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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 3, Issue 1, January- June (2012), © IAEME
82
FINITE ELEMENT ANALYSIS FOR STRUCTURAL RESPONSE OF
RCC COOLING TOWER SHELL CONSIDERING ALTERNATIVE
SUPPORTING SYSTEMS
Esmaeil Asadzadeh
1 PROF. Mrs. A. RAJAN
2 Mrudula S. Kulkarni
3
SahebaliAsadzadeh4
1Graduate Student,Maeer’s Maharashtra Institute of Technology Pune-411038, University of
Pune, India, Email:es.asadzadeh@gmail.com 2
Professor,Maeer’s Maharashtra Institute of TechnologyPune-411038, University of Pune,
India,Email: kmrajan2806@yahoo.co.in 3Head of the department of Maeer’s Maharashtra Institute of TechnologyPune-411038
mrudula.kulkarni@mitpune.edu.in 4
Professor, Islsmic Azad University of Maragheh,Faculty of Engineering (Civil),Iran
saliasadzadeh@yahoo.com
ABSTRACT
Hyperbolic RCC free standing cooling towers constitute an important component of systems dealing
with thermal power generation or nuclear power generations. Keeping in view modern requirements
these structures constitute high rise structural systems.it is a normal practice to adopt one of the
following kind of supports to the shell part of the tower.
1. Fixity at the base
2. I type of column support at the base
3. V type of column support at the base
With a view to compare the relative influence of the supports on the structural response offered by the
shell for available case history Finite Element Analysis employing higher order Mindlin formulation
have been undertaken. The comparison has been made of the self-weight loading, static wind loading
and pseudo static seismic activities the loads are calculated as per the recommendation of relevant IS
codes.
Keywords: Hyperbolic RCC Cooling Towers, Finite Element Analysis, Wind Analysis, Pseudo static
Analysis, Shell Structures
1. INTRODUCTION R/C cooling towers constitute important component of the thermal and nuclear power plants.
With the ever growing demand for the requirements of power supply, more and more numbers of such
towers are planned; not only this but to cater to the larger requirements their heights are on increase.
The towers with the height exceeding 150m are being planned everywhere in the world, including
India.
INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND
TECHNOLOGY (IJCIET)
ISSN 0976 – 6308 (Print) ISSN 0976 – 6316(Online)
Volume 3, Issue 1, January- June (2012), pp. 82-98
© IAEME: www.iaeme.com/ijciet.html
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IJCIET
© I A E M E
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The tower structural system has two main components. These are thin walled tower shell and the
supporting columns. As far as the column supports are concerned the same are chosen from the
alternative arrangement of I type and V type. It would be of importance to compare the relative
behaviour of these alternative systems for the same tower shell. The proposed work deals with such
aspect.
Some of the earlier and generic finite element analysis of cooling towers are reported by J.G.A. Croll,
F. Kaleli, K.O. Kemp, J. Munro, (1979), outlined a simplified method for analysing the elastic stresses
in geometrically imperfect cooling tower shells based on the replacement of the imperfection by an
appropriate additional normal pressure. Hyun-ock Jang and Chang-shik Min, (2001), A design is
performed to check the design strength under a consistent design load; therefore, to verify the
adequacy of the design algorithm developed. Based on the equilibrium consideration for the ultimate
limit state of reinforcement in tension and cracked concrete in compression, an iterative numerical
computational algorithm was developed. Lang, ( 2002), presented the extension of the linear static
shell ring element to account for non-linear kinematic relation and non-linear material response in the
shell. Orlando M. (2001) discussed the wind induced interference effect on two adjacent cooling
tower through pressure measurements on cooling tower models in a boundary layer wind tunnel.
Viladkar, (2006) studied the effect of soil-structure interaction on the design forces of shell, racker
columns and raft foundation as compared to fixed base case. Long-yuan Loo Wen-da, (1989), the
post-buckling analysis of cooling tower shell with discrete fixed support and under the action of wind
loads and dead load is studied. KarisiddappaM. N. Viladkar, (1998), represents the tower shell by
semi-loof shell elements and the supporting columns by semi-loof beam elements. The column ends
are assumed to be fixed at their bases. The analysis has been carried out for only the dead load.
