Helsinki University of Technology Laboratory of Steel Structures Publications 29 Teknillisen korkeakoulun tersrakennetekniikan laboratorion julkaisuja 29

Espoo 2003 TKK-TER-29

ADVANCED STEEL STRUCTURES

1. STRUCTURAL FIRE DESIGN 2. FATIGUE DESIGN

Wei Lu Pentti Mkelinen

AB TEKNILLINEN KORKEAKOULUTEKNISKA HGSKOLANHELSINKI UNIVERSITY OF TECHNOLOGYTECHNISCHE UNIVERSITT HELSINKIUNIVERSITE DE TECHNOLOGIE DHELSINKI

Helsinki University of Technology Laboratory of Steel Structures Publications 29 Teknillisen korkeakoulun tersrakennetekniikan laboratorion julkaisuja 29

Espoo 2003 TKK-TER-29

ADVANCED STEEL STRUCTURES

1. Structural Fire Design

2. Fatigue Design

Wei Lu Pentti Mkelinen Helsinki University of Technology Department of Civil and Environmental Engineering Laboratory of Steel Structures Teknillinen korkeakoulu Rakennus- ja ympristtekniikan osasto Tersrakennetekniikan laboratorio

Distribution: Helsinki University of Technology Laboratory of Steel Structures P.O. Box 2100 FIN-02015 HUT Tel. +358-9-451 3701 Fax. +358-9-451 3826 E-mail: srt-sihteerit@hut.fi Teknillinen korkeakoulu ISBN 951-22-6732-2 ISSN 1456-4327 Yleisjljenns - Painoprssi Espoo 2003

PREFACE This report is prepared in the Laboratory of Steel Structures at Helsinki University of Technology (HUT) in 2003. This work is a part of the project Tersrakennetekniikan opetusmateriaalin ajanmukaistaminen (Teaching material updating for advanced steel structures). This project is financially supported by TKK/Opintotoimikunta (joint student-faculty committee in HUT), which is gratefully acknowledged. This report was developed to use as a part of teaching materials either for graduate courses Rak-83.122 Advanced Steel Structures or for postgraduate studies Rak-83.J. Two topics are included in this report: structural fire design and fatigue design. The structure of each topic is basically composed of three parts: theoretical backgrounds, design rules and worked examples. The design rules that are presented in this report are based on ENV 1991-1 (1994): Eurocode 1-Basis of design and actions on structures-Part 1: Basis of design; EN 1991-1-2 (2002): Eurocode 1: Actions on structures Part 1-2: General actions-Actions on structures exposed to fire; ENV 1993-1-1 (1992): Eurocode 3: Design of Steel Structures-Part 1.1: General rules and rules for buildings; and ENV 1993-1-2 (1995): Eurocode 3: Design of Steel Structures-Part 1.1: General rules-structural fire design. The materials used in the part of structural fire design are based on the books and papers that are collected, and researches that have been carried out in the Laboratory of Steel Structures. The materials used in the part of fatigue design are based on materials available in the Laboratory of Steel Structures and the materials distributed in the short course Fatigue of Materials and Structures organized by Laboratory for Mechanics of Materials at HUT. I would like to express my thanks to these authors and organizers. The authors wish to express gratitude for Lic.Sc. (Tech.) Olli Kaitila, Lic.Sc. (Tech.) Jyri Outinen, Mr. Olavi Tenhunen and D.Sc. (Tech.) Zhongcheng Ma for providing extra materials, nice discussions and useful comments. Many thanks go to secretary Mrs. Elsa Nissinen for her kind assistance. Wei Lu, D.Sc. (Tech.) Espoo, August 2003

CONTENTS

PREFACE ........................................................................................................................................... 3

CONTENTS........................................................................................................................................ 4

1 STRUCTURAL FIRE DESIGN................................................................................................ 6 1.1 INTRODUCTION...................................................................................................................... 6

1.1.1 Development of fire in buildings .................................................................................. 6 1.1.2 Fire safety..................................................................................................................... 7 1.1.3 Fire protection.............................................................................................................. 7 1.1.4 Structural fire safety design methods ........................................................................... 8

1.2 DESIGN CURVES AND FIRE MODELS...................................................................................... 9 1.2.1 Nominal temperature-time curves ................................................................................ 9 1.2.2 Natural fire models: compartment fires or parametric fires...................................... 10 1.2.3 Natural fire models: localized fire models ................................................................. 15 1.2.4 Natural fire models: advanced fire models ................................................................ 15

1.3 MATERIAL PROPERTIES OF STEEL AT ELEVATED TEMPERATURE........................................ 16 1.3.1 Mechanical properties of materials ........................................................................... 16 1.3.2 Thermal properties ..................................................................................................... 23

1.4 PASSIVE PROTECTION FOR STEELWORK .............................................................................. 26 1.4.1 Fire protection systems .............................................................................................. 26 1.4.2 Thermal properties of fire protection systems............................................................ 28

1.5 HEAT TRANSFER IN STEEL................................................................................................... 29 1.5.1 Type of heat transfer................................................................................................... 29 1.5.2 Heat transfer equation for steel.................................................................................. 30

1.6 MECHANICAL ANALYSIS OF STRUCTURAL ELEMENT .......................................................... 37 1.6.1 Required fire resistance time...................................................................................... 37 1.6.2 Mechanical actions..................................................................................................... 41 1.6.3 Design value of material temperature........................................................................ 42 1.6.4 Design value of fire resistance time ........................................................................... 43 1.6.5 Critical temperature ................................................................................................... 44 1.6.6 Load bearing capacity................................................................................................ 45

1.7 DESIGN OF STEEL MEMBERS EXPOSED TO FIRE .................................................................. 47 1.7.1 Design methods .......................................................................................................... 47 1.7.2 Classification of cross-sections .................................................................................. 47 1.7.3 Tension members........................................................................................................ 47 1.7.4 Moment resistance of beams ...................................................................................... 48 1.7.5 Lateral-torsional buckling.......................................................................................... 49

1.7.6 Compression members with Class 1, Class 2 or Class 3 cross-section ..................... 49 1.8 USE OF ADVANCED CALCULATION MODELS ....................................................................... 50 1.9 GLOBAL FIRE SAFETY DESIGN ............................................................................................ 51 1.10 DESIGN EXAMPLE ACCORDING TO EUROCODE 3.................................................................. 52

1.10.1 Introduction ................................................................................................................ 52 1.10.2 Design loads and load distribution in the frame ........................................................ 54 1.10.3 Fire resistance and protection of a tension member BE ............................................ 54 1.10.4 Fire resistance and protection of steel beam AB........................................................ 58

1.11 REFERENCES........................................................................................................................ 62

2 FATIGUE DESIGN.................................................................................................................. 64 2.1 INTRODUCTION .................................................................................................................... 64

2.1.1 Different approaches for fatigue analysis .................................................................. 64 2.1.2 A short history to fatigue ............................................................................................ 65

2.2 FATIGUE LOADING .............................................................................................................. 66 2.3 STRESS METHODS................................................................................................................ 67

2.3.1 Standard fatigue tests ................................................................................................. 68 2.3.2 S-N curves................................................................................................................... 69 2.3.3 One dimensional analysis for fatigue assessment ...................................................... 76

2.4 STRAIN METHODS ............................................................................................................... 77 2.4.1 Cyclic material law..................................................................................................... 77 2.4.2 Fatigue life.................................................................................................................. 79

2.5 CRACK PROPAGATION METHODS ........................................................................................ 82 2.5.1 Characteristic of fatigue surfaces............................................................................... 82 2.5.2 Fatigue mechanism..................................................................................................... 83 2.5.3 Linear elastic fracture mechanics .............................................................................. 84 2.5.4 Crack propagation under fatigue load ....................................................................... 86 2.5.5 Short crack behavior .................................................................................................. 88

2.6 FATIGUE ANALYSIS UNDER VARIABLE LOADS.................................................................... 88 2.6.1 Fatigue testing under variable loading ...................................................................... 88 2.6.2 Palmgren-Miner rule.................................................................................................. 89 2.6.3 Cycle counting ............................................................................................................ 90 2.6.4 Crack propagation under variable loading................................................................ 92

2.7 FATIGUE ANALYSIS OF WELDED COMPONENTS................................................................... 93 2.7.1 Factors affecting the fatigue life................................................................................. 94 2.7.2 S-N methods for evaluating fatigue life ...................................................................... 96 2.7.3 Crack propagation method....................................................................................... 106

2.8 CALCULATION EXAMPLES ACCORDING TO EUROCODE 3................................................... 107 2.8.1 Introduction .............................................................................................................. 107 2.8.2 Given values ............................................................................................................. 108 2.8.3 Stress calculations .................................................................................................... 108 2.8.4 Assessment for the trolley carrying the full load of 150 kN ..................................... 111 2.8.5 Assessment for the trolley returning empty .............................................................. 113 2.8.6 Assessment for the trolley returning carrying load of 70 kN ................................... 113 2.8.7 Assemblage of the calculated damage and determination of the fatigue life ........... 114

2.9 REFERENCES...................................................................................................................... 115

1 STRUCTURAL FIRE DESIGN

1.1 Introduction

1.1.1 Development of fire in buildings A real fire in a building grows and decays in accordance with the mass and energy balance within the compartment in which it occurs. The energy released depends upon the quantity and type of fuel available and upon the ventilation conditions. Figure 1.1 illustrates that the fire in a building can be divided into three phases: the growth or pre-flashover period, the fully developed or post-flashover fire and the decay period [2]. The most rapid temperature rise occurs in the period following flashover, a point at which all organic materials in a compartment spontaneously combust. Anyone who has not escaped from a compartment before flashover is unlikely to survive.

