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[Cbca] steel framing - engenharia

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[Cbca] steel framing - engenharia

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  155. 155. HVHo}HVGRWLSR8HTXDQGRVXEPHWLGDVj FRPSUHVVmRXQLIRUPH6mRWDPEpPDSUHVHQWD GDVDVIRUPXODo}HVSDUDDVVHo}HVGRWLSR8HH GRWLSR=HVXEPHWLGDVjIOH[mRHPUHODomRDR HL[RSHUSHQGLFXODUjDOPDHVHo}HVGRWLSRFDU WRODH8HTXDQGRVXEPHWLGDVjIOH[mRHPUHOD omR DR HL[R SDUDOHOR j DOPD HVWDQGR RV HQULMHFHGRUHVGHERUGDFRPSULPLGRV RP R REMHWLYR GH VLPSOLILFDU R GLPHQVLRQDPHQWRD$%171%5FRQ WpPDLQGDDOJXPDVLQIRUPDo}HV~WHLVSDUDTXH VHMDP GLVSHQVDGDV DV YHULILFDo}HV GD IODPEDJHPSRUGLVWRUomR RPSRUWDPHQWRSyVFUtWLFRGHHOH PHQWRVHVEHOWRV±0pWRGRGDODUJXUDHIHWLYD $ DQiOLVH GR FRPSRUWDPHQWR SyVFUtWLFR FRQGX]LGD DWUDYpV GDV HTXDo}HV GLIHUHQFLDLV QmROLQHDUHVGHHTXLOtEULRpFRPSOH[DGHYHQGR VH UHFRUUHU D PpWRGRV QXPpULFRV H FRPSXWDFLRQDLV 3DUDVLPSOLILFDomRGRWUDWDPHQWRGDVFKD SDVHVEHOWDVHPUHJLPHSyVFUtWLFRYRQ.DUPDQ SURS{VRPpWRGRGDODUJXUDHIHWLYDTXHFRQVL GHUDDUHGXomRGDULJLGH]GDFKDSDGHODUJXUD LQLFLDOEDWUDYpVGHXPDFKDSDVXEVWLWXWDGHODU JXUDHIHWLYDEHVHQGR EH E (VWHFRQFHLWR p HVTXHPDWLFDPHQWHDSUHVHQWDGRQDILJXUD )LJXUD 'LVWULEXLomR QmROLQHDU GDV WHQV}HV H ODUJXUDV HIHWLYDV GH XPD FKDSD VLPSOHVPHQWH DSRLDGD 3DUDDFKDSDDSUHVHQWDGDQDILJXUD DQWHVGHVHUDWLQJLGDDVXDFDUJDFUtWLFDDGLVWUL EXLomRGDVWHQV}HVORQJLWXGLQDLVLQWHUQDVDRORQ JRGDODUJXUDGHVWDFKDSDWHQVmR σ QDGLUHomR [
  156. 156. VHID]GHIRUPDXQLIRUPH$SDUWLUGRLQVWDQWH HPTXHDFDUJDFUtWLFDpDWLQJLGDHVWDQGRDLQGD HPHVWDGRGHVHUYLoRRFRUUHXPDUHGLVWULEXLomR QmROLQHDU
  157. 157. GDVWHQV}HVORQJLWXGLQDLVLQWHUQDVH RDSDUHFLPHQWRVLPXOWkQHRGHGHVORFDPHQWRV SHUSHQGLFXODUHVDRSODQRGDFKDSD3DUDYRQ .DUPDQDWHQVmRFUtWLFDGDFKDSDIODPEDGDGH ODUJXUDEH pLJXDOD σ HTXHpRYDORUGDWHQVmR Pi[LPD σ PD[DWXDQGRDRORQJRGDVDUHVWDVSD UDOHODVD[ $SDUWLUGHVWDFRQFHLWXDomRSRGHVHLQWUR GX]LURFRQFHLWRGHHVEHOWH]UHODWLYDGDGRSHOD HTXDomR
