asce 78 - structural fire protection
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SPECIAL
NOTICE
The material presented
in
thi s
publication has been
prepared
in
accordance
wth
generally recognized
engineering principles and practices, and is for generai
information only. This information should not
be
used
without first securing competent advice
wth
respect
to
its
suitability for any general or specific application.
The contents
of
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
reference made
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
any
fund,
whether express
or
imptied, concerning
the
accuracy, completeness, suitability or utility of any
information, apparatus, product, or process discussed
in ths
publication, and assumes no liability therefor.
Anyone utilizing
this
information assumes all liability
arising
from
such
use,
incfuding but not limited to
infringement
of
any patent
or
patents.
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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
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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
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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
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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
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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
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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
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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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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.
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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
..................................
2.2.3.4 Deformation Properties
...................................
-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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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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CONTENTS
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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CONTENTS
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 ..................................
5.2.2 Fire Resistance
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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CONTENTS
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 ......................
-Expanded Shale Aggregate Concrete ..............
A.2.1.3 Coefficient of Thermal Expansion of Concretes...
-Siliceous and Carbonate Aggregate Concretes
..
-Expanded Shale Aggregate Concrete ..............
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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A S C E
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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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2
STRUCTURAL
FIRE
PROTECTION: MANUAL
OF
PRACTICE
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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BUILDING DESIGN AND FIRE SAFETY
3
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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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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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BUILDING DESIGN AND FIRE SAFETY
5
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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6
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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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A S C E 7 8
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BUILDING DESIGN AND
FIRE
SAFETY
7
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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STRUCTURAL
FIRE
PROTECTION: MANUAL OF PRACTICE
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).
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BUILDING DESIGN AND FIRE SAFETY
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
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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.
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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).
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STRUCTURAL
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PROTECTION: MANUAL OF PRACTICE
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.
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PRINCIPLES
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STRUCTURAL FIRE PROTECTION
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.
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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-
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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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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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16
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
92
m
0 7 5 9 b 0 0 0021820 490
m
PRINCIPLES
OF
STRUCTURAL FIRE PROTECTION
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
78
7 2 O757600
0023823
327 D
U
z
C Y
W
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
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I
A S C E 78 92
m
0 7 5 î b 0 0 0023822 2 b 3
m
PRINCIPLESOF STRUCTURAL FIRE PROTECTION
19
T E M P E R A T U R E , O F
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
=
T E M P E R A T U R E ,
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
L T T W
20
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
2.2.1.2 Mechanical Properties
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.
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ASCE
7 8 92
0759600
0021824 0 3 b
N
E
E
z
vi
v>
W
@L
I-
vi
PRINCIPLES OF STRUCTURAL FIRE PROTECTION
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
T E M P E R A T U R E ,
C
Figure 2.9 -Stren gth of some steels at high temperature.
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- - ` ` ,
` , ,
` , ,
` ` ` , ,
` ` ` ` ,
` , , ,
` ` ,
` , , - ` - ` , ,
` , ,
` ,
` , ,
` - - -
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A S C E
78 92 O759600
0021825 T 7 2
22
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
2.2.1.3 Deformation Properties
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
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A S C E
78
92 H 0759600
0 0 2 L ô 2 b
909 9
PRINCIPLES OF STRUCTURAL
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
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A S C E
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92 m
0759600 0023827
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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
-
-
PRINCIPLES OF STRUCTURAL FIRE PROTECTION
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).
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` ` ` ,
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` , , - ` - ` , ,
` , ,
` ,
` , ,
` - - -
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26 STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
T E M P E R A T U R E , F
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.
T E M P E R A T U R E ,
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.
T E M P E R A T U R E , C
Figure 2.14-Specific heat for different types of concrete.
U
+-
I
Y
2 0
-
U
0
a
rn
-
1
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A S C E 78 92 759600
002L830
3 3 T
PRINCIPLES
OF
STRUCTURAL FIRE PROTECTION
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.
2.2.2.2 Mechanical Properties
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
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ASCE
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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.
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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
PRINCIPLES OF STRUCTURAL FIRE PROTECTION
29
Figure 2.17-Influence of cement-aggregate ratio and load conditions on the
concrete strength.
T E M P E R A T U R E ,
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.
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ASCE 7 8 92
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
T E M P E R A T U R E , O F
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
T E M P E R A T U R E , C
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
T E M P E R A T U R E , C
Figure 2.19-Compressive stren gth of carbonate aggregate concrete at high
temperatures and after cooling.
T E M P E R A T U R E , F
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
T E M P E R A T U R E , C
Figure 2.20-Compressive strength of siliceous aggregate concrete at high
temperatures and after cooling.
