1

STRUCTURAL ANALYSIS AND DESIGN OF A REINFORCED CONCRETE CYLINDRICAL TANK

Miguel Meneses miguel.meneses@ist.utl.pt

M.Sc. Thesis in Civil Engineering – Extended Abstract

October 2013

ABSTRACT

This work presents as its main objective the analysis and structural design of a reinforced concrete cylindrical

tank, originally conceived in the middle of the last century. The most relevant aspects in light of the structural

Eurocodes are covered, which include specific regulations that apply to reservoirs.

The main durability requirements in order to ensure proper operation of these constructions over their lifetime

are addressed. It is described how to quantify indirect actions, through a temporal evaluation of the joint effect

of concrete shrinkage and creep, by applying the effective modulus method.

The structural behavior of cylindrical shells in presence of static forces is analyzed in detail, and simplified

calculation methods are introduced. Using the finite element method, it is further assessed the influence of the

deformability of the soil on the stresses generated in the structure.

It is performed a seismic analysis of the tank, in which the distribution of the hydrodynamic pressure on the walls

are found, and different forms for combining the pressure components are examined. In addition, based on the

finite element method, a modal analysis of the structure is carried out and the seismic stresses are attained.

The structure is designed based on the provisions included in the relevant Eurocodes, wherein the criteria for

limiting crack width in tanks stand out. A reinforcement solution for the original structure’s geometry is found

considering a rigid homogeneous foundation soil.

Lastly, a non-linear analysis was conducted on a generic frame corner with different reinforcement detailing, in

order to assess its efficiency in terms of ductility and resistance. Further in, the same type of analysis is applied

to the node joining the wall and the slab bottom of the tank.

Keywords: Cylindrical tanks, Reinforced concrete, Structural analysis, Structural design, Seismic analysis, Non-

linear analysis

1. INTRODUCTION

Reservoirs are liquid, gas or solid retaining

structures that may be conceived in a wide range of

structural solutions, since there are several types of

different applications that possess different

requirements, which can be in terms of contained

substance aggressiveness, operational conditions,

size, or site conditions.

In Portugal, it has been common practice to use

reinforced or prestressed concrete in liquid

retaining structures (tanks), namely in water supply

systems and waste-water treatment plants, due to

its lower cost. Reinforced concrete can provide long

life with low maintenance costs, but only if

appropriately designed and constructed. However,

steel structures have advantage when there is a

need for complete tightness.

This work’s main objective is to cover the most

relevant matters of analysis and design for ground

reinforced concrete cylindrical tanks, by studying a

2

tank originally conceived by Santarella [1] (Figure 1),

in light of the new regulations (Eurocodes).

This tank has a full capacity of 1113 m3, by

possessing a 8,2 m radius, and a maximum depth of

5,4 m. The ground slab, walls and dome have,

respectively, 0,1 m, 0,2 m and 0,08 m thickness. The

retained liquid is mineral oil (γ = 9,5 kN/m3).

FIGURE 1 – TANK STUDIED

2. DURABILITY

Traditionally, concrete’s performance is based

exclusively on its compressive strength, which

defines the design of the structure in ultimate limit

state. However, in the last decades, there has been

a growing concern towards the problems RC

structures tend to show during their lifetime.

The ability of concrete to satisfy not only the safety

criteria but functionality and aesthetics as well is

dependent on other parameters, related with its

composition and production, and also with the

execution of the construction in site and the

maintenance and inspection procedures that need

to be carried on.

This topic is even more important in RC tanks,

because this structures experience, during most of

their live span, high permanent loads, and are in

contact with the retained liquid that often induce

corrosion problems to concrete and reinforcement

that need to be evaluated. In case they’re buried,

large areas of the construction are in permanent

contact with potentially aggressive soils. Also,

because of tightness requirements, high demands

for crack control and impermeability take place.

In order to define the durability requirements, it is

first necessary to identify the aggressive substances

and its transportation mechanisms, and the

reactions involved in deterioration.

The Portuguese norm Esp. LNEC E 464 [2] classifies

environmental actions into six categories (Table 1),

based on type and severity of exposure that the

construction will experience.

