NBR 6118.2023 - Projeto de Estruturas de Concreto
March 24, 2024 | Author: Anonymous | Category: N/A
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NORMA BRASILEIRA
ABNT NBR 6118 Quarta edição 28.08.2023
Projeto de estruturas de concreto
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Design of concrete structures
ICS 91.080.40
ISBN 978-85-07-09632-0
Número de referência ABNT NBR 6118:2023 242 páginas
© ABNT 2023 Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
ABNT NBR 6118:2023
© ABNT 2023 7RGRVRVGLUHLWRVUHVHUYDGRV$PHQRVTXHHVSHFL¿FDGRGHRXWURPRGRQHQKXPDSDUWHGHVWDSXEOLFDomRSRGHVHU UHSURGX]LGDRXXWLOL]DGDSRUTXDOTXHUPHLRHOHWU{QLFRRXPHFkQLFRLQFOXLQGRIRWRFySLDHPLFUR¿OPHVHPSHUPLVVmRSRU escrito da ABNT. ABNT $Y7UH]HGH0DLRDQGDU 20031-901 - Rio de Janeiro - RJ 7HO )D[ DEQW#DEQWRUJEU ZZZDEQWRUJEU
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Sumário
Página
Prefácio .............................................................................................................................................xvi Introdução .......................................................................................................................................xviii 1 Escopo ................................................................................................................................1 2 Referências normativas .....................................................................................................1 7HUPRVHGH¿QLo}HV ...........................................................................................................3 'H¿QLomRUHODWLYDDRVHQYROYLGRVQRSURFHVVRFRQVWUXWLYR..........................................5 6LPERORJLD ..........................................................................................................................5 *HQHUDOLGDGHV.....................................................................................................................5 6tPERORVEDVH ....................................................................................................................6 *HQHUDOLGDGHV.....................................................................................................................6 /HWUDVPLQ~VFXODV ..............................................................................................................6 /HWUDVPDL~VFXODV ..............................................................................................................7 /HWUDVJUHJDV ......................................................................................................................9 6tPERORVVXEVFULWRV ........................................................................................................10 *HQHUDOLGDGHV...................................................................................................................10 /HWUDVPLQ~VFXODV ............................................................................................................ 11 /HWUDVPDL~VFXODV ............................................................................................................12 4.3.4 Números ............................................................................................................................12 5HTXLVLWRVJHUDLVGHTXDOLGDGHGDHVWUXWXUDHDYDOLDomRGDFRQIRUPLGDGHGRSURMHWR ....12 5HTXLVLWRVGHTXDOLGDGHGDHVWUXWXUD ............................................................................12 &RQGLo}HVJHUDLV .............................................................................................................12 &ODVVL¿FDomRGRVUHTXLVLWRVGHTXDOLGDGHGDHVWUXWXUD ..............................................13 5HTXLVLWRVGHTXDOLGDGHGRSURMHWR ...............................................................................13 4XDOLGDGHGDVROXomRDGRWDGD .......................................................................................13 &RQGLo}HVLPSRVWDVDRSURMHWR ......................................................................................13 'RFXPHQWDomRGDVROXomRDGRWDGD ...............................................................................14 $YDOLDomRGDFRQIRUPLGDGHGRSURMHWR ..........................................................................14 'LUHWUL]HVSDUDGXUDELOLGDGHGDVHVWUXWXUDVGHFRQFUHWR .............................................15 ([LJrQFLDVGHGXUDELOLGDGH .............................................................................................15 9LGD~WLOGHSURMHWR ...........................................................................................................15 0HFDQLVPRVGHHQYHOKHFLPHQWRHGHWHULRUDomR ...........................................................15 *HQHUDOLGDGHV...................................................................................................................15 0HFDQLVPRVSUHSRQGHUDQWHVGHGHWHULRUDomRUHODWLYRVDRFRQFUHWR........................15 0HFDQLVPRVSUHSRQGHUDQWHVGHGHWHULRUDomRUHODWLYRVjDUPDGXUD..........................16 6.3.4 Mecanismos de deterioração da estrutura propriamente dita .....................................16 $JUHVVLYLGDGHDPELHQWDO .................................................................................................16 &ULWpULRVGHSURMHWRTXHYLVDPDGXUDELOLGDGH ..............................................................17 6LPERORJLDHVSHFt¿FDGHVWDVHomR ................................................................................17 'UHQDJHP ..........................................................................................................................17 7.3 Formas arquitetônicas e estruturais ..............................................................................18 4XDOLGDGHGRFRQFUHWRGHFREULPHQWR...........................................................................18 © ABNT 2023 - Todos os direitos reservados
iii
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ABNT NBR 6118:2023
7.7 7.8 8 8.2 8.3 8.3.2 8.4 9 9.2.2 iv
'HWDOKDPHQWRGDVDUPDGXUDV .........................................................................................20 &RQWUROHGD¿VVXUDomR ....................................................................................................20 Medidas especiais ............................................................................................................21 Inspeção e manutenção preventiva................................................................................21 Propriedades dos materiais ............................................................................................21 6LPERORJLDHVSHFt¿FDGHVWDVHomR ................................................................................21 Concreto............................................................................................................................22 &ODVVHV ..............................................................................................................................22 0DVVDHVSHFt¿FD ..............................................................................................................22 &RH¿FLHQWHGHGLODWDomRWpUPLFD ....................................................................................23 5HVLVWrQFLDjFRPSUHVVmR ..............................................................................................23 5HVLVWrQFLDjWUDomR.........................................................................................................23 5HVLVWrQFLDQRHVWDGRPXOWLD[LDOGHWHQV}HV ................................................................24 5HVLVWrQFLDjIDGLJD .........................................................................................................24 0yGXORGHHODVWLFLGDGH ....................................................................................................24 &RH¿FLHQWHGH3RLVVRQHPyGXORGHHODVWLFLGDGHWUDQVYHUVDO ....................................25 'LDJUDPDVWHQVmRGHIRUPDomR .......................................................................................26 )OXrQFLDHUHWUDomR...........................................................................................................27 Aço de armadura passiva ................................................................................................28 &DWHJRULD ...........................................................................................................................28 Tipo de superfície aderente.............................................................................................28 0DVVDHVSHFt¿FD ..............................................................................................................29 &RH¿FLHQWHGHGLODWDomRWpUPLFD ....................................................................................29 0yGXORGHHODVWLFLGDGH ....................................................................................................29 'LDJUDPDWHQVmRGHIRUPDomRUHVLVWrQFLDDRHVFRDPHQWRHjWUDomR .......................29 &DUDFWHUtVWLFDVGHGXWLOLGDGH ..........................................................................................30 5HVLVWrQFLDjIDGLJD .........................................................................................................30 6ROGDELOLGDGH ....................................................................................................................30 Aço de armadura ativa .....................................................................................................30 &ODVVL¿FDomR ....................................................................................................................30 0DVVDHVSHFt¿FD ..............................................................................................................30 &RH¿FLHQWHGHGLODWDomRWpUPLFD ...................................................................................30 0yGXORGHHODVWLFLGDGH ...................................................................................................30 'LDJUDPDWHQVmRGHIRUPDomRUHVLVWrQFLDDRHVFRDPHQWRHjWUDomR .......................30 &DUDFWHUtVWLFDVGHGXWLOLGDGH ..........................................................................................31 5HVLVWrQFLDjIDGLJD .........................................................................................................31 5HOD[DomR..........................................................................................................................31 Comportamento conjunto dos materiais .......................................................................32 6LPERORJLDHVSHFt¿FDGHVWDVHomR ................................................................................32 'LVSRVLo}HVJHUDLV...........................................................................................................34 *HQHUDOLGDGHV...................................................................................................................34 Níveis de protensão .........................................................................................................34 9HUL¿FDomRGDDGHUrQFLD .................................................................................................34 © ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
ABNT NBR 6118:2023
9.5 9.5.1 9.5.2 9.6 9.6.1 9.6.2 9.6.3
3RVLomRGDEDUUDGXUDQWHDFRQFUHWDJHP ......................................................................34 9DORUHVGDVUHVLVWrQFLDVGHDGHUrQFLD...........................................................................34 $QFRUDJHPGDVDUPDGXUDV .............................................................................................35 &RQGLo}HVJHUDLV .............................................................................................................35 $QFRUDJHPGHDUPDGXUDVSDVVLYDVSRUDGHUrQFLD ......................................................36 $QFRUDJHPGHIHL[HVGHEDUUDVSRUDGHUrQFLD .............................................................38 $QFRUDJHPGHWHODVVROGDGDVSRUDGHUrQFLD ................................................................39 $QFRUDJHPGHDUPDGXUDVDWLYDV ¿RVHFRUGRDOKDVSUpWUDFLRQDGDV SRUDGHUrQFLD ... 39 $QFRUDJHPGHHVWULERV ...................................................................................................40 $QFRUDJHPSRUPHLRGHGLVSRVLWLYRVPHFkQLFRV.........................................................41 Emendas das barras ........................................................................................................42 Tipos ..................................................................................................................................42 Emendas por traspasse ...................................................................................................42 (PHQGDVSRUOXYDVURVTXHDGDVRXSUHQVDGDV .............................................................45 (PHQGDVSRUVROGD ..........................................................................................................45 Protensão ..........................................................................................................................47 Força de protensão ..........................................................................................................47 Introdução das forças de protensão ..............................................................................48 Perdas da força de protensão .........................................................................................49 6HJXUDQoDHHVWDGRVOLPLWHV ...........................................................................................54 &ULWpULRVGHVHJXUDQoD ....................................................................................................54 (VWDGRVOLPLWHV ................................................................................................................54 (VWDGRVOLPLWHV~OWLPRV (/8 ........................................................................................54 (VWDGRVOLPLWHVGHVHUYLoR (/6 ....................................................................................55 $o}HV.................................................................................................................................55 6LPERORJLDHVSHFt¿FDGHVWD6HomR................................................................................55 $o}HVDFRQVLGHUDU ..........................................................................................................56 *HQHUDOLGDGHV...................................................................................................................56 &ODVVL¿FDomRGDVDo}HV ..................................................................................................56 $o}HVSHUPDQHQWHV .........................................................................................................56 *HQHUDOLGDGHV...................................................................................................................56 $o}HVSHUPDQHQWHVGLUHWDV ...........................................................................................57 $o}HVSHUPDQHQWHVLQGLUHWDV .........................................................................................57 $o}HVYDULiYHLV ................................................................................................................61 $o}HVYDULiYHLVGLUHWDV ...................................................................................................61 $o}HVYDULiYHLVLQGLUHWDV ................................................................................................62 $o}HVH[FHSFLRQDLV .........................................................................................................63 9DORUHVGDVDo}HV ............................................................................................................63 9DORUHVFDUDFWHUtVWLFRV ....................................................................................................63 9DORUHVUHSUHVHQWDWLYRV ...................................................................................................64 9DORUHVGHFiOFXOR ............................................................................................................64 &RH¿FLHQWHVGHSRQGHUDomRGDVDo}HV .........................................................................64 &RH¿FLHQWHVGHSRQGHUDomRGDVDo}HVQRHVWDGROLPLWH~OWLPR (/8 ......................64
© ABNT 2023 - Todos os direitos reservados
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
ABNT NBR 6118:2023
12 13.2.1 13.2.4 13.2.5 13.4.1 14.3 vi
&RH¿FLHQWHVGHSRQGHUDomRGDVDo}HVQRHVWDGROLPLWHGHVHUYLoR (/6 ...............66 &RPELQDo}HVGHDo}HV ...................................................................................................66 *HQHUDOLGDGHV...................................................................................................................66 &RPELQDo}HV~OWLPDV ......................................................................................................66 &RPELQDo}HVGHVHUYLoR .................................................................................................68 Resistências .....................................................................................................................69 6LPERORJLDHVSHFt¿FDGHVWDVHomR ................................................................................69 9DORUHVFDUDFWHUtVWLFRV ....................................................................................................70 9DORUHVGHFiOFXOR ............................................................................................................70 5HVLVWrQFLDGHFiOFXOR .....................................................................................................70 7HQV}HVUHVLVWHQWHVGHFiOFXOR ......................................................................................70 5HVLVWrQFLDGHFiOFXORGRFRQFUHWR ...............................................................................70 &RH¿FLHQWHVGHSRQGHUDomRGDVUHVLVWrQFLDV ..............................................................71 &RH¿FLHQWHVGHSRQGHUDomRGDVUHVLVWrQFLDVQRHVWDGROLPLWH~OWLPR (/8 ...........71 &RH¿FLHQWHVGHSRQGHUDomRGDVUHVLVWrQFLDVQRHVWDGROLPLWHGHVHUYLoR (/6 .....72 9HUL¿FDomRGDVHJXUDQoD ................................................................................................72 &RQGLo}HVFRQVWUXWLYDVGHVHJXUDQoD ..........................................................................72 &RQGLo}HVDQDOtWLFDVGHVHJXUDQoD ...............................................................................72 (VIRUoRVUHVLVWHQWHVGHFiOFXOR .....................................................................................72 (VIRUoRVVROLFLWDQWHVGHFiOFXOR.....................................................................................72 /LPLWHVSDUDGLPHQV}HVGHVORFDPHQWRVHDEHUWXUDVGH¿VVXUDV ..............................72 6LPERORJLDHVSHFt¿FDGHVWD6HomR................................................................................72 'LPHQV}HVOLPLWHV............................................................................................................73 Introdução .........................................................................................................................73 9LJDVHYLJDVSDUHGH........................................................................................................73 3LODUHVHSLODUHVSDUHGH ...................................................................................................73 Lajes ..................................................................................................................................74 Furos e aberturas .............................................................................................................75 &DQDOL]Do}HVHPEXWLGDV..................................................................................................76 'HVORFDPHQWRVOLPLWHV ....................................................................................................76 &RQWUROHGD¿VVXUDomRHSURWHomRGDVDUPDGXUDV.......................................................79 Introdução .........................................................................................................................79 /LPLWHVSDUD¿VVXUDomRHSURWHomRGDVDUPDGXUDVTXDQWRjGXUDELOLGDGH ...............79 &RQWUROHGD¿VVXUDomRTXDQWRjDFHLWDELOLGDGHVHQVRULDOHjXWLOL]DomR ..................80 $QiOLVHHVWUXWXUDO .............................................................................................................81 6LPERORJLDHVSHFt¿FDGHVWDVHomR ................................................................................81 3ULQFtSLRVJHUDLVGDDQiOLVHHVWUXWXUDO ..........................................................................81 2EMHWLYRGDDQiOLVHHVWUXWXUDO .........................................................................................81 3UHPLVVDVQHFHVViULDVjDQiOLVHHVWUXWXUDO ..................................................................82 $SOLFDomRGRVUHVXOWDGRVREWLGRVFRPRVPRGHORVGHDQiOLVHVHPUHJLPHOLQHDU .....82 $SOLFDomRGRVUHVXOWDGRVREWLGRVFRPRVPRGHORVGHDQiOLVHVHPUHJLPHQmR OLQHDU ..................................................................................................................................83 Hipóteses básicas ............................................................................................................83 © ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
ABNT NBR 6118:2023
14.6.1 14.7.1 14.7.6 14.7.7 15.4.3
&RQGLo}HVGHHTXLOtEULR...................................................................................................83 &RQGLo}HVGHFRPSDWLELOLGDGH .......................................................................................83 &DUUHJDPHQWRPRQRW{QLFR .............................................................................................83 (OHPHQWRVHVWUXWXUDLV......................................................................................................83 (OHPHQWRVOLQHDUHV...........................................................................................................83 (OHPHQWRVGHVXSHUItFLH ..................................................................................................84 0pWRGRVGHDQiOLVHHVWUXWXUDO.........................................................................................84 *HQHUDOLGDGHV...................................................................................................................84 $QiOLVHOLQHDU ....................................................................................................................85 $QiOLVHOLQHDUFRPUHGLVWULEXLomR ...................................................................................85 $QiOLVHSOiVWLFD ................................................................................................................85 $QiOLVHQmROLQHDU.............................................................................................................86 $QiOLVHDWUDYpVGHPRGHORVItVLFRV................................................................................86 (VWUXWXUDVGHHOHPHQWRVOLQHDUHV ...................................................................................86 Hipóteses básicas ............................................................................................................86 &DUDFWHUL]DomRGDJHRPHWULD ..........................................................................................87 $UUHGRQGDPHQWRGRGLDJUDPDGHPRPHQWRVÀHWRUHV..................................................90 $QiOLVHOLQHDUFRPRXVHPUHGLVWULEXLomR .....................................................................91 $QiOLVHQmROLQHDU.............................................................................................................93 (VWUXWXUDVXVXDLVGHHGLItFLRV±$SUR[LPDo}HVSHUPLWLGDV ........................................93 (VWUXWXUDVFRPHOHPHQWRVGHSODFD ...............................................................................95 Hipóteses básicas ............................................................................................................95 &DUDFWHUL]DomRGDJHRPHWULD ..........................................................................................95 $QiOLVHOLQHDUFRPRXVHPUHGLVWULEXLomR .....................................................................95 $QiOLVHSOiVWLFD ................................................................................................................96 $QiOLVHQmROLQHDU.............................................................................................................96 Lajes maciças ...................................................................................................................96 Lajes nervuradas ..............................................................................................................97 /DMHVOLVDVHODMHVFRJXPHOR ...........................................................................................97 (VWUXWXUDVFRQWHQGRRXWURVHOHPHQWRV .........................................................................98 9LJDVSDUHGHHSLODUHVSDUHGH ........................................................................................98 %ORFRV ...............................................................................................................................98 ,QVWDELOLGDGHHHIHLWRVGHRUGHP ................................................................................99 6LPERORJLDHVSHFt¿FDGHVWD6HomR................................................................................99 &DPSRGHDSOLFDomRHFRQFHLWRVIXQGDPHQWDLV ...........................................................99 3ULQFtSLREiVLFRGHFiOFXOR ...........................................................................................100 5HODo}HVPRPHQWRFXUYDWXUD .......................................................................................100 ,PSHUIHLo}HVJHRPpWULFDV .............................................................................................101 'H¿QLo}HVHFODVVL¿FDomRGDVHVWUXWXUDV ...................................................................102 (IHLWRVJOREDLVORFDLVHORFDOL]DGRVGHRUGHP.......................................................102 (VWUXWXUDVGHQyV¿[RVHHVWUXWXUDVGHQyVPyYHLV ..................................................103 Contraventamento..........................................................................................................103 (OHPHQWRVLVRODGRV........................................................................................................103
© ABNT 2023 - Todos os direitos reservados
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
ABNT NBR 6118:2023
16.1 16.3 17.2.1 17.2.2 17.2.4 viii
'LVSHQVDGDFRQVLGHUDomRGRVHVIRUoRVJOREDLVGHRUGHP .................................104 *HQHUDOLGDGHV.................................................................................................................104 3DUkPHWURGHLQVWDELOLGDGHD ........................................................................................104 &RH¿FLHQWHJz ..................................................................................................................105 $QiOLVHGHHVWUXWXUDVGHQyV¿[RV ...............................................................................105 $QiOLVHGHHVWUXWXUDVGHQyVPyYHLV ...........................................................................106 *HQHUDOLGDGHV.................................................................................................................106 $QiOLVHQmROLQHDUFRPRUGHP ..................................................................................106 &RQVLGHUDomRDSUR[LPDGDGDQmROLQHDULGDGHItVLFD..................................................106 $QiOLVHGRVHIHLWRVORFDLVGHRUGHP ........................................................................107 $QiOLVHGHHOHPHQWRVLVRODGRV .....................................................................................107 *HQHUDOLGDGHV.................................................................................................................107 'LVSHQVDGDDQiOLVHGRVHIHLWRVORFDLVGHRUGHP ..................................................107 'HWHUPLQDomRGRVHIHLWRVORFDLVGHRUGHP .............................................................108 &RQVLGHUDomRGDÀXrQFLD .............................................................................................. 111 $QiOLVHGHSLODUHVSDUHGH .............................................................................................. 111 *HQHUDOLGDGHV................................................................................................................. 111 'LVSHQVDGDDQiOLVHGRVHIHLWRVORFDOL]DGRVGHRUGHP ......................................... 111 3URFHVVRDSUR[LPDGRSDUDFRQVLGHUDomRGRHIHLWRORFDOL]DGRGHRUGHP ........... 112 ,QVWDELOLGDGHODWHUDOGHYLJDV ........................................................................................ 113 3ULQFtSLRVJHUDLVGHGLPHQVLRQDPHQWRYHUL¿FDomRHGHWDOKDPHQWR ....................... 114 Objetivo ........................................................................................................................... 114 3ULQFtSLRVJHUDLV ............................................................................................................ 115 *HQHUDOLGDGHV................................................................................................................. 115 9LVmRJOREDOHORFDO ........................................................................................................ 115 6HJXUDQoDHPUHODomRDRV(/8 .................................................................................... 115 6HJXUDQoDHPUHODomRDRV(/6 GHVHPSHQKRHPVHUYLoR ....................................... 115 Critérios de projeto ........................................................................................................ 116 'XUDELOLGDGH.................................................................................................................... 117 &DVRGHFDUJDVFtFOLFDV ................................................................................................. 117 'LPHQVLRQDPHQWRHYHUL¿FDomRGHHOHPHQWRVOLQHDUHV ............................................. 117 6LPERORJLDHVSHFt¿FDGHVWDVHomR .............................................................................. 117 (OHPHQWRVOLQHDUHVVXMHLWRVDVROLFLWDo}HVQRUPDLV(VWDGROLPLWH~OWLPR .............120 Introdução .......................................................................................................................120 Hipóteses básicas ..........................................................................................................120 'XWLOLGDGHHPYLJDV........................................................................................................122 Armaduras ativas e passivas ........................................................................................123 3URFHVVRDSUR[LPDGRSDUDRGLPHQVLRQDPHQWRjÀH[mRFRPSRVWDREOtTXD ..........125 (OHPHQWRVOLQHDUHVVXMHLWRVDVROLFLWDo}HVQRUPDLV±(VWDGRVOLPLWHVGHVHUYLoR ....125 *HQHUDOLGDGHV.................................................................................................................125 (VWDGROLPLWHGHGHIRUPDomR ........................................................................................126 (VWDGROLPLWHGH¿VVXUDomR...........................................................................................128 (VWDGROLPLWHGHGHVFRPSUHVVmRHGHIRUPDomRGH¿VVXUDV ....................................130 © ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
ABNT NBR 6118:2023
17.4.1 17.5.1 17.7.2 18.2.1 18.2.2 18.2.3 18.3.4 18.3.6 18.4.1 18.4.3 18.6 19.4.1
$UPDGXUDVORQJLWXGLQDLVPi[LPDVHPtQLPDV ............................................................131 (OHPHQWRVOLQHDUHVVXMHLWRVjIRUoDFRUWDQWHí(VWDGROLPLWH~OWLPR .......................133 Hipóteses básicas ..........................................................................................................133 9HUL¿FDomRGRHVWDGROLPLWH~OWLPR ..............................................................................136 (OHPHQWRVOLQHDUHVVXMHLWRVjWRUomRí(VWDGROLPLWH~OWLPR ....................................139 Torção uniforme .............................................................................................................139 7RUomRHPSHU¿VDEHUWRVGHSDUHGH¿QD .....................................................................142 (VWDGROLPLWHGH¿VVXUDomRLQFOLQDGDGDDOPDí)RUoDFRUWDQWHHWRUomR ...............144 6ROLFLWDo}HVFRPELQDGDV ..............................................................................................144 )OH[mRHWRUomR ...............................................................................................................144 Torção e força cortante..................................................................................................145 'HWDOKDPHQWRGHHOHPHQWRVOLQHDUHV ...........................................................................145 6LPERORJLDHVSHFt¿FDGHVWD6HomR..............................................................................145 'LVSRVLo}HVJHUDLVUHODWLYDVjVDUPDGXUDV.................................................................146 Arranjo das armaduras ..................................................................................................146 Barras curvadas .............................................................................................................146 Mudanças de direção das armaduras ..........................................................................146 3URWHomRFRQWUDÀDPEDJHPGDVEDUUDV .......................................................................147 9LJDV ................................................................................................................................147 *HQHUDOLGDGHV.................................................................................................................147 $UPDGXUDORQJLWXGLQDO ...................................................................................................147 $UPDGXUDWUDQVYHUVDOSDUDIRUoDFRUWDQWH...................................................................150 Armadura para torção ....................................................................................................151 $UPDGXUDGHSHOH ...........................................................................................................152 Armadura de suspensão ...............................................................................................152 $UPDGXUDVGHOLJDomRPHVDDOPDRXWDOmRDOPD ........................................................152 3LODUHV.............................................................................................................................152 Introdução .......................................................................................................................152 $UPDGXUDVORQJLWXGLQDLV ...............................................................................................153 Armaduras transversais ................................................................................................153 3LODUHVSDUHGH.................................................................................................................154 Cabos de protensão .......................................................................................................154 $UUDQMRORQJLWXGLQDO .......................................................................................................154 $UUDQMRWUDQVYHUVDO ........................................................................................................155 'LPHQVLRQDPHQWRHYHUL¿FDomRGHODMHV .....................................................................157 6LPERORJLDHVSHFt¿FDGHVWDVHomR ..............................................................................157 'LPHQVLRQDPHQWRHYHUL¿FDomRGHODMHVí(VWDGROLPLWH~OWLPR ...............................158 'LPHQVLRQDPHQWRHYHUL¿FDomRGHODMHVí(VWDGRVOLPLWHVGHVHUYLoR ....................159 (VWDGROLPLWHGHGHIRUPDomR ........................................................................................159 (VWDGRVOLPLWHVGH¿VVXUDomRHGHGHVFRPSUHVVmRRXGHIRUPDomRGH¿VVXUDV .....159 $UPDGXUDVORQJLWXGLQDLVPi[LPDVHPtQLPDV ............................................................159 )RUoDFRUWDQWHHPODMHVHHOHPHQWRVOLQHDUHVFRP bw t 5d .......................................160 Lajes sem armadura para força cortante .....................................................................160
© ABNT 2023 - Todos os direitos reservados
ix
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
ABNT NBR 6118:2023
19.4.2 20.3.1 20.3.2 20.4 21.2.1 21.3 22.4.1 x
Lajes com armadura para força cortante .....................................................................162 'LPHQVLRQDPHQWRGHODMHVjSXQomR ...........................................................................162 0RGHORGHFiOFXOR ..........................................................................................................162 'H¿QLomRGDWHQVmRVROLFLWDQWHQDVVXSHUItFLHVFUtWLFDVC e C' ................................162 'H¿QLomRGDWHQVmRUHVLVWHQWHQDVVXSHUItFLHVFUtWLFDVCC’ e C” ...........................167 &RODSVRSURJUHVVLYR......................................................................................................170 9HUL¿FDomRGHHOHPHQWRVHVWUXWXUDLVSURWHQGLGRV .....................................................171 'HWDOKDPHQWRGHODMHV ...................................................................................................172 3UHVFULo}HVJHUDLV .........................................................................................................172 %RUGDVOLYUHVHDEHUWXUDV ..............................................................................................172 /DMHVVHPYLJDV ..............................................................................................................173 Armaduras passivas ......................................................................................................173 Lajes protendidas...........................................................................................................174 Armaduras de punção ...................................................................................................176 /DMHVDUPDGDVFRPWHODVVROGDGDVQHUYXUDGDV ..........................................................176 $QFRUDJHPGDVWHODVVROGDGDVQHUYXUDGDVQRDSRLRVREUHYLJDV ...........................176 (PHQGDVGHDUPDGXUDVHPWHODVVROGDGDVQHUYXUDGDV ............................................176 5HJL}HVHVSHFLDLV ..........................................................................................................176 'H¿QLomR .........................................................................................................................176 5HJL}HVGHLQWURGXomRGHFDUJDVFRQFHQWUDGDV ........................................................177 Pressão de contato em área reduzida ..........................................................................177 $UWLFXODo}HVGHFRQFUHWR ..............................................................................................178 5HJLmRGHLQWURGXomRGDSURWHQVmR .............................................................................178 &DUJDVDSOLFDGDVQDVXSHUItFLHGHHOHPHQWRVHVWUXWXUDLV .........................................179 Furos e aberturas ...........................................................................................................179 *HQHUDOLGDGHV.................................................................................................................179 3DUHGHVHYLJDVSDUHGH .................................................................................................180 )XURVTXHDWUDYHVVDPDVYLJDVQDGLUHomRGDDOWXUD .................................................180 $EHUWXUDVHPODMHV .........................................................................................................181 1yVGHSyUWLFRVHOLJDo}HVHQWUHSDUHGHV ...................................................................181 /LJDo}HVGHHOHPHQWRVHVWUXWXUDLVSUpPROGDGRV .....................................................181 -XQWDVGHFRQFUHWDJHP .................................................................................................181 (OHPHQWRVHVSHFLDLV ......................................................................................................182 6LPERORJLDHVSHFt¿FDGHVWDVHomR ..............................................................................182 'H¿QLo}HV .......................................................................................................................182 0pWRGRGHELHODVHWLUDQWHV ...........................................................................................183 3URFHGLPHQWRSDUDDSOLFDomRGRPpWRGR ....................................................................183 3DUkPHWURVGHUHVLVWrQFLDGHFiOFXORGDVELHODVHUHJL}HVQRGDLV ..........................184 3DUkPHWURVGHUHVLVWrQFLDGHFiOFXORGRVWLUDQWHV.....................................................184 9LJDVSDUHGH ...................................................................................................................184 Conceituação .................................................................................................................184 &RPSRUWDPHQWRHVWUXWXUDO ...........................................................................................184 0RGHORVGHFiOFXOR .......................................................................................................185 © ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
ABNT NBR 6118:2023
22.5.2 22.6 22.6.1 22.7.1 24.3 24.5.3 24.5.6
'HWDOKDPHQWR..................................................................................................................185 &RQVRORVHGHQWHV*HUEHU.............................................................................................186 &RQVRORV .........................................................................................................................186 Dentes Gerber.................................................................................................................190 Sapatas............................................................................................................................191 Conceituação ..................................................................................................................191 &RPSRUWDPHQWRHVWUXWXUDO ............................................................................................192 0RGHORGHFiOFXOR ..........................................................................................................192 'HWDOKDPHQWR..................................................................................................................192 %ORFRVVREUHHVWDFDV ....................................................................................................193 Conceituação ..................................................................................................................193 &RPSRUWDPHQWRHVWUXWXUDO ............................................................................................193 0RGHORGHFiOFXOR ..........................................................................................................193 'HWDOKDPHQWR..................................................................................................................194 $o}HVGLQkPLFDVHIDGLJD .............................................................................................195 6LPERORJLDHVSHFt¿FDGHVWDVHomR ..............................................................................195 *HQHUDOLGDGHV.................................................................................................................195 (VWDGROLPLWHGHYLEUDo}HVH[FHVVLYDV ........................................................................195 (VWDGRVOLPLWHV~OWLPRVSURYRFDGRVSRUUHVVRQkQFLDRXDPSOL¿FDomRGLQkPLFD .....196 (VWDGROLPLWH~OWLPRGHIDGLJD ......................................................................................196 $o}HVFtFOLFDV.................................................................................................................196 &RPELQDo}HVGHDo}HVDFRQVLGHUDU ...........................................................................197 0RGHORGHFiOFXOR ..........................................................................................................197 9HUL¿FDomRGDIDGLJDGRFRQFUHWR ................................................................................199 9HUL¿FDomRGDIDGLJDGDDUPDGXUD ...............................................................................200 (VWDGRVOLPLWHVGHVHUYLoR ............................................................................................202 &RQFUHWRVLPSOHV ...........................................................................................................203 6LPERORJLDHVSHFt¿FDGHVWD6HomR..............................................................................203 &DPSRGHDSOLFDomR.......................................................................................................204 Materiais e propriedades ...............................................................................................204 -XQWDVHGLVSRVLo}HVFRQVWUXWLYDV...............................................................................204 3URMHWRHVWUXWXUDO ...........................................................................................................204 *HQHUDOLGDGHV.................................................................................................................204 7HQV}HVUHVLVWHQWHVGHFiOFXOR ....................................................................................204 Dimensionamento ..........................................................................................................205 7HQV}HVHGHIRUPDo}HVQDÀH[mR ................................................................................206 7HQV}HVGHFLVDOKDPHQWR ..............................................................................................207 Torção ..............................................................................................................................207 &iOFXORGHVHo}HVVXEPHWLGDVjFRPSUHVVmRHjIRUoDFRUWDQWH .............................207 (VWDELOLGDGHJOREDO.........................................................................................................208 (OHPHQWRVHVWUXWXUDLVGHFRQFUHWRVLPSOHV ................................................................208 3LODUHVSDUHGH.................................................................................................................208 %ORFRVGHIXQGDomR .......................................................................................................209
© ABNT 2023 - Todos os direitos reservados
xi
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
24.6.4 25.1 25.2
3LODUHV..............................................................................................................................209 Arcos ...............................................................................................................................210 ,QWHUIDFHVGRSURMHWRFRPDFRQVWUXomRXWLOL]DomRHPDQXWHQomR ..........................210 Aceitação do projeto ......................................................................................................210 Recebimento do concreto e do aço .............................................................................210 0DQXDOGHXWLOL]DomRLQVSHomRHPDQXWHQomR............................................................210
Anexos Anexo A LQIRUPDWLYR (IHLWRGRWHPSRQRFRQFUHWRHVWUXWXUDO .................................................... 211 $ *HQHUDOLGDGHV................................................................................................................. 211 $ 'HIRUPDo}HVGRFRQFUHWR ............................................................................................. 211 A.2.1 Introdução ....................................................................................................................... 211 $ )OXrQFLDGRFRQFUHWR ..................................................................................................... 211 $ *HQHUDOLGDGHV................................................................................................................. 211 A.2.2.2 Hipóteses ........................................................................................................................212 $ 9DORUGDÀXrQFLD .............................................................................................................213 A.2.3 Retração do concreto ....................................................................................................215 A.2.3.1 Hipóteses básicas ..........................................................................................................215 $ 9DORUGDUHWUDomR ............................................................................................................215 $ ,GDGHHHVSHVVXUD¿FWtFLDV ............................................................................................218 $ ,GDGH¿FWtFLDGRFRQFUHWR ..............................................................................................218 $ (VSHVVXUD¿FWtFLDGDSHoD ............................................................................................219 $ 'HIRUPDomRWRWDOGRFRQFUHWR ......................................................................................219 $ 'HIRUPDo}HVQDDUPDGXUD ............................................................................................220 Anexo B LQIRUPDWLYR Índice remissivo ..........................................................................................221 )LJXUDV )LJXUD±(VWDGROLPLWHGHGHVFRPSUHVVmRSDUFLDO .....................................................................5 )LJXUD±5HVLVWrQFLDQRHVWDGRPXOWLD[LDOGHWHQV}HV ............................................................24 )LJXUD±'LDJUDPDWHQVmRGHIRUPDomRLGHDOL]DGR...................................................................26 )LJXUD±'LDJUDPDGHWHQVmRGHIRUPDomRSDUDDQiOLVHQmROLQHDU ........................................27 )LJXUD±'LDJUDPDWHQVmRGHIRUPDomRELOLQHDUGHWUDomR ......................................................27 )LJXUD±'LDJUDPDWHQVmRGHIRUPDomRSDUDDoRVGHDUPDGXUDVSDVVLYDV ..........................29 )LJXUD±'LDJUDPDWHQVmRGHIRUPDomRSDUDDoRVGHDUPDGXUDVDWLYDV ...............................31 )LJXUD ±$QFRUDJHPFRPEDUUDVWUDQVYHUVDLVVROGDGDV .........................................................36 )LJXUD ±(VWULERFRPJDQFKRHP ......................................................................................40 )LJXUD ±$QFRUDJHPGHDUPDGXUDWUDQVYHUVDOSRUPHLRGHEDUUDVVROGDGDV .......................41 )LJXUD ±(PHQGDVVXSRVWDVFRPRQDPHVPDVHomRWUDQVYHUVDO ..........................................43 )LJXUD ±$UPDGXUDWUDQVYHUVDOQDVHPHQGDV ...........................................................................44 )LJXUD ±(PHQGDVSRUVROGD ......................................................................................................46 )LJXUD ±,QWURGXomRGDSURWHQVmR .............................................................................................49 )LJXUD±,PSHUIHLo}HVJHRPpWULFDVJOREDLV ............................................................................59 xii
© ABNT 2023 - Todos os direitos reservados
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
ABNT NBR 6118:2023
)LJXUD±,PSHUIHLo}HVJHRPpWULFDVORFDLV ..............................................................................60 )LJXUD±(QYROWyULDPtQLPDGHRUGHP .................................................................................61 )LJXUD±'LPHQV}HVOLPLWHVSDUDDEHUWXUDVGHODMHVFRPGLVSHQVDGHYHUL¿FDomR ...........76 )LJXUD±7UHFKRVUtJLGRV ...........................................................................................................87 )LJXUD±/DUJXUDGHPHVDFRODERUDQWH ...................................................................................88 )LJXUD±/DUJXUDHIHWLYDFRPDEHUWXUD ....................................................................................89 )LJXUD±$OWXUDHODUJXUDHIHWLYDVGHXPDVHomRWUDQVYHUVDO ................................................89 )LJXUD±9mRHIHWLYR ..................................................................................................................90 )LJXUD±$UUHGRQGDPHQWRGHGLDJUDPDGHPRPHQWRVÀHWRUHV ............................................90 )LJXUD±&DSDFLGDGHGHURWDomRGHUyWXODVSOiVWLFDV............................................................92 )LJXUD±$SUR[LPDomRHPDSRLRVH[WUHPRV ...........................................................................94 )LJXUD ±)DL[DVGHODMHSDUDGLVWULEXLomRGRVHVIRUoRVQRVSyUWLFRVP~OWLSORV .................98 )LJXUD±5HODomRPRPHQWRFXUYDWXUD ...................................................................................101 )LJXUD±(QYROWyULDPtQLPDFRPRUGHP............................................................................102 )LJXUD±(IHLWRVGHRUGHPORFDOL]DGRV..............................................................................103 )LJXUD±&RPSULPHQWRHTXLYDOHQWHe ..................................................................................................... 112 )LJXUD±$YDOLDomRDSUR[LPDGDGRHIHLWRGHRUGHPORFDOL]DGR ...................................... 113 )LJXUD±'RPtQLRVGHHVWDGROLPLWH~OWLPRGHXPDVHomRWUDQVYHUVDO ..............................122 )LJXUD±5LJLGH]HTXLYDOHQWHSDUDYmRVGHYLJDVFRQWtQXDV ...............................................127 )LJXUD±&RQFUHWRGHHQYROYLPHQWRGDDUPDGXUD ................................................................129 )LJXUDí)OH[RWRUomRGHSHU¿OFRPSDUHGHVRSRVWDV .........................................................143 )LJXUDí0XGDQoDGHGLUHomRGDVDUPDGXUDV ......................................................................146 )LJXUDí3URWHomRFRQWUDÀDPEDJHPGDVEDUUDV .................................................................147 )LJXUDí&REHUWXUDGRGLDJUDPDGHIRUoDGHWUDomRVROLFLWDQWHSHORGLDJUDPDUHVLVWHQWH ... 149 )LJXUD í&RPSULPHQWRGHDQFRUDJHPQHFHVViULR ...............................................................161 )LJXUD í3HUtPHWURFUtWLFRHPSLODUHVLQWHUQRV .....................................................................163 )LJXUD í3HUtPHWURFUtWLFRHPSLODUHVGHERUGD ....................................................................165 )LJXUD í3HUtPHWURFUtWLFRHPSLODUHVGHFDQWR ....................................................................166 )LJXUD í'H¿QLomRGDDOWXUD~WLOQRFDVRGHFDSLWHO.............................................................166 )LJXUD í3HUtPHWURFUtWLFRQRFDVRGHRFRQWRUQR&DSUHVHQWDUUHHQWUkQFLD ....................167 )LJXUD í3HUtPHWURFUtWLFRMXQWRjDEHUWXUDQDODMH ..............................................................167 )LJXUD í'LVSRVLomRGDDUPDGXUDGHSXQomRHPSODQWDHFRQWRUQRGDVXSHUItFLH crítica C” .........................................................................................................................169 )LJXUD í'LVSRVLomRGDDUPDGXUDGHSXQomRHPFRUWH.......................................................170 )LJXUD í$UPDGXUDFRQWUDFRODSVRSURJUHVVLYR ................................................................171 )LJXUD í(IHLWRIDYRUiYHOGRVFDERVLQFOLQDGRV .................................................................171 )LJXUDí%RUGDVOLYUHVHDEHUWXUDVGDVODMHVPDFLoDV .........................................................173 )LJXUDí/DMHVVHPYLJDV ........................................................................................................174 )LJXUD±'LVSRVLomRGHFDERVHPIDL[DH[WHUQDGHDSRLR ...................................................175 )LJXUDí5HJL}HVGHSUHVVmRORFDOL]DGD ...............................................................................178 )LJXUDí5HJLmRGHDUWLFXODomRGHFRQFUHWR .........................................................................178 )LJXUDí3UHVV}HVMXQWRDXPSLQRHPEXWLGRHPXPHOHPHQWRHVWUXWXUDOGHFRQFUHWR ..179 )LJXUDí$EHUWXUDVHPYLJDVSDUHGHGHFRQFUHWRDUPDGR ..................................................180 © ABNT 2023 - Todos os direitos reservados
xiii
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
ABNT NBR 6118:2023
)LJXUDí$EHUWXUDYHUWLFDOHPYLJDV.......................................................................................181 )LJXUDí6LWXDo}HVWtSLFDVGHUHJL}HV' ...............................................................................183 )LJXUDí'RLVWLSRVFRPXQVGHYLJDVSDUHGHHPUHODomRDRFDUUHJDPHQWR .....................184 )LJXUDí$UPDomRWtSLFDGHYLJDSDUHGHFRPh d .............................................................186 )LJXUDí0RGHORELHODWLUDQWHSDUDFRQVRORFXUWR ................................................................187 )LJXUDí$UPDGXUDWtSLFDGHXPFRQVRORFXUWR ....................................................................189 )LJXUDí0RGHORELHODWLUDQWHSDUDXPGHQWH*HUEHU ...........................................................190 )LJXUDí%ORFRFRPHVWDFDVWUDFLRQDGDV..............................................................................194 )LJXUDí'H¿QLomRGDVWHQV}HVVc1 e Vc2 .............................................................................199 )LJXUD±)RUPDWRGDVFXUYDVGHUHVLVWrQFLDFDUDFWHUtVWLFDjIDGLJD FXUYDV61 para o aço .......................................................................................................................202 )LJXUDí'LDJUDPDGHFiOFXORWHQVmRGHIRUPDomRGRFRQFUHWRFRPFRQVLGHUDomR GDÀXrQFLD.......................................................................................................................206 )LJXUDí6HomRÀH[RFRPSULPLGD ..........................................................................................208 )LJXUD$í9DULDomRGHHccf t ......................................................................................................213 )LJXUD$í9DULDomRGHEf t .........................................................................................................215 )LJXUD$í9DULDomRGHEs t .........................................................................................................217 7DEHODV 7DEHOD±&ODVVHVGHDJUHVVLYLGDGHDPELHQWDO &$$ ...............................................................17 7DEHOD±&RUUHVSRQGrQFLDHQWUHDFODVVHGHDJUHVVLYLGDGHHDTXDOLGDGHGRFRQFUHWR .....18 7DEHOD±&RUUHVSRQGrQFLDHQWUHDFODVVHGHDJUHVVLYLGDGHDPELHQWDOHRFREULPHQWR QRPLQDOSDUD'c = 10 mm ................................................................................................20 7DEHOD±9DORUHVFDUDFWHUtVWLFRVVXSHULRUHVGDGHIRUPDomRHVSHFt¿FDGHUHWUDomR Hcs tt0 HGRFRH¿FLHQWHGHÀXrQFLDM tt0 ..............................................................28 7DEHOD±9DORUGRFRH¿FLHQWHGHDGHUrQFLDK1..........................................................................29 7DEHOD±9DORUHVGH fck @ onde fFWP e fckVmRH[SUHVVRVHPPHJDSDVFDO 03D sendo fFNMt03DHVWDVH[SUHVV}HVSRGHPWDPEpPVHUXVDGDVSDUDLGDGHVGLIHUHQWHVGHGLDV
© ABNT 2023 - Todos os direitos reservados
23
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ABNT NBR 6118:2023
8.2.6
5HVLVWrQFLDQRHVWDGRPXOWLD[LDOGHWHQV}HV
(VWDQGRRFRQFUHWRVXEPHWLGRjVWHQV}HVSULQFLSDLVV3 t V2 t V1GHYHVHWHU V1 t± fctk V3 d fckV1 VHQGRDVWHQV}HVGHFRPSUHVVmRFRQVLGHUDGDVSRVLWLYDVHDVGHWUDomRQHJDWLYDVRHVWDGRPXOWLD[LDO GHWHQV}HVGHYHVHUYHUL¿FDGRFRQIRUPHLOXVWUDGRQD)LJXUD
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
fct
fc
σ1
fc
σ3
)LJXUD±5HVLVWrQFLDQRHVWDGRPXOWLD[LDOGHWHQV}HV 8.2.7
5HVLVWrQFLDjIDGLJD
9HUH 8.2.8
0yGXORGHHODVWLFLGDGH
2 PyGXOR GH HODVWLFLGDGH (ci GHYH VHU REWLGR VHJXQGR R PpWRGR GH HQVDLR HVWDEHOHFLGR QD $%171%5H$%171%5VHQGRFRQVLGHUDGRQHVWD1RUPDRPyGXORGHGHIRUPDomR WDQJHQWHLQLFLDOREWLGRDRVGLDVGHLGDGH 4XDQGR QmR IRUHP UHDOL]DGRV HQVDLRV SRGHVH HVWLPDU R YDORU GR PyGXOR GH HODVWLFLGDGH LQLFLDO XVDQGRDVH[SUHVV}HVDVHJXLU (ci = D(Â fck para concretos com fck 03D f Eci = 21, 5 ⋅ 103 ⋅ αE ⋅ ⎛⎜ ck + 1, 25⎞⎟ ⎝ 10 ⎠
13
SDUDFRQFUHWRVFRPfck !03D
sendo D( SDUDEDVDOWRHGLDEiVLR D( SDUDJUDQLWRHJQDLVVH D( SDUDFDOFiULR D( SDUDDUHQLWR onde (ci e fckVmRGDGRVHPPHJDSDVFDO 03D 24
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
2 PyGXOR GH GHIRUPDomR VHFDQWH SRGH VHU REWLGR VHJXQGR PpWRGR GH HQVDLR HVWDEHOHFLGR QD$%171%5H$%171%5RXHVWLPDGRSHODH[SUHVVmR (cs = DiÂ(ci sendo f αi = 0, 8 + 0, 2 ⋅ ck ≤ 1, 0 80 $ GHIRUPDomR HOiVWLFD GR FRQFUHWR GHSHQGH GD FRPSRVLomR GR WUDoR GR FRQFUHWR HVSHFLDOPHQWH da natureza dos agregados.
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
1DDYDOLDomRGRFRPSRUWDPHQWRGHXPHOHPHQWRHVWUXWXUDORXVHomRWUDQVYHUVDOSRGHVHUDGRWDGR PyGXORGHHODVWLFLGDGH~QLFRjWUDomRHjFRPSUHVVmRLJXDODRPyGXORGHGHIRUPDomRVHFDQWH(cs. 1RFiOFXORGDVSHUGDVGHSURWHQVmRSRGHVHUXWLOL]DGRHPSURMHWRRPyGXORGHHODVWLFLGDGHLQLFLDO(ci. 2 PyGXOR GH HODVWLFLGDGH HP XPD LGDGH PHQRU TXH GLDV SRGH VHU DYDOLDGR SHODV H[SUHVV}HV a seguir:
⎡fckj ⎤ Eci (t ) = ⎢ ⎥ ⎣ fck ⎦
0,5
⋅ EciSDUDRVFRQFUHWRVFRPfck 03D
0,3 ⎡fckj ⎤ Eci (t ) = ⎢ ⎥ ⋅ EciSDUDRVFRQFUHWRVFRPfck!03D ⎣ fck ⎦
onde (ci W pDHVWLPDWLYDGRPyGXORGHHODVWLFLGDGHGRFRQFUHWRHPXPDLGDGHHQWUHGLDVHGLDV fFNM 8.2.9
pDUHVLVWrQFLDFDUDFWHUtVWLFDjFRPSUHVVmRGRFRQFUHWRQDLGDGHHPTXHVHSUHWHQGHHVWLPDU RPyGXORGHHODVWLFLGDGHHPPHJDSDVFDO 03D &RH¿FLHQWHGH3RLVVRQHPyGXORGHHODVWLFLGDGHWUDQVYHUVDO
3DUDWHQV}HVGHFRPSUHVVmRPHQRUHVTXHfcHWHQV}HVGHWUDomRPHQRUHVTXHfctRFRH¿FLHQWH de Poisson Q SRGH VHU WRPDGR FRPR LJXDO D H R PyGXOR GH HODVWLFLGDGH WUDQVYHUVDO *c LJXDO a (cs
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
8.2.10 'LDJUDPDVWHQVmRGHIRUPDomR 8.2.10.1 Compressão 3DUDWHQV}HVGHFRPSUHVVmRPHQRUHVTXHfcSRGHVHDGPLWLUXPDUHODomROLQHDUHQWUHWHQV}HV H GHIRUPDo}HV DGRWDQGRVH SDUD PyGXOR GH HODVWLFLGDGH R YDORU VHFDQWH GDGR SHOD H[SUHVVmR constante em 8.2.8. 3DUD DQiOLVHV QR HVWDGROLPLWH ~OWLPR SRGHP VHU HPSUHJDGRV R GLDJUDPD WHQVmRGHIRUPDomR LGHDOL]DGRPRVWUDGRQD)LJXUDRXDVVLPSOL¿FDo}HVSURSRVWDVQD6HomR Vc fck
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
0,85 Kcfcd
Hc2
⎧3DUDfck n ⎪ ⎡ ⎛ εc ⎞ ⎤ ⎪Para fck σc = , ηc fcd ⎢ − ⎜ − ⎥ ⎝ εc2 ⎟⎠ ⎥ ⎨⎪3DUDfck ⎣⎢ ⎦ ⎪3DUDf ck ⎩
Hcu
Hc
≤ 03D ηc = > 40 MPa: ηc = ( 40 fck )1 3 ≤ 03D Q = > 03D Q = + [( − fck ) ]4
)LJXUD±'LDJUDPDWHQVmRGHIRUPDomRLGHDOL]DGR 2V YDORUHV D VHUHP DGRWDGRV SDUD RV SDUkPHWURV Hc2 GHIRUPDomR HVSHFt¿FD GH HQFXUWDPHQWR GRFRQFUHWRQRLQtFLRGRSDWDPDUSOiVWLFR HHcu GHIRUPDomRHVSHFt¿FDGHHQFXUWDPHQWRGRFRQFUHWR QDUXSWXUD VmRGH¿QLGRVDVHJXLU — SDUDFRQFUHWRVGHFODVVHVDWp& Hc2 Å Hcu Å — SDUDFRQFUHWRVGHFODVVHV&DWp& Hc2 ÅÅ(fck± Hcu ÅÅ> ±fck @4 9HULQGLFDomRVREUHRYDORUGH fcd em 12.3.3.
26
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
3DUDDDQiOLVHHVWUXWXUDOQmROLQHDUSRGHDOWHUQDWLYDPHQWHVHUXWLOL]DGRRGLDJUDPDGHWHQVmRGHIRUPDomR SDUDDFRPSUHVVmRVLPSOHVGHFXUWDGXUDomRUHSUHVHQWDGRQD)LJXUD
)LJXUD ± 'LDJUDPD GH WHQVmRGHIRUPDomR SDUD DQiOLVH QmR OLQHDU 3DUDXWLOL]DomRGRJUi¿FRQD)LJXUDDGRWDU fcm
fck 03D
3DUDFDUJDVGHORQJDGXUDomRRVHIHLWRVGDÀXrQFLDGHYHPVHUFRQYHQLHQWHPHQWHFRQVLGHUDGRV 8.2.10.2 Tração 3DUDRFRQFUHWRQmR¿VVXUDGRSRGHVHUDGRWDGRRGLDJUDPDWHQVmRGHIRUPDomRELOLQHDUGHWUDomR indicado na Figura 8.4. Vct fctk 0,9 fctk
arctg(Eci) 0,15 ‰
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ABNT NBR 6118:2023
$7DEHODIRUQHFHRYDORUGRFRH¿FLHQWHGHÀXrQFLDM(tt0 HGDGHIRUPDomRHVSHFt¿FDGHUHWUDomR Hcs(tt0 HPIXQomRGDXPLGDGHPpGLDDPELHQWHHGDHVSHVVXUD¿FWtFLDAc uRQGHAcpDiUHDGD VHomRWUDQVYHUVDOHupRSHUtPHWURGDVHomRHPFRQWDWRFRPDDWPRVIHUD2VYDORUHVGHVWD7DEHOD VmRUHODWLYRVDWHPSHUDWXUDVGRFRQFUHWRHQWUH&H&SRGHQGRVHHQWUHWDQWRDGPLWLORVFRPR YiOLGRV SDUD WHPSHUDWXUDV HQWUH & H & (VVHV YDORUHV VmR YiOLGRV SDUD FRQFUHWRV SOiVWLFRV HGHFLPHQWR3RUWODQGFRPXP 'HIRUPDo}HVHVSHFt¿FDVGHYLGDVjÀXrQFLDHjUHWUDomRPDLVSUHFLVDVSRGHPVHUFDOFXODGDVVHJXQGR indicação do Anexo A.
