NISTIR 7563

DRAFT For Public Comments 

Best Practice Guidelines for

Structural Fire Resistance Design of

Concrete and Steel Buildings

National Institute of Standards and Technology

Technology Administration, U.S. Department of Commerce

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NISTIR 7563 DRAFT For Public Comments 

Best Practice Guidelines for

Structural Fire Resistance Design of 

Concrete and Steel Buildings

Long T. Phan 

Therese P. McAllister

John L. Gross 

Building and Fire Research Laboratory 

National Institute of Standards and Technology

Morgan J. Hurley 

Society of Fire Protection Engineers

Editors 

February 2009

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

Patrick Gallagher, Deputy Director

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Abstract 

This document is intended to provide practicing engineers and building code officials with a 

technical resource that contains the current “best practice” for fire-resistant design of concrete 

and steel structures. The report provides a review of existing U.S. and international guidelines 

and design standards, which use approaches that range from simple prescriptive methods to

sophisticated software programs with advanced methods of analysis under a wide range of 

realistic fire conditions. Basic concepts of risk-informed decision making for mitigating fire 

risk, and a general framework for assessing fire risk to building construction and for developing 

structural design requirements for fire conditions are described. Current best knowledge in 

thermal and mechanical properties and behaviors of normal strength concrete, high strength 

concrete, structural steel, and several major groups of common fire protection materials at 

elevated temperatures, which are necessary for performance-based engineering calculation, are 

presented. Modern fire-resistant design methodologies for concrete and steel structures are 

discussed, including methods based on standard fire tests as well as performance-based

engineering analysis methods that involve heat transfer and structural analysis at elevated 

temperatures. 

This report is not intended to provide step-by-step design procedures. Rather, it provides general 

guidance on the approaches to, and practical aspects of, implementing a fire-resistant design 

approach for concrete and steel buildings. The guidance includes key concepts and examples for 

identifying performance objectives, conducting risk analyses, selecting design fire scenarios and

fire exposure curves, and implementing heat transfer and structural response analyses for the 

structural fire-resistant design of concrete and steel structures.

Keywords: building codes; concrete structures; design fire scenarios; fire-resistant design; fire 

risk mitigation; performance-based fire engineering; steel structures; structural response analysis; 

thermal analysis.

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Disclaimers: 

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

technical communications. In this document however, works of authors outside 

NIST are cited which describe measurements in certain non-SI units. Thus, it 

is more practical to include the non-SI unit measurements from these

references.

(2) Certain trade names or company products are mentioned in the text to 

specify adequately the experimental procedure and equipment used. In no case 

does such identification imply recommendation or endorsement by the National 

Institute of Standards and Technology, nor does it imply that the products

are the best available for the purpose.

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Preface

This best practices document is prepared as part of the response to the recommendations from 

the October 2003 NIST-SFPE Workshop for Development of a National R&D Roadmap for 

Structural Fire Safety Design and Retrofit of Structures. The workshop was jointly organized by 

the Society of Fire Protections Engineers (SFPE) and the National Institute of Standards and 

Technology (NIST) with guidance from an industry steering team comprising of representatives 

of the American Institute of Steel Construction (AISC), the American Society of Civil Engineers 

(ASCE), Portland Cement Association (PCA), Underwriters Laboratories (UL), Arup Fire, and 

National Fire Protection Association (NFPA). The document aims to integrate information on 

current “best practices” in fire resistance engineering in the United States and overseas with 

current best knowledge in fire risk assessment and characterization, material properties and 

responses at high temperatures, and thermal and structural response calculation methods into a 

single source document, and to provide engineers and code enforcement officials with a technical 

resource for use in their approach to fire resistance design and evaluation of concrete and steel 

structures. 

This best practices guidance document provides the current best information to enable the use of 

the performance-based design approach for fire resistance design of those structures whose 

performance objectives might exceed the objectives intended by current codes. It is a nonconsensus, non-mandatory document. As such, it does not represent a minimum standard of care

and is not intended to supersede any existing standards currently in practice. Where current best 

practices are represented in existing standards, the standards are discussed and referenced. 

The preparation of this document was coordinated by Mr. Bernard Murphy of the Multihazard 

Mitigation Council (MMC) of the National Institute of Building Sciences (NIBS). Under NIST 

guidance, the MMC convened an industry steering group that included Daniel Falconer 

(American Concrete Institute, ACI), James Rossberg (ASCE), Jason Krohn (Precast/Prestressed 

Concrete Institute, PCI), John Ruddy (AISC, formerly Structural Affiliates International, Inc.), 

and Morgan Hurley (SFPE) to provide guidance in defining the scope of the document, 

developing the working outline, and recommending appropriate chapter authors. To that end, the 

MMC selected the following individuals who are experts in various fields of structural and fire 

safety engineering to serve as chapter authors: Farid Alfawakhiri (AISI), Andy Buchanan 

(University of Canterbury), Donald Dusenberry (Simpson Gumpertz & Heger Inc.), Bruce 

Ellingwood (Georgia Institute of Technology), Morgan Hurley (SFPE), Jim Milke (University of

Maryland), Stephen Pessiki (Lehigh University), and Long Phan (NIST). Subsequently, the 

MMC convened an introductory planning meeting with the authors and the industry steering 

group, organized an internal workshop at NIBS for presentation and review of the 60 % draft 

document and an invited workshop in Washington, D.C. for the presentation and comments on 

the 90 % draft document. A select group of 65 individuals representing the engineering and

construction industry was invited to attend the 90 % draft workshop and to provide comments. 

Following this workshop, the MMC coordinated the incorporation of comments into an interim 

draft document and posted the document on the NIST FTP website for further comments. 

Comments provided were subsequently included in this the final version of the Best Practice 

Guidelines for Structural Fire Resistance Design of Concrete and Steel Buildings. 

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Table of Contents

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

Preface .....................................................................................................................................v 

Table of Contents .......................................................................................................................... vii 

List of Figures .............................................................................................................................. xiii 

List of Tables .................................................................................................................................xv

Chapter 1 Introduction................................................................................................. 1 

1.1 Basic Evacuation Concepts and Goals ....................................................................................1 

1.2 Purpose of These Guidelines ..................................................................................................3 

1.3 Scope ......................................................................................................................................4 

1.4 References ...............................................................................................................................5 

Chapter 2 Existing Guidelines for Fire Resistance Design of Concrete and Steel 

Structures ................................................................................................... 7

2.1 Introduction .............................................................................................................................7 

2.2 Legislative Environment .........................................................................................................7 

2.2.1 Prescriptive Codes ......................................................................................................7 

2.2.2 Performance-Based Codes ..........................................................................................7 

2.2.3 Eurocodes ....................................................................................................................9 

2.3 Structural Design for Fire Conditions .....................................................................................9 

2.3.1 Design Objectives .......................................................................................................9 

2.3.2 Design Process ............................................................................................................9 

2.3.3 Loads for Structural Fire Design ...............................................................................10 

2.3.4 Design Equation ........................................................................................................10 

2.4 Levels of Sophistication in the Design Process ....................................................................11 

2.5 Fire Severity ..........................................................................................................................12 

2.5.1 Fire Severity for Design ............................................................................................12 

2.5.2 Standard Fire Exposure .............................................................................................12 

2.5.3 Realistic Fire Exposure .............................................................................................14 

2.5.4 Time Equivalence .....................................................................................................15 

2.6 Fire Resistance of Elements Exposed to the Standard Fire ..................................................16 

2.6.1 Failure Criteria ..........................................................................................................17 

2.6.2 Approvals ..................................................................................................................17 

2.7 Fire Resistance of Buildings Exposed to Real Fires .............................................................18 

2.7.1 Design of Steel Buildings Exposed to Fire ...............................................................18 

2.7.2 Multi-story Frame Buildings.....................................................................................18 

2.8 Materials Standards ...............................................................................................................19 

2.8.1 U.S.A.........................................................................................................................20 

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 2.8.1.1 Steel............................................................................................................20 

 2.8.1.2 Concrete .....................................................................................................21 

2.8.2 Canada.......................................................................................................................21 

2.8.3 Eurocodes ..................................................................................................................21 

2.8.4 European Countries ...................................................................................................24 

2.8.5 Australia and New Zealand .......................................................................................24 

2.9 Conclusions ...........................................................................................................................24 

2.10 References .............................................................................................................................25 

Chapter 3 Decision Framework for Fire Risk Mitigation......................................... 31

3.1 Introduction ...........................................................................................................................31 

3.2 Performance Objectives and Risk Assessment for Natural and Man-Made Hazards ...........33 

3.2.1 Performance-Based Engineering ..............................................................................33 

3.2.2 Risk and Its Analysis—Hazard, Consequences, Context .........................................35 

3.3 Fire Hazard Modeling ...........................................................................................................39 

3.3.1 Incidence of Fires ......................................................................................................39 

3.3.2 Characteristics of Fire Exposure Curves...................................................................41 

3.4 Structural Engineering for Fire Conditions ...........................................................................46 

3.4.1 Performance Objective..............................................................................................46 

3.4.2 General Fire Risk Mitigation Strategies ...................................................................46 

3.4.2.1 Event Control/Fire Protection Systems ......................................................47 

3.4.2.2 Structural Engineering Analysis ................................................................48 

 3.4.3 Structural Design by Engineering Analysis ..............................................................48 

3.4.3.1 Design-Basis Fire Scenarios ......................................................................48 

3.4.3.2 Thermal Effects on Structural Components and Systems..........................49 

3.4.3.3 Strength Requirements and Deformation Limits .......................................50 

3.4.3.4 Required Attributes of Advanced Analysis ...............................................53 

3.4.3.5 Simplified Methods of Analysis ................................................................53 

 3.4.4 Structural Design by Performance-Based Testing ....................................................54 

3.5 Summary ...............................................................................................................................54 

3.6 References .............................................................................................................................55 

Chapter 4 Design of Concrete Structures................................................................ 61

4.1 Introduction ...........................................................................................................................61 

4.1.1 Scope .........................................................................................................................62 

4.1.2 Technical Basis for Calculating Fire Resistance of Concrete Construction .............62 

4.2 Material Properties ................................................................................................................63 

4.2.1 Normal Strength Concrete ........................................................................................64 

 4.2.1.1 Thermal Properties .....................................................................................64 

 4.2.1.1.1 Thermal Conductivity ..............................................................64 

4.2.1.1.2 Volumetric Specific Heat .........................................................65 

4.2.1.1.3 Density .....................................................................................65 

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 4.2.1.2 Mechanical Properties ................................................................................66 

4.2.1.2.1 Compressive Strength ..............................................................66 

4.2.1.2.2 Modulus of Elasticity ...............................................................69 

4.2.1.2.3 Shear Modulus .........................................................................70 

4.2.1.2.4 Tensile Strength .......................................................................70 

4.2.1.2.5 Coefficient of Thermal Expansion ...........................................71 

 4.2.2 High Strength Concrete.............................................................................................72 

 4.2.2.1 Thermal Properties .....................................................................................72 

4.2.2.2 Mechanical Properties ................................................................................72 

4.2.2.2.1 Compressive Strength ..............................................................72 

4.2.2.2.2 Modulus of Elasticity ...............................................................75 

 4.2.3 Steel Reinforcement ..................................................................................................76 

4.2.3.1 Thermal Properties .....................................................................................76 

4.2.3.2 Mechanical Properties ................................................................................76 

4.3 Thermal Analysis ..................................................................................................................76 

4.3.1 ASTM E119 Exposure ..............................................................................................77 

4.3.2 Other Fire Exposures ................................................................................................82 

4.4 Structural Analysis ..............................................................................................................84 

4.4.1 Performance Criteria .................................................................................................84 

4.4.2 Analysis of Flexural Members (Beams and Slabs) ...................................................85 

4.4.2.1 Simply Supported, Thermally Unrestrained, Flexural Members ...............85 

4.4.2.2 Simply Supported, Thermally Restrained, Flexural Members ..................88 

4.4.2.3 Continuous Flexural Members ...................................................................91 

 4.4.3 Analysis of Compression Members ..........................................................................95 

4.4.3.1 Ultimate Load Calculation—Simplified Method .......................................95 

4.4.3.2 Beam–Column Calculation Method ..........................................................99 

4.4.3.3 Mathematical Model ................................................................................101 

 4.4.4 Shear and Torsion ...................................................................................................102 

 4.4.5 Spalling and Spalling Mitigation ............................................................................102 

4.5 References ...........................................................................................................................104 

4.6 Appendix A from Lie (1992) ..............................................................................................109 

4.7 Commentary/Appendix .......................................................................................................111 

4.8 Mathematical Model for Concrete Columns (Lie and Velikkol 1991) ...............................113 

Chapter 5 Design of Steel Structures..................................................................... 121

5.1 Introduction ................................................................................................................121 

 5.1.1 Scope ................................................................................................................121 

5.2 Material Properties ..............................................................................................................121 

5.2.1 Structural Steel ........................................................................................................122 

 5.2.1.1 Thermal Properties of Steel .....................................................................122 

 5.2.1.1.1 Thermal Expansion of Steel ...................................................122 

5.2.1.1.2 Specific Heat of Steel .............................................................125 

5.2.1.1.3 Thermal Conductivity of Steel ...............................................126 

 5.2.1.2 Mechanical Properties of Steel ................................................................128 

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 5.2.1.2.1 Stress-Strain Relationship – Eurocode Approach ..................130 

 5.2.1.2.2 Stress-Strain Relationship – NIST Approach ........................133 

 5.2.2 Fire Protection Materials.........................................................................................141 

5.2.2.1 Spray-Applied Fire-Resistive Materials (SFRM) ....................................142 

5.2.2.2 Intumescent Coatings ...............................................................................143 

5.2.2.3 Gypsum Board Products ..........................................................................145 

5.2.2.4 Fibrous Board and Mat Products .............................................................148 

5.2.2.5 Concrete and Masonry ..............................................................................148 

5.3 Design Procedures ..............................................................................................................149 

5.3.1 Design by Qualification Testing .............................................................................149 

5.3.1.1 Individual Protection ................................................................................151 

5.3.1.2 Structural Steel Columns .........................................................................152 

5.3.1.3 Steel Framed Floors and Roofs ................................................................152 

5.3.1.4 Steel Trusses ............................................................................................152 

5.3.1.5 Connections...............................................................................................153 

 5.3.2 Design by Engineering Analysis .............................................................................153 

5.3.2.1 Heat Transfer Analysis ............................................................................154 

5.3.2.2 Critical Temperatures...............................................................................157 

5.3.2.3 Simple Calculation Models ......................................................................159 

5.3.2.4 Advanced Calculation Models .................................................................162 

5.4 References ...........................................................................................................................163 

Chapter 6 General Applications of Guidelines...................................................... 171

6.1 Performance Objectives and Risk Assessment ...................................................................171 

6.1.1 Performance Objectives ..........................................................................................172 

6.1.2 Risk Assessments ....................................................................................................172 

6.2 Design Fires ...................................................................................................174 

6.2.1 Factors That Affect Fire Severity ...........................................................................174 

 6.2.1.1 Fuel Arrangement ....................................................................................174 

 6.2.1.2 Composition and Amount of Fuel............................................................174 

 6.2.1.3 Ventilation Characteristics and Compartment Geometry ........................176 

 6.2.1.4 Thermal Properties ...................................................................................178 

6.2.2 Fires in a Compartment ...........................................................................................178 

6.2.3 Design Fires and Fire Scenarios .............................................................................179 

6.2.4 Predictive Methods for Fire Modeling ....................................................................180 

 6.2.4.1 Time Equivalence Methods .....................................................................180 

 6.2.4.2 Fire Exposure Curves and Parametric Equations.....................................180 

 6.2.4.3 Fire Modeling with Computer Programs .................................................181 

 6.2.4.4 Selecting a Predictive Method for Fire Modeling....................................182 

6.3 Heat Transfer Analysis ...................................................................................................183 

 6.3.1 Heat Transfer Mechanisms .....................................................................................183 

 6.3.2 Heat Transfer Analysis Methods ............................................................................185 

 6.3.3 Temperature Data for Structural Analysis ..............................................................185 

6.4 Analytical Approaches to Fire-Resistant Design ................................................................186 

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6.4.1 Prescriptive Building Code Requirements ..............................................................186 

6.4.2 Standardized Analytical Approaches ......................................................................186 

6.4.3 Computational Analytical Approaches ...................................................................187 

6.4.4 Selecting an Approach ............................................................................................188 

6.5 Fire Resistant Design Considerations .................................................................................188 

6.5.1 Fuel Control ............................................................................................................189 

6.5.2 Control of Fire Spread ............................................................................................189 

6.5.3 Ventilation Control .................................................................................................190 

6.5.4 Fire Resistance and Protection of Construction Materials ......................................190 

6.6 Fire-Resistant Design of Concrete Structures .....................................................................191 

 6.6.1 Concrete Floor Beams.............................................................................................191 

 6.6.2 Untested Concrete Component Capacity in Design Fires.......................................191 

 6.6.3 Restraint of Continuous Concrete Floors ................................................................192 

 6.6.4 Thermal Expansion Effects .....................................................................................192 

 6.6.5 Reinforced Concrete Floor Sagging........................................................................193 

 6.6.6 Cooling Phase Effects .............................................................................................193 

 6.6.7 Design of Reinforced Concrete Components .........................................................193 

6.7 Fire-Resistant Design of Steel Structures ...........................................................................194 

 6.7.1 Steel Behavior at Elevated Temperatures ...............................................................194 

 6.7.2 Composite Floor Behavior at Elevated Temperatures ............................................195 

 6.7.3 Design of Composite Floor Section ........................................................................196 

 6.7.4 Passive Fire Protection for Steel Components ........................................................196 

6.8 References ...........................................................................................................................197 

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List of Figures

2.1 Hierarchical Relationship for Performance-Based Design .....................................................8 

2.2 Standard Time–Temperature Curves ....................................................................................13 

2.3 Typical Time–Temperature Curves for Given Ventilation Factor and Different 

Fuel Loads (MJ/m2 of Total Internal Surface Area) .............................................................15 

2.4 Alternative Design Procedures in the Structural Eurocodes .................................................23 

3.1 Underrated Fire Load with Respect to Floor Area in General/Clerical Offices in

the United States ...................................................................................................................43 

3.2 Comparison of Calculated Fire Exposures to ASTM E119 and Compartment 

Fire Test ................................................................................................................................45 

4.1 Thermal Conductivity of Four “Limiting” Concretes ...........................................................65 

4.2 Volumetric Specific Heat of Normal Weight and Lightweight Aggregate Concretes .........66 

4.3 Stress–Strain Curves at Elevated Temperature for Normal and Lightweight 

Aggregate Concretes .............................................................................................................67 

4.4 Compressive Strength of Siliceous Aggregate .....................................................................68 

4.5 Compressive Strength of Carbonate Aggregate ....................................................................68 

4.6 Compressive Strength of Lightweight Concrete ...................................................................69 

4.7 Modulus of Elasticity of Concrete at Elevated Temperatures ..............................................70 

4.8 Shear Modulus of Concrete at Elevated Temperatures.........................................................71 

4.9 Coefficient of Thermal Expansion of Concrete ....................................................................71 

4.10 Relative Compressive Strength of HSC under the Stressed Test Method ............................73 

4.11 Relative Compressive Strength of HSC under the Unstressed Test Method ........................73 

4.12 Relative Compressive Strength of HSC under the Unstressed Residual Property Test 

Method ..................................................................................................................................74 

4.13 Relative Compressive Strength of HSC for Design Applications ........................................74 

4.14 Modulus of Elasticity of HSC at Elevated Temperature ......................................................75 

4.15 Strength–Temperature Relationships for Various Steels ......................................................77 

4.16 Modulus of Elasticity–Temperature Relationships for Steel ................................................77 

4.17 Temperatures Within Normal Weight Concrete Slabs or Panels During ASTM E119 

Exposure ...............................................................................................................................78 

4.18 Temperatures Within Sand–Lightweight Concrete Slabs or Panels During ASTM E119 

Exposure ...............................................................................................................................79 

4.19 Temperature on Vertical Centerline of Stemmed Units at 1 Hour of ASTM E119 

Exposure ...............................................................................................................................79 

4.20 Temperature on Vertical Centerline of Stemmed Units at 2 Hours of ASTM E119 

Exposure ...............................................................................................................................80 

4.21 Temperature on Vertical Centerline of Stemmed Units at 3 Hours of ASTM E119 

Exposure ...............................................................................................................................80 

4.22 Temperature on Vertical Centerline of Stemmed Units at 4 Hours of ASTM E119 

 Exposure ...............................................................................................................................81 

4.23 Graphical Heat Transfer Solution for ASTM E119 Exposure of Slab .................................81 

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4.24 Moment Diagram for Simply Supported Flexural Element ..................................................86 

4.25 Nomograms Relating Thrust Parameter, Strain Parameter, and Ratio of CrossSectional Area to Heated Perimeter ......................................................................................89 

4.26 Estimate of Midspan Deflection, Reference Specimens .......................................................90 

4.27 Moment Diagram for a Two-Span Continuous Beam ..........................................................91 

4.28 Uniformly Loaded Member Continuous (or Fixed) at One Support ....................................93 

4.29 Uniformly Loaded Member Continuous at Supports............................................................94 

4.30 Reference Specimen............................................................................................................111 

4.31 Maximum Thrust: Reference Specimen .............................................................................112 

4.32 Correlation Specimens ........................................................................................................113 

4.33 Arrangement of Layers in Circular Section ........................................................................114 

4.34 Arrangement of Elementary Layers in Rectangular Section ..............................................114 

4.35 Arrangement in Quarter Section of Circular .......................................................................118 

4.36 Stress–Strain Network in Quarter Section of Rectangular .................................................118 

4.37 Load Deflection Analysis ...................................................................................................119 

5.1 Thermal Elongation of Structural Steel at Elevated Temperatures ....................................123 

5.2 Instantaneous Coefficient of Thermal Expansion ...............................................................125 

5.3 Specific Heat of Structural Steel at Elevated Temperatures ...............................................126 

5.4 Thermal Conductivity of 12 Low-alloy Steels as a function of Temperatures ...................127 

5.5 Thermal Conductivity of Structural Steel at Elevated Temperatures .................................128 

5.6 Strength and Elasticity Reduction Factors for Structural Steel at Elevated 

Temperatures.......................................................................................................................131 

5.7 Stress–Strain Relationships for Structural Steel at Elevated Temperatures .......................133 

5.8 Comparison of Modulus of Elasticity of Structural Steels at Elevated Temperatures .......134 

5.9 Example of the NIST predicted vs. experimental true stress-true strain behavior of an A572 

structural steel .....................................................................................................................136 

5.10 A comparison of engineering stress vs. strain data computed using NIST approach, the 

Eurocode model, and the WTC experimental data .............................................................137 

5.11 Elevated temperature yield stress normalized by room temperature yield stress ...............139 

5.12 Computed stress-strain curves for an ASTM A572 Grade 50 steel ....................................140 

5.13 Typical Temperature History of a Steel Member Protected with Gypsum Board ..............146 

5.14 Specific Heat of Type X Gypsum Board Core ...................................................................147 

5.15 Thermal Conductivity of Type X Gypsum Board Core ......................................................147 

5.16 Perimeter D for Steel Column Sections ..............................................................................150 

5.17 Perimeter D for Steel Beam Sections..................................................................................151 

5.18 Moment Envelopes Before and During Fire .......................................................................160 

5.19 Typical Positive Moment Force Resultants ........................................................................161 

5.20 Typical Negative Moment Force Resultants.......................................................................162 

6.1 Phases of Fire Development for a Fire in an Envelope ......................................................176 

6.2 Relationship Between Temperature and Time as a Function of Fuel Load ........................177 

6.3 Relationship Between Temperature and Time as a Function of Ventilation ......................179

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List of Tables

2.1 Dead and Live Load Factors for Fire Design .....................................................................10 

2.2 Three Alternative Methods of Comparing Fire Severity with Fire Resistance .................11 

2.3 Alternative Methods of Verifying Fire Performance .........................................................12 

2.4 ASTM E119 and ISO 834 Time–Temperature Curves......................................................14 

3.1 Building Performance Matrix ............................................................................................34 

3.2 Fire Occurrence ..................................................................................................................40 

3.3(a) Fire Load with Respect to Floor Area (MJ/m2) (CIB W14 1983, 1980) ...........................43 

3.3(b) Fire Load in Offices with Respect to Floor Area (MJ/m2

) (Culver 1976) .........................44 

3.3(c) Fire Load with Respect to Floor Area (MJ/m2) (ECCS 2001)...........................................44 

5.1 Reduction Factors KT for Stress–Strain Relationships of Structural Steel at

Elevated Temperatures.....................................................................................................131 

5.2 Parameters for Equation 5.12 ...........................................................................................135 

5.3 True stress-true strain values for an A572 Grade 50 structural steel using equations 5.13 

and 5.14 ............................................................................................................................136 

5.4 Thermal Properties of Common Fire Protection Material ...............................................142 

5.5 Critical Temperatures for Structural Steel Members .......................................................159 

5.6 Literature references for Figure 5.8 .................................................................................164 

5.7 Literature references for Figure 5.11 ...............................................................................164 

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1

Chapter 1 

Introduction

Long Phan, Ph.D., P.E., National Institute of Standards and Technology 

1.1 BASIC EVALUATION CONCEPTS AND GOALS

Current fire protection strategy for a building often incorporates a combination of active 

and passive fire protection measures. Active measures, such as fire alarm and detection 

systems or sprinklers, require either human intervention or automatic activation and help 

control fire spread and its effect as needed at the time of the fire. Passive fire protection 

measures are built into the structural system by: 

• Choice of building materials

• Dimensions of building components 

• Compartmentation, and 

• Fire protection materials

These control fire spread and its effect by providing sufficient fire resistance to prevent 

loss of structural stability within a prescribed time period, which is based on the 

building’s occupancy and fire safety objectives. Materials and construction assemblies 

that provide fire resistance, measured in terms of fire endurance time, are commonly 

referred to as fire resistance-rated-construction or fire-resistive materials and 

construction in the current two model building codes: International Building Code 2006 

(ICC 2006) and the Building Construction and Safety Code, NFPA 5000 (NFPA 2006).

Current U.S. practice for fire resistance design of structures is principally based on the 

provisions of locally adopted codes that are usually based on the model building codes. 

The codes specify minimum required fire endurance times (or fire endurance ratings) for 

building elements and accepted methods for determining their fire endurance ratings. 

The permitted methods for determining fire endurance ratings include: 

1. Qualification testing, which requires the building element to be tested under a 

standard fire exposure (more details in Section 2.5.2) in accordance with the 

procedure and criteria set forth in ASTM E 119 (2007) or NFPA 251 (2006), 

or 

2. Analytical methods as prescribed by ACI/TMS 216.1 (ACI, 2007), 

ASCE/SFPE 29 (2005), and ANSI/AISC 360 (2005). 

ACI/TMS 216.1 (TMS: The Masonry Society) prescribes calculation methods for 

determining equivalent fire resistance ratings for structural members and barrier 

assemblies made of concrete, concrete masonry, and clay masonry that would have been 

equivalently achieved in the ASTM E 119 standard fire test. ASCE/SFPE 29 prescribes 

similar calculation methods but with additional calculation methods for steel and wood 

construction. 

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The prescriptive approach to fire safety engineering is simple to implement and enforce 

and is satisfactory in meeting the codes’ stated intent, which is: 

“...to establish the minimum requirements to safeguard the public health, 

safety and general welfare through structural strength, means of egress 

facilities, stability, sanitation, adequate light and ventilation, energy 

conservation, and safety to life and property from fire and other hazards 

attributed to the built environment.” (ICC 2006) 

However, as will be further articulated in the introduction to Chapter 3 of these 

guidelines, there is also a growing recognition that the current prescriptive, componentbased method only provides a relative comparison of how similar building elements 

performed under a standard fire exposure and does not provide information about the 

actual performance (i.e., load-carrying capacity) of a component or assembly in a real fire 

environment, nor of the system as a whole or its connections. The prescriptive method 

also does not provide how the structural system as a whole or its connections will 

perform in a standard fire exposure, nor does it account for the effects of thermal 

expansion on the strength and stability of a structural system. Therefore, this method 

cannot be used to quantify the maximum possible fire endurance time of a structure 

without undergoing collapse. Thus, for a certain class of buildings such as high-rises or 

other important structures which, due to the longer evacuation time or the significance of 

the buildings, may be required to survive beyond the unquantified system fire endurance 

time without structural collapse using prescriptive methods, a performance-based fire 

resistance approach may provide a more rational method for achieving the necessary fire 

resistance more consistent with the needed level of protection. A performance-based fire 

resistance approach considering the evolution of the building’s structural capacity as it 

undergoes realistic (non-standard) fire exposures is thus a desirable alternative fire 

resistance design method for those structures. This approach may also be used with a 

standard fire if that is deemed appropriate. 

Fire can affect a building’s structural capacity in two ways: 

1. Prolonged exposure of structural components or subsystems to elevated 

temperatures degrades their engineering properties, thus resulting in the 

reduction of overall structural capacity. 

2. Exposure to elevated temperature may induce internal forces (due to restraint 

of thermal expansion) or axial deformations in structural members due to 

plastic and creep strains or buckling, which may adversely affect the global 

stability of the building. 

For steel structures, the effect of geometric nonlinearity is likely to be significant because 

of large deformation that may occur. For concrete structures, lateral displacement of 

columns at slab–column joints due to thermal expansion of the slabs might pose 

additional risk to the global stability of the structure. Further, because steel has relatively 

small thermal mass and high thermal conductivity, temperature is more likely to be nearly 

uniform across most steel sections while concrete components can have steep thermal 

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3

gradients near their surface, which may cause surface spalling. Consideration of the 

evolution of the building’s structural capacity and global stability requires a performancebased fire engineering approach that explicitly considers structural fire loads in the design 

process to achieve a rational fire safety design. 

1.2 PURPOSE OF THESE GUIDELINES

These best practice guidelines are a result of a collaborative effort initiated by NIST as 

part of its World Trade Center (WTC) Response Plan and through its Safety of 

Threatened Building R&D program. NIST is collaborating with representatives of the 

American Concrete Institute (Daniel Falconer), the American Society for Civil Engineers 

(James Rossberg), the Precast/Prestressed Concrete Institute (Jason Krohn), the American 

Institute of Steel Construction (John Ruddy, formerly with Structural Affiliates 

International, Inc.), and the Society of Fire Protection Engineers (Morgan Hurley), who 

served as steering committee members and provided technical oversight. Individual 

experts in the fields of structural and fire safety engineering authored the chapters in this 

document: 

Chapter 1 Long Phan, NIST 

Chapter 2 Andy Buchanan, University of Canterbury 

Chapter 3 Bruce Ellingwood, Georgia Institute of Technology 

Chapter 4 Jim Milke, University of Maryland 

Stephen Pessiki, Lehigh University

Long Phan, NIST 

Chapter 5 Farid Alfawakhiri, American Iron and Steel Institute

Chapter 6 Donald Dusenberry, Simpson Gumpertz & Heger Inc. 

Morgan Hurley, Society of Fire Protection Engineers 

The guidelines were produced under the coordination of Mr. Bernard Murphy of the 

Multi-Hazard Mitigation Council (MMC) of the National Institute of Building Sciences

(NIBS). NIST, together with Morgan Hurley (SFPE), assumed the role of technical 

editors to provide consistency between chapters and to add additional technical 

information reflecting new knowledge gained in the course of the WTC investigation. 

Individuals who contributed in this regard include Dilip Banerjee (NIST, Building and 

Fire Research Laboratory) and William Luecke (NIST, Materials Science and 

Engineering Laboratory).

These best practice guidelines are a non-consensus, non-mandatory document. It is 

intended to be a technical resource that provides the most complete information for 

structural fire-resistant design at present. As a non-mandatory document, it does not 

represent a minimum standard of care. 

These guidelines aim to integrate information on current practice in fire resistance 

engineering in the United States and overseas with current best knowledge in fire risk 

assessment and characterization, material responses at high temperatures, and thermal 

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4

and structural response calculation methods into a single source document, and to provide 

engineers and code enforcement officials with a technical resource for use in their 

approach to fire resistance design and evaluation of concrete and steel structures. They 

are not intended to supersede any existing standards currently in practice. Rather, they 

provide the current best information to enable the use of an alternate performance-based 

design process for fire resistance design of those structures. Where current best practices 

are represented in existing standards, the standards are discussed and referenced.

1.3 SCOPE

The information presented in this document is limited to passive fire protection measures 

only. The material properties and calculation procedures in Chapters 4 and 5 are based 

on the assumption that intervention by active fire protection measures such as sprinklers 

or firefighters is nonexistent. While active fire protection systems are an important 

component of a fire protection strategy, active systems may fail and human intervention 

may not be timely, leaving passive fire resistance measures as the only fire protection. 

Since these guidelines focus only on the structural fire resistance calculation and not the 

larger structural fire safety strategies, the issue of “trade-offs” between active and passive 

fire protection measures is not considered. 

The information in these guidelines is also limited to concrete and steel. Other common 

building construction materials such as masonry and wood are not included since they are 

less likely to be used as the main structural material in high-rise construction, which is 

the type of construction more likely to utilize the performance-based fire resistance 

design approach. 

Chapter 2 presents a review of existing U.S. and international guidelines and design 

standards for fire safety design of concrete and steel structures. It also discusses general 

considerations for structural design for fire conditions and the different levels of 

sophistication in the fire design process currently permitted by the Eurocodes. 

Chapter 3 outlines the decision framework for fire risk mitigation that includes a 

discussion of performance objectives for fire-resistant design, fire hazard modeling, and 

steps involved in structural engineering for fire conditions. 

Chapter 4 provides information on material properties of concrete and steel reinforcement 

as functions of temperature and design procedures with discussions of methods for 

thermal and structural analyses of cast-in-place and precast concrete construction.

Chapter 5 provides information on material properties of structural steel and fire 

protection materials and discusses methods for structural fire design of steel members.

Chapter 6 provides general guidance on structural fire resistant design approaches, 

including technical considerations for fire modeling issues, and discusses practical 

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5

aspects of implementing these design approaches for applications to design of concrete 

and steel structures.

1.4 REFERENCES

ACI (2007), “Code Requirements for Determining Fire Resistance of Concrete and 

Masonry Construction Assemblies,” ACI/TMS 216.1-07, Farmington Hills, Michigan:

American Concrete Institute.

ANSI/AISC (2005), “Specification for Structural Steel Buildings,” ANSI/AISC 360-05, 

American Institute of Steel Construction, Inc., Chicago, Illinois.

ASCE/SFPE (2005), Standard Calculation Methods for Structural Fire Protection, 

ASCE/SEI/SFPE 29-05, Reston, VA: American Society of Civil Engineers.

ASTM (2007), Standard Test Methods for Fire Tests of Building Construction and 

Materials, E119-07a, West Conshohocken, Pa.: American Society for Testing and 

Materials.

ICC (2006), International Building Code, Falls Church, Va.: International Code Council. 

NFPA (2006), Building Construction and Safety Code, NFPA 5000, Quincy, Mass.: 

National Fire Protection Association.

NFPA (2006), “Standard Methods of Tests of Fire Endurance of Building Construction 

and Materials,” NFPA 251, Quincy, Mass.: National Fire Protection Association. 

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6

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7

Chapter 2 

Existing Guidelines for Fire Resistance Design of Concrete and 

Steel Structures

Andy Buchanan, Ph.D., University of Canterbury 

2.1 INTRODUCTION

This chapter describes existing international guidelines and design standards for 

structural fire resistance of concrete and steel structures. These guidelines and standards 

range from very simple prescriptive documents to textbooks and sophisticated codes that 

allow advanced methods of analysis under a wide range of realistic conditions. There is 

focus on current U.S. developments and on the Structural Eurocodes, which are the most 

comprehensive suite of documents for structural fire design at the present time. 

This chapter also benchmarks the international status of development and adoption of 

design standards for structural fire resistance of concrete and steel structures, within the 

overall codes and standards context. 

2.2 LEGISLATIVE ENVIRONMENT

The legislative environment differs greatly among countries. Many countries are moving 

at various speeds to adopt performance-based codes, or to move from a prescriptive code 

environment to a more performance-based environment.

2.2.1 Prescriptive Codes

In the United States there are two main building codes: the International Building Code 

(ICC 2006) and the NFPA Building Construction and Safety Code (NFPA 2006). Both of 

these codes specify fire resistance ratings in a prescriptive environment. Designers have 

the freedom to select materials and assemblies to meet these requirements using the 

methods described below in Section 2.6. 

2.2.2 Performance-Based Codes

Until recently, structural design for fire resistance in all countries has been based on 

prescriptive building codes, with little or no opportunity for designers to take a rational 

engineering approach to the provision of fire safety. Recently, many countries have 

adopted performance-based building codes, which allow designers to use any fire safety 

strategy they wish, provided that adequate safety can be demonstrated. In general terms, a 

prescriptive code states “how a building is to be constructed” whereas a performancebased code states “how a building is to perform” (Buchanan 2001). An important part of 

performance-based design is identification of the severity and probability of the design 

hazards.

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8

In the development of new codes, many countries have adopted a multi-level approach to 

fire resistance design as shown in Figure 2.1. At the highest levels, there is legislation 

specifying the overall goals, functional objectives, and required performance that must be 

achieved in all buildings. At a lower level, there is a selection of alternative means of 

achieving those goals. The three most common options are to: 

1. Comply with a prescriptive “acceptable solution” 

2. Comply using an “approved calculation method” 

3. Carry out a performance-based “alternative design” from engineering 

principles using all the information available

FIGURE 2.1. Hierarchical Relationship for PerformanceBased Design (Buchanan 2001)

Standard calculation methods for all aspects of fire resistance design have not yet been 

developed for widespread use, so compliance with performance-based codes in most 

countries is usually achieved by simply meeting the requirements of “acceptable 

solutions” (a “deemed-to-satisfy” solution), or alternatively carrying out a performancebased “alternative design” based on fire engineering principles. Alternative designs can 

often be used to justify variations from the “acceptable solution” in order to provide cost 

savings or other benefits.

Codes differ around the world. They all have the objectives of protecting life and 

property from the effects of fire, but the emphasis between life safety and property 

protection varies considerably. The code environment in England, Australia, and some 

Scandinavian countries is similar to that in New Zealand (described by Buchanan 1994, 

2000). 

Moves toward performance-based codes are being taken slowly. More background on 

performance-based design in the U.S. context is given by Custer and Meacham (1997) 

and SFPE (2000). NFPA 5000 (2006) and ICC Performance Code (2006) include 

specific provisions that address performance-based design. 

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9

2.2.3 Eurocodes

For more than 25 years, European countries have been working on a new coordinated set 

of structural design standards known as the Structural Eurocodes. These are 

comprehensive documents that bring together diverse European views on all aspects of 

structural design for all main structural materials. The Eurocodes are being prepared by 

the European Committee for Standardization (CEN) under an agreement with Commission 

of the European Community. The Eurocodes recognize the need for member countries to 

set national safety standards that may vary from country to country, so each country’s 

national standard will comprise the full text of the Eurocode with local modifications in a 

supporting document. More details are given later in this chapter. 

2.3 STRUCTURAL DESIGN FOR FIRE CONDITIONS

Structural design for fire conditions is multi-faceted. It can be done in a very simple 

approximate way or with more and more detail considering more and more of the 

important variables. Whatever the level of complexity, it is essential for the designer to 

know what is being achieved and what assumptions are being made. A recent book 

giving an overview of the whole field, including fire severity, fire resistance, and design 

of concrete, steel, and timber structures, is given by Buchanan (2001). Some of the 

material in the book is summarized below in Section 2.8.3. 

 

2.3.1 Design Objectives

For any design outside a simple prescriptive requirement, fire safety objectives must be 

established first. The overall design framework needs to set objectives for property 

protection and safety of occupants and fire fighters for a range of design hazards. Design 

for fire safety is often split into active and passive fire protection. A major component of 

passive fire protection is fire resistance, which is only one component of the overall fire 

safety strategy. Structural design for fire safety is a subset of fire resistance.

Structural elements can be provided with fire resistance for either controlling the spread 

of fire or preventing structural collapse, or both, depending on the functional 

requirements for the particular building. This chapter concentrates on the latter.

2.3.2 Design Process

Most codes recognize that structural design for fire conditions is conceptually similar to 

structural design for normal temperature conditions. Before making any design, it is 

essential to establish clear objectives and determine the severity of the design fire. The 

design can be carried out using either working stress or ultimate strength (LRFD) format. 

The main differences of fire design compared with normal temperature design are that, at 

the time of a fire:

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10

• The applied loads are less.

• Internal forces may be induced by thermal expansion.

• Strengths of materials may be reduced by elevated temperatures.

• Cross section areas may be reduced by charring or spalling.

• Smaller safety factors can be used because of the low likelihood of the event. 

• Deflections may be important as they may affect strength and global stability. 

• Different failure mechanisms need to be considered.

The above factors may be different for different materials. 

2.3.3 Loads for Structural Fire Design

The most likely loads at the time of a fire are much lower than the maximum design loads 

specified for normal temperature conditions. This is especially true for members that 

have been designed for load combinations including wind, snow, or earthquake, or for 

members sized for deflection control or architectural reasons. For this reason, different 

design loads and load combinations are used. It is generally assumed that there is no 

explosion or other structural damage associated with the fire. Loads on members could 

be much higher if other members are removed or distressed. 

Most codes refer to an “arbitrary point-in-time load” to be used for the fire design 

condition. As an example, the ASCE document (ASCE 2005) gives the design load 

combination for fire Uf as

 Uf = 1.2Dn + 0.5 Ln 

where Dn and Ln are the design levels of dead and live load respectively, from the 

standard. 

The Eurocode recommendations differ slightly as shown in Table 2.1, with two values: 

the first is for storage occupancies with semi-permanent loads such as library books or 

other stored items, and the second is for all other occupancies. 

TABLE 2.1. Dead and Live Load Factors for Fire Design

Dead load Storage load Other live load

U.S.A. (ASCE 2005) 1.2Dn 0.5 Ln 0.5 Ln

Ellingwood and Corotis (1991) Dn 0.5 Ln 0.5 Ln

Eurocode (EC1 1994) Dn 0.9 Ln 0.5 Ln

New Zealand (SNZ 1992) Dn 0.6 Ln 0.4 Ln

2.3.4 Design Equation

The fundamental step in designing structures for fire safety is to verify that the fire 

resistance of the structure (or each part of the structure) is greater than the severity of the 

fire to which the structure is exposed. This verification requires that: 

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11

Fire resistance ≥ Fire severity

Where: 

Fire resistance = A measure of the ability of the structure to resist collapse, 

fire spread, or other failure during exposure to a fire of 

specified severity 

Fire severity = A measure of the destructive impact of a fire, or a measure of 

the forces or temperatures that could cause collapse or other 

failure as a result of the fire

As shown in Table 2.2, there are three alternative methods of comparing fire severity 

with fire resistance. The verification may be in the time domain, the temperature

domain, or the strength domain, using different units, which can be confusing if not 

understood clearly. The first two domains are based on the fire resistance rating (FRR), 

which is the time to failure under standard fire conditions, expressed in different units but 

giving the same result. The third domain (strength) is most often used with realistic fires 

where it has to be shown that the structure will not fail at any point during the full process 

of fire development and decay. 

TABLE 2.2. Three Alternative Methods of Comparing Fire Severity with Fire 

Resistance

Domain Units

FIRE RESISTANCE ≥ FIRE SEVERITY

Time minutes 

or hours

Time to failure

(FRR) 

≥ Fire duration as calculated 

or specified by code 

Temperature °C Steel temperature to

cause failure 

≥ Maximum steel temperature reached during the fire 

Strength kN or 

kN.m

Load capacity

(strength/stability) at 

elevated temperature 

≥ Applied load during 

the fire

2.4 LEVELS OF SOPHISTICATION IN THE DESIGN PROCESS

One of the difficulties in describing or specifying fire-resistant design of structures is that 

there are many different levels of sophistication in the design process with regard to the 

part (or parts) of the structure being considered, the fire exposure, and the structural 

analysis under fire conditions. 

Three levels of specifying design for fire performance (as described in the structural 

Eurocodes) are: 

1. Tabulated data 

2. Simplified calculation methods 

3. Advanced calculation models 

Three possible levels of analysis of structural behavior are:

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12

1. Single member analysis

2. Analysis of sub-assemblage or part of the structure

3. Global structural analysis of the whole structure 

Four possible levels of fire exposure are: 

1. Code-specified time of exposure to the standard fire 

2. Time of exposure to the standard fire equivalent to a complete burnout 

3. Parametric fire based on the standard fire with a decay phase

4. Independently calculated exposure of expected real fire

Table 2.3 (adapted from EC2 2002) illustrates the applicability of three levels of 

specifying design for fire performance, showing where each can be used for single 

members, parts of a structure, or global structural analysis. 

TABLE 2.3. Alternative Methods of Verifying Fire Performance

Tabulated 

data

Simplified calculation 

methods

Advanced calculation 

models

Member analysis YES 

Standard fire 

only

YES 

Standard fire and 

parametric fire

YES 

Parametric fire or real fire

Design from first principles

Analysis of parts 

of the structure

NO YES 

Standard fire and 

parametric fire

YES 

Parametric fire or real fire

Design from first principles

Global structural 

analysis

NO NO YES 

Parametric fire or real fire

Design from first principles

2.5 FIRE SEVERITY

2.5.1 Fire Severity for Design

The fire severity to be used for design depends on the legislative environment and on the 

design philosophy. In a prescriptive code, the design fire severity is usually prescribed by 

the code with little or no room for discussion. In a performance-based code, the design 

fire is usually recommended to be a complete burnout, or in some cases a shorter time of 

fire exposure that only allows for escape, rescue, or firefighting (Buchanan 2001). The 

equivalent time of a complete burnout is the time of exposure to the standard test fire that 

would result in an equivalent impact on the structure. 

2.5.2 Standard Fire Exposure

Most countries rely on large-scale fire resistance tests to assess the fire performance of 

building materials and structural elements. The time–temperature curve used in fire 

resistance tests is called the standard fire. Full-size tests are preferred over small-scale 

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13

tests because they allow the method of construction to be assessed, including the effects 

of thermal expansion, shrinkage, local damage, and deformation under load. 

