Asce 78 - Structural Fire Protection

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The contents

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thi s

publication are not intended to

be

and should not be construed to

be a

standard

of the.

American Society of Civil Engineers (ASCE) and are

not

intended for

use as a

reference

in

purchase

specifications, contracts, regulations, statutes, or any

other îegai document.

No

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in ths

publication

to

any specific

method, product, process, or service constitutes or

implies an endorsement, recommendation, or warranty

thereof by ASCE.

ASCE makes no representation or warranty

of

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fund,

whether express

or

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ASCE Manuals and Reports on Engineering PracticeNo.78

Structural

Fire

Protection

A S C E 78

92

m

07.59600 0023787 339

m

AMERICAN SOCIETY of CIVIL ENGINEERS


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ASCE 7 8

92

7 5 9 b 0 0 0 0 2 1 7 8 8 2 7 5 W

ASCE Manuals and Reports on Engineering PracticeNo.

78

Structural

Fire

Protect

on

T.T.

Lie, Editor

Prepared by the

ASCE Committee on Fire Protection

Structural Division

American Society of Civ il Engineers

E. L.

Schaffer, Chairman

R. W. Fitzgerald, Past Chairman

K. H.

Almand

J.

R.

Barnett

B.

Bresler

J. .

Fitzgerald

R.

i?

Fleming

W.

L .

Gamble

R.

G.

Gewain

F.

S. Harvey

D. B. Jeanes

R .

H. Iding

T.T.

Lie

T.

D. Lin

5. E .

Magnusson

J . R.

Milke

M. M.

Rudick

Published by the

American Society

of

Civil Engineers

345

East 47th Street

New York, New York

10017-2398


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A S C E 7 8

92

0759b00 002L789 101

ABSTRACT

This manual, Structurai Fire Protection: Manual

of

Practice

(Manual andReport 78) , is intended o provide a basis for the

development of new standards for the calculation of the fire

resistance of structural members.

It

provides information on

current techniques and developments

to

improve fire safety in

buildings. While it deals main1 with structural fire safety, related

subjects are also discussed. {he manual consists of two parts.

The material in Part 1, which consists

of

three chapters, is mainly

descriptive. Chapter 1 deals with various aspects related

to

structural fire protection, including building codes and the role

of structural fire protection. Chapter 2 discusses the develop-

ment of fire in enclosures and the effect of fire on the behavior

of concrete, steel, and wood, including the properties of these

materials at elevated temperatures. Chapter 3 describes meth-

ods for the calculationof the fire resistanceof various structural

members. Part 2, which consists

of

Chapters 4 and 5, deals with

the development

of

fire and the calculation of fire resistance using

mathematical models, respectively. t is hoped that,

in

addition

to

providing a basis for new standards, this manual will also be

useful to architects, engineers, building officials and students

in any branch concerned with structural fire safety.

L i b r a r y of Cong r es s Ca tal og i ng - i n - Pub l i c a t i on Da ta

Structural fire protection: manual of practice/T.T. Lie, editor;

prepared by the ASCE Committee on Fire Protection, Struo

tural Division, American Society of Civil Engineers.

p. cm.

-

ASCE manuals and reports of engineering

practice; no. 78)

Includes bibliographical references and index.

1. Fire prevention.

I.

Lie,

T.

T.

II.

American Society of Civil

ISBN 0-87262-888-4

Engineers. Committee on Fire Protection. 11. Series.

TD9145S85 1992

693' .82

-

c20 92-23885

CIP

The material presented n this publication has been pre-

pared in accordance with generally recognized engineering

principles and practices, and

is

for general information only.

This information should not be used without first securing

competent advice with respect to its suitability for any general

or specific application.

The contents of this publication are not intended to be

and should not be construed o be a standard of the American

Society of Civil Engineers (ASCE) and are not intended for

use as a reference in purchase specifications, contracts, reg-

ulations, statutes, or any other legal document.

No reference made in this publication

to

any specific

method, product, process, or service constitutes or implies

an endorsement, recommendation, or warranty thereof by

ASCE.

ASCE makes no representationor warranty of any kind,

whether express or implied, concerning the accuracy, com-

pleteness, suitability or utility of any information, apparatus,

product, or process discussed in this publication, and

assumes no liability therefor.

Anyone utilizing this information assumes all liability

arising from such use, including but not limited to infringe-

ment of any patent or patents.

Authorization to photocopy material for internal or personal

use under circumstances not falling within the fair use provi-

sions of the Copyright Act is granted by ASCE

to

libraries and

other users registered with the Copyright Clearance Center

(CCC) Transactional Reporting Service, provided that the

base fee of

$1.00

per article plus .15 per page s paid directly

to

CCC, 27 Congress Street, Salem, MA 01970. The identifi-

cation for ASCE Books is O-87262/92.

$1 +

.15. Requests for

special permission or bulk copying should be addressed

to

Reprintc/PermissionsDepartment.

Copyright

@

1992 by the American Society of Civil Engineers,

All Rights Reserved.

Library of Congress Catalog Card No: 92-23885

Manufactured in the United States of America.

ISBN 0-87262-888-4


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A S C E 78 92 0759b00

0023790

923

MANUALS AND REPORTS ON ENGINEERING PRACTICE

(As developed by the ASCE Technical Procedures Commitee, July

1930,

and

revised March 1935, February 1962, April 1982)

A

manual or report in this series consists

of

an orderly presentation of facts on

a particular subject, supplemented by an analysis of limitations and applications

of

these facts. it contains information useful to the average engineer in his

everyday work, rather than the findings that may be useful only occasionally or

rarely. It is not in any sense a “standard,” however; nor is it so elementary or so

conclusive as to provide a “rule

of

thumb” for nonengineers.

Furthermore, material in this series, in distinction from a paper (which

expresses only one person’s observations or opinions),

is

the work of a committee

or group selected to assemble and express information on a specific topic. As often

as practicable the committee is under the direction of one or more

of

the Technical

Divisions and Councils, and the product evolved has been subjected to review by

the Executive Committee

of

that Division or Council. As a step in the process

of

this review, proposed manuscripts are often brought before the members

of

the

Technical Divisions and Councils for comment, which may serve as the basis for

improvement. When published, each work shows the names

of

the committees

by which

i t

was compiled and indicates clearly the several processes through

which it was compiled and indicates clearly the several processes through which

it has passed in review, in order that its merit may be definitely understood.

In February 1962 (and revised in April, 1982) the Board of Direction voted to

establish:

A series entitled ’Manuals and Reports on Engineering Practice, to include the

Manuals published and authorized to date, future Manuals

of

Professional

Practice, and Reports on Engineering Practice. All such Manual or Report

material of the Society would have been refereed in a manner approved by the

Board Committee on Publications and would be bound, with applicable

discussion, in books similar to past Manuals. Numbering would be consecutive

and would be a continuation of present Manual numbers. In some cases

of

reports

of

joint committees, bypassing of Jounral publications may be autho-

rized.


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AVAILABLE* MANUALS

AND

REPORTS

OF

ENGINEERING

PRACTICE

Number

10

13

14

31

33

34

35

36

37

40

41

42

44

45

46

47

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

Technical Procedures for City Surveys

Filtering Materials

for

Sewage Treatment Plants

Accommodation

of

Utility Plant Within the Rights-of-way of Urban

Streets and Highways

Design

of

Cylindrical Concrete Shell Roofs

Cost Control and Accounting for Civil Engineers

Definitions of Surveying and Associated Terms

A List of Translations of Foreign Literature on Hydraulics

Wastewater Treatment Plant Design

Design and Construction of Sanitary and Storm Sewers

Ground Water Management

Plastic Design in Steel-A Guide an d Commentary

Design of Structures to Resist Nuclear Weapons Effects

Report on Highway an d Bridge Surveys

Consulting Engineering-A Guide

for

the Engagement of Engineering

Services

Report on Pipeline Location

Selected Abstracts on Structural Applications of Plastics

Urban Planning Guide

Report on Small Craft Harbors

Survey of Current Structural Research

Guide for the Design of Steel Traiismission Towers

Criteria for Maintenance of Multilane Highways

Sedimentation Engineering

Guide to Employment Conditions for Civil Engineers

Subsurface Investigation for Design and Construction of Foundations

of Buildings

Management, Operation and Maintenance of Irrigation and Drainage

Systems

Structural Analysis and Design of Nuclear Plant Facilities

Computer Pricing Practices

Gravity Sanitary Sewer Design and Construction

Introductory Manual on Computer Services

Existing Sewer Evaluation and Rehabilitation

Structural Plastics Design Manual

Manual on Engineering Surveying

Construction Cost Control

Structural Plastics Selection Manual

Wind Tunnel Model Studies

of

Buildings and Structures

Aeration-A Wastewater Treatment Process

Sulfide in Wastewater Collection and Treatment Systems

Evapotranspiration and Irrigation Water Requirements

Agricultural Salinity Assessment and Management

Design of Steel Transmission Structures

Quality in the Constructed Pr o j e c t a Guide for Owners, Designers,

and Constructors

Guidelines for Electrical Transmission Line Structural Loading

Right-of-waySurveying

Design of Municipal Wastewater Treatment Plants

Design and ConstructionofUrbanStormwater Management Systems

Structural Fire Protection

_

‘Numbers

1,

2,3 ,4 , 5 ,6 ,7 ,8 ,9 ,

11, 12, 15,

16, 17,

18,

19,21), 2 1 , z , 23, 24, 25,26,27 , 28,

29,

30

I2

38,39,43,

and

48

are out of print.


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A S C E 76 7 2

rn

0 7 5 q b o o o 0 2 3 7 7 2 7 T b

PREFACE

Fire is the primary cause of loss of life and property in buildings in

North America. Stimulated by conflagrations in many parts of the world,

techniques to control or mitigate the effects of fire have been developed

over the last

two

decades. Significant advances have been made in the

development of knowledge of basic fire phenomena and fire dynamics

in addition to the development of methods to protect buildings and

their occupants against fire. Attention to techniques, materials, and

details now enables the designer to confine a fire to only one part of

a building, where a few years ago the entire building would have been

lost. The ability to prevent spread of fire and to protect the building

occupants does not automatically assure fire safety, however. Fire safety

measures must be consciously incorporated into the design and con-

struction processes from the preliminary planning to the completion of

the construction.

While it is possible to improve considerably the fire safety design of

buildings, there is a lack in attention on the part of architects and

engineers to firesafety provisions (National Commission on Fire Pre-

vention and Control 1973). One of the reasons cited is the insufficient

availability of training in professional education and practice, leading

to lack of or low levels of awareness of the principles and applications

of fire protection in buildings. Whereas training is given in numerous

institutions in many areas of building design, and many books and

manuals are available in these areas, this is not the case in the area of

fire.

The main objective of the Manual is to document selected data that

over the years have been produced in the area of fire safety and to

transfer this knowledge to the building design practitioner. Because the

area of fire safety is very wide, mainly structural fire safety provisions

and related subjects are discussed.

A

considerable amount of research has been carried out in the area

of structural fire protection in recent years. The use of numerical tech-

niques has made it possible to develop mathematical models that sim-

ulate the behavior of various structural members in fire. A large number


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A S C E

7 8 9 2

m

0 7 5 î b 0 0 0023793 b 3 2

m

of models that calculate the fire resistance of structural members now

exists. Most of the models have been programmed for computer

processing.

Much data on the thermal and mechanical properties of various build-

ing materials at elevated temperatures have also been produced in

recent years. Knowledge of these properties, which are used as input

data for the computer programs, is essential to be able to predict the

behavior of structural members during exposure to fire. Methods for

estimating the expected severity of building fires and temperature-time

relations that characterize the severity of these fires have also been

developed. At present much information exists for the determination

of the required fire protection for various structural members.

In the Manual all the subjects mentioned above and several more are

discussed. Although the Manual was written with the aim to provide

a basis for the development of new standards for the calculation of fire

resistance, it is hoped that it will also be used by architects, engineers,

building officials, and students in any branch concerned with structural

fire safety.

T. T. Lie

Principal Research Officer

Institute for Research in Construction

National Research Council of Canada


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A S C E

7 8

92

O759600 0021794 579

ACKNOWLEDGEMENTS

The authors wish to thank all who contributed to the Manual. The

manual was reviewed

by

a Peer Review Committee, consisting of the

following members:

Charles Culver, Director (Chairman)

Office of Construction, Maritime and Health Engineering Support

Occupational Safety and Health Administration

Washington, D.C.

Roger Wildt

Construction Marketing Manager

Bethlehem Steel Corporation

Bethlehem, Pennsylvania

Paul R. DeCicco, PE

Mainview, New York

Thomas Seymor, Director

Office of Safety Standards Programs

Occupational Safety and Health Administration

Washington, D.C.

Robert White, Wood Scientist

Fire Safety

of

Wood Products

Forest Products Laboratory

Madison, Wisconsin

Daniel Gross, Senior Research Engineer

Building and Fire Research Laboratory

National Institute of Science and Technology

Gaithersburg, Maryland

Contributions to the Manual were received from the concrete, steel,

and wood industries, research organizations, universities, and con-

sulting firms. Authors who made substantial contributions to the var-


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A S C E

7 8

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0759600

0021775

405

ious chapters of the Manual are mentioned in the footnotes to each

chapter.

Special thanks is extended to the Institute for Research in Construc-

tion (IRC), National Research Council of Canada, for the provision of

considerable staff time during the writing of the manual. The typing

and editing of the numerous drafts of the document were conducted

by

IRC's National Fire Laboratory, and the drawings prepared by IRC's

Graphics Unit.


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A S C E 7 8 9 2

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341

m

EXECUTIVE SUMMARY

The writing of the Manual was initiated by the Committee on Fire

Protection in the Structural Division of the American Society of Civil

Engineers. It was written with the aim of providing information on

current techniques and developments to improve fire safety in build-

ings. It deals mainly with structural fire safety, although related subjects

are also discussed.

The Manual consists of

two

parts: The objective of Part

1,

consisting

of Chapters 1-3, is to introduce the subject matter to the building design

practitioner who has had no experience with fire other than in work

with building codes. The material in this part is mainly descriptive.

In Chapter

1,

various aspects related to structural fire protection are

discussed, including building codes, their background and purpose,

and the role structural fire protection plays in building fire safety.

Chapter 2 discusses the development of fire in enclosures and the

effect of exposure to fire on common materials of construction, which

includes concrete, steel, and wood. A large part of the chapter deals

vated temperatures. In order to understand and eventually predict the

performance of structural members in a fire, knowledge of the material

properties that determine the behavior of a member at elevated tem-

peratures is essential. A part of Chapter

2

deals with experimental

evaluation of the fire resistance of structural members and describes

the most common testing methods to determine the fire resistance of

these members.

Chapter 3 provides methods that will enable the determination of

the fire resistance of various building elements with the aid of simplified

formulas and rules. Also, references are given in which fire resistance

ratings, obtained from test results, can be found for a large number of

building elements. In addition, extension rules are given that will enable

the interpretation of test or calculated results for conditions that differ

from those in the test or calculation. The materials considered in this

chapter are concrete, steel, and wood, eventually in combination with

I

with the thermal and mechanical properties of these materials at ele-


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A S C E 78 92 0 7 5 9 b 0 0 0023797 2 8 8

various other materials used as insulation, such as gypsum board and

sprayed mineral fibre.

in Part 2, which consists of Chapters

4

and 5, the technical bases of

the material in Part 1 is described.

This

will enable those interested to

obtain more knowledge about the background of the material in Part

1.

Chapter 4 discusses various temperature-time relations for real world

and for standard fires. Analytical expressions are given that describe

Characteristic temperature curves as a function of the significant param-

eters for various fire conditions commonly met with in practice. Expres-

sions are also given for the standard fire curve used in North America

and for the fire curve adopted by the International Organization for

Standardization.

In Chapter 5, a large number of mathematical models for the calcu-

lation of fire resistance by numerical methods are described. Because

mainly metric units were used in the literature dealing with these models,

the same units were also used

in

this chapter. Most of the models have

been programmed for computer processing.

Material related to test methods, codes, and standards are mainly

based on North American practices. In several other areas, however,

such as calculation methods, properties of materials and fire protection

methods, the material is more general in scope.

The Manual is intended to provide a text that can be used as a basis

for the development of new standards for the prediction of fire resist-

ance by calculation. It has been reviewed by several members of the

Committee on Fire Protection during the writing of the Manual and,

subsequently, after completion of the writing by an independent

Peer Review Committee, consisting of the members mentioned in the

Acknowledgement in this Manual.

COPYRIGHT 2003; American Society of Civil Engineers Document provided by IHS Licensee=IHS Dealers/IHSINTL003, User=SOPORTE,

08/14/2003 08:59:48 MDT Questions or comments about this message: please callthe Document Policy Management Group at 1-800-451-1584.

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A S C E 7 8 9 2 0 7 5 9 b 0 0 0 0 2 3 7 9 8 3 1 4

CONTENTS

PART

1

CHAPTER 1

.

BUILDING DESIGN AND FIRE SAFETY ..................

1.1

BUILDING CODES

..............................................................

1.2 MODEL CODES ..................................................................

1.3 ROLE OF CODES AND STANDARDS ...................................

1.4

DESIGN FOR FIRE RESISTANCE ..........................................

1.4.2

Fire Resistance Assessment

..........................................

1.4.2.1

Testing

..........................................................

1.4.2.2

Calculation of Fire Resistance

...........................

1.4.1 Fire Resistance Requirements

.......................................

CHAPTER

2.

PRINCIPLES

OF

STRUCTURAL FIRE PROTECTION

.

2.1 FIRE CEVERITY ...................................................................

2.1.1

2.2

EFFECT OF FIRE ON COMMON MATERIALS OF

CONSTRUCTION

................................................................

2.2.1 Steel .........................................................................

Fire Development in a Room

.......................................

2.2.1.1

Thermal Properties .........................................

-Thermal Conductivity ..................................

-Specific Heat...............................................

-Thermal Diffusivity

......................................

2.2.1.2 Mechanical Properties

.....................................

-Modulus of Elasticity ...................................

-Strength .....................................................

2.2.1.3 Deformation Properties

...................................

-Thermal Expansion

......................................

-Creep Properties

.........................................

1

11

11

11

14

17

17

17

18

18

20

20

20

22

22

23


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A S C E

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CONTENTS

2.2.2 Concrete ...................................................................

2.2.2.1 Thermal Properties .........................................

-Thermal Conductivity

..................................

-Specific Heat

...............................................

-Thermal Diffusivity

......................................

2.2.2.2 Mechanical Properties .....................................

-Modulus of Elasticity

...................................

-Strength

.....................................................

2.2.2.3 Deformation Properties ...................................

-Thermal Expansion

......................................

2.2.3 Wood .......................................................................

2.2.3.2 Thermal Properties .........................................

-Thermal Conductivity

..................................

-Kinetics ......................................................

-Heat Generation ..........................................

2.2.3.3 Mechanical Properties .....................................

-Tensile Strength ..........................................

-Compressive Strength

..................................


...................................

-Thermal Expansion......................................

-Creep Properties

.........................................

2.2.3.1 Rate of Charring

............................................

-Specific Heat...............................................

-Modulus of Elasticity

...................................

-Creep Properties

.........................................

2.3 PRINCIPLES OF ACHIEVING STRUCTURAL FIRE

RESISTANCE ......................................................................

2.3.1 Mechanisms of Protection............................................

2.3.1.1 Thickness of Protection ...................................

2.3.1.3 Ablation ........................................................

2.3.1.4 Calcination

....................................................

2.3.1.5 Intumescence .................................................

2.3.1.2 Thermal Conductivity

.....................................

2.3.1.6 Dehydration ..................................................

2.3.1.7 Transpiration

.................................................

2.3.1.8 Reflection

......................................................

2.3.2 Fire Protection Methods ..............................................

2.3.2.1 Insulation

......................................................

2.3.2.2 Capacitive Protection

......................................

2.3.3 Construction Techniques .............................................

Classification of Building Construction

..............

2.3.3.2 Structural Systems

..........................................

2.4 EVALUATION OF FIRE PERFORMANCE...............................

2.4.1 Fire Resistance Testing Methods

...................................

2.4.1.1 ASTM E119 Test Standard ...............................

2.4.2 Calculation Methods ...................................................

2.3.3.1

24

24

24

25

27

27

27

27

33

33

34

36

38

40

41

41

42

42

42

42

43

43

45

45

45

45

46

46

46

46

46

46

47

48

48

48

48

49

49

49

51

55

55

56

57


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ASCE 7 8

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CONTENTS

CHAPTER 3. FIRE RESISTANCE OF BUILDING ELEMENTS

.........

3.1

3.1

CALCULATION OF FIRE RESISTANCE .................................

3.1.1

Steel .........................................................................

3.1.1.1 Steel Columns

................................................

-Steel Columns Protected by Low Density

Protection...................................................

-Steel Columns Protected by Gypsum

Wallboard...................................................

-Steel Columns Protected by Concrete

.............

-Other Types of Protection for Hollow Steel

-Unprotected Steel Columns ..........................

Columns ....................................................

3.1.1.2 Floor, Roof and Beam Assemblies.....................

3.1.1.3

Steel Trusses

..................................................

3.1.1.4 Load Bearing Walls.... ...........................

Concrete ...................................................................

3.1.2.1

Reinforced Concrete Columns ..........................

3.1.2.2 Monolithic Concrete Slabs ...............................

3.1.2.3

3.1.2.4 Hollow Concrete Slabs

....................................

3.1.2.6

Simply Supported (Unrestrained) Slabs and

Beams

...........................................................

3.1.2.7

Continuous Beams and Slabs

...........................

3.1.2.8 Fire Resistance of Floor Slabs and Roofs

3.1.2.9 Examples.......................................................

Double Layer Concrete Slabs............................

3.1.2.5

Composite Slabs .............................................

Subjected to Thermal Restraints ........................

-Example 1-Determination of Cross Sectional

Area and Length of Negative Reinforcement

Required in a Two-span Slab to Provide

Three-hour Fire Resistance ...........................

-Example 2-Verification that an Exterior-bay

Floor Panel Qualifies for a Two-hour Fire

-Example 3-Verification that an Interior-bay

Floor Panel Qualifies for a Three-hour Fire

Resistance Rating

........................................

Resistance Rating

.........................................

3.1.3 Timber ......................................................................

3.1.3.1 Light Frame Assemblies

..................................

3.1.3.2

One Hour Fire Resistive Exposed Wood

Members

.......................................................

3.2 FIRE RESISTANCE DETERMINED BY TESTING ......................

3.3 EXTENSION RULES A N D GUIDELINES FOF FIRE

RESISTANCE

......................................................................

3.3.1

Definition of Terms ....................................................

63

63

63

64

64

67

67

70

70

72

75

76

77

79

80

81

82

82

84

86

88

93

93

98

104

111

111

113

117

117

118


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3.3.2 Variation of Material Properties .....

3.3.2.1 Steel .............................................................

3.3.2.2 Concrete .......................................................

3.3.2.3 Wood ...........................................................

3.3.3 Variation of Dimensions

......................

3.3.3.1 Concrete

.......................................................

3.3.4 General Rules

............................................................

PART 2

CHAPTER 4

.

FIRE TEMPERATURE-TIME RELATIONS .................

4.1 FIRE TEMPERATURES

.........................................................

4.1.1

4.1.2 Possible Fire Severities ................................................

4.1.4

4.1.5 Standard Fire Curve

...................................................

Nomenclature .....................................................................

Parameters Determining the Fire Temperature Course .....

4.1.3 Characteristic Temperature Curves

................................

Expressions for Characteristic Temperature Curves .........

CHAPTER 5.

CALCULATION OF TEMPERATURE AND FIRE

RESISTANCE OF STRUCTURAL MEMBERS

.............

5.1 TEMPERATURE OF FIRE EXPOSED MEMBERS

......................

5.1.1 Temperature of Protected Steel.....................................

5.1.1.1 Calculation Method ........................................

5.1.1.2 Equations for the Outer Boundary of Insulation ..

5.1.1.3 Equations for the Inside of Insulation

................

5.1.1.4 Equations for the Inner Boundary of Insulation

and for the Steel Core

.....................................

5.1.1.5 Auxiliary Equations

........................................

5.1.1.6 Comparison with Test Results

..........................

5.1.2 Temperature of Unprotected Steel

.................................

5.1.3 Temperature of Rectangular Concrete Columns ..............

5.1.4 Temperature of Square Concrete Columns .....................

5.1.4.1 Division of Cross-section into Elements

.............

5.1.4.2 Equations for the Fire-Concrete Boundary ..........

5.1.4.3 Equations for Inside the Concrete

.....................

5.1.4.4 Auxiliary Equations ........................................

5.1.4.5 Effect of Moisture

...........................................

5.1.5 Temperature of Circular Concrete Columns....................

5.1.5.1 Division of Cross-section into Elementary Layers

5.1.5.2 Equations for the Fire-Concrete Boundary ..........

119

119

120

123

125

125

126

137

138

138

140

141

142

151

158

159

159

160

160

162

165

165

170

170

172

172

172

173

174

174

175

175

176

176

177



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5.1.5.3 Equations for Inside the Concrete .....................

5.1.5.4 Equations for the Centre of the Concrete ...........

5.1.5.5 Effect of Moisture ...........................................

5.1.5.6 Stability Criterion ......... ............................

5.1.5.7 Procedure of Calculation of Column

Temperatures

.................................................

5.1.6 Temperature of Composite Concrete Floor and Roof

Slabs ........................................................................

5.1.6.1 Division of Cross-section into Elementary Layers

5.1.6.2 Equations for the Fire-Slab Boundary ................

5.1.6.3 Equations for the Inside of the Slab ..................

5.1.6.4 Equations for the Boundary Slab and Asbestos

Pad ... ................................

5.1.6.5 Equati he Inside of the Asbest

5.1.6.6 Equations for the Boundary Asbestos Pad and

Air ...................... .........

5.1.6.7 Stability Criterion ...........................................

5.1.6.8 Procedure for Calculation of Slab Temperatures

..

5.1.7 Temperature of Circular Concrete Filled Steel Columns

...

5.1.7.1 Division of Cross-section in Elementary Layers ...

5.1.7.2 Equations for the Fire-Steel Boundary

...............

5.1.7.3 Equations for the Inside of the Steel .................

5.1.7.4 Equations for the Steel-Concrete Boundary

........

5.1.7.5 Equations for the Inside of the Concrete

............

5.1.7.6 Stability Criterion

...........................................

5.1.7.7 Effect of Moisture ...........................................

5.1.8 Temperature of Semi-infinite Wood Slabs

5.1.8.1 Temperature Distribution .................................

5.1.8.2 Charring Rate ..................................

5.1.9 Temperature of Finite Wood Members ..........................

5.2 FIRE RESISTANCE OF STRUCTURAL MEMBERS ............

5.2.1 Fire Resistance

of

Steel Members ..................................


of

Concrete Members ............................

5.2.2.1 Fire Resistance

of

Concrete Floor and Roof Slabs

5.2.2.2 Fire Resistance

of

Reinforced Concrete Columns .

-Equations for steel in the column ..................

-Equations for concrete in the column .............

5.2.3 Fire Resistance of Concrete Filled Tubular Steel Columns

.

5.2.3.1 Division of Cross-section into Annular Elements.

5.2.3.2

5.2.3.3

5.2.3.4

5.2.4.1

Calculation of Strength during Fire ...................

Equations for the Steel ....................................

Equations for the Concrete ..............................

5.2.4 Fire Resistance of Wood Member .............. ...

Fire Resistance of Glued-Laminated Timber

........

-Beams

........................................................

-Columns ....................................................

178

178

178

179

180

180

180

181

182

182

183

183

183

184

184

184

185

186

186

186

187

187

188

188

189

190

193

193

193

193

194

196

199

201

201

202

203

204

204

206

207

207



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5.2.4.2

5.2.4.3

Fire Resistance of Glued-Laminated Beams

(Composite Models)........................................

Fire Resistance of Light-Frame Members............

5.3 REMARKS ..........................................................................

NOMENCLATURE

...............................................................

-Protected Steel, Reinforced Concrete and Concrete Filled Steel

Columns

..........................................................................

-Glued-laminated Timber ....................................................

-Composite Floor and Roof Slabs

.........................................

APPENDIX

MATERIAL PROPERTIES AND PHYSICAL CONSTANTS

...............

A.l STEEL PROPERTIES

............................................................

A.l .l Thermal Properties

.....................................................

A.1.1.1 Thermal Capacity of Steel

................................

A.1.1.2 Thermal Conductivity of Steel ..........................

A.1.1.3 Coefficient of Thermal Expansion of Steel ..........

A

.

1.2 Mechanical Properties .................................................

A.1.2.1 Stress-strain Relations for Steel (Version

1)

........

A.1.2.2 Stress-strain Relations for Steel (Version 2) ........

A.2 CONCRETE PROPERTIES

....................................................

A.2.1 Thermal Properties .....................................................

A.2.1.1 Thermal Capacity of Concretes .........................

-Siliceous Aggregate Concrete ........................

-Carbonate Aggregate Concrete

......................

-Expanded Shale Aggregate Concrete ..............

A.2.1.2 Thermal Conductivity

of

Concretes ...................

-Siliceous Aggregate Concrete ........................

-Pure Quartz Aggregate Concrete ...................

-Carbonate Aggregate Concrete ......................


A.2.1.3 Coefficient of Thermal Expansion of Concretes...

-Siliceous and Carbonate Aggregate Concretes

..


A.2.2 Mechanical Properties

.................................................

A.2.2.1 Stress-strain Relations for Siliceous, Carbonate

and Expanded Shale Aggregate Concretes

.........

A.3 WATER PROPERTIES

..........................................................

A.3.1 Thermal Capacity of Water ..........................................

A.3.2 Heat of Vaporization of Water ......................................

A.4 PHYSICAL CONSTANTS ..................... ............................

INDEX

......................................................................................

210

210

211

218

218

220

221

222

222

222

222

223

223

223

223

224

225

225

225

225

226

226

227

227

227

228

228

228

228

228

228

228

229

229

229

229

231


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ter

1

BUILDING DESIGN AND

FIRE

SAFETY

The basic fire safety objectives are to protect life and property. These

objectives can be achieved in buildings in various ways. One of the

most important is prevention of the outbreak of fire. If fire occurs, the

objective is to reduce the growth of the fire. Some fires, however,

become large in spite of preventive measures.

To

protect building oc-

cupants and property at this stage of the fire it is essential to confine

the fire and to provide means that permit safe evacuation of people

from the fire area.

The effectiveness and cost of all these measures can be influenced

by the building designer. Electrical and heating systems, for example,

are the cause of many fires in buildings. Attention to design and in-

stallation of such systems can contribute to the prevention of fire.

Measures to retard or combat fire growth that are related to building

design are the use of low fire hazard materials, providing fire detection

and extinguishing systems, and provisions to facilitate fire department

operations. These measures are in addition

to

those used to control the

combustibles that are brought into a structure on a regular basis as part

of the function of a structure, i.e. residence, warehouse for fuels, etc.

Measures to protect people against the hazards of the spread of fire

and its combustion products strongly affect the design of a building.

Preventing the spread of smoke and hot gases and providing adequate

exits or safety areas are a part of these measures.

Probably the closest measures related to building design are those

for the confinement of a fire. These measures include providing ade-

quate structural fire resistance, and fire barriers capable of delaying or

preventing spread of fire from one room to another. Methods and

materials used for fire protection, dimensions and location of building

Principal authors:

R.

W .

Fitzgerald

T. T.

Lie


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members and of materials used for fire protection, all affect the fire

performance of the members in a building.

The following section covers various aspects related to structural fire

protection, including building codes, their background and purpose,

and the role structural fire protection plays in building fire safety.

References for literature that has been consulted and which contains

more detailed information on these subjects is given at the end of this

chapter.

1.1

BUILDING CODES

Building codes have been in existence since about

2250

B.C., when

Hammurabi established in Babylon a law that protects building occu-

pants against the hazards resulting from faulty construction. Early Greek

and Roman laws had the objective of limiting loss of life caused by

building collapse to that in one property. These laws included provi-

sions for control of materials

of

construction, size of buildings, and

inspection of construction.

Laws to control the effects of fire were also introduced a long time

ago. Progress was often prompted by the occurrence of serious fires,

such as that of Rome in

70

B.C. or London in 1666, when these cities

were entirely destroyed. As a result of the serious fires that occurred

periodically in London in the Middle Ages, numerous laws to control

construction were enacted. These laws included a ban on thatch roofs

and required existing thatch roofs to be replaced with tile roofing.

Chimneys were required to be constructed of stone, tile, or plaster

instead of timber. After disastrous fires in 1664 and

1666,

regulations

were enacted that specified not only the kinds of construction to be

used but the locations where each type was permissible. Regulations

also governed timber sizes, thicknesses of walls, and the number of

stories to which a building could be built. In addition, inspectors or

surveyors were appointed to enforce the provisions.

Records of the settlements in North America indicated that building

regulations were also adopted early in their history. A significant step

was taken in New England in the mid-to-late 1800s or early

1900s.

At

that time, many poorly constructed or poorly managed textile mills

were destroyed by fire. Some mills, however, were built, and managed

to high safety standards, but the insurance companies were not inter-

ested in compensating for the reduced fire risk in these mills.

To

avoid

paying for serious fire losses that were occurring in some mills over

which they had no control, mill owners formed mutual insurance com-

panies whose members agreed to maintain certain levels of fire safety

design and fire prevention procedures thus qualifying for less costly

insurance coverage.

These companies found that experimentation with methods of con-

struction and fire-protection devices, particularly with automatic sprin-


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Model building codes have gained wide recognition throughout North

America. These codes have been developed by organizations whose

members have a wealth of experience in the building regulatory field.

The first model code in the United States was prepared by repre-

sentatives of the fire insurance industry in response to the serious losses

from conflagrations that occurred in cities across the country. Boston,

New York, Chicago, Baltimore, and San Francisco all suffered devas-

tating fires in the late 1800s. The National Board of Fire Underwriters,

(now American Insurance Association (AIA)), was deeply concerned

by these enormous fire losses and developed a recommended building

code the primary purpose of which was to reduce fire hazards and the

loss from fire. This was called the National Building Code. It consisted

of comprehensive building regulations suitable for adoption as law by

municipalities and it established a basic pattern for the development of

building codes throughout the country. This first model code has been

revised and republished numerous times since it was first published in

1905. The most recent revision of the National Building Code is the

1976 edition. In 1980, responsibility for the maintenance of the National

Building Code was transferred to the National Conference of States on

~

kler systems that were just beginning to be developed, produced worth-

while results.

The activities of these mutual insurance companies led to the for-

mation of Factory Mutual Laboratories in 1866 and Underwriters Lab-

oratories, Inc. in 1894. Each provided facilities for testing fire protection

devices and equipment. The outcome of this early testing resulted in

criteria and standards not only for general building design but also for

fire-protection equipment and devices. However, the lack of uniform

national standards was a serious weakness in achieving the sought-

after level of fire protection.

The 1904 Baltimore conflagration provided evidence of the need not

only for uniform standards but also for building regulations to minimize

the occurrence of such catastrophic fires. This fire reached such pro-

portions in its first hours that urgent appeals for aid were sent not only

to neighbouring cities but to more distant cities such as Philadelphia,

New York, and Washington, D.C. as well. Apparatus and men were

sent to Baltimore, but much of the apparatus could not be used because

hose couplings used by these other cities would not fit the Baltimore

hydrants. Before being finally contained, the fire swept over 140 city

acres (or 80 blocks) and destroyed about 2500 buildings.

In the following year, 1905, the National Board of Fire Underwriters

published a "model" code in an effort to standardize building regula-

tions.

1.2 MODEL CODES


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Building Codes and Standards (NCSBCS). Subsequent to this, NCSBCS

gave the Code back to AIA, and the AIA subsequently gave the Building

Officials and Code Administrators International Inc. (BOCA) the right

to use the title ”National Building Code.” BOCA, founded in 1915 as

the Building Officials Conference Õf America, first published its model

code, the Basic Building Code, in 1950. Revised editions of the code

are published every three years and code revisions are considered every

year. The Basic Building Code has gained wide acceptance in many

states and municipalities in the United States, largely in the north and

east. In 1984, the title of this Code was changed to the BOCA Basic/

National Building Code, and in 1987, to the BOCA National Building

Code.

In 1927, the Pacific Coast Building Officials Conference, now the

International Conference of Building Officials (ICBO), drafted and adopted

the first edition of the Uniform Building Code at its sixth annual meet-

ing. The code has gained wide acceptance in states west of the Missis-

sippi. It was the first model code to establish distinct fire resistance

rating requirements for specific types of construction. The ICBO pro-

cesses revisions to the Uniform Building Code annually and publish

new editions every three years.

The Southern Building Code Congress International, Inc. (SBCCI)

was organized in 1945 by building officials and inspectors from the

southeastern part of the United States. The SBCCI first published the

Southern Standard Building Code in 1946. Now known as the Standard

Building Code, it is revised annually and new editions are published

every three years.

The three building officials’ organizations that publish model building

codes process their code changes by an open consensus process. Op-

portunity for public participation at hearings is provided and action on

proposed changes is by vote of member building officials representing

local and state jurisdictions.

The Life Safety Code, although not a building code,

is

the predom-

inant overall guide to safety from fire for buildings occupants in the

United States. Work on the code started in 1913 by the National Fire

Protection Association (NFPA). Known originally as the Building Exits

Code, the title was changed in 1966 to the Code for Safety to Life from

Fire in Buildings and Structures. The Code, often referred to as NFPA

101, is frequently used as a supplement to building codes. New editions

are published every three years.

The National Building Code of Canada was developed and is main-

tained by the Associate Committee on the National Building Code of

the National Research Council of Canada. The members of the Associate

Committee are appointed by the National Research Council and rep-

resent all interests of the building construction industry in Canada.

First published in 1941, revised editions of the National Building Code

of

Canada are published every five years. The Code, although volun-


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tary, is widely adopted by municipal, provincial, and other government

agencies of Canada. Its background and concepts have been developed

almost entirely in Canada and its approach to many fire protection

matters is quite different from model code practice in the United States.

For that reason alone, it is a valuable resource document for code

researchers.

1.3

ROLE

OF CODES AND STANDARDS

Codes and standards have similar but separate functions. Codes are

usually broader in scope and include in their framework references to

many standards. Codes usually are intended to become mandatory

regulations through legislation.

A building code specifies minimum requirements for design and con-

struction of buildings and structures. These minimum requirements are

established to protect health and safety of the public and generally

represent a compromise between optimum safety and economic feasi-

bility. Features covered include structural design, fire protection, means

of egress, light, sanitation, and interior finish.

There are two types of building codes. Type one, specification codes,

spell out in detail what materials can be used, the maximum or mini-

mum size of a building, and how components should be assembled.

Type two, performance codes, detail the objective to be met and es-

tablish criteria for determining if the objective has been met. The de-

signer and builder are, thus, allowed freedom in selecting construction

methods and materials as long as it can be shown that the performance

criteria can be met. Performance-oriented building codes still embody

a fair amount of specification-type requirements, but the provision exists

for substitution of alternate methods and materials, if they can be proven

adequate.

Standards are generally considered to be a set of conditions or re-

quirements to be met by a material, product, process, or procedure.

Standards may also describe a method of testing to determine physical,

functional, or performance characteristics of materials or products. The

most extensive use of the standards is their adoption into the building

code by reference, thus keeping the building codes to a workable size

and eliminating much duplication of effort. As a result of the reliance

of codes on nationally recognized standards, there is substantial con-

sistency between building codes. Such standards are also used by spec-

ification writers in the design stage of a building to provide guidelines

for the bidders and contractors.

Most national standards are developed by standards writing orga-

nizations. These organizations follow procedures for standards devel-

opment, designed to obtain a national consensus of all groups affected


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by the standards including consumers, producers, designers, govern-

ment, and independent experts.

Standards referenced in building codes can generally be classified as

materials standards, engineering practice standards, and testing stan-

dards.

Materials standards generally establish minimum requirements of

quality as measured by composition, mechanical properties, dimen-

sions, and uniformity of product. They include provisions establishing

methods of sampling and testing for verification of such quality.

Engineering practice standards include basic design procedure, en-

gineering formulas, and special provisions intended to provide a sat-

isfactory level of performance. A s in the case of materials standards,

engineering practice standards may be sufficiently comprehensive to

include methods of testing to verify performance. An example might

be a structural design specification which includes provisions limiting

its application to materials meeting certain levels of quality and strength,

and also providing for the testing of structural assemblies whose per-

formance must be evaluated on that basis.

Testing standards generally pertain to the methods and procedures

employed to establish levels of quality or performance of materials or

assemblies. Included are procedures for measuring such charactenstics

as structural strength and stability, permeability, durability, combus-

tibility or flammability, and fire resistance.

Provisions for fire resistance are specified in all the building codes

mentioned earlier. These provisions include requirements for fire resis-

tance, which are given partly in the form of required performances and

partly in the form of specifications, such as materials and dimensions

needed to obtain the required fire resistances. The building codes also

specify recognized codes and standards for fire resistance design and

assessment. Fire resistance design requirements and assessments will

be discussed in more detail in the following sections.

1.4 DESIGN FOR FIRE RESISTANCE

Building codes and insurance considerations are important factors in

design decision making. Historically, both have influenced and greatly

improved the safety of buildings. However, codes, standards, and in-

surance requirements alone are insufficient to provide attainable fire

safety levels in the buildings constructed today. To achieve this, the

building designer must play a more active role in the fire safety design

of the building. Conscious, integrated design for building fire safety

must be a part of the architectural design process if it is to be effective

and economical. All members of the traditional building design team

should include, as an integral part of their work, fire safety in the

design process, in the same manner that spatial, structural, mechanical,


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and electrical provisions are now incorporated. The earlier in the design

process that fire safety objectives are established, alternate methods of

accomplishing these objectives are identified, and engineering design

decisions are made, the more effective and economical the final results

will be.

Several factors play a role in designing for fire resistance. They include

fire resistance requirements, materials and methods used for fire pro-

tection, and methods for assessing fire resistance.

In the following sections, fire resistance requirements and assessment

of fire resistance will be briefly discussed. More on these subjects ap-

pears in Chapters 2 and 3. The principles of structural fire protection

are discussed in Chapter 2.

1.4.1

Fire Resistance Requirements

The fire resistance of a building component or assembly is its ability

to withstand exposure to fire without loss of load bearing function, or

to act as a barrier against spread of fire, or both. In North America,

building code requirements for fire resistant design are currently ex-

pressed, almost exclusively, in terms of the length of time that a con-

struction can withstand exposure to a standard fire without losing its

load bearing or fire separating function. This length of time is a measure

of the fire performance of the component or assembly, and is termed

the ”fire resistance” of the construction. The term ”fire endurance’’ is

popularly used to describe both the duration of load bearing and fire

separating function for assemblies tested according to North American

Standards.

The fire resistance requirements in the building codes are usually a

function of such factors as fire load, building occupancy, height, and

area. In actual practice, however, the severity of a fire and thus the

required fire resistance is a function of additional factors, which are not

considered in present building codes. These factors include the prop-

erties of the material of the walls enclosing the fire, and the dimensions

of the openings in the walls through which air can be supplied to the

fire and heat lost to the surroundings.

A noticeable difference between the standard fire temperature curve

and an actual fire temperature curve is that the standard fire temper-

ature continues to rise with time, whereas the temperature in an actual

fire decreases after reaching a maximum temperature. This is illustrated

in Fig. 1.1where the standard fire curve and a fire curve for a burnout

fire in actual practice are shown. It should be noted here, however,

that with the exception of Japan, the fire temperature curves used

throughout the world are very close to that of the North American

Standard.

Evaluating the fire performance of a construction exposed to a real

world fire instead

of

a standard fire will probably give more accurate

information on the fire performance of the construction. The current


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1 2 0 0

1 0 0 0

8 0 0

<

6 0 0

S

4 0 0

2 0 0

O

O

œ

æ

+

E

Y

a

Y

I-

-

-

2 0 0 0

-

IME-TEMPERATURE

CURVE

U

ACTUAL F I RE

æ

O

-

1 6 0 0

Y

œ

-

O

2

4 6 8 1 0 1 2 1 4 16

TIME, h

Figure 1.1 -Time-temperature curves of standard fire and actual

fire.

method of expressing fire resistance requirements and performances in

terms of standard fire resistance is a well established method, however.