  158. 158. VHQGR λSG DHVEHOWH]UHODWLYDGDFKDSDSHUIHLWD HPHVWDGRGHVHUYLoRHRFiOFXORGDODUJXUD HIHWLYDGHVWDFKDSDHIHWXDGRSHODHTXDomR
  159. 159. )XQGDPHQWRVGRVSHUILVIRUPDGRVDIULR 6HJXQGRRFULWpULRGHYRQ.DUPDQUHIHUHQ WHDRHVWXGRGDVFKDSDVHVEHOWDVQRHVWDGROLPL WH~OWLPRSRGHVHDGPLWLUTXHRFRODSVRGDFKD SDpDOFDQoDGRTXDQGRDWHQVmRPi[LPD σ HDWLQ JHRYDORUGDUHVLVWrQFLDDRHVFRDPHQWRGRPD WHULDOI $SDUWLUGHVWDDSUR[LPDomRDLJXDOGDGH WRPDDIRUPD
  160. 160. 1HVWHFDVRRVHJXQGRPHPEURGDHTXDomR HVWiDVVRFLDGRjHVEHOWH]UHODWLYDGDVHomR QRHVWDGROLPLWH~OWLPR λ S RXVHMD
  161. 161. 'HVWDIRUPDQRLQVWDQWHGRFRODSVRGDFKDSD WHPVHTXH
  162. 162. $IRUPXODomRGHYRQ.DUPDQpDSOLFiYHOjV FKDSDVLGHDLVSHUIHLWDVHTXDo}HVH
  163. 163. RPUHODomRjVFKDSDVUHDLVGHYHVHFRQVLGH UDUTXHHODVVmRSRUWDGRUDVGHGLYHUVDVLPSHU IHLo}HVRULXQGDVJHUDOPHQWHGRVSURFHVVRVGH IDEULFDomRDWpVHFKHJDUDRV3))1HVWHFDVR KiVHPSUHXPDGLPLQXLomRGDFDUJD~OWLPDGD FKDSDHDPDJQLWXGHGHVWDPLQRUDomRHVWiDV VRFLDGDDRVQtYHLVGDVLPSHUIHLo}HVLQLFLDLV$ SDUWLUGHVWDVYHULILFDo}HVGLYHUVRVDXWRUHVSUR SXVHUDPRXWUDVIyUPXODVSDUDRFiOFXORGDFDUJD ~OWLPDGHFKDSDVHVEHOWDVLPSHUIHLWDV $IRUPXODomRPDLVGLIXQGLGDLQWHUQDFLRQDO PHQWHHDGRWDGDHPGLYHUVDVQRUPDVWpFQLFDVp DGH:LQWHUTXHIRLSURSRVWDSDUDRHVWDGROLPLWH ~OWLPRGHHVFRDPHQWRSRUFRPSUHVVmRGDFKD SDFRQIRUPHHTXDomR
  164. 164. 1RHVWDGROLPLWH~OWLPRDIyUPXODGH:LQWHU DSUHVHQWDH[FHOHQWHVUHVXOWDGRV1RHQWDQWRHVWD IRUPXODomRQmRDSUHVHQWDUHVXOWDGRVVDWLVIDWyULRV SDUDRFRPSRUWDPHQWRSyVFUtWLFRDQWHVGRFR ODSVR0HVPRDVVLPSDUDRFiOFXORGRVGHVOR FDPHQWRVWDOFRPRHVSHFLILFDPGLYHUVDVQRUPDV WpFQLFDVSRGHVHXWLOL]DUDIyUPXODGH:LQWHUDSH QDVWURFDQGRQDIyUPXOD λS SRU λSGFRQIRUPH DSUHVHQWDDHTXDomRREWHQGRVHXPFRP SRUWDPHQWRPXLWRIOH[tYHOGDFKDSDFRPSUHYLV}HV WHyULFDVGHPDVLDGDPHQWHFRQVHUYDGRUDV
  165. 165. 1ROLPLDUGDIODPEDJHPORFDOSDUDRTXDO EH E= GHWHUPLQDVHSDUD S λ RYDORU LJXDOD VHQGRHQWmRHVWDHVEHOWH]UHODWLYDGHVLJ QDGDGH λ 2$PHULFDQ,URQDQG6WHHO,QVWLWXWH$,6,
  166. 166. H R(8522'(DGRWDPDOpPGDH[SUHVVmRGH :LQWHUIyUPXODVPDLVSUHFLVDVSDUDRFiOFXORGRV GHVORFDPHQWRVHDVVLPUHSUHVHQWDURFRPSRUWD PHQWRHPVHUYLoRGHFKDSDVHVEHOWDVFRPDV GXDVERUGDVYLQFXODGDVDRXWURVHOHPHQWRVQD GLUHomRORQJLWXGLQDOGRSHUILO $ ILJXUD DSUHVHQWD DV IRUPXODo}HV DGRWDGDV SHOR$,6, $,6,
