MODELO NO-LINEAR INELSTICO PARA ANLISE DE ESTRUTURAS

METLICAS APORTICADAS EM CONDIES DE INCNDIO

Alexandre Landesmann

TESE SUBMETIDA AO CORPO DOCENTE DA COORDENAO DOS

PROGRAMAS DE PS-GRADUAO DE ENGENHARIA DA UNIVERSIDADE

FEDERAL DO RIO DE JANEIRO COMO PARTE DOS REQUISITOS

NECESSRIOS PARA A OBTENO DO GRAU DE DOUTOR EM CINCIAS EM

ENGENHARIA CIVIL.

Aprovada por:

________________________________________________

Prof. Eduardo de Miranda Batista, D.Sc.

________________________________________________

Prof. Jos Luis Drummond Alves, D.Sc.

________________________________________________

Prof. Ronaldo Carvalho Battista, Ph.D.

________________________________________________

Prof. Ricardo Hallal Fakury, D.Sc.

________________________________________________

Prof. Paulo de Mattos Pimenta, Dr.-Ing.

________________________________________________

Prof. Valdir Pignatta e Silva, D.Sc.

RIO DE JANEIRO, RJ - BRASIL

DEZEMBRO DE 2003

ii

LANDESMANN, ALEXANDRE

Modelo No-Linear Inelstico para Anlise

de Estruturas Metlicas Aporticadas em

Condies de Incndio [Rio de Janeiro] 2003

XXIII, 295 p. 29,7 cm (COPPE/UFRJ,

D.Sc., Engenharia Civil, 2003)

Tese - Universidade Federal do Rio de

Janeiro, COPPE

1. Estruturas de ao 2. Incndio 3. Modelo

Computacional 3. Plasticidade

I. COPPE/UFRJ II. Ttulo ( srie )

iii

A DEUS por tudo,

Aos meus pais, Henry e Catharina, e minha irm, Miriam,

A Carol.

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Agradecimentos:

Ao meu orientador, Professor Eduardo de Miranda Batista, pela competncia,

dedicao, aconselhamento e amizade minha sincera gratido.

Ao Professor Jos Luis Drummond Alves, pela valiosa co-orientao e pelo importante

estmulo nas diversas etapas do desenvolvimento deste trabalho de pesquisa.

Ao Professor Francisco Claudio Pereira de Barros da Comisso Nacional de Energia

Nuclear CNEN, pelo constante incentivo, apoio e amizade.

Ao Engenheiro Artur Correa Filho da CNEN, pelo apoio e compreenso, demonstrados

durante todas as etapas deste estudo.

A todos meus colegas de trabalho na CNEN, em especial, aos Engenheiros Ricardo

Colosimo, Humberto Teixeira e Ronaldo Pollis, pelo apoio e amizade no decorrer desta

jornada.

Comisso Nacional de Energia Nuclear, pelo apoio institucional, que viabilizou o

desenvolvimento deste trabalho de pesquisa.

A todos meus colegas da COPPE/UFRJ, especialmente, Hisashi Inoue, Santigo

Venncio, Danilo Fernandes, Maurcio Alves e Tiago de Oliveira, pela amizade,

companheirismo e diversas colaboraes neste perodo de convivncia.

COPPE/UFRJ, em particular, ao Programa de Engenharia Civil, representado por

todos seus Professores e Funcionrios, o meu sincero agradecimento.

Aos professores Roger Plank e Ian Burgess da Universidade de Sheffield (UK) pela

precisa orientao durante minha estadia naquela instituio.

Ao Professor Jean-Marc Franssen da Universidade de Lige (Blgica) pela permisso

de utilizao do Programa de Anlise Estrutural SAFIR, largamente utilizado nesta

pesquisa para fins de validao dos nossos resultados.

Coordenao de Aperfeioamento de Pessoal de Nvel Superior CAPES, pelo

auxlio financeiro, que possibilitou a realizao do Programa de Doutorado no Brasil

com Estgio no Exterior (PDEE), durante o perodo de Novembro/2002 a

Fevereiro/2003 junto a Universidade de Sheffield (UK).

v

Resumo da Tese apresentada COPPE/UFRJ como parte dos requisitos necessrios

para a obteno do grau de Doutor em Cincias (D.Sc.)

