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MODELO NÃO-LINEAR INELÁSTICO PARA ANÁLISE DE ESTRUTURAS METÁLICAS APORTICADAS EM CONDIÇÕES DE INCÊNDIO Alexandre Landesmann TESE SUBMETIDA AO CORPO DOCENTE DA COORDENAÇÃO DOS PROGRAMAS DE PÓS-GRADUAÇÃO DE ENGENHARIA DA UNIVERSIDADE FEDERAL DO RIO DE JANEIRO COMO PARTE DOS REQUISITOS NECESSÁRIOS PARA A OBTENÇÃO DO GRAU DE DOUTOR EM CIÊNCIAS EM ENGENHARIA CIVIL. Aprovada por: ________________________________________________ Prof. Eduardo de Miranda Batista, D.Sc. ________________________________________________ Prof. José 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

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Page 1: METÁLICAS APORTICADAS EM CONDIÇÕES DE INCÊNDIO …

MODELO NÃO-LINEAR INELÁSTICO PARA ANÁLISE DE ESTRUTURAS

METÁLICAS APORTICADAS EM CONDIÇÕES DE INCÊNDIO

Alexandre Landesmann

TESE SUBMETIDA AO CORPO DOCENTE DA COORDENAÇÃO DOS

PROGRAMAS DE PÓS-GRADUAÇÃO DE ENGENHARIA DA UNIVERSIDADE

FEDERAL DO RIO DE JANEIRO COMO PARTE DOS REQUISITOS

NECESSÁRIOS PARA A OBTENÇÃO DO GRAU DE DOUTOR EM CIÊNCIAS EM

ENGENHARIA CIVIL.

Aprovada por:

________________________________________________

Prof. Eduardo de Miranda Batista, D.Sc.

________________________________________________

Prof. José 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

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LANDESMANN, ALEXANDRE

Modelo Não-Linear Inelástico para Análise

de Estruturas Metálicas Aporticadas em

Condições de Incêndio [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 aço 2. Incêndio 3. Modelo

Computacional 3. Plasticidade

I. COPPE/UFRJ II. Título ( série )

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A DEUS por tudo,

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

A Carol.

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Agradecimentos:

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

dedicação, aconselhamento e amizade – minha sincera gratidão.

Ao Professor José Luis Drummond Alves, pela valiosa co-orientação e pelo importante

estímulo nas diversas etapas do desenvolvimento deste trabalho de pesquisa.

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

Nuclear – CNEN, pelo constante incentivo, apoio e amizade.

Ao Engenheiro Artur Correa Filho da CNEN, pelo apoio e compreensão, 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.

À Comissão 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

Venâncio, Danilo Fernandes, Maurício Alves e Tiago de Oliveira, pela amizade,

companheirismo e diversas colaborações neste período de convivência.

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

todos seus Professores e Funcionários, o meu sincero agradecimento.

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

precisa orientação durante minha estadia naquela instituição.

Ao Professor Jean-Marc Franssen da Universidade de Liège (Bélgica) pela permissão

de utilização do Programa de Análise Estrutural – SAFIR, largamente utilizado nesta

pesquisa para fins de validação dos nossos resultados.

À Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – CAPES, pelo

auxílio financeiro, que possibilitou a realização do Programa de Doutorado no Brasil

com Estágio no Exterior (PDEE), durante o período de Novembro/2002 a

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

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Resumo da Tese apresentada à COPPE/UFRJ como parte dos requisitos necessários

para a obtenção do grau de Doutor em Ciências (D.Sc.)