All provisions and ratings in North American codes and standards are

based on exposure to the standard fire. There is also a large amount

of information on the standard fire resistances of numerous building

components and assemblies. Therefore, in the field of structural fire

protection, the use of the standard fire resistance is still needed at this

stage, although in various cases fire resistance requirements and per-

formances can also be based on exposure to real world fires, which

probably will give less conservative results.

Part 1 of this Manual will mainly deal with structural fire protection

based on exposure to a fire of a severity given by the standard fire

curve. Exposure to real world fires of various severities will be discussed

only briefly in this Part and in more detail in Part 2 of the Manual.

1.4.2 Fire Resistance Assessment

1.4.2.1

Testing

A common method to assess fire resistance is by subjecting speci-

mens, such as beams, columns, walls, and floors or assemblies to a fire

test. In North America, fire resistance has historically been determined

through laboratory tests conducted in accordance with procedures de-

veloped by the American Society for Testing and Materials (ASTM).


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -




9

The most widely used of these procedures are described in the ”Stand-

ard Methods of Fire Tests of Building Construction and Materials,”

ASTM

E119. This test method is used to evaluate walls, partitions,

beams, columns, floor, and roof assemblies. Similar procedures are used

for determining the fire resistance of door and window assemblies. In

addition to ASTM, other organizations such as the National Fire Pro-

tection Association (NFPA), Underwriters Laboratories, Inc. (UL), Un-

derwriters Laboratories

of

Canada (ULC), and the Standards Council

of Canada also publish fire test methods which are virtually identical

to those developed by ASTM and are generally considered to be equiv-

alent. In all these methods, the fire resistance is expressed in the time

that the specimen meets specified criteria of performance during ex-

posure to a standard fire.

There are three criteria in the standard test method. They concern

load-bearing capacity, integrity, and for fire barriers, temperature rise

on the unexposed face. In many cases, not all criteria have to be sat-

isfied. Beams and columns, for example, are required only to demon-

strate ability to carry load for the fire resistance period. Non-bearing

walls, if used as a fire separation, only have to meet the requirement

of integrity and the requirement that limits the temperature rise on the

unexposed face. A more comprehensive discussion of the ASTM test

procedure is given in Section 2.4 of Chapter

2

of this manual and in

Boring et al 1981 and Babrauskas and Williamson 1978. These references

also describe the historical development of fire resistance testing.

1.4.2.2

Calculation

of

Fire Resistance

Progress in the field of theoretical prediction of fire resistance has

been rapid in recent years. In many cases the fire resistance of building

components and assemblies can be determined, not only by testing,

but also by calculation. Calculation of fire resistance is far less expensive

and time-consuming than conducting fire resistance tests, which are

usually performed on large scale test specimens.

Calculation of fire resistance involves the calculation of fire temper-

ature, and the temperature, deformation and strength of

the

building

construction. Because these variables are time dependent, the calcula-

has simplified it. Common methods to calculate fire resistance are finite

difference and finite element methods. In Section 2.4, Chapter 2 of Part

fire resistance. In Part 2, a numerical technique for the calculation of

fire resistance is described in detail.

At present, much effort is made in many countries in the world to

promote calculation of fire resistance. Mathematical models for the cal-

culation of fire resistance, using numerical techniques, give the most

accurate results. Such models have been developed for many cases at

present but often the calculation can only be performed by large com-

I

tion procedure is complex, although the use of high speed computers

1 of the manual, more information is given on calculation methods for


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` -

` , ,

` , ,

` ,

` , ,

` - - -



ASCE

78 9 2

m

0759600 00218L3 2 5 0

m


0

puters. Its application for fire resistance calculation is therefore re-

stricted at this stage. A method more suitable for general application

and incorporation in codes and manuals is the use of simplified formulas

that approximately give the same results as those obtained from the

mathematical model. Such formulas can be derived by making a large

number of computer runs, using validated mathematical models, and

expressing the results of these runs in simple approximate formulas or

rules, that can be processed manually or with desk calculators.

Formulas for the assessment of the fire resistance of various building

elements made of steel, concrete, and timber are given in Section 3.1

of Chapter

3

of Part 1 of this manual. In Section 3.3 of Chapter

3

rules

are given that enable the interpretation of test or calculated results for

conditions that differ from those in the test or calculation.

REFERENCES

Babrauskas, V. and Williamson, R.B. (Aug. and Nov. 1978). "The historical

basis of fire resistance testing." Part

I

and Part II, Fire Technology,

14(3),

184-

Boring, D.F., Spence, J.C., Wells, W.G. (1981). Fire protecfion through modern

building codes. American Iron and Steel Institute, Washington, D.C.

Bresler, B. "Fire protection of modern buildings: Engineering response to new

problems," North Carolina State University, Department of Civil Engineering,

Raleigh, North Carolina.

Fitzgerald, R.W. (1981). Fundamentals of firesafe building design. National Fire

Protection Association, Section 5, Chapter 1,Fifteenth Edition, NFPA, Quincy,

MA.

Fitzgerald, R.W. (1981).

Structural integrity during fire.

National Fire Protection

Association, Section 5, Chapter 8, Fifteenth Edition, NFPA, Quincy, MA.

Lie, T.T. (1972). Fire and buildings. Applied Science Publishers Ltd., London.

National Commission on Fire Prevention and Control. (1973). "America burn-

ing.'' Superintendent of Documents, U.S. Government Printing Office, Wach-

ington, D.C.

Nelson, H.E. (1981). Building construction. National Fire Protection Association,

Section 5, Chapter 5, Fifteenth Edition, NFPA, Quincy, MA.

Nelson, H.E. (1981).Classification of build ing construction . National Fire Protection

Association, Section 5, Chapter

4,

Fifteenth Edition, NFPA, Quincy, MA.

Stevens,

R.E.

"Building codes and standards" (1981). Fire Protection Handbook,

National Fire Protection Association, Section 5, Chapter

13,

Fifteenth Edition,

NFPA, Quincy, MA.

U.S. Federal Emergency Management Agency. (1980) "Multiprotection design

manual." Part 3, Fire, U.S.G.P.O., Washington, D.C.

194; 14(4), 304-316.


--``,`,,`,,`̀ `,,````,`,,,̀ `,`,,-`-`,,`,,`,`,,`---



Chapter 2

PRINCIPLES OF STRUCTURAL

FIRE PROTECTION

2.1

FIRE SEVERITY

2.1.1

Fire Development in

a

Room

Conventionally, the development of a fire in a room is divided into

three periods: growth period, period of full development, and decay

period (Fig.

2.1).

Normally,

a

fire starts with the ignition of a single

product. It may then

go

out or may grow into a fully developed fire.

The start of the full development period is usually preceded by a phe-

nomenon referred to as flashover which is characterized by an almost

instantaneous spread of flame over all combustible surfaces.

During the earlier phases of the growth period, the evacuation of

occupants presents no problem and the risk of failure of structural

elements

is

negligible. The risk of failure begins with the onset of full

fire development, when the temperature rises rapidly and the burning

assumes a quasi-steady-state character.

The word “severity” is commonly used to describe the potential of

fires to spread by destruction. Recently, as a result of ongoing research

concerning the development of a fire and the involvement of combus-

tibles, airflow, and room boundaries, the nature of the definition of fire

severity has changed. It has long been usual to regard the temperature

of the fire gases in the room as the embodiment of the destructive

potential of fire, and the boundaries of the room as passive participants

in the fire process that merely respond to the destructive conditions

imposed on them. Furthermore, the area under the temperature-time

curve has been looked upon as a measure of the severity of fire. This

concept suggests with some qualification that if for two fires the areas

under the temperature-time curves above a specific baseline are the

same, they are of identical severity (Fig. 2.2).


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , ,

,̀ ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E

78 92

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0759600 0021815

023

STRUCTURAL

FIRE


I

Figure 2 . 2-Generalized temperature course for fire in a room.

GROWTH

PERIOD

-

2

LASHOVER

T I M E

A

/

Y

cx

3

a

cx

Y

n-

a

Y

T I M E

Figure 2.2-Illustration of the concept characterizing the sm er ity of fires by

their area under the temperature-time curves. According to the

concept, the tw o fires described

by

curves

A

and

B

are of equal

severity.


-

- ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E 7 8 92

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0 7 5 î b 0 0 0 0 2 L 8 L b TbT

m

PRINCIPLES

OF


13

It has been proven that it is inaccurate to regard the temperature of

the fire gases as the principal descriptor of fire severity. The temperature

of fire gases is the result

of

a strong and complex interaction between

the fire gases and the room. By virtue of that interaction, it appears

permissible and more convenient to look at fire severity through the

effect on the room boundaries. Recent investigations revealed that the

so-called "normalized heat load' on the room boundaries is an accurate

measure of the fire's destructive potential. The heat load is the total

heat absorbed by the room boundaries (per unit surface area) during

the fire incident, Normalization is achieved by dividing the heat load

by the thermal inertia of the boundaries.

Since the heat load is the time integral of the heat flux into the room

boundaries, the concept of normalized heat load can be illustrated as

shown in Fig. 2.3, where fires A and B are of equal severity (destructive

potential).

Numerous theoretical and experimental studies have indicated that

the destructive potential of fires depends mainly on five factors:

0 Total fire load (total mass of combustibles),

Ventilation parameter (characterizing the rate of inflow of air into the

Total area of the room's internal surfaces,

Thermal inertia of the room's boundaries (low for insulating materials,

Fraction

of

energy of volatile combustibles released within the room per

room),

high for conductors),

unit time.

A

T

I ME

Figure 2.3-I llustration of the concept

of

characterizing the severity

of

fires

by

the normalized heaf load. According to the concept, the two

fires described by curves A and

B

are of equal severity.


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E 78 92 0759600

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14


It has been found that the nature of fire depends substantially on

the nature of fuel: on whether the fuel is charring (cellulosics in general)

or noncharring (most plastics). Much of the information available for

room fires has been derived from room-burns employing cellulosics.

Among non-charring fuels, mainly pool-like burning of plastics has

so

far been studied.

A

multitude of calculations for cellulosic fuel has indicated that the

severity of fire, as expressed by the normalized heat load,

increases less than in proportion to the fire load,

decreases as the ventilation of the room increases, and

decreases as the thermal inertia of the room boundaries increases.

In practice, the ability of the room boundaries to withstand the de-

structive potential of fire is determined by subjecting specimens of the

room boundaries to standard test fires. Standard tests are idealized

simulations of room fires, conceived to develop according to a unique

temperature-time curve. The normalized heat load imposed on the test

specimen during a standard test fire is calculable. Because of the unique-

ness of the standard temperature-time curve, the normalized heat load

on the specimen is a function of the duration of test only.

Clearly, the boundaries of the room should be constructed

of

building

elements that are capable of withstanding in standard fire tests the

same normalized heat load as they are expected to be subjected to in

an actual room fire. The length of exposure to test fires that ensures

the imposition of a specified normalized heat load is referred to as “fire

resistance” time.

The rest of this chapter will deal only with ”standard” fires, i.e. those

specified for standard test fires.

Standard temperature-time curves used in various countries for test-

ing of building elements are shown in Fig. 2.4. It can be seen that, with

the exception of that of Japan for times greater than 2 hours, there are

no significant differences between the various curves. The temperature-

time relation adopted in IS0

834

by the International Organization of

Standardization is given in Table

2.1.

In Table

2.2

the ASTM

E119

temperature-time relation is given, which is the standard relation used

in North America.

2.2 EFFECT

OF FIRE

ON COMMON MATERIALS

OF CONSTRUCTION

In order to understand and eventually predict the performance of

structural members in a fire, the material properties that determine the

behaviour of a member at elevated temperatures must be understood.

Regardless of type, all building materials will experience a certain degree

of degradation when exposed to severe fires. At some point, the ele-


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` ,

, ` ,

` , ,

` - - -



1 3 0 0

1 2 0 0

1 1 0 0

U

O

1 0 0 0

w

Li-

4

Li-

u

L

W

+

w

+

9 0 0

S

8 0 0

E 7 0 0

U

6 O0

5 0 0

4 0 0

I

Time in Minutes

5

10

15

30

60

90

120

180

240

360

A S C E 7 8 92

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0 7 5 î b 0 0 002L818 A32 W

PRINCIPLES OF STRUCTURAL FIRE PROTECTION

15

Temperature rise

556

659

718

821

925

986

1,029

1,090

1,133

1,193

/>

A:-

. -

.....

-.

I ' ' 2 q 2 3 0 0

2 2 0 0

y

y\

2 1 0 0

2000

fi 4 1 8 0 0 .

W

1 7 0 0

5

1 6 0 0

1 5 0 0

2

I-

w

{'

U S T R A L I A

G R E A T B R I T A I N

k i c w

CAI

AM^

~ / C A N A D A

i

I

- .-I

, . L I , L L - L - I . Y

"

\ U . S . A . 1 4 0 0

1 3 0 0

1 2 0 0

B E L G I U M

D E N M A R K

F I N L A N D 5 - I T A L Y

4

-

U . S . S . R .

R L A N D

-+io0

N O R W A Y

7 -

J A P A N

S W E D E N

W E S T G E R M A N Y

1

2

3 4 5 6 7 8

O U R A T I O N ,

h

Figure 2.4-Standard fire temperature-time relations used in various

countries

for

testing

of

building elements.

TABLE

.1.

Standard fire temperature-time

relation.


- - ` ` ,

` , ,

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` ` ,

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` , ,

` , ,

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ASCE

7 8 3 2 m 075 îb00 0023839 7 7 3 m

16


Temperature

F

68

1,000

1,300

1,399

1,462

1,510

1,550

1,548

1,613

1,638

1,661

1,681

1,700

1,718

1,735

1,750

1,765

1,779

1,792

1,804

1,815

1,826

1,835

1,843

1,862

1,862

1,875

1,999

1,900

1,912

1,925

Temperature

C

20

538

704

760

795

821

843

862

878

892

905

916

927

937

946

955

963

971

978

985

991

996

1,001

1,006

1,010

1,017

1,024

1,031

1,038

1,045

1,052

Time

h:min

Time

h:min

0:00

0:05

0:lO

0:15

0:20

0:25

0:30

0:35

0:40

0:45

050

0:55

l:oo

1:05

1:lO

1:15

1:20

1:25

1:30

1:35

1:40

1:45

1:50

1:55

2:oo

2:lO

2:20

2:30

2:40

2:50

3:OO

3:lO

3:20

3:30

3:40

3:50

4:OO

4:lO

420

4:30

4:40

4:50

5:OO

5:lO

5:20

5:30

5:40

5:50

6:OO

6:lO

6:20

6:30

6:40

6:50

7OO

7:lO

720

7:30

7:40

7:50

800

Temperature

F

1,938

1,950

1,962

1,975

1,988

2,000

2,012

2,025

2,038

2,050

2,062

2,075

2,088

2,100

2,112

2,125

2,138

2,150

2,162

2,175

2,188

2,200

2,212

2,225

2,238

2,250

2,262

2,275

2,288

2,300

~

Temperature

"C

1,059

1,066

1,072

1,079

1,086

1,093

1,100

1,107

1,114

1,121

1,128

1,135

1,142

1,149

1,156

1,163

1,170

1,177

1,184

1,191

1,198

1,204

1,211

1,218

1,225

1,232

1,239

1,246

1,253

1,260

vated temperatures will adversely affect the material's strength and

rigidity and therefore its structural performance. The material may also

burn, melt, spall, warp, expand, shrink or deflect.

For

the most common

structural materials, i.e. steel, concrete, and wood, it can generally be

assumed that the influence of temperature will not become significant

until or unless flashover occurs, thereby bringing the fire compartment

to the fully developed stage.

Unlike wood, steel and concrete are noncombustible and therefore

do not add to the severity of the fire. The properties of all these ma-

terials, however, will vary with an increase in temperature. Material


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A S C E 78

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PRINCIPLES

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17

properties that affect the behaviour of structural members exposed to

fire will be discussed in more detail in Part 2, Chapter 5. Some of the

material properties may be expressed by equations, giving their value

as a function of temperature. For several of the properties, the de-

pendence on temperature can only be shown in graphs. For a number

of the properties, more than one relationship between the property and

temperature

is

given in this manual. In such cases, the relationships

given in this chapter are generally more simplified than those given in

the Appendix. The relations given in the Appendix are suitable for use

in mathematical models programmed for computer processing. Com-

pilations of values of material properties at elevated temperatures are

given in Lie 1972 and Harmathy 1983.

2.2.1 Steel

2.2.1.1 Thermal Properties

The material properties that affect the temperature rise and distri-

bution in a structural steel section are its thermal conductivity and

specific heat.

Thermal Conductivity:

The temperature rise in a steel member as a

result of heat flow is a function of the thermal conductivity of the

material. The value of this property varies somewhat with chemical

composition at room temperature; however, at elevated temperatures

it may be considered identical for most structural steels. Figure 2.5

illustrates the typical variation in steel's thermal conductivity with tem-

perature. This variation may be expressed approximately by the follow-

ing equations (U.S.D.A. Agricultural Handbook No. 72 1987):

k = -

0.022T

+

48

k

= 28.2

for

O 5

T 900°C

for T > 900°C

where:

k

=

Thermal conductivity, W/m"C

T =

Steel temperature, "C

This thermal conductivity is high in comparison with that of materials

commonly used as a protection of steel (about

100

times). Because of

its relatively high thermal conductivity, the assumption that steel is a

perfect conductor, implying uniform temperatures of the steel section,

is widely used in the determination of the fire performance of steel

members. In reality, temperature gradients do exist in steel sections

which may result in internal stresses. The temperature differential across

a structural section will also be affected by the heat sink characteristics

of adjoining members. The best example of this effect is a concrete slab

resting on a steel beam.



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A S C E

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7 2 O757600

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1 0 .

18 STRUCTURAL

FIRE

PROTECTION: MANUAL

OF

PRACTICE

T E M P E R A T U R E , O F

3 2 1000

2000

I I I

I

I

5 o t

O/

2 0 0 4 0 0

6 0 0 8 0 0 1 0 0 0 1 2 0 0

T E M P E R A T U R E ,

C

10

U

O

2 5

c

2

m

2 0

>

>

I-

-

-

1 5

3

n

æ

O

10

2

a

s

E

5 =

+-

O

Figure 2.5-Thermal conductivity of steel at elevated temperatures.

Specific Heat: The specific heat of the material is the characteristic that

describes the amount of heat input required to raise a unit mass of

material a unit of temperature. For most structural steels, its value

increases gradually with temperature. At 540°C

(1000 F),

however, there

is a steep increase in specific heat over a narrow temperature range.

This

is

illustrated in Fig. 2.6, where the volumetric specific heat (product

of specific heat and density) of the steel is plotted as a function of

temperature. Because of a wide scatter of reported data in this narrow

range, and because of its minor overall influence on behaviour in fire,

a constant value of 600 J/kg K for the specific heat of steel for the entire

temperature range is a good approximation. (Equations in which the

peak is taken into account and that are suitable for computer processing,

are given in the Appendix).

Thermal Difusivify: The thermal diffusivity of a material is a measure

of how effectively the heat is dissipated through the material. It is equal

to the ratio of the thermal conductivity to the volumetric specific heat

of the material. The larger the value of thermal diffusivity, the faster


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,`

` ,` , ,-` -` , ,` , ,` ,` , ,` ---



I

A S C E 78 92

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PRINCIPLESOF STRUCTURAL FIRE PROTECTION

19


1

12, 2 , l o loo I

2 o p o

1 7 5

-

-

-

Figure

2.6

U

O

1 5 0

3

L

m

1 2 5 -

a

1 0 0 u

c

W

I

-

U

U

W

Ln

-

- 1 5

a

u

- 5 0 E

B

c

w

3

- 2 5

2 2

q

>

>

= O

O

200 400

6 0 0 800

1 0 0 0 1 2 0 0

=


C

-Volum etric specific heat for steel at elevated temperatures.

the heat is transported away from the surface being heated. The value

of thermal diffusivity is determined by the following relationship:

a

=

k/pc

where:

a

= thermal diffusivity

k

= thermal conductivity

p = density

c

=

specific heat

Since the values of thermal conductivity and specific heat vary with

elevated temperatures, the value of thermal diffusivity will also vary.

Because it may be readily calculated from the equations given for ther-

mal conductivity and specific heat, values for thermal diffusivity will

not be shown here.


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A S C E 78 92 0757600 O023823

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20



Modulus

of EZasticity: The modulus of elasticity of steel decreases with

increasing temperature, as shown in Fig. 2.7. The modulus for ferrite

steels decreases nearly linearly with temperature up to about

500°C

(932°F). Above this temperature, the modulus decreases more rapidly.

This relationship is also true for hot-rolled alloyed bars used in pre-

stressed concrete.

However, the modulus of elasticity for cold-drawn steel (used for

prestressing wire) is typically

20%

lower than the values for hot-rolled

steel over a temperature range of

20

to

700°C (68

to

1292°F).

(See Ap-

pendix for equations for the modulus of elasticity of steel.)

Strength: There are two values that typically characterize the strength

of hot-rolled structural steel: its yield and tensile strengths. Figure 2.8

illustrates typical stress-strain curves for steel at various temperatures

(Harmathy and Stanzak

1970).

Yield strength is generally the basis for

the design of steel structures at working loads. It is characterized (at

room temperature) by a distinct point on the stress-strain curve at which

a pronounced increase in strain is observed without a corresponding

increase in applied stress. At elevated temperatures, this characteristic

diminishes until the curve becomes "rounded." Under these conditions,

the value of yield strength is defined by the "offset" method. Figure

2.9

shows the variation of this characteristic yield strength with tem-

perature. Note that the yield strength is reduced by 50% at about

600°C.

TEMPERATURE, F

32

200

400 6 0 0

800 1000

1 2 0 0

1 4 0 0

2 0 0

m

c:

2 1 5 0

x

rr)

E

9

-

2

+

100

U

O

TEMPERATURE,

C

Figure 2.7-Modulus of elasticity of steel

at

elevated temperatures.


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,`

, ,` ---



ASCE

7 8 92

0759600

0021824 0 3 b

N

E

E

z

vi

v>

W

@L

I-

vi


21

6 0 0 1

20 c , 200°C

\

6 0 0 ° C

0 0

1O0

O

5 0

._

VI

2d

6 0 .

vi

vi

W

4 0

E

vi

2 0

i

O O . O 2

O .

04

O . 06

O . 08

O . 1 0 O . 1 2

S T R A I N

Figure 2.8-Stress-stra in curues for

a

mild steel ( A S T M

A36)

at various

temperat ures.

T E M P E R A T U R E , F

3 2

4 0 0

8 0 0 1 2 0 0

.O0

8 0

6 0

4 0

2 0

n

-

U L TI MATEI

HIGH STRENGTH

ALLOY B A R S

í

ULT

I

MATE)

-

-

O 2 0 0

4 0 0 6 0 0


C

Figure 2.9 -Stren gth of some steels at high temperature.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E

78 92 O759600

0021825 T 7 2

22


Equations have been developed to describe the variation of the yield

strength of steel with temperature (Lie and Stanzak 1974) which can

be given by:

or by (European Convention for Constructional Steelwork):

Fy

=

Fyo i + TJ(767 tn(TC/1750))) O < T , I 00°C

Fy

= Fyo (108

-

T~/lOOO)/(T,

-

440))

600" <

T , 1000°C

where:

Fy

=

yield stress at elevated temperatures

Fyo = yield stress at room temperature

T , = temperature of steel, "F

T, = temperature of steel, "C

(See Appendix for equations of yield strength and of stress-strain curves

for various steels).

The tensile or ultimate strength of hot-rolled steel, as illustrated in

Figure 2.9, is the maximum strength achieved before failure. The effect

of temperature on this property is similar to that on yield strength with

the exception of a temporary 25% increase in strength in the 150-370°C

(302-698°F) range (Figure 2.9). From this point, tensile strength de-

creases to values approaching yield strength at 760°C (1400°F).

The strength changes in cold-drawn steel are different in character

from the changes found in hot-rolled steel at elevated temperatures.

As

shown in Fig. 2.9, the cold-drawn steel loses its strength at relatively

lower temperatures.

e

= ( T ,

-

6a)/iaoo


Thermal Expansion: The thermal expansion of steels can be related to

its temperature by a coefficient of expansion, which can be defined as

the expansion of a unit length of the steel when it is raised one degree

in temperature. The effect of expansion and contraction of the member

on the surrounding structure is an important consideration to the struc-

tural integrity of the building during exposure to elevated temperatures.

The coefficient of thermal expansion is reported to be basically the same

for all typical structural steels. Its value increases with increasing tem-

peratures. Beyond 650°C (1202"F), the value

of

the coefficient decreases

to zero at approximately 815°C (1502°F) and then begins to increase

again. This is due to a molecular transformation in the steel at this

temperature range. The order of magnitude of thermal expansion of

steel is given in Fig. 2.10. It should be noted, however, that lower


--``,`,,`,,``̀ ,,````,`,,,`̀ ,`,,-`-`,,`,,`,`,,`---



A S C E

78

92 H 0759600

0 0 2 L ô 2 b

909 9


FIRE

PROTECTION

TEMPERATURE,

F

2 0 0 4 0 0 6 0 0 8 0 0 1000 1 2 0 0

0

0 1 0 3 2

2 0 0 4 0 0 6 0 0 8 0 0 1000 1 2 0 0

I I

O08

-

006 -

0 0 4 -

O 0 2

-

I

I I I I

23

O 1 0 0 2 0 0

300

4 0 0 5 0 0 6 0 0

TEMPERATURE, C

Figure 2.10-Th erma l expansion of ferrite steels.

values are reported for prestressing steel. The following equation de-

scribes, for temperatures up to 650°C (1200 F), the influence of tem-

perature on the coefficient of thermal expansion (American Institute of

Steel Construction

1970).

Equations covering higher temperatures are

given in the Appendix:

a =

(11

+ 0.0062 T ) x

where:

u

=

coefficient of thermal expansion

T

=

steel temperature,

"C

Creep Properties:

Creep may be defined as the time dependent defor-

mation of a material. Creep is characterized by three periods: primary,

secondary, and tertiary (Fig. 2.11). ,The primary creep begins with load

application and is reflected by a continuous but decreasing strain after

the elastic deformation. Deformation, which then continues at a con-

stant strain rate for a given temperature, is the secondary creep. Finally,

tertiary creep begins when, under the same conditions, the strain rate

begins

to

increase, eventually leading to failure by rupture. At the

elevated temperatures of a fire, deformation proceeds at a varying rate

depending on both temperature and length of time. Ultimate failure as

a result of increasing strain will eventually result in failure at a load


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E

78

92 m

0759600 0023827

845

24

STRUCTURAL FIRE PROTECTION: MANUAL

OF

PRACTICE

O

TIME

Figure

2.11 -Typical

creep

curve.

less than that sustained at its beginning. From a practical point

of

view,

the secondary creep is the most important. The creep depends not only

on the temperature but it is also strongly dependent on the stress in

the steel.

Creep

of

structural steels becomes significant at temperatures above

450°C (842°F). The influence of creep on fire performance may be eval-

uated by the use of strength values determined at a strain (or heating)

rate equivalent to that achieved during fire. It may alternatively be

evaluated through the use of creep equations (Harmathy

1967).

2.2.2

Concrete

2.2.2.1

Thermal Properties

The thermal properties of concrete are found to vary widely with the

type and quantity of the aggregate in the concrete.

Thermal Conductivity: The thermal conductivity of concrete is usually

taken as invariant with respect to direction of heat flow. For normal

weight concrete, it tends to decrease with increasing temperature. This

is illustrated in Fig. 2.12, where the order

of

magnitude

of

the thermal

conductivity of normal weight concrete

is

given as a function of tem-

perature. The value and change of the thermal conductivity with tem-

perature, however, depends on the degree of crystallinity of the ag-

gregate. The higher the

crystallinity,

the higher is the thermal conductivity

and its decrease with temperature. A typical crystalline material in


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--` ` ,` , ,` , ,` ` `

, ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



ASCE 7 8

92

O759600 0021826 7 8 1

O

5 -

I I I 1 I I

-

0 -

-

-

-

0 -

L I G H T W E I G H T

-

-


25

- 1 . 6

L L

c

S

- 1 . 2 2

m

z-

0 . 8

n

z

O

u

5

E

Y

0 1

I I I I I I I I I o

O

2 0 0 4 0 0 6 0 0 8 O0

TEMPERATURE, C

Figure 2.12-Thermal conductivity of normal weight and lightweight

concrete as a function of temperature.

concrete is quartzite, which is often the main component in siliceous

aggregate.

The thermal conductivity of lightweight concretes tends to increase

with temperature, but is nearly constant as shown in Fig.

2.12.

Specific Heat:

Typical ranges for the volumetric specific heat (product

of specific heat and density) for normal weight and lightweight con-

cretes (Harmathy and Allen 1973, Harmathy 1970) are shown in Fig.

2.13. The peak at the 500°C (932°F) temperature range is caused by the

character of the specific heat of the cement paste, which shows a sharp

peak at about

500°C.

The water in the concrete may also have a sub-

stantial effect on the value of the specific heat of the concrete.

A study was made of the variation in the specific heat as a function

of temperature for concretes made with three different types of aggre-

gates: gravel, limestone, and a lightweight aggregate (Collett and Tav-

ernier 1976). The results are shown in Fig. 2.14. It can be seen that the

specific heat increases slowly with increasing temperature for all ag-

gregates. The type of aggregate has only a small influence on the specific

heat. Although the many variables affecting the specific heat of a given

concrete batch make it difficult to establish a constant value for this

property, the results indicate that

1170

J/kg"C (0.28 Btu/lb"F) is a rea-

sonable approximation of the specific heat of concrete (Fig. 2.14).


- - ` ` ,

` , ,

` , ,

` ` ` , ,

`

` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



26 STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE


1200

1 6 0 0

0 0 8 0 0

iL

-

. .

E

- 6

a

+ - 5

Y

I

U

U

- 4

-

u

m

3

2 2

lY

c

i

o

O

g 400 6 O0 800 ;

O 2 0 0

T E M P E R A T U R E , C

Figure 2.13-Ranges of volumetric specific heats of normal weight

and

lightweight concretes.


F

,

Z q O

4qO 6 q O 8 q O l O y 0 12,OO ,

LL

.

0

O .

E 8 0 0

o

G R A V E L

u,

0 L I M E S T O N E

-

A L I G H T W E I G H T

O 1 0 0

2 0 0 300

400 5 0 0 6 0 0

7 0 0

rn

4 0 0 O.


Figure 2.14-Specific heat for different types of concrete.

U

+-

I

Y

2 0

-

U

0

a

rn

-

1


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E 78 92 759600

002L830

3 3 T

PRINCIPLES

OF


27

Thermal Diffusivity:

As with steel, the thermal diffusivity of concrete

is a function of the thermal conductivity, specific heat and density of

the concrete. Accordingly, the thermal diffusivity will vary in value

with the change in thermal conductivity and specific heat.


Modulus of Elasticity: Values for modulus of elasticity of concrete made

with three types of aggregates are shown in Fig. 2.15. All three concretes

experienced a rapid loss in elastic modulus as temperature increased.

At 200°C (392”F), the modulus is from 70-80% of the modulus at room

temperature. At 400°C (752”F), the modulus is from 40-50% of the

original value. From reported data, it appears that aggregate type and

concrete strength do not significantly effect moduli at high tempera-

tures. Test data of the modulus of elasticity of concrete shows that the

original values are not restored upon cooling (Harada 1961). Actual

recovery is found to be both a function of the exposure temperatures,

and the time since exposure (Fig. 2.16). Recovery is never actually

complete. This must be taken into account when considering reusability

of concrete after a fire.

Strength: The compressive strength of concrete at elevated tempera-

tures will vary according to the type of aggregate, cement to aggregate

ratio, and the degree of loading, among other factors. The effect of

cement to aggregate ratio and different load conditions are illustrated

in Fig. 2.17 (Malhotra 1956).

Figs. 2.18, 2.19, and 2.20 also show the compressive strength of

concretes made with different types of aggregates (Abrams 1971). Spec-

imens heated to test temperature with no superimposed load and tested

hot are designated as ”unstressed.” Strengths of specimens heated

while stressed to

0.4

f: and then tested hot are designated as ”stressed

to 0.4

fc,”

where f:

=

28-day moist cure compressive strength. The

“unstressed residual” strengths were determined from specimens heated

to test temperature, cooled to room temperature, stored at 75% relative

humidity for 6 days and then tested in compression.

It was found that the applied stress levels during heating of 0.25 to

0.55 f: had little effect on the strength obtained and that the original

concrete strengths of between 27.6 MN/m2 (4000 psi) and 44.8 MN/m2

(6500 psi) had little effect on the percentage of strength retained at test

temperature. In Fig. 2.19, the ”unstressed” sanded specimens were

made with sand replacing 60% of the lightweight fines, by volume. The

unsanded lightweight concrete was the kind used in the manufacture

of masonry block. In the results reported, the ”stressed’ strengths are

higher than the ”unstressed” strengths, and that the ”unstressed’ re-

sidual strengths were lower in all cases than strengths determined by

the other two procedures.

The influence of various aggregates on the elevated temperature com-

pressive strength is shown in Fig. 2.21 (Pettersson 1965). As can be


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - `

, ,

` , ,

` ,

` , ,

` - - -



ASCE

78

92 W

0 7 5 9 b 0 0

0023833 2 7 6

28

STRUCTURAL

FIRE

PROTECTION: MANUAL

OF

PRACTICE

TEMPERATURE, I F

32

4

O0

8 0 0 1 2 0 0

;o 1 0 0

4

c

2.

8 0

U

O

e

u- 6 0

g

Y

4 0

vi

Y

O

2 0

2 0

vi

1

æ

n

O

2 0 0

4 0 0 8 0 0

TEMPERATURE,

C

Figure 2.15-Modulus of elasticity of concrete.

1

E,

= 2.6 x

id

k N / m L ì

(E,

=

5.5

x

lo6

p s i )

I I I I I

i 1

O

1 2 3 4

5

6 7

8

9 1 0 1 1 1 2

TIME. month

Figure 2.16-Natural recovery

of

the modulus of elasticity

of

a normal

weight concrete heated at various temperatures.


--``,`,,`,,`̀ `,,````,`,,,`̀ ,`,,-`-`,,`,,`,`,,`---



A S C E

7 8 92

0 7 5 9 b 0 0

0023832 302

TEMPERATURE,

F

TEMPERATURE,

F

32 200

400

600

800

1

12032 200 400 600 800 loo0

110

I

1 2 0 r

l

I

1 I

l 1

110 - CEMENT:AGGREGATE RATIO - - -

10

- - -UNLOADED - - --- COOLED DOWN

8

O

O I l I I I

10

O

100

200

300

400

500

600

100

200

Mo

400 500 600

TEMPERATURE, OC TEMP ERA TURE C

a )

INFLUENCE

OF LOADING AND

b l

DIFFERENCES N

COMPRESSIVE TRENGTH

CEMENT-AGGREGATE U T I 0 O N THE

COMPRESSIVE STRENGTH

OF

A NORMAL

WEIGH T CONCRETE AT ELEVATED

TEMPERATURES

BETWEEN HOT A ND COOLED DOW N

NORMAL WEIGHT CONCRETE


29

Figure 2.17-Influence of cement-aggregate ratio and load conditions on the

concrete strength.


F

3 2 4 0 0 8 0 0 1 2 0 0 1 6 0 0

i

SSED'- '\

R E S I D U A L

( S A N D E D ) \\,(UNSANDEDI -

i

0 1 ..

z- 4 0

-

<

x

-

A V G . I N I T I A L

fi

F UNSANO ED CO NCRET E= 1 7 . 9 M N/ r n 2 ( 2 6 0 0

ps?ì\\

A V G . I N I T I A L f O F S A N DE D C O N C R E T E z 2 6 . 9 M N l m 2 ( 3 9 0 0 psiJ

rl

2 0

Figure 2.28-Compressive strength of lightweight concrete at high

temperatures and after cooling.

COPYRIGHT 2003; American Society of Civil Engineers Document provided by IHS Licensee=IHS Dealers/IHSINTL003, User=SOPORTE,08/14/2003 08:59:48 MDT Questions or comments about this message: please call


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,

` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



ASCE 7 8 92

O759600

0023833 O49

30



3 2 400 8 0 0 1200 1600

A 100

0

Y

80 -

'

8

8

'

I-

z

-

O

E 6 0

- UNSTRESSED

M x < .

o

R E S I D U A L

Y

z 4 0

-

œ

Y

>

v>

Y

œ

L

2 0

-

A V G . I N I T I A L f = 26.91 M N d (39W s i )

2i

O

3 0

I I I

1 I

I

I

I

800

200

4 0 0

600


v>

2 0

-

A V G . I N I T I A L f = 26.91 M N d (39W s i )

Y

f

L

2i

O

3 0

I I I

1 I

I

I

I

800

200

4 0 0

600


Figure 2.19-Compressive stren gth of carbonate aggregate concrete at high



O

\ STRESSED TO

0.4

f

-

Y

UNSTRESSED

R E S I D U A L

O

ip

\

~

L

I

O I I I

I l I 1

I

u 0

800

200 4 0 0 600


Figure 2.20-Compressive strength of siliceous aggregate concrete at high



--``,`,,`,,``̀ ,,````,`,,,̀ `,`,,-`-`,, ,̀,`,`,,`---



A S C E

78

92 0759600

0023834

T 8 5

PRINCIPLESOF STRUCTURAL FIRE

PROTECTION

31


Figure 2.21-Influence of the aggregate

on

the compressive sfr en gf h

of

concrete

a t

elevated temperatures.

seen, actual strengths will increase for some aggregates while others

begin to decline immediately. These values, however, all tend to merge

as temperatures reach 800°C (1472°F).

Few results have been reported of tests to determine tensile strength

under elevated temperature. Fig.

2.22

shows the effect of temperature

on split-cylinder tensile strength of a siliceous aggregate concrete (FIP/

CEB

Committee 1978).

As

with other mechanical properties of concrete under limited ex-

posure (Le. up to 500°C (932"F)), the compressive strength of the ma-

terial will be largely restored given adequate recovery time. Fig. 2.23

illustrates the influence of both the degree of exposure and the length

of recovery time on the concrete strength (Harada 1961).


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E

7 8 9 2 m

0759600

0023835

9 3 3 m

32


TEMPERATURE, F

Figure 2.22 -

-

W

E

I-

V

R A P I D HEATING

5 0

-

-

L n

æ

W

e

2 5

-

Y

O

6e

I I I

2 0

200 4 0 0 6 0 0

8 0 0

O

TEMPERATURE, C

-Effect of temperature on split-cylinder tensile strength of

a

siliceous aggregate concrete.

1 2 0

I

1 1 1 1 1 1 1 1 1 1 1

z 1 1 0

+

PIl,

I I I I I I

œ

+

v>

O

1 2

3

4

5

6

7 8 9 1 0 1 1 1 2

O

T IME,

m o n t h

Figure 2.23-Natural recovery

of

the compressive streng th

of a

normal

weight concrete, heated a t various temperatures.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E 7 8

92

0759600 0023836

858


33

2.2.2.3

Deformation Properties

Thermal Expansion:

The thermal expansion data for concrete made with

different aggregates are shown in Fig. 2.24 (Pettersson 1965, Saito 1965).

Most concretes expand with increasing temperature. The thermal ex-

pansion is not a linear function of temperature but increases with in-

creasing temperature. Sanded expanded-shale concrete has the most

nearly linear and lowest expansion-versus-temperature relationship over

the temperature range of 20-875°C (60- 1607°F).

The thermal expansion of concrete is influenced by cement, water

content, aggregate type, and age. An investigation of the effect

of

different load levels on thermal expansion of a siliceous-aggregate con-

crete heated at a rate of 5°C (9"F)/min s shown in

Fig.

2.25 (Anderberg

1976). As can be seen, the thermal expansion was sharply reduced with

increasing levels of stress.


2 0 0 400 6 0 0 800 1O00

1200

2

1.

6

-

S A N D S T O N E

1 . 2

-

-

0 . 8

-

-

0 .4

-

-

-

- 0 . 4

-

-

P E R L I T E

- 0 . 8 ~

O

I

I I

I I 1

1O0 2 0 0

300

4 0 0 5 0 0

6 0 0 700


C

Figure

2.24-

Expansion with temperature

of

concretes made with various

aggregates.


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---




1 . 5 ,

2 , 4qO , 8O , 12,OO

1.

o

o . 5

se

æ

-

a

cc

f

v,

O

- 0 . 5

-1. o

O 200 400 6 0 0 8 0 0


C

Figure 2.25-Effect of load levels

on

concrete deformation.

Generally, soft aggregates exhibit relatively little influence on expan-

sion while cement paste will shrink, causing overall shrinkage. Hard

aggregates have a more pronounced effect, however, and might even

experience a change in the molecular structure. The best example of

this is quartz, which goes through a transformation at approximately

570°C (1058°F) and again at 870°C (1598"F), as shown in Fig. 2.26. The

influence of the quartz content in a gravel aggregate is illustrated in

Fig. 2.27.

A s

can be seen, the quartz transformation influences the

expansion characteristics during both the heating and cooling periods.

The effect of final dehydration of the concrete at approximately 800°C

(1472°F)

leads to a rather rapid shrinkage of the concrete.

Creep Properties:

Creep

of

concrete is determined by various factors.

The most important are the temperature of the concrete and the stress

in it.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



~

A S C E 7 8

92 0 7 5 9 b 0 0 0023838 620

PRINCIPLES

OF


35

T E M P E R A T U R E , OF

2 , 4 2 4 0 0 8 q O 12pO 16;o 2 0 p o

1

2 . 2

X

u

1 . 4

1 . 2

1. o

o.

8

-

O .

6

O

U

w

u

æ

O

v> o . 4

a

r x

o. 2

O

æ

X

W

-

B.

T R A N S F O R M A T I O N

-

B - Q U A R T Z

+

T R I D Y M I T E

-

-

A . T R A N S F O R ¡ W T I O N

-

-

-

O

2 0 0

4 0 0

6 0 0 8 0 0

1 0 0 0 1 2 0 0


Figure 2.26-Expansion with temperature

of a

material mainly quartz

(Heating rate:

5°C

per minute).

Data on creep at high temperatures of a carbonate aggregate concrete,

for a 5-hour test period are shown graphically in Fig. 2.28 (Cruz 1968).

After heating to test temperature, a load equal to

45%

of

room-

temperature strength of the concrete was maintained during the test

period. For this concrete, creep increased with temperature only mod-

erately to

320°C

(608°F). Above this point, the increase in creep was

much greater. The age, moisture conditioning, type, and strength of

concrete, and stress-strength ratio have all been found

to

influence the

creep of concrete at high temperatures.

Fig. 2.29 shows creep information for two stress levels, i.e. 22.5%

and

45%

of the concrete strength, and several concrete temperatures

for a 3-hour period (Harmathy 1967). From these data it appears that

creep plays a very limited role in the overall behaviour of concrete

except when the temperature is above

400°C

(752°F).


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



ASCE 78 92 0759b00 0023 839 5 6 7

36


OF

PRACTICE


" F

3 2

4

O0 800

1200 1 6 0 0 2 0 0 0

1.2

c2 1 . 0

_I O. 8

I

l-

z

Y

2

U

= O. 6

z

o. 4

-

c>

O

f$

o.

2

: o

U

c

2

- 0 . 2

o

@=

p .

w

-0.4

z - 0 . 6

cn - 0 . 8

- 1 . 0

O

z

<

x

-

Y

I

1

TO B E R MOR TE

-

- A . T R A N S F O R N I T I O N

a

- Q U A R T Z -+B - Q U A R T Z

-

- 1 . 2

O

200 400

6

O0

8 0 0 1 0 0 0

1 2 0 0


Figure 2.27-Expansion of a concrete made with gravel aggregate during

heating and cooling dow n period (Rate of temperature change:

5°C

per minute).

2.2.3

Wood

When a structural wood member is exposed to fire, a char layer is

formed at the exposed surface. The fire resistance of the member de-

pends on the extent of wood charring and the load-carrying capacity

of the remaining uncharred portions of the structural wood elements.

