Study the Effects of Seismic and Wind Loads on Hyperbolic Cooling Tower

8/19/2019 Study the Effects of Seismic and Wind Loads on Hyperbolic Cooling Tower

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“TO STUDY THE EFFECT OF SEISMIC AND WIND LOADS ON

HYPERBOLIC COOLING TOWER OF VARYING DIMENSIONS AND

RCC SHELL THICKNESS”

DISSERTATION:

Submitted to Visvesvaraya Technological University, Belgaum

In partial fulfillment of the requirement for the award of the degree of

MASTER OF TECHNOLOGY

IN

STRUCTURAL ENGINEERING

By:

PRASHANTH .NUSN: 1GC11CSE05

Under the Guidance of:

SAYEED SULAIMAN

Assistant Professor

Dept of Civil Engineering, G.C.E,

Ramanagaram-571511

DEPARTMENT OF CIVIL ENGINEERING

GHOUSIA COLLEGE OF ENGINEERING

RAMANAGARAM-5715112012-2013


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SYNOPSIS:

Natural draught cooling towers are very common in modern day thermal and nuclear power

stations. These towers with very small shell thickness are exceptional structures by their

sheer size and sensitivity to horizontal loads. This paper deals with to study the effect of

seismic and wind loads on hyperbolic cooling of varying dimensions and rcc shell thickness.

For the purpose of comparison an existing cooling tower is consider as reference, (BTPS,

Karnataka).For other models the dimensions and rcc shell thickness is varied with respect to

reference cooling tower.

Bellary thermal power station is a power generating unit near kudithini village in Bellary

taluk, Bellary district and karnataka state. Basic wind speed is 39 m/sec, risk co-efficient

factor K 1 shall be taken as 1.06, terrain category shall be 2 and corresponding values shall be

taken for K 2, risk co-efficient factor K 3 shall be taken as 1.0. The seismic zone is zone III,

importance factor (I) is 1.5.

The boundary condition of the cooling tower has been top end free and bottom end is fixed.

The material properties of the cooling tower have young modulus 31GPa, Poisson Ratio 0.15

and density of RCC 25 Kg/m3. These cooling towers have been analyzed for seismic & wind

loads using Finite Element Analysis (ANSYS v.10). The seismic load will be carried out for 0.5g, 0.6g& 0.7g in accordance with IS: 1893 (part 1)-2002 and by modal analysis and wind

loads on these cooling towers have been calculated in the form of pressures by using the

design wind pressure coefficients as given in IS: 11504-1985 code along with the design

wind pressures at different levels as per IS: 875 (Part 3) - 1987 code. The analysis has been

carried out using 8-noded 93 Shell Element.

The out come & result are Max Deflection, Max Principal Stress & Strain, Max Von mises

Stress & Strain are mapped & tabulated.


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ACKNOWLEDGEMENT

This satisfaction and euphoria that accompany the successful completion of any task would

be but incomplete without mentioning the names of the people who made it possible, whose

constant guidance and encouragement crowned the efforts with success.

I convey my regard to SAYEED SULAIMAN, Assistant Professor, Department of Civil

Engineering, GCE, for his valuable insights and suggestions offered during the course of the

Project work.

I express my deep gratitude to Dr. MOHAMED ILYAS ANJUM, Vice principal, Prof. &

HOD, Department of Civil Engineering, GCE for providing support and encouragement.

I express my thanks to Dr. MOHAMED HANEEF, Principal, for providing congenial

atmosphere to work in.

I express my thanks to PRAKASH, Chief Engineer, and KPCL for providing data to our

Project work.

I express my thanks to KIMDHASAIAH, Executive Engineer, and KPCL for helping to our

project work.

I express my thanks to Sunil Reddy for Guidance of ANSYS Software to our project work.

I also thank full to our Family and Friends. Their Constant faith in our sincerity has helped

us to stay confident in the entire course of the project.

I thank all the Teaching Staff , Supporting Staff who have directly or indirectly helped us in

successful completion of our project work.

