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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
6
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.
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