ACI 117M-10

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ACI 307-08

Reported by ACI Committee 307

Code Requirements for Reinforced

Concrete Chimneys (ACI 307-08)

and Commentary

An ACI Standard

Copyright American Concrete Institute

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--`,,`,````,,,`,,`,,```,,,,````,-`-`,,`,,`,`,,`---Code Requirements for Reinforced Concrete Chimneys

and Commentary

November 2008

ISBN 978-0-87031-307-3

American Concrete Institute

®

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--`,,`,````,,,`,,`,,```,,,,````,-`-`,,`,,`,`,,`---ACI 307-08 supersedes --`,,`,````,,,`,,`,,```,,,,````,-`-`,,`,,`,`,,`---ACI 307-98, was adopted August 19, 2008, and published November 2008.

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307-1

ACI Committee Reports, Guides, Manuals, Standard Practices, and Commentaries are intended for guidance in planning, designing, executing, and inspecting construction. This Commentary is intended for the use of individuals who are competent to evaluate the significance and limitations of its content and recommendations and who will accept responsibility for the application of the material it contains. The American Concrete Institute disclaims any and all responsibility for the stated principles. The Institute shall not be liable for any loss or damage arising therefrom.

Reference to this Commentary shall not be made in contract documents. If items found in this document are desired by the licensed design professional to be a part of the contract documents, they shall be restated in mandatory language.

ACI 307-08

This code gives material, construction, and design requirements for cast-in-place and precast reinforced concrete chimneys. It sets forth minimum loadings for design and contains methods for determining the concrete 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.

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 vertically and circumferentially, are included in this code. These methods permit the licensed design professional to establish minimum concrete and reinforcement requirements.

The Commentary discusses some of the background and considerations of Committee 307 in developing the provisions contained in “Code Requirements for Reinforced Concrete Chimneys (ACI 307-08).” Two appendixes provide the derivation of the equations for nominal strength and temperature stresses. Commentary provisions begin with an “R,” such as “R1.1.1,” and are shown in italics.

Keywords: chimneys; compressive strength; concrete construction;

earth-quake-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 R0—Introduction, p. 307-2 Chapter 1—General, p. 307-3 1.1—Scope 1.2—Drawings 1.3—Regulations 1.4—Notation Chapter 2—Materials, p. 307-7 2.1—General 2.2—Cement 2.3—Aggregates 2.4—Reinforcement

Chapter 3—Construction requirements, p. 307-7

3.1—General 3.2—Concrete strength 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—Loads and general design criteria, p. 307-8

4.1—General 4.2—Wind loads

Victor A. Bochicchio Thomas D. Joseph Robert A. Porthouse Randolph W. Snook John J. Carty Jagadish R. Joshi Ronald E. Purkey John C. Sowizal Samuel Dilcer Faris A. Malhas Denis J. Radecki Barry J. Vickery Shu-Jin Fang David C. Mattes Scott D. Richart Edward L. Yordy Sigmund A. Freeman

The committee acknowledges the late Milton Harstein for his contribution to the development of these code requirements.

David J. Bird Chair

Code Requirements for Reinforced Concrete

Chimneys (ACI 307-08) and Commentary

An ACI Standard

Reported by ACI Committee 307

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--`,,`,````,,,`,,`,,```,,,,````,-`-`,,`,,`,`,,`---4.3—Earthquake loads

4.4—Special design considerations and requirements 4.5—Wind deflection criteria

Chapter 5—Design of chimney shells: strength method, p. 307-17

5.1—General 5.2—Design loads 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. 307-22

6.1—General

6.2—Vertical temperature stresses 6.3—Circumferential temperature stresses

Chapter 7—References, p. 307-23

7.1/R7.1—Referenced standards/Referenced standards and reports

R7.2—Cited references

Appendix A—Derivation of equations for nominal strength, p. 307-25

Appendix B—Derivation of equations for temperature stresses, p. 307-29

R0—INTRODUCTION

As industry expanded in the years immediately following World War I and, as a result of the development of large pulverized coal-fired boilers for the electric power-generating utilities in the 1920s, a number of large reinforced concrete chimneys were constructed to accommodate these new facilities. A group of interested engineers who foresaw the potential need for many more such chimneys, and who were members of the American Concrete Institute, embarked on an effort to develop rational design criteria for these structures. The group was organized into ACI Committee 505 (predecessor to the present Committee 307) to develop such criteria in the early 1930s.

Committee 505 submitted a “Proposed Standard Specifica-tion for the Design and ConstrucSpecifica-tion of Reinforced Concrete Chimneys,” an outline of which was published in the ACI

JOURNAL (ACI Committee 505 1934). This specification was adopted as a tentative standard in February 1936. Although this tentative standard was never accepted by ACI as an official standard, it was used as the basis for the design of many chimneys. As these chimneys aged, inspections revealed considerable cracking. When the industrial expansion began following World War II, other engineers recognized the need for developing an improved design specification for reinforced concrete chimneys.

In May 1949, Committee 505 was reactivated to revise the tentative standard specification, embodying modifications that were found desirable during the years it had been in use. The section dealing with the temperature gradient through the

chimney lining and the chimney shell was completely revised and extended to cover different types and thicknesses of linings and both unventilated and ventilated air spaces between the lining and the concrete shell. In 1954, this specification was approved as ACI 505-54 (ACI Committee 505 1954).

The rapid increase in the size and height of concrete chimneys being built in the mid-1950s raised further questions about the adequacy of the 1954 version of the specification, especially in relation to earthquake forces and the effects of wind.

In May 1959, the ACI Board of Direction reactivated Committee 505 (renamed Committee 307) to review the standard and to update portions with the latest design techniques and the then-current knowledge of the severity of the operating conditions that prevailed in large steam plants. The material in the standard was reorganized, charts were added, and the methods for determining loads due to wind and earthquakes were revised. The information on design and construction of various types of linings was amplified and incorporated in an appendix. That version included criteria for working stress design. It was planned to add ultimate strength criteria in a future revision.

In preparing the earthquake design recommendations for ACI 307-69 (ACI Committee 307 1969), the committee incorporated the results of theoretical studies by adapting them to existing United States codes. The primary problems in this endeavor stemmed from the uncertainties still inherent in the definition of earthquake forces and from the difficulty of selecting the proper safety and serviceability levels that might be desirable for various classes of construction. Committee investigations revealed that with some modifications (such as the K factor), the base shear equations developed by the Seismology Committee of the Structural Engineers’ Association of California (SEAOC) could be applied to chimneys. Similarly, the shape of the force, shear, and moment distributions, as revised in their 1967 report, were also suitable for chimneys. A use factor (U factor) ranging from 1.3 to 2.0 was introduced in the specification, and it was emphasized that the requirements of Section 4.5 of ACI 307-69 that related to seismic design could be superseded by a rational analysis based on evaluation of the seismicity of the site and modal response calculations. The modifications were approved in ACI 307-69. In that version, the commentary and derivation of equations were published separately as a supplement to ACI 307-69.

