NETHERLANDS INSTITUTE FOR METALS RESEARCH TECHNICAL UNIVERSITY OF EINDHOVEN TNO BUILT ENVIRONMENT AND GEOSCIENCES

Netherlands Institute for Metals Research

Report 1 Literature Study on Aluminium Structures Exposed to Fire

Date June, 2005

Author(s) J. Maljaars Tel +31 15 276 3464 Fax +31 15 276 3016 E-mail [email protected]

Report no. O 2005.14 Number of pages 128 Number of appendices 6 Sponsor Netherlands Institute of Metals Research (NIMR) Project name PhD Aluminium Structures exposed to fire Description This report is a background document on the PhD research “Local buckling of aluminium sections exposed to fire”

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Preface

This report gives the results of a literature study to aluminium structures exposed to fire. The report is a background document for the PhD research “Local buckling of slender aluminium sections exposed to fire”. This research is carried out under project number MC1.02147 in the framework of the Strategic Research programme of the Netherlands Institute for Metals Research in the Netherlands (www.nimr.nl).

The author would like to thank Dr. J.H.H. Fellinger (TNO Built Environment and Geosciences), B.W.E.M. van Hove (TNO Built Environment and Geosciences and Eindhoven University of Technology) Prof. H.H. Snijder (Eindhoven University of Technology), Prof. F. Soetens (TNO Built Environment and Geosciences and Eindhoven University of Technology) and Ir. L. Twilt (TNO Built Environment and Geosciences) for their continuous support in the establishment of this report. TNO Built Environment and Geosciences is kindly acknowledged for the provision of test facilities, work place and software. Further, Prof. T. Höglund (KTH, Royal Institute of Technology, Stockholm), G.J. Kaufman (Alcoa, USA), S. Lundberg (Hydro Aluminium Structures, Norway), Prof. Dr. F.M. Mazzolani and his group at the University of Naples "Federico II" and Dr. J. Mennink (TNO Built Environment and Geosciences) are acknowledged for providing additional information on articles and papers and on the background of the Eurocode for aluminium structures.

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Summary

This report gives the results of a literature study to aluminium structures exposed to fire. The report is a background document for the PhD research “Local buckling of slender aluminium sections exposed to fire”.

Especially the low density, low melting point and high thermal conductivity cause aluminium structures to be sensitive to fire, compared to steel. Thermal properties of aluminium alloys are sufficiently known to be able to make a fire design of an aluminium structure.

Results of tensile tests show that the strength and stiffness reduce already at moderately elevated temperatures. The strength reduction depends on the alloy and the temper. For some alloys (the heat treatable ones), the strength reduction depends on the thermal exposure period.

Basically, codes for aluminium or steel structures exposed to fire (EN 1999-1-2 [7] and EN 1993-1-2 [4] respectively) distinguish the same failure mechanisms as in normal temperature design. The few tests on aluminium components found in literature confirm this. However because of changes in mechanical properties, visco-plastic behaviour and thermal expansion, other failure mechanisms may become decisive in fire compared to room temperature.

Thermal expansion may result in large deformations or, when thermal expansion is partially or entirely restrained, in high internal stresses. The coefficient of thermal expansion of aluminium is approximately two times that of steel. Additionally, creep may on the one hand decrease the material strength, and on the other hand result in large deformations and / or relaxation of stresses.

Contrarily to steel structures, only a few fundamental studies were carried out to fire exposed aluminium structures and no experience of aluminium structures in real fires is available. The amount of calculation models in the Eurocode for fire design of aluminium structures, EN 1999-1-2 [7], is therefore limited and many calculation models are not validated with tests. For some important failure mechanisms, such as failure of connections and local buckling, no calculation models are incorporated in the code. Studies to these failure mechanisms on which general conclusions could be based are not found in literature.

Because of the thin wall thicknesses usually applied in aluminium extruded sections, in combination with the high ratio between strength and modulus of elasticity, aluminium structures are relatively sensitive to local buckling. It is a first and essential step to determine a mechanical response model for local buckling of aluminium at elevated temperature.

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Symbol list

Chapter 2 “+” = To be combined with η = Reduction factor, ratio between design value of actions in fire and design value of actions for fundamental combination ψ0 = Factor for combination value of a variable action ψ1 = Factor for the frequent value of a variable action ψ2 = Factor for the quasi-permanent value of a variable action γG = Partial factor for a permanent action, also accounting for model uncertainties and dimensional variations γP = Partial factor for prestressing actions γQ = Partial factor for a variable action Ad = Design value of an accidental action (fire action) Gk,j = Characteristic value of permanent action j P = Relevant representative value of a prestressing action Qk,1 = Characteristic value of the leading variable action 1 Qk,i = Characteristic value of the accompanying variable action i

Chapter 3 Index p = insulation layer Index al = aluminium α = Coefficient of heat transfer by convection εm = Emissivity of the member εf = Emissivity of the flames λ = Conductivity ρ = Density θg = Gas temperature [ºC] θm = Member temperature [ºC] σ = Constant of Stephan-Bolzman (=5,67 . 108 W/m2K4) c = Specific heat q = Heat flow dp = Thickness of the insulation layer hrad = Radiative heat flux hcon = Convective heat flux ksh = Correction factor for the shadow effect qcon = Convective heat flow qrad = Radiative heat flow t = Time A = Exposed surface area per unit length Q = Accumulated heat Tm = Temperature of the member [Kelvin] Tr = Effective radiation temperature of the environment [Kelvin] V = Volume of the member per unit length

Chapter 4 αT = Coefficient of linear thermal expansion ε = Strain ε& = Strain rate εb = Homogeneous strain (strain at ultimate stress) εcr = Creep strain

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εcr,0 = Primary creep strain ν = Poisson ratio (or coefficient of lateral contraction) θlower = Temperature of the bottom flange θupper = Temperature of the top flange

ρo,haz = Ratio between 0,2% proof stress in heat affected zone and in parent material at room temperature σ = Stress f0,1 = 0,1 % proof stress f0,2 = 0,2 % proof stress at room temperature f0,2,θ = 0,2 % proof stress at elevated temperature θ f0,2,θ,haz = 0,2% proof stress of the heat affected zone at elevated temperature θ fc,x%, y min = Stress level to obtain a creep deformation of x % after y minutes under stress fp = Proportional limit fr = Rupture stress at room temperature fr,θ = Rupture stress at elevated temperature θ fu = Tensile strength at room temperature fu,θ = Tensile strength at elevated temperature fy = Yield stress h = Beam height k0,2,θ = Relative value of the 0,2% proof stress at elevated temperature θ m = Strain rate sensitivity index n = Strain hardening exponent t = Time tT = Temperature compensated time A50 = Strain at rupture C = Alloy- and temper-dependent constant, chosen such that the stress values of all tests fall on the same master curve E = Modulus of elasticity at room temperature Eθ = Modulus of elasticity at elevated temperature θ G = Shear modulus ∆H = Activation energy required for creep K = Constant in the stress-strain-strain rate relation L = Beam span PLM = Larson-Miller time-temperature parameter R = Universal gas constant T = Member temperature Z = Constant slope of the creep strain – temperature compensated time curve

Chapter 5 χ = Buckling factor ν = Coefficient of lateral contraction (Poisson ratio) τ = Plasticity reduction factor ε = Slenderness parameter at room temperature σ = Stress εθ = Slenderness parameter at elevated temperature θ σav = Average value for the stress σcr = Critical stress at room temperature σcr,θ = Critical stress at elevated temperature θ σmax = Maximum stress in a plate in the post-buckling range λrel = Relative slenderness σu,MK = Ultimate buckling stress according to method Mennink ∆y = shift of the neutral axis

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a = Plate dimension in direction of the load (length) b = Plate dimension perpendicular to load direction (width) beff = Effective width bw = Beam width e = Eccentricity

e0 = Eccentricity before loading eT = Eccentricity caused by bending due to unequal thermal expansion f0,2 = 0,2 % proof stress at room temperature f0,2 = 0,2% proof stress f0,2,θ = 0,2 % proof stress at elevated temperature θ fp = Proportionality limit at room temperature fp,θ = Proportionality limit at elevated temperature θ fy = Yield stress k = Spring stiffness kcr = Buckling factor kE,θ = Relative value of the modulus of elasticity of aluminium at elevated temperature θ k0,2,θ = Relative value of the 0,2% proof stress of aluminium at elevated temperature θ n = Ratio critical load / applied load ni = Constant depending on the cross-section class q = Lateral load t = Plate thickness u = Lateral deflection u0 = Initial lateral deflection w = Deflection out of plane x = Distance along span A = Area of the cross-section Aeff = Effective area E = (initial) modulus of elasticity Es = Secant modulus of elasticity Et = Tangent modulus of elasticity Eθ = Modulus of elasticity at elevated temperature θ F = Applied force in vertical direction (action) Fcr = Critical (elastic) buckling load H = Applied force in horizontal direction (action) Ieff = Effective second moment of inertia Iy = Second moment of inertia L = Length / span Lk = Buckling length MA = Moment around position A Mi = Internal moment Mu = External moment Npl = Plastic capacity of the column Nu,EC9 = Ultimate buckling resistance according to EN 1999-1-1 Nu,R = Ultimate buckling resistance according to method Ranby Nu,VK = Ultimate buckling resistance according to method Von Karman Nu,W = Ultimate buckling resistance according to method Winter Weff = Effective section modulus

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Contents

1 Introduction ...... 13

2 General remarks on fire design and structural aluminium...... 15 2.1 Steps in a fire design ...... 15 2.1.1 Fire resistance requirements...... 15 2.1.2 Actions 15 2.1.3 Gas temperature...... 16 2.1.4 Member temperature ...... 16 2.1.5 Mechanical properties at elevated temperature ...... 17 2.1.6 Response of the structure ...... 17 2.2 Overview of alloys and treatments ...... 19 2.2.1 Alloy indication system...... 19 2.2.2 Treatment indication...... 20

3 Heating of fire exposed aluminium...... 23 3.1 Gas temperature...... 23 3.2 Member temperature ...... 25 3.2.1 Conduction ...... 25 3.2.2 Convection ...... 27 3.2.3 Radiation ...... 27 3.2.4 Simple calculation model for heating of members...... 28 3.3 Relevant thermal properties of aluminium alloys...... 29 3.3.1 Melting temperature ...... 29 3.3.2 Density 29 3.3.3 Specific heat ...... 29 3.3.4 Thermal conductivity ...... 30 3.3.5 Emissivity and reflection...... 31 3.4 Evaluation of thermal properties ...... 33

4 Mechanical properties of aluminium alloys ...... 35 4.1 Thermal expansion ...... 35 4.2 Shape of the stress-strain relation...... 36 4.2.1 Room temperature ...... 36 4.2.2 Elevated temperature...... 38 4.3 0,2% proof stress...... 42 4.3.1 Room temperature ...... 42 4.3.2 Elevated temperature...... 44 4.4 Ultimate tensile strength...... 53 4.4.1 Room temperature ...... 53 4.4.2 Elevated temperature...... 55 4.5 Strength of Heat affected Zone...... 62 4.5.1 Room temperature ...... 62 4.5.2 Elevated temperature...... 62 4.6 Modulus of elasticity and Poisson ratio...... 63 4.6.1 Room temperature ...... 63 4.6.2 Elevated temperature...... 64 4.7 Ultimate strain ...... 69 4.7.1 Room temperature ...... 69

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4.7.2 Elevated temperature...... 70 4.8 Visco-plastic behaviour...... 72 4.8.1 Strain rate dependency ...... 72 4.8.2 Introduction to creep ...... 74

4.8.3 Creep rupture stress...... 74 4.8.4 Influence of creep on the strength for stress levels lower than the rupture stress ...... 82 4.8.5 Creep deformations ...... 84 4.8.6 Modelling of creep ...... 86 4.8.7 Creep in EN 1999-1-2 ...... 88 4.9 Evaluation of mechanical properties ...... 89

5 Structural behaviour of fire exposed aluminium structures ...... 93 5.1 Overview of failure mechanisms and evaluation methods...... 93 5.2 Cross-sectional resistance...... 94 5.2.1 Members loaded in tension...... 94 5.2.2 Members loaded in bending ...... 95 5.3 Connections...... 96 5.4 Global buckling of members ...... 96 5.4.1 Introduction to buckling ...... 96 5.4.2 Flexural, torsional and flexural-torsional buckling ...... 100 5.4.3 Lateral-torsional buckling (Art. 4.2.2.3)...... 105 5.4.4 Interaction of buckling phenomena (Art. 4.2.2.4 (6))...... 105 5.5 Local buckling...... 105 5.5.1 Critical load...... 106 5.5.2 Inelastic material ...... 110 5.5.3 Buckling resistance of plates at room temperature...... 111 5.5.4 Local buckling at elevated temperature...... 117 5.5.5 Classification...... 118 5.6 Behaviour of entire structures or parts of structures...... 122 5.6.1 Verification according to EN 1999-1-2 [7] ...... 122 5.6.2 Numerical research to frames...... 123 5.7 Evaluation of structural behaviour ...... 124

6 Conclusions and recommendations...... 127 6.1 Conclusions ...... 127 6.2 Recommendations ...... 128

References ...... 129

Appendices A Tests on the capacity of beams B Tests on welded connections C Tests on columns in compression (Amdahl et al.) D Tests on columns in compression and bending (Langhelle) E Tests on a stressed skin structure F Numerical models on the evaluation of entire aluminium structures exposed to fire

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1 Introduction

This report gives the results of a literature study to aluminium structures exposed to fire. It gives an overview of (thermal and mechanical) material properties of aluminium alloys at elevated temperature. The alloys considered are alloys that are of interest for structural applications. The temperatures and exposure times considered are those that are of interest for fire situations. The report also gives an overview of the structural behaviour of aluminium components exposed to elevated temperature. In this respect, the simple calculation models in the Eurocode that provides rules for aluminium structures exposed to fire, EN 1999-1-2 [7], are evaluated. Literature with respect to insulation of aluminium is not referred to in this document.

In this research, fire design and structural aluminium come together. Chapter 2 gives an introduction in both areas. Chapter 3 concerns the heating of aluminium structural elements exposed to fire. The effect heating has on aluminium alloys, in particular the reduction of mechanical properties and thermal expansion, is elaborated in chapter 4. Chapter 5 discusses the structural behaviour of fire exposed aluminium components and structures, based on the reduction of these mechanical properties. Conclusions and recommendations are given in chapter 6.

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2 General remarks on fire design and structural aluminium

Fire design of aluminium structures is a relatively new subject both in design and research areas. In this research, fire design and structural aluminium come together. This chapter gives an introduction in both areas. The steps that should be carried out when a fire design has to be made are shown in paragraph 2.1. Paragraph 2.2 gives an overview of aluminium alloys as well as treatments to improve the mechanical behaviour.

2.1 Steps in a fire design

The fire design of a structure is made in such a way, that people are able to escape safely before the structure collapses due to a fire. Besides fire spread to adjacent buildings has to be avoided. This chapter describes the steps that should be carried out when a fire design has to be made.

2.1.1 Fire resistance requirements

The requirement should be determined for the period after flash-over during which the structure should remain its load bearing or separating function. This so-called requirement on the fire resistance is given in national and international regulations. The requirement in The Netherlands is 0, 30, 60, 90 or 120 minutes, depending on occupation, height of the highest floor and fire load density.

2.1.2 Actions

The actions working on the structure have to be determined. The Eurocode for actions on structures exposed to fire, EN 1991-1-2 [2], classifies actions on structures from fire exposure as accidental actions. The Eurocode that provides the basis of structural design, EN 1990 [1], specifies the combinations of actions that should be taken into account for accidental design situations. The specifications in this code are based on risk analyses of the occurrence of load situations. Compared to room temperature, the design values of permanent and variable actions in an accidental design situation are reduced. Equation (2.1) gives the combination of actions for persistent or transient design situations, which is the fundamental combination for room temperature, and equation (2.2) gives the combination of actions for accidental design situations, according to EN 1990 [1].

γ+γ+γ+γψ ∑∑G,jk,jG "" P P"" Q,1k,1 Q "" Q,i0,ik,i Q (2.1) j1≥> i1 ++ +ψψ() + ψ ∑∑Gk,j""P""A"" d 1,1 or 2,1 Q k,1 "" 2,i Q k,i (2.2) j1≥> i1

Symbols are explained in the symbol list on page 3.

The differences between the accidental situation (as in case of fire) and the combinations for persistent or transient design situations are that: • The accidental load (fire) is taken into account; • Partial factors for permanent and variable actions are set to unity; • The frequent value or quasi-permanent value of the leading variable action is taken into account instead of the characteristic value. The choice between the frequent of quasi- permanent value in case of fire is given in the National Annex of EN 1991-1-2 [2]. The use of the quasi-permanent value is recommended in EN 1991-1-2 [2];

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• The quasi-permanent values of the other variable actions are taken into account instead of the combination values. Partial factors and factors for combination values, frequent values and quasi-permanent values of variable actions may be specified in the National Annex.

Factors for combination values, frequent values and quasi-permanent values depend on the type of variable action. In case the values in the National Annex are set equal to the recommended values in EN 1990 [1], the design value of the permanent action is reduced to 85%. Table 2.1 gives the design values of some variable actions for accidental design situations as a percentage of the design values of actions for permanent or transient design situations, in case the values in the National Annex are set equal to the recommended values in EN 1990 [1].

Table 2.1 – Design values of variable actions in accidental situations relative to design values in permanent situations for recommended values of partial, combination, frequent and quasi-permanent factors in EN 1990 [1]

Type of action Leading variable action Accompanying variable actions Imposed load in office or 20 % 29 % residential buildings Imposed load in shopping 40 % 57 % buildings Imposed load on roofs 0 % - Wind load on buildings 0 % 0 % Snow load on buildings 0 % 0 %

The reduction factor η is defined as the ratio between the design value of the effects of actions in fire (equation (2.2)) and the design value of the effects of actions for the fundamental combination (equation (2.1)). Because the dead weight of aluminium structures is in general low compared to the summation of variable loads, the reduction factor η is relatively low, compared to more conventional structural materials such as steel.

2.1.3 Gas temperature

The gas temperature as a function of the time should be determined. EN 1991-1-2 [2] gives several possibilities for the relation between time and temperature. Either a standardised temperature-time curve could be applied, or a relation between time an temperature could be determined for the structure considered, taking into account the specific fire design parameters of the structures. These possibilities, together with the advantages and disadvantages, are given in paragraph 3.1.

2.1.4 Member temperature

Based on the relation between time and gas temperature, the temperature in each aluminium member can be determined as a function of the time. To determine the member temperature, the thermal properties of the structural member have to be known. These properties in case of aluminium alloys are given in paragraph 3.3.

The temperature inside a member can be determined using equations given in the parts of the different Eurocodes dealing with fire design. These equations are given in paragraph 3.2. The application of these equations is limited to structures with a uniform temperature distribution. The

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equation for insulated members is further limited to a standard fire. For more accurate predictions of the member temperature as a function of the gas temperature, heat flow analysis can be carried out numerically, e.g. with Finite Element Programs. Applying such programs, it is also possible to determine temperature gradients that may be apparent in the structure.

2.1.5 Mechanical properties at elevated temperature

The mechanical properties of materials depend on the temperature. Having determined the temperatures of the structural members, the mechanical properties at these temperatures can be determined. In case of aluminium, three important effects are present when exposed to elevated temperatures: • Thermal expansion may lead to elongation and / or thermal stresses and strains. This is described in paragraph 4.1. • The shape of the stress-strain relation changes. The strength and stiffness decrease at elevated temperature and the strain at rupture changes. These phenomena are given in paragraphs 4.2 up to 4.7. • Creep is time dependent deformation, which may lead to fracture. It is accelerated by increase in stress and / or temperature. While creep is normally neglected at room temperature, it may become significant at elevated temperature. Creep is discussed in paragraph 4.8.

2.1.6 Response of the structure

The last step is to determine the mechanical response of the structure and to verify whether the structure is able to carry the load during the required fire resistance time. EN 1999-1-2 [7] provides the possibility to analyse the entire structure, parts of the structure or to divide the structure in individual components and verify each component. The structure may then be checked using tabulated data, simple calculation models or advanced calculation models.

Figure 2.1 gives an overview of the possibilities to evaluate the fire design of a structure. The rows represent the way the structure is modelled and the columns indicate existing possibilities to model the fire.

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Fire model Generalised fire Parametric fire Field models curves curves

Model of the structure components

t = f(x1,x2,…) t = f(x1,x2,…)

Parts of the structure

Entire structure

Figure 2.1 – Overview of possibilities to evaluate the fire design of a structure (source: PAO Course “Hybride constructies”, Delft University of Technology)

Where individual components are checked on the standard fire, it is in general possible to apply tabulated data as well as simple calculation models. In case of aluminium structures, the amount of available tabulated data is limited; simple calculation models are applied in this case. Also advanced models can be applied. In case of individual components checked on parametric fire curves, it is to some extend possible to apply tabulated data and simple calculation models. Advanced models can be applied. For all other combinations of structure modelling and fire modelling, tabulated data and simple calculation models are not provided. Advanced models should then be applied.

It seems inappropriate to put much effort in accurately modelling the structure, but to apply a fire that does not take the specific structure into account, i.e. to apply a standard fire curve in combination with a part of the structure or the entire structure. It may be unsafe to apply checks on individual components in combination with an advanced fire model, because then the uncertainties in structural behaviour remain, while the overestimation of the temperature reduces. The green boxes in Figure 2.1 indicate the most logical combinations of modelling the structure and the fire.

Information on simple an advanced mechanical response models for verification of individual aluminium members are given in chapter 5.

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2.2 Overview of alloys and treatments

The properties of aluminium at ambient and at elevated temperature depend on the alloy and the treatment. For a basic understanding of the similarities and differences in properties and

behaviour, it is necessary to outline the different alloys and treatments.

2.2.1 Alloy indication system

A distinction is made between wrought alloys and cast alloys. Wrought aluminium alloys are alloys with which the cast ingot is mechanically worked by processes such as rolling, drawing, extruding and forging (TALAT [10]). In this overview, it is focussed on wrought alloys, as wrought alloys are most applied in structures.

A wide variety of mechanical properties exist between different alloys. The selection of the alloy to be applied in load-bearing structures depends on aspects such as strength, ductility, weldability, resistance to corrosion and price. Most commercial aluminium alloys are indicated by a four-digit number, administrated by the Aluminum Association. The first of the four digits in the designation indicates the alloy group in terms of the mayor alloying element. In the overview below, attention is paid to the selection criteria for structural application (TALAT [10], Altenpohl [11], Davis [27], Kaufman [55] and Koser [57]). - 1xxx Pure aluminium (99,00 % purity or higher). These alloys are soft, ductile and of little structural interest because of the low strength; - 2xxx Copper. These alloys require solution heat treatment (paragraph 2.2.2) to achieve optimum strength. They have limited cold formability, except in the annealed condition, and less corrosion resistance than other alloys. Besides, they are more difficult to weld, although differences in weldability exist between the alloys in this series. Applications are found in airplanes; - 3xxx Manganese. By the addition of manganese, the strength increases significantly, without a mayor loss in ductility or corrosion resistance. The strength is however not sufficient to be a competitive material for applications in load-bearing structures. Applications are roofing sheets, vehicle panels and food preservations; - 4xxx Silicon. The addition of silicon lowers the melting point. These alloys are therefore applied as welding wires, brazing filler alloys and cladding; - 5xxx Magnesium. These alloys have moderately high strength in combination with good corrosion resistance, high toughness and good weldability, even at thickness up to 200 mm. Applications are bridges, ship structures, living quarters on drilling platforms, helicopter decks, chemical plants, pressure vessels and rail vehicles; - 6xxx Magnesium and Silicon. These alloys have excellent strength in combination with good corrosion resistance and ease of formability. Because of the good formability, these alloys are often applied for extrusions. Applications are the same as for 5xxx alloys, where 5xxx alloys are applied for sheets and plates and 6xxx alloys for extrusions. - 7xxx Zinc. These alloys are among the alloys with the highest strength. They are however difficult and costly to fabricate and not weldeable by routine commercial processes. The ductility of most of these alloys is less than in case of most other series. Main applications are in military objects, especially the aircraft industry. - 8xxx Other elements, for example iron nickel and lithium. By adding lithium, the strength increases, but also the modulus of elasticity increases, while the density decreases. Welding of these alloys is not possible. Al-Li alloys are applied in airplanes. Iron and nickel provide strength with little loss in electrical conductivity. They are used for conductors.

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2.2.2 Treatment indication

Increase in strength of aluminium alloys is possible by treatment, indicated by the temper. Possible treatments are precipitation hardening and work hardening (TALAT [10], Altenpohl [11],

Kammer [51], Langhelle [62]).

Precipitation hardening Wrought alloys can be divided in heat treatable and non-heat treatable alloys. In case of precipitation or heat treatable alloys (alloys in 2xxx, 6xxx and 7xxx series), the amount of alloying element(s) that can be dissolved in aluminium at higher temperature is higher than at ambient temperature. This fact is used to increase the strength of the alloy in precipitation hardening: First, a large amount of the alloying element(s) is dissolved in aluminium at a temperature just below the melting temperature (point A in Figure 2.2). This stage is called solution heat treatment. Following, rapid quenching takes place, which leaves the alloy in a supersaturated, unstable condition (point B in Figure 2.2)). The unstable condition gradually changes in a stable condition by the formation of precipitate particles. These particles impede plastic deformation by slip, through which extra strength is obtained, which is called ageing. Tempers T4 and lower indicate that aging takes place at room temperature, which is called naturally ageing. Because naturally ageing occurs gradually for most alloys, the strength of an alloy of this temper usually increases during the entire lifetime of a structure. To speed up ageing, it is possible to bring the supersaturated alloy at an elevated temperature (120 to 180 ºC) for a specific period of time (mostly several hours) in a conditioned way, which is called artificially ageing. Vacancies in the structure are then more mobile and the alloying elements diffuse more quickly. Tempers T5 and higher indicate alloys in artificially aged condition. The process is schematically shown in Figure 2.3.

L = liquid condition A α = random solid solution C] o of Mg and Si atoms in the aluminium matrix Temperature [ Temperature

B

Mass % Mg Si 2

Figure 2.2 – Al Mg2 Si phase diagram (after Mondolfo [89])

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T Solution heat

treatment + 500 ºC

Artificial ageing + 175 ºC

O ≤ T4 ≥ T5 t + 5 hr + 10-15 hr

Figure 2.3 – Heat treatments schematically described (after TALAT [10])

Work hardening Whenever aluminium products are fabricated by rolling, extruding, drawing or bending, work is done on the metal. When deformations are applied below the metal’s recrystallisation temperature, it not only forms the metal, but also increases the strength due to the fact that the dislocation density increases. When stress is applied, dislocations trying to glide on different slip planes interact causing a “traffic jam” that prevents them from moving, so that the strength increases. In general, alloys in series 3xxx and 5xxx are regarded as non-heat treatable. For these alloys, work hardening is an option to strengthen the alloys. Work hardening can also be applied to heat- treated alloys to further strengthen the material.

Indication system for treatments The treatments are indicated by the temper. For both heat treatable and non-heat treatable alloys, the following tempers are applied: - F As fabricated (this denotes an undefined stress enhancement above the annealed state); - O Annealed (or soft). A selection of tempers in case of non-heat treatable alloys is: - H1x Strain hardened to specified strength; - H2x Strain hardened and partially annealed; - H3x Strain hardened and stabilized by low temperature treatment; - Hx1 1/8 hard; - Hx2 Quarter hard; - Hx4 Half hard; Degree of cold working - Hx6 Three quarter hard; - Hx8 Fully hard (maximum amount of cold work which is commercially practical) - Hx9 Extra hard - Hxxx The last digit indicates that the standard fabrication practices have been varied for a special application

A selection of tempers in case of heat treatable alloys is: - T1 Cooled from an elevated temperature and naturally aged; - T2 Cooled from an elevated temperature, cold worked and naturally aged; - T3 Solution heat-treated, cold worked and naturally aged; - T4 Solution heat-treated and naturally aged; - T5 Cooled from an elevated temperature and artificially aged;

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- T6 Solution heat-treated and artificially aged; - T7 Solution heat-treated and overaged / stabilised (beyond the point of maximum strength); - T8 Solution heat-treated, cold worked and then artificially aged;

- T9 Solution heat-treated, artificially aged and then cold worked; - T10 Cooled from an elevated temperature, cold worked, and artificially aged; - Tx51 Stress-relieved by stretching after solution-heat treating; - Tx510Stress-relieved by stretching of extruded rod, bar and shapes which receive no further straightening after stretching; - Tx511Stress-relieved by stretching of extruded rod, bar and shapes which receive minor straightening after stretching; - Tx52 Stress-relieved by compressing after solution-heat treating; - Tx53 Stress-relieved by thermal treatment.

In a welded structure, the temperature induced by welding influences the material properties of certain area of parent material around the weld. This area is called the heat affected zone (HAZ). In the heat affected zone, both precipitation and work hardening are (partially) destroyed, depending on the time and temperature induced by welding. The influence of welding on precipitation hardening is larger than on work hardening.

The treatment possibilities are illustrated in Figure 2.4.

Not treated Treated

Tempers x Cold worked x, 5xx starting with H x, 3xx 1xx Cold worked and Tempers Temper O 2xxx, 6xxx, 7xxx 2 precipitation treated T3 T5 T8 T9 xxx, 6xxx, 7xxx Precipitation Tempers

treated T2 T4 T6 T7

Figure 2.4 – Overview of treatment possibilities

The PhD research focuses on alloys 5083 O, 6063 T6 and 6082 T6. These alloys are widely applied in load-bearing structures because of a combination of moderate to high strength, good corrosion resistance and good weldability.

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Literature Study on Aluminium Structures Exposed to Fire

3 Heating of fire exposed aluminium

This chapter elaborates the heating of fire exposed aluminium structures. Paragraph 3.1 gives a general overview of fire concepts applied in structural engineering and the resulting time- temperature curves. Paragraph 3.2 gives the general equation for heat transfer to a (structural) member and gives an overview of the thermal properties that determine this heat transfer. The quantification of these properties for aluminium is given in paragraph 3.3. Paragraph 3.4 gives an evaluation of heating of aluminium structures.

3.1 Gas temperature

The information in this paragraph has been derived from EN 1991-1-2 [2] and from Twilt [107]. A temperature-time relation in case of a fire is, for structural applications, usually schematised according to the thick line in Figure 3.1. The three phases distinguished in a fire are the growth phase, the fully developed phase and the decay phase.

Growth Fully Decay phase developed phase phase

temperature

Flash-over

Start of the fire

time Figure 3.1 – Phases distinguished in a fire

Gas temperature, heating rate and fire duration depend on many factors. Important factors, which are distinguished in EN 1991-1-2 [2] are: - Amount and type of combustible material. The net caloric values of combustible materials in a fire compartment are used to determine the fire load density [MJ/m2]; - Thermal properties of the boundary enclosure as the walls, floor and ceiling of the compartment may conduct and absorb heat; - Amount and sizes of openings: ventilation is an important parameter that influences the maximum temperature and the fire duration. At low ventilation, the temperature development is limited by the presence of fresh air, so that the fire is ventilation controlled. At higher temperatures, the fire is fuel load controlled. High ventilation may lead to fast exhaust of hot gas and supply of cold gas, which limits the maximum temperature. The maximum gas temperature thus occurs in between an entirely opened and an entirely closed structure. - Occurrence of flash-over: At a certain temperature, combustible material that initially did not participate in the fire will ignite spontaneously (flash-over). Resulting, the entire fire compartment is on fire and the gas temperature will increase significantly. When flash-over does not occur, the fire remains localised with only moderately elevated temperature (Figure 3.1).

The actual gas temperature thus depends on the lay-out of the structure. As it used to be complicated to determine the actual gas temperature for each structure, generalised temperature- time curves were traditionally applied for verification of the fire resistance of a structure. These

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curves are independent of the specific layout of the structure, they are a simplified representation of a real fire. The most applied generalised curve is the standard temperature-time relation (standard fire), represented by the dotted line in Figure 3.1. It is mainly chosen because of standardisation reasons of laboratory facilities. Other generalised curves are the hydrocarbon curve and the external fire curve (Figure 3.2). EN 1991-1-2 [2] gives the possibility to apply these generalised curves for verification of structures. It also provides the possibility to apply a natural fire concept.

1200

Hydrocarbon 1000 Standard 800 External 600

Temperature [º C] Temperature 400

200

0 0 20 40 60 80 100 120 Time [min] .

Figure 3.2 – Generalised temperature-time curves

A natural curve is determined for each fire compartment specifically, using the above mentioned factors for the structure considered. As such a curve is related to the specific fire compartment, it is in most cases less conservative than the generalised temperature time curves. A second difference is that the extinction phase is taken into account in case of natural fires. Natural fire concepts are in particular interesting for aluminium structures, as aluminium is relatively sensitive to elevated temperature. Active fire fighting measures have proven to be effective. However it is possible that such measures are not activated when a fire occurs. Based on the probability that the fire is actively extinguished, reduction factors are determined. In EN 1991-1-2 [2], active fire fighting measures are taken into account in natural fire concepts by multiplying the characteristic fire load with these reduction factors. Factors are also provided to take account of compartment floor area and occupancy, as these parameters influence the fire activation risk.

Figure 3.3 gives some examples of natural temperature-time curves.

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1200

1000

Different fire load 800

Different 600 ventilation

Temperature [ºC] Temperature 400

200

0 0 20 40 60 80 100 120 Time [min] .

Figure 3.3 – Example of a natural temperature-time curve

When the gas temperature in the fire design of a structure is determined, this information is used to determine the temperature of the structural members. The following paragraph considers heat transfer from a fire to (structural) components.

3.2 Member temperature

Most of the equations for heat transfer or, in general, the study on thermodynamics, were derived in the 19th century. The equations are written down in many textbooks. The derivation of the equations in this chapter is based on Jakob [49] and Carslaw and Jaeger [26]. Transfer of heat inside a solid (by direct contact) is called conduction. Paragraph 3.2.1 gives the basic equation for heat transfer by conduction. The boundary conditions for this equation are determined by the heat flow to the surface of the member. This heat flow is the summation of heat flow by convection and heat flow by radiation. Convection and radiation are discussed in paragraphs 3.2.2 and 3.2.3, respectively.

3.2.1 Conduction

Heating of mass costs energy. The accumulated heat energy (∆Q) due to a temperature increase . (∆θm) of a body with a certain mass (ρ V) depends on a material dependent property called the specific heat (c). This specific heat denotes the amount of energy to be added to a unit mass of a body to increase its temperature with one degree.

∆=()θ ⋅ρ θθ ⋅⋅∆ Qcm ()mm V (3.1)

The process whereby heat flows from regions of higher temperature to regions of lower temperature is called heat flow (q). Heat flow is defined as the amount of heat added to the material per unit time, q = ∆Q/∆t. Considering an amount of material with thickness ∆x and surface A, the relation between the heat flow and the heating rate is given in equation (3.2).

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∆θ qc=⋅⋅∆⋅⋅()θρθ() xA m (3.2) mm ∆t

The one-dimensional heat flow through a material depends on the temperature gradient and a material specific quantity, called the thermal conductivity (λ).The basic law of heat conduction originates from Biot [18] and is given in equation (3.3). The definition of thermal conductivity is thus the quantity of heat that passes in unit time through a plate of unit area and unit thickness when its opposite faces differ in temperature by one degree.

