313_Public_Discussion_Draft.pdf

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This draft is not final and is subject to revision. This draft is for public review and comment.

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Design Specification for Concrete Silos and Stacking Tubes for Storing Granular Materials (ACI 3

313-14) and Commentary 4

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Reported by ACI Committee 313 6

Shahriar Shahriar 7

Chair 8

William D. Arockiasamy 9 William H. Bokhoven 10

Patrick B. Ebner 11 Stephen G. Frankosky 12

Timothy A. Harvey 13 F. Thomas Johnston 14

David C. Mattes 15 Rodney M. Nohr 16 John E. Sadler 17

Michael D. Simpson 18 Bill J. Socha 19

20 Consulting Members 21

22 Donald Midgley 23 John M. Rotter 24 Jonathan G. M. Wood25

26 27

28 29

This Design Specification provides material, design, and construction requirements for 30

concrete silos, stave silos, and stacking tubes for storing granular materials, including design and 31

construction requirements for cast-in-place or precast and conventionally reinforced or post-32

tensioned silos. 33

Silos and stacking tubes require design considerations not encountered in building structures. 34

While this Design Specification refers to ACI 318 for several requirements, static and dynamic 35

loading from funnel, mass, concentric, and asymmetric flow in silos; special loadings on stacking 36

tubes; and seismic and hopper bottom design are also included. 37

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313 Public Discussion

Draft

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Keywords: asymmetric flow; bins; funnel flow; granular materials; hoppers; mass flow; silos. 1

CONTENTS 2

Chapter 1—General 3

1.1—Scope 4

1.2—Documentation 5

1.3—Regulations/Inspections 6

Chapter 2—Notation and definitions 7

2.1—Notation 8

2.2—Definitions 9

Chapter 3—Reference standards 10

Chapter 4—Materials 11

4.1—General 12

4.2—Cement and Concrete 13

4.3—Aggregates 14

4.4—Water 15

4.5—Admixtures 16

4.6—Reinforcement 17

4.7—Precast concrete staves 18

4.8—Tests of materials 19

Chapter 5—Construction requirements 20

5.1—General 21

5.2—Sampling and testing concrete 22

5.3—Details and placement of reinforcement 23

5.4—Forms 24

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5.5—Concrete placing and finishing 1

5.6—Concrete protection and curing 2

5.7—Lining and coating 3

5.8—Tolerances for slipformed and jumpformed structures 4

Chapter 6—Design 5

6.1—General 6


6.3—Loads 8

6.4—Wall design 9

6.5—Hopper design 10

6.6—Column design 11

6.7—Foundation design 12

Chapter 7—Concrete stave industrial silos 13

7.1—Scope 14

7.2—Coatings 15

7.3—Erection tolerances 16

7.4—Wall design 17

7.5—Hoops for stave silos 18

7.6—Concrete stave testing 19

Chapter 8—Post-tensioned concrete silos 20

8.1—Scope 21

8.2—Post-tensioning systems 22

8.3—Tendon systems 23

8.4—Bonded tendons 24

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8.5—Unbonded tendons 1

8.6—Post-tensioning ducts 2

8.7—Details and placement of nonprestressed reinforcement 3

8.8—Wall openings 4

8.9—Stressing records 5

8.10—Design 6

8.11—Vertical bending moment and shear due to post-tensioning 7

8.12—Tolerances 8

Chapter 9—Concrete stacking tubes 9

9.1—Scope 10

9.2—General layout 11

9.3—Loads 12

9.4—Load factors and strength-reduction factors 13

9.5—Tube wall design 14

9.6—Foundation or reclaim tunnel 15

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CHAPTER 1—GENERAL 17

1.1—Scope 18

This Design Specification covers the design and construction of concrete silos, stave silos, and 19

stacking tubes for storing granular materials. 20

For the design of these structures, initial filling and flow loading shall be considered. This 21

Design Specification is supplemental to ACI 318-11 for design and ACI 301-10 for construction, 22

where indicated. 23

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1.1.1 Specific inclusions— Industrial stave silos for storage of granular materials are included in 1

these specifications. The application to precast concrete is limited to industrial stave silos. Effect 2

of hot stored material is included in this Design Specification. 3

1.1.2 Specific exclusions—Silos for storing silage are not included in this Design Specification. 4

This Design Specification does not consider any chemical reaction between the silo reinforced 5

concrete and the stored granular material. 6

1.1.3 Hierarchy of standards—Whenever the requirements of this Design Specification are more 7

stringent than the requirements of ACI 318-11, the requirements of this Design Specification shall 8

govern. 9

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1.2—Documentation 11

1.2.1 Project drawings and specifications for silos shall be prepared under the direct supervision 12

of and bear the seal of the licensed design professional. 13

1.2.2 Contract documents shall show all features of the work, naming the stored materials assumed 14

in the design and stating their properties, including the size and position of all structural 15

components, connections, and reinforcing steel; the specified concrete strength; and the specified 16

strength or grade of reinforcement and structural steel. 17

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1.3—Regulations/Inspections 19

1.3.1 This Design Specification supplements legally adopted building code in all matters 20

pertaining to concrete silo and stacking tubes for storing granular materials. 21

1.3.2 Construction shall be inspected throughout the various work stages by or under the 22

supervision of a licensed design professional or a qualified inspector. 23

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1

CHAPTER 2—NOTATION AND DEFINITIONS 2

2.1—Notation 3

The terms in this list are used in the Design Specification and as needed in the commentary. 4

A = effective tension area of concrete surrounding the tension reinforcement and having the 5

same centroid as that reinforcement, divided by the number of bars; when the 6

reinforcement consists of different bar sizes, the number of bars shall be calculated as 7

the total area of reinforcement divided by the area of the largest bar used. 8

Ā = critical ratio 9

Af = area of flow channel, ft2 (m2) 10

As = area of hoop or tension reinforcement, in.2 (mm2)per unit height 11

Asilo = cross-sectional area of silo, ft2 (m2) 12

Aw = effective cross-sectional area (horizontal projection) of an individual stave, in.2 (mm2) 13

B = constant used to compute n 14

Cd = over pressure factor 15

dc = distance from bar centerline towards surface, used to calculate design crack width, in. 16

D = silo inside diameter, ft (m) 17

D′ = effective outlet diameter, ft (m) 18

E = effects of earthquake, or related internal moments and forces 19

Ec = modulus of elasticity for concrete, psi (MPa) 20

Ecc = distance from center of silo to center of outlet (eccentricity of outlet), ft (m) 21

Ep = modulus of elasticity of post-tensioning reinforcement, psi (MPa) 22

Es = modulus of elasticity of reinforcement, psi (MPa) 23

eo = distance from center of silo to apex of eccentric hopper, ft (m) 24

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Fu = required hoop or horizontal tensile strength, lb (N) per unit height of wall 1

fc = specified compressive strength of concrete, psi (MPa) 2

fci = compressive strength of concrete at time of initial stressing, psi (MPa) 3

fpu = specified tensile strength of -prestressing steel, wires, or strands, psi (MPa) 4

fpy = specified yield strength of prestressing steel, wires, or strands, psi (MPa) 5

fs = calculated stress in reinforcement at initial (filling) pressures, psi (MPa) 6

fse = effective stress in post-tensioning reinforcement (after allowance for all losses), psi 7

(MPa) 8

fy = specified yield strength of nonprestressed reinforcement, psi (MPa) 9

h = wall thickness, in. (mm) 10

h’b = height from hopper apex to effective outlet of hopper, ft (m) 11

hh = height of hopper from apex to top of hopper, ft (m) 12

hs = height of sloping top surface (repose volume) of stored material, ft (m) 13

hst = height of stave specimen for compression test, in. (mm) 14

hy = depth below top of hopper to point in question, ft (m) 15

h1 = core wall thickness, in. (mm) 16

H’ = depth from the effective depth of the repose volume to the apex of the hopper, ft (m) 17

k = ratio of p to q 18

lstg = amount of vertical stagger between horizontal stave joints, ft (m) 19

Lw = length of design flow channel perimeter in contact with wall, ft (m) 20

Mneg = negative (tension outside face) circumferential bending moments caused by 21

asymmetric filling or emptying under service load conditions, ft-lb (m-N)per unit 22

height 23

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Mpos = positive (tension inside face) circumferential bending moment caused by asymmetric 1

filling or emptying under service load conditions, ft-lb (m-N) per unit height 2

M = circumferential bending strength for an assembled circular group of silo staves, ft-lb 3

(m-N) per unit height; the statical moment or sum of absolute values of M,pos and M,neg 4

M,neg = the calculated bending strength in the negative moment zone (tension on the outside 5

face), ft-lb (m-N) per unit height 6

M,pos = the calculated bending strength in the positive moment zone (tension on the inside 7

face), ft-lb (m-N) per unit height 8

Mt = thermal bending moment per unit width of height of wall (consistent units), ft-lb/ft (m-9

N/m) 10

n = constant used to computer qy 11

Pf = perimeter of flow channel, ft (m) 12

Pnw = nominal axial load strength of stave wall per unit perimeter, lb (N) 13

Pnw,buckling = nominal axial load strength of the stave wall as limited by buckling, lb (N) 14

Pnw,joint = nominal axial load strength of the stave wall as limited by the stave joint, lb (N) 15

Pnw,stave = nominal axial load strength of the stave wall as limited by the shape of the stave, lb (N) 16

p = initial (filling) horizontal pressure due to stored material, psf (N/m2) 17

pn = pressure normal to hopper surface at a depth below top of hopper, psf (N/m2) 18

ps = horizontal pressure within static material around flow channel(s), psf (N/m2) 19

q = initial (filling) vertical pressure due to stored material, psf (N/m2) 20

qf = vertical design pressure in the nonconverging section of the flow channel, psf (N/m2) 21

qo = initial vertical pressure at top of hopper, psf (N/m2) 22

qs = vertical pressure within static material around flow channels(s), psf (N/m2) 23

qy = vertical pressure at a distance hy below top of hopper, psf (N/m2) 24

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r = silo inside radius, ft (m) 1

R = ratio of area to perimeter of horizontal cross section of storage space 2

Rf = ratio of area to perimeter for a flow channel, ft (m) 3

s = bar spacing, in. (mm) 4

vn = initial friction force per unit area between stored material and hopper surface, lb (N) 5

V = total vertical frictional force on a unit length of wall perimeter above the section in 6

question, lb (N) 7

w = design crack width, in. (mm) 8

ws = width of stave specimen for compression test, in. (mm) 9

W = wind load, or related internal moments and forces, psf (N/m2) 10

Wt = tension force per stave from wind overturning moment, lb (N) 11

Y = depth from the effective depth of the repose volume to point in question, ft (m) 12

YEFF = vertical distance from the top of the discharge opening to the effective depth of the 13

repose volume, ft (m) 14

Y = diameter of the flow channel, ft (m) 15

T = temperature difference between inside face and outside face of wall, degrees Fahrenheit 16

(degrees Celcius) 17

= constant used to compute B 18

δ = effective angle of internal friction, degrees 19

= weight per unit volume for stored material, pcf (kg/m3) 20

= angle of hopper from vertical, degrees 21

f = angle of flow channel with vertical, degrees 22

μ = coefficient of friction between stored material and wall or hopper surface 23

ν = Poisson’s ratio for concrete, assumed to be 0.2 24

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= strength-reduction factor or angle of internal friction, degrees 1

′ = angle of friction between material and wall and hopper surface, degrees 2

ρ = angle of repose, degrees 3

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2.2—Definitions 5

The following terms are defined for general use in this Design Specification. Specialized 6

definitions appear in individual chapters. 7

aeration pressures—air pressures caused by injection of air for mixing or homogenizing, or for 8

initiating flow near discharge openings. 9

asymmetric flow—flow pattern in which the flow channel is not centrally located. 10

concentric flow—flow pattern in which the flow channel has a vertical axis of symmetry 11

coinciding with that of the silo and discharge outlet. 12

discharging—process of emptying the material by gravity from the silo. 13

effective angle of internal friction )—a measure of combined friction and cohesion of 14

material— approximately equal to the angle of internal friction for free flowing or coarse materials, 15

but significantly higher for cohesive materials. 16

expanded flow—flow pattern in which a mass flow hopper is used directly over the outlet to 17

expand the flow channel diameter beyond the maximum stable rathole diameter. 18

expanded flow silo—silo equipped with a self-cleaning hopper section above a mass flow hopper 19

section. 20

filling—the process of loading the material by gravity into the silo. 21

flow channel—channel of moving material that forms above a discharge opening. 22

flow pressures—stored material pressures during flow. 23

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funnel flow—flow pattern in which the flow channel forms within the material; material 1

surrounding the flow channel remains at rest during discharge. 2

hopper—converging portion at the bottom of a silo making the transition from a silo to one or 3

more outlets. 4

initial filling pressure—pressures during filling and settling of material, but before discharge has 5

started. 6

jackrod—a vertical steel pipe or solid rod embedded in a silo wall, used in slipform silo construction. The 7

slipform lifting jacks are supported by and ride up the jackrods, advancing the wall forms vertically. 8

jumpformed silo—silo constructed typically using three segments of fixed forms; the bottom 9

segment is moved to the top position after the concrete at bottom level gains adequate strength. 10

mass flow—flow pattern in which all material is in motion whenever any of it is withdrawn. 11

overpressure factor—multiplier applied to the initial filling pressure to provide for pressure 12

increases that occur during discharge. 13

plane flow hopper—hopper with two flat sloping sides and two vertical ends. 14

pressure zone—that zone within the silo subjected either directly or indirectly to pressure from 15

stored material. 16

pyramidal hopper—hopper with polygonal flat sloping sides. 17

rathole—a flow channel configuration which, when formed in surrounding static material, 18

remains stable after the contents of the flow channel have been discharged. 19

self-cleaning hopper—hopper that is sloped steeply enough to cause material, which has 20

remained static during funnel flow, to slide off of it when the silo is completely discharged. 21

stable arch dimension—maximum dimension up to which a material arch can form and remain 22

stable. 23

silo—any upright container for storing bulk granular material. 24

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slipformed silo—silo constructed using a continuously moving form. 1

stacking tube—relatively slender, free-standing tubular concrete structure used to lower 2

material in a controlled fashion from a conveyor to a storage pile. 3

stave silo—silo assembled from small precast concrete units called staves, usually having tongue 4

and groove joints, and held together by exterior adjustable steel hoops. 5

tilted hopper—hopper that has its axis tilted from the vertical. 6

transition hopper—hopper with flat and curved surfaces. 7

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CHAPTER 3—REFERENCE STANDARDS 10

American Concrete Institute 11

ACI 117-10 Specification for Tolerances for Concrete Construction and Materials and 12

Commentary 13

ACI 301-10 Specifications for Structural Concrete 14

ACI 318-11 Building Code Requirements for Structural Concrete and Commentary 15

ACI 305.1-06 Specification for Hot Weather Concreting 16

ACI 306.1-90 Standard Specification for Cold Weather Concreting (Reapproved 2002) 17

ACI 308.1-11 Specification for Curing Concrete 18

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American Society of Civil Engineers 20

ASCE/SEI 7-10 Minimum Design Loads for Buildings and Other Structures 21

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ASTM International 23

ASTM A47/A47M-99(2009) Standard Specification for Ferritic Malleable Iron Castings 24

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ASTM A123/A123M-12 Standard Specification for Zinc (Hot-Dip Galvanized) Coatings on 1

Iron and Steel Products 2

ASTM A153/A153M-09 Standard Specification for Zinc Coating (Hot-Dip) on Iron and 3

Steel Hardware 4

ASTM A615/A615M-13 Standard Specification for Deformed and Plain Carbon-Steel Bars 5

for Concrete Reinforcement 6

ASTM A821/A821M-10 Standard Specification for Steel Wire, Hard-Drawn for Prestressed 7

Concrete Tanks 8

ASTM A1008/A1008M-13 Standard Specification for Steel, Sheet, Cold-Rolled, Carbon, 9

Structural, High-Strength Low-Alloy, High-Strength Low-Alloy 10

with Improved Formability, Solution Hardened, and Bake 11

Hardenable 12

ASTM A1064/A1064M-13 Standard Specification for Carbon-Steel Wire and Welded Wire 13

Reinforcement, Plain and Deformed, for Concrete 14

ASTM C55-11 Standard Specification for Concrete Building Brick 15

ASTM C109/C109M-13 Standard Test Method for Compressive Strength of Hydraulic 16

Cement Mortars (Using 2-in. or [50-mm] Cube Specimens) 17

ASTM C140-13 Standard Test Methods for Sampling and Testing Concrete 18

Masonry Units and Related Units 19

ASTM C150/C150-12 Standard Specification for Portland Cement 20

ASTM C309-11 Standard Specification for Liquid Membrane-Forming Compounds 21

for Curing Concrete 22

ASTM C426-10 Standard Test Method for Linear Drying Shrinkage of Concrete 23

Masonry Units 24

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ASTM C595/C595M-13 Standard Specification for Blended Hydraulic Cements 1

ASTM C648/04(2009) Standard Test Method for Breaking Strength of Ceramic Tile 2

ASTM C845/C845M-12 Standard Specification for Expansive Hydraulic Cement 3

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CHAPTER 4—MATERIALS 5

4.1—General 6

All materials and tests of materials shall conform to the ASTM standards specified in ACI 7

301-10. For materials that are not specifically provided for, the design strength and permissible 8

stress shall be established by tests. 9

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4.2—Cement and Concrete 11

4.2.1 Cement shall conform to the requirements of ACI 301-10, 4.2. 12

4.2.2 The minimum specified concrete compressive strength shall be 4000 psi (28 MPa) at 28 days. 13

4.2.3 Concrete that will be exposed to cycles of freezing and thawing shall be air entrained. Air 14

content shall not exceed that required by ACI 301-10, 4.2.2.4. 15

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4.3—Aggregates 17

The nominal maximum dimension of aggregate for slipformed silo walls shall not exceed one-18

eighth of the narrowest dimension between sides of wall forms, or exceed three-fourths of the 19

minimum clear distance between individual reinforcing bars or vertical bundles of bars. 20

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4.4—Water 22

Water used in mixing concrete shall conform to the requirements of ACI 301-10, 4.2.1.3. 23

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4.5—Admixtures 1

Admixtures used in concrete shall conform to the requirements of ACI 301-10, 4.2.2.5, and 2

shall be subject to prior approval by the licensed design professional. 3

4

4.6—Reinforcement 5

4.6.1 Hoop post-tensioning rods shall be hot-dip galvanized or otherwise protected from corrosion. 6

Post-tensioning connectors, nuts, and lugs shall either be hot-dip galvanized or made from 7

corrosion-resistant castings or corrosion-resistant steel. Galvanizing shall conform to ASTM 8

A123/A123M or ASTM A153/A153M. 9

4.6.2 Malleable iron castings shall conform to ASTM A47/A47M. 10

4.6.3 Steel reinforcement shall conform to the requirements of ACI 301-10. 11

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4.7—Precast concrete staves 13

4.7.1 Materials for staves manufactured by the dry-pack vibratory method shall conform to ASTM 14

C55. 15

4.7.2 Before a stave is used in a silo, drying shrinkage shall have caused the stave to come within 16

10 percent of its equilibrium weight and length as defined by ASTM C426. 17

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4.8—Tests of materials 19

4.8.1 Tests of materials used in construction shall be specified by the licensed design professional. 20

4.8.2 Tests of materials shall be in accordance with the applicable ASTM standards. The complete 21

record of such tests shall be available for inspection during the progress of the work, and a 22

complete set of these documents shall be preserved by the licensed design professional for at least 23