  167. 167. H SHOR (8522'((6
  168. 168. FRQVWDQGRDLQGDD VROXomRGH:LQWHUDGDSWDGDSDUDDSUHYLVmRGR FRPSRUWDPHQWRGDFKDSDHPUHJLPHSyVFUtWLFR )LJXUD RPSDUDomR HQWUH DOJXPDV IRUPXODo}HV SDUD R FiOFXOR GD ODUJXUD HIHWLYD
  169. 169. 1RWHVHQDILJXUDTXHDVIRUPXODo}HV GR$,6,HGR(8522'(TXDQGRFRPSDUDGDV FRPDGH:LQWHUDGDSWDGDDSUHVHQWDPPDLRUHV UHVLVWrQFLDVHPUHJLPHSyVFUtWLFROHYDQGRSRU WDQWRDRSURMHWRGHHVWUXWXUDVDLQGDPDLVOHYHV
  170. 170. DStWXOR 3UHVFULo}HVGD$%17 1%5
  171. 171. 3UHVFULo}HVGD$%171%5 2WH[WRGD$%171%5IXQGD PHQWDGRQRPpWRGRGRVHVWDGRVOLPLWHVIRLHOD ERUDGRFRPEDVHQDVSUHVFULo}HVGR$,6, $,6,
  172. 172. LQFOXLQGRDOJXPDVUHFRPHQGDo}HVH SURFHGLPHQWRVGR(XURFRGH(6
  173. 173. HGD QRUPDDXVWUDOLDQD$61=6
  174. 174. SURFX UDQGRVHPSUHHVWDEHOHFHUFRPSDWLELOLGDGHFRP RXWUDVQRUPDVEUDVLOHLUDVUHODFLRQDGDVDRWHPD 2PpWRGRGRVHVWDGRVOLPLWHVEDVHLDVHQD DSOLFDomRGHFRHILFLHQWHVGHVHJXUDQoDWDQWRjV Do}HVQRPLQDLVTXDQWRjVUHVLVWrQFLDVQRPLQDLV $SDUWLUGHFRPELQDo}HVGDVDo}HVGHFiOFXOR GHWHUPLQDPVHRVHIHLWRVGHFiOFXORGDVDo}HV TXHVmRFRPSDUDGRVFRPDVUHVLVWrQFLDVGHFiO FXOR(VWHPpWRGRXWLOL]DXPSURFHVVRGHYHULIL FDomRQRTXDODHVWUXWXUDpDQDOLVDGDHPYiULDV VLWXDo}HVH[WUHPDVVXEGLYLGLGDVQRVHVWDGRVOL PLWHV~OWLPRVHHVWDGRVOLPLWHVGHXWLOL]DomR 1RSUHVHQWHFDStWXORVmRDSUHVHQWDGDVH FRPHQWDGDVDOJXPDVGDVSUHVFULo}HVGD$%17 1%5UHODFLRQDGDVFRPRVPRGRVGH IODPEDJHPORFDO±LQFOXLQGRRPRGRGLVWRUFLRQDO GRVHOHPHQWRVGDVHomRWUDQVYHUVDOGRSHUILO FRQVLGHUDGDVSHORDXWRUFRPRDVPDLVVLJQLILFD WLYDV SDUD R FRQKHFLPHQWR GR IHQ{PHQR GD IODPEDJHPORFDOHGHVXDLQWHUDomRFRPRVPR GRVGHIODPEDJHPJOREDOGRV3))(VVDVSUHV FULo}HVIRUDPXWLOL]DGDVQDVROXomRSDUFLDOGRV H[HPSORVGHFiOFXORDSUHVHQWDGRVQRFDStWXOR RTXHQmRGLVSHQVDDUHDOL]DomRGHRXWUDVYHULIL FDo}HVFDEtYHLVHPFDGDFDVRWDLVFRPRHIHLWR VKHDUODJ EDUUDVVXMHLWDVDIRUoDVFRQFHQWUDGDV VHP HQULMHFHGRUHV WUDQVYHUVDLV HIHLWR ZHE FULSSOLQJ