∆θ qA=−λθ() ⋅ m (3.3) ∆x

The accumulated heat in a layer of the material with thickness ∆x causes a temperature difference between the surface where heat enters and the surface where it leaves the body. Equation (3.4) gives the heat entering the body on one surface, and equation (3.5) gives the heat leaving the body on the opposite surface.

dQ dθ 1 =−λ ⋅A m (3.4) dtdx

dQ d ⎛⎞dddθθθ2 2 =−λθ ⋅ +mmm ∆ =− λ ⋅ − λ ⋅ ∆ (3.5) A ⎜⎟xA A2 x dt dx⎝⎠ dx dx dx

The difference between the heat entering and the heat leaving the body is the accumulated heat stored inside the body:

∆= − Q dQ12 dQ (3.6)

Equations (3.1), (3.4), (3.5) and (3.6) result in the differential equation for heat conduction for a one-dimensional situation:

d 2θθd λθρm =⋅⋅c() m (3.7) dxd2 m t

In case of a three dimensional situation, the accumulated heat is the summation of the heat entering and leaving in three directions. Equation (3.7) can be extended to equation (3.8).

∂∂∂222θθθd θ λλλm ++=⋅⋅mmc() θρ m (3.8) ∂∂∂x222yzm dt

In the derivation of equation (3.8), it was assumed that the thermal conductivity (λ) is independent of the temperature. For the common case of a dependency of the thermal conductivity on the temperature, equation (3.9) applies. This equation is known as the Fourier equation, as Fourier [40] applied it in his theory of heat.

∂∂∂∂∂∂θθθ⎛⎞ dθ ⎛⎞λθ() ++=⋅⋅ λθ() ⎛⎞ λθ() () θ ρ m ⎜⎟mmmm⎜⎟ ⎜⎟c (3.9) ∂∂∂∂∂∂x ⎝⎠xy⎝⎠ yz ⎝⎠ z dt

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This equation forms the basis to determine the temperature development in the cross-section of a non-combustible member.

3.2.2 Convection

Convection is the transfer of heat by the motion of or within hot or cold fluids (gases or liquids). This is also a form of conduction, but it involves a material that flows because of the ensuing temperature and pressure differences. The heat flow by convection (qcon) can be approximated by a linear dependency on the temperature difference between the gas (θg) and the member surface (θm). Newton [90] proposed the simplified equation (3.10).

θθ=⋅⋅ α θ − θ qAcon() g, m ( g m ) (3.10)

The convection coefficient (α) is independent of the material. The magnitude of the convection coefficient depends on the actual velocity of the air during the fire. EN 1991-1-2 [2] specifies values for this parameter depending on the nominal temperature-time curve applied. o In case of a standard temperature-time curve, α = 25 W/m2K; o In case of an external fire curve, α = 25 W/m2K; o In case of a hydrocarbon time curve, α = 50 W/m2K; o In case of a simplified, natural fire model, α = 35 W/m2K. The convection coefficients for the first three temperature-time curves were average values of measurements in fire furnaces (Twilt [107]). The convection coefficient of natural fires depends on the fire, and the value given is recommended in Twilt [107].

3.2.3 Radiation

Radiation carries heat through the emission and absorption of photons (electromagnetic radiation). The frequencies emitted are related to blackbody radiation. The heat flow by radiation of a blackbody (qrad) was determined by Stefan [101] and theoretically proved by Boltzmann [20], equation (3.11).

()=⋅⋅σ 4 −4 qradTT r, m A( T r T m ) (absolute temperatures Tr and Tm) (3.11)

In which the constant of Stefan Boltzmann (σ) is equal to 5,67 . 108 W/m2K4. The effective radiation temperature (Tr) depends on the type of fire. According to EN 1991-1-2 [2], the radiation temperature may be represented by the gas temperature T around that member, in case of fully fire-engulfed members. No guidance is given for other situations.

In case of a non-ideal radiation source, and a real member instead of a black body, the left hand side of equation (3.11) should be multiplied with the emissivity of the radiation source (εf) and the emissivity of the receiving member (εm).

()=⋅⋅⋅⋅−εεσ 4 4 qradTT r, m f m A( T r T m ) (absolute temperatures Tr and Tm) (3.12)

The emissivity of the member (εm) indicates the energy radiated by a real object relative to the energy radiated of a black body of the same temperature. It is closely related to reflectivity: the best reflecting surface being the poorest emitter. The member emissivity varies among different materials and is for real objects always smaller than 1,0.

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Concerning the radiation source, the emissivity of the flames of a fire (εf) depends on the type of combustible material (oil, gas or wood) and on the covering of the fire furnace or fire compartment (Twilt [107]). EN 1991-1-2 [2] specifies that εf is taken in general as 1,0.

EN 1991-1-2 [2] allows the radiation coefficient to be multiplied by a configuration factor (ksh), in order to be able to take a shadow effect into account. The configuration factor is specified at 1,0, unless the codes for materials at elevated temperature give specific data to account of position and shadow effects. The configuration factor specified in EN 1999-1-2 [7] is however taken into account for the total transmission coefficient (which is the sum of the radiation coefficient and the convection coefficient) instead of solely the radiation coefficient.

3.2.4 Simple calculation model for heating of members

Simple calculation models in the Eurocode for fire exposed steel structures EN 1993-1-2 [4] and the Eurocode for fire exposed aluminium structures EN 1999-1-2 [7] are based on solving equation (3.9) under the assumption of uniform temperature distribution over the cross-section of the member, i.e. assuming an infinitely large coefficient thermal conductivity (λ). Equation (3.9) then reduces to equation (3.1), with boundary conditions determined by convection and radiation:

dθ c⋅⋅ρθθVqm =(), + qTT(), (3.13) dt con g m rad r m

As the heat flow by conduction and convection depends on the temperature of the member (θ), the temperature increase of the member ∆T after a certain period ∆t is determined by incrementally solving equation (3.13). • The codes apply the heat flux ( h ) of a member, which is equal to the heat flow (q) divided by the surface (A). The expression applied in the codes is:

1 A •• ∆=θθθ⎛⎞() +() ∆ ≤ mshk ⎜⎟hhTTcon gm,, rad rm t (time step 5 sec) (3.14) cV⋅ ρ ⎝⎠

The incremental time step (∆t) is set to 5 seconds maximum in order not to diverge from the real solution. Equation (3.14) shows that the incremental temperature is directly related to the ratio between surface (A) and volume (V). This ratio is called the section factor.

In many cases, aluminium members will have to be insulated in order to meet the required fire resistance. In case of dry insulation materials, the heating rate of the aluminium member depends mainly on the ratio of the thermal conductivity of the insulation material (λp) and the thickness of the insulation layer (dp). EN 1999-1-2 [7] provides the equation (3.15) for heating of insulated aluminium members. This semi-empirical relation was proposed by Wickström [111] based on a research to insulated steel structures.

λθ ()/dA⎡⎤1 φ ∆=θθθθpm p p () − ∆−te()/10 −∆1 (time step ≤ 30 sec) ⋅+ρφ⎢⎥g m g cVal al ⎣⎦1/3 (3.15) c ⋅ ρ A With φ = p ppd and ∆θ ≥ 0 ⋅ ρ p cal al V

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Equation (3.15) may also be applied for insulation materials that release moist. The delay that occurs by releasing moist is, according to the Dutch code NEN 6072 [8], taken into account in the values for the specific heat of the insulation material (cp), to be determined in tests.

3.3 Relevant thermal properties of aluminium alloys

Aluminium structural components are non-combustible. The most important effect of a fire on aluminium structures is an increase in temperature. According to the equations in the previous paragraph, the temperature of a member as a function of the gas temperature depends on some material dependent parameters. These parameters are the specific heat, the density, the thermal conductivity and, in case of a member that is not protected, on the emissivity of the member surface. The values for these properties are given for aluminium and compared to steel in this paragraph.

The influence of the aluminium alloy and of the treatments is of minor importance for most thermal properties.

3.3.1 Melting temperature

The melting temperature of aluminium depends on the alloy and ranges from 660 ºC for 99,99 % pure aluminium to 500 ºC for some magnesium alloys. The melting temperature of most structural alloys ranges from 590 ºC to 650 ºC (TALAT [10]). The melting temperature of steel is approximately 1500 ºC. The strength of steel is negligible for temperatures exceeding 1200 ºC.

3.3.2 Density

The density (ρ) of aluminium varies only little with the temperature. The density of pure aluminium decreases from 2700 kg/m3 at room temperature to 2600 kg/m3 at 500 ºC (Kammer [51]). The density of aluminium alloys at room temperature ranges from 2650 to 2800 kg/m3 for most structural alloys (Kammer [51]). EN 1991-1-2 [2] specifies that the density of aluminium may be taken as 2700 kg/m3 independent of the temperature. This is approximately 1/3 of the density of steel.

3.3.3 Specific heat

In an overview of 17 alloys from different alloy series given in Kammer [51], the specific heat (c) varies from 860 to 900 J/kg K at a temperature of 20 ºC. For alloys in series 3xxx, 5xxx and 6xxx (25 in total), Davis [27] gives values ranging from 887 to 904 J/kg K. The variation of the specific heat between alloys is thus small. Kammer [51] also gives test results on the specific heat of pure aluminium at elevated temperature. Figure 3.4 gives the test results on pure aluminium, together with the values given in EN 1999-1-2 [7] for aluminium alloys. Lundberg [76], who gives the background to the values for the specific heat in the code, refers to the data in Kammer [51]. No data is however given for the specific heat of aluminium alloys at elevated temperature in Kammer [51].

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2000

1600

1200

c [J/kg K] [J/kg c 800 Kammer 400 EN 1999-1-2 0 0 200 400 600 Temperature [ºC]

Figure 3.4 – Specific heat for alloys specified by EN 1999-1-2 [7] and tests on pure aluminium (Kammer [51])

According to data in EN 1999-1-2 [7] and EN 1993-1-2 [4], the specific heat of aluminium is 2,1 times higher at room temperature and 1,7 times higher at 550 ºC than that of steel. Thus it requires more energy to heat a mass unit of aluminium than it is to heat the same mass of steel. However, heating of a member is related to the product of the specific heat times the density (c x ρ) (see equations (3.9), (3.14) and (3.15)). This product is called the thermal capacitance or volumetric heat capacity. The density of aluminium is approximately 1/3 of that of steel. As a result, the thermal capacitance of aluminium is lower than that of steel (Figure 3.5), meaning that it requires less energy to heat a volume unit of aluminium than to heat the same volume of steel.

6.0E+06

K] 4.0E+06 3 [J/m ρ

c x 2.0E+06 aluminium steel 0.0E+00 0 200 400 600 Temperature [ºC]

Figure 3.5 – Thermal capacitance (specific heat (c) times density (ρ)) of aluminium (EN 1999-1-2 [7]) and steel (EN 1993-1-2 [4])

3.3.4 Thermal conductivity

Tests are carried out to determine the thermal conductivity (λ) of aluminium. The conductivity is determined for many alloys at room temperature. Data is given e.g. in Kammer [51], Davis [27], Brandes [22], DiNenno 0 and Holman [46]. In Kammer [51], the thermal conductivity of pure aluminium is also given at elevated temperature (up to a temperature of 400 ºC) and for some

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alloys up to 100 ºC. Lundberg [76] gives references on which the data in EN 1999-1-2 [7] are based. These data are given in Figure 3.6. The figure shows that the thermal conductivity varies for various alloys. Data in Davis [27] shows that the thermal conductivity also depends on the temper. The data given for the thermal conductivity for soft annealed alloys (temper O) is in all

cases higher than the thermal conductivity for work hardened or precipitation hardened tempers of the same alloy.

300 Tests on pure 250 commercial alu K Tests on aluminium 200 alloys EC9, alu alloys 1xxx, 150 3xxx and 6xxx EC9, alu alloys 2xxx, 100 4xxx, 5xxx, 7xxx EC3, steel hermal conductivity [W/m 50 T

0 0 100 200 300 400 500 Temperature [ºC]

Figure 3.6 – Thermal conductivity measurements on pure aluminium and aluminium alloys and thermal conductivity of aluminium (EN 1999-1-2 [7]) and steel (EN 1993-1- 2 [4])

Figure 3.6 also gives the thermal conductivity for aluminium alloys according to EN 1999-1-2 [7] and that of steel according to EN 1993-1-2 [4]. Two relations are given between the thermal conductivity and the temperature for aluminium alloys, the series of the alloy considered determines which of these relations has to be applied. According to the codes, the thermal conductivity of aluminium is 2,7 up to 3,6 times higher than that of steel at 20 ºC, and 5,0 up to 6,0 times higher at 500 ºC.

In structures, usually relatively thin wall thicknesses are applied for aluminium components. Because of the high thermal conductivity in combination with thin wall thickness, usually a uniform temperature distribution over the cross-section of aluminium members is assumed. It is possible that the high thermal conductivity also leads to an elevated temperature in the part of the component or structure that is not directly exposed to fire.

The relations between thermal conductivity and temperature in EN 1999-1-2 [7] are an approximation of the real thermal conductivity of a specific alloy. However, the thermal conductivity is so large, that a uniform temperature distribution in the member occurs even for the highest heating rates during a fire. The exact value for the thermal conductivity is therefore less important.

3.3.5 Emissivity and reflection

Aluminium structures have to be insulated in most cases in order to meet fire safety requirements. In some cases however, only a part of the structure has to be insulated. The temperature of the

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non-insulated parts then depends, among others, on the emissivity of the member (εm) (equation (3.12)).

The emissivity of plain aluminium is relatively low. TALAT [10] mentions an emissivity that is lower than 10% of that of a black body at the same temperature with the same surroundings. Plain aluminium thus reflects about 90% of the heat radiation that falls on it. For old oxidised aluminium however, the reflection of heat radiation is lower. For polished aluminium the reflection can be up to 97%. At higher temperatures, the reflection of heat radiation decreases.

According to Kammer [51], the influence of alloying element on the emissivity coefficient is small. The test results of Table 3.1 and Table 3.2 are reported in this book. Holman [46] also carried out tests, presented in Table 3.3. In order to check these values in a fire situation, Twilt [106] carried out one test on aluminium and one test on steel. The coefficient of convective heat 2 transfer (αcon) was taken as 25 kW/m K in these tests. For aluminium, the emissivity coefficient resulting from the tests was equal to 0,06, for steel, the emissivity coefficient was 0,4. All test results are given in Lundberg [71].

Table 3.1 – Emissivity coefficient, depending on the temperature of the radiation source according to Kammer [51]

Temperature 10 ºC – 65 ºC 538 ºC Description new old new old Bright foil 0.03 0.05 0.05 0.10 Bright roof sheets 0.05 0.20 0.10 0.20 Bright rolled sheets 0.08 0.20 0.11 0.20

Table 3.2 – Emissivity coefficient, for various surface conditions according to Kammer [51]

Description Emissivity coefficient Highly polished 0.04 - 0.06 Bright rolled 0.05 - 0.07 Pickled 0.06 - 0.08

Table 3.3 – Emissivity coefficient, for various surface conditions according to Holman [46]

Surface description Emissivity coefficient Surface temperature Highly polished plate 0.039 - 0.057 226 – 576 ºC Commercial sheet 0.09 100 ºC Heavily oxidized 0.20 - 0.31 148 – 504 ºC Surfaced roofing 0.216 38 ºC

TALAT [10] provides a rule of thumb of 0.2 for the coefficient of emissivity of plain aluminium. The coefficient of emissivity of plain aluminium specified by EN 1999-1-2 [7] is 0,3. This value is low when compared to steel: EN 1993-1-2 [4] specifies a coefficient of emissivity of 0.7 for steel.

In case of real fires, however, the surfaces are almost always (partially) covered with sooth. For covered surfaces, the coefficient of emissivity is different compared to plain surfaces. EN 1999-1- 2 [7] specifies a coefficient of emissivity of 0.7 for covered (e.g. soothed, but also painted) aluminium surfaces. This coefficient is equal to the value given for covered steel surfaces.

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3.4 Evaluation of thermal properties

Especially the low density and the high thermal conductivity of aluminium result in relatively rapid heating of aluminium compared to steel. Figure 3.7 gives an example of the uniformly

distributed temperature of two sections with different section factors of aluminium compared to the heating rates of the same sections of steel. The gas temperature is according to the standard fire (ISO 834), specified in EN 1991-1-2 [2]. The uniformly distributed temperature in the structural elements is determined using the equations in EN 1999-1-2 [7], EN 1993-1-2 [4] and EN 1991-1-2 [2], with the assumption that the component surface is soothed. These equations correspond to equations (3.11) up to (3.14).

600

Tgas

θ alu.0.8 400 θ Heating of alu.2 square hollow θ sections tx50x50 steel.0.8 200 temperature [deg C] t = 0,8 mm (dashed) θ steel.2 t = 2,0 mm (continuous) aluminium (dark grey) steel (light grey) 0 02468 timet [min]

Figure 3.7 – Example of the uniform temperature of aluminium components compared to steel

It is shown that the heating rate of the aluminium sections is higher than that of steel sections with equal dimensions of the cross-section. Because of the thin wall thickness usually applied for aluminium components, the heating of aluminium components is even more rapid. This last aspect is thus an important design condition for the fire design of an aluminium structure.

The rapid heating of unprotected aluminium compared to the low melting temperature (both in reference to steel) cause aluminium to be sensitive to fire. Consequently, many aluminium structures need insulation in order to remain their load-bearing function during the required fire resistance time.

Considering the thermal properties of aluminium, the specific heat and the thermal conductivity are known for many alloys at room temperature, and in case of pure aluminium also at elevated temperature. The variation in specific heat is small for different alloys at room temperature. For the data in EN 1999-1-2 [7], it is assumed that this variation is also small at elevated temperature, so that the measured specific heat of pure aluminium at elevated temperature is also representative for aluminium alloys. The thermal conductivity varies between alloys. It is so high that a uniform temperature distribution in is to be expected in structural components engulfed in flame.

The coefficient of emissivity of plain aluminium depends on the condition (age) of the surface and on the temperature. The value of 0.3 for the coefficient of emissivity for plain aluminium specified

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by EN 1999-1-2 [7] seems conservative for most cases. However, as many structures need insulation so that the emissivity of plain aluminium is consequently not relevant. In case of unprotected members, the structural components inside the area on fire will be soothed. As the amount of sooth on the structural component during the fire is unpredictable, codes can only provide a global value for the emissivity.

Table 3.4 gives an overview of the relevant thermal properties. In this table, it is indicated whether the properties are known, or whether more research is necessary. In conclusion no further research to the thermal properties of aluminium alloys is necessary.

Table 3.4 – Overview of relevant thermal properties

Thermal property Status Remarks Melting temperature Known Density Known Specific heat Known Tests results at elevated temperature exist for pure aluminium. These results are assumed to be representative for aluminium alloys as well Thermal conductivity Partially known Only a few test results are available on alloys at (but irrelevant) elevated temperature. The exact value of the thermal conductivity is however irrelevant. Emissivity Known The exact emissivity of plain aluminium depends on age and surface

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4 Mechanical properties of aluminium alloys

The previous chapter discussed the temperatures of fire exposed aluminium structures. In the current chapter, the mechanical material behaviour due to these temperatures is discussed. The structural response of aluminium to elevated temperatures is triple: - Thermal expansion (paragraph 4.1); - Changes in the stress-strain relation (paragraph 4.2 up to 4.7); - Visco-plastic behaviour (creep) (4.8). Paragraph 4.9 gives the evaluation of the mechanical properties.

4.1 Thermal expansion

Thermal expansion leads to a change in the force distribution of statically undetermined structures. In case thermal expansion is restrained, high internal stresses in may occur. Where a temperature gradient across the cross-section is present in a component, unequal thermal expansion results, leading to non-uniform thermal stresses. At high external stress levels approaching the 0,2% proof stress, yielding of the material occurs and, while thermal deformations remain, thermal stresses flow off the material.

Davis [27] give average coefficients of linear thermal expansion (α) for temperatures between 20 and –50, 100, 200 or 300 ºC for various alloys. Kammer [51] gives the average coefficients of linear thermal expansion for temperatures between 20 and 100, 200 or 300 ºC for aluminium alloys and up to 500 ºC for pure commercial aluminium. The data show that the coefficient of linear thermal expansion is almost equal for different alloys. The same conclusion is made in TALAT [10]. The relative thermal elongation in EN 1999-1-2 [7] is based on the data for pure commercial aluminium in Kammer [51]. The data is given in Figure 4.1.

30 30

25 25 20 20 Values in Pure /K] /K]

-6 Aluminium -6 Aluminium 15 EN 1999-1-2 15 aluminium alloys (Davis) alloys (Kammer)

[x10 (Kammer) [x10

α 10 10 α Values in EN 1999-1-2 5 5

0 0 0 200 400 600 0 200 400 600 Temperature [oC] Temperature [oC]

Figure 4.1 – Coefficient of linear thermal expansion between 20 ºC and indicated temperature of tests and according to EN 1999-1-2 [7] (Data source: left-hand Davis [27], right-hand Kammer [51])

The relative thermal elongation of aluminium, specified by EN 1999-1-2 [7], and of steel, specified by EN 1993-1-2 [4] are compared in Figure 4.2.

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Relative thermal elongation 0.020

0.015

l/l aluminium

∆ 0.010 steel

0.005

0.000 0 200 400 600 800 1000 1200 o T ( C)

Figure 4.2 –Thermal elongation of aluminium (EN 1999-1-2 [7]) and of steel EN 1993-1-2 [4])

Thermal expansion of aluminium is approximately two times the thermal expansion of steel. On the other hand, the modulus of elasticity of aluminium is only one third of the modulus of elasticity of steel. Still, thermal expansion of aluminium may lead to significant changes in load and stress distributions and may cause plasticity even for low externally applied loads. As an example Eberwien [34] did numerical research on the behaviour of aluminium simple frames consisting of a beam supported by two columns. She concluded that thermal expansion of the beam results in a bending moment in the column, which amounts in some cases 40% of the bending capacity of the columns at elevated temperature.

4.2 Shape of the stress-strain relation

The stress-strain relation is in most cases determined in tensile tests. The stress-strain relations and values for the specific properties in the stress-strain relations are the engineering stresses and strains in tension.

4.2.1 Room temperature

A typical σ-ε diagram for an aluminium alloy is compared with that of mild steel in Figure 4.3.

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350

300

f0,2 = 250

] 200 2

150 [N/mm

σ 100 aluminium alloy (5083 H34) mild steel (S235) 50

0 0,2 % 0 0.005 0.01 0.015 0.02 0.025 0.03 ε [-]

Figure 4.3 – Typical σ-ε diagrams of mild steel and of aluminium alloys (after Galambos [42] and TALAT [10], with values according to EN 1993-1-1 [3] and EN 1999-1-1 [6])

Aluminium alloys applied in load-bearing structures do not have a clearly defined yield point as in case of mild steel. For engineering applications, usually the arbitrary chosen value of the 0,2% proof stress is applied as the border between linear-elastic material behaviour and non-linear behaviour. This 0,2% proof stress is the stress at a permanent strain of 0,2 % of the original specimen length. The Eurocode for aluminium structures, EN 1999-1-1 [6] applies the 0,2% proof stress in verification rules for members. Apart from the 0,2% proof stress (f0,2), other typical properties of the σ-ε diagram are the modulus of elasticity (E), proportional limit (fp), 0,1% proof stress (f0,1), tensile strength (fu), strain at tensile strength, also called the homogeneous strain (εb) and strain at rupture, also called the ultimate strain (A50). As shown in Figure 4.4, these properties vary widely per alloy. The characteristic value of some of these properties given in EN 1999-1-1 [6] of some alloys widely applied in structures in Europe is given in Table 4.1. The values given here are minimum guaranteed values, the actual properties for f0,2 and fu are normally larger than these values.

σ (N/mm2)

ε (%)

Figure 4.4 – Engineering stress strain curves of some alloys (source Soetens and Van Hove [95])

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Table 4.1 – f0,2 and fu of some alloys according to EN 1999-1-1 [6]

2 2 Alloy f0,2 [N/mm ] fu [N/mm ] f0,2/fu [- A50 [%] ]

3005 H26 160 195 0,82 3 5052 H34 150 230 0,65 4 5083 O 125 275 0,45 11 5083 H34 250 340 0,74 4 6063 T6 190 220 0,86 10 6082 T6 260 310 0,84 8 7020 T6 280 350 0,80 7

The Ramberg-Osgood law is often applied in to model the stress-strain relation for design purposes (equation (4.1)). According to this law, the strain (ε) at any point in the stress-strain relation is equal to the elastic strain, equal to the stress (σ) divided by the modulus of elasticity (E), and the plastic strain. The plastic strain is modelled as a function of the strain at the yield stress (ε0 = 0,002 in case of aluminium), the ratio between stress level (σ) and the yield stress (fε0 = f0,2 in case of aluminium), and the hardening factor (n), expressing the strain hardening of the alloy. Large values of n indicate small strain hardening, while small values indicate large strain hardening. The factor n thus depends on the alloy and treatment and is determined by evaluation of f0,1 and f0,2 in equation (4.1). The strain hardening factor can thus be determined according to equation (4.2). EN 1999-1-1 [6] gives the strain hardening factor for each alloy and temper indicated. For more information on the Ramberg-Osgood law, see Mazzolani [78].

n σσ⎛⎞ εε=+ 0 ⎜⎟ (4.1) Ef⎜⎟ε ⎝⎠0 ln2 n = (4.2) ⎛⎞f0,2 ln ⎜⎟ ⎝⎠f0,1

4.2.2 Elevated temperature

At elevated temperature, the shape of the stress-strain relation changes. As an example, Figure 4.5 up to Figure 4.8 give the engineering stress-strain relation of the heat treatable alloy 6082 in tempers T4 and T6 at room temperature and at 250 ºC, resulting from tensile tests carried out by Eberg et al. [35]. The left graph shows the entire σ-ε diagram and the right graph gives the detail concerning the 0,2% proof stress. Note that the scales of the axes are not equal for the graphs presented. Figure 4.9 gives the stress-strain relation at various temperatures of the non-heat treatable alloy 5457 in temper O.

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AA6082 T4, 25 ºC

Figure 4.5 – σ-ε diagram of alloy 6082 T4 at 25 ºC (Source: Eberg et. al. [35])

AA6082 T4, 250 ºC

Figure 4.6 – σ-ε diagram of alloy 6082 T4 at 250 ºC (Source: Eberg et. al. [35])

AA6082 T6, 25 ºC

Figure 4.7 – σ-ε diagram of alloy 6082 T6 at 25 ºC (Source: Eberg et. al. [35])

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AA6082 T6, 250 ºC

Figure 4.8 – σ-ε diagram of alloy 6082 T6 at 250 ºC (Source: Eberg et. al. [35])

Figure 4.9 – Stress-strain relation of alloy 5754 O at various temperatures for a strain rate of 0,002 /sec (source: Van den Boogaard [21])

According to the figures and to tabulated values of the f0,2 and fu, strain hardening decreases at elevated temperature, i.e. the difference between the ultimate tensile strength and the 0,2 % proof stress decrease at increasing temperature. Also the homogeneous strain (εb) decreases at elevated temperature. Reliable data on the proportional limit at elevated temperature were not found in literature, so it is not known whether or not the ratio fp / f0,2 changes at elevated temperature. Mild steel shows an elastic-plastic behaviour at room temperature, and an inelastic behaviour at elevated temperature, in which case the proportional limit is lower than the yield stress (2 % proof stress). This is shown for example in the tensile tests in Thor [104]. In case of most aluminium alloys and tempers, the homogeneous strain decreases while the ultimate strain increases.

The stress-strain relations depend on the strain rate with which the tensile test is carried out. This effect is so small that it is neglected at room temperature, but becomes important at elevated temperature. More information on the strain rate dependency is given in paragraph 4.8.1.

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All tensile tests at elevated temperature found in literature were steady state tests, in which deformation was applied and increased until rupture occurred, while the temperature was kept constant at a certain elevated level. The exposure period at elevated temperature before the tensile test was carried out varied in the tests. Transient state tests, in which the load remains constant while the temperature is increased from ambient temperature to critical temperature, are closer to the actual load situation of most structures when exposed to fire.

The steady state tests at elevated temperature are usually carried out after a certain thermal exposure period, i.e. a period at constant elevated temperature before the load is applied (Figure 4.10).

heating loading

Thermal exposure period Load

Temperature = beginning of loading = failure

Time Time

Figure 4.10 – Procedure applied in steady state tests (left-hand heating, right-hand loading)

Steady state tensile tests on various alloys with various exposure times varying from 15 minutes to 10.000 hours were reported by Voorhees and Freeman [110] and Kaufman [55]. The data in Voorhees and Freeman [110] origin from several laboratories. One of the two major data sources referred to applied a strain rate of 0,005/min up to yielding and 0,10/min up to rupture. The other source applied a stress of 0,575 N/mm2sec up to yielding and a deformation of 0,05/min up to rupture. The strain rate in the tests on which the data in Kaufman [55] are based was maintained at about 0,005 / min up to yielding. The rate was subsequently increased to a crosshead motion of about 0,05 / min. The alloys incorporated in these reports are limited to those frequently applied in the USA. Tensile tests on alloy 6082, which is applied in many structures in Europe, are reported in Hepples and Wale [45] (crosshead displacement rate 4,02 mm/min), Broli and Mollersen [23], Amdahl et al. [14] (testing rate not mentionned), Kleive and Gustavsen [56] (2,4 mm/min), Langhelle [62] (2 mm/min or 5 mm/min), Bergli and Moe [17] (testing rate not mentionned), Krokeide [59] (2 mm/min up to yielding, 6 mm/min up to rupture) and Kaspersen and Sørås [54] (2 mm/min up to yielding, 4 or 5 mm/min up to rupture).

Kaufman [55] gives the most extensive overview of tensile test and creep test results at elevated temperature. It is noted that Kaufman [55] gives the average value of tests instead of individual test results. Each of the values results from analysis of many test results for specimens of the respective alloy and temper. It is not mentioned on how many tests one value is based. Some of the values given by Kaufman [55] are based on Voorhees and Freeman [110], so that these two sources cannot be regarded as independent.

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Average values of tensile tests are also provided in Davis [27]. However in case of alloys for which the thermal exposure period influences the mechanical properties, Davis [27] gives minimum values for thermal exposure periods up to 10.000 hours. These data are not relevant for

fire exposed structures. Considering the good correspondence between the data in Kaufman [55] and Davis [27], it is likely that the same database of tensile tests has been used to derive average values. The data given in Davis [27] are therefore not referred to in this chapter.

Some important typical properties of the stress-strain relations of the documented tests given above are elaborated in the following paragraphs. This concerns the 0,2 % proof stress (f0,2), the tensile strength (fu), the modulus of elasticity (E) and the strain at rupture (A50). No information was found about the proportional limit (fp), the 0,1 % proof stress (f0,1) and the strain at the tensile strength (εb), so these properties are not discussed here. The PhD research focuses on alloys 5083, 6063 and 6082 (paragraph 2.2). Therefore, in discussing the properties, first a general overview of the alloys is given, and then special attention is paid to alloys 5083, 6063 and 6082.

4.3 0,2% proof stress

The 0,2% proof stress is applied in the Eurocodes for aluminium structures in the verification rules for members. It is therefore one of the most important characteristics of the stress-strain relations.

4.3.1 Room temperature

The 0,2 % proof stress varies widely among alloys and tempers. In general, alloys in the 3xxx series, and some in the 5xxx series, have relatively low strength. Most alloys in the 5xxx series have medium strength, provided that they are hardened to some extend. Alloys in the 6xxx series also have medium strength, provided that they are heat-treated. The highest strengths are achieved for alloys in the 7xxx and the 2xxx in heat treated condition(TALAT [10]). As an example of this, Figure 4.11 gives characteristic values of the 0,2% proof stress of various alloys, grouped by alloy series. Each dot represents a certain combination of alloy and temper. The values given originate from Kaufman [55]. Figure 4.12 gives characteristic values of the heat-treatable alloys from Figure 4.11, grouped by temper. Figure 4.13 gives these values for non-heat treatable alloys. It is shown that alloys in the annealed condition have an 0,2 % proof stress that is considerably lower than when hardened or heat-treated and that the 0,2 % proof stress increases as more work is done.

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0,2% proof stress, 24 oC 700

600

500 ] 2 400 series 2xxx [N/mm 300 0,2 series 3xxx f series 4xxx 200 series 5xxx series 6xxx 100 series 7xxx

0 2xxx 3xxx 5xxx 6xxx 7xxx Alloy series

Figure 4.11 – Characteristic values for the 0,2 % proof stress for alloy series (data source: Kaufman [55])

0,2 % proof stress, heat treatable alloys, 24 oC 700

600 O 500 T1 T3, T36, T37 ] 2 400 T4, T451 T5, T53, T5311 [N/mm 300 0,2

f T6, T6x, T6xx T7, T7x, T7xx 200 T8, T8x, T8xx T9 100

0 OT1T3T4T5 T6 T7 T8T9 Temper

Figure 4.12 – Characteristic values for the 0,2 % proof stress for heat treatable alloys (data source: Kaufman [55])

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0,2 % proof stress, non-heat treatable alloys, 24 oC 400

350

300 O

] 250 Hx1 2 H12, H32, H323 200 H14, H34, H343 [N/mm 0,2 f 150 H25 H18, H38 100 H19

50

0 O Hx1 Hx2 Hx4 Hx5Hx8 Hx9 Temper

Figure 4.13 – Characteristic values for the 0,2 % proof stress for non-heat treatable alloys (data source: Kaufman [55])

4.3.2 Elevated temperature

The 0,2 % proof stress of aluminium at elevated temperature depends on the temperature, on the alloy and treatment and, for some treatments, on the time of exposure at elevated temperature. Figure 4.14 gives the relative value of the 0,2% proof stress, f0,2,θ / f0,2, as a function of the temperature for different alloys and tempers, resulting from the tensile tests results given in Voorhees and Freeman [110], after a thermal exposure period of 30 minutes. It is shown that the relative value for the 0,2% proof stress varies significantly per alloy and temper. In general, the largest reduction in the 0,2 % proof stress occurs between 100 ºC and 350 ºC.

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2014 T6 1.2 3003 O 3003 H14 1 3003 H18 5052 O 0.8 5052 H34 [-]

0,2 5052 H38 0.6 / f

θ 5083 O 0,2, f 5083 H113 0.4 5086 O 5086 H34 0.2 5454 O 5454 H32 0 0 100 200 300 400 500 6061 T6 6063 T6 Temperature [oC] 7075 T6

Figure 4.14 – 0,2% proof stress resulting from tests for various alloys and tempers after an exposure period of 30 minutes (data source: Voorhees and Freeman [110])

Kaufman [55] documented tensile test results of 158 different alloys and tempers at various elevated temperatures. For each of the alloys and tempers listed, the ratio between the 0,2 % proof stress at elevated temperature and the 0,2 % proof stress at room temperature is determined. The average value of these ratios for all alloys and tempers are given in Figure 4.15. Values are shown for a thermal exposure period of 6, 30 and 600 minutes. The standard deviation of the relative value of the 0,2 % proof stress for a thermal exposure period of 30 minutes is also shown in the figure. The variation in the relative value of the 0,2 % proof stress between different alloys and tempers is large even for moderately elevated temperatures.

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1.20

1.00 t = 6 min

0.80 t = 30 min [-]

0,2 t = 600 min 0.60 / f θ 0,2,

f 0.40

0.20

0.00 0 100 200 300 400 500 600 Temperature [ºC]

Figure 4.15 – Relative value of the 0,2 % proof stress of all alloys listed in Kaufman [55]

The influence of temperature on the strength of alloys is discussed in detail in the following paragraphs, separately for non-heat treatable and heat-treatable alloys.

Non-heat treatable alloys The test results show that at room temperature, the strength of an alloy in cold worked condition is higher than the strength of the same alloy in annealed condition. At elevated temperature, this difference in strength gradually vanishes. This is caused by the fact that the favourable matrix obtained through cold working is destroyed above the recrystallisation temperature, so that the alloy is in annealed temper. Below the recrystallisation temperature, recovery already starts, causing the dislocation density to decrease as the dislocations rearrange to a configuration of minimum energy (Verdier et al. [109]). In some cases, for example for alloy 5083, the strength of the cold worked alloy at a certain temperature may even be (slightly) lower than the strength of the alloy in annealed condition at the same temperature (Figure 4.16). The reason for this is unknown.