Figure 1.1 Typical temperature development in a compartment [2]

In the pre-flashover phase, the room temperature is low and the fire is local in the compartment. This period is important for evacuation and fire fighting. Usually, it has not significant influence on the structures. After flashover, the fire enters into the fully developed phase, in which the temperature of the compartment increase rapidly and the overall compartment is engulfed in fire. The highest temperature, the highest rate of heating and the largest flame occur during this phase, which gives rise to the most structural damage and much of the fire spread in buildings. In the decaying period, which is formally identified as a stage after the temperature falling to 80 percent of its peak value, the temperature decreases gradually. It is worth to point out that this period is also important to the structural fire engineering because for the insulated steel structures and unprotected

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steel structures of low section factor, the internal temperature of cross-section will still increase significantly even though in the decaying periods [12].

1.1.2 Fire safety Fire safety design is an important aspect of building design. A properly designed building system greatly reduces the loss of the life and the property of finical losses in, or in the neighborhood of, building fires. Current fire safety concepts are defined as optimal packages of integrated structural, technical and organizational fire precaution measures, which allow well defined objectives agreed by the owner, the fire authority and the designer, to be fulfilled [8]. The essential requirements for the limitation of fire risks have to be fulfilled in the following ways:

o The load-bearing capacity of the construction can be assumed for a specific period of time; o The generation and spread of fire and smoke within the works are limited; o The occupants can leave the works or can be rescued by other means o The safety of rescue teams is taken into consideration.

The central objective of fire safety in the current Fire Codes is to confine the fire within the compartment in which it started. These consist of a collection of requirements, only or mostly related to the structural fire resistance of load-bearing elements and to walls and slabs necessary to guarantee the compartmentation. It should be noticed that the objectives of fire safety are a historical concept, in which the contents can be changed with the development of fire science. Besides, the additional objective can also be implemented if the client or authorities require a particular building or a project.

1.1.3 Fire protection Structural fire protection is only one part of the package of fire safety measure used in a building. There are two broad groups of measures [1]:

o Fire prevention, designed to reduce the chance of a fire occurring; o Fire protection, designed to mitigate the effects of a fire should it nevertheless occur.

Fire prevention includes eliminating or protecting possible ignition sources in order to prevent a fire occurring. Fire protection measures may be passive or active, which are used according to the phase of fire development as shown in Figure 1.2 [5]. Active measures [1] include detection and alarm, fire extinction, and smoke control, all of which may be operated manually or automatically. Early detection and extinction lead to early fire fighting and decease the risk of a large fire. For instance, the combination of automatic sprinklers and a designed smoke-control system has been used to protect people escaping from fire in large buildings. Passive measures include structural fire protection, layout of escape routes, fire brigade access routes, and control of combustible materials of construction [1]. Normally for pre-flashover fires,

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passive protection includes selection of suitable materials for building contents and interior linings that do not support rapid flame spread in the growth period. In post-flashover fires, passive protection is provided by structures and assemblies, which have sufficient fire resistance to prevent both spread of fire and structural collapse. The controls of fire spread include controlling fire spread within the room of origin, to adjacent room, to other storeys and to other buildings. The most important component of passive fire protection is fire resistance of the structure.

Figure 1.2 Fire evolution and fire protection [5]

Often a combination of the above measures is applied. Ideally, the fire safety design concept should allow for a certain between the various measures i.e. emphasis on one or two of the possible measures should lead to relaxation of the remaining one(s). For instance, a sprinkler installation would lead to reduce overall requirements for the fire resistance. Such a trade off is not generally accepted at present but needs to be pursued with the appropriate authorities [5].

1.1.4 Structural fire safety design methods Currently, the design methods may be classified into two classes, i.e. [12]

o Methods related to fire resistance only; o Methods related to global fire safety.

The first category of methods concerns the verification methods of fire resistance. The Eurocodes are for the time being strictly limited to this category. The method related to fire resistance is governed by two basic models: a heat model and a structural model. The heat model defines the evolution of air temperature, the convective and radiative boundary conditions and the spreading of fire in a fire affected room if possible. The structural model defines elements or parts of the structures, thus allowing the prediction of the temperature increase in the structure or in elements ensuring compartmentation, of the collapse temperature or the collapse time for a given load. To

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date, the use of a conventional fire scenario based on the ISO standard fire curve is common practice in Europe and elsewhere. Safety level in buildings referring to fully developed mainly. The second category is based on the fire risk assessment technology, which is being developed for particular buildings, important structures or individual projects. The purpose of developing the global fire safety concept is to establish the basis for realistic and credible assumptions to be used in fire situation for thermal actions, active measures and structural response.

1.2 Design Curves and Fire Models When dealing with fire resistance, the ignition stage is generally neglected, although this stage is generally the most critical for human life since it is during this stage that toxic gases are produced and the temperature can reach 100 C and more. To select the relevant fire model, the fire scenarios need to be defined. It is a selection of the possible worst cases as far as the location and the amount of fire load are concerned [5]. For instance:

o In a small room, it is assumed a fully developed fire, using the maximum fire load which can be in the compartment;

o In a large room, at least two assumptions can be made, either a uniformly distributed fire load leading to a fully developed fire in the compartment or localized fires depending on the possible location of the fire load;

o For element located outside the facade of the building, flames coming through windows and doors will be considered.

A design fire shall be expressed as a relationship between temperature, time and space location, which may be [5]:

o A nominal temperature-time curve uniform in the space; o A real fire either specified in terms of parametric fire exposure, or given by an analytical

formula for localized fire, or obtained by computer modeling.

1.2.1 Nominal temperature-time curves The nominal temperature-time curves are a set of curves, in which no physical parameters are taken into account. The main purpose of the prescription of the nominal curves was to make the fire resistance tests reproducible. The ability of fire resistance of building elements can be evaluated under the same heating curve [18]. Fire resistance times specified in most national building regulations relate to test performance when heated according to an internationally agreed time-temperature curve defined in ISO834 (or Eurocode 1 Part 2-2), which does not represent any type of natural building fire. This standard temperature-time curve involves an ever-increasing air temperature inside the considered compartment, even when later on all consumable materials have been destroyed. This has become the standard design curve, which is used in furnace testing of components. The quoted value of fire

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resistance time does not therefore indicate the actual time for which a component will survive in a building fire, but is a like-against-like comparison indicating the severity of a fire that the component will survive [17]. Where the structure for which the fire resistance is being considered is external, and the atmosphere temperatures are therefore likely to be lower at any given time (which means that the temperatures of the building materials will be closer to the corresponding fire temperatures), a similar External Fire curve may be used. In cases where storage of hydrocarbon materials makes fires extremely severe a Hydrocarbon Fire curve is also given. The formula for describing these curves are given as follows [3]: for standard temperature-time curve g = 20+345log10(8t+1) ( 1.1 )

for external fire curve g = 660(1-0.687e-0.32t-0.313e-3.8t)+20 ( 1.2 )

for hydrocarbon curve g = 1080(1-0.325e-0.167t-0.675e-2.5t)+20 ( 1.3 )

These three nominal temperature-time curves according to these formulas are shown in Figure 1.3.

Figure 1.3 Nominal temperature-time curves

1.2.2 Natural fire models: compartment fires or parametric fires Before get into the details of this model, the following definitions are clarified [2]:

o Heat of combustion or the calorific value of material is defined as the amount of heat in calories evolved by the combustion of one-gram weight of a substance [MJ/kg].

0

200

400

600

800

1000

1200

0 30 60 90 120 150

Time (min)

Tem

pera

ture

( C

)

Standard Fire

External Fire

Hydrocarbon Fire

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o Mass loss rate is defined as the mass of fuel that is vaporized from the solid or liquid fuel per

unit time [kg/s].

o Burning rate is the amount of fuel that is burned within the compartment in terms of airflow per unit time [kg/s]. This is distinct from the mass loss rate and is dependent on the available oxygen.

o Heat release rate is defined as the rate at which the heat is released [J/s] and can be measured

experimentally or obtained by calculation. It is the source of the gas temperature rise and the driving force behind the spreading of gas and smoke.