PRASHANTH N


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CONTENTS:

Abstract i

List of Tables iv

List of Figures v

Abbreviations viii

CHAPTER-I: INTRODUCTION OF COOLING TOWER

1.1 General Introduction 1

1.2 Types of cooling tower 2

1.3 Component of natural draft cooling tower 4

1.4 Cooling tower materials 5

1.5 IS11504-1985 Recommendation 6

1.6 Advantage of cooling tower 7

1.7 Details of Bellary thermal power plant 7

1.8 Objective 8

1.9 Origination of Thesis 8

CHAPTER-II: LITERATURE REVIEW

2.1 Introduction 10

2.2 Review of hyperbolic cooling tower 10-13

CHAPTER-III: ANALYSIS OF RCC SHELL

3.1 General Introduction 14

3.2 Reinforced Concrete Thin Shell Structure 15

3.3 Classification of Shell 17

CHAPTER-IV: INTRODUCTION TO FEM PACKAGE USED ANSYS

4.1 FEA Program 18

4.2 Materials Models 20

4.3 Element Library 20

4.4 Procedure Library 21

4.5 FEA Program 22


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CHAPTER-V: ELEMENT USED FOR ANALYSIS OF THE PROJECT

5.1 Shell 93: Description 26

5.2 Shell 93: Input Data 26

5.3 Shell 93: Input Summary 28

5.4 Shell 93: Assumption & Restriction 29CHAPTER-VI: ANALYSIS PROCEDURE & CALCULATIONS

6.1 Description of Geometry of cooling tower 30

6.2 Earthquake forces 35

6.3 Wind load 40

6.4 Analysis steps involved in finite Element Modeling 49

CHAPTER-VII: TABULATION AND RESULTS

7.1 Static analysis 527.2 Modal analysis 55

7.3 Response spectrum analysis 57

7.4 Wind analysis 63

CHAPTER-VIII: SUMMARY AND CONCLUSIONS 66

CHAPTER-IX: RECOMMENDATION FOR FUTURE STUDIES 67

REFERENCES 68APPENDIX A- JOURNAL PAPER

APPENDIX B- Geometrical drawing of BTPS

APPENDIX C- IS Codes

1. IS: 11504:1985., Criteria for structural design of reinforced concrete natural draught

cooling tower, New Delhi, India: Bureau of Indian standards.

2. IS 1893 (part 1): 2002 Criteria for earthquake resistant design structure.

3. IS: 875 (Part3):1987. Code of practice for design loads (other than earthquake loads)

for buildings and structures. New Delhi, India: Bureau of Indian Standards.


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LIST OF TABLES:

Table 5.1: Shell 93 real constants 28

Table 6.1: Geometric details of hyperbolic cooling tower 31Table 6.2: Input geometry values to create model in ANSYS for CT1 32

Table 6.3: Input geometry values to create model in ANSYS for CT2 33

Table 6.4: Input geometry values to create model in ANSYS for CT3 34

Table 6.5: Design spectrum for 0.5g 37



Table 6.8: Result of variation hourly mean wind speed with height for CT1 41Table 6.9: Result of variation hourly mean wind speed with height for CT2 42

Table 6.10: Result of variation hourly mean wind speed with height for CT3 42

Table 6.11: Gust factor calculation result for CT1 45

Table 6.12: ANSYS input wind pressure for CT1 45

Table 6.13: Gust factor calculation result for CT2 46

Table 6.14: ANSYS input wind pressure for CT 47

Table 6.15: Gust factor calculation result for CT3 48Table 6.16: ANSYS input wind pressure for CT3 48

Table 7.1: Static analysis results 55

Table7.2: Modal analysis results 57

Table 7.3: Response spectrum analysis result for 0.5g 59



Table 7.4: Wind load analysis results 65


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LIST OF FIGURES:

Fig1.1: Group of cooling towers 1

Fig1.2: Historical development of cooling tower 2

Fig1.3: Cross flow of cooling tower 3

Fig1.4: Counter flow of cooling tower 3Fig1.5: Fabrication of supporting columns 4