TABLE 1 - EXPOSURE CLASSES

Description Designation

No risk of corrosion or attack X0

Corrosion induced by

carbonation

XC1 / XC2 / XC3 /

XC4

Corrosion induced by chlorides XD1 / XD2 / XD3

Corrosion induced by chlorides

from sea water XS1 / XS2 / XS3

Freeze/Thaw attack XF1 / XF2

Chemical attack XA1 / XA2 / XA3

Based on this information, the same norm defines

the protective measures that need to be taken,

which are centered on minimum concrete cover

over reinforcement and concrete mix. For tanks,

this requirements might be higher, due to the

impermeability needs. For example, British norm BS

8007 [3], that regulates design of RC tanks, states

that concrete should possess minimum cement

content of 325 kg/m3, maximum water/cement

ratio of 0,55, or 0,50 if pulverized-fuel ash is

present, and minimum characteristic cube strength

at 28 days not less than 35 MPa.

In the tank studied, the ground slab was classified

as exposure class XC2, while the remainder

elements were set at class XC4. Because of the

elevated slenderness of the slab and dome, they can

only afford one set of reinforcement. The nominal

reinforcement covers were established 3,5 cm at

the walls and dome, and 4 cm at the slab.

3. ACTIONS ON TANKS

Actions on tanks are identified in Eurocode 1-4 [4].

Besides the actions that are accounted in most

cases, there are some loads that apply specifically to

tanks, such as hydrostatic pressure, suction on

unloading due to inadequate ventilation, loads

resultant from filling process, thermal loads from

3

liquid, or accidental loads (due to overfilling, or

spills, for example).

Unlike other type of structures, tanks are very

sensitive to cracking and therefore it is essential to

correctly quantify actions that will be present in

service limits states. Thus, the definition of indirect

actions (imposed loads), such as temperature

variation and concrete shrinkage and creep, achieve

special relevance and are frequently determinant.

In tanks, the following situation should be

accounted when considering thermal loads [5]:

- Thermal actions from climatic effect due to the

variation of shade air temperature and solar

radiation;

- Temperature distribution for normal and

abnormal process conditions;

- Effects arising from interaction between the

structure and its contents during changes (e.g.

shrinkage of the structure against stiff solid

contents);

The total shrinkage strain is composed mainly by the

drying and autogenous components. The drying

shrinkage is a function of the migration of the water

through the hardened concrete and develops slowly

over a several year period and it relates more to

higher water/cement ratio concretes. On other

hand, the autogenous shrinkage develops in the

early days after casting.

FIGURE 2 – TEMPORAL EVOLUTION OF SHRINKAGE EXTENSION

It is clear that higher strength concrete, that possess

a higher cement mix, will develop lower shrinkage

extension. However, higher cement content has its

downside. Heat is evolved as cement hydrates, and

subsequent cooling can cause early cracking, which

can be controlled by appropriate measures.

Temporal evolution of shrinkage extension was

calculated for the tank and is presented in Figure 2.

Under constant stress, concrete gradually allows for

greater deformations, which can be measured as:

𝜀𝑐𝑐(𝑡∞, 𝑡0) = 𝜑(𝑡∞, 𝑡0) ∙ (𝜎𝑐/𝐸𝑐) (3.1)

Where 𝜑(𝑡∞, 𝑡0) is creep coefficient, that

represents the ratio between the deformation at

time 𝑡∞ and at time of loading 𝑡0.

Temporal evolution of creep coefficient was

calculated for the tank, for two different loading

times (Figure 3).

FIGURE 3 - TEMPORAL EVOLUTION OF CREEP COEFICIENT

Because of effect of ageing of concrete, namely

creep, in situations where a load is applied during

large periods of time, the elastic modulus can’t be

assumed as constant. For direct actions, this

consideration doesn’t change much, as the stresses

in structure counter directly the applied loads.

However, stresses caused by imposed loads (e.g.

shrinkage) are directly proportional to the

material’s stiffness.

The effects of creep and shrinkage can’t be

evaluated separately because they’re

interdependent: Shrinkage origins creep that

diminishes its effect over the structure.