MODELO NO-LINEAR INELSTICO PARA ANLISE DE ESTRUTURAS

METLICAS APORTICADAS EM CONDIES DE INCNDIO

Alexandre Landesmann

Dezembro/2003

Orientadores: Prof. Eduardo de Miranda Batista

Prof. Jos Luis Drummond Alves

Programa: Engenharia Civil

Este trabalho dedicado ao desenvolvimento de um modelo computacional

para anlise no-linear elastoplstica de estruturas de ao, planas e aporticadas, sob

condies de incndio. A primeira etapa do processo de anlise, traduzida pela

determinao da variao do campo de temperaturas de sees-transversais expostas ao

fogo, realizada por meio de procedimento numrico no-linear transiente de

transferncia de calor, desenvolvido com base na formulao geral do Mtodo dos

Elementos Finitos (MEF). O comportamento estrutural numericamente investigado

por meio de princpios de plasticidade concentrada, que fazem uso de modelos refinados

de rtulas plsticas, funes de estabilidade, mdulos tangentes e superfcies inelsticas

de reduo de resistncia, permitindo-se assim, estimar o tempo crtico de resistncia ao

fogo, associado formao de mecanismos de colapso estrutural. Os resultados obtidos,

para um grupo selecionado de estruturas aporticadas, so examinados tomando-se por

base o Programa SAFIR e recomendaes previstas pela normatizao nacional e

internacional, vigente.

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Abstract of Thesis presented to COPPE/UFRJ as a partial fulfillment of the

requirements for the degree of Doctor of Science (D.Sc.)

SECOND-ORDER INELASTIC MODEL FOR THE ANALYSIS OF STEEL-

FRAMED STRUCTURES UNDER FIRE CONDITIONS

Alexandre Landesmann

December/2003

Advisors: Prof. Eduardo de Miranda Batista

Prof. Jos Luis Drummond Alves

Department: Civil Engineering

This work is dedicated to the development of a computational model for the

inelastic second-order analysis of plane steel-framed structures under fire conditions.

The first step of the analysis process, represented by the determination of the variation

of the transversal temperature field, is performed by a numerical transient nonlinear

heat transfer procedure, that was developed on the general basis of the Finite Element

Method (FEM). The structural behavior is numerically tracked by the concept of

concentrated plasticity, making use of refined plastic hinges models, stability functions,

tangent modulus models and gradual inelastic plastic surfaces, allowing the estimation

of the fire-resistance critical time, associated with the development of the structural

collapse mechanism. The numerical results, for a selected group of framed structures,

are examined in contrast with the SAFIR computational program results as well as

recommendations proposed by national and international standards.

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Sumrio

Captulo 1: INTRODUO

1.1 Motivao ................................................................................................... 1

1.2 Importncia da anlise estrutural no contexto da engenharia de

incndio....................................................................................................... 3

1.3 Pesquisa bibliogrfica sobre a anlise de estruturas de ao sob

fogo .............................................................................................................. 9

1.4 Mtodo das rtulas plsticas..................................................................... 16

1.5 Organizao deste trabalho ...................................................................... 19

Captulo 2: ANLISE TRMICA 2.1 Introduo ..................................................................................................22

2.2 Curvas de incndio ....................................................................................24

2.3 Modelo trmico simplificado segundo EC-3 ...........................................27

2.3.1 Elementos estruturais sem proteo contra incndio...................................27

2.3.2 Elementos estruturais com material de proteo contra incndio ...............33

2.4 Elemento unidimensional de transferncia de calor ..............................35

2.4.1 Elementos estruturais sem proteo trmica................................................35

2.4.2 Elementos estruturais protegidos contra incndio .......................................44

2.5 Verificao dos modelos trmicos implementados .................................48

2.5.1 Elementos estruturais sem proteo trmica................................................50

2.5.2 Elementos estruturais protegidos contra incndio .......................................54

2.6 Considerao da variao de temperatura na seo-transversal pelo

mtodo de anlise avanada......................................................................57

2.6.1 Seo-transversal equivalente......................................................................57

2.6.2 Limites equivalentes de resistncia plstica ................................................61

2.6.3 Esforos de engastamento perfeito devido variao de temperatura ........62

2.6.4 Temperatura de referncia ...........................................................................64

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Captulo 3: ANLISE ESTRUTURAL

