Doctoral Thesis
PERFORMANCE-BASED FIRE ENGINEERING FOR CIVIL ENGINEERING STRUCTURAL DESIGN
by
Michał Malendowski
Supervisor: dr. hab. inż. Adam Glema,
Submitted in partial fulfilment of the requirements for the degree, Doctor of Philosophy (Ph.D.), in Structural Engineering,
in the Faculty of Civil and Environmental Engineering, Poznan University of Technology, Poznan, Poland
Poznan, 2018
SUMMARY
(summary in English and Polish) (streszczenie w języku angielskim i w języku polskim) English summary
In this work, the problem of the structural behaviour in natural fire is considered. The performance- based structural fire engineering approach is used. Hence, models called in Eurocodes advanced calculation models are used for structural analyses. According to Eurocodes, these models are design methods in which engineering principles are applied in a realistic manner to specific applications. Thus, analysis objectives are defined in terms of performance criteria. In this work, the fire resistance of the structure is used as performance criterion.
An integrated framework for analysis of structures in natural fire is developed. It integrates analyses of the fire development in a building, heat transfer from fire to the structure, and the response of the structure in fire. In the developed framework, all the models being used are based on the mathematical models describing the physical processes. The fire modelling is done with the use of Computational Fluid Dynamics (CFD) models. For the solution of mechanical problem of a structural response, a nonlinear finite element method is incorporated. The heat transfer between the fire environment and the structural members is modelled using an original heat transfer model. The heat transfer model creates a link between the CFD fire analyses and analyses of structures in fire.
The work starts with a theoretical elaboration about modelling of physical phenomena observed in buildings during a fire. These considerations are divided into parts describing fire modelling, modelling of mechanical phenomena occurring in the structure during a fire, and heat transfer between the fire and the structure. In the first part, mathematical models for fluid flow, turbulences, combustion, soot production, and radiation, are described. The special concern is put into the mutual relationship between these phenomena and necessity of including of them in fire modelling. In a second part, considerations are directed into mechanical phenomena. A special concern is put into the sources of nonlinearities arising during fire. Both geometrical and material nonlinearities are taken into account.
The direct source of these nonlinearities is a high temperature in structures in fire. It causes additional thermal strains, as well as reduces material properties. Considerations in this part provide the extensive theoretical background for the analyses of the structures with respect to the developed performance-based framework. Therefore, the influence of nonuniform temperature field inside cross-section on the stiffness of beam elements is highlighted, as well as qualitative explanation of mechanical processes in fire is given. In the last part of the theoretical considerations, the problem of heat exchange between the fire and the structure is formulated. Mathematical models of convection, radiation, and conduction are introduced, as well as the concept of an adiabatic surface temperature (AST) is presented. An original, analytical solution for an AST is given.
The heat transfer model is an original research contribution. It establishes a coupling between fire
analyses, carried out using CFD-based approach, and structural response analyses, that use finite
element method modelling. The developed heat transfer model is dedicated for analyses of heat
transfer between the fire and framed members. In framed structures, the projection of structural
elements inside the CFD grid is impossible in practical cases. Steel framed structures are good
representation of this problem. In these kinds of structures, the cross-sectional dimensions are too
small, to accurate include them in CFD grids of practically used sizes.
to quantify a thermal exposure around the cross-section of structural element. Introducing virtual surfaces as for measurement does not influence the fluid flow. Hence, they do not have to fit a computational grid, so they can be arbitrarily placed in a computational domain in any direction.
Virtual surfaces are set to be adiabatic. Hence, the output quantity is the adiabatic surface temperature (AST). AST allows to quantify the thermal exposure taking into account both convection and radiation at a particular point in a certain direction. In the heat transfer model, for radiation calculations, virtual surfaces take a form of black body radiators which interacts with cross-section surfaces.
An analytical solution for an adiabatic surface temperature is derived. The solution has been implemented by developers of fire development CFD solver called FDS. Thanks to this implementation, the practical usage of the developed heat transfer model became possible. Additionally, this solution, after some modifications, contributed to experimental measurements of fire exposure. It allowed to calculate an AST, based on a plate thermometers output, using a closed-form formula. This has been used in a validation process of the heat transfer model. The laboratory tests of steel sections exposed to a localised fires are an integral part of this research.
A mechanically based method for determination of fire scenarios is a complementary element of the developed performance-based framework. It supports the selection of the worse placement of a localised fire based on mechanical premises. It finds the structural element, or group of structural elements, with the highest importance in load-bearing. Next, the localised fire is placed in the CFD model, in the vicinity of such chosen structural element.
A calculation example of structural response in natural fire is presented at the end of the thesis. These analyses aims to show the effectiveness of the developed framework. The offshore structures factory is chosen as an exemplary structure. The structure is capable to carry on significant loads in normal conditions, resulted from the operation of heavy cranes. Thus, it is presumed, that the structure is robust in fire, since the cranes do not operate. The resistance of the structure in fire is checked according to the developed framework. Despite the conclusion about the fire resistance, the example is used to indicate the phenomena, which are possible to be observed when the developed framework is applied, but could not be observed using simplified models.
It is concluded, that the effects caused by the nonuniform temperature distribution inside the cross-
section can importantly influence the structural response of the system. It is shown, that the developed
heat transfer model enables effective calculations of temperature field inside steel sections and further
use of these results in mechanical analyses of the structure. The developed framework utilises
capabilities in prediction of structural behaviour of beam finite elements, which stiffness is updated
during the analysis. This allows to analyse entire structural systems, where the temperature field is
evaluated in a detailed way. In this work, also the method for determination of position of localised
fire is proposed. The method is based on the identification of structural elements that play crucial role
in load bearing. It has been proven, that the developed integrated framework for analysis of structures
in natural fire enables effective analyses of the physical phenomena observed in fire, considering fire
development, heat transfer to structure, and structural response.
możliwości obliczania konstrukcji na wypadek pożaru, które w obowiązujących normach do projektowania (eurokodach) nazwane są zaawansowanymi modelami obliczeniowymi. Cytując zapisy normowe, w przypadkach stosowania zaawansowanych modeli obliczeniowych, konieczne jest stosowanie modeli obliczeniowych wykorzystujących w sposób realistyczny zasady inżynierii pożarowej. Cele analiz odnoszą się wtedy do parametrów użytkowych (ang. „Performance-based analyses”). W niniejszej pracy jako główny parametr użytkowy przyjęto nośność konstrukcji w pożarze.
Sprawdza się zatem, czy nośność konstrukcji jest zachowana w czasie trwania pożaru.
Aby umożliwić sprawdzenie nośności konstrukcji w pożarze, opracowano zintegrowane podejście służące analizie rozwoju pożaru w budynku oraz analizie pracy konstrukcji budowlanej w pożarze.
W podejściu tym posłużono się modelami pożaru, przepływu ciepła pomiędzy pożarem i konstrukcją, oraz pracy konstrukcji, zbudowanymi z wykorzystaniem modeli matematycznych opisujących odpowiednie procesy fizyczne. Problem rozwoju pożaru analizuje się stosując modele komputerowej mechaniki płynów (CFD). Problem analizy pracy konstrukcji w pożarze rozwiązuje się poprzez stosowanie algorytmów metody elementów skończonych (MES) do rozwiązywania problemów nieliniowych. Autorski model przepływu ciepła pomiędzy środowiskiem pożaru a elementami konstrukcyjnymi stanowi połączenie pomiędzy wymienionymi modelami (CFD i MES).