For a more rigorous analysis on the evolution of

total deformation, the effective modulus method

can be used, based on the equation:

𝜀𝑐(𝑡, 𝑡0) =𝛥𝜎𝑐(𝑡, 𝑡0)

𝐸𝑐,𝑒𝑓𝑓 (𝑡, 𝑡0) (3.2)

𝐸𝑐,𝑒𝑓𝑓 (𝑡, 𝑡0) can be calculated by equation (3.3).

0,0E+00

5,0E-05

1,0E-04

1,5E-04

2,0E-04

2,5E-04

3,0E-04

3,5E-04

4,0E-04

0 500 1.000 1.500 2.000

ε (-)

t (days)Autogenous Drying Total

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

0 500 1.000 1.500

𝜙(t0,t)

t (days)t0 = 7 days t0 = 40 days

4

𝐸𝑐,𝑎𝑗𝑢𝑠𝑡 =𝐸𝑐

1 + 𝜒(𝑡, 𝑡0) ∙ 𝜙(𝑡, 𝑡0) (3.3)

𝜒(𝑡, 𝑡0) represents the ageing coeficient, and

assumes values less than one. This parameter

relates the deformation caused by a load that grows

concomitantly with creep, such as shrinkage, with

the deformation caused by a constant load. Its

precise value can be obtained in the work of Bazant

[6] but generally 0,8 is a good estimate.

Based on this method, the resulting stress from

shrinkage in the tank, for a fully restrained element,

was obtained (Figure 4). The maximum occurs at

around 3000 days, where σcs=3,2 MPa, εcs=0,36‰

and Ec,eff=8,89 GPa. Because all this values maintain

practically unchanged, the shrinkage can be

obtained at infinite time (it’s easier to calculate),

and the stresses can be calculated applying an

elastic modulus of Ec/3. This observations combine

with those of Camara & Figueiredo [7]. According to

the same authors, the uniform temperature

variation, that take place slowly during months’

time, can be calculated with Ec/2. This value was

also applied in uniform temp. variation to account

for same cracking due to its high value (Table 2).

TABLE 2 – INDIRECT LOADS APPLIED TO THE TANK

Load Value Ec,eff

Shrinkage - 30 °C 10 GPa

Uniform temp. variation ± 20 °C 15 GPa

Diferential temp. variation ± 15 °C 15 GPa

Admitting that the ground slab is cast first, only half

of the shrinkage load was applied in this element.

Both temperature variation loads were applied

solely on the top part of the structure, to account

the 3 m high embankment (Figure 1) sheltering

effect against solar radiation.

4. STRUCTURAL ANALYSIS

4.1. STRUCTURAL BEHAVIOR OF CYLINDRICAL TANKS

A cylindrical tank is an axisymmetric structure. If the

load is also axisymmetric, then the same stresses

will be generated along any meridian section of the

tank.

The lateral deformation resistance of the wall,

facing a hydrostatic load inside out, can be divided

into two components:

- Resistance provided by a set of infinitesimal

horizontal ring beams, that develop axial traction

forces (hoop forces) (Nϕ);

- Resistance provided by a set of infinitesimal

vertical cantilevered beams that develop shear

force and bending moment (M and V).

Logically, the cantilevered beams resistance

depends on the stiffness of the connection between

the wall and the ground slab. For a given height, the

larger the radius of the tank is, more stresses are

absorbed by the vertical cantilevers, because the

sections get increasingly more plane. On other

hand, the higher the tank gets, more stresses are

driven into the ring beams, since the deformed

shape of the cantilevers increase in height, in

opposition to the ring beams, offering lower

stiffness.

The last description represents the typical structure

behavior of a fixed tank wall: predominance of

horizontal axial forces in the middle and upper part

of the wall, and predominance of bending in the

lower part of the wall (Figure 5).

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

0

5

10

15

20

25

30

35

0 200 400 600 800 1.000 1.200 1.400 1.600 1.800 2.000

σcs

= E

c,ef

f (t)

x ε

ct (

t)

(MP

a)

Ec,e

ffj (

GP

a)

t (days)Adjusted elasticity modulus Resultant tension of restrained concrete shrinkage

FIGURE 4 – TEMPORAL EVOLUTION OF THE RESULTING TENSION DUE TO RESTRAINED SHRINKAGE

5

FIGURE 5 – TYPICAL FORCES CONFIGURATION IN A FIXED WALL

The configuration of the forces in the wall, in case

of rigid connection, can change drastically

depending on the behavior of the the ground slab.