The most widely used standard test specifications are ASTM E119 (ASTM 2007), NFPA 

251 (NFPA 2006), UL 263 (UL 2003), and ISO 834 (ISO 1975). Other national standards 

include British Standard BS 476, Parts 20-23 (BSI 1987), Canadian Standard CAN/ULCS101-04 (ULC 2004), and Australian Standard AS 1530, Part 4 (SAA 1990). The 

standard time–temperature curves from ASTM E119 and ISO 834 are compared in Figure 

2.2. They are seen to be rather similar. All other international fire resistance test 

standards specify similar time–temperature curves.

FIGURE 2.2. Standard Time–Temperature Curves 

The ASTM E119 curve is defined by a number of discrete points, which are shown in 

Table 2.4 along with the corresponding ISO 834 temperatures. Several equations 

approximating the ASTM E119 curve are given by Lie (2002), the simplest of which 

gives the temperature T (°C) as

[ ] 0

)79553.3 T 1750 e 41.170 Tth

th −= + + −

Where:

th = Time (hours) 

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14

TABLE 2.4. ASTM E119 and ISO 834 Time–Temperature Curves

Time

(min)

ASTM E119

Temperature (°C)

ISO 834

Temperature (°C)

0 20 20

5 538 576

10 704 678

30 843 842

60 927 945

120 1010 1049

240 1093 1153

480 1260 1257

The ISO 834 specification (ISO 1975) defines the temperature T (°C) by the following 

equation: 

 T = 345 log10 (8 t + 1) + T0

Where:

t = Time (minutes) 

 T0 = Ambient temperature (°C)

Figure 2.2 also shows two alternative design fires from the Eurocode (EC1 2002). The 

upper curve is the hydrocarbon fire curve, intended for use where a structural member is 

engulfed in flames from a large pool fire. The temperature T (°C) is given by

 T = 1080 (1 - 0.325e -0.167t - 0.675e -2.5t ) + T0

Where:

 t = Time (minutes)

 T0 = Ambient temperature (°C)

The lower curve is intended for design of structural members located outside a burning 

compartment. Unless they are engulfed in flames, exterior structural members will be 

exposed to lower temperatures than members inside a compartment. The temperature for 

external members is given by

 T = 660 (1 - 0.687e -0.32t - 0.313e -3.8t) + T0

2.5.3 Realistic Fire Exposure 

If a fire in a typical room is allowed to grow without intervention, assuming sufficient 

fuel and ventilation, temperatures will increase as the radiant heat flux to all objects in the 

room increases. At a critical level of heat flux, all exposed combustible items in the room 

will ignite, leading to a rapid increase in both heat release rate and temperature. This 

transition is known as flashover, after which the fire is often referred to as a “postflashover fire,” “fully developed fire,” or “full room involvement.” 

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15

As an example of realistic fire exposure in a compartment, Figure 2.3 shows typical 

time–temperature curves for post-flashover fire exposure from Magnusson and 

Thelandersson (1970) (often referred to as the “Swedish” fire curves). These are derived 

from heat balance calculations for the burning rate of ventilation-controlled fires. Very 

different curves are predicted for different ventilation factors and fuel loads. In a similar 

approach, Lie (2002) performed heat balance calculations for post-flashover fires with a 

range of ventilation factors and different wall lining materials. Law (1983) used the 

results from a large number of small-scale tests to propose a simple design method for 

predicting fire duration and temperatures. The Eurocode (EC1 2002) gives an equation 

for “parametric” fires, allowing a time–temperature relationship to be produced for any 

combination of fuel load, ventilation openings, and wall lining materials to give an 

approximation to the Swedish curves. 

These and other approaches have been assessed and compared in the recent engineering 

guide from SFPE (2004), which recommends the use of the Law method for most 

applications, with the Magnusson and Thelandersson method and the Lie method 

recommended in certain cases.

FIGURE 2.3. Typical Time–Temperature Curves for Given Ventilation 

Factor and Different Fuel Loads (MJ/m2 of Total Internal Surface Area) 

(Magnusson and Thelandersson 1970)

Computer programs for calculating temperatures in post-flashover room fires using 

single-zone models include COMPF2 (Babrauskas 1979), Ozone (Franssen et al. 1999), 

FASTLite (Buchanan 1997), and CFIRE (Yii 2003). 

2.5.4 Time Equivalence

The concept of equivalent fire severity is used to relate the severity of an expected real 

fire to the standard test fire. This is important when designers want to use published fire 

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16

resistance ratings from standard tests with estimates of real fire exposure. There are 

several methods of comparing real fires to the standard test fire, the most common being 

the time equivalence formula given in Eurocode 1 (EC1 2002), which gives the 

equivalent time te (min) as

 te = kb w ef 

Where:

 ef = Fuel load (MJ/m2 of floor area)

kb = A parameter to account for different compartment linings, generally 

0.07 min m

2

/MJ

w = Ventilation factor, given by

 ( )

w

Hr b

v

v h

=





 



 + −

+

















>

6 0

0 62

90 0 4

1 0 5

0 3 4

. . . .

. α

α

 Hr = Compartment height (m)

αv = Av / Af 0.05 ≤ αv ≤ 0.25 

αh = Ah / Af αh ≤ 0.20 

 bv = 12.5 (1 + 10 αv - αv

2

 ) 

 Af = Floor area of the compartment (m2) 

 Av = Area of vertical openings in the walls (m2

) 

 Ah = Area of horizontal openings in the roof (m2) 

The equivalent fire severity is very useful where the details of the compartment are 

known and where the designer wishes to use published fire resistance ratings for selection 

of construction elements. 

2.6 FIRE RESISTANCE OF ELEMENTS EXPOSED TO THE 

STANDARD FIRE

Fire resistance is a measure of the ability of a building element to resist a fire, usually the 

time for which the element can meet certain criteria during exposure to a standard fire 

resistance test. A building element is a structural member such as a beam or a column, a 

non-structural element such as a partition or door, or a combination such as a floor or 

load-bearing wall. Individual materials do not possess fire resistance. Fire resistance is a 

property assigned to building elements that are constructed from a single material or a 

mixture of materials. A fire resistance rating is the fire resistance assigned to a building 

element on the basis of a test or some other approval system. Some countries use the 

terms fire rating, fire endurance rating, or fire resistance level, which are usually 

interchangeable.

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17

2.6.1 Failure Criteria

The three failure criteria for fire resistance are stability, integrity, and insulation. To 

meet the stability criterion in a standard fire resistance test, a structural element must 

perform its load-bearing function and carry the applied loads for the duration of the test 

without structural collapse. The integrity and insulation criteria are intended to test the 

ability of a barrier to contain a fire, to prevent fire spreading from the room of origin. To 

meet the integrity criterion, the test specimen must not develop any cracks or fissures that 

allow flame or hot gases to pass through the assembly. To meet the insulation criterion, 

the temperature of the cold side of the test specimen must not exceed a specified limit, 

usually an average increase of 140°C and a maximum increase of 180°C at a single point 

(ASTM 2007). 

An increasing international trend is for fire codes to specify the required fire resistance 

separately for stability, integrity, and insulation. For example, a typical load-bearing wall 

may have a specified fire resistance rating of 60/60/60, which means that a 1-hour rating 

is required for stability, integrity and insulation, respectively. If the wall was non-loadbearing, the specified fire resistance rating would be - /60/60. A fire door with a glazed 

panel may have a specified rating of - /30/ - , which means that this assembly requires an 

integrity rating of 30 minutes, with no requirement for stability or insulation. 

2.6.2 Approvals

Most countries require that fire resistance tests be certified by a recognized testing 

laboratory or approvals agency. In North America, independent testing organizations 

such as Underwriters Laboratories (UL 2004) and the Southwest Research Institute 

(SWRI 2004) maintain registers of fire resistance ratings. Most of these ratings are based 

on standard tests. Ratings based on these approvals are listed in some national building 

codes (e.g., NBCC 1995, ICC 2006). Some countries may need to use approvals from 

other countries, so that in New Zealand, for example, a register of approved listings is 

maintained by the national standards organization (SNZ 1991). Some trade organizations 

(e.g., ASFPCM 1988, Gypsum Association 2003) maintain industry listings of approvals 

for products manufactured or used by their members. Listings generally fall into three 

categories: generic ratings, proprietary ratings, or calculation methods. 

Generic fire resistance ratings, or “tabular ratings,” are listings that assign fire resistance 

to typical materials such as concrete or steel. Generic ratings are derived from full-scale 

fire resistance tests carried out over many years and are widely used because they can be 

applied to commonly available materials in any country. However, generic ratings make 

no allowance for the size and shape of the fire-exposed member or the level of load. 

Proprietary fire resistance ratings apply to proprietary products made by specific 

manufacturers, so they may be more accurate than generic ratings but cannot be applied 

to similar products from other manufacturers. 

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18

As fire engineering develops, it is becoming feasible to assess fire resistance of structural 

members and some assemblies by calculation. Some listing agencies and national design 

codes now include approved calculation methods for assessing fire resistance. 

Calculation methods must be based on full-scale fire resistance test results of similar 

assemblies. Calculations can be used for predicting insulation and load-bearing response 

but not integrity. 

An increasing number of listed fire resistance ratings are based on expert opinion. The 

opinion will state whether the assembly would be considered likely to pass a test, based 

on observations of similar successful tests, calculations, and the considered experience of 

the testing and approving personnel. 

2.7 FIRE RESISTANCE OF BUILDINGS EXPOSED TO REAL 

FIRES

2.7.1 Design of Steel Buildings Exposed to Fire

Whole buildings or significant assemblies in whole buildings cannot be designed 

economically by the simple methods described above. It becomes necessary to use 

specialist computer programs for analysis of fire-exposed structures (the “advanced” 

calculation method in Eurocodes). Such programs will impose deformations on the 

structure and calculate the total strain in each member resulting from those deformations. 

The stress-related strain will be calculated, leading to derivation of the internal forces in 

each member for comparison with the applied loads. The advanced method is essential 

for any structures with structural redundancies. The calculated fire resistance of an 

individual member can be very different from the resistance calculated considering the 

member to be part of a frame or a building. 

2.7.2 Multi-story Frame Buildings

In recent years, the fire performance of large-frame structures has been shown in some 

instances to be better than the fire resistance of the individual structural elements (Moore 

and Lennon 1997). These observations have been supported by extensive computer 

analyses, including Franssen, Schleich, and Cajot (1995) who showed that, when axial 

restraint from thermal expansion of the members is included in the analysis of a frame 

building, the behavior is different from that of the column and beam analyzed separately. 

A large series of full-scale fire tests was carried out between 1994 and 1996 in the 

Cardington Laboratory of the Building Research Establishment in England. A full-size 

eight-story steel building was constructed with composite reinforced concrete slabs on 

exposed metal decking, supported on steel beams with no applied fire protection other 

than a suspended ceiling in some tests. The steel columns were fire-protected. A number 

of fire tests were carried out on parts of one floor of the building, resulting in steel beam 

temperatures up to 1000 °C, leading to deflections up to 600 mm but no collapse and 

generally no integrity failures (Martin and Moore 1997). 

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19

The good performance of the floor/beam systems in such buildings has been attributed to 

a complex interrelated sequence of events, described rather simply as follows (Buchanan 

2001): 

1. The fire causes heating of the beams and the underside of the slab.

2. The slab and beam deform downwards as a result of thermal bowing. 

3. Thermal expansion causes compressive axial restraint forces to develop in the 

beams.

4. The reaction from the stiff surrounding structure causes the axial restraint 

forces to become large.

5. The yield strength and modulus of elasticity of the steel reduce steadily. 

6. The downward deflections increase rapidly due to the combined effects of the 

applied loads, thermal bowing, and the high axial compressive forces. 

7. The axial restraint forces reduce due to the increased deflections and the 

reduced modulus of elasticity, limiting the horizontal forces on the 

surrounding structure.

8. Higher temperatures lead to a further reduction of flexural and axial strength 

and stiffness. 

9. The slab–beam system deforms into a catenary, resisting the applied loads 

with tensile membrane forces.

10. As the fire decays, the structural members cool down and attempt to shorten in 

length. 

11. High tensile axial forces are induced in the slab, the beam, and the beam 

connections. 

These actions can take place in two or three dimensions, depending on the geometry of 

the building and the layout of the structure. The large deformations are often 

accompanied by local buckling of steel members.

Modern computing power has recently made it possible to model the structural response 

of buildings exposed to fires. Computer modeling has been used to help interpret the 

behavior of the Cardington building. Some of the studies have found that the building 

can be modeled using two-dimensional sub-frames rather than the complete threedimensional frame, but others have emphasized the three-dimensional behavior. The 

development of tensile membrane action in reinforced concrete or composite 

steel/concrete floors is described by Lim et al. (2004). 

2.8 MATERIALS STANDARDS

In most countries, the materials standards for structural design provide methods of 

assessing or calculating fire resistance. These often use the three levels shown in Table 

2.2. 

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20

2.8.1 U.S.A.

Structural design for fire resistance in the United States has not moved to performancebased design as quickly as in Europe. A very useful overview of the effects of fires on

structures is given by Lie (1992). Existing building codes include prescriptive 

requirements for fire resistance, which have not changed greatly in recent years, and the 

current movement from regional to national building codes (IBC, NFPA codes) has not 

been accompanied by significant changes in design for fire resistance. However, several 

background documents have recently been published (e.g., SFPE 2004) that will 

eventually lead to changes in materials standards. 

Guidance on the severity of fire exposure on structural elements for both fully developed 

fires and for fire plumes is given in SFPE 2004. 

The most recent U.S.-based standard for structural fire calculations is the joint 

ASCE/SFPE Standard 29-05 (ASCE/SFPE 2005), which gives simple calculation 

methods for all main materials of construction. Most of the methods in this document are 

empirical methods strongly based on standard fire resistance testing, with very little 

guidance on sophisticated analysis or design from first principles. 

Industry groups for particular materials (steel, concrete, and timber) are also developing 

standards and guidance documents for structural fire resistance.

2.8.1.1 Steel

The American Institute of Steel Construction (AISC) is the principal organization 

providing documentation for design of steel structures. The AISC, March 2005 

Specification for Structural Steel Buildings (ANSI/AISC 350-05) provides for design of 

steel structures for fire conditions. Specifically, the 2005 Specification addresses design 

by engineering analysis and provides guidance on load combinations and required 

strength, design-basis fires and both simple and advanced methods of analysis. Simple 

methods of analysis are applicable to individual members while advanced methods are 

applicable to entire steel building frames. Additionally, ANSI/AISC 360-05 gives basic 

information on thermal and mechanical properties of steel and concrete at elevated 

temperatures. 

The American Institute of Steel Construction (AISC 2003) recently commissioned a 

major strategy report on integrating the structural engineering and fire engineering of 

steel structures. The report gives a survey of existing codes and standards, plus 

background information on fire testing, analysis, and design methods for steel structures. 

The SFPE Handbook of Fire Protection Engineering (SFPE 2002) has a chapter on steel 

design that gives an overview of steel structures’ performance in fire, but this does not 

give sufficient information for the advanced calculation methods in Eurocode 3. 

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21

The American Iron and Steel Institute has published a manual for load and resistance 

factor design of cold-formed steel framing members (AISI 1991). 

2.8.1.2 Concrete

The American Concrete Institute is the principal organization providing documentation 

for design of concrete structures. ACI/TMS 216.1-07, Code Requirements for 

Determining Fire Resistance of Concrete and Masonry Construction Assemblies,

provides basic information for design of concrete structures to resist standard fire 

exposure. This document is being updated with new guidance for fire design.

The Concrete Reinforcing Steel Institute has a handbook on fire resistance of reinforced 

concrete (CRSI 1980), and the SFPE Handbook of Fire Protection Engineering (SFPE 

2002) has a chapter on concrete design that gives an overview of concrete structures 

performance in fire.

2.8.2 Canada

Most design standards (concrete, wood, and steel) in Canada refer to the National 

Building Code of Canada (NBCC 2005) for fire resistance specifications, and a new 

standard for fiber-reinforced plastics (FRP) is CSA-S806, which was published in 2002 

and includes design charts for the fire resistance design of FRP-reinforced concrete slabs.

Guidance for design of concrete structures in fire is given by Harmathy (1993), who 

draws on Canadian research and experience.

2.8.3 Eurocodes

By far the most comprehensive international documents for structural design of buildings 

and structures in fire conditions are the Structural Eurocodes. The main codes follow, 

with details in the list of references in Section 2.10 below: 

• EN 1991 Eurocode 1 Basis of design and actions on structures

• EN 1992 Eurocode 2 Design of concrete structures

• EN 1993 Eurocode 3 Design of steel structures

• EN 1994 Eurocode 4 Design of composite steel and concrete structures

• EN 1995 Eurocode 5 Design of timber structures

• EN 1996 Eurocode 6 Design of masonry structures

• EN 1997 Eurocode 7 Geotechnical design

• EN 1998 Eurocode 8 Design provisions for earthquake resistance of 

structures

• EN 1999 Eurocode 9 Design of aluminum alloy structures

Most of these have substantial fire sections (100 pages or more). 

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22

Most European countries also have a national “Annex” to provide various nationally 

determined parameters and other information, sometimes in the form of a “National 

Application Document.” There will be an opportunity to review the Eurocodes at fiveyear intervals, and there may be a maintenance group to answer questions or correct any 

errors in the shorter term.

Most of the Structural Eurocodes include the following statement: 

“A full analytical procedure for structural fire design would take into 

account the behavior of the structural system at elevated temperatures, the 

potential heat exposure and the beneficial effects of active and passive fire 

protection systems, together with the uncertainties associated with these 

three features and the importance of the structure (consequences of 

failure).

“At the present time it is possible to undertake a procedure for determining 

adequate performance which incorporates some, if not all, of these 

parameters and to demonstrate that the structure, or its components, will 

give adequate performance in a real building fire. However, where the 

procedure is based on a nominal (standard) fire the classification system, 

which call for specific periods of fire resistance, takes into account 

(though not explicitly), the features and uncertainties described above.”

Design can then be at various levels in a hierarchy, as shown in Figure 2.4, which 

identifies both the prescriptive and the performance-based approaches. In general, the 

simplest designs will be at the far left-hand side of Figure 2.4 (tabulated data for single 

members in a prescriptive environment), with the most sophisticated designs being at the 

right-hand side of Figure 2.4 (advanced calculation models for entire structures). 

All the Structural Eurocodes include the following sections: 

• Basis of design 

 Fire exposure 

 Verification methods

 Methods of structural analysis 

• Material properties

 Mechanical properties

 Thermal properties 

• Design procedures

 Tabulated data

 Simple calculation methods 

 Advanced calculation methods 

• Construction details 

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23

Tabulated

Data

Simple

Calculation

Models

Advanced

Calculation

Models

Calculation of

Mechanical Actions

at Boundaries

Member

Analysis

Simple

Calculation

Models

(if available)

Advanced

Calculation

Models

Calculation of

Mechanical Actions

at Boundaries

Analysis of Part

of the Structure

Advanced

Calculation

Models

Selection of

Mechanical

Actions

Analysis of

Entire Structure

Prescriptive Rules

(Thermal Actions given by Nominal Fire

SimpleCalculation

Models

(if available)

Advanced

Calculation

Models

Calculation of

Mechanical

 Actions

at Boundaries

Member

Analysis

Advanced

Calculation

Models

Calculation of

Mechanical

Actions

at Boundaries

Analysis of

Part of the

Structure

Advanced

Calculation

Models

Selection of

Mechanical

 Actions

Analysis of

Entire

Structure

Selection of Simple or Advanced

Fire Development Models

Performance-Based Code

(Physically based Thermal Actions)

Project Design

FIGURE 2.4. Alternative Design Procedures in the Structural Eurocodes 

(EC2 2002)

The fire exposure allows for standard or realistic fire design curves to be used. The 

simple calculation methods are for predicting the behavior of single members based on 

simple assumptions. The advanced calculation methods provide the principles for 

computer analyses based on fundamental physical behavior for both thermal analysis and 

mechanical behavior. These analyses need to take into account factors such as transient 

temperature gradients, variation of thermal properties with temperature, axial and flexural 

restraint, thermally induced forces, and thermally induced deformations, throughout the 

duration of the expected fire. The effects of creep are not explicitly included in the 

advanced calculation methods, but the stress–strain relationships have been modified to 

include creep in an indirect way. 

The Eurocodes include information that does not generally appear in other fire codes, 

such as comprehensive expressions for thermal and mechanical properties at elevated 

temperatures and stress-strain relationships at elevated temperatures. This is very useful 

for any analytical modeling of fire behavior of structures. The tabulated listings in the 

Eurocodes are far more extensive than most other codes, the particular benefit to 

designers being that the tables include the improved fire resistance for members that are 

loaded below their design strength at the time of a fire.

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24

2.8.4 European Countries

All the major European countries have been involved in development of the Eurocodes, 

but they have also been maintaining parallel development of national codes that are used 

for everyday design. The transition to design office use of the Eurocodes is expected to 

be slow in most countries, depending on the rate at which the existing national codes are 

phased out. 

In the United Kingdom, a comprehensive recent publication, Structural Response and 

Fire Spread Beyond the Enclosure of Origin (BSI 2003), is a “Published Document” in 

support of BS 7974, Application of Fire Safety Engineering Principles to the Design of 

Buildings (BSI 2001). BS 7974 is currently the most comprehensive code of practice for 

specific fire engineering design in any country. 

The U.K. Published Document (150 pages) is complementary to the Structural Eurocodes 

and provides data and guidance for calculating the fire exposure and fire resistance 

(structural and non-structural) for a wide range of materials and assemblies. The 

document recognizes that detailed structural analysis of complex load-bearing structural 

frames is beyond the scope of such a guidance document. More detail is given in specific 

material codes such as the Code of Practice for Design of Structural Steelwork (BSI 

1990). 

2.8.5 Australia and New Zealand 

The Australian and New Zealand fire codes permit specific fire engineering design in a 

similar performance-based environment. However, the minimum fire ratings specified by 

the New Zealand prescriptive documents are much lower than in Australia and many 

other countries because of more emphasis on life safety than property protection. The 

fire requirements in the structural design codes are rather simplistic, using tabulated 

values for reinforced concrete, for example, or specifying that standard tests should be 

used for establishing fire resistance ratings. All fire resistance values are based on 

standard fire exposure with little or no mention of realistic fires. Alternative calculations 

are permitted but, unlike Europe, very little guidance is given (Buchanan 2000). A useful 

Guide for the Design of Fire Resistant Barriers and Structures has recently been 

published in Australia (England et al. 2000). 

2.9 CONCLUSIONS

• The international community is moving toward performance-based 

engineering standards for structural design in fire conditions. 

• The Structural Eurocodes provide the most comprehensive current codified 

source of information on design for structural fire resistance.

• There is a developing spectrum of fire design methods ranging from simple 

tabulated data to advanced structural analysis and design techniques. 

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25

• The more simple the design method, the more conservative the underlying 

assumptions need to be in order to provide the desired level of protection 

against collapse in fire.

• A major limitation on structural design for fire conditions is assessment of the 

fire scenario and the resulting fire temperatures. 

• Advanced structural analysis and design of buildings in fire conditions are 

more difficult than for normal temperature conditions. 

2.10 REFERENCES

ACI (2007), “Code Requirements for Determining Fire Resistance of Concrete and 

Masonry Construction Assemblies,” ACI/TMS 216.1-07, Farmington Hills, Mich.: 

American Concrete Institute.

AISC (2005), Steel Construction Manual, 13th ed., Chicago: American Institute of Steel 

Construction. 

AISC (2003), “Strategy for Integrating Structural and Fire Engineering of Steel 

Structures,” Report prepared by Ove Arup & Partners for American Institute of Steel 

Construction. 

AISI (1991), Load and Resistance Factor Design Specification for Cold-Formed Steel 

Structural Members, Washington: American Iron and Steel Institute. 

ASCE (2005), Minimum Design Loads for Buildings and Other Structures, SEI/ASCE 7-

05, New York: American Society for Civil Engineers.

ASCE/SFPE (2005), Standard Calculation Methods for Structural Fire Protection, 

ASCE/SEI/SFPE 29-05, Reston, VA: American Society of Civil Engineers. 

ASFPCM (1988), Fire Protection for Structural Steel in Buildings, U.K.: Association of 

Specialist Fire Protection Contractors and Manufacturers.

ASTM (2007), Standard Test Methods for Fire Tests of Building Construction and 

Materials, E119-07a, West Conshohocken, Pa.: American Society for Testing and 

Materials.

Babrauskas, V. (1979), COMPF2: A Program for Calculating Post-Flashover Fire 

Temperatures, NBS Technical Note 991, National Bureau of Standards.

BSI (1987), Fire Tests on Building Materials and Structures, BS 476 (Parts 1 to 23), 

U.K.: British Standards Institution. 

BSI (1990), “Structural Steelwork for Use in Building” – Part 8: Code of Practice for 

Fire Design, BS 5950-8, U.K.: British Standards Institution. 

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26

BSI (2001), Application of Fire Safety Engineering Principles to the Design of Buildings 

- Code of Practice, BS 7974:2001, U.K.: British Standards Institution. 

BSI (2003), Application of Fire Safety Engineering Principles to the Design of Buildings 

- Part 3: Structural Response and Fire Spread Beyond the Enclosure of Origin (Subsystem 3), Published Document PD 7974-3, U.K.: British Standards Institution. 

Buchanan, A.H. (1994), “Fire Engineering for a Performance Based Code, Fire Safety 

Journal. 23:1 (1994) 1-16.

Buchanan, A.H. (1997), “Modeling Post Flashover Fires with FASTLite,” Journal of Fire 

Protection Engineering 9:3 (1997) 1-11. 

Buchanan, A.H., ed. (2000), Fire Engineering Design Guide, New Zealand: Centre for 

Advanced Engineering, University of Canterbury. 

Buchanan, A.H. (2001), Structural Design for Fire Safety, U.K.: John Wiley & Sons, Ltd. 

CRSI (1980), Reinforced Concrete Fire Resistance, Chicago: Concrete Reinforcing Steel 

Institute.

Custer, R.L.P., and B.J. Meacham (1997), Introduction to Performance-Based Fire 

Safety, Society of Fire Protection Engineers and National Fire Protection Association. 

EC1 (2002), Eurocode 1: Actions on Structures. ENV 1991, Part 1-2: General Actions—

Actions on Structures Exposed to Fire, Brussels: European Committee for Standardization.

EC2 (2002), Eurocode 2: Design of Concrete Structures. ENV 1992, Part 1-2: General 

Rules—Structural Fire Design, Brussels: European Committee for Standardization.

EC3 (2002), Eurocode 3: Design of Steel Structures. ENV 1993, Part 1-2: General 

Rules—Structural Fire Design, Brussels: European Committee for Standardization.

EC4 (2003), Eurocode 4: Design of Composite Steel and Concrete Structures. ENV 1994, 

Part 1-2: General Rules—Structural Fire Design, Brussels: European Committee for 

Standardization.

EC5 (1994), Eurocode 5: Design of Timber Structures. ENV 1995, Part 1-2: General 

Rules—Structural Fire Design, Brussels: European Committee for Standardization.

EC6 (1995), Eurocode 6: Design of Masonry Structures. ENV 1996, Part 1-2: General 

Rules—Structural Fire Design, Brussels: European Committee for Standardization.

Ellingwood, B.R., and R.B. Corotis (1991), “Load Combinations for Buildings Exposed 

to Fires,” Engineering Journal, American Institute of Steel Construction 28:1 (1991) 37-

44. 

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27

England, J.P., S.A. Young, M.C. Hui, and N. Kurban (2000), Guide for the Design of Fire 

Resistant Barriers and Structures. Melbourne: Building Control Commission. 

Feasey, R., and A.H. Buchanan (2002), “Post-flashover Fires for Structural Design,” Fire 

Safety Journal 37 (2002) 83-105. 

Franssen, J-M., J-B. Schleich, and L-G. Cajot (1995), “A Simple Model for the Fire 

Resistance of Axially Loaded Members According to Eurocode 3,” Journal of 

Constructional Steel Research 35 (1995) 49-69. 

Franssen, J.-M., V.K.R. Kodur, and J. Mason (2002), User’s manual for SAFIR2001 free: 

A computer program for analysis of structures at elevated temperature conditions, Liege, 

Belgium: University of Liege.

Franssen, J-M., et al. (1999), Competitive Steel Buildings Through Natural Fire Safety 

Concept, Draft Final Report, Part 2, Luxembourg: Profil Arbed Centre de Recherches. 

Gypsum Association (2003), Fire Resistance Design Manual, 17th ed., Washington: 

Gypsum Association. 

Harmathy,T.Z. (1993), Fire Safety Design and Concrete, Essex, England: Longman 

Scientific & Technical.

ICC (2006), International Building Code, Falls Church, Va.: International Code Council. 

ICC (2003b), Performance-Based Building Design Concepts: A Companion Document to 

the ICC PC, Falls Church, Va.: International Code Council. 

ICC (2006), ICC Performance Code for Buildings and Facilities, Falls Church, Va.: 

International Code Council. 

ISO (1975), Fire Resistance Tests—Elements of Building Construction, ISO 834 – 1975, 

International Organization for Standardization. 

Law, M. (1983), “A Basis for the Design of Fire Protection of Building Structures,” The 

Structural Engineer 61A:5 (1983). 

Lie, T.T. (1992) (ed.), “Structural Fire Protection,” ASCE Manuals and Reports of 

Engineering Practice No 78, New York: American Society of Civil Engineers. 

Lie, T.T. (2002), “Fire Temperature-Time Relations,” Chapter 4-8, SFPE Handbook of 

Fire Protection Engineering, 3rd ed., Bethesda, Md.: Society of Fire Protection 

Engineers. 

Lim, L., A.H. Buchanan, P.J. Moss, and J-M. Franssen (2004), “Computer Modeling of 

Restrained Reinforced Concrete Slabs in Fire Conditions,” ASCE Journal of Structural 

Engineering 130:12 (December 2004) 1964-1971. 

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28

Magnusson, S.E., and S. Thelandersson (1970), Temperature-Time Curves of Complete 

Process of Fire Development: Theoretical Study of Wood Fuel Fires in Enclosed Spaces, 

Acta Polytechnica Scandinavica, Civil Engineering and Building Construction Series 65. 

Martin, D.M., and D.B. Moore (1997), Introduction and Background to the Research 

Programme and Major Fire Tests at BRE Cardington, Proceedings, London: National 

Steel Construction Conference. 

Moore, D.B., and T. Lennon (1997), “Fire Engineering Design of Steel Structures,” 

Progress in Structural Engineering and Materials 1:1 (1997) 4-9. 

NBCC (1995), National Building Code of Canada, Ottawa: National Research Council of 

Canada.

NFPA (2006), “Standard Methods of Tests of Fire Endurance of Building Construction 

and Materials,” NFPA 251, Quincy, Mass.: National Fire Protection Association. 

NFPA (2006), Building Construction and Safety Code, NFPA 5000, Quincy, Mass.: 

National Fire Protection Association.

SAA (1990), Fire Resistance Tests of Elements of Structure, AS 1530.4-1990, Standards 

Association of Australia.

SFPE (2000), Engineering Guide: Performance-Based Fire Protection, Bethesda, Md.: 

Society of Fire Protection Engineers. 

SFPE (2002), SFPE Handbook of Fire Protection Engineering, Bethesda, Md.: Society 

of Fire Protection Engineers. 

SFPE (2004), Engineering Guide: Fire Exposures to Structural Elements, Bethesda, Md.: 

Society of Fire Protection Engineers. 

SNZ (1991), Fire Properties of Building Materials and Elements of Structure,. 

Miscellaneous Publication No. 9, Wellington: Standards New Zealand. 

SWRI (2004), Directory of Listed Products, San Antonio, Texas: Southwest Research 

Institute, Department of Fire Technology.

UL (2003), Fire Tests of Building Construction and Materials, UL 263, Northbrook, Ill.: 

Underwriters Laboratories Inc.

UL (2004), Fire Resistance Directory, Northbrook, Ill.: Underwriters Laboratories Inc. 

ULC (2004), Standard Methods of Fire Endurance Tests of Building Construction and 

Materials, CAN/ULC-S101-04, Toronto: Underwriters Laboratories of Canada. 

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29

Yii (2003), “Modelling the Effects of Fuel Types and Ventilation Openings on PostFlashover Compartment Fires,” Fire Engineering Research Report 03/1, New Zealand: 

University of Canterbury. 

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30

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Chapter 3 

Decision Framework for Fire Risk Mitigation

Bruce R. Ellingwood, Ph.D., P.E., Georgia Institute of Technology 

3.1 INTRODUCTION

The public generally has been well served by building code provisions for fire protection and fire 

safety. Since the early 20th century, code requirements for passive fire protection traditionally 

have been derived from building component qualification testing (according to ASTM Standard 

E119, in the United States). Prescriptive code design requirements and methods (e.g., 2003 

International Building Code, Sections 703 and 720; NFPA Building Construction and Safety 

Code, NFPA 5000, Section 8.2.2) stipulate acceptance criteria (in the form of fire ratings) that 

are based on a component surviving a “standard” fire for a prescribed rating period. From a 

practical viewpoint, the traditional approach has proved relatively easy to implement and to 

codify and enforce through building regulation. Fire ratings can be useful for classification 

purposes or for making comparisons of performance of structural components and other building 

products under standardized conditions as well as for demonstrating code compliance. On the 

other hand, such prescriptive requirements and ratings often are simplistic and seldom are 

indicative of actual building performance during a fire. They are based on experience and are 

usually, but not always, conservative. They stipulate an unrealistic fire (one that presumes an 

inexhaustible fuel supply during the rating period), do not distinguish differences in 

compartment ventilation or surface composition, and do not account for realistic structural loads, 

thermal effects, or conditions of structural restraint. They do not account for innovations that 

have taken place in modern building construction. Perhaps most importantly, they focus on fires 

that are localized in compartments (implied by the requirement that floors and walls are to be 

heated on only one side) and do not address the impact of the fire on the structural system as a 

whole. As a result, current fire protection practices may lead to inefficient, uneconomical, and 

occasionally inadequate design solutions. The performance of building systems during realistic 

fires often is better than anticipated (Buchanan 2001). Despite this, building structural 

components and systems that are known to perform acceptably under realistic fire exposures may 

be penalized or not permitted by current practices (Milke 1985; Meacham 1997; Kruppa 2000; 

Bennetts and Thomas 2002). Finally, the specific performance objectives of most prescriptive 

fire protection provisions are not well articulated, making it difficult to apply them to nonroutine design situations. 

The new paradigm of performance-based engineering, where there is a strong motivation to seek 

alternatives to ratings based on prescriptive design and qualification testing, is moving the 

building design profession in this direction in the area of fire safety assurance. Performancebased engineering enhances the prospect of clarifying the intent of the code, overcoming the 

need to rely on prescriptive design solutions that may be disconnected from reality, and 

providing a framework for innovative design solutions. In contrast to traditional prescriptive 

approaches to fire protection, performance-based fire engineering (PBFE) requires a systematic 

approach to identifying building performance objectives and quantitative structural analysis tools 

to verify that these objectives have been achieved. In the United States, performance-based 

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32

engineering solutions for fire protection are permitted under the “alternate means and methods” 

or “equivalency” provisions of model building codes (e.g., Section 1.5 of NFPA 5000; 

Section 104.11 of the IBC; and the performance-based design option in Chapter 5 of 

NFPA 5000). However, the lack of technical methods and data has inhibited their 

implementation for all but special buildings. With recent advances in fire science and advanced 

structural analysis as a design tool, it is becoming possible to consider realistic fire scenarios and 

fire effects on the building’s structural system as a whole as part of the design process (Buchanan 

2001; SFPE 2000). 

In an era when prescriptive building code requirements for fire protection were the norm, 

structural engineers seldom were responsible for fire protection of building structural systems. 

Such protection has been mainly the responsibility of the project architect and, occasionally, a 

fire protection engineer. This state of affairs is changing with the move toward PBFE. There are 

a number of instances where structural engineering for fire conditions may add value to the 

building design process. One case in point is when innovative architectural expressions can be 

inhibited by customary fire resistance rating requirements (Siu 2004). Another is by providing a 

level of performance for buildings of unique social or economic importance beyond the 

traditional goals of safeguarding lives and property, for example in protecting irreplaceable 

building contents against the consequence of building failure. In some cases, a building owner 

may wish to assess general structural integrity and the likelihood of progressive collapse if fire 

protection has been removed by the effect of other abnormal loads (Liew and Chen 2004). 

Finally, nonconforming fire code issues with existing construction can be addressed efficiently 

with PBFE prior to undertaking costly rehabilitation. 

A fire with the potential to damage a building structure severely is a low-probability event in 

comparison with the events that give rise to other loads and structural actions that are common to 

structural engineering analysis and design. Severe fires can lead to ultimate structural limit 

states such as gross inelastic deformation, instability, or partial or total building collapse. The 

science of fire-resistant structural design is at an early stage of development, and the structural 

engineering profession lacks the customary engineering tools to attack the problem. Many 

building codes and standards such as ASCE Standard 7-05 (ASCE 2005) contain a requirement 

to provide general structural integrity, which is aimed at mitigating events that are outside the 

design envelope. These provisions generally lack specifics, however, and structural engineers 

find them difficult to apply. 

Most factors that determine building safety under fire conditions are uncertain in nature. In the 

presence of uncertainty, no building system can be engineered and constructed to be absolutely 

risk free from the effects of fire. Rather, the fire risk must be managed by a combination of 

measures involving architectural and structural engineering, building systems engineering, and 

occupant education. With their extensive provisions for fire safety, building codes are (and have 

been) key tools for managing fire risk in building construction in the interest of public safety, but 

the risks addressed by code provisions have been managed judgmentally. The aftermath of 

recent natural and man-made disasters has necessitated a re-evaluation of such judgmental 

approaches to risk management. Mitigation of risk from low-probability/high-consequence 

events, such as fire, through the added dimension of structural analysis and design requires a 

different approach from the one taken in present building codes. Questions regarding alternative 

or innovative fire protection strategies and required structural strength to withstand a severe fire 

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33

can only be answered from a risk perspective. The move toward PBFE will require riskinformed assessments of fire hazards and alternative strategies for hazard mitigation.

This chapter introduces basic concepts of modern risk-informed decision making and suggests a 

framework for developing and implementing structural design requirements for mitigating fire 

risk in the current building regulatory climate. 

3.2 PERFORMANCE OBJECTIVES AND RISK ASSESSMENT FOR 

NATURAL AND MAN-MADE HAZARDS

Performance-based fire engineering requires quantitative goal setting and documentation on the 

part of the design team. Risk measures are important in PBFE since they become the basis for 

measuring compliance with performance objectives, for comparing alternatives, and for 

highlighting the role of uncertainty in the decision process. 

3.2.1 Performance-Based Engineering 

Performance-based engineering (PBE) is evolving to enable new building technologies and 

structural design to better meet heightened public expectations and to enable more reliable 

prediction and control of building performance. The perception that some structural systems 

designed to code by current building practices have failed to perform satisfactorily during recent 

natural and man-made disasters certainly has provided impetus for the move toward PBE, but the 

desire to minimize arbitrariness and add value to the building process also is a significant 

motivator. Efforts in this regard are well under way in Europe, Australia, New Zealand, Canada 

(where the expected PBE work product for the 2005 National Building Code of Canada is 

termed an “objective-based code”), and the United States (ICC 2003; NFPA 2002). 

Performance-based engineering is based on: 

• A hierarchical set of explicitly stated functional requirements related to building 

category and hazard intensity 

• Quantitative criteria to ensure minimum attributes (e.g., strength, stiffness, durability) 

necessary to meet those requirements

• Evaluation methods (analysis or test) by which satisfaction of the criteria can be 

measured

• Extensive commentaries to explain the basis of the criteria and evaluation methods 

and to provide guidance in their application (Hamburger 1996; Ellingwood 1998) 

To date, PBE has focused particularly on two areas: fire engineering and earthquake engineering. 

The motivating factors behind PBE in the fire engineering area are strongly economic in nature. 

The Society of Fire Protection Engineers (SFPE) is moving its standards program for fireresistant design toward PBFE (SFPE 2000), and the American Institute of Steel Construction 

(AISC) has developed a new Appendix 4 on structural design for fire conditions. The 

International Council for Research and Innovation in Building and Construction (CIB) has 

ongoing work on performance-based fire-safety design through its Working Commission W14 

(1983; Thomas et al. 1986; 2001), and the European Convention for Constructional Steelwork 

(ECCS) has developed a model performance-based fire engineering code (ECCS 2001). Such 

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34

activities on the international scene will accelerate the development of improved quantitative 

methods for engineering structures for fire safety.

Performance objectives for fire-resistant design now appear in the two Model Codes (ICC 2006; 

NFPA 2006). For example, Section 1701.3.11 of the ICC Performance Code for Buildings and 

Facilities (ICC 2006) states that: 

“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 properties, and 

any fire protection features.”

Sections 5.2.2 and 5.2.3 of NFPA’s Building Construction and Safety Code (NFPA 5000)

contain similar statements. The intent of such statements seems clear, but the wording is vague, 

and many engineers (and code officials) are unwilling to undertake the responsibility (liability) 

associated with implementing the concept in design.

Most proposals for PBE have included a performance matrix in which one axis describes event 

severity (e.g., small, medium, large) or frequency, while the second axis identifies building 

occupancy classifications such as those that appear in Table 1-1 of ASCE Standard 7-05 (ASCE 

2005). A common factor in these proposals is a multi-tiered approach to design. The stipulated 

event impacts (e.g., minor, moderate, severe) are placed at the intersections of rows and columns 

in the matrix to define the level of performance expected for each occupancy classification. An 

illustration of such a matrix developed for the ICC Performance Code (ICC 2006) is provided in 

Table 3.1. Such matrices have been developed mainly for natural hazards—the earthquake 

hazard, in particular. Interpreting Figure 3.1, one might expect that a “large” fire would have a 

severe impact on Category I occupancies (temporary or storage facilities with low hazard to 

human life), a high impact on Category II occupancies (office or multi-story residential 

buildings) and a moderate impact on Category III facilities (e.g., hospitals, schools). As an 

alternative, it might be observed that Table 3.1 could be re-arranged to display severity (or 

frequency) of the event on the vertical axis and consequence on the horizontal axis, placing 

building occupancy categories at the intersections of rows and columns in the matrix. (Such a 

format was followed in an early proposal by the Structural Engineers Association of California 

for performance-based earthquake design.) While such performance matrices are useful for 

TABLE 3.1. Building Performance Matrix 

(ICC 2006)

“Size” of 

event

Perf. 

Group I 

Perf. 

Group II 

Perf. Group 

III

Perf. 

Group IV 

V. Large Severe Severe High Mod 

Large Severe High Mod Mild

Medium High Mod Mild Mild

Small Mod Mild Mild Mild

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35

organizing the design process, their applicability to PBFE bears further examination because, in 

contrast to earthquake-related performance, the building performance during fire evolves during 

the event depending on the fire suppression systems that are called into play. 

Risk analysis tools are essential to the success of PBFE for measuring compliance with 

performance objectives, for comparing alternatives, and for highlighting the role of uncertainty 

in the decision process (Ellingwood 2005b). 

3.2.2 Risk and Its Analysis—Hazard, Consequences, Context

Risk involves hazard, consequences, and context (Elms 1992; Stewart and Melchers 1997). The 

hazard is a potentially harmful event, action, or state of nature. The potential for a fire in a 

building is a hazard. The occurrence of the hazardous event has consequences—building 

damage or collapse, loss of life or personal injury, economic losses, or damage to the 

environment—that must be measured in some manner, as described below. Finally, there is the 

context, which provides a frame of reference for the risk analysis, assessment, and decision. As 

stakeholders in a building risk assessment and decision process, individuals, management 

groups, government agencies, or other decision makers may view risk differently. Individuals 

seldom undertake risky activities without an expectation of some benefit. Most individuals or 

small groups are risk averse (implying that they require a substantial increase in value or benefit 

in return for accepting marginal increases in risk). On the other hand, governments and large 

corporations, which may be self-insured, tend to be risk neutral. Willingness on the part of 

individuals to accept risk depends on whether the risk is undertaken voluntarily or involuntarily 

(Starr 1969) and whether the individual perceives that he or she can manage the risky situation. 

Incidents involving large numbers people are viewed differently from incidents involving 

individuals. The element of familiarity or dread or the unknown in perception of risk plays a 

significant role in risk acceptance. The context also is determined by the necessity for risk 

management and how additional investment in risk reduction is balanced against available 

resources. 

Building codes and structural design practice aim at delivering building products and systems 

with risks that the public finds acceptable. Despite the advances in structural reliability analysis 

and acceptance of probability-based structural codes (Galambos et al. 1982; Ellingwood et al. 

1982), it remains unclear exactly what is acceptable risk in the built environment. Like other 

risks, acceptable risk in building construction is relative in the sense that it can be determined 

only in the context of: 

• What is acceptable in other activities

• What investment is required to marginally reduce the risk

• What losses might be incurred if the risk were to increase

To a building occupant, any risk below the (unknown) threshold is acceptable. To a developer, 

on the other hand, any risk above the threshold represents wasted cost. 

Annual mortality statistics in the United States provide a psychological yardstick, of sorts, in 

measuring and discussing risk in terms of annual frequency, although these risks are not truly 

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36

comparable to building risk. For the healthy adult population, the mortality risk from 

cardiovascular disease and cancer is on the order of 10-3/year. At the other extreme, the de 

minimis risk, that risk below which society normally does not impose any regulatory guidance, is 

on the order of 10-7/year (Pate-Cornell 1994). Between these annual frequencies of 10-3/year and 

10-7/year is a gray area in which measures to reduce risk usually are traded off against increments 

in cost of risk reduction. For the sake of illustrating the role of risk in PBFE in this chapter, we 

may take 10-6/year as the upper threshold of acceptable risk (measured in terms of annual 

frequency) due to fires in building construction. In terms of order of magnitude, this is not 

inconsistent with the failure probability of building systems from other natural events 

(Ellingwood 2001). In first-generation LRFD (load and resistance factor design) (Galambos et 

al. 1982; Ellingwood et al. 1982), the target member limit state probability involving formation 

of the first plastic hinge was approximately 0.001 in 50 years (corresponding to a “reliability 

index” of about 3.0); annualized, this is on the order of 10-5. The annual probability of partial or 

total collapse of a redundant structural frame is approximately one order of magnitude less, or on 

the order of 10-6/yr. Note that such comparisons assume that “risk” is equivalent to “annual 

probability or frequency.” 