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
7DEHOD±9DORUHVFDUDFWHUtVWLFRVVXSHULRUHVGDGHIRUPDomRHVSHFt¿FDGHUHWUDomR Hcs tt0 HGRFRH¿FLHQWHGHÀXrQFLDM tt0 8PLGDGHPpGLD ambiente
40
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8.3 Aço de armadura passiva 8.3.1
&DWHJRULD
1RV SURMHWRV GH HVWUXWXUDV GH FRQFUHWR DUPDGR GHYH VHU XWLOL]DGR DoR FODVVL¿FDGR SHOD $%17 1%5 FRP R YDORU FDUDFWHUtVWLFR GD UHVLVWrQFLD GH HVFRDPHQWR QDV FDWHJRULDV &$&$H&$2VGLkPHWURVHVHo}HVWUDQVYHUVDLVQRPLQDLVGHYHPVHURVHVWDEHOHFLGRV QD$%171%5 8.3.2
Tipo de superfície aderente
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
3DUDRVHIHLWRVGHVWD1RUPDDFDSDFLGDGHDGHUHQWHHQWUHRDoRHRFRQFUHWRHVWiUHODFLRQDGDDR FRH¿FLHQWHK1FXMRYDORUHVWiHVWDEHOHFLGRQD7DEHOD 7DEHOD±9DORUGRFRH¿FLHQWHGHDGHUrQFLDK1
8.3.3
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
3RGHVHDGRWDUSDUDDPDVVDHVSHFt¿FDGRDoRGHDUPDGXUDSDVVLYDRYDORUGHNJP3. 8.3.4
&RH¿FLHQWHGHGLODWDomRWpUPLFD
2YDORUGH&SRGHVHUFRQVLGHUDGRSDUDRFRH¿FLHQWHGHGLODWDomRWpUPLFDGRDoRSDUDLQWHUYDORV GHWHPSHUDWXUDHQWUH&H& 8.3.5
0yGXORGHHODVWLFLGDGH
1DIDOWDGHHQVDLRVRXYDORUHVIRUQHFLGRVSHORIDEULFDQWHRPyGXORGHHODVWLFLGDGHGRDoRSRGHVHU DGPLWLGRLJXDOD*3D 8.3.6
'LDJUDPDWHQVmRGHIRUPDomRUHVLVWrQFLDDRHVFRDPHQWRHjWUDomR
2 GLDJUDPD WHQVmRGHIRUPDomR GR DoR H RV YDORUHV FDUDFWHUtVWLFRV GD UHVLVWrQFLD DR HVFRDPHQWR fyk GD UHVLVWrQFLD j WUDomR fstk H GD GHIRUPDomR QD UXSWXUD Huk GHYHP VHU REWLGRV GH HQVDLRV GHWUDomRUHDOL]DGRVVHJXQGRD$%171%5,62 2YDORUGH fyk para os aços sem patamar GHHVFRDPHQWRpRYDORUGDWHQVmRFRUUHVSRQGHQWHjGHIRUPDomRSHUPDQHQWHGH 3DUDRFiOFXORQRVHVWDGRVOLPLWHGHVHUYLoRH~OWLPRSRGHVHXWLOL]DURGLDJUDPDVLPSOL¿FDGRPRVWUDGR QD)LJXUDSDUDRVDoRVFRPRXVHPSDWDPDUGHHVFRDPHQWR Vs fyk fyd
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)LJXUD±'LDJUDPDWHQVmRGHIRUPDomRSDUDDoRVGHDUPDGXUDVSDVVLYDV © ABNT 2023 - Todos os direitos reservados
29
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
(VWHGLDJUDPDpYiOLGRSDUDLQWHUYDORVGHWHPSHUDWXUDHQWUH&H&HSRGHVHUDSOLFDGRSDUD tração e compressão. 8.3.7
&DUDFWHUtVWLFDVGHGXWLOLGDGH
2VDoRV&$H&$TXHDWHQGDPDRVYDORUHVPtQLPRVGHfstfy e HukLQGLFDGRVQD$%171%5 SRGHPVHUFRQVLGHUDGRVGHDOWDGXWLOLGDGH2VDoRV&$TXHREHGHoDPWDPEpPjVHVSHFL¿FDo}HV GHVWD1RUPDSRGHPVHUFRQVLGHUDGRVGHGXWLOLGDGHQRUPDO (PHQVDLRVGHGREUDPHQWRDUHDOL]DGRVGHDFRUGRFRPD$%171%5,62HXWLOL]DQGR RVGLkPHWURVGHSLQRVLQGLFDGRVQD$%171%5QmRSRGHRFRUUHUUXSWXUDRX¿VVXUDomR 8.3.8
5HVLVWrQFLDjIDGLJD
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
9HU 8.3.9
6ROGDELOLGDGH
3DUDTXHXPDoRVHMDFRQVLGHUDGRVROGiYHOVXDFRPSRVLomRGHYHREHGHFHUDRVOLPLWHVHVWDEHOHFLGRV QD$%171%5 $HPHQGDGHDoRVROGDGDGHYHVHUHQVDLDGDjWUDomRVHJXQGRD$%171%5$IRUoDGHUXSWXUD PtQLPDPHGLGDQDEDUUDVROGDGDGHYHVDWLVID]HURHVSHFL¿FDGRQD$%171%5HRDORQJDPHQWR VREFDUJDGHYHVHUWDOTXHQmRFRPSURPHWDDGXWLOLGDGHGDDUPDGXUD2DORQJDPHQWRWRWDOSOiVWLFR PHGLGRQDEDUUDVROGDGDGHYHDWHQGHUDXPPtQLPRGH
8.4 Aço de armadura ativa 8.4.1
&ODVVL¿FDomR
2V YDORUHV GH UHVLVWrQFLD FDUDFWHUtVWLFD j WUDomR GLkPHWUR H iUHD GRV ¿RV H GDV FRUGRDOKDV EHP FRPRDFODVVL¿FDomRTXDQWRjUHOD[DomRDVHUHPDGRWDGRVHPSURMHWRVmRRVQRPLQDLVLQGLFDGRVQD $%171%5HQD$%171%5UHVSHFWLYDPHQWH 8.4.2
0DVVDHVSHFt¿FD
3RGHVHDGRWDUSDUDDPDVVDHVSHFt¿FDGRDoRGHDUPDGXUDDWLYDRYDORUNJP3. 8.4.3
&RH¿FLHQWHGHGLODWDomRWpUPLFD
2YDORUGH&SRGHVHUFRQVLGHUDGRSDUDFRH¿FLHQWHGHGLODWDomRWpUPLFDGRDoRSDUDLQWHUYDORV GHWHPSHUDWXUDHQWUH&H& 8.4.4
0yGXORGHHODVWLFLGDGH
2YDORUGRPyGXORGHHODVWLFLGDGHGHYHVHUREWLGRHPHQVDLRVRXIRUQHFLGRSHORIDEULFDQWH1DIDOWD GHGDGRVHVSHFt¿FRVSRGHVHFRQVLGHUDURYDORUGH*3DSDUD¿RVHFRUGRDOKDV 8.4.5
'LDJUDPDWHQVmRGHIRUPDomRUHVLVWrQFLDDRHVFRDPHQWRHjWUDomR
2 GLDJUDPD WHQVmRGHIRUPDomR GHYH VHU IRUQHFLGR SHOR IDEULFDQWH RX REWLGR DWUDYpV GH HQVDLRV UHDOL]DGRVVHJXQGRD$%171%5 30
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
2VYDORUHVFDUDFWHUtVWLFRVGDUHVLVWrQFLDDRHVFRDPHQWRFRQYHQFLRQDOfpykGDUHVLVWrQFLDjWUDomRfptk HRDORQJDPHQWRDSyVUXSWXUDHukGDVFRUGRDOKDVGHYHPVDWLVID]HURVYDORUHVPtQLPRVHVWDEHOHFLGRV QD $%17 1%5 2V YDORUHV GH fpyk fptk H GR DORQJDPHQWR DSyV UXSWXUD Huk GRV ¿RV GHYHP DWHQGHUDRTXHpHVSHFL¿FDGRQD$%171%5 3DUDFiOFXORQRVHVWDGRVOLPLWHGHVHUYLoRH~OWLPRSRGHVHXWLOL]DURGLDJUDPDVLPSOL¿FDGRPRVWUDGR na Figura 8.6. Vp fptk fptd
fpyk
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
fpyd
arctg(Ep) Hpu
Hp
)LJXUD±'LDJUDPDWHQVmRGHIRUPDomRSDUDDoRVGHDUPDGXUDVDWLYDV (VWHGLDJUDPDpYiOLGRSDUDLQWHUYDORVGHWHPSHUDWXUDHQWUH&H& 8.4.6
&DUDFWHUtVWLFDVGHGXWLOLGDGH
2V ¿RV H FRUGRDOKDV FXMR YDORU GH Huk IRU PDLRU TXH R PtQLPR LQGLFDGR QDV $%17 1%5 H$%171%5UHVSHFWLYDPHQWHSRGHPVHUFRQVLGHUDGRVFRPRWHQGRGXWLOLGDGHQRUPDO 2Q~PHURPtQLPRGHGREUDPHQWRVDOWHUQDGRVGRV¿RVGHSURWHQVmRREWLGRVHPHQVDLRVVHJXQGR D$%171%5GHYHDWHQGHUDRTXHpLQGLFDGRQD$%171%5 8.4.7
5HVLVWrQFLDjIDGLJD
9HU 8.4.8
5HOD[DomR
$UHOD[DomRGH¿RVHFRUGRDOKDVDSyVKD& 3NW(x @sup 3t(x >3NW(x @LQI 3t(x Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
9.6.1.4
9DORUHVGHFiOFXORGDIRUoDGHSURWHQVmR
2VYDORUHVGHFiOFXORGDIRUoDGHSURWHQVmRQRWHPSR t VmRGDGRVSHODH[SUHVVmR 3GW(x Jp 3t(x VHQGRRYDORUGHJpHVWDEHOHFLGRQD6HomR 9.6.2 9.6.2.1
Introdução das forças de protensão *HQHUDOLGDGHV
$VWHQV}HVLQGX]LGDVQRFRQFUHWRSHODVDQFRUDJHQVGHSURWHQVmRVRPHQWHSRGHPVHUFRQVLGHUDGDV OLQHDUPHQWHGLVWULEXtGDVQDVHomRWUDQVYHUVDOGRHOHPHQWRHVWUXWXUDODXPDGLVWkQFLDGDH[WUHPLGDGH GHVVDVDUPDGXUDVFKDPDGDGLVWkQFLDGHUHJXODUL]DomRGHWHUPLQDGDFRPEDVHQRTXHpHVWDEHOHFLGR em 9.6.2.2 e 9.6.2.3. $VDUPDGXUDVSDVVLYDVQHVVDV]RQDVGHLQWURGXomRGHIRUoDVGHYHPVHUFDOFXODGDVGHDFRUGRFRP DVGLVSRVLo}HVGD6HomR 9.6.2.2
&DVRVGHSyVWUDomR
1R FDVR GRV HOHPHQWRV SyVWUDFLRQDGRV D GLVWkQFLD GH UHJXODUL]DomR GDV WHQV}HV SRGH VHU GHWHUPLQDGDDGPLWLQGRVHTXHDGLIXVmRGDIRUoDVHIDoDDSDUWLUGDDQFRUDJHPQRLQWHULRUGHXPkQJXOR GHDEHUWXUDEWDOTXHWJE YHU)LJXUD 4XDQGRWDOGLIXVmRSDUWLQGRGDDOPDDWLQJHRSODQRPpGLRGDPHVDSRGHVHDGPLWLUTXHDGLIXVmR DRORQJRGDPHVDVHID]WDPEpPFRQIRUPHRkQJXORGHDEHUWXUDE.
48
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
mesa β
alma
β β
cabo cabo
β
mesa
β
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
β
)LJXUD ±,QWURGXomRGDSURWHQVmR 9.6.2.3
&DVRVGHSUpWUDomR
1RFDVRGHHOHPHQWRVSUpWUDFLRQDGRVDGLVWkQFLDGHUHJXODUL]DomRp GHYHVHUREWLGDSHODH[SUHVVmR p = h2 + (0, 6 bpt ) ≥ bpt 2
onde h pDDOWXUDGRHOHPHQWRHVWUXWXUDO 3DUD DV VHo}HV QmR UHWDQJXODUHV R FRPSULPHQWR GH UHJXODUL]DomR SRGH VHU FDOFXODGR GH IRUPD VHPHOKDQWHjLQGLFDGDHP 9.6.3 9.6.3.1
Perdas da força de protensão *HQHUDOLGDGHV
2 SURMHWR GHYH SUHYHU DV SHUGDV GD IRUoD GH SURWHQVmR HP UHODomR DR YDORU LQLFLDO DSOLFDGR SHOR DSDUHOKR WHQVRU RFRUULGDV DQWHV GD WUDQVIHUrQFLD GD SURWHQVmR DR FRQFUHWR SHUGDV LQLFLDLV QDSUpWUDomR GXUDQWHHVVDWUDQVIHUrQFLD SHUGDVLPHGLDWDV HDRORQJRGRWHPSR SHUGDVSURJUHVVLYDV 9.6.3.2
Perdas iniciais da força de protensão
&RQVLGHUDPVHLQLFLDLVDVSHUGDVRFRUULGDVQDSUpWUDomRDQWHVGDOLEHUDomRGRGLVSRVLWLYRGHWUDomR e decorrentes de: D DWULWRQRVSRQWRVGHGHVYLRGDDUPDGXUDSROLJRQDOFXMDDYDOLDomRGHYHVHUIHLWDH[SHULPHQWDOPHQWH HPIXQomRGRWLSRGHDSDUHOKRGHGHVYLRHPSUHJDGR E HVFRUUHJDPHQWRGRV¿RVQDDQFRUDJHPFXMDGHWHUPLQDomRGHYHVHUH[SHULPHQWDORXGHYHPVHU DGRWDGRVRVYDORUHVLQGLFDGRVSHORIDEULFDQWHGRVGLVSRVLWLYRVGHDQFRUDJHP
© ABNT 2023 - Todos os direitos reservados
49
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ABNT NBR 6118:2023
F UHOD[DomR LQLFLDO GD DUPDGXUD IXQomR GR WHPSR GHFRUULGR HQWUH R DORQJDPHQWR GD DUPDGXUD HDOLEHUDomRGRGLVSRVLWLYRGHWUDomR G UHWUDomR LQLFLDO GR FRQFUHWR FRQVLGHUDGR R WHPSR GHFRUULGR HQWUH D FRQFUHWDJHP GR HOHPHQWR HVWUXWXUDOHDOLEHUDomRGRGLVSRVLWLYRGHWUDomR $ DYDOLDomR GDV SHUGDV LQLFLDLV GHYH FRQVLGHUDU RV HIHLWRV SURYRFDGRV SHOD WHPSHUDWXUD TXDQGR RFRQFUHWRIRUFXUDGRWHUPLFDPHQWH 9.6.3.3
Perdas imediatas da força de protensão
9.6.3.3.1
&DVRGDSUpWUDomR
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
$YDULDomRGDIRUoDGHSURWHQVmRHPHOHPHQWRVHVWUXWXUDLVFRPSUpWUDomRSRURFDVLmRGDDSOLFDomR GDSURWHQVmRDRFRQFUHWRHHPUD]mRGRVHXHQFXUWDPHQWRGHYHVHUFDOFXODGDHPUHJLPHHOiVWLFR FRQVLGHUDQGRVH D GHIRUPDomR GD VHomR KRPRJHQHL]DGD 2 PyGXOR GH HODVWLFLGDGH GR FRQFUHWR DFRQVLGHUDUpRFRUUHVSRQGHQWHjGDWDGHSURWHQVmRFRUULJLGRVHKRXYHUFXUDWpUPLFD 9.6.3.3.2
&DVRGHSyVWUDomR
3DUDRVVLVWHPDVXVXDLVGHSURWHQVmRDVSHUGDVLPHGLDWDVVmRDVGHYLGDVDRHQFXUWDPHQWRLPHGLDWR GRFRQFUHWRDRDWULWRHQWUHDVDUPDGXUDVHDVEDLQKDVRXRFRQFUHWRDRGHVOL]DPHQWRGDDUPDGXUD MXQWRjDQFRUDJHPHjDFRPRGDomRGRVGLVSRVLWLYRVGHDQFRUDJHPFRPRGHWDOKDGRHP a 9.6.3.3.2.3. 9.6.3.3.2.1 Encurtamento imediato do concreto 1RVHOHPHQWRVHVWUXWXUDLVFRPSyVWUDomRDSURWHQVmRVXFHVVLYDGHFDGDXPGRVnJUXSRVGHFDERV SURWHQGLGRVVLPXOWDQHDPHQWHSURYRFDXPDGHIRUPDomRLPHGLDWDGRFRQFUHWRHFRQVHTXHQWHPHQWH DIURX[DPHQWRGRVFDERVDQWHULRUPHQWHSURWHQGLGRV$SHUGDPpGLDGHSURWHQVmRSRUFDERSRGHVHU FDOFXODGDSHODH[SUHVVmR n − 1⎞ * ΔσS = αS ( t ) ⎜⎛ ⎟ σFSJ ⎝ 2n ⎠ onde σ*FSJ
p D WHQVmR QR FRQFUHWR DGMDFHQWH DR FDER UHVXOWDQWH SURYRFDGD SHOR HIHLWR FRQMXQWR GDSURWHQVmR FRPSUHVVmR DSyVDVSHUGDVSRUDWULWRHSRUDFRPRGDomRGDDQFRUDJHP HSHORHIHLWRGDFDUJDSHUPDQHQWH WUDomR PRELOL]DGDQRLQVWDQWHt0VHQGRSRVLWLYDVH de compressão.
9.6.3.3.2.2 Perdas por atrito 1RVHOHPHQWRVHVWUXWXUDLVFRPSyVWUDomRDSHUGDSRUDWULWRSRGHVHUGHWHUPLQDGDSHODH[SUHVVmR ΔP( x ) = P i ⎡⎣1 − e − (μΣα + kx ) ⎤⎦ onde 3 i pRYDORUGH¿QLGRHP x p D DEVFLVVD GR SRQWR RQGH VH FDOFXOD '3 PHGLGD D SDUWLU GD DQFRUDJHP H[SUHVVD HP PHWURV P 6D pDVRPDGRVkQJXORVGHGHVYLRHQWUHDDQFRUDJHPHRSRQWRGHDEVFLVVD[H[SUHVVDHP
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
UDGLDQRV UDG
P pRFRH¿FLHQWHGHDWULWRDSDUHQWHHQWUHRFDERHDEDLQKD1DIDOWDGHGDGRVH[SHULPHQWDLV SRGHVHUHVWLPDGRFRPRDVHJXLU YDORUHVHPUDGLDQRV P HQWUHFDERHFRQFUHWR VHPEDLQKD P HQWUHEDUUDVRX¿RVFRPPRVVDVRXVDOLrQFLDVHEDLQKDPHWiOLFD P HQWUH¿RVOLVRVRXFRUGRDOKDVHEDLQKDPHWiOLFD P HQWUH¿RVOLVRVRXFRUGRDOKDVHEDLQKDPHWiOLFDOXEUL¿FDGD
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
P HQWUHFRUGRDOKDHEDLQKDGHSROLSURSLOHQROXEUL¿FDGD N pRFRH¿FLHQWHGHSHUGDSRUPHWURSURYRFDGDSRUFXUYDWXUDVQmRLQWHQFLRQDLVGRFDER1DIDOWD GHGDGRVH[SHULPHQWDLVSRGHVHUDGRWDGRRYDORUP P 9.6.3.3.2.3 3HUGDVSRUGHVOL]DPHQWRGDDUPDGXUDQDDQFRUDJHPHDFRPRGDomRGDDQFRUDJHP $V SHUGDV GHYHP VHU GHWHUPLQDGDV H[SHULPHQWDOPHQWH RX DGRWDGRV RV YDORUHV LQGLFDGRV SHORV IDEULFDQWHVGRVGLVSRVLWLYRVGHDQFRUDJHP 9.6.3.4 9.6.3.4.1
3HUGDVSURJUHVVLYDV *HQHUDOLGDGHV
2V YDORUHV SDUFLDLV H WRWDLV GDV SHUGDV SURJUHVVLYDV GH SURWHQVmR GHFRUUHQWHV GD UHWUDomR H GD ÀXrQFLDGRFRQFUHWRHGDUHOD[DomRGRDoRGHSURWHQVmRGHYHPVHUGHWHUPLQDGRVFRQVLGHUDQGRVH DLQWHUDomRGHVVDVFDXVDVSRGHQGRVHUXWLOL]DGRVRVSURFHVVRVLQGLFDGRVHP D 1HVVHVSURFHVVRVDGPLWHVHTXHH[LVWDDGHUrQFLDHQWUHDDUPDGXUDHRFRQFUHWRHTXHRHOHPHQWR HVWUXWXUDOSHUPDQHoDQRHVWiGLR, 9.6.3.4.2
3URFHVVRVLPSOL¿FDGRSDUDRFDVRGHIDVHV~QLFDVGHRSHUDomR
(VVHFDVRpDSOLFiYHOTXDQGRVmRVDWLVIHLWDVDVFRQGLo}HVVHJXLQWHV D DFRQFUHWDJHPGRHOHPHQWRHVWUXWXUDOEHPFRPRDSURWHQVmRVmRH[HFXWDGDVFDGDXPDGHODV HPIDVHVVX¿FLHQWHPHQWHSUy[LPDVSDUDTXHVHGHVSUH]HPRVHIHLWRVUHFtSURFRVGHXPDIDVH VREUHDRXWUD E RV FDERV SRVVXHP HQWUH VL DIDVWDPHQWRV VX¿FLHQWHPHQWH SHTXHQRV HP UHODomR j DOWXUD GD VHomRGRHOHPHQWRHVWUXWXUDOGHPRGRTXHVHXVHIHLWRVSRVVDPVHUVXSRVWRVHTXLYDOHQWHVDR GHXP~QLFRFDERFRPVHomRWUDQVYHUVDOGHiUHDLJXDOjVRPDGDViUHDVGDVVHo}HVGRVFDERV FRPSRQHQWHVVLWXDGRQDSRVLomRGDUHVXOWDQWHGDVIRUoDVQHOHVDWXDQWHV FDERUHVXOWDQWH 1HVVH FDVR DGPLWHVH TXH QR WHPSR t DV SHUGDV H GHIRUPDo}HV SURJUHVVLYDV GR FRQFUHWR H GR DoRGHSURWHQVmRQDSRVLomRGRFDERUHVXOWDQWHFRPDVWHQV}HVQRFRQFUHWRVFSJ positivas para FRPSUHVVmRHDVWHQV}HVQRDoRVp0SRVLWLYDVSDUDWUDomRVHMDPGDGDVSRU Δσp (t,t0 ) =
εFV (W W ) (S + αS (W ) σFSJϕ (W W ) + σS χ (W W ) χp + χc αp ηρp
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
σp0
Δεpt (t t0 ) = Δεct (W W0 ) =
(p
χ ( t t 0 ) −
σFSJ (ci28
Δσp (t t0 )
ϕ ( W W 0 ) −
(p
χp
Δσc (t t0 ) χc + |Hcs(tt0 _ (ci28
onde F(t,t0 ±OQ>±\ (t,t0 @ Fc M (t,t0 Fp F (t,t0
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
A η = 1 + ep2 c Ic Up= Ap$c αp =
(p (ci
α p (t ) =
(p (ci (W )
onde
VFSJ
pDWHQVmRQRFRQFUHWRDGMDFHQWHDRFDERUHVXOWDQWHSURYRFDGDSHORHIHLWRFRQMXQWR GD SURWHQVmR FRPSUHVVmR DSyV WRGDV DV SHUGDV LPHGLDWDV DWULWR DFRPRGDomR HHQFXUWDPHQWR HSHORHIHLWRGDFDUJDSHUPDQHQWH WUDomR PRELOL]DGDQRLQVWDQWHt0 VHQGRSRVLWLYDVHGHFRPSUHVVmR
M (tt0
pRFRH¿FLHQWHGHÀXrQFLDGRFRQFUHWRQRLQVWDQWHtSDUDSURWHQVmRHFDUJDSHUPDQHQWH DSOLFDGDVQRLQVWDQWHt0
ıp0
pDWHQVmRQDDUPDGXUDDWLYDDSyVWRGDVDVSHUGDVLPHGLDWDVQRLQVWDQWHt0 e sempre SRVLWLYDSRUVHUGHWUDomR
F(tt0
pRFRH¿FLHQWHGHÀXrQFLDGRDoR
Hcs(tt0
pDUHWUDomRQRLQVWDQWHtGHVFRQWDGDDUHWUDomRRFRUULGDDWpRLQVWDQWHt0FRQIRUPH
\(tt0
pRFRH¿FLHQWHGHUHOD[DomRGRDoRQRLQVWDQWHt para protensão e carga permanente PRELOL]DGDQRLQVWDQWHt0
'Vc(tt0
pDYDULDomRGDWHQVmRGRFRQFUHWRDGMDFHQWHDRFDERUHVXOWDQWHHQWUHt0 e t
'Vp(tt0
pDYDULDomRGDWHQVmRQRDoRGHSURWHQVmRHQWUHt0 e t
U p
pDWD[DJHRPpWULFDGDDUPDGXUDGHSURWHQVmR
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
ep
pDH[FHQWULFLGDGHGRFDERUHVXOWDQWHHPUHODomRDREDULFHQWURGDVHomRGRFRQFUHWR
Ap
pDiUHDGDVHomRWUDQVYHUVDOGRFDERUHVXOWDQWH
Ac
pDiUHDGDVHomRWUDQVYHUVDOGRFRQFUHWR
Ic
pRPRPHQWRFHQWUDOGHLQpUFLDQDVHomRGRFRQFUHWR
3DUDSURWHQVmRDGHUHQWHFRQVLGHUDURVYDORUHVORFDLVGDVWHQV}HVHSDUDSURWHQVmRQmRDGHUHQWH FRQVLGHUDURYDORUPpGLRGDVWHQV}HV2VYDORUHVPpGLRVGHYHPVHUFDOFXODGRVHQWUHVHo}HVGH¿QLGDV SHORVSRQWRVGHLQÀH[mRGRVFDERVQRFDVRGHSURWHQVmRH[WHUQDRXDRORQJRGHWRGRFRPSULPHQWR para o caso de protensão interna.
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
9.6.3.4.3
Processo aproximado
(VVHSURFHVVRSRGHVXEVWLWXLURHVWDEHOHFLGRHP GHVGHTXHVDWLVIHLWDVDVPHVPDVFRQGLo}HV GHDSOLFDomRHTXHDUHWUDomRQmRGL¿UDHPPDLVGHGRYDORU> 10±M(t0 @ 2YDORUDEVROXWRGDSHUGDGHWHQVmRGHYLGDjÀXrQFLDUHWUDomRHUHOD[DomRFRPVFSJHPPHJDSDVFDO HFRQVLGHUDGRSRVLWLYRVHIRUGHFRPSUHVVmRpGDGRSRU D SDUDDoRVGHUHOD[DomRQRUPDO 51 YDORUHPSRUFHQWDJHP Δσp (t∞ ,t0 ) σp 0
= 18,1 +
αp 47
[ϕ (t∞,t0 )]1,57 (3 + σc,p0g )
E SDUDDoRVGHUHOD[DomREDL[D 5% YDORUHPSRUFHQWDJHP Δσp (t∞ ,t0 ) σp 0
= 7, 4 +
αp
1,07 ϕ (t∞ ,t0 )] (3 + σc,p0g ) [ 18, 7
onde Vp0 9.6.3.4.4
pDWHQVmRQDDUPDGXUDGHSURWHQVmRGHYLGDH[FOXVLYDPHQWHjIRUoDGHSURWHQVmRQR instante t0. 0pWRGRJHUDOGHFiOFXOR
4XDQGR DV Do}HV SHUPDQHQWHV FDUJD SHUPDQHQWH RX SURWHQVmR VmR DSOLFDGDV SDUFHODGDPHQWH HP LGDGHV GLIHUHQWHV SRUWDQWR QmR VmR VDWLVIHLWDV DV FRQGLo}HV HVWDEHOHFLGDV HP GHYH VHU FRQVLGHUDGD D ÀXrQFLD GH FDGD XPD GDV FDPDGDV GH FRQFUHWR H D UHOD[DomR GH FDGD FDER separadamente. 3RGHVHUFRQVLGHUDGDDUHOD[DomRLVRODGDGHFDGDFDERLQGHSHQGHQWHPHQWHGDDSOLFDomRSRVWHULRU GHRXWUDVDo}HVSHUPDQHQWHV
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
9.6.3.4.5
5HOD[DomRGRDoR
$LQWHQVLGDGHGDUHOD[DomRGRDoRGHYHVHUGHWHUPLQDGDSHORFRH¿FLHQWH\(t,t0 FDOFXODGRSRU ψ (t , t 0 ) =
Δσpr (t , t0 ) σpi
onde 'Vpr (tt0 pDSHUGDGHWHQVmRSRUUHOD[DomRSXUDGHVGHRLQVWDQWHt0 do estiramento da armadura DWpRLQVWDQWHt considerado.
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
2V YDORUHV PpGLRV GD UHOD[DomR PHGLGRV DSyV K j WHPSHUDWXUD FRQVWDQWH GH & SDUD DV SHUGDV GH WHQVmR UHIHULGDV D YDORUHV EiVLFRV GD WHQVmR LQLFLDO GH D GD UHVLVWrQFLD FDUDFWHUtVWLFD fptk (\1000 VmRGH¿QLGRVQD7DEHOD 2VYDORUHVFRUUHVSRQGHQWHVDWHPSRVGLIHUHQWHVGHKVHPSUHD&SRGHPVHUGHWHUPLQDGRV DSDUWLUGDVHJXLQWHH[SUHVVmRGHYHQGRRWHPSRVHUH[SUHVVRHPGLDV 0,15 ⎛ t − t0 ⎞ ψ (t , t0 ) = ψ1000 ⎜ ⎝ 41, 67⎟⎠
3DUDWHQV}HVLQIHULRUHVDfptkDGPLWHVHTXHQmRKDMDSHUGDGHWHQVmRSRUUHOD[DomR 3DUDWHQV}HVLQWHUPHGLiULDVHQWUHRVYDORUHV¿[DGRVQD7DEHODSRGHVHUIHLWDLQWHUSRODomROLQHDU 3RGHVHFRQVLGHUDUTXHSDUDRWHPSRLQ¿QLWRRYDORUGH\ (tt0 pGDGRSRU\ (tt0 #\1000.
10 6HJXUDQoDHHVWDGRVOLPLWHV 10.1 &ULWpULRVGHVHJXUDQoD 2VFULWpULRVGHVHJXUDQoDDGRWDGRVQHVWD1RUPDEDVHLDPVHQD$%171%5
10.2 (VWDGRVOLPLWHV 3DUDRVHIHLWRVGHVWD1RUPDGHYHPVHUFRQVLGHUDGRVRVHVWDGRVOLPLWHV~OWLPRVHRVHVWDGRVOLPLWHV de serviço.
10.3 (VWDGRVOLPLWHV~OWLPRV (/8 $ VHJXUDQoD GDV HVWUXWXUDV GH FRQFUHWR GHYH VHPSUH VHU YHUL¿FDGD HP UHODomR DRV VHJXLQWHV HVWDGRVOLPLWHV~OWLPRV D HVWDGROLPLWH~OWLPRGDSHUGDGRHTXLOtEULRGDHVWUXWXUDDGPLWLGDFRPRFRUSRUtJLGR E HVWDGROLPLWH~OWLPRGHHVJRWDPHQWRGDFDSDFLGDGHUHVLVWHQWHGDHVWUXWXUDQRVHXWRGRRXHP SDUWH GHYLGR jV VROLFLWDo}HV QRUPDLV H WDQJHQFLDLV DGPLWLQGRVH D UHGLVWULEXLomR GH HVIRUoRV LQWHUQRVGHVGHTXHVHMDUHVSHLWDGDDFDSDFLGDGHGHDGDSWDomRSOiVWLFDGH¿QLGDQD6HomR H DGPLWLQGRVH HP JHUDO DV YHUL¿FDo}HV VHSDUDGDV GDV VROLFLWDo}HV QRUPDLV H WDQJHQFLDLV
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
WRGDYLDTXDQGRDLQWHUDomRHQWUHHODVIRULPSRUWDQWHHODHVWDUiH[SOLFLWDPHQWHLQGLFDGDQHVWD 1RUPD F HVWDGROLPLWH~OWLPRGHHVJRWDPHQWRGDFDSDFLGDGHUHVLVWHQWHGDHVWUXWXUDQRVHXWRGRRXHP SDUWHFRQVLGHUDQGRRVHIHLWRVGHVHJXQGDRUGHP G HVWDGROLPLWH~OWLPRSURYRFDGRSRUVROLFLWDo}HVGLQkPLFDV YHU6HomR H HVWDGROLPLWH~OWLPRGHFRODSVRSURJUHVVLYR I
HVWDGROLPLWH~OWLPRGHHVJRWDPHQWRGDFDSDFLGDGHUHVLVWHQWHGDHVWUXWXUDQRVHXWRGRRXHP SDUWHFRQVLGHUDQGRH[SRVLomRDRIRJRFRQIRUPHD$%171%5
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
J HVWDGROLPLWH~OWLPRGHHVJRWDPHQWRGDFDSDFLGDGHUHVLVWHQWHGDHVWUXWXUDFRQVLGHUDQGRDo}HV VtVPLFDVGHDFRUGRFRPD$%171%5 K RXWURVHVWDGRVOLPLWHV~OWLPRVTXHHYHQWXDOPHQWHSRVVDPRFRUUHUHPFDVRVHVSHFLDLV
10.4 (VWDGRVOLPLWHVGHVHUYLoR (/6 (VWDGRVOLPLWHV GH VHUYLoR VmR DTXHOHV UHODFLRQDGRV DR FRQIRUWR GR XVXiULR H j GXUDELOLGDGH DSDUrQFLDHERDXWLOL]DomRGDVHVWUXWXUDVVHMDHPUHODomRDRVXVXiULRVVHMDHPUHODomRjVPiTXLQDV HDRVHTXLSDPHQWRVVXSRUWDGRVSHODVHVWUXWXUDV $ VHJXUDQoD GDV HVWUXWXUDV GH FRQFUHWR SRGH H[LJLU D YHUL¿FDomR GRV HVWDGRVOLPLWH GH VHUYLoR GH¿QLGRVHP (PFRQVWUXo}HVHVSHFLDLVSRGHVHUQHFHVViULRYHUL¿FDUDVHJXUDQoDHPUHODomRDRXWURVHVWDGRV OLPLWHVGHVHUYLoRQmRGH¿QLGRVQHVWD1RUPD
11 $o}HV 11.1 6LPERORJLDHVSHFt¿FDGHVWD6HomR 'H IRUPD D VLPSOL¿FDU D FRPSUHHQVmR H SRUWDQWR D DSOLFDomR GRV FRQFHLWRV HVWDEHOHFLGRV QHVWD 6HomRRVVtPERORVPDLVXWLOL]DGRVRXTXHSRGHULDPJHUDUG~YLGDVHQFRQWUDPVHDVHJXLUGH¿QLGRV $VLPERORJLDDSUHVHQWDGDQHVWDVHomRVHJXHDPHVPDRULHQWDomRHVWDEHOHFLGDQD6HomR'HVVD IRUPDRVVtPERORVVXEVFULWRVWrPRPHVPRVLJQL¿FDGRTXHRVDSUHVHQWDGRVHP )±Do}HV YHU7DEHODVH MGPtQ±PRPHQWRWRWDOGHRUGHPGHFiOFXORPtQLPRTXHSRVVLELOLWDRDWHQGLPHQWRGDYHUL¿FDomR GDVLPSHUIHLo}HVORFDOL]DGDVGHXPODQFHGHSLODU JI±SDUWHGRFRH¿FLHQWHGHSRQGHUDomRGDVDo}HVJITXHFRQVLGHUDDYDULDELOLGDGHGDVDo}HV JI±SDUWHGRFRH¿FLHQWHGHSRQGHUDomRGDVDo}HVJITXHFRQVLGHUDDVLPXOWDQHLGDGHGHDWXDomRGDV Do}HV JI ± SDUWH GR FRH¿FLHQWH GH SRQGHUDomR GDV Do}HV JI TXH FRQVLGHUD RV GHVYLRV JHUDGRV QDV FRQVWUXo}HVHDVDSUR[LPDo}HVIHLWDVHPSURMHWRGRSRQWRGHYLVWDGDVVROLFLWDo}HV © ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
Jq±FRH¿FLHQWHGHSRQGHUDomRSDUDDVDo}HVYDULiYHLVGLUHWDV Jqs ±FRH¿FLHQWHGHSRQGHUDomRSDUDDDomRYDULiYHOHVWDELOL]DQWH Jgn±FRH¿FLHQWHGHSRQGHUDomRSDUDDVDo}HVSHUPDQHQWHVQmRHVWDELOL]DQWHV JHg ±FRH¿FLHQWHGHSRQGHUDomRSDUDDVDo}HVLQGLUHWDVSHUPDQHQWHV UHWUDomRRXÀXrQFLD JHq±FRH¿FLHQWHGHSRQGHUDomRSDUDDVDo}HVLQGLUHWDVYDULiYHLV WHPSHUDWXUD Jn ±FRH¿FLHQWHGHDMXVWHGHJITXHFRQVLGHUDRDXPHQWRGHSUREDELOLGDGHGHRFRUUrQFLDGHGHVYLRV UHODWLYRV VLJQL¿FDWLYRV QD FRQVWUXomR DSOLFDGR HP SLODUHV SLODUHVSDUHGHV H ODMHV HP EDODQoR FRPGLPHQV}HVPHQRUHVTXHFHUWRVYDORUHV T1±GHVDSUXPRGHXPHOHPHQWRYHUWLFDOFRQWtQXR
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
\M±IDWRUGHUHGXomRGHFRPELQDomRSDUDDVDo}HVYDULiYHLVGLUHWDV \0H±IDWRUGHUHGXomRGHFRPELQDomRSDUDDVDo}HVYDULiYHLVLQGLUHWDV \0±IDWRUGHUHGXomRGHFRPELQDomRSDUD(/8 \1±IDWRUGHUHGXomRGHFRPELQDomRIUHTXHQWHSDUD(/6 \2 ±IDWRUGHUHGXomRGHFRPELQDomRTXDVHSHUPDQHQWHSDUD(/6
11.2 $o}HVDFRQVLGHUDU 11.2.1 *HQHUDOLGDGHV 1DDQiOLVHHVWUXWXUDOGHYHVHUFRQVLGHUDGDDLQÀXrQFLDGHWRGDVDVDo}HVTXHSRVVDPSURGX]LUHIHLWRV VLJQL¿FDWLYRVSDUDDVHJXUDQoDGDHVWUXWXUDHPH[DPHOHYDQGRVHHPFRQWDRVSRVVtYHLVHVWDGRV OLPLWHV~OWLPRVHRVGHVHUYLoR 11.2.2 &ODVVL¿FDomRGDVDo}HV $VDo}HVDFRQVLGHUDUFODVVL¿FDPVHGHDFRUGRFRPD$%171%5HPSHUPDQHQWHVYDULiYHLV e excepcionais. 3DUDFDGDWLSRGHFRQVWUXomRDVDo}HVDFRQVLGHUDUGHYHPUHVSHLWDUVXDVSHFXOLDULGDGHVHDVQRUPDV DHODDSOLFiYHLV $ DomR GD iJXD SRGH VHU FRQVLGHUDGD FRPR SHUPDQHQWH YDULiYHO RX HVSHFLDO GHSHQGHQGR GD VLWXDomRFRQIRUPHDV$%171%5H$%171%5
11.3 $o}HVSHUPDQHQWHV 11.3.1 *HQHUDOLGDGHV $o}HVSHUPDQHQWHVVmRDVTXHRFRUUHPFRPYDORUHVSUDWLFDPHQWHFRQVWDQWHVGXUDQWHWRGDDYLGDGD FRQVWUXomR7DPEpPVmRFRQVLGHUDGDVSHUPDQHQWHVDVDo}HVTXHDXPHQWDPQRWHPSRWHQGHQGRD XPYDORUOLPLWHFRQVWDQWH $VDo}HVSHUPDQHQWHVGHYHPVHUFRQVLGHUDGDVFRPVHXVYDORUHVUHSUHVHQWDWLYRVPDLVGHVIDYRUiYHLV para a segurança.
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
11.3.2 $o}HVSHUPDQHQWHVGLUHWDV $V Do}HV SHUPDQHQWHV GLUHWDV VmR FRQVWLWXtGDV SHOR SHVR SUySULR GD HVWUXWXUD SHORV SHVRV GRV HOHPHQWRVFRQVWUXWLYRV¿[RVGDVLQVWDODo}HVSHUPDQHQWHVHGRVHPSX[RVSHUPDQHQWHV 11.3.2.1 Peso próprio 1DVFRQVWUXo}HVFRUUHQWHVDGPLWHVHTXHRSHVRSUySULRGDHVWUXWXUDVHMDDYDOLDGRFRQIRUPH &RQFUHWRVHVSHFLDLVGHYHPWHUVXDPDVVDHVSHFt¿FDGHWHUPLQDGDH[SHULPHQWDOPHQWHHPFDGDFDVR SDUWLFXODUHRDFUpVFLPRGHFRUUHQWHGDPDVVDGDDUPDGXUDDYDOLDGRFRQIRUPH 11.3.2.2 3HVRGRVHOHPHQWRVFRQVWUXWLYRV¿[RVHGHLQVWDODo}HVSHUPDQHQWHV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
$V PDVVDV HVSHFt¿FDV GRV PDWHULDLV GH FRQVWUXomR FRUUHQWHV SRGHP VHU DYDOLDGDV FRP EDVH QRV YDORUHVLQGLFDGRVQD$%171%5 2VSHVRVGDVLQVWDODo}HVSHUPDQHQWHVVmRFRQVLGHUDGRVFRPRVYDORUHVQRPLQDLVLQGLFDGRVSHORV UHVSHFWLYRVIRUQHFHGRUHV 11.3.2.3 Empuxos permanentes &RQVLGHUDPVH SHUPDQHQWHV RV HPSX[RV GH WHUUD H RXWURV PDWHULDLV JUDQXORVRV TXDQGR IRUHP DGPLWLGRVFRPRQmRUHPRYtYHLV &RQVLGHUDPVHUHSUHVHQWDWLYRVRVYDORUHVFDUDFWHUtVWLFRV)NVXS ou )NLQIFRQIRUPHD$%171%5 2HPSX[RGHYHVHUFRQVLGHUDGRFRQIRUPHDV$%171%5$%171%5H$%171%5 11.3.3 $o}HVSHUPDQHQWHVLQGLUHWDV $VDo}HVSHUPDQHQWHVLQGLUHWDVVmRFRQVWLWXtGDVSHODVGHIRUPDo}HVLPSRVWDVSRUUHWUDomRHÀXrQFLD GRFRQFUHWRGHVORFDPHQWRVGHDSRLRLPSHUIHLo}HVJHRPpWULFDVHSURWHQVmR 11.3.3.1 Retração do concreto $GHIRUPDomRHVSHFt¿FDGHUHWUDomRGRFRQFUHWRSRGHVHUFDOFXODGDFRQIRUPHLQGLFDGRQR$QH[R$ 1DJUDQGHPDLRULDGRVFDVRVSHUPLWHVHTXHDUHWUDomRVHMDFDOFXODGDVLPSOL¿FDGDPHQWHDWUDYpV GD7DEHODSRULQWHUSRODomR(VVD7DEHODIRUQHFHRYDORUFDUDFWHUtVWLFRVXSHULRUGDGHIRUPDomR HVSHFt¿FD GH UHWUDomR HQWUH RV LQVWDQWHV t0 e t Hcs (tt0 HP DOJXPDV VLWXDo}HV XVXDLV YHU6HomR 1RVFDVRVFRUUHQWHVGDVREUDVGHFRQFUHWRDUPDGRHPIXQomRGDUHVWULomRjUHWUDomRGRFRQFUHWR LPSRVWDSHODDUPDGXUDVDWLVID]HQGRRPtQLPRHVSHFL¿FDGRQHVWD1RUPDRYDORUGHHcs (tt0 SRGH VHUDGRWDGRLJXDODî(VVHYDORUpYiOLGRSDUDHOHPHQWRVHVWUXWXUDLVGHGLPHQV}HVXVXDLV HQWUHFPHFPVXMHLWRVDXPLGDGHDPELHQWHQmRLQIHULRUD 2YDORUFDUDFWHUtVWLFRLQIHULRUGDUHWUDomRGRFRQFUHWRpFRQVLGHUDGRQXOR 1RVHOHPHQWRVHVWUXWXUDLVSHUPDQHQWHPHQWHVXEPHWLGRVDGLIHUHQWHVFRQGLo}HVGHXPLGDGHHPIDFHV RSRVWDVDGPLWHVHYDULDomROLQHDUGDUHWUDomRDRORQJRGDHVSHVVXUDGRHOHPHQWRHVWUXWXUDOHQWUHRV GRLVYDORUHVFRUUHVSRQGHQWHVDFDGDXPDGDVIDFHV © ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
$VGHIRUPDo}HVLPSRVWDVXQLIRUPHVQDVSHoDVFRPRDTXHODVGHFRUUHQWHVGHUHWUDomREHPFRPR WHPSHUDWXUDHÀXrQFLDGRFRQFUHWRGHYHPVHUYHUL¿FDGDV2VHIHLWRVGHYLGRVDHVVDVGHIRUPDo}HV SRGHP VHU PLQLPL]DGDV SHOD FULDomR GH MXQWDV GH FRQFUHWDJHP RX GH GLODWDomR $ FRQVLGHUDomR GHGHIRUPDo}HVLPSRVWDVGLIHUHQFLDLVGHQWURGDPHVPDSHoDGHFRUUHQWHVSRUH[HPSORGHSDUWHV FRPHVSHVVXUDVPXLWRGLIHUHQWHVGHYHPVHUVHPSUHFRQVLGHUDGDV 11.3.3.2 )OXrQFLDGRFRQFUHWR $V GHIRUPDo}HV GHFRUUHQWHV GD ÀXrQFLD GR FRQFUHWR SRGHP VHU FDOFXODGDV FRQIRUPH LQGLFDGR no Anexo A.
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Nos casos em que a tensãoVc(t0 QmRYDULDVLJQL¿FDWLYDPHQWHSHUPLWHVHTXHHVVDVGHIRUPDo}HV VHMDPFDOFXODGDVVLPSOL¿FDGDPHQWHSHODH[SUHVVmR ϕ (t∞ ,t0 )⎥ ⎢ 1 εc (t∞ ,t0 ) = σc (t0 ) ⎢ + ⎥ ⎣Ec (t0 ) Ec (28) ⎦ onde Hc (tt0
pDGHIRUPDomRHVSHFt¿FDWRWDOGRFRQFUHWRHQWUHRVLQVWDQWHVt0 e t
Vc (t0
pDWHQVmRQRFRQFUHWRGHYLGDDRFDUUHJDPHQWRDSOLFDGRHPt0
M(tt0
p R OLPLWH SDUD R TXDO WHQGH R FRH¿FLHQWH GH ÀXrQFLD SURYRFDGR SRU FDUUHJDPHQWR DSOLFDGRHPt0.
