Table of Contents

Cover

Series

Title

FOREWORD

PREFACE TO THE 2^ND EDITION

PREFACE 1^ST EDITION

NOTATIONS

Chapter 1: INTRODUCTION

1.1. RELATIONS BETWEEN DIFFERENT EUROCODES
1.2. SCOPE OF EN 1993-1-2
1.3. LAYOUT OF THE BOOK

Chapter 2: MECHANICAL LOADING

2.1. GENERAL
2.2. EXAMPLES
2.3. INDIRECT ACTIONS

Chapter 3: THERMAL ACTION

3.1. GENERAL
3.2. NOMINAL TEMPERATURE-TIME CURVES
3.3. PARAMETRIC TEMPERATURE-TIME CURVES
3.4. ZONE MODELS
3.5. CFD MODELS
3.6. LOCALISED FIRES
3.7. EXTERNAL MEMBERS

Chapter 4: TEMPERATURE IN STEEL SECTIONS

4.1. INTRODUCTION
4.2. THE HEAT CONDUCTION EQUATION AND ITS BOUNDARY CONDITIONS
4.3. ADVANCED CALCULATION MODEL. FINITE ELEMENT SOLUTION OF THE HEAT CONDUCTION EQUATION
4.4. SECTION FACTOR
4.5. TEMPERATURE OF UNPROTECTED STEELWORK EXPOSED TO FIRE
4.6. TEMPERATURE OF PROTECTED STEELWORK EXPOSED TO FIRE
4.7. INTERNAL STEELWORK IN A VOID PROTECTED BY HEAT SCREENS
4.8. EXTERNAL STEELWORK
4.9. VIEW FACTORS IN THE CONCAVE PART OF A STEEL PROFILE
4.10. TEMPERATURE IN STEEL MEMBERS SUBJECTED TO LOCALISED FIRES
4.11. TEMPERATURE IN STAINLESS STEEL MEMBERS

Chapter 5: MECHANICAL ANALYSIS

5.1. BASIC PRINCIPLES
5.2. MECHANICAL PROPERTIES OF CARBON STEEL
5.3. CLASSIFICATION OF CROSS SECTIONS
5.4. EFFECTIVE CROSS SECTION
5.5. FIRE RESISTANCE OF STRUCTURAL MEMBERS
5.6. DESIGN IN THE TEMPERATURE DOMAIN. CRITICAL TEMPERATURE
5.7. DESIGN OF CONTINUOUS BEAMS
5.8. FIRE RESISTANCE OF STRUCTURAL STAINLESS STEEL MEMBERS
5.9. DESIGN EXAMPLES

Chapter 6: ADVANCED CALCULATION MODELS

6.1. GENERAL
6.2. THERMAL RESPONSE MODEL
6.3. MECHANICAL RESPONSE MODEL
6.4. SOME COMPARISONS BETWEEN THE SIMPLE AND THE ADVANCED CALCULATION MODELS

Chapter 7: JOINTS

7.1. GENERAL
7.2. STRENGTH OF BOLTS AND WELDS AT ELEVATED TEMPERATURE
7.3. TEMPERATURE OF JOINTS IN FIRE
7.4. BOLTED CONNECTIONS
7.5. DESIGN FIRE RESISTANCE OF WELDS
7.6. DESIGN EXAMPLES

Chapter 8: THE COMPUTER PROGRAM “ELEFIR-EN”

8.1. GENERAL
8.2. BRIEF DESCRIPTION OF THE PROGRAM
8.3. DEFAULT CONSTANTS USED IN THE PROGRAM
8.4. DESIGN EXAMPLE

Chapter 9: CASE STUDY

9.1. DESCRIPTION OF THE CASE STUDY
9.2. FIRE RESISTANCE UNDER STANDARD FIRE
9.3. FIRE RESISTANCE UNDER NATURAL FIRE

REFERENCES

Annex A: THERMAL DATA FOR CARBON STEEL AND STAINLESS STEEL SECTIONS

A.1. THERMAL PROPERTIES OF CARBON STEEL
A.2. SECTION FACTOR A_m/V [m^-1] FOR UNPROTECTED STEEL MEMBERS
A.3. SECTION FACTOR A_p/V [m^-1] FOR PROTECTED STEEL MEMBERS
A.4. TABLES AND NOMOGRAMS FOR EVALUATING THE TEMPERATURE IN UNPROTECTED STEEL MEMBERS SUBJECTED TO THE STANDARD FIRE CURVE ISO 834
A.5. TABLES AND NOMOGRAMS FOR EVALUATING THE TEMPERATURE IN PROTECTED STEEL MEMBERS SUBJECTED TO THE STANDARD FIRE CURVE ISO 834
A.6. THERMAL PROPERTIES OF SOME FIRE PROTECTION MATERIALS
A.7. THERMAL PROPERTIES OF STAINLESS STEEL
A.8. TABLES AND NOMOGRAMS FOR EVALUATING THE TEMPERATURE IN UNPROTECTED STAINLESS STEEL MEMBERS SUBJECTED TO THE STANDARD FIRE CURVE ISO 834
A.9. THERMAL PROPERTIES OF SOME FIRE COMPARTMENT LINING MATERIALS

