##### Document Text Contents

Page 1

Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

1

Design of Circular Concrete Tanks

1. Introduction

Conventionally reinforced (non-prestressed) circular concrete tanks have been used

extensively in municipal and industrial facilities for several decades.

The design of these structures requires that attention be given not only to strength

requirements, but to serviceability requirements as well. A properly designed tank must be

able to withstand the applied loads without cracks that would permit leakage. The goal of

providing a structurally sound tank that will not leak is achieved by providing the proper

amount and distribution of reinforcement, the proper spacing and detailing of construction

joints, and the use of quality concrete placed using proper construction practices.

A thorough review of the latest report by ACI Committee 350 entitled Environmental

Engineering Concrete Structures1

is essential in understanding the design of tanks. The latest

edition (1983) of that document recommends that, unless noted otherwise, the structural

design should conform to Building Code Requirements for Reinforced Concrete (ACI 318-89).

2. Loading Conditions

A tank must be designed to withstand the loads that it will be subjected to during many years

of use. But it is equally important to consider loads during construction. An example of some

of the loading conditions that must be considered for a partially buried tank is shown in Fig. 1.

The tank must be designed and detailed to withstand the forces from each of these loading

conditions. The tank may also be subjected to uplift forces from hydrostatic pressure on the

bottom of the slab when the tank is empty. Therefore, it is important for the design engineer to

determine all possible loading conditions on the structure. According to ACI 350, the full

effects of the soil loads and water pressure must be designed for without the benefit of

resistance of the loads which could minimize the effects of each other.

Page 2

Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

2

3. Design Methods

Two approaches currently exist for the design of reinforced concrete members:

1) Strength Design

2) Allowable Stress Design (referred in ACI Code as the Alternate Design method).

The Strength Design method became the commonly adopted procedure for conventional

buildings after the 1963 revision to the ACI Building Code, and constitutes the basic

procedure of design in the present ACI Building Code (ACI 318-89) with the Alternate

Design method in an appendix (Appendix A).

Until recently, the use of strength design for municipal and other facilities was

considered inappropriate due to the lack of reliable assessment of crack widths at

service loads. The advances in this area of knowledge in the last two decades has led to

the acceptance of the strength design method for municipal liquid retaining structures in

general and circular concrete tanks in particular.

The latest ACI Committee 350 report recommends procedures for the use of both

Allowable Stress Design, and Strength Design for liquid retaining structures.

The new recommendations by Committee 350 for strength design essentially suggest

inflated load factors to control service load crack widths to fall in the range of (0.1 mm.

to 0.2 mm).

The following. discussion describes the alterations in the design methods of ACI 318 provided

by ACI 350.

Strength Design Method The load combinations to determine the required strength, U, are

given in Section 9.2 in ACI318. The ACI 350 requires the following two modifications to that

section.

Modification 1 The load factor to be used for lateral liquid pressure, F, is taken as 1.7

rather than the value of 1.4 specified in ACI 318. This value of 1.7 may be over

conservative for some tanks, since they are filled to the top only during leak testing or

because of accidental overflow. Since leak testing usually occurs only once and since most

tanks are equipped with overflow pipes, some designers have considered using the load

factor of 1.4 in an attempt to reduce the amount of required steel which results in less

shrinkage restraint.

Modification 2 ACI 350 requires that the value of U be increased by using a multiplier

called the sanitary coefficient. The sanitary coefficient will increase the design loads to

provide a more conservative design with less cracking. The increased required strength is

given by:

Required strength = Sanitary coefficient x U

where the sanitary coefficient equals:

1.3 for flexure

1.65 for direct tension

1.3 for shear beyond that of the capacity provided by the Concrete.

Working Stress Design

ACI 350 implies in its document that the maximum allowable stress for Grade 60 (4200

Kg/cm2) reinforcing steel is 2100 Kg/cm2 (0.5fy). This is considerably larger than the

(1680 Kg/cm2

ACI 350 recommends the allowable stress in hoop tension for Grade 60 (4200 Kg/cm

) allowed in Appendix A of ACI 318-89.

