Comportamento à flexão de vigas de madeira reforçadas com perfis de aço fixados com diferentes parafusos: análise experimental e computacional
Este artigo verificou o comportamento estrutural à flexão de três configurações de vigas mistas de madeira e perfis de aço, por meio do método de homogeneização da seção mista, ensaios experimentais e simulação computacional. Foram analisadas viga de madeira sem reforço (V-SR), com perfis de chapa d...
- Autores:
-
Ehrenbring, Hinoel Zamis
Vidal, Marcelo
Hannich Aires, Rafael
Christ, Roberto
Braatz, Simone
Schneider, Diego
Tutikian, Bernardo
Pacheco, Fernanda
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2023
- Institución:
- Corporación Universidad de la Costa
- Repositorio:
- REDICUC - Repositorio CUC
- Idioma:
- por
- OAI Identifier:
- oai:repositorio.cuc.edu.co:11323/10404
- Acceso en línea:
- https://hdl.handle.net/11323/10404
https://repositorio.cuc.edu.co/
- Palabra clave:
- Vigas
Estruturas mistas
Simulação computacional
Madeira
Reforço metálico
Beams
Mixed structures
Computer simulation
Wood
Metallic reinforcement
- Rights
- openAccess
- License
- Atribución 4.0 Internacional (CC BY 4.0)
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dc.title.por.fl_str_mv |
Comportamento à flexão de vigas de madeira reforçadas com perfis de aço fixados com diferentes parafusos: análise experimental e computacional |
dc.title.translated.none.fl_str_mv |
Bending behavior of wooden beams reinforced with steel profiles: experimental and computational analysis |
title |
Comportamento à flexão de vigas de madeira reforçadas com perfis de aço fixados com diferentes parafusos: análise experimental e computacional |
spellingShingle |
Comportamento à flexão de vigas de madeira reforçadas com perfis de aço fixados com diferentes parafusos: análise experimental e computacional Vigas Estruturas mistas Simulação computacional Madeira Reforço metálico Beams Mixed structures Computer simulation Wood Metallic reinforcement |
title_short |
Comportamento à flexão de vigas de madeira reforçadas com perfis de aço fixados com diferentes parafusos: análise experimental e computacional |
title_full |
Comportamento à flexão de vigas de madeira reforçadas com perfis de aço fixados com diferentes parafusos: análise experimental e computacional |
title_fullStr |
Comportamento à flexão de vigas de madeira reforçadas com perfis de aço fixados com diferentes parafusos: análise experimental e computacional |
title_full_unstemmed |
Comportamento à flexão de vigas de madeira reforçadas com perfis de aço fixados com diferentes parafusos: análise experimental e computacional |
title_sort |
Comportamento à flexão de vigas de madeira reforçadas com perfis de aço fixados com diferentes parafusos: análise experimental e computacional |
dc.creator.fl_str_mv |
Ehrenbring, Hinoel Zamis Vidal, Marcelo Hannich Aires, Rafael Christ, Roberto Braatz, Simone Schneider, Diego Tutikian, Bernardo Pacheco, Fernanda |
dc.contributor.author.none.fl_str_mv |
Ehrenbring, Hinoel Zamis Vidal, Marcelo Hannich Aires, Rafael Christ, Roberto Braatz, Simone Schneider, Diego Tutikian, Bernardo Pacheco, Fernanda |
dc.subject.proposal.por.fl_str_mv |
Vigas Estruturas mistas Simulação computacional Madeira Reforço metálico |
topic |
Vigas Estruturas mistas Simulação computacional Madeira Reforço metálico Beams Mixed structures Computer simulation Wood Metallic reinforcement |
dc.subject.proposal.eng.fl_str_mv |
Beams Mixed structures Computer simulation Wood Metallic reinforcement |
description |
Este artigo verificou o comportamento estrutural à flexão de três configurações de vigas mistas de madeira e perfis de aço, por meio do método de homogeneização da seção mista, ensaios experimentais e simulação computacional. Foram analisadas viga de madeira sem reforço (V-SR), com perfis de chapa de aço dobrada fixada com parafuso tipo prisioneiro (V-PRI) e autoatarraxante (V-AUT). Foram realizados ensaios de flexão por 3 pontos, obtendo a força de ruptura e deslocamentos. Verificou-se que a forma ruptura das vigas foi similar em todas as configurações, ocorrendo na parte tracionada, sem apresentar flambagem lateral dos perfis de aço ou deformação plástica dos parafusos. Notou-se que a inserção dos perfis de aço ocasionou um aumento na resistência das vigas mistas, sendo de 100% nas vigas com perfis de chapa de aço dobrada fixada com parafuso tipo prisioneiro (V-PRI) e de 32% nas vigas com perfis de chapa de aço dobrada fixada com parafuso tipo autoatarraxante (V-AUT). As simulações pelo método dos elementos finitos apresentaram valores mais próximos ao comportamento na flexão das vigas V-SR e V-PRI no regime elástico (ELS). O método de homogeneização da seção mista mostrou-se mais próximo dos resultados experimentais nas vigas de madeira reforçadas (V-PRI e V-AUT). |
publishDate |
2023 |
dc.date.accessioned.none.fl_str_mv |
2023-08-23T21:26:35Z |
dc.date.available.none.fl_str_mv |
2023-08-23T21:26:35Z |
dc.date.issued.none.fl_str_mv |
2023 |
dc.type.spa.fl_str_mv |
Artículo de revista |
dc.type.coar.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
dc.type.content.spa.fl_str_mv |
Text |
dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/ART |
dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.coarversion.spa.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
format |
http://purl.org/coar/resource_type/c_2df8fbb1 |
status_str |
publishedVersion |