Fig1.6: climbing construction of shell 4

Fig1.7: Location of BTPS 8

Fig3.1: Aircraft hangar, Orly, France 15

Fig4.1: Components of general purpose finite element analysis program 19

Fig4.2: ANSYS graphical user interface 23

Fig5.1: Shell 93: geometry 26Fig6.1: Geometry of BTPS 30

Fig6.2: Response spectra graph for 0.5g 37



Fig7.1: key points to create CT model 52

Fig7.2: Geometric model 52

Fig7.3: Boundary condition 52Fig7.4: Thickness of rcc shell 52

Fig7.5: Element number in model 53

Fig7.6: Node number in model 53

Static analysis:

Fig7.7: Deflection for CT1 53

Fig7.8: Principal stress for CT1 54

Fig7.9: Principal strain for CT1 54Fig7.10: Von mises stress for CT1 54

Fig7.11: Von mises strain for CT1 54


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Modal Analysis:


Fig7.13: Von mises stress for CT1 56


Fig7.15: Principal stress for CT1 56Fig7.16: Principal strain for CT1 56

Response spectrum analysis for 0.5g:



Fig7.19: Principal strain for CT1 58

Fig7.20: Von mises stress for CT1 58Fig7.21: Von mises strain for CT1 58












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Wind Analysis:

Fig7.32: Applied wind pressure for CT1 63



Fig7.35: Principal strain for CT1 64Fig7.36: Von mises stress for CT1 65



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ABBREVIATIONS

For the purpose of this standard, the following letter symbols shall have the meaning indicated

against each:

IS: 11504-1985: criteria for structural design of reinforced concrete

natural draught cooling towers

r th= throat radius

r th/b= slope of the asymptote of the generating hyperbola

D= base diameter at basin sill level

Ee= modulus of elasticity of concrete (short term modulus)

Fn= Fourier coefficient of nib term

d = thickness of the shell

H= total tower height above basin sill level

MФ= meridional moment per unit length of the middle surface

Mθ= circumferential moment per unit length of the middle surface

MθФ, MФф= twisting moments per unit length of the middle surface

n= nth

harmonic

NФ= meridional stress resultant per unit length of middle surface

Ne= circumferential stress resultant per unit length of middle surface

NθФ, NФθ = shearing stress resultants per unit length of middle surface

p'= design wind pressure coefficient

p= a constant reference load intensity per unit area of middle surface

per = critical buckling pressure

PФ, Pθ, Pz =load components per unit area of middle surface

Qθ, QФ = transverse shear stress resultants per unit length of middle surface

R 0= horizontal radius

r b = base radius

H b= vertical distance from the throat to basin sill level


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r t= top radius

Ht= vertical distance from the throat to the top of the shell

Y= vertical coordinates

< f > = angle between vertical and the normal to an element of the shell

Θ= the circumferential angle

γ= Poisson's ratio of concrete

IS 875 (part 3)-1987: Code of practice design loads (other than earthquake)

A = surface area of a structure or part of a structure

Ae= effective frontal area

Az = an area at height z

b= breadth of a structure or structural member normal to the wind stream. in the horizontal

plane

Ct= force coefficient/drag coefficient

Cfn= normal force coefficient

C't= frictional drag coefficient

C p= pressure coefficient

C pe= external pressure coefficient

CPt= internal pressure coefficient

d = depth of a structure or structural member parallel to wind stream

D= diameter of cylinder

F= force normal to the surface

Fn= normal force

Ft= transverse force

F'-= frictional force;

h = height of structure above mean ground level

hx = height of development of a velocity profile at a distance x down wind from a change in

terrain category

k1, k2, k3 = Multiplication factors


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K= Multiplication factor

l = length of the member or greater horizontal dimension of a building

pa = design wind pressure

pz = design wind pressure at height z

pe = external pressure

p1= internal pressure

Re = Reynolds number

Vb = regional basic wind speed

Vz = design wind velocity at height z

x = distance down wind from a change in terrain category

θ = wind angle from given axis

α = inclination of the roof to the horizontal

β = effective solidity ratio

ф = solidity ratio

z = a height or distance above the ground

ε = average height of the surface roughness

IS 1893 (Part 1): 2002: Criteria for earthquake resistant design of

structures

Ah= Design horizontal seismic coefficient

Ak =Design horizontal acceleration spectrum value for mode k of vibration

bi = ith Floor plan dimension of the building perpendicular to the direction of force

c =Index for the closely-spaced modes

d = Base dimension of the building, in meters, in the direction in which the seismic force is

considered.