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A S C E
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92 0759600
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PRINCIPLESOF STRUCTURAL FIRE
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31
T E M P E R A T U R E , C
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).
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A S C E
7 8 9 2 m
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0023835
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32
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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.
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A S C E 7 8
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PRINCIPLES OF STRUCTURAL FIRE PROTECTION
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.
T E M P E R A T U R E , F
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
T E M P E R A T U R E ,
C
Figure
2.24-
Expansion with temperature
of
concretes made with various
aggregates.
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T E M P E R A T U R E , O F
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
T E M P E R A T U R E ,
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.
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~
A S C E 7 8
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PRINCIPLES
OF
STRUCTURAL FIRE PROTECTION
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
T E M P E R A T U R E , C
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).
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ASCE 78 92 0759b00 0023 839 5 6 7
36
STRUCTURAL FIRE PROTECTION: MANUAL
OF
PRACTICE
T E M P E R A T U R E ,
" 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
T E M P E R A T U R E , C
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.
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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.
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38
STRUCTURAL FIRE PROTECTION: MANUAL
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
T E M P E R A T U R E ,
C
Figure
2.30-
Density of wood as a function of temperature.
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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-
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
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PRINCIPLES
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STRUCTURAL FIRE PROTECTION
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
T E M P E R A T U R E ,
C
Figure 2.32-Thermal conductivity of wood
as
a function of temperature.
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42 STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
T E M P E R A T U R E ,
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.
2.2.3.3 Mechanical Properties
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
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PRINCIPLES
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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
T E M P E R A T U R E ,
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.
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44 STRUCTURAL FIRE PROTECTION: MANUAL
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O
O
5 0 1O0 1 5 0
2 O0 250 3 0 0
T E M P E R A T U R E , C
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
T E M P E R A T U R E ,
C
Figure 2.36-Compressive strength of wood us u function of temperature.
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PRINCIPLES OF STRUCTURAL
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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.
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
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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
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.
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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.
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PRINCIPLES
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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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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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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PRINCIPLES
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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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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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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PRINCIPLES OF STRUCTURAL FIRE PROTECTION
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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PRINCIPLES OF STRUCTURAL FIRE PROTECTION
55
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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PRINCIPLES OF STRUCTURAL FIRE PROTECTION
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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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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
> 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.
REFERENCES
Abrams, M.S. (1971). "Compressive strength of concrete at temperatures to
1600°F." Temperature and Concrete, Special Publication SP-25, American Concrete
Institute, Detroit, MI.
American Institute of Steel Construction. (1970).Manual of steel construction. 7th
edition, AISC, New York, NY.
American Society
for
Testing and Materials. (1985). Standard methods offire tests
of building construction and materials, ANSIIASTM Eîî9. Philadelphia, PA.
Anderberg,
Y.
and Thelandersson,
S.
(1976). "Stress and deformation charac-
teristics of concrete at high temperatures-Experimental investigation and
material behaviour model." Bulletin
54,
Division
of
Structural Mechanics and
Concrete Construction, Lund Institute of Technology, Lund, Sweden.
Babrauskas,
V .
and Williamson,
R.B.
(1978). "The historical basis of fire resist-
ance testing-Part
I
and Part II."
Fire Technology,
14(3), 184-194; 14(4), 304-
316.
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STRUCTURAL FIRE PROTECTION:
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PRACTICE
Boring, D.E., Spence, J.C., and Wells, W.G. (1981). Fire protection through
modern building codes. American Iron and Steel Institute, Washington, D.C.
Collet,
Y.
and Tavernier, E. (1976). ”Etude des proprietes du beton soumis a
des temperatures elevees.” Groupe de Travail, “Comportement ,du Materiau
Beton en Fonction de la Temperature,” Bruxelles, Belgium.
Cruz, C.R. (1968). ”Apparatus for measuring creep of concrete at high tem-
peratures.“ PCA Research Department Bulletin
225,
Skokie, IL.
European Convention for Constructional Steelwork. (1983). “European rec-
ommendations for the fire safety of steel structures.” ECCS-Technical Com:
mif fee
3 , Elsevier, Amsterdam, The Netherlands.
European Convention for Constructional Steelwork. (1981). “European rec-
ommendations for the fire safety of steel structures.” Level I: Calculation of
the Fire Resistance of Load Bearing Elements and Structural Assemblies Ex-
posed to the Standard Fire,
Technical Committee
3-Fire
Safety of Steel
Structures,
Delft, Netherlands.