Annex B: INPUT DATA FOR NATURAL FIRE MODELS

B.1. INTRODUCTION
B.2. FIRE LOAD DENSITY
B.3. RATE OF HEAT RELEASE DENSITY
B.4. VENTILATION CONTROL
B.5. FLASH-OVER

Annex C: MECHANICAL PROPERTIES OF CARBON STEEL AND STAINLESS STEEL

C.1. MECHANICAL PROPERTIES OF CARBON STEEL
C.2. MECHANICAL PROPERTIES OF STAINLESS STEEL

Annex D: TABLES FOR SECTION CLASSIFICATION AND EFFECTIVE WIDTH EVALUATION

Annex E: SECTION FACTORS OF EUROPEAN HOT ROLLED IPE AND HE PROFILES

Annex F: CROSS SECTIONAL CLASSIFICATION OF THE EUROPEAN HOT ROLLED IPE AND HE PROFILES

F.1. CROSS SECTIONAL CLASSIFICATION FOR PURE COMPRESSION AND PURE BENDING
F.2. CROSS SECTIONAL CLASSIFICATION FOR COMBINED COMPRESSION AND BENDING MOMENT

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List of Tables

Chapter 2: MECHANICAL LOADING

Table 2.1 – Recommended values of the coefficients ψ for buildings

Chapter 3: THERMAL ACTION

Table 3.1 – Values of t_lim as a function of the growth rate

Chapter 4: TEMPERATURE IN STEEL SECTIONS

Table 4.1 – Definition of section factors for unprotected steel members
Table 4.2 – Definition of section factors for protected steel members
Table 4.3 – Some examples of section factors
Table 4.4 – Coefficient of heat transfer by convection and view factor
Table 4.5 – Box value of the section factor
Table 4.6 – Temperatures after 30 and 60 min of ISO 834 exposure
Table 4.7 – Section factors for HEB profiles
Table 4.8 – Classification of cars
Table 4.9 – Values of the rate of heat release of four burning class 3-cars
Table 4.10 – Distances r between the axis of the flame and the position where the temperature is evaluated
Table 4.11 – Maximum temperatures of the main beam

Chapter 5: MECHANICAL ANALYSIS

Table 5.1 – Relation between calculation models, structural schematization and fire model
Table 5.2 – Reduction factors for carbon steel for the design at elevated temperatures
Table 5.3 − Reduction factors k_0.2p,θ for carbon steel
Table 5.4 − Maximum slenderness for compression parts of cross section
Table 5.5 – Equivalent uniform moment factors C₁
Table 5.6 – Equivalent uniform moment factors
Table 5.7 – Mechanical properties at room temperature
Table 5.8 – Mechanical properties at 600 °C, Class 1, 2, 3 and 4 cross section
Table 5.9 – Factors for determination of strain and stiffness of stainless steel at elevated temperatures for Stainless Steel 1.4301

Chapter 7: JOINTS

Table 7.1 – Strength Reduction Factors for Bolts and Welds

Chapter 9: CASE STUDY

Table 9.1 − Steel section temperatures
Table 9.2 − Effects of actions (compression is negative)
Table 9.3 − Results of the mechanical analyses
Table 9.4 − Characteristics of the localised fire

Annex B: INPUT DATA FOR NATURAL FIRE MODELS

Table B.1 – Characteristic fire load densities q_f,k [MJ/m²] for different occupancies
Table B.2 – Factor δ_q1 for different floor areas
Table B.3 – Factor δ_q2 for different types of occupancy
Table B.4 – Fire growth rate and RHR density for different types of occupancy

