Techniques of performance-based design in fire safety have developed notably in the past two decades. One of the reasons for departing from the prescriptive methods is the ability of performance-based methods to form a scientific basis for the cost-risk-benefit analysis of different fire safety alternatives. Apart from few exceptions, observation of past fires has shown that the structure’s contribution to the overall fire resistance was considerably underestimated. The purpose of this research is to outline a risk-based design approach for structures in fire. Probabilistic methods are employed to ascertain uniform reliability indices in line with the classical trend in code development. Modern design codes for complex phenomena such as fire have been structured to facilitate design computations. Prescriptive design methods specify fire protection methods for structural systems based on laboratory controlled and highly restrictive testing regimes. Those methods inherently assume that the tested elements behave similarly in real structures irrespective of their loading, location or boundary conditions. This approach is contested by many researchers, and analyses following fire incidents indicated alarming discrepancy between anticipated and actual structural behaviour during real fires. In formulating design and construction codes, code writers deal with the inherent uncertainties by setting a ceiling to the potential risk of failure. The latter process is implemented by specifying safety parameters, that are derived via probabilistic techniques aimed at harmonising the risks ensuing different load scenarios. The code structure addresses the probability of failure with adequate detail and accuracy. The other component of the risk metric, namely the consequence of failure, is a subjective field that assumes a multitude of variables depending on the context of the problem. In codified structural design, the severity of failure is implicitly embodied in the different magnitudes of safety indices applied to different modes of structural response. This project introduces a risk-based method for the design of structures in fire. It provides a coherent approach to a quantified treatment of risk elements that meets the demands of performance-based fire safety methods. A number of proposals are made for rational acceptable risk and reliability parameters in addition to a damage index with applications in structural fire safety design. Although the example application of the proposed damage index is a structure subjected to fire effects, the same rationale can be easily applied to the assessment of structural damage due to other effects.

As the engineering profession moves from prescriptive or “deemed-to-satisfy” approaches towards design methodologies based on quantification of performance, sophisticated modelling tools are increasingly needed, especially when complex combinations of demand and capacity are encountered. Recourse is invariably made to advanced computational tools to provide high fidelity solutions to large and complex problems, such as the response of structural systems or components to thermomechanical actions. Software packages based on the finite element method are most commonly used for such analyses. There are some essential prerequisites to effective use of advanced computational software for complex nonlinear problems, which are often ignored, particularly in professional practice. These include a thorough understanding of the underlying mechanics of the problem under consideration; a good appreciation of the approximation methods for modelling the problem properly (e.g. the choice between elements, continuum or structural, low or high order interpolation, degree of mesh refinement necessary and so on); and perhaps most importantly ensuring that the software is reliable and is able to reproduce established fundamental solutions to an acceptable degree of accuracy. This thesis attempts to address most of these issues but focusses primarily on the last mentioned prerequisite and provides a range of novel and unprecedented fundamental solutions for beams, plates, and shallow shells subject to moderate or extreme thermomechanical loads such as those resulting from a fire. Geometric and material nonlinearities are included in the proposed formulations along with the most common idealised boundary conditions. Thermally induced deformations generate large displacements and require the solutions to account for geometric nonlinearity, while material nonlinearity arises from the degradation of the material at elevated temperatures. In the context of structural performance under extreme thermal action (such as fire), a finite element procedure is employed to analytically characterise generic temperature distributions through the thickness of a structural component arising from different types of fire exposure conditions including: a “short hot” fire leading to a high compartment temperature over a relatively short duration; and a “long cool” fire with lower compartment temperatures, but over a longer duration. Results have shown that despite the larger area under the long cool fire time-temperature curve, which traditionally represented the fire severity, the effect of the short hot fire on the nonlinear responses of beams, plates, and shallow shells is more pronounced. Also, the effect of temperature-dependent material properties is found to be more pronounced during the short hot fire rather than the long cool fire. Comparison studies have confirmed that while the current numerical and theoretical approaches for analysing of thin plates and shells are often computationally intensive, the proposed approach offers an adequate level of accuracy with a rapid convergence rate for such structures. The solutions developed can be used to: verify software used for modelling structural response to thermomechanical actions; help students and professionals appreciate the fundamental mechanics better; provide relatively quick solutions for component level analyses; and visualise internal load paths and stress trajectories in complex structural components such as composite shells that can help engineers develop deeper insights into the relevant mechanics. The formulations developed are versatile and can be used for other applications such as laminated composite or orthotropic shallow shells. A very significant by-product of developing such fundamental solutions is their potential use in the development of highly accurate hybrid elements for very efficient modelling of large problems. While this has not been fully developed and implemented in the current work, the requisite theoretical framework has been developed and reported in one of the appendices, which can be used to develop such elements and implement on an appropriate software platform.

