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Manual Pontes e Viadutos em Vigas Mistas.pdf
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- 160. ) ) )Y ≤ = 2VHQULMHFHGRUHVWUDQVYHUVDLVLQWHUPHGLiULRV GHYHPSUHIHUHQFLDOPHQWHVHUIHLWRVGHFKDSDV SDUDRVSHUILVVROGDGRV(OHVSRGHPVHUHP SDUHVXPHQULMHFHGRUGHFDGDODGRGDDOPDGD YLJDFRPOLJDomRFRPDPHVDFRPSULPLGD(OHV SRGHPFRQWXGRVHUIHLWRVGHXPHQULMHFHGRU VLPSOHVGHXPODGRGDFKDSDGHDOPD 2PRPHQWR GH LQpUFLD GH TXDOTXHU WLSRGH HQULMHFHGRUWUDQVYHUVDOHPUHODomRDRSODQR PpGLRGDDOPDQmRGHYHVHUPHQRUTXH - W G , Z = RQGH − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = G K - PDVQmRPHQRUTXH , 0RPHQWRGHLQpUFLDPtQLPRSHUPLWLGRSDUD TXDOTXHUWLSRGHHQULMHFHGRUWUDQVYHUVDOHPFP - 5HODomRGHULJLGH]QHFHVViULDSDUD XP HQULMHFHGRUWUDQVYHUVDOSDUDDFKDSDGHDOPD G HVSDoDPHQWRHQWUHHQULMHFHGRUHVHP FHQ WtPHWURV $iUHDGDVHomRWUDQVYHUVDOGRVHQULMHFHGRUHV WUDQVYHUVDLVLQWHUPHGLiULRVQmRGHYHVHUPH QRUTXH ( ) Z FU Y Y Z W ) ) ) I W K % $ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = ( ) U HQULMHFHGR FU ) WV EV ) ≤ = RQGH EV ODUJXUDGRHQULMHFHGRU WV HVSHVVXUDGRHQULMHFHGRU % SDUDHQULMHFHGRUHVHPSDUHV % SDUDFDQWRQHLUDVVLPSOHV % SDUDFKDSDVVLPSOHV FDOFXODGRQRLWHP 1RWD4XDQGRDiUHD³$´ VHDSUR[LPDUGH]HUR RXIRU QHJDWLYD RVHQULMHGRUHV WUDQVYHUVDLV GHYHPDWHQGHUDSHQDVDRPRPHQWRGHLQpUFLD PtQLPR 4XDQGRRVHQULMHFHGRUHVVmRHPSDUHVRPR PHQWRGHLQpUFLDGHYHVHUWRPDGRHPUHODomR D OLQKD GH FHQWUR GD DOPD 4XDQGR RV HQULMHFHGRUHVVmRGHFKDSDVLPSOHVRPRPHQ WRGHLQpUFLDGHYHVHUWRPDGRHPUHODomRj IDFHHPFRQWDWRFRPDFKDSDGDDOPD 2VHQULMHFHGRUHVWUDVYHUVDLVLQWHUPHGLiULRVQmR SUHFLVDPDSRLDUQDPHVDWUDFLRQDGD$GLVWkQ FLDHQWUHDH[WUHPLGDGHGDVROGDGRHQULMHFHGRU HDH[WUHPLGDGHPDLVSUy[LPDGRILOHWHGHVRO GDGDPHVDFRPDDOPDQmRGHYHVHUPHQRU TXHW Z RXPDLRUTXHW Z 2VHQULMHFHGRUHV QRVSRQWRVGHFDUJDVFRQFHQWUDGDVGHYHPVHU FRORFDGRVHPSDUHVHFDOFXODGRVGHDFRUGR FRPRLWHP
- 161. 1RUPDVHVWUXWXUDLV $ODUJXUDGDFKDSDRXDDEDHPSURMHomRGH XPDFDQWRQHLUDGHXPHQULMHFHGRULQWHUPHGLi ULRQmRGHYHVHUPHQRUTXHPPPDLV GDDOWXUDGDDOPDGDYLJDHHOHGHYHSUHIHUHQFL DOPHQWHQmRVHUPHQRUTXHóGDODUJXUDWRWDO GDPHVDGDYLJD$HVSHVVXUDGDFKDSDRXGD DED HP SURMHomR GH FDQWRQHLUDV GH XP HQULMHFHGRUQmRGHYHVHUPHQRUTXHGD VXDODUJXUD(QULMHFHGRUHVWUDQVYHUVDLVLQWHU PHGLiULRVSRGHPVHUGHDoR$ (QULMHFHGRUHVORQJLWXGLQDLV $GLVWkQFLDyWLPDHQWUHDOLQKDGHFHQWURGD FKDSDGHXPHQULMHFHGRUORQJLWXGLQDOHDIDFH LQWHUQDGDPHVDFRPSULPLGD³GV´pGH K SDUD SHUILVVLPpWULFRV3DUDXPSHUILODVVLPpWULFRD GLVWkQFLD³GV´GHYHVHUGHWHUPLQDGDSHODHTXD omRDEDL[R FS EV I I KFV GV + = RQGH GV GLVWkQFLDGRHQULMHFHGRUORQJLWXGLQDOjIDFH LQIHULRUGDPHVDFRPSULPLGD KFV DOWXUDGDDOPDHPFRPSUHVVmRSDUDD VHomRGHDoRQmRPLVWD 2HQULMHFHGRUORQJLWXGLQDOGHYHVHUSURSRUFLR QDGRSDUDTXH ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = K G W K , Z RQGH , 0RPHQWR GH LQpUFLD PtQLPR SDUD R HQULMHFHGRUORQJLWXGLQDOHPUHODomRjVXDH[ WUHPLGDGHHPFRQWDFWRFRPDFKDSDGDDOPD HPFP $HVSHVVXUDGRHQULMHFHGRUORQJLWXGLQDOQmR GHYHVHUPHQRUTXH ) EV WV ≥ RQGH WV HVSHVVXUDGRHQULMHFHGRU EV ODUJXUDGRHQULMHFHGRU ) WHQVmRGHHVFRDPHQWRGRHQULMHFHGRU $WHQVmRQRHQULMHFHGRUQmRGHYHVHUPDLRUTXH DWHQVmRDGPLVVtYHOEiVLFDSDUDRPDWHULDOXVD GRQRHQULMHFHGRU 2VHQULMHFHGRUHVORQJLWXGLQDLVVmRXVXDOPHQ WHFRORFDGRVGHXPODGRVRPHQWHGDFKDSDGD DOPD(OHVQmRQHFHVVLWDPVHUFRQWtQXRVHSR GHPVHUFRUWDGRVQDVVXDVLQWHUFHo}HVFRP RVHQULMHFHGRUHVWUDQVYHUVDLVLQWHUPHGLiULRV (QULMHFHGRUHVGHDSRLR 3HUILV6ROGDGRV 1RVDSRLRVGHH[WUHPLGDGHGHYLJDVVROGDGDV HQRVDSRLRVLQWHUPHGLiULRVGHYLJDVVROGDGDV FRQWtQXDVGHYHPVHUFRORFDGRVHQULMHFHGRUHV (OHVGHYHPVHHVWHQGHUDWpRPDLVSUy[LPR SRVVtYHOGDERUGDVGDFKDSDGDVPHVDV'H YHPVHUIHLWRVGHFKDSDVFRORFDGDVHPDPERV RVODGRVGDFKDSDGDDOPD2VHQULMHFHGRUHV GHDSRLRGHYHPVHUFDOFXODGRVFRPRFROXQDV HVXDOLJDomRFRPDDOPDGHYHVHUSURMHWDGD SDUDWUDQVPLWLUDUHDomRWRWDOSDUDRVDSDUH OKRVGHDSRLR 3DUDHQULMHFHGRUHVFRPSRVWRVGHGXDVFKDSDV DVHomRGDFROXQDGHYHVHUFRPSRVWDGDVGXDV FKDSDVPDLVXPDSDUWHFHQWUDGDGDFKDSDGD DOPDFXMDODUJXUDQmRVHMDPDLRUTXH YH]HV DHVSHVVXUDGDDOPD3DUDHQULMHFHGRUHVFRP SRVWRVGHTXDWURRXPDLVFKDSDVDVHomRGD FROXQDGHYHLQFOXLUDVFKDSDVHDSDUWHGDDOPD IHFKDGDSHODVTXDWURRXPDLVFKDSDVPDLVXPD ODUJXUDGDDOPDQmRPDLRUTXH YH]HVDVXD HVSHVVXUD 2UDLRGHJLUDomRGHYHVHUFDOFXODGRHPUHOD omRDRHL[RTXHSDVVDSHODOLQKDGHFHQWURGD DOPD2VHQULMHFHGRUHVGHYHPVHUXVLQDGRVMXQ WRjPHVDGDTXDOUHFHEHPDUHDomRRXVROGD GRVSRUVROGDGHSHQHWUDomRWRWDO6RPHQWHD