Praca rozpoczyna się od opracowania teoretycznego dotyczącego modelowania zjawisk fizycznych obserwowanych w budynkach podczas pożaru. Rozważania podzielono na części opisujące modelowanie pożaru, modelowanie zjawisk mechanicznych zachodzących w konstrukcji i modelowanie przepływu ciepła pomiędzy pożarem a konstrukcją. W pierwszej części zostały opisane modele matematyczne wykorzystywane w mechanice płynów, począwszy od równań przepływu (Naviera-Stokesa), poprzez równania opisujące turbulencje, spalanie, produkcję sadzy, kończąc na promieniowaniu. Zwrócono uwagę na wzajemność tych zjawisk i konieczność ich sprzężenia przy opisywaniu pożaru. W drugiej części skupiono się na modelowaniu zjawisk mechanicznych. Szczególną uwagę zwrócono na źródła nieliniowości występujące podczas analizy konstrukcji w pożarze:
nieliniowości geometryczne, jak i materiałowe. Ich źródłem jest przede wszystkim wysoka temperatura w konstrukcji podczas pożaru. Wywołuje ona dodatkowe odkształcenia termiczne, jak również redukuje parametry materiału. Rozważania w tej części stanowiłą teoretyczne sformułowanie dla analiz realizowanych z wykorzystaniem opracowanego podejścia. Zwrócono uwagę przede wszystkim na nierównomierny rozkład temperatury oraz jego wpływ na sztywność elementów konstrukcyjnych, jak również opisano jakościowo mechanikę zjawisk zachodzących w konstrukcji podczas pożaru.
W ostatniej części opisu teoretycznego, dotyczącej przepływu ciepła, wprowadzono matematyczne modele opisujące zjawiska konwekcyjnego przepływu ciepła, radiacyjnego przepływu ciepła oraz przewodnictwa, jak również wprowadzono pojęcie temperatury powierzchni adiabatycznej (AST) oraz wyprowadzono analityczne rozwiązanie pozwalające na obliczenie wartości AST.
Model przepływu ciepła stanowi oryginalną część tej pracy. Jego opracowanie pozwoliło na połączenie analiz rozwoju pożaru, wykorzystujących modele CFD, oraz analiz pracy konstrukcji, wykorzystujących modele MES. Opracowany model przepływu ciepła jest dedykowany do obliczania przepływu ciepła pomiędzy środowiskiem pożaru, a konstrukcją budynku złożoną z elementów prętowych. Dokładne odwzorowanie tego typu elementów konstrukcyjnych w modelach CFD jest w praktyce niemożliwe.
Jako czytelną ilustracją tego problemu posłużono się konstrukcjami stalowymi, w których gabaryty przekroju są zbyt małe, aby jednoznacznie odtworzyć je wewnątrz stosowanych w praktyce siatek CFD.
Model przepływu ciepła wykorzystuje wirtualne powierzchnie, które wprowadza się do modeli CFD, w
celu zbadania oddziaływań termicznych w otoczeniu przekroju elementu konstrukcyjnego.
wpływają na przepływ, jak również mogą być dowolnie umiejscowione i zorientowane (niezależnie od siatki CFD). Powierzchnie te określa się jako adiabatyczne i dokonuje się odczytu ich temperatury.
Temperatura ta, zwana temperaturą powierzchni adiabatycznej (AST), pozwala na ilościowe określenie oddziaływania termicznego w danym punkcie, w danym kierunku (wpływ konwekcji i promieniowania).
W modelu przepływu ciepła, przy analizie promieniowania, powierzchnia ta przyjmuje postać doskonale czarnego promiennika i odpowiednio oddziałuje z powierzchniami przekroju elementu konstrukcyjnego.
W celu wyznaczenia temperatury powierzchni adiabatycznej wyprowadzono analityczne rozwiązanie równania równowagi cieplnej na powierzchni adiabatycznej. Rozwiązanie to zostało zaimplementowane przez twórców programu FDS, służącego analizom CFD rozwoju pożaru, przez co możliwe stało się wykorzystanie autorskiego modelu przepływu ciepła w praktyce. Dodatkowo pokazano, że po niewielkich modyfikacjach, zaproponowane rozwiązanie pozwala na pomiar eksperymentalny AST przy pomocy termoelementów płytkowych. Wykonano eksperymenty służące weryfikacji eksperymentalnej opracowanego modelu przepływu ciepła.
Elementem zaproponowanego podejścia służącego analizie pracy konstrukcji w pożarze jest opracowana metoda wspomagająca wybór scenariusza pożarowego w zakresie określenia położenia pożaru zlokalizowanego. Bazuje ona wyborze elementu konstrukcyjnego, lub grupy elementów konstrukcyjnych, których znaczenie przy przenoszeniu obciążeń statycznych jest największe.
Następnie, pożar umieszcza się w modelu CFD w najbliższym otoczeniu elementu konstrukcyjnego wskazanego na podstawie opracowanej metody. Wybór scenariusza jest więc dokonywany na przesłankach mechanicznych.
Przykład obliczeniowy analizy konstrukcji w pożarze umiejscowiony jest na końcu pracy. Służy on do zobrazowania skuteczności opracowanego podejścia. Wybrano przykład konstrukcji stalowej budynku fabryki konstrukcji platform oceanicznych. Konstrukcja tego budynku, z uwagi na ciężkie suwnice pracujące wewnątrz niej, przenosi znaczące obciążenia w normalnej sytuacji obliczeniowej. Postuluje się więc, że w przypadku pożaru, gdy obciążenia od pracy suwnic nie są brane pod uwagę, będzie ona stosunkowo odporna na pożar. Nośność tej konstrukcji w pożarze sprawdza się z wykorzystaniem opracowanego podejścia. Dodatkowo, przykład ten wykorzystuje się do omówienia możliwości modelowania zjawisk, które występują w konstrukcji podczas pożaru. Wskazuje się, że w konstrukcji podczas pożaru występują zjawiska, które symulowane być mogą jedynie przy wykorzystaniu odpowiednio złożonych modeli obliczeniowych.
W pracy wykazano, że zjawiska wynikające z nierównomiernego rozkładu temperatury wewnątrz
przekrojów elementów konstrukcyjnych mogą mieć istotny wpływ na odpowiedź mechaniczną
konstrukcji. Pokazano, że opracowany model przepływu ciepła pozwala w sposób skuteczny obliczać
pole temperatury wewnątrz przekrojów elementów stalowych, a następnie wykorzystywać te
obliczenia do analizy mechanicznej konstrukcji. Opracowane podejście pozwala na zastosowanie
belkowych elementów skończonych, których sztywność jest liczona w każdym kroku analizy, do
modelowania numerycznego elementów konstrukcyjnych,. Dzięki temu, w praktyce mogą być
analizowane całe systemy konstrukcyjne, w których pole temperatury odwzorowane jest w sposób
szczegółowy. W pracy wskazano również na możliwość określenia położenia pożaru zlokalizowanego z
wykorzystaniem metody znajdowania elementu konstrukcyjnego, lub grupy elementów
konstrukcyjnych, o szczególnym znaczeniu przy przenoszeniu obciążeń statycznych. Udowodniono, że
opracowane zintegrowane podejście, służące zarówno analizie rozwoju pożaru w budynku, jak i
określaniu wpływu pożaru na pracę konstrukcji budowlanej, pozwala w skuteczny sposób opisywać
zjawiska fizyczne obserwowane w pożarze.