2YDORUGHM(tt0 SRGHVHUFDOFXODGRSRULQWHUSRODomRGRVYDORUHVGD7DEHOD(VVD7DEHODIRUQHFH RYDORUFDUDFWHUtVWLFRVXSHULRUGHM(tt0 HPDOJXPDVVLWXDo}HVXVXDLV YHU6HomR 2YDORUFDUDFWHUtVWLFRLQIHULRUGHM(tt0 pFRQVLGHUDGRQXOR 11.3.3.3 'HVORFDPHQWRVGHDSRLR 2VGHVORFDPHQWRVGHDSRLRVyGHYHPVHUFRQVLGHUDGRVTXDQGRJHUDUHPHVIRUoRVVROLFLWDQWHVVLJQL¿FDWLYRV HPUHODomRDRFRQMXQWRGDVRXWUDVDo}HVLVWRpTXDQGRDHVWUXWXUDIRUKLSHUHVWiWLFDHPXLWRUtJLGD 2GHVORFDPHQWRGHFDGDDSRLRGHYHVHUDYDOLDGRHPIXQomRGDVFDUDFWHUtVWLFDVItVLFDVGRPDWHULDO GHIXQGDomRFRUUHVSRQGHQWH&RPRUHSUHVHQWDWLYRVGHVVHVGHVORFDPHQWRVGHYHPVHUFRQVLGHUDGRV RVYDORUHVFDUDFWHUtVWLFRVVXSHULRUHVGksupFDOFXODGRVFRPDYDOLDomRSHVVLPLVWDGDULJLGH]GRPDWHULDO GHIXQGDomRFRUUHVSRQGHQWHHPSULQFtSLRDRTXDQWLOGDUHVSHFWLYDGLVWULEXLomRGHSUREDELOLGDGH 2VYDORUHVFDUDFWHUtVWLFRVLQIHULRUHVSRGHPVHUFRQVLGHUDGRVQXORV 2FRQMXQWRGHVVHVGHVORFDPHQWRVFRQVWLWXLVHHPXPD~QLFDDomRDGPLWLQGRVHTXHWRGRVHOHVVHMDP PDMRUDGRVSHORPHVPRFRH¿FLHQWHGHSRQGHUDomR 11.3.3.4 ,PSHUIHLo}HVJHRPpWULFDV 1D YHUL¿FDomR GR HVWDGROLPLWH ~OWLPR GDV HVWUXWXUDV UHWLFXODGDV GHYHP VHU FRQVLGHUDGDV DV LPSHUIHLo}HV JHRPpWULFDV GR HL[R GRV HOHPHQWRV HVWUXWXUDLV GD HVWUXWXUD GHVFDUUHJDGD (VVDV LPSHUIHLo}HVSRGHPVHUGLYLGLGDVHPGRLVJUXSRV LPSHUIHLo}HVJOREDLVHLPSHUIHLo}HVORFDLV
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
(PERUD DV LPSHUIHLo}HV JHRPpWULFDV VHMDP SHUPDQHQWHV DV VROLFLWDo}HV SRU HODV SURGX]LGDV WrP a mesma natureza da ação que as provocam. 11.3.3.4.1 ,PSHUIHLo}HVJOREDLV 1D DQiOLVH JOREDO GHVVDV HVWUXWXUDV VHMDP HODV FRQWUDYHQWDGDV RX QmR GHYH VHU FRQVLGHUDGR XP GHVDSUXPRGRVHOHPHQWRVYHUWLFDLVFRQIRUPHPRVWUDD)LJXUD
1
θ1 =
H
100
θa
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
θa = θ1
H 1 + 1/n 2
n prumadas de pilares
onde T1min SDUDHVWUXWXUDVUHWLFXODGDVHLPSHUIHLo}HVORFDLV T1máx H
pDDOWXUDWRWDOGDHGL¿FDomRH[SUHVVDHPPHWURV P
n
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3DUDHGLItFLRVFRPSUHGRPLQkQFLDGHODMHVOLVDVRXFRJXPHORFRQVLGHUDUTa = T1. 3DUDSLODUHVLVRODGRVHPEDODQoRGHYHVHDGRWDUT1 $ FRQVLGHUDomR GDV Do}HV GH YHQWR H GHVDSUXPR GHYH VHU UHDOL]DGD GH DFRUGR FRP DV VHJXLQWHV SRVVLELOLGDGHV D 4XDQGR GD DomR GR YHQWR IRU PDLRU TXH D DomR GR GHVDSUXPR FRQVLGHUDVH VRPHQWH a ação do vento. E 4XDQGR D DomR GR YHQWR IRU LQIHULRU D GD DomR GR GHVDSUXPR FRQVLGHUDVH VRPHQWH o desaprumo respeitando a consideração de TPtQFRQIRUPHGH¿QLGRDFLPD F 1RVGHPDLVFDVRVFRPELQDVHDDomRGRYHQWRHGHVDSUXPRVHPQHFHVVLGDGHGDFRQVLGHUDomR do TPtQ1HVVDFRPELQDomRDGPLWHVHFRQVLGHUDUDPEDVDVDo}HVDWXDQGRQDPHVPDGLUHomR HVHQWLGRFRPRHTXLYDOHQWHVDXPDDomRGRYHQWRSRUWDQWRFRPRFDUJDYDULiYHODUWL¿FLDOPHQWH DPSOL¿FDGDSDUDFREULUDVXSHUSRVLomR $FRPSDUDomRSRGHVHUIHLWDFRPRVPRPHQWRVWRWDLVQDEDVHGDFRQVWUXomRHHPFDGDGLUHomRH VHQWLGRGDDSOLFDomRGDDomRGRYHQWRFRPGHVDSUXPRFDOFXODGRFRPTaVHPDFRQVLGHUDomRGRTPtQ. 127$
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
11.3.3.4.2 ,PSHUIHLo}HVORFDLV 1RFDVRGHHOHPHQWRVTXHOLJDPSLODUHVFRQWUDYHQWDGRVDSLODUHVGHFRQWUDYHQWDPHQWRXVXDOPHQWH YLJDV H ODMHV GHYH VHU FRQVLGHUDGD D WUDomR GHFRUUHQWH GR GHVDSUXPR GR SLODU FRQWUDYHQWDGR >YHU)LJXUDD @ 1RFDVRGRGLPHQVLRQDPHQWRRXYHUL¿FDomRGHXPODQFHGHSLODUGHYHVHUFRQVLGHUDGRRHIHLWRGR GHVDSUXPRRXGDIDOWDGHUHWLOLQHLGDGHGRHL[RGRSLODU>YHU)LJXUDVE HF UHVSHFWLYDPHQWH@ Pilar de contraventamento
Pilar contraventado
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Elemento de travamento
θ1
θ1
a) Elementos de travamento (tracionado ou comprimido)
ea
Hi
θ1
ea
θ1
H i/2
b) Falta de retilineidade c) Desaprumo do pilar no pilar
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60
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
My
M1d,mín,yy = Nd (0,015 + 0,03b)
M1d,mín,yy (M1d,mín,x,M 1d,mín,y)
M1d,mín,xx = Nd (0,015 + 0,03h)
h
M1d,mín,xx
- M1d,mín,xx b
Mx
(Seção transversal) M1d,mín,x M1d,mín,xx
2
+
M1d,mín,y M1d,mín,yy
2
=1
- M1d,mín,yy
(Envoltória mínima de 1ª ordem)
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Sendo: M1d,mín,xxe M1d,mín,yy as componentes em flexão composta normal e M1d,mín,x e M1d,mín,y as componentes em flexão composta oblíqua
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61
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ABNT NBR 6118:2023
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
F SDUDHOHPHQWRVHVWUXWXUDLVFXMDPHQRUGLPHQVmRHVWHMDHQWUHFPHFPDGPLWHVHTXHVHMD IHLWDXPDLQWHUSRODomROLQHDUHQWUHRVYDORUHVDFLPDLQGLFDGRV $HVFROKDGHXPYDORUHQWUHHVVHVGRLVOLPLWHVSRGHVHUIHLWDFRQVLGHUDQGRVHGDGLIHUHQoDHQWUH DVWHPSHUDWXUDVPpGLDVGHYHUmRHLQYHUQRQRORFDOGDREUD (PHGLItFLRVGHYiULRVDQGDUHVGHYHPVHUUHVSHLWDGDVDVH[LJrQFLDVFRQVWUXWLYDVSUHVFULWDVSRUHVWD 1RUPD SDUD TXH VHMDP PLQLPL]DGRV RV HIHLWRV GDV YDULDo}HV GH WHPSHUDWXUD VREUH D HVWUXWXUD GD construção. 11.4.2.2 9DULDo}HVQmRXQLIRUPHVGHWHPSHUDWXUD
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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63
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
11.6.2 9DORUHVUHSUHVHQWDWLYRV $VDo}HVVmRTXDQWL¿FDGDVSRUVHXVYDORUHVUHSUHVHQWDWLYRVTXHSRGHPVHU D RVYDORUHVFDUDFWHUtVWLFRVFRQIRUPHGH¿QLGRHP E YDORUHVFRQYHQFLRQDLVH[FHSFLRQDLVTXHVmRRVYDORUHVDUELWUDGRVSDUDDVDo}HVH[FHSFLRQDLV F YDORUHVUHGX]LGRVHPIXQomRGDFRPELQDomRGHDo}HVFRPR
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
— YHUL¿FDo}HV GH HVWDGRVOLPLWHV ~OWLPRV TXDQGR D DomR FRQVLGHUDGD FRPELQD FRP D DomR SULQFLSDO 2V YDORUHV UHGX]LGRV VmR GHWHUPLQDGRV D SDUWLU GRV YDORUHV FDUDFWHUtVWLFRV SHOD expressão\0Fk TXH FRQVLGHUD PXLWR EDL[D D SUREDELOLGDGH GH RFRUUrQFLD VLPXOWkQHD GRV YDORUHVFDUDFWHUtVWLFRVGHGXDVRXPDLVDo}HVYDULiYHLVGHQDWXUH]DVGLIHUHQWHV YHU — YHUL¿FDo}HVGHHVWDGRVOLPLWHVGHVHUYLoR(VWHVYDORUHVUHGX]LGRVVmRGHWHUPLQDGRVDSDUWLU GRVYDORUHVFDUDFWHUtVWLFRVSHODVH[SUHVV}HV\1Fk e \2FkTXHHVWLPDPYDORUHVIUHTXHQWHV HTXDVHSHUPDQHQWHVUHVSHFWLYDPHQWHGHXPDDomRTXHDFRPSDQKDDDomRSULQFLSDO 11.6.3 9DORUHVGHFiOFXOR 2VYDORUHVGHFiOFXOR)dGDVDo}HVVmRREWLGRVDSDUWLUGRVYDORUHVUHSUHVHQWDWLYRVPXOWLSOLFDQGRRV SHORVUHVSHFWLYRVFRH¿FLHQWHVGHSRQGHUDomRJIGH¿QLGRVHP
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64
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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0
0
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\2
/RFDLVHPTXHQmRKi SUHGRPLQkQFLDGHSHVRVGH equipamentos que permanecem ¿[RVSRUORQJRVSHUtRGRVGHWHPSR QHPGHHOHYDGDVFRQFHQWUDo}HV de pessoas E
/RFDLVHPTXHKiSUHGRPLQkQFLD de pesos de equipamentos que SHUPDQHFHP¿[RVSRUORQJRV SHUtRGRVGHWHPSRRXGHHOHYDGD concentração de pessoas c
%LEOLRWHFDDUTXLYRVR¿FLQDV e garagens
Vento
3UHVVmRGLQkPLFDGRYHQWRQDV HVWUXWXUDVHPJHUDO
0
Temperatura
9DULDo}HVXQLIRUPHVGHWHPSHUDWXUD HPUHODomRjPpGLDDQXDOORFDO
&DUJDVGH XWLOL]DomRGH HGL¿FDo}HV
a E c
JI
3DUDRVYDORUHVGH\1UHODWLYRVjVSRQWHVHSULQFLSDOPHQWHSDUDRVSUREOHPDVGHIDGLJDYHU6HomR ÈUHDVFRPRFXSDomRUHVLGHQFLDORXKRVSHGDJHPHiUHDVGHDFHVVRUHVWULWR ÈUHDVFRPRFXSDomRFRPHUFLDOGHHVFULWyULRVORMDVHVWDo}HVGHSDVVDJHLURVHGLItFLRVS~EOLFRVHiUHDV GHDFHVVRS~EOLFR
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
2VYDORUHVGDV7DEHODVHSRGHPVHUPRGL¿FDGRVHPFDVRVHVSHFLDLVDTXLQmRFRQWHPSODGRV de acordo com a ABNT NBR 8681. 2 YDORU GR FRH¿FLHQWH GH SRQGHUDomR GH FDUJDV SHUPDQHQWHV GH PHVPD RULJHP HP XP GDGR FDUUHJDPHQWRGHYHVHURPHVPRDRORQJRGHWRGDDHVWUXWXUD$~QLFDH[FHomRpRFDVRGDYHUL¿FDomR GDHVWDELOLGDGHFRPRFRUSRUtJLGR 11.7.2 &RH¿FLHQWHVGHSRQGHUDomRGDVDo}HVQRHVWDGROLPLWHGHVHUYLoR (/6 (P JHUDO R FRH¿FLHQWH GH SRQGHUDomR GDV Do}HV SDUD HVWDGRVOLPLWHV GH VHUYLoR p GDGR SHOD expressão: JI = JI onde
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
JI WHPYDORUYDULiYHOFRQIRUPHDYHUL¿FDomRTXHVHGHVHMDID]HU YHU7DEHOD JI SDUDFRPELQDo}HVUDUDV JI = \1SDUDFRPELQDo}HVIUHTXHQWHV JI = \2SDUDFRPELQDo}HVTXDVHSHUPDQHQWHV
11.8 &RPELQDo}HVGHDo}HV 11.8.1 *HQHUDOLGDGHV 8PFDUUHJDPHQWRpGH¿QLGRSHODFRPELQDomRGDVDo}HVTXHWrPSUREDELOLGDGHVQmRGHVSUH]tYHLV GHDWXDUHPVLPXOWDQHDPHQWHVREUHDHVWUXWXUDGXUDQWHXPSHUtRGRSUHHVWDEHOHFLGR $ FRPELQDomR GDV Do}HV GHYH VHU IHLWD GH IRUPD TXH SRVVDP VHU GHWHUPLQDGRV RV HIHLWRV PDLV GHVIDYRUiYHLVSDUDDHVWUXWXUD DYHUL¿FDomRGDVHJXUDQoDHPUHODomRDRVHVWDGRVOLPLWHV~OWLPRVH DRVHVWDGRVOLPLWHVGHVHUYLoRGHYHVHUUHDOL]DGDHPIXQomRGHFRPELQDo}HV~OWLPDVHGHFRPELQDo}HV GHVHUYLoRUHVSHFWLYDPHQWH 11.8.2 &RPELQDo}HV~OWLPDV 8PDFRPELQDomR~OWLPDSRGHVHUFODVVL¿FDGDFRPRQRUPDOHVSHFLDORXGHFRQVWUXomRHH[FHSFLRQDO 11.8.2.1 &RPELQDo}HV~OWLPDVQRUPDLV (PFDGDFRPELQDomRGHYHPHVWDULQFOXtGDVDVDo}HVSHUPDQHQWHVHDDomRYDULiYHOSULQFLSDOFRP VHXVYDORUHVFDUDFWHUtVWLFRVHDVGHPDLVDo}HVYDULiYHLVFRQVLGHUDGDVVHFXQGiULDVFRPVHXVYDORUHV UHGX]LGRVGHFRPELQDomRFRQIRUPH$%171%5 11.8.2.2 &RPELQDo}HV~OWLPDVHVSHFLDLVRXGHFRQVWUXomR (P FDGD FRPELQDomR GHYHP HVWDU SUHVHQWHV DV Do}HV SHUPDQHQWHV H D DomR YDULiYHO HVSHFLDO TXDQGR H[LVWLU FRP VHXV YDORUHV FDUDFWHUtVWLFRV H DV GHPDLV Do}HV YDULiYHLV FRP SUREDELOLGDGH QmR GHVSUH]tYHO GH RFRUUrQFLD VLPXOWkQHD FRP VHXV YDORUHV UHGX]LGRV GH FRPELQDomR FRQIRUPH ABNT NBR 8681. 11.8.2.3 &RPELQDo}HV~OWLPDVH[FHSFLRQDLV (PFDGDFRPELQDomRGHYHP¿JXUDUDVDo}HVSHUPDQHQWHVHDDomRYDULiYHOH[FHSFLRQDOTXDQGR H[LVWLUFRPVHXVYDORUHVUHSUHVHQWDWLYRVHDVGHPDLVDo}HVYDULiYHLVFRPSUREDELOLGDGHQmRGHVSUH]tYHO 66
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
GHRFRUUrQFLDVLPXOWkQHDFRPVHXVYDORUHVUHGX]LGRVGHFRPELQDomRFRQIRUPH$%171%5 1HVVHFDVRVHHQTXDGUDPHQWUHRXWUDVVLVPRHLQFrQGLR 11.8.2.4 &RPELQDo}HV~OWLPDVXVXDLV 3DUDIDFLOLWDUDYLVXDOL]DomRHVVDVFRPELQDo}HVHVWmRGLVSRVWDVQD7DEHOD 7DEHOD±&RPELQDo}HV~OWLPDV FRQWLQXD
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
&RPELQDo}HV ~OWLPDV (/8
Normais
Descrição
&iOFXORGDVVROLFLWDo}HV
(VJRWDPHQWR da capacidade resistente para HOHPHQWRV estruturais de concreto armado a
Fd = γ gFgk + γ εgFεgk + γ q (Fq1k + Σψ 0jFqjk ) + γ εqψ 0 ε Fεqk
(VJRWDPHQWR da capacidade resistente para HOHPHQWRV estruturais de concreto protendido
'HYHVHUFRQVLGHUDGDTXDQGRQHFHVViULRDIRUoDGHSURWHQVmR FRPRFDUUHJDPHQWRH[WHUQRFRPRVYDORUHV3kmáx e 3NPtQ para a IRUoDGHVIDYRUiYHOHIDYRUiYHOUHVSHFWLYDPHQWHFRQIRUPHGH¿QLGR QD6HomR
Perda do HTXLOtEULR como corpo UtJLGR
S ()sd t S ()nd )sd Jgs *skRd )nd Jgn *nkJq Qnk Jqs QVPLQRQGH Qnk Q1k ¦\MQMN
Especiais ou de construção E
Fd = γ gF gk + γ εgFεgk + γ q (Fq1k + Σψ 0jFqjk ) + γ εqψ 0ε Fεqk
Excepcionais E
Fd = γ gFgk + γ εgFεgk + Fq1exc + γ qΣψ 0jFqjk + γ εq ψ 0ε Fεqk
onde )d
pRYDORUGHFiOFXORGDVDo}HVSDUDFRPELQDomR~OWLPD
)gk
UHSUHVHQWDDVDo}HVSHUPDQHQWHVGLUHWDV
)Hk
UHSUHVHQWD DV Do}HV LQGLUHWDV SHUPDQHQWHV FRPR D UHWUDomR )Hgk e variáveis como a temperatura )Hqk
)qk
UHSUHVHQWDDVDo}HVYDULiYHLVGLUHWDVGDVTXDLV)q1kpHVFROKLGDSULQFLSDO
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
7DEHOD FRQFOXVmR JgJHgJqJHq
YHU7DEHOD
\RM\oH
YHU7DEHOD
)sd
UHSUHVHQWDDVDo}HVHVWDELOL]DQWHV
)nd
UHSUHVHQWDDVDo}HVQmRHVWDELOL]DQWHV
*sk
pRYDORUFDUDFWHUtVWLFRGDDomRSHUPDQHQWHHVWDELOL]DQWH
Rd
pRHVIRUoRUHVLVWHQWHFRQVLGHUDGRHVWDELOL]DQWHTXDQGRKRXYHU
*nk
pRYDORUFDUDFWHUtVWLFRGDDomRSHUPDQHQWHLQVWDELOL]DQWH m
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Qnk = Q1k +
∑ ψ ojQjk j= 2
Qnk
pRYDORUFDUDFWHUtVWLFRGDVDo}HVYDULiYHLVLQVWDELOL]DQWHV
Q1k
pRYDORUFDUDFWHUtVWLFRGDDomRYDULiYHOLQVWDELOL]DQWHFRQVLGHUDGDSULQFLSDO
\RM e QMN
VmRDVGHPDLVDo}HVYDULiYHLVLQVWDELOL]DQWHVFRQVLGHUDGDVFRPVHXYDORUUHGX]LGR
QVPtQ
p R YDORU FDUDFWHUtVWLFR PtQLPR GD DomR YDULiYHO HVWDELOL]DQWH TXH DFRPSDQKD REULJDWRULDPHQWHXPDDomRYDULiYHOLQVWDELOL]DQWH
a
1R FDVR JHUDO GHYHP VHU FRQVLGHUDGDV LQFOXVLYH FRPELQDo}HV RQGH R HIHLWR IDYRUiYHO GDV FDUJDV SHUPDQHQWHVVHMDUHGX]LGRSHODFRQVLGHUDomRGHJg 1RFDVRGHHVWUXWXUDVXVXDLVGHHGLItFLRVHVVDV FRPELQDo}HVTXHFRQVLGHUDPJgUHGX]LGR QmRSUHFLVDPVHUFRQVLGHUDGDV E Quando ) q1k ou )q1excDWXDUHPHPWHPSRPXLWRSHTXHQRRXWLYHUHPSUREDELOLGDGHGHRFRUUrQFLDPXLWR EDL[D\MSRGHVHUVXEVWLWXtGRSRU\M(VWHSRGHVHURFDVRSDUDDo}HVVtVPLFDVHVLWXDomRGHLQFrQGLR
11.8.3 &RPELQDo}HVGHVHUYLoR 11.8.3.1 &ODVVL¿FDomR 6mR FODVVL¿FDGDV GH DFRUGR FRP VXD SHUPDQrQFLD QD HVWUXWXUD H GHYHP VHU YHUL¿FDGDV FRPR HVWDEHOHFLGRDVHJXLU D TXDVHSHUPDQHQWHV SRGHPDWXDUGXUDQWHJUDQGHSDUWHGRSHUtRGRGHYLGDGDHVWUXWXUDHVXD FRQVLGHUDomRSRGHVHUQHFHVViULDQDYHUL¿FDomRGRHVWDGROLPLWHGHGHIRUPDo}HVH[FHVVLYDV E IUHTXHQWHV UHSHWHPVHPXLWDVYH]HVGXUDQWHRSHUtRGRGHYLGDGDHVWUXWXUDHVXDFRQVLGHUDomR SRGH VHU QHFHVViULD QD YHUL¿FDomR GRV HVWDGRVOLPLWHV GH IRUPDomR GH ¿VVXUDV GH DEHUWXUD GH¿VVXUDVHGHYLEUDo}HVH[FHVVLYDV3RGHPWDPEpPVHUFRQVLGHUDGDVSDUDYHUL¿FDo}HVGH HVWDGRVOLPLWHV GH GHIRUPDo}HV H[FHVVLYDV GHFRUUHQWHV GH YHQWR RX WHPSHUDWXUD TXH SRGHP FRPSURPHWHUDVYHGDo}HV F UDUDV RFRUUHPDOJXPDVYH]HVGXUDQWHRSHUtRGRGHYLGDGDHVWUXWXUDHVXDFRQVLGHUDomRSRGH VHUQHFHVViULDQDYHUL¿FDomRGRHVWDGROLPLWHGHIRUPDomRGH¿VVXUDV
68
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
11.8.3.2 &RPELQDo}HVGHVHUYLoRXVXDLV 3DUDIDFLOLWDUDYLVXDOL]DomRHVVDVFRPELQDo}HVHVWmRGLVSRVWDVQD7DEHOD
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
7DEHOD±&RPELQDo}HVGHVHUYLoR &RPELQDo}HV de serviço (/6
Descrição
&RPELQDo}HV quase permanentes de serviço &43
1DVFRPELQDo}HVTXDVHSHUPDQHQWHV GHVHUYLoRWRGDVDVDo}HVYDULiYHLVVmR FRQVLGHUDGDVFRPVHXVYDORUHVTXDVH permanentes \2 )qk
&RPELQDo}HV frequentes de VHUYLoR &)
&iOFXORGDVVROLFLWDo}HV
Fd,ser = Σ Fgi,k + Σψ 2 jFqj,k
1DVFRPELQDo}HVIUHTXHQWHVGHVHUYLoR DDomRYDULiYHOSULQFLSDO)q1 pWRPDGDFRPVHXYDORUIUHTXHQWH Fd,ser = Σ Fgik + ψ1 Fq1k + Σψ 2 j Fqjk \1 )q1kHWRGDVDVGHPDLVDo}HVYDULiYHLV VmRWRPDGDVFRPVHXVYDORUHVTXDVH permanentes \2 )qk
1DVFRPELQDo}HVUDUDVGHVHUYLoRDDomR &RPELQDo}HV YDULiYHOSULQFLSDO)q1 raras de pWRPDGDFRPVHXYDORUFDUDFWHUtVWLFR)q1k Fd,ser = Σ Fgik + Fq1k + Σψ1jFqjk HWRGDVDVGHPDLVDo}HVVmRWRPDGDVFRP VHUYLoR &5 VHXVYDORUHVIUHTXHQWHV\1 )qk onde )GVHU pRYDORUGHFiOFXORGDVDo}HVSDUDFRPELQDo}HVGHVHUYLoR )q1k
pRYDORUFDUDFWHUtVWLFRGDVDo}HVYDULiYHLVSULQFLSDLVGLUHWDV
\1
pRIDWRUGHUHGXomRGHFRPELQDomRIUHTXHQWHSDUD(/6
\2
pRIDWRUGHUHGXomRGHFRPELQDomRTXDVHSHUPDQHQWHSDUD(/6
12 Resistências 12.1 6LPERORJLDHVSHFt¿FDGHVWDVHomR 'H IRUPD D VLPSOL¿FDU D FRPSUHHQVmR H SRUWDQWR D DSOLFDomR GRV FRQFHLWRV HVWDEHOHFLGRV QHVWD 6HomRRVVtPERORVPDLVXWLOL]DGRVRXTXHSRGHULDPJHUDUG~YLGDVHQFRQWUDPVHDVHJXLUGH¿QLGRV $VLPERORJLDDSUHVHQWDGDQHVWD6HomRVHJXHDPHVPDRULHQWDomRHVWDEHOHFLGDQD6HomR'HVVD IRUPDRVVtPERORVVXEVFULWRVWrPRPHVPRVLJQL¿FDGRDSUHVHQWDGRHP I±5HVLVWrQFLD YHU6HomR Jm1 ± 3DUWH GR FRH¿FLHQWH GH SRQGHUDomR GDV UHVLVWrQFLDV Jm TXH FRQVLGHUD D YDULDELOLGDGH GD UHVLVWrQFLDGRVPDWHULDLVHQYROYLGRV © ABNT 2023 - Todos os direitos reservados
69
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
Jm2 ± 3DUWH GR FRH¿FLHQWH GH SRQGHUDomR GDV UHVLVWrQFLDV Jm TXH FRQVLGHUD D GLIHUHQoD HQWUH D UHVLVWrQFLDGRPDWHULDOQRFRUSRGHSURYDHQDHVWUXWXUD Jm3 ± 3DUWH GR FRH¿FLHQWH GH SRQGHUDomR GDV UHVLVWrQFLDV Jm TXH FRQVLGHUD RV GHVYLRV JHUDGRV QDFRQVWUXomRHDVDSUR[LPDo}HVIHLWDVHPSURMHWRGRSRQWRGHYLVWDGDVUHVLVWrQFLDV
12.2 9DORUHVFDUDFWHUtVWLFRV 2VYDORUHVFDUDFWHUtVWLFRV fkGDVUHVLVWrQFLDVVmRRVTXHHPXPORWHGHPDWHULDOWrPXPDGHWHUPLQDGD SUREDELOLGDGHGHVHUHPXOWUDSDVVDGRVQRVHQWLGRGHVIDYRUiYHOSDUDDVHJXUDQoD
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
8VXDOPHQWHpGHLQWHUHVVHDUHVLVWrQFLDFDUDFWHUtVWLFDLQIHULRUfNLQIFXMRYDORUpPHQRUTXHDUHVLVWrQFLD PpGLD fm HPERUD SRU YH]HV KDMD LQWHUHVVH QD UHVLVWrQFLD FDUDFWHUtVWLFD VXSHULRU fNVXS FXMR YDORU pPDLRUTXHfm. 3DUDRVHIHLWRVGHVWD1RUPDDUHVLVWrQFLDFDUDFWHUtVWLFDLQIHULRUpDGPLWLGDFRPRVHQGRRYDORUTXH WHPDSHQDVGHSUREDELOLGDGHGHQmRVHUDWLQJLGRSHORVHOHPHQWRVGHXPGDGRORWHGHPDWHULDO
12.3 9DORUHVGHFiOFXOR 12.3.1 5HVLVWrQFLDGHFiOFXOR $UHVLVWrQFLDGHFiOFXORfdpGDGDSHODH[SUHVVmR fd =
fk γm
12.3.2 7HQV}HVUHVLVWHQWHVGHFiOFXOR $VWHQV}HVUHVLVWHQWHVGHFiOFXORVRd ouWRd VmRHVWDEHOHFLGDVSDUDDGHWHUPLQDomRGDVVROLFLWDo}HV UHVLVWHQWHVGHFiOFXORTXHQmRGHSHQGDPGLUHWDPHQWHGDVUHVLVWrQFLDVPHGLGDVFRQYHQFLRQDOPHQWH HPHQVDLRVGHFRUSRVGHSURYDSDGURQL]DGRVGRVPDWHULDLVHPSUHJDGRV2VYDORUHVGHVRd e WRd são HVWDEHOHFLGRVHPFDGDFDVRSDUWLFXODUDSDUWLUGDVWHRULDVGHUHVLVWrQFLDGRVHOHPHQWRVHVWUXWXUDLV considerados. 12.3.3 5HVLVWrQFLDGHFiOFXORGRFRQFUHWR 1R FDVR HVSHFt¿FR GD UHVLVWrQFLD GH FiOFXOR GR FRQFUHWR fcd DOJXQV GHWDOKHV DGLFLRQDLV VmR QHFHVViULRVFRQIRUPHGHVFULWRDVHJXLU D TXDQGRDYHUL¿FDomRVHID]HPGDWD jLJXDORXVXSHULRUDGLDVDGRWDVHDH[SUHVVmR fcd =
f ck γc
1HVVH FDVR R FRQWUROH GD UHVLVWrQFLD j FRPSUHVVmR GR FRQFUHWR GHYH VHU IHLWR DRV GLDV GHIRUPDDFRQ¿UPDURYDORUGHfckDGRWDGRQRSURMHWR E TXDQGRDYHUL¿FDomRVHID]HPGDWDjLQIHULRUDGLDVDGRWDVHDH[SUHVVmR fckj f fcd = ≅ β1 ck γc γc
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
sendo E1DUHODomRfFNMfck dada por: E1 = exp {s>± t @` onde s SDUDFRQFUHWRGHFLPHQWR&3,,,H,9 s SDUDFRQFUHWRGHFLPHQWR&3,H,, s = SDUDFRQFUHWRGHFLPHQWR&39$5, t pDLGDGHHIHWLYDGRFRQFUHWRH[SUHVVDHPGLDV (VVDYHUL¿FDomRGHYHVHUIHLWDDRVtGLDVSDUDDVFDUJDVDSOLFDGDVDWpHVVDGDWD
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
$LQGDGHYHVHUIHLWDDYHUL¿FDomRSDUDDWRWDOLGDGHGDVFDUJDVDSOLFDGDVDRVGLDV 1HVVHFDVRRFRQWUROHGDUHVLVWrQFLDjFRPSUHVVmRGRFRQFUHWRGHYHVHUIHLWRHPGXDVGDWDV DRVt GLDVHDRVGLDVGHIRUPDDFRQ¿UPDURVYDORUHVGHfFNM e fckDGRWDGRVQRSURMHWR
12.4 &RH¿FLHQWHVGHSRQGHUDomRGDVUHVLVWrQFLDV $VUHVLVWrQFLDVGHYHPVHUPLQRUDGDVSHORFRH¿FLHQWH Jm = Jm1 Jm2 Jm3 12.4.1 &RH¿FLHQWHVGHSRQGHUDomRGDVUHVLVWrQFLDVQRHVWDGROLPLWH~OWLPR (/8 2VYDORUHVSDUDYHUL¿FDomRQRHVWDGROLPLWH~OWLPRHVWmRLQGLFDGRVQD7DEHOD 7DEHOD±9DORUHVGRVFRH¿FLHQWHVJc e Js &RPELQDo}HV
Concreto Jc
Aço Js
Normais
(VSHFLDLVRXGHFRQVWUXomR
([FHSFLRQDLV
3DUDDH[HFXomRGHHOHPHQWRVHVWUXWXUDLVQRVTXDLVHVWHMDPSUHYLVWDVFRQGLo}HVGHVIDYRUiYHLV SRU H[HPSOR PiV FRQGLo}HV GH WUDQVSRUWH RX DGHQVDPHQWR PDQXDO RX FRQFUHWDJHP GH¿FLHQWH SRU FRQFHQWUDomRGHDUPDGXUD RFRH¿FLHQWHJcGHYHVHUPXOWLSOLFDGRSRU 3DUDHOHPHQWRVHVWUXWXUDLVSUpPROGDGRVHSUpIDEULFDGRVGHYHVHUFRQVXOWDGDD$%171%5 $GPLWHVHQRFDVRGHWHVWHPXQKRVH[WUDtGRVGDHVWUXWXUDGLYLGLURYDORUGHJcSRU $GPLWHVHQDVREUDVGHSHTXHQDLPSRUWkQFLDRHPSUHJRGHDoR&$VHPDUHDOL]DomRGRFRQWUROH GHTXDOLGDGHHVWDEHOHFLGRQD$%171%5GHVGHTXHRFRH¿FLHQWHGHSRQGHUDomRSDUDRDoR VHMDPXOWLSOLFDGRSRU © ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
12.4.2 &RH¿FLHQWHVGHSRQGHUDomRGDVUHVLVWrQFLDVQRHVWDGROLPLWHGHVHUYLoR (/6 2VOLPLWHVHVWDEHOHFLGRVSDUDRVHVWDGRVOLPLWHVGHVHUYLoR YHU6Ho}HV H QmRQHFHVVLWDP GHPLQRUDomRSRUWDQWRJm
12.5 9HUL¿FDomRGDVHJXUDQoD 1DYHUL¿FDomRGDVHJXUDQoDGDVHVWUXWXUDVGHFRQFUHWRGHYHPVHUDWHQGLGDVDVFRQGLo}HVFRQVWUXWLYDV HDVFRQGLo}HVDQDOtWLFDVGHVHJXUDQoD 12.5.1 &RQGLo}HVFRQVWUXWLYDVGHVHJXUDQoD 'HYHPVHUDWHQGLGDVDVH[LJrQFLDVHVWDEHOHFLGDV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
— QRVFULWpULRVGHGHWDOKDPHQWRFRQVWDQWHVQDV6Ho}HVH — QDVQRUPDVGHFRQWUROHGRVPDWHULDLVHVSHFLDOPHQWHD$%171%5 — QRFRQWUROHGHH[HFXomRGDREUDFRQIRUPH$%171%5 H1RUPDV%UDVLOHLUDVHVSHFt¿FDV 12.5.2 &RQGLo}HVDQDOtWLFDVGHVHJXUDQoD $VFRQGLo}HVDQDOtWLFDVGHVHJXUDQoDHVWDEHOHFHPTXHDVUHVLVWrQFLDVQmRSRGHPVHUPHQRUHVTXHDV VROLFLWDo}HVHGHYHPVHUYHUL¿FDGDVHPUHODomRDWRGRVRVHVWDGRVOLPLWHVHWRGRVRVFDUUHJDPHQWRV HVSHFL¿FDGRVSDUDRWLSRGHFRQVWUXomRFRQVLGHUDGRRXVHMDHPTXDOTXHUFDVRGHYHVHUUHVSHLWDGD a condição: Rd t Sd 3DUDDYHUL¿FDomRGRHVWDGROLPLWH~OWLPRGHSHUGDGHHTXLOtEULRFRPRFRUSRUtJLGRRd e Sd devem DVVXPLURVYDORUHVGHFiOFXORGDVDo}HVHVWDELOL]DQWHVHGHVHVWDELOL]DQWHVUHVSHFWLYDPHQWH 12.5.3 (VIRUoRVUHVLVWHQWHVGHFiOFXOR 2VYDORUHVGHFiOFXORGRVHVIRUoRVUHVLVWHQWHVVmRGHWHUPLQDGRVDSDUWLUGRVYDORUHVGHFiOFXORGDV UHVLVWrQFLDVGRVPDWHULDLVDGRWDGRVQRSURMHWRRXGDVWHQV}HVUHVLVWHQWHVGHFiOFXORFRPRGH¿QLGR em 12.3.1. 3DUDDSOLFDo}HVHVSHFt¿FDVYHU6Ho}HV H 12.5.4 (VIRUoRVVROLFLWDQWHVGHFiOFXOR $VVROLFLWDo}HVGHFiOFXORVmRFDOFXODGDVSDUDDFRPELQDomRGHDo}HVFRQVLGHUDGDGHDFRUGRFRP DDQiOLVHHVWUXWXUDO YHU6HomR
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© ABNT 2023 - Todos os direitos reservados
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ABNT NBR 6118:2023
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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© ABNT 2023 - Todos os direitos reservados
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ABNT NBR 6118:2023
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
14 $QiOLVHHVWUXWXUDO 14.1 6LPERORJLDHVSHFt¿FDGHVWDVHomR 'H IRUPD D VLPSOL¿FDU D FRPSUHHQVmR H SRUWDQWR D DSOLFDomR GRV FRQFHLWRV HVWDEHOHFLGRV QHVWD 6HomRRVVtPERORVPDLVXWLOL]DGRVRXTXHSRGHULDPJHUDUG~YLGDVHQFRQWUDPVHDVHJXLUGH¿QLGRV $VLPERORJLDDSUHVHQWDGDQHVWDVHomRVHJXHDPHVPDRULHQWDomRHVWDEHOHFLGDQD6HomR'HVVD IRUPDRVVtPERORVVXEVFULWRVWrPRPHVPRVLJQL¿FDGRTXHRVDSUHVHQWDGRVHP a ±GLVWkQFLDHQWUHVHo}HVGHPRPHQWRÀHWRUQXOR bHI±ODUJXUDHIHWLYD
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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© ABNT 2023 - Todos os direitos reservados
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ABNT NBR 6118:2023
14.2.2 3UHPLVVDVQHFHVViULDVjDQiOLVHHVWUXWXUDO $DQiOLVHHVWUXWXUDOGHYHVHUIHLWDDSDUWLUGHXPPRGHORHVWUXWXUDODGHTXDGRDRREMHWLYRGDDQiOLVH (PXPSURMHWRSRGHVHUQHFHVViULRPDLVGHXPPRGHORSDUDUHDOL]DUDVYHUL¿FDo}HVSUHYLVWDVQHVWD Norma. 2 PRGHOR HVWUXWXUDO SRGH VHU LGHDOL]DGR FRPR D FRPSRVLomR GH HOHPHQWRV HVWUXWXUDLV EiVLFRV FRQIRUPH GH¿QLGR HP IRUPDQGR VLVWHPDV HVWUXWXUDLV UHVLVWHQWHV TXH SHUPLWDP UHSUHVHQWDU GHPDQHLUDFODUDWRGRVRVFDPLQKRVSHUFRUULGRVSHODVDo}HVDWpRVDSRLRVGDHVWUXWXUD
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
14.2.4 $SOLFDomRGRVUHVXOWDGRVREWLGRVFRPRVPRGHORVGHDQiOLVHVHPUHJLPHQmROLQHDU 2V UHVXOWDGRV REWLGRV QD DQiOLVH HVWUXWXUDO FRQVLGHUDQGR PHLRV FRQWtQXRV TXH UHSUHVHQWHP DGHTXDGDPHQWHDUHRORJLDGRFRQFUHWRHVXDLQWHUDomRFRPDDUPDGXUDVLPXODQGRDVQmROLQHDULGDGHV GRFRQFUHWR GLDJUDPDWHQVmRGHIRUPDomRH¿VVXUDomR HGDDUPDGXUD GLDJUDPDWHQVmRGHIRUPDomR SRGHPVHUXVDGRVSDUDDYDOLDURGHVHPSHQKRGDHVWUXWXUDHPVHUYLoRRXPHVPRQDUXSWXUD 2 GLPHQVLRQDPHQWR GDV DUPDGXUDV QmR SRGH VHU UHDOL]DGR DSHQDV D SDUWLU GRV HVIRUoRV RX GDV WHQV}HVUHVXOWDQWHVGHVWDDQiOLVHSRUH[HPSORGHWUDomRQXPDFHUWDUHJLmRGRPRGHOR$VDUPDGXUDV GHYHPVHPSUHUHVSHLWDUDVTXDQWLGDGHVQHFHVViULDVPtQLPDVHPi[LPDVH[LJLGDVSRUHVWD1RUPD VHJXQGRDWHRULDGHFRQFUHWRHVWUXWXUDOEHPFRPRRVFULWpULRVGHGHWDOKDPHQWRSUHVFULWRVSRUHOD
14.3 Hipóteses básicas
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
14.3.1 &RQGLo}HVGHHTXLOtEULR $VFRQGLo}HVGHHTXLOtEULRGHYHPVHUQHFHVVDULDPHQWHUHVSHLWDGDV $VHTXDo}HVGHHTXLOtEULRSRGHPVHUHVWDEHOHFLGDVFRPEDVHQDJHRPHWULDLQGHIRUPDGDGDHVWUXWXUD WHRULDGHRUGHP H[FHWRQRVFDVRVHPTXHRVGHVORFDPHQWRV DOWHUHPGHPDQHLUD VLJQL¿FDWLYD RVHVIRUoRVLQWHUQRV WHRULDGHRUGHPYHU6HomR 14.3.2 &RQGLo}HVGHFRPSDWLELOLGDGH 4XDQGRDVFRQGLo}HVGHFRPSDWLELOLGDGHQmRIRUHPYHUL¿FDGDVQRHVWDGROLPLWHFRQVLGHUDGRGHYHP VHU DGRWDGDV PHGLGDV TXH JDUDQWDP GXWLOLGDGH DGHTXDGD GD HVWUXWXUD QR HVWDGROLPLWH ~OWLPR UHVJXDUGDGRXPGHVHPSHQKRDGHTXDGRQRVHVWDGRVOLPLWHVGHVHUYLoR 14.3.3 &DUUHJDPHQWRPRQRW{QLFR $GPLWHVHFDUUHJDPHQWRPRQRW{QLFRDWpRHVWDGROLPLWHFRQVLGHUDGRQDVHVWUXWXUDVXVXDLVGHVGHTXH DUHVSRVWDDFLFORVGHFDUJDHGHVFDUJDHPVHUYLoRQmRVROLFLWHRFRQFUHWRDWHQV}HVGHFRPSUHVVmR DFLPDGHfck.
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83
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
14.4.1.2 3LODUHV (OHPHQWRV OLQHDUHV GH HL[R UHWR XVXDOPHQWH GLVSRVWRV QD YHUWLFDO HP TXH DV IRUoDV QRUPDLV GH compressão são preponderantes. 14.4.1.3 Tirantes (OHPHQWRVOLQHDUHVGHHL[RUHWRHPTXHDVIRUoDVQRUPDLVGHWUDomRVmRSUHSRQGHUDQWHV 14.4.1.4 Arcos (OHPHQWRV OLQHDUHV FXUYRV HP TXH DV IRUoDV QRUPDLV GH FRPSUHVVmR VmR SUHSRQGHUDQWHV DJLQGR RX QmR VLPXOWDQHDPHQWH FRP HVIRUoRV VROLFLWDQWHV GH ÀH[mR FXMDV Do}HV HVWmR FRQWLGDV HP VHX SODQR
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
14.4.2 (OHPHQWRVGHVXSHUItFLH (OHPHQWRV HP TXH XPD GLPHQVmR XVXDOPHQWH FKDPDGD GH HVSHVVXUD p UHODWLYDPHQWH SHTXHQD HPIDFHGDVGHPDLVSRGHQGRUHFHEHUDVGHVLJQDo}HVDSUHVHQWDGDVHPD 14.4.2.1 3ODFDV (OHPHQWRV GH VXSHUItFLH SODQD VXMHLWRV SULQFLSDOPHQWH D Do}HV QRUPDLV D VHX SODQR $V SODFDV GHFRQFUHWRVmRXVXDOPHQWHGHQRPLQDGDVODMHV3ODFDVFRPHVSHVVXUDPDLRUTXHGRYmRGHYHP VHUHVWXGDGDVFRPRSODFDVHVSHVVDV 14.4.2.2 &KDSDV (OHPHQWRV GH VXSHUItFLH SODQD VXMHLWRV SULQFLSDOPHQWH D Do}HV FRQWLGDV HP VHX SODQR$V FKDSDV GH FRQFUHWR HP TXH R YmR IRU PHQRU TXH WUrV YH]HV D PDLRU GLPHQVmR GD VHomR WUDQVYHUVDO VmR XVXDOPHQWHGHQRPLQDGDVYLJDVSDUHGH 14.4.2.3 Cascas (OHPHQWRVGHVXSHUItFLHQmRSODQD 14.4.2.4 3LODUHVSDUHGH (OHPHQWRV GH VXSHUItFLH SODQD RX FDVFD FLOtQGULFD XVXDOPHQWH GLVSRVWRV QD YHUWLFDO H VXEPHWLGRV SUHSRQGHUDQWHPHQWHjFRPSUHVVmR3RGHPVHUFRPSRVWRVSRUXPDRXPDLVVXSHUItFLHVDVVRFLDGDV 3DUDTXHVHWHQKDXPSLODUSDUHGHHPDOJXPDGHVVDVVXSHUItFLHVDPHQRUGLPHQVmRGHYHVHUPHQRU TXHGDPDLRUDPEDVFRQVLGHUDGDVQDVHomRWUDQVYHUVDOGRHOHPHQWRHVWUXWXUDO
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84
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
3DUDVLWXDo}HVGHYHUL¿FDo}HVGHSURMHWRVRXREUDVMiH[HFXWDGDVQmRFRQIRUPLGDGHVLGHQWL¿FDGDV DWUDYpV GH XP GHVVHV PpWRGRV GH DQiOLVH HVWUXWXUDO QmR VHUmR DFHLWDV FRPR LPSXJQDo}HV 3DUD DFHLWDomRGHVVHSURMHWRRXREUDpVX¿FLHQWHPRVWUDUDFRQIRUPLGDGHFRPDQRUPDSRUXPGRVRXWURV PpWRGRVGHDQiOLVHHVWUXWXUDO 2VPpWRGRVGHDQiOLVHGHDDGPLWHPTXHRVGHVORFDPHQWRVGDHVWUXWXUDVmRSHTXHQRV 14.5.2 $QiOLVHOLQHDU $GPLWHVHFRPSRUWDPHQWRHOiVWLFROLQHDUSDUDRVPDWHULDLV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
1DDQiOLVHJOREDODVFDUDFWHUtVWLFDVJHRPpWULFDVSRGHPVHUGHWHUPLQDGDVSHODVHomREUXWDGHFRQFUHWR GRV HOHPHQWRV HVWUXWXUDLV (P DQiOLVHV ORFDLV SDUD FiOFXOR GRV GHVORFDPHQWRV QD HYHQWXDOLGDGH GD¿VVXUDomRHVWDGHYHVHUFRQVLGHUDGD 2VYDORUHVSDUDRPyGXORGHHODVWLFLGDGHHRFRH¿FLHQWHGH3RLVVRQGHYHPVHUDGRWDGRVGHDFRUGR FRPRDSUHVHQWDGRHPH GHYHQGRHPSULQFtSLRVHUFRQVLGHUDGRRPyGXORGHHODVWLFLGDGH secante(cs. 2V UHVXOWDGRV GH XPD DQiOLVH OLQHDU VmR XVXDOPHQWH HPSUHJDGRV SDUD D YHUL¿FDomR GH HVWDGRV OLPLWHVGHVHUYLoR 2VHVIRUoRVVROLFLWDQWHVGHFRUUHQWHVGHXPDDQiOLVHOLQHDUSRGHPVHUYLUGHEDVHSDUDRGLPHQVLRQDPHQWRGRVHOHPHQWRVHVWUXWXUDLVQRHVWDGROLPLWH~OWLPRPHVPRTXHHVVHGLPHQVLRQDPHQWRDGPLWD DSODVWL¿FDomRGRVPDWHULDLVGHVGHTXHVHJDUDQWDXPDGXWLOLGDGHPtQLPDjVSHoDV 14.5.3 $QiOLVHOLQHDUFRPUHGLVWULEXLomR 1DDQiOLVHOLQHDUFRPUHGLVWULEXLomRRVHIHLWRVGDVDo}HVGHWHUPLQDGRVHPXPDDQiOLVHOLQHDUVmR UHGLVWULEXtGRVQDHVWUXWXUDSDUDDVFRPELQDo}HVGHFDUUHJDPHQWRGR(/8 1HVVHFDVRDVFRQGLo}HVGHHTXLOtEULRHGHGXWLOLGDGHGHYHPVHUREULJDWRULDPHQWHVDWLVIHLWDV 7RGRV RV HVIRUoRV LQWHUQRV GHYHP VHU UHFDOFXODGRV GH PRGR D JDUDQWLU R HTXLOtEULR GH FDGD XP GRV HOHPHQWRV HVWUXWXUDLV H GD HVWUXWXUD FRPR XP WRGR 2V HIHLWRV GH UHGLVWULEXLomR GHYHP VHU FRQVLGHUDGRVHPWRGRVRVDVSHFWRVGRSURMHWRHVWUXWXUDOLQFOXVLYHQDVFRQGLo}HVGHDQFRUDJHPH FRUWHGHDUPDGXUDVHQDVIRUoDVDDQFRUDU &XLGDGRVHVSHFLDLVGHYHPVHUWRPDGRVFRPUHODomRDRVFDUUHJDPHQWRVGHJUDQGHYDULDELOLGDGH $VYHUL¿FDo}HVGHFRPELQDo}HVGHFDUUHJDPHQWRGH(/6RXGHIDGLJDSRGHPVHUEDVHDGDVQDDQiOLVH OLQHDUVHPUHGLVWULEXLomR'HXPDPDQHLUDJHUDOpGHVHMiYHOTXHQmRKDMDUHGLVWULEXLomRGHHVIRUoRV QDVYHUL¿FDo}HVHPVHUYLoR 14.5.4 $QiOLVHSOiVWLFD $DQiOLVHHVWUXWXUDOpGHQRPLQDGDSOiVWLFDTXDQGRDVQmROLQHDULGDGHVSXGHUHPVHUFRQVLGHUDGDV DGPLWLQGRVHPDWHULDLVGHFRPSRUWDPHQWRUtJLGRSOiVWLFRSHUIHLWRRXHODVWRSOiVWLFRSHUIHLWR(VWHWLSR GHDQiOLVHGHYHVHUXVDGRDSHQDVSDUDYHUL¿FDo}HVGH(/8 $DQiOLVHSOiVWLFDGHHVWUXWXUDVUHWLFXODGDVQmRSRGHVHUDGRWDGDTXDQGR D VHFRQVLGHUDPRVHIHLWRVGHVHJXQGDRUGHPJOREDO © ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
E QmRKRXYHUVX¿FLHQWHGXWLOLGDGHSDUDTXHDVFRQ¿JXUDo}HVDGRWDGDVVHMDPDWLQJLGDV 1R FDVR GH FDUUHJDPHQWR FtFOLFR FRP SRVVLELOLGDGH GH IDGLJD GHYHVH HYLWDU R FiOFXOR SOiVWLFR REVHUYDQGRVHDVSUHVFULo}HVFRQWLGDVQD6HomR 14.5.5 $QiOLVHQmROLQHDU 1DDQiOLVHQmROLQHDUFRQVLGHUDVHRFRPSRUWDPHQWRQmROLQHDUJHRPpWULFRHGRVPDWHULDLV 7RGDDJHRPHWULDGDHVWUXWXUDEHPFRPRWRGDVDVVXDVDUPDGXUDVSUHFLVDPVHUFRQKHFLGDVSDUD TXHDDQiOLVHQmROLQHDUSRVVDVHUHIHWXDGDSRLVDUHVSRVWDGDHVWUXWXUDGHSHQGHGHFRPRHODIRL armada.
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
&RQGLo}HVGHHTXLOtEULRGHFRPSDWLELOLGDGHHGHGXWLOLGDGHGHYHPVHUQHFHVVDULDPHQWHVDWLVIHLWDV $QiOLVHVQmROLQHDUHVSRGHPVHUDGRWDGDVWDQWRSDUDYHUL¿FDo}HVGHHVWDGRVOLPLWHV~OWLPRVFRPR SDUDYHUL¿FDo}HVGHHVWDGRVOLPLWHVGHVHUYLoR 3DUDDQiOLVHGHHVIRUoRVVROLFLWDQWHVQRHVWDGROLPLWH~OWLPRRVSURFHGLPHQWRVDSUR[LPDGRVGH¿QLGRV QD6HomRSRGHPVHUDSOLFDGRV 14.5.6 $QiOLVHDWUDYpVGHPRGHORVItVLFRV 1DDQiOLVHDWUDYpVGHPRGHORVItVLFRVRFRPSRUWDPHQWRHVWUXWXUDOpGHWHUPLQDGRDSDUWLUGHHQVDLRV UHDOL]DGRVFRPPRGHORVItVLFRVGHFRQFUHWRFRQVLGHUDQGRRVFULWpULRVGHVHPHOKDQoDPHFkQLFD $ PHWRGRORJLD HPSUHJDGD QRV H[SHULPHQWRV GHYH DVVHJXUDU D SRVVLELOLGDGH GH REWHU D FRUUHWD LQWHUSUHWDomRGRVUHVXOWDGRV 1HVWHFDVRDLQWHUSUHWDomRGRVUHVXOWDGRVGHYHVHUMXVWL¿FDGDSRUPRGHORWHyULFRGHHTXLOtEULRQDV VHo}HVFUtWLFDVHDQiOLVHHVWDWtVWLFDGRVUHVXOWDGRV 6HIRUSRVVtYHOXPDDYDOLDomRDGHTXDGDGDYDULDELOLGDGHGRVUHVXOWDGRVSRGHVHDGRWDUDVPDUJHQV GHVHJXUDQoDSUHVFULWDVQHVWD1RUPDFRQIRUPHDV6Ho}HVH&DVRFRQWUiULRTXDQGRVyIRU SRVVtYHODYDOLDURYDORUPpGLRGRVUHVXOWDGRVGHYHVHUDPSOLDGDDPDUJHPGHVHJXUDQoDUHIHULGD QHVWD1RUPDFREULQGRDIDYRUGDVHJXUDQoDDVYDULDELOLGDGHVDYDOLDGDVSRURXWURVPHLRV 2EULJDWRULDPHQWHGHYHPVHUREWLGRVUHVXOWDGRVSDUDWRGRVRVHVWDGRVOLPLWHV~OWLPRVHGHVHUYLoR DVHUHPHPSUHJDGRVQDDQiOLVHGDHVWUXWXUD 7RGDVDVDo}HVFRQGLo}HVHSRVVtYHLVLQÀXrQFLDVTXHSRVVDPRFRUUHUGXUDQWHDYLGDGDHVWUXWXUD devem ser convenientemente reproduzidas nos ensaios. (VVH WLSR GH DQiOLVH p DSURSULDGR TXDQGR RV PRGHORV GH FiOFXOR VmR LQVX¿FLHQWHV RX HVWmR IRUD do escopo desta Norma. 3DUDRFDVRGHSURYDVGHFDUJDGHYHPVHUDWHQGLGDVDVSUHVFULo}HVGD6HomR
14.6 (VWUXWXUDVGHHOHPHQWRVOLQHDUHV 14.6.1 Hipóteses básicas (VWUXWXUDVRXSDUWHVGHHVWUXWXUDVTXHSRVVDPVHUDVVLPLODGDVDHOHPHQWRVOLQHDUHV YLJDVSLODUHV WLUDQWHVDUFRVSyUWLFRVJUHOKDVWUHOLoDV SRGHPVHUDQDOLVDGDVDGPLWLQGRVHDVVHJXLQWHVKLSyWHVHV D PDQXWHQomRGDVHomRSODQDDSyVDGHIRUPDomR 86
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
E UHSUHVHQWDomRGRVHOHPHQWRVSRUVHXVHL[RVORQJLWXGLQDLV F FRPSULPHQWROLPLWDGRSHORVFHQWURVGHDSRLRVRXSHORFUX]DPHQWRFRPRHL[RGHRXWURHOHPHQWR HVWUXWXUDO 14.6.2 &DUDFWHUL]DomRGDJHRPHWULD 14.6.2.1 7UHFKRVUtJLGRV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
2V WUHFKRV GH HOHPHQWRV OLQHDUHV SHUWHQFHQWHV j UHJLmR FRPXP DR FUX]DPHQWR GH GRLV RX PDLV HOHPHQWRVSRGHPVHUFRQVLGHUDGRVUtJLGRV QyVGHGLPHQV}HV¿QLWDV GDPDQHLUDFRPRpLOXVWUDGR na Figura 14.1.