O interesse pelo estudo de estruturas em situação de incêndio vem aumentando dadas as inúmeras ocorrências internacionais, que resultaram em colapso estrutural de edificações. As recentes revisões das normas técnicas brasileiras reforçam a preocupação de organismos públicos e da comunidade técnica. A contribuição deste trabalho é determinar como os esforços resistentes em perfis isolados de aço são afetados pela ação térmica provenientes do incêndio, ou melhor, em função das variáveis que modelam o incêndio natural. Para tanto foi desenvolvido o programa de computador STRESFIRE capaz de calcular a ação térmica conforme curvas paramétricas, a transferência de calor para a peça de aço e o esforço resistente em função da temperatura na formulação a ser apresentada na revisão da NBR 14323:1999. / The interest by study of structures in fire situation has increased due to several international occurrences, which resulted in structural collapse of buildings. The recent revisions of the Brazilian technical standards reinforce the concern of public organisms and technical community. The contribution of this work is determine how the structural resistance of isolated steel element is affected by fire thermal action, in other words, the variables that model the natural fire. A software STRESFIRE was developed, which calculates the temperatures in the compartment, the heat transfer to steel member and the fire resistance by analytical methods.

O presente trabalho teve como objetivo principal estudar, em caráter essencialmente numérico via ANSYS v9.0, a elevação de temperatura em seções transversais de elementos estruturais de aço e mistos de aço e concreto, com vistas a uma avaliação das equações propostas pelo método simplificado de cálculo da NBR 14323:1999, em especial, para situações em que não ocorra aquecimento uniforme por todos os lados do elemento. São apresentados modelos numéricos de seções transversais de elementos estruturais de aço, mistos de aço e concreto e, em caráter complementar, de madeira, em situação de incêndio, para avaliar a evolução dos níveis de temperatura ao longo do tempo. São também construídos e analisados modelos numéricos com vistas à análise do efeito da elevação de temperatura no comportamento mecânico em vigas de aço de um edifício de interesse. A determinação dos níveis de temperatura em seções transversais de elementos estruturais, obtidas com base nas prescrições normativas da NBR 14323:1999, conduzem a resultados satisfatórios, porém, com temperaturas próximas as temperaturas máximas obtidas numericamente. Para os casos usuais não contemplados pela NBR 14323:1999 fica evidente a necessidade do emprego de modelo avançado de cálculo ou de estudos com vistas ao desenvolvimento de ferramentas analíticas para emprego em tais situações. Com relação à análise do efeito da elevação de temperatura no comportamento mecânico, os fatores de redução de resistência para as vigas em situação de incêndio obtidos via ANSYS resultaram inferiores àqueles obtidos via TCD v5.0, com base na análise da seção transversal e procedimentos normativos. / This research presents a study, within the context of numerical analysis with ANSYS v9.0, in which the main goal has been driven to obtain the rise of temperature in steel and composite steel-concrete structural elements cross sections with the purpose of evaluating the temperature determination by normative equations proposed in brazilian standard NBR 14323:1999, considering the simple calculation model, specially in situations with not uniform exposition of the elements cross sections to the fire. Numerical models of steel, composite steel-concrete and wooden structural elements cross sections in fire situation are presented to evaluate the levels of temperature throughout the time. Numerical models to analyze the effect of the rise of temperature in the mechanical behavior of steel beams of a building of interest are also presented. The temperature levels obtained for structural elements by prescriptions of NBR 14323:1999 lead to satisfactory results but with temperatures near to the maximum temperatures obtained numerically. For the usual cases not contemplated by the NBR 14323:1999, is evident the necessity of employing advanced calculation models or studies for the development of analytical methods for such situations. With respect to the analysis of temperature rising effects in the mechanical behavior, the reduction factors for the resistance in fire situation, obtained by ANSYS, resulted smaller than those ones obtained by TCD v5.0, with base on the analysis of elements cross sections and normative procedures.