- 162. SDUWHGRHQULMHFHGRUIRUDGDVROGDGDPHVDFRP DDOPDGHYHVHUFRQVLGHUDGDHIHWLYDPHQWHDSRL DGD $HVSHVVXUD GDVFKDSDV GR HQULMHFHGRUGH DSRLRQmRGHYHVHUPHQRUTXH ) E W ′ ≥ $WHQVmRDGPLVVtYHOjFRPSUHVVmRHDSUHV VmRGHHVPDJDPHQWRQRHQULMHFHGRUQmRGHYHP H[FHGHU RV YDORUHV HVSHFLILFDGRV QR LWHP 7UHOLoDV KDSDV SHUIXUDGDV H EDUUDV WUHOLoDGDV $IRUoDGHFLVDOKDPHQWRQRUPDOjVEDUUDVQRSOD QRGHFRQWUDYHQWDPHQWRVRXFKDSDVSHUIXUDGDV GHYHUiVHUFRQVLGHUDGDGLYLGLGDLJXDOPHQWHHQ WUHWDLVSODQRVSDUDOHORV$IRUoDGHFLVDOKDPHQWR GHYHUiLQFOXLUDo}HVGHYLGRDRSHVRSUySULR PDLVTXDOTXHURXWUDIRUoDH[WHUQD3DUDHOHPHQ WRVFRPSULPLGRVXPDIRUoDDGLFLRQDOGHYHUiVHU DGLFLRQDGDFRPRREWLGRSHODVHJXLQWHIyUPXOD ( ) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + + = ) U O U O 3 9 RQGH 9 IRUoDFRUWDQWHQRUPDOHP N1 3 FRPSUHVVmRQRUPDODGPLVVtYHOHP N1 O FRPSULPHQWRGDEDUUDHP FP U UDLRGHJLUDomRGRHL[RHPUHODomRDRSODQR GHIODPEDJHPHP FP ) WHQVmRGHHVFRDPHQWRPtQLPDGRWLSRGH DoRXVDGRHPN1FP %DUUDVFRPSULPLGDV(VSHVVXUD GRPDWHULDO %DUUDV FRPSULPLGDV SULQFLSDLVGHYHUmR VHU SURMHWDGDVGHIRUPDTXHRVVHXVHOHPHQWRVSULQ FLSDLVGHVXDVHomRVHMDPFRQHFWDGRVGLUHWD PHQWHjVFKDSDVGHOLJDomRSLQRVRXRXWURVHOH PHQWRV 2 FHQWURGHJUDYLGDGHGDXPDVHomRFRPSRVWD GHYHUiFRLQFLGLURPDLVSUy[LPRSRVVtYHOFRPR FHQWURJHRPpWULFRGDVHomR3UHIHUHQFLDOPHQ WHRVVHJPHQWRVGDVHomRGHYHPVHUOLJDGRV HPDOPDVRXFKDSDVSHUIXUDGDV 3DUDSODFDVDSRLDGDVHPXPODGRDEDVHPSUR MHomRGHFDQWRQHLUDVRXFKDSDVSHUIXUDGDVD HVEHOWH]EWGDFKDSDRXDEDGDFDQWRQHLUD TXDQGRXVDGDHPHOHPHQWRVFRPSULPLGRVQmR SRGHUiVHUVXSHULRUD D I W E = PDVHPQHQKXPFDVREWSRGHUiVHUVXSHULRU DSDUDEDUUDVSULQFLSDLVHSDUDEDUUDV VHFXQGiULDV 1RWDEpDGLVWkQFLDHQWUHDH[WUHPLGDGHGD FKDSDRXH[WUHPLGDGHGDSHUIXUDomRHRSRQWR GHDSRLR
- 164. EW
- 165. 1RUPDVHVWUXWXUDLV 3DUDFKDSDVDSRLDGDVQDVGXDVH[WUHPLGD GHVRXDOPDVGHVHJPHQWRVGHHOHPHQWRVSULQ FLSDLVSDUDHOHPHQWRVGHVHomRFDL[mRIRUPD GRVSRUFKDSDVVHo}HVODPLQDGDVRXVHJPHQ WRVGHFRPSRQHQWHVFRPFRYHUSODWHVUHODomR EWGHFKDSDVSULQFLSDLVRXDOPDVGHVHJPHQ WRVFRPSULPLGRVQmRGHYHUiXOWUDSDVVDURYD ORUREWLGRSHODIyUPXOD D I W E = PDVHPQHQKXPFDVR EW GHYHUiVHUPDLRUTXH 1RWDE pDGLVWkQFLDHQWUHSRQWRVGHDSRLRGD FKDSDHHQWUHUDL]GHPHVDVSDUDDOPDVGH VHJPHQWRVODPLQDGRV
- 168. RXDOPDVOLJDQGR FKDSDVSULQFLSDLVRXVHJPHQWRVDUHODomREW GHFKDSDVGHFRYHUSODWHVVyOLGDVRXDOPDV TXDQGRFRPSULPLGDVQmRGHYHUiXOWUDSDVDUR YDORUREWLGRSHODIyUPXOD D I W E = PDVHPQHQKXPFDVR EWGHYHUiVHUPDLRUTXH 1RWD E pDGLVWkQFLDOLYUHHQWUHDSRLRV
