1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
-
Upload
sukhwinder-singh-gill -
Category
Documents
-
view
34 -
download
0
description
Transcript of 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
1/97
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
2/97
DESIGN FOR FIRE RESISTANCE
OF
PRECAST PRESTRESSED CONCRETE
SECOND EDITION
by
Armand H. Gustaferro and Leslie D. Martin
Prepared for thePCI FIRE COMMITTEE (1988)
Paul C. Breeze, Chairman
James P. BarrisRonald G. BurgLouis T. CaimiStanley CummingWilliam L. GambleJames R. Gaston*Armand H. Gustaferro*
David W. Hanson*Robert T. HaugThomas W. HedbergDaniel P. Jenny
Milo J. NimmerWalter J. Prebis*Thomas J. Rowe
*Past Chairman
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
3/97
MNL-124-89
Copyright 1989By Prestressed Concrete Institute
First Edition, first printing, 1977
First Edition, second printing, 1982
Second Edition, 1989
All rights reserved. This manual or any part thereof may
not be reproduced in any form without the written permission
of the Prestressed Concrete Institute.
ISBN 0-937040-41-X
Printed in U.S.A.
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
4/97
- v -
1988 COMMITTEE STATEMENT
The Committee is indeed pleased that soon after its initial publication, theInternational Conference of Building Officials issued an evaluation report (No.3264) on the use of the manual. Similarly, the Building Officials and Code Administrators International issued Research Report No. 78-49 in 1979. The 1984BOCA Basic/National Building Code and the 1987 BOCA National Building Codereference the manual and permit its use for determining the f ire resistance ratingsof precast prestressed concrete. Other codes such as the South Florida BuildingCode and the Wisconsin Administrative Code also permit use of the manual.
It has been gratifying to the Committee that the manual has gained such broad
acceptance.
PC/ Fire Committee
COMMITTEE STATEMENT
The purpose of this manual is to provide an analytical method of evaluatingthe fire endurance of structures made of precast and prestressed concrete. The
manual brings together information from many sources, and presents the data
in a convenient form. Example problems illustrate the use of the design aids and
principles outlined in the text.
In recent years, building officials, architects, and engineers have become increasingly aware of the unreliability of results of fire tests. Through the use ofthe engineering principles outlined in this manual, a greater degree of reliabilityin predicting fire endurance of structures or assemblies can be achieved.
It is the hope of the PCI Fire Committee that building codes will adopt provisions permitting engineering analyses as the basis for estab lishing the fire endurance of a structure.Building codes should encourage the use of such engineeringanalyses by permitting a reduction in the fire rating requirements when suchanalyses are performed.
The Committee feels that this manual represents a landmark contribution todesigners, building officials, and insurance underwriters who are concerned withfire safety of buildings . Not only does this manual present a rational design approach for the safety of precast prestressed concrete structures, but also it placesprecast and prestressed concrete in the forefront of a long overdue frontier -that of structural design for fire resistance.
PC! Fire Committee
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
5/97
-vi-
PREFACE
The fact that the strengths of steel and concrete diminish during the sustained
high temperatures of a building fire is well known to both ex perts and laymen in
the fields of fire protection and structural engineering . It may be something of a
revelation that the principles of structural engineering are still valid, regardless of
the intensity or duration of a fire.
After the development and acceptance of ultimate strength design procedures
for reinforced concrete, it seemed apparent that the same principles would apply at
high temperatures, providing the strength of the materials at high temperatures
were utilized. An extensive research program at the Portland Cement Association
Research and Development Laboratories in Skokie, Illinois, during the 1960's de m
onstrated that the strength of these materials, and hence the ultimate capacity and
fire endurance period, could be accurately predicted. This has led to the rationaldesign procedures described in this manual. Application of these design procedures
to result of tests conducted at PCA, Underwriters Laboratories, Inc., and elsewhere
have shown that the fire endurance period of a concrete assembly can be predicted
with about the same precision as the load carrying capacity of an assembly tested
at room temperature.
Designs based on this method of analysis have been approved by several build
ing officials and government agenc ies. Among the first to recognize this method
was the Wisconsin Administrative Code.Although,to our knowledge, this is the first
published text on this subject, an earlier version in loose-leaf fo rm was prepared by
the authors for the Wisconsin Precast Prestressed Concrete Association.
The authors wish to express their appreciation to the Prestressed Concrete In
stitute for sponsoring the publication of this document,and especially to the members of the PCI Fire Committee task group for their va luable comments and review
of this text. These members were: William D. Givens, Chairman, George Adam, Gary
Ehlenbeck, James R. Gaston, and David J. LaGue.
The authors also thank the Portland Cement Asso ciation for the valuable re
search work which led to this development, and to Underwriters Laborato ries, Inc.,
for making data available which corroborated much of the research.
While this manual pertains to the design for fire resistance of precast, pre
stressed concrete, the principles and techniques are based upon general structura l
des ign theory and are therefore applicable to other structural materials.
Armand H. Gustaferro
Leslie D. Martin
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
6/97
- vii -
PREFACE TO SECOND EDITION
The use of this manual for eleven years indicated that improvements could be
made without changing the character of the manual. Several parts have been re
written to clarify the text and some new material has been added. Most changes
were editorial.
Fire tests and research studies conducted since 1977 have confirmed the prin
ciples outlined in the manual. For example, comprehensive series of tests designed
to study the shear behavior of concrete beams exposed to fire conducted in Ger
many and in America showed that beams which are designed adequately for shear
under normal conditions do not fail in shear when exposed to fire. Thus, no change
was made in the text, except to reference the reports of those tests.
A section has been added on precast concrete cover sections used to protect
steel columns. In addition, the section on post-fire examination has been broadened.Thanks are due to the PCI Fire Committee for suggesting many of the changes
and for reviewing the revisions. Special thanks to Walter J. Prebis, David W. Hanson,
Daniel P. Jenny, and Paul C. Breeze for their valuable comments and support.
Armand H. Gustaferro
Leslie D. M artin
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
7/97
-9-
TABLE OF CONTENTS
Committee Statement ................................................................................................................v
Preface ..............................................................................................................................................vi
Table of Contents ......... . .............., ........................................................ ix
Notation .............................................................................................................................................1
Glossary of Terms .......................................................................................................................... 3
CHAPTER 1 GENERAL ..... ............... . . . . . . .. ............... . . . . . . . . ............. 5
1.1 Standard Fire Tests of Building Construction and Materials ........ . .. 5
1.1.1 End Point Criteria .. ..................... .. .. ................. .. .. 7
1.2 Application Of Structural Engineering
Princ iples to Design For Fire Safety 7
CHAPTER 2 PROPERTIES OF STEEL AND
CONCRETE AT HIGH TEMPERATURES ................................. 9
2.1 Steel ..................................................................... 9
2.2 Concrete ................................................................. 9
CHAPTER 3 TEMPERATURES WITHIN CONCRETE
SLABS AND BEAMS DURING FIRES .......................... .. . ...... 11
3.1 Slabs ........ . . . . .............. . ... . ...................... . . . . . .......... 11
3.2 Beams ..... .. .. .......... .. . . . . . . . ................... . . . . . . .............. 11
3.2.1 Beam Isotherm Diagrams .............. .. .. .. .. .. ....... ...... .. . 11
3.3 Spray-Applied Coatings ......................... .. .. ............. .. .. ... 13
CHAPTER4 SIMPLY SUPPORTED SLABS AND BEAMS . ..................... ....... 15
4.1 Structural Behavior ...................... ,.............................. 15
4.2 Test Ver if ication ............ .. . . . .................. ...................... 164.3 Design A ids . . . . ......................................................... 16
CHAPTER 5 CONTINUOUS BEAMS AND SLABS .................................... 21
5.1 Structural Behavior . . . . . ............................ ...... .............. 21
5.2 Test Verification .. . . . . ...................................... ............. 21
5.3 Calculation Procedures ................ . . .. ....... ....... . . . . . .... ....... 23
5.4 Detailing Precautions ......... .. . . ................. . . ... . . . ............ . 24
CHAPTER 6 FIRE ENDURANCE OF SLABS AND BEAMS
IN WHICH RESTRAINT TO THERMAL EXPANSION OCCURS .. . . .. .. .. 29
6.1 Structural Behavior . ., ................... .. .. .. .. ............. .. .. ...... 29
6.2 Test Verification ... .. .. ............... .. .. .. ................. .. .......... 296.3 Ca lculation Procedures .................................... .. .. .......... 30
6.4 Interpretation of Appendi x X3 of ASTM E119-88 ............... ........ 33
CHAPTER 7 FIRE ENDURANCE DETERMINED
BY HEAT TRANSMISSION REQUIREMENTS OF ASTM E119 .......... 39
7.1 General ....., . ........................................................... 39
7.2 Single Course Slabs ........................... .......................... 39
7.3 Multi-Course Assemb Iies ........ . . . . . . .............. ... . . . . . . .. ........ 41
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
8/97
-10
CHAPTER 8
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
CHAPTER 9
9.1
9.2
9.3
ARCHITECTURAL PRECAST CONCRETE ........................................................ 47
General.................................................................................................................. 47
One- and Two-Course Panels ........................................................................... 47
Equivalent Thickness .......................................................................................... 47
8.3.1 Hollow-Core Panels ................................................................................ 47
8.3.2 Ribbed Panels ......................................................................................... 49Sandwich Panels ................................................................................................. 50
Window Walls ................................................................................................. 52
Treatment of Joints ............................................................................................. 53
Precast Concrete Column Covers ..................................................................... 53
Detailing Precautions .......................................................................................... 57
8.8.1 Fire Stopping Between Floors and Wall Panels .................................. 58
MISCELLANEOUS PROBLEMS ......................................................................... 59
Protection of Openings .................................................................................. 59
Special Use Structures ....................................................................................... 62
Protection of Connections and Joints ............................................................... 62
9.3.1 Connections .............................................................................................. 629.3.2 Joints ......................................................................................................... 63
9.4 Post-Fire Examination ....... . . . . ............... . . . . .... . . . . .... . 64
CHAPTER 10
APPENDIX A
APPENDIX B
SELECTED BIBLIOGRAPHY . . . ............ . .... . . . . ............. 67
71
DERIVATION OF EQUATIONS AND DESIGN AIDS...................................... 83
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
9/97
-1-
NOTATION
a = depth of equivalent rectangular stress block
at ultimate load, and is equal to A P.fPJ0.85
fcb or A.fy!0.85 f b (in.)