In 1970, the document was reissued with corrections of typographical errors. This issue of ACI 307-69 was also designated ANSI A158.1-1970. At the time, as a result of numerous requests, the commentary and derivation of equations were bound together with the specification.

ACI 307-79 (ACI Committee 307 1979) updated its requirements to agree with the then-accepted standard practices in the design and construction of reinforced concrete chimneys. The major changes included the requirement that two layers of reinforcing steel be used in the walls of all chimneys (previously, this only applied to chimney walls thicker than 18 in.) and the requirement that horizontal sections through the chimney wall be designed for the radial wind pressure distribution around the chimney. Formulas

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--`,,`,````,,,`,,`,,```,,,,````,-`-`,,`,,`,`,,`---were included to compute the stresses under these conditions. Many revisions of less importance were included to bring the specification up to date.

The editions of the specifications before 1979 included appendixes on the subjects of chimney linings and accessories. In 1971, Committee 307 learned of buckling problems in steel chimney liners. The committee also noted that, in modern power plant and process chimneys, environmental regulations required treatment of the effluent gases that could result in extremely variable and aggressively corrosive conditions in the chimneys. These facts led the committee to agree that the task of keeping the chimney liner recommendations current was not a responsibility of an ACI committee and could be misleading to licensed design professionals using the chimney specification. By committee consensus, the reference to chimney liner construction was dropped from future editions of the specification. Committee 307 then made a recommendation to the Brick Manufacturers’ Association and the American Society of Civil Engineers that each appoint a task force or a committee for the development of design criteria for brick and steel liners, respectively. The Power Division of ASCE took up the recommendation and appointed a task committee that developed and published a design guide in 1975 titled “Design and Construction of Steel Chimney Liners” (ASCE Task Committee on Steel Chimney Liners 1975). ASTM established two task forces for chimney liners: one for brick and one for fiberglass-reinforced plastic.

The committee had extensive discussion on the question of including strength design in the 1979 specification. The decision to exclude it was based on the lack of experimental data on hollow concrete cylinders to substantiate this form of analysis for concrete chimneys. The committee continued, however, to consider strength design, and encouraged experiments in this area.

Shortly after ACI 307-79 was issued, the committee decided to incorporate strength design provisions and update the wind and earthquake design requirements.

ACI 307-88 (ACI Committee 307 1988) incorporated significant changes in the procedures for calculating wind forces as well as requiring strength design rather than working stress. The effects of these and other revisions resulted in designs with relatively thin walls governed mainly by steel area and, in many instances, across-wind forces.

The subject of across-wind loads dominated the attention of the committee between 1988 and 1995, and ACI 307-95 (ACI Committee 307 1995) introduced modified procedures to reflect more recent information and thinking.

Precast chimney design and construction techniques were introduced as this type of design became more prevalent for chimneys as tall as 300 ft.

The subject of noncircular shapes was also introduced in ACI 307-95. Due to the infinite array of possible configurations, however, only broadly defined procedures were presented.

Because of dissimilarities between the load factors required by ACI 307 and 318, the committee added guidelines for determining bearing pressures and loads to size and design chimney foundations.

The major changes incorporated into the ACI 307-95 were: • Modified procedures for calculating across-wind loads; • Added requirements for precast concrete chimney columns;

• Added procedures for calculating loads and for

designing noncircular chimney columns;

• Deleted exemptions previously granted to smaller

chimneys regarding reinforcement and wall thickness; and • Deleted static equivalent procedures for calculating

earthquake forces.

For the ACI 307-98 (ACI Committee 307 1998), revisions to the ASCE 7-95 relating to wind and seismic forces required several changes to be made to the ACI 307-95. The changes incorporated into the ACI 307-98 were:

• Site-specific wind loads were calculated using a 3-second gust speed determined from Fig. 6-1 in ASCE 7-95, instead of the previously used fastest-mile speed; • Site-specific earthquake forces were calculated using

the effective peak velocity-related acceleration contours determined from Contour Map 9-2 in ASCE 7-95 instead of previously designated zonal intensity;

• The vertical load factor for along-wind forces was

reduced from 1.7 to 1.3;

• The vertical load factor for seismic forces was reduced from 1.87 to 1.43;

• The load factor for across-wind forces was reduced

from 1.40 to 1.20; and

• The vertical strength reduction factor φ was reduced from 0.80 to 0.70.

The reduced load factors should be used in concert with the revised strength reduction factor and the wind and seismic loads specified in ASCE 7-95.

Revisions to ASCE 7 again caused Committee 307 to revisit and revise ACI 307-98. The changes incorporate applicable ASCE 7-02 wind and seismic load factors and methods. The changes to the ACI 307-98 were:

• Included procedure in Section 4.3, Earthquake load,

compatible with ASCE 7-02 and the ASCE 7 seismic risk maps;

• Updated the load factors and load combinations to be more in line with ASCE 7-02 values and presentation; and

• Changed the vertical strength reduction factor φ back to 0.80.

As stated previously, the current methods in this document can only be used in conjunction with the ASCE 7-02.

CHAPTER 1—GENERAL 1.1—Scope

This code covers the minimum design and construction requirements of circular cast-in-place or precast reinforced concrete chimney shells. If other shapes are used, their design shall be substantiated in accordance with the principles used herein. This code does not include the design of linings, but does include 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 on top of 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

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--`,,`,````,,,`,,`,,```,,,,````,-`-`,,`,,`,`,,`---continuity and stability. The use of precast panels as stay-in-place forms is considered cast-in-stay-in-place construction.

R1.1 For this revision, ACI 307-98 was updated to an ACI

code. ACI 307, “Code Requirements for Reinforced Concrete Chimneys,” is written for new construction. The committee acknowledges that the general analytical procedures and requirements contained in ACI 307 are appropriate for the investigation and retrofitting of existing chimneys. The committee recognizes, however, that not all code requirements, such as Section 4.4, will be feasible or appropriate when retrofitting existing chimneys.

The scope of ACI 307-95 was expanded to include precast chimney shells. Additional information can be found in PCI manuals (PCI 1977, 1985). Warnes(1992) provides further guidelines on connection details for precast structures. Additional information is given in ACI 550R.

1.2—Drawings

Drawings of the chimney shall be prepared showing 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 accessories.

1.3—Regulations

1.3.1 This code supplements local building regulations

and shall govern in all matters pertaining to reinforced concrete chimney design and construction.

1.3.2 Consideration shall be given to the regulations of the

Federal Aviation Administration with respect to chimney heights and aviation obstruction lighting and marking (AC70-7460-1K), and the standards of the Underwriters Laboratories (UL 96A) regarding lightning protection and grounding.