2 years after completion of the construction. 24

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4.8.3 All material tests shall be performed by an accredited testing agency. 1

4.8.4 The results of mechanical tests of silo staves and stave assemblies shall be used as criteria 2

for structural design of stave silos. Application of the test results is given in Chapter 7. 3

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CHAPTER 5—CONSTRUCTION REQUIREMENTS 5

5.1—General 6

Concrete quality control, methods of determining concrete strength, field tests, concrete 7

proportions and consistency, mixing and placing, formwork, details of reinforcement, and 8

structural members shall conform to ACI 301-10, except as specified otherwise herein. 9

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5.2—Sampling and testing concrete 11

Concrete shall be evaluated and tested in accordance with ACI 301-10, 1.6. 12

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Horizontal reinforcement shall be accurately placed and adequately supported prior to placing 15

concrete. It shall be physically secured to vertical reinforcement or other adequate supports to 16

prevent displacement during movement of forms or placement of concrete. 17

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5.4—Forms 19

5.4.1 Calculations and drawings for the design, fabrication, and erection of a slipform or jumpform 20

system for a silo or stacking tube wall shall bear the registration stamp of an engineer licensed to 21

practice in the location where the silo or stacking tube wall is to be constructed. 22

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5.5—Concrete placing and finishing 24

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5.5.1 Construction joints in slipform silo walls shall not be permitted unless shown on the contract 1

documents or specifically approved by the licensed design professional responsible for the wall 2

design. Construction joints in jumpform silo walls shall be constructed as shown on the contract 3

documents or as required by the licensed design professional responsible for the wall design. Prior 4

to the start of silo construction, the licensed design professional and contractor shall agree on 5

construction details to be used in case of an unplanned construction joint. In the event of an 6

interruption in slipform wall construction, the licensed design professional shall be notified 7

immediately. 8

9

5.5.2 Concrete shall be deposited within 5 ft (1.5 m) of its final position in a way that will prevent 10

segregation and shall not be worked or vibrated a distance of more than 5 ft (1.5 m) from the point 11

of initial deposit. 12

5.5.3 Wall surface voids shall be filled where required in accordance with ACI 301-10, 5.3.3.3, 13

with mortar made from the same materials (cement, sand, and water) as used in the wall. For 14

slipform construction, wall surface voids shall be filled within 2 hours after forms have been raised 15

or removed. For jumpform construction, wall surface voids shall be filled when required by the 16

contract documents, or as required by the licensed design professional responsible for the wall 17

design. 18

5.5.4 Surface finish shall be specified in the contract documents. 19

5.5.5 Surface fins and protrusions in jumpform walls shall be removed where they exceed the Class 20

D Formed Surface Irregularities provision, as defined by ACI 117-10, 4.8.3, or as required by the 21

licensed design professional responsible for the wall design. 22

23

5.6—Concrete protection and curing 24

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5.6.1 Cold weather concrete placement shall comply with ACI 306.1. 1

The requirements of ACI 306.1 govern over those of ACI 301-10. 2

5.6.2 Hot weather concrete placement shall comply with ACI 305.1-06. The requirements of ACI 3

305.1 govern over those of ACI 301-10. 4

5.6.3 Curing methods shall comply with ACI 308.1-98. 5

5.6.4 For slipform construction, curing measures shall be provided before the exposed exterior 6

wall surfaces begin to dry, but after the patching and finishing are completed. For jumpform 7

construction, curing shall be provided as soon as possible after forms are advanced and any 8

incidental patching is completed. Wall surfaces shall be protected against damage from rain, 9

running water, or freezing. 10

5.6.5 Curing compound shall not be used on the inside surfaces of silos, unless required by the 11

contract documents, or unless specified by the licensed design professional. When curing of 12

interior surfaces is required, nontoxic compounds and ventilation or other methods of ensuring 13

worker safety shall be used. 14

5.6.6 Curing compound shall be a nonstaining, resin-base type conforming to ASTM C309 and 15

shall be applied in accordance with the manufacturer’s instructions. Wax-based curing compounds 16

shall not be permitted. If a curing compound is used on the interior surfaces of a silo to be used for 17

storing materials for food, the compound shall be nontoxic, nonflaking, and otherwise 18

nondeleterious. 19

20

5.7—Lining and coating 21

5.7.1 Lining or coating material used to protect the structure from wear and abrasion, or used to 22

enhance flowability, shall be noncontaminating to the stored material. 23

19


5.7.2 Lining materials installed in sheet form shall be fastened to the structure with all seams sealed 1

to prevent entrance of stored material behind the lining. 2

3

5.8—Tolerances for slipformed and jumpformed structures 4

5.8.1 Translation of silo centerline or spiraling of the silo wall about the vertical axis of the silo 5

(lateral departure from the nominal centerline): 6

For heights 100 ft (30 m) or less………………+/- 3 in. (75 mm) 7

For heights greater than 100 ft (30 m)………… 1/400 times the height, but not more than +/- 8

4 in. (100 mm) 9

5.8.2 Inside diameter or distance between walls: 10

For each 10 ft (3 m) of diameter or distance….. +/- 1/2 in. (12 mm) but not more than +/- 3 in. 11

(75 mm) 12

5.8.3 Cross-sectional dimensions of: 13

Walls .......................... +1 in. (25 mm), - 3/8 in. (10 mm) 14

5.8.4 Deviation from the specified locations of openings, embedded plates, or anchors: 15

Vertical +/- 3 in. (75 mm) 16

Horizontal +/- 1 in. (25 mm) 17

5.8.5 Other tolerances shall be in accordance with ACI 117. Plus (+) tolerance increases the 18

amount or dimension to which it applies, or raises a deviation from level. Minus (-) tolerance 19

decreases the amount or dimension to which it applies, or lowers a deviation from level. Where 20

only one signed tolerance is specified (+ or -), there is no tolerance in the opposing direction. 21

22

CHAPTER 6—DESIGN 23

6.1—General 24

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6.1.1 Silos (Fig. 6.1.1) and stacking tubes shall be designed to resist all applicable forces, 1

including: 2

(a) Dead loads: weight of the structure and attached items including equipment dead loads 3

supported by the structure 4

(b) Live loads: granular material loads including those from flow, floor, and roof live loads; 5

equipment loads; positive and negative air pressure; and forces from earth or from materials 6

stored against the outside of the silo or stacking tube 7

(c) Wind, snow, and seismic loads 8

(d) Thermal forces, including those due to temperature differences between inside and 9

outside faces of wall 10

(e) Forces due to differential settlement of foundations. 11

12

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Fig. 6.1.1––Examples of vertical cross sections of silos used to determine the height of the 14

hopper. Other configurations are possible. 15

16

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6.1.2 Structural members shall be proportioned for adequate strength and stiffness. Pressures and 1

forces shall be calculated and combined using methods provided in Chapter 6 for silos and 2

Chapter 9 for stacking tubes. Design of reinforced or prestressed concrete members, such as 3

foundations, floors, and roofs not covered herein shall be in accordance with ACI 318-11. 4

6.1.3 The thickness of silo or stacking tube walls shall not be less than 6 in. (150 mm) for 5

reinforced cast-in-place and precast concrete. The thickness of precast staves used in externally 6

reinforced stave silo walls shall not be less than 2 in. (50 mm) 7

6.1.4 Load factors shall conform to ACI 318-11, 9.2 and this section. Strength-reduction factors 8

shall conform to ACI 318-11, 9.3. 9

6.1.4.1 The load factor for granular material shall be: 10

(a) 1.6 for load combinations with dead and live loads that do not include wind (W) or seismic 11

(E) loads 12

(b) 1.2 for load combinations that include wind (W) or seismic (E) loads, where the wind (W) 13

or seismic (E) loads are additive to the gravity loads 14

(c) 0.9 for load combinations that include seismic (E) loads, where the seismic (E) loads 15

counteract gravity loads. 16

17


6.2.1 In slipformed concrete structures, the reinforcement size, spacing, configuration, 19

dimensions, and lap splice details shall be such that the placement of reinforcement is achieved 20

without any omission and without any interference with the slipform operation. 21

6.2.2 Provide reinforcement to resist axial forces, tension forces due to bending moments, and 22

shear forces, taking into consideration the effect of the connection of the wall to the roof, silo 23

bottom, and adjoining walls in silo groups. 24

22


6.2.3 Provide horizontal ties to resist forces that tend to separate adjoining silos of monolithically 1

constructed silo groups. 2

6.2.4 The minimum ratio of horizontal reinforcement area to gross concrete area of the wall shall 3

be 0.0025. Horizontal reinforcement shall not be spaced farther apart than three times the wall 4

thickness, or farther apart than 18 in. (450 mm) Unless determined otherwise by analysis, 5

horizontal reinforcement at the bottom of the pressure zone shall be continued at the same size 6

and spacing for a distance below the pressure zone equal to at least four times the thickness h of 7

the wall above. 8

6.2.5 The minimum ratio of vertical reinforcement area to gross concrete area of the wall shall be 9

0.0020. The minimum vertical reinforcing bar size in the silo wall shall be No. 4 (No. 13). The 10

maximum horizontal spacing of vertical bars shall be 18 in. (450 mm) for exterior walls and 11

interior walls of monolithically cast silo groups. Jack rods left in place during slipform 12

construction shall not be considered as vertical reinforcement. 13

6.2.6 Dowels shall be provided at the bottom of columns and pilasters and also at portions of 14

walls serving as columns. Dowels shall also be provided as needed to resist wind or seismic 15

forces at the bottom of walls. Dowel spacing, size, and quantity shall be determined by analysis. 16

Dowels shall be developed on both sides of the shear plane in accordance with shear-friction 17

provisions of ACI 318-11, 11.6.4. 18

6.2.7 In circular silo walls, lap splices of horizontal and vertical reinforcement shall be staggered. 19

In circular silos, adjacent horizontal and vertical reinforcement lap splices shall be staggered by a 20

distance not less than one lap length or 3 ft (0.9 m). Adjacent hoop reinforcement lap splices 21

shall not coincide in vertical array more frequently than every third bar. In noncircular silos, lap 22

splices need not be staggered. Reinforcement splices in circular and noncircular silos shall be 23

23


checked for conformance to development and anchorage requirements of ACI 318-11, Chapter 1

12. 2

6.2.8 Reinforcement at wall openings 3

6.2.8.1 Openings in pressure zone—Stress concentrations at openings shall be analyzed and 4

adequate reinforcement shall be designed and provided accordingly. 5

6.2.8.2 Unless determined otherwise by analysis, horizontal reinforcement interrupted by an 6

opening shall be replaced by adding a minimum of 1.2 times the area of the interrupted 7

horizontal reinforcement, one-half above the opening and one-half below. 8

Additional vertical reinforcement shall be added to the wall on each side of the opening. 9

The added vertical reinforcement shall be calculated by assuming that a strip of wall, 4h in width 10

on each side of the opening, is an unsupported column within the opening height. This column 11

supports its own share of the vertical load plus one-half of the load acting over the wall opening 12

within a height equal to the opening width. The minimum added vertical reinforcement area for 13

each side shall be one-half of the reinforcement area eliminated by the opening. 14

6.2.8.3 Reinforcement development at openings—Unless determined otherwise by analysis, the 15

reinforcement provided to replace the interrupted reinforcement at an opening shall extend in 16

each direction beyond the opening. The minimum extension each way shall be the greater of (a), 17

(b), and (c): 18

(a) The development length of the reinforcement per ACI 318-11 Section 12.2 19

(b) 24 in. (600 mm) 20

(c) One-half the opening dimension in a direction perpendicular to the reinforcing bars being 21

considered. 22

6.2.8.4 Narrow vertical walls between openings—Unless determined otherwise by analysis, wall 23

sections 8h in width or less between openings shall be designed as columns. 24

24


6.2.9 The minimum center-to-center spacing of adjacent specified rows of horizontal or hoop 1

reinforcing shall be five bar diameters. Replacement or additional hoop reinforcing placed at 2

wall openings are allowed to be placed closer than five bar diameters, but must meet the bar 3

spacing requirements of ACI 318. 4

6.2.10 The lap length of horizontal and vertical reinforcement in silo walls shall be not less than: 5

(a) The lap length specified by ACI 318-11, 12.15, for Class B splices 6

(b) The length of circular reinforcing bars in slipformed silos shall be increased by 6 in. (150 7

mm) to facilitate assurance of the minimum required lap length. This provision to increase 8

reinforcing bar length does not apply to vertical bars. 9

In determining the lap length, horizontal bars in jumpformed structures shall be assumed as 10

top bars. Concrete thickness covering the reinforcement at lap splices shall be at least that 11

specified in ACI 318-11, 12.2, for that particular splice, but not less than 1 in. (25 mm). The 12

horizontal distance from the center of the bars to the face of wall shall be not less than two and a 13

half bar diameters. 14

6.2.11 Silo walls that are 9 in. (230 mm) or more in thickness shall have two layers of horizontal 15

and vertical reinforcement. 16

6.2.12 In walls with a single layer of reinforcement, reinforcement to resist thermal bending 17

moments shall be placed within that layer. 18

In walls with two-layers of reinforcement, reinforcement to resist thermal bending moments 19

shall be added to the layer nearer to the colder face. 20

6.2.13 In singly-reinforced circular walls, the main hoop reinforcement shall be placed closer to 21

the outer face. 22

25


6.2.14 Reinforcement in silo and stacking tube walls shall not be bundled. Reinforcement that is 1

to be field bent shall be clearly identified on the drawings and shall be bent in accordance with 2

ACI 301-10, 3.2.2. 3

6.2.15 The minimum concrete cover provided for reinforcement shall conform to ACI 318-11, 7.7 4

for cast-in-place concrete (nonprestressed), except as noted in 6.2.10 herein. 5

6

6.3—Loads 7

6.3.1 Stored material pressures and loads 8

6.3.1.1 Stored material pressures and loads against silo walls and hoppers shall be determined in 9

accordance with 6.3.2 through 6.3.5. Pressures shall include initial (filling) pressures, air 10

pressures, and pressure increases or decreases caused by withdrawal of material from concentric 11

or eccentric outlets. 12

6.3.1.2 Any method of pressure computation for determining the horizontal and vertical 13

pressures and frictional design forces within the silo shall be permitted provided such methods 14

are either based on generally accepted principles or methods that have been verified empirically 15

or by test. 6.3.1.3 Where properties of stored materials vary, pressures shall be calculated using 16

combinations of properties given in 6.3.2.1(e). 17

18

26


1

Fig. 6.3.2.1––Dimensions for use in calculation of pressures and loads for walls and 2

hoppers. 3

4

6.3.2 Pressures and loads for walls 5

6.3.2.1 Pressures due to initial filling (Fig. 6.3.2.1) shall be calculated by the following 6

(a) With reference to Fig. 6.3.2.1, the initial (filling) vertical pressure at depth Y of the stored 7

material shall be calculated by 8

27


RkYek

Rq /1

(6.3.2.1a) 1

(b) The initial (filling) horizontal pressure at depth Y in Fig. 6.3.2.1 shall be calculated by 2

p = kq (6.3.2.1b) 3

(c) The lateral pressure ratio k shall be calculated by 4

k = 1 – sin (6.3.2.1c) 5

where is the angle of internal friction 6

(d) The vertical friction load per unit length of wall perimeter at depth Y in Fig. 6.3.2.1 shall 7

be calculated by 8

V = (Y – q) R (6.3.2.1d) 9

(e) Where , μ′, and k vary, the following combinations shall be used with maximum 10

i. Minimum μ′ and minimum k for maximum vertical pressure q 11

ii. Minimum μ′ and maximum k for maximum lateral pressure p 12

iii. Maximum μ′ and maximum k for maximum vertical friction force V. 13

6.3.2.2 Concentric flow—The horizontal wall design pressure above the hopper for concentric 14

flow patterns shall be obtained by multiplying the initial filling pressure calculated according to 15

Eq. (6.3.2.1b) by an overpressure factor (Cd) of 1.6. 16

6.3.2.3 Asymmetric flow— Pressures due to asymmetric flow from concentric or eccentric 17

discharge openings shall be considered in design of silo walls. Refer to Sections 6.4.4.2 through 18

6.4.4.7.. 19

The effect of asymmetric flow on design pressures, and the method used to design the silo wall 20

shall be determined by the licensed design professional based on silo geometry; flow 21

characteristics; material properties; material and surface finish of the hopper; and position, type, 22

and configuration of the silo discharge. 23

28


6.3.3 Pressures and loads for hoppers 1

6.3.3.1 Initial (filling) pressures below the top of the hopper: 2

(a) The initial vertical pressure at depth hy below top of hopper shall be calculated by 3

qy = qo + hy (6.3.3.1a) 4

where qo is the initial vertical pressure at the top of the hopper calculated by Eq. (6.3.2.1a); 5

(b) The initial pressure normal to the hopper surface at a depth hy below top of hopper shall 6

be the larger of Eq. (6-6) and (6-7) 7

tantan

tanyn

qp (6.3.3.1b) 8

or 9

pn = qy (sin2 + k cos2) (6.3.3.1c) 10

(c) The initial friction force per unit area of hopper wall surface shall be calculated by 11

vn = pn tan (6.3.3.1d) 12

when Eq. (6.3.3.2b) is used to determine pn and by 13

vn = qy (1 – k) sin cos (6.3.3.1e) 14

when Eq. (6.3.3.2c) is used to determine pn. 15

6.3.3.2 Funnel flow hoppers—Design pressures at and below the top of a funnel flow hopper 16

shall be calculated using Eq. (6.3.3.1a) through (6.3.3.1e) with qo multiplied by an overpressure 17

factor Cd of 1.45 for concrete hoppers and 1.60 for steel hoppers. The vertical design pressure at 18

the top of the hopper need not exceed Y, where Y is the effective depth of the stored material 19

from the top of the hopper. 20

6.3.3.3 Mass flow hoppers—Design pressures at and below the top of mass flow hoppers shall be 21

calculated by 6.3.3.3(a) through 6.3.3.3(d). 22

(a) The vertical pressure at depth hy below the top of the hopper shall be calculated by 23

29


n

h

yho

n

h

yhyhy h

hhq

h

hhhh

nq

1

11

(6.3.3.3a) 1

where qo (the initial vertical pressure at the top of the hopper) is calculated by Eq. (6.3.2.1a), and 2

for circular cones 3

tan

2Bn (but not less than 1.0) (6.3.3.3b) 4

for plane flow hoppers 5

tan

Bn (but not less than 1.0) (6.3.3.3c) 6

where 7

)(2cossin1

)(2sinsin

B (6.3.3.3d) 8

and 9

sin

sinarcsin2/1 (6.3.3.3e) 10

(b) The pressure normal to the hopper surface at a depth hy below the top of the hopper shall 11

be calculated by 12

yn qp)(2cossin1

)2cos(sin1

(6.3.3.3f) 13

(c) The unit friction load between the stored material and hopper surface is calculated by Eq. 14

(6.3.3.2d), with pn calculated by Eq. (6.3.3.3f). 15

(d) In no case shall the design pressure in a mass flow hopper be taken less than the design 16

pressure calculated by 6.3.3.2. 17

6.3.3.4 In multiple outlet hoppers, the condition that initial pressures exist above some outlets 18

and design pressures exist above others shall be considered in the design of the hoppers and 19

supporting structures. 20

30


6.3.4 Pressures for flat bottoms 1

6.3.4.1 Initial filling pressures on flat bottoms shall be calculated by Eq. (6.3.2.1a), with Y taken 2

as the effective depth of the stored material from the top of the hopper. 3

6.3.4.2 Vertical design pressures on flat bottoms shall be obtained by multiplying the initial 4

filling pressures calculated according to 6.3.4.1 by an overpressure factor Cd of 1.35 for concrete 5

bottoms and 1.50 for steel bottoms. The vertical design pressure need not exceed Y. 6

