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- Herausgeber: Wiley-VCH
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
This book explains and illustrates the rules that are given in the Eurocodes for designing steel structures subjected to fire. After the first introductory chapter, 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 is dedicated to the models which represent the thermal actions created by the fire. Chapter 4 describes the procedures to 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 is used to determine the load bearing capacity of the steel structure. Chapter 6 presents the essential features that characterize the advanced calculation models, for thermal and mechanical response. The methods used to evaluate the fire resistance of bolted and welded connections are described in Chapter 7. 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 previous chapters.
For this second edition the content has been revised and extended. The book contains some new sections, e.g. a comparison between the simple and the advanced calculation, as well as additional examples.
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Table of Contents
Cover
Series
Title
Copyright
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
ELEFIR - EN
End User License Agreement
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
0.2
p,θ
for carbon steel
Table 5.4 − Maximum slenderness for compression parts of cross section
Table 5.5 – Equivalent uniform moment factors
C
1
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/m
2
] for different occupancies
Table B.2 – Factor
δ
q
1
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
Guide
Cover
Table of Contents
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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 – 1ST EDITION REVISED SECOND IMPRESSIONLuís Simões da Silva, Rui Simões and Helena Gervásio
FIRE DESIGN OF STEEL STRUCTURES – 2ND EDITIONJean-Marc Franssen and Paulo Vila Real
DESIGN OF PLATED STRUCTURESDarko Beg, Ulrike Kuhlmann, Laurence Davaine and Benjamin Braun
FATIGUE DESIGN OD STEEL AND COMPOSITE STRUCTURESAlain Nussbaumer, Luís Borges and Laurence Davaine
DESIGN OF COLD-FORMED STEEL STRUCTURESDan Dubina, Viorel Ungureanu and Raffaele Landolfo
AVAILABLE SOON
DESIGN OF JOINTS IN STEEL AND COMPOSITE STRUCTURESJean-Pierre Jaspart, Klaus Weynand
DESIGN OF COMPOSITE STRUCTURESMarkus Feldman and Benno Hoffmeister
DESIGN OF STEEL STRUCTURES FOR BUILDINGS IN SEISMIC AREASRaffaele Landolfo, Federico Mazzolani, Dan Dubina and Luís Simões da Silva
ECCS – SCI EUROCODE DESIGN MANUALS
DESIGN OF STEEL STRUCTURES, U. K. EDITIONLuís Simões da Silva, Rui Simões, Helena Gervásio and Graham Couchman
INFORMATION AND ORDERING DETAILS
For price, availability, and ordering visit our website www.steelconstruct.com.For more information about books and journals visit www.ernst-und-sohn.de.
FIRE DESIGN OF STEEL STRUCTURES
2ND EDITION
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
Jean-Marc Franssen
Paulo Vila Real
Design of Steel Structures
2nd Edition, 2015
Published by:ECCS – European Convention for Constructional [email protected]
Sales:Wilhelm Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin
All rights reserved. No parts of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner.
ECCS assumes no liability with respect to the use for any application of the material and information contained in this publication.
Copyright © 2015 ECCS – European Convention for Constructional Steelwork
ISBN (ECCS): 978-92-9147-128-7ISBN (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 MooreBCSA Director of Engineering
PREFACE TO THE 2ND 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 κ
1
and κ
2
);
– New references have been included.