A = cross sectional area of a member sub-
jected to thrust (in.2) Chapter 6
Ac = cross sectional area of a concrete member
(in.2)
As = area of reinforcing steel (in.2)
AP = area of prestressing steel (in.2)
b = width of compression zone (for use in flex-
ural calculations) (in.)
b = width of a beam or joist at centroid of re-inforcement (for use in estimating tem
perature during fire exposure) (in.)
c,, c2 = width of space between end of member
and vertical face of restraining member (in.)
Fig. 6.6
d = distance between centroid of reinforce
ment and extreme compression fiber (in.)
dT = distance between line of action of thrust
at the supports and extreme compression
fiber (in.) Chapter 6
e = distance between line of action of thrust
and the centroidal axis (in.) Chapter 6
E = modulus of elasticity of concrete (psi -or
ksi)
f = compress ive strength of concrete (psi or
ksi)
fcb = concrete fiber stress at bottom fiber (psi)
fps = stress in prestressing steel in flexural
member at ultimate load (ksi)
fpu = ultimate strength of prestressing steel (ksi)
f. =stress inhot-rolled steel (ksi)
fv = yield strength of hot-rolled steel (ksi)
h = overall depth of flexural member (in.)
h = unbraced height of column (in.) Chapter 6
H = height of wall (ft) Chapter 6
= moment of inertia of cross section (in.4)
lc r = moment of inertia of cracked cross section
of flexural member ( in.
4
kh = coefficient of horizontal soil force (psf)
kP = passive soil pressure (psf)
I = span length (ft or in.)
I = heated length of a flexural member (in.)
Chapter 6
!:::./ = increase in length due to thermal expan-
sion (in.) Chapter 6
M = service load bending moment ; in genera l
M = Md + M, in which subscripts d and Iindicate dead and live loads (in.-k or ft-k)
Mn = nominal moment strength (in.-k or ft-k)
MT = moment due to thrust resulting from re
straint of thermal expansion (in.-k or ft-k)
Chapter 6
Mu = ultimate resisting bending moment (in.-k
or ft-k)
P,, P2, P3 = concentrated loads applied to test
specimen (kips) Chapter 5
PP = passive soil force (lb or k ips)
R = fire endurance of a composite assembly
as determined by the criteria for temperature rise of the unexposed surface (min)
Chapters 7 and 8
R,, R2, Rn = fire endurance of one course of a
composite assembly as determined by the
criteria for temperature rise of the unex
posed surface (min) Chapters 7 and 8
s = heated perimeter of a member, i.e., that
portion of the perimeter of a section of a
member, normal to the direction of the
thermal thrust, which is exposed to fire
(in.) Chapter 6
s = rib spacing (in.) Chapter 8
t = thickness (in.)
tc = equivalent thickness (in.) Section 8.3.2
T = thermal thrust (lb or kips)
u = distance from bottom of slab or beam to
a point within the member, e.g., the dis
tance from the underside of a slab to the
center of a prestressing strand (in.)
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
10/97
-2-
= effective u, for use with wide beams (in.)
Section 4.3
= distance from the side of a beam or joist
to a point within the member (in.)
w = uniformly distributed load on a flexural
member, in general w = wd + w, in whichthe subscripts d and I indicate dead and
live loads (lb or k per ft or in.)
x = distance along length of a flexural mem
ber from a support to a point in question(in. or ft)
= distance along length of a flexural mem
ber from support to point of zero moment
(in. or ft) Fig. 5.1
x, = distance along length of a flexural mem
ber from support to point of maximum
positive moment (in. or ft) Fig. 5.1
= distance along length of a flexural member between points of zero moment (in. or
ft) Fig. 5.6
= distance from centroidal axis of flexural
member to extreme bottom fiber (in.)
z =A/s (in.) Chapter 6
Zb = section modulus of cross section with ref-
erence to bottom fiber = l/yb (in.3)
= unit weight of soil (pcf)
6. = deflection (in.)
6.l = increase in length due to thermal expan-
sion (in.) Chapter 6
8 = temperature (F)
8s = temperature of steel (F)
PP = Aps/bd
= capacity reduction factor from ACI 318-83;
for flexure = 0.90
w = Asf/bdf
Wp =Apsfpjbd f
Subscripts
b = with reference to the bottom fiber
d =as affected by dead load
= as affected by live load
min = minimum
p = of prestressing steel
s = of reinforcing steelu = ultimate
x = at a distance x from a support. Chapter 5
0, 1 = of reference specimens and member in
question. Chapter 6
8 = as affected by temperature
Superscripts
+ and indicate positive and negative momentregions
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
11/97
-3-
GLOSSARY OF TERMS
Built-up roofing - roof covering consisting of at
least 3-ply, 15-lb type felt and not having in excess
of 1.20 lb per square foot of hot-mopped asphalt
without gravel surfacing.
Carbonate aggregate concrete- concrete made
with aggregates consisting mainly of calcium or
magnesium carbonate, e.g., limestone or dolo
mite.
Cellular concrete - a lightweight insulating con
crete made by mixing a preformed foam with
portlandcement slurryand having a dryunit weight
of about 30 pct.
Cold-drawn steel - uncoated steel used inprestressing wire or strand. Does not include high
strength alloy steel bars used for post-tensioning
tendons.
Critical temperature - the temperature at which
the strength of the steel is the same as the stress
inthe steel.
End point criteria - the conditions of acceptance
foranASTM E119 fire test.
Fire endurance - a measure of the elapsed time
during which a material or assembly continues to
exhibit fire resistance under specified conditionsof test and performance .As applied to elements
of buildings it shall be measured by the methods
and to the criteria defined in ASTM E119. (Defined
inASTM E176)
Fire rate - an insurance term indicating the an
nual premium per $100 of insurance.
Fire resistance - the property of a material or
assembly to withstand fire or to give protection
from it. As applied to elements of buildings, it is
characterized by the ability to confine a fire or to
continue to perform a given structural function,or both. (Defined inASTM E176)
Fire resistance rating (sometimes called fire rat
ing,fire resistance classification, or hourly rating)
- a legal term defined in building codes,usually
based on fire endurances. Fire resistance ratings
are assigned by building codes for various types
of construction and occupancies and are usually
given in half-hour increments.
Fire test - see standard fire test.
Glass fiber board - fibrous glass roof insulationconsisting of inorganic glass fibers formed into
rigid boards using a binder. The board has a top
surface faced with asphalt and kraft reinforced with
fiber.
Gypsum wallboard, Type X - a mill-fabricated
product made of a gypsum core containing spe
cial minerals and encased in a smooth, f inished
paper on the face side and liner paper on the back,
and conforming to the requirements ofASTM C36.
Heat transmission end point - an acceptance cri
terion of ASTM E119 limiting the temperature riseof the unexposed surface temperatu re to an av
erage of 250F or a maximum of 325F at any one
point.
High strength alloy steel bars - uncoated bars
used for post-tensioning conforming to the re
quirements of ASTMA722.
Hot-rolled steel - uncoated steel used in rein
forcing barsorstructuralsteel members.
lntumescent mastic - a solvent-base spray-ap
plied coating which reacts to heat at about 300F
by foaming to a multicellular structure having10 to 15 times its initial thickness.
Isotherm - a line drawn on the cross section of
a member connecting points of the same temper
ature.
Lightweight aggregate concrete- concrete made
with aggregates of expanded clay, shale, slag, or
slate or sintered fly ash, and weighing about 85
to 115 pct.
Mineral board - a rigid felted thermal insulation
board consisting of either felted mineral fiber or
cellular beads of expanded aggregate formed intoflat rectangular units.
Normal weight concrete - any concrete made
with natural aggregates, cement, and water hav
ing a unit weight of about 140 to 155 pct.
Perl te concrete - a lightweight insulating con
crete having a dry unit weight of about 30 pcf
made with perlite concrete aggregate. Perlite ag
gregate is produced from a volcanic rock which,
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
12/97
-4-
when heated, expands to form a glass-like mate
rial of cellular structure.
Restrained assembly classification - the classi
fication derived from fire tests of floors, roofs, or
beams in accordance with acceptance criteria of
ASTM E119. Such a classification is considered to
be applicable in buildings when (1) the surround
ing or supporting structure is capable of resisting
the thermal expansion induced by a standard fire,
or (2) the assembly has structural continuity over
supports or has structural continuity with its sup
port.
Sand-lightweight concrete - concrete made with
a combination of expanded clay, shale, slag, or
slate or sintered fly ash and natural sand. Its unit
weight is generally between 105 and 120 pcf.
Siliceous aggregate concrete - concrete made
with normal weight aggregates consisting mainly
of silica or compounds other than calcium or
magnesium carbonate.
Spray-applied coatings, sprayed insulation - see
intumescent mastic, sprayed mineral fiber, or ver
miculite cementitious material.
Sprayed mineral fiber - a blend of refined min
eral fibers and inorganic binders. Water is added
during the spraying operation, and the untamped
unit weight is about 13 pcf.
Standard fire exposure - the time-temperature
relationship defined byASTM E119, and shown
in Fig. 1.1.
Standard fire test - the test prescribed by ASTME119.