Annex C: MECHANICAL PROPERTIES OF CARBON STEEL AND STAINLESS STEEL

Table C.1 – Nominal values of yield strength f_y and ultimate tensile strength f_u for hot rolled structural steel
Table C.2 – Nominal values of yield strength f_y and ultimate tensile strength f_u for structural hollow sections
Table C.3 – Steel constitutive law at elevated temperatures
Table C.4 – Stress-strain relationship for S235 carbon steel at elevated temperatures
Table C.5 – Stress-strain relationship for S275 carbon steel at elevated temperatures
Table C.6 – Stress-strain relationship for S355 carbon steel at elevated temperatures
Table C.7 – Stress-strain relationship for S460 carbon steel at elevated temperatures
Table C.8 – Reduction factors for carbon steel for the design of class 4 sections at elevated temperatures
Table C.9 – Nominal values of the yield strength f_y, the ultimate tensile strength f_u and Young’s modulus E for structural stainless steels according to EN 10088
Table. C.10 – Parameters for defining stress-strain relationship for stainless steel at elevated temperatures
Table C.11 – Reduction factors of stainless steel at elevated temperatures

Annex D: TABLES FOR SECTION CLASSIFICATION AND EFFECTIVE WIDTH EVALUATION

Table D.1 – Maximum with-to-thickness ratios for compression parts
Table D.2 – Maximum with-to-thickness ratios for compression parts
Table D.3 – Maximum with-to-thickness ratios for compression parts
Table D.4 – Internal compression elements
Table D.5 – Outstand compression elements

List of Illustrations

Chapter 1: INTRODUCTION

Figure 1.1 – Relationships between different Eurocodes

Chapter 3: THERMAL ACTION

Figure 3.1 – Comparison between two nominal temperature-time curves
Figure 3.2 – Examples of parametric time-temperature curves
Figure 3.3 – Flame on the floor and not impacting the ceiling
Figure 3.4 – Flame on the floor and impacting the ceiling
Figure 3.5 – Relationship between the impinging flux and the steel temperature in a steady state situation
Figure 3.6 – Configuration factor for two parallel surfaces
Figure 3.7 – Configuration factor for two perpendicular surfaces
Figure 3.8 – Configuration factor when point P is outside the radiating surface

Chapter 4: TEMPERATURE IN STEEL SECTIONS

Figure 4.1 – Steel profile exposed to fire on all four sides
Figure 4.2 – Finite element mesh used
Figure 4.3 – Temperature field of an HE 400 B heated on all four sides
Figure 4.4 – The section factor
Figure 4.5 – Influence of shape on the shadow effect
Figure 4.6 – Influence of section factor A_m/V on the temperature rise in HEB profiles
Figure 4.7 – Influence of the use of a constant value of the steel specific heat of 600 J/(KgK)
Figure 4.8 – Temperature as a function of the massivity factor for various times for unprotected sections subjected to the ISO 834 fire
Figure 4.9 – Temperature as a function of time for various massivity factors for unprotected sections subjected to the ISO 834 fire
Figure 4.10 – Temperature development in a compartment with a parametric fire and the corresponding temperature of an unprotected HE 220 B
Figure 4.11 – Temperature in protected steelwork
Figure 4.12 – Time delay due to the moisture content
Figure 4.13 – Temperature as a function of the modified massivity factor for various times, for protected profiles subjected to the ISO 834 curve
Figure 4.14 – Temperature as a function of time for various modified massivity factors, for protected profiles subjected to the ISO 834 curve
Figure 4.15 – Influence of the parameter ϕ, in a heavy fire insulation material a) Eq. (4.19); b) Eq. 4.23 with Eq. (4.25); c) Eq. 4.19 with ϕ = 0 or Eq. (4.23)
Figure 4.16 – Influence of the parameter, ϕ, in light weight fire insulation material
Figure 4.17 – Temperature of an unprotected HE 220 A heated by the parametric fire from example 3.3
Figure 4.18 – Temperature of a HE 220 A heated by the parametric fire of example 3.3
Figure 4.19 – Temperature of a HE 220 B protected with gypsum boards
Figure 4.20 – Steel beam with a heat screen underneath (elevation)
Figure 4.21 – Protected steel column with heat screens on both sides (plan view)
Figure 4.22 – Two elevations of the façade of a hotel
Figure 4.23 – Shape of the flame
Figure 4.24 – Emitting and receiving surfaces for radiative heat (A_e - emitting surface; A_r - receiving surface)
Figure 4.25 – View factors for an HE 400 B
Figure 4.26 – Emitting (AB) and receiving (CD) surfaces for radiative heat.
Figure 4.27 – Length of the flame
Figure 4.28 – Gas and unprotected IPE 300 temperature development when the flame does not impinge the ceiling
Figure 4.29 – Gas and unprotected IPE 300 temperature development when the flame is impinging the ceiling
Figure 4.30 – Temperature development of gas and protected IPE 300 when the flame does not impinge the ceiling
Figure 4.31 – Temperature development of Gas and protected IPE 300 when the flame impinges the ceiling
Figure 4.32 – a) Rate of heat release of a single class3 car fire; b) Rate of heat release of a single class 3 car fire with a delay of 12 minutes
Figure 4.33 – Fire scenarios and sequence of ignition
Figure 4.34 – Flame length development for a single burning car
Figure 4.35 – a) Scheme showing the distance r; b) Distances to be considered for scenario 2
Figure 4.36 –Temperature development. a) Scenario 1; b) Scenario 2; c) Scenario 3 d) Scenario 4; e) Scenario 5; f) Scenario 1 with the beam protected
Figure 4.37 – Specific heat of stainless steel and carbon steel as a function of temperature
Figure 4.38 – Conductivity of stainless steel and carbon steel as a function of temperature
Figure 4.39 – Temperature development of a carbon steel and a stainless steel IPE 450, heated on four sides by the ISO 834 fire curve
Figure 4.40 – Thermal diffusivity of carbon steel and stainless steel