3.1 Anlise avanada de estruturas................................................................69

3.2 Considerao de efeitos no-lineares geomtricos..................................71

3.2.1 Restries e consideraes gerais para elemento de viga-coluna................71

3.2.2 Funes de estabilidade para elemento de viga-coluna...............................73

3.2.3 Relao de rigidez tangente .........................................................................77

3.2.4 Aplicaes com modelos de funes de estabilidade ..................................80

3.2.5 Fatores de amplificao de momentos fletores............................................83

3.3 Conceito de mdulo tangente....................................................................91

3.3.1 Adaptao do conceito de anlise avanada s prescries da NBR-8800 .94

3.3.2 Considerao do efeito de temperatura........................................................101

3.3.3 Resistncia de barras comprimidas, segundo EC-3/Parte-2 (2001) ............102

3.3.4 Modelo de mdulo tangente segundo o Eurocdigo ...................................105

3.3.5 Estudos com modelos de mdulos tangentes...............................................107

3.4 Modelo inelstico de reduo de rigidez flexional ..................................115

3.5 Considerao de ligaes semi-rgidas.....................................................123

3.5.1 Modelo de ligao semi-rgida KISHI e CHEN (1990) ..............................125

3.5.2 Modificao da rigidez do elemento devido presena de ligaes...........127

Captulo 4: RESULTADOS

4.1 Introduo .................................................................................................. 131

4.2 Vigas isoladas em condies de incndio ................................................. 134

4.3 Pilares isolados sob ao de incndio ....................................................... 143

4.4 Prtico plano sob ao de incndio .......................................................... 155

4.5 Prtico plano industrial sob ao de incndio......................................... 166

4.6 Edifcio industrial sob ao de incndio .................................................. 169

4.7 Anlise comparativa dos resultados......................................................... 177

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Captulo 5: CONSIDERAES FINAIS 5.1 Breve resumo do presente trabalho ......................................................... 176

5.2 Concluses .................................................................................................. 178

5.3 Sugestes para trabalhos futuros ............................................................. 181

6. Referncias bibliogrficas ......................................................................... 185

Anexo A: IMPLEMENTAO COMPUTACIONAL A.1 Introduo .................................................................................................. 203

A.2 Entrada de dados para o programa de anlise trmica ......................... 204

A.3 Entrada de dados para o programa de anlise estrutural ..................... 209

A.4 Procedimentos de solues numricas ..................................................... 224

Anexo B: RESULTADOS COM MODELO DE ANLISE TRMICA B.1 Introduo .................................................................................................. 231

B.2 Variao do campo de temperaturas ....................................................... 233

B.3 Seo-transversal equivalente .................................................................. 245

Anexo C: VERIFICAES ESTRUTURAIS EM TEMPERATURA

AMBIENTE C.1 Introduo .................................................................................................. 268

C.2 Prtico plano tipo portal ........................................................................ 271

C.3 Prtico plano tipo industrial .................................................................. 273

C.4 Edifcio de seis andares ............................................................................ 275

C.5 Parmetros adimensionais padronizados para ligaes com

cantoneiras.................................................................................................. 277

C.6 Prtico de oito andares.............................................................................. 281

C.7 Exemplo de aplicao em projeto............................................................. 289

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ndice de figuras:

Captulo 1: Introduo

Figura 1.1: Fases de um incndio natural, comparadas com curva

padronizada temperatura-tempo (ISO 834-1, 1999). ......................... 4

Figura 1.2: Medidas de segurana contra incndio em edificaes...................... 6

Figura 1.3: Principais etapas seguidas pelo procedimento computacional

desenvolvido....................................................................................... 20

Captulo 2: Anlise Trmica

Figura 2.1: Comparao entre diferentes curvas de incndio, previstas

pelo EC-1/Parte-2 (2001).................................................................27

Figura 2.2: Diviso da seo-transversal de perfis I ou H para

utilizao do modelo trmico simplificado......................................28

Figura 2.3: Calor especfico do ao (ca) em funo da temperatura

(EC-3/Parte-2, 2001)........................................................................30

Figura 2.4: Elemento finito trmico unidimensional (1D) com funes de

interpolao lineares (Ni e Nj) ..........................................................36

Figura 2.5: Discretizao da seo-transversal por meio de elementos

unidimensionais (1D) para anlise trmica......................................37

Figura 2.6: Condutividade trmica do ao a em funo da temperatura,

segundo modelo recomendado pelo EC-3/Parte-2 (2001) ...............38

Figura 2.7: Balano trmico em cada elemento 1D; contribuio do fluxo

de calor para anlise trmica............................................................39

Figura 2.8: Esquema de integrao temporal pelo mtodo dos trapzios

para soluo do sistema de equaes transientes de

temperatura ......................................................................................42

Figura 2.9: Aplicao do elemento trmico unidimensional para anlise

de perfis metlicos envolvidos por material de proteo

contra incndio.................................................................................44

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Figura 2.10: Simulao de perfis metlicos protegidos por material de

revestimento trmico por meio de elementos trmicos

unidimensionais ...............................................................................46