Background Parametric fire models provide a simple means to take into account the most important physical phenomenon that may influence the development of a fire in a particular building. Like nominal fires, they consist of time temperature relationships, but these relationships contain some parameters represent particular aspects of the reality. Normally, three parameters are included in these models, namely, the fire load present in the compartment, the openings in the walls and/or in the roofs, and the type and nature of the different walls of the compartment. These models assume that the temperature is uniform in the compartment, which limits the application to post-flashover fires in compartment of moderated dimensions. These models require the following data: fire load density, rate of heat release and heat losses. a. Fire load density Fire load density is defined as the total amount of combustion energy per unit of floor area and is the source of the fire development. The fire load is composed of the building components such as wall and ceiling linings, and building contents such as furniture. The characteristic value of fire load density is provided by: qf.k = [Mk.iHuil]/A ( 1.4 )

where

Mk.i is the combustible materials [kg] Hui is the net calorific value [MJ/kg]; Mk.i Hui is the total amount of energy contained in material and released assuming

complete combustion. l is the optional factor to accessing protected fire load. For instance by putting

it into a cabinet. A is the floor area.

b. Rate of heat release ( RHR ) The calculation of RHR is different from ventilation controlled fire to fuel controlled fire. The fuel controlled fire refers to the case that there is always enough oxygen to sustain combustion. While for

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the ventilation controlled fire, the size of openings in the compartment enclosure is factor to control the amount of the air to enter the compartment. When fire is ventilation controlled, according to Kawagoe (1958), the burning rate m [kg/s] can be calculated as [2]

m = 0.092 AvHv ( 1.5 ) Where Av is the area of the openings (m2) and Hv is the height of the openings (m). This equation is derived from the experiments for a room with a single opening. Despite the findings showing that the burning rate depends on the shape of the room and the width of the window proportion to the wall in which it is located, this equation is formed the basis of most post-flashover fire calculation. The corresponding ventilation controlled heat released rate (MW) for steady burning is calculated as [1]:

Qvent = m Hui ( 1.6 )

The duration of fire can be calculated as: tb = E/Qvent ( 1.7 )

where E is the energy content of fuel available for combustion (MJ). In addition, the amount of ventilation in a fire compartment is described by the opening factor O (m0.5) given by O = AvHeq/At ( 1.8 ) where Heq is weighted average window heights on all walls (m) and At is total area of enclosures (walls, ceiling and floor, m2). If this formula is multiplied by gravity g, then the product is related to the velocity of gas flow through openings. Researches show that if the ventilation openings were enlarged, a condition would be reached beyond which the burning rate would be independent on the size of the opening and would be determined instead by the surface and burning characteristics of the fuel. For the fuel controlled fire, the duration of the fire can be assumed as 25 min for slow fire growth rate, 20 min for medium growth rate and 15 min for fast growth rate. The RHR can be calculated as Qfuel = E / tlim ( 1.9 )

When the duration is not known, the RHR is estimated from the information about the fuel and the temperatures in the fire compartment. In the current Eurocode[3], the RHR is implicitly calculated using AvHeq. c. Heat losses Heat losses suffered by the combustion gases are important factors to the temperature development of a compartment fire. Heat losses occur to the compartment boundaries by convection and radiation and by the ventilation flow [3]. The most popular way to model the heat losses to the compartment boundaries is through the concept of the thermal inertia, b, of the wall material, i.e. b = c ( 1.10 ) where is heat conductivity (W/mK); c is the heat capacity (J/kgK) and is mass density (kg/m3).

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Parametric temperature-time curves Current Eurocode[3] gives an equation for parametric temperature-time curves for any combination of fuel load, ventilation openings and wall lining materials. The equation of temperature g (C) for heating phase is provided by g = 1325(1-0.324e-0.2t*-0.204e-1.7t*-0.472e-19t*)+20 ( 1.11 ) where t* is fictitious time (hours) given by t* = t ( 1.12 ) where t is the time (hours) and = (O/b)2/(0.04/1160)2 ( 1.13 ) In the case of compartment with O = 0.04 m0.5 and b = 1160 J/m2s0.5K, the parameter curve is almost exactly the ISO curve. The maximum temperature occurred at t* = t*max where t*max = tmax ( 1.14 ) with tmax = max [(0.210-3qt.d/O); tlim] ( 1.15 )

The time tmax corresponding to the maximum temperature is given by tlim in case the fire is fuel controlled. If tmax is given by (0.210-3qt.d/O), the fire is ventilation controlled. When tmax = tlim, t* is the temperature formula is replaced by t* = tlim ( 1.16 ) with lim = (Olim/b)2/(0.04/1160)2 ( 1.17 ) where Olim = 0.110-3qt.d/tlim ( 1.18 )

If O > 0.04 and qt.d < 75 and b < 1160, lim has to be multiplied by k given by k = 1+ [(O-0.04)/0.04][(qt.d-75)/75][(1160-b)/1160] ( 1.19 )

This is due to the fact that the influence of the openings is still present when the fire is fuel controlled. [3] uses a reference decay rate equal to 625 C per hour for fires with duration less than half an hour, decreasing to 250 C for fires with duration greater than two hours. The temperature curves in the cooling period are given by g = max 625 (t*-t*maxx) ( 1.20 ) for t* 0.5 g = max 250(3-t*max) (t*-t*maxx) ( 1.21 ) for 0.5 < t* 2 g = max 250 (t*-t*maxx) ( 1.22 ) for t* > 2, where t* = t; tmax = (0.210-3qt.d/O) and x = 1.0 if tmax > tlim , or x = tlim / t*max if tmax = tlim .

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Examples The effects of the fire load density and the ventilation of the fire compartment on the gas temperature are shown in Figure 1.4 and Figure 1.5. These calculations are based on the formula given above with the parameters given in the figures, which are based on the seminar materials [16]. These curves are suitable for using as alternatives of nominal curve of internal members of a compartment.

Figure 1.4 Parametric temperature-time curves considering the effects of openings

Figure 1.5 Parametric temperature-time curves considering the effects of fire loads

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1.2.3 Natural fire models: localized fire models The models mentioned above have assumed a fully developed fire occurs and the same temperature conditions throughout the fire compartment. However, in some circumstances, possibly in a large space where there are no nearly combustibles, or in a fire partially controlled by sprinklers, there could be a localized fire which has much less impact on the building structure than a fully developed fire. The thermal actions of a localized fire can be assessed using the analytical formula that takes into account the relative height of the flame to the ceilings. These formulas are given in [3] and [5].

1.2.4 Natural fire models: advanced fire models Two kinds of numerical models are available to model the real fires: multi zone models and field models. The multi zone models are used when the fire is localized, e.g. in the growth phase of a fire. The fire compartment is divided into a hot zone, with a uniform temperature, above a fresh air zone and a fire plume that feeds the hot zone just above the fire. A two-zone model is shown in Figure 1.6. For each of the zones, the heat and mass balance is solved. (Semi) empirical relations govern plume entrainment, irradiative heat exchange between zones and mass flow through openings to adjoining compartments. Particularly, the (growth of the) fire size should be taken as an input besides the parameters mentioned in the one zone model [18]. The application of this model is mainly in pre-flashover conditions, in order to know the smoke propagation in buildings, and estimate the life safety in function of toxic gas concentration temperature, radiative flux and optical density.

Figure 1.6 Zone model [10]

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Field models are also called Computational Fluid Dynamics (CFD) models. These models are based on two or three dimensional heat and mass transport, solving the equations of conservation of mass, momentum and energy for discrete points in the enclosed compartment. In this model, material properties and boundary conditions may be defined as the function of temperatures. The fire simulation problem represents one of the most difficult areas in computational fluid dynamics: the numerical solution of re-circulating, three dimensional turbulent, generating eddies or vortices of many sizes. The energy contained in large vortices cascades down to smaller and smaller vortices until it diffuses into heat. Eddies exist down to the size where the viscous forces dominate over inertial forces and energy is dissipated into heat. Field models will provide accurate information about temperatures from the pieces of the fire room [18]. The complexity and the CPU time needed with field models allow few applications of such model in respect to fire resistance particularly for fully developed fire. In fire domain the use of field model is often reduced to the application of smoke movement.

1.3 Material Properties of Steel At Elevated Temperature

1.3.1 Mechanical properties of materials When structural components are exposed to fire, they experience temperature gradients and stress gradients, which are both varied with time. Mechanical properties of materials for fire design purpose must be consistent with the anticipated fire exposure.