dc.identifier.citation.spa.fl_str_mv |
Ehrenbring HZ, Vidal M, Aires RH, Christ R, Braatz S, Schneider D, et al.. Comportamento à flexão de vigas de madeira reforçadas com perfis de aço fixados com diferentes parafusos: análise experimental e computacional. Matéria (Rio J) [Internet]. 2023;28(1):e20220308. Available from: https://doi.org/10.1590/1517-7076-RMAT-2022-0308 |
dc.identifier.issn.spa.fl_str_mv |
1517-7076 |
dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/11323/10404 |
dc.identifier.doi.none.fl_str_mv |
10.1590/1517-7076-RMAT-2022-0308 |
dc.identifier.instname.spa.fl_str_mv |
Corporación Universidad de la Costa |
dc.identifier.reponame.spa.fl_str_mv |
REDICUC - Repositorio CUC |
dc.identifier.repourl.spa.fl_str_mv |
https://repositorio.cuc.edu.co/ |
identifier_str_mv |
Ehrenbring HZ, Vidal M, Aires RH, Christ R, Braatz S, Schneider D, et al.. Comportamento à flexão de vigas de madeira reforçadas com perfis de aço fixados com diferentes parafusos: análise experimental e computacional. Matéria (Rio J) [Internet]. 2023;28(1):e20220308. Available from: https://doi.org/10.1590/1517-7076-RMAT-2022-0308 1517-7076 10.1590/1517-7076-RMAT-2022-0308 Corporación Universidad de la Costa REDICUC - Repositorio CUC |
url |
https://hdl.handle.net/11323/10404 https://repositorio.cuc.edu.co/ |
dc.language.iso.spa.fl_str_mv |
por |
language |
por |
dc.relation.ispartofjournal.spa.fl_str_mv |
Revista Materia |
dc.relation.references.spa.fl_str_mv |
[1] BOLINA, F.L., TUTIKIAN, B.F., HELENE, P.R.L., Patologia de estruturas, São Paulo, Oficina de Textos, 2019. [2] NOWAK, T., JASIENKO, J., KOTWICA, E., et al., “Strength enhancement of timber beams using steel plates – review and experimental tests”, Drewno, v. 59, n. 196, pp. 75–80, 2016. [3] CARNEIRO, F.F.O.D., “Reforço de vigas de madeira com elementos de aço em obras de reabilitação”, Tese de M.Sc., Universidade do Porto, Porto, Portugal, 2012. [4] LINKOV, V., “Effect of humidity on the wooden beams of the composite section”, E3S Web of Conferences, v. 110, pp. 01087, 2019. doi: http://dx.doi.org/10.1051/e3sconf/201911001087. [5] GATO, A.C., Madera: patologia y tratamento, 1 ed., Espanha, Bubok Publishing, 2007. [6] LOBÃO, M.S., DELLA LÚCIA, R.M., MOREIRA, M.S.S., et al., “Caracterização das propriedades físico-mecânicas da madeira de eucalipto com diferentes densidades”, Revista Árvore, v. 28, n. 6, pp. 889–894, 2004. http://dx.doi.org/10.1590/S0100-67622004000600014. [7] YANG, H., LIU, W., LU, W., et al., “Flexural behavior of FRP and steel reinforced glulam beams: experimental and theoretical evaluation”, Construction & Building Materials, v. 106, pp. 550–563, 2016. doi: http://dx.doi.org/10.1016/j.conbuildmat.2015.12.135. [8] ARRIAGA, F., PERAZA, F., ESTEBAN, M., et al., Intervención em estructuras de madeira, Espanha, AITIM, 2002. [9] CASTO, V. G., GUIMARÃES, P. P., Deterioração e preservação da madeira, 1 ed., Mossoró, EdUFERSA, 2018. [10] SOUZA, A.S.C., Ligações em estruturas de aço, 1 ed., São Carlos, EdUFSCar, 2015. [11] ALVES FILHO, A., Elementos finitos: a base da tecnologia CAE, vol. 6, Rio de Janeiro, Saraiva Educação, 2018. [12] HASSANIEH, A., VALIPOUR, H.R., BRADFORD, M.A., “Load-slip behaviour of steel-cross laminated timber (CLT) composite connections”, Journal of Constructional Steel Research, v. 122, pp. 110–121, 2016. doi: http://dx.doi.org/10.1016/j.jcsr.2016.03.008. [13] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS, NBR 6892-1: Materiais metálicos – Ensaio de tração parte 1: Método de ensaio à temperatura ambiente, Rio de Janeiro, ABNT, 2018. [14] INSTITUTO DE PESQUISAS TECNOLÓGICAS, Fichas de características das madeiras brasileiras, 2 ed., São Paulo, IPT, 1989. [15] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS, NBR 14087: Peças de madeira serrada, Rio de Janeiro, ABNT, 2002. [16] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS, NBR 15522: Laje pré-fabricada – Avaliação do desempenho de vigotas e pré-lajes sob carga de trabalho, Rio de Janeiro, ABNT, 2007. [17] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS, NBR 8800: Projeto de estruturas de aço e de estruturas mistas de aço e concreto de edifícios, Rio de Janeiro, ABNT, 2008. [18] INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, ISO 4017: Fasteners – Hexagon head screws – Product grades A and B, Genebra, ISO, 2014. [19] INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, ISO 7089: Plain washers – Normal series – Product grade A, Genebra, ISO, 2000. [20] INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, ISO 4032: Hexagon regular nuts (style 1) – Product grades A and B, Genebra, ISO, 2012. [21] INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, ISO 7050: Cross-recessed countersunk (flat) head tapping screws, Genebra, ISO, 2011. [22] CARRASCO, E.V.M., OLIVEIRA, A.L.C., MANTILLA, J.N.R., “Influência da temperatura na resistência e no módulo de elasticidade em madeira de híbridos de eucaliptos”, Ciência Florestal, v. 26, n. 2, pp. 389–400, 2016. doi: http://dx.doi.org/10.5902/1980509822740. [23] SZUCS, C.A., TEREZO, R.F., VALLE, A., et al., Estruturas de madeira, Florianópolis, UFSC, 2015. [24] ZENID, J.G., Madeira na construção civil, Instituto de Pesquisas Tecnológicas, São Paulo, 2011. [25] FORTI, N.C.S., FORTI, T.L.D., JACINTHO, A.E.P.G.A., et al., “Análise de vigas mistas de concreto e madeira pelo método dos elementos finitos”, Revista IBRACON de Estruturas e Materiais, v. 8, n. 