- 170. EW 4XDQGRDWHQVmRGHFRPSUHVVmRpLJXDODR YDORUOLPLWHGH)DUHODomREWGRVVHJ PHQWRVLQGLFDGRVDFLPDQmRSRGHUiVHUPDLRU TXHRVYDORUHVPRVWUDGRVDEDL[RSDUDRVVH JXLQWHVJUDXVGHDoRV 3DUDFKDSDVSHUIXUDGDVDSRLDGDVQDVGXDV H[WUHPLGDGHVSDUDHOHPHQWRVGHVHomRFDL [mRIRUPDGRVGHFKDSDVSHUIXUDGDVOLJDQGRHOH PHQWRVSULQFLSDLVRXVHJPHQWRVDUHODomR EW GHFKDSDVSHUIXUDGDVTXDQGRFRPSULPLGDVQmR GHYHUiXOWUDSDVVDURYDORUREWLGRSHODIyUPXOD D I W E = PDVHPQHQKXPFDVR EWGHYHUiVHUPDLRUTXH 1RWD E pDGLVWDQFLDOLYUHHQWUHSRQWRVGH DSRLR$DWHQomRpGLULJLGDDRVUHTXLVLWRVSDUD DHVSHVVXUDGDFKDSDQDVSHUIXUDo}HVFKDPD GDGHDSRLDGDHPXPODGRTXHWDPEpPGHYH UiVHUVDWLVIHLWD
- 171. 4XDQGRDWHQVmRGHFRPSUHVVmRpLJXDODR YDORUOLPLWHGH ) DUHODomR EW GDVFKDSDV SHUIXUDGDVQmRSRGHUiVHUPDLRUTXHRVYDOR UHVPRVWUDGRVDEDL[RSDUDRVVHJXLQWHVJUDXV GHDoRV 7HQVmRGHHVFRDPHQWR PtQLPDN1FP
- 173. EW
- 176. VHMDLQIHULRUjVHWH2DFDEDPHQWR GDVVROGDVGHSHQHWUDomRGHYHUiVHUHVPH ULOKDGRFRPDVXSHUItFLHOLVD ±7HQV}HVFRPELQDGDV 7RGRVRVHOHPHQWRVVXMHLWRVjDomRVLPXOWk QHDGHWHQV}HVGHFRPSUHVVmRD[LDOHIOH[mR GHYHUmRVHUGLPHQVLRQDGRVSDUDDWHQGHUDRV VHJXLQWHVUHTXLVLWRV I ) I I ) I I ) D D P[ E[ D H[ P E D H + − ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + − ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ≤ H I ) I ) I ) D E[ E[ E E + + ≤ QRVSRQWRVGHDSRLR
- 177. RQGH ( ) ) ( )6 . / U H E E E = π I D WHQVmRD[LDOFDOFXODGD I E[ RXI E WHQVmRGHIOH[mRFDOFXODGDHP UHODomRDRVHL[RV;HUHVSHFWLYDPHQWH ) D WHQVmRD[LDOTXHVHULDSHUPLWLGDVHD IRUoDD[LDOH[LVWLVVHVR]LQKD ) E[ ) E WHQVmRGHIOH[mRTXHVHULDSHUPLWLGD VHRPRPHQWRIOHWRUH[LVWLVVHVR]LQKRHPUH ODomRDRVHL[RV;HHGHDFRUGRFRPDWDEH OD )¶ H WHQVmRGHIODPEDJHPGH(XOHUGLYLGD SHORIDWRUGHVHJXUDQoD . E IDWRUGHFRPSULPHQWRHIHWLYRQRSODQR GHIOH[mR / E GLVWkQFLDVHPFRQWHQomRODWHUDOQRSODQR GHIOH[mR U E UDLRGHJLUDomRQRSODQRGHIOH[mR P[ P FRHILFLHQWHHPUHODomRDRVHL[RV; H )6 IDWRUGHVHJXUDQoDLJXDOD 9LJDVPLVWDV *HQHUDOLGDGHV (VWDVHomRWUDWDGDVHVWUXWXUDVFRPSRVWDVGH YLJDVPHWiOLFDVHODMHVGHFRQFUHWRXQLGDVSRU FRQHFWRUHVGHFLVDOKDPHQWR (VSHFLILFDo}HVJHUDLVSDUDSURMHWRVGHHVWUX WXUDVHVSHFtILFDVGHFRQFUHWRHDoRVHUmRDSOL FDGDVDHVWUXWXUDVFRQVWLWXtGDVSRUYLJDVPLV WDVRQGHWDLVHVSHFLILFDo}HVIRUHPDSOLFiYHLV $VYLJDVPLVWDVHODMHVGHYHUmRVHUSURMHWDGDV HDVWHQV}HVFDOFXODGDVSHORPpWRGRGRPR PHQWRGHLQpUFLDFRPSRVWRHFRQVLVWHQWHFRP DVSURSULHGDGHVSUpGHWHUPLQDGDVGRVYiULRV PDWHULDLVXVDGRV $UHODomRHQWUHRPyGXORGHHODVWLFLGDGHGR DoR(D N1FP