It would be tempting to assert that the acceptable risk for PBFE should be set so that the PBFE 

design alternatives are at least as safe as those that comply with existing prescriptive 

requirements. This line of thinking is analogous to that followed in first-generation LRFD, 

which was calibrated (in an overall reliability sense) to existing structural design practice. When 

applied to PBFE, however, this approach is questionable. The calibration process for structural 

components subjected to dead, live, wind, and snow load drew upon years of successful 

experience in designing for those common loads using recognized principles of structural 

mechanics and behavior. In contrast, fire is a low-probability event; moreover, the current fireresistant design approach cannot be tied in any meaningful experiential way to real structural 

demands, behavior, or response. May (2004) has argued that, rather than to argue about what is 

acceptable risk, performance-based engineering should aim at developing tools that would allow 

a stakeholder or decision maker to make informed choices about how to manage the risk. 

Building risk must be measured quantitatively to be useful in decision making. The risk metric 

can be expressed as a probability of failure to meet a performance objective. That probability 

can be evaluated from the following equation: 

P[Loss > θ ] = ΣHΣLSΣD P[Loss> θ|D] P[D|LS] P[LS|H] P[H] (3.1) 

Where:

P[A] = Probability of event A 

P[A|B] = (Conditional) probability of event A, given the occurrence of event B 

θ = An appropriate loss metric: severe injury or death, direct damage costs, 

loss of opportunity costs, etc. 

P[LS|H] = Conditional probability of a structural limit state

P[D|LS] = Conditional probability of damage state (e.g., negligible, minor, 

moderate, severe)

P[Loss > θ|D] = Conditional probability of loss 

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37

The probability, P[H], defines the hazard probabilistically. In applications familiar to many 

structural engineers (e.g., wind, earthquake, and flood hazard), it often is expressed as a function 

of the intensity of the event (wind speed, spectral acceleration, or flood stage) and in that form is 

termed the “hazard curve.”

As an alternative, the risk assessment may be based on a set of stipulated scenario events rather 

than on a hazard with a random intensity, depending on the preferences of the decision-maker. 

Each scenario represents a description of fire development in time, from ignition through full 

development and decay, with key features identified that distinguish it from other fires. For a 

scenario fire, the risk metric in Eq. 3.1 becomes a conditional probability: 

P[Loss > θ|Hs] = ΣLSΣD P[Loss > θ|D] P[D|LS] P[LS|Hs] (3.2) 

in which Hs = scenario event(s) selected. Specific interpretations of Eqs. 3.1 and 3.2 for fireresistant design are discussed below in Section 3.3. 

Equations 3.1 and 3.2 deconstruct the risk analysis into its major constituents and enable the 

design team and decision makers (representing different technical disciplines) to focus on 

strategies where risk mitigation is most likely to be achieved successfully and economically. 

The likelihood of the hazard is measured by P[H] (or by its mean annual frequency, λH; as noted 

below, the two are indistinguishable for rare events). The probabilities P[LS|H] or P[LS|Hs] are 

determined by structural engineering analysis. The P[D|LS] describes the damage state for the 

structural system in terms of the structural response quantities computed from the structural 

analysis. Finally, the conditional probability, P[Loss > θ|D], describes the probability of loss, 

given a specific damage state. Both approaches have their advantages and drawbacks in specific 

situations. Eq. 3.1 can be used to assess risk for a spectrum of events and to estimate losses over 

time (often on an annual basis, as that is the common way of reporting λH and resulting losses). 

On the other hand, it may not be practical to identify and/or analyze the full spectrum of hazards. 

Furthermore, the occurrence of some hazards, such as deliberate fires or other acts of 

malevolence directed at specific targets, cannot be modeled probabilistically at the current state 

of the art of risk analysis. Scenario analysis (Eq. 3.2) usually considers a relatively small 

number of hazardous situations, each of which may be described in considerable detail (Hurley 

2004). This approach allows the decision makers to focus on events that are deemed to be 

particularly significant to building performance and facilitates communication of the designbasis events to the building stakeholders. However, the probability of each scenario seldom is 

calculated. Thus, the probabilities in Eq. 3.2 are conditional in nature, and as a consequence the 

loss probabilities cannot be annualized or benchmarked against other commonplace risks. 

A key ingredient of risk management is identification of appropriate risk metrics for the event 

{Loss > θ} in Eqs. 3.1 and 3.2. For purposes of this chapter, this event should be interpreted in a 

broad sense. Structural codes traditionally have been concerned first and foremost with public 

safety (preventing loss of life or personal injury for a normative set of design hazards) and 

property protection, and in this context the collapse of a building, or a large portion of it, is a 

surrogate for all other metrics. Occupant and public safety will continue to be the primary 

objectives of building codes in performance-based engineering. Other performance metrics—

direct economic losses from building contents damage, indirect losses due to interruption of 

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38

function, foregone opportunities, and loss of amenity—traditionally have not been addressed by 

the building regulatory community but may be of concern to certain stakeholder groups for 

certain types of building facilities. Some in the building community have voiced the opinion that 

an appropriate performance objective for fire-resistant structural design is for the building system 

to survive burnout without structural collapse. The purpose here is not to judge the merits of 

these alternative performance objectives (that is a major ingredient of the goal-setting in PBFE 

that must occur among stakeholders), but rather to note that Eqs. 3.1 and 3.2 are sufficiently 

general to be adapted to a variety of decision contexts. In any event, it is important that the 

building design team arrives at a common understanding of how risk is to be measured since this 

will be required in evaluating whether the performance objectives for the project are met. 

Investment in risk reduction invariably must be balanced against available resources. There 

currently are many such trade-offs in the area of fire protection (e.g., reductions in hourly ratings 

if sprinklers are provided), but the effect of the trade-off on performance is not quantified 

(Beyler 2004). Considering each of the hazards term by term in Eq. 3.1 (or hazard scenarios in 

Eq. 3.2), one can estimate the probability of unacceptable loss due to each hazard (or scenario) 

and the relative contribution of each to overall building risk. This overall risk must be limited to 

a socially acceptable value through a combination of professional practice and building 

regulation. Strategies for reducing risks from various hazards or fire scenarios may be directed 

toward different aspects of structural behavior and performance. For example, in earthquake 

engineering, such strategies would be aimed at the lateral force-resisting system, while for fire 

they would be aimed at enhancing the integrity of the structure subjected to gravity loads in a 

degraded or damaged condition. It is unwise to invest large sums in marginally reducing the 

risk from one hazard or scenario while others go unaddressed. Accordingly, the building design 

team must attempt to identify and document major sources of risk as part of the PBFE process. 

Those sources that contribute only trivially to risk should be screened out so that structural 

design and fire protection can focus on risk mitigation strategies that maximize the return (risk 

reduction) on investment. While the scenario analysis (Eq. 3.2) cannot provide a perspective on 

the overall risk to the building from fire in comparison to risk from other natural or man-made 

hazards, specific scenario risks are more easily evaluated and communicated among members of 

the design team and project stakeholders and their relative importance established. Furthermore, 

scenarios are far more easily implemented in building regulation. Accordingly, initial 

implementation of PBFE in structural engineering practice is likely to be scenario-based.

Efforts should be made to identify and analyze all uncertainties that affect the risk metric and to 

display them clearly in the risk assessment. Specific sources of uncertainty in analyzing 

structural response to fires would include: 

• Scenario identification

• Fire load density

• Compartment ventilation

• Structural modeling

• Thermal and mechanical properties of steel and concrete

• Limitations in supporting databases

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39

Uncertainties in engineering risk analysis come in two basic types, designated as aleatoric 

and epistemic. Aleatoric uncertainties represent inherent randomness that is irreducible 

(at the customary scales of engineering analysis) and cannot be eliminated by further 

analysis or testing. Fire load density, occupancy live loads, and strengths of structural 

frames are examples of engineering parameters that are inherently random. Such 

parameters are represented by probability distributions, and the uncertainties are 

propagated through the risk analysis (Eqs. 3.1 and 3.2) to yield a point estimate of risk, 

i.e., “The probability of building collapse is less than 10-5/yr.” In contrast, epistemic or 

knowledge-based uncertainties depend on the engineering models and supporting 

databases and can be reduced (at additional cost) by using improved or advanced (and 

usually more complex) models and more complete databases. When these uncertainties 

are propagated through the risk analysis, they yield an “interval” estimate of risk (in a 

Bayesian sense, since the databases invariably are limited): “I am 90 % confident that the 

probability of building collapse is less than 10-5/yr.” While a statement of such 

probabilities may not be required as part of every design decision, displaying the 

epistemic uncertainty in the risk assessment is important. The display is a manifestation 

of the confidence in the modeling that supports the decision process. Either overstating 

or understating the epistemic uncertainty can distort the risk mitigation policy. 

3.3 FIRE HAZARD MODELING 

Section 3.2 provided a general framework for assessing the risk to building construction 

from natural and man-made hazards, including fires. In this section, these methods are 

considered as they apply specifically to the assessment of fire risk. According to the 

National Fire Protection Association, there were approximately 1.7 million fire starts 

reported in the United States in 2002, leading to approximately 3,400 fatalities and 

property damage of $10 billion. These risks were not randomly distributed across the 

building inventory, however, since approximately 80 % of the fatalities and 75 % of the 

economic losses were concentrated in the residential sector. Single-family residences and 

low-rise multifamily apartments typically are not engineered and thus would fall outside 

the scope of the risk analysis and engineering solutions proposed in these guidelines. 

These guidelines are directed toward engineered construction in residential/commercial 

buildings, offices, public assembly facilities, schools, hospitals, and similar occupancies. 

The fire hazard, defined by the terms P[H] or the postulated scenarios, Hs in Eqs. 3.1 and 

3.2, depends on the incidence of fires, as well as the fire load (through the building 

occupancy), compartment dimensions, thermal and ventilation characteristics, and 

operability of active fire suppression, smoke-control, and air handling systems (sprinklers 

and smoke and heat vents). 

3.3.1 Incidence of Fires

The random occurrence of rare (accidental) events such as fires is commonly modeled as 

a Poisson process. In its simplest formulation, if the occurrences of events are 

statistically independent, the probability of occurrence in any interval of time, ∆t, is λ∆t, 

and the probability of two or more simultaneous events is essentially zero, then if N(t) = 

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40

the number of events that occur in (0,t), the probability that r events occur in that interval 

is (Stewart and Melchers 1997)

P[N(t) = r] = (λt) r exp(-λt)/r!; r = 0,1,2,3... (3.3) 

It may be shown that the expected (average) number of events in (0,t) is λt; hence λ = 

mean rate of occurrence of the Poisson events. Furthermore, the probability of at least 

one event in (0,t) is 

P[N(t) > 1] = 1 – P[N(t) = 0] = 1 – exp(-λt) (3.4) 

If the events are very rare, then the probability of one occurrence in (0,t) is approximately 

equal to λt. Accordingly, if the probabilities and frequencies of occurrence of the hazard 

are annualized, P[Fire] ≈ λFire. As noted previously, it is questionable to model deliberate 

acts that target specific buildings for sociopolitical impact by this approach since such 

acts do not occur randomly in the building population at large. 

The ignition of fire can be modeled as a Poisson event, with a mean rate of occurrence, 

λIgn that is related to floor area, Af. This mean rate of occurrence is summarized in Table 

3.2 for several common building occupancies (CIB W14 1983; SFPE/SEI 2003). The 

values presented were selected for illustration of what might be typical for a broad 

occupancy category and may not be accurate for specific buildings. The mean rate is on 

the order of 0.5 x 10-6/m2/yr to 1.0 x 10-6/m2/yr for common occupancies. There is 

evidence that the ignition rate is proportional to √Af rather than Af in very large 

compartments, where the fuel load may not be uniformly distributed over the floor area. 

The rate of ignition may also depend on the age of the building and level of maintenance 

(Bennetts and Thomas 2002), which are not reflected in the table. Following ignition, the 

likelihood of a fully developed compartment fire with the potential to cause significant 

structural damage depends on the presence and timely activation of fire and smoke 

detection and suppression systems and quick response of the fire department. For 

example, if the reliability of the sprinkler system is on the order of 0.9 – 0.95 (Beyler 

2004) and fire department response times are typical of urban areas, the probability of a 

fully developed fire in urban hotels and schools, given ignition, is on the order of 0.01 

(CIB W14 1983). Thus, in modern code-compliant building systems, such conditions 

occur in a relatively small percentage of cases. The occurrence of full-development fires 

is also described by a Poisson process (with random selection), with mean rate of 

occurrence equal to the product of P[Full development|Ignition] and λIgn. This rate, 

denoted λH, is on the order of 10-8/m2

/yr and is equivalent to the term P[H] in Eq. 3.1. 

TABLE 3.2. Fire Occurrence

Occupancy Mean rate x 10-6/m2/yr P[Flashover|ignition]

Office 1 to 2 10-3 to 10-2

Dwelling 2 to 5 10-1

Hotel 0.5 10-3 to 10-2

Commercial 1.0 10-2

School 0.5 10-3

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41

While this annual frequency is order of magnitude only, it is not inconsistent with fire 

occurrence statistics reported independently. For example, Clifton and Feeney (2004) 

remark that the probability of a fully developed fire occurring over the 50-year life of a 

multi-story office building with sprinklers in New Zealand is on the order of 0.5 %. For a 

multi-story building with 10,000 m2 of leasable space, this corresponds to an annual 

frequency of approximately 1 x 10-4/yr, about what one would expect from the above 

formulation. Similarly, Bennetts and Thomas (2002) report a “fire start frequency rate” 

of approximately 2 x 10-3/apartment/year in the United States. At an average apartment 

area of 110 m2, this corresponds to an annual frequency of 1.8 x 10-5/m2/yr, an incidence 

that is one order of magnitude higher than that in Table 3.2 for “dwellings,” which 

includes both single-family residences and apartments. It often is sufficient in risk 

analysis to estimate such frequencies to an order of magnitude to evaluate engineering 

alternatives.

3.3.2 Characteristics of Fire Exposure Curves

Once a fire has ignited, its subsequent severity and impact on the structural system 

depend on the fire load (amount, type, distribution, and surface characteristics), 

compartment ventilation, compartment geometry, and thermal characteristics of the 

compartment bounding surface. The ASTM E119/E1529/ISO exposures describe a longduration moderately severe post-flashover fire but do not address specifically any of the 

factors above. The monotonic increase implies that the supply of fuel is inexhaustible 

and there is no cooling phase. For example, in ISO Standard 834, the time-temperature 

curves are given by

T(t) = 20 + 345 log10(1 + 8t) (cellulose) (3.5a) 

T(t) = 20 + 1080 [1 – 0.325 e-0.167t + 0.675 e-2.5t] (hydrocarbon) (3.5b) 

in which T is given in °C and t is in minutes. It should be noted that a temperaturecontrolled standard test such as that specified by ASTM (2002)or ISO may not imply a 

constant compartment fuel load since structural elements with high thermal mass require 

more fuel to maintain the furnace temperatures than lightweight construction materials. 

Furthermore, combustible structural assemblies contribute to the fuel load, reducing the 

fuel otherwise required to maintain furnace temperatures, making their comparison with 

the performance of non-combustible assemblies difficult. 

The primary factors affecting fire development and the temperature history in a building 

compartment during a real fire are the fire load per unit area, qt = WM/At; the ventilation 

parameter, Ao h ; the opening factor, F = Ao At

h , which controls the rate of combustion; 

and the thermal properties of the compartment lining materials (CIB W14 1986; SFPE 

2004). Parameter Ao denotes the total area (m2) of door and window openings in the 

compartment, h = average height (m) of the openings, At is total area (m2) of the 

compartment bounding surface, M is total mass (kg) of combustibles in the compartment, 

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42

and W = effective heat of combustion, which for a building fire involving normal 

building contents is taken as 18.6 MJ/kg (8,000 Btu/lb). (Chemical fires may have a 

different W, depending on the nature of the fuel.) When a building contains materials 

that pose a high fire hazard, involving high fuel loads, flammable liquids, or explosive 

materials, a special analysis of fire hazard and fire exposure (temperature and duration) 

should be conducted. 

Fire load surveys have provided data to describe fire loads for common occupancies, 

often in terms of fire load density obtained from the calorific value of combustible 

material. These data usually are reported in terms of fire load per unit floor area, qf, 

although occasionally they are reported as load, qt, with respect to total area of the 

compartment bounding surface. The fire load is random in intensity and spatial 

distribution, but generally is reported as an equivalent uniformly distributed load with 

respect to floor area. A histogram for fire load in a general/clerical office in the United 

States (equivalent weight of combustibles having a calorific value of 18.6 MJ/kg (8,000 

Btu/lb), (Culver 1976) is shown in Figure 3.1. Tables 3.3(a) through 3.3(c) summarize 

some of the fire load data from the United States and Europe that might be considered in 

selecting a fire load, qf (MJ/m2

), with respect to compartment floor area. Appendix 1 of 

(CIB W14 1986) summarizes fire loads, qf, from a variety of studies in Europe and the 

United States. There are significant variations in qf from occupancy to occupancy and 

from study to study for a given occupancy. For example, for general offices, the mean 

value of qf (in MJ/m2) = 420 (ECCS 2001), 390 (CIB W14 1983), 598 (Culver 1976), and 

348 (Kumar and Rao 1997). As a further benchmark for comparison, the Cardington fire 

tests (Newman, Robinson, and Bailey 2000) were conducted with fire loads of 372

MJ/m2 to 744 MJ/m2 (floor area), assuming an effective heat of fuel of 18.6 MJ/kg. The 

data summarized in Table 3.3 present the mean and standard deviation of qf and its 80th

and 90th percentiles. (The ECCS 111 (2001) has recommended that the design fire load 

be taken at the 80th percentile.) It is notable that the coefficient of variation (COV) in fire 

load is 0.30 for all occupancies in the ECCS 111 recommendations, a value that is 

substantially less than that measured in both Culver’s (1976) 

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43

FIGURE 3.1. Underrated Fire Load with Respect to Floor Area in 

General/Clerical Offices in the United States (Culver 1976) [1 psf = 47.88 Pa)

and Kumar and Rao’s (1997) surveys (approximately 0.60). Moreover, it is substantially 

less than the COVs in load intensities measured in most modern surveys of live loads in 

the United States and Western Europe, which tend to be on the order of 0.50 to 0.60, 

depending on the loaded area. 

TABLE 3.3(a). Fire Load with Respect to Floor Area (MJ/m2) (CIB W14, 

1983; 1986)

Occupancy Mean Standard deviation 80%ile 90%ile

Offices 420 309 680 740

Dwellings 

(bedroom)

640 135 750 810

Hotels 345 92 420 472

Schools (primary) 285 79 360 415

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44

TABLE 3.3(b). Fire Load in Offices with Respect to Floor Area (MJ/m2) 

(Culver 1976)

Occupancy Mean Standard deviation 80%ile 90%ile

General/clerical offices 598 358 898 1,046

Conference rooms 425 425 714 969

File, storage rooms 1,112 1,020 1,968 2,400

TABLE 3.3(c). Fire Load with Respect to Floor Area (MJ/m2

) (ECCS 2001)

Occupancy Mean Standard deviation 80%ile 90%ile

Office 420 126 511 584

Dwelling 780 234 948 1,085

Hotel 310 93 377 431

Shopping center 600 180 730 835

Schools 285 86 347 397

Hospitals 230 69 280 320

Theaters 300 90 365 420

The fire loads reported above are obtained, for the most part, from building surveys. By 

their nature, such surveys capture the fuel load at an arbitrary point in time. It should 

also be noted that fuel loads, like other occupancy loads, vary during the life of a building 

as tenancies and occupancy classifications change. Fuel loads during periods of 

remodeling, rehabilitation, or construction may be relatively high, at a time when 

protection systems may not be functioning. Such loads would not be reflected in Tables 

3.3(a) through 3.3(c). Clearly, there is a need for further research on fire loads for 

common building occupancies. 

To evaluate the time–temperature curve for a fully developed (post-flashover) fire 

resulting from a given fire scenario, a post-flashover condition can be assumed in which 

thermal conditions are homogeneous throughout the compartment, the fire is ventilation 

controlled, and no combustion occurs outside the compartment. Most post-flashover fires 

satisfy these conditions. The volumetric flow of air into the compartment is proportional 

to the ventilation factor Ao√ h, in which Ao = total area (m2) of door or window openings 

in the compartment and h = average height of openings; thus, the total rate of heat release 

within the compartment is also proportional to Ao√h. The duration of the burning phase 

of the fire then is proportional to MW/(Ao√ h). A solution to the energy balance equation 

then yields the compartment temperature, T, as a function of time, t, in terms of opening 

factor F, qt, and the thermal properties of the compartment interior surface, which 

defines the fire exposure (e.g., Magnusson and Thelandersson 1974; SFPE 2004). Such 

relations have been verified experimentally. To illustrate, it was assumed that At = 4Af, 

noting that for typical rooms the total surface area is three to five times the floor area. 

Based on these data, two fire exposure curves were developed to simulate a compartment 

fire test conducted at the National Bureau of Standards (now National Institute of 

Standards and Technology). The fire load was qt = 100 MJ/m2 (qf ≈ 400 MJ/m2

) and the 

two opening factors believed to be typical in light occupancies: F = 0.04 m1/2 and 0.08 

m1/2. These fire exposures are compared to the standard ASTM E119 (2007) exposure 

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45

and the temperatures measured in the fire test in Figure 3.2. Temperatures measured in 

the compartment fire increase more rapidly after flashover than indicated by the ASTM 

standard fire exposure, but the fire duration is relatively short and the temperatures decay 

for an extended period (fuel-controlled phase). Knowledge of the fuel load and 

compartment ventilation can be used to generate a fire exposure that matches a natural 

fire quite well. Such fires can be approximately parameterized (Buchanan 2001; ECCS 

2001; SFPE 2004). 

FIGURE 3.2. Comparison of Calculated Fire Exposures to ASTM E119 and 

Compartment Fire Test. (Fire load is referenced to total compartment bounding 

area, At.)

The above analysis yields one fire exposure curve for a compartment. The fuel source, 

arrangement, and load, and the compartment ventilation and composition of its bounding 

surfaces constitute one fire scenario. A “scenario” is a set of conditions—fire protection, 

ignition, nature/configuration of fuel, ventilation, etc.—that define the fire exposure 

curve used in design (SFPE 2000). In structural engineering of frames for fire protection 

in most multi-tenant buildings, several fire scenarios may have to be considered. This is 

considered further in Section 3.4.3.1. 

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3.4 STRUCTURAL ENGINEERING FOR FIRE CONDITIONS

This section considers the structural integrity aspects of fire protection. Once the designbasis events are determined, the principles of structural analysis used in designing for fire 

conditions are similar to those used for other hazards, but the conditional nature of the 

limit states leads to some differences that will become apparent in the following 

discussion. General design strategies require a statement of performance objectives and a 

general approach to risk management. Specific technical engineering approaches then 

can be developed along two lines: design by engineering analysis and design by 

qualification testing. 

3.4.1 Performance Objective

The primary performance objective underlying structural engineering for fire conditions 

is that of life safety. Fire safety levels should depend on the nature of the fire hazard and 

building occupancy, height of the building, presence of active and passive fire mitigation 

measures, and the effectiveness of firefighting. Given the occurrence of a fire, three limit 

states traditionally have been considered (Buchanan 2001): 

1. Heat transmission leading to unacceptable rise in temperature on unexposed 

surfaces

2. Breach of barrier due to loss of integrity 

3. Loss of load-bearing capacity (or, for short, insulation/integrity/stability) 

Other specific performance objectives must be determined by the stakeholders in the 

building process. Performance-based engineering, in contrast to traditional prescriptive 

approaches that essentially follow a design recipe, involves goal-setting and 

documentation on the part of the design team. Performance objectives for fire-resistant 

design might include, but are not necessarily limited to the following (e.g, ICC 2006; 

NFPA 2003; CIB W14 2001): 

• Life safety of building occupants 

• Life safety for firefighters entering the building

• Survival of burn-out of building contents 

• Preservation of paths of entrance/egress 

• Protection of property (including adjacent buildings) or minimal disruption of 

business operation 

• Protection of the environment 

• Protection of civil infrastructure 

3.4.2 General Fire Risk Mitigation Strategies

Fire risk mitigation and fire safety measures can be aimed at three levels: 

1. Preventing the outbreak of fires through elimination of ignition sources or 

hazardous practices

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2. Preventing fire development (flames and smoke) through early detection and 

suppression 

3. Preventing loss of life or structural collapse through provision of general 

structural integrity, compartmentation, fire protection systems, and other 

measures

Proper management of building risk involves examining each of the terms in Eqs. 3.1 or 

3.2 as part of the decision process. Structural engineering for fire is concerned primarily 

with maintaining compartmentation (limiting spread) and general structural integrity.

3.4.2.1 Event Control/Fire Protection Systems 

Event control focuses on the term P[H] in Eq. 3.1. One principle of risk management of 

man-made hazards is that it usually is more cost-effective to prevent or control a situation 

than to deal with one that has progressed beyond the initial stage. In other words, if P[H] 

≈ λH can be limited to (approximately) the de minimis threshold, then further structural 

engineering measures for fire protection to reduce the other terms in the risk equation are 

not necessary. For many types of building construction this may be the most costeffective strategy for risk mitigation. If one building performance objective is to protect 

the building and its contents from significant damage (for example, in a financial 

institution, record-keeping facility, or museum), or to minimize the likelihood that 

damage to adjacent buildings may occur (as in a historic district), it is important to 

minimize the likelihood of a major fire ever developing. High levels of structural 

integrity may not be particularly useful for such applications if the contents are 

essentially irreplaceable or costs of contents damage are significant.

Conversely, if P[H] is one or two orders above the de minimis threshold, further 

investigation of that hazard is warranted. (It is interesting to note that the National 

Building Code of Canada (1996) specifies a threshold for the consideration of 

“abnormal” loads at 10-4/yr. If the likelihood of the event is greater than that threshold, 

consideration of the event must be documented.) The evaluation of P[H] has several 

dimensions: likelihood of ignition, flashover, and behavior of the building occupants 

when confronted with the threat. The effectiveness of nonstructural measures, such as 

sprinklers, vents, and intervention, first by occupants and subsequently by firefighters 

once they arrive on the scene, are taken into account in the risk analysis through the term 

P[H] in Eq. 3.1. Collapsing these factors into one term may appear to oversimplify what 

may be a complex systems analysis. An event tree formulation may be helpful in 

visualizing the alternatives and in identifying plausible scenarios (Mowrer 2004). Such 

an event tree should include the probability that the sprinklers malfunction, the 

probability that the building ventilation system is operating properly, and the likelihood 

that emergency personnel arrive at a state where the fire can still be controlled, and the 

probability that passive protection will not have been damaged or destroyed by ancillary 

events.

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3.4.2.2 Structural Engineering Analysis 

Structural engineering measures to design fire resistance into the building structural 

system directly affect the terms P[LS|H] and P[D|LS] in Eq. 3.1. For simplicity in 

structural code development (e.g., AISC 2005), the term P[Loss> θ|D] P[D|LS] in Eq. 3.1 

may be collapsed into one conditional probability, P[DS|LS], in which DS = damage state 

identified as being consistent with the performance objectives for the building project. 

The damage state might be stipulated as “moderate damage” or “collapse,” depending on 

the performance objective. If the overall risk (measured by annual frequency) is to be 

limited to less than 10-6, then the engineering measures for fire protection must ensure 

that

ΣLSP[DS|LS]P[LS|H] < 10-6/λH (3.6) 

This criterion can be satisfied with a combination of passive fire protection and structural 

engineering measures, as described in the following section. Consistent with the idea of 

risk differentiation among different building occupancies that is implied in Table 3.1, one 

might specify that 10-6 in Eq. 3.6 be replaced by 10-5 for buildings in which the 

consequences are less severe and with 10-7 for essential facilities that cannot be 

evacuated, such as hospitals. Such risk differentiations are made only indirectly in 

current building regulations, if at all (through such devices as “importance factors”), and 

should be carefully debated before implementation. 

3.4.3 Structural Design by Engineering Analysis

A structurally significant fire results in imposed deformations on the building structure, 

and the forces developed in an indeterminate building frame are self-limiting in nature. 

Moreover, the strength and stiffness of structural materials are temperature dependent 

(degrading to only a fraction of the ambient strength and stiffness at temperatures as high 

as 1,000°C) in a fully developed compartment fire. Results of recent full-scale building 

fire tests (Newman, Robinson, and Bailey 2000) indicate that advanced structural 

analysis can reproduce the actual behavior of the structure quite well.

3.4.3.1 Design-Basis Fire Scenarios

A scenario identifies a set of conditions—sources of ignition, nature and configuration of 

fuel, ventilation, patterns of growth and spread of smoke, availability of active fire 

detection and protection systems, etc.—that can be used as a basis for verifying that the 

performance objectives of the design have been achieved. In risk analysis and 

management, scenario analyses are commonly used to answer “what if” questions. It is 

not possible to identify all possible scenarios, but an effort must be made to identify those 

that are dominant contributors to fire risk. 

The performance option in the NFPA 5000 Building Construction and Safety Code

stipulates eight scenarios (Section 5.5.2), but not all must be evaluated fully (Section 

5.5.1.3). Section 1701.3.15 of the ICC Performance Code requires scenarios that “can be 

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reasonably expected to impact in buildings as designed or constructed” but does not 

require a specific number of scenarios. The number of design scenarios must be kept to a 

manageable size since the number of possible scenarios may become quite large in 

complex facilities. Stipulating an excessive number of scenarios (e.g., involving ignition 

and development in different parts of the building) may discourage engineers from 

applying PBFE and cause them to regress to traditional prescriptive or deemed-to-satisfy 

provisions. 

Each fire scenario ultimately produces a fire exposure curve that can be used in advanced 

structural analysis to assess the structural response during the heating and cooling phases 

following exhaustion of combustibles. Typically, three types of fire scenario might be 

considered (Hurley 2004). The first and most important would involve a fully developed 

(post-flashover) fire with involvement of all combustibles within the compartment 

(similar to the one illustrated in Figure 3.2). This scenario would stipulate the amount 

and distribution of fuel, compartment ventilation, and the type of materials forming the 

floor, walls, and ceiling of the compartment. The second, and related, scenario involves 

window flames that escape the enclosure of a post-flashover fire to heat exterior 

structural elements. The third would consider the impact of local fire plumes adjacent to 

exposed and unprotected structural elements; this scenario may occur in large 

compartments where fuel is not distributed uniformly and there is little interaction with 

the enclosure. The SFPE Engineering Guide: Fire Exposures to Structural Elements

(SFPE 2004) provides additional information on the analysis of local fire plumes. 

Scenarios should include the possibility that sprinklers (if present) fail to function. At a 

greater level of sophistication, some scenarios may involve fires spreading to several 

adjacent compartments or floors in the course of fire development. The development of 

fire exposure curves for multiple-compartment fires is highly complex (Beyler 2004). In 

the last decade, computational fluid dynamics (CFD) models have become widely used 

by fire protection engineers to simulate the behavior of fires in buildings (SFPE 

Handbook, 4th ed.). While there is extensive validation of these models in situations 

where the fire's heat release rate is known or specified (NUREG-1824), there has been 

less validation work for post-flashover fires, fire growth and spread, and under-ventilated 

fires. 

3.4.3.2 Thermal Effects on Structural Components and Systems 

The fire exposure, nature of heat transfer, and thermal properties of the material govern 

the development of temperatures (and thus thermal strains) in the structural components 

and system. If the temperature is essentially uniform in the compartment, these 

temperatures can be determined from the numerical solution of the heat flow (diffusion) 

equation. Assuming heat flow in two dimensions and homogeneous and isotropic 

thermal conductivity, 

ρCp ∂T/∂t = k ∇2

T (3.7) 

in which T = T(x,y,t) represents the temperature within the structural element at 

coordinate (x,y), ρ = density, thermal parameters Cp = specific heat (typically 600 J/kg K 

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50

for steel and 900 J/kg K for concrete), and k = thermal conductivity (typically 45 W/m K 

for steel and 1.4 W/m K for concrete). The thermal parameters may be temperature 

dependent (ECCS 2001). Assuming that the heat flow across the boundary due to the fire 

is caused by both convection and radiation, the boundary condition at the exposed surface 

for the solution of Eq. 3.7 is 

– k ∂T/∂n = hc(Tg – Ts) + Vεσ (Tg

4

 – Ts

4

) (3.8) 

Where:

n = Direction of heat flow at the boundary 

hc = Convection coefficient (typically 25 W/m2 K)

V = Radiation view factor

ε = Resultant emissivity (typically about 0.8 for hot surfaces and luminous 

flames)

σ = Stefan-Boltzman constant (5.67 x 10-8 W/m2 K4) 

Tg, Ts = Absolute temperatures of compartment (e.g., Figure 3.2) and surface, 

respectively

Analytical solutions to Eqs. 3.7 and 3.8 are difficult to obtain, and finite element or finite 

difference approaches generally are necessary for all but simple structural member tests. 

In the finite element formulation, Eqs. 3.7 and 3.8 become, 

C ∂T/∂t + K T = Q (3.9) 

Where:

C = Heat capacity matrix

K = Thermal conductivity matrix

Q = External heat input 

T = Temperature vector

A number of programs are available to perform the thermal analysis (Milke 2002). 

Simplified analytical and graphical methods are available for computing temperature 

develop-ment in simple beams and columns. Some of these methods are summarized in 

T.T. Lie et al. (1992). 

3.4.3.3 Strength Requirements and Deformation Limits 

Limit states design is well accepted for structural engineering for occupancy and 

environmental loads. Structural engineering for fire conditions must adopt a similar 

approach. The structural actions resulting from the design-basis fire or alternative fire 

scenarios must be integrated into the structural analysis and design process. This section 

summarizes the probabilistic basis for appropriate combinations of loads to facilitate fireresistant structural design and recommends specific load combinations for this purpose 

(Ellingwood and Corotis 1991; Ellingwood 2005a). The probabilistic basis is essential 

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for measuring compliance with performance objectives, for comparing alternatives, and 

for making the role of uncertainty in the decision process transparent. 

Structural loads vary randomly in space and time. Modern structural reliability theory 

has illuminated the analysis of load combinations, and has led to design load 

combinations that have a specified probability of being exceeded (ASCE 2005). The 

bases for the probabilistic modeling of loads and load combinations have been published 

in the archival literature (e.g., Ellingwood et al. 1982). To summarize, both theoretical 

analysis and simulation have shown that when two or more loads that vary in time are 

combined, the maximum combined effect, U, during time interval (0,t) occurs when one 

load achieves its maximum (or “principal” value during 0,t while the other loads are at 

their companion values. In other words, if one were combining the structural action due 

to the fire, T, with dead load, D, and occupancy live load, L, one would consider 

U = Max [D + L + T] = D + max [max L + T, L + max T] (3.10) 

Equation 3.10 is a simple statement of the “principal action–companion action” load 

combination scheme that is the basis for all modern limit states structural codes 

worldwide (ASCE 7-05; Eurocode 1 1994). Since fire is a very rare event with a 

duration that measures in hours in any local region within the building, the probability 

that a fire occurs concurrent with the maximum live load is negligible—in fact, it is on 

the order of 10-9/yr (Ellingwood and Corotis 1991; Ellingwood 2005 —so the term “max 

L + T” in Eq. 3.10 is simply equal to max L, which is addressed by the ordinary gravity 

load design criteria in ASCE Standard 7-05. The L in “L + max T” is the “companion 

action live load, or the value expected to act at the time of the design-basis fire, 

represented by max T. Surveys of live loads (e.g., Culver 1976; Ellingwood and Corotis 

1991) show that the mean value of this companion action live load generally is on the 

order of 25 % to 30 % of the nominal live load specified in ASCE Standard 7-05. 

Reasoning along these lines, one can develop a suitable set of load combinations 

involving fire and gravity load effects. Such combinations are required for limit states 

design based on advanced structural analysis but could also be used for designing a 

suitable fire test of a structural component or assembly. Observing the reliability 

constraint in Eq. 3.6 limiting the collapse probability to less than 10-6/yr and noting that 

λH typically is on the order 10-5 to 10-4/yr, the load factors in the principal 

action/companion action load combination are adjusted until the probability that the 

combined structural action, U, exceeds the design action, Ud, is equal to approximately 

0.05 to 0.1. This iterative process yields

 Ud = (0.9 or 1.2)D + T + 0.5L + (0.5Lr or 0.2S) (3.11) 

in which T (replacing term “max T” for simplicity) denotes the structural action (force or 

deformation) resulting from the postulated fire scenario (discussed below). The loads D, 

L, Lr, and S are the nominal loads in ASCE Standard 7-05. As might be observed from 

the brief review of probabilistic load models presented above, the companion actions 

0.5L, 0.5Lr, and 0.2S represent the most probable values of load on the structure at the 

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52

time of the fire. When gravity effects stabilize the structure, the load factor on D is 0.9 

rather than 1.2, and the live load is set equal to zero. Equation 3.11 is found in 

Commentary 2.5 of ASCE Standard 7-05 (ASCE 2005) and in Appendix 4 of the new 

AISC 2005 Specification (AISC 2005). A similar relationship is found in Eurocode No. 

1 (1998) and in the ECCS model code on fire engineering (ECCS 2001). Probabilistic 

event combination analyses show that neither wind nor earthquake effects need to be 

considered in checking the overall behavior of a building frame during a severe fire 

(Ellingwood 2005a). It should be emphasized that because of the nonlinear nature of the 

structural system response to severe fires, the loads and structural actions should be 

factored prior to performing the structural analysis. 

The structural action, T, is determined from an analysis of the fire exposures that arise 

from postulated fire scenarios for design. Since these are “design-basis” events, the load 

factor is set equal to 1.0. In the Eurocode and ECCS, it is recommended that T be 

developed from the 80th percentiles of the fire load densities, such as those presented in 

Tables 3.3(a) through (c); these fire densities are permitted to be reduced by as much as 

50%, depending on the presence of active fire protection systems in the building. 

However, it should be noted that the role of various active protection measures in 

reducing fire risk is already taken into account, in an average sense, in the value of λH in 

Eq. 3.6 on which load combination Eq. 3.11 is based. In these circumstances, any 

adjustments to these fire densities should be viewed with caution. 

The lateral stability of building frames normally is ensured by designing the frames for 

lateral forces from wind and/or earthquake effects. However, few building frames are 

perfectly symmetric or symmetrically loaded by gravity loads. Moreover, columns and 

beams are not perfectly straight, nor are fabrication and erection procedures perfect. 

Consequently, even a “perfect” frame is subject to sway. If this sway is not accounted 

for, or if the imposed deformations from the fire give rise to significant frame 

deformations, large secondary (P-∆) forces will develop in the frame and lead to overall 

instability of the frame under gravity loads. This occurrence can be mitigated by 

stipulating that the lateral stability of the building frame be checked by imposing a small 

notional lateral force equal in magnitude to 0.002ΣP at each floor level, in which the term 

ΣP is the cumulative gravity force due to the summation of dead and live loads acting on 

the story above that level. This approach to ensuring lateral stability under gravity loads 

has been recommended by the Structural Stability Research Council (SSRC 1998) and is 

being implemented in several modern standards (AISC 2005; NBCC 2005). Structural 

elements that provide lateral stability and are exposed to heating from the fire should 

receive particular attention in fire-resistant structural design.

The above load combinations determine the required strength of the building frame 

(strength that must be provided in design) from structural analysis. The design strength is 

determined by (ACI 2005; AISC 2005): 

 Required strength (Ud) < Design strength (φ Rn) (3.12) 

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53

in which Rn = nominal strength stipulated in the material specification or code (e.g., 

strength in tension, flexure, shear, or compression) and φ = resistance factor that takes 

into account uncertainties in the determination of Rn and mode and consequences of 

failure. The design strength and deformations should be calculated taking the elevated 

temperature properties of the structural materials into account (AISC 2005; ACI 2005). 

The stability check of the frame should include second-order forces arising from 

differential heating of the structural system. The selection of specific resistance factors 

for governing structural limit states is the responsibility of standard-writing groups for the 

individual construction materials and is outside the scope of this chapter. Although some 

have suggested that the resistance factors for fire (and other accidental loads) should be 

set equal to 1.0 (ECCS 2001), the structural properties of steel and concrete at the 

elevated temperatures in a severe fire are more uncertain than the corresponding 

properties under normal conditions. Engineers who would err in the direction of 

conservatism might use resistance factors that are the same as those used for normal 

design. 

3.4.3.4 Required Attributes of Advanced Analysis 

The analysis must include both thermal response and mechanical response of structural 

components and systems. Thermal and mechanical properties of structural materials are 

temperature-dependent (Gustaferro and Martin 1989; ECCS 2001), as described in detail 

in Chapters 4 for steel and 5 for concrete. Unfortunately, there currently is no standard 

ASTM test for determining structural properties at fire temperatures. The deterioration in 

structural strength and stiffness with increasing temperatures, nonlinear material 

behavior, effects of thermal expansion, and large deformations should be taken into 

account. The appropriate limit states include excessive deflections, connection fractures, 

and overall and local buckling. The analysis should allow for the nature of the failure 

observed in fire tests of structural systems (Lim et al. 2004). For example, the 

Cardington tests showed that, in structural frames with fire-protected columns and floor 

slabs supported by unprotected steel beams, the floor systems supported the load through 

the development of two-way membrane action rather than flexural action. Thus, the 

analysis should take such behavior into account. Furthermore, for fire-induced limit 

states that are relevant for progressive collapse mitigation, a finite element (FE) platform 

with nonlinear analysis capabilities generally would be required for structural systems 

analysis. 

3.4.3.5 Simplified Methods of Analysis

Simplified methods of analysis may be sufficient when structural design for fire 

conditions involves structural members and components rather than systems and when 

the element is exposed to essentially uniform heat flux on all sides (e.g., Milke 1985; Lie 

and Almand 1990; Lie 1992; Buchanan 2001; Bennett and Thomas 2002; Bailey 2004). 

Some general guidelines are provided in Appendix 4 of the AISC Specification (2005), in 

Chapter X of AISC Steel Design Guide 19 (Ruddy et al.2003), and in the 

recommendations of ACI Committee 216 (2007). ASCE/SFPE Standard 29-05 (ASCE 

2005) also contains a number of relatively simple analytical methods. However, Section 

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54

1.2.1 of ASCE/SFPE Standard 29-05 states that the methods are intended to produce fire 

resistance rating times for concrete, timber and wood, masonry, and steel construction 

that are equivalent to those obtained from a standard ASTM E119 fire test, and to 

produce results that are an alternative to laboratory test results. ASCE/SFPE Standard 

29-05 also states (Section 1.3.1) that it may provide results that do not describe the 

performance for natural fires. Accordingly, the methods in ASCE/SFPE Standard 29-05 

may not always be suitable for demonstrating compliance under natural fires. 

3.4.4 Structural Design by Performance-Based Testing

Design by testing is an acceptable alternative to design by analysis in performance-based 

fire engineering. Fire testing in support of PBFE should demonstrate compliance with 

the performance objectives, a different goal than that in traditional fire testing which is 

focused on demonstrating that the component tested meets the three criteria in ASTM 

Standard E119 during the required rating period. In contrast, performance-based testing 

should strive to replicate the same basic attributes—fire exposure, superposed gravity 

loads, conditions of restraint—identified as being essential in advanced analysis. Such 

tests of building structural systems seldom would be feasible as a design tool, but tests of 

key structural components could be considered and performed on a case-by-case basis. 

While procedures for performing such a test have yet to be standardized, the move 

toward an acceptance of performance-based fire engineering by structural engineers and 

the code community may provide incentives for their development. 

3.5 SUMMARY

Practical design solutions can be developed to achieve performance-based engineering 

objectives for fire resistance, and protection can be expressed in terms of acceptable risk. 

Adoption of PBFE as an alternative approach to fire safety assurance would have a 

number of benefits. Foremost among these is the flexibility it provides in designing to 

meet mutually agreed-upon building performance objectives including, but not 

necessarily limited to, life safety and property protection for specific building occupancy 

categories and anticipated risks. The ability to consider fire protection alternatives, to 

trade off investments in additional fire protection above the code minimums against 

benefit received, and to reduce or eliminate unnecessary fire protection would add 

significant economic value to design of certain building structural systems.

Performance-based fire engineering requires a different approach to building planning 

and design from what is customary as well as better integration of the stakeholders, 

building design team, and the building code community. At the outset, a thoughtful 

approach must be taken to establishing performance objectives and identifying possible 

fire scenarios to check compliance with those objectives. This requires a systems 

approach, and involvement of project stakeholders early in the planning stages of design, 

and a degree of integration of traditional architectural and structural design functions. In 

the technical arena, the structural engineering task will become more complex. 

Advanced analysis methods may be warranted for major buildings or where additional 

investment in design is warranted by the nature of the building project or can be shown to 

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55

have a major economic benefit. Large-scale fire testing has demonstrated the power of 

modern advanced analysis methods. Many of the analytical (thermo-structural modeling) 

tools are becoming accessible, and a more widespread demand for such tools will make 

them more user friendly. On the other hand, not all PBFE solutions require advanced 

analysis; some can be achieved using relatively simple structural calculations. Finally, 

PBFE should include an assessment of uncertainties and must carry with it recognition of 

the need to make trade-offs between performance and cost.