FIP/CEB. (1978). “FIPCEB Report on Methods of Assessment of Fire Resistance
of Concrete Structural Members.” Wexham Springs, Great Britain.
Gerhards, C.C. (1982). Effect
of
moisture content and temperature
on
mechan-
ical properties of wood: an analysis of immediate effects.
Wood and Fiber,
Hadvig, S. (1981). Charring of wood in buiiding fires. Technical University
of
Denmark, Lyngby, Denmark.
Hall, G.S., Saunders, R.G., Allcorn, R.T., Jackman, P.E., Hickey, M.W., and
Fitt R. (1971). Fire performance of timber-A literature survey. Timber Research
Development Association, High Wycombe, England.
Harada, T. (1961). Research
on
fire proof of concrete and reinforced concrete construc-
tion.
Tokyo Institute of Technology, Tokyo, Japan.
Harmathy, T.Z. (1967). “A comprehensive creep model.”
Journal of Basic Engi-
neering,
Transactions of the American Society for Mechanical Engineering,
Vol. 89.
Harmathy, T.Z. (1970). ”Thermal properties of concrete at elevated tempera-
tures.”
ASTM Journal
of
Materials,
5(1),
47-74.
Harmathy, T.Z. (1983). Properties of building materials at elevated temperatures.
National Research Council Canada, NRCC 20956.
Harmathy, T.Z., and Allen, L.W. (1973). ”Thermal properties of selected ma-
sonry unit concretes.” Journal of the American Concrete ln dus fr y, No. 70.
Harmathy, T.Z. and Stanzak, W.W. (1970). ”Elevated temperature tensile and
creep properties of some structural and prestressing steels.” Fire Test Per-
formance STP-464,
American Society for Testing and Materials, Philadelphia,
PA.
Hebert,
R.V.
(1975). “Steel and Fire Safety as Required in the National Building
Code of Canada.” Canadian Steel Industries Construction Council Manual.
14(1), 4-36.
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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
PRINCIPLES OF STRUCTURAL FIRE PROTECTION
61
International Standard. (1975). Fire Resistance Tests-Elements of Building
Construction.
I S 0 834.
Knudson, R.M., Schniewind, A.P. (1975). "Performance of structural wood
members exposed to fire."
Forest Products Journal,
25(2).
Lie, T.T. (1972). "Fire and buildings." Applied Science Publishers, Ltd., Lon-
don.
Lie, T.T. and Stanzak, W.W. (1974). "Empirical method for calculating fire
resistance of protected steel columns."
Engineeying Journal,
Transactions of
the Canadian Society for Civil Engineering, Vol. 57.
Lie, T.T. and Stanzak, W.W. (1973). "Fire resistance of protected steel columns."
Engineering Journal,
American Institute of Steel Construction, 10(3), 82-94.
Magnusson, S.E., Pettersson,
O.,
and Thor, J. (1976). "Fire engineering design
of steel structures."
Publication
No.
50,
Swedish Institute of Steel Construction,
Stockholm, Sweden.
Maku, T. (1954). "Studies on the heat conduction in wood." Kyobo University,
Bulletin of the Wood Research Institute,
13, 1-80.
Malhotra, H.L. (1956). "The effect of temperature on the compressive strength
of concrete."
Magazine of Concrete Research,
8(23), 85-94.
Mikkola, E. (1990). "Charring of wood."
V T T Research Reports 68 9,
Espoo: Tech-
nical Research Centre of Finland, Espoo, Finland.
Montle, J.F. and Mayhan, K.G. (1974). "The role of magnesium oxychloride as
a fire-resistive material."
Fire Technology,
10(3), 201-210.
Nussbaum, R. (1988). "The effect of low concentration fire retardant impregna-
tions on wood charring rate and char yield."
Journal of Fire Sciences,
6, July/
August.
Ouchi, T. (1988). "Thermal conductivity of wood at high temperatures."
Pro-
ceedings of the 1988 International Conference on Timber Engineering,
Forest Prod-
ucts Research Society, 441-447.
Pettersson,
O.
(1965). "Structural fire engineering research today and tomor-
row." Acta Polytechnica Scandinavica,
Civil Engineering and Building Construc-
tion Series No. 33,
Stockholm, 42-55.
Roberts, A.F. (1971). "The heat of reaction during the pyrolysis of wood."
Combustion and Flame,
17.
Saito, H. (1965). "Explosive spalling of prestressed concrete in fire." BRI Oc-
casional Report No. 22,
Building Research Institute, Ministry of Construction,
Tokyo, p. 18.
Schaffer,
E.L.