Eixo do elemento normal
h2 h1
Trecho rígido
0,3 h1
0,3 h2
)LJXUD±7UHFKRVUtJLGRV 14.6.2.2 /DUJXUDFRODERUDQWHGHYLJDVGHVHomR7 4XDQGRDHVWUXWXUDIRUPRGHODGDVHPDFRQVLGHUDomRDXWRPiWLFDGDDomRFRQMXQWDGHODMHVHYLJDV HVVHHIHLWRSRGHVHUFRQVLGHUDGRPHGLDQWHDDGRomRGHXPDODUJXUDFRODERUDQWHGDODMHDVVRFLDGD jYLJDFRPSRQGRXPDVHomRWUDQVYHUVDO7 $ FRQVLGHUDomR GD VHomR 7 SRGH VHU IHLWD SDUD HVWDEHOHFHU DV GLVWULEXLo}HV GH HVIRUoRV LQWHUQRV WHQV}HVGHIRUPDo}HVHGHVORFDPHQWRVQDHVWUXWXUDGHXPDIRUPDPDLVUHDOLVWD $ ODUJXUD FRODERUDQWH bI GHYH VHU GDGD SHOD ODUJXUD GD YLJD bw DFUHVFLGD GH QR Pi[LPR GD GLVWkQFLDaHQWUHSRQWRVGHPRPHQWRÀHWRUQXORSDUDFDGDODGRGDYLJDHPTXHKDMDODMHFRODERUDQWH $ GLVWkQFLD a SRGH VHU HVWLPDGD HP IXQomR GR FRPSULPHQWR GR WUDPR FRQVLGHUDGR FRPR VH apresenta a seguir: — YLJDVLPSOHVPHQWHDSRLDGD a — WUDPRFRPPRPHQWRHPXPDVyH[WUHPLGDGH a — tramo com momentos nas duas extremidades: a — WUDPRHPEDODQoR a . $OWHUQDWLYDPHQWHRF{PSXWRGDGLVWkQFLDaSRGHVHUIHLWRRXYHUL¿FDGRPHGLDQWHH[DPHGRVGLDJUDPDV GHPRPHQWRVÀHWRUHVQDHVWUXWXUD © ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
1RFDVRGHYLJDVFRQWtQXDVSHUPLWHVHFDOFXOiODVFRPXPDODUJXUDFRODERUDQWH~QLFDSDUDWRGDVDV VHo}HVLQFOXVLYHQRVDSRLRVVREPRPHQWRVQHJDWLYRVGHVGHTXHHVVDODUJXUDVHMDFDOFXODGDDSDUWLU GRWUHFKRGHPRPHQWRVSRVLWLYRVRQGHDODUJXUDUHVXOWHPtQLPD 'HYHPVHUUHVSHLWDGRVRVOLPLWHVb1 e b3FRQIRUPHLQGLFDGRQD)LJXUD bf b3
b1
c
b4
c
b1
b2
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
bw
bw
bf
b3
bw
b1 ≤ 0,5b2
b1 ≤ 0,1a
b3 ≤ b4
b3 ≤ 0,1a
b1
)LJXUD±/DUJXUDGHPHVDFRODERUDQWH 4XDQGR D ODMH DSUHVHQWDU DEHUWXUDV RX LQWHUUXSo}HV QD UHJLmR GD PHVD FRODERUDQWH D YDULDomR GDODUJXUDHIHWLYD bHI GDPHVDGHYHUHVSHLWDURPi[LPRbIHOLPLWDo}HVLPSRVWDVSHODVDEHUWXUDV FRQIRUPHPRVWUDD)LJXUD
88
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
Abertura 2
1
bf
1
2
bef
)LJXUD±/DUJXUDHIHWLYDFRPDEHUWXUD 14.6.2.3 0tVXODVHYDULDo}HVEUXVFDVGHVHo}HV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
1D RFRUUrQFLD GH PtVXOD RX YDULDomR EUXVFD GH VHomR WUDQVYHUVDO Vy GHYH VHU FRQVLGHUDGD FRPR SDUWHHIHWLYDGDVHomRDTXHODLQGLFDGDQD)LJXUD 2 1
hef ou bef
hef ou bef 2 1
1 2
)LJXUD±$OWXUDHODUJXUDHIHWLYDVGHXPDVHomRWUDQVYHUVDO 14.6.2.4 9mRVHIHWLYRVGHYLJDV 2YmRHIHWLYRSRGHVHUFDOFXODGRSRU ef = 0 + a1 + a2 com a1LJXDODRPHQRUYDORUHQWUH t1Hh Ha2LJXDODRPHQRUYDORUHQWUH t2Hh FRQIRUPH )LJXUD
© ABNT 2023 - Todos os direitos reservados
89
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
h
0
0
t1
t2
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
D $SRLRGHYmRH[WUHPRE $SRLRGHYmRLQWHUPHGLiULR
)LJXUD±9mRHIHWLYR 14.6.3 $UUHGRQGDPHQWRGRGLDJUDPDGHPRPHQWRVÀHWRUHV 2 GLDJUDPD GH PRPHQWRV ÀHWRUHV SRGH VHU DUUHGRQGDGR VREUH RV DSRLRV H SRQWRV GH DSOLFDomR GH IRUoDV FRQVLGHUDGDV FRQFHQWUDGDV H HP QyV GH SyUWLFRV (VVH DUUHGRQGDPHQWR SRGH VHU IHLWR GHPDQHLUDDSUR[LPDGDFRQIRUPHLQGLFDGRQD)LJXUD
ΔM
ΔM2
ΔM1
ΔM’
ΔM2
ΔM’
ΔM1
ΔM =
t /2
t /2
t
R1
R2
R
R2 - R1 4
t
ΔM’ = Rt /8
ΔM1 = R1 t /4 ΔM2 = R2 t /4
)LJXUD±$UUHGRQGDPHQWRGHGLDJUDPDGHPRPHQWRVÀHWRUHV
90
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
14.6.4 $QiOLVHOLQHDUFRPRXVHPUHGLVWULEXLomR $SOLFDPVHjVHVWUXWXUDVGHHOHPHQWRVOLQHDUHVDVFRQGLo}HVJHUDLVH[SUHVVDVHPH HDVFRQGLo}HVHVSHFt¿FDVDSUHVHQWDGDVHPD 14.6.4.1 9DORUHVGHULJLGH] 3DUDRFiOFXORGDULJLGH]GRVHOHPHQWRVHVWUXWXUDLVSHUPLWHVHFRPRDSUR[LPDomRWRPDURPyGXOR GHHODVWLFLGDGHVHFDQWH (cs YHU HRPRPHQWRGHLQpUFLDGDVHomREUXWDGHFRQFUHWR 3DUD YHUL¿FDomR GDV ÀHFKDV GHYHP REULJDWRULDPHQWH VHU FRQVLGHUDGDV D ¿VVXUDomR H D ÀXrQFLD XVDQGRSRUH[HPSORRFULWpULRGH
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
14.6.4.2 5HVWULo}HVSDUDDUHGLVWULEXLomR $VUHGLVWULEXLo}HVGHPRPHQWRVÀHWRUHVHGHWRUomRHPSLODUHVHOHPHQWRVOLQHDUHVFRPSUHSRQGHUkQFLD GH FRPSUHVVmR H FRQVRORV Vy SRGHP VHU DGRWDGDV TXDQGR IRUHP GHFRUUHQWHV GH UHGLVWULEXLo}HV GHPRPHQWRVGHYLJDVTXHDHOHVVHOLJXHP 4XDQGRIRUHPXWLOL]DGRVSURFHGLPHQWRVDSUR[LPDGRVDSHQDVXPDSHTXHQDUHGLVWULEXLomRpSHUPLWLGD HPHVWUXWXUDVGHQyVPyYHLV YHU $VUHGLVWULEXLo}HVLPSOtFLWDVHPXPDDQiOLVHGHVHJXQGDRUGHPGHYHPVHUUHDOL]DGDVGHDFRUGRFRP D6HomR 14.6.4.3 /LPLWHVSDUDUHGLVWULEXLomRGHPRPHQWRVHFRQGLo}HVGHGXWLOLGDGH A FDSDFLGDGH GH URWDomR GRV HOHPHQWRV HVWUXWXUDLV p IXQomR GD SRVLomR GD OLQKD QHXWUD QR (/8 4XDQWRPHQRUIRU[GWDQWRPDLRUVHUiHVVDFDSDFLGDGH 3DUDSURSRUFLRQDURDGHTXDGRFRPSRUWDPHQWRG~WLOHPYLJDVHODMHVDSRVLomRGDOLQKDQHXWUDQR(/8 GHYHREHGHFHUDRVVHJXLQWHVOLPLWHV ࣰD xd dSDUDFRQFUHWRVFRPfck d03D ࣰE xd dSDUDFRQFUHWRVFRP03D fck d 90 MPa. (VVHVOLPLWHVSRGHPVHUDOWHUDGRVVHIRUHPXWLOL]DGRVGHWDOKHVHVSHFLDLVGHDUPDGXUDVFRPRSRU H[HPSORRVTXHSURGX]HPFRQ¿QDPHQWRQHVVDVUHJL}HV 4XDQGR IRU HIHWXDGD XPD UHGLVWULEXLomR UHGX]LQGRVH XP PRPHQWR ÀHWRU GH M para GM HP XPD GHWHUPLQDGD VHomR WUDQVYHUVDO D SURIXQGLGDGH GD OLQKD QHXWUD QHVVD VHomR xd SDUD R PRPHQWR reduzido GMGHYHVHUOLPLWDGDSRU ࣰD xd d (G± SDUDFRQFUHWRVFRPfck d03D ࣰE xd d(G± SDUDFRQFUHWRVFRP03D fck d 90 MPa. 2FRH¿FLHQWHGHUHGLVWULEXLomRGHYHDLQGDREHGHFHUDRVVHJXLQWHVOLPLWHV D G t SDUDHVWUXWXUDVGHQyVPyYHLV E GtSDUDTXDOTXHURXWURFDVR © ABNT 2023 - Todos os direitos reservados
91
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
3RGHVHUDGRWDGDUHGLVWULEXLomRIRUDGRVOLPLWHVHVWDEHOHFLGRVQHVWD1RUPDGHVGHTXHDHVWUXWXUD VHMD FDOFXODGD PHGLDQWH R HPSUHJR GH DQiOLVH QmR OLQHDU RX GH DQiOLVH SOiVWLFD FRP YHUL¿FDomR H[SOtFLWDGDFDSDFLGDGHGHURWDomRGDVUyWXODVSOiVWLFDV 14.6.4.4 $QiOLVHQmROLQHDUFRPYHUL¿FDomRH[SOtFLWDGDURWDomRSOiVWLFDVROLFLWDQWH 3DUDYHUL¿FDo}HVGHHVWDGRVOLPLWHV~OWLPRVSRGHVHUHIHWXDGDDDQiOLVHSOiVWLFDGDHVWUXWXUDFRP DVLPXODomRGHUyWXODVSOiVWLFDVORFDOL]DGDVQDVVHo}HVFUtWLFDV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
e REULJDWyULD D YHUL¿FDomR GDV URWDo}HV QDV UyWXODV SOiVWLFDV FRUUHVSRQGHQWHV DRV PHFDQLVPRV DGRWDGRV TXH QmR SRGHP VXSHUDU D FDSDFLGDGH GH URWDomR SOiVWLFD GDV VHo}HV WUDQVYHUVDLV correspondentes. 2OLPLWHGDURWDomRSOiVWLFDVROLFLWDQWHIXQomRGDSURIXQGLGDGHGDOLQKDQHXWUDQRHVWDGROLPLWH~OWLPR± ÀH[mRVLPSOHVSDUDRPRPHQWRÀHWRUVROLFLWDQWHM6GGDVHomRFUtWLFDGDGDQD)LJXUDFRUUHVSRQGH jUD]mRad RQGHa = M6GV6GVHQGRV6GDIRUoDFRUWDQWHQHVWDVHomR3DUDRXWUDVUHODo}HVad PXOWLSOLFDURVYDORUHVH[WUDtGRVGD)LJXUDSHORIDWRU (a d ) 3. 35 I:bfck= 20 bab50bMPa,bCA-50 30
II:bfck= 90 bMPa,bCA-50
I 25
III:bfck= 20 bab50bMPa,bCA-60
II
IV:bfck= 90 bMPa,bCA-60 θpl
20
III
(mrad) 15
IV
10
5
0 0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
(x/d) ELU
)LJXUD±&DSDFLGDGHGHURWDomRGHUyWXODVSOiVWLFDV $ YHUL¿FDomR GD FDSDFLGDGH GH URWDomR GH UyWXODV SOiVWLFDV GHYH VHU IHLWD SDUD FDGD XPD GDV FRPELQDo}HV GH FDUUHJDPHQWR FRQVLGHUDGDV $WHQomR HVSHFLDO GHYH VHU GDGD j YHUL¿FDomR GD ¿VVXUDomRQDVUyWXODVSDUDFRQGLo}HVGHVHUYLoR 3DUD FODVVHV GH FRQFUHWR HQWUH & H & p YiOLGD D LQWHUSRODomR OLQHDU GRV YDORUHV REWLGRV QD )LJXUD
92
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
e GLVSHQVDGD QD DQiOLVH SOiVWLFD FRQIRUPH LWHP D YHUL¿FDomR H[SOtFLWD GD FDSDFLGDGH GH URWDomRSOiVWLFDSUHVFULWDDFLPDGHVGHTXHDSRVLomRGDOLQKDQHXWUDVHMDOLPLWDGDHP xd dVHfck d03D xd dVHfck!03D 14.6.5 $QiOLVHQmROLQHDU $QiOLVHV QmR OLQHDUHV VmR SHUPLWLGDV WDQWR SDUD YHUL¿FDo}HV GH HVWDGRVOLPLWHV ~OWLPRV FRPR SDUD YHUL¿FDo}HVGHHVWDGRVOLPLWHVGHVHUYLoR 14.6.6 (VWUXWXUDVXVXDLVGHHGLItFLRV±$SUR[LPDo}HVSHUPLWLGDV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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ABNT NBR 6118:2023
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ABNT NBR 6118:2023
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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ABNT NBR 6118:2023
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ABNT NBR 6118:2023
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
F HPHVWUXWXUDVGHPDWHULDOGHFRPSRUWDPHQWRQmROLQHDUFRPLPSHUIHLo}HVJHRPpWULFDVLQLFLDLV QmRKiSHUGDGHHVWDELOLGDGHSRUELIXUFDomRGRHTXLOtEULRSRGHQGRQRHQWDQWRKDYHUSHUGDGH HVWDELOLGDGHTXDQGRDRFUHVFHUDLQWHQVLGDGHGRFDUUHJDPHQWRRDXPHQWRGDFDSDFLGDGHUHVLVWHQWHGDHVWUXWXUDSDVVDDVHUPHQRUGRTXHRDXPHQWRGDVROLFLWDomR SRQWROLPLWHVHPUHYHUVmR 2VFDVRVD HE SRGHPRFRUUHUSDUDHVWUXWXUDVGHPDWHULDOGHFRPSRUWDPHQWROLQHDURXQmROLQHDU (IHLWRVGHRUGHPVmRDTXHOHVTXHVHVRPDPDRVREWLGRVHPXPDDQiOLVHGHSULPHLUDRUGHP HP TXH R HTXLOtEULR GD HVWUXWXUD p HVWXGDGR QD FRQ¿JXUDomR JHRPpWULFD LQLFLDO TXDQGR D DQiOLVH GR HTXLOtEULRSDVVDDVHUHIHWXDGDFRQVLGHUDQGRDFRQ¿JXUDomRGHIRUPDGD 2VHIHLWRVGHRUGHPHPFXMDGHWHUPLQDomRGHYHVHUFRQVLGHUDGRRFRPSRUWDPHQWRQmROLQHDUGRV PDWHULDLVSRGHPVHUGHVSUH]DGRVVHPSUHTXHQmRUHSUHVHQWDUHPDFUpVFLPRVXSHULRUDQDV UHDo}HVHQDVVROLFLWDo}HVUHOHYDQWHVQDHVWUXWXUD Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
15.3 3ULQFtSLREiVLFRGHFiOFXOR $ DQiOLVH HVWUXWXUDO FRP HIHLWRV GH RUGHP GHYH DVVHJXUDU TXH SDUD DV FRPELQDo}HV PDLV GHVIDYRUiYHLVGDVDo}HVGHFiOFXORQmRRFRUUDSHUGDGHHVWDELOLGDGHQHPHVJRWDPHQWRGDFDSDFLGDGH UHVLVWHQWHGHFiOFXOR $ QmR OLQHDULGDGH ItVLFD SUHVHQWH QDV HVWUXWXUDV GH FRQFUHWR DUPDGR GHYH VHU REULJDWRULDPHQWH considerada. $GHIRUPDELOLGDGHGRVHOHPHQWRVGHYHVHUFDOFXODGDFRPEDVHQRVGLDJUDPDV WHQVmRGHIRUPDomR GRVPDWHULDLVGH¿QLGRVQD6HomR$WHQVmRGHSLFRGRFRQFUHWRGHYHVHULJXDODfcdMiLQFOXtGR RHIHLWRGHFDUJDPDQWLGD 5VFK HDGRDoRGHYHVHULJXDODfydFRPRVYDORUHVGHJc e JsXWLOL]DGRV SDUDR(/8 $YHUL¿FDomRGDFDSDFLGDGHUHVLVWHQWHGHYHVHUIHLWDFRQIRUPHSUHVFULo}HVGD6HomR 3RVVtYHLVLQFHUWH]DVQDVFDUDFWHUtVWLFDVGRVDSRLRVGDHVWUXWXUDHQDGHIRUPDELOLGDGHGHVWDGHYHP VHUFRQVLGHUDGDVQDDQiOLVH 15.3.1 5HODo}HVPRPHQWRFXUYDWXUD 2SULQFLSDOHIHLWRGDQmROLQHDULGDGHItVLFDSRGHHPJHUDOVHUFRQVLGHUDGRDWUDYpVGDFRQVWUXomRGD UHODomRPRPHQWRFXUYDWXUDSDUDFDGDVHomRFRPDUPDGXUDVXSRVWDFRQKHFLGDHSDUDRYDORUGD IRUoDQRUPDODWXDQWH 3RGHVHUFRQVLGHUDGDWDPEpPDIRUPXODomRGHVHJXUDQoDHPTXHVHFDOFXODPRVHIHLWRVGHRUGHP GDVFDUJDVPDMRUDGDVGHJIJITXHSRVWHULRUPHQWHVmRPDMRUDGRVGHJIFRPJI FRPDVHJXLQWH equação: SGWRW = JI S() onde n ⎡γ ⎞⎤ γ ⎛ ψ ojFqjk ⎟ ⎥ F = ⎢ f Fgk + f ⎜ Fq1k + γ f3 ⎝ ⎠ ⎥⎦ ⎢⎣ γ f3 2
∑
100
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
3DUDHVFROKDGDFRPELQDomRGHDo}HVHGRVFRH¿FLHQWHVJI e \0YHUD6HomR $VVLPDUHODomRPRPHQWRFXUYDWXUDDSUHVHQWDRDVSHFWRGD)LJXUD M
Secante
Curva obtida com 1,10 fcd e NRd
Jf3
MRd MRd
γf3
arctg (EI )sec
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
ELU
B
Curva obtida com 0,85 Kcfcd
Rigidez secante
A
1/r
)LJXUD±5HODomRPRPHQWRFXUYDWXUD $FXUYDFKHLD$%REWLGDFRQVLGHUDQGRRYDORUGHIRUoDQRUPDOLJXDODNRdJITXHDIDYRUGDVHJXUDQoD SRGHVHUOLQHDUL]DGDSHODUHWD$%pXWLOL]DGDQRFiOFXORGDVGHIRUPDo}HV $FXUYDWUDFHMDGDREWLGDFRPRVYDORUHVGHFiOFXORGDVUHVLVWrQFLDVGRFRQFUHWRHGRDoRpXWLOL]DGD VRPHQWHSDUDGH¿QLURHVIRUoRUHVLVWHQWHMRd correspondente a NRd SRQWRPi[LPR $UHWD$%pFDUDFWHUL]DGDSHODULJLGH]VHFDQWH (, secTXHSRGHVHUXWLOL]DGDHPSURFHVVRVDSUR[LPDGRV SDUDÀH[mRFRPSRVWDQRUPDORXREOtTXD 'H¿QHVHFRPRULJLGH]VHFDQWHDGLPHQVLRQDONsecRYDORUGDGRSRU κ sec = (El )sec
( A c ⋅ h2 ⋅ fcd )
onde h pDDOWXUDGDVHomRFRQVLGHUDGD (VVHYDORUGDULJLGH]VHFDQWHDGLPHQVLRQDOSRGHVHUFRORFDGRHPFRQMXQWRFRPRVYDORUHV~OWLPRV de NRd e MRdHPiEDFRVGHLQWHUDomRIRUoDQRUPDOPRPHQWRÀHWRU 15.3.2 ,PSHUIHLo}HVJHRPpWULFDV $VLPSHUIHLo}HVJHRPpWULFDV JOREDOHORFDO GHYHPVHUFRQVLGHUDGDVGHDFRUGRFRPRSUHVFULWRHP 11.3.3.4. 3DUD SLODUHV GH VHomR UHWDQJXODU TXDQGR KRXYHU D QHFHVVLGDGH GH FDOFXODU RV HIHLWRV ORFDLV GH RUGHPDYHUL¿FDomRGRPRPHQWRPtQLPRSRGHVHUFRQVLGHUDGDDWHQGLGDTXDQGRQRGLPHQVLRQDPHQWR DGRWDGRREWpPVHXPDHQYROWyULDUHVLVWHQWHTXHHQJOREHDHQYROWyULDPtQLPDFRPRUGHPFXMRV PRPHQWRVWRWDLVVmRFDOFXODGRVDSDUWLUGRVPRPHQWRVPtQLPRVGHRUGHPHGHDFRUGRFRP
© ABNT 2023 - Todos os direitos reservados
101
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
$FRQVLGHUDomRGHVWDHQYROWyULDPtQLPDSRGHVHUUHDOL]DGDDWUDYpVGHGXDVDQiOLVHVjÀH[mRFRPSRVWD QRUPDO FDOFXODGDV GH IRUPD LVRODGD H FRP PRPHQWRV ÀHWRUHV PtQLPRV GH RUGHP DWXDQWHV QRV H[WUHPRVGRSLODUQDVVXDVGLUHo}HVSULQFLSDLV
My
M1d,mín,yy
M1d,mín,yy (Flexão composta normal em torno de y)
Md,tot,mín,yy M1d,mín,xx
h
Md,tot,mín,yy M1d,mín,yy
- M1d,mín,xx
b
M1d,mín,xx Md,tot,mín,xx
- Md,tot,mín,xx
(Seção transversal)
M1d,mín,yy
Mx
(Flexão composta normal em torno de x)
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
M1d,mín,xx 2
Md,tot,mín,x Md,tot,mín,y + Md,tot,mín,xx Md,tot,mín,yy
- M1d,mín,yy
2
=1
Md,tot,mín,xx - Md,tot,mín,yy M1d,mín,xx
(Envoltória mínima com 2a ordem) Sendo: Md,tot,mín,xx e Md,tot,mín,yy as componentes em flexão composta normal e Md,tot,mín,x e Md,tot,mín,y as componentes em flexão composta oblíqua
)LJXUD±(QYROWyULDPtQLPDFRPRUGHP
15.4 'H¿QLo}HVHFODVVL¿FDomRGDVHVWUXWXUDV 15.4.1 (IHLWRVJOREDLVORFDLVHORFDOL]DGRVGHRUGHP 6RE D DomR GDV FDUJDV YHUWLFDLV H KRUL]RQWDLV RV QyV GD HVWUXWXUD GHVORFDPVH KRUL]RQWDOPHQWH 2V HVIRUoRV GH RUGHP GHFRUUHQWHV GHVVHV GHVORFDPHQWRV VmR FKDPDGRV HIHLWRV JOREDLV GH RUGHP 1DV EDUUDV GD HVWUXWXUD FRPR XP ODQFH GH SLODU RV UHVSHFWLYRV HL[RV QmR VH PDQWrP UHWLOtQHRVVXUJLQGRDtHIHLWRVORFDLVGHRUGHPTXHHPSULQFtSLRDIHWDPSULQFLSDOPHQWHRVHVIRUoRV VROLFLWDQWHVDRORQJRGHODV (PSLODUHVSDUHGH VLPSOHVRXFRPSRVWRV SRGHVHWHUXPDUHJLmRTXHDSUHVHQWDQmRUHWLOLQHLGDGH PDLRUGRTXHDGRHL[RGRSLODUFRPRXPWRGR1HVVDVUHJL}HVVXUJHPHIHLWRVGHRUGHPPDLRUHV FKDPDGRV GH HIHLWRV GH RUGHP ORFDOL]DGRV YHU )LJXUD 2 HIHLWR GH RUGHP ORFDOL]DGR DOpPGHDXPHQWDUQHVVDUHJLmRDÀH[mRORQJLWXGLQDODXPHQWDWDPEpPDÀH[mRWUDQVYHUVDOKDYHQGR DQHFHVVLGDGHGHDXPHQWDUDDUPDGXUDWUDQVYHUVDOQHVVDVUHJL}HV
102
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
N M
2a ordem localizado
2a ordem localizado
)LJXUD±(IHLWRVGHRUGHPORFDOL]DGRV Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
15.4.2 (VWUXWXUDVGHQyV¿[RVHHVWUXWXUDVGHQyVPyYHLV $V HVWUXWXUDV VmR FRQVLGHUDGDV SDUD HIHLWR GH FiOFXOR GH QyV ¿[RV TXDQGR RV GHVORFDPHQWRV KRUL]RQWDLVGRVQyVVmRSHTXHQRVHSRUGHFRUUrQFLDRVHIHLWRVJOREDLVGHRUGHPVmRGHVSUH]tYHLV LQIHULRUHV D GRV UHVSHFWLYRV HVIRUoRV GH RUGHP 1HVVDV HVWUXWXUDV EDVWD FRQVLGHUDU RVHIHLWRVORFDLVHORFDOL]DGRVGHRUGHP $VHVWUXWXUDVGHQyVPyYHLVVmRDTXHODVRQGHRVGHVORFDPHQWRVKRUL]RQWDLVQmRVmRSHTXHQRVH HPGHFRUUrQFLDRVHIHLWRVJOREDLVGHRUGHPVmRLPSRUWDQWHV VXSHULRUHVDGRVUHVSHFWLYRV HVIRUoRV GH RUGHP 1HVVDV HVWUXWXUDV GHYHP VHU FRQVLGHUDGRV WDQWR RV HVIRUoRV GH RUGHP JOREDLVFRPRRVORFDLVHORFDOL]DGRV 7RGDYLDKiHVWUXWXUDVHPTXHRVGHVORFDPHQWRVKRUL]RQWDLVVmRJUDQGHVHTXHQmRREVWDQWHSRGH VHUGLVSHQVDGDDFRQVLGHUDomRGRVHIHLWRVGHRUGHPSRUVHUHPSHTXHQDVDVIRUoDVQRUPDLVH SRUWDQWRSHTXHQRVRVDFUpVFLPRVGRVGHVORFDPHQWRVSURGX]LGRVSRUHODV LVVRSRGHDFRQWHFHUSRU H[HPSORHPSRVWHV 15.4.3 Contraventamento 3RU FRQYHQLrQFLD GH DQiOLVH p SRVVtYHO LGHQWL¿FDU GHQWUR GD HVWUXWXUD VXEHVWUXWXUDV TXH GHYLGR j VXD JUDQGH ULJLGH] D Do}HV KRUL]RQWDLV UHVLVWHP j PDLRU SDUWH GRV HVIRUoRV GHFRUUHQWHV GHVVDV Do}HV(VVDVVXEHVWUXWXUDVVmRFKDPDGDVVXEHVWUXWXUDVGHFRQWUDYHQWDPHQWR 2V HOHPHQWRV TXH QmR SDUWLFLSDP GD VXEHVWUXWXUD GH FRQWUDYHQWDPHQWR VmR FKDPDGRV HOHPHQWRV contraventados. $V VXEHVWUXWXUDV GH FRQWUDYHQWDPHQWR SRGHP VHU GH QyV ¿[RV RX GH QyV PyYHLV GH DFRUGR FRP DVGH¿QLo}HVGH 15.4.4 (OHPHQWRVLVRODGRV 6mRFRQVLGHUDGRVHOHPHQWRVLVRODGRVRVVHJXLQWHV D RVHOHPHQWRVHVWUXWXUDLVLVRVWiWLFRV E RVHOHPHQWRVFRQWUDYHQWDGRV F RVHOHPHQWRVGDVHVWUXWXUDVGHFRQWUDYHQWDPHQWRGHQyV¿[RV © ABNT 2023 - Todos os direitos reservados
103
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
G RVHOHPHQWRVGDVVXEHVWUXWXUDVGHFRQWUDYHQWDPHQWRGHQyVPyYHLVGHVGHTXHDRVHVIRUoRV QDVH[WUHPLGDGHVREWLGRVHPXPDDQiOLVHGHRUGHPVHMDPDFUHVFHQWDGRVRVGHWHUPLQDGRV SRUDQiOLVHJOREDOGHRUGHP
15.5 'LVSHQVDGDFRQVLGHUDomRGRVHVIRUoRVJOREDLVGHRUGHP 15.5.1 *HQHUDOLGDGHV 2V SURFHVVRV DSUR[LPDGRV DSUHVHQWDGRV HP H SRGHP VHU XWLOL]DGRV SDUD YHUL¿FDU DSRVVLELOLGDGHGHGLVSHQVDGDFRQVLGHUDomRGRVHVIRUoRVJOREDLVGHDRUGHPRXVHMDSDUDLQGLFDU VHDHVWUXWXUDSRGHVHUFODVVL¿FDGDFRPRGHQyV¿[RVVHPQHFHVVLGDGHGHFiOFXORULJRURVR 1DDQiOLVHGHHVWDELOLGDGHJOREDOTXHWUDWDDHVWUXWXUDFRPRXPWRGRRYDORUUHSUHVHQWDWLYRGRPyGXOR GHGHIRUPDomRVHFDQWHFRQIRUPHSRGHVHUPDMRUDGRHP
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
15.5.2 3DUkPHWURGHLQVWDELOLGDGHD 8PDHVWUXWXUDUHWLFXODGDVLPpWULFDSRGHVHUFRQVLGHUDGDFRPRVHQGRGHQyV¿[RVVHVHXSDUkPHWUR GHLQVWDELOLGDGHDIRUPHQRUTXHRYDORUD1FRQIRUPHDH[SUHVVmR α = H tot Nk (EcsIc ) onde D1 Q VH n d 3 D1
VH n t 4
onde n
pRQ~PHURGHQtYHLVGHEDUUDVKRUL]RQWDLV DQGDUHV DFLPDGDIXQGDomRRXGHXPQtYHO SRXFRGHVORFiYHOGRVXEVROR
Htot p D DOWXUD WRWDO GD HVWUXWXUD PHGLGD D SDUWLU GR WRSR GD IXQGDomR RX GH XP QtYHO SRXFR GHVORFiYHOGRVXEVROR N k
pRVRPDWyULRGHWRGDVDVFDUJDVYHUWLFDLVDWXDQWHVQDHVWUXWXUD DSDUWLUGRQtYHOFRQVLGHUDGR SDUDRFiOFXORGHHtot FRPVHXYDORUFDUDFWHUtVWLFR
(csIc UHSUHVHQWDRVRPDWyULRGRVYDORUHVGHULJLGH]GHWRGRVRVSLODUHVQDGLUHomRFRQVLGHUDGD 1RFDVRGHHVWUXWXUDVGHSyUWLFRVGHWUHOLoDVRXPLVWDVRXFRPSLODUHVGHULJLGH]YDULiYHO DRORQJRGDDOWXUDSRGHVHUFRQVLGHUDGRRYDORUGDH[SUHVVmR(csIcGHXPSLODUHTXLYDOHQWH de seção constante. 2YDORUGH IcGHYHVHUFDOFXODGRFRQVLGHUDQGRDVVHo}HVEUXWDVGRVSLODUHV $ULJLGH]GRSLODUHTXLYDOHQWHGHYHVHUGHWHUPLQDGDGDVHJXLQWHIRUPD — FDOFXODU R GHVORFDPHQWR GR WRSR GD HVWUXWXUD GH FRQWUDYHQWDPHQWR VRE D DomR GR FDUUHJDPHQWRKRUL]RQWDOQDGLUHomRFRQVLGHUDGD — FDOFXODUDULJLGH]GHXPSLODUHTXLYDOHQWHGHVHomRFRQVWDQWHHQJDVWDGRQDEDVHHOLYUHQR WRSRGHPHVPDDOWXUDHtotWDOTXHVREDDomRGRPHVPRFDUUHJDPHQWRVRIUDRPHVPR GHVORFDPHQWRQRWRSR 104
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
2YDORUOLPLWHD1 SUHVFULWRSDUDn tpHPJHUDODSOLFiYHOjVHVWUXWXUDVXVXDLVGHHGLItFLRV 3DUD DVVRFLDo}HV GH SLODUHVSDUHGH H SDUD SyUWLFRV DVVRFLDGRV D SLODUHVSDUHGH DGRWDU D1 1RFDVRGHFRQWUDYHQWDPHQWRFRQVWLWXtGRH[FOXVLYDPHQWHSRUSLODUHVSDUHGHDGRWDUD1 4XDQGR VyKRXYHUSyUWLFRVDGRWDUD1 15.5.3 &RH¿FLHQWHJz 2FRH¿FLHQWHJzGHDYDOLDomRGDLPSRUWkQFLDGRVHVIRUoRVGHVHJXQGDRUGHPJOREDLVpYiOLGRSDUD HVWUXWXUDVUHWLFXODGDVGHQRPtQLPRTXDWURDQGDUHV(OHSRGHVHUGHWHUPLQDGRDSDUWLUGRVUHVXOWDGRV GHXPDDQiOLVHOLQHDUGHSULPHLUDRUGHPSDUDFDGDFDVRGHFDUUHJDPHQWRDGRWDQGRVHRVYDORUHV GHULJLGH]GDGRVHP 2YDORUGHJzSDUDFDGDFRPELQDomRGHFDUUHJDPHQWRpGDGRSHODH[SUHVVmR
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
γz =
1 ΔM tot,d 1− M1,tot,d
onde MWRWG p R PRPHQWR GH WRPEDPHQWR RX VHMD D VRPD GRV PRPHQWRV GH WRGDV DV IRUoDV KRUL]RQWDLV GD FRPELQDomR FRQVLGHUDGD FRP VHXV YDORUHV GH FiOFXOR HP UHODomR jEDVHGDHVWUXWXUD 'MWRWG pDVRPDGRVSURGXWRVGHWRGDVDVIRUoDVYHUWLFDLVDWXDQWHVQDHVWUXWXUDQDFRPELQDomR FRQVLGHUDGD FRP VHXV YDORUHV GH FiOFXOR SHORV GHVORFDPHQWRV KRUL]RQWDLV GH VHXV UHVSHFWLYRVSRQWRVGHDSOLFDomRREWLGRVGDDQiOLVHGHRUGHP &RQVLGHUDVHTXHDHVWUXWXUDpGHQyV¿[RVVHIRUREHGHFLGDDFRQGLomRJz d
15.6 $QiOLVHGHHVWUXWXUDVGHQyV¿[RV 1DVHVWUXWXUDVGHQyV¿[RVRFiOFXORSRGHVHUUHDOL]DGRFRQVLGHUDQGRFDGDHOHPHQWRFRPSULPLGR LVRODGDPHQWH FRPR EDUUD YLQFXODGD QDV H[WUHPLGDGHV DRV GHPDLV HOHPHQWRV HVWUXWXUDLV TXH DOL FRQFRUUHPRQGHVHDSOLFDPRVHVIRUoRVREWLGRVSHODDQiOLVHGDHVWUXWXUDHIHWXDGDVHJXQGRDWHRULD GHRUGHP $DQiOLVHGRVHIHLWRVORFDLVGHRUGHPGHYHVHUUHDOL]DGDGHDFRUGRFRPRHVWDEHOHFLGRHP 6REDDomRGHIRUoDVKRUL]RQWDLVDHVWUXWXUDpVHPSUHFDOFXODGDFRPRGHVORFiYHO2IDWRGHDHVWUXWXUD VHU FODVVL¿FDGD FRPR VHQGR GH QyV ¿[RV GLVSHQVD DSHQDV D FRQVLGHUDomR GRV HVIRUoRV JOREDLV GHRUGHP 2 FRPSULPHQWR HTXLYDOHQWH e GR HOHPHQWR FRPSULPLGR SLODU VXSRVWR YLQFXODGR HP DPEDV DV H[WUHPLGDGHVGHYHVHURPHQRUGRVVHJXLQWHVYDORUHV e = h e =
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
onde 0 p D GLVWkQFLD HQWUH DV IDFHV LQWHUQDV GRV HOHPHQWRV HVWUXWXUDLV VXSRVWRV KRUL]RQWDLV TXH YLQFXODPRSLODU h
pDDOWXUDGDVHomRWUDQVYHUVDOGRSLODUPHGLGDQRSODQRGDHVWUXWXUDHPHVWXGR
pDGLVWkQFLDHQWUHRVHL[RVGRVHOHPHQWRVHVWUXWXUDLVDRVTXDLVRSLODUHVWiYLQFXODGR
15.7 $QiOLVHGHHVWUXWXUDVGHQyVPyYHLV 15.7.1 *HQHUDOLGDGHV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
1D DQiOLVH HVWUXWXUDO GH HVWUXWXUDV GH QyV PyYHLV GHYHP VHU REULJDWRULDPHQWH FRQVLGHUDGRV RV HIHLWRVGDQmROLQHDULGDGHJHRPpWULFDHGDQmROLQHDULGDGHItVLFDHQRGLPHQVLRQDPHQWRGHYHPVHU REULJDWRULDPHQWHFRQVLGHUDGRVRVHIHLWRVJOREDLVHORFDLVGHRUGHP 15.7.2 $QiOLVHQmROLQHDUFRPRUGHP 8PDVROXomRDSUR[LPDGDSDUDDGHWHUPLQDomRGRVHVIRUoRVJOREDLVGHRUGHPFRQVLVWHQDDYDOLDomR GRVHVIRUoRV¿QDLV RUGHPRUGHP DSDUWLUGDPDMRUDomRDGLFLRQDOGDVDo}HVKRUL]RQWDLVGD FRPELQDomRGHFDUUHJDPHQWRFRQVLGHUDGDSRU Ȗz(VVHSURFHVVRVypYiOLGRSDUDȖz 15.7.3 &RQVLGHUDomRDSUR[LPDGDGDQmROLQHDULGDGHItVLFD 3DUDDDQiOLVHGRVHVIRUoRVJOREDLVGHRUGHPHPHVWUXWXUDVUHWLFXODGDVFRPQRPtQLPRTXDWUR DQGDUHVSRGHVHUFRQVLGHUDGDDQmROLQHDULGDGHItVLFDGHPDQHLUDDSUR[LPDGDWRPDQGRVHFRPR ULJLGH]GRVHOHPHQWRVHVWUXWXUDLVRVYDORUHVVHJXLQWHV — ODMHV
(, sec (c,c
— YLJDV
(, sec (c,c para As¶z As e ((, sec (cIc para As¶ As
— SLODUHV
(, sec (c,c
onde Ic pRPRPHQWRGHLQpUFLDGDVHomREUXWDGHFRQFUHWRLQFOXLQGRTXDQGRIRURFDVRDVPHVDV FRODERUDQWHV (c pRYDORUUHSUHVHQWDWLYRGRPyGXORGHGHIRUPDomRGRFRQFUHWRFRQIRUPH 2V YDORUHV GH ULJLGH] DGRWDGRV QHVWD VXEVHomR VmR DSUR[LPDGRV H QmR SRGHP VHU XVDGRV SDUD DYDOLDUHVIRUoRVORFDLVGHRUGHPPHVPRFRPXPDGLVFUHWL]DomRPDLRUGDPRGHODJHP (PHVWUXWXUDVGHHGL¿FDo}HVFRPPHQRVGHTXDWURDQGDUHVHPTXHDVIRUoDVYHUWLFDLVQRVSLODUHV VHMDPSHTXHQDV N6G Ac fcd FRPRHPDOJXQVJDOS}HVDUHGXomRGHULJLGH]GRVHOHPHQWRV HVWUXWXUDLVGHYHVHUDYDOLDGDGHIRUPDHVSHFt¿FD
106
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
15.7.4 $QiOLVHGRVHIHLWRVORFDLVGHRUGHP $ DQiOLVH JOREDO GH RUGHP IRUQHFH DSHQDV RV HVIRUoRV QDV H[WUHPLGDGHV GDV EDUUDV GHYHQGR VHUUHDOL]DGDXPDDQiOLVHGRVHIHLWRVORFDLVGHRUGHPDRORQJRGRVHL[RVGDVEDUUDVFRPSULPLGDV GHDFRUGRFRPRSUHVFULWRHP 2VHOHPHQWRVLVRODGRVSDUD¿QVGHYHUL¿FDomRORFDOGHYHPVHUIRUPDGRVSHODVEDUUDVFRPSULPLGDV UHWLUDGDVGDHVWUXWXUDFRPFRPSULPHQWReGHDFRUGRFRPRHVWDEHOHFLGRHPSRUpPDSOLFDQGR VHjVVXDVH[WUHPLGDGHVRVHVIRUoRVREWLGRVDWUDYpVGDDQiOLVHJOREDOGHRUGHP
15.8 $QiOLVHGHHOHPHQWRVLVRODGRV 15.8.1 *HQHUDOLGDGHV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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γ n1 = 1 +
λ − 140 ≥1 140
15.8.2 'LVSHQVDGDDQiOLVHGRVHIHLWRVORFDLVGHRUGHP 2V HVIRUoRV ORFDLV GH RUGHP HP HOHPHQWRV LVRODGRV SRGHP VHU GHVSUH]DGRV TXDQGR R tQGLFH GHHVEHOWH]IRUPHQRUTXHRYDORUOLPLWHO1HVWDEHOHFLGRQHVWDVXEVHomR 2tQGLFHGHHVEHOWH]GHYHVHUFDOFXODGRSHODH[SUHVVmR O = e i 1RFDVRGHSLODUHQJDVWDGRQDEDVHHOLYUHQRWRSRRYDORUGHe pLJXDOD1RVGHPDLVFDVRV DGRWDURVYDORUHVFDOFXODGRVFRQIRUPH 2YDORUGHO1GHSHQGHGHGLYHUVRVIDWRUHVPDVRVSUHSRQGHUDQWHVVmR — D H[FHQWULFLGDGH UHODWLYD GH RUGHP e1h QD H[WUHPLGDGH GR SLODU RQGH RFRUUH R PRPHQWR GHRUGHPGHPDLRUYDORUDEVROXWR — DYLQFXODomRGRVH[WUHPRVGDFROXQDLVRODGD — DIRUPDGRGLDJUDPDGHPRPHQWRVGHRUGHP 2YDORUGHO1SRGHVHUFDOFXODGRSHODH[SUHVVmR λ1 =
25 + 12,5e1 /h αb
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
onde dO1 d 90 HRQGHRYDORUGHDEGHYHVHUREWLGRFRQIRUPHHVWDEHOHFLGRDVHJXLU D SDUDSLODUHVELDSRLDGRVVHPFDUJDVWUDQVYHUVDLV M αb = 0, 60 + 0, 40 B ≥ 0, 40 MA sendo tDE t
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onde MA e MB VmRRVPRPHQWRVGHRUGHPQRVH[WUHPRVGRSLODUREWLGRVQDDQiOLVHGHRUGHP QRFDVRGHHVWUXWXUDVGHQyV¿[RVHRVPRPHQWRVWRWDLV RUGHPRUGHPJOREDO QRFDVRGHHVWUXWXUDVGHQyVPyYHLV'HYHVHUDGRWDGRSDUDMARPDLRUYDORUDEVROXWR DRORQJRGRSLODUELDSRLDGRHSDUDMBRVLQDOSRVLWLYRVHWUDFLRQDUDPHVPDIDFHTXH MAHQHJDWLYRHPFDVRFRQWUiULR E SDUDSLODUHVELDSRLDGRVFRPFDUJDVWUDQVYHUVDLVVLJQL¿FDWLYDVDRORQJRGDDOWXUD DE F SDUDSLODUHVHPEDODQoR ĮE G SDUD SLODUHV ELDSRLDGRV RX HP EDODQoR FRP PRPHQWRV PHQRUHV TXH R PRPHQWR PtQLPR HVWDEHOHFLGRHP DE 15.8.3 'HWHUPLQDomRGRVHIHLWRVORFDLVGHRUGHP 15.8.3.1 %DUUDVVXEPHWLGDVDÀH[RFRPSUHVVmRQRUPDO 2 FiOFXOR SRGH VHU IHLWR SHOR PpWRGR JHUDO RX SRU PpWRGRV DSUR[LPDGRV GH DFRUGR FRP RX $FRQVLGHUDomRGDÀXrQFLDpREULJDWyULDSDUDO! FRQIRUPH 15.8.3.2 0pWRGRJHUDO &RQVLVWHQDDQiOLVHQmROLQHDUGHRUGHPHIHWXDGDFRPGLVFUHWL]DomRDGHTXDGDGDEDUUDFRQVLGHUDomR GDUHODomRPRPHQWRFXUYDWXUDUHDOHPFDGDVHomRHFRQVLGHUDomRGDQmROLQHDULGDGHJHRPpWULFDGH maneira não aproximada. 2PpWRGRJHUDOpREULJDWyULRSDUDO >140. 108
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
15.8.3.3 Métodos aproximados 15.8.3.3.1 *HQHUDOLGDGHV $GHWHUPLQDomRGRVHVIRUoRVORFDLVGHRUGHPSRGHVHUIHLWDSRUPpWRGRVDSUR[LPDGRVFRPRRGR SLODUSDGUmRHRGRSLODUSDGUmRPHOKRUDGR 15.8.3.3.2 0pWRGRGRSLODUSDGUmRFRPFXUYDWXUDDSUR[LPDGD 3RGH VHU HPSUHJDGR DSHQDV QR FiOFXOR GH SLODUHV FRP O d FRP VHomR FRQVWDQWH H DUPDGXUD VLPpWULFDHFRQVWDQWHDRORQJRGHVHXHL[R
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
$QmROLQHDULGDGHJHRPpWULFDpFRQVLGHUDGDGHIRUPDDSUR[LPDGDVXSRQGRVHTXHDGHIRUPDomRGD EDUUDVHMDVHQRLGDO $QmROLQHDULGDGHItVLFDpFRQVLGHUDGDDWUDYpVGHXPDH[SUHVVmRDSUR[LPDGDGDFXUYDWXUDQDVHomR FUtWLFD 2PRPHQWRWRWDOPi[LPRQRSLODUGHYHVHUFDOFXODGRSHODH[SUHVVmR 2 1 Md,tot = αb M1d,A + Nd e ≥ M1d,A 10 r VHQGRrDFXUYDWXUDQDVHomRFUtWLFDTXHSRGHVHUDYDOLDGDSHODH[SUHVVmRDSUR[LPDGD 1 0, 005 0, 005 = ≤ r h ( ν + 0, 5 ) h onde Q= Nd Ac fcd onde h
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109
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ABNT NBR 6118:2023
2PRPHQWRWRWDOPi[LPRQRSLODUGHYHVHUFDOFXODGRDSDUWLUGDPDMRUDomRGRPRPHQWRGHRUGHP SHODH[SUHVVmR MSd,tot =
αb M1d,A ≥ M1d,A λ2 1− 120 κ ν
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(P XP SURFHVVR GH GLPHQVLRQDPHQWR WRPDVH M5GWRW = M6GWRW (P XP SURFHVVR GH YHUL¿FDomR RQGHDDUPDGXUDpFRQKHFLGDM5GWRWpRPRPHQWRUHVLVWHQWHFDOFXODGRFRPHVVDDUPDGXUDHFRP Nd = N6G = NRd. As variáveis hQMG$ e DEVmRDVPHVPDVGH¿QLGDVQDVXEVHomRDQWHULRU8VXDOPHQWHGXDVRXWUrV LWHUDo}HVVmRVX¿FLHQWHVTXDQGRVHRSWDUSRUXPFiOFXORLWHUDWLYR 2 SURFHVVR DSUR[LPDGR DFLPD HP XP FDVR GH GLPHQVLRQDPHQWR UHFDL QD IRUPXODomR GLUHWD GDGDDEDL[R
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
HPDSHQDVWUrVVHo}HV QDVH[WUHPLGDGHV$H%HHPXPSRQWRLQWHUPHGLiULRRQGHVHDGPLWHDWXDU concomitantemente os momentos MGWRWQDVGXDVGLUHo}HV [H\ 15.8.4 &RQVLGHUDomRGDÀXrQFLD $FRQVLGHUDomRGDÀXrQFLDGHYHREULJDWRULDPHQWHVHUUHDOL]DGDHPSLODUHVFRPtQGLFHGHHVEHOWH] O! HSRGHVHUHIHWXDGDGHPDQHLUDDSUR[LPDGDFRQVLGHUDQGRDH[FHQWULFLGDGHDGLFLRQDOecc dada a seguir: ϕNsg ⎛ ⎞ ⎛ Msg ⎞ N N − e sg ⎜ ⎟ ecc = ⎜ + ea ⎟ 2, 718 −1 ⎟ ⎝ Nsg ⎠⎜ ⎝ ⎠
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© ABNT 2023 - Todos os direitos reservados
111
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ABNT NBR 6118:2023
E DHVEHOWH]OiGHFDGDOkPLQDGHYHVHUPHQRUTXHSRGHQGRRFiOFXORGHVVDHVEHOWH]Oi ser HIHWXDGRDWUDYpVGDH[SUHVVmRGDGDDVHJXLU λi = 3, 46 ei hi RQGHSDUDFDGDOkPLQD ei pRFRPSULPHQWRHTXLYDOHQWH hi pDHVSHVVXUD
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
onde a i
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15.10 ,QVWDELOLGDGHODWHUDOGHYLJDV $VHJXUDQoDjLQVWDELOLGDGHODWHUDOGHYLJDVGHYHVHUJDUDQWLGDDWUDYpVGHSURFHGLPHQWRVDSURSULDGRV &RPRSURFHGLPHQWRDSUR[LPDGRSRGHVHDGRWDUSDUDYLJDVGHFRQFUHWRFRPDUPDGXUDVSDVVLYDV RXDWLYDVVXMHLWDVjÀDPEDJHPODWHUDODVVHJXLQWHVFRQGLo}HV b t 0 b t EÀ h onde b pDODUJXUDGD]RQDFRPSULPLGD h pDDOWXUDWRWDOGDYLJD
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113
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ABNT NBR 6118:2023
0 pRFRPSULPHQWRGRÀDQJHFRPSULPLGRPHGLGRHQWUHVXSRUWHVTXHJDUDQWDPRFRQWUDYHQWDPHQWRODWHUDO EÀ pRFRH¿FLHQWHTXHGHSHQGHGDIRUPDGDYLJD YHU7DEHOD 7DEHOD±9DORUHVGHEÀ Valores de βfl
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114
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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ABNT NBR 6118:2023
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ABNT NBR 6118:2023
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ABNT NBR 6118:2023
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)LJXUD±'RPtQLRVGHHVWDGROLPLWH~OWLPRGHXPDVHomRWUDQVYHUVDO 5XSWXUDFRQYHQFLRQDOSRUGHIRUPDomRSOiVWLFDH[FHVVLYD — UHWDD WUDomRXQLIRUPH — GRPtQLR WUDomRQmRXQLIRUPHVHPFRPSUHVVmR — GRPtQLR ÀH[mRVLPSOHVRXFRPSRVWDVHPUXSWXUDjFRPSUHVVmRGRFRQFUHWR Hc < Hcu e com RPi[LPRDORQJDPHQWRSHUPLWLGR 5XSWXUDFRQYHQFLRQDOSRUHQFXUWDPHQWROLPLWHGRFRQFUHWR — GRPtQLR ÀH[mRVLPSOHV VHomRVXEDUPDGD RXFRPSRVWDFRPUXSWXUDjFRPSUHVVmRGRFRQFUHWR e com escoamento do aço (Hs t Hyd — GRPtQLR ÀH[mRVLPSOHV VHomRVXSHUDUPDGD RXFRPSRVWDFRPUXSWXUDjFRPSUHVVmRGRFRQcreto e aço tracionado sem escoamento (Hs Hyd — GRPtQLRD ÀH[mRFRPSRVWDFRPDUPDGXUDVFRPSULPLGDV — GRPtQLR FRPSUHVVmRQmRXQLIRUPHVHPWUDomR — UHWDE FRPSUHVVmRXQLIRUPH 17.2.3 'XWLOLGDGHHPYLJDV 1DV YLJDV p QHFHVViULR JDUDQWLU ERDV FRQGLo}HV GH GXWLOLGDGH UHVSHLWDQGR RV OLPLWHV GD SRVLomR GDOLQKDQHXWUD [G GDGRVHPVHQGRDGRWDGDVHQHFHVViULRDUPDGXUDGHFRPSUHVVmR $LQWURGXomRGDDUPDGXUDGHFRPSUHVVmRSDUDJDUDQWLURDWHQGLPHQWRGHYDORUHVPHQRUHVGDSRVLomR GDOLQKDQHXWUD [ TXHHVWHMDPQRVGRPtQLRVRXQmRFRQGX]DHOHPHQWRVHVWUXWXUDLVFRPUXSWXUD IUiJLO$UXSWXUDIUiJLOHVWiDVVRFLDGDDSRVLo}HVGDOLQKDQHXWUDQRGRPtQLRFRPRXVHPDUPDGXUD de compressão. 122
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ABNT NBR 6118:2023
17.2.4 Armaduras ativas e passivas 17.2.4.1 *HQHUDOLGDGHV $VIRUoDVQDVDUPDGXUDVSRGHPVHUFRQVLGHUDGDVFRQFHQWUDGDVQRFHQWURGHJUDYLGDGHFRUUHVSRQGHQWH VHDGLVWkQFLDGHVWHFHQWURGHJUDYLGDGHDRFHQWURGDDUPDGXUDPDLVDIDVWDGDPHGLGDQRUPDOPHQWH jOLQKDQHXWUDIRUPHQRUTXHGHh. $VDUPDGXUDVODWHUDLVGHYLJDVSRGHPVHUFRQVLGHUDGDVQRFiOFXORGRVHVIRUoRVUHVLVWHQWHVGHVGH TXHHVWHMDPFRQYHQLHQWHPHQWHDQFRUDGDVHHPHQGDGDV 17.2.4.2 Protensão
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
17.2.4.2.1 *HQHUDOLGDGHV 1DYHUL¿FDomRGR(/8GHYHPVHUFRQVLGHUDGRVDOpPGRHIHLWRGHRXWUDVDo}HVDSHQDVRVHVIRUoRV VROLFLWDQWHVKLSHUHVWiWLFRVGHSURWHQVmR2VLVRVWiWLFRVGHSURWHQVmRQmRSRGHPVHULQFOXtGRV $FRQVLGHUDomRGDVDUPDGXUDVDWLYDVQRVHVIRUoRVUHVLVWHQWHVGHYHVHUIHLWDDSDUWLUGRVGLDJUDPDV WHQVmRGHIRUPDomRHVSHFL¿FDGRVHPHGDFRQVLGHUDomRGRVSUpDORQJDPHQWRVGHODV (VVHV SUpDORQJDPHQWRV GHYHP VHU FDOFXODGRV FRP EDVH QDV WHQV}HV LQLFLDLV GH SURWHQVmR FRP YDORUHVGHFiOFXOR YHU HFRPDFRQVLGHUDomRGHSHUGDVQDLGDGHtHPH[DPH YHU 17.2.4.3 (VWDGROLPLWH~OWLPRQRDWRGDSURWHQVmR 17.2.4.3.1 *HQHUDOLGDGHV $OpP GDV KLSyWHVHV EiVLFDV DSUHVHQWDGDV HP GHYHP DLQGD VHU UHVSHLWDGDV DV VHJXLQWHV KLSyWHVHVVXSOHPHQWDUHV D FRQVLGHUDVH UHVLVWrQFLD FDUDFWHUtVWLFD GR FRQFUHWR fFNM DTXHOD FRUUHVSRQGHQWH j LGDGH ¿FWtFLD j HPGLDV QRDWRGDSURWHQVmRVHQGRTXHDUHVLVWrQFLDGHfFNMGHYHVHUFODUDPHQWHHVSHFL¿FDGD QRSURMHWR E SDUDHVWDYHUL¿FDomRDGPLWHPVHRVVHJXLQWHVYDORUHVSDUDRVFRH¿FLHQWHVGHSRQGHUDomRFRP DVFDUJDVTXHHIHWLYDPHQWHDWXDUHPQHVVDRFDVLmR Jc Js Jp QDSUpWUDomR Jp QDSyVWUDomR JI SDUDDVDo}HVGHVIDYRUiYHLV JI SDUDDVDo}HVIDYRUiYHLV
© ABNT 2023 - Todos os direitos reservados
123
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ABNT NBR 6118:2023
17.2.4.3.2 9HUL¿FDomRVLPSOL¿FDGD $GPLWHVHTXHDVHJXUDQoDHPUHODomRDRHVWDGROLPLWH~OWLPRQRDWRGHSURWHQVmRVHMDYHUL¿FDGDQR HVWiGLR , FRQFUHWR QmR ¿VVXUDGR H FRPSRUWDPHQWR HOiVWLFR OLQHDU GRV PDWHULDLV GHVGH TXH DV VHJXLQWHVFRQGLo}HVVHMDPVDWLVIHLWDV D DWHQVmRPi[LPDGHFRPSUHVVmRQDVHomRGHFRQFUHWRREWLGDDWUDYpVGDVVROLFLWDo}HVSRQGHUDGDV de Ȗp HȖI QmRSRGHXOWUDSDVVDURVVHJXLQWHVYDORUHV fFNM para fck03D >± fFNM± @fFNMSDUD fck 03D
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
E DWHQVmRPi[LPDGHWUDomRGRFRQFUHWRQmRSRGHXOWUDSDVVDUYH]DUHVLVWrQFLDjWUDomR fctm FRUUHVSRQGHQWHDRYDORUfFNMHVSHFL¿FDGR F TXDQGR QDV VHo}HV WUDQVYHUVDLV H[LVWLUHP WHQV}HV GH WUDomR GHYH KDYHU DUPDGXUD GH WUDomR FDOFXODGD QR HVWiGLR ,, 3DUD HIHLWRV GH FiOFXOR QHVVD IDVH GD FRQVWUXomR D IRUoD QHVVD DUPDGXUDSRGHVHUFRQVLGHUDGDLJXDOjUHVXOWDQWHGDVWHQV}HVGHWUDomRQRFRQFUHWRQRHVWiGLR, (VVDIRUoDQmRSRGHSURYRFDUQDDUPDGXUDFRUUHVSRQGHQWHDFUpVFLPRVGHWHQVmRVXSHULRUHV D03DQRFDVRGH¿RVRXEDUUDVOLVDVHD03DHPEDUUDVQHUYXUDGDV 17.2.4.4 (VWDGROLPLWHGHVHUYLoR 'HYHPVHUDWHQGLGDVDVYHUL¿FDo}HVGR(/6HVWDEHOHFLGDVQD7DEHODGHDFRUGRFRPRQtYHOGH SURWHQVmRGH¿QLGRHPSURMHWR 17.2.4.4.1 Limites de tensão de compressão 7HQV}HV GH FRPSUHVVmR H[FHVVLYDV QR FRQFUHWR VRE FDUJDV HP VHUYLoR SRGHP SURYRFDU ¿VVXUDV ORQJLWXGLQDLVHHOHYDGDVSHUGDVGHSURWHQVmRSRUÀXrQFLD3DUDHYLWDUHVVHVHIHLWRVGHYHPVHOLPLWDU DVWHQV}HVGHFRPSUHVVmRGRFRQFUHWRDXPQtYHODSURSULDGR 3DUDSURWHQVmRFRPSOHWD 1tYHO HSURWHQVmROLPLWDGD 1tYHO DVWHQV}HVQRFRQFUHWRHPVHUYLoR FRQVLGHUDQGRDVHomRQmR¿VVXUDGDHDSyVWRGDVDVSHUGDVGHSURWHQVmR QmRSRGHPH[FHGHURV VHJXLQWHVOLPLWHV D QDFRPELQDomRTXDVHSHUPDQHQWH±fFN E QDFRPELQDomRIUHTXHQWH±fFN F QDFRPELQDomRUDUD±fck VRPHQWHSDUDSURWHQVmRFRPSOHWD1tYHO 17.2.4.4.2 Limites de tensão de tração $OLPLWDomRGDVWHQV}HVGHWUDomRQRFRQFUHWRpXPDPHGLGDDGHTXDGDSDUDUHGX]LUDSUREDELOLGDGH GH¿VVXUDomR'HSHQGHQGRGRHVWDGROLPLWHFRQVLGHUDGR(/6)H(/6'GLIHUHQWHVOLPLWHVGHWHQVmR GHYHPVHUDSOLFDGRVWRPDQGRVHFRPREDVHDVHomRQmR¿VVXUDGDGRFRQFUHWR 4XDQGR D WHQVmR GH WUDomR Pi[LPD QR FRQFUHWR QR (/6) YHU D7DEHOD H[FHGHU Į fctm DVHomRSDVVDDWUDEDOKDUQR(VWiGLR,, VHomR¿VVXUDGD 1R(/6'FRQVLGHUDVHDWHQVmROLPLWHQXOD de tração. 124
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ABNT NBR 6118:2023
17.2.5 3URFHVVRDSUR[LPDGRSDUDRGLPHQVLRQDPHQWRjÀH[mRFRPSRVWDREOtTXD 1DVVLWXDo}HVGHÀH[mRREOtTXDVLPSOHVRXFRPSRVWDSRGHVHUDGRWDGDDDSUR[LPDomRGDGDSHOD expressão de interação: α
α
⎡ M Rd,x ⎤ ⎡ M Rd,y ⎤ ⎢ ⎥ +⎢ ⎥ =1 ⎣M Rd,yy ⎦ ⎣M Rd,xx ⎦ onde
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
M5G[ e M5G\
VmR DV FRPSRQHQWHV GR PRPHQWR UHVLVWHQWH GH FiOFXOR HP ÀH[mR REOtTXD FRPSRVWD VHJXQGR RV GRLV HL[RV SULQFLSDLV GH LQpUFLD [ H \ GD VHomR EUXWD FRPXPDIRUoDQRUPDOUHVLVWHQWHGHFiOFXORNRdLJXDOjQRUPDOVROLFLWDQWHN6G. (VVHVVmRRVYDORUHVTXHVHGHVHMDREWHU
M5G[[ e M5G\\ VmRRVPRPHQWRVUHVLVWHQWHVGHFiOFXORVHJXQGRFDGDXPGRVUHIHULGRVHL[RVHP ÀH[mRFRPSRVWDQRUPDOFRPRPHVPRYDORUGHNRd(VVHVYDORUHVVmRFDOFXODGRVDSDUWLUGRDUUDQMRHGDTXDQWLGDGHGHDUPDGXUDHPHVWXGR D
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fct p D UHVLVWrQFLD j WUDomR GLUHWD GR FRQFUHWR FRQIRUPH FRP R TXDQWLO DSURSULDGR DFDGDYHUL¿FDomRSDUWLFXODU3DUDGHWHUPLQDomRGRPRPHQWRGH¿VVXUDomRGHYHVHUXVDGR © ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
o fFWNLQI QR HVWDGROLPLWH GH IRUPDomR GH ¿VVXUDV H R fFWP QR HVWDGROLPLWH GH GHIRUPDomR H[FHVVLYD YHU 1RFDVRGDXWLOL]DomRGHDUPDGXUDVDWLYDVGHYHVHUFRQVLGHUDGRRHIHLWRGDSURWHQVmRQRFiOFXOR GRPRPHQWRGH¿VVXUDomR 17.3.2 (VWDGROLPLWHGHGHIRUPDomR
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
$YHUL¿FDomRGRVYDORUHVOLPLWHVHVWDEHOHFLGRVQD7DEHODSDUDDGHIRUPDomRGDHVWUXWXUDPDLV SURSULDPHQWHURWDo}HVHGHVORFDPHQWRVHPHOHPHQWRVHVWUXWXUDLVOLQHDUHVDQDOLVDGRVLVRODGDPHQWH HVXEPHWLGRVjFRPELQDomRGHDo}HVFRQIRUPHD6HomRGHYHVHUUHDOL]DGDDWUDYpVGHPRGHORVTXH FRQVLGHUHPDULJLGH]HIHWLYDGDVVHo}HVGRHOHPHQWRHVWUXWXUDORXVHMDTXHOHYHPHPFRQVLGHUDomR DSUHVHQoDGDDUPDGXUDDH[LVWrQFLDGH¿VVXUDVQRFRQFUHWRDRORQJRGHVVDDUPDGXUDHDVGHIRUPDo}HVGLIHULGDVQRWHPSR $GHIRUPDomRUHDOGDHVWUXWXUDGHSHQGHWDPEpPGRSURFHVVRFRQVWUXWLYRDVVLPFRPRGDVSURSULHGDGHVGRVPDWHULDLV SULQFLSDOPHQWHGRPyGXORGHHODVWLFLGDGHHGDUHVLVWrQFLDjWUDomR QRPRPHQWR GHVXDHIHWLYDVROLFLWDomR(PIDFHGDJUDQGHYDULDELOLGDGHGRVSDUkPHWURVFLWDGRVH[LVWHXPDJUDQGH YDULDELOLGDGHGDVGHIRUPDo}HVUHDLV1mRVHSRGHHVSHUDUSRUWDQWRJUDQGHSUHFLVmRQDVSUHYLV}HV GHGHVORFDPHQWRVGDGDVSHORVSURFHVVRVDQDOtWLFRVSUHVFULWRV 17.3.2.1 $YDOLDomRDSUR[LPDGDGDÀHFKDHPYLJDV 2PRGHORGHFRPSRUWDPHQWRGDHVWUXWXUDSRGHDGPLWLURFRQFUHWRHRDoRFRPRPDWHULDLVGHFRPSRUWDPHQWRHOiVWLFRHOLQHDUGHPRGRTXHDVVHo}HVDRORQJRGRHOHPHQWRHVWUXWXUDOSRVVDPWHUDV GHIRUPDo}HVHVSHFt¿FDVGHWHUPLQDGDVQRHVWiGLR,GHVGHTXHRVHVIRUoRVQmRVXSHUHPDTXHOHVTXH GmRLQtFLRj¿VVXUDomRHQRHVWiGLR,,HPFDVRFRQWUiULR 'HYH VHU XWLOL]DGR QR FiOFXOR R YDORU GR PyGXOR GH HODVWLFLGDGH VHFDQWH (cs GH¿QLGR QD 6HomR VHQGRREULJDWyULDDFRQVLGHUDomRGRHIHLWRGDÀXrQFLD 17.3.2.1.1 )OHFKDLPHGLDWDHPYLJDVGHFRQFUHWRDUPDGR 3DUDXPDDYDOLDomRDSUR[LPDGDGDÀHFKDLPHGLDWDHPYLJDVSRGHVHXWLOL]DUDH[SUHVVmRGHULJLGH] HTXLYDOHQWHGDGDDVHJXLU ⎧⎪⎛ Mr ⎞ 3 ⎡ ⎛ M r ⎞ 3 ⎤ ⎪⎫ (El )eq,t0 = Ecs ⎨⎜ ⎟ Ic + ⎢1 − ⎜ ⎟ ⎥ III ⎬ ≤ Ecs Ic ⎢⎣ ⎝ Ma ⎠ ⎥⎦ ⎪⎭ ⎪⎩⎝ Ma ⎠ onde Ic pRPRPHQWRGHLQpUFLDGDVHomREUXWDGHFRQFUHWR Es Ecs Ma pRPRPHQWRÀHWRUQDVHomRFUtWLFDGRYmRFRQVLGHUDGRRXVHMDRPRPHQWRPi[LPRQRYmR SDUDYLJDVELDSRLDGDVRXFRQWtQXDVHPRPHQWRQRDSRLRSDUDEDODQoRVSDUDDFRPELQDomR GHDo}HVFRQVLGHUDGDQHVVDDYDOLDomR I,, pRPRPHQWRGHLQpUFLDGDVHomR¿VVXUDGDGHFRQFUHWRQRHVWiGLR,,FDOFXODGRFRPα e =
Mr pRPRPHQWRGH¿VVXUDomRGRHOHPHQWRHVWUXWXUDOFXMRYDORUGHYHVHUUHGX]LGRjPHWDGHQR FDVRGHXWLOL]DomRGHEDUUDVOLVDV (cs pRPyGXORGHHODVWLFLGDGHVHFDQWHGRFRQFUHWR 126
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ABNT NBR 6118:2023
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
3DUDYmRVGHYLJDVFRQWtQXDVTXDQGRIRUQHFHVViULDPDLRUSUHFLVmRSRGHVHDGRWDUSDUDDULJLGH] HTXLYDOHQWHRYDORUSRQGHUDGRFRPRFULWpULRHVWDEHOHFLGRQD)LJXUD
)LJXUD±5LJLGH]HTXLYDOHQWHSDUDYmRVGHYLJDVFRQWtQXDV (P FDGD WUHFKR D ULJLGH] HTXLYDOHQWH GHYH VHU FDOFXODGD FRP (,,, considerando as armaduras H[LVWHQWHVQRWUHFKRHFRPMaLJXDODM1Mv e M2 respectivamente. Pode-se adotar a1C e a2CDSUR[LPDGDPHQWHLJXDLVD 17.3.2.1.2 &iOFXORGDÀHFKDGLIHULGDQRWHPSRSDUDYLJDVGHFRQFUHWRDUPDGR $ ÀHFKD DGLFLRQDO GLIHULGD GHFRUUHQWH GDV FDUJDV GH ORQJD GXUDomR HP IXQomR GD ÀXrQFLD SRGH VHUFDOFXODGDGHPDQHLUDDSUR[LPDGDSHODPXOWLSOLFDomRGDÀHFKDLPHGLDWDSHORIDWRUDIGDGRSHOD expressão: αf =
Δξ 1 + 50ρ'
onde ρ' =
As ' bd
[ pXPFRH¿FLHQWHIXQomRGRWHPSRTXHSRGHVHUREWLGRGLUHWDPHQWHQD7DEHODRXVHU FDOFXODGRSHODVH[SUHVV}HVVHJXLQWHV '[ [(t ±[(t0 [(t t t para t dPHVHV [(t SDUDt!PHVHV © ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
7DEHOD±9DORUHVGRFRH¿FLHQWH[ em função do tempo 7HPSR t meses
0
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
t0 DLGDGHHPPHVHVUHODWLYDjGDWDGHDSOLFDomRGDFDUJDGHORQJDGXUDomRFRQVLGHUDQGRVH como t RPRPHQWRGDFRQFUHWDJHP1RFDVRGHSDUFHODVGDFDUJDGHORQJDGXUDomRVHUHP DSOLFDGDVHPLGDGHVGLIHUHQWHVSRGHVHWRPDUSDUDt0RYDORUSRQGHUDGRDVHJXLU t0 =
ΣP i t0i ΣP i
onde 3i UHSUHVHQWDDVSDUFHODVGHFDUJD t0i pDLGDGHHPTXHVHDSOLFRXFDGDSDUFHOD3iH[SUHVVDHPPHVHV 2YDORUGDÀHFKDWRWDOGHYHVHUREWLGRPXOWLSOLFDQGRDÀHFKDLPHGLDWDSRU DI 17.3.2.1.3 )OHFKDHPYLJDVFRPDUPDGXUDVDWLYDV 1RV HOHPHQWRV HVWUXWXUDLV FRP DUPDGXUDV DWLYDV p VX¿FLHQWH FRQVLGHUDU (, eq = (csIc GHVGH TXH QmR VHMD XOWUDSDVVDGR R HVWDGROLPLWH GH IRUPDomR GH ¿VVXUDV &DVR FRQWUiULR D H[SUHVVmR FRPSOHWD GH SRGH VHU DSOLFDGD GHVGH TXH I,, Mr e Ma VHMDP FDOFXODGRV FRQVLGHUDQGR RHOHPHQWRHVWUXWXUDOGHFRQFUHWRVXEPHWLGRjFRPELQDomRGHDo}HVHVFROKLGDDFUHVFLGDGDSURWHQVmR UHSUHVHQWDGDFRPRDomRH[WHUQDHTXLYDOHQWH JHUDQGRIRUoDQRUPDOHPRPHQWRÀHWRU YHU 3DUDFRQVLGHUDomRGDGHIRUPDomRGLIHULGDQRWHPSREDVWDPXOWLSOLFDUDSDUFHODSHUPDQHQWHGDÀHFKD LPHGLDWDDFLPDUHIHULGDSRU M RQGHMpRFRH¿FLHQWHGHÀXrQFLD YHU 17.3.3 (VWDGROLPLWHGH¿VVXUDomR 17.3.3.1 *HQHUDOLGDGHV (VWD 6HomR GH¿QH RV FULWpULRV SDUD D YHUL¿FDomR GRV YDORUHVOLPLWHV HVWDEHOHFLGRV HP SDUD D DEHUWXUD GH ¿VVXUDV QRV HOHPHQWRV HVWUXWXUDLV OLQHDUHV DQDOLVDGRV LVRODGDPHQWH H VXEPHWLGRV jFRPELQDomRGHDo}HVFRQIRUPHD6HomR 17.3.3.2 &RQWUROHGD¿VVXUDomRDWUDYpVGDOLPLWDomRGDDEHUWXUDHVWLPDGDGDV¿VVXUDV 2 YDORU GD DEHUWXUD GDV ¿VVXUDV SRGH VRIUHU D LQÀXrQFLD GH UHVWULo}HV jV YDULDo}HV YROXPpWULFDV GDHVWUXWXUDGLItFHLVGHVHUHPFRQVLGHUDGDVQHVVDDYDOLDomRGHIRUPDVX¿FLHQWHPHQWHSUHFLVD$OpP GLVVRHVVDDEHUWXUDVRIUHWDPEpPDLQÀXrQFLDGDVFRQGLo}HVGHH[HFXomRGDHVWUXWXUD 128
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
3RUHVVDVUD]}HVRVFULWpULRVDSUHVHQWDGRVDVHJXLUGHYHPVHUHQFDUDGRVFRPRDYDOLDo}HVDFHLWiYHLV GRFRPSRUWDPHQWRJHUDOGRHOHPHQWRPDVQmRJDUDQWHPDYDOLDomRSUHFLVDGDDEHUWXUDGHXPD¿VVXUD HVSHFt¿FD 3DUDFDGDHOHPHQWRRXJUXSRGHHOHPHQWRVGDVDUPDGXUDVSDVVLYDHDWLYDDGHUHQWH H[FOXLQGRVHRV FDERVSURWHQGLGRVTXHHVWHMDPGHQWURGHEDLQKDV TXHFRQWURODPD¿VVXUDomRGRHOHPHQWRHVWUXWXUDO deve ser considerada uma área AcrGRFRQFUHWRGHHQYROYLPHQWRFRQVWLWXtGDSRUXPUHWkQJXORFXMRV ODGRVQmRGLVWHPPDLVGHIGRHL[RGDEDUUDGDDUPDGXUD YHU)LJXUD 127$ eFRQYHQLHQWHTXHWRGDDDUPDGXUDGHSHOHIiGDYLJDQDVXD]RQDWUDFLRQDGDOLPLWHDDEHUWXUD GH¿VVXUDVQDUHJLmRAcriFRUUHVSRQGHQWHHTXHVHMDPDQWLGRXPHVSDoDPHQWRPHQRURXLJXDODI.
