHMH COHMH 5 CXeM HavpymeH H MOK 62, 63 TpexcofiHa KOHCTpyKHH 5 HeCHMMeTpHqHOrO CTpOeHHH 6 npeHMyecTBa H HeoCTaTKH 5, 7 C paccoeHM 173, 176 xapawrBpCTHK 6, 7, 13 TpexcoflHa o60oqKa 5 HaHpeHHo-eopMpoaHHoe COCTO- He 184, 194 OHTHMH3aH ffO Macce 275 c »KeCTKHM 3anoHTeeM 182, 187 ffaHroyTaMH 188 yCTOflqßOCTb 220, 222, 229, 239, 244, 249, 252 xapaKTepcTHKH 5 TpexcofiHa acTHa 5 eCMMeTpqoro cTpoeHn 44, 49, 53 OnTHM3aH nO Macce 265, 267, 270, 271 C H3OTpOUHIMH HecyHMH COHM}] 57 EOHHTeeM.61 C nopeneHeM 135 CMMeTpqHoro cTpoeHa 61 yCToflqHOCTb 141, 146, 156, 159, 163, 165, 171, 172 xap aKTepHcTnK 5 bHa >KeCTKOCTb 13 ebHa Macca EaHefl 6 COBHIfi npee npoqHocTH npH caTHH 33, 35--39 npH cre 33, 35 33, 36, 37, 39 CTOqHDOCTb KOHHqCKHX H CpHqCKHX O60OqK 249 KpHBOHHefiHHX naHenefl 255 yx coe 40 acT 141, 146, 156, 159, 163, [65, 171, 172 ¢Tepnefl pnecnx oöooeK 220, 222, 229, 239, 244, 25 poeKTspoae pex¢ox fi 260, ropT 260 oTnaoe 279 pa¢a o 8, 9, 262 a yeTo paccoen PaccoeHH TpeXC0flHX KOHCTpyKKHfl BHRHHe Ha napaMeTp 281 BHHHHe Ha npOHOCTb 291 accHHaKs 173 BCTBHTebHOCTb K paccoeHHSM 292 eTnHOCTb 276 0FIABIEH 14E peHc3oBHe ............................. OCHOBHbIe O603HaqeHHH ....................... Faaßa 1. OCHOBHbe CBeJeHH 0 TpexcofiHbX KOHCTpyKqHX ........ I.I. O6tne OHHTHH ..................... 1.2. HpenMyeCTBa H HeoCTaTKH TpexCOfiHUX KOHCTpyKRHfi... 1.3. OCOöeHHOCTH paOT TpexcofiHX KOHCTpyKKHfi ...... 1.4. MaTepHaa, UpHMeHeMe a H3FOTOBeHH 3eMeHTOB Tpex- COfiHX KOHCTpyKH .................. 1.5. T KOHCTpyKRHfi .................... Faaßa 2. Ctnp. Fana 3. 11 16 Faßa 4. PacqeT 3anonHHTen TpexcofiHx KOHCTpyKH ........ 22 2.1. Tn 3aoaHTeaefi ................... 22 2.2. l-Ieo3anonTen ................... 24 2.3. 3anonTeH ncKpeTO cTpyKTyp ........... 31 PacqeT nepeMemeuufi u HanpgeHHfi B Tpexc,OfiHbX nOCKHX npMo- yFo]bHbX HIaCTHHax ..................... 3.1. PacqeT IIIaCTHH HeCHMMeTpHqHOFO CTpOeHH, CBOOHO oepTblX o ByM KpoKaM  »r6aex o asnpqecKo OBepX- HOCT .......................... 44 3.2. PacqeT rIaCTHH HeCHmmeTpHqHOrO CTpOeHH, 3aIeMleHHblX IByM KpOMKaM H H3rHOaeMIX IO IBIIHHIpHqeCKOfi IOBepXHOCTH 49 3.3. PaceT IIaCTHH HeCHMMeTpHqHoro CTpOeHH» HMeIOIHX OIHy aieMaeHHyo H o£Hy CBOOOIHyO KpOMKy H H3rHOaeMbX IIHJIHHIpHqeKOfi noBepxHoCTH ............. 