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Table of Contents
                            (ACI 307-95)
CONTENTS
CHAPTER 1—GENERAL
CHAPTER 2—MATERIALS
CHAPTER 3—CONSTRUCTION REQUIREMENTS
CHAPTER 4—SERVICE LOADS AND GENERAL DESIGN CRITERIA
CHAPTER 5—DESIGN OF CHIMNEY SHELLS—STRENGTH METHOD
CHAPTER 6—THERMAL STRESSES
                        
Document Text Contents
Page 1

307-1

This standard gives material, construction, and design requirements for
cast-in-place and precast reinforced concrete chimneys. It sets forth mini-
mum loadings for design and contains methods for determining the con-
crete and reinforcement required as a result of these loadings. The method
of analysis applies primarily to circular chimney shells; however, a general
procedure for analysis of noncircular shapes is included.

This standard is written in explicit, mandatory language, and as such, is
intended for reference in project specifications.

Equations are provided for determining the temperature gradient through
the concrete resulting from the difference in temperature of the gases inside
the chimney and the surrounding atmosphere. Methods for combining the
effects of dead and wind (or earthquake) loads with temperature both verti-
cally and circumferentially are included in the standard. These methods
permit the designer to establish minimum concrete and reinforcement
requirements.

This standard refers extensively to “Building Code Requirements for
Reinforced Concrete” (ACI 318); construction requirements are generally
in accordance with ACI 318; and notation is in accordance with ACI 104.

Keywords: chimneys; compressive strength;concrete construction;
earthquake-resistant structures; formwork (construction); foundations; high
temperature; linings; loads (forces); moments; openings; precast concrete;
quality control ;reinforced concrete; reinforcing steels; specifications;
static loads; strength; structural analysis;structural design; temperature;
thermal gradient; wind pressure.

CONTENTS

Chapter 1—General, p. 307-2
1.1—Scope
1.2—Drawings
1.3—Regulations
1.4—Reference standards

Chapter 2—Materials, p. 307-2
2.1—General
2.2—Cement

2.3—Aggregates
2.4—Reinforcement

Chapter 3—Construction requirements, p. 307-2
3.1—General
3.2—Concrete quality
3.3—Strength tests
3.4—Forms
3.5—Reinforcement placement
3.6—Concrete placement
3.7—Concrete curing
3.8—Construction tolerances
3.9—Precast erection

Chapter 4—Service loads and general design criteria, p.
307-3

4.1—General
4.2—Wind loads
4.3—Earthquake loads
4.4—Special design considerations and requirements
4.5—Deflection criteria

Chapter 5—Design of chimney shell—Strength method,
p. 307-8

5.1—General
5.2—Applied forces
5.3—Required strength
5.4—Design strength
5.5—Nominal moment strength—Circular shells
5.6—Noncircular shapes
5.7—Design for circumferential bending

Chapter 6—Thermal stresses, p. 307-12
6.1—General
6.2—Vertical temperature stresses

ACI 307-95 supersedes ACI 307-88 and became effective Mar. 1, 1995.
Copyright © 1995, American Concrete Institute.
All rights reserved including rights of reproduction and use in any form or by any

means, including the making of copies by any photo process, or by any electronic or
mechanical device, printed, written, or oral, or recording for sound or visual reproduc-
tion or for use in any knowledge or retrieval system or device, unless permission in
writing is obtained from the copyright proprietors.

Standa rd Practice for the Design and Construction of
Reinforced Concrete Chimn eys (ACI 307-95)

Reported by ACI Committee 307

ACI Committee Reports, Guides, Standard Practices, and
Commentaries are intended for guidance in designing, planning,
executing, or inspecting construction and in preparing specifica-
tions. Reference to these documents shall not be made in the
Project Documents. If items found in these documents are de-
sired to be part of the Project Documents, they should be
phrased in mandatory language and incorporated in the Project
Documents.