Improving building fire safety by adopting PBFE methods is likely to provide economic 

incentive. For the majority of buildings, current methods of fire protection and 

demonstration of code compliance appear satisfactory and will continue to be used. On 

the other hand, PBFE gives the building design team and structural engineer additional 

quantitative tools for fire safety assurance in situations where prescriptive limits found in 

traditional codes may be highly restrictive or unsuitable, where safety benefits may be 

realized for unique facilities by better quantification of their structural fire resistance, or 

where innovative architectural expressions can be inhibited by customary fire resistance 

rating requirements. In addition, nonconforming fire code issues with existing 

construction can be addressed efficiently with PBFE prior to undertaking costly 

rehabilitation. To take full advantage of these new tools, structural engineers will have to 

develop a competency for fire-resistant structural analysis and design through education, 

and become comfortable in accepting this additional design challenge and responsibility. 

3.6 REFERENCES

Fire risk assessment of buildings is an interdisciplinary endeavor. The past two decades 

have seen the development of an extensive literature on risk assessment and the 

performance of building structural systems exposed to severe fires. Structural analysis 

and decision tools and experimental data on performance of structural components and 

systems have been covered extensively, and the field continues to evolve rapidly. The 

following bibliography, tailored to a structural engineering audience, provides a point of 

departure for further study of the field. Many of the references listed are cited in this 

chapter. References that are suitable as a starting point for independent study are 

indicated with an asterisk. 

ACI (2005), “Building Code Requirements for Structural Concrete,” ACI Standard 318-

05, Farmingham Hills, Mich.: American Concrete Institute.

ACI Committee 216 (2007), “Code Requirements for Determining Fire Resistance of 

Concrete and Masonry Construction Assemblies,” ACI 216.1-07/TMS 0216.1-07, 

Farmington Hills, Mich.: American Concrete Institute.

AISC (2005), Specification for Structural Steel Buildings, Chicago American Institute of 

Steel Construction, Inc.

ASCE (2005), Standard Calculation Methods for Structural Fire Protection, 

ASCE/SFPE Standard 29-05, Reston, Va.: American Society of Civil Engineers. 

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56

ASCE (2005), Minimum Design Loads for Buildings and Other Structures, ASCE 

Standard 7-05, Reston, Va.: American Society of Civil Engineers.

ASTM (2007), Standard Methods of Fire Tests of Building Construction and Materials, 

ASTM Standard E119-07a, West Conshohocken, Pa.: American Society for Testing and 

Materials.

Bailey, C.G. (2004), “Membrane Action of Slab/Beam Composite Floor Systems in 

Fire,” Engrg. Struct. 26(12): 1691-1703. 

*Bennetts, I.D., and I.R. Thomas, “Design of Steel Structures Under Fire Conditions,” 

Progress in Struct. Engrg. and Materials 4:1 (2002) 6-17. 

Beyler, C. (2004), “Relationship Between Structural Fire Protection Design and Other 

Elements of Fire Safety Design,” Proc. NIST-SFPE Workshop for Development of a 

National R & D Roadmap for Fire Safety Design and Retrofit of Structures, NISTIR 

7133:100-106, April. 

*Buchanan, A.H. (2001), Structural design for fire safety, Chichester, U.K.: John Wiley 

and Sons, Ltd. 

CIB W14 (1983), “A conceptual approach towards a probability-based design guide on 

structural fire safety,” Fire Safety Journal 6:1 (1983) 1-79. 

CIB W14 (1986), “Design guide—structural fire safety,” P.H. Thomas, Coordinator, Fire 

Safety Journal 10:2 (1986) 75-137. 

*CIB W14 (2001), “Rational safety engineering approach to fire resistance of buildings,” 

CIB Report No. 269, Rotterdam: Int. Council for Research and Innovation in Building 

and Construction, 2001. 

Clifton, G.D., and M.J. Feeney (2004), “Fire Engineering Applications to Multi-Story 

Steel Structures,” Modern Steel Construction, Chicago: AISC, March 2004. 

Culver, C.G. (1976), “Survey Results for Fire Loads and Live Loads in Office 

Buildings,” Building Science Series No. 85, Washington: National Bureau of Standards. 

*ECCS Technical Committee 3 (2001), Model code on fire engineering, Document No. 

111, Brussels: European Convention for Constructional Steelwork. 

Ellingwood, B.R., et al. (1982), “Probability-Based Load Criteria: Load Factors and Load 

Combinations,” J. Struct. Div. ASCE 108:5 (1982) 978-997. 

Ellingwood, B.R., and R.B. Corotis (1991), “Load Combinations for Buildings Exposed 

to Fires,” Engrg. J. AISC 28:1 (1991) 37-44. 

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Ellingwood, B. (1998), “Reliability-based performance concept for building 

construction,” in Struct. Engrg. Worldwide, Proc. Struct. Engrg. World Congress 1998, 

Elsevier, Paper T178-4 (CD-ROM).

Ellingwood, B. (2001), “Acceptable Risk Bases for the Design of Structures,” Progress 

in Struct. Engrg. and Materials 3:2 (2001) 170-179. 

*Ellingwood, B.R. (2005a), “Load Combination Requirements for Fire-Resistant 

Structural Design,” J.Fire Protection Engrg. 15:1 (2005) 43-61. 

*Ellingwood, B.R. (2005b), “Progressive Collapse-Resistant Design: Acceptable Risk 

Bases,” in Best Practices for Mitigating Risk of Progressive Collapse, H.S. Lew, ed., 

Washington: National Institute of Building Sciences.

European Prestandard ENV 1991-2-7 (1998), “Eurocode 1: Basis of design and actions 

on structures, Part 2-7: Accidental actions,” Brussels: Comite Europeen de 

Normalization 250. 

Galambos, T.V., et al. (1982), “Probability-Based Load Criteria: Assessment of Current 

Design Practice,” J. Struct. Div. ASCE 108:5 (1982) 959-977. 

Gewain, R.G., and E.W.J. Troup (2001), “Restrained Fire Resistance Ratings in 

Structural Steel Buildings,” Engrg. Journal AISC 38:2 (2001) 78-89. 

Gustaferro, A.H., and L.D. Martin (1989), PCI Design for Fire Resistance of Precast 

Prestressed Concrete, 2nd ed., Chicago: Prestressed Concrete Institute.

Hamburger, R.O. (1996), “Implementing performance-based seismic design in structural 

engineering practice,” Proc. 11th World Conf. on Earthquake Engrg., Paper 2121, 

Elsevier Science Ltd.

Hurley, M. (2004), “Design Fire Scenarios,” Proc. NIST-SFPE Workshop for 

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63-75. 

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Chapter 4 

Design of Concrete Structures 

James Milke, Ph.D., P.E., University of Maryland 

Stephen Pessiki, Ph.D., Lehigh University 

Long Phan, Ph.D., P.E., National Institute of Standard and Technology 

4.1 INTRODUCTION 

Concrete construction may serve as a fire-resistant barrier and/or as a load-bearing component of 

a structure. Thus, an analysis of the fire resistance of concrete construction may need to assess 

the characteristics of the construction relative to one or both of these functions. In particular: 

 An assembly serving as a barrier to prevent the spread of fire, such as a floor-ceiling 

assembly or a wall, contributes to the fire protection strategy of compartmentation. 

As such, the barrier needs to be a sufficient insulator, limiting heat transmission to the 

unexposed side of the barrier. This is assessed by adopting limits for temperature rise 

on the surface of the unexposed side of the barrier. ASTM E119 (ASTM 2007) limits 

the average temperature rise above ambient on the unexposed side to 139 °C. 

 The fire resistance of an assembly serving as a barrier is assessed via a heat transfer 

analysis. The purpose of the heat transfer analysis is to confirm that the temperature 

rise on the unexposed side of the assembly resulting from the fire exposure meets 

established limits. The heat transfer analysis requires the dimensions and geometry 

of the assembly and the thermal material properties (see Section 4.2). In addition, the 

fire exposure needs to be characterized (see Chapters 2 and 3). 

 A load-bearing assembly needs to maintain its structural integrity, supporting the 

weight of the structure and its contents, despite the effects of the fire exposure. To 

achieve this aspect of performance, the load-carrying ability of the structural element 

needs to be preserved, in spite of changes in mechanical properties associated with an 

increase in temperature of the structural element and the imposition of thermal strain. 

 A fire resistance assessment of load-bearing assemblies requires both a heat transfer 

and structural analysis. The heat transfer analysis requires information similar to that 

for a barrier, but now is conducted to assess temperatures of reinforcing elements or a 

temperature distribution within the assembly. Based on this information, a structural 

analysis is conducted that assesses load-carrying ability or structural stability, 

accounting for changes in material properties, spalling, and induced thermal strains. 

Concrete columns are an example of an assembly that needs to satisfy only the structural 

integrity criterion. In contrast, walls and floor–ceiling assemblies are examples of barriers that 

are also load bearing and thus would need to satisfy both considerations in order to be considered 

fire resistant. 

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62

The design of concrete construction for fire resistance can be based on engineering principles 

incorporated into calculation procedures described in this chapter (Milke 1999). A variety of 

procedures are available to estimate the fire resistance of concrete flexural members and concrete 

columns. These procedures range from the application of algebraic equations to finite element 

computer models. 

The calculation methods included in this chapter are based primarily on research conducted by 

the Portland Cement Association (PCA). Much of the research was sponsored by the Precast/ 

Prestressed Concrete Institute (PCI) and the PCA (specific references from this research are cited 

throughout this chapter). This chapter summarizes the technical basis for the calculation 

methods, presents the methods, and provides examples to illustrate their application. The 

information presented in this chapter is drawn from ACI 216.1-07, the 6th edition of the PCI 

Design Handbook (PCI 2004); PCI manual, MNL-124-89, Design for Fire Resistance of Precast 

Prestressed Concrete (PCI 1989); the Concrete Reinforcing Steel Institute manual, Reinforced 

Concrete Fire Resistance (CRSI 1980), as well as results of recent studies. These references are 

recognized as the principal references in the field and for years were recognized by the model 

codes as acceptable resource documents for determining fire resistance ratings of concrete 

construction by other than prescriptive means. 

4.1.1 Scope 

Concrete buildings exist in many forms. For example, concrete buildings may be cast-in-place, 

precast on site (tilt-up construction), or precast in a manufacturing facility. Concrete buildings 

may be made with mild steel reinforcement or prestressing steel reinforcement. For prestressed 

concrete, the construction may be pretensioned or post-tensioned, and bonded or unbonded. The 

methods described in this chapter apply to this wide range of types of concrete structural 

members and assemblies. For global structural analysis of entire concrete building in fire, 

advanced calculation models, developed based on acknowledged engineering principles and 

assumptions of the theory of structural mechanics, as generally described in the Eurocode as well 

as in section 3.4.3 of this report, may be used with the effects of thermal expansions and large 

deformations, degradation of concrete material properties and potential concrete spalling as 

prescribed in section 4.2, appropriately taken into account. 

4.1.2 Technical Basis for Calculating Fire Resistance of Concrete Construction 

Current practice in the design of concrete structures for fire is based on hundreds of fire tests of 

cast-in-place and precast concrete assemblies. These fire tests have been performed on a variety 

of structural assemblies including beams, slabs, columns, and walls. 

Reports of a number of tests of flexural elements sponsored by PCI have been issued by 

Underwriters Laboratories (UL). Most of the reports have been reprinted by PCI, and the results 

of the tests are the basis for UL’s listings and specifications for non-proprietary products such as 

double tee beams and hollow-core slabs. PCA has also conducted many fire tests of precast 

flexural elements, including simply supported and continuous slabs and beams. Test results 

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63

published as Research and Development Bulletins available from PCA also have been the basis 

for papers published elsewhere. 

Fire tests of reinforced concrete columns have been conducted by PCA and the National 

Research Council of Canada. While no tests are known to have been conducted for prestressed 

concrete columns, results from tests of reinforced columns are considered to be equally 

applicable to prestressed concrete columns with adjustment made for the difference in thermal 

properties between mild reinforcing steel and prestressing strand as appropriate. Concrete cover 

requirements are less for precast concrete assemblies manufactured under controlled conditions 

in a precast plant. This may also influence the relative behavior of cast-in-place columns as 

compared with precast concrete columns, as discussed more fully later in the chapter. 

The fire resistance of concrete walls is normally governed by the ASTM E119 criteria for 

temperature rise of the unexposed surface rather than by structural behavior during fire tests. 

This is due to the low level of stresses under service load, even in concrete bearing walls. In 

most cases, the concrete cover for steel reinforcement required by code exceeds that required for 

fire protection so there is, in effect, reserve structural fire resistance within the concrete wall. 

Although many of the tests performed over the years were conducted to determine fire ratings for 

specific structural elements, many of the tests were performed in conjunction with broad research 

studies whose objectives have been to understand the behavior of concrete elements subjected to 

fire. The knowledge gained from these tests has resulted in the development of listings of fireresistive concrete building assemblies and procedures for determining the fire resistance of 

precast concrete members by calculation. 

The remainder of this chapter reviews material properties, including their dependence on 

temperature, and computational methods for heat transfer and structural analyses of reinforced 

and prestressed concrete assemblies exposed to fire. 

4.2 MATERIAL PROPERTIES 

This section on material properties of concrete at elevated temperatures is divided into two major 

sections. The first section presents information on material properties for normal strength 

concrete (NSC). The second section presents information on material properties for high 

strength concrete (HSC). In these guidelines, NSC is defined as concrete with a compressive 

strength less than 83 MPa (12,000 psi), and HSC is defined as concrete with a compressive 

strength greater than 83 MPa. 

The concrete material properties required for thermal and structural calculations are thermal and 

mechanical properties. The thermal properties described include thermal conductivity, 

volumetric specific heat, and density. The mechanical properties include concrete compressive 

strength, modulus of elasticity, shear modulus, tensile strength, and coefficient of thermal 

expansion. These properties are required for engineering analyses in typical design applications. 

Additional properties may also be required in more advanced analyses. These include: 

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64

 Porosity 

 Moisture content 

 Poisson’s ratio 

 Creep parameters 

In some cases, multiple sources of data for material properties are provided. These are included 

to demonstrate the range in property values that have been determined, where the variations are 

attributable primarily to variations in the experimental procedure used to determine the 

properties. In general, standard experimental procedures are not available to assess the noted 

material properties over the range of temperatures of interest for concrete. 

4.2.1 Normal Strength Concrete 

4.2.1.1 Thermal Properties 

At a minimum, an unsteady conduction heat transfer analysis requires the following material 

properties to be known: 

 Thermal conductivity,  (W/mK) 

 Specific heat, Cp (J/kgK) 

 Density,  (kg/m3) 

The reported thermal properties of concrete are obtained from small-scale tests. Full-scale 

members are likely to perform differently, especially with regard to moisture migration. 

Therefore, these properties should be considered to be useful only for developing estimates of 

the thermal response of a concrete structural member. 

4.2.1.1.1 Thermal Conductivity 

Thermal conductivity, , of concrete is primarily a function of concrete densities and aggregate 

type. Values of  for concrete with density ranging from 800 kg/m3

 to 2,400 kg/m3 are listed in 

ACI 216.1 (ACI 2007). For simple analyses, the following averaged values may be used for the 

thermal conductivity of NSC with normal weight and light weight aggregate (EC2 2002): 

Normal weight aggregate NSC:  = 1.3 W/mK 

Lightweight aggregate NSC:  = 0.5 W/mK 

For more comprehensive analysis where temperature-dependent thermal conductivity is needed, 

correlations are provided in Appendix A of this chapter (Section 4.6) and are also graphically 

depicted in Figure 4.1 (Harmathy 1970a; Harmathy and Allen, 1973). The thermal conductivity 

of normal weight aggregate concrete is greater than that of lightweight aggregate concrete, which 

makes lightweight concretes better insulators than normal weight concretes. This affects the heat 

transmission aspect of fire resistance for normal weight and lightweight aggregate concrete slabs 

and walls as well as the temperature rise of any reinforcement within the concrete (for concrete 

walls, slabs, and columns). 

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65

FIGURE 4.1. Thermal Conductivity of Different 

Structural Concretes (Schneider, 1988) 

4.2.1.1.2 Volumetric Specific Heat 

Volumetric specific heat, .Cp, For simple analyses, the following values may be used for the 

volumetric specific heat of concrete (EC2 2002): 

Normal weight concrete: .Cp = 2.6 MJ/m3

K 

Lightweight concrete: .Cp = 1.5 MJ/m3

K 

The volumetric specific heat of concrete at elevated temperatures is illustrated in Figure 4.2 

(Harmathy 1970b). Again, the volumetric specific heat differs for the two aggregates, with the 

normal weight aggregate concretes having a greater volumetric specific heat than the lightweight 

aggregate concretes. As with thermal conductivity, this will affect the temperature rise within 

and on the unexposed surface of the concrete member. Correlations to determine the volumetric 

specific heat at selected temperatures are included in Appendix A (Section 4.6 below). 

4.2.1.1.3 Density 

Concrete density, , does not vary significantly over the temperature range typically associated 

with common fires. In general, concrete density decreases with increasing temperature. This is 

due mostly to mass loss incurred in the heat-induced release and evaporation of free and 

chemically-bound waters in unsealed concrete. For calculation purpose, the densities of 

structural concretes commonly used in concrete building construction can be taken as 1760 

Temperature (C) 

Thermal Conductivity, (

) 

(W/m.K)

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66

kg/m3

 (110 lb/ft3) for light weight aggregate concrete, and 2330 kg/m3 (145 pcf) for normal 

weight aggregate concrete. Lightweight aggregate concrete is more commonly used in precast 

concrete construction for elements such as double tee roof framing members. Normal weight 

aggregate concrete is most commonly used in cast-in-place construction. 

FIGURE 4.2. Volumetric Specific Heat of Normal Weight 

(Concretes 1 and 2) and Lightweight Aggregate 

(Concretes 3 and 4) Concretes (Harmathy 1970b) 

4.2.1.2 Mechanical Properties 

Concrete temperature-dependent mechanical properties, including compressive and tensile 

strength, modulus of elasticity, shear modulus, and coefficient of thermal expansion are 

discussed in this section. 

4.2.1.2.1 Compressive Strength 

The typical compressive strength value, f’c, specified for design is the 28-day compressive 

strength. Prestressed construction also includes a requirement for the compressive strength of 

the concrete at the time of load transfer due to prestressing. The requirement for high early 

strength to allow the load transfer to occur soon after concrete placement (8 to 12 hours) often 

leads to actual 28-day compressive strengths that significantly exceed the specified design value. 

Stress–strain curves for normal and lightweight aggregate concretes at elevated temperatures are 

provided in Figure 4.3 (Harmathy 1993). The slope of the curve decreases with increasing 

temperature, indicating a decline in the modulus of elasticity with temperature, as is confirmed in 

subsequent figures in this section. 

Temperature (C) 

Volumetric Specific Heat, (Cp) 

(MJ m-3/K)

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67

FIGURE 4.3. Stress–Strain Curves at Elevated Temperature for Normal 

and Lightweight Aggregate Concretes (Harmathy 1993) 

Concrete compressive strength varies differently at elevated temperatures depending on the 

stress and heating conditions. In laboratory tests, concrete compressive strength at elevated 

temperature are typically evaluated using three different test methods, called stressed, 

unstressed, and unstressed residual property test method. Each test method yields results with 

different application. 

1. Stressed test method: Apply a constant load to the test sample (ranging from 25% to 

55 % of ultimate room-temperature compressive strength), heat the sample to its 

target temperature, allow time for steady state temperature condition to be achieved 

within the test sample (near uniform temperature), and increase the load to failure. 

Mechanical properties determined using this method are applicable for use in 

calculating structural response of concrete members whose main function is to carry a 

large portion of compressive load, such as columns. Figure 4.4 shows the variation 

with respect to temperature of compressive strength obtained under this test method 

for normal weight and lightweight aggregate NSC (Phan, 2002). 

2. Unstressed test method: Heat the unloaded sample to its target temperature, allow 

time for near uniform temperature to be achieved within the test sample, and increase 

the load to failure. Mechanical properties determined using this method are applicable 

for use in calculating structural response of concrete members whose main function is 

to serve as barrier and carry only minor compressive load, such as partition walls or 

beams. Figure 4.5 shows variation of compressive strength of NSC obtained by 

various studies under the unstressed test method (Phan, 2002) 

3. Unstressed residual property test method: Heat the unloaded sample to its target 

temperature, allow the sample to cool to room temperature, and increase the load to 

failure. This information is particularly relevant to post-fire integrity assessments of 

concrete construction. Figure 4.6 shows variation of compressive strength of NSC 

obtained by various studies under the unstressed residual properties test method 

(Phan, 2002) 

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68

Designers should refer to properties determined from the test method that most closely relates to 

the application being considered, e.g., in a design application, properties of loaded samples 

(stressed test method) should be considered. In contrast, a post-fire integrity analysis should 

consider the data from tests where the sample was heated and then allowed to cool prior to the 

application of a load (unstressed residual properties test method). 

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000

Abrams (Carbonate)

Abrams (Siliceous)

Abrams (Lightweight)

Relative Compressive Strength

Temperature (oC)

FIGURE 4.4. Relative Compressive Strength of NSC (normal and lightweight 

aggregate) under Stressed Test Condition 

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000

Castillo

Diederich

Abrams (Carbonate)

Abrams (Siliceous)

Abrams (Lightweight)

Furumura

Relative Compressive Strength

Temperature (oC)

FIGURE 4.5. Relative Compressive Strength of NSC (normal and 

lightweight aggregate) under Unstressed Test Condition 

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69

 

FIGURE 4.6 Relative Compressive Strength of NSC (normal and lightweight 

 aggregate) under Unstressed Residual Strength Test Condition

The following correlations, proposed by Lie (1992), provide estimates of the compressive 

strength at elevated temperature for NSC made with siliceous, carbonate, or expanded shale 

aggregate. These estimates are conservative and can be used to determine NSC compressive 

strength in calculation methods where compressive strength at elevated temperature is required. 

cTc 0,,  ff for T  450 °C (4.1) 





 



    1000

20 353.2011.2 0,,

T ff cTc for T > 450°C (4.2) 

4.2.1.2.2 Modulus of Elasticity 

The variation in the modulus of elasticity, Ec of NSC over a range of temperatures is provided in 

Figure 4.7 (Cruz 1966). Similar reductions in the elastic modulus as a function of temperature 

are evident for both the lightweight aggregate concrete and the normal weight concrete. 

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000

Abrams (Carbonate)

Abrams (Siliceous)

Abrams (Lightweight)

Morita

Relative Compressive Strength

Temperature (oC)

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70

FIGURE 4.7. Modulus of Elasticity of NSC at Elevated 

Temperatures (Cruz 1966) 

4.2.1.2.3 Shear Modulus 

The shear modulus at elevated temperatures is presented in Figure 4.8. 

4.2.1.2.4 Tensile Strength 

The tensile strength of concrete is often empirically expressed as a product of a multiplier, , and 

the square root of the compressive strength, where  depends on the concrete density and the type 

of test. The American Concrete Institute (ACI 318 1989) suggests the following relationship for 

the two strengths at room temperature: 

c t ff '  620 (4.3) 

Where: 

f

’

c = Compressive ultimate strength (Pa) 

ft = Tensile ultimate strength (Pa) 

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71

FIGURE 4.8. Shear Modulus of Concrete at 

Elevated Temperatures (ACI 216 1989) 

The tensile strength of concrete is relatively small, typically about 10% of the compressive 

strength, and is usually neglected in practical design applications. 

4.2.1.2.5 Coefficient of Thermal Expansion 

The coefficient of thermal expansion is used to predict thermally induced loads and curvatures in 

a structure. The coefficient of thermal expansion of concrete was measured by Cruz at elevated 

temperatures (see Figure 4.9). Correlations to fit the data by Cruz were provided by Lie (1992) 

and are provided in Section 4.6 (Appendix A). 

FIGURE 4.9 Coefficient of Thermal Expansion of Concrete (ACI Committee 216 2007) 

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72

4.2.2 High Strength Concrete 

HSC is more widely used in columns of cast-in-place construc-tion or in heavily loaded flexural 

elements such as precast prestressed inverted tee girders. In pretensioned construction, the need 

for a sufficiently large compressive strength at early age to allow the transfer of prestress often 

leads to an actual 28-day compressive strength that exceeds the specified 28-day compressive 

strength. 

4.2.2.1 Thermal Properties 

Studies (Van Geem et al., 1996; Burg and Ost, 1994) have shown high strength concrete and 

normal strength concrete has very similar thermal properties. Thus thermal properties provided 

in section 4.2.1.1 can also be used for analysis of high strength concrete. 

4.2.2.2 Mechanical Properties 

4.2.2.2.1 Compressive Strength 

As with the data for the compressive strength of NSC, the compressive strength for HSC also 

varies differently at elevated temperature depending on the stress and temperature levels. The 

data for compressive strength is reflected in Figures 4.10 to 4.12 (Phan, 2003, 2007). Phan 

proposes that, for design purposes, the compressive strength of HSC be selected from Figure 

4.13 (Phan, 2003, 2007). 

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73

FIGURE 4.10. Relative Compressive Strength of HSC 

under the Stressed Test Method (Phan, 2003, 2007) 

FIGURE 4.11. Relative Compressive Strength of HSC 

under the Unstressed Test Method (Phan, 2003, 2007) 

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000

Phan (2002)

Castillo (1990)

Khoury (1999)

Relative Strength

Temperature (oC)

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000

Phan (2002)

Castillo (1990)

Hammer (1995)

Diederichs (1995)

Furumura (1995)

Khoury (1999)

Relative Strength

Temperature (oC)

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74

FIGURE 4.12. Relative Compressive Strength of HSC 

under Unstressed Residual Property Test Method 

(Phan, 2003, 2007) 

0.0

0.2

0.4

0.6

0.8

1.0

0 200 400 600 800 1000

Temperature (°C)

Strength at Temp./

Strength at Ambient Temp.

FIGURE 4.13. Relative Compressive Strength of HSC for 

Design Applications (Phan, 2003) 

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000

Phan, 2002

Hertz, 1991

Morita, 1992

Felicetti, 1996

Khoury, 1999

Relative Strength

Temperature (oC)

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75

Correlations to describe the line segments in Figure 4.13 are: 

cc 20,  ff T  50 °C 

 ff cc 20,    0056.28.1 T 50 °C < T  100 °C 

c 72.0 c 20,  ff 100 °C < T  350 °C 

 ff cc 20,    00168.31.1 T 350 °C < T  778 °C 

 0 c f T > 778 °C 

4.2.2.2.2 Modulus of Elasticity 

The variation in the modulus of elasticity, Ec, of HSC made of limestone coarse aggregate over a 

range of temperature is provided in Figure 4.14 (Phan, 2001). The data were obtained under 

three different test methods (see Section 4.2.1.2.1) and show that the variation of HSC’s modulus 

of elasticity is not significantly influenced by the stress the stress level during heating. In 

addition, the variation of HSC’s modulus of elasticity at elevated temperature in general follows 

the trend observed for NSC’s modulus of elasticity (see Figure 4.7). 

0

0.2

0.4

0.6

0.8

1

0 100 200 300 400 500 600 700

Stressed Test

Unstressed Test

Unstressed Residual Test

Modulus of Elasticity, E,

100% of Initial Eo

Temperature ( oC)

FIGURE 4.14. Modulus of Elasticity of HSC at Elevated 

Temperature (Phan, 2001) 

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76

4.2.3 Steel Reinforcement 

Both cast-in-place and precast concrete building structures are reinforced in a variety of ways. 

Types of reinforcement include mild steel reinforcement bars, wire mesh, high-strength 

prestressing wire, and strand and high-strength bars. The discussion in this section applies to all 

types of steel reinforcement commonly used in cast-in-place and precast concrete building 

structures. For structural steel, discussion is provided in Chapter 5. 

Heat transfer through steel reinforcement is usually neglected given the relatively small amount 

of steel mass in a concrete assembly. As such, thermal properties of steel reinforcement are 

usually unnecessary in design applications. However, there are cases where it may be necessary 

to include the presence of the steel reinforcement in the thermal analysis. One example may be a 

heavily reinforced element of relatively small overall dimensions, such as a concrete corbel. A 

second example may be a detail that includes embedded steel hardware such as plates or angles 

welded to the main reinforcement in a member. The steel hardware may be exposed and thus 

provide a direct path to conduct heat to the reinforcement. In this situation, the temperature of 

the reinforcement may not be the same as the surrounding concrete, or the steel may more 

readily conduct heat into the concrete, thereby necessitating that the presence of the steel be 

considered in the analysis. 

4.2.3.1 Thermal Properties 

The thermal properties of steel reinforcement may be considered to be the same as for structural 

steel (see Chapter 5). 

4.2.3.2 Mechanical Properties 

Variations in mechanical properties of steel reinforcement, including yield strength fy and 

modulus of elasticity Ey at elevated temperatures are shown in Figures 4.15 and 4.16. 

4.3 THERMAL ANALYSIS 

There are two purposes for conducting thermal (heat transfer) analyses of fire-exposed concrete 

assemblies: 

1. Assess heat transmission to the unexposed side, i.e., compare the temperature rise on 

the surface of the unexposed side to performance criteria. 

2. Provide input to structural analysis, i.e., determine the temperature of the steel 

reinforcements or temperature distribution through the assembly. 

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77

FIGURE 4.15. Strength–Temperature Relationships for 

Various Steel Reinforcements (ACI 216.1-07) 

FIGURE 4.16. Modulus of Elasticity–Temperature 

Relationships for Steel (Weigler and Fischer 1964) 

4.3.1 ASTM E119 Standard Fire Exposure 

Heat transfer through concrete members exposed to the conditions associated with the ASTM 

E119 standard fire exposure has been studied by numerous individuals. These studies have 

resulted in: 

 Tables to identify the minimum thickness of concrete required to limit the 

temperature rise on the surface of the unexposed side to acceptable limits (according 

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78

to ASTM E119). These tables form the basis of the equivalent thickness method in 

ASCE/SFPE 29. 

 Graphical methods to assess temperature rise at specific locations of interest within 

the concrete, i.e., at the location of reinforcement elements. 

 Computer algorithms to assess temperature rise in reinforced concrete columns. 

Numerous graphical solutions of the temperature distribution within fire-exposed structural 

members have been presented in the literature. However, most of the graphical solutions are 

limited to cases involving the standard ASTM E119 exposure. 

Graphs of the type presented in Figures 4.17 and 4.18 provide the temperature distribution within 

concrete slabs based on data from tests with the ASTM E119 standard fire exposure (Abrams 

and Gustaferro 1968). Graphs are provided for three aggregates: siliceous, carbonate and sandlightweight. These graphs are applicable for determining the temperature at a particular depth 

into a concrete slab, often at the location of reinforcing or pre-stressing steel within the slab. 

Additional graphs are available to determine the temperature rise on the unexposed surface of 

concrete slabs, beams, and columns exposed to the ASTM E119 test as a function of thickness 

and aggregate (ACI 216.1-07.) According to the review by Hosser et al. (1994), the graphical 

thermal analysis procedure included in the PCI guide (1989) provides good agreement with 

actual test data. 

FIGURE 4.17. Temperatures Within Normal Weight Concrete Slabs or 

Panels During ASTM E119 Exposure (Abrams and Gustaferro 1968) 

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79

FIGURE 4.18. Temperatures Within Sand–

Lightweight Concrete Slabs or Panels 

During ASTM E119 Exposure (Abrams and 

Gustaferro 1968) 

Similarly, graphical solutions are presented for stemmed units exposed to the standard ASTM 

E119 fire exposure. Examples are presented in Figures 4.19 to 4.22. 

FIGURE 4.19. Temperatures on Vertical Centerline of Stemmed Units 

at 1 Hour of ASTM E119 Exposure (Ehm and van Postel 1967) 

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80

FIGURE 4.20. Temperatures on Vertical Centerline of Stemmed Units 

at 2 Hours of ASTM E119 Exposure (Ehm and van Postel 1967) 

FIGURE 4.21. Temperatures on Vertical Centerline of Stemmed Units 

at 3 Hours of ASTM E119 Exposure (Ehm and van Postel 1967) 

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81

FIGURE 4.22. Temperatures on Vertical Centerline of Stemmed Units 

at 4 Hours of ASTM E119 Exposure (Ehm and van Postel 1967) 

Lie (1972) provided a series of graphs for one-dimensional analyses of the temperature 

distribution in walls or slabs exposed on one or two sides to the ASTM E119 exposure as 

illustrated in Figure 4.23. The graphs can also be used for two-dimensional assemblies such as 

columns or beams by applying the principle of superposition. Because the material properties 

are assumed to be temperature-dependent, average properties need to be identified. 

FIGURE 4.23. Graphical Heat Transfer Solution for 

ASTM E119 Exposure of Slab (Lie 1972) 



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82

Legend for Figure 4.23: 

a = Thermal diffusivity of concrete (m2

/s) 

l = Thickness of slab (m) 

N = Biot number 

t = Duration of exposure (s) 

T = Temperature of concrete at position x (°C) 

Tm = Mean exposure temperature (°C) 

To = Initial temperature (°C) 

 = Heat transfer coefficient (W/m2°C) 

 = Fourier number 

 = Dimensionless temperature 

Limitations of the graphical analyses include the following: 

 The graphical methods apply only for exposures associated with ASTM E119. 

Consequently, if this analysis is being conducted to assess the response of a concrete 

assembly to an alternative fire exposure, an approach described in Section 4.3.2 

should be applied. 

 Graphical solutions cannot be readily incorporated into computer-based methods that 

require the temperature of the assembly as input. So, while a graphical method may 

be relatively easy to apply, it may be tedious, and perhaps not very accurate 

(depending on the legibility of the graph), to input the results of the graphical analysis 

into a structural calculation. 

Numerous algorithms are available to evaluate the thermal response of concrete slabs. Because 

the principal application of these algorithms is to assess the heat transfer in concrete sections 

exposed to non-standard fires, these methods are discussed in the next section. 

4.3.2 Other Fire Exposures 

A limited number of graphical solutions are available to describe the exposure from natural fires, 

e.g., the graphs presented by Pettersson, Magnusson, and Thor (1976) (see Section 2.5.3). Other 

solutions could potentially be developed, perhaps expanding the approach by Pettersson, 

Magnusson, and Thor. 

Until other methods are developed, computer-based calculations are necessary to determine the 

temperature rise within concrete sections. Lie and Allen (1972) formulated a finite difference 

model to analyze the heating of circular reinforced concrete columns exposed to the standard 

fire. In addition, finite difference models were developed for concrete floor slabs (Lie 1978) and 

square reinforced concrete columns (Lie et al. 1984). 

Ellingwood and Shaver (1980) and Ellingwood (1991) discuss the results of algorithms assessing 

the temperature distribution in concrete slabs and beams exposed to a variety of fire conditions. 

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83

Ahmed and Hurst (1995, 1998) applied a one-dimensional, finite difference analysis of the 

coupled heat and mass transfer through carbonate and siliceous aggregate concrete slabs and 

multi-layered gypsum wallboard-and-stud assemblies. Dehydration and evaporation phenomena 

and changes in porosity were considered by the model. 

Heat transfer models that are widely available and have been applied to analyze the thermal 

response of assemblies exposed to fires include HEATING7 (Childs 1999), FIRES-T3 (Bresler 

Iding, and Nizamuddin 1977), TASEF-2 (Sterner and Wickstrom 1990) and HEAT (Munukutla 

1989). 

The numerical models are capable of assessing the heat transfer through concrete slabs as a result 

of exposure to the standard fire described in ASTM E119 or other defined fire exposures. 

Boundary conditions to characterize the fire are stipulated by convective and radiative 

parameters. 

The numerical heat transfer models need to possess the following characteristics in order to 

address heating due to any fire exposure: 

 Time-varying exposure conditions, including a wide range of possible conditions, 

ranging from a steady heat flux to non-linear conditions 

 Temperature-dependent material properties 

More advanced analyses should consider models such as those by Ahmed and Hurst (1995, 

1998) that include mass and moisture transport and pore pressure analysis. 

Limitations of the numerical analyses include the following: 

 Most of the models assume that the material is homogeneous, with changes permitted 

only to account for variation in properties due to temperature. As such, changes due to 

the formation of cracks or pockets of moisture/water vapor are neglected. These can 

significantly affect the heat transfer process. 

 Some thermal properties that vary with temperature may not be well characterized due 

to lack of data. If the properties are not known, a test program will need to be conducted 

to evaluate the unknown properties. 

 Moisture migration and pressure build-up in pores are not addressed, except in 

specialized models. These effects will affect the heat transfer within a concrete 

assembly and will need to be accounted for either explicitly or implicitly. 

 Spalling is not considered. Changes in the thickness of a concrete element due to 

spalling, formation of cracks, and changes in the surface characteristics can have a 

significant effect on heat transfer. 

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84

4.4 STRUCTURAL ANALYSIS 

This section describes the analytical procedures that can be applied to all concrete construction to 

evaluate their structural response at elevated temperatures. Some differences exist between castin-place and precast construction, and between reinforced and prestressed concrete. These 

differences are noted in the appropriate locations in the section. 

Evaluating the structural performance of concrete structures at elevated temperatures involves 

many of the usual propositions of the mechanics of reinforced and prestressed concrete (plane 

section behavior, strain compatibility between steel and concrete, etc.). The analytical 

procedures described here differ from the usual design calculations in that the properties of the 

materials (steel and concrete) at elevated temperatures are used in the calculations, and the 

effects of temperature on the distribution of forces in the structure must also be considered. 

As an alternative to the use of calculation models described in these guidelines, a design may be 

based on the results of tests. The tests may be conducted in accordance with standard 

procedures, e.g., ASTM E119, or may be uniquely defined. Where unique tests are conducted, 

such tests need to be well documented, providing at least the same amount of information 

concerning the performance of the assembly as provided by calculations such as those described 

in this section. 

4.4.1 Performance Criteria 

Where load-bearing ability is required in the case of fire, concrete structures need to be designed 

and constructed to maintain their load-bearing function during the time period of interest. A 

structural analysis may be applied to assess load capacity or structural stability of fire-exposed 

sections. The performance criterion is stipulated as: 

 Sn  Qd (4.4) 

Where: 

Sn = Nominal required strength at elevated temperature  

Qd = Demand 

This statement of required performance is general and applies to all structural actions. The 

nominal strength of interest may be a bending moment, axial force, shear force, or torque. 

Similarly, the demand is represented by the internal bending moment, axial force, shear force, 

and torque at a section resulting from the self weight of the structure, superposed dead load, 

superposed live load, and the moment created by thermal effects. As a specific example, the 

nominal strength may be the nominal bending moment capacity and the demand may be the 

internal bending moment in equilibrium with external loads. In equation form, this strength 

requirement would be Mn  Md. 

As an alternative to the strength criterion in Equation 4.4, deflection criteria may be adopted to 

assess serviceability of the concrete member. While deflection criteria are not explicitly 

stipulated in the standard test protocols used in North America to assess fire resistance, they may 

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85

be adopted by the stakeholders of a performance-based analysis. Similarly, post-fire serviceability could be adopted by some stakeholders, though that is also not considered in current 

standard fire resistance test protocols. 

4.4.2 Analysis of Flexural Members (Beams and Slabs) 

A rational design method can be applied to calculate the strength of a flexural concrete element 

subjected to fire loading. Because the method of support is an important factor affecting 

structural behavior of flexural elements during a fire, the discussion that follows deals with three 

conditions of support: 

1. Simply supported, thermally unrestrained, flexural members 

2. Continuous flexural members 

3. Simply supported, thermally restrained, flexural members 

4.4.2.1 Simply Supported, Thermally Unrestrained, Flexural Members 

The moment capacity analysis formulated for reinforced and prestressed concrete flexural 

members accounts for the composite nature of the assembly. The analysis of concrete slabs and 

beams is based on methods of analysis used in room temperature concrete design adapted for fire 

resistance analyses, with support from large-scale test data from the Portland Cement 

Association. 

Figure 4.24 illustrates the behavior of a simply supported prestressed concrete beam exposed to 

fire from beneath. The ends of the beam are free to rotate, and the beam is free to elongate 

(thermally unrestrained). The steel reinforcement consists of straight prestressing strands located 

near the bottom of the beam. With the underside of the beam exposed to fire, the bottom expands 

more than the top, and the resulting curvature causes the beam to deflect downward. Also, the 

strength of the reinforcement and concrete near the bottom of the beam will decrease as the 

temperature rises. When the strength of the reinforcement reduces to less than that required to 

support the beam and any superposed load, flexural failure will occur. In essence, the moment 

demand, Md, remains practically constant during the fire exposure, but the resisting moment, or 

nominal moment capacity, Mn, is reduced as the reinforcement and the concrete near the bottom 

lose strength. 

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86

FIGURE 4.24. Moment Diagram for Simply Supported, Thermally 

Unrestrained, Flexural Element (PCI 2004) 

Because steel reinforcement is parallel to the axis of the beam, the design moment strength is 

constant throughout the length (CRSI 1980; PCI 1989; ACI 318 2005): 





 



  2



 

a ssn dfAM (4.5) 

Where: 

Mn = Moment capacity (lb-in.) 

fs = Critical stress in steel (psi) 

As = Cross-sectional area of reinforcement steel (in.2) 

d = Distance from extreme compression fiber to centroid of steel (in.) 

a = Depth of equivalent rectangular stress block (in.) 

bf

f

a

c

s

85.0

A

 s 

 

f’c = Compressive strength of concrete (psi) 

b = Width of beam (in.) 

in which θ signifies the effects of elevated temperatures. Note that As and d are not affected, but 

fs is reduced based on the reinforcement temperature achieved (see Section 4.2). Similarly, the 

equivalent stress block depth, a, is reduced to maintain horizontal force equilibrium in the 

section as fs is reduced. The concrete strength at the top of the beam, c

f , is generally not reduced 

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87

significantly because the temperature rise in the upper portion of the slab is typically relatively 

modest, if for no other reason than because of the heat transmission limit for fire resistance. For 

prestressed concrete, the tendon stress fs can be determined from Equation 18-3 of the 

ACI 318-05 Code (ACI Committee 318 2005). 

If the beam is uniformly loaded, the moment diagram is parabolic with a maximum value at midspan of: 

8

2 wl M  (4.5) 

Where: 

w = Dead plus live load per unit of length (k/in.) 

l = Span length (in.) 

As noted in Equation 4.4, flexural failure is assumed to occur when Mnθ is reduced to Md. The 

usual ACI load factors and strength reduction factors are not applied (see Chapter 3). Thus, in 

this approach, the fire endurance depends on the applied loading and on the strength–temperature 

characteristics of the steel. In turn, the duration of the fire before the “critical” reinforcement 

temperature is reached depends on the protection afforded to the reinforcement. 

Design problems involving the above equations can be solved utilizing data on the strength–

temperature relationships for steel and concrete, and information on temperature distributions 

within concrete members during fire exposures (see the previous sections of this chapter). 

The temperature of the reinforcement steel used in the analysis needs to be representative of the 

temperature of all positive reinforcing steel. Where reinforcement is located at multiple 

distances from an exposed surface, an “effective u,” or u , is used when applying Equation 4.5. 

The value of u is determined as: 







  n

i

i

n

i

ii

A

Au

u

1

1 (4.6) 

For a beam, the representative temperature of the positive reinforcing steel is equal to the 

temperature attained in the concrete at an average position, u , measured from the closest 

exposed surface. Where the difference in distance of a particular bar or strand to two exposed 

surfaces is not more than 25 %, for the purpose of this calculation, the distance to the surface for 

that bar or strand is 1⁄2 of the average of the two distances. This procedure does not apply to 

bundled bars or bundled strands. 

The strength of the reinforcing steel is determined at the temperature resulting from the fire 

exposure, as determined following the heat transfer analysis methods described in the previous 

section and given the material properties presented in Section 4.2.3. 

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88

In addition, thin beams, such as in concrete single- or double-tee beams, are expected to 

experience a faster increase in temperature as a result of fire exposure. In some analysis 

methods, any portion of concrete that attains a threshold temperature is neglected, though the 

specific threshold temperature cited varies from 500 °C to 760 °C between publications and may 

also depend on the aggregate (Buchanan 2001; PCI 1989; CRSI 1980). 

One important difference between cast-in-place and precast concrete construction is the amount 

of concrete cover required over the reinforcement required by ACI 318 (2005) or ASCE/SFPE 

29 (1999). In general, precast concrete construction manufactured under plant control conditions 

requires less cover concrete than cast-in-place concrete. The justification for this difference is 

that better control can be exerted over formwork dimensions, placement of reinforcement, 

concrete quality, and curing procedures in a precast plant than in the field. While this better 

control may contribute to greater quality, a precast concrete element may have less concrete 

cover over the main longitudinal reinforcement (mild steel or prestressing steel), and therefore 

the steel temperature will increase more quickly than a similar cast-in-place concrete specimen. 

While the cast-in-place and precast construction may both satisfy minimum concrete cover 

requirements, there may be less reserve capacity in a precast element with less cover than a 

similar cast-in-place element. 

4.4.2.2 Simply Supported, Thermally Restrained, Flexural Members 

If a fire occurs beneath a portion of a large concrete floor (or roof), the heated portion of the 

floor will expand and push against the surrounding portion of the floor not involved in the fire. 

As a result, the unheated portion exerts compressive forces on the heated portion and creates 

restraint against thermal expansion. In general, restraint improves the performance of a member 

subjected to fire. 

If restrained, the heated section will exert a force when attempting to expand against adjoining 

members. The force exerted on adjoining members is referred to as “thrust”, T. In order to 

develop a moment from the thrust force and moment arm, dT, two aspects must be true. 

1. Adjoining members must be able to withstand the thrust force. 

2. The line of action is not co-located with the neutral axis. If the line of action is below 

the neutral axis, the thrust acts similar to a prestressing force, thereby inducing a 

negative moment. A negative moment is beneficial to simply supported flexural 

members that need to resist an applied positive moment. 