  175. 175. HGHVORFDPHQWRVOLPLWHVHQWUHRXWURV 6mRWDPEpPDSUHVHQWDGRVDSHQDVRVFUL WpULRVSDUDRGLPHQVLRQDPHQWRGDVOLJDo}HVSD UDIXVDGDVSUySULDVHPDLVXWLOL]DGDVSDUDRVLV WHPD/6) 9DORUHV Pi[LPRV UHFRPHQGDGRV SDUDDUHODomRODUJXUDHVSHVVXUD $UHODomRODUJXUDHVSHVVXUDGRVHOHPHQWRV EW
  176. 176. TXHUHSUHVHQWDVHXtQGLFHGHHVEHOWH]JHR PpWULFDGHYHUHVSHLWDUOLPLWHVPi[LPRVDILPGH QmR VH REWHUHP HOHPHQWRV H[FHVVLYDPHQWH GHIRUPiYHLV(VWHVYDORUHVOLPLWHVGHEWVHUYHP SDUDVHSUHYHQLUGHIRUPDo}HVH[FHVVLYDVGHYL GDVjIODPEDJHPORFDOSURYRFDQGRRQGXODo}HV YLVtYHLVHQmRGHVHMiYHLVQRVHOHPHQWRVGRVSHU ILVPHVPRSDUDFDUJDVGHVHUYLoR $WDEHODDSUHVHQWDRVYDORUHVPi[LPRV UHFRPHQGDGRVSDUDDUHODomRODUJXUDHVSHVVX UD GH XP HOHPHQWR GHVFRQVLGHUDQGR HQULMHFHGRUHVLQWHUPHGLiULRVVHQGRWDHVSHV VXUDGDFKDSDGHDoRTXHFRQVWLWXLRSHUILOVHP RUHYHVWLPHQWRPHWiOLFR $VGHILQLo}HVGRVHOHPHQWRVWLSRV$$H$/ VmRDSUHVHQWDGDVQRLWHP 0RGRGHIODPEDJHPORFDOGHFKDSD $VROXomRGRSUREOHPDGRFRPSRUWDPHQWR SyVFUtWLFRGHFKDSDVIRLSURSRVWDSRUYRQ.DUPDQ HpUHSUHVHQWDGDSRUXPVLVWHPDGHHTXDo}HV GLIHUHQFLDLVGHHTXLOtEULR9iULRVPpWRGRVSRGHP VHUXWLOL]DGRVDILPGHVHREWHUVROXo}HVDSUR[L PDGDVSDUDHVWHSUREOHPDFRPRRPpWRGRGDV SHUWXUEDo}HVRPpWRGRGDVGLIHUHQoDVILQLWDVRX DLQGDXPPpWRGRVHPLYDULDFLRQDO $ FRPSOH[LGDGH GDV VROXo}HV EDVHDGDV QRVPpWRGRVFLWDGRVDQWHULRUPHQWHFRQGX]LXDR GHVHQYROYLPHQWRGHPpWRGRVVLPSOLILFDGRVSDUD R WUDWDPHQWR GDV FKDSDV HVEHOWDV HP UHJLPH SyVFUtWLFR'HQWUHHVWHVRGHJUDQGHDFHLWDomR HDPSODPHQWHDGRWDGRSRUWRGDVDVQRUPDVWpF QLFDVQDFLRQDOHLQWHUQDFLRQDLVpRPpWRGRGD ODUJXUDHIHWLYDFRQIRUPHDSUHVHQWDGRHP
  177. 177. DVRDVHUDQDOLVDGR ≤ 6HJXLQGRHVWDILORVRILDGHFiOFXORD$%17 1%5HVWDEHOHFHTXHQRFiOFXORGD UHVLVWrQFLDHGRVGHVORFDPHQWRVGHSHUILVIRU PDGRVSRUHOHPHQWRVHVEHOWRVDIODPEDJHPOR FDOGHHOHPHQWRVWRWDOPHQWHRXSDUFLDOPHQWHFRP SULPLGRVGHYHVHUFRQVLGHUDGDSRUPHLRGHODU JXUDVHIHWLYDV (OHPHQWRVWLSR$$HWLSR$/ 1RFiOFXORGDUHVLVWrQFLDGDVEDUUDVGHYH VHUFRQVLGHUDGDDUHGXomRGHVXDUHVLVWrQFLD GHYLGDjIODPEDJHPORFDOGHVHXVHOHPHQWRV GHWHUPLQDQGRVHDVODUJXUDVHIHWLYDVEHIGRVHOH PHQWRVGDVHomRWUDQVYHUVDOTXHVHHQFRQWUHP WRWDORXSDUFLDOPHQWHVXEPHWLGRVDWHQV}HVQRU PDLVGHFRPSUHVVmRFRQIRUPHVHJXH ÂWRGRVRVHOHPHQWRVWLSR$$LQGLFDGRVQD WDEHODHRVHOHPHQWRVWLSR$/LQGLFD GRVQDWDEHODVHPLQYHUVmRQRVLQDOGD WHQVmRψ ≥