1.3.1.1 Components of strains The deformation of steel at elevated temperature is described by assuming that the change in strain consists of three components: mechanical or stress-related strain, thermal strain and creep strain [1]. Stress-related strain Figure 1.7 shows the stress-strain curves at various temperatures for S275 steel in Eurocode 3. It can be seen that the steel suffers a progressive loss of strength and stiffness at temperature increases. The change can be seen at temperatures as low as 300C. Although melting does not happen until about 1500C, only 23% of the ambient-temperature strength remains at 700C. At 800C this has reduced to 11% and at 900C to 6% [17]. A value of yield strength is required at elevated temperature. Most normal construction steel has well-defined yield strength at normal temperatures, but this disappears at elevated temperatures as shown in Figure 1.7. In Eurocode 3 [7], the 2% proof strength is used as the effective yield strength. However, Kaitila [9] summarizes the possible values for yield strength at elevated temperature from the literatures: Ala-Outinen and Myllymki, and Ranby suggested the use of the 0.2% proof stress for the effective yield strength at elevated temperature; In the Steel Construction Institute (SCI) recommendation, the use of 0.5% proof stress is suggested for members failing by buckling in

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compression (mainly columns) and the 1.5% proof stress fro members failing in bending (mainly beams); and Kirby and Preston recommend using 1% proof stress as the effective yield strength.

Figure 1.7 Reduction of stress-strain properties with temperature for S275 steel (EC3 curves) [17]

The modulus of elasticity is needed for buckling calculations and for elastic deflection calculation, but these are rarely attempted under fire conditions because elevated temperatures lead rapidly to plastic deformations. For the fire design of individual structural members such as simply supported beams that are free to expand during heating, the stress-related strain is the only component that needs to be considered. If the reduction of strength with temperature is known, member strength at elevated temperature can easily be calculated using simple formulae. The stress-related strains in fire-exposed structures may be well above yield levels, resulting in extensive plastification, especially in buildings with redundancy or restraint to thermal expansion. Computer modeling of fire-exposed structures requires knowledge of stress-strain relationships not only in loading, but also in unloading, as members deform and as structural members cool in real fires [1]. Thermal strain Thermal strain is the thermal expansion (L/L) that occurs when most materials are heated, with expansion being related to the increase in temperature. Thermal strains is not important for fire design of simply supported members, but must be considered for frames and complex structural systems, especially where members are restrained by other parts of structure since thermal strains can induce large internal forces [1].

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Creep strain Creep is the term that describes long-term deformation of materials under constant load. Under most conditions, creep is only a problem for members with very high permanent loads. Creep is relatively insignificant in structural steel at normal temperatures. However, it becomes very significant at temperatures over 400 or 500C and highly depends on the stress level. At higher temperatures, the creep deformations in steel can accelerate rapidly, leading to plastic behavior. Creep strain is not usually included explicitly in fire engineering calculations because of the added complexity. This applies to both hand and computer methods. The effects of creep are usually allowed for implicitly by using stress-strain relationships that include an allowance for the amount of creep that might be expected in a fire-exposed member [1].

1.3.1.2 Testing regimes Constant temperature tests of material can be carried out in the following four regimes [1]:

1) The most common test procedure to determine stress-strain relationship is to impose a constant rate of increase of strain and to measure the load, from which the stress can be derived;

2) A similar regime is to control the rate of increase of load and measure the deformation; 3) A creep test is one in which the load is kept constant and deformation over time is measured; 4) A relaxation test is one in which a constant initial deformation is imposed and the reduction

in load over time is measured. Two other possible test regimes are available when the effects of changing temperature are added.

5) A transient creep test is that the specimen is subjected to initial load, then the temperature is increased at a constant rate while the load is maintained at a constant level, and the deformations are measured.

6) An alternative is that the applied load is varied throughout the test in order to maintain a constant level of strain as temperature is increased at a constant rate.

The most common of these are regimes (1) and (5). The regime (1) tests depend on the rate of loading because of the influence of the creep. The region (5) tests depend on the rate of temperature increase. The stress-strain relationships at elevated temperature can be obtained directly from steady-state tests at certain elevated temperatures (Regime 1) or they can be derived from the results of transient tests. This procedure can be demonstrated from the following example, i.e. the small-scale tensile tests of steel at high temperature [15]. This research has been carried out in the Laboratory of Steel Structures at Helsinki University of Technology from the years 1994-2001 in order to investigate mechanical properties of several structural steels at elevated temperatures by using mainly the transient state tensile test method.

19

The testing device is illustrated in Figure 1.8. The oven, in which test specimen is situated during the tests, was heated using three separate temperature controlled resistor elements. The air temperature is measured with three separate temperature-detecting elements. The steel temperature was measured accurately from the test specimen using temperature-detecting element that was fastened to the specimen during the heating.

Figure 1.8 High temperature tensile testing device [15]

During the transient test, the specimen is under a level of constant load and a constant rise of temperature. The temperature and the strain are measured; the temperature and strain curve are recorded. The results are then converted into stress-strain relations using the scheme shown in Figure 1.9. Thermal elongation, which has been measured separately [14], is subtracted from the total strain.

Figure 1.9 Converting the stress-strain curves from the transient state test results [15]

In the steady-state tests, the test specimen was heated up to a specific temperature, and then a normal tensile test was carried out. The mechanical properties can be determined directly from the

20

recorded stress-strain curve. The comparisons of Comparison of the steady state and transient state test results of structural steel S350GD+Z at temperature 800C are shown in Figure 1.10. It can be seen that the results using these two testing methods are different.

Figure 1.10 Comparison of the steady state and transient state test results of structural steel S350GD+Z at temperature 800C [15]

1.3.1.3 Mechanical properties provided in Eurocode 3 The steel grades in Eurocode 3 [7] are based on EN 10025 (S235, S275, S355) and EN 10113 (S420, S460). The mechanical properties of steel at 20 C is taken as those given in Eurocode 3, Part 1.1 for normal design. The stress-strain relationship at elevated temperature is given in Figure 1.11 and can be used to determine the resistance to tension, compression, moment or shear. This is suitable for the heating rate from 2 to 50 K/min.

Strain range Stress Tangent modulus p. Ea. Ea.

p. < < y. fp. - c + (b / a)[a2 - (y. - )2]0.5 b(y. - ) / {a[a2 - (y. - )2]0.5} y. t. fy. 0 t. < < u. fy.[1 - ( - t.) / (u. - t.)] -

= u. 0.00 - Parameters p. = fp. / Ea. , y. = 0.02, t. = 0.15 , u. = 0.20 Functions a2 = (y. - p.)(y. - p. + c / Ea.)

b2 = c(y. - p.) Ea. + c2 c = (fy. - fp.)2 / [(y. - p.) Ea. - 2(fy. - fp.)]

21

fy. is the effective yield strength; fp. is the proportional limit; Ea. is the slope of the linear elastic range; p. is the strain at proportional limit

y. is the yield strain; t. is the limiting strain for yield strength u. is the ultimate strain

Figure 1.11 Stress-strain relationship for steel at elevated temperature (Eurocode 3) [7]

The variations of the reduction factor for effective yield strength, for proportional limit and for the slope of the linear elastic range are shown in Figure 1.12 [17]. The reduction factors, relative to the appropriate value at 20 C, are given in Table 1.1.

Figure 1.12 Reduction factors for stress-strain relationship of steel at elevated temperature [17]

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000 1200

Temperature (C)

Red

uctio

n fa

ctor Effective yield strength

Slope of linear elastic range

Proportional limit

22

Table 1.1 Reduction factors for stress-strain relationship of steel at elevated temperatures [7]

Reduction factors at temperature relative to the value at 20 C Steel temperature

a Effective yield strength ky. = fy. / fy Proportional limit

kp. = fp. / fy Slope of the linear elastic range

kE. = Ea. / Ea 20 1.000 1.000 1.000

100 1.000 1.000 1.000 200 1.000 0.807 0.900 300 1.000 0.613 0.800 400 1.000 0.420 0.700 500 0.780 0.360 0.600 600 0.470 0.180 0.310 700 0.230 0.075 0.130 800 0.110 0.050 0.090 900 0.060 0.0375 0.0675

1000 0.040 0.0250 0.0450 1100 0.020 0.0125 0.0225 1200 0.000 0.0000 0.0000

Note: For intermediate values of the steel temperature, linear interpolation may be used As an example, Figure 1.13 illustrates the stress-strain relationship for steel grade S 355 at elevated temperature using the values given above. For steel grade S355, the yield strength is 355 MPa and the elastic modulus is 210 000 MPa. In Figure 1.13, no strain hardening is included. However, for temperature below 400 C, the alternative strain hardening option can be used according to Annex B in Eurocode 3, Part 1.2 [7].