1.4—Notation

A_s = area of reinforcing steel at top and bottom of opening, in.2 (Chapter 4)

B = band-width parameter (Chapter 4)

Cb = coefficient of thermal conductivity of chimney’s

uninsulated lining or insulation around steel liner, Btu⋅in./(h⋅ft2_{⋅°F) of thickness/h/°F difference in}

temperature (Chapter 6)

C_c = coefficient of thermal conductivity of concrete of chimney shell, Btu⋅in./(h⋅ft2_{⋅°F) of thickness/h/°F}

difference in temperature (12 for normalweight concrete) (Chapter 6)

C_dr = drag coefficient for along-wind load (Chapter 4)

C_E = end-effect factor (Chapter 4)

C_L = rms lift coefficient (Chapter 4)

C_Lo = rms lift coefficient modified for local turbulence (Chapter 4)

C_s = coefficient of thermal conductivity of insulation filling in space between lining and shell, Btu⋅in./ (h⋅ft2⋅°F) of thickness/h/°F difference in temperature (3 for lightweight concrete) (Chapter 6)

c = ratio of distance from extreme compression fiber to neutral axis for vertical stresses to total thickness t (Chapter 6)

c′ = c for circumferential stresses (Chapter 6)

D = dead load (Chapter 5)

d = diameter of chimney, ft (Chapter 4)

db = mean diameter of uninsulated lining or insulation

around liner, ft (Chapter 6)

dbi = inside diameter of uninsulated lining or insulation

around liner, ft (Chapter 6)

d_c = mean diameter of concrete chimney shell, ft (Chapter 6)

d_ci = inside diameter of concrete chimney shell, ft (Chapter 6)

d_co = outside diameter of concrete chimney shell, ft (Chapter 6)

d_s = mean diameter of space between lining and shell, ft (Chapter 6)

d(b) = bottom outside diameter of chimney, ft (Chapter 4)

d(b) = mean diameter at bottom of chimney, ft (Chapter 4)

d(h) = top outside diameter of chimney, ft (Chapter 4)

d(h) = mean diameter at top of chimney, ft (Chapter 4)

d(u) = mean outside diameter of upper third of chimney, ft (Chapter 4)

d(z) = outside diameter of chimney at height z, ft

(Chapter 4)

d(z_cr) = outside diameter of chimney at critical height z_cr, ft (Chapter 4)

E = earthquake loads or forces (Chapter 5)

E_c = modulus of elasticity of concrete, psi (Chapter 6)

E_ck = modulus of elasticity of concrete, kip/ft2 (Chapter 4)

E_s = modulus of elasticity of reinforcement, psi (Chapters 5 and 6)

F_a = acceleration-based site coefficient at 0.2-second period (Section 4.3)

F_V = velocity-based site coefficient at 1.0-second period (Section 4.3)

F1A = strouhal number parameter (Chapter 4)

F1B = lift coefficient parameter (Chapter 4)

f = frequency, Hz (Chapter 4)

f_c′ = specified compressive strength of concrete, psi (Chapter 4)

f_c′′(c) = f_c′ modified for temperature effects, circumferential,

psi (Chapter 5)

f_c′′(v) = f_c′ modified for temperature effects, vertical, psi

(Chapter 5)

f _CTC′′ = maximum circumferential stress in concrete due to temperature inside chimney shell, psi (Chapters 5 and 6)

f _CTV′′ = maximum vertical stress in concrete inside chimney shell due to temperature, psi (Chapters 5 and 6)

f_STC = maximum stress in outside circumferential reinforcement due to temperature, psi (Chapters 5 and 6)

f_STV = maximum stress in outside vertical reinforcement due to temperature, psi (Chapters 5 and 6)

f STV′′ = maximum stress in inside vertical reinforcement

due to temperature, psi (Chapters 5 and 6)

fy = specified yield strength of reinforcing steel, psi

(Chapters 4 and 5)

f_y′(c) = f_y modified for temperature effects, circumferential,

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--`,,`,````,,,`,,`,,```,,,,````,-`-`,,`,,`,`,,`---psi (Chapter 5)

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

G = across-wind peaking factor (Chapter 4)

Gr(z) = gust factor for radial wind pressure at height z

(Chapter 4)

G_w_′ = gust factor for along-wind fluctuating load (Chapter 4)

g = acceleration due to gravity, 32.2 ft/s2 (Chapter 4)

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

I = importance factor for wind design (Chapter 4)

I_E = occupancy importance factor from Section 4.3.2 (Chapter 4)

i = local turbulence parameter (Chapter 4)

K = parameter for nominal moment strength (Chapter 5)

K1 = parameter for nominal moment strength (Chapter 5)

K2 = parameter for nominal moment strength (Chapter 5)

K₃ = parameter for nominal moment strength (Chapter 5)

K_d = wind directionality factor (Chapter 4)

K_e = E_s/f_y (Chapter 5 and Appendix E)

K_i = coefficient of heat transmission from gas to inner surface of chimney lining when chimney is lined, or to inner surface of chimney shell when chimney is unlined, Btu/ft2/h/°F difference in temperature (Chapter 6)

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

K_r = coefficient of heat transfer by radiation between outside surface of lining and inside surface of concrete chimney shell, Btu/ft2/h/°F difference in temperature (Chapter 6)

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

k = ratio of wind speed V to critical wind speed Vcr

(Chapter 4)

ka = aerodynamic damping parameter (Chapter 4)

k_ao = mass damping parameter of small amplitudes (Chapter 4)

k_s = equivalent sand-grained surface roughness factor (Chapter 4)

L = correlation length coefficient (Chapter 4)

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

M_a = peak base moment, ft⋅lb (Chapter 4)

M_a(z) = moment induced at height z by across-wind loads, ft⋅lb (Chapter 4)

M_i(z) = maximum circumferential bending moment due to radial wind pressure, at height z, tension on inside, ft-lb/ft (Chapter 4)

Ml(z) = moment induced at height z by mean along-wind

load, ft-lb (Chapter 4)

Mn = nominal moment strength at section, ft-lb

(Chapter 5 and Appendix A)

M_o(z) = maximum circumferential bending moment due to radial wind pressure, at height z, tension on

outside, ft⋅lb/ft (Chapter 4)

M_u = factored moment at section, ft-lb (Chapter 5 and Appendix A)

Mw(b)= bending moment at base due to mean along-wind

load, ft⋅lb (Chapter 4)

Mw(z)= combined design moment at height z for

across-wind and along-across-wind loads, ft-lb (Chapter 4)

n = modular ratio of elasticity, E_s/E_c (Chapter 6)

n₁ = number of openings entirely in compression zone (Chapter 5 and Appendix A)

P_cr = pressure due to wind at critical speed, lb/ft2 (Chapter 4)