6.3.5 Design pressures in homogenizing silos shall be taken as the larger of (a) and (b): 7

(a) When air pressure is not present, compute pressures according to 6.3.2 and 6.3.3 8

(b) When air pressure and volume are sufficient to fluidize the total depth of stored material, 9

compute pressures by 10

p = q = 0.6Y (6.3.5) 11

where is the nonaerated weight per unit volume of the stored material. 12

6.3.6 The pressures and forces calculated in accordance with 6.3.1 through 6.3.5 are due only to 13

stored material. The effects of dead load; floor and roof live load; and snow, ice, thermal, wind, 14

seismic force, internal air pressure, and forces from earth or materials stored against the outside 15

of the silo shall be considered in combination with stored material loads. 16

6.3.7 Wind force—Wind force on silos shall be considered generated by positive and negative 17

pressure acting concurrently. The pressure shall be not less than that required by the local 18

building code for the locality and height zone in question. Wind pressure distributions shall take 19

into account adjacent silos or structures. Circumferential bending due to wind on the empty silo 20

shall be considered. 21

6.3.8 Seismic forces—Silos and stacking tubes shall be designed to withstand the seismic forces 22

in accordance with ASCE/SEI 7-10. The design shall consider the full range of material loading 23

from empty to full. It shall be permitted to consider the interaction between the silo and the 24

31


stored material using an appropriate structural analysis procedure found in ASCE/SEI 7-10. 1

Unless otherwise determined by analysis, the effective density of the stored material, used to 2

compute seismic forces in accordance with ASCE/SEI 7-10, shall be equal to . 3

6.3.9 Thermal effects—The thermal effects of hot or cold stored materials and hot or cold air 4

shall be considered. For circular walls or wall areas with total restraint to warping (as at corners 5

of rectangular silos), the thermal bending moment per unit of wall height or width shall be 6

calculated by 7

Mt = Ec h2 c T/12 (1 – v) (6.3.9) 8

9

and c = thermal coefficient of expansion of concrete. It shall be 10

permitted to reduce Ec or h to reflect the development of a cracked moment of inertia if such 11

assumptions are compatible with the planned performance of the silo wall at service loads. 12

13

6.4—Wall design 14

6.4.1 Minimum wall thickness for silos shall be in accordance with 6.1.3. Minimum wall 15

reinforcement for cast-in-place silos shall be in accordance with 6.2. The wall thickness for stave 16

silos shall be in accordance with Chapter 7.4.2. 17

6.4.2 Walls shall have design strengths at all sections at least equal to the required strength 18

calculated for the factored forces, moments, and shears in accordance with 6.1.4. 19

6.4.3 Design of walls subject to axial load or to combined flexure and axial load shall be in 20

accordance with ACI 318-11, Chapter 10. Design of walls subject to shear shall be in 21

accordance with ACI 318-11, Chapter 11. 22

6.4.4 Circular walls in pressure zone 23

32


6.4.4.1 For concentric flow, circular silo walls shall be designed for hoop tension due to 1

horizontal pressures computed in accordance with 6.3.2.2. The minimum wall hoop 2

reinforcement shall be in accordance with 6.2.4. 3

6.4.4.2 For asymmetric flow, circular silo walls shall be designed for the effect of combined 4

axial tension, bending moments, and shear forces due to nonuniform pressures using either the 5

Flow Channel Method of 6.4.4.3 through 6.4.4.6 or the Eccentricity Method of 6.4.4.7. 6

Asymmetric loading in homogenizing silos shall conform to 6.4.4.8. 7

The choice of design method shall be made by the licensed design professional taking into 8

account the stored material properties and flow characteristics; the configuration, construction, 9

material, and surface finish of the silo bottom or hopper; and the industry's experience with 10

similar full-size silos. 11

The Eccentricity Method of design shall not be used for silos containing materials with an 12

effective angle of internal friction, δ, of more than 40 degrees. 13

The Eccentricity Method of design shall not be used for asymmetric loading in homogenizing 14

silos. 15

The minimum wall hoop reinforcement shall be as required by 6.4.4.1. 16

6.4.4.3 Design pressures for asymmetric flow patterns shall be determined by selecting design 17

flow channel(s) that come in contact with the silo wall over an appropriate height of the wall and 18

by computing pressures in static and flowing materials after flow begins in accordance with 19

6.4.4.4 through 6.4.4.6. The design pressures shall be used to determine silo wall tensions, 20

moments, and shears in the silo wall. 21

In determining tensions, moments, and shears, any method of structural analysis shall be 22

acceptable that results in a realistic approximation of the behavior of the wall and considers the 23

following: 24

33


a) Restraint or fixity provided by common walls of adjacent silos, interstices, or both 1

b) Interaction between the silo wall and the stored material; the stiffness of the material within 2

the flow channel boundary shall be taken as not more than 10 percent of the stiffness of the 3

static material 4

c) Effect of wall cracking . 5

Redistribution of bending moments from negative moment (MOF) zones to positive moment 6

(MIF) zones shall be permitted in accordance with ACI 318-11, 8.4. 7

Reductions to shear capacity of the wall caused by axial hoop tension shall be considered. Shear 8

reinforcement to supplement wall shear strength shall be in accordance with ACI 318-11, 9

Chapter 11. 10

6.4.4.4 The design flow channel configuration(s) shall be specified by the licensed design 11

professional based on experience and field observations of flow in silos with comparable 12

configurations and stored materials. Configuration of the assumed design flow channel(s) shall 13

be shown on the project drawings. 14

Unless otherwise determined by analysis or field observation, the design flow channel shall be 15

assumed to contact the silo wall from the top of the hopper to the top of the material and the flow 16

channel diameter shall be estimated using Fig. 6.4.4.4. The selected flow angle θf and channel 17

diameter Y shall be representative of actual flow channels normally found in the type of silo 18

considered. 19

In case of a side discharge, where the outlet is in the silo wall, the flow channel shall be 20

assumed to contact the wall from the bottom of the outlet to the top of the material. 21

Stored material variability, variations in flow channel location or configuration, and silo wall 22

serviceability, such as crack width under cyclic loading, shall be addressed. 23

24

34


1

2

Fig. 6.4.4.4––Flow channel diameter (Giunta 1969). 3

4

6.4.4.5 Vertical design pressure in the flow channel at depth y below the top surface of the flow 5

channel shall be calculated by 6

7

fRfky

f

ff e

k

Rq /1

(6.4.4.5a) 8

Horizontal design pressure in the flow channel at depth y below the surface of the stored material 9

shall be calculated as 10

ff kqp

(6.4.4.5b) 11

12

Cd = 1.0 for both flow and static pressures. 13

6.4.4.6 Vertical design pressure in the static material at any depth y below the surface of the 14

stored material shall be calculated by 15

35


fsilo

ffsilos AA

qAqAq

(6.4.4.6a) 1

where fA is the summation of the plan areas of all flow channels that are active at depth y. 2

The horizontal design pressure in the static material at any depth y below the surface of the 3

stored material shall be calculated by 4

ss kqp (6.4.4.6b) 5

6.4.4.7 The Eccentricity Method of design shall be used only on silos containing material with an 6

effective angle of internal friction of 40 degrees or less. 7

For the Eccentricity Method of design, the horizontal wall design pressure above the hopper 8

calculated in accordance with 6.3.2.2 shall be increased. The calculated increase shall be 25 9

percent of the static pressure when the discharge opening eccentricity ECC equals the silo radius 10

(D/2). In cases where the discharge is less than fully eccentric, the calculated increase shall be 11

ECC /(D/2) times 25 percent of the static pressure. 12

The material effective depth, YEFF, shall be taken as the vertical distance from the top of the 13

discharge opening to the top of the stored material. For silos where the ratio of YEFF to diameter 14

is two or less, the pressure increase shall be considered constant from the top of the discharge to 15

a height of 1.0D, and then reduce linearly to zero at the top of the stored material. 16

For silos where the ratio of YEFF to diameter is greater than two, the pressure increase shall be 17

considered constant from the top of the discharge to a height of 1.5D, and then reduce linearly to 18

zero at the top of the stored material. 19

The increased design pressures shall be uniformly applied around the circumference of the silo. 20

6.4.4.8 For homogenizing silos, circular silo walls shall be designed for hoop tension due to 21

horizontal pressures calculated in accordance with 6.3.5. For partially fluidized silos, circular 22

36


silo walls shall be designed for combined hoop tensions, bending moments and shear forces due 1

to non-uniform horizontal pressures computed in accordance with 6.4.4.2. 2

The minimum wall hoop reinforcement shall be in accordance with 6.2.4. 3

6.4.5 Walls in the pressure zone of square, rectangular, or polygonal silos shall be designed for 4

combined axial tension, bending moments, and shear forces due to horizontal pressure from 5

stored material. 6

6.4.6 Walls below the pressure zone shall be designed as walls subjected to vertical load and 7

applicable lateral loads. 8

6.4.7 Design axial strength per unit area Pnw for walls in which buckling, including local 9

buckling, does not control, shall be calculated by Eq. (6.4.7) 10

Pnw = 0.55fc (6.4.7) 11

in which the strength-reduction factor is 0.65. 12

6.4.8 For walls in the pressure zone, wall thickness and reinforcing shall be so proportioned that, 13

under initial (filling) pressures, the calculated crack width at 2.5 bar diameters from the center of 14

bar (dc = 2.5 bar diameters) shall not exceed 0.010 in. (0.25 mm) (Fig. 6.4.8). The crack width 15

(in. (mm)) shall be calculated by 16

30001.0 Adfw cs (6.4.8) 17

37


1

Fig. 6.4.8––Effective tension area A for crack width computation. 2

3

6.4.9 The continuity between a wall and a suspended hopper shall be considered in the wall 4

design. 5

6.4.10 Walls shall be reinforced to resist forces and moments due to continuity of walls in 6

monolithically constructed silo groups. The effects of load patterns of both full and empty cells 7

shall be considered. 8

6.4.11 Walls at each side of an opening shall be designed as columns. The column width shall 9

not exceed four times the wall thickness. 10

11

6.5—Hopper design 12

6.5.1 Loads—Silo hoppers shall be designed to withstand forces from stored materials calculated 13

according to 6.3.3 and other loads such as mechanical equipment and support platforms. Seismic 14

38


forces shall be determined using provisions of 6.3.8. Thermal effects due to stored material shall 1

also be considered. 2

6.5.2 Suspended hoppers 3

6.5.2.1 Suspended conical hopper shells shall be considered subject to circumferential and 4

meriodinal (parallel to hopper slope) tension membrane forces. 5

6.5.2.2 Suspended pyramidal hopper walls shall be considered subject to combined tension 6

membrane forces, flexure, and shear. 7

6.5.2.3 The maximum calculated crack width of reinforced concrete suspended hoppers shall 8

meet the requirements of 6.4.8. 9

6.5.2.4 The minimum wall thickness of suspended reinforced concrete hoppers shall be 5 in. (125 10

mm). 11

6.5.2.5 Hopper supports shall have adequate strength to resist the hopper reactions. 12

6.5.3 Flat bottoms 13

6.5.3.1 For horizontal bottom slabs, the design shall consider the dead load; the vertical design 14

pressure (from stored material) calculated at the top of the slab according to 6.3.4.2; and the 15

thermal effects, if any, from stored material. If hopper forming fill is present, the weight of the 16

fill shall be considered as dead load. 17

18

6.6—Column design 19

The maximum area of vertical reinforcement in columns supporting silos or silo bottoms 20

shall be 0.02 times the gross area of the column. 21

22

6.7—Foundation design 23

39


6.7.1 Except as prescribed, silo foundations shall be designed in accordance with ACI 318-11, 1

Chapter 15. 2

6.7.2 The overpressure effects from stored material, as defined in 6.3.2.2, 6.3.3.2, and 6.3.4.2, 3

shall be neglected in the design of silo foundations. 4

6.7.3 Unsymmetrical loading of silo groups and the effect of lateral loads shall be considered in 5

foundation design. 6

6.7.4 Differential settlement of silos within a group shall be considered in foundation, wall, and 7

roof design. Estimations of differential settlement, creep, shrinkage, or temperature changes 8

shall be based on a realistic assessment of such effects occurring in service. 9

10

CHAPTER 7—CONCRETE STAVE INDUSTRIAL SILOS 11

7.1—Scope 12

This chapter applies to precast concrete stave silos that are used only for storing granular 13

bulk material. It does not apply to farm silos for storage of silage. 14

15

7.2—Coatings 16

7.2.1 Interior and exterior coatings shall be applied to the staves where specified. 17

7.3—Erection tolerances 18

7.3.1 For vertical alignment of the center point, the actual center point of the silo shall not vary 19

from its theoretical axis:Per 10 ft (3 m) of height. . . . . . . . . . . . . .+/- 1 in. (25 mm) 20

7.3.2 Rotational (spiral) of the vertical stave joint: 21

Per 10 ft (3 m) of height. . . . . . . . . . . . . .+/- 1 in. (25 mm) 22

7.3.3 Bulging of stave wall— 23

For any 10 ft (3 m) of height . . . . . . . . . . 1 in. (25 mm) 24

40


For entire height. . . . . . . . . . . . . . . .3 in. (75 mm) 1

7.3.4 The measured inside shell diameter at any section shall not vary from the specified 2

diameter by more than 1 in. (25 mm) or .1 times the specified diameter (ft (m)), whichever is 3

greater.7.3.5 Hoops—In no case shall a lower quantity of hoops be placed than specified in the 4

design. The vertical spacing requirement shall not deviate from specified design by: 5

Hoop Vertical Spacing. . . . . . . . . . . . . . . . . . . . .+/- 1 in. (25 mm) 6

7

7.4—Wall design 8

7.4.1 Loads, design pressures, and forces—Loads, design pressures, and vertical forces for stave 9

silo design shall be determined as specified in Chapter 6. Overpressure or impact, and the effects 10

of eccentric discharge openings, wind, snow, thermal effects, and seismic forces shall all be 11

considered. Strength requirements shall be satisfied in accordance with7.4 through 7.6 and 12

referenced tests in 7.6. 13

7.4.2 Wall thickness—The required stave silo wall thickness shall be determined considering 14

circular bending, compression, tension, and buckling, but shall in no case be less than 2 in. (50 15

mm). 16

7.4.3 Circular bending—Unless a more detailed analysis is performed, the circumferential 17

bending strength M shall satisfy (a) and (b): 18

(a) In the case of wind acting on an unbraced wall or an empty silo 19

M D2w/8 (7.4.3a) 20

where w is strength-level wind pressure. Where wind pressure w has not been reduced by a 21

directionality factor, 0.8w must be used in place of w in Eq. (7.4.3a); and 22

(b) In the case of unequal interior pressures from asymmetric filling or emptying 23

negpos MM6.1M (7.4.3b) 24

41


1

M, pos 1.0 Mpos (7.4.3c) 2

3

where 1.6 and 1.0 are load factors, and Mpos + Mneg are determined by the Flow Channel Method 4

in accordance with Section 6.4.4.2 through 6.4.4.7.. 5

The following strength relationships shall be satisfied 6

0.875(Asfy – Fu)h M (7.4.3d) 7

8

0.375(Asfy – Fu)h M, pos (7.4.3e) 9

10

If Eq. (7.4.3d) and (7.4.3e) are not satisfied, a complete circular assembly of staves, such as 11

described in Fig. R7.6b shall be tested to prove satisfactory strength. 12

7.4.4 Compression and buckling—The design axial load strength per unit perimeter, Pnw, shall 13

be taken as the smaller of that calculated by Eq. (7.4.4a) through (7.4.4c) 14

Pnw = 0.50Pnw, stave (7.4.4a) 15

Pnw = 0.55Pnw, joint (7.4.4b) 16

Pnw = 0.55Pnw, buckling (7.4.4c) 17

where is 0.65, and Pnw, stave, Pnw, joint, and Pnw, buckling are determined by computation of 18

properties, or proven by tests of stave assemblies such as described by Fig. R7.6a. The variable 19

Pnw, buckling shall take into account the maximum eccentricities from out-of-plane deviations 20

allowed in 7.3. 21

The wall thickness shall be such that Pnw shall not be exceeded by any appropriate 22

combination of applicable forces as specified in 6.1. 23

42


7.4.5 Forces due to overturning—The empty silo shall have a factor of safety not less than 1.33 1

against wind or earthquake overturning forces. Computation shall be based on a shape factor for 2

rough-surfaced cylinders for wind loads and not more than 0.9 times the calculated dead load of 3

structure. If anchorage is necessary, the following shall be satisfied where anchors attach to the 4

stave wall 5

6

)WorE(2'fA5 cw (7.4.5a) 7

and 8

)WorE(2lapFfA1.0 uys (7.4.5b) 9

10

where, is 0.65, the force (Asfy - Fu) is per unit length of wall height, lap is the amount of 11

vertical stagger in feet between horizontal stave joints, and W is the strength-level wind uplift. 12

The limitations of Eq. (7.4.5b) shall be imposed unless tests, such as described by Fig. R7.4.4a, 13

indicate greater strength. 14

7.4.6 Wall openings—Wall openings in stave silos shall be framed in such a way that the vertical 15

and horizontal bending and tensile strengths of the wall are not reduced by the opening. 16

17

7.5—Hoops for stave silos 18

7.5.1 Size and spacing—Except as noted, the size and spacing of external hoops for stave silos 19

shall be calculated in the same manner as horizontal reinforcement of circular, cast-in-place 20

silos. In computing the hoop reinforcing, it is permitted to use an average design pressure over a 21

wall height equal to 30 times its thickness. Hoops shall be 1/2 in. (12 mm) minimum in diameter. 22

The maximum spacing shall not exceed the stave height or 10 times the wall thickness. 23

43


7.5.2 Calculating steel area—When calculating the required size and spacing of stave silo hoops, 1

the hoop net area shall be used and taken as the lesser of (a) and (b): 2

(a) The area of the rod 3

(b) The root area of the thread. 4

If lugs or mechanical fasteners induce bending deformations or strains in the hoop that 5

reduce the yield strength of the hoop, appropriate restrictions in the available strength of the 6

hoop/lug assembly shall be considered. 7

7.5.3 Tensioning—Initial stave silo hoop tension shall be such that, after all losses from 8

shrinkage, creep, elastic shortening, and temperature changes, the required vertical and circular 9

strength and stiffness of the stave assembly is maintained. 10

11

7.6—Concrete stave and stave assembly testing 12

7.6.1 Compressive strength of the concrete staves shall conform to the requirements of the 13

contract documents. Concrete design strength shall not be taken less than 4000 psi (28 MPa). 14

15

CHAPTER 8—POST-TENSIONED CONCRETE SILOS 16

8.1—Scope 17

8.1.1 Provisions in this chapter apply to cast-in-place concrete silo walls post-tensioned with 18

high-strength steel meeting the requirements of ACI 318-11, Chapter 18. Pretensioned systems, 19

where the reinforcement is stressed before the concrete is cast, are not covered herein. Wire 20

wrapping systems are not covered herein. Wire-wrapping systems are covered in ACI 372R-13. 21

