INT ERNATIONAL JOURNAL OF CIVIL ENGINEERING AND ... ELEMENT...Esmaeil Asadzadeh 1 PROF. Mrs. A....

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:[email protected] 2

Professor,Maeer’s Maharashtra Institute of TechnologyPune-411038, University of Pune,

India,Email: [email protected] 3Head of the department of Maeer’s Maharashtra Institute of TechnologyPune-411038

[email protected] 4

Professor, Islsmic Azad University of Maragheh,Faculty of Engineering (Civil),Iran

[email protected]

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

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ISSN 0976 – 6308 (Print) ISSN 0976 – 6316(Online)

Volume 3, Issue 1, January- June (2012), pp. 82-98

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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



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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.



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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.



88



89



90

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.



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Figure 7 Variation of In-plane forces with height at Ɵ=0


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.



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.


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.



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


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


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.



98

[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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