Steel temperature end point - the acceptance
criterion of ASTM E119 defining the limiting steel
temperatures for unrestrained assembly classifi
cations based on the results of a fire test of a re
strained specimen, i.e., 1100F average or 1300F
maximum for structura l steel, 1100F average for
reinforcing steel, and 800F for cold-drawn pres
tressing steel. For restrained classifications of
beams spaced more than four feet on centers,theselimits must not be exceeded for the first half of
the fire endurance period.
Structural end point - the acceptance criterion
of ASTM E119 which states that the specimen shallsustain the applied load without collapse.
Unrestrained assembly classification - a classi
fication derived from fire tests of floors, roofs, or
beams in accordance with the acceptance criteria
ofASTM E119. Such a classification is considered
applicable in buildings when the conditions for arestrained assembly classification are not met.
Vermiculite cementitious material - a cementi
tious mill-mixed material to which water is added
to form a mixture suitable for spraying. The mix
ture has a wet unit weight of about 55 to 60 pct.
Vermiculite concrete - a lightweight insulating
concrete made with vermiculite concrete aggre
gate which is a laminated micaceous material pro
duced by expanding the ore at high temperatures.
When added to a portland cement slurry the re
sulting concrete has a dry unit weight of about 30pct.
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
13/97
-5-
CHAPTER ONE
GENERAL
In the interest of life safety and property pro
tection, building codes require that the resistance
to fire be considered in the design of buildings.
The degree of fire resistance required is depen
dent on the type of occupancy, the size of the
building, its location (proximity to property lines
and within established zones), and, insome cases,
the amount and type of fire detection and extin
guishing equipment available in the structure.
In addition to the life safety considerations,
casualty insurance companies and owners are
concerned about the damage that is inflicted upon
the structure and its contents during a fire. Insur
ance rates are usually substantially lower for
buildings with higher fire resistance ratings.
Fire resistance ratings have, in the past, been
assigned to various building components on the
basis of results of standard fire tests. Such tests
leave much to be desired. In addition to being
expensive and time consuming, fire tests often
yield results that are misleading. Because of these
shortcomings, a considerable research effort has
been expended to develop procedures and data
for the rational design of structural members forfire resistance.
nace design and the heat capacity of the test as
sembly. For example, the amount of fuel consumed
during a fire test of an exposed concrete floor
specimen is likely to be 10 to 20 percent greater
than that used during a test of a floor with an
insulated ceiling, and considerably greater than
for a combustible assembly. However, this fact is
not recognized when assigning or specifying fire
resistance ratings.
The standard, ASTM E119, specifies the min
imum sizes of specimens to be exposed in fire
tests. For floors and roofs, at least 180 sq ft must
be exposed to fire from beneath, and neither di
mension can be less than 12 ft. For tests of walls,
either loadbearing or non-loadbear ing, the mini
mum specified area is 100 sq ft with neither di
mension less than 9 ft. The minimum length for
columns is specified to be 9 ft,while for beams it
is 12 ft.
During fire tests of floors, roofs, beams, load
bearing walls, and columns, the maximum per
missible superimposed load as requ ired or
permitted by nationally recognized standards is
2500 -----.------.------.-----..,
1.1 STANDARD FIRE TESTS OF BUILDING
CONSTRUCTION AND MATERIALS
The fire resistive properties of building com
ponents are measured and specified according to
a common standard, ASTM E119.12>* Fire endurance is defined as the period of resistance to the
standard fire exposure which elapses before an
"end point" is reached.
The standard fire exposure is defined by the
time-temperature relationship of the fire shown in
Fig. 1.1, and is required by ASTM E119. This fire
represents combustion of about 10 lb of wood (with
0
wcc 2000 >---- -:::>I-
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
14/97
-6-
applied. A load other than the maximum may be
applied but the results then apply only to the re
stricted load condition. The standard permits al
ternate tests of large steel beams and columns in
which a superimposed load is not required, but
the end point criteria are modified.
Floor and roof specimens are exposed to fire
from beneath, beams from the bottoms and sides,
walls from one side, and columns from all sides.
ASTM E 119 distinguishes betwee n "re-
strained" and "unrestrained" assemblies. Re
strained in this case means that thermal expansion
of the specimen is restricted during the fire test.
Two classifications can be derived from fire tests
of restrained specimens, "unrestrained" and "re
strained."ASTM E119 includes a guide, Table 1.1,
for classifying construction as restrained or un
restrained. It can be noted that cast-in-place and
most precast concrete constructions are consid
ered to be restrained.
TABLE 1.1
EXAMPLES OF TYPICAL RESTRAINED AND UNRESTRAINED
CONSTRUCTION CLASSIFICATIONS (from Appendix X3 of ASTM E119-88)
I. Wall Bearing:Single span and simply supported end spans of multiple bays:..
( 1) Open-web steeljoists or steel beams, supporting concrete slab,precast units ormetal decking
(2) Concrete slabs, precast units, or metal decking
Interior spans of multiple bays:(1) Open-web steel joists, steel beams or metal decking, supporting continuous
concrete slab(2) Open-web steeljoists or steel beams, supporting precast units or metal decking(3) Cast-in-place concrete slab systems
(4) Precast concrete where the potential thermal expansion is resisted by adjacentconstructionb
II. Steel framing:(1) Steel beams welded , riveted,or bolted to the framing members(2) All types of cast-in-place floor and roof systems (such as beam-and-slabs, flat
slabs, panjoists, and waffle slabs) where the floor or roof system is secured to theframing members
(3) All types of prefabricated floor or roof systems where the structural members aresecured to the framing members and the potential thermal expansion of the flooror roof system is resisted by the framing system or the adjoining floor or roofconstructionb
Ill. Concrete framing:(1) Beams securely fastened to the framing members
(2) All types of cast-in-place floor or roof systems (such as beam-and-slabs, flat slabs,
panjoists, and waffle slabs) where the floor system is cast with the framingmembers
(3) Interior and exterior spans of precast systems with cast-in-place joints resulting inrestraint equivalent to that which would exist in condition Jll (1)
(4) All types of prefabricated floor or roof systems where the structural members aresecured to such systems and the potential thermal expansion of the floor or roofsystems is resisted by the framing system or the adjoining floor or roofconstructionb
IV. Wood constructionAll types
unrestrained
unrestrained
restrained
unrestrained
restrained
restrained
restrained
restrained
restrained
restrained
restrained
restrained
restrained
unrestrained
Floor and roof sys tems can be considered restrained when they are tied into walls with or without tie beams, the walls being designed anddetailed to resist thermal thrust from the floor or roof system .For example, res istance to po tential thermal expansion is considered to be achieved when :
(1) Continuous structural concrete topping is used,(2) The space between the ends of precast units or between the ends of units and the vertical face of supports is filled with concrete or mortar,
or(3) The space between the ends of precast units and the vertical fac es of supports, or betw een the ends of solid or hollow core slab units does
not exceed 0.25 percent of the length for normal weight concrete members or 0.1 percent of the length for structural lightweight concretemembers.
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
15/97
-7-
1.1.1 End Point Criteria:
(a) Loadbearing specimens must sustain the
applied loading - collapse is an obvious
end point(structuralend point).
(b) Holes, cracks, or fissures through which
flames or gases hot enough to ignite cot
ton waste must not form (flame passage
end point).(c) When the temperature increase of the
unexposed surface of floors, roofs, or walls
reaches an average of 250F or a maxi
mum of 325F at any one point (heat trans
mission end point).
(d) In alternate tests of large steel beams (not
loaded during test) the end point occurs
when the steel temperature reaches an
average of 1000F or a maximum of 1200F
at any one point.
Unrestrained assembly classifications can be derived from fire tests of restrained specimens. When
based on results of fire tests of restrained speci
mens, additional end point criteria for unres
trained floor, roof and beam classifications are:
(a) Structural steel members: temperature of
the steel at any one section must not ex
ceed an average of 1100F or a maximum
of 1300F.
(b) Concrete structural members: average
temperature of the tension steel at any
section must not exceed 800F for colddrawn prestressing steel or 1100F for
reinforcing bars.
(c) Multiple open-web steel joists: average
temperature must not exceed 1100F.
Addit ional end point criteria for restrained assem
bly classifications are:
(a) Beams spaced more than 4 ft on centers:
limiting steel temperatures for unrestrained as
sembly classifications derived from fire tests of
unrestrained specimens. Restrained assemblyclassifications cannot be obtained from fire tests
of unrestrained specimens.
Walls and partitions must meet the same
structural, flame passage, and heat transmission
end points described above. In addition, they must
sustain a hose stream test (s imulating, in a specified manner, a fire fighter's hose stream).
1.2 APPLICATION OF STRUCTURAL
ENGINEERING PRINCIPLES TO
DESIGN FOR FIRE SAFETY
In designing a structural member to resist ser
vice loads, the member is proportioned so that its
capacity to resist loads is somewhat greater than
the anticipated loads to be placed on the member,
as illustrated in Fig. 1.2(a). If the loads applied to
the structure exceed the anticipated loads by a
certain margin, as in the case of a load test, a
structural "end point" (failure) will occur, as in
Fig. 1.2(b).
At elevated temperatures , the strengths of
construction materials diminish. If the strength re
duction is enough, as may occur during a sus
tained fire, then a structural end point will also
occur, even if the applied loads do not exceed
those anticipated (Fig. 1.2(c)). Therefore, if the
temperature of the materials at a given time dur-
Jt' ' ' ' ' ' ' ' ' ' I l l l l l l l l l l
s, ;olwdm"'.M
Theoretical momentcapacity. M.
(a)
the above steel temperatures must not be
exceeded for classifications of 1 hr or less;
for classifications longer than 1 hr, the
above temperatures must not be exceeded for the first half of the classificalb)
Structural end pointdu e to overload
M =M.
tion period or 1 hr,whichever is longer.