MODELO NÃO-LINEAR INELÁSTICO PARA ANÁLISE DE ESTRUTURAS

METÁLICAS APORTICADAS EM CONDIÇÕES DE INCÊNDIO

Alexandre Landesmann

Dezembro/2003

Orientadores: Prof. Eduardo de Miranda Batista

Prof. José Luis Drummond Alves

Programa: Engenharia Civil

Este trabalho é dedicado ao desenvolvimento de um modelo computacional

para análise não-linear elastoplástica de estruturas de aço, planas e aporticadas, sob

condições de incêndio. A primeira etapa do processo de análise, traduzida pela

determinação da variação do campo de temperaturas de seções-transversais expostas ao

fogo, é realizada por meio de procedimento numérico não-linear transiente de

transferência de calor, desenvolvido com base na formulação geral do Método dos

Elementos Finitos (MEF). O comportamento estrutural é numericamente investigado

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

de rótulas plásticas, funções de estabilidade, módulos tangentes e superfícies inelásticas

de redução de resistência, permitindo-se assim, estimar o tempo crítico de resistência ao

fogo, associado à formação de mecanismos de colapso estrutural. Os resultados obtidos,

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

base o Programa SAFIR e recomendações previstas pela normatização 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. José 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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Sumário

Capítulo 1: INTRODUÇÃO

1.1 Motivação ................................................................................................... 1

1.2 Importância da análise estrutural no contexto da engenharia de

incêndio....................................................................................................... 3

1.3 Pesquisa bibliográfica sobre a análise de estruturas de aço sob

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

1.4 Método das rótulas plásticas..................................................................... 16

1.5 Organização deste trabalho ...................................................................... 19

Capítulo 2: ANÁLISE TÉRMICA 2.1 Introdução ..................................................................................................22

2.2 Curvas de incêndio ....................................................................................24

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

2.3.1 Elementos estruturais sem proteção contra incêndio...................................27

2.3.2 Elementos estruturais com material de proteção contra incêndio ...............33

2.4 Elemento unidimensional de transferência de calor ..............................35

2.4.1 Elementos estruturais sem proteção térmica................................................35

2.4.2 Elementos estruturais protegidos contra incêndio .......................................44

2.5 Verificação dos modelos térmicos implementados .................................48

2.5.1 Elementos estruturais sem proteção térmica................................................50

2.5.2 Elementos estruturais protegidos contra incêndio .......................................54

2.6 Consideração da variação de temperatura na seção-transversal pelo

método de análise avançada......................................................................57

2.6.1 Seção-transversal equivalente......................................................................57

2.6.2 Limites equivalentes de resistência plástica ................................................61

2.6.3 Esforços de engastamento perfeito devido à variação de temperatura ........62

2.6.4 Temperatura de referência ...........................................................................64

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Capítulo 3: ANÁLISE ESTRUTURAL

3.1 Análise avançada de estruturas................................................................69

3.2 Consideração de efeitos não-lineares geométricos..................................71

3.2.1 Restrições e considerações gerais para elemento de viga-coluna................71

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

3.2.3 Relação de rigidez tangente .........................................................................77

3.2.4 Aplicações com modelos de funções de estabilidade ..................................80

3.2.5 Fatores de amplificação de momentos fletores............................................83

3.3 Conceito de módulo tangente....................................................................91

3.3.1 Adaptação do conceito de análise avançada às prescrições da NBR-8800 .94

3.3.2 Consideração do efeito de temperatura........................................................101

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

3.3.4 Modelo de módulo tangente segundo o Eurocódigo ...................................105

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

3.4 Modelo inelástico de redução de rigidez flexional ..................................115

3.5 Consideração de ligações semi-rígidas.....................................................123

3.5.1 Modelo de ligação semi-rígida KISHI e CHEN (1990) ..............................125

3.5.2 Modificação da rigidez do elemento devido à presença de ligações...........127

Capítulo 4: RESULTADOS

4.1 Introdução .................................................................................................. 131

4.2 Vigas isoladas em condições de incêndio ................................................. 134

4.3 Pilares isolados sob ação de incêndio ....................................................... 143

4.4 Pórtico plano sob ação de incêndio .......................................................... 155

4.5 Pórtico plano industrial sob ação de incêndio......................................... 166

4.6 Edifício industrial sob ação de incêndio .................................................. 169

4.7 Análise comparativa dos resultados......................................................... 177

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Capítulo 5: CONSIDERAÇÕES FINAIS

5.1 Breve resumo do presente trabalho ......................................................... 176

5.2 Conclusões .................................................................................................. 178

5.3 Sugestões para trabalhos futuros ............................................................. 181

6. Referências bibliográficas ......................................................................... 185

Anexo A: IMPLEMENTAÇÃO COMPUTACIONAL

A.1 Introdução .................................................................................................. 203