  178. 178. E Eλ
  179. 179. λ ≤ E
  180. 180. HI SS Â HOHPHQWRV$/LQGLFDGRVQDWDEHODFRP LQYHUVmRQRVLQDOGDWHQVmRψ
  181. 181. E Eλ
  182. 182. λ ≤ E
  183. 183. HI FSS F 6HQGREDODUJXUDGRHOHPHQWREDODUJXUD FGDUHJLmR FRPSULPLGDGR HOHPHQWRFDOFXODGD FRPEDVHQDVHomRHIHWLYDH λ S RtQGLFHGHHV EHOWH]UHGX]LGRGRHOHPHQWRGHILQLGRFRPR EHI EF SDUD λ S ≤
  184. 184. 2QGHWpDHVSHVVXUDGRHOHPHQWRNpR FRHILFLHQWHGHIODPEDJHPORFDODVHUFDOFXODGR GHDFRUGRFRPDWDEHODSDUDHOHPHQWRV$$ RXGHDFRUGRFRPDWDEHODSDUDHOHPHQWRV $/ σ pDWHQVmRQRUPDOGHFRPSUHVVmRDVHU GHWHUPLQDGDVHJXQGRRVVHJXLQWHVSURFHGLPHQ WRV D
  185. 185. (VWDGROLPLWH~OWLPRGHHVFRDPHQWRGDVHomR 3DUDFDGDHOHPHQWRWRWDOPHQWHRXSDUFLDO PHQWHFRPSULPLGR σpDPi[LPDWHQVmRGHFRP SUHVVmRFDOFXODGDSDUDDVHomRHIHWLYDTXHRFRU UHTXDQGRDVHomRDWLQJHRHVFRDPHQWR 4XDQGRDPi[LPDWHQVmRpGHWUDomR σ SRGHVHUFDOFXODGDDGPLWLQGRVHGLVWULEXLomROL QHDUGHWHQV}HV1HVWHFDVRDVHomRHIHWLYD GHYHVHUGHWHUPLQDGDSRUDSUR[LPDo}HVVXFHV VLYDV 7DEHOD 9DORUHV Pi[LPRV UHFRPHQGDGRV SDUDDUHODomRODUJXUDHVSHVVXUD
  186. 186. ≥ 9DORUPi[LPRGD UHODomRODUJXUD HVSHVVXUDEW
  187. 187. P D[ (OHPHQWRFRPSULPLGR$$WHQGRXPD ERUGDYLQFXODGDDDOPDRXPHVDHD RXWUDDHQULMHFHGRUGHERUGDVLPSOHV 3DUDHYLWDUGHIRUPDo}HVH[FHVVLYDVGR HOHPHQWRUHFRPHQGDVHEW
  188. 188. PD[ (OHPHQWRFRPSULPLGR$$WHQGRXPD ERUGDYLQFXODGDDDOPDHDRXWUDD PHVDRXRXWURWLSRGHHQULMHFHGRUGH ERUGDFRP,V,DH'EFRQIRUPH $OPDGHSHUILV8QmRHQULMHFLGRVVXMHLWD jFRPSUHVVmRXQLIRUPH (OHPHQWRFRPSULPLGRFRPDPEDVDV ERUGDVYLQFXODGDVDHOHPHQWRV$$3DUD HYLWDUGHIRUPDo}HVH[FHVVLYDVGR HOHPHQWRUHFRPHQGDVHEW
  189. 189. PD[ (OHPHQWRFRPSULPLGR$/RX$$FRP HQULMHFHGRUGHERUGDWHQGR,V,DH 'EFRQIRUPH3DUDHYLWDU GHIRUPDo}HVH[FHVVLYDVGRHOHPHQWR UHFRPHQGDVHEW
  190. 190. PD[ $OPDGHYLJDVVHPHQULMHFHGRUHV WUDQVYHUVDLV $OPDGHYLJDVFRPHQULMHFHGRUHV WUDQVYHUVDLVDSHQDVQRVDSRLRVH VDWLVID]HQGRDVH[LJrQFLDVGHGD $%171%5 $OPDGHYLJDVFRPHQULMHFHGRUHV WUDQVYHUVDLVQRVDSRLRVH LQWHUPHGLiULRVVDWLVID]HQGRDV H[LJrQFLDVGHGD$%171%5 'E ≤ FRQIRUPH 3DUD HYLWDU