P_u = factored vertical load, lb (Chapter 5 and Appendix A)

p(z) = pressure due to mean hourly design wind speed at height z, lb/ft2 (Chapter 4)

p_r(z) = radial wind pressure at height z, lb/ft2 (Chapter 4)

Q = stress level correction parameter (Chapter 5)

Q′ = parameter for nominal moment strength (Chapter 5) Q1 = parameter for nominal moment strength (Chapter 5)

Q2 = parameter for nominal moment strength (Chapter 5)

Q₃ = parameter for nominal moment strength (Chapter 5)

R = response modification factor for concrete chimney from Section 4.3.2 (Chapter 4)

R = parameter for nominal moment strength (Chapter 5)

R_L = response modification factor for liner (Chapter 4)

r = average radius of section, ft (Chapter 5)

r_q = 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 height z, ft (Chapter 4)

S₁ = mapped maximum considered earthquake, 5% damped, spectral response acceleration at a period of 1 second (Section 4.3)

S_a = design spectral response acceleration (Section 4.3)

SaM = the maximum spectral response acceleration for

site-specific procedures (Section 4.3)

SD1 = the design spectral response acceleration at a

period of 1 second (Section 4.3)

S_DS = the design spectral response acceleration at short periods (Section 4.3)

S_M1 = the maximum considered earthquake, 5% damped, spectral response acceleration at a period of 1 second adjusted for site class effects (Section 4.3)

S_MS = the maximum considered earthquake, 5% damped, spectral response acceleration at short periods adjusted for site class effects (Section 4.3)

S_p = spectral parameter (Chapter 4)

S_sv = mode shape factor (Section 4.2)

S_s = mapped maximum considered earthquake, 5% damped, spectral response acceleration at short periods (Section 4.3)

S_t = strouhal number (Chapter 4)

s = center-to-center spacing of chimneys, ft (Chapter 4)

T = normal temperature effect, °F (Chapter 6)

T = period of structure (Section 4.3)

T₁ = fundamental period of vibration for unlined shell,

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--`,,`,````,,,`,,`,,```,,,,````,-`-`,,`,,`,`,,`---seconds per cycle (Chapter 4)

T₂ = second mode period of vibration for unlined shell, seconds per cycle (Chapter 4)

Ti = maximum specified design temperature of gas

inside chimney, °F (Chapter 6)

To = minimum temperature of outside air surrounding

chimney, °F (Chapter 6)

T_o = seismic parameter (Section 4.3)

T_x = temperature drop across concrete shell, °F (Chapter 6)

t = thickness of concrete shell, in. (Chapters 5 and 6)

t = concrete thickness at opening, in. (Chapter 4)

t_b = thickness of uninsulated lining or insulation around steel liner, in. (Chapter 6)

t_s = 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 (Chapter 4)

t(h) = thickness of concrete shell at top, ft (Chapter 4)

Uc = required circumferential strength (Chapter 5)

Uv = required vertical strength (Chapter 5)

V = basic wind speed, mph (Chapter 4)

V_cr = critical wind speed for across-wind loads, corre-sponding to fundamental mode, ft/s (Chapter 4)

V_cr2 = critical wind speed for across-wind loads corre-sponding to second mode, ft/s (Chapter 4)

V_r = V(I0.5), mph (Chapter 4)

V = mean hourly wind speed at (5/6)h varying over range of 0.50 and 1.30V(z_cr), ft/s (Chapter 4)

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

V(h) = mean hourly wind speed at top of chimney, ft/s

(Chapter 4)

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

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

(Chapter 4)

W = wind load (Chapter 5)

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)

w′(h) = fluctuating along-wind load per unit length at top

of chimney, lb/ft (Chapter 4)

w′(z) = fluctuating along-wind load per unit length at

height z, lb/ft (Chapter 4)

w₁(z) = mean along-wind load per unit length as given by Eq. (4-27), lb/ft (Chapter 4)

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

w_a(z) = across-wind load per unit length at height z, lb/ft (Chapter 4)

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

Ymax = maximum lateral deflection of top of chimney, ft

(Chapter 4)

y = total (SRSS or CQC) lateral displacement of concrete chimney, ft (Chapter 4)

y_L = total (SRSS or CQC) lateral displacement of

liner, ft (Chapter 4)

Z_c = exposure length, ft (Chapter 4)

z = height above ground, ft (Chapter 4)

z_cr = height corresponding to V_cr, ft (Chapter 4) α = on chimney cross section, one-half of the central

angle subtended by neutral axis, radians (Chapter 5) αte = thermal coefficient of expansion of concrete and

of reinforcing steel, 0.0000065 per °F (Chapter 6) β = one-half of the central angle subtended by an opening on the chimney cross section, radians (Chapter 5 and Appendix A)

β1 = factor in Section 10.2.7.3 of ACI 318 (Chapters 5

and 6)

βa = aerodynamic damping factor (Chapter 4)

βs = fraction of critical damping for across-wind load

(Chapter 4)

γ = one-half of the central angle subtended by the centerlines of two openings on chimney cross section, radians (Chapter 5 and Appendix A) γ1 = ratio of inside face vertical reinforcement area

(Chapter 6)

γ2 = ratio of distance between inner surface of

chimney shell and outside face vertical reinforce-ment to total shell thickness (Chapter 6)

γ1′ = ratio of inside face circumferential reinforcement

area to outside face circumferential reinforcement area (Chapter 6)

γ2′ = ratio of distance between inner surface of

chimney shell and outside face circumferential reinforcement to total shell thickness (Chapter 6)

γd = d(h)/d(b) (Chapter 4)

δ = γ – β for two symmetric openings partly in compression zone, radians (Chapter 5)

εm = maximum concrete compressive strain (Chapter 5

and Appendix A)

λ = τ – n₁β, radians (Chapter 5) λ1 = μ + ψ – π, radians (Chapter 5)

μ = angle shown on Fig. 5.1(a), radians (Chapter 5 and Appendix A)

τ = angle shown on Fig. 5.1(a), radians (Chapter 5 and Appendix A)

ψ = angle shown on Fig. 5.1(a), radians (Chapter 5 and Appendix A)

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

reinforcement per unit of height to total area of concrete shell per unit of height (Chapter 6) ρa = specific weight of air, 0.0765 lb/ft3 (Chapter 4)

ρck = mass density of concrete, kip-s2/ft4 (Chapter 4)

ρt = ratio of total area of vertical reinforcement to total

area of concrete shell cross section (Chapter 5) φ = strength reduction factor (Chapter 5 and

Appendix A) ωt = ρt fy/fc′ (Chapter 5)

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--`,,`,````,,,`,,`,,```,,,,````,-`-`,,`,,`,`,,`---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 throughout the construction of the chimney. The cement used shall conform to the requirements for Types I, II, III, or V of ASTM C150, or Type IS or IP of ASTM C595.