- 181. Q (D(F a a a a a DFLPDGH RQGH I FN 5HVLVWrQFLDGRFRQFUHWRjFRPSUHVVmR GHWHUPLQDGRSRUWHVWHFRPFRUSRGHSURYDFL OtQGULFRFRPDLGDGHGHGLDV Q 5HODomRHQWUHRPyGXORGHHODVWLFLGDGHGR DoRSDUDRGRFRQFUHWR 2HIHLWRGDGHIRUPDomROHQWDSDUDFDUJDVGH ORQJDGXUDomRGHYHVHUFRQVLGHUDGRQRSURMH WRGDVYLJDVPLVWDVTXHWrPFDUJDVSHUPDQHQ WHVDJLQGRVREUHDVHomRPLVWD1HVWDVHVWUXWX UDVDVWHQV}HVHRFLVDOKDPHQWRKRUL]RQWDOSUR GX]LGRSHODVFDUJDVSHUPDQHQWHVTXHDJHP VREUHDVHomRPLVWDGHYHUmRVHUFDOFXODGDV SDUDRYDORUGH³Q´GDGRSHODWDEHODDFLPDRX SHORVHXYDORUPXOWLSOLFDGRSRU RTXHIRUQHFHU DVWHQV}HVGHFLVDOKDPHQWRPDLVDOWDV 6H IRUXVDGRFRQFUHWRFRPFDUDFWHUtVWLFDV H[SDQVLYDVRSURMHWRGDYLJDPLVWDGHYHVHU XVDGRFRPFXLGDGRHGHYHPVHUIHLWDVSUHYL V}HVQRSURMHWRSDUDDFRPRGDUDH[SDQVmR $VVHo}HVPLVWDVGHYLJDVELDSRLDGDVRXHP UHJL}HVGHPRPHQWRSRVLWLYRGHYLJDVFRQWtQX DVGHYHPVHUGHSUHIHUrQFLDSURSRUFLRQDGDV GHIRUPDTXHRHL[RQHXWURILTXHDEDL[RGDVX SHUItFLHVXSHULRUGRSHUILOGHDoR2FRQFUHWR QDSDUWHWUDFLRQDGDQmRGHYHVHUFRQVLGHUDGR QDUHVLVWrQFLDDRVPRPHQWRV1DVUHJL}HVGH PRPHQWRQHJDWLYRGHYLJDVFRQWtQXDVVRPHQWH DVDUPDGXUDVGDODMHSRGHPVHUFRQVLGHUDGDV DJLQGRMXQWRFRPDYLJDGHDoRQDUHVLVWrQFLD DRVPRPHQWRV 'HYHPVHUSUHYLVWDVDQFRUDJHQVPHFkQLFDVQDV UHJL}HVGHVHo}HVFRPSRVWDVGHIRUPDDWUDQV IHULUDVWHQV}HVGHVHQYROYLGDVQDLQWHUIDFHHQ WUHR DoRH RFRQFUHWR2 FRQFUHWRGRODGR WUDFLRQDGRGRHL[RQHXWURSRGHVHUFRQVLGHUD GRQRFiOFXORGRPRPHQWRGHLQpUFLDSDUDYHUL ILFDomRGDVGHIRUPDo}HVHQDGHWHUPLQDomR GDULJLGH]SDUDRFiOFXORGRVPRPHQWRVHFRU WDQWHV $V YLJDVPHWiOLFDVHVSHFLDOPHQWHVHQmR HVFRUDGDVSRUHVFRUDPHQWRVLQWHUPHGLiULRV GHYHPVHUYHULILFDGDVSDUDHVWDELOLGDGHHUH VLVWrQFLDQRSHUtRGRGHWHPSRHPTXHRFRQ FUHWRpODQoDGRHDQWHVGDVXDFXUD RQHFWRUHVGHFLVDOKDPHQWR 2VPHLRVPHFkQLFRVXVDGRVQDMXQomRGDYLJD GHDoRFRPRFRQFUHWRFRPDILQDOLGDGHGH GHVHQYROYHUDUHVLVWrQFLDDRFLVDOKDPHQWRQH FHVViULDSDUDSURGX]LUDDomRPLVWDGHYHUmR HVWDUGHDFRUGRFRPDVHVSHFLILFDo}HVGRVUHV SHFWLYRVPDWHULDLV 2VFRQHFWRUHVGHFLVDOKDPHQWRGHYHPVHUGH WLSRVTXHSHUPLWDPDFRPSOHWDFRPSDFWDomRGR FRQFUHWRGHIRUPDDJDUDQWLUTXHWRGDDVXSHU ItFLHHVWDUiHPFRQWDWRFRPRFRQFUHWR(OHVGH YHPVHUFDSD]HVGHUHVLVWLUDDPERVPRYLPHQ WRVHQWUHRFRQFUHWRHRDoRKRUL]RQWDLVHYHU WLFDLV $VFDSDFLGDGHVGHUHVLVWrQFLDGRVFRQHFWRUHV GHFLVDOKDPHQWRWLSR 6WXGH 9LJD8VmRGDGDV QRLWHP2VFRQHFWRUHVWLSR9LJD8 GHYHPWHUXPILOHWHPtQLPRGH PP DRORQ JRGDEDVHGRSHUILO8 2VFRQHFWRUHVGHYHUmRSHQHWUDUQRFRQFUHWR QRPtQLPR PP DFLPDGDIDFHLQIHULRUGDODMH HGHYHPWHUDFLPDGRVHXWRSRXPFREULPHQWR GHFRQFUHWRQmRPHQRUGRTXH PP $GLVWkQFLDOLYUHHQWUHDH[WUHPLGDGHGDPHVD GDYLJDHDH[WUHPLGDGH GRVFRQHFWRUHVGH
