1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI

7/13/2019 1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI

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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


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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.


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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


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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


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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


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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


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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


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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.)


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= 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


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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,


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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.


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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-


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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.


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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.


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.


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


18/97

10


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 -


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 -


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


22/97

14


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


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


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 -


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 -


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


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


29/97

M

M /

FIR E EXPOSURE = 18' I'" -5'-+- -20' + 5'

O D

CHAPTER FIVE

CONTINUOUS BEAMS AND SLABS


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.


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

-'--


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 -


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


33/97

- 24 -


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


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


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_._


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.


38/97

CHAPTER SIX

FIRE ENDURANCE OF SLABS AND BEAMS

. IN WHICH RESTRAINT TO THERMAL EXPANSION OCCURS


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

Documents

1 Design of Fire Resistance Precsat Pre Stressed Concrete PCI