A.2 Entrada de dados para o programa de análise térmica ......................... 204

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

A.4 Procedimentos de soluções numéricas ..................................................... 224

Anexo B: RESULTADOS COM MODELO DE ANÁLISE TÉRMICA

B.1 Introdução .................................................................................................. 231

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

B.3 Seção-transversal equivalente .................................................................. 245

Anexo C: VERIFICAÇÕES ESTRUTURAIS EM TEMPERATURA

AMBIENTE

C.1 Introdução .................................................................................................. 268

C.2 Pórtico plano tipo ‘portal’ ........................................................................ 271

C.3 Pórtico plano tipo ‘industrial’ .................................................................. 273

C.4 Edifício de seis andares ............................................................................ 275

C.5 Parâmetros adimensionais padronizados para ligações com

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

C.6 Pórtico de oito andares.............................................................................. 281

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

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Índice de figuras:

Capítulo 1: Introdução

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

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

Figura 1.2: Medidas de segurança contra incêndio em edificações...................... 6

Figura 1.3: Principais etapas seguidas pelo procedimento computacional

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

Capítulo 2: Análise Térmica

Figura 2.1: Comparação entre diferentes curvas de incêndio, previstas

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

Figura 2.2: Divisão da seção-transversal de perfis ‘I’ ou ‘H’ para

utilização do modelo térmico simplificado......................................28

Figura 2.3: Calor específico do aço (ca) em função da temperatura

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

Figura 2.4: Elemento finito térmico unidimensional (1D) com funções de

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

Figura 2.5: Discretização da seção-transversal por meio de elementos

unidimensionais (1D) para análise térmica......................................37

Figura 2.6: Condutividade térmica do aço λa em função da temperatura,

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

Figura 2.7: Balanço térmico em cada elemento 1D; contribuição do fluxo

de calor para análise térmica............................................................39

Figura 2.8: Esquema de integração temporal pelo método dos trapézios

para solução do sistema de equações transientes de

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

Figura 2.9: Aplicação do elemento térmico unidimensional para análise

de perfis metálicos envolvidos por material de proteção

contra incêndio.................................................................................44

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Figura 2.10: Simulação de perfis metálicos protegidos por material de

revestimento térmico por meio de elementos térmicos

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

Figura 2.11: Comparação entre variação de temperatura para o grupo de

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

Figura 2.12: Comparação entre variação de temperatura para o grupo de

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

Figura 2.13: Variação de temperatura para perfis selecionados, protegidos

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

Figura 2.14: Variação de temperatura para perfis selecionados, protegidos

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

Figura 2.15: Segmentação da seção-transversal em função do aumento de

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

Figura 2.16: Variação dos fatores de redução do aço em função da

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

Figura 2.17: Alongamento do aço (εθ) em função da temperatura, segundo

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

Capítulo 3: Análise Estrutural

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

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

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

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

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

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

Figura 3.4: Curvas de deslocamento para diferentes condições de

imperfeição geométrica inicial.........................................................81

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

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

Figura 3.6: Comparação entre os fatores de amplificação de momento

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

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solução teórica e especificações do LRFD (1999), para

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

Figura 3.7: Comparação entre os fatores de amplificação de momento

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

solução teórica e especificações do AISC-LRFD (1999), para

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

Figura 3.8: Amplificação de momento obtidos pela solução teórica,

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

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

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

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

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

Figura 3.11: Reduções inelásticas de rigidez devido ao efeito da força

axial, obtidos a partir das curvas de resistência da

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

Figura 3.12: Curvas de resistência de barras comprimidas para diferentes

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

Figura 3.13: Curvas de resistência de barras comprimidas para diferentes

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

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

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

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

Figura 3.15: Redução inelástica de rigidez devido ao efeito da força axial,

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

Figura 3.16: Modelo de barra isolada empregada nas análises numéricas

para comparação entre o modelo de módulo tangente e as

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

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

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

temperatura ambiente, para curva de flambagem ‘b’