It is proposed to undertake preliminary design for RCC cooling tower combined with its supporting
system. To do so the linear finite element analysis would be employed to determine the structural
response.
The actual problem being considered is in the form of a cooling tower supported on two
alternative column supporting systems as shown in figure 1.
Figure 1 Alternative column supporting systems
The aim of the proposed work is to compute the response of these alternative tower systems to
determine their relative merits. The points to be considered are:
1. The stresses in the tower region in the vicinity of support junctions, the deformations at the throat
of the tower and the deflections at the top of the tower.
2. The results for the following load conditions are derived for the completeness of the required
comparisons.
a. Self-weight of the structural system.
b. Wind load as per IS875 subject to Pune region.
c. Pseudo static seismic forces computed through modal analysis as per the recommendation of
IS1893.
The principle data of the tower system is as presented in tables 1, 2 and 3.
The radius r of the shell at height z(m) is found by Takashi Hara, (2004) as
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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The parameters a, b and ∆r are shown in Table 1, Table 2 and Table 3.
TABLE1. CONFIGURATION PARAMETERES
Heig
ht(z)
9.17m-125m 125m-176m
a
b
∆r
51.9644
113.9896
-15.3644
0.2578
8.0293
36.3422
TABLE2. RADIUS AND THICKNESS OF THE SHELL
Lintel Node Top
Height(z)
Radius(m)
Thickness(m)
9.17m
58.72m
1.05m
125m
36.6m
0.24m
176m
38m
0.2m
TABLE3. MATERIAL PROPERTIES
Concrete
Elastic Modulus
Poisson’s Ratio
Density
Compressive
Strength
Tensile Strength
34Gpa
0.167
0.0023kg/cm3
36Mpa
2.7Mpa
Reinforecement
Elastic Modulus
Yield Stress
206Gpa
500Mpa
The complete information presented above is taken up from literature Takashi Hara, (2004).
The finite element modelling will be carried out through two nodded line elements for representing
the column supports and second orders Mindlin elements for representing the tower shell.
The finite element analysis for the proposed work is conducted through application of well-known
analysis software SAP 2000 Ver.14.
2. SELF WEIGHT ANALYSIS
2.1 Displacements
For the self-weight the displacements are symmetrical about axis of symmetry and the same
are of quiet insignificant order. For the sake of illustrative comparison variation of radial
displacements over the height of the tower is provided on figure 2.
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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Figure 2 Variation of radial displacement with height
Following observations could be made:
For all the support types the radial displacements above the base of the shell structure are more or less
same indicating the inward movement up to the throat level, and subsequently small radial movement
in outward direction is developed.
Between the support level and the base of the shell structure a considerable amount of the
outward moment maybe observed which in case of V type support is almost six times that of I type
support.
2.2 In-plane Forces
Stress resultants (NX,NY,NXY) representing the In-plane normal force in local X direction,
normal force in local y direction and shear force over the local (X,Y) plane are having following
characteristics. Once more their variations over the height are shown in figure 3.
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Figure 3 Variation of In-plane forces with height
It may be observed that:
a) From height of 32.34 meter the top of the tower (NX, NY, NXY) have identical variation with
height for all kinds of supports.
b) For the portions below the height of 32.34 meter the (NY, NXY) are almost similar for all the
support conditions.
c) For NX the variation below the height of 32.34 meter is dependent on the type of support
condition varying compared to the value for fix support. For both I type and V type supports,
the sign of the force is reversed. In addition, for the V type of support the value is almost 6
times of that of the value for the fixed base.
2.3 Bending Moments Bending moments (MX, MY, MXY) represent the moments around the plate surface such
that MX and MY represent the moments around X and Y axis, whereas MXY denotes the twisting
moment. Their variations over the height of the tower are shown in figure 4.