2.3—Aggregates

2.3.1 Concrete aggregates shall conform to ASTM C33. 2.3.2 The maximum size of coarse aggregate shall be not

larger than 1/8 of the narrowest dimension between inside and outside forms nor larger than 1/2 the minimum clear distance between reinforcing bars.

R2.3.2 This requirement differs from the ACI 318 because

most walls are 8 in. thick, and 3/4 or 1 in. aggregate works best with 8 ft forms.

2.4—Reinforcement

Reinforcement shall conform to ASTM A615/A615M, A996/A996M, or A706/A706M. Other deformed reinforce-ment with a specified minimum yield strength f_y exceeding 60,000 psi shall be permitted provided that the ultimate tensile strain shall equal or exceed 0.07.

R2.4 Refer to R5.1.2 for explanation of ultimate tensile

strain limits.

CHAPTER 3—CONSTRUCTION REQUIREMENTS 3.1—General

Concrete quality, methods of determining strength of concrete, field tests, concrete proportions and consistency, mixing and placing, and formwork and details of reinforce-ment shall be in accordance with ACI 318, except as stated otherwise.

3.2—Concrete strength

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 strength tests (consisting of the average of two cylinders per each test) per 8-hour shift (slipform) or per lift (jump form). For precast sections, a minimum of two sets shall be taken from each class of concrete cast each day and from each 100 yd3 of concrete placed each day.

R3.3 Requirements for testing precast concrete units were

added in ACI 307-95.

3.4—Forms

R3.4 Shear transfer within precast concrete shells should

be considered in design, especially if the structure has vertical as well as horizontal construction joints.

3.4.1 Forms for the chimney shell shall be made of metal,

wood, or other suitable materials. If unlined wooden forms

are used, they shall be of selected material with tongue-and-groove joints and shall be kept continuously wet to prevent shrinking and warping due to exposure to the elements. Form oil shall not be used unless it is a nonstaining type and it has been established that specified protective coatings or paint can be applied to concrete exposed to form oil.

3.4.2 Forms shall be sufficiently tight to prevent leakage

of mortar.

3.4.3 Load shall not be placed on the concrete structure until

that portion of the structure has attained sufficient strength to safely support its weight and the loads placed thereon.

3.4.4 Forms shall be removed in such manner as to ensure

the safety of the structure. Forms shall be permitted to be removed after the concrete has hardened to a sufficient strength to maintain its shape without damage and to safely support all loads on it, including temporary construction loads.

3.4.5 Ties between inner and outer chimney shell forms

shall not be permitted.

3.4.6 Construction joints shall be properly prepared to

facilitate bonding. As a minimum requirement, all laitance and loose material shall be removed.

3.5—Reinforcement placement

R3.5 The size, spacing, and location of vertical cores

within precast concrete chimney shells will be determined by geometry and steel area requirements. It is important that the design of precast chimneys complies with the minimum spacing requirements of ACI 318 when arranging reinforcement within the cores to permit proper bar splicing and concrete placement.

3.5.1 Circumferential reinforcement shall be placed

around the exterior of, and secured to, the vertical reinforcement bars. All reinforcing bars shall be tied at intervals of not more than 2 ft. Bars shall be secured against displacement within the tolerances of the ACI 318.

R3.5.1 Particular attention shall be paid to placing and

securing the circumferential reinforcement so that it cannot bulge or be displaced during the placing and working of the concrete so as to result in less than the required concrete cover over this circumferential reinforcement.

3.5.2 Vertical reinforcement projecting above the forms

for the chimney shell or cores of precast sections shall be temporarily supported so as to prevent the breaking of the bond with the freshly placed concrete.

R3.5.2 It is important to protect the early bond set.

Vertical bars are subjected to movement due to wind forces. Vertical bars should be tied together or braced to prevent damaging the bond.

3.5.3 Not more than 50% of bars shall be spliced along any

horizontal or vertical plane unless specifically permitted and approved by the licensed design professional.

3.5.4 For reinforcement in cast-in-place chimneys, the

minimum concrete cover shall be 2 in. For reinforcement in precast units manufactured under plant-controlled conditions, the minimum concrete cover shall be 1.5 in.

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--`,,`,````,,,`,,`,,```,,,,````,-`-`,,`,,`,`,,`---3.6—Concrete placement

Cast-in-place concrete placement shall conform to ACI 318, and shall be placed in layers no greater than 16 in. Vertical construction joints for cast-in-place chimney shells shall not be used. Where used, horizontal construction joints for cast-in-place and precast concrete shall be approximately evenly spaced throughout the height of the chimney shell. Grout for setting precast sections shall have a specified compressive strength equal to or greater than the specified compressive strength of the set precast sections.

3.7—Concrete curing

3.7.1 Immediately after the forms have been removed, all

necessary finishing of concrete shall commence.

3.7.2 As soon as finishing has been completed, both faces

of concrete shall be cured by coating with a membrane-curing compound or other method approved by the licensed design professional. The curing compound shall comply with ASTM C309, and shall be applied in strict accordance with the manufacturer’s recommendations. If coatings are to be applied to the concrete, the curing compound shall be of a type compatible with these coatings.

3.8—Construction tolerances

R3.8 A quality control program should be established to

measure, document, and verify compliance with the construction tolerance requirements of this code. The program should identify the type, number, and frequency of the measurements required to document each of the areas specified in this code.

3.8.1 The chimney shell shall be constructed within the

tolerance limits set forth herein.

3.8.1.1 Vertical alignment of centerpoint—The actual

centerpoint of the shell shall not vary from its theoretical axis by more than 0.001 times the height of the shell, or 1 in., whichever is greater. Locally, the actual centerpoint of the shell shall not change horizontally by more than 1 in. for any 10 ft of vertical rise.

3.8.1.2 Diameter—The measured outside shell diameter

at any section shall not vary from the specified diameter by more than 1 in. plus 0.01 times the specified or theoretical diameter.

3.8.1.3 Wall thickness—The measured wall thickness

shall not vary from the specified wall thickness by more than –1/4 in., +1/2 in. for walls 10 in. thick or less, or by more than –1/2 in., +1 in. for walls greater than 10 in. thick. A single wall thickness measurement is defined as the average of at least four measurements taken at a uniform spacing over a 60-degree arc. A negative tolerance decreases the overall thickness, and a positive tolerance increases the overall thickness.

3.8.2 Openings and embedments—Tolerances on the size

and location of openings and embedments in the shell cannot be uniformly established due to the varying degrees of accuracy required, depending on the nature of their use. Appropriate tolerances for opening and embedment sizes and locations shall be established for each chimney.

3.9—Precast erection

3.9.1 Precast sections shall be erected in a manner and at a

rate that ensures that sufficient strength has been attained in grout, core concrete, and all connecting components to safely support construction and applicable design loads.