Assuming the vertical hydrostatic pressure is

countered directly by the soil above, and

consequently doesn’t generate any stresses, the

main question relies on how does the system

behave under the vertical axial loads and bending

moments transferred from the walls.

FIGURE 6 – STRESSES DISTRIBUTION ON SOIL

On soft soils and stiff slabs, the soil’s reaction will be

distributed along the entire slab (curve 1 on Figure

6). On other hand, having hard soils and relatively

slender slabs, the slab will deform easily near the

edges, which will generate a concentrated reaction

by the soil near those areas (curve 2).

In general, more deformable soils will generate

more stresses in the slab, as the reactions migrate

to the center. This can easily be pictured by

imagining the system inverted, where the walls act

like columns.

In the tank studied, the slab is extended beyond the

walls. In this case, another factor arises under

deformable soil. In the situation where there is no

embankment loads acting on the outside portion

(during test phase), the vertical component of the

hydrostatic pressure will cause displacements on

the ground, which by turn will produce reactions

under the entire slab. Consequently, the outside

portion of the slab will act as a cantilever,

generating large bending moments (Figure 7).

When the tank is empty and the embankment is in

place, the condition is reversed.

FIGURE 7 – OUTSIDE SLAB ACTING AS CANTILEVER

4.2. MODELLING

The structural behavior of the cylindrical tanks are

highly dependent on the type of connection

between the wall and the ground slab that can be

fixed, pinned or simply supported. In this work, the

tank (Figure 1), having rigid connection, was

evaluated through two FEM models, in which one of

them the slab isn’t extended beyond the walls and

has no roofing (model A). The software used was

CSI’s SAP2000.

FIGURE 8 - F.E.M. MODEL B IN SAP2000

To evaluate the influence of deformability, each

model was run under four different soil stiffness

(ks), modeled with Winkler springs (Table 3).

TABLE 3 - WINKLER SPRINGS APPLIED IN F.E.M. MODELS

Soil ks (kN/m3)

Extremely deformable 5.000

Deformable 40.000

Very stiff 200.000

Undeformable 2E10

The results were validated by comparison with the

ones obtained from the Hangan-Soare method, and

with the exact solutions provided by differential

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equations deduced from elasticity theory (for fixed

base wall only).

4.3. RESULTS

Due to limited space, only some of the results will

be shown. Except otherwise stated (Figure 15), all

data refers to the combination of dead load and

hydrostatic pressure (PP+PH).

- Model A

It can be observed in the following figures that, as previously discussed, the soil’s deformability plays a major role on the stresses in both wall and ground slab, due to the rotation of the node linking the elements, while hoop force is less affected.

FIGURE 9 - SLAB - RADIAL MOMENT

FIGURE 10 - WALL - VERTICAL MOMENT

FIGURE 11 - WALL - HOOP FORCE

- Model B

When the slab is extended, the soil’s deformability

influence over the stresses on the wall decays,

because the node no longer experiences large

rotation. On other hand, bending moment in the

slab is greatly increased due to the difference on

vertical loading between interior and exterior

sections.

FIGURE 12 - SLAB - RADIAL MOMENT

FIGURE 13 – WALL - VERTICAL MOMENT

FIGURE 14 - SLAB - RADIAL MOMENT

Lastly, it can be observed in Figure 15 that imposed

deformations can have a big impact on overall wall

stresses. The slab limitation on the walls contraction

due to shrinkage causes large hoop forces on the

botton of the wall. The same effect happens

between the bottom and top areas of the wall on

account of only the top experiencing uniform

temperature variation.