The nominal bending moment capacity of a thermally restrained beam or slab is: 

,Rn Th  MMM n (4.7) 

Mn is determined by the equation presented above for simply supported members. The moment 

caused by the thrust resulting from the restraint, MTh, is determined as: 

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89





 





1  1 2

Th

Th Th

a dTM (4.8) 

Where: 

 T1 = Thermally-induced thrust 

 1 = Mid-span deflection 

 dTh = Distance between the top of the member and the thrust line at the supports 

 aTh = Depth of equivalent stress block for the thrust force 

If the standard ASTM E119 fire exposure is considered, the thermally induced thrust, T1, can be 

determined from the nomograms given in Figure 4.25 (PCI 1989): 

FIGURE 4.25. Nomograms Relating Thrust Parameter, Strain Parameter, and 

Ratio of Cross-Sectional Area to Heated Perimeter (PCI 1989) 

Where: 

T = Thrust force (lb) 

A = Cross-sectional area (in2

) 

E = Modulus of elasticity (psi) 

Z = Dimensionless geometric parameter = A/S 

A = Cross-sectional area (in2

) 

S = Heated perimeter (in) 

The distance between the top of the member and the line-of-action for the thrust force at the 

supports depends on the support conditions. Empirically, the position of the line of action of the 

thrust force was observed to be at or near the bottom of the stems in the multiple-T slabs. Thus, 

a conservative approach is to assume the location to be equal to 10 % of the depth of the slab 

above the bottom at the supports. 

Where the standard ASTM E119 fire exposure is considered, the mid-span deflection, 1, is 

determined as: 

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90

Normal-weight concrete: 

























  

31 log61 3500

11

1

1

2

1

1

EA

T

y

l

b

o (4.9) 

Lightweight concrete: 

























  

74 log61 3500

11

1

1

2

1

1

EA

T

y

l

b

o (4.10)

Where: 

1 = Deflection for a restrained slab (in.) 

0 = Deflection for an unrestrained slab (in.) 

b

cb

bb Ey

lf

yEZ

MI

EI

wl

48

5

48

5

384

5 4 2 2

 

yb1 = Distance from centroid to extreme fiber (in.) 

If a fire exposure other than the standard fire exposure is considered, the thermally induced 

thrust, T1, the line of action of the thrust force, and the mid-span deflection, 1 need to be 

determined by an advanced computational method or test. 

The depth of the equivalent compressive stress block for the thrust force, aT, is determined as: 

bf

fAT

a

c

psps

T 85.

  (4.11) 

dT is estimated to be 90 % of the overall depth of the section, and  is determined from 

Figure 4.26. Both of these guidelines are only applicable given exposure conditions from the 

ASTM E119 standard test. 

FIGURE 4.26. Estimate of Midspan 

Deflection, Reference Specimens (PCI 1989) 

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91

The actual location of the line of action the thrust force, dT, for a concrete member depends on: 

 Time duration of fire exposure 

 Shape of the member 

 Concrete compressive strength 

 Amount of reinforcement 

 Relative stiffness of the flexural member and the adjoining frame 

 Amount of expansion permitted 

4.4.2.3 Continuous Flexural Members 

Continuous members undergo changes in reactions and internal forces when subjected to fire, 

referred to as “moment redistribution.” Temperature gradients through the depth of the beam or 

slab create curvature, which, when integrated along the length of the element, creates deflection. 

The continuity of support condition creates reaction forces that are superposed with the reactions 

due to applied loads. 

The moment diagrams for a two-span continuous beam whose underside is exposed to fire are 

presented in Figure 4.27. With the underside of the beam exposed to fire, the bottom of the 

beam expands more than the top. The resulting curvature increases the downward reaction at the 

interior support. This action results in a redistribution of moments: the negative moment at the 

interior support increases while the positive moments decrease. 

FIGURE 4.27. Moment Diagram for a TwoSpan Continuous Beam (PCI 2004) 

For the situation shown in Figure 4.27 (fire exposing the underside of the continuous beam or 

slab), the negative moment reinforcement remains cooler than the positive moment reinforcement because it is better protected from the fire. In addition, the redistribution that occurs during 

fire exposure may cause a sufficient increase in negative bending moment and yielding of the 

negative moment reinforcement. Thus, a relatively large increase in negative moment can 

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92

develop throughout the test. The resulting decrease in positive moment means that the positive 

moment reinforcement can be heated to a higher temperature before failure will occur. 

Therefore, the fire endurance of a continuous concrete beam is generally significantly longer 

than that of a simply supported beam having the same cover and the same applied loads. 

It is possible to design the reinforcement in a continuous beam or slab for a particular fire 

endurance period. From Figure 4.27, the beam is expected to collapse when the positive moment 

capacity, M+

nθ, is reduced to the value of the maximum redistributed positive moment at a 

distance x1 from the outer support. 

The aspects to consider in a fire resistance analysis of a continuous slab are: 

 Positive moment capacity 

 Negative moment capacity 

 Lengths of reinforcement 

For a uniformly loaded, symmetrical interior span with equal end moments, the positive moment 

capacity is determined using the method outlined for simply supported sections. The required 

negative moment capacity is: 

 

n  n - M wl M

8

2

(4.12)

The required length of the negative moment reinforcement is: 

w

M - l

 x n



 2 

2 0 (4.13) 

The available negative moment capacity is determined using the method outlined for simply 

supported sections with the following modifications. Because the concrete in compression will 

be located on the exposed side, the temperature of the concrete is determined at a location equal 

to half of the depth of the equivalent rectangular compressive stress block. The compressive 

strength of the concrete is then determined based on this temperature. 

Figure 4.28 depicts a uniformly loaded beam or slab continuous (or fixed) at one support and 

simply supported at the other. Also shown is the redistributed applied moment diagram at 

failure. 

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93

FIGURE 4.28. Uniformly Loaded Member 

Continuous (or Fixed) at One Support (PCI 2004) 

For a uniformly loaded end span, the positive moment capacity is determined as for an interior 

span, but the minimum, nominal negative moment capacity is determined as: 

2

2

2

n

2 2

 M

wl

M wl wl n



  

 (4.14) 

The required length of the negative moment reinforcement in the end span is determined as: 

wl

M

 x

- 2 nθ

0  (4.15) 

In most cases, redistribution of moments occurs early during the course of a fire, and the 

negative moment reinforcement can be expected to yield before the negative moment capacity 

has been reduced by the effects of fire. In such cases, the length of x0 is increased, i.e., the 

inflection point moves toward the simple support. If the inflection point moves beyond the point 

where the bar stress cannot be developed in the negative moment reinforcement, sudden failure 

may result. 

A symmetrical beam or slab in which the end moments are equal is illustrated in Figure 4.29. 

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94

FIGURE 4.29. Uniformly Loaded Member 

Continuous at Supports (PCI 2004) 

In this case, 

 

  M n

wl - 8

 M

2

n (4.16) 

w

M - l

 x n



 8 

2 0 (4.17) 

To determine the maximum value of x0, the value of w should be the minimum service load 

anticipated, and 













 

n

2

M - 

8

wl should be substituted for  M n . 

For any given fire endurance period, the value of  M n can be determined by the procedures 

given above. Then the value of  M n can be determined, followed by the necessary lengths of 

the negative moment reinforcement. 

The amount of moment redistribution that can occur depends on the amount of negative moment 

reinforcement. Tests have clearly demonstrated that in most cases the negative moment 

reinforcement will yield, so the negative moment capacity is reached early during a fire test, 

regardless of the applied loading. The designer must exercise care to ensure that a secondary 

type of failure does not occur. To avoid a compression failure in the negative moment region, 

the amount of negative moment reinforcement should be small enough so that 

   ss c  fdbfA  is less than 0.30, before and after reductions in fy, b, d, and c

f are taken 

into account. Furthermore, the negative moment bars or welded wire reinforcement must be long 

enough to accommodate the complete redistributed moment and change in the inflection points. 

It should be noted that the worst condition occurs when the applied loading is smallest, such as 

the dead load plus partial or no live load. It is recommended that at least 20% of the maximum 

negative moment reinforcement extend throughout the span. 

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95

Many of the precast concrete elements used in building structures (e.g., hollow-core planks, 

double-tee beams, and inverted tee beams) are used as simply supported elements. As such, the 

development of secondary shears due to thermal effects is often not a consideration. In contrast, 

much of the cast-in-place building construction is continuous, and consideration needs to be 

given to the effects of this continuity as described above. 

4.4.3 Analysis of Compression Members 

The axial-flexural behavior of concrete columns in fire may be governed by buckling strength. 

Allen and Lie (1974) evaluated the buckling of reinforced concrete columns by conducting an 

analysis of the strains through the cross section at mid-span. Stress resultants were applied to 

determine the strain distribution through the cross section. The total strain was related to the 

curvature in the column. Buckling behavior is noted when the radius of curvature decreases without 

limit. The analysis compared favorably with experimental data (Harmathy 1993). 

4.4.3.1 Ultimate Load Calculation—Simplified Method 

Dotreppe, Franssen, and Vanderzeypen (1999) evaluated the fire resistance of concrete columns 

based on tabulated data containing dimensions of the cross section and concrete cover. 

Dotreppe, Franssen, and Vanderzeypen developed a quick and efficient design method for 

determination of the ultimate load capacity in the case of a prescribed fire resistance, as well as 

determination of the fire resistance of a column in a building. This design formula is related to 

the plastic crushing load at elevated temperatures, which is reduced by the buckling coefficient 

for eccentrically loaded columns and a nonlinear amplification term for eccentric loads. The 

results are calibrated on experimental results. Spalling of concrete, slenderness ratio, and 

varying concrete cover are taken into account. 

Limitations of this design method include the following (Dotreppe, Franssen, and Vanderzeypen 

1999): 

1. Columns with longitudinal bars with diameter   25mm. 

2. Method is calibrated on experimental results. 

3. )(1  t and )( 2  t were considered using rectangular cross sections. However, the 

formulation can be extended to circular columns. 

4. Nu-theoretical / Nu-test ~ 0.4 – 1.4 ; mean = 0.9. 

5. )(1  t and )( 2  t are limited to siliceous aggregate columns subjected to ISO 834, 

ASTM E119, and ULC S 101 fires. 

6. λ (slenderness ratio) ≤100. 

7. 0.04 m2 ≤ Ac ≤ 0.2 m2

. 

8. h/b ≥ 1⁄2 (with h ≤ b). 

9. 20 mm ≤ c ≤ 50 mm. 

10. e ≤ h/2 (Note: Even if column is axially loaded, an eccentricity e = 10 mm should be 

adopted.) 

The principal equation for this method is expressed as Equation 4.18: 

-- DRAFT -- -- DRAFT --
96

 ) u    p (*)()()( tNtttN (4.18) 

Where: 

 t)( = Describes spalling as a function of time 

 ) (t = Buckling coefficient for concentrically loaded columns 

Np(t) = Plastic crushing load 

Nu(t) = Ultimate load capacity 

For short columns: Nu(t) = Np(t) (4.19) 

For long columns: (4.20)

The following steps are used in the simplified method for ultimate load calculation: 

Step 1: Calculate Plastic Crushing Load 

 (4.21)

 

 Determine correlation factors: 

 2 )*(1

1 )(

1

1 a ta

t



  (4.22) 

 5.0

1 *3.0   Aa c (4.23) 

 25.0

2

  Aa c (4.24) 

 0

111.0046.0

9.0 1)( 2 

  c

t  t

 

Step 2: Calculate Spalling Factor 

 for t < 0.5 hour 

 for t > 0.5 hour 

Step 3: Calculate Buckling Coefficient 

 

 Determine slenderness: 

 for   20 100 1)(    (4.25) 

 

tNtttN )(*)()()( u  p   

p cc ys  1   2 **)(**)()( fAtfAttN

  3.01)( tt

 t  85.0)(

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97

25 10.3

)(

1

/10 1

)( )(





 



 



 he t

 for 20 < λ ≤ 70 

5

200

225 7.0

20 80.0)(





 



 





 



 

c

  (4.26) 

 for   70 

5

200

225

70

7.0

20 80.0)(





 



  



 









 



 

 c

  (4.27) 

Determine buckling coefficient: (4.28) 

where, 

 e = load eccentricity (mm) 

 h = smaller dimension of the cross section (mm) 

 λ = slenderness ratio 

 c = concrete cover (mm) 

 Ac = concrete area (m2

) 

 As = steel area (m2

) 

 fc = compressive strength of concrete (N/mm2

) 

 fy = yielding strength of steel (N/mm2) 

 t = time or fire resistance (h) 

 

Modifications to Simplified Formula:

1. Aggregate factor described by Tan and Tang [2004] based on studies by 

Lie and Woollerton [1998] and Lie and Kodur [1996]: 

 agg = 1.0 for siliceous; 0.9 for carbonate aggregate 

2. ASTM E119 fire exposure factor by Tan and Tang [2004]: 

 ISO = 1.0 for ISO 834 fire; and 0.85 for ASTM E119 fire 

 

 Apply modifications to time (t) with te: te = agg 

*ISO *t 

Example: 

Ultimate load (Nu) calculation for a given fire resistance rating (Rf) 

Given: A 200 mm x 300 mm column with 6 #4 bars (diameter of 12 mm) that is 3.90 meters in 

length. The column is eccentrically loaded, with hinges at both ends. The column has a fire 

resistance rating of 2 hours based on ISO 834 standard fire exposure 

 

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98

 Parameters: 

 Ac = 200 x 300 mm 6  12 mm L = 3.90 m 

 c = 25 mm e = 20 mm hinged at both ends 

 fc = 35.7 N/mm2

 fy = 493 N/mm2 Rf = 120 min 

 Calculation: 

 λ = kL/r = 67.5 Assume k = 1.0 (effective length) 

 Ac = 0.06m2

 As = 6.8*10-4 m2 

 5.0

1 *3.0   Aa c = 1.22 

 25.0

2

  Aa c = 2.02 

 2 )*(1

1

1

1 a  ta

  = 0.38 

 111.0046.0

9.0

2 1

  c

t  = –0.42 

 since  2 ≥ 0  2 = 0 

 Therefore, 

 

 20 < λ ≤ 70 

5

200

225 7.0

20 80.0





 



 





 



 

c

  = 0.34 

 

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99

25 10.3

)(

1

/10 1

)(





 



 



 he

Calculate buckling coefficient: 

 = 0.25 

 

 Calculate spalling factor: 

 

 Since t > 0.5 hr 

 Determine ultimate load: 

 

4.4.3.2 Beam–Column Calculation Method 

Tan and Tang (2004) extend the Rankine method (typically used to describe the critical buckling 

load in steel column design) to predict the fire resistance of reinforced concrete columns 

subjected to fire conditions. This method does not include non-uniform temperature and stress 

distribution across member sections, and the induced mechanical stresses due to thermal 

expansion and thermal gradient. In addition, other secondary effects such as initial crookedness 

are ignored. 

The general form of the Rankine model applied to reinforced concrete columns in fire conditions 

is as follows: 

)(

1

)(

1

)(

1

Rr ppr eer tPutPutP   (4.29) 

where upr and uer are the respective plastic and elastic critical load reduction factor and account 

for load eccentricity or applied moment (for axially loaded columns, uer is typically unity). Pp(t) 

and Pe(t) are the respective plastic and elastic critical axial loads. 

This method includes the calculation of the modified normalized slenderness ratio, t)( r . For 

reinforced concrete columns, this term is typically less than 0.5, which also explains the 

insignificance of secondary effects compared with steel columns. 

)(* )(

)( )( t

u

u

tP

tP

t

er

pr

er

pr

r  (4.30) 

Where,  t)( is the slenderness ratio. 

The reinforced concrete column buckling curves can then be determined from the modified 

buckling coefficient, Nr(t): 

 t  85.0)(

Nu     1 cc   2 ys   173**** kNfAfA

-- DRAFT -- -- DRAFT --
100

2

)(1

1

)()(

)( )( tP t

P

tP

tP tN

pr pr r

R

r   (4.31) 

However, both the buckling coefficient and the normalized slenderness ratios depend on fire 

exposure time, in which the plastic collapse load Ppr(t) and the elastic critical load Per(t) decrease 

with time.

To account for the reduction in plastic collapse load and elastic critical load, Tan and Tang 

introduce Ppr(t) and Per(t) in terms of ambient loads Ppr(0) and Per(0). 

 ) 0()()( pr   PttP prp and ) 0()()( er   PttP ere (4.32) 

t)(  p and ) (t e are reduction factors accounting for the deterioration of material yield strength 

and elastic modulus. Modified normalized buckling and modified normalized slenderness ratio 

are also expressed in these terms, as follows: 

)0( )(

)( 1

)( )0(

2

r

e

p

p

r

t

t

t

N









 and )0(* )0(

)0(

)0(

)0( )0(   

er

pr

eer

ppr

er

pr

r u

u

Pu

Pu

P

P

 (4.33) 

Hertz (1993) suggests that  

a

e p   tt )()( , where a is between 1 and 2. From Dotreppe, 

Franssen, and Vanderzeypen a=1. With a=1, 

 

)0(1

)( )0( 2

r

p

r

t

N

   (4.34) 

The plastic crushing load and elastic critical load can then be calculated, as follows: 

Pp(0) = Qc(0) + Qyr(0) = 0.85f’c(0)Ac +fyr(0)Asr (4.35) 

 

2

2 )0(2.0 )0(

e

srsrcc

e L

IEIE

P

   (ACI Committee 318 2005) (4.36) 

Where: 

Qc(0) and Qyr(0) = Plastic crushing load from concrete and the steel reinforcement 

f’c and Ec(0) = Concrete strength and elastic modulus 

fyr(0) and Esr(0) = Yield strength and elastic modulus of steel reinforcement 

Ac and Asr = Area of concrete and steel rebar 

Ic and Isr = Second moment of area of concrete and steel rebar at centroid 

-- DRAFT -- -- DRAFT --
101

Temperature effects on steel reinforcement and concrete materials are considered by applying the 

)(1  t and )( 2  t from Dotreppe, Franssen, and Vanderzeypen (1999) to the material models. 

The plastic reduction factor, ) (t  p , is determined from Equations 4.29, 4.30, 4.32, and 4.33 and 

then used in Equation 4.31 to determine the normalized buckling coefficient. Then, the ultimate 

load can be calculated from the Rankine load formula. 

Using a similar approach, the Rankine model is further applied to eccentrically loaded reinforced 

concrete columns in fire conditions. A bilinear P-M interaction diagram is constructed from the 

ultimate axial compressive load, the balance point, and the ultimate bending capacity. Note: The 

P-M interaction curve shrinks with increasing temperature. Temperature effects are accounted 

for by applying the )(1  t and )( 2  t factors mentioned earlier. 

Better correlations are achieved with this method than the Dotreppe, Franssen, and 

Vanderzeypen method (Tan and Tang 2004). 

4.4.3.3 Mathematical Model 

Lie and Celikkol (1991) evaluated the buckling of circular reinforced concrete columns. Lie and 

Irwin (1993) also evaluated the buckling of reinforced concrete columns with rectangular cross 

sections. In both studies, a mathematical model was proposed to predict the fire resistance of both 

circular and rectangular concrete columns. A thermal analysis was conducted using finite 

difference techniques to attain a temperature profile across the column cross section as a function of 

time. Effects of moisture were included for the temperature profiles. The strength of the column 

was determined by load deflection analysis assuming linear curvature from the pin end to the midheight of the column, and a relationship between mid-height deflection and curvature. The axial 

strain was varied until the internal mid-height moment was in equilibrium with the applied moment. 

Load deflection curves were calculated for each time step during the fire exposure until the 

maximum load the column can carry was determined. Spalling was not considered in this study. 

Alternatively, thermo-mechanical models, similar to that reported by Dotreppe, Franssen, and 

Vanderzeypen may be applied to assess the structural response of fire-exposed concrete columns. 

The anticipated behavior of cast-in-place and precast concrete columns is similar. Precast 

columns are often reinforced with mild steel reinforcement, the same as for cast-in-place 

columns. In addition, a precast column may include a prestressing force to control stresses 

during handling and erection. Often this prestressing force is provided with debonded posttensioned steel strands. The magnitude of the prestress is small and will not greatly influence 

behavior. Two principal differences in construction may create differences in behavior: 

1. Concrete cover requirements are less for precast concrete columns than cast-in-place 

columns. Because the main longitudinal reinforcement is distributed around the 

perimeter of a column, all the reinforcement in a precast concrete column can be 

expected to increase in temperature (and therefore reduce in strength) more quickly 

than the reinforcement in a similar cast-in-place column. 

2. Precast concrete columns are most often constructed as prismatic multistory elements. 

In fact, the cross-sectional dimensions of a precast concrete column often remain 

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102

constant throughout the height of a building structure. In contrast, the cross section 

dimensions of a cast-in-place column are more likely to change every several floors. 

This may result in a greater overstrength in the upper story columns of a precast 

concrete building than with a cast-in-place concrete building. This greater overstrength will provide greater inherent fire resistance for the upper story column. 

4.4.4 Shear and Torsion 

Little information exists in the published literature about the shear and torsion behavior of 

concrete members in fires. Most of the structural fire tests that have been performed have 

focused on the flexural behavior of beams and slabs and on the axial behavior of columns. 

In the beam flexural tests, the beams were carrying shear force as well as bending moment, so 

the shear strengths of the beams were also evaluated in the tests. Of the many structural fire tests 

performed on simply supported elements (unrestrained and restrained), no shear failures were 

reported. Only one shear failure has been reported in a test of a continuous beam. However, in 

that test, the shear reinforcement was under-designed for the service load in the absence of fire. 

As explained earlier, in the case of continuous beams, additional reaction forces develop as a 

result of thermal effect, and these reaction forces alter the distribution of internal shear. 

Therefore, careful attention needs to be paid to the shear demands in continuous flexural 

members in fires. 

In the absence of experimental data created for a particular design application, the behavior of 

concrete members in shear and torsion subjected to a fire loading should be calculated using the 

procedures in ACI 318 (2005), allowing for the effects of temperature on material properties and 

on the distribution of internal shear and torsion demands. In particular, this means that the 

effects of elevated temperatures on the yield strength of transverse reinforcement should be 

included in the calculation of the nominal shear strength, Vn, and nominal torsion strength, Tn. 

The influence of thermal effects on the magnitude of the internal shear force may be particularly 

important. 

4.4.5 Spalling and Spalling Mitigation 

Spalling refers to the delaminating or breaking away of a surface layer of concrete due to 

exposure to elevated temperature. There are many variations of spalling. Two types of concrete 

spalling that are more critical in structural performance point of view are explosive spalling and 

corner spalling. Explosive spalling, which tends to occur very suddenly and violently early in 

the fire exposure process, is widely observed in laboratory tests of small material specimens and 

structural elements (Phan, 2005, 2007, 2008; Bailey, 2002; Kalifa et al., 2000; Hertz, 1992) as 

well as real structures in accidental fires (Ulm et al., 1997). Corner spalling, which is often 

observed along the corners of rectangular or square concrete columns or beams, is a more 

gradual and less violent process. 

While corner spalling is primarily the result of unrestrained thermal expansion in the transverse 

direction of the beams or columns, explosive spalling effects a larger surface area and has been 

shown to be primarily pore pressure-driven. The complex mechanism of explosive spalling and 

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103

factors contributing to its occurrences has been explained in details by Phan (2005, 2007, 2007). 

Briefly, exposure to elevated temperature triggers the transformation and mass transport of 

moisture in concrete that results in the buildup of internal pore pressure and potential for 

explosive spalling as free water residing in the concrete pores and chemically-bound water in the 

concrete matrix undergo transformation from liquid to a gaseous phase, expand in volume, and 

transport through the concrete with increasing concrete temperature. High strength concrete is 

found to be more susceptible to explosive spalling than normal strength concrete due to its low 

permeability and thus reduced ability to successfully mitigate the buildup of internal pressure. 

Spalling is significant in terms of structural fire performance because of the consequent 

reduction in the concrete cover causing the reinforcing steel to be heated more quickly, leading 

to premature loss of overall structural capacity. A secondary effect is the reduction in the overall 

slab thickness causing the unexposed surface temperature to increase more quickly. The amount 

of thickness reduction and the area of the slab affected are usually not large enough to cause 

problems with heat transmission through the slab (without otherwise causing very a substantial 

temperature increase in the steel reinforcement). Spalling itself is not identified as one of the 

endpoint criteria in ASTM E119. 

The following is important information on explosive spalling that is useful for structural fire 

design and modeling purposes: 

 The temperature of concrete (at the depth where spalling is expected to occur) when 

explosive spalling occurs is between 220 C and 280 C. 

 Spalling depth typically varies between 25 mm and 75 mm. 

The susceptibility of spalling by higher strength concrete may be abated through material design, 

reinforcement detailing, curing conditions, and use of additives such as polypropylene fibers. 

Studies (Phan, 2005, 2007, 2008) have shown that the addition of at least 1.5 kg/m3

 of 

polypropylene fibers significantly reduced the buildup of pore pressure and tendency for 

explosive spalling in high strength concrete. Use of 135 bent seismic hook for stirrups in 

columns has also been found to reduce the tendency for spalling in columns (Kodur, 2005; ACI 

216.1-07, 2007). The likelihood of spalling appears to increase for: 

 High incident heat flux in the early stages of fire development 

 Siliceous aggregate concretes and high-strength concretes 

 Concretes with high moisture content ( 2 % by mass) 

 Stress level: 

 Thin elements under high stress (i.e., prestressed concrete) 

 Abrupt changes in geometry and at connections to other structural members 

 Concretes with low porosity/permeability 

 

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104

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Phan, L., and N.J. Carino (2001), “Mechanical Properties of High-Strength Concrete at Elevated 

Temperatures, NISTIR 6726, Gaithersburg, Md.: National Institute of Standards and 

Technology. 

Phan, L.T., and N.J. Carino (2003), “Code Provisions for High Strength Concrete StrengthTemperature Relationship at Elevated Temperatures,” RILEM Materials and Structures 36 

(March 2003) 91-98. 

Phan, L.T. (2005), “Pore Pressure in High Strength Concrete at High Temperature,” Third 

International Conference on Construction Materials: Performance, Innovations and Structural 

Implications (ConMat ’05), Vancouver, Canada, August, 2005. 

Phan, L.T., (2007) “ Spalling and Mechanical Properties of High Strength Concrete at High 

Temperature,” Proceedings of the 5th International Conference on Concrete Under Severe 

Conditions: Environment and Loading (CONSEC’07), Tours, France, June 2007, pp. 1595-

1608, Volume 2. 

Phan, L.T., (2008) “Pore Pressure and Explosive Spalling in Concrete,” RILEM Materials and 

Structures Journal (Accepted for publication: January, 2008) 

-- DRAFT -- -- DRAFT --
108

Sanjayan, G., and L.J. Stocks (1993), “Spalling of High-Strength Silica Fume Concrete in Fire,” 

ACI Structural J., Technical Paper No. 90-M18 (March-April 1993) 170-173. 

Shirley, S.T., R.G. Burg, and A.E. Fiorato (1988), “Fire Endurance of High-Strength Concrete 

Slabs,” ACI Materials J. (March-April 1988) 102-108. 

Sterner, E., and U. Wickstrom (1990), “TASEF—Temperature Analysis of Structures Exposed to 

Fire,” Fire Technology SP Report 1990: 05, Boras: Swedish National Testing Institute. 

Tan, K.H., and C.Y. Tang (2004), “Interaction Formula for Reinforced Concrete Columns in Fire 

Conditions,” ACI Structural J., Technical Paper No. 101-S03 (January-February 2004) 19-28. 

Underwriters’ Laboratories of Canada (2004), Fire Tests of Building Construction and 

Materials, ULS Std. CAN4-S101, Toronto: Underwriters’ Laboratories of Canada. 

Weigler, H., and R. Fischer (1964), “Beton bei Temperaturen von 100 C bis 750 C,” Beton 

Herstellung und Verwedung, Dusseldorf (February 2, 1964) 33-46. 

-- DRAFT -- -- DRAFT --
109

4.6 Appendix A from Lie (1992) 

for 200 C  T   400 C c cc  2.7 106  J m 3  C

 1 

for 400 C  T   500 C c cc  ( ) 10 0.013T 2.5  6  J m 3  C

 1 

for 500 C  T   600 C c cc  ( ) 10 0.013T 10.5 

6  J m 3  C 1 

for T 600 C    c cc  2.7 106  J m 3  C

 1 

Thermal conductivity

for 0 C  T 800 C kc 0.00085T 1.9 W m 1  C 1

 

T 800 C kc 1.22 W m 1  C 1 

Coefficient of thermal expansion

c ( ) 10 0.008 T  6  6 

Concrete Properties

Stress-strain relations

for c max  f

c f'c 1

c max 

3 max 

















2



















where max 0.0025 6.0T 0.04T2    10 6 

and for 0 C  T 450 C f'c f'co

for 450 C  T 874 C f'c f'c 2.011 2.353

T 20 

1000











  











for T 874 C f'c 0

Thermal capacity

for 0 T    200 C c cc  ( ) 10 0.005T 1.7 

6  J m 3  C 1 

-- DRAFT -- -- DRAFT --
110

 s cs  ( ) 10 0.086T 73.35 

6  J m 3  C 1 

for T 800 C    s cs  4.55 106  J m 3  C 1 

Thermal conductivity

for 0 C  T 900 C ks 0.022T 48 W m 1  C 1

 

T 900 C ks 28.2 W m 1  C 1 

Coefficient of thermal expansion

for T 1000 C    s ( ) 10 0.004 T  12  6  C 1 

T 1000 C    s 16 106  C 1 

Water Properties w cw 4.2 106  J m 3  C 1 

Heat of vaporization: w 2.3 106  J kg 1 

Steel Properties

Stress-strain relations

for s p  f

y f ( ) T 0.001 

0.001

s 

where p 4 10 6  f

yo 

and f T 0.001 ( ) 50 0.04T  ( ) 1 exp 30    ( ) 0.001   0.03T  6.9

for s p  f

y

f T 0.001 ( ) 

0.001

p  f T s p      0.001  

   f T 0.001 ( ) 

Thermal capacity

for 0 T    650 C s cs  ( ) 10 0.004T 3.3 

6  J m 3  C 1 

for 650 C  T   725 C s cs  ( ) 10 0.068T 38.3  6  J m 3  C 1 

for 725 C  T 800 C

-- DRAFT -- -- DRAFT --
111

Specifics of columns and furnace

f 0.75 emissivity of column furnace fire

c 0.8 emissivity of concrete

KL 2.0 m effective length of columns

l 3.5 m length of column that contributes to axial deformations

 0.05 concentration of moisture in insulation by volume

4.7 Commentary/Appendix 

Information on T and dT is based on experimental research by Issen, Gustaferro and Carlson 

(1970). The experimental program consisted of 40 standard fire resistance tests conducted by the 

Portland Cement Association. 

The first 25 tests were conducted to provide a set of reference tests that could be used to obtain 

data to examine the accuracy of predictions from the analytical method. The 25 tests included 13 

normal weight (carbonate) and 12 lightweight double-T slabs that were 16 feet long. The 

specimens were both prestressed and reinforced concrete designs. The expansion permitted in 

the tests ranged from 0.04 to 1.40 in. A diagram of a reference specimen is provided in Figure 

4.30. 

FIGURE 4.30. Reference Specimen (CRSI 1980) 

-- DRAFT -- -- DRAFT --
112

The maximum thrust measured from the reference specimens is plotted in the graph in Figure 

4.31. As expected, the thrust increased with a decrease in the amount of expansion permitted. 

FIGURE 4.31. Maximum Thrust: Reference Specimens (CRSI 1980)

In the next phase of the experimental program, 15 tests were conducted with “correlation 

specimens.” These specimens used different geometries and aggregates to observe differences in 

behavior. The analytical method developed from the reference specimens was adapted with the 

data from the correlation specimens for increased applicability. 

The 15 specimens consisted of:

• 12 beams and slabs

 Four 14 x 18 ft restrained slabs (restrained longitudinally and laterally) 

 8 beams restrained longitudinally 

• 3 miscellaneous specimens (siliceous)

 2 embedded electrical, underfloor ducts 

 1 pan-joist with spray applied protection 

The correlation specimens are depicted in Figure 4.32. Further details on the correlation 

specimens are:

• Properties of steel and concrete: 

 Prestressing steel: fsu = 262 ksi 

 Reinforcing steel: fy = 66 ksi 

 Concrete: fc = 5 ksi 

• Applied load: factor of safety = 1.8, i.e., applied moment was 56% of ambient 

temperature moment capacity per American Concrete Institute code.

-- DRAFT -- -- DRAFT --
113

• Applied load: factor of safety = 1.8, i.e., applied moment was 56% of ambient 

temperature moment capacity per American Concrete Institute code.

FIGURE 4.32. Correlation Specimens (CRSI 1980)

Agreement between the predicted and measured thrust is ± 15% for beams and –20 to +10 % for 

slabs, with a pan–joist slab at 80%. 

4.8 Mathematical Model for Concrete Columns (Lie and Celikkol 

1991)

Step 1: Calculation of Temperatures Using Finite Difference Method

Divide the column into concentric layers M (for circular column, Figure 4.33) and a triangular 

network (for rectangular sections, Figure 4.34). Assume the columns are exposed to the standard 

fire described by ASTM E119 or CAN4-S101 (ULC 2004). 

 

-- DRAFT -- -- DRAFT --
114

FIGURE 4.33. Arrangement of Layers in FIGURE 4.34. Arrangement of 

Circular Section Elementary Layers in 

Rectangular Section 

 

Equation for ASTM E119 time–temperature curve: 

 

 

 

Temperature expression for outer concrete layer: 

 

 Circular section: 

 

 

 

 

Rectangular section: 

 Elements along x-axis: 

 

 

 

]})273()273[({ ))[(4/5( ]

)1(2 4

1

4

1 1

1

1

1   

 

  j j

j fcf

ww

j

cc

j j T T

M cc

tM TT 



T t t j

f   41.170])79553.3exp(1[75020

)( ))[(4/5 )](

))(2/3(

2 21

1 1

21 jj

j

ww

j

cc

jj

TT

M cc

tkkM    

  

  





 















 

 



 

  j

n

j

n

j

n

j

n

j

nww

j

ncc

j

n

j

n TT

kk

cc

t TT ,1)1(,2

,1)1(,2

2

,1 ,1

,1

1

,1 2

( )

)[( ]

2



  ])273()273[(2  2

( ) 4

,1

4

,1)1(,2

,1)1(,2 















 

 

 j

n

j

cf f

j

n

j

n

j

n

j

n TT T T

kk



-- DRAFT -- -- DRAFT --
115

 

Elements along y-axis: 

 

 

 

 

 

 

Temperature expression for inside concrete layers: 

 Circular section: 

 

 Rectangular section: 

 

 

Temperature expression for center of concrete column: 

 Circular section: 

 

Temperatures along lines of symmetry:

 Rectangular section: 

 

)(2/1[( ))( ))[((2 ] 2 1 1

1 j

m

j

m

j

m

j

j m

mww

j

mcc

j

m

j

m TTkkmM

ccmM

t TT      



  





  





  













 

 



 

  j

Nm

j

Nm

j

Nm

j

Nm

j

Nmww

j

Nmcc

j

Nm

j

Nm T T

kk

cc

t TT ,)1(),1(

,)1(),1(

2

, ,

,

1

, 2

( )

)[( ]

2



  ])273()273[(2  2

( ) 4

,

4

,)1(),1(

,)1(),1( 















 

 

 j

Nm

j

cf f

j

Nm

j

Nm

j

Nm

j

Nm T T T T

k k



)(2/1( )( )] 1 1

j

m

j

m

j

m

j

m   TTkkmM 

  





 















 

 



 

  j

nm

j

nm

j

nm

j

nm

j

nmww

j

nmcc

j

nm

j

nm TT

kk

cc

t TT ,)1(),1(

,)1(),1(

2

, ,

,

1

, )[( ]  2

    j

nm

j

nm

j

nm

j

j nm

nm

j

nm

j

nm

j

nm TT

kk

TT

kk

,)1(),1(

,)1(),1(

,)1(),1(

,)1(),1(

2 2 















 

















 

 







 





 















 

 

 j

nm

j

nm

j

nm

j

nm TT

kk

,)1(),1(

,)1(),1(

2

( )( ) )[( ]

2

2 1 1

1 j

M

j

M

j

M

j

j M

Mww

j

Mcc

j

M

j

M TTkk

cc

t TT    



  





1

3,

1

1,

   j

m

j

m TT 1),1(

1

),1(







  jnM

j

nM TT

-- DRAFT -- -- DRAFT --
116

Calculate effect of moisture: 

 i) Initial Volume of Moisture 

 Outer layer: 

 Circular section: 

 Rectangular (x-axis): 

 Rectangular (y-axis): 

 Inner layers: 

 

 Circular section: 

 

 Rectangular: 

Center: 

 

 ii) Evaporation of volume with time 

 Outer Layer: 

 Circular section: 

Rectangular (x-axis): 

 

 

 

1

2

1  MV  ))(4/5( 

V n ,1 n

2

,1 2

)( 

 

V Nm ,Nm

2

, 2

)( 

 

m  mMV  m

2  ))((2

  





 















  

 

 j

n

j

n

j

n

j

n

ww

n TT t kk

V ,1)1(,2

,1)1(,2

,1 2

( )



  j

n

j

n

j

n

j

n TT

kk

,1)1(,2

,1)1(,2

2 















 

 



])273()273[(2  4

,1

4   j

n

j

cf  Tf T

V nm ,nm

2

, 2

)( 

 

VM  M

2  )(4/1

 ])273()273[()1( 2 4

1

4

1  

  j j

fcf

ww

M T T t V  







    ))( 2 )(2/3( 21

21 jj

jj

TT kk M

-- DRAFT -- -- DRAFT --
117

Rectangular (y-axis): 

 

 

 Inner Layers: 

 

 Circular section: 

 

 Rectangular section: 

 

 

 Center: 

 Circular section: 

 

))( 2 )(2/1[( 2

1

1 j

m

j

m

j

m

j

m

ww

m TT kk mM t V  



  







  





 















  

 

 j

Nm

j

Nm

j

Nm

j

Nm

ww

mN T T t k k

V ,)1(),1(

,)1(),1(

, 2

( )



  j

Nm

j

Nm

j

Nm

j

Nm T T

kk

,)1(),1(

,)1(),1(

2  













 

 



])273()273[(2  4

,

4  j

Nm

j

cf  Tf T

  





 















  

 

 j

Nm

j

nm

j

nm

j

nm

ww

nm TT t kk

V ,)1(),1(

,)1(),1(

,  2

  j

Nm

j

nm

j

nm

j

nm T T

k k

,)1(),1(

,)1(),1(

2 















 

 



 





  













 

 

 j

nm

j

nm

j

nm

j

nm TT

kk

,)1(),1(

,)1(),1(

2

))( 2 ( 1

1 j

M

j

M

j

M

j

M

ww

M TT kkt V    







)])( 2 )(2/1( 1

1 j

m

j

m

j

m

j

m TT kk mM    

  j

Nm

j

nm

j

nm

j

nm TT

kk

,)1(),1(

,)1(),1(

2  













 

 



-- DRAFT -- -- DRAFT --
118

Step 2: Set Stability Criterion 

The time increment must satisfy the following equation to minimize the error in 

temperature calculations: 

 

 

Step 3: Calculation of Column Strength 

 Divide cross section into annular elements. 

 

 Determine temperature of annular concrete element: 

 

 Circular section (Figure 4.35): 

 

 Rectangular section (Figure 4.36): 

 

Note: Temperature differences in steel rebar are often small. Steel rebar will be assumed to 

have the temperature of the concrete section at the location of the rebar center. 

FIGURE 4.35. Arrangement in Quarter FIGURE 4.36. Stress–Strain 

Sections of Circular Columns Network in Quarter Section of 

 Rectangular 

Using the relationship between column mid-height deflection and curvature: 

 12

)(

2 KL Y   

 

layer

j

m

j

m

annular

j

nm

TT

T ) 2 ()( 1

,

  

triangular

j

nm

j

nm

squarenm

Tt

T















    

2 )( )2(,)1(),1(

,

h CmW

2

max  /*675

(7200 )

)()(

max max

2

min







 

hk

c

t cc

-- DRAFT -- -- DRAFT --
119

For any given curvature, the axial strain is varied until the internal moment at the midsection is 

in equilibrium with the applied moment given by: 

 Load x (deflection + eccentricity) 

 Assumptions: 

1. Properties are as defined in Appendix. 

2. Concrete has no tensile strength. 

3. Plane sections remain plane. 

4. The reduction of column length before 

exposure to fire, consisting of free 

shrinkage of concrete, creep, and 

shortening of column due to load, are 

negligible. 

5. Spalling is not considered. 

 Equations for concrete: 

 

 Concrete strain to the right of y-axis: 

 

 

 c

Rc cT

x ( )() 

 Concrete strain to the left of y-axis: 

 

 c

Lc cT

x ( )() 

 Where: 

 cT  )( = Thermal expansion of concrete, mm-1 

  = Axial strain of the column, mm-1 

 xc = Horizontal distance from center of the element to vertical plane through 

y-axis of column section, m 

   Radius of curvature 

 

Equations for steel: 

 

 Steel strain to the right of y-axis: 



 s

Rs sT

x ( )() 

 

 Steel strain to the left of y-axis: 



 s

Lc sT

x )()( 

FIGURE 4.37. Load Deflection 

Analysis 

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Chapter 5 

Design of Steel Structures 

Farid Alfawakhiri, Ph.D., American Iron and Steel Institute 

 

5.1 INTRODUCTION

Structural steel frames are widely used in virtually all types of buildings and industrial 

installations. Fire-resistant design of structural steel framing is often required, depending on the 

fire risks associated with the structure, the magnitude of potential losses due to structural failures 

caused by fire, and the accumulated performance record of similar structures in past fire 

incidents. While fire risks and consequences are discussed in earlier chapters, Beitel and 

Iwankiw (2002) provide a comprehensive review of fire-associated structural failure incidents in 

buildings higher than three stories. 

5.1.1 Scope 

This chapter reviews the background and practical methods of fire-resistant design in structural 

steel and consists of two parts. The first part covers the thermal and mechanical properties of 

structural steel at elevated temperatures. Additionally, several major groups of materials used 

for the fire protection of structural steel are discussed including insulating properties at elevated 

temperatures and practical guidance for their use. The second part discusses modern fireresistant design methodologies for structural steel, covering methods based on standardized tests 

and the more sophisticated engineering analysis methods involving heat transfer and structural 

analysis at elevated temperatures. 

This chapter does not include details for the fire protection design of open web steel joists 

(sometimes referred as “bar joists”) or light-gauge cold formed steel structures. For these topics, 

the reader is referred to other publications (Design 2003, NAHB 2004). 

5.2 MATERIAL PROPERTIES 

The thermal and mechanical properties of most materials change substantially within the 

temperature range associated with building fires (up to 1200 oC). At elevated temperatures, 

structural steel undergoes physio-chemical processes that essentially change its composition, 

structure, and properties. Most of its material properties are temperature dependent and 

determination of the properties is sensitive to testing method and conditions such as heating rate, 

temperature gradient, strain rate, etc. An extensive summary of elevated temperature properties 

of steel and other building materials is provided in The SFPE Handbook of Fire Protection 

Engineering (Kodur and Harmathy 2002). 

Harmathy (1983) was among the first researchers to systematically investigate and document the 

properties of common construction materials at elevated temperatures. He cited the lack of 

adequate knowledge of the behavior of building materials at elevated temperatures as the most 

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disturbing trend in fire safety engineering, noting that there has been a tendency to use “national” 

(“typical,” “proprietary,” “empirical,” etc.) values for material properties in numerical 

computations; in other words, values that ensure agreement between experimental and analytical 

results. Harmathy warned that this practice might lead to a proliferation of theories that lack 

general validity. 

As more research has been conducted in the last two decades, the state of knowledge of the 

properties of common construction material at elevated temperature has improved considerably. 

However, applied materials research in the field of structural fire engineering continues to face 

numerous difficulties, especially in the area of materials used to protect steel. Some of the 

processes that affect these materials under heat exposure, such as moisture migration, 

intumescence, erosion, and spalling, are difficult to quantify or standardize in simple terms for 

engineering analysis. Many of the fire protection materials have proprietary formulations that 

are not readily available to the researcher or designer. The absence of generally accepted 

standard procedures to measure the heat transfer properties of fire protection materials (for the 

full range of temperatures associated with building fires) is a primary reason for the wide 

variation of conductivity and specific heat properties reported in the literature. However, 

standard procedures for regression analysis of the contribution of protection materials to fire 

resistance have been recently established in Europe (ENV 13381-1:2005, ENV 13381-2:2002, 

ENV 13381-4:2002). 

In addition to the fact that elevated temperature properties of common fire protection materials 

are not generally available from the manufacturers, results of standard fire resistance tests of 

construction assemblies offer little technical information as well. This is because, in general, 

only the fire resistance rating achieved is reported to the public (the sponsor of the test, of 

course, has access to the entire test report). Thus, while it is possible to deduce at least bulk 

insulating properties of the fire protection materials from the rate of heating of the structural 

steel, without access to the actual recorded data, the tests provide little quantitative information. 

5.2.1 Structural Steel 

The performance of structural steel in fires is characterized by its thermal properties and 

mechanical properties. Thermal properties are necessary to predict the temperature rise in steel 

resulting from fire exposure and the resulting free thermal expansion, and include coefficients of 

thermal expansion, specific heat, and thermal conductivity. Prediction of mechanical behavior 

requires the stress-strain relationship of steel at elevated temperatures and may be represented by 

such parameters as elastic modulus, yield and ultimate strengths, and creep behavior. Poisson’s 

ratio is generally considered to be invariant over the range of temperatures of interest and may be 

taken as 0.3. The effects on mechanical properties of the phase change that occurs generally 

between 700 °C and 850 °C are often neglected. For heat transfer calculations, steel density can 

be assumed constant at 7850 kg/m3

. The temperature-dependent thermal and mechanical 

properties of steel are discussed here. 