3.9.2 Precast sections shall be grouted to level, and joints

shall be sealed. Shear keys shall be installed if required by the licensed design professional.

CHAPTER 4—LOADS AND GENERAL DESIGN CRITERIA

4.1—General

R4.1 For the 1995 edition, the Committee re-evaluated the

previous exemptions regarding two-face reinforcement and minimum wall thickness for chimneys 300 ft or less in height and less than 20 ft in diameter. Recent information has indicated that two-face circumferential reinforcement is necessary to minimize vertical cracking due to radial wind pressures and reverse thermal gradients due to the effects of solar heating. Reverse thermal gradients due to solar heating may be more pronounced when the air space between the column and lining is purged by pressurization fans and gas temperatures are low. Further, the current committee believes that two-face reinforcement should be required in all chimney columns, regardless of size, considering the aggressive environment surrounding chimneys.

4.1.1 The chimney shell shall be designed for the effects

of gravity, temperature, wind, and earthquake in accordance with ACI 318, except as stated otherwise.

4.1.2 The chimney shell shall be designed for load

combinations in accordance with the provisions of Chapter 5.

4.1.3 Minimum shell thickness

4.1.3.1 The chimney shell shall not be less than 8 in.

thick when cast in place, or less than 7 in. thick when composed of precast sections.

R4.1.3.1 A minimum wall thickness of 8 in. (7 in. if

precast) is required to provide for proper concrete placement within and around two curtains of reinforcement.

4.1.3.2 The chimney shell thickness, through openings,

shall not be less than 1/24 times the height of the opening over a vertical distance extending from 1/2 the height of the opening below the sill of the opening to 1/2 the height of the opening above the top of the opening. Properly designed buttresses or other means of lateral restraint may be permitted in place of this requirement. However, the buttresses or other means of lateral restraint shall not be included when calculating vertical strength.

R4.1.3.2 The committee expressed concern regarding

edge buckling of relatively thin walls through regions where tall openings are present. The simplified procedure given in this section will give approximately the same results as the procedures of Section 10.10 of ACI 318-02 (ACI Committee 318 2002).

The committee defines a buttress to be rectangular or square in shape and can project either inside or outside (or both) the chimney wall. A buttress provides additional stability to the thin wall design.

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--`,,`,````,,,`,,`,,```,,,,````,-`-`,,`,,`,`,,`---If jamb buttresses are used, they should be placed homogeneously with the section or adequately tied to ensure composite action.

4.1.3.3 When the inside diameter of the shell exceeds 28 ft,

the minimum thickness shall be increased 1/8 in. for each 1 ft increase in inside diameter.

4.1.4 Shell and liner interaction—A chimney shell that

supports lining loads shall comply with the requirements of this standard with the lining in place. The loads on the concrete shell shall include any lining loads resulting from dead load, thermal, wind, or seismic loads.

4.1.5 Design for temporary construction loads—When

temporary access openings are used during construction, they shall be designed as permanent openings.

4.1.6 Foundation considerations

4.1.6.1 The maximum foundation bearing pressure shall

be established using service chimney loads.

R4.1.6.1 Service loads are defined in Section 2.4 of

ASCE 7-02.

4.1.6.2 The foundation shall be designed by the strength

method in accordance with the procedures of ACI 318. The foundation design shall be based on a pseudo-bearing pres-sure distribution, or pile loads, using the loading combina-tions given in Section 5.3.1.

R4.1.6.2 Foundation design—The pseudo-bearing

pres-sure/pile loads should be computed by multiplying the unfac-tored dead and axial bending loads by their appropriate load factor from Sections 5.3.1.

4.1.6.3 The minimum factor of safety against overturning

shall be 1.50 using service loads.

4.1.6.4 Design shall include the effects of radiant heat of

gases on any part of the foundation, including the foundation floor area that is exposed within the liner and concrete floors supported from the concrete shell.

4.2—Wind loads

4.2.1 General—Reinforced concrete chimneys shall be

designed to resist the wind forces in both the along-wind and across-wind directions. In addition, the hollow circular cross section shall be designed to resist the loads caused by the circumferential pressure distribution.

The reference design wind speed in mph, which shall be denoted as V_r, shall be the 3-second gust wind speed at 33 ft over open terrain, where V_r = (I)0.5V. This speed V shall be

as specified by ASCE 7-02. The importance factor I for all chimneys shall be 1.15. Topographic effects referenced in Section 6.5.7.1 of ASCE 7-02 are omitted.

At a height z ft above ground, the mean hourly design speed V(z) in ft/s shall be computed from Eq. (4-1)

(4-1)

The provisions with respect to wind load take into account dynamic action, but are simplified and result in equivalent static loads. A properly substantiated dynamic analysis shall be permitted in place of these provisions.

R4.2.1 The basic wind speed V in the ACI 307-98 standard

was revised from fastest-mile to a 3-second gust speed to reflect the changes published in ASCE 7-02. Equation (4-1) was modified accordingly. In Eq. (4-1), 1.47 converts wind speed from mph to ft/s, and 0.65 converts the 3-second gust speed to a mean hourly speed. The revised power law coefficient 0.154 (as an approximation of 1/6.5) came from Table 6.2 of ASCE 7-02 for Exposure C and for flexible or dynamically sensitive structures; the increase in the exponent increases the calculated pressures over the chimney height for the same speed.

The 3-second gust speed is always higher than the previously specified fastest-mile speed. A fastest-mile wind speed may be converted to a 3-second gust speed for normal speeds of interest in chimney design using

3-second gust V = 1.0546 (fastest mile V + 11.94) The relationship between a 3-second gust speed and any other averaging time can be found in texts such as Wind

Effects on Structures (Simiu and Scanlon 1986).

The procedure was determined from simplified dynamic analyses that resulted in equivalent static load distributions. This approach requires that a wind speed averaged over a period approximately 20 minutes to 1 hour be used as a basis for design. Equation (4-1) permits the mean hourly speed at height z to be determined from the basic design speed that is the 3-second gust speed at 33 ft over open country. The conversion is based on the relationship recommended by Hollister (1969). The specified wind loads presume that the chimney is located in open country. In rougher terrains, the overall loads will be reduced, but for a tall chimney (with a height of approximately 650 ft), the reduction is not likely to exceed 20%.

In Eq. (4-1), V_r is the product of the square root of the importance factor I, and V, the basic wind speed as charted and defined in ASCE 7-02. I can be used to vary probability as well as to classify the importance of the structure. All chim-neys should be designed to be part of an essential facility classified as a Category IV structure. The importance factor of 1.15 for Category IV buildings and structures corresponds to a mean recurrence interval of 100 years. Additional infor-mation can be found in ASCE 7-02.