Chapter 5: MECHANICAL ANALYSIS

Figure 5.1 – Time (1), load (2), and temperature (3) domains for a nominal fire
Figure 5.2 – With parametric or natural fires a)
Figure 5.3 – Structural schematisation. a) Global structure, b) Substructures, c) Members
Figure 5.4 – Stress-strain relationship for carbon steel S235 at elevated temperatures
Figure 5.5 – Stress-strain relationship for carbon steel at elevated temperatures
Figure 5.6 – Reduction factors for the stress-strain relationship of carbon steel at elevated temperatures (see Fig. 3.2 from EN 1993-1-2)
Figure 5.7 – Reduction factors for the yield strength, k_y,θ, at elevated temperatures
Figure 5.8 − Internal and outstand elements a) Rolled section; b) Hollow section; c) Welded section
Figure 5.9 − Local buckling of the upper flange of a beam subject to bending (ESDEP, 1995)
Figure 5.10 − Moment-rotation curves
Figure 5.11 − Pattern of normal stresses for: a) Class 1or Class 2; b) Class 3
Figure 5.12 − Plastic and elastic M-N interaction curves
Figure 5.13 − M-N interaction curves
Figure 5.14 − Pattern of normal stresses distribution for combined bending and axial compression. a) and b) Elastic stress distribution; c) elastoplastic stress distribution; d) Plastic stress distribution
Figure 5.15 − The three possible methodologies to reach the ultimate limit state a) Ultimate elastic limit state; b) Ultimate plastic limit state
Figure 5.16 − Plastic interaction diagram with the pair (N_Ed; M_y,ult)
Figure 5.17 − Pattern of normal stresses for Class 1 or 2 I-section. Positive – Compression (C and C’); Negative – Tension (T)
Figure 5.18 − Plastic interaction diagram with the pair (N_ult, M_y,ult)
Figure 5.19 − Reaching the ultimate elastic limit state amplifying only M_y,Ed a) Actual direct strength diagram; b) Direct strength diagram at ultimate limit state
Figure 5.20 − Reaching the ultimate elastic limit state amplifying only M_y,Ed
Figure 5.21 − Reaching the ultimate elastic limit state amplifying simultaneously N_Ed and M_y,Ed a) Actual direct strength diagram; b) Direct strength diagram at ultimate limit state
Figure 5.22 − Reaching the ultimate elastic limit state amplifying simultaneously N_Ed and M_y,Ed
Figure 5.23 − Change of the class in a beam-column using the second methodology
Figure 5.24 − Ratio as a function of the temperature
Figure 5.25 − Shrinkage of the M-N interaction curve with the increasing temperature, during a fire
Figure 5.26 − Class 4 cross section. a) For axial force; b) For bending moment
Figure 5.27 − Stress-strain relationship
Figure 5.28 – Buckling lengths l_fi of columns in braced frames
Figure 5.29 – Cross section with non-uniform temperature distribution
Figure 5.30 – Non-uniform steel temperature distribution across the cross section
Figure 5.31 – Non-uniform steel temperature distribution along the beam
Figure 5.32 – Reduction of the yield strength, in the shear area, due to the shear force a) Class 1 or Class 2; b) Class 3
Figure 5.33 – Reduction of the yield strength due to the shear force
Figure 5.34 – Lateral-torsional buckling of a slender cantilever beam
Figure 5.35 – Simple I-beam with fork supports under uniform moment
Figure 5.36 – Influence of the level of the application of the load
Figure 5.37 – Influence of the shape of the bending moment diagram on the lateral torsional buckling resistance moment
Figure 5.38 – Shear buckling in a plate girder in fire situation
Figure 5.39 – Bending and axial force interaction
Figure 5.40 – Bending and axial force interaction for rectangular solid sections
Figure 5.41 – Critical temperature, related to degree of utilisation
Figure 5.42 – Flowchart for evaluating the critical temperature
Figure 5.43 – Typical collapse mechanisms for a continuous beam
Figure 5.44 – End beam mechanism
Figure 5.45 – Intermediate beam mechanism
Figure 5.46 – Stress-strain relationships of carbon steel S 235 and stainless steel 1.4301 in fire situation at 20 °C (from EN 1993-1-2)
Figure 5.47 – Stress-strain relationships of carbon steel S 235 and stainless steel 1.4301 at 600 °C
Figure 5.48 – Stress-strain relationships of carbon steel S 235 and stainless steel 1.4301 at 20 °C for 0 ≤ ε ≤ 0.02
Figure 5.49 – Stress-strain relationships of carbon steel S 235 and stainless steel 1.4301 at 600 °C for 0 ≤ ε ≤ 0.02
Figure 5.50 – Reduction factors: a) strength reduction factor; b) reduction factor for the Young’s modulus
Figure 5.51 – as a function of the temperature
Figure 5.52 – Elements of a cross section
Figure 5.53 – Steel temperatures after 30 min of standard fire exposure
Figure 5.54 – Comparison of the temperatures obtained from EC3 and EC4
Figure 5.55 – Plastic stress distribution after 30 min of standard fire exposure and location of the plastic neutral axis (n. a.)
Figure 5.56 – Beam-column in a braced frame
Figure 5.57 – Effective cross section
Figure 5.58 – Dimensions of the built up cross section
Figure 5.59 – Effective throat thickness of the fillet weld
Figure 5.60 – Effective^p width b_eff of outstand compression elements (EN 1993-1-5)
Figure 5.61 – Effective^p width b_eff = b_e1 + b_e2 of internal compression elements (EN 1993-1-5)
Figure 5.62 – Effective cross section when subjected to uniform compression
Figure 5.63 – Compression and tension parts of the web
Figure 5.64 – Effective^p width b_eff = b_e1 + b_e2 of internal compression elements (EN 1993-1-5)
Figure 5.65 – Effective cross section when subjected only to moment about the major axis
Figure 5.66 – Continuous beam
Figure 5.67 – Bending diagram and shear forces
Figure 5.68 – Combined bending and tension