The char layer is considered to have practically no strength. There is

also loss of strength and rigidity of the uncharred wood because of its

elevated temperature. If the rate

of

charring of the wood and its strength

and deformation properties are known as a function

of

temperature,

the time during which the member can support the load, i.e. its fire

resistance, can be calculated.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



ASCE

7 8 92 0759600 0023840

289

D

PRINCIPLES OF STRUCTURAL FIRE PROTECTION 37

O . 0 0 4

r

649°C í1200 F)

O . 0 0 4

o.

O 0 2

t

649°C (1200°F)

t

1

E o .

O02

z

-

2

0 . 0 0 1

I

I

I

w l I I

316 C,(60O0F)

I

1

I I I

l

I-

O

a

Y

0 . 0 0 1 I 1 I I

o 149°C í3OO F)

0 -

o . O 0 1

I

1

I

O

1

O

1 2 3 4

5

T E S T

TIME,

h

Figure 2.28-Creep

of

a carbonate aggregate concrete at various

temperatures. (Applied stress = 12.42

M N h 2

1800 psi),

f h = 27.6

M N h 2

4000 psi)

o. 5 I I

L OAD: 22.5%

O

1

2 3

T I M E ,

h

i

OAD:

45%

- 400°C (752°F)

-

O 1 2 3

TIME,

h

Figure 2.29-Effect of temperature and stress level on creep.


--``,`,,`,,`̀ `,,````,`,,,̀ `,`,,-`-`,,`,,`,`,,`---



ASCE

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92 0757600 002L841 115

38


OF

PRACTICE

2.2.3.1 Rate of Charring

By converting wood to char and gas, thermal degradation (pyrolysis)

results in a reduction in the wood density. Thermogravimetric analyses

(Schaffer

1967,

Tang

1967)

has shown the density of wood heated at a

rate similar to that formed in burning wood members decreases ap-

proximately in the manner shown in Fig. 2.30. The charring rate gen-

erally refers to the linear rate at which wood is converted to char. Under

standard fire exposure, the charring rates tend to be fairly constant

after a higher initial charring rate. There is a fairly distinct demarcation

between char and uncharred wood. The base of the char layers is wood

reaching a temperature of approximately 300°C

(550°F).

To determine

the charring rate, one can use either empirical equations or theoretical

models based on chemical and physical principals. Some of the theo-

retical models are discussed in Section

5.1.9.

Expressions for charring rate in the standard ASTM

E 119

test are

the result of many experimental studies. It is generally assumed that

the transverse-to-grain char rate is a constant

0.6

m d m i n ( l-Y2 in./hr.)

for all woods, when subjected to the standard fire exposure. There are

differences among species associated with their density, chemical com-

position, and permeability. Chemical composition affects the kinetics

of pyrolysis and the percentage weight of the residual char. In addition,

the moisture content of the wood affects the charring rate. The influence

of the moisture content and density of the wood on the charring rate

is illustrated in Fig. 2.31 for Douglas-fir exposed to the standard test.

It can be seen that the charring rate decreases with increasing density

of the wood and also with increasing moisture content. It is reasonable

150

>

+

I

-

I

I I I

125

z

W

n

-I 100

Q

I-

-

-

æ 75

-

U

5 0

25

I-

z

E

I

O

100 200 300

400

5 0 0

600

700 800

900

1000

1100


C

Figure

2.30-

Density of wood as a function of temperature.


--``,`,,`,,`̀ `,,````,`,,,`̀ ,`,,-`-`,,`,,`,`,,`---



A S C E

7 8

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0021842 O51

PRINCIPLES

OF STRUCTURAL

FIRE PROTECTION

39

0 . 8

-

0 . 7 -

t

.-

E

E

E

- 0 . 6 -

g

0 . 5

I

. 4

-

-

cd

cd

o

U

O

0 . 3 .

w

I-

cx

a

0 . 2 -

0 . 1

-

- C O N T E N T

I B Y

W E I G H T I

O

300 400 5 O0 600

D E N S I T Y , k g / m 3

condition ) for various moisture contents w hen exposed

to

ACTM standard fire.

Figure 2.31-Rate of charring of Douglas fir as

a

function of its density (dry

to modify the 0.6 mm/min approximately to 0.4 mm/min for moist and

dense wood or

0.8

mm/min for dry and light wood.

Assumption of a constant charring rate is reasonable when the mem-

ber or panel product is thick enough to be treated as a semi-infinite

slab. For smaller dimensions, the charring rate increases once the tem-

perature at the center of the member or at the unexposed surface of

the panel begins to rise. The charring rate parallel to the grain of wood

is

approximately twice the transverse to the grain (Hall et al.

1971).

As

a beam or column chars, the corners become rounded. The rounding

is generally considered to have a radius equivalent to the char depth

on the sides. The effect of fire-retardant treatment and adhesives on

fire resistance depends on the type of adhesive or treatment. Lumber

bonded with phenolic or resorcinol adhesives has a charring rate con-


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , , `

, ,

` ,

` , ,

` - - -



ASCE 7 8

92 0759600 0021843 T î 8

40


sistent with that of solid wood. Fire-retardant treatments are designed

to reduce flamespread. The fire retardant's effect on charring rate may

be to only slightly increase the time until ignition of the wood. Some

fire retardants reduce flammability by lowering the temperature at which

charring occurs. This may increase the charring rate. A few retardants

have been found to improve charring resistance (Schaffer 1974, Nuss-

baum 1988). The charring rate in a real fire depends upon the severity

of the fire to which the wood is exposed. The fire severity depends

upon such factors as the available combustible material (fire load) and

the available air supply (design opening factor). Using these factors,

equations have been developed for char depth at a given time (Hadvig

1981). Charring rate generally varies linearly with external heat flux

(Nussbaum 1988, Mikkola 1990).

2.2.3.2

Thermal

Properties

Most wood properties are functions of density, moisture content,

grain orientation, and temperature. Chemical composition may also be

a factor. Wood is a hygroscopic material, which gains or loses moisture

depending upon the temperature and relative humidity of the sur-

rounding air. Moisture content of wood is calculated by dividing the

weight of water in wood by the weight of oven-dry wood. It is usually

expressed as percentage. Under the conditions stated in ASTM E 119

(23" C,

50%

relative humidity), wood has an equilibrium moisture con-

tent of 9%.

The oven-dry density of wood can range from 160 to over 1000 kg/

m3, but most species are in the 300-700 kg/m3 range (U.S.D.A. Agr.

Hdbk #72 1987). The density of wood relative to the density of water,

i.e., specific gravity, is often used to express the density. The specific

gravity of wood is normally based on the oven-dry weight and the

volume at some specified moisture content, but in some cases the oven-

dry volume is used.

The fiber (grain) orientation is important because wood is an ortho-

tropic material. The longitudinal axis is parallel to the fiber or grain.

The two transverse directions (perpendicular to the grain) are the radial

and tangential axes. The radial axis is normal to the growth rings and

the tangential axis is tangent to the growth rings.

Property data for wood can be found in the Wood Handbook: Wood as

un Engineering Material

(U.S.D.A. Agr. Hdbk #72 1987) and various other

wood science reference books. The preponderance of property data is

often limited to temperatures below 100°C. In fire resistance analysis,

temperature can have a significant influence on the properties of wood.

Properties at temperatures associated with a fire can be found in articles

on the various theoretical charring models (Section 5.1.9). For purposes

of illustrating the general nature of the thermal properties of wood,

graphs from Knudson and Schniewind (1975) are shown here. Better


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E

3 8 92 0759600 0023844 924

D

PRINCIPLES

OF


41

thermal property data are still needed for char and wood at the higher

temperatures.

Thermal conductivity:

Both density and moisture content affect the

thermal conductivity of wood. The transverse thermal conductivity of

wood at elevated temperatures is shown in Fig. 2.32 (Knudson and

Schniewind 1975). The room temperature value is for Douglas-fir at

12% moisture content. Initially the thermal conductivity increases with

temperature (Segment A). Based on work on wood described in Maku

(1954) the thermal conductivity of both wood and char was assumed

to be proportional to its absolute temperature.

A

thermal conductivity

for charcoal (0.041 W/m-W0.024 BTU-ft/hr-ft'-"F) was applied at 350°C.

A straight line relationship (segment E) was assumed between

200 C,

temperature at which wood begins to degrade into flammable volatiles,

and 350°C, temperature at which char has a nearly uniform density. In

recent tests (Ouchi

1988)

it was found that the thermal conductivity of

wood initially at

11

moisture content increases linearly with temper-

ature up to around

lOO"C,

and then gradually decreases at the same

rate up to temperature

of

300°C. The thermal conductivity of wood

decreases as its moisture content decreases.

Specific H eat:

For temperatures up to 140"C, the specific heat of wood

has been shown to have a linear relationship with temperature. Segment

A

of Fig. 2.33 represents the combined specific heat of wood plus that

0.250

-

I I ;I

I I

I

I

I I I

I

I

o

O

E

- 0.200

t

I

I

>

>

+-

-

-

O. 150

I3

æ

O

u

A

n

=l

.100

E

w

W

I

+

I

O . 050 I I

O 100 200

300

400

500

600 700 800 900 1000 1100


C

Figure 2.32-Thermal conductivity of wood

as

a function of temperature.



--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E

7 8

92

0 7 5 9 b 0 0 0021845 8bO


2.5

U

' 2.0

m

Y

Y

-

I-

a

w 1.5

I

U

-

LL

U

W

v,

-

0-

1.

o

I

; I

I

I

I \

I \

I \

I

E

o. 5

O

100

200 300

400 500

600

700 800 900 1000

1100


C

Figure 2.33-Specific heut of wood

as

a function of temperature.

of

10%

moisture. The sharp peak between 99.5 and 104.4"C was added

to represent the latent heat of vaporization of the water within the

wood. Segment C is consistent with segment

A

without the addition

for moisture. Using a value for charcoal (690 J/kg "C or 0.165 Btuílb

F),

a constant value was assumed for temperatures above 350°C. Segment

D was obtained by connecting segment C and E by a straight line

between 200°C and 350°C.

Kinetics: Thermal gravimetric analysis techniques (TGA) are generally

used to determine the kinetic constants and char yield of wood exposed

to elevated temperatures. The kinetics

of

mass loss due to thermal

degradation shown in Fig. 2.30 are generally expressed by an Arrhenius

equation.

Heut Generufion: The heat of reaction for wood pyrolysis has been

highly disputed. Published estimates

of

the overall heat

of

reaction

during the pyrolysis of wood range from 370 kJ/kg endothermic to 1700

kJíkg exothermic (Roberts 1971). In some recent models, it has been

assumed to be zero.


Mod ul us of Elasticity: The modulus of elasticity of wood, with a mois-

ture content between O-12%, decreases slowly with temperatures up

to 180-2OO0C, as shown in Fig. 2.34 (Gerhards 1982). Above 200°C there


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



ASCE

7 8

92 0759b00 0021846 7 T 7 W

PRINCIPLES

OF


l

I I

I I

v>

3

43

3 O0

E

W

a

O

O 5 0 1O0 1 5 0 2 0 0 2 5 0


C

Figure 2.34-Modulus

of

elasticity of wood

as

a

function

of

temperature.

is some evidence that it decreases more rapidly. There is a spread in

reported results.

Tensile Strength:

The tensile strength parallel to grain exhibits a small

linear decrease to about 200°C. Above 200°C, the effect becomes greater

(Gerhards 1982, Schaffer 1984, Schaffer 1973). A linear relationship that

approximately reflects the decrease of the tensile strength of wood,

with a moisture content between 0-12%, is shown in Fig. 2.35 (Knudson

and Schniewind 1975). The tensile strength of unheated wood is about

110

MPa, while heated, the tensile strength reduces to about 24% at

300°C. After cooling and reconditioning to a moisture content of 12%,

a substantial part of the tensile strength is regained, as shown in Fig.

2.35.

Compressive Strength: The compressive strength parallel to grain de-

creases more rapidly with temperature than the tensile strength (Schaf-

fer 1984, Schaffer 1973). An approximate linear relationship for wood

with a moisture content between 0-12%, is shown in Fig. 2.38 (Knudson

and Schniewind 1975). The compressive strength of unheated wood

decreases linearly with temperature until approximately

20%

of the

initial strength remains at 300°C. After cooling and reconditioning to a

moisture content of 12%, the compressive strength increases to ap-

proximately the original strength, as shown in Fig. 2.36.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E

78

92

W

0757600

0023847 b 3 3

44 STRUCTURAL FIRE PROTECTION: MANUAL

OF

PRACTICE

O

O

5 0 1O0 1 5 0

2 O0 250 3 0 0


Figure 2.35-Tensile strength of

wood

us u function of temperature.

1 2 0

I

I

I

1 0 0

-

R E C O N D

I T 1 O N E D

80

-

6 0

-

40

-

2 0

-

I

I I I l

5 0

1O0 1 5 0 200 2 5 0 3 0 0

O

1 0 0

'

80

6 0

40

2 0

I

I I I l I

5 0

1O0 1 5 0 200 2 5 0 3 0 0

O


C

Figure 2.36-Compressive strength of wood us u function of temperature.


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E 78

92 759600

0023848

5 7 T


FIRE

PROTECTION 45

2.2.3.4

Deformation P roperties

Thermai Expansion:

The deformation of wood due to elevated tem-

perature is generally ignored in fire resistance analysis of wood. Tem-

peratures above 100°C reduce the moisture content of wood and results

in shrinkage of the wood. The amount of shrinkage will depend on the

original moisture content, the species, and the grain orientation. At

most, shrinkage will be

12%

and 8% in the tangential and radial direc-

tions, respectively. In the longitudinal direction, the average values for

shrinkage in going from green to ovendry are between 0.1 and

0.2%

for most species of wood (U.S.D.A. Agr. Hdbk #72 1987). For certain

typical types of wood known as reaction wood, the longitudinal shrink-

age can be much greater. Completely dry wood does have a positive

thermal expansion coefficient. In tests of both hardwoods and soft-

woods, the parallel-to-grain values have ranged from about 0.0000031

to 0.0000045 per

"C

(U.S.D.A. Agr. Hdbk #72 1987). The linear expan-

sion coefficients across the grain range from about

5

to over

10

times

greater than the parallel-to-grain coefficients and are proportional to

the wood density.

Creep Properties;

In parallel-to-grain tensile tests, creep deformation

has been correlated to a nonlinear (in stress) viscoelastic-plastic model

which included terms for separate mechanically induced and thermally-

induced responses (Schaffer 1978). Both recoverable and irrecoverable

creep components exhibited the same temperature dependency nec-

essary for simple thermorheologic behavior (Schaffer 1977).

2.3

PRINCIPLES OF

RESISTANCE

ACHIEVING STRUCTURAL

FIRE

Structural fire resistance can be achieved in various ways. Construc-

tions

of steel, which have a high thermal conductivity, may attain high

temperatures very fast. Because at high temperatures steel loses its

strength, steel constructions usually have to be protected to obtain

substantial fire resistance. Constructions of concrete and wood, which

are less conductive and therefore attain high temperatures at a lower

rate than steel, can often

be

used unprotected.

There are several methods to prevent structural members from reach-

ing excessive temperatures. The most common is by providing insu-

lation. Insulation can be obtained or improved in various ways. Prob-

ably the most important are increasing the thickness of the insulation,

and using a material with a low thermal conductivity as insulation.

There are other more or less important mechanisms that can be utilized

to obtain insulation. These are the heat absorbing chemical and physical

reactions that take place in various materials, and mechanisms known

as transpiration and reflection (Montle and Mayhan 1974). In the fol-

lowing, the various mechanisms for achieving insulation will be briefly

discussed.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E 7 8 92

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0021849

4 0 6

46


2.3.1

Mechanisms of Protection

2.3.1.1 Thickness

of

Protection

As a rule, the fire resistance

of

a building element increases at least

proportionally to the thickness of the insulation. For protected steel,

such as columns and beams, the fire resistance increases approximately

proportionally to the thickness

of

the insulation (Lie and Stanzak 1973).

For fire separations, such as floors and walls, the fire resistance, based

on attainment of a critical temperature at the unexposed face, increases

progressively with the thickness of the fire separation.

2.3.1.2 Thermal Conductivity

According to the basic equation for heat conduction, the rate with

which heat is conducted from one point to another in

a

material, is

proportional to the thermal conductivity of the material. Roughly, this

is also true for the heat conducted from the fire exposed surface to the

unexposed face of a slab, or to a protected steel member or to reinforcing

steel, through the protection. Therefore, the thermal conductivity has

a strong influence on the fire resistance of building elements. The

thermal conductivity of building materials varies in a wide range. Nor-

mally, the thermal conductivity of a material increases with the density

of the material. Approximate values of the thermal conductivity of

commonly used building materials under fire conditions, derived from

existing data (Lie 1972, Magnusson et al. 1976, European Convention

for Construction Steelwork

1981)

are given in Table 2.3. It can be seen

that sprayed mineral fibre in the density range of 250-350 kgím3 (15.6-

21.8 lb/fS) have the lowest thermal conductivity of the listed materials.

2.3.1.3 Ablation

Ablation is a process in which

a

material is removed by melting,

vaporization, or erosion. These processes may require a large amount

of heat and therefore may considerably retard the temperature rise of

a fire exposed object. For example, evaporation of water at the unex-

posed face of slablike building elements normally contributes substan-

tially to the thermal fire resistance of these elements.

2.3.1.4 Calcination

C a 0

+ COz.

This reaction requires heat.

Calcination takes place during the chemical reaction CaC03

4

2.3.1.5 Intumescence

Some coatings swell to a layer of insulating foam of substantial thick-

ness when exposed to heat. Retardation

of

temperature rise of building

elements protected with intumescent coatings is caused mainly by the


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E

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PRINCIPLES

OF

STRUCTURAL

FIRE

PROTECTION

47

TABLE .3. Approximate values for the thermal conductivity of

various materials under fire conditions.

Material

Sprayed mineral fibre

Cementitious mixture

Perlite or vermiculite plates

Asbestos silicate sheets

Fibre silicate sheets

Wood

Gypsum slabs

Mineral wool slabs

Cellular concrete

Cellular concrete

Cellular concrete

Light weight concrete

Clay brick, and lime brick

Normal weight concrete


Steel

(mainly amorphous aggregate)

(mainly crystalline aggregate)

Density

kg/m3

(lb/ft3)

250-350

(15.6-21.8)

800

-1

O00

(49.9

-

62.4)

300-800

(18.7 49.9)

800

(49.9)

450-900

(28.1-56.2)

600

(37.4)

800

(49.9)

(7.5

-

9.4)

600

(37.4)

1000

(62.4)

1300

(81.1)

1600

(99.8)

2000

(124.8)

2200

(137.2)

2200

(137.2)

7800

(490.0)

120-150

Thermal Conductivity

WImT

(Btuift

WF)

0.10

(0.058)

0.10

(0.058)

0.15

(0.087)

0.15

(0.087)

0.15

(0.087)

0.20

(0.116)

0.20

(0.116)

0.25

(0.143)

0.30

(0.173)

0.45

(O.

260)

0.65

(0.376)

0.80

(0.462)

1.20

(0.694)

1.30

(0.751)

1.70

(O. 983)

35.0

(20.2)

insulative effect of this layer. However, a considerable amount of heat

is absorbed in generating the chemical reaction that forms the foam,

and heat is required to drive the liberated gases from the protective

layer.

2.3.1.6 Dehydration

This is a process in which water of crystallization is removed by

heating. Often materials contain free water and bound water of crys-

tallization. This water will be removed in certain temperature regions.



--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



48


For example, free water in the pores of a material will be removed at

temperatures near the boiling point of water, and water of crystallization

at higher temperatures. In these regions, most of the heat supplied to

the material will be used for removal of the water, and only a small

amount is available for raising the temperature of the material. An

example is gypsum, which consists at room temperature of CaSO,

2H,O and some free water. When heated, free water is removed at

about 100°C and water of crystallization in the region between 150 and

220°C. Because the large amount

of

heat that is required to remove the

water of crystallization, the temperature of the gypsum remains ap-

proximately constant for a long time in this temperature region. This

is an often observed phenomena during fire resistance tests in which

gypsum board is exposed to fire. A considerable gain in fire resistance

can be obtained by protecting a building element with gypsum board.

2.3.1.7 Transpiration

When gases are produced by heating a material, often a porous

structure will be formed. Energy is required to drive these gases through

the materials, which may considerably increase the fire resistance of

building elements made of such materials.

2.3.1.8 Reflection

If

the surface of a material is smooth and shiny and it is exposed to

radiant heat, a large amount of the heat may be reflected. In this case,

the surface stays cooler and less heat is transferred into the material

than in a surface that is rough, and dull in appearance.

2.3.2

Fire Protection Methods

2.3.2.1 Insulation

Insulations used as fire protection include gypsum, perlite, and ver-

miculite board, mineral fibre, ceiling panels and tiles, portland cement

concrete, portland cement plaster, masonry materials, and intumescent

coatings. The insulation can be used as a membrane fire protection. In

this method, a fire-resistive barrier is placed between the potential fire

source and the member to be protected. Another method is by direct

application of the fire protection. In this method, the fire protection

materials generally come into actual contact with all or part of the

surface of the structural components to be protected. The direct-applied

fire protection method is widely used to protect structural steel. In Fig.

2.37, typical steel column sections protected with an insulating cover

are shown. Protective covers that follow the contour of the steel as

illustrated in Figs. 2.37 (a), (b) and (d) are known as contour protections.

Protections that do not follow the entire steel surface and enclose the

steel as shown in Figs. 2.37 (c) and

e) ,

are known as box protections.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



ASCE

7 8

92

m

0 7 5 9 b 0 0

0023852

T T O

m

PRINCIPLES

OF

STRUCTURAL

FIRE

PROTECTION

Im

C )

49

( e )

Figure 2.37-Typical steel column sections with insulation.

2.3.2.2

Capacitive Protection

The method of capacitive fire protection is based on using the heat

capacity of a material to absorb heat. In this way, the temperature rise

of a fire exposed building element is delayed and its fire resistance

increased. Examples in which the heat capacity of a material is used to

gain fire resistance are concrete-filled and water-filled hollow steel col-

umns. In the case of water filling, part of the heat supplied to the steel

is used for heating and evaporation of the water. In the case of concrete

filling, the concrete absorbs some of the heat supplied to the member;

most of the gain in fire resistance, however, is obtained by the contri-

bution of the concrete to the load carrying capacity of the column.

2.3.3 Construction

Techniques

2.3.3.1

Classifica tion of Building Construction

It has been well recognized that certain buildings, constructed with

particular materials, behave better in fires than others. The recognition

has been reflected in insurance practices which, in turn, have influenced

building code requirements. North American building codes and fire

insurance practices classify buildings in a number of different ways.

All of the classifications, however, are derived from five fundamental

construction types (Boring et al.

1981):

a . Fire-Resistive

b. Non-Combustible


--``,`,,`,,`̀ `,,````,`,,,̀ `,`,,-`-`,, ,̀,`,`,,`---



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50


c.

Exterior-Protected Ordinary

d.

Heavy Timber

e. Wood Frame

These descriptive names are now being discontinued because they no

longer define the construction types as precisely as needed. However,

the names are helpful in tracing the development

of

classification of

building construction types.

In general, the term fire-resistive building construction means that

the load bearing building elements, such as walls, beams and columns

have a fire resistance rating. In the United States, the term fire-resistive

construction implies that the bearing walls and principal supporting

members have a fire resistance rating of 4 or 3 hr depending on the

requirements in the code under consideration. Secondary structural

members and non-loadbearing partitions enclosing stairwells and other

vertical openings are required to have a

3

or 2 hour fire resistance

rating. Other non-bearing partitions must be constructed of non-com-

bustible materials. A non-combustible construction is normally consid-

ered to be a building constructed of materials that do not contribute

fuel to a fire. When the interior structural members and floors are of

non-combustible materials with fire resistance ratings of one hour or

less, the type of construction is generally identified as non-combustible.

Most codes subdivide the non-combustible classification into protected

and unprotected types.

For combustible types of construction, the model codes in the United

States employ three broad classifications: Exterior-Protected Ordinary,

Heavy Timber, and Wood Frame. Exterior-Protected Ordinary and Wood

Frame types each include two sub-types: protected and unprotected.

In most respects, they are almost identical except for their exterior wall

requirements. Heavy Timber construction is unique because it is iden-

tified by detailed requirements mainly relating to the size of structural

members and their connections. Properties such as combustibility or

fire resistance are not specifically included

in

the requirements for Heavy

Timber construction, with the exception that exterior walls are required

to be of non-combustible construction.

The National Building Code of Canada does not classify buildings in

the traditional manner as is done in the U.S. codes, but rather specifies

fire-resistive requirements for the structural components of a building,

depending on its occupancy, number of stories and floor area. In this

code, iwo basic types of construction are recognized: combustible and

non-combustible construction. These are further subdivided by the char-

acteristics under fire conditions of the materials used in construction,

as shown in Table 2.4.

The National Building Code

of

Canada establishes the areas for the

sub-types of construction identified in the table by placing them into

three groups which are based upon fire-safety characteristics, combus-


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

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` , ,

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A S C E 7 8 92 0759600

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51

TABLE

.4.

Types of construction and their fire safety characteristics

according to the National Building Code of Canada.

Basic Type of

Construction

Combustible

Construction

Noncombustible

Construction

(Hebert 1975)

-

Group

1

II

III

-

Sub-Types

Wood Frame

Wood post and beam

Plank

Plastic

Other unprotected

combustible

Heavy timber

construction and other

protected combustible

construction

Unprotected steel

construction

Ordinary prestressed

concrete

Thin unprotected

reinforced masonry

Other unprotected

noncombustible

construction

Steel construction with

fire resistance

Masonry with fire

resistance

Reinforced concrete with

fire resistance

Characteristics

(under fire conditions)

Fuel Contributing and

Unstable

Fuel Contributing but

partially stable as to

degree

of

fire resistance

Non-fuel contributing but

unstable

Nonfuel contributing and

stable as to the degree of

fire resistance

tibility or non-combustibility, and stability

or

instability under fire con-

ditions. These groups are:

Group I -Construction limited to the smallest of buildings

Group II -Construction limited to small and intermediate buildings

Group III-Construction may be used

for

all buildings, and is mandatory for

the largest and highest buildings, and for some smaller buildings

with hazardous occupancies.

2.3.3.2 Structural Systems

Each

new building is unique. In producing it, the designer integrates

the function and structure into a definable form. Because form, function,


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and building technology all have both flexibility and constraints, over

the years certain building practices have evolved. These practices have

led to several reasonably well-defined framing systems utilizing the

common structural materials, i.e., structural steel, reinforced concrete,

prestressed concrete, and timber.

Buildings are essentially a grouping of horizontal and vertical sur-

faces, attached in some manner to provide a series of volumes of space.

Some elements of the horizontal and vertical surfaces are critical to the

stability of the structure. Other elements either are non-essential for

structural stability, or are of limited importance. Foundations, while

important, are not of great significance in structural design for fire loads.

Therefore, only the elements of the superstructures are considered here.

In order to identify the role of the elements in a system, their function

in a system will be discussed. For load-bearing elements, this role is

similar under both normal conditions and fire conditions.

These elements can be divided into horizontal and vertical elements

in the following manner (U.S.F.E.M.A.

1980):

1. Non-loadbearing surfaces

a. Ceilings

b. Partitions

a. Roof

b. Floor

a .

Intermediate flexural supports, such as beams

b. Primary flexural supports, such as girders

a. Columns

b. Load-bearing walls

2. Deck

3. Horizontal supports

4. Vertical supports

The elements

of

the building described in this manner are inde-

pendent of the materials of construction. In certain systems, some dis-

tinctions of the elements blend together. However, this way of arrang-

ing the elements does offer a convenient method of identification of

the role of the various elements, that progressively increase in signif-

icance for structural safety.

Non-loadbearing ceilings and partitions support only their

own

weight.

Consequently, their collapse, from a structural point of view, is not

significant. From a functional, environmental, and firesafety viewpoint

these elements are important, and in order to integrate these with the

structural systems, they are included here.

Fig. 2.38 illustrates a common structural system using structural steel

beams and girders and a continuous reinforced concrete floor slab. This

system may be regarded as the “base system.” The reinforced concrete

slab is the floor deck, mentioned under 2b in the preceding outline.

Reinforced concrete floor slabs are seldom less than

4

inches

(100

mm)

thick, and in one-way slabs of the type shown in Fig. 2.38, they may



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53

G I R D E R

BEAM

REINFORCED

c

\

G I R D E R

G I R D E R

Figure 2.38-Typical structural sys tem using structural steel and reinforced

concrete.

be as much as 7 or

8

inches (175 or

200

mm) thick. The thickness

depends upon several factors, the spacing of the supporting floor beams

being one of the most significant parameters.

Reinforcing steel carries the tensile forces of flexure, and is placed in

those regions of tension in the continuous concrete slab. This would

be at the top of the slab over the supporting beams, and at the bottom

of the slab between beams. The clear distance from the surface of the

slab to the reinforcing steel is usually about one inch (25.4 mm).

The reinforced concrete slab is supported by steel beams. The beams

are defined as the intermediate flexural framing (3a of the outline). The

spacing of these beams could be as close as four feet, but it is generally

between

6

feet and 12 feet

(1.8

and 3.7

m).

The steel beams are supported by steel girders, which are defined as

the primary flexural framing (3b of the outline). Interior girders support

beams from both sides. In addition, the interior partitions are often

located over and under these girders. This enables the girders to be

hidden in the construction. Exterior girders, called spandrels, support

floor beams from one side, and often the exterior wall also. The girders

span between the supporting columns. In many common buildings,

this distance is usually between 12 and 24 feet (3.7 and 7.3 m).

The columns support the girders, and, as such, effectively support

the floor. Since columns are framed vertically in line, the lower columns

support not only the floor girders of a particular floor, but also the


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54 STRUCTURAL FIRE

PROTECTION: MANUAL

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PRACTICE

columns for all floors above. They are the primary supports and are,

therefore, critical to the structural integrity of the building.

The seriousness of failure increases with each succeeding element

shown in the outline. Localized failure of a floor slab will merely involve

a small area

of

a building. Failure of

a

floor beam is somewhat more

serious, but is still somewhat localized. Failure of a girder becomes far

more critical. Not only does it affect a significant area, but also it can

trigger progressive failure due to other flexural members being required

to support increased loads. In addition, failure of one or two girders

can cause instability of a column leading to a progressive collapse. The

columns are, of course, the most critical of the building superstructure

elements.

A

column failure, depending on its location can trigger ex-

tensive collapse damage in a building.

The outline

of

the building elements and the description of the simple

deck, beam, girder, and column support functions can be used as a

framework to identify quickly other forms of building construction. Fig.

2.39, for example, illustrates a slab, beam, girder, column system case

monolithically of reinforced concrete. The functions of the elements are,

of course, the same as those described in Fig. 2.38. From the "base

system" various other systems can be derived

(U.S.F.E.M.A. 1980).

Figure 2.39-Monolithically cast reinforced concrete.


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2.4

EVALUATION

OF

FIRE PERFORMANCE

The most common way to determine the fire performance of building

elements, such as beams, columns, walls and floors is by testing. This

performance is usually expressed as a fire resistance, which may be

defined as its ability to withstand exposure to fire without

loss

of load

bearing function or ability to act as a barrier to spread of fire.

Fire resistance testing has been carried out in several countries for

about a century (Babrauskas and Williamson 1978). At present, tests

are carried out according to specifications of the particular country

concerned or according to international standards. The most common

international standard for the determination of fire resistance is the IS0

834

Standard; the most common standard in North America is the ASTM

Standard method E119.

2.4.1 Fire Resistance Testing Methods

The purpose of fire resistance testing is to obtain information on the

ability of structural elements to confine a fire to the compartment where

it started. In general, to confine a fire, elements must possess such

resistance to heat exposure that they will not allow excessive heat

transmission to other compartments. This implies that the elements

must have a certain thermal resistance and must not collapse during

the fire or develop openings that will permit hot gases to flow to other

compartments. During a fire resistance test, this is examined under

conditions that are made as similar as possible to those met within fully

developed fires.

The most common method to determine fire resistance is to expose

a test specimen to a standard fire in specially constructed test furnaces

(IS0 1975, ASTM). The time during which the specimen can withstand

the fire, i.e. meets specified criteria of performance, is the fire resistance

of the specimen. There are three criteria in the standard test method.

They concern structural stability, integrity, and for fire barriers, tem-

perature rise on the unexposed face.

In many cases, not all criteria have to be satisfied. Beams and col-

umns, for example, are required only to demonstrate ability to carry

load for the fire resistance period. Because their fire resistance depends

on the applied load, they may have several fire resistance ratings. This

is also the case for load-bearing walls. Non-bearing walls, if used as a

fire separation, only have to meet a requirement that limits the tem-

perature rise on the unexposed face.

Although there are many test standards, the test methods described

in the various standards are in principle the same. In the following,

the ASTM

E119

test method, which is the basis of the standards used

in North America, will be briefly discussed.


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STRUCTURAL

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2.4.1.1

ASTM E119 Test Standard

The test method described in the ASTM E119 test standard, titled

"Standard Methods of Fire Tests of Building Construction and Mate-

rials" is often cited as the "Standard Fire Test." This test is applicable

to assemblies of masonry units and to composite assemblies of structural

materials for buildings. They include bearing and non-bearing walls

and partitions, columns, girders, beams, slabs, and composite slab and

beam assemblies for floors and roofs. The test is only intended to

register performance during the period of fire exposure. It should not

be construed that the assembly has any suitability for use after the fire

exposure.

The test specimens must be constructed in the same manner as the

representative building assembly. The size of the sample

is

determined

by the type of component (e.g., walls, columns, beams, etc.) being

tested and by the minimum dimensions of the test furnace specified

by the test standard. The specimen must be protected during and after

fabrication to ensure the normality of its quality and condition at the

time of the test. When the material contains moisture as, for example,

wood or concrete, it is tested in an air-dry condition.

A furnace for the determination of the fire resistance of building

elements consists, in general, of a chamber in which the temperature

can be controlled to follow a predetermined temperature-time relation

(see Table 2.1 and

2.2).

The furnace chamber is heated by liquid fuel,

such as oil or kerosene, or by gas such as propane. Normally, the

furnaces are equipped with devices for measuring temperature and test

specimen deformations, and also for loading the test specimens. There

are furnaces that can apply heat to the underside of a floor assembly,

to one side of a wall assembly, or to all four sides of a column assembly.

Thermocouples are used to determine the temperature near, but not

on, the exposed surface. Other thermocouples are placed in contact

with the unexposed surface to measure the temperature at various

locations on that surface.

The fire test on the specimen with its applied load, if any, is continued

until failure occurs, or until the specimen has withstood the test con-

ditions for a time equal to that specified in the conditions of acceptance.

When the conditions of acceptance require a hose stream test, a test

specimen is subjected to the impact, erosion, and cooling effects

of

a

hose stream, immediately after exposure to fire.

The test results are reported as the time, to the nearest minute, of

the resistance of the assembly to the failure, as defined in the standards.

In addition, the type of restraint provided by the test apparatus against

expansion, contraction, and rotation is reported.

The standard test is only intended to register the performance during

the period of fire exposure. Again, it should not be construed that the

building element or assembly has any suitability for use after the fire

exposure.



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2.4.2 Calculation

Methods

Calculation of the fire resistance of a building element involves the

determination of the temperatures and deformations of the element,

and its strength during exposure to fire. Because all these quantities

vary with time, the calculation procedure is often complex. Develop-

ment of numerical calculation methods and the use of high-speed com-

puters, however, have greatly contributed in simplifying these calcu-

lations.

The calculation of fire resistance is performed in various steps. The

first step is the calculation of the temperatures in the fire exposed

building element. These temperatures are determined by finite differ-

ence or finite element methods. In Chapter

5

of this manual, the cal-

culation of temperatures in solid or composite members of concrete or

steel by a finite difference method, is discussed in more detail.

As

an

example, the calculated temperatures in a cross-section of a 12 x 12

in. (300

x 300

mm) concrete column, after exposure to the standard

fire for two hours, are shown in Fig. 2.40.

The next step in the calculation procedure of fire resistance is the

calculation of the deformation and stresses in the column for various

times during exposure to fire. This is followed by the calculation of the

strength

of

the column during the exposure.

Because of the temperature rise, the strength of the concrete de-

creases. Shown in Fig. 2.41 is how, after exposure to a standard fire

for

two

hours, the strength of the concrete varies with the location in

the column. At this stage, the strength of the concrete near the surface

is reduced to zero. A substantial part of the concrete has a strength

varying from 40-80% of the initial strength. A small part of the concrete

near the center still has its original strength.

If

the exposure to fire

continues, a stage will be reached at which the column can no longer

support the applied load. At this point the column collapses.

The fire resistance of the column decreases with increasing load. The

relation between fire resistance and load is shown in Fig. 2.42. With

the aid of this relation, the fire resistance of the column can be deter-

mined for any given load. For the column under consideration (cross-

section of 12

X

12 in. (300 x

300

mm)), and, for example, a load equal

to

30

of the initial column strength, the fire resistance is about

3

hours.

Using procedures similar to those described above, methods for the

calculation of the fire resistance of various building elements have been

developed over the years.

Although it

is

possible to use these procedures for the calculation of

fire resistance, it is elaborate and can, at present, only be performed

by large computers. At this stage, therefore, its application for fire

resistance calculation is still restricted.

A

method more suitable for

general application and incorporation in present codes or manuals, is

the use of simplified formulas that approximately give the same results


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ASCE

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92

9 0 7 5 î b 0 0

0 0 2 L B b l i T O 3

58


> 8 0 0 C

600-800°C

4 0 0 -6 0 0 °C

< 4 0 0 C

Figure 2.40-Temperatures in

300

x

300 mm

(12 x 12 in .) column affer

two hours exposure.

Figure 2.41 -Strength of concrete in

300

x

300 mm

(12 >

after tw o hours exposure.

12 in. column


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PRINCIPLES OF STRUCTURAL FIRE PROTECTION 59

1 0 0

8 0

6 0

40

2 0

n

I- -I

-

O

0 . 5 1 . 0 1.5 2 . 0 2 . 5

3 . 0

3.5 4 . 0

F I

RE RES ISTANCE,

h

Figure 2.42-Relatiun between fire resistance and load fur a 300 x 300

mm

(12 x 12

in.)

reinforced

concrete

column.

as those obtained from the mathematical model. Such formulas can be

derived by making a large number of computer runs, using validated

mathematical models, and expressing the results

of

these runs in simple

approximate formulas or rules, that can be processed by hand or desk

calculators. Such formulas and simplified rules as well as information,

derived from tests, for the determination of fire resistance will be given

in the next chapter.

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S.

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--



A S C E

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60

STRUCTURAL FIRE PROTECTION:

MANUAL OF

PRACTICE

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` ,

, ` ` ` , ,

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` , , ,

` ` ,

` , , - ` - ` , ,

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` , ,

` - - -



ASCE 7 8 92 7 5 ï b 0 0

0 0 2 1 8 b 4

712


61

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,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



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OF

PRACTICE

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3,

Fire, Washington, D.C.


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A S C E 78 92 0759b00 002LBbb

595

Chapter 3

FIRE

RESISTANCE OF BUILDING ELEMENTS

In the following, methods will be given to determine, with the aid

of simplified formulas and rules, the fire resistance of various building

elements. Also references will be given in which fire resistance ratings,

obtained from test results, can be found for a large number of building

elements. In addition, there will be a discussion of extension rules that

enable the interpretation of test or calculated results for conditions that

differ from those in the test or calculation. The three most commonly

used building materials are considered, i.e. steel, concrete, and timber,

eventually in combination with various other materials used as insu-

lation, such as gypsum board and sprayed mineral fiber.

It should be noted that it is also possible to treat the effect of elevated

temperatures in the same manner as that of other structural loading

conditions. Design equations can be derived in which elevated tem-

perature effects are taken into account by modification factors to classical

resistance factors. This approach has been developed in Culver et al.

1973, Ossenbruggen et al. 1973, and Uddin and Culver 1975.

3 .1

CALCULATION

OF

FIRE

RESISTANCE

3.1.1 Steel

Steel, like all building materials, loses strength if it is heated to high

temperatures. Often a critical steel temperature can be indicated at

which the steel has lost so much strength that the safety factor against

failure becomes less than 1 . In this case, the calculation of failure of

the building element can be reduced to the calculation of the temper-

atures of the steel. North American standards assume a critical or failure

Principal Authors:

K.H.

Almand, T.T. Lie, and T.D. Lin

63


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E 7 8

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64

STRUCTURAL

FIRE PROTECTION:

MANUAL

OF

PRACTICE

temperature of 538°C

(iOOO°F)

for structural steel. It is a typical actual

failure temperature for columns under full design load. This tempera-

ture is also regarded as the failure temperature in calculations of fire

resistance of steel members. If a load is applied to the member, the

test is continued until the member actually fails, which, depending on

the load intensity, may occur at a higher or lower steel temperature.

3.1.1.1 Steel

Columns

Research has shown that the temperature of a steel column in fire is

a function of its weight-to-heated-perimeter ratio (see explanation in

section 3.3.2.1, Guideline 2). The heated perimeter concept is demon-

strated in Figures 3.1 and 3.2. A common method to prevent rapid loss

of strength in a steel column is to insulate it, typically with low density

materials. Figures 3.1 and 3.2 show typical contour and box-type in-

sulation configurations.

Steel Columns Protected by Low Density Protection:

Based

on

theoretical

and experimental studies

[4-61,

the following expression has been de-

rived for the fire resistance of steel sections protected by light insulating

materials:

In this formula:

R

C l , C , = material constants that are known for a specific protecting

W

D

h

As noted above, the material constants C1 and C2 are specific to a

given protection material. For cases in which the values of

C ,

and

C ,

are not known, however, generally conservative assessment of the fire

resistance

of

protected steel columns can be made using the equations:

For protections with

a

density íp) in the range:

20 <

p

50

lb/ft3

= the fire resistance of the column (minutes)

material

= weight of the steel column per foot length (lb/ft)

=

developed heated perimeter (inches) (see Figs. 3.1 and 3.2)

=

thickness of protection (inches)

for protections consisting

of

chemicallv stable materials

such as vermiculite, perlite

(2)

and sprayed mineral fibres with

various binders, and dense

mineral wool.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



ASCE 78 92

0 7 5 9 b O O 0 0 2 1 8 b 8

3 b 8

FIRE RESISTANCE OF

BUILDING

ELEMENTS

65

e - 7

mllb

. . . . . . . . . . . . . .

. . . . . . . . . . . . .

D =

2 ( a

+ b ) D

=

2 í a +

b )

D

=

2 í a + b )

pl)

. . . . . . . . . . .

. . . . . . . . . . . . .

D = 2 í a + b ) D = 2 ( a + b )

D = 3 . 1 4 b D = 2 ( a + b i

Figure 3.1 -Sections

and

heated perimeter

D of

steel columns with

a

box

protection.

for protections containing cement

+

72 h (3)

pastes or gypsum such

as

cementitious

i

mixtures and plasters.

For all above mentioned protections in the density range:

20

p 20 lb/ft3

for small round and square columns

protection (h 2 1.5 in.).

for all other shapes and

protection.

h

(4)

(width less than 6 in.) and thick

h

(5)

sizes and any thickness of


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,`

, , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E 78 92 0 7 5 9 b 0 0

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2 T 4

66

STRUCTURAL

FIRE

PROTECTION: MANUAL

OF

PRACTICE

D = 4 a + 2 b D =

4 a

+ 2 b

D

= Z i a

+

b i D = 3 . 1 4 b

D = 2 i a t b )

D = 3 . 1 4 b

Figure 3.2-Sections

of

steel

columns

protected by

a

contour protection.

More accurate evaluation of the fire resistance of protected steel col-

umns can be obtained by determining

Cl

nd

C,

empirically from small-

or large-scale fire resistance tests in accordance with Appendix

P

of the

Standard Building Code (Southern Building Code Congress Int’l. Inc.

1988). The following formulas have been developed for two types of

spray applied

low

density fire protection: cementitious and mineral

fibre (AIS1 1980).*

Cementitious material:

*Not applicable

to

columns with a fire resistance of less than one (1)hour.