Região de envolvimento de φi com área Acri
7,5 φi
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Linha Neutra
7,5 φi
φi Armadura de pele tracionada da viga
φj
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φi σsi 3σsi 12, 5 η1 Esi fctm
wk =
φi σsi ⎛ 4 ⎞ + 45⎟ ⎜ ⎠ 12, 5 η1 Esi ⎝ ρri
onde VsiIi(siUri
VmRGH¿QLGRVSDUDFDGDiUHDGHHQYROYLPHQWRHPH[DPH
Acri
pDiUHDGDUHJLmRGHHQYROYLPHQWRSURWHJLGDSHODEDUUDIi
(si
pRPyGXORGHHODVWLFLGDGHGRDoRGDEDUUDFRQVLGHUDGDGHGLkPHWURIi
Ii
pRGLkPHWURGDEDUUDTXHSURWHJHDUHJLmRGHHQYROYLPHQWRFRQVLGHUDGD
Uri
p D WD[D GH DUPDGXUD SDVVLYD RX DWLYD DGHUHQWH TXH QmR HVWHMD GHQWUR GH EDLQKD HPUHODomRjiUHDGDUHJLmRGHHQYROYLPHQWR Acri
Vsi
pDWHQVmRGHWUDomRQRFHQWURGHJUDYLGDGHGDDUPDGXUDFRQVLGHUDGDFDOFXODGD QRHVWiGLR,,
© ABNT 2023 - Todos os direitos reservados
129
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
1RV HOHPHQWRV HVWUXWXUDLV FRP SURWHQVmR Vsi p R DFUpVFLPR GH WHQVmR QR FHQWUR GH JUDYLGDGH GD DUPDGXUD HQWUH R HVWDGROLPLWH GH GHVFRPSUHVVmR H R FDUUHJDPHQWR FRQVLGHUDGR 'HYH VHU FDOFXODGRQRHVWiGLR,,FRQVLGHUDQGRWRGDDDUPDGXUDDWLYDLQFOXVLYHDTXHODGHQWURGHEDLQKDV 2 FiOFXOR QR HVWiGLR ,, TXH DGPLWH FRPSRUWDPHQWR OLQHDU GRV PDWHULDLV H GHVSUH]D D UHVLVWrQFLD j WUDomR GR FRQFUHWR SRGH VHU IHLWR FRQVLGHUDQGR D UHODomR De HQWUH RV PyGXORV GH HODVWLFLGDGH GRDoRHGRFRQFUHWRLJXDOD K1 p R FRH¿FLHQWH GH FRQIRUPDomR VXSHU¿FLDO GD DUPDGXUD FRQVLGHUDGD GDGR HP SDUD DSDVVLYDHVXEVWLWXtGRSRUKp1SDUDDDWLYDFRQIRUPH 1DVYLJDVXVXDLVFRPDOWXUDPHQRUTXHPSRGHVHFRQVLGHUDUDWHQGLGDDFRQGLomRGHDEHUWXUD GH¿VVXUDVHPWRGDDSHOHWUDFLRQDGDVHDDEHUWXUDGH¿VVXUDVFDOFXODGDQDUHJLmRGDVEDUUDVPDLV WUDFLRQDGDVIRUYHUL¿FDGDHVHH[LVWLUXPDDUPDGXUDODWHUDOTXHDWHQGDDRGHVFULWRHP Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
17.3.3.3 &RQWUROHGD¿VVXUDomRVHPDYHUL¿FDomRGDDEHUWXUDGH¿VVXUDV 3DUDGLVSHQVDUDDYDOLDomRGDJUDQGH]DGDDEHUWXUDGH¿VVXUDVHDWHQGHUDRHVWDGROLPLWHGH¿VVXUDomR SDUDDEHUWXUDVPi[LPDVHVSHUDGDVGDRUGHPGHPPHPFRQFUHWRDUPDGRHPPHPFRQFUHWR FRPDUPDGXUDVDWLYDV XPHOHPHQWRHVWUXWXUDOGHYHVHUGLPHQVLRQDGRUHVSHLWDQGRDVUHVWULo}HVGD 7DEHOD TXDQWR DR GLkPHWUR Pi[LPR Imáx H DR HVSDoDPHQWR Pi[LPR smáx GDV DUPDGXUDV SDVVLYDVEHPFRPRDVH[LJrQFLDVGHFREULPHQWR 6HomR HGHDUPDGXUDPtQLPD YHU A tensão VsiGHYHVHUGHWHUPLQDGDQRHVWiGLR,, 7DEHOD±9DORUHVPi[LPRVGHGLkPHWURHHVSDoDPHQWRFRPEDUUDVGHDOWDDGHUrQFLD Tensão na barra
9DORUHVPi[LPRV &RQFUHWRVHPDUPDGXUDVDWLYDV
&RQFUHWRFRPDUPDGXUDVDWLYDV
Vsi ou 'Vpi MPa
Imáx mm
smáx cm
Imáx mm
smáx cm
160
32
30
20
200
16
240
20
20
10
280
16
8
320
10
6
-
360
10
-
-
400
8
-
-
-
'VpipRDFUpVFLPRGHWHQVmRQDDUPDGXUDSURWHQGLGDDGHUHQWHHQWUHDWRWDOREWLGDQRHVWiGLR,,HD GHSURWHQVmRDSyVDVSHUGDV 17.3.4 (VWDGROLPLWHGHGHVFRPSUHVVmRHGHIRUPDomRGH¿VVXUDV 1RVHOHPHQWRVHVWUXWXUDLVRQGHVHXWLOL]DPDUPDGXUDVGHSURWHQVmRSRGHVHUQHFHVViULDDYHUL¿FDomR GDVHJXUDQoDHPUHODomRDRVHVWDGRVOLPLWHVGHGHVFRPSUHVVmRHGHIRUPDomRGH¿VVXUDV 130
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
(VVDYHUL¿FDomRSRGHVHUIHLWDFDOFXODQGRVH DPi[LPDWHQVmRGHWUDomRGRFRQFUHWRQRHVWiGLR, FRQFUHWRQmR¿VVXUDGRHFRPSRUWDPHQWRHOiVWLFROLQHDUGRVPDWHULDLV 17.3.5 $UPDGXUDV ORQJLWXGLQDLV Pi[LPDV H PtQLPDV 17.3.5.1 Princípios básicos $UXSWXUDIUiJLOGDVVHo}HVWUDQVYHUVDLVTXDQGRGDIRUPDomRGDSULPHLUD¿VVXUDGHYHVHUHYLWDGD FRQVLGHUDQGRVHSDUDRFiOFXORGDVDUPDGXUDVXPPRPHQWRPtQLPRGDGRSHORYDORUFRUUHVSRQGHQWH DR TXH SURGX]LULD D UXSWXUD GD VHomR GH FRQFUHWR VLPSOHV VXSRQGR TXH D UHVLVWrQFLD j WUDomR GR FRQFUHWR VHMD GDGD SRU fFWNVXS GHYHQGR WDPEpP REHGHFHU jV FRQGLo}HV UHODWLYDV DR FRQWUROH GDDEHUWXUDGH¿VVXUDVGDGDVHP
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
$ HVSHFL¿FDomR GH YDORUHV Pi[LPRV SDUD DV DUPDGXUDV GHFRUUH GD QHFHVVLGDGH GH VH DVVHJXUDU FRQGLo}HV GH GXWLOLGDGH H GH VH UHVSHLWDU R FDPSR GH YDOLGDGH GRV HQVDLRV TXH GHUDP RULJHP jV SUHVFULo}HVGHIXQFLRQDPHQWRGRFRQMXQWRDoRFRQFUHWR 17.3.5.2 9DORUHVOLPLWHV SDUD DUPDGXUDV ORQJLWXGLQDLV GH YLJDV 17.3.5.2.1 Armadura de tração $DUPDGXUDPtQLPDGHWUDomRHPHOHPHQWRVHVWUXWXUDLVDUPDGRVRXSURWHQGLGRVGHYHVHUGHWHUPLQDGD SHORGLPHQVLRQDPHQWRGDVHomRDXPPRPHQWRÀHWRUPtQLPRGDGRSHODH[SUHVVmRDVHJXLUUHVSHLWDGD DWD[DPtQLPDDEVROXWDGH MGPtQ W0IFWNVXS onde W0
p R PyGXOR GH UHVLVWrQFLD GD VHomR WUDQVYHUVDO EUXWD GH FRQFUHWR UHODWLYR j ¿EUD PDLV WUDFLRQDGD
fFWNVXS pDUHVLVWrQFLDFDUDFWHUtVWLFDVXSHULRUGRFRQFUHWRjWUDomR YHU $OWHUQDWLYDPHQWHDDUPDGXUDPtQLPDSRGHVHUFRQVLGHUDGDDWHQGLGDVHIRUHPUHVSHLWDGDVDVWD[DV PtQLPDVGHDUPDGXUDGD7DEHOD 7DEHOD ± 7D[DV PtQLPDV GH DUPDGXUD GH ÀH[mR SDUD YLJDV FRP VHomR WUDQVYHUVDO UHWDQJXODU
© ABNT 2023 - Todos os direitos reservados
131
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
(PHOHPHQWRVHVWUXWXUDLVH[FHWRHOHPHQWRVHPEDODQoRFXMDVDUPDGXUDVVHMDPFDOFXODGDVFRPXP PRPHQWRÀHWRULJXDORXPDLRUDRGREURGHMdQmRpQHFHVViULRDWHQGHUjDUPDGXUDPtQLPD1HVWH FDVRDGHWHUPLQDomRGRVHVIRUoRVVROLFLWDQWHVGHYHFRQVLGHUDU GHIRUPDULJRURVDWRGDVDVFRPELQDo}HVSRVVtYHLVGHFDUUHJDPHQWRDVVLPFRPRRVHIHLWRVGHWHPSHUDWXUDGHIRUPDo}HVGLIHULGDVH UHFDOTXHVGHDSRLR'HYHVHWHUDLQGDHVSHFLDOFXLGDGRFRPRGLkPHWURHHVSDoDPHQWRGDVDUPDGXUDVGHOLPLWDomRGH¿VVXUDomR 17.3.5.2.2 9DORUHVPtQLPRVSDUDDDUPDGXUDGHWUDomRVREGHIRUPDo}HVLPSRVWDV (PHOHPHQWRVHVWUXWXUDLVRQGHRFRQWUROHGD¿VVXUDomRVHMDLPSUHVFLQGtYHOSRUUD]}HVGHHVWDQTXHLGDGH RXHVWpWLFDVQDIDOWDGHXPPpWRGRPDLVULJRURVRGHDYDOLDomRGRVHVIRUoRVJHUDGRVSHODUHVWULomR GHGHIRUPDo}HVLPSRVWDVHGHVGHTXHVHMDPWRPDGDVPHGLGDVWHFQROyJLFDVTXHUHVWULQMDPHVVHV HVIRUoRVDDUPDGXUDPtQLPDGHWUDomRSDUDFRQWUROHGD¿VVXUDomRSRGHVHUFDOFXODGDSHODUHODomR
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
As = N Nc fFWHI ActVs onde A s
pDiUHDGHDUPDGXUDQD]RQDWUDFLRQDGD
Act
pDiUHDGHFRQFUHWRQD]RQDWUDFLRQDGD
Vs
p D WHQVmR Pi[LPD SHUPLWLGD QD DUPDGXUD LPHGLDWDPHQWH DSyV D IRUPDomR GD ¿VVXUD 8PYDORUPHQRUTXHDUHVLVWrQFLDGHHVFRDPHQWRSRGHVHUQHFHVViULRSDUDVDWLVID]HURV OLPLWHVGHDEHUWXUDGH¿VVXUDV YHU7DEHOD
fFWHI pDUHVLVWrQFLDPpGLDjWUDomRHIHWLYDGRFRQFUHWRQRLQVWDQWHHPTXHVHIRUPDPDVSULPHLUDV ¿VVXUDV (P PXLWRV FDVRV ± FRPR DTXHOHV HP TXH DV GHIRUPDo}HV SUHSRQGHUDQWHV LPSRVWDV UHVXOWDP GH GLVVLSDomR GR FDORU GH KLGUDWDomR ± LVVR SRGH RFRUUHU HP LGDGH HQWUHGLDHGLDVDSyVDPROGDJHPDGHSHQGHUGDVFRQGLo}HVDPELHQWHVGDIRUPDGR HOHPHQWRHVWUXWXUDOGDQDWXUH]DGDVIRUPDVHGRWLSRGHFLPHQWRXWLOL]DGR9DORUHVGHfFWHI SRGHPVHUREWLGRVFRPDX[tOLRGDVHTXDo}HVGHDGRWDQGRDUHVLVWrQFLDGRFRQFUHWRj FRPSUHVVmRQDLGDGHHPTXHVHVXS}HDRFRUUrQFLDGD¿VVXUDomR4XDQGRHVVDLGDGHQmR SXGHUVHUGH¿QLGDFRPYDORUFRQ¿iYHOUHFRPHQGDVHDGRWDUYDORUPtQLPRGHUHVLVWrQFLDj WUDomRLJXDOD03D N
pXPFRH¿FLHQWHTXHFRQVLGHUDRVPHFDQLVPRVGHJHUDomRGHWHQV}HVGHWUDomR
D QRFDVRGHGHIRUPDo}HVLPSRVWDVLQWUtQVHFDV — QRFDVRJHUDOGHIRUPDGHVHomR N — HPVHo}HVUHWDQJXODUHV N SDUDKdP — N SDUDKtP — LQWHUSRODUOLQHDUPHQWHRVYDORUHVGHNSDUDYDORUHVGHKHQWUHPHP E QRFDVRGHGHIRUPDo}HVLPSRVWDVH[WUtQVHFDV N Nc
p XP FRH¿FLHQWH TXH FRQVLGHUD D QDWXUH]D GD GLVWULEXLomR GH WHQV}HV QD VHomR LPHGLDWDPHQWHDQWHVGD¿VVXUDomRFRPRVVHJXLQWHVYDORUHV
— kc SDUDWUDomRSXUD 132
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
— Nc SDUDÀH[mRVLPSOHV — Nc SDUDDVQHUYXUDVGHHOHPHQWRVHVWUXWXUDLVSURWHQGLGRVRXVREÀH[mRFRPSRVWDHP VHo}HVYD]DGDV FHOXODURXFDL[mR — Nc SDUDDPHVDWUDFLRQDGDGHHOHPHQWRVHVWUXWXUDLVSURWHQGLGRVRXVREÀH[mRFRPSRVWD HPVHo}HVYD]DGDV FHOXODURXFDL[mR — R YDORU GH Nc SRGH VHU LQWHUSRODGR HQWUH FRUUHVSRQGHQWH DR FDVR GH ÀH[mR VLPSOHV H ]HUR TXDQGR D DOWXUD GD ]RQD WUDFLRQDGD FDOFXODGD QR HVWiGLR ,, VRE RV HVIRUoRV TXH FRQGX]HPDRLQtFLRGD¿VVXUDomRQmRH[FHGHURPHQRUGRVGRLVYDORUHV hHP
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
17.3.5.2.3 $UPDGXUDGHSHOH $PtQLPDDUPDGXUDODWHUDOGHYHVHUAFDOPDHPFDGDIDFHGDDOPDGDYLJDHFRPSRVWDSRU EDUUDVGH&$RX&$FRPHVSDoDPHQWRQmRPDLRUTXHFPHGHYLGDPHQWHDQFRUDGDQRV DSRLRVUHVSHLWDGRRGLVSRVWRHPQmRVHQGRQHFHVViULDXPDDUPDGXUDVXSHULRUDFP2P SRUIDFH (PYLJDVFRPDOWXUDLJXDORXLQIHULRUDFPSRGHVHUGLVSHQVDGDDXWLOL]DomRGDDUPDGXUDGHSHOH $V DUPDGXUDV SULQFLSDLV GH WUDomR H GH FRPSUHVVmR QmR SRGHP VHU FRPSXWDGDV QR FiOFXOR GD DUPDGXUDGHSHOH 17.3.5.2.4 Armaduras de tração e de compressão A soma das armaduras de tração e de compressão (AsAs¶ QmRSRGHWHUYDORUPDLRUTXHAc FDOFXODGD QD UHJLmR IRUD GD ]RQD GH HPHQGDV GHYHQGR VHU JDUDQWLGDV DV FRQGLo}HV GH GXWLOLGDGH requeridas em 14.6.4.3. 17.3.5.3 9DORUHVOLPLWHVSDUDDUPDGXUDVORQJLWXGLQDLVGHSLODUHV 17.3.5.3.1 9DORUHVPtQLPRV $DUPDGXUDORQJLWXGLQDOPtQLPDGHYHVHU AVPtQ Ndfyd tAc 17.3.5.3.2 9DORUHVPi[LPRV AVPi[ Ac $ Pi[LPD DUPDGXUD SHUPLWLGD HP SLODUHV GHYH FRQVLGHUDU LQFOXVLYH D VREUHSRVLomR GH DUPDGXUD H[LVWHQWHHPUHJL}HVGHHPHQGDGHYHQGRVHUWDPEpPUHVSHLWDGRRGLVSRVWRHP
17.4 (OHPHQWRVOLQHDUHVVXMHLWRVjIRUoDFRUWDQWH(VWDGROLPLWH~OWLPR 17.4.1 Hipóteses básicas $VSUHVFULo}HVDVHJXLUDSOLFDPVHDHOHPHQWRVOLQHDUHVDUPDGRVRXSURWHQGLGRVVXEPHWLGRVDIRUoDV FRUWDQWHVHYHQWXDOPHQWHFRPELQDGDVFRPRXWURVHVIRUoRVVROLFLWDQWHV © ABNT 2023 - Todos os direitos reservados
133
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
1mRVHDSOLFDPDHOHPHQWRVGHYROXPHODMHVYLJDVSDUHGHHFRQVRORVFXUWRVTXHVmRWUDWDGRVHP RXWUDV6Ho}HVGHVWD1RUPD $V FRQGLo}HV ¿[DGDV SRU HVWD 1RUPD SDUD HOHPHQWRV OLQHDUHV DGPLWHP GRLV PRGHORV GH FiOFXOR TXHSUHVVXS}HPDDQDORJLDFRPPRGHORHPWUHOLoDGHEDQ]RVSDUDOHORVDVVRFLDGRDPHFDQLVPRV UHVLVWHQWHVFRPSOHPHQWDUHV GHVHQYROYLGRV QRLQWHULRUGRHOHPHQWR HVWUXWXUDOHWUDGX]LGRV SRUXPD FRPSRQHQWHDGLFLRQDOVc. 17.4.1.1 &RQGLo}HVJHUDLV 17.4.1.1.1 7RGRV RV HOHPHQWRV OLQHDUHV VXEPHWLGRV D IRUoD FRUWDQWH FRP H[FHomR GRV FDVRV LQGLFDGRV HP GHYHP FRQWHU DUPDGXUD WUDQVYHUVDO PtQLPD FRQVWLWXtGD SRU HVWULERV FRP WD[DJHRPpWULFD
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
ρsw =
fct,m Asw ≥ 0, 2 bw s senα fywk
onde Asw
pDiUHDGDVHomRWUDQVYHUVDOGRVHVWULERV
s
pRHVSDoDPHQWRGRVHVWULERVPHGLGRVHJXQGRRHL[RORQJLWXGLQDOGRHOHPHQWRHVWUXWXUDO
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pDLQFOLQDomRGRVHVWULERVHPUHODomRDRHL[RORQJLWXGLQDOGRHOHPHQWRHVWUXWXUDO
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pDODUJXUDPpGLDGDDOPDPHGLGDDRORQJRGDDOWXUD~WLOGDVHomRUHVSHLWDGDDUHVWULomR LQGLFDGDHP
fywk
pDUHVLVWrQFLDFDUDFWHUtVWLFDDRHVFRDPHQWRGRDoRGDDUPDGXUDWUDQVYHUVDO
fFWP
pGDGRHP
17.4.1.1.2 6mRH[FHomRDRGHVFULWRHP D RVHOHPHQWRVHVWUXWXUDLVOLQHDUHVFRPbw!d (em que dpDDOWXUD~WLOGDVHomR FDVRTXHGHYH VHUWUDWDGRFRPRODMH YHU E DVQHUYXUDVGHODMHVQHUYXUDGDVGHVFULWDVHPD HE TXHWDPEpPSRGHPVHUYHUL¿FDGDV FRPRODMHV1HVVHFDVRGHYHVHUWRPDGDFRPREDVHDVRPDGDVODUJXUDVGDVQHUYXUDVQRWUHFKR FRQVLGHUDGR SRGHQGR VHU GLVSHQVDGD D DUPDGXUD WUDQVYHUVDO TXDQGR DWHQGLGR R GLVSRVWR HP F RVSLODUHVHHOHPHQWRVOLQHDUHVGHIXQGDomRVXEPHWLGRVSUHGRPLQDQWHPHQWHjFRPSUHVVmRTXH DWHQGDPVLPXOWDQHDPHQWHQDFRPELQDomRPDLVGHVIDYRUiYHOGDVDo}HVHPHVWDGROLPLWH~OWLPR FDOFXODGDDVHomRHPHVWiGLR,jVFRQGLo}HVVHJXLQWHV — HPQHQKXPSRQWRGHYHVHUXOWUDSDVVDGDDWHQVmRfctk — V6Gd VcVHQGRVcGH¿QLGRHP 1HVVHFDVRDDUPDGXUDWUDQVYHUVDOPtQLPDpDGH¿QLGDQD6HomR 134
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
17.4.1.1.3 $ DUPDGXUD WUDQVYHUVDO Asw SRGH VHU FRQVWLWXtGD SRU HVWULERV IHFKDGRV QD UHJLmR GH DSRLRGDVGLDJRQDLVHQYROYHQGRDDUPDGXUDORQJLWXGLQDO RXSHODFRPSRVLomRGHHVWULERVHEDUUDV GREUDGDV HQWUHWDQWRTXDQGRIRUHPXWLOL]DGDVEDUUDVGREUDGDVHVWDVQmRSRGHPVXSRUWDUPDLVGR TXHGRHVIRUoRWRWDOUHVLVWLGRSHODDUPDGXUD 17.4.1.1.4 3RGHPVHUXWLOL]DGDVEDUUDVYHUWLFDLVVROGDGDVFRPELQDGDVFRPHVWULERVIHFKDGRVPDQWLGD DSURSRUomRUHVLVWHQWHHVWDEHOHFLGDHPTXDQGRHVVDVEDUUDVIRUHPDQFRUDGDVGHDFRUGR FRP (QWUHWDQWR TXDQGR HVVDV EDUUDV QmR IRUHP FRPELQDGDV FRP HVWULERV QD SURSRUomR LQGLFDGD HP RV HOHPHQWRV ORQJLWXGLQDLV VROGDGRV GHYHP REULJDWRULDPHQWH FRQVWLWXLU DWRWDOLGDGHGDDUPDGXUDORQJLWXGLQDOGHWUDomR 17.4.1.1.5 2 kQJXOR GH LQFOLQDomR D GDV DUPDGXUDV WUDQVYHUVDLV HP UHODomR DR HL[R ORQJLWXGLQDO GRHOHPHQWRHVWUXWXUDOGHYHHVWDUVLWXDGRQRLQWHUYDORd Dd
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
17.4.1.1.6 2VHVSDoDPHQWRVPi[LPRVHPtQLPRVHQWUHHOHPHQWRVGDDUPDGXUDGHYHPDWHQGHUjV H[LJrQFLDVGD6HomR 17.4.1.2 &RQGLo}HV UHODWLYDV DRV HVIRUoRV VROLFLWDQWHV 17.4.1.2.1 &DUJDV SUy[LPDV DRV DSRLRV 3DUDRFiOFXORGDDUPDGXUDWUDQVYHUVDOQRFDVRGHDSRLRGLUHWR VHDFDUJDHDUHDomRGHDSRLRIRUHP DSOLFDGDVHPIDFHVRSRVWDVGRHOHPHQWRHVWUXWXUDOFRPSULPLQGRR YDOHPDVVHJXLQWHVSUHVFULo}HV D
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E
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$VUHGXo}HVLQGLFDGDVQHVWDVHomRQmRVHDSOLFDPjYHUL¿FDomRGDUHVLVWrQFLDjFRPSUHVVmRGLDJRQDO GRFRQFUHWR1RFDVRGHDSRLRVLQGLUHWRVHVVDVUHGXo}HVWDPEpPQmRVmRSHUPLWLGDV 17.4.1.2.2 (IHLWR GD FRPSRQHQWH WDQJHQFLDO GD IRUoD GH SURWHQVmR 1RYDORUGHV6GGHYHVHUFRQVLGHUDGRRHIHLWRGDSURMHomRGDIRUoDGHSURWHQVmRQDVXDGLUHomRFRP RYDORUGHFiOFXORFRUUHVSRQGHQWHDRWHPSRtFRQVLGHUDGR(QWUHWDQWRTXDQGRHVVHHIHLWRIRUIDYRUiYHO DDUPDGXUDORQJLWXGLQDOGHWUDomRMXQWRjIDFHWUDFLRQDGDSRUÀH[mRGHYHVDWLVID]HUDFRQGLomR Ap fpydAs fyd t V6G 17.4.1.2.3 (OHPHQWRV HVWUXWXUDLV FRP DOWXUD YDULiYHO $IRUoDFRUWDQWHTXHpUHVLVWLGDSHODDOPDGDVYLJDVGHDOWXUDYDULiYHOSRGHVHUDYDOLDGDSRU
onde V6GUHG
pDIRUoDFRUWDQWHUHGX]LGDFRQVLGHUDQGRRHIHLWRGHDOWXUDYDULiYHO
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
Ec
pRkQJXORHQWUHREDQ]RGHFRPSUHVVmRHRHL[RORQJLWXGLQDOGRHOHPHQWRHVWUXWXUDO
Et
pRkQJXORHQWUHDDUPDGXUDGHWUDomRHRHL[RORQJLWXGLQDOGRHOHPHQWRHVWUXWXUDO
T
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z pREUDoRGHDODYDQFDGDVIRUoDVUHVXOWDQWHVLQWHUQDV 2VVLQDLVGHEc eEtGHYHPVHUREWLGRVFRQVLGHUDQGRRVHQWLGRGDVIRUoDV¿QDLVGHFRPSUHVVmRHGH WUDomRGDÀH[mRFRPDIRUoDFRUWDQWHFRQFRPLWDQWH $H[SUHVVmRDFLPDFRQVLGHUDDUHGXomRGDIRUoDGHFRPSUHVVmRQDÀH[mRTXDQGRH[LVWHIRUoDFRUWDQWH concomitante.
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
17.4.2 9HUL¿FDomRGRHVWDGROLPLWH~OWLPR 17.4.2.1 &iOFXORGDUHVLVWrQFLD $UHVLVWrQFLDGRHOHPHQWRHVWUXWXUDOHPXPDGHWHUPLQDGDVHomRWUDQVYHUVDOGHYHVHUFRQVLGHUDGD VDWLVIDWyULDTXDQGRYHUL¿FDGDVVLPXOWDQHDPHQWHDVVHJXLQWHVFRQGLo}HV V6Gd VRd2 V6Gd VRd3 = VcVsw onde V6G
pDIRUoDFRUWDQWHVROLFLWDQWHGHFiOFXORQDVHomR
VRd2
p D IRUoD FRUWDQWH UHVLVWHQWH GH FiOFXOR UHODWLYD j UXtQD GDV GLDJRQDLV FRPSULPLGDVGHFRQFUHWRGHDFRUGRFRPRVPRGHORVLQGLFDGRVHPRX
VRd3 = Vc Vsw pDIRUoDFRUWDQWHUHVLVWHQWHGHFiOFXORUHODWLYDjUXtQDSRUWUDomRGLDJRQDORQGH VcpDSDUFHODGHIRUoDFRUWDQWHDEVRUYLGDSRUPHFDQLVPRVFRPSOHPHQWDUHVDR GDWUHOLoDHVswDSDUFHODUHVLVWLGDSHODDUPDGXUDWUDQVYHUVDOGHDFRUGRFRP RVPRGHORVLQGLFDGRVHPRX 1D UHJLmR GRV DSRLRV RV FiOFXORV GHYHP FRQVLGHUDU DV IRUoDV FRUWDQWHV DJHQWHV QDV UHVSHFWLYDV IDFHVOHYDQGRHPFRQWDDVUHGXo}HVSUHVFULWDVHP 17.4.2.2 0RGHORGHFiOFXOR, 2PRGHOR,DGPLWHGLDJRQDLVGHFRPSUHVVmRLQFOLQDGDVGHT HPUHODomRDRHL[RORQJLWXGLQDO GR HOHPHQWR HVWUXWXUDO H DGPLWH DLQGD TXH D SDUFHOD FRPSOHPHQWDU Vc WHQKD YDORU FRQVWDQWH independentemente de V6G. D YHUL¿FDomRGDFRPSUHVVmRGLDJRQDOGRFRQFUHWR VRd2 Dv2 fcd bw d 136
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ABNT NBR 6118:2023
onde Dv2 ífck HfckH[SUHVVRHPPHJDSDVFDO 03D E FiOFXORGDDUPDGXUDWUDQVYHUVDO VRd3 = VcVsw onde Vsw = (AswV d fywd (sen DFRVD Vc QRVHOHPHQWRVHVWUXWXUDLVWUDFLRQDGRVTXDQGRDOLQKDQHXWUDVHVLWXDIRUDGDVHomR Vc 9c0QDÀH[mRVLPSOHVHQDÀH[RWUDomRFRPDOLQKDQHXWUDFRUWDQGRDVHomR
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Vc 9c0 MoM6GPi[ d 2Vc0QDÀH[RFRPSUHVVmR Vc0 fctd bw d fctd = fFWNLQIJc onde b w
pDPHQRUODUJXUDGDVHomRFRPSUHHQGLGDDRORQJRGDDOWXUD~WLOd HQWUHWDQWRQRFDVR GHHOHPHQWRVHVWUXWXUDLVSURWHQGLGRVTXDQGRH[LVWLUHPEDLQKDVLQMHWDGDVFRPGLkPHWUR I > bwDODUJXUDUHVLVWHQWHDFRQVLGHUDUGHYHVHU bw±6I QDSRVLomRGDDOPDHP TXHHVVDGLIHUHQoDVHMDPDLVGHVIDYRUiYHOFRPH[FHomRGRQtYHOTXHGH¿QHREDQ]R WUDFLRQDGRGDYLJD
d
pDDOWXUD~WLOGDVHomRLJXDOjGLVWkQFLDGDERUGDFRPSULPLGDDRFHQWURGHJUDYLGDGH GDDUPDGXUDGHWUDomR HQWUHWDQWRQRFDVRGHHOHPHQWRVHVWUXWXUDLVSURWHQGLGRVFRP FDERVGLVWULEXtGRVDRORQJRGDDOWXUDdQmRSUHFLVDVHUWRPDGRFRPYDORUPHQRUTXH hGHVGHTXHH[LVWDDUPDGXUDMXQWRjIDFHWUDFLRQDGDGHIRUPDDVDWLVID]HURGHVFULWR HP
s
pRHVSDoDPHQWRHQWUHHOHPHQWRVGDDUPDGXUDWUDQVYHUVDOAswPHGLGRVHJXQGRRHL[R ORQJLWXGLQDOGRHOHPHQWRHVWUXWXUDO
fywd
pDWHQVmRQDDUPDGXUDWUDQVYHUVDOSDVVLYDOLPLWDGDDRYDORUfydQRFDVRGHHVWULERV HDGHVVHYDORUQRFDVRGHEDUUDVGREUDGDVQmRVHWRPDQGRSDUDDPERVRVFDVRV YDORUHV VXSHULRUHV D 03D HQWUHWDQWR QR FDVR GH DUPDGXUDV WUDQVYHUVDLV DWLYDV RDFUpVFLPRGHWHQVmRGHYLGDjIRUoDFRUWDQWHQmRSRGHXOWUDSDVVDUDGLIHUHQoDHQWUH fpydHDWHQVmRGHSURWHQVmRQHPVHUVXSHULRUD03D
D
p R kQJXOR GH LQFOLQDomR GD DUPDGXUD WUDQVYHUVDO HP UHODomR DR HL[R ORQJLWXGLQDO GR HOHPHQWRHVWUXWXUDOSRGHQGRVHWRPDUd D d
M0
pRYDORUGRPRPHQWRÀHWRUTXHDQXODDWHQVmRQRUPDOGHFRPSUHVVmRQDERUGDGDVHomR tracionada por M6GPi[SURYRFDGDSHORVHVIRUoRVLVRVWiWLFRVGHSURWHQVmRHSHODVIRUoDV normais de diversas origens concomitantes com V6GVHQGRHVVDWHQVmRFDOFXODGDFRP YDORUHVGHȖI e ȖpLJXDLVDH UHVSHFWLYDPHQWH RVPRPHQWRVFRUUHVSRQGHQWHV DHVVDVIRUoDVQRUPDLVQmRSRGHPVHUFRQVLGHUDGRVQRFiOFXORGHVVDWHQVmRSRLVVmR
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
considerados em M6GPi[ GHYHPVHUFRQVLGHUDGRVDSHQDVRVPRPHQWRVLVRVWiWLFRVGH SURWHQVmR GHYHPVHUFRQVLGHUDGDVWRGDVDVSHUGDVGHSURWHQVmRQDGHWHUPLQDomRGDV IRUoDVQRUPDLVHGRVPRPHQWRVLVRVWiWLFRVGHSURWHQVmR ⎛W ⎞ ⎛W ⎞ 0 = 3G ⎜ 1 + HS ⎟ + 16G ⎜ 1⎟ VHQGRW1RPyGXORGHUHVLVWrQFLDQD¿EUDPDLVWUDFLRQDGD ⎝ Ac ⎠ ⎝ Ac ⎠ M6GPi[ pRPRPHQWRÀHWRUGHFiOFXORPi[LPRQDVHomRHPDQiOLVH DOWHUQDWLYDPHQWHSRGHVHU WRPDGRDSHQDVQDVHomRFRPPDLRUYDORUGHM6GPi[QRVHPLWUDPRHPDQiOLVHQHVVH FDVR D UHODomR M0M6GPi[ ¿FD FRQVWDQWH QR VHPLWUDPR H M0 GHYH VHU FDOFXODGR QD mesma seção que atua M6GPi[ RVPRPHQWRVLVRVWiWLFRVGHSURWHQVmRQmRSRGHPVHU FRQVLGHUDGRVQHVVHFiOFXORDSHQDVRVKLSHUHVWiWLFRV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
F GHFDODJHPGRGLDJUDPDGHIRUoDQREDQ]RWUDFLRQDGR 4XDQGRDDUPDGXUDORQJLWXGLQDOGHWUDomRIRUGHWHUPLQDGDDWUDYpVGRHTXLOtEULRGHHVIRUoRVQDVHomR QRUPDODRHL[RGRHOHPHQWRHVWUXWXUDORVHIHLWRVSURYRFDGRVSHOD¿VVXUDomRREOtTXDSRGHPVHUVXEVWLWXtGRVQRFiOFXORSHODGHFDODJHPGRGLDJUDPDGHIRUoDQREDQ]RWUDFLRQDGRGDGDSHODH[SUHVVmR VSd,máx ⎡ ⎤ a = d ⎢ (1 + cotg α ) − cotg α ⎥ ≤ d ⎣ 2 (VSd,máx − Vc ) ⎦ onde a = dSDUD_VVGPi[ | d |Vc| a tdQRFDVRJHUDO a tdSDUDHVWULERVLQFOLQDGRVD (VVDGHFDODJHPSRGHVHUVXEVWLWXtGDDSUR[LPDGDPHQWHSHODFRUUHVSRQGHQWHGHFDODJHPGRGLDJUDPD GHPRPHQWRVÀHWRUHV $ GHFDODJHP GR GLDJUDPD GH IRUoD QR EDQ]R WUDFLRQDGR SRGH WDPEpP VHU REWLGD VLPSOHVPHQWH HPSUHJDQGRDIRUoDGHWUDomRHPFDGDVHomRGDGDSHODH[SUHVVmR
)6GFRU =
M6G a M6GPi[ + 96G ≤ z d zmáx
onde M6GPi[
pRPRPHQWRÀHWRUGHFiOFXORPi[LPRQRWUHFKRHPDQiOLVH
zmáx
RYDORUGH]TXHFRUUHVSRQGHDRYDORUGHM6GPi[.
17.4.2.3 0RGHORGHFiOFXOR,, 2PRGHOR,,DGPLWHGLDJRQDLVGHFRPSUHVVmRLQFOLQDGDVGHTHPUHODomRDRHL[RORQJLWXGLQDOGRHOHPHQWR HVWUXWXUDO FRP T YDULiYHO OLYUHPHQWH HQWUH H $GPLWH DLQGD TXH D SDUFHOD FRPSOHPHQWDU VcVRIUDUHGXomRFRPRDXPHQWRGH V6G. D YHUL¿FDomRGDFRPSUHVVmRGLDJRQDOGRFRQFUHWR VRd2 Dv2 fcd bw d sen2 T (cotg DFRWJT com: Dv2 ±fck HfckHPPHJDSDVFDO 138
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ABNT NBR 6118:2023
E FiOFXORGDDUPDGXUDWUDQVYHUVDO VRd3 = VcVsw onde Vsw = (AswV d fywd (cotg DFRWJT VHQD Vc HPHOHPHQWRVHVWUXWXUDLVWUDFLRQDGRVTXDQGRDOLQKDQHXWUDVHVLWXDIRUDGDVHomR Vc = Vc1QDÀH[mRVLPSOHVHQDÀH[RWUDomRFRPDOLQKDQHXWUDFRUWDQGRDVHomR Vc = Vc1 M0M6GPi[ Vc1QDÀH[RFRPSUHVVmRFRP
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Vc1 = Vc0 quando V6Gd Vc0 Vc1 = 0 quando V6G = VRd2LQWHUSRODQGRVHOLQHDUPHQWHSDUDYDORUHVLQWHUPHGLiULRV 6mRPDQWLGDVDQRWDomRHDVOLPLWDo}HVGH¿QLGDVHP F GHVORFDPHQWRGRGLDJUDPDGHPRPHQWRVÀHWRUHV 6HIRUHPPDQWLGDVDVFRQGLo}HVHVWDEHOHFLGDVHPF RGHVORFDPHQWRGRGLDJUDPDGHPRPHQWRVÀHWRUHVDSOLFDQGRRSURFHVVRGHVFULWRQHVWD6HomRGHYHVHU ⎡ V6GPi[ ⎤ a = , d ⎢ ( FRWJθ + FRWJα ) − FRWJα ⎥ ≤ d ⎣(V6GPi[ − VF ) ⎦ onde a tdQRFDVRJHUDO atdSDUDHVWULERVLQFOLQDGRVD 3HUPDQHFHYiOLGDSDUDRPRGHOR,,DDOWHUQDWLYDSDUDDREWHQomRGDIRUoDGHWUDomRGDGDHPF
17.5 (OHPHQWRVOLQHDUHVVXMHLWRVjWRUomRí(VWDGROLPLWH~OWLPR 17.5.1 Torção uniforme 17.5.1.1 *HQHUDOLGDGHV $VFRQGLo}HV¿[DGDVSRUHVWD1RUPDSUHVVXS}HPXPPRGHORUHVLVWHQWHFRQVWLWXtGRSRUWUHOLoDHVSDFLDO GH¿QLGD D SDUWLU GH XP HOHPHQWR HVWUXWXUDO GH VHomR YD]DGD HTXLYDOHQWH DR HOHPHQWR HVWUXWXUDO a dimensionar. $VGLDJRQDLVGHFRPSUHVVmRGHVVDWUHOLoDIRUPDGDSRUHOHPHQWRVGHFRQFUHWRWrPLQFOLQDomRTXH SRGHVHUDUELWUDGDSHORSURMHWRQRLQWHUYDORd T d 17.5.1.2 &RQGLo}HVJHUDLV 6HPSUH TXH D WRUomR IRU QHFHVViULD DR HTXLOtEULR GR HOHPHQWR HVWUXWXUDO GHYH H[LVWLU DUPDGXUD GHVWLQDGDDUHVLVWLUDRVHVIRUoRVGHWUDomRRULXQGRVGDWRUomR(VVDDUPDGXUDGHYHVHUFRQVWLWXtGDSRU HVWULERVYHUWLFDLVSHULIpULFRVQRUPDLVDRHL[RGRHOHPHQWRHVWUXWXUDOHEDUUDVORQJLWXGLQDLVGLVWULEXtGDV © ABNT 2023 - Todos os direitos reservados
139
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
DR ORQJR GR SHUtPHWUR GD VHomR UHVLVWHQWH FDOFXODGD GH DFRUGR FRP DV SUHVFULo}HV GHVWD 6HomR HFRPDWD[DJHRPpWULFDPtQLPDGDGDSHODH[SUHVVmR As ⎫ heue ⎪⎪ fctm FRPfywk ≤ 03D ⎬ ≥ , Asw ⎪ fywk ρsw = bw s ⎭⎪ ρs =
1HVWDH[SUHVVmRSDUDVHo}HVYD]DGDVbwpLJXDOjVRPDGDODUJXUDGDVDOPDVPDLVH[WHUQDVGDVHomR
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
4XDQGR D WRUomR QmR IRU QHFHVViULD DR HTXLOtEULR FDVR GD WRUomR GH FRPSDWLELOLGDGH p SRVVtYHO GHVSUH]iODGHVGHTXHRHOHPHQWRHVWUXWXUDOWHQKDDFDSDFLGDGHDGHTXDGDGHDGDSWDomRSOiVWLFD H TXH WRGRV RV RXWURV HVIRUoRV VHMDP FDOFXODGRV VHP FRQVLGHUDU RV HIHLWRV SRU HOD SURYRFDGRV (PUHJL}HVRQGHRFRPSULPHQWRGRHOHPHQWRVXMHLWRDWRUomRVHMDPHQRURXLJXDODKSDUDJDUDQWLU XP QtYHO UD]RiYHO GH FDSDFLGDGH GH DGDSWDomR SOiVWLFD GHYHVH UHVSHLWDU D DUPDGXUD PtQLPD GHWRUomRHOLPLWDUDIRUoDFRUWDQWHWDOTXH Vsd dVRd2. 17.5.1.3 5HVLVWrQFLDGRHOHPHQWRHVWUXWXUDOí7RUomRSXUD $GPLWHVHVDWLVIHLWDDUHVLVWrQFLDGRHOHPHQWRHVWUXWXUDOHPXPDGDGDVHomRTXDQGRVHYHUL¿FDUHP VLPXOWDQHDPHQWHDVVHJXLQWHVFRQGLo}HV T6G d T5G T6G d T5G T6G d T5G onde T5G UHSUHVHQWDROLPLWHGDGRSHODUHVLVWrQFLDGDVGLDJRQDLVFRPSULPLGDVGHFRQFUHWR T5G UHSUHVHQWD R OLPLWH GH¿QLGR SHOD SDUFHOD UHVLVWLGD SHORV HVWULERV QRUPDLV DR HL[R GR HOHPHQWRHVWUXWXUDO T5G UHSUHVHQWD R OLPLWH GH¿QLGR SHOD SDUFHOD UHVLVWLGD SHODV EDUUDV ORQJLWXGLQDLV SDUDOHODV DRHL[RGRHOHPHQWRHVWUXWXUDO 17.5.1.4 Geometria da seção resistente 17.5.1.4.1 6Ho}HVSROLJRQDLVFRQYH[DVFKHLDV $VHomRYD]DGDHTXLYDOHQWHVHGH¿QHDSDUWLUGDVHomRFKHLDFRPHVSHVVXUDGDSDUHGHHTXLYDOHQWH he dada por: he ≤
A u
he t 2 c1 onde A pDiUHDGDVHomRFKHLD
140
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
u pRSHUtPHWURGDVHomRFKHLD c1 pDGLVWkQFLDHQWUHRHL[RGDEDUUDORQJLWXGLQDOGRFDQWRHDIDFHODWHUDOGRHOHPHQWRHVWUXWXUDO &DVRAuUHVXOWHPHQRUTXHc1SRGHVHDGRWDUhe = Au d bwíc1HDVXSHUItFLHPpGLDGDVHomR FHOXODUHTXLYDOHQWHAeGH¿QLGDSHORVHL[RVGDVDUPDGXUDVGRFDQWR UHVSHLWDQGRRFREULPHQWRH[LJLGR QRVHVWULERV 17.5.1.4.2 6HomRFRPSRVWDGHUHWkQJXORV 2 PRPHQWR GH WRUomR WRWDO GHYH VHU GLVWULEXtGR HQWUH RV UHWkQJXORV FRQIRUPH VXD ULJLGH] HOiVWLFD OLQHDU &DGD UHWkQJXOR GHYH VHU YHUL¿FDGR LVRODGDPHQWH FRP D VHomR YD]DGD HTXLYDOHQWH GH¿QLGD HP$VVLPRPRPHQWRGHWRUomRT6GLTXHFDEHDRUHWkQJXORi pGDGRSRU
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
TSdi = TSd
a i3 b i Σa i3 b i
onde a i UHSUHVHQWDRVODGRVPHQRUHVGRVUHWkQJXORV b i UHSUHVHQWDRVODGRVPDLRUHVGRVUHWkQJXORV 17.5.1.4.3 6Ho}HVYD]DGDV 'HYHVHUFRQVLGHUDGDDPHQRUHVSHVVXUDGHSDUHGHHQWUH — DHVSHVVXUDUHDOGDSDUHGH — DHVSHVVXUDHTXLYDOHQWHFDOFXODGDVXSRQGRDVHomRFKHLDGHPHVPRFRQWRUQRH[WHUQRGDVHomR vazada. 17.5.1.5 9HUL¿FDomRGDFRPSUHVVmRGLDJRQDOGRFRQFUHWR $UHVLVWrQFLDGHFRUUHQWHGDVGLDJRQDLVFRPSULPLGDVGHFRQFUHWRGHYHVHUREWLGDSRU TRd2 Dv2 fcd Ae he sen 2 T onde Dv2 ífckFRPfckH[SUHVVRHPPHJDSDVFDO 03D onde T pRkQJXORGHLQFOLQDomRGDVGLDJRQDLVGHFRQFUHWRDUELWUDGRQRLQWHUYDORd T d Ae pDiUHDOLPLWDGDSHODOLQKDPpGLDGDSDUHGHGDVHomRYD]DGDUHDORXHTXLYDOHQWHLQFOXLQGR DSDUWHYD]DGD he p D HVSHVVXUD HTXLYDOHQWH GD SDUHGH GD VHomR YD]DGD UHDO RX HTXLYDOHQWH QR SRQWR considerado. © ABNT 2023 - Todos os direitos reservados
141
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
17.5.1.6 &iOFXORGDVDUPDGXUDV 'HYHPVHUFRQVLGHUDGDVHIHWLYDVDVDUPDGXUDVFRQWLGDVQDiUHDFRUUHVSRQGHQWHDXPD~QLFDSDUHGH HTXLYDOHQWHVHQGRTXH D D UHVLVWrQFLD GHFRUUHQWH GRV HVWULERV QRUPDLV DR HL[R GR HOHPHQWR HVWUXWXUDO p GDGD SHOD expressão: TRd3 = (A90s fywd 2Ae cotg T onde fywd pRYDORUGHFiOFXORGDUHVLVWrQFLDDRHVFRDPHQWRGRDoRGDDUPDGXUDSDVVLYDOLPLWDGD D03D
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
E DUHVLVWrQFLDGHFRUUHQWHGDVDUPDGXUDVORQJLWXGLQDLVpGDGDSHODH[SUHVVmR TRd4 = ( As ue ) 2 Ae fywd tg θ onde As
pDVRPDGDViUHDVGDVVHo}HVGDVEDUUDVORQJLWXGLQDLV
ue
pRSHUtPHWURGHAe.