Figure 4 Variation of moments over the height
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It may be observed that:
a) The variation of moments (MX, MY, MXY) for the height 43.92 meter and above up to the
top of the tower is identical for all type of supports.
b) For I type support below the height of 43.92 meter up to the base of the shell structure
variation of MX is same as that due to fixed base. However for the V type of support the
variation of MX shows larger values compared to that of for the base and at the base of the
shell the value is almost 50% more than the value for the fixed base.
c) For MY the V type of support has value lesser than the value of fixed support though for
entire region below 43.92 meter height, up to the base of the shell the trend of variation is
similar. For I type of support the sign for the moment is reversed though the value of the
moment is quite small.
d) Below the height of 43.92 meter up to the base of the shell the nature of variation is different
for both I type and V type at support compared to that of the fixed base. At the base the values
are larger compared to that due to fixed base with maximum being for the V type support and
lesser for the I type of support.
3. WIND LOAD ANALYSIS The wind loads are calculated as per the recommendations offered in IS 875 1987. These are applied
as direct nodal actions and the analysis is performed.
3.1 The loads are calculated with respect to following data as per IS 875 1987.
a) Wind speed= 39 m/s
b) Terrain category=1
c) Structure class= C
d) Risk coefficient(K1 factor)=1.06
e) Topography (K3 factor)=1
3.2 Displacements As is the common practice the variation of radial displacement with the height is provided in
figure 5 by considering vertical line at Ɵ=0.
Figure 5 Radial displacement variation with height at Ɵ=0
It may be observed that qualitatively the trend of variation is same for all type of supports. However
much larger radial displacements occur with I type and V type supports. This is because the base of
the shell structure which happens to be connected to column supports renders the total structural
system as if it is having support flexibility at the base of the shell. The I type of supports relatively
display larger flexibility than that for V type of support.
It would be of interest to display the displacements suffered by horizontal sections of the
tower at various levels. The complete details are shown in figure 6.
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 3, Issue 1, January- June (2012), © IAEME
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Figure 6 Distorted profiles at various levels of the shell tower
From those details following observations could be made:
a) The degree of distortion increases with height of the tower.
b) From the base it starts ovalization, which continues to grow with the height.
c) As the throat level is approached, the deformed shape manifests in all directions with the
reversal of curvatures and the trend continues up to the top of the tower.
d) The distortion is minimum with fixed base, intermediate with V support and maximum with I
support up to the height of about 90 meter. At further levels right up to the top of the tower,
the tower with V support displays greater distortion compared to that due to I support.
3.3 In-plane Forces Stress resultants (NX,NY,NXY) represent the In-plane normal force in local X direction,
normal force in local y direction and shear force over the local (X,Y) plane have the following
characteristics. Once more at Ɵ=0, their variation over the height are shown in figure 7.
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 3, Issue 1, January- June (2012), © IAEME
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Figure 7 Variation of In-plane forces with height at Ɵ=0
Following observations could be made:
a) For the tower height of 32.34 meters to the top of the tower the variation of (NX, NY) is more
or less same For all types at supports.
b) Below the region 32.34 meters up to the base of the shell structure the variation of NX is
dependent on the type of supports. Now I type of support, at the base of the shell, displays a
value five times as much the value of the fixed base. For V type of support, at the base level
the sign is reversed and the value is about three times as much the value of the fixed base.
c) The nature of the variation for NY below 32.34 meters and up to the base of the shell is more
or less similar, however the values compared to the value for fixed base are marginally
different for I and V type of supports.
d) For NXY, variation above the height of 32.34 meters up to the top of the tower is same for
fixed support and V type support. For I type support the variation is same from 101.83 meters
up to top of the tower. The nature of variation for NXY in case of V type support is similar to
that of fixed support. For I type of the support the variation below the height of 101.83
meters up to the 20.75 meters shows reversal in sign and subsequently by maintaining same
trend it approaches at the base value slightly larger than that of V support.