List of Tables ... viii
Notation ... ix
Acknowledgment ... xiii
1. Introduction ... 1
1.1. State-of-the-art ... 1
1.1.1. Performance-based fire engineering ... 1
1.1.2. Advancements in solving of structural fire engineering problems ... 6
1.2. Research objectives and the concept of the thesis ... 8
2. Theoretical background ... 11
2.1. Fluid dynamics in fire engineering ... 11
2.1.1. Fundamental laws of fluid dynamics and heat transfer ... 11
2.1.2. Turbulence modelling... 17
2.1.3. Combustion ... 19
2.1.4. Soot production ... 21
2.1.5. Radiation ... 22
2.2. Nonlinear solid mechanics in performance-based structural fire design ... 25
2.2.1. Formulation of a linear elastic problem ... 25
2.2.2. Finite Element Method in linear elastic problems ... 26
2.2.3. Large strain-displacement formulation ... 27
2.2.4. Material nonlinearity in structural fire engineering problems ... 31
2.2.5. Stiffness of a structural element in fire ... 36
2.2.6. Solution of a nonlinear problem ... 39
2.3. Physical bases for heat exchange between the fire environment and the structure ... 44
2.3.1. Convective heat flux ... 44
2.3.2. Radiative heat flux ... 46
2.3.3. Adiabatic surface temperature ... 47
2.3.4. Heat conduction ... 53
3. Coupling between the fire and the mechanical models ... 55
3.1. Incompatibility between CFD and FEM models for steel framed structures ... 55
3.2. Development of a heat transfer model ... 57
3.2.1. Virtual surfaces ... 57
3.2.2. Shadow effect ... 59
3.2.3. Heat transfer model formulation ... 59
3.3.1. Approximate calculation of view factors ... 67
3.3.2. Verification of view factors calculation method ... 70
3.3.3. Finite difference method approximation of a conduction problem ... 71
3.4. Verification and Validation ... 76
3.4.1. Furnace tests with uniform thermal exposure of a cross-section ... 77
3.4.2. Furnace tests with nonuniform thermal exposure of a cross-section... 79
3.4.3. Compartment fire tests ... 82
3.4.4. Localised fire tests ... 84
3.4.5. Summary ... 93
3.5. CFD-FEM coupling procedure ... 93
3.5.1. Setting CFD output ... 94
3.5.2. Heat transfer calculations ... 94
4. Mechanically based method for determination of fire scenarios ... 97
4.1. Complexity and robustness of frame structures ... 97
4.2. The idea of the method ... 98
4.3. Theoretical bases ... 100
4.4. Complexity measures ... 101
4.5. Method implementation ... 102
4.6. Verification ... 104
5. Exemplary analysis of a structure subjected to fire ... 115
5.1. Actions ... 115
5.1.1. Fire actions ... 117
5.1.2. Permanent loads ... 117
5.1.3. Imposed loads ... 118
5.1.4. Snow load ... 118
5.1.5. Wind load... 119
5.1.6. Combinations of actions ... 120
5.2. Preliminary analyses ... 121
5.2.1. Design according to Eurocode simple calculation model ... 122
5.2.2. Response to uniform ISO 834 fire exposure ... 122
5.3. Numerical models ... 124
5.3.1. CFD fire model ... 124
5.3.2. FEM mechanical model ... 127
5.4. Fire scenario determination ... 129
5.5. CFD-FEM coupling ... 131
5.6.2. Fire-structure heat transfer results ... 135
5.6.3. Effect of combinations of actions on the mechanical response of the structure in fire 145 5.6.4. Local response of the structure in fire ... 147
5.6.5. Global response of the structure in fire ... 164
5.6.6. Summary ... 173
6. Concluding remarks ... 175
References ... 179
Figure 1. Alternative design procedures (according to Eurocode 1991-1-2) ... 3
Figure 2. Available methods to define the Fire Behaviour, Thermal Response and Structural Behaviour (elaborated according to [165] and [60]) ... 4
Figure 3. Phenomena modelled by various structural analysis methods. Dashed arrows represent non-straight- forward approach (reproduced according to [176]). ... 6
Figure 4. The proposed integrated framework for performance-based analyses of structures in fire. ... 9
Figure 5. Framework for field modelling in fire engineering [189]. ... 12
Figure 6. Eulerian (a) and Lagrangian (b) approaches for derivation of governing equations. ... 12
Figure 7. Transport property 𝜙 fluctuation with time at some point in a turbulent flow [189]. ... 17
Figure 8.Time scales for field modelling related problems... 20
Figure 9. Change of intensity 𝐼𝜆 in monochromatic pencil of radiation of direction 𝑠... 22
Figure 10. Local coordinate system and degrees of freedom at element’s node. ... 28
Figure 11. Geometric relations for displacement of an arbitrary point on the cross-section. ... 30
Figure 12. Yield stress in relation to accumulated plastic strain 𝜀𝑢𝑝 and material temperature 𝜃. ... 33
Figure 13. Discretisation of cross-section: a) fibre element approach, b) division of cross-section into points. . 37
Figure 14. Illustration of the temperature and strain field on the stresses induced in a cross-section: a) division of cross-section and indication of the differences in the temperature over the fields, b) strain field, c) stress field. ... 38
Figure 15. Path dependence of solution in structural fire engineering problems. ... 40
Figure 16. Newton’s method. ... 41
Figure 17. Illustration of the temperature-displacement path for an pre-tensioned prismatic bar, neglecting the effect of thermal elongation. ... 42
Figure 18. Producing of a force increment by inclusion of thermal strain profile. ... 43
Figure 19. Illustration of the three fundamental heat transfer mechanisms. ... 44
Figure 20. Effects of incident radiation on fluid-solid surface. ... 46
Figure 21. Physical model of an adiabatic surface. ... 47
Figure 22. Relationship between 𝜃𝐴𝑆𝑇 and 𝜀𝑠/ℎ𝑐 ratios [103]. ... 50
Figure 23. Comparison between exact and approximate solutions for 𝜃𝑔 = 20°C and 𝜃𝑔 = 500°C (graphs overlap) [103]. ... 51
Figure 24. Scheme of the plate thermometer. ... 51
Figure 25. Differences between the actual shapes of the steel profiles and their approximations in CFD model. Orthogonal direction of the profiles correspond to the coordinate system of CFD model. ... 56
Figure 26. Differences between the actual shapes of the steel profiles and their approximations in CFD model. Orthogonal direction of the profiles are 45° rotated with respect to the coordinate system of CFD model. ... 57
Figure 27. a) Exemplary projection of a steel section in CFD model; b) Set of virtual surfaces surrounding the element’s cross-section ... 58
Figure 28. Shapes of virtual boxes for different cross-sections. ... 58
Figure 29. Shadow effect. ... 59
Figure 30. Illustration of the geometrical relations between 3 radiating surfaces. ... 61
Figure 31. Illustration of reciprocal radiation between 3 radiating surfaces, on the example of I-section, where one surface is a black body radiator. ... 64
Figure 32. Illustration of parameters used in equation (221). ... 66
Figure 33. Cross-section scheme for an explanation of heat transfer model implementation: a) cross-section division into parts and corresponding temperature points; b) distinguished surfaces on the cross- section perimeter; c) distinguished surfaces on a virtual box. ... 66
Figure 34. Set of information have to be provided to resolve radiation problem in a cross-section: a) cross- section division into parts and corresponding temperature points, section’s dimensions; b) surfaces related to surface 20 and coordinates of their middle points; c) widths of surfaces and their normal directions. ... 67
Figure 35. Vertices of a single surface at the boundary of cross-section ... 69