8.1.2 Requirements of Chapters 1, 4, 5, and 6 (where not in conflict with this chapter) shall apply 22

to post-tensioned concrete silos, unless specifically stated otherwise. 23

44


8.1.3 Provide sufficient prestressed and nonprestressed reinforcement to resist all hoop tensile 1

forces and bending moments. 2

3

8.2—Post-tensioning systems 4

8.2.1 Permitted post-tensioning systems for silos shall be bonded internal tendons in embedded 5

ducts, or unbonded external strands with protective cover. 6

8.2.2 Internal tendons consist of strands or bars inside ducts embedded in the concrete. The 7

embedded ducts shall be grouted after tensioning of the strands. 8

8.2.3 Unbonded external strands use high-strength strands that are placed around the silo and 9

post-tensioned individually. The strands and splices shall be protected from the environment. 10

11

8.3—Tendon systems 12

8.3.1 Wall thickness h for silos with tendons in embedded ducts shall be not less than 10 in. (250 13

mm). The wall thickness shall be sufficient to prevent the compression stress from exceeding 14

0.55 fci at the time of initial stressing. 15

8.3.2 The center-to-center spacing of tendons shall not exceed three times the wall thickness h or 16

h1, as applicable, but no more than 42 in. (1 m). 17

8.3.3 The clear spacing between embedded tendon ducts shall be at least the greatest of (a), (b), 18

and (c): 19

(a) Three times the duct diameter 20

(b) 6 in. (150 mm) 21

(c) The minimum anchorage spacing for the chosen post-tensioning system. 22

8.3.4 The minimum clear spacing between unbounded external tendon ducts shall be at least the 23

greatest of (a), (b), and (c): 24

45


(a) The duct diameter 1

(b) ¾ in. (20 mm) 2

(c) The clear spacing required for external strand splicing hardware. 3

8.3.5 Horizontal embedded tendon ducts shall be located interior to the exterior vertical 4

nonprestressed reinforcement. 5

8.3.6 Stressing points shall be located at vertical pilasters on the outside of the walls, at wall 6

intersections, or at blockouts. In determining the number of stressing locations, friction loss, and 7

local concentrations of the post-tensioning force shall be considered. Blockout sizes and 8

locations shall be such that, at the time of initial stressing, the compressive stress in the net 9

concrete wall area shall not exceed 0.55fci. 10

8.3.7 Reinforcement shall be provided at stressing locations to resist forces created by the post-11

tensioning operation. 12

8.3.8 Tendon ducts shall be supported to maintain location within vertical and horizontal 13

tolerances. 14

8.3.9 Tendon anchor locations shall be staggered such that stressing locations do not coincide in 15

vertical array more often than every second tendon. 16

8.3.10 After stressing is completed, anchorage and end fittings shall be permanently protected 17

against corrosion. Where protective plastic fittings are exposed to sunlight, they shall be resistant 18

to ultraviolet light. Blockouts and pockets shall be filled with a nonshrink grout that will bond to 19

and develop the strength of the adjacent concrete. 20

21

8.4—Bonded tendons 22

8.4.1 Anchorages and couplers for bonded tendons shall meet the requirements of ACI 318-11, 23

18.21. 24

46


8.4.2 Grout materials, proportioning, mixing, and pumping grout shall conform to ACI 318-11, 1

18.18 or Post-Tensioning Institute M55.1-12: Specification for Grouting of Post-Tensioned 2

Structures. 3

4

8.5—Unbonded tendons 5

8.5.1 Anchorages and couplers for unbonded tendons shall develop 100 percent of fpu without 6

exceeding the anticipated set. 8.5.2 External, nongalvanized, unbonded tendons shall be coated 7

with a protective lubricant and encased in protective ducts to provide protection from corrosion 8

and ultraviolet radiation for the intended useful life of the structure. The ducts shall be 9

continuous over the entire zone to be unbonded and shall prevent intrusion of cement paste, 10

water, or both, and the loss of coating materials during concrete placement. The anchorage and 11

end fittings shall be protected as specified in 8.3.9. 12

13

8.6—Post-tensioning ducts 14

8.6.1 Tendon ducts shall be mortar-tight and nonreactive with concrete, tendons, or the grout. 15

The minimum metal duct wall thickness shall be 0.012 in. (0.30 mm). Metal ducts shall be 16

prebent to conform to the intended circular shape and intended radial position. Metal ducts shall 17

be spliced at each joint. Duct splices shall be staggered and ducts shall be installed free of kinks 18

or unspecified curvature changes. Plastic ducts shall not be spliced and shall be connected to 19

trumpets at the anchorage points. Ducts shall be supported at intervals as necessary to meet 20

tolerances specified in 8.13.2. 21

8.6.2 Ducts for grouted single wire, strand, or bar tendons shall have an inside diameter at least 22

1/4 in. (6 mm) larger than tendon diameter. 23

47


8.6.3 Ducts for grouted multiple wire, strand, or bar tendons shall have an inside cross-sectional 1

area at least two times the net area of tendons. 2

8.6.4 In addition to meeting the requirements of 8.6.2 and 8.6.3, duct diameter shall be 3

compatible with tendon installation requirements, taking into consideration curvature of wall, 4

duct length, potential blockage, and silo configuration. 5

8.6.5 Ducts shall be kept clean and free of water. Grouting shall be performed as soon after post-6

tensioning as possible. When grouting is delayed, the exposed elements of the system shall be 7

protected against intrusion of water or any foreign material that is detrimental to the system. 8

8.6.6 Ducts for grouted tendons shall be capable of transferring bond between tendons and grout 9

to the surrounding concrete. 10

11

8.7—Details and location of nonprestressed reinforcement 12

8.7.1 Vertical nonprestressed reinforcement shall be provided to withstand bending moments due 13

to post-tensioning, banding of post-tensioning reinforcement at openings, stored material loads 14

(partially full and full), temperature, and other loading conditions to which the walls are 15

subjected. The minimum area of vertical nonprestressed reinforcement provided shall be as 16

required by Chapter 6. 17

8.7.2 Horizontal nonprestressed reinforcement shall be provided to resist bending moments in 18

accordance with 8.10.5. Bending due to differential temperature, nonuniform pressures of stored 19

material, asymmetric flow of material, and shrinkage and temperature effects during the period 20

between completion of wall construction and start of post-tensioning shall be considered. The 21

minimum total area of such reinforcement shall meet the requirements of Chapter 6. 22

23

8.8—Wall openings 24

48


8.8.1 Nonprestressed reinforcement at wall openings shall meet the requirements of 6.2.8. Axial 1

forces, bending moments, and shear forces due to flaring of post-tensioned tendons shall be 2

considered in the design of such reinforcement. 3

8.8.2 Where post-tensioning reinforcement would cross wall openings in pressure zones, the 4

post-tensioning reinforcement shall be flared to pass immediately above and below the opening. 5

The length of flare, measured from the center of the opening, shall be not more than the silo 6

diameter or less than six times the opening height. Horizontal and vertical stress concentrations 7

resulting from flaring of tendons around openings shall be considered for cases of both full and 8

empty silos. Minimum spacing requirements shall be observed at all locations. 9

10

8.9—Stressing records 11

8.9.1 Stressing procedures and results shall be documented and the records submitted to the 12

licensed design professional and preserved for the period specified on the project drawings and 13

project specifications, but not less than 2 years. Records shall include type, size, and source of 14

strand or bars; date of stressing; jacking pressures; sequence of stressing; elongation before and 15

after anchor set; any deviations from expected response from jacking; and name of the inspector. 16

17

8.10—Design 18

8.10.1 Design shall satisfy both strength requirements and concrete stresses at service conditions. 19

All critical load stages during the life of the structure from the time post-tensioning stress is first 20

applied shall be considered. 21

8.10.2 Silo walls shall be designed to resist all applicable loads as specified in Chapter 6, plus the 22

effect of post-tensioning forces during and after tensioning. Stress concentrations and edge 23

49


restraint at wall junctions with silo roof, bottom, and wall intersections or other intersecting 1

structural members, such as hopper supports, shall be considered. 2

8.10.3 Concrete stress shall not exceed the values provided in Chapter 6 and in ACI 318-11, 3

18.4, except as provided in Table 8.10.3 herein. 4

5

Table 8.10.3—Maximum permissible stresses in concrete*

Axial compression 0.225 fc

Combined axial compression and bending: extreme fiber 0.45 fc

Axial tension, psi 6 fc�� fc��a)

Combined axial tension and bending: extreme fiber, psi 12 fc fcMPa)

*At service loads, after allowance for all losses. 6

7

8.10.4 Tensile stress in strands or bars of tendon systems shall not exceed (a) or (b): 8

(a) During jacking. . . . . . . . . . . . . . . . . . . 0.80 fpu or 0.94 fpy 9

whichever is smaller, but not more than maximum value recommended by the manufacturer of 10

tendons or anchorages 11

(b) Immediately after anchoring. . . . . . . . . . 0.70 fpu 12

Average stress in strands or bars of tendon systems shall not exceed (c) or (d): 13

(c) Immediately after stressing. . . . . . . . . . . 0.70 fpu 14

(d) After all losses. . . . . . . . . . . . . . . . . . . . 0.55 fpu. 15

8.10.5 Required area of reinforcement—The amount of post-tensioned reinforcement furnished 16

shall be as required to resist the hoop tension due to horizontal pressures calculated according to 17

6.3.2.2. In silo walls subjected to combined hoop tension and bending, resistance to bending 18

shall be provided by non-post-tensioned reinforcement. 19

50


8.10.6 Unless more accurate information is available from the manufacturer or by independent 1

test data, the following values shall be used for the modulus of elasticity Ep: 2

Bars. . . . . . . . . . . . . . . . . . . . . . 29 x 106 psi (200 x 103 MPa) 3

Strands. . . . . . . . . . . . . . . . . . 28.5 x 106 psi (197 x 103 MPa) 4

8.10.7 Nonprestressed reinforcement 5

8.10.7.1 The amount of nonprestressed reinforcement shall be determined by the strength design 6

method as required in ACI 318-11. The minimum amount of nonprestressed reinforcement 7

provided shall be as required by 8.7 and 8.8. 8

8.10.7.2 Design shall not be based on a yield strength of reinforcement fy in excess of that 9

permitted by ACI 318-11, 9.4. 10

8.10.7.3 The modulus of elasticity Es of nonprestressed reinforcement shall be taken as 29 x 106 11

psi (200 x 103 MPa). 12

8.10.8 Where a circular wall is post-tensioned within a distance of 10 wall thicknesses of a roof, 13

silo bottom, foundation, or other intersecting structural member, the minimum initial concrete 14

circumferential compression stress, for a height of wall extending from 0.4 Dh to 1.1 , 15

shall be: 16

Edges unrestrained. . . . . . . . . . . . . . . . . 280 psi (2.0 MPa). 17

Edges restrained. . . . . . . . . . . . . . . . . . . 140 psi (1.0 MPa). 18

8.10.9 Losses—Prestress losses that are used to establish the effective stress fse shall be 19

determined using the provisions of ACI 318-11, 18.6. 20

21

8.11—Vertical bending moment and shear due to post-tensioning 22

Nonprestressed vertical reinforcement shall be provided to resist vertical bending moments 23

and shear forces due to post-tensioning. 24

Dh

51


1

8.12—Tolerances 2

8.12.1 The tolerance for placement of ducts at support points, relative to position shown on the 3

project drawings, shall be +/-1 in. (25 mm) vertically or horizontally. 4

8.12.2 The tolerance for duct vertical sag or horizontal displacement between support points 5

shall be +/-1/2 in. (13 mm). 6

7

CHAPTER 9—CONCRETE STACKING TUBES 8

9.1—Scope 9

This chapter covers the design and construction of reinforced concrete stacking tubes. 10

Requirements of Chapters 1 through 6 shall be applicable to stacking tubes unless specifically 11

stated otherwise. 12

13

9.2—General layout 14

The inside diameter of a stacking tube shall be sufficient to prevent arching across the tube. 15

Wall discharge openings shall be sufficient to prevent arching across the openings and allow free 16

flow of material from the stacking tube. 17

Discharge openings over the height of the tube shall be located as to minimize the effects of 18

circumferential bending from uneven loads. Where a concentric discharge is provided inside the 19

tube through the reclaim tunnel roof at the bottom of the stacking tube, it shall be sufficient to 20

prevent arching across the opening and prevent the formation of a stable rathole in the tube. 21

22

9.3—Loads 23

52


All vertical and lateral loads that are inside or outside the stacking tube shall be considered. 1

The following loads shall be considered for the design of stacking tubes. 2

9.3.1 Vertical loads at top of tube 3

(a) The vertical reaction from the weight of the conveyor and headhouse structure 4

(b) The vertical reaction from the walkway live load, headhouse floor live load, and the 5

weight of material carried by the conveyor. 6

9.3.2 Horizontal loads at top of tube 7

9.3.2.1 Acting perpendicular to the conveyor: 8

(a) The horizontal reaction from wind on the conveyor and headhouse 9

(b) The horizontal reaction from seismic force on the conveyor and headhouse. 10

9.3.2.2 Acting parallel to the conveyor: 11

(a) The horizontal reaction due to the belt pull, including tension from start-up 12

(b) The horizontal reaction due to thermal expansion or contraction of the conveyor support 13

structure; such force shall be taken as not less than 10 percent of the total (dead plus live) vertical 14

reaction of the conveyor system on the top of the tube, unless provision is made to reduce the 15

loads with rollers or rockers 16

(c) Longitudinal wind and seismic loads on the conveyor. 17

9.3.3 Vertical loads over height of tube 18

(a) The weight of the tube 19

(b) The vertical drag force from the material stored inside the tube 20

(c) The vertical drag force from a complete pile of material stored outside the tube 21

(d) The vertical drag force from a partial pile of material stored outside the tube. 22

9.3.4 Horizontal loads over height of tube 23

(a) Wind action on the exposed portion of the tube 24

53


(b) Seismic action on the mass of the tube 1

(c) Unbalanced forces acting on the tube as a result of a partial pile of material stored around 2

the tube 3

(d) Seismic action on the material stored inside the tube 4

(e) Seismic action on the pile stored on the outside of the tube. 5

6

9.4—Load factors and strength-reduction factors 7

9.4.1 Load factors, load combinations, and strength-reduction factors shall be in accordance with 8

6.1.4. 9

10

9.5—Tube wall design 11

9.5.1 The stacking tube shall be designed as a cantilevered beam fixed at the top of the 12

foundation or reclaim tunnel roof. The minimum concrete wall strength shall be as required by 13

the most severe combination of loads at the base of the tube and at every level. 14

9.5.2 The stacking tube wall shall be reinforced vertically and horizontally. For wall thicknesses 15

of 9 in. or more, reinforcement shall be provided on each face. The vertical reinforcement shall 16

resist the maximum tension resulting from the combination of vertical loads and overturning 17

moments. In addition, the vertical reinforcing adjacent to the openings shall resist the forces and 18

moments resulting from the bending action of the wall between the openings. The minimum ratio 19

of vertical reinforcement to gross concrete area shall be 0.0025. 20

9.5.3 Horizontal reinforcement shall resist circumferential forces and moments and horizontal 21

tension caused by the redistribution of vertical loads around the openings. Horizontal 22

reinforcement that is discontinuous at openings shall be replaced by adding not less than 60 23

54


percent of the interrupted reinforcement above the top and 60 percent below the bottom of the 1

opening. The minimum ratio of horizontal reinforcement to gross concrete area shall be 0.0025. 2

3

9.6—Foundation or reclaim tunnel 4

The foundation and reclaim tunnel shall support all horizontal and vertical loads imposed on 5

them by the tube or by the material above and adjacent to the tube and reclaim tunnel. 6

7

COMMENTARY 8

9

INTRODUCTION 10

This Commentary presents considerations and assumptions in developing provisions of the 11

Design Specification. Initial filling (static) pressures are exerted by the stored material at rest. Flow 12

pressures differ from initial filling pressures, and are exerted by the stored material during flow. 13

Comments on specific provisions of the Design Specification are made using corresponding 14

chapter and section numbers of the Design Specification. References cited in the commentary are 15

listed in the Commentary References. 16

17

CHAPTER R1—GENERAL 18

R1.1— Scope 19

Silo failures have alerted licensed design professionals to the inadequacy of designing silos for 20

only static pressures due to stored material at rest. Those failures motivated researchers to study 21

the variations of pressures and flow of materials. Research has established that pressures during 22

withdrawal can be significantly higher (Turitzin 1963; Pieper and Wenzel 1964; Reimbert and 23

Reimbert 1987, 1980) or significantly lower than those present when the material is at rest. The 24

55


excess (above static pressure) is called overpressure, and the shortfall is called underpressure. One 1

of the causes of overpressure is the switch from active to passive conditions that occurs during 2

material withdrawal (Jenike et al. 1972). Underpressures can occur at a flow channel, and 3

overpressures can occur away from the flow channel at the same level (Colijn and Peschl 1981; 4

Homes 1972; Bernache 1968). Underpressures concurrent with overpressures cause 5

circumferential bending in the silo wall. Impact during filling can cause the total pressure to exceed 6

the static pressure. Whereas overpressures and underpressures are generally important in deeper 7

silos, impact loading is usually significant for shallow bins (bunkers) in which large volumes of 8

material are dumped suddenly. Some stored granular materials have sufficient cohesion and 9

unconfined compressive strength to form large arches or cavities during discharge. The collapse 10

of these arches and cavities can develop significant impact loads when the material above strikes 11

the wall or floor. This document does not provide methods for calculation of such loads. The 12

probability of forming arches and cavities can be reduced by using hopper and discharge 13

equipment designs that reflect results from flowability testing of the stored material. 14

Overpressure, underpressure, or impact should be considered in the structural design of silos if 15

present. 16

Initial filling (static) pressures are exerted by the stored material at rest. Flow pressures differ 17

from initial filling pressures, and are exerted by the stored material during flow. 18

19

R1.2—Documentation 20

Silos and stacking tubes are unusual structures. Many licensed design professionals are 21

unfamiliar with computation of their design loads and with their design and detail requirements. 22

Design computations and the preparation of project drawings and project specifications for silos, 23

56


bunkers, and stacking tubes should be done under the supervision of a licensed design professional 1

experienced in the design of such structures. 2

If possible, the properties of the stored materials to be used in the design should be obtained 3

from tests of the actual materials to be stored or from records of tests of similar materials 4

previously stored. Properties assumed in the design should be stated in the contract documents. 5

6

R1.3—Regulations/Inspections 7

Investigations of silo damage, deterioration failures frequently reveal omitted or mislocated 8

reinforcement, inadequate or misaligned reinforcement splices, and inadequate reinforcement 9

cover. 10

The quality and performance of slipformed concrete silo structures depend on construction 11

workmanship. The best materials and design will not be effective unless the construction is in 12

accordance with project documents. For example, during slipform operations, the proper 13

placement of reinforcement is a critical task. In addition, horizontal lifts, buckled jackrods, and 14

concrete delaminations can occur if the concrete sets too rapidly, the slipform is improperly 15

battered, or jackrods are overloaded. Similar considerations are associated with the quality and 16

performance of jumpformed concrete silos. 17

Continuous field inspection of construction activity helps ensure conformance with the project 18

requirements. The committee recommends that field inspection of construction activity be 19

performed by or under the supervision of a licensed design professional. Field inspection of 20

construction activity does not relieve the contractor of the responsibility to conform to project 21

requirements. 22

23

57


1

CHAPTER R2—NOTATION AND DEFINITIONS 2

R2.1—Commentary notation 3

The following additional terms are used in the Commentary, but are not used in the Design 4