3.4 Bending Moments Bending moments (MX, MY, MXY) represent the moments around the plate surface such
that MX and MY represent the moments around X and Y axis, whereas MXY denotes the twisting
moment. Their variations over the height of the tower are shown over figure 8.
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Figure 8 Variation of bending moments with height at Ɵ=0
Once more the variation of the moments over the height are plotted at Ɵ=0.
Following observations could be made:
a) The variation of the MX from throat level to the top of the tower is same for all type of
supports. For the height of 125 meters to the base of the shell structure, I type and V type
qualitatively display the similar trend of variation compared to that of the fixed base. In
general the values are highest for V type of support and intermediate for I type.
b) The variation of MY from the height of 43.92 meters to the top of the tower is same for all
types of supports. At the base of the shell, maximum value develops for the I type of support
whereas for V type of support the value is quite small.
c) The variation of MXY from the height of 67.09 to the top of the tower is same for all type of
supports. Below the height of 67.09 up to the base of the shell tower, the variation gradually
differs in nature, wherein right at the base for I support very high value develops with reversal
of sign, whereas for V support value is only slightly larger compared to the value for the fixed
base.
4 PSEUDO STATIC SEISMIC FORCES The tower systems are subjected to pseudo static forces derived through application of
recommendations contained in IS 1893 2002. This involves considerations to the modal
characteristics of the structural systems, along with the prescribed earthquake response spectrum. For
this the SAP2000 software is utilized.
4.1 Modal Frequencies For the purpose of evaluating the pseudo static seismic forces, the modal characteristics in
respect of first twelve natural modes are derived. The details are presented in table 4.
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Table 4. Modal Characteristics
MODAL FREQUENCIES
MODE
Fixed I Type V type
Frequency
rad/sec rad/sec rad/sec
1 2.5135 2.4804 2.4295
2 2.5135 2.4804 2.4295
3 2.5742 2.507 2.5087
4 2.5742 2.507 2.5087
5 2.9223 2.922 2.889
6 2.9223 2.922 2.889
7 3.331 2.9249 2.922
8 3.331 2.9249 2.922
9 3.6365 3.5368 3.2791
10 3.6365 3.5368 3.2791
11 4.4418 3.5846 3.6365
12 4.5835 3.6365 3.6365
It may be observed that more or less, the frequencies are insensitive to the type of supports.
Hence the pseudo static seismic forces are also independent of the support types.
4.2 Evaluation of Pseudo Static Seismic Forces
The earthquake loads are calculated as per the recommendations offered in IS 1893 2002. These are
applied as direct nodal actions and the analysis is performed. The data is as given below:
a) Seismic zone factor =.16 for Pune area
b) Soil type = II
c) Importance factor( I) = 1.5
d) Response reduction factor (R) = 5
e) Eccentricity ratio = 0.05
4.3 Displacements As is the common practice the variation of radial displacement with the height is provided in
figure 9 by considering vertical line at Ɵ=0.
Figure 9 Radial displacement variation with height at Ɵ=0
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It may be observed that the I type support has greater flexibility compared to that of V type
support, as far as the radial displacement at the base of the shell structure concerned. The subsequent
behaviour is that of vertical cantilever subjected to horizontal forces.
4.4 In-plane forces Stress resultants (NX,NY,NXY) represent the In-plane normal force in local X direction,
normal force in local y direction and shear force over the local (X,Y) plane have following
characteristics. Once more at Ɵ=0, their variation over the height are shown in figure 10.
Figure 10 Variation of In-plane forces with height at Ɵ=0
It may be observed that variation characteristics over the height of the structure are more or less same
as that observed in case of wind load, however the seismic response displays In-plane forces of the
order of about 25% more than that due to wind loads.
4.5 Bending Moments Bending moments (MX, MY, MXY) represent the moments around the plate surface such
that MX and MY represent the moments around X and Y axis, whereas MXY denotes the twisting
moment. Their variations over the height of the tower are shown over figure 11.