2)

reinforcing steel as is 1400 Kg/cm2 (fy/3).

Page 3

Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

3

4. Modification according to ACI 350-06

Load Combinations

Required strength U shall be at least equal to the effects of factored loads in the following

equations. The effect of one or more loads not acting simultaneously shall be investigated.

1.4( )

1.2( ) 1.6( ) 0.5( )

1.2 1.6( ) (1.0 0.8 )

1.2 1.6 1.0 0.5( )

1.2 1.2 1.0 1.6 1.0 0.2

U D F

U D F T L H Lr o rS o rR

U D Lr or S or R L or W

U D W L Lr o rS o rR

U D F E H L S

U

= +

= + + + + +

= + +

= + + +

= + + + + +

= 0.9 1.2 1.6 1.6

0.9 1.2 1.0 1.6

D F W H

U D F E H

+ + +

= + + +

Required strength U for other than compression controlled sections, shall be multiplied by

the following environmental durability factor (Sd

𝑆𝑆𝑑𝑑 =

∅𝑓𝑓𝑦𝑦

𝛾𝛾𝑓𝑓𝑠𝑠

≥ 1.0

). In the case of shear design, this factor is

applied to the excess shear strength carried by shear reinforcement only.

where

𝛾𝛾 =

factored load

unfactored load

fs is the permissible tensile stress in reinforcement

For tension-controlled sections and shear strength contributed by reinforcement, in

calculation of the Sd the effects of code-prescribed load factors and φ factors can be

eliminates and applies an effective load factor equal to fy/fs

with φ factors set to 1.0.

𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑑𝑑 𝑆𝑆𝑆𝑆𝑅𝑅𝑅𝑅𝑆𝑆𝑆𝑆𝑆𝑆ℎ ≥

𝑓𝑓𝑦𝑦

𝑓𝑓𝑠𝑠

𝑆𝑆𝑅𝑅𝑅𝑅𝑆𝑆𝑅𝑅𝑆𝑆𝑅𝑅 𝐿𝐿𝐿𝐿𝐿𝐿𝑑𝑑

Permissible Stresses

Direct and hoop tensile stress in normal environmental exposures fs = 20 ksi (138 Mpa)

Direct and hoop tensile stress in severe environmental exposures fs = 17 ksi (117 Mpa)

Shear stress carried by shear reinforcement in normal environmental exposures

fs = 24 ksi (165 Mpa)

Shear stress carried by shear reinforcement in severe environmental exposures

fs = 20 ksi (138 Mpa)

Strength reduction factor φ shall be as follows:

Tension-controlled sections φ=0.90

Compression-controlled sections,

o Members with spiral reinforcement φ=0.70

o Other reinforced members φ=0.65

Shear and torsion φ=0.75

Bearing on concrete φ=0.65

Page 4

Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

4

5. Wall Thickness

Typically, in the design of reinforced concrete members, the tensile strength of concrete is

ignored. Any significant cracking in a liquid containing tank is unacceptable. For this reason,

it must be assured that the stress in the concrete from ring tension is kept at minimum to

prevent excessive cracking. Neither ACI 350 or ACI 318 provide guidelines for the tension

carrying capacity for this condition. The allowable tensile strength of concrete is usually

between 7% an 12% of the compressive strength. A value of 10% c the concrete strength will

be used here.

According to ACI 350, reinforced concrete walls 3 meter high or taller, which are in contact

with liquid, shall have a minimum thickness of 30 cm.

Shrinkage Effect

As concrete dries and loses moisture, it contracts in size. This contraction (drying shrinkage),

if constrained, will produce tensile stresses that may exceed the capacity of the concrete and

cause cracking.

Figure 2(a) illustrates a block of concrete with a bar as shown, but otherwise unrestrained.

The height of the block is chosen as one unit 1m, since tension in a circular ring of a tank wall

is computed for that height.