4, 2015. doi: http://dx.doi.org/10.1590/S1983-41952015000400006. [26] RIBEIRO, P.G., “Utilização de técnicas não destrutivas para caracterização de madeiras de Pinus caribaea Var. hondurensis e de Eucalyptus grandis”, Tese de M.Sc., Universidade de Brasília, Brasília, 2009. [27] CALLISTER, W.D., RETHWISCH, D.G., Ciência e Engenharia de Materiais: uma introdução, 9 ed., São Paulo, LTC, 2016. [28] CANALLI, I., “Estudo do comportamento de estrutura mista de concreto e perfil pultrudado de PRFV sob flexão”, Tese de M.Sc., Universidade Federal de Santa Catarina, Florianópolis, 2010. [29] AUTENGRUBER, M., LUKACEVIC, M., GRÖSTLINGER, C., et al., “Numerical assessment of wood moisture content-based assignments to service classes in EC 5 and a prediction concept for moistureinduced stresses solely using relative humidity data”, Engineering Structures, v. 245, n. 15, pp. 1128– 1149, 2021. doi: http://dx.doi.org/10.1016/j.engstruct.2021.112849. [30] OUDJENE, M., TRAN, V.D., MEGHLAT, E., et al., Numerical Models for self-tapping screws as reinforcement of timber structures and joints, In: Word Conference on Timber Engineering – WCTE, Vienna, Austria, 2016. [31] KARAGÖZ IŞLEYEN, Ü., KESIK, H.I., “Experimental and numerical analysis of compression and bending strength of old wood reinforced with CFRP strips”, Structures, v. 33, pp. 259–271, 2021. doi: http://dx.doi.org/10.1016/j.istruc.2021.04.070. [32] YANG, Y., LIU, J., XIONG, G., “Flexural behavior of wood beams strengthened with HFRP”, Construction & Building Materials, v. 43, pp. 118-124, 2013. doi: http://dx.doi.org/10.1016/j.conbuildmat.2013.01.029. [33] JELUŠIČ, P., KRAVANJA, S., “Flexural analysis of laminated solid wood beams with different shear connections”, Construction & Building Materials, v. 174, pp. 456–465, 2018. doi: http://dx.doi. org/10.1016/j.conbuildmat.2018.04.102. [34] LI, C., WANG, X., RAN, L., et al., “PtoMYB92 is a transcriptional activator of the lignin biosynthetic pathway during secondary cell wall formation in Populus tomentosa”, Plant & Cell Physiology, v. 56, n. 12, pp. 2436-2446, 2015. doi: http://dx.doi.org/10.1093/pcp/pcv157. PubMed PMID: 26508520. [35] CZIBULA, C., SEIDLHOFER, T., GANSER, C., et al., “Longitudinal and transverse low frequency viscoelastic characterization of wood pulp fibers at different relative humidity”, Materialia, v. 16, pp. 101094, 2021. doi: http://dx.doi.org/10.1016/j.mtla.2021.101094. [36] OLIVEIRA, M.A.M.E., “Ligações com pinos metálicos em estruturas de madeira”, Tese de M.Sc., Universidade de São Paulo, São Carlos, 2001. [37] PACHECO, F., SOUZA, R.P., CHRIST, R., et al., “Determination of volume and distribution of pores of concretes according to different exposure classes through 3D microtomography and mercury intrusion porosimetry”, Structural Concrete, v. 19, n. 5, pp. 1419–1427, 2019. doi: http://dx.doi.org/10.1002/ suco.201800075. [38] YOU, R., ZHU, N., DENG, X., et al., “Variation in wood physical properties and effects of climate for different geographic sources of Chinese fir in subtropical area of China”, Scientific Reports, v. 11, n. 1, pp. 4664, 2021. doi: http://dx.doi.org/10.1038/s41598-021-83500-w. PubMed PMID: 33633125. [39] TIAN, Q., WANG, X., LI, C., et al., “Functional characterization of the poplar R2R3-MYB transcription factor PtoMYB216 involved in the regulation of lignin biosynthesis during wood formation”, PLoS One, v. 8, n. 10, pp. e76369, 2013. doi: http://dx.doi.org/10.1371/journal.pone.0076369. PubMed PMID: 24204619. [40] GOWHARI ANAKARI, A.R., FAKOOR, M., “General mixed mode I/II fracture criterion for wood considering T-stress effects”, Materials & Design, v. 31, n. 9, pp. 4461–4469, 2010. http://dx.doi. org/10.1016/j.matdes.2010.04.055. [41] FENG, X., XIAO, H., CHEN, B., “Experimental study on splitting strength of sawn lumber loaded perpendicular to grain by bolted steel-wood-steel connections”, Journal of Building Engineering, v. 44, pp. 44, 2021. http://dx.doi.org/10.1016/j.jobe.2021.102554. [42] DAPPER, P., EHRENDRING, H., PACHECO, F., et al., “Ballistic impact resistance of UHPC plates made with hybrid fibers and low binder content”, Sustainability, v. 13, n. 23, pp. 13410, 2021. http://dx. doi.org/10.3390/su132313410. |
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Atribución 4.0 Internacional (CC BY 4.0) |
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Universidade Federal do Rio de Janeiro - UFRJ |
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Atribución 4.0 Internacional (CC BY 4.0)https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Ehrenbring, Hinoel ZamisVidal, MarceloHannich Aires, RafaelChrist, RobertoBraatz, SimoneSchneider, DiegoTutikian, BernardoPacheco, Fernanda2023-08-23T21:26:35Z2023-08-23T21:26:35Z2023Ehrenbring HZ, Vidal M, Aires RH, Christ R, Braatz S, Schneider D, et al.. Comportamento à flexão de vigas de madeira reforçadas com perfis de aço fixados com diferentes parafusos: análise experimental e computacional. Matéria (Rio J) [Internet]. 