Chapter 6: ADVANCED CALCULATION MODELS

Figure 6.1 – Temperature in a HE300A heated on 4 sides after 30 minutes of standard fire
Figure 6.2 – Temperature in a HE300A heated on 3 sides after 30 minutes of standard fire
Figure 6.3 – Temperature in a HE300A with a concrete slab on the upper flange
Figure 6.4 – Temperature in a HE200A inserted in a concrete wall after 60 minutes of standard fire
Figure 6.5 – Temperature in a composite joint (courtesy of Elisabetta Alderighi, Univ. of Pisa)
Figure 6.6 – Large displacements in a steel frame partially subjected to the fire (Courtesy of COPERFIL Construccion)
Figure 6.7 – Bending moment distribution in a 3D frame
Figure 6.8 – Deformed shape of a cellular beam modelled by shell elements
Figure 6.9 – Deformed shape and compression forces in a composite floor
Figure 6.10 – Temperature evolution with different models
Figure 6.11 – Temperature distribution with two different models

Chapter 7: JOINTS

Figure 7.1 – Reduction factors for structural steel (ky), bolts (kb) and welds (kw)
Figure 7.2 – Temperature profile within the depth of a joint in which the connected beam supports a concrete slab
Figure 7.3 – Bolted joint of a member subject to tension
Figure 7.4 – Symbols for spacing of fasteners (EN 1993-1-1)
Figure 7.5 – Welded tension joint
Figure 7.6 – Double angle cleat. Beam-to-column connection

Chapter 8: THE COMPUTER PROGRAM “ELEFIR-EN”