If the bar is left out as in Fig. 2(b) (which is obviously out of scale), shrinkage will shorten the

1-unit long block a distance of εsh, which denotes the shrinkage per unit length. The presence

of the steel bar prevents some of the shortening of the concrete εs < ε

The steel shortens a distance ε

sh

s and accordingly is subject to compressive stress fs, while

concrete will elongate a distance (εsh - εs ) and will subject to tensile stress fct

.

εsh = εs + ε

ε

c

s = εsh - ε

s

sh

s c

f f

=

E E

ctε −

c

s shf = fs ctε E n−

Considering equilibrium, the total tension in the concrete must equal the total compression in

the steel

s sA f = fc ctA

( )s sh sA f = fs ct c ctε E n A−

1m

εsh

εc

1m

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Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

5

sh

s

f =

+nA

s s

ct

c

ε E A

A

s

T

f =

+nAct cA

sh

s

T+

f =

+nA

s s

ct

c

ε E A

A

For a rectangular section of 100 cm height and with t width, then Ac= 100 t and As= T/f

s

shT+ f

f =

100 +n

f

s

s

ct

s

T

ε E

T

t

sh f f=

100f f

s s ct

s ct

ε E n

t T

+ −

This formula may be used to estimate the wall thickness. The value of εsh ,coefficient of

shrinkage for reinforced concrete, is in the range of 0.0002 to 0.0004. The value of εsh for

plain concrete ranges from 0.0003 to 0.0008. The shrinkage coefficient for plain concrete was

used to derive Equation 2 which would require a value of εsh

between 0.0003 and 0.0008.

However, this equation has traditionally used the value of 0.0003, the average value for

reinforced concrete, with success.

Example

For f c= 300 kg/cm2 and fy = 4200 kg/cm2, Es=2.04*106

f

kg/cm2 evaluate the wall thickness t

necessary to prevent cracks resulting from shrinkage plus tensile forces.

ct = 0.1(300) = 30 kg/cm

fs= 4200/3 = 1400 kg/cm

2

215100 300 261540 /cE kg cm= =

2

, n= 8

( )6sh 0.003(2.04*10 ) 1400 8 30f f= 0.00042

100f f 100*1400*30

s s ct

s ct

ε E n

t T T T

+ −+ −

= =

Where T is in kg

t= 0.42 T

where T is in tons.

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Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

6

6. Reinforcement

1. The amount, size, and spacing of reinforcing bars has a great effect on the extent of

cracking.

2. The amount of reinforcement provided must be sufficient for strength and

serviceability including temperature and shrinkage effects.

3. The designer should provide proper details to ensure that cracking will occur at joints

and that joints are properly leak proofed.

4. The size of reinforcing bars should be chosen recognizing that cracking can be better

controlled by using a larger number of small diameter bars rather than fewer larger

diameter bars.

5. Spacing of reinforcing bars should be limited to a maximum of 30 cm.

6. Minimum concrete cover for reinforcement in the tank wall should be at least 5cm.

7. The wall thickness should be sufficient to keep the concrete from cracking. If the

concrete does crack, the ring steel must be able to carry all the ring tension alone.

0.9uS

y

T

A

f

φ

φ

= =

8. It is desirable to use a higher allowable steel stress so that less steel is used, resulting

in less restraint shrinkage and smaller tensile stresses in the concrete.

9. The required length of the splice is a function of many factors. The length depends on

the class of splice required, the clear cover, the clear distance between adjacent bars,

and the size of the bar. Other factors affecting splice length include: the type of

concrete used (lightweight or normal weight), bar coating, if used, and the amount of

fresh concrete cast below the bar.

10. In circular tanks, the location of horizontal splices should be staggered. Splices should

be staggered horizontally by not less than one lap length or 90 cm and should not

coincide in vertical arrays more frequently than every third bar.

Page 7

Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

7

7. Crack Control

Crack widths must be minimized in tank walls to prevent leakage and corrosion of

reinforcement.