(b) Beams spaced 4 ft or less on centers and
slabs are not subjected to steel tempera
ture limitations.
r3lllilln l]]JJW]E::::'"'";",I --M.,. II IL--- -----___ J
Note that there are no limiting temperatures
for reinforcing steel or prestress ing steel for re
strained classifications of slabs. Also, there are no
(c) -....... M.Fig. 1.2 Comparison of moment diagrams for a structural load
test and a structural fire test.
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
16/97
-8-
ing a fire are known, or can be assumed (similar
to the assumption of live loads), and the strength
of the material at that temperature is known, then
the capacity of the member can be determined.
Much of the research effort mentioned previ
ously has been devoted to the effects of high tem
perature on the properties of concretes and steels
used in precast and prestressed concrete struc
tural members, and in determining the tempera tures within a c onc rete member during the
"standard fire." Thus, in the case of precast and
prestressed concrete enough is known to design
for fire safety using structural engineering prin
ciples.
In the design of a strucutral member, the ratio
of the load carrying capacity of the anticipated
applied loads is often expressed in terms of the
"factor of safety." In designing for fire, the "factor
of safety" is contained within the fire resistance
classification rating. Thus, a member with a 4-hr.
rating would have a greater "factor of safety" for
a particular situation than one with a 2-hr. rating.
The introduction to ASTM E119-88 states: "When
a factor of safety exceeding that inherent in the
test conditions is desired, a proportional increase
should be made in the specified time-classifica
tion period."
The design methods and examples in this
manual are consistent with the strength (ultimate)
design principles of the "Building Code Requirements for Reinforced Concrete (ACI 318-83)." Be
cause the factors of safety in the design for fire
are included in the ratings, the load factors and
capacity reduction factor are equal to 1.0 when
designing for fire resistance in order to be consis
tent with the conditions of acceptance in ASTM
E119.
Most of the example problems in this manual
deal with precast, prestressed concrete. Neverthe
less, the principles apply not only to precast con
struction but also to cast-in-place post-tensioned
concrete and reinforced concrete.
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
17/97
-9-
CHAPTER TWO
PROPERTIES OF STEEL AND CONCRETE
AT HIGH TEMPERATURES
At temperatures encountered in fires, the
strength and modulus of elasticity of both steel
and concrete diminish.
2.1 STEEL
Fig. A.1 in Appendix A shows strengths of un
coated hot-rolled and cold-drawn stee ls and high
strength alloy steel bars at high temperatures.
Strengths are shown as percentages of room
temperature strengths. For hot-rolled steel, such
as reinforcing bars, data are shown for yield
strength, while for high strength alloy steel bars
and c
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
18/97
10
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
19/97
CHAPTER THREE
TEMPERATURES WITHIN CONCRETE
SLABS AND BEAMS DURING FIRES
3.1 SLABS
Figs. A.3. 1, A.3.2, and A.3.3 in Appendix A show
temperatures within solid or hollow-core concrete
slabs during standard fire tests. 161l The three fig
ures represent the three aggregate types used in
most structural concretes. Carbonate aggregates
include limestone, limerock and dolomite, i.e..
those consisting of calcium and/or magnesium
carbonate. Such aggregates undergo a chemicalchange at temperatures above about 1250F dur
ing which carbon dioxide is released. This reac
tion consumes heat and the residual material tends
to retard the flow of heat. Siliceous aggregates
are those consisting principally of silicon dioxide.
These include quartzites,granites, basalt, and most
other hard rocks other than limestone, limerock
and dolomite. These aggregates do not undergo
chemical changes at the temperatures encoun
tered in fire tests. The data in Fig.A.3.3 for sand
lightweight aggregate concrete applies to con
cretes weighing about 115 pcf. For lighter con
cretes the temperatures are slightly lower.
The curves are applicable to slabs of any
thickness provided that the slab thickness is at
least 1 in. thicker than the curve being used. For
example,if a steel bar is centered 1 in. above the
underside of a carbonate aggregate concrete slab
at least 2 in. thick, exposed to an ASTM E119 fire
from beneath, its temperature will reach 1100F at
about 2 hr 23 min (see Fig. A.3. 1). Thus, if the
"critical temperature " is 1100F, the fire endur
ance of the slab would be 2 hr 23 min.
The curves are reasonably accurate for esti
mating the concrete temperature within the lower
portion of hollow-core slabs. Data developed at
Underwriters Laboratories, Inc., during several full
scale fire tests of hollow-core floor assemblies
show that the strand temperatures are in reason
able agreement with the data in Figs. A.3. 1 through
A.3.3 . Tests of small spec imensP8> further show
that the data are also applicable to roof assem
blies consisting of hollow-core slabs with roof in-
sulation and built-up roofing.
3.2 BEAMS
Graphs of temperatures within beams are not
as simple as those for slabs because beams are
heated from more than one face. Temperatures
within beams and joists during fire exposure are
affected by the width of the section as well as by
cover. Fig. A.4 shows temperatures along the vertical centerlines of beams 3 to 10 in. wide. The
data were developed from results of f ire tests of
prestressed stemmed units at Underwriters Lab
oratories and of beam and joist sections at Port
land Cement Association.
The data inFig.A.4 apply to rectangular beams
and to stems of tee-shaped members.Much of the
data came from stems having tapered sides, i.e.,
the width of stems were narrower at the bottom
than at the top. In such cases, the temperature
along the vertical centerline at a distance, u,from
the bottom was plotted for the width of the section, b,at the location a distance u from the bot
tom. The following example illustrates the use of
Fig. A.4.
Problem 3. 1:
Estimate the temperature at 2 hr test time of
the prestressing steel in a sand-lightweight
concrete joist having a width of 5 in. at the
bottom, 7 in. at the top, and 18 in. deep. The
centroid of the steel is 6 in. above the bottom
of the unit.
Solution:
b = 5.00 + 6(2.00)/18 = 5.67"
u = 6"From the graph for 2-hr sand-lightweight con
crete in Fig. A.4(2). the temperature is about
720F.
3.2.1 Beam Isotherm Diagrams
Fig. 3.1 shows temperatures within concrete
11 -
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
20/97
TLL
0au.I
80)
0
LOLL
000M 0
0LO
12''
0,...0
M
lJ0,...
o
-0Cl
112"
80 -
8 - 00)
0
. 5" 11/2 Hr
3"
2 Hr l H r 3 Hr
(a) NORMAL WEIGHT CONCRETE (b) SAND-LIGHTWEIGHT CONCRETE
I
Fig. 3. 1 Temperatures within beams at various exposure periods. (a) 6 x 12-in. normal weight concrete beam at 1/2 hr and 2 hr;
(b) 10 x 12-in sand-lightweight concrete beam at 1 hr and 3 hr.
beams at various times during standard fire ex
posure. It would be possible to show similar dis
tribution within many sizes of beams made with
different aggregates at various periods of expo
sure to a standard fire. A comprehensive set of
such diagrams would be voluminous and inter
polating between such diagrams is tedious.
As indicated above, Fig. A.4 shows the tem
peratures along the vertical centerlines of stemmed
units, not the temperature distribution throughout
the cross section. However, it is possible to esti
mate the temperatures throughout the cross sec
tion by constructing "isotherm diagrams." The
method is outlined below and in Fig. 3.2.
Problem 3.2:
Estimate the temperature distribution in a 9 x
20-in. normal weight concrete beam at 1112 hr
fire test time.
Solution:
(1) Draw the cross section outline to a con
venient scale as shown in Fig. 3.2(b).
(2) From Fig. A.4(11/z) determine the temper-
atures along the vertical centerline for b
= 9 in., and plot them on a convenient
scale as shown in Fig. 3.2(a). Note that the
vertical scale corresponds to that of the
beam cross section. Some judgment is
needed in extrapolating the curve above
u = 10 in. and below u = 11/z in. As aguide for values below u = 1112 in., the
exposed surfac e of the beam will be
somewhat cooler than the furnace atmo
sphere, which is 1792F at 1112 hr (ASTM
E119).
(3) From the e vs. u curve just drawn, determine the u values for e = 900, 700, 500,300F (and/or otr convenient values) and
plot these points along the vertial center
line as shown in Fig. 3.2(b).
(4) In this case e = 900F at u = 1.2 in. Thus,there are isotherms for 1100, 1300, 1500,
and possibly 1700F between u = 0 and u
= 1.2 in. It is Iikely that the isotherm for
1700F occurs only near the corner, as
shown in Fig. 3.2(b). The isotherms should
12 -
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
21/97
be located closer together near the sur
face, so points for 1100, 1300, and 1500F
are marked accordingly along the center
line.
(5) Locate point A where u = b/2, in this case
where u=
4.5 in.(6) From point A, draw construction lines AB,
AC, and AD which are horizontal, and at
angles of 30 and 60 from the horizontal
respectively.
(7) Draw lines horizontally from the points onthe centerline where e = 500, 700, . . .1500F to line AD.
(8) Locate along line AB points where the
temperatures are 500, 700, . . . 1500F. The
distances from B to these points are slightly
less than the corresponding distances
along the centerline from the bottom ofthe beam.
(9) From those points on AB draw lines es
sentially vertical (though they may slope
slightly toward the side of the beam) to
line AC, and to the top of the beam.
(10) Connect the corresponding isotherms be
tween lines AC and AD with curves, as
shown.
(11) Draw isotherms above point A, roughly
parallel to the others.
Isotherm diagrams can be prepared with
(2), and (3) above, and constructing the
isotherms by approximating the shapes of
those in Fig. 3.1.
3.3 SPRAY-APPLIED COATINGS
Temperatures within concrete members ex
posed to fire are lowered if the fire-exposed sur
face is coated with an insulating materia1.17oi Fig.
A.5 gives data on three types of insulating mate
rial, sprayed mineral fiber (SMF), vermiculite type
cementitious material (VCM), and intumescent
mastic (IM). Data are given in terms of equivalent
concrete thickness. It should be noted that values
for intumescent mastic are applicable only for fire
endurances of 2 hours or less. Data for SMF and
VCM are applicable for as long as 4 hours.