Figure 8.1 – First screen of the software Elefir-EN
Figure 8.2 – Dialog box for user-defined sections
Figure 8.3 – Options for fire exposure. a) four sides; b) three sides
Figure 8.4 – Options for fire protection. a) contour encasement; b) hollow encasement
Figure 8.5 – Heating curves and option for the effect of moisture content
Figure 8.6 – Localised fires. a) Hesquestad method; b) Hasemi method
Figure 8.7 – RHR – Rate of Heat Release. a) According Eurocode 1; b) User-defined curve
Figure 8.8 – Dialog box for defining the compartment dimensions
Figure 8.9 – Dialog box for defining parametric fires
Figure 8.10 – Dialog box for defining localised fires
Figure 8.11 – Main menu
Figure 8.12 – Safety factors
Figure 8.13 – Menu tools
Figure 8.14 – Wall lining materials
Figure 8.15 – Fire protection materials
Figure 8.16 – Options menu
Figure 8.17 – Reduction factors a) Reduction factors function of the temperature; b) Temperature function of the reduction factors
Figure 8.18 – Possible load cases for bending
Figure 8.19 – Development of the compartment and steel temperature for a parametric fire. a) Unprotected member; b) and c) Protected member
Figure 8.20 – Dialog box for the global plastic analysis of continuous beams
Figure 8.21 – Dialog box for bending
Figure 8.22 – Dialog box for bending with lateral-torsional buckling
Figure 8.23 – HE 220 B under major axis load and bracing system
Figure 8.24 – M_y,fi,Ed bending diagram
Figure 8.25 – M_y,fi,Ed bending diagram for LTB

Chapter 9: CASE STUDY

Figure 9.1 − Schematic representation of the characteristic wind load
Figure 9.2 − Axial forces under dead load
Figure 9.3 − Bending moments under dead load and wind load
Figure 9.4 − Buckling length in the columns a) in the plane of the frame; b) out of the plane of the frame
Figure 9.5 − Plan view of an horizontal bracing system
Figure 9.6 − Deformed shape at room temperature under dead loads
Figure 9.7 − Deformed shape under dead loads at elevated temperature
Figure 9.8 – 3D model with the supports
Figure 9.9 – Deformation of the 3D model at collapse
Figure 9.10 − Development of the gas temperature
Figure 9.11 − Zone subjected to the localised fire

Annex A: THERMAL DATA FOR CARBON STEEL AND STAINLESS STEEL SECTIONS

Figure A.1 – Specific heat of carbon steel
Figure A.2 – Conductivity of carbon steel
Figure A.3 – Thermal elongation of carbon steel
Figure A.4 – Specific heat of stainless steel as a function of the temperature
Figure A.5 – Thermal conductivity of stainless steel as a function of the temperature
Figure A.6 – Thermal elongation of stainless steel as a function of the temperature

Annex B: INPUT DATA FOR NATURAL FIRE MODELS

Figure B.1 – Evolution of the RHR as a function of time
Figure B.2: – Evolution of the flame length as a function of time
Figure B.3 – Modification of the RHR curve in case of ventilation control - Principle
Figure B.4 – Modification of the RHR curve in case of ventilation control - Example
Figure B.5 – Modification of the RHR curve in case of flash-over

Annex C: MECHANICAL PROPERTIES OF CARBON STEEL AND STAINLESS STEEL

Figure C.1 – Stress-strain relationship for carbon steel at elevated temperatures
Figure C.2 – Stress-strain relationship for S235 carbon steel at elevated temperatures
Figure C.3 – Stress-strain relationship for S275 carbon steel at elevated temperatures
Figure C.4 – Stress-strain relationship for S355 carbon steel at elevated temperatures
Figure C.5 – Stress-strain relationship for S460 carbon steel at elevated temperatures
Figure C.6 – Alternative stress-strain relationship for steel allowing for strain-hardening
Figure C.7 – Alternative stress-strain relationship for steel allowing for strain-hardening for different temperatures
Figure C.8 – Reduction factors for the stress-strain relationship of cold formed and hot rolled thin walled steel at elevated temperatures
Figure C.9 – Stress-strain relationship for stainless steel at elevated temperatures
Figure C.10 – Stress-strain relationship of the stainless steel 1.4301 at 1100 ºC

ECCS EUROCODE DESIGN MANUALS

ECCS EDITORIAL BOARD

Luís Simões da Silva (ECCS)

António Lamas (Portugal)

Jean-Pierre Jaspart (Belgium)

Reidar Bjorhovde (USA)

Ulrike Kuhlmann (Germany)

DESIGN OF STEEL STRUCTURES – 1^ST EDITION REVISED SECOND IMPRESSION
Luís Simões da Silva, Rui Simões and Helena Gervásio

FIRE DESIGN OF STEEL STRUCTURES – 2^ND EDITION
Jean-Marc Franssen and Paulo Vila Real

DESIGN OF PLATED STRUCTURES
Darko Beg, Ulrike Kuhlmann, Laurence Davaine and Benjamin Braun

FATIGUE DESIGN OD STEEL AND COMPOSITE STRUCTURES
Alain Nussbaumer, Luís Borges and Laurence Davaine