-10,0

-5,0

0,0

5,0

10,0

15,0

20,0

4,925,746,567,388,20r (m)

Mr (kNm/m)

PP+PH: Ks=5PP+PH: Ks=40PP+PH: Ks=200PP+PH: Ks=2E7

[MN/m3]

0,0

1,0

2,0

3,0

4,0

5,0

6,0

-20 -15 -10 -5 0 5 10 15 20 25

h (m)

Mv (kNm/m)

PP+PH: Ks=5PP+PH: Ks=40PP+PH: Ks=200PP+PH: Ks=2E7PP+PH: Encastrado

[MN/m3]

0,0

1,0

2,0

3,0

4,0

5,0

6,0

-5050150250350

h (m)

Nϕ (kN/m)

PP+PH: Ks=5PP+PH: Ks=40PP+PH: Ks=200PP+PH: Ks=2E7PP+PH: Encastrado

[MN/m3]

-10,0

-5,0

0,0

5,0

10,0

15,0

20,0

25,0

30,0

4,925,746,567,388,209,02r (m)

Mr (kNm/m)

PP+PH: Ks=5PP+PH: Ks=40PP+PH: Ks=200PP+PH: Ks=inf.

[MN/m3]

0,0

1,0

2,0

3,0

4,0

5,0

6,0

-10 -5 0 5 10 15 20 25 30 35

h (m)

Mv (kNm/m)

PP+PH: Ks=5PP+PH: Ks=40PP+PH: Ks=200PP+PH: Ks=2E7

[MN/m3]

0,0

1,0

2,0

3,0

4,0

5,0

6,0

-5050150250350

h (m)

N (kN/m)

PP+PH: Ks=5PP+PH: Ks=40PP+PH: Ks=200PP+PH: Ks=2E7

[MN/m3]

7

FIGURE 15 – WALL – HOOP FORCE (R – SHRINKAGE; TUN –

UNIF. NEGATIVE TEMP. VAR.; TDP – DIF. POSITIVE TEMP VAR.)

5. SEISMIC ANALYSIS

The dynamic response of cylindrical tanks to seismic

loads is a complex problem that involves the

interaction between the retaining liquid and the

deformation of the structure and the ground itself.

Therefore, several simplified mechanical models

have been proposed in order to turn the seismic

analysis simpler through the determination of

equivalent static forces, based on some hypothesis.

One of the first models was presented by Housner

[8], that assumes the tank being completely

anchored at their base and the walls rigid. According

to this model, under a horizontal acceleration of the

ground, the liquid will produce hydrodynamic

pressures that can be divided into two components:

1 – Impulsive component – The wall’s motion forces

a fraction of the liquid to move combined with the

structure. Because the structure is assumed rigid,

the entire system undergoes the same acceleration

that the ground.

2 – Convective component – The tank’s motion

excites the liquid, generating oscillation at the

surface, whose motion is independent from the

remainder of the system. This portion exhibit its

own vibration modes, which simpler ones are

characterized by high vibrational periods, where

only the first one is accounted for.

Thereby, globally this model resumes to two masses

mi and mc rigidly connected to the tank at heights hi

and hc. The first one (impulsive) experiences the

ground’s acceleration (together with the tank’s

mass) while the second one (convective)

experiences the spectral acceleration linked to its

vibration period.

However, it has been shown later that assuming

that the tank is rigid can be non-conservative. In

fact, due to the tank’s bending flexibility, the

impulsive liquid and tank’s joint acceleration should

correspond to the natural fundamental vibration

frequency of the system, which can be several times

higher than the peak ground acceleration.

Therefore, recent models, including the one present

in Eurocode 8-4 [9], introduce a third, flexible,

component (Figure 16).

FIGURE 16 - MECHANICAL MODEL INCLUDED IN EUROCODE 8-4

The maximum pressure distribution on the tank wall

relative to the three components were calculated

according to Eurocode 8-4 [9] (Figure 17). This

distribution varies circumferentially according to

function cos(ϕ). It was applied the response

spectrum for most aggravating seismic action in

Portuguese territory.

FIGURE 17 – HYDRODYNAMIC PRESSURE DISTRIBUTION

It should be noted that the convective component

acceleration should be deduced using the elastic

response spectrum, because it is assumed that the

liquid doesn’t have any energy dissipation capacity.

The other components should limit the behavior

0,0

1,0

2,0

3,0

4,0

5,0

6,0

-200 0 200 400

h (m)

Nϕ (kN/m)

R

TUN

TDP

0,0

1,0

2,0

3,0

4,0

5,0

6,0

0,0 2,0 4,0 6,0 8,0 10,0 12,0

h (m)

p (kN/m2)Convective Impulsive Flexible

8

coefficient to q=1,5 due to the tank’s low

redundancy.