300

250 5083 O

] 200 2 5083 H113 150 [N/mm θ 0,2, f 100

50

0 0 100 200 300 400 500 600 Temperature [oC]

Figure 4.16 – Tensile test results - 0,2% proof stress of alloy 5083 in different tempers (data source: Voorhees and Freeman [110])

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Recrystallisation and recovery require time. It is therefore expected that the strength at elevated temperature of work-hardened non-heat treatable alloys depends on the thermal exposure period. However, the tensile tests results tabulated by Voorhees and Freeman [110] and by Kaufman [55] show that the thermal exposure period does not significantly influence the 0,2% proof stress for non-heat treatable alloys for the studied thermal exposure period of 0,1 up to 10.000 hours. Exceptions are alloys 5005 and 5050, for which a thermal exposure period of 600 minutes gave a slightly lower value for the 0,2 % proof stress than a thermal exposure period of 30 minutes. Engstrom and Sandstrom [37] came to the same conclusion.

Langhelle and Eberg [63] however found an influence of the thermal exposure period on the 0,2 % proof stress of alloy 5083 H34. They carried out tensile tests on alloys 5754 H34 and 5083 H34 at test temperatures of 200 and 225 ºC with the following thermal exposure periods: ƒ Heating from room temperature to the temperature at which the tension test was carried out (referred to as test temperature) in 20 minutes. The tensile tests were carried out directly after this test temperature was reached (indicated in Figure 4.17 with ‘20 min’). ƒ Heating from room temperature to test temperature took place in 60 minutes. The tensile test were carried out directly after the test temperature was reached (60 min). ƒ Heating from room temperature to test temperature took place in 60 minutes. The tensile test was carried out 60 minutes after the test temperature was reached (60+60 min). The 0,2% proof stresses are given in Figure 4.17. (Note: the scales of the vertical axes in this figure are not equal).

AA 5083 H34 AA 5754 H34 250 180 ] ] 160 2 2 200 140 120 150 100 80 100 60 20 min 20 min 50 60 min 40 60 min 0,2% proof stress [N/mm 0,2% proof stress 60+60 min 0,2% [N/mm proof stress 20 60+60 min 0 0 200 225 200 225 o o Temperature [ C] Temperature [ C]

Figure 4.17 – 0,2% proof stress for alloys AA 5754 H34 and AA 5083 H34 determined after various thermal exposure periods

A physical explanation is not available for the fact that alloy 5083 H34, tested at 225 ºC with heating schedule 60 + 60 minutes, gives an 0,2 % proof stress that is higher than the 0,2 % proof stress of the test with a heating schedule of 60 minutes. The amount of tests results with different thermal exposure periods is too little for a general conclusion on the influence of the thermal exposure period on the strength of alloy 5083 H34. The data in Kaufman [55] and in Voorhees and Freeman [110] shows no influence of the thermal exposure period of alloy 5083 in other tempers (O, H113 and H321).

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Heat-treatable alloys The reaction of heat-treatable alloys strongly depends on the temper. Tests show that the strength of artificially aged alloys (tempers T5-T8) decreases at increasing temperature. However, the strength of naturally aged alloys (tempers T1-T4) increases at moderately elevated temperatures, whereas the strength decreases at higher temperatures (Figure 4.18 and Figure 4.19). This may be explained by artificial ageing, i.e. the ageing process speeds up at moderately elevated temperature. The turning point from increase to decrease in strength in the tests reported occurs at a temperature of approximately 200 ºC for a thermal exposure period of 0,5 and 1,0 hour. From this point, the strength of the naturally aged alloy approaches that of the same alloy in artificially aged temper. In case of some other alloys, the strength of the alloy in naturally aged temper first decreases slightly (up to a temperature of approximately 150 ºC), subsequently increases (up to a temperature of approximately 200 ºC) and then decreases again. An example of this is shown in Figure 4.20 for alloy 6082 in tempers T1 and T6 after a thermal exposure period of 20 minutes. 250

200 6063 T1 6063 T6 ] 2 150 [N/mm θ 100 0,2, f

50

0 0 100 200 300 400 500 600 Temperature [oC]

Figure 4.18 – 0,2% proof stress of alloy 6063 in various tempers after a thermal exposure period of 30 min (data source: Voorhees and Freeman [110])

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6063-O Extrusions 6063 0,2% proof stress 6063-T1 Extrusions 250 6063-T5 Extruded rod 6063-T6

6063-T6 Extrusions 200 ] 2 150 [N/mm θ 100 0,2, f

50

0 0 100 200 300 400 500 600 Temperature [oC]

Figure 4.19 –0,2 % proof stress of alloy 6063 in various tempers after a thermal exposure period of 30 min (data source: Kaufman [55])

350 300 6082 T6 250 ] 2 6082 T4 200 [N/mm

θ 150 0,2, f 100 50

0 0 100 200 300 400 500 600

Temperature [oC]

Figure 4.20 – f0,2,θ for alloy 6082 in tempers T4 and T6 (Eberg et al. [35] and Langhelle [62])

The test data shows that at higher temperatures, the strength difference between an alloy in a heat- treated temper and the same alloy in annealed condition vanishes at certain elevated temperature. A reasonable explanation is as follows: when a solution heat-treated alloy is exposed to an elevated temperature, a larger percentage of alloying elements can be dissolved in aluminium, so that the supersaturated stage gradually changes into the annealed stage and the extra strength obtained through solution heat-treatment gradually vanishes. In general, alloys in these tempers show the largest reduction of the strength at elevated temperature.

Cold working increases the strength at room temperature. However, as in case of non-heat treatable alloys, the strength of cold worked heat-treated alloys (e.g. temper T8) is lower than the

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strength of alloys without cold working (e.g. temper T6) at certain elevated temperature, see Figure 4.21. The reason for this is not known.

6061-T6 -T651 -T6511 6061 0,2% proof stress 6061-T8 350

300

250 ] 2 200 [N/mm

θ 150 0,2, f 100

50

0 0 100 200 300 400 500 600 Temperature [ºC]

Figure 4.21 – 0,2 % proof stress of alloy 6061 in tempers T6 and T8 after a thermal exposure period of 30 min (data source: Kaufman [55])

The formation and destroy of precipitate particles requires time. Test results show that the strength of heat-treated alloys indeed depends on the thermal exposure period. This is shown in Figure 4.22 for alloy 6063 T6 and in Figure 4.23 for alloy 6082 T6. (Heat treatable alloys in temper O experience no influence of the thermal exposure period.)

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6063-T6 Extrusions, 0,2% proof stress 250

200 ]

2 6 min 150 30 min

[N/mm 600 min θ 0,2,

f 100

50

0 0 100 200 300 400 500 600 Temperature [ºC]

Figure 4.22 – 0,2% proof stress of alloy 6063-T6 after thermal exposure periods of 6 min, 30 min and 600 min (data source: Kaufman [55])

Hepples and Wale [45] carried out tensile tests on alloy AA 6082 T6 after various thermal exposure periods. The specimens were brought at test temperature with a heating rate of 0,33 ºC/s (19,8 ºC/min). Three test series were carried out: the load was applied directly after the test temperature was achieved and after holding times of 60 minutes and 120 minutes. Results are given in Figure 4.23.

6082-T6, 0,2 % proof stress 350

300

250

] 0 min 2 200 60 min

[N/mm 120 min θ 150 0,2, f 100

50

0 0 100 200 300 400 500 600 Temperature [ºC]

Figure 4.23 – 0,2 % proof stress for alloy AA6082 T6 after various thermal exposure periods [38]

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Values for the 0,2 % proof stress in EN 1999-1-2 [7] EN 1999-1-2 [7] provides the ratio between the 0,2% proof stress at elevated temperature and the 0,2 % proof stress at room temperature of some alloys and tempers, which can be used for heating periods up to two hours. The data provided are not differentiated to the thermal exposure period.

According to Lundberg [67], the data provided in EN 1999-1-2 [7] for all alloys except for 6082 are based on the tensile tests reported in Voorhees and Freeman [110] and Engstrom and Sandstrom [37]. The thermal exposure periods at constant temperature in Voorhees and Freeman [110] are 30 minutes, 60 minutes or 600 minutes and more. In order to make the data applicable for 2 hours, Engstrom and Sandstrom [37] reinterpreted the tests described by Voorhees and Freeman [110]. They applied a time-temperature parameter in order to be able to use the data of tests after various exposure periods for generating data at an exposure period of 2 hours. The time- dependent parameter used is described by Sandström and Widestig [93]:

=+() PLM TtClog (4.3)

In which PLM is the Larson-Miller time-temperature parameter. The 0,2 % proof stress after 2 hours should be divided by this factor to obtain the 0,2 % proof stress after t hours. C is an alloy- and temper-dependent constant, chosen such that the stress values of all tests fall on the same master curve. The data in the code are set equal to data resulting from Engström and Sandström [37].

The values for alloy 6082 in EN 1999-1-2 [7] are based on Hepples and Wale [45] (who applied a time of 0, 60 and 120 minutes at constant elevated temperature prior to testing), Broli and Mollersen [23] (no information documented on the thermal exposure period), Amdahl et al. [14] (exposure period of 20 minutes), Kleive and Gustavsen [56] (heating in 1,5 hour, subsequently 30 minutes at constant elevated temperature before testing), Langhelle [62] (exposure period of 20 minutes) and Bergli and Moe [17] (heating in 20 to 45 minutes, subsequently 30 minutes at constant elevated temperature before testing).

The relative value of the 0,2% proof stress in EN 1999-1-2 [7] is only provided for a limited number of all alloys and tempers listed in EN 1999-1-1 [6]. This is due to lack of data for the other alloys at elevated temperatures. However, Kaufman [55] gives data for some of these other alloys. This data base has not yet been applied as a source for the values in EN 1999-1-2 [7]. The code also gives the relative value of the 0,2% proof stress of some alloys and tempers that are not listed in EN 1999-1-1 [6].

The relative value of the 0,2 % proof stress at a temperature of 100 ºC is 1,0 for all alloys and tempers. However, tests reported by Kaufman [55] show that especially for heat treatable alloys with temper T6, a significant reduction of the 0,2% proof stress already occurs at this temperature.

According to Lundberg [67], the data for alloy AA5083 in temper H113 in the EN 1999-1-2 [7] are based on tensile tests data in Voorhees and Freeman [110]. However, the data in the code differ considerably from those in Voorhees and Freeman [110]. The reason for this is not known.

In Figure 4.24, the maximum and minimum relative value of the 0,2% proof stress of the various aluminium alloys listed in EN 1999-1-2 [7] is compared with the relative value of the yield strength and the proportional limit of steel, as given in EN 1993-1-2 [4]. It is shown that the 0,2% proof stress of aluminium reduces faster than the yield strength of mild steel. It should be noted though that the yield strength of mild steel is traditionally determined as the strength at a total

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strain of 2,0 %. The 0,2 % proof stress of mild steel is in between the curve for the proportional limit and the yield strength.

1.20

1.00 [-] alu, fo ,st ⎯ steel, fy y, 0.80 steel, fp alu, fo

andk 0.60 ,st ⎯ p,

, k 0.40 ,alu ⎯ o,

k 0.20

0.00 0 200 400 600 800 1000 1200 T [oC]

Figure 4.24 – Relative value of the 0,2% proof stress aluminium (EN 1999-1-2 [7]) compared to relative value of the yield stress and the proportional limit of steel (EN 1993- 1-2 [4])

4.4 Ultimate tensile strength

EN 1999-1-2 [7] applies the 0,2 % proof stress for most checks. The ultimate tensile strength is applied in EN 1999-1-2 [7] in case of checks on connections. Further, maximum values on the ratio between f0,2 and fu are set in order to obtain enough redundancy of the structure.

4.4.1 Room temperature

In general, the same conclusions as drawn for the 0,2 % proof stress are valid for the tensile strength. Characteristic ultimate tensile strengths for the distinguished series of alloys are given in Table 4.2.

Table 4.2 – Typical ultimate tensile strengths of different alloy series (Kaufman [55])

Alloy series Range of ultimate tensile strength [N/mm2] 1xxx 70 to 185 2xxx 185 to 425 3xxx 110 to 285 4xxx 170 to 380 5xxx 125 to 350 6xxx 125 to 400 7xxx 220 to 605 8xxx 113 to 240

The ratio between 0,2% proof stress and tensile strength also depends on alloy and temper. In general, this ratio is lower for alloys with less treatment. In case of non-heat treatable alloys, this

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ratio varies from approximately 0,4 for soft to 0,9 for the hardest tempers. In case of heat treatable alloys, this ratio is approximately 0,85 for fully heat-treated alloys (TALAT [10]). Figure 4.25 gives the ratio between the 0,2% proof stress and the tensile strength according to data in Kaufman [55] for heat treatable alloys in various tempers. Figure 4.26 gives this ratio for non- heat treatable alloys in various tempers. In both figures, each dot represents a certain combination of alloy and temper.

0,2 % proof stress / tensile strength, heat treatable alloys, 24 oC 1.00 0.90 0.80 O 0.70 T1 T3, T36, T37 0.60 T4, T451 [-] u

/ f 0.50 T5, T53, T5311 0,2 f 0.40 T6, T6x, T6xx T7, T7x, T7xx 0.30 T8, T8x, T8xx 0.20 T9 0.10 0.00 OT1T3T4T5 T6 T7 T8T9 Temper

Figure 4.25 – Ratio between 0,2 % proof stress and tensile strength for heat treatable alloys in various tempers at room temperature (data source: Kaufman [55])

0,2 % proof stress / tensile strength, non-heat treatable alloys, 24 oC 1.00 0.90 0.80 O 0.70 Hx1 0.60 H12, H32, H323 [-] u H14, H34, H343

/ f 0.50

0,2 H25 f 0.40 H18, H38 0.30 H19 0.20 0.10 0.00 O Hx1 Hx2 Hx4 Hx5Hx8 Hx9 Temper

Figure 4.26 – Ratio between 0,2 % proof stress and tensile strength for non-heat treatable alloys in various tempers at room temperature (data source: Kaufman [55])

The strength in compression and in bending is approximately equal to the tensile strength (Kammer [51]).

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4.4.2 Elevated temperature

In general, the conclusions drawn for the 0,2 % proof stress at elevated temperature are also valid

for the ultimate tensile strength at elevated temperature. In the following paragraph, the tensile strength of various alloys and tempers relative to the value at room temperature are given. The paragraph hereafter gives the ratio between the 0,2 % proof stress and the tensile strength at elevated temperature.

Relative values for the tensile strength Figure 4.27 gives the ratio between the tensile strength at a certain elevated temperature and the tensile strength at room temperature resulting from tests published by Kaufman [55]. Different background colours indicate different alloy series. The dot series represent the test temperature. The figure shows that the major part of the reduction in strength occurs for a temperature between approximately 100 and 350 ºC. It also shows that the strength reduction of alloys in 7xxx series occurs on average at lower temperatures than alloys in other series. The scatter in relative strength is larger in case of alloys in the 2000 and 6000 series than in case of other alloys. At a temperature of 100 ºC, the relative tensile strength of non-heat treatable alloys (alloys in series 3xxx and 5xxx) is larger than in case of non-heat treatable alloys. As the scatter in relative strength increases at increasing temperature, this is less evident at temperatures higher than 100 ºC.

1.20

1.00

0.80 100 deg C [-] u 204 deg C 0.60 / f

u, 316 deg C f 371 deg C 0.40 538 deg C

0.20

0.00 2xxx 3xxx 5xxx 6xxx 7xxx Alloy series

Figure 4.27 – Relative value for the tensile strength for various alloys after a thermal exposure period of 30 min (data source: Kaufman [55])

As an example of the influence of the thermal exposure period, Figure 4.28 gives the tensile strength after 6 and 600 minutes relative to the tensile strength after 30 minutes at a temperature of 316 ºC. In case of series 3xxx and 5xxx, the tensile stress after a thermal exposure period of 6 or 600 minutes is equal to the tensile stress after a thermal exposure period of 30 minutes (value of 1,00 in Figure 4.28). This indicates that, as concluded for the 0,2 % proof stress, the thermal

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exposure period has no influence on the tensile strength in case of non-heat treatable alloys. Figures of the tensile test results at other temperatures show the same independence for non-heat treatable alloys, and dependence for heat treatable alloys. At temperatures of approximately 200 ºC, alloys in series 7xxx show the largest dependency on thermal exposure period. This changes at a temperature of approximately 300 ºC; the thermal exposure period has most influence for series 2xxx and 6xxx in case of temperatures exceeding 300 ºC.

316 ºC 1.40

1.20

1.00 [-] 0.80 u, ,30 min ,30 u,

/ f 0.60

u, ,x min 6 min / 30 min f 0.40 600 min / 30 min

0.20

0.00 2xxx 3xxx 5xxx 6xxx 7xxx Alloy series

Figure 4.28 – Relative value for the tensile strength for various alloys after various thermal exposure period at a temperature of 316 ºC (data source: Kaufman [55])

For each of the alloys and tempers listed in Kaufman [55], the ratio between the ultimate tensile strength at elevated temperature and the tensile strength at room temperature. The average value of these ratios for all alloys and tempers are given in Figure 4.29. Values are shown for a thermal exposure period of 6, 30 and 600 minutes. The standard deviation of the relative value of the tensile strength for a thermal exposure period of 30 minutes is also shown in the figure. The standard deviation is smaller as in case of the 0,2 % proof stress. This may be due to the fact that the scatter in 0,2 % proof stress between different alloys and tempers at room temperature is larger than the scatter in ultimate tensile stress, but it may also be caused by the fact that it is difficult to accurately measure the 0,2 % proof stress at elevated temperature.

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1.20

1.00 t = 6 min

0.80 t = 30 min

[-] t = 600 min u 0.60 /f u,q f 0.40

0.20

0.00 0 100 200 300 400 500 600 Temperature [ºC]

Figure 4.29 - Relative value of the ultimate tensile strength of all alloys listed in Kaufman [55]

Ratio between 0,2 % proof stress and tensile strength According to the tensile tests reported in Kaufman [55], Voorhees and Freeman [110], Langhelle [62]and Van den Boogaard [21], the absolute value of the difference between the 0,2 % proof stress and the tensile strength for most alloys and tempers decreases at increasing temperature. This is shown in Figure 4.30 for alloy 5083 and in Figure 4.31 and Figure 4.32 for alloy 6063.

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5083-O 5083-H113 400 400 tensile strength (K) tensile strength (VF) 350 tensile strength (VF) 350 0,2% pr str (VF)

0,2% pr str (K) 300 300 ] ] 2 2 0,2% pr str (VF) 250 250 [N/mm [N/mm θ θ 200 200 0,2, 0,2, and f and f 150 150 θ θ u, u, f f 100 100

50 50

0 0 0 200 400 600 0 200 400 600 Temperature [oC] Temperature [oC]

5083-H321 400 tensile strength (K) 350 0,2% pr str (K)

300 ] 2 250 [N/mm θ 200 0,2,

150 and f θ u, f 100

50

0 0 200 400 600 Temperature [oC]

Figure 4.30 – 0,2 % proof stress and tensile strength of alloy 5083 in tempers O, H321 and H113 after a thermal exposure period of 30 min (data source: K = Kaufman [55] and VF = Voorhees and Freeman [110])

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6063-O Extrusions 6063-T1 Extrusions 250 250

tensile strength (K) 200 200 tensile strength (K) 0,2% proof stress (K) tensile strength (VF)

] ] 0,2 % pr str (K) 2 2 0,2 % pr str (VF) 150 150 [N/mm [N/mm θ θ 0,2, 0,2, 100 100 and f and f θ θ u, u, f f

50 50

0 0 0 200 400 600 0 200 400 600 Temperature [oC] Temperature [oC]

6063-T5 Extruded rod 6063-T6 250 250 tensile strength (K) tensile strength (K) tensile strength (VF) 0,2% pr str (K) 200 0,2% pr str (K) 200 0,2% pr str (VF) ] ] 2 2

150 150 [N/mm [N/mm θ θ 0,2, 0,2, 100 100 and f and f θ θ u, u, f f

50 50

0 0 0 200 400 600 0 200 400 600 Temperature [ºC] Temperature [oC]

Figure 4.31 – 0,2 % proof stress and tensile strength of alloy 6063 in tempers O, T1, T42 and T6 after a thermal exposure period of 30 min (data source: K = Kaufman [55] and VF = Voorhees and Freeman [110])

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σ [N/mm2] ε [%] 6063 T6

Figure 4.32 – 0,2 % proof stress, tensile strength and strain at rupture of alloy 6063 T6 after a thermal exposure period of 30 min (Source: Aluminium Konstruksjons och materiallaera [13])

Figure 4.33 gives the proof stress and the tensile strength of tests carried out in Norway on alloy 6082 in tempers T4 and T6. The tests are documented in Hepples and Wale [45], Broli and Mollersen [23], Amdahl et al. [14], Kleive and Gustavsen [56], Langhelle [62] and Bergli and Moe [17].

In case of temper T6 at elevated temperature, and also for temper T4 at temperatures exceeding 225 ºC, the 0,2% proof stress coincides with the tensile strength. This does not correspond to the general behaviour of the alloys tested in the USA (Kaufman [55] and Voorhees and Freeman [110]). Other tensile test results on alloy 6082 were not found. More data is necessary to determine whether the behaviour of this alloy at elevated temperature is indeed different from the other alloys, or whether the tensile tests were not carried out correctly.

6082 T4 6082 T6 350 400

300 tensile strength 350 tensile strength

] 0,2% proof stress 0,2% proof stress 2

] 300

250 2 250 200 [N/mm θ [N/mm ,θ 200 0,2, 150 0,2 150 and f and f and θ θ u, u,

f 100 f 100 50 50

0 0 0 200 400 600 0 200 400 600 Temperature [ºC] Temperature [ºC]

Figure 4.33 – 0,2 % proof stress and tensile strength of alloy 6082 T4 and T6 after a thermal exposure period ranging from 15 to 120 minutes

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Figure 4.34 gives the ratio between the 0,2 % proof stress and the tensile strength at a temperature of 204 ºC for all combinations of heat treatable alloys and tempers listed in Kaufman [55]. Figure 4.35 gives these results for all non-heat treatable alloys listed in Kaufman [55].

0,2 % proof stress / tensile strength, heat treatable alloys, 204 oC 1.00 0.90 0.80 O 0.70 T1 T3, T36, T37 0.60

[-] T4, T451 u,

/ f 0.50 T5, T53, T5311 0,2,

f 0.40 T6, T6x, T6xx T7, T7x, T7xx 0.30 T8, T8x, T8xx 0.20 T9 0.10 0.00 OT1T3T4T5 T6 T7 T8T9 Temper

Figure 4.34 – Ratio between 0,2 % proof stress and tensile strength for heat treatable alloys in various tempers at 204 ºC (data source: Kaufman [55])

Proof stress / tensile strength, 204 oC 1.20

1.00

0.80 [-] u,

/f 0.60 series 2xxx 0,2,

f series 3xxx 0.40 series 4xxx series 5xxx series 6xxx 0.20 series 7xxx

0.00 2xxx 3xxx 5xxx 6xxx 7xxx Alloy series

Figure 4.35 – Ratio between 0,2 % proof stress and tensile strength for non-heat treatable alloys in various tempers at 204 ºC (data source: Kaufman [55])

At room temperature, the ratio between the 0,2 % proof stress and the tensile strength of non-heat treatable alloys was on average approximately 0,4 for alloys in temper O up to 0,9 for the hardest tempers. At elevated temperature, the difference in strength between different tempers decreases,

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and consequently the ratio approaches one value for different tempers. The data in Kaufman [55] show that at elevated temperature, the ratio in case of non-heat treatable alloys is approximately 0,7 for temperatures between 200 and 400 ºC.

At room temperature, the ratio for heat treatable alloys was approximately 0,5 for alloys in temper O up to 0,85 for fully heat-treated alloys. At elevated temperature, this ratio first increases to an average value of 0,7 for alloys in temper O and 0,9 for alloys in other tempers at a temperature of 200 ºC. At increasing temperature, the ratio reduces to approximately 0,8 at a temperature of 400 ºC for all tempers.

It should be mentioned that the strength at elevated temperature depends on the time at stress, resulting in strain rate dependency and creep. The tests in Van den Boogaard [21] show that the strain rate dependency is larger on the ultimate tensile strength than on the 0,2 % proof stress. A possible explanation for the larger decrease of the tensile strength, compared to the 0,2 % proof stress at increasing temperature is that creep rates occurring are so high for high stress levels, that they influence the results of the tensile tests at high stress levels even during the short period in which the tensile test is carried out, see paragraph 4.8. It is possible that creep dominates the behaviour in the test at stress levels higher than the 0,2% proof stress. If this is the case, the σ-ε diagram depends on the rate with which stress is applied during the tensile test. Also Voorhees and Freeman [110] remark that the results depend on the load rate applied in the tensile test. For most structures exposed to fire, transient state tensile tests are more representative than the steady state tests reported in literature. In these tests, influence of creep is implicitly taken into account. It is therefore recommended to determine material properties with transient state tests.

Values for the tensile strength in EN 1999-1-2 [7] EN 1999-1-1 [6] uses the ultimate tensile strength in the checks on connections. EN 1999-1-2 [7] gives no simple calculation models for connections. In all simple calculation models given in EN 1999-1-2 [7], the 0,2% proof stress at elevated temperature is used. Therefore, EN 1999-1-2 [7] only gives values for the relative 0,2% proof stress at elevated temperature, and not for the ultimate tensile strength at elevated temperature. However, data on the ultimate tensile strength are required when using advanced calculation models, prescribed in section 4.3 of EN 1999-1-2 [7] or when material plasticity is required, e.g. for plates with a hole. In Lundberg [67], it is stated that an elastic-perfect plastic material curve is to be assumed.

4.5 Strength of Heat affected Zone

The heat affected zone is the zone in the parent material next to a weld with material properties influenced by the welding process.

4.5.1 Room temperature

During welding, annealing of the weld and the heat-affected zone takes place. Consequently, a part of the strengthening effect of hardening may be lost in the heat-affected zone. Therefore, EN 1999-1-1 [6] provides reduction factors for the strength of the heat-affected zone at room temperature (ρ0,2,haz), depending on the alloy and the temper. The reduction factors are equal to 1,0 for soft annealed alloys (temper O) and smaller than 1,0 for alloys in other tempers.

4.5.2 Elevated temperature

EN 1999-1-2 [7] prescribes that the reduced strength in the heat affected zones must be taken into account for welded connections. A reduction for the strength of the heat affected zone is also taken

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into account in case of simple calculation models of members with a non-uniform temperature distribution. In these simple calculation models, the same reduction factor (ρ0,2,haz) is taken into account as given in EN 1999-1-1 [6] for room temperature design. Additionally, the reduction of the strength to take account of the elevated temperature of the heat affected zone is taken equal to

the reduction of the strength (kθ) of the material that is not influenced by welds, i.e. the parent material. The 0,2% proof stress of the heat affected zone at elevated temperature is thus:

=⋅ρ ⋅ f0,2,θθ ,hazkf 0,2,haz 0,2 (4.4)

In reality however, the strength reduction due to the elevated temperature of the heat-affected zone is probably less than the reduction for parent material (for tempers other than O), as annealing already took place during welding. It is thus expected that EN 1999-1-2 [7] gives conservative verification rules for the heat affected zone, as loss of strength due to annealing is taken into account twice.

A strength reduction for the heat-affected zone is not specified in the verification rules for uniform temperature distribution in EN 1999-1-2 [7]. This does not match with the rules for non-uniform temperature distribution.

Only one tensile test on a welded specimen at elevated temperature is found in the literature. This test is described in Annex B. Both the specimen at room temperature and that at elevated temperature failed through rupture in the weld. A conclusion on the strength reduction of a weld due to elevated temperature based on this single test is inappropriate.

Langhelle [62] carried out column buckling tests on columns with and without welds, made of alloy 6082 T6. At room temperature, the buckling load of columns with welds was lower than that of identical columns without welds. At elevated temperature however, the welded columns had approximately equal critical temperature as columns without welds, but with the same dimensions and load. This strengthens the expectation described above. Results of the column buckling tests carried out by Langhelle [62] are given in Annex B.

4.6 Modulus of elasticity and Poisson ratio

4.6.1 Room temperature

At room temperature, the modulus of elasticity can properly be determined by measuring the increase in length over a certain distance along the specimen. This can either be done by displacement indicators, or by strain gauges. Mennink [85] recommends the use of strain gauges, stating that this results in more accurate measurements. It is further recommended to measure both sides of the specimen, using two gauges, in order to correct for bending and twisting. In order to obtain results not influenced by adjustment of the specimen to the applied load (e.g. straightening), the specimen should be loaded to a certain magnitude, subsequently unloaded to e.g. 10 % of the proof stress and finally reloaded again until rupture occurs. The modulus of elasticity should be determined in the unloading-reloading cycle. Note that measuring the increase in length over the clamps does not give accurate values for the modulus of elasticity, as slip between the specimen and the clamps influences the measured displacements in this case.

The modulus of elasticity measured with this method varies between 65.500 N/mm2 and 72.400 N/mm2 for most commercially applied alloys (TALAT [10]). The temper has no significant

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influence on the modulus of elasticity. The modulus of elasticity provided by codes is 70.000 N/mm2, independent of the alloy. This value is one third of that of steel. Mennink [85] found a modulus of elasticity in tensile tests on alloys in the 6xxx series of approximately 66.000 N/mm2.

The modulus of elasticity in compression is approximately 2 % higher than in tension for most alloys (Kaufman [55]).

The Poisson ratio (which is the coefficient of lateral contraction) given in EN 1999-1-1 [6] is ν = 0,3. This value is equal to the value for steel. Measurements show that the Poisson ratio is actually approximately ν = 0,35 in case of aluminium and aluminium alloys (Kammer [51], Mondolfo [89]). The Poisson ratio is expected to rise in the inelastic range of the stress-strain curve, as the fully plastic value for incompressible, isotropic materials is νp = 0,5. Gerhard and Becker [43] proposed the following relationship for the inelastic Poisson ratio, with ν and νp are the elastic and fully plastic Poisson ratios, respectively, and Et is the tangential modulus of elasticity.

E ν =−νννt () − (4.5) ipE p

4.6.2 Elevated temperature

Modulus of elasticity Measuring displacements at elevated temperature is complicated, as strain gauges have a maximum temperature at which they function (usually approximately 200 ºC) and also displacement indicators cannot sustain high temperatures, so they must be placed outside the fire furnace. At elevated temperature, an alternative method is therefore sometimes applied. In this method, (sound) waves are sent through a specimen and reflected. The reflection time is a measure for the (linear elastic) stiffness of the specimen. This method is applied e.g. by Mondolfo [89] to determine the modulus of elasticity of pure aluminium. The modulus of elasticity determined with this alternative method is referred to as the dynamic modulus of elasticity, whereas in the method with tensile tests, it is called the static modulus of elasticity.

Measurements using one of the methods given above show that also the modulus of elasticity decreases with increasing temperature. However, while the two methods give approximately equal results at room temperature, the dynamic modulus of elasticity at elevated temperature seems to be larger than the static modulus of elasticity. This is shown in Figure 4.36, which gives the static modulus of elasticity for series 3xxx, 5xxx and 6xxx according to data in Kaufman [55], the dynamic modulus of elasticity according to measurements in Mondolfo [89] and by Richter and Hanitzsch [92], and the values given in EN 1999-1-2 [7]. A possible explanation for the difference in modulus of elasticity determined with the two methods is that visco-plastic behaviour becomes important at elevated temperature. This may reduce the modulus of elasticity in case of specimens under stress, such as in case of the static modulus of elasticity. Data on the influence of visco-plastic behaviour on the modulus of elasticity were not found in literature. As this research concerns aluminium structures subjected to loads, it is further concentrated on the static modulus of elasticity.

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The data for the modulus of elasticity in EN 1999-1-2 [7] are based on the former Norwegian Standard NS 3478 [9]. The data in the Norwegian Standard are based on Essem [38]. The modulus of elasticity according to EN 1999-1-2 [7] corresponds reasonable with the data of the static modulus of elasticity of various alloys in series 3xxx, 5xxx and 6xxx in Kaufman [55].

80000

70000

60000 ]

2 50000

40000 [N/mm θ

E 30000 adiabatic 20000 isothermal 10000 EN 1999-1-2

0 0 100 200 300 400 500 600 TemperatureT [oC]

Figure 4.36 – Comparison of the static modulus of elasticity (Kaufman [55]) and the dynamic modulus of elasticity (Mondolfo [89], Richter and Hanitzsch [89]) for aluminium alloys at elevated temperature

The values in EN 1999-1-2 [7] also correspond reasonable with test data on alloy 6082 by Langhelle [62], Krokeide [59] and Kleive and Gustavsen [56] (Figure 4.37). 80000 70000 60000 ] 2 50000 40000 [N/mm θ

E 30000 6082 T6 20000 6082 T4 10000 EN 1999-1-2 0 0 100 200 300 400 500 600 Temperature [oC]

Figure 4.37 – Modulus of elasticity according to EN 1999-1-2 [7] and according to various tensile tests on alloy AA 6082 T6 and T4

According to the data in Kaufman [55], the variation in modulus of elasticity between different alloys is larger at elevated temperature than at room temperature, see Figure 4.38. Furthermore, there is no difference in the modulus of elasticity between different tempers of the same alloy. Also, the variation in the modulus of elasticity between different alloys within the same series is negligible for most alloys. However, as indicated in Figure 4.38, exceptions occur.

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According to the tabulated data, the modulus of elasticity is independent of the thermal exposure period, i.e. independent of the time at elevated temperature before application of the load.

Modulus of elasticity

90000

80000

70000

60000 ] 2 50000

40000

E [N/mm 24 ºC 30000 100 ºC 149 ºC 20000 204 ºC 10000 316 ºC 371 ºC 0 2000 3000 5000 6000 7000 Alloy series

Figure 4.38 – Modulus of elasticity of various alloys (data source: Kaufman [55])

At 250 ºC, the modulus of elasticity is reduced to approximately 80% of the modulus of elasticity at ambient temperature. No test data were found on the static modulus of elasticity for temperatures exceeding 370 ºC. The values in EN 1999-1-2 [7] are thus not verified for temperatures exceeding this temperature.

Figure 4.39 gives a comparison between the relative value of the modulus of elasticity of aluminium according to EN 1999-1-2 [7], and of steel according to EN 1993-1-2 [4]. The figure shows that the modulus of elasticity of aluminium reduces faster at increasing temperature than that of steel. However, the slopes of the steepest parts of the curves (between kE,θ = 0,6 and kE,θ = 0,1) are approximately equal.

1.20

1.00 aluminium alloys steel 0.80

0.60 / E [-] / E θ E 0.40

0.20

0.00 0 200 400 600 800 1000 1200 Temperature [oC]

Figure 4.39 – Relative value of the modulus of elasticity of aluminium (EN 1999-1-2 [7]) and steel (EN 1993-1-2 [4])

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Ratio 0,2 % proof stress / modulus of elasticity The ratio between the 0,2 % proof stress and the modulus of elasticity is an important indicator for the sensitivity to buckling. The higher this ratio, the more sensitive to buckling (paragraph 5.4 and 5.5).

The ratio between the 0,2 % proof stress and the modulus of elasticity largely depends on the temper. The ratio of most alloys in annealed temper increases slightly up to a temperature of 200 ºC. , after which it decreases rapidly. The ratio of work hardened, non-heat treatable alloys remains approximately constant up to a temperature of 150 ºC, after which it decreases. The ratio of naturally aged alloys increases slightly up to 200 ºC, after which it decreases. In case of artificially aged alloys, the ratio decreases at increasing temperature from room temperature on.