Figure 38. Identical, parallel, directly opposed rectangles (F2-3). ... 72 Figure 39. Two rectangles with one common edge and included angle of 𝛷 (F4-5). ... 73 Figure 40. Finite difference method implementation: a) exemplary discretisation of a cross-section, b) projection of dummy nodes. ... 74 Figure 41. Differences between the extremal measured temperatures in selected tests: left – ratio between minimum and maximum temperature, right – difference between maximum and minimum temperature. ... 77 Figure 42. Comparison of steel temperature predictions by the Wang’s model, current model with averaged temperatures and experimental results (Test-40, Am/V = 76 m-1). ... 78 Figure 43. Comparison of steel temperature predictions by the Wang’s model, current model with averaged temperatures and experimental results (Test-72, Am/V = 133 m-1). ... 78 Figure 44. Comparison of steel temperature predictions by the Wang’s model, current model with averaged temperatures and experimental results (Test-82, Am/V = 149 m-1). ... 78 Figure 45. Model configuration for validation against furnace tests. ... 79 Figure 46. Comparison of steel temperature predictions by the current model (solid line) and temperatures measured during experiment. Upper flange, cross-section 254x146. ... 80 Figure 47. Comparison of steel temperature predictions by the current model (solid line) and temperatures measured during experiment. Upper flange, cross-section 203x203. ... 80 Figure 48. Comparison of steel temperature predictions by the current model (solid line) and temperatures measured during experiment. Web, cross-section 254x146. ... 80 Figure 49. Comparison of steel temperature predictions by the current model (solid line) and temperatures measured during experiment. Web, cross-section 203x203. ... 80 Figure 50. Comparison of steel temperature predictions by the current model (solid line) and temperatures measured during experiment. Lower flange, cross-section 254x146. ... 80 Figure 51. Comparison of steel temperature predictions by the current model (solid line) and temperatures measured during experiment. Lower flange, cross-section 203x203. ... 80 Figure 52. Comparison of steel temperature predictions by the current model (solid line) and temperatures measured during experiment. Upper flange, cross-section 203x133. ... 81 Figure 53. Comparison of steel temperature predictions by the current model (solid line) and temperatures measured during experiment. Upper flange, cross-section 356x171. ... 81 Figure 54. Comparison of steel temperature predictions by the current model (solid line) and temperatures measured during experiment. Web, cross-section 203x133. ... 81 Figure 55. Comparison of steel temperature predictions by the current model (solid line) and temperatures measured during experiment. Web, cross-section 356x171. ... 81 Figure 56. Comparison of steel temperature predictions by the current model (solid line) and temperatures measured during experiment. Lower flange, cross-section 203x133. ... 81 Figure 57. Comparison of steel temperature predictions by the current model (solid line) and temperatures measured during experiment. Lower flange, cross-section 356x171. ... 81 Figure 58. Experimental set-up of tests carried out by Wickström et al. [187]... 82 Figure 59. Exemplary validation graph for validation against the compartment fire (see Appendix 1)... 83 Figure 60. a) Instrumentation of measuring stations in tests carried out by Wickström et al. [187]; b) heat transfer model: virtual surfaces and temperature points. ... 83 Figure 61. Error evaluation of heat transfer model. Experimental data from [187]: Station-A, Test-2 and Test-3.
... 84 Figure 62. Error evaluation of heat transfer model. Experimental data from [187]: Station-B, Test-2 and Test-3.
... 84 Figure 63. Error evaluation of heat transfer model. Experimental data from [187]: Station-C, Test-2 and Test-3.
... 84 Figure 64. Experimental configuration for Tests 1-3 (dimensions in cm). ... 85 Figure 65. Experimental configuration for Tests 4-5 (dimensions in cm). ... 85
Figure 68. Steel temperature measurement points in vertically placed specimens. ... 86
Figure 69. Configuration of thermal exposure measurement: Tests 1-3. ... 87
Figure 70. Configuration of thermal exposure measurement: Tests 4-5. ... 87
Figure 71. Configuration of thermal exposure measurement: Tests 6. ... 88
Figure 72. Exemplary validation graph for validation against the localised fire (see Appendix 2). ... 88
Figure 73. a) heat transfer model virtual surfaces and temperature points; b) Instrumentation of measuring stations horizontal specimens; c) Instrumentation of measuring stations vertical specimens. ... 89
Figure 74. Error evaluation of heat transfer model. Own experimental data: Test-1, all sections. ... 90
Figure 75. Error evaluation of heat transfer model. Own experimental data: Test-2, all sections. ... 90
Figure 76. Error evaluation of heat transfer model. Own experimental data: Test-3, all sections. ... 91
Figure 77. Error evaluation of heat transfer model. Own experimental data: Test-4, all sections. ... 91
Figure 78. Error evaluation of heat transfer model. Own experimental data: Test-5, all sections. ... 92
Figure 79. Error evaluation of heat transfer model. Own experimental data: Test-6, all sections. ... 92
Figure 80. Data exchange scheme in CFD-FEM coupling. ... 94
Figure 81. Example of an event tree used for risk assessment of selected fire scenarios (reproduced from [131]). ... 99
Figure 82. The idea of mechanically based method for determination of fire scenarios ([100]). ... 100
Figure 83. Example of decomposition of statically indeterminate structure: a) initial structure, b) substructures ([100]). ... 101
Figure 84. Scheme of the mechanically based method for determination of fire scenarios. ... 103
Figure 85. Results of mechanically based method for determination of fire scenarios for simple cases. ... 104
Figure 86. 2D model for demonstration of the mechanically based method for determination of fire scenarios. ... 105
Figure 87. Results from analyses of 2D frame for extreme values of 𝑚 and 𝑛. ... 105
Figure 88. Relationship between stiffness of column 1 and stiffness of beam, and a) total elastic work of initial system, b-d) performance factors of subsequent substructures... 106
Figure 89. Relationship between stiffness of column 1 and stiffness of beam, and importance factors of subsequent elements. ... 107
Figure 90. Relationship between stiffness of column 1 and stiffness of beam, and importance factors of elements selected as variables in method. ... 107
Figure 91. 3D model for verification of the mechanically based method for determination of fire scenarios. .. 108
Figure 92. Shape of substructures for model used in verification of the mechanically based method for determination of fire scenarios. ... 109
Figure 93. Deflection shapes of substructures of the 3D frame under symmetrical, equally distributed load. .. 109
Figure 94. Elementary contributions for total elastic work of the 3D frame under symmetrical, equally distributed load. ... 110
Figure 95. Results from analyses of 3D frame for extreme values of 𝑚 and 𝑛 and symmetrical load. ... 111
Figure 96. Results from analyses of 3D frame for extreme values of 𝑚 and 𝑛 and unsymmetrical load. ... 112
Figure 97. Relationship between stiffness of column 4 and stiffness of beams, and importance factors of columns in 3D frame examples with a) symmetrical and b) unsymmetrical loads. ... 113