Figure 1.13 Stress-strain relationship for S355 at elevated temperature

23

Hot-rolled reinforcing bars are treated in Eurocode 4 in similar fashion to structural steels, but cold-worked reinforcing steel, whose standard grade is S500, deteriorates more rapidly at elevated temperatures than do the standard grades. Its strength reduction factors for effective yield and elastic modulus are shown in Figure 1.14. It is unlikely that reinforcing bars or mesh will reach very high temperatures in a fire, given the insulation provided by the concrete if normal cover specifications are maintained. The very low ductility of S500 steel (it is only guaranteed at 5%) may be of more significance, in which high strains of mesh in slabs are caused by the progressive weakening of supporting steel sections [17].

Figure 1.14 EC3 Strength reduction for structural steel (SS) and cold-worked reinforcement (Rft) at high temperatures [17]

1.3.2 Thermal properties Such material properties as density, specific heat and thermal conductivity are needed for heat transfer calculation in solid materials. Density, , is the mass of the material per unit volume in kg/m3. Specific heat, cp, is the amount of heat required to heat a unit mass of material by one degree with unit of J/kgK. Thermal conductivity, , represents the rate of heat transferred through a unit thickness material per unit temperature difference with unit of W/mK. Two other derived properties which are often needed, i.e. the thermal diffusivity given by /c with unit of m2/s and thermal inertia given by =c with unit of W2s/m4K2. When materials with low thermal inertia are exposed to heating, surface temperature increase rapidly, so that these materials ignite more readily. In the following sections, the values of some thermal properties provided in Eurocode 3 [7] are described.

0 300 600 900 1200

100

80

60

40

20

% of normal value

Temperature (C)

Effective yield strength(at 2% strain)

Elastic modulus

SSRft

SS

Rft

24

1.3.2.1 Specific heat In Eurocode 3, Part 1.2 [7], the specific heat of steel (J/kgK) may be determined as follows:

ca = 425 + 7.7310-1a - 1.6910-3a2 - 2.2210-6a3 (20C a < 600C) ca = 666 + 13002 / (738 - a) (600C a < 735C) ca = 545 + 17820 / (a - s731) (735C a < 900C) ca = 650 (900C a 1200C)

The variation of specific heat with temperature is illustrated in Figure 1.15. The value of specific heat undergoes a very dramatic change in the range 700-800C. The apparent sharp rise to an "infinite" value at about 735C is actually an indication of the latent heat input needed to allow the crystal-structure phase change to take place. When simple calculation models are being used a single value of 600J/kgK is allowed, which is quite accurate for most of the temperature range but does not allow for the endothermic nature of the phase change.

Figure 1.15 Variation of the specific heat of steel with temperature [17]

1.3.2.2 Thermal conductivity The thermal conductivity of steel may be defined as follows [7] a = 54-3.3310-2a (20C a < 800C) a = 27.3 (800C a 1200C) The variation of thermal conductivity with temperature is shown in Figure 1.16. For simple design calculations the constant conservative value of 45W/mC is allowed.

5000

0 200 400 600 800 1000 1200

Temperature (C)

Specific Heat(J/kgK)

4000

3000

2000

1000

ca=600 J/kgK(EC3 simple calculationmodels)

25

Figure 1.16 Eurocode 3 representations of the variation of thermal conductivity of steel with temperature [17]

1.3.2.3 Thermal elongation In most simple fire engineering calculations thermal expansion of materials is neglected, but for steel members which support a concrete slab on the upper flange the differential thermal expansion caused by shielding of the top flange and the heat-sink function of the concrete slab causes a thermal bowing towards the fire in the lower range of temperatures. In Eurocode 3, Part 1.2 [7], the thermal elongation is defined as the function of temperature and may be determined as follows: l /l = 1.210-5a+0.410-8a2-2.41610-4 (20C a < 750C) l /l = 1.110-2 (750C a 860C) l /l = 210-5a-6.210-3 (860C < a 1200C) where, l is the length at 20C; l is the temperature induced expansion; and a is the steel temperature. The variation of thermal elongation with temperature is illustrated in Figure 1.17. When the exposed steel sections reach a certain temperature range within which a crystal-structure change takes place and the thermal expansion temporarily stops. In simple calculation models, the relationship between thermal elongation and steel temperature may be considered to be constant. In this case the elongation may be determined from l /l = 1410-6(a-20) ( 1.23 )

10

20

30

40

50

60

0 200 400 600 800 1000 1200

Thermalconductivity(W/mK)

Temperature (C)

a=45 W/mK (EC3 simple calculation models)

26

Figure 1.17 Thermal elongation of steel as a function of the temperature ( Eurocode 3, Part 1.2) [7]

1.4 Passive Protection for Steelwork

1.4.1 Fire protection systems The traditional approach to fire resistance of steel structures has been to clad the members with insulating material. This may be in alternative forms [17]:

o Boarding (plasterboard or more specialized systems based on mineral fiber or vermiculite) fixed around the exposed parts of the steel members. This is fairly easy to apply and creates an external profile that is aesthetically acceptable, but is inflexible in use around complex details such as connections. Ceramic fiber blanket may be used as a more flexible insulating barrier in some cases.

o Sprays that build up a coating of prescribed thickness around the members. These tend to use vermiculite or mineral fiber in a cement or gypsum binder. Application on site is fairly rapid, and does not suffer the problems of rigid boarding around complex structural details. Since the finish produced tends to be unacceptable in public areas of buildings these systems tend to be used in areas that are normally hidden from view, such as beams and connections above suspended ceilings.

o Intumescent paints, which provide a decorative finish under normal conditions, but which foam and swell when heated, producing an insulating char layer which is up to 50 times as thick as the original paint film. They are applied by brush, spray or roller, and must achieve a specified thickness that may require several coats of paint and measurement of the film thickness.

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0 200 400 600 800 1000 1200

Temperature (C)

Elon

gatio

n

27

All of these methods are normally applied as a site operation after the main structural elements are erected. This can introduce a significant delay into the construction process, which increases the cost of construction to the client. The only exception to this is that some systems have recently been developed in which intumescents are applied to steelwork at the fabrication stage, so that much of the site-work is avoided. However, in such systems there is clearly a need for a much higher degree than usual of resistance to impact or abrasion. These methods can provide any required degree of protection against fire heating of steelwork, and can be used as part of a fire engineering approach. However traditionally thicknesses of the protection layers have been based on manufacturers data aimed at the relatively simplistic criterion of limiting the steel temperature to less than 550C at the required time of fire resistance in the ISO834 standard fire. Fire protection materials are routinely tested for insulation, integrity and load-carrying capacity in ISO834 furnace test. Material properties for design are determined from the results by semi-empirical means. Full or partial encasement of open steel sections in concrete is occasionally used as a method of fire protection, particularly in the case of columns for which the strength of the concrete, either reinforced or plain, can contribute to the ambient-temperature strength. In the case of hollow steel sections concrete may be used to fill the section, again either with or without reinforcing bars. In fire this concrete acts to some extent as a heat sink, which slows the heating process in the steel section. In a few buildings hollow-section columns have been linked together as a system and filled with water fed from a gravity reservoir. This can clearly dissipate huge amounts of heat, but at rather high cost, both in construction and maintenance. The most recent design codes are explicit about the fact that the structural fire resistance of a member is dependent to a large extent on its loading level in fire, and also that loading in the fire situation has a very high probability of being considerably less than the factored loads for which strength design is performed. This presents designers with another option that may be used alone or in combination with other measures. A reduction in load level by selecting steel members that are stronger individually than are needed for ambient temperature strength, possibly as part of a strategy of standardizing sections, can enhance the fire resistance times, particularly for beams. This can allow unprotected or partially protected beams to be used. The effect of loading level reduction is particularly useful when combined with a reduction in exposed perimeter by making use of the shielding and heat sink effects of the supported concrete slab. The traditional down stand beam (Figure 1.18) gains some advantage over complete exposure by having its top flange upper face totally shielded by the slab; supporting the slab on shelf angles welded to the beam web keeps the upper part of the beam web and the whole top flange cool, which provides a greater enhancement. The recent innovation of Slimflor beams, in which an unusually shallow beam section is used and the slab is supported on the lower flange, either by pre-welding a plate across this flange or by using an asymmetric steel section, leaves only the lower face of the bottom flange exposed. Alternative fire engineering strategies are beyond the scope of this lecture, but there is an active encouragement to designers in the Eurocodes to use agreed and validated advanced calculation models for the behavior of the whole structure or sub-assemblies. The clear implication of this is

28

that designs which can be shown to gain fire resistance overall by providing alternative load paths when members in a fire compartment have individually lost all effective load resistance are perfectly valid under the provisions of these codes. This is a major departure from the traditional approach based on the fire resistance in standard tests of each component. In its preamble Eurocode 3 Part 1-2 also encourages the use of integrated fire strategies, including the use of combinations of active (sprinklers) and passive protection, although it is acknowledged that allowances for sprinkler systems in fire resistant design are at present a matter for national Building Regulations.