The ratio is given in Figure 4.40 for alloy 5083, in Figure 4.41 for alloy 6061 and in Figure 4.42 for alloy 6082. The modulus of elasticity was not provided for alloy 6063.

Contrary to the general behaviour of most aluminium alloys, the ratio between the yield strength and the modulus of elasticity of mild steel increases at increasing temperature, until a temperature of 900 ºC (based on data in EN 1993-1-2 [4]).

5083, 0,2% proof stress / modulus of elasticity 0.0035

0.0030

0.0025 [-] θ 0.0020 5083-O / E θ 0.0015 5083-H321 0,2, f 0.0010

0.0005

0.0000 0 100 200 300 400 Temperature [ºC]

Figure 4.40 – Ratio between 0,2 % proof stress and modulus of elasticity for alloy 5083 (data source: Kaufman [55])

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6061, 0,2% proof stress / modulus of elasticity 0.0050 6061-O 0.0045 6061-T4,-T451 6061-T6,-T651,-T6511 0.0040 6061-T8 0.0035

[-] 0.0030 θ 0.0025 / E θ

0,2, 0.0020 f 0.0015 0.0010 0.0005 0.0000 0 100 200 300 400 Temperature [ºC]

Figure 4.41 – Ratio between 0,2 % proof stress and modulus of elasticity for alloy 6061 (data source: Kaufman [55])

6082, 0,2% proof stress / modulus of elasticity 0.0050 0.0045 0.0040 6082-T4 0.0035 6082-T6

[-] 0.0030 θ 0.0025 / E / θ

0,2, 0.0020 f 0.0015 0.0010 0.0005 0.0000 0 100 200 300 400 Temperature [ºC]

Figure 4.42 – Ratio between 0,2 % proof stress and modulus of elasticity for alloy 6082 (data source: Langhelle [62] and Kleive and Gustavsen [56])

Shear modulus and Poisson ratio The shear modulus (G) has the following relation with the Poisson ratio (ν) and the modulus of elasticity (E):

E G = (4.6) 21()+ν

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Mondolfo [89] gives an overview of experiments in which the dynamic modulus of elasticity and the dynamic shear modulus are determined. The experimental results are given in Figure 4.43.

Figure 4.43 – Dynamic modulus of elasticity and shear modulus of experiments in various test series (source: Mondolfo [89])

Based on this figure, Mondolfo [89] concludes that the Poisson ratio tends to rise with increasing temperature. (Values are not provided.) However, based on this figure, the decrease in modulus of elasticity is larger than the decrease in shear modulus. This indicates that, instead of rising, the Poisson ratio decreases at increasing temperature.

It should be noted that the dynamic shear modulus at room temperature, which is approximately 22.000 N/mm2 according to Figure 4.43 does not correspond to the static shear modulus at room temperature (approximately 26.000 N/mm2). No information was found regarding the static shear modulus or Poisson ratio at elevated temperature. Tests are required to determine the static shear modulus.

4.7 Ultimate strain

4.7.1 Room temperature

The strain at rupture (ultimate strain) is often used as a measure for ductility (TALAT [10]). The strain at rupture depends largely on the treatment. In case of non-heat treatable alloys in the annealed condition, this measure is 35 % (for a measuring length of 50 mm), while in fully strain- hardened condition, this measure may reduce to 3 % (TALAT [10]). According to the test data in Kaufman [55], the strain at rupture in case of heat treatable alloy of temper T6 is approximately 10 to 20 %. In case of temper T4, this measure is approximately 25 %. The strain at rupture also varies per alloy. In general, alloys with high strength have smaller strain at rupture than alloys with low strength, although exceptions occur.

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4.7.2 Elevated temperature

Tests show that the ultimate strain at elevated temperature depends on the strain rate (paragraph 4.8.1). According to test data (Kaufman [55], Voorhees and Freeman [110]), the strain at rupture

of non-heat treatable alloys increases at increasing temperature, until a temperature of approximately 400 ºC. The corresponding strain at rupture may then be larger than 150 %. At higher temperatures, the strain at rupture remains approximately constant. The strain at rupture for alloy 5083 in various tempers is given in Figure 4.44. The data provided show no dependency of the temper on the strain at rupture. Also the thermal exposure period does not influence the strain at rupture.

In case of heat treatable alloys however, the strain at rupture depends on the treatment. • The strain at rupture of alloys in temper O increases at increasing temperature; • In case of artificially aged tempers, the strain at rupture remains approximately constant until a temperature of approximately 250 ºC. At higher temperatures, the strain at rupture increases and may exceed the strain at rupture of temper O. A physical explanation of this behaviour was not found; • In case of naturally aged tempers, the strain at rupture may first decrease at moderately elevated temperature, due to artificial ageing. At higher temperatures, the difference between aged alloys vanishes, so that the strain at rupture of naturally aged tempers corresponds to that of artificially aged tempers. Figure 4.44 gives the strain at rupture for alloy 6063 in various tempers, according to data by Kaufman [55] and Voorhees and Freeman [110]. Figure 4.45 gives the strain at rupture for alloy 6082 in tempers T4 and T6, according to Norwegian tests.

The figures show that the scatter in measured rupture strain is relatively large at elevated temperature. Measurements on alloy 6063 (Figure 4.44) indicate that the strain at rupture at temperatures exceeding 400 ºC for tempers T1 and T6 are larger than the strain at rupture for temper O. It is however expected that the alloy with any treatment would be in annealed condition at these temperatures, so that all tempers would behave as temper O. An explanation for the difference in strain at rupture between various tempers at temperatures exceeding 400 ºC was not found in literature.

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200 180 5083-O (K) 5083 O (VF) 160

5083-H321 (K) 140 5083 H113 (VF) 120

[%] 100 50 A 80 60 40 20 0 0 100 200 300 400 500 600 o Temperature [ C]

Figure 4.44 – Strain at rupture of alloy 5083 (data source: K = Kaufman [55], VF = Voorhees and Freeman [110])

200 180 6063 O (K) 6063 T1 (K) 160 6063 T42 (VF) 140 6063 T5 (K) 120 6063 T6 (K)

[%] 100

50 6063 T6 (VF) A 80 60 40 20 0 0 100 200 300 400 500 600 Temperature [ºC]

Figure 4.45 – Strain at rupture of alloy 6063 (data source: K = Kaufman [55], VF = Voorhees and Freeman [110])

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60

50 6082 T6 6082 T4 40

[%] 30 50 A 20

10

0 0 100 200 300 400 Temperature [oC]

Figure 4.46 – Strain at rupture of alloy 6082

Some authors, e.g. Koser [57], recommend to use the relative energy absorption of the material for stresses higher than the 0,2% proof stress as a measure for the ductility, instead of the strain at rupture. Although the strain at rupture increases at increasing temperature, Figure 4.5 up to Figure 4.8 show that the energy absorption may for heat-treated alloys decrease at increasing temperature up to approximately 250 ºC. The two definitions of ductility given above may thus result in a different evaluation of the ductile behaviour of aluminium at elevated temperature.

4.8 Visco-plastic behaviour

The time under stress may influence the strength and deformations. This time dependency is related to visco-plastic behaviour of the material. This visco-plastic behaviour exhibits in two ways: - Dependency on the strain rate; - Dependency on the load level during the thermal exposure period (creep). These phenomena are discussed in the following paragraphs.

4.8.1 Strain rate dependency

Test results by Kumar and Swaminathan [60] and Van den Boogaard [21] show that the strain rate with which the tensile test is carried out has a significant influence on the strength determined in tensile tests at elevated temperature, i.e. higher strengths are found at higher strain rates. As an example, Figure 4.47 up to Figure 4.49 give the stress-strain relations of alloy 5754 O for different strain rates. The strain rate dependency is caused by phenomena such as remobilisation and annihilation of dislocations (Van den Boogaard [21]). The dependency on the strain rate increases at increasing temperature. Note that the strain rate effect at room temperature is so small that it is neglected for structural applications.

Dieter [28] proposed equation (4.7) for the relation between the true stress (σ), the true strain (ε) and the strain rate (ε& ):

n m σεε=⋅⋅K & (4.7)

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In which K is a constant and n and m are the strain hardening exponent and the strain rate sensitivity index, respectively. These parameters depend on the temperature.

Figure 4.47 – Stress-strain relation of alloy 5754 O at various temperatures for a strain rate of 0,002 /sec (source: Van den Boogaard [21])

Figure 4.48 – Stress-strain relation of alloy 5754 O at various temperatures for a strain rate of 0,02 /sec (source: Van den Boogaard [21])

Figure 4.49 – Stress-strain relation of alloy 5754 O at various temperatures for a strain rate of 0,1 /sec (source: Van den Boogaard [21])

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4.8.2 Introduction to creep

Creep is time dependent distortion of material due to loading. Creep results in elongation of material and decrease in strength and stiffness. Kraus [58] gives an extended overview of creep

behaviour of metals. Creep deformations are divided in primary creep with decreasing creep rate, in secondary creep with constant creep rate and in tertiary creep with increasing creep rate, see Figure 4.50. Creep rupture takes place at the end of the tertiary stage. creep rupture creep strain

Primary Secondary Tertiary time

Figure 4.50 – Creep deformation of metals divided in primary, secondary and tertiary creep

The amount of creep depends on the temperature, the time of exposure and the stress level.

Creep is present for long exposure periods in aluminium structures at room temperature. The influence of creep at room temperature, however, is such that it is usually neglected. EN 1999-1-1 [6], does not explicitly take creep into account. At elevated temperature, the tertiary stage may already be reached for creep periods of less than two hours. Hence, creep may become important in fire situations.

Voorhees and Freeman [110] and Kaufman [55] give elongation percentages after various exposure periods and the time to rupture of various alloys and tempers at various stress levels at elevated temperature. Kaspersen and Soras [54], Krokeide [59] and Broli and Mollersen [23] carried out creep tensile tests on alloy AA6082 T6 at various temperatures with various stress levels. Their results are discussed in Eberg et al. [35] and in Langhelle [62]. Also Hepples and Wale [45] carried out creep tensile tests on alloy AA6082 T6. Creep test results at temperatures exceeding 320 ºC were barely found in literature. The data apply to creep tests during a period of constant elevated temperature. In fire situations, the temperature increases until collapse occurs. Transient state tests were however not found in literature.

The following paragraphs discuss successively the creep rupture stress, the influence of creep on the strength at lower creep levels, creep deformations and the way creep is implemented in EN 1999-1-2 [7]. No information was found concerning creep influence on the modulus of elasticity.

4.8.3 Creep rupture stress

The creep rupture stress indicates the stress that will cause rupture (failure of the specimen) under sustained constant load during a certain time. Kaufman [55] gives data on the creep rupture stress of some alloys resulting from creep tensile tests after a creep period of 6 min, 60 min and 600 min. the following procedure was followed to determine the creep rupture stress (Figure 4.51): • The specimen was heated to a certain elevated temperature;

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• The specimen was loaded to a certain load; • Rupture (due to creep) occurred after a certain period;

The specified stresses are based on tests over a range of stresses plotted in a curve, and the stresses for creep rupture after a creep period 6 min, 60 min and 600 min were picked from the curve. Original test results are not reported.

heating loading

Creep rupture period

Failure Load

Temperature Failure

Time Time

Figure 4.51 – Tests to determine the creep rupture stress in Kaufman [55] (left-hand heating, right-hand loading)

The ultimate tensile strength determined in short time tensile tests was given for thermal exposure periods of 30 min and 600 min. In Figure 4.52 up to Figure 4.55, the creep rupture stress is compared to the short time tensile strength. Each of the figures gives the ratio between creep rupture stress and tensile strength at a certain temperature. Each solid diamond represent the ratio between creep rupture stress after a creep period of 6 minutes and tensile strength after a thermal exposure period of 30 minutes (fr,6 min/fu,30 min) of a specific combination of an alloy and temper. The square open dots represent the ratio between creep rupture stress after a creep period of 30 minutes and tensile strength after a thermal exposure period of 30 minutes (fr,30 min/fu,30 min). The solid triangles represent the ratio between creep rupture stress after a creep period of 600 minutes and tensile strength after a thermal exposure period of 600 minutes (fr,600 min/fu,600 min).

According to the figures, a moderately elevated temperature (200 ºC) and a creep time of 6 min already results in a creep rupture stress that is lower than the tensile strength. The figures show that the ratio between creep rupture stress and short time ultimate tensile strength is lower for non-heat treatable alloys than for heat treatable alloys. For these alloys, also the ratio between 0,2 % proof stress and ultimate tensile strength is lower.

At a temperature of 316 ºC, it is shown that the ratio between the creep rupture stress and the tensile strength for a number of alloys and tempers in series 5xxx are exactly equal. Though, data for each alloy was accumulated and analysed separately. According to the author of this database, the reason for the curves of different alloys coming together, especially at very high temperatures, is that the limits of aluminum alloy behavior are approached.

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T = 24 oC 1.20

1.00 ]

u 0.80

0,1 h 0.60 1 h [relative tof [relative r 10 h f 0.40

0.20

0.00 2000 3000 5000 6000 7000 Alloy series

Figure 4.52 – Ratio between creep rupture stress and tensile strength at a temperature of 24 ºC for various alloys according to data by Kaufman [55]

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T = 100 oC 1.20

1.00 ]

u 0.80 0,1 h 0.60 1 h [relative to f

r 10 h f 0.40

0.20

0.00 2000 3000 5000 6000 7000 Alloy series

Figure 4.53 – Ratio between creep rupture stress and tensile strength at a temperature of 100 ºC for various alloys according to data by Kaufman [55]

T = 204 oC 1.20

1.00 ]

u 0.80 0,1 h 0.60 1 h [relative to f

r 10 h f 0.40

0.20

0.00 2000 3000 5000 6000 7000 Alloy series

Figure 4.54 – Ratio between creep rupture stress and tensile strength at a temperature of 204 ºC for various alloys according to data by Kaufman [55]

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T = 316 oC 1.20

1.00 ]

u 0.80 0,1 h 0.60 1 h [relative to f

r 10 h f 0.40

0.20

0.00 2000 3000 5000 6000 7000 Alloy series

Figure 4.55 – Ratio between creep rupture stress and tensile strength at a temperature of 316 ºC for various alloys according to data by Kaufman [55]

For each of the alloys and tempers listed in Kaufman [55], the ratios between the creep rupture stress and the tensile strength (fr,6 min / fu,30 min), (fr,60 min / fu,30 min) and (fr,600 min / fu,600 min) are determined. The average value of these ratios for all alloys and tempers are given in Figure 4.56. The standard deviation of fr,60 min / fu,30 min is also shown in the figure. The figure shows that creep becomes increasingly important at increasing temperature.

1.20

1.00 ] u 0.80

0.60 t = 6 min

[relative to f to [relative 0.40 r

f t = 60 min 0.20 t = 600 min

0.00 0 100 200 300 400 Temperature [ºC]

Figure 4.56 - Ratios between creep rupture stress and tensile strength for the alloys and tempers listed in Kaufman [55]

According to the data on all alloys and tempers listed in Kaufman [55] and Voorhees and Freeman [110], the applied stress on specimens for which creep rupture occurred within 60 minutes was on average between the 0,2% proof stress and the ultimate tensile strength, for temperatures up to 200 ºC. At higher temperatures, the creep rupture stress for all alloys and tempers is on average lower than the 0,2 % proof stress.

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In case of non-heat treatable alloys, the ratio between creep rupture stress and tensile strength varies little between different tempers of the same alloy. In case of heat-treatable alloys, his ratio varied for various tempers of the same alloy.

For non-heat treatable alloys, the creep rupture stress is already significantly lower than the tensile strength at a temperature of 100 ºC. At increasing temperature, the influence of creep on the strength did not increase significantly. For heat treatable alloys however, the influence of creep on strength increases for increasing temperatures. As an example of this, Figure 4.57 gives tensile strengths and creep rupture stress of the non-heat treatable alloy 5083 and Figure 4.58 gives this data for the heat treatable alloy 6061. The data for alloy 6063 is slightly different from the data on other alloys in the 6xxx series (Figure 4.59). This is partly caused by the fact that the tensile strength after a thermal exposure period of 600 minutes is higher than after a thermal exposure period of 30 minutes. This was not found for other alloys, and it is possibly caused by measurement errors or scatter in test results. (It should be noted that the axis in the figures have different scales).

5083-O 5083-H321 350 350 Tensile strength 30 min Tensile strength 30 min Tensile strength 600 min Tensile strength 600 min 300 300 Creep time = 6 min Creep time = 6 min ] ] 2 Creep time = 60 min 2 250 Creep time = 60 min 250 Creep time = 600 min Creep time = 600 min 200

200 [N/mm [N/mm θ θ r, r, 150 150 and f f and and f f and θ θ

u, 100 u,

100 f f 50 50

0 0 0 200 400 600 0 200 400 600 Temperature [ºC] Temperature [ºC]

Figure 4.57 – Tensile strength and creep rupture stress of alloy 5083 according to data by Kaufman [55]

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6061-O 6061-T6 -T651 -T6511 Extrusions 140 Tensile strength 30 min 350 Tensile strength Tensile strength 600 min 30 min 120 300 Creep time = 6 min Tensile strength

] ]

Creep time = 60 min 2 600 min 2 100 250 Creep time = 600 min Creep time = 6 80 200 min [N/mm [N/mm θ θ r, r, Creep time = 60 150 60 min and f and and f θ θ Creep time = u, u, f 40 f 100 600 min

20 50

0 0 0 200 400 600 0 200 400 600 Temperature [ºC] Temperature [ºC]

Figure 4.58 – Tensile strength and creep rupture stress of alloy 6061 according to data by Kaufman [55]

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6063-O Extrusions 6063-T5 Extrusions 100 250 Tensile strength 30 min Tensile strength 0.5 h 90 Tensile strength 600 min Tensile strength 10 h Creep time = 6 min 200 Creep time = 0.1 h 80 ] ]

2 Creep time = 60 min 2 Creep time = 1 h 70 Creep time = 600 min 60 150 Creep time = 10 h [N/mm [N/mm θ θ r, 50 r, 40 100 and f and and f f and θ θ u,

u, 30 f f 20 50 10 0 0 0 200 400 600 0 200 400 600 Temperature [ºC] Temperature [ºC]

6063-T6 250

200 ] 2

150 [N/mm θ r, 100 Tensile strength 30 min and f f and θ Tensile strength 600 min u, f 50 Creep time = 6 min Creep time = 60 min 0 Creep time = 600 min 0 200 400 600 Temperature [ºC]

Figure 4.59 – Tensile strength and creep rupture stress of alloy 6063 according to data by Kaufman [55]

Kaspersen and Soras [54] and Krokeide [59] carried out creep tests on alloy AA6082 T6 at various temperatures with various stress levels. Their results are discussed in Eberg et al. [35] and in Langhelle [62]. The time to rupture of the axially loaded test specimens is given in Table 4.3. Six other creep tests are carried out on specimens loaded with a combination of axial force and bending moment. These tests are not reported here, as the results depend on the ratio between axial force and bending moment applied in the tests. The amount of tests is too little to be able to determine a relation between this ratio and creep.

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Table 4.3 – Creep tests on alloy 6082 T6 by Krokeide [59] and by Kaspersen and Soras [54]

Temperature Stress level 0,2% proof Stress level / 0,2% Time to Ultimate 2 2 [ºC] [N/mm ] stress [N/mm ] proof stress [-] rupture [hrs] creep strain 200 201 223 0.90 0.5 231 156 173 0.90 0.4 270 100 111 0.90 0.19 250 60 1) 9.8 2) 6.0 % 250 70 1) 4.4 2) 12.3 % 250 85 1) 1.6 2) 22.5 % 250 95 1) 0.81 2) 10.0 % 250 105 1) 0.72 2) 16.9 % 1) Values for the 0,2% proof stress at a temperature of 250 ºC are not reported. 2) Given values are estimated from the results presented in graphs

The tests showed a strong impact of the stress level on the time to rupture. For high stress levels, close to the 0,2% proof stress at elevated temperature, it is possible that rupture due to creep occurs within 60 minutes.

4.8.4 Influence of creep on the strength for stress levels lower than the rupture stress

The previous paragraph discussed creep rupture stress at constant elevated temperature. In order to use this data for transient state situations, in which the load remains constant and the temperature increases, it is relevant to know whether creep at lower stress levels influences the strength. In this respect, a limited number of tests was found in literature in which specimens were loaded to a certain extent during a period at constant elevated temperature. After this creep period, the load was increased until rupture occurred, as in a normal tensile test (Figure 4.60).

heating loading

Tensile test Creep period

Load Stress level in creep period

Temperature = beginning tensile test = failure

Time Time

Figure 4.60 – Creep tests with load levels lower than creep rupture stress (left-hand heating, right-hand loading)

To determine the influence of creep on the material properties of alloy 6082, Eberg et al. [35] carried out tensile tests after a creep period. The test procedure was slightly different from that indicated in Figure 4.60:

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ƒ The specimen was heated to the test temperature and held at this temperature 10 minutes before loading; ƒ The specimen was loaded to the predefined stress level; ƒ The specimen was held at constant temperature and stress level allowing creep to

develop. The holding period for most tests was two hours; ƒ The specimen was unloaded to zero and subsequently reloaded to rupture (tensile test). The test results are summarised in Table 4.4. The data in this table are estimated from the strain – time graphs and the stress-strain figures of the tensile tests reported in Eberg et al. [35].

Table 4.4 – Tensile tests after a creep period on alloy AA 6082 T6 (Eberg et al. [35])

2) 2) 2) T [ºC] Stress Creep Total strain f0,2 fu A50 during creep period after creep [N/mm2] [N/mm2] [%] [N/mm2] [min] period 1) 150 60 120 0.103 % 229 234 23 150 80 120 0.169 % 231 266 21 150 100 120 0.160 % 237 244 21 150 130 120 0.263 % 224 232 22 200 60 194 3) 0.164 % 4) 4) 4) 200 80 120 0.219 % 183 188 24 200 90 232 3) 0.213 % 185 190 23 200 100 120 0.239 % 191 193 23 200 120 120 0.307 % 189 190 22 1) The given strain is the summation of elastic strain and creep strain 2) The values tabulated for f0,2, fu and A50 refer to the tensile test at elevated temperature carried out after the creep period 3) Longer creep periods were applied because little creep developed during the first two hours 4) Creep rupture occurred, so the tensile test could not be carried out

Eberg et al. [35] conclude that the strain-time curves are seen to have the characteristic shape of the primary and secondary creep phases. When evaluating the curves however, the creep rate accelerated just before the specimen was unloaded to zero and subsequently reloaded to rupture, indicating that the tertiary creep phase just started. No discussion of the test results was given. Unfortunately, no tests were carried out without creep on specimens from the same extrusion length. The ratio between the stress applied during the creep period and the 0,2 % proof stress determined in the final tensile test was 0,26 up to 0,63. For this ratio and for the temperatures applied, i.e. 150 and 200 ºC, the tests show no correlation between the stress applied during the creep period and the strength determined in the subsequent tensile test.

Hepples and Wale [45] carried out tensile tests on alloy 6082 T6 after a creep period with a stress level of 30 % of the proof stress at room temperature. Three different holding periods were applied: directly after the specimen was heated, after a holding period of one hour or after a holding period of two hours. Tests were carried out for temperatures up to 250 ºC. At this temperature, the strength decreases to such an extend that the preload is equal to 87 % of the 0,2 % proof stress of the tensile test at 250 ºC. At 200 ºC, the preload is equal to 47 % of the 0,2 % proof stress.

The results were compared with test results without preloading. It was concluded that pre-loading to 30% of the proof stress at room temperature (= up to 87 % of the 0,2 % proof stress at elevated

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temperature) has no significant influence on the 0,2% proof stress and on the ultimate tensile strength. However, the ductility was significantly reduced.

Too few test results are available to conclude whether or not stress levels lower than the creep

rupture stress have significant influence on the strength.

4.8.5 Creep deformations

Individual test results reported by Voorhees and Freeman [110] show a large scatter in creep deformations at rupture, varying from less than 1 % to more than 50 %, depending on the alloy.

Kaufman [55] gives the stress at which creep deformations of 1,0%, 0,5%, 0,2% and 0,1% occur after 6 min, 60 min and 600 min. In order to obtain an impression of the relevance of such creep deformations, creep deformation is compared to the deformation by thermal expansion and by strains in the stress-strain relation. For this purpose, a uniformly loaded, simply supported beam with a span of 7,2 m is considered according to Figure 4.61. The height of the beam is chosen as 1/25 times the span.

Figure 4.61 – Beam for which thermal and creep deformations are compared

The derivation of the deflection at midspan due to thermal expansion or creep is relatively simple. Equation (4.8) gives the deflection due to thermal expansion and equation (4.9) allows the calculation of the deflection due to creep.

α ⋅ L2 ⋅∆T w = T (4.8) T 8h ∆L L2 w = ⋅ (4.9) c L 8h

• The vertical deflection at midspan due to the load at room temperature is estimated at 1/250 times the span. This is approximately 30 mm. • When, in a fire, the upper flange is 50 ºC colder than the lower flange, the upper flange will expand less than the lower flange. Provided thermal expansion is not restrained and assuming a linear thermal expansion coefficient of 2,5.10-5/ºC (independent of the temperature), the deflection at midspan caused by difference in thermal expansion is also approximately 30 mm. • In case the compressed upper flange shortens because of 0,1 % creep deformation and the lower flange in tension elongates with 0,1 %, the first order deflection at midspan is 45 mm (assuming a linear relation between the stress and the creep deformation). A creep percentage of 0,2 % results in a deflection at midspan of 90 mm, 0,5 % results in 225 mm and 1,0 % results in an extremely large deflection of 450 mm.

In case of a column, thermal expansion is equal to 0,1 % at a temperature of 60 ºC. Thermal expansion is equal to 0,2 % at a temperature of 100 ºC, equal to 0,5 % at a temperature of 220 ºC and equal to 1,0 % at 400 ºC.

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The proportional limit of aluminium alloys applied in structures is reached at a strain of approximately 0,2 to 0,3 %. The 0,2 % proof stress is reached at a total strain of approximately 0,5 %. It is concluded that a creep strain of 0,1 % or 0,2 % is already relevant in structural applications.

Creep strains of 1 % may result in very large deformations.

For each of the 101 combinations of alloys and tempers listed in Kaufman [55], the ratios between the stress level to obtain 0,5 % creep stress and the tensile strength (fc,0.5%, 6 min / fu,30 min), (fc,0.5%, 60 min / fu,30 min) and (fc,0.5%, 600 min / fu,600 min) were determined. The average value of these ratios for all alloys and tempers are given in Figure 4.56. The standard deviation of fc,0.5%, 60 min / fu,30 min is also shown in the figure.

1.20

1.00 ] u 0.80

0.60

[relative to f to [relative 0.40 t = 6 min

c,0.5% t = 60 min f 0.20 t = 600 min 0.00 0 100 200 300 400 Temperature [ºC]

Figure 4.62 - Ratios between the stress resulting in creep deformations of 0,5 % and the tensile strength for the alloys and tempers listed in Kaufman [55]

Again, a large difference exist between the creep elongation of heat-treatable and non-heat treatable alloys, see e.g. Figure 4.63 and Figure 4.64.

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5083-O, time under stress = 1 h 5083-H321, time under stress = 1 h 300 300 Creep rupture stress Creep rupture stress Stress at 1,0% creep Stress at 1,0% creep 250 250 Stress at 0,5% creep Stress at 0,5% creep Stress at 0,2% creep 200 Stress at 0,2% creep 200 ] ] Stress at 0,1% creep 2 2 Stress at 0,1% creep 150 150 [N/mm [N/mm σ σ 100 100

50 50

0 0 0 200 400 600 0 200 400 600 T [oC] T [oC]

Figure 4.63 – Creep rupture stress and stress levels for various percentages of creep of alloy 5083 after a creep period of 1,0 h (Data source: Kaufman [55])

6063-O Extrusions, time under stress = 1 h 6063-T5 Extrusions, time under stress = 1 h Creep rupture stress 90 250 Creep rupture stress 80 Stress at 1,0% creep Stress at 1,0% creep Stress at 0,5% creep Stress at 0,5% creep 70 200 Stress at 0,2% creep Stress at 0,2% creep 60 ] Stress at 0,1% creep 2 ]

Stress at 0,1% creep 2 50 150 40 [N/mm [N/mm σ 100 30 σ 20 50 10

0 0 0 100 200 300 400 500 0 100 200 300 400 500 T [oC] T [oC]

Figure 4.64 – Creep rupture stress and stress levels for various percentages of creep of alloy 6061 after a creep time of 1 h (Data source: Kaufman [55])

Creep tests on alloy 6082 T6 at temperatures of 50, 100, 150 and 200 ºC with various stress levels are carried out by Broli and Mollersen [23]. Results are discussed in Eberg et al. [35]. For the lowest temperature examined, 50 ºC, creep is seen to be negligible for all stress levels except for stresses close to the 0,2% proof stress. At increasing temperature, creep becomes more pronounced and especially for the highest stress levels examined the presence of creep strains is evident.

4.8.6 Modelling of creep

The Dorn-Harmathy creep model is usually applied to model primary and secondary creep of steel at elevated temperature. In contrast to most other creep theories, with the Dorn-Harmathy creep model it is possible to account for a temperature variation in time. The model is based on the

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assumption by Dorn [33] that the effect of the temperature can be discounted in an adaptation of the time. The creep strain (εcr) then depends on the stress level (σ) and on a temperature- compensated time (tT), according to equation (4.10).

∆ H t − t = edRT t (4.10) T ∫0

The temperature-compensated time depends on the material, through the activation energy required for creep (∆H [cal/mol]). R is the universal gas constant [cal/mol K]. The curve expressing the relation between the creep strain (εcr) and the temperature-compensated time (tT) is linear during the secondary creep phase. The slope of this curve, denoted with Z = dεcr/dtT, depends on the stress level (σ). The intersection of the line with this constant creep strain rate with the vertical axis is a measure for the primary creep (εcr,0), which also depends on the stress level (σ). This is indicated in Figure 4.65.

cr ε

tT

Figure 4.65 – Relations between creep strain (εcr) and temperature-compensated time (tT)

Harmathy [44] gave a mathematical relation between the creep strain (εcr) and tT, Z and εcr,0:

ε − ⎛⎞Z ⋅t ε = cr,0 cosh1 2 T (4.11) t ⎜⎟ε ln 2 ⎝⎠cr,0

The material-dependent parameters in the Dorn-Harmathy model are the ratio ∆H/R and, dependent on the stress level, Z and εcr,0. These parameters can be determined with creep tests at constant temperature and stress. In this case, equation (4.10) reduces to:

∆ − H =⋅ R⋅T tT te (4.12)

Considering the fact that the creep strain (εcr) is assumed to depend only on the stress level (σ) and the temperature-compensated time (tT), the ratio ∆H/R can be solved when at least two tests are carried out with equal stress levels (σ) at a different temperature (T), and of these tests data are

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available on the time at which the creep strains are equal. In that case, the values for tT should be equal. Z can be solved using equation (4.13):

∆ ddεεdt d εH Z ==⋅=⋅cr cr cr e R⋅T (4.13) dtTT dt dt dt

When ∆H/R has been determined, Z can be determined for each test when the creep strain rate dεcr/dt is measured in the test. If the calculated values of Z are plotted in a diagram as a function of the stress (σ) for steel, it is found that measurements with high stress levels are usually close to a straight line in a diagram plotted with the Z-axis on a logarithmic scale, and measurements with low stress levels are usually close to a straight line in a diagram plotted with both the Z-axis and the stress-axis on a logarithmic scale (Thor [104]). The values of εcr,0 can be determined for each test when Z is known. If the calculated values of εcr,0 are plotted in a diagram as a function of the stress (σ) for steel, it is found that the measurements are usually close to a straight line in a diagram plotted with both the εcr,0-axis and the stress-axis on a logarithmic scale (Thor [104]). Evaluation of the application of the Dorn-Harmathy creep model for various steel grades is given in Thor [104].

With the creep data in Kaufman [55], it could be verified whether or not the Dorn-Harmathy model can also be applied for aluminium alloys.

4.8.7 Creep in EN 1999-1-2

EN 1999-1-2 [7] gives no explicit reduction of the material strength due to creep. Creep is explicitely taken into account in the verification rules for flexural and torsional buckling of columns and beam columns, by multiplying the normal force with a factor 1,2. The code specifies that this factor is a reduction factor for the design resistance due to the temperature dependent creep of aluminium alloys (see paragraph 5.4 of this document). Lundberg ([72], [74] and [75]) gives the background to the rules in EN 1999-1-2 [7] concerning creep. According to background document [72], it is assumed that the 0,2% proof stress is sufficiently conservative, so that creep effects in the design may be neglected in the material properties at elevated temperature. Background document [75] gives guidelines for incorporation of creep in future versions of EN 1999-1-2 [7]. Three different stages, with increasing complexness and accuracy, are proposed. Next to the current rule, these stages comprise: • Different buckling curves, depending on the fire resistance requirement, implicitly taking account of creep could be determined for relevant alloys. • Explicit formulas for calculation of creep increments to be considered in non-linear structural analyses could be given for application of advanced calculation methods. In the document, it is questioned whether simple uni-axial models would be sufficient to simulate total structural behaviour.

In background document [74], it is stated that only moderate differences in maximum creep strain values are obtained when the total fire time is set to 30 min, 60 min, 90 min and 120 min, assuming a linear temperature development from room temperature to the maximum temperature. It is concluded in the document that it seems to be necessary to consider the creep problem for all four fire resistance periods mentioned above.

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4.9 Evaluation of mechanical properties

Mechanical properties of aluminium depend on the temperature. At elevated temperature, the 0,2% proof stress, the tensile strength and the modulus of elasticity of aluminium decrease, while

creep, which is normally neglected at room temperature in structural designs, may become significant at elevated temperature. The mechanical properties of aluminium reduce faster than those of steel at increasing temperature.

The decrease in strength depends on temperature, alloy, temper and time of exposure at elevated temperature. In case of heat-treated alloys, the temper changes gradually when they are subjected to a period at elevated temperature. The strength of heat treated, naturally aged alloys (tempers ≤ T4) may increase at moderately elevated temperature, because of artificial ageing. At higher temperatures, the strength reduces at increasing temperature and alloys in these tempers then show similar strength as artificially aged alloys (tempers ≥ T5). In case of cold-worked alloys, the extra strength at room temperature obtained through cold working gradually vanishes at elevated temperature.

Tests show that the creep rupture stress for rupture within one hour is for most alloys and tempers lower than the 0,2 % proof stress for temperatures higher than 200 ºC. In case of temperatures below 200 ºC, the creep rupture stress is in most cases between the 0,2 % proof stress and the tensile strength. Non-heat treatable alloys show more influence of creep on the strength than heat treatable alloys.

Creep deformations of 0,5 % may have an important influence on the structural behaviour. Tests show that the stresses at which these creep deformations occur may be up to 30 % of the 0,2 % proof stress at temperatures of 200 to 300 ºC in case of non-heat treatable alloys. For heat treatable alloys, this percentage is 80 %.

Thermal expansion may influence the internal load and stress distributions in structures. The coefficient of thermal expansion of aluminium is approximately two times that of steel.

Almost all tensile tests found in literature are carried out after a heating period at a constant temperature, during which the specimens were unloaded (steady state). The material properties listed in EN 1999-1-2 [7] are based on these tensile tests. The creep tests found in literature were carried out with a constant load level during a period with constant temperature. In a fire, however, the temperature increases and the load is usually assumed to remain constant. In order to obtain material properties that are closer to the real behaviour in fire, it is recommended to carry out tensile tests with constant load and heating rates that are present during fires (transient state tests). Influence of creep and possible changes in the temper on the material properties are implicitly taken into account in these tests.