Figure 98. Relationship between stiffness of column 4 and stiffness of beams, and importance factors of columns 2 and 4 in 3D frame example with symmetrical load. ... 113
Figure 99. Sketch of frame no. 6. ... 115
Figure 100. Sketch of ground floor plan. ... 116
Figure 101. Rate of heat release curve. ... 118
Figure 102. Ratio between the amount of heat released and the total heat released. ... 118
Figure 103. Values of shape coefficients for drifted and undrifted snow load. ... 119
Figure 104. Actions acting on a single frame (on the example of frame 6 and D6 fire position). ... 120
Figure 105. Critical temperatures of the main structural elements of frame 6. ... 122
Figure 106. Failure mechanisms with respect to combinations of actions ([102]). ... 123
Figure 109. Plan view of CFD model at z=2.0 m. ... 126
Figure 110. Plan view of CFD model at z=5.0 m. ... 126
Figure 111. Plan view of CFD model at z=12.5 m. ... 127
Figure 112. 3D Abaqus beam element: a) Temperature points, temperature interpolation; b) section integration points. ... 128
Figure 113. Plot of 3D Abaqus model of the structure (beams’ cross-section rendered). ... 128
Figure 114. Plot of exemplary frame from 3D Abaqus model of the structure (beams’ cross-section rendered). ... 128
Figure 115. Normalised columns’ performance factors 𝜓𝑖 for determination of fire scenario. ... 130
Figure 116. Fire scenario. ... 131
Figure 117. Matching temperature points of heat transfer model to temperature points of structural model (see Figure 112). ... 132
Figure 118. Comparison between heat release rates modelled and obtained. ... 133
Figure 119. Gas temperature distributions in longitudinal and transverse cross-sections of the design fire. .... 134
Figure 120. Gas temperature distributions in longitudinal and transverse cross-sections of the amplified fire.135 Figure 121. Visible flames at the peak heat release rate of the amplified fire (smoke removed from the visualisation). ... 135
Figure 122. Cross-sections selected for verification of a performance of the developed heat transfer model. 136 Figure 123. Development of AST boundary conditions and a temperature field inside cross-sections for BOX- sections in a design fire. ... 137
Figure 124. Development of AST boundary conditions and a temperature field inside cross-sections for I-sections in a design fire. ... 138
Figure 125. Development of AST boundary conditions and a temperature field inside cross-sections for BOX- sections in an amplified fire. ... 139
Figure 126. Development of AST boundary conditions and a temperature field inside cross-sections for I-sections in an amplified fire... 140
Figure 127. Inclination of radiation surface resulted from the increase of the heat release rate. ... 140
Figure 128. Temperature profiles at selected BOX-sections in a design fire and their Abaqus approximation. . 141
Figure 129. Temperature profiles at selected I-sections in a design fire and their Abaqus approximation. ... 142
Figure 130. Temperature profiles at selected BOX-sections in an amplified fire and their Abaqus approximation. ... 143
Figure 131. Temperature profiles at selected I-sections in an amplified fire and their Abaqus approximation. 144 Figure 132. Absolute values of displacements of point P5 during fire. ... 146
Figure 133. Values of displacements of point P5 during fire, relative to initial state at the beginning of fire. ... 146
Figure 134. Local response of the structure to fire, at time 25.5 min: mean section temperature, plastic equivalent strain, von Mises stress. ... 148
Figure 135. Local response of the structure to fire, at time 33.3 min: mean section temperature, plastic equivalent strain, von Mises stress. ... 149
Figure 136. Local response of the structure to fire, at time 40.0 min: mean section temperature, plastic equivalent strain, von Mises stress. ... 150
Figure 137. Local response of the structure to fire, at time 50.0 min: mean section temperature, plastic equivalent strain, von Mises stress. ... 151
Figure 138. Local response of the structure to fire, at time 60.0 min: mean section temperature, plastic equivalent strain, von Mises stress. ... 152
Figure 139. Temperature development in cross-section A. ... 154
Figure 140. Temperature development in cross-section B. ... 154
Figure 141. Temperature development in cross-section C. ... 155
Figure 142. Temperature development in cross-section D. ... 155
Figure 143. Temperature development in cross-section E. ... 155
Figure 144. Maximum temperature difference histories in cross-sections A-E. ... 156
Figure 147. Bending moments at the base of columns. ... 158
Figure 148. Vertical reactions at the base of columns... 158
Figure 149. Illustration of the lifting forces source in columns adjacent to the fire exposed column. ... 159
Figure 150. Temperature development in cross-section P. ... 160
Figure 151. Temperature development in cross-section R. ... 160
Figure 152. Temperature development in cross-section S. ... 160
Figure 153. Visualisation of mechanical effects on the restrained cross-section with nonuniform temperature field. ... 161
Figure 154. Plastic equivalent strains development in cross-section P1. ... 162
Figure 155. Normal stresses development in cross-section P1. ... 162
Figure 156. Plastic equivalent strains development in cross-section P2. ... 162
Figure 157. Normal stresses development in cross-section P2. ... 162
Figure 158. Plastic equivalent strains development in cross-section R1. ... 163
Figure 159. Normal stresses development in cross-section R1. ... 163
Figure 160. Plastic equivalent strains development in cross-section R2. ... 163
Figure 161. Normal stresses development in cross-section R2. ... 163
Figure 162. Plastic equivalent strains development in cross-section S1. ... 163
Figure 163. Normal stresses development in cross-section S1. ... 163
Figure 164. Plastic equivalent strains development in cross-section S2. ... 164
Figure 165. Normal stresses development in cross-section S2. ... 164
Figure 166. Mean section temperatures for the structure exposed to design fire at time 25.5 min. ... 165
Figure 167. Mean section temperatures for the structure exposed to design fire at time 33.3 min. ... 165
Figure 168. Mean section temperatures for the structure exposed to design fire at time 40.0 min.. ... 165
Figure 169. Mean section temperatures for the structure exposed to design fire at time 50.0 min.. ... 166
Figure 170. Mean section temperatures for the structure exposed to design fire at time 60.0 min.. ... 166
Figure 171. Mean section temperatures for the structure exposed to amplified design fire at time 25.5 min. . 166
Figure 172. Mean section temperatures for the structure exposed to amplified design fire at time 33.3 min. . 167
Figure 173. Mean section temperatures for the structure exposed to amplified design fire at time 40.0 min. . 167
Figure 174. Mean section temperatures for the structure exposed to amplified design fire at time 50.0 min. . 167
Figure 175. Mean section temperatures for the structure exposed to amplified design fire at time 60.0 min. . 168
Figure 176. Structural model view with displacement measurement points and cross-section being analysed. ... 168
Figure 177. Deformation development at time 40 min for structure exposed to design fire. ... 169
Figure 178. Deformation development at time 50 min for structure exposed to design fire. ... 170