The flexible component’s acceleration was

calculated using the absolute response spectra

instead of relative (to the ground’s movement)

since there is evidence that within the normal

frequency range where the liquid-structure

normally lies in, the value of these accelerations are

similar.

The three components were combined using the

square root sum of squares rule (SRSS).

FIGURE 18 - COMBINED HYDRODYNAMIC PRESSURE DIST.

The Eurocode 8-4 also features a simplified method

that quickly provides solely the total basal shear

force and overturning moment, which was also

applied.

Subsequently, it was conducted the procedure

proposed by Virella [10], which consists on adding

masses proportional to the impulsive hydrodynamic

distribution to the tank wall in a F.E.M model, a

modal analysis was carried on (SAP2000 model was

used again). Three models were formed to evaluate

the influence of the wall-slab connection stiffness.

It was observed that the tank possesses a major

vibration mode that shows approximately 80% mass

participation factor (Figure 19). Its deformed shape

resembles that from a cantilever.

FIGURE 19 - MASS PARTICIPATION FACTORS

Introducing the response spectrum in the software,

seismic induced stresses in the walls were obtained.

This stresses correspond to the impulsive-flexible

component only, as the convective component is

not accounted for in this procedure. It can be

observed in Figure 20 that the seismic stresses (SIS)

are relatively low when compared to the ones

relative to dead load and hydrostatic pressure

(PP+PH). This happens because all hydrodynamic

pressure is applied in a single direction and most of

the force is transmitted to the foundation by

membrane (tangential) shear with only small

vertical bending.

FIGURE 20 – VERTICAL BENDING MOMENT IN WALL

Due to the low seismic stresses, because in tanks

quasi-permanent loads are close to maximum loads

in ultimate state limit, and since high crack

limitation take place in order to fulfill tightness

requirements, it’s clear that the seismic

combination of actions will not be limiting. This

remarks correlate with observed damage resulting

from earthquakes in RC tanks, consisting mainly in

rigid body sliding occurrences and soil rupture.

The EC8 simplified method should therefore

provide with enough information (basal shear force

and overturning moment) to design the base

anchorage and check for global equilibrium.

Logically, these conclusions don’t apply to steel

tanks, in which ultimate state limit will be limiting,

and in addition the flexible component force might

be higher due to this type of tank’s higher

vibrational period (the range of periods referred

lays in the initial ascending curve of the response

spectrum)

6. STRUCTURAL DESIGN

0,0

1,0

2,0

3,0

4,0

5,0

6,0

0,0 10,0 20,0 30,0 40,0 50,0 60,0

h (m)

p (kN/m2)SRSS ABS Hydrostatic

0,00

0,20

0,40

0,60

0,80

1,00

0,0200,0300,0400,0500,0600,070

Mas

s p

arti

cip

atio

n

fact

or

T (s)Fixed Pinned Rigid

0,0

1,0

2,0

3,0

4,0

5,0

6,0

-10 -5 0 5

h (m)

Mv (kNm/m)

SISSIS+PP+PH (max)SIS+PP+PH (min)PP+PH

9

Eurocode 2-3 [5] introduces specific design

provisions for liquid retaining tanks and classifies

tanks based on its requirements for leakage.

The tank being studied classifies as

tightness class 1, where according to the regulation,

leakage should be limited to a small amount and

some surface staining or damp patches are

acceptable. In this class, any cracks which can be

expected to pass through the full thickness of the

section should be limited to wk1.

Where the full thickness of the section is

not cracked, the provisions of Eurocode 2-1-1 (in

which the cracking limits are based on exposure

classification) apply. This condition is valid if at least

50 mm or 0,2 times the section thickness is

permanently experiencing pressure at all times,

under quasi-permanent loading.

The cracking limit wk1 is calculated as a

function of the ratio between the height of liquid hL

and the element thickness t. For ℎ𝐿/ℎ ≤ 5, 𝑤𝑘1 =

0,2 𝑚𝑚, and for ℎ𝐿/ℎ ≥ 35, 𝑤𝑘1 = 0,05 𝑚𝑚. For

intermediate ratios a linear interpolation can be

made (Figure 21).