5.2.1.1 Thermal Properties of Steel 

5.2.1.1.1 Thermal Expansion of Steel 

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Steel expands when it is heated and the coefficient of thermal expansion (CTE) can be used to 

predict the expansion as a function of temperature, T. That is, 

∆l/l = α(T) ∆T (5.1)

where, 

∆l = change in length due to temperature rise 

 l = initial length of the steel member 

α(T) = coefficient of thermal expansion 

∆T = change in temperature 

The thermal elongation of a uniformly heated steel member, ∆l/l, may be determined from the 

following, taken from Eurocode 3 (EN 1993-3-2): 

∆l/l = –2.416(10-4)+1.2(10-5)T+0.4(10-8)T2

 for 20 oC ≤ T ≤ 750 oC (5.2a) 

∆l/l = 11(10-3) for 750 oC < T ≤ 860 oC (5.2b) 

∆l/l = –6.2(10-3)+2.0(10-5)T for 860 oC < T ≤ 1200 oC (5.2c) 

where, 

l = length of the steel member at 20 oC 

∆l = change in length due to temperature rise 

T = steel temperature, oC 

The variation of the thermal elongation of steel with temperature is illustrated in Figure 5.1. 

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

Steel Temperature (oC)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Thermal Elongation (%)

FIGURE 5.1. Thermal Elongation of Structural Steel at Elevated 

Temperatures (EN 1993-1-2: 2005) 

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The coefficient of thermal expansion, α, (see Eq. 5.1) varies with temperature and is equal to the 

slope of the relative elongation curve shown in Fig. 5.1. Note that steel begins to undergo a 

phase change at temperatures around 750 °C and, in fact begins to contract rather than expand. 

Because the phase change is not instantaneous, the behavior of steel in the range of 750 °C to 

860 °C depends on the rate of heating. And, since the rate of heating is not known, the relative 

thermal elongation in this temperature range is taken to be constant and equal to 11 %. The 

coefficient of thermal expansion may be obtained by differentiating Eqs. 5.2a to 5.2c giving, 

α = 1.2(10-5)+0.8(10-8)T for 20 oC ≤ T ≤ 750 oC (5.3a) 

α = 0 for 750 oC < T ≤ 860 oC (5.3b) 

α = 2.0(10-5) for 860 oC < T ≤ 1200 oC (5.3c) 

Results for pure iron and for several low alloy steels have been reported by Touloukian et al. 

(1977). Banovic et al. (2005) note that the results are generally insensitive to composition and 

microstructure and recommend that the coefficient of thermal expansion be taken as that for pure 

iron which may be expressed in the form of a cubic polynomial as 

α (T) = α0 + α1T + α2T2

 + α3T3 (5.4) 

 

where: 

α0 = 7.3633 x 10-6 

α1 = 1.8723 x 10-8 

α2 = -9.8382 x 10-12 

α3 = 1.6718 x 10-16

T is measured in Kelvin (°C+273) and the expression is valid over the range 

 300 K < T < 900 K (approx. 20 °C < T < 630 °C) 

A plot of the instantaneous coefficient of thermal expansion (expressed in °C) for both Eq. 5.3a 

(i.e., T ≤ 750 oC) and 5.4 is shown in Figure 5.2. 

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125

1.00E-05

1.10E-05

1.20E-05

1.30E-05

1.40E-05

1.50E-05

1.60E-05

1.70E-05

1.80E-05

0 200 400 600 800

Temperature ( ̊C)

Coefficient of Thermal Expansion

(1/ ̊C)

Eq. 5.4

Eq. 5.3a

FIGURE 5.2 Instantaneous Coefficient of Thermal Expansion

Banovic recommends that, for temperatures in excess of 700 °C, the instantaneous coefficient of 

thermal expansion should be determined for the particular steel in question. 

For simple calculation models, the relationship between thermal elongation and steel temperature 

may be considered to be linear (see Fig. 5.1) and the coefficient of thermal expansion (slope of 

the curve in Fig. 5.1) may be taken as a constant, 

α =1.4(10-5) / °C (5.5) 

5.2.1.1.2 Specific Heat of Steel 

The specific heat of steel, cs, valid for all structural grades, may be determined from the 

following, also taken from Eurocode 3 (EN 1993-3-2): 

cs = 425 +7.73(10-1)T-1.69(10-3)T2

+2.22(10-6)T3 J/kgoC for 20 oC ≤ T ≤ 600 oC (5.6a) 

cs = 666 + 13002

 738-T J/kgoC for 600 oC < T ≤ 735 oC (5.6b) 

cs = 545 + 17820

 T-731 J/kgoC for 735 oC < T ≤ 900 oC (5.6c) 

cs = 650 J/kgoC for 900 oC < T ≤ 1200 oC(5.6d) 

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126

where, 

T = steel temperature, oC 

The variation of the specific heat with temperature is illustrated in Figure 5.3. 

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

Steel Temperature (oC)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Specific Heat [ J / (kg oC) ]

FIGURE 5.3. Specific Heat of Structural Steel at Elevated Temperatures (EN 

1993-1-2: 2005) 

In simple calculation models, the specific heat of steel may be considered to be independent of 

temperature with an average value of cs = 600 J/kgoC. 

5.2.1.1.3 Thermal Conductivity of Steel 

Thermal conductivity properties of steel are required for determining the temperatures of steel 

members subjected to heat flux or fire exposure. Unlike the thermal properties just discussed, 

coefficient of thermal expansion and specific heat, thermal conductivity is affected by the 

microstructure of the steel. Fig. 5.4 shows the thermal conductivity as a function of temperature 

for twelve low-alloy steels as reported by Banovic (2005). This figure serves to illustrate the 

variability of thermal conductivity for various steel compositions and also plots the expression 

recommended in Eurocode 3 as described next. 

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FIGURE 5.4. Thermal Conductivity of 12 Low-alloy Steels as a function of 

Temperatures (from Banovic 2005) 

Eurocode 3 recommends that the thermal conductivity of steel, ks, independent of structural 

grades, be determined from the following: 

ks = 54 –3.33(10-2)T W/moC for 20 oC ≤ T ≤ 800 oC (5.7a) 

ks = 27.3 W/moC for 800 oC < T ≤ 1200 oC (5.7b) 

where, 

T = steel temperature, oC 

The variation of the thermal conductivity with temperature, as recommended by Eurocode, is 

illustrated in Figure 5.5. 

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0 100 200 300 400 500 600 700 800 900 1000 1100 1200

Steel Temperature (oC)

0

5

10

15

20

25

30

35

40

45

50

55

Thermal Conductivity [ W / (m oC) ]

FIGURE 5.5. Thermal Conductivity of Structural Steel at Elevated 

Temperatures (EN 1993-1-2: 2005) 

In simple calculations models, the thermal conductivity of steel may be considered to be 

independent of temperature with an average value of ks = 45 W/moC. 

5.2.1.2 Mechanical Properties of Steel 

Structural steel begins to lose its strength and stiffness at temperatures above 300 C and 

eventually melts at about 1500 C (Lawson and Newman 1990). The mechanical properties of 

steel at temperatures above 450 C are strongly affected by creep, i.e., both stress and 

temperature histories influence steel deformations. In the combined heating and deformation of 

steel, the total strain in this temperature range can be separated into three components: the 

thermal strain, the instantaneous stress-related strain, and the time-dependent creep strain. 

Therefore, mechani-cal properties of steel can be established by following a number of different 

test procedures. The three main test parameters are the heating process, application and control 

of load, and control of strain. A clear distinction is made between isothermal “steady-state” tests 

and anisothermal “transient” tests (Anderberg 1983). 

During the steady-state tests, the specimen is first heated to the intended steady temperature (the 

specimen is allowed to expand freely during this initial heating period) and then loaded using 

one of the following methods: 

 Stress rate controlled test 

 Strain rate controlled test 

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 Creep test, where the specimen is loaded to the intended level and kept constant while 

the deformations are recorded over time 

 Relaxation test, where the specimen is loaded to the intended initial strain that is kept 

constant while the reduction in stress is recorded over time 

In the United States, the first two types of steady-state tests mentioned above are standardized 

under ASTM designation E21-92. Steady-state test data for North American structural steel 

grades have been reported in the literature (Harmathy and Stanzak 1970, Brockenbrough and 

Johnston 1981). 

During the transient tests, the specimen is first loaded to the intended level of stress which is then 

kept constant, while the specimen is steadily heated and the temperature–deformation 

relationship is recorded. The stress-strain relationship for a particular temperature can then be 

obtained by interpolation from a family of transient test curves for different stress levels. 

Another variation of transient tests is where the specimen is first restrained against thermal 

expansion (i.e., initially not loaded) and then steadily heated while the temperature–load 

relationship is recorded (compressive load develops in this test due to the restrained thermal 

expansion of the specimen). 

During a building fire, the loaded steel structure is subjected to transient processes with varying 

temperature and stress. Therefore, transient tests could be claimed to be more realistic, and 

many researchers consider transient test data as an essential part of information for fire-resistant 

design purposes. Kirby and Preston (1988) demonstrated that, at small strains, transient data 

produce slightly more conservative results than steady-state tests. However, at larger strains 

there was negligible difference between the minimum properties derived from either type of test. 

In the late 1970s, RILEM Committee 44-PHT over a five-year period conducted the first 

comprehensive international survey of high-temperature test data for structural and other steel 

grades, including North American grades. The final report (Anderberg 1983) concluded that the 

relative decrease in strength at elevated temperatures was almost the same for all structural 

grades, regardless of the initial strength of steel at room temperature. This observation led to the 

development of a single strength retention model for structural steel (of all grades) at elevated 

temperatures, first adopted by ECCS (1983). The model implicitly accounted for hightemperature creep associated with heating rates expected for steel during fires (2 C/min to 

50 C/min). Later, more detailed experimental and analytical studies by Cooke (1988); Jerath, 

Cole, and Smith (1980): Kirby (1983); Kirby and Preston (1988) and others eventually led to the 

adoption of a complete stress–strain relationship model for structural steel at elevated 

temperatures in Eurocode 3 (EN 1993-1-2: 2005) and ECCS (2001). 

As part of its investigation into the collapse of the World Trade Center towers (WTC 1 and 2) 

and Building 7 (WTC 7), NIST developed an elevated temperature true stress-true strain 

relationship based on data reported in the technical literature and on tests it conducted. Both the 

Eurocode and NIST approaches are described here. 

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5.2.1.2.1 Stress-Strain Relationship - Eurocode Approach 

In the Eurocode 3 approach, three temperature-dependent parameters are used to define the 

stress-strain behaviour of steel at elevated temperatures: 

1. The slope of the linear elastic range, ET 

2. The proportional limit stress, fp 

3. The yield stress, fy 

The yield stress is taken as the stress at 2 % strain (ε = 0.02) and is termed the “effective yield 

stress.” An ellipse is fit between the proportional limit and the effective yield stress and beyond 

a strain of 2 %, the stress strain relationship is flat up to a strain of 15 % (ε= 0.15). The 

temperature-dependence of each parameter is normalized to a room temperature value; E = 

210,000 MPa for ET, and Fy at 20 oC determined from the ε = 0.002 (0.2 %) offset yield strength. 

Accordingly, the stress f at strain ε for structural steel at elevated temperatures may be 

determined from the following expressions: 

f = ε ET for 0 ≤ ε < ε p = fp / E (5.8a) 

f = (b/a) ( a2 - (0.02- ε)

2

 ) 0.5 + fp – c for ε p ≤ ε ≤ 0.02 (5.8b) 

f = fy for 0.02 < ε ≤ 0.15 (5.8c) 

f = 20 fy (0.2 – ε ) for 0.15 < ε ≤ 0.20 (5.8d) 

f = 0 for ε ≥ 0.20 (5.8e) 

where: 

a

2

 = (0.02 - ε p) (0.02 - ε p+ c / ET) (5.8f) 

b2

 = ET (0.02 - ε p) c + c2 (5.8g) 

c = (fy - fp)

2

 / ( ET (0.02 - ε p) – 2 (fy - fp) ) (5.8h) 

Table 5.1 gives, for steel elevated temperatures T, the reduction factors k T to be applied to the 

appropriate values of the steel modulus of elasticity, E, and the specified minimum yield stress 

Fy at 20 oC in order to determine the parameters in Equations 5.8. For intermediate values of the 

temperature, linear interpolation may be used. For simple computation models, the proportional 

limit could be taken as the yield stress, i.e., fp = fy. 

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131

TABLE 5.1. Reduction Factors k T for Stress–Strain Relationships of Structural 

Steel at Elevated Temperatures 

Steel Temperature 

T (oC) 

k E, T = ET / E k p, T = fp / Fy k y, T = fy / Fy k u, T = fu / Fy

 20 1.00 1.00 1.00 1.25 

 100 1.00 1.00 1.00 1.25 

 200 0.90 0.807 1.00 1.25 

 300 0.80 0.613 1.00 1.25 

 400 0.70 0.42 1.00 1.00 

 500 0.60 0.36 0.78 0.78 

 600 0.31 0.18 0.47 0.47 

 700 0.13 0.075 0.23 0.23 

 800 0.09 0.05 0.11 0.11 

 900 0.0675 0.0375 0.06 0.06 

1000 0.045 0.025 0.04 0.04 

1100 0.0225 0.0125 0.02 0.02 

1200 0.00 0.00 0.00 0.00 

Figure 5.6 illustrates the reduction factors listed in Table 5.1. 

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

Steel Temperature (oC)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Retention Factors

k u, T = fu / Fy

k y, T = fy / Fy

k p, T = fp / Fy

k E, T = ET / E

FIGURE 5.6. Strength and Elasticity Reduction Factors for Structural Steel at 

Elevated Temperatures (EN 1993-1-2: 2005) 

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132

For temperatures below 400oC, the stress–strain relationships may be extended by the strain 

hardening option, provided local instability is prevented and the ratio fu / Fy is limited to 1.25. 

The ultimate stress fu at elevated temperatures may be determined using the following: 

fu = 1.25 fy for 20 oC ≤ T ≤ 300 oC (5.9a) 

fu = fy (2.0-0.0025T) for 300 oC < T < 400 oC (5.9b) 

fu = fy for 400 oC ≤ T ≤ 1200 oC (5.9c) 

Where: 

T = Steel temperature, oC 

For strains ε higher than 2%, the stress–strain relationships allowing for strain hardening could 

be determined as follows: 

f = fy + 50 (ε - 0.02) (fu - fy) for 0.02 < ε < 0.04 (5.10a) 

f = fu for 0.04 ≤ ε ≤ 0.15 (5.10b) 

f = 20 fu (0.2 – ε ) for 0.15 < ε ≤ 0.20 (5.10c) 

f = 0 for ε ≥ 0.20 (5.10d) 

The effect of strain hardening could be considered only if the analysis is based on advanced 

calculation models (see Section 5.3.2). This is allowed only if it is proven that local failures 

(local buckling, shear failure, spalling, etc.) do not occur because of increased strains. 

The stress–strain relationships of Equations 5.8 are valid for increasing temperature (heating) 

histories. For decreasing temperature (cooling) histories, these relationships can be used as a 

sufficiently precise approximation. 

Figure 5.7 illustrates the stress-strain relationships described by Equations 5.8 through 5.10. 

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133

0 2 4 6 8 10 12 14 16 18 20

Strain  (%)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Normalised Stress f / Fy

T 100°C

T 300°C

T=400°C

T=200°C

T=300°C

T=350°C

T=500°C

T=600°C

T=700°C

T=800°C

T=900°C

T=400°C

FIGURE 5.7. Stress–Strain Relationships for Structural Steel at Elevated 

Temperatures (ECCS 2001) 

The residual yield stress fyR and tensile strength fuR of steel heated to a maximum temperature 

Tmax and having cooled down to the ambient temperature of 20oC may be determined as follows: 

fyR = Fy for 20 oC ≤ Tmax ≤ 800 oC (5.11a) 

fuR = Fu for 20 oC ≤ Tmax ≤ 800 oC (5.11b) 

fyR = 0.9 Fy for 800 oC < Tmax ≤ 1200 oC (5.11c) 

fuR = 0.9 Fu for 800 oC < Tmax ≤ 1200 oC (5.11d) 

5.2.1.2.2 Stress-Strain Relationship - NIST Approach 

In support of the World Trade Center collapse investigation, NIST characterized the hightemperature stress-strain behavior of seventeen different steels recovered from the collapse site. 

The steels in this group represent construction steels with specified yield strengths in the range of 

36 ksi to 100 ksi (248 MPa to 689 MPa). The data set included examples of plates, heavyweight 

shapes, and lightweight shapes. Full stress-strain data as a function of temperature were obtained 

for nine of the steels. In addition, a survey of the technical literature was conducted to obtain 

existing data on stress-strain behavior of other construction steels. This background information 

is reported in NIST NCSTAR 1-3D (Luecke 2005). These data were subsequently reanalyzed to 

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134

develop general models for the tensile stress-strain behavior of construction steels as a function 

of temperature. 

Modulus of Elasticity 

Using stress-strain data for three steels recovered from the WTC towers collapse, the following 

expression was obtained for modulus of elasticity (slope of linear portion of - curve up to the 

proportional limit) of structural steel: 

where, 

3

3

2

210 )(  TeTeTeeTE

e0 = 206 Gpa = 29900 ksi 

e1 = 0.043 GPa/oC = -6.3 ksi/oC

e2 = –3.510-5 GPa/oC2

 = -5x10-3 ksi/oC2 

e3 = –6.610-8 GPa/oC3

 = -9.6x10-6 ksi/oC3

(5.12)

The constant term, e0, was taken as the average value of modulus of elasticity of three steels 

tested at room temperature. Equation 5.12 is plotted in Figure 5.8. Also, plotted are experimental 

values for two 55 ksi (379 MPa) plates and one 50 ksi (344 MPa) plate tested by NIST and for 

results reported for nine series of tests obtained from the technical literature (see NIST NCSTAR 

1-3D). Values obtained using the Eurocode 3 reduction factors (Table 5.1) are also plotted as a 

comparison to the NIST model. 

0

50

100

150

200

250

0 200 400 600 800 1000

Temperature, degree C

Young's Modulus (GPa)

1 NIST

2 Eurocode

3 55ksi plat e WTC-Exp-1

4 55ksi plat e WTC-Exp-3

5 50ksi 50mm plat e WTC-Exp-4

6 Carbon St eel [ C<0.3 %]

7 Carbon St eel [ C>0.3 %]

8 Structural Steels

9 AISI 1015 St eel

10 AISI 1015 St eel

11 Aust enit e

12 Ferrit e

13 ASTM A36 St eel

14 ASTM A36 St eel

1

3-5 12

14

7

6 11

13

2

8

9

10

FIGURE 5.8. Comparison of Modulus of Elasticity of Structural 

Steels at Elevated Temperatures (See Table 5.6 for references). 

Stress-Strain Relationship - True Stress-True Strain 

A simple, phenomenological model for the relation between true stress and true strain is the 

power-law strain-hardening expression: 

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135

n  K (5.13)

The above equation can be expressed as a function of temperature using the following 

expressions for K and n: 

 





































  

 



 

1

2

exp 43

k

k

T

y

FkkK (5.14a)

 





















































































 

1

2

exp 43

n

n

T

y

Fnnn (5.14b)

where, Fy is the room temperature yield strength of steel. 

The remaining parameters in Equations 5.14a and 5.14b can be determined by best fit to 

experimental data. Values are given in Table 5.2 for the steels tested by NIST (Fy of 36 ksi to 

100 ksi) and should give good results for steels with room temperature yield strengths in the 

range of 36 ksi to 65 ksi. 

TABLE 5.2. Parameters for Equation 5.12. 

Parameter Value Units 

1 k 4.92 

2 k 575 oC 

3 k 734 MPa 

4 k 0.315 

1 n 4.51 

2 n 637 oC 

n3 0.329 

4 n -4.23 x 10-4 MPa-1

An example is provided below for an ASTM A572 Grade 50 steel with a measured room 

temperature yield strength of 52.5 ksi (362 MPa). In this example, the true stress is computed at 

three temperatures (20 oC, 400 oC, and 600 oC) using Equations 5.13 and 5.14 and coefficients 

given in Table 5.2. The computed values are shown in Table 5.3. Figure 5.9 shows a plot of 

these computed values along with experimental data obtained by NIST. 

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136

TABLE 5.3. True stress-true strain values for an A572 Grade 50 

structural steel using Equations 5.13 and 5.14. 

True Stress Calculation

True Strain True (MPa) True (ksi) True (MPa) True (ksi) True (MPa) True (ksi)

0.001 252 36.5 245 35.5 140 20.3

0.01 377 54.7 350 50.8 169 24.6

0.02 426 61.8 390 56.6 179 26.0

0.03 458 66.4 416 60.3 185 26.9

0.04 481 69.8 435 63.0 190 27.5

0.05 501 72.6 450 65.3 193 28.0

0.1 566 82.0 501 72.7 205 29.7

0.15 607 88.1 534 77.4 212 30.7

0.2 639 92.7 558 81.0 217 31.4

0.25 665 96.4 578 83.8 221 32.0

20 C 400 C 600 C

FIGURE 5.9. Example of the NIST predicted vs. experimental 

true stress-true strain behavior of an A572 structural steel. 

Note that the phenomenological model used here cannot reproduce a yield plateau that is 

observed in uniaxial tensile tests at room temperature. However, such stress-strain behavior is 

generally not evident in hot rolled sections with residual stresses. Further, a yield plateau is not 

observed at elevated temperatures. 

Engineering Stress-Engineering Strain 

Engineering stress and engineering strain data are often of more interest to engineers than true 

stress and true strain data. The following expressions can be used to convert true stress and true 

strain to engineering stress and engineering strain: 

0

100

200

300

400

500

600

700

0 0.05 0.1 0.15 0.2 0.25 0.3

True Strain

True Stress, Mpa

0

20

41

61

81

102

True Stress, ksi

NIST 20 C

Exp 20 C

NIST 400 C

Exp 400 C

NIST 600 C

Exp 600 C

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137

 )(exp



  E (5.15a)

 1

E

E 



 (5.15b)

As an example, consider true stress and true strain values of 88.1 ksi (607 MPa) and 0.15, 

respectively, corresponding to 20 oC as shown in Table 5.3. The engineering stress and 

engineering strain are obtained by substitution into Equations 5.15a and 5.15b, giving 

σE = 88.1 / exp(0.15) = 75.8 ksi 

E = 88.1 / 75.8 - 1 = 0.16 

 or 

σE = 607 / exp(0.15) = 522 MPa 

E = 607 / 522 - 1 = 0.16 

The engineering stress vs. engineering strain values for an A572 Grade 50 structural steel as 

computed above are plotted in Figure 5.10 for 20 oC, 400 oC and 600 oC. Also plotted in the 

figure are the corresponding engineering stress and strain data obtained from experiments and 

from the Eurocode 3 model. Note that, for the Eurocode model, values for temperatures below 

400 oC were computed assuming strain hardening using with the equations provided in Annex A 

of Eurocode 3. 

FIGURE 5.10. A comparison of engineering stress vs. strain data 

computed using NIST approach, the Eurocode model, and the 

WTC experimental data. 

0

100

200

300

400

500

600

0.00000 0.05000 0.10000 0.15000 0.20000 0.25000

Engineering Strain

Engineering Stress (MPa)

0

17

35

52

70

87

Engineering Stress (ksi)

NIST 20 C

Exp 20 C

EC 20 C

NIST 400 C

Exp 400 C

EC 400 C

NIST 600 C

Exp 600 C

EC 600 C

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138

Yield Stress 

The stress-strain relationship (Equation 5.13) is a power-law work-hardening model that was 

fitted to a large range of strain (i.e., from zero to 0.15 or greater). This model works well for 

large strains, but does not capture the linear elastic behavior of steels at small strains. For 

analysis purposes, the linear elastic portion of the stress-strain curve can be modeled separately 

up to the yield stress (as defined by a 0.002 strain offset), and the power-law work-hardening 

model can be used to provide stress-strain data beyond the yield stress. 

Since the yield stress varies with temperature, a relationship is required for the yield stress at 

elevated temperatures. Equation 5.16 (see Luecke 2005) gives the ratio of the yield stress at an 

elevated temperature to the yield stress at room temperature (where elevated temperature yield 

stresses are also defined at a 0.002 offset strain). 

 

  2

2

2 2

1 1

1 2

1

exp 2 1

)20(

)(

0 A

m

s

T

m

s

T A

CF

TF

R

y

y 





































 















  (5.16)

Figure 5.11 is a plot of the normalized yield stress ratio for data from WTC structural steels and 

from the technical literature. Tests conducted by NIST followed ASTM E21, Standard Test 

Methods for Elevated Temperature Tension Tests of Metallic Materials, using a loading rate of 

d/dt = 0.005/min ± 0.002/min. Data from the technical literature are plotted for only those 

steels tested at strain rates d/dt ≤ 0.007/min, the upper limit for tests that conform to the 

requirements of ASTM E21. The solid (blue) line is given by Equation 5.16, where A2 = 0.075, 

m1 = 8.07, m2 = 1.0, s1 = 635 oC, and s2 = 539 oC. 

The Eurocode defines separate curves for the proportional limit and the yield stress. However, 

the yield stress at elevated temperatures is defined at a 0.02 offset strain in the Eurocode. The 

upper (blue) dashed line in Figure 5.11 is the Eurocode 3 yield stress at 0.02 offset strain 

normalized to the room-temperature yield stress at 0.002 offset strain. The lower (red) dashed 

line in Figure 5.11 is the Eurocode 3 proportional limit, normalized to the room temperature 

yield stress at 0.002 offset strain. 

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139

FIGURE 5.11. Elevated temperature yield stress normalized by 

room temperature yield stress (see Table 5.7 for references). 

For analysis purposes, a temperature dependent stress-strain relationship can be developed based 

on the relationships for the elastic modulus (Equation 5.12), yield stress (Equation 5.16), and true 

stress-true strain (Equations 5.15a and 5.15b). An example of a stress-strain relationship based 

on these relationships for an ASTM A572, Grade 50 steel is shown in Figure 5.12. The modulus 

of elasticity (Equation 5.12) and yield stress (the room temperature yield stress multiplied by R 

from Equation 5.16) were determined for 20 °C, 400 °C, and 600 °C. The strain at the yield 

stress could be slightly offset from the 0.002 value, depending on where the modulus of elasticity 

and yield stress intersect. Discrete strains greater than that at the yield stress were selected (for a 

tabular input format) and the corresponding stresses were determined with Equations 5.13 and 

5.14. These true stress and true strain values were converted to engineering stress and strain 

using Equations 5.15a and 5.15b. Figure 5.12 (a) is a plot of the elevated temperature 

relationship up to a strain of 0.2, and Figure 5.12 (b) shows the lower portion of the curve to a 

strain of 0.05. 

By adjusting the chemistry of a steel, one can obtain improved properties under fire exposure. 

Such steels, sometimes called “fire-resistive steels” have been shown to produce a different 

decay curve than that in the above illustration. The reduction in yield stress with temperature for 

a given fire-resistive steel can be obtained from Equation 5.16 using parameters established from 

elevated temperature tension test data using, for example, ASTM E 21 standard test methods. 

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000

Temperature, degree C

f=Fy(T)/Fy

SM A490

ASM E-SA516

T1

T1a

A36

Cor-Ten

A440

Tri-Ten

AS3679.1

AS3678 XLERPlate

BS4360 Gr 50B

S355*****

S460M ***

SM 400A

60 ksi HSLA Plate

100 ksi Plate

A36 14WF184

50ksi A242 angle

A36 Angle

EC YS Red Fac

EC Prop Limit

NIST FY(T)

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140

0

100

200

300

400

500

600

700

0 0.05 0.1 0.15 0.2

True Strain

True Stress (MPa)

-20

0

20

41

61

81

102

True Stress (ksi)

20 C

20 C Discretized

400 C

400 C Discretized

600 C

600 C Discretized

(a) 

0

100

200

300

400

500

0 0.01 0.02 0.03 0.04 0.05

True Strain

True Stress (MPa)

0

15

29

44

58

73

True Stress (ksi)

20 C

20 C Discretized

400 C

400 C Discretized

600 C

600 C Discretized

(b) 

FIGURE 5.12. Computed stress-strain curves for an ASTM 

A 572 Grade 50 steel. 

Strain rate effects can be addressed by adding a strain-rate sensitivity term, m(T), to Equation 

5.13: 

n

Tm

K







)(

0















  

 5.17

where 0  is the strain rate under which the original data were developed. 

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141

5.2.2 Fire Protection Materials 

Fire protection materials and systems are designed to delay the temperature rise in structural 

steel, usually through one or more of the following mechanisms: 

 Low thermal conductivity 

 High effective heat capacity 

 Heat-absorbing physical reactions (e.g., transpiration, evaporation, sublimation, ablation) or 

chemical reactions (e.g., endothermic decomposition, pyrolysis) 

 Intumescence, i.e., formation of a thicker insulating foam upon heating 

 Reradiation 

The common fire protection materials that provide one or more of these mechanisms function 

generally in one of three ways (in addition to radiation shielding): 

1. Mostly insulating—These are low-conductivity, lightweight, spray-applied fireresistive materials (SFRM); mineral fiberboard products; and ceramic wool wraps. 

2. Energy absorbing—These are most commonly gypsum-based or concrete-based 

products, each of which releases water of crystallization when exposed to high 

temperatures. 

3. Intumescent—Applied as multi-layer paint, these coating systems expand upon 

exposure to high temperatures, forming an insulating layer. They are traditionally 

more expensive but provide many benefits, including reduced weight, durability, 

aesthetic appeal, good adhesion, and the option for off-site application that saves 

construction time on site. 

Fire protection materials could be classified as organic or inorganic, depending on the chemistry 

of their major components. Therefore, SFRM are often referred to as inorganic systems, while 

intumescent coatings are often referred to as organic systems. 

SFRM products today are the most common type of fire protection for structural steel. Gypsum 

board and mineral fiber board products, intumescent coatings, and ceramic wool wraps are 

common alternatives. Plaster, clay tile, concrete, and masonry enclosures, commonly used to 

protect steel a few decades ago, are not very common in modern fire protection. For the most 

comprehensive list of commercial products used in fire-resistant designs, refer to the Underwriters Laboratories (UL) Directory (Fire 2004). It should also be noted that steel itself is an 

effective fire-protective material when used in the form of wrapping sheets (e.g., UL Designs 

X101, X203, X526) to provide protective and reflective shielding, or in the form of meshes, 

banding straps, and wire ties (e.g., UL Designs Y714, XR614, X204, X205) to help fire 

protection materials maintain their integrity under heat exposure. Other fire protection methods 

for structural steel involve rain screens (sprinklers designed to protect steel members) or filling 

tubular structures with concrete or water. 

Table 5.4 lists the thermal properties of some common fire protection materials suggested by 

ECCS (1995) for simplified heat transfer calculation models (see Section 5.3.2.1). Note that the 

values reported are for room temperature only and thermal properties of many fire protection 

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142

materials in common use are known to be temperature dependent. NIST NCSTAR 1-6A, 

Chapter 6 provides temperature dependent properties of several SFRMs (Carino et al., 2005). 

More detailed discussion of common fire protection materials is provided below. 

TABLE 5.4. Thermal Properties of Common Fire Protection 

Material (ECCS 1995)

5.2.2.1 Spray-Applied Fire-Resistive Materials (SFRM) 

Most SFRM utilize either mineral fiber or cementitious materials to insulate steel from the heat 

of a fire. Mineral fiber and vermiculite acoustical plaster on metal lath are two of the frequently 

used SFRM on steel columns, beams, and joists. These popular commercial products have 

proprietary formulations, and, therefore, it is imperative to follow closely the manufacturer’s 

recommendations for mixing and application. 

The mineral fiber mixture combines the mineral fibers, binders (usually, Portland cement based), 

air, and water. Mineral fiber fire protection material is spray-applied with specifically designed 

equipment that feeds the dry mixture of mineral fibers and various binding agents to a spray 

nozzle, where water is added to the mixture as it is sprayed on the surface to be protected. In the 

final cured form, the mineral fiber coating is usually lightweight, essentially non-combustible, 

chemically inert, and a poor conductor of heat. 

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143

Cementitious SFRM are composed of a binder material mixed with aggregates. Various 

additives and foaming agents are also often mixed in. The common binders are calcined gypsum 

and Portland cement. Some formulations use magnesium oxychloride, magnesium oxysulfate, 

calcium aluminate, calcium phosphate, or ammonium sulfate. Common aggregates are 

vermiculite and perlite. Some manufacturers have substituted polystyrene beads for the 

vermiculite aggregate. The frequently used vermiculite acoustical plaster is a cementitious 

product composed of gypsum binder and perlite or vermiculite lightweight aggregates. 

Cementitious SFRM can be classified by their density as low-density (about 240 kg/m3

), 

medium-density (320 kg/m3

 to 430 kg/m3), and high-density (640 kg/m3 to 1280 kg/m3) 

products. Higher density SFRM products (1600 kg/m3

 to 2400 kg/m3) are essentially concrete 

mixtures. 

Lie (1992) suggests the approximate value of k = 0.1 W/moC for mineral fiber SFRM products 

with densities ρ = 250 kg/m3

 to 350 kg/m3, and cementitious SFRM products with densities 

ρ = 800 kg/m3

 to 1000 kg/m3. Ruddy et al. (2003) suggest the following representative thermal 

properties for lightweight SFRM (both mineral fiber and cementitious): 

c = 0.754 kJ/kgoC 

k = 0.135 W/moC 

ρ = 293 kg/m3

The durability characteristics and on-site application quality of SFRM are regulated by the 

following standards: 

 ASTM E605, “Standard Test Methods for Thickness and Density of Sprayed FireResistive Material Applied to Structural Members” 

 ASTM E736, “Standard Test Method for Cohesion/Adhesion of Sprayed FireResistive Materials Applied to Structural Members” 

 ASTM E759, “Standard Test Method for Effect of Deflection on Sprayed FireResistive Material Applied to Structural Members” 

 ASTM E760, “Standard Test Method for Effect of Impact on Bonding of Sprayed 

Fire-Resistive Material Applied to Structural Members” 

 ASTM E761, “Standard Test Method for Compressive Strength of Sprayed FireResistive Material Applied to Structural Members” 

5.2.2.2 Intumescent Coatings 

An intumescent coating has the appearance of a thick film or paint. When exposed to a fire, it 

chars, foams, and expands significantly in thickness. To retain this insulating layer, reinforcing 

is sometimes required at sharp corners, such as the flange tips of a wide-flange shape. 

The intumescent mechanism involves the interaction of four types of compounds (Yandzio, 

Dowling, and Newman 1996): 

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144

1. Inorganic acid, or material yielding an acid at temperatures of 100 to 300 C. 

Ammonium polyphosphates, yielding phosphoric acid, are common for this purpose. 

2. A polyhydric compound rich in carbon (such as starch) that reacts with the acid to 

form carbonaceous char. 

3. A spumific agent that decomposes to liberate large volumes of non-combustible gases 

(including carbon dioxide, ammonia, and water vapor). Production of theses gases 

causes the carbonaceous char to foam and expand into a thick (up to 100 times thicker 

that original) protective layer. 

4. A binder or resin that softens at a predetermined temperature and helps preventing 

gases from escaping. 

A review of chemical and physical phenomena that occur within intumescent coatings upon 

heating, and various approaches to model intumescent behavior, has been provided by Butler 

(1997). 

Two distinct categories of intumescent coating are manufactured: water or solvent based (also 

referred to as intumescent paints or thin film coatings), and epoxy based (also referred to as 

mastics or thick film coatings). Water and solvent-based coatings are thinner (usually up to 

5 mm) and mostly intended for controlled environments inside buildings, although some systems 

are available for external exposures. Epoxy-based coatings are thicker (up to 45 mm) and are 

mostly used for petro-chemical installations. 

In many instances, the intumescent coating is actually a system of multiple coats with different 

properties and functions. The base coat (or primer coat) is formulated to provide a strong bond 

to the steel substrate, while the top coat (or the sealing/decorative coat) is formulated to provide 

a durable aesthetically appealing finished surface. The intermediate layer of the fire protective 

intumescent material is usually applied in multiple coats to achieve the desired protection 

thickness, allowing sufficient time for each coat to dry before applying the next coat. Therefore, 

depending on the design thickness, the application of intumescent coatings could be a lengthy 

and costly process. Cost-effective solutions are often achieved through the over-design of 

structural steel, i.e., increasing the size (the W/D ratio) of steel sections, that results in the 

reduction of the design thickness of intumescent protection and the reduction in the overall cost 

of construction. 

All intumescent coating products are proprietary and their thermal properties have rarely been 

reported in the open literature, although special proprietary software (Lawson, Oshatogbe, and 

Newman 2002) provides predictions of steel section (protected by intumescent coating) 

temperatures under standard fire exposure. Hamins (1998) reported the dry density of eight 

different intumescent coatings ranging within 1.1 g/cm3

 to 1.6 g/cm3. After 30 minutes of 

heating in this study, the measured expansion factors for the char ranged between 2 and 56, and 

the measured mass loss (attributed to vaporization) ranged between 38% and 66%, suggesting a 

reduction in char density (compared to the original coating density) of up to about 100 times. An 

earlier study by Anderson, Ketchum, and Mountain (1988) reported measurements of the thermal 

conductivity of 13 different intumescent chars that averaged 0.096 (±0.033) W/moC. 

-- DRAFT -- -- DRAFT --
145

The only public document in the United States to regulate the on-site application and quality of 

intumescent coatings is the AWCI Technical Manual 12-B (1998). Off-site (workshop) application of intumescent coatings, with subsequent on-site erection of coated structural steel, is 

relatively rare in the United States. Off-site application has been more popular in the United 

Kingdom (Yandzio, Dowling, and Newman 1996). 

5.2.2.3 Gypsum Board Products 

Gypsum board consists of a non-combustible core (usually, of not less than 65 % gypsum) and 

paper laminated surfaces to form flat sheets available in a range of sizes. Special fire-resistant 

types of gypsum board are usually used for fire protection. Type X and “Type C” (because of 

the letter “C” usually appearing in the designation of the associated products) board are the fireresistant products most widely used in North America. These products have a specially 

formulated gypsum core in order to provide a greater fire resistance (of building systems) than 

regular gypsum board of the same thickness. 

Type X gypsum board is defined (ASTM C36-97) as the board that would provide the following 

minimum fire resistance ratings for the assemblies described: 

 One hour for a non-load-bearing cold formed steel frame wall with galvanized 

92x35x0.5 mm steel studs spaced 600 mm o.c. and a single layer of 15.9 mm thick 

gypsum board on each side. The 1200 mm wide gypsum board sheets should be 

attached to the studs using 25 mm long drywall screws spaced 200 mm o.c. along 

edges and ends, and 300 mm o.c. along intermediate studs. All joints should be 

oriented parallel to, and located over, studs and staggered on opposite sides of the 

assembly. 

 Two hours for a non-load-bearing cold formed steel framed wall with galvanized 

64x35x0.5 mm steel studs spaced 600 mm o.c. and two layers of 12.7 mm thick 

gypsum board on each side. The gypsum board sheets should be 1200 mm wide. The 

base layer sheets should be attached to the studs using 25 mm long drywall screws 

spaced 300 mm o.c. along board edges, ends, and along intermediate studs. Base 

layer joints should be oriented parallel to, and located over, studs and staggered on 

opposite sides of the assembly. The face layer sheets should be attached using 41 mm 

long drywall screws spaced 300 mm o.c. along board edges, ends, and along 

intermediate studs. Face layer joints should be oriented parallel to, and located over, 

studs, offset 600 mm from base layer joints, and staggered on opposite sides of the 

assembly. 

Type C gypsum board does not have an associated product standard. Type C products are 

advertised by gypsum board manufacturers as exhibiting superior fire performance characteristics (compared to Type X products) and exceeding the ASTM requirements for Type X gypsum 

board. 

Gypsum (calcium sulphate) dihydrate, CaSO42H2O, the major component of the gypsum board 

core, contains chemically bound water of crystallization (about 21% by weight) in addition to a 

small amount of free moisture. The fire retarding property of gypsum board products derives 

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146

primarily from this water content. When the gypsum board is exposed to fire, the water of 

crystallization is gradually released and evaporated, consuming large amounts of energy in the 

process and delaying heat transmission through the board. Therefore, gypsum board effectively 

acts as a fire barrier until most of its water content is driven out. As shown in Figure 5.13, the 

temperature of the protected steel directly behind the fire-exposed gypsum board remains around 

the boiling temperature of water (100 C) for the duration of the delay. The dehydration (release 

of water of crystallization) of gypsum dihydrate proceeds in two phases. The first phase, known 

as calcination, is associated with the formation of gypsum hemihydrate (semihydrate), 

CaSO41/2H2O, at temperatures in the range of 80 C to 150 C. The second phase of 

dehydration occurs at higher temperatures when the gypsum hemihydrate is transformed to 

gypsum anhydrite, CaSO4. In the case of fire near gypsum products, calcination of the core 

starts at the fire-exposed surface and penetrates through the thickness of the board. The progress 

of calcination is retarded by the layer of calcined gypsum on the fire-exposed surface, which 

adheres well to the inner uncalcined layers. 

FIGURE 5.13. Typical Temperature 

History of a Steel Member Protected 

with Gypsum Board 

The thermo-physical properties of the gypsum board (Alexander 1982) could vary depending on 

the composition of the core and depending on the methods used to derive the properties. Figures 

5.14 and 5.15 illustrate the typical variation of the specific heat and the thermal conductivity, 

respectively, of the gypsum board core with temperature. The plots reflect the expressions 

proposed by Sultan (1996) based on tests conducted on Type X gypsum board specimens. 

Specific heat measurements were carried out at a heating rate of 2 C/min. The dehydration of 

gypsum resulted in the two peaks that appear in the specific heat curve at temperatures around 

100 C and 650 C. 

The Gypsum Association (Gypsum 1998) lists typical mechanical properties, at room 

temperature, for some North American gypsum board products. Little is known about the 

mechanical properties of the gypsum board at elevated temperatures because these properties are 

Time

0

100Temperature ( C)

Fire Temperature

 Steel Stud

Average Temperature

Delay in Temperature Rise

-- DRAFT -- -- DRAFT --
147

difficult to obtain experimentally. However, the tensile strength of the gypsum board has a 

significant effect on its performance in fire. Gypsum board shrinks significantly at elevated 

temperatures (up to 1.5% by the time it reaches 600 C). When this shrinkage is restrained, 

considerable tensile stresses build up in the board, causing cracks within the field of the board 

and/or near the attachment screws. 

FIGURE 5.14. Specific Heat of Type X Gypsum Board Core 

FIGURE 5.15. Thermal Conductivity of Type X Gypsum 

Board Core 

Even dehydrated gypsum board acts as a shield against fire flames and associated radiation 

emissions. The enhanced fire performance of Type X and Type C gypsum board derives 

0 100 200 300 400 500 600 700 800 900 1000

Temperature ( C)

0

5

10

15

20

Specific Heat [kJ/(kg C)]

Sultan (1996)

Heating Rate : 2 C/min

0 100 200 300 400 500 600 700 800 900 1000

Temperature ( C)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Thermal Conductivity [W/(m C)]

Sultan (1996)

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148

primarily from the improved ability of these products to stay in place for an extended period of 

time. This improved ability is usually achieved through reduced shrinkage and increased 

strength characteristics of the gypsum core. Special additives are used in the proprietary 

formulations of fire-resistant boards to reduce their shrinkage (often clay and vermiculite) at 

elevated temperatures. Reinforcement fibres (usually glass fibres) are added to improve the 

mechanical properties of the boards. Type X and Type C products are usually of higher density 

than regular gypsum board. 

5.2.2.4 Fibrous Board and Mat Products 

Although mineral fiberboard and similar mat products are usually more expensive than SFRM, 

they are relatively easy to install and maintain since no wet processes are involved. They are 

often used in retrofit applications and projects where speed and dry process are of importance. 

Mineral fiberboard fire protection products are usually semi-rigid, while the mat products are 

fully flexible. These proprietary products are often supplied with an outer sheathing (aluminum 

foil or similar). They are fixed to structural steel using a wide variety of methods: steel weld 

pins with non-return washers, wire ties, special nails, screws, and, sometimes, bonding agents. 

Some protection systems also involve sealing of the joints with special tape. 

Fibrous insulation products used for fire protection of structural steel range in density from 

100 kg/m3 to 320 kg/m3

 (generally, insulations used for high-temperature applications are much 

denser than standard insulations used for climate protection of premises). Their heat transfer 

properties over the full range of fire temperatures have been rarely reported in literature. Pelanne 

(1978) discusses the mechanisms of heat transfer through fibrous insulations and graphically 

illustrates the thermal conductivity for several insulation products at mean temperatures of up to 

760 oC. He points out that the thermal conductivity of lighter insulations tends to increase 

sharply with temperature, but this effect is much less pronounced for denser insulation products. 

Lie (1992) suggests an approximate temperature-independent value of k = 0.25 W/moC for 

mineral wool boards with densities of ρ = 120 kg/m3

 to 150 kg/m3. 

5.2.2.5 Concrete and Masonry 

For the purposes of determining the fire resistance ratings of structural steel protected with 

concrete or masonry, Tables 720.5.1(2) and 720.5.1(3) of the IBC (2000) and Tables 5-1 through 

5-3 of ASCE 29-99 suggest the following temperature-independent thermal properties 

(cc is specific heat, mc is moisture content, kc is thermal conductivity and ρc is density): 

For normal weight concrete: 

cc = 0.84 kJ/kgoC mc = 4 % kc = 1.64 W/moC ρc = 2323 kg/m3

 

For lightweight concrete: 

cc = 0.84 kJ/kgoC mc = 5 % kc = 0.61 W/moC ρc = 1762 kg/m3

 

For concrete masonry: 

-- DRAFT -- -- DRAFT --
149

cc = 0.84 kJ/kgoC, mc = 0 %, while kc values range from 0.36 W/moC to 1.45 W/moC, 

depending on the density (ρc ranging from 1281 kg/m3

 to 2403 kg/m3) 

For clay masonry: 

cc = 1.00 kJ/kgoC, mc = 0 %, and kc values range from 2.16 W/moC to 3.89 W/moC, 

depending on the density (ρc ranging from 1922 kg/m3

 to 2082 kg/m3) 

5.3 DESIGN PROCEDURES 

The design of structural steel for fire resistance usually falls in one of the two broad categories of 

relevant design procedures: design by qualification testing (sometimes referred to as prescriptive 

methods), discussed in Section 5.3.1, and the more sophisticated design by engineering analysis 

(sometimes referred to as equivalency methods or performance-based methods) (see Section 

5.3.2). While the overwhelming majority of U.S. fire-resistant design decisions are based on 

qualification testing, performance-based designs are increasingly gaining popularity and 

acceptance in the last few decades, especially in complex and high-profile projects, such as 

airports (Baldassarra and Romine 1988), museums and universities (Lane 2000), arts centers 

(Chen and Gemeny 2004), and other public buildings (Siu 2005). 