Figura 2.11: Comparao entre variao de temperatura para o grupo de

perfis selecionados, assumindo-se exposio em 3 faces ................51

Figura 2.12: Comparao entre variao de temperatura para o grupo de

perfis selecionados, assumindo-se exposio em 4 faces ................52

Figura 2.13: Variao de temperatura para perfis selecionados, protegidos

por material de revestimento, expostos ao fogo em 3 faces ............54

Figura 2.14: Variao de temperatura para perfis selecionados, protegidos

por material de revestimento, expostos ao fogo em 3 faces ............55

Figura 2.15: Segmentao da seo-transversal em funo do aumento de

temperatura; (a) sistema de coordenadas dos segmentos.................58

Figura 2.16: Variao dos fatores de reduo do ao em funo da

temperatura (EC-3/Parte-2, 2001)....................................................58

Figura 2.17: Alongamento do ao () em funo da temperatura, segundo

modelo sugerido pelo EC-3/Parte-2 (2001). ....................................63

Captulo 3: Anlise Estrutural

Figura 3.1: Elemento de viga-coluna submetido a foras axiais e

momentos de extremidade. ..............................................................73

Figura 3.2: Deslocamentos nodais do elemento viga-coluna, para os ns

sistemas local e global. ....................................................................77

Figura 3.3: Sistemas de foras equivalentes para o elemento de viga-

coluna...............................................................................................79

Figura 3.4: Curvas de deslocamento para diferentes condies de

imperfeio geomtrica inicial.........................................................81

Figura 3.5: Modelo de pilar isolado adotado nas avaliaes do efeito P-

delta..................................................................................................85

Figura 3.6: Comparao entre os fatores de amplificao de momento

obtidos pelo modelo de funes de estabilidade (PNL-F),

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soluo terica e especificaes do LRFD (1999), para

relaes P/Pe inferiores a 0,4. ..........................................................86

Figura 3.7: Comparao entre os fatores de amplificao de momento

obtidos pelo modelo de funes de estabilidade (PNL-F),

soluo terica e especificaes do AISC-LRFD (1999), para

relaes P/Pe entre 0,5 e 0,9. ...........................................................87

Figura 3.8: Amplificao de momento obtidos pela soluo terica,

especificaes do AISC-LRFD (1999) e NBR-8800 (1986). ..........88

Figura 3.9: Comparao entre curvas de flambagem de pilares (a-d)

adotadas pela NBR-8800 (1986) e pelo AISC-LRFD (1999)..........96

Figura 3.10: Comparao entre curvas de flambagem de pilares (a-d)

adotadas pela NBR-8800 (1986) e as curvas pseudo-elsticas........97

Figura 3.11: Redues inelsticas de rigidez devido ao efeito da fora

axial, obtidos a partir das curvas de resistncia da

NBR-8800 (1986) e AISC-LRFD (1999). .......................................100

Figura 3.12: Curvas de resistncia de barras comprimidas para diferentes

nveis de temperatura, segundo NBR-14323 (1999). ......................102

Figura 3.13: Curvas de resistncia de barras comprimidas para diferentes

nveis de temperatura, segundo EC-3/Parte-2 (2001). .....................104

Figura 3.14: Comparao entre as curvas de flambagem de Euler, EC-

3/Parte-2 (2001) e NBR-14323 (1999), em condies de

temperatura ambiente (20oC). ..........................................................104

Figura 3.15: Reduo inelstica de rigidez devido ao efeito da fora axial,

obtido a partir da curva de resistncia do EC-3/Parte2 (2001). .......107

Figura 3.16: Modelo de barra isolada empregada nas anlises numricas

para comparao entre o modelo de mdulo tangente e as

curvas de resistncia do AISC-LRFD (1999) e da

NBR-8800 (1986). ...........................................................................108

Figura 3.17: Comparao entre resultados de viga-coluna isolada sob

temperatura ambiente, para curva de flambagem a

(NBR-8800, 1986). ..........................................................................109

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Figura 3.18: Comparao entre resultados de viga-coluna isolada sob

temperatura ambiente, para curva de flambagem b

(NBR-8800, 1986). ..........................................................................109

Figura 3.19: Comparao entre resultados de viga-coluna isolada sob

temperatura ambiente, para curva de flambagem c

(NBR-8800, 1986). ..........................................................................110

Figura 3.20: Comparao entre resultados de viga-coluna isolada sob

temperatura ambiente, para curva de flambagem d

(NBR-8800, 1986). ..........................................................................110

Figura 3.21: Comparao entre resultados de viga-coluna isolada sob

temperatura ambiente, para curva de flambagem original do

AISC-LRFD (1999). ........................................................................111

Figura 3.22: Comparao entre os resultados obtidos com o modelo de

mdulo tangente e as curvas de resistncia do EC-3/Parte-2,

para valores de esbelteza entre 0,1 e 0,9..........................................113

