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NIST Technical Note 1842

Structural Design for Fire: A 

Survey of Building Codes and 

Standards

Dat Duthinh

http://dx.doi.org/10.6028/NIST.TN.1842
This publication is available free of charge from http://dx.doi.org/10.6028/NIST.TN.1842

NIST Technical Note 1842 

Structural Design for Fire: A 

Survey of Building Codes and

Standards 

Dat Duthinh

Materials and Structural Systems Division

Engineering Laboratory

This publication is available free of charge from:

http://dx.doi.org/10.6028/NIST.TN.1842

September 2014

U.S. Department of Commerce 

Penny Pritzker, Secretary

National Institute of Standards and Technology 

Willie May, Acting Under Secretary of Commerce for Standards and Technology and Acting Director 
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Certain commercial entities, equipment, or materials may be identified in this

document in order to describe an experimental procedure or concept adequately.

Such identification is not intended to imply recommendation or endorsement by the

National Institute of Standards and Technology, nor is it intended to imply that the

entities, materials, or equipment are necessarily the best available for the purpose. 

National Institute of Standards and Technology Technical Note 1842

Natl. Inst. Stand. Technol. Tech. Note 1842, 120 pages (September 2014) 

CODEN: NTNOEF

This publication is available free of charge from: 

http://dx.doi.org/10.6028/NIST.TN.1842
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iii

Abstract

This document is a critical assessment of building codes and standards pertaining to structural 

design for fire from the United States, Canada, European Union members, Japan, New Zealand 

and Australia. These countries were selected because of their vigorous research activities on 

this topic, and the relevance of their engineering practice to that in the US. In the US, there is a 

dynamic interplay between various consensus-based code writing bodies (such as the 

International Building Code), and professional associations (such as the Society of Fire 

Protection Engineers, the National Fire Protection Association, the American Society for Testing 

and Materials, the American Society of Civil Engineers, the American Institute for Steel 

Construction, the American Concrete Institute International, and the Precast/prestressed 

Concrete Institute), which can produce authoritative and influential guidance documents. It has 

been necessary to study not just the codes and standards, but also the specifications and guides 

where applicable. The review presents both prescriptive and performance-based standards, but 

puts more emphasis on the latter, and topics that are the subject of current research or in need 

of updating. The structural materials covered are steel, concrete and composites of steel and 

concrete. The assessment identifies gaps in U.S. codes and standards for the design of 

structures for fire. 

Keywords: building codes; building standards; concrete; fire; steel; steel-concrete composite; 

structural engineering.
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iv

Disclaimer

The policy of the NIST is to use the International System of Units (SI) in its 

technical communications. In this document, however, building codes and

standards in the US are referenced in both customary (as is the practice in US 

construction industry) and SI units.
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v

CONTENTS

Abstract............................................................................................................................................................. iii

List of figures...................................................................................................................................................... x

List of tables....................................................................................................................................................... xi

CHAPTER 1 INTRODUCTION AND SCOPE.............................................................................................. 1

CHAPTER 2 STRUCTURAL DESIGN FOR FIRE: PRESCRIPTIVE AND PERFORMANCE STANDARDS..... 2

2.1 Prescriptive design........................................................................................................................... 2

2.1.1 USA: The International Building Code IBC 2012.......................................................................... 3

2.1.2 Eurocode......................................................................................................................................... 5

2.1.3 New Zealand Building Regulations 1992, reprinted 10 April 2012........................................... 6

2.1.4 Australian Building Codes Board, National Construction Code, 2012..................................... 8

2.1.5 2010 National Building Code of Canada (NBCC).......................................................................... 9

2.2 Performance-based structural fire design.................................................................................. 9

2.2.1 USA: Society for Fire Protection Engineering (SFPE)................................................................... 10

2.2.2 USA: International Code Council Performance Code for Buildings and Facilities, 2012...... 11

2.2.3 USA: American Institute of Steel Construction Steel (2011) AISC Construction Manual..... 11

2.2.4 Eurocode 1 (2010): Actions on Structures Part 1-2: General Actions - Actions on 

Structures Exposed to Fire........................................................................................................................... 12

2.2.5 New Zealand Building Regulations 1992, reprinted 10 April 2012........................................... 14

2.2.6 The Building Code of Australia, National Construction Code Series 2012............................... 15

2.2.7 2010 National Building Code of Canada (NBCC).......................................................................... 16

2.2.8 Canadian Standards Association CSA S16-09 Limit States Design of Steel Structures........... 16

2.2.9 The Building Standard Law of Japan........................................................................................... 17

2.3 Load combinations involving fire.................................................................................................. 17

2.3.1 AISC 2011 14th Ed. Appendix 4 Structural Design for Fire Conditions..................................... 17

2.3.2 Eurocode........................................................................................................................................... 18

2.3.3 Australia / New Zealand Standard AS/NZS 1170.0.2002........................................................... 18

2.3.4 2010 National Building Code of Canada (NBCC).......................................................................... 18

2.3.5 The Building Standard Law of Japan August 2011...................................................................... 19

2.4 Critical assessment.......................................................................................................................... 19

References...................................................................................................................................................... 19

CHAPTER 3 FIRE EXPOSURE.................................................................................................................... 22

3.1 Standard fires................................................................................................................................... 22

3.1.1 ASTM E119 (2012) Standard Test Methods for Fire Tests of Building Construction and 

Materials.......................................................................................................................................................... 22

3.1.2 ASTM E1529-13 Standard Test Methods for Determining Effects of Large Hydrocarbon 

Pool Fires on Structural Members and Assemblies.................................................................................... 23

3.1.3 Other standard time-temperature curves................................................................................... 24

3.1.4 Time equivalence............................................................................................................................ 25

3.2 EUROCODE parametric fire curves............................................................................................... 27

3.3 Design fires and fire scenarios...................................................................................................... 29

3.3.1 SFPE S.01 2011 SFPE Engineering standard on calculating fire exposures to structures..... 29

3.3.2 NFPA 5000 Building Construction and Safety Code Handbook (2003)................................... 30

3.3.3 NFPA 557 Standard Determination of Fire Loads for Use in Structural Fire Protection 

Design (2012).................................................................................................................................................. 31

3.3.4 AISC 2011 14th Ed. Appendix 4 Structural Design for Fire Conditions.................................... 32
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3.3.5 ISO/TS 16733 (2006) Fire Safety Engineering- Selection of design fire scenarios and 

design fires...................................................................................................................................................... 33

3.3.6 Eurocode........................................................................................................................................... 33

3.3.7 New Zealand Building Regulations 1992, reprinted 10 April 2012............................................ 34

3.3.8 AS 1530.4–2005 Methods for fire tests on building materials, components and structures.... 37

3.3.9 The Building Standard Law of Japan August 2011..................................................................... 37

3.4 Localized fire exposure................................................................................................................. 39

3.4.1 SFPE S.01 2011 Engineering standard on calculating fire exposures to structures.............. 39

3.4.2 Localized fires from Eurocode Annex C DIN EN 1991 1-2:2010-12......................................... 40

3.5 Critical assessment.......................................................................................................................... 41

References...................................................................................................................................................... 42

CHAPTER 4 STEEL STRUCTURES............................................................................................................ 45

4.1 Prescriptive methods...................................................................................................................... 45

4.1.1 USA: ASCE/SEI/SFPE 29-05 Standard Calculation Methods for Structural Fire Protection.. 45

4.1.2 USA: The International Building Code IBC 2012, Chapter 7: Fire and Smoke Protection 

Features.......................................................................................................................................................... 46

4.1.3 National Building Code of Canada (NBCC) 2010 vol. 2 Appendix D Fire-performance ratings 47

4.2 Performance-based methods....................................................................................................... 47

4.2.1 Methods for predicting temperatures in fire-exposed structures.......................................... 47

4.2.2 Eurocode 3: Design of steel structures- Par 1-2: General rules- structural fire design......... 49

4.2.3 USA: AISC 2011 14th Ed. Appendix 4 Structural Design for Fire Conditions.......................... 55

4.2.4 Canadian Standards Association CSA S16-09 Limit States Design of Steel Structures.......... 60

4.2.5 New Zealand and Australia........................................................................................................... 64

4.2.6 The Building Standard Law of Japan August 2011 – Steel........................................................ 65

4.3 Critical assessment.......................................................................................................................... 68

References...................................................................................................................................................... 71

Appendix: 2% yield strain and 0.2% proof strain...................................................................................... 73

CHAPTER 5 REINFORCED CONCRETE STRUCTURES.............................................................................. 74

5.1 Calculation methods for concrete in USA.................................................................................... 74

5.1.1 ASCE/SEI/SPFE 29-05 Standard Calculation Methods for Structural Fire Protection........... 74

5.1.2 ACI 216.1-07/ TMS 0216-07.......................................................................................................... 75

5.1.3 ACI 216R-89 Guide for Determining the Fire Endurance of Concrete Elements................... 78

5.1.4 USA: The International Building Code IBC 2012......................................................................... 81

5.1.5 The Society of Fire Protection Engineers....................................................................................... 81

5.1.6 Spalling prevention measures in USA.......................................................................................... 84

5.2 Calculation methods for concrete in Europe.............................................................................. 84

5.2.1 Simple one-dimensional thermal calculation for concrete (Wickstrom, 2008)................... 86

5.2.2 High-strength concrete ............................................................................................................... 86

5.2.3 Spalling.............................................................................................................................................. 87

5.3 Calculation methods for concrete used in New Zealand and Australia................................... 88

5.4 2010 National Building Code of Canada, Division B, Appendix D, Fire performance ratings... 88

5.5 The Building Standard Law of Japan, August 2011..................................................................... 89

5.6 Critical assessment.......................................................................................................................... 91

References...................................................................................................................................................... 91

CHAPTER 6 COMPOSITE STRUCTURES.................................................................................................... 93
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6.1 AISC 2011 14th ed. Appendix 4 Structural design for fire conditions - composite floor 

members......................................................................................................................................................... 93

6.2 ASCE /SEI/SFPE 29-05 Standard calculation methods for structural fire protection –

concrete-filled hollow steel tubes (Section 5.2.3)..................................................................................... 93

6.3 National Building Code of Canada 2010....................................................................................... 94

6.4 The Building Standard Law of Japan, Aug. 2011......................................................................... 95

6.5 EUROCODE 4: EN 1994-1-2, Aug. 2005 - Design of composite steel and concrete structures –

Part 1-2: general rules - structural fire design........................................................................................... 95

6.6 Composite members in New Zealand (NZS 3404) and Australia (AS 4100)............................ 97

6.7 Critical assessment.......................................................................................................................... 98

References...................................................................................................................................................... 98

CHAPTER 7 PRESTRESSED CONCRETE STRUCTURES............................................................................. 101

7.1 PCI 3rd ed. 2011: Design for fire resistance of precast/prestressed concrete...................... 101

7.2 International Building Code 2012.................................................................................................. 102

7.3 ASCE/SEI/SFPE 29-05....................................................................................................................... 102

7.4 EUROCODE 2-1-2 Design of concrete structures........................................................................ 103

7.5 New Zealand and Australia............................................................................................................ 103

7.6 2010 National Building Code of Canada, Division B, Appendix D, Fire performance ratings.. 103

7.7 The Building Standard Law of Japan, August 2011..................................................................... 104

7.8 Critical assessment.......................................................................................................................... 104

References...................................................................................................................................................... 104

CHAPTER 8 RECOMMENDATIONS........................................................................................................... 106

8.1 Develop slab membrane tension provisions in US building codes for steel beam-concrete 

slab composites in fire............................................................................................................................. 106

8.2 Develop US code provisions for spalling of concrete, especially high-strength concrete... 106

8.3 Develop US performance code provisions for steel connections in fire.................................. 106

8.4 Improve steel stress-strain relationships at elevated temperatures in future US 

performance building code........................................................................................................................... 107

8.5 Update provisions for plate buckling strength at elevated temperatures, and asses need 

for revision of other design equations due to change in shape of steel stress-strain curve at 

elevated temperatures................................................................................................................................ 107

8.6 Investigate effects of temperature gradient on simple design equations of steel and 

composite structures..................................................................................................................................... 107

8.7 Expand scope of US code provisions for concrete-filled tube (CFT) columns......................... 108

8.8 In US performance-based codes, develop methodology for analyzing parts of structure 

most affected by fire..................................................................................................................................... 108

8.9 Continue development of design fires and fire models............................................................ 109

References...................................................................................................................................................... 110
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viii

List of Figures

Chapter 2 Structural design for fire: prescriptive and performance standards

Figure 2.1 Design procedure according to the Eurocode prescriptive codes........................................ 5

Figure 2.2 Hierarchical Relationship for Performance-Based Design (Buchanan 2001)...................... 9

Figure 2.3 Design procedure for the Eurocode performance-based codes.......................................... 14

Chapter 3 Fire Exposure 

Figure 3.1 ASTM E119 standard time-temperature curves....................................................................... 24

Figure 3.2 Standard time-temperature curve used in furnace fire tests, cooling curves, curves 

representing the temperatures in a typical occupancy test, and equivalent areas; adapted from 

Ingberg (1928)................................................................................................................................................ 25

Chapter 4 Steel Structures

Figure 4.1 Reduction factors for the stress-strain relationship of carbon steel at elevated 

temperatures................................................................................................................................................. 50

Figure 4.2 Comparison of compression and flexural strengths at 500 °C (932 °F) – 

Takagi and Deierlein (2007).......................................................................................................................... 57

Figure 4.3 Comparison of compression and flexural strengths at 500°C (932°F)................................ 62

Figure 4.4 Variation of mechanical properties of steel with temperature........................................... 64

Figure 4.5: Eurocode (CEN 2001) stress-strain curves of steel at elevated temperatures from 100°C 

to 900°C ............................................................................................................................................................. 73

Chapter 5 Reinforced Concrete Structures

Figure 5.1 Strength of various types of reinforcement and concrete at high temperatures 

(ACI 216.1-07)................................................................................................................................................. 76

Figure 5.2 Temperature distribution in a normal-weight concrete rectangular unit.......................... 77

Figure 5.3 Moment diagram for one half of a continuous three-span beam before and during fire 

exposure.......................................................................................................................................................... 79

Figure 5.4 Nomographs relating thrust parameter, strain parameter, and ratio of cross-sectional 

area to heated perimeter............................................................................................................................. 80

Figure 5.5 Redistributed applied bending moment diagram................................................................... 82

Figure 5.6 Coefficient kcθ for decrease of characteristic strength fck of normal weight concrete with 

siliceous (1) or calcareous (2) aggregates................................................................................................... 85

Figure 5.7 High-strength concrete strength reduction factor fc,θ / fck at high temperatures for 

Class 1 (C55/67 and C60/75), Class 2 (C70/85 and C80/95) and Class 3 (C90/105) concrete. 

Class (f ck,cylinder / f ck,cube), fck = characteristic strength.............................................................................. 86
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ix

List of Tables

Chapter 2 Structural Design for Fire: Prescriptive and Performance Standards

Table 2.1 Prescriptive design documents from various countries............................................................. 4

Table 2.2 Fire resistance rating requirements for building elements (hours)...................................... 4

Table 2.3 Fire resistance rating (hours) requirements for exterior walls based on fire separation 

distance........................................................................................................................................................... 4

Table 2.4 Acceptable Solutions, New Zealand Building Code................................................................. 6

Table 2.5 Building classes (National Construction Code of Australia, 2012)......................................... 8

Table 2.6 Building types (National Construction Code of Australia, 2012)............................................ 8

Table 2.7 Performance design documents from various countries ........................................................ 10

Table 2.8 Heat flux between buildings....................................................................................................... 16

Chapter 3 Fire Exposure 

Table 3.1 Conditions of acceptance for beams and floor and roof assemblies................................... 23

Table 3.2 Fire frequency............................................................................................................................... 31

Table 3.3 Fraction c of structurally significant fires in office/business occupancies........................... 32

Table 3.4 Fire load density............................................................................................................................ 32

Table 3.5 List of 10 fire design scenarios.................................................................................................... 34

Table 3.6 Pre-flashover design fire characteristics................................................................................... 35

Table 3.7 Design Fire Load Energy Density (FLED) for use in modeling fires in C/VM2...................... 36

Table 3.8 Fire load density ql per unit floor area: excerpt from Notification 1433.............................. 37

Table 3.9 Heat release rate qb: excerpt from Notification 1433............................................................ 38

Table 3.10 Local fire temperature rise coefficient: excerpt from Notification 1433........................... 39

Chapter 4 Steel Structures

Table 4.1 Stress-strain reduction factors in EC3........................................................................................ 50

Table 4.2 High-temperature tensile data for structural steel................................................................. 70

Chapter 5 Reinforced Concrete Structures

Table 5.1 Fire resistance of concrete walls, floors and roofs.................................................................. 74

Table 5.2 Minimum cover for non-prestressed reinforcement in concrete beams............................ 75

Table 5.3 Minimum concrete column dimension..................................................................................... 75

Table 5.4 Excerpt from IBC Table 722.2.3 for an FRR of 3 h.................................................................... 81

Table 5.5 Location of thermal thrust line................................................................................................... 83

Table 5.6 Minimum dimensions and cover thickness for RC members................................................ 89

Chapter 6 Composite Structures

Table 6.1 Values of constant a (ASCE)........................................................................................................ 94

Table 6.2 Values of constant a (NBCC)....................................................................................................... 94

Chapter 7 Prestressed Concrete Structures

Table 7.1 Restrained and unrestrained fire rating based on tests......................................................... 102

Table 7.2 Minimum cover thickness - inches (mm).................................................................................. 102

Table 7.3 Minimum cover for prestressed reinforcement in beams 40 in2(26 000 mm2) 

or greater in area........................................................................................................................................... 103

Table 7.4 Minimum thickness of concrete cover over steel tendons in prestressed concrete 

beams............................................................................................................................................................. 104
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1

Structural Design for Fire:

A Survey of Building Codes and Standards

Chapter 1 Introduction and Scope

This document is a critical assessment of building codes and standards pertaining to structural design for 

fire from the United States, Canada, European Union members, Japan, New Zealand and Australia. 

These countries were selected because of their vigorous research activities on this topic, and the 

relevance of their engineering practice to that in the US. In the US, there is a dynamic interplay between 

various consensus-based code writing bodies (such as the International Building Code), and professional 

associations (such as the Society of Fire Protection Engineers, the National Fire Protection Association, 

the American Society of Testing and Materials, the American Society of Civil Engineers, the American 

Institute for Steel Construction AISC, the American Concrete Institute International ACI, and the 

Precast/prestressed Concrete Institute), which can produce authoritative and influential guidance 

documents. It has been necessary to study not just the codes and standards, but also the specifications 

and guides where applicable. The review presents both prescriptive and performance-based standards, 

but puts more emphasis on the latter, and topics that are the subject of current research or in need of 

updating. The structural materials covered are steel, concrete and composites of steel and concrete. 

The assessment identifies gaps in U.S. codes and standards for the design of structures for fire. 

The document is organized in eight chapters. Chapter 1 introduces the scope of the survey. Chapter 2 

presents the concepts behind prescriptive and performance-based standards. Chapter 3 reviews 

methods used to model fires, including standard fires, as well as various fire scenarios and design fires. 

Chapters 4 to 7 review design and analysis methods for structures made of steel (Ch. 4), reinforced 

concrete (Ch. 5), steel-concrete composites (Ch. 6) and prestressed concrete (Ch. 7). Finally, Chapter 8 

offers recommendations for future work that addresses the identified gaps in US building codes and 

standards.
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2

Chapter 2 Structural Design for Fire: Prescriptive and 

Performance Standards

There is general agreement that the goals of structural design against fire are to limit risks to the 

individual and society, to directly exposed or neighboring property, and to the environment. To meet 

these goals, fire protection requirements use the prescriptive format, e.g., they specify the permissible 

materials for buildings, the thickness of insulation, or the minimum acceptable spacing between 

buildings. This is the traditional approach that continues to this day. In the early 1970s, performancebased approaches were developed, following an evolution in the understanding of fire and building 

performance in fire. Performance-based methods allow the designers to account for the unique features 

and uses of buildings and promote a better understanding of how buildings perform in fire. Compared to 

prescriptive methods, performance-based approaches have a greater potential to promote innovation 

and cost savings, but require more expertise.

2.1 Prescriptive Design

Traditionally, building codes have specified prescriptive methods to improve fire safety in buildings. 

These methods use:

• fixed values, such as maximum travel distance, minimum fire resistance ratings and minimum 

features of required systems, such as detection, alarm, suppression and ventilation;

• Safety factors, typically historically based, used to account for uncertainties inherent in the data, 

and to achieve the desired excess capacity;

• Exposure to a standard fire, such as ASTM E119 (2012) or ISO 834 (2002). The standards that 

focus on fire exposure (time-temperature curves) and fire scenarios, such as NFPA 5000, are 

discussed in Chapter 3.

Most prescriptive codes include an equivalency clause that allows the use of performance-based 

methods to satisfy the intent of the code. Table 2.1 lists various codes and standards that follow a 

prescriptive format and are studied in the present document.
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Table 2.1 Prescriptive design documents from various countries

Country Title Document type Year

USA The International Code Council International Building 

Code

Building code 2012

USA ASCE/SEI/SFPE 29-05 Standard Calculation Methods 

for Structural Fire Protection 1,3

Standard 2005

USA ACI 216.1-07/ TMS 0216-07 Code requirements for 

determining fire resistance of concrete and masonry 

assemblies1

Standard 2007

USA PCI 3rd ed. Design for fire resistance of precast

/prestressed concrete2

Standard 2011

Europe Eurocode1- 1-2: Actions on structures exposed to fire Building code 2010

New Zealand NZS 3404: Part 1:1997 (with Oct. 2007 amendments, 

currently applicable in 2013) Steel Structures

Standard3

Standard 1997, 2007

New Zealand NZS 3101: Part 1: 2006 (with Aug. 2008 amendments) 

Concrete Structures1

Standard 2006, 2008

New Zealand Building Regulations Building code 1992 2012

Australia AS 4100-1998 Steel Structures - Section 12 Fire3Standard 1998

Australia AS 3600 - 2009 Concrete structures1Standard 2009

Australia Building Code of Australia, Vol. 1, Part C, Fire 

Resistance

Building code 2012

Canada CSA A23.3-04 Design of Concrete Structures4Standard 2004

Canada CAN/CSA-S16-09 Limit States Design of Steel 

Structures3

Standard 2009

Canada National Building Code of Canada Building code 2010

Japan Building Standard Law Building code 2000, 2011

1 will be discussed further in Chapter 5

2 will be discussed further in Chapter 6

3 will be discussed further in Chapter 4

4

fire is not mentioned. This standard will not be discussed further.

2.1.1 USA: The International Building Code IBC 2012 

The International Building Code is a comprehensive building code that establishes minimum regulations 

for building systems using prescriptive and performance-based provisions. The first edition, issued by 

the International Code council (ICC) in 2000, was the culmination of efforts to unify three building codes 

that were in effect in various parts of the US, namely the codes issued by the Building Officials and Code 

Administrators International (BOCA), the International Conference of Building Officials (ICBO), and the 

Southern Building Code Congress International (SBCCI). The IBC follows a three –year updating 

schedule.

Fire resistance rating is determined in compliance with the test procedures set forth in ASTM E119 (see 

Chapter 3) or UL 263. If alternative methods are used, the fire exposure and acceptance criteria 
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4

specified in ASTM E119 or UL 263 should be used (Sections 703.2 and 703.3 of IBC 2012). The test 

specimen is deemed acceptable if it can sustain the applied load during the fire resistance test without 

passage of flame or gases hot enough to ignite cotton waste for a period ( tclass) equal to that for which 

classification is desired. For walls or partitions, and restrained or unrestrained beams and floor and roof 

assemblies, transmission of heat should not raise the temperature on the unexposed surface more than 

250°F (139°C) above its initial temperature. Chapter 6 of the IBC 2012, Types of Construction, specifies 

the fire resistance rating requirements (in hours) for various types of construction and occupancy (Table 

2.2, adapted from Table 601 of IBC 2012), and for exterior walls based on fire separation distance (Table 

2.3, adapted from Table 602 of IBC 2012). The fire separation distance is defined as the distance 

measured perpendicular to the building face and from it to 1) the closest interior lot line, 2) the 

centerline of a street, an alley, or a public way, or 3) an imaginary line between two buildings on the 

property.

Table 2.2 Fire resistance rating requirements for building elements (hours)

Building element Type I Type II Type III Type IV Type V

A B A B A B HT A B

Primary structural frame 3 2 1 0 1 0 HT 1 0

Bearing walls

Exterior 3 2 1 0 2 2 2 1 0

Interior 3 2 1 0 1 0 1/HT 1 0

Types I and II: construction made of non-combustible materials;

Type III: exterior walls of non-combustible materials, interior building elements of any material;

Type IV: exterior walls of non-combustible materials, interior building elements of solid or laminated 

wood;

Type V: construction material of any permitted type.

Occupancy A: Assembly (defined by IBC as gathering of people);

Occupancy B: Business (office, professional or service transactions, including storage of records);

HT: heavy timber.

Table 2.3 Fire resistance rating (hours) requirements 

for exterior walls based on fire separation distance

Fire separation 

distance X 

Type of 

construction

Occupancy

group H

Occupancy group 

F-1, M, S-1

Occupancy group A, B, 

E, F-2, R, S-2, U

X < 5 ft 

X < 1.5 m

All 3 2 1

5 ft ≤ X < 10 ft 

1.5 m ≤ X < 3.0 m

IA

Others

3

2

2

1

1

1

10 ft ≤ X < 30 ft 

3.0 m ≤ X < 9.1 m

IA, IB

IIB, VB

Others

2

1

1

1

0

1

1

0

1

X ≥ 30 ft 

X ≥ 9.1 m

All 0 0 0
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Occupancy F-1: Hazardous materials, explosives;

Occupancy F-2: Hazardous materials, combustible liquids or gases;

Occupancy M: Mercantile (shops);

Occupancy R: Residential (hotels, group homes);

Occupancy S-1: Moderate hazard storage (furniture);

Occupancy s-2: Low hazard storage (food, metals);

Occupancy U: Utility (barns).

The IBC references other standards, such as those of the American Society of Civil Engineers (ASCE), the 

American Concrete Institute International (ACI), The Masonry Society (TMS), the Precast/Prestressed 

Concrete Institute (PCI) and the American Institute of Steel Construction (AISC). Other prescriptive 

standards used in the US include ACI 216.1-07/ TMS 0216-07 Code requirements for determining fire 

resistance of concrete and masonry assemblies, and PCI 3rd ed. 2011 Design for fire resistance of 

precast/prestressed concrete. These prescriptive requirements will be covered in Chapters 5 and 7 

respectively. ASCE/SEI/SPFE 29-05 Standard Calculation Methods for Structural Fire Protection show 

how to calculate the equivalent fire resistance, in terms of hours, of concrete, timber, masonry and steel 

members, that would be achieved under the standard ASTM E119 fire test. The standard does not 

provide any guidance about the structural performance of members or structures under fire. 

2.1.2 Eurocode

Figure 2.1 Design procedure according to the Eurocode prescriptive codes

(EN 1991 1-2:2010-12, also in Phan et al. 2010 NIST TN 1681)

Prescriptive rules 

(thermal actions given by 

nominal fire)

Analysis of a 

member

Determination of 

mechanical actions and 

boundary conditions

Tabulated 

data

Simple 

calculation 

models

Advanced 

calculation 

models

Analysis of 

part of the 

structure

Determination of 

mechanical actions and 

boundary conditions

Simple 

calculation 

models (if 

available)

Advanced 

calculation 

models 

Analysis of 

entire 

structure

Selection of 

mechanical 

actions

Advanced 

calculation 

models 
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The Eurocode (EN 1991 1-2:2010-12) also includes prescriptive design recommendations, as shown in 

Fig. 2.1. The prescriptive approach uses nominal fires to generate thermal actions, and the rest of the 

analysis is similar to the performance-based approach. The standard temperature-time curve is 

described in Chapter 3. Figure 2.1 lays out clearly the different types of analysis expected in fire design, 

corresponding to the level of individual members, parts of the structure, and the entire structure. For 

each type of analysis, the loads, boundary conditions and analytical models available are listed. No 

equivalent framework exists in US codes (e.g., IBC 2012 or ASCE/SEI/SPFE 29-05), which tend to focus on 

individual members.

2.1.3 New Zealand Building Regulations 1992, reprinted 10 April 2012

There are seven Acceptable Solutions (AS), listed in Table 2.4, that are deemed to comply with the New 

Zealand Building Code. As stated at the beginning of this chapter, the New Zealand Building Code shares 

with all codes the same principles on structural design for fire, namely, to limit risks to the individual and 

society, to directly exposed or neighboring property, and to the environment. Following is some of the 

Commentary attached to the AS, which go into greater detail.

Table 2.4 Acceptable Solutions (AS), New Zealand Building Code

Applies to Risk 

group

Description

C/AS1 Single household units and 

small multi-unit dwellings

SH Houses, townhouses and small multi-unit dwellings.

C/AS2 Non-institutional buildings 

for sleeping

SM Permanent accommodation, e.g., apartments; transient 

accommodation, e.g., hotels, motels, hostels, 

backpackers; education accommodation.

C/AS3 Care or detention facilities SI Institutions, hospitals (excluding special facilities), 

residential care, resthomes, medical day treatment 

(using sedation), detention facilities (excluding prisons).

C/AS4 Public access and

educational facilities

CA Crowds, halls, recreation centers, public libraries (< 2.4 

m storage height), cinemas, shops, personal services, 

schools, restaurants and cafes, early childhood centers.

C/AS5 Business, commercial and

low-level storage buildings 

WB Offices, laboratories, workshops, manufacturing 

(excluding foamed plastics), factories, processing, cool 

stores (capable of < 3.0 m storage height) and other 

storage buildings capable of < 5.0 m storage height, 

light aircraft hangars.

C/AS6 High-level storage and 

other high-risk buildings

WS Warehouses (capable of ≥ 5.0 m storage height), cools 

stores (capable of ≥ 3.0 m storage height), trading and 

bulk retail (≥ 3.0 m storage height).

C/AS7 Vehicle storage and

parking buildings 

VP Vehicle parking – within a building or a separate

building.

General principles

External walls and roofs must be constructed to avoid vertical and horizontal fire spread.
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The necessary protection may be achieved by one or more of:

a) Separation distance between buildings;

b) Using building elements that have a fire resistance rating (FRR);

c) Restricting the use of combustible surface finishes;

d) Limiting the areas of external walls and roofs that are close to a title boundary and that do not have

an FRR;

e) Providing parapets, spandrels or aprons; and 

f) Protecting the building with an automatic fire sprinkler system.

Fire resistance ratings

To prevent fire spread or structural collapse, the Acceptable Solutions require building elements to have

FRRs. The level of FRR required depends on the risk group of the building. An FRR comprises three 

numbers, which give time values in minutes for structural adequacy, integrity and insulation:

a) Structural adequacy is usually provided by primary elements within a firecell. (A firecell is any space 

including a group of contiguous spaces on the same or different levels within a building, which is 

enclosed by any combination of fire separations, external walls, roofs, and floors.)

Primary elements include building elements which are part of the structure, and those providing support 

to other elements with an FRR within the same or adjacent firecells. Examples are: columns, beams, 

floors and walls (which may also be fire separations). 

b) Integrity is usually provided by secondary elements. Examples are fire separations, which are internal 

partitions and floors. Primary elements forming an integral part of a fire separation are also rated for 

integrity.

c) Insulation applies to fire separations and is required where the transmission of heat through the

element may endanger occupants on the other side or cause fire to spread to other firecells or adjacent 

buildings. For example, insulation is necessary for fire separation between sleeping spaces, or for 

protecting a safe path.

General requirements for FRRs

When applying FRRs to building elements such as walls and columns, it is necessary to consider the face 

of the element that will be exposed to fire. For example, if the required FRR is different on each side of 

the separation, the higher of the required ratings applies to both sides of the separation. In the case of 

floors, it is only required to rate the floor on the underside, as it is unusual for fires to burn through a 

floor and spread downwards. Columns, beams and other structural framing elements must either have 

the same FRR as the element they are attached to, or be designed so that, if they do collapse during a 

fire, this would not cause the collapse of the fire rated element.

Stability of building elements having an FRR

Vertical stability

For building elements required to have an FRR:

a) Primary elements in a vertical orientation (e.g., walls and columns) shall be rated for structural 

adequacy under the design dead and live loads and any additional loads caused by the fire.

b) Primary elements in a horizontal orientation (e.g., floors and beams) shall be supported by primary 

elements with at least an equivalent structural adequacy rating.