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Figure 11 Variation of bending moments with height at Ɵ=0
Once more the variation of the moments over height are plotted at Ɵ=0.
It may be observed that
a) From the height of 43.92 meters up to the top of the tower the pattern of the variation is same
for all type of supports. It should be noted that the sign of bending moment MX changes from
the height of 101.83 meters. At the base of the shell structure V type support displays about
five times as much in the case of the fixed base. On the other hand for I type of support it is
about 2.5 times more than that due to fixed base.
b) The variation of MY over the height as a pattern similar to that observed in case of wind load
however the values are almost 25% more in comparison with that due to wind load.
c) The variation of MXY over the height as a pattern similar to that observed in case of wind
load however the values are almost 19% more in comparison to that due to wind load.
4.6 COMPARISONS
In the above presentation various details concerning structural response of the tower with respect to
three types of supports, namely fixed support, I type support and V type support have been elaborately
presented. For practical purpose, however it would be of interest to provide a comprehensive view of
these details. This will offer a rational means for the comparison with respect of influence of the type
of supports on the structural response. In view of this the comparison of displacements suffered and
the forces and moments induced at the three critical locations over the height of the tower are
considered. These are base of the tower shell, throat of the tower and top of the tower.
4.6.1 Structural Response for Self Weight of the Structure In table 5 the structural response details in respect of self-weight of the structure are
presented.
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Table 5. Structural response against self-weight of the structure at Ɵ=0
BASE Throat
Top
Fixed I Type V Type Fixed I Type V Type Fixed I Type V Type
U 0 0.002412 0.012605 0.000089 0.000089 0.000089 0.000069 0.000069 0.00007
NX -1536951 -159045 5900179 -76022.7 -76022.8 -76022.7 8516.3 8516.31 8516.3
NY -9221844 -9655580 -9914431 -572612 -572611 -572611 -23986.1 -23986.1 -23986.1
NXY -3911059 -3393831 -2794496 -53282 -53281.9 -53281.9 297.86 297.86 297.86
MX -662191 -625377 -929460 -22510.8 -22510.9 -22510.9 3980.54 3980.49 3980.45
MY -759222 93477.08 -535816 -3071.9 -3071.94 -3071.93 576.44 576.43 576.42
MXY -22368.2 128377.1 218478.6 1788.49 1788.48 1788.48 109.17 109.17 109.16
4.6.2 Structural Response for Wind Loads In table 6 the structural response details in respect of wind load are presented.
Table 6 Structural response against wind load at Ɵ=0
BASE Throat Top
Fixed I Type V Type Fixed I Type V Type Fixed I Type V Type
U 0 0.006243 0.001344 0.002211 0.005355 0.006236 0.000903 -0.000971 0.001002
NX -96393.9 -491736.68 316132.48 17800.97 17222.62 16894.69 25108.89 25335.92 25412.21
NY -437768.29 -389318.28 -460936.19 -18606.03 -17329.93 -16209.96 -5621.63 -5620.86 -5634.28
NXY -169980.72 -119545.72 -95188.51 2516.42 3422.9 3271.56 -8555.82 -8494.13 -8583.66
MX -3223.64 -11822.95 -18366.44 -761.87 -1128.62 -1354.49 1999.89 2244.66 2342.82
MY -129.45 -254257.34 -28820.49 -580.05 -790.47 -820.95 290.15 338.99 338.99
MXY 1341.43 -46378.1 7842.16 231 238.24 259.37 -43.01 -36.66 -26.61
4.6.3 Structural Response for Earthquake Forces
In table 7 the structural response details in respect of earthquake forces are
presented.