DESIGN OF COLD-FORMED STEEL STRUCTURES
Dan Dubina, Viorel Ungureanu and Raffaele Landolfo

AVAILABLE SOON

DESIGN OF JOINTS IN STEEL AND COMPOSITE STRUCTURES
Jean-Pierre Jaspart, Klaus Weynand

DESIGN OF COMPOSITE STRUCTURES
Markus Feldman and Benno Hoffmeister

DESIGN OF STEEL STRUCTURES FOR BUILDINGS IN SEISMIC AREAS
Raffaele Landolfo, Federico Mazzolani, Dan Dubina and Luís Simões da Silva

ECCS – SCI EUROCODE DESIGN MANUALS

DESIGN OF STEEL STRUCTURES, U. K. EDITION
Luís Simões da Silva, Rui Simões, Helena Gervásio and Graham Couchman

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Design of Steel Structures

2^nd Edition, 2015

Published by:
ECCS – European Convention for Constructional Steelwork
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ISBN (ECCS): 978-92-9147-128-7
ISBN (Ernst & Sohn): 978-3-433-03143-8

FOREWORD

Designing for fire is an important and essential requirement in the design process of buildings and civil engineering structures. Within Europe the fire resistance requirements for buildings are specified in the national Building Regulations. All buildings must meet certain functional requirements and these are usually linked to the purpose and height of the building. For the purpose of this publication, the most important requirement is for the building to retain its stability for a reasonable period. This requirement has traditionally been linked to the required time of survival in the standard fire test. The most common method of designing a steel structure for the fire condition is to design the building for the ambient temperature loading condition and then to cover the steel members with proprietary fire protection materials to ensure that a specific temperature is not exceeded. Although this remains the simplest approach for the majority of regular steel framed buildings, one of the drawbacks with this approach is that it is often incorrectly assumed that there is a one to one correspondence between the survival time in the standard fire test and the survival time in a real fire. This is not the case and real fire can be more or less severe than the standard fire test depending on the characteristics of the fire enclosure.

The fire parts of the Eurocodes set out a new way of approaching structural fire design. To those more familiar with the very simple prescriptive approach to the design of structures for fire, the new philosophy may appear unduly complex. However, the fire design methodology in the Eurocodes affords the designer much greater flexibility in his approach to the subject. The options available range from a simple consideration of isolated member behaviour subject to a standard fire to a consideration of the physical parameters influencing fire development coupled with an analysis of the entire building.

The Eurocode process can be simplified into three components consisting of the characterisation of the fire model, a consideration of the temperature distribution within the structure and an assessment of the structural response to the fire. Information on thermal actions for temperature analysis is given in EN 1991-1-2 and the method used to calculate the temperature rise of structural steelwork (either protected or unprotected) is found in EN 1993-1-2. The design procedures to establish structural resistance are set out in EN 1993 but the actions (or loads) to be used for the assessment are taken from the relevant parts of EN 1991.

This publication follows this sequence of steps. Chapter 2 explains how to calculate the mechanical actions (loads) in the fire situation based on the information given in EN 1990 and EN 1991. Chapter 3 presents the models that may be used to represent the thermal actions. Chapter 4 describes the procedures that may be used to calculate the temperature of the steelwork from the temperature of the compartment and Chapter 5 shows how the information given in EN 1993-1-2 may be used to determine the load bearing capacity of the steel structures. The methods used to evaluate the fire resistance of bolted and welded connections are described in Chapter 7. In all of these chapters the information given in the Eurocodes is presented in a practical and usable manner. Each chapter also contains a set of easy to follow worked examples.

Chapter 8 describes a computer program called ‘Elefir-EN’ which is based on the simple calculation model given in the Eurocode and allows designers to quickly and accurately calculate the performance of steel components in the fire situation. Chapter 9 looks at the issues that a designer may be faced with when assessing the fire resistance of a complete building. This is done via a case study and addresses most of the concepts presented in the earlier chapters. Finally the annexes give basic information on the thermal and mechanical properties for both carbon steel and stainless steel.

The concepts and fire engineering procedures given in the Eurocodes may seem complex to those more familiar with the prescriptive approach. This publication sets out the design process in a logical manner giving practical and helpful advice and easy to follow worked examples that will allow designers to exploit the benefits of this new approach to fire design.

David Moore
BCSA Director of Engineering

PREFACE TO THE 2^ND EDITION

The first edition of Fire Design of Steel Structures was published by ECCS as paperback in 2010. Since 2012, this publication is also available in electronic format as an e-book. Nevertheless, the interest for this publication was so high that it appeared rapidly that the paper copies would be sold out within a short time and a second edition would have to be printed.