Horizontal stability

Building elements required to have an FRR shall:

a) Be cantilevered from a structural base having an equal or greater FRR;
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b) Be supported within the firecell by other building elements having an equal or greater FRR;

c) Be supported by primary elements outside the firecell.

Other prescriptive methods for structural fire design in New Zealand are found in NZS 3404: Part 1:1997 

(with Oct. 2007 amendments, currently applicable in 2013) Steel Structures (see Chapter 4 of this 

report), and NZS 3101: Part 1: 2006, (with amendments Aug. 2008) Concrete Structures Chapter 4: 

Design for fire resistance. The latter document states the same principle as the New Zealand Building 

Regulations, namely, that a member shall be designed to have an FRR that meets or exceeds the 

required fire resistance for the criteria of structural adequacy, integrity and insulation. The criteria for 

integrity shall be considered to be satisfied if the member meets the criteria for both insulation and 

structural adequacy for that period, if applicable. This topic will be discussed further in Chapter 5 of this 

report.

2.1.4 Australian Building Codes Board, National Construction Code, 2012 

Vol. 1, Specification C1.1, Fire Resistance Construction

The Fire Resistance Level (FRL) for various building elements is specified for various building classes 

(Table 2.5) and types (Table 2.6). The FRL is given in minutes for structural adequacy/ integrity/

insulation. For example, a fire-resisting lift or stair shaft for an industrial building three-story high (class 

8, type B) is required to have an FRL of 240/120/120.

Table2.5 Building classes (National Construction Code of Australia 2012)

1 Single houses or attached dwellings separated by a fire-resisting wall

2 Buildings with multiple separate dwellings

3 Hotels, schools, detention centers

4 Only dwelling in a building of Class 5, 6, 7, 8 or 9

5 Office buildings

6 Retail shops, professional service buildings

7 Car parks, wholesale shops or storage

8 Laboratories, industrial facilities

9 Buildings of a public nature

10 Non-habitable buildings

Table2.6 Building types (National Construction Code of Australia 2012)

Number of stories Building classes 2, 3, 9 Building classes 5, 6, 7, 8

4 or more A A

3 A B

2 B C

1 C C

Other Australian building standards that include prescription against fire include Australian Standards 

AS 4100-1998 Steel Structures - Section 12 Fire (see Chapter 4), and Australian Standards AS 3600 -

2009 Concrete structures (see Chapter 5).The latter is a prescriptive standard which specifies minimum 

dimensions and protection for a given fire rating. Standard calculation methods are used, but with 

material properties at ambient replaced by those at elevated temperatures. 
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2.1.5 2010 National Building Code of Canada (NBCC)

To meet the objectives of the National Building Code, designers may use prescriptive acceptable 

solutions. Fire resistance rating (FRR) are determined from tests or calculated on the basis of Appendix 

D of the NBCC (See Chapter 5). Supporting members shall have an FRR not less than that of the 

supported members. It is noteworthy that in Canadian Standards Association CSA A23.3-04 Design of 

Concrete Structures, fire is not mentioned, except compliance with applicable building code.

Discussion of the prescriptive methods in The Building Standard Law of Japan (BSL-J) 2011 Fire 

Resistance Verification Method is deferred to later chapters.

2.2 Performance-based structural fire design

In the codes and standards reviewed, there is general agreement that the performance goals of 

structural design against fire are to limit risks to the individual and society, to directly exposed or 

neighboring property, and to the environment. Satisfactory performance can be demonstrated by 

engineering analysis or qualification testing. To achieve these overall goals, many countries are currently 

developing performance-based standards that would allow designers flexibility in the use of new 

materials and technology, while possibly reducing cost. According to Buchanan (2001), performancebased design starts with the setting of general, high-level goals, and then gets more specific with the 

definition of functional objectives and performance requirements that guide the designers to meet 

these goals. At the design level, performance-based standards recommend acceptable solutions and 

approved calculation methods, but leave open the possibility of alternative designs, provided these can 

be proven to meet the performance goals (Fig. 2.2). Compliance with performance-based codes can be 

attained by using either prescriptive methods (sometimes called acceptable solutions or approved 

calculation methods), or performance-based design (PBD). Following is a review of various guides, 

codes and standards that follow a performance-based format (Table 2.7).

Figure 2.2 Hierarchical Relationship for Performance-Based Design 

(Buchanan 2001, Phan et al. 2010 NIST TN 1681)
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Table 2.7 Performance-based design documents from various countries

Country Title Document type Year

USA SFPE Engineering Guide to Performance-Based Fire 

Protection

Guide 2007

USA The International Code Council Performance Code for 

Buildings and Facilities

Building code 2012

USA AISC Specifications

Structural Design for Fire Conditions

Appendix to 

standards

2011

Europe Eurocode1- 1-2: Actions on structures exposed to fire

Eurocode2- 1-2: Design of concrete structures -

structural fire design1

Eurocode3- 1-2: Design of steel structures –

structural fire design3

Eurocode4- 1-2: Design of composite steel and 

concrete structures - structural fire design2

Building code

Building code

Building code

Building code

2002

2010

2005

2010

New Zealand Building Regulations Building code 1992, 2012

Australia Building Code of Australia, Vol. 1, Part C, Fire 

Resistance

Building code 2012

Canada National Building Code of Canada Building code 2010

Canada CAN/CSA-S16-09 Limit States Design of Steel 

Structures3

Standard 2009

Japan Building Standard Law Building code 2000, 2011

1 will be discussed further in Chapter 5

2 will be discussed further in Chapter 6

3 will be discussed further in Chapter 4

2.2.1 USA: Society for Fire Protection Engineering (SFPE)

Engineering Guide to Performance-based Fire Protection, 2nd edition, 2007

The SFPE Guide provides a general framework for performance-based design against fire. The first step 

is to define performance objectives, which are to mitigate the consequences of fire in buildings in terms 

of loss of life, financial cost on property, impact on operations and the environment, or maximum 

allowable conditions. These conditions include stability of structure, integrity of partitions, maximum 

temperature, extent of fire and smoke spread, and spread of combustion products.

The second step is to develop performance criteria, i.e., assign threshold values for temperature of 

materials and gases, toxic gas emission, thermal effects on structures, fire spread, fire barrier damage, 

structural integrity, damage to exposed properties and the environment, etc. These can be stated as 

either deterministic criteria, e.g., preventing flashover in the room of fire origin, or probabilistic criteria, 

e.g., reducing the probability of flashover below a threshold value.

The third step is to develop design fire scenarios, which are reviewed in Chapter 3. The fourth step is to 

develop trial designs for fire protection systems, construction features such as fire barriers, and 

operational procedures that meet the specified performance criteria for the design fire scenarios. The 
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fifth and final step is to evaluate the trial designs and select the final design based on effectiveness, 

reliability, availability and cost.

2.2.2 USA: The International Code Council Performance Code for Buildings and Facilities, 

2012

For fire impact management, the goal is to provide an acceptable level of fire safety performance in 

facilities in case of fire and to protect people during egress and rescue operations. 

The functional objectives are to: 

 Mitigate the spread of fire so that people not directly adjacent or involved in the ignition shall 

not suffer serious injury or death, and so that property losses are limited; 

 Protect adjacent buildings and facilities from fire and smoke; and 

 Allow firefighters to perform their function safely.

The performance requirements are (only fire spread and structural aspects are listed here):

 Design fire events shall realistically reflect the ignition, growth and spread potential of fires; For 

each design fire scenario considered, the analysis shall include the ignitability of the first item, 

the peak heat release rate of the first item ignited, the heat release rate and expected fire 

growth, and the overall fuel load, geometry and ventilation of the space and adjoining spaces;

 Design fires shall have appropriate factors of safety that reflect the uncertainties in their 

development and what level of damage is considered tolerable;

 Interior surface finishes shall resist the spread of fire and limit the generation of unacceptable 

levels of smoke, toxic gases and heat;

 Building materials shall limit fire growth and size to controllable levels;

 Facilities shall be arranged, constructed, and maintained so as to limit the impact of a fire on the 

structural integrity of the facility;

 Structural members and assemblies shall have a fire resistance appropriate to their function, the 

fire load, the predicted fire intensity and duration, the fire hazard, the height and use of the 

building, the proximity to other structures and any fire protection features;

 Exterior wall and roof assemblies shall restrict the spread of fire to and from adjacent buildings 

and from exterior fire sources; and shall resist the spread of fire by limiting their contribution to 

fire growth and development.

2.2.3 USA: American Institute of Steel Construction Steel (2011) “AISC Construction Manual,

Appendix 4: Structural Design for Fire Conditions,” 14th Ed. 

The AISC lists the following performance requirements: 

 The structure should maintain its load-bearing function under the design-basis fire.

 It should also satisfy displacement constraints to maintain fire barrier and compartmentalization 

requirements. 

 Satisfactory performance can be demonstrated by engineering analysis or qualification testing.

As part of general structural integrity requirements, the structural system should be able to sustain local 

damage due the design basis fire and maintain a stable continuous load path to the foundation. The 

structural frame should have adequate strength and deformation capacity to withstand the structural 
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actions caused by the design basis fire, within prescribed limits of deformation. Furthermore, the 

connections should be designed to allow the connected members to develop their full strength .

To satisfy the performance requirements, two methods of engineering analysis are possible:

a simple analysis that assumes the support and restraint conditions remain unchanged from normal 

temperatures is allowed for evaluating the performance of individual members during fire exposure. If 

member temperatures are below 200 ̊C (400 ̊F) material properties may be assumed unchanged from 

normal temperatures.

An advanced analysis of the effects of the design basis fire on the structure includes a thermal and a 

mechanical analysis. The mechanical analysis should account for the temperature dependence of 

material properties, the effects of thermal expansion, large deformations, and possible changes in 

boundary conditions and connection fixity. All relevant limit states, such as excessive deflections, 

connection fractures, overall and local buckling should be considered.

Satisfaction of performance requirements can also be met by qualification testing, which refers to 

prescriptive methods of determining fire resistance of components or assemblies through standard fire 

tests or approved equivalence calculation methods.

2.2.4 Eurocode 1 (2010): “Actions on Structures Part 1-2: General Actions - Actions on 

Structures Exposed to Fire”

According to the Eurocode, the goals of fire protection are to limit risks with respect to the individual 

and society, neighboring property, and the environment or directly exposed property, in the case of fire. 

Functional objectives for structures in the event of fire address:

• Load bearing resistance of the construction can be demonstrated for a specified period of time;

• Generation and spread of fire and smoke within the works are limited;

• Spread of fire to neighboring construction works is limited;

• Occupants can leave the building or can be rescued by other means; and

• Safety of rescue teams is taken into consideration.

Structural members and partitions must comply with the following performance criteria for a specified 

period of time under exposure to the design basis fire:

• Stability or mechanical resistance (criterion R): the structure should be able to maintain its load 

bearing function and provide a stable load path to the foundation; 

• Integrity (criterion E): the fire should not create new openings in the structure, whose integrity 

limits the spread of fire and smoke within the burning building and to neighboring construction, 

and the provision of oxygen to the fire. This criterion sets limits on deformation and cracking to 

maintain fire barrier and compartmentalization requirements. The criteria of stability and 

integrity require that the structure maintains adequate strength and is able to sustain local 

damage within prescribed limits of deformation; and 

• Insulation (criterion I): limits that can differ between countries are placed on the average 

temperature rise and maximum temperature on unexposed surfaces. For example, at the time 
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of maximum gas temperature, on surfaces not exposed to fire, the average temperature rise 

should be less than Δθ1 = 140 K, and the maximum temperature rise at any point should be less 

than Δθ2 = 180 K. For parametric fires, during the decay phase, the recommended values are 

Δθ1 = 200 K and Δθ2 = 240 K, unless specified otherwise by national codes.

These performance criteria are designed to allow the occupants to escape or be rescued, and to ensure 

the safety of emergency responders. 

Three levels of analysis are possible: member analysis, analysis of part of the structure, or analysis of the 

entire structure. In member analysis, a structural member is considered isolated and unaffected by 

indirect fire actions, except those resulting from thermal gradients. Indirect actions are actions that 

result from constrained thermal expansion of the members themselves, differing thermal expansion 

within statically indeterminate members, thermal gradients within cross sections, or thermal expansion 

of adjacent members. While this type of analysis is directly comparable with furnace tests and can be 

used to calculate fire rating or insulation thickness, it cannot capture the response of a structural frame 

or the development of alternative load paths in the entire structure. At the next level, analysis of parts 

of the structure, indirect actions within the subassembly are considered, but time-dependent 

interactions with other parts of the structure are not. In other words, the boundary conditions of the 

subassembly are assumed unchanged from those at ambient temperature. At the highest level, global 

structural analysis, indirect actions are considered throughout the structure. Changes in boundary 

conditions and connection fixity, development of new load paths, such as by catenary or membrane 

action, etc., are accounted for. This type of analysis usually requires the capability to handle nonlinear 

geometric and material behavior. The flowchart in Fig. 2.3 describes the design procedure outlined in 

the Eurocode performance-based codes. 

A structural fire analysis starts with selection of the relevant design fire scenarios, from which a set of 

design fires is determined. Next, temperature evolution within the structural members is calculated 

using a nominal time-temperature curve (prescriptive approach) or a parametric fire model or fire 

simulation (performance-based approach). The Eurocode performance-based codes (Fig. 2.3) use 

physically-based thermal actions. The designer has the choice of selecting fire models suitable for the 

physical characteristics of the situation such as compartment dimensions, openings, ventilation, calorific 

size and dimensions of the fuel load, and fire protection measures. Fire models are described further in 

Chapter 3. Depending on the project requirements, the fire performance analysis can be performed at 

three different levels: 1) individual members, 2) parts of the structure, or 3) the entire structure. The 

analysis includes all mechanical actions and appropriate boundary conditions and uses advanced

calculation models, but member analyses may use alternative simple calculation models when available. 

Calculation of the mechanical behavior of the structure exposed to fire can be performed in the time 

domain (fire resistance ≥ required fire resistance time, generally given in national fire regulations), the 

strength domain (design value of member resistance at time t ≥ design value of relevant effects of 

actions at t) or the temperature domain (design value of material temperature ≤ design value of critical 

material temperature).
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Fig. 2.3 Design procedure for the Eurocode performance-based codes

(EN 1991 1-2:2010-12, also in Phan et al.2010 NIST TN 1681)

2.2.5 New Zealand Building Regulations 1992, reprinted 10 April 2012

The New Zealand Building Regulations follow a performance-based format. The objectives of the fire 

clauses (C1) are to:

1. Safeguard people from an unacceptable risk of injury or illness caused by fire;

2. Protect other property from damage caused by fire;

3. Facilitate firefighting and rescue operations.

Clause C3 deals with fire affecting areas beyond the fire source. The functional requirements are:

1. Low probability of injury or illness to people not in close proximity to fire;

2. Low probability of fire spread vertically or horizontally across relevant boundaries;

3. For buildings higher than 10 m where upper floors contain sleeping quarters or other property, 

design for low probability of external vertical fire spread to upper floors in the building.

In terms of performance, requirements for building materials are defined depending on how the 

occupants intend to use the relevant building area, and whether the building is protected by automatic 

sprinklers or not. Other performance standards include:

1. sleeping areas in buildings not protected by an automatic fire sprinkler system must be able to 

withstand a minimum critical radiant flux of 4.5 kW/m2 when exposed to ISO 9239-1:2010;

Performance-based codes 

(physically based thermal actions)

Selection of simple or 

advanced fire development models

Analysis of 

a member

Determination of 

mechanical actions and 

boundary conditions

Simple calculation 

models 

(if available)

Advanced 

calculation 

models

Analysis of 

part of the 

structure

Determination of 

mechanical actions and 

boundary conditions

Advanced 

calculation 

models 

Analysis of 

entire 

structure

Selection of 

mechanical 

actions

Advanced 

calculation 

models 
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2. buildings must be designed and constructed so that fire does not spread more than 3.5 m 

vertically from the fire source over the external cladding of multi-level buildings; 

3. buildings must be designed and constructed so that in the event of fire in the building, the 

received radiation at the relevant boundary of the property does not exceed 30 kW/m2, and at a 

distance of 1 m beyond the relevant boundary of the property does not exceed 16 kW/m2;

4. buildings must be constructed from materials that, when subjected to a radiant flux of 30 

kW/m2, do not ignite for 30 minutes for importance levels 3 and 4, and 15 minutes for 

importance levels 1 and 2. There are five building importance levels (defined in Clause A3): 

- level 1: low risk to human life, such as minor storage facilities;

- level 2: normal risk to human life (all buildings not listed in the other levels);

- level 3: higher level of risk to occupants, such as schools or buildings where more than 300 

congregate in one area;

- level 4: buildings essential to post-disaster recovery or associated with hazardous materials;

- level 5: buildings whose failure pose catastrophic risk to a large area (100 km

2

) or a large number 

of people (100 000).

5. buildings must be designed and constructed with regard to the likelihood and consequence of 

failure of any fire safety system intended to control fire spread.

The functional requirements for structural stability are (C6):

1. low probability of injury or illness to occupants;

2. low probability of injury or illness to emergency personnel;

3. low probability of direct or consequential damage to adjacent property.

Some of the performance standards for structural stability follow:

1. Structural systems must remain stable during and after fire to protect other property, taking 

into account: fire severity, automatic fire sprinkler system, any other active fire safety system, 

and the likelihood of failure of any fire safety system;

2. Structural systems must remain stable during and after fire to provide firefighters safe access to 

floors;

3. Collapse of structural elements with lesser fire resistance must not cause the collapse of 

elements that are required to have higher fire resistance.

The New Zealand Building Regulations do not offer any guidance about calculation methods, such as for 

individual structural members, parts of a structure, or the entire structure. 

2.2.6 The Building Code of Australia, National Construction Code Series 2012,

Vol. 1, Part C, Fire Resistance

The Building Code of Australia follows a performance-based format and is similar to New Zealand’s.

There are differences in some of the numbers, e.g., the Australian requirements equivalent to New 

Zealand’s performance requirements 3 and 4 read as follows:

CV1: To avoid the spread of fire between buildings in adjoining allotments, a building will not cause heat 

flux in excess of those shown in Table 2.8. Conversely, a building located at the distances listed in Table 

2.6 must be capable of withstanding the heat flux without ignition (note: no duration is given).
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Table 2.8 Heat flux between buildings

Location Heat flux

On boundary 80 kW/m2

1 m from boundary 40

3 m from boundary 20

6 m from boundary 10

2.2.7 2010 National Building Code of Canada (NBCC)

The National Building Code of Canada follows an objective-based format and applies at the time of 

construction and reconstruction while the National Fire Code applies to the operation and maintenance 

of the fire-related features of buildings in use.

The objective for fire (or structural) safety, according to the NBCC are to limit the probability that, as a 

result of the design or construction of the building, a person in or adjacent to the building will be 

exposed to an unacceptable risk of injury due to fire (or structural failure).

Functional statements: 

The objectives of this Code are achieved by measures, such as those described in the acceptable 

solutions, that are intended to allow the building or its elements to perform the following functions: 

- To limit the severity and effects of fire and explosions;

- To retard the effects of fire on areas beyond its point of origin;

- To retard failure or collapse due to the effects of fire;

- To support and withstand expected loads and forces;

- To limit or accommodate dimensional change;

- To limit movement under expected loads and forces;

- To limit the risk of injury to persons as a result of contact with hot surfaces or substances;

- To minimize the risk of release of hazardous substances;

- To limit the spread of hazardous substances beyond their point of release;

- To maintain appropriate air and surface temperatures;

2.2.8 Canadian Standards Association CSA S16-09 “Limit States Design of Steel Structures” 

Annex K: Structural design for fire conditions

The development (CISC Commentary 2010) of CSA S16-09 Annex K parallels that of AISC Appendix 4. In 

Canada until recently, the design of steel structures for fire conditions followed the standard design 

equations at normal temperature, but with material properties altered on account of elevated 

temperatures. Takagi and Deierlein (2009) showed that this approach was unconservative and their 

work was instrumental in bringing about Annex K as part of the 2009 edition of CSA S16. The new 

approach is similar to that in AISC and agrees well with Eurocode methods. The structural design 

equations for fire apply for steel temperatures greater than 200°C and are consistent in form with 

(albeit more complicated than) their counterparts for ambient temperature. This will be discussed 

further in Chapter 5.
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2.2.9 The Building Standard Law of Japan (BSL-J) 2011

The performance standard states that, when principal building parts are heated during a normal fire, 

the parts must not deform, melt, crack or undergo any other damage detrimental to structural strength. 

The performance requirements are: (1) Principal building parts must withstand the heat of a fire that 

could be expected to occur inside the building until the end of the fire; (2) External walls must withstand 

the heat of a normal fire occurring in the area surrounding the building until the end of the fire.

Since 2000 (Notification 1433 was issued in May 2000 and included in BSL-J 2004 and 2011), there are 

three alternative routes to design for structural safety against fire:

Route A (Specific Provisions) is prescriptive and consists in meeting or exceeding, for example, the 

minimum dimensions and cover thickness for reinforced concrete members and minimum insulation 

thickness for steel members. 

Routes B (Ordinary Verification Method) and C (Advanced Verification Method) are performance-based. 

Route B includes Verification Methods that are prescriptive, but deemed to satisfy the performance 

requirements. Route C is intended for new technology, requires approval of the cabinet minister in 

charge, and allows the use of advanced methods, but these are not provided by the building code.

Route B is now described. The technical criteria for fire-resistive performance are stated in BSL-J Article 

107 Technical criteria re. fire resistive performance (2011 Enforcement Order p. 83):

1. Stability: When exposed to a normal fire (ISO 834 or ASTM E119), structural members must not 

undergo damage detrimental to structural resistance for given periods, e.g., for beams and 

columns, 1 h for the 4 uppermost stories, 2 h for the next 10 stories down, and 3 h for the 15th 

(counting from the top)and lower stories. 

2. Insulation: For 1 h in a normal fire, the temperature of surfaces not directly exposed to fire must 

not reach the ignition temperature of combustibles (maximum 200°C, average 160°C on 

surface).

3. Integrity: When exposed to a normal fire for 1 h, exterior walls and roofs must not crack or 

undergo damage that could allow the fire to spread.

The “Fire Resistance Verification Method” operates in the time domain and can be used to prove 

compliance with these functional requirements. The main idea is to ensure that the critical time to 

failure tfr (S) under service load S exceeds the fire duration tf.

tfr (S) > tf

Details on how to satisfy this criterion will be described in later chapters.

2.3 Load combinations involving fire

The last part of this chapter deals with load combinations from various countries involving fire.

2.3.1 AISC 2011 14th Ed. Appendix 4 Structural Design for Fire Conditions

ASCE 7-10 Minimum Design Loads for Buildings and Other Structures 2010
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In the US, based on the work of Ellingwood and Corotis (1991), the load combination that applies to fires 

is the one for extraordinary events:

(0.9 or 1.2) D + Ak + 0.5 L + 0.2 S (2.5.1- ASCE 7-10)

where Ak = extraordinary event, which includes fire, D = dead load, L = live load, and S = snow load. The 

dead load is multiplied by 0.9 if it has a stabilizing effect, otherwise it is multiplied by 1.2 as in the other 

load combinations. The companion loads are multiplied by a factor less than 1 because of the small 

probability of joint occurrence of fire and the design live, snow or wind load. The wind term 0.2 W

present in previous editions has been replaced by a requirement to check for lateral stability. 0.5 L and 

0.2 S correspond approximately to the mean of the yearly maximum of live and snow loads.

2.3.2 Eurocode 

From Eurocode EN 1990 “Basis of structural design”, the load combination involving fire is: 

1.0 D + Fire + 1.0 IP + γ1 INP + γ2 W

where IP = imposed, permanent load, INP = Imposed, non-permanent load, and W = wind load.

γ1 = 1.0 for INP in escape stairs and lobbies, γ1 = 0.5 for INP in offices for general use, and γ1 = 0.8 for 

INP in all other areas. In particular snow load on roofs may be ignored. γ2 = 0 when designing for 

boundary conditions to control external fire spread, and γ2 = 0.33 in all other cases.

2.3.3 Australia / New Zealand Standard AS/NZS 1170.0.2002

From Australia / New Zealand Standard AS/NZS 1170.0.2002, the load combination for ultimate limit 

state for fire is:

G + thermal actions arising from the fire + ψlQ

where

G = permanent action (self-weight or “dead” action);

Q = imposed action (due to occupancy and use, “live” action);

ψl = factor for determining quasi-permanent values (long term) of actions;

ψl = 0.4 for floors of residences, offices, parking, retail, and ψl = 0.6 for storage and other uses.

2.3.4 2010 National Building Code of Canada (NBCC)

Tables 4.1.3.2A and B of division B list all load combinations, including dead, live, snow, wind, 

earthquakes, and cranes, but none of them involve fire. According to Appendix A, load combinations 

involving fire are relegated to Commentary A of the User’s Guide. Fire is treated as an accidental load 

and the following load combination applies:

D + TS + (αL or 0.25 S)
This publication is available free of charge from http://dx.doi.org/10.6028/NIST.TN.1842

19

α = 1.0 for storage areas, equipment areas and service rooms, and 0.5 for other occupancies (the basis 

for the factor of 0.5 is the work by Ellingwood and Corotis, 1991); D = dead load; L = live load; S = snow 

load; and Ts = short-term, variable effect caused by imposed deformations due to variations in 

temperature or moisture content or a combination thereof. Ts can be taken as zero for statically 

determinate structures.

2.3.5 The Building Standard Law of Japan August 2011:

From The Building Standard Law of Japan August 2011 p. 554 (2004), p. 115 (2011): when calculating 

resistance to fire, the full dead and live loads (plus snow load where relevant) are applied. 

1.0 D + Fire + 1.0 L

2.4 Critical assessment

All prescriptive building codes and standards surveyed specify fire rating depending on occupancy, type 

of structure and structural component, and based on criteria of stability, integrity (ignition of material 

separated from fire by barrier with required integrity, propagation of smoke) and insulation (maximum 

and average temperatures on surfaces not directly exposed to fire). Of the testing methods used to 

establish fire rating, ASTM E 119 puts particular emphasis on restrained versus unrestrained end 

conditions of beams and floor and roof assemblies. 

There is also general agreement on the objectives and a framework for performance-based structural 

design against fire. Eurocode is the most detailed in listing three methods of analysis available 

(individual structural member, part of the structure, or the entire structure) and the level of 

sophistication required for each method. AISC lists two methods of analysis, simple or advanced, 

depending on whether the effects of temperature on boundary conditions are accounted for or not. It is 

recommended that US performance-based codes develop methodology for analyzing parts of a 

structure most affected by fire.

For the foreseeable future, a dual approach, prescriptive and performance-based, will continue to be 

used. Compliance with performance-based codes can be attained by using prescriptive methods 

deemed as acceptable solutions. On the other hand, most prescriptive codes include an equivalency 

clause that allows the use of performance-based methods to satisfy the intent of the code.

References

American Concrete Institute (2007) “ACI 216.1-07/TMS 0216-07 Code requirements for Determining fire 

Resistance of Concrete and Masonry Assemblies,” Farmington Hills, MI

American Institute of Steel Construction Steel (2011) “AISC Construction Manual, Appendix 4: Structural 

Design for Fire Conditions,” 14th Ed. Chicago, IL, USA
This publication is available free of charge from http://dx.doi.org/10.6028/NIST.TN.1842

20

American Society of Civil Engineers (2007) “ASCE/SEI/SFPE 29-05 Standard Calculation Methods for 

Structural Fire Protection,” Reston, VA, USA

American Society of Civil Engineers (2010) “ASCE 7-10 Minimum Design Loads for Buildings and Other 

Structures,” Reston, VA, USA

ASTM E119 (2012) “Standard Test Methods for Fire Tests of Building Construction and Materials,” 

American Society for Testing and Materials, West Conshohocken, Pa

Australian Building Codes Board (2012) “Building Code of Australia,” National Construction Code Series 

Vol. 1, Part C, Fire Resistance, Canberra, ACT, Australia

Australia / New Zealand Standard AS/NZS 1170.0.2002 “Structural Design Actions: Part 0: General 

Principles,” (previously NZS 4203:1992, AS 1170.1-1989 and AS 2867-1986), Sydney, NSW, Australia and

Wellington, NZ

Buchanan, A.H. (2001) “Structural Design for Fire Safety,” John Wiley & Sons, Ltd., Chichester, UK

Building Center of Japan (2011) “The Building Standard Law of Japan,” Tokyo, Japan

Canadian Institute of Steel Construction (2010) “Commentary on CSA S16-09 Annex K: Structural design 

for Fire conditions,” CISC, Markham, Ontario, Canada

Canadian Standards Association (2004) “CAN/CSA-S16-01 Limit States Design of Steel Structures,”

Toronto, ON, Canada 

Canadian Standards Association (2004) “CSA A23.3-04 Design of Concrete Structures,” Toronto, ON, 

Canada 

Ellingwood B. and Corotis R.B. (1991) “Load combinations for buildings exposed to fires,” Engg. J. AISC 

28 (1) 37-44

Eurocode 1 (2010): “Actions on Structures Part 1-2: General Actions - Actions on Structures Exposed to 

Fire,” DIN EN 1991 1-2:2010-12, CEN, Brussels, Belgium

Eurocode EN 1990:2002 (2010) “Basis of structural design,” CEN, Brussels, Belgium

International Code Council (2012) “Performance Code for Buildings and Facilities” Country Club Hills, IL, 

USA

ISO 834-8:2002 “Fire resistance tests -- Elements of building construction,” International Organization 

for Standardization, Ch. de la Voie-Creuse, CP 56 CH-1211, Geneva 20, Switzerland 

National Research Council Canada (2010) “National Building Code of Canada 2010” (NBCC), Institute of 

Research in Construction, Ottawa, ON, Canada

New Zealand Building Regulations (1992, reprinted 2012), Wellington, NZ
This publication is available free of charge from http://dx.doi.org/10.6028/NIST.TN.1842

21

Phan, L.T., McAllister, T.P., Gross, J.L. and Hurley, M.J. (2010) “Best Practice Guidelines for Structural Fire 

Resistance Design of Concrete and Steel Buildings,” NIST TN 1681, National Institute of Standards and 

Technology, Gaithersburg, MD 201899

Prestressed Concrete Institute PCI (2011) “Design for fire resistance of precast/prestressed concrete,” 3

rd

ed. Chicago, IL, USA

Society for Fire Protection Engineering (2007) “SFPE Engineering Guide to Performance-based Fire 

Protection,” 2

nd ed., Bethesda, MD, USA

Standards Australia (1998) “AS 4100-1998 Steel Structures,” Sydney, NSW, Australia

Standards Australia (2009) “AS 3600-2009 Concrete structures,” Sydney, NSW, Australia 

Standards New Zealand (2007) “NZS 3404 Part 1: 1997 (with Oct. 2007 amendments, currently 

applicable in 2013) Steel Structures”, Wellington, NZ

Standards New Zealand (2008) “NZS 3101 Part 1: 2006 (with Aug. 2008 amendments, currently 

applicable in 2013) Concrete Structures”, Wellington, NZ

Takagi, J. and Deierlein, G.G. (2009) “Proposed design equations for CAN/CSA S16 Appendix K Provisions

for steel members at high temperatures,” Report prepared for the Canadian Institute of Steel 

Construction, Jan. 22
22

Chapter 3 Fire Exposure

The question of what fire to design or rate a building for is of fundamental importance. All building 

codes use standard fires and, in the case of performance-based design, more realistic, physically-based 

fires, which include compartment fires and localized fires (pre-flashover fires in large spaces, § 3.4).

3.1 Standard fires

Standard fire tests serve to compare the relative performance of building materials and small-scale 

assemblies, although they may not be representative of actual fires. Temperatures in most standard 

fires continue to rise over time whereas actual fires have growth, full development and decay phases. 

Furthermore, standard fire tests cannot approximate the full-scale complex structural performance of 

buildings, which includes the effects of thermal expansion, connection behavior, large deflections, 

possible loss of stability, and development of alternative load paths. In addition, furnace temperatures 

have uncertainties up to 100°C (ASCE Engineering Practice No. 114 (2009) Appendix A), and furnace 

tests often involve short-span specimens, which may require a difficult extrapolation to full-scale. 