Figura 3.23: Comparao entre os resultados obtidos com o modelo de

mdulo tangente e as curvas de resistncia do EC-3/Parte-2,

para valores de esbeltez entre 1,1 e 1,9............................................114

Figura 3.24: Modelos inelsticos para reduo de rigidez flexional

propostos por LIEW e WHITE (1993) em condies de

temperatura ambiente.......................................................................116

Figura 3.25: Curvas de resistncia plstica e de incio de plastificao

obtidas em funo das prescries do EC-3 (2003) e do

AISC-LRFD (1999). ........................................................................117

Figura 3.26: Relao tenso-deformao para o ao em condies de

temperatura elevada, segundo o EC-3/Parte-2 (2001). ....................119

Figura 3.27: Modificao da relao tenso-deformao do ao em funo

da temperatura, segundo o modelo proposto pelo

EC-3/Parte-2 (2001).........................................................................120

Figura 3.28: Modelos polinomial de 4o grau proposto para o fator de

reduo de rigidez flexional para as temperaturas no ao ()

entre 100oC e 1200oC.......................................................................122

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Figura 3.29: Comportamento de curvas momento-rotao, para ligaes

semi-rgidas segundo o modelo de KISHI e CHEN (1990).............126

Figura 3.30: Elemento viga-coluna, modificado devido a presena de

ligaes de extremidade semi-rgidas. .............................................128

Captulo 4: Resultados

Figura 4.1: Modelo estrutural de viga isolada em condies de incndio;

(a) seo-transversal do perfil exposto ao incndio nas trs

faces inferiores. ................................................................................ 134

Figura 4.2: Comparao entre os deslocamentos verticais em funo do

tempo de incndio normalizado, para o modelo de viga

isolada. ............................................................................................. 135

Figura 4.3: Comparao entre os deslocamentos verticais elsticos em

funo do tempo de incndio normalizado. ..................................... 138

Figura 4.4: Variao da configurao deformada do modelo de viga

simples, sob fator de carga =0,6. ................................................... 139

Figura 4.5: Comparao entre temperaturas para o perfil IPE-360

exposto ao fogo em 3 faces: (a) temperaturas na seo a 600

segundos; (b) idem para 1800 segundos; (c) idem para 3600

segundos........................................................................................... 140

Figura 4.6: Modelo estrutural de pilares isolados; (a) perfil exposto ao

fogo em 3 faces: mesa inferior e alma; (b) idem para 4 faces:

alma e mesas. ................................................................................... 143

Figura 4.7: Deslocamentos horizontais em funo do tempo de incndio,

para o modelo de pilar isolado formado pelo perfil IPE-360. ......... 145

Figura 4.8: Deslocamentos horizontais em funo do tempo de incndio,

para o modelo de pilar isolado formado pelo perfil W-360............. 145

Figura 4.9: Distribuio de temperaturas para o perfil IPE-360 exposto

ao fogo em 4 faces; (a) temperaturas ao longo da seo-

transversal no tempo de 600 segundos; (b) idem para 1800

segundos; (c) idem para 3600 segundos. ......................................... 147

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Figura 4.10: Distribuio de temperaturas para o perfil W-360 exposto ao

fogo em 3 faces; (a) temperaturas a 600 segundos; (b) 1800

seg.; (c) 3600 seg. ............................................................................ 148

Figura 4.11: Distribuio de temperaturas para o perfil W-360 exposto ao

fogo em 4 faces(a) temperaturas a 600 segundos; (b) 1800

seg.; (c) 3600 seg. ............................................................................ 148

Figura 4.12: Superfcies de resistncia plstica da seo-transversal do

perfil IPE-360 exposta ao fogo em 3 e 4 faces. ............................... 149

Figura 4.13: Superfcies de resistncia plstica da seo-transversal do

perfil W-360 aquecido em 3 e 4 faces. ............................................ 150

Figura 4.14: Mdulos elsticos equivalentes: EA e EI em funo do

tempo de incndio para os perfis IPE-360 e W-360, expostos

em 3 e 4 faces................................................................................... 151

Figura 4.15: Variao de esforos axiais equivalentes: Py e P, em funo

do tempo de incndio para o perfil IPE-360, exposto ao fogo

em 3 e 4 faces................................................................................... 152