DL = Response quantity due to dead load

edi = Design eccentricity to be used at floor i calculated as per 7.8.2

esi = Static eccentricity at floor i defined as the distance between centre of mass and center of

rigidity


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TO STUDY THE EFFECT OF SEISMIC AND WIND LOADS ON HYPERBOLIC COOLING

TOWER OF VARYING DIMENSIONS AND RCC SHELL THICKNESS

DEPT. OF CIVIL, GCE Page 1

CHAPTER-1

INTRODUCTION OF HYPERBOLIC COOLING

TOWER:

1.1 GENERAL INTRODUCTION:

Hyperbolic cooling towers are large, thin shell reinforced concrete structures which

contribute to environmental protection and to power generation efficiency and reliability.

Hyperbolic reinforced concrete cooling towers are widely used for cooling large quantities of

water in thermal power stations, refineries, atomic power plants, steel plants, air conditioning

and other industrial plants. Natural-draught cooling towers are used in nuclear power plants

as heat exchangers. These shell structures are submitted to environmental loads such as

seismic and thermal gradients that are stochastic in nature. Due to the complexity of the

building procedure, uncertainties in the material properties as well as differences between the

theoretical and the real geometry also exist. A series of a hyperbolic cooling tower as shown

in Fig1.1

Fig 1.1: Group of cooling tower

Figure 1.2 summarizes the historical development of natural draft cooling towers. Technical

cooling devices first came into use at the end of the 19th century. The well-known hyperbolic

shape of cooling towers was introduced by two Dutch engineers, Van Iterson and Kuyper,

who in 1914 constructed the first hyperboloid towers which were 35 m high. Soon, capacities

and heights increased until around 1930, when tower heights of 65 m were achieved. The


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first such structures to reach higher than 100 m were the towers of the High Marnham Power

Station in Britain. Today’s tallest cooling towers, located at several EDF nuclear power

Plants in France, reach heights of about 170 m. And it is predicted that 200 m high towers

will be constructed in the early 21st century.

FIG.1.2: Historical development of Natural draft cooling tower

1.2 TYPES OF COOLING TOWERS:

This section describes the two main types of cooling towers: the natural draft and mechanicaldraft cooling towers.

1.2.1 NATURAL DRAFT COOLING TOWER:

The natural draft or hyperbolic cooling tower makes use of the difference in temperature

between the ambient air and the hotter air inside the tower. As hot air moves upwards

through the tower (because hot air rises), fresh cool air is drawn into the tower through an air

inlet at the bottom. Due to the layout of the tower, no fan is required and there is almost no

circulation of hot air that could affect the performance. Concrete is used for the tower shell

with a height of up to 200 m. These cooling towers are mostly only for large heat duties

because large concrete structures are expensive. There are two main types of natural draft

towers:


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1. Cross flow tower (Figure 1.3): air is drawn across the falling water and the fill is

located outside the tower

2. Counter flow tower (Figure 1.4): air is drawn up through the falling water and the fill

is therefore located inside the tower, although design depends on specific site

conditions.

Fig 1.3: Cross flow cooling tower Fig1.4: Counter flow cooling tower

1.2.2 MECHANICLA DRAFT COOLING TOWER:

Because of their huge shape, construction difficulties and cost, natural draft towers have beenreplaced by mechanical draft towers in many installations. Mechanical draft towers have

large fans to force or draw air through circulated water. The water falls downwards over fill

surfaces, which helps increase the contact time between the water and the air. Cooling rates

of mechanical draft towers depend upon various parameters; such as fan diameter and speed

of operation, fills for system resistance, etc. There are two different classes of mechanical

draft cooling towers:

1. Forced draft:

2. Induced draft:


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1.3 COMPONENTS OF NATURAL DRAFT COOLING

TOWER:

The most prominent component of a natural draft cooling tower is the huge, towering shell.