O interesse pelo estudo de estruturas em situação de incêndio vem aumentando dadas as inúmeras ocorrências internacionais, que resultaram em colapso estrutural de edificações. As recentes revisões das normas técnicas brasileiras reforçam a preocupação de organismos públicos e da comunidade técnica. A contribuição deste trabalho é determinar como os esforços resistentes em perfis isolados de aço são afetados pela ação térmica provenientes do incêndio, ou melhor, em função das variáveis que modelam o incêndio natural. Para tanto foi desenvolvido o programa de computador STRESFIRE capaz de calcular a ação térmica conforme curvas paramétricas, a transferência de calor para a peça de aço e o esforço resistente em função da temperatura na formulação a ser apresentada na revisão da NBR 14323:1999. / The interest by study of structures in fire situation has increased due to several international occurrences, which resulted in structural collapse of buildings. The recent revisions of the Brazilian technical standards reinforce the concern of public organisms and technical community. The contribution of this work is determine how the structural resistance of isolated steel element is affected by fire thermal action, in other words, the variables that model the natural fire. A software STRESFIRE was developed, which calculates the temperatures in the compartment, the heat transfer to steel member and the fire resistance by analytical methods.

O presente trabalho teve como objetivo principal estudar, em caráter essencialmente numérico via ANSYS v9.0, a elevação de temperatura em seções transversais de elementos estruturais de aço e mistos de aço e concreto, com vistas a uma avaliação das equações propostas pelo método simplificado de cálculo da NBR 14323:1999, em especial, para situações em que não ocorra aquecimento uniforme por todos os lados do elemento. São apresentados modelos numéricos de seções transversais de elementos estruturais de aço, mistos de aço e concreto e, em caráter complementar, de madeira, em situação de incêndio, para avaliar a evolução dos níveis de temperatura ao longo do tempo. São também construídos e analisados modelos numéricos com vistas à análise do efeito da elevação de temperatura no comportamento mecânico em vigas de aço de um edifício de interesse. A determinação dos níveis de temperatura em seções transversais de elementos estruturais, obtidas com base nas prescrições normativas da NBR 14323:1999, conduzem a resultados satisfatórios, porém, com temperaturas próximas as temperaturas máximas obtidas numericamente. Para os casos usuais não contemplados pela NBR 14323:1999 fica evidente a necessidade do emprego de modelo avançado de cálculo ou de estudos com vistas ao desenvolvimento de ferramentas analíticas para emprego em tais situações. Com relação à análise do efeito da elevação de temperatura no comportamento mecânico, os fatores de redução de resistência para as vigas em situação de incêndio obtidos via ANSYS resultaram inferiores àqueles obtidos via TCD v5.0, com base na análise da seção transversal e procedimentos normativos. / This research presents a study, within the context of numerical analysis with ANSYS v9.0, in which the main goal has been driven to obtain the rise of temperature in steel and composite steel-concrete structural elements cross sections with the purpose of evaluating the temperature determination by normative equations proposed in brazilian standard NBR 14323:1999, considering the simple calculation model, specially in situations with not uniform exposition of the elements cross sections to the fire. Numerical models of steel, composite steel-concrete and wooden structural elements cross sections in fire situation are presented to evaluate the levels of temperature throughout the time. Numerical models to analyze the effect of the rise of temperature in the mechanical behavior of steel beams of a building of interest are also presented. The temperature levels obtained for structural elements by prescriptions of NBR 14323:1999 lead to satisfactory results but with temperatures near to the maximum temperatures obtained numerically. For the usual cases not contemplated by the NBR 14323:1999, is evident the necessity of employing advanced calculation models or studies for the development of analytical methods for such situations. With respect to the analysis of temperature rising effects in the mechanical behavior, the reduction factors for the resistance in fire situation, obtained by ANSYS, resulted smaller than those ones obtained by TCD v5.0, with base on the analysis of elements cross sections and normative procedures.