2023;28(1):e20220308. Available from: https://doi.org/10.1590/1517-7076-RMAT-2022-03081517-7076https://hdl.handle.net/11323/1040410.1590/1517-7076-RMAT-2022-0308Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/Este artigo verificou o comportamento estrutural à flexão de três configurações de vigas mistas de madeira e perfis de aço, por meio do método de homogeneização da seção mista, ensaios experimentais e simulação computacional. Foram analisadas viga de madeira sem reforço (V-SR), com perfis de chapa de aço dobrada fixada com parafuso tipo prisioneiro (V-PRI) e autoatarraxante (V-AUT). Foram realizados ensaios de flexão por 3 pontos, obtendo a força de ruptura e deslocamentos. Verificou-se que a forma ruptura das vigas foi similar em todas as configurações, ocorrendo na parte tracionada, sem apresentar flambagem lateral dos perfis de aço ou deformação plástica dos parafusos. Notou-se que a inserção dos perfis de aço ocasionou um aumento na resistência das vigas mistas, sendo de 100% nas vigas com perfis de chapa de aço dobrada fixada com parafuso tipo prisioneiro (V-PRI) e de 32% nas vigas com perfis de chapa de aço dobrada fixada com parafuso tipo autoatarraxante (V-AUT). As simulações pelo método dos elementos finitos apresentaram valores mais próximos ao comportamento na flexão das vigas V-SR e V-PRI no regime elástico (ELS). O método de homogeneização da seção mista mostrou-se mais próximo dos resultados experimentais nas vigas de madeira reforçadas (V-PRI e V-AUT).This paper verified the structural behavior of three configurations of composite beams of wood and steel profiles, analytically by the mixed section homogenization method (MHSM), by experimental tests and simulated by the finite element method (FEM). Unreinforced wooden beam (V-SR), with bent steel sheet profiles fixed with stud (V-PRI) and self-tapping (V-AUT) screws were analyzed. The flexural behavior was analyzed by 3 points of these elements, represented by the load and displacement. It was found that the beam failure form was the same in all configurations, occurring in the tensioned part, without lateral buckling of the steel profiles or plastic deformation of the screws. It was noted that the insertion of steel profiles caused an increase in the strength of the composite beams, being 100% in the V-PRI sample and 32% in the V-AUT. The FEM simulations showed values closer to the bending behavior of the V-SR and V-PRI beams in the elastic regime (ELS). The experimental results of the V-AUT beams were more compatible with the mixed section homogenization model.13 páginasapplication/pdfporUniversidade Federal do Rio de Janeiro - UFRJBrazilhttps://www.scielo.br/j/rmat/a/YMqkqZMYJfrPzc9MtCg5K6C/abstract/?lang=enComportamento à flexão de vigas de madeira reforçadas com perfis de aço fixados com diferentes parafusos: análise experimental e computacionalBending behavior of wooden beams reinforced with steel profiles: experimental and computational analysisArtículo de revistahttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Revista Materia[1] BOLINA, F.L., TUTIKIAN, B.F., HELENE, P.R.L., Patologia de estruturas, São Paulo, Oficina de Textos, 2019.[2] NOWAK, T., JASIENKO, J., KOTWICA, E., et al., “Strength enhancement of timber beams using steel plates – review and experimental tests”, Drewno, v. 59, n. 196, pp. 75–80, 2016.[3] CARNEIRO, F.F.O.D., “Reforço de vigas de madeira com elementos de aço em obras de reabilitação”, Tese de M.Sc., Universidade do Porto, Porto, Portugal, 2012.[4] LINKOV, V., “Effect of humidity on the wooden beams of the composite section”, E3S Web of Conferences, v. 110, pp. 01087, 2019. doi: http://dx.doi.org/10.1051/e3sconf/201911001087.[5] GATO, A.C., Madera: patologia y tratamento, 1 ed., Espanha, Bubok Publishing, 2007.[6] LOBÃO, M.S., DELLA LÚCIA, R.M., MOREIRA, M.S.S., et al., “Caracterização das propriedades físico-mecânicas da madeira de eucalipto com diferentes densidades”, Revista Árvore, v. 28, n. 6, pp. 889–894, 2004. http://dx.doi.org/10.1590/S0100-67622004000600014.[7] YANG, H., LIU, W., LU, W., et al., “Flexural behavior of FRP and steel reinforced glulam beams: experimental and theoretical evaluation”, Construction & Building Materials, v. 106, pp. 550–563, 2016. doi: http://dx.doi.org/10.1016/j.conbuildmat.2015.12.135.[8] ARRIAGA, F., PERAZA, F., ESTEBAN, M., et al., Intervención em estructuras de madeira, Espanha, AITIM, 2002.[9] CASTO, V. G., GUIMARÃES, P. P., Deterioração e preservação da madeira, 1 ed., Mossoró, EdUFERSA, 2018.[10] SOUZA, A.S.C., Ligações em estruturas de aço, 1 ed., São Carlos, EdUFSCar, 2015.[11] ALVES FILHO, A., Elementos finitos: a base da tecnologia CAE, vol. 6, Rio de Janeiro, Saraiva Educação, 2018.[12] HASSANIEH, A., VALIPOUR, H.R., BRADFORD, M.A., “Load-slip behaviour of steel-cross laminated timber (CLT) composite connections”, Journal of Constructional Steel Research, v. 122, pp. 110–121, 2016. doi: http://dx.doi.org/10.1016/j.jcsr.2016.03.008.[13] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS, NBR 6892-1: Materiais metálicos – Ensaio de tração parte 1: Método de ensaio à temperatura ambiente, Rio de Janeiro, ABNT, 2018.[14] INSTITUTO DE PESQUISAS TECNOLÓGICAS, Fichas de características das madeiras brasileiras, 2 ed., São Paulo, IPT, 1989.[15] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS, NBR 14087: Peças de madeira serrada, Rio de Janeiro, ABNT, 2002.[16] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS, NBR 15522: Laje pré-fabricada – Avaliação do desempenho de vigotas e pré-lajes sob carga de trabalho, Rio de Janeiro, ABNT, 2007.[17] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS, NBR 8800: Projeto de estruturas de aço e de estruturas mistas de aço e concreto de edifícios, Rio de Janeiro, ABNT, 2008.[18] INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, ISO 4017: Fasteners – Hexagon head screws – Product grades A and B, Genebra, ISO, 2014.