Randolph W. Snook
Chairman

David J. Bird Milton Harstein Niran G. Shah
Victor A. Bochicchio Erick N. Larson John C. Sowizal
William F. Brannen Robert A. Porthouse Barry V. Vickery
John J. Carty Ronald E. Purkey Chung-Yee John Wei
Phillip B. Davidson Scott D. Richart Winston W. Yau
Shu-Jin Fang Wadi S. Rumman Edward L. Yordy

Page 2

307-2 ACI STANDARD

6.3—Circumferential temperature stresses

Appendix A—Notation, p. 307-14

CHAPTER 1—GENERAL

1.1—Scope
This standard covers the design and construction of circu-

lar cast-in-place or precast reinforced concrete chimney
shells. If other shapes are used, their design shall be substan-
tiated in accordance with the principles used herein. The
standard does not include the design of linings, but includes
the effects of linings on the concrete shell.

A precast chimney shell is defined as a shell constructed
wholly from precast reinforced concrete sections, assembled
one atop another, to form a freestanding, self-supporting
cantilever. Vertical reinforcement and grout are placed in
cores as the precast sections are erected to provide structural
continuity and stability. The use of precast panels as stay-in-
place forms is considered cast-in-place construction.

1.2—Drawings
Drawings of the chimney shall be prepared showing all

features of the work, including the design strength of the
concrete, the thickness of the concrete chimney shell, the
size and position of reinforcing steel, details and dimensions
of the chimney lining, and information on chimney accesso-
ries.

1.3—Regulations
1.3.1 The design and construction of the chimney shall

meet the requirements of all ordinances and regulations of
authorities having jurisdiction, except that where such re-
quirements are less conservative than the comparable re-
quirements of this standard, this standard shall govern.

1.3.2 Consideration shall be given to the recommendations
of the Federal Aviation Administration with respect to chim-
ney heights and aviation obstruction lighting and marking,
and the standards of the Underwriters Laboratories regarding
lightning protection and grounding.

1.4—Reference standards
Standards of the American Concrete Institute, the Ameri-

can National Standards Institute, and the American Society
for Testing and Materials referred to in this standard are list-
ed in the following with their serial designations, including
the year of adoption or revision, and are declared to be a part
of this standard as if fully set forth herein.

ACI 104-71 Preparation of Notation for Concrete
(Revised 1982) (Reapproved 1987)
ACI 318-89 Building Code Requirements for Re-
(Revised 1992) inforced Concrete
ASCE 7-88 Minimum Design Loads for Buildings

and Other Structures
ASTM A 615-89 Standard Specification for Deformed

and Plain Billet Steel Bars for Con-
crete Reinforcement

ASTM A 617-87 Standard Specification for Axle-Steel
Deformed and Plain Bars for Concrete
Reinforcement

ASTM A 706-89 Standard Specification for Low-Alloy
Steel Deformed Bars for Concrete Re-
inforcement

ASTM C 33-90 Standard Specification for Concrete
Aggregates

ASTM C 150-89 Standard Specification for Portland
Cement

ASTM C 309-89 Standard Specification for Liquid
Membrane-Forming Compounds for
Curing Concrete

ASTM C 595-89 Standard Specification for Blended
Hydraulic Cement

CHAPTER 2—MATERIALS

2.1—General
All materials and material tests shall conform to ACI 318,

except as otherwise specified herein.

2.2—Cement
The same brand and type of cement shall be used through-

out the construction of the chimney. The cement used shall
conform to the requirements for Type I, Type II, Type III, or
Type V of ASTM C 150, or Type IS or Type IP of ASTM C
595.

2.3—Aggregates
2.3.1 Concrete aggregates shall conform to ASTM C 33.
2.3.2 The maximum size of coarse aggregate shall be not

larger than1/8 of the narrowest dimension between forms nor
larger than1/2 the minimum clear distance between reinforc-
ing bars.