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

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

temperatura ambiente, para curva de flambagem ‘c’

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

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

temperatura ambiente, para curva de flambagem ‘d’

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

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

temperatura ambiente, para curva de flambagem original do

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

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

módulo tangente e as curvas de resistência do EC-3/Parte-2,

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

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

módulo tangente e as curvas de resistência do EC-3/Parte-2,

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

Figura 3.24: Modelos inelásticos para redução de rigidez flexional

propostos por LIEW e WHITE (1993) em condições de

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

Figura 3.25: Curvas de resistência plástica e de início de plastificação

obtidas em função das prescrições do EC-3 (2003) e do

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

Figura 3.26: Relação tensão-deformação para o aço em condições de

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

Figura 3.27: Modificação da relação tensão-deformação do aço em função

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

redução de rigidez flexional para as temperaturas no aço (ηθ)

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

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Figura 3.29: Comportamento de curvas momento-rotação, para ligações

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

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

ligações de extremidade semi-rígidas. .............................................128

Capítulo 4: Resultados

Figura 4.1: Modelo estrutural de viga isolada em condições de incêndio;

(a) seção-transversal do perfil exposto ao incêndio nas três

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

Figura 4.2: Comparação entre os deslocamentos verticais em função do

tempo de incêndio normalizado, para o modelo de viga

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

Figura 4.3: Comparação entre os deslocamentos verticais elásticos em

função do tempo de incêndio normalizado. ..................................... 138

Figura 4.4: Variação da configuração deformada do modelo de viga

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

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

exposto ao fogo em 3 faces: (a) temperaturas na seção 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 função do tempo de incêndio,

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

Figura 4.8: Deslocamentos horizontais em função do tempo de incêndio,

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

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

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

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

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

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Figura 4.10: Distribuição 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: Distribuição 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: Superfícies de resistência plástica da seção-transversal do

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

Figura 4.13: Superfícies de resistência plástica da seção-transversal do

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

Figura 4.14: Módulos elásticos equivalentes: EAθ e EIθ em função do

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

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

Figura 4.15: Variação de esforços axiais equivalentes: Pyθ e Pθ, em função

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

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

Figura 4.16: Variação de esforços axiais equivalentes: Pyθ e Pθ, em função

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

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

Figura 4.17: Momentos equivalentes normalizados: Mpθ e Mθ, em função

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

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

Figura 4.18: Momentos equivalentes normalizados: Mpθ e Mθ, em função

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

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

Figura 4.19: Modelo de pórtico plano tipo “portal” adaptado de VOGEL

(1985), sob condições de incêndio normalizado; (a) perfis

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

Figura 4.20: Comparação entre deslocamentos horizontais do modelo de

pórtico plano em função do tempo de incêndio, obtidos pelos

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

diferentes níveis de carregamento aplicado (ψ)............................... 157

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Figura 4.21: Configuração deformada do pórtico plano para diferentes

intervalos de tempo de incêndio, ψ=0,4........................................... 159

Figura 4.22: Índices plásticos associados à flexão (ηθ*) para a estrutura do

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

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

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

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

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

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

Figura 4.24: Distribuição 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 resistência plástica para os perfis HEA-340 e

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

Figura 4.26: Variação normalizada da resistência axial e esforço axial de

engastamento, em função do tempo de incêndio. ............................ 164

Figura 4.27: Variação do momento plástico e momento de engastamento

perfeito em função do tempo de incêndio para os perfis

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

Figura 4.28: Redução dos módulos elásticos equivalentes: EAθ e EIθ em

função do tempo de incêndio para os perfis HEA-340 e

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

Figura 4.29: Configuração geométrica inicial e carregamento externo do

modelo de pórtico plano industrial; (a) seção-transversal do

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

Figura 4.30: Comparação entre os deslocamentos horizontais em função

do tempo de incêndio normalizado, obtidos pelos programas

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

em regime elástico. .......................................................................... 167