Figure 1.18 Inherent fire protection to steel beams [17]

1.4.2 Thermal properties of fire protection systems Typical values of thermal properties of insulating materials are given in Table 1.2, from ECCS (1995) [1].

Table 1.2 Thermal properties of insulation materials

Materials Density i

(kg/m3)

Thermal conductivity i

(W/mK)

Specific heat ci

(J/kgK)

Equilibrium moisture content

% Sprays Sprayed mineral fiber 300 0.12 1200 1 Perlite or vermiculite plaster

350 0.12 1200 15

High density perlite or vermiculite plaster

550 0.12 1200 15

Boards: Fiber-silicate or fiber-calcium silicate

600 0.15 1200 3

Gypsum plaster 800 0.20 1700 20 Compressed fiber boards Mineral wool, fiber silicate 150 0.20 1200 2

Downstand beam

Shelf-angle beam

Slimflor beam

29

1.5 Heat Transfer in Steel

1.5.1 Type of heat transfer Heat transfer involves the following three processes: conduction, convection and radiation, which can occur separately or together depending on the circumstances. Conduction Conduction is the mechanism for heat transfer in solid materials. In materials that are good conductors of heat, the heat is transferred by interaction involving free electrons. In materials that are poor conductors, heat is conducted via mechanical vibrations of molecular lattice. Conduction of heat is an important factor in the ignition of solid surfaces, and in fire resistance of barriers and structural members. In the steady state, the heat transfer by conduction is directly proportional to the temperature gradient between two points and the thermal conductivity, , i.e. [1] hD = d/dx ( 1.24 )

where hD is the heat flow per unit area (W/m2), is the thermal conductivity (W/mK), is the temperature (C), and x is the distance in the direction of heat flow (m). In the transit state, i.e. the temperatures are changing with time, the amount of heat required to change the temperature of the materials must be included. For one dimension heat transfer by conduction with no internal heat being released, the governing equation is [1] 2 / 2x=(1/)/( / t) ( 1.25 )

where t is time (s) and = /c is thermal diffusivity (m2/s). These equations can be solved using analytical, graphical or numerical methods. Convection Convection is heat transfer by the movement of fluids, either gases or liquids. Convective heat transfer is an important factor in flame spread and in the upward transport of smoke and hot gases to the ceiling or out of window from a compartment fire. For given conditions, the heating transfer is proportional to the temperature difference between to materials, so that the heat flow per unit area can be calculated using [1]

hD =c ( 1.26 )

where c is the convective heat transfer coefficient (W/m2K) and is the temperature difference between the surface of the solid and the fluid (C). In Eurocode 3, Part 1.2 [7], the coefficient of heat transfer by convection is given as follows:

30

Table 1.3 Coefficient of heat transfer by convection

c (W/m2K) Exposed sides the standard temperature-time curve is used 25 the external fire curve is used 25 the hydrocarbon temperature-time is used 50 the simplified fire models are used 35 the advanced fire models are used 35 Unexposed side of separating members the radiation effects are not included 4 the radiation effects are included 9

Radiation Radiation is transfer of energy by electromagnetic waves that can be travel through a vacuum or through a transparent solid or liquid. Radiation is the main mechanism for heat transfer from flames to fuel surfaces, from hot smoke to building objects and from a burning building to an adjacent building. The heat flow per unit area can be calculated as [1]:

hD = [(e + 273) 4 (r +273 ) 4] ( 1.27 )

where is the configuration factor that is a measure of how much of the emitter is seen by the receiving surface. is the resultant emissivity of two surface and can be calculated as =1/(1/r + 1/e - 1). is the Stefan-Boltzmann constant and its value is = 5.67 10-8 W/m2K4. e is the temperature of emitting surface (C) and r is the temperature of receiving surface (C).

1.5.2 Heat transfer equation for steel The rise of temperature in a structural steel member depends on the heat transfer between any two elements that are at different temperature. Conduction, radiation and convection are the modes by which thermal energy flows from regions of high temperature to those of low temperature. On the external surfaces of the elements, all three mechanisms are present. Inside the element, heat is transferred from point to point only by conduction. Calculation of heat transfer requires knowledge of the geometry of element, thermal properties of the materials and heat transfer coefficient at boundaries. Practical difficulties are that some of thermal properties are temperature dependent as shown in 1.3.2.

1.5.2.1 General equation The general approach to study the increase of the temperature in structural elements exposed to fire is based on the integration of the Fourier-differential equation for transient conduction inside the member. This equation is given as [16]:

31

dtdch

zzyyxx net

)()()()(

=+

+

+

D ( 1.28 )

where x, y, and z is the Cartesian coordinates inside the structural element; is thermal conductivity; is the density; c is the specific heat and hD is the net heat flux that is due to convection and radiation, i.e.

neth = cneth . + rneth . ( 1.29 )

where, the net convective heat flux can be determined by

cneth . = c (g - m) ( 1.30 )

in which c is the coefficient of heat transfer by convection, g is the gas temperature in the vicinity of the fire exposed member (C) and m is the surface temperature of the member (C). The net radiative heat flux component per unit of surface area is determined by:

rneth . = [(r + 273) 4 (m +273 ) 4] ( 1.31 )

in which r is the effective radiation temperature of the fire environment (C). The solution of Fourier-differential equation can be obtained when the initial and boundary conditions are known. For fire, the initial conditions consist of the temperature distribution at the beginning of the analysis (usually the room temperature before fire); boundary conditions must be defined on every surface of the structure, for instance, boundaries exposed to fire and boundaries unexposed to fire. Usually fire simulations are based on the temperature history of the fire, for instance the standard fire curve. However, any other any fire conditions can be assumed, using other type of temperature-time curves. Numerical methods are necessary to solve this equation. Many computer programs are available and it is possible to carry out thermal analysis for very complex structural elements. For instance, Ma and Mkelinen [11] in the Laboratory of Steel Structures at HUT has developed a computer program to perform temperature analysis of steel-concrete composite slim floor structures exposed to fire based on this heat transfer equation. As an example, Figure 1.19 shows the section shape of a new slim floor beam, which is composed of a three-plate-welded beam, a profiled steel deck and a concrete slab over the steel deck. Figure 1.20 shows the temperature distribution of this slim floor beam under standard temperature-time curve when the fire exposure is 60 minutes. In many cases, the general form of the equation can be greatly simplified. For instance, thermal conductivity, density and specific can be assumed to be independent of temperature; internal heat generation is absent or can be neglected; and three-dimensional problems can be studied as two-dimensional or one dimensional idealizations.

32

Figure 1.19 Section shape of new slim floor beam [11]

Figure 1.20 Temperature distribution of the new slim floor beam under ISO fire (60 minutes) [11]

1.5.2.2 Temperature calculation for unprotected steel members Since the thermal conductivity is high enough to allow the difference of temperature in the cross-section to be neglected. This assumption means that thermal resistance to heat flow is negligible. Any heat supplied to the steel section is instantly distributed to give a uniform steel temperature. With this assumption, the energy balance can be made based on the principle that the heat entering the steel over the exposed surface area in a small time step t (s) is equal to the heat required to raise temperature of the steel by (C), i.e. [1]

60

117

183

Concrete

Rannila 120

Steel Deck

Reinforcement Mesh

Asymmetric

Steel Beam

10

20

400

200

18

fillet weld

fillet weld

33

heat entering = heat to raise temperature

neth Am t = a ca V a ( 1.32 )

and the temperature increase of steel can be calculated as

a.t = (Am/V)(1/a ca) neth t ( 1.33 )

where neth is the heat flow per unit area (W/m2) and is given by:

neth = c (g - m) + [(r + 273) 4 (m +273 ) 4] ( 1.34 )

The meanings and the values of other symbols are given in Table 1.4.

Table 1.4 Parameter values for exterminating temperature increase

Symbols Meanings Values according to Eurocode Unit a Density of steel 7850 kg/m3 ca Specific heat of steel see 1.3.2.1 or 600 for a simple calculation model J/kgK c Coefficient of heat transfer

by convection see Table 1.3 W/m2K

Configuration factor can be taken as 1. A lower value may be chosen to consider position and shadow effect

----

Resultant emissivity of two surface

can be calculated as =mf with m = 0.8 and f = 1.0, = 0.8

-----

Stefan-Boltzmann constant 5.67 10-8 W/m2K4 g Temperature of gas nominal temperature-time curve or parametric

temperature-time curves C

r Effective radiation temperature of the fire environment

r = g C

Am/V Section factor see Table 1.6 1/m a.t Temperature change of steel Calculation results C

Solving the increasemental equation step by step gives the temperature development of the steel element during the fire. A spreadsheet for calculating steel temperatures is shown in Table 1.5. In order to assure the numerical convergence of the solution, some upper limit must be taken for the time increasement t. In Eurocode 3, Part 1.2 [7], it suggested that the value of t should not be taken as more than 5 seconds.