(1967). "Charring rate of selected woods-Transverse to grain."
U.S.
Forest Service Research Paper FPL69,
U.S. Dept. Agri., For. Prod. Lab.,
Madison, WI.
Schaffer,
E.L.
(1974). "Effect of fire retardant impregnations on wood charring
rate." Journal of Fire and Flammability, Fire Retardant Chemical Supplement,
1. 96.
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62
STRUCTURAL
FIRE
PROTECTION: MANUAL
OF
PRACTICE
Schaffer,
E.L.
(1984). “Structural fire design: wood.”
U.S. Forest Service Research
Paper FPL 450, U.S.
Dept. Agri., For. Prod. Lab., Madison, WI.
Schaffer,
E.L.
(1973). “Effects
of
Pyrolytic Temperatures on the Longitudinal
Strength
of
Dry Douglas-fir.”
A S T M
J.
of
Testing and Evaluation, 1(4),
319-329.
Schaffer,
E.L.
(1978). “Influence
of
heat on the longitudinal creep of
dry
Douglas-
fir.”
Structural Use of Wood in Adverse Environments,
Robert W. Meyer, and
Robert.
M.
Kellogg, eds. Van Nostrand Reinhold
Co.,
New York, NY.
Schaffer,
E.L.
(1977). “State of structural timber fire endurance.”
Wood and Fiber.
Tang, W.K. (1967). “Effect of inorganic salts on pyrolysis of wood, alpha-
cellulose, and lignin determined by dynamic thermogravimetry.”
U . S . Forest
Service Research Paper FPL-71, U.S.
Dept. Agri., For. Prod. Lab., Madison, WI.
U S D A Agr. Hdbk. No.
72. (1987). “Wood handbook: Wood as an engineering
material” Superintendent of Documents, Washington, D.C.
U.S.
Federal Emergency Management Agency. (1980).
Multiprofection design
manual,
Fire Section, TR
20,
Part
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
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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.
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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
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A S C E 78 92 0 7 5 9 b 0 0
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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.
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A S C E 7 8
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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
7 8 92 0
0 7 5 9 b 0 0
0023873 952
68
STRUCTURAL
FIRE
PROTECTION: MANUAL OF PRACTICE
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.
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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)
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70 STRUCTURAL
FIRE
PROTECTION: MANUAL OF PRACTICE
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
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A S C E 7 8
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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
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72 STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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-
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FIRE RESISTANCE OF BUILDING ELEMENTS 73
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
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ASCE
78 92
m
0 7 5 9 b 0 0
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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.
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` , ,
` ,
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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),
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STRUCTURAL FIRE PROTECTION: MANUAL
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
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FIRE RESISTANCE
OF
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.
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
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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.
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STRUCTURAL
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PROTECTION: MANUAL OF PRACTICE
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
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FIRE RESISTANCE
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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)
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82
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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)
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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
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78
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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)
Normal weight concrete
(Dominantly carbonate
aggregate)
Lightweight concrete
04 STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
-
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- -
` ` ,
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A S C E 78 92
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075îb00 002L88B L5 b
m
FIRE RESISTANCE OF BUILDING ELEMENTS
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
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A S C E
78 92 m 0759b00
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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
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- - ` ` ,
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ASCE 78 92
0759600 O023890 804
D
FIRE RESISTANCEOF BUILDING ELEMENTS
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.
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A S C E
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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.
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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;
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A S C E 7 8
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0757600 0021893
513
90 STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
NORMAL WEIGHT CONCRETE
I
CARBONATE
OR /
NORMAL WEIGHT CONCRETE
(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.
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- - ` ` ,
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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.
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A S C E
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3 î b
2 0
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92
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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 ' '
T E M P E R A T U R E , C
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
FIRE RESISTANCE OF BUILDING ELEMENTS
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).
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A S C E
78
92
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L b 9
STRUCTURAL
FIRE
PROTECTION: MANUAL
OF
PRACTICE
4
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FIRE RESISTANCE OF BUILDING ELEMENTS
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STRUCTURAL
FIRE
PROTECTION: MANUAL
OF
PRACTICE
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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A S C E
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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A S C E 78
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FIRE RESISTANCE
OF
BUILDING ELEMENTS
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STRUCTURAL FIRE PROTECTION: MANUAL
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A S C E
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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A S C E 7 8
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STRUCTURAL FIRE PROTECTION: MANUAL
OF
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STRUCTURAL FIRE PROTECTION:
MANUAL
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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
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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
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114 STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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.
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92 0759b00
O021918 713
FIRE RESISTANCE OF BUILDING ELEMENTS 115
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.)