Specification. 5

As = compression steel area, in.2 (mm2) 6

d = effective depth of flexural member, in. (mm) 7

d, d = distances from face of wall to center of reinforcement nearest that face, in. (mm) 8

EI = flexural stiffness of wall, lb-in.2 (N-mm2) 9

e, e,e = eccentricities, in. (mm) 10

F = radial force on the wall that results from the stressing (jacking) of the tendon, lb (N) 11

Kt = thermal resistance of wall, °F/in. (°C/mm) 12

Mmax = maximum vertical bending moment per unit width of wall 13

Mu = required flexural strength per unit height of wall, ft-lb (m-N) 14

My = vertical bending moment per unit width caused by force F on the wall, ft-lb (m-N) 15

Ti = temperature inside mass of stored material, °F (°C) 16

To = exterior dry-bulb temperature, °F (°C) 17

Vhy = shear per unit width caused by a force F on the wall, lb (N) 18

Vmax = maximum shear force per unit width of wall, lb (N) 19

y = distance above and below tendon location, in. (mm) 20

c, p = angle of conical or plane flow hopper with vertical, degrees 21

f = angle of flow channel with vertical, degrees 22

t = angle of flow channel axis with vertical, degrees 23

p = factor relating to Poisson’s ratio, silo diameter, and wall thickness 24

58


R2.2—Definitions 1

silo—the term silo includes both deep bins and shallow bins; the latter are sometimes called 2

bunkers. Wherever the term silo is used in the Design Specification, it should be interpreted as 3

meaning a silo, bin, or bunker of any proportion, shallow or deep. 4

stave silo—stave silos are used principally in agriculture for storing chopped silage, but are used 5

for storing granular materials in other industries. The Design Specification covers industrial stave 6

silos, but does not cover silos storing silage. The methods of computing pressures due to granular 7

material are the same for industrial stave silos as for other silos. Design of stave silos, however, 8

relies heavily on strength and stiffness tests; consequently, the Design Specification includes 9

several design requirements that are peculiar to stave silos only. 10

11

12

CHAPTER R4—MATERIALS 13

R4.2—Cements 14

R4.2.1 To minimize variations in concrete color, cement for exposed parts of silos or bunkers 15

should be of one particular type and brand of cement. 16

In general, the types of cement permitted by ACI 318-11, 3.2, are permitted herein, except as 17

noted. There is some variation in the physical properties of each type of cement. Type I cement 18

that is very finely ground (a fineness modulus greater than 2000) can act in the same manner as 19

Type III and cause placing difficulties by accelerating the initial set during a slipform operation. 20

Types IS and IP are not recommended for use in slipform or jumpform concrete because of 21

long initial setting time and low strength at an early age. 22

59


R4.2.2 Performance and design requirements for concrete mixtures should meet the requirements 1

of ACI 301-10. Concrete mixtures should be proportioned to produce a required average 2

compressive strength determined in accordance with ACI 301-10. 3

Historically, concrete mixtures with a slump of 4 in. (100 mm) have been used successfully 4

for construction of slipformed silo walls under a variety of field conditions. High-range water-5

reducing admixtures (HRWRAs) have been successfully used to increase slump without adversely 6

affecting the water-cement ratio or strength. 7

R4.2.3 Concrete is considered exposed to freezing and thawing when, in a cold climate, the 8

concrete is in almost continuous contact with moisture before freezing. 9

Entrained air in concrete will provide some protection against damage from freezing. 10

11

R4.5—Admixtures 12

The use of admixtures in concrete silo walls is a common method of controlling the initial set 13

of concrete and, therefore, the rate at which slipforms or jumpforms may be raised. During the 14

construction operation, the amount of admixture can be adjusted in the field to suit the ambient 15

conditions and so maintain a constant rate of rise for the forms. 16

Concrete that includes accelerators or retarders should be placed in uniform depths in the 17

slipform or jumpforms to maintain a consistent time of initial set at any wall elevation. 18

When using admixtures, trial batches should be made and evaluated for potential problems 19

with set and for adverse effects on the slip-form operation. 20

Similarly, admixtures are commonly used in mortar, parge coatings, protective coatings, and 21

grout for post-tensioning ducts. Trial batches should be made and evaluated when required to 22

substantiate mix designs. 23

24

60


1

R4.8—Test of Materials 2

R4.8.2 Completion of the construction is the date at which the owner accepts the project or when 3

the certificate of occupancy is issued, whichever date is later. 4

5

CHAPTER R5—CONSTRUCTION REQUIREMENTS 6

7

R5.3—Details and placement of reinforcement 8

Bars that are not tied can move during vibration or be mislocated. Failures have occurred because 9

of incorrect spacing of horizontal steel; therefore, a positive means of controlling location is 10

essential. The practice of floating hoop reinforcement in slip form construction is prohibited. 11

12

R5.4—Forms 13

Guidelines for the design, fabrication, erection, and operation of a slipform or jumpform 14

system for a silo or stacking tube wall are given in ACI 347. 15

Slipform and jumpform systems should be designed, constructed, and operated by or under the 16

supervision of persons experienced in this type of construction. Hurd (2005) and Camellerie (1959, 17

1971) contain a general description of the vertical slipform process. 18

The advancement rate of the slipform system should be slow enough that concrete exposed 19

below the bottom of the forms is capable of supporting itself and the concrete placed above it, but 20

rapid enough to prevent concrete from bonding to the forms. 21

The advancement of the jumpform system should be scheduled or timed such that hardened 22

concrete is capable of supporting the jumpform system, the construction loads, and the fresh 23

concrete placed above it. 24

61


1

R5.5—Concrete placing and finishing 2

During the construction of slipformed silo or stacking tube walls, the concrete placing 3

operation can be interrupted due to an unavoidable field condition, resulting in an unplanned 4

construction joint. 5

During the construction of a jumpform wall, construction joints occur at regular intervals, 6

as defined by the height of the jumpform lifts. The construction details of such expected 7

construction joints are typically shown on the contract documents. 8

The licensed design professional should consider construction joint orientation, reinforcing 9

bar splices, surface cleanliness, and joint preparation when preparing the contract documents. 10

R5.5.6 Slipformed walls are typically finished as the bottom of the moving slipform is raised, 11

exposing newly placed concrete. Jumpform wall surfaces are typically not exposed until several 12

hours or days after the concrete is poured. Jumpform wall surfaces typically have an as-cast finish, 13

as described by ACI 117. 14

R5.5.7 Small surface fins or protrusions are typically removed from jumpform walls only when 15

they interfere with form placement or they constitute a hazard. The Class D irregularity 16

provisions of ACI 117, 4.8.3, allow irregularities of approximately 1 in. (25 mm) size. 17

18

R5.6—Concrete protection and curing 19

R5.6.1 A guide to cold weather concreting is presented in ACI 306R. 20

R5.6.2 A guide to hot weather concreting is presented in ACI 305R. 21

R5.6.3 Procedures for curing of concrete are presented in ACI 308R. Curing compounds, where 22

required, are applied to walls after any surface voids are addressed. 23

62


In some cases, atmospheric conditions are such that excess water from bleeding of concrete 1

as placed in the forms is sufficient to keep the surface of the newly formed walls moist for several 2

days, and no additional provisions for curing are needed. Where deck forms or other enclosures 3

retain the atmosphere in a highly humid condition, no additional curing measures are needed. 4

Construction during moderate to high relative humidity and low to moderate winds will typically 5

not require additional curing methods. These conditions are very often true of the inside face of 6

silo wall construction. 7

When the aforementioned conditions cannot be met, a curing compound may be used or a water 8

spray or mist applied to keep the wall surface continuously moist. The amount of water should be 9

carefully regulated to avoid damage to the concrete by erosion. If a curing compound is not used, 10

the concrete should not be allowed to have a dry surface for at least 5 days. 11

R5.6.5 Curing compound may be undesirable on the interior surfaces that are in contact with the 12

stored material. As the curing compound is abraded, it contaminates the stored material. Such 13

compound, if present, modifies the friction between the interior wall surface and the stored 14

material. 15

16

17

CHAPTER R6—DESIGN 18

R6.1—General 19

R6.1.3 Experience has shown that slipformed walls thinner than 6 in. (150 mm) are difficult to 20

construct. When slip-forming thin walls, concrete can more easily be lifted by friction between 21

the forms and the freshly-placed concrete, causing horizontal and vertical planes of weakness or 22

actual separation. 23

24

63


R6.2—Details and placement of reinforcement 1

R6.2.1 Figures R6.2.1a and R6.2.1b illustrate typical reinforcing patterns at wall intersections, 2

ring beams, and wall openings. The illustrated details are not mandatory, but are examples to aid 3

the licensed design professional. 4

5

6

7

Fig. R6.2.1a––Reinforcement pattern at intersecting walls. 8

9

64


1

Fig. R6.2.1b––Miscellaneous details. 2

3

R6.2.2 The licensed design professional should be aware that bending moments may occur in 4

silos of any shape. Bending moments will be present in walls of silo groups, especially when 5

some cells are full and some are empty (Safarian and Harris 1984; Stalnaker and Harris 1992). 6

They may also occur when flow patterns change or when some cells are subjected to initial 7

(filling) pressures whereas others are subjected to design (flow) pressures (Jenike 1977). 8

65


The walls of interstices and pocket bins will have axial forces, bending moments, and shear 1

forces, and may cause axial forces, bending moments, and shear forces in the silo walls to which 2

they are attached. 3

Wall bending moments in a circular silo are difficult to evaluate accurately, but do exist. 4

They result from nonuniform pressures around the circumference during discharge, especially 5

eccentric discharge. They can also result from temperature differential, structural continuity, and 6

materials stored against the outside of the silo. 7

R6.2.3 Forces that tend to separate silos of monolithically constructed silo groups can occur 8

when some cells are full and some empty (Safarian and Harris 1984), such as four empty cells 9

with a full interstice. They can also result from nonuniform pressure around the circumference, 10

thermal expansion, seismic loading, or differential foundation settlement. 11

R6.2.4 Horizontal hoop tension (or tension plus shear and bending moment) does not cease 12

abruptly at the bottom of the pressure zone. The portion of the wall below the pressure zone has 13

strains and displacements comparable with those of the wall at the bottom of the pressure zone. 14

Therefore, the pattern of main horizontal reinforcement should be continued downward from the 15

bottom of the pressure zone for a distance equal to four times the thickness h of the wall above. 16

Because the wall below the pressure zone frequently has sizeable openings, that wall may 17

need to be designed (usually as a deep beam) to span those openings. In this case, reinforcement 18

areas should be adequate for deep beam action. 19

R6.2.5 Vertical reinforcement in silo walls helps distribute lateral load irregularities vertically to 20

successive layers of horizontal reinforcement. In addition, it resists vertical bending and tension 21

due to the following causes: 22

a) Temperature changes in the walls when the wall is restrained or not free to move in 23

the vertical direction 24

66


b) Wall restraint at roof, floor, or foundation 1

c) Eccentric loads, such as those from hopper edges or ancillary structures 2

d) Concentrated loads at the transition between the cylindrical and converging section of 3

a flow channel 4

e) Temperature differentials between inside and outside wall surfaces or between silos 5

(Safarian and Harris 1970) 6

f) Splitting action from bond stresses at lapped splices of hoop bars. 7

To provide access for concrete buggies in slipform construction, vertical reinforcement may 8

be spaced farther apart at specified access locations. Vertical reinforcement should not be 9

omitted for this purpose; only the spacing should be affected, larger than specified at the access 10

location, and smaller than specified on each side. Buggy pathway locations and widths should 11

be specified on the drawings. 12

R6.2.7 The possibility of bond failure, with subsequent splitting, is greater where bars are closely 13

spaced, as at lap splices (Ferguson and Krishbaswamy 1971). Staggering of lap splices increases 14

the average bar spacing. With adjacent splices, one splice failure can trigger another. With 15

staggered splices, this possibility is less likely. 16

R6.2.8 Reinforcement at wall openings 17

R6.2.8.1 Reinforcement at openings consists of vertical bars, horizontal bars, diagonal bars, and 18

shear reinforcement. The area of added reinforcement should be determined by analysis, 19

including deep beam action (tension, flexure, and shear) when applicable (Safarian and Harris 20

1974). 21

R6.2.8.2 The required area of horizontal reinforcement should be determined by analysis. The 20 22

percent minimum increase in the area of horizontal reinforcement is to limit cracking at stress 23

67


concentrations next to the opening. Bar spacing and clearances frequently become critical where 1

such extra reinforcement is added. 2

R6.2.8.3 Reinforcement development at openings—The distance that reinforcement should be 3

extended to replace the strength that would otherwise be lost at the opening depends not only on 4

development length, but also on the proportions of the opening. Horizontal extension should be 5

longer for deep openings than for shallow openings. Similarly, vertical extension should be 6

longer for wide openings than for narrow openings. In each case, the extension length depends 7

on the opening dimension perpendicular to the bar direction. 8

R6.2.9 The five-bar diameter minimum spacing of specified horizontal bar rows ensures more 9

concrete between bars and helps prevent possible brittle bond failures. 10

R6.2.10 Additional bar length is specified for hoop bars in walls of slipformed silos because bars 11

may easily be misplaced longitudinally, leading to reduced lap at one end of the bars. For 12

rectangular or polygonal silos, where the shape of the bar prevents longitudinal misplacement of 13

horizontal bars at a splice, the additional bar length may not be required. 14

R6.2.11 Caution should be exercised in selecting walls thinner than 9 in. (230 mm), because such 15

walls will not generally accommodate two curtains of reinforcement. Two-face reinforcement 16

substantially improves performance of a wall subjected to both tension and bending forces. 17

R6.2.12 Both horizontal and vertical thermal tensile stress will occur on the colder side of the 18

wall. Where thermal stress adds significantly to stress due to stored material, additional 19

reinforcement is required by 6.3.9. 20

Better crack-width control on the outside face is possible when the horizontal reinforcement 21

is near the outer face. Also, because this is frequently the colder face, reinforcement so placed is 22

in a better position to resist thermal stress. Care should be taken to ensure adequate concrete 23

68


cover over the bars on the outside surface to prevent bond splitting failures and reinforcement 1

corrosion. 2

Crack-width control and concrete cover on the inside face are also important to lessen the 3

effects of abrasion due to flow and to reduce the possibility that corrosive elements from the 4

stored material may damage the reinforcement. 5

R6.2.13 Singly reinforced circular walls, with the reinforcement placed near the outside face, 6

may not effectively resist bending moments that cause tension on the inside face of the wall. 7

R6.2.14 Because no reinforcing bars can project beyond the face of a slipform silo wall, dowels 8

that project into abutting walls, slabs, or silo bottoms are frequently field bent. 9

If reinforcing bars are welded or have items welded to them, it is essential to know the carbon 10

content of the bars to select the proper procedure and materials for the weld. 11

R6.2.15 The minimum cover for reinforcing bars placed on the inside face of silo walls should be 12

1 in. (25 mm). Additional cover should be provided where required by 6.2.10. 13

14

R6.3—Loads 15

R6.3.1.2 Generally, American practice to compute wall pressures is to use Janssen’s (1885) 16

formula (Eq. (6.3.2.1a), although Rankine’s method is sometimes used for silos with small 17

height-diameter ratios. Methods other than Janssen’s may be used to compute wall pressures. 18

There are a large variety of hopper pressure formulas available in the literature, including Jenike 19

(1977), Gaylord and Gaylord (1984), McLean (1985), and Walker (1966). All are based on 20

different assumptions, and may yield significantly different pressure distributions. 21

R6.3.1.3 To compute pressures, certain properties of the stored material must be known or 22

assumed. There are many tables in the technical literature listing such properties as silo design 23

parameters. In using those parameters for structural analysis, however, the designer should be 24

69


aware that they are, at best, a guide. Unquestioned use may lead to an unsafe design. This 1

situation exists because of a long-maintained effort to associate design parameters with the 2

generic name of the material to be stored, neglecting the wide range of properties that such a 3

name may cover. The usual design parameters, density, internal friction angle, and wall friction 4

angle, all used in computing pressures, are affected by: 5

(a) Conditions of the material—moisture content, particle size, gradation, and angularity of 6

particles 7

(b) Operating conditions—consolidation pressure, time in storage, temperature, rate of 8

filling, and amount of aeration. 9

The licensed design professional should use physical and flow properties of the stored 10

material from reliable sources. Table R6.3.1.3 provides examples of physical properties for 11

various materials. Actual physical properties of specific materials may vary from the properties 12

shown in the table. Upper and lower bounds of properties should be determined by testing the 13

material in question. If the actual material to be stored is unavailable, the bounds should be 14

determined by testing or by examining representative materials from other similar installations. 15

Note that the physical properties noted in the table for some materials show a wide range of 16

values, demonstrating the variability in the properties that affect pressures and flow in silos. 17

Values shown in the table should be used with caution. 18

Table R6.3.1.3—Example physical properties of granular materials 19

Density Coefficient of friction

lb/ft3 kg/m3

Angle of internal

friction

Effective angle of internal

friction Against concrete

Against steel

Cement, clinker 88 1410 33 42-52 0.6 0.3 Cement, portland 84-100 1345-1600 24-30 40-50 0.40-0.80 0.30 Clay 106-138 1700-2200 15-40 50-90 0.2-0.5 0.36-0.7 Coal, bituminous 50-65 800-1040 32-44 33-68 0.55-0.85 0.30

70


Coal, anthracite 60-70 960-1120 24-30 40-45 0.45-0.50 0.30 Coke 32-61 515-975 35-45 50-60 0.50-0.80 0.50-0.65 Flour 38 610 40 23-30 0.30 0.30 Fly ash 50-112 865-1800 35-40 37-42 0.60-0.80 0.47-0.70 Gravel 100-125 1600-2000 25-35 36-40 0.40-0.45 0.29-0.42 Grains (small): wheat corn, barley, beans (navy, kidney), oats, rice, rye

44-62 735-990 20-37 28-35 0.29-0.47 0.26-0.42

Gypsum, lumps 100 1600 38-40 45-62 0.5-0.8 0.38-0.48 Iron ore 165 2640 40-50 50-70 0.5-0.8 0.4-0.7 Lime, calcined, fine

70-80 1120-1280 30-35 35-45 0.5-0.7 0.5-0.6

Lime, calcined, coarse

58-75 930-1200 40 40-45 0.5-0.8 0.3-0.5

Limestone 84-127 1340-2730 39-43

45-80

0.3-0.8 0.55-0.70

Manganese ore 125 2000 40 — — — Sand 100-125 1600-2000 25-40 30-50 0.40-0.70 0.35-0.50 Soybeans, peas 50-60 800-960 23 — 0.25 0.20 Sugar, granular 53-63 1000 35 33-40 0.43 —

1

2

R6.3.2 Pressures and loads for walls 3

R6.3.2.1 The licensed design professional should consider an appropriate degree of variability in 4

, k, and μ. The design should be based on maximum with appropriate combinations of 5

maximum and minimum values of k and μ. 6

Equation (6.3.2.1a) assumes concentric filling and uniform axisymmetric pressure 7

distribution. In the case of eccentrically filled silos in which the elevation of the material surface 8

at the wall varies significantly around the perimeter, the pressure distribution will not be 9

axisymmetric. 10

R6.3.2.2 During initial filling and during discharge, even when both are concentric, 11

overpressures occur because of imperfections in the cylindrical shape of the silo, nonuniformity 12

in the distribution of particle sizes, and convergence at the top of hoppers or in flow channels. 13