3.1.1 ASTM E119 (2012) Standard Test Methods for Fire Tests of Building Construction and 

Materials 

The standard fire prescribed by ASTM E119 is used by various building and fire codes in the US and 

around the world to define the period of resistance before a building element being tested loses its 

structural integrity or its ability to contain the fire. A time-temperature curve (Fig. 3.1) is defined and 

used in a furnace to heat the element to be tested, which is also loaded to the appropriate load 

condition specified under nationally recognized structural design criteria. A close approximation of the 

ASTM E119 curve is provided by Lie (2002):

T = 750 (1 − e

−3.79553√th) + 170.41√th + 20

where T = temperature °C and th = time in hours. 

The test specimen is deemed acceptable if it can sustain the applied load during the fire resistance test 

without passage of flame or gases hot enough to ignite cotton waste for a period (tclass) equal to that 

for which classification is desired. For walls or partitions, and restrained or unrestrained beams and floor 

and roof assemblies, transmission of heat should not raise the temperature on the unexposed surface 

more than 250°F (139°C) above its initial temperature.

For loaded columns, the condition of acceptance is the ability to sustain load for the desired period. For 

unloaded, protected columns, the condition of acceptance is that the heat transmitted through the 

protection does not raise the average steel temperature at any one of four sections above 1000°F

(538°C) or does not raise the steel temperature above 1200°F (649°C) at any measured point. 
23

The conditions of acceptance take into account the stiffness of contiguous construction. If connections 

have sufficient rigidity to resist thermal expansion and rotation, fire resistance is improved. Thus, the 

conditions of acceptance are stricter for beams and floor and roof assemblies with unrestrained ends 

than with restrained ends (Table 3.1). The average temperature limit in Table 3.1 corresponds to the 

temperature at which half of the tensile strength of high strength alloy steel bars, or cold-drawn 

prestressing steel, and half of the yield strength of hot rolled steel have been lost (ACI 216.1-07).

Table 3.1 Conditions of acceptance for beams and floor and roof assemblies

Ends Type Spacing Max. temp. ≤ Average temp. ≤ Duration

Restrained steel > 4 ft > 1.2 m 1300°F 704°C 1100°F 593°C t ≥ tclass⁄2 and t ≥ 1 h

steel ≤ 4 ft ≤ 1.2 m 1300°F 704°C 1100°F 593°C t ≥ tclass⁄2 and t ≥ 1 h

PC* > 4 ft > 1.2 m 1300°F 704°C 800°F 427°C t ≥ tclass⁄2 and t ≥ 1 h

RC* > 4 ft > 1.2 m 1300°F 704°C 1100°F 593°C t ≥ tclass⁄2 and t ≥ 1 h

Unrestrained steel > 4 ft > 1.2 m 1300°F 704°C 1100°F 593°C t ≥ tclass

steel ≤ 4 ft ≤ 1.2 m 1300°F 704°C 1100°F 593°C t ≥ tclass

PC* 1300°F 704°C 800°F 427°C t ≥ tclass

RC* 1300°F 704°C 1100°F 593°C t ≥ tclass

*For prestressed (PC) and reinforced concrete (RC), temperatures are measured at tension steel.

For loaded, unrestrained beams supporting floors and roofs, the specimen should sustain the applied 

load during the rating period. The specimen is deemed as not sustaining the applied load when both the 

following conditions are exceeded: a maximum total deflection of Lc

2⁄(400d), and after the total 

deflection has been exceeded, a maximum deflection rate per minute determined over 1 min interval of 

Lc

2⁄(9000d), where Lc = clear span of the beam and d = beam depth from extreme fiber to extreme 

fiber.

3.1.2 ASTM E1529-13 Standard Test Methods for Determining Effects of Large Hydrocarbon 

Pool Fires on Structural Members and Assemblies

This standard applies to hydrocarbon processing industry facilities and other facilities potentially 

subjected to these types of fires. The specified fire exposure provides an average total cold wall heat 

flux on all exposed surfaces of 50 000 Btu/h/ft2(158 kW/m2) to be attained within 5 min of test 

exposure and maintained for the duration of the test. The temperature of the environment that 

generates this heat flux is at least 1500°F (815°C) after the first 3 min of the test, and between 1850°F

(1010°C) and 2150°F (1180°C) at all times after the first 5 min of the test (Fig. 3.1). This test gets hotter 

faster than ASTM E119, which is equivalent to a heat flux of 11 100 Btu/h/ft2(35 kW/m2) at 5 min and 

37 400 Btu/h/ft2(118 kW/m2) at 60 min. 
24

Figure 3.1 Standard time-temperature curves (Phan et al. 2010 NIST TN 1681)

3.1.3 Other standard time-temperature curves

2010 National Building Code of Canada (NBCC)

In Canada, fire resistance rating (FRR) is determined based on CAN/ULC-S101 “Fire endurance tests of 

building construction and materials.” The time-temperature curve is identical to ASTM 119 (Parkinson 

and Kodur, 2006). FRR can also be assigned on the basis of calculations shown in Appendix D of NBCC. 

Supporting members should have an FRR not less than that of the supported members. FRR will be 

addressed in more detail in Chapters 4, 5, 6 and 7.

Eurocode

In Europe, a number of other fire curves are used (Eurocode 1, Part 1-2, 2010). The following notation is 

used: θg= gas temperature °C, t = time (min).

ISO 834 Standard temperature-time curve (fig. 3.1), which is very close to ASTM E119:

θg = 345 log10 (8 t + 1) + 20

External fire curve:

θg = 660 (1 − 0.687 e

−0.32t − 0.313 e−3.8t

) + 20

Hydrocarbon fire curve:

θg = 1080(1 − 0.325 e

−0.167t − 0.675 e−2.5t

) + 20
25

Most standard fire temperature continues to rise with time, whereas the temperature in an actual fire 

decreases after reaching a maximum temperature. 

3.1.4 Time equivalence

Standardized fire tests are applied for the purpose of designing fire protection or selecting member size 

to ensure that the temperature in individual protected structural members and components does not 

exceed a limiting value over a given time. Time is the measure specified in building codes and depends 

on the building use, height and area. How to compare the severity of different fire tests or real fires has 

been the subject of much research.

Equal area

Figure 3.2 Standard time-temperature curve used in furnace tests, cooling curves, curves representing 

the temperatures in a typical occupancy test, and equivalent areas. Adapted from Ingberg (1928).

Ingberg (1928) developed the equal area method, whereby an approximate comparative measure of fire 

severity is obtained by assuming that the area under the average temperature-time curve from a burnout test, expressed in degree-hours, gives severity equivalent to an equal area under the standard curve 

and the cooling curve applicable for the given period. Only temperatures above a baseline are important 

for both the standard curve and the occupancy test curve. Ingberg recommended a baseline of 150°C, 

which is the ignition point for ordinary combustible materials, and 300°C for incombustible structural 
26

members. In Fig. 3.2, adapted from Ingberg’s (1928) paper, an occupancy fire test lasting 3 h 20 min is 

equivalent to a 3 h standard fire, the last hour of which is taken by the temperature decay curve.

Ingberg compared the area under the time-temperature curve of burn-out tests with standard fire tests, 

neglecting the area below 300°C, and developed the following time-equivalence:

te = k1L

"

where te = time equivalent (min), L” = fire load (wood) per unit floor area (kg/m2 or lbm/ft2), and k1 = 1 

min∙m2/kg or 5 min∙ft2/lbm. This formula assumes that the area under any time-temperature curve from 

ignition through decay provides a comparative measure of fire severity, which in turn is only a function 

of the fire load. Ingberg’s work became widely accepted as the basis for establishing fire endurance, but 

its limitations include neglect of the effects of ventilation, fuel type, fuel and compartment geometry, 

and boundary properties. The equal temperature method overcomes some of these limitations, but is 

much more complicated.

Equal temperature

Consider a structural element under a real post-flashover fire. If the same element is subjected to a 

standard fire such as ISO 834 and attains the same maximum temperature as in the real fire after a time 

te , then te is defined as the equivalent severity of the real fire. This equal temperature concept accounts 

for the effects of fuel load density, ventilation openings, compartment dimensions, and enclosure 

thermal properties, and is more realistic than the equal area concept. Eurocode 1, Part 1-2, Annex F

(2002) defines the fire exposure equivalent to a standard fire exposure, depending on 

• the design fire load density, 

• the ventilation factor, 

• a material correction factor, and 

• a conversion factor that depends on the thermal properties of the enclosure. 

The Eurocode defines the time-equivalent as follows: te = qf,d kb wf kc (min)

Each of the parameters is explained below:

qf,d = fire load density on floor area (MJ/m2) qf,d = qf,k m δq1 δq2 δn where

qf,k = fire load density dependent on occupancy (e.g., average for office space is 420 MJ/m2);

m = combustion factor (e.g., 0.8 for cellulosic materials);

δq1 = compartment size fire activation risk factor (e.g., 1.10 for 25 m2);

δq2 = occupancy type fire activation risk factor (e.g., 1.00 for offices, hotels, and residences);

δn = active firefighting factor (e.g., 0.61 for automatic water extinguishing system);

kb = boundary thermal properties factor, defaults to 0.07 min∙m2/MJ;

kc = material correction factor for structural sections (kc = 1 for protected steel or concrete, kc = 13.7 × O

for unprotected steel, O = opening factor defined below );

wf = ventilation factor, calculated as follows:

wf = (

6

H

)

0.3

[0.62 +

90(0.4 − αv

)

4

1 + bvαh

] ≥ 0.5

where
27

αv = Av /Af = ratio of the area of façade vertical openings to the compartment floor area 0.025 ≤ αv ≤ 0.25;

αh = Ah /Af = ratio of the area of roof horizontal openings to the compartment floor area;

bv = 12.5 (1 + 10 αv – αv

2

) ≥ 10;

H = compartment height.

For small fire compartments (defined in the Eurocode as Af ≤ 100 m2) without roof openings, wf may be 

calculated as:

wf =

Af

At√O

where

O = Av√h⁄At with 0.02 ≤ O ≤ 0.20 is the opening factor; and

At = total area of inside compartment surfaces, including window area.

The design is deemed to satisfy code if the design time-equivalent te,d is less than the design value of the 

standard fire resistance of the members tfi,d . Time equivalent methods only apply after flashover has 

occurred. They are essentially refined versions of simple element performance in fire, they cannot 

address frame performance or structure bearing capacity. Furthermore, the equivalent times are 

empirical and should not be used in situations beyond the specific compartment test data upon which 

the formulas are based (Lane 2008). 

3.2 Eurocode parametric fire curves

For performance-based design, Eurocode allows the use of simple fire models based on physical 

parameters. Eurocode parametric time-temperature curves have a heating phase and a cooling phase, 

are based on the equal temperature method, and deal with the temperature evolution in a more 

realistic fashion than a standard fire does. Eurocode 1, Part 1-2, Annex A describes the parametric 

temperature-time curves for post-flashover fires. In the heating phase:

θg = 20 + 1325 (1 − 0.324 e

−0.2t

∗

− 0.204 e

−1.7t

∗

− 0.472 e

−19t

∗

)

t

∗ = Γ t

where

θg = gas temperature; 

t

∗ = modified or scaled time;

t = time (h);

Γ = a function of compartment properties (size of openings, properties of boundaries, etc. Γ = 1 yields 

the ISO 834 standard fire, Γ < 1 for more slowly growing fires, and Γ > 1 for faster growing fires.

Γ = (

O⁄0.04

b⁄1160)

2

0.02 ≤ O =

Av

At

√heq = opening factor ≤ 0.20

100 ≤ b = √ρcλ ≤ 2200 value at ambient temperature may be used for b
28

Av = total area of vertical openings on all walls;

At = total area of enclosure (walls, ceiling and floor, including openings);

heq = weighted average of window heights on all walls;

ρ = density of boundary enclosure (;

c = specific heat of boundary enclosure;

λ = thermal conductivity of boundary enclosure.

The maximum temperature θmax in the heating phase occurs at 

tmax

∗ = Γ tmax

tmax = max [

0.0002 qt,d

O

; tlim]

50 ≤ qt,d = qf,d Af At ≤ 1000 MJ m2 ⁄ ⁄

where

qt,d = design value of fire load density related to total surface area At of the enclosure;

qf,d = design value of fire load density related to floor area Af;

tlim = time of maximum temperature for fuel controlled fires (= 15, 20, 25 min for fast, medium and 

slow fire growth respectively);

0.0002 qt,d

O

 is the time of maximum temperature for ventilation controlled fires.

In the cooling phase: 

θg = θmax − 625(t

∗ − x tmax∗

) for tmax

∗ ≤ 0.5

θg = θmax − 250(3 − tmax

∗

)(t

∗ − x tmax∗

) for 0.5 < tmax

∗ < 2

θg = θmax − 250(t

∗ − x tmax∗

) for tmax

∗ ≥ 2

where

tmax

∗ = Γ

0.0002 qt,d

O

x = 1.0 if tmax > tlim ; or x =

Γtlim

tmax

∗

if tmax = tlim

Eurocode 1, Part 1-2, Annex E specifies 

• fire load densities, which include factors for combustion, 

• activation risk, 

• firefighting measures, as well as

• characteristic fire load densities for various occupancies.
29

3.3 Design fires and fire scenarios

Unlike design fires for smoke control or egress time, design fires for structural assessment are mostly 

concerned with post-flashover fires. The reasons are that structures are affected by peak temperatures 

and fire duration beyond the incipient and growth phases of a fire. The following paragraphs emphasize 

compartment fires, but it is important to note that, for very large spaces with specific pockets of fuel, 

such as an airport terminal, flashover is unlikely to occur, and local fires affecting one or two columns in 

a long span structure may be more relevant.

3.3.1 SFPE S.01 2011 SFPE Engineering standard on calculating fire exposures to structures

The standard covers fully developed fires, arising from within an enclosure, or from a localized fire not 

affected by an enclosure. All required design fire scenarios have exposure greater than or equal to 

30 kW. The required enclosure fire scenarios are:

1. Most likely compartment, space or area that could be involved in a fire;

2. Compartment, space or area with the largest potential or anticipated mass of combustible 

material;

3. Compartment, space or area with the largest potential volume;

4. Compartment, space or area containing structural elements that may lead to structural failure 

upon exposure to design fire.

The required local fire scenarios, discussed at the end of the chapter, are:

5. Compartment, space or area with the largest potential concentrated fuel load;

6. An external fire that exposes the structure.

Potential for flashover

The potential for flashover is based on consideration of wall linings, compartment geometry, ventilation, 

and fuel quantity and orientation. For rectangular parallelepiped spaces that a) are not too large; b) 

have one or more vertical openings; c) have known thermal conductivity and thickness of compartment 

lining materials; d) have a width to depth ratio between 0.5 and 2.0; and e) have no mechanical 

ventilation or flow-through wind, the heat release rate required for flashover can be estimated by one 

of the following two methods:

Method of McCaffrey, Quintiere and Harkleroad (1981):

Q̇ = 610(hkAA0√H0)

1/2

hk = √kρc⁄t

Method of Thomas (1981):

Q̇ = 7.8A + 378A0√H0

where

Q̇ = heat release rate required for flashover (kW);

hk = effective heat transfer coefficient (kW/m2/K);

A = total surface area of compartment (m2);

A0 = total opening area (m2);

H0 = height of opening (m);

k = thermal conductivity of wall lining material (kW/m/K);

ρ = density of compartment surface material (kg/m3);
30

c = specific heat of compartment surface material (kJ/kg/K);

t = exposure time (s).

For all other cases, engineering analysis methods should be used, with the criterion that flashover 

occurs when the upper layer temperature exceeds 600°C or the heat flux to the floor exceeds 20 kW/m2.

Enclosure fires

SFPE S.01 2011 recommends two methods to calculate the post-flashover gas temperature evolution in 

a compartment.

Method 1: assumes a constant fire temperature of 1200°C after a growth time and until burnout, when 

the fuel is consumed, after which the temperature decays at a rate of 7 °C/min. The burnout time τb is 

given by:

τb =

EAf

90A0√H0

where Af = floor area (m2).

Method 2: Tanaka’s refined method (1996) calculates the ventilation controlled post-flashover transient 

fire temperatures for the room of origin.

T = βF,1(2.50 + βF,1)T∞ + T∞ , for βF,1 ≤ 1.00

T = βF,1(4.50 − βF,1)T∞ + T∞ , for βF,1 > 1.00

where

βF,1 = (

A0√H0

A

)

1

3

⁄

(

t

kρc)

1

6

⁄

T = temperature of enclosure (K);

T∞ = 300 K;

A = total surface area of compartment, excluding openings (m2).

The mass burning rate is (Kawagoe and Sekine, 1963): ṁ = 0.1 A0√H0

and the burnout time is: τb = M⁄ṁ , where

M = mass of available combustible material (kg);

ṁ = mass burning rate (kg/s).

3.3.2 NFPA 5000 Building Construction and Safety Code Handbook (2003) 

Ch. 5 Performance-based option

According to the NFPA 5000 Building Code, at a minimum, a fire scenario consists of the following:

1. Ignition factors (source, location and material);

2. At least one heat release rate curve;

3. Occupant locations;

4. Occupant characteristics;

5. Special factors (shielded, systems unreliable, open door).

NFPA 5000 recommends the following methods to select fire scenarios:

a. statistical analysis of fire experience of similar buildings, e.g., fast fire growth in room contents, 

to select common scenarios;
31

b. refine common scenarios, e.g., flammable liquids in means of egress, to select high challenge 

scenarios;

c. special problems, e.g., sprinklers or fire detector out of commission, to select special scenarios.

More specifically, NFPA recommends eight fire scenarios:

1. Occupancy-specific and representative of typical fire for that occupancy. This first scenario must 

explicitly specify the following: occupant activities; number and location of occupants; room 

size; furnishings and contents; fuel properties and ignition sources; ventilation conditions; first 

item ignited and its location. Example: a hospital room with two occupied beds, fire initially 

involving one bed and room door open.

2. Ultrafast developing fire in the primary means of egress, with interior doors open at the start of 

the fire. This scenario is intended to address reduction in the number of available means of 

egress. Example: fire in clothing rack in corridor.

3. Fire starts in a normally unoccupied room that can endanger a large number of occupants in 

other areas. Example: fire starts in a storage room adjacent to the largest occupiable room in 

the building.

4. Fire originates in a concealed wall space or ceiling space adjacent to a large, occupied room. 

5. A slow developing fire, shielded from fire protection systems, close to a high occupancy area. 

Example: cigarette in a trash can.

6. Most severe fire resulting from the largest possible fuel load characteristic of normal operation. 

7. Outside fire exposure.

8. Fire originates in ordinary combustibles in a room where each active or passive fire protection 

feature is rendered ineffective.

3.3.3 NFPA 557 Standard Determination of Fire Loads for Use in Structural Fire Protection 

Design (2012)

This document provides standard methods and values for fire loads in a risk framework.

The frequency of structurally significant fires fss is calculated as follows:

fss = c × ff × Af

where

c =fraction of fires that are structurally significant; ff = fire frequency (fires/m2/year);

Af =floor area (m2). The fire frequency ff is given for various occupancies:

Table 3.2 Fire frequency

Occupancy Fire frequency (fires/m2/year)

Office, business 6×10-6

Religious properties 6×10-6

Eating, drinking establishments 81×10-6

Other public assembly buildings 10×10-6

Educational buildings 10×10-6

Facilities that care for the sick 16×10-6

Stores, mercantile buildings 16×10-6

Places where people sleep other than homes 43×10-6
32

The fraction c depends on the occupancy, the type of construction and the fire protection.

Table 3.3 Fraction c of structurally significant fires in office/business occupancies

Type of 

construction

No detection

No alarm

No sprinklers

No detection

No alarm

Sprinklers present

Detection present

Alarm present

No sprinklers

Detection present

Alarm present

Sprinklers present

Fire resistive 0.13 0.04 0.07 0.03

...

Unprotected 

wood frame

0.37 0.12 0.20 0.07

The fire load density Qf is the sum of the fixed fire load density Qf,f and the contents fire load density 

Qf,c.

Qf = Qf,f + Qf,c

The mean and variance of the sum are the sum of the means and variances.

Qf

̅̅̅̅ = Qf,f̅̅̅̅̅ + Qf,c̅̅̅̅̅

σf

2 = σf,f2 + σf,c2

Table 3.4 Fire load density

Fire load density Occupancy or construction Mean Standard deviation

Contents Office, business 600 MJ/m2 500 MJ/m2

Fixed Non-combustible 130 MJ/m2 40 MJ/m2

If a more detailed fire load density needs to be calculated, the heat of combustion for products made 

entirely of wood or products with fire performance superior to that of non-fire retarded materials can 

be assumed to be 15 MJ/kg unless specific information is available.

The design fire load density Qfd is a function of the risk objective F.

Qfd = Qf

̅̅̅̅ −

√6

π

σf

[0.577 + ln (−lnF)]

F = 1 −

Rs

fss

where 

Rs =risk performance criterion for structural collapse (say 10-6/year).

3.3.4 AISC 2011 14th Ed. Appendix 4 Structural Design for Fire Conditions. 

Design-basis fires should take into account the fuel load characteristic of occupancy and the heat flux or 

temperatures for the duration of the fire. Alternatively, ASTM E119 may be used. The kinds of fire that 

need to be considered include localized fire, post-flashover compartment fires, and exterior fires. Active 

fire protection systems need to be accounted for.
33

3.3.5 ISO/TS 16733 (2006) “Fire Safety Engineering- Selection of design fire scenarios and 

design fires” 

ISO/TS 16733 (Hadjisophocleous and Mehaffey, 2008) recommends the following steps for identifying 

and selecting fire scenarios:

1. Location of fire;

2. Type of fire (smoldering, pre- or post-flashover);

3. Potential fire hazards (from intended use of facility);

4. Systems impacting on fire (fire safety systems);

5. Occupant response;

6. Event tree (alternative event sequences);

7. Consideration of probability;

8. Consideration of consequence;

9. Risk ranking;

10. Final selection and documentation.

The potential fire locations to be considered are:

1. Fires in rooms with large number of occupants or valuable property;

2. Fires that render parts of means of egress unusable;

3. Fires that commence within building assemblies and remain undetected while growing in 

intensity in concealed places;

4. Localized fires and/or post-flashover fires that could challenge the structure and 

compartmentalization in the building;

5. Fire locations that are challenging for proposed active measures (e.g., fires that are shielded 

from sprinkler sprays, fires at center of a space that generate large volume of smoke).

3.3.6 Eurocode

Eurocode 1, Part 1.2, Annex D, 2002 allows the use of advanced fire models for post-flashover 

conditions, for example, one-zone models, where homogeneous conditions prevail through the 

compartment; two-zone models, where combustion products accumulate in a layer beneath the ceiling, 

with a horizontal interface; and computational fluid dynamics models.

The many factors that affect fire development include:

• Form of ignition source;

• Type of fuel first ignited;

• Secondary fuel ignited and fire spread;

• Location of fire;

• Compartment geometry;

• Time of doors and windows closing or opening;

• Ventilation;

• Type of construction and interior finish materials;

• Form of intervention (fire suppression systems, fire department, etc.).
34

Part of the characterization of the design fire scenario is the establishment of a design fire curve, which 

typically encompasses ignition, growth (pre-flashover), flashover (fully developed phase), and postflashover (decay and burnout phases). 

Factors that affect whether flashover occurs or not include:

• Surface area of enclosure A;

• Area of enclosure openings A0; 

• Effective height of openings H0; 

• Heat release rate of fuel;

• Ventilation;

• Thermal properties of compartment boundaries.

Trial designs are developed in order to propose fire protection systems, construction features and 

operations to meet performance criteria using design fire scenarios. Trial designs are evaluated and 

selected based on effectiveness, reliability, availability and cost.

3.3.7 New Zealand Building Regulations 1992, reprinted 10 April 2012

Table 3.5 List of 10 fire design scenarios

Design scenario Expected method

Keeping people safe

BE Fire blocks exit Solved by inspection

UT Fire in a normally unoccupied room 

threatening occupants of other rooms

ASET/RSET analysis or provide separating elements 

/suppression compliant with a recognized standard

CS Fire starts in a concealed space Provide separating elements/suppression or automatic 

detection compliant with a recognized standard

SF Smoldering fire Provide automatic detection and alarm system 

compliant with a recognized standard

IS Rapid fire spread involving surface 

linings

Suitable materials used (proven by testing)

CF Challenging fire1 ASET/RSET analysis

RC Robustness check2 Modified ASET/RSET analysis

Protecting other property

HS Horizontal fire spread Calculate radiation from unprotected areas as specified

VS Vertical fire spread Suitable materials used (proven by testing) and 

construction features specified (e.g., aprons/spandrels 

/sprinklers) as required to limit vertical fire spread.

Firefighting operations

FO Firefighting operations Demonstrate firefighter safety

1The challenging fires are intended to represent credible worst case scenarios in normally occupied 

spaces that will challenge the fire protection features of the building.

2Robustness check: The fire design is checked to ensure that the failure of a critical part of the fire safety 

system will not result in the design not meeting the objectives of the Building Code, which include 

structural stability during and after fire.
35

A series of documents called Verification Methods or Acceptable Solutions are published to provide one 

way to show compliance with the New Zealand Building Regulations (1992). Other ways are explained in 

general terms in the main document. C/VM2 (Ministry of Business, Innovation and Employment, 2013) 

provides the framework for fire safety design and sets out ten design scenarios (Table 3.5) that must be 

considered and designed for, where appropriate, in order to achieve compliance with NZBC C: 

Protection from Fire (Dept. of Building and Housing Extract, 2012). A flowchart is provided to guide the 

designer through the process, taking into account the number of occupants, occupants’ characteristics, 

building use, availability of sprinklers, etc. C/VM2 uses the following acronyms:

FLED = fire load energy density MJ/m2;

ASET = available safe egress time;

RSET = required safe egress time.

Design fire characteristics

Analysis for a number of the design scenarios is based on the use of ‘design fires’. These are defined by 

one or more of the following parameters:

a) Fire growth rate

b) Peak heat release rate (HRR)

c) Fire load energy density (FLED)

d) Species production (CO, CO2, water, soot)

e) Heat flux, and

f) Time.

Verification Method C/VM2 also provides parameters and modeling instructions for the various phases 

of design fires.

Pre-flashover design fires

In most cases (i.e., for all buildings, including storage buildings, that are capable of storage to a height of 

less than 3.0 m) the pre-flashover design fire is assumed to grow as a fast t

2

fire (fire growth rate (W) = 

46.9 t

2 with t in seconds), up to flashover or until the HRR reaches the peak (20 MW) or becomes 

ventilation limited. See Table 3.6 for other buildings.

Table 3.6 Pre-flashover design fire characteristics

Building use Fire growth 

rate (W)

Species Radiative 

fraction

Peak 

HRR

All buildings including storage with a 

stack height of less than 3.0 m

46.9 t

2

Ysoot = 0.07 kg/kg

YCO = 0.04 kg/kg

ΔHC = 20 MJ/kg

YCO2 = 1.5 kg/kg

YH2O = 1.0 kg/kg

0.35

20 MW

Carparks (no stacking) 11.7 t

2

Storage with a stack height between 

3.0 m and 5.0 m above the floor

188 t

2

Storage with a stack height of more 50 MW

than 5.0 m above the floor and car 

parks with stacking systems

0.68 t

3H

NOTE: t = time in seconds; H = height of storage in m; Y = yield kg/kg; ΔHC = heat of combustion

Post-flashover design fires

Flashover is assumed to occur when the average upper layer temperature first reaches 500°C. For 

uncontrolled fires, the burning rate is assumed to be governed by the ventilation limit or the peak HRR, 
36

whichever is less. Post-flashover fires are unlikely to be required in the modeling of sprinklered 

buildings.

Full burnout design fires

Table 3.7 Design Fire Load Energy Density (FLED) for use in modeling fires in C/VM2

Design 

FLED 

(MJ/m2)

Activities in the space or room Examples

400

1. Display or other large open spaces; or 

other spaces of low fire hazard where 

the occupants are awake but may be 

unfamiliar with the building.

1. Art galleries, auditoriums, bowling alleys, 

churches, clubs, community halls, court rooms, 

day care centres, gymnasiums, indoor 

swimming pools

2. Seating areas without upholstered 

furniture

2. School classrooms, lecture halls, museums, 

eating places without cooking facilities

3. All spaces where occupants sleep 3. Household units, motels, hotels, hospitals,

residential care institutions

4. Working spaces and where low fire 

hazard materials are stored

4. Wineries, meat processing plants, 

manufacturing plants

5. Support activities of low fire hazard 5. Car parks, locker rooms, toilets and 

amenities, service rooms

800

1. Spaces for business 1. Banks, personal or professional services, 

police stations (without detention)

2. Seating areas with upholstered 

furniture, or spaces of moderate fire 

hazard where the occupants are awake 

but may be unfamiliar with the building

2. Nightclubs, restaurants and eating places, 

early childhood centres, cinemas, theatres, 

libraries

3. Spaces for display of goods for sale 

(retail, non-bulk)

3. Exhibition halls, shops and other retail (non 

bulk)

1200

1. Spaces for working or storage with 

moderate fire hazard

1. Manufacturing and processing moderate fire 

load

2. Storage up to 3.0 m high other than foamed 

plastics

2. Workshops and support activities of 

moderate fire hazard

3. Maintenance workshops, plant and boiler 

rooms

400/tier 

of car 

storage

Spaces for multi-level car storage Car stacking systems. The design floor area 

over which the design FLED applies is the total 

actual car parking area

800/m

height,

with a

minimum

of 2400

1. Spaces for working or storage with 

high fire hazard

1. Chemical manufacturing and processing, 

feed mills, flour mills

2. Storage over 3.0 m high of combustible 

materials, including climate controlled storage

2. Spaces for display and sale of goods 

(bulk retail)

3. Bulk retail (over 3.0 m high)
37

The ‘full burnout design fire’ for structural design and for assessing the fire resistance of separating 

elements is based on complete burnout of the firecell with no intervention. For the full burnout design 

fire, all the fuel shown in Table 3.7 is allowed to burn. There are three choices for modeling the full

burnout design fire:

a) Use a time-equivalent formula to calculate the equivalent fire severity and specify building 

elements with a fire resistance rating not less than the calculated fire severity. If the calculated 

value is less, an equivalent fire severity of 20 minutes is used. The time equivalence formula is

taken from Annex E of Eurocode DD ENV 1991-2-2.

b) Use a parametric time versus gas temperature formula to calculate the thermal boundary 

conditions (time/temperature) for input to a structural response model, or

c) Construct an HRR versus time structural design fire. Then, taking into account the ventilation 

conditions, use a fire model or energy conservation equations to determine suitable thermal 

boundary conditions (time/temperature/flux) for input to a structural response model.

3.3.8 AS 1530.4 – 2005 Methods for fire tests on building materials, components and 

structures

Standard heating conditions are similar to those of Eurocode, where T is in °C, and t is in min.

T = 345 log10 (8 t + 1) + 20

3.3.9 The Building Standard Law of Japan August 2011

As mentioned in Chapter 2, the “fire resistance verification method” can be used to prove compliance 

with the functional requirements. The main idea is to ensure that the critical time to failure tfr (S)

under service load S exceeds the fire duration tf. 

tfr (S) > tf

In order to satisfy this inequality, the fire duration is first defined.

Table 3.8 Fire load density ql per unit floor area: excerpt from Notification 1433 

Category Fire load density MJ/m2

dwelling 720 

office 560

classroom 400

restaurant 480

theater 400

parking garage 240

storage 2000

Fire duration tf (min)

tf =

Qr

60 qb

where

Qr = fire load (MJ). See Table 3.8;

qb = heat release rate of combustible material in compartment (MW). See Table 3.9.
38

Table 3.9 Heat release rate qb: excerpt from Notification 1433 

Burn factor Heat release rate qb (MW)

x ≤ 0.081 1.6 x Afuel

0.081 < x ≤ 0.1 0.13 Afuel

x > 0.1 (2.5 x e

−11x + 0.048)Afuel

where

x = burn factor =

fop

Afuel

= max {∑(

Aop√Hop

Afuel

,

Ar√Hr

70Afuel)}

fop = effective ventilation factor (m5⁄2) = max {∑(Aop√Hop ,

Ar√Hr

70 )}

Aop = area of openings in walls, floor and ceiling (m2);

Hop = vertical distance from top edge to bottom edge of openings in walls, floor and ceiling (m);

Ar = floor area (m2);

Hr = average height of ceiling above floor (m);

Afuel = surface area of combustible = 0.26 ql

1⁄3

Ar +∑φAf

ql = fire load density (MJ m2 ⁄ )

Af = areas of interior surface finish of floor, walls and ceiling (m2);

φ = oxygen consumption coefficient.