ACI 318- 89

A criterion for flexural crack width is provided in ACI 3 18-

89 (10.6.4).

s cz f d A=

where,

z = quantity limiting distribution of flexural reinforcement.

fs= calculated stress in reinforcement at service loads, ksi.

dc= thickness of concrete cover measured from extreme tension fiber to center of bar

located closest thereto, in.

A = effective tension area of concrete surrounding the flexural tension reinforcement

having the same centroid as that reinforcement, divided by the number of bars, sq in.

ACI 3 18-89 does not allow z to exceed 175 kips/in. for interior exposure and 145 kips/in. for

exterior exposure. These values of z correspond to crack widths of 0.016 in. and 0.013 in.,

respectively. ACI 350 has stricter requirements. The limiting value of z specified in ACI 350

is 115 kips/in. For severe environmental exposures, the quantity z should not exceed 95

kips/in..

ACI 318- 02

A more practical method which limit the maximum reinforcement spacing after Cod 95

The Maximum Spacing S of reinforcement closest to the surface in tension

9500

2.5

7560

c

s

s

C

f

S

f

−

≤

Where

Cc

0.6s yf f≅

is the clear cover from the nearest surface of concrete in tension zone to surface of flexural

reinforcement.

Joints in the circular tank walls will allow dissipation of temperature and shrinkage.

Maximum length of wall placed at one time will usually not exceed 60 ft (18m), with

30 ft (10m) to 50ft (15m) being more common. Note that water stops should be used in

all joints to prevent the possibility of leakage. The cracking from temperature and

shrinkage will be a function of the base restraint. A sliding wall has no base fixity and

this will have less restraint than tanks with fixed bases. Tanks with fixed bases tend to

develop shrinkage cracks just above the slab

Page 8

Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

8

8. Types of Wall Joints

The structural behavior of circular cylindrical tank walls, subject to the action of hydrostatic

pressure varies according to the type of joint between wall and other elements (base and roof

if any). There are three main types of joints free (or sliding), fixed and hinged Any case in

practice can be analyzed by combination of these cases.

1- Free Joint (Sliding joint)

No restraint for motion of wall due to liquid rressure

For this type of joint the elastic line of the wall is a straight line and the wall resists the liquid

pressure by ring action.( i.e. by horizontal strips only ). with respect to base, no indeterminate

stresses are created. To ensure water tightness in- the joint a copper plate may be placed to

join the wall and floor.

2- Fixed Joint (Continuous joint)

In this case, no allowance for motion or rotation is allowed for wall base (or top). Wall will

carry liquid pressure partly by ring and partly by cantilever action (combined resistance by

both vertical and horizontal strips). There is a connecting moment between wall and base. To

obtain the required fixation, vertical reinforcement extends across the joint as shown. Good.

bond qualities are obtained. by the following procedure:

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Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

9

After the concrete is placed and has stiffened sufficiently but is not thoroughly hardened.

(about 6 hours) clean the joint surface with a pressure water jet. Then cover the joint and keep

it continuously wet. Before new concrete is placed, flush the old surface with 1:2 Portland

cement mortar. Vibrate the new concrete and. keep it moist for several days.

2- Hinged Joint

It may sometimes be desirable to avoid transmitting moment between Wall and base; in such

cases we used a hinged joint which allows for rotation as shown in a) and b)

A wall rigidly connected to the base may however be considered hinged if the soil underneath

is liable to rotate as shown in-case C.

In deep circular tanks, with the wall rigidly connected to the floor, the liquid pressure will be

mainly resisted by ring action. Due to the fixation of the wall to the floor, the horizontal

displacement of the wall at its foot cannot be fully developed and the pressure resisted by ring

action will decrease to zero at the point of fixation.

The small part of the liquid pressure at the foot of the wall that has not been resisted in the

horizontal direction by ring action will be resisted in the vertical direction by cantilever action

creating bending moments in the wall. In this case, the maximum ring tension T takes place

at 0.8 to 0.9 H and is given TRmaxR = 0.80 to 0.90 w HR

Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

1

Design of Circular Concrete Tanks

1. Introduction

Conventionally reinforced (non-prestressed) circular concrete tanks have been used

extensively in municipal and industrial facilities for several decades.