[19] INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, ISO 7089: Plain washers – Normal series – Product grade A, Genebra, ISO, 2000.[20] INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, ISO 4032: Hexagon regular nuts (style 1) – Product grades A and B, Genebra, ISO, 2012.[21] INTERNATIONAL ORGANIZATION FOR STANDARDIZATION, ISO 7050: Cross-recessed countersunk (flat) head tapping screws, Genebra, ISO, 2011.[22] CARRASCO, E.V.M., OLIVEIRA, A.L.C., MANTILLA, J.N.R., “Influência da temperatura na resistência e no módulo de elasticidade em madeira de híbridos de eucaliptos”, Ciência Florestal, v. 26, n. 2, pp. 389–400, 2016. doi: http://dx.doi.org/10.5902/1980509822740.[23] SZUCS, C.A., TEREZO, R.F., VALLE, A., et al., Estruturas de madeira, Florianópolis, UFSC, 2015.[24] ZENID, J.G., Madeira na construção civil, Instituto de Pesquisas Tecnológicas, São Paulo, 2011.[25] FORTI, N.C.S., FORTI, T.L.D., JACINTHO, A.E.P.G.A., et al., “Análise de vigas mistas de concreto e madeira pelo método dos elementos finitos”, Revista IBRACON de Estruturas e Materiais, v. 8, n. 4, 2015. doi: http://dx.doi.org/10.1590/S1983-41952015000400006.[26] RIBEIRO, P.G., “Utilização de técnicas não destrutivas para caracterização de madeiras de Pinus caribaea Var. hondurensis e de Eucalyptus grandis”, Tese de M.Sc., Universidade de Brasília, Brasília, 2009.[27] CALLISTER, W.D., RETHWISCH, D.G., Ciência e Engenharia de Materiais: uma introdução, 9 ed., São Paulo, LTC, 2016.[28] CANALLI, I., “Estudo do comportamento de estrutura mista de concreto e perfil pultrudado de PRFV sob flexão”, Tese de M.Sc., Universidade Federal de Santa Catarina, Florianópolis, 2010.[29] AUTENGRUBER, M., LUKACEVIC, M., GRÖSTLINGER, C., et al., “Numerical assessment of wood moisture content-based assignments to service classes in EC 5 and a prediction concept for moistureinduced stresses solely using relative humidity data”, Engineering Structures, v. 245, n. 15, pp. 1128– 1149, 2021. doi: http://dx.doi.org/10.1016/j.engstruct.2021.112849.[30] OUDJENE, M., TRAN, V.D., MEGHLAT, E., et al., Numerical Models for self-tapping screws as reinforcement of timber structures and joints, In: Word Conference on Timber Engineering – WCTE, Vienna, Austria, 2016.[31] KARAGÖZ IŞLEYEN, Ü., KESIK, H.I., “Experimental and numerical analysis of compression and bending strength of old wood reinforced with CFRP strips”, Structures, v. 33, pp. 259–271, 2021. doi: http://dx.doi.org/10.1016/j.istruc.2021.04.070.[32] YANG, Y., LIU, J., XIONG, G., “Flexural behavior of wood beams strengthened with HFRP”, Construction & Building Materials, v. 43, pp. 118-124, 2013. doi: http://dx.doi.org/10.1016/j.conbuildmat.2013.01.029.[33] JELUŠIČ, P., KRAVANJA, S., “Flexural analysis of laminated solid wood beams with different shear connections”, Construction & Building Materials, v. 174, pp. 456–465, 2018. doi: http://dx.doi. org/10.1016/j.conbuildmat.2018.04.102.[34] LI, C., WANG, X., RAN, L., et al., “PtoMYB92 is a transcriptional activator of the lignin biosynthetic pathway during secondary cell wall formation in Populus tomentosa”, Plant & Cell Physiology, v. 56, n. 12, pp. 2436-2446, 2015. doi: http://dx.doi.org/10.1093/pcp/pcv157. PubMed PMID: 26508520.[35] CZIBULA, C., SEIDLHOFER, T., GANSER, C., et al., “Longitudinal and transverse low frequency viscoelastic characterization of wood pulp fibers at different relative humidity”, Materialia, v. 16, pp. 101094, 2021. doi: http://dx.doi.org/10.1016/j.mtla.2021.101094.[36] OLIVEIRA, M.A.M.E., “Ligações com pinos metálicos em estruturas de madeira”, Tese de M.Sc., Universidade de São Paulo, São Carlos, 2001.[37] PACHECO, F., SOUZA, R.P., CHRIST, R., et al., “Determination of volume and distribution of pores of concretes according to different exposure classes through 3D microtomography and mercury intrusion porosimetry”, Structural Concrete, v. 19, n. 5, pp. 1419–1427, 2019. doi: http://dx.doi.org/10.1002/ suco.201800075.[38] YOU, R., ZHU, N., DENG, X., et al., “Variation in wood physical properties and effects of climate for different geographic sources of Chinese fir in subtropical area of China”, Scientific Reports, v. 11, n. 1, pp. 4664, 2021. doi: http://dx.doi.org/10.1038/s41598-021-83500-w. 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PubMed PMID: 24204619.[40] GOWHARI ANAKARI, A.R., FAKOOR, M., “General mixed mode I/II fracture criterion for wood considering T-stress effects”, Materials & Design, v. 31, n. 9, pp. 4461–4469, 2010. http://dx.doi. org/10.1016/j.matdes.2010.04.055.[41] FENG, X., XIAO, H., CHEN, B., “Experimental study on splitting strength of sawn lumber loaded perpendicular to grain by bolted steel-wood-steel connections”, Journal of Building Engineering, v. 44, pp. 44, 2021. http://dx.doi.org/10.1016/j.jobe.2021.102554.[42] DAPPER, P., EHRENDRING, H., PACHECO, F., et al., “Ballistic impact resistance of UHPC plates made with hybrid fibers and low binder content”, Sustainability, v. 13, n. 23, pp. 13410, 2021. http://dx. doi.org/10.3390/su132313410.128VigasEstruturas mistasSimulação computacionalMadeiraReforço metálicoBeamsMixed structuresComputer simulationWoodMetallic reinforcementPublicationORIGINALComportamento à flexão de vigas de madeira reforçadas com perfis de aço.pdfComportamento à flexão de 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ada en las Obras Colectivas.