There is a need to carry out tensile tests on alloys and tempers that are listed in EN 1999-1-1 [6] and often applied in structures, but that are not yet listed in EN 1999-1-2 [7]. Besides, material properties of the heat-affected zone at elevated temperature should be determined with tensile tests.

In order to draw conclusions on the influence of primary and secondary creep on the stress-strain relation, tests should be carried out with a load level during the creep period that is lower than the creep rupture load. Tensile tests should subsequently be carried out after this creep period. In conclusion, Figure 4.66 gives the time-temperature and time-load relations of most of the tests

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found in literature, while Figure 4.67 gives the time-temperature and time-load relations of recommended tests.

heating loading

Load Temperature Steady state tensile test Creep rupture test

Time Time

Figure 4.66 – Relations between temperature, load and time of the tests found in literature

heating loading Load

Temperature Steady state tensile test Creep rupture test Transient state test

Time Time

Figure 4.67 – Relations between temperature, load and time of recommended tests

Table 4.5 gives an overview of the mechanical properties at elevated temperature. In this table, it is indicated whether the properties are known, or whether more research is necessary.

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Table 4.5 – Overview of mechanical properties at elevated temperature

Mechanical property Status Remarks

Shape of the stress- Known Less strain hardening is apparent as at room temperature. strain relation The relation depends on the strain rate. Proportional limit Not known Not documented for the tensile tests carried out 0,2 % proof stress Partially Known for a limited amount of alloys. known No transient state tensile tests were found in literature. Tensile strength Partially See yield strength. known Limited information was found on the homogeneous strain (εb). Weld / HAZ Not known The strength of the weld and the HAZ at elevated properties temperature should be determined. Modulus of Partially No test data for temperatures exceeding 370 ºC. elasticity known Poisson ratio Not known No tests found to determine the static shear modulus Creep Partially The influence of creep on strength for stress levels lower known than the creep rupture stress is not known; The influence of creep on stiffness is not known; It is not known whether creep has influence in transient state situations.

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5 Structural behaviour of fire exposed aluminium structures

Knowing the mechanical properties of fire exposed aluminium alloys, these properties can be used to evaluate the behaviour of an aluminium structure exposed to fire. This is the subject of the current chapter. The chapter starts with an overview of failure mechanisms. Following, the evaluation of individual members, of parts of a structure and of entire structures is discussed.

5.1 Overview of failure mechanisms and evaluation methods

Basically, codes for aluminium or steel structures exposed to fire (EN 1999-1-2 [7] and EN 1993- 1-2 [4] respectively) distinguish the same failure mechanisms as in normal temperature design. However because of changes in material properties, other failure mechanisms may become decisive in fire compared to room temperature. Additional, thermal expansion may result in large deformations or, when thermal expansion is partially or entirely restrained, in high internal stresses. Visco-plastic material behaviour may on the one hand decrease the material strength, and on the other hand result in large deformations and / or relaxation of stresses.

The following relevant failure modes of aluminium structures when exposed to fire are distinguished in EN 1999-1-2 [7]: - The combination of cross-sectional forces applied on a member may exceed the resistance of the cross-section. Cross-sectional forces may be the result of externally applied actions or they may develop because of thermal expansion. The cross-sectional resistance of members in tension and bending is discussed in paragraph 5.2; - Connections between members may fail. Paragraph 5.3 discusses the strength of connections; - Deformations may become such that compatibility between parts of the structure is no longer maintained. Deformations may increase dramatically during a fire because of influence of creep, because of the development of plastic hinges, because of reduction in material stiffness or stiffness of connections and because of thermal expansion; - Buckling of members that are partly or entirely in compression may occur. The buckling modes that can be distinguished are buckling of the entire member (elaborated in paragraph 5.4) or local buckling of the cross-section (paragraph 5.5). Interaction between local and global buckling may also occur.

EN 1999-1-2 [7] gives simple calculation models for individual components. When evaluating individual components, only the effects of thermal deformations resulting from thermal gradients across the cross-section need to be considered. The effects of axial or in-plain thermal expansions may be neglected. Additional, the boundary conditions at supports and ends of a member may be assumed to remain unchanged throughout the fire exposure. The simple calculation models in EN 1999-1-2 [7] consist of analytical equations for failure mechanisms of components. In the simple calculation models, the partial factors for resistance of cross-sections and for resistance of members subjected to instability are replaced by the partial factor for fire. The recommended value for this partial factor is 1,0.

EN 1999-1-2 [7] also provides the possibility to apply advanced calculation models to check an individual component, to check a part of the structure or to check the entire structure. In this case, the relevant failure mode during fire exposure, the temperature-dependent material properties and member stiffness and effects of thermal expansions and deformations shall be taken into account. In the fire design, deformations at ultimate limit state, implied by the calculation method, shall be limited to ensure that compatibility is maintained between all parts of the structure.

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The advanced calculation models applied shall be validated based on relevant test results. Sensitivity analyse shall be carried out on critical parameters (buckling length, element sizes, load level). The application of advanced models is the subject of paragraph 5.6.

5.2 Cross-sectional resistance

5.2.1 Members loaded in tension

The thermal conductivity of aluminium is so high that in many cases the temperature will be uniformly distributed. In this case the resistance of the cross-section can be determined by multiplying the strength at elevated temperature with the section area.

A non-uniform temperature distribution may occur for members that are protected at some sides and not protected at other sides. This could for example be the case for members in a partition wall that is heated at one side and not heated directly at the opposite side. When a non-uniform temperature distribution over the cross-section is present, thermal expansion in different parts of the cross section is unequal. As the part of the cross-section with the highest temperature tends to expand more than colder parts, compression stresses may develop in the part with the highest temperature. The component that was initially loaded in tension, is then loaded in bending at elevated temperature. At increasing temperature during the fire, the 0,2 % proof stress reduces and after a certain time it approaches the externally applied tension load. In case of elastic-perfectly plastic material behaviour, the internal stresses by thermal expansion then flow off and the member is, at its critical temperature, again loaded in tension. However, the σ-ε diagrams at elevated temperature in paragraph 4.2.2 show that the strength may reduce at a relatively small plastic strain of 0,6 to 1,0 %. The assumption of elastic-perfectly plastic material behaviour is thus not justified for all aluminium alloys at elevated temperature. Tests on members in tension with a non-uniform temperature distribution were not found in literature.

Article 4.2.2.2 in EN 1999-1-2 [7] gives simple calculation models both for a uniformly distributed temperature and a non-uniformly distributed temperature. The calculation model for uniformly distributed temperature the resistance of the cross-section can be determined by multiplying the strength at elevated temperature with the section area. In case of a non-uniform temperature distribution, the contribution of each part of the cross- section with a specific temperature is taken into account by using the reduced 0,2% proof stress at that temperature for the specific part of the cross-section. The strength of the entire cross-section is obtained by the summation of the strengths of the individual parts. The calculation model thus assumes elastic-perfectly plastic material behaviour.

In case of a heat affected zone in tension members with a non-uniform temperature distribution, EN 1999-1-2 [7] specifies that the 0,2% proof stress should be multiplied with the reduction coefficient for the weld at room temperature and by the relative value of the 0,2% proof stress at elevated temperature. As indicated in paragraph 4.5, the strength reduction at elevated temperature of the heat affected zone may give conservative results, as the reduction of the strength of the heat-affected zone through annealing is then taken into account twice. In case of a uniform temperature distribution, a reduction for welding of the strength of heat- affected zones is not specified. This seems to be inconsistent.

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5.2.2 Members loaded in bending

The actual cross-sectional bending capacity depends on the rotation capacity of the cross section. In order to provide simple verification rules, EN 1999-1-2 [7] gives a classification system for

cross-sections. The rotation capacity of members in classes 1 and 2 is such that the plastic capacity of the cross-section can be reached without instability problems. In case of members in class 3, the elastic capacity with the 0,2 % proof stress in the furthest fibre can be reached. Members in class 4 buckle before the 0,2 % proof stress is reached in the furthest fibre. The classification system is elaborated more extensively in paragraph 5.5.5.

For members in bending with a uniform temperature distribution, the cross-sectional resistance may be obtained by multiplying the 0,2 % proof stress at elevated temperature with the section modulus. For members with a non-uniform temperature distribution, the same considerations apply as for members in tension.

Tests on tubes of alloy 6082 in bending at elevated temperature were carried out by Amdahl et al. [15]. These tubes are not sensitive to lateral-torsional buckling and the capacity of the beam thus depends on the capacity of the cross-section. The tests are difficult to use for verification of mechanical response models, because the beam ends were substantially colder than the rest of the specimens. As the beam ends were clamped (i.e. the rotation in plain was restrained), a mechanism occurred after plastic hinges developed near the beam ends and in the middle section. The critical temperature thus depended on the cross-sectional capacities of both the warmer middle cross- section and of the colder beam-ends. Besides, test temperature, time at elevated temperature and loads were different in all tests. It is therefore difficult to draw conclusions on the influence of individual parameters on the capacity of the beams. The tests are described and discussed in Annex A.

Four reports are found in literature in which tests on insulated aluminium beams are described, carried out by CTICM [97], [98], [99] and [100]. The tests are conducted to determine the fire resistance classification of insulated beams for various values of the insulation thickness, the amount of loads and the load magnitude. No additional information about the behaviour of aluminium beams at elevated temperature result from these tests. Therefore they are not evaluated here.

Article 4.2.2.3 in EN 1999-1-2 [7] provides rules for the bending capacity of beams in all classes with a uniform temperature distribution. For these situations, the beam capacity at room temperature should be multiplied with the relative value of the 0,2% proof stress. For non-uniform temperature distribution, rules are provided for beams in classes 1 and 2. As in case of members in tension, the contribution of each part of the cross-section with a specific temperature is taken into account by using the reduced 0,2% proof stress at that temperature. For beams in classes 3 and 4 with a non-uniform temperature distribution, the beam capacity is calculated according to a uniform temperature distribution with a temperature equal to the maximum temperature in the section.

Only in case of members with a non-uniform temperature distribution of classes 1 and 2, the 0,2% proof stress of the heat affected zone should be determined by multiplying the 0,2% proof stress at elevated temperature with the reduction coefficient for the weld at room temperature. No specifications are given for the reduction of the strength of the heat affected zone in case of members of classes 3 and 4 or for members of classes 1 and 2 with uniform temperature distribution.

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5.3 Connections

Almost no research was found to the behaviour of aluminium connections exposed to fire. Both on the strength and on the stiffness of aluminium connections, data is lacking.

At elevated temperature, the difference in strength between the heat affected zone and the parent material may disappear, as indicated in paragraph 4.5.

According to Langhelle [64], it is often assumed in the analysis of a structure that the connections remain intact and that the forces developed in the different members will be transferred through the joints to neighbour members. This assumption is only correct when the overall capacity of the connection at least maintains the same relative capacity as the members joined by the connection. In order to verify this assumption, tests were carried out on welded connections. The amount of tests was however too little to draw general conclusions on the behaviour of welded connections. The tests are described in Annex B.

With the two-dimensional computer program Tasef v. 3.0, temperature gradients in insulated aluminium plates with a bolt through the plates are compared with a steel connection with the same dimensions. The comparison is described in Lundberg [73]. The temperature gradients in case of the aluminium connection were lower than in case of the steel connection.

EN 1999-1-2 [7] does not provide a simple calculation model for the strength of connections at elevated temperature. A statement is made for fire protected connections: the resistance of connections between members need not be checked provided that the thermal resistance of the fire protection of the connection is not less than the minimum value of the thermal resistance of the fire protection of any of the aluminium members joined by that connection. Furthermore, for welded connections the reduced strength in the heat-affected zones must be taken into account.

The code specifies that the boundary conditions at supports and ends of a member may be assumed to remain unchanged throughout the fire exposure. This implicitly assumes that the stiffness of connections (and of the adjacent members) remains unchanged throughout the fire. (Besides, it assumes that restrained thermal expansion does not influence the structural behaviour.)

5.4 Global buckling of members

Prevention of buckling is one of the main criteria for the dimensioning of components in compression, and in some cases also for components in bending. This paragraph starts with an introduction to buckling. Following, different types of buckling of members are discussed.

5.4.1 Introduction to buckling

Stability problems Consider an infinitely stiff column with linear elastic material behaviour according to Figure 5.1. The column, loaded in compression, is hinged supported in one end (A) and supported by a horizontal spring with linear stiffness k in the other end (B).

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u F F H B B . H = k u

L L

A A

Figure 5.1 – Model of an infinitely stiff column

The compression load F multiplied by a possible lateral deflection u generates the expelling moment around A, while the repulsing moment is generated by the spring load H multiplied by the length of the column. The lateral deflection u multiplied by the spring stiffness forms the load in the spring. Hence, equilibrium of moments in A is described according to equation (5.1).

= ⋅ − ⋅ = ⋅ − ⋅ ⋅ M A F u H L F u k u L (5.1)

As no moment can be applied in A, MA is equal to zero. This gives two possibilities: • The horizontal deflection is equal to zero, u = 0. • The compression load F is equal to the product of spring stiffness and length, F = k.L, in which case the horizontal deflection is undetermined. The latter possibility is a case of instability. Characteristic is that the deflection cannot be determined. The first case occurs for compression loads smaller than the product of spring stiffness and length. The load-deflection diagram is thus according to line (a) in Figure 5.2. The . load F = k L at which bifurcation occurs is called the critical load (Fcr) or Euler load.

Post-buckling behaviour It is possible that the spring stiffness depends on the deformation of the spring, hence H = k(u).u. For example, the load-displacement relation according to line b in Figure 5.2 occurs when the spring becomes stiffer for increasing deformations (positive post-buckling behaviour), line c occurs when the spring becomes less stiff for increasing deformations (negative post-buckling behaviour) and line d occurs when the stiffness of the spring depends on the direction of the deformation. The way the structure reacts to lateral deformations is called post-buckling behaviour. Note that the deformations on the horizontal axis in Figure 5.2 are small, so that geometric non-linearity does not yet influence the post-buckling behaviour. The load at which lateral deformations suddenly occur is called the critical load or Euler buckling . load, Fcr = k(0) L.

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b F b

d

a Fcr a

d

c c a, b, c, d

u

Figure 5.2 – Load-lateral deflection diagrams

Influence of geometric imperfections Real structures always have certain initial geometric imperfections, such as initial out of straightness, loads that apply not exactly in the centre of the bar or initial non-straightness of members. The influence of geometrical imperfections on buckling can be investigated when assuming an initial deflection u0 for the column in Figure 5.1. The system of equations for this problem is:

= + ∆ u uo u (5.2) F ⋅u = k(u) ⋅ ∆u ⋅ L (5.3)

Using equations (5.2) and (5.3), the total deflection u can be described as a function of the initial deflection uo:

k(u) ⋅ L F u = u = cr u (5.4) ⋅ − o − o k(u) L F Fcr F

Introducing n as the ratio between the critical load and the applied load, equation (5.5) arises.

n u = u (5.5) n −1 o

In case of small loads, n is large and the total deformation approaches the initial deformation. In case of loads approaching the critical load, n approaches the value of 1 and the total deformation becomes infinite. The stiffness of the system is apparently reduced with a factor n/(n-1). As an example, the load-deflection diagram of an initially imperfect system in case of a linear spring stiffness is indicated with a grey line in Figure 5.3.

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u0 u

Figure 5.3 – Load deflection diagram in case of an initially imperfect system

Influence of yielding and residual stresses In many structures, interaction between yielding and instability occurs. This causes that also structures with a horizontal or positive post-buckling behaviour eventually fail. The load-bearing resistance through yielding usually decreases at increasing lateral displacement. The ultimate strength is obtained by the intersection of buckling and plasticity. Residual stresses may decrease the ultimate strength.

Buckling Buckling is a type of instability in which a member loaded (partially) in compression deflects in a direction perpendicular to the direction in which the load is applied. Important types of buckling are given in Figure 5.4.

Buckling of members in compression Buckling of members in Local buckling bending Flexural Torsional Flexural- Lateral-torsional buckling Of a plate Of a member torsional

Figure 5.4 – Buckling of members in compression (left-hand), buckling of members in bending (middle) and local buckling (right-hand) (Source for the left-hand and middle pictures: Over Spannend Staal [96])

These types of buckling are discussed separately in the following paragraphs.

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5.4.2 Flexural, torsional and flexural-torsional buckling

This paragraph gives the derivation of the critical load for flexural buckling and discusses the buckling curves for flexural buckling. Torsional and flexural-torsional buckling can be dealt with

in a similar way.

Critical load for flexural buckling One of the most well known types of buckling is that of a flexible column according to Figure 5.5. Euler was the first to derive the buckling load of a column. His derivation has been noted in many books on instability, such as Timoshenko and Gere , Bleich [19] and Galambos [42].

F F F

u(x) u(x)

L L L

Figure 5.5 – Buckling of a flexible column

The internal moment in the bended column is given in equation (5.6). The external moment applied on the column is equal to equation (5.7).

d 2ux() Mx()=⋅ EI (5.6) iydx2 = ⋅ M u (x) F u(x) (5.7)

Equilibrium is achieved when the internal moment equals the external moment. Hence:

2 dux()−= F 2 ux( ) 0 (5.8) dx EI y

The general solution for equation (5.8) is:

⎛⎞F ⎛⎞F ux()=⋅ A cos⎜⎟ x +⋅ B sin ⎜⎟ x (5.9) ⎜⎟EIEI ⎜⎟ ⎝⎠yy ⎝⎠

Boundary conditions u(0) = 0, u(L) = 0 are satisfied when A = 0 and u(x) is according to equation (5.10), in which m is a natural number.

⎛ m ⋅π ⎞ u(x) = B ⋅sin⎜ x ⎟ (5.10) ⎝ L ⎠

Substitution of equation (5.10) in (5.8) results:

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2 ⎛⎞()mπ Fm⎛⎞⋅π ⎜⎟−⋅Bxsin =0 (5.11) ⎜⎟LEI2 ⎜⎟ L ⎝⎠y ⎝⎠

Equation (5.11) can be solved when B is zero, i.e. when no lateral deflection occurs and the load is lower than the critical load, or when the part of the equation between brackets is zero, hence: m22π EI F = y (5.12) cr L2

The smallest value for the critical load is found for m = 1. The middle picture in Figure 5.5 gives the deflected shape in case m=1. The right-hand picture gives the deflected shape for m=2. The critical load thus depends on the modulus of elasticity. This property decreases for increasing temperature. Other support conditions are covered by introducing the buckling length (Lbuc) (equation (5.13)). This buckling length is related to the wavelength of the first buckling mode. In case of the hinged column in Figure 5.5, Lbuc = L. In case of a column clamped at both sides Lbuc = 0,5 L and in case of a column clamped at one side and free at the other side Lbuc = 2 L.

m22π EI = y Fcr 2 (5.13) Lbuc

The critical load in equation (5.12) is valid for a linear elastic material. Shanley [94] showed that in case of inelastic material, the modulus of elasticity in equation (5.12) should be replaced by the tangential modulus of elasticity (Et). The definition of the tangential modulus of elasticity (Et) and the secant modulus of elasticity (Es) is given in Figure 5.6. The figure shows that the value of Et depends on the strain (ε). In an iterative process, the value of Fcr should be found for which the stress at buckling corresponds to the strain at Et. The method is described in Bleich [19].

400 350 300 ]

2 250 200

[N/mm 150 stress-strain curve Initial mod. of el. (E) 100 Tangent mod. of el. (Et) 50 Secant mod. of el. (Es) 0 0 0.005 0.01 0.015 0.02 0.025 ε [-]

Figure 5.6 – Modulus of elasticity and secant and tangent mod. of el. at 250 N/mm2 for alloy 5083 H34

In the simple calculation models in EN 1999-1-1, the elastic critical buckling load is applied, i.e. applying equation (5.13) and using the initial modulus of elasticity E also in case of alloys with an

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inelastic stress-strain relation. The influence of inelastic material is taken into account by introducing a different buckling curve.

Ultimate buckling resistance

Inelastic material behaviour and yielding, initial geometric imperfections and residual stresses may cause the ultimate buckling resistance of aluminium columns to be smaller than the critical elastic buckling load. Mazzolani [78] gives an overview of the influence of each of these variables on the buckling load (at room temperature).

Buckling curves defined in the Eurocodes for steel and aluminium give the ultimate buckling resistance as a function of a parameter called the relative slenderness. Buckling curves take into account influences of yielding, initial geometric imperfections and residual stresses. The relative slenderness (λrel) can be determined using equation (5.14).

N A⋅ L 2 f λ = pl = k ⋅ 0 (5.14) rel π 2 ⋅ Fcr I y E

Equation (5.14), shows that the relative slenderness depends on the ratio between the 0,2% proof stress and the modulus of elasticity. A large value of this relative slenderness, corresponding to a slender column, indicates that the column is sensitive to buckling, while a small value, corresponding to a stocky column, indicates that failure is dominated by reaching the plastic capacity. The buckling curves defined in the Eurocodes for steel and aluminium are given in Figure 5.7. The horizontal axes give the relative slenderness, the vertical axes give the buckling foactor. In order to obtain the ultimate buckling resistance, this buckling factor should be multiplied with the cross-sectional resistance.

steel aluminium 1.0 1.0 a 0.8 class A b 0.8 class B c 0.6 0.6 d [-] [-] χ χ 0.4 fire 0.4

0.2 0.2

0.0 0.0 0.0 1.0 2.0 3.0 0.0 1.0 2.0 3.0 λrel [-] λrel [-]

Figure 5.7 – Buckling curves in EN 1993 for steel and in EN 1999 for aluminium

In an experimental research on fire exposed steel members in compression, it was concluded that the correlation between the buckling resistance and the slenderness determined with material properties at elevated temperature is better than the correlation between buckling resistance and slenderness determined with material properties at ambient temperature. (Franssen et al. [41] and Talamona et al. [103]). Based on this research, EN 1993-1-2 [4] specifies that the relative

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slenderness of steel columns subjected to buckling should be determined using the material properties at elevated temperature. Based on the same research, EN 1993-1-2 [4] gives an alternative buckling curve for steel columns at elevated temperature. This curve is less favourable than the buckling curves at room temperature in the Eurocode EN 1993-1-1 [3], see Figure 5.7.

A reasonable explanation for the fact that the buckling curve at elevated temperature should be less favourable is the following: Shanley [94] showed that the critical buckling load depends on the tangential modulus of elasticity. The relative slenderness is however determined using the (initial, linear elastic) modulus of elasticity and the yield stress. At room temperature, the stress- strain curve of mild steel can be regarded as elastic-perfectly plastic. Thus, the proportional limit is equal to the yield stress and the initial modulus of elasticity applies up to the yield stress. At elevated temperature however, the stress-strain curve of steel is inelastic. The proportional limit lower than the yield strength and the tangential modulus of elasticity decreases between the proportional limit and the yield strength. The buckling curve at elevated temperature implicitly takes the inelastic material properties into account.

A similar research was not carried out for aluminium. For fire exposed aluminium columns, the same buckling curves apply as for room temperature design (see Figure 5.7). As aluminium shows inelastic material behaviour at normal temperature, the buckling curves for aluminium already account for inelastic material properties: curve ‘A’ in Figure 5.7 should be applied for alloys with material characteristics approaching an elastic-perfectly plastic behaviour, while curve ‘B’ should be applied for alloys for which the proportional limit is considerably lower than the 0,2 % proof stress. Data on the proportionality limit at elevated temperature was not found in literature. It is therefore uncertain whether the difference between the proportionality limit and the 0,2 % proof stress decreases or increases at elevated temperature. It is therefore not known whether the buckling curve at normal temperature is appropriate, conservative or unsafe for fire exposed aluminium columns.

EN 1999-1-2 [7] specifies that the relative slenderness should be determined with material properties at room temperature. The ratio between the reduction coefficient of the modulus of elasticity and the relative value of the 0,2% proof stress of the alloys listed in EN 1999-1-2 [7] generally increases at increasing temperature (Lundberg [67]). Consequently, the calculation model overestimates the value for the relative slenderness at elevated temperature. This may lead to conservative ultimate buckling resistance at elevated temperature.

Creep influence Paragraph 5.4.2 shows that lateral deflection in the column increase for increasing load, until buckling occurs. As indicated in paragraph 4.8, creep strains develop at elevated temperature. For a member in compression, the lateral deflection might increase in time at elevated temperature, because of creep. Because of this, the bending moment in the column increases and collapse might occur. This phenomenon is called creep buckling (Langhelle [62]). In order to take creep into account in the verification rules for columns, EN 1999-1-2 [7] specifies a factor with which the design value of the load should be multiplied. The value for this factor is specified at 1,2, independent of the elevated temperature and the time of exposure to this temperature. The value for this creep factor is not based on experimental or numerical data.

Tests on buckling of columns at elevated temperatures are carried out by Amdahl et al. [14]. Aluminium tubes (probably round tubes) of alloy 6082 were tested with a length of 2000 mm, a diameter of 150 mm and a thickness of 5 mm. One of the tests was carried out at a constant temperature in which the load was increased step-wise, so that creep could develop.

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Langhelle et al. carried out a more extensive test series on aluminium columns in bending and compression, which are subjected to flexural buckling. The tests are reported in Langhelle [36], Langhelle et al. [64] and Eberg et al. [36]. The sections tested were square tubes 120 mm x 7 mm and 120 mm x 5 mm of alloy 6082 T4 and

T6 and a buckling length of 1900 mm. The load was applied with an eccentricity of 8 mm. The ratio between the stress caused by normal force and the maximum stress caused by bending was thus 4,5 for t=7 mm and 4,6 for t=5 mm. Based on the deformations measured, it was concluded in both studies that the influence of creep was moderate until the last load level, where an accelerating creep effect was observed. This eventually leaded to global buckling. The test series of Amdahl et al. [14] is discussed in Annex C.

Langhelle [36], [64] and [36] also carried out transient state tests with increasing temperature and constant load during heating. The same types of specimens were applied as in the creep tests elaborated above. Tests carried out with a relatively low heating rate, so that the fire resistance period was 60 minutes, gave the same critical temperature as tests with a relatively high heating rate, so that the fire resistance period was 20 minutes. The critical temperature, apart from one test, was ranging from 220 to 290 ºC. and the ratio between the load applied in the transient state tests and the ultimate resistance at room temperature was ranging from 0,35 to 0,61. Based on this, it was concluded that for the parameter field considered, creep has no influence on the ultimate buckling resistance of columns in transient state situations. When comparing the resistance determined in the tests with the resistance determined with the calculation model in EN 1999-1-2 [7], it was concluded that the calculation model in the code is more conservative at elevated temperature than at room temperature. This conservativeness could either be based on the fact that the properties at room temperature are used to determine the relative slenderness at elevated temperature, or on the fact that creep was not detected in the tests, yet a creep factor of 1,2 was incorporated in the calculation model. The research of Langhelle [36], [64] and [36] is discussed in Annex D.

Columns with temperature gradients over the cross-section In case of a column with a temperature gradient over the cross-section, EN 1993-1-2 [4] and in EN 1999-1-2 [7] allow the same calculation models to be applied as for uniform temperature distribution, but with applying the value for the 0,2 % proof stress of the part with the maximum temperature applied for the entire cross-section. However, unequal thermal expansion may cause large initial bending of the column and / or internal stresses. Ranby [91] carried out a numerical and empirical research to buckling of steel C-sections in a wall. The C-section is first subjected to flexural buckling, but as the temperature rises, the gypsum boards at the fire-exposed side will crack and a temperature gradient will develop over the cross section of the C-section. Consequently, a bending moment develops and the section is subjected to flexural-torsional buckling. Mechanical response models are being proposed for flexural and torsional-flexural buckling at elevated temperature. The models are based on an equation given in the European code for design of steel structures- plated structural elements, EN 1993-1-3 (currently EN 1993-1-5 [5]), and take into account the following properties: - The reduced 0,2 % proof stress for the average temperature over the cross-section (note that the yield strength is not used); - Eccentricity due to unequal thermal expansion of the section; - Eccentricity due to the shift in neutral axis due to the difference in modulus of elasticity due to temperature differences over the cross-section; - The bending stiffness of the cross-section taking into account the difference in modulus of elasticity due to temperature differences over the cross-section.

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Research to buckling of steel components at elevated temperature was also reported in Zhao et al. [113]. Also in this research, it is accounted for eccentricity due to unequal thermal expansion of the section. A simplification applied in this research is that the slenderness parameter λrel is calculated at room temperature. The simplification is based on the fact that for the cold-formed

steel considered, the ratio f0,2,θ / Eθ varies only slightly with the temperature.

5.4.3 Lateral-torsional buckling (Art. 4.2.2.3)

A member loaded in bending may be subjected to flexural torsional buckling. In this case, the compression flange may reach its critical load, while the tension flange does not buckle. As a result, the beam may rotate about it’s longitudinal axis and it may deflect in lateral direction. Mazzolani [78] gives an overview of lateral-torsional buckling of aluminium beams.

The procedure to check lateral-torsional buckling of beams in EN 1999-1-1 [6] is basically similar to that for flexural buckling of a column, i.e. the elastic critical load should first be determined and the ultimate resistance can then be determined using a prescribed buckling curve.

EN 1999-1-2 [7] also provides a rule for beams subjected to lateral-torsional buckling at elevated temperature. Independent of the temperature distribution, the buckling resistance at elevated temperature may be determined by multiplication of the buckling resistance at room temperature and the relative value of the 0,2 % proof stress at maximum temperature. As for columns subjected to buckling, the relative slenderness should be determined at room temperature and the same buckling curve applies as for room temperature. In contradiction to columns subjected to buckling, a creep factor with which the load on the beam should be multiplied is not specified for beams subjected to buckling. According to Lundberg [67], the stresses are low in case of lateral-torsional buckling, and creep will be negligible. Therefore, no creep factor is taken into account.

No tests are found in the literature on beams subjected to lateral-torsional buckling at elevated temperature.

5.4.4 Interaction of buckling phenomena (Art. 4.2.2.4 (6))

EN 1999-1-2 [7] provides simple calculation models for beam-columns (i.e. members loaded by a combination of compression and bending) at elevated temperature. The verification rules for room temperature design in EN 1999-1-1 [6] apply with some modifications. These modifications are: - The normal force in the column (action) should be multiplied with a factor to take account of creep effects. The value for this factor is specified at 1,2, independent on the elevated temperature and the time of exposure to this temperature; - The bending moment resistance and the normal force resistance of the beam-column should be determined according to the simple calculation models provided by EN 199-1-2 [1] for pure bending and pure compression. This means that the relative value of the 0,2% proof stress is taken into account in the resistance of the beam-column. For flexural, torsional and lateral-torsional buckling, the relative slenderness should be determined at room temperature.

5.5 Local buckling

Local buckling is especially important for aluminium structures, because of the low modulus of elasticity and the thin wall thickness usually applied in sections. As this document is a literature study belonging to a project on local buckling of slender aluminium sections exposed to fire, local buckling is discussed here more extensively than other failure mechanisms.

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5.5.1 Critical load

Buckling of plates is extensively investigated and written down in many books on stability and buckling, such as Timoshenko and Gere [105], Bleich [19] and Galambos [42].

Assumptions in thin plate theory The equation of equilibrium of a plate, which forms the basis of the equation of the critical load of a plate, is based on the theory of plate bending. Some assumptions apply in the theory of plate bending: 1. The thickness of the plate is considered small compared with other dimensions; 2. The deflections are small (i.e. less than the thickness of the plate); 3. The middle plane of the plate does not stretch during bending. This middle plane remains a neutral surface, analogous to the neutral axis of a beam; 4. Plane sections rotate during bending to remain normal to the neutral surface and do not distort, so that the stresses and strains are proportional to their distance form the neutral surface; 5. The loads are entirely resisted by bending and twisting of the plate elements. The effect of shear forces is neglected.

Equilibrium The equation of equilibrium of a plate loaded in compression and bending has been derived by Saint Venant:

∂4w ∂4w ∂4w t ⎛ q ∂2w ∂2w ∂2w ⎞ + 2 + = ⎜ +σ + 2σ + σ ⎟ (5.15) 4 2 2 4 ⎜ xx 2 xy yy 2 ⎟ ∂x ∂x ∂y ∂y D ⎝ t ∂x ∂x∂y ∂y ⎠ Et 3 D = (5.16) 12()1−ν 2

The critical stress of a plate can be derived by omitting the lateral load (q) in equation (5.15). As an example, consider the rectangular plate with dimensions ‘a’ and ‘b’ according to Figure 5.8. The plate is loaded in compression by a uniformly distributed load along the edges and simply supported at edges (on which the load is applied) and sides (parallel to the load direction).The critical load of a plate with these loading and boundary conditions was first determined by Bryan [24].

b

x y

w(x,y)

a w (x,y)

Figure 5.8 – Buckling of a simply supported plate

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For the plate considered, σxy and σyy are equal to zero and σxx = σ, thus:

∂4w ∂4w ∂4w t ⎛ ∂2w ⎞ + 2 + = ⎜σ ⎟ (5.17) ∂x4 ∂x2∂y2 ∂y4 D ⎜ ∂x2 ⎟ ⎝ ⎠

The boundary conditions for solving equation (5.17) are that the lateral deformation at the plate sides and edges are equal to zero, i.e. w(0,y) = 0, w (a,y) = 0, w(x,0) = 0 and w(x,b) = 0. The solution for this equation is:

⎛ m⋅π ⎞ ⎛ n ⋅π ⎞ w(x, y) = A⋅sin⎜ x ⎟ ⋅sin⎜ y ⎟ (5.18) ⎝ a ⎠ ⎝ b ⎠

In which m and n are natural numbers. Substituting equation (5.18) in (5.17) results:

4 2 2 4 2 ⎡⎛ mπ ⎞ ⎛ mπ ⎞ ⎛ nπ ⎞ ⎛ nπ ⎞ ⎛ mπ ⎞ t ⎤ ⎛ m ⋅π ⎞ ⎛ m ⋅π ⎞ ⎢⎜ ⎟ + 2⎜ ⎟ ⎜ ⎟ + ⎜ ⎟ − ⎜ ⎟ σ ⎥A⋅sin⎜ x ⎟ ⋅sin⎜ y ⎟ = 0 ⎣⎢⎝ a ⎠ ⎝ a ⎠ ⎝ b ⎠ ⎝ b ⎠ ⎝ a ⎠ D ⎦⎥ ⎝ a ⎠ ⎝ b ⎠ (5.19) Equation (5.19) can be solved when A is zero, i.e. when no lateral deflection occurs and the load is lower than the critical stress, or when the part of the equation between brackets is zero, hence:

2 π 2a 2 D ⎛ m2 n2 ⎞ σ = ⎜ + ⎟ (5.20) cr 2 ⎜ 2 2 ⎟ m t ⎝ a b ⎠

The lowest value of the critical stress is found for n = 1, i.e. the plate buckles in such a mode that there is one half-wave in the direction perpendicular to compression. Expression (5.20) can be rewritten according to equations (5.21) and (5.22), provided n = 1.

π 2D σ = k (5.21) cr cr tb2 m2b2 a2 k = + + 2 (5.22) cr a2 m2b2

The lowest value for the critical stress is found for the lowest value of kcr. This is the case when m multiplied by b is closest to a. (Note that m is a natural number). This means that the middle picture in Figure 5.8 indicates the buckled shape when b is approximately equal to a (m=1) and that the right-hand picture indicates the buckled shape when b is approximately equal to ½.a (m=2). Figure 5.9 gives the buckling factor kcr as a function of the ratio a/b.