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E 7 8

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R 0759h00 0023870 T l b

FIRE RESISTANCE OF BUILDING ELEMENTS 67

Mineral fibre material:

R =

6 3 - + 4 2

h

io

(7 )

Steel Columns Protected by

Gypsum

Wallboard:

A common protection for

steel columns is to box it in using gypsum wallboard. Based on the

results of accumulated fire-test data, an empirical equation has been

developed to determine the fire resistance of columns protected by

gypsum wallboard (AIS1 1980, Flemington 1980). This equation can be

given as:

where:

R =

fire resistance (minutes)

W weight of steel column and gypsum wallboard protection per

foot length (lb/ft)

h = thickness of gypsum wallboard (inches)

D =

developed heated perimeter (inches), which as shown in Fig. 3.1

may be defined as the inside perimeter of the fire protection

To derive the total weight W' of both the column and its gypsum

wallboard protection, the following formula can be used:

h D

144

W W

+

50-

(9)

where W = Weight of the steel per foot (lb/ft).

To improve structural integrity of gypsum board during exposure to

fire, in general, a gypsum board reinforced with inorganic fibre is used.

These types of board are usually classified by accredited testing labo-

ratories, like Underwriters Laboratories in North America. In addition,

the gypsum wallboard needs to be supported by methods that prevent

its dislocation. Examples of these methods are shown in Figs. 3.3 and

3.4.

Steel

Columns Protected

by

Concrete: Concrete encasement is another

form of protection for steel columns. Empirical formulas have been

developed to predict the fire resistance of concrete protected steel col-

umns (Lie and Harmathy 1974). In Fig. 3.5, three types of encasements

are shown for which the fire resistance can be determined by calcula-

tion. In the derivation of the formulas, attainment of a temperature of

1000°F (538°C)

of

the steel was regarded as failure of the steel. Note



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A S C E

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0023873 952

68

STRUCTURAL

FIRE


1 1

2 2

3 3

S N A P - L O C K P I T T S B U R G H SEAM L A P

C O R N E R JO I N T D E T A I L S ( A )

1.

STRUCTURAL MEMBER 3. SHEET STEEL

2.

G Y P S U M W A L LB O AR D

4.

SHEET STEEL SCREWS

Figure 3.3-Column protection designed with sheet-steel covers.

*

3

2

4

1

L A Y E R

2 L A Y E R S

6

5 5

1 . S T R U C T U R A L MEMBER

2 . S T E EL S T U D S

4 4

3 .

G Y P S U M W A L L B O A R D

( T Y P E

X )

3 L A Y E R S

4

L A Y E R S

4 .

S TE EL C O R N E R B E A D

5 . T I E W I R E

6 .

S H E E T M E T A L A N G L E

Figure 3.4-Column protection designed w ith steel studs and corner beads or

angles.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



ASCE 7 8 92 0 7 5 9 b 0 0 0 0 2 3 8 7 2 8 9 9

FIRE RESISTANCE OF BUILDING ELEMENTS

69

Figure 3.5-Concrete-protected structural steel columns (1) Square shape

protection with a uni form thickness of concrete cover

on

a l l sides

( 2 )

Rectangular shape wit h varying thickness of concrete cover

and ( 3 ) Encasement having a l l re-entrant spaces filled with

concrete.

that this implies that the contribution of the concrete to support the

load is zero.

For a normal weight concrete protection of uniform thickness on all

sides and square shape (Fig.

3.5

type

(l)) ,

he fire resistance is given

by:

H

R = 11 + 19h1.6

(1

+ 94

[

(10)

P&

( L

+ 4

and for a lightweight concrete protection by

H

R

=

11

(E) . + 23h1.6

{

1

+

94

[

] O }

(11)

Pch

( L + h )

where:

R

=

fire resistance at equilibrium moisture condition, here assumed to

W

=

weight of steel per foot length (lbíft)

D = developed heated perimeter of steel columns (in.) (See Fig. 3.5)

h = thickness of concrete cover (in.) (see note if the thickness is not

uniform)

L

=

interior dimensions of one side of a square concrete box protection

(in.) (see note if the box protection is not square)

H

=

thermal capacity of steel column at ambient temperature

(= 0.11 W Btu/ft"F) (see note for column type No. 3 in Fig. 3.5,

which has all re-entrant spaces fiiled with concrete)

be

4%

of the concrete by volume (minutes)

pc

= concrete density (1bífS)


--` `

,̀ , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



70 STRUCTURAL

FIRE


Notes:

1) If the concrete box protection is not square, or if the concrete cover

I

thickness is not constant

(Fig. 3.5

type (2)), k and L shall be taken as

the average values i.e.

k

=

%(h,

+

h2)

and

L

=

%(LI

+

L,)

2) If the steel column is completely encased in concrete, with all reentrant

spaces filled (Fig. 3.5 type

(3)),

the thermal capacity of the concrete

within the re-entrant space may be added to the thermal capacity of the

steel column, increasing the value of H to:

H

=

0.11

w

+

(L,L, -

720

I

where

L ,

=

steel column flange width (in.)

L, = depth of steel column (in.)

A, = cross sectional area

of

the steel column (in.2)

3) Formulas

10-12

are identical to those given in

AISI

1980 or Lie and

Harmathy 1974, except that conservative values of the thermal properties

and a practical value of the moisture content have been substituted in

these formulas. If the thermal properties of the concrete under consid-

eration are known, the fire resistance of the column can also be deter-

mined using the formulas in AISI 1980 or Lie and Harmathy 1974.

Unprotected Steel Columns:

Unprotected steel columns of small cross-

sectional area have, in general, a fire resistance of not more than 10-

20 minutes. However, heavier columns are capable of much better fire

performance. Based on theoretical and experimental studies, the fol-

lowing formulas have been developed for the calculation of the fire

resistance of unprotected steel columns

AISI

1980:

0.7

R =

10.3

(E) for WID < 10

0.8

R

=

8.3

(

for W/D 2 10

where:

R

= fire resistance (minutes)

W =

weight of steel column per ft length (lb/ft)

D

= developed heated perimeter of the steel section (in.) (See Fig. 3 .6)

Other Types of Protection for Hollow Steel Columns:

There are

two

rela-

tively new types of fire protection for hollow steel columns. One

is

concrete filling. At room temperature, the concrete carnes

a

share

of

the load; during fire it acts as a heat sink, protecting the steel and


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E 7 8

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M

0 7 5 9 b U U

002L874

b b L

FIRE RESISTANCEOF BUILDING ELEMENTS

D

=

4 a

+

2 b

D

= 4 a

+

2 b

71

D = 2 ( a

+ b ) D

= 3 . 1 4 b

01

01

D

= 2 ( a + b )

D = 3 . 1 4 b

Figure 3.6-Sections of unprotected steel columns.

taking on more load as steel strength

is

reduced. Calculation procedures

have been developed to predict the fire resistance of loaded concrete

filled columns (Flemington 1980, Int't. Committee for the Study and

Development of Tubular Structures 1976, Lie 1984).

A second method

of

protection for hollow columns is water filling.

The water inside the column will absorb the heat transferred from the

fire to the column. The heat is dissipated by evaporation of the water

and circulation of the water to other non-exposed areas of a chosen

loop system

of

water filled steel. The quantity of water required is a

function of the surface area

of

the steel exposed to the heat of a fire,

the fire length and its intensity. Based on the heat transferred to

a

column during a standard fire and the heat needed to evaporate water,

the quantity of water necessary to prevent excessive temperature rise

of the steel can be evaluated (Flemington 1980, Miller and Ife 1974).


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A S C E

78

92 0759b00 0023875 5 T 8 W


The following formula describes the quantity of external storage water

required to achieve fire resistance using this technique:

vw

= 3.92. A

. 9

.

10-7

where:

V , =

required external storage water, m3

A

= surface area of the column, m2

9

= heat transferred to the column during a fire test per unit surface

=

150740

for

7 4

hour fire rating

=

225260 for

1

hour fire rating

= 580960

for

2

hour fire rating

=

785460

for

3

hour fire rating

= 1014640 for 4 hour fire rating

area, kJ/m2

The water in the system is generally treated with potassium carbonate

in quantities sufficient to prevent freezing during winter, and potassium

nitrate to inhibit corrosion.

3.1.1.2

Floor,

Roof and Beam Assemblies

When considering the fire resistance of steel floor, roof and beam

assemblies, the concept of assembly restraint must first be understood.

When a beam is fire tested alone or as part of the floor or roof assembly,

it expands as it is heated. Floor test furnaces encase the specimen in a

rigid restraining frame.

If

the beam is built tightly into the frame, the

frame resists its expansion and moments are generated in the beam.

Often these moments are beneficial, in other words, of opposite sign

to those generated by gravity loads on the member. Benefits increase

with an increase in the composite action between the beam and any

floor deck it supports. Because restraint in some degree is a reality in

actual construction, and because it has proved beneficial in fire, many

steel floor and beam assemblies are fire tested in a restrained condition.

However, end conditions are not well specified in the fire test and the

degree of restraint provided is not measured or indeed constant during

the test. Since critical temperatures are a function of support conditions,

it has proved impossible to assign a single critical temperature as a

failure criteria for restrained beam and floor assemblies. In these tests,

the assembly must sustain the load for the entire fire resistance period.

The critical temperature of beams is much better understood and has

been researched and experimentally investigated to the point where

the limits

of 593°C (1100°F)

when the beam is part of an assembly and

538°C (1000°F) when the beam is tested alone, are now listed as critical

temperature criteria in the fire test standard.

W I D

concepts can also be applied to assess protection requirements

for steel beams in both restrained and unrestrained assemblies to pre-


--``,`,,`,,`̀ `,,````,`,,,̀ `,`,,-`-`,, ,̀,`,`,,`---



ASCE 78

92

0757600 0023876

434


vent the attainment of the 1000°F critical temperature. For steel beams

protected

by

a low-density protection, the same formulas as for the

steel columns, given in Section 3.1 .1 .1 (equations

1-7),

can be used to

determine their fire resistance.

In

the case of beams, only three sides

of the beam are exposed to fire (Fig.

3.7

and

3.8).

The top of the beam

is assumed to be a floor or roof

slab,

made of a perfectly insulating

material. Thus, there is

no

heat exchange between the floor or roof slab

and the steel. Because only three sides of the beam are exposed to heat,

the values of the heated perimeter D of beams in these formulas are

smaller than those of the corresponding column. As a result, the fire

resistance of a beam, i.e., the time to reach a specific failure temperature

lTTp

h F v

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . .

I

.:.

. ,

.

,:: . ;

:

:

I

D = a + 2 b D = a + 2 b

a

U

D = a + 2 b D = a + 2 b D = a + 2 b

Tnr

. . . . . . . . .. . . . . .

I

. . . . . . . . . . . .

I

. . . . . . . . . . .

ka-' k-J

D - a t 2 b D = a + 2 b

Figure

3.7-Sections and heated perimeter

D

of

steel beams

with

a box

profection



- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - `

- ` , ,

` , ,

` ,

` , ,

` - - -



ASCE

78 92

m

0 7 5 9 b 0 0

0021877 370

m

74

STRUCTURALFIRE PROTECTION: MANUAL OF PRACTICE

b y g

.

. .

.: . . . . . .

: . . . .

.

. _ . . . . .

. . . . . . . . . . .

,

. . . . . . . . .

TrT

.. :.. .. :.

, ..

. .

.

,

. .

.

.

. . . .

.

. . .

.

.

.

.

. . .

.

.

U

D

=

3 a

t 2 b

D = 3 a t 2b

w

D = a t 2 b

Figure 3.8-Sections of steel beams protected by a contour protection.

in the steel is relatively longer than that for a column. In addition,

because the floor or roof on top of the beam normally absorbs heat

transmitted through the beam, which is not taken into account in the

formulas, the fire resistances calculated using these formulas, are rel-

atively more conservative for the beam than those for the column.

For beams protected by spray-applied protections, a scaling formula

(Int'l. Committee for the Study and Development of Tubular Structures

1976) has been developed that enables substitution of one beam for

another by varying the thickness of the protection. Provided the deck

is the same and D' is calculated for three-sided exposure only, the

following beam substitution equation, which has achieved code ac-

ceptance, can be used:

W 2 / D , + 0.6

h ,

=

(

W,ID, +

0.6)

h2

where:

h

W

D

=

thickness of spray-applied fire protection (inches).

=

weight of steel beam (lb/ft).

= heated perimeter of the steel beam (inches). Note, see

Figure 3.7 and 3.8.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



ASCE 7 8 92 0 7 5 9 b 0 0 0 0 2 1 8 7 8 2 0 7

FIRE

RESISTANCE

OF

BUILDING ELEMENTS

75

Subscript 1

=

refers to the substitute beam and required protection

Subscript

2 =

refers to the beam and protection thickness specified in

thickness.

the reference fire tested design.

Use of this equation is subject to these limitations:

1) The equation applies to beams having

WID

values not less than 0.37,

2) h , cannot be less than Yi inch, and

3)

the Unrestrained Beam Rating in the tested design is not less than one

hour.

One of the least understood factors affecting the fire resistance of

steel beams is the influence of roof deck or floor slab construction.

Normally, these roof and floor constructions act as heat sinks by ab-

sorbing heat from the beam and thus delaying the temperature rise of

the beam. Concrete slabs are known to have a large delaying influence

on the temperature rise of the beam. In contrast, insulated roof decks

absorb little heat from the beam, resulting in higher beam temperatures

than those in the case of the concrete slab construction.

Other deckíslab construction details can also influence the tempera-

ture of protected steel beams. In some cases, for example, in the case

of an unprotected steel deck, it may not act as a heat sink but transmits

heat into the top flange of a steel beam from the surrounding fire.

The overall behaviour of these floors, roof, and beam assemblies is

complex and no simple formula has been developed to predict their

performance or to translate their performance in a fire test to actual

structural behaviour in buildings. The American Iron and Steel Institute

has developed a finite element computer program to analyze the struc-

tural behaviour of these assemblies, known as FASBUS

II

(Jeanes

1985).

With its use, the complex problem

of

floor assembly structural response

to fire can be mapped.

3.1.1.3

Steel Trusses

Large-scale steel trusses (such as those forming part of a staggered

truss or interstitial truss system) cannot, because of their size, be loaded

and tested in conventional fire resistance test furnaces (several unloaded

tests have been carried out).

Building codes recognize three acceptable procedures for the fire

protection of these systems (Culver 1973):

(1) Individual member protection-Each truss web or chord member is

evaluated

a s

if it were a stand alone column in a fire test furnace: thus,

the

WID

formulae discussed in Section

3.1.1.1

may be used to evaluate

overall truss fire resistance based on the least resistance provided by

individual members.

( 2 )

Envelope protection-When the truss serves as a vertical barrier to the

horizontal spread of fire (for example, full storey staggered trusses),


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E

7 8

92

W

0 7 5 9 b 0 0 0021879 143

76


OF

PRACTICE

D

-

3 a

t

2 b D =

3 a t

2 b

w

D = a + 2 b

Figure 3.9-Sections of unprotected steel beams.

the entire truss may be encased in a wall and protected with gypsum

wall board covering. In this case, special fire resistance ratings based

on wall criteria, are applied.

(3) Membrane protection-When the truss is part of a system that provides

a horizontal barrier to the vertical spread

of

fire (such as an interstitial

truss/ceiling assembly), the

truss

is protected by membrane protection

below the bottom chord and open web steel joist (OWSJ) floor assembly

ratings may be conservatively applied. (The interstitial truss members

have a much higher

WID

ratio than the webs and chords of OWSJ.)

3.1.1.4 Load

Bearing Walls

Many structural steel wall assemblies are fire tested unloaded, so

insulative criteria are the only ones applied to them. Thus calculation

procedures, such as the scaling formula (AIS1 1984), shown below, are

applicable to them.

r/rref= (L/L,,) .7

(17)

where the subscript ref refers to a reference material, and

r

=

fire resistance

L = wall (or slab) thickness


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



ASCE 7 8

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0759600 0023880 965

FIRE RESISTANCE

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BUILDING ELEMENTS

77

The structural performance of a load bearing steel stud wall can be

related to the attainment of a critical temperature by the studs in the

wall, and is a function of the load applied to them. Stud temperatures

are not presently used as a failure criteria in the standard fire test. The

American Iron and Steel Institute has published a design method for

calculating the fire resistance of load bearing steel stud walls. The

method is based on a room temperature design method, elevated tem-

perature strength tests on cold formed steel studs and several full-scale

fire resistance tests on gypsum wallboard protected assemblies. Figure

3.10

shows the relationship between fire resistance and the load applied

to the studs expressed as a percentage of room temperature design

load (AIS1

1981,

Klipstein

1980).

3.1.2

Concrete

For concrete members, the development of approximate formulas to

predict their fire resistance is more difficult than for steel. In general,

the temperature in a cross-section of a concrete member is not as uni-

form during fire exposure as that in a steel section.

As

a consequence,

the thermal and mechanical properties of the concrete vary not only

with time but also with the location in the section. This non-uniformity

and, in addition, the wide range in which the properties of concrete

can vary at elevated temperatures are complicating factors in the cal-

culation of fire resistance of concrete members and in the derivation of

general formulas for the prediction of their fire resistance.

For a number of concrete building elements, Le., reinforced concrete

columns and slab-like elements, such as monolithic and double layer

walls and floors, and masonry, approximate formulas have been de-

veloped to calculate their fire resistance.

Most of the formulas for slab-like concrete elements (Fig. 3.11 (a), (b)

and

(c))

assume that the slab failed due to excessive heat transfer through

it. In a standard ASTM fire test (ASTM

1985),

an average rise in tem-

perature of

250°F

on the unexposed surface is regarded as failure. This

temperature rise was also regarded as the failure temperature criterion

in the development of the formulas for the prediction of the fire resist-

ance of slabs. The fire resistance of the slab, known as the ”thermal

fire resistance,” is the time elapsed to reach a temperature rise of

250°F

at the unexposed face of the slab.

In the derivation of approximate formulas for the fire resistance of

composite floor and roof slabs (Fig.

3.11

(d)) with steel reinforcement,

however, an additional failure criterion for the reinforcing or prestress-

ing steel was considered. The composite slab was regarded to have

failed if the steel temperature reached 1100°F for reinforcing steel and

800°F for prestressing steel. Formulas were developed for these slabs

that give the minimum cover thickness to the steel to obtain a specific

fire resistance.


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E

7 8 92 0 7 5 9 b 0 0 0 0 2 3 8 8 3 B T 3

78


O

O

4

Il

*

E

E

u;

U

N

O

æ

II

-

4

O

I

In O 2

In

O

O P, In N

d O

O

O u

r c j

+-

3

k

-29

d / l d =

tll

O I l V t l a v o 1


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



ASCE 7 8

92

0 7 5 9 b 0 0

002L882

738

FIRE RESISTANCE OF

BUILDING

ELEMENTS

79

For slabs and beams, also, methods have been developed to evaluate

their structural fire resistance, Methods exist for simply supported and

continuous slabs and beams, and for floors and roofs in which restraint

to thermal expansion occurs. These methods and the approximate for-

mulas for the calculation of the fire resistance of reinforced concrete

columns and the slab-like elements, shown in Fig. 3.11, will be given

in the following sections. Also, examples will be given to illustrate

calculation techniques for assessing the structural fire resistance of slabs

and beams.

3.1.2.1 Reinforced Concrete Columns

Based on theoretical and experimental studies (Lie and Allen 1972,

Lie et al. 1984), formulas have been derived for the calculation

of

the

fire resistance of reinforced concrete columns. In these formulas, the

minimum dimensions for reinforced concrete columns and minimum

concrete cover for vertical steel reinforcements to obtain a specific fire

resistance are given. The formulas take into account the type of con-

crete, the effective length of the column and the area of the vertical

reinforcement. According to these formulas, the minimum dimension

of a rectangular column tmin (in.) for obtaining a fire resistance

R ( h )

is

fmin

=

3.2f(X

+

1)

for normal weight siliceous aggregate concrete, when the design con-

dition of the column is defined in columns

2

and

4

of Table

3.1,

tmin

=

3.2f(R + 0.75)

(19)

for normal weight carbonate aggregate concrete, when the design con-

dition of the column is defined in columns 2 and 4 of Table 3.1,

tmin =

4f(R

+

1)

‘ b - 4

L1 L1 b2

L1

M O NO L I T H I C DO UBL E- L AYER

HO L L O W CO M PO SI T E

S L A B C O N F I G U R A T I Q N

S L A B

S L A B

Figure

3 .22

-

lab-like building elements.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E 7 8

92

0 7 5 9 b 0 0 0 0 2 1 8 8 3 b 7 4

80

STRUCTURAL

FIRE


TABLE

.1 .

Values of f .

Where kh is more than 12 ft

but not more than 24 ft

t

is not more

than 12 in. and

Overdesign Where kh is not

p is not more All other

Factor**

more than

12

ft than 3 percent cases

1.00

1.0 1.2

1.0

1.25 0.9 1.1 0.9

1.50

0.8 1.0

0.8

Column

1

2

3

4

*For round columns the diameter must be not less than 1.2 times the value determined

by equations (18)-(21).

**Overdesign factor is the ratio of the calculated load carrying capacity of the column to

the column strength required to carry the specified loads determined in conformance

with AC1 318-89 “Building Code Requirements for Reinforced Concrete”

for normal weight siliceous or carbonate aggregate concrete, when the

design condition of the column is defined in column 3 of Table 3.1,

and

tmin = 3f(R

+

1) (21)

for lightweight concrete, where

f

takes into account overdesign, effective

length and percentage of steel. Values of f are given in Table 3.1. In

this table:

k = the effective length factor obtained from AC1318-89”Building Code

h = unsupported length of the column (ft)

p = the area of vertical reinforcement in the column as a percentage

In addition to a minimum dimension of the column, there is also a

minimum cover requirement to prevent the steel from reaching exces-

sive temperatures. The minimum cover Cmin(in.) to the vertical rein-

forcement is for all concretes:

Requirements for Reinforced Concrete”

of the column area

for R 5 3 hr Cmin= R or 2 in., whichever is less (22)

for

R

> 3 hr

Cmin=

1/2 (R

-

3)

+

2

(23)

3.1.2.2 Monolithic Concrete

Slabs

The fire resistance of dry monolithic normal weight concrete slabs

(Fig. 3.11(a))based on obtaining

a

failure temperature rise of 250°F at


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



ASCE 78 92 W

0759600 0021884

500

FIRE RESISTANCE

OF

BUILDING ELEMENTS

81

the unexposed surface can be given by the following semi-empirical

formula (Harmathy 1970, Allen and Harmathy 1972):

where

RI

= the fire resistance of slab based on heat transmission criterion (hr)

L = thickness of slab (ft)

p

=

density of concrete (lb/fP)

c

=

specific heat of concrete (Btu/lb"F)

k

=

thermal conductivity of concrete (Btu/ft h"F)

following conservative values may

be

used for these properties:

k

=

1.0 Btu/ft h°F for normal weight concrete,

k

=

0.45 Btu/ft h°F for Iightweight concrete, and

c

= 0.20

Btu/lb"F for both concretes.

If

no data on the thermal properties of the concrete are available, the

In this case, equation 24 becomes for normal weight concrete

R I = 0.03 p'.' L' '

(25)

and for lightweight concrete

RI =

0.05 (26)

3.1.2.3

Double Layer Concrete Slabs

For assemblies of two concrete slabs separated by a continuous air

gap of any thickness (Fig.

3.11

(b)), an analogous formula as that of

the monolithic slab is applicable. The fire resistance of these slabs in

dry condition, based on obtaining a failure temperature rise of 250°F at

the unexposed surface, can be given by the following semi-empirical

formula

[21]:

where

R = the thermal fire resistance of the slab (hr)

LI =

thickness of one layer of the slab (ft)

p = density of the concrete (lb/ft3)

c

=

specific heat of the concrete (BtdlWF)

k

=

thermal conductivity of the concrete (Btdft h"F)



--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



ASCE 7 8 92 0 7 5 î b 0 0

002L885

447

82


If no data on the thermal properties of the concrete are available, the

following conservative values may be used for these properties:

k = 1.0 Btu/ft

h F

for normal weight concrete,

k

=

0.45

Btu/ft h"F for lightweight concrete, and

c

=

0.20 Btu/lb"F for both concretes.

In this case, equation 27 becomes for normal weight concrete

R ,

=

0.13

p'.'

(28)

and for lightweight concrete

R2 =

0.216

p ' . '

(29)

3.1.2.4

Hollow Concrete Slabs

With the aid of the equations given in the previous sections for the

monolithic concrete slab (section 3.1.2.2) and for the double layer slab

(section 3.1.2.3), the fire resistance of the hollow slab (Fig. 3.11 (c)) can

be derived. This slab may be regarded as a monolithic slab at the

locations of the webs and as a double layer slab at the location of the

cavity.

The fire resistance of these slabs in dry condition, based on attaining

a temperature rise of 250°F at the side away from the fire, can be given

by the following semi-empirical formula (Harmathy

1970):

where

R = the thermal fire resistance of the hollow slab (hr) (see Fig. 3.10(c))

R , = the thermal fire resistance of the monolithic slab (hr) (section

R,

=

the thermal fire resistance of the double layer slab (hr) (section

b, =

thickness of a web (ft)

b2 =

distance between the centrelines of two webs (ft)

3.1.2.5 Com posite Slabs

Theoretical and experimental studies (Lie

1978,

Abrams and Gusta-

ferro 1969) were carried out to predict the fire resistance of composite

concrete slabs, consisting of a layer of normal weight concrete and a

layer of lightweight concrete (Fig.

3.11(d)). Using

the results of these

3.1.2.2)

3.1.2.3)


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` ,

,-` -` , ,` , ,` ,` , ,` ---



A S C E 7 8

92

m

0759600 0 0 2 L 8 8 b 383

m

Material

of

Top Layer

Type

X gypsum

wallboard

Cellular

Vermiculite and perlite concrete

concrete (Density 25-35 lb/ft3)

(Density

35

1bifP or less)

aggregate

Gypsum sand plaster

Portland cement with sand

Terrazzo

FIRE

RESISTANCE

OF BUILDING

ELEMENTS

83

Base slab of Base slab

of

normal weight lightweight

concrete concrete

3 2%

2 1

2

1 3 ~

1

2

1%

1

1 7 4

1 %

studies, approximate formulas have been derived for the calculation of

the fire resistance of these slabs. The fire resistance, based on obtaining

a failure temperature rise of 250°F at the unexposed face, can, for slabs

in equilibrium in an environment of 50-75% Relative Humidity, be

given when the base slab consists of normal weight concrete by

and when the base slab consists of lightweight concrete by

l 2 +

d l

- d2

+

-

(32)

where

R =

fire resistance of slab (hr)

1 = total thickness of slab (in.)

d

= thickness of base slab (in.)

and 1 - d is not less than 1 in.

If the base slab is covered by a top layer of a material other than

normal weight or lightweight concrete, the top layer thickness may be

converted to an equivalent thickness of one of these concretes. The

equivalent thickness may be added to the thickness of the base slab for

calculating the fire resistance of the composite slab using equations (31)

or (33). Table 3.2 lists, for several materials, the factors by which the

thickness of the top layer has to be multiplied to obtain the equivalent

thickness.

In addition to failure by exceeding a temperature rise of

250°F

at the

unexposed surface, floor and roof assemblies may also fail because of


--` ` ,` , ,` , ,` ` ` ,

,̀ ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



ASCE

78

92

0 7 5 î b 0 0 0021887

2 L T

Base Slab

Concrete Type

Reinforced concrete (all types)

Prestressed concrete normal

weight concrete (dominantly

siliceous aggregate)


(Dominantly carbonate

aggregate)

Lightweight concrete


Fire Resistance

Y2 %

1

1%

0.65 0.65

0.8

0.83

0.8 1.0 1.25 1.65

0.8

0.85 1.1 1.45

0.8 0.8

0.9 1.25

excessive temperature rise of the prestressing or reinforcing steel in the

slab. The critical steel temperature, i.e., the temperature at which the

steel can no longer support the loading, is assumed to be equal to that

specified by ASTM

E119

(ASTM

1985)

for floor and roof slabs. This is

800°F

for prestressing steel and

1100°F

for reinforcing steel. By calcu-

lating the thickness of the concrete cover over the steel that is needed

to prevent the steel from reaching the critical temperature before a

given time, the minimum cover thickness to obtain this can be deter-

mined. The minimum concrete cover over the main reinforcement for

composite concrete floor and roof slabs

is

given in Table 3.3.

3.1.2.6 Sim ply Supported (Unrestrained) Slabs and Beam s

Structural Behaviour: Figure 3.12 illustrates a simply supported rein-

forced concrete slab. The reinforcement consists of straight bars located

near the bottom of the slab. If the underside of the slab is exposed to

fire, the bottom of the slab will expand more than the top, resulting in

a deflection of the slab. The tensile strength of the concrete and steel

near the bottom of the slab will decrease as the temperature increases.

When the strength of the steel at elevated temperature reduces to that

of the stress in the steel, flexural collapse will occur (Gustaferro and

Selvaggio

1967).

The nominal moment strength will be constant

throughout the length:

where:

A, = the area

of

the reinforcing steel

fy = the yield stress

of

the reinforcing steel

TABLE.3.

Minimum cover over reinforcement to obtain a specific

fire resistance

(in.).

lours

2

1.1

2.0

1.75

1.55

-


- -

` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E 78 92

m

075îb00 002L88B L5 b

m


M

+

M

1

A T O h

85

A T 2 h

Figure 3.12-Moment diagrams for sim ply supported beam or slab before

and

during fire exposure.

d = the distance from the centroid of the reinforcing steel to the ex-

treme compressive fibre

a = the depth of the equivalent rectangular compressive stress block

at ultimate load, and is equal to A,fy/0.85fib where f i = the cyl-

inder compressive strength of the concrete and b is the width of

the slab.

If

the slab is uniformly loaded, the moment diagram will be parabolic

with a maximum value at midspan:

w12

8

M Y -

(34)

where:

w

=

dead plus live load per unit of length, and

= span length

It is generally assumed that, during a fire, the dead and live loads

remain constant. However, the material strengths are reduced so that

the retained moment capacity is:

in which

8

signifies the effects of elevated temperatures. Note that

A

and d are not affected, but fye is reduced. Similarly a, is reduced, but


--``,`,,`,,`̀ `,,````,`,,,`̀ ,`,,-`-`,,`,,`,`,,`---



A S C E

78 92 m 0759b00

002L889

O92

m

86

STRUCTURAL FIRE PROTECTION:MANUAL OF PRACTICE

the concrete strength at the top of the slab, f i is generally not reduced

signihcantly. If, however, the compressive zone of the concrete is heated,

an appropriate reduction should be assumed.

Flexural failure can be assumed to occur when M,, is reduced to M .

From this expression, it can be noted that the fire resistance depends

on the load intensity and the strength-temperature characteristics of

steel. In turn, the duration of the fire until the "critical" steel temper-

ature

is

reached depends upon the protection afforded to the reinforce-

ment. Usually, the protection consists of the concrete cover, i.e., the

thickness of concrete between the fire exposed surface and the rein-

forcement. In some cases, additional protective layers of insulation or

membrane ceilings might be present.

3.1.2.7 Continuous

Beams and Slabs

Sfr uc fur al Behaviour:

Structures that are continuous or otherwise stat-

ically indeterminate, undergo changes in stresses when subjected to

fire (Abrams et al. 1976, Institute for Structural Materials and Building

Structures 1959).

Such changes in stress result from temperature gradients within struc-

tural members, or changes in strength of structural materials at high

temperatures, or both.

Figure 3.13 shows a continuous beam whose underside is exposed

to fire. The bottom of the beam becomes hotter than the top and tends

to expand more than the top. This differential heating causes the ends

of the beam to tend to lift from their supports, thus increasing the

reaction at the interior support. This action results in a redistribution

of moments, i.e., the negative moment at the interior support increases

while the positive moments decrease.

During the course of a fire, the negative moment reinforcement (Fig.

3.13) remains cooler than the positive moment reinforcement because

it is better protected from the fire. Thus, the increase in negative mo-

ment can be accommodated. Generally, the redistribution that occurs

is sufficient to cause yielding of the negative moment reinforcement.

The resulting decrease in positive moment means that the positive

moment reinforcement can be heated to a higher temperature before

failure will occur. Thus, it is apparent that the fire resistance of a

continuous reinforced concrete beam is generally significantly longer

than that of a similar simply supported beam loaded to the same mo-

ment intensity.

Detailing Precautions: It should be noted that the amount of redistri-

bution that occurs is sufficient to cause yielding of the negative moment

reinforcement. Since, by increasing the amount of negative moment

reinforcement, a greater negative moment will be attracted, care must

be exercised in designing the member to assure that flexural tension

will govern the design. To avoid a compressive failure in the negative

moment region, the amount of negative moment reinforcement should


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



ASCE 78 92

0759600 O023890 804

D


87

be small enough so that w, i.e., A,f,lbd f : , is less than about 0.30 even

after reductions due to temperature in

f,,

f k ,

b,

and

d

are taken into

account. Furthermore, the negative moment reinforcing bars must be

long enough to accommodate the complete redistributed moment and

change in the location of inflection points. It is recommended that at

least

20% of

the maximum negative moment reinforcement in the span

extend throughout the span.

Estimating Structural Fire Resistance:

It is possible to design the rein-

forcement in a continuous beam or slab for a particular fire endurance

period. From the lowermost diagram of Fig. 3.13, the beam can be

expected to collapse when the positive moment capacity,

M,t,,

is re-

duced to the value indicated by the dashed horizontal line, i.e., when

the applied moment at a point x1 from the outer support, M,, = M:e.

For a uniform applied load,

w,

wl

x , wx: M A X ,

-

M,t,

2 1

M,,

=

2

1 M ,

I 2 w

x

= - - -

lta

F I

R E

+

M O

- A T 3 h

Figure 3.13 -Moment diagrams for one half of

a

continuous three-span beam

before and during fire exposure.


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E

7 8

92 0759600

0023893

740

88

STRUCTURAL

FIRE

PROTECTION: MANUAL

OF

PRACTICE

and

also

x g

=

2x,

For a symmetrical interior bay,

x , = 112

or

(37)

(38)

3.1.2.8

Fire Resistance of Floor Slabs and Roofs Subjected to Thermal

Restraints

Sfructurd Behaviour:

If a fire occurs beneath a small interior portion

of a large reinforced concrete slab, the heated portion will tend to

expand and push against the surrounding part of the slab. In turn, the

unheated part of the slab exerts compressive forces on the heated por-

tion. The compressive force, or thrust, acts near the bottom of the slab

when the fire first occurs, but as the fire progresses, the line of action

of the thrust rises (Selvaggio and Carlson 1962).

If

the surrounding slab

is thick and heavily reinforced, the thrust forces that occur can be quite

large; but considerably less than those calculated by use of elastic prop-

erties of concrete and steel together with appropriate coefficients of

expansion. At high temperatures, creep and stress relaxation play an

important role. Nevertheless, the thrust is generally great enough to

increase the fire resistance significantly. In most fire tests of restrained

assemblies, the fire resistance is determined by temperature rise of the

unexposed surface rather than by structural considerations, even though

the steel temperatures often exceed 800°C (1500°F) (Abrams et al. 1976,

Lin and Abrams

1983,

Issen et al. 1970).

The effects of restraint to thermal expansion can be characterized as

shown in Fig. 3.14. The thermal thrust acts in a manner similar to an

external prestressing force, which, in effect, increases the positive mo-

ment capacity.


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` ,

,-` -` , ,` , ,` ,` , ,` ---



ASCE

7 8

92

0759600

0023892

6 8 7

FIRE RESISTANCE

OF

BUILDING ELEMENTS

CENTROIDAL

A X I S

4-c 3

- - - - -.

T

FIXED F I R E MOVEABLE

S U P P O R T

SUPPORT

M n

89

‘ I M I

M

T - O

A T

O

h

CURVE

DUE

TO

DEFLECTION OF BEAM

‘

M

dMngT 3

h

Figure 3.14-Moment diagrams for axially restrained beam during fire

exposure. Note that u t

3

h M,, is less than

M

and effect of

axial restraint permit beam to continue to support load.

Estimating Structural Fire Resistance:

The increase in bending moment

capacity is similar to the effect of “fictitious reinforcement” located along

the line of action of the thrust (Salse and Gustaferro 1971, Salse and

Lin 1976). It is assumed that the “fictitious reinforcement” has a strength

(force) equal to the thrust.

By

this approach, it is possible to determine

the magnitude and location of the required thrust to provide a given

fire endurance. The procedure for estimating thrust requirements is:

(1) determine temperature distribution at the required fire test duration;

( 2 )

determine the retained moment capacity for that temperature distri-

bution;

(3) if the applied moment, M , is greater than the retained moment capacity

M,,,

estimate the midspan deflection at the given fire test time (if

M,,

is greater than M, no thrust is needed);

(4) estimate the line of action of the thrust;

( 5 )

calculate the magnitude of the required thrust,

T;

(6) calculate the ”thrust parameter,” TIAE, where A is the gross cross-

sectional area of the section resisting the thrust and

€

is the concrete

modulus of elasticity prior to fire exposure (Issen et al. 1970);

(7) calculate Z ‘ defined as Z‘ =

A/s

in which 5 is the “heated perimeter”

defined as that portion of the perimeter of the cross section resisting

the thrust exposed to fire;

(8)

enter Fig. 3.15 with the appropriate thrust parameter and Z’ value

and determine the ”strain parameter,” AlIl;


--` ` ,` , ,` , ,` `

` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E 7 8

92

0757600 0021893

513


i o

O

4

x

W

4

I-

\

uuu I

SANDED-LIGHTWEIGHT

CONCRETE

500

-

400 -

300 -

100

-

I

= o

5 600

a

L 500

3 400

I-

300

200

1O0

4

&

I-

V,

ct


I

CARBONATE

OR /


(CARBONATE

OR

-

SILICEOUS)

REINFORCED

o.

0100

o. 0050

o.

O020

o. O010

0.0005

-1

a

2

\

&

0.0002

W

0.0001

5

0.0100 Q

0.0050

5

0.0020 =;

a

a

pz

o.

O010

o.

O005

o. O002

o.

o001

Figure 3.15-Nomogram relating thrust, stra in, and

Z’

ratio (issen et al.

1970).

(9) calculate A l by multiplying the strain parameter by the heated length

of

the member; and

(10) determine

if

the surrounding or supporting structure can support the

thrust T with a displacement no greater than

AlIl.

Example

3

in Section

3.1.2.9 illustrates this procedure.

The above explanation is greatly simplified because, in reality, re-

straint is quite complex, and can be likened to the behaviour of a flexural

member subjected

to

an axial force. Interaction diagrams (Abrams et

al. 1971) can be constructed for a given cross section at a particular

stage of a fire, e.g.,

2

hr of a standard fire exposure.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



1

1

1

U

O

W

oc

3

I-

cd

W

a

a

z

W

I-

FIRE RESISTANCE

OF

BUILDING ELEMENTS

91

A S C E

78

92

m

0 7 5 î b 0 0 002L894

4 5 T

m

8 0 0

7 0 0

6 0 0

o

O

5 0 0

W

oc

3

I-

oi

a

4 0 0 w

a

z

W

+

3 0 0

2 0 0

1

O0

3 0

4 5 6 0 9 0 120 1 8 0 2 4 0

F I R E

T E S T TIME, min

Figure 3.16 -Temperatures wi thin slabs dur ing tests -siliceous aggregate

concrete.


--``,`,,`,,`̀ `,,````,`,,,̀ `,`,,-`-`,,`,,`,`,,`---



A S C E

7 8 92 0 7 5 9 b 0 0 0021895

3 î b

2 0

o

92


I

-

H I G H S T R E N G T H

A L L O Y B A R S ( ULT IM A T E )

' 1 ' ' l ' '


Figure

_I

a

-

I-

æ

-

-

U

O

Se

I

c

a

æ

W

E

I-

v1

3.17-

n

200

- - I C O L D - D R A WN WI R E OR

S T R A N D ( U L T I MA T E )A \ \ I

4 0

I

TEMPERATURE,

C

O 200 400 6 0 0 8 0 0

..

I I

I

.

I

\

\

-STRESSED TO 0.4 f i

I

-

\

UNSTRESSED RESIDUAL

-

1

-

A V G . I N I T I A L

f \

=

3900 ps i (27

M P a )

I

ILICEOUS AGGREGATE CONCRETE

\

O 4 O0 800 1200 1 6 0 0

TEMPERATURE,

F

Figure 3.18-Compressive strength of siliceous aggregate concrete at high

temperafures and affe r cooling.


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C O L Q

8


93

,

I

.

BARS

TOP

BARS

13 # 3

-

O T T O M B A R S

I

I

t -4----~+----

9 w 4

B O T T O M

1 6 W 4

TOP BARS

ARS BARS

t

Figure 3.19-Steel layout in the exterior panel.

The guidelines in

ASTM

E119 for determining conditions of restraint

are useful for preliminary design purposes. Basically, interior bays of

multibay floors or roofs can be considered to be restrained and the

magnitude and location

of

the thrust are generally of academic interest

only.

3.1.2.9

Examples

cussed in Sections 3.1.2.6, 3.1.2.7 and 3.1.2.8.

The three examples that follow illustrate calculation techniques dis-

Example

1

Determination of Cross Sectional Area and Length of Negative

Reinforcement Required in a Two-span Slab to Provide Three-hour Fire

Resistance

Given:

A

two-span siliceous aggregate concrete slab 6.0 in. (150

mm)

thick, reinforced for positive moment with #4 Grade 60 bars on

6.0

in

(150 mm) centres with 0.75 in (19 mm) cover. Each span is 18.0 ft (5.5

m) and superimposed load is 42 psf

(2.0

kPa). Concrete has a unit

weight of

150

pcf (2400

kg/m3)

and a specified compressive strength

of

4000

psi (28 MPa).


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E

78

92

0 7 5 9 b 0 0 0 0 2 1 8 9 7

L b 9

STRUCTURAL

FIRE

PROTECTION: MANUAL

OF

PRACTICE

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A S C E

7 8

92 W 0 7 5 9 b 0 0

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STRUCTURAL

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PROTECTION: MANUAL

OF

PRACTICE


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FIRE RESISTANCE

OF

BUILDING ELEMENTS

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A S C E

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A S C E 78 92 D 0759600

0023903

292

100

STRUCTURAL

FIRE


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A S C E 78

92

m

0759600

002190b

T T L

W

FIRE RESISTANCE

OF

BUILDING ELEMENTS

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A S C E

7 8

92 0759b00 0023907 938

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OF

PRACTICE

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7 8 92

0759600 0021908

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A S C E

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0759600 0021910 4 2 2

FIRE

RESISTANCE OF BUILDING ELEMENTS

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A S C E 7 8

92

m

0 7 5 9 b 0 0

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A S C E

7 8

92

0759600

0023733 331 9

110

STRUCTURAL FIRE PROTECTION:

MANUAL

OF PRACTICE


--

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ASCE

78 92 0 7 5 î b 0 0 002LîL4 078

FIRE RESISTANCE OF

BUILDING

ELEMENTS

I / ï ( 1 3 x 3 )

'

/

-

C O L

O L * p L

-;* 4 ? 1 6 * 4

CI

E

-

L

1/2 ( 1 3 x 3 )

-

3/4 i n . ( 1 9 mm) C O V E R

7 x 4

TOP

BA RS 1 6 x 4 TOP BARS

c

y3

i

BOTTOM BARS

-L

3/4 i n . (19 mm) C O V E R

I

L

18

f t (5 .5 m)

1

Figure 3.20-Reinforcing details in column strip.

C O L U M N S T R I P

15 *S A l 9 in. (229 m m ì

TOP BARS SPACING

10*4

AT 1 2 - 1 /2 i n .

(318 mm)

16

in,

(406

mm)

SQ

C O L

ln

19-2/3 f l .

(6

m)

ZI

f t

(6.4

m)

M I D D L E

S T R I P

I l

4 AT

10

i n .

(254 mm) SPACING -,

(230

mm) SPACING

SLAB

THICKNESS

= 7 in . (178

mm)

6.1 i n .

(155

mm)

(32 mm)

f

/ f l , f f f f l f f f f l f l l f l l / l f f f ~

T I

_ _

T I > ' ,

60

C)

l h

Uk1400

F (7,

-0.9 i n .

111

(23

mm)

Figure 3.21 -Location of restraining forces.