The authors took the opportunity of this second edition to review their own manuscript. The standards that are described and commented in this book, namely EN 1991-1-2 and 1993-1-2, are still in application in the same versions as those that prevailed at the time of writing the first edition. It was nevertheless considered that an added value would be given by, first, rephrasing some sentences or sections that had generated questions by some readers but, above all, adding some new material for the benefit of completeness.

The new material namely comprises:

– A section dealing with the thermal response of steel members under several separate simultaneous localised fires, including one worked example with multiple fire scenarios in a car park (Chapter 4);
– An important section on classification of cross sections. The case of combined bending and axial force, including one worked example comparing different methodologies to obtain the position of the neutral axis, has been added (Chapter 5);
– A worked example of a beam-column with Class 4 cross section (Chapter 5);
– A new section with comparisons between the simple and the advanced calculation models in Chapter 6 (shadow factor – including one example, buckling curves and adaptation factors κ₁ and κ₂ );
– New references have been included.

Jean-Marc Franssen
Paulo Vila Real
June 2015

PREFACE 1^ST EDITION

When a fire breaks out in a building, except in very few cases, the structure has to perform in a satisfactory manner in order to meet various objectives such as, e.g., to limit the extension of the fire, to ensure evacuation of the occupant or to allow safe operations by the fire brigade. Steel structures are no exception to this requirement.

Eurocode 3 proposes design methods that allow verifying whether the stability and resistance of a steel structure is ensured. A specific Part 1-2 of Eurocode 3 is dedicated to the calculation of structures subjected to fire. Indeed, the fact that the stress-strain relationship becomes highly non-linear at elevated temperatures, plus the fact that heating leads to thermal expansion with possible restraint forces, make the rules derived for ambient temperature inaccurate in the fire situation.

After a long evolution and maturation, the Eurocodes have received the status of European standards. The fire part of Eurocode 3 is EN 1993-1-2. This makes the application of these rules mandatory in member states of the European Community. In many other parts of the world, these standards are considered as valuable pieces of information and their application may be rendered mandatory, either by law or by contractual imposition.

Nevertheless, standards are not written with pedagogic objectives. Yet, for a designer who has not been involved in the research projects that are at the base of the document, some questions may arise when the rules have to be applied to practical cases.

The objective of this book is to explain the rules, to give some information about the fundamental physics that is at the base of these rules and to show by examples how they have to be applied in practice. It is expected that a designer who reads this book will reduce the probability of doing a non appropriate application of the rules and, on the contrary, will be in a better position to make a design in a situation that has not been explicitly foreseen in the code.

A design in the fire situation is based on load combinations that are different from those considered at room temperatures. Actions on structures from fire exposure are classified as accidental actions and the load combinations for the fire situation are given in the Eurocode, EN 1990. The thermal environment created by the fire must also be defined in order to calculate the temperature elevation in the steel sections and different models are given in part 1.2 of Eurocode 1 for representing the fire. In order to encompass in one single document all aspects that are relevant to the fire design of steel structures, this book deals with the fire part of Eurocode 1 as well as that of Eurocode 3.

The requirements, i.e., for example, the duration of stability or resistance that has to be ensured to the structure, is not treated in the Eurocodes. This aspect is indeed very often imposed by the legal environment, especially when using a prescriptive approach, or has to be treated separately by, for example, a risk analysis based on evacuation time. In line with the Eurocodes, this book does not deal with the requirement.

A computer program, Elefir-EN, which has been developed for the fire design of structural members in accordance with the simple calculation models given in the Eurocodes, is supplied with this book. The software is an essential tool for structural engineers in the design office, enabling quick and accurate calculations to be produced, reducing design time and the probability of errors in the application of the equations. It can also be used by academics and students.

The program has been carefully checked for reliability and do not contain any known errors, but the authors and the publisher assume no responsibility for any damage resulting from the use of this program. No warranty of any type is given or implied concerning the correctness or accuracy of any results obtained from the program. It is the responsibility of the program user to independently verify any analysis results. Please contact the authors if any errors are discovered. The program is licensed to the purchasers of this book who are strongly encouraged to register in its web site so that any updated version can be delivered.

Jean-Marc Franssen
Paulo Vila Real
March 2010

Eurocode 1: Actions on structuresPart 1-2 – General actions – Actions on structures exposed to fireEurocode 3: Design of steel structuresPart 1-2 – General rules – Structural fire design

Eurocode 1: Actions on structures
Part 1-2 – General actions – Actions on structures exposed to fire
Eurocode 3: Design of steel structures
Part 1-2 – General rules – Structural fire design