The fire load Qr consists of the fuel load from the floor plus the finish parts of walls, floor and ceiling of 

the room in question and adjoining rooms. In this summation, the fire loads from adjoining rooms are 

multiplied by heat penetration coefficients that depend on openings.

Fire severity and duration

Mc Caffery’s parametric equation for post-flashover compartment fires is used. The fire temperature 

Tf(°C) is a power function of time t (min):

Tf = α t

1⁄6

α is the fire temperature rise coefficient (°C/min1/6) and balances heat released by combustibles and 

lost through boundaries and openings:

α = 1280 (

 

qb

√∑(Ac

Ih

)√fop)

 

2/3

where

Ac = surface area of walls, floor and ceiling of compartment (m2);

Ih = thermal inertia = √kρc unless listed otherwise (in table in Notification 1433 p. 98);

k = thermal conductivity (kW/m/K);

ρ = mass density (kg/m3);

c = specific heat (kJ/kg/K)
39

The standard fire temperature curve ISO 834 is approximated closely by α = 460 °C/min1/6(Kohno 

2006).

A local fire temperature rise coefficient αlis also provided to account for the height z of a structural 

member above the floor (Table 3.10). This assumes a localized fire that grows to 3 MW in 20 minutes 

(Harada et al. 2004).

Table 3.10 Local fire temperature rise coefficient: excerpt from Notification 1433 

z (m) αl

z ≤ 2 500

2 < z ≤ 7 500 – 100 (z – 2)

z > 7 0

3.4 Localized fire exposure

For very large spaces (with an open floor area greater than 465 m2 or 5000 ft2) with specific pockets of 

fuel, or rectangular rooms with aspect ratios greater than 5, flashover is unlikely to occur, and local 

fires affecting one or two columns in a long span structure may be more relevant. Examples include 

airport terminals, shopping malls, warehouses and factories. 

3.4.1 SFPE S.01 2011 Engineering standard on calculating fire exposures to structures

SFPE recommends checking two local fire scenarios:

1. Compartment, space or area with the largest potential concentrated fuel load.

2. An external fire that exposes the structure.

Localized fire exposure

The document provides guidance for the total incident heat flux and fire duration for surfaces that are 

immersed or in contact with the thermal plume or flame zone of a concentrated fuel load. The methods 

presented apply to fires greater than 30 kW and specific geometric configurations. The incident heat flux 

to structural members should not be less than 20 kW/m2, which is the threshold for ignition of common 

combustible materials in an enclosure. The design fire should be the most severe fire exposure in terms 

of incident heat flux and exposure duration for a given fuel package.

a) Unconfined fire and fire below ceiling: 

Maximum flame height: Fh = H − 1.02 Deff + 0.23(Q̇)

0.4

where

Fh = maximum flame height (m);

H = fuel package height (m);

Q̇ = heat release rate (kW);

Deff = effective fire diameter; πDeff

2 ⁄4 = L W

L = length of fuel package (m);

W = width of fuel package (m).

Three cases are of interest: 

1. Fh ≥ HT (height of exposed object):

The exposure heat flux is 120 kW/m2 and the fire duration τd (s) is:
40

τd =

M ∙ ΔHc

(

HT + 1.02Deff

0.23 )

5

2

⁄

where ΔHc = effective heat of combustion (kJ/kg).

2. HT > Fh ≥ HT/2 

The exposure heat flux is 20 kW/m2 and the fire duration is:

τd =

M ∙ ΔHc

(

HT⁄2 + 1.02Deff

0.23 )

5

2

⁄

3. HT/2 > Fh

The method is not applicable.

b) Fire adjacent to wall – with or without ceiling effect:

The exposure heat flux is 120 kW/m2 and the fire duration is:

τd =

M ∙ ΔHc

Q̇

c) Fire adjacent to corner – with or without ceiling effect:

1. If Fh < HT/2, heat flux < 20 kW/m2 and method is not applicable.

2. For Fh ≥ HT/2, the maximum flame height is: Fh = H + 0.03 Deff (

Q̇

Deff

5⁄2)

1⁄2

.

If Fh ≥ HT, the exposure heat flux is 120 kW/m2 and the fire duration is:

τd =

M ∙ ΔHc

(

HT − H

0.03Deff

)

2

Deff

5⁄2

If HT/2 ≤ Fh < HT, the exposure heat flux is 20 kW/m2 and the fire duration is:

τd =

M ∙ ΔHc

(

HT/2 − H

0.03Deff

)

2

Deff

5⁄2

3.4.2 Localized fires from Eurocode Annex C DIN EN 1991 1-2:2010-12 

Eurocode 1: Actions on Structures Part 1-2: General Actions-Actions on Structures Exposed to Fire,

Annex C gives the flame vertical length Lf (m) of a localized fire as a function of the fire diameter D (m) 

and heat release rate Q (W):
41

Lf = −1.02 D + 0.0148 Q

2⁄5

If the flame is not impacting the ceiling, the temperature θ(z) in the plume along the vertical axis of the 

flame is given by:

θ(z) = 20 + 0.25Qc

2⁄3

(z − z0)

−5⁄3 ≤ 900

where

Qc = convective part of heat release rate, Qc = 0.8 Q by default, Q = heat release rate;

z = height from floor along flame axis (m);

z0 = −1.02 D + 0.00524 Q

2⁄5 = virtual origin of axis.

If the flame impacts the ceiling, the heat flux ḣ (W/m2) on the ceiling is given by:

ḣ = 100 000 if y ≤ 0.30

ḣ = 136 300 to 121 000 y if 0.30 < y < 1.0

ḣ = 15 000 y

−3.7

if y ≥ 1.0

y =

r + H + z′

Lh + H + z′

where

r = radial coordinate of point on ceiling where heat flux is calculated;

H = vertical distance to ceiling from fire source;

z’ = vertical coordinate of virtual heat source (equivalent point source);

z

′ = 2.4 D (QD

∗2⁄5 − QD∗2⁄3

) when QD

∗ < 1.0

z

′ = 2.4 D (1.0 − QD

∗2⁄5

) when QD

∗ ≥ 1.0

QD

∗ =

Q

1.11 ∙ 106 ∙ D2.5

The horizontal flame length at the ceiling level, measured from the flame axis is:

Lh = 2.9 H QH

∗ 0.33 − H

QH

∗ = non − dimensional heat release rate =

Q

1.11 ∙ 106 ∙ H2.5

3.5 Critical Assessment

All building codes studied use standard fire time-temperature curves for comparing the relative 

performance of building materials and small-scale assemblies, designing fire protection, and selecting 

structural member sizes through fire resistance ratings (in hours). Standard fire temperature curves 

continue to rise with time, whereas the temperature in an actual fire decreases after reaching a 

maximum temperature. Parametric fires, which are based on physical parameters, attempt to deal with 

the temperature evolution in a more realistic fashion. In the US, SFPE recommends a number of 

parametric fire models that are comparable to those of Eurocode. However, the time of exposure to a 

standard fire equivalent to a real fire (to achieve the same maximum temperature) is more clearly 

defined by Eurocode than by US standards.
42

The best measure of the accuracy of any time-temperature relationship for enclosure fires is by 

comparison with experimental results. One of the more extensive data sets is the CIB (Conseil 

International du Batiment), which consists of 321 tests conducted in a coordinated international testing 

program (Thomas and Heselden, 1972). Based on a comparison of various formulas for calculating the 

temperature at various times in a compartment fire, Thomas (2008) concludes that it is better to rely on 

well-documented and well-tested computer models. The reasons for this conclusion include:

. For many enclosures of practical significance, the assumption of uniformity of conditions is not valid.

. The maximum temperature measured anywhere in an enclosure may grossly overestimate fire severity 

in particular locations.

. Major changes in maximum temperatures and fire duration occur, particularly for low ventilation.

. The manner of ignition has little effect on maximum temperatures and duration of burning.

. The lining materials have significant effect on both maximum temperature and duration of burning.

Law (1997) reviewed time-equivalent formulas and generally concluded that they do not accurately 

represent fire temperature and duration, especially in deep compartment fires, and do not differentiate 

between short, hot fires and longer, cooler fires that have the same equivalent time.

Researchers have suggested various modifications to the Eurocode parametric curves based on 

comparison with output from program COMPF2 (Babrauskas, 1979). ASCE (2009) compares Eurocode 

time-temperature parametric curves with the proposed modified Eurocode curves, as well as curves 

proposed by Lie and by Petterson for various values of thermal inertia, fuel load, and ventilation factor. 

ASCE (2009) notes that the modified Eurocode curves predict the highest fire severity.

Most of the building codes studied also have elaborate recommendations on the fire scenarios that a 

building should be designed for. Unlike design fires for smoke control or egress time, design fires for 

structural assessment are mostly concerned with post-flashover fires. In the US, both NFPA and SFPE 

provide extensive recommendations on the fire scenarios to be investigated, and these are comparable 

to the fire scenarios listed in Eurocode and ISO. Of all the documents studied, the New Zealand Building 

Regulations have the most detailed fire scenarios, with design Fire Load Energy Densities for various 

spaces and occupancies.

According to data contained in CIB W14 (1986), the total fuel load in a typical office ranges between 

635 MJ/m2 and 3900 MJ/m2. The wood equivalent, assuming an average heat of combustion of 

12.5 MJ/kg, is 35 kg/m2to 217 kg/m2 of floor area. This generally agrees with the range suggested by 

SFPE and NFPA as likely to produce a ventilation-controlled fire, which forms the basis for design (ASCE 

2009).

For very large spaces, post-flashover fires are unlikely to occur and local fires affecting one or two 

columns in a long span structure may be more relevant. SFPE and Eurocode are at a comparable level of 

sophistication on localized fires.

References

AISC (2011) “AISC Construction Manual, Appendix 4: Structural Design for Fire Conditions,” 14th Ed. 

American Institute of Steel Construction Steel, Chicago, IL, USA
43

AS 1530.4 – 2005 “Methods for fire tests on building materials, components and structures”, Standards 

Australia, Sydney, NSW, Australia

ASCE Manuals and Reports on Engineering Practice No. 114 (2009) “Performance-Based Design of 

Structural Steel for Fire conditions,” Parkinson, D.L., Kodur, V. and Sullivan, P.D., ed.

ASTM E119 (2012) “Standard Test Methods for Fire Tests of Building Construction and Materials,” 

American Society for Testing and Materials, West Conshohocken, Pa

ASTM E1529-13 (2013) “Standard Test Methods for Determining Effects of Large Hydrocarbon Pool Fires 

on Structural Members and Assemblies,” American Society for Testing and Materials, West 

Conshohocken, Pa

Babrauskas, V. (1979 “COMPF2-A Program for Calculating Post-Flashover Fire Temperatures,” NBS TN 

991, National Bureau of Standards, Washington, DC

Building Center of Japan (2011) “The Building Standard Law of Japan,” Tokyo, Japan

CIB W14 Workshop (1986) “Design Guide - Structural Fire Safety”, Fire Safety J. vol. 10, no. 2, pp. 77-137

Dept. of Building and Housing (2012) “Extract from the New Zealand Building Code: Clauses C1-C6: 

Protection from Fire, and Clause A3: Building Importance Levels”, Wellington, NZ

Eurocode 1: Actions on Structures Part 1-2: General Actions-Actions on Structures Exposed to Fire

DIN EN 1991 1-2:2010-12, including Annex A, Annex C, Annex D, 2002, Annex E, Annex F, 2002

Hadjisophocleous, G. and Mehaffey, J.R. (2008) “Fire Scenarios,” SFPE Handbook of Fire Protection 

Engineering 4th ed. Chapter 5.11

Harada, K., Ohmiya, Y., Natori, A., Nakamichi, A. (2004) “Technical basis on structural fire resistance 

design in building standards law of Japan” Fire and Materials, 28:323-341 DOI:10.1002/fam.857

Ingberg, S.H. (1928) “Tests of the severity of building fires,” Quarterly of the National Fire Protection 

Association, vol. 22, no. 1, July, pp. 43-61, Boston, MA

ISO/TS 16733 (2006) “Fire Safety Engineering- Selection of design fire scenarios and design fires,” 

International Organization for Standardization, Geneva, Switzerland

Kawagoe, K. and Sekine, T. (1963) “Estimation of Fire Temperature‐Time Curve in Rooms,” Occasional 

Report No.11, Building Research Institute, Tokyo, Japan 

Kohno, M. (2006) “Outline of the fire resistance verification method in the Building Standard Law of 

Japan” 38th Joint Meeting US-Japan Panel on Wind and Seismic Effects, 15-20 May, Gaithersburg, MD

Lane, B. (2008) “Approaches to calculating structural fire resistance,” NFPA Fire Protection Handbook, 

12th ed., Vol. II, Chap. 19.5, Cote, A.E. Ed. National Fire Protection Association, Quincy, MA. USA pp. 

19.77-19.126
44

Law, M. (1997) “Review of Formulae for T-Equivalent,” Fire Safety Science, Proc. 5th Int. Symp., pp.985-

996.

Lie, T.T. (2002) “Fire Temperature-Time Relations,” Hdbk Fire Protection Engg, 3rd. ed. Chapter 4.8, SFPE, 

Bethesda, MD

McCaffrey, B.J. , Quintiere, J.G. and Harkleroad , M.F. (1981) ‘‘Estimating Room Temperatures and the

Likelihood of Flashover Using Fire Test Data Correlations,’’ Fire Technology, Vol. 17, No. 2, pp. 98-119

Ministry of Business, Innovation and Employment (2013) “C/VM2 Verification Method: Framework for 

Fire Safety Design for New Zealand Building Code Clauses C1-C6 Protection from Fire,” Wellington, NZ

National Research Council Canada (2010) “National Building Code of Canada 2010” (NBCC), Institute of 

Research in Construction, Ottawa, ON, Canada

New Zealand Building Regulations (1992, reprinted 2012), Wellington, NZ

NFPA 5000 (2003) “Building construction and safety code handbook,” Ch. 5 Performance-based option, 

National Fire Protection Association, Quincy, MA

NFPA 557 (2012) “Standard Determination of Fire Loads for Use in Structural Fire Protection Design,”

National Fire Protection Association, Quincy, MA

Parkinson, D.L. and Kodur, v. (2006) “Performance-Based Design of Structural Steel for Fire conditions: a 

Calculaiton Methodology,” ASCE Structures Congress, St. Louis, MO

Phan, L.T., McAllister, T.P., Gross, J.L. and Hurley, M.J. (2010) “Best Practice Guidelines for Structural Fire 

Resistance Design of Concrete and Steel Buildings,” NIST TN 1681, National Institute of Standards and 

Technology, Gaithersburg, MD 201899

SFPE S.01 (2011) “SFPE Engineering standard on calculating fire exposures to structures,” Society for Fire 

Protection Engineering, Bethesda, MD

Tanaka, T., Sato, M. and Wakamatsu, T. (1996) “Simple Formula for Ventilation Controlled Fire 

Temperatures,” 13th US/Japan Government Cooperative Program on Natural Resources (UJNR), 

Gaithersburg, MD, NISTIR 6030 June 1997 pp. 341-356 also Fire Science and Technology, 1997, Vol. 17, 

No. Special Issue, pp. 15-27

Thomas. P.H. (1981) “Testing products and materials for their contribution to flashover in rooms,” Fire

Materials, 5:103-111

Thomas, I. (2008) “Enclosure Fire Temperature-Time Estimation,” SPFE Hdbk of Fire Protection 

Engineering , 4th ed. , ©SPFE, NFPA Pub., Quincy, MA, pp. 4.208-4.227

Thomas, P. and Heselkden, A (1972) “fully Developed Fires in Single Compartments,” CIB Rept. 20, Fire 

Research Note 923, Fire Research Station, Borehamwood, UK
45

Chapter 4 Steel Structures

This chapter covers the design of steel structures to resist fire, according to various national building 

codes and guidance documents. Traditionally, prescriptive methods have been specified to achieve a 

certain fire resistance rating measured in exposure time to a standard fire. More recently, performancebased methods have been developed to calculate the resistance of structural members exposed to more 

realistic fires, taking into account the decreased strength and stiffness of steel at elevated temperatures. 

4.1 Prescriptive methods

4.1.1 USA: ASCE/SEI/SFPE 29-05 Standard Calculation Methods for Structural Fire Protection

This standard provides methods to calculate the equivalent fire resistance, in terms of hours, of 

concrete, timber, masonry and steel members that would be achieved under the standard ASTM E119 

fire test, or by comparative engineering analysis. This standard does not provide any guidance about 

the structural performance of members or structures under fire.

Columns: The procedures for determining the fire resistance R (in hours) of column assemblies (i.e., 

steel columns encased in insulation) are based on the mass per unit length W (lbm/ft or kg/m) or the 

cross sectional area A (in2 or mm2), the heated perimeter D or P (in or mm) of the steel section, and the 

thickness h (in or mm) of the fire protection. 

For gypsum wallboard protection:

R = c1 (

h

2

W′

D

)

0.75

W′ = W + c2hD

where

c1 = 2.17 (h, in, lbm); c1 = 1.60 (h, mm, kg);

W’ = total mass per unit length of steel column and protection.

c2 = 50⁄144 lbm, ft; c2 = 0.0008 kg, m

For spray-applied protection on wide-flange columns:

R = (C1 W⁄D + C2

)h

For spray-applied protection on tubular columns:

R = C1

′h A⁄P + C2′

where C1, C2, C1

′

and C2

′

are material constants.

Concrete-filled hollow steel columns: In addition to W, D and h, R (in hours) is also dependent on the 

concrete specified compressive strength fc’ (ksi or MPa), the column effective length KL (ft or mm) and 

the compressive force due to the unfactored dead and live loads C (kips or kN).
46

R = 0.58a

fc

′ + 2.90

KL − 3.28D

2√

D

C

or R = a

fc

′ + 20

60(KL − 1000)

D

2√

D

C

SI units

Columns encased in concrete or masonry: In addition to some of the quantities listed above, the fire 

resistance rating R of steel columns encased in concrete or masonry depends also on the properties of 

the enclosure, namely moisture content m (% of volume), thermal conductivity kc (Btu/h/ft/°F or 

W/m/K), thermal capacity H (Btu/ft/°F or J/m/K), density ρc (lbm/ft3 or kg/m3), specific heat cc

(Btu/lbm/°F or J/kg/K), thickness h (in or mm)and side length L = inside perimeter of protection/4 (in or 

mm).

R = R0

(1 + 0.03m)

R0 = 0.17 (

W

D

)

0.7

+ 0.28

h

1.6

kc

0.2

[1 + 26 (

H

ρccch(L + h)

)

0.8

]

R0 = 1.22 (

W

D

)

0.7

+ 0.0027

h

1.6

kc

0.2

[1 + 31000 (

H

ρccch(L + h)

)

0.8

] SI units

Beams, girders and trusses: The procedure for determining the fire resistance rating R of beams, girders 

and trusses is similar to that used for columns. The heated perimeter D does not include the top of the 

top flange, which is shielded from direct fire exposure by floor or roof decks. The rating accounts for 

restrained or unrestrained conditions. 

The following formulas are provided to calculate the thickness h of the spray-applied insulation on a 

non-standard beam (subscript 2) in relation to a standard, approved beam (subscript 1):

h2 = (

W1⁄D1 + 0.60

W2⁄D2 + 0.60) h1 W

lbm

ft ,D and h in

h2 = (

W1⁄D1 + 0.036

W2⁄D2 + 0.036) h1 W

kg

m

,D and h mm

4.1.2 USA: The International Building Code IBC 2012, Chapter 7: Fire and Smoke Protection 

Features 

This standard is based on ASCE/SEI/SPFE 29-05 “Standard Calculation Methods for Structural Fire 

Protection”, but it does not contain any provision on concrete-filled hollow steel columns, and it treats 

the fire resistance of steel columns protected by concrete or clay masonry units separately from the fire 

resistance of steel columns protected by concrete. The standard does not provide any guidance about 

the structural performance of members or structures under fire.

Table 721.1 of IBC 2012 prescribes the minimum thickness of various types of insulation for various fire 

resistance ratings (FRR) of structural members. For example, an FRR of 3 h requires a 2 in (50 mm) 

protective cover of concrete for a steel column. 
47

The FRR of steel assemblies depends on the size of the element and the type of protection provided, and 

is calculated based on the W/D concept, i.e., the ratio of average weight per unit length W to the heated 

perimeter D. For a wide-flanged steel column protected with sprayed fire-resistant material for example, 

R = [C1

(W⁄D) + C2

]h where R is the fire resistance (minutes), h is the thickness of the insulation (in) 

and C1 and C2 are material constants. The required thickness of sprayed fire-resistant material on larger 

or smaller steel beams can be calculated from the required thickness for approved restrained or 

unrestrained beams by the same ASCE ratio mentioned in the previous section.

4.1.3 National Building Code of Canada (NBCC) 2010 vol. 2 Appendix D Fire-performance 

ratings

Section D-2.6 provides the minimum thickness of concrete or masonry protective covering for steel 

columns. Equivalent thicknesses of plaster or gypsum-sand plaster are also listed. These values are 

based on the M/D (kg/m) ratio of the column mass m to the heated perimeter D of the column section 

in m. Section D-2.7 provides the minimum thickness of protective covering for steel beams for FRR 

between 30 min and 4 h. Table D-2.6.1.A specifies the minimum thickness of concrete or masonry 

protection for steel columns, e.g., for an FRR of 1h, a monolithic concrete cover of 25 mm is required.

4.2 Performance-based methods

Furnace tests are used to determine the fire resistance rating and the thickness of protection for 

individual structural members. Because the results are directly comparable to furnace tests, the analysis 

of single members typically form the basis for structural design against fire, whereby all relevant 

structural responses due to axial force, shear, flexure, buckling, lateral torsional buckling, etc. are 

verified. With the progress of structural software, the development of faster computers, and the 

construction of bigger test facilities, progress is being made in moving beyond single member behavior 

to capture the full frame response, including the effects of thermal expansion, the strength of 

connections under fire, and the potential development of alternate load paths. Performance-based 

methods start with various fire exposures described in Chapter 3, then calculate the temperature in the 

fire-exposed structure.

4.2.1 Methods for predicting temperatures in fire-exposed structures 

SFPE Fire Protection Engineering, 4th ed. 2008

The total heat flux q̇tot

"

transferred from a fire to a structural member is:

q̇tot

" = εs σ(Tr4 − Ts4

) + h(Tg − Ts)

where

εs = emissivity of target surface;

σ = Stefan-Boltzman constant = 5.6696 × 10-8 W/(m2∙K

4

);

h = convective heat transfer coefficient;

Tg = gas absolute temperature;

Tr = radiation absolute temperature;

Ts = surface absolute temperature.
48

The adiabatic surface temperature TAST, measured approximately by a plate thermometer, is the 

temperature of a perfectly insulated surface exposed to radiation and convection, and is defined by:

εs σ(Tr

4 − TAST

4

) + h(Tg − TAST) = 0

Then the total heat transfer can be rewritten as:

q̇tot

" = εs σ(TAST

4 − Ts

4

) + h(TAST − Ts)

For unprotected steel structures the transient steel temperature is:

As

[εsσ(TAST

4 − Ts

4

) + h(TAST − Ts)] = csρsVs

∂Ts

∂t

where

As = fire exposed area;

cs = steel specific heat capacity;

t = time;

Vs = volume per unit length of steel section; 

ρs = steel density.

For insulated steel structures, to a good approximation, the fire exposed surface temperature is the 

same as the fire temperature, and the total heat transfer qtot to the steel in steady state is: 

qtot = As

(ki⁄di)(Tf − Ts)

where

ki = thermal conductivity of insulation material; 

di = thickness of insulation material; 

Tf = fire temperature (Tr = Tg = Tf in fire engineering);

Ts = steel temperature.

If the heat capacity of the insulation is negligible relative to that of steel, transient steel temperature can 

be obtained from the heat balance equation:

As

ki

di

(Tf − Ts) = cs ρs Vs

∂Ts

∂t

For a constant fire temperature rise and constant material properties, the solution is:

Ts − T0 = (Tf − T0)(1 − e

−t⁄τ

)

τ =

cs ρs Vs

As

(ki⁄di)

=

cs ρs

(di⁄ki)

As⁄Vs

where τ is the characteristic response time, Asthe cross section area per unit length of steel section 

and As⁄Vsthe shape factor or section factor. For heavily insulated sections, a simple approximation is to 
49

lump 1⁄3 of the insulation heat capacity with that of steel (normally the heat capacity of the insulation has 

an insignificant influence on the temperature rise of the steel section).

4.2.2 Eurocode 3: Design of steel structures- Par 1-2: General rules- structural fire design

BS EN 1993-1-2:2005 also DIN EN 1993-1-2:2010-12

Structural fire design must meet two basic requirements:

1. maintain load bearing function during fire;

2. maintain separation requirement between elements by limiting deformations.

Eurocode 3 defines the stress-strain relationship of carbon steel at elevated temperatures as follows:

- a linear, elastic part: 

for ε ≤ εp

(T) σ = εE(T)

- a nonlinear, transition part:

for εp

(T) < ε < εy(T) σ = Fp(T) − c +

b

a

√a

2 − (εy

(T) − ε)

2

- a constant, plastic part:

for εy

(T) ≤ ε ≤ εt(T) σ = Fy(T)

- a linear, decreasing part to failure:

for εt

(T) < ε < εu(T) σ = Fy(T)

1 − (ε − εt

(T))

εu

(T) − εt(T)

where

ε = strain;

εp

(T) = Fp(T)⁄E(T) = strain at proportional limit;

εy

(T) = 0.02 = yield strain;

εt

(T) = 0.15 = limiting strain for yield strength;

εu

(T) = 0.20 = ultimate strain;

σ = stress;

E(T) = Young’s modulus at temperature T;

Fp

(T) = proportional limit at temperature T;

Fy

(T) = effective yield strength at temperature T;

a

2 = (εy

(T) − εp(T)) (εy(T) − εp(T) +

c

E(T)

)

b

2 = c (εy

(T) − εp(T))E(T) + c

2

c =

(Fy

(T) − Fp(T))

2

(εy

(T) − εp(T)) E(T) − 2 (Fy(T) − Fp(T))

Note that Eurocode defines the yield stress Fy at 2% strain. The Appendix at the end of this chapter 

compares the values at various temperatures of the yield stress at 2% strain and at 0.2 % offset (proof or 

plastic strain). Material properties are reduced from characteristic (room temperature) values by 

reduction factors that depend on temperature (Fig. 4.1, Table 4.1). 
50

Kp

(T) =

Fp(T)

Fp0

Ky

(T) =

Fy(T)

Fy0

KE

(T) =

E(T)

E0

Fp = proportional limit

Fy = yield stress

E = Young′s modulus

Figure 4.1 Reduction factors for the stress-strain relationship of carbon steel at elevated 

temperatures (EN 1993-1-2:2010, also Phan et al. 2010 NIST TN 1681)

Table 4.1 Stress-strain reduction factors in EC3

Temperature °C Ky

(T) Kp(T) KE

(T)

20 1.000 1.000 1.000

100 1.000 1.000 1.000

200 1.000 0.807 0.900

300 1.000 0.613 0.800

400 1.000 0.420 0.700

500 0.780 0.360 0.600

600 0.470 0.180 0.310

700 0.230 0.075 0.130

800 0.110 0.050 0.090

900 0.060 0.038 0.068

1000 0.040 0.025 0.045

1100 0.020 0.013 0.023

1200 0 0 0

Eurocode defines four classes of cross section, with class 1 the least susceptible to local buckling and 

class 4 the most susceptible. Class 1 (plastic) cross sections can form plastic hinges with the rotation 

capacity required for plastic analysis. Class 2 (compact) sections can also develop their plastic moment 

resistance, but have limited rotation capacity because of local buckling. In class 3 (semi-compact) 
51

sections, the extreme fibers in compression can reach the yield strength, assuming an elastic stress 

distribution, but local buckling is likely to prevent development of the plastic moment resistance. In class 

4 (slender) sections, local buckling will occur before any part of the section reaches yield. The limits 

between classes are established by the factor:

ε = 0.85 √235⁄Fy

where Fy is the yield strength in MPa at 20°C and the reduction factor 0.85 accounts for elevated 

temperatures.

Simple calculations: the capacity method

Load bearing function is maintained if the design effect of actions for the fire design situation is less than 

or equal to the corresponding design resistance of the steel member, which is calculated by modifying 

the resistance at ambient temperature by accounting for the mechanical properties of steel at elevated 

temperature. Usually, this is done by assuming a uniform temperature in the cross section. [The 

following notation is adopted from Takagi and Deierlein (2007), and differs slightly from EC3].

Tension members:

N(T) = Ky(T)N0

N(T) = design tensile resistance at temperature T;

N0 = design tensile resistance at ambient temperature;

Ky(T) = reduction factor for yield strength.

Compression members: 

For members subjected to inelastic flexural buckling (Class 1, 2 and 3 sections), the design buckling 

resistance Pcr,EC3

(T) at a uniform temperature T is:

Pcr,EC3(T) = χ(T) Py(T)

where Py(T) is the yield load at T and χ(T) is a reduction factor that depends on the slenderness ratio 

λ̅(T) and imperfection factor α.

χ(T) =

1

φ(T) + √φ2(T) − λ̅2(T)

≤ 1.0

φ(T) = 0.5[1 + αλ̅(T) + λ̅2(T)]

λ̅(T) = √

Fy(T)

Fe(T)

= λ̅

0√

Ky(T)

KE(T)

α = 0.65√235⁄Fy0

where

λ̅

0 = slenderness ratio at ambient temperature;

Fy

(T) = yield stress at T;

Fe

(T) = Euler buckling stress at T;

Fy0 = yield stress at ambient temperature;
52

Ky

(T),KE(T) = reduction factors for yield strength and for modulus of elasticity.

The above formulation is similar to that at ambient temperature (subscript 0)

Pcr0,EC3 = χ0Py0

χ0 =

1

φ0 + √φ0

2 − λ̅

0

2

≤ 1.0

φ0 = 0.5[1 + α(λ̅

0 − 0.2) + λ̅

0

2

]

λ̅

0 = √

Fy0

Fe0

=

KL

πr √

Fy0

E0

Fe0 =

π

2E0

(KL⁄r)

2 = Euler buckling stress

where

0.13 ≤ α ≤ 0.76 is an imperfection factor;

K = end fixity factor;

L = column length;

r = radius of gyration.

For column buckling, only curve c - the more conservative of four possible curves - is used at high 

temperatures. The use of curve c is due to a more severe influence of initial imperfections than for 

ambient conditions and additional bending due to non-uniform temperatures. 

Beams 

The design lateral torsional buckling resistance of a laterally unrestrained member with a class 1 or 2 

cross section with a uniform temperature is:

Mcr,EC3(T) = χLT(T) Mp(T)

where

Mp(T) = plastic moment at temperature T;

χLT(T) = reduction factor that depends on the slenderness ratio λ̅

LT(T) and imperfection factor αLT.

λ̅

LT0 = slenderness ratio at ambient temperature.

χLT(T) =

1

φLT(T) + √φLT

2

(T) − λ̅

LT

2

(T)

≤ 1.0

φLT(T) = 0.5[1 + αLTλ̅

LT(T) + λ̅

LT

2

(T)]

λ̅

LT(T) = λ̅LT0√

Ky(T)

KE(T)

αLT = 0.65√235⁄Fy0

The above formulation is similar to that at ambient temperature (subscript 0).

Mcr0,EC3 = χLT0Mp0
53

χLT0 =

1

φLT0 + √φLT0

2 − λ̅

LT0

2

≤ 1.0

φLT0 = 0.5[1 + αLT(λ̅

LT0 − 0.2) + λ̅

LT0

2

]

λ̅

LT0 = √

Mp0

Mcr0,e

Mp0 = ZxFy0

Mcr0,eis the elastic critical moment for lateral torsional buckling, α is an imperfection factor that 

depends on the section proportions, and Zx is the plastic section modulus about the strong axis. It is 

seen that the strength formulations for the flexural buckling of columns and the lateral torsional 

buckling of beams at ambient and at temperature T are consistent. 