  191. 191. 3UHVFULo}HVGD$%171%5 $ILJXUDDSUHVHQWDDOJXPDVFRQILJXUDo}HVGHJUDGLHQWHGHWHQVmRSDUDXPHOHPHQWRGRWLSR $$ )LJXUD ± ([HPSOR GH HOHPHQWRV VROLFLWDGRV SRU JUDGLHQWH GH WHQVmR D
  192. 192. (VWDGROLPLWH~OWLPRGHIODPEDJHPGDEDUUD 4XDQGRDEDUUDpVXEPHWLGDjFRPSUHVVmRFRQVLGHUDVH σ ρIVHQGR ρ RIDWRUGHUHGXomR DVVRFLDGRjIODPEDJHPFRQIRUPH 4XDQGRDEDUUDpVXEPHWLGDjIOH[mRFRQVLGHUDVH σ ρ )/7IVHQGR ρ )/7 RIDWRUGHUHGXomR DVVRFLDGRjIODPEDJHPODWHUDOFRPWRUomRFRQIRUPH $$%171%5DSUHVHQWDDLQGDDVSUHVFULo}HVSDUDRFiOFXORGHGHVORFDPHQWRVHP EDUUDVFRPVHo}HVWUDQVYHUVDLVFRQVWLWXtGDVSRUHOHPHQWRVHVEHOWRVTXHGHYHVHUIHLWRSRUDSUR[LPD o}HVVXFHVVLYDVFRQVLGHUDQGRDUHGXomRGHVXDULJLGH]SURYRFDGDSHODIODPEDJHPORFDO
  193. 193. 7DEHOD±/DUJXUDHIHWLYDHFRHILFLHQWHVGHIODPEDJHPORFDOSDUDHOHPHQWRV$$
  194. 194. 3UHVFULo}HVGD$%171%5 7DEHOD±/DUJXUDHIHWLYDHFRHILFLHQWHVGHIODPEDJHPORFDOSDUDHOHPHQWRV$/
  195. 195. /DUJXUDHIHWLYDGHHOHPHQWRVXQL IRUPHPHQWHFRPSULPLGRVFRPHQULMHFHGRUGH ERUGD $$%17 1%5 DSUHVHQWD DV HVSHFLILFDo}HVSDUDRFiOFXORGDODUJXUDHIHWLYD GHHOHPHQWRVXQLIRUPHPHQWHFRPSULPLGRVFRP HQULMHFHGRULQWHUPHGLiULRRXFRPHQULMHFHGRUGH ERUGD1RHQWDQWRYLVDQGRRVH[HPSORVGHDSOL FDomRGRFDStWXORQRSUHVHQWHPDQXDOVHUmR DSUHVHQWDGDVDSHQDVDVSUHVFULo}HVUHODWLYDV DRVHOHPHQWRVXQLIRUPHPHQWHFRPSULPLGRVFRP HQULMHFHGRUGHERUGD 3DUDHVVHVHOHPHQWRVRFiOFXORGDODUJXUD HIHWLYDGHYHVHUUHDOL]DGRFRQVLGHUDQGRVHRYD ORUGHUHIHUrQFLDGRtQGLFHGHHVEHOWH]UHGX]LGR GRHOHPHQWRGDGRSRU
  196. 196. 2QGH σ p D WHQVmR QRUPDO GHILQLGD HP NpRFRHILFLHQWHGHIODPEDJHPORFDO'E GVmRDVGLPHQV}HVLQGLFDGDVQDILJXUDGHI pDODUJXUDHIHWLYDGRHQULMHFHGRUFDOFXODGDFRQ IRUPHGV pDODUJXUDHIHWLYDUHGX]LGDGR HQULMHFHGRUHDGRWDGDQRFiOFXORGDVSURSULHGD GHVGDVHomRHIHWLYDGRSHUILO $V pDiUHDUHGX]LGDGRHQULMHFHGRUFDOFX ODGDFRQIRUPHLQGLFDGRQHVWDVHomRHDGRWDGD QRFiOFXORGDVSURSULHGDGHVGDVHomRHIHWLYDGR SHUILO ,DpRPRPHQWRGHLQpUFLDGHUHIHUrQFLDGR HQULMHFHGRULQWHUPHGLiULRRXGHERUGD $HIH,VVmRUHVSHFWLYDPHQWHDiUHDHIHWLYD