This shell is supported by diagonal, meridional, or vertical columns bridging the air inlet.

The columns, made of high-strength reinforced concrete, are either prefabricated or cast in

situ into moveable steel forms. After the erection of the ring of columns and the lower edge

member, the climbing formwork is assembled and the stepwise climbing construction of the

cooling tower shell begins (Figure 1.5). Fresh concrete and reinforcement steel are supplied

to the working site by a central crane anchored to the completed parts of the shell, and are

placed in lifts up to 2 m high (Figure 1.6). After sufficient strength has been gained, the

complete forms are raised for the next lift to enhance the durability of the concrete and to

provide sufficient cover for the reinforcement; the cooling tower shell thickness should not

be less than 16 to 18 cm. The shell itself should be sufficiently stiffened by upper and lower

edge members. In order to achieve sufficient resistance against instability, large cooling

tower shells may be stiffened by additional internal or external rings. These stiffeners may

also serve as a repair or rehabilitation tool.

Fig1.5: Fabrication of supporting columns Fig1.6: Climbing construction of shell


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1.4 COOLING TOWER MATERIALS:

Cooling tower structures are constructed using a variety of materials. While package cooling

towers are generally constructed with fiber glass, galvanized steel or stainless steel in specialsituation, many possibilities exits for field erected structure. Field erected towers can be

constructed of redwood, fiber glass, steel or concrete. Each material has advantage &

disadvantage.

1. Galvanized steel :

The most cost-effective material of construction for packaged tower in G-235 hot dip

galvanized steel, from both structural & corrosion resistance stand point. G-235 is the

heaviest galvanizing mill commercially available and offers a substantial amount of

protection as compared to the lighter zinc thickness used several decades ago, providing

reliable corrosion protection for most HVAC and industrial system water chemistries. The

most common upgrade from G-235 galvanized steel in type 304 stainless steel. Parts that are

submerged during operation and at shutdown can benefit the most by upgrading to stainless

steel.

2. Stainless steel:

Type 304 stainless steel construction is recommended for cooling tower that are to be used in

a highly corrosive environment.

3. Concrete Towers:

Large field erected towers for power plant and refinery applications are constructed of

concrete. Concrete towers will last more than 40 yrs, but they are the most expensive to

build, because of their cost. They represent only 2-3% of all field erected towers some times

concrete construction is also used for architectural reasons (where the tower is disguised to

look like or blend with a building) or the cooling towers is designed as a structure with a life

expectancy equal to the facility it serves.


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4. Fiber Reinforced plastic towers:

Currently the first growing segment of the cooling tower market is structure built with

pultruded FRP sections. This inert inorganic material is strong, light weight, chemically

resistant and able to handle a range of PH values fire-retardant.FRP can eliminate the cost of

a fire protection system, which can equal 5-12% of the cost of a cooling tower.

1.5 IS: 11504-1985 RECOMMENDATIONS FOR COOLING

TOWER:

· The following loading should be considered

1. Dead load

2. Wind load

3. Earthquake forces

4. Thermal resistant loads

5. Construction loads

6. Any other loads such as snow loads, foundation settlement etc

· Tower design considerations

1. Size and shape: The base diameter, air intake, opening height, tower height

and throat diameter are basically designed by thermal consideration

2. Spacing: It is recommended that cooling towers in group be spaced at clear

distance of not less than 0.5 times the base diameter of the largest cooling

tower in the group.

3. Tower shell analysis: This shall be in accordance with general accepted

principles of structural mechanics and sound engineering practices.

The following stipulations are made:

ü Analysis shall be as per the accepted theories of elasticity

applicable to thin shell of revolution.

ü For elastic analysis concrete may be assumed to be un-cracked,

homogeneous and isotropic.