For beam-column strength, EC3 provides the following equations:

Pu

Pcry,EC3(T)

+ kLT(T)

Mux(T)

Mcr,EC3(T)

≤ 1.0

Pcry,EC3(T) = χ(T)Py(T)

kLT(T) = 1 − μLT(T)

Pu

Pcry,EC3(T)

μLT(T) = 0.165̅λy

(T) − 0.15 ≤ 0.9

where

Pu = factored axial load;

Mux

(T) = factored bending moment about the strong axis;

Pcr,EC3(T) = critical axial strength for flexural buckling;

Mcr,EC3(T) = critical bending moment for lateral torsional buckling;

μLT(T) for pin-ended beam-column subjected to uniform end moments.

For class 4 cross sections other than tension members, the load bearing function is assumed maintained 

if the steel temperature is less than a critical temperature, recommended to be 350°C unless otherwise 

specified.

The critical temperature method

As an alternative to the capacity method, verification may be carried out in the temperature domain. 

When deformation or stability does not need to be considered, a critical temperature θa,cr for steel can 

be defined for a uniform temperature distribution and an utilization factor μ0:

θa,cr = 39.19 ln (

1

0.9674 μ0

3.833 − 1) + 482

The degree of utilization μ0 is the ratio of the design effect of actions for the fire situation (reduced dead 

and live loads, e.g., 1.0 D + 0.5 L for office occupancy), including the effects of thermal expansion and 

deformations, to the corresponding design resistance in the fire situation. For unprotected members, 

θa,cr = 554°C for μ0 = 0.60 and θa,cr = 526°C for μ0 = 0.70 for examples. This temperature is 

assumed uniform over the cross section, and therefore a lumped mass heat transfer analysis is sufficient 
54

(Lane 2008). Due to instability effects (e.g., lateral torsional buckling) and the sensitivity of various 

modes of failure to temperature gradients, the strength reduction factors that apply to structural 

members are not the same as would apply to the material. 

The EC3 document includes steel temperature development ∆θa,tfor unprotected steelwork as a 

function of the net heat flux ḣ

net,d , the section factor (ratio of cross section area Am to volume V of 

member per unit length), material properties (specific heat ca and unit mass ρa of steel), a shadow 

factor ksh, and time ∆t. 

∆θa,t = ksh

Am⁄V

caρa

ḣ

net,d∆t

For protected steelwork, the thickness and thermal properties of insulation are included in the equation.

∆θa,t =

λp(Ap⁄V)(θg,t − θa,t)

dpcaρa

(1 + φ⁄3)

∆t − (e

φ⁄10 − 1)∆θg,t

φ =

cpρp

caρa

dp Ap⁄V

where

Ap⁄V = section factor ;

= ratio of cross section area of protection material Ap to volume of member V per unit length;

cp = specific heat of protection material; 

dp = thickness of protection material;

ρp = unit mass of protection material;

λp = thermal conductivity of protection material;

θg,t = ambient gas temperature at time t.

In addition to the simple methods described above, advanced calculation methods can be used with 

any heating curve to calculate the thermal and mechanical responses of the structure. EN 1993-1-2 also 

includes the following annexes:

Annex A: strain-hardening of carbon steel at elevated temperatures.

Annex B: heat transfer to external steelwork, including beams and columns partially or fully engulfed in 

flames.

Annex C: stainless steel. Proof strength is defined at 0.2 % plastic strain ( fp0.2, as in US).

Annex D: joints. The strength of bolts and welds is reduced from that at ambient by a temperaturedependent reduction factor listed in Table D1. The temperature of a joint may be calculated from the 

ratio of exposed area to volume of the connected members in the vicinity of the joint, or from the 

temperature θ0 of the bottom flange at midspan:

θh = 0.88 θ0

[1 − 0.3 h⁄D] for h ≤ 400 mm

θh = 0.88 θ0 for h > 400 mm and h ≤ D⁄2

θh = 0.88 θ0

[1 + 0.2(1 − 2 h⁄D)] for h > 400 mm and h > D⁄2

where

θh = temperature at height h above bottom of beam;

D = depth of beam.

Annex E: class 4 cross sections
55

For the design under fire conditions using simplified calculation models, the design yield strength of 

steel should be taken as the 0.2% proof strength, fp0.2,θ, with the reduction factor

kp0.2,θ = fp0.2,θ⁄fy

kp0.2,θ is tabulated in Table E1.

Single elements in local heating

The methodology for single elements applies to post-flashover fires as well as to local fires, where 

temperature gradients may be more severe, with potential adverse consequences on the stability of 

columns and frames. 

Connections in fire

EC3 states that the fire resistance of a bolted or welded connection may be assumed to be sufficient if 

the fire protection on the connection is as effective on the joint as it is on the members, and the 

utilization of the joint is less than or equal to the maximum utilization of any of the connected members. 

4.2.3 USA: AISC 2011 14th Ed. Appendix 4 Structural Design for Fire Conditions

This appendix has been recently updated with the work of Takagi and Deierlein (2007).

Unprotected steel members

Appendix 4 proposes a formula for the rise in steel temperature that is a function of the weight to 

perimeter ratio, the difference in temperature between the fire and the steel, and a heat transfer 

coefficient, which is the sum of a convective and a radiative coefficient. Unfortunately, the radiative 

coefficient is itself a function of the unknown steel temperature to the third power, and the time step 

associated with this approach is recommended not to exceed 5 s.

Protected steel members

The simple method is applicable to steel members with contour insulation (i.e., that follows the shape of 

the section). Application of the method to box insulation will overestimate the steel temperatures. The 

temperature of the outside surface of the insulation is assumed to be the fire temperature, and 

temperature in the steel section is determined by thermal conduction through the insulation material. 

Two formulas are provided, depending on whether the heat capacity of the insulation material can be 

neglected or not. Ideally material properties used should be functions of temperature, but if these 

functions are not known, then insulation properties at 500°C (932°F ) and steel properties at 300°C 

(572°F) may be used. Time steps should not exceed 5 s.

External Steelwork

Temperature rise is proportional to the heat flux incident on the steel member and inversely 

proportional to the weight to perimeter ratio of the section.

Advanced calculation method

A computer model is required that accounts for exposure conditions based on the design fire, and 

characterized by a heat flux, or a temperature time history, along with radiation and convection 

parameters. Temperature-dependent material properties are used to calculate temperature variation in 

time and space within the steel members and the insulation material.
56

Material properties at elevated temperatures

Mechanical properties of steel with yield strength less than 448 MPa (65 ksi), defined at a yield strain of 

2%, and of normal or light weight concrete with compressive strength less than 55 MPa (8000 psi) are 

given for temperatures up to 1200°C (2200°F). These properties (see Section 4.2.2) are adopted from 

Eurocode 3 (2010) and Eurocode 4 (2005) and therefore the yield stress is defined at 2% strain 

consistently with Eurocode.

Structural Design Requirements

General structural integrity: The structural system should be able to sustain local damage due the design 

basis fire and maintain a stable continuous load path to the foundation. The structural frame should 

have adequate strength and deformation capacity to withstand the structural actions caused by the 

design basis fire, within prescribed limits of deformation. Connections should be able to develop the 

strength of the connected members in fire or resist the forces, moments and deformations obtained by 

analysis of the structure under the applicable load combinations that include the design basis fire:

(0.9 or 1.2)D + T + 0.5L + 0.2S

where

D = nominal dead load

L = nominal occupancy live load

S = nominal snow load

T = nominal forces and deformations due to the design basis fire.

Advanced analysis

An advanced analysis of the effects of the design basis fire on the structure includes a thermal and a 

mechanical analysis. The thermal analysis produces a temperature field in each structural element and 

should account for the presence of insulation. The mechanical analysis results in forces and 

deformations in the structural system subjected to the response calculated in the thermal analysis. The 

mechanical analysis should account for the temperature dependence of material properties, the effects 

of thermal expansion, large deformations, and possible changes in boundary conditions and connection 

fixity. All relevant limit states, such as excessive deflections, connection fractures, overall and local 

buckling should be considered.

Simple analysis

A simple analysis that assumes the support and restraint conditions remain unchanged from normal 

temperatures is allowed for evaluating the performance of individual members during fire exposure. If 

temperatures are below 200°C (400°F) material properties may be assumed unchanged from normal

temperatures.

Tension members

The thermal response of a tension member may be calculated by a one-dimensional heat transfer 

equation with heat input determined from the design-basis fire. The design strength equations for 

normal temperatures may be used, with the mechanical steel properties changed to correspond to the 

maximum steel temperature assumed to apply uniformly over the entire cross section. 

Compression members

For the simple analysis, one dimensional heat transfer from the design-basis fire is permitted 

(temperature is uniform over the cross section and the length of the member). The nominal 

compressive strength for flexural buckling Fcr(T) is given by:
57

Fcr(T)

Fy(T)

= 0.42λ(T)(A4.2)

λ(T) = √

Fy(T)

Fe(T)

where Fy(T) = yield stress at temperature T, Fe(T) = Euler buckling stress at temperature T, and the 

same equation number is given as in AISC 2011. This equation and others below come from the work of 

Takagi and Deierlein (2007). The 2005 AISC Specifications used the standard strength equations, such as 

E3.2 below, with the modulus of elasticity E, the yield strength Fy and the ultimate strength Fu reduced 

by appropriate factors due to elevated temperatures. Takagi and Deierlein (2007), however, showed 

that these equations are unconservative (Fig. 4.2), especially in the inelastic range, and the change in the 

shape of the stress-strain curve (more gradual yielding at elevated temperatures) needs to be taken into 

account in addition to the changes in E, Fy and Fu. This suggestion was adopted in AISC 2011. Eq. A4.2 is 

similar, but not identical in form to the equation for inelastic flexural buckling under normal 

temperature:

Fcr

Fy

= 0.658Fy⁄Fe for Fy

Fe

≤ 2.25 (E3.2)

Fcr

Fe

= 0.877 for

Fy

Fe

> 2.25

a Compression strength Pcr(T) Py ⁄ (T) vs. L⁄r b Flexural strength Mcr(T) Mp ⁄ (T) vs. λ = Lb⁄ry

Figure 4.2 Comparison of compression and flexural strengths at 500 °C (932 °F)

 Takagi and Deierlein (2007), AISC Construction Manual, Appendix 4 (2011)

 Copyright 2011 American Institute of Steel Construction, reprinted with permission

Using the same notation as Eurocode:

λ̅

0

2 =

Fy0

Fe0

λ̅2

(T) =

Fy(T)

Fe(T)
58

Fcr0 = 0.658λ̅

0

2

Fy0 for λ̅

0

2 ≤ 2.25

Fcr0 = 0.877Fe0 for λ̅

0

2 > 2.25

Fcr(T) = 0.42λ̅(T)Fy(T)

Flexural members

In general, the formulas used for flexural members at room temperature apply, with the proviso that 

material properties are now temperature dependent. Takagi and Deierlein (2007) have shown that this 

approach can be unconservative, and where their work applies, new formulas have been adopted for 

the lateral-torsional buckling of laterally unbraced doubly-symmetric members and channels bending 

about their major axis and having compact webs and flanges:

a) When Lb ≤ Lr (T)

Mn

(T) = Cb [Mr(T) + [Mp(T) − Mr(T)][1 −

Lb

Lr(T)

]

cx

] (A4.3)

b) When Lb > Lr (T)

Mn

(T) = Fcr(T)Sx (A4.4)

where

Fcr(T) =

Cbπ

2E(T)

(Lb⁄rts)

2

√1 + 0.078

Jc

Sxh0

(

Lb

rts

)

2

(A4.5)

Lr

(T) = 1.95 rts

E(T)

FL(T)

√

Jc

Sxh0

+ √(

Jc

Sxh0

)

2

+ 6.76 [

FL(T)

E(T)

]

2

(A4.6)

Mr

(T) = SxFL(T) (A4.7)

FL

(T) = Fy(kp − 0.3ky) (A4.8)

Mp

(T) = ZxFy(T) (A4.9)

cx = 0.53 +

T

450 ≤ 3.0 where T is in °F (A4.10)

cx = 0.6 +

T

250 ≤ 3.0 where T is in °C (A4.10M)

c = 1 for doubly-symmetric I-sections; c =

h0

2

√

Iy

Cw

 for channels;

Cb = lateral-torsional buckling modification factor for non-uniform moment diagram;

Cw = warping constant;

E = Young’s modulus;

Fcr = critical stress; 

FL = magnitude of flexural stress in compression flange at which flange local buckling or lateral-torsional 

buckling is influenced by yielding;

Fy = specified yield strength; 

h0 = distance between the flange centroids;

Iy = out-of-plane moment of inertia;

J = torsional constant;

kp = Fp(T)⁄Fy = ratio of proportional stress at T to specified yield strength at room temperature;

ky = Fy(T)⁄Fy = ratio of yield stress at T to specified yield strength at room temperature;

Lb = distance between points that are braced against lateral displacement of the compression flange or 

braced against twist of the cross section;
59

Lp = limiting laterally unbraced length for the limit state of yielding;

Lr = limiting laterally unbraced length for the limit state of inelastic lateral torsional buckling;

Mn = nominal flexural strength;

Mp = plastic bending moment;

Mr = elastic moment at onset of yielding;

rts = effective radius of gyration; rts

2 =

√IyCw

Sx

ry = radius of gyration about y-axis;

Sx = elastic section modulus about x-axis; 

T = temperature;

Zx = plastic section modulus about x-axis.

Compared to the AISC equations for room temperature (below), the above equations distinguish 

between only two regions of behavior (elastic and inelastic lateral-torsional buckling), instead of three 

(elastic, inelastic lateral-torsional buckling and full plastic bending). This is because, at elevated 

temperatures, the critical moment drops off quickly from the plastic moment at small slenderness 

values, and the full plastic bending region is no longer significant. In the calculation of Lr (Eqs. A4.6 and 

F2.6), the initial yield stress FL is replaced by the proportional limit stress minus the residual stress 

estimated to be 30% of the yield strength. For comparison, the AISC equations for lateral-torsional 

buckling at room temperature are also shown below:

a) When Lb ≤ Lp , the limit state of lateral-torsional buckling does not apply. The limit state of 

yielding is:

Mn = Mp = FyZx (F2.1)

b) When Lp < Lb ≤ Lr ,

Mn = Cb [Mp − (Mp − 0.7 FySx) (

Lb − Lp

Lr − Lp

)] ≤ Mp (F2.2)

c) When Lb > Lr ,

Mn = FcrSx ≤ Mp (F2.3)

where

Fcr(T) =

Cbπ

2E

(

Lb

rts

)

2

√1 + 0.078

JC

Sxh0

(

Lb

rts

)

2

(F2.4)

Lp = 1.76 ry√

E

Fy

(F2.5)

Lr = 1.95 rts

E

0.7 Fy

√

JC

Sxh0

+ √(

JC

Sxh0

)

2

+ 6.76 [

0.7 Fy

E

]

2

(F2.6)

Mp0 = plastic moment

Mr0 = initial yield moment (reduced to account for residual stresses)

E0 , G0 = elastic moduli. 

Beam-column strength 

AISC uses a bilinear combination of the ratio of axial and bending effects.
60

For

Pu

Pcry,AISC(T)

≥ 0.2,

Pu

Pcry,AISC(T)

+

8

9

Mux

Mcrx,AISC(T)

≤ 1.0 (H1 − 1a)

For

Pu

Pcry,AISC(T)

< 0.2,

Pu

2Pcry,AISC(T)

+

Mux

Mcrx,AISC(T)

≤ 1.0 (H1 − 1b)

where

Pu = factored axial load;

Mux = factored bending moment about strong axis;

Pcry, AISC (T) = critical axial strength for flexural buckling about weak axis;

Mcrx, AISC(T) = critical bending moment for lateral-torsional buckling.

These equations are unchanged from previous editions, but Pcry, AISC (T) and Mcrx, AISC(T) are now calculated 

by the new formulas above (Eq. A4.2 adapted for buckling about the weak axis, and Eq. A4.3 or A4.4). 

Design by qualification

AISC also allows prescriptive design in conformance with ASTM E119 and ASCE-SFPE 29-05 Standard 

Calculation Method for Structural Fire Protection. AISC notes that restrained conditions exist for floor 

and roof assemblies and individual beams when the surrounding members and connections can resist 

thermal expansion throughout the range of elevated temperatures. 

4.2.4 Canadian Standards Association CSA S16-09 “Limit States Design of Steel Structures” 

Annex K: Structural design for fire conditions

The development (CISC Commentary 2010) of CSA S16-09 Annex K parallels that of AISC 2011 Appendix 

4. In Canada until recently, the design of steel structures for fire conditions followed the standard design 

equations at normal temperature, but with material properties altered on account of elevated 

temperatures. Takagi and Deierlein (2009, Fig. 4.4) showed that this approach was unconservative and 

their work was instrumental in bringing about Annex K as part of the 2009 edition of CSA S16. The 

approach is similar to that of AISC and agrees well with Eurocode methods. The equations for design for 

fire apply for temperatures greater than 200°C and are consistent in form with (albeit more complicated 

than) their counterparts for ambient temperature.

Calculation of temperatures in steel

Unprotected steel:

A first order analysis assumes uniform temperature over the member and typically uses lumped heat 

capacity analysis. The temperature rise ∆Tsis:

∆Ts =

a

cs

(M⁄D)

(TF − Ts)∆t

where

a = ac + ar = heat transfer coefficient; 

ac = convective heat transfer coefficient ≅ 25 W/(m2⋅ °C);

ar = radiative heat transfer coefficient =

5.67 × 10−8εF

TF − Ts

(TF

4 − Ts

4

);

cs = steel heat capacity;
61

εF = emissivity;

M⁄D = ratio of steel mass per unit length to perimeter exposed to fire;

TF = fire temperature;

Ts = steel temperature;

∆t = time increment < 5 s.

For protected steel members, two cases are considered:

If the thermal capacity of the protection is negligible compared to that of steel, i.e.,

cs M⁄D > 2 dp ρp cp

where

dp = thickness of protection,

ρp = density of protection,

cp = thermal capacity of protection, 

then the temperature rise of the steel member is:

ΔTs =

kp

cs dp M⁄D

(TF − Ts)∆t

where kp = conductivity of protection.

If the thermal capacity of the protection needs to be considered, then the temperature rise is:

ΔTs =

kp

dp

TF − Ts

cs M⁄D + dp ρp cp⁄2

∆t

For external steelwork, the temperature rise is:

ΔTs =

q

"

cs M⁄D

∆t

Alternatively, a more advanced model can be used to calculate the temperature rise in the member.

The mechanical properties of steel at elevated temperatures are the same as in Eurocode.

Three levels of structural design are possible:

a) Analysis of individual elements, accounting for reduction in resistance and stiffness with 

temperature, but ignoring the effects of restraint to thermal expansion and bowing;

b) Analysis of substructures where the effects of restrained thermal expansion and thermal bowing 

are considered by incorporating geometric and material nonlinearities;

c) Global analysis where restrained thermal expansion, thermal bowing, material degradation and 

geometric nonlinearity are considered.

CSA S-16 column strength at high temperatures

Pcr(T) = [1 + λ(T)

2dn]−1⁄(dn)AFy(T)

where

λ(T) = √

Fy(T)

Fe(T)

=

KL

r

√

Fy(T)

π

2E(T)

λ(T) = column slenderness ratio;

A = column cross section area;
62

d = 0.6 ;

Fe

(T) = Euler buckling load at temperature T;

Fy

(T) = yield strength at temperature T;

KL = column effective length;

n as given for nominal strength (below); 

Pcr(T) = column strength at temperature T;

r = radius of gyration of column cross section.

CSA S-16 column strength at ambient temperature

Pcr0 = [1 + λ

2n]−1⁄nAFy0

where

λ = √

Fy0

Fe0

=

KL

r

√

Fy0

π

2E0

subscript 0 is for ambient temperature;

n = 1.34 for hot-rolled, fabricated structural sections, and hollow structural sections;

n = 2.24 for doubly symmetric welded three-plate members with flange edges oxy-flame-cut, and

hollow structural sections.

Pcr(T) Py ⁄ (T) vs. L⁄r Mcr(T) Mp ⁄ (T) vs. λ = Lb⁄ry

Figure 4.3 Comparison of compression and flexural strengths at 500°C (932°F) (S and W stand for strong 

and weak axis buckling strength respectively) - Takagi and Deierlein (2009), Frater (2010) 

Copyright 2009 Canadian Steel Construction Council, reprinted with permission

Fig. 4.3a compares various column strength curves, AISC 2005, CSA S16-01 (reprinted 2005), AISC 

proposed (adopted as Appendix 4 in 2010), CSA proposed (adopted as Annex K in 2009), Eurocode 

(2003) with finite-element (FE) simulations of a wide flange column (W 14 x 90 Gr. 50 or W 360 x 134, 

Fy =345 MPa) buckling about the strong (S) or weak axis (W). The new AISC and CSA curves are in much 

closer agreement with Eurocode and FE results, compared with the old curves, which were 

unconservative, especially in the inelastic range. 
63

CSA S-16 beam strength at high temperatures

Mcr(T) = CKMp

(T) + (1 − CK)Mp(T) [1 − (

CKMp

(T)

Mu

(T)

)

0.5

]

Cz(T)

where

CK = 0.12;

Mcr(T) = nominal beam strength at temperature T;

Mp

(T) = plastic moment using Fy(T);

Mu

(T) = elastic critical moment at temperature T;

T = temperature °C;

Mu

(T) =

ω2π

L

√E(T)IyG(T)J + IyCw (

πE(T)

L

)

2

ω2 = moment gradient, same as for ambient temperature (see below);

Cw = warping constant;

E = Young’s modulus;

G = shear modulus;

Iy = out-of-plane moment of inertia;

J = torsional constant; 

L = length of unbraced portion of beam; and

Cz

(T) =

T + 800

500 ≤ 2.4

CSA S-16 beam strength at ambient temperature

For Mu0 > 0.67 Mp0 Mcr0 = 1.15 Mp0 (1 −

0.28 Mp0

Mu

) ≤ Mp0

For Mu0 ≤ 0.67 Mp0 Mcr0 = Mu0

where

Mu0 =

ω2π

L

√E0IyG0J + IyCw (

πE0

L

)

2

ω2 = moment gradient;

ω2 = 1.75 + 1.05κ + 0.3κ

2 ≤ 2.5 for unbraced lengths subject to end moments;

ω2 = 1.0 when the bending moment at any point within the unbraced length is larger than the larger

end moment or when there is no effective lateral support for the compression flange at one of the ends 

of the unsupported length;

κ = the ratio of the smaller factored moment to the larger factored moment at opposite ends of the

unbraced length, positive for double curvature and negative for single curvature.

Fig. 4.3b compares various beam strength curves, AISC 2005, CSA S16-01 (reprinted 2005), AISC 

proposed (adopted as Appendix 4 in 2010), CSA proposed (adopted as Annex K in 2009), Eurocode 

(2003) with finite-element (FE) simulations of a wide flange beam (W 14 x 22 Gr. 50 or W 360 x 32.9, 

Fy =345 MPa) buckling in torsional-flexural mode about the strong (S) or weak axis (W). The new AISC 

and CSA curves are in much closer agreement with Eurocode and FE results, compared with the old 

curve, which were unconservative, especially in the inelastic range.
64

The factored resistance is obtained by multiplying the nominal resistance with the same resistance 

factor φ as for ambient temperature. Qualification testing is an acceptable alternative to design by 

analysis for providing fire resistance.

4.2.5 New Zealand and Australia 

NZS 3404: Part 1:1997 (with Oct. 2007 amendment) Steel Structures Standard current in Jan. 2013, 

Chapter 11 “Fire”

Australian Standards AS 4100-1998 Steel Structures - Section 12 Fire

These standards cover steel building elements required to have a fire resistance rating (FRR for New 

Zealand, fire-resistance level FRL for Australia), i.e., a period of structural adequacy (PSA) under a 

standard fire exposure. The FRR or FRL depends on the thickness of protection for protected members, 

and the section factor for unprotected members. The section factor (SF) is defined as either the ratio of 

the surface area exposed to fire to the mass of steel, or the ratio of the heated perimeter to the cross 

section area. The PSA may be calculated as the duration from the start of the fire test to the time when 

the steel temperature reaches a limiting value Tl. It may also be determined by tests or by structural 

analysis accounting for the effects of temperature on material properties. The variation of the yield 

strength and modulus of elasticity of steel vs. temperature is given as follows (Fig. 4.4, AS 4100-1998):

Figure 4.4 Variation of mechanical properties of steel with temperature, adapted from AS 4100-1998

Yield strength ratio = ky,T =

905−T

690

≤ 1.0 for 215°C < T ≤ 905°C

Young’s modulus at elevated temperatures is defined by the ratio kE,T:

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 1000

Yiled strength ratio or modulus of elasticity ratio

Steel temperature T °C

yield strength ratio

modulus of elasticity ratio
65

kE,T = 1.0 +

T

2000 ln(T⁄1100)

for 0 < T ≤ 600 °C

kE,T =

690 [1 − (T⁄1000)]

T − 53.5

for 600 < T ≤ 1000 °C

According to AS 4100 and NZS 3404, a steel member is expected to yield at a limiting temperature which 

accounts for the ratio of the load in fire to the capacity at ambient temperature (load ratio r). (In 

contrast, the Eurocode degree of utilization μ0 is the ratio of the design effect of actions for the fire 

situation to the corresponding design resistance in the fire situation). From the definition of the yield 

strength, the limiting temperature = Tl = 905 − 690 r.

The resistance time of protected and unprotected steel against a standard fire is given by the same 

formulas used in the Design Manual on the European Recommendations for Fire Safety of Steel 

Structures (European Convention for Constructional Steelwork, Brussels, Belgium, 1985).

For unprotected members, formulas for the time t in minutes at which the limiting temperature Tlis 

attained is given for members exposed on three or four sides:

t = −5.2 + 0.0221 Tl + 0.433 Tl⁄SF for three-sided exposure,

t = −4.7 + 0.0263 Tl + 0.213 Tl⁄SF for four-sided exposure,

SF = ksm = ratio of exposed area to mass, 2 m2/tonne ≤ ksm ≤ 35 m2/tonne, or

SF =

Hp

7.85A

= ratio of exposed perimeter to area, 15 m-1 ≤ Hp⁄A ≤ 275 m-1

For protected members, the time to reach the limiting temperature Tlis determined by tests.

Connections to protected members should be protected with the maximum thickness required for any 

of the members. Connections to unprotected members are designed using the limiting temperature and 

the section factor of the connection components. They should achieve the same or lower load ratio as 

the members being connected.

4.2.6 The Building Standard Law of Japan August 2011 - Steel

Calculation of critical time to failure of structural steel elements

The procedure starts with calculation of structural stresses under normal temperature. Next, the critical 

steel temperature is determined for various possible failure modes. The steel temperature rise is then 

computed for the cross section geometry and insulation that apply. Finally the time to critical condition 

is obtained and compared with the fire duration. 

The decrease of yield strength of steel with temperature is governed by:

κ(T) =

σy(T)

F

=

700 − T

375 for T > 325°C

where

F = nominal yield strength (at 1% strain) at normal temperature;

T = temperature °C ;

σy

(T) = yield strength at temperature T. 

Steel Columns

The critical member temperature Tcr is governed by overall buckling, local buckling, thermal 

deformation, and allowable temperature (Notification 1433 p. 101).
66

Tcr = min(TB, TLB, TDP, 550°C)

where

TB = maximum temperature for overall buckling of steel columns;

TLB = maximum temperature for local buckling of steel columns;

TDP = maximum temperature for thermal deformation of steel columns.

550°C is the critical temperature of joints. 

Overall buckling of steel columns

The slenderness ratio λ is defined as:

λ = √

F

σE

=

le

πi √

F

E

where

E = modulus of elasticity at normal temperature;

le = effective column length;

i = minimum radius of gyration;

σE = Euler buckling stress.

The axial stress for overall buckling σB is similar to that for normal temperature (Harada 2004):

σB

F

=

1 − 0.24λ

2

1 + 0.267λ

2

From σB, TB can be calculated:

for λ < 0.1, TB is governed by yielding;

for 0.1 ≤ λ < 1, TB = max {tangent modulus value, inelastic buckling value}. More precisely,

for λ < 0.1, TB = 700 − 375 p

for 0.1 ≤ λ < 1, TB = max {700 − 375p − 55.8(p + 30p

2

)(λ − 0.1), 500√1 −

p(1 + 0.267λ

2)

1 − 0.24λ

2

}

where

p = ratio of axial force P to column capacity at normal temperature =

P

FAc

Ac = column cross section area.

Local buckling of steel columns

TLB = 700 −

375

min(RLBO, 0.75)

where RLBO is a reduction factor that depends on the width or diameter to thickness ratio and is 

tabulated for H-, hollow square and cylindrical sections.

Deformations of steel columns

TDP = 20 + 18000⁄√S
67

where S = floor area of room that column faces (m2) and TDP is in °C . For example, for a very large room 

S = 1000 m2, TDP = 589 °C . See explanation below for deformations of steel beams.

Steel beams

Consider a steel beam of span 2l with fixed ends under uniformly distributed load w. At bending 

failure, plastic hinges that develop plastic bending moment MpB form at the ends and midspan:

w (2l)

2⁄8 = 2 MpB ⇔ wl2 = 4 MpB

The critical temperature for flexural failure of steel beams is therefore:

TBcr = 700 − 375 wl

2⁄(4 MpB)

Notification 1433 p. 109 covers a more general case for the critical beam temperature Tcr .

Tcr = min (TBcr, TDP, 550°C)

TBcr = 700 −

750l

2

(w1 + w2)

MpB(√RB1 + RB3 + √RB2 + RB3)

2

where

TBcr = critical temperature for flexural failure of steel beam;

2l = beam span;

w1 = uniformly distributed load;

w2 = uniformly distributed load equivalent to concentrated loads;

MpB = FZpBx⁄1000 = normal temperature plastic moment N/m;

F = specified design yield strength N mm2 ⁄ ;

ZpBx , ZpBy = plastic section modulus about strong, weak axis mm3 ;

RB1, RB2 = 1 for fixed ends, 0 otherwise;

RB3 = 1 when top of beam is rigidly connected to slab, RB3 = ZpBy⁄ZpBx otherwise.

Deformations of steel beams

TDP = 20 + 18000⁄√S

where S = floor area of room that beam faces (m2) and TDP is in °C. 

The following explanation is adapted from Harada (2004):

Take a steel frame under fire where all the beams are heated to TDP. The beam length can be taken as 

√S , so the beam thermal elongation is ∆l = 1.2 × 10−5

(TDP − T0)√S, where T0 is the normal 

temperature and 1.2 × 10−5/°C is the coefficient of thermal expansion of steel. If the story drift is 

limited to ∆l⁄4.32 = 1⁄20, where a story height of 4.32 m is assumed, then 

TDP = T0 +

4.32

20

1

1.2 × 10−5√S

= 20 +

18000

√S

Connections

The critical temperature for steel connections is 550°C.
68

Retained fire-resistance time of protected steel beams and columns

From Tcr , the retained fire-resistance time tfr of protected steel columns against enclosure fire, in 

minutes, can be calculated from formulas that take into account (Notification 1433 p. 100, 102, 108, 

110):

- the properties of the insulating material, such as cross sectional area Ai, heated perimeter 

Hi, thermal resistance and heat capacity;

- the properties of the steel member, such as cross sectional area As and heated perimeter 

Hs;

- the fire exposure, such as the fire temperature rise coefficient α, the temperature rise delay 

time coefficient aw (due to insulation), and the member temperature rise coefficient h

(which depends on the steel cross section geometry).

tfr = max [

9866

α

3⁄2

{

2

h

{

1

ln{h

16 (Tcr − 20)⁄1250}

} +

aw

(Hi⁄Ai)

2

}, (

Tcr − 20

α

)

6

]

The member temperature rise coefficient h is:

h =

φK0

(Hs⁄As)

{1 +

φR

Hi⁄Ai

}{1 +

φC(Hs⁄As

)

2(Hi⁄Ai

)

}

φ = Hi⁄Hs = ratio of heated perimeters of insulation to steel section;

K0 = basic temperature rise rate (tabulated);

R = thermal resistance coefficient (depends on insulation and steel shape);

C = heat capacity ratio (depends on insulation).

aw,K0 and R are determined from heating tests of insulated steel members. The term aw

(Hi⁄Ai)

2

is the 

delay in temperature rise due to evaporation of water in the insulation.