b.	Distribuir copias o fonogramas de las Obras, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública, incluyéndolas como incorporadas en Obras Colectivas, según corresponda.

c.	Distribuir copias de las Obras Derivadas que se generen, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública.
Los derechos mencionados anteriormente pueden ser ejercidos en todos los medios y formatos, actualmente conocidos o que se inventen en el futuro. Los derechos antes mencionados incluyen el derecho a realizar dichas modificaciones en la medida que sean técnicamente necesarias para ejercer los derechos en otro medio o formatos, pero de otra manera usted no está autorizado para realizar obras derivadas. Todos los derechos no otorgados expresamente por el Licenciante quedan por este medio reservados, incluyendo pero sin limitarse a aquellos que se mencionan en las secciones 4(d) y 4(e).

4. Restricciones.
La licencia otorgada en la anterior Sección 3 está expresamente sujeta y limitada por las siguientes restricciones:

a.	Usted puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra sólo bajo las condiciones de esta Licencia, y Usted debe incluir una copia de esta licencia o del Identificador Universal de Recursos de la misma con cada copia de la Obra que distribuya, exhiba públicamente, ejecute públicamente o ponga a disposición pública. No es posible ofrecer o imponer ninguna condición sobre la Obra que altere o limite las condiciones de esta Licencia o el ejercicio de los derechos de los destinatarios otorgados en este documento. No es posible sublicenciar la Obra. Usted debe mantener intactos todos los avisos que hagan referencia a esta Licencia y a la cláusula de limitación de garantías. Usted no puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra con alguna medida tecnológica que controle el acceso o la utilización de ella de una forma que sea inconsistente con las condiciones de esta Licencia. Lo anterior se aplica a la Obra incorporada a una Obra Colectiva, pero esto no exige que la Obra Colectiva aparte de la obra misma quede sujeta a las condiciones de esta Licencia. Si Usted crea una Obra Colectiva, previo aviso de cualquier Licenciante debe, en la medida de lo posible, eliminar de la Obra Colectiva cualquier referencia a dicho Licenciante o al Autor Original, según lo solicitado por el Licenciante y conforme lo exige la cláusula 4(c).