Figure 179. Deformation development at time 60 min for structure exposed to design fire. ... 170
Figure 180. Deformation development at time 40 min for structure exposed to design fire amplified 5 times.170 Figure 181. Deformation development at time 50 min for structure exposed to design fire amplified 5 times.171 Figure 182. Deformation development at time 60 min for structure exposed to design fire amplified 5 times.171 Figure 183. Longitudinal expansion of the structure measured between selected points (see Figure 176). ... 172
Figure 184. Transverse expansion of the structure measured between selected points (see Figure 176). ... 172
Figure 185. Vertical expansion of the structure measured between selected points (see Figure 176). ... 172
LIST OF TABLES
Table 1. Possible types of design approaches with respect to structural model. ……….. 2Table 2. Application domain of different design methods under fire situation . ……… 3
Table 3. Selected performance-based structural fire engineering design examples and methods used in them. ………. 5
Table 4. Derivation of parameters for view factors calculation according to Mitalas and Stephenson’s contour integration method, based on illustrative draw in Figure 32. ……… 65
Table 6. Dimensions, and the geometric relationships for a rectangular virtual box. ……….………. 68
Table 7. Coordinates of vertices of an arbitrary surface, with the emphasise of unknown values, see Figure 35. ………. 69
Table 8. Analytical solutions for view factors for different configurations, according to Figure 36, see Howell [57]. ……….. 71
Table 9. Average error and standard deviation of errors with respect to number of edge division in an approximated scheme of view factors calculations ……… 71
Table 10. Parameters of 2D model given for demonstration of the method. ……… 105
Table 11. Parameters of 3D model given for demonstration of the method. ……… 108
Table 12. Permanent and imposed loads. ……….. 118
Table 13. Values of wind pressure coefficients and wind pressure regarding to particular building zone. ….. 120
Table 14. Combinations of actions. ……….. 121
Table 15. Combinations of actions for 2D model of frame 6 exposed to ISO 834 fire [102]. ………. 123
Table 16. Fire resistance time for each combinations of action and each bay [102]. ……….. 123
Table 17. Solid phase sections and their layers. ……….. 125
Table 18. Positions and values of loads imposed by cranes. ……….. 131
Table 19. Types of cross-section used in presentation of heat transfer results. ……….. 136
NOTATION
(The list of notations is divided into problems they concern) Operators
∇ is the gradient operator
div(𝒂) = ∇ ∙ 𝒂 the divergence of vector 𝒂
∆ is the Laplace operator equal to ∇2
Fluid Dynamics
𝑒 internal energy of a thermodynamic system 𝒇 force vector
ℎ enthalpy of a thermodynamic system 𝑘𝑔 thermal conductivity of fluid (gas)
𝑚 mass
𝑛 number of moles in a perfect gas equation
𝒏 unit vector orthogonal and directed outwards to an analysed surface 𝑝 static pressure
𝑝𝑠𝑔𝑠 volumetric pressure in a subgrid-scale
𝑡 time
𝐶𝑣 constant volume specific heat
𝑫 rate of strain (deformation) tensor in Newtonian fluids model 𝑰 unit tensor
𝑀 molecular weight of a gas mixture in a perfect gas equation
𝑅𝑢 universal gas constant (8.31431 kJ kmol−1K−1) in a perfect gas equation 𝑆𝐶𝑉 surface enclosing control volume
𝑺 deviatoric part of stress tensor in Large Eddy Simulation approximate solution of governing equations for fluid flows
𝑻 stress tensor in Newtonian fluids model 𝑻𝑠𝑔𝑠 the subgrid-scale (SGS) stress tensor
𝑉 volume occupied by gas in a perfect gas equation 𝜃𝑔 temperature of fluid (gas)
𝜇 dynamic viscosity 𝜇𝑡 turbulent viscosity
𝒗 velocity vector, often referring to fluid velocity
𝜌 density
𝜏𝑖𝑗𝑠𝑔𝑠 component of stress tensor 𝑻𝑠𝑔𝑠, in a subgrid-scale 𝜙 intensive property symbol
Φ extensive property symbol Ω𝐶𝑉 control volume
Combustion modelling
∆ℎ𝑓,𝛼0 heat of formation of species 𝛼
𝑚̇𝛼′′′ the mean chemical mass production rate of species 𝛼 per unit volume 𝑞̇′′′ heat release rate for per unit volume
𝑟 stochiometric air requirement for fuel 𝑊𝑖 molecular weight of the i-th substance
𝑋H fraction of the atoms in the soot that are hydrogen
𝑍𝐹, 𝑍𝐴, 𝑍𝑃 stochiometric masses for fuel, air and products, respectively 𝛾CO fraction of fuel mass converted into carbon monoxide
𝛾Soot fraction of fuel mass converted into smoke particulate 𝜏𝑚𝑖𝑥 time scale for mixing
Radiation modelling
𝑐 velocity of radiation (speed of light)
𝒓 spatial position vector in given coordinate system.
𝐼(𝒓, 𝒔) total intensity that radiant energy incident normally on the infinitesimally small cross-section 𝑑𝐴 during time interval 𝑑𝑡, at position 𝒓, from direction 𝒔
𝐼𝜆 spectral intensity that radiant energy incident normally on the infinitesimally small cross-section 𝑑𝐴 during time interval 𝑑𝑡
𝐼𝜆(𝑏𝑙𝑎𝑐𝑘 𝑏𝑜𝑑𝑦)
black body intensity
𝜅𝑎,𝜆 local spectral absorption coefficient for a wavelength 𝜆 𝜆 wavelength of radiation
𝜎𝑠,𝜆 local spectral scattering coefficient for a wavelength 𝜆 𝜎 Stefan-Boltzmann constant (5.67 ∙ 10−8 W/m2K)
𝒇 global nodal force vector
𝑢𝑖, 𝒖 displacement field vector in indicial notation and matrix notation, respectively
𝑩, 𝑩̃ geometrical matrices that describes the strain in an arbitrary point of the finite element, caused by unit displacements at degrees of freedom for general problem and linear elastic problem,
respectively
𝐶𝑖𝑗𝑘𝑙 elasticity tensor in indicial notation
𝑫, 𝑫̃ elasticity tensors for general problem and linear elastic problem, respectively 𝑫𝑒𝑝∗ elasto-plastic constitutive matrix
𝐸𝑖𝑗 finite strains tensor in indicial notation
𝑲, 𝑲̃ global stiffness matrices for general problem and linear elastic problem, respectively 𝑵 shape functions matrix
𝓢, 𝓢̃ tree-dimensional strain operators for general problem and linear elastic problem, respectively 𝜇 and 𝜆 are Lamé constants
𝜀𝑖𝑗, 𝜺 strain tensor in indicial notation and matrix notation, respectively 𝜺𝑒, 𝜺𝑖 elastic, and inelastic components of strain tensor, respectively 𝜺𝑝, 𝜺𝑡ℎ, 𝜺𝑐𝑟 plastic, thermal and creep components of strain tensor, respectively
𝜀
𝑢𝑝is an accumulated plastic strain
𝜃 temperature at a given material point 𝜿 kinematic hardening parameter 𝜅 isotropic hardening parameter
𝑑𝜆 proportionality constant, often referred as the ‘plastic consistency’ parameter 𝜎𝑖𝑗, 𝝈 stress tensor in indicial notation and matrix notation, respectively
𝜳𝑛+1 residual vector of a solution of a nonlinear system of equations at 𝑡𝑛+1 discrete time
Heat transfer:
𝑐𝑝 specific heat capacity at constant pressure ℎ𝑐, coefficient of heat transfer by convection 𝑘𝑔 gas conductivity
𝑞̇ heat flux 𝑞̇′′ heat flux density
𝑞̇𝑐𝑜𝑛 convective part of the net heat flux absorbed by the body 𝑞̇𝑐𝑜𝑛′′ convective part of the net heat flux density absorbed by the body 𝑞̇𝑖𝑛𝑐 incident radiation
𝑞̇𝑖𝑛𝑐′′ incident radiation density
𝑞̇𝑛𝑒𝑡 net heat flux absorbed by the body 𝑞̇𝑛𝑒𝑡′′ net heat flux density absorbed by the body 𝑞̇𝑛𝑒𝑡,𝑠′′ net heat flux density reaching the solid surface (s) 𝑞̇𝑟𝑎𝑑 radiative part of the net heat flux absorbed by the body 𝑞̇𝑟𝑎𝑑′′ radiative part of the net heat flux density absorbed by the body 𝑞̇𝑟𝑒𝑓𝑙𝑐 reflected radiation
𝒔 unit vector normal to the surface 𝐶 natural convection coefficient
𝐶𝑃𝑇 heat capacity of the Inconel plate plus a third of the heat capacity of the insulation pad of the plate thermometer
𝐸̇ rate of increase of the energy