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A S C E 7 8

92

0 7 5 9 b 0 0 002LïI15 TO4

112 STRUCTURAL FIRE PROTECTION: MANUAL

OF

PRACTICE

3.1.3 Timber

member or assembly depends on three items:

When attention is given to all details, the fire resistance of a wood

1.

performance of its protective membrane

(if

any)

2. extent of charring

of

the structural wood element, and

3. load-carrying capacity of the remaining uncharred portions of the struc-

tural wood elements.

In recent years,

two

fire resistance design procedures have gained U.S.

and Canadian building code acceptance. Due to differences in the var-

ious codes, specifics need to be verified for a given code. In addi-

tion, other procedures and models have been proposed or are being

developed.

3.1.3.1

Light Frame

Assemblies

Gypsum board and plywood panelling are two common types of

protective membrane, which is the first line of resistance in a fire in

wood construction. The contribution of the protective membrane to the

fire resistance rating of a light-frame assembly is clearly illustrated in

the component additive calculation procedure.

The component additive calculation procedure

is

a method to deter-

mine conservatively the fire resistance ratings of load-bearing light-

frame wood floor assemblies and of load-bearing and nonload bearing

wall assemblies. With this procedure, one assumes that times can be

assigned to the types and thicknesses of protective membranes and

that an assembly with

two

or more protective membranes has a fire

resistance rating at least that of the sum of the times assigned

for

the

individual layers and the times assigned to the framing. The procedure

was developed by the National Research Council of Canada. It has both

U.S. and Canadian Code acceptance.

The times assigned to the protective membrane (Table 3.4), the fram-

ing (Table

3.5),

and other factors (Table 3.6) are based on empirical

correlation with actual ASTM E 119 tests of assemblies. The fire rating

of an assembly is the sum of the appropriate items from Tables 3.4,

3.5, and 3.6. Depending on the codes, the rating for the assembly is

limited to ether 60 or 90 minutes. The times given in Table 3.4 are

based on the membrane’s contribution to the total fire rating of the

assembly. The times assigned to the protective membranes are not the

“finish ratings:” of the material cited

in

test reports or listings. (A finish

rating is defined as the time for an average temperature rise of 139°C

or maximum rise of 181°C on the fire exposed side of the wood framing.)

There are minimum requirements for the membrane on the side not

exposed to fire (Tables3.7 and 3.8) in order to assure that the assembly

does not fail because of fire penetration or heat transfer through as-

sembly. Instead of being one of the combinations listed in Tables 3.7


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` -

--



A S C E 7 8 9 2 E 0 7 5 ï b 0 0

0 0 2 1 9 L b

940

FIRE

RESISTANCE

OF BUILDING ELEMENTS

113

TABLE .4.

Time assigned to protective membranes.