2.4—Reinforcement
Reinforcement shall conform to ASTM A 615, A 617, or

A 706, of grade or grades referred to in the project specifica-
tions.

CHAPTER 3—CONSTRUCTION REQUIREMENTS

3.1—General
Concrete quality, methods of determining strength of con-

crete, field tests, concrete proportions and consistency, mix-
ing and placing, and formwork and details of reinforcement
shall be in accordance with ACI 318, except as stated other-
wise herein.

3.2—Concrete quality
The specified concrete compressive strength shall not be

less than 3000 psi at 28 days.

3.3—Strength tests
The 28-day compressive strength of the concrete shall be

determined from a minimum of two sets of cylinders (con-
sisting of three specimens each) per 8-hr shift (slipform) or

Page 8

307-8 ACI STANDARD

be computed using the SRSS over a minimum of five normal
modal responses. SRSS means taking the square root of the
sum of the squares of modal maxima.

4.4—Special design considerations and requirements
4.4.1 Two layers of vertical and circumferential reinforc-

ing are required. The total vertical reinforcement shall be not
less than 0.25 percent of the concrete area. The outside ver-
tical reinforcement shall be not less than 50 percent of the to-
tal reinforcement. Outside face vertical bars shall not be
smaller than #4 and spaced not over 12 in. on centers. Inside
face vertical reinforcement shall consist of vertical bars not
smaller than #4 and spaced not over 24 in. on centers.

4.4.2 The total circumferential reinforcement shall not be
less than 0.20 percent of the concrete area. The circumferen-
tial reinforcement in each face shall be not less than 0.1 per-
cent of the concrete area at the section.

Spacing of outer face circumferential reinforcement shall
not exceed the wall thickness or 12 in. Spacing of circumfer-
ential reinforcing on the inner face shall not exceed 12 in.
The minimum size of circumferential reinforcing bars shall
be #3.

4.4.3 The circumferential reinforcement for a distance of
0.2d(h) from the top of the chimney or 7.5 ft, whichever is
greater, shall be at least twice the amount required by Sec-
tion 5.7.

4.4.4 Where a segment between openings is critical as re-
lated to the height of the openings, this segment shall be in-
vestigated as a beam-column. Where more than two open-
ings occur at the same elevation, appropriate design methods
consistent with the cases shown by Fig. 5.5.1(a), (b), and (c)
shall be used.

4.4.5 In addition to the reinforcement determined by de-
sign, extra reinforcement shall be provided at the sides, top,
bottom, and corners of these openings as hereinafter speci-
fied. This extra reinforcement shall be placed near the out-
side surface of the chimney shell as close to the opening as
proper spacing of bars will permit. Unless otherwise speci-
fied, all extra reinforcement shall extend past the opening a
minimum of the development length.

4.4.6 At each side of the opening, the additional vertical
reinforcement shall have an area at least equal to the design
steel ratio times one-half the area of the opening. The extra
reinforcement shall be placed within a distance not exceed-
ing twice the wall thickness unless otherwise determined by
a detailed analysis.

4.4.7 At both the top and bottom of each opening, addi-
tional reinforcement shall be placed having an area at least
equal to one-half the established design circumferential rein-
forcement interrupted by the opening, but the areaAs of this
additional steel at the top and also at the bottom shall be not
less than that given by Eq. (4-32), unless otherwise deter-
mined by a detailed analysis.

(4-32)

where
fc′ = specified compressive strength of concrete, psi
t = concrete thickness at opening, in.
l = width of opening, in.
fy = specified yield strength of reinforcing steel, psi

One-half of this extra reinforcement shall extend com-
pletely around the circumference of the chimney, and the
other half shall extend beyond the opening a sufficient dis-
tance to develop the bars in bond. This steel shall be placed
as close to the opening as practicable, but within a height not
to exceed three times the thicknesst.