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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
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A S C E 78
92 m 0759600
0021921
208
m
118
STRUCTURAL FIRE PROTECTION: MANUAL
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.
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A N Y
STEEL
S E C T I O N
FIRE RESISTANCE OF BUILDING ELEMENTS
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
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120 STRUCTURAL
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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.
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FIRE RESISTANCE OF
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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
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122
STRUCTURAL
FIRE
PROTECTION: MANUAL OF PRACTICE
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. 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
C O N C R E T E C O N C R E T E
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
C O N C R E T E C O N C R E T E
. ~ .
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
are more favorable than those of siliceous aggregate concrete from the
point of view of heat transmission. Therefore, it takes more time to
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ASCE 7 8 92 0759b00 0023926 8 9 T D
FIRE RESISTANCE OF BUILDING ELEMENTS
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
C O N C R E T E C O N C R E T E
.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
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STRUCTURAL
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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
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ASCE
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FIRE RESISTANCEOF BUILDING ELEMENTS
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.
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ASCE 7 8 92 0 7 5 9 b 0 0
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STRUCTURAL FIRE PROTECTION: MANUAL
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(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).
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FIRE RESISTANCE OF
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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
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STRUCTURAL FIRE PROTECTION: MANUAL
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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.
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FIRE
RESISTANCE
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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.
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130
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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).
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FIRE RESISTANCE OF BUILDING ELEMENTS
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
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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.
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FIRE RESISTANCE
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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.
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
REFERENCES
Abrams,
M.S.,
et al. (1976). "Fire endurance of continuous reinforced concrete
beams." Prelimina
y
Report of the Ten th Congress of the International Association
for Bridge and Structural Engineering, Portland Cement Association, Skokie, IL.
Abrams,
M.S.
and Gustaferro, A.H. (1969). "Fire endurance of two-course floors
and roofs."
Journal of the American Concrete Insti tute ,
66(2), 92-102.
Abrams, M.S., Gustaferro, A.H. and Salse, E.A.B. (1971). "Fire tests of concrete
joist floors and roofs." Research and Development Bulletin No. RD006.01B, Port-
land Cement Association, Skokie, IL.
Allen, L.W. and Harmathy, T.Z. (1972). "Fire endurance of selected concrete
masonry units." Journal of the American Concrete Insti tute , 69,
American Concrete Institute. (1987). Guide for determining the fire endurance of
concrete elements. AC1
21
6R81.
American Insurance Services Group. (1985). Fire resistance ratings. New York,
NY.
American Iron and Steel Institute. (1976).Designing fire protection or steel trusses.
Washington, D.C.
American Iron and Steel Institute. (1980).Designing fire protection or steel columns.
Third Edition, Washington, D.C.
Amencan Iron and Steel Institute. (1981). Fire Resistance Ratings of Load-Bearing
Steel Stud Walls. Washington,
D.C.
American Iron and Steel Institute. (1984). Design ing fire protection for steel beams.
Washington, D.C.
American Society for Testing and Materials. (1985).Standard Methods of Fire Tests
of Building Construction and Materials, AN SII AS TM E l 19-83, Philadelphia, PA.
Brick Institute of America. (1974). "Technical notes on brick construction."
Technical Note No. 16, McLean, VA,
Canadian Standards Association. (1984). Code for the engineering design of wood,
C S A standard 086, Rexdale, Ontario.
Culver, C.G., Aggarwal,
V .
and Ossenbruggen,
P.
(1973). "Buckling of columns
at elevated temperatures." Journal of the Structural D ivision, ASCE, 99(ST4),
Fitzgerald, R.W. (1986). "Structural integrity during fire." Fire Protection iia nd -
book,
National Fire Protection Association, 16th ed., Section 7, Chapter 8,
Quincy, MA. 7-82 to 7-108.
Flemington, R.A. (1980). "Fire protection of hollow structural section." Technical
Bulletin
21,
Stelco Inc., Toronto, Canada.
Gustaferro, A.H. (1970). "Temperature criteria at failure."
Fire Test Performance,
STP-464,
American Society for Testing and Materials, Philadelphia, PA, 68-
84.
715-726.
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FIRE RESISTANCE
OF
BUILDING ELEMENTS
135
Gustaferro, A.H. and Selvaggio, S.L. (1967). "Fire endurance of simply-supported
prestressed concrete slabs." Journal, Prestressed Concrete Institute, 12(1), 37-
52.
Gypsum Association. (1978). Fire resistance design manual. Evanston, IL.
Harmathy, T.Z. (1965). "Ten rules of fire endurance rating." Fire Technology,
1(2), 93-102.