Descriution of Finish Time, minutes

~~~

Yi inch Douglas fir plywood, phenolic bonded

Yi nch Douglas fir plywood, phenolic bonded

5/s inch Douglas fir plywood, phenolic bonded

Yi inch gypsum board

Y2 inch gypsum board

7 s inch gypsum board

Y2

inch Type X gypsum board

7 s inch Type X gypsum board

Double 3% inch gypsum board

Y z +

Yu inch gypsum board

Double

Yi

nch bypsum board

5

10

15

10

15

20

25

40

25

35

40

Notes:

1.

On wall, gypsum board shall be installed with the long dimension parallel to framing

members with all joints finished However, 5/s inch Type

X

gypsum wallboard may be

installed horizontally with the horizontal joints unsupported.

2. On floorlceiling or rooficeiling assemblies, gypsum board shall be installed with the

long dimension perpendicular to framing members and shall have all joints finished.

TABLE

.5 .

Time assigned to wood-frame components.

Description of Frames Time, minutes

Wood studs,

16

inches on center

Wood joists,

16

inches on center

Wood roof and floor truss assemblies 24 inches on center

20

10

5

TABLE

.6.

Time assigned for additional protection.

Description of Additional Protection I Time, minutes

Add to the fire endurance rating of wood studs walls

if

the spaces

between the studs are filled with rockwool or slag mineral wool

batts weighing not less than Vi 1b.isq. ft. of wall surface.

walls if the spaces between the studs are filled with glass fiber

batts weighing not less than

?4

1b.isq. ft. of wall surface

15

Add to the fire endurance rating of non-load bearing wood stud 5


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



ASCE 78 92

0759b00

0021917 887


TABLE

.7. Minimum requirement for the membrane on exterior face

of walls

(Any

combination of sheathing, paper (if

required) and exterior finish).

Sheathing Paper Exterior Finish

%

inch T&G lumber

% e

inch exterior grade plywood

Y 2

inch gypsum board paper

Y4

inch hardboard metal siding,

Lumber siding

Wood shingles and shakes

Y4

inch ext. grade plywood

Stucco on metal lath

Masonry veneer

Sheathing

None None Ya inch ext. grade plywood

TABLE .8.

Minimum requirement for flooring or roofing

membranes.

Assemblv

Floor

Roof

Structural

members

Wood

Wood

Subfloor or roof

deck

Yi inch plywood

or

'Y16

inch T&G

softwood lumber

Y2

inch plywood or

l 6

inch T&G

softwood lumber

Finish flooring

or roofing

Hardwood or softwood

flooring on building paper

or Resilient flooring, parquet

floor, felted-synthetic-fiber

floor coverings, carpeting, or

ceramic tile

on

Ys in. thick

panel-type underlay; or

Ceramic tile i-Ya in. mortar

bed.

Finish roofing material with

or without insulation

and 3.8, the membrane on the side not exposed to fire (the outside)

may be any membrane listed in Table 3.4with a rated time of 15minutes

or greater.


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



ASCE

78

92 0759b00

O021918 713


3.1.3.2 One Hour Fire Re sistiv e Exposed W oo d Members

If timber structural members are exposed to fire, a char layer is formed

at the exposed surface. The thickness of this layer grows continuously

at an approximately constant rate. Because the char layer has practically

no strength, the load carrying capacity of the member decreases.

As

the charring proceeds, a time will be reached when the uncharred part

is reduced to a size at which the member can no longer support the

load. By calculating the time it takes to reach the critical size, the fire

resistance of the member can be determined. Such calculations have

been carried out for glue laminated timber beams and columns exposed

on three or four sides to fire, and simplified formulas have been derived

for the prediction of their fire resistance (Lie

1977).

According to these

formulas, the fire resistance of glue-laminated timber beams and col-

umns can be given as follows:

Beams heated on 4 sides

R =

2.54jB [4 - 2(B/D)]

(37)

Beams heated on 3 sides

R = 2.54fB(4 -

B / D )

(38)

Columns heated on

4

sides

R =

2.54fB(3

-

B/D)

(39)

Columns heated on 3 sides

R = 2.54 fB(3 - B/2D)

(40)

where

R = the fire resistance of a beam or column (min)

B

= the smaller side of a beam or column before exposure to fire (in.)

D = the larger side of a beam or column before exposure to fire (in.)


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E 78 92 0759600 0023939 b5T

116

STRUCTURALFIRE PROTECTION: MANUAL OF PRACTICE

c

1.

1.

1.

1.

1.

1.

O 2 5

5 0

75

1 0 0

L O A D , % O F A L L O W A B L E L O A D

Figure 3.22-Factor f as a function of load for timber columns and beams.

f = factor taking into account the load and for columns the effective

K = the effective length factor

L

= the unsupported length of column (in.)

Equations 38 and

40

apply for the case where the unexposed face is

the smaller side of the beam or column. Where one of the larger sides

of a beam or column is not exposed to fire, conservative values of the

fire resistance of the members can be obtained, using equation 37 for

the beam and equation 39 for the column.

length as shown in Fig.

3.22

Note to formulas (37) to

(40):

*The formulas are applicable for wood beam or column with minimum

nominal dimension of 6 in. The net finish width for a nominal 6-in.

glued laminated member is

5%

in.

The factor

f

depends on the load and, for columns, also on the

effective length as shown in Fig.

3.22. If

a load is applied that is lower

than the allowable load the fire resistance of a member increases. The

higher fire resistance of a member that is overdesigned is expressed by

a higher value of

f .

With respect to fire, a member may be regarded as

overdesigned if it is designed to resist accidental loads, such as seismic,

wind and snow loads. The load on the beam or column may be assumed

to be equal to the full specified dead load and live load plus

30

of

the design snow load.

This procedure is contained within the Council of American Building

Officials (CABO) Report No. NER-250 (National Evaluation Board 1984)

and the supplement to the

National Building Code of Canada

(National

Research Council of Canada 1990).

Connectors and fasteners relating to support of the member must be

protected for equivalent fire-resistive construction. Where minimal

1-


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A S C E

78 '72 m 0759600 O023920 371 m

FIRE

RESISTANCE

OF BUILDING

ELEMENTS

117

hr fire endurance is required, connectors and fasteners must be pro-

tected from fire exposure by 1% in. of wood, fire-rated gypsum board,

or any coating approved for a 1hour rating. NER-250 includes diagrams

giving typical details of such protection.

There

is

often a high-strength tension laminate on the bottom of

glued-laminated timber beams. As a result, it is required (NER-250) that

a core lamination be removed, the tension zone moved inward, and

the equivalent of an extra nominal 2-in.-thick outer tension lamination

be added to ensure that there is still a high-strength laminate left after

fire exposure.

3.2 FIRE

RESISTANCES DETERMINED BY TESTING

Over the years, thousands of fire tests have been conducted on many

types of materials and combinations of materials. Most of the tests were

conducted to satisfy regulatory requirements. Very comprehensive doc-

uments containing fire test results for various structural members such

as beams, columns, floors, roofs, walls and partitions are the Fire Aesist-

ance Directory

(Underwriters Laboratories 1988), the

List

of

Equipment

and

Materials

(Underwriters Laboratories of Canada 1980), and that pub-

lished by the American Insurance Services Group (1985). These docu-

ments are updated every year.

Other documents containing fire test results are more restrictive in

that one inorganic material is used to provide fire resistance for the

elements of the building. One such document is the Fire Resistance Design

Manual (Gypsum Association 1978). Designs in this manual use gypsum

products to provide fire resistance for walls, partitions, floor ceilings,

columns, beams, and roof decks. Another document of the latter type

is

Technical Note

i 6 on brick construction (Brick Institute of America

1974), that gives several designs using brick in combination with other

materials.

Most of the information in the above mentioned documents are based

on results of tests on building elements made with proprietary mate-

rials. Ratings for a large number of building elements made with generic

materials are given in the NFPA Fire Protection Handbook (Fitzgerald 1986)

and in the National Building Code of Canada (National Research Council

of Canada 1990).

3.3

EXTENSION RULES AND GUIDELINES FOR

FIRE

RESISTANCE

In a test, the fire resistance of a building element is usually deter-

mined for one specific condition with regard to the factors that deter-

mine its fire performance, such as materials used in the specimen, its

dimensions, load, etc. For any other condition, a new test is required


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E 78

92 m 0759600

0021921

208

m

118


OF

PRACTICE

which is a costly and time consuming method for determining fire

resistance. By calculation of fire resistance, which can be carried out at

a fraction of the time and cost involved in testing, the range of con-

ditions for which the fire resistance can be determined can be consid-

erably extended. A further extension of this range can be obtained by

using experimentally or theoretically derived rules and guidelines that

enable the interpretation of test or calculated results for conditions that

differ from those in the test or calculation.

In the following, several extension rules and guidelines will be given

for the assessment of the fire resistance of various building elements.

The rules are for building elements made with steel, concrete, or timber,

with or without protection. Only rules and guidelines will be given for

variation in conditions that will produce equal or higher fire resistances

than those under the conditions in the test or in the calculations. They

are divided into guidelines that take into account the effect on the fire

resistance

( R )

of the building element due to:

1) variation of material properties, or

2)

variation of dimensions.

In addition, a number of generally valid rules will be given. In all cases,

it is assumed that the variations do not introduce higher stresses in

load bearing elements.

Where necessary, the rules and guidelines will be briefly explained.

More information is given in Fire Technology (Harmathy 1965), in which

the author introduced ten general rules for fire resistance. More infor-

mation is also given in other sources, where the basis

of

several of the

extension rules given below can be found (Stanzak and Lie 1973, Har-

mathy 1970, Lie 1978, Abrams and Gustaferro 1969, Gustaferro and

Selvaggio 1967, and Lie 1972).

3.3.1 Definition of Terms

To

facilitate the use of the rules and guidelines, definitions of a few

often used terms will first be given before dealing with the rules.

Structural fire resistance:

the ability of a construction to withstand the

thermal effects of fire without loss of its load bearing function.

Thermal fire resistance:

the ability

of

a fire separation to withstand the

thermal effects of fire without excessive heat transmission through it.

DeveIoped

heuted

perimeter: for protected steel elements, the perimeter

of the protection at the interface between steel and insulation (see Figs.

3.1-3.5, 3.7,3.8). For unprotected steel elements, this perimeter is equal

to the outer perimeter of the steel (see Figs.

3.6,

3.9). The developed

heated perimeter is equal to the area per unit length of the steel element

through which heat is supplied to the steel.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

`

` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E

7 8 92

O759600

O023922

344

A N Y

STEEL

S E C T I O N


119

S A M E

STEEL

S E C T I O N

3.3.2

Variation of Material Properties

3.3.2.1 Steel

Guideline

I:

The structural fire resistance of a protected or unprotected

steel element may increase with the ratio of the strength

of

the steel

to the load applied. (See Fig.

3.1,

3.2and

3.5-3.9

for examples of these

steel elements.)

(STRENGTH$ > (STRENGTH$

NOTE: This may not be the case if other failure criteria apply.

Guideline

2:

The structural fire resistance of protected and unprotected

steel elements increases with the ratio of the weight of the steel to the

developed heated perimeter

D

(see Figs.

3.1,

3 .2 and

3.5-3.9

for the

developed heated perimeter

D of

various steel sections).

WE IGH T STEEL W EIG HT STEEL

HEATED PERIMETER

SECT I ON S E C T I O N


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E

7 8

' i 2

=

0759600 0023923

080

120 STRUCTURAL

FIRE

PROTECTION: MANUAL

OF

PRACTICE

Explanation:

If the weight of the steel

is

increased, more heat is needed

to raise the temperature of the steel to the failure temperature. If the

area through which the heat is supplied to the steel is increased, it will

take less time to reach the failure temperature. This area is, for a unit

length

of

the protected steel elements, equal to the developed heated

perimeter D.Note that the accuracy of the above guideline is dependent

upon the shape of the steel section. For example, for wide flange shapes

and angles, the area through which heat is supplied to the steel is less

than that corresponding to the developed heated perimeter D , because

the fire exposed area is reduced between the flanges or legs. Therefore,

the validity of the rule is restricted to similar shapes.

3.3.2.2 ConCrete

Guideline

1: The structural fire resistance of a concrete building ele-

ment increases with the strength of the concrete,

if

the same type of

concrete is used.

(STRENGTH l > ( S T R E N G T H $

( R St r u c ' 1

>

( R s t r u c ' p

Explanation:

The fire resistance of concrete elements increases with

the strength of the concrete if subjected to the same load. For a specific

strength, siliceous aggregate concrete elements have lower fire resist-

ances than carbonate aggregate corxrete elements; and normal weight

concrete elements often have lower fire resistances than lightweight

concrete elements. Therefore the rule is only valid if the same type of

concrete is used.

Guideline

2: The use of carbonate aggregate instead of siliceous ag-

gregate is beneficial for the structural fire resistance of concrete or

concrete protected building elements, if the strength of the concrete

is

not decreased.


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E 78

92

W

0?.59b00 0021924 T I ?

W

FIRE RESISTANCE OF

BUILDING

ELEMENTS

121

C A R B O N A T E

S

I L I C E O U S

A G G R E G A T E A G G R E G A T E

, N Y B E A M

i

R C O L U M N

q .

. A - . A

A

-

'-

S E C T I O N S E C T I O N

e :4

A

A

4 . -

. ' .

, ..a.. .

.a.

.

y _ _

.,. . . ._

. e

SAME SECTION

NY WALL OR FLOOR

(MONOLITHIC OR HOLLOW)

*:. a :

.

4 . - . P .

w

. P . . o . . .

.

, w

. .

d

Explanation: The thermal properties of carbonate aggregate concrete

are more favorable than those of siliceous aggregate concrete from the

point of view of heat transmission. Carbonate aggregate concrete is also

more ductile than siliceous aggregate concrete.

Guiúeíine

3 :

The use of carbonate aggregate instead

of

siliceous ag-

gregate is beneficial for the thermal fire resistance of fire separating

building elements.

C A R B O N A T E

S I

L

I

C E O U

S

C O N C R E T E C O N C R E T E

SAME SECTION

N Y W A L L OR FLOOR

(MONOLITHIC OR H OL L OW)

( R t h e r m > ( R t h e r m


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



122

STRUCTURAL

FIRE


Explanation:

The thermal properties of carbonate aggregate concrete


point of view of heat transmission. Therefore, the rate of temperature

rise at the unexposed face of the wall or floor will be lower for the

carbonate concrete slab than for the siliceous concrete slab.

Guideline 4:

The use of lightweight concrete instead of normal weight

concrete increases the thermal fire resistance of fire separating building

elements.

L I G H T W E I G H T N O R M A L W E I G H T


SAME SECTION

N Y WAL L OR FL OOR

(MONOLITHIC OR H OL L OW)

( R t h e r r n

> ( R t h e r m

Explanafion:

The thermal properties of lightweight concrete are more

favorable than those of normal weight concrete from the point of view

of heat transmission. Therefore, the rate of temperature rise at the

unexposed face of the wall or floor will be lower for the lightweight

concrete slab than for the normal weight concrete slab.

Guideline 5:

The structural fire resistance of multilayer reinforced or

prestressed concrete slabs increases if, in the bottom layer, carbonate

aggregate is used instead of siliceous aggregate.

C A R B O N A T E

S

I L

I

C E O U S


. ~ .

d . .

A ' . d . .

.a

. - . .

.

d . . p . . . ~ . .

A NY CONCRETE SAME CONCRETE

A ,

. . Q . . _ , *.. . . .- . ,

- 4 .

. . . a . . .

e . .

a..

P

, * .

. - - - . . - - . . 4 . - . O . . e . . - = >

CARBONATE SIL ICEOUS

d. . _ P . . . P . . ...

1 & . . . . P . . . - . Q - . . - - . -

. .

( Rs ruc'

(

R s t r u c '

1

Explanation:

The thermal properties of carbonate aggregate concrete


point of view of heat transmission. Therefore, it takes more time to


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



ASCE 7 8 92 0759b00 0023926 8 9 T D


123

reach the failure temperature of the reinforcing or prestressing steel if

the steel is protected by carbonate concrete than if it is protected by

siliceous concrete.

Guideline

6:

The structural fire resistance of multilayer reinforced con-

crete slabs increases if, in the bottom layer, lightweight concrete is used

instead of normal weight concrete.

L I G H T W E I G H T N O R M A L W E I G H T


.A.

, - . .

d.'. D . ' . . * . . A .

..a.

AN Y CONCRETE SAME CONCRETE

, *:.

. . 4 _ . . . ...o. <.d

. . c . .

. b : .: A...'*

~

< . , . .

4 . . . . C I . . - 4 .

.

.i ,

..a:.*

L IG HT W EIG HT NO RMAL W Ei G HT

. L I . .

. . 4 .

. 4 , . . . a

. . a

. P

_ . . .

;

- 4 , .

. v . , < - . -

> ( R ì

Struz

2

R

ì

s t r u c

Explanation: The thermal properties of lightweight concrete are more

favorable than those of normal weight concrete from the point of view

of transmission of heat in the concrete. Therefore, it takes more time

to reach the failure temperature of the reinforcing steel if it is protected

by lightweight concrete than if it is protected by normal weight concrete.

3.3.2.3

Wood

Guideline 1:

The structural fire resistance of wood building elements

increases with the strength of the wood, if its density

or

moisture

content is not decreased.

(STRENGTH$

A N Y

W O O D

S E C T I O N

S A M E WOOD

SECT

ION

Explanation: If

wood is exposed to fire, a char layer is formed that

grows

in thickness with time. The fire resistance of a building element

of wood is the time it takes to reduce the uncharred part of the section


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E 78

92 m

0759600

0021927 7 2 b m

124

STRUCTURAL

FIRE

PROTECTION: MANUAL

OF

PRACTICE

to a critical size at which it can no longer support the applied load. For

a specific load, the critical size reduces if the strength of the wood is

increased. Thus, the time to failure increases with the strength of the

wood. The failure time, however, depends also on the rate of charring,

which increases

if

the density or the moisture content of the wood is

reduced. In this case, the rule may not be valid.

Guideline 2: The structural fire resistance of wood building eIements

increases with the density of the wood, if the same species is used.

A N Y W O O D

SP EC I ES

A N D S E C T I O N

(Rstruc’l

> (DENSITY12

S A M E W OO D

SP EC I ES

>

( R 1

strut 2

Explanation:

The higher the density of the wood, the lower is the rate

of charring of the wood.

In

this case, it takes more time to reduce the

section of the element to a size at which the element can no longer

support the load. Because different species may differ in the properties

that determine the fire resistance of the element, such

as

strength, the

rule is only valid for the same species.

Guideline

3:

The thermal fire resistance of wood fire separations in-

creases with the density of the wood, if the same species is used.

( D E N S I T Y ) 1

>

( D E N S I T Y $

-

SAME SPECIES

AND SECTION

ANY WOOD WALL

OR

FLOOR

(MONOLITHIC

OR

HOLLOW)

Explanation:

Attainment

of

excessive temperatures at the unexposed

face of wood walls or floors is caused by penetration of the burning of


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



ASCE

7 8 9 2 0 7 5 9 b 0 0

0021928

b b 2


125

the wood through the wall or floor towards the unexposed face. The

higher the density of the wood, the lower is the rate of burning through

the wall or floor.

3.3.3

Variation

of

Dimensions

3.3.3.1 Concrete

ing elements increases with the thickness of the cover to the steel.

GuideIine 2

;The structural fire resistance

of

reinforced concrete build-

i-

r

1

i O V ERI1

4

L

?-

cl

>

i

7

p

Guideline 2:

The structural fire resistance of reinforced concrete build-

ing elements increases with amount of the reinforcing steel.


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,

` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



ASCE 7 8 92 0 7 5 9 b 0 0

0023927 5 T 9

126


OF

PRACTICE

(SEC TION AL AREA STEEL$

>

C 1

(

R s t ruc'

>

(S EC TIO NA L AR EA STEEL),

. . . . . . ' . .

.

:4 .

. .

a d'

, . . .

3.3.4

General

Rules

Rule

1:

The thermal fire resistance

of

a construction consisting

of

a

number

of

parallel layers

is

greater than the sum of the thermal fire

resistance of the individual layers (from Harmathy

1965;

see

this

paper

for explanation).


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E 78

9 2

0759b00 0021930 2 1 0

FIRE RESISTANCE OF

BUILDING

ELEMENTS

127

L A Y E R S L A Y E R S

COMB

I N E D

S E P A R A T E D

Rule

2:

The thermal fire resistance of a construction usually does not

decrease with the addition of further layers (from Harmathy 1965; see

this paper for explanation).

A D D I T I O N

OF L A Y E R


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,`

` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E

78 92

D 0759600

0023733 357

128


OF

PRACTICE

Rule

3:

Filling of cavities with a noncombustible structural material is

beneficial for the structural fire resistance of columns and walls.

S T R U C T U R A L

M A T E R I A L

I N C A V I T Y

A I R I N

C A V I T Y

o

R s t r u c ’ l

Explanation: Structural material functions as a thermal resistance if it

lies between the fire and the load bearing component

to

be protected.

When it lies behind the load bearing component, it also functions as a

heat sink, for example, in the case of hollow steel filled with a structural

material. In addition, the material contributes to the strength of the

member.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

`

, , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E i 8 92 m 0 7 5 9 b 0 0

0023932 093 m

FIRE

RESISTANCE

OF BUILDING ELEMENTS

129

Rule 4: The structural resistance

of

a construction increases with the

addition of further layers at the fire-exposed surface.

A D D I T I O N O F L A Y E R

A T

F I

R E - E X P O S E D

S U R F A C E

Explanation:

The addition of a layer at the fire-exposed surface will

delay the temperature rise and loss of strength

of

the construction.

If

a layer is added at the unexposed surface, the layer may act as an

insulator. In this case, the temperature rise of the construction and

components, such as reinforcing steel, will be accelerated.

Rule 5:

The thermal fire resistance of a construction containing con-

tinuous air layers or cavities is greater than that of a similar construction,

built without air layers or cavities (Harmathy

1965).

W I T H W I T H O U T

A I R L A Y E R A I R L A Y E R

Explanation:

The air layer provides additional thermal resistance.


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



130


Rule 6: The further a n air. layer is located from the fire-exposed surface,

the more beneficial is its effect on the thermal fire resistance of a con-

struction (from Harmathy 1965; see this paper for explanation).

D I S T A N C E

A I R L A Y E R - F I R E

Rule

7:

The thermal fire resistance of a construction cannot be in-

creased by increasing the thickness of a completely enclosed air layer

(from Harmathy 1965; see this paper for explanation).

T H I N T H I C K

A I R L A Y E R A I R L A Y E R

Rule

8:

Layers of materials of low thermal conductivity are better

utilized on the side of the construction that is exposed to the fire

(Harmathy 1965).


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E 7 8 92 0 7 5 9 b 0 0 00211934 9 6 6


131

I N S U L A T O R I N S U L A T O R A T

A T F I R E S I D E U N E X P O S E D S I D E

Explanation: The layer with

low

thermal conductivity functions as an

insulator and the layer with high conductivity as an heat sink. Therefore

materials in the layers, such as reinforcing steel, and materials on the

unexposed surface are better protected

if

the insulating layer is utilized

on the fire side.

Rule 9: The presence of moisture, if it does not result in explosive

spalling, is beneficial to fire resistance (Harmathy 1965; see this paper

for explanation).

MO

I S T D R Y

( R s t

ruc)

’

‘

Rst

r

uc)

( R t h e r m > R t h e r m


--`

` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E 7 8 92 W 0759600 0023935 8 T 2

132


Rule 70: Reduction of the length of a column or the span of a beam

or floor is beneficial for the structural fire resistance of these members.

(LENGTH$

< \ L ENGT H$

( S P A N $ < (S A N I 2

O R

( S P A N ì l

P-----

r

.

Explanation: During exposure to fire, the strength of a member reduces

gradually until it can no longer support the load on it. The strength of

a member increases if its span or length is reduced. Therefore, for a

given load, the time to failure or the fire resistance of the member also

increases if the length or span of the member is reduced.

Rule 11:

The structural fire resistance of a member increases with

reduction of the load to which it is subjected.


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



ASCE 7 8 Ti? 075îbU0 0021936 739

FIRE RESISTANCE

OF

BUILDING ELEMENTS

133

Explanation: During exposure to fire, the strength of a member reduces

gradually until it can no longer support the applied load. The lower

the load, the lower the strength needed to support the load. Therefore,

the time to failure or the fire resistance of the member increases if the

load is reduced.

Rule 12: Load-supporting elements, such as beams, girders and joists,

yield higher fire resistance when subjected to fire tests as parts of floor,

roof or ceiling assemblies than they do when tested separately (Har-

mathy 1965; see this paper for explanation).

B E A M T E S T E D A S B E A M T E S T E D

P A R T O F F L O O R S E P A R A T E L Y

‘Rs t ruc’

’

% t r u c ) *

Rule

23:

The structural fire resistance of continuous floor slabs or

beams is greater than that of simply supported floors or beams.

s

I M P L Y

C O N T I N U O U S S U P P O R T E D

M E M B E R M E M B E R

( Rst ruc) > ( Rst

ruc’p

Explanation:

When a continuous member

is

heated from below, a

negative temperature moment is created which reduces the positive

moment in the span. Owing to the counteracting moments in the span,

stresses in the lower reinforcement of concrete members or in the lower

part of steel members will be reduced, and this will lead to an increase

of the failure temperature of the steel.


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E 7 8

92 0759b00 0021937 b 7 5

134


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y

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715-726.


--` ` ,` , ,` , ,` ` ` ,

,̀ ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



FIRE RESISTANCE

OF

BUILDING ELEMENTS

135

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Pro-

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W.

W. (1973). "Fire resistance of protected steel columns."

Engineering Journal,

American Institute of Steel Construction, 10(3),



--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



136 STRUCTURAL

FIRE


Lin, T.D. and Abrams, Melvin S. (1983). ”Simulation of realistic thermal re-

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SP-80, American Concrete Institute, Detroit, pp. 1-68.

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Fire Technology,

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proach.‘’ Stelco Inc., Toronto, Canada.

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NRCC, No. 17724, Ottawa.

Ossenbruggen, P., Aggarwal, V . and Culver, C. (1973). “Steel column failure

under thermal gradients.” Journa l of the Structural Division, ASCE, 9Y(ST4),

727- 739.

Salse, E.A.B. and Gustaferro, A.H. (1971). “Structural capacity of concrete

beams during fires a s affected by restraint and continuity.” Proceedings, 5th

CiB Congress, International Council for Building Research, Studies and Doc-

umentation, Rotterdam, 199-204.

Salse, E.A. and Lin, T.D. (1976). ”Structural fire resistance of concrete.” Journal

of the structural Division, ASCE, 102(ST1), 51-63.

Celvaggio,

S.L.

and Carlson, C.C. (1962). “Effect of restraint on fire resistance

of

prestressed concrete.” Symposium

on

Fire Test Methods,

STP-344,

American

Society for Testing and Materials, Philadelphia, PA, 91-115.

Selvaggio, S.L., and Carlson, C.C. (1967). ”Restraint in fire tests

of

concrete

floors and roofs.”

Fire Test Methods-Restraint of Smoke, STP-422,

American

Society for Testing and Materials, Philadelphia, PA, 21-39.

Southern Building Code Congress International Inc. (1988). Standard building

code. Birmingham, AL.

Stanzak, W . W . and Lie, T.T. (1973). “Fire resistance of unprotected steel col-

umns.’’ Journa l of the Structural Division, ASCE, 9Y(ST5),

Uddin, T. and Culver, C. (1975). ”Effects of elevated temperature on structural

members.”

Journa l of the Structural Division,

ASCE, 101(ST7), 1531-1544.

Underwriters Laboratories Inc. (1988).

Fire resistance directory.

Northbrook,

IL.


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A S C E

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Chapter

4

FIRE

TEMPERATURE-TIME RELATIONS

The intensity and duration of fire in buildings can vary in a wide

range, and several studies have been carried out to investigate the

determining factors. At present, it is possible to estimate the temper-

ature course of fire in enclosures under various conditions, provided

the values of the parameters that determine it are known.

Several of these parameters, however, such as amount and surface

area of the combustible materials, are unpredictable as they change

with time and often vary from compartment to compartment in a build-

ing. It is not possible, therefore, to know at the time a building is

erected, the temperature course of a fire to which objects in that building

might be exposed during its service life.

It is possible, however, to indicate for any enclosure a temperature-

time curve that, with reasonable likelihood, will not be exceeded during

the lifetime of the building. Such curves are useful as a basis for the

fire-resistive design of buildings. They can also facilitate studies of fire

resistance of building components exposed to fires of various intensity

and duration.

In this Chapter, analytical expressions will be given that describe

characteristic temperature curves as a function of the significant param-

eters for various fire conditions commonly met with in practice.

Expressions will also be given for the standard fire curve used in

North America and for the fire curve adopted by the International

Organization for Standardization

(KO).

Principal Author: T. T.Lie.

137


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4.1

FIRE TEMPERATURES

The temperature course of a fire in an enclosure may be divided into

three periods:

the growth period,

the fully developed period, and

the decay period.

These periods are illustrated in Fig.

4.1,

where an idealized fire tem-

perature course is shown. During the growth period, heat produced

by the burning materials is accumulated in the enclosure. As a result,

other materials may be heated

so

severely that they also ignite. At this

stage of the fire, the gas temperatures rise very quickly to high values.

The rather sudden ignition of these gases and materials in all parts

of

the room is called "flash-over." After the flash-over, the fully developed

period starts. Because the temperatures in the enclosure are relatively

low in the growth period, their influence on the fire resistance of struc-

tural members is negligible. In fire resistance studies, therefore, the

growth period can be disregarded. Actual risk of failure of structural

members or fire separations begins when the fire reaches the fully

developed stage. In this stage, temperatures

of

about 1000°C or higher

can be reached and the heat transferred from the fire to structural

members may substantially reduce their strength. This risk also exists

in the decay period.

4.1.1

Parameters Determining the Fire Temperature Course

The most important parameters that determine the temperature course

of a fire were first shown by Kawagoe and Sekine (Kawagoe and Sekine

1963) and by Odeen (Odeen 1963), who estimated the heat balance for

fires in enclosed spaces. Usually part of the heat produced during a

fire in an enclosure will be absorbed by the walls and contents, a part

by the gases, and a part will be lost by radiation and convection from

windows

(Fig. 4.2).

There is also loss of chemical energy that could

have been released as heat because of outflow of unburned gases, which

burn outside the endosure. In addition, there is loss of unburned particles.

To be able to determine the temperature course, it is necessary to

know at each moment during a fire the rate at which heat is produced

and the rate at which heat is lost to exposed materials and surroundings.

Several of the parameters that determine heat production and heat

losses, such as material properties, room dimensions, wall construction,

window area, and emissivity of the flames and exposed materials, can

be determined with reasonable accuracy. Others that are known ap-

proximately are the amount of gases that burn outside the room, the

loss of unburned particles through windows, and the temperature dif-

ferences in the room.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



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0021942 T32

D

FIRE TEMPERATURE-TIME RELATIONS

139

O 0 0

U N O o 3 ~ O N O O O O O N

N N N M d d d d \ O U N m

I I I

I

I

O O O O O O

O O O O O O

m .Li

U N

O

O

-3 N O

d d d

3 , ' 3 t l r l l V t 1 3 d W 3 1

\

-

O


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



ASCE

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140

STRUCTURAL

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PROTECTION: MANUAL

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i

w

Q R

C _ j

Q W -

-

I

Q R = R A D I A T I O N L O S S E S

Q , = HEAT CO NT ENT O F I NF L O W I NG A I R

QL = HEAT CONTENT OF OUTFLOWING GASES

Q W = HEAT LOSSES TO THE WALLS

Q c = HEAT PRODUCED BY C O M B U S T I O N

Q G = R I S E OF THE HEAT CONTENT

OF

THE GASES

I N

THE

ENCLOSURE

Figure 4.2-Heat balance for an enclosure during a fire.

There are several parameters, however, whose magnitude cannot be

predicted. Usually they change with time, and therefore their value at

the time of occurrence of a fire is determined by chance. Such param-

eters include the amount, surface area and arrangement of the com-

bustible contents, velocity and direction of wind and the outside tem-

perature. The influence of wind (Thomas and Heselden

1972)

and that

of fire load can be substantial. Surveys show, for instance, that the

variability of fire loads in various types

of

buildings is such that devia-

tions in the order of

50%

or more from the most probable fire load are

common (Lie

1972).As

a consequence, variability

of

fire load alone may

easily cause deviations from the most probable temperature course of

hundreds of degrees centigrade in temperature and 50% or more in fire

duration.

4.1.2

Possible Fire Severities

Owing to the substantia1 influence of uncertain factors, it is impossible

to predict accurately the temperatures to which building components


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A S C E

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FIRE

TEMPERATURE-TIME RELATIONS

141

will be exposed during their service life. Even if the analysis to predict

fire temperature courses in enclosures is perfect, it is very improbable

that a certain predicted temperature course will occur.

The fire temperature to which building components will most likely

be exposed during the use of a building are the relatively low temper-

atures of a fire that has been extinguished before it reaches the fully

developed stage. There is a small, although not insignificant, chance

of occurrence of a fully developed fire. In this case, and assuming that

the fire cannot be influenced by sprinkler or other built-in suppression

systems or by action of the fire brigade, the fire will be controlled either

by the surface area of the materials that can participate in the burning

or by the rate of air supply through the openings (Odeen 1963, Thomas

et al. 1967).

Whether the fire will be largely controlled by surface area or venti-

lation depends on the amount of combustible contents. Unless its quan-

tity, surface area, and arrangement are controlled, or the size of the

windows and floor area made such that the possibility of a ventilation-

controlled fire becomes remote (Lie 1972, Harmathy 1972), the type of

fire that may occur is unpredictable. According to statistical data, com-

bustible contents of 10-60 kg per m2 of floor area are normal, and there

is a considerable probability of enclosures having a combustible content

of

40-100 kg/m2 (Lie 1972). It is probable that in the latter range, as

confirmed by experiments (Thomas et al. 1967, Kawagoe 1958), the fire

will be mainly ventilation controlled, even when large window openings

are present. It is likely that the greater the space behind the windows,

or to a certain extent, the deeper the enclosure, the more material or

surface area it will contain and therefore the greater will be the prob-

ability of a ventilation-controlled fire. Usually a ventilation-controlled

fire is the more severe fire, and because of the substantial probability

of its occurrence, it is common to base fire resistance requirements for

buildings on the assumption that fire severities will be controlled by

ventilation.

4.1.3

Characteristic Temperature Curves

It is possible to indicate for any enclosure a characteristic temperature-

time curve whose effect, with reasonable likelihood, will not be ex-

ceeded during the lifetime of the building. Such curves are useful as a

basis for the fire-resistance design of buildings. They can also facilitate

studies of fire resistance of building components exposed to fires of

different severity.

There are several reports that present the temperature course of fires

in fully developed and decay periods (Kawagoe and Sekine 1963, Odeen

1963, Harmathy 1972, Magnusson and Thelandersson 1970, Tsuchiya

and Sumi 1971). In all of these studies, a procedure is followed in which

the fire temperatures are determined by solving a heat balance for the

enclosure under consideration.


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



ASCE 7 8 92 0759600

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42

For the fully developed period and ventilation-controlled fires, there

is reasonable agreement in the temperatures found in the various stud-

ies, except for rather shallow rooms of limited size. In the latter case,

the amount of combustible gases that burn outside may increase in

such a way with increasing ventilation that the temperature decreases

(Harmathy 1972).

There is less agreement in the results of the various studies for the

decay period due, partly, to the complexity of the processes that de-

termine the temperature in that period.

So

far, rates of decay of tem-

perature can only

be

established empirically or by making conservative

or

highly idealized assumptions. Because of the different approaches

in deriving the rates of decay, there is a rather wide spread in the

results of the various studies. Fortunately, the influence of temperature

variation in the decay period on the maximum temperatures reached

in building components is relatively small (Kawagoe 1967). For the

purpose of deriving a temperature-time curve that, with reasonable

probability, will not be exceeded during the lifetime of the building, it

will be sufficient to use a curve that only approximately reflects the

effect of heating in the decay period. This is further explained in

Fig. 4.3.

In this figure, curve "a" illustrates a fire temperature curve derived

theoretically for a certain building. The probability of occurrence

of

a

fire with a more severe effect than shown by the curve is once in 50

years. Curve "b" illustrates a fire temperature curve for the same build-

ing, but it is assumed that the rate of burning remains constant until

all combustible materials are consumed, whereupon the fire tempera-

ture drops linearly to room temperature. Although curve "b" differs in

shape from curve "a," their heating effect is approximately the same.

If curve b' s used instead of curve "a," the probability of occurrence

of a more severe fire than that represented by the relevant curve may

change somewhat, for instance, from once in fifty years to somewhat

more or less than fifty years. In practice this means that virtually the

same fire safety will be provided whether curve "a" or curve

b

is

used for the fire-resistance design of a building. The use of curve "b"

instead of curve "a" has the advantage that it is easier to define.

4.1.4 Expressions for Characteristic Temperature Curves

In the following, analytical expressions are given that describe char-

acteristic temperature curves as a function of the significant parameters

for various fire conditions commonly met with in practice. For the fully

developed period, the derivation of these curves will be based on the

temperature curves for ventilation-controlled fires calculated according

to the method described by Kawagoe and Sekine (1963).

The temperatures attained in ventilation-controlled fires are described

(in addition to the thermal properties of the material bounding the


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E 7 8 92

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0759600 0021946 688

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~ C U O C O ~ d C U O O O O O N

C U C U N d . + d d d C O \ O r r N m

I I I I I

O O O O O O O O

O O O O

O O

O

d Cu

O 00 \o Tr

N

d d d

1

43

d

m

N

d

O


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



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534

144

STRUCTURAL

FIRE


enclosure) by a parameter, known as the opening factor F (see also

Nomenclature for the definition of symbols and the units used):

A f i *

AT

F = -

where

A

is area of the openings in the enclosure, H is height of the

openings, and A , is area of the bounding surfaces (walls and floor and

ceiling, including openings).

The rate of burning,

R,

of the combustible materials in the enclosure

is given by

R = 330 ATH (2)

and thus,

if

Q

is the fire load per unit area of the surfaces bounding

the enclosure, the duration of the fire

T

is determined by:

For given thermal properties of the material bounding the enclosure,

the heat balance can be solved for the temperature as a function of the

opening factor F . Besides depending on

F ,

the temperature course is

also a function of the thermal properties of the material bounding the

enclosure.

In this study, two materials have been chosen as representative

bounding materials: one with thermal properties resembling those of a

heavy material (high heat capacity and conductivity) and one repre-

senting those of a light material (low heat capacity and conductivity).

The thermal properties

of

these materials are given in Table 4.1. In

practice, materials with a density of approximately 1600 kg/m3 or more,

e.g., normal weight concretes, sand lime brick and most clay bricks,

can be considered as belonging to the group of heavy materials. Those

with a density of less than 1600 kg/m3, e.g., lightweight and cellular

concretes and plasterboard, can be regarded as belonging to the group

of light materials.

Using the method described in Kawagoe 1967, the temperature course

of fires in enclosures has been calculated for the two chosen bounding

materials and for various values

of

the opening factor (Lie 1974). The

conditions for which the calculations have been performed are shown

in Table

4.1

and the results of the calculations in Figures 4.4 and 4.5.

The curves in these figures were used as a basis for the derivation of

*The method

of

calculating

A f i

for openings of unequal height

is

described

in Magnusson and Thelandersson 1970, Kawagoe 1967.


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



ASCE 7 8 92 0 7 5 9 b 0 0

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145

TABLE .1.

Information on the enclosure.

Factor

k

PC

A T

H

E

a'

a

C

G

9

7 0

V

Ax

At

D

Description

Thermal conductivity of bounding material:

1.16 W/m K for a heavy material (p 2 1600 kg/m3)

0.58 W/m K for a light material (p < 1600 kg/m3)

Volumetric specific heat of bounding material:

2150

x

lo3

J/m3K for a heavy material (p

2

1600 kg/m3)

1075

X

lo3 J/m3Kfor a light material (p

<

1600 kg/m3)

Total inner surface area bounding the enclosure including window area:

Window height: 1.8 m

Emissivity for radiation transfer between hot gases and inner bounding

Coefficient of heat transfer by convection between fire and inner bounding

Coefficient

of

heat transfer between outer bounding surface area and

Specific heat of combustion gases: 1340 J/Nm3"C

Volume of combustion gas produced by burning 1 kg of wood: 4.9 Nm3/kg

Heat released in the enclosure by burning

1

kg of wood: 10.77 x lo6 Jikg

Initiai temperature: 20°C

Volume of enclosure": 1000 m3

Thickness of elementary layers of bounding material: 0.03 m

Time increment: 0.0004167 hr

Thickness of bounding material: 0.15 m

1000 m2

surface of the enclosure: 0.7

surface area: 23 W/m2K

surroundings: 23 W/m*K

"It can be shown that the influence of the volume of the enclosure on the fire temperature

is negligible.

temperature curves for fire resistance design. It was found that these

temperature curves could be reasonably described by the expression:

T

= 250

( 1 0 F ) O . l l F O . 3

, -F2t [3

( i

-

e-0.6t)

where

T

= the fire temperature in OC = time in hr, F = opening

factor in

mii2,

and

C =

a constant taking into account the influence of

the properties of the boundary material on the temperature. C =

O

for

heavy materials (p 2 1600

kg/m3), and

C = 1

for light materials

(p <

1600

kg/m3).

The expression is valid for

0.08

t r - + 1

F

(5)



- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E

78

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0759600

0023947 397

146


O 0

~ c ~ ~ o m y > ~ ~ u o o o o o

N V c I I - 4 . - + 4 + d m \ O d V m

O O O

O

O

O

O O

O

O

Cu

O O O

w

O

d hl O 00

.o

4

-4 d

3 ,

’3ä

l l V ä 3 d

W

31



--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E

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FIRE TEMPERATURE-TIME RELATIONS 147

O

u N o w a ~ N o o o o o

C \ 1 N N - d d d d w a u N

O O O O O O

O

O O

O

O Q O

O

U N

O m a N

a

II

U

Cu

m

m

h

a

rn

U

pr,

N

&

3

f

W

z

-

I-

?

.o9

a

rsi


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ASCE 78

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0759600

0023953 T 4 5

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I I

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I

I

I

I

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I

l

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\:

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A S C E

7 8

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W

0 7 5 9 b 0 0 0023952 983

W


0.01

F

0.15

If

t

>

(0.08/F)

+

1,

a value of

t

=

(0.08/F)

+

1

should be used.

If

F

>

0.15, a value of F = 0.15 should be used.

The temperature-time curves evaluated from equation

4

and those

obtained by solving the heat balance for the enclosure are shown in

Figures 4.6 and 4.7 for various values of the opening factor.

It is seen that with the aid of the analytical expression, temperature

curves can be developed that reasonably describe the curves derived

from solving the heat balance.

As discussed previously, the temperatures in the decay period are

more difficult to calculate due to the complexity of the processes that

determine the temperature in this period. On the other hand, if the

temperature variations are not very large, the influence of such varia-

tions in the decay period on the temperature attained in exposed build-

ing components are, in general, relatively small. Therefore, describing

the temperature course in the decay period by a temperature-time re-

lation that approximately reflects the decrease of temperature in this

period is sufficient.

According to the experimental data of Kawagoe (1958), the rate of

decrease of a fire with a fully developed period of less than one hour

is roughly 10°C per minute and that of a fire with a fully developed

period of more than one hour is 7°C per minute. The Swedish code

assumes a rate of decrease of

10°C

per minute irrespective of the du-

ration of the fully developed period of the fire (Magnusson and

Thelandersson 1970). A comparison with semi-empirical data developed

by Magnusson and Thelandersson (1970) shows that the assumption

of a rate of decrease of 10°C per minute is too fast for fires of long

duration and too slow for fires of short duration. According to Har-

mathy (1972), who studied several experimental fires of relatively short

duration (Butcher et al. 1966, Butcher et al. 1968), the rate of decrease

of temperature for such fires is in the order of 15-20°C per minute.

In general, the longer the duration of the fully developed period, the

lower the rate of decrease of temperature. Using this information, the

following expressions have been derived for the temperature course of

fire in the decay period:

(6)

~

and

I

with the condition

T =

20

if

T <

20°C

( 8 )


--``,`,,`,,`̀ `,,````,`,,,``,`,,-`-`,,̀ ,,`,`,,`---



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STRUCTURAL

FIRE

PROTECTION: MANUAL

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PRACTICE

i ,

' 3ä

í l l V ä 3 d l i V 3 2

O 0

O 0

U N

N N

O 00

\ O U

N O O O O O N

N

d d d d

W \O U N m

h

.-n

7

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

g

O O O O O

O

O

O

O O O O O O O

U N O W \o U N

d d

.-I

3,

' 3 ä

íll

Vä

3

dW

31


- - ` ` ,

` , ,

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` ` ` ` ,

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` ` ,

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` , ,

` ,

` , ,

` - - -



A S C E 7 8 92 W 0 7 5 9 b 0 0 0 0 2 3 9 5 4 7 5 4 W

FIRE TEMPERATURE-TIME

RELATIONS 151

In the above equations,

T

= fire temperature, 7

=

time at which the

decay starts as given by Equation 3, t = time under consideration

( t >

T), and T = temperature given by Equation 4 at the time t =

T .

The temperature curves obtained from equations

4

and

7

are illus-

trated in Figure

4.8

for various fire loads (Le., based on total bounding

surface area) and an opening factor of 0.05. In Figure 4.9, the influence

is shown of the openings on the fire temperature course. It can be seen

that the fire load determines the duration of the fire, whereas the

openings influence both the duration and the intensity of the fire. In

Figure

4.10,

a characteristic temperature curve is compared with the

temperatures measured at several places in a room during an experi-

mental fire (Kawagoe and Sekine 1963). It is seen that the curve de-

veloped from the analytical expression reasonably characterizes the tem-

peratures obtained during the experimental fire. It is somewhat con-

servative, but satisfactory to use as a design curve for fire resistance.

4.1.5 Standard Fire Curve

In studies of fire resistance, it is common to expose building elements

to heating in accordance with a standard temperature-time relation. The

standard temperature-time curves used in various countries are shown

in Figure

4.11.

It can be seen that there are no significant differences

between the various standard curves. The values of the curve adopted

by

IS0

834

are given in Table

4.2.

Those used in North America (ASTM

1985)

are given in Table

4.3.

There are also analytical expressions for several of the standard m e s .

The expression that describes the IS0 curve

is:

T -

To =

345

log,,

(8t + 1)

(9)

where t

=

time in minutes, T

=

fire temperature in OC and To = initial

temperature in

"C.

For the curve used in North America, several analytical expressions

exist (Williams-Leir

1973).

One of the expressions is of the form of a

sum of exponential functions:

T - To =

al

(1

- ea49

+

u2

(1

-

ea5*)

+ u3

(1 -

en@)

(10)

where u, = 532 for OC, 957 for O F ; u2 = - 86 for OC, - 334 for OF a3 =

820 for O C , 1476

for

OF ; a4 = -0.6; a5 = 3; a6 = -12.

The extreme deviation from the values given in Table 4.2 are -26°C

at 45 min; + 48°C at 3.5 hours;

-

8°C at

8

hours.

This form is suitable for use in analytical heat flow calculations be-

cause when it is used as a boundary condition, the heat transfer equa-

tions are integrable.



- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

`

, ,

` ,

` , ,

` - - -



A S C E 78 92

0 7 5 9 b 0 0

0 0 2 1 9 5 5 b90


OF

PRACTICE

52

h

o

'3ä l l l V ä 3 d W31

a-

8

d N O W \o . J N O O O O O N

x

m e

B

E

O O

O

O

O O

O

O

O

O

O

O O O O

w

N O 00

\o

-a

N

2

d d

3,

' 3 ä

n l V ä 3

d

W

31


--` ` ,` , ,` , ,` ` ` ,

,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E

78 92

W

0759600 0 0 2 1 9 5 6 5 2 7

W


3 , ‘3ä l V ä 3 d W 3 1

N N d d d d d m \ D g N m

N O W - W N O O O O O N

O O O O O O

O

O O

O O O

O

N O

m

rD N

d d

3,

‘ 3ä

n l V ä 3 d W 3 1

>

I

2

Cu


--``,`,,`,,`̀ `,,````,`,,,``,`,,-`- ,̀,`,,`,`,,`---



A S C E

78

92

m

O759600 0023957

4 b 3

m


U N O W a U N O O O O O N

N

N N 4 d d

d

00 u3 U N m O

n

W

>

I I

1’

U

Ln

m

O

m

Ln

N

O

N

Ln

d

O

+

Ln

O

O

O

O

O O O

O

O

N

O O

O

O

O

N

O m

u3

4

O

O

d

3 ,

‘ 3 t l n l V t l 3 d W 3 1

E

W

-

c


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



1 3 0 0

I

4 0 0

1 2 0 0

~

D U

R A T IO N , h

Figure 4.11 -Standard fire tempera ture-time relations used in various

countries for testing of building elements.

1 1 0 0

Time in Minutes

O

5

10

15

30

60

90

120

180

240

360

o

O 1000

W

rx

+ 9 0 0

a

w

w

a

S

8 0 0

W

I-

W

2 7 0 0

U

Temperature rise fire

O C )

O

556

659

71

8

821

925

986

1,029

1,090

1,133

1,193

6

O0

5

O0

ASCE 7 8

7 2

m

0 7 5 7 b 0 0 002L958 3 T T

m


-

- 1 9 0 0

- 1 8 0 0

- 1 7 0 0 ,

- 6 0 0

s

O

W

I-

A U S T R A L I A

G R E A T B R I T A I N

N E W Z E A L A N D

B E L G I U M

D E N M A R K

W

-

1 3 0 0

- U . S . S . R .

I I

F I N L A N D

5

- I T A L Y

F R A N C E

6 - S W I T Z E R L A N D

I E T H E R L A N D S

'r

I

-

N O R W A Y 7

-

J A P A N

S W E D E N

W EST G E R M A N Y

-

I I I

8 0 0

O 1 2

3 4

5 6 7

8


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ASCE

7 8

9 2

0 7 5 9 b 0 0 0023959

236

156

STRUCTURAL

FIRE


A set of expressions that more accurately approximates the values

given in Table 4.2 is:

T

- To

= al tanh a,f + az tanh a,f

+ u3

tanh

a ,

t

<

2

(11)

T

-

To = 906.7

+

41.67f, t

2

2 for

C

T - To = 1632 + 75f, t 2

2

for O F

(12)

(13)

TABLE

.3. Standard fire temperature-time relation used in

Time

h:min

0:oo

005

0:lO

0:15

0:20

0:25

0:30

0:35

040

0:45

050

0:55

1:oo

1:05

1 : l O

1:15

1:20

1:25

1:30

1:35

1:40

1:45

1:50

1:55

2:oo

2:lO

2:20

2:30

2:40

2:50

3:OO

North America (ÂSTM E119).

Temperature

F

68

1,000

1,300

1,399

1,462

1,510

1,550

1,548

1,613

1,638

1,661

1,681

1,700

1,718

1,735

1,750

1,765

1,779

1,792

1,804

1,815

1,826

1,835

1,843

1,862

1,862

1,875

1,999

1,900

1,912

1,925

Temperature

"C

20

538

704

760

795

821

843

862

878

892

905

916

927

937

946

955

963

971

978

985

991

996

1,001

1,006

1,010

1,017

1,024

1,031

1,038

1,045

1,052

Time

h:min

3:lO

3:20

3:30

3:40

3:50

4:OO

4:lO

4:20

4:30

4:40

4:50

5:OO

5:lO

5:20

5:30

5:40

5:50

6:OO

6:lO

6:20

6:30

6:40

6:50

700

710

720

730

740

7:50

8:00

Temperature

F

1,938

1,950

1,962

1,975

1,988

2,000

2,012

2,025

2,038

2,050

2,062

2,075

2,088

2,100

2,112

2,125

2,138

2,150

2,162

2,175

2,188

2,200

2,212

2,225

2,238

2,250

2,262

2,275

2,288

2,300

Temperature

"C

1,059

1,066

1,072

1,079

1,086

1,093

1,100

1,107

1,114

1,121

1,128

1,135

1,142

1,149

1,156

1,163

1,170

1,177

1,184

1,191

1,198

1,204

1,211

1,218

1,225

1,232

1,239

1,246

1,253

1,260


--``,`,,`,,``̀ ,,````,`,,,`̀ ,`,,-`-`,,`,,`,`,,`---



A S C E 7 8

92

m

0 7 5 9 b 0 0 0 0 2 3 9 b O

T 5 8 W


where ul = 580 for OC, 1044 for OF;

u,

=

-276.8 for O C 498.2 for

O F ;

u3

= 714.4 for OC 1286 for OF u, = 0.8429; u5 = 0.9736;

u6

= 8.910.

The maximum deviation of the temperature after 20 minutes, given

by expressions

11,

12, and

13,

from the values tabulated in Table 4.2,

is

-7°C

at 40 min.

Another temperature-time relation, given in Fackler (1959), has the

form:

T

-

To = u

[i -

exp (-3.79553 v? ]+

b V l

(14)

where

u =

750 for

OC,

1350 for

O F , b =

170.41 for

OC,

306.74 for "F and

t = time in hours.

This expression is frequently used and is a reasonably accurate ap-

proximation of the relation between temperature and time given in

Table 4.2.

REFERENCES

American Society for Testing and Materials. (1985). Standard methods of fire tests

of

building construction and materials, AN SI IA ST M

E l 19,

Philadelphia, PA.

Butcher, E.G., Bedford, G.K., and Fardell, P.J. (1968). "Further experiments

on temperatures reached by steel in buildings." Symposium No. 2, Behaviour

of Structural Steel in Fire, Paper No.

1 ,

H.M. Stationery Office, London,

England.

Butcher, E.G., Chitty, T.B., and Ashton, L.A. (1966). "The temperatures at-

tained by steel in building fires."

Fire Research Technical Paper

No. 14, H.M.

Stationery Office, London, England.

Fackler, J .P. (1959). "Concernant la resistance au feu des elements de construc-

tion." (In French). Cahier 299, Centre Scientifique et Technique du Bâtiment,

France.

Harmathy, T.Z. (1972). "A new look at compartment fires, Part I and Part II."

Fire Technology, 8(3), 196-217; 8(4), 326-351.

International Standards Organization. (19

).

Fire resistance tests-Elements of

building construction, International Standard IS0 834.

Kawagoe, K. (1958). "Fire behaviour in rooms."

Report No.

27, Building Research

Institute, Ministry of Construction, Tokyo, Japan.

Kawagoe,

K.

(1967). "Estimation of fire temperature-time curve in rooms."

Research Paper No. 29, Building Research Institute, Tokyo, Japan.

Kawagoe, K., and Sekine, T. (1963). "Estimation of fire temperature-time curve

in rooms."

B.R.I. Occasional Report No.

I l , Building Research Institute, Min-

istry of Construction, Tokyo, Japan.

Lie, T.T. (1972). Fire and buildings. Applied Science Publishers Limited, London,

19-22.


--``,`,,`,,̀ ``,,````,`,,,``,`,,-`-`,,̀ ,,`,`,,`---



A S C E 78

92 D

0759600 002LîbL

994

158


Lie, T.T. (1972).

Fire and buildings.

Applied Science Publishers Limited, London,

Lie, T.T. (1974). “Characteristic temperature curves for various fire seventies.”

Fire Technology, 10(4), 315-326.

Magnusson, S.E.,

and Thelandersson, S. (1970). “Temperature-time curves of

complete process of fire development. Theoretical study of wood fuel fires

in enclosed spaces.” Civil Engineering and Building Construction Series

No.

65,

Acta Polytechnica Scandinavica, Stockholm, Sweden.

Odeen,

K.

(1963). “Theoretical study

of

fire characteristics in enclosed spaces.”

Bulletin 1O,

Division of Building Construction, Royal Institute of Technology,

Stockholm, Sweden.

Thomas, P.H., and Heselden, A.J.M. (1972). “Fully-developed fires in single

compartments.” Fire Research Note N o. 923, Building Research Establishment,

Fire Research Station, Borehamwood, England.

Thomas, P.H., Heselden, A.J.M., and Law, M. (1967). ’’Fully-developed com-

partment fires; two kinds of behaviour.” Fire Research Technical Paper No. 18,

H.M. Stationery Office, London.

Tsuchiya, Y. and Sumi, K. (1971). ”Computation of the behaviour of fire in an

enclosure.” Combustion and F lame, 16, 131.

Williams-Leir, G . (1973). “Analytical equivalents of standard fire temperature

curves.” Fire Technology, 9(2), 132-136.

9-11.

NOMENCLATURE

A = area of the openings in the enclosure, m2

A , =

area of the internal bounding surfaces, m2

C

= constant

F = opening factor, m1’2

H

= height

of

openings in the enclosure,

m

Q = fire load per unit area of the internal bounding surfaces, kg/m2

R

=

rate

of

burning, kg/hr

T

=

fire temperature,

“C

T , = fire temperature at the time

T,

“C

t = time, hr

T

=

time at which the temperature starts to decline, hr



--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



ASCE

78 92 0759600 0023962

8 2 0

5.1

TEMPERATURE OF FIRE EXPOSED MEMBERS

Several methods exist for predicting temperatures of structural mem-

bers that are exposed to fire. It is possible to determine temperatures

in fire exposed members experimentally, but also by analytical, nu-

merical, graphical, or analogue methods. Of the theoretical methods

the numerical method is used most at present.