- 185. YH]HVDPHQRUHVSHVVXUDGDODMH 3DUDYLJDVTXHWrPPHVDGHODMHGHXPODGR VRPHQWHDODUJXUDHIHWLYDGDPHVDQmRGHYH UiH[FHGHU GRFRPSULPHQWRGRYmRGDYLJD RXYH]HVDHVSHVVXUDGDODMHRXòGDGLV WkQFLDGHFHQWURDFHQWURSDUDDSUy[LPDYLJD 7HQV}HV $VWHQV}HVPi[LPDVGHFRPSUHVVmRHWUDomR HPYLJDVQmRHVFRUDGDVGXUDQWHDFRORFDomR GDVFDUJDVSHUPDQHQWHVGHYHPVHUDVRPD GDVWHQV}HVSURGX]LGDVSHODVFDUJDVSHUPD QHQWHVDJLQGRVREUHDVYLJDVGHDoRLVRODGDV HDVWHQV}HVSURGX]LGDVSHODVVREUHFDUJDV DJLQGRVREUHDVHomRPLVWD4XDQGRDVYLJDV VmRHVFRUDGDVFRPDSRLRVLQWHUPHGLiULRVGX UDQWHDFRQFUHWDJHPTXHSHUPDQHFHPDWpTXH RFRQFUHWRDWLQMDGDVXDUHVLVWrQFLDSUHYLV WDSDUDGLDVDVWHQV}HVGHYLGDVjVFDUJDV SHUPDQHQWHVHjVFDUJDVPyYHLVGHYHUmRVHU FDOFXODGDVFRPEDVHQDVSURSULHGDGHVGDVH omRPLVWD LVDOKDPHQWR LVDOKDPHQWRKRUL]RQWDO $GLVWkQFLDPi[LPDHQWUHFRQHFWRUHVQmRGH YHUiH[FHGHUDFPH[FHWRVREUHDSRLRVLQ WHUPHGLiULRV GH YLJDV FRQWtQXDV RQGH HVSDoDPHQWRVPDLRUHVGHYHPVHUXVDGRVSDUD HYLWDUFRORFDUFRQHFWRUHVHPUHJL}HVGDPHVD FRPWHQV}HVDOWDVGHWUDomR $UHVLVWrQFLDDRFLVDOKDPHQWRKRUL]RQWDOGHYH VHUIHLWDSRUFRQHFWRUHVGHFLVDOKDPHQWRPH FkQLFRVFRORFDGRVQDLQWHUIDFHHQWUHRFRQFUH WR H D YLJD GH DoR 2V FRQHFWRUHV GH FLVDOKDPHQWRGHYHPVHUGLVSRVLWLYRVPHFkQL FRVFRORFDGRVWUDQVYHUVDOPHQWHjPHVDGDYLJD D LQWHUYDORV UHJXODUHV RX YDULiYHLV 2V FRQHFWRUHVGHFLVDOKDPHQWRGHYHPVHUFDOFX ODGRVSDUDD IDGLJD HYHULILFDGRVSHOD UHVLVWrQ FLD~OWLPD )DGLJD $IDL[DGHYDULDomRGRFLVDOKDPHQWRKRUL]RQWDO GHYHVHUFDOFXODGDSHODIyUPXOD , 4 9 6 U U = RQGH 6 U )DL[D GH YDULDomR GR FLVDOKDPHQWR KRUL]RQWDOQDMXQomRGDODMHFRPDYLJDQR SRQWRGRYmRHPFRQVLGHUDomR 9 U )DL[DGHYDULDomRGDIRUoDFRUWDQWHGHYLGR j FDUJDPyYHO PDLVLPSDFWRSDUD TXDOTXHU VHomR$IDL[DGDIRUoDFRUWDQWHGHYHVHUWRPDGD FRPRDGLIHUHQoDHQWUHRVYDORUHVPtQLPRVH Pi[LPRVGDHQYROWyULDGHFRUWDQWHLQFOXLQGR FDUJDVSHUPDQHQWHV