Problem 3.3:
Determine the temperature at 3 hr of a strand
2 in. above the bottom of a normal weight
concrete joist if the width at that location is 5
in. and the joist is coated with 7/8-in. thickness
of SMF.
Solution:
Equivalent concrete thickness, from Fig. A.5 is
2.25 in. for joists.
b = 5.0 + 2(2.25) = 9.5"
u = 2.0 + 2.25 = 4.25"From Fig. A.4(3), temperature 700F
adequate precision by following steps ( 1),
Fig. 3.2 Example of construction of isotherm diagrams.
- 13 -
20------ ---------
15b = 9"Norma I weight c ancrete
1-1/2 hours
:!!: 10,,,
5
0 1-............._-L...._ L..-_.___. L-100 300 500 700 900
e, TEMPERATU RE, F(a)
-
9"
(bl
c1500
==:::.d 1700
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
22/97
14
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
23/97
ti
CHAPTER FOUR
SIMPLY SUPPORTED SLABS AND BEAMS
4.1 STRUCTURAL BEHAVIOR
Assume that a simply supported prestressed
concrete slab is exposed to fire from below, that where
c/>Apsf ps (d -a/2) ... 4.1
the ends of the slab are free to rotate, and that
expansion can occur without restriction. Also as
sume that the reinforcement consists of straight
strands located near the bottom of the slab. With
the underside of the slab exposed to fire, the bot
tom will expand more than the top and the slab
will deflect downward; also, the strength of the
steel and concrete near the bottom will decrease
as the temperature rises. When the strength of the
steel diminishes to that required to support the
slab, flexural collapse will occur. In essence, the
applied moment remains practically constant dur
ing fire exposure, but the resisting moment ca
pacity is reduced as the steel weakens.
Fig. 4.1 illustrates the behavior of a simply
supported slab exposed to fire from beneath, as
described above. Because strands are parallel to
the axis of the slab, the ultimate moment capacity
is constant throughout the length:
1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 I J
FIR E
Aps = the cross sectional area of the prestress
ing steel, in.2
fps = the stress in the prestressing steel at ul
timate load, ksi
d = the distance between the centroid of theprestressing steel and the extreme com
pression fiber, in.
a = the depth of the equivalent rectangular
stress block at ultimate load, in., and is
equal to Apsfps/0.85fcb, where f is the
compressive strength, ksi, of the con
crete and b is the width of the slab, in.
Mn = nominal moment strength, in.-k
In lieu of an analysis based on strain compat
ability the value of fps can be assumed to be:
... 4.2
where fpu is the ultimate tensile strength of the
prestressing steel, ksi.
If the slab is uniformly loaded, the moment dia
gram will be parabolic with a maximum value at
midspan of:
M,, = moment capacitywhere
w12M
8
Mn= reduced moment capacity
Fig. 4.l Moment diagrams for simply supported beam or slab
before and during fire exposure.
- 15 -
w = dead plus live load per unit of length, k/
in.
I =span length, in.
As the mater ial strengths diminish with ele
vated temperatures, the retained moment capac
ity becomes:
... 4.3
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
24/97
in which e signifies the effects of high temperatures. Note that Aps and d are not affected, but fps
is reduced. Similarly, a is reduced, but the con
crete strength at the top of the slab, f . is generally
not reduced significantly because of its lower
temperature. If, however, the compressive zone
of the concrete is heated above about 900F, an
appropriate reduction should be included in the
calculation of ay.
Flexural failure can be assumed to occur when
M n 11 is reduced to M. From this expression, it can
be seen that the fire endurance depends on the
applied loading and on the strength-tern perature
characteristics of the steel.
In turn, the duration of the fire before the "crit
ical" steel temperature is reached depends upon
the protection afforded to the reinforcement.
4.2 TEST VERIFICATION
To verify the theory described above, the Port
land Cement Association sponsored a series of
fire tests of simply supported prestressed con
crete slabs.(451 During the tests, the temperature
of the prestressing steel was monitored and the
steel temperature at the time when collapse was
imminent was used in calculating M n 11 For these
tests, a comparison of Mn and M is shown in Fig.
4.2 Note that the values are nearly equal, clearly
illustrating that the moment capacity during a fire
can be predicted, and that behavior during fires follows basic engineering principles.
Of all of the fire tests performed on simply
supported prestressed or reinfor ced concrete
beams or slabs, none has failed in shear. Because
of the relatively small sizes of test furnaces, some
very short specimens with very large end shear
forces have been fire tested. Thus it seems evi
dent that simply supported concrete slabs or beams
which have shear capacities required by ACI 318
will not fail in shear if exposed to fire.
4.3 DESIGN AIDS
Fig. A.6 shows graphically the relationships
between moment intensity (M/Mn) and critical steel
temperatures for various values of wP. The deri
vation of these relationships is given in Appendix
B.
Figs. A.7.1, A.7.2, and A.7.3 show graphically
the relationships between moment intensity and
"u" distance for various fire endurances and ag
gregate types. The following example illustrates
the use of the graphs.
Problem 4.1
Determine the fire endurance of a simply sup
ported (unrestrained) hollow-core slab, 10 in.
deep, 48 in. wide, reinforced wit six 1/2-in.
250 ksi strands centered 1-3/4 in. above the
bottom of the slab. The span is 28 ft, the dead
load is 65 psf and the live load is 50 psf. Con
crete is made with siliceous aggregate withf = 5 ksi.
Solution:
Cg
/,l
::.:
i-
M = 4(55 + 50)(28)2
= 41.1 ft-ki s8(1000) p
Mn =Apsfps (d - a/2)
Aps = 6(0.144) = 0.864 sq. in.
d = 10.0 - 1.75 = 8.25 in.
f = [ - 0.5(0.864)(250) ]= 236 k ips 250 1 48(8.25)(5) S
0.864(236)
a=
0.85(5)(48)=
1.00 in.Mn = 0.864(236)(8.25 - 0.50)/12
= 131.7 ft-kips
M/Mn =45.1/131.7 = 0.34
_ Apsfpu 0.864( 250) 1
0 100
M,.. IN.-KIPS
200 300
Wp = bdf = 48(8.25)(5) = 01
From Fig. A.7.2 with M/Mn = 0.34, wP = 0.11,and u = 1.75 in., the fire endurance is about
Fig. 4.2 Comparison of M"" and M from fire tests of simply supported slabs.14"
2 hr 30 min.
- 16 -
0 Test resu l ts
200
100
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
25/97
Figs.A.7.1, A.7.2,and A.7 .3 can also be used
for beams wider than about 10 in. in which the
strands are spaced uniformly in horizontal rows.For such beams, an "effective u", designated u,should be Cised. Effective u is the average of the
distances between the centers of the individual
strands and the nearest fire-exposed surface, as
suming that the values for the corner strands are
reduced one-half, to account for the side expo
sure. The procedure does not apply to bundled
strands.
Problem 4.2:
Determine the fire endurance for a simply
supported unrestrained prestressed concrete
beam shown. Assume siliceous aggregate
concrete with M/Mn = 0.50 and wP = 0.25.
Solution:In the illustration, the u distance of strands 1,
3, 5, 6, and 7 from the nearest fire exposed
surface is 2-1/2 in.,strand 2 is 4-1/2in., and
strands 4 and 8 are assumed for this purpose
hollow-core slab with a simply supported un
restrained span of 25 ft and a fire endurance
of 3 hr.
Given:
h = 8 in.; u = 1.75 in.; eight 1/2-in. 250 ksi
strands;Aps = 8(0. 144) = 1.152 in.2; b = 48in.; d = 8 - 1.75 = 6.25 in; wd = 60 psf;carbonate aggregate concrete; l = 25 ft.
Solution:
(a) Estimate strand temperature at 3 hr from
Fig.A.3 .1, (Js at 3 hr at 1.75 in.above fire
exposed surface = 925F.
(b) Determine fpullfrom Fig. A.1. For cold-drawn
steel at 925F, fpuli = 32.5% fpu = 81 ksi
(c) Determine Mn 11 and w
f = 81 (1 - 0.5(1.152)(81) )psi! 48(6.25)(5)
= 78.5 ksi
1.152(78.5)4
to be 1/2 x 2-1/2 = 1.25 in. 0.85(5)(48) = 0.4 in.
M"8 = 1.152(78.5)(6.25 - 0.44/2)/12
= 45.4 ft-kips
8(45.4)( 1000)w =
(25)2(4)= 145 psf
1 2 3
4 5 6 7 8 '
w, = w - wd = 145 - 60 = 85 psf(d) Calculate maximum allowable w, at room
temperature
-0.5( 1.152)(250))
i--- i---
;;:
I ""fps = 250 (1 48(6.25)(5)
= 226 ksi
1.152(226)2Y," 2'h"
12..a
0.85(5)(48) = 1'28 in.
Therefore,
u = 5(2.5) + 1(4.5) + 2(1.25)
M u = 0.9(1.152)(226)(6.25 - 0.64)/ 12
109.5 ft-kips
8( 109.5)( 1000)8 wu = (25)2(4) = 350 psf
= 2.44 in.
From Fig.A.7.2, the fire endurance is about 3
With load factors of 1.4 (dead load) +1.7 (live load):
hr 15 min. 350 - 1.4(60)w1 =1.7
f= 156 ps
Problem 4.3:
Determine the maximum safe superimposed
load that can be supported by an 8-in. deep
Conclusion: w1 = 85 < 156 :.85 psf governs
Note: This problem can also be solved
through the use of Fig. A.7.1
17 -
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
26/97
1
1
M
w = 1.152(250) = 0.19p 48(6.25)(5)
At 3 hr for u = 1.75 in. and wP = 0.19M/Mn = 0.375
From step (d) above, Mu = 109.5 ft-kips
(e) Estimate temperatures and strengths of
strand and rebars
From Fig. A.4(3), at c.g.s.