The numerical method has several advantages. Various heat transfer

problems for which no analytical solution can be found, for example,

because of complex shape of the member, can be solved numerically.

In addition, by solving the heat transfer equations numerically, it is

possible to take into account the temperature dependence of the ma-

terial properties.

A

disadvantage of the numerical method is that it is laborious and

time consuming. With the aid of high speed computers, however, the

calculation time can be reduced substantially. But the preparations be-

fore a calculation can be executed, such as programming and deter-

mination of the material properties as functions of temperature, still

require a large amount of work and time. If, however, the material

properties are known and a program for calculating the temperatures

in the member is already available, the calculation can be made in a

very short time.

The most common method for the calculation of temperatures in

members are the finite difference method (Dusinberre 1961) and the

finite element method (Zienkiewiczand Cheung 1967). In the following,

a versatile finite difference calculation method (Lie 1977) is discussed.

I

t

Chapter 5

CALCULATION OF TEMPERATURE AND FIRE

RESISTANCE OF STRUCTURAL MEMBERS

Principal

Authors:

T .

T.

Lie

R. H. White

159


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E

7 8 92 m 0759600 002Lîb3 7b7 m

1

60


OF

PRACTICE

The method designed originally for the calculation of the temperatures

in protected steel columns, is also suitable for the calculation

of

tem-

peratures in monolithic building components such as solid concrete

columns, beams, and walls. It can also be used for the calculation of

temperatures of any system in which a perfect conductor or well-stirred

fluid is enclosed in an encasement, for example, water-filled hollow

steel columns or beams, and exposed to a radiative heat source of

varying temperature.

5.1.1 Temperature of Protected Steel

5.1.1.1 Calculation Method

The calculation procedure is based on an improved version of a finite

difference method, which offers the advantage

of

a network of points

with which the corners of rectangular configurations can be reached

without difficulties (Harmathy 1970). It was applied in a study describ-

ing the heat flow in fireexposed steel columns protected by an insulating

material (Lie and Harmathy 1972, see Figure

5.1).

It was later extended

to take into account other configurations and the possibility of heat

generation or heat absorption by the protecting material.

In this method, the cross section

of

the insulating protection is divided

into several elementary regions as shown in Fig. 5.2. They are square

inside the insulation and triangular at its boundaries. The temperature

b

a

A

b

4

4

b

d

A

4

Figure 5.1-Cross section

of

a typical protected steel column.


--` ` ,

` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E

7 8 92 m

0759600

0023964 b T 3 m

CALCULATION

OF

TEMPERATURE AND FIRE RESISTANCE

161

at the center

of

each element is taken as representative

of

that of the

entire element. The representative point for each triangular boundary

element

is

located on the hypotenuse.

Because the thermal conductivity of steel is normally at least 20 times

higher than that

of

the protection, steel will be considered as a perfect

conductor. This implies that the temperature of the steel core will be

assumed to be uniform over its entire volume. Consequently, the two-

dimensional network need not be extended over the cross-sectional

area of the steel core. Instead the subdivision of the steel core can be

done in a more convenient way as will be described later. Furthermore,

it will

be

assumed that the capacity

of

the air enclosed by the protection

is negligible in comparison with that of the steel.

For reasons of symmetry, only one-quarter of the section need be

considered when calculating the temperature distribution in a cross-

section.

As

shown in Fig.

5.2

in an

x-y

coordinate system the repre-

K

Figure 5.2-The arrangement

of

the elementary regions

of a

one-quarter

section

of

column protection.


- - ` ` ,

` , ,

` , ,

` ` `

, ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E

3 8 92 0359600 0021965 5 3 T

9


62

sentative point of the protection I or the region

R,,,,

has the coor-

dinates x =

(rn

-

i

A e / e and y = ( n - 1) A [ / G . The points rn =

1 and n = 1 coincide with the origin x

= O

and y = O. m increases in

the

x

direction and attains a value m=M at the boundary A-B, where

as

n

increases in the

y

direction and has a value

n

=

N at the boundary

B-C. As can be seen in the figure, only those points of the

x-y

plane

are defined for which (m +

n )

is an odd number.

To calculate the temperature history of the insulation and steel, a

heat equation is written for each elementary region for the times j A t

where

j

= O,

1, 2 . . .

and

A t

is an appropriate time increment. With

the aid of these equations, the temperature of each region can be suc-

cessively evaluated for any time t = j + 1 ) A t if the temperature at

the time t = j A t is known.

It should be mentioned that the applicability of the method to be

described is not limited to protected steel columns. It can be applied

to any assembly consisting of a central core

of

a well-stirred material

or a material with relatively high thermal conductivity, surrounded by

a rectangular envelope of much lower conductivity, which is exposed

to heating on all four sides, By removing the core and extending the

insulation to the centre of the section, it can also be used for the

calculation of the temperature history of monolithic columns or beams.

Moisture movement is not taken into account in the model. The effect

of moisture on the temperature rise of steel is in general small, and in

most cases negligible. Under normal conditions, usually assumed to be

an environment of about

50%

relative humidity and 20°C temperature,

most inorganic building materials do not hold more than 1 moisture

by volume. For such materials, the effect of moisture on the time to

reach the critical steel temperature is a few percent and not significant.

Concretes, however, may hold 3-6

of

moisture. Experiments and

calculations, using a model in which it is assumed that the moisture

moves to the inner surface of the insulation and evaporates at this

surface, indicate that the predicted failure times will be on the safe side

by about 10-15% (Lie and Harmathy 1972). It is possible to make a

correction for the effect of moisture using a semi-empirical method. It

is also possible to take the effect of moisture into account by assuming

that evaporation of moisture takes place when the temperature in a

specific region reaches 100°C. At this stage, all heat is used for the

evaporation and the temperature stays constant until all moisture has

been evaporated.

5.1.1.2 Equations for the O uter Boundary of Insulation

In a fire, heat is transferred from the fire to an exposed object by

convection and radiation. According to existing information, the heat

transferred in a typical case by convection to an object is less than

10%

of the radiative heat (Trinks and Mawhinney

1961).

It is well known

that above a certain level of the coefficient of heat transfer, which is


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E

7 8 92

m 0 7 5 î b O O

002Lîbb 476 m

CALCULATION OF TEMPERATURE AND FIRE RESISTANCE 1

63

easily obtained in fires and furnaces, the temperature of the surface of

the exposed object will be very close to the temperature of the envi-

ronment. In this region, changes of the order of

10%

will have little

effect on the surface temperature and thus on the temperature in the

exposed object. Therefore, to simplify the heat transfer model, the

convective heat transfer may be neglected.

Furthermore, it may be assumed that the radiative heat transfer to

the exposed object is approximately that of a black body. As explained

subsequently, this assumption will cause only a small error.

In an actual fire, heat is received from luminous flames, which have

a high emissivity. If the thickness of the flames is sufficient, the em-

issivity may reach values of about 0.9 or higher, and thus approaches

that of a black body. For the same reason as in the case of convection,

an error of the order of 10% in the radiative heat transfer will have

little effect on the surface temperatures of the exposed object if the heat

transfer

is

high. The high heat transfer from fires is simulated in fur-

naces by making them large,

so

that the flames have sufficient thickness,

and by selecting furnace wall materials that produce wall temperatures

close to the flame temperature. In the present study, a column is con-

sidered that is exposed to fire on four sides. It will be assumed that

the fire temperature follows a standard temperaturetime relation ac-

cording to that specified in

ASTM

E119-83 (1985), although the calcu-

lation procedure is valid for any other temperature-time relation. Several

analytical expressions that approximately describe this curve exist

(Williams-Leir 1973). Here, the following expression will be used (Lie

and Harmathy 1972):

T, = To + 750 (1 - exp (-3.79533 G 170.41

d

(1)

where T f and

To

are, respectively, the fire and ambient temperature in

"C and t

is

the time after the start of the fire in hours. (The symbols

used are defined in the Nomenclature section of this chapter.)

The heat transmitted from the fire to an elementary surface region

R M , n

along the boundary

A-B

(see Fig. 5.2) during the period

jAt

t

(i

+

12)At for a unit height

of

the column can be written as

I

fl &TE~

(Tf

+

273)4

-

FM , n

+

273)*]At

where

u

= Stefan-Boltzmann constant

E~ = emissivity of the protection.

(Values of material properties and physical constants are given in the

Appendix.)

From the region

RM

heat is transferred by conduction to the

two

neighbouring regions, R,- i),(n This heat can be

nd R,, - ) , (n +


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



ASCE 78

92

0 7 5 9 b 0 0

0021967

302

164


given as

k{M-

l ) , ( n +

1)

+ ‘k l

(T M,n

T { M - i ) , ( n + i ) )

2

(3)

where k

=

thermal conductivity of the protection.

During exposure, heat may be generated in the protecting material,

because of decomposition of the material. It is also possible that heat

is absorbed because of dehydration or transformation processes in the

material. If Q is the rate of heat generation (+)

or

absorption ( - ) per

unit volume, then the heat gain or loss in an elementary region

R M , n r

because of this heat generation or absorption, is for a time period

At

2

(At)’ QAt

(4)

1

The sensible heat absorbed by the element in this period

is

1

-

AL)’ ( P C ) ~ , ~TG,; -

Ti

,TJ

2

(5)

where

p =

density of the protection

c = specific heat of the protection.

following heat balance for an elementary region R M,n s obtained:

By adding all heat gains and losses given by equations (2)-(5), the

1

-

(Ag)’ ( p ~ ) i M , ~I? ,;

-

pM,fl)

2

= fl

LUE^

[(q

+ 273)* - (T;,fl+ 273)4]At

1

2

-

(At)’ QAt

The temperature

TZ :

t the time

( j

+ 1)At for an elementary region



--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` -

--



CALCULATION OF TEMPERATURE AND FIRE RESISTANCE

165

R M , n can be solved for from the equation (6). For an elementary region

RM,n

along the boundary B-C (Fig.

5.2)

the temperature

Tm+N

can be

derived in a similar manner.

In equation

(6)

the quantities, p, c, k, e,, and Q are assumed to

be known.

If

the temperatures in all elementary regions at the time

t = jAt

are known, the temperatures in these regions at the time

t =

( j + 1)At can be calculated from these equations.

By

using the newly

calculated temperatures of the various regions as initial temperature

and repeating the calculation process, the temperatures at the times

( j + 2)At ,

( j

+

3)At ,

etc., can be derived for each elementary region.

5.1.1.3

Equations

for

the Inside

of

Insulation

In the same way as for elementary regions at the outer boundary,

the temperatures in the insulation can be calculated by writing heat

balance equations for the inside elementary regions. For a region

Rm,n

represented by point

P,,,,

the heat balance equation for a unit height

of the column and a time period At is

+

Q(At.)'At

(7)

The temperature

(i +

l )Af

can be solved for from equation (7).

of an inside elementary region Rm,nat the time

5.1.1.4

Equations

for

the Inner B ou nd ay

of

Insulation and

for

the

Steel

Core

To describe the heat transfer along the inner boundary of the insu-

lation, a model presented in a previous paper (Lie and Harmathy 1972)

will be used.

As

shown in Fig. 5.1, a certain fraction of the inner surface

of the insulation of a protected steel column

is

usually in direct contact

with the steel core, and a fraction (1

-

ci) is separated from the steel

core by an air gap. The mechanism of heat transfer along the areas of

contact is conduction. Heat is transferred through the air gap by ra-

diation and convection. Because the radiative heat transfer is predom-

inant at temperatures normally found in protected steel columns during


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -





A S C E 7 8 9 2

0757600

O 0 2 1 9 7 0 9 T 7

CALCULATION

OF


167

M - K -

2) pieces. It is assumed that a fraction of each elementary

mass is in direct contact with the adjacent elementary insulation surface,

and thus receives heat from the insulation by conduction, while a

fraction (1 -

a)

of its mass is at some distance from the elementary

surface and receives heat by radiation. By varying from

O

to

1,

all

possible practical conditions, including pure radiative and pure con-

ductive heat transfer to the steel core, can be simulated. If the steel is

everywhere in contact with the insulation, for example, in the case of

tubular steel columns, a

=

1. If there is no contact, as in the case of

a wall built around the steel without touching it, a

=

O.

In the case of

the column shown in Fig. 5.1,

(Y

is approximately 0.5.

In

practice, the

shape and size of the columns are known and

a

can be estimated, but

considering the worst case of (Y = 1 is probably sufficient.

Along the boundary

D-E

(see Fig. 5.2), the radiative heat transferred

to the steel core from the elementary region

R ( Mp K+l ) , n

through a frac-

tion (1 - a) f the inner surface of the insulation bounding this region

is during the period j A t t ( j + 1)At

(1

- a)

~ C U Ë

[ ( T / M - K + l ) , n +

273)4-

(Tir

+ 273)4]At

(8)

where E = emissivity factor =

l / [ ( l /&J

(UEJ-

11

In the same period, heat is transferred by conduction from the neigh-

bouring regions to each triangular elementary region

R(M-K+

at the

inner surface of the insulation, and to each fraction

of

the elementary

steel masses that are in contact with the inner insulation surface. Since,

by assumption, steel is regarded as a perfect conductor, the tempera-

tures of those fractions of elementary steel masses that are in direct

contact with the insulation surface are identical to those of the adjacent

elementary regions of insulation. Consequently, their presence can be

taken into account by adding their heat capacities to those of the ad-

jacent elementary insulation regions.

By adding all heat gains and losses, the following heat balance equa-

tion can be written for a period

jht t 5 j +

1)At for each triangular

elementary region

R ( M p K + l ) , n

and each fraction of steel attached to it:

L

2



- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E 78 92 0 7 5 9 b O O 0023973 8 3 3

168


where

c , ) I ; ~ - ~ + ~ ) , , ~

the specific heat of steel at a temperature of T(M-K+l),n

W

with

attached steel fraction along the boundary D-E at the time ( j + i ) At ,

can be found by solving equation

(9)

for this temperature. For the

boundary E-F (Fig.

5.2),

the temperature

Tc:N-L+I) of

an elementary

region R,,r,(N + with attached steel fraction can be derived in a similar

manner.

One of the parameters still unknown in equation

(9)

is the steel

temperature Ti,,

of

that part of the steel that receives heat by radiation.

Although the model assumes that the steel temperature is uniform,

evaluation of Ti,. is necessary, as an intermediate step in the procedure

of calculation of the uniform steel temperature. This steel temperature

is obtained later by adding all enthalpies of the steel elements, part of

which are heated by radiation and part by conduction, and dividing

the sum by the heat capacity of the steel.

Ti, can be derived in a similar way to the temperatures of the ele-

mentary regions in the insulation by writing a heat balance for the steel.

From such a heat balance, it follows that the temperature Ti,: at the

time

( j +

1)At is given by

= mass of the steel core

The temperature T/,& K+i),nof an elementary region

M - K

+ ( T i t , ( N - L+ l ) +

273)4

rn =

3.5

..

Although the temperature field in the protection may be of interest

in other cases, e.g., if the protection is made of concrete and contributes

to carrying the loading, normally the temperature

of

the steel core is

of primary importance. Because this temperature often determines the

strength of the steel, knowledge of it is essential for predicting the time

of

collapse of building components.



- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E 78 7 2

O759600

O023972 7 ï T

CALCULATION OF TEMPERATURE AND

FIRE

RESISTANCE

169

The steel core temperature can be derived by equating the enthalpy

of the steel core to that

of

the sum of the enthalpies of all steel pieces

constituting the steel core. This results in the following equation:

2 a

c,dT

=

TL: ' N - L + M - K - 2

where

q+'

=

the steel core temperature at the time

( j +

1)At

cs

=

the specific heat

of

steel.

According to available data (Liley et al. 1963, British Iron Steel Re-

search Ass'n. 1953), the specific heat of steel may, in the temperature

range of 0-650"C, be given as a function of its temperature T by the

expression

(12)

,

=

440 + 0.478T

where

c,

is in J/kg"C and

T

in

" C .

(See the Appendix for more accurate

expressions and higher temperatures.)

Substitution of

c,

in equation (11)and integrating gives, for the steel

core temperature,

where

a

=

0.239

b

=

440

a

d = - 2

N

- L

+ M

- K - 2

+

0.239(Ti~(',-L+1,)2]

+

a[440T{:'

+

0.239(Ti:')2]


- - ` `

, ` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E 78

92

m

0759b00 0023973 b o b

m

170


5.1.1.5 Au xiliay Equations

To

calculate the temperatures of the elementary regions along the

lines of symmetryA-D and

ï -C,

it is necessary to know the temperatures

of the regions

P,,i,l

and

Pl.,,.

These temperatures are obtained by equat-

ing the temperatures of symmetrical points. Thus, along line

A-D:

(14)

i+' =

Ti+'

ni,1 n1,3

and along line

F-C:

(15)

i f1 = Tif1

I,n 3,

n

With the aid of equations

(6),

(7),

(9), (10)

and

(13)-(15),

it is now

possible to calculate the temperature distribution in the insulation, on

its boundaries, and the temperature of the steel core for any

( j

+ 1)At

time level, if the temperatures at the

jAt

level are known. Initially, only

the temperatures at the

t = O

level, which are usually equal to room

temperature, are known. Starting from these temperatures, the tem-

perature history of the protection and the steel core can be determined

up to any specified time or temperature level with the aid of the afore-

mentioned equations.

It is known that the solutions are not stable for all values of the mesh

width

A[

and time increment

At.

In order to insure that any error

existing in the solution at some time level will not be amplified in the

subsequent calculations, a stability criterion has to be satisfied which,

for a selected value of At, limits the maximum value of

At

(Dusinberre

1961).

For fire-exposed columns and beams, the criterion of stability

is usually most restrictive along the boundary

A-B

between fire and

insulation.

5.1.1.6 Comparison wi th Test Results

In previous studies (Lie and Harmathy

1970,

Konicek and Lie

1974),

calculated results were compared with experimental results for a num-

ber of steel sizes and protecting materials. The comparisons showed

that, for these cases, the maximum deviation between calculated and

experimental temperatures was about

15%,

which may be regarded as

reasonably accurate in the field of fire engineering. A few of the com-

parisons are shown in Figs.

5.4-5.6.

In Figs.

5.4

and

5.5,

measured

and calculated steel temperatures are compared for protected steel col-

umns that were exposed to heating at temperatures according to the

standard temperature-time relation given by equation (14). In Fig.

5.6,

the comparison is for a column that was exposed to heating according

to a temperature-time curve that resembles an actual fire temperature

curve.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

`

, ,

` - - -



ASCE 7 8

92

m

0 7 5 9 b 0 0 0023974

542 m

I I

5 0 0

-

-

4 0 0 -

300

-

-

X P E R I M E N T A L

C A L C U L A T E D -

--

-

I

1

171

ALCULATION

OF


1100

U

750 o

Y

rx

+

Q

rx

w

I T

400 2

I-

32

O

o

W

rx

3

c

<

rx

w

L

I-

T I M E ,

m i n

Figure 5.4-Steel temperature as a func tion of time (size steel core: 15 x 15

cm; insulation of insu lating fire brick).

o

o

W

rx

3

c

rx

W

L

w

a

s

Figure 5.5-Steel temperature as a function of time (size steel core: 20 x 20

cm; insulation

of

heuy lay brick).



--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E

78

'72 0 7 5 ' 7 b 0 0

0023975

489

1

72


9 o o c

a

Y

+

300

2 0 0

Y

1100 u-

œ

æ

+

U

œ

750 a

Y

c

400

1O0

I I I l

I

I

O

3 2

O 20

4 0

60 8 0 1 0 0 1 2 0

140 160

TIME, m i n

core: 25 x 25 em; insulation of vermiculite board).

Figure 5.6-Steel and furnace temperature as a fun ction of time (size steel

5.1.2

Temperature of Unprotected Steel

For unprotected steel with a rectangular or square cross-section, the

temperatures can be calculated by modifying the method described in

Section

5.1.1

for protected steel. In this modification, the steel in the

cavity behind the insulation is removed and the thickness of the in-

sulation is increased until it reaches the center of the section. In ad-

dition, the thermal properties of the insulation have to be replaced by

that of the steel. An example of the calculation method is given for a

square steel section in Stanzak and Lie

1973.

5.1.3

Temperature

of

Rectangular Concrete Columns

The temperature of a concrete column with rectangular cross section

can be calculated by modifying the method for calculating the temper-

atures in protected steel, described in Section5.1.1. In this modification,

the steel in the cavity behind the insulation is removed and the thickness

of the insulation is increased until it reaches the center of the section.

In addition, the thermal properties of the insulation have to be replaced

by those of the concrete.

5.1.4 Temperature

of

Square Concrete Columns

The equations that determine the temperatures in square concrete

columns, exposed to fire on four sides, have been published in several


--``,`,,`,,`̀ `,,````,`,,,̀ `,`,,-`-`,, ,̀,`,`,,`---



A S C E 7 8

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0759600 0021976

315

m


173

papers. Also, many tests were carried out to validate the calculation

method (Lie et al.

1984).

It can be used for the calculation of temper-

atures in any object with square cross section,

of

which the thermal

properties are known as a function

of

temperature. The equations that

describe the calculation method are given below, and the equations

that describe the thermal properties are given for a number of materials

in the Appendix.

5.1.4.2

Divis ion of Cross-Section in to Elements

To calculate the temperatures in the column, the cross-sectional area

of the column is subdivided into a number of elements, arranged in a

triangular network (Fig.

5.7).

The elements are square inside the column

and triangular at the surface. For the inside elements, the temperature

at the center

is

taken as representative of the entire element. For the

triangular surface elements, the representative points are located on

the center of each hypotenuse.

'

7

cy>

a

r-4

I

E

X

Figure 5.7-Trian gular network

of

elements

in

a one-eighth section of

column.



--` ` ,` , ,` , ,` `

` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---





A S C E 7 8 9 2

m

0 7 5 9 b 0 0 0021978 198

m

CALCULATION

OF


5.1.4.4 Auxilia

y

Equations

To

calculate the temperatures of the elements along the lines

of

sym-

metry

A-C

and

B-C,

the temperature has to satisfy the following sym-

metry conditions:

line A-C

In order to ensure that any error existing in the solution at some

time level will not be amplified in subsequent calculations, a stability

criterion has to be satisfied which, for

a

selected value of

AC,

limits the

maximum of the time step

(AT).

Following the method described in

Dusinberre (1961),

it can be derived that for the fire-exposed column

the criterion of stability is most restrictive along the line rn + 1, between

fire and concrete. It is given by the condition:

where the maximum value of the coefficient of heat transfer during

exposure to the standard fire

(hmax)

s approximately

3 x lo6

J/m2h"C

(147

Btu/ft2h"F).

5.1.4.5 Effect

of

Moisture

The effect of moisture

is

taken into account by assuming that in each

element, the moisture starts

to

evaporate when the temperature of the

element reaches

100°C

(212°F). During the period of evaporation, all

the heat supplied to an element is used for evaporation of the moisture,

until the element is dry. From a heat balance equation, the moisture

concentration in an element at the firekoncrete boundary, at the time


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,`

, ,` ,` , ,` ---



ASCE 78 92

m

0 7 5 ï b 0 0 0021979

024

m

176


T = ( j + AT is given by:

+ GA(cJE~E~[(T/273)4

-

(T<,n

+

273)4]

Similarly, the moisture concentration in an element inside the concrete

at the time

T = ( j + AT

is given by:

With the aid of equations (16) to

(23) ,

and the relevant material

properties given in Appendix

A,

the temperature distribution in the

column and on its surface can be calculated for any time

(T =

( j + A AT), if the temperature distribution at the time jA7 is known.

Starting from a temperature of 20°C (68"F), the temperature history of

the column can be calculated by repeated application of equations

(16)

to (23).

5.1.5

Temperature

of

Circular

Concrete

Columns

5.1.5.2 Divis ion

of

Cross-section in to Elementary Layers

To calculate the temperature in the column, the cross-sectional area

of the column is subdivided into a number of concentric layers ( M ) . AS

illustrated in Fig.

5.8,

the outer layer, which is exposed to fire, has a

thickness of 1/2(AE).This is also the thickness of the layer at the centre

of the column. The thickness of the other layers in the concrete is equal

to

AE.

For each layer, the temperature at the location

of

the points

pm

is taken as representative

of

that of the entire layer.


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



B

F I

A S C E 7 8

92 0759600

0023980 846


177

Figure 5.8-Arrangement of elementary layers in section of circular concrete

column.

5.1.5.2 Equations f or the F ire-Concrete Bounday

It is assumed that the entire surface of the column is exposed to the

heat of a fire whose temperature course follows that of the standard

fire described in ASTM-E119 (1985). This temperature course can be

approximately described by the following expression (Lie and Harmathy

1972):

Tj =

20

+ 750[1 - exp(-3.79553G)] + 170.41G (24)

where

t

is the time in hours and

Tj

is the fire temperature in

C

at time

f

=

jA t . (The symbols used are defined in the Nomenclature.)


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E 78 92

D 0 7 5 9 b 0 0

0023983 7 8 2 9

1

78


The temperature rise in each layer can be derived by making a heat

balance for them. For the elementary layer at the surface of the column,

the temperature at the time t =

( i + 1)Af

is given by the expression:

x

{sep, [(Ti

+

273)4-

( T i

+ 273)4]}

5.1.5.3 Equations

for

Inside the Concrete

perature at the time

t = ( j + 1)At

is given by

For the layers in the concrete, except for the center layer, the tem-

5.1.5.4

Equations

for

the Center

of

the Concrete

given by

For the center layer, the temperature at the time t = i + 1)At is

2A.t

TM l= TI +

[(PFJL + Pw~u>+Ll(At)z

x

(kL-1

+

k a,q)(TL-I -

T L )

(27)

5.1.5.5 Effect

of

Moisture

The effect of moisture in the concrete on the column temperatures

is taken into account by assuming that, in each layer, the moisture

starts to evaporate when the temperature reaches

100°C.

In the period

of

evaporation, all the heat supplied to a layer is used for evaporation

of the moisture until the layer is dry.

For the concrete layer at the boundary between fire and concrete,

the initial volume of moisture is given by

VI = T ( M - 5/4)(A()*+,

(28)

From a heat balance equation it can be derived that, per unit length of

the column, the volume

AVl,

evaporated in the time

At

from the con-



- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -




FIRE

RESISTANCE

179

Crete boundary layer, is

AV, =

M -

~ ) A & J E ~ E ,

( T j

+

273)4

- (T,

+ 273)4]

P W L

- (M - 3 / 2 ) ( y ) ( T i

i +

ki -

Ti)}

For the concrete layers inside the column, except for the layer at the

boundary between concrete and fire and the centre layer, the initial

volume of moisture is given by

Similarly, as for the boundary concrete layers, it can be derived that,

per unit length

of

the column, the volume

AV,,

evaporated in the

time

At from this layer is

For the concrete center layer, the, initial volume of moisture is

5.1.5.6

Stabi l i ty

Criterion


time level will not be amplified in the subsequent calculations, a stability

criterion has to be satisfied; for a selected value of

AC,

this limits the

maximum time step

At.

From a heat balance equation, it can be derived

that, per unit length of the column, the volume AVm, evaporated in

the time At from the center layer, is

Following the method described in Dusinberre

1961,

it can be derived

that for the fire-exposed column, the criterion of stability is most re-


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E

7 8

92 D 0759600

002L963 555

D

180


strictive along the boundary between fire and concrete. It is given by

the condition

where (pgJmin is the minimum value of the heat capacity of the concrete,

kmax,

the maximum value of its thermal conductivity and

h,,,

the max-

imum value of the coefficient of heat transfer to be expected during the

exposure to fire. For exposure to the standard fire, the maximum value

of the coefficient of heat transfer

h,,,

is approximately 675 W/(m2"C).

5.1.5.7 Procedure for Calculation of Column Temperatures


(24)-(34),

and the relevant material prop-

erties given in the Appendix, the temperature distribution in the column

and on its surface can be calculated for any time, T = (j +

l )At,

if the

temperature distribution at the time jAt is known. Starting from an

initial temperature of

20°C,

the temperature history of the column can

be calculated by repeated application of equations

(24)-(34).

5.1.6

Temperature of Composite Concrete Floor and

Roof

Slabs

To

calculate the temperature history of a concrete floor or roof slab,

a finite difference method, described in the following section (Lie 1978),

can be used.

5.1.6.1

Division

of Cross-Section int o Elementay Layers

In this method, the cross-section of the slab is divided into a number

of elementary layers as shown in Fig. 5.9. It is assumed that the slab

is

exposed to fire from below, and that it is covered at the top by an

asbestos pad according to the specifications in ASTM E119 (1985).

The thickness of the layers is

Ax

with the exception of the boundary

layers, which are

1/2Ax

thick. Each layer is represented by a point

P,,,.

The temperature in each elementary layer is assumed to be uniform

and equal to that of the representative point. In Fig. 5.9, a composite

slab is shown consisting of two laminar concrete slabs, the lower made

of concrete type n , and the upper of concrete type n,. The thickness

of the (concrete),, slab is

(M,

-

l)Ax,

that of the (concrete),, slab is

For each elementary layer, a heat transfer equation is written for the

time t = j A t , where j = O, 1,

2

. . . and

A t

is an appropriate time

increment. With the aid of these equations, the temperature of each

layer can be successively evaluated for any time t = (j +

1)At

if the

temperature at the time t = jbt is known.

(M, - MJAx.


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



ASCE 7 8 92 0759600

0023984

491


181

Figure 5.9-Arrangem ent

of

elementary layers in composite dab.

I

5.1.6.2

Equations for the Fire-Slab Boundary

The temperature course of the fire to which the slab is exposed is

assumed to follow the temperature-time relation specified in ASTM

E119 (1985). This curve can be described approximately by the following

expression (Lie and Harmathy 1972):

T j

= To +

1,350[1

-

exp( -3.795532/5)] + 3 0 6 . 7 4 ~

(35)

where t is the time in hours, Tj is the fire temperature in O F at the time

t

=

jA t ,

and

To

is the initial fire temperature. (The symbols used are

defined in the Nomenclature section of this chapter.)

The temperature at the time t

= ( j

+ 1)At of the boundary elementary



--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E 78

92 0759600

0023985

3 2 8

182


layer of the slab, represented by the point pi, can be given by:

5.1.6.3 Equations for the Inside of the Slab

For an elementary layer represented by a point P,, located inside the

slab but not at the boundary of two layers of different material, the

temperature at the time

t

=

( j + 1)At is given by:

1

’, + k’,+1

- (

)<n. -

T r2+l)

(37)

For a boundary elementary layer inside the slab, represented by the

point

P,,

and composed partly of concrete type n, and partly

of

concrete

type nz (Figure

l ) ,

the temperature is given by:

5.1.6.4 Equations for the Boundary Slab and Asb esto s Pud

According to the specifications in ASTM

E119,

temperatures

of

the

unexposed face of the slab should be measured under an asbestos pad

of prescribed dimensions and properties. In the calculation of these

temperatures, it is assumed that the heat flow through the slab and

asbestos pad is one-dimensional. The equation that determines the

temperature at the time

t = ( j + 1)At

of the unexposed face

of

the

concrete slab, i.e., the boundary slab and asbestos pad, is in this case:


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,`

, ,` ---



A S C E

7 8

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0759bOO 0 0 2 1 9 8 b

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m


183

5.1.6.5 Equ ations for the Inside

of

the Asbesto s Pad

(i + 1)At of an elementary layer represented by a point P, is:

For the inside of the asbestos pad, the temperature at the time t =

5.1.6.6

Equations for the Boundary Asbestos Pad and Air

At the boundary of the asbestos pad and air, heat is transferred from

the pad to the air by convection and radiation. For the heat transferred

by convection from the asbestos pad to the ambient air, the conventional

expression given in Spiers (1961)has been used in the derivation of the

heat transfer equations. It follows that the temperature of the asbestos

pad at the boundary pad and ambient air at the time t = ( j + 1)At is

given by:

where

pá

= density

of

asbestos

[ 7 ] : 31 .2

Ib ft-3

c',

= specific heat of asbestos [16]:

0 .25

Btu lb-*"F-'

k', =

thermal conductivity of asbestos [7]: 0.0316 Btu ft-'h-'"F-*

y = coefficient expressing convective heat transfer from pad to air [15]:

0.1823 Btu ft-3h-10F-1.25

5.1.6.7 Sta bility Criterion



criterion must be satisfied, which, for a selected value of Ax, limits the

maximum value of At. For fireexposed composite slabs made of con-

crete, this criterion is:

where

(pc),,,

=

the minimum value of the volumetric specific heat of concrete

met in practice: 13 Btu ftV3"FP1


--``,`,,`,,`̀ `,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E i 8

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0021987 1 T O

184

STRUCTURAL FIRE PROTECTION: MANUALOF PRACTICE

k,,,

h,,,

=

the maximum value of the thermal conductivity of concrete

met in practice: 1.6 Btu f t-*h-*"Fp1

= the maximum value of the coefficient of heat transfer attained

in

practice at fire-exposed concrete surfaces:

147

Btu ftp2h-'"F-'

5.1.6.8 Procedure

for

Calculation of Slab Temperatures

With the aid of equations (35)-(42), the temperatures, at any point

of the composite slab, can be calculated in successive steps for any time

t =

jAf.

Initially, at time t =

O,

the slab and asbestos pad are at room

temperature, here assumed to be 68°F. The first step is to calculate the

temperatures in the various layers of the slab and asbestos pad for the

time t = At. These are now used as initial temperatures for the cal-

culation of the temperatures at the time f =

2At.

This process is repeated

until the critical temperatures are exceeded. For the derivation of the

approximate formulas given in section

3.1.2.4

for the calculation of the

fire resistance of composite concrete slabs, the critical temperatures,

specified in ASTM E119 (1985), were selected. These are a temperature

rise of

250°F

at the unexposed face of the concrete slab, a temperature

at the location of the centre of the steel of 800°F for prestressing steel,

and a temperature of

1100°F

for reinforcing steel.

As can be seen in the equations, in order to calculate the temperatures

of the slab, it is necessary to know the thermal properties of the con-

cretes of which the slab is composed. Conservative values of these

properties, which were used in the derivation of the approximate for-

mulas, are given in Lie

(1978).

Equations for the thermal properties of

various types of concretes as a function of temperature are given in the

Appendix.

5.1.7

Temperature of Circular Concrete Filled Steel Columns

a finite difference method, described in Lie

(1984),

can be used.

To calculate the temperatures in circular concrete filled tubular steel,

5.1.7.1 Division

of

Cross-section into Elementay Layers

In this method, the crosssectional area of the column is subdivided

into a number of concentric layers as illustrated in Fig.

5.10.

Along any

radius a point

P,

representing the temperature of a layer ( m ) , s located

at a distance

(m -

1)Ae from the boundary. There are

M,

layers in the

steel and

((M,

-

M,)/2)

+

1

layers in the concrete.

M,

and

M,

are

selected in such a way that

M,

-

M,

is an even number. The outer

layer of steel, which is exposed to fire, has a thickness of

1/2(Ae).

The

layer of steel at the boundary between steel and concrete is also

1/2(Ae)

thick. The thickness of all other layers in the steel is AE. This is also

the thickness of the layer of concrete at the boundary between steel

and concrete, and that at the center of the column. The thickness of

the other layers in the concrete is equal to

2(A5).


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E

78 92 0759600 0021988 037


185

5.1.7.2

Equations

for

the

Fire-Steel

Boundary

It is assumed that the entire surface of the column is exposed to the

heat of a fire whose temperature course follows that of the standard

described approximately by the following expression:

I

fire described in ASTM E119 (1985). This temperature course can be

ï f

= 20 + 750[1

-

exp(-3.79553 m)] 1 7 0 . 4 1 m

(43)

where T is the time in hours, ï'f is the fire temperature in C at the time

T

= j h . (The symbols used are defined in the Nomenclature.)

The temperature rise in each layer can be derived by making a heat

balance for it. For an elementary layer at the surface of the column,


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E 7 8 92 0759600 O 0 2 3 9 8 9 T 7 3

186


OF

PRACTICE

the temperature at a time

T = (i +

AT

is

given by the expression:

2(Mz -

1)

M2

- 5 / 4 ) ( P S C S W

A t

{+' =

T{ +

(UE,E/

[ (T j

+

273)4

-

(T i

+

2 7 3 ) 4 ] }

AT

5.1.7.3 E quation fo r the Inside

of

the Steel

perature rise at time

T = (j

+ AT, is given by:

For the layers in the steel, except for the boundary layers, the tem-

I(M2

-

m

+ 1/21 x

(kL1-1

+ k M ? , 1 - 1 - Tin)

- ( M z -

m

-

W k L I

+

k',,l+i)(T ,l - T' f l + 1)1

5.1.7.4 Equation

f o r

the Bounday Steel-Concrete

temperature rise at time

T =

i + AT is:

TI ']

=

TI

For the layer at the boundary between the steel and concrete, the

M l M I

5.1.7.5 Equations

for

the Inside

of

the Concrete

For the layers in the concrete, except for the layer at the boundary

between the concrete and steel and the center layer, the temperature

rise at time

T

= (j +

A AT, is given by:


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



ASCE

7 8 92

0 7 5 9 b 0 0 O023990

795

I

5.1.7.7 Effect

of

Moisture

The effect of moisture in the concrete is taken into account by as-

suming that, in each layer, the moisture starts to evaporate when the

temperature reaches

100°C.

In the period of evaporation, all the heat

supplied to a layer is used for evaporation of the moisture until the

layer is dry. From a heat balance equation, it can be derived that, per

unit length of the column, the volume of moisture AV,,, evaporated

in time A T from the concrete layer at the boundary between steel and

concrete, is


187

For the center concrete layer, the temperature rise at time T

=

( j

+ AT, is given by:

5.1.7.6 Stability Criterion



criterion has to be satisfied; for a selected value of

At,

this limits the

maximum time step. For the column exposed to fire, the criterion of

stability is most restrictive along the boundary between fire and steel.

It is given by the condition

where ( p s ~ s ) m i ns the minimum value of the heat capacity of the steel,

k, the maximum value of its thermal conductivity and hmaXthe max-

imum value of the coefficient of heat transfer to be expected during the

exposure to fire. Approximate values for these quantities are:

(pscJmin

=

3.6

x

lo6

J

m-3KK1

(k,),,, =

47 W

m-'K-'

hmax

= 4s(T,J3 =

675

W m-2K-' for T, = 1500 K


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E 78

92 W O757600 O023773

b 2 3

188


The total volume of moisture in this layer is

Similarly, it can be derived that the volume of moisture

AVm,

evap-

orated in the time

AT

from a layer inside the concrete, i.e., not located

at the boundaries, is:

The total volume of moisture in an inside concrete layer is:

For the center, the volume of moisture AVM2 evaporated from the

concrete in the time AT is:

The total volume of moisture in the center layer is:

With the aid of equations (43)-(55), and the relevant material prop-

erties given in the Appendix, the temperature distribution in the column

and on its surface can be calculated for any time, 7 = ( j + AT, if the

temperature distribution at the time jA7 is known. Starting from an

initial temperature of

20°C,

the temperature history

of

the column can

be calculated by repeated applications of equations (43)-(55).

5.1.8

Temperatures of Semi-infinite Wood

Slabs

After about 15-20 min in the standard E 119 test, a quasi-steady-

state charring rate is developed. Assuming that there is a constant

temperature at the base of the transient char layer and a constant rate

of charring, an equation has been developed to describe the temperature

distribution in the uncharred wood below the char-wood interface

(Schaffer

1965).

The equation is:


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E

7 8

9 2

W

0 7 5 9 b 0 0 O023992 5bA

W

CALCULATION OF TEMPERATUR E AND FIRE RESISTANCE 189

where

T =

temperature at location

x

T,,

=

char-wood interface temperature of 288°C (550°F)

To = initial wood temperature

zi

x

olq = thermal diffusivity

=

assumed constant rate of charring

= depth into wood from char-wood interface

5.1.8.2 Charting

Rate

As discussed in Section 2.2.3.1, it is generally assumed that the con-

stant transverse-to-grain char rate is 0.6 min/mm for all wood, when

subjected to the standard fire exposure. There are differences among

species associated with their density, chemical composition, and perme-

ability.

The British Code of Practice fur the Structural Use of Timber (Malhotra

1982) divides species into three groups. The assigned charring rates

(m dm in ) are:

1. Western red cedar 0.83

2. Oak utile, keruing (gurjun), teak, greenheart 0.50

3.

All other listed structural species 0.66

Charring rates as a function of density and moisture content for white

oak, Douglas fir and southern pine are reported in Schaffer (1967). The

regression equations for B (min per mm, the reciprocal of charring rate)

were:

B = 0.79 [(28.726 + 0.578

M)

p + 4.1871 for Douglas fir

B =

0.79 [(20.036

+

0.403

M) p +

7.5191 for white oak

(57)

(59)

B = 0.79 [(5.832 + 0.120 M) p

+

12.8621 for southern pine

(58)

where

M

= percent moisture content, and

p =

dry specific gravity

(White 1988; White and Nordheim 1992). The equations are:

A more generic equation for all species also has been developed

t =

rn

x, 1.23

and

rn

=

-.147 + .O00564 p + .O121 u + .532fc

(61)


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E 78 92 O759600 0021993 4 T 4

5.1.9

Temperature of Finite Wood Members

Assumption of a constant charring rate is reasonable when the mem-

ber or panel product is thick enough to be treated as a semi-infinite

slab. For smaller dimensions, the charring rate increases once the tem-

perature has risen above the initial temperature at the center

of

the

member or at the unexposed surface of the panel. Theoretical models

allow calculation of the charring rate for geometries other than a semi-

infinite slab and for nonstandard fire exposures. Most theoretical models

for wood charring not only define the charring rate but provide results

for the temperature gradient. Considerable efforts have gone into de-

veloping theoretical models for wood charring. Unfortunately, no com-

pletely satisfactory model has yet been developed. The problems as-

sociated with the theoretical analysis of the burning

of

wood, including

structural effects and internal heat transfer, kinetics of the pyrolysis

reactions, net

of

reactions of the pyrolysis reactions, and variations of

thermal properties during pyrolysis are reviewed in Roberts (1971). The

major problems are the formulation of a mathematical model for the

complex chemical and physical processes and the acquisition of reliable

data for use in the model.

The Factory Mutual model (SPYVAP) includes terms for internal con-

vection of volatiles and thermal properties as functions

of

temperature

and density. This model has been further revised to include moisture

absorption (Atreya

1983).

The energy conservation equation in this

model is:

190


where

f = time, min

x , = char depth from original fire-exposed surface, mm

p

= density from oven dry weight and volume, kg/m3

u = moisture content, pct.

f, = char contraction factor, dimensionless

Equation (61) is based on data for

x ,

of 10 to 40 mm. The char contraction

factor is the fractional shrinkage of the wood layer as it is degraded to

char. It

is

related to the lignin content and anatomy of the wood. Some

values for f c are (White 1988; White and Nordheim 1992).

Engelmann spruce

Western red cedar

Southern Pine

Redwood

Hard maple

Yellow poplar

Red Oak

Basswood

0.84

0.78

0.59

0.86

0.59

0.67

0.70

0.54



- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` `

, ` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E

7 8

92

0 7 5 9 b 0 0 0021994

330

C, = specific heat (calig OC)

K =

thermal conductivity (calicm OCs)

T =

temperature

(K)

t = time

(s)

X = distance (cm)

p =

density (gicm3)

M, = outward mass

flux

of volatile gases (gicm’s)

H = thermal-sensible specific enthalpy (cal@

Q =

endothermic heat of decomposition of wood for a unit mass of

i,

j

= parameters to simulate cracking, between O and

1;

subscripts:

x

=

ambient

w

=

virgin wood

c

=

char

q = volatile gases

a =

unpyrolyzed active material

rn

= moisture

~

f

=

final value

s = solid wood

In equation 62, the material has been broken up into its components

(wood, water, and char). The term on the left side of the equal sign

represents the energy stored at a given location as indicated by the

increase or decrease of the temperature with time at that location. The

first term on the right side of the equal sign represents the thermal

conduction of energy away from or into the given location. The second

term on the right represents the energy transferred in or out of a location

as a result of the temperature gradient. The parameter

j

eliminates the

convection term if the pyrolysis gases are escaping through cracks or

fissures in the wood. The third term on the right side represents the

volatiles generated (calig at

T,)

I

CALCULATION

OF

TEMPERATURE AND

FIRE

RESISTANCE

191

+ i 1 - j -

M -

( ;

. d X


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



192

STRUCTURAL FIRE PROTECTION: MANUALOF PRACTICE

energy absorbed (endothermic reaction) or energy given off (exothermic

reaction) as the wood undergoes pyrolysis or thermal degradation. The

last term represents the heat absorbed with vaporization of the water.

The conservation of mass equation is:

It ensures that the mass of gases equals the mass loss due to thermal

degradation of the wood and vaporization of the moisture. The decom-

position kinetics equation for wood is usually the Arrhenius equation:

where

A =

frequency factors (l/s)

E = activation energy (kcalímole), and

R

=

gas constant.

The model in Atreya (1983) also used an Arhenius equation as a mois-

ture desorption kinetics equation for vaporization of the water in the

wood, which is

a P m

-

-

Amp,,,exp ( -

E,/RT)

at

Moisture desorption and surface recession were not considered until

recently. There may be not only moisture desorption but also an in-

crease in moisture content behind the char front caused by moisture

movement away from the surface (White and Schaffer 1981). The CMA

model (White and Schaffer 1978) developed for NASA provides good

results for oven-dry wood, because it includes surface recession but

does not take into account moisture desorption. Fredlund 1988 describes

a theoretical model for charring wood, which includes mass transfer as

well as heat transfer. Total pressure is assumed to be the driving force

in the mass transfer of the pyrolysis gases and water vapor.

Surface recession may be due to char shrinkage or char oxidation. In

his model Parker (1986) takes char shrinkage parallel and normal to the

surface into account. In Fredlund (1988), it is assumed that the surface

recession is due to char oxidation. Dimensional, phenomenological,

approximate analytical and exact numerical solutions for wood chamng

have been presented in Kanury (1975). Other models are described in

Havens (1969), Knudson and Schniewind (1975), Kansa et al. (1977),

Hadvig and Paulsen (1976), and Tinney (1965).


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,`

, , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



ASCE 7 8 92 O ï S î b O O

0023996

L O 3


193

5.2 FIRE RESISTANCE OF STRUCTURAL MEMBERS

5.2.1

Fire Resistance of Steel Members

For steel members, often a critical steel temperature can be indicated

at which the steel has lost so much strength that it can no longer support

the load. In these cases, the calculation of the fire resistance of the steel

members can be reduced to the calculation of the temperature

of

the

steel. North American standards assume that the critical temperature

condition is reached when the average temperature in a steel section

has reached 538°C (1000°F). In the derivation of the formulas for the

calculation of the fire resistance of protected and unprotected steel in

Chapter

3,

sections 3.1.1.1-3.1.1.6, this temperature was also regarded

as the failure temperature of the steel members.

Using more precise methods for the calculation of fire resistance, for

example, by taking into account the influence of load or temperature

gradients in the steel, is possible. However, no validated and generally

accepted method exists at present. The validity of the approximate

formulas for steel members given in Chapter 3, however, has been

thoroughly examined experimentally and theoretically by research and

testing organizations and by the steel industry. They are generally used

in North America for the calculation of the fire resistance of steel mem-

bers, and may be regarded as methods that produce, in the specified

range of their validity, conservative values for the fire resistance of

these members.

5.2.2

Fire Resistance of Concrete Members

For concrete members, their fire resistance can usually not be deter-

mined by calculating a single critical temperature as in the case of steel.

In general, the temperature in a cross-section of a concrete member is

not as uniform during fire exposure as that in a steel section.

A s

a

consequence, the thermal and mechanical properties of the concrete

vary not only with time but also with the location in the section. This

non-uniformity and, in addition, the wide range in which the properties

of concrete can vary at elevated temperatures are complicating factors

in the calculation of fire resistance of concrete members. For a number

of members, however, methods have been developed to calculate their

fire resistance.

5.2.2.1 Fire Re sistan ce of Concrete Floor and Roof Slab s

In some cases, namely if the members are supported by reinforcing

or prestressing steel, such as many concrete floor and roof slabs, it is

possible to derive their fire resistance by calculating the steel temper-

ature. According to ASTM E119 (1985) the critical steel temperature is

800°F

(427°C) for prestressing steel and

1100°F

(593°C) for reinforcing

steel. In addition, the slab is regarded to have failed if the temperature



--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E 78 92 0 7 5 9 b 0 0

0023997

O g T

.

194

STRUCTUR AL FIRE PRO TECTION: MANUAL

OF

PRACTICE

. . . .

.

.

.

rise at the unexposed face of the slab exceeds 250°F (139°C). These

temperature criteria were also used in the derivation of the formulas

for the calculation of the fire resistance of the slabs given in Chapter

3, Sections 3.1.2.2-3.1.2.5. The temperature of the slabs was calculated

using the method described in Section

5 .1 .6 .

5.2.2.2 Fire Resistance of Reinforced Concrete

Columns

The fire resistance of reinforced concrete columns can be calculated

if the temperatures of the column are known. These temperatures can

be derived using the methods described in Sections 5.1.3 and

5.1.4.

Here, a method will be described for the calculation of the fire resis-

tance of square reinforced concrete columns (Lie et al. 1984). Similar

methods can be used for the calcuIation of the fire resistance of rectan-

gular and circular reinforced concrete columns.

To simplify the calculation of the deformations and stresses in the

column, the triangular network shown in Fig.

5.7,

which was used for

the calculation of the temperatures of the column, is transformed into

a square network. In Fig. 5.11, a quarter section of this network, con-

sisting of square elements arranged parallel to the

x -

and z-axis of the

section, are shown. The width of each element of this network is A. /

fl. he temperatures, deformations and stresses of each element are

represented by those of the center for the element. The temperature at

the center of each element is obtained by averaging the temperatures

of the elements in the triangular network according to the relation:

+

X

Figure 5.11 -Square network of elements

in

a quarter section of column.



--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,

` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E 78 92 0759bOO 002 3998 T8b

CALCULATIONOF

TEMPERATURE

AND FIRE RESISTANCE

195

where the subscripts 'square' and 'triangular' refer to the elements of

the square and triangular network.

During exposure to fire, the strength of the column decreases with

the duration of exposure. The strength of the column can be calculated

by a method based on load-deflection analysis which, in turn, is based

on a stress-strain analysis of cross-sections (Allen and Lie

1974).

In this

method, the columns, which are fixed at the ends during the tests, are

idealized as pin-ended columns of reduced length KL (Fig. 5.12). The

load on the test columns is intended to be concentric. To represent

imperfections in the columns, an initial deflection yo = 2.5 mm (0.1 in.)

is assumed.

The curvature of the column is assumed to vary from zero at pin-

end to mid-height according to a straight line relation, as illustrated in

Fig. 5.12. For such a relation, the deflection at mid-height ( y ) , in terms

of the curvature

x)of

the column at this height, can be given by:

t

Figure 5.12-Load-deflection analysis.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -





ASCE 7 8

9 2

m

0 7 5 î b 0 0 O022000 2 3 2

m

CALCULATIONOF TEMPERATURE AND FIRE RESISTANCE

197

The stresses in the elements of the network can be calculated using

stress-strain relations derived from data provided by Ingberg and Sale

(1926), and Witteveen, Twilt and Bylaard (1977). These relations include

the effect of creep at elevated temperatures and were obtained at heating

rates approximately the same as those that occur in a fire in actual

practice. The relations have been generalized for other structural steels

by assuming that, for a given temperature, the curves are the same for

all steels, but the stress below which the stress-strain relation is linear,

is proportional to the yield strength of the steel. This is illustrated in

Fig. 5.13, where the stress-strain curves at 20°C (68°F) are shown for a

steel with a yield strength of 250 MPa (36 ksi) and for the reinforcing

steel, which has a yield strength of 443 MPa (64.3 ksi). In Fig. 5.14 the

stress-strain curves of the reinforcing steel are shown for various tem-

peratures. Recent studies show that the curves produce conservative

results. They can be used, however, for cases where the role of the

steel in determining the fire resistance of the member is secondary, for

example, for reinforcing steel or for concrete filled steel.

If

the steel

plays a primary role in determining the fire resistance, as is the case

in, for example, protected structural steel members, the stress-strain

relations are too conservative. For such cases, less conservative stress-

strain relations, which were developed recently, are given in Section

A.1.2.2 in the Appendix. The equations that describe the relations,

5 0 0

400

m

a

E 300

m

m

g

200

+

m

100

I

I I I

I I

I

l

I l

O

O O . 0 0 4 o . O08

0 . 0 1 2 0 . 0 1 6

o.

0 2 0

S T R A I N ,

E

Figure 5.13-Stress-strain curves for tw o steels at

20°C.


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



198


I l 1

I

T 20°C

T = 200°C

-

T = 400°C

-

T = 600°C

-

T

=

800°C

600

500

m 400

E

* 300

a

vl

w

w

I-

* 200

100

O

O o .

o1 0 . 0 2

O .

0 3 O.

0 4 O . 0 5

S T R A I N , E

Figure 5.24-Stre ss-strain curves for the reinforcing sfeel at various

temperatures (yield strength

= 443 MPa) .

shown

in

Fig. 5.14, between the stress in the steel

( ï J ,

he strain (EJ

and the temperature of the steel (T) are as follows:

for

f

T,O

.001)

f y

= 0.001 E s

where

Ep =

4

x

10-6fyo

and

f(T,O.OOl)

=

(50

-

0.04T)

X [1 - exp((-30 + 0 . 0 3 T ) a ) J

x 6.9


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E

78 ci2

0 7 5 î b 0 0

O022002

005

where

( E ~ ) ~free strain due to thermal expansion of the concrete,

E

2

p

= radius of curvature.

The stresses in the elements are calculated using stress-strain relations

based on the work of Ritter (1899) and Hognestad (1951). These relations

have been slightly modified

to

take into account the creep of concrete

at elevated temperatures. The modifications are based on results of

work by Schneider and Haksever (1976) and consist of a movement of

the maxima in the stress-strain curves to higher strains with higher

temperatures. These curves are shown in Fig. 5.15 for a concrete with

a cylinder strength

of 35

MPa (5ksi). The equations that describe these

curves are as follows:

for

= axial strain of the column,

= horizontal distance of the center of the element to the vertical

I

plane through the x-axis of the column section,

Ec

Emax

CALCULATION

OF


199

f(T/o.001)

E p

+

f(T/(E,

- E p +

0.001))

-

f(T,0.001)

(73)

0.001

Y =

With the aid of equations (56)-(61), the stresses at mid-height in the

steel can be calculated for any value of the axial strain (E), curvature

(Up)

and temperature ( r ) . From these stresses, the load that the steel

carries and the contribution of the steel to the moments can be derived.

Equations for concrete in the column:

for elements at the right of the x-axis (Fig. 5.11) can be given by:

In the same way as for steel, the strain in the concrete causing stress

and for elements at the left of the x-axis by:



- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E 78 92

W 0759600

0022003 T 4 L 9

200


OF

PRACTICE

I I

1

0

n

E

V

V)

w

E

I-

V

30

20

10

n

O

o. o 1 o. 0 2

O .

0 3

O .

0 4 O .

0 5

S T R A I N , E

Figure 5.15-Stress-strain curves fo r concrete ut various temperatures

(compressive strength

=

35

M Pa) .

for

f c = f: [1 - (

E'3F,:92]

where

f c

= fL if T

<

450°C

E =

0.0025

+ (6.OT

+ 0.04T2)

x

(80)

In these equations

fc

f ;

=

compressive strength of concrete at temperature

T ,

=

cylinder strength

of

concrete at temperature T,


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



CALCULATION OF TEMPERA TURE AND FIRE RESISTANCE 201

= cylinder strength of concrete at

20°C

(68"F),

=

strain of the concrete,

=

strain corresponding to maximum stress.

E,