$DUPDGXUDORQJLWXGLQDOGHWRUomRGHiUHDWRWDO AsSRGHWHUDUUDQMRGLVWULEXtGRRXFRQFHQWUDGR PDQWHQGRVH REULJDWRULDPHQWH FRQVWDQWH D UHODomR ΔAs'u RQGH 'u p R WUHFKR GH SHUtPHWUR GDVHomRHIHWLYDFRUUHVSRQGHQWHDFDGDEDUUDRXIHL[HGHEDUUDVGHiUHDΔAs. 1DVVHo}HVSROLJRQDLVHPFDGDYpUWLFHGRVHVWULERVGHWRUomRGHYHVHUFRORFDGDSHORPHQRVXPD EDUUDORQJLWXGLQDO 17.5.2 7RUomRHPSHU¿VDEHUWRVGHSDUHGH¿QD 17.5.2.1 *HQHUDOLGDGHV 4XDQGR R HOHPHQWR HVWUXWXUDO VRE WRUomR SXGHU VHU DVVLPLODGR D XP SHU¿O DEHUWR GH SDUHGH ¿QD RSURMHWRGHYHFRQWHPSODUDOpPGDWRUomRXQLIRUPHWDPEpPRVHIHLWRVGDÀH[RWRUomR 17.5.2.2 &RQVLGHUDo}HVJHUDLV 1RFDVRJHUDODWRUomRXQLIRUPHHDÀH[RWRUomRPDQLIHVWDPVHGHIRUPDFRPSDWLELOL]DGDGLYLGLQGR HQWUH VL R FDUUHJDPHQWR H[WHUQR GH IRUPD YDULiYHO DR ORQJR GR HOHPHQWR HVWUXWXUDO &RQVLGHUDQGR DERDFDSDFLGDGHGHDGDSWDomRSOiVWLFDGRVHOHPHQWRVHVWUXWXUDLVjWRUomRSHUPLWHVHGHVSUH]DUXP GHVVHVPHFDQLVPRVGHVGHTXHRFRQVLGHUDGRQmRWHQKDULJLGH]PHQRUTXHRGHVSUH]DGR 2VYDORUHVGHULJLGH]GHYHPVHUFDOFXODGRVFRQVLGHUDQGRVHRVHIHLWRVGD¿VVXUDomRSRGHQGRVHU DGRWDGRGDULJLGH]HOiVWLFDQRFDVRGDWRUomRXQLIRUPHHQRFDVRGDÀH[RWRUomR 17.5.2.3 5LJLGH]jÀH[RWRUomR 1DIDOWDGHFiOFXORPDLVSUHFLVRTXDQGRRSHU¿OSRVVXLUSDUHGHVRSRVWDVSDUDOHODVRXDSUR[LPDGDPHQWH SDUDOHODV FDVR GH SHU¿V , & = 8 H DQiORJRV DV TXDLV SRVVDP UHVLVWLU SRU ÀH[mR GLIHUHQFLDGD 142
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
jVROLFLWDomRGHÀH[RWRUomRDULJLGH]HVWUXWXUDOGHVVHSHU¿OPHGLGDSRUH[HPSORSHORFRH¿FLHQWH GH PROD HP TXLORQHZWRQV PHWUR SRU UDGLDQR N1PUDG SRGH VHU FDOFXODGD SHOD H[SUHVVmR YHU )LJXUD r = TT sendo T = (a1a2 z
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
onde T
pRPRPHQWRH[WHUQRTXHSURYRFDWRUomRFRQVLGHUDGRDSOLFDGRQRPHLRGRYmR
z
pDGLVWkQFLDHQWUHRVHL[RVGDVSDUHGHVH
T
pDURWDomRGDVHomRSURYRFDGDSHODÀH[mRGLIHUHQFLDGDGDVSDUHGHVRSRVWDVH
a1
pDÀHFKDSURYRFDGDSHODÀH[mRGDSDUHGHVREDWXDomRGDIRUoD) Tz
a2
pDÀHFKDSURYRFDGDSHODÀH[mRGDSDUHGHVREDWXDomRGDIRUoD) Tz de sentido oposto jTXHVHDSOLFDjSDUHGH
1RFiOFXORGDVÀHFKDVa1 e a2GHYHVHUFRQVLGHUDGDPHWDGHGDULJLGH]HOiVWLFDGDVSDUHGHV bf
a2
θ
a1 T
bf F
z
F
onde bI pDODUJXUDGHFRODERUDomRDVVRFLDGDDFDGDSDUHGHFRQIRUPH )LJXUDí)OH[RWRUomRGHSHU¿OFRPSDUHGHVRSRVWDV 17.5.2.4 5HVLVWrQFLDjÀH[RWRUomR $UHVLVWrQFLDjÀH[RWRUomRGHWRGRRHOHPHQWRHVWUXWXUDOSRGHVHUFDOFXODGDDSDUWLUGDUHVLVWrQFLD jÀH[mRGDVSDUHGHVRSRVWDVSHODH[SUHVVmRVHJXLQWH TRd = ')5GPtQ z
© ABNT 2023 - Todos os direitos reservados
143
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ABNT NBR 6118:2023
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ABNT NBR 6118:2023
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ABNT NBR 6118:2023
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ABNT NBR 6118:2023
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ABNT NBR 6118:2023
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ABNT NBR 6118:2023
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ABNT NBR 6118:2023
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
18.3.3.3 (OHPHQWRVHVWUXWXUDLVDUPDGRVFRPEDUUDVGREUDGDV 18.3.3.3.1 $QFRUDJHP 1R FDVR GH EDUUDV GREUDGDV UHVLVWHQWHV j WUDomR SURYRFDGD SRU IRUoDV FRUWDQWHV R WUHFKR UHWR GH DQFRUDJHPGHYHVHUPDLRURXLJXDODEQHF YHU 18.3.3.3.2 (VSDoDPHQWRORQJLWXGLQDO 2HVSDoDPHQWRORQJLWXGLQDOHQWUHEDUUDVGREUDGDVQmRSRGHVHUVXSHULRUD smáx d FRWJD onde DpRkQJXORGHLQFOLQDomRGDEDUUDGREUDGD 18.3.4 Armadura para torção $DUPDGXUDGHVWLQDGDDUHVLVWLUDRVHVIRUoRVGHWUDomRSURYRFDGRVSRUWRUomRGHYHVHUFRQVWLWXtGD SRUHVWULERVQRUPDLVDRHL[RGDYLJDFRPELQDGRVFRPEDUUDVORQJLWXGLQDLVSDUDOHODVDRPHVPRHL[R HGHYHVHUSURMHWDGDGHDFRUGRFRPDVSUHVFULo}HVGH &RQVLGHUDPVHHIHWLYRVQDUHVLVWrQFLDRVUDPRVGRVHVWULERVHDVDUPDGXUDVORQJLWXGLQDLVFRQWLGRVQR LQWHULRUGDSDUHGH¿FWtFLDGDVHomRYD]DGDHTXLYDOHQWH YHU 2V HVWULERV SDUD WRUomR GHYHP VHU IHFKDGRV HP WRGR R VHX FRQWRUQR HQYROYHQGR DV EDUUDV GDV DUPDGXUDVORQJLWXGLQDLVGHWUDomRHFRPDVH[WUHPLGDGHVDGHTXDGDPHQWHDQFRUDGDVSRUPHLRGH JDQFKRVHPkQJXORGH 'HYHPVHUREHGHFLGDVDVSUHVFULo}HVGHUHODWLYDVDRGLkPHWURGDVEDUUDVTXHIRUPDPR HVWULERHDRHVSDoDPHQWRORQJLWXGLQDOGRVPHVPRV $VEDUUDVORQJLWXGLQDLVGDDUPDGXUDGHWRUomRSRGHPWHUDUUDQMRGLVWULEXtGRRXFRQFHQWUDGRDRORQJR GRSHUtPHWURLQWHUQRGRVHVWULERVHVSDoDGDVQRPi[LPRHPPP 'HYHVHUHVSHLWDUDUHODomRΔAs Δu RQGH'upRWUHFKRGHSHUtPHWURGDVHomRHIHWLYDFRUUHVSRQGHQWH DFDGDEDUUDRXIHL[HGHEDUUDVGHiUHDΔAs H[LJLGDSHORGLPHQVLRQDPHQWR $VVHo}HVSROLJRQDLVGHYHPFRQWHUHPFDGDYpUWLFHGRVHVWULERVGHWRUomRSHORPHQRVXPDEDUUD
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
18.3.5 $UPDGXUDGHSHOH $DUPDGXUDGHSHOHFDOFXODGDGHDFRUGRFRPGHYHVHUGLVSRVWDGHPRGRTXHRDIDVWDPHQWR HQWUHDVEDUUDVQmRXOWUDSDVVHdHFP 18.3.6 Armadura de suspensão 1DVSUR[LPLGDGHVGHFDUJDVFRQFHQWUDGDVWUDQVPLWLGDVjYLJDSRURXWUDVYLJDVRXHOHPHQWRVGLVFUHWRV TXHQHODVHDSRLHPDRORQJRRXHPSDUWHGHVXDDOWXUDRX¿TXHPQHODSHQGXUDGRVGHYHVHUFRORFDGD armadura de suspensão.
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
$ DUPDGXUD GH VXVSHQVmR GHYH VHU VRPDGD j DUPDGXUD GH FLVDOKDPHQWR GHYLGD j IRUoD FRUWDQWH HRXDRPRPHQWRWRUVRU 1RFDVRGHYLJDVQmRSHQGXUDGDVDDUPDGXUDGHVXVSHQVmRSRGHVHUGLVSRVWDQDYLJDGHDSRLRHQD YLJDDSRLDGD1DYLJDGHDSRLRGHYHVHUSRVWRXPPtQLPRGHGDDUPDGXUDFDOFXODGDGRWLUDQWH HPXPDH[WHQVmRPi[LPDHTXLYDOHQWHDhviga apoioFRQVLGHUDGDDPHWDGHGHVWDDOWXUDSDUDFDGDXP GRVODGRVDSDUWLUGRSRQWRGHFUX]DPHQWR1DYLJDDSRLDGDGHYHVHUSRVWRXPPi[LPRGHGD DUPDGXUD FDOFXODGD GR WLUDQWH HP XPD H[WHQVmR Pi[LPD HTXLYDOHQWH D hviga apoiada FRQVLGHUDGD DPHWDGHSDUDFDGDXPGRVODGRVDSDUWLUGRSRQWRGHFUX]DPHQWR&DVRDYLJDDSRLRHRXDYLJD DSRLDGDQmRVHHVWHQGHUDOpPGRSRQWRGHFUX]DPHQWRWRGDDDUPDGXUDGHYHVHUSRVWDQDH[WHQVmR máxima correspondente a hviga 1RFDVRGHYLJDVQmRSHQGXUDGDVFRPIDFHVVXSHULRUHVFRLQFLGHQWHVSRGHVHUDSOLFDGRXPIDWRUGH UHGXomRGDFDUJDGHVXVSHQVmRGDGRSRU ±hdhviga apoio RQGHhdpDGLIHUHQoDGHQtYHOPHGLGD HQWUHDVIDFHVLQIHULRUHVGDVYLJDVHhviga apoiopDDOWXUDGDYLJDGHDSRLR 'H¿QHVHXPDVLWXDomRGHYLJDSHQGXUDGDTXDQGRDIDFHLQIHULRUGDYLJDDSRLDGDHVWiDEDL[RGDIDFH LQIHULRUGDYLJDGHDSRLR 18.3.7 $UPDGXUDVGHOLJDomRPHVDDOPDRXWDOmRDOPD 2VSODQRVGHOLJDomRHQWUHPHVDVHDOPDVRXWDO}HVHDOPDVGHYLJDVGHYHPVHUYHUL¿FDGRVFRP UHODomRDRVHIHLWRVWDQJHQFLDLVGHFRUUHQWHVGDVYDULDo}HVGHWHQV}HVQRUPDLVDRORQJRGRFRPSULPHQWR GD YLJD WDQWR VRE R DVSHFWR GH UHVLVWrQFLD GR FRQFUHWR TXDQWR GDV DUPDGXUDV QHFHVViULDV SDUD UHVLVWLUjVWUDo}HVGHFRUUHQWHVGHVVHVHIHLWRV $V DUPDGXUDV GH ÀH[mR GD ODMH H[LVWHQWHV QR SODQR GH OLJDomR SRGHP VHU FRQVLGHUDGDV SDUWH GD DUPDGXUDGHOLJDomRTXDQGRGHYLGDPHQWHDQFRUDGDVFRPSOHPHQWDQGRVHDGLIHUHQoDHQWUHDPEDV VH QHFHVViULR$ VHomR WUDQVYHUVDO PtQLPD GHVVD DUPDGXUD HVWHQGHQGRVH SRU WRGD D ODUJXUD ~WLO HDGHTXDGDPHQWHDQFRUDGDGHYHVHUGHFP2 por metro.
18.4 3LODUHV 18.4.1 Introdução $V H[LJrQFLDV TXH VHJXHP UHIHUHPVH DRV SLODUHV FXMD PDLRU GLPHQVmR GD VHomR WUDQVYHUVDO QmR H[FHGDFLQFRYH]HVDPHQRUGLPHQVmRHQmRVmRYiOLGDVSDUDDVUHJL}HVHVSHFLDLV YHU6HomR 4XDQGRDSULPHLUDFRQGLomRQmRIRUVDWLVIHLWDRSLODUGHYHVHUWUDWDGRFRPRSLODUSDUHGHDSOLFDQGRVH RGLVSRVWRHP
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
18.4.2 $UPDGXUDVORQJLWXGLQDLV 18.4.2.1 'LkPHWURPtQLPRHWD[DGHDUPDGXUD 2 GLkPHWUR GDV EDUUDV ORQJLWXGLQDLV QmR SRGH VHU LQIHULRU D PP QHP VXSHULRU D GD PHQRU GLPHQVmRWUDQVYHUVDO $ WD[D JHRPpWULFD GH DUPDGXUD GHYH UHVSHLWDU RV YDORUHV Pi[LPRV H PtQLPRV HVSHFL¿FDGRV HP 18.4.2.2 'LVWULEXLomRWUDQVYHUVDO
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
$VDUPDGXUDVORQJLWXGLQDLVGHYHPVHUGLVSRVWDVQDVHomRWUDQVYHUVDOGHIRUPDDJDUDQWLUDUHVLVWrQFLDDGHTXDGDGRHOHPHQWRHVWUXWXUDO(PVHo}HVSROLJRQDLVGHYHH[LVWLUSHORPHQRVXPDEDUUDHP FDGDYpUWLFH HPVHo}HVFLUFXODUHVQRPtQLPRVHLVEDUUDVGLVWULEXtGDVDRORQJRGRSHUtPHWUR 2HVSDoDPHQWRPtQLPROLYUHHQWUHDVIDFHVGDVEDUUDVORQJLWXGLQDLVPHGLGRQRSODQRGDVHomRWUDQVYHUVDOIRUDGDUHJLmRGHHPHQGDVGHYHVHULJXDORXVXSHULRUDRPDLRUGRVVHJXLQWHVYDORUHV — PP — GLkPHWURGDEDUUDGRIHL[HRXGDOXYD — YH]DGLPHQVmRPi[LPDFDUDFWHUtVWLFDGRDJUHJDGRJUD~GR 3DUDIHL[HVGHEDUUDVGHYHVHFRQVLGHUDURGLkPHWURGRIHL[H φn = φ n . (VVHVYDORUHVVHDSOLFDPWDPEpPjVUHJL}HVGHHPHQGDVSRUWUDVSDVVHGDVEDUUDV 4XDQGRHVWLYHUSUHYLVWRQRSODQRGHFRQFUHWDJHPRDGHQVDPHQWRSRUPHLRGHDEHUWXUDODWHUDOQDIDFH GDI{UPDRHVSDoDPHQWRGDVDUPDGXUDVGHYHVHUVX¿FLHQWHSDUDSHUPLWLUDSDVVDJHPGRYLEUDGRU 2HVSDoDPHQWRPi[LPRHQWUHHL[RVGDVEDUUDVRXGHFHQWURVGHIHL[HVGHEDUUDVGHYHVHUPHQRU RXLJXDODGXDVYH]HVDPHQRUGLPHQVmRGDVHomRQRWUHFKRFRQVLGHUDGRVHPH[FHGHUPP 18.4.3 Armaduras transversais $ DUPDGXUD WUDQVYHUVDO GH SLODUHV FRQVWLWXtGD SRU HVWULERV H TXDQGR IRU R FDVR SRU JUDPSRV VXSOHPHQWDUHVGHYHVHUFRORFDGDHPWRGDDDOWXUDGRSLODUVHQGRREULJDWyULDVXDFRORFDomRQDUHJLmR GHFUX]DPHQWRFRPYLJDVHODMHV 2 GLkPHWUR GRV HVWULERV HP SLODUHV QmR SRGH VHU LQIHULRU D PP QHP D GR GLkPHWUR GD EDUUD LVRODGDRXGRGLkPHWURHTXLYDOHQWHGRIHL[HTXHFRQVWLWXLDDUPDGXUDORQJLWXGLQDO 2HVSDoDPHQWRORQJLWXGLQDOHQWUHHVWULERVPHGLGRQDGLUHomRGRHL[RGRSLODUSDUDJDUDQWLURSRVLFLRQDPHQWRLPSHGLUDÀDPEDJHPGDVEDUUDVORQJLWXGLQDLVHJDUDQWLUDFRVWXUDGDVHPHQGDVGHEDUUDV ORQJLWXGLQDLVQRVSLODUHVXVXDLVGHYHVHULJXDORXLQIHULRUDRPHQRUGRVVHJXLQWHVYDORUHV — PP — PHQRUGLPHQVmRGDVHomR — 24 ISDUD&$ISDUD&$ © ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
3RGHVHUDGRWDGRRYDORUIt < IGHVGHTXHDVDUPDGXUDVVHMDPFRQVWLWXtGDVGRPHVPRWLSRGHDoR HRHVSDoDPHQWRUHVSHLWHWDPEpPDOLPLWDomR ⎛ φ2 ⎞ 1 smáx = 90 000 ⎜ t ⎟ ⎜ φ ⎟ fyk ⎝ ⎠ com fykHPPHJDSDVFDO 4XDQGRKRXYHUQHFHVVLGDGHGHDUPDGXUDVWUDQVYHUVDLVSDUDIRUoDVFRUWDQWHVHWRUomRHVVHVYDORUHV GHYHPVHUFRPSDUDGRVFRPRVPtQLPRVHVSHFL¿FDGRVHPSDUDYLJDVDGRWDQGRVHRPHQRUGRV OLPLWHVHVSHFL¿FDGRV 127$ &RPYLVWDVDJDUDQWLUDGXWLOLGDGHGRVSLODUHVUHFRPHQGDVHTXHRVHVSDoDPHQWRVPi[LPRVHQWUH RVHVWULERVVHMDPUHGX]LGRVHPSDUDFRQFUHWRVGHFODVVH&D& FRPLQFOLQDomRGRVJDQFKRVGH SHORPHQRV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
18.5 3LODUHVSDUHGH 1RFDVRGHSLODUHVFXMDPDLRUGLPHQVmRGDVHomRWUDQVYHUVDOH[FHGDHPFLQFRYH]HVDPHQRUGLPHQVmRDOpPGDVH[LJrQFLDVFRQVWDQWHVQHVWDVXEVHomRHHPGHYHWDPEpPVHUDWHQGLGRRTXH HVWDEHOHFHD6HomRUHODWLYDPHQWHDHVIRUoRVVROLFLWDQWHVQDGLUHomRWUDQVYHUVDOGHFRUUHQWHVGH HIHLWRVGHHRUGHQVHPHVSHFLDOGRVHIHLWRVGHRUGHPORFDOL]DGRV $DUPDGXUDWUDQVYHUVDOGHSLODUHVSDUHGHGHYHUHVSHLWDUDDUPDGXUDPtQLPDGHÀH[mRGHSODFDVVH HVVDÀH[mRHDDUPDGXUDFRUUHVSRQGHQWHIRUHPFDOFXODGDV&DVRFRQWUiULRDDUPDGXUDWUDQVYHUVDO SRUPHWURGHIDFHGHYHUHVSHLWDURPtQLPRGHGDDUPDGXUDORQJLWXGLQDOSRUPHWURGDPDLRUIDFH GDOkPLQDFRQVLGHUDGD
18.6 Cabos de protensão 18.6.1 $UUDQMRORQJLWXGLQDO 18.6.1.1 Traçado $ DUPDGXUD GH SURWHQVmR SRGH VHU UHWLOtQHD FXUYLOtQHD SROLJRQDO RX GH WUDoDGR PLVWR UHVSHLWDGD D H[LJrQFLD UHIHUHQWH j DUPDGXUD QD UHJLmR GRV DSRLRV FRQIRUPH D H E (P DSRLRV LQWHUPHGLiULRVGHYHVHUGLVSRVWDXPDDUPDGXUDSURORQJDPHQWRGDVDUPDGXUDVGRVYmRVDGMDFHQWHV FDSD]GHUHVLVWLUDXPDIRUoDGHWUDomRLJXDOD FSd = (a d ) ΔVd + Nd ≥ FSd,mín = 0, 2Vd 1HVVDH[SUHVVmR'VdpDPi[LPDGLIHUHQoDGHIRUoDFRUWDQWHGHXPODGRSDUDRRXWURGRDSRLRHNd DIRUoDGHWUDomRHYHQWXDOPHQWHH[LVWHQWH$DUPDGXUDDGLVSRUQHVVHDSRLRpDREWLGDSDUDRPDLRU dos )6GFDOFXODGRVSDUDFDGDXPGRVODGRVGRDSRLR 18.6.1.2 Curvaturas $V FXUYDWXUDV GDV DUPDGXUDV GH SURWHQVmR GHYHP UHVSHLWDU RV UDLRV PtQLPRV H[LJLGRV HP IXQomR GRGLkPHWURGR¿RGDFRUGRDOKDRXGDEDUUDRXGRGLkPHWURH[WHUQRGDEDLQKD 2 HVWDEHOHFLPHQWR GRV UDLRV PtQLPRV GH FXUYDWXUD SRGH VHU UHDOL]DGR H[SHULPHQWDOPHQWH GHVGH TXHGHFRUUHQWHGHLQYHVWLJDomRDGHTXDGDPHQWHUHDOL]DGDHGRFXPHQWDGD'LVSHQVDVHMXVWL¿FDWLYD GRUDLRGHFXUYDWXUDDGRWDGRGHVGHTXHHOHVHMDVXSHULRUDPPHPUHVSHFWLYDPHQWHQRV FDVRVGH¿RVEDUUDVHFRUGRDOKDV
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
4XDQGRDFXUYDWXUDRFRUUHUHPUHJLmRSUy[LPDjIDFHGRHOHPHQWRHVWUXWXUDOSURYRFDQGRHPSX[RQR YD]LRGHYHPVHUSURMHWDGDVDUPDGXUDVTXHJDUDQWDPDPDQXWHQomRGDSRVLomRGRFDERVHPDIHWDU a integridade do concreto nessa região. 18.6.1.3 &XUYDWXUDQDVSUR[LPLGDGHVGDVDQFRUDJHQV 1DVUHJL}HVSUy[LPDVGDVDQFRUDJHQVRVUDLRVPtQLPRVGHFXUYDWXUDGRV¿RVFRUGRDOKDVRXIHL[HV SRGHPVHUUHGX]LGRVGHVGHTXHGHYLGDPHQWHFRPSURYDGDDSRVVLELOLGDGHGHUHGXomRSRUHQVDLRV 1HVVDVUHJL}HVGHYHP¿FDUJDUDQWLGDVDUHVLVWrQFLDGRFRQFUHWRHPUHODomRDRIHQGLOKDPHQWRHD PDQXWHQomRGDSRVLomRGRFDERTXDQGRHOHSURYRFDUHPSX[RQRYD]LR 18.6.1.4 Fixação durante a execução
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
$SHUPDQrQFLDGDDUPDGXUDGHSURWHQVmRHPVXDSRVLomRGXUDQWHDH[HFXomRGRHOHPHQWRHVWUXWXUDO deve ser garantida por dispositivos apropriados. 18.6.1.5 Extremidades retas 2V FDERV GH SURWHQVmR GHYHP WHU HP VXDV H[WUHPLGDGHV VHJPHQWRV UHWRV TXH SHUPLWDP RDOLQKDPHQWRGHVHXVHL[RVFRPRVHL[RVGRVUHVSHFWLYRVGLVSRVLWLYRVGHDQFRUDJHP2FRPSULPHQWR GHVVHV VHJPHQWRV QmR SRGH VHU LQIHULRU D FP 1R FDVR GH PRQRFRUGRDOKDV HQJUD[DGDV HVWH YDORUSRGHVHUGHFP 18.6.1.6 3URORQJDPHQWRGHH[WUHPLGDGH 2VFDERVGHSURWHQVmRGHYHPWHUSURORQJDPHQWRVGHH[WUHPLGDGHTXHVHHVWHQGDPDOpPGDVDQFRUDJHQVDWLYDVFRPFRPSULPHQWRDGHTXDGRj¿[DomRGRVDSDUHOKRVGHSURWHQVmR 18.6.1.7 Emendas $VEDUUDVGDDUPDGXUDGHSURWHQVmRSRGHPVHUHPHQGDGDVGHVGHTXHSRUURVFDHOXYD 6mR SHUPLWLGDV DV HPHQGDV LQGLYLGXDLV GH ¿RV FRUGRDOKDV H FDERV SRU GLVSRVLWLYRV HVSHFLDLV GH H¿FLrQFLDFRQVDJUDGDSHORXVRRXGHYLGDPHQWHFRPSURYDGDSRUHQVDLRVFRQFOXVLYRV 2WLSRHDSRVLomRGDVHPHQGDVGHYHPHVWDUSHUIHLWDPHQWHFDUDFWHUL]DGRVQRSURMHWR 18.6.1.8 $QFRUDJHQV $VDQFRUDJHQVSUHYLVWDVGHYHPUHVSHLWDURGLVSRVWRHP 18.6.2 $UUDQMRWUDQVYHUVDO 18.6.2.1 %DLQKDV 18.6.2.1.1 Protensão interna com armadura aderente $VEDLQKDVGDDUPDGXUDGHSURWHQVmRGHYHPVHUPHWiOLFDVSURMHWDGDVFRPGLkPHWURDGHTXDGRjOLYUH PRYLPHQWDomRGRVFDERVDRVLVWHPDH[HFXWLYRHPSUHJDGRHFDSD]HVGHUHVLVWLUVHPGHIRUPDomR DSUHFLiYHO j SUHVVmR GR FRQFUHWR IUHVFR H DRV HVIRUoRV GH PRQWDJHP $OpP GLVVR GHYHP VHU HVWDQTXHVUHODWLYDPHQWHjSDVWDHjDUJDPDVVDSRURFDVLmRGDFRQFUHWDJHP © ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
18.6.2.1.2 Protensão interna com armadura não aderente $VEDLQKDVSRGHPVHUGHPDWHULDOSOiVWLFRFRPSURWHomRDGHTXDGDGDDUPDGXUD 18.6.2.1.3 Protensão externa $V EDLQKDV SRGHP VHU GH PDWHULDO SOiVWLFR UHVLVWHQWH jV LQWHPSpULHV H FRP SURWHomR DGHTXDGD da armadura. 18.6.2.2 $JUXSDPHQWRGHFDERVQDSyVWUDomR
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
2VFDERVDORMDGRVHPEDLQKDVSRGHPFRQVWLWXLUJUXSRVGHGRLVWUrVHTXDWURFDERVQRVWUHFKRVUHWRV GHVGHTXHQmRRFRUUDPGLVSRVLo}HVHPOLQKDFRPPDLVGHGRLVFDERVDGMDFHQWHV1RVWUHFKRVFXUYRV SRGHPVHUGLVSRVWRVDSHQDVHPSDUHVFXMDVFXUYDWXUDVHVWHMDPHPSODQRVSDUDOHORVGHPRGRDQmR H[LVWLUSUHVVmRWUDQVYHUVDOHQWUHHOHV 18.6.2.3 Espaçamentos mínimos 2VHOHPHQWRVGDDUPDGXUDGHSURWHQVmRGHYHPHVWDUVX¿FLHQWHPHQWHDIDVWDGRVHQWUHVLGHPRGR D¿FDUJDUDQWLGRRVHXSHUIHLWRHQYROYLPHQWRSHORFRQFUHWR 2V DIDVWDPHQWRV QD GLUHomR KRUL]RQWDO YLVDP SHUPLWLU D OLYUH SDVVDJHP GR FRQFUHWR H TXDQGR IRU HPSUHJDGRYLEUDGRUGHDJXOKDDVXDLQWURGXomRHRSHUDomR2VYDORUHVPtQLPRVGRVHVSDoDPHQWRV HVWmRLQGLFDGRVQDV7DEHODVH 7DEHODí(VSDoDPHQWRVPtQLPRVí&DVRGHSyVWUDomR Espaço livre Disposição das bainhas
a
a
h (horizontal)
v (vertical)
≥ φext
≥ φext
≥ 4 cm
≥ 5 cm
≥ 1,2 φext
≥ 1,5 φext
≥ 4 cm
≥ 5 cm
av
ah
av
ah
ah
onde φext é o diâmetro externo da bainha.
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
7DEHODí(VSDoDPHQWRVPtQLPRVí&DVRGHSUpWUDomR Espaço livre
Disposição dos fios ou cordoalhas
av
ah
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
av
ah
av
ah
a
a
h (horizontal)
v (vertical)
≥2φ
≥2φ
≥ 1,2 dmáx
≥ 1,2 dmáx
≥ 2 cm
≥ 2 cm
≥3φ
≥3φ
≥ 1,2 dmáx
≥ 1,2 dmáx
≥ 2,5 cm
≥ 2 cm
≥3φ
≥3φ
≥ 1,2 dmáx
≥ 1,2 dmáx
≥ 3 cm
≥ 3 cm
onde φ é o diâmetro do fio ou cordoalha; dmáx é a dimensão máxima do agregado graúdo.
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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© ABNT 2023 - Todos os direitos reservados
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ABNT NBR 6118:2023
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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161
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ABNT NBR 6118:2023
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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163
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ABNT NBR 6118:2023
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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onde Ne
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
19.5.3.3 Tensão resistente na superfície crítica C’ HP HOHPHQWRV HVWUXWXUDLV RX WUHFKRV FRP armadura de punção $YHUL¿FDomRGHWHQV}HVQDVXSHUItFLHFUtWLFDC’ GHYHVHUHIHWXDGDFRPRDVHJXLU
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(VVDDUPDGXUDGHYHVHUSUHIHUHQFLDOPHQWHFRQVWLWXtGDSRUWUrVRXPDLVOLQKDVGHFRQHFWRUHV studs FRPH[WUHPLGDGHVDODUJDGDVGLVSRVWDVUDGLDOPHQWHDSDUWLUGRSHUtPHWURGRSLODU&DGDXPDGHVVDV H[WUHPLGDGHVGHYHHVWDUDQFRUDGDIRUDGRSODQRGDDUPDGXUDGHÀH[mRFRUUHVSRQGHQWH 19.5.3.4 'H¿QLomR GD VXSHUItFLH FUtWLFD C” 4XDQGRIRUQHFHVViULRXWLOL]DUDUPDGXUDWUDQVYHUVDOHODGHYHVHUHVWHQGLGDHPFRQWRUQRVSDUDOHORV a C¶ DWp TXH HP XP FRQWRUQR C” DIDVWDGR d GR ~OWLPR FRQWRUQR GH DUPDGXUD YHU )LJXUDV H QmRVHMDPDLVQHFHVViULDDUPDGXUDLVWRpWsd d WRd1 FRQIRUPH C” > 2d < 2d 2d C”
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169
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ABNT NBR 6118:2023
C”
C”
2d
2d
≤ 0,75d
≤ 0,75d ≤ 0,50d
≤ 0,50d
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— tensão resistente de compressão do concreto no contorno CFRQIRUPH — WHQVmR UHVLVWHQWH j SXQomR QR FRQWRUQR C’ FRQVLGHUDQGR D DUPDGXUD GH SXQomR FRQIRUPH — WHQVmRUHVLVWHQWHjSXQomRQRFRQWRUQRC´VHPDUPDGXUDGHSXQomRFRQIRUPH 19.5.3.5 $UPDGXUDGHSXQomRREULJDWyULD 1RFDVRGHDHVWDELOLGDGHJOREDOGDHVWUXWXUDGHSHQGHUGDUHVLVWrQFLDGDODMHjSXQomRGHYHVHUSUHYLVWDDUPDGXUDGHSXQomRPHVPRTXHW6GVHMDPHQRUTXHWRd1(VVDDUPDGXUDGHYHHTXLOLEUDUXP PtQLPRGHGH)6G. 19.5.4 &RODSVRSURJUHVVLYR 3DUDJDUDQWLUDGXWLOLGDGHORFDOHDFRQVHTXHQWHSURWHomRFRQWUDRFRODSVRSURJUHVVLYRDDUPDGXUD GHÀH[mRLQIHULRUTXHDWUDYHVVDRFRQWRUQRCGHYHHVWDUVX¿FLHQWHPHQWHDQFRUDGDDOpPGRFRQWRUQR C’ ou C”FRQIRUPH)LJXUD HGHYHVHUWDOTXH fyd AVFFS tā)6G onde AVFFS pRVRPDWyULRGHWRGDVDViUHDVGDVEDUUDVLQIHULRUHVTXHFUX]DPFDGDXPDGDVIDFHV GRSLODU )6G
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
)LJXUD í$UPDGXUDFRQWUDFRODSVRSURJUHVVLYR
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
20 'HWDOKDPHQWRGHODMHV 20.1 3UHVFULo}HVJHUDLV $V DUPDGXUDV GHYHP VHU GHWDOKDGDV QR SURMHWR GH IRUPD TXH GXUDQWH D H[HFXomR VHMD JDUDQWLGR o seu posicionamento durante a concretagem. 4XDOTXHUEDUUDGDDUPDGXUDGHÀH[mRGHYHWHUGLkPHWURQRPi[LPRLJXDOD h
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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20.2 %RUGDVOLYUHVHDEHUWXUDV $VERUGDVOLYUHVHDVIDFHVGDVODMHVPDFLoDVMXQWRDVDEHUWXUDVGHYHPVHUDGHTXDGDPHQWHSURWHJLGDV SRUDUPDGXUDVWUDQVYHUVDLVHORQJLWXGLQDLV2VGHWDOKHVWtSLFRVVXJHULGRVSDUDDUPDGXUDFRPSOHPHQWDU PRVWUDGRVQD)LJXUDVmRLQGLFDWLYRVHGHYHPVHUDGHTXDGRVHPFDGDVLWXDomRFRQVLGHUDQGR DGLPHQVmRHRSRVLFLRQDPHQWRGDVDEHUWXUDVRFDUUHJDPHQWRDSOLFDGRQDVODMHVHDTXDQWLGDGHGH EDUUDVTXHHVWiVHQGRLQWHUURPSLGDSHODVDEHUWXUDV
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
ABNT NBR 6118:2023
)LJXUD í %RUGDV OLYUHV H DEHUWXUDV GDV ODMHV PDFLoDV
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
Barras Barras Barras Barras inferiores superiores inferiores superiores
Região dos apoios Região central
Faixa interna
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
y
Faixa externa
% mínima da armadura total
≥ 0,35
50
≥ 0,25
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≥ 0,25
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Restante ≥ 15 cm 100 ≥ 0,25
Armadura contra colapso progressivo
100 ≥ 15 cm 33 Restante Eixo de apoio externo
Face de apoio
Eixo de apoio interno
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
ABNT NBR 6118:2023
)LJXUD±'LVSRVLomRGHFDERVHPIDL[DH[WHUQDGHDSRLR 20.3.2.3 Espaçamento mínimo entre cabos ou feixes de cabos (QWUHFDERVRXIHL[HVGHFDERVRXHQWUHFDERVHDUPDGXUDVSDVVLYDVGHYHVHUPDQWLGRXPHVSDoDPHQWRPtQLPRGHFP 20.3.2.4 Cobrimento mínimo 2FREULPHQWRPtQLPRGHFDERVHPUHODomRjIDFHGHDEHUWXUDVQDVODMHVGHYHVHUGHFP 20.3.2.5 Desvio 2GHVYLRQRSODQRGDODMHGHXPFDERRXIHL[HGHFDERVGHYHSURGX]LUXPDLQFOLQDomRPi[LPDGH QDFRUGDLPDJLQiULDTXHXQHRLQtFLRDR¿PGHVVHWUHFKRPDQWHQGRRVHXGHVHQYROYLPHQWRGHDFRUGR FRPXPDFXUYDSDUDEyOLFDHPSODQWD$RORQJRGRGHVYLRRFRQMXQWRGHFDERVRXIHL[HVGHYHHVWDU GLVSRVWRGHWDOIRUPDDPDQWHUXPDGLVWkQFLDPtQLPDGHFPHQWUHFDERVQDUHJLmRFHQWUDOGDFXUYD 3DUDRVFDVRVHPTXHRGHVYLRH[FHGDRVOLPLWHVHVSHFL¿FDGRVGHYHVHUSUHYLVWDDUPDGXUDFDSD] GHUHVLVWLUjIRUoDSURYRFDGDSRUHVVHGHVYLR 20.3.2.6 Armaduras passivas e ativas 'HVGHTXHGHYLGDPHQWHFRPSURYDGDDVXDH¿FLrQFLDSRGHVHFRQVLGHUDURVFDERVSURWHQGLGRVFRP FXUYDWXUDDGHTXDGDFRPRSDUWHGDDUPDGXUDFRQWUDRFRODSVRSURJUHVVLYRSUHYLVWRHP $OpP GLVVR QR PtQLPR GRLV FDERV HP FDGD GLUHomR RUWRJRQDO GHYHP SDVVDU SHOR LQWHULRU GD DUPDGXUD ORQJLWXGLQDOFRQWLGDQDVHomRWUDQVYHUVDOGRVSLODUHVRXHOHPHQWRVGHDSRLR$SRVLomRGHVWHVFDERV GHYHHVWDUFODUDPHQWHUHJLVWUDGDQRSURMHWR
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
6REUHRVDSRLRVGDVODMHVOLVDVRXFRJXPHORSURWHQGLGDVGHYHPVHUGLVSRVWDVQRPtQLPRTXDWUREDUUDV QDIDFHWUDFLRQDGDHPXPDIDL[DTXHQmRH[FHGDDODUJXUDGRDSRLRDFUHVFLGDGHYH]DDOWXUDWRWDO GDODMHSDUDFDGDODGR$VEDUUDVGHYHPVHUHVSDoDGDVHPQRPi[LPRFPHHVWHQGLGDVDWpXPD GLVWkQFLDPtQLPDGHGRYmROLYUHQDGLUHomRGDDUPDGXUDFRQVLGHUDGDDSDUWLUGDIDFHGRDSRLR 1DV ODMHV SURWHQGLGDV SRU PRQRFRUGRDOKDV QmR DGHUHQWHV QR Pi[LPR TXDWUR FDERV SRGHP VHU GLVSRVWRVHPIHL[H
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
P
P
P
Elevação
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Planta
a) Fendilhamento anelar
b) Fendilhamento lateral
c) Fendilhamento
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c
3c
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⎧ ⎪ c/ 8 ⎪ ⎨ ⎪ 2 cm ⎪ ⎩
3c
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Volume a ser fretado
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
GDV DUPDGXUDV SDUD UHVLVWLU DV IRUoDV GH WUDomR Mi PHQFLRQDGRV QHVWD 1RUPD WDPEpP DUPDGXUDV FRPSOHPHQWDUHVGLVSRVWDVQRFRQWRUQRHQRVFDQWRVGDVDEHUWXUDV 2VOLPLWHVSDUDDVGLPHQV}HVGHIXURVHDEHUWXUDVFRQVWDPQD6HomR1RVFDVRVHPTXHHVWHV OLPLWHVQmRVHMDPDWHQGLGRVDYHUL¿FDomRHVWUXWXUDOSRGHVHUIHLWDSHORPpWRGRGHELHODVHWLUDQWHV FRQIRUPHD6HomR 21.3.2 3DUHGHVHYLJDVSDUHGH
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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Abertura h
h Abertura
a) Abertura considerada normal
b) Abertura considerada prejudicial
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180
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
b Furo de diâmetro menor que b/3
Maior que 5 cm e duas vezes o cobrimento
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Viga
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181
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ABNT NBR 6118:2023
22 (OHPHQWRVHVSHFLDLV 22.1 6LPERORJLDHVSHFt¿FDGHVWDVHomR $VLPERORJLDDSUHVHQWDGDQHVWD6HomRVHJXHDPHVPDRULHQWDomRHVWDEHOHFLGDQD6HomR'HVWD IRUPDRVVtPERORVVXEVFULWRVWrPRPHVPRVLJQL¿FDGRTXHRVDSUHVHQWDGRVHP fcd1±WHQVmRUHVLVWHQWHPi[LPDQRFRQFUHWRHPYHUL¿FDo}HVSHORPpWRGRGHELHODVHWLUDQWHVHP UHJL}HVFRPWHQV}HVGHFRPSUHVVmRWUDQVYHUVDORXVHPWHQV}HVGHWUDomRWUDQVYHUVDOHHP QyVRQGHFRQÀXHPVRPHQWHELHODVGHFRPSUHVVmR QyV&&&
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
fcd2 ±WHQVmRUHVLVWHQWHPi[LPDQRFRQFUHWRHPYHUL¿FDo}HVSHORVPpWRGRGHELHODVHWLUDQWHVHP UHJL}HV FRP WHQV}HV GH WUDomR WUDQVYHUVDO H HP QyV RQGH FRQÀXHP GRLV RX PDLV WLUDQWHV WUDFLRQDGRV QyV&77RX777 fcd3 ± WHQVmR UHVLVWHQWH Pi[LPD QR FRQFUHWR HP YHUL¿FDo}HV SHORV PpWRGR GH ELHODV H WLUDQWHV HPQyVRQGHFRQÀXLXPWLUDQWHWUDFLRQDGR QyV&&7
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182
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
b1) Apoio de viga
c1) Transversina
h1
h
h2
h1
a1) Mudança brusca de seção
h2 h
b2) Cargas concentradas em vigas
c2) Consolo
h1
a2) Nó de pórtico
h
h2
h h1
h
h2 2h
a3) Vigas com aberturas
h h2
h h2
b3) Introdução de forças concentradas
h
h h2
h
b4) Viga parede
a4) Fundação
c3) Dente Gerber
h h
h
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
h
h1
h1
h1
h
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183
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ABNT NBR 6118:2023
$VELHODVLQFOLQDGDVGHYHPWHUkQJXORGHLQFOLQDomRFXMDWDQJHQWHHVWHMDHQWUHHHPUHODomR DRHL[RGDDUPDGXUDORQJLWXGLQDOGRHOHPHQWRHVWUXWXUDO $VYHUL¿FDo}HVGDVELHODVWLUDQWHVHQyVVmRHIHWXDGDVDSDUWLUGDVIRUoDVREWLGDVQDDQiOLVHGDWUHOLoD LVRVWiWLFDVREDDomRGRVLVWHPDDXWRHTXLOLEUDGRGHIRUoDVDWLYDVHUHDWLYDVQDWUHOLoD 22.3.2 3DUkPHWURVGHUHVLVWrQFLDGHFiOFXORGDVELHODVHUHJL}HVQRGDLV 3DUDDYHUL¿FDomRGHWHQV}HVGHFRPSUHVVmRPi[LPDVQDVELHODVHUHJL}HVQRGDLVVmRGH¿QLGRVRV VHJXLQWHVSDUkPHWURV fcd1 Dv2 fcd ELHODVSULVPiWLFDVRXQyV&&& fcd2 Dv2 fcd ELHODVDWUDYHVVDGDVSRUPDLVGHXPWLUDQWHRXQyV&77RX777
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
fcd3 Dv2 fcd ELHODVDWUDYHVVDGDVSRUWLUDQWH~QLFRRXQyV&&7 22.3.3 3DUkPHWURVGHUHVLVWrQFLDGHFiOFXORGRVWLUDQWHV $iUHDGHDoRDVHUDSOLFDGDHPFDGDWLUDQWHpGDGDSRU F As = Sd fyd
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a) Carregamento superior
h
b) Carregamento inferior
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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ABNT NBR 6118:2023
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ABNT NBR 6118:2023
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ABNT NBR 6118:2023
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ABNT NBR 6118:2023
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
3DUDEDUUDVFRPItPPGHYHVHUYHUL¿FDGRRIHQGLOKDPHQWRHPSODQRKRUL]RQWDOXPDYH]TXH SRGHRFRUUHURGHVWDFDPHQWRGHWRGDDPDOKDGDDUPDGXUD 22.6.4.1.2 $UPDGXUDGHDUUDQTXHGRVSLODUHV $VDSDWDGHYHWHUDOWXUDVX¿FLHQWHSDUDSHUPLWLUDDQFRUDJHPGDDUPDGXUDGHDUUDQTXH 22.6.4.1.3 6DSDWDVÀH[tYHLV 'HYHPVHUDWHQGLGRVRVUHTXLVLWRVUHODWLYRVjVODMHVHSXQomR YHU6Ho}HV H
22.7 %ORFRVVREUHHVWDFDV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
22.7.1 Conceituação %ORFRV VmR HVWUXWXUDV GH YROXPH XVDGDV SDUD WUDQVPLWLU jV HVWDFDV H DRV WXEXO}HV DV FDUJDV GH IXQGDomRSRGHQGRVHUFRQVLGHUDGRVUtJLGRVRXÀH[tYHLVSRUFULWpULRDQiORJRDRGH¿QLGRSDUDVDSDWDV 22.7.2 &RPSRUWDPHQWRHVWUXWXUDO 22.7.2.1 %ORFRUtJLGR 2FRPSRUWDPHQWRHVWUXWXUDOVHFDUDFWHUL]DSRU D WUDEDOKRjÀH[mRQDVGXDVGLUHo}HVXVXDOPHQWHVLPXODGRSRUELHODVHWLUDQWHVPDVFRPWUDo}HV HVVHQFLDOPHQWH FRQFHQWUDGDV QDV OLQKDV VREUH DV HVWDFDV UHWLFXODGR GH¿QLGR SHOR HL[R GDV HVWDFDVFRPIDL[DVGHODUJXUDLJXDODYH]VHXGLkPHWUR E IRUoDVWUDQVPLWLGDVGRSLODUSDUDDVHVWDFDVHVVHQFLDOPHQWHSRUELHODVGHFRPSUHVVmRGHIRUPD HGLPHQV}HVFRPSOH[DV F WUDEDOKRDRFLVDOKDPHQWRWDPEpPHPGXDVGLUHo}HVQmRDSUHVHQWDQGRUXtQDVSRUWUDomRGLDJRQDO HVLPSRUFRPSUHVVmRGDVELHODVDQDORJDPHQWHjVVDSDWDV 22.7.2.2 %ORFRÀH[tYHO 3DUDHVVHWLSRGHEORFRGHYHVHUUHDOL]DGDXPDDQiOLVHPDLVFRPSOHWDGHVGHDGLVWULEXLomRGRVHVIRUoRV QDVHVWDFDVGRVWLUDQWHVGHWUDomRGRFLVDOKDPHQWRDWpDQHFHVVLGDGHGDYHUL¿FDomRGDSXQomR 22.7.3 0RGHORGHFiOFXOR 3DUD FiOFXOR H GLPHQVLRQDPHQWR GRV EORFRV VmR DFHLWRV PRGHORV WULGLPHQVLRQDLV OLQHDUHV RX QmR OLQHDUHVHPRGHORVELHODWLUDQWHWULGLPHQVLRQDLV(VVHVPRGHORVGHYHPFRQWHPSODUDGHTXDGDPHQWH RVDVSHFWRVGHVFULWRVHP 1DUHJLmRGHFRQWDWRHQWUHRSLODUHREORFRRVHIHLWRVGHIHQGLOKDPHQWRGHYHPVHUFRQVLGHUDGRV FRQIRUPH UHTXHULGR HP SHUPLWLQGRVH D DGRomR GH XP PRGHOR GH ELHODV H WLUDQWHV SDUD a determinação das armaduras. 6HPSUHTXHKRXYHUIRUoDVKRUL]RQWDLVVLJQL¿FDWLYDVRXIRUWHDVVLPHWULDRPRGHORGHYHFRQWHPSODU DLQWHUDomRVRORHVWUXWXUD © ABNT 2023 - Todos os direitos reservados