M-- 0.375(109.5)
0.9- 45 .6 ft-k1' ps
w =8(45.6)( 1000)
(25)2 (4)
6 f= 14 ps
w1 = 146 - 60 = 86 psf.
Problem 4.4:
Provide 3-hr fire endurance (structurally) by
adding strands and/or rebars to an 8DT16 + 2for a 29-ft span with a live load of 40 psf. Sim
= 3(6.67) + 1(8) - 0 .U 4 - 7. In .
ple support, no restraint, normal weight concrete, f'c = 5 ksi, topping concrete f'c = 4 ksi,
fpu = 270 ksi, b = 96 in., strand pattern shown
at u = 7 in., b = 4.75 in., ()5
fpull = 0.10fpu = 27.0 ksi
= 1200F
below:
Topping ! 4 ""
;:: --- - -... :- .. 1r--------15 J14-7) "'I
I I
at u = 8.25 in., b = 4.93 in., ()5 = 1165F
fvo = 0.42 fv = 0.42(60) = 25.2 ksi
(f) Calculate Mno
adjusted fps8
\ --+-- Ap s = 6W.153 f = 0.918 in.2 =27 (1_ 0.5(8) (0.153)(27 .0) ) = 26.9 ksiI\ +I--r "' d = 18 - 6.67 = 1 1.33 in. 96(11)(4)---r--o : wd =
IJ I i 1 W1 =
3 314" w =
Solution:
539 plf
8( 40) = 320 plf859 plf
adjusted a 0
8(0.153( 26.9) + 4(0.79)(25.2)-----------= 0.34 in.
96(0.85)(4)
Mno due to strand:
(a) Estimate strand temperature at 3 hr from
Fig. A.4(3)
6.67at c.g.s. b = 3.75 + (2) = 4.70 in.
Avg. {)5 = 1215F
(b) Estimate fpuo from Fig. A.1
fpuO = 0.095 fpu = 0.095(270) = 25.65 ksi
(c) Calculate Mn8 and compare with Mfps& = 25.6 ksi
a11 = 0.07 in.
Mno = 0.918(25.6)(11.33 - 0.04)/12
= 22.1 ft-kips
M = 0.859(29)2/8 = 90.3 ft-kips
(d) Try adding one 1/2 in. 270 ksi strand at u
= 8 in. and two #8 Grade 60 reinforcing
bars at u = 7.25 and 9.25 in. in each stem.
Mno = 8(0.153)(26.9)( 11.00- 0.17)/12
= 29.7 ft-kips
Mna due to rebars:
Mno =4(0.79)(25.2)(9.75- 0.17)/12
= 63.5 ft-kips
Total capacity = 29.7 + 63.5 = 93.2 ft-kips> 90.3 ft-kips :. OK
Problem 4.5:
Provide 3-hr fire endurance by applying spray
insulation to an 8DT24 + 2 double tee sectionof normal weight concrete with a strand pat
tern 88-DI as shown below:
Span = 46 ft simple support, unrestrained,
superimposed dead load = 10 psf, live load
= 50 psf.
w1 = 400 pit, wd = 618 + 80 = 698 pit
18 -
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
27/97
- 19 -
I,
5-3/4" 'r, I5-3/4" I
to----. r-----+--1
-,..-- :.;,.
c-,,N
4-1 /2" 270K
Strands Per Stem
c.g.s. --
Co
N
3-3/4"
@ Ends
c.g.s. --,--+--
LJ3-3/4"@ Midspan
Solution:1.5(698 + 400)(46)2
OOO
b = 4.00 + 2(2.25) = 8.50 in.
From Fig.A.4(3), (JS = 750F
Applied M = 1= 3485 in.-kips
Capacity Mn = 7225 in.-kips
M 3485
-=--
=0 482
Mn 7225 .
at midspan,d = 26 - 2.75 = 23.25 in.
- = 8(0.153)(270) = 0.05w p 96(23.25)(3)
From Fig. A.6, the critical steel temperature
for M/Mn = 0.482 and wp = 0.05 is 810F.
at midspan c.g.s.2.75 .
b = 3.75 + 22(2) = 4.00 In.
Try 1/2-in coating of sprayed mineral fiber or
vermiculite cementitious mixture. The equivalent concrete thickness from Fig.A.5 is 1.35
in. for joists.
Therefore u = 2.75 + 1.35 = 4.10 in.
and b = 4.00 + 2(1.35) = 6.70 in.
From Fig. A.4(3), (JS = 1000F at 3 hr;too high.
Try 718 in. coating. Equivalent concrete thick
ness = 2.25 in.
u = 2.75 + 2.25 = 5.00 in.
Try 3/4 in. coating. Equivalent concrete thick
ness = 1.95 in.
u = 2.75 + 1.95 = 4.70 in.
b = 4.00 + 2(1.95) = 7.90 in.Os = 830F, too high; use 7/8-in. coating.
Apply 7/8 in. thickness of coating to lower 12
in.of stems andfeather to 0 in. at top of stems.
b
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
28/97
- 29 -
( m.-k K
Problem 4.6:
Provide 2-hr fire endurance for an 8DT24 + 2double tee section of normal weight concrete
shown in problem 4.5. A ceiling or sprayed
insulation cannot be used because of environmental considerations. Span = 46 ft simple
support, unrestrained; superimposed dead
load = 10 psf; live load = 50 psf. Strand pattern can be changed to accommodate addi
tional reinforcement.
Solution:
Applied M at midspan = 3485 in.-k (see Prob
lem 4.5)
Determine Mno at midspan at 2 hr
U = 2.75 in.; b = 4.00 in.; (}ps = 1220F
fpul! = 0.09 (270) = 24.3 ksi
fpsl! 0.98 (24.3) = 23.8 ksi
(Eq. 18-3 of ACI 318-83 could be used to cal
culate fpsol
1/2" St rand
1" H.S.A. Bar--+--
#8 Rebar --+---3!
1/2" Strand-+--------+-- v lD J: i 3485 OK
Note that #7 rebars can be used in place of
the #8 bars, in which case Mn u = 893 +
= 8(0.153)(23.8) = 0 12a o 0.85(3)(96)
-1.20
841)1.58
+ 2010 = 3541 . > 34850
M no = 8(0.153)(23.8)(23.25 -0.06) =676 in.-k
M - M no = 2809 in.-k
Assume deformed high strength alloy steel
bars, fpu = 150 ksi with 8 = 1150F.
fpul! = 0.38 (150) = 57 ksi; fpso = 55.9 ksi
assume (d - 0.5a) = 18.6 in.
2809
The added bars need not extend to the ends
of the member if calculation of M no and M at
various points along the length indicate that
without the bars Mnii > M. A development
length of 40 bar diameters should be provided
beyond the point where the bar is no longerneeded. Additional stirrups should be pro
vided in the regions of cut-off points.
A -b -55.9(18.6)
= 2.70 in.2 It may be advisable to re-calculate stresses at
transfer and for service load conditions using Try one 1-in. dia. H.S.A. bar plus one #8 bar
per stem in the pattern shown. Steel param
eters are tabulated below:
the section properties of the transformed sec
tion.
A. u b 8@2 hr fpuH/fpu f puH f psH
Strand 1.224 in.2 5.19 in. 4.22 in. 1140F 0.135 36.4 ksi 35.7 ksi
Rebars 1.58 4.00 4.11 1170 0.41 24.6* 24.6*
H.S.A. bars 1.70 5.00 4.20 1150 0.39 58.5 57.3
*fyH
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
29/97
M
M /
FIR E EXPOSURE = 18' I'" -5'-+- -20' + 5'
O D
CHAPTER FIVE
CONTINUOUS BEAMS AND SLABS
5.1 STRUCTURAL BEHAVIOR
Continuous members undergo changes in
stresses when subjected to fire, resulting from
temperature gradients within the structural mem
bers, or changes in strength of the materials at
high temperatures ,or both.
Fig. 5.1 shows a continuous beam whose un
derside is exposed to fire. The bottom of the beam
becomes hotter than the top and tends to expand
more than the top. This differential temperature
causes the ends of the beam to tend to lift from their supports thereby increasing the reaction at
the interior support. This action results in a redis
tribution 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 mo
ment reinforcement (Fig. 5.1) remains cooler than
the positive moment reinforcement because it is
better protected from the fire. Thus the increase
in negative moment can be accommodated. Gen
erally the redistribution that ocurs 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 a failure
will occur . Therefore, the fire endurance of a con
tinuous concrete beam is generally significantly
longer than that of a simply supported beam hav
ing the same cover and loaded to the same mo
ment intensity.
and two others 3 ft 6 in. from the supports. Two
bottom bars were cut off 4 ft 2 in. from the sup
ports.
I -lj I l I j j
[ l IFIRE FIRE
M"
n
AT O HR
Fig. 5.1 Moment diagrams for continuous 2-span beam be
fore and during fir e exposure.
5.2 TEST VERIFICATION
A series of tests was conducted at the Port
land Cement Association to investigate the be
havior of continuous beams exposed to fire.
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
30/97
::
(/)
One spec imen was tested as a simply sup
ported beam, i.e., the cantilever loads P, and P3were omitted. The P2 loads were 4.36 kips each.
The applied moment (dead plus live load) was
equal to 50% of the calculated theoret ical moment
strength at midspan and the fire endurance proved
to be about 1 hr 25 min.In another test, loads were applied on the can
tilevers as well as midspan so that the resulting
applied moments were 50% of the ultimate at the
- 150
-100
(/) - 509;0
I- + 50u..+ 100
I-2UJ
- 1500 -100
supports as well as at midspan. The P2 loads were11.27 kips, and the cantilever loads at the beg in
ning of the test were 13.47 kips. During the tests
the cantilever ends (points A and B) were kept at
::! - 500
+ 50
a constant elevation by changing the loads P, and
P3. This was done to simulate the behavior of a
continuous beam subjected to fire in one span.