𝐾𝑃𝑇 heat conduction coefficient for the heat lost by conduction through the insulation pad plus along the Inconel plate of the plate thermometer
𝑰(𝒓, 𝒔) surface incident intensity, where 𝒓 is the position vector and 𝒔 is the surface normal vector 𝐹𝑘−𝑗 a proportion of radiation which leaves surface k that hits surface j (view factor)
𝑄 heat energy
𝑄̇ the net rate of heat added to the system
𝑄̇s rate of heat added or removed by the heat source on the control volume, e.g. due to chemical reactions and/or radiation
𝑆 surface area
𝑊̇ net rate of work done by pressure and viscous forces 𝛼 isotropic thermal diffusivity in the solid body 𝛼𝑠 surface absorptivity coefficient
𝜀𝑠 surface emissivity coefficient
𝜀𝑃𝑇 emissivity coefficient of the plate thermometer surface 𝜃𝐴𝑆𝑇 adiabatic surface temperature (AST)
𝜃𝑔 gas temperature
𝜃𝑠 solid surface temperature 𝜃𝑃𝑇 plate thermometer temperature
𝜆 isotropic thermal conductivity in the solid body 𝜌 density of the solid body
ACKNOWLEDGMENT
The author expresses his thanks to dr hab. inż. Adam Glema, prof. of Poznan University of Technology, for his supervision, advices and huge support. Many thanks are also directed to dr inż. Janusz Dębiński, for his general advices and comments he was sharing with me during this research.
From October 2011 to September 2015, financial support was provided from Ruukki Construction OY within scientific grant 11-962/2011-14. From October 2016 to September 2017 the research was financially supported by the National Science Centre of Poland under the Etiuda-4 project.
The experimental work was completely sponsored by the Building Research Institute of Poland, with the support of dr inż. Paweł Sulik and dr inż. Wojciech Węgrzyński. This support is gratefully acknowledged.
Osobne podziękowania chciałem złożyć wszystkim moim nabliższym, których wsparcie jest nieocenione…
… a w szczególności dziękuję mojej żonie.
1. INTRODUCTION
Destructive power of the fire on the building structures is commonly known since the dawn of history.
Historical sources, from antiquity, show, that apparently trivial ignition of fire can finally result in difficult to manage fires, which consequences are so significant, that refurbishment may took many years. The list of most meaningful fires in modern history, together with exemplification of their environmental impact can be found e.g. in [107]. In the context of this thesis, the Great Fire of London (1666) was the extremely important event. The rules and law regulations, developed as a consequence of that fire, was the first prescriptive guidelines in “modern” history, aims in the reduction of the risk of the fire and the size of its effects [88]. For hundreds of years, up to late ‘80s of XX century, the most of the knowledge about the fire safety was empirical based and the safety aspects were mainly defined by arbitrary prescriptive regulations concerning construction materials, construction products, but also building itself and their placement. Those regulations, the same like nowadays, tended to guarantee a satisfactory level of people’s and property’s safety. The one of the biggest breakthrough, in the history of structural fire safety, was development of temperature-time curve for fully developed fire in compartment, called today ISO 834 curve (or cellulosic curve, or standard nominal fire curve). This achievement allowed for standardisation of fire tests of structural materials and structural elements, and the methodology originated then, is widely used for today. However, modern engineering approaches tend to predict the physical phenomena based on trustworthy models, rather than base on the prescriptive rules. These type of approaches are generally called performance-based approaches. The methodology that uses performance-based approaches in the field of fire safety engineering is called performance-based fire engineering. The design that uses performance-based approaches to fulfil design objectives is called performance-based design.
1.1. S
TATE-
OF-
THE-
ART1.1.1. Performance-based fire engineering
Performance-based fire engineering (PBFE) is used in many different areas concerning civil engineering. PBFE is basically the approach based on idea of design fire safety of the buildings, objects, etc. in such a way, to meet certain criteria resulting from the fire safety requirements that need to be fulfilled. Contrary to a standard prescriptive approach, those requirements concern particularly the operational goals of designed object, e.g. instead of saying that the fire protection paint thickness should be equal to certain value, in performance-based approach the rule can be connected to requirement of providing safety by avoiding the overheating of members during fire.
The goal of applying PBFE approach in civil engineering is mainly to avoid the risk of fire and provide satisfactory level of people’s and fire brigades’ safety during the fire, as well as to reduce the property losses caused by the fire and its implications. In order to make PBFE feasible, there is a need of development of set of a multi-discipline methods and regulations that allow engineers to make more sophisticated analyses of construction systems in fire than standard prescriptive methods.
Although, performance-based fire engineering approach involves assessment of many components resulting from requirements of fire safety, this contribution is placed in structural fire engineering field (SFE). In performance-based structural fire engineering, design objectives are related to the performance of the structure in fire, i.e. ensuring the lack of partial and/or complete structural collapse during the specified period of the fire. Hence, performance-based fire engineering considerations require coupling of three types of analyses: fire modelling, thermal analysis and structural analysis.
The workflow in performance-based structural fire engineering problems is widely described in [165],
where the methodology for different objectives and complexities of buildings is shown. It is
summarised in Figure 2, where possible approaches for modelling of fire behaviour, thermal response,
and structural behaviour are given. More detailed information about the methods used in the performance-based structural fire engineering, theoretical bases of these methods, referring to specific physical phenomena, material properties and mathematical models of material behaviour, etc.
are given in [176]. Good practical guidance to structural design according performance-based rules, mostly concerned UK regulations, can be also found in [89] and [60].
Generally, the design process carried out by structural engineer starts with the collection of all the actions and their combinations acting on a structure. The same approach is always a start point for the structural fire design. However, in structural fire design, contrary to standard design, the temperature caused by fire is taken into account as the main variable action that influences the structural response. Let here refer to Eurocode EN 1990 [170] as the main part of set of codes that establishes the basis for using Eurocodes for structural design. The combination of actions used here is called combination for accidental design situation and the accidental action A
drepresents the design value of an indirect thermal action due to fire. Depending on the type of analysis, this action should be accordingly taken in analysis of structures in fire.