71


A minimum Cd overpressure factor of 1.6 is recommended for concentric flow silos, even 1

when they are of a mass flow configuration. The recommended factor recognizes that even 2

though higher and lower point pressures are measured in full-size silos, they are distributed 3

vertically through the stiffness of the silo wall and can be averaged over larger areas for 4

structural design. The 1.6 overpressure factor Cd is in addition to the load factor required by 6.1.4 5

(design pressure = load factor × Cd × initial filling pressure). 6

Licensed design professionals are cautioned that the overpressure factor provided in 6.3.2.2 7

for concentric flow and is not intended for asymmetric flow. 8

R6.3.2.3 Asymmetric flow can result from the presence of one or more eccentric outlets, from 9

nonuniform distribution of material over a concentric outlet, or even from nonuniform flow 10

through a center outlet. 11

R6.3.3 Pressures and loads for hoppers 12

R6.3.3.1 Hopper pressures are more complex to predict than wall pressures. The pressure 13

distribution will be more sensitive to the variables discussed in R6.3.1.3. There is a significant 14

diversity within the technical literature with regard to hopper pressures (Walker 1966; DIN 1055 15

1987; ISO 11697:1995; Standards Association of Australia 1989). Equations (6.3.3.1a) through 16

(6.3.3.1e), which are based on Walker’s (1966) method, provide a generally acceptable method 17

to estimate initial pressures in hoppers. Equation (6.3.3.1a) reflects Walker’s assumption of an 18

incompressible material and, therefore, yields conservative pressures near the outlets of steep 19

hoppers. Some pressure measurements reported in the technical literature (Clague and Wright 20

1973; Blight 1988), however, are not significantly lower than those predicted by Eq. (6.3.3.1a) in 21

the lower part of the hopper. 22

Equations (6.3.3.1b) and (6.3.3.1d) generally control for steep smooth hoppers where the 23

friction along the material-hopper interface is fully developed. Equations (6.3.3.1c) and 24

72


(6.3.3.1e) generally control for shallow hoppers where the friction along the material-hopper 1

interface is not fully developed. The value of k to be used in Eq. (6.3.3.1c) should be 2

conservatively calculated by Eq. (6.3.2.1c). Because of the uncertainty inherent in hopper 3

pressure estimates, the engineer should check Eq. (6.3.3.1b) and (6.3.3.1c), and use the equation 4

that yields the larger pn. 5

While lower hopper pressures may be justified, a hopper failure can result in significant 6

damage or total collapse of a silo; therefore, the use of the slightly conservative procedure of Eq. 7

(6.3.3.1a) through (6.3.3.1e) is recommended. Pressures on gates and feeders at hopper outlets 8

are usually lower than the pressures calculated using Eq. (6.3.3.1a). 9

R6.3.3.2 Funnel flow occurs only when the outlet is large enough for the material to flow 10

without forming a stable arch or rathole, and the hopper walls are not sufficiently smooth or 11

sufficiently steep to develop a mass flow pattern. To obtain a self-cleaning condition, the hopper 12

slope should be steep enough to cause the material to slide off of it when the silo is discharged 13

completely. Jenike (1964) suggests ′ + 25 degrees. Some designers select such that tan 14

> 1.5 tan ′for hoppers having flat surfaces and 1.5 2 tan ′ for conical hoppers or the valley of 15

pyramidal hoppers. The slope of a funnel flow hopper should be selected to avoid the possibility 16

of mass flow that is discussed further inR6.3.3.3. 17

The recommended overpressure factors for hoppers and flat bottoms are intended to cover 18

dynamic loads that normally occur during funnel flow. 19

Collapse of large arches and ratholes can subject the silo to severe shock loads that can cause 20

structural damage. Such loading requires additional analysis and design that is not covered 21

herein. Selection of silo and hopper configurations and flow control devices that minimize the 22

potential for forming stable arches and ratholes is highly recommended. A common approach is 23

to select an expanded flow pattern. An expanded flow pattern is typically a two-slope hopper, 24

73


with a lower mass flow section and an upper self-cleaning section. The boundary between the 1

mass flow and self-cleaning sections should be chosen to minimize the potential for forming 2

stable arches and ratholes. 3

R6.3.3.3 Mass flow occurs only when the outlet is large enough for the material to flow without 4

arching, the flow control device permits flow through the entire outlet, and the hopper walls are 5

smooth enough and steep enough to allow material to slide. 6

Jenike (1964, 1967) provided design information in graph form for selecting the slopes of 7

two common shapes of hoppers (conical and plane flow). Approximate slopes necessary for mass 8

flow to occur may be estimated using Fig. R6.3.3.3a. The occurrence of mass flow or funnel 9

flow depends on the hopper slope angles c and p and the hopper wall friction angle ′. The 10

region labeled uncertain on the graphs of Fig. R6.3.3.3a indicates conditions for which flow may 11

shift abruptly between funnel flow and mass flow, with large masses of material being in 12

nonsteady flow and the consequent development of shock loads (Carson and Johanson 1977). 13

Such flow conditions will also lead to nonsymmetric flow patterns and, hence, to nonsymmetric 14

loads on the silo. Selecting hopper slopes in the uncertain region should be avoided. 15

Other hopper configurations include pyramidal and transition hoppers. For mass flow to 16

develop in a pyramidal hopper, the slope of the hopper valleys should be steeper than c. For 17

transition hoppers, the side slope should be steeper than p, and the slope of the curved end walls 18

should be steeper than c. For tilted hoppers with one vertical side, mass flow will develop when 19

the included angle is greater than 1.25c or 1.25p. 20

21

22

74


1

Fig. R6.3.3.3a––Mass flow versus funnel flow bounds. 2

3

Figure R6.3.3.3b is a flow chart showing a recommended procedure for selecting a silo 4

hopper configuration. Detailed procedures for computing hopper slopes and outlet sizes are 5

given by Jenike (1964). 6

75


Mass flow results in high pressures at the top of the hopper (at and directly below the 1

transition). Methods for computing mass flow pressures are given by Jenike (1977, 1967) and 2

Walker (1966). The two methods result in slightly different pressure distributions, with Jenike 3

yielding peak pressures at the transition higher than Walker. Comprehensive reviews of hopper 4

pressures are given in Gaylord and Gaylord (1984), Rotter (1990), and Ooi and Rotter (1991). 5

Equations (6.3.3.3e) through (6.4.8) are based on Walker (1966). 6

Pressures in mass flow tilted hoppers, where the angle between the hopper axis and the 7

vertical does not exceed c or p, may be calculated using 6.3.3.3, with taken as the angle 8

between the hopper axis and the hopper surface. 9

10

Fig. R6.3.3.3b––Flow chart for selecting hopper configuration. 11

12 R6.3.3.4 In multiple-outlet hoppers, flow may occur over some outlets whereas initial filling 13

pressures exist over others. The differential lateral pressures on hopper segments between outlets 14

can be substantial. 15

76


R6.3.4 Pressures for flat bottoms 1

R6.3.4.1 Equation (6.3.2.1a) assumes a uniform vertical pressure distribution across the diameter 2

of the silo. Vertical pressures may be lower at the wall and higher at the center of the silo, 3

particularly if the silo height-diameter ratio is low. Such pressure variations should be considered 4

in the design of flat bottom floors. 5

R6.3.5 Pressures in homogenizing silos—Homogenizing silos are those in which air pressure is 6

used to mix dust-like materials. The material being mixed may behave as a fluid; thus, the 7

possibility of hydrostatic pressures should be considered. The factor 0.6 reflects the fact that the 8

suspended particles are not in contact, and the average density is less than for the material at rest. 9

Partially aerated silos may experience aeration pressure directly additive to nonaerated inter-10

granular pressures (Anderson 1985). Refer to 6.3.2.3 for computing design pressures in partially 11

fluidized silos. 12

Some homogenizing silos are aerated in sequential sectors. The walls of such silos can be 13

subjected to large pressure differentials between aerated and non-aerated sectors. Such pressure 14

differentials can lead to significant vertical and horizontal bending moments. 15

R6.3.8 The determination of seismic forces and moments on a stacking tube due to a surrounding 16

pile of granular material should consider the relative stiffness of the tube and the material. Large 17

shear forces and moments may result, especially for tall stacking tubes, in areas of high seismic 18

risk. 19

R6.3.9 Thermal effects—Computation of bending moments due to thermal effects requires 20

determining the temperature differential through the wall. To determine this differential, the 21

licensed design professional should consider the rates at which heat flows from the hot material 22

to the inside surface of the wall, through the wall thickness, and from the wall to the atmosphere. 23

There are two distinct and different conditions to be analyzed. 24

77


1. The worst thermal condition is usually found in the wall above the hot material surface, 1

where the air is maintained at a high temperature while fresh hot material is fed into the silo. In 2

that portion of the wall, high thermal loads will coexist with wall dead load and no material 3

loads. 4

2. A less severe condition exists below the hot material surface, where temperatures fall as 5

heat flows through the wall to the outside and a temperature gradient develops through some 6

thickness of the granular material (Bohm 1956). In that portion of the wall, material loads will 7

coexist with reduced thermal loads. 8

The temperature differential may be estimated by (Safarian and Harris 1970) 9

T = (Ti – To – 80F) Kt (T = (Ti – To – 45C) Kt) (R6.3.9) 10

where Kt for cement is given by Fig. R6.3.9. 11

Other methods for computing bending moments due to thermal effects are available (Turitzin 12

1963; Theimer 1969; Broersma 1972; Jenkyn 1994). 13

The licensed design professional should also recognize that structural steel items like roof 14

beams inside a concrete silo will expand and contract more rapidly than the concrete and cause 15

an overstress at contact areas if space for expansion is not provided. Provision should also be 16

provided for vertical thermal expansion at roof beam bearings. 17

The bending moments induced in a silo wall are affected by the stiffness of the wall. An 18

adjustment to Ec or h may be made to account for the reduced stiffness of a cracked wall, where 19

appropriate. It is recommended that the stiffness used for analysis should not be lower than that 20

provided in ACI 318 for cracked walls in compression. 21

78


1

Fig. R6.3.9––Determination of Kt for a wall of a cement storage silo 2

3

R6.4—Wall design 4

R6.4.2 Storage of hot materials can cause appreciable thermal stresses in the walls of silos. 5

Thermal stresses may or may not occur concurrently with the maximum hoop forces. 6

The reinforcement added for thermal bending moments should be placed near the cooler 7

(usually outside) face of the wall. In singly reinforced walls, it should be added to the main hoop 8

reinforcement, which should be near the outside face. In walls with two-layer reinforcing, the 9

entire amount should be added to the outer layer. For simplicity, an equal amount is often added 10

to the inner layer to avoid having bar sizes or spacings differ from one layer to the other. 11

Horizontal and vertical thermal moments will be present in the wall above the hot material 12

surface, and should be considered in the design. Where the vertical dead load compressive stress 13

is low, added vertical temperature reinforcement may be required. 14

79


R6.4.3 Strength design of walls subject to combined axial tension and flexure should be based on 1

the stress and strain compatibility assumptions of ACI 318-11, Chapter 10, and on the 2

equilibrium between the forces acting on the cross section at nominal strength. For small 3

eccentricity, Fig. R6.4.3 (e = Mu/Fu < h/2 - d) the required tensile reinforcement area per unit 4

height may be calculated by 5

)( ddf

eFA

y

us

(R6.4.3a) 6

on the side nearest to force Fu, and 7

)( ddf

eFA

y

us

(R6.4.3b) 8

on the opposite side. The variables As and As are both in tension. For large eccentricity (e = 9

Mu/Fu > h/2 - d), refer to Safarian and Harris (1974). 10

11

Fig. R6.4.3––Axial tension and flexure with small eccentricity. 12

13

R6.4.4 Circular walls in pressure zone 14

R6.4.4.1 Even though circular walls of concentric flow silos are analyzed as being subject to 15

hoop tension only, bending moments can occur due to temperature differentials, wind, seismic, 16

or differential settlement effects. The hoop tensions, bending moments and shear forces should 17

be combined according to 6.4.2 and the wall thickness and hoop reinforcement determined 18

according to 6.4.3. 19

80


R6.4.4.2 Although the Flow Channel Method is applicable to all silos, it is more commonly used 1

for silos storing stronger, higher δ materials where definitive flow channels occur. The method 2

calculates variation in pressure around the perimeter of the silo based on design flow channel(s). 3

The circumferential moments, radial shears, and tensions resulting from these variations are then 4

determined by structural analysis and used to select the wall thickness and reinforcement. Sadler 5

et al. (1995) provides general guidelines for designing silo walls based on flow channel 6

considerations. 7

The Eccentricity Method is commonly used for silos storing weaker, lower δ materials where 8

flow channel boundaries may not be easily definable. The method increases the normal amount 9

of hoop tension reinforcement by a calculated percentage based on the offset of an eccentric 10

discharge point when compared with the silo diameter. The resulting increased hoop 11

reinforcement increases the ability of the wall to resist forces resulting from asymmetric flow. 12

The Eccentricity Method is not to be used in cases when the effective angle of internal friction of 13

the material, δ, under service conditions of moisture, gradation, and compaction exceeds 40 14

degrees. 15

The two methods may or may not yield comparable results. 16

The overpressure factor Cd in 6.3.2.2 is not intended to cover asymmetric flow situations. 17

R6.4.4.3 Any rational method of structural analysis that recognizes the stiffness and passive 18

resistance of the static material may be used to estimate bending moments. Finite element 19

models with differential pressures on their shell elements that exclude the stiffness of stored 20

materials can provide unreasonably large bending moments and shear forces. 21

Figure R6.4.4.3 from Sadler et al. is a design aid used to estimate moments for D/h ratios and 22

different Lw/D ratios. The figure provides moment coefficients for a single flow channel and for 23

81


two diametrically opposed flow channels, based upon the ratio of the Silo diameter, D, to the silo 1

wall thickness, h. 2

The design aid is based on a linear elastic finite element model of a slice of unit height of the silo 3

wall and static material. For monolithically constructed silo groups and silos with unusual 4

configurations, a three-dimensional finite element model as opposed to a slice model may be 5

required. 6

Compared with an uncracked wall analysis, a cracked wall analysis results in lower bending 7

moments. A reduced wall thickness to simulate the effect of a cracked wall moment of inertia 8

may be used for h in this design aid. Wall cracking assumptions should be compatible with the 9

planned performance of the silo wall at service loads. 10

11

12

MTOTAL = C1 (ps – pf) D2 13 MIF = C2 MTOTAL 14

MOF = MTOTAL - MIF 15 16

Fig. R6.4.4.3––Moment coefficients (Sadler et al. 1995). 17 18

82


If the difference between ps and pf is known, the coefficients C1 and C2 can be used to determine 1

MTOTAL and the wall moments MOF and MIF. The higher negative (MOF) moments at the edges of 2

flow channels may be redistributed to the lower positive (MIF) zone at the center channel, to help 3

equalize the area of reinforcement between the inside and outside faces of the wall. Using same 4

bar size and spacing in both faces simplifies placement, especially for slip-formed walls. 5

Reinforcement for bending should typically be carried around the entire perimeter of the silo to 6

cover flow channels that might meander laterally away from the outlet and over the height of the 7

silo wall. 8

Although analysis may show hoop tension varying around the silo circumference, maximum 9

hoop tension is recommended at all locations for design. 10

R6.4.4.4 Selection of a design flow channel should be based on an understanding of material 11

flow and experience with asymmetric flow in comparable silos storing comparable materials. 12

Flow channels that form over outlet openings are often observed in the field from silo roof 13

openings; sizes, locations, and limits can be defined by scouring or abrasion marks on the silo 14

walls. 15

Figure 6.4.4.4 (Giunta 1969) is a useful analytical starting point for estimating θf and Y based on 16

δ. Whereas δ is a good measure of the ability of the material to form definitive flow channels, δ 17

as measured in shear strength tests on small samples may not be representative of the complete 18

range of particle sizes in the silo. Therefore, when selecting design flow channel configuration(s) 19

based on δ, the licensed design professional should place more reliance on observed behavior in 20

full-size silos than on shear test results and Fig. 6.4.4.4. 21

The channel should rarely be assumed to be plumb, but should be tilted toward the nearest wall 22

where coarse material accumulates from segregation during filling, as shown in Fig. R6.4.4.4. 23

The channel should be assumed to increase in size at the included angle 2 f from its apex until 24

83


it reaches diameter Y , after which it continues without further expansion. The tilt angle t 1

should be taken not less than f and may be conservatively set equal to , making the flow 2

channel start at the top of the hopper. 3

Actual flow channels that develop in silos will most likely differ from the design flow channel 4

assumed; therefore, a reasonably full range of variations in size and locations should be explored. 5

6

7

Fig. R6.4.4.4––Tilted Design Flow Channel. 8

9

R6.4.4.5 Vertical and horizontal pressures exerted by the flowing material, which are less than 10

the pressures exerted by the static or nonflowing material, result in circular flexing of the silo 11

wall. In applications where the converging portion of the flow channel is in contact with the wall, 12

84


Rf varies in depth and an incremental (layer by layer) solution of Eq. (6.4.4.5a) and (6.4.4.5b) is 1

required. The generalized form of Eq. (R6.4.4.5) is useful for this purpose. 2

ffff Rkyt

Rky

f

ff eqe

k

Rq //1

(R6.4.4.5) 3

4

where qt is the surcharge on the top layer being considered. 5

Alternatively, the material pressures within the converging portion of the flow channel may 6

be calculated using mass flow pressure formulas in 6.3.3.1. Such formulas will result in a less 7

conservative design (a smaller difference between pf and p) at and below the transition. The 8

opposite will be true near the outlet. 9

In Eq. (6.4.4.5a), µ’f may be conservatively taken equal to tan . Alternatively, a weighted 10

average for µ’ following the procedure given in Sadler et al. (1995) may be used. 11

12

R6.4.4.6 Geometry dictates that as the number and size of flow channels of a multiple-outlet silo 13

increase, the pressures in the static material and the resulting moments increase significantly. 14

Therefore, it is important to consider realistic combinations of flow channels and not arbitrarily 15

assume all discharge feeders will be interlocked and operated together. 16

17

R6.4.4.7 The eccentricity method described here was introduced in 4.4.2.4 of the ACI 313-77 18

Commentary. Even though it was not retained in subsequent updates of ACI 313, it has been 19

used with success in the grain industry. 20

The Eccentricity Method is not appropriate for design of silos with small or zero eccentricities if 21

the flow channel can deviate laterally above the opening and contact the wall as shown in Fig. 22

R6.4.4.4. 23

85


1

2

3

4

5

R6.4.4.8 Aeration systems that fluidize only portions of the silo subject silo walls to non-uniform 6

horizontal pressure. Design pressures should be computed by 6.3.2.3. Hoop tensions, bending 7

moments and shear forces should be computed by 6.4.4.2. 8

R6.4.5 Suggested procedures for the analysis and design of noncircular silo walls are given in 9

Safarian and Harris (1984). 10

R6.4.7 Equation (6.4.7) is obtained from ACI 318-11, Eq. (14-1) for walls. Proportions of cast-11

in-place circular silo walls are such that buckling due to vertical compression ordinarily does not 12

control, and the axial load compressive strength given by Eq. (6.4.7) need not be reduced for 13

slenderness effects. 14

For silos of unusual proportions and for some silo walls next to openings, however, the 15

design vertical compressive strength may be less than given by Eq. (6.4.7). Suggested formulas 16

for such conditions are given in Safarian and Harris (1984) and Baker et al. (1981). 17