Utbredningen av en brand inuti en byggnad kan leda till global eller lokal strukturell kollaps, särskilt i stålramkonstruktioner. Faktum är att stålkonstruktioner är särskilt utsatta för termiska angrepp på grund av ett högt värde av stålkonduktivitet och tvärsnitten med små tjockleken. Som en viktig aspekt av konstruktionen bör brandsäkerhetskrav uppnås antingen enligt föreskrivande regler eller enligt antagande av prestationsbaserad brandteknik. Trots möjligheten att använda enkla metoder som involverar membersanalys kombinerat med nominella brandkurvor, är en mer exakt analys av det termomekaniska beteendet hos en stålkonstruktion ett tilltalande alternativ eftersom det kan leda till mer ekonomiska och effektiva lösningar genom att ta hänsyn till möjliga gynnsamma mekanismer. Denna analys kräver vanligtvis utredning av delar av strukturen eller till och med av hela strukturen. För detta ändamål och för att få en djupare kunskap om strukturelementens beteende vid förhöjd temperatur bör numerisk simulering användas. I denna avhandling utvecklades och användes termomekaniska finita element som är lämpliga för analys av stålkonstruktioner utsätta för brand. Relevanta fallstudier utfördes. Utvecklingen av både ett termomekaniskt skal- och 3D balkelement baserade på en korotationsformulering presenteras. De flesta relevanta strukturfall kan undersökas på ett adekvat sätt genom att antingen använda något av dessa element eller kombinera dem. Korotationsformuleringen är väl lämpad för analyser av strukturer där stora förskjutningar, men små töjningar förekommer, som i fallet med stålkonstruktioner i brand. Elementens huvuddrag beskrivs, liksom deras karakterisering i termomekaniskt sammanhang. I detta avseende övervägdes materialnedbrytningen på grund av temperaturökningen och den termiska expansionen av stål vid härledningen av elementen. Dessutom presenteras en grenväxlingsprocedur för att utföra preliminära instabilitetsanalyser och få viktig inblick i efterknäckningsbeteendet hos stålkonstruktioner som utsätts för brand. Tillämpningen av de utvecklade numeriska verktygen ges i den del av avhandlingen som ägnas åt det publicerade forskningsarbetet. Flera aspekter av knäckningen av stålkonstruktionselement vid förhöjd temperatur diskuteras. I Artikel I tillhandahålls överväganden om påverkan av geometriska imperfektioner på beteendet hos komprimerade stålplattor och kolonner vid förhöjda temperaturer, liksom implikationer och resultat av användningen av grenväxlingsprocedur. I Artikel II valideras det föreslagna 3D-balkelementet genom meningsfulla fallstudier där torsionsdeformationer är signifikanta. De utvecklade balk- och skalelementen används i en undersökning av knäckningsmotstånd hos komprimerade vinkel-, Tee- och korsformade stålprofiler vid förhöjd temperatur som presenteras i Artikel III. En förbättrad knäckningskurva för design presenteras i detta arbete. Som ett exempel på tillämpningen av principerna för brandsäkerhetsteknik presenteras en omfattande analys i Artikel IV. Två relevanta brandscenarier identifieras för den undersökta byggnaden, som modelleras och analyseras i programmet SAFIR. / The ignition and the propagation of a fire inside a building may lead to global or local structural collapse, especially in steel framed structures. Indeed, steel structures are particularly vulnerable to thermal attack because of a high value of steel conductivity and of the small thickness that characterise the cross-sections. As a crucial aspect of design, fire safety requirements should be achieved either following prescriptive rules or adopting performance-based fire engineering. Despite the possibility to employ simple methods that involve member analysis under nominal fire curves, a more accurate analysis of the thermomechanical behaviour of a steel structural system is an appealing alternative, as it may lead to more economical and efficient solutions by taking into account possible favourable mechanisms. This analysis typically requires the investigation of parts of the structure or even of the whole structure. For this purpose, and in order to gain a deeper knowledge about the behaviour