4.3 Critical assessment

Much progress has been achieved in the last decade or so in moving beyond prescriptive methods that 

ensure a certain fire resistance rating by specifying minimum protection thickness or section 

dimensions. New performance-based methods allow the designer greater flexibility by providing 

guidance for calculating the temperature of members exposed to more realistic fires based on physical 

parameters, and more accurate determination of member temperature, stiffness and strength. The 

work of Takagi and Deierlein (2007, 2009) has been instrumental in improving the standards for fire 

design of steel structures in the USA and Canada, and making the prediction of behavior as close to 

computer simulation and experimental results as Eurocode is, while maintaining consistency of 

formulation with design equations at ambient temperature. 

AISC has a simple method, where boundary conditions are assumed unchanged from ambient 

temperature conditions, and an advanced method, that accounts for thermal expansion and changes in 

end conditions. In comparison, Eurocode offers the designer three methods of calculations, the 

intermediate one being an analysis of a part of the structure, wherein the boundaries of the part of the 

structure are unchanged from ambient, but within the part of the structure, thermal expansion and 

changes in boundary conditions and material properties are accounted for. Two additional things 
69

Eurocode has, but AISC does not, are guidance on connections in fire, and the temperature method. The 

latter is an alternative to the capacity method, whereby verification is carried out in the temperature 

domain, assuming a uniform temperature distribution and an utilization factor. The Japanese Building 

Standard Law has a simple limit formula for the deformation of beams and columns under fire, which 

AISC does not have.

Connections

Several codes contain prescriptive methods to ensure the strength of steel connections in fire, such as 

limiting the temperature in steel connections to 550°C (Japan), protecting connections with the 

maximum insulation thickness required for any of the connected members (New Zealand), or limiting 

the utilization of connections to not exceed that of the connected members (Eurocode, New Zealand). 

(At 550°C steel retains about 60 % of its yield strength Fy at ambient temperature and allowable stress 

design commonly uses 0.60 Fy as a limit.) In the Eurocode, the temperature of a joint may be calculated 

from the ratio of exposed area to volume of the connected members in the vicinity of the joint, or from 

the temperature of the bottom flange at midspan. Eurocode 3-1.8:2005 states that the fire resistance of 

a bolted or welded connection may be assumed to be sufficient if the fire protection on the connection 

is as effective on the joint as it is on the members, and the utilization of the joint is less than or equal to 

the maximum utilization of any of the connected members. In contrast, AISC 2011 14th Ed. Construction 

Manual Appendix 4 Structural Design for Fire Conditions presents only general structural integrity 

requirements for connections.

It is recommended that US performance code provisions for steel connections in fire be developed

beyond the present general structural integrity requirements. This development is particularly needed 

because elevated temperatures may cause new load paths to develop (e.g., development of tensile 

membrane action), and thermal expansion may cause gaps to close, thus potentially developing tension 

or compression in a connection, where none existed at ambient temperature. One promising approach 

is to extend to elevated temperatures the component method used in Eurocode 3-1.8:2005, whereby a 

joint is modeled as an assembly of rigid links and extensional springs, whose load-deformation curves 

represent different joint components that can be summed to represent the total joint response. The 

joint components may include tension, compression and shear zones. The tension zone may include 

bolts, column web, beam web in tension, column flange and end plate in bending; the compression zone 

may include beam flange, beam web, and column web; and the shear zone may include beam and 

column web panels and bolts. 

Research on connection behavior at elevated temperatures includes work by Da Silva et al. (2001), who 

used the ratios of strength to stiffness of various joint components and modified them to account for 

temperature effects by considering the sequence of yield of the components; and by Kirby (1995), who 

observed thread stripping in bolts tested between 530°C and 740°C. Recent finite-element calculations 

by Franssen (2004) showed that temperatures in joints are higher than predicted by Eurocode 

3-1.2:2005 (although still lower than in the connected members) because the dimensions of joint 

components are an order of magnitude smaller than those of the connected members, and the 

influence of the connected members can be felt in the joint. There is a need for a systematic study of 

the performance of connections in fire in order to move beyond prescriptive methods. 

Stress-strain curves

Takagi and Deierlein (2007, 2009) have shown the importance of using the complete stress-strain curve 

of steel at elevated temperatures, rather than just accounting for the influence of temperature on the 

yield strength and modulus of elasticity. It is recommended that better steel stress-strain relationships 
70

at elevated temperature be incorporated in future US performance building codes. Recent work at NIST 

is a step in that direction (Luecke et al. 2011):

for ε < Sy⁄E σ = Eε

for ε ≥ Sy⁄E σ = [RSy

0 + (k3 − k4Sy0

)exp (− (

T

k2

)

k1

) (ε −

RSy

0

E

)

n

] (

ε̇

ε0̇

)

m

where

E = E0 + e1T + e2T

2 + e3T3

R = exp [−

1

2

(

T

∗

r3

)

r1

−

1

2

(

T

∗

r4

)

r2

]

m = m0 + m3 [1 − exp (− (

T

m2

)

m1

)]

ε = ln(l⁄l0

) = true strain 

 = natural log of current length over original length;

Table 4.2 High-temperature

tensile data for structural steel

ε̇ = true strain rate; Parameter Value

ε0̇ = reference true strain rate = 8.333 × 10−5s

−1

 in ASTM E8; r1 5.708

σ = true stress = force / current area; r2 1.000

E = modulus of elasticity; r3 590°C

E0 = modulus of elasticity at room temperature; r4 919°C

R = retained strength, usually Sy/Sy

0

; k1 8.294

Sy = measured yield strength; k2 538°C

Sy

0 = measured yield strength at room temperature; k3 959 MPa

T = temperature °C; k4 0.766

T

∗ = T − 20; n 0.483

e1 , e2 , e3 = curve-fitting empirical constants; m0 0.0108

k1 , k2 , k3 , k4 = curve-fitting empirical constants; m1 7.308

m = strain rate sensitivity parameter; m2 613°C

m0 , m1 , m2 , m3 = curve-fitting empirical constants; m3 0.126

n = strain-hardening exponent; ε0̇ 8.333 × 10−5

s

−1

r1 , r2 , r3 , r4 = curve-fitting empirical constants. E0 206.0 GPa

e1 −4.326 × 10−2GPa/°C

An updated version of this model has been submitted to the e2 −3.502 × 10−5GPa/°C2

AISC Engineering Journal for publication (Luecke et al. 2013). e3 −6.592 × 10−8GPa/°C3

Unlike the Eurocode 3 formulation, the NIST model explicitly describes the time-dependent nature of 

the strength of steel at high temperature. For untested steels, it predicts the stress-strain behavior using 

only the measured room-temperature yield strength, Sy. On a subset of eight steels, the model predicts

the stress-strain behavior slightly better than the equally complicated Eurocode 3 model. For three 

structural steels from the literature and not used in the development of the model, the NIST constitutive 

relations and the Eurocode 3 model predict stress-strain behavior with similar quality.
71

Plate buckling

Compared with ambient temperature, the stress-strain curve of steel at elevated temperatures deviates 

from linearity at lower strains (see Appendix at the end of this chapter). This leads to lower plate 

buckling strength than the ultimate buckling load determined by equating the plate edge stress with 

yield stress (defined at 2% strain). Selamet and Garlock (2013) have shown that the direct mapping 

from ambient to elevated temperatures of the current equations for plate buckling strength can lead to 

unconservative predictions. Earlier criticisms by Takagi and Deierlein (2007, 2009) of the 

unconservativeness of this direct mapping in wide-flange sections led to changes in US and Canadian 

steel design specifications for compression and flexural members. It is recommended that the equations 

for plate buckling strength at elevated temperatures be updated, and a critical assessment be made of 

the possible need to revise other design equations due to the change in shape of the stress-strain curve 

at elevated temperatures. The adoption of a new stress-strain formulation similar to NIST proposal 

would be an additional reason to update steel design equations for fire.

Effects of temperature gradient 

Many of the simple design equations in US building codes assume a uniform temperature over the 

entire cross section, or even over the entire length of a member. When the temperature is not uniform, 

stresses redistribute from the hot parts of the cross section to the cooler parts. As the temperature 

increases, the hotter parts of the section reach their limiting temperature, yield plastically, and transfer 

load to cooler regions, which still behave elastically. This load transfer continues until the cool regions 

become plastic and the member fails. It is recommended that building codes account for temperature 

gradients where necessary with the aid of design equations, without requiring designers to perform a 

detailed finite-element analysis. 

Eurocode accounts for a temperature gradient along the beam depth for the purpose of evaluating the 

strength of joints. In a recent paper, Agarwal et al. (2014) proposed design equations for steel columns 

exposed to uneven heating by addressing additional limit states. They noted that thermal gradients in a 

column cross section can reduce the load carrying capacity for two reasons: column deformations due to 

uneven thermal expansion (bowing) and asymmetry in the column cross section due to uneven 

degradation of material properties (yield stress and elastic modulus).

References

American Institute of Steel Construction Steel (2011) “AISC Construction Manual, Appendix 4: Structural 

Design for Fire Conditions,” 14th Ed., AISC, Chicago, IL, USA

American Society of Civil Engineers (2007) “ASCE/SEI/SFPE 29-05 Standard Calculation Methods for 

Structural Fire Protection,” Reston, VA, USA

Canadian Institute of Steel Construction (2010) “Commentary on CSA S16-09 Annex K: Structural design 

for Fire conditions,” CISC, Markham, Ontario, Canada

Building Center of Japan (2011) “The Building Standard Law of Japan,” Tokyo, Japan

Eurocode 3: Design of steel structures- Part 1-2: General rules - structural fire design, BS EN 1993-1-

2:2005 also DIN EN 1993-1-2:2010-12, CEN, Brussels, Belgium
72

Eurocode 4: Design of composite steel and concrete structures- Part 1-2: General rules - structural fire 

design, DIN EN 1994-1-2:2010-12, EN 1994-1-2:2005 + AC:2008, CEN, Brussels, Belgium

European Convention for Constructional Steelwork (1985) “Design Manual on the European 

Recommendations for Fire Safety of Steel Structures,” Brussels, Belgium

International Code Council (2012) “International Building Code” Country Club Hills, IL, USA

Franssen, M. (2004) “Numerical determination of 3D temperature fields in steel joints,” Fire and 

Materials, 28, 63-82

Frater, G. (2010) “CIST Commentary on CSA S19-09 Annex K Structural Design for Fire Conditions,” 

Canadian Institute of Steel Construction, Markham, Ont., Canada

Harada, K., Ohmiya, Y., Natori, A., Nakamichi, A. (2004) “Technical basis on structural fire resistance 

design in building standards law of Japan” Fire and Materials, 28:323-341 DOI:10.1002/fam.857

Lane, B. (2008) “Approaches to calculating structural fire resistance,” NFPA Fire Protection Handbook, 

12th ed., Vol. II, Chap. 19.5, Cote, A.E. Ed. National Fire Protection Association, Quincy, MA. USA pp. 

19.77-19.126

Luecke, W., Banovic, S.W., and McColskey, J.D. (2011) “High-temperature tensile constitutive data and

models for structural steels in fire,” NIST Technical Note 1714, National Institute of Standards and 

Technology, Gaithersburg, MD 20899

Luecke, W. E., Gross, J. L., and McColskey, J. D. (2013) “High-temperature, tensile, constitutive models 

for structural steel in fire,” submitted to AISC Engineering Journal, AISC, Chicago, IL, USA

National Research Council Canada (2010) “National Building Code of Canada 2010” (NBCC), Institute of 

Research in Construction, Ottawa, ON, Canada, Vol. 2 Appendix D: Fire-performance Ratings

Selamet, S. and Garlock, M. (2013). "Plate Buckling Strength of Steel Wide-Flange Sections at Elevated 

Temperatures." ASCE J. Struct. Eng., 139 (11), 1853-1865, online 3 Nov 2012 

http://dx.doi.org/10.1061/(ASCE)ST.1943-541X.0000769

Standards Australia (1998) “Steel structures,” AS 4100-1998, Section 12: Fire, Homebush, NSW, Australia

Standards New Zealand (1997) “Steel structures standard,” NZS 3404:Part 1:1997, Wellington, NZ 

(current in 2013) Chapter 11: Fire

Takagi, J. and Deierlein, G.G. (2007) “Strength design criteria for steel members at elevated 

temperatures,” Journal of Constructional Steel Research, Elsevier, 63, 1036–1050

Takagi, J. and Deierlein, G.G. (2009) “Proposed design equations for CAN/CSA S16 Appendix K Provisions

for steel members at high temperatures,” Report prepared for the Canadian Institute of Steel 

Construction, Jan. 22
73

Wickstrom, U. (2008) “Methods for predicting temperatures in fire-exposed structures,” SFPE Fire 

Protection Engineering, 4th ed. Chapter 4.9, Society of Fire Protection Engineers, Bethesda, MD. USA

Appendix: 2% yield strain and 0.2% proof strain

Figure 4.5: Eurocode (CEN 2001) stress-strain curves of steel at elevated temperatures 

from 100°C to 900°C with yield stresses: σy,2% (red hollow circles, 2% strain) and σy,offset

(red squares, 0.2% proof or plastic strain). From Selamet and Garlock (2013).

Copyright 2013 American Society of Civil Engineers, reprinted with permission
74

Chapter 5 Reinforced Concrete Structures

The simplest and most common method for the fire design of reinforced concrete (RC) members is to 

ensure that sections have the required thickness, and reinforcement the required cover. In addition, 

well detailed reinforcement with adequate tying enables moment redistribution, and axial restraint 

allows arch/membrane action to occur in fire events. 

5.1 Calculation methods for concrete in USA

Building codes for concrete structures in the US differentiate between aggregate types, with carbonate 

concrete having better spalling resistance to fire than siliceous concrete. Member size and cover 

thickness are given for restrained or unrestrained beams and slabs, for prestressed or passively 

reinforced members. Continuous unrestrained members have longer fire endurance than simply 

supported members because they can redistribute moments, resulting eventually in failure of negative 

reinforcement over the supports. In concrete design for ambient conditions, the amount of negative 

reinforcement is limited to avoid compressive, brittle failure of the member.

5.1.1 ASCE/SEI/SPFE 29-05 Standard Calculation Methods for Structural Fire Protection

This standard provides methods to calculate the equivalent fire resistance, in terms of hours, of 

concrete, timber, masonry and steel members that would be achieved under the standard ASTM E119 

(2012) fire test. It does not provide any guidance about the structural performance of members or 

structures under fire. The guidelines apply to concrete with specified compressive strength less than 

10 000 psi or 69 MPa. 

Walls: The minimum equivalent thickness to provide equivalent fire resistance of one to four hours is 

given for load bearing and non-bearing walls of different types of plain and reinforced concrete. Joints 

between precast concrete wall panels must be insulated and guidance is also given about the thickness 

required for different types of insulation.

Floor and roof slabs: The minimum equivalent thickness to provide equivalent fire resistance of one to 

four hours is given.

Table 5.1 Fire resistance of concrete walls, floors and roofs

Minimum Equivalent Thickness for Fire Resistance Rating (h)

Concrete Aggregate 1 h 1.5 h 2 h 3 h 4 h

Type in. mm in. mm in. mm in. mm in. mm

Siliceous 3.5 89 4.3 109 5.0 127 6.2 157 7.0 178

Carbonate 3.2 81 4.0 102 4.6 117 5.7 145 6.6 168

Sand-lightweight 2.7 69 3.3 84 3.8 97 4.6 117 5.4 137

Lightweight 2.5 64 3.1 79 3.6 91 4.4 112 5.1 130
75

Concrete cover over reinforcement: The minimum concrete cover over prestressed or passive positive 

moment reinforcement for floor, roof slabs and beams to provide an equivalent fire resistance of one to 

four hours is given. For slabs and beams, different minimum concrete cover thicknesses apply for 

restrained or unrestrained (free to expand under temperature change) situations. 

Table 5.2 Minimum cover for non-prestressed reinforcement in concrete beams

Thickness of Cover for Fire Resistance Rating

Beam Width 1 h 1.5 h 2 h 3 h 4 h

in. mm in. mm in. mm in. mm in. mm in. mm

Restrained

5 127 3/4 19 3/4 19 3/4 19 1 25 1 1⁄4 32

7 178 3/4 19 3/4 19 3/4 19 3/4 19 3/4 19

≥ 10 ≥ 254 3/4 19 3/4 19 3/4 19 3/4 19 3/4 19

Unrestrained

5 127 3/4 19 1 25 1 1⁄4 32 — — — —

7 178 3/4 19 3/4 19 3/4 19 1 3⁄4 44 3 76

≥ 10 ≥ 254 3/4 19 3/4 19 3/4 19 3/4 19 1 3⁄4 44

Columns: The minimum dimension of RC columns of different types of concrete for fire resistance rating 

of 1 to 4 h is given.

Table 5.3 Minimum concrete column dimension

Minimum Column Dimension

Concrete Aggregate 1 h 1.5 h 2 h 3 h 4 h

Type in. mm in. mm in. mm in. mm in. mm

Siliceous 8 203 9 229 10 254 12 305 14 356

Carbonate 8 203 9 229 10 254 11 279 12 305

Sand-lightweight 8 203 81⁄2 216 9 229 101⁄2 267 12 305

5.1.2 ACI 216.1-07/ TMS 0216-07 

Code requirements for determining the fire resistance of concrete and masonry assemblies

Fire resistance rating is measured in terms of hours of exposure to the standard fire defined by ASTM 

E119 (2012), e.g., the fire rating for siliceous aggregate concrete with a minimum equivalent thickness 

of five inches (127 mm) is two hours. Formulas are provided to calculate the equivalent thickness of 

non-uniform sections, such as ribbed or undulating panels, and sections consisting of multiple layers. 

The code also gives minimum cover thickness to protect prestressed or passive steel reinforcement 

against fire. Distinction is made between restrained and non-restrained members. Most cast-in-place or 

precast construction is restrained, whereas single spans and simply-supported end spans of multiple 

bays are unrestrained. For example, the minimum cover for the non-prestressed reinforcement of a 

restrained beam rated for two hours is 3⁄4 in (19 mm). The data is the same as presented above since the 

ASCE 29-05 standards are taken from ACI 216.

Normal design procedures for concrete structures apply, with the material properties as functions of 

temperature (Fig. 5.1). 
76

Strength of flexural reinforcement steel bar and 

strand at high temperatures

Compressive strength of siliceous aggregate 

concrete at high temperatures and after cooling

Compressive strength of carbonate aggregate 

concrete at high temperatures and after cooling

Compressive strength of semi-lightweight 

concrete at high temperatures and after cooling

Figure 5.1 Strength of various types of reinforcement and concrete at high temperatures (ACI 216.1-07)

Copyright 2007 American Concrete Institute International, reprinted with permission

The unfactored full service load (i.e., load factor of 1.0 for both dead and live loads) is assumed constant 

for the entire fire resistance period. The compressive strength of various types of concrete and the 

tensile strength of steel bars and prestressed steel are given as functions of temperature in the form of 

graphs. The strength of concrete hotter than 1400°F (760°C) is neglected, thus resulting in a reduced 

effective depth. 

For continuous beams and slabs, the fire resistance of flexural members is determined by the value of 

the redistributed maximum positive moment. As a continuous beam or slab is heated from below, its 

bottom expands more than its top, resulting in the ends tending to lift off, positive moments to decrease 

and negative moments at interior supports to increase. It is therefore advantageous to increase the 
77

negative moment capacity. This will be explained in greater detail below (Figs. 5.3 and 5.5). To avoid 

compressive failure in the negative moment region, however, the tension reinforcement in these 

regions is limited to ω = ρ fy fc ⁄

′ ≤ 0.30, where ρ = As⁄(bd), As

is the area of steel reinforcement of 

yield strength fy, fc

′

is the concrete compressive strength, and b and d are the width and depth of the 

beam or slab strip. The negative moment reinforcement should be long enough to accommodate the 

redistributed moment and the change in location of inflection points. More details are provided below 

in ACI 216R-89 Guide for Determining the Fire Endurance of Concrete Elements.

The code provides minimum dimensions for columns with concrete strength less than 12 000 psi (83 

MPa) for fire ratings from one to four hours. The fire rating of steel columns protected by concrete 

depends on the thickness of the concrete, its degree of moisture, as well as the perimeter to weight 

ratio of the steel section. 

ACI 216.1-07 includes charts that provide the temperature θ for various exposure time t, concrete depth

u from the fire exposed surface, and types of aggregate (Fig. 5.2). For concrete masonry, the code 

provides guidance on how to calculate an equivalent thickness, and how to apply that thickness to 

calculate the fire rating of steel columns protected by concrete masonry.

at 1 hour of fire exposure at 2 hours of fire exposure

Figure 5.2 Temperature distribution in a normal weight concrete rectangular unit (ACI 216.1-07)

Copyright 2007 American Concrete Institute International, reprinted with permission
78

5.1.3 ACI 216R-89 Guide for Determining the Fire Endurance of Concrete Elements

(Reapproved 2001, now discontinued by ACI. Although discontinued, it is covered here because of its 

usefulness for understanding the update in SFPE 29, discussed in Section 5.1.5 of this chapter.)

This guide provides the empirical data, the methods and examples for calculating the fire endurance of 

concrete beams, columns, walls, and one-way and two-way slabs. The Guide includes charts that 

provide the temperature θ for various exposure time t, concrete depth u from the fire exposed surface, 

and types of aggregate. It also includes curves that give the strength at various temperatures of 

reinforcing steel and concrete of various aggregates. From these graphs, the temperature of the bottom 

steel (u is calculated at the center of the bar, i.e., at concrete cover plus bar radius) and of the top 

concrete can be determined. For corner bars, u is divided by two. The depth of the rectangular stress 

block and the nominal moment capacity are calculated from the familiar formulas:

aθ =

Asfyθ

0.85 bfcθ

′

Mnθ = Asfyθ(d − aθ⁄2)

where

aθ = depth of the rectangular stress block at temperature θ;

As = area of bottom steel reinforcement;

b = width of beam or slab strip;

d = section depth;

fcθ

′ = concrete strength at temperature θ;

fyθ = yield strength of steel at temperature θ;

Mnθ = nominal bending capacity at temperature θ.

Since fcθ

′

is evaluated at aθ⁄2, iterations are theoretically required to calculate aθ. In practice, the top 

concrete remains fairly cool and its properties are close to ambient. Thus, the computational method to 

calculate the nominal (positive) bending capacity Mnθ of a beam or a one-way slab exposed for a time t

to a fire from below follows the standard procedure, but with the material properties modified from 

ambient to temperature θ.

A similar procedure is followed for the computation of the nominal negative moment capacity. Here, the 

top steel is relatively cool, and its properties are close to ambient. The bottom concrete is directly 

exposed to fire, and any concrete whose temperature exceeds 1400°F (760°C) is deemed to have lost its 

strength. The method therefore includes an additional step, which is the determination from charts of 

the depth of the concrete rendered ineffective.

Continuous beams and slabs

As continuous beams and slabs are heated from below, their bottom expands more than their top, thus 

causing the ends to lift and more moment to redistribute to the interior supports while positive 

moments decrease. The Guide provides a method to account for this effect (Figs. 5.3 and 5.5): 
79

1. From statics, express the moment equation for an end span of length l heated to a temperature 

θ. For a beam uniformly loaded by w, with one end simply supported, the nominal positive 

moment Mnθ

+

at x1 is:

Mx1 =

wlx1

2

−

wx1

2

2

−

Mnθ

−

x1

l

= Mnθ

+

where Mnθ

−

is the negative nominal moment at the interior support at temperature θ. 

2. Calculate the location x1 from the simple support of the maximum positive moment by 

differentiation:

x1 =

l

2

−

Mnθ

−

wl

3. Calculate the negative moment at the interior support from the previous two steps:

Mnθ

− = m − 2m (√Mnθ

+ ⁄m) where m = wl

2⁄2

@ 3 hr

Figure 5.3 Moment diagram for one half of a continuous

three-span beam before and during fire exposure (ACI 216R-89)

Copyright 1989 American Concrete Institute International, reprinted with permission
80

Restraint to thermal expansion

If restraint to thermal expansion is provided, a compressive thrust develops near the bottom of the slab. 

Its line of action rises as the fire progresses, but remains below the section centroid even after the 

maximum downward deflection is subtracted. Thus the thrust acts as a prestressing force which causes 

the slab to deflect upward. Restraint to thermal expansion increases the positive nominal moment and 

the fire resistance considerably. The procedure to account for it is complicated, even with the aid of 

nomographs (Fig. 5.4):

1. Determine the temperature distribution at the fire exposure duration;

2. Determine the retained nominal moment capacity Mnθ at that temperature;

3. If the applied moment M < Mnθ, there is no need to calculate the restraint to thermal 

expansion. If M ≥ Mnθ, calculate midspan deflection;

4. Estimate the line of action of the thrust;

5. Calculate the required thrust T;

6. Calculate the thrust parameter T⁄(AE) where A is the gross section area resisting the thrust 

and E is the modulus of elasticity of concrete at ambient temperature; 

7. Calculate Z

′ = A⁄s, where s is the heated perimeter of the section resisting the thrust;

8. From Z

′

and T⁄(AE), find the strain parameter ∆l⁄l using nomographs (Fig. 4); 

9. Calculate ∆l by multiplying the strain parameter with the length of the heated member;

10. Determine if the supports can provide T with a displacement no greater than ∆l.

Figure 5.4 Nomographs relating thrust parameter, strain parameter, 

and ratio of cross-sectional area to heated perimeter (ACI 216R-89)

Copyright 1989 American Concrete Institute International, reprinted with permission

Fire resistance of reinforced concrete columns

Columns larger than twelve inches (305 mm) in diameter or side are assigned a fire resistance of three 

or four hours in most building codes in North America. The Guide provides test results that support this 

recommendation. 
81

5.1.4 USA: The International Building Code IBC 2012 

Chapter 7 Fire and Smoke Protection Features.

These standards provide methods to calculate the equivalent fire resistance, in terms of hours, of 

concrete, timber, masonry and steel members, that would be achieved under the standard ASTM E119 

fire test. It does not provide any guidance about the structural performance of members or structures 

under fire.

Table 721.1 of IBC 2012 prescribes the minimum thickness of various types of insulation for various fire 

resistance ratings (FRR) of structural members. For example, an FRR of 3 h requires a 2 in (50 mm) 

protective cover of concrete for a steel column. Table 722.2.3 prescribes the minimum cover thickness 

for reinforced (RC) or prestressed concrete (PC) slabs and beams. Table 5.4 presents an excerpt for a 3h 

FRR.

Table 5.4 Excerpt from IBC Table 722.2.3 for an FRR of 3 h

restrained unrestrained

slab RC 3⁄4 in (19 mm) 11⁄4 in (32 mm)

Slab, siliceous aggregate PC 3⁄4 in (19 mm) 23⁄8 in (60 mm)

beam 7 in (178 mm) wide RC 3⁄4 in (19 mm) 13⁄4 in (44 mm)

beam 8 in (203 mm) wide PC 13⁄4 in (44 mm) 5 in (127 mm)

For concrete floors, walls and partitions, an FRR of 3 h requires a minimum thickness of 6.2 in (157 mm) 

for siliceous aggregate concrete and 5.7 in (145 mm) for carbonate aggregate concrete respectively

(Table 721.1 of IBC 2012). For RC columns with concrete strength less than 12 000 psi (83 MPa), an FRR 

of 3 h requires minimum dimensions of 12 in (305 mm) for siliceous aggregate, 11 in (279 mm) for 

carbonate aggregate, and 10.5 in (267 mm)for sand-lightweight concrete. For concrete strength greater 

than 12 000 psi (83 MPa), the minimum column dimension is 24 in (610 mm) for FRR between 1 and 4 h.

Chapter 7 of IBC also provides guidance on how to calculate fire resistance for situations not covered by 

tables. For example, for ribbed or undulating panels, an equivalent thickness is defined based on the 

ratio of the net cross sectional area to the width. 

5.1.5 The Society of Fire Protection Engineers

(Analytical methods for determining fire resistance of concrete members, C. Fleischmann, A. Buchanan, 

and J. Chang, SFPE Handbook of Fire Protection Engineering, 4th Ed. 2008) presents equations for 

calculating the fire resistance of simply supported beams and slabs, continuous unrestrained flexural 

members, and members restrained against thermal expansion. It also gives formulas for computing the 

axial thrust in members restrained against thermal expansion and heated from below. The effect is 

similar to that of a prestressing force, as presented (above) in the discontinued ACI 216 R-89 ACI Manual 

of Concrete Practice, of which the SFPE chapter can be considered to be an update.
82

The SFPE chapter generalizes the redistribution of moments for continuous unrestrained flexural 

members under fire to the case of unequal end moments Mnθ1

−

and Mnθ2

−

. The minimum positive 

moment Mnθ

+

at temperature θ required for a beam of length L uniformly loaded by w is (Fig. 5.5):

Figure 5.5 Redistributed applied bending moment diagram

(Fleischmann et al., SFPE Handbook of Fire Protection Engineering, 4th Ed. 2008)

Copyright 2008 Society of Fire Protection Engineers, reprinted with permission

Mnθ

+ =

(Mnθ1

− − Mnθ2−

)

2

2wL

2 −

Mnθ1

− + Mnθ2−

2

+

wL

2

8

This moment occurs at a distance from end 1 of: 

x1 =

L

2

+

Mnθ1

− − Mnθ2−

wL

When Mnθ1

− = 0 , one obtains the moment redistribution formulas of ACI 216R-89 for a simply 

supported end span. The thrust due to restraint of thermal expansion helps reduce the length of the top 

bars. The following procedure is used to account for this effect:

1. Because negative reinforcement generally yields early in fire due to moment redistribution, 

design reinforcement for the maximum (not the actual) negative moment Mmax

− that the section 

can bear at an interior support. 

2. Calculate the distance from the first interior support to the point of inflection (zero moment), 

assuming full dead load and half live load x0 = 2Mmax

− ⁄(wL) .
83

3. Use ACI specifications for the development length of the top bars beyond the inflection point 

(1/16 of clear span or 12 bar diameters, whichever is greater).

4. If desired, use resistance to thermal expansion to reduce Mmax

− and length of top bars. Start 

with the bar length required for gravity loading only and calculate the corresponding negative 

moment Mn

− = x0wL⁄2. The thrust T caused by resistance to thermal expansion must 

produce MT = Mmax

− − Mn− to reduce the bar length required under fire to the same length as 

under gravity only.

5. Assume the location of the thrust T, say 12 mm from the bottom (Table 5.5 provides the 

estimation of location), and calculate T from MT , the deflection ∆ (assumed to be 0), and an 

assumed depth of the compression stress block aθ

+

. Check that the assumed stress block is 

correct by equilibrium T = MT

(dT − ∆ − aθ

+ ⁄ ) = 0.85 fc

′b aθ

+

 (b is section width).

Table 5.5 Location of thermal thrust line

*distance above bottom of member; h = overall depth of the joist and slab

6. Calculate the axial strain caused by T acting on the entire section, and the ratio Z of section 

area to heated perimeter. Use nomographs (Fig. 5.4) to read the counteracting strain the rest of 

the structure must provide to resist thermal expansion.

7. Verify that the structure has the strength and stiffness to resist the thrust and expand no more 

than calculated in step 6.

8. Verify that the bar length is sufficient in the absence of resistance to thermal expansion under 

the actual negative moment.

Reinforced concrete columns

Reinforced concrete columns generally perform well under fire because:

 columns are large enough to prevent the core from losing significant strength even during 

prolonged fire exposure;

 ties or spirals contain the concrete within the core; and

 the vertical reinforcing bars are protected by at least 48 mm (1 7⁄8 in) of cover.

Reinforced concrete frame

Individual members can be designed for fire by simplified methods, but moment-resisting frames 

require detailed computer analysis. 

Reinforced concrete walls

Usually heat transmission rather than load bearing governs the fire endurance of walls.

Type of construction Fire exposure (hour) Location of thrust line at supports*

Solid slab 2

3

4

25 mm (1 in)

32 mm (1 1⁄4 in)

38 mm (1 1⁄2 in)

Slab-and-joist ≤ 2

2 to 4

0.1 h

0.15 h
84

5.1.6 Spalling prevention measures in USA

There is no specific recommendation.

5.2 Calculation methods for concrete in Europe

Eurocode 2: Design of concrete structures – Part 1-2: general rules – structural fire design (includes AC 

2008) English translation of DIN EN 1992-1-2:2010-12

EC 2-1-2 allows three levels of analysis: individual members, part of the structure, and global analysis. 