Jean-Marc FranssenPaulo Vila RealJune 2015
PREFACE 1ST 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 FranssenPaulo Vila RealMarch 2010
NOTATIONS
Latin lower case letters
b
material parameter in the walls, width of a steel section, width of a plate
c
specific heat, width of a plate in an open steel section
c
a
specific heat of steel
c
p
specific heat of protection material
d
diameter of a circular hollow section
d
eq
characteristic size of a structural member
d
f
flame thickness
d
p
thickness of a fire protection material
f
factor for the effect of non-uniform bending moment distribution on lateral torsional buckling
f
b
stress due to bending moment
f
c
stress due to axial force
f
0.2
p
,θ
0.2% proof strength
f
p,θ
limit of proportionality of steel at temperature
θ
f
u
ultimate strength at 20 ºC
f
u,θ
ultimate strength of steel at temperature
θ
f
y
yield strength at 20 ºC
f
y,θ
effective yield strength of steel at temperature
θ
h
height of an opening, height of a radiating surface, height of a steel section, height of a component being considered above the bottom of the beam
impinging heat flux
heat flux at the surface of a steel element
h
eq
averaged height of the vertical openings
h
w
depth of the web
i
radius of gyration of a cross section
k
multiplication factor in the parametric fire model
k
2%
,θ
correction factor for the determination of the yield strength of stainless steel at elevated temperature
k
b,θ
reduction factor for bolts
k
p
0.2
θ
reduction factor for the 0.2% proof strength
k
E,θ
reduction factor for the Young's modulus
k
E,θ
,
com
reduction factor for the Young’s modulus at the maximum steel temperature in the compression flange
k
p,θ
reduction factor for the limit of proportionality
k
sh
correction factor for the shadow effect
k
u,θ
reduction factor for tensile strength of stainless steel at elevated temperature
k
w
effective length factor referring to end warping
k
w,θ
reduction factor for welds
k
y,θ
reduction factor for the effective yield strength
k
y,θ
,
com
reduction factor for the yield strength of steel at the maximum temperature in the compression flange
k
y,θ,web
reduction factor for the yield strength at the web temperature
θ
web
k
z
effective length factor referring to end rotation on plan
k
θ
reduction factor for a strength or deformation property
k
σ
plate buckling factor
l
length of a member
l
fi
buckling length in fire situation
p
moisture content of a protection material
q
c
heat flux by convection
q
cr
combine heat flux by convection and radiation
q
Ed
design value of a distributed load in the normal situation
q
f,d
design value of the fire load density related to the floor area
q
fi,Ed
design value of a distributed load in the fire situation
q
r
heat flux by radiation
q
t,d
design value of the fire load density related to the total area of enclosure
r
horizontal distance from the fire plume, distance between an emitting an a receiving surface, root fillet
t
time, thickness of the walls in a hollow section, plate thickness in general
t
*
expanded time in the parametric fire model
t
f
flange thickness
t
fi,d
design value of the fire resistance
t
fi,req
required fire resistance time
t
lim
limit time in the parametric fire model
t
max
duration of the heating phase in the parametric fire model
t
v
length of the horizontal plateau in a heating curve
t
w
thickness of the web
w
width of a radiating surface
w
t
sum of the window widths
x
cartesian coordinate
y
parameter in a localised fire model, cartesian coordinate
z
vertical elevation in a fire plume
z'
vertical position of the virtual heat source
z
g
level of the application of the load
z
i
distance from the plastic neutral axis to the centroid of an elemental area
z
0
vertical position of the virtual origin of the fire source
Latin upper case letters
A
area of a wall, cross section area of a steel member, surface area of a member exposed to the heat flux
A
c
gross cross sectional area of a plate
A
c,eff
effective area of the compression zone of a plate
A
d
indirect fire actions
A
m
surface area of a member exposed to the heat flux
A
m
/V
section factor of unprotected sections
A
p
/V
section factor of protected sections
[
A
m
/V
]
b
box value of the section factor
A
f
floor area
A
fire
area of a fire source
A
p
appropriate area of fire protection material per unit length of a member
A
t
total area of an enclosure, including the openings
A
v
area of a vertical opening, shear area
C
matrix of capacity, compression force
C'
compression force
D
the diameter of a fire, depth of a beam
D/W
ratio for the external members
E
Young’s modulus of steel
E
a,θ
Young’s modulus of steel at temperature
θ
E
d
effects of actions in the normal situation
E
fi,d
design effect of actions for the fire situation
E
fi,d,t
design effect of actions for the fire situation at time
t
EI
z
flexural stiffness of a section
EI
w
warping stiffness of a section
F
thermal load vector
F
b,Rd
design bearing resistance of bolts at normal temperature