FIGURE 21 - RECOMENDED VALUES FOR WK1

The dome, which is not in contact with the retained

liquid, had it’s crack width limited to 0,3 mm,

accordingly to its exposure class XC4. In the other

elements, wk1 applied (Table 4).

TABLE 4 - WK1 LIMITS APPLIED IN THE STRUCTURE

Element

o

z (m) hL (m) t (m) hL/t wk1 (mm)

Wall

3,4 2,0 0,2 10 0,175

1,4 4,0 0,2 20 0,125

0,4 5,0 0,2 25 0,100

Slab - 5,4 0,1 54 0,050

Beam - 0,1 0,4 0,25 0,200

All elements had their crack width calculated at

every section by a MS Excel application that

calculates, for a pair of axial force and bending

moment, the extensions in steel and concrete and

consequently its stresses, and hence is able, based

on Eurocode 2-1-1 formulation, to calculate crack

width. Therefore, reinforcement was attributed

based on an iterative procedure.

Ultimate limit states were also verified and at no

case was limiting. In fact, that wouldn’t be

expected, because at service the loads have

practically the same values and the cracking

requirements limit stresses in reinforcement at

around 50 to 90 MPa, which represents about 20%

of design strength value for reinforcement steel.

It should be noted that the reinforcement was

designed without altering the structure’s original

geometry and doesn’t represent an optimum

solution, which would imply increasing the

thickness of both the bottom slab and the dome.

Also, this design was possible by considering a very

rigid homogeneous foundation soil (characterized

by 200 MN/m3).

7. FINAL REMARKS

Reinforced concrete water retaining structures

possess some unique characteristics because of

high loads that withstand during most of their

lifespan and the tightness requirements that is the

major parameter on its design, by imposing high

cracking limitations.

Because of these, indirect loads must be careful

quantified and its effects properly analyzed.

The structural analysis involving different ground

stiffness concludes that this is a very important

parameter that can greatly increase stresses both in

the ground slab and in the wall.

Lastly, it was found that seismic loads should

generally not influence design of reinforcing steel,

although its global effect on the links to the

foundation can’t be ignored.

MAIN REFERENCES

[1] Santarella, Luigi (1953). Il Cemento Armato, Volume II – Le Applicazioni alle Construzioni Civili ed Industriali - Tridicesima Edizione Rifatta. Editore Ulrico Hoepli, Milano.

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[2] LNEC E464 (2007). Betões: Metodologia prescritiva para uma vida útil de projecto de 50 e de 100 anos face às acções ambientais. Laboratório Nacional de Engenharia Civil (LNEC), Lisboa.

[3] British Standards Institution (1987). British Standard 8007: Code of practice for design of concrete structures for retaining aqueous liquids. British Standards Institution, London.

[4] EN 1991-4 (2006). Eurocode 1: Actions on structures – Part 4: Silos and tanks. European Committee for Standardization (CEN), Brussels.

[5] EN 1992-3 (2006). Eurocode 2: Design of concrete structures – Part 3: Liquid retaining and containment structures. European Committee for Standardization (CEN), Brussels.

[6] Bazant, Zdenek (1972). Prediction of Concrete Creep Effects Using Age-Adjusted Effective Modulus Method. Journal of the American Concrete Institute, Vol. 69, 212-217.

[7] Camara, José; Figueiredo, Carlos (2012). Concepção de Edifícios com grande área de implantação. Encontro Nacional Betão Estrutural – BE2012, Faculdade de Engenharia da Universidade do Porto, Porto.

[8] Housner, George W. (1963). The dynamic behavior of water tanks. Bulletin of the Seismological Society of America, Vol. 53, No.2, 381-387.

[9] EN 1998-4 (2006). Eurocode 8: Design of structures for earthquake resistance – Part 4: Silos, tanks and pipelines. European Committee for Standardization (CEN), Brussels.

[10] Virella, Juan C.; Godoy, Luis A.; Suárez, Luis E. (2006). Fundamental modes of tank-liquid systems under horizontal motions. Engineering Structures, 28, 1450-1461.