The design of these structures requires that attention be given not only to strength

requirements, but to serviceability requirements as well. A properly designed tank must be

able to withstand the applied loads without cracks that would permit leakage. The goal of

providing a structurally sound tank that will not leak is achieved by providing the proper

amount and distribution of reinforcement, the proper spacing and detailing of construction

joints, and the use of quality concrete placed using proper construction practices.

A thorough review of the latest report by ACI Committee 350 entitled Environmental

Engineering Concrete Structures1

is essential in understanding the design of tanks. The latest

edition (1983) of that document recommends that, unless noted otherwise, the structural

design should conform to Building Code Requirements for Reinforced Concrete (ACI 318-89).

2. Loading Conditions

A tank must be designed to withstand the loads that it will be subjected to during many years

of use. But it is equally important to consider loads during construction. An example of some

of the loading conditions that must be considered for a partially buried tank is shown in Fig. 1.

The tank must be designed and detailed to withstand the forces from each of these loading

conditions. The tank may also be subjected to uplift forces from hydrostatic pressure on the

bottom of the slab when the tank is empty. Therefore, it is important for the design engineer to

determine all possible loading conditions on the structure. According to ACI 350, the full

effects of the soil loads and water pressure must be designed for without the benefit of

resistance of the loads which could minimize the effects of each other.

Page 2

Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

2

3. Design Methods

Two approaches currently exist for the design of reinforced concrete members:

1) Strength Design

2) Allowable Stress Design (referred in ACI Code as the Alternate Design method).

The Strength Design method became the commonly adopted procedure for conventional

buildings after the 1963 revision to the ACI Building Code, and constitutes the basic

procedure of design in the present ACI Building Code (ACI 318-89) with the Alternate

Design method in an appendix (Appendix A).

Until recently, the use of strength design for municipal and other facilities was

considered inappropriate due to the lack of reliable assessment of crack widths at

service loads. The advances in this area of knowledge in the last two decades has led to

the acceptance of the strength design method for municipal liquid retaining structures in

general and circular concrete tanks in particular.

The latest ACI Committee 350 report recommends procedures for the use of both

Allowable Stress Design, and Strength Design for liquid retaining structures.

The new recommendations by Committee 350 for strength design essentially suggest

inflated load factors to control service load crack widths to fall in the range of (0.1 mm.

to 0.2 mm).

The following. discussion describes the alterations in the design methods of ACI 318 provided

by ACI 350.

Strength Design Method The load combinations to determine the required strength, U, are

given in Section 9.2 in ACI318. The ACI 350 requires the following two modifications to that

section.

Modification 1 The load factor to be used for lateral liquid pressure, F, is taken as 1.7

rather than the value of 1.4 specified in ACI 318. This value of 1.7 may be over

conservative for some tanks, since they are filled to the top only during leak testing or

because of accidental overflow. Since leak testing usually occurs only once and since most

tanks are equipped with overflow pipes, some designers have considered using the load

factor of 1.4 in an attempt to reduce the amount of required steel which results in less

shrinkage restraint.

Modification 2 ACI 350 requires that the value of U be increased by using a multiplier

called the sanitary coefficient. The sanitary coefficient will increase the design loads to

provide a more conservative design with less cracking. The increased required strength is

given by:

Required strength = Sanitary coefficient x U

where the sanitary coefficient equals:

1.3 for flexure

1.65 for direct tension

1.3 for shear beyond that of the capacity provided by the Concrete.

Working Stress Design

ACI 350 implies in its document that the maximum allowable stress for Grade 60 (4200

Kg/cm2) reinforcing steel is 2100 Kg/cm2 (0.5fy). This is considerably larger than the

(1680 Kg/cm2

ACI 350 recommends the allowable stress in hoop tension for Grade 60 (4200 Kg/cm

) allowed in Appendix A of ACI 318-89.