Figura 4.16: Variao de esforos axiais equivalentes: Py e P, em funo

do tempo de incndio para o perfil W-360, exposto ao fogo

em 3 e 4 faces................................................................................... 153

Figura 4.17: Momentos equivalentes normalizados: Mp e M, em funo

do tempo de incndio para o perfil IPE-360, exposto ao fogo

em 3 e 4 faces................................................................................... 154

Figura 4.18: Momentos equivalentes normalizados: Mp e M, em funo

do tempo de incndio para o perfil W-360, exposto ao fogo

em 3 e 4 faces................................................................................... 154

Figura 4.19: Modelo de prtico plano tipo portal adaptado de VOGEL

(1985), sob condies de incndio normalizado; (a) perfis

expostos ao fogo nas trs faces internas: alma e mesa inferior. ...... 156

Figura 4.20: Comparao entre deslocamentos horizontais do modelo de

prtico plano em funo do tempo de incndio, obtidos pelos

programas PNL-F e SAFIR (FRANSSEN et al., 2000), para

diferentes nveis de carregamento aplicado ()............................... 157

xvi

Figura 4.21: Configurao deformada do prtico plano para diferentes

intervalos de tempo de incndio, =0,4........................................... 159

Figura 4.22: ndices plsticos associados flexo (*) para a estrutura do

prtico plano deformada sob fator de carga de 0,4; no

instante de 960s................................................................................ 160

Figura 4.23: Distribuio de temperaturas para o perfil HEA-340 exposto

ao fogo em 3 faces; (a) distribuio de temperaturas ao longo

da seo-transversal no instante de 600 segundos; (b) idem

para 1800 segundos; (c) idem para 3600 segundos. ........................ 161

Figura 4.24: Distribuio de temperaturas para o perfil HEB-300 exposto

ao fogo em 3 faces; (a) 600 segundos; (b) 1800 seg.;

(c) 3600 seg...................................................................................... 162

Figura 4.25: Curvas de resistncia plstica para os perfis HEA-340 e

HEB-300, para diferentes instantes do incndio padronizado......... 163

Figura 4.26: Variao normalizada da resistncia axial e esforo axial de

engastamento, em funo do tempo de incndio. ............................ 164

Figura 4.27: Variao do momento plstico e momento de engastamento

perfeito em funo do tempo de incndio para os perfis

HEA-340 e HEB-300. ...................................................................... 164

Figura 4.28: Reduo dos mdulos elsticos equivalentes: EA e EI em

funo do tempo de incndio para os perfis HEA-340 e

HEB-300 adotados no modelo de prtico plano. ............................. 165

Figura 4.29: Configurao geomtrica inicial e carregamento externo do

modelo de prtico plano industrial; (a) seo-transversal do

perfil IPE-360. ................................................................................. 166

Figura 4.30: Comparao entre os deslocamentos horizontais em funo

do tempo de incndio normalizado, obtidos pelos programas

PNL-F e SAFIR, para o modelo de prtico plano industrial,

em regime elstico. .......................................................................... 167

Figura 4.31: Desenvolvimento da configurao deformada do prtico

plano industrial para diferentes instantes do incndio, obtido

pelo programa PNL-F ...................................................................... 168

xvii

Figura 4.32: Modelo de edifcio de 4 andares sob incndio; (a) pilares

expostos em 3 faces; (b) idem para 4 faces; (c) vigas expostas

em 3 faces; (d) carregamentos vertical; (e) 50% do vento

proposto LEON et al. (1996). .......................................................... 169

Figura 4.33: Relao momento-rotao segundo o modelo tri-linear

proposto por LEON et al. (1996) para ligaes semi-rgidas. ......... 171

Figura 4.34: Distribuio de ligaes semi-rgidas para o edifcio de

4 andares proposto por LEON et al. (1996)..................................... 172

Figura 4.35: Variao de deslocamento horizontal do edifcio de 4 andares

(LEON et al., 1996), sob diferentes condies de incndio,

obtidos pelos programas PNL e SAFIR

(FRANSSEN et al., 2000). .............................................................. 172

Figura 4.36: Variao da configurao deformada do edifcio de 4 andares

adaptado de LEON et al. (1996) no tempo de incndio,

obtido pelo programa PNL-F........................................................... 175

Figura 4.37: Superfcies de resistncia plstica para diferentes instantes do

incndio padronizado para os perfis: W21x44 (3 e 4 faces) e

W14x82............................................................................................ 176