For individual member analysis, only the effects of thermal deformations resulting from thermal 

gradients across the cross section need to be considered, but thermal expansion and changes in 

boundary conditions from ambient conditions may be ignored. For analysis of part of the structure, the 

boundary conditions of the part are assumed unchanged from ambient conditions, but within the part of 

the structure to be analyzed, changes in material properties, thermal expansion and deformations are 

accounted for. Finally, for global analysis, all relevant modes of failure, changes in material properties 

and boundary conditions, thermal expansion and deformation are considered.

For standard fire exposure, members must satisfy three criteria:

- E for integrity or maintenance of fire and smoke separation function;

- I for insulation or limiting the temperature on the unexposed faces;

- and R for load bearing.

EC 2-1-2 provides tables for minimum dimensions, minimum cover thickness and design criteria for 

beams (R), columns (R), walls (R, E, I), and slabs (R, E, I). For example, for a rectangular column exposed 

to fire on more than one side, and loaded to a degree of utilization (defined as the ratio of design axial 

load in fire to design resistance at ambient temperature) of 0.5, a standard fire resistance of R90 (in 

minutes) requires a minimum column width of 300 mm and a minimum cover of 45 mm (defined as the 

distance from the center of the main bars to the nearest exposed surface and called axis distance).

The most commonly used design tool, recognized by EC 2-1-2, for concrete members in a compartment 

with a post-flashover fire is the 500°C (932°F) isotherm originally developed by Anderberg (1993). In this 

simplified method, concrete is assumed to have full ambient strength at temperatures less than 500°C, 

and zero strength above 500°C. The reinforcement, however, has reduced strength depending on the 

temperature. If the residual capacity, calculated according to these simple rules, is sufficient to carry the 

load factored for the fire limit state, then the section is deemed acceptable. EC2 provides 500°C

isotherms for various sections (beams, columns and thick slabs) at 30, 60, 90, 120 min of a standard fire. 

As an alternative, EC2 also allows the use of advanced calculation methods, which entail a heat transfer 

analysis and a structural analysis following fundamental physical behavior. The advanced analysis of 

concrete structures in fire must account for the degradation of material properties at elevated 

temperatures (Fig. 5.6). Nonlinear behavior of the structure must often be modeled as well. Due to the 

low thermal conductivity of concrete, an accurate representation of temperature gradients is necessary 

(Section 5.2.1). If moisture content is neglected, results would tend to be conservative as the thermal lag 
85

due to water evaporation at 100°C is not observed. Cracking is usually deduced from high tensile strain 

regions, as in a smear crack model. Spalling is usually not modeled explicitly, but the thickness of the 

spalled layer can be assumed and removed at appropriate stages in the analysis (Lane, 2008). 

Figure 5.6 Coefficient kc

(θ) for decrease of characteristic strength fck of normal weight concrete 

with siliceous (solid line) or calcareous aggregates (dashed line) (data from EN 1992-1-2:2010)

An intermediate method, detailed in Annex B of EC2-1-2, is the zone method for calculating fire 

resistance to bending moments and axial forces. The zone method applies to small sections and slender 

columns fully engulfed in a post-flashover fire modeled as a standard fire. The zone method divides the 

member into three or more zones of near equal temperature, calculates the capacity of these zones 

using material properties at elevated temperatures, and sums them up. Typically, a zone of damaged 

concrete at the surface does not contribute to the section capacity.

Annex D provides a simplified calculation method for shear, torsion and anchorage. Shear resistance in 

fire can be a problem for precast, pretensioned members with thin webs. Stirrups conduct heat 

efficiently and achieve a near uniform temperature over their length. As they pass through zones with 

different temperatures (the top of a beam is generally cooler than the bottom and the corners), the 

usual assumption of assigning to the reinforcing steel the same temperature as to the concrete is not 

strictly true.

Annex E provides simplified methods for the fire design of beams and slabs with uniform loading 

amenable to linear analysis at ambient temperature. As well, it provides simplified methods for simply 

supported beams and slabs and for moment redistribution (not to exceed 15 %) in continuous members. 

In particular, it provides a formula for the curtailment length of reinforcement over the supports, which 

should be checked because the point of contra-flexure may have moved due to elevated temperatures. 

What it does not provide is a simplified method for axially restrained beams and slabs, as can be found 

in the SFPE Handbook of Fire Protection Engineering. Axial restraint results in thrust, which is equivalent 

to additional reinforcement.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 1000 1200

Strength reduction factor 

kc

Temperature °C
86

5.2.1 Simple one-dimensional thermal calculation for concrete (Wickstrom, 2008)

According to Eurocode 2, for standard fire exposure (defined in ISO 834) and normal weight concrete, 

the temperature at time t (in hours) and any depth x (in meters) inside a concrete slab uniformly 

heated on one surface is:

Tx = (1 − 0.062 t

−0.88)[0.16 ln (t x2 ⁄ ) − 0.70] 345 log (480 t + 1)

Wickstrom (1989) extended this approach to various parametric fires and material properties.

5.2.2 High strength concrete

EC 2-1-2 Section 6 addresses high strength concrete and provides strength reduction factors at high 

temperatures (Fig. 5.7).

Figure 5.7 High strength concrete strength reduction factor (fc,θ⁄fck) at high temperatures for 

Class 1 (C55/67 and C60/75), Class 2 (C70/85 and C80/95) and Class 3 (C90/105) concrete. 

Class (fck,cylinder/fck,cube), fck = characteristic strength (data from EN 1992-1-2:2010).

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200

Strength reduction factor

Temperature°C

Class1

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200

Strength reduction factor

Temperature°C

Class 2

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200

Strength reduction factor

Temperature°C

Class 3

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000 1200

Strength reduction factor

Temperature°C

Class1

Class 2

Class 3
87

In general, the same methodology applies as for normal strength concrete, but with a factor k. For 

columns and walls, the reduced concrete thickness is calculated from the depth of the 500°C isotherm 

increased by k, which in effect changes the isotherm to 460°C for Class 1 and 400°C for Class 2 (caption 

of Fig. 5.7 defines classes). For beams and slabs, the calculated moment capacity corresponding to the 

500°C isotherm is reduced by a factor 0.85 ≤ km ≤ 0.98.

5.2.3 Spalling

An important phenomenon to consider for concrete in fire is spalling, which is due to the build-up of 

pressure caused by the evaporation of water in the pores. The major factors affecting spalling are:

- concrete strength, with high strength concrete more susceptible to spalling than normal 

strength concrete.

- the type of aggregate; limestone aggregates are less susceptible to spalling than silica, quartzite 

and granite aggregates; and concrete that uses manufactured lightweight aggregates is found 

unlikely to spall.

- the heating rate; a faster rate increases the risk of spalling.

- the dimensions of the member and cover thickness.

- large compressive stresses, and the amount of restraint against thermal expansion.

- high moisture content (over 5 % by volume or 2 % to 3 % by mass of dense concrete).

- the most important parameter is the permeability, which can be controlled by the addition of 

polypropylene fibers. 

For covers exceeding 40 mm to 50 mm, the use of the following measures to alleviate spalling is 

acceptable:

- a protective layer of plaster, vermiculite or similar material, sprayed or applied manually;

- a false ceiling as a fire barrier;

- lightweight aggregates;

- sacrificial steel, such as welded steel fabric placed within the concrete cover at 20 mm from the 

concrete face.

In addition, Eurocode EC 2-1-2 recommends limiting the moisture content of concrete to control 

explosive spalling. The recommended limiting moisture content by mass is mc = 3 %. If the moisture 

content exceeds mc , spalling effect on load bearing may be assessed by assuming local loss of cover to 

one reinforcing bar or bundle of bars in the cross section, then calculating the ensuing rise in 

temperature and the reduced load bearing function R. Eurocode provides specific provisions for 

prevention of spalling in high strength concrete. For concrete with cube strength between 55 MPa and 

80 MPa, or cylinder strength between 67 MPa and 95 MPa (55/67 < C grade < 80/95), and with fly ash 

content less than 6 % of cement weight, the recommendations for normal strength concrete apply. If 

the fly ash content is higher than 6 %, further measures are necessary. Likewise, for 

80/95 < C grade < 90/105, at least one of the following measures must be provided:

A. A reinforcement mesh with nominal cover of 15 mm, wire diameter not less than 2 mm, pitch 

not more than 50 mm × 50 mm. The nominal cover to the main reinforcement should not be 

less than 40 mm.
88

B. Show by testing or experience that the concrete used exhibits no spalling under fire exposure.

C. Protective layers demonstrated to prevent spalling under fire.

D. Include in the concrete mixture more than 2 kg/m3 of monofilament polypropylene.

If it can be shown (by member virtual removal) that a frame remains stable when an individual member 

has lost its strength due to a local fire, then spalling prevention is not required for that member. 

Normally, members impinged on by flames, or whose reinforcement cover temperature exceeds 100°C,

must be designed to prevent spalling (Lane 2008). 

5.3 Calculation methods for concrete used in New Zealand and Australia

New Zealand Standards Concrete Structure Standard - Part 1: The design of concrete structures

NZS 3101: Part 1: 2006, with amendments Aug. 2008, Chapter 4: Design for fire resistance

The standards start out by mentioning performance criteria: “A member shall be designed to have a fire 

resistance rating (FRR) for each of structural adequacy, integrity and insulation equal to or greater than 

the required fire resistance. The criteria for integrity shall be considered to be satisfied if the member 

meets the criteria for both insulation and structural adequacy for that period, if applicable.”

To achieve these performance criteria, prescriptive tables are provided for minimum dimensions 

corresponding to various FRR (from 30 to 240 minutes) for the structural adequacy of slabs and simply 

supported or continuous beams. Similar tables are provided for columns and walls, with an additional 

parameter, namely, the load level ηfi , taken as 0.7 or calculated as ηfi = Nf

∗⁄Nu , where Nf∗

is the 

factored design axial load in fire conditions, and Nu is the axial load capacity at normal temperature. The 

standard provides guidance on the thickness of insulation required to achieve a given FRR, and also 

allows the calculation of FRR by recognized methods, such as Eurocode 2. 

Australian Standards AS 3600 - 2009 Concrete structures

AS 3600, like NZS 3101, specifies minimum dimensions and cover thickness for concrete sections to 

achieve a given fire rating or duration of resistance to a standard fire. Standard calculation methods are 

used, but with material properties at ambient replaced by those at elevated temperatures.

Spalling prevention measures in Australia and New Zealand

There are no specific recommendations, but reference is made to British Standards BS 8110 Part 2, 

Clauses 4.1.6 and 4.1.7. These are similar to Eurocode provisions described above.

5.4 2010 National Building Code of Canada, 

Division B, Appendix D, Fire Performance Rating

This Appendix prescribes minimum dimensions and cover thickness for various structural members. 

Table D-2.2.1.A lists the minimum thickness of reinforced and prestressed concrete floor and roof slabs, 
89

e.g., for 1 h fire resistance rating, the minimum thickness for type S concrete is 90 mm, for type N, it is 

87 mm, and for type L40S or Type L concrete, it is 72 mm. Table D-2.2.1.B gives the minimum concrete 

cover over reinforcement in concrete slabs, e.g., for 1 h fire resistance rating, the minimum cover for 

type S, N, L40S or L concrete is 20 mm for reinforced concrete (RC) slabs, and 25 mm for prestressed 

concrete (PC) slabs. Table D-2.6.1.A provides the minimum thickness of concrete or masonry protection 

to steel columns, e.g., for an FRR of 1h, monolithic concrete protection of 25 mm is required. Table D2.9.1 shows the minimum cover to principal steel reinforcement in RC beams, e.g., for 1 h rating, 20 mm 

is required. Table D-2.10.1 specifies the minimum cover over steel tendons in PC beams, e.g., for beams 

made of type S or N concrete and with areas between 260 and 970 cm2, 1 h rating requires 50 mm

minimum cover. 

The minimum dimensions of a rectangular RC column is required to be t (mm) = 75 f (R+1) for all types L 

and L40S concrete, where R is the required fire resistance rating in hours and f is a factor that depends 

on the effective length factor k, the unsupported length h of the column, the ratio ρ of vertical 

reinforcement area to column area, and the overdesign factor ODF, which is the ratio of the calculated 

load carrying capacity to the column strength required to carry the specified loads. For example, f = 1.2 

for ODF = 1.00, 3.7 m < kh ≤ 7.3 m, t ≤ 300 mm, and ρ ≤ 3%. For R = 3 h, t = 75 × 1.2 (3+1) = 360 mm > 

300 mm. Therefore choose f = 1.0 (all other cases) and t = 75 × 1.0 (3+1) = 300 mm (Section D2.8.2). 

Supporting members are required to have an FRR not less than that of the supported members.

CSA Standard A23.3-04 (2004) Design of concrete structures

This standard has no specific provisions concerning fire.

5.5 The Building Standard Law of Japan, August 2011

The code gives minimum dimensions and cover thickness for RC members (Hasegawa, 2013).

Table 5.6 Minimum dimensions and cover thickness for RC members

Member Fire resistance 

time, min

Minimum 

dimension, mm

Minimum cover 

thickness, mm

Load bearing walls 60 70 30

120 100 30

Columns 60 30

120 250 30

180 400 30

Beams 60, 120,180 30

Floors 60 70 20

120 100 20

In general, when the minimum cover depth is 20 mm larger than the cover depth required for normal 

environment, the verification for fire resistance can be omitted. For normal environment, cover 

thickness is specified to alleviate corrosion due to carbonation. When no fire resistance is required, the 

minimum concrete cover is the larger of the reinforcing bar diameter and the cover that meets 

durability requirement, plus a margin of construction error (Standard specifications for concrete 

structures - 2007).
90

Notification 1433, Reinforced concrete (RC) members, p. 104

This document provides detailed calculation methods for fire resistance. The retained fire resistance 

time of RC columns and beams depends on the thermal degradation depth and should not be less than 

the time it takes the fire to reach a temperature of 480°C. RC columns and beams with standard 

strength at normal temperature Fc ≤ 60 MPa , minimum width/length ≤ 10 and concrete cover ≥ 3 cm, 

have retained fire resistance time tfr in minutes:

tfr = max

{

 

 

16772(cd)

2

α

3⁄2 (ln 0.673

(cd)

1⁄3

)

2

, (

480

α

)

6

}

 

 

where

α = fire temperature rise coefficient (°C/min1/6). The fire temperature Tf°C is (Chapter 3):

Tf = α t

1⁄6

, with t = time (min);

c = thermal property coefficient = 0.21 for normal concrete, 0.23 for lightweight concrete;

d = thermal degradation depth mm.

For RC columns, a thermal degradation depth (p. 104) less than twice the concrete cover is calculated 

for columns loaded beyond (2⁄3)FcAc

d = min {

Ac − 3P (2Fc ⁄ )

Hc

, 2ds}

Ac = column cross section area;

Hc = heated perimeter of column cross section;

P = compressive force on column;

ds = minimum value of concrete cover in heated parts.

For RC beams a similar but more complicated equation is provided for the thermal degradation depth.

RC walls

RC load-bearing walls with standard strength at normal temperature Fc ≤ 60 MPa and concrete cover 

≥ 3 cm, have retained fire resistance time tfr in minutes:

tfr = min

[

 

 

 

 

max

{

 

 

16772(cd)

2

α

3⁄2 (ln 0.673

(cd)

1⁄3

)

2

, (

480

α

)

6

}

 

 

,

118.4 cDD

2

α

3⁄2

]

 

 

 

 

where

cD = thermal insulating coefficient = 1.0 for normal concrete, 1.2 for lightweight concrete. 

D = wall thickness mm.

The thermal degradation depth is given by:

d = min {D −

3P

2Fc

, 2ds

}

where P = load on wall N/mm.

For non load-bearing walls, 

tfr =

118.4 cDD

2

α

3⁄2
91

5.6 Critical assessment

All building codes studied have a prescriptive method, whereby minimum member dimensions and 

reinforcement cover are prescribed for a given rating of time of exposure to a standard fire. 

Performance-based methods allow more precise determination of fire resistance by calculating the 

temperature distribution throughout the member and accounting for the reduction in strength and 

stiffness of the materials. Isotherms are provided by most codes for common members exposed to a 

standard fire. Beyond a certain temperature, concrete is considered so degraded that its contribution to 

member strength can be neglected. Redistribution of moments in continuous members, development of 

axial thrust due to restraint against thermal expansion, special provisions for high strength concrete, and 

design to resist spalling are among the issues that some codes address in greater detail than others. 

In the US, the SFPE handbook and ACI 216 have a more detailed method on how to account for the axial 

thrust generated by resistance to thermal expansion than any method found in Eurocode 2utilization

but in several other aspects, Eurocode is more complete than US standards. These include: methods for 

preventing spalling, thickness of spalled layer to remove in design calculations; account for the actual 

degree of utilization of the concrete member in fire design; strength reduction in high-strength concrete 

(up to 90 MPa or 13 ksi cylinder strength) at elevated temperatures. (ACI 216 does not provide guidance 

on high strength concrete, whereas IBC 2012 specifies minimum dimensions for columns made of 

concrete 83 MPa or 12 ksi or above in strength for a given fire resistance rating.) In addition, ACI 

neglects the strength of concrete above 760°C, whereas Eurocode neglects it above 500°C, a rather 

significant difference worth exploring further.

It is recommended that US code provisions for spalling of concrete, especially high strength concrete be 

developed.

References

American Concrete Institute (2007) “ACI 216.1-07/TMS 0216-07 Code requirements for Determining fire 

Resistance of Concrete and Masonry Assemblies,” Farmington Hills, MI

American Concrete Institute (2001) “ACI 216R-89 Guide for Determining the Fire Endurance of Concrete 

Elements,” (reapproved 2001, now discontinued by ACI) Farmington Hills, MI

American Society of Civil Engineers (2007) “ASCE/SEI/SFPE 29-05 Standard Calculation Methods for 

Structural Fire Protection,” Reston, VA, USA

Anderberg, Y. (1993) “Computer simulation and a design method for fire exposed concrete columns,” 

Report 92-50 Fire Safety Design, Lund, Sweden

ASTM E119 (2012) “Standard Test Methods for Fire Tests of Building Construction and Materials,” 

American Society for Testing and Materials, West Conshohocken, Pa

Building Center of Japan (2011) “The Building Standard Law of Japan,” Tokyo, Japan
92

Canadian Standards Association (2004) “CSA A23.3-04 Design of Concrete Structures,” Toronto, ON, 

Canada 

Eurocode 2 (2010) “Design of concrete structures – Part 1-2: general rules – structural fire design 

(includes AC 2008),” English translation of DIN EN 1992-1-2:2010-12, CEN, Brussels, Belgium

Fleischmann, C., Buchanan, A. and Chang, J. (2008) “Analytical methods for determining fire resistance 

of concrete members,” SFPE Handbook of Fire Protection Engineering, 4th Ed., NFPA, Quincy, MA

Hasegawa, T. (2013) hasegawa-t2qq@mlit.go.jp “Introduction to the Building Standard Law, version Feb 

2013,” Building Center of Japan, Tokyo, Japan

International Code Council (2012) “International Building Code,” Chapter 7: Fire and Smoke Protection 

Features, Country Club Hills, IL, USA

Japan Society of Civil Engineers (2007) “Standard specifications for concrete structures-2007-Design,”

Section 10.7, Tokyo, Japan

Lane, B. (2008) “Approaches to calculating structural fire resistance,” NFPA Fire Protection Handbook, 

12th ed., Vol. II, Chap. 19.5, Cote, A.E. Ed. National Fire Protection Association, Quincy, MA. USA pp. 

19.77-19.126

National Research Council Canada (2010) “National Building Code of Canada 2010” (NBCC), Division B,

Appendix D, Fire performance rating, Institute of Research in Construction, Ottawa, ON, Canada

New Zealand Standards (2006) “NZS 3101: Concrete Structures Standard - Part 1: The Design of Concrete 

Structures 2006, with amendments Aug. 2008,” Chapter 4: Design for Fire Resistance, Wellington, NZ

Standards Australia (2009) “AS 3600-2009 Concrete structures,” Sydney, NSW, Australia 

Wickstrom, U. (1989) “Natural fires for design of steel and concrete structures- a Swedish approach,” 

Int. Symp. on Fire Engg. for Building Structures and Safety, Inst. of Engrs, Australia, Nat. Conf. Pub. 

89/16, Melbourne.

Wickstrom, U. (2008) “Methods for predicting temperatures in fire-exposed structures,” SFPE Fire 

Protection Engineering, 4th ed. 
93

Chapter 6 Composite Structures

The most common composite steel and concrete members are concrete floor slabs connected to steel 

sheeting or beams by shear studs, hollow steel sections filled with reinforced concrete, or hot rolled 

steel sections encased in concrete. The strength of composite slabs is severely influenced by fire 

because the steel sheeting under fire loses its strength as external reinforcing. Composite slabs, 

however, still provide good performance under fire because of axial restraint, moment redistribution 

and internal reinforcement.

6.1 AISC 2011 14th Ed. Appendix 4 Structural Design for Fire Conditions -

Composite floor members

For the simplified analysis, the AISC Specifications allow the use of 1D heat transfer equations, whereby 

the temperature is assumed to be uniform from the bottom flange to midweb, and to decrease linearly 

by no more than 25 % from midweb to the top flange. The mechanical properties of the steel beam are 

taken as functions of temperature. 

AISC Steel Design Guide 19 (2003) provides more detailed guidance. The concrete properties are 

unchanged from ambient as the temperature on the top of the slab does not rise dramatically. The 

neutral axis is assumed to be within the concrete slab for the purpose of calculating the positive 

moment capacity, which is the sum of the moment capacities of the top flange, the web and the bottom 

flange, calculated at elevated temperatures. The location of the neutral axis is verified using concrete 

properties at ambient temperature. For negative moment capacity, an iterative approach is used, with 

the assumptions that the steel reinforcement of the slab is fully yielded in tension and the neutral axis is 

located in the web in the first iteration. A change in the moment distribution in continuous beams as 

temperature increases (see Section 5.1.3, continuous beams and slabs) is also accounted for.

6.2 ASCE /SEI/SFPE 29-05 Standard Calculation Methods for Structural Fire 

Protection - Concrete-filled hollow steel tubes (Section 5.2.3)

In composite concrete filled hollow steel sections, the concrete acts as a heat sink and slows the 

temperature rise of the steel column; it also assumes an increasing part of the axial load as the steel 

weakens under fire; and it inhibits local buckling of the steel section. ASCE gives the fire resistance 

rating R ≤ 2 hrs of hollow steel columns filled with unreinforced normal weight concrete as:

R = 0.58 a

fc

′ + 2.90

KL − 3.28 D

2 √

D

C

in US units
94

R = a

fc

′ + 20

60 (KL − 1000)

D

2 √

D

C

in SI units

where

a = constant given in Table 6.1;

fc

′ = 28-day compressive strength of concrete; 5.80 ≤ fc′ ≤ 2.90 ksi or 40 ≤ fc′ ≤ 20 MPa ;

KL = effective length of column; 6.5 ≤ KL ≤ 13 ft or 2000 ≤ KL ≤ 4000 mm ;

D = outside diameter of circular column; 5.5 ≤ D ≤ 16 in or 140 ≤ D ≤ 410 mm ;

D = outside dimension of square column; 5.5 ≤ D ≤ 12 in or 140 ≤ D ≤ 305 mm ;

D = least outside dimension of rectangular column; 5.5 ≤ D ≤ 12 in or 140 ≤ D ≤ 305 mm ;

C = compressive force due to unfactored dead load and live load (kips or kN) ≤ design strength of 

concrete core.

Table 6.1 Values of constant a (ASCE)

Aggregate Circular columns Square or rectangular columns

siliceous 0.07 0.06

carbonate 0.08 0.07

These equations are based on an extensive series of test, performed by the National Research Council of 

Canada, of unprotected concrete filled steel columns, 3.810 m in length, with ends rotationally 

restrained and exposed to ASTM E119 fire. The tests comprise various types of concrete (siliceous or 

carbonate aggregate, normal or high strength); types or reinforcement (none, steel bars, steel fibers); 

square and circular hollow steel sections of various dimensions; and load ratios (Kodur, 1998; Lie and 

Chabot, 1992; Lie and Kodur, 1996). Typical test results show axial expansion at the beginning of the 

fire, followed by sharp contraction, then a more gradual contraction. A final drastic contraction occurs 

just before failure. 

6.3 National Building Code of Canada 2010

The same SI formula as above is recast for the capacity Cmax of the concrete-filled steel column with a 

given fire rating R in minutes, with a given in Table 6.2:

Cmax = (

a(fc

′ + 20)D2.5

R(KL − 1000)

)

2
95

 Table 6.2 Values of constant a (NBCC)

Concrete

type

Steel

reinforcement

Reinforcement

ratio %

Circular

columns

Square

columns

* S: coarse aggregate is granite, 

quartzite, siliceous gravel or 

other dense materials 

containing at least 30% quartz, 

chert or flint; 

+ N: coarse aggregate is cinders, 

brick, blast furnace slag, 

limestone, calcareous gravel, 

trap rock, sandstone or similar 

dense materials containing at 

least 30% quartz, chert or flint.

S* Plain 0 0.070 0.060

S Fiber ≈ 2 0.075 0.065

S Bar 1.5 to 3 0.080 0.070

S Bar 3 to 5 0.085 0.075

N

+ Plain 0 0.080 0.070

N Fiber ≈ 2 0.085 0.075

N Bar 1.5 to 3 0.090 0.080

N Bar 3 to 5 0.095 0.085

6.4 The Building Standard Law of Japan Aug. 2011

No special provision is available for composite construction. For methods of fire-resistive construction 

other than those explicitly mentioned, the retained fire resistance time against enclosure fire tfr is 

calculated by (Notification 1433 Aug. 2011 p. 105):

tfr = tA (

460

α

)

3⁄2

where

tA = fire resistance rating (min);

α = fire temperature rise coefficient.

6.5 Eurocode 4: EN 1994-1-2, Aug. 2005 - Design of composite steel and 

concrete structures – Part 1-2: General rules - structural fire design

Simple calculation models are given for slabs, beams and columns of steel-concrete composite 

construction under standard fire exposure. Columns are assumed to be heated all around, whereas 

beams supporting floors are heated from the three lower sides. For composite slabs and beams, the 

bending design resistance is governed by plastic theory (or ultimate strength), whereby the concrete 

contribution is modeled by the rectangular stress block and the tension reinforcement is at yield. 

Material properties are multiplied by a reduction factor that is a function of temperature. For composite 

beam-slab systems with full shear connection, Eurocode 4 Part 1.2 method consists in obtaining the 

temperature distribution in the cross section exposed to a standard fire, dividing the section into slices 

of approximately the same temperature, calculating the plastic bending moment of each cross sectional 

slice, and summing them up. A protected composite slab is assumed to have fulfilled its load bearing 

function R if the temperature of the steel sheet is less than or equal to 350°C when heated from below 

by a standard fire. 

In case of design by partial shear connection in a fire situation, the variation of longitudinal shear forces 

in function of the heating needs to be considered. For composite beams with no concrete encasement 

around the beam, the temperature of the stud connectors and of the concrete may be taken as 80 % 
96

and 40 % respectively of the temperature of the upper flange of the beam. If the beam is partially 

encased in concrete, it may be assumed that there is no reduction in the shear resistance of the 

connectors welded to the effective width of the upper flange. The limiting temperature approach can be 

used (see Section 4.2.2, Chapter 4). Reflecting the lower heating rate of the shear connectors, EC4-1-2 

specifies a higher limiting temperature for partial shear connections than for full shear connections.

Slab membrane action in fire

The load bearing calculation of a composite slab in fire typically assumes one-way spanning, in the 

direction of the concrete rib. This simplification is conservative compared to the tensile membrane 

behavior that occurs in reality. 

EC4 also allows the use of yield line theory for the fire design of continuous slabs. Minimum 

reinforcement at supports and midspan is specified to ensure sufficient deformation capacity. For 

positive (sagging) bending, the concrete in compression is at the top and is required to be below 140°C 

(284° F) per insulation standard. Therefore, ambient material properties may be used. The contribution 

from the unprotected steel decking is usually ignored because it might debond under direct fire attack. 

Tension is resisted by the reinforcement in the ribs, whose temperature can be calculated with the aid 

of nomograms. For negative bending of a continuous slab, the compression face is exposed to fire and 

sees a steep temperature gradient. As mentioned above, it is then necessary to divide the slab, including 

the ribs, into layers of varying temperature and integrate the contributions of all layers with their 

reduced stiffness and strength properties.

According to Lane (2008), simple design guidance based on Bailey’s analysis (Bailey et al., 2000) of the 

Cardington frame fire tests and similar tests in Australia and Europe were published by the Steel 

Construction Institute of the UK (Guide SCI-P288, Newman et al., 2000, 2006). By accounting for the 

tensile membrane action of composite slabs in fire, the guide allows secondary beams in composite 

steel-framed structures to be left unprotected. The recommendations are restricted to non-sway frames 

with composite steel decks similar to the Cardington tests. The slabs should be made of normal or light 

weight concrete with reinforcement mesh and steel decking of trapezoidal or reentrant geometry. The 

design method, based on a standard fire exposure and the yield line theory of slabs, is comprised of 

tables for various beam spans, reinforcement meshes, slab profiles and loads. 

The maximum fire resistance achievable with the use of the Guide is 60 minutes. Slab reinforcement 

detailing is governed by limits on deflections (span/30) to ensure that compartmentalization is not 

breached and steel stresses do not exceed fy /2. The method requires that the floor be divided into 

rectangles of less than 9 m span, with the rectangles supported by unprotected beams surrounded by 

other rectangles with fully protected beams. Primary and edge beams must be protected. The Guide 

accounts for the additional loads induced on the beams by the membrane action of the floor slab. The 

2006 edition of the Guide (SCI-P288) also accounts for the catenary behavior of the beams, and extends 

the method to orthotropic slab reinforcement. Usmani and Cameron (2004) extended the method 

further by modeling the deflected shape of the slab with a cubic polynomial before calculating the 
97

membrane forces. Further refinement includes the pulling in of columns under high floor membrane 

action based on the work of Wang (1996, 2005) and published by HERA in New Zealand (Clifton, 1998).

Composite columns

EN4-1-2 gives a detailed fire design method for composite columns. Three approaches are presented: 

1) tabulated data, 2) simple calculations, and 3) advanced calculations. 

Design tables are available for a limited range of load ratios and steel sections, and steel columns of 

buckling length less than 4.5 m. Simple calculation methods (Annex H) are also limited to buckling 

lengths less than 4.5 m, but can be used for any section and any load ratio. Tabulated data are available 

for columns heated all around by a standard fire, with the same temperature distribution over their 

whole length. The tables account for the column load level, which is the ratio between the relevant 

design effect of actions in fire and the design resistance for ambient temperature.

Under “simple calculations” for columns, the design value of the plastic resistance for axial compression 

in fire is the sum of the contributions of the steel profile, the reinforcing bars and the concrete, with 

material properties reduced at elevated temperature. A complicated step by step approach is necessary, 

whereby, at each value of column strain, the plastic resistance and the Euler buckling load are 

calculated. The Euler buckling load is evaluated using the tangent modulus at the appropriate column 

strain and temperature. When the plastic resistance equals the Euler buckling load, that load is the 

design compressive strength of the composite column. 

Advanced calculation methods are based on fundamental physical behavior and provide a realistic 

analysis of structures exposed to fire. They account for mechanical actions, geometrical imperfections, 

thermal actions, temperature-dependent material properties, geometric non-linear effects and nonlinear material properties, including the effects of unloading. The influence of moisture migration on the 

thermal response of the concrete and the fire insulation may be neglected.

6.6 Composite members in New Zealand (NZS 3404) and Australia (AS 4100)

The limiting temperature method is also used. Composite columns are designed within the performance

-based framework. In New Zealand, Clifton (2006) developed the Slab Panel Method (SPM) to take into 

account the inelastic reserve strength of composite slab construction. The SPM formulates Bailey et al.’s

(2000) tensile membrane action of composite slabs, observed in the Cardington tests, for general 

application to steel framed buildings with composite floors on steel deck. SPM applies to concrete floor 

systems integral with supporting steel beams in buildings subjected to fully developed fires. Under these 

conditions, and especially if steel members are unprotected, the inelastic demand on the floor system 

can be considerable. SPM estimates this demand and compares it to the reserve strength made 

available by large deformations of the composite floor. SPM also calculates the minimum detailing 

requirements to ensure the expected deformations can be achieved without failure of reinforcement or 

connections. The highest inelastic demand on the connections occurs during the cooling phase, when 

large tension forces develop. Improvements of SPM over Bailey et al.’s approach include 1) the 
98

incorporation of the supporting beams directly into the flexural/tensile capacity of the slab, 2) a check of 

the shear capacity of the slab, and 3) an update on the limits on maximum slab deflection (Oliver et al.