2)

reinforcing steel as is 1400 Kg/cm2 (fy/3).

Page 3

Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

3

4. Modification according to ACI 350-06

Load Combinations

Required strength U shall be at least equal to the effects of factored loads in the following

equations. The effect of one or more loads not acting simultaneously shall be investigated.

1.4( )

1.2( ) 1.6( ) 0.5( )

1.2 1.6( ) (1.0 0.8 )

1.2 1.6 1.0 0.5( )

1.2 1.2 1.0 1.6 1.0 0.2

U D F

U D F T L H Lr o rS o rR

U D Lr or S or R L or W

U D W L Lr o rS o rR

U D F E H L S

U

= +

= + + + + +

= + +

= + + +

= + + + + +

= 0.9 1.2 1.6 1.6

0.9 1.2 1.0 1.6

D F W H

U D F E H

+ + +

= + + +

Required strength U for other than compression controlled sections, shall be multiplied by

the following environmental durability factor (Sd

𝑆𝑆𝑑𝑑 =

∅𝑓𝑓𝑦𝑦

𝛾𝛾𝑓𝑓𝑠𝑠

≥ 1.0

). In the case of shear design, this factor is

applied to the excess shear strength carried by shear reinforcement only.

where

𝛾𝛾 =

factored load

unfactored load

fs is the permissible tensile stress in reinforcement

For tension-controlled sections and shear strength contributed by reinforcement, in

calculation of the Sd the effects of code-prescribed load factors and φ factors can be

eliminates and applies an effective load factor equal to fy/fs

with φ factors set to 1.0.

𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑑𝑑 𝑆𝑆𝑆𝑆𝑅𝑅𝑅𝑅𝑆𝑆𝑆𝑆𝑆𝑆ℎ ≥

𝑓𝑓𝑦𝑦

𝑓𝑓𝑠𝑠

𝑆𝑆𝑅𝑅𝑅𝑅𝑆𝑆𝑅𝑅𝑆𝑆𝑅𝑅 𝐿𝐿𝐿𝐿𝐿𝐿𝑑𝑑

Permissible Stresses

Direct and hoop tensile stress in normal environmental exposures fs = 20 ksi (138 Mpa)

Direct and hoop tensile stress in severe environmental exposures fs = 17 ksi (117 Mpa)

Shear stress carried by shear reinforcement in normal environmental exposures

fs = 24 ksi (165 Mpa)

Shear stress carried by shear reinforcement in severe environmental exposures

fs = 20 ksi (138 Mpa)

Strength reduction factor φ shall be as follows:

Tension-controlled sections φ=0.90

Compression-controlled sections,

o Members with spiral reinforcement φ=0.70

o Other reinforced members φ=0.65

Shear and torsion φ=0.75

Bearing on concrete φ=0.65

Page 4

Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

4

5. Wall Thickness

Typically, in the design of reinforced concrete members, the tensile strength of concrete is

ignored. Any significant cracking in a liquid containing tank is unacceptable. For this reason,

it must be assured that the stress in the concrete from ring tension is kept at minimum to

prevent excessive cracking. Neither ACI 350 or ACI 318 provide guidelines for the tension

carrying capacity for this condition. The allowable tensile strength of concrete is usually

between 7% an 12% of the compressive strength. A value of 10% c the concrete strength will

be used here.

According to ACI 350, reinforced concrete walls 3 meter high or taller, which are in contact

with liquid, shall have a minimum thickness of 30 cm.

Shrinkage Effect

As concrete dries and loses moisture, it contracts in size. This contraction (drying shrinkage),

if constrained, will produce tensile stresses that may exceed the capacity of the concrete and

cause cracking.

Figure 2(a) illustrates a block of concrete with a bar as shown, but otherwise unrestrained.

The height of the block is chosen as one unit 1m, since tension in a circular ring of a tank wall

is computed for that height.