GRHQULMHFHGRUHRPRPHQWRGHLQpUFLDGDVHomR EUXWDGRHQULMHFHGRUHPUHODomRDRVHXHL[RSULQ FLSDOSDUDOHORDRHOHPHQWRDVHUHQULMHFLGR 2FHQWUyLGHHRVPRPHQWRVGHLQpUFLDGR HQULMHFHGRUGHYHPVHUDVVXPLGRVHPUHODomRj VXDVHomREUXWD $UHJLmRGDVGREUDVHQWUHRHQULMHFHGRUHR HOHPHQWRDVHUHQULMHFLGRQmRGHYHVHUFRQVLGH UDGD FRPR SDUWHLQWHJUDQWH GR HQULMHFHGRU GH ERUGD 3DUDRHQULMHFHGRUUHSUHVHQWDGRQDILJXUD ,V GWVHQ θ
  197. 197. $HI GHIW
  198. 198. 3DUDRFiOFXORGDUHVLVWrQFLDGHSHUILVIRU PDGRVSRUHOHPHQWRVFRPHQULMHFHGRUGHERUGD GHYHVHUFRQVLGHUDGDDUHGXomRGHVXDUHVLVWrQ FLDSURYRFDGDSHODIODPEDJHPORFDOGHWHUPLQDQ GRVH DV ODUJXUDV HIHWLYDV GR HOHPHQWR H GR HQULMHFHGRUGHDFRUGRFRPRVHJXLQWHSURFHGL PHQWR DVR, λ S ≤ HQULMHFHGRUGHERUGDQmRpQHFHVViULR EHI E GV GHI SDUDHQULMHFHGRUGHERUGDVLPSOHV
  199. 199. $V $HI SDUDRXWURVWLSRVGHHQULMHFHGRU
  200. 200. DVR,, λ S ,D Wλ S@
  201. 201. EHI ,V,D
  202. 202. EHI
  203. 203. ≤ EHI
  204. 204. EHI EHI ±EHI
  205. 205. EHIGHYHVHUFDOFXODGDFRQIRUPHRQGH N ,V,D
  206. 206. ND
  207. 207. ≤ ND
  208. 208. ND 'E
  209. 209. ≤ SDUDHQULMHFHGRUGH ERUGDVLPSOHVFRPƒ ≤ θ ≤ ƒH'E ≤ RQGH θ pLQGLFDGRQDILJXUD GV ,V,D
  210. 210. GHI ≤ GHI
  211. 211. 3UHVFULo}HVGD$%171%5 ND SDUDRXWURVWLSRVGHHQULMHFHGRU $V ,V,D
  212. 212. $HI ≤ $HI
  213. 213. DVR,,, λ S ≥ ,D λ S@W
  214. 214. N ,V,D
  215. 215. ND
  216. 216. ≤ ND
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  218. 218. 3DUDRVSHUILV8VLPSOHVVHPHQULMHFHGRUHV GHERUGD
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  222. 222. 3UHVFULo}HVGD$%171%5 )ODPEDJHPGDEDUUDSRUIOH[mRSRU WRUomRRXSRUIOH[RWRUomR 2YDORUGDIRUoDQRUPDOGHFRPSUHVVmRUH VLVWHQWHGHFiOFXOR1F5GGHYHVHUFDOFXODGRSHOD VHJXLQWHH[SUHVVmR 1F5G ρ $HI I γ γ
  223. 223. 2QGH ρ pRIDWRUGHUHGXomRDVVRFLDGRj IODPEDJHPJOREDOGDEDUUDSRGHQGRVHUGHWHU PLQDGR SRU PHLR GD WDEHOD GD $%17 1%5RXFDOFXODGRSHODVHTXDo}HV
  224. 224. β α λ
  225. 225. λ @