4.4.8 For openings larger than 2 ft wide, diagonal reinforc-
ing bars with a total cross-sectional area in square inches of
not less than1/5 of the shell thickness in inches shall be
placed at each corner of the opening. For openings 2 ft wide
or smaller, a minimum of two #5 reinforcing bars shall be
placed diagonally at each corner of the opening.

4.5—Deflection criteria
The maximum lateral deflection of the top of a chimney

under all service conditions, prior to the application of load
factors, shall not exceed the limits set forth by Eq. (4-33):

Ymax = 0.04h (4-33)

where
Ymax = maximum lateral deflection, in.
h = chimney height, ft

CHAPTER 5—DESIGN OF CHIMNEY SHELLS—
STRENGTH METHOD

5.1—General
5.1.1 Except as modified herein, design assumptions shall

be in accordance with ACI 318, Chapter 10. The chimney
shell shall be designed by the strength method.

5.1.2 The equivalent rectangular concrete stress distribu-
tion described in Section 10.2.7 of ACI 318 and as modified
herein shall be used. For vertical strength the maximum
strain on the concrete is assumed to be 0.003 and the maxi-
mum strain in the steel is assumed to be 0.07. Whichever val-
ue is reached first shall be taken as the limiting value.

In lieu of the equivalent rectangular concrete compressive
stress distribution used in this chapter, any other relationship
between concrete compressive stress and strain may be as-
sumed that results in prediction of the strength of hollow cir-
cular sections in substantial agreement with results of
comprehensive tests.

5.1.3 The design and detailing of precast chimney shells
shall emulate the design of cast-in-place chimney shells un-
less specifically excepted herein. Particular attention should
be given to the spacing and reinforcement of cast-in-place
cores and closures joining precast units to ensure that the re-
qirements of this and other applicable standards are met.

5.1.4 Refer to Section 5.7 for design procedures of noncir-
cular shells.

As
0.06f c′tl

f y
----------------------=

Page 15

REINFORCED CONCRETE CHIMNEYS 307-15

fy′(v) = fy modified for temperature effects, vertical, psi
(Chapter 5)

F1A = strouhal number parameter (Chapter 4)
F1B = lift coefficent parameter (Chapter 4)
g = acceleration due to gravity, 32.2 ft/sec2 (Chap-

ter 4 and Commentary Chapter 4)
G = across-wind peaking factor (Chapter 4)
Gr(z) = gust factor for radial wind pressure at heightz

(Chapter 4 and Commentary Chapter 4)
Gw′ = gust factor for along-wind fluctuating load

(Chapter 4 and Commentary Chapter 4)
h = chimney height above ground level, ft (Chapter

4 and Commentary Chapter 4)
i = local turbulence parameter (Chapter 4)
I = importance factor for wind design in Chapter 4

and ASCE 7
k = ratio of wind speed, (V), to the critical wind

speed, (Vcr)
ka = aerodynamic damping parameter (Chapter 4)
kao = mass damping parameter of small amplitudes

(Chapter 4)
ks = equivalent sand grained surface roughness fac-

tor (Commentary Chapter 4)
K = parameter for nominal moment strength in

Chapter 5 or horizontal force factor for earth-
quake design in the Commentary Introduction

Ke = Es/fy (Chapter 5)
Ki = coefficient of heat transmission from gas to in-

ner surface of chimney lining when chimney is
lined, or to inner surface of chimney shell when
chimney is unlined, Btu/ft2/hr/deg F difference
in temperature (Chapter 6)

Ko = coefficient of heat transmission from outside
surface of chimney shell to surrounding air,
Btu/ft2/hr/deg F difference in temperature
(Chapter 6)

Kr = coefficient of heat transfer by radiation be-
tween outside surface of lining and inside sur-
face of concrete chimney shell, Btu/ft2/hr/deg
F difference in temperature. (Chapter 6)