53 3.4. Hpornöb H HanpaKea npn nonepeqo  npoIoao-nonepeqo HOM I43rHöe flaCTHH C HecyuI4MI COaMH 3 pa3JIHqHblX H3OTpOI'[- HbIX MaTepHaIOß ..................... 57 3.5. Hpoon»o-nonepebfl »r6 I'[/IaCTHH ........... 59 3.6. TpexcnoflHa naCTHa CHMMeTpHqHoro CTpOeHHH, HarpyKeHHa co¢p eoToqeI4 HIM MoMeHTOM l'I p I4/IO:eH HII M K OIHOMy H3 ecyx coe ............. • ........ 61 3.7. Hapeo-eopMpoaoe COCTOe Io2aCTHH C H3oTpoI- HIMH ecyM COM  aaoTee« p COKbX cxeMax narpye ....................... 61 3.8. I-Ip6mKeoe opeeee npor6o  anpKefi nolpen- /IeHHIIX I'I/IaCTHH ..................... 135 "CTOqHBOCTb cTepxHefi H nacTHH ............... 4.1. rCTOqHBOCTb cTepKHefl ................. 2 4.2. PacqeT Ha o6y yCTOqHBOCTb HaCTHH C 3anOHHTe.qeM cpeHeH KeCKOCTH .................... 4.3. ¢'CTOqHBOCTb CTHH C MaoKeCTKHM H3OTpOHHM 3aHOHH- TeeM .......................... 139 139 141 146 
Faaa 5. Faa 6. Faaßa 7. 02 4.4. rCTOqHBOCTI TpexcJIOfHblX nJIaCTHH C MaJIo)KeCTKHM OpTOTpon- HblM 3anOJIHHTedleM .................... 156 4.5. I-IJIaCTHHa C ,KeCTKHM H3OTpOnHbIM 3anO3IHHTedleM ...... 159 4.6. rCTOqHBOCTb noIaCTHH C )KeCTKHM OpTOTpOnHblM 3aIIOJIHHTeJIeM I40pTOTpOnHblMH BHeILIHHMH CJIOflMH ............. 163 4.7. YCTOfiqnBOC*b npaMoyroJIbHX nJIaCTnH HecnMeTpnqnoro cTpo- enna npn c)KaTnn n cßnre ................ 165 4.8. Y'CTOqHBOCTIa cKaTUX I'[.rlaCTHH C Ma$1ofi ,KeCTKOCTbIO npn n3- rnöe necylnX C$1OeB .................. 171 4.9. /MiecTnan yCTOfiqnBOCTb n.acTnll ............... 172 4.10. PacqeT TpexCIOfiHblX KOHCTpyKRnfi C pacc21oeHnnMn . . . 173 PacùeT nepeteiaennfi n uanpn¢eHnfi n Tpexcaofinmx ttnannJpnùe- CKnX 060oqKax .................. 5.1. O6ume noloKeHni .................... 5.2. CneTpnqHoe HarpyKeHne noayöecKoHeqHo OöOIOqKn CnM- MeTpHqHO[ CTpyKTypbI C JIerKHM 3anoJIHnTe,qeM ycHJInIMn IOMeHTaIn, ]leficTByonIn B nonepeqHoI ceqeHnn ...... 5.3. CneTpnqHoe Harpy)KeHne noIyöeCKOHeqHOfi nJI 6eCKOHeqHOfi O00IOqKn HeCntMeTpnqHOfi cTpyKTypbI C meCTKnt sanoJIHTeJiet ycnJIntn nJin OMeHTa, ]IeficTByoln B nonepeqHo ceqe- HnH ........................... 5.4. CnMeTpnqnoe HarpymeHe O6OJIOqKn paßHoepno pacnpeeJIeH- nofi no noßepxnoCT narpy3Ko .............. 5.5. CnMMeTpnqHOe HarpyKeHne KOpOTKOf'i OO.OqKH C KeCTKIM no.rlnnTedleM nonepeqnbIMH yCH.rIHflMn H MOMeHTaMn, JeICTByIO- IKHMH B TOpIaX ..................... 