2008). AS/NZS 2327: Composite Structures is planning a 2014 release of a new standard for composite 

steel-concrete buildings, which will be informed by overseas standards such as AISC and Eurocode, but 

will also include SPM for fire design. The new standard acknowledges that, for indeterminate systems in

fire, there is a significant degree of redundancy that provides additional structural capacity that cannot

be addressed by considering single elements within a building (Uy, 2013).

6.7 Critical assessment

Eurocode has made extensive use of the results of the Cardington tests to provide guidance on the 

development of tensile membrane action, leading to savings in fireproofing and more efficient design of 

composite reinforced concrete (RC) floor slab-steel beam systems. In the US, the performance in fire of 

composite floor systems comprising a concrete deck poured over corrugated steel sections supported by 

open-web joists (NCSTAR 1 (2005)) or conventional beams (NCSTAR 1A (2008)) was studied by NIST as 

part of the World Trade Center investigation. NCSTAR 1 (2005) noted that deflections greater than 

span/20 were required for tensile membrane action to develop in the case of concrete slabs supported 

by open web joists, but this form of construction is less widely used than the conventional steel beamconcrete slab. As there are differences in construction methods between the US and Europe, the results 

of the Cardington tests may not be directly applicable to the US. Guidance is needed on when tensile 

membrane action can be relied upon in fire, e.g., the reinforcement, anchorage, boundary conditions 

required, as appropriate to US construction.

The challenge, as always, is to produce design methods that are safe, not overly conservative, and 

simple to use. This challenge is illustrated by the difference in approach between North America and 

Europe on the design of concrete-filled steel tubular columns. US standards are based on Canadian 

tests, and are therefore limited to the range of geometries and concrete types of these tests. (Eurocode 

standards are more complete, but more complex, although simplified methods are also offered.)

There is also a need for more research and standards for composite columns within a structural 

assembly. For CFT columns, the steel tube may experience local buckling at the ends or along the length 

under fire exposure. If local buckling occurs at the ends, then the column should be considered pinned, 

but there is no clear guidance on when that happens, only indications that the location of the local 

buckling depends on the axial load, the thickness of the steel tube, and the bond between the steel tube 

and the concrete core (Wang, 2005).

It is therefore recommended that further research be undertaken to 1) develop guidance appropriate to 

US construction techniques for the development of tensile membrane action of steel beam-concrete 

slab composites under fire; and 2) expand the scope of US code provisions for concrete-filled tube (CFT) 

columns.

References

American Institute of Steel Construction Steel (2011) “AISC Construction Manual, Appendix 4: Structural 

Design for Fire Conditions,” part of “Specifications for Structural Steel Buildings,“ (adopted 2010), 14th

Ed., AISC, Chicago, IL, USA
99

American Institute of Steel Construction Steel (2003) “Fire Resistance of Structural Steel Framing,” Steel 

Design Guide 19, AISC, Chicago, IL, USA

American Society of Civil Engineers (2007) “ASCE/SEI/SFPE 29-05 Standard Calculation Methods for 

Structural Fire Protection,” Reston, VA, USA

Bailey, C.G., White, D.S. and Moore, D.B. (2000) “The Tensile Membrane Action of Unrestrained 

Composite Slabs Simulated under Fire Conditions,” Engineering Structures, Vol. 22, 1583-1595

Building Center of Japan (2011) “The Building Standard Law of Japan,” Tokyo, Japan

Clifton, G.C. (2006) “Slab Panel Method – Design of composite steel floor systems for severe fires,” 3rd 

Edition, HERA Report R4-131, Heavy Engineering Research Association, Manukau City, New Zealand.

Clifton, G.C. (1998) “Draft for Development: Design Procedures for the Inelastic Floor System Frame 

Response of Multi-Storey Steel Framed Buildings in Fully Developed Natural Fires,” Technical Report R4-

90-DD, Heavy Engineering Research Association, Manukau City, New Zealand

Eurocode 4: EN 1994-1-1, Dec. 2004, with corrigendum Apr. 2009 - Design of composite steel and 

concrete structures – Part 1-1: General rules and rules for buildings, CEN, Brussels, Belgium

Eurocode 4: EN 1994-1-2, Aug. 2005, with corrigendum Jul. 2008 - Design of composite steel and 

concrete structures – Part 1-2: General rules - structural fire design, CEN, Brussels, Belgium

Kodur, V.K.R. (1998) “Performance of High Strength Concrete-Filled Steel Columns Exposed to Fire,” Can. 

J. of Civil Engg. Vol. 25, 975-981 

Lane, B. (2008) “Approaches to calculating structural fire resistance,” NFPA Fire Protection Handbook, 

12th ed., Vol. II, Chap. 19.5, Cote, A.E. Ed. National Fire Protection Association, Quincy, MA. USA pp. 

19.77-19.126

Lie, T.T. and Chabot, M. (1992) “Experimental Studies on the Fire Resistance of Hollow Steel Columns 

Filled with Plain Concrete,” IR 611, NRCC, Ottawa, Ont. 

Lie, T.T. and Kodur, V.J.R. (1996) “Fire Resistance of Steel Columns Filled with Bar-Reinforced Concrete,” 

ASCE J. of Structural Engg. Vol. 122, No.1, 30-36 

National Research Council Canada (2010) “National Building Code of Canada 2010” (NBCC), Institute of 

Research in Construction, Ottawa, ON, Canada

Newman, G., Robinson, J.T. and Bailey, C. (2000) “Fire Safe Design: A New Approach to Multi-Storey Steel 

Framed Buildings,” SCI Pub. 288, Steel Construction Institute, Ascot, Berkshire, UK

Newman, G., Robinson, J.T. and Bailey, C. (2006) “Safe Design: A New Approach to Multi-Storey Steel 

Framed Buildings,” SCI Pub. 288, 2nd ed., Steel Construction Institute, Ascot, Berkshire, UK

Oliver, S., Feeney, M., Jones, B. (2008) “Dependable Performance of Steel Structures in Fire with Case 

Studies,” Proc. Structural Eng. Assoc. of California, 77th SEAOC Annual Convention , Big Island, Hawaii
100

Standards Australia (1998) “Steel structures,” AS 4100-1998, Section 12: Fire, Homebush, NSW, Australia

Standards New Zealand (1997) “Steel structures standard,” NZS 3404: Part 1:1997, Wellington, NZ 

(current in 2013) Chapter 11: Fire

Usmani, A.S. and Cameron, N.J.K. (2004) “Limit capacity of reinforced Concrete Floor Slabs in Fire,”

Cement and Concrete Composites, Vol. 26, No. 2, 127-140

Uy, B. (2013) “AS/NZS 2327 Composite Structures: a new standard for composite-steel concrete 

buildings,” Steel Innovations, Feb., Christchurch, NZ

Wang, Y.C. (1996) “Tensile Membrane Action in Slabs and its Application to the Cardington Fire Tests,”

Proc. 2nd Cardington Conf., BRE, Cardington, UK, Mar. 

Wang, Y.C. (2005) “Performance of steel-concrete composite structures in fire,” Prog. Struct. Engng. 

Mater.7, 86-102, Wiley-Interscience
101

Chapter 7 Prestressed Concrete Structures

7.1 PCI 3rd ed. 2011: Design for fire resistance of precast/prestressed concrete 

By the Fire Subcommittee of the Prestressed Concrete Institute Building Code Committee

The basis for the fire resistance rating of prestressed, precast members is the standard fire defined by 

ASTM E119. The guide provides isotherms for various cross sections at various time exposures to the 

standard fire, and methods for calculating the fire rating of slabs and beams under various conditions: 

simply supported, continuous, or with resistance to thermal expansion. The methods are similar to 

those used for reinforced concrete members, and are the same as for ambient temperature, but with 

material properties as functions of temperature (also provided by the guide). For example, the retained 

moment capacity Mnθ at temperature θ is:

Mnθ = Apsfpsθ(d − aθ⁄2)

where

Aps = area of prestressing steel;

fpsθ = nominal strength of prestressing steel at temperature θ;

d = section depth;

aθ = depth of equivalent rectangular stress block at temperature θ, determined by

Apsfpsθ = 0.85fcθ

′ aθb

b = section width;

fcθ

′ = compressive strength of concrete at temperature θ. If the compressive zone is on top, as in simply 

supported beams and slabs, the concrete is generally cool enough that fcθ

′ ≅ fc

′

.

The PCI Manual also discusses restrained fire-resistive ratings at some length. It had been surmised that 

restraint boundary conditions introduced in fire tests could not be depended on in actual buildings. This 

assumption proved incorrect because actual buildings have shown tremendous structural redundancy in 

resisting thermal expansion due to fire. Thus the original ratings (obtained from tests prior to 1970) 

were kept intact due to the restrained test procedures. Unrestrained ratings can be based on the results 

of restrained fire tests, provided additional criteria are observed: when cold-drawn prestressing steel 

reaches a temperature of 430°C (800°F) or reinforcing steel reaches 600°C (1100°F), the member is 

assumed to be at the point of failure and is given an unrestrained rating for that time period. If, on the 

other hand, unrestrained rating is derived from unrestrained fire tests, then there is no limiting 

temperature on prestressing or passive reinforcement. Similarly, there is no limiting temperature for 

reinforcing or prestressing steel in the case of restrained rating of slabs based on restrained fire tests. 

There are, however, temperature limits for restrained rating of beams based on restrained tests: 

tension steel must not exceed on average 430°C (800°F) for cold-drawn prestressing steel or 600°C

(1100°F) for reinforcing steel for beams longer than 1.22 m (4 ft) on center with a rating of 1 h or less, or 
102

for the larger of 1 h or the first half of a rating period longer than 1 h (Table 7.1). Restraint is provided to 

a heated part of a floor that experiences a reduction in strength and stiffness, but is surrounded by 

cooler structural members that are able to anchor the development of membrane action in the heated 

slab. 

Table 7.1 Restrained and unrestrained fire rating based on tests

Rating Based on tests Temperature limits

unrestrained unrestrained none

unrestrained restrained prestressing steel < 430°C (800°F) or reinforcing steel < 600°C (1100°F)

restrained restrained none for slabs;

for beams longer than 1.22 m (4 ft) and 

for t = tr = fire rating ≤ 1 h or if tr > 1 h, for t = max(1 h,tr⁄2), 

prestressing steel < 430°C (800°F) or reinforcing steel < 600°C (1100°F) 

The procedure for accounting for the thrust developed by resistance to thermal expansion for 

continuous beams and slabs is similar to that presented by the SFPE (Analytical methods for determining 

fire resistance of concrete members, by C. Fleischmann, A. Buchanan, and J. Chang, SFPE Handbook of 

Fire Protection Engineering, 4th Ed. 2008) referenced in Chapter 5.

7.2 International Building Code 2012

The IBC prescribes the minimum cover thickness for prestressed or post-tensioned tendons. Table 7.2 is 

an excerpt from IBC Table 721.1(1).

Table 7.2 Minimum cover thickness - inches (mm)

Insulation 

material

Structural part 

to be protected

Member type Beam 

width

Fire resistance period

4 h 3h 2 h 1 h

Carbonate, 

lightweight, 

sand 

lightweight 

and siliceous 

aggregate 

concrete

Bonded 

pretensioned 

reinforcement

Beams or 

girders

4 (102) 3 (76) 2.5 (64) 1.5 (38)

Solid slabs 2 (51) 1.5 (38) 1 (25)

Bonded or 

unbonded 

post-tensioned 

tendons

Unrestrained 

members

Solid slabs 2 (51) 1.5 (38)

Beams or 

girders

8 (203) 4.5 (114) 2.5 (64) 1.75 (44)

>12 (305) 3 (76) 2.5 (64) 2 (51) 1.5 (38)

Restrained 

members

Solid slabs 1.25 (32) 1 (25) 0.75 (19)

Beams or 

girders

8 (203) 2.5 (64) 2 (51) 1.75 (44)

>12 (305) 2 (51) 1.75 (44) 1.5 (38)

The minimum thickness of prestressed or precast slabs and walls for various fire rating periods is the 

same as for reinforced concrete members.

7.3 ASCE/SEI/SFPE 29-05

Besides containing some of the same tables as IBC (Table 7.2), ASCE 29-05 also specifies minimum 

covers for prestressed concrete beams 40 in2(26 000 mm2) or greater in area regardless of beam widths. 
103

Table 7.3 Minimum cover for prestressed reinforcement

in beams 40 in2(26 000 mm2) or greater in area

Concrete Aggregate Type Cross Section Area 

in.2(103 mm2)

Thickness in. (mm) of Cover for Fire Resistance Rating

1 h 1.5 h 2 h 3 h 4 h

RESTRAINED

All 40–150 (26–97) 1.5 (38) 1.5 (38) 2 (51) 2.5 (64)

Carbonate or siliceous 150–300 (97–194) 1.5 (38) 1.5 (38) 1.5 (38) 1.75 (44) 2.5 (64)

Carbonate or siliceous >300 (194) 1.5 (38) 1.5 (38) 1.5 (38) 1.5 (38) 2 (51)

Lightweight or sand-lightweight >150 (97) 1.5 (38) 1.5 (38) 1.5 (38) 1.5 (38) 2 (51)

UNRESTRAINED

All 40–150 (26–97) 2 (51) 2.5 (64)

Carbonate or siliceous 150–300 (97–194) 1.5 (38) 1.75 (44) 2.5 (64)

Carbonate or siliceous >300 (194) 1.5 (38) 1.5 (38) 2 (51) 3 (76) 4 (102)

Lightweight or sand-lightweight >150 (97) 1.5 (38) 1.5 (38) 2 (51) 3 (76) 4 (102)

7.4 Eurocode 2-1-2 Design of concrete structures

Reinforced and prestressed concrete structures are treated in the same document. There is no separate 

methodology for prestressed concrete, however, the mechanical properties at elevated temperatures 

for cold-drawn tendons are listed separately from those of reinforcing bars. Based on a utilization factor 

of 0.7, the critical temperature is 400°C for prestressing bars and 350°C for strands and wires. (For 

comparison, the critical temperature is 500°C for reinforcing bars.) If no special check is made, the cover 

should be increased by 10 mm for prestressing bars, corresponding to a critical temperature of 400°C, 

and 15 mm for strands and wires, corresponding to a critical temperature of 350°C. The critical 

temperature determines the cover thickness required for a given duration under standard fire exposure.

7.5 New Zealand and Australia

New Zealand Standards Concrete Structure Standard - Part 1: the design of concrete structures

NZS 3101: Part 1: 2006, with amendments Aug. 2008, Chapter 4: Design for fire resistance

Australian Standards AS 3600 - 2009 Concrete structures

The cover should be increased by 10 mm for prestressing bars, and 15 mm for strands and wires,

compared to its thickness for reinforcing bars.

7.6 2010 National Building Code of Canada, Division B, Appendix D, Fire 

Performance Rating 

This Appendix prescribes minimum dimensions and cover thickness for various structural members. 

Table D-2.2.1.A lists the minimum thickness of reinforced and prestressed concrete floor and roof slabs, 

e.g., for 1 h fire resistance rating, the minimum thickness for type S concrete is 90 mm, for type N is 87 

mm and for type L40S or Type L concrete is 72 mm. Slab thickness is the same, whether the 

reinforcement is prestressed or not. Table D-2.2.1.B gives the minimum concrete cover over 

reinforcement in concrete slabs, e.g., for 1 h fire resistance rating, the minimum cover for type S, N, 
104

L40S or L concrete is 20 mm for reinforced concrete slabs, and 25 mm for prestressed concrete slabs. 

Table D-2.10.1 (shown here as Table 7.4) specifies the minimum cover over steel tendons in PC beams. 

The effect of end restraint on fire resistance is not accounted for.

Table 7.4 Minimum thickness of concrete cover over 

steel tendons in prestressed concrete beams (mm)

Type of 

concrete

Area of beam 

cm2

Fire-resistance rating

30 min 45 min 1 h 1.5 h 2 h 3 h 4 h

260 to 970 25 39 50 64

S or N 970 to 1940 25 26 39 45 64

Over 1940 25 26 39 39 50 77 102

L

# Over 970 25 25 25 39 50 77 102

#

L is lightweight concrete in which all the aggregate is expanded slag, expanded clay, expanded shale or 

pumice. Concrete types S and L are defined in Table 6.2.

CSA Standard A23.3-04 (2004) Design of concrete structures

This standard has no specific provisions concerning fire.

7.7 The Building Standard Law of Japan, August 2011

This standard has no specific provisions concerning prestressed concrete structures in fire.

7.8 Critical assessment

All codes studied use the same methodology for prestressed concrete structures as for reinforced 

concrete structures. Certain parameters are changed to reflect the greater effect of elevated 

temperatures on prestressing steel than on reinforcing steel, such as an increase in concrete cover for 

the same fire resistance rating, or a lower critical temperature for strands and tendons than for 

reinforcing bars. 

Some of the observations for reinforced concrete structures are repeated here: In the US, the PCI has a 

more detailed method on how to account for the axial thrust generated by resistance to thermal 

expansion than any method found in the Eurocode, but in several other aspects, Eurocode is more 

complete than US standards. These include: methods for preventing spalling, thickness of spalled layer 

to remove in design calculations; account for the actual degree of utilization of the concrete member in 

fire design; strength reduction in high-strength concrete (up to 90 MPa or 13 ksi cylinder strength) at 

elevated temperatures.

References

American Society of Civil Engineers (2007) “ASCE/SEI/SFPE 29-05 Standard Calculation Methods for 

Structural Fire Protection,” Reston, VA, USA
105

ASTM E119 (2012) “Standard Test Methods for Fire Tests of Building Construction and Materials,” 

American Society for Testing and Materials, West Conshohocken, Pa

Building Center of Japan (2011) “The Building Standard Law of Japan,” Tokyo, Japan

Canadian Standards Association (2004) “CSA A23.3-04 Design of Concrete Structures,” Toronto, ON, 

Canada 

Eurocode 2 (2010) “Design of concrete structures – Part 1-2: general rules – structural fire design 

(includes AC 2008),” English translation of DIN EN 1992-1-2:2010-12, CEN, Brussels, Belgium

International Code Council (2012) “International Building Code,” Chapter 7: Fire and Smoke Protection 

Features, Country Club Hills, IL, USA

National Research Council Canada (2010) “National Building Code of Canada 2010” (NBCC), Division B,

Appendix D, Fire performance rating, Institute of Research in Construction, Ottawa, ON, Canada

New Zealand Standards (2006) “NZS 3101: Concrete Structures Standard - Part 1: The Design of Concrete 

Structures 2006, with amendments Aug. 2008,” Chapter 4: Design for Fire Resistance, Wellington, NZ

Prestressed Concrete Institute PCI (2011) “Design for fire resistance of precast/prestressed concrete,” 3

rd

ed. Chicago, IL, USA

Standards Australia (2009) “AS 3600-2009 Concrete structures,” Sydney, NSW, Australia 
106

Chapter 8 Recommendations

This chapter offers recommendations about future work covering gaps in US building codes for 

structural design for fire.

8.1 Develop slab membrane tension provisions in US building codes for steel 

beam-concrete slab composites in fire

Steel beam-concrete slab composites are a fairly common form of construction that has been shown (by 

the Cardington tests) to be more resilient under fire than first thought. Provided the slab has adequate 

steel reinforcement and the connections of the slab with perimeter beams can resist the required 

tension, tensile membrane action can develop in the slab under fire after significant deflection. In this 

case, secondary beams may be left unprotected, thus potentially leading to more economical fire 

protection. It is therefore recommended that US building codes develop slab membrane tension 

provisions appropriate to US construction methods for steel beam-concrete slab composites under fire.

8.2 Develop US code provisions for spalling of concrete, especially high 

strength concrete

An important phenomenon to consider for concrete, especially high strength concrete, in fire is spalling, 

which is due to the build-up of pressure caused by the evaporation of pore water. Spalling removes the 

concrete cover and its insulating effect. The subsequent direct exposure of the steel reinforcement to 

fire is very detrimental to the fire resistance of reinforced concrete structures. Much research has been 

done in the US and elsewhere on this topic, and there is general agreement on causes and remedies, but 

these have yet to find their way into US building codes. There is a need for US building codes to include 

ways to design for spalling of concrete, especially high strength concrete.

8.3 Develop US performance code provisions for steel connections in fire

The AISC Construction Manual (14th Ed. 2011, Appendix 4: Structural Design for Fire Conditions) contains 

the general structural integrity requirement that connections should be able to develop the strength of 

the connected members in fire or resist the forces, moments and deformations obtained by analysis of 

the structure under the applicable load combinations that include the design basis fire. 

Further guidance is especially needed since elevated temperatures may cause new load paths to 

develop (e.g., development of tensile membrane action), and thermal expansion may cause gaps to 

close, thus potentially developing tension or compression in a connection, where none existed at 

ambient temperature. One promising approach is to extend to elevated temperatures the component 

method, whereby a joint is modeled as an assembly of rigid links and extensional springs, whose loaddeformation curves represent different joint components that can be summed to represent the total 

joint response. 
107

8.4 Improve steel stress-strain relationships at elevated temperatures in 

future US performance building codes 

Takagi and Deierlein (2007) have shown the importance of using the complete stress-strain curve of 

steel at elevated temperatures, rather than just accounting for the influence of temperature on the yield 

strength and modulus of elasticity. The current version of AISC (2011) 14th Ed. “Construction Manual, 

Appendix 4: Structural Design for Fire Conditions” adopts the EC3 (2005) stress-strain formulation, and 

recent work at NIST shows further progress. Unlike the EC3 formulation, the NIST model (Luecke et al. 

2011) explicitly describes the time-dependent nature of the strength of steel at high temperature. For 

untested steels, it predicts the stress-strain behavior using only the measured room-temperature yield 

strength. On a subset of eight steels, the model predicts the stress-strain behavior slightly better than 

the equally complicated EC3 model. For three structural steels from the literature and not used in the 

development of the model, the NIST constitutive relations and the EC3 model predict stress-strain 

behavior with similar quality.

8.5 Update provisions for plate buckling strength at elevated temperatures, 

and asses need for revision of other design equations due to change in shape of 

steel stress-strain curve at elevated temperatures

Compared with ambient temperature, the stress-strain curve of steel at elevated temperatures deviates 

from linearity at lower strains. This leads to lower plate buckling strength than the ultimate buckling 

load determined by equating the plate edge stress with yield stress (defined at 2% strain). Selamet and 

Garlock (2013) have shown that the direct mapping from ambient to elevated temperatures of the 

current equations for plate buckling strength can lead to unconservative predictions. Earlier criticisms 

by Takagi and Deierlein (2007, 2009) of the unconservativeness of this direct mapping in wide-flange 

sections led to changes in US and Canadian steel design specifications for compression and flexural 

members. It is recommended that the equations for plate buckling strength at elevated temperatures be 

updated, and a critical assessment be made of the possible need to revise other design equations due to 

the change in shape of the stress-strain curve at elevated temperatures. The adoption of a new stressstrain formulation similar to NIST proposal would be an additional reason for such an assessment.

8.6 Investigate effects of temperature gradient on simple design equations of 

steel and composite structures

Many of the simple design equations in US building codes assume a uniform temperature over the 

entire cross section, or even over the entire length of a member. This assumption ignores the 

redistribution of stresses that takes place from the hotter parts of the cross section to the cooler parts,

when temperatures are not uniform. As the temperature increases, the hotter parts of the section reach 

their limiting temperature, yield plastically, and transfer load to cooler regions, which still behave 

elastically. This load transfer continues until the cool regions become plastic and the member fails. 

Researchers have noted that thermal gradients in a column cross section can reduce the load carrying 

capacity for two reasons: column deformations due to uneven thermal expansion (bowing) and 

asymmetry in the column cross section due to uneven degradation of material properties (yield stress 
108

and elastic modulus)( Agarwal et al. 2014). It should be noted that Eurocode 3.1-8 (2005) accounts for a 

temperature gradient along the beam depth for the purpose of evaluating the strength of joints. 

It is recommended that US building codes include provisions to account for temperature gradients 

where necessary, preferably with the aid of design equations, which would obviate the need for a 

detailed finite-element analysis. 

8.7 Expand scope of US code provisions for concrete-filled tube (CFT) columns 

For concrete-filled tube (CFT) columns, the US approach (ASCE /SEI/SFPE 29-05) is empirical (based on 

Canadian tests) and simple, but limited to the range of columns tested. US codes need to provide a 

method that covers column geometries beyond those tested. There is also a need for more research and 

standards for composite columns within a structural assembly. For CFT columns, the steel tube may 

experience local buckling at the ends or along the length under fire exposure. If local buckling occurs at 

the ends, then the column should be considered pinned, but there is no clear guidance on when that 

happens.

8.8 In US performance-based codes, develop methodology for analyzing parts 

of structure most affected by fire 

The building codes and standards studied all agree on the performance goals of structural design for 

fire. The framework of a performance-based code is also well in hand, e.g., the possibility of performing 

fire-structure analysis in the time, temperature, or strength domain. The need to continue to have 

simple prescriptive codes, and the need for consistency of newly developed performance-based codes 

with existing prescriptive provisions are also acknowledged in the building codes and standards studied. 

The development of means, preferably simple and accurate, to achieve these performance goals 

continue to be the subject of active research. Most developed is the analysis of single members, both 

prescriptive and performance-based. Traditionally, furnace tests have provided the basis for the fire 

rating of single members and the prescriptive requirements to meet the rating. Single members are also 

simple enough that it is often possible to develop user-friendly rules that govern their behavior in fire 

through rational thermal and structural analyses, although nonlinear analysis can be used when needed. 

The next level, analysis of part of the structure, needs further development in the US. In this analysis, a 

part that is most affected by the fire or of greatest interest is studied in detail, but its boundaries are 

assumed unaffected by the fire and the same as ambient. Finally, at the highest level, global analysis of 

the structure on fire takes into account all important nonlinearities in material and structural behavior, 

and changes in boundary conditions. The building codes studied agree on the general goals and 

methods, but the details depend on the individual situations to be investigated.

At present there is a shortage of simple design rules that can be used for analysis of part of the 

structure. The development of tensile membrane action can be considered to result from an analysis of 

a part of a structure, namely a slab with its surrounding frame of beams and columns. 
109

8.9 Continue development of design fires and fire models

The selection of fire scenarios and design fires to be considered is a crucial step in a fire-structural 

analysis. Much progress has been achieved by many countries over the last several decades, based on 

statistics of fire loads and their dependence on building use and occupancy. Scenarios that must be 

considered include those that are most detrimental to the stability of the structure, and those that are 

most likely to occur. Probability theory and event tree analysis offer pathways to decision.

The standard fire temperature – time curves in many countries are quite similar. They are most useful 

for testing structural members in furnaces and comparing the effectiveness of various protection 

methods. Furthermore, specialized fire curves have been developed for particular situations, such as 

hydrocarbon fires and tunnel fires. In response to the criticism that the standard fire does not capture 

realistic fires, parameterized fire curves have been developed by Eurocode for compartments under 

flashover conditions, using physically based parameters that capture the effects of openings, fuel load, 

fuel geometry, compartment dimensions, etc. Research is continuing to develop formulas for situations 

that do not fit these parameters. 

The problem with fire is that it is, in essence, a nonlinear phenomenon in its effects, with radiation a 

function of the 4th power of temperature. Therefore, superposition does not work, and it is necessary to 

investigate complete individual fire scenarios, rather than simple fire situations that can be combined, in 

a similar fashion to load cases that can be superposed and influence lines that can be developed for 

linear elastic analysis. 

Great strides have been achieved in determining the fire scenarios that must be studied, whether for 

the evacuation of occupants, the safety of firefighters, the threat to neighboring buildings, or the 

stability of the structure in fire. Most of the efforts have focused on compartment fires, the conditions 

that lead to flashover, and the evolution of temperature for various compartment geometries, openings, 

and fuel loads. Building codes from various countries have adopted various empirical fire models, and it 

is unlikely that one fire model will emerge as a universal choice in the foreseeable future. More recently, 

local fires in expanses too large for flashover to occur have also been modeled. For compartment and 

local fires, there exist a number of software based on computational fluid dynamics, calibrated and 

verified by experiments, such as FDS (Fire Dynamics Simulator, McGrattan et al. 2013), that are in 

continuous development and can be used in a great many situations. As always in the case of powerful, 

general purpose tools, they require experience and judgment on the part of the users.

Much remains to be done, along the same line as previous development: expand statistics on fire loads 

for various building use and occupancy, in particular for fuel surface area and fuel arrangement, which 

are less well known than fire load density (see for example NFPA 557 (2012), described in Section 3.3 of 

this report); continue development of simplified fire models (e.g., the t

6 model used in the Japanese 

Building Code 2011) for ordinary design, for post-flashover compartment fires and localized fires; 

develop new models that overcome some of the limitations of existing models, such as room aspect 

ratios; continue development of software for fire modeling; improve understanding of behavior of fire 

in large compartments and of localized fires near complex geometries; continue fire tests to calibrate 

and verify all these models; study various common structural arrangements to narrow down what the 

most detrimental fires are; provide guidance on how to apply the results of a design fire to structural 
110

analysis, etc. In this last regard, several possibilities exist. For example, the New Zealand Standard 

(2012) recommends three modeling choices for the full burnout design fire, when all the fuel available is 

allowed to burn:

a) Use a time-equivalent formula to calculate the equivalent fire severity and specify building 

elements with a fire resistance rating not less than the calculated fire severity; 

b) Use a parametric time versus gas temperature formula to calculate the thermal boundary 

conditions (time/temperature) for input to a structural response model, or

c) Construct a heat release rate versus time curve. Then, taking into account the ventilation 

conditions, use a fire model or energy conservation equations to determine suitable thermal 

boundary conditions (time/temperature/flux) for input to a structural response model.

References

Agarwal, A. Choe, L. and Varma, A.H. (2014) “Fire design of steel columns: effects of thermal gradients,” 

J. Constructional Steel Research, Vol. 93, 107-118

American Institute of Steel Construction (2011) “AISC Steel Construction Manual, Appendix 4: Structural 

Design for Fire Conditions,” 14th Ed., AISC, Chicago, IL, USA

ASCE /SEI/SFPE 29-05 (2007) “Standard Calculation Methods for structural Fire Protection, Concretefilled hollow steel tubes (Section 5.2.3),” Reston, VA, USA

Building Center of Japan (2011) “The Building Standard Law of Japan,” Tokyo, Japan

Eurocode 3 (2005) “Design of steel structures- Part 1-2: General rules - structural fire design,” BS EN 

1993-1-2:2005 also DIN EN 1993-1-2:2010-12, CEN, Brussels, Belgium

Eurocode 3 (2005) “Design of steel structures- Part 1-8 Design of joints,” CEN, Brussels, Belgium

Luecke, W., Banovic, S.W., McColskey, J.D. (2011) “High-temperature tensile constitutive data and

models for structural steels in fire,” NIST Technical Note 1714, National Institute of Standards and 

Technology, Gaithersburg, MD 20899

McGrattan, K., Hostikka, S., McDermott, R., Floyd, J., Weinschenk, C., Overholt, K. (2013) “Fire Dynamics 

Simulator User’s Guide, 6th ed.” NIST SP 1019, National Institute of Standards and Technology, 

Gaithersburg, MD 20899

New Zealand Building Regulations (1992, reprinted 2012), Wellington, NZ

NFPA 557 (2012) “Standard Determination of Fire Loads for Use in Structural Fire Protection Design,”

National Fire Protection Association, Quincy, MA

Selamet, S. and Garlock, M. (2012). "Plate Buckling Strength of Steel Wide-Flange Sections at Elevated 

Temperatures." J. Struct. Eng., 10.1061/(ASCE)ST.1943-541X.0000769 (Nov. 3, 2012)
111

Takagi, J. and Deierlein, G.G. (2007) “Strength design criteria for steel members at elevated 

temperatures,” Journal of Constructional Steel Research, Elsevier, 63, 1036–1050

Takagi, J. and Deierlein, G.G. (2009) “Proposed design equations for CAN/CSA S16 Appendix K Provisions

for steel members at high temperatures,” Report prepared for the Canadian Institute of Steel 

Construction, Jan. 22