Figura 4.31: Desenvolvimento da configuração deformada do pórtico

plano industrial para diferentes instantes do incêndio, obtido

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

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Figura 4.32: Modelo de edifício de 4 andares sob incêndio; (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: Relação momento-rotação segundo o modelo tri-linear

proposto por LEON et al. (1996) para ligações semi-rígidas. ......... 171

Figura 4.34: Distribuição de ligações semi-rígidas para o edifício de

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

Figura 4.35: Variação de deslocamento horizontal do edifício de 4 andares

(LEON et al., 1996), sob diferentes condições de incêndio,

obtidos pelos programas PNL e SAFIR

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

Figura 4.36: Variação da configuração deformada do edifício de 4 andares

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

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

Figura 4.37: Superfícies de resistência plástica para diferentes instantes do

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

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

Figura 4.38: Redução dos módulos elásticos equivalentes: EAθ e EIθ em

função do tempo de incêndio para os perfis: W21x44 e

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

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

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Índice de tabelas

Capítulo 2: Análise Térmica

Tabela 2.1: Perímetros expostos para elementos que compõem a seção-

transversal de perfis metálicos ‘I’ ou ‘H’. .......................................32

Tabela 2.2: Propriedades de elementos unidimensionais utilizados na

discretização de seções-transversais de perfis metálicos ‘I’ ou

‘H’ envolvidos por material de proteção contra incêndio................47

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

selecionados para análise térmica entre os diferentes modelos

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

Tabela 2.4: Propriedades térmicas do material de proteção contra

incêndio adotado nas análises de comparação de variação de

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

Tabela 2.5: Diferenças percentuais entre resultados térmicos, para perfis

metálicos sem a presença de material de proteção contra

incêndio............................................................................................53

Tabela 2.6: Diferenças percentuais entre resultados térmicos, para perfis

metálicos envolvidos por material de proteção contra

incêndio............................................................................................56

Tabela 2.7: Fatores de redução das propriedades mecânicas do aço para

diferentes níveis de temperatura ......................................................59

Tabela 2.8: Diferenças percentuais para propriedades de seções

equivalentes, de perfis metálicos desprotegidos, expostos ao

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

Tabela 2.9: Diferenças percentuais para propriedades de seções

equivalentes, de perfis metálicos desprotegidos, expostos ao

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

Tabela 2.10: Diferenças percentuais para propriedades de seções

equivalentes, de perfis metálicos protegidos, expostos ao

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

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Tabela 2.11: Diferenças percentuais para propriedades de seções

equivalentes, de perfis metálicos protegidos, expostos ao

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

Capítulo 3: Análise Estrutural

Tabela 3.1: Comparação entre valores de funções de estabilidade.....................76

Tabela 3.2: Diferenças entre os fatores máximos de amplificação de

momento para diferentes valores de carga axial e momento

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

Tabela 3.3: Comparação entre os fatores máximos de amplificação de

momento, para momentos fletores com o mesmo sentido

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

Tabela 3.4: Comparação entre fatores máximos de amplificação 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 inércia (NBR-8800, 1986)....................95

Tabela 3.6: Fator de imperfeição para curvas de flambagem

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

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

Tabela 3.8: Constantes para as expressões analíticas do fator de redução

de rigidez inelástico .........................................................................99

Tabela 3.9: Constantes para fator de redução de rigidez inelástico

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

Tabela 3.10: Diferença entre as curvas de resistência originais

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

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

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

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

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

aço entre 20oC e 1200oC. .................................................................115

Tabela 3.12: Limites de tensão-deformação para o aço em condições de

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

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

flexional, em função da temperatura do aço. ...................................121

Capítulo 4: Resultados

Tabela 4.1: Tempo Crítico de Resistência ao Fogo (TCRF) obtido pelos

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

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

Tabela 4.2: Comparação entre valores de flechas máximas elásticas

obtidos pelos programas PNL-F e SAFIR para diferentes

níveis de momento fletor, após 1h de incêndio. .............................. 139

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

diferentes níveis de carregamento aplicado (ψ) para o pórtico

plano tipo “portal”. .......................................................................... 158

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

diferentes condições de aquecimento do pórtico de 4 andares

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

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xxi

Lista de símbolos:

Letras romanas

A área da seção-transversal, área do elemento

Ae superfície da seção-transversal exposta ao fogo

Am área da seção-transversal material de proteção térmica

Aθ área equivalente da seção-transversal

b características térmicas do material de fechamento do compartimento

B1 fator de amplificação de momento fletor

B2 fator de amplificação de momento fletor

bf largura da mesa de perfil metálico

ca calor específico do aço

cm calor específico do material de proteção contra incêndio

Cm fator de homogeneização de momentos fletores

dci deslocamento locais do elemento viga-coluna

dgi grau de liberdade em coordenadas globais

E módulo elástico (módulo de Young)

EAθ módulo elástico equivalente associado à rigidez axial

EIθ módulo elástico equivalente associado à rigidez flexional

Et módulo tangente

fp,θ tensão limite proporcional

fy tensão de escoamento para temperatura ambiente

h altura total da alma de perfil metálico

Hcr matriz de transferência de calor por convecção e por radiação

hw altura útil da alma de perfil metálico

Iθ momento de inércia equivalente

k segmento básico da seção-transversal

ka fator de correção empírico para análises em condições de incêndio

Kt matriz de condução de calor

L comprimento do elemento

ℓ comprimento do elemento

M matriz de massa concentrada

M momento de extremidade

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xxii

Mp20 momento plástico para temperatura ambiente (ou simplesmente Mp)

Mpθ momento plástico em função da temperatura

n parâmetro de forma de ligações semi-rígidas

Ni funções de interpolação lineares

O fator de abertura para o compartimento

P esforço axial

p perímetro exposto da seção-transversal

Pcr carga crítica de Euler, também adotado (Pe)

Py20 resistência plástica axial para temperatura ambiente (ou simplesmente Py)

Pyθ resistência plástica axial em função da temperatura

q fluxo de calor

qt,d densidade de carga de incêndio acondicionada no compartimento

Rcr vetor de transferência de calor por convecção e por radiação

Rkt rigidez tangente da ligação

rs comprimento de raio de solda de perfil metálico

S1 funções de estabilidade

S2 funções de estabilidade

tf espessura da mesa de perfil metálico

tlim taxa de crescimento do incêndio

tm espessura do material de proteção contra incêndio

tw espessura da alma de perfil metálico

u perímetro efetivo da seção-transversal

u/A fator de massividade de elementos estruturais de aço sem proteção contra incêndio

um perímetro efetivo da seção-transversal envolvida por material de proteção

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

Letras gregas:

j fluxo de calor por unidade de área

la coeficiente de condução de calor do aço

ra massa específica do aço

ac coeficiente de transferência de calor por convecção

jc fluxo de calor por unidade de área associado à convecção

qg temperatura do ambiente

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xxiii

lm condutividade térmica do material de proteção contra incêndio

qm temperatura na superfície do aço

rm massa específica do material de proteção

ar coeficiente de transferência de calor por radiação

jr fluxo de calor por unidade de área associado à radiação

x comprimento qualquer do elemento de viga-coluna

α estado de esforços combinados, momento fletor e esforço axial

β fator de imperfeição

βθ fator de forma específico para análises em condições de incêndio

∆t intervalo de tempo

∆θa,t elevação de temperatura do aço em função do tempo t

εres coeficiente de emissividade resultante

εθ alongamento do aço em função da temperatura

η parâmetros de redução de rigidez sob temperatura ambiente

ηθ parâmetros de redução de rigidez em função da temperatura

Θ rotação de extremidade do elemento

θ temperatura

θ0 temperatura do ambiente antes do início do aquecimento

θa temperatura do aço

θmax temperatura máxima dada pela fase de aquecimento

Θr rotação relativa entre a viga e a coluna

θref temperatura de referência

κE,θ fator de redução do módulo elástico

κp,θ fator de redução do limite proporcional

κy,θ fator de redução do limite de escoamento

λ parâmetro de esbeltez para barras comprimidas

ξ armazenagem relativa de calor do material de proteção térmica

χ fator de correção

ε deformação

σ tensão

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