of structural members at elevated temperature, numerical simulation should be employed. In this thesis, thermomechanical finite elements, suited for the analyses of steel structures in fire, were developed and exploited in numerical simulation of relevant case studies. The development of a shell and of a 3D beam thermomechanical finite element based on a corotational formulation is presented. Most of the relevant structural cases can be adequately investigated by either using one of these elements or combining them. The corotational formulation is well suited for the analyses of structures in which large displacements, but small strains occur, as in the case of steel structures in fire. The main features of the elements are described, as well as their characterization in the thermomechanical context. In this regard, the material degradation due to the temperature increase and the thermal expansion of steel were considered in the derivation of the elements. In addition, a branch-switching procedure to perform preliminary instability analyses and get important insight into the post-buckling behaviour of steel structures subjected to fire is presented. The application of the developed numerical tools is provided in the part of the thesis devoted to the published research work. Several aspects of the buckling of steel structural elements at elevated temperature are discussed. In paper I, considerations about the influence of geometrical imperfections on the behaviour of compressed steel plates and columns at elevated temperatures are provided, as well as implications and results of the employment of the branch-switching procedure. In Paper II, the proposed 3D beam element is validated for meaningful case studies, in which torsional deformations are significant. The developed beam and shell elements are employed in an investigation of buckling resistance of compressed angular, Tee and cruciform steel profiles at elevated temperature presented in Paper III. An improved buckling curve for design is presented in this work. Furthermore, as an example of the application of Fire Safety Engineering principles, a comprehensive analysis is proposed in Paper IV. Two relevant fire scenarios are identified for the investigated building, which is modelled and analysed in the software SAFIR.

Tesis por compendio / [ES] El fuego es uno de los principales riesgos que pueden afectar a las estructuras de acero. El impacto del fuego en estas estructuras es muy adverso y complejo de simular, principalmente en escenarios de fuego realistas, donde el calentamiento en los miembros de acero no es uniforme y en miembros de acero esbeltos porque fallan prematuramente por la aparición de abolladuras locales. Para predecir con exactitud la respuesta de las estructuras de acero al fuego, se han desarrollado modelos avanzados y complejos de EF con elementos de cáscara y sólidos. Sin embargo, estos modelos son costosos desde el punto de vista computacional, lo que complica la realización de análisis más complejos que requieren muchas simulaciones en poco tiempo y con bajos costes computacionales. Por lo tanto, es necesario desarrollar modelos computacionales sencillos, precisos y de bajo coste, tan fiables como los modelos de cáscara, que abran el camino más fácilmente hacia la modelización de problemas estructurales de acero más complejos en situación de incendio. En esta tesis se presentan propuestas sencillas y de bajo coste computacional para simular la respuesta mecánica de estructuras de acero en condición de incendio utilizando un elemento finito de viga de Timoshenko de Ansys. Una de las propuestas consiste en una nueva metodología para el análisis en 3D de estructuras de acero sometidas a temperaturas no uniformes por el fuego. Las otras consisten en dos estrategias de modelización para analizar el pandeo lateral torsional en miembros de acero de clase 4 a temperaturas elevadas. Las propuestas simplifican significativamente la modelización estructural y se validan satisfactoriamente con resultados numéricos y experimentales. Esto significa que problemas complejos de ingeniería de incendio, como los análisis probabilísticos