- 186. 4 0RPHQWRHVWiWLFRGDiUHDGHFRPSUHVVmR GH FRQFUHWR WUDQVIRUPDGD RX GD iUHD GD DUPDGXUDORQJLWXGLQDOGRFRQFUHWRHPUHJL}HV GH PRPHQWR QHJDWLYR HP UHODomR DR HL[R QHXWURGDYLJDPLVWD , 0RPHQWRGH,QpUFLDGDVHomRPLVWDQDV UHJL}HVGHPRPHQWRSRVLWLYRRXRPRPHQWRGH LQpUFLDGDYLJDGHDoRLQFOXLQGRRXH[FOXLQGRD iUHDGDVDUPDGXUDVGRFRQFUHWRQDVUHJL}HV GHPRPHQWRQHJDWLYR
- 188. $ IDL[D GH YDULDomR DGPLVVtYHO SDUD R FLVDOKDPHQWR KRUL]RQWDO =U HPWI SDUD XP FRQHFWRULQGLYLGXDOpDVHJXLQWH 3DUDFRQHFWRUHVGHYLJD8 = U EZ 3DUD6WXGVVROGDGRV SDUD KVGV!
- 189. = U α GV RQGH Z FRPSULPHQWRGDYLJD8HPFPPHGLGD WUDQVYHUVDOPHQWHDGLUHomRGDPHVDGDYLJD GV GLkPHWURGRVWXGFP KV DOWXUDGRVWXGFP α SDUDFLFORV SDUDFLFORV SDUDFLFORV SDUDPDLVGHFLFORV E SDUDFLFORV SDUDFLFORV SDUDFLFORV SDUDPDLVGHFLFORV 2HVSDoDPHQWRQHFHVViULRHQWUHFRQHFWRUHV p GHWHUPLQDGR GLYLGLQGRVH D IDL[D GH FLVDOKDPHQWRDGPLVVtYHOSDUDRFLVDOKDPHQWR KRUL]RQWDOGHWRGRVRVFRQHFWRUHVGHXPDGH WHUPLQDGDVHomRWUDQVYHUVDOn= U
- 190. SHODIDL[D GHFLVDOKDPHQWRKRUL]RQWDO 6 U 6REUHDSRLRV LQWHUQRV GH YLJDVFRQWtQXDVRHVSDoDPHQWR SRGHVHUPRGLILFDGRSDUDHYLWDUDFRORFDomR GHFRQHFWRUHVHPORFDLVGHDOWDWHQVmRQDPHVD WUDFLRQDGD PDQWHQGR R Q~PHUR WRWDO GH FRQHFWRUHVLQDOWHUDGR 5HVLVWrQFLD~OWLPD 2Q~PHURGHFRQHFWRUHVFDOFXODGRSDUDDIDGL JDGHYHUiVHUYHULILFDGRSDUDJDUDQWLUVHRV FRQHFWRUHVVmRDGHTXDGRVSDUDDUHVLVWrQFLD ~OWLPD 2Q~PHURGHFRQHFWRUHVGHFLVDOKDPHQWRQH FHVViULRGHYHUiVHUPDLRURXLJXDODRQ~PHUR GDGRSHODIyUPXOD X 6 3 1 φ = RQGH 1 1~PHURGHFRQHFWRUHVHQWUHSRQWRVGH PRPHQWR SRVLWLYR Pi[LPR H R DSRLR PDLV SUy[LPR 6 X 5HVLVWrQFLD ÒOWLPD GR FRQHFWRU GH FLVDOKDPHQWRFRPRGDGRDEDL[R φ )DWRUGHUHGXomR 3 )RUoDQDODMHFRPRGHILQLGDDVHJXLUFRPR 3RX3 1RVSRQWRVGHPRPHQWRSRVLWLYRPi[LPRD IRUoDQDODMHVHUiRPHQRUYDORUGDVIyUPXODV V ) $ 3 = RX F F FN W E I 3 = RQGH $ V ÈUHDWRWDOGDVHomRGHDoRLQFOXLQGR FKDSDVGHUHIRUoRFRYHUSODWHV
- 192. 2Q~PHURGHFRQHFWRUHV1 QHFHVViULRHQWUH RVSRQWRVGHPRPHQWRSRVLWLYRPi[LPRHSRQ WRVDGMDFHQWHVGHPRPHQWRQHJDWLYRPi[LPR GHYHUiVHULJXDORXPDLRUGRTXHRQ~PHURGDGR SHODIyUPXOD X 6 3 3 1 φ + = 1RVSRQWRVGHPRPHQWRQHJDWLYRPi[LPRD IRUoDQDODMHpGDGRSRU ∗ = U U V ) $ 3 RQGH $ V U ÈUHDWRWDOGDVDUPDGXUDVGRFRQFUHWRQR DSRLRLQWHUPHGLiULRGHQWURGDODUJXUDHIHWLYD ) U /LPLWHGHHVFRDPHQWRHVSHFLILFDGRSDUD RDoRGDVDUPDGXUDV $UHVLVWrQFLD~OWLPDGRVFRQHFWRUHVGH FLVDOKDPHQWRpGDGRSRU 3DUD9LJDV8 F FN ZX IX ( I Z W W 6X ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = 3DUD6WXGVSDUDKVGV!