Harmathy, T.Z. (1970). "Thermal performance of concrete masonry walls and
fire." Special Technical Publication 464, American Society for Testing and Ma-
terials, Philadelphia, PA.
Institute for Structural Materials and Building Structures. (1959). "Fire test of
a simple, statically indeterminant beam." Delft. (English Translation, SLA
Translation Center, John Crerar Library, Chicago.)
International Committee for the Study and Development of Tubular Structures.
(1976). CIDECT Document 15A76136.
Issen, L.A., Gustaferro, A.H. and Carlson, C.C. (1970). "Fire tests of concrete
members: An improved method for estimating restraint forces." Fire Test
Performance, STP-464, American Society for Testing and Materials, Philadel-
phia, PA, 153-185.
Jeanes, David C. (1985). "Application of the computer in modelling fire en-
durance of structural steel floor systems." Fire Safety Journal, 9.
Kìipstein, K.H. (1980). "Behavior of cold-formed steel studs in fire tests."
Pro-
ceeding, Fifth Specialty Conference, University of Missouri-Rolla.
Lie, T.T. (1972). Fire and Buildings. Applied Science Publishers Ltd., Barking,
England.
Lie, T.T. (1977). "A method for assessing the fire resistance of laminated timber
beams and columns." Canadian Journal of Civil Engineering, 4(2), 161 169.
Lie, T.T. (1978). "Calculation of the fire resistance of composite concrete floor
and roof slabs." Fire Technology, 14(1).
Lie, T.T. (1984). "A procedure to calculate fire resistance of structural members."
Fire and Materials,
8(1).
Lie, T.T. and Allen,
D.E.
(1972). "Calculation of the fire resistance of reinforced
concrete columns." Technical Paper No. 378, Division of Building Research,
National Research Council of Canada.
Lie, T.T. and Harmathy, T.Z. (1974). "Fire endurance of concrete-protected
steel columns." Journal of the American Concrete Institute, ( i) ,
Lie, T.T., Lin, T.D., Allen, D.E. and Abrams,
M.S.
(1984). "Fire resistance of
reinforced concrete columns." Technical Paper
No.
378 Division of Building
Research, National Research Council of Canada.
Lie, T.T. and Stanzak,
W.
W. (1973). "Fire resistance of protected steel columns."
Engineering Journal,
American Institute of Steel Construction, 10(3),
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136 STRUCTURAL
FIRE
PROTECTION: MANUAL OF PRACTICE
Lin, T.D. and Abrams, Melvin S. (1983). ”Simulation of realistic thermal re-
straint during fire test of floors and roofs,” Fire Safety of Concrete structures,
SP-80, American Concrete Institute, Detroit, pp. 1-68.
McGuire, J.J., Stanzak, W.W., and Law, M. (1975). “The scaling of fire resistance
problems.”
Fire Technology,
ll(3).
Miller, G.D. and Ife, L.W. (1974). “Steel Fire Protection: An Engineering Ap-
proach.‘’ Stelco Inc., Toronto, Canada.
National Research Council of Canada. (1990).
Supplement to the National Building
Code of Canada,
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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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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STRUCTURAL
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PROTECTION: MANUAL
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PRACTICE
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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ASCE
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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
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d d d
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STRUCTURAL
FIRE
PROTECTION: MANUAL
OF
PRACTICE
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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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.
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STRUCTURAL FIRE PROTECTION: MANUAL
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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
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m
FIRE TEMPERATURE-TIME RELATIONS
~ 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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144
STRUCTURAL
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PROTECTION: MANUAL OF PRACTICE
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.
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ASCE 7 8 92 0 7 5 9 b 0 0
0023948
450
FIRE TEMPERATURE-TIME RELATIONS
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)
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A S C E
78
92
0759600
0023947 397
146
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
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O O
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O O O
w
O
d hl O 00
.o
4
-4 d
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A S C E
78
92
0 O759600
0023950 O09
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
92
0759600
0023953 T 4 5
I 48
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
I I
I
I
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\
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l
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\:
I
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A S C E
7 8
92
W
0 7 5 9 b 0 0 0023952 983
W
FIRE TEMPERATURE-TIME RELATIONS 149
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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150
STRUCTURAL
FIRE
PROTECTION: MANUAL
OF
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
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U N O W \o U N
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íll
Vä
3
dW
31
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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.