y de optimización, pueden tratarse con mucha más facilidad, lo que representa un paso importante hacia la aplicación generalizada de enfoques basados en el desempeño para tratar los efectos del fuego en las estructuras de acero. / [CA] El foc és un dels principals riscos que poden afectar les estructures d'acer. L'impacte del foc en estes estructures és molt advers i complex de simular, principalment en escenaris de foc realistes, on el calfament en els membres d'acer no és uniforme i en membres d'acer esvelts perquè fallen prematurament per l'aparició d'abonyegadures locals. Per a predir amb exactitud la resposta de les estructures d'acer al foc, s'han desenvolupat models avançats i complexos d'elements finits de corfa i sòlids. No obstant això, estos models són computacionalment costosos, la qual cosa complica la realització d'anàlisi més complexos que requerixen moltes simulacions en poc de temps i amb baixos costos computacionals. Per tant, és necessari desenvolupar models computacionals senzills, precisos i de baix cost, tan fiables com els models de corfa, que òbriguen el camí més fàcilment cap a la modelització de problemes estructurals d'acer més complexos en situació d'incendi. En esta tesi es presenten propostes senzilles i de baix cost per a simular la resposta mecànica d'estructures d'acer en condició d'incendi utilitzant un element finit de biga de Timoshenko d'Ansys. Una de les propostes consistix en una nova metodologia per a l'anàlisi en 3D d'estructures d'acer sotmeses a temperatures no uniformes pel foc. Les altres consistixen en dos estratègies de modelització per a analitzar el bombament lateral torsional en membres d'acer de classe 4 a temperatures elevades. Les propostes simplifiquen significativament la modelització estructural i es validen satisfactòriament amb resultats numèrics i experimentals. Açò significa que problemes complexos d'enginyeria d'incendi, com les anàlisis probabilístiques i d'optimització, poden tractar-se amb molta més facilitat, la qual cosa representa un pas important cap a l'aplicació generalitzada d'enfocaments basats en l'exercici per a tractar els efectes del foc en les estructures d'acer. / [EN] Fire is one of the main hazards that can affect steel structures. The impact of fire on these structures is highly adverse and complex to simulate, mainly in realistic fire scenarios, where heating in steel members is non-uniform and in slender steel members because they fail prematurely by local buckling. In order to accurately predict the response of steel structures to fire, advanced and complex FE models with shell and solid elements have been developed. However, these shell models are computationally expensive, complicating the carrying out of more complex analyses that require many simulations in a short time and at low computational costs. Therefore, there is a need to develop simple, accurate, and low-cost computational models as reliable as shell-type models that open the path more easily towards modeling more complex steel structural problems in fire conditions. This thesis presents simple and low-cost proposals to simulate the mechanical response of steel structures under fire using Timoshenko's beam-type finite element available in Ansys. One of the proposals consists of a new methodology for the 3D-analysis of steel frames subjected to non-uniform temperatures by fire. The others consist of two modeling strategies for analyzing the lateral-torsional buckling in class-4 steel structural members at elevated temperatures. The proposals significantly simplify the structural modeling and satisfactorily validate numerical and experimental results. That means that complex fire engineering problems, such as probabilistic and optimization analyses, can be handled much more easily, representing a significant step toward the generalized application of performance-based approaches to deal with fire effects on steel structures. / Pallares Muñoz, MR. (2022). New Proposals for Modeling the Thermo-Mechanical Response of Steel Structures Under Fire Using Beam-Type Finite Elements [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/182768 / TESIS / Compendio