193
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
22.7.4 'HWDOKDPHQWR 22.7.4.1 %ORFRVUtJLGRV 22.7.4.1.1 $UPDGXUDGHÀH[mR $DUPDGXUDGHÀH[mRGHYHVHUGLVSRVWDHVVHQFLDOPHQWH PDLVGH QDVIDL[DVGH¿QLGDVSHODV HVWDFDVFRQVLGHUDQGRRHTXLOtEULRFRPDVUHVSHFWLYDVELHODV $VEDUUDVGHYHPVHHVWHQGHUGHIDFHDIDFHGREORFRHWHUPLQDUHPJDQFKRQDVGXDVH[WUHPLGDGHV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
'HYHVHDVVHJXUDUDDQFRUDJHPGDVDUPDGXUDVGHFDGDXPDGHVVDVIDL[DVVREUHDVHVWDFDVPHGLGD DSDUWLUGDVIDFHVLQWHUQDVGDVHVWDFDV 1RFDVRGHHVWDFDVWUDFLRQDGDVDDUPDGXUDGDHVWDFDGHYHVHUDQFRUDGDQRWRSRGREORFRFRQIRUPH LOXVWUDD)LJXUD$OWHUQDWLYDPHQWHSRGHPVHUXWLOL]DGRVHVWULERVTXHJDUDQWDPDWUDQVIHUrQFLD GDIRUoDGHWUDomRDWpRWRSRGREORFR Md Fd
d
h
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)LJXUDí%ORFRFRPHVWDFDVWUDFLRQDGDV 22.7.4.1.2 Armadura de distribuição 3DUD FRQWURODU D ¿VVXUDomR GHYH VHU SUHYLVWD DUPDGXUD SRVLWLYD DGLFLRQDO LQGHSHQGHQWHPHQWH GD DUPDGXUD SULQFLSDO GH ÀH[mR HP PDOKD XQLIRUPHPHQWH GLVWULEXtGD HP GXDV GLUHo}HV RUWRJRQDLV FRUUHVSRQGHQWHDGRWRWDOGDVIRUoDVGHWUDomRHPFDGDXPDGHODV 22.7.4.1.3 Armadura de suspensão 6HIRUSUHYLVWDDUPDGXUDGHGLVWULEXLomRSDUDPDLVGHGRVHVIRUoRVWRWDLVRXVHRHVSDoDPHQWR HQWUHHVWDFDVIRUPDLRUTXHWUrVYH]HVDDOWXUDGREORFRGHYHVHUSUHYLVWDDUPDGXUDGHVXVSHQVmR SDUDDSDUFHODGHFDUJDDVHUHTXLOLEUDGD
194
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
22.7.4.1.4 $UPDGXUDGHDUUDQTXHGRVSLODUHV 2EORFRGHYHWHUDOWXUDVX¿FLHQWHSDUDSHUPLWLUDDQFRUDJHPGDDUPDGXUDGHDUUDQTXHGRVSLODUHV 22.7.4.1.5 $UPDGXUDODWHUDOHVXSHULRU (PEORFRVFRPGXDVRXPDLVHVWDFDVHPXPD~QLFDOLQKDpREULJDWyULDDFRORFDomRGHDUPDGXUDV ODWHUDLVHVXSHULRU (PEORFRVGHIXQGDomRGHJUDQGHVYROXPHVpFRQYHQLHQWHDDQiOLVHGDQHFHVVLGDGHGHDUPDGXUDV FRPSOHPHQWDUHV 22.7.4.2 %ORFRVÀH[tYHLV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
'HYHPVHUDWHQGLGRVRVUHTXLVLWRVUHODWLYRVjVODMHVHSXQomR YHU6Ho}HV H
23 $o}HVGLQkPLFDVHIDGLJD 23.1 6LPERORJLDHVSHFt¿FDGHVWDVHomR 'H IRUPD D VLPSOL¿FDU D FRPSUHHQVmR H SRUWDQWR D DSOLFDomR GRV FRQFHLWRV HVWDEHOHFLGRV QHVWD 6HomRRVVtPERORVPDLVXWLOL]DGRVRXTXHSRGHULDPJHUDUG~YLGDVHQFRQWUDPVHDVHJXLUGH¿QLGRV $VLPERORJLDDSUHVHQWDGDQHVWD6HomRVHJXHDPHVPDRULHQWDomRHVWDEHOHFLGDQD6HomR'HVVD IRUPDRVVtPERORVVXEVFULWRVWrPRPHVPRVLJQL¿FDGRTXHRVDSUHVHQWDGRVHP fn±IUHTXrQFLDQDWXUDO fcrit ±IUHTXrQFLDFUtWLFD
23.2 *HQHUDOLGDGHV $VDo}HVGLQkPLFDVSRGHPSURYRFDUHVWDGRVOLPLWHVGHVHUYLoRHHVWDGRVOLPLWHV~OWLPRVSRUYLEUDomR H[FHVVLYDRXSRUIDGLJDGRVPDWHULDLV
23.3 (VWDGROLPLWHGHYLEUDo}HVH[FHVVLYDV $DQiOLVHGDVYLEUDo}HVSRGHVHUIHLWDHPUHJLPHOLQHDUQRFDVRGDVHVWUXWXUDVXVXDLV 3DUD DVVHJXUDU FRPSRUWDPHQWR VDWLVIDWyULR GDV HVWUXWXUDV VXMHLWDV D YLEUDo}HV GHYHVH DIDVWDU R Pi[LPR SRVVtYHO D IUHTXrQFLD QDWXUDO GD HVWUXWXUD fn GD IUHTXrQFLD FUtWLFD fcrit TXH GHSHQGH GDGHVWLQDomRGDUHVSHFWLYDHGL¿FDomR$FRQGLomRDVHJXLUGHYHVHUDWHQGLGD fn!fcrit $UHODomRLQGLFDGDpXPDDYDOLDomRVLPSOL¿FDGDGRSUREOHPDGDYLEUDomRHPHVWUXWXUDVVHQGRDVXD DGRomRXPDGHFLVmRTXH¿FDDFULWpULRGRSURMHWLVWDSRGHQGRQmRFRQVWLWXLUXPDVROXomRDGHTXDGD SDUDRSUREOHPDHPTXHVWmR
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
1RVFDVRVHVSHFLDLVHQDTXHOHVHPTXHRVUHTXLVLWRVGHVWDVXEVHomRQmRSXGHUHPVHUDWHQGLGDV GHYHVHUIHLWDXPDDQiOLVHGLQkPLFDPDLVDFXUDGDFRQIRUPHHVWDEHOHFLGRHP1RUPDV,QWHUQDFLRQDLV HQTXDQWRQmRH[LVWLU1RUPD%UDVLOHLUDHVSHFt¿FD $VIUHTXrQFLDVQDWXUDLVGDHVWUXWXUDGHYHPVHUGHWHUPLQDGDVSRUXPDDQiOLVHPRGDOFRPSXWDFLRQDO RXH[SHULPHQWDO$VPDVVDVDVHUHPFRQVLGHUDGDVQHVWDDYDOLDomRFRUUHVSRQGHPDRVSHVRVGH¿QLGRV QDVFRPELQDo}HVGHVHUYLoRIUHTXHQWHGHDFRUGRFRP 4XDQGRDDomRFUtWLFDpRULJLQDGDSRUXPDPiTXLQDDIUHTXrQFLDFUtWLFDSDVVDDVHUDGDRSHUDomRGD PiTXLQD1HVVHFDVRSRGHQmRVHUVX¿FLHQWHDIDVWDUDVGXDVIUHTXrQFLDVSUySULDHFUtWLFD3ULQFLSDOPHQWH TXDQGRDPiTXLQDpOLJDGDGXUDQWHRVHXSURFHVVRGHDFHOHUDomRpXVXDOPHQWHQHFHVViULRDXPHQWDU DPDVVDRXRDPRUWHFLPHQWRGDHVWUXWXUDSDUDDEVRUYHUSDUWHGDHQHUJLDHQYROYLGD
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
1DIDOWDGHYDORUHVGHWHUPLQDGRVH[SHULPHQWDOPHQWHSRGHVHDGRWDURVYDORUHVLQGLFDGRVQD7DEHOD para fcrit. 7DEHODí)UHTXrQFLDFUtWLFDSDUDYLEUDo}HVYHUWLFDLVSDUDDOJXQVFDVRVHVSHFLDLVGH HVWUXWXUDVVXEPHWLGDVDYLEUDo}HVSHODDomRGHSHVVRDV Caso
fcrit Hz
Ginásio de esportes e academias de ginástica
6DODVGHGDQoDRXGHFRQFHUWRVHPFDGHLUDV¿[DV
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23.5 (VWDGROLPLWH~OWLPRGHIDGLJD 23.5.1 $o}HVFtFOLFDV $IDGLJDpXPIHQ{PHQRDVVRFLDGRDDo}HVGLQkPLFDVUHSHWLGDVTXHSRGHVHUHQWHQGLGRFRPRXP SURFHVVRGHPRGL¿FDo}HVSURJUHVVLYDVHSHUPDQHQWHVGDHVWUXWXUDLQWHUQDGHXPPDWHULDOVXEPHWLGR DRVFLODomRGHWHQV}HVGHFRUUHQWHVGHVVDVDo}HV 1mRVmRWUDWDGDVQHVWD1RUPDDVDo}HVGHIDGLJDGHDOWDLQWHQVLGDGHFDSD]HVGHSURYRFDUGDQRV FRPPHQRVGHUHSHWLo}HV $VDo}HVGHIDGLJDGHPpGLDHEDL[DLQWHQVLGDGHHQ~PHURGHUHSHWLo}HVDWpGHFLFORV VmRFRQVLGHUDGDVQDVGLVSRVLo}HVHVWDEHOHFLGDVQHVWD6HomR3DUDDFRQVLGHUDomRGRHVSHFWURGH Do}HVDGPLWHVHTXHSRGHPVHUH[FOXtGDVDTXHODVGHYHtFXORVFRPFDUJDWRWDODWpN1SDUDRFDVR de pontes rodoviárias. 196
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
3DUD D FRPELQDomR GH Do}HV GH XP GHWHUPLQDGR HVSHFWUR GH FDUJDV FRQVLGHUDVH YiOLGD D UHJUD GH 3DOPJUHQ0LQHU RX VHMD VXS}HVH TXH RV GDQRV GH IDGLJD DFXPXODPVH OLQHDUPHQWH FRP R Q~PHURGHFLFORVDSOLFDGRDFHUWRQtYHOGHWHQV}HVGHYHQGRVHREHGHFHUjH[SUHVVmR n
∑ Nii ≤ 1 onde ni
pRQ~PHURGHUHSHWLo}HVDSOLFDGDVVREFRQGLomRSDUWLFXODUGHWHQV}HV
N i
p R Q~PHUR GH UHSHWLo}HV TXH FDXVDULD D UXSWXUD SRU IDGLJD SDUD D PHVPD FRQGLomR GH WHQV}HVDSOLFDGDV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
23.5.2 &RPELQDo}HVGHDo}HVDFRQVLGHUDU (PERUD R IHQ{PHQR GD IDGLJD VHMD FRQWURODGR SHOD DFXPXODomR GR HIHLWR GHOHWpULR GH VROLFLWDo}HV UHSHWLGDVDYHUL¿FDomRGDIDGLJDSRGHVHUIHLWDFRQVLGHUDQGRXPD~QLFDLQWHQVLGDGHGHVROLFLWDomR H[SUHVVRSHODFRPELQDomRIUHTXHQWHGHDo}HV YHU6HomR GDGDDVHJXLU m
Fd,ser =
∑
n
Fgik + ψ1 Fq1k +
i =1
∑ ψ2 j Fqjk j =2
3DUDDYHUL¿FDomRGDIDGLJDGHYHVHUDGRWDGRRYDORUGRIDWRUGHUHGXomR\1FRQIRUPHRWLSRGHREUD HGHSHoDHVWUXWXUDO Para pontes rodoviárias: \1 SDUDYHUL¿FDomRGDVYLJDV \1 SDUDYHUL¿FDomRGDVWUDQVYHUVLQDV \1 SDUDYHUL¿FDomRGDVODMHVGHWDEXOHLUR 3DUDSRQWHVIHUURYLiULDV \1 3DUDYLJDVGHURODPHQWRGHSRQWHVURODQWHV \1 (P FDVRV HVSHFLDLV GH SRQWHV URODQWHV GH RSHUDomR PHQRV IUHTXHQWH RQGH R Q~PHUR GH FLFORV pVLJQL¿FDWLYDPHQWHPHQRUTXHî6DUHVLVWrQFLDjIDGLJDSRGHVHUDXPHQWDGDFRQIRUPH 23.5.3 0RGHORGHFiOFXOR 3DUDYHUL¿FDomRGDIDGLJDVHMDGRFRQFUHWRRXGRDoRRVHVIRUoRVVROLFLWDQWHVSRGHPVHUFDOFXODGRV HPUHJLPHHOiVWLFR
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
2FiOFXORGDVWHQV}HVGHFRUUHQWHVGHÀH[mRFRPSRVWDSRGHVHUIHLWRQRHVWiGLR,,RQGHpGHVSUH]DGD DUHVLVWrQFLDjWUDomRGRFRQFUHWR 2 FiOFXOR GDV WHQV}HV GHFRUUHQWHV GD IRUoD FRUWDQWH HP YLJDV GHYH VHU IHLWR SHOD DSOLFDomR GRV PRGHORV , RX ,, FRQIRUPH H UHVSHFWLYDPHQWH FRP UHGXomR GD FRQWULEXLomR GR FRQFUHWRFRPRDVHJXLU — QRPRGHOR,RYDORUGHVcGHYHVHUPXOWLSOLFDGRSHORIDWRUUHGXWRU — QRPRGHOR,,DLQFOLQDomRGDVGLDJRQDLVGHFRPSUHVVmRTGHYHVHUFRUULJLGDSHODHTXDomR tg θcor = tg θ ≤ 1 devendo-se adotar:
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
JI Jc Js 3DUDRFiOFXORGRVHVIRUoRVVROLFLWDQWHVHDYHUL¿FDomRGDVWHQV}HVDGPLWHVHRPRGHOROLQHDUHOiVWLFR FRPDUHODomR αe HQWUHRVPyGXORVGHGHIRUPDomRGRDoRHGRFRQFUHWR αe = (s (cs SRGHQGR QHVWHFDVRVHUDGRWDGRLJXDOD 3DUD R FiOFXOR GDV WHQV}HV QR DoR GD DUPDGXUD SDVVLYD RX DWLYD DGHUHQWH SRGHVH FRQVLGHUDU R FRPSRUWDPHQWR HOiVWLFR OLQHDU FRPSDWLELOL]DQGR DV GHIRUPDo}HV H PXOWLSOLFDQGR D WHQVmR QR DoR SHOR IDWRU Ks SDUD OHYDU HP FRQWD D GLIHUHQoD GH DGHUrQFLD HQWUH R DoR GH SURWHQVmR H R DoR da armadura passiva. 1+ ηs =
Ap As
φ 1+ ξ s φp As Ap
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pDiUHDGHDUPDGXUDSDVVLYD
Ap
pDiUHDGDDUPDGXUDDWLYD
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pRPHQRUGLkPHWURGRDoRGDDUPDGXUDSDVVLYDQDVHomRFRQVLGHUDGD
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[
pDUHODomRHQWUHDVUHVLVWrQFLDVGHDGHUrQFLDGRDoRGHSURWHQVmRHGRDoRGDDUPDGXUD SDVVLYD DOWDDGHUrQFLD
9DORUHVGH[QDSyVWUDomR [ SDUDDoRGHSURWHQVmROLVR 198
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
[ SDUDFRUGRDOKDV [ SDUD¿RVHQWDOKDGRV [ SDUDEDUUDVQHUYXUDGDV 9DORUHVGH[QDSUpWUDomR [ SDUDFRUGRDOKDV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
[ SDUDDoRVHQWDOKDGRV 2FULWpULRHVWDEHOHFLGRSDUDDYHUL¿FDomRGDIDGLJDGHFRUUHQWHGHIRUoDFRUWDQWHQDVYLJDVVHEDVHLD QD UHGXomR GD FRQWULEXLomR GR FRQFUHWR H GH HVTXHPDV DOWHUQDWLYRV DYDOLDGD D SDUWLU GD UHGXomR GDUHVLVWrQFLDjWUDomRGRFRQFUHWRVREFDUJDFtFOLFDHTXLYDOHQWHDDGRWDUSDUDFLFORVGD UHVLVWrQFLDjWUDomRHVWiWLFD,VVRFRUUHVSRQGHDUHGX]LURYDORUVcGDFRQWULEXLomRGRFRQFUHWRGH GR VHX YDORU HVWiWLFR QR FDVR GR 0RGHOR , 3DUD R 0RGHOR ,, QmR Ki D QHFHVVLGDGH GHVVD UHGXomRVHQGRVX¿FLHQWHDFRUUHomRGRkQJXORGDVELHODV 23.5.4 9HUL¿FDomRGDIDGLJDGRFRQFUHWR 23.5.4.1 Concreto em compressão (VVDYHUL¿FDomRSDUDRFRQFUHWRHPFRPSUHVVmRpVDWLVIHLWDVH KFJUDG JIVFPi[ d fFGIDG sendo fcdIDG fcd KFJUDG =
1 1, 5 − 0, 5 ( σc1
σc 2 )
onde KFJUDG pXPIDWRUTXHFRQVLGHUDRJUDGLHQWHGHWHQV}HVGHFRPSUHVVmRQRFRQFUHWR |Vc1_
p R PHQRU YDORU HP PyGXOR GD WHQVmR GH FRPSUHVVmR D XPD GLVWkQFLD QmR PDLRU TXH PPGDIDFHVREDFRPELQDomRUHOHYDQWHGHFDUJDV )LJXUD
|Vc2_
p R PDLRU YDORU HP PyGXOR GD WHQVmR GH FRPSUHVVmR D XPD GLVWkQFLD QmR PDLRU TXH PPGDIDFHVREDPHVPDFRPELQDomRGHFDUJDXVDGDSDUDFiOFXORGH_Vc1_ )LJXUD σc2 300 mm
σc1
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199
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
23.5.4.2 Concreto em tração $YHUL¿FDomRGDIDGLJDGRFRQFUHWRHPWUDomRpVDWLVIHLWDVH JI VFWPi[ d fFWGIDG onde fFWGIDG fFWGLQI 23.5.5 9HUL¿FDomRGDIDGLJDGDDUPDGXUD (VVD YHUL¿FDomR p VDWLVIHLWD VH D Pi[LPD YDULDomR GH WHQVmR FDOFXODGD 'Vs SDUD D FRPELQDomR IUHTXHQWHGHFDUJDVVDWLV¿]HU JI 'V6V d 'fVGIDG Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
RQGHRVYDORUHVGH'fVGIDGVmRGDGRVQD7DEHOD 7DEHODí3DUkPHWURVSDUDDVFXUYDV61 :RHOOHU SDUDRVDoRVGHQWURGRFRQFUHWRa FRQWLQXD $UPDGXUDSDVVLYDDoR&$ 9DORUHVGHǻfVGIDGPtQSDUDu106FLFORV MPa ࢥ mm
Caso 10
16
20
22
32
40
TipoE
190
190
190
180
T1
DPtQ 8ࢥSDUDࢥPP DPtQ ࢥSDUDࢥ < 20 mm DPtQ 3ࢥSDUDࢥPP
90
90
90
100
90
T1
$PELHQWHPDULQKR e &ODVVH,9
110
110
110
110
110
110
110
110
T4
%DUUDVVROGDGDV e LQFOXLQGR VROGDSRUSRQWRRXGDV H[WUHPLGDGHV HFRQHFWRUHV PHFkQLFRV
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$UPDGXUDDWLYDSDUDDoRV&3 5%H&35% Caso
9DORUHVGHǻfVGIDGPtQSDUDu106FLFORV MPa
3UpWUDomR FRP¿RVUHWRV RXFRUGRDOKDVUHWDV
200
T1
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
7DEHOD FRQFOXVmR $UPDGXUDDWLYDSDUDDoRV&3 5%H&35% 9DORUHVGHǻfVGIDGPtQSDUDu106FLFORV MPa
Caso 3yVWUDomRDGHUHQWH — &DERVUHWRVRXFDERV FXUYRVHPEDLQKDV SOiVWLFDV
140
T
— &DERVFXUYRVHP EDLQKDVPHWiOLFDV
110
T6
— 'LVSRVLWLYRVGHHPHQGD
T
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
a
$GPLWHVHSDUDFHUWL¿FDomRGHSURFHVVRVSURGXWLYRVMXVWL¿FDURVYDORUHVGHVWD7DEHODHPHQVDLRVGH EDUUDVDRDU(VVHVYDORUHVGHYHPVHUFDOFXODGRVGHDFRUGRFRPD$%171%5 E 9HUD7DEHOD c DpRGLkPHWURGRSLQRGHGREUDPHQWR d 9DORUHVREWLGRVSHODPXOWLSOLFDomRGRIDWRUUHGXWRUȟHPIXQomRGRGLkPHWURGRSLQRGHGREUDPHQWR'H GRGLkPHWURGDEDUUDࢥVHQGRȟ Dࢥ. e $PDLRULDGDVFXUYDV61LQWHUFHSWDDFXUYDGDEDUUDUHWDFRUUHVSRQGHQWH1HVVHVFDVRVDUHVLVWrQFLDj IDGLJDGDEDUUDUHWDpYiOLGDSDUDQ~PHURGHFLFORVPHQRUGRTXHRGRSRQWRGHLQWHUVHomR
7DEHODí7LSRVGDFXUYD61 Tipo
N*
k1
k2
T1
106
9
T2
106
3
T3
106
3
T4
10
3
T
106
T6
106
T
106
10
$IXQomRGDUHVLVWrQFLDjIDGLJDSDUDRDoRUHSUHVHQWDGDHPHVFDODORJORJ YHU)LJXUD FRQVLVWH HPVHJPHQWRVGHUHWDGDIRUPD 'f6GIDG mîN = constante.
© ABNT 2023 - Todos os direitos reservados
201
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ABNT NBR 6118:2023
log Δ fsd, fad
curva 1 m = k1
curva 2 m = k2
N*
log N
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
)LJXUD±)RUPDWRGDVFXUYDVGHUHVLVWrQFLDFDUDFWHUtVWLFDjIDGLJD FXUYDV61 para o aço (PQHQKXPFDVRGHYHVHFRQVLGHUDUUHVLVWrQFLDjIDGLJDPDLRUTXHDGDEDUUDUHWD 1R FDVR HP TXH VH SRVVD FRPSURYDU H[SHULPHQWDOPHQWH TXH R DoR D VHU XWLOL]DGR QD HVWUXWXUD DSUHVHQWD FDUDFWHUtVWLFDV GH UHVLVWrQFLD j IDGLJD VXSHULRUHV jV DTXL LQGLFDGDV SHUPLWHVH R XVR GHVVDVFDUDFWHUtVWLFDVQRFiOFXOR 1RFDVRGDVPDUFDVGHLGHQWL¿FDomRGRIDEULFDQWHHVWHGHYHDSUHVHQWDURVYDORUHVGHUHVLVWrQFLD jIDGLJDFRQVHTXHQWHVGHHYHQWXDOFRQFHQWUDomRGHWHQV}HVSURYRFDGDVSHORIRUPDWRGRUHOHYRGD PDUFDQDEDUUD &RQVLGHUDVHTXHRVYDORUHVDSUHVHQWDGRVSDUDDUHVLVWrQFLDjIDGLJDGRVDoRVGDDUPDGXUDSDVVLYD UHIHUHPVHDEDUUDVQHUYXUDGDVGHDOWDDGHUrQFLDQDVTXDLVDVVDOLrQFLDVWUDQVYHUVDLVHORQJLWXGLQDLV não se cruzam nem apresentam: r < 0, 5 h onde h pDDOWXUDGDVDOLrQFLD r
pRUDLRGDFXUYDGHFRQFRUGkQFLDGDVDOLrQFLDFRPRFRUSRGDEDUUD
1D IDOWD GH GDGRV H[SHULPHQWDLV HVSHFt¿FRV TXH FRPSURYHP TXH EDUUDV TXH QmR UHVSHLWHP HVVD FRQ¿JXUDomRVDWLVID]HPD7DEHODSHUPLWHVHXWLOL]iODVFRPXPDUHGXomRGHGDÀXWXDomR GDWHQVmROLPLWHGDGDQD7DEHOD
23.6 (VWDGRVOLPLWHVGHVHUYLoR $V PRGL¿FDo}HV LQWURGX]LGDV SHOD UHSHWLomR GDV VROLFLWDo}HV SRGHP DIHWDU VLJQL¿FDWLYDPHQWH DVHVWUXWXUDVGRSRQWRGHYLVWDGHVHXFRPSRUWDPHQWRHPVHUYLoRSDUWLFXODUPHQWHQRTXHGL]UHVSHLWR DR DSDUHFLPHQWR GH ¿VVXUDV QmR H[LVWHQWHV VRE Do}HV HVWiWLFDV DR DJUDYDPHQWR GH ¿VVXUDomR MiH[LVWHQWHHDRDXPHQWRGDVGHIRUPDo}HV
202
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
2 DXPHQWR GDV GHIRUPDo}HV p SURJUHVVLYR VRE Do}HV GLQkPLFDV FtFOLFDV H VRPDVH DR DXPHQWR GHGHIRUPDo}HVGHFRUUHQWHVGDÀXrQFLD1DIDOWDGHGDGRVH[SHULPHQWDLVFRQFOXVLYRVRHIHLWRFtFOLFR SRGHVHUHVWLPDGRSHODH[SUHVVmR
(
)
an = a1 ⎡⎣1, 5 − 0, 5 exp − 0, 05 n 0,25 ⎤⎦ onde an pDGHIRUPDomRQRHQpVLPRFLFORGHYLGRjFDUJDPi[LPD a1 pDGHIRUPDomRQRSULPHLURFLFORGHYLGRjFDUJDPi[LPD n pRQ~PHURGHFLFORV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
24 &RQFUHWRVLPSOHV 24.1 6LPERORJLDHVSHFt¿FDGHVWD6HomR 'H IRUPD D VLPSOL¿FDU D FRPSUHHQVmR H SRUWDQWR D DSOLFDomR GRV FRQFHLWRV HVWDEHOHFLGRV QHVWD 6HomRRVVtPERORVPDLVXWLOL]DGRVRXTXHSRGHPJHUDUG~YLGDVHQFRQWUDPVHDVHJXLUGH¿QLGRV $VLPERORJLDDSUHVHQWDGDQHVWD6HomRVHJXHDPHVPDRULHQWDomRHVWDEHOHFLGDQD6HomR'HVVD IRUPDRVVtPERORVVXEVFULWRVWrPRPHVPRVLJQL¿FDGRTXHRVDSUHVHQWDGRVHP ea±H[FHQWULFLGDGHDGLFLRQDO exey±H[FHQWULFLGDGHVQDVGLUHo}HV[\ exaeya±H[FHQWULFLGDGHVDGLFLRQDLVQDVGLUHo}HV[\ Ae±iUHDH¿FD] Hc ±GHIRUPDomRHVSHFt¿FDGRFRQFUHWR HFOLP±GHIRUPDomRjFRPSUHVVmRGRFRQFUHWRQDUXSWXUD Hct±GHIRUPDomRGHWUDomRQRFRQFUHWR HFWOLP±GHIRUPDomRGHWUDomRGRFRQFUHWRQDUXSWXUD Vcmd ±WHQVmRQRFRQFUHWRFRPSULPLGRPpGLDGHFiOFXOR WTRd±WHQVmRGHFLVDOKDPHQWRUHVLVWHQWHjWRUomRGHFiOFXOR WwRd±WHQVmRGHFLVDOKDPHQWRUHVLVWHQWHjIRUoDFRUWDQWHGHFiOFXOR WRd±WHQVmRGHFLVDOKDPHQWRUHVLVWHQWHGHFiOFXOR
© ABNT 2023 - Todos os direitos reservados
203
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
24.2 &DPSRGHDSOLFDomR 2 FRQFUHWR VLPSOHV HVWUXWXUDO GHYH WHU JDUDQWLGDV DOJXPDV FRQGLo}HV EiVLFDV FRPR FRQ¿QDPHQWR ODWHUDO FDVR GH HVWDFDV RX WXERV FRPSUHVVmR HP WRGD VHomR WUDQVYHUVDO FDVR GH DUFRV DSRLR YHUWLFDOFRQWtQXRQRVRORRXHPRXWUDSHoDHVWUXWXUDO FDVRGHSLODUHVSDUHGHVEORFRVRXSHGHVWDLV 1mR p SHUPLWLGR R XVR GH FRQFUHWR VLPSOHV HP HVWUXWXUDV VXMHLWDV D VLVPRV RX D H[SORV}HV H HP FDVRVRQGHDGXWLOLGDGHVHMDTXDOLGDGHLPSRUWDQWHGDHVWUXWXUD
24.3 Materiais e propriedades 'HYHPVHUDWHQGLGDVDVH[LJrQFLDVSDUDFRQFUHWRFRQVWDQWHVQD6HomRXWLOL]DQGRVHFRQFUHWRGD FODVVH&D& $%171%5
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
24.4 -XQWDVHGLVSRVLo}HVFRQVWUXWLYDV $V MXQWDV GH GLODWDomR GHYHP VHU SUHYLVWDV SHOR PHQRV D FDGD P 1R FDVR GH VHU QHFHVViULR DIDVWDPHQWR PDLRU GHYHP VHU FRQVLGHUDGRV QR FiOFXOR RV HIHLWRV GD UHWUDomR WpUPLFD GR FRQFUHWR FRPRFRQVHTXrQFLDGRFDORUGHKLGUDWDomR GDUHWUDomRKLGUiXOLFDHGDVYDULDo}HVGHWHPSHUDWXUD 4XDOTXHUDUPDGXUDHYHQWXDOPHQWHH[LVWHQWHQRFRQFUHWRVLPSOHVGHYHWHUPLQDUSHORPHQRVDFP GDVMXQWDV ,QWHUUXSo}HVGHFRQFUHWDJHPVySRGHPVHUIHLWDVQDVMXQWDV 'HYHVHUJDUDQWLGDDHVWDELOLGDGHODWHUDOGDVSHoDVGHFRQFUHWRVLPSOHVSRUPHLRGHFRQWUDYHQWDPHQWRV YHU6HomR
24.5 3URMHWRHVWUXWXUDO 24.5.1 *HQHUDOLGDGHV 2VHOHPHQWRVHVWUXWXUDLVGHFRQFUHWRVLPSOHVGHYHPVHUSURMHWDGRVSHORPpWRGRGRVHVWDGRVOLPLWHV XVDQGRRVPHVPRVFRH¿FLHQWHVGHSRQGHUDomRMiSUHVFULWRVSDUDRFRQFUHWRDUPDGR YHU6Ho}HV H $UHVLVWrQFLDjWUDomRGRFRQFUHWRSRGHVHUFRQVLGHUDGDQRFiOFXORGHVGHTXHVRERHIHLWRGDVDo}HV PDMRUDGDVQmRVHMDPH[FHGLGRVRVYDORUHV~OWLPRVWDQWRQDWUDomRFRPRQDFRPSUHVVmR 1RFDVRGHFDUUHJDPHQWRVGHORQJDGXUDomRGHYHVHUFRQVLGHUDGDDÀXrQFLDGRFRQFUHWRFRQIRUPH 6HomR 24.5.2 7HQV}HVUHVLVWHQWHVGHFiOFXOR 24.5.2.1 $WHQVmRPi[LPDQDV¿EUDVGHFRQFUHWRVLPSOHVGHYLGDjVFDUJDVHHVIRUoRVPDMRUDGRVQmR SRGHH[FHGHURVYDORUHVGDVWHQV}HVUHVLVWHQWHVGHFiOFXOR(PWRGRVRVFDVRVGHDSOLFDomRGRFRQFUHWR VLPSOHVHVWUXWXUDOGHYHVHUDGRWDGRJc î 1RFDVRGDWUDomRHVWDWHQVmRPi[LPDGHYH VHUEDVHDGDQRYDORUFDUDFWHUtVWLFRLQIHULRUGDUHVLVWrQFLDjWUDomRFRQIRUPHWDOTXH f fctd = ctk,inf γc 204
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
24.5.2.2 2V YDORUHV GDV WHQV}HV UHVLVWHQWHV GH FiOFXOR YDORUHVOLPLWHV GDV WHQV}HV GHWHUPLQDGDV FRPDVVROLFLWDo}HVDWXDQWHVGHFiOFXOR VmRGDGRVDVHJXLU — ¿EUDH[WUHPDjFRPSUHVVmR VcRd fcd — ¿EUDH[WUHPDjWUDomR VctRd fctd. 24.5.2.3 2VYDORUHVGDVWHQV}HVGHFLVDOKDPHQWRUHVLVWHQWHVGHFiOFXORUHODWLYDVjIRUoDFRUWDQWHHP SHoDVOLQHDUHVVmRGDGRVDVHJXLU — WwRd fFWGQDÀH[mRVLPSOHVHQDÀH[RWUDomR — WwRd fctd Vcmdfck QDÀH[RFRPSUHVVmR
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
VHQGRDGHWHUPLQDomRGDLQÀXrQFLDGDIRUoDQRUPDOH[WHUQDGHFRPSUHVVmRGDGDSHORIDWRU Vcmdfck d 2 24.5.2.4 2 YDORU GD WHQVmR GH FLVDOKDPHQWR UHVLVWHQWH GH FiOFXOR HP ODMHV GH FRQFUHWR VLPSOHV VXEPHWLGDVDÀH[mRRXÀH[RWUDomRGHYHVHUFDOFXODGRSRU WRd fctd d03D 24.5.2.5 2YDORUGDWHQVmRGHFLVDOKDPHQWRUHVLVWHQWHGHFiOFXORQRVHOHPHQWRVHVWUXWXUDLVVXEPHWLGRV DWRUomRVLPSOHVGHYHVHUFDOFXODGRSRU WTRd fctd d03D 3HoDVFXUYDVRXTXHHVWHMDPVXMHLWDVDWRUomRGHHTXLOtEULRQmRSRGHPVHUGHFRQFUHWRVLPSOHV 24.5.2.6 2YDORUGDWHQVmRGHFLVDOKDPHQWRUHVLVWHQWHGHFiOFXORjSXQomRQRFRQWRUQRC’ GHYHVHUFDOFXODGRSRU WRd fctd d03D 24.5.3 Dimensionamento $VREUDVGHFRQFUHWRVLPSOHVSRGHPWHUDUPDGXUDGHGLVWULEXLomRTXHQmRSRGHVHUFRQVLGHUDGDQR FiOFXORGRVHVIRUoRVUHVLVWHQWHVPDVTXHSRGHVHUFRQVLGHUDGDSDUDGLPLQXLURHIHLWRGD¿VVXUDomR (OHPHQWRV GH FRQFUHWR FRP DUPDGXUD PHQRU TXH D PtQLPD GHYHP VHU GLPHQVLRQDGRV FRPR GH FRQFUHWRVLPSOHV,VWRQmRVHDSOLFDjDUPDGXUDXVDGDSDUDWUDQVIHULUHVIRUoRVDHOHPHQWRVGHFRQFUHWR VLPSOHV 'HYHVHUDWHQGLGRRGLVSRVWRQDV6Ho}HVHVREUHGXUDELOLGDGH 1R FiOFXOR GH WHQV}HV FDXVDGDV SRU ÀH[mR ÀH[mR FRPSRVWD H WHQV}HV WDQJHQFLDLV GHYH VHU FRQVLGHUDGDDVHomRWUDQVYHUVDOWRWDOGRHOHPHQWRH[FHWRQRFDVRGHFRQFUHWRODQoDGRFRQWUDRVROR RQGHDDOWXUDWRWDO hDVHUFRQVLGHUDGDGHYHVHUFPPHQRUTXHDUHDO
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
24.5.4 7HQV}HVHGHIRUPDo}HVQDÀH[mR 24.5.4.1 'LDJUDPDWHQVmRGHIRUPDomRGRFRQFUHWR 8WLOL]DQGR DV KLSyWHVHV GH FiOFXOR HVWDEHOHFLGDV HP DV GHIRUPDo}HV QDV ¿EUDV H[WUHPDV GHYHPVHUOLPLWDGDVSRU — Hc d HFOLP — Hct d HFWOLP &RPR VLPSOL¿FDomR SRGHVH DGPLWLU TXH R GLDJUDPD WHQVmRGHIRUPDomR WHP D FRQ¿JXUDomR GH SDUiERODUHWkQJXORWDQWRQDFRPSUHVVmRFRPRQDWUDomR'HYHVHUFRQVLGHUDGDDÀXrQFLDGRFRQFUHWR SDUDRVFDUUHJDPHQWRVGHORQJDGXUDomR )LJXUD
0,0035
0,002
0,001
- 0,00035 - 0,0002
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
0,85 fcd
εc
)LJXUDí'LDJUDPDGHFiOFXORWHQVmRGHIRUPDomRGRFRQFUHWRFRPFRQVLGHUDomR GDÀXrQFLD 24.5.4.2 /LPLWHVGDVGHIRUPDo}HVPpGLDV 'DPHVPDIRUPDDVGHIRUPDo}HVPpGLDVGHYHPVHUOLPLWDGDVFRPRDVHJXLU — QD FRPSUHVVmR FRP SHTXHQD H[FHQWULFLGDGH QD ¿EUD GLVWDQWH h da mais comprimida: Hc d — QDWUDomRFRPSHTXHQDH[FHQWULFLGDGHQD¿EUDGLVWDQWHh da mais tracionada: Hct d 24.5.4.3 7HQV}HVUHVLVWHQWHVGHFiOFXOR &RPR VLPSOL¿FDomR DGLFLRQDO SRGHP VHU DGRWDGRV YDORUHV SDUD DV WHQV}HV UHVLVWHQWHV GH FiOFXOR como a seguir: — para a região tracionada: VctRd fctdFRQVWDQWHFDOFXODGRFRPRVHXYDORULQIHULRU — SDUDDUHJLmRFRPSULPLGD GLDJUDPDOLQHDUGHWHQV}HVFRPSLFRVcRd fcd.
206
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
24.5.5 7HQV}HVGHFLVDOKDPHQWR 24.5.5.1 $VWHQV}HVGHFLVDOKDPHQWRWwdSDUDVHomRUHWDQJXODUGHYHPVHUOLPLWDGDVSRU YHU Wwd = (3 V6G b h d WRd onde h pDDOWXUDWRWDOGDVHomRWUDQVYHUVDOGRHOHPHQWRHVWUXWXUDO 24.5.5.2 $ WHQVmR Pi[LPD GH FLVDOKDPHQWR Wwd GHYH VHU FDOFXODGD SDUD D IRUoD FRUWDQWH D XPD GLVWkQFLDhGDIDFHGRDSRLR3DUDVHo}HVPDLVSUy[LPDVGRDSRLRDGPLWHVHHVVHPHVPRYDORUGH IRUoDFRUWDQWH
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
24.5.5.3 1RFDVRGHODMHVQmRSRGHVHUIHLWDDUHGXomRGRYDORUGDIRUoDFRUWDQWHQRVDSRLRVHD WHQVmRGHFLVDOKDPHQWRGHYHVHU YHU Wwd d WRd 24.5.6 Torção $V WHQV}HV SURYHQLHQWHV GD WRUomR GHYHP VHU FDOFXODGDV SHODV IyUPXODV GD WHRULD GD HODVWLFLGDGH HVHXVHIHLWRVGHYHPVHUDFUHVFLGRVDRVSURYHQLHQWHVGRVRXWURVHVIRUoRVVROLFLWDQWHVD¿PGHVHUHP H[DPLQDGRVFRPRHVWDGRP~OWLSORGHWHQVmR 1RVHOHPHQWRVVXEPHWLGRVDWRUomRHÀH[mRVLPSOHVRXFRPSRVWDDVWHQV}HVGHYHPVHUFDOFXODGDV separadamente para a torção (WTd HSDUDDIRUoDFRUWDQWH Wwd GHYHQGRREHGHFHUjVUHODo}HV — para torção: WTd d WTRd — SDUDIRUoDFRUWDQWH Wwd d WwRd — SDUDWRUomRHIRUoDFRUWDQWH WwdWwRdWTdWTRd d 1. 24.5.7 &iOFXORGHVHo}HVVXEPHWLGDVjFRPSUHVVmRHjIRUoDFRUWDQWH 24.5.7.1 *HQHUDOLGDGHV 6mRFRQVLGHUDGRVRVFDVRVGHVHo}HVFRPSULPLGDVSRUIRUoDQRUPDOHVHo}HVVXMHLWDVDFRPSUHVVmR HDIRUoDFRUWDQWHDWXDQGRVLPXOWDQHDPHQWH IRUoDGHFRPSUHVVmRLQFOLQDGD 24.5.7.2 &iOFXORVLPSOL¿FDGRGHVHo}HVFRPSULPLGDV 1DVVHo}HVGHHOHPHQWRVGHFRQFUHWRVLPSOHVVXEPHWLGDVDIRUoDGHFRPSUHVVmRNdDSOLFDGDHPXP ponto *FRPDVH[FHQWULFLGDGHVex e eyHPUHODomRDRVHL[RV[H\UHVSHFWLYDPHQWH YHU)LJXUD R FiOFXOR GHYH VHU UHDOL]DGR DSOLFDQGRVH HVVD IRUoD QR SRQWR *1 (e1x e1y TXH UHVXOWH R PDLV GHVIDYRUiYHOHQWUHRVGRLVVHJXLQWHV *1x (exexaey RX G1y (exeyeya sendo exa hx tFP
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
eya hy t 2 cm. onde hx e hyVmRDVGLPHQV}HVPi[LPDVGDVHomR y hx
3ax
G1y eya G
ey
0 ex
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
ay
G1x x exa
ax
hy
a) Pontos de aplicação virtuais
G1 3ay
b) Seção eficaz
)LJXUDí6HomRÀH[RFRPSULPLGD A tensão Vd GHYH VHU FDOFXODGD DGRWDQGRVH GLVWULEXLomR XQLIRUPH GH WHQV}HV QD VHomR H¿FD] WULDQJXODU GH iUHD Ae YHU )LJXUD FRP EDULFHQWUR QR SRQWR GH DSOLFDomR YLUWXDO *1 GD IRUoD QRUPDOFRQVLGHUDQGRLQDWLYRRUHVWRGDVHomR$FRQGLomRGHVHJXUDQoDGHYHVHUYHUL¿FDGDSRU V6G = N6GAe d VcRd fcd 24.5.7.3 &iOFXORVLPSOL¿FDGRGHVHo}HVjFRPSUHVVmRHjIRUoDFRUWDQWH (P XPD VHomR GH XP HOHPHQWR GH FRQFUHWR VLPSOHV VREUH D TXDO DWXH XPD IRUoD LQFOLQDGD GH FRPSUHVVmRFRPVXDVFRPSRQHQWHVGHFiOFXORN6G e V6GDSOLFDGDQRSRQWR*FDOFXODVHRSRQWRGH DSOLFDomRYLUWXDO*1HDiUHDH¿FD]AeFRQIRUPHHVWDEHOHFLGRHP$VFRQGLo}HVGHVHJXUDQoD GHYHPVHUFDOFXODGDVSRU V6G = N6GAe d VcRd fcd Wwd = V6GAe d WwRd 24.5.8 (VWDELOLGDGHJOREDO (PWRGDDHVWUXWXUDGHYHVHUYHUL¿FDGDDHVWDELOLGDGHJOREDO
24.6 (OHPHQWRVHVWUXWXUDLVGHFRQFUHWRVLPSOHV 24.6.1 3LODUHVSDUHGH 3LODUHVSDUHGH GH FRQFUHWR VLPSOHV GH VHomR UHWDQJXODU SRGHP VHU GLPHQVLRQDGRV SHOD HTXDomR GDGDDVHJXLUTXDQGRDUHVXOWDQWHGHWRGDVDVFDUJDVGHFiOFXORHVWLYHUGHQWURGRWHUoRPpGLRGD HVSHVVXUDGRSLODUSDUHGH NSd ≤ NRd = 0, 63 fcd Ac ⎡1 − ( α 32 h )2 ⎤ ⎣ ⎦ sendo D TXDQGRQmRH[LVWLUHPUHVWULo}HVjURWDomRQRWRSRHQDEDVHGRSLODUSDUHGH 208
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
D TXDQGRH[LVWLUDOJXPDUHVWULomRFRQWUDURWDomRQRWRSRQDEDVHRXHPDPEDVDVH[WUHPLGDGHVGRSLODUSDUHGH onde
pDGLVWkQFLDYHUWLFDOHQWUHDSRLRV
h pDDOWXUDWRWDOGDVHomRWUDQVYHUVDOGRSLODUSDUHGH D pRIDWRUTXHGH¿QHDVFRQGLo}HVGHYtQFXORQRVDSRLRV 2 FRPSULPHQWR KRUL]RQWDO GR SLODUSDUHGH D VHU FRQVLGHUDGR SDUD FDGD FDUJD YHUWLFDO FRQFHQWUDGD QRWRSRQmRSRGHXOWUDSDVVDU — DGLVWkQFLDGHFHQWURDFHQWURHQWUHFDUJDV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
— GLVWkQFLDHQWUHDSRLRVDFUHVFLGDGHTXDWURYH]HVDHVSHVVXUDGRSLODUSDUHGH $HVSHVVXUDGRSLODUSDUHGHQmRSRGHVHUPHQRUTXH — GDDOWXUDWRWDORXGRFRPSULPHQWRYHUWLFDOQmRDSRLDGR — FP — FPQRFDVRGHSLODUHVSDUHGHSDUHGHVGHIXQGDo}HVRXGHVDSDWDVFRUULGDV 1DVDEHUWXUDVGDVSRUWDVRXMDQHODVGHYHPVHUSUHYLVWDVSHORPHQRVGXDVEDUUDVGHI PP TXHVHSURORQJXHPFPDSDUWLUGRVkQJXORVUHHQWUDQWHV 'HYHVHUJDUDQWLGDDHVWDELOLGDGHJOREDOGRFRQMXQWRHDMXQomRHQWUHRVSDLQpLV 24.6.2 %ORFRVGHIXQGDomR 1mRSRGHVHUXVDGRFRQFUHWRVLPSOHVSDUDEORFRVVREUHHVWDFDV $iUHDGDEDVHGHEORFRVGHIXQGDomRGHYHVHUGHWHUPLQDGDDSDUWLUGDWHQVmRDGPLVVtYHOGRVROR SDUDFDUJDVQmRPDMRUDGDV$HVSHVVXUDPpGLDGREORFRQmRSRGHVHUPHQRUGRTXHFP 2 GLPHQVLRQDPHQWR GDV VHo}HV WUDQVYHUVDLV GHYH VHU IHLWR SHOR PpWRGR GRV HVWDGRVOLPLWHV 2PRPHQWRÀHWRUPDMRUDGRGHYHVHUGHWHUPLQDGRQDVHomRFUtWLFDTXHSRGHVHUFRQVLGHUDGDQDIDFH GDFROXQDRXSDUHGH $IRUoDFRUWDQWHPDMRUDGDGHYHVHUFDOFXODGDSDUDDVHomRFUtWLFDQDIDFHGDFROXQDSHGHVWDORXSDUHGH e não pode superar: V6G d Ac WwRd 24.6.3 3LODUHV 3LODUHV GH FRQFUHWR VLPSOHV GHYHP VHU FDOFXODGRV GD PHVPD PDQHLUD TXH RV SLODUHVSDUHGH YHU HQDDXVrQFLDGHDo}HVODWHUDLVDFDUJDDWXDQWHGHYHHVWDUGHQWURRXQROLPLWHGRQ~FOHR FHQWUDOGHLQpUFLDGDVHomR1RFDVRGHDWXDUHPFRQFRPLWDQWHPHQWHDo}HVODWHUDLVFRPRRYHQWR DV VHo}HV GHYHP VHU YHUL¿FDGDV VHP FRQVLGHUDU D UHVLVWrQFLD j WUDomR GR FRQFUHWR 1HVVH FDVR a parte comprimida da seção deve conter o centro de gravidade. $Pi[LPDWHQVmRGHFRPSUHVVmRQRHVWDGROLPLWH~OWLPRFRPDo}HVPDMRUDGDVQmRSRGHXOWUDSDVVDU RYDORUGHVcRd. © ABNT 2023 - Todos os direitos reservados
209
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
$PHQRUGLPHQVmRGHSLODUHVGHYHVHUFPRXGHVXDDOWXUD 24.6.4 Arcos 2VDUFRVGHFRQFUHWRVLPSOHVGHYHPVHUSURMHWDGRVGHWDOIRUPD TXHQRHVWDGROLPLWH ~OWLPRQmR DSDUHoDPWHQV}HVGHWUDomRHPQHQKXPDVHomRWUDQVYHUVDO 'HYHVHUJDUDQWLGDDHVWDELOLGDGHJOREDOGRDUFRSRGHQGRVHUFRQVLGHUDGRXPDXPHQWRGHPRPHQWRV ÀHWRUHVSRUHIHLWRVGHRUGHPDWpXPPi[LPRGHDFLPDGRVPRPHQWRVGHRUGHP
25 ,QWHUIDFHVGRSURMHWRFRPDFRQVWUXomRXWLOL]DomRHPDQXWHQomR
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
25.1 Aceitação do projeto &DEH DR FRQWUDWDQWH SURFHGHU DR UHFHELPHQWR GR SURMHWR TXDQGR FXPSULGDV DV H[LJrQFLDV GHVWD 1RUPDHPSDUWLFXODUDTXHODVSUHVFULWDVQD6HomR 9HUL¿FDGD D H[LVWrQFLD GH QmR FRQIRUPLGDGHV GHYH VHU HPLWLGR WHUPR GH DFHLWDomR SURYLVyULR GR SURMHWRQRTXDOGHYHPFRQVWDUWRGDVDVSHQGrQFLDV 1D IDOWD GH KDELOLWDomR WpFQLFD GR FRQWUDWDQWH SDUD D DFHLWDomR GR SURMHWR HOH GHYH GHVLJQDU XP SUHSRVWROHJDOPHQWHKDELOLWDGRSDUDWDO 8PDYH]VDQDGDVDVSHQGrQFLDVGHYHVHUHPLWLGRRWHUPRGHDFHLWDomRGH¿QLWLYDGRSURMHWR
25.2 Recebimento do concreto e do aço 2FRQFUHWRHRDoRGHYHPVHUUHFHELGRVGHVGHTXHDWHQGLGDVWRGDVDVH[LJrQFLDVGDV$%171%5 $%171%5$%171%5$%171%5H$%171%5
25.3 0DQXDOGHXWLOL]DomRLQVSHomRHPDQXWHQomR 'H SRVVH GDV LQIRUPDo}HV GRV SURMHWRV PDWHULDLV H SURGXWRV XWLOL]DGRV H GD H[HFXomR GD REUD GHYHVHUSURGX]LGRSRUSUR¿VVLRQDOKDELOLWDGRGHYLGDPHQWHFRQWUDWDGRSHORFRQWUDWDQWHXPPDQXDO GH XWLOL]DomR LQVSHomR H PDQXWHQomR (VVH PDQXDO GHYH HVSHFL¿FDU GH IRUPD FODUD H VXFLQWD RV UHTXLVLWRVEiVLFRVSDUDDXWLOL]DomRHDPDQXWHQomRSUHYHQWLYDQHFHVViULRVSDUDJDUDQWLUDYLGD~WLO SUHYLVWDSDUDDHVWUXWXUDFRQIRUPHLQGLFDGRQD$%171%5 3DUWHVGDHVWUXWXUDTXHPHUHoDPFRQVLGHUDomRHVSHFLDOFRPYLGD~WLOGLIHUHQWHGRWRGRGHYHPVHU FRQWHPSODGDVFRPRDSDUHOKRVGHDSRLRMXQWDVGHPRYLPHQWRHWF (OHPHQWRV QmR HVWUXWXUDLV TXH SRVVDP LQÀXLU QR SURFHVVR GH GHWHULRUDomR GDV HVWUXWXUDV FRPR FKDSLQV UXIRV FRQWUDUUXIRV LQVWDODo}HV KLGUiXOLFDV H LPSHUPHDELOL]Do}HV GHYHP VHU YLVWRULDGRV periodicamente.