F
b,t,Rd
design bearing resistance of bolts in the fire situation
F
t,Rd
design tension resistance of bolts at normal temperature
F
ten,t,Rd
design tension resistance of bolts in the fire situation
F
v,Rd
design shear resistance of a bolt per shear plane in the normal situation
F
v,t,Rd
fire design resistance of a bolt loaded in shear
F
w,Rd
design weld resistance per unit length at normal temperature
F
w,t,Rd
design weld resistance per unit length in the fire situation
G
shear modulus
G
k
characteristic value of a permanent action
GI
t
torsional stiffness of a section
H
altitude above mean sea level, vertical distance from the fire source to the ceiling
I
second moment of area
I
f
radiative heat flux from an opening
I
t
torsion constant
I
w
warping constant
I
z
second moment of area about the minor axis, radiative heat flux from a flame
K
matrix of conductivity
L
column length, unrestrained length of the beam
L
f
vertical length of a flame
L
h
horizontal flame length
L
L
vertical extension of a flame above the top of the window
L
X
distance from the window
M
bending moment
M
b,fi,t,Rd
design lateral-torsional buckling resistance moment at time
t
M
cr
elastic critical moment for lateral-torsional buckling
M
el
elastic moment
M
Ed
design value of a bending moment in the normal situation
M
fi,Ed
design value of a bending moment in the fire situation
M
fi,t,Rd
design value of bending moment resistance in the fire situation
M
fi,θ,Rd
design moment resistance of a cross section with a uniform temperature
θ
a
M
N,fi,Rd
design plastic moment resistance reduced due to the axial force
M
pl
plastic moment
M
Q
maximum moment due to lateral load only
M
Rd
design resistance for bending for normal temperature design
M
y,V,fi,Rd
design plastic resistance moment in fire situation, allowing for the shear force effect
N
axial force
N
b,fi,Ed
design value of the compression force in fire situation
N
b,fi,t,Rd
design buckling resistance at time t of a compression member
N
b,fi,θ,Rd
design resistance of a compression member, with a uniform steel temperature
θ
a
N
fi,Ed
design value of axial force in the fire situation
N
fi,t,Rd
design value of axial resistance force in the fire situation
N
fi,θ,Rd
design resistance of a tension member with a uniform temperature
θ
a
N
Rd
design resistance of the cross section for normal temperature
O
opening factor of an opening
P
perimeter of a section exposed to the fire, prestressing load
Q
rate of heat release of a fire
internal heat source
Q
c
convective part of the rate of heat release
non-dimensional rate of heat release, related to
D
non-dimensional rate of heat release, related to
H
Q
k
characteristic value of a variable action
Q
k,
1
characteristic value of the leading variable action
R
fire resistance criterion for load bearing capacity
R
fi,d,t
design value of the resistance in the fire situation at time
t
RHR
f
maximum rate of heat release per square meter
T
tension force
T
f
temperature in the fire compartment
T
W
flame temperature at the window
T
Z
temperature of the flame along the axis, flame temperature
V
volume of the member per unit length
V
fi,Ed
design value of a shear force in fire situation
V
fi,t,Rd
design shear resistance at time
t
V
pl,Rd
design plastic shear resistance of a gross cross section for normal temperature design
V
Rd
design shear resistance of a gross cross section for normal temperature design
W
el,y
elastic section modulus
W
pl,y
plastic section modulus
W
2
size of the fire compartment perpendicular to wall 1
X
d,fi
design values of mechanical material properties in fire situation
X
k
characteristic value of a strength or deformation property
Greek lower case letters
α
parameter for time integration, convective heat transfer coefficient, imperfection factor for buckling curves or for lateral torsional buckling
α
c
coefficient of convection
α
cr
combined convection and radiation coefficient
α
f
absorptivity of a flame
α
r
coefficient of heat transfer by radiation
β
M,y
equivalent uniform moment factor about the y-y axis
β
M,z
equivalent uniform moment factor about the z-z axis
β
M,LT
equivalent uniform moment factor for lateral torsional buckling
γ
G
partial safety factor for the permanent action
γ
M,fi
partial safety factor for the relevant material property, for the fire situation
γ
M
0
partial safety factor for the resistance of cross sections
γ
Q,
1
partial safety factor for the leading variable action
ε
emissivity, parameter for section classification
ε
f
emissivity of a fire, emissivity of a flame
ε
m
surface emissivity of a member
ε
p,θ
strain at the proportional limit at elevated temperature
ε
y,θ
yield strain at elevated temperature
ε
t,θ
limiting strain for yield strength at elevated temperature
ε
u,θ
ultimate strain at elevated temperature
η
fi
reduction factor for the loads in the fire situation
θ
temperature
θ
a
,
com
maximum temperature in the compression flange
θ
a
,
cr
critical temperature of steel