If the bar is left out as in Fig. 2(b) (which is obviously out of scale), shrinkage will shorten the

1-unit long block a distance of εsh, which denotes the shrinkage per unit length. The presence

of the steel bar prevents some of the shortening of the concrete εs < ε

The steel shortens a distance ε

sh

s and accordingly is subject to compressive stress fs, while

concrete will elongate a distance (εsh - εs ) and will subject to tensile stress fct

.

εsh = εs + ε

ε

c

s = εsh - ε

s

sh

s c

f f

=

E E

ctε −

c

s shf = fs ctε E n−

Considering equilibrium, the total tension in the concrete must equal the total compression in

the steel

s sA f = fc ctA

( )s sh sA f = fs ct c ctε E n A−

1m

εsh

εc

1m

Page 5

Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

5

sh

s

f =

+nA

s s

ct

c

ε E A

A

s

T

f =

+nAct cA

sh

s

T+

f =

+nA

s s

ct

c

ε E A

A

For a rectangular section of 100 cm height and with t width, then Ac= 100 t and As= T/f

s

shT+ f

f =

100 +n

f

s

s

ct

s

T

ε E

T

t

sh f f=

100f f

s s ct

s ct

ε E n

t T

+ −

This formula may be used to estimate the wall thickness. The value of εsh ,coefficient of

shrinkage for reinforced concrete, is in the range of 0.0002 to 0.0004. The value of εsh for

plain concrete ranges from 0.0003 to 0.0008. The shrinkage coefficient for plain concrete was

used to derive Equation 2 which would require a value of εsh

between 0.0003 and 0.0008.

However, this equation has traditionally used the value of 0.0003, the average value for

reinforced concrete, with success.

Example

For f c= 300 kg/cm2 and fy = 4200 kg/cm2, Es=2.04*106

f

kg/cm2 evaluate the wall thickness t

necessary to prevent cracks resulting from shrinkage plus tensile forces.

ct = 0.1(300) = 30 kg/cm

fs= 4200/3 = 1400 kg/cm

2

215100 300 261540 /cE kg cm= =

2

, n= 8

( )6sh 0.003(2.04*10 ) 1400 8 30f f= 0.00042

100f f 100*1400*30

s s ct

s ct

ε E n

t T T T

+ −+ −

= =

Where T is in kg

t= 0.42 T

where T is in tons.

Page 6

Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

6

6. Reinforcement

1. The amount, size, and spacing of reinforcing bars has a great effect on the extent of

cracking.

2. The amount of reinforcement provided must be sufficient for strength and

serviceability including temperature and shrinkage effects.

3. The designer should provide proper details to ensure that cracking will occur at joints

and that joints are properly leak proofed.

4. The size of reinforcing bars should be chosen recognizing that cracking can be better

controlled by using a larger number of small diameter bars rather than fewer larger

diameter bars.

5. Spacing of reinforcing bars should be limited to a maximum of 30 cm.

6. Minimum concrete cover for reinforcement in the tank wall should be at least 5cm.

7. The wall thickness should be sufficient to keep the concrete from cracking. If the

concrete does crack, the ring steel must be able to carry all the ring tension alone.

0.9uS

y

T

A

f

φ

φ

= =

8. It is desirable to use a higher allowable steel stress so that less steel is used, resulting

in less restraint shrinkage and smaller tensile stresses in the concrete.

9. The required length of the splice is a function of many factors. The length depends on

the class of splice required, the clear cover, the clear distance between adjacent bars,

and the size of the bar. Other factors affecting splice length include: the type of

concrete used (lightweight or normal weight), bar coating, if used, and the amount of

fresh concrete cast below the bar.

10. In circular tanks, the location of horizontal splices should be staggered. Splices should

be staggered horizontally by not less than one lap length or 90 cm and should not

coincide in vertical arrays more frequently than every third bar.

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Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

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7. Crack Control

Crack widths must be minimized in tank walls to prevent leakage and corrosion of

reinforcement.