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m=1 m=3 m=5 m=2 m=4 m=1 m=2 8

7

m=3 6

5 m=4 m=5 kcr 4 m=1 3 m=2 2 m=3 m=4 1 m=5

0 0123456 a/b

Figure 5.9 – Buckling factor kcr as a function of the ratio a/b for different values of m

Figure 5.9 shows that a lower boundary for kcr for the plate considered is 4. This results in the equation for the critical stress: π 2 2 σ = E ⎛⎞t crk cr ⎜⎟ (5.23) 12() 1−ν 2 ⎝⎠b

Boundary conditions The above elaboration of the critical stress concerns a plate simply supported at all sides. Various authors have studied the critical stress of plates with other boundary conditions, such as clamped or free sides. Their results are summarised by Gerhard and Becker [43]. The critical stress of plates with other boundary conditions can also be expressed according to equation (5.23), with different values for buckling factor kcr. Table 5.1 gives an overview of the lower values of kcr for plates with simply supported edges and various supports of the sides.

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Table 5.1 – Minimum values for kcr for plates with simply supported edges and various supports of the sides

Type of plates Boundary conditions kcr Both sides simply supported 4,00

Internal parts One side clamped, other side simply supported 5,50

Both sides clamped 7,00

One side simply supported, other side free 0,43 Outstands One side clamped, other side free 1,25

In practice, boundary conditions as given in Table 5.1 not always occur. In many cases, different plates of a section or a structure interact. The boundary conditions may then be in between purely hinged and purely clamped. The critical load of the section depends on the buckling length of the individual plates (Mennink [85]).

Figure 5.10 gives some examples. The plates in the rectangular hollow section according to the left-hand picture are usually considered hinged. The buckling lengths of the different plates are however not equal, so interaction occurs and the buckling length of the section is in between the individual buckling lengths of the different plates of the section. In case of a large difference in plate widths of the individual plates, it is possible that the plates with a smaller width remain intact. In such a case, the plates with a larger width can be considered as clamped. A similar case is found for U-sections as indicated in the middle picture of Figure 5.10. In this case, interaction between buckling of outstands and internal part may occur. The buckled shape of a square hollow section is according to the right-hand picture in Figure 5.10. The buckling lengths of the individual plates of this section are equal, consequently the plates can be considered as simply supported.

Figure 5.10 – Local buckling of a rectangular hollow section, U-section and square hollow section

More information on interaction of plates in real sections is given in Mennink [85].

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5.5.2 Inelastic material

The equations for the critical stress in the previous paragraph are valid for linear elastic material. In that case, the value of the tangential modulus of elasticity is equal to the initial modulus of

elasticity at all stress levels. Aluminium however has inelastic material characteristics.

As local buckling causes stresses both in the direction of loading and perpendicular to this direction, the buckling load depends on the material characteristics in both directions. As aluminium shows anisotropic behaviour at yielding, it is not possible to simply replace the initial modulus of elasticity (E) by the tangential modulus of elasticity (Et) in the equation of the critical load, as applied by Shanley [94] in case of column buckling (Bleich [19]).

Applying the principle of virtual work, Stowell [102] determined the value for the factor η with which the critical elastic buckling load should be multiplied (equation (5.24)). This factor η depends on the support conditions. In his equations for inelastic buckling, he applied a Poisson ratio of 0,5, related to the incompressibility condition of the theory of plasticity. The values for η are given in Table 5.2.

πη2 2 σ = E ⎛⎞t crk cr ⎜⎟ (5.24) 12() 1−ν 2 ⎝⎠b

Table 5.2 – Factor η with which the critical elastic buckling load should be multiplied to account for inelastic material behaviour (Stowell [102])

Type of Boundary conditions η plates ⎛ ⎞ Both sides simply Es 1 1 1 3 Et ⎜ + + ⎟ supported E ⎜ E ⎟ Internal ⎝ 2 2 4 4 s ⎠ parts E ⎛ 1 3 E ⎞ s ⎜ + + t ⎟ Both sides clamped ⎜0,352 0,648 ⎟ E ⎝ 4 4 Es ⎠ One side simply E supported, other side s free E Outstands ⎛ ⎞ One side clamped, Es 1 3 Et ⎜0,428 + 0,572 + ⎟ other side free ⎜ ⎟ E ⎝ 4 4 Es ⎠

Bleich [19] proposed a simpler equation for the critical stress of a plate of inelastic material. He showed that his approach gives a lower border of the critical stress determined by the approach of Stowell [102]. Bleich [19] assumed that the tangent modulus of elasticity Et is effective in direction of the load and that the initial modulus of elasticity E is valid in the direction perpendicular to the load. He incorporated a plasticity reduction factor τ = Et/E for inelastic buckling of plates in the general equation of equilibrium (5.17):

∂ 4 w ∂ 4 w ∂ 4 w t ⎛ ∂ 2 w ⎞ τ + 2 τ + = ⎜σ ⎟ (5.25) 4 2 2 4 ⎜ 2 ⎟ ∂x ∂x ∂y ∂y D ⎝ ∂x ⎠

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It should be noted in that this equation, the factor τ in the second term of the left-hand side of equation (5.25) is arbitrarily chosen. It should have a value between 1 and τ. Elaboration of equation (5.25) results in the following equation for the critical stress:

π 2 2 σ = τ E ⎛ b ⎞ cr kcr ⎜ ⎟ (5.26) ()1−ν 2 ⎝ t ⎠

This equation applies for plates with all boundary conditions.

5.5.3 Buckling resistance of plates at room temperature

Post buckling behaviour A plate with linear elastic material characteristics does not collapse when reaching the elastic critical load. This is due to the fact that the parts of the plate near the supports are able to bear a higher load than the elastic critical load. Consequently, the stress distribution in the plate is uniform until the elastic critical load is reached and non-uniform at higher loads, as shown in Figure 5.11. σ > σ σ ≤ σ av cr cr σ cr

Figure 5.11 – Stress distribution in simply supported internal plates (Von Karman [53])

The post buckling behaviour of a plate can be analysed by using large deflection theory. Von Karman [52] derived the system of equations for this case. The equations are too complicated to be used in daily practice, however, for a limited number of boundary conditions, the system of equations was solved (Allen and Bulson [11]). For the investigated support conditions, the elastic post buckling stiffness (E*) of a plate with linear elastic material turns out to be linear for loads up to two times (Galambos [42]) or five times (Allen and Bulson [11]) the critical stress. Figure 5.12 shows the initial and post buckling stiffness of a plate and gives values for the post buckling stiffness for various support conditions.

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2

Boundary conditions Postbuckling

* E stiffness Simply supported, sides straight E* = 0,5 E cr

σ but free to move laterally 1 / Simply supported, sides free E* = 0,408 E σ Clamped, sides straight but free E* = 0,497 E buckling E to move laterally One edge simply supported, E* = 0,444 E other edge free 0 012 ε / εcr

Figure 5.12 – Post buckling stiffness of plates (Allen and Bulson [11])

Mennink [85] showed with Finite Element analyses that in case of long plates such as in real sections, mode jumping may occur. Mode jumping is the phenomenon that, at increasing deformation, the plate with initially e.g. 6 buckles along the length, corresponding to the first buckling mode, suddenly jumps into a deformation pattern with e.g. 8 buckles along the length. This mode jumping may be accompanied by a sudden drop of the load.

Initial imperfections Figure 5.13 shows the deflections of a plate with an initial out-of-flatness (grey line) in reference to the deflections of a plate without imperfections (black line). These curves are based on research by Hu et al. [48] and apply for plates of linear-elastic material. The left-hand picture gives the relation between the stress and the axial displacement (u) and the right-hand picture gives the relation between the stress and the maximum lateral displacement of the plate (w). It is shown that the initial imperfection has mainly influence on the load-displacement trajectory near the critical load. At loads far below the critical load, the lateral deflection is only slightly larger than the initial imperfection and at loads higher than the critical load, the large lateral deflection approaches that of an initially perfect plate.

F F

Fcr Fcr

u w

Figure 5.13 – Post buckling behaviour of plates (Allan and Bulson [11])

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Ultimate buckling resistance of mild steel The above given elaboration of the post buckling behaviour is valid for linear elastic material. Because of the occurrence of yielding, the stresses in the plates near the supported sides are subjected to a maximum. Hence, the ultimate strength of the plate depends both on the critical stress and the yield stress. Von Karman [53] introduced the effective with approach to determine the ultimate buckling resistance of steel plates. His approach is based on the simplification that the maximum force carried out on the plate, i.e. the stress distribution in the plate multiplied by the plate width, is described by an effective width multiplied by the material strength, as indicated by the following equation (see Figure 5.14):

b σ dy = b σ (5.27) ∫ eff max 0 b

½be ½be

σ max

σcr

Figure 5.14 – Effective width approach

Determination of the ultimate strength is now reduced to determining the effective width. This effective width represents a plate with such width, that the plate just buckles when the compressive stress reaches the yield stress. The effective width approach can be described in a similar way as applied for the ultimate resistance of columns, i.e. introducing the relative slenderness (λρ,rel) and the buckling factor (beff / b).

f λ = y (5.28) ρ ,rel σ cr b 1 eff = (5.29) λ b ρ,rel =⋅=⋅ Nu Afbteff y eff f y (5.30)

With the elastic critical stress (σcr) according to equation (5.23) Winter [112] carried out an extensive amount of tests on cold-formed steel sections. He concluded that for plates with initially imperfections and residual stresses, the effective width approach of Von Karman resulted in general in too high ultimate buckling resistances. He defined a modification on the effective width approach of Von Karman, resulting in equation (5.31) instead of equation (5.29) for simply supported internal parts. For simply supported outstands, equation (5.32) was proposed:

b 1 ⎛⎞1 eff =⋅−10,25 (5.31) λλ⎜⎟ b ρρ,,rel⎝⎠ rel

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b 1,19⎛⎞ 1 eff =⋅−10,30 (5.32) λλ⎜⎟ b ρρ,,rel⎝⎠ rel

Winter [112] also concluded that the effective width approach can also be applied to loads lower than the ultimate resistance. By using the maximum stress in the plate (σmax) instead of the yield stress (fy) in determining the relative slenderness (equation (5.28)), the equation can be applied to service loads as well as to the ultimate resistance. Mechanical response models to determine the ultimate local buckling resistance in modern codes are based on equation (5.31). In EN 1993-1-1 [3], the value 0,25 in equation (5.31) is replaced by 0,22.

Ultimate buckling resistance of aluminium The above approach is based on steel and valid for a material with a yield limit. In case of inelastic material behaviour as apparent for aluminium, it may be necessary to modify the approach. Local buckling of aluminium sections has been studied extensively. Some of the most resent studies are discussed here:

Langseth, Hopperstad and Tryland, [47] and [66] carried out stub column tests on square hollow sections and cruciform sections. For evaluating the strength, it was proposed to apply Stowell’s equation (5.24) for the critical stress and the effective width method of Von Karman (equation (5.29)) for the ultimate resistance. Thus, the ultimate resistance depends on the strain hardening behaviour of the alloy. The Poisson ratio in the inelastic range to determine the critical stress was assumed according to equation (4.5).

Mazzolani et all. [61], [79], [80], [82], [83] and [84] carried out an extensive amount of stub column tests on square hollow sections, rectangular hollow sections and C-channels. In order to let local buckling be the decisive failure mechanism, and not global buckling or interaction between local and global buckling, the length of the columns was very short (often between one and two times the width of the largest plate of which the column is composed). Based on the results, the following calculation model was proposed to determine the ultimate buckling resistance: • For members buckling in the inelastic range, the same calculation model was proposed as described by Langseth, Hopperstad and Tryland, [47] and [66]. For these members the influence of initial imperfections was not taken into account in the calculation model. • For members buckling in the elastic range, the ultimate resistance is based on the elastic critical load, i.e. on equation (5.23). Only for these members, a correction for initial imperfections was considered. The proposed effective width for this case is according to equation (5.33). The value of 0,11 was considered to be representative for average imperfections.

b σσ⎛⎞ eff =−cr10,11 cr (5.33) σσ⎜⎟ b max⎝⎠ max

It was shown that the ultimate load and the load-displacement diagrams determined with the above described method corresponded well with that determined in tests. Also, an equation was proposed for the critical load of sections composed of plates with different slenderness. The above described effective width method and the effective thickness method (EN 1999-1-1, equations (5.36) up to (5.38)) were checked with the experimental results.

Mofflin and Dwight [88] carried out stub column tests and numerical simulations of simply supported internal parts and outstands. For unwelded plates, the out-of-flatness applied in the

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calculations was 1/1000 times the section width. For welded plates, this out-of-flatness was 5/1000 times the section width, together with a distribution of residual stresses. The research resulted in a proposal for buckling curves for slender plates in compression (Mazzolani [78]).

Mennink [85] carried out stub column tests and numerical simulations of plates and sections, resulting in a proposal for a calculation model for interaction of buckling of plates in sections with arbitrary cross-section. It was concluded that for plates that buckle elastically, significant post-buckling strength is developed. Little post-buckling strength develops in plates that buckle inelastically, i.e. when the critical stress is larger than the proportional limit. For such, less slender plates the inelastic buckling strength provides a lower bound for the ultimate buckling resistance. The same conclusion was made by Jombock and Clark [50]. The equations provided by Mennink [85] to determine the average stress at the ultimate buckling resistance (σu,Mk) are as follows:

σσσ< =+ crpf ⇒ uMk, 0,68 cr 0,32f p (5.34) σ ≥ σ = σ cr f p ⇒ u,Mk cr (5.35)

Note that the critical stress in equation (5.35) should be determined for inelastic material.

Mainly based on the test results by Mazzolani et al. [61], [79], [80], [82], [83] and [84], a mechanical response model for local buckling of aluminium plates in compression was drafted for the Eurocode for aluminium structures, EN 1999-1-1 [6]. Instead of an effective width, EN 1999-1-1 [6] applies an effective plate thickness. Although Bulson and Cullimore [25] noted that “the reduced thickness method has no physical meaning and used unwisely can lead to confusion and subsequent error”, it was still proposed for the Eurocode (Landolfo and Mazzolani [61]). The critical buckling load and the ultimate resistance depends on the strain hardening behaviour, which is different for each alloy and temper. In order to simplify the calculation model, the code accounts for the strain hardening behaviour by dividing the alloys into two classes. Alloys divided in class A experience small strain hardening; i.e. the proportional limit is close to the 0,2 % proof stress. Alloys divided in class B experience large strain hardening; i.e. the proportional limit is considerably smaller than the 0,2 % proof stress. The code provides a calculation model for each of these classes, which makes it possible to let the calculation model be dependent on the values of the initial modulus of elasticity and the 0,2 % proof stress instead of the entire stress-strain relation.

The code also distinguishes members with and without longitudinal welds. The code makes no distinction in simply supported and clamped plates. Independent of the actual boundary conditions, all plates are conservatively treated simply supported.

250 1 E ε == (5.36) ff0,216,733 0,2 CC ρ =−12 (5.37) βε ()β ε 2 =⋅ρρ ⋅ ⎯⎯→=⋅ Nu btf0,2 Nup Nl (5.38)

In these equations, β is the slenderness parameter, which, for uniform compression, is equal to the width-to-thickness ratio of the plate. The coefficients of C1 and C2 are set depending on the alloy

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class, on whether or not welds are applied and on whether internal parts or outstands are applied. Applying a Poisson ratio equal to 0,3 and the equation for the elastic critical stress according to equation (5.23), equations (5.36) and (5.37) can be rewritten in a similar way as applied for global buckling:

f λ = 0,2 (5.39) ρ,rel σ cr c ⎛⎞1 ρ =−1 1 c (5.40) λλ⎜⎟2 ρρ,,rel⎝⎠ rel

Again, the 0,2 % proof stress is applied as the yield limit. Note that the elastic critical stress with the initial modulus of elasticity should be applied in equation (5.39), and not the critical stress for inelastic material. Thus, equation (5.23) should be applied and not equation (5.24) or (5.26). Influence of inelastic material on the ultimate resistance is taken into account by modified factors c1 and c2 in equation (5.40).

The relations between factors c1 and C1, and factors c2 and C2, are given in equations (5.41) and (5.42). Table 5.3 gives the values for factors c1 and c2 according to the code, when they are rewritten according to these equations.

2 12() 1− 0,3 C C c ==1 0,06286 1 (5.41) 1 16,73⋅π kk 2 12() 1− 0,3 C C c ==220,06286 (5.42) 2 ⋅π 16,73 C11kCk

Table 5.3 – Values for factors c1 and c2 according to EN 1999-1-1 [6]

Material classification Internal part Outstand

c1 c2 c1 c2 Class A, without welds 1,0 0,22 0,96 0,23 Class A, with welds 0,91 0,21 0,86 0,21 Class B, without welds 0,91 0,21 0,86 0,21 Class B, with welds 0,79 0,19 0,77 0,19

As equation (5.40) for aluminium is written in the same way as equations (5.31) and (5.32) for steel sections, it is possible to compare the mechanical response models for local buckling of uniformly compressed plates. In case of class A alloys, the buckling curve is equal to that of steel. For outstands of class A alloys, the mechanical response model is slightly less favourable than that of steel. Local buckling of class B alloys, the buckling curves are less favourable than in case of class A material. The buckling curves are shown in Figure 5.15. It is remarkable that the buckling curve for outstands is more favourable than the buckling curve of internal parts of steel, while it is less favourable in case of aluminium. The reason for this has not been found in literature.

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1.2

1

0.8

[-] 0.6

ρ internal, class A outstand, class A 0.4 internal, class B outstand, class B 0.2 internal, Steel outstand, Steel

0 00.511.522.5

λρ,rel

Figure 5.15 – Buckling curves for local buckling of aluminium and steel plates

5.5.4 Local buckling at elevated temperature

Research on local buckling of aluminium members at elevated temperature was not found in literature. EN 1999-1-2 [7] gives no rules for local buckling at elevated temperature of aluminium columns. These rules are also not provided for steel columns at elevated temperature in EN 1993- 1-2 [4]. A limited amount of studies was found on local buckling of fire exposed thin walled steel plates or sections.

Ranby [91] carried out an empirical and numerical research to thin walled C-sections. It is suggested to apply the same models for the local buckling resistance at elevated temperature as are currently applied in EN 1993-1-1 [3] for room temperature, i.e. applying equation (5.31). The modulus of elasticity that should be applied in the calculation model is the initial modulus of elasticity at elevated temperature (Eθ). As steel exhibits an inelastic stress-strain curve at elevated temperature, the 0,2 % proof stress is applied instead of the yield strength. It was noted that the results would not have been significantly different, had the 0,1 % proof stress been used. The critical stress is determined for elastic material, i.e. applying equation (5.23).

It was concluded that with this model, the ultimate local buckling resistance corresponds to that of Finite Element analyses in which the entire inelastic material properties were applied. It was further concluded that initial deflections have the same relative influence on the load bearing resistance at room temperature as in case of fire.

The results show that, with the typical values for the load reduction factor of 0,6, the maximum steel temperature with regard to the load bearing resistance is larger than 350 ºC, which is the current limit in EN 1993-1-2 [4]. The maximum steel temperature is rather in the range of 450 ºC.

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Uy and Bradford [108] carried out a numerical research, applying the finite strip method, to local buckling of cold-formed steel sections in composite steel-concrete structural elements at elevated temperature. They suggest applying equation (5.43) for the critical stress in case of buckling in the

elastic range and (5.44) in case of buckling in the inelastic range.

Eθ σ θ = σ for σ θ ≤ f θ (5.43) cr, cr,room E cr, p, f σ = σ p,θ σ > cr,θ cr,room for cr,θ f p,θ (5.44) f p

Research to local buckling of steel components at elevated temperature was also reported in Zhao et al. [113]. In this research, the slenderness parameter λrel is calculated at room temperature. This simplification is based on the fact that for the cold-formed steel considered, the ratio f0,2,θ / Eθ varies only slightly with the temperature.

Restrained thermal expansion may result in large stresses in the elastic range. In case of members that are not sensitive to local buckling, the 0,2 % proof stress reduces and finally approaches the externally applied load. The internal stresses by thermal expansion then flow off, and the critical temperature of a member with a uniform temperature distribution can be approximated by neglecting restrained thermal expansion. In case of members that are sensitive to local buckling, however, the member collapses before the 0,2 % proof stress is reached. Restrained thermal expansion may in this case influence the critical temperature. Research on the influence of restrained thermal expansion on local buckling was not found in literature.

A research to local buckling at elevated temperature should provide information on the following questions: - The stress-strain relation of aluminium alloys changes at elevated temperature. How does this influence the critical load? - Is the effective width approach, as applied in EN 1999-1-1 [6] and based on the research of Winter [112], also valid for fire-exposed aluminium? - What is the influence of creep on local buckling? - In case thermal expansion is restrained, how does this affect the ultimate buckling resistance? - In case of sections with a temperature gradient over the cross-section, how does unequal thermal expansion affect the ultimate buckling resistance?

5.5.5 Classification

The previous paragraph considered local buckling of plates in uniform compression. In a similar way, local buckling of plates in bending can be considered. The rotation capacity of members in bending may be limited by the occurrence of local buckling of the section. The deformation at which local buckling occurs can be determined with tests or Finite Element analyses, but no simple calculation model is available that can be incorporated in codes. Yet, the rotation capacity of sections is important in the design of structures, as it determines the possibility to apply plastic moment resistance and to allow redistribution of forces and moments. Therefore, the Eurocodes on steel and aluminium structures provide a classification system of cross-sections, in which the section is classified depending on the sensitivity to local bucking.

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Room temperature The classification depends on the deformation at which the member fails due to local buckling. The allowed response calculation models and the verification rules for members depend on the classification of cross-sections. In EN 1999-1-1 [6], cross-sections are divided into four classes.

The classification is illustrated in Figure 5.16. The horizontal axis shows the actual rotation of the section divided by the rotation corresponding to the attainment of the 0,2 % proof stress. The vertical axis of this figure shows the actual moment divided by the elastic moment. The latter is determined by multiplying the 0,2 % proof stress (f0,2) with the elastic section modulus (Wel).

Class 1: (Ductile) Sections in which local buckling occurs after extended deformation, or does not occur at all. The plastic capacity of the cross-sections can be achieved for these sections and the deformation capacity is sufficient to make redistribution of forces possible. Class 2: (Compact) The plastic capacity of the cross-sections can develop before buckling occurs. The deformation capacity is limited because of local buckling and therefore insufficient to make redistribution of forces possible. Class 3: (Semi-compact) Local buckling occurs after the 0,2% proof stress is reached in the extreme fibre of the member, but before the full plastic capacity is reached. The design value of the capacity of the cross-section may be determined with the theory of elasticity. Class 4: (Slender) Local buckling occurs before the 0,2% proof stress is reached in one or more parts of the cross-section. Buckling thus occurs in the elastic range. Only in case of these cross-sections, a check on the local buckling capacity is necessary.

[-]

0,2 Class 1 α 5 M / M Class 2

α0 Class 3 1

Class 4

1 φ / φ 0,2 [-]

Figure 5.16 – Classification of the cross-section of aluminium members

Mazzolani and Piluso [81] give the outline of a proper classification system of aluminium. • The border between classes 4 and 3 is obvious; class 4 sections buckle in the elastic range, while class 3 (and lower) sections buckle in the inelastic range; • The border between classes 3 and 2 is set as the plastic moment, equal to the 0,2 % proof stress (f0,2) multiplied with the plastic section modulus (Wpl). Note that in case of inelastic material, such as aluminium alloys, this plastic moment has no physical meaning. The factor α0, indicating the border between class 3 and class 2 sections in Figure 5.16, is thus equal to the geometrical shape factor (α0 = Wpl / Wel);

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• The border between classes 2 and 1 is set as the moment at which the curvature is equal to 5 times the curvature corresponding to the attainment of the 0,2 % proof stress. This moment is . denoted as α5 M0,2. The limit value of the curvature has been chosen taking into account the most unfavourable failure conditions for the less ductile materials.

The global rotation capacity (R) and the stable part of the global rotation capacity (R0) were defined as follows:

φφ− φ R ==−c 0,2 c 1 (5.45) φφ 0,2 0,2 φφ− φ R ==−u 0,2 u 1 (5.46) 0 φφ 0,2 0,2

In which the rotations φu and φc correspond to the attainment of the ultimate resistance (Mu) and the collapse moment, respectively, the latter defined at the intersection with the elastic moment line (Figure 5.17). [-] 0,2

M / M 1

R0

R

1 φu / φ 0,2 φc / φ 0,2 φ φ / 0,2 [-] Figure 5.17 – Definition of rotation capacity in Mazzolani and Piluso [81]

Tests and numerical simulations to determine a classification system were described e.g. by Faella et al. [39], Moen et al. [86], Moen et al. [87] and De Matteis et al. [77]. From these studies, it is concluded that the most important parameters influencing the rotation capacity are: • The slenderness of the plates of which the member is composed. Smaller slenderness results, as expected, in a larger rotation capacity; • The material strain hardening. Larger strain hardening; i.e. a larger ratio between fu and f0,2, results in a larger rotation capacity; These parameters provide variations of a similar range, both for the global rotation capacity and the stable part of the rotation capacity.

Less important parameters influencing the rotation capacity are: • The geometrical shape factor α0; • The restraining influence of the web on the compression flange, i.e. interaction between buckling of flanges and web; • The moment gradient, expressed by the ratio between span and beam height. This parameter only affected the unstable part of the rotation capacity.

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The borders between the classes in EN 1999-1-1 [6] are given as the relative plate slenderness. The variation in strain hardening between alloys and tempers is only globally taken into account by giving different borders for class A and class B material. The geometrical shape factor, restraining influence of the web on the compression flange and moment gradient are not considered in the classification. The borders between classes are given as the ratio between β and ε, Table 5.4.

Table 5.4 – Borders between classes (ratios β/ε)

Material classification Internal part Outstand Class Class Class Class Class Class 1-2 2-3 3-4 1-2 2-3 3-4 Class A, without welds 11 16 22 3 4,5 6 Class A, with welds 9 13 18 2,5 4 5 Class B, without welds 13 16,5 18 3,5 4,5 5 Class B, with welds 10 13,5 15 3 3,5 4

Note that only two classes are applied for members loaded in uniform compression. These classes are class 4, for which the ultimate resistance is limited by local buckling in the elastic range, and classes 1-3, for which the ultimate resistance is determined by multiplying the 0,2 % proof stress with the gross area of the cross-section.

Elevated temperature In EN 1999-1-2 [7], the same classification applies at elevated temperature as for room temperature for aluminium structures. This means that it is not accounted for changes in material properties. Contrarily, EN 1993-1-2 [4] specifies that the 0,2 % proof stress and modulus of elasticity at elevated temperature should be applied in the determination of the classification.

Lundberg [70] gives the background to the classification of fire exposed aluminium sections. The slenderness parameter ε and therefore the buckling factor ρ in equation (5.36) changes at elevated temperature, as the ratio between the 0,2 % proof stress and the modulus of elasticity changes at elevated temperature. For the alloys listed in both EN 1999-1-1 [6] and EN 1999-1-2 [7], Lundberg [70] gives the ratio between the modulus of elasticity and the 0,2% proof stress, normalised at room temperature as a function of the temperature (Figure 5.18). The parameter on the vertical axis in this figure is the slenderness parameter at elevated temperature divided by the slenderness parameter at room temperature:

ε k θ θ = E, (5.47) ε ko,θ

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Figure 5.18 – Relative value of the slenderness parameter as a function of the temperature

Contrary to steel, the ratio between the slenderness at elevated temperature and the slenderness at room temperature generally increases for increasing temperature in case of the alloys in Figure 5.18. The lowest value of the normalised ratio is 0,97. Using the same classification in fire design as at normal temperature is therefore expected to give conservative results for these alloys.

Note that the shape of the stress-strain relation changes at elevated temperature. As shown by Faella et al. [39], the rotational capacity of aluminium components depends on the entire stress- strain relation. For a proper classification system at elevated temperature, the entire stress-strain relation should therefore be regarded and not only the 0,2 % proof stress.

No literature has been found in which the classification at elevated temperature was checked.

5.6 Behaviour of entire structures or parts of structures

Instead of evaluating each component of which a structure is composed, EN 1999-1-2 [7] also provides the possibility to evaluate a part of a structure or the entire structure. Paragraph 5.6.1 outlines the evaluation of parts of the structure or the entire structure.

No tests are found in literature on the behaviour of entire, aluminium structures at elevated temperature. One test series was found considering a part of a structure, i.e. a stressed skin structure. This research is discussed in Annex E. Two numerical studies on the behaviour of frames ate elevated temperature were found. These are discussed in paragraph 5.6.2.

5.6.1 Verification according to EN 1999-1-2 [7]

If the structure is divided in parts and each part is checked individually, the code specifies that: - The part of the structure to be analysed should be specified on the basis of the potential thermal expansions and deformations such, that their interaction with other parts of the structure can be approximated by time-independent support and boundary conditions during fire exposure;

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- Within the part of the structure to be analysed, the relevant failure mode in fire exposure, the temperature-dependent material properties and member stiffness, effects of thermal expansions and deformations shall be taken into account; - The boundary conditions at supports and forces and moments at boundaries of the part of the

structure may be assumed to remain unchanged throughout the fire exposure.

Compared to evaluation of each individual component, analysis of a part of a structure better approaches the real behaviour of a fire exposed structure, as (restrained) thermal expansion of members in the part considered should be taken into account. Because of the first specification, thermal expansion of the rest of the structure cannot have major influence on the part of the structure considered.

EN 1999-1-2 [7] also provides the possibility to evaluate the structure or the entire structure. When this approach is chosen, the relevant failure mode in fire exposure, the temperature- dependent material properties and member stiffness and effects of thermal deformations shall be taken into account.

As EN 1999-1-2 [7] provides no simple calculation models for parts of a structure or entire structures, advanced calculation models should be applied. These models should include the determination of: - The development and distribution of the temperature within structural members (thermal response model); - The mechanical behaviour of the structure or of any part of it (mechanical response model). In the mechanical response model, it should be accounted for the relevant failure modes as outlined in paragraph 5.1.

Advanced calculation models may be used in association with any heating curve, provided that the material properties are known for the relevant temperature range. The deformations at ultimate limit state implied by the calculation method shall be limited to ensure that compatibility is maintained between all parts of the structure. The advanced calculation models applied shall be validated based on relevant test results. A sensitivity analysis shall be carried out on critical parameters (buckling length, element sizes, load level).

As the development and validation of an advanced model is complicated and sometimes time consuming, advanced models are not yet much applied. On the other hand, these models may give the best approximation of the real structural behaviour during a fire. Besides, redistribution of forces can only be taken into account when the entire structure is evaluated at once. Advanced response models may therefore result in more economical structures.

Natural fire concepts may be applied in combination with advanced mechanical response models. This is beneficial, because natural fire concepts provide the most realistic fire scenarios, which are specific for the structure in consideration. This is another reason why advanced response models may result in more economical structures.

5.6.2 Numerical research to frames

Faggiano et al. [30], [31], [32] carried out numerical analyses of frames composed of various alloys exposed to a standard fire. In the research, the Ramberg-Osgood model was applied to describe the entire stress-strain relation at elevated temperature.

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Also Eberwien [34] carried out a numerical study on the behaviour of frames. A parameter study was carried out in which loads, overall dimensions and dimensions of the cross-sections were varied. The critical temperatures of these frames were determined by code checking (component behaviour) and with FEM analyses.

The simple frames considered in both studies are shown in Figure 5.19. The studies and their results are discussed in Annex F.

Figure 5.19 – Frames numerically researched by Faggiano [30], [31] and [32] and Eberwien [34]

Eberwien [34] noted that redistribution of forces (and the resulting higher critical temperature) is only possible if a large rotation capacity is available in the plastic hinges. Local buckling might prevent large rotations in the plastic hinges. However, with the beam elements used in the numerical analyses, it is not possible to detect local buckling. The rotation capacities that are required for redistribution of forces are not realistic. Data on rotation capacities of connections and local bucking in members at elevated temperatures are not available.

The research shows the necessity to study the rotation capacity with respect to local buckling, in order to make redistribution of forces possible.

5.7 Evaluation of structural behaviour

Basically, codes for aluminium or steel structures exposed to fire (EN 1999-1-2 [7] and EN 1993- 1-2 [4] respectively) distinguish the same failure mechanisms as in normal temperature design. The few tests on aluminium components found in literature confirm this. However because of changes in material properties, other failure mechanisms may become decisive in fire compared to room temperature. Additional, thermal expansion may result in large deformations or, when thermal expansion is partially or entirely restrained, in high internal stresses. Creep may on the one hand decrease the material strength, and on the other hand result in large deformations and / or relaxation of stresses.

The verification rules for fire exposed components in EN 1999-1-2 [7] are basically equal to the rules at room temperature in EN 1999-1-1 [6], but with taking the reduced value for the 0,2 % proof stress into account. Contrarily to steel structures, only a few fundamental studies were carried out to fire exposed aluminium structures and no experience of aluminium structures in real fires is available. The amount of calculation models in EN 1999-1-2 [7] is therefore limited, and most calculation models are not validated with tests. For some important failure mechanisms, such as failure of connections and local buckling, no calculation models are incorporated in the code. Studies to these failure mechanisms on which general conclusions could be based are not found in literature.

Concerning connections, research is necessary for drafting a calculation model. This research should focus on strength, stiffness and rotation capacity.

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Because of the thin wall thicknesses usually applied in aluminium extruded sections, in combination with the high ratio between strength and modulus of elasticity, aluminium structures are relatively sensitive to local buckling. Besides, in case of components in bending, the deformation at which local bucking occurs determines whether redistribution of forces is possible, whether the moment resistance of the cross-section can be determined using the theory of plasticity or elasticity and in the latter case, whether the yield stress can be reached in the extreme fibres. The classification of the cross-section at elevated temperature is set equal to the classification at room temperature. Research is necessary to determine whether adaptation of the classification at elevated temperature is necessary. It is therefore a first and essential step to determine a mechanical response model for local buckling of aluminium at elevated temperature. A research to local buckling at elevated temperature should provide information on the following questions: - The stress-strain relation of aluminium alloys changes at elevated temperature. How does this influence the critical load? - Is the effective width approach, as applied in EN 1999-1-1 [6] and based on the research of Winter [112], also valid for fire-exposed aluminium? - What is the influence of creep on local buckling? - In case thermal expansion is restrained, how does this affect the ultimate buckling resistance? - In case of sections with a temperature gradient over the cross-section, how does unequal thermal expansion affect the ultimate buckling resistance? - What are appropriate borders of the classification of cross-sections?

In case of flexural, torsional or torsional-flexural buckling, the relative slenderness according to EN 1999-1-2 [7] shall be determined using the 0,2 % proof stress and the modulus of elasticity at room temperature. The normal force should be multiplied with a factor 1,2 to take creep effects into account. In a research to flexural buckling of steel columns, it was concluded that the correlation between the relative slenderness and the buckling resistance is better when the relative slenderness is determined with material properties at elevated temperature instead of room temperature. Besides, an alternative buckling curve was proposed for fire. Research is necessary to determine whether a similar approach leads to more accurate results for aluminium columns. EN 1999-1-2 [7] specifies that possible temperature gradients over the cross-section should be accounted for in the design. However the calculation models for flexural, torsional or torsional- flexural buckling seem not to account for a reduction of the ultimate resistance because of bending of the component due to unequal thermal expansion.

In a research to flexural buckling of beam-columns (Langhelle [62]), transient state tests were carried out with a constant heating rate. The critical temperature in tests with a high heating rate (failure after 20 minutes) was approximately equal to tests with a lower heating rate (failure after 60 minutes). Based on this, it is concluded that creep has no important influence on the buckling resistance of the beam-columns for the studied parameter field.

Table 5.5 gives an overview of the behaviour of aluminium components at elevated temperature. In this table, it is indicated whether the properties are known, or whether more research is necessary.