b.	Usted no puede ejercer ninguno de los derechos que le han sido otorgados en la Sección 3 precedente de modo que estén principalmente destinados o directamente dirigidos a conseguir un provecho comercial o una compensación monetaria privada. El intercambio de la Obra por otras obras protegidas por derechos de autor, ya sea a través de un sistema para compartir archivos digitales (digital file-sharing) o de cualquier otra manera no será considerado como estar destinado principalmente o dirigido directamente a conseguir un provecho comercial o una compensación monetaria privada, siempre que no se realice un pago mediante una compensación monetaria en relación con el intercambio de obras protegidas por el derecho de autor.

c.	Si usted distribuye, exhibe públicamente, ejecuta públicamente o ejecuta públicamente en forma digital la Obra o cualquier Obra Derivada u Obra Colectiva, Usted debe mantener intacta toda la información de derecho de autor de la Obra y proporcionar, de forma razonable según el medio o manera que Usted esté utilizando: (i) el nombre del Autor Original si está provisto (o seudónimo, si fuere aplicable), y/o (ii) el nombre de la parte o las partes que el Autor Original y/o el Licenciante hubieren designado para la atribución (v.g., un instituto patrocinador, editorial, publicación) en la información de los derechos de autor del Licenciante, términos de servicios o de otras formas razonables; el título de la Obra si está provisto; en la medida de lo razonablemente factible y, si está provisto, el Identificador Uniforme de Recursos (Uniform Resource Identifier) que el Licenciante especifica para ser asociado con la Obra, salvo que tal URI no se refiera a la nota sobre los derechos de autor o a la información sobre el licenciamiento de la Obra; y en el caso de una Obra Derivada, atribuir el crédito identificando el uso de la Obra en la Obra Derivada (v.g., "Traducción Francesa de la Obra del Autor Original," o "Guión Cinematográfico basado en la Obra original del Autor Original"). Tal crédito puede ser implementado de cualquier forma razonable; en el caso, sin embargo, de Obras Derivadas u Obras Colectivas, tal crédito aparecerá, como mínimo, donde aparece el crédito de cualquier otro autor comparable y de una manera, al menos, tan destacada como el crédito de otro autor comparable.

d.	Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:

i.	Regalías por interpretación y ejecución bajo licencias generales. El Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública o la ejecución pública digital de la obra y de recolectar, sea individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), las regalías por la ejecución pública o por la ejecución pública digital de la obra (por ejemplo Webcast) licenciada bajo licencias generales, si la interpretación o ejecución de la obra está primordialmente orientada por o dirigida a la obtención de una ventaja comercial o una compensación monetaria privada.

ii.	Regalías por Fonogramas. El Licenciante se reserva el derecho exclusivo de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, los consagrados por la SAYCO), una agencia de derechos musicales o algún agente designado, las regalías por cualquier fonograma que Usted cree a partir de la obra (“versión cover”) y distribuya, en los términos del régimen de derechos de autor, si la creación o distribución de esa versión cover está primordialmente destinada o dirigida a obtener una ventaja comercial o una compensación monetaria privada.

e.	Gestión de Derechos de Autor sobre Interpretaciones y Ejecuciones Digitales (WebCasting). Para evitar toda confusión, el Licenciante aclara que, cuando la obra sea un fonograma, el Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública digital de la obra (por ejemplo, webcast) y de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, ACINPRO), las regalías por la ejecución pública digital de la obra (por ejemplo, webcast), sujeta a las disposiciones aplicables del régimen de Derecho de Autor, si esta ejecución pública digital está primordialmente dirigida a obtener una ventaja comercial o una compensación monetaria privada.