30
a... 20
Fig.5.4 Moment diagrams before and during fire test."""
Other tests in that series have yielded infor
mation on beams that were continuous over onesupport simulating the condition shown in Fig. 5.1.
Also, tests were conducted with unsymmetricP, and P3 were such that the mo
zCl
o0 2
HR
--'3 4
loadings, i.e.,
ments over the supports were different. In one
case, the applied negative moments at the sup
ports were 40% and 50% of the respective ulti
mate capacities, and the midspan applied moment
was 50% of the capacity. Under this condition a
greater redistribution of moments occurred, and
the fire endurance was greater than 4 hr. There have also been some fire tests of pre
Fig. 5.3 Change in P, and P3 to keep A and B at constantelevation.,.,.,
Fig. 5.3 shows the changes in cantilever loads
during the test. Note that early in the test, P, andP3 increased sharply and then leveled off. Note
also that P2 loads were kept constant. The fire test
was continued for 3-1/2 hr.
The moment diagrams in Fig. 5.4 show graph
ically the behavior of the specimen during the fire
test. At the beginning of the test, the maximum
applied moments were half the ultimate moment
capacities. Note that the moment capacity dia
grams are stepped. These steps are shown at thecut-off points, and indicate graphically the reduc
tion in moment capacity within the bar anchorage
length. Note that at 3-1/2 hr the applied negative
moment had great ly increased, and the applied
positive moment had decreased. The negative
moment capacity had not decreased very much,
but the positive moment capacity was approach
ing positive moment. The test was stopped when
the midspan deflection began to increase rapidly.
cast prestressed concrete units joined in such a
manner so as to effect continuity over the sup
ports. These tests have verified that yielding of
the negative moment reinforcing bars occurs early
during a fire test. In some tests, continuity was
achieved through the use of negative moment re
inforcement within a cast-in-place topping. In other
tests, in which no topping was used, negative mo
ment reinforcing bars were spliced and welded
over the supports. Results of these tests have ver
ified the method of calculating fire endurance of
continuous structures.
It should be noted that when beams which are
continuous over one support (e.g., such as that
shown in Fig. 5.1) are ex posed to fire, both the
moment and the shear at the interior support in
crease. Such a redistribution of shear results in a
severe stress condit ion. However, of the several
fire tests in which that condition was simulated,
failure occurred only in one beam.158) In that test,
the shear reinforcement was inadequate, even for
service load conditions without fire, as judged by
- 22 -
nuI
/pl- - -=-o.-_:_:_:_:.
P3
-'--
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
31/97
-x =-
the shear requirements of ACI 318. Thus it ap
pears from available test data that members which
are designed for shear strength in accordance with
ACI 318 will perform satisfactorily in fire situa
tions, i.e., failure will not occur prematurely due
to a shear failure.
(51 x = x,, Mx = M ;11
M 11 = w/2 w/2
... 5.2a
5.3 CALCULATION PROCEDURES
It is possible to design the reinforcement in a
continuous beam or slab for a particular fire en
durance period. From Fig. 5.1, the beam can be
expected to collapse when the positive moment
capacity, M 6, is reduced to the value indicated
by the dashed horizontal line, i.e., when the re
distributed moment at point x,, from the outer
support, Mx1 = M 8Fig. 5.5 shows a uniformly loaded beam or
slab continuous (or fixed) at one support and sim
ply supported at the other. Also shown is the re
distributed applied moment diagram at failure.
M, 11
..Jll 1 1 I I I I 1 1 I III I I I I I I I I I I )
' J I j
2 y -;;? ... 5.3
Fig. 5.6 shows a symmetrica l beam or slab in
which the end moments are equal.
M 1111
(A 1 1 1 1':', , 1 1 5!..._ )
I--------i
Fig. 5.6 Symmetrical uniformly loaded member continuous
at both supports.
M o = w/2/8 - M 11
wx _ M
8- n8
... 5.4
x, ... 5.5
Fig. 5.5 Uniformly loaded member continuous at one sup
port.
x, ... 5.1
2M 11
0 wl ... 5.2
In most cases, redistribution of moments oc
curs early during the course of a fire before the
negative moment capacity has been reduced by
the effects of fire. In such cases, the length of x0
is increased, i.e.,the inflection point moves toward
the simple support. For such cases.
M & ... 5.62 2 w
To determine the maximumvalue of x0, the value
of w should be the minimum service load antici
pated, and (-M + w/2/8) should be substitutedfor M 11 inEq. 5.6.
For any given fire endurance period, the value
of M 11 can be calculated by the procedures given
in Chapter 4. Then the value of M 11 can be cal
culated by use of Eq. 5.3 or 5.4 and the necessary
lengths of the negative moment reinforcement can
be determined from Eq. 5. 1 or 5.6. Use of these
equations is illustrated in the example problems
that follow .
- 23 -
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
32/97
2
5.4 DETAILING PRECAUTIONS
It should be noted that the amount of moment
redistribution that can occur is dependent upon
the amount of negative moment reinforcement.
Tests have clearly demonstrated that the negative
moment reinforcement will yield, so the negativemoment capacity is reached early during a fire
test, regardless of the applied loading. The de
signer must exercise care to ensure that a sec
ondary type of failure will not occur. To avoid a
compression failure in the negative moment re
gion, the amount of negative moment reinforce
ment should be small enough so that w11, i.e.,Asfv ol
Assume u = 1.75 in.; then d = 12 - 1.75
10.25 in. Assume a = 1 in.; fps = 240 ksi
A 12(30.25) = 0 17 in 2/ftps = 0.90(240){ 10.25-1/2)
0
Use nine 3/8-in. 250 ksi strands per 4-ft wide
unit
Ap5 = 9(0.08)/4 = 0.180 in.2/ft
Calculate Mn 11 at 4 hr:
From Fig. A.3.1, for u = 1.75 in. at 4 hr,
Os = 1010F
From Fig. A.1, fpufl = 0.24 fpu = 60.0 ksib11d 0f8, is less than 0.30, before and after reductions in fv, b, d andfare taken into account. Fur
fpso = 58.8 ksi and a 11 = 0.35 in.
thermore, the negative moment bars or mesh must
be long enough to accommodate the complete
redistributed moment and change in the inflectionpoints. It should be noted that the worst condition
occurs when the applied loading is smallest, such
as dead load plus partial or no live load. It is rec
ommended that at least 20% of the maximum
negative moment reinforcement be extended
throughout the span.
Problem 5. 7 :
Design a floor using hollow-core slabs and
topping for 22-ft span for 4-hr fire endurance.
Service loads = 175 psf dead (including structure) and 150 psf live. Use 10-in. slabs with 2-
in. topping, carbonate aggregate concrete.
Continuity can be achieved at both ends. (This
is for the first floor of a wood frame apartment
building with automobile parking in the base
ment.) Usef = 5000 psi, fpu = 250 ksi,andf(topping) = 3000 psi.
Solution A:
Design slabs as simple spans with positive
moment reinforcement to resist gravity loads
and provide negative moment reinforcement
for fire conditions.
Wu = 1.4(175) + 1.7(150) = 500 psf = 0.5 ksf
M 11 = 0.180(58.8)(10.07)/12 = 8.88 ft-kips/ft
M = (175 + 150)(22)2/8000 = 19.66 ft-kips/ft
Assuming that M ne at wall and M 0 at interiorsupport are equal:
I___22' .....,
M 11 = M - M 11
Mnll = 19.66 - 8.88 = 10.78 ft-kips/ftNeglect concrete in negative moment region
above 1400F, i.e., from Fig. A.3.1,neglect bot
tom 5/8 in. Assume steel in negative moment
region is centered in topping. Then d = 12 -
0.63 - 1.0 = 10.37 in. To account for tem
peratures of 1200F to 1400F in compressive
zone in negative moment region, use fe =
0.9 f = 4500 psi (see Fig. A.2.). Because steel
in topping is relatively cool, use fv11 = 0.90fv
= 54 ksi. Assume a11 = 0.5 in.
d - II = 10.37 - 0.25 = 10.12 in.
Mo 12 - 0 23 . 2/ft
Mu = wJ2/8 = 0.5(22)2/8 = 30.25 ft-kips/ft fv(dI ) - . 7 In.
- a"'
]-----=-=2-2- 1-------==-2-2-' - ......1...(_
22' -dr
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
33/97
- 24 -
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
34/97
. 12
I 1
0
8
Extend 20% of A throughout length of slab;
0.2(0.237) = 0.047 in.2
Use 6 x 6 - W2.9 x W2.9 wwf throughout
and #4 Grade 60 at 13 in. on centers.
As = 0.058 + 13 (0.20) = 0.242 in.i.tftCheck M o
M 8 = 0.32(58.4)(10.25 - 0.31)/12
= 15.48 ft-kips/ft
M = 19.66 ft-kips/ft
Required M no = 19.66 - 15.48 = 4.18 ft-kips/ft
Assume d - a /2 = 10.25 in.; fv = 54 ksi
A = 4.18(12) = 0 091 . 2/fta- = As fyo = 0.28 . s 54(10.25) . In.
80.85f b
M 8 =A.fve (d -
in.
8
) = 0.242(54)(10.37 -Use at least 20 percent throughout span, e.g.,
6 x 6 - W2 .1 x W2 .1
0.14)/12 = 11.14 ft-kips/ft > 10.9 OK
Calculate bar cutoff points
x0 is maximum when M is minimum
Assume Mmin = Mct + 1/2(M1); and calculate
M = 13.14 ft-kips/ft
Mmin = (0.175 + 0.075)(22) 2/8
= 15.12 ft-kips/ft
M;;n = 15.12 - 13.14 = 1.98 ft-kips/ft
From Eq. 5.6
max x0 = 2 - 2 V
wwf A. = 0.041 in.2/ft = 45 % req'dAplus 6 x 6 - W2.9 x W2.9 wwf over supports.