Table 7 Structural response against earthquake forces at Ɵ=0
BASE Throat Top
Fixed I Type V Type Fixed I Type V Type Fixed I Type V Type
U 0.000054 0.00789 0.002076 0.004383 0.010157 0.010895 0.008348 0.012731 0.017355
NX -205792.62 -636997.62 685526.95 14127.95 14183.77 14555.42 81681.4 76428.78 77022.89
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NY -1016460.6 -940943.98 -1069391.3 -102172.77 -95712.57 -96256.33 3161.37 2994.02 2989.97
NXY -424133.45 -311937 -281255.1 -8047.28 -6326.09 -7120.04 1869.15 1941.11 1797.53
MX -10727.22 -25696.26 -51130.96 6426.72 6446.29 6516.54 29113.17 27296.21 27503
MY -23806.82 -316192.09 -61894.02 2307.78 2152.78 2281.79 4110.46 3879.31 3884.2
MXY -1216.36 -54592.36 19528.33 1035.95 967.01 994.83 1127.31 1038.51 1052.22
U – Radial displacement in meter
(NX, NY, NXY) In-plane forces in terms of Newton per meter
(MX, MY, MXY) Bending moments in terms of Newton meter per meter
4.7 CONCLUSIONS On the basis of various details presented above following broad conclusions could be drawn.
a) In general it has been observed that the I type of supports create higher flexibility at the base
of the tower as compared to the V type of supports. In fact the V type of the supports behaves
in a manner similar to fixed support at the base.
b) The presentation above deals with discussions regarding variations of various structural
response details over the height of the tower. These details are providing the information
regarding the vertical line at Ɵ=0. The comparison of the response in respect of dead load,
wind load and seismic load has been generally undertaken this offers qualitative nature of the
comparisons. On the other hand quantitative information supporting above observations have
been presented in table 5, 6 and table 7. These permits following specific conclusions
1. For self-weight all the parameters of response details are more or less independent of
the type of supports at the throat level and at the top.
2. An important observation is in respect of deflection suffered. At the base the I type of
support displays almost five time that of the V type support. At the throat the
difference is negligible whereas at the top V type of the support indicates almost ten
times the deflection of the I type of the support. However the sign of the deflections
are opposite.
3. An important observation is in respect of deflection suffered. At the base the I type of
support displays almost four time that of the V type support. At the throat the
difference is negligible whereas at the top V type of the support indicates almost 1.5
times the deflection of the I type of the support.
REFERENCES
[1] J.G.A. Croll, F. Kaleli, K.O. Kemp, J. Munro, (1979) “A simplified approach to the analysis of
geometrically imperfect cooling tower shells “ pp. 92-98.
[2] Hyun-ock Jang and Chang-shik Min, (2001),“Design and Inelastic Behaviour of Hyperbolic
Cooling Tower.
[3] Lang C., Meiswinkel R. and Filippou C.( 2002), “Non-linear analysis of shells of revolution with
ring elements. Engineering Structures”. 24: 163-177.
[4] Orlando M. (2001).” Wind-induced interference effects on two adjacent cooling towers”.
Engineering Structures. 23: 979-992.
[5] Viladkar M.N., Karisiddappa Bhargava P. and Godbole P.N. (2006). Static soil-structure
interaction response of hyperbolic cooling towers to symmetrical wind loads. Engineering Structures.
28: 1236-1251.
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 3, Issue 1, January- June (2012), © IAEME
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[6] Long-yuan Loo Wen-da,(1989), “Nonlinear buckling analysis of hyperbolic cooling towers shell
with ring stiffeners” (Shanghai Institute of Appl. Math. and Mech., Shanghai) pp. 113-118
[7] KarisiddappaM. N. Viladkar, P. N. Godbole and Prem Krishna,(1998), “Finite element analysis of
column supported hyperbolic cooling towers using semi-loof shell and beam elements12” pp. 75-85.
[8] Takashi Hara.(2004) “Dynamic response of R/C cooling tower shell considering supporting
systems” Tokuyama College of Technology.
[9] IS 875 1987 (Part3): Wind Loads on Buildings and Structures
[10] IS 1893 2002 (part1): Criteria for Earthquake resistant Design of Structures
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