5.3.1 Design by Qualification Testing 

Qualification fire resistance testing in accordance with ASTM E119 (or very similar standards, 

UL 263 and NFPA 251) is used extensively in the United States to satisfy building code 

requirements for fire resistance. As it relates to structural steel, AISC Steel Design Guide 19 

(Ruddy et al. 2003) and Facts for Steel Buildings: Fire (Gewain, Iwankiw, and Alfawakhiri 

2003) provides a detailed discussion of building code requirements and approved fire-resistant 

design methods for steel-framed floors and roofs, and structural steel beams, columns and 

trusses, and connections. 

Fire-resistant construction assemblies (walls, floors, roofs) and elements (beams, columns) that 

perform satisfactorily in standard fire resistance tests (ASTM E119, UL 263, NFPA 251) are 

documented (along with their respective hourly ratings) in building codes, standards, test reports 

and special directories of testing laboratories. Over the years, a considerable amount of 

accumulated test data has allowed the standardization of many fire-resistant designs involving 

generic (non-proprietary) materials such as steel, wood, concrete, masonry, clay tile, Type X 

gypsum wallboard, and various plasters. These generalized designs and methods are documented in building codes and standards, e.g., in IBC Sections 719 and 720 or in the ASCE/SFPE 

29 standard, with detailed explanatory figures, tables, formulas, and charts. Fire-resistant 

designs that incorporate proprietary (pertaining to specific manufacturers and/or patented) 

materials are documented by test laboratories in relevant test reports and special directories. The 

largest single source of such proprietary fire resistance designs is the Underwriters Laboratories 

(UL) Directory (Fire 2004), updated annually. It contains a variety of designs for columns (X 

and Y series), walls (U and V series), floors (D and G series), roofs (P series), and beams (N and 

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150

S series). Several other accredited laboratories, such as Intertek Testing Services (ITS) and 

Omega Point Laboratories (OPL), also conduct standard fire-resistance tests and publish details 

of fire resistant designs in their directories (ITS 2004; OPL 2004). 

To comply with fire resistance rating requirements specified by the building code, the designer 

usually selects suitable fire-resistant designs from the above sources. It should be noted, 

however, that listed designs must be followed in every detail to ensure the fire resistance rating. 

Departures from listed designs are often difficult to justify to the satisfaction of building 

officials. Additional testing could be required to establish fire-resistance ratings for new design 

configurations that have not been tested or listed before. 

W/D Ratios 

It has been long recognized that the rate of temperature rise in a structural steel member depends 

on its weight and the surface area exposed to heat. Therefore, the factor commonly used in fire 

resistant design is W/D, where W is defined as the weight per unit length of the steel member, 

and D is the inside perimeter of the fire protection, as illustrated in Figure 5.16 for columns 

(exposed to fire on four sides) and Figure 5.17 for beams (exposed to fire on three sides). 

Similar A/P factors are used in the fire-resistant design of tubular column sections, where A is 

the section area and P is the section perimeter. Accurate values of W/D and A/P ratios for 

various sections and configurations are listed in Tables 1-36 through 1-53 of the AISC LRFD 

Manual (Manual 2001) and Appendix A of the AISC Steel Design Guide 19 (Ruddy et al. 2003). 

FIGURE 5.16. Perimeter D for Steel Column Sections 

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FIGURE 5.17. Perimeter D for Steel Beam Sections 

It should be noted that the W/D ratio approach does not apply to open web steel joists (Design

2003) or light-gauge cold-formed steel sections (NAHB 2004). 

Structural steel sections with larger W/D ratios (or A/P ratios) experience slower rates of 

temperature rise in the steel and, therefore, exhibit extended fire resistance performance in fire 

tests and in real fire incidents. W/D and A/P ratios are often used in correlations and formulas, 

developed over the years from a large number of tests, for the determination of fire resistance 

and for the adjustment of fire protection thickness, depending on the size of the steel section. 

Similar concepts are adopted in Europe and other countries; however, their correlations usually 

incorporate the inverted (compared to W/D) ratio Hp/A, where Hp is the inside perimeter of fire 

protection, and A is the steel section area. 

5.3.1.1 Individual Protection 

The International Building Code (2000) requires that fire-rated columns, beams, girders, trusses, 

and other structural members “shall be individually protected on all sides for the full length” 

where the structural element supports: 

 More than two floors (or more than one floor and one roof), or 

 A load-bearing wall, or 

 A non-load-bearing wall that is more than two stories high 

The requirement applies to most columns in multi-story buildings and effectively prohibits 

protecting more than one column in a single fire protection enclosure. This individual protection 

requirement also prohibits the protection of important and “critical” beams, girders, and trusses 

by fire-resistive ceiling membranes. However, ceiling protection (shielding more than one beam, 

girder, or truss by a single fire-resistant membrane) can be used for regular beam, girder, or truss 

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152

systems supporting one floor, or transfer beams, girders, and trusses supporting not more than 

two floors. 

Where required for trusses, the “individual” protection is accomplished through the enclosure of 

the entire individual truss for its full height and length (usually by gypsum wallboard) or through 

the enclosure of each truss element by a spray-applied fire resistive material, intumescent 

coating, gypsum board, or other acceptable protection. 

5.3.1.2 Structural Steel Columns 

The International Building Code prescribes many column fire-resistant designs using generic 

(non-proprietary) materials such as concrete, masonry, plaster, and gypsum wallboard. Also, the 

International Building Code contains several equations (with W/D variable) and relevant tables 

for the calculation of fire resistance of steel columns protected with generic materials. Further, 

the International Building Code allows the adjustment of thickness of proprietary SFRM 

materials based on the W/D ratio of the column section. The ASCE/SFPE 29 standard contains 

very similar provisions for steel columns. In addition, the latter provides an equation for the 

determination of fire resistance of concrete-filled tubular steel columns (for up to 2 hours). 

Fire-resistant steel column designs using proprietary materials, such as SFRM and intumescent 

coatings, are listed under the X and Y series designation of the UL directory. A notable 

exception is UL Design X107 that does not use proprietary materials; the design is for a generic 

1-hour rated W-section steel column with concrete-encased web (and exposed flanges). 

5.3.1.3 Steel Framed Floors and Roofs 

Test standards (ASTM E119, UL 263, NFPA 251) specify dual, restrained and unrestrained, 

classification of fire resistance ratings for floors, roofs, beams, and girders. Floor/roof 

assemblies and individual beams/girders are usually tested, under maximum design load, in the 

restrained condition (i.e., where the thermal expansion of the test specimen is resisted by test 

frame), which is representative of the field conditions in most cases. The resulting restrained 

ratings determined during the tests are representative of the actual fire resistance of the 

specimens. However, in the same tests, unrestrained ratings are also determined based on certain 

steel temperature limits. These unrestrained ratings are sometimes used for field conditions 

where the thermal expansion of a certain beam or floor segment is not expected to be resisted by 

surrounding construction, e.g., as in the case of a cantilevered beam or floor. Table C1.1 of UL 

263 (and similar tables in ASTM E119 and NFPA 251) provide guidance on the cases where 

unrestrained ratings are recommended. An extensive discussion of this subject is provided by 

Gewain and Troup (2001). 

5.3.1.4 Steel Trusses 

The inherently large size of truss assemblies does not allow their adequate fire resistance testing 

in standard furnaces. However, several conservative approaches have been developed over the 

years for truss fire protection. One common approach is to protect each truss element to the 

same level as a column of a similar or smaller section size. Another approach, sometimes used 

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153

for lighter trusses, is to apply proven fire-resistant joist designs to heavier trusses. Both 

approaches are based on the rationale that larger/heavier truss elements would heat up more 

slowly than smaller column sections or lighter joists under similar fire exposures. 

The column designs in the International Building Code apply equally to truss elements protected 

with generic (non-proprietary) materials. Further, the International Building Code specifies the 

method of adjustment of thickness of proprietary SFRM based on the W/D ratio of the protected 

steel section and the number of fire-exposed sides. For truss elements exposed to fire on four 

sides (vertical, diagonal, and sometimes bottom chord elements), the four-side W/D ratio should 

be used in this procedure. Where truss elements directly support floor or roof construction (top 

chord and, sometimes, bottom chord elements, as in staggered truss systems), the W/D ratio for 

three-side exposure is used, as for beams and girders. Similar provisions are specified in the 

ASCE/SFPE 29 standard. 

Proprietary UL designs for columns (X and Y series) and, sometimes, walls (U and V series), 

floors (D and G series), roofs (P series), and beams (N and S series) can also be used for trusses. 

Notably, UL Design U436 is especially useful for the fire-resistant design of staggered trusses 

protected within a gypsum wallboard envelope. 

5.3.1.5 Connections 

There are no standard fire resistance tests or associated ratings for structural connections in any 

material (although beam-to-girder connections are sometimes included within floor assembly 

tests). The approach adopted by building codes for many decades has been to protect 

connections to the same level as the adjacent structural member with the highest fire resistance 

rating. For example, the International Building Code specifies that “where columns require a 

fire-resistant rating, the entire column, including its connections to beams and girders, shall be 

protected.” This approach may often be satisfactory since connection failures have rarely been 

reported during fire incidents. In general, three factors are believed to delay temperature rise 

within connections during fires: 

 SFRM application methods may result in higher than specified protection thickness in 

the corners of beam-to-column and/or beam-to-girder connections. 

 The connections contain more steel material (i.e., more thermal capacity to absorb 

heat) as a result of the overlapping plates and/or section elements. 

 The corner configuration of connections limits their exposure to fire heat radiation, 

while the proximity of connections to several steel members facilitates heat 

dissipation from the heated connection to adjacent cooler members. 

It should be noted that the forces resisted by connections in real fire incidents may be 

significantly different from design forces. Also, multiple compartment fires and fires extending 

simultaneously over multiple floors may result in temperatures within connections that equal 

those of the connected members. Finally, the effects of thermal expansion of the structural 

system can lead to connection failure. 

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5.3.2 Design by Engineering Analysis 

For a given heat exposure history (fire scenario), the engineering analysis of a steel structure 

would involve two major stages. First, heat transfer analysis is conducted (using simple or 

advanced calculation models, described in Section 5.3.2.1) to establish the temperature field 

history in the structure. In the second stage, the structural analysis of the heated steel structure is 

performed using one of the following methodologies: 

 The critical temperature approach (described in Section 5.3.2.2). This is the simplest 

analysis methodology and involves determining critical temperatures (limiting 

temperatures) for various steel elements, and ensuring (adjusting section size and/or 

protection thickness) that these critical temperatures are not exceeded for the required 

time in the design fire scenario. 

 Simple calculation methods (described in Section 5.3.2.3). These are generally 

“hand” calculation methods, although they are not necessarily simple to use (in fact, 

several computer programs have been developed to make these methods easier to 

apply). These calculation methods are based on well-established principles, such as 

plastic analysis of sections, and they usually are used to analyze a single member at a 

time. They often involve simplifying assumptions, such as neglect of thermal 

expansion, temperature independence, and idealization of structural boundary 

conditions (degrees of freedom of member ends), approximation of second-order 

effects, and simplified material property models. 

 Advanced calculation methods (described in Section 5.3.2.4). These are generally 

finite element models incorporating geometrical and material nonlinearities, and they 

are usually used to analyze assemblies of structural components and/or entire building 

systems. The many assumptions and approximations in advanced calculation models 

are usually of a higher order of refinement than in simple calculation methods; 

therefore, a higher degree of accuracy is expected. Because significant expense is 

involved in advanced modeling and calculation, these methods are rarely used for 

routine design projects. Presently, they are primarily used to investigate unusual or 

novel structural configurations, understand frame behavior in fires, conduct 

parametric research studies, and to develop design aids. 

5.3.2.1 Heat Transfer Analysis 

Simplified heat transfer models generally assume the uniformity of temperature across the steel 

section at any time during the fire exposure (heating history). This assumption holds very well 

(due to the high conductivity of steel) for unprotected steel members and also where the 

structural steel member is uniformly protected on all sides and uniformly exposed to fire on all 

sides. For instance, steel section temperatures close to uniform are usually observed in standard 

fire resistance tests on unprotected or uniformly protected structural steel columns. Non-uniform 

temperatures could develop in steel members that have non-uniform protection and/or in cases of 

non-uniform fire exposures. For example, some temperature differences between the top and 

bottom flanges are usually observed in standard fire resistance tests on protected structural steel 

beams supporting concrete slabs (although this temperature difference is neglected where 

simplified heat transfer models are used). 

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155

Other significant approximations often used with simplified heat transfer models are 

temperature-independent (approximated) heat transfer properties for structural steel and fire 

protection materials (e.g., properties listed in Table 5.4) although, ideally, temperature-dependent 

properties could also be used with the simplified models. 

Using the simplifying assumption of uniform section temperature for an unprotected structural 

steel member exposed to a compartment fire, the incremental temperature rise in the steel 

member in a short time period can be determined (Malhotra 1982) from: 

  tTT

D

W

c

a T sF

s

s 





 



  (5.18) 

where: 

ΔTs = Temperature rise in steel (°C), 

D = Inner perimeter of fire protection, as defined in Figures 5.10 and 5.11 (m) 

cs = Specific heat of steel (J/(kg°C)) 

W = Steel section weight per unit length (kg/m) 

TF = Fire temperature (K) 

Ts = Steel temperature (K) 

Δt = Time step (s) 

and the heat transfer coefficient, a, is determined from: 

 aaa rc (5.19) 

where: 

ac = Convective heat transfer coefficient (W/(m2°C)) 

ar = Radiative heat transfer coefficient (W/(m2°C)), defined as: 

  44

8 1067.5

sF

SF

F

r TT

TT

x

a   

  (5.20) 

where: 

F = Emissivity (dimensionless)

For a standard test furnace exposure, the convective heat transfer coefficient, ac, can be 

conservatively approximated as ac = 25 W/m2°C (ECCS 2001). The conservative value for the 

emissivity parameter F is 0.8 (ECCS 2001). 

For the accuracy of temperature history calculations, the time step, t, should be reasonably 

small (e.g., not exceeding 10 seconds). It should also be noted that Equation 5.18 could be used 

for unprotected external steel members (members located outside the building envelope) and/or 

unprotected steel members exposed to localized fires. For these cases, the convective and 

radiative heat transfer coefficients are appropriately reduced, depending on the configuration of 

the considered fire scenario (ECCS 2001). 

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156

For protected structural steel members, the additional conservative simplifying assumption of 

outer protection surface having the temperature of the fire is employed (Malhotra 1982). Hence, 

for steel columns and beams with contour or box protection configurations, Equation 5.18 

becomes: 

t dc

D

W

c

TT

d

k

T

ppp

s

sF

p

p

s 



























 

2

 (5.21) 

where: 

kp = Thermal conductivity of the protection material (W/(moC)) 

cp = Specific heat of the protection material (J/(kgoC)) 

ρp = Density of the protection material (W/moC) 

dp = Protection thickness (m) 

and the other parameters are as defined earlier for Equation 5.18. 

Equation 5.21 could be further simplified (Malhotra 1992) by conservatively neglecting the 

thermal capacity of the protection material: 

  tTT

D

W dc

k

T sF

ps

p

s   (5.22) 

This approximation is appropriate where the thermal capacity of the protection material is much 

less than that of the steel, such that the following inequality holds: 

s 2d > W/Dc p  p c p (5.23) 

Where large temperature differences across a steel section could be expected (e.g., in columns 

partially embedded in masonry walls, or beams partially embedded in a concrete slab), and also 

for complex protection and/or heat exposure configurations and any other cases where a higher 

degree of refinement and accuracy is desirable, the temperature field history in structural steel 

members can be determined using the more advanced calculation models that usually incorporate 

the following actions: 

 Utilize finite element methods of analysis, allowing for the determination of the 

temperature variations within the construction assembly and the steel section. 

 Where necessary, appropriately model the temperature-dependent heat transfer 

properties of materials. 

 Where necessary, take into account the effects of cracking, spalling, or other types of 

high-temperature material erosion or degradation. 

While many of the general-purpose finite-element programs with suitable heat transfer routines 

could be used to implement advanced calculations, several advanced special-purpose fire-related 

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157

programs have been developed over the years for heat transfer analysis, including FIRES-T3 

(SFPE 1995), TASEF (Sterner and Wickstrom 1990), and SAFIR (Franssen et al. 2000). 

5.3.2.2 Critical Temperatures 

Although no standard in the United States specifies critical steel temperatures for performancebased designs, the critical average section temperatures commonly used in the United States are 

538oC for steel columns and 593oC for steel beams (similar to temperature acceptance criteria 

adopted in ASTM E119) regardless of the loads applied to structural members. In Europe (BS 

5950 1990, prEN 1993-1-2: 2003, prEN 1994-1-2: 2003, ECCS 2001), critical temperatures for 

steel members are specified depending on the so-called applied load level, or load ratio, R, i.e., 

critical temperatures depend on both the type of the structural member and the load level. The 

critical temperatures, however, are independent of time and also independent of the shape or size 

of the steel section. 

Lawson and Newman (1990) provide a comprehensive summary of critical steel temperatures in 

accordance with the British Standard (BS 5950 1990), which defines the load ratio as: 

x y

g c b yy

MF M

R

A p M pZ

  for members in compression (columns) (5.24a) 

c

M R

M for members in bending (beams) (5.24b) 

x y

e y cx cy

MF M

R

A pM M

  for members in tension (5.24c) 

where: 

Ag = Gross cross-sectional area (mm2) 

Ae = Effective area in tension (mm2) 

pc = Compressive strength of member at room temperature (MPa) 

py = Design strength of steel at room temperature (MPa) 

Zy = Elastic section modulus about the minor axis (mm3) 

Mb = Buckling resistance moment capacity about major axis at room temperature 

(N mm) 

Mc = Bending moment capacity (at room temperature), including the lateral torsional 

buckling capacity where applicable (N mm) 

Mcx = Bending moment capacity about the major axis at room temperature (N mm) 

Mcy = Bending moment capacity about the minor axis at room temperature (N mm) 

F = Axial load at the fire limit state (N) 

M = Applied moment at the fire limit state (N mm) 

Mx = Applied moment about the major axis at the fire limit state (N mm) 

My = Applied moment about the minor axis at the fire limit state (N mm) 

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158

Once the load ratios are calculated from Equations 5.24, the critical temperatures can be 

determined by interpolating the values in the relevant British Standard (BS 5950 1990) table, 

reproduced here in Table 5.5. For compression members in braced frames (where the loading is 

predominantly axial and the bending is comparatively small), the standard distinguishes two 

ranges of slenderness ratios (cases 1 and 2 in Table 5.5). It should also be noted the standard 

treats columns in sway frames more conservatively by adopting a single critical temperature of 

520oC, regardless of slenderness and load ratios. 

For members in bending, BS 5950 (1990) specifies higher critical temperatures for steel beams 

supporting concrete or composite floors (cases 3 and 4 in Table 5.5) where the beams could be 

exposed to fire on three sides only. Beams not supporting concrete or composite floors are 

assigned lower critical temperatures (cases 5 and 6 in Table 5.5). The standard also reduces the 

critical temperatures for steel and composite beams protected with materials that have not 

demonstrated their adhesion properties in fire tests (cases 4 and 6 in Table 5.5). Protection 

materials with proven ability to remain in place during large deformations in fire tests qualify the 

beams for higher critical temperatures (cases 3 and 5 in Table 5.5). 

The critical temperature method could be used in combination with either simplified or advanced 

heat transfer models to determine the required protection thickness or to confirm that no 

protection is necessary. Where advanced heat transfer models are used and there is significant 

temperature variation across the steel section, the hotter flange temperatures should be checked 

against the critical temperature. 

The critical temperature method was developed based on compilations of experimental 

measurements and analytical extrapolations further confirmed by tests (Lawson and Newman 

1990). Very similar concepts were later adopted for the critical temperature methods specified in 

Eurocode 3 (EN 1993-1-2: 2005), Eurocode 4 (EN 1994-1-2: 2005), and the ECCS Model Code 

(ECCS 2001), although they resulted in critical temperatures slightly different from those in BS 

5950 (1990). Lawson and Newman (1996) discuss these differences in detail. 

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159

TABLE 5.5. Critical Temperatures for Structural Steel Members (Lawson and 

Newman 1990) 

Case 

Number Description of member 

Limiting temperatures (oC) at load 

ratios: 

0.7 0.6 0.5 0.4 0.3 0.2 

(1) 

(2) 

Braced members in compression: 

- slenderness ratio  70 

- slenderness ratio  180 

510 

460 

540 

510 

580 

545 

615 

590 

655 

635 

710 

635 

(3) 

(4) 

Members in bending supporting 

concrete or composite deck floors: 

- unprotected, or protected with 

materials with proven “stickability” 

- all other protected members 

590 

540 

620 

585 

650 

625 

680 

655 

725 

700 

780 

745 

(5) 

(6) 

Members in bending not supporting 

concrete or composite deck floors: 

- unprotected, or protected with 

materials with proven “stickability” 

- all other protected members 

520 

460 

555 

510 

585 

545 

620 

590 

660 

635 

745 

690 

(7) Members in tension 460 510 545 590 635 690 

5.3.2.3 Simple Calculation Models 

Provisions for simple methods of analysis for the performance-based fire-resistant design of steel 

and composite structures have been recently introduced in the United States for the first time 

(AISC 2005). These simple methods are based on AISC design provisions for the capacity of 

structural steel and composite members at room temperature, adjusted for the deterioration of the 

mechanical properties of steel and concrete at elevated temperatures. The provisions cover 

simple methods for tension, compression and flexural steel members and also for composite floor 

members. The major limitations and simplifications associated with the simple methods of 

analysis are stated as follows: 

“The methods of analysis in this section are applicable for the evaluation of 

performance of individual members at elevated temperature during exposure to 

fire. The support and restraint conditions (forces, moments and boundary 

conditions) applicable at normal temperatures may be assumed to remain 

unchanged throughout the fire exposure.” 

Similar simple calculation models have been specified in Europe (BS 5950 1990, prEN 1993-1-

2: 2003, prEN 1994-1-2: 2003, ECCS 2001) for more than a decade now, having a similar 

limitation of applicability to individual members or analysis of parts of the structure only, and 

using similar assumptions of temperature-independent boundary conditions. 

Among simple calculation methods, the most intensive in terms of the calculation effort are 

probably the methods for the plastic bending moment capacity. The AISC Steel Design Guide 19 

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160

(Ruddy et al. 2003) provides a step-by-step procedure for the calculation of flexural capacity of 

composite floor beams at elevated temperatures, based on earlier research (Ioannides and Mehta 

1997) and consistent with newly proposed AISC provisions (AISC 2005). Under fire conditions, 

the rotational restraint provided by the continuity of the composite floor assembly results in the 

redistribution of bending moments to beam ends, as illustrated in Figure 5.18, so that the factored 

applied ultimate bending moment Mu (for the fire load combination) is resisted by both the 

positive flexural design strength b M+

n and the negative flexural design strength b M -n of the 

composite beam, so that: 

 Mu  b (M+

n + M -n) (5.25) 

Where : 

b = 0.9 = resistance factor for composite beams in bending 

M+

n = Positive nominal flexural strength of the composite beam (N mm) 

M -

n = Negative nominal flexural strength of the composite beam (N mm) 

FIGURE 5.18. Moment Envelopes Before 

and During Fire (Ioannides and Mehta 1997) 

The positive nominal flexural strength M+

n is determined (in most cases) as the sum of moment 

couples of the section resultant forces, shown in Figure 5.19. The resultant FT of tensile forces 

takes into account the deterioration of steel yield strength in the components of the steel section 

at their elevated temperatures: 

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161

 FT = Ftf + Fw + Fbf (5.26) 

where: 

Ftf = Yield capacity of the top flange at its elevated temperature (N) 

Ftf = Yield capacity of the web at its elevated temperature (N) 

Ftf = Yield capacity of the bottom flange at its elevated temperature (N) 

FIGURE 5.19. Typical Positive Moment 

Force Resultants (Ioannides and Mehta 

1997) 

The concrete in the compression zone is modeled to achieve its full plastic capacity at the strain 

of 0.003, assuming the temperature at the top surface of the concrete slab does not increase 

dramatically. The compressive resultant FC (equal in magnitude to FT) would then be located at 

the middle of the standard equivalent rectangular block of depth a calculated from 

0.85 '

T

c f

F

a

f b  (5.27) 

where: 

fc' = Compressive strength of concrete (Mpa) 

bf = Effective width of concrete slab (mm) 

If the depth a of the equivalent compression block is less than the concrete slab depth, then the 

neutral axis of the composite section lies within the slab, and no further iterations are required. 

Otherwise, partial compression of the steel section should be assumed, and the location of the 

neutral axis should be adjusted until the equilibrium of the tensile and compressive resultants in 

the composite section is satisfied (before the flexural strength is calculated). 

The negative nominal flexural strength Mn at the ends of the composite beam is usually provided 

by the concrete slab reinforcement (parallel with the beam) with the top flange acting together in 

tension, and forming flexural couples with the remaining portions of the steel beam section 

acting in compression, as illustrated in Figure 5.20, which assumes the neutral axis passing along 

the bottom surface of the top flange. The tensile resultant FT and compressive resultant FC in 

this case are: 

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162

 FT = FRB + Ftf (5.28) 

 FC = Fw + Fbf (5.29) 

where: 

FRB = Tensile yield capacity of concrete slab reinforcement 

FIGRE 5.20. Typical Negative Moment 

Force Resultants (Ioannides and Mehta 

1997) 

If the equilibrium condition for the tensile and compressive resultants is satisfied (FT = FC), no 

further iterations are required, and the negative nominal flexural strength is calculated as the sum 

of the resultant moment couples. Otherwise, the position of the neutral axis should be adjusted 

until the equilibrium condition is satisfied before the flexural strength is calculated. 

For the above procedures (and similar procedures for the plastic bending moment capacity of 

non-composite steel beams), if the temperatures within the steel or composite section vary 

considerably, the section could be divided into a larger number of elements so that the temperature in each element would be reasonably approximated as uniform. For a large number of 

section elements, a suitable computer program is usually used for calculations. One such 

program, AFCB (available for free download at www.asc.arcelor.com), calculates the capacities 

of composite steel beams in accordance with Eurocode 4 (EN 1994-1-2: 2005). 

5.3.2.4 Advanced Calculation Models 

Advanced calculated models could be applied to a single member, an assembly, or to the entire 

building frame. The newly proposed AISC provisions (AISC 2005) describe the requirement for 

advanced methods of structural analysis for performance-based fire resistant design as follows: 

“The mechanical response results in forces and deflection in the structural system 

subjected to the thermal response calculated from the design-basis fire. The 

mechanical response shall take into account explicitly the deterioration in strength 

and stiffness with increasing temperature, the effects of thermal expansions and 

large deformations. Boundary conditions and connection fixity must represent the 

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163

proposed structural design. Material properties shall be defined as per Section 

4.2.3. The resulting analysis shall consider all relevant limit states, such as 

excessive deflections, connection fractures, and overall or local buckling.” 

Similar requirements for advanced calculation models have been specified in Europe (EN 1993-

1-2: 2005, EN 1994-1-2: 2005, ECCS 2001) for many years: 

 When a global structural analysis for the fire situation is carried out, the relevant 

failure mode in fire exposure, the temperature-dependent material properties, and 

member stiffnesses, as well as the effects of thermal expansions and deformations 

(indirect fire actions), shall be taken into account. 

 Advanced calculation models for mechanical response shall be based on the 

acknowledged principles and assumptions of the theory of structural mechanics, 

taking into account the effects of temperature. The mechanical response shall also 

take account of the combined effect of mechanical actions, geometrical imperfections 

and thermal actions, the temperature-dependent mechanical properties of materials, 

geometrical nonlinear effects, and the effects of non-linear material properties, 

including the effects of unloading on the structural stiffness. The effects of the 

thermally induced strains and stresses, both due to temperature rise and due to 

temperature differentials, shall be considered. The deformations at ultimate limit 

state, given by the calculation model, shall be limited as necessary to ensure that 

compatibility is maintained between all parts of the structure. 

 A verification of the calculation results shall be made on basis of relevant test results. 

The critical results shall be checked, by means of a sensitivity analysis, to ensure that 

the model complies with sound engineering principles. 

To address specific fire resistance problems, several special-purpose finite element computer 

programs had been developed over the years, most notably SAFIR (Franssen et al. 2000) and 

VULCAN (Huang et al. 2003). In the last decade, the development of advanced calculation 

models has intensified significantly in connection with large-scale fire experiments carried out 

on the Cardington steel-framed building (Kirby 1999), with the main focus on the behavior of 

unprotected steel-framed composite floors using general-purpose finite element programs, such 

as ABAQUS, DIANA, LS-DYNA, and ANSYS. The ABAQUS-based model has been 

reportedly used in practical fire-resistant design applications in the United Kingdom (Ove Arup 

2003), and SAFIR was used in at least one practical design in the United States (Chen and 

Gemeny 2004). 

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5.4 REFERENCES 

TABLE 5.6. Literature references for Figure 5.8 

Steels Reference 

WTC 55 ksi and 50 ksi steels Luecke (2005) 

C < 0.3%, C > 0.3% ASME Boiler and Pressure Vessel Code 

(2004) 

Structural steels Brockenbrough (1968) 

1015 steel Clark, High-temperature Alloys, Pitman 

Publishing (1953) 

1015 steel Garafolo, ASTM STP 129 (1952) 

Austenite, Ferrite Koester, Z. Metallk. 39 (1948) 

Not specified Stanzak, Tall (cited in Uddin J Struct Div 

ASCE 107 [7] p5131 Table 1) 

TABLE 5.7. Literature references for Figure 5.11 

Steels Reference 

SMA490 Chijiiwa (1993) 

ASME-SA516 Gowda, B.C. (1978) 

T1, A36 Brockenbrough (1968) 

T1a, Cor-Ten, A440, Tri-Ten Holt (1964) 

AS3679.1 Poh (1998) 

AS3678 XLERPlate Chen (2006) 

BS4360 Gr 50B Kirby (1988) 

S355, S460M Outinen (2001) 

SM400A Sakumoto (1999) 

60 ksi HSLA plate, 100 ksi plate, A36 

12WF161, A36 14WF184, 50ksi A242 

angle, A36 angle 

Luecke (2005) 

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Brockenbrough, R.L., and B.G. Johnston (1981), USS Steel Design Manual, Pittsburgh, Pa.: R.L. 

Brockenbrough and Assoc. Inc.. 

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Butler, K.M. (1997), “Physical Modeling of Intumescent Fire Retardant Polymers,” Chapter 15 

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Gaithersburg, MD, September 

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Development and practical application of fire-resistant steel for buildings. Nippon Steel 

Technical Report 58, Nippon Steel, 1993. UDC669.14.018.291 : 699.81. 

Clark, C.L. 1953. High-temperature Alloys. Pitman, New York. 

Cooke, G.M.E. (1988), “An Introduction to the Mechanical Properties of Structural Steel at 

Elevated Temperatures,” Fire Safety Journal 13 (1988) 45-54. 

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EN 1993-1-2: 2005, Eurocode 3: Design of Steel Structures—Part 1-2: General Rules, 

Structural Fire Design, Stage 49 Draft, Brussels: European Committee for Standardisation, 

2005. 

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ENV 13381-1: 2005, Test Methods for Determining the Contribution to the Fire Resistance of 

Structural Members—Part 1: Horizontal Protective Membranes, Brussels: European Committee 

for Standardisation, 2005. 

ENV 13381-2: 2002, Test Methods for Determining the Contribution to the Fire Resistance of 

Structural Members—Part 1: Vertical Protective Membranes, Brussels: European Committee for 

Standardisation, 2002. 

ENV 13381-4: 2002, Test Methods for Determining the Contribution to the Fire Resistance of 

Structural Members—Part 1: Applied Protection to Steel Members, Brussels: European 

Committee for Standardisation, 2002. 

Franssen, J.M., V.K.R. Kodur, and J. Mason (2000), User’s manual for SAFIR2001: a computer 

program for analysis of structures submitted to the fire, Liege, Belgium: University of Liege. 

Garofalo, F., Malenock, P.R., and Smith, G.V. (1952), The Influence of Temperature on the 

Elastic Constants of Some Commercial Steels. Symposium on Determination of Elastic 

Constants. ASTM Special Technical Publication 129. 10-27. 

Gewain, R.G., E.W.J. Troup (2001), “Restrained Fire Resistance Ratings in Structural Steel 

Buildings,” Engineering Journal 38:2 (2001). 

Gewain, R.G., N.R. Iwankiw, and F. Alfawakhiri (2003), Facts for Steel Buildings: Fire, 

Chicago: American Institute of Steel Construction. 

Gowda, B.C. (1978), Tensile properties of SA516, grade 55 steel in the temperature range of 

25 oC–927 oC and strain rate range of 10−4 to 10−1 sec−1/in. George V. Smith, editor, 

Characterization of Materials for Service at Elevated Temperatures, pages 145–158, New York, 

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Montreal Pressure Vessel & Piping Conference, Montreal, Quebec, Canada, June 25–29 1978. 

Gypsum Association (1998), Gypsum Board: Typical Mechanical and Physical Properties, 

GA-235-98, Washington: Gypsum Association. 

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of Some Structural and Prestressing Steels”, ASTM STP 464, West Conshohocken, Pa.: 

American Society for Testing and Materials, pp 186-208. 

Holt, J. M. (1964) Short-time elevated-temperature tensile properties of USS Cor-Ten and USS 

Tri-Ten high-strength low-alloy steels, USS Man-Ten (A 440, high strength steel, and ASTM A 

36 steel. Progress Report 57.19-901(1), United States Steel Corporation. 

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Huang, Z., I.W. Burgess, and R.J. Plank (2003), “Modelling Membrane Action of Concrete Slabs 

in Composite Buildings in Fire. Part I: Theoretical Development,” ASCE Journal of Structural 

Engineering 129:8 (2003) 1093-1102. 

Huang, Z., I.W. Burgess, and R.J. Plank (2003), “Modelling Membrane Action of Concrete Slabs 

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International Building Code (ICC 2000), Falls Church, Va.: International Code Council. 

Intertek Testing Services NA Inc. (2004), Directory of Listed Products (ITS 2004), Cortland, 

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Ioannides, S.A., and S. Mehta (1997), “Restrained vs. Unrestrained Fire Ratings: A Practical 

Approach,” Modern Steel Construction (May 1997). 

Jerath, V., K.J. Cole, and C.I. Smith (1980), Elevated Temperature Tensile Properties of 

Structural Steels Manufactured by the British Steel Corporation, Report T/RS/1189/11/80/C, 

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Kirby, B. (1983), The Behaviour of Structural Steels Manufactured by BSC under Stress 

Controlled Anisothermal Creep Conditions, Report SH/RS/3664/4/83/B, BSC Sheffield 

Laboratories (October 1983). 

Kirby, B. (1999), The Behaviour of Multi-Storey Steel Framed Buildings in Fires, A European 

Joint Research Program, U.K.: British Steel Swinden Technology Centre. 

Kirby, B.R., and Preston (1988), “High Temperature Properties of Hot-Rolled, Structural Steels 

for Use in Fire Engineering Design Studies,” Fire Safety J. 13 (1988) 27-37. 

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The SFPE Handbook of Fire Protection Engineering, 3rd ed., Bethesda, Md.: Society of Fire 

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Metallkd. 39(1).1-9. 

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Chapter 6 

General Application of Guidelines

Donald O. Dusenberry, P.E., Simpson Gumpertz & Heger Inc. 

Morgan J. Hurley, P.E., Society of Fire Protection Engineers 

Performance-based design of structures for fire resistance requires the collaboration of fire 

protection engineers and structural engineers. Fire protection engineers typically analyze fire 

environments and the transfer of heat from the fire to the elements of a structure. Structural 

engineers use the results of the heat transfer analysis to determine the structural response, 

considering thermally induced strains and the effects of changes of material properties at 

elevated temperatures. Typically this collaboration is most effective when fire resistance is 

considered as early as the conceptual design stage, when flexibility in structural concepts allows 

the fire resistance considerations to influence the structural design. 

Designing structural fire resistance on a performance basis generally includes the following steps

(see SFPE 2006, SFPE 2007 and Aktan 2007): 

1. Predict the thermal environment surrounding a building structure (or portion thereof) in 

the event of a fire. This is generally accomplished by modeling the fire.

2. Determine the thermal response of the structure by conducting heat transfer analyses. 

Most fire models provide temperature boundary conditions, which must be translated into 

heat flux boundary conditions to determine the thermal response of the structure. 

3. Evaluate the structural response. This involves evaluation of the impacts of temperaturedependent material properties and stresses due to thermal expansion and contraction. 

Hence, material and geometry nonlinearities often are important.

Underlying these three steps, if a risk assessment is part of the design, is a risk analysis for the 

identified fire hazards, the response of the structural system, and the associated consequences of 

failures that might be induced by fires.

This chapter provides general guidance on the approaches to and practical aspects of

implementing a fire resistant design for conventional applications. 

Section 6.1 reviews key concepts for identifying performance objectives and conducting risk 

analyses, with examples. Section 6.2 discusses considerations for identifying fire scenarios and 

developing fire exposure curves. Sections 6.3 and 6.4 discuss heat transfer analyses and analyses 

of structural response to elevated temperatures. Section 6.5 discusses fire resistant structural 

design. Sections 6.6 and 6.7 discuss design issues particular to concrete and steel structures, 

respectively.

6.1 PERFORMANCE OBJECTIVES AND RISK ASSESSMENT

Chapter 3 presented a detailed framework for developing performance goals and objectives, 

conducting risk assessments, and selecting a risk mitigation approach for performance based 

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design of fire resistant conventional construction. This section discusses implementing this 

approach in the design process. 

6.1.1 Performance Objectives

Performance objectives, which must be fulfilled to achieve the goals of the performance-based 

design, often are derived from code-based requirements, sometimes with additional goals that 

satisfy the mission of the owner or other parties. For instance, a primary goal in building codes 

is life safety of building occupants. Other goals might address protection of property, business 

continuity, or life safety risk for firefighters. 

Specific criteria should be established for each performance objective to identify how it will be 

met. For instance, structural performance objectives for life safety could provide structural 

resistance that allows adequate time for occupant evacuation (note that this does not address 

firefighter safety or preservation of building contents). 

Overall fire safety design strategies for a building might include: 

• Appropriate compartmentation for limiting heat transmission and fire and smoke 

spread

• Intact egress paths or safe havens 

• Appropriate passive fire protection for the structural system

• Active fire suppression systems to control fire growth

A subset of fire safety design strategies for the structural system might include: 

• Structural integrity to ensure that architectural features remain intact (e.g., limit frame 

deflections so that fire barriers are not breached) 

• Adequate structural stiffness and strength for columns, floors, and connections 

Other performance objectives for fire resistant design might include life safety of firefighters 

(e.g., no partial or global collapse of the structure), protection of property (including adjacent 

buildings), survival of building contents (e.g., bank, library, or museum contents), protection of 

infrastructure (e.g., integrity of gas lines or electrical substations), or protection of the 

environment (e.g., no chemical spills). 

6.1.2 Risk Assessments

The risk analysis should be addressed at the start of the project, and continued through the design 

process. Owners and their consultants must make decisions to manage and mitigate risk through 

combinations of prudent design and risk acceptance. 

For a risk assessment to be useful, it must be expressed in quantitative terms. Risk can be 

defined as the potential rate at which consequences (e.g., economic, life, or other types of losses) 

may occur for a given structure and its associated hazards. 

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Chapter 3 states that the probability of a loss can be evaluated from the following equation: 

P[Loss > θ ] = ΣHΣLSΣD P[Loss> θ|D] P[D|LS] P[LS|H] P[H] (3.1) 

Where:

P[A] = Probability of event A 

P[A|B] = (Conditional) probability of event A, given the occurrence of event B 

θ = An appropriate loss metric: severe injury or death, direct damage costs, 

loss of opportunity costs, etc. 

P[LS|H] = Conditional probability of a structural limit state

P[D|LS] = Conditional probability of damage state (e.g., negligible, minor, 

moderate, severe)

P[H] = Probability of a hazard occurrence 

P[Loss > θ|D] = Conditional probability of loss

As an alternative, the risk assessment may be based on a set of stipulated scenario events rather 

than on a hazard with a random intensity, depending on the preferences of the decision-maker. 

For a fire scenario, the risk metric in Eq. 3.1 becomes a conditional probability: 

P[Loss > θ|Hs] = ΣLSΣD P[Loss > θ|D] P[D|LS] P[LS|Hs] (3.2) 

where: 

Hs = Fire scenario event(s)

These expressions from Chapter 3 can be simply restated as:

Risk = ΣH Probability of failure x Consequence of failure

where the summation is evaluated for the fire hazard, H, or for all identified fire scenarios, Hs. 

For a risk analysis, the fire hazard can be expressed either probabilistically or as a set of fire 

scenarios (see Ch. 3) with a probability of occurrence for each fire scenario. While tables of fire 

occurrence rates are useful, the designer must be careful to include other factors that may affect 

an individual building. For instance, buildings sited in locations where wildfires occur could 

have a greater probability of fire ignition than buildings that are remote from such hazards. 

Occupancies that involve storage of volatile fluids and buildings with outdated and overloaded 

electrical systems could have a greater probability of ignition. 

Unfortunately, there might not be reliable data leading to precise assessments of fire hazards 

under unusual conditions. In some cases, data might be held by organizations that monitor fire 

occurrences (e.g., the National Fire Protection Association). In many cases the engineer must 

apply judgment to determine factors for fire hazards that will contribute to the risk assessment.

Fire suppression systems affect the frequency of fully developed fires, given that fire ignition has 

occurred. The effect of these systems generally is considered only in risk and probabilistic 

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analyses of fire occurrence rates (see Section 3.2.2). In scenario-based analyses, effectiveness 

and reliability of suppression systems are considered only when selecting fire scenarios to be 

evaluated. 

The probability of failure (i.e., exceeding a structural limit state or failing a performance 

objective), and the resulting damage state, are based on the results of structural analyses. Since 

structural behavior can be highly nonlinear when thermal effects and temperature dependent 

properties of construction materials are included in the analysis, care must be given to analysis 

approaches (e.g., linear approaches usually are insufficient) and a clear definition of what 

constitutes “failure” must be established in consideration of the selected analysis approach. 

Risk analysis can be used to make comparisons against risks for similar types of construction or 

to identify the factors that contribute to the overall risk. A comparative risk analysis cannot 

guarantee specific levels of performance, but it can provide guidance on how to (1) reduce risks 

associated with the performance objectives, and (2) develop prudent and effective designs based 

on the best available information. 

6.2 DESIGN FIRES

Fire protection engineers, through collaboration with structural engineers, must identify the 

relevant fire environments for structural analyses and design. This requires consideration of the 

factors that affect fire severity, fire growth within compartments, design fire definitions, fuel 

loads, fire resistance ratings, and fire modeling. 

6.2.1 Factors That Affect Fire Severity

Each fire and its severity are affected by the following factors: 

• The arrangement of fuel in the fire compartment

• The composition and amount of fuel 

• Ventilation characteristics

• The geometry of the compartment

• Thermal properties of the compartment walls, floor and ceiling

6.2.1.1 Fuel Arrangement 

The arrangement of fuel determines whether a fire can be treated as uniform over a compartment 

or as a discrete fire location within a compartment. If the fuel is well distributed over the floor 

area of the compartment, it is usually assumed that the fire conditions are uniform throughout the 

enclosure. Conversely, if the fuel is concentrated over a portion of a floor area, an assumption 

that the fire exposure would not be uniform would be more appropriate. 

6.2.1.2 Composition and Amount of Fuel 

The composition and amount of fuel in an enclosure can affect the peak temperatures and the 

duration of burning. In Figure 6.1, characteristic curves plotted using the method developed by 

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Magnusson and Thelandersson (1970) show the theoretical relationship between peak fire 

temperature and time as a function of fuel load in the compartment. 

All predictive methods were developed on the basis of wood (or other cellulosic materials) as 

fuel (SFPE, 2004). Some methods specify the fuel load on the basis of mass, while others 

require input on the basis of caloric value of fuel. The methods developed based on wood crib 

fires reasonably predict maximum fire temperatures. However, special attention is required 

when compartments contain significant quantities of non-cellulosic fuels and ventilation is not 

expected to control the burning rate. Predictive methods based on burning wood cribs should be 

appropriate for most compartments of interest. 

Many hydrocarbon-based materials, such as plastics, have approximately twice the heat of 

combustion of wood. More energy is required to cause wood to release flammable vapors than is 

needed for plastics (Karlsson and Quintiere 1999), so that wood has a lower rate of mass loss and 

longer burning durations. However, heat energy that is released per mass of available oxygen is 

essentially constant for a wide variety of fuels (Huggett 1980; Drysdale 1999). 

Two approaches can be used to estimate the fuel load in a compartment. Typically for design, 

fuel loads can be determined from tabulated values that are based on occupancy. Alternatively, 

for an existing structure or for occupancies that are not included in tables of fuel loads, 

combustible furnishings and contents can be inventoried. Masses, and therefore fuel loads, of 

the combustible items anticipated for the compartment can be determined by their weights or by 

measuring their dimensions and multiplying their volumes by effective densities. 

Chapter 3 summarized available information on expected fire loads (fuels) in buildings with 

various occupancies. Tables 3.3(a), 3.3(b), and 3.3(c) relate results from different studies 

conducted at different times over a period of approximately 25 years. When assessing fire loads, 

engineers need to consider matters such as whether the expected occupancy of the building under 

design would generate fire loads that are atypical for the general occupancy category and 

building type. 