Ks = coefficient of heat transfer between outside
surface of lining and inside surface of shell for
chimneys with ventilated air spaces, Btu/ft2/hr/
deg F difference in temperature (Chapter 6)

K1, K2, K3=parameters for nominal moment strength
(Chapter 5)

l = width of opening in concrete chimney shell, in.
(Chapter 4)

L = length coefficient (Chapter 4)
Ma(z) = moment induced at heightz by across-wind

loads, ft-lb (Chapter 4)
Mi(z) = maximum circumferential bending moment

due to radial wind pressure, at heightz, tension
on inside, ft-lb/ft (Chapter 4)

Ml(z) = moment induced at heightz by mean along-
wind load, ft-lb (Chapter 4)

Mn = nominal moment strength at section (Chapter
5)

Mo(z) = maximum circumferential bending moment
due to radial wind pressure, at heightz, tension
on outside, ft-lb/ft (Chapter 4)

Mu = factored moment at section (Chapter 5)
Mw(b) = bending moment at base due to mean along-

wind load, ft-lb (Chapter 4)
Mw(z) = combined design moment at heightz for

across-wind and along-wind loads (Chapter 4)
n = modular ratio of elasticity,Es/Ec (Chapter 6)
n1 = number of openings entirely in compression

zone (Chapter 5)
p(z) = pressure due to mean hourly design wind speed

at heightz, lb/ft2 (Chapter 4)
pr(z) = radial wind pressure at heightz, lb/ft

2 (Chapter
4 and Commentary Chapter 4)

Pcr = pressure due to wind at critical speed (Chapter
4)

Pu = factored vertical load (Chapter 5)
Q = stress level correction parameter (Chapter 5

and Commentary Chapter 5)
Q′, Q1, = parameters for nominal moment strength
Q2, Q3 (Chapter 5)
r = average radius of section (Chapter 5)
rq = ratio of heat transmission through chimney

shell to heat transmission through lining for
chimneys with ventilated air spaces (Chapter
6)

r(z) = mean radius at heightz, ft (Chapter 4)
R = parameter for nominal moment strength (Chap-

ter 5)
s = center-to-center spacing of chimneys, ft (Chap-

ter 4 and Commentary Chapter 4)
Sp = spectral parameter (Chapter 4)
Ss = mode shape factor (Chapter 4)
St = strouhal number (Chapter 4)
t = thickness of concrete shell (Chapters 5 and 6)
tb = thickness of uninsulated lining or insulation

around steel liner, in. (Chapter 6)
ts = thickness of air space or insulation filling the

space between lining and shell, in. (Chapter 6)
t(b) = thickness of concrete shell at bottom, ft (Chap-

ter 4)
t(h) = thickness of concrete shell at top, ft (Chapter 4)
T = normal temperature effect (Chapter 6)
Ti = maximum specified design temperature of gas

inside chimney, deg F (Chapter 6)
To = minimum temperature of outside air surround-

ing chimney, deg F (Chapter 6)
Tx = temperature drop across concrete shell (Chap-

ter 6)
T1 = fundamental period of vibration for unlined

shell, sec per cycle (Chapter 4 and Commen-
tary Chapter 4)

T2 = second mode period of vibration for unlined
shell, sec per cycle (Chapter 4 and Commen-
tary Chapter 4)

Uc = required circumferential strength (Chapter 5)
Uv = required vertical strength (Chapter 5)

Page 16

307-16 ACI STANDARD

V = basic wind speed, mph (ASCE 7 and Chapter
4)

Vcr = critical wind speed for across-wind loads, cor-
responding to the fundemental mode ft/sec
(Chapter 4)

Vcr2 = critical wind speed for across-wind loads cor-
responding to the second mode