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A S C E 78 92
0 7 5 9 b 0 0
0 0 2 1 9 5 5 b90
STRUCTURAL FIRE PROTECTION: MANUAL
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
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O O O O
w
N O 00
\o
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2
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3,
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d
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31
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A S C E
78 92
W
0759600 0 0 2 1 9 5 6 5 2 7
W
FIRE TEMPERATURE-TIME RELATIONS 153
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
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A S C E
78
92
m
O759600 0023957
4 b 3
m
154 STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
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` ` ` , ,
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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
FIRE TEMPERATURE-TIME RELATIONS 155
-
- 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
PROTECTION: MANUAL OF PRACTICE
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
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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
FIRE TEMPERATURE-TIME RELATIONS 157
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.
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A S C E 78
92 D
0759600 002LîbL
994
158
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
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ASCE
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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
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A S C E
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60
STRUCTURAL FIRE PROTECTION: MANUAL
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.
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CALCULATION
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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.
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A S C E
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
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A S C E
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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 +
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ASCE 78
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164
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
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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
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A S C E 7 8 9 2
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CALCULATION
OF
TEMPERATURE AND FIRE RESISTANCE
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
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` ,
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A S C E 78 92 0 7 5 9 b O O 0023973 8 3 3
168
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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.
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A S C E 78 7 2
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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]
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A S C E 78
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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.
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` , ,
` ,
`
, ,
` - - -
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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
TEMPERATURE AND FIRE RESISTANCE
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).
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A S C E
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
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CALCULATION OF TEMPERATURE AND FIRE RESISTANCE
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.
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m
CALCULATION
OF
TEMPERATURE AND FIRE RESISTANCE
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
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176
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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.
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F I
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CALCULATION OF TEMPERATURE AND FIRE RESISTANCE
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.)
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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-
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CALCULATION OF TEMPERATURE AND
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
In order to ensure 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; 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-
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
With the aid of equations
(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.
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CALCULATION OF TEMPERATURE AND FIRE RESISTANCE
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
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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:
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CALCULATION OF TEMPERATURE AND FIRE RESISTANCE
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
In order to ensure that any error existing in the solution at some
time level will not be amplified in the subsequent calculations, a stability
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
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A S C E i 8
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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).
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A S C E
78 92 0759600 0021988 037
CALCULATION OF TEMPERATURE AND FIRE RESISTANCE
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,
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A S C E 7 8 92 0759600 O 0 2 3 9 8 9 T 7 3
186
STRUCTURAL FIRE PROTECTION: MANUAL
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:
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ASCE
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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
CALCULATION OF TEMPERATURE AND FIRE RESISTANCE
187
For the center concrete layer, the temperature rise at time T
=
( j
+ AT, is given by:
5.1.7.6 Stability Criterion
In order to ensure 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; 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
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A S C E 78
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188
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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:
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A S C E
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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)
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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
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
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A S C E
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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
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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).
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ASCE 7 8 92 O ï S î b O O
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CALCULATION OF TEMPERATURE AND FIRE RESISTANCE
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
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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.
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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.
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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.
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198
STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
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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
TEMPERATURE AND FIRE RESISTANCE
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:
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A S C E 78 92
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STRUCTURAL FIRE PROTECTION: MANUAL
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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,
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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.
5.2.3 Fire Resistance
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
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- ` , ,
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202
A S C E
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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.
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A S C E 78 92 0759600 O022006 750 E
CALCULATION OF TEMPERATURE AND FIRE RESISTANCE
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
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A S C E 78 92 0759600 0022007 b î 7
204
STRUCTURAL FIRE PROTECTION: MANUAL
OF
PRACTICE
With the aid of equations
(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
With the aid of equations
(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
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A S C E
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92
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I where
CALCULATION
OF
TEMPERATURE AND FIRE RESISTANCE
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,
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STRUCTURAL
FIRE
PROTECTION: MANUAL OF PRACTICE
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.)
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A S C E 78
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CALCULATION OF TEMPERATURE AND FIRE RESISTANCE
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
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208
STRUCTURAL FIRE PROTECTION: MANUAL
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
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ASCE 78 92 0 7 5 î b 0 0
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CALCULATION OF TEMPERATURE AND
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
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STRUCTURAL FIRE PROTECTION: MANUAL OF PRACTICE
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
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A S C E 78
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CALCULATION OF TEMPERATURE AND FIRE RESISTANCE
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
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A S C E 78 92 0757600 0022015
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212
STRUCTURAL FIRE PROTECTION: MANUAL
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).
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CALCULATION
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- - ` ` ,
` , ,
` , ,
` ` ` , ,
` ` ` ` ,
` , , ,
` ` ,
` , , - ` - ` , ,
` , ,
` ,
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` - - -
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6th Edition, World Press Conference,
London, England.