It is generally acceptable to rely on published data. However, there are circumstances for which 

specific evaluations of fire ignition risks and fire loads are important. When a specific building 

will house activities that involve conditions not normally found in similar occupancies, specific 

evaluations can be essential. An example could be an office building that will contain fuel 

storage capacity for backup site power generation. The presence of petroleum fuel storage and 

handling capability in this application warrants special consideration. In this example, the 

engineer should assess:

• The quantity of fuel on the premises 

• The reliability of the fuel containment systems

• The fire load generated by a spill (SFPE 2002, pp. 3-24 to 3-26) relative to fire loads 

normally associated with office building occupancies

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6.2.1.3 Ventilation Characteristics and Compartment Geometry 

Compartment gas temperatures and burning rates are influenced by the available ventilation. In 

ventilation-limited fires, the rate of airflow into the enclosure will govern the heat release rate 

inside the enclosure, and fuel vapors that cannot burn inside the enclosure will burn outside once 

they encounter fresh air. 

Fuel in well-ventilated compartments (e.g., with ventilation factor Fv = 0.12 m-1/2 in Figure 6.2) 

tends to burn more quickly and create higher peak temperatures than fuel in compartments that 

have restricted airflow (e.g., with Fv = 0.02 m-1/2 in Figure 6.2). Hence, access to oxygen during 

a fire must be evaluated.

The shapes and locations of openings in a fire compartment are important. Most fire exposure 

curves assume openings in walls (rather than floors or ceilings) and that the associated airflow is 

induced by buoyancy. When airflow is buoyancy driven, the flow rate through openings is a 

function of the distance above or below the plane at which the pressure in a compartment is the 

same as the pressure outside the compartment (the neutral plane) (Drysdale 1999). Above the 

neutral plane, the pressure is higher than the ambient pressure, and heated gas flows out of the 

compartment through openings. Below the neutral plane the pressure is lower than ambient, so 

air flows into the compartment.

Time

Temperature 

500

200

300

100

50

Fuel Load (MJ/m2)

FIGURE 6.1. Relationship between Temperature and Time as a Function of Fuel 

Load (adapted from Magnusson and Thelandersson, 1970)

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Given ventilation openings in vertical surfaces, tall window openings tend to ventilate 

compartments more efficiently than do shallow windows, resulting in a higher ventilation factor 

and possibly hotter and shorter fires. Through tall windows, convection encourages cool air with 

oxygen to flow into the compartment in the lower portion of the window and hot fumes 

generated by the fire to flow out the upper portion of the window. Convection currents are 

weaker when windows are shallow in height. This fact is represented in the ventilation factor, 

Fv, used in the Swedish curves (Magnesson and Thelandersson 1970). 

Fire exposure curves, such as those shown in Fig. 6.1, and empirical equations are generally 

based on an assumption that ventilation openings are in vertical surfaces. Compartments with 

openings in horizontal surfaces, such as stairwell openings between floors in office spaces, 

require special attention with methods applicable to such conditions (see Section 6.2.5.3). 

Predictive methods based on available fire exposure curves are also based on an assumption that 

the compartments are “well stirred,” i.e., that the temperature in the compartment is uniform. 

This assumption can break down in compartments that are irregularly shaped. SFPE (2004) 

investigated the ability of various methods to predict fires in compartments that were long and 

narrow with the ventilation opening on one of the shorter sides. This study showed that some 

existing methods provide reasonable predictions of fire severity in long and narrow 

compartments. See Section 6.2.2 for additional information. 

Time

Temperature

Fv=0.12

Fv=0.04

Fv=0.02

FIGURE 6.2. Relationship between Fire Temperature and Time as a Function of 

Ventilation (adapted from Magnusson and Thelandersson, 1970)

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6.2.1.4 Thermal Properties

The thermal properties of the construction materials and furnishings in an enclosure also 

influence gas temperature histories during fires. Gas temperatures in compartments with low 

thermal inertia (defined as the product of density, specific heat, and thermal conductivity) tend to 

be hotter than gas temperatures in compartments with higher thermal inertias (SFPE 2004). The 

surfaces with higher thermal inertia absorb more heat energy from the fire-induced environment, 

reducing gas temperatures, whereas less heat energy is absorbed by materials with lower thermal 

inertia. 

6.2.2 Fires in a Compartment

The rate of burning in fully developed fires is primarily controlled by either ventilation or fuel. 

In ventilation-controlled burning, the rate of combustion depends on the volume of available air; 

if there is insufficient air, combustibles will be incompletely burned and flames may extend out 

the windows to complete combustion of the unburned gaseous fuel mixture. In fuel-controlled 

burning, the rate of combustion depends on the surface area of the fuel, especially in large wellventilated rooms with limited amounts of combustible surfaces. 

As fires develop in compartments, the increasing gas temperatures in the upper layer of the 

compartment generate increasing radiant heat flux that heats all objects in the compartment. At a 

critical level of heat flux, all exposed combustible items in the compartment simultaneously 

begin to burn, leading to a rapid increase in both the heat release rate and gas temperatures. This 

transition is referred to as flashover, and fires after this transition are often referred to as ‘postflashover’ fires or ‘fully developed’ fires, as shown in Fig. 6.3 (Buchanan 2001). 

The primary threat to most structures arises during the fully-developed stage of burning and, for 

insulated steel or concrete structures, possibly during the decay stage as cooling occurs (SFPE 

2004). Figure 6.3 illustrates the phases of fire development for a room fire. 

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FIGURE 6.3. Phases of Fire Development for a Fire in an Enclosure 

(adapted from SFPE 2004).

Generally, fully developed fires are assumed to involve entire rooms or enclosures. Where fire 

barriers are not provided, the entire building, or at least an entire floor, generally is assumed to 

be fully involved. 

If a building contains multiple areas that are enclosed with fire-rated boundaries, then it may be 

necessary to consider separate fire scenarios in each enclosed area. Fire rated boundaries include 

partitions with fire-rated door and wall construction that extends from floor slab to floor slab or 

from the floor slab to a fire-rated suspended ceiling. Partitions that stop at unrated suspended 

ceilings are not fire boundaries. 

6.2.3 Design Fires and Fire Scenarios 

A design fire is defined to be a time-temperature curve of the gases in one or more compartments 

and possibly on multiple floors and a fire scenario describes all the conditions required for a 

particular fire event. A time-temperature curve, or fire exposure curve, is the quantitative 

measure of the fire scenario and its supporting conditions. 

Factors that affect fire development include the following conditions: 

• Compartment size

• Furnishings and contents 

• Fuel properties 

• Ignition sources 

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• Ventilation conditions 

• First item ignited and its location

A large number of design fire scenarios may be possible. A set of credible fire scenarios should 

be selected to represent the fire hazard. Resources from SFPE (2007), ICC (2006), and NFPA 

(2006) can provide guidance, information, and methodologies for developing fire design 

scenarios.

6.2.4 Predictive Methods for Fire Modeling

There are three approaches to generating time-temperature data for analysis: 

1. Time equivalence methods that use standard fire data in combination with compartment 

features. 

2. Fire exposure curves and/or parametric equations based on experimental data of realistic 

fire conditions, as described in Section 2.5.2 and shown in Fig. 3.2. 

3. Computer analysis of fire scenarios 

6.2.4.1 Time Equivalence Methods

Time equivalence methods allow designers to use standard fire exposures as a basis for 

qualifying fire protection products and systems under prescriptive building code approaches, as 

discussed in Section 2.5.2. Time equivalents are determined by adjusting time-temperature data 

for compartment fires to determine the duration in the standard test that would have the same 

heating effect as a compartment fire. 

As with the standard fire test, time equivalent methods only consider individual elements or 

subsystems; structural system behavior cannot be addressed with this approach. Time 

equivalence methods are suitable for compartments with similar dimensions for width and 

length; long, narrow compartments are not satisfactorily correlated by these methods (Law 

1997). 

6.2.4.2 Fire Exposure Curves and Parametric Equations

For most performance-based designs, fire exposure curves or parametric equations are 

satisfactory approximations of actual fire conditions that occur in a building. Most fire exposure 

curves and parametric equations approximate temperatures in fully developed fires as uniform 

throughout the compartment (the one-zone model). Buchanan (2001) and SFPE (2004) describe 

the underlying assumptions for and applicability of many of the available fire exposure curves. 

Fire exposure curves and equations have been developed to account for the effects of the 

following parameters:

• Fuel load (unit weight) 

• Area and height of ventilation areas

• Enclosure geometry (width, depth, height, and total surface area of enclosure)

• Thermal properties of compartment construction materials and furnishings 

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The amount of ventilation in a compartment is often described by the ventilation factor (or 

opening factor) Fv: 

t

VV

V A

HA

F = (m-1/2) (6.1) 

Where:

 AV = Area of openings

 At = Total surface area of the compartment

 HV = Height of openings 

In some compartments, the assumption of uniform temperatures does not hold. Compartment 

geometry and the distribution of ventilation sources can cause the fire to burn preferentially close 

to sources of ventilation, and for the fire to move away from the ventilation opening(s) only as 

the fuel is consumed. Nevertheless, some models can reasonably predict fire conditions in 

compartments where preferential burning occurs (SFPE 2004, McGrattan 2002). 

Compartment fires where the ventilation factor changes over time are difficult to analyze using 

available curves and equations. None of these references accounts directly for window breakage 

or partition failure. Designers using these references often overcome this limitation by selecting

ventilation characteristics that yield an upper bound fire exposure. This process may involve 

investigating several realistic estimates of ventilation factors, since both peak temperature and 

fire duration are affected by ventilation.

Law’s method (1983), which estimates the maximum gas temperature, is appropriate for all 

roughly cubic compartments (height to width ratio between 0.5 and 2.0) and for long, narrow 

compartments with a ventilation factor, Fv, greater than 0.56 m1⁄2 created by openings on only one 

of the shorter sides. 

Law’s method does not predict temperatures during the decay phase. To account for the fire 

decay phase while using Law’s method, designers often assume a decay rate of 7 °C/min for fires 

with predicted durations of 60 minutes or more, or 10 °C/min if the predicted duration is less 

than 60 min. 

The Magnusson and Thelandersson method and the Lie method can be used for long, narrow, 

under-ventilated compartments with openings on one of the shorter sides. The Magnusson and 

Thelandersson method is appropriate for 1/Fv in the range of 45 m-1⁄2 to 85 m-1⁄2, the Lie method is 

appropriate when 1/ Fv is approximately 345 m-1⁄2. 

6.2.4.3 Fire Modeling with Computer Programs

Three classes of fire models have been programmed for computer analyses of gas temperatures 

in a room or compartment.. 

1. Empirical models are based on correlations with full-scale fire experiments. 

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2. "Zone" models treat the compartment as either one or two homogeneous volumes in 

which conservation of mass, momentum, and energy are computed in a dynamic process. 

3. "Field" models are based on computational fluid dynamics (CFD). Field models use a 

three-dimensional grid to model the changes in gas and surface temperatures over the 

room volume. 

Some of these models analyze for a user-specified heat release rate; some predict the heat release 

rate based on user-specified material properties of the combustibles. All three classes of fire 

models address fully developed fires. The choice of model depends on the reliability of fuel and 

thermal property data and the desired degree of accuracy. 

For compartments with size, aspect ratio, and contents that are comparable to those used for fullscale experiments, the empirical models are appropriate tools. 

Zone models are appropriate for a well-stirred combustion chamber. Some zone models, such as 

COMPF2 (Babrauskas 1979), were designed specifically to model fully developed fires. Others 

are more general and used primarily to model smoke and heat movement through structures. 

These models have been applied with mixed success to the prediction of fully developed

conditions (Luo, He, Beck 1997 and Buchanan 2001). 

Field models can reproduce flashover conditions (NIST 2005f), but the degree of accuracy 

depends on the quality of the input data. Validation studies (e.g., US NRC 2007) have been 

performed to quantify the accuracy of the various types of models. The designer should review 

the documentation for the individual fire model for references to validation work to judge if the 

model is appropriate for the task at hand. 

 

An international survey of available computer programs for zone and field model that predict fire 

and smoke growth and spread can be found in Olenick and Carpenter (2003). 

6.2.4.4 Selecting a Predictive Method for Fire Modeling

The steps involved in selecting the appropriate fire exposure curve follow from the selection of 

the design fire. The designer establishes realistic fire loads and ventilation factors. In some 

cases, effects of compartment size and wall lining materials can be evaluated and introduced into 

the selection process. These considerations often lead directly to the selection of the appropriate 

fire exposure curve.

The challenge for engineers is to ensure that the fire exposure curves are reasonably conservative

(i.e., do not underestimate temperatures or durations) and that the design fire scenarios are 

consistent with the performance objectives for the building. While much attention has been 

focused on computer modeling in recent years, fire exposure curves and parametric equations are 

still representative of the state of the art for estimating fire exposure curves for fully developed 

enclosure fires. SFPE (2004) provides guidance on selecting methods that will provide bounding 

predictions. 

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6.3 HEAT TRANSFER ANALYSIS 

Heat transfer analyses provide estimates of structural component temperatures as a function of 

time and location in a compartment. 

6.3.1 Heat Transfer Mechanisms

Heat is transferred to the structure from the compartment gases and soot through radiation and 

convection. The rate of heat transfer by each mechanism can change during the course of a fire.

The surface temperature of an object exposed to a fire can be (1) assumed equal to the gas 

temperature, or (2) estimated from radiative and convective heat transfer analyses. With the first 

approach, the temperature history of the object is determined by calculating the conductive heat 

transfer through its layers of material (e.g., the insulation and steel section of an enclosed 

column). This approach is relatively simple to apply. However, this simple estimation is 

unlikely to provide bases to evaluate transient stress states since the rates at which components 

of composite elements heat also depend on the section surface areas and masses, factors not

considered in the approach. 

The second approach generally yields higher fidelity. Following is a brief introduction to

radiative and convective heat transfer analysis. SFPE (2002, pp. 1-1 to 1-89) and any number of 

engineering text books (Incropera and DeWitt 2002) provide more thorough explanations. 

Thermal radiation often dominates heat transfer from a fire to the solid surfaces of a 

compartment. The radiative heat transfer is proportional to the difference in the effective 

temperatures of the fire and the surface to the 4th power. If the fire and the surface are assumed to 

be perfect (or black body) absorbers and emitters of radiation (an approximation that is 

surprisingly reasonable), the steady-state rate of heat transferred from the fire to the surface by 

radiation, Qr (W), can be approximated by:

Qr = F2-1 σ A2 (T1

4

 – T2

4

) 

where:

F2-1 Radiative view factor between the surface and the fire

σ Stefan-Boltzmann constant (5.669 ·10-8 W/m2 K4) 

A2 area of the surface receiving heat from the fire (m2) 

T1 effective temperature of the fire ( K)

T2 average temperature of the surface (K) 

The absorptivity, α, of a real surface is the fraction of the heat absorbed when compared to a 

perfect surface. In fires, the absorptivity is about equal to its emissivity, ε, and varies with the 

amount of soot in the flame. Since it is common during fires for soot to increase in concentration 

and to deposit on the exposed surfaces of the structure, thereby increasing the emissivity of both 

the fire and the surfaces, the rate of heat transferred by thermal radiation changes. 

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The radiation view factor accounts for the geometry of the fire and of the surface’ It is a measure 

of the fraction of energy leaving the surface that is exposed to the fire. For example, objects’ 

surfaces directly facing a fire may “see” the entire fire volume and be heated intensely by 

radiation. However, the back side of exposed objects is shielded and may not receive any heat 

directly from the fire. Even so, the shielded sides of exposed objects may be heated by radiation 

from other surfaces, by the hot smoke layer some distance from the fire source, or by convective 

heat transfer. 

Radiation heat transfer can be complex, and the simplified calculations suggested above, while 

generally more accurate than estimating objects’ temperatures solely from gas temperatures, still 

might not yield high accuracy for complicated exposures. 

Convective heat transfer is always present in a structure fire, but it increases in importance 

relative to radiative heat transfer as the temperature of the environment decreases. The simplest 

approach to estimating the heat transfer from a gas to a surface due to convection, Qc, is with the 

following expression: 

Qc = h As (Ts – Tf) 

 

where:

h convective heat transfer coefficient (W/m

2

⋅°C) 

As area of the surface exposed to the gas (m2 ) 

Ts temperature of the surface (°C) 

Tf temperature of the gas (°C) 

The convective heat transfer coefficient is a complex function of the gas velocity, the gas 

properties, and the gas and surface temperatures. The value for h is generally found to lie 

between 10 W/m2-°C and 30 W/m2-°C (SFPE 2004). 

The convective and radiative components are normally additive, and provide the boundary 

condition for the conduction analysis. The initial temperature, thermal properties, and geometry 

of the structural components must be specified to determine the temperature, T, everywhere in 

the structure using the following general equation: 

∂2T + ∂2T + ∂2T = ρc ∂T

∂x2 ∂y

2

 ∂z

2

 k ∂t 

where:

T temperature in the structure (°C) 

x, y, z defines the position in the structure (m) 

t time (s)

k structural material thermal conductivity (W/m-°C) 

c specific heat of the structural material (J/kg-°C) 

ρ density of the structural material (kg/m3

) 

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If the heat transfer into the structure is primarily one dimensional and the thermal conductivity is 

constant, then, under steady-state conditions, the convective and radiative components of heat 

transfer are balanced by the conduction normal to the surface, and the above equation reduces to 

 -k dT = Qc + Q

6.3.2 Heat Transfer Analysis Methods

r 

 dx A 

where A is the area of the surface.

The heat transferred to the structure will continue as long as the temperature of the gas is higher 

than the temperature of the surface. Once the fire burns itself out, heat transfer by surface 

radiation and convection will cool the structure. 

Heat transfer analyses can range from simple one-dimensional (or lumped mass) equations such 

as those suggested in section 6.3.2 to analyses with finite element software, depending on the 

complexity of the geometry and heat flow. While some of the most rudimentary analyses 

(principally, one-dimensional analyses) can be performed by hand, practical and efficient 

analyses normally require computer-based solutions. Two- and three-dimensional heat transfer 

analyses are sufficiently complex problems, particularly when heat flows through different 

materials with dissimilar thermal properties, that they require computer-based solutions. Finite 

element software can represent the salient characteristics of materials of construction and 

insulation, including the effects of air gaps and the various modes of heat transfer (radiation, 

convection, and conduction) in complicated geometries. 

Finite element analyses use solid elements for heat transfer analysis. Temperature dependent 

thermal, strength, and stiffness properties of steel, concrete, and fire protection materials are 

given in the following sources. Chapter 4 gives concrete properties. Chapter 5 and Harmathy 

(1983) give steel and fire protection material properties. Temperature dependent properties of 

structural steels can also be found in NIST 2005b. NIST 2005d has temperature dependent 

properties of the passive fire protection used in the WTC towers, and NIST 2005e has 

temperature dependent data for concrete. 

For compartment fires, an emissivity of 1.0 and a convective heat transfer coefficient of 30 

W/m2

⋅°C can be conservatively assumed, though the value may range between 10 W/m2⋅°C and

30 W/m2

⋅°C (SFPE 2004). 

6.3.3 Temperature Data for Structural Analysis

A heat transfer analysis will produce temperature profiles that may vary across the sections and 

along the lengths of components. This information usually needs to be converted to input for 

structural analyses software. Since, the capabilities of various software differ and designers 

might decide to analyze to levels of precision that allow approximations, the component 

temperature data need to be reduced to be compatible with the structural response analysis 

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program and the goals of the designer. For instance, the designer might need to approximate 

non-linear temperature profiles as linear if the analysis program can not receive as input nonlinear profiles between nodes along the length or across the member section. 

The temperature histories from the heat transfer analysis should be reviewed before selecting a 

time interval for the structural analysis input of temperature data. For example, a 120 min fire 

scenario may produce relatively rapid heating in the first 30 min to 60 min, followed by cooling

at a slower rate. The time interval for the analysis of the heating portion of the time-temperature 

relationship should capture the temperature rise through linear interpolation between data points

(NIST 2005e). The same time interval could be used for the more gradual temperature changes 

typically associated with cooling, or the time interval could be increased if the time-temperature 

curve can be adequately simulated with large time increments. 

6.4 ANALYTICAL APPROACHES FOR FIRE-RESISTANT DESIGN

6.4.1 Prescriptive Building Code Requirements 

Building codes specify fire-resistance rating requirements (in terms of hours) for performance of 

building components under exposure to the standard fire. Fire ratings are usually determined by 

testing (e.g., following ASTM E 119). Catalogues of components with specified construction 

details and their approved fire rating are available for selecting an appropriate protection 

configuration that is consistent with the architecture and goals of the project. When this 

approach is used, designers need to consider connections between rated structural components. 

For instance, if columns have a required 3 hour rating, and floor beams and girders have a 

required 2 hour rating, the design may specify that the connections be protected according to the 

higher rating (i.e., match the column level of protection). 

The standard fire approach gives relative levels of protection required for overall building 

performance. By verifying structural component performance in accordance with standard fires, 

manufacturers of fire protection products are certifying their products according to a common 

standard. Performance of components and the structural system during actual fires requires a 

comparison between actual conditions and conditions during standard fire tests. Codification of 

performance levels based on exposures to standard fires does not necessarily ensure that the 

structural system will, indeed, be able to sustain the effects of a real fire for the duration implied 

by the rating.

6.4.2 Standardized Analytical Approaches

For designs where pre-qualified details based on standard fire testing are not available, analytical 

approaches for determining fire resistance of many common structural systems are available in 

reference documents such as Standard Calculation Methods for Structural Fire Protection

(ASCE/SEI/SFPE 29-99 1999) and Standard Method for Determining Fire Resistance of 

Concrete and Masonry Construction Assemblies (ACI 216.1-97/TMS 0216.1-97 1997). These 

standard methods provide procedures for determining fire resistance to standard ASTM E 119 

fires, in terms of hours, before reaching defined endpoint criteria for common structural 

components and type of fire protection. 

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Both ASCE/SEI/SFPE 29-99 and ACI 216.1-97/TMS 0216.1-97 present design information and 

methods for computing a fire resistance rating for geometries for which there is no rating 

established by test, and determining an appropriate thickness of insulating materials. These 

references guide designers on the selection of sprayed fire protection, concrete cover thickness, 

enclosures of gypsum products, enclosures with masonry or concrete, and other means to add fire 

resistance to steel components. These references also provide guidance for detailing connections 

and gaps between components to minimize the potential for fire spread. 

Both ASCE/SEI/SFPE 29-99 and ACI 216.1-97/TMS 0216.1-97 provide means to quantify the 

minimum thickness of concrete for a component to meet required fire resistance ratings. For 

instance, methods are given for determining the effective thickness of tapered webs in concrete 

components and the effective thickness of hollow core panels. These methods and others

establish a consistent approach for determining a fire resistance rating of untested configurations 

that are similar to configurations with fire resistance ratings established by ASTM E119 tests. 

ASCE/SEI/SFPE 29-99 also provides guidance on fire resistance calculations for steel, wood, 

and masonry. For steel sections, it specifies how to calculate geometric parameters such as 

“heated perimeter” and “section factor” of rolled steel sections as a function of flange width, 

depth, and web thickness for a number of configurations. The section factor is expressed in 

several ways, but it is essentially the ratio of the heated surface area to the mass (volume). The 

Manual of Steel Construction for Load and Resistance Factor Design (AISC 2001) has tables that 

list the section factor ratio as the weight per foot divided by the section perimeter for 4 cases: 3 

sides of a steel beam (one flange protected from heat exposure), 4 sides of a steel beam, 3 sides 

of a box perimeter for a steel beam in an enclosure (one flange protected from heat exposure), 

and 4 sides of a box perimeter for a steel beam in an enclosure. 

Prescribed definitions of geometric parameters allow users to access charts, graphs, and tables in 

which fire resistance parameters are presented. For instance, ACI 216.1-97/TMS 0216.1-97 lists 

minimum equivalent thicknesses of concrete walls to achieve specific fire resistance ratings as a 

function of concrete aggregate type. These ASCE and ACI references also prescribe minimum 

cover over reinforcing steel and prestressing steel in concrete beams, and other factors that 

determine fire resistance, to achieve specific resistance ratings relative to the standard fire 

resistance requirements specified in building codes. 

The methods discussed above have the limitation that only the performance of individual 

components is considered. Structural system performance at elevated temperatures is not 

addressed. 

6.4.3 Computational Analytical Approaches

To determine the structural system response or the structural behavior of components and 

subsystems to design fires, one or more of the following analyses can be conducted to provide 

the required data: 

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• Fire modeling with hand calculations, parametric equations, or computer programs to 

develop fire exposure curves (e.g., gas temperature vs. time curves) for design fire 

scenarios.

• Heat transfer analyses to compute temperature histories of structural components. 

• Structural analysis with service gravity loads and elevated temperature histories to 

determine deformations and stresses due to thermal expansion, reduced stiffness and 

strength, and plastic and creep strains. 

Computer programs for fire modeling will give gas temperature-time histories, which are needed

as input data for heat transfer analyses to determine temperature profiles through component 

cross sections. With some software packages, component stresses and deformations can be 

evaluated simultaneously with the determination of temperatures; with others, temperature 

profiles are computed separately and then provided as input for structural analyses. Chapters 4 

and 5 listed a number of computer programs that can analyze concrete and steel structures. 

Typically, if a finite element analysis package offers an option to solve heat transfer and 

structural response in a single analysis, it uses solid elements. While some software have 

features that partially automate the analyses for certain mechanical systems, such as engines or 

radiators, such conveniences generally do not exist for beam and shell elements normally 

needed for structural analyses. The analyst must first conduct a heat transfer analysis with solid 

elements and then translate equivalent temperatures to the nodes of beam and shell elements for 

the structural analysis.

6.4.4 Selecting an Approach

Standard fire, time equivalence, and fire exposure curves and parametric equations are used for 

designing fire resistance for most typical structures. A performance based approach should be 

used when building stakeholders (owners, insurers, regulators, etc.) wish to understand how the 

building will actually perform in fire or wish to minimize risks through structural fire resistant 

design. If a performance based design approach uses analytical procedures instead of standard 

fire testing or approved analytical approaches, the design team should involve the building code 

officials early in the process to determine what the building officials will require for approval of 

the design. 

Recommendation 28 of the NIST investigation of the World Trade Center collapse suggested 

that appropriate design professionals (fire protection engineers and structural engineers) provide 

the standard of care when designing structures to resist fires in buildings that employ “innovative 

structural and fire safety systems” (NIST 2005a). This suggests that methods that consider the 

actual response of the structure to fire (i.e., performance based approaches) be used in buildings 

with innovative structural systems. 

6.5 FIRE RESISTANT DESIGN CONSIDERATIONS

Fire safety is provided in a building by a combination of active fire suppression and passive fire 

protection. Active fire suppression includes firefighting and automatic devices, such as 

sprinklers, to control the spread of fire. Passive fire protection includes measures, such as fire 

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barriers, that control the spread of fire or insulations, such as concrete cover and spray-applied 

fire protection that delay the effects of fire on the structure. These guidelines address the fire 

resistance provided by passive fire protection measures that prevent structural collapse in fire. 

The following approaches can enhance fire resistance in buildings: 

• Control fuel quantity and locations. 

• Control fire spread. 

• Control ventilation characteristics. 

• Protect construction materials.

6.5.1 Fuel Control

Designers usually have limited control over the fuels that are built into or brought into buildings. 

In large measure, the occupancy determines the fuel load inside buildings since much of the fuel 

in buildings is derived from its contents. 

On the other hand, designers, working with their clients, can make certain fuel-related decisions 

that can impact fire severity. Owners and their consultants should consider carefully the fuel 

load associated floor, wall, and ceiling finishes to minimize the avoidable potential for fires to 

ignite, spread, and grow. 

For instance, ceramic floor tile and concrete-based floor finishes add no fuel to a building, and 

they have the added advantage of providing thermal inertia that absorbs heat and reduces fire 

severity. Painted plasterboard walls over metal studs contribute less fuel to a fire than do wood 

finishes and many manufactured cubicle partition systems. Similarly, plasterboard ceilings 

constitute lower fuel load (and better fire barriers) than do certain ceiling tiles.

Owners and their consultants can often control decisions about locations of fuels for power 

sources. To the extent that such fuels are needed for heating, air conditioning, backup power, or 

other purposes, options for placement and isolation within facilities and associated risks should 

be reviewed. 

6.5.2 Control of Fire Spread

Effective compartmentation of interior spaces can limit fire spread by creating barriers among 

spaces. Features of effective compartmentation include fire-rated partitions and proper 

protection of penetrations through these partitions. Fire-rated partitions prevent the passage of 

flames, hot gases, and heat transmission to the unexposed side of the barrier. This is typically 

accomplished by having the barrier extend from floor slab to floor slab, particularly if non-fire 

rated ceiling tiles are used in the facility. 

Additionally, architectural and functional features can effectively impact the potential for fires to 

spread. For instance, window size, orientation, and spacing from floor to floor can contribute to 

the fire intensity by influencing how easily fire spreads from one floor to another. Tall windows, 

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closely spaced from floor to floor, in general are more likely to contribute to vertical spread than 

are smaller windows with deep spandrel panels in between. 

6.5.3 Ventilation Control

Because ventilation affects the temperature and duration of compartment fires, selection of 

ventilation characteristics can be used as part of a design strategy. Most predictive methods use 

the “ventilation factor” (see 6.2.1.3), the area of the ventilation opening multiplied by the square 

root of its height, as input. Judicious selection of opening geometry can be used to reduce fire 

severity in a compartment.

6.5.4 Fire Resistance and Protection of Construction Materials

Most materials of construction require insulation to achieve resistances that are commensurate 

with performance requirements in building codes. The amount of protection that designers must 

provide depends on the inherent resistance of the construction materials, geometry of structural 

components, function in the structural system, and performance objectives for the building. 

Fire protection for structural components is accomplished by some form of insulation, usually as 

applied coatings, encasement of components, and enclosures around components that separates 

the structural component from the fire environment. 

Some protection products and systems maintain a barrier to the transmission of heat by their 

static structure and form (e.g., enclosing steel columns in a fire-rated enclosure). Other 

protection means dissipate heat energy by physical or chemical transformations. Physical 

transformations include release of entrapped moisture (e.g., heat of hydration for bound water in 

spray applied insulation). Chemical transformations include endothermic decomposition and 

heat-induced expansion to create insulation layers (e.g., intumescent coatings). Examples of 

these products and system types are discussed in Section 5.1.2. 

The selection of materials for critical structural components will have a direct impact on 

strategies for providing fire resistance. For example, reinforced concrete components with 

appropriate detailing can sustain the effects of fire temperatures for relatively long periods if they 

have an adequate concrete cover over the steel reinforcement (see Sections 4.3.1 and 4.4.3). The 

concrete cover over the steel reinforcement acts as insulation, and delays temperature rise in the 

steel reinforcement if it does not spall or crack during the fire event. The dimensions and the 

thermal conductivity of concrete components may be designed so that substantial time is 

required for the temperature of the steel reinforcement to rise to damaging levels. 

Brick and concrete masonry components are similar in behavior to concrete components: they 

are relatively large in dimension and tend to insulate any embedded reinforcing steel.

Steel structural components subject to fire exposure generally need protective insulating layers 

such as spray applied insulation, enclosures, or concrete coatings for fire protection. This is 

particularly true for lightweight steel systems such as cold-formed steel components and 

fabricated components such as steel joists, which have large surface-area-to-volume ratios. 

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Some building codes place criteria (i.e., allowable building height and floor area) on buildings as 

a function of occupancy, combustibility of materials of construction, and levels of protection. In 

those circumstances, the occupancy and size of a building can affect the suitability of certain 

materials of construction. 

6.6 FIRE-RESISTANT DESIGN OF CONCRETE STRUCTURES

This section discusses design practices for common types of concrete construction and the 

response of reinforced concrete structural components under exposure to fire, with an emphasis 

on concrete floor systems. Refer to Buchanan (2001) for worked examples of concrete 

component designs for fire exposure. 

6.6.1 Concrete Floor Beams

A reinforced concrete beam supporting a concrete floor will have positive moment steel 

positioned near the bottom of the beam at midspan. The top of the beam usually is integral with 

the concrete slab and is, therefore, substantially isolated from exposure to high temperatures 

from a fire below. Since conventional flexural design of beams neglects the concrete below the 

neutral axis, loss in strength in this portion of the concrete component does not have a significant 

impact on load-carrying capacity. The integrity of the steel reinforcement in this region, on the 

other hand, is critical. The concrete cover over the steel reinforcement acts as an insulator. 

Thus, when a concrete beam is exposed to fire, the temperature increases rapidly at the section 

surfaces but more slowly at the interior. The temperature profile across the section drops 

substantially within a short distance from the exposed surface, resulting in a highly nonlinear 

temperature profile. Since concrete has a relatively large heat capacity and density, there can be 

a significant time lag before the temperature of the steel reinforcement increases. Hence, the 

temperature of the steel reinforcement lags the concrete surface temperature. 

During initial phases of a serious fire, the concrete cover normally will remain intact, providing 

insulation to the steel reinforcement. However, high temperatures weaken concrete, produce 

high stresses due to thermal expansion, and generate vapor pressures within the concrete which 

may cause spalling (see 4.4.5). 

If the concrete cover over the reinforcing steel spalls during the progression of a fire, the steel is 

exposed directly to the fire environment. Without insulation, the steel heats rapidly, with a 

corresponding reduction in strength and stiffness. Even if the concrete does not spall, the 

temperature of the steel reinforcement may rise if there is sufficient fire duration (ACI 216.1 

1997). 

6.6.2 Untested Concrete Component Capacity in Design Fires

When a specific design is not addressed by standard fire test results, and when informed 

judgment will not allow designers to adapt test results, designers need to conduct analyses to 

validate fire resistance designs. These analyses can follow two paths: 

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1. Rely on published charts that show the theoretical temperature at depth into concrete 

components as a function of duration in standard exposure fires (Section 4.3.1). 

2. Conduct heat transfer analyses to determine internal temperature increases as a 

function of time. 

Standard fire exposure charts can be adapted to show approximate theoretical temperatures 

inside concrete components during realistic fires. Some rules for determining direct relations are 

available (Section 4.3.2), and designers can rely on fire conversion formulas (Section 2.5.4) that 

give equivalent standard fire exposure times for realistic fires when fire load, ventilation, and 

compartment surface materials are known. Heat transfer analyses are useful when standard 

exposure curves cannot be used and when conversions from realistic fire exposures to standard 

fire exposures are impractical or insufficiently accurate.

With either approach, the goal is to determine the temperature of the steel reinforcement due to 

the fire exposure, and to find the conditions and durations at which the load carrying capacity of 

the concrete component has been reduced so that it no longer supports the design service load. 

The design service load for analysis of fire effects is usually taken as the “point-in-time” load 

rather than the full load when such loads control for non-fire conditions, which may be taken as

1.2 DL + 0.5 LL (see Table 2.1). 

6.6.3 Restraint of Continuous Concrete Floors

Continuous concrete floors may not fail when the positive moment flexural steel at midspan has 

inadequate strength for the design service loads. Plastic hinges need to form at the support 

points in addition to the midspan before a failure mechanism is created. In concrete structures 

with continuous beams, the steel reinforcement for negative moment resistance is embedded in 

the slab near the top of the beam, and is likely to be relatively protected from the heat in the fire 

compartment. Hence, formation of negative moment hinges due to reduction in steel 

reinforcement capacity usually trails the formation of positive moment hinges. 

6.6.4 Thermal Expansion Effects

Fully developed fires in a compartment generate intense heat in the compartment. However, 

adjacent compartments are usually not significantly heated. As the fire spreads in a building, 

new areas sequentially become hot as the fire intensifies locally while an area of previously 

intense fire begins to cool. 

In a fire environment, forces generated by restraining thermal expansion may have additional 

effects on component and system survivability. Differences in temperatures of structural 

components within a structural system may create restraining forces that affect the load-carrying 

capacity in structural components. For instance, when a fire first begins to heat structural 

components, those components will expand and push against adjacent structure. If there is 

continuity within the structural system and adequate strength in the surrounding structural 

components to resist forces due to thermal expansion, the heated components may develop 

significant compressive forces. 

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In reinforced concrete floor beams, thermally induced compression can initially counteract the 

effects of reduced strength in steel reinforcement due to heating. As the steel tensile strength is 

being reduced, thermal expansion effects are generating compressive forces and reducing the 

demand on the steel reinforcement, prolonging the load-carrying life of the beam. However, 

thermally induced compressive forces along the beam length may also generate P-Δ moments at 

the center of the beam, which would increase demand on the steel reinforcement. 

6.6.5 Reinforced Concrete Floor Sagging

As steel reinforcement temperatures increase, steel stiffness and strength will reduce and floor 

beams will begin to sag. This deformation could signal failure to contain the fire in the 

compartment if the floor sagging is sufficient to cause a breach in the fire barrier (e.g., a gap or 

opening between the floor and the walls). However, large deformations do not necessarily mean 

that beams have failed to perform adequately in a fire, particularly if the performance goal is 

prevention of collapse. 

In structural systems with adequate continuity, large deformations and a significant loss of 

stiffness can generate tensile forces in the floor beams. Once deflections become large, the 

weakened reinforcing steel usually has adequate strength to support the applied loads with the 

beam acting primarily as a tension member. For this mechanism to develop, splices in the 

reinforcing steel need to function, and there must be sufficient continuity and strength in the 

beam detailing and in the structural system around the bay with large deformations to support the 

tensile reactions generated at the ends of the beam.

6.6.6 Cooling Phase Effects

Assuming that heated beams do not collapse during the fully developed phase of a fire, they may

develop significant additional forces during the cooling phase. Surviving components that 

previously expanded and sagged under the influence of heat will begin to cool and contract. This 

contraction pulls inward on the adjacent structure, particularly if components were deformed

during the fire event. Floor beams with thermally induced compressive loads that were sufficient 

to cause plastic strains to develop may experience tension as contraction during cooling reduces, 

and possible reverses, the compressive forces on adjacent components. 

During a fire event, the sequence of reinforcing steel yielding, concrete weakening and spalling, 

midspan and end supports undergoing large rotations, floor beams developing compressive and 

tensile forces may cause stresses that exceed the level normally expected in concrete 

components, particularly for steel reinforcement details at connections. 

6.6.7 Design of Reinforced Concrete Components

Conventional design of reinforced concrete components usually does not consider the loadcarrying capacity after flexural failure. For unrestrained, determinate components, failure 

usually is assumed when the first plastic hinge forms. For continuous beams, approaches for 

determining the benefits gained by compression while restraining component expansion (when 

connections and the surrounding structure can sustain the forces associated with restraint of 

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expansion) and by redistribution of moments that occurs as hinges form are presented in Chapter 

4. 

When analyses show that the strength of reinforced concrete cannot provide adequate resistance 

to the effects of fire, within the limitations of other design constraints, the designers have two 

principal options: change the configuration of the components or apply methods to modify the 

design-basis fire.

Configuration changes can take the following forms: 

• Add restraint. 

• Add continuity. 

• Increase concrete cover over reinforcing steel.

• Increase the area of reinforcing steel. 

Each of these options adds resistance at a cost. The designer needs to anticipate cost, together 

with other goals of the design, when selecting the best method or combination of methods. 

Normally, the addition of restraint and continuity to systems is costly and potentially disruptive 

to the intended behavior of structural systems and may affect space usage. Enhancement of 

concrete cover can usually be accomplished at a modest cost, with the benefit of additional 

insulation provided for the steel reinforcement. Introduction of additional reinforcing steel 

(beyond that required for design loads under ambient conditions) to provide reserve moment 

capacity also can be accomplished at a modest cost. Steel reinforcement can often be increased 

in diameter or added without changing the profile of reinforced concrete components. 

When changes in the design of components does not emerge as the preferred approach to adding 

fire resistance, the performance of reinforced concrete components can be enhanced with many 

of the same fire protection methods that are available for structural components of other 

construction materials: concrete components can be insulated from the harsh fire temperatures. 

To evaluate these methods, the designer will need to refer to qualifying fire tests or pursue heat 

transfer and structural response analyses to evaluate the effectiveness of various protection 

methods. 

6.7 FIRE-RESISTANT DESIGN OF STEEL STRUCTURES

This section discusses design practices for common types of steel construction and the response 

of steel structural components and composite floor systems under exposure to fire. Refer to 

Buchanan (2001) for worked examples of steel component designs for fire exposure. 

6.7.1 Steel Behavior at Elevated Temperatures

As discussed in Chapter 5, unprotected steel components are sensitive to the effects of fire. The 

relatively high thermal conductivity of steel (at least 27.3 W/m2

K as compared to approximately 

1.3 W/m2

K for normal weight concrete) and generally thin proportions of steel components make 

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unprotected steel structures susceptible to rapid heating when exposed to fires. For this reason, 

steel components in structures usually require passive fire protection. 

When structural steel component temperatures exceed 400 °C, the yield strength and modulus of 

elasticity begin to decrease (Milke 2002, NIST 2005b). As temperatures increase in a steel 

section, its yield strength and elastic modulus decrease. When the yield strength is reduced to the 

applied stress level, the steel section will begin to yield (i.e., deform under plastic strains and, 

possibly, creep strains). At the same time, reduced stiffness will increase deflections.

6.7.2 Composite Floor Behavior at Elevated Temperatures

Heating of a composite floor initially causes thermal expansion, which in turn, subjects the floor 

section and adjacent framing to compressive loads. If a steel beam acts compositely with a 

concrete slab, the most highly stressed element of the steel beam is typically the bottom flange. If

the bottom flange yields as steel temperatures increase, the neutral axis shifts upward. Since thin 

webs make only minor contributions to moment resistance, yielding of the bottom flange can 

result in rapid and significant loss of moment capacity as the cross section yielding progresses 

rapidly upward through the web. 

If a composite section is heated sufficiently, large deformations and sagging may occur. The 

temperature gradients in the steel beam and slab will induce thermal bowing, where the floor 

section will bow downward to relieve the differential thermal expansion. The connections and 

surrounding framing will be subject to compressive loads from thermal expansion. 

Consider a section of the composite floor that includes a beam and tributary area of the slab, with 

a protected beam (i.e., insulated with passive fire protection). If the floor section is heated from 

fires below, typically the bottom flange will have the highest temperatures, as it heats first, with 

a temperature gradient through the web to the top flange. The top flange will be considerably 

cooler (often by several hundred degrees), due to contact with the thermal mass of the slab, 

which acts as a heat sink. If the bottom flange temperatures reduce the yield strength to equal

the applied loads, the composite section will develop plastic strains at the point of highest load, 

which is often near the midspan of simply supported floors. If the plastic strains result in a 

plastic hinge forming at the highly loaded section, the floor may ‘hang’ between supports. If the 

sagging increases to the point that the composite floor is supporting its loads through tensile 

loads at its connections, then the floor section is often described as being supported through 

catenary action. The top flange and steel reinforcement of the slab will attempt to carry the 

tensile stresses, if the remaining capacity is greater than the supported loads.

Six fire tests of an 8-story steel framed structure with composite floors was carried out by a 

research team at the Building Research Establishment (BRE) in Cardington, Bedfordshire to: (1) 

gain understanding of the natural fire resistance of such structures, (2) correlate data and 

observations with predictive numerical models, and (3) establish a more rational design 

methodology for steel framed building response to fire (British Steel 1999). There are a number 

of reports and papers written that summarize the test data, observations, and numerical analysis 

of the tests. British Steel (1999) and O’Connor (2003) are given as summary papers. 

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6.7.3 Design of Composite Floor Section

The design of steel components for fire exposure is usually based on the assumption that positive 

and negative moments are limited to the plastic moment, which is based on a reduced yield 

strength and stiffness based on the maximum temperature estimates. 

The flexural capacity of a composite floor section is determined by calculation of the plastic 

moment across the steel beam and slab section for the estimated maximum temperature that the 

steel beam components will reach due to the design fires. When determining the flexural 

capacity for a thermal condition, one should also consider the possible reduction in the stiffness 

and strength of the concrete and whether the concrete can support the compressive load (meaning 

that a hinge has not formed and the beam still has some flexural capacity) or if the concrete will 

crush (signaling the limit of flexural capacity).

Steel beams connections can be designed to carry increased tensile loads for the condition where 

hinges develop in a composite floor section and cause tensile loads at the supports. Large 

deformations associated with loss of stiffness and flexural yielding can allow the full cross 

section of steel beams to act as tensile elements as long as the connections can sustain the 

substantial deformations associated with large hinge rotations and the surrounding structure can

support the forces induced by tension in the beam.

It is not common to design for loss of flexural capacity. However, conventional design does 

allow full redistribution of moment between the positive and negative moment regions to 

account for the formation of full hinges at these locations. For steel components to develop full 

plastic hinges they must be adequately braced at hinge locations to undergo the associated 

rotations. In addition, the designer must consider the integrity of the bracing element; it must 

also be designed with consideration for the effects of temperature on its strength and stiffness.

6.7.4 Passive Fire Protection for Steel Components

Common methods to protect steel components from the effects of fire include spray-on fire 

resistive materials (SFRM), intumescent coatings, and enclosures of gypsum board, mineral 

fiberboard, concrete, masonry, or similar materials (Section 5.1.2, Milke 2002). Each of these 

protection systems provides its insulating function through one or more mechanisms: low 

thermal conductivity, high heat capacity, heat-absorbing reactions, or formation of insulation 

layers through expansion. 

Each protection system has its set of advantages regarding cost, aesthetics, weight, and ease of 

installation. The systems with perhaps the longest history of use generally are relatively easy to 

install by trade personnel. Systems, such as enclosures with gypsum or mineral fiberboard 

products, are easy to install and relatively lightweight. Non-combustible enclosures of masonry 

materials are also relatively easy to install on columns (but not beams), but they have a weight 

premium that should be considered in design. SFRM coatings are lightweight, but generally 

require an enclosure to conceal their unfinished appearance unless they are applied in areas 

where finishes need not have high aesthetic qualities. SFRM products are somewhat vulnerable 

to damage over time, particularly in areas where work may be done by other trades. An 

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inspection and maintenance program by the owner can address any loss in integrity of the SFRM 

coating.

Some of the less-traditional approaches to fire protection of steel, such as intumescent coatings, 

are still costly when compared to other approaches and often need to be applied by specialty 

contractors. Some intumescent coatings can be applied as the final finish for exposed steel 

components, thereby adding to the steel framing appearance for architectural purposes. 

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