The simplified provisions of this standard do not preclude the use of more detailed methods, and the results of a full dynamic analysis employing accepted approaches and recognizing the flow profile and turbulence levels at a specific site may be used in place of the standard provisions. The approximate methods have, however, been tested against more detailed analyses using probabilistic (Vickery 1969; Vickery and Basu 1985) and deterministic (Rumman 1985) approaches. These methods gave acceptable results.

4.2.2 Along-wind load: circular shapes—The along-wind

load, w(z) per unit length at any height z ft, shall be the sum of the mean load w(z) and the fluctuating load w′(z).

The mean load w(z) in lb/ft shall be computed from Eq. (4-2)

w(z) = C_dr(z) × d(z) × p(z) (4-2) V z( ) (1.47)Vr z 33 ---⎝ ⎠ ⎛ ⎞0.154 0.65 ( ) × =

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--`,,`,````,,,`,,`,,```,,,,````,-`-`,,`,,`,`,,`---where

C_dr(z) = 0.65 for z < h – 1.5d(h) (4-3)

C_dr(z) = 1.0 for z ≥ h – 1.5d(h) (4-4) and 1.5d(h) shall not exceed 50 ft

p(z) = 0.00119K_d[V(z)]2 (4-5) where Kd = 0.95 for circular chimneys.

The fluctuating load w′(z), lb/ft, shall be taken equal to (4-6)

where M_w(b) is the base bending moment, lb-ft, due to w(z), and

(4-7)

where V(33) is determined from Eq. (4-1) for z = 33 ft. For preliminary design and evaluation of the critical wind speed V_cr, as described in Section 4.2.3.1, the natural period of an unlined chimney T₁, in seconds per cycle, shall be permitted to be approximated using Eq. (4-8). For final design, however, the period shall be computed by dynamic analysis

(4-8)

The mass and structure properties of the chimney lining shall be included in the calculation of the period.

R4.2.2 The recommended drag coefficients are consistent

with slender chimneys [h/d(h) > 20] with a relative surface roughness on the order of 10–4 to 10–5. Some reduction in the drag coefficient C_dr with decreasing h/d(h) can be expected, but unusually rough (for example, ribbed) chimneys would have higher values of C_dr. The variations of C_dr with roughness and aspect ratio are discussed by Basu (1982) and Vickery and Basu (1984).

The total load per unit length is computed as the sum of the mean component w(z) and the fluctuating component w′(z). The dynamic component was evaluated using a slightly modified form of the gust factor approaches described by Davenport (1967), Vickery (1969), and Simiu et al. (1977). The base moment is evaluated using the gust factor approach, but the loads producing this moment are approx-imated by a triangular distribution rather than a distribution matching the mean. Equation (4-7) is a simple empirical fit to values of G_w_′ computed as before for a structural

damping of 1.5% of critical. Except for referencing V as the 3-second gust speed, no revisions have been made to the procedures for calculating along-wind loads.

For the 2008 revision, the directionality factor K_d was added to Eq. (4-5). The 1.5 × d(h) is now limited to 50 ft, and the factor of 2 in 4.4.3 is removed. Also, the numeric coefficient was revised to correct for a previous error.

The natural period of the chimney may include the effect of foundation and soil interaction.

4.2.3 Across-wind load: circular shapes

R4.2.3 No revisions were made to the procedures for

calculating across-wind forces in the 2008 version.

In 1995, the committee had numerous user comments and discussions regarding the procedures included in the 1988 standard for across-wind forces. Virtually all of the commentators felt that the 1988 procedures were unduly conservative, especially in the absence of any record of structural failure. As a result of these discussions, and with the availability of new data and full-scale observations, the procedures for calculating across-wind loads were extensively revised.

A general solution for the across-wind response of circular chimneys with any geometry was developed by Vickery (1993). These procedures, based on Vickery’s general solution, were simplified to some extent, which requires that their application be restricted to certain geometries. Similar models have provided the basis for vortex-induced forces incorporated by the National Building Code of Canada (Canadian Commission on Building and Fire Codes 1995) and the ASME/ANSI STS-1.

Circular chimneys outside the bounds of these procedures, or where a flare or strong taper (nozzle) exists for more than one diameter near the top, may be conservatively analyzed using the procedures of Section 4.2.3.3 of ACI 307-88 or by the general approach put forth by Vickery (1993).

The procedures for determining shedding forces, however, are not materially affected by the configuration of the lower third of the shell, which may range from plumb to any degree of taper.

Noncircular shapes may be more sensitive to across-wind forces and may require analyses beyond the scope of this standard.

Equation (4-18) establishes a basis for increasing structural damping from a minimum of 1.0% to a maximum of 4.0% when the wind speed V exceeds V(z_cr). Structural damping of 1% of critical is consistent with measured values and moderate stress levels with little cracking. Damping of 4.0%, which would be permitted when V = 1.30V(z_cr), is more consistent with damping values permitted in seismic design.

Eight sample chimneys were studied using the 1988 and 1995 procedures. The geometry is in Table R4.1, and a more detailed description is in 307-88. Fatigue damage was also considered using the procedures put forth by Vickery (1993). The committee concluded that a case-by-case analysis of fatigue in circular chimneys that would require a supplemental working stress analysis was not necessary, as fatigue stresses in the sample chimneys were within acceptable limits.

Results using the 1988 and 1995 procedures are compared in Table R4.1. These chimneys were selected from a group of projects where the aspect ratio h/d is at or near 10, where peak excitation is normally found. Note that w′ z( ) 3.0z×Gw′×Mw( )b h3 ---= Gw′ 0.30 11.0 T[ ₁×V 33( )]0.47 h+16 ( )0.86 ---+ = T₁ 5 h 2 d b( ) --- ρck Eck --- t h( ) t b( ) ---⎝ ⎠ ⎛ ⎞0.3 =

(13)

--`,,`,````,,,`,,`,,```,,,,````,-`-`,,`,,`,`,,`---for Chimneys 7 and 9, the critical wind speed exceeds the design wind speed, permitting modification of both damping (Eq. (4-18)) and M_a (Eq. (4-10)), which signifi-cantly reduces the base moments.

4.2.3.1 General—Across-wind loads due to vortex

shedding in the first and second modes shall be considered in the design of all chimney shells when the critical wind speed V_cr is between 0.50 and 1.30 V(z_cr). Across-wind loads need not be considered outside this range.