R6.4.8 The primary concern of crack control is to minimize crack width. In terms of protecting 18

the reinforcement from corrosion, however, surface crack width appears to be relatively less 19

important than previously believed. Therefore, it is usually preferable to provide a greater 20

thickness of concrete cover even though this will lead to wider surface cracks. Construction 21

practices directed towards minimizing drying shrinkage will have significant impact on crack 22

control. Additional information on this subject is found in ACI 318-11, 10.6, and in ACI 23

Committee 224R-01. 24

86


Similarly, to protect against splitting of the concrete around the reinforcement, the minimum 1

center-to-center spacing and the minimum concrete cover of the reinforcement should be limited 2

to those prescribed by 6.2.9 and 6.2.10, even though this may also lead to wider surface cracks. 3

The design crack width limit of 0.010 in. (0.25 mm) under initial filling conditions results in 4

reasonable reinforcement details that reflect experience with existing silos. The actual crack 5

width will, in all probability, be different than the calculated design crack width, and will vary 6

depending on the amount of cover provided. Equation (6.4.8), given in Section 4.8 of ACI 7

Committee 224-01 (Reapproved 2008), does not reflect the effects of excessive drying shrinkage 8

that can result in a significant increase in crack width. In Eq. (6.4.8), fs is the stress in the hoop 9

reinforcement under initial filling pressures calculated by Eq. (6.3.2.1a) through (6.3.2.1c) (at 10

service load level, load factor = 1.0; overpressure factor = 1.0). 11

12

R6.5—Hopper design 13

R6.5.1 Loads—Hoppers should be designed to withstand flow pressures in accordance with 14

6.3.3.2 and 6.3.3.3, in addition to other loads described in this chapter. 15

R6.5.2 Formulas for computing stresses in hoppers are found in Safarian and Harris (1984), 16

Gaylord and Gaylord (1984), Rotter (1990), and Ooi and Rotter (1991). The design of structural 17

steel hoppers should be in accordance the requirements of the American Institute of Steel 18

Construction “Steel Construction Manual,” 14th Edition (2011). 19

R6.5.2.5 The design of hopper supports should consider potential differential horizontal and 20

vertical movements between the hopper support and silo walls. Such movements may induce 21

forces and moments not otherwise anticipated. 22

23

R6.6—Column design 24

87


Under sustained compressive load, creep in a reinforced concrete column causes the concrete 1

stress to reduce, transferring load to the steel reinforcement. With subsequent sudden unloading, 2

the concrete may be in tension and develop horizontal cracks. This condition is more pronounced 3

in columns with large ratios of reinforcement-to-concrete area. (Dipasquale, 1981) 4

The problem of such cracking is seldom experienced in normal building structures because 5

dead load exceeds vertical live load and extreme unloading cannot occur. In storage silos, 6

however, live load (stored materials) usually accounts for the major portion of the load, and can 7

be quickly removed. Thus, the horizontal cracking of heavily reinforced silo support columns 8

can be severe. 9

Such cracking will be serious if it is accompanied by vertical cracking, as could occur with 10

high bond stress during unloading. This latter condition can be dangerous, and can be prevented 11

by the following: 12

a) If lateral forces are not a problem, the vertical reinforcement ratio should be kept low to 13

prevent horizontal cracking upon unloading. 14

b) If lateral forces have to be resisted, larger columns with a low reinforcement ratio should 15

be used. 16

17

R6.7—Foundation design 18

R6.7.3 Unsymmetrical loading should be considered for its effect on stability (against 19

overturning), soil pressures, and structural design of the foundation. 20

21

CHAPTER R7—CONCRETE STAVE INDUSTRIAL SILOS 22

R7.2—Coatings 23

88


Coatings are often specified for the inside and/or outside face of stave silo walls to protect 1

the stored material from moisture infiltratation, to protect the staves from hazardous stored 2

materials, or to protect the staves and stave hoops from weathering. The coating material, where 3

required, should be chosen to be consistent with the properties of the stored material, the stave 4

concrete and the steel hoops. 5

Interior coatings, where specified, typically consist of a single operation, three-coat plaster 6

(parge) application of fine sand and cement worked into the stave surface and joints in such a 7

manner as to become an integral part of the wall. The final finish is typically steel troweled 8

smooth. 9

Exterior coatings, where specified, typically consist of thick cement slurry brushed or 10

otherwise worked into the surface and joints of the staves to provide maximum joint rigidity and 11

water-tightness. 12

13

R7.3—Erection tolerances 14

A quality control program should be established to measure, document, and verify 15

compliance with the construction tolerance requirements of this document. The program should 16

identify the type, number and frequency of the measurements required to document each of the 17

areas specified in this document.R7.3.2 Spiraling results when staves are tilted slightly so that, 18

even though their outer faces are vertical, their edges are inclined. Such misplacement causes 19

vertical joint lines to be long-pitch spirals rather than plumb lines. The resulting assembly 20

appears to spiral. 21

R7.3.3 A bulge is the vertical out-of-plane deviation of a stave wall as measured from a straight-22

edge or string and shall be measured over a 10 ft (3 m) section of wall height. 23

R7.3.4 The measured inside shell diameter shall be taken at regular intervals as established by 24

89


the quality control program. The diameter of the silo is measured in feet for the tolerance 1

calculation. 2

3

R7.4—Wall design 4

R7.4.1 Loads, design pressures, and forces—The pressure formulas in Chapter 6 are not 5

applicable to silos storing silage. Guidance for farm silo design is given in International Silo 6

Association (1981). 7

R7.4.2 Wall thickness—Stave silo strength depends not so much on the strength of any one 8

component as on the way these components and their connections act when assembled. 9

Therefore, stave assembly tests are needed to determine joint shear strength (tension) and vertical 10

compressive strength, as well as vertical and horizontal wall stiffness and bending strength. 11

Recommended tests are given in R7.6. 12

R7.4.3 Circular bending—Because of thin walls and a multitude of vertical joints, stave silos 13

have less circular rigidity than monolithic silos. If joints are not shaped so they can be pointed 14

with grout after erection, they are free to rotate and allow the silo to assume an oval shape. 15

Decreased circular strength also results from the placement of steel hoops on the exterior surface. 16

When the curvature of the wall increases, the hoops add to circular strength; however, when the 17

curvature decreases, the hoops add minimal strength. While a stave wall has the undesirable 18

tendency to go out-of-round if it is not stiff enough, it also has the desirable ability to redistribute 19

circumferential bending moments from weaker positive moment (tension inside face) zones to 20

stronger negative moment zones (tension outside face). 21

The circular strength and stiffness of a stave silo can be increased by additional hoops, 22

thicker staves, or better vertical joint details. The strength of any particular stave design is 23

difficult to determine without testing full-scale stave assemblies. It can be estimated, however, 24

90


that the total statical moment strength is typically not more than 0.875(As fy-Fu)h and that the 1

positive moment strength is typically not more than 0.375(Asfy-Fu)h. 2

Equation (7.4.3b) requires the total statical moment strength to be 1.6 times the total moment 3

acting on the wall. Equation (7.4.3c) requires the positive moment strength to be 1.0 times the 4

positive moment acting on the wall. It is assumed a portion of the positive moments will 5

redistribute to the negative moment zones and the factor of safety against total failure will be 6

maintained, even though there may be some cracking on the inside face in the positive moment 7

zones. 8

Equations (7.4.3d) and (7.4.3e) simply restate Eq. (7.4.3b) and (7.4.3c) in terms of the actual 9

wall thickness and hoops supplied. The term (NAsfy - Fu) represents the excess hoop capacity 10

supplied for bending. The quantity 0.875h in Eq. (7.4.3d) represents the approximate distance 11

between the tension force in the hoops (assumed 1/2 in. diameter) and the compression block. 12

The quantity 0.375h in Eq. (7.4.3e) represents the approximate distance between the tension 13

force in the hoops and the triangular compression block in the wall, assuming compression exists 14

across the entire depth (h) of the wall. 15

When calculating circumferential bending from unequal pressures, the magnitudes and 16

distribution of moments can be affected by assumptions about where and to what extent the stave 17

wall cracks under the tension and bending loads. The circumferential tension force from filling 18

pressures, Fu, can reduce the circumferential bending capacity and stiffness available to resist 19

unequal pressures and significant circular deformation can occur. 20

Because of the flexibility of stave walls, unexpected distress can result where walls are 21

restrained from free movement by attached structures or internal hoppers. 22

91


R7.4.4 Compression and buckling—Deformation from asymmetric flow, particularly over a side 1

withdrawal, can reduce the wall curvature and increase the possibility of the wall buckling under 2

vertical loads. 3

The Pnw,stave in Eq. (7.4.4a) is the nominal axial load strength obtained from tests illustrated 4

by Fig. R7.4.4a or Fig. R7.4.4b. The Pnw,joint in Eq. (7.4.4b) is the strength from tests illustrated 5

by Fig. R7.4.4b, and is typically lower. The Pnw,buckling in Eq. (7.4.4c) is obtained by test, or by a 6

combination of test results and published methods of computing critical buckling strength, and 7

should take into account the sometimes large out-of-plane deviations found in stave silo walls. 8

R7.4.5 Forces due to overturning—Silo walls are subjected to vertical tension when the silo has 9

insufficient self-weight to resist overturning from wind or earthquake overturning. In such cases, 10

anchor straps secured to the foundation are extended up the silo wall an appropriate distance and 11

secured to the hoops. Where the straps are discontinued, the wall must resist the remaining 12

tension. Tension failure of the wall can occur if the stave breaks in tension or if the stave slips 13

out of the lapped position depicted in Fig. R7.4.4b. Compliance with Eq. (7.4.5a), which assumes 14

the tensile strength of concrete is 5√f’c (0.42√f’c), will prevent a tension failure of the concrete in 15

the stave. Compliance with Eq. (7.4.5b), which assumes the coefficient of sliding friction of 16

concrete on concrete is 0.1, will prevent slipping of the stave from the lapped position. The force 17

W or E in Eq. (7.4.5a) and (7.4.5b) is doubled because only half of the staves are continuous at 18

any horizontal joint. 19

20

R7.5—Hoops for stave silos 21

R7.5.1 Hoops are typically of galvanized steel. The exterior cement paste coating, when used, is 22

typically applied over top of the stave hoops, providing additional protection. 23

24

92


R7.5.2 Calculating steel area—Typical hoop connector lugs are configured to allow the 1

connected hoop ends to splice by offsetting and overlapping. As the hoops are tightened, the lugs 2

through which the hoops pass rotate slightly because of the offset. This causes the hoops to bend 3

slightly where they enter the lug. 4

R7.5.3 Tensioning—Hoops generally consist of three or more rods connected by lugs of 5

malleable iron or pressed steel. Even though tightening is done only at the lug, within a short 6

time the hoop stress will be uniform along the entire hoop length. 7

8

R7.6—Concrete stave and stave assembly tests 9

The compressive strength of concrete staves should be in accordance with the following 10

paragraphs. 11

A test section should consist of the full width of a solid stave with the height of this section 12

being twice the thickness of the stave shown in Fig. 7.6c. The stave should be tested in a 13

conventional compression testing machine, being loaded by the machine in the same manner as it 14

is loaded in the silo wall. 15

When testing a cored stave, a section should be cut with a height twice the thickness of the 16

stave shown in Fig. 7.6d. The maximum depth, however, should include only one complete core, 17

and no portion of a core should be present on either top or bottom of the test specimen. 18

The selection and required number of test sections and the procedures for capping and testing 19

the test sections should conform to ASTM C140. 20

The average minimum compressive strength on the effective cross-sectional area, Aw, should 21

be at least 4000 psi (28 MPa) at 28 days. The average of any five consecutive stave strength tests 22

should be equal to or greater than the specified concrete strength and not more than 20 percent of 23

the tests should have a compressive strength value less than the specified strength. 24

93


1

2

The following are tests of individual staves: 3

a) Compressive strength tests to determine Pnw, stave are defined by earlier paragraphs. 4

Compressive test samples should be cut from five or more randomly selected staves. The 5

specimens shown in Fig. R7.4.4a and R7.4.4b are full stave width with height equal to 6

twice the stave thickness. The compressive load is vertical, with the specimen positioned 7

as for use in the silo wall. 8

b) Flexural strength measures concrete quality and can be used instead of the compressive 9

strength test. Bending specimens are cut from five or more randomly selected staves. The 10

specimen length is sufficient to permit testing on a 24 in. (600 mm) simple span with 11

concentrated midspan load. End reactions and midspan load are distributed across the full 12

width of the specimen and are applied through padded bearing plates 2 in. (50 mm) wide. 13

The span direction is parallel to the vertical direction of the stave in the silo. Test speed is 14

not over 0.05 in. (0.13 mm) per minute. The bending strength is calculated as the bending 15

modulus of rupture. 16

The following are tests of stave assemblies that may be used to establish properties and 17

prove strength of assembled staves: 18

a) Joint shear strength (tension), that is, resistance to sliding, can be determined by testing a 19

group of three staves as shown in Fig. R7.4.4a. Lateral confining forces simulate the 20

forces applied by hoop prestress in the unloaded actual silo. The test measures the 21

vertical pull necessary to cause the center stave to slide with respect to the two adjacent 22

staves. The word tension describes this test because such joint shear and sliding result 23

from vertical wall tension from wind load on the empty silo. 24

94


b) Figure R7.4.4b shows a test for stave joint compressive strength Pnw,joint. It measures the 1

compressive force that can be transferred from stave to stave across a horizontal joint. 2

Joints and surfaces should be grouted, coated, or both, in the manner that will be used in 3

the actual silo. 4

c) Figure R7.6a is a test for determining vertical stiffness. An assembly four staves high by 5

four wide is coated in the manner that will be used in the actual silo. Confining forces are 6

applied to the assembly in a manner that simulates the prestress force (after losses) of the 7

hoop rods. Lateral load is applied and deflections measured. From loads and deflections, 8

the value of effective EI, and then effective wall thickness, can be calculated for use in 9

obtaining Pnw,buckling. 10

d) Fig. R7.6b is a test for horizontal strength and stiffness. The assembled staves are coated 11

similarly to how they will be used in the actual silo. Deflection and load values are 12

measured. The effective EI and wall thickness are then calculated from test results for use 13

in silo design. 14

When the Fig. R7.6b test is used to determine circular bending strength for purposes of 15

checking resistance to bending from asymmetric pressures, the hoops should be loosened an 16

appropriate amount to simulate the loss of compression across the vertical joints that would 17

occur from the internal pressure of the stored material. 18

There are no standards (ASTM or otherwise) for the tests of stave assemblies described in 19

R7.6. The tests are not to be considered proof tests used to assure that a certain strength 20

specified by a designer or code authority has been met. They are rather to provide guidance to a 21

contractor and the licensed design professional in determining what strengths might reasonably 22

be relied upon with their particular assembly of staves and in their particular application. 23

24

95


1

Fig. R7.4.4a—Stave assembly joint shear (tension) test. 2

3

4

5

Fig. R7.4.4b—Stave assembly compression test. 6

7

96


1

Fig. R7.6a—Stave assembly test for vertical stiffness. 2

3

Fig. R7.6b—Stave assembly test for horizontal stiffness. 4

97


1

Fig. 7.6c—Solid stave. 2

3

4

Fig. 7.6d—Hollow stave. 5

6

7

CHAPTER R8—POST-TENSIONED CONCRETE SILOS 8

R8.1—Scope 9

R8.1.3 Concrete silo wall strength and performance can be improved by the addition of post-10

tensioning forces to the wall to resist hoop tension forces. Observations by committee members 11

have shown that when the wall is subjected to significant bending, conventional reinforcement 12

should be used in addition to the post-tensioning. Use of full post-tensioning alone can cause 13

compression overstress and failure when the wall is subject to significant circumferential 14

bending. 15

R8.1.2 Requirements of this Design Specification sometimes differ from those of ACI 318-11 16

because the severity of silo loadings and field operating conditions differ substantially from 17

those of buildings. 18

98


1

R8.2—Post-tensioning systems 2

R8.2.1 Wire wrapping systems, which are tendons or wires wound continuously around the 3

outside of the silo, are sometimes suited to making repairs to distressed silos but are not covered 4

in this Design Specification. Guidance on techniques and procedures for wrapped systems is 5

available in ACI 372R. 6

R8.2.2 Exterior ducts or strands with special protective coatings can be left exposed if 7

constructed to withstand the surrounding atmospheric condition; otherwise, they are usually 8

protected with shotcrete. 9

10

R8.3—Tendon systems 11

R8.3.1 A minimum 10 in. (250 mm) wall thickness is recommended to provide adequate room 12

for placing and controlling the location of tendons and conventional reinforcement. 13

R8.3.4 In slipform construction, embedded tendon ducts are normally placed near the center of 14

the wall. 15

R8.3.5 Jacking locations should be spaced uniformly around the circumference of the silo to 16

avoid unnecessary concentrations of stresses. Wall pilasters should be located and proportioned 17

to avoid reverse curvature of the tendons. Radial forces from reverse curvature should be 18

considered in the design of the pilaster and its web reinforcement. Spiral reinforcement should be 19

placed at trumpet locations to control bursting forces. 20

R8.3.6 Horizontal tie reinforcement should be provided in pilasters to prevent radial forces from 21

continuing tendons and forces from anchored tendons from splitting the wall. Ties to resist 22

splitting forces should be provided at pilasters common to two silos, as at wall intersections 23

shown in Fig. R8.3.6. 24

99


R8.3.7 Horizontal (radial) tie reinforcement, shown in Fig. R8.3.6, is provided in walls between 1

pilasters and between inner and outer main horizontal bars to resist radial tensile stresses. 2

R8.3.9 Dry-packed mortar consisting of one part shrinkage-compensating cement and two parts 3

sand is recommended for filling blockouts and pockets. 4

5

Fig. R8.3.6––Circumferential post-tensioning anchorage details. 6

7

R8.4—Bonded tendons 8

100


R8.4.2 Any anchorage encasement material in contact with the grout and exposed to the 1

environment should be resistant to degradation from sunlight and have an effective life 2

equivalent to that of the concrete. 3

4

R8.5—Unbonded tendons 5

R8.5.1 Cyclic loading and unloading of the silo that might lead to fatigue failure of anchorages 6

or couplers shall be considered in the selection of anchorages. A discussion of the factors to 7

consider in cases of cyclic loading that might lead to premature fatigue failures are found in ACI 8

215R. 9

10

R8.6—Post-tensioning ducts 11

Semirigid metal tendon ducts are usually available in 20 ft (6 m) lengths. Flexible plastic ducts 12

are usually available in 400 ft (120 m) rolls. Metal ducts are typically corrugated and prebent to 13

conform to the intended circular shape and radial position. Metal ducts require splices at 14

approximately 20 ft (6 m) intervals. 15

Because plastic ducts come in 400 ft (120 m) lengths, splices are needed only at points where 16

the ducts terminate and are connected to trumpets at anchorage points. 17

Plastic ducts, however, should be tied for support at more frequent intervals than semirigid 18

ducts to prevent sag and shifting during concrete placement and vibration. 19

Concrete placing and compacting should be completed carefully to avoid punching holes in 20

the duct, which allows concrete to fill it. In the event ducts are punctured, concrete should be 21

removed and holes patched while the concrete is still workable. 22

R8.6.3 Post-tensioning suppliers typically recommend the necessary duct diameter for a given 23

tendon profile based on anchorage, installation, and grouting requirements. 24

101


1

R8.10—Design 2

R8.10.3 In post-tensioned silos, a residual compressive stress in the silo wall of approximately 3