Stanzak, W.W. and Lie, T.T., (1973). “Fire resistance of unprotected steel col-
umns.’’
Journal of the Structural Divis ion,
ASCE, 99(ST5), 9719.
Tinney,
E.R.
(1965).
Tenth Symposium Int.
on
Combustion,
The Combustion In-
stitute, Pittsburg, PA.
Trinks, W., and Mawhinney, M.W. (1961). industrial furnaces. Carnegie Inst.
Technology, Wiley, New York, N.Y.
White,
R.H.
(1988). ”Chamng rate of different wood species.” Ph.D. Disser-
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E119 Exposure.”
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28(1), 5-30.
WI, 432-440.
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- - ` ` ,
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` , ,
` ,
` , ,
` - - -
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A S C E 78 72
W
0 7 5 9 b 0 0
O022020
020
CALCULATION
OF
TEMPERATURE
AND
FIRE RESISTANCE
217
White, R.H., Schaffer,
E.L.
(1978). ”Application of CMA program to wood
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White, R.H., Schaffer, E.L. (1981). ”Transient moisture gradient
in
fire-exposed
wood slab.” Wood and Fiber, 13(17), 296.
White, R.H., Schaffer, E.L., Woeste, F.E. (1984). “Replicate fire endurance tests
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Wickstrom, U. (1979). ”TASEF-2, A computer program for temperature analysis
of structures exposed to fire.” Report
No.
79-2, Lund Institute of Technology,
Department of Structural Mechanics, Lund, Sweden.
Williams-Leir, G. (1973). “Analytical equivalents of standard fire temperature
curves.” Fire Technology, 9(2), 132-136.
Williamson, T.G. (1982).
Evaluation, maintenance, and upgrading
of
wood structures.
American Society of Civil Engineers, New York,
N.Y.
Witteveen, J., Twilt,
L.
and Bylaard,
F.S.K.
(1977). “The stability of braced and
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umn Strength, Liege.
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(1967).The fin iteelem ent method in structural
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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
STRUCTURAL FIRE PROTECTION: MANUAL
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
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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)
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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
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` ` ,
` , ,
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` , ,
` ,
` , ,
` - - -
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A S C E 78 92 0759600 O022026 549 m
MATERIAL PROPERTIES AND PHYSICAL CONSTANTS
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,
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A S C E 78
92 0759600 0022028
311
MATERIAL PROPERTIES AND PHYSICAL CONSTANTS
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
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226
STRUCTURAL
FIRE
PROTECTION: MANUAL OF PRACTICE
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
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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-'
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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
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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,
temperature calculation 183
Boundary slab and asbestos pad,
temperature calculation 182-
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
93-110; steel 63-77; timber
111-117
23
i
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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
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A S CE 7 8 92 W 0759600 O022035 5 5 1
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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,
resistance calculation 193-194
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
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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;
extension rules and guide-
lines 117-136; testing 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&-2ۈ -
Expanded shale, siliceous and car-
bonate aggregate concretes,
166-169
stress-strain relations, formula
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,
temperature calculation 159-
192; circular concrete columns
176- 180; circular concrete
filled steel columns 184-188;
composite concrete floor and
17-24; wood 36-45
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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
of structural members 193-
211; nomenclature 218-221;
remarks 21 1-212; temperature
of fire exposed members 159-
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;
extension rules and guide-
lines 117-136; testing 117
Fire resistance, calculation, building
elements 63-117; concrete
77-110; concrete examples
93-110; steel 63-77; timber
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,
resistance calculation 193-194
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
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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;
temperature calculation 165
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-
crete 193-201; concrete filled
tubular steel columns 201-
204; steel 193; wood 204-211
Members, structurai, calculation of
temperature and fire resis-
tance 159-221; fire resistance
223-225
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ASCE
78 92 W
O759600
O022039 I T 7
D
INDEX 237
Members, structurai,
(continued)
of structural members 193-
21
1;
nomenclature 21
8-
221;
remarks 21 1-212; temperature
of fire exposed members 159-
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
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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
93-110; steel 63-77; timber
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
resistance calculation 193-194
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,
stress-strain relations, formula
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
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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-
crete 193-201; concrete filled
tubular steel columns 201-
204; steel 193; wood 204-211
Structural members, calculation of
temperature and fire resis-
tance 159-221; fire resistance
of structural members 193-
211; nomenclature 218-221;
remarks 21 1-212; temperature
of fire exposed members 159-
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
of structural members 193-
211; nomenclature 218-221;
remarks 211-212; temperature
of fire exposed members 159-
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
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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