Then, depending on the complexity of the structure and design objectives, some practical decisions about the design process must be taken, in order to make the design rational and feasible. This preliminary decision is usually taken, consciously or unconsciously, with the reference to Table 1.
So, depending on the structural model in use, particular design approaches are enforced.
Regarding fire models, two possibilities can be distinguished: nominal fire curves and natural fires. The former consist of ISO 834 curve (the most common, called standard fire curve), but also hydrocarbon fire curve and external fire curve. All of them are included in Eurocode 1991-1-2 [20] and they can be used to evaluate the thermal exposure of structures in fire. Natural fires are defined as all the other than nominal curves approaches used to describe both qualitatively and quantitatively the fire.
Contrary to nominal fire curves, natural fires take into account the specific conditions that exist in the designed object, i.e. thermal parameters of walls, ventilation conditions, fire load.
Table 1. Possible types of design approaches with respect to structural model.
Element Substructure Structure
Prescriptive
approach + + — — —
↓ Performance-based structural fire engineering approaches ↓ Simple calculation
models + + + —
Advanced
calculation models + + + + +
The choice of existing fire model is somehow related to structural model have been chosen. According to [140], the first correspondence between model of thermal exposure and structural model (element, substructure, structure) was given by Witteveen in 1983. Witteveen findings were adopted by Purkiss and finally rearranged by other researchers. The resulted tables of application domain of different design methods under fire situation (Table 2) can be found in several publications, i.e. [51], [170].
Above strategy and application procedures are all given in Eurocode 1991-1-2 [20] in a straight-forward
decision tree (Figure 1). No matter what design procedure is chosen; no matter if tabulated data,
simple calculation model or advance calculation model is used, there is always one, physically based
scheme of analysis of structures in fire. Regardless the fire condition or fire model and material of the
structure, all the analyses must consist of three parts: (1) fire definition, (2) determination of
temperature field inside the structure, (3) determination of mechanical response of structure. There
are several methods for evaluation of those three inherent ingredients of each analysis, which are presented in Figure 2.
Figure 1. Alternative design procedures (according to Eurocode 1991-1-2) Table 2. Application domain of different design methods under fire situation .
Type of analysis Tabulated data Simple calculation models
Advanced calculation models Member analysis - nominal fires - nominal fires
- natural fires
- nominal fires - natural fires Analysis of a part of the
structure x - nominal fires - nominal fires
- natural fires Global structural
analysis x x - nominal fires
- natural fires
An excellent collection of real buildings designed with the use of performance-based fire safety engineering methods is given in [175]. Several examples show how those methods are used in order to satisfy design objectives. First of all, it is seen that such kind of design is used for rather extraordinary buildings, from structural or functional point of view. So, there are examples of administrative buildings, sport centres, shopping centres, exhibition centres, industrial buildings, as well as some complex residential buildings, bridge and a couple of different refurbishments. All and all, the practical projects, where design is supported by performance-based fire safety engineering methods, follows
Design Procedures
Prescriptive Rules (Thermal Actions given by Nominal Fire)
Analysis of a Member Analysis of Part of the Structure Analysis of Entire Structure
Determination of Mechanical Actions and Boundary Cond.
Selection of Mechanical Actions
Tabulated Data
Simple Calulation Models
Advanced Calulation Models Performance-Based Code (Physically based Thermal Actions)
Selection of Simple or Advanced Fire Development Models
Analysis of a Member Analysis of Part of the Structure Analysis of Entire Structure
Selection of Mechanical Actions
Simple Calulation Models
Advanced Calulation Models Determination of Mechanical
Actions and Boundary Cond.
Determination of Mechanical Actions and Boundary Cond.
Determination of Mechanical Actions and Boundary Cond.
mainly the provisions given by fire parts of Eurocodes (in Europe) or other modern design codes that exist in North America or other parts of the World.
Figure 2. Available methods to define the Fire Behaviour, Thermal Response and Structural Behaviour (elaborated according to [165] and [60])
The real design examples, given in [175], can be selected in such a way, to indicate the current state- of-the-art of practical usage of performance-based approach in structural fire engineering (see Table 3). It makes the list given in Table 3 enough short to be quickly readable, but enough comprehensive to really show the way the performance-based design is used nowadays in practical engineering cases.
According to the summary given in Table 3, currently the most of the projects base on the simple temperature-time relationships to define the fire. Nevertheless, most of the examples given in Table 3 do not use ISO 834 curve, but approaches that define the temperature-time relationship by taking into account the actual situation in analysing space, i.e. the fire load, heat release rate, ventilation and obstruction condition. However, choice of a single temperature-time curve influences the way the thermal response is calculated. The advanced heat transfer models, able to calculate the non-uniform temperature field in a structural cross-section, are used only when concrete or composite structures are considered. Otherwise, the simple heat transfer model for steel structures, known from EN 1993- 1-2 [33] is used. Structural analyses take an advantage of the development of finite element method and are usually tailored to the example considered. Nonetheless, the choice of heat transfer model influences the results possible to obtain from mechanical analyses, e.g. applying uniform temperature to steel members, when substructure or entire structure is calculated, will not reflect the phenomena of thermal bowing, what can be substantial in some cases.
Fire Behaviour
Thermal Response
Structural Behaviour
Localised Fire Fully Developed Fire
Plume Models Zone Models
CFD
Standard Fire Test Curves (Nominal Fires)
Time Equivalence Natural Fire Curves
Zone Models CFD
Test Data Simple Heat
Transfer Models
Advanced Heat Transfer Models
Member Behaviour
Substructure Behaviour
Entire Structure Behaviour
Table 3. Selected performance-based structural fire engineering design examples and methods used in them.
Object
Fire Model Thermal Response Model Structural Analysis Model Nominal Fire,
Natural Fire Curve, One Zone Fire, Localised fire
Two Zone
Fire, CFD Test Data
Simple Heat Transfer
Model
Advanced Heat Transfer
Model
Member Analysis
Substructure Analysis
Entire Structure
Analysis ADMINISTRATIVE BUILDINGS:
1. Courthouse of Naples 1 1 1
2.Heron Tower, London 1 1 1
3. Adidas Laces 1 1 1
4. The Pinnacle, London 1 1 1
5. Britomart East,
Auckland 1 1
6. 4 Kingdom Street,
London 1 1 1
SPORT CENTRES:
7. The Spalladium Hall,
Split 1 1 1
8. Salmisaari Sports
Center, Helsinki 1 1 1
SHOPPING CENTRES:
9. IKEA, Tampere 1 1
10. Centrum Galerie
Dresden 1
EXHIBITION CENTRES:
11. The Oeiras
Exhibitions Centre 1 1 1
INDUSTRIAL BUILDINGS:
12. Production and Storage Hall, Czech Republic
1 1 1
13. Boiler House in
Ledvice Power Plant 1 1 1
14. Industrial Building,
Spain 1 1 1 1
15. Factory Building,
Athens 1 1 1
RESIDENTIAL BUILDINGS:
16. C.A.S.E. Project or
L’Aquila 1 1 1
17. Modular Steel
System for Hotel Rooms 1 1 1
18. Blessed Trinity RC
School, Burnley 1 1 1
19. ME Hotel Aldwych,
London 1 1 1
SUM: 14 4 1 10 6 8 9 2