  226. 226. 6HQGR α RIDWRUGHLPSHUIHLomRLQLFLDO 1RVFDVRVGHIODPEDJHPSRUIOH[mRRVYD ORUHVGH D YDULDPGHDFRUGRFRPRWLSRGHVHomR HHL[RGHIODPEDJHPFRQIRUPHWDEHODWHQGR YDORU GLIHUHQWH SDUD FDGD XPD GDV FXUYDV GH IODPEDJHPFRQIRUPHVHVHJXH FXUYDD α FXUYDE α FXUYDF α 'HYHVHFRQVLGHUDUDFXUYDEHPWRGRVRV FDVRVGHIODPEDJHPSRUWRUomRRXSRUIOH[RWRU omR 2tQGLFHGHHVEHOWH]UHGX]LGRSDUDEDUUDV FRPSULPLGDV λ GHYHVHUFDOFXODGRSRU
  227. 227. 1RWHVHQDHTXDomRTXHRHIHLWRGD IODPEDJHPORFDOpOHYDGRHPFRQWDQDGHILQLomR GDiUHDHIHWLYDGDVHomRWUDQVYHUVDOGDEDUUD$HI TXHSRUVXDYH]pFDOFXODGDFRPEDVHQDVODU JXUDVHIHWLYDVGRVHOHPHQWRVDSDUWLUGDVIyUPX ODVDSUHVHQWDGDVQRLWHPSDUDXPQtYHOGH WHQVmR σ ρI 1RFiOFXORGH σSRGHVHGHWHUPLQDURYD ORUGH ρ GHIRUPDDSUR[LPDGDWRPDQGRVHGLUH WDPHQWH$HI $SDUDRFiOFXORGH λ GLVSHQVDQ GRSURFHVVRLWHUDWLYR $IRUoDQRUPDOGHIODPEDJHPHOiVWLFDGD EDUUD1HFRUUHVSRQGHDRSULPHLURPRGRGHLQV WDELOLGDGHGDEDUUDLJXDOSRUWDQWRDRPHQRUGRV YDORUHVGHFDUJDFUtWLFDGHIODPEDJHPSRUIOH[mR RXSRUIOH[RWRUomRGHYHQGRVHUGHWHUPLQDGDD SDUWLUGRVLWHQVRX 1DWDEHODTXHDSUHVHQWDDFODVVLILFD omRGDVVHo}HVHUHVSHFWLYDVFXUYDVGHUHVLV WrQFLDjFRPSUHVVmRDVVRFLDGDVjIODPEDJHP SRUIOH[mRGDVEDUUDVDVGXDVREVHUYDo}HVFLWD GDVHVWmRUHODFLRQDGDVFRPDUHVLVWrQFLDDRHV FRDPHQWRHDXPHQWRGDUHVLVWrQFLDDRHVFRD PHQWRGHYLGRDRHIHLWRGRWUDEDOKRDIULR 6HJXQGRD$%171%5DUH VLVWrQFLDDRHVFRDPHQWRXWLOL]DGDQRSURMHWRGHYH VHUDGRWDGDFRPRXPGRVYDORUHVHVWDEHOHFLGRV DVHJXLU Â2EVHUYDomRDUHVLVWrQFLDDRHVFRD PHQWRGRDoRYLUJHPDQWHVGDVRSHUDo}HV GHIRUPDomRDIULR
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  231. 231. [ [ [ π =
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  233. 233. 1 π =
  234. 234. Â IODPEDJHPHOiVWLFDSRUWRUomR ⎤ 1
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  238. 238. 1 π =
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  241. 241. @ [ U
  242. 242. @
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  244. 244. U 1H1H[
  245. 245. 1H1H
  246. 246. 1H1HW
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  250. 250. γ
  251. 251. F5G GLVW 3DUD ≤ λ GLVW ≤ 1F5G $Iλ GLVW±
  252. 252. @ γ
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