Table 1.5 Spreadsheet calculation for temperatures of unprotected steel section [1]

Time Steel temperature a

Fire temperature g

Temperature change in steel a

t1 = t Initial steel temperature a0

Fire temperature half way through time step (at t / 2)

Calculating from increasemental equation with a and g from this row

t2 = t1 + t a + a a Temperature for previous row

Fire temperature half way through time step (at t1+t / 2)

Calculating from increasemental equation with a and g from this row

34

An important parameter in determining the rise of temperature of the steel section is section factor, Am/V (sometimes given as F/V or A/V or Hp/V in different countries). The section factors for some of the unprotected steel members in Eurocode 3, Part 1.2[7] are shown in Table 1.6.

Table 1.6 Section factor for unprotected steel members [7]

Open section exposed to fire Am/V: Perimeter / Section area

Open section exposed to fire on three sides Am/V: Surface exposed to fire / Section area

Hollow section or welded box section with uniform thickness exposed to fire on all sides if t

35

insulation material). The calculation of steel temperature rise a.t in a time increment t is now concerned with balancing the heat conduction from the exposed surface with the heat stored in the insulation layer and the steel section:

( ) ( ) tgtatgpaa

ppta etV

Ac

d.

10/... 13/1

1/

+= but 0. ta ( 1.35 )

in which the relative heat storage in the protection material is given by the term

VA

dcc p

paa

pp

= ( 1.36 )

in which Ap/V section factor for protected steel member, where Ap is generally the inner perimeter of the protection material and the values are shown in Table 1.7.

Table 1.7 Section factors of steel members insulated by fire protection materials[7]

Sketch Description Section factor (Ap/V)

Contour encasement of uniform thickness

Steel perimeter / Steel section area

Hollow encasement of uniform thickness

2(b+h) / Steel section area

Contour encasement of uniform thickness to fire on three sides

(Steel perimeter-b) / Steel section area

Hollow encasement of uniform thickness exposed to fire on three sides

(2h+b) / Steel section area

Normally, the section factors represent the ratio of the effective surface exposed to fire to the volume of the element. When there is a protective coating, the surface to be taken into account is not

36

the external surface of the profile but the inner steel surface. cp is the specific heat of protection material; p is thermal conductivity of the fire protection material; p is the density of fire protection material. These values are given in Table 1.2. dp is the thickness of fire protection material. The value of t should not be taken as more than 30 seconds. Fire protection materials often contain a certain percentage of moisture that evaporates at about 100C, with considerable absorption of latent heat. This causes a dwell in the heating curve for a protected steel member at about this temperature while the water content is expelled from the protection layer. The incremental time-temperature relationship above does not model this effect, but this is at least a conservative approach. A method of calculating the dwell time is given, if required, in the European pre-standard for fire testing.

1.5.2.4 Example: temperature analysis for both unprotected and protected steel members The following example shows the temperature analysis of steel beam with three-side exposure to fire and box protection with gypsum board under standard fire. The cross-section and the required parameter of the gypsum board are given in Figure 1.21. The results of temperature-time curves for unprotected steel beam and protected beam together with the standard fire curve are shown in Figure 1.22. The thickness of 12.5 mm gypsum board is used and it can be seen that with this thickness, the temperature of steel beam drops dramatically at 30 minutes.

Figure 1.21 Cross-section of steel beam and properties of protection material

Figure 1.22 Temperature-time curves of unprotected and protected steel beam together with standard fire

37

1.6 Mechanical Analysis of Structural Element Fire resistance is a measure of the ability of building element to resist a fire. Fire resistance is most often quantified as the time to which the element can meet certain criteria during an exposure to a standard fire test. Structural fire resistance can also be quantified using temperature or load capacity of a structural element exposed to a fire. Verification of fire resistance should be in one of the following domain [3]:

o Time domain: tfi.d tfi.requ o Strength domain Rfi.d.t Efi.d.t o Temperature domain d cr.d

where tfi.d is the design value of fire resistance; tfi.requ is the required fire resistance time; Rfi.d.t is the design value of the resistance of the member in the fire situation at time t; Efi.d.t is the design value of the relevant effects of actions in the fire situation at time t; d is the design value of material temperature; cr.d is the design value of critical material temperature. tfi.requ, Efi.d.t, d are the variables to describe fire severity. Fire safety is a measure of the destructive impact of a fire, or measure of the forces or temperatures that could cause collapse or other failure as a result of the fire. tfi.d, Rfi.d.t, and cr.d are used to describe the fire resistance.

1.6.1 Required fire resistance time The required fire resistance time is usually a time of standard fire exposure specified by a building code, or the equivalent time of standard fire exposure calculated for a real fire in building.

1.6.1.1 Standard fire exposure Required fire resistance time are specified in National Codes, for instance, in Finland, the required fire resistance time is prescribed in E1 National Building Code of Finland, Structural Fire Safety, Regulation, Helsinki, Ministry of the Environment (cited with abbreviation: RakMK E1), and E2 National Building Code of Finland, Fire Safety in Industrial and Warehouse buildings, Helsinki, Ministry of the Environment (cited with abbreviation: RakMK E2). Required fire resistance time normally depends on factors such as: type of occupancy, height and size of the building, effectiveness of fire brigade action, and active measures such as vents and

38

sprinklers [5]. An overview of fire resistance requirements in various European countries as a function of above factors is given in Table 1.8 [5]. From this table it shows that

o For one storey buildings, no or low requirements are needed and ISO-fire class is possibly up to R30;

o For 2 to 3 storeys buildings, no up to medium requirements are needed and ISO-fire class is possibly up to R60;

o For more than 3 storey buildings, medium requirements are needed and ISO-fire class is R60 to R120;

o For tall buildings, high requirements are needed and ISO-fire class is R90 and more. Although quite large variations exist, the required fire resistance time is not beyond 90 to 120 minutes. If requirements are set, the minimum values are 30 minutes (some countries have minimum requirements of 15 or 20 minutes). Intermediate values are usually given in steps of 30 minutes, leading to a schema of 30, 60, 90, 120, ... minutes.

1.6.1.2 Equivalent time of fire exposure Equivalent time of fire exposure is a quantity which relates a non-standard or natural fire exposure to the standard fire, i.e. an equivalent time of exposure to standard fire is supposed to have the same severity as a real fire in the compartment. This equivalent can be determined based on equal area concept, maximum temperature concept and minimum load capacity concept [1]. The key difference lies in the definition of severity. Equal area concept Figure 1.23 illustrates the concept first proposed by Ingberg (1928), by which two fires are considered to have equivalent severity if the areas under each curves are equal, above a certain temperature (150 or 300 C). This has little theoretical significance because the product of temperature and time is not heat as expected. However, his work formed the starting points of current regulations of fire class [1].

Figure 1.23 Equivalent fire severity on equal area concept [1]

39

Table 1.8 Minimum Periods (minutes) for elements of structure [5]

In the following building types According to the regulations of Building

type n h H X L b x(*) S B CH D F I L NL FIN SP UK

Y 0 0 0 30*2 0/60 (7)

0 0 0 - 0*1 Industrial hall

1 0 10 20 100 50 2

N 0 (1)*3 (1) 30*2 30/90 (7)

0-60 0 0 - 0*1

Y 0 0 0 0 H 60/90 (7)

30 0 0 90 0*1 Commercial center and shop

1 0 4 500 80 80 4

N (1) (1)*3 (1) 30 V 90/120 (7)

(3) 0 30 90 0*1

Y 0 0 (2) 60 (8)(9) 30 0 60(4) 90 30 Dancing 2 5 9 1000 60 30 4 N 0 30 90 60 60 30 0 60(5) 90 60

Y 60(6) 0 30*3

(2) 60 (8) (10)

90 60 60(4) 60 60 School 4 12 16 300 60 20 4

N 60(6) 60 90 60 60 90 60 60(5) 60 60

Y 60(6) 0 30*3

(2) 60 (8) (9)

90 60 60(4) 60 30 Small rise office building

4 10 13 50 50 30 2

N 60(6) (1)*3 90 60 60 90 60 60(5) 60 60

Y 60(6) 30 60*3

(2) 60 (8) (11)

90 60 60(4) 90 60 Hotel 6 16 20 60 50 30 2

N 60(6) 60 90 60 60 90 60 60(5) 90 60

Y 120 60 (2) 60 (8)(12) 90/120 120 60(4) 120 90 Hospital 8 24.5 28 60 70 30 2 N 120 90 90 60 120 120 120 60(5) 120 90

Y 120 60 90*3

(2) 120 (8) (9)

90 60 120 (4)

120 120 Medium rise office building

11 33 37 50 50 30 2

N 120 90 90 120 90 120 90 120 (5)

120 (3)

Y 120 90 90 120 (8) (9)

120 90 120 (4)

120 120 High rise office building

31 90 93 100 50 50 2

N 120 90(3) (3) 120 120 (3) 90 120 (5)

120 (3)

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Maximum temperature concept Maximum temperature concept developed by Law, Pettersson et al. and others is to define the equivalent fire severity as the time of exposure to the standard fire that would result in the same maximum temperature in a steel member as would occur in a complete burnout of the fire compartment as shown in Figure 1.24 [1]. This concept is widely used and current Eurocode is based on this method.