5. Representaciones, Garantías y Limitaciones de Responsabilidad.
A MENOS QUE LAS PARTES LO ACORDARAN DE OTRA FORMA POR ESCRITO, EL LICENCIANTE OFRECE LA OBRA (EN EL ESTADO EN EL QUE SE ENCUENTRA) “TAL CUAL”, SIN BRINDAR GARANTÍAS DE CLASE ALGUNA RESPECTO DE LA OBRA, YA SEA EXPRESA, IMPLÍCITA, LEGAL O CUALQUIERA OTRA, INCLUYENDO, SIN LIMITARSE A ELLAS, GARANTÍAS DE TITULARIDAD, COMERCIABILIDAD, ADAPTABILIDAD O ADECUACIÓN A PROPÓSITO DETERMINADO, AUSENCIA DE INFRACCIÓN, DE AUSENCIA DE DEFECTOS LATENTES O DE OTRO TIPO, O LA PRESENCIA O AUSENCIA DE ERRORES, SEAN O NO DESCUBRIBLES (PUEDAN O NO SER ESTOS DESCUBIERTOS). ALGUNAS JURISDICCIONES NO PERMITEN LA EXCLUSIÓN DE GARANTÍAS IMPLÍCITAS, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

6. Limitación de responsabilidad.
A MENOS QUE LO EXIJA EXPRESAMENTE LA LEY APLICABLE, EL LICENCIANTE NO SERÁ RESPONSABLE ANTE USTED POR DAÑO ALGUNO, SEA POR RESPONSABILIDAD EXTRACONTRACTUAL, PRECONTRACTUAL O CONTRACTUAL, OBJETIVA O SUBJETIVA, SE TRATE DE DAÑOS MORALES O PATRIMONIALES, DIRECTOS O INDIRECTOS, PREVISTOS O IMPREVISTOS PRODUCIDOS POR EL USO DE ESTA LICENCIA O DE LA OBRA, AUN CUANDO EL LICENCIANTE HAYA SIDO ADVERTIDO DE LA POSIBILIDAD DE DICHOS DAÑOS. ALGUNAS LEYES NO PERMITEN LA EXCLUSIÓN DE CIERTA RESPONSABILIDAD, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

7. Término.

a.	Esta Licencia y los derechos otorgados en virtud de ella terminarán automáticamente si Usted infringe alguna condición establecida en ella. Sin embargo, los individuos o entidades que han recibido Obras Derivadas o Colectivas de Usted de conformidad con esta Licencia, no verán terminadas sus licencias, siempre que estos individuos o entidades sigan cumpliendo íntegramente las condiciones de estas licencias. Las Secciones 1, 2, 5, 6, 7, y 8 subsistirán a cualquier terminación de esta Licencia.

b.	Sujeta a las condiciones y términos anteriores, la licencia otorgada aquí es perpetua (durante el período de vigencia de los derechos de autor de la obra). No obstante lo anterior, el Licenciante se reserva el derecho a publicar y/o estrenar la Obra bajo condiciones de licencia diferentes o a dejar de distribuirla en los términos de esta Licencia en cualquier momento; en el entendido, sin embargo, que esa elección no servirá para revocar esta licencia o que deba ser otorgada , bajo los términos de esta licencia), y esta licencia continuará en pleno vigor y efecto a menos que sea terminada como se expresa atrás. La Licencia revocada continuará siendo plenamente vigente y efectiva si no se le da término en las condiciones indicadas anteriormente.

8. Varios.

a.	Cada vez que Usted distribuya o ponga a disposición pública la Obra o una Obra Colectiva, el Licenciante ofrecerá al destinatario una licencia en los mismos términos y condiciones que la licencia otorgada a Usted bajo esta Licencia.

b.	Si alguna disposición de esta Licencia resulta invalidada o no exigible, según la legislación vigente, esto no afectará ni la validez ni la aplicabilidad del resto de condiciones de esta Licencia y, sin acción adicional por parte de los sujetos de este acuerdo, aquélla se entenderá reformada lo mínimo necesario para hacer que dicha disposición sea válida y exigible.

c.	Ningún término o disposición de esta Licencia se estimará renunciada y ninguna violación de ella será consentida a menos que esa renuncia o consentimiento sea otorgado por escrito y firmado por la parte que renuncie o consienta.

d.	Esta Licencia refleja el acuerdo pleno entre las partes respecto a la Obra aquí licenciada. No hay arreglos, acuerdos o declaraciones respecto a la Obra que no estén especificados en este documento. El Licenciante no se verá limitado por ninguna disposición adicional que pueda surgir en alguna comunicación emanada de Usted. Esta Licencia no puede ser modificada sin el consentimiento mutuo por escrito del Licenciante y Usted.
 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