- 193. VF F FN VF $ ( I $ 6X ≤ = RQGH ( F PRGXORGHHODVWLFLGDGHGRFRQFUHWRHP N1FP SRGHVHUWRPDGRFRPR FN F I ( = FRPI FN HP03D 6 X UHVLVWrQFLD~OWLPDGHXPFRQHFWRU LQGLYLGXDO N1 $ VF iUHDGDVHomRGRVWXGFP W IX HVSHVVXUDPpGLDGDPHVDGDYLJD8FP W ZX HVSHVVXUDGDDOPDGDYLJD8FP Z FRPSULPHQWRGRFRQHFWRUGHYLJD8HP FP I FN UHVLVWrQFLDjFRPSUHVVmRGRFRQFUHWRD GLDVN1FP GV GLkPHWURGRVWXGFP LVDOKDPHQWRYHUWLFDO $WHQVmRGHFLVDOKDPHQWRQDYLJDPLVWDGHYH VHUGHWHUPLQDGDVXSRQGRTXHDDOWXUDGDDOPD GDYLJDGHDoRUHFHEHDWRWDOLGDGHGRHVIRUoR FRUWDQWHGHVSUH]DQGRVHDVPHVDVGDYLJDH RFRQFUHWRGDODMH2FLVDOKDPHQWRpVXSRVWR XQLIRUPHPHQWHGLVWULEXtGRDRORQJRGDiUHD EUXWDGDDOPD 'HIRUPDo}HV $VSURYLV}HVGRLWHPHPUHODomRDGH IRUPDo}HVGHYLGDVjFDUJDPyYHOPDLVLPSDF WRWDPEpPVmRDSOLFiYHLVjVYLJDVPLVWDV 4XDQGRDVYLJDVQmRVmRHVFRUDGDVFRPDSRL RVLQWHUPHGLiULRVGXUDQWHDFRQFUHWDJHPGD ODMHDGHIRUPDomRGHYLGRDRSHVRGDODMHH RXWUDVFDUJDVFRORFDGDVDQWHVTXHRFRQFUHWR DWLQMD GDVXDUHVLVWrQFLDHVSHFLILFDGDSDUD GLDVGHYHVHUFDOFXODGDFRPEDVHQDVH omRVHPDDomRFRPSRVWD
- 199. (VSHVVXUDGDODMHFP
- 200. TXDQGRDJHPFRQWLQXDPHQWHVmRWDPEpPLQFRU SRUDGRVQDFDWHJRULDGHFDUJDSHUPDQHQWH 3HVRHVSHFtILFRGRVPDWHULDLV 3DUDHIHLWRGRSURMHWRSRGHPVHUDGRWDGRVRV SHVRVHVSHFtILFRVDSDUHQWHVGRTXDGURDEDL[R SDUDRVPDWHULDLVGHFRQVWUXomREDVHDGRVQD 1%5 3RGHVHGLVSHQVDUQRYRFiOFXORGDVVROLFLWD o}HV TXDQGR R SHVR SUySULR REWLGR GR GLPHQVLRQDPHQWRGHILQLWLYRGDHVWUXWXUDQmRGL IHULUPDLVGRTXHGRSHVRSUySULRLQLFLDOPHQ WHDGPLWLGRSDUDRFiOFXOR DUJDVPyYHLV RQVWLWXLomRGDVFDUJDVPyYHLV $VFDUJDVPyYHLVGHFiOFXORIL[DGDVQDVQRU PDVQmRFRLQFLGHPFRPDVFDUJDVUHDLVTXH FLUFXODPQDVHVWUDGDV1DVSRQWHVURGRYLiUL DVDVFDUJDVURGRYLiULDVGHFiOFXOR1%5
- 202. $oR RQFUHWRDUPDGR RQFUHWRVLPSOHV $UJDPDVVDGHFLPHQWRHDUHLD RQFUHWRDVIDOWLFR 0DGHLUDWLSRSHURED