4.2.3.2 Analysis—When the outside shell diameter at h/3 is

less than 1.6 times the top outside diameter, across-wind loads shall be calculated using Eq. (4-9), which defines the peak base moment M_a

(4-9)

×

Equation (4-9) defines the peak base moment Ma for

values of V, where V is evaluated between 0.5 and 1.30V(zcr). When V ≥ V(zcr), Ma shall be multiplied by

(4-10)

where G = 4.0, and S_sv= 0.57 (first mode) and 0.18 (second mode). C_L = C_LoF_1B (4-11) where C_Lo = –0.243 + 5.648i – 18.182i2 (4-12) where (4-13) Ma G g ----SsvCL ρa 2 ---Vcr 2 d u( )h2 π 4(βs+βa) ---× 1/2 = Sp 2L h d u( ) ---+CE ⎝ ⎠ ⎛ ⎞ ---⎝ ⎠ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎛ ⎞1/2 1.0 0.95 V–V z( )cr V z( )cr ---⎝ ⎠ ⎜ ⎟ ⎛ ⎞ – i 1 loge (5/6)h Zc ---⎝ ⎠ ⎛ ⎞ ---=

Table R4.1—Comparison of results: along-wind plus across-wind moments, 1988 versus 1995 procedures

Description of chimneys

Chimney Height, ft Top outside diameter, ft Bottom outside diameter, ft Tapers VI, mph h/d at (5/6)h Frequency, hz 6 485 47.67 53.50 3 85.0 10.17 0.485 13 500 52.17 52.17 1 76.8 09.58 0.428 7 534 51.09 61.55 1 74.9 10.11 0.591 8 545 33.00 55.00 1 85.6 14.86 0.432 9 613 73.00 73.00 1 74.9 08.40 0.406 12 978 71.50 114.58 3 74.9 13.68 0.295 2 275 28.00 28.00 1 85.6 09.82 0.752 4 375 20.00 32.00 1 85.6 17.05 0.529

Calculated wind speeds Chimney

Per ACI 307-88 Per ACI 307-95

V_cr, mph V(z_cr), mph V(z_cr), mph _{V, mph} V_cr, mph _k 6 78.9 93.9 93.3 88.3 77.8 1.135 13 76.2 84.0 83.5 83.5 76.3 1.094 7 106.4 84.8 84.3 84.3 105.2 0.802 8 54.0 96.0 95.5 55.2 48.6 1.135 9 101.1 86.4 85.9 85.9 104.9 0.820 12 72.0 92.3 91.7 66.0 66.0 1.000 2 71.8 87.2 86.7 86.7 71.5 1.214 4 39.7 91.1 90.6 45.3 34.6 1.310

Factored base wind moments in ft-tons Chimney

Per ACI 307-88, RMS combined along- and across-wind: Bs = 0.015;

LF = 1.40

Per ACI 307-95, RMS combined along- and across-wind: Bs = 0.010;

LF = 1.40

Per ACI 307-88 and ACI 307-95 along-wind only: LF = 1.70 6 270,600 209,200 160,900 13 283,500 224,100 148,000 7 447,800 238,100 165,100 8 117,500 79,400 161,200 9 971,700 459,100 320,700 12 1,475,800 977,400 865,300 2 39,800 34,100 28,600 4 16,500 11,600 43,800

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--`,,`,````,,,`,,`,,```,,,,````,-`-`,,`,,`,`,,`---Z_c= 0.06 ft. (4-14) but not > 1.0 or < 0.20 ρa = 0.0765 lb/ft3 (4-15) St = 0.25F1A (4-16) where F_1A = 0.333 + 0.206log_e (4-17) but not > 1.0 or < 0.60 (4-18) but not < 0.01 or > 0.04 (4-19) k_a= k_aoF_1B (4-20) where (4-21) where (4-22) (4-23) where B = 0.10 + 2i (4-24) L = 1.20 C_E = 3

After solving for M_a, across-wind moments at any height,

M_a(z), shall be calculated based on the corresponding mode shape of the chimney column.

4.2.3.3 Second mode—Across-wind response in the second

mode shall be considered if the critical wind speed V_cr2, as

computed by Eq. (4-25), is between 0.50 and 1.30V(z_cr), where V(z_cr) is the mean hourly wind speed at (5/6)h

(4-25)

The period T₂ in seconds per cycle for an unlined shell may be estimated by Eq. (4-26). For final design, T₂ shall be calculated by dynamic analysis

(4-26)

where t(h) and t(b) are the thicknesses at the top and bottom, respectively, and d(h) and d(b) are the mean diameters at the top and bottom, respectively.

The effect of a shell-supported liner on the period of the second mode shall also be included in the design.

Any method based on the modal characteristics of the chimney shall be used to estimate the across-wind response in the second mode.

4.2.3.4 Grouped chimneys—When two identical chimneys

are in close proximity, the across-wind load shall be increased to account for the potential increase in vortex-induced motions. In such cases, the lift coefficient C_L in Eq. (4-11) shall be modified as follows

a. If s/d(z_cr) > 12.75, C_L is unaltered; and

b. If 3 < s/d(z_cr) < 12.75, C_L shall be multiplied by: [0.26

– 0.015s/d(z_cr)] + [2 – s/12d(z_cr)].

For chimneys that are not identical and for identical chimneys where s/d(z_cr) < 3, the value of C_L shall be established by reference to model tests or observations or test reports of similar arrangements.

R4.2.3.4 Interactions between closely spaced cylindrical

objects have been studied in considerable detail, but virtually all of the test results are for subcritical values of Reynolds numbers, and their applicability to chimneys is highly questionable. Even with the scale effects introduced by the inequality of the Reynolds number, however, the wind tunnel is presently the only tool that will provide guidance as to the likely magnitude of interference effects. A review of interference effects was given by Zdravkokvich (1977). Vickery (1993) attributed the amplification of shedding forces to increased turbulence and additional buffeting effects that formed the basis for revisions made to this section.

At center-to-center spacings s in excess of two to three diameters, the prime interference effect is related to across-wind excitation due to shedding. The recommendations in Section 4.2.3.4 are based on the results of Vickery and Daly (1984), and were obtained at subcritical values of the Reynolds number. The first term in the modifier (c) is an enhancement factor to account for buffeting due to vortexes shed by the upstream structure; the second term accounts for small-scale turbulence. The same reference also contains results for two cylinders of different sizes, with the upstream structure having a diameter 25% greater than the diameter d of F_1B –0.089 0.337loge h d u( ) ---+ = Vcr fd u( ) St ---= h d u( ) ---βs 0.01 0.10 V[ –V z( )cr ] V z( )cr ---+ = βa kaρad u( ) 2 wt u( ) ---= kao 1.0 – 1+5i ( ) 1 k–1 i+0.10 ---+ ⎝ ⎠ ⎛ ⎞ ---= k V Vcr ---= Sp k 1.5 B0.5π0.25 --- 1 2 --- 1 k 1 – – B ---⎝ ⎠ ⎛ ⎞2 – exp = V_cr2 5d u( ) T₂ ---= T₂ 0.82 h 2 d b( ) --- ρck Eck --- t h( ) t b( ) --- 0.09 d h( ) d b( ) --- –0.22 =