ACI 318- 89

A criterion for flexural crack width is provided in ACI 3 18-

89 (10.6.4).

s cz f d A=

where,

z = quantity limiting distribution of flexural reinforcement.

fs= calculated stress in reinforcement at service loads, ksi.

dc= thickness of concrete cover measured from extreme tension fiber to center of bar

located closest thereto, in.

A = effective tension area of concrete surrounding the flexural tension reinforcement

having the same centroid as that reinforcement, divided by the number of bars, sq in.

ACI 3 18-89 does not allow z to exceed 175 kips/in. for interior exposure and 145 kips/in. for

exterior exposure. These values of z correspond to crack widths of 0.016 in. and 0.013 in.,

respectively. ACI 350 has stricter requirements. The limiting value of z specified in ACI 350

is 115 kips/in. For severe environmental exposures, the quantity z should not exceed 95

kips/in..

ACI 318- 02

A more practical method which limit the maximum reinforcement spacing after Cod 95

The Maximum Spacing S of reinforcement closest to the surface in tension

9500

2.5

7560

c

s

s

C

f

S

f

−

≤

Where

Cc

0.6s yf f≅

is the clear cover from the nearest surface of concrete in tension zone to surface of flexural

reinforcement.

Joints in the circular tank walls will allow dissipation of temperature and shrinkage.

Maximum length of wall placed at one time will usually not exceed 60 ft (18m), with

30 ft (10m) to 50ft (15m) being more common. Note that water stops should be used in

all joints to prevent the possibility of leakage. The cracking from temperature and

shrinkage will be a function of the base restraint. A sliding wall has no base fixity and

this will have less restraint than tanks with fixed bases. Tanks with fixed bases tend to

develop shrinkage cracks just above the slab

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8. Types of Wall Joints

The structural behavior of circular cylindrical tank walls, subject to the action of hydrostatic

pressure varies according to the type of joint between wall and other elements (base and roof

if any). There are three main types of joints free (or sliding), fixed and hinged Any case in

practice can be analyzed by combination of these cases.

1- Free Joint (Sliding joint)

No restraint for motion of wall due to liquid rressure

For this type of joint the elastic line of the wall is a straight line and the wall resists the liquid

pressure by ring action.( i.e. by horizontal strips only ). with respect to base, no indeterminate

stresses are created. To ensure water tightness in- the joint a copper plate may be placed to

join the wall and floor.

2- Fixed Joint (Continuous joint)

In this case, no allowance for motion or rotation is allowed for wall base (or top). Wall will

carry liquid pressure partly by ring and partly by cantilever action (combined resistance by

both vertical and horizontal strips). There is a connecting moment between wall and base. To

obtain the required fixation, vertical reinforcement extends across the joint as shown. Good.

bond qualities are obtained. by the following procedure:

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Dr. Mohammed Arafa Design of Special Concrete Structures ENGC 6330

9

After the concrete is placed and has stiffened sufficiently but is not thoroughly hardened.

(about 6 hours) clean the joint surface with a pressure water jet. Then cover the joint and keep

it continuously wet. Before new concrete is placed, flush the old surface with 1:2 Portland

cement mortar. Vibrate the new concrete and. keep it moist for several days.

2- Hinged Joint

It may sometimes be desirable to avoid transmitting moment between Wall and base; in such

cases we used a hinged joint which allows for rotation as shown in a) and b)

A wall rigidly connected to the base may however be considered hinged if the soil underneath

is liable to rotate as shown in-case C.

In deep circular tanks, with the wall rigidly connected to the floor, the liquid pressure will be

mainly resisted by ring action. Due to the fixation of the wall to the floor, the horizontal

displacement of the wall at its foot cannot be fully developed and the pressure resisted by ring

action will decrease to zero at the point of fixation.

The small part of the liquid pressure at the foot of the wall that has not been resisted in the

horizontal direction by ring action will be resisted in the vertical direction by cantilever action

creating bending moments in the wall. In this case, the maximum ring tension T takes place

at 0.8 to 0.9 H and is given TRmaxR = 0.80 to 0.90 w HR