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Table 5.5 – Overview of component behaviour at elevated temperature

Component behaviour Status Remarks

Local buckling - critical stress Partially known No information on the influence of changes in the stress-strain relation - buckling resistance Partially known No information on the validity of the effective width approach of fire exposed aluminium - creep influence Not known - thermal expansion Not known No information on the influence of restrained thermal expansion and, in case of a temperature gradient, the influence of bending Classification Partially known Applying the same classification as at room temperature seems conservative Members in tension Known Members in compression or bending - relative slenderness Partially known Relative slenderness and buckling factor in code are equal to room temperature design. Is this justified? - buckling resistance Partially known No research is available to determine an appropriate buckling curve for fire exposed aluminium. - creep influence Partially known Creep factor of 1,2 (or 1,0 for lateral- torsional buckling) not verified with tests - thermal expansion Partially known In case of a temperature gradient, no information on the influence of bending because of unequal thermal expansion Connections Not known No information on the strength, stiffness and rotation capacity of members

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6 Conclusions and recommendations

6.1 Conclusions

Thermal properties that determine the temperature of fire exposed members are the thermal capacitance (=specific heat times density), the thermal conductivity, and the fire protection (or the emissivity of the member for unprotected members). Most of these thermal properties are known for aluminium alloys. Especially the low density, low melting point and high thermal conductivity cause aluminium structures to be sensitive to fire, compared to steel.

Mechanical properties of aluminium alloys are determined in steady state tests, i.e. with a heating period at a constant temperature prior to testing, and no load applied during the heating period. A limited amount of test data was found resulting from creep tests, also carried out with a heating period at a constant temperature, loaded during the entire heating period. Transient state tests, in which the temperature increases during testing until the critical temperature is reached, and the load is applied from the beginning of heating, were not found in literature. Such test give a better approximation of the real behaviour of fire exposed materials.

The steady state and creep tests showed that the strength and stiffness reduce already at moderately elevated temperatures. The strength reduction depends on the alloy and the temper. For some alloys (the heat treatable ones), the strength reduction depends on the thermal exposure period. Further, the strength at elevated temperature also depends on the load, as creep influences the strength at elevated temperature. The extra strength obtained by solution heat treatment and / or cold working gradually vanishes at elevated temperature.

Basically, codes for aluminium or steel structures exposed to fire (EN 1999-1-2 [7] and EN 1993- 1-2 [4] respectively) distinguish the same failure mechanisms as in normal temperature design. The few tests on aluminium components found in literature confirm this. However because of changes in material properties, other failure mechanisms may become decisive in fire compared to room temperature. Thermal expansion may result in large deformations or, when thermal expansion is partially or entirely restrained, in high internal stresses. The coefficient of thermal expansion of aluminium is approximately two times that of steel. Additionally, creep may on the one hand decrease the material strength, and on the other hand result in large deformations and / or relaxation of stresses.

Contrarily to steel structures, only a few fundamental studies were carried out to fire exposed aluminium structures and no experience of aluminium structures in real fires is available. The amount of calculation models in the Eurocode for fire design of aluminium structures, EN 1999-1- 2 [7], is therefore limited and many calculation models are not validated with tests. For some important failure mechanisms, such as failure of connections and local buckling, no calculation models are incorporated in the code. Studies to these failure mechanisms on which general conclusions could be based are not found in literature.

Because of the thin wall thicknesses usually applied in aluminium extruded sections, in combination with the high ratio between strength and modulus of elasticity, aluminium structures are relatively sensitive to local buckling. It is a first and essential step to determine a mechanical response model for local buckling of aluminium at elevated temperature.

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In case of other global buckling phenomena, EN 1999-1-2 [7] provides simple calculation models. These models are however validated with tests. The application of a creep factor of 1,2 and the determination of the relative slenderness in EN 1999-1-2 [7] are subject of discussion.

6.2 Recommendations

In order to obtain material properties that are closer to the real behaviour in fire, it is recommended that tensile tests with constant load and heating rates that are present during fires (transient state tests) be carried out. Influence of creep and possible changes in the temper on the material properties are implicitly taken into account in these tests.

It is recommended to carry out a research to local buckling at elevated temperature, which provides answers to the following questions: - The stress-strain relation of aluminium alloys changes at elevated temperature. How does this influence the critical load? - Is the effective width approach, as applied in EN 1999-1-1 [6] and based on the research of Winter [112], also valid for fire-exposed aluminium? - What is the influence of creep on local buckling? - In case thermal expansion is restrained, how does this affect the ultimate buckling resistance? - In case of sections with a temperature gradient over the cross-section, how does unequal thermal expansion affect the ultimate buckling resistance? - What are appropriate borders of the classification of cross-sections?

It is recommended to carry out a research to the strength, the stiffness and the rotation capacity of fire exposed aluminium connections.

It is recommended to carry out a research to global buckling of aluminium components, which determines - Whether the relative slenderness should be determined with material properties at room temperature or at elevated temperature; - Whether or not an alternative buckling curve should be determined at elevated temperature; - The influence of creep is on global buckling; - (In case of sections with a temperature gradient over the cross-section) The influence of bending caused by unequal thermal expansion on the ultimate buckling resistance. For this research to global buckling, research on fire exposed steel structures may be used as a guidance.

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References

[1] EN 1990 Eurocode 0: Basis of structural design

[2] EN 1991-1-2 Eurocode 1: Actions on structures – Part 1-2: General actions – Actions on structures exposed to fire

[3] EN 1993-1-1 Eurocode 3: Design of steel structures – Part 1-1: General Structural Rules, February 2004

[4] EN 1993-1-2 Eurocode 3: Design of steel structures – Part 1-2: General Rules – Structural fire design, September 2003

[5] EN 1993-1-5 Eurocode 3: Design of steel structures – Part 1-5: Plated structural elements, February 2003

[6] EN 1999-1-1 Eurocode 9: Design of aluminium structures – Part 1-1: General Structural Rules, February 2004

[7] EN 1999-1-2 Eurocode 9: Design of aluminium structures – Part 1-2: General Rules – Structural fire design, September 2003

[8] NEN 6072 Rekenkundige bepaling van de brandwerendheid van bouwdelen (Staalconstructies), December 1999

[9] Norsk Standard NS 3478, Brannteknisk dimensjonering av bygningskonstruksjoner Beregning (Design for structural members for fire resistance), 1. utgave oktober 1979

[10] TALAT, Training in Aluminium Application Technologies, European Aluminium Association (http://www.eaa.net/education/TALAT/index.htm)

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[14] Amdahl, J. Eberg, E. and Langhelle, N.K. Experimental and theoretical investigation of aluminium tubes subjected to temperature loads SINTEF, report no. STF70 93140, 1993

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[26] Carslaw, H.S. and Jaeger, J.C.

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Conduction of heat in solids 2nd edition, Oxford University Press, 1959, ISBN 0 19 853303 9

[27] Davis, J.R.

ASM specialty handbook, Aluminum and aluminum alloys ASM International, 1993, ISBN 0-87170-496-X

[28] Dieter, G.E. Mechanical Metallurgy McGraw-Hill, London, 1988

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[30] Faggiano, B. De Matteis, G. Landolfo, R. Mazzolani, F.M. The influence of material modelling on the fire resistance of aluminium alloy structures INALCO (International Aluminium Conference), Cleveland, 2004

[31] Faggiano, B. De Matteis, G. Landolfo, R. Mazzolani, F.M. Effects of high temperatures on the resistance of aluminium alloy structures 7th International Conference on Modern Building Materials, Structures and Tehniques, Vilnius, May 2004

[32] Faggiano, B. De Matteis, G. Landolfo, R. Mazzolani, F.M. On the fire resistance of aluminium alloy structures COST C12 – Improvement of Buildings’ Structural Quality by New Technologies, Innsbruck, January 2005, pp. 267-276

[33] Dorn, J.E. Some Fundamental Experiments on High Temperature Creep. Journal of the Mechanics and Physics of Solids, Vol. 3, 1954

[34] Eberwien Entwicklung eines allgemeinen Verfahrens zur Berechnung von Versagenstemperaturen an Aluminiumkonstructionen des EC 9-1-2 PhD University of Hannover, 2003

[35] Eberg, E. Amdahl, J. and Langhelle, N.K. Experimental investigation of creep behaviour of aluminium at elevated temperatures SINTEF, report no. STF22 F96713, 1996

[36] Eberg, E. Langhelle N.K. and Amdahl, J. Experimental investigation of creep buckling behaviour of aluminium tubes subjected to temperature loads SINTEF, report no. STF70 F95223, 1995

[37] Engström and Sandström Evaluation of high temperature strength values of aluminium alloys Aluminium 69.11, p. 1007-1013, 1993

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[38] Essem, G. Aluminium Data 8-61 Hållfasthet vid hög und låg temperatur, samt andre data 1975

[39] Faella, C. Mazzolani, M. Piluso V. and Rizzano, G. Local buckling of aluminium members: testing and classification Journal of Structural Engineering, 2000, vol 126-3 pages 353-360

[40] Fourier, J.B.J. Théorie analytique de la chaleur 1822, English translation by Freeman, Cambridge, 1878

[41] Franssen, J.M. Taloma, D. Kruppa, J. and Cajot, L.G. Stability of Steel Columns in Case of Fire: Experimental Evaluation Journal of Structural Engineering, 1998, vol 124-2 pages 158-163

[42] Galambos, T.B. Stability design criteria for metal structures 5th edition, John Wiley & Sons, Inc, 1998. ISBN 0-471-12742-6

[43] Gerhard G. and Becker H. Handbook of Structural Stability, Part 1 – Buckling of flat plates Technical note 3781, NACA, 1957

[44] Harmathy, T. Z. Deflection and Failure of Steel-Supported Floors and Beams in Fire National Research Council, Division of Building Research, Paper No 195, 1966

[45] Hepples and Wale High temperature tensile properties of 6082-T651

[46] Holman, J.P. Heat Transfer McGraw-Hill Publishing Company, 1990, ISBN 0-07-909388-4

[47] Hopperstad, O.S., Langseth, M., Tryland, T. Ultimate strength of aluminium alloy outstands in compression: experiments and simplified analysis Thin-Walled Structures, Vol. 34, pp. 279-294, 1999

[48] Hu, P.C. Lundquist, E.E. Badvord, S.B. Effects of small deviations from flatness on the effective width and buckling of plates in compression Technical note 1124, NACA

[49] Jakob, M. Heat transfer Volume 1, John Wiley & Sons, Inc. 1949

[50] Jombock, J.R. and Clark, J.W. Postbuckling Behaviour of Flat Plates

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Transactions of the American Society of Civil Engineers, Vol 127, part I, p. 227-240, 1962

[51] Kammer, C.

Aluminium Taschenbuch teil 1, Grundlagen und Werkstoffe Aluminium Verlag Düsseldorf 2002. ISBN 3-87017-274-6

[52] Von Karman, T. Festigkeitsprobleme im Maschinenbau Enzyklopädie der mathematischen Wissenschaften, Band 4, Leipzig 1910

[53] Von Karman, T. Sechler, E.E. Donnell, L.H. The Strength of Thin Plates in Compression Transactions of the American Society of Mechanical Engineers, Vol. 54, p. 53-56, 1932

[54] Kaspersen and Sørås Krypeffekter i brannbelastede aluminiumskonstruksjoner 1994

[55] Kaufman, J.G. Properties of aluminium alloys – Tensile, creep and Fatigue data at high and low temperatures ASM international, 1999

[56] Kleive and Gustavsen Mekansike egenskaper ved kortvarige eleverte temperaturer for aluminiumlegering 6082- T6

[57] Koser, J Konstruieren mit aluminium Aluminium-Verlag Düsseldorf, 1990, ISBN 3-87017-196-0

[58] Kraus, H. Creep analysis Wiley, 1980, ISBN 0-471-06255-3

[59] Krokeide Brannbelastede konstruksjonskomponenter I aluminium

[60] Kumar, D.R. Swaminathan, K. Tensile deformation behaviour of two aluminium alloys at elevated temperature Materials at high temperatures Vol. 16, No. 4 pp 161-172, 1999

[61] Landolfo, R. Mazzolani, F.M. Different approaches in the design of slender aluminium alloy sections Thin-Walled Structures Vol. 27, No. 1 pp. 85-102, 1997

[62] Langhelle, N.K. Experimental validation and calibration of nonlinear finite element models for use in design of aluminium structures exposed to fire

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PhD Norwegian University of Science and Technology Trondheim, 1999, ISBN 82-471- 0376-1

[63] Langhelle, N.K. and Eberg, E.

Ultimate strength testing of aluminium stressed skin structures at elevated temperatures Marintek, report no. 22L103.00.01, 1999

[64] Langhelle, N.K. Ultimate strength testing of steel and aluminium connections at elevated temperatures Marintek, report no. 22L105.00.01, 2001

[65] Langhelle, N.K. Eberg, E. Amdahl, J. and Lundberg, S. Buckling tests of aluminium columns at elevated temperatures 15th Offshore Mechanics and Arctic Engineering Conference (OMAE), Firenze, 1996

[66] Langseth, M. Hopperstad, O.S. Local Buckling of Square Thin-Walled Aluminium Extrusions Thin-Walled Structures, Vol. 27, No. 1, pp. 117-126, 1997

[67] Lundberg, S. Mechanical properties at elevated temperature for aluminium alloys CEN/TC 250/SC 9/PT Fire/N-27, 2003

[68] Lundberg, S. Formula for compression members CEN/TC 250/SC 9/PT Fire/N-18, 2002

[69] Lundberg, S. Comments to Draft prEN 1999, Part 1.2 CEN/TC 250/SC 9/PT 4/N 88, 1996

[70] Lundberg, S. Classification CEN/TC 250/SC 9/PT Fire/N-26, 1995

[71] Lundberg, S. Emissivity of Aluminium Alloys CEN/TC 250/SC 9/PT 4/N 83, 1995

[72] Lundberg, S. Design of aluminium alloy structures for fire resistance – influence of creep – Concluding remarks CEN/TC 250/SC 9/PT 4/N 73, 1995

[73] Lundberg, S. Thermal calculation of insulated bolted connection CEN/TC 250/SC 9/PT 4/N 64, 1995

[74] Lundberg, S. Creep model for 6082 aluminium alloy CEN/TC 250/SC 9/PT 4/N 57, 1995

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[75] Lundberg, S. Design of aluminium alloy structures for fire resistance – influence of creep – Technical note

CEN/TC 250/SC 9/PT 4/N 48, 1994

[76] Lundberg, S. Thermal properties of aluminium alloys CEN/TC 250/SC 9/PT 4/N 32

[77] De Mattheis, G., Moen, L.A. Langseth, M. Landolfo, R. Hopperstad, O.S. Mazzolani, F.M. Cross-sectional classification for aluminium beams – parametric study Journal of Structural Engineering, Vol. 127, No. 3, pp. 271-279

[78] Mazzolani, F.M. Aluminium alloy structures Pitman, 1985, ISBN 0-273-08653-7

[79] Mazzolani, F.M. Faella, C. Puliso, V., Rizzano, G. Assessment of the stub column test for aluminium alloys 2nd conference of Coupled Instabilities in Metal Structures, CIMS, Liège, 1996

[80] Mazzolani, F.M., Faella, C. Puliso, V. Rizzano, G. Experimental Analysis of Aluminium Alloy SHS-Members Subjected to Local Buckling under Uniform Compression 5th International Colloquium on Structural Stability, SSRC, Brazilian Session, Rio de Janeiro, 1996

[81] Mazzolani, F.M. Piluso, V. Prediction of the Rotation Capacity of Aluminium Alloy Beams, Thin-Walled Structures Vol. 27, No. 1, pp. 103-116, 1997

[82] Mazzolani, F.M., Faella, C. Puliso, V. Rizzano, G. Local Buckling of Aluminium Alloy RHS-members: Experimental Analysis XVI Congresso C.T.A., Italian Conference on Steel Construction, Ancona, 1997

[83] Mazzolani, F.M., Faella, C. Puliso, V. Rizzano, G. Local Buckling of Aluminium Channels under Uniform Compression: Experimental Analysis Fourth International Conference on Steel and Aluminium Structures, Espoo, Finland, 1999

[84] Mazzolani, F.M., Puliso, V. Rizzano, G. Experimental analysis of aluminium alloy channels subjected to local buckling under uniform compression Giornate Italiane Della Constuzione in Acciaio, Venice, 2001

[85] Mennink, J. Cross-sectional stability of aluminium extrusions PhD University of Eindhoven 2002, ISBN 90-386-1546-9

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[86] Moen, L.A. De Matteis, G. Hopperstad, O.S. Langseth, M. Landolfo, R. and Mazzolani, F.M. Rotational capacity of aluminium beams under moment gradient. II: Numerical

simulations Journal of Structural Engineering, 1999, vol 125-8 pages 910-920

[87] Moen, L.A. Hopperstad, O.S. and Langseth, M. Rotational capacity of aluminium beams under moment gradient. I: Experiments Journal of structural engineering, 1999, vol 125 (8) pp 910-920

[88] Mofflin, D.S. Dwight, J.B. Buckling of aluminium plates in compression In Behaviour of Thin-walled tructres, ed. B J. Rhodes and J. Spence, Elsevier, pp. Journal of structural engineering, 1984, pp 399-427

[89] Mondolfo, L.F. Aluminium Alloys- Structure and Properties Butterworths, 1976

[90] Newton, I. Philosophical Transactions of the Royal Society, London, 22, p 824, 1701

[91] Ranby, A. Structural Fire Design of Thin Walled Steel Sections Luleå University of Technology, 1999

[92] Richter, E. Hanitzsch, E. Der Elastizitätzmodul und andere physikalische Eigenschaften von Aluminiumwerkstoffen, Teil 1 Aluminium 70 (1994)9/10, p 570/574

[93] Sandström, R. and Widestig, P. High temperature yield and tensile strengths of aluminium alloys Aluminium 68.4, p 330-333, 1992

[94] Shanley, F.R. Inelastic Column Theory Journal of Aeronautical Science, Vol. 14 No. 5

[95] Soetens, F. and Van Hove, B.W.E.M. Bouwen met aluminium Lectures at Eindhoven, university of Technology, 1999

[96] Various authors Over Spannend Staal, Construeren A Staalbouwkundig Genootschap, 1997, ISBN 90-72830-20-2

[97] Station d’essais au feu du CTICM process-verbal de classement de resistance au feu. Essai no 82 U 47 / T 47 1982

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[98] Station d’essais au feu du CTICM process-verbal de classement de resistance au feu. Essai no 82 U 48 / T 48 1982

[99] Station d’essais au feu du CTICM process-verbal de classement de resistance au feu. Essai no 83 G 2 / T 2 1983

[100] Station d’essais au feu du CTICM process-verbal de classement de resistance au feu. Essai no 83 G 3 / T 3 1983

[101] Stefan, J. Sitzungsberichte Deutsche Kais. Akademie Der Wissenschaften Wien, math.-naturwiss. Klasse 79, p 391, 1879

[102] Stowell, E.Z. A Unified Theory of Plastic Buckling of Columns and Plates Technical note no.1556, 1948, NACA

[103] Talamona, D. Franssen, J.M. Schleich, J.B. and Kruppa J. Stability of Steel Columns in Case of Fire: Numerical Modeling Journal of Structural Engineering, 1997, vol 123-6 pages 713-720

[104] Thor, J. Deformations and critical loads of steel beams under fire exposure conditions National Swedish Building Research D 16, 1973

[105] Timoshenko, S.P. and Gere, J.M. Theory of elastic stability Mc Graw and Hill, 2nd edition, 1961

[106] Twilt, L. Global investigation into the resultant emissivity of aluminium alloys CEN/TC 250/SC 9/PT 4/N 70

[107] Twilt, L. Valorisatie project natuurlijk brandconcept 2001

[108] Uy, B. Bradford, M.A. Local Buckling of Cold Formed Steel in Composite Structural Elements at Elevated Temperatures Journal of Constructuional Steel Research 34 (1995) pp. 53-73

[109] Verdier, M. Bréchet, Y. and Guyot, P. Recovery of AlMg alloys: flow stress and strain-hardening properties Acta Materialia, Vol 47(1), pp. 127-134, 1998

[110] Voorhees H.R. and Freeman J.W.

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Report on the elevated-temperature properties of aluminium and magnesioum alloys Americal Society of Testing Materials, STP No. 291, 1960

[111] Wickström, U.

Temperature analysis of heavily-insulated steel structures exposed to fire Fire Safety Journal, Vol 9(3), pp. 281-285, 1985

[112] Winter, G. Strength of Thin Steel Compression Flanges Transactions of the American Society of Civil Engineers. Vol. 112, pp. 527-554, 1947

[113] Zhao, B. Kruppa, J. Renaud, C. O’ Connor, M. Mecozzi, E. Azpiazu, W. Demarco, T. Karlstrom, P. Jumppanen, U. Kaitila, O. Oksanen T. and Salmi, P. Calculation rules of lightweight steel sections in fire situations CTICM, ECSC project no 7210 PR 254, 2003

Report 1 | Appendix A.1/8 Literature Study on Aluminium Structures Exposed to Fire

A Tests on the capacity of beams

Tests on tubes of alloy 6082 in bending at elevated temperature were carried out by Amdahl et al. [15]. First the tests are described. Second some remarks are given on the experiments.

A.1 Description of tests

The tubes had a length of approximately 2400 mm, a diameter of 150 mm and a thickness of 5 mm. Note that it is not reported whether round or square tubes were used, however, based on the load transfer detail shown, it is expected that the tubes were round (Figure A 1). The tubes were made of alloy AA6082, the temper is not reported.

Figure A 1 – Test set-up and load transfer detail applied in the bending tests by Amdahl et al. [15]

The beams were restrained against rotations perpendicular to the longitudinal axis at the beam ends, see Figure A 2. Some beams were axially restrained at both supports, while others were free in axial direction, so that the statical system according to Figure A 3 was applied.

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Figure A 2 – Supports applied in the bending tests by Amdahl et al. [15] (left fixed, right roll with fixation against rotations perpendicular to the longitudinal axis)

Figure A 3 – Statical systems applied in the bending tests by Amdahl et al. [15] (left axially restrained, right axially free)

The beams were heated electrically by ceramic mat elements. The number of elements and the positions along the specimen were not reported. The beams were insulated with blankets of ceramic fibres to prevent loss of heat. Four thermoelements were used to record the temperature at the following points: left end, at midspan and at both quarter-points. In all tests, the temperature at the tube end was significantly lower than measured in the central region of the tubes.

Various tests series were conducted. The results are listed in Table A 1. Results are discussed below:

1. Series 1: two axially restrained beams (system according to the left picture in Figure A 3) were tested at room temperature. In test 2, the transverse force displacement relation was linear up to approximately 70 kN, where it is assumed that initial yielding and formation of plastic hinges at the two end sections take place. At a load level of 94 kN, the bolts fixing the tube ends fractured and the test had to be stopped before the tube was fully plastified (plastic hinges at both ends and at the mid section). The force displacement curve of test 3 indicates that significant yielding occurred and that membrane action contributed to carry the imposed load. At a load equal to 116 kN, a fracture occurred at one of the tube ends. The load corresponded to the theoretical capacity of 120 kN.

2. Series 2: three axially restrained beams (system according to the left picture in Figure A 3) were tested at elevated temperature. The three tests had a different collapse mechanism, as

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indicated in Table A 1. In all tests it was observed that in the initial phase of loading the tube behaved linearly, see e.g. Figure A 4. When tests with various temperature levels were compared, the temperature influence on the initiation of yielding was also clearly visible. The level of plastification reached in the individual test cases depended on the collapse

mechanism. The indentation at the actuator force application was significant.

Figure A 4 – Force-displacement diagram of test 4 of the bending tests by Amdahl et al. [15]

3. Series 3: one axially restrained beam (system according to the left picture in Figure A 3) was tested at elevated temperature, during which creep deformations were measured. After the test temperature was reached, an initial load of 20 kN was applied. Then the load was increased with steps of 5 kN and held constant for a certain period. The holding times varied between 15 and 60 minutes. (Note that this is in contradiction to the reported load-time plot, which indicates that the holding times were ranging from approximately 2 minutes to 30 minutes, Figure A 5.) Results are given in Figure A 6. In the left graph, the displacement in mid-span is given as function of the time. The lines in the graph refer to the displacement of the actuator (lastcelle), the upper flange of the specimen (Ror O) and the lower flange (Ror N). The right graph gives the relation between the load on the vertical axis and the displacement on the horizontal axis. The amount of creep deformation occurring for each combination of load level and holding time may be deducted from the individual transverse displacement versus time relationships.

It should be noted that also the local tube deformations at the load application point is a function of time.

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Figure A 5 – Load - time relation applied in test 7 of the bending tests by Amdahl et al. [15]

Figure A 6 – Load, displacements and time in test 7 of the bending tests by Amdahl et al. [15]

4. Series 4: one axially free beam (system according to the right picture in Figure A 3) was tested at room temperature. Initial yielding occurred at approximately 65 kN and at 95 kN the tube was fully plastified. The test was stopped when fracture occurred at one tube end hinge.

5. Series 5: two axially free beams (system according to the right picture in Figure A 3) were tested at elevated temperature. The collapse mechanism in the two tests was fracture in one of the plastic hinges. Other observations made are as described for series 2 (axially restrained beams tested at elevated temperature).

6. Series 6: two axially free beams (system according to the right picture in Figure A 3) were tested at elevated temperature, during which creep deformations were measured. After the test temperature was reached, an initial load of 20 kN was applied. Then the load was increased with steps of 5 or 10 kN and held constant for a certain period. The holding times varied between 15 and 60 minutes. The load-time plot of both tests is given in Figure A 7. Results are shown in Figure A 8 for test 11 and Figure A 9 for test 12. In the left graphs of these figures, the displacement in mid-span is given as function of the time. The right graphs give the relation between the load on the vertical axis and the displacement on the horizontal axis.

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Figure A 7 – Load - time relations applied in tests 11 and 12 of the bending tests by Amdahl et al. [15]

Figure A 8 – Load, displacements and time in test 11 of the bending tests by Amdahl et al. [15]

Figure A 9– Load, displacements and time in test 12 of the bending tests by Amdahl et al. [15]

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Table A 1 – Results beam tests (Amdahl et al. [15])

Series Specimen Time at elevated Temp Max load Collapse temp [min] 1) . [ºC] [kN] mechanism 2) 1. Room temperature, 2 - 20 100 A axially restrained 3 - 20 116 B 2. Elevated temperature, 4 25 + 10 150 88.4 C axially restrained 5 30 + 55 200 79.8 D 6 30 + 5 250 72.3 B 3. Elevated temperature, 7 35 + 150 250 82.9 B axially restrained, creep test 4. Room temperature, 8 - 20 94.1 B axially free 5. Elevated temperature, 9 25 + 25 200 76.6 B axially free 10 30 + 20 250 65.7 B 6. Elevated temperature, 11 50 + 85 200 60.2 B axially free, 12 50 + 135 250 50.6 B creep tests 1) Indicated is the time during which the specimen was heated to test temperature and the period at test temperature before collapse occurred 2) Collapse mechanisms: A. Bolts fixing tube to plug ruptured B. Fracture occurred in plastic hinge C. Endplate- plug weld ruptured D. Bolts fixing end plate ruptured

A.2 Remarks on the tests

Comments about the test set-up: It is shown that the temperature at the beam end was significantly lower than the temperature in mid-span for all tests at elevated temperature. The temperature at the end was approximately 60% of the temperature in the central region. As the beam ends had a lower temperature than indicated in Table A 1, the relation between temperature and maximum loads given are not representative for real fire situations. The expression “fully plastified” applied in the report probably refers to the existence of one plastic hinge in mid-span and two plastic hinges at the beam ends.

Axial restraining applied in series 1, 2 and 3 has two influences on the load situation of the specimens: Before the development of three plastic hinges, thermal expansion is restrained, causing axial compression in the beam. This extra load might cause the three plastic hinges to develop at a lower externally applied load. After three plastic hinges have developed and significant deformation has occurred, membrane action in the beam might transfer a part of the externally applied load, causing an increase in the maximum (collapse) load. This effect is visible when the maximum loads in Table A 1 are compared (the axially restrained beams show higher maximum loads than the axially free beams).

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For the axially restrained beams, deformation of the test rig and / or deformation of the supports might cause the beam to be not fully restrained against axial displacements. Axial displacement was measured but unfortunately not reported for the axially restrained beams. It is unclear to what extend the types of connections in Figure A 3 prevent rotations perpendicular to the longitudinal axis.

Comments about the test results: For test five, the temperature before testing in the specimen was not constant, but it varied between approximately 210 ºC and 140 ºC. During this period, the specimen was loaded and unloaded two times before the final load was applied. The loads applied in the first load cycles were significantly higher than the finally applied load, at which collapse occurred. This is remarkable, as the temperature in the beam during the second load cycle was approximately equal to the temperature at the finally applied load. The load-time history and the temperature-time history of test 5 are given in Figure A 10. It seems more convenient to leave test 5 out of consideration.

Figure A 10 – Load, temperature and time in test 5 of the bending tests by Amdahl et al. [15]

As tests 1, 4 and 5 show another collapse mechanism than the other tests, the resulting maximum loads found in these tests should not be compared with the other test results. Because of differences in thermal exposure times applied in the tests, the test results should be compared to each other with caution.

As expected, all tests in one series show that the maximum load decreases at increasing temperature.

The force – displacement graphs and the displacement – time graphs in Figure A 6, Figure A 8 and Figure A 9 show that the largest creep deformations occur at load levels close to the maximum load. Creep deformations are however also visible at the lowest load levels applied. The maximum load in tests 11 and 12, including creep effects, is significantly lower than the maximum load of comparable tests without creep (tests 9 and 10 respectively). However, test 7, including creep effects, results in a significantly higher maximum load than test 6, without creep effects. In the last load phase in test 7, when large creep deformations were detected, the holding times are so low that it is possible that extra creep could not have been developed in this phase. A conclusion about the influence of creep on the beam capacity only based on these three tests is inappropriate. The combination of the temperature and the total test times is not representative for almost all fire situations in real structures.

The tests were carried out in order to study the behaviour of aluminium beams at elevated temperatures and to provide data for the verification of the material model adopted in the

Appendix A.8/8 Report 1 | Literature Study on Aluminium Structures Exposed to Fire

computer program USFOS. However, a comparison with simulations of the tests in USFOS is not reported. Tensile tests in order to determine the material properties were not carried out.

Report 1 | Appendix B.1/4 Literature Study on Aluminium Structures Exposed to Fire

B Tests on welded connections

According to Langhelle [64], it is often assumed in the analysis of a structure that the connections remain intact and that the forces developed in the different members will be transferred through the joints to neighbour members. This assumption is only correct when the overall capacity of the connection at least maintains the same relative capacity as the members joined by the connection. In order to verify the assumption, some tests on welded connections were carried out. First, the tests are described. Second, some remarks are given on the tests.

B.1 Description of tests

Tests were carried out on aluminium simple plate X-connections loaded in tension (Figure B 1) and on T-joints loaded in tension (Figure B 2) of alloy AA 6082 T6

Figure B 1 – X connections tested by Langhelle [64]

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One X connection was tested at room temperature and one at a temperature of 200 ºC. The collapse behaviour of both connections was similar. Rupture occurred in the weld for both tests, due to lack of through thickness welding, which resulted in sudden failure. The behaviour of the connection at elevated temperature was slightly more

ductile. The ultimate stress for the connection at room temperature was approximately 155 N/mm2. This is much lower than the ultimate stress of alloy AA6082 T6, which is 325 N/mm2. Note that it is not reported how and where this ultimate strength is determined. The relative ultimate stress is determined by dividing the test capacity at elevated temperature by the test capacity at room temperature. The ultimate stress for the connection at 200 ºC was 74% of the ultimate stress for the connection at room temperature. The relative value of the 0,2% proof stress at 200 ºC is 0.70 according to EN 1999-1-2 [7].

A similar research to steel connections resulted in a reduction of the ultimate stress in the X-connection of 0.62 at a temperature of 500 ºC. EN 1993-1-2 [4] gives a relative value of 0.78 of the yield stress.

Figure B 2 – T joints tested by Langhelle [64]

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The T-joints consisted of I-260 sections welded perpendicular to each other. One T- joint was tested at room temperature and one at 200 ºC. The collapse behaviour of the specimen was similar. Failure for both specimen occurred in the weld, which resulted in sudden failure. The ultimate stress of the connection tested at room temperature was 2 160 N/mm , which was again lower than expected. The reduction coefficient for ultimate capacity of the connection at 200 ºC was 0.77. (The relative value of the 0,2% proof stress at 200 ºC is 0.70 according to EN 1999-1-2 [7].) A similar research to steel connections resulted in a reduction of the ultimate stress in the X-connection of 0.5 at a temperature of 500 ºC.

B.2 Remarks on the tests

Both for the aluminium and the steel connections, the connections fail because the ultimate tensile strength was reached. This ultimate strength in the tests was compared to the yield stress in the codes. As the ratio between ultimate strength and yield stress changes at elevated temperature, this is actually not a good comparison. As explained in paragraph 4.5, the relative strength of the weld and the heat affected zone at elevated temperature is probably higher than the relative strength of the parent material with temper T6, because annealing already took place during the welding process. It would therefore be convenient to compare the test results not only with the relative strength at elevated temperature of temper T6, but also with the relative strength of temper O. However, no data are available on tensile tests carried out on alloy AA6082 temper O.

A general conclusion on the behaviour of aluminium connections based on these two tests at elevated temperature is inappropriate. No test results are found in literature on aluminium connections loaded in bending. More data on the behaviour of connections at elevated temperature are required. These data comprise not only strength, but also stiffness and rotation capacities. It should be focussed on the most common failure mode in real connections, i.e. failure in the weld or in the heat affected zone.

Appendix B.4/4 Report 1 | Literature Study on Aluminium Structures Exposed to Fire

Report 1 | Appendix C.1/6 Literature Study on Aluminium Structures Exposed to Fire

C Tests on columns in compression (Amdahl et al.)

Tests on buckling of columns at elevated temperatures are carried out by Amdahl et al. [14].

C.1 Description of tests

Aluminium tubes were tested with a length of 2000 mm, a diameter of 150 mm and a thickness of 5 mm. Imperfections are measured before testing. It is not reported whether the tubes were square or round. The tubes are made of alloy AA6082, the temper is not reported. The test set-up and the support of the columns are illustrated in Figure C 1.

Figure C 1 – Test set-up and support in the column buckling tests by Amdahl et al. [14]

The columns were heated electrically by 12 ceramic mat elements (low voltage heating elements): three elements around the perimeter at four positions along the tube. The columns were insulated with blankets of ceramic fibres to prevent loss of heat. The temperature was measured at three points: in mid span and at the quarter points. Various tests series were conducted. The results are listed in Table C 1. Results are discussed below:

1. In test series 1 (two tests), column buckling tests were carried out at room temperature. In both tests a strong interaction with local buckling was observed.

2. In test series 2 (two tests), the tubes were subjected to controlled heating, while the tube ends were restrained against axial displacement. Buckling is therefore caused by thermal expansion. Different heating rates were applied for the tests, so that buckling of the first specimen occurred after 55 minutes and buckling of the second column occurred after 10 minutes.

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3. Test series 3 (one test) was conducted with the same boundary and test conditions as in series 2. However, the test was stopped once the axial force dropped to approximately half of the ultimate strength. The corresponding lateral deflection at mid-span was only 25 mm. Accordingly, the amount of plastic deformation was

relatively moderate. A significant gradient in temperature distribution was detected. After buckling, the specimen was allowed to cool down to ambient temperature before it was subjected to axial compression, to detect the residual buckling strength.

4. Test series 4 (two tests) was conducted at a constant temperature of 220 ºC. The specimens were heated to the test temperature in approximately 20 to 25 minutes. The temperature was kept constant for a period of approximately 25 to 30 minutes. Following, load was applied until buckling occurred. The ultimate strength differed quite much for both specimens, although the material properties and nominal test conditions apparently were similar. However, due to substitution of one of the electrical heating elements, a uniform temperature distribution was not well achieved for specimen 2.