210
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
Anexo A LQIRUPDWLYR (IHLWRGRWHPSRQRFRQFUHWRHVWUXWXUDO
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
A.1
*HQHUDOLGDGHV
$VSUHVFULo}HVGHVWH$QH[RWrPFDUiWHULQIRUPDWLYRTXHSRGHPQDIDOWDGHGDGRVPHOKRUHVVHUXVDGDVQRSURMHWRGHHVWUXWXUDVFRPFRQFUHWRVGRJUXSR,HGRJUXSR,,GD$%171%5 FREHUWRVSRU HVWD1RUPD2XWURVYDORUHVSRGHPVHUXVDGRVGHVGHTXHFRPSURYDGRVH[SHULPHQWDOPHQWHSRUPHLR GHHQVDLRVUHDOL]DGRVGHDFRUGRFRP1RUPDV%UDVLOHLUDVHVSHFt¿FDVOHYDQGRHPFRQWDYDULDo}HVQDV FDUDFWHUtVWLFDVHSURSULHGDGHVGRVFRPSRQHQWHVGRFRQFUHWRRXDLQGDGHVGHTXHUHVSDOGDGRVSRU 1RUPDV,QWHUQDFLRQDLVRXOLWHUDWXUDWpFQLFD
A.2 A.2.1
'HIRUPDo}HVGRFRQFUHWR Introdução
4XDQGRQmRKiLPSHGLPHQWRjOLYUHGHIRUPDomRGRFRQFUHWRHDHOHpDSOLFDGDQRWHPSRt0XPD WHQVmRFRQVWDQWHQRLQWHUYDORt±t0VXDGHIRUPDomRWRWDOQRWHPSRtYDOH Hc (t Hc (t0 Hcc (t Hcs (t onde İc (t0 ıc (t0 (ci (t0 p D GHIRUPDomR LPHGLDWD SRU RFDVLmR GR FDUUHJDPHQWR FRP (ci (t0 FDOFXODGRSHODH[SUHVVmRFRQVWDQWHHP Hcc (t >Vc (t0 (ci28@M (tt0 pDGHIRUPDomRSRUÀXrQFLDQRLQWHUYDORGHWHPSR tt0 FRP(ci28 FDOFXODGRSHODPHVPDH[SUHVVmRSDUDj GLDV Hcs (t pDGHIRUPDomRSRUUHWUDomRQRLQWHUYDORGHWHPSR tt0
A.2.2 A.2.2.1
)OXrQFLDGRFRQFUHWR *HQHUDOLGDGHV
$GHIRUPDomRSRUÀXrQFLDGRFRQFUHWR Hcc pFRPSRVWDGHGXDVSDUWHVXPDUiSLGDHRXWUDOHQWD $GHIRUPDomRUiSLGD Hcca pLUUHYHUVtYHOHRFRUUHGXUDQWHDVSULPHLUDVKDSyVDDSOLFDomRGDFDUJD TXHDRULJLQRX$GHIRUPDomROHQWDpSRUVXDYH]FRPSRVWDSRUGXDVRXWUDVSDUFHODV DGHIRUPDomR OHQWDLUUHYHUVtYHO HFFI HDGHIRUPDomROHQWDUHYHUVtYHO Hccd Hcc = HccaHFFIHccd HFWRW = HcHcc = Hc M M = MaMIMd © ABNT 2023 - Todos os direitos reservados
211
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
onde Ma pRFRH¿FLHQWHGHGHIRUPDomRUiSLGD MI pRFRH¿FLHQWHGHGHIRUPDomROHQWDLUUHYHUVtYHO Md pRFRH¿FLHQWHGHGHIRUPDomROHQWDUHYHUVtYHO A.2.2.2
Hipóteses
3DUDRFiOFXORGRVHIHLWRVGDÀXrQFLDTXDQGRDVWHQV}HVQRFRQFUHWRVmRDVGHVHUYLoRDGPLWHPVH DVVHJXLQWHVKLSyWHVHV
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
D DGHIRUPDomRSRUÀXrQFLDHccYDULDOLQHDUPHQWHFRPDWHQVmRDSOLFDGD E SDUDDFUpVFLPRVGHWHQVmRDSOLFDGRVHPLQVWDQWHVGLVWLQWRVRVUHVSHFWLYRVHIHLWRVGHÀXrQFLDVH VXSHUS}HP F DGHIRUPDomRUiSLGDSURGX]GHIRUPDo}HVFRQVWDQWHVDRORQJRGRWHPSR RVYDORUHVGRFRH¿FLHQWH MaVmRIXQomRGDUHODomRHQWUHDUHVLVWrQFLDGRFRQFUHWRQRPRPHQWRGDDSOLFDomRGDFDUJDHD VXDUHVLVWrQFLD¿QDO G RFRH¿FLHQWHGHGHIRUPDomROHQWDUHYHUVtYHOMdGHSHQGHDSHQDVGDGXUDomRGRFDUUHJDPHQWR R VHX YDORU ¿QDO H R VHX GHVHQYROYLPHQWR DR ORQJR GR WHPSR VmR LQGHSHQGHQWHV GD LGDGH GRFRQFUHWRQRPRPHQWRGDDSOLFDomRGDFDUJD H RFRH¿FLHQWHGHGHIRUPDomROHQWDLUUHYHUVtYHOMI depende de: — XPLGDGHUHODWLYDGRDPELHQWH 8 — FRQVLVWrQFLDGRFRQFUHWRQRODQoDPHQWR — HVSHVVXUD¿FWtFLDGDSHoDK¿F YHU$ — LGDGH¿FWtFLDGRFRQFUHWR YHU$ QRLQVWDQWH W0 GDDSOLFDomRGDFDUJD — LGDGH¿FWtFLDGRFRQFUHWRQRLQVWDQWHFRQVLGHUDGR W I
212
SDUDRPHVPRFRQFUHWRDVFXUYDVGHGHIRUPDomROHQWDLUUHYHUVtYHOHPIXQomRGRWHPSRFRUUHVSRQGHQWHVjVGLIHUHQWHVLGDGHVGRFRQFUHWRQRPRPHQWRGRFDUUHJDPHQWRVmRREWLGDVXPDVHP UHODomRjVRXWUDVSRUGHVORFDPHQWRSDUDOHORDRHL[RGDVGHIRUPDo}HVFRQIRUPHD)LJXUD$
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Deformação lenta irreversível
εccf
t01
t02
t03
t Tempo
)LJXUD$í9DULDomRGHHccf t A.2.2.3
9DORUGDÀXrQFLD
No instante t DGHIRUPDomRGHYLGDjÀXrQFLDpGDGDSRU εcc ( t,t0 ) = ε cca + εccd + ε ccf =
σc ϕ ( t,t0 ) Ec 28
com (c28PyGXORGHGHIRUPDomRWDQJHQWHLQLFLDOSDUDj GLDVTXHGHYHVHUREWLGRVHJXQGR HQVDLRHVWDEHOHFLGRQD$%171%54XDQGRQmRIRUHPUHDOL]DGRVHQVDLRVHQmRH[LVWLUHP GDGRVPDLVSUHFLVRVVREUHRFRQFUHWRXVDGRSRGHPVHUXWLOL]DGRVYDORUHVFRQIRUPH 2FRH¿FLHQWHGHÀXrQFLDM (t, t0 YiOLGRWDPEpPSDUDDWUDomRpGDGRSRU ϕ ( t , t0 ) = ϕa + ϕf∞ [βf ( t ) − βf ( t0 )] + ϕd ∞βd onde t
pDLGDGH¿FWtFLDGRFRQFUHWRQRLQVWDQWHFRQVLGHUDGRH[SUHVVDHPGLDV
t0
pDLGDGH¿FWtFLDGRFRQFUHWRDRVHUIHLWRRFDUUHJDPHQWR~QLFRH[SUHVVDHPGLDV
t0i
pDLGDGH¿FWtFLDGRFRQFUHWRDRVHUIHLWRRFDUUHJDPHQWRH[SUHVVDHPGLDV
Ma
pRFRH¿FLHQWHGHÀXrQFLDUiSLGDGHWHUPLQDGRSHODH[SUHVVmR ⎡ f (t ) ⎤ ϕa = 0, 8 ⎢1 − c 0 ⎥ , para concretos de classes C20 a C45. ⎣ fc ( t∞ ) ⎦ ⎡ f (t ) ⎤ ϕa = 1, 4 ⎢1 − c 0 ⎥ , para concretos de classes C50 a C90. ⎣ fc ( t∞ ) ⎦
© ABNT 2023 - Todos os direitos reservados
213
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
onde fc ( t0 ) pDIXQomRGRFUHVFLPHQWRGDUHVLVWrQFLDGRFRQFUHWRFRPDLGDGHGH¿QLGDHP fc ( t∞ ) MI = M1cāM2c pRYDORU¿QDOGRFRH¿FLHQWHGHGHIRUPDomROHQWDLUUHYHUVtYHOSDUDFRQFUHWRVGH FODVVHV&D& MI āM1cāM2c pRYDORU¿QDOGRFRH¿FLHQWHGHGHIRUPDomROHQWDLUUHYHUVtYHOSDUDFRQFUHWRV GHFODVVHV&D&
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
M1c pRFRH¿FLHQWHGHSHQGHQWHGDXPLGDGHUHODWLYDGRDPELHQWHUH[SUHVVRHPSRUFHQWDJHP HGDFRQVLVWrQFLDGRFRQFUHWRGDGDSHOD7DEHOD$ M2c
pRFRH¿FLHQWHGHSHQGHQWHGDHVSHVVXUD¿FWtFLDh¿FGDSHoDGH¿QLGDHP$
ϕ2c =
42 + h 20 + h
onde h
pDHVSHVVXUD¿FWtFLDSRQGHUDGDJāh¿FH[SUHVVDHPFHQWtPHWURVVHQGRJGH¿QLGR QD7DEHOD$
EI(t RXEI (t0 pRFRH¿FLHQWHUHODWLYRjGHIRUPDomROHQWDLUUHYHUVtYHOIXQomRGDLGDGHGRFRQFUHWR YHU)LJXUD$ Md
pRYDORU¿QDOGRFRH¿FLHQWHGHGHIRUPDomROHQWDUHYHUVtYHOTXHpFRQVLGHUDGRLJXDO D
Ed(t
p R FRH¿FLHQWH UHODWLYR j GHIRUPDomR OHQWD UHYHUVtYHO IXQomR GR WHPSR t ± t0 GHFRUULGRDSyVRFDUUHJDPHQWR
β d (t ) =
t − t0 + 20 t − t0 + 70
t 2 + At + B βf ( t ) = t 2 + Ct + D onde A = 42h3±h2h % h3±h2h± C ±h3h2 h D h3± h2h hpDHVSHVVXUD¿FWtFLDSRQGHUDGDLJXDOD γ ⋅ hILF H[SUHVVDHPPHWURV P VHQGRJGH¿QLGRQD 7DEHOD$3DUDYDORUHVGHhIRUDGRLQWHUYDOR h DGRWDPVHRVYDORUHVH[WUHPRV FRUUHVSRQGHQWHV
214
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
tpRWHPSRH[SUHVVRHPGLDV t t βf(t) 1,0 0,9 0,8 0,7
a≤
ad er
0,6
nd
0,5
a íci
po
ict
0,4
ss
pe
Es
0,3
af ur
m m 0,1 m 2 , 0 m 0,4
5 0,0
m 0,8 m ,6 ≥1
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
0,2 0,1 0,0 1
t 3
10
100
1 000
10 000
Idade fictícia do concreto em dias
)LJXUD$í9DULDomRGHEf t
A.2.3 A.2.3.1
Retração do concreto Hipóteses básicas
2YDORUGDUHWUDomRGRFRQFUHWRGHSHQGHGD D XPLGDGHUHODWLYDGRDPELHQWH E FRQVLVWrQFLDGRFRQFUHWRQRODQoDPHQWR F HVSHVVXUD¿FWtFLDGDSHoD A.2.3.2
9DORUGDUHWUDomR
(QWUHRVLQVWDQWHVt0 e tDUHWUDomRpGDGDSRU Hcs (tt0 Hcs>Es(t ±Es(t0 @ onde Hcs = H1s H2s Hcs
pRYDORU¿QDOGDUHWUDomR
H1s
pRFRH¿FLHQWHGHSHQGHQWHGDXPLGDGHUHODWLYDGRDPELHQWHHGDFRQVLVWrQFLDGRFRQFUHWR YHU7DEHOD$
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
H2s ε2s =
pRFRH¿FLHQWHGHSHQGHQWHGDHVSHVVXUD¿FWtFLDGDSHoD 33 + 2h 20, 8 + 3h
onde pDHVSHVVXUD¿FWtFLDSRQGHUDGDJāh¿FH[SUHVVDHPFHQWtPHWURVVHQGRJGH¿QLGR QD7DEHOD$
h
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Es(t RXEs(t0 pRFRH¿FLHQWHUHODWLYRjUHWUDomRQRLQVWDQWHt ou t0 )LJXUD$ t
pDLGDGH¿FWtFLDGRFRQFUHWRQRLQVWDQWHFRQVLGHUDGRH[SUHVVDHPGLDV
t0
pDLGDGH¿FWtFLDGRFRQFUHWRQRLQVWDQWHHPTXHRHIHLWRGDUHWUDomRQDSHoDFRPHoD DVHUFRQVLGHUDGRH[SUHVVDHPGLDV
7DEHOD$í9DORUHVQXPpULFRVXVXDLVSDUDDGHWHUPLQDomRGDÀXrQFLDHGDUHWUDomR
Ambiente
8PLGDGH U
Retração 104 H1s EF
)OXrQFLD M1c DF
Abatimento de acordo com a ABNT NBR 16889 cm ±
±
±
±
±
±
Jd
Na água
±
(PDPELHQWH PXLWR~PLGR imediatamente acima da água
90
±
±
±
$RDUOLYUHHP JHUDO
±
±
±
(PDPELHQWH seco
40
±
±
±
a E c d
M1c ±USDUDDEDWLPHQWRQRLQWHUYDORGHFPD FPHU d 104 H1s ± U ± U2 ± U3 U4 SDUDDEDWLPHQWRVGHFP D FPHd U d 2V YDORUHV GH M1c e H1s para U d H DEDWLPHQWR HQWUH FP H FP VmR PHQRUHV H SDUD DEDWLPHQWRVHQWUHFPHFPVmRPDLRUHV J H[S ±U SDUDU d
127$ 3DUD HIHLWR GH FiOFXOR DV PHVPDV H[SUHVV}HV H RV PHVPRV YDORUHV QXPpULFRV SRGHP VHU HPSUHJDGRVQRFDVRGHWUDomR 127$ 3DUD R FiOFXOR GRV YDORUHV GH ÀXrQFLD H UHWUDomR D FRQVLVWrQFLD GR FRQFUHWR p DTXHOD FRUUHVSRQGHQWHjREWLGDFRPRPHVPRWUDoRVHPDDGLomRGHVXSHUSODVWL¿FDQWHVHVXSHUÀXLGL¿FDQWHV
216
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
3 2 ⎛ t ⎞ ⎛ t ⎞ ⎛ t ⎞ +B ⎜ A + ⎜⎝ ⎟⎠ ⎜⎝ ⎟⎠ ⎝ 100⎟⎠ 100 100 β s (t ) = 3 2 ⎛ t ⎞ + C ⎛ t ⎞ +D ⎛⎜ t ⎞⎟ + E ⎜⎝ ⎟ ⎜⎝ ⎟ ⎝ 100⎠ 100⎠ 100⎠
onde A B = 116h3±h2h± C h3±h
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
D íh3h2 h± ( ± h4h3h2± h h pDHVSHVVXUD¿FWtFLDSRQGHUDGDLJXDOD γ ⋅ hILF H[SUHVVDHPPHWURV P VHQGRJGH¿QLGRQD 7DEHOD$3DUDYDORUHVGHhIRUDGRLQWHUYDOR h DGRWDPVHRVYDORUHVH[WUHPRV FRUUHVSRQGHQWHV t
pRWHPSRH[SUHVVRHPGLDV t t βs(t)
1,0 0,9 0,8
5m
,0
0,7
a
0,6
d ra de
≤0
1
0,
n
ia tíc
0,5
ra su
0,4
po
m 2
0,
fic
m
4
0,
es
m
p
Es
0,3
8
0,
m
0,2 0,1 0,0 1
,6
m
≥1
t 3
10
100
1 000
10 000
Idade fictícia do concreto, em dias
)LJXUD$í9DULDomRGHEs t
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
A.2.4
,GDGHHHVSHVVXUD¿FWtFLDV
A.2.4.1
,GDGH¿FWtFLDGRFRQFUHWR
$LGDGHDFRQVLGHUDUpDLGDGH¿FWtFLD D tHI HPGLDVTXDQGRRHQGXUHFLPHQWRpIHLWRjWHPSHUDWXUD DPELHQWHGH&HQRVGHPDLVFDVRVTXDQGRQmRKRXYHUFXUDDYDSRUDLGDGHDFRQVLGHUDUpD LGDGH¿FWtFLDGDGDSRU t =α
Ti + 10 Δtef,i 30 i
∑
onde
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
t
pDLGDGH¿FWtFLDH[SUHVVDHPGLDV
D p R FRH¿FLHQWH GHSHQGHQWH GD YHORFLGDGH GH HQGXUHFLPHQWR GR FLPHQWR QD IDOWD GH GDGRV H[SHULPHQWDLVSHUPLWHVHRHPSUHJRGRVYDORUHVFRQVWDQWHVQD7DEHOD$ Ti
pDWHPSHUDWXUDPpGLDGLiULDGRDPELHQWHH[SUHVVDHPJUDXV&HOVLXV &
'tHIL pRSHUtRGRH[SUHVVRHPGLDVGXUDQWHRTXDODWHPSHUDWXUDPpGLDGLiULDGRDPELHQWHTi pode ser admitida constante. 127$
(VVDH[SUHVVmRQmRVHDSOLFDjFXUDDYDSRU
7DEHOD$í9DORUHVGDÀXrQFLDHGDUHWUDomRHPIXQomRGDYHORFLGDGHGH endurecimento do cimento &LPHQWR3RUWODQG &3
D )OXrQFLD
'HHQGXUHFLPHQWROHQWR &3,,,H&3,9WRGDVDVFODVVHV GHUHVLVWrQFLD
1
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2
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3
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1
/HJHQGD &3,H&3,6í&LPHQWR3RUWODQGFRPXP &3,,(&3,,)H&3,,=í&LPHQWR3RUWODQGFRPSRVWR &3,,,í&LPHQWR3RUWODQGGHDOWRIRUQR &3,9í&LPHQWR3RUWODQGSR]ROkQLFR &39$5,í&LPHQWR3RUWODQGGHDOWDUHVLVWrQFLDLQLFLDO 56í&LPHQWR3RUWODQGUHVLVWHQWHDVXOIDWRV SURSULHGDGHHVSHFt¿FDGHDOJXQVGRVWLSRVGHFLPHQWRFLWDGRV
218
© ABNT 2023 - Todos os direitos reservados
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ABNT NBR 6118:2023
A.2.4.2
(VSHVVXUD ¿FWtFLD GD SHoD
'H¿QHVHFRPRHVSHVVXUD¿FWtFLDRVHJXLQWHYDORU hILF =
2Ac uar
onde Ac
pDiUHDGDVHomRWUDQVYHUVDOGDSHoD
uar
pDSDUWHGRSHUtPHWURH[WHUQRGDVHomRWUDQVYHUVDOGDSHoDHPFRQWDWRFRPRDU
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
A.2.5
'HIRUPDomR WRWDO GR FRQFUHWR
4XDQGR Ki YDULDomR GH WHQVmR DR ORQJR GR LQWHUYDOR LQGX]LGD SRU Do}HV H[WHUQDV RX DJHQWHV GHGLIHUHQWHVSURSULHGDGHVUHROyJLFDV LQFOXLQGRVHDUPDGXUDFRQFUHWRVGHGLIHUHQWHVLGDGHVHWF DGHIRUPDomRWRWDOQRFRQFUHWRSRGHVHUFDOFXODGDSRU σ (t ) σ ( t ) εc (t ) = c 0 + c 0 ϕ (t , t0 ) + εcs (t , t0 ) + Ec (t0 ) Ec 28
t
∫
τ = t0
∂σc ⎛ 1 αϕ ( τ, t0 )⎞ + ⎜ ⎟ dτ ∂τ ⎝ Ecτ Ec 28 ⎠
HPTXHRVWUrVSULPHLURVWHUPRVUHSUHVHQWDPDGHIRUPDomRQmRLPSHGLGDHDLQWHJUDOHRVHIHLWRV GDYDULDomRGHWHQV}HVRFRUULGDVQRLQWHUYDOR 3HUPLWHVHVXEVWLWXLUHVVDH[SUHVVmRSRU
1DVH[SUHVV}HVGHHc W 'Vc (ttt0
pDYDULDomRWRWDOGHWHQVmRQRFRQFUHWRQRLQWHUYDOR ttt0
D
pRFRH¿FLHQWHFDUDFWHUtVWLFRTXHWHPYDORUYDULiYHOFRQIRUPHRFDVR
1RFiOFXORGHSHUGDVGHSURWHQVmRHPFDVRVXVXDLVRQGHDSHoDSRGHVHUFRQVLGHUDGDFRPR FRQFUHWDGDGHXPDVyYH]HDSURWHQVmRFRPRDSOLFDGDGHXPDVyYH]SRGHVHDGRWDUU D e admitir (c(tt0 (c28 FRPR IRL IHLWR HP 2EVHUYDU TXH DTXHOD VXEVHomR FRQVLGHUD TXHRFRH¿FLHQWHGHÀXrQFLDGRFRQFUHWR M = MaMI MdpXPFRH¿FLHQWHGHGHIRUPDomROHQWD LUUHYHUVtYHOFRPDVSURSULHGDGHVGH¿QLGDVSDUDMI. 1RV RXWURV FDVRV XVXDLV SRGHVH FRQVLGHUDU D PDQWHQGR (c (tt0 z (c28 sempre que VLJQL¿FDWLYR (VVDDSUR[LPDomRWHPDYDQWDJHPGHWUDWDUMFRPRXPD~QLFDIXQomRVHPVHSDUDUMaMIHMd. eSRVVtYHOVHSDUDUMaMIHMdPDVSDUDLVVRpQHFHVViULRDSOLFDUDH[SUHVVmRLQWHJUDODRSUREOHPD HPHVWXGR$H[SUHVVmRVLPSOL¿FDGDQmRVHDSOLFDQHVVHFDVR
© ABNT 2023 - Todos os direitos reservados
219
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
(VSHFLDODWHQomRGHYHVHUGDGDDRVFDVRVHPTXHDVIXQGDo}HVVmRGHIRUPiYHLVRXSDUWHGDHVWUXWXUD QmRDSUHVHQWDGHIRUPDomROHQWDFRPRpRFDVRGHWLUDQWHVPHWiOLFRV
A.3 A.3.1 YDOH
'HIRUPDo}HVQDDUPDGXUD 4XDQGRDDUPDGXUDpVROLFLWDGDHPVLWXDomRDQiORJDjGHVFULWDHP$VXDGHIRUPDomR
σ (t ) σ (t ) ε s ( t ) = s 0 + s 0 χ ( t , t0 ) Es Es onde
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Vs (t0 (spDGHIRUPDomRLPHGLDWDSRURFDVLmRGRFDUUHJDPHQWR >Vs (t0 (s@F (t, t0 pDGHIRUPDomRSRUÀXrQFLDRFRUULGDQRLQWHUYDORGHWHPSR t, t0 HFRQVLGHUDGD sempre que Vs (t0 !fptk. A.3.2 4XDQGRDOLYUHGHIRUPDomRSRUÀXrQFLDpLPSHGLGDHPVLWXDomRDQiORJDjGHVFULWDHP$ SDUDRFRQFUHWRDGHIRUPDomRWRWDOSRGHVHUFDOFXODGDSRU σ (t ) σ (t ) Δσ ( t , t0 ) ε s ( t ) = s 0 + s 0 χ ( t , t0 ) + s [1 + χ ( t , t0 )] Es Es Es onde 'Vs (tt0 pDYDULDomRWRWDOGHWHQVmRQDDUPDGXUDQRLQWHUYDOR tt0
220
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Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
Anexo B LQIRUPDWLYR Índice remissivo
Aberturas no concreto ........ )LJXUD)LJXUD)LJXUDVH Aço Aço de armadura passiva ...............................................................................................................8.2.3
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Aço de armadura ativa ....................................................................................................................8.2.4 5HFHELPHQWRGRFRQFUHWRHGRDoR $o}HV .................................................................................................................................................11 Ação do vento...............................................................................................................................11.4.1.2 Ação da água ............................................................................................................................ 11.4.1.3 $o}HVFtFOLFDV $o}HVGLQkPLFDV $o}HVH[FHSFLRQDLV $o}HVSHUPDQHQWHVH7DEHOD $o}HVYDULiYHLV7DEHODH7DEHOD &RH¿FLHQWHVGHSRQGHUDomRGDVDo}HV &RPELQDomRGHDo}HV7DEHODV7DEHOD7DEHOD 9DORUHVGDVDo}HV —
9DORUHVFDUDFWHUtVWLFRV......................................................................................................... 11.6.1
—
9DORUHVGHFiOFXOR................................................................................................................ 11.6.3
—
9DORUHVUHSUHVHQWDWLYRV
Aderência .................................................................................................................................. Aditivos $JUHJDGR
© ABNT 2023 - Todos os direitos reservados
221
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
$JUHVVLYLGDGHDPELHQWDO .................................................................................................................6.4 &ODVVHV ................................................................................................................................ 7DEHOD &RUUHVSRQGrQFLDHQWUHFODVVHGHDJUHVVLYLGDGHHTXDOLGDGHGRFRQFUHWR .......................... 7DEHOD &RUUHVSRQGrQFLDHQWUHFODVVHGHDJUHVVLYLGDGHHFREULPHQWRQRPLQDOSDUD'c = 10 mm ... 7DEHOD $ORQJDPHQWRHSUpDORQJDPHQWR ...... $QiOLVHHVWUXWXUDO ..............................................................................................................................14 $QFRUDJHP ........................................................................................................................................9.4
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Arcos ............................................................................................................................. Área reduzida Pressão de contato em..................................................................................................................21.2.1 Armadura .................................................... $GHUrQFLD .......................................................................................................................ver Ancoragem Ancoragem .................................................. $UPDGXUDGHSHOH ......................................................................................................H $UPDGXUDGHSXQomRREULJDWyULD ................................................................................................ $UPDGXUDVORQJLWXGLQDLVPtQLPDVHPi[LPDV .............................................. 7DEHOD 9DORUHVOLPLWHVSDUDDUPDGXUDVORQJLWXGLQDLVGHYLJDV ....................................... H7DEHOD 9DORUHVOLPLWHVSDUDDUPDGXUDVORQJLWXGLQDLVGHSLODUHV ............................................................ Armadura passiva...................................................................................................................H Armadura ativa ................................................................................................................H —
3UpWUDFLRQDGD ......................................................................................................................
—
3yVWUDFLRQDGD...........................................................................................................3.1.8 e 3.1.9
&iOFXORGHDUPDGXUDV ....................................................................................... H &REULPHQWRGDDUPDGXUD...................................................................................................H 'HIRUPDo}HVQDDUPDGXUD ............................................................................................................... A.3 'HWDOKDPHQWRGHDUPDGXUDV ............................................................................................................. —
Armaduras de punção ...........................................................................................................20.4
—
%ORFRVVREUHHVWDFDV...........................................................................................................
—
&DERVGHSURWHQVmR .............................................................................................................18.6
222
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
ABNT NBR 6118:2023
—
&ULWpULRVGHSURMHWRYLVDQGRDGXUDELOLGDGH .............................................................................
—
&RQVRORV ..........................................................................................................................22.3.1.4
—
'HQWHV*HUEHU .................................................................................................................22.3.2.4
—
(OHPHQWRVOLQHDUHV .............................................................................................................18.2.1
—
/DMHVVHPYLJDVHFRPDUPDGXUDSDVVLYD.........................................................................20.3.1
—
/DMHVSURWHQGLGDV ................................................................................................................20.3.2
—
3LODUHV ....................................................................................................................................18.4
—
3LODUHVSDUHGH .......................................................................................................................
—
6DSDWDV................................................................................................................................22.4.4
—
9LJDV ......................................................................................................................................18.3
—
9LJDVSDUHGH .......................................................................................................................22.2.4
'HWHULRUDomRGDDUPDGXUD...............................................................................................................6.3.3 (PHQGDV ............................................................................................................................................ Proteção das armaduras ..................................................................................................................13.4 9HUL¿FDomRGDIDGLJDGDDUPDGXUD ................................................................................................ $UWLFXODo}HV .................................................................................................................................21.2.2 %ORFRV ...................................................................................................................H &iOFXOR (VIRUoRVUHVLVWHQWHVGHFiOFXOR ..................................................................................................... (VIRUoRVVROLFLWDQWHVGHFiOFXOR..................................................................................................... 9DORUHVGHFiOFXORGDIRUoDGHSURWHQVmR ....................................................................................9.6.1.4 9DORUHVGHFiOFXORGDVDo}HV ........................................................................................................ 11.6.3 9DORUHVGHFiOFXORGDVUHVLVWrQFLDV..................................................................................................12.3 —
7HQV}HVUHVLVWHQWHVGHFiOFXOR ............................................................................................12.3.2
—
5HVLVWrQFLDGHFiOFXORGRFRQFUHWR .....................................................................................12.3.3
&DQDOL]Do}HVHPEXWLGDV .............................................................................................................13.2.6 Capitéis /DMHV .............................................................................................................................................. Punção .....................................................................................................................................
© ABNT 2023 - Todos os direitos reservados
223
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
Característicos 9DORUHVFDUDFWHUtVWLFRVGDVDo}HV ................................................................................................. 11.6.1 9DORUHVFDUDFWHUtVWLFRVGDVUHVLVWrQFLDV...........................................................................................12.2 &DUJD &DUJDVDFLGHQWDLVSUHYLVWDVSDUDRXVRGDFRQVWUXomR ............................................................. .11.4.1.1 &RQVLGHUDomRGHFDUJDVYDULiYHLVHPHVWUXWXUDVXVXDLVGHHGLItFLRV±$SUR[LPDo}HV permitidas ................................................................................................................................... 5HJL}HVGHLQWURGXomRGHFDUJDVFRQFHQWUDGDV ..............................................................................21.2
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
&KRTXHV Do}HVGLQkPLFDV ...................................................................................................... 11.4.2.3 Cimento ......................................................................................................................................... &XUYDWHyULFDGHFUHVFLPHQWRGDUHVLVWrQFLDjFRPSUHVVmRGRFRQFUHWR .....................................12.3.3 9DORUHVGHÀXrQFLDHUHWUDomRHPIXQomRGDYHORFLGDGHGHHQGXUHFLPHQWRGR cimento ....................................................................................................................$H7DEHOD$ &LVDOKDPHQWRHIRUoDFRUWDQWH $UPDGXUDWUDQVYHUVDOSDUDIRUoDFRUWDQWH —
%DUUDGDDUPDGXUDORQJLWXGLQDOGREUDGD .............................................................................18.2.2
—
3LODUHV ..................................................................................................................................18.4.3
—
9LJDV ....................................................................................................................................18.3.3
&RQFUHWRVLPSOHV ....................................................................................H (OHPHQWRVOLQHDUHVVXMHLWRVDIRUoDVFRUWDQWHV (/8 ..................................................................... (OHPHQWRVOLQHDUHVVXMHLWRVDIRUoDFRUWDQWHHWRUomR HVWDGROLPLWHGH¿VVXUDomR LQFOLQDGDGDDOPD ............................................................................................................................ (OHPHQWRVOLQHDUHVVXEPHWLGRVDVROLFLWDo}HVFRPELQDGDV............................................................. )DGLJDFiOFXORGDVWHQV}HVGHFRUUHQWHVGDIRUoDFRUWDQWHHPYLJDV ......................................... )RUoDFRUWDQWHHPODMHVHHOHPHQWRVOLQHDUHVFRP bwd ................................................................19.4 /DMHVQHUYXUDGDV ........................................................................................................................13.2.4.2 /DMHVFRPDUPDGXUDSDUDIRUoDFRUWDQWH.......................................................................................19.4.2 /DMHVVHPDUPDGXUDSDUDIRUoDFRUWDQWH.......................................................................................19.4.1 /DMHVVXEPHWLGDVjSXQomR ........................................................................................................... 5HJL}HVHVSHFLDLV&DUJDVDSOLFDGDVQDVXSHUItFLHGHHOHPHQWRVHVWUXWXUDLV ............................21.2.4 5HVLVWrQFLDDRFLVDOKDPHQWRGDVROGDGHEDUUDVWUDQVYHUVDLVVROGDGDV ......................9.4.2.2 e 9.4.6.2
224
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
9LJDVSDUHGHHSLODUHVSDUHGH ......................................................................................................14.8.1 &ODVVHVGHDJUHVVLYLGDGHDPELHQWDO ......................................................YHU$JUHVVLYLGDGHDPELHQWDO Cobrimento da armadura ................................................................................................H &RH¿FLHQWH &RH¿FLHQWHGHFRQIRUPDomRVXSHU¿FLDOGRDoR ...............................................................................8.3.2 &RH¿FLHQWHGHGLODWDomRWpUPLFDGRDoR DUPDGXUDDWLYD ..............................................................8.4.3 &RH¿FLHQWHGHGLODWDomRWpUPLFDGRDoR DUPDGXUDSDVVLYD ..........................................................8.3.4
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
&RH¿FLHQWHGHGLODWDomRWpUPLFDGRFRQFUHWR..................................................................................8.2.3 &RH¿FLHQWHGHÀXrQFLDGRFRQFUHWR ............................................................................ 8.2.11 e Anexo A &RH¿FLHQWHVGHPDMRUDomRGDVDo}HVSDUDSLODUHVHSLODUHVSDUHGH .................... H7DEHOD &RH¿FLHQWHGHPDMRUDomRGRVHVIRUoRVJOREDLVGHRUGHPSDUDREWHQomRGRV ¿QDLVGHRUGHP......................................................................................................................... &RH¿FLHQWHGH3RLVVRQGRFRQFUHWR ................................................................................................8.2.9 &RH¿FLHQWHVGHSRQGHUDomRGDVDo}HV ........................................................ H7DEHODVH &RH¿FLHQWHVGHSRQGHUDomRGDVUHVLVWrQFLDV ........................................................... H7DEHOD &RH¿FLHQWHVGHSRQGHUDomRSDUDRHVWDGROLPLWH~OWLPRQRDWRGDSURWHQVmR ......................... &RH¿FLHQWHGHUHGLVWULEXLomRGHPRPHQWRV ..............................................................H Compressão (VWDGROLPLWHGHFRPSUHVVmRH[FHVVLYD (/6&( ......................................................................... 5HVLVWrQFLDjFRPSUHVVmRGRFRQFUHWR...........................................................................................8.2.4 'LDJUDPDWHQVmRGHIRUPDomRGRFRQFUHWRHPFRPSUHVVmR......................................................8.2.10.1 9HUL¿FDomRGDIDGLJDGRFRQFUHWRjFRPSUHVVmR ....................................................................... Concreto ...........................................................................................................................................8.2 $UWLFXODo}HVGHFRQFUHWR ...............................................................................................................21.2.2 &RQFUHWRVLPSOHV .................................................................................................................................24 'H¿QLo}HVGHFRQFUHWRHVWUXWXUDO .......................................................................................................3.1 (IHLWRGRWHPSRQRFRQFUHWRHVWUXWXUDO.......................................................................................Anexo A )OXrQFLDGRFRQFUHWR ..........................................................................................H$QH[R$$ 0HFDQLVPRVSUHSRQGHUDQWHVGHGHWHULRUDomRUHODWLYRVDRFRQFUHWR ..............................................6.3.2 4XDOLGDGHGRFRQFUHWRHFREULPHQWR.................................................................................................. © ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
5HFHELPHQWRGRFRQFUHWRHGRDoR .................................................................................................. 5HVLVWrQFLDGHFiOFXORGRFRQFUHWR ...............................................................................................12.3.3 Retração do concreto ................................................................................................ 11.3.3.2 e Anexo A 9HUL¿FDomRGDIDGLJDGRFRQFUHWR ................................................................................................. &RQVRORV ......................................................................................................................................22.3.1 Deformação 'HIRUPDomRGHFRUUHQWHGDÀXrQFLDGRFRQFUHWR....................................................... 11.3.3.2 e Anexo A 'HIRUPDomRHVSHFt¿FDGHUHWUDomRGRFRQFUHWR ....................................................... 11.3.3.1 e Anexo A
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
'LDJUDPDVWHQVmRGHIRUPDomR ....................................................................................... YHU'LDJUDPDV (VWDGROLPLWHGHGHIRUPDomRSDUDHOHPHQWRVOLQHDUHVVXMHLWRVDVROLFLWDo}HVQRUPDLV ................ (VWDGROLPLWHGHGHIRUPDomRSDUDODMHV ........................................................................................19.3.1 'HIRUPDomROHQWD .............................................................................................................. YHU)OXrQFLD Dentes Gerber ..............................................................................................................................22.3.2 'HVORFDPHQWR 'HVORFDPHQWRV ..................................................................................................................... YHU)OHFKDV 'HVORFDPHQWRVGHDSRLR ............................................................................................................ 11.3.3.3 'HVORFDPHQWRVOLPLWHV .............................................................................................. H7DEHOD 'LDJUDPD 'LDJUDPDVWHQVmRGHIRUPDomRSDUDRFRQFUHWR .....................)LJXUDVH 'LDJUDPDWHQVmRGHIRUPDomRSDUDRDoR DUPDGXUDSDVVLYD ..................................H)LJXUD 'LDJUDPDWHQVmRGHIRUPDomRSDUDRDoR DUPDGXUDDWLYD ........................................H)LJXUD 'LPHQVLRQDPHQWRHYHUL¿FDomR %ORFRVVREUHHVWDFDV ....................................................................................................................... &RQVRORV.......................................................................................................................................22.3.1 'HQWHV*HUEHU ...............................................................................................................................22.3.2 (OHPHQWRVGHFRQFUHWRVLPSOHV...........................................................................................................24 (OHPHQWRVOLQHDUHVVXMHLWRVDVROLFLWDo}HVQRUPDLV (/8 ............................................................... (OHPHQWRVOLQHDUHVVXMHLWRVDVROLFLWDo}HVQRUPDLV (/6 ...............................................................
226
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
(OHPHQWRVOLQHDUHVVXMHLWRVDIRUoDVFRUWDQWHV (/8 ...................................................................... (OHPHQWRVOLQHDUHVVXMHLWRVDWRUomR (/8 ..................................................................................... (OHPHQWRVOLQHDUHVVXMHLWRVDIRUoDFRUWDQWHHWRUomR (/GH¿VVXUDomRLQFOLQDGDGDDOPD .......... (OHPHQWRVOLQHDUHVVXEPHWLGRVDVROLFLWDo}HVFRPELQDGDV............................................................. )DGLJD (/8 .................................................................................................................................... Juntas de concretagem ....................................................................................................................21.6 /DMHV (/8 ......................................................................................................................................19.2 /DMHV (/6 .......................................................................................................................................19.3 /DMHVHHOHPHQWRVOLQHDUHVFRP bw tGVXMHLWRVDIRUoDFRUWDQWH ...................................................19.4 /DMHVVXMHLWDVjSXQomR .................................................................................................................... Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
/LJDo}HVGHHOHPHQWRVHVWUXWXUDLVSUpPROGDGRV ............................................................................ 1yVGHSyUWLFRVHOLJDo}HVHQWUHSDUHGHV ........................................................................................21.4 5HJL}HVGHLQWURGXomRGHFDUJDVFRQFHQWUDGDV ..............................................................................21.2 5HJL}HVFRPIXURVHDEHUWXUDV ........................................................................................................21.3 6DSDWDV ............................................................................................................................................22.4 9LJDVSDUHGH ....................................................................................................................................22.2 'LPHQV}HVOLPLWHVGRVHOHPHQWRVHVWUXWXUDLV ...........................................................................13.2 'XUDELOLGDGHGDHVWUXWXUDGHFRQFUHWR &ULWpULRVGHSURMHWRYLVDQGRDGXUDELOLGDGH ........................................................................................... 'LUHWUL]HVSDUDGXUDELOLGDGHGDVHVWUXWXUDVGHFRQFUHWR .......................................................................6 'XUDELOLGDGH .....................................................................................................................................16.4 /LPLWHVSDUD¿VVXUDomRHSURWHomRGDVDUPDGXUDVTXDQWRjGXUDELOLGDGH ..................................13.4.2 'XWLOLGDGH 'XWLOLGDGHHPYLJDV ....................................................................................................................... 5HGLVWULEXLomRGHPRPHQWRVHFRQGLo}HVGHGXWLOLGDGHHPHVWUXWXUDVGHHOHPHQWRV OLQHDUHV .......................................................................................................................................14.6.4.3 5HGLVWULEXLomRGHPRPHQWRVHFRQGLo}HVGHGXWLOLGDGHHPHVWUXWXUDVFRPHOHPHQWRVGH SODFD .......................................................................................................................................... (IHLWRVGHRUGHP ........................................................................................................................... $QiOLVHGRVHIHLWRVORFDLVGHRUGHP.......................................................................................... 'HWHUPLQDomRGRVHIHLWRVORFDLVGHRUGHP ............................................................................... © ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
'LVSHQVDGDDQiOLVHGRVHIHLWRVORFDLVGHRUGHP .....................................................H (IHLWRVJOREDLVORFDLVHORFDOL]DGRVGHRUGHP......................................................................... 3URFHVVRDSUR[LPDGRSDUDFRQVLGHUDomRGRHIHLWRORFDOL]DGRGHRUGHP ................................ Emendas............................................................................................................................................ Esforços (VIRUoRVUHVLVWHQWHVGHFiOFXOR ..................................................................................................... (VIRUoRVVROLFLWDQWHVGHFiOFXOR.....................................................................................................
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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228
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
'LkPHWURGRVSLQRVGHGREUDPHQWRSDUDHVWULERV................................................................. 7DEHOD (OHPHQWRVHVWUXWXUDLVDUPDGRVFRPHVWULERV —
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229
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ABNT NBR 6118:2023
(VSDoDPHQWRPtQLPRHQWUHFDERVRXIHL[HVGHFDERVHPODMHVVHPYLJDV ..............................20.3.2.3 )LVVXUDVDEHUWXUDGH¿VVXUDVH¿VVXUDomR &RQWUROHGD¿VVXUDomR FULWpULRVGHSURMHWR ..................................................................................... 'LPHQVLRQDPHQWRHYHUL¿FDomRGHHOHPHQWRVOLQHDUHV —
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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231
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ABNT NBR 6118:2023
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Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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232
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
0yGXORGHHODVWLFLGDGH Aço de armadura ativa —
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© ABNT 2023 - Todos os direitos reservados
233
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ABNT NBR 6118:2023
— 3LODUSDGUmRSDUDSLODUHVGHVHomRUHWDQJXODUVXEPHWLGRVjÀH[mRFRPSRVWD REOtTXD ..................................................................................................................................... 'LPHQV}HVGHSLODUHVHSLODUHVSDUHGH .......................................................................... H 'LPHQVLRQDPHQWR............................................................................................................................... 'LVSHQVDGDDQiOLVHGRVHIHLWRVORFDLVGHRUGHP ..................................................................... ,PSHUIHLo}HVORFDLV .............................................................................................. 11.3.3.4.2 e 11.3.3.4.3 3LODUHV GH¿QLomR .......................................................................................................................14.4.1.2
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
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© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
—
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236
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
5HODomRiJXDFLPHQWR....................................................................................................H7DEHOD 5HJL}HVHVSHFLDLV .............................................................................................................................21 Resistência Aço de armadura ativa —
5HVLVWrQFLDjIDGLJD ..............................................................................................................
—
'LDJUDPDWHQVmRGHIRUPDomRUHVLVWrQFLDDRHVFRDPHQWRHjWUDomR .................................
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Aço de armadura passiva —
5HVLVWrQFLDjIDGLJD ..............................................................................................................8.3.8
—
'LDJUDPDWHQVmRGHIRUPDomRUHVLVWrQFLDDRHVFRDPHQWRHjWUDomR .................................8.3.6
&RQFUHWR —
5HVLVWrQFLDjFRPSUHVVmR.....................................................................................................8.2.4
—
5HVLVWrQFLDjWUDomR ..............................................................................................................
—
5HVLVWrQFLDQRHVWDGRPXOWLD[LDOGHWHQV}HV .....................................................8.2.6 e Figura 8.1
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5HVLVWrQFLDjIDGLJD ..............................................................................................................
5HVLVWrQFLDV .......................................................................................................................................12 —
9DORUHVFDUDFWHUtVWLFRV............................................................................................................12.2
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9DORUHVGHFiOFXOR..................................................................................................................12.3
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—
•
5HVLVWrQFLDGHFiOFXOR .................................................................................................12.3.1
•
7HQV}HVUHVLVWHQWHVGHFiOFXOR.....................................................................................12.3.2
•
5HVLVWrQFLDGHFiOFXORGRFRQFUHWR ..............................................................................12.3.3
&RH¿FLHQWHVGHSRQGHUDomRGDVUHVLVWrQFLDV ........................................................................12.4 •
&RH¿FLHQWHVGHSRQGHUDomRGDVUHVLVWrQFLDVQRHVWDGROLPLWH~OWLPR (/8 .............12.4.1
•
&RH¿FLHQWHVGHSRQGHUDomRGDVUHVLVWrQFLDVQRHVWDGROLPLWHGHVHUYLoR (/6 ........12.4.2
9HUL¿FDomRGDVHJXUDQoD ....................................................................................................... •
&RQGLo}HVFRQVWUXWLYDVGHVHJXUDQoD .........................................................................
•
&RQGLo}HVDQDOtWLFDVGHVHJXUDQoD ............................................................................
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(VIRUoRVUHVLVWHQWHVGHFiOFXOR ....................................................................................
•
(VIRUoRVVROLFLWDQWHVGHFiOFXOR....................................................................................
•
9DORUHVGDVUHVLVWrQFLDVGHDGHUrQFLD ...........................................................................9.3.2
5HVVRQkQFLD ...................................................................................................................................23.4 Retração ........................................................................................................... H$ © ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
Ruína e ruptura (VWDGROLPLWH~OWLPR (/8 ...............................................................................................................3.2.1 &DSDFLGDGHUHVLVWHQWHGDHVWUXWXUD.............................................................................................. 'RPtQLRVGHFiOFXOR ..............................................................................................................)LJXUD Sapatas ............................................................................................................................................22.6 Seção 'RPtQLRVGHHVWDGROLPLWH~OWLPRGHXPDVHomRWUDQVYHUVDO ................................................)LJXUD
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
Geometria da seção resistente................................................................................................... —
6Ho}HVSROLJRQDLVFRQYH[DVFKHLDV .............................................................................
—
6HomRFRPSRVWDGHUHWkQJXORV .....................................................................................
—
6Ho}HVYD]DGDV ...........................................................................................................
6HJXUDQoD 6HJXUDQoDHHVWDGRVOLPLWHV ...............................................................................................................10 &ULWpULRVGHVHJXUDQoD .....................................................................................................................10.1 9HUL¿FDomRGDVHJXUDQoD ................................................................................................................. —
&RQGLo}HVFRQVWUXWLYDVGHVHJXUDQoD .................................................................................
—
&RQGLo}HVDQDOtWLFDVGHVHJXUDQoD .....................................................................................
—
(VIRUoRVUHVLVWHQWHVGHFiOFXOR ...........................................................................................
—
(VIRUoRVVROLFLWDQWHVGHFiOFXOR ...........................................................................................
6HJXUDQoDHPUHODomRDRV(/8....................................................................................................16.2.3 6HJXUDQoDHPUHODomRDRV(/6 GHVHPSHQKRHPVHUYLoR .........................................................16.2.4 Serviço &RH¿FLHQWHVGHSRQGHUDomRGDVDo}HVQRHVWDGROLPLWHGHVHUYLoR (/6 .................................. &RH¿FLHQWHVGHSRQGHUDomRGDVUHVLVWrQFLDVQRHVWDGROLPLWHGHVHUYLoR (/6 .........................12.4.2 &RPELQDo}HVGHVHUYLoR Do}HV .................................................................................................. 11.8.3 —
&ODVVL¿FDomR..................................................................................................................... 11.8.3.1
—
&RPELQDo}HVGHVHUYLoRXVXDLV ....................................................................................... 11.8.3.2
'LPHQVLRQDPHQWRHYHUL¿FDomRGHODMHV(VWDGRVOLPLWHVGHVHUYLoR ...............................................19.3 (OHPHQWRVOLQHDUHVVXMHLWRVDVROLFLWDo}HVQRUPDLV(VWDGRVOLPLWHVGHVHUYLoR .............................. (VWDGRVOLPLWHVGHVHUYLoR (/6 ......................................................................................................10.4 (VWDGRVOLPLWHVGHVHUYLoR IDGLJD ...................................................................................................23.6 238
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
6HJXUDQoDHPUHODomRDRV(/6 GHVHPSHQKRHPVHUYLoR .........................................................16.2.4 6LPERORJLD .......................................................................................................................H 6ROGD (PHQGDVSRUVROGD.......................................................................................................................... 6ROGDELOLGDGH .................................................................................................................................8.3.9 6ROLFLWDo}HV &iOFXORGDVVROLFLWDo}HVGHFRPELQDo}HVGHDo}HV ................................................ 7DEHODVH Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
(OHPHQWRVOLQHDUHVVXMHLWRVDVROLFLWDo}HVQRUPDLV ......................................................................... (OHPHQWRVOLQHDUHVVXMHLWRVDVROLFLWDo}HVQRUPDLV (/6 ............................................................... (OHPHQWRVOLQHDUHVVXMHLWRVDIRUoDVFRUWDQWHV (/8 ...................................................................... (OHPHQWRVOLQHDUHVVXMHLWRVDWRUomR (/8 ..................................................................................... (OHPHQWRVOLQHDUHVVXMHLWRVDIRUoDFRUWDQWHHWRUomR (/GH¿VVXUDomRLQFOLQDGDGDDOPD ........... (OHPHQWRVOLQHDUHVVXEPHWLGRVDVROLFLWDo}HVFRPELQDGDV............................................................. (VIRUoRVVROLFLWDQWHVGHFiOFXOR..................................................................................................... (VIRUoRVVROLFLWDQWHVGHFiOFXOR FRQFUHWRVLPSOHV ................................................................... ,QWHUDomRGHVROLFLWDo}HVQRUPDLVHWDQJHQFLDLV ....................................................................... /DMHVHHOHPHQWRVOLQHDUHVFRPEw tGVXMHLWRVDIRUoDFRUWDQWH...................................................19.4 /DMHVVXMHLWDVDSXQomR ................................................................................................................... 5HJL}HVGHLQWURGXomRGHFDUJDVFRQFHQWUDGDV ..............................................................................21.2 Suspensão Armadura de suspensão %ORFRVVREUHHVWDFDV .............................................................................................................. &RQVRORV..................................................................................................................................22.3.1.4.4 'HQWHV*HUEHU .........................................................................................................................22.3.2.4.2 (OHPHQWRVOLQHDUHV ........................................................................................................................18.3.6 Temperatura 9DULDo}HVXQLIRUPHVGHWHPSHUDWXUD.......................................................................................... 11.4.2.1 9DULDo}HVQmRXQLIRUPHVGHWHPSHUDWXUD................................................................................... 11.4.2.2 Torção © ABNT 2023 - Todos os direitos reservados
239
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
Armadura para torção................................................................................................................... 18.3.4 (OHPHQWRVOLQHDUHVVXMHLWRVDWRUomR±(VWDGROLPLWH~OWLPR ............................................................ —
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
—
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•
&RQGLo}HVJHUDLV ........................................................................................................
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5HVLVWrQFLDGRHOHPHQWRHVWUXWXUDO±7RUomRSXUD ......................................................
•
Geometria da seção resistente ...................................................................................
•
9HUL¿FDomRGDFRPSUHVVmRGLDJRQDOGRFRQFUHWR.......................................................
•
&iOFXORGDVDUPDGXUDV ...............................................................................................
7RUomRHPSHU¿VDEHUWRVGHSDUHGH¿QD ............................................................................. •
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5LJLGH]jÀH[RWRUomR .................................................................................................
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5HVLVWrQFLDjÀH[RWRUomR ..........................................................................................
(VWDGROLPLWHGH¿VVXUDomRLQFOLQDGDGDDOPD±)RUoDFRUWDQWHHWRUomR ........................................ 6ROLFLWDo}HVFRPELQDGDV .................................................................................................................. —
—
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$UPDGXUDORQJLWXGLQDO ................................................................................................
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5HVLVWrQFLDGHEDQ]RFRPSULPLGR .............................................................................
7RUomRHIRUoDFRUWDQWH ....................................................................................................... •
*HQHUDOLGDGHV ...........................................................................................................
Torção ........................................................................................................................................... Tração 'LDJUDPDVWHQVmRGHIRUPDomRGRFRQFUHWRjWUDomR ...............................................................8.2.10.2 'LDJUDPDWHQVmRGHIRUPDomRUHVLVWrQFLDDRHVFRDPHQWRHjWUDomR —
Aço da armadura passiva ......................................................................................................8.3.6
—
Aço de armadura ativa...........................................................................................................
(OHPHQWRVOLQHDUHV$UPDGXUDVGHWUDomRQDÀH[mRVLPSOHVDQFRUDGDVSRUDGHUrQFLD ......18.3.2.3.1 (OHPHQWRVOLQHDUHV$UPDGXUDGHWUDomRQDVVHo}HVGHDSRLR ................................................18.3.2.4 *DQFKRVGDVDUPDGXUDVGHWUDomR DQFRUDJHPGHDUPDGXUDSDVVLYDSRUDGHUrQFLD ..............9.4.2.3 5HVLVWrQFLDGRFRQFUHWRjWUDomR .................................................................................................... 9DORUHVOLPLWHVSDUDDUPDGXUDVORQJLWXGLQDLVGHYLJDV............................................................... 240
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
—
Armadura de tração .......................................................................................................
—
9DORUHVPtQLPRVSDUDDDUPDGXUDGHWUDomRVREGHIRUPDo}HVLPSRVWDV.....................
—
$UPDGXUDGHSHOH ..........................................................................................................
—
Armaduras de tração e de compressão ........................................................................
9HUL¿FDomRGDIDGLJDGRFRQFUHWRHPWUDomR ............................................................................. 8WLOL]DomR &RQWUROHGDDFHLWDomRTXDQWRjDFHLWDELOLGDGHVHQVRULDOHjXWLOL]DomR ........................................13.4.3 ,QWHUIDFHVGRSURMHWRFRPDFRQVWUXomRXWLOL]DomRHPDQXWHQomR ....................................................
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
0DQXDOGHXWLOL]DomRLQVSHomRHPDQXWHQomR ................................................................................ 9DORUHV 9DORUHVGHFiOFXORGDIRUoDGHSURWHQVmR ....................................................................................9.6.1.4 9DORUHVGHFiOFXORGDVDo}HV ....................................................................................................... 11.6.3 9DORUHVGHFiOFXORGDVUHVLVWrQFLDV..................................................................................................12.3 9DORUHVFDUDFWHUtVWLFRVGDVDo}HV ................................................................................................. 11.6.1 9DORUHVFDUDFWHUtVWLFRVGDVUHVLVWrQFLDV..........................................................................................12.2 Vento Ação do vento ............................................................................................................................ 11.4.1.2 Vibração (VWDGROLPLWHGHYLEUDo}HVH[FHVVLYDV ................................................................................3.2.8 e 23.3 9LJDV $QFRUDJHPGDDUPDGXUDLQIHULRUGDYLJD ................................................................................22.3.2.4.4 $YDOLDomRDSUR[LPDGDGDÀHFKDHPYLJDV ................................................................................. —
)OHFKDLPHGLDWDHPYLJDVGHFRQFUHWRDUPDGR .............................................................
—
&iOFXORGDÀHFKDGLIHULGDQRWHPSRSDUDYLJDVGHFRQFUHWRDUPDGR ............................
—
)OHFKDHPYLJDVFRPDUPDGXUDVDWLYDV ........................................................................
'XWLOLGDGHHPYLJDV ....................................................................................................................... (VWUXWXUDVGHHOHPHQWRVOLQHDUHV ....................................................................................................14.6 —
+LSyWHVHVEiVLFDV............................................................................................................... 14.6.1
—
&DUDFWHUL]DomRGDJHRPHWULD...............................................................................................14.6.2 •
7UHFKRVUtJLGRV ............................................................................................................14.6.2.1
•
/DUJXUDFRODERUDQWHGHYLJDVGHVHomR7 .................................................................14.6.2.2
© ABNT 2023 - Todos os direitos reservados
241
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
ABNT NBR 6118:2023
•
0LVXODVHYDULDo}HVEUXVFDVGHVHo}HV ....................................................................14.6.2.3
•
9mRVHIHWLYRVGHYLJDV...............................................................................................14.6.2.4
'LPHQVLRQDPHQWR................................................................................................................................ )XURVTXHDWUDYHVVDPDVYLJDVQDGLUHomRGDDOWXUD ....................................................................21.3.3 )XURVTXHDWUDYHVVDPYLJDVQDGLUHomRGHVXDODUJXUD............................................................. ,QVWDELOLGDGHODWHUDOGHYLJDV .......................................................................................................... Paredes e vigas-parede ................................................................................................................21.3.2 9DORUHVOLPLWHVSDUDDUPDGXUDVORQJLWXGLQDLVGHYLJDV.............................................................. 9LJDV GH¿QLomR .........................................................................................................................14.4.1.1
Exemplar para uso exclusivo - UNIVERSIDADE DO VALE DO RIO DOS SINOS – UNISINOS - 92.959.006/0008-85
9LJDV GHWDOKDPHQWR ......................................................................................................................18.3 —
*HQHUDOLGDGHV .....................................................................................................................18.3.1
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$UPDGXUDORQJLWXGLQDO ..........................................................................................................18.3.2
—
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4XDQWLGDGHPtQLPD ..................................................................................................18.3.2.1
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'LVWULEXLomRWUDQVYHUVDO ............................................................................................18.3.2.2
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'LVWULEXLomRORQJLWXGLQDO.............................................................................................18.3.2.3
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$UPDGXUDGHWUDomRQDVVHo}HVGHDSRLR .................................................................18.3.2.4
$UPDGXUDWUDQVYHUVDOSDUDIRUoDFRUWDQWH ...........................................................................18.3.3 •
*HQHUDOLGDGHV ..........................................................................................................18.3.3.1
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(OHPHQWRVHVWUXWXUDLVDUPDGRVFRPHVWULERV ...........................................................18.3.3.2
•
(OHPHQWRVHVWUXWXUDLVDUPDGRVFRPEDUUDVGREUDGDV ..............................................18.3.3.3
•
Armadura para torção...................................................................................................18.3.4
•
$UPDGXUDGHSHOH .........................................................................................................
•
Armadura de suspensão ..............................................................................................18.3.6
•
$UPDGXUDVGHOLJDomRPHVDDOPDRXWDOmRDOPD ........................................................
9LJDVFRQWtQXDV ......................................................................................................................... 9LJDVSDUHGH $QiOLVHHVWUXWXUDOFRPYLJDVSDUHGHHSLODUHVSDUHGH ..................................................................14.8.1 1yVGHSyUWLFRVHOLJDo}HVHQWUHSDUHGHV ........................................................................................21.4 Paredes e vigas-parede ...............................................................................................................21.3.2 9LJDVHYLJDVSDUHGH GLPHQV}HV ..............................................................................................13.2.2 9LJDVSDUHGH ....................................................................................................................................22.2
242
© ABNT 2023 - Todos os direitos reservados
Nota: Este procedimento é cópia não controlada quando impresso. É válido o documento disponível na Intranet Corporativa. Somente para uso interno
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