5.6. CnIIeTpHq}Ioe HarpyKeHne paßHOIep}io pacnpeJleaeHHOfi no rIOBepXHOCTn Harpy3KOfl O60.qOqKn C ,KeCTKnM 3ano.riHnTe.rleM, no¢penaeHHOfi qaCTO nocTaßlennblMn ynpyrnMn mnaHroyTamn 5.7. HanpnKeHHO-eqbopmnpoßaHHOe COCTOnnne O60$1OqKn, Harpy- KeHHOfl na OnH CaOfi .................. 5.8. PacqeT HanpKeHHO-JleqbopmnpoaHHOrO COCTOHnn npn npoaßOIbHblX HarpyaKax ....... IlpoeKTnpoùaIne Tpexcaofinmx naacT}m n o6oaoqeK ....... 7.1. Oömne npnnnnbt npOeKTUpoßann ........... 7.2. PemeHn HeKOTOpblX 3aJaq OnTHMaIbHOrO npOeKTpoßannn.. 7.3. Cpamtenue maccoßofi sqbqbeTtmnOCTU TpeXCaOfmblX naacTun u O60IOqeK t /pyrnx TtnOß TOHKOCTeHHblX KOnCTpyKnfi... 7.4. HeKoTOpe peKoMeH/aRIn o pi6liKeHHOMy OnTnMaIbHOty ipOeKTHpOßanHIO ..................... 178 178 178 182 184 187 188 189 194 220 9-20 222 29 9-44 249 255 257 260 260 265 9-76 279 7.5. BonaHle JleteKToß Tl4na paccloennn Ha napaMeTpb TpeXClOf- HblX nJiaCTnH ....................... 281 7.6. F[pOeKTnpoßaHne Tpexc2aoflnblX KOHCTpyKI2rlf'i c yqeToM paccaoe- nur ........................... 283 7.7. Ocnoßnble nyTn cnn.xKennH iMiHflnnn pflccJloennfi Ha npoqnocTb Tpexc.rIOfiHblX KOnCTpyKILnI ................ 291 7.8. PacqeT KpnTHqeCKHX uapaMeTpoß paccloenn TpexcIonblX n.rlaCTnH n O60.rIOqeK ............. 297 CnncoK anepaTypbl. 299 I'IpeJIMeTI41Ifi yKa3aTe,rlb ........................ 300 
Baaaaap Hasoaaeaau Koöeaea, Jlea Maxaäaosw Koaapcsaä, Cepaa HeaHomlq Taobeee PACqET TPEXCJIOIIHblX KOHCTPKIHI Pe, aawrop H. A. ,qeöe,ena Xy,Ko:Ke¢TBeHHt,If'I pela«wop 14. K. Kanpaaona YlepeiaeT xy,aO:aHHga A. H. Kona.ena TeXHH'ecgHf pe,aaI<Top H. B. Taopeengo Koppeop Jl. . lllaöamoaa a O. E. /lama«a I/Iß J¢_o 3456 C,a8o B 8a6op 29.07.83. YIo/lncaso B neaTb 23.12.83. T-22926. • opMaT 60X901/I«. ByMara Tnorpaqbca J¢2 2. rapHTypa .qTepaTypHal. l-[eqaTb BlICOl¢aI. CI. Ileq. i. 19,0. Yca. Kp.-OTT. 19,0. Y.-8a,. a. 19,80. TnpaK I1800 K8. 3aKa3 177. lea I p. 30 . Op,ea Tpy,oßoro Kpacoro 3aen 88JlaTeIbCTBO «NiamnOCTpOene» 107076, /M.ocKBa, CTpOMbIHCKI4I nep., 4 21eHHHrpaJlc¢a THnorpadpH J¢_o 6 op,ea Tpy,oßoro KpacHoro 3HaMeH -leHHHI'paJ[CKOI'O ooeHHeHHil «TexHHqeCKa KHHFa> HM. EBFeHHH CoKo.qoßo CoIO3rloaHrparlpoMa rlp FocyIapCTBe8OM KOMI4TeTe CCCP rlo Jle31aM Ha/IaTe_3IbCTB, rloiJrpaHu  ¢HKOfl ToproßIm 193144, r. JIe8rpa,, ya. Moceeo, I0.