θ
a
,max
maximum steel temperature in a section
θ
cr,d
design value of the critical temperature
θ
d
design value of steel temperature
θ
g
gas temperature
θ
h
temperature at height
h
of the steel beam
θ
m
surface temperature of a steel member
θ
max
gas temperature at the end of the heating phase
θ
r
radiation temperature of the fire environment
θ
(
z
)
temperature in a fire plume
θ
web
average temperature of a web
θ
0
bottom flange temperature of a steel beam remote from the connection
θ
∞
surrounding ambient temperature
k
1
adaptation factor for non-uniform temperature across the cross section
k
2
adaptation factor for non-uniform temperature along the beam
λ
thermal conductivity, member slenderness
λ
f
effective thermal conductivity of a fire protection material
λ
1
eulerian slenderness
λ
a
thermal conductivity of steel
λ
p
thermal conductivity of protection material
non-dimensional slenderness at room temperature
non-dimensional slenderness for lateral torsional buckling
normalised plate slenderness
non-dimensional slenderness for the temperature
θ
a
µ
0
degree of utilization
ν
Poisson’s ratio
ρ
specific density, reduction factor for plate buckling
ρ
a
specific density of steel
σ
Stephan Boltzmann constant, equal to 5.67
×
10
-8
W/m
2
K
4
σ
c
compression stress
σ
cr
elastic critical buckling stress
σ
t
tension stress
τ
F
free burning duration time
χ
fi
reduction factor for flexural buckling in the fire design situation
χ
LT,fi
reduction factor for lateral-torsional buckling in the fire design situation
ψ
ratio between tension and compression stress, ratio between bending moments at both ends of a member
ψ
1
coefficient for the frequent value of an action
ψ
2
coefficient for the quasi-permanent value of an action
ψ
fi
coefficient for the variable loads in the fire situation, equal to
ψ
1
or ψ
2
Greek upper case letters
Γ
expansion coefficient in the parametric fire model
D
prefix for increment
φ
amount of heat stored in the protection
φ
f
overall configuration factor of a member from an opening
φ
pl
rotation needed to form a fully plastic stress distribution
Φ
geometrical configuration factor
Chapter 1INTRODUCTION
1.1. RELATIONS BETWEEN DIFFERENT EUROCODES
The structural Eurocodes are a set of reference documents recognised by the Member States of the European Community and of the European Free Trade Association as a suitable means for demonstrating the compliance of building structures with the essential requirements listed in the Council Directive 89/106/CEE on construction products, in particular essential requirement No. 1, mechanical resistance and stability, and essential requirement No. 2, safety in case of fire.
EN 1990 forms the basic document of all Eurocodes because it gives the basis of design, i.e., the principles and the requirements for safety, serviceability and durability of structures. It is thus the first document to read when the fire resistance of a structure has to be evaluated.
The Eurocode philosophy is based on the concept of limit states, either ultimate limit states or serviceability limit states. The occurrence of limit states is verified according to a semi-probabilistic approach. This means that deterministic verifications are being carried out on the base of design values of applied loads and material strength. The design values are obtained from characteristic values, corresponding to 5% or 95% probability of occurrence, multiplied or divided by partial safety factors. The partial safety factors have been calibrated by the code writers to ensure that the probability of occurrence of the limit states is lower than a defined accepted probability, but the real probability of occurrence in a particular design is not known to the designer.
The fire resistance of a structure can be assessed using the Eurocodes provided the structure has been designed according to the rules given in the Eurocodes for the ambient temperature situation. The design at room temperature is based on EN 1991, where the actions on structures are defined independently of the material of the structure. The mechanical behaviour of steel structures in buildings at room temperature is assessed on the basis of EN 1993-1-1.
In the fire situation, the combinations of actions are different from those at room temperature. EN 1991-1-2 gives the combinations for mechanical actions that have to be applied to the structure in the fire situation, as well as the fire actions, i.e., the thermal environment created by the fire. This Eurocode is independent of the material of the structure. Characteristic values of the loads are required to determine the mechanical load combinations applied to the structure; the characteristic values are given in EN 1991-1-1, 1991-1-3 and 1991-1-4.
For steel structures, EN 1993-1-2 gives the rules for calculating the temperature development in the structure together with the rules for calculating the mechanical behaviour of the structure at elevated temperatures.