40 psi (0.28 MPa)should be maintained under service load of 1.5 times initial filling pressures 4

plus thermal loads to minimize the likelihood of open cracks (Safarian and Harris 1995). 5

A careful evaluation should be made of the expected cracking and the effects such cracking 6

can have on protection of the post-tensioning tendons from weather or abrasion (Johnston 1990). 7

R8.10.7.2 ACI 318-11, 9.4, does not permit designs based on a yield strength fy in excess of 8

80,000 psi (550 MPa), except for prestressing steel. In addition to the upper limit of 80,000 psi 9

(550 MPa) for yield strength of nonprestressed reinforcement, there are other limitations on the 10

yield strength in ACI 318-11, 9.4. 11

12

R8.10.8 The height limits given in 8.10.8 for the transition zone have been obtained by shell 13

analysis. Specified minimum levels of initial compressive stress are lower than recommended by 14

ACI 372R because some cracking can be tolerated, whereas cracking in liquid storage tanks 15

cannot be tolerated. 16

R8.10.9 Formulas for estimating losses from anchorage set and tendon elongation within the jack 17

and for calculation of the length influenced by anchor set are found in the PTI Post Tensioning 18

Manual (2006) and AASHTO (2010) LRFD Bridge Design.. Methods of estimating prestress 19

losses due to elastic shortening and time-dependent losses are found in the PTI (2006) and 20

AASHTO (2010) documents noted above, the PCI Prestressed Concrete Institute (2010) Design 21

Handbook, 7th Edition , and Zia et al. (1979). 22

23

R8.11—Vertical bending moment and shear due to post-tensioning 24

102


Vertical bending moment will be caused whenever a tendon is tensioned due to inward 1

movement of the wall at the tendon location, whereas the wall at some distance above and below 2

that tendon is relatively unaffected. During prestressing, vertical bending moment is also caused 3

by the restraint to inward movement of the wall offered by the foundation, nonsliding roofs, and 4

silo bottom slabs. These bending moments should be considered in design (ACI Committee 344 5

1980). Bending moments may be calculated using finite element methods or estimated using 6

approximate methods (ACI Committee 344 1980; Timoshenko and Woinowsky-Krieger 1959; 7

Beyer 1948; Girkmann et al. 1959; Flugge 1957; and Born 1960). 8

9

CHAPTER R9—CONCRETE STACKING TUBES 10

R9.2—General layout 11

Stacking tubes, also known as lowering tubes, are free-standing tubular structures used to stack 12

conical piles of granular bulk materials, similar to Fig. R9.2a. They are used to reduce dust 13

emissions and support the stacking conveyor and headhouse. Concrete stacking tubes typically 14

vary in diameter from 10 to 16 ft (3 to 5 m) and in wall thickness from 6 to 16 in. (150 to 400 15

mm). Stacking tubes typically have a round cross section, but square stacking tubes have also 16

been constructed. 17

The bulk material is discharged into the top of the tube, and as material builds up in the 18

bottom, it spills out through the wall openings to form a conical pile. Openings are generally 19

equipped with hinged dust flaps and arranged in symmetric 90- or 180-degree patterns. The 20

materials segregate during the stockpiling process. The less flowable fines collect in and adjacent 21

to the tube. The coarse material collects at the foot of the pile. 22

Stacking tubes are frequently built directly over conveyor-equipped tunnels that reclaim 23

material by gravity from the pile above. Typically, tunnel reclaim openings are furnished on 24

103


either side of the tube. Sometimes openings are furnished directly under the tube, similar toFig. 1

R9.2b. Even though the latter location is less effective in reclaiming from the pile, it does inhibit 2

plugging of the tube. 3

Operators of stacking tube systems frequently work on top of the piles with bulldozers to 4

push materials toward and away from the tube during stockpiling and reclaiming. Bulldozers 5

create additional fines and compact the material into a denser state. This action, added to 6

densification of fines from accumulating weight, frequently causes flow problems in the tube 7

vicinity. Such problems include: 8

a) Equipment and workers falling into ratholes when the material around or over a rathole 9

collapses. A stable rathole forms when the stockpiled material gains sufficient cohesion and 10

internal strength to arch horizontally around a flow channel and remain stable even after the 11

flowing material is gone. Stable ratholes have been observed from 5 to 20 ft (1 m to 6 m) in 12

width. 13

b) Walls of dense material that can collapse while reclaiming the material 14

c) Arches that prevent material from flowing into or out of the stacking tube openings 15

d) Arches in the upper portions of tubes with cavities below; collapse of the arches when 16

cleaning from below can injure personnel and structurally damage the tube 17

e) Structural damage to tube walls and dust flaps by dozer operators reclaiming material close 18

to the tube 19

f) Failure of open dust-flaps from entrapment and settlement of the surrounding pile. 20

Stacking tube diameters, outlet opening sizes, wall thicknesses, reclaim opening configurations, 21

and dust-flap designs that will minimize potential problems should be chosen. 22

23

R9.3—Loads 24

104


The design of the stacking tube (Safarian and Harris 1985a, b; Wu 1975; Reimbert and Reimbert 1

1974) should consider the most severe probable loading condition the tube might experience 2

from operation of the stockpiling and reclaiming system. Many loading combinations should be 3

considered in the analysis and design of a stacking tube. The licensed design professional should 4

consider all possible combinations of operational and environmental loads as well as stockpile 5

loads that result from a bulldozed pile sloping down to the tube, or a full conical pile, a partially 6

drawn down pile, or from no pile at all. 7

Reclaim hoppers large enough to prevent stable ratholes should be used if possible; if they 8

are not, the tube design should consider the uneven lateral loading that might result from a pile 9

that is complete, except for a stable rathole on one side of the tube. The design should also 10

consider all likely configurations of bulldozed and excavated material. 11

Stockpiling conveyor system loads are usually transmitted to the top of the stacking tube 12

through a headhouse structure. Eccentricity between the applied loads and tube should be 13

considered in the design. 14

Stiffness of the tube relative to the conveyor structure should be assessed when analyzing 15

longitudinal loads from the conveyor. 16

17

R9.4—Load factors and strength-reduction factors 18

Load factors used in the analysis and design of a stacking tube should be chosen to reflect the 19

likelihood of them occurring simultaneously. Conveying equipment is often designed for large 20

motor startup or upset condition loadings. The licensed design professional should determine 21

which conditions are most probable during routine operations. 22

23

R9.6—Foundation or reclaim tunnel 24

105


The vertical loads (Wu 1975) that the bulk material pile imparts on the stacking tube, reclaim 1

tunnel, and foundation should be carefully considered if the pile is supported on compressible 2

soils while the tube is supported on rigid foundations. In this case, the stacking tube and other 3

associated rigid structures can be subjected to extremely large negative skin friction loads as the 4

pile settles relative to the tube, tunnel, and foundation. 5

Careful consideration should also be given to the effect of differential foundation settlement. 6

7

Fig. R9.2a––Stacking tube elevation. 8

106


1

Fig. R9.2b––Reclaim tunnel under stacking tube. 2

107


1

2

COMMENTARY REFERENCES 3

American Concrete Institute 4

ACI 117-10 Specification for Tolerances for Concrete Construction and Materials and 5

Commentary 6

ACI 215R- (92) Considerations for Design of Concrete Structures Subjected to Fatigue 7

Loading (Reapproved 1997) 8

ACI 224-01 Control of Cracking in Concrete Structures (Reapproved 2008) 9

ACI 301-10 Specifications for Structural Concrete 10

ACI 305R-10 Guide to Hot Weather Concreting 11

ACI 306R-10 Guide to Cold Weather Concreting 12

ACI 308R-01 Guide to Curing Concrete (Reapproved 2008) 13

ACI 318-11 Building Code Requirements for Structural Concrete and Commentary 14

ACI 347-04 Guide to Formwork for Concrete 15

ACI 372R-03 Design and Construction of Circular Wire and Strand-Wrapped Prestressed 16

Concrete Structures 17

18

American Association of State Highway and Transportation Officials 19

AASHTO HB-17-02 Specifications for Highway Bridges 20

21

International Organization for Standardization 22

ISO 11697:1995 Bases for Design of Structures—Loads Due to Bulk Materials 23

24

108


ACI Committee 224, 1986, “Cracking of Concrete Members in Direct Tension,” ACI 1

JOURNAL, Proceedings V. 83, No. 1, Jan.- Feb., pp. 3-13. 2

ACI Committee 344, 1980, “Design and Construction of Circular Prestressed Concrete 3

Structures,” ACI JOURNAL, Proceedings V. 67, No. 9, Sept., pp. 657-672. 4

ACI Committee 443, 1976, “Prestressed Concrete Bridge Design,” ACI JOURNAL, 5

Proceedings V. 73, No. 11, Nov., pp. 597-612. 6

American Institute of Steel Construction, Inc., 2010, Manual of Steel Construction, 7

fourteenth edition, Chicago, IL, pp. 1578 8

Anderson, E. Y., 1985, “Wall Pressures and Flow Patterns in Fly Ash Silos Due To Various 9

Aerations,” International Journal of Bulk Solids Storage in Silos, V. 1, No. 4, pp. 1-7. 10

Baker, E. H.; Kovalevsky, L.; and Rish, F. L., 1981, Structural Analysis of Shells, Robert E. 11

Krieger Publishing Company, New York. 12

Bernache, P. L., 1968, “Flow of Dry Bulk Solids on Bin Walls,” No. 68-MH-16, ASME, 13

New York. 14

Beyer, K., 1948, Die Statik in Stahlbetonbau, Springer, Berlin. 15

Bishara, A. G.; Vedaie, B.; and Togni, C., 1996, Discussion of “Designing Silo Walls for 16

Flow Patterns,” ACI Structural Journal, V. 93, No. 1, Jan.‐Feb., pp. 145‐150. 17

Blight, G. E., 1988, “A Comparison of Measured Pressures in Silos with Code 18

Recommendations,” Bulk Solids Handling, V. 8, No. 2, Apr., pp. 145, 153. 19

Bohm, F., 1956, “Zur Berechnung Runder Silozellen fur Zementlagerung,” Beton und 20

Stahlbetonbau, Berlin, Feb., pp. 29-36. 21

Born, J., 1960, “Practishe Schalenstatik Bd. 1, die Rotationsschalen, Wilhelm Ernst and 22

Sohn, Berlin. 23

109


Broersma, G., 1972, Behavior of Granular Materials, Stam Technical Publications, 1

Culemborg, 265 pp. 2

BS 2810 Precast Concrete Stave Silos for Grain Storage. 3

Camellerie, J. F., 1959, “Slip Form Details and Techniques,” ACI JOURNAL, Proceedings 4

V. 55, No. 10, Apr., pp. 1131-1140. 5

Camellerie, J. F., 1971, “Slip Forms,” Handbook of Heavy Construction, McGraw-Hill Book 6

Co., NY, pp. 21-117 to 21-129. 7

Carson, J. W., and Johanson, J. R., 1977, “Vibrations Caused by Solids Flow in Storage 8

Bins,” Proceedings of the Industrial and Scientific Conference Management, Inc., Chicago, May, 9

pp. 236-243. 10

Clague, K., and Wright, H., 1973, “Pressures in Bunkers,” Iron and Steel International, Aug., 11

pp. 336-346. 12

Colijn, H., and Peschl, V., 1981, “Non-Symmetrical Bin Flow Problems,” International 13

Journal of Storing and Handling Bulk Materials, V. 6, No. 3, pp. 79-96. 14

DIN 1055, Teil 6, Deutsche Norm, Lastannahmen fur Bauten, Lasten in Silozellen, Design 15

Loads for Building Silos, Beuth Verlag, Berlin, 1987. 16

DiPasquale. Raymond, Why Concrete Columns can Crack, Concrete Construction, Volume 17

26, No. 9, Septemeber 1981, pg. 737 18

19

Ferguson, P. M., and Krishbaswamy, C. M., 1971, “Tensile Lap Splices, Part 2; Design 20

Recommendations for Retaining Wall Splices and Larger Bar Splices,” Center for Highway 21

Research, University of Texas, Austin, TX. 22

Flugge, W., 1957, Statik und Dynamik der Schalen, Springer, Berlin. 23

110


Gaylord, E. H., and Gaylord, C. N., 1984, Design of Steel Bins for Storage of Bulk Solids, 1

Prentice-Hall, Inc., Englewood Cliffs, NJ. 2

Girkmann, K., 1959, “Flachentraqwerke,” Springer, Wien. 3

Giunta, J.S., 1968, Flow Patterns of Granular Materials in Flat Bottom Bins, The American 4

Society of Mechanical Engineers, Paper No. 68 MH-1. 5

Hurd, M. K., 2005, Formwork for Concrete, SP-4, seventh edition, American Concrete 6

Institute, Farmington Hills, MI, 500 pp. 7

Homes, A. G., 1972, “Lateral Pressures of Granular Materials in Silos,” Publication No. 72-8

MH-30, ASME, NY. 9

International Silo Association, 1981, “Recommended Practice for Design and Construction 10

of; Top Unloading Monolithic Farm Silos; Bottom Unloading Monolithic Farm Silos; Top 11

Unloading Concrete Stave Farm Silos; and Bottom Unloading Concrete Stave Farm Silos,” V. 1-12

4, Luxemburg, WI. 13

Janssen, H. A., 1885, “Versuche uber Getreidedruck in Silozellen,” VDI Zeitschrift, 14

Dusseldorf, V. 39, Aug., pp. 1045-1049. 15

Jenike, A. W., 1964, “Storage and Flow of Solids,” Bulletin No. 123, Engineering 16

Experiment Station, University of Utah, Salt Lake City, Nov., 196 pp. 17

Jenike, A. W., 1967, “Quantitative Design of Mass Flow Bins,” Powder Technology 18

(Lausanne), V. 1, pp. 237-244. 19

Jenike, A. W., 1977, “Load Assumptions and Distributions in Silo Design,” Norwegian 20

Society of Chartered Engineers Conference on Construction of Concrete Silos, Oslo, Jan. 21

Jenike, A. W.; Johanson, J. R.; and Carson, J. W., 1972, “Bin Loads, Parts 2, 3 and 4,” No. 22

72-MH-1, 2, 3, American Society of Mechanical Engineers, NY. 23

111


Jenkyn, R. T., 1994, “How to Calculate Thermal Loadings in Silos,” Bulk Solids Handling, 1

V. 14, No. 2, Apr.-June, pp. 345-349. 2

Johnston, T., 1990, “How to Design Large-Diameter Silos that Last,” Powder and Bulk 3

Engineering, CSC Publishing, Minneapolis, MN, May, pp. 43-53. 4

McLean, A. G., 1985, “Initial Stress Fields in Converging Channels,” Bulk Solids Handling, 5

V. 5, No. 2, Apr., pp. 49-54. 6

Ooi, J. Y., and Rotter, J. M., 1991, “Elastic Predictions of Pressures in Conical Silo 7

Hoppers,” Engineering Structures, V. 13, No. 1, Jan., pp. 2-12. 8

Pieper, K., and Wenzel, F., 1964, “Druckverhaltnisse,” Silozellen, Verlag von Wilhelm Ernst 9

and Sohn, Berlin. 10

Post-Tensioning Institute, 2006, Post-Tensioning Manual, sixth edition, Farmington Hills, 11

MI, 354 pp. 12

Prestressed Concrete Institute, 2010, Design Handbook, seventh edition, Chicago, IL 13

14

Reimbert, M. L., and Reimbert, A. M., 1974, Retaining Walls, Trans Tech Publications, 15

Clausthal, West Germany, 284 pp. 16

Reimbert, A. L., and Reimbert, A. M., 1980, “Pressures and Overpressures in Vertical and 17

Horizontal Silos,” Proceedings of the International Conference on Design of Silos for Strength 18

and Flow, University of Lancaster, Sept., 16 pp. 19

Reimbert, M. L., and Reimbert, A. M., 1987, Silo—Theory and Practice, second edition, 20

Lavoisier Publishing, Inc., NY, 564 pp. 21

Rotter, J. M., 1990, “Structural Design of Light Gauge Silo Hoppers,” Journal of Structural 22

Engineering, ASCE, V. 116, No. 7, July, pp. 1907-1922. 23

112


Sadler, J. E.; Johnston, F. T.; and Mahmoud, M. H., 1995, “Designing Silo Walls for Flow 1

Patterns,” ACI Structural Journal, V. 93, No. 1, Jan.-Feb., pp. 145-150. 2

3

Safarian, S. S., and Harris, E. C., 1970, “Determination of Minimum Wall Thickness and 4

Temperature Steel in Conventionally Reinforced Circular Concrete Silos,” ACI JOURNAL, 5

Proceedings V. 67, No. 7, July, pp. 539-547. 6

Safarian, S. S., and Harris, E. C., 1974, “Silos and Bunkers,” Handbook of Concrete 7

Engineering, Chapter 17, M. Fintel, ed., NY, pp. 491-535. 8

Safarian, S. S., and Harris, E. C., 1984, “Design and Construction of Silos and Bunkers,” 9

Van Nostrand Reinhold, ed., NY. 10

Safarian, S. S., and Harris, E. C., 1985a, “Loads for Design of Stacking Tubes for Granular 11

Materials,” International Journal of Storing and Handling Bulk Materials, Trans Tech 12

Publications, Clausthal-Zellerfeld, West Germany, V. 5, No. 2, Apr. 13

Safarian, S. S., and Harris, E. C., 1985b, “Design of Stacking Tubes for Granular Materials,” 14

International Journal of Storing and Handling Bulk Materials, Trans Tech Publications, 15

Clausthal-Zellerfeld, West Germany, V. 5, No. 4, Aug. 16

Safarian, S. S., and Harris, E. C., 1995, “Design of Partially Post-Tensioned Circular 17

Concrete Silo Walls,” Concrete International, Apr., pp. 43-47. 18

Stalnaker, J. J., and Harris, E. C., 1992, “Bending Moment in Silo Walls Due to Structural 19

Continuity,” ACI Structural Journal, V. 89, No. 2, Mar.-Apr., pp. 159-163. 20

Standards Association of Australia, 1989, “Loads on Bulk Solids Containers,” Standards 21

Australia, ed., Sydney, Oct. 22

Theimer, O. F., 1969, “Ablauf fordernde Trichterkonstruktionen von Silozellen,” 23

Augbereitungs-Technik, No. 10, pp. 547-556. 24

113


Timoshenko, S., and Woinowsky-Krieger, S., 1959, Theory of Plates and Shells, McGraw-1

Hill Book Co., Second ed., NY, 580 pp. 2

Turitzin, A. M., “Dynamic Pressure of Granular Material in Deep Bins,” Proceedings, 3

ASCE, V. 89, ST2, April 1963, pp. 49-73. 4

Walker, D. M., 1966, “Approximate Theory for Pressure and Arching in Hoppers,” Chemical 5

Engineering Science, V. 21, pp. 975-997. 6

Wu, T. H., 1975, “Retaining Walls,” Foundation Engineering Handbook, H. Winterkorn, and 7

F. Hsai-Yang, eds., Van Nostrand Reinhold, New York, pp. 402-417. 8

Zia, P.; Preston, H. K.; Scott, N. L.; and Workman, E. B., 1979, “Estimating Prestress 9

Losses,” Concrete International: Design and Construction, V. 1, No. 6, June, pp. 32-38. 10

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