With the aid of equations (74)-(80), the stresses in each of the concrete

elements at midsection can be calculated for any value of the axial strain

(E)

and curvature

(Up).

From these stresses, the load that the concrete

carries and the contribution of the concrete to the moments can be

derived.


of

Concrete-Filled Tubular Steel Columns

The fire resistance of concrete filled tubular steel columns can be

calculated if the temperatures in the concrete and the steel are known.

These temperatures can be derived using the methods described in

Section

5.1.7.

Here, a method will be described for the calculation of the fire resis-

tance of circular concrete filled steel columns (Lie 1984).A sirrular method

can be used for the calculation of the fire resistance of rectangular

concrete filled steel columns.

5.2.3.1 Divis ion

of

cross-section into annular elements

To calculate the fire resistance of the circular column, the cross sec-

tional area of the column is subdivided into a number of annular ele-

ments. In Fig. 5.16, the arrangement of the elements is shown in a

quarter section of the column. The arrangement of elements in the three

other quarter sections is identical to this. In radial direction, the sub-

division is the same as that shown in Fig. 5.10, where the cross-section

is divided into concentric layers. In tangential direction, each quarter

layer is divided into N, lements. The temperature, representative of

an element, is assumed to be that at the center of the element. It is

obtained by taking the average of the temperatures at the tangential

boundaries of each element, previously calculated with the aid of equa-

tions

(43)-(55).

in the steel, the representative temperature

is

Thus for an element

Ti, + Ti,,,

layer

and for an element

in the concrete

\

L

/ layer


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - `

- ` , ,

` , ,

` ,

` , ,

` - - -



202

A S C E

7 8

92

0759600

O022005

814


B O U N D A R Y

F I R E - S T E E L

X - A X I S

/

B O U N D A R Y L

Z - A X I S

M2 - 2, N

1

S T E E L

- C O N C

R E T E

Figure 5.16-Arrangement of elements in quarter section of concrete-filled

tubular steel column.

where the subscripts annular and layer refer to the annular elements

shown in Fig.

5.16

and the element layers shown in Fig.

5.10.

Similarly, it is assumed that the stresses and deformations at the

centre of an element are representative of the whole element.

5.2.3.2 Calculation of Strength During Fire

During exposure to fire, the strength of the column decreases with

the duration of exposure. The strength

of

the column can be calculated

by a method based on a load deflection analysis described in Allen and

Lie (1974). In this method, the columns, which are fixed at the ends

during the tests, are idealized as pin-ended columns of length

K L

(Fig.

5.12). The load on the column

is

intended to be concentric. Due to

imperfections of the columns and the loading device, a small initial

deflection yo

=

0.1 in. (2.5 mm), is assumed.


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E 78 92 0759600 O022006 750 E


203

The curvature of the column is assumed to vary from pin-end to mid-

height according to a straight line relation, as illustrated in Fig. 5.12.

For such a relation, the deflection at mid-height y, in terms of the

curvature

x

of the column at this height, can be given by

For any given curvature, and thus for any given deflection at mid-

height, the axial strain is varied until the internal moment at the mid-

section is in equilibrium with the applied moment given by the product

of

load and total deflection.

In this way, a load deflection curve can be calculated for specific

times during the exposure to fire. From these curves, the strength of

the column, i.e., the maximum load that the column can carry, can be

determined for each time. In the calculation of column strength, the

following assumptions were made:

(1)

The properties of the concrete and steel are those described by equations

(70)-(73) for the steel, equations (76)-(80) for the concrete, and

by

the

relevant equations given in the Appendix.

As

mentioned earlier, the

stress-strain relations for the steel given by the equations (70)-(73) are

conservative. Instead of these equations, the recently developed equa-

tions given in the Appendix (Version

2),

which are less conservative,

can be used for the stress-strain relations of structural steel.

(2)

Concrete has no tensile strength.

(3) Plane sections remain plane.

Based on these assumptions, the change of column strength during

the exposure to fire can be calculated using the network of annular

elements shown in Fig. 5.16. The equations to calculate the strength of

the column during exposure to fire are described below.

5.2.3.3

Equations for the Steel in the Column

The strain in an element

of

the steel can be given as the sum of the

thermal expansion

of

the steel the axial strain of the column e

and the strain due to bending of the column zJp, where z , is the

horizontal distance of the steel element to the vertical plane through

the x-axis

of

the column section, and p is the radius of curvature. For

the steel at the right of the x-axis the strain ( E , ) ~ is given by

(84)

2

(&,)R

=

+

E

+

P

For the steel elements at the left of the x-axis the strain ( E ~ ) ~s given


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E 78 92 0759600 0022007 b î 7

204


OF

PRACTICE


(84)

and (85) and the stress-strain relations

given by equations (70)-(73), the stresses at mid-section in the steel

can be calculated for any value of the axial strain

E

and curvature

Up.

From these stresses, the load the steel carries and the contribution of

the steel to the moments can be derived.

5.2.3.4 Equations for the Concrete in the Column

(Fig. 5.16) can be given by

The strain in the concrete for the elements at the right of the x-axis

and for the elements at the left of the x-axis by

where

(ET)c = the thermal expansion of the concrete

E

z

vertical plane through the x-axis of the column section

p


(84)-(87)

and the stress-strain relations for

the steel (equations (70)-(72)) and those for concrete (equations (76)-

@ O ) ) , the stresses in each of the steel and concrete elements at mid-

section can be calculated for any value of the axial strain

E

and curvature

Up.

From these stresses, the load that the column carries and the

contribution of each element to the internal moment at midsection can

be derived.

=

the axial strain of the column

=

the horizontal distance from the center of the element to the

=

the radius of curvature.

5.2.4

Fire Resistance

of

Wood

Member

When a structural member of timber is exposed to fire, the material

will generally be ignited. During the combustion of the material, a char

layer is formed at the exposed surface.

As

the chamng proceeds, a moment will be reached when the mem-

ber can no longer support its load and it will collapse. To calculate the

fire resistance of the member, the time is calculated for which the


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -

` , ,` , ,` ,` , ,` ---



A S C E

78

92

m

0759b00 O022008 523

m

I where

CALCULATION

OF


205

member is capable of supporting its load

[40-441.

This time depends

on:

1. the rate of charring,

2.

the temperature distribution in the uncharred

part

of

the member, and

3. the strength and deformation properties of the material as a function

of temperature.

This section deals with calculating the fire endurance time for a given

member or assembly in the standard tests. In the future, fire resistance

evaluations will include natural fires and probabilistic-based metho-

dologies that will permit an overall fire safety evaluation. The current

state of the art in the development of such methodologies for fire

exposed timber structures have been reviewed

in

Pettersson and Jonsson

(1988).

The rate of charring of wood depends on various factors (Schaffer

1967). The temperature distribution in the uncharred part of the member

depends on the rate of charring, on the temperature of the burning

material at the surface of the uncharred wood, and its thermal prop-

erties. The thermal properties of wood normally depends on the type

of wood and its temperature (Odeen 1970, Knudson and Schniewind

1975). This also applies to the strength and deformation properties of

wood (Rogowski 1970, Schaffer 1977). Calculation of fire resistance of

timber structural members based on temperature distribution in the

member, material strength, and deformation is possible in principle

(Knudson and Schniewind 1975). However, lack of knowledge of the

various processes that take place during exposure to fire, such as the

combustion processes under the char layer and outside the member,

the heat transfer from the fire to the member, and the movement of

moisture in the material, as well as inadequate knowledge of material

properties at elevated temperature, makes it difficult at present to de-

termin the fire resistance accurately in this way.

There are basically two approaches to evaluating the load carrying

capacity: to evaluate the remaining section either as a single homoge-

neous material or as a composite

of

layers with different properties.

The most common approach in accounting for the

loss

in strength and

stiffness of the entire uncharred region are fractions (Y of their room

temperature values. For bending rupture of a beam, an equation of this

type would be

M

=

applied moment (design load),

S

=

section modulus of uncharred member,


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - -

-



A S C E

7 8 92

0759600 0022009 4 b T

206

STRUCTURAL

FIRE


u.

=

modulus of rupture at room temperature

t

=

time

This approach was used in the glued-laminated model of Section 5.2.4.1

and the light-frame floor model of Section 5.2.4.3. The second approach

to evaluating the fire endurance of a wood member is to assume that

the uncharred region consists of layers. In such a model, the com-

pressive and tensile strengths and modulus of elasticity of each layer

are assumed to be fractions of the room temperatures values. In another

type of model with layers, an equivalent zero-strength layer is calcu-

lated. This composite model approach was used in the glued-laminated

model of Section 5.2.4.1. The grade of the lumber is generally assumed

not to be a factor in the fire resistance of a wood member loaded to

full allowable stresses as in the

standard fire resistance test. When

individual sawn timbers were loaded in bending to the same proportion

of characteristic strength and directly exposed to fire, there were no

significant differences in the times to failure between the high grade

and low grade material (Noren 1988). The fire resistance of joints is a

critical item that is sometimes overlooked. As noted in Section 3.1.3.2,

CABO Report No. NER-250 requires that connectors and fasteners re-

lating to support of the large timber members be protected for equiv-

alent fire-resistive construction. Diagrams are given for typical protec-

tion methods. An extensive literature survey of work done in West

Germany, Denmark, Sweden, and Norway on the fire resistance of

joint details

in

loadbearing timber construction

is

given in Carling (1989).

Recent tests have shown that 14.5 mm thick gypsum board is capable

of providing 60 minutes fire resistance ratings

to

nailed plywood or

steel gusset connections for glulam members (Lim and King 1990, King

and Glowinski 1988).

5.2.4.1 Fire Resistance of Glued-Laminated Timber

The prediction of fire resistance of timber structural members can be

considerably simplified and reasonably accurate results obtained if a

semi-empirical method (Imaizumi 1962, Odeen 1970, Lie 1977) is used

for determining the fire resistance. In this method, the following as-

sumptions are made.

(a) The member

is

exposed to a standard fire, in this case one meeting the

definition in

ASTM E119

(White and Schaffer

1978).

(b) The fire resistance of the member is the time for which the member is

capable of supporting its load. This load

is a

fraction k of the ultimate

load.

(c) Due to temperature rise, the compressive strength and the modulus

of

elasticity of the uncharred part of the member is reduced. The effect

of this reduction can be taken into account by using, in the calculation,

reduced values of the compressive strength and the modulus

of

elas-

ticity.

(It

is assumed that these values are a fraction a of their values

before exposure to fire.)



--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E 78

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0 7 5 9 b 0 0 0022010

181


207

(d) The rate

of

penetration

of

the charring can be given approximately by

a constant average value

ß.

Beams

From these assumptions, it can be derived (Lie 1977) that the depth

d at which a beam fails (critical depth) is determined, for a beam that

is heated on all sides, by the relation

= (d/D)*

K BID

-

(Y d / D -

(1

- B / D )

where B and D are the breadth (smaller side) and depth (larger side)

of the beam before the fire. (The symbols used are defined in the

Nomenclature section of this chapter.)

When the critical depth of the beam and the rate of penetration of

the charring are known, the time tb4to reach this critical depth is given

by

In the derivation of equation

(88) ,

it is assumed that the beam is

exposed to heating on all sides. In practice, the top of the beam is often

protected by a floor or roof construction,

so

that only three sides of

the beam are exposed to heating. In a manner similar to that used in

the case of heating on four sides, it can be derived, for this case, that

the critical depth d of the beam, i.e., the depth of the unburnt part of

the beam at the time of failure, is determined by

= (d/D)’

BID

-

CL BID

- 2

(1

-

d / D )

and its fire resistance tb,, which

is

equal to the time to reach this critical

depth, is given by

t

=

( D -

d ) / ß

(91)

For slender beams, the fire endurance of the member may be a function

of lateral buckling of the member. Procedures have been developed to

calculate the times of failure due to lateral buckling (Reyer and Schlich

1988, Fredlund 1979).

Columns

depth and fire resistance of columns.

Relations, similar to those for beams, can be derived for the critical


--``,`,,`,,`̀ `,,````,`,,,̀ `,`,,-`-`,,̀ ,,`,`,,`---



208


OF

PRACTICE

According to standard structural design formulas for columns, the

relation for short columns between the load p , stress u, and area

A

of

the cross section is given by

p

=

UA

It is assumed that, during the exposure to fire, a load p , is applied.

According to equation

(92),

the relation between this load, the stress

in the column, and the dimensions of the column is given by

p ,

= crBD

where B and D are the breadth (smaller side) and depth (larger side)

of the column before the fire.

During the fire, the size of the uncharred part of the column de-

creases. If this part is sufficiently short, failure occurs when the stress

in the column reaches a value equal to the compressive strength of the

uncharred part of the column. Thus, at the time of failure:

where u, is the compressive strength of the wood before exposure to

the fire, and

b

and d are the breadth and depth of the uncharred part

of the column at failure. From equations

(93)

and

(94),

it follows that

the critical breadth b is determined by the relation

uBD

= aucbd (95)

Since B

-

b

=

D

- d ,

and

duc =

K, equation

(95)

for the critical

breadth can also be written as

b

-

-

BID

-

OL blB

-

(1

-

DIB)

B

For long columns, which fail by buckling, the critical breadth can be

derived using Euler’s formula

p ’ = n2EA/(Wr)’

where p ’ is the buckling load,

E

is the modulus of elasticity of the wood

before exposure

to

fire,

L

is the effective length

of

the column and

Y

is

the radius

of

gyration.

Assuming that a load

p a = kp’

is applied and that the radius of

gyration

r

=

B / m ,

he relation between load, column dimensions,

and material properties at the start of exposure to fire is


--``,`,,`,,`̀ `,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



ASCE 78 92 0 7 5 î b 0 0

O022032 T 5 4 W


FIRE

RESISTANCE

209

p a

=

kr2EDB3/12L2

(98)

At the time of failure, this relation becomes

p a = n2aEdb3/12L2 (99)

From equations

(96)

and (lOO), it follows that, for long columns, the

critical breadth is determined by

K

DIB

-

(Y b/B - (1 - V/B)

Equations (85) and (89) show that the critical breadth is determined

by an expression dependent on

n,

where

n

is an exponent having a

value of n = 1 for short columns and

n

= 3 for long columns. It is

plausible that the critical breadth of intermediate columns is given by

a similar expression where 1

<

n

< 3 .

Thus, the general form of the

equation that determines the critical breadth

of

a column is

K

D /B

(Y b/B

-

(1

- V/B)

-

where 1I 3 .

of columns heated on four sides is given by

In the same way as for the fire resistance of beams, the fire resistance

In the derivation of equation

(loi),

it is assumed that the column is

exposed to heating on all sides. In practice, one side of the column

may be protected

by,

for example, a wall, so that only three sides of

the column are exposed to heating. For a column of which one of the

smaller sides is protected, it can be derived in a manner, similar to that

used in the case of exposure on four sides, such that the critical breadth

b of the column, i.e., the breadth of the unburnt part of the column at

the time of failure, is determined by

- DIB ($)

OL DIB

- 2

(1 - b/B)

and its fire resistance

t c3 ,

which is equal to the time to reach this critical

breadth, is given by

(104)

c3 = ( B

- b)/ß


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E

78 32 0753b00

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o


With the aid of equations (88)-(104), the fire resistance of beams and

columns exposed to fire on four and three sides can be calculated.

Although solving the equations does not represent a great problem,

graphical or numerical methods have to be used to calculate the critical

size of the section of the timber member and its fire resistance. In the

study where the equations were presented (Lie 1977), an attempt was

made to derive formulas in which the fire resistance is expressed ex-

plicitly as a function of the parameters that determine it. The results,

which were based on a rate of charring of 0.6 mdmin, are given in

Chapter 3, Section

3.1.3.

5.2.4.2

Fire Resistance

of

Glued-Laminated Beams (Composite Models)

A second approach to evaluating the fire endurance of a wood mem-

ber

is

to assume that the uncharred region consists of layers. In a model

with layers, the compressive and tensile strengths and modulus of

elasticity of each layer are assumed to be fractions of the room tem-

perature values. In one model (Schaffer et al. 1986), a single

38

mm

heated layer with reduced properties was used to analyze a beam using

transformed section analysis.

To

develop a more practical procedure,

the single layer model was used to calculate an equivalent zero-strength

layer, 6. For bending, the 6 was estimated to be 8 mm (0.3 in.) thick.

This zero-strength layer,

S,

was added to the char depth to obtain the

total zero-strength layer. The rest of the member was then evaluated

using room temperature property values. For fire damaged members,

Williamson (1982) recommended

6

of 6 mm

(0.25

in.) for designs con-

trolled by tension) and the use

of 100%

of the original basic allowable

stresses in calculation of load capacity.

As part of the effort to get U.S. code acceptance of the one-hour fire

resistive exposed wood member procedure (Section 3.1 .3 .2) , a layer

model was developed for the fire endurance of fire-exposed wood beams

(King and Glowinski 1988). This elastic transformed section model di-

vides the fire-exposed beam into four layers: a char layer, two layers

of wood at elevated temperatures and the central core at room tem-

perature. The inclusion of two layers at elevated temperatures makes

it possible to use the model for smaller members.

5.2.4.3 Fire Resistance of Light-Frame Members

The empirical reduction approach has been applied to the fire en-

durance of fire-exposed unprotected wood joist floor assemblies. In this

model, the strength reduction factor

01

was modified to account for the

small size of the member. The selection term was

1

a =

B

+

2 0


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E 78

9 2 0 7 5 9 b 0 0

00220l14

8 2 7


21

1

where

tf = failure time, and

y = empirical thermal degrade parameter.

The empirical thermal degrade parameter includes the effect of load

sharing between the joists and the T-beam action of the sheathing as

well as the loss of strength due to temperature rise of the uncharred

wood section. The model has been experimentally evaluated (White et

al. 1984, Schaffer et al. 1988). When a mean modulus of rupture at

room temperature is used to define the joist population, the analysis

indicated that 0.2 was an appropriate value for the thermal degrade

parameter y. The model has been extended to floor-truss assemblies

(Schaffer and Woeste 1979, 1981), and used as part of a first-order

second-moment reliability analysis of floor assemblies (Schaffer and

Woeste 1981a, 1981b).

A

more general approach to calculate the fire

resistance of light-frame assemblies requires the determination of the

temperature development in the assembly.

A

finite-element heat trans-

fer model has been applied to wood stud wall assemblies (Gammon

1987) and another heat transfer model has been applied to the calcu-

lation of the fire resistance of wood-based boards and wall constructions

(Fredlund 1990). The modelling of heat transfer in timber and gypsum

products has not gained wide acceptance due to the difficulties involved

with the accurate determination of material thermal properties and the

development of models for the pyrolysis, combustion, and mass transfer

processes. Support conditions can have an impact on the structural

performance of a loadbearing wall. It was found (Konig and Kallsner

1988) that better predictions were obtained when the axially loaded

wood studs were modeled with a compressible intermediate layer be-

tween the end surface of the stud and the support plate.

A

fire resistance model for wood beams based on mass loss versus

strength data was proposed in

Do

and Springer (1983a-c). The work

included a program to predict the temperature and mass

loss

within

the wood member. The input data came from small scale tension,

compression, and shear tests done on specimens that had previously

been heated in a muffle oven.

5.3

REMARKS

In this Chapter, a large number of mathematical models for the cal-

culation of the fire resistance of various building members are described.

Most

of

the methods are included because they are the bases of the

approximate formulas for the calculation of fire resistance given in

Chapter 3. These methods have been validated by comparing calculated

times to failure with experimental results. The methods have been

programmed by the National Research Council of Canada for computer


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S C E 78 92 0757600 0022015

7b3

212


OF

PRACTICE

processing. Many other methods and computer programs for the cal-

culation of fire resistance exist, however. Several of these and literature

that provide information on fire resistance calculation methods are in-

cluded in the following references: Reyer and Schlich (1988), Fredlund

(1979), Schaffer et al. (1986), Williamson (1982), King and Glowinski

(1988), White et al. (1984), Schaffer et al. (1988), Schaffer and Woeste

(1979, 1979, 1981), Gammon (1987), Fredlund (1990), Groom (1989),

Konig and Kallsner (1988),Do and Springer (1983a-c), Haksever (1975,

1977), Klingcch (1975), Iding et al. (1977, Wickstrom (1979), Bresler and

Iding (1982), Forsen (1983), Quast et al. (1984),

CEC

Research (1982,

1985), Jeanes (1985), Pettersson (1986), and CTICM (1982).

REFERENCES

Allen, D.E. and Lie, T.T. (1974). "Further studies of the fire resistance of

reinforced concrete columns." NRCC 14047, National Research Council of

Canada, Division of Building Research, Ottawa.

American Society for Testing and Materials. (1985). Standard methods offire tests

of building constructions and materials. Designation E119-83, Philadelphia, PA.

Atreya, A. (1983). "Pyrolysis: ignition and fire spread on horizontal surfaces

of wood." Ph.D. Thesis, Harvard University, Cambridge, MA.

Bender, D.A., Woeste, F.E. and Schaffer, E.L. (1985). "Reliability formulation

for the strength and fire endurance of glued-laminated beams." Research Paper

FPL 460,

U.S. Department of Agriculture, Forest Service, Forest Products

Laboratory, Madison, WI.

Bresler, B. and Iding, R.HJ. (1982). "Effect of fire exposure on steel frame

buildings." (Computer Program FASBUS II), Final Report, Vols. 1 and 2 , to

American Iron and Steel Institute, Wiss, Janney, Elstner Associates, Inc.,

Emeryville, CA.

British Iron Steel Res. Assoc, (1953). Physical constants of some commercial steels

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CALCULATION

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W

0 7 5 9 b 0 0

O022020

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CALCULATION

OF

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FIRE RESISTANCE

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A S C E

78

92

9

0 7 5 î b 0 0

O022023

Tb 7

m

Nomenclature

(Corresponding

to Chapter

5)

PROTECTED STEEL, REINFORCED CONCRETE, AND

CONCRETE-FILLED STEEL COLUMNS

Notation

f :

f :o

h

I

k

K

L

=

coefficient

=

coefficient

=

specific heat

(J

kgP1"CP*)

= coefficient

=

eccentricity of load (m)

=

compressive strength of concrete at temperature

=

cylinder strength of concrete at temperature T

= cylinder strength of concrete at room tempera-

=

strength of steel at temperature T (MPa)

=

yield strength of steel at room temperature (MPa)

=

yield strength

of

steel at room temperature

T

=

coefficient of heat transfer at fire exposed surface

=

o, 1, 2, . . .

= thermal conductivity

(W

m-*"C-')

= effective length factor, number of mesh points

in and on the insulation along the x-axis (Section

5.1.1)

= unsupported length

of

column

( m ) ,

number

of

mesh points in and on the insulation along the

y-axis

(Section 5.1.1)

T (MPa)

(MP4

ture (MPa)

(MPa)

(W m-*OC - I )

218


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A S C E

7 8

92

0 7 5 î b 0 0

O 0 2 2 0 2 2

î T 3 W

NOMENCLATURE (CORRESPONDING TO CHAPTER

5)

219

m

M

Ml

M ,

n

N

N,

P

Q

R

f

T

V

Y

X

z

Greek Letters

a

= 1,

2,

3, .

.

,

=

number of mesh points along the x-axis

= number of points P in the steel section in radial

direction

=

total number of points

P

in the column section

in radial direction

=

1,

2, 3,

.

.

.

= number

of

mesh points along the y-axis (Section

=

number of elements in tangential direction

= point

= rate of heat generation or absorption (J m-3h-1)

= elementary region

=

time (h)

=

temperature ("C)

= coordinate

=

volume of water in an element (m3)

=

lateral deflection of column at mid-height ( m ) ,

coordinate

=

coordinate

5.1.1), or along z-axis (Section 5.1.4)

=

coefficient of thermal expansion ("C-l), fraction

(Section 5.1.1)

=

increment or difference

=

mesh width ( m )

= emissivity strain (m m-')

=

emissivity factor = 1/

-

+

-

-

1

(ic is

1

=

heat of vaporization

(J

kg-l)

= density (kg rnp3), radius of curvature ( m )

= Stefan-Boltzmann constant (W m-2K-4)

= time (h)

=

concentration of moisture (fraction

of

volume)

= curvature of column at midheight (m-l)

Subscripts

a

=

average

c

= of concrete

i

m ,

M

ml

Mi, M,

max = maximum

=

of the fire

= of the insulation

= at a mesh point in the mth or Mth column, re-

=

at the points

rn,

MI, M, in radial direction

f

spectively (Sections 5.1.1 and 5.1.4)


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A S C E 78 92 0 7 5 9 b 0 0

0022023

8 3 T

220


OF

PRACTICE

min

n , N

n ,

N,

L

P

r

R

T

Superscripts

O

S

W

i

= minimum

= at a mesh point in the nth or Nth row, respec-

= at the points

n,

N, in tangential direction

=

left of the x-axis

= initial at room temperature

= pertaining to proportional stress-strain relation

=

pertaining to radiation

= right of the x-axis

= of steel

= pertaining to temperature

=

of water

tively (Sections

5.1.1

and 5.1.4)

=

at

t

=

jAt,

or

t

=

jA7

COMPOSITE FLOOR AND ROOF SLABS

Notations

C

C

d

h

i

k

1

P

R

t

T

X

Greek letters

= specific heat, Btu 1bP1'FP1

= minimum cover thickness, in.

= thickness of lower layer, in.

=

coefficient of heat transfer at fireexposed surface,

=

o, 1,

2,

. . .

= thermal conductivity, Btu h-'ft-''F-'

= thickness of slab, in.

= point

=

fire resistance of slab, h

= time, h

= temperature, O F

= coordinate, ft

Btu ft-,h-'"F-'

= coefficient expressing convective heat transfer

=

increment

= emissivity

=

density

=

Stefan-Boltzmann constant

=

0.1713

x l o p 8

Btu

from pad to air:

0.1823

Btu ft-2h-ioF-1.25

h - ft-2°F-

Subscripts

a = of asbestos

f

= of the fire

rn, M, MI, M,,

.

. . = at a point in the n-th, M-th, Ml-th, M,-th .

.

.

elementary layer


--``,`,,`,,``̀ ,,````,`,,,` ,̀`,,-`-`,,`,,̀ ,`,,`---



A S C E 78 92 0 7 5 î b O O 8022024 ï ï b

NOMENCLATURE (CORRESPONDINGTO CHAPTER 5)

max = maximum value of

min

=

minimum value of

n , nl ,

n2,

.

.

.

n =

initial

Superscripts

i

=

concrete type

= at

t

=

jAt

GLUED -LAMINATED TIMBER

22

Notation

A

= area of cross section (m2)

b

B

d

D

E

k

L

n

P

PL3

r

P

t b 3

tb4

t C 4

a

ß

U

c c

tc3

=

breadth of uncharred part of member at the time

of failure (larger side of column, smaller side of

beam) (m)

=

breadth of member before exposure to fire (larger

side of column, smaller side of beam) (m)

= depth of uncharred part of member at the time

of failure (smaller side of column, larger side of

beam) (m)

=

depth of member before exposure to fire (smaller

side of column, larger side of beam) (m)

=

modulus of elasticity (N/m2)

=

ratio between applied load and ultimate load

=

effective length of column (m)

=

exponent taking into account the dependence of

the critical depth of columns on column length

= load (N/m2)

=

applied load (N/m2)

=

buckling load (N/m2)

=

radius of gyration (m)

= fire resistance of beams heated on three sides

(min)

=

fire resistance of beams heated on four sides

(min)

=

fire resistance of columns heated on four sides

(min)

= a factor that takes into account the reduction of

compressive 'strength (or modulus of elasticity)

due to temperature rise in the uncharred part of

column or beam

= rate of penetration of the charring (&min)

=

stress (N/m2)

=

compressive strength of the wood before expo-

= fire resistance of columns heated on three sides

sure to fire (N/m2)

(min)


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -`

, ,` , ,` ,` , ,` ---



A S C E

7 8 92

0759b00 0022025

602

Appendix

MATERIAL PROPERTIES

AND

PHYSICAL CONSTANTS

(See Nomenclature section for definiton of symbols)

In this Appendix, the values are given of the material properties and

physical constants used in the mathematical models for the generation

of

the formulas for fire resistance given in Chapter 3. In general, con-

servative values were used in the mathematical models, which are

described in Chapter 5. For a number of cases, more accurate and less

conservative values became available with progress

of

time. These val-

ues are also included in this Appendix. Instead of tabulated values,

approximate equations are given that describe the relationship between

the properties and temperature. The use of such equations facilitates

the application

of

the mathematical models for the calculation of fire

resistance. All models described in Chapter 5 were programmed for

computer processing by the Institute for Research in Construction

of

the National Research Council of Canada.

A. l

STEEL PROPERTIES

A. l . l Thermal

Properties

A.l.l.l Thermal Ca pacity of Steel

for O I I 50°C

psc5=

(0.004T

+ 3.3) x lo6

m-30C-1

for 650°C

<

T

725°C

p5c5= (0.068T - 38.3) x lo6

m-30C-1

222


- -

` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E 78 92 0759600 O022026 549 m


223

for 725°C < T 800°C

p,c, =

(-0.086T +

73.35)

x l o 6

J

mP3"C-l

for

T

>

800°C

psc, =

4.55

x l o 6 J

m-30C-1

A.1.1.2

Thermal Conductiv i ty of Steel

for O I 900°C

k, = -0.022T +

48

W

m-'"C-'

for T

> 900°C

k ,

= 28.2 W m-'"C-'

A.1.1.3

Coefficient

of

Thermal Expansion

of

Steel

for T < 1000°C

a,

=

(0.004T

+

12)

x

10-6"C-1

for T 2 1000°C

A.1.2 Mechanical

Properties

A.1.2.1

Stress-strain Relations for Steel (Version

1)

(More conservative than Version

2,

but may be used for reinforcing

steel or concrete-filled steel, where the role of the steel in carrying the

load at failure point is secondary.)

for

E,

f ( T , 0.001)

f y =

0.001

Es

where

E p = 4 x 10-6fy,


- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -





A S C E 78

92 0759600 0022028

311


225

for 600

< T <

1000°C

340

-

0.34T

T - 240 fyo

tT

=

and the modulus

of

elasticity

by

the equations

[47]:

for O

<

T 600°C

for 600

< T

< 1000°C

690

-

0.69T

T

-

53.5

T = E o

A.2

CONCRETE PROPERTIES

A.2.1

Thermal Properties

A.2.1.1 Thermal Ca pacity of Concretes

Siliceous Aggregate Concrete

for

O

T

I

00°C

pccc =

(0.005T +

1.7)

X

lo6

J m-30C-1

for 200°C

<

T 400°C

pcc, =

2.7

x lo6 J m-3"C-1

for 400°C

<

T 5 500°C

pccc = (0.013T - 2.5) x l o6 J

m-30C-1

for 500°C < T 5 600°C

~

pccc

=

(-0.013T +

10.5)

X l o6

J

m-30C-1


--

` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



226

STRUCTURAL

FIRE


for

T

>

600°C

pcc,

=

2.7 x

l o 6

J

m-30C-1

Carbonate Aggregate Concrete

for O T I

00°C

pee,

= 2.566 x

lo6

J mP3"C-'

for

400

< T I

10°C

pee, =

(0.1765T - 68.034)

X lo6

J mP3"C-'

for

410

< T

445°C

pcc, =

(-0.05043T

+

25.00671) x

lo6

J m-3"C-1

for

445

< T 5

500°C

p,c,

=

2.566 x

l o 6

J

m-3 C-1

for

500

< T

635°C

pccc

=

(0.01603T

-

5.44881)

x lo6

J m-3"C-1

for

635

< T I

15°C

pccc

= (0.16635T

-

100.90225) x

lo6

J

rnP3"C-'

for

715

< T I

85°C

pccc

=

(-0.22103T

+

176.07343)

x

l o 6 J m-30C-:

for T

>

785°C

pccc = 2.566 x lo6 J m-3"C-1

Expanded Shale Aggregate Concrete

for

O

I 5

400°C

p,c,

=

1.930

x

lo6

J

m-3"C-1


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,`

, ,-` -` , ,` , ,` ,` , ,` ---



227

ATERIAL PROPERTIES AND PHYSICAL CONSTANTS

for

400 < T 5

420°C

pcc,

=

(0.0772T - 28.95)

x

106J m-3"C-1

for

420

<

T

435°C

pcc, =

(-0.1029T

+

46.706) x 106

J

mP3"C-l

for

435 <

T

600°C

pccc

=

1.930 x

l o 6

J m-30C-1

for 600 < T

700°C

p,c,

=

(0.03474T

-

18.9140) x

106

m-30C-1

for

700 <

T

720°C

pee, =

(-0.1737T + 126.994) x

106

m-30C-1

for T

>

720°C

pcc,

= 1.930 x

lo6 J

m-30C-1

A.2.1.2 Thermal Con duct ivi ty of Concretes

for O

T

I 00°C

Siliceous

Aggregate Concrete

k,

=

-0.000625T

+ 1.5

W m-'OC-l

for

T

> 800°C

Pure Q uartz Aggregate Concrete

for

O

4 T

800°C

k , =

-

0.00085T + 1.9 W m-*"C-'

for T

> 800°C

k ,

=

1.22 W

m-'"C-'


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---





A S C E 78

3 2

O753600 0022032 842

229

ATERIAL PROPERTIES AND PHYSICAL CONSTA NTS

where

f :

= fo

if T I 50°C

f c = fi, 12.011 - 2.353

f T

2 450°C

1000

E,,~

= 0.0025 +

(6.OT

+ 0.04TZ)

x

A.3 WATER PROPERTIES

A.3.1 Thermal Capacity of Water

pc = 4.2 x

lo6

J m-30C-1

A.3 .2

Heat of Vaporization of Water

X,

= 2.3 x lo6

J

kg-’

A .4 PHYSICAL CON STANT S

a =

Stefan-Boltzmann constant:

5.67

x lop8

W

m P 2

K - *

E~

=

emissivity

of

fire: 1

E, = emissivity

of

steel: 0.9

E, = emissivity of concrete: 0.9


- - ` `

, ` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E 78 92 0759600

0022033

7 8 9

-A-

Ablation protection 46

AC1 318-89 80

Actual fire-standard fire time tem-

perature curves 7-8

Aggregate concrete 25-37; slab cal-

culations 93-98; tem eratures

25-26, 91-92, 121-152

Aggre ate concrete formula values,

226, 228; expanded shale 226-

228; Ure quartz 227; siliceous

225-528

Aggregate-cement ratio and load

conditions 29

Air and boundary asbestos pad,

temperature calculation 183

Air layers 129-130

Allo bars, stren th 21, 92

Annular elements, steel column 202

Area time temperature curves, se-

verity of fire 12

Asbestos pad and boundary slab,

temperature calculation 182-

183

Asbestos pad elementa layer,

composite slab 1 8 .

Assemblies of floor, roof and beam

72-75

Assemblies, timber, light frame

112-114

Assessment, fire resistance design

8-10,

calculation 9-10; test-

in 8 9

AS T M & i ~ t e s ttandard 56

ASTM S-36 steel ield, strength 92

Axially restrainedrbeam 89

-B-

Basalt 31

Bay floor panel 98-110

Beads, corner 68

Beam as part of floor, effect on

Beam span, effect on resistance 132

Beam, roof and floor assemblies

t

a

erma1 properties, carbonate,

Angres, corner 6i

resistance 132

72-75

Beams, concrete 84-89; continuous

86-88; steel 73-76; timber

115-117

Beams, continuous vs. simply sup-

ported 132

Beams, timber, glue laminated,

resistance calculation 207;

composite models 210

285

-

$6

Bendin ru ture of wood beam

Boltzmann-Stefan constant 229

Boundary asbestos pad and air,


Boundary slab and asbestos pad,


183

Boundary steel-concrete, tempera-

ture calculation 188

Box protection, steel beams 73;

steel columns 65

Brick, insulation, temperature cal-

culation 171

Building design and fire safety

1-10;

codes 2-6; fire resis-

tance design 6-10; model

codes 3-5; standards 5-6

Building elements testing, standard

fire tem erature-time rela-

tions 15g

Buildin elements, fire resistance

6f-136; calculation 63-117;

extension rules and guide-

lines 117-136; testing 117

c

-L-

CABO, report

No.

NER-250 116-117

Calcination protection 46

Calculation methods, concrete 77-

110; evaluation of fire per-

formance 57-62; examples

93-110; fire resistance design

9-10, 63-117; steel 63-77;

timber 112-117

Calculation of fire resistance, build-

ing elements 63-117; concrete

77-

110;

concrete examples


111-117

23

i


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,

` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E 7 8 92 7 5 9 b 0 0 0022034 b L 5

232 INDEX

Calculation of temperature and fire

resistance of structural mem-

bers 159-221; fire resistance

of structural members 193-

211;

nomenclature 218-221;remarks 21 1-212; temperature

of fire exposed members 159-

192

Calculation, fire resistance, struc-

tural members 193-211; con-

crete 193-201; concrete filled

tubular steel columns 201-

204; steel 193; wood 204-211

Canada, National Building Code of

50-51, 116

Capacitive protection 49

Carbonate ag regate concrete 27-

30,

35,

i',

121-122; thermal

roperties, formula values

526, 228

shale aggregate concretes,

stress-strain relations, formula

values, 228-229

Carbonate, siliceous and expanded

Cavitv filling

of

columns and walls

'1

28

confitions 29

Cellulosic fuel 14

Cement-a gregate ratio and load

Cementitious material 65-66

Center concrete temperature calcu-

lation 178

Characteristics

of

construction

types, under fire 49-51

Charring rate of wood 38-40

Charring rate, semi-infinite, tem-

perature calculation 189- 190

Circular concrete columns, temper-

ature calculation 176-180

Circular concrete filled steel col-

umns, tem erature calcula-

tion 184-1f8

49-51

Classification, building construction

Codes, building 2-6

Coefficient, thermal expansion,

steel 223; concrete 228; col-

umn 185

Column length, effect on resistance

132

Columns and walls, cavity filling 128

Columns, concrete circular, temper-

ature calculation 176- 180;

concrete rectangular, temper-

ature calculation 172

Columns, reinforced concrete, cal-

culation methods 57-59;

resistance calculation, 79-80,

194-196

Columns, steel, circular concrete,

temperature calculation

184-

188

Columns, steel, concrete filled tu-

bular, resistance calculation

Columns, steel, concrete filled, no-

menclature, calculation of

resistance 218-220

Columns, steel, insulation protec-

tion 48-49, tem erature cal-

culation 160-16f

Columns, steel, resistance calcula-

tion 64-72; concrete protec-

tion 67-70; gypsum wall-

board protection 67; hollow

steel columns 70-72; low

density protection 64-67; un-

protected 70

Columns, timber 115-117, glue

laminated, resistance calcula-

tion 207-210

Combustible construction, safety

characteristics 49-51

Composite concrete floor and roof

201-204

slabs, temperature calculation

180-184

Composite floor and roof slabs, no-

menclature, resistance calcula-

tion 220-221

Composite slabs 82-84

Compressive strength, concrete 29-

31;

siliceous a gregate con-

crete 92;

W O O f 4 3 - 4 4

ro rams, finite element,

comp;FxJs41 75

Computer programs, calculation of

resistance 211-212

Concrete beams 84-89

Concrete boundary tem erature

calculation 174,

18

Concrete center temperature calcu-

lation 178

Concrete columns, calculation

methods 57-59; resistance

calculation 79-80

Concrete columns, tem erature cal

culation, circular 776-180; -

rectan ular 172; s uare 172

Concrete cohmns, rein2orced.

resistance calculation 194-196


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



A S CE 7 8 92 W 0759600 O022035 5 5 1

W

INDEX

233

Concrete filled steel columns, circu-

lar, temperature calculation,

Concrete filled steel columns, no-

menclature, calculation of

resistance 218-220

Concrete filled tubular steel col-

umns, resistance calculation

Concrete floor and roof slabs,


Concrete members, calculation of

fire resistance 193-201

Concrete rotection, steel columns

67- 70

184-188

201-204

Concrete slabs, composite 82-84;

continuous 86-88; double

layer 81-82; hollow 82; mon-

olithic 80-81; siliceous con-

crete 93-98; simply su ported

84-86; unrestrained 8 2 8 6

Concrete, carbonate aggre ate,

thermal ro erties, krmula

values 2f6, %8

Concrete, composite, floor and roof

slabs, temperature calculation

Concrete, expanded shale aggre-

gate, stress-strain formula

values 228-229; thermal

roperties formula values

Concrete, extension range variation

120-123

Concrete, fire effect on 24-36; de-

formation roperties 33-37;

mechanicafproperties 27-32;

thermal properties 24-27

Concrete, formula values 225-229

Concrete, inner, temperature calcu-

lation 174, 177

Concrete, pure quartz aggregate,

thermal roperties, formula

values 2f7

Concrete, reinforced, nomenclature,

calculation of resistance 218-

220

Concrete, resistance calculation 77-

110; examples 93-110

Concrete, siliceous ag re ate 91,

121-122; slab cafcuktions 93;

thermal ro erties formula

values J5-528

Concrete-steel boundar , empera-

ture calculation 1

i

180-184

Y

26-228

Conductivity values 47; formula

values, concrete 227-228;

steel 223

Conductivity, concrete 24-25, steel

17; wood 41

Constants, physical 229

Construction materials,effect of fire

on 14-45; concrete 24-36;

steel 17-24; wood 36-45

Construction techni ues 49-54;

classification 41-51; structural

systems 51 -54

Continuous beams and slabs 86-88

Continuous vs. simply supported

floors or beams 132

Contour protection, steel beams 74;

steel columns 66

Corner ba floor panel 98-104;

bea& or angles 68; joint de-

tails 68

Council of American Building Offi-

ciais, re Ort No. NER-250

116-117

Creep, concrete 34-37; steel 23-24;

wood 45

Cross sectional area determination,

siliceous aggregate concrete

slab 93-98

Crushed clinker 31

Curve, thermal conductivity

18;

volumetric specific heat, steel

19

Curve tem eratures, standard fire

1.51-757

Curves, characteristic temperature

141-142; expressions 142-151

Curves, time-temperature 8, 12-15

-D-

D

perimeter, steel beams 73-74;

steel columns 65-66, 69, 71;

steel trusses 76

Decay period temperature-time

curve 142-143; expressions

149

Deformation pro erties, concrete

33-36; steey22-23; wood 45

Dehydration protection 47-48

Dehydration tobermorite gel 36

Density of materials 47; steel 64-66;

wood 38-39, 42, 124

Design, fire resistance 6-10; assess-

ment 8; calculation 9-10; re-

quirements

7-8;

testing 8-9


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



ASCE 78 92

0 7 5 9 b 0 0

0022036 498

234 INDEX

Design, fire safety 1-10; codes 2-6;

fire resistance design 6-10;

model codes 3-5; standards

13

nition) 118

5-6

Destructive potential of fire, factors

Developed heated perimeter (defi-

Development of room fire 11-14

Diffusivity, concrete 27; steel 18-19

Double la er concrete slabs 81-82

Douglas plywood protective

membrane 112-114

Douglas fir rate of charring 38-39

Duration curve 15, 155

-E-

Effect of fire on construction mate-

rials 14-45; concrete 24-36;

steel 17-24; wood 36-45

Elasticity, concrete 27-28; steel 20;

wood 42-43

Elementary layers arrangement,

com osite slab 181; concrete

f J

lle tubular steel column 185

Elementary layers, circular concrete

columns 176-177

Elementary region of inner surface

of

insulation, protected steel

Elements testing, building, stan-

dard fire temperature-time re-

lations 155

Elements, building, fire resistance

63-136; calculation 63-117;



Enclosures, area and height anal ti

cal expressions 142, 144-145;

-

heat balance during a fire

138, 140; tem erature-time

curves

î4i-î.Fi

Equation of steel thermal conduc-

tivity 17

Equilibrium moisture condition 69

Equivalent thickness, multiplying

factors 83

Evaluation of fire performance 55-

59; resistance testing 55-56;

calculation 57-62

Exam les, concrete resistance calcu-

Pation techniques 93-110

Expanded shale 33; thermal

ro er

ties formula values 22&-2€à -

Expanded shale, siliceous and car-

bonate aggregate concretes,

166-169


values, 228-229

Expanded slag 33

Expansion coefficient, steel 223;

concrete 228

Expansion, concrete 33-35; steel 22;

wood 45

Exposed structural members, tem-

perature calculation 159-192;

circular concrete columns

176- 180; circular concrete

filled steel columns 184-188;

composite concrete floor and

roof slabs 180-184; finite

wood members 190-192; pro-

tected steel 160-172; rectan-

gular concrete columns 172;

semi-finite wood slabs 188-

190; s uare concrete columns

172-176; unprotected steel

172

Expressions, characteristic tempera-

ture curves 142-151

Extension ran e of fire resistance,

rules a n i guidelines 117- 136;

definition of terms 118; gen-

eral rules 126-136; variation

of dimensions 125-126; varia-

tion of material properties

Exterior panel, concrete 98-

110;

steel layout 93

Exterior protected ordinary con-

struction techniques 50-51

External storage water 72

-F-

F, values 80, 116

Factor, Overdesign 80

Failure vs. load time, steel stud

FASBUS

II

finite element computer

119-125

walls 78

program 75

Ferrite steels. thermal exDansion 23

Finite woodmembers, tfmperature

Fire development in a room 11-14

Fire effect on construction materials

calculation 190- 192

14-45; concrete 24-36; steel

Fire exposed structural members,


192; circular concrete columns

176- 180; circular concrete

filled steel columns 184-188;

composite concrete floor and

17-24; wood 36-45


--``,`,,`,,```,,````,`,,,``,`,,-`-`,,`,,`,`,,`---



ASCE 7 8 92

m

0759b00 0022037 324

m

INDEX 235

Fire exposed structural members,

(con inueù)

roof slabs 180-184; finite

wood members 190-192; pro-

tected steel 160-172; rectan-

gular concrete columns 172;

semi-finite wood slabs 188-

190;

s

uare concrete columns

172-176; unprotected steel

172

Fire protection principles

11

-62;

achieving resistance 45-54;

evaluation of fire performance

55-59; fire effect on construc-

tion materials 14-45; fire se-

verity 11-14

Fire resistance and temperature of

structural members, calcula-

tion 159-221; fire resistance


211; nomenclature 218-221;

remarks 21 1-212; temperature


192

Fire resistance desi n 6 10; assess

ment 8; calcufatioi 9-10; re--

quirements 7-8; testing 8-9

construction techniques 49-

54; mechanisms 46-48; meth-

Fire resistance, building elements

63-136; calculation 63-117;



Fire resistance, calculation, building

elements 63-117; concrete

77-110; concrete examples


Fire resistance, structural members,

calculation 193-211; concrete

193-201; concrete filled tubu-

lar steel columns 201-204;

steel 193; wood 204-211

Fire resistive construction ty es,

safety characteristics 4a)-51

Fire safety and building design

1-10; codes 2-6; fire resis-

tance design 6-10; model

codes 3-5; standards 5-6

Fire severity 11-14

Fire slab boundary, composite con-

crete, temperature calculation

181-182

Fire tem erature-time relations

133) 158; expressions for tem-

Fire resistance principles 45-54;

ods 48-49

112-117

perature curves 142-151; no-

menclature 158; parameters of

temperature course 138-140;

ossible fire severities 140-

157; temperature curves, 141-

142

Fire-steel boundary, tem erature

calculation 185- 18g

Flat plate construction 98-110

Floor and roof slabs, composite

concrete, temperature calcula-

tion 180-184

Floor and roof slabs, composite,

nomenclature, resistance cal-

culation 220-221

Floor and roof slabs, concrete,


Floor panels 98-110

Floor slabs subjected to thermal re-

straints 88-93

Floor span, effect on resistance 132

Floor truss and roof assemblies,

Floor, roof and beam assemblies

P

41; standard fire curve 151-

wood 112-114

72-75

-

. -

Floors, continuous vs. simply sup-

ported 132

Foreign countries standard fire tem-

Frame assemblies, timber

112-

114

perature time relations 15, 155

-G-

Glue laminated timber beams and

Glue laminated timber, nomencla-

columns 115-117

ture, resistance calculation

221

Glue laminated timber, resistance

calculation 206-210

Granite 33

Gravel 36; specific heat 25-26

Growth-develo ed decay period of

Guidelines and rules, extension

fire 138-r39

-

range of fire resistance 117-

136; definition of terms 118;

general rules 126-136; varia-

tion of dimensions 125-126;

variation of material proper-

ties 119-125

Gypsum board protective mem-

Gypsum wallboard protection, steel

brane 112-114

columns 67; steel stud walls

78



- - ` ` ,

` , ,

` , ,

` ` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



A S C E

7 8

92 0 7 5 ï b 0 0 0022038

260

236 INDEX

-H-

Heat balance for an enclosure dur-

Heat eneration, wood 42

Heat kad curves 13

Heat transfer model for elementary

region, protected steel 166

Heat, specific (see Specific heat)

Heat, va orization of water, for-

muya values 229

Heated perimeter, developed (defi-

nition)

118

Heavy timber 50-51

Hollow concrete slabs 82; steel col-

umns 70-72

-1-

Idealized temperature course of fire

Inner concrete temperature calcula-

Inner surface of insulation, pro-

ing a fire 138, 140

139

tion 174, 177

tected steel, heat transfer

model 166; temperature calcu-

lation 165

Insulation 48; steel column sections

49; brick 171; vermiculite

board 172

Insulation, inner surface, protected

steel heat transfer model 166;


Insulation, outer boundary, tem-

perature calculation 162-165

Interior bay floor panel 104-110

Intumescence rotection 46-47

IS0 834, s tangrd fire tem erature-

time relation 155-15t

-I-

Joint details 68

Joists, wood 112

Jura limestone 31

-K-

Kinetics, wood 42

-L-

Laminated timber, resistance calcu-

lation 206-210; nomenclature

221

Layers arrangement, elementary,

concrete filled tubular steel

column 185

Layers, combined vs. individual

126-127, 129

Layers, elementary, in composite

slab 181

Length of column, effect on resis-

tance 132

Length of negative reinforcement

93

-

98

Light frame assemblies, timber

112-114

Light frame wood members, resis-

tance calculation 210-211

Lightweight concrete, specific heat

25-28; compressive stren th

27, 29; extension range lf2-

123

Limestone 33; specific heat 25-26

Load bearing wails 76-77

Load deflection analysis, resistance

calculation 195

Load factor, timber columns and

beams 116

Load levels effect on concrete de-

formation 34

Load vs. failure time for steel stud

walls 78

Loadin and cement-aggregate ratio

Loads, fire, characteristic tempera-

ture curves 152

Location of restraining forces, tim-

ber beams and columns

111

Low densiíy protection, steel col-

umns 64-67

Lumber, protective membrane 114

28

-M-

Material properties and physical

constants, formula values

222-229; concrete 225-229;

h sical constants 229; steel

2 -225; water 229

Materials of construction, effect of

fire on 14-45; concrete 24-36;

steel 17-24; wood 36-45

Mechanical pro erties, concrete 27-

32; steel &-22; wood 42-44

Mechanical properties formula val-

ues, concrete 228-229; steel

Mechanisms, fire protection 46-48

Members, structural, calculation of

fire resistance 193-211; con-



204; steel 193; wood 204-211

Members, structurai, calculation of

temperature and fire resis-

tance 159-221; fire resistance

223-225


--` ` ,` , ,` , ,`

` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



ASCE

78 92 W

O759600

O022039 I T 7

D

INDEX 237

Members, structurai,

(continued)


21

1;

nomenclature 21

8-

221;



192

Mineral fibre material 67

Model building codes 3-5

Modulus of elasticity, concrete 27-

28; steel 20; wood 42-43

Moisture 131

Moisture condition, equilibrium 69

Moisture content, Douglas fir 39

Moisture effect, circular concrete

columns 178-179; circular

concrete filled steel columns

187-188; square concrete col-

umns 175-176

Moment diagrams, axially re-

strained beam 89; continuous

beam 87-88; sim 1 sup-

orted beam or siai

85

Monogthic concrete slabs 80-81

Monolithicall cast reinforced con-

Multiplying factors for equivalent

-N-

National Building Code of Canada50-51, 116

Negative reinforcement length, sili-

ceous aggregate concrete slab

Nomenclature, calculation of resis-

tance 218-221; composite

floor and roof slabs 220-221;

glue laminated timber 221;

protected steel, reinforced

concrete, concrete filled steel

columns 218-220

Nomenclature, fire temperatures

158

Noncombustible construction,

safety characteristics 49-51

Noncombustible material filling of

column and wall cavities 128

Normal Wei ht concrete 27-29, 32,

122-1 3

Normalized heat load curves 13

-0-

Opening factor influence 153

Outer boundary of insulation, tem-

Overdesign factor 80

crete 5 J

thickness 83

93-98

perature calculation, pro-

tected steel 162-165

-P-

Panels, corner ba 98 104; interior

bay 104-1iJ

-

Panels, steel 93

Parameters, fire temperature course

138-140

Performance of fire, evaluation 55-

59

Perimeter

D,

steel beams 73-74;

steel columns 65-66, 69, 71;

steel trusses 76

Perimeter, developed heated (defi-

nition)

118

Perlite 33

Physical constants 229

Pittsbur h seam corner joints 68

Plywoocf, Douglas fir, protective

membrane 112-114

Principles, fire protection 11-62;

achieving resistance 45-54;

evaluation of fire performance

55-62; fire effect on construc-

tion materials 14-45; fire se-

verity 11-14

construction techniques 49-

54; mechanisms 46-48; meth-

Programs, computer, calculation of

resistance 211-212

Protected steel, nomenclature, cal-

culation of resistance 218-220

Protected steel, temperature calcu-

lation 160-172; auxiliary

equations 170; calculation

method 160-162; com arison

with test results 170-h; in-

side of insulation 165; outer

boundar of insulation 162-

165; steey core 165-169

Protection from fire, principies

11-

62; achieving resistance 45-

54;

evaluation of fire perform-

ance 55-62; fire effect on con-

struction materials 14-45; fire

severity 11-14

Principies, fire resistance 45-54;

ods 48-49

Pumice 33

-Q-

Quartz aggregate concrete, pure,

thermal roperties, formula

values 2f7

Quartz expansion 35-36

-R-

Rectangular concrete col+ns, tem-

perature calculation 172



- - ` ` ,

` , ,

` , ,

`

` ` , ,

` ` ` ` ,

` , , ,

` ` ,

` , , - ` - ` , ,

` , ,

` ,

` , ,

` - - -



ASCE

78

92

D

0757600 0022040 919

238

INDEX

Reflection protection 48

Reinforced concrete columns, calcu-

lation methods 57-59; resist-

ance calculation 79-80; 194-

196

Reinforced concrete slab, steel

structural system 52-53

Reinforced concrete, nomenclature,

calculation of resistance 218-

220

Reinforcement, negative 93-98

Reinforcing steel stress-strain

curves, resistance calculation

Relation

of

standard fire time-

temperature tables 15- 16

Requirements, fire resistance design

7-8

Resistance and temperature of struc-

tural members, calculation

159-221; fire resistance of

structural members 193-211;

nomenclature 218-221; re-

marks 211-212; temperature of

fire exposed members 159-192

Resistance calculation, building

elements 63-117; concrete

77-110; concrete examples


Resistance design 6-10; assessment

testing 8-9; calculation 9-10;

requirements 7-8

Resistance, building elements 63-

136; calculation 63-117; ex-

tension rules and uidelines

117-136; testing 1f7

Resistance, principles 45-54; con-

struction techniques 49-54;

mechanisms 46-48; methods

48-49

Resistance, structural members, cal-

culation 193-211; concrete

193-201; concrete filled tubu-

lar steel columns 201-204;

steel 193; wood 204-211

Restraining forces location, timber

beams and columns 115

Restraints, thermal 88-93

Rhine sand 31

Roof and floor slabs, composite

Roof and floor slabs, composite,

197-198

112-117

concrete, temperature calcula-

tion 180-184

nomenclature, resistance cal-

culation 220-221

Roof and floor slabs, concrete,

Roof and floor truss assemblies,

Roof, floor and beam assemblies

Roofs subjected to thermal re-

Room fire development 11-14

Rules and guidelines, extension


wood 112-114

72-75

straints 88-93

range of fire resistance 117-

136; definition of terms 118;

general rules 126-136; varia-

tion of dimensions 125-126;

variation of material proper-

ties 119-125

Rupture, steel 24; wood beam 205-

-S-

Safety and building design 1-10;

codes 2-6; fire resistance de-

sign 6-10; model codes 3-5;

standards 5-6

Safety characteristics, types of con-

struction 51

Sandstone 33

Semi-infinite wood slabs, tempera-

ture calculation 188-190

Severities, temperatures 140-141

Severity, room fire 11-14

Shale aggregate concrete, ex-

Shale, expanded 33, stress-strain

formula values, 228-229

Sheet steel covers 68

Siliceous a gregate concrete 27-30,

32-35, 121-122; slab calcula-

tion 93-98; slab temperatures

91; thermal pro erties for-

mula values 225)-228

shale aggregate concretes,


values, 228-229

Simply supported (unrestrained)

slabs and beams 84-86

Simply supported vs. continuous

floors or beams 132

Slab boundary, composite concrete,

temperature calculation

181

-

182

Slab-like building elements 79

Slabs subjected to thermal re-

206

anded, thermal pro erties,

Formula values 226-

f

8

Siliceous, carbonate and expanded

straints 88-93


--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,` , , ,` ` ,` , ,-` -`

, ,` , ,` ,` , ,` ---





ASCE 7 8

92

0759b00 0022042 791

240 INDEX

Strain-stress relations,

(continued)

ag regate concretes, formula

vakes, 228-229

Strain-stress relations, steel, for-

mula values 223-225

Strength calculation, tubular steel

columns 202-203

Strength, concrete 27-32; concrete

column 57-59; steel 20-22;

Stress-strain curves for reinforcing

steel, resistance calculation

197-198

Stress-strain curves, concrete 37;

mild steel 21

Stress-strain curves, concrete,

resistance calculation

200

Stress-strain relations for siliceous,

carbonate and expanded shale

ag regate concretes, formula

vakes, 228-229

Stress-strain relations, steel, for-

mula values 223-225

Structural fire protection principles

11-62; achieving resistance

45-54; evaluation of fire per-

formance 55-62; fire effect on

construction materials 14-45;

fire severity 11-14

Structural fire resistance (definition)

118

Structural members, calculation of

fire resistance 193-211; con-



204; steel 193; wood 204-211

Structural members, calculation of

temperature and fire resis-

tance 159-221; fire resistance





192

wood 43-44, 123

Structural systems 51-54

Studs, steel 68; wells 78; wood 113

Symmetry temperature calculation,

elementary regions 170;

square concrete columns 175

-T-

Tables of standard fire temperature-

time relation 15-16

Temperature and fire resistance of

structural members, calcula-

tion 159-221; fire resistance



remarks 211-212; temperature


192

.

Temperature-time curves, concrete

28, 32; steel 8. 12. 15

Temperature-time curves, room fire

11-14; standard fire-actual fire

Temperature-time relations, stan-

dard fire, tables 15-16, 156;

building elements testing 155

Temperature-time relations, fire

137- 158; expressions for tem-

perature curves 142-151; no-

menclature 158; parameters of

temperature course 138-140;

ossible fire severities 140-

P41;

standard fire curve 151-

157; temperature curves, 141-

142

Tensile strength, concrete 32; wood

43-44

Test standard, ASTM E119 stan-

7-8

dard 56'

Testin

,

ire resistance design 8-9,

f5-56; building: elements 15,

127, 155; conc&e slabs 91

Thermal capacity, water, formula

values 229

Thermal conductivity protection

46

-

47

Thermal conductivit

,

concrete 24-

25; steel 17-1J wood 41

Thermal diffusivety, steel 18-19

Thermal ex ansion, concrete 33;

steel 'i;-23; wood 45

Thermal fire resistance (definition)

118

Thermal pro erties, concrete 24-27;

steel lfl-19; wood 40-42

Thermal properties formula values,

concrete 225-228; steel 222-

223

Thermal restraints, floor slabs and

roofs 88-93

Thickness equivalent, 85; multipl

ing factors 83; protection 4 J -

Thrust parameter 90

Timber 50-51; beams 115-117; col-

umns 115-117

Timber, glue laminated, nomencla-

ture, resistance calculation

221



--` ` ,` , ,` , ,` ` ` , ,` ` ` ` ,`

, , ,` ` ,` , ,-` -` , ,` , ,` ,` , ,` ---



A S C E 78 92 0759600 0022043 628

INDEX 241

Time assigned to rotective mem-

branes 112-713

Time-tem erature curves, concrete

28, g2; steel

8,

12, 15

Time-temperature curves, room fire

11-14; standard fire-actual

fire 7-8

Crete 120-123; steel 119-120;

wood 123-125

Ventilation controlled fires 142- 150

Verification techniques, resistance

Vermiculite board insulation 172

Volumetric specific heat, concrete

ratings 98-110