5. Test series 5 (one test) was carried out at a constant temperature of 200 ºC and an increasing load. Heating to test temperature occurred in approximately 45 minutes. Following, a load of 240 kN was applied. The axial load was subsequently increased to the following levels: 300 kN, 330 kN and 360 kN. Between each level, the temperature was kept constant for a certain period of time. At each level the jack position is adjusted manually to compensate for creep. The load-time history is given in Figure C 1.

Figure C 2 – Load time history of creep test in Amdahl et al. [14]

The influence of creep was moderate until the last load level, where an accelerating creep effect was observed, which eventually leaded to global buckling. Creep buckling occurred approximately 40 minutes after the last load increase. The total duration of the test, including the heating period, was 130 minutes.

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Almost all tests showed interaction between global and local buckling, which is considerably more important than for steel columns with similar geometry, according to the authors. A recommendation is made to study local buckling.

Table C 1 – Results column buckling tests (Amdahl et al. [14])

Series Specimen Heating rate Buckling Critical [deg ºC / min] load [kN] temp [ºC] 1. Normal 7 - 700 20 temperature 8 - 660 20 2. Axially restrained 6 3.53 370 193 (buckling due to 4 19.35 400 190 thermal expansion) 3. Residual strength 1 7.25 360 174 400 20 4. Constant 5 (5.85) 360 219 temperature 2 (5.09) 270 220 5. Creep buckling 3 (4.47) 360 200

The tests in series 1, 2 and 4 were simulated with Finite Element models consisting of beam elements in the program USFOS. In order to determine the 0,2% proof stress and the modulus of elasticity at elevated temperature, four tensile tests were carried out at 150 ºC and two tensile tests at 300 ºC.

In general, the simulations agree fairly well with tests, although discrepancies are observed: - For thermal induced buckling, the critical temperature found by USFOS was lower than the test value; - The capacity predicted in terms of bending moment – axial force interaction is somewhat overestimated by USFOS at elevated temperature and underestimated at ambient temperature. This is obviously due to sensitivity to the actual material characteristics and their modelling in USFOS. - Local buckling is important for (at least) the post-buckling behaviour of members subjected to end compression. Without local buckling, the capacity is much over- predicted by USFOS. No attempt has been made to utilize the local buckling option in USFOS, because this is only relevant for steel tubes. I do not follow this statement.

No comparison was made with the buckling resistance resulting from the verification rules in EN 1999-1-1 [6] and EN 1999-1-2 [7].

C.2 Remarks on the tests

Comments about the test set-up The column length was 2 m. From the pictures presented in Amdahl et al. [14] and in Langhelle [62], it is expected that the same set-up was used. If this is the case, the buckling length is somewhat smaller than 2,0 m, approximately 1,8 m (see Annex D). The applied buckling length in the numerical analyses is not reported.

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Although an eccentricity was applied in the load application in Langhelle [62], it is assumed that no eccentricity was applied in the load application in the current study, because this is not mentioned. The temperature was only measured in midspan, at the upper quarter and at the lower

quarter. The reported temperature distributions show that the temperature gradient in the beam can be significant in some tests. This raises questions to the heating procedure and the reliability of the results.

Comments about the test results The difference in buckling load between the tests in series 1 (ambient temperature) is relatively large. A possible explanation for this difference is the initial imperfection (non-straightness) of the columns. This imperfection was 1 mm for specimen 7 and 3 mm for specimen 8. The difference in buckling load between the tests in series 2 (buckling due to thermal expansion) is also relatively large, although the test temperature was almost equal. The test with the lowest heating rate (longest thermal exposure period) resulted in the lowest load. This could indicate that creep buckling occurred for this test. A conclusion about the influence of creep based on these single test is however inappropriate. In a more extended test program on beam-columns, Langhelle [62] found no influence of creep during the first hour of thermal exposure. In the current study, no creep deformation was reported. The reason for the difference in buckling loads is therefore unclear. The buckling resistance of the test in series 3 (residual strength) is remarkably low compared to the resistances of the tests in series 2: both the temperature and the applied load in the first phase of series 3 are lower than in case of series 2. Besides, it is reported that deformations in this phase were low for series 3, indicating that the degree of plasticity is relatively moderate. Yet the buckling load in the second phase, after cooling down to 20ºC, was approximately equal to the buckling loads at elevated temperature, found in series 2. This is remarkable because TALAT [10] shows that the strength after cooling of alloy AA 6082 is substantially higher than the strength at elevated temperature. A possible explanation for the low buckling resistance of series 3 is that the temperature distribution in the column is unequal. However, the temperature in Table C 1 is the maximum temperature measured in midspan. The temperatures at quarter points were only approximately 200 ºC. This makes the buckling load found in the test even more remarkable. The difference in buckling loads between the tests in series 4 (constant temperature) is large. An axial temperature gradient was found in the specimen with the lowest buckling load. After the heating period, the temperature at the lower quarter point was approximately 280 ºC, while the temperatures in midspan and at the higher quarter point were 200 ºC. At the moment the load was applied, the temperature in midspan was approximately 220 ºC, the temperature at the higher quarter point was approximately 180 ºC and the temperature at the lower quarter point was approximately 240 ºC. However, the difference between the buckling loads seems to be too large to contribute entirely to the temperature gradient. For test series 5 (creep buckling), the reported conclusion that the influence of creep was moderate until the last load level, where an accelerating creep effect was observed, could not be drawn from the graphs presented. On the other hand, this phenomenon is visible in the test results of beam-columns, reported by Langhelle [62], see Annex D.

The small amount of tests in each series and the relatively large difference in buckling loads between tests in the same series raises questions about the suitability to use the tests for validation of numerical models.

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Comments about the numerical models Tensile tests to determine material properties are carried out at 150 ºC and 300 ºC. The material properties outside the tested area are merely guessed. The tensile tests at 150 ºC, and therefore also the course of the 0,2% proof stress incorporated in the numerical

models, do not correspond to other tensile tests reported in literature (see paragraph 4.3). The modulus of elasticity resulting from the tensile tests differ significantly from each other and do not correspond at all to other tensile tests reported in literature. The modulus of elasticity used in the numerical models therefore not corresponds with the data from the tensile tests carried out. However, the modulus of elasticity also not corresponds to the values given in EN 1999-1-2 [7]. The source of the modulus of elasticity is thus unknown. The way of incorporating strain hardening is unclear.

Contrary to what is stated, the correspondence between tests and simulations cannot always be regarded as “fairly well”. For thermal induced buckling, the graphs show that the axial force in the numerical simulation is higher than the axial force in the test for temperatures lower than the critical temperature. This could be caused by a difference in modulus of elasticity at elevated temperature between test and simulation, but it could also be caused by deformation of the test rig in which the column is placed, so that axial displacement in the tests is not completely prevented. Both causes could explain the reported lower critical temperature found in the simulations. The material properties used in the simulation of specimen 1 (series 3, i.e. residual strength test) after cooling to room temperature are not listed. Both the use of properties at maximum elevated temperature or at room temperature would be inappropriate. For all tests, a strong interaction between local buckling and global buckling was reported. It is not clear whether or how local buckling was incorporated in the numerical models. In this literature research, the performance of the finite element program used was not checked, but in more conventional finite element programs, local buckling cannot be detected by beam elements.

The test program was carried out in order to study the behaviour of aluminium columns at elevated temperatures. The purpose of the tests was to provide data for verification of the material model adopted in the Finite Element program USFOS. For the reasons described above, the entire test program and the simulations are questionable. Conclusions about the behaviour of columns at elevated temperature based on this study are therefore inappropriate. A more extended test program to study buckling and creep buckling is carried out on beam-columns by Langhelle [62], see Annex D. It is therefore more convenient to draw conclusions on buckling and creep buckling based on beam- columns.

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D Tests on columns in compression and bending (Langhelle)

Langhelle et al. carried out tests on beam-columns. The tests are reported in Langhelle [62], Langhelle et al. [65] and Eberg et al. [36].

D.1 Description of tests

The sections tested were square tubes 120 mm x 7 mm and 120 mm x 5 mm with a length of 2100 mm. Some specimen consisted of two sections of 1050 mm welded together. The buckling length of the columns in the set-up was 1900 mm. The load was applied with an eccentricity of 8 mm. The ratio between the stress caused by normal force and the maximum stress caused by bending was thus 4,5 for t=7 mm and 4,6 for t=5 mm. The tubes were made of alloy AA6082. Some specimens were made of temper T4, others of temper T6.

The specimens were heated electrically by ceramic mat elements (low voltage heating elements): four elements around the cross-section at four positions along the specimens. The specimens were insulated with blankets of ceramic fibres to prevent loss of heat. The temperature was measured at seven points along the specimens, including both ends. Tests on a dummy were carried out to determine the optimal distance between the heating units in order to obtain a temperature distribution that was as uniform as possible. The results show that the temperatures at all measured positions are almost equal in all tests carried out.

Tensile tests were conducted at room temperature and at the elevated temperatures at which the columns were tested. Results are discussed in paragraph 4.3. The dimensions of the cross-section of the column, the imperfections in the cross- section and out-of-straightness were measured. The cross-sections were initially distorted with initial bowing in the range of +/- 1 mm. The out-of-straightness was negligible for the columns without welds and 0,4 to 2,7 mm for the welded columns.

The tests are simulated with Finite element models in ABAQUS and in USFOR. In both cases, the models consisted of beam elements.

The capacity of the tested columns was also determined using the simple calculation models in EN 1999-1-2 [7], NS 3471 and BS 8118. These capacities were determined by using the relative value of the 0,2 % proof stress, k0,2,θ, according to the codes, and according to the tensile tests. The following comments are made to the EN 1999 calculations: - For welded columns of temper T6, the 0,2% proof stress specified of the heat affected zone is 0,65 of the 0,2% proof stress of parent material. This factor is taken into account both at room temperature design and at elevated temperature. A reduction for the heat affected zone is not taken into account for temper T4. In addition, a partial safety coefficient of 1,1 is applied in the calculations of axial force and bending moment capacity for welded columns. - When measured material properties are applied, the section classification is different from that based on nominal code values. The section classification changes for columns without welds of temper T6 and welded columns of temper T4

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with wall thickness 7 mm, giving increased slenderness. This introduces a reduction of the shape factor, giving a reduction in bending moment capacity, thus the capacity becomes lower while the yield strength is higher. The importance of these two factors varies for the different columns and materials.

Various test series were conducted: 1. Series 1: tests at ambient temperature. The results are given in Table D 1. Presented are only the results of the test, the ABAQUS simulation and the calculation according to EN 1999 with the 0,2% proof stress according to the tensile tests. The collapse stresses according to EN 1999 were reported in diagrams. The values given in Table D 1 are estimated from these diagrams.

For temper T4 no influence was detected of the weld on the test capacity. For temper T6, this influence was detected. The two columns with temper T6 and a wall thickness of 5 mm have a significant different collapse stress. The source of this difference is unknown, however, based on strain measurements and visual observations it is concluded that local buckles occur simultaneously to global collapse for these columns. If this is the case, increased variability in the results should be expected. The collapse behaviour of both tests was “violent”, with a sudden loss of capacity.

The capacity of test 18 (welded column of temper T6) was considerably higher than predicted by EN 1999. This is caused by the unfavourable section classification for this column because of the high 0,2% proof stress at room temperature.

There is a good correspondence between the test capacities and the numerical capacities determined with USFOS and ABAQUS. The load - axial displacement trajectories were also similar.

Comments: EN 1999 provides conservative capacities for temper T6. The difference between code capacity and test capacity is largest for the welded column T6, indicating that the reduction of the strength heat affected zone taken into account in the code is exaggerated for this specific beam-column.

Table D 1 – Tests on beam-columns at room temperature, carried out by Langhelle [62]

No Temper t [mm] welded Collapse stress [N/mm2] Test ABAQUS EN 1999 1 T4 7 122 124 118 3 T4 7 123 17 T4 7 welded 122 124 118 2 T6 7 216 207 195 4 T6 7 211 18 T6 7 welded 165 163 130 26 T6 5 195 200 180 27 T6 5 220

2. Series 2: test with constant load and constant heating rate. Two heating rates were applied, resulting in duration of the tests of approximately 20 minutes and 60 minutes for heating rates of 5 ºC/min and 12 ºC/min respectively. The critical

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temperatures resulting from the tests are compared to the temperatures determined with the numerical models in Table D 2. In the simple calculation models in EN 1999, the temperature is input of the calculation and the result is the maximum applicable load. The critical temperature resulting from the tests is taken to

determine the capacity according to the EN 1999. These capacities are compared to the loads applied on the tests in Table D 3.

Tests with different heating rates result in similar critical temperatures. This indicates that annealing and creep have no significant influence on the capacity for a thermal exposure period up to one hour and for the parameter field studied. The critical temperatures of welded columns of temper T4 were almost equal to columns without welds, independent of the applied heating rates. This is similar to the behaviour experienced at room temperature. For temper T6, the difference in capacity between columns with and without welds is reduced for increasing temperatures. There is still a difference in critical temperature for the columns tested with a stress of 110 N/mm2 (approximately 225 ºC for the welded column and 255 ºC for the columns without welds), but at 75 N/mm2, welded columns have almost equal critical temperatures (approximately 287 ºC). Column no 19 (specimen without welds with temper T4, tested at a higher stress level) gave an unexpected low critical temperature. No other columns were taken from this extrusion length, and none of the tensile test specimens are taken from this material. Therefore it is not possible to confirm whether the material properties of this column correspond to those of the other tested columns. The control measurements of the dimensions did not reveal any irregularities.

The capacities according to EN 1999 are in general much lower than the capacities resulting from the tests. Creep is not present in these tests and therefore the applied reduction coefficient yields conservative results. To avoid this, Langhelle [62] proposes that an additional assumption for applying the reduction coefficient could be established. If the period spend at a temperature higher than 170 ºC is less than 20 minutes, the reduction coefficient 1,2 could be replaced by 1,0. This suggestion is strictly relevant only for the stress levels applied in the present study. Additional tests should be conducted before a specified “time limit” could be established.

When the material properties according to the EN 1999 are used, the code capacities are much lower than the test capacities in all cases.

As the different heating rates applied do not seem to influence the capacities, creep is not incorporated in the finite element models to simulate these tests. Only for specimens with temper T6 and a load level of 110 N/mm2, the weld is included in the model by adapting the material properties (the 0,2% proof stress at the position of the weld was modelled as 70% of the 0,2% proof stress of the parent material). In general, there is good correspondence between the critical temperatures resulting from tests and from ABAQUS. One exception is test 19, for which the critical temperature found in the test is much lower than expected.

In general, the numerical analyses yield a higher stiffness in the elastic range. This is not only valid for series 2, but also for series 1 and 3. Some possible error sources are: 1. Non-plain ends of the columns may cause yielding and plastic deformation of parts of the cross section in the initial stages of loading; 2. Premature yielding of parts of the cross-section due to residual stresses from fabrication may casue a reduced stiffness;

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3. If the spherical surfaces supporting the ends of the columns experience any deformation during the test, this would reduce the stiffness measured in the tests. However, considering the supports, possible deformations of end supports are considered to be negligible;

4. The total column length is 2100 mm. The buckling length of the modelled column is 1906 mm. This difference in length causes the stiffness in the analysis to be 110 % of the stiffness in the test.

Table D 2 – Tests on beam-columns with constant heating rate, carried out by Langhelle [62]

No temper t welded stress utilization heating Critical temp [ºC] [mm] [N/mm2] 1) rate Test ABAQUS [ºC/min] 6 T4 7 75 0.61 4.6 286 282 7 T4 7 75 0.61 13 290 19 T4 7 102 0.84 4.7 157 270 23 T4 7 welded 75 0.61 12.2 283 282 24 T4 7 welded 75 0.61 5.4 290 10 T6 7 75 0.35 5 287 285 9 T6 7 75 0.35 12 270 5 T6 7 110 0.51 4.7 259 244 8 T6 7 110 0.51 12.4 253 21 T6 7 welded 75 0.45 4.9 287 285 22 T6 7 welded 75 0.45 11.1 285 20 T6 7 welded 110 0.67 3.8 223 213 29 T6 5 75 0.38 4.7 276 263 28 T6 5 110 0.50 4.7 241 224 1) The utilization is added to the data provided by Langhelle [62]. The utilization is in this respect determined as the load applied on the specimen in series 2 (elevated temperature) divided by the capacities found in series 1 (room temperature).

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Table D 3 – Tests on beam-columns with constant heating rate, carried out by Langhelle [62]

2 No Temper t welded heating Critical utilization stress [N/mm ] [mm] rate temp [ºC] 1) Test EN 1999 6 T4 7 4.6 286 0.61 75 7 T4 7 13 290 0.61 75 19 T4 7 4.7 157 0.84 102 23 T4 7 welded 12.2 283 0.61 75 24 T4 7 welded 5.4 290 0.61 75 10 T6 7 5 287 0.35 75 65 9 T6 7 12 270 0.35 75 78 5 T6 7 4.7 259 0.51 110 94 8 T6 7 12.4 253 0.51 110 89 21 T6 7 welded 4.9 287 0.45 75 44 22 T6 7 welded 11.1 285 0.45 75 43 20 T6 7 welded 3.8 223 0.67 110 79 29 T6 5 4.7 276 0.38 75 58 28 T6 5 4.7 241 0.50 110 100 1) The utilization is added to the data provided by Langhelle [62]. The utilization is in this respect determined as the load applied on the specimen in series 2 (elevated temperature) divided by the capacities found in series 1 (room temperature).

3. Series 3: tests with constant temperature and increasing load. For these tests, an initial load of 50 or 75 N/mm2 was applied. Then, the temperature was elevated to test temperature in approximately 20 minutes. Following, the temperature was kept constant for a period of 15 minutes before the first load increase was applied. The load was increased every 15 minutes until creep buckling occurred. The total test duration was 70 to 180 minutes. Results are given in Table D 4. An example of a load – time diagram applied and the resulting lateral displacement – time diagram is given in Figure D 1.

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Figure D 1 – Load, lateral displacement and time for creep buckling test no. 15 by Langhelle [62]

For test 11, it was not possible to keep the temperature constant during the complete test period.

In these tests, significant creep deformations were detected at the highest stress levels. The columns consequently failed through creep buckling. The highest test temperature gave the lowest collapse stress and the shortest duration of the tests. Different load histories did not seem to affect the test results. The temperature applied in test 14 was almost identical to the critical temperature in test 5 (series 2). The collapse strain in test 14 was 73 N/mm2, which was considerably lower than the stress level applied in the test with constant heating rate (110 N/mm2). The difference is attributed to the effects of creep.

Creep was therefore incorporated in ABAQUS. The parameters for the creep models applied were derived from tests carried out by Kaspersen and Soras [54]. In general, there is good correspondence between test capacities and numerical capacities for a temperature of approximately 200 ºC. For a temperature of 250 ºC, the numerical capacities are lower than the test capacities. A possible explanation is

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that the parameters in the creep model applied are not appropriate for a temperature of 250 ºC.

In general, there is good correspondence between capacities according to EN 1999

and test capacities, except for temperatures above 250 ºC. Then the test capacity is lower than the capacity according to the code. This indicates that creep is most pronounced at the highest temperatures. In some cases, calculation according to EN 1999 results in higher capacities than resulting from the tests. This could indicate that for these columns, the value of 1,2 for the factor that takes creep into account is inappropriate. It should be mentioned however that some test durations were exceeding the maximum time of exposure to elevated temperatures, apparent in real fires. When the material properties according to the EN 1999 are used, the code capacities are much lower than the test capacities in all cases.

More column buckling tests should be conducted at constant temperature, to obtain column buckling curves with well defined creep development.

Table D 4 – Tests on beam-columns with constant temperature, carried out by Langhelle [62]

No Temp t weld init. utiliza Temp Collapse stress [N/mm2] 1) [mm] stress tion [ºC] Test ABAQU EN 1999 [N/mm2] S 16 T4 7 50 0.41 259 64 59 15 T4 7 75 0.61 210 123 124 12 T4 7 75 0.61 198 131 121 25 T4 7 weld 75 0.61 223 112 118

14 T6 7 50 0.23 261 73 59 82 11 T6 7 75 0.35 malfunctioning of heating system 13 T6 7 75 0.35 204 131 128 128 31 T6 7 50 0.23 264 69 59 71 30 T6 7 75 0.35 222 122 119 113 1) The utilization is added to the data provided by Langhelle [62]. The utilization is in this respect determined as the load applied on the specimen in series 3 (elevated temperature) divided by the capacities found in series 1 (room temperature).

D.2 Remarks on the tests

Load increments and holding times are not constant in the constant temperature tests, so caution has to be made when test results are compared to each other. The long thermal exposure periods in series 3 are not representative for almost all real structures exposed to fire.

The capacities according to EN 1999 (using measured material data) are slightly lower than the test capacities at room temperature (series 1) and at constant temperature (series 3). For tests with constant heating rates (series 2) however, a larger difference was found. EN 1999 gives conservative results for this series, as indicated in Figure D 2. The difference in test method between series 2 and series 3 is the holding time

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applied in series 3 and the longer test period. The difference in results could therefore indicate that either creep or the long heating period decreases the resistance of series 3. The combination of the thermal exposure period and the temperatures applied in series 3 is not representative for almost all real structures exposed to fire.

Figure D 2 –Capacities found in tests compared with capacities according to codes (Langhelle et al. [65])

The interaction formulas for a combination of bending and compression at elevated temperature were not evaluated. This interaction also influences the capacities according to the codes. For specimen 19 (series 2), the resistance found in the test was much lower than the resistance according to the numerical simulation. It should be noted that the utilization (ratio between stress level and collapse stress at ambient temperature) is highest for this column, so that this column is on the edge of the parameter field. Unfortunately, only one heating rate is applied to this combination of specimen and initial stress. A possibility that could explain (a part of) the difference is that artificial ageing might occur for temper T4 at elevated temperature, causing an increase in the 0,2% proof stress. Besides, because of artificial ageing, there exists a large scatter in material properties for temper T4 at elevated temperature, see Figure 4.20.However, considering the high utilization, the capacity according to ABAQUS seems too high.

The numerical models consisted of beam elements. Local buckling cannot be detected by the applied beam elements in ABAQUS. The program USFOS is not studied, so it is unclear whether local buckling can be detected by the USFOS models. However, for test series one, a strong interaction between local and global buckling was detected in some tests. The good correspondence between tests and simulations could indicate that

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local buckling has no significant influence on the capacity for the beam-columns considered. The specimens in the tests at elevated temperature (series 2 and 3) were insulated, so visible inspection was not possible for these series.

The reported difference in stiffness in the elastic range between the tests and the numerical simulations could also be caused by a difference in modulus of elasticity. It is not reported which values were chosen for the modulus of elasticity in the numerical model, but it is assumed that the values according to EN 1999 were used. Tensile tests carried out by Moen et al. [87] resulted in a modulus of elasticity of approximately 66700 N/mm2 for alloy AA6082 tempers T4 and T6 at room temperature. The difference with the value given in the code is 5%.

As reported, creep deformations were visible in series 3. It would have been interesting to determine to what extend creep decreases the buckling load of a column. Unfortunately, no simulations with ABAQUS are reported for series 3 in which creep was not incorporated. The influence of creep on the buckling load is therefore still unknown, so that evaluation of the value for the creep factor taken into account in EN 1999-1-2 [7] is not possible, based on this work.

Creep may influence the beam capacity for the following reasons: The lateral deflection may increase because of creep, resulting in an increase of the moment in the middle of the column. This reduces the buckling load; Creep may reduce strength and stiffness of the material. This reduces the buckling load. No distinction between these phenomena is given in the study. In the numerical model, no reductions in strength and stiffness of the material because of creep were taken into account (second reason). The correspondence between tests and numerical results at a temperature of 200 ºC indicates that the influence of the second reason is negligible, at least for this temperature (in combination with the rest of the parameter field considered).

Tests in series 3 cover only a limited temperature range (200 – 260 ºC). Tests at other temperatures should be carried out (both column buckling tests and creep tests on small specimen).

In the research with tests conducted on columns, beams and beam-columns, it is reported that interaction between global buckling and local buckling was present. However, the numerical models used by Langhelle [62] to simulate the tests only supported global buckling. The good correspondence between numerical and test results for beam-columns indicate that, for the studied geometries, the influence of local buckling on the beam resistance was limited.

D.3 Buckling in EN 1999-1-2 [7], based on Langhelle [62]

Lundberg [67] gives two proposals for changes in the formula in EN 1999-1-2 [7], which are based on the work carried out by Langhelle [62]: 1. Adaptation of the relative values of the 0,2% proof stress at elevated temperature. The capacities according to the code then correspond better with the capacities found in the buckling tests by Langhelle [62]. Applying the new relative values, the code capacities are still on the safe side.

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2. Adaptation of the creep factor. Creep is more likely to occur at higher temperatures. At about 250 ºC, it seems that a factor 1,2 is correct, but at lower temperatures it seems to be too high. For unprotected columns the heating rate is too high to give significant creep deformations. For protected columns creep has to be included in

the simple calculation model. A temperature dependent reduction factor is proposed:

η = θ cr 1,0 for al < 150 ºC (1) η = + θ − θ ≥ cr 1 0,004( al 190) for al 150 ºC (2)

In the equation: ⎛ γ ⎞ N = k ⋅ N ⋅⎜ M1 ⎟ b, fi,t,Rd 0,θ ,max b,Rd ⎜η ⋅γ ⎟ ⎝ cr M , fi ⎠

(3) With: ηcr = creep factor θal = temperature of aluminium Nb,fi,t,Rd = buckling resistance at elevated temperature k0,θ,max = relative value of the 0,2% proof stress of aluminium at maximum elevated temperature θal, max Nb,Rd = buckling resistance at room temperature γM1 = partial safety factor for members subjected to buckling γM,fi = partial safety factor for fire conditions

No significant influence of creep was detected on columns tested at constant heating rate (series 2). Therefore, the new proposal gives conservative values for these tests. Capacities determined with the new proposal correspond better with the capacities resulting from the tests with constant heating rates (series 3) than the current simple calculation model in EN 1999-1-2 [7].

Some remarks can be made about these proposals: • First proposal: In the reported comparison for evaluation of the new proposal concerning the relative value of the 0,2% proof stress at elevated temperature, the creep factor with value 1,2 is taken into account. For a proper evaluation however, the creep factor should not be taken into account, because no influence of creep on the resistance was detected for series 2. Possibly, the calculation model would not always give resistances on the safe side, had the creep factor not been taken into account. • Second proposal: The proposal was not given by Langhelle [62]. The origin of the equations is not reported. The proposal is only evaluated based on 5 tests on alloy AA6082 T6 with constant temperatures ranging from 200 to 260 ºC. The validity of the equations outside this parameter field is not checked. For temperatures between 150 ºC and 190 ºC, the creep factor is smaller than 1,0, which is nonsense. Although a more sophisticated creep factor replacing the current constant 1,2 is desired, more data are necessary to determine a well evaluated equation for the creep factor.

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E Tests on a stressed skin structure

Amdahl et al. [16] and Langhelle and Eberg [63] conducted a test series on a part of a structure, i.e. a stressed skin structure (Figure E 1). Such structures are often applied on offshore platforms.

E.1 Description of tests

Dimensions of the specimens are given in Figure E 2. Alloy AA 5754 H34 was applied for the web and alloy AA 5083 H34 was used for the flanges and end plates.

The specimen were restrained along one end and loaded at the other end. Figure E 3 shows the deformed structure after testing. One test was conducted at room temperature, one test at 200 ºC and one test at 225 ºC. The temperature of the specimen end connected to the rig was lower than the average temperature in the tests at elevated temperature.

Figure E 1 – Stressed skin structure applied in the tests by Langhelle and Eberg [63]

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Figure E 2 – Dimensions of the stressed skin structure

Figure E 3 – Deformed structure after testing at room temperature

Tensile tests were conducted on the materials of which the stressed skin structures were constructed. Results are given in Figure E 4.

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Figure E 4 – Data tensile tests carried out for the stressed skin structures

The load displacement diagrams of the three tests carried out are given in Figure E 5. In the specimen tested at room temperature, a tension field is developed along the diagonal of the web. The difference between the load level when the first buckle occurs and the ultimate load is only 10%. After a displacement of approximately 60 mm, a crack occurs at the lower right corner of the specimen, in the heat affected zone. This crack grows, causing a rapid loss of capacity.

In the specimen tested at 200 ºC, no crack occurred, despite the large deformations. The heating of the weld not only reduces the strength, but also increases the ductility of the material.

The specimen tested at 225 ºC gave some unexpected results. The behaviour of this specimen was anticipated to be similar to the test at 200 ºC, but with a lower capacity. However, the capacity was much lower than expected. The specimen experiences a large deformation after what was first believed to be the ultimate load. The test is terminated after a displacement of 100 mm.

Cracks were only found in the specimen tested at room temperature. This could indicate that the difference in capacity between welded and parent material is reduced at elevated temperature and / or the ductility of the weld and the heat affected zone increases at elevated temperature.

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Figure E 5 – Load displacement diagrams of the stressed skin structures

EN 1999-1-2 [7] and BS 8118 give no specific calculation models for stressed skin structures at elevated temperature. However, in EN 1999-1-2 [7] a general statement is made that the capacity at elevated temperature is equal to the capacity at room temperature multiplied by k0,2,θ (the relative value of the 0,2% proof stress at elevated temperature). This procedure is followed for both codes in order to determine the design capacity of the structure. These design capacities are compared with the test results in Figure E 6. It is shown that the safety level at room temperature is much larger than the safety level at elevated temperature.

Figure E 6 – Comparison of test results with code capacities for stressed skin structures

E.2 Remarks on the tests

The heating period and the time at constant temperature are not mentioned. No explanation is given for the low stiffness in the beginning of loading of the specimen tested at 200 ºC. The relative capacity of the specimen tested at 200 ºC was approximately 0,69.

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The ultimate load of the specimen tested at 225 ºC is not known, because the test was terminated after a displacement of 100 mm. It was stated that the behaviour of the material at elevated temperature was more ductile than the behaviour at room temperature. Indeed, the behaviour of the structures at

elevated temperature was more ductile than the behaviour of the structure at room temperature. However, it depends on the alloy and temper whether the material behaviour is more ductile at elevated temperature, see paragraph 4.7. The ductile behaviour of the structure at elevated temperature may also be caused by the fact that the difference between the strength of the heat affected zone and the strength of the parent material is expected to decrease at increasing temperature, see paragraph 5.6.1. When the strength of the heat affected zone is equal to the strength of the parent material at the test temperature, deformations are not limited to the heat affected zone, but they may occur in the entire structure. This results in a more ductile behaviour.

A general conclusion on the behaviour of stressed skin structures based on these three tests is inappropriate.

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F Numerical models on the evaluation of entire aluminium structures exposed to fire

Faggiano et al. [30], [31], [32] carried out numerical analyses of frames composed of various alloys exposed to a standard fire. In the research, the Ramberg-Osgood model was applied to describe the entire stress-strain relation at elevated temperature. Eberwien [34] carried out a numerical study on the behaviour of frames. A parameter study was carried out in which loads, overall dimensions and dimensions of the cross- sections were varied.

F.1 Description of numerical models and results

The frames investigated in Faggiano et al. [30], [31], [32] and Eberwien [34] is shown in Figure F 1. The critical temperatures of the frames, with varying values for loads, overall dimensions and dimensions of the cross-sections, were determined by code checking (component behaviour) and with FEM analyses.

In both studies, a uniform temperature distribution in the aluminium members was assumed. In the FEM analyses, beam elements were used. Local and lateral-torsional buckling are therefore not incorporated in the research, but flexural buckling is. The studies considered unprotected frames. Creep is not taken into account in the FEM analyses in both studies.

Figure F 1 – Frames numerically researched by Faggiano [30], [31] and [32] and Eberwien [34]

In Eberwien [34], the critical temperatures according to the FEM analyses were approximately 30ºC higher than the critical temperatures using the code. The following explanations are given for this difference: - In code checking, the relative slenderness has to be determined at the room temperature. As the 0,2% proof stress decreases at elevated temperatures, the slenderness at elevated temperatures decreases and the resistance increases. The contribution of this effect is approximately 10ºC; - The normal force in the right column is larger than in the left column. The first plastic hinge will therefore arise in the top of the right column. Following the code (component check), the structure is assumed to be collapsed by then. However, in the FEM analysis the temperature is allowed to rise before the second hinge occurs in the right column. In case of stocky frames, the contribution of this effect is about 10ºC and in case of slender frames, the contribution is negligible. - No explanation is given for the remaining 10-20ºC.

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Eberwien [34] also analysed a frame with hinged columns and a localised fire. Due to the stiff connection between the beam and the third column, the critical temperature of the right frame in Figure F 2 is 60 degrees Celsius higher than the critical temperature of the left frame.

= heated by localised fire

Figure F 2 – Frames with hinged column

Eberwien [34] noted that redistribution of forces (and the resulting higher critical temperature) is only possible if a large rotation capacity is available in the plastic hinges. Local buckling might prevent large rotations in the plastic hinges. The rotation capacities that are required for redistribution of forces are not realistic. Data on rotation capacities of connections and local bucking in members at elevated temperatures are not available.

F.2 Remarks on the numerical models

Creep is not taken into account in the FEM analyses in both studies. In Eberwien [34] it was concluded that creep is not important during the first hour of thermal exposure. However, in paragraph 4.8 it is shown that creep may become significant for this exposure period. Had there been a temperature gradient, creep deformations could not have been neglected. Besides creep may reduce the strength for this exposure period.

In Faggiano et al. [30], [31] and [32], it is concluded that for all alloys, the structure should be insulated in order to meet the required fire resistance period. It is also concluded that elastic-perfectly plastic material behaviour, using the 0,2 % proof stress as the yield limit, in all cases leads to conservative values of the critical temperature. However, as shown in paragraphs 5.4 and 5.5, the buckling resistance of members composed of inelastic material may be lower than the buckling resistance of elastic material. In case buckling is the decisive failure mechanism, it could be that elastic- perfectly plastic material behaviour leads to unsafe values of the critical temperature. Moreover, paragraph 4.2.2 showed that the strength at elevated temperature may decrease at relatively low strains (0,6 – 1,0 %). This was not accounted for in the research. The parameters in the Ramberg-Osgood model in Faggiano et al. [30], [31] and [32], are based on data of the 0,2 % proof stress, tensile strength and strain at rupture according to data in Davis [27]. The data provided in Davis [27] are however valid for thermal exposure periods of 10.000 hours. These data are inappropriate to use for fire exposure.

To determine the relative slenderness, Eberwien [34] recommends to use the 0,2% proof stress at elevated temperature. However, in that case also the modulus of elasticity

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at higher temperatures should be used. In that case, the relative slenderness at elevated temperature is still smaller than at room temperature, but it is higher compared with the case in which only the 0,2% proof stress at elevated temperature was used.

Other explanations for the differences between EN 1999-1-2 [7] and the FEM calculations, which are not noted by Eberwien [34], may be: - In the method of EN 1999-1-2 [7], creep is taken into account by a multiplication factor of 1,2 for the normal forces on columns. It is not clear whether this factor was also taken into account in the FEM analyses; - It is possible that the relation between the relative slenderness and the buckling factor described in EN 1999-1-1 [6] (which should also be applied in case of fire according to EN 1999-1-2 [7]) is too conservative for the structure under consideration. It is possible that the combination rules for bending and axial force in EN 1999-1-1 [6] (which should also be used in case of fire according to EN 1999-1-2 [7]) are too conservative for the columns considered.

It should be noted that the development of the temperature in the structural elements was not subject of study. It should be studied whether an increase of the critical temperature of 30 to 60ºC makes a relevant increase in the time that the structure resists the fire.

The research shows the necessity to study the rotation capacity with respect to local buckling, in order to make redistribution of forces possible.