Vr = VI (Chapter 4), mph
V = mean hourly wind speed at 5/6h varying over a

range of 0.50 and 1.30V(zcr), ft/sec
V(h) = mean hourly wind speed at top of chimney, ft/

sec (Chapter 4)
V(z) = mean hourly design wind speed at heightz, ft/

sec (Chapter 4)
V(zcr) = mean hourly design wind speed at 5/6h, ft/sec

(Chapter 4)
V(33) = mean hourly wind speed at a height of 33 ft, ft/

sec (Chapter 4)
w(z) = total along-wind load per unit length at height

z, lb/ft (Chapter 4)
w(z) = mean along-wind load per unit length at height

z, lb/ft (Chapter 4 and Commentary Chapter 4)
w′(h) = fluctuating along-wind load per unit length at

top of chimney, lb/ft (Commentary Chapter 4)
w′(z) = fluctuating along-wind load per unit length at

heightz, lb/ft (Chapter 4)
wa(h) = across-wind load per unit length at top of chim-

ney, lb/ft (Chapter 4)
wa(z) = across-wind load per unit length at heightz, lb/

ft (Chapter 4)
wt(u) = average weight per unit length for top third of

chimney, lb/ft (Chapter 4)
w1(z) = mean along-wind load per unit length as given

by Eq. (4-27), lb/ft (Chapter 4)
W = wind load (Chapter 5)
Ymax = maximum lateral deflection of top of chimney,

in. (Chapter 4)
z = height above ground, ft (Chapter 4 and Com-

mentary Chapter 4)
zcr = height corresponding toVcr (Chapter 4)
Zc = exposure length factor (Chapter 4)
α = on the chimney cross section, one-half the cen-

tral angle subtended by the neutral axis (Chap-
ter 5 and Commentary Chapter 5)

αte = thermal coefficient of expansion of concrete
and of reinforcing steel, 0.0000065 per deg F
(Chapter 6)

ß = on the chimney cross section, one-half the cen-
tral angle subtended by an opening (Chapter 5

and Commentary Chapter 5)
βa = aerodynamic damping factor (Chapter 4)
ßs = fraction of critical damping for across-wind

load (Chapter 4)
ßl = factor defined in Section 10.2.7.3 of ACI 318

(Chapter 6)
γ = on the chimney cross section, one-half the cen-

tral angle subtended by the center lines of two
openings (Chapter 5)

γd = d(h)/d(b) (Chapter 4)
γ1 = ratio of inside face vertical reinforcement area

(Chapter 6)
γ2 = ratio of distance between inner surface of

chimney shell and outside face vertical rein-
forcement to total shell thickness (Chapter 6)

γ1′ = ratio of inside face circumferential reinforce-
ment area to outside face circumferential rein-
forcement area (Chapter 6)

γ2′ = ratio of distance between inner surface of
chimney shell and outside face circumferential
reinforcement to total shell thickness (Chapter
6)

δ = γ - ß, for two symmetric openings partly in
compression zone (Chapter 5)

εm = maximum concrete compressive strain (Chap-
ter 5 and Commentary Chapter 5)

λ = τ - n1ß (Chapter 5)
λ1 = µ + ψ - π (radians) (Chapter 5)
µ, τ, ψ = angles shown on Fig. 5.5.1(a) (Chapter 5)
π = 3.1416 (Chapter 5)
ρ = ratio of area of vertical outside face reinforce-

ment to total area of concrete shell (Chapter 6)
ρ′ = ratio of area of circumferential outside face re-

inforcement per unit of height to total area of
concrete shell per unit of height (Chapter 6)

ρa = specific weight of air, 0.075 lb/ft3 (Chapter 4)
ρck = mass density of concrete, kip-sec2/ft4 (Chapter

4)
ρt = ratio of total area of vertical reinforcement to

total area of concrete shell cross section (Chap-
ter 5)

φ = strength reduction factor (Chapter 5 and Com-
mentary Chapter 5)

ωt = ρt fy/fc′ (Chapter 5)

Adopted as a standard of the American Concrete Institute to supersede ACI 307-88,
in accordance with the Institute's standardization procedure.

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