A;= 0.041 + 0.058 = 0.099 in.2/ft
Neglect concrete above 1400F in negative mo
ment region, as in Solution A, and check M ne
0.087(60)
ae = 0.85(4.5)(12) = 0.11 in.
M 8 = 0.099(54)(10.37 - 0.06)/12
= 4.59 ft-kips/ft
With dead load + 1/2 (live load). and M" 5.42ft-kips/ft (ca lculated for room temperatures)
M,;,in = 15.12 - 5.42 = 9.70 ft-kips/ft22 1
=- - -2 2
= 7 02 ft. From Eq. 5.6
Thus the negative moment reinforcement must
extend 7.02 ft plus bond development length from
the supports. Bars should be staggered, e.g., half
22 1max x = --
2 2
8(9.70) = 2 19 ft0.25 .
should be cut off at 8 ft from support and half 6
ft from support; the mesh should extend through
out the span.
Solution 8:
Use maximum pos1t1ve moment reinforce
ment and provide negative moment reinforce
ment needed for fire.
Assume max strand = sixteen 3/8 in.250 ksi/
4-ft unit.
From Fig. A.3. 1.,8.= 1010F
From Fig. A.1, fpull = 0.24 fpu = 60 ksi
Calculate f pse = 58.4 ksi and a 8 = 0.61 in.
Aps = 16(0.08)/4 = 0.32 in.2/ft
Use 6 x 6 - W2.1 x W2 .1 continuous throughout
plus 6 x 6 - W2.9 x W2 .9 for a distance of 3.25
ft from the support. Mesh must extend into walls
which must be designed for the moment induced
at the top.
Problem 5.2:
Use Fig. A.7.3 to determine the amount of
negative moment reinforcement needed to
provide a 3- hr fire endurance for sand- light
weight hollow-core slabs, 8 in. deep,5 ksi con
crete, with 2-in. (4 ksi) composite topping, 48
in. wide, with seven 7/ 16-in. 250 ksi strands.
Slabs span 25 ft of an exterior bay (no re
straint to thermal expansion) .Dead load = 65
- 25 -
8(1.98)
0.250
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
35/97
-26 -
2
bdf SI
7 3
psf, live load = 100 psf. Strands are centered
1-3/4-in. above bottom of slab.
Solution:
Determine capacity Mn:
Assume f 0 incompressive zone = 0.8f'c
= 4 ksi
Assume d - afl/2 = 8.1 in. and fv,1 = 54 ksi
A _ 24.6(12) _ .Aps = 7(0.108) = 0.756 in.2
d = 10 - 1.75 = 8.25 in.
s - 54(8.1) - 0.675 in.
h - 0.675(54) - .c eek a8 - 0. ( ) - 0.22 in.
fps = f pu (1 - 0.
5Ap.f pu) = 235 k .
c
ApJps 1 09 .a = 0.85fb = in.
85 4 48
d - ai2 = 8.25 - 0.11 = 8.14 in. > 8.1 OK
Use 6 x 6 - W2.1 x W2.1 wwf throughoutplus #5Grade 60 at 16 in. in negative moment
Mn =Apsfp5(d - a/2)/12 = 114.1 ft-kips region.
- 48Fr F A
om . . ,. _ _ 0.756(250) A. = 4(0.041) + (0.20) = 0.764 in.2
1619. with wP -
48( _ )( )8 25 4
= 0.12 and u = 1.75, at 3 hr M/Mn = 0.35M = 0.35(114.1) = 40.0 ft-kips = M 11
Calculate x0 for dead load plus one-half live
load.
From Eq. 5.3
nH 2 W vWf2-
Mno =0.764
_ (24.6) = 27.8 ft- kips0 67
M- = w/2 - 12
w/2 = 4(65 + 100)(25)211000 = 412.5 ft-kips
loading = 4(0.065 + 0.050) = 0.46 k/ft; M =34.0 ft-kips (calculated for room tempera
tures)
From Eq. 5.2a
. 412.5M =
-412.5 /2(40.0) = 24.6 ft-kips 2Mn 2(34.0)
n11 --2
'412.5 XO = -;;/ = 0.46(25) = 5.91 ft
DetermineA.; neglect concrete above 1400F
in negative moment region. From Fig.A.3.3
neglect3/4in.above bottom, and assume steel
centered in topping.
d = 10 - 3/4 - 1 = 8.25 in.
Half of #4 bars should extend 7 ft each side
of interior support and half 5 ft.
Use #4 Grade 60 at 16 in. x 12 ft and alter
nate.
Ji
Je.g. of strand
33' 33'
tl6 - 1/2"-270K 00
DL = 72 psf 0-5"
SECTION AA
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
36/97
-27 -
bdfo ks1
2
V
Problem 5.3: 1063M = - 1063 2(55.4)
Design double-tees for 33-ft bays of the 2-span
layout shown. Fire endurance of 3 hr req'd.
Live load = 40 psf, superimposed dead load
11
Estimate fv11
--
2 1063
= 10 psf. Use 2-in. topping (4000 psi). Normal
weight concrete.
Solution:
Determine retained positive moment capacity
at 3 hr. If capacity is insufficient to support
loads, provide negative moment reinforce
ment.
From Fig. A.4(3)
6 67
From Fig.A.3.1, for u = 3 in. (bottom of slabto center of steel) e "" 630F
From Fig. A.1, fy 11 "" 0.81fy = 48.6 ksi
Assume d - - a,,- /2 ""' 12 in.
A = M;11 = 3.87 in.2" fy11(d-a11/2)
Check w 8 with f v8 = 48.6 ksi,neglect concreteabove 1400F.
at 3 hr: for b = (2) + 514 Effective "b" per stem ""' 3 in. so b for two
Ops = 1010F= 5.95 in. and u = 6.67 in.
stems = 6 in.,d = 15.5 in.,f 11 = 4 ksi
_ A:tvn
From Fig. A.1
w8 = bdf11
= 0.51 > 0.30 too high
fpuS = 0.24 fpu = 0.24(270) = 64.8 ksi
Aps = 6(0.153) = 0.918 in.2
d = 18 - 6.67 = 11.33 in.
fpsO = fpulJ (1 -0.5Ap.fpuB)
= 64.4.
Apsfpsfl .
ao = 0.85fb = 0.18 in.
d - aJ 2 = 11.24 in.
M8 =Apsf (d - a0/2)/12 = 55.4 ft-kips
M = 8(72 + 10 + 40)(33) 2/8000= 132.9 ft-kips
Since M > Mno use continuity reinforcement:
From Eq. 5.3
M- = w/2 - w12nll 2 Wj2
:. Increase M 11 by adding rebars
Try adding one #7 per stem,
A. = 1.20 in.2, at u = 8 in.
8b = (2) + 5 = 6.14 in.
14
From Fig. A.4(3) o.= 960FFrom Fig. A.1 fv8 = 0.67(60) = 40.2 ksi
A5fv8 +Apsfps8 .as = 0.85bf s = 0.33 in.
d - as = 11.33 - 0.17 = 11.16 inp
ao .d. - 2 = 10 - 0.17 = 9.83 in.
M8= 0.918(64.4)(11.16)/12
+ 1.20(40.2)(9.83)/12 = 94.5 ft-kips
w/2 = 8(72 + 10 + 40)(33) 2/1000
1063 ft-kips
1063Mn8-
2- 1063
2(94.5) .= 83.3 ft-kips
1063
e_._
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
37/97
-28-
For negative moment
Assume d - a8/2 = 12 in., fvo = 48.6 ksi
A - _ 83.3(12) _ .
This is OK but try 6 x 6 - W2.1 x W2.1 plus
6 #4 Grade 60
2
s - 48.6(12) - 1.71 In.
h k 1.71(48.6)
A; = 8(0.041) + 6(0.20)
=1.528 in.2
c ec w 0 =6
(15
. )( ) = 0.22 < 0.30 OK - 1.5285 4 a o = .1648 (3.92) = 3.63 in.
Try 6 x 6 - W2.1 x W2.1 wwf plus 12 #3
Grade 60
A. = 8(0.041) + 12(0.11) = 1.648 in.2
check Mn0; neglect concrete above 1400F at
3 hr
f 8 = 0.8(5) = 4 ksi (Fig. A.2)
a o_ A;fvo
0.85f8b
M;0 = 1.528(48.6)( 15.5 - 1.82)/12
= 84.7 ft-kips >83.3 OK
Determine x0 for dead load plus half live load;
w = 8(82 + 20) = 816 plf, and M n = 121.6ft-kips (calculated),
2M; 2(121.6) O9
1.648(48.6)0.85(4)(6) = 3.92 in.
XO = --;;/ = 0.816(33) = ft
d - a 8/2 = 15.5 - 3.92/2 = 13.54 in.
M;0 = 1.648(48.6)(13.54)/12
= 90.4 ft-kips > 83.3
Use 6 x 6 - W2. 1 x W2.1 wwf throughout
plus #4 Grade 60 x 16 ft at 16 in. o.c. Alter
nate bars so that they extend 10 ft and 6 ft
from support centerline.
-
7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI
38/97
CHAPTER SIX
FIRE ENDURANCE OF SLABS AND BEAMS
. IN WHICH RESTRAINT TO THERMAL EXPANSION OCCURS
6.1 STRUCTURAL BEHAVIOR
If a fire occurs beneath a portion of a large
floor or roof, such as beneath a concrete floor slab
in one interior bay of a multi-bay building, the
heated portion will expand and push against the
surrounding unheated portion. In turn, the un
heated portion exerts compressive forces on the
heated portion. The compressive force, or thrust,
acts near the bottom of the slab when the fire
starts, but as the f