Figura 4.38: Reduo dos mdulos elsticos equivalentes: EA e EI em

funo do tempo de incndio para os perfis: W21x44 e

W14x82 (3 e 4 faces) adotados no modelo de 4 andares

adaptado de LEON et al. (1996). ..................................................... 176

xviii

ndice de tabelas

Captulo 2: Anlise Trmica

Tabela 2.1: Permetros expostos para elementos que compem a seo-

transversal de perfis metlicos I ou H. .......................................32

Tabela 2.2: Propriedades de elementos unidimensionais utilizados na

discretizao de sees-transversais de perfis metlicos I ou

H envolvidos por material de proteo contra incndio................47

Tabela 2.3: Fatores de massividade para o grupo de perfis metlicos

selecionados para anlise trmica entre os diferentes modelos

implementados. ................................................................................49

Tabela 2.4: Propriedades trmicas do material de proteo contra

incndio adotado nas anlises de comparao de variao de

temperatura. .....................................................................................50

Tabela 2.5: Diferenas percentuais entre resultados trmicos, para perfis

metlicos sem a presena de material de proteo contra

incndio............................................................................................53

Tabela 2.6: Diferenas percentuais entre resultados trmicos, para perfis

metlicos envolvidos por material de proteo contra

incndio............................................................................................56

Tabela 2.7: Fatores de reduo das propriedades mecnicas do ao para

diferentes nveis de temperatura ......................................................59

Tabela 2.8: Diferenas percentuais para propriedades de sees

equivalentes, de perfis metlicos desprotegidos, expostos ao

fogo em 3 faces. ...............................................................................66

Tabela 2.9: Diferenas percentuais para propriedades de sees

equivalentes, de perfis metlicos desprotegidos, expostos ao

fogo em 4 faces. ...............................................................................67

Tabela 2.10: Diferenas percentuais para propriedades de sees

equivalentes, de perfis metlicos protegidos, expostos ao

fogo em 3 faces. ...............................................................................67

xix

Tabela 2.11: Diferenas percentuais para propriedades de sees

equivalentes, de perfis metlicos protegidos, expostos ao

fogo em 4 faces. ...............................................................................68

Captulo 3: Anlise Estrutural

Tabela 3.1: Comparao entre valores de funes de estabilidade.....................76

Tabela 3.2: Diferenas entre os fatores mximos de amplificao de

momento para diferentes valores de carga axial e momento

aplicado. ...........................................................................................89

Tabela 3.3: Comparao entre os fatores mximos de amplificao de

momento, para momentos fletores com o mesmo sentido

(MA/MB 0).....................................................................................90

Tabela 3.4: Comparao entre fatores mximos de amplificao de

momento fletor, para momentos fletores opostos

(MA/MB < 0).....................................................................................90

Tabela 3.5: Curvas de flambagem para perfis tipo I ou H, fletidos

segundo seu eixo de maior inrcia (NBR-8800, 1986)....................95

Tabela 3.6: Fator de imperfeio para curvas de flambagem

(NBR8800, 1986).............................................................................95

Tabela 3.7: Fator de escala curvas de flambagem elsticas................................97

Tabela 3.8: Constantes para as expresses analticas do fator de reduo

de rigidez inelstico .........................................................................99

Tabela 3.9: Constantes para fator de reduo de rigidez inelstico

aproximados por polinmios de quarto-grau ...................................100

Tabela 3.10: Diferena entre as curvas de resistncia originais

(NBR8800, 1986 e LRFD-AISC, 1999) (A) e os resultados

obtidos com respectivo modelo de mdulo tangente (B). ...............112

Tabela 3.11: Diferena entre curvas de resistncia (EC-3/Parte-2, 2001)

(A) e resultados pelo modelo de mdulo tangente PNL-F

(B), para valores de esbeltez entre 0,1 e 1,9; temperatura no

ao entre 20oC e 1200oC. .................................................................115

Tabela 3.12: Limites de tenso-deformao para o ao em condies de

temperatura elevada, segundo o EC-3/Parte-2 (2001). ....................119

xx

Tabela 3.13: Coeficientes polinomiais para o fator de reduo de rigidez

flexional, em funo da temperatura do ao. ...................................121

Captulo 4: Resultados

Tabela 4.1: Tempo Crtico de Resistncia ao Fogo (TCRF) obtido pelos

programas PNL-F e SAFIR (FRANSSEN et al., 2000) para o

modelo de viga isolada. ................................................................... 137