Figure 1.24 Equivalent fire severity based on maximum temperature concept [1]

Minimum load capacity concept In this concept, the equivalent fire severity is the time of exposure to the standard fire that would result in the same load bearing capacity as the minimum which would occur in a complete burnout of the fire compartment as shown in Figure 1.25 [1]. The load bearing capacity of a structural member exposed to the standard fire decreases continuously, but the strength of the same member exposed to a natural fire increases after the fire enters the decay period and the steel temperature decreases.

Figure 1.25 Equivalent fire severity based on minimum load capacity concept [1]

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Equivalent time of fire exposure in Eurocode The equivalent time of ISO fire exposure is defined by [3] te.d = (qf.d kb wf) kc or te.d = (qf.d kb wt) kc ( 1.37 )

where qf.d is the design fire load density; kb is the conversion factor; wf is the ventilation factor and kc is the correction factor function of the material composing structural cross-sections.

1.6.2 Mechanical actions Mechanical actions include actions from normal conditions of use and indirect fire actions. Indirect actions may occur as result of restrained thermal expansion and depend on the temperature development in the structural system and different in stiffness. A typical example of indirect action due to fire is temperature-induced stress due to non-uniform temperature distribution over the cross-section. In normal condition of use, the load combination for ultimate limit state verification in Eurocode is defined as [6]: E d = GG k + Q1Q k1 + QiQ ki ( 1.38 )

The actions during fire exposure is in accordance with the accidental design situation and the load combination is defined as [6]: E fi.d = GAG k + 1.1Q k1 + 2.iQ ki + Ad ( 1.39 )

where

G = 1.35 Partial factor for permanent loads: strength design Q = 1.5 Partial factor for variable loads: strength design

GA = 1.0 Partial factor for permanent loads: accidental design situations 1.1 Table 1.9 Combination factor: variable loads 2.i Table 1.9 Combination factor: variable loads E d Design value of effects of actions from normal design

E fi.d Constant design value in fire exposure G k Characteristic value of permanent action

Q k1 Characteristic value of dominant variable action Q ki Characteristic value of other variable actions Ad Design value of accidental action: indirect action in fire

Due to the low probability that both fire and extreme severity of external actions occur at the same time and indirect actions not being considered for standard fire exposure, the above two formulas can be simplified as: E d = GG k + Q1Q k1 ( 1.40 )

in normal condition, and E fi.d = GAG k + 1.1Q k1 ( 1.41 )

in fire situation. The values of combination factors are given in Table 1.9.

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Table 1.9 Values of combination factor [6]

Actions 0 1 2 Imposed loads in buildings, category (EN 1991-1-1) Category A: domestic, residential areas Category B: office areas Category C: congregation areas Category D: shopping areas Category E: storage areas Category F: traffic area, vehicle weight = 30 kN Category G: traffic area, 30 kN < vehicle weight = 160 kN Category H: roofs

0.7 0.7 0.7 0.7 1.0 0.7 0.7 0

0.5 0.5 0.7 0.7 0.9 0.7 0.5 0

0.3 0.3 0.6 0.6 0.8 0.6 0.3 0

Snow loads on building (see EN 1991-1-3)* Finland, Iceland, Norway, Sweden Remainder of CEN member States, for sites located at altitude H > 1000 m a.s.l H = 1000 m a.s.

0.7

0.7 0.5

0.5

0.5 0.2

0.2

0.2 0

Wind loads on buildings (see EN 1991-1-4) 0.6 0.2 0 Temperature (non-fire) in building (see EN 1991-1-5) 0.6 0.5 0 Note: value of may be set by national annex * for countries not mentioned above, see relevant local conditions

The reduction factor can be defined either as [3] fi = E fi.d.t / R d ( 1.42 )

in which the loading in fire is taken as a proportion of ambient-temperature design resistance when global structural analysis is used, or [3] fi = E fi.d.t / E d ( 1.43 )

in which loading in fire is taken as a proportion of ambient-temperature factored design load when simplified design of individual members is used and only the principal variable action is used together with the permanent action. This may be expressed in terms of the characteristic loads and their factors as

1.1.

1.1.1

kQkG

kkGAfi QG

QG

+

+= ( 1.44 )

1.6.3 Design value of material temperature The design value of material temperature, d, is the maximum temperature reached in fire or temperature at the time specified by code. This temperature can be determined using heat transfer analysis.

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1.6.4 Design value of fire resistance time Fire resistance time can be described using fire resistance class (grade), or fire resistance level, or fire resistance rating. Fire resistance rating is normally assigned starting with 15 and 30 minutes, and continuing in whole numbers of hours or parts of hours, for instances, 30/60/90 minutes. Fire resistance rating can be obtained using full-scale fire resistance test, calculation or expert opinions. These ratings are listed in various documents maintained by testing authorities, code authorities or manufacturers and can be classified into three categories, i.e. generic ratings, which apply to typical materials, proprietary ratings, which are linked to particular manufacturers, and approved calculation methods. Full-scale testing is the most common method of obtaining fire resistance ratings [1]. Fire resistance tests are carried out on representative specimens of building elements. For example, if a representative sample of a floor system has been exposed to the standard fire for at least two hours while meeting the specified failure criteria, a similar assembly can be assigned a two hour fire resistance rating for use in a real building. For fire resistance testing, most European countries have standards similar to ISO 834 and in the United States, Canada and some other countries is ASTM E119. The relevant British Standards are BS 476 Parts 20-23 (BSI, 1987) [1]. The test is mainly carried out in a furnace that is composed of a large steel box lined with firebricks or ceramic fiber blanket. The furnace will have a number of burners, most often fuelled with gas but sometimes with fuel oil. There exist an exhaust chimney, several thermocouples for measuring gas temperatures and usually a small observation. The most common apparatus for full-scale fire resistance testing is the vertical wall furnace. The minimum size specified by most testing standards is 3.03.0 m2 (ISO 834 or ASTM E119). Some furnaces are 4.0 m tall [1]. Three failure criteria for fire resistance testing are stability, integrity and insulation [1]. To meet the stability criteria, a structural element must perform its loading bearing function and carry the applied loads for the duration of the test without structural collapse. The integrity and insulation criteria are intended to test the ability of a barrier to contain a fire, to prevent fire spreading from the room of origin. To meet the integrity criterion, the test specimen must not develop any cracks or fissures that allow smoke or hot gases to pass through the assembly. To meet the insulation criterion, the temperature of the cold side of the test specimen must not exceed a specified limit, usually an average increase of 140 C and a maximum increase of 180 C at a single point. Fire resistance of building elements, such as walls, beams, columns and doors etc., depends on many factors including the severity of the fire test, the material, the geometry and support conditions of the element, restraint from the surrounding structure and the applied loads at the time of the fire. Furnace testing using the standard time-temperature atmosphere curve is the traditional means of assessing the behavior of frame elements in fire, but the difficulties of conducting furnace tests of representative full-scale structural members under load are obvious. The size of furnaces limits the size of the members tested, usually to less than 5m, and if a range of load levels is required then a separate specimen is required for each of these. Tests on small members may be unrepresentative of the behavior of larger members.

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A further serious problem with the use of furnace tests in relation to the behavior of similar elements in structural frames is that the only reliable support condition for a member in a furnace test is simply supported, with the member free to expand axially. When a member forms part of a fire compartment surrounded by adjacent structure which is unaffected by the fire its thermal expansion is resisted by restraint from this surrounding structure. This is a problem that is unique to the fire state, because at ambient temperatures structural deflections are so small that axial restraint is very rarely an issue of significance. Axial restraint can in fact work in different ways at different stages of a fire; in the early stages the restrained thermal expansion dominates, and very high compressive stresses are generated, but in the later stages when the weakening of the material is very high the restraint may begin to support the member by resisting pull-in. Furnace tests that allow axial movement cannot reproduce these restraint conditions at all; in particular, in the later stages a complete collapse would be observed unless a safety cut-off criterion is applied. In fact a beam furnace test is always terminated at a deflection of not more than span/20 for exactly this reason. Only recently has any significant number of fire