Tabela 4.2: Comparao entre valores de flechas mximas elsticas

obtidos pelos programas PNL-F e SAFIR para diferentes

nveis de momento fletor, aps 1h de incndio. .............................. 139

Tabela 4.3: TCRF obtidos pelos programas PNL-F e SAFIR para

diferentes nveis de carregamento aplicado () para o prtico

plano tipo portal. .......................................................................... 158

Tabela 4.4: TCRF obtidos pelos programas PNL-F e SAFIR para

diferentes condies de aquecimento do prtico de 4 andares

(LEON et al. ,1996). ........................................................................ 173

xxi

Lista de smbolos:

Letras romanas

A rea da seo-transversal, rea do elemento

Ae superfcie da seo-transversal exposta ao fogo

Am rea da seo-transversal material de proteo trmica

A rea equivalente da seo-transversal

b caractersticas trmicas do material de fechamento do compartimento

B1 fator de amplificao de momento fletor

B2 fator de amplificao de momento fletor

bf largura da mesa de perfil metlico

ca calor especfico do ao

cm calor especfico do material de proteo contra incndio

Cm fator de homogeneizao de momentos fletores

dci deslocamento locais do elemento viga-coluna

dgi grau de liberdade em coordenadas globais

E mdulo elstico (mdulo de Young)

EA mdulo elstico equivalente associado rigidez axial

EI mdulo elstico equivalente associado rigidez flexional

Et mdulo tangente

fp, tenso limite proporcional

fy tenso de escoamento para temperatura ambiente

h altura total da alma de perfil metlico

Hcr matriz de transferncia de calor por conveco e por radiao

hw altura til da alma de perfil metlico

I momento de inrcia equivalente

k segmento bsico da seo-transversal

ka fator de correo emprico para anlises em condies de incndio

Kt matriz de conduo de calor

L comprimento do elemento

comprimento do elemento

M matriz de massa concentrada

M momento de extremidade

xxii

Mp20 momento plstico para temperatura ambiente (ou simplesmente Mp)

Mp momento plstico em funo da temperatura

n parmetro de forma de ligaes semi-rgidas

Ni funes de interpolao lineares

O fator de abertura para o compartimento

P esforo axial

p permetro exposto da seo-transversal

Pcr carga crtica de Euler, tambm adotado (Pe)

Py20 resistncia plstica axial para temperatura ambiente (ou simplesmente Py)

Py resistncia plstica axial em funo da temperatura

q fluxo de calor

qt,d densidade de carga de incndio acondicionada no compartimento

Rcr vetor de transferncia de calor por conveco e por radiao

Rkt rigidez tangente da ligao

rs comprimento de raio de solda de perfil metlico

S1 funes de estabilidade

S2 funes de estabilidade

tf espessura da mesa de perfil metlico

tlim taxa de crescimento do incndio

tm espessura do material de proteo contra incndio

tw espessura da alma de perfil metlico

u permetro efetivo da seo-transversal

u/A fator de massividade de elementos estruturais de ao sem proteo contra incndio

um permetro efetivo da seo-transversal envolvida por material de proteo

um/A fator de massividade para elementos com material de proteo contra fogo

Letras gregas:

j fluxo de calor por unidade de rea

la coeficiente de conduo de calor do ao

ra massa especfica do ao

ac coeficiente de transferncia de calor por conveco

jc fluxo de calor por unidade de rea associado conveco

qg temperatura do ambiente

xxiii

lm condutividade trmica do material de proteo contra incndio

qm temperatura na superfcie do ao

rm massa especfica do material de proteo

ar coeficiente de transferncia de calor por radiao

jr fluxo de calor por unidade de rea associado radiao

x comprimento qualquer do elemento de viga-coluna

estado de esforos combinados, momento fletor e esforo axial

fator de imperfeio

fator de forma especfico para anlises em condies de incndio

t intervalo de tempo

a,t elevao de temperatura do ao em funo do tempo t

res coeficiente de emissividade resultante

alongamento do ao em funo da temperatura

parmetros de reduo de rigidez sob temperatura ambiente

parmetros de reduo de rigidez em funo da temperatura

rotao de extremidade do elemento

temperatura

0 temperatura do ambiente antes do incio do aquecimento

a temperatura do ao

max temperatura mxima dada pela fase de aquecimento

r rotao relativa entre a viga e a coluna

ref temperatura de referncia

E, fator de reduo do mdulo elstico

p, fator de reduo do limite proporcional

y, fator de reduo do limite de escoamento

parmetro de esbeltez para barras comprimidas

armazenagem relativa de calor do material de proteo trmica

fator de correo

deformao

tenso

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