ü Attention in drawn to the possibility of Wind induced

vibrations in the shell.


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Fig 1.7: Location of BTPS

1.8 OBJECTIVE:

1. To analyze the hyperbolic cooling tower by using finite element analysis (FEA).

2. For the purpose of comparison an existing tower should be considering, bellary

thermal power plant (details from KPCL, Bangalore) and studied the seismic and

wind loads of hyperbolic cooling tower.

3. For other models dimensions and rcc shell thickness is varied with respect to

reference tower.

4. Analysis has been carried out using 8 noded 93 shell elements using ANSYS V.10.

5. The out come of result is Max deflection, Max Principal stress & strain & Von mises

stress & strain.

1.9 ORGANIZATION OF THESIS:

CHAPTER 1: INTRODUCTION OF HYPERBOLIC COOLING TOWER

CHAPTER 2: LITERATURE REVIEW

CHAPTER 3: REINFORCED CONCRETE SHELL

CHAPTER 4: INTRODUCTION TO FEM PACKAGE USED ANSYS

CHAPTER 5: DETAILS OF ELEMENT UTILIZED FOR THIS ANALYSIS

CHAPTER 6: ANALYSIS PROCEDURE AND CALCULATION


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CHAPTER 7: TABULATION AND RESULTS

CHAPTER 8: CONCLUSSION

CHAPTER 9: RECOMMENDATIONS FOR FURTHER STUDIES

REFERENCES

APPENDIX A: JOURNAL PAPER

APPENDIX B: GEOMETRIC DRAWING OF BTPS

APPENDIX C:

1) IS: 11504:1985., Criteria for structural design of reinforced concrete natural draught

cooling tower, New Delhi, India: Bureau of Indian standards.

2) IS: 875 (Part3):1987. Code of practice for design loads (other than earthquake loads)

for buildings and structures. New Delhi, India: Bureau of Indian Standards.

3) IS 1893 (part 1): 2002 Criteria for earthquake resistant design structure.


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CHAPTER-2

REVIEW OF LITERATURE:

2.1 INTRODUCTION:

The field of finite element analysis of shells and shell structures has been very widely researched

consequently enormous literature was available regarding various aspects of their behavior. It

would be impossible to cover all such publications; therefore some selected segments of the

literature were presented herein by the way providing the literature survey. The important aspect

in such publications was concisely presented in the form of the abstracts of the subject matter

presented in such publications. Hence, it was opined that the listing of the abstracts of theselected segment of the literature should serve the purpose of literature review adequately. The

literature available on the investigations on the hyperbolic cooling tower is presented.

2.2 REVIEWS ON HYPERBOLIC COOLING TOWER:

Ø Response of natural draught cooling tower to wind load.

Journal: ARPN Journal of Engineering and Applied Sciences, VOL. 7, NO. 1, JANUARY

2012 ISSN 1819-6608,

Author: G. Murali.

This paper deals with the study of two cooling towers of 122m and 200m high above ground

level. These cooling towers have been analyzed for wind loads using ANSYS software by

assuming fixity at the shell base. The wind loads on these cooling towers have been

calculated in the form of pressures by using the circumferentially distributed design wind

pressure coefficients as given in IS: 11504-1985 code along with the design wind pressures at

different levels as per IS:875 (Part 3)- 1987 code. The analysis has been carried out using 8-

noded shell element (SHELL 93) with 5 degrees of freedom per node.

The results of the analysis include: Membrane forces, Bending moments. The vertical

distribution of membrane forces and bending moments along 0° and 70° meridians and the


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circumferential distributions at base, throat and top levels have been studied for both the

cooling towers. For circumferential distribution, non-dimensional values have been obtained

by normalizing the membrane forces and bending moments using the reference values at 0°

meridian.

Ø Finite element analysis for structural response of cooling

tower shell considering alternative supporting systems:

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

Author: Esmaeil Asadzadeh.

He studied the following kind of supports to the shell part of the tower. Such as Fixity at the

base, I type of column support at the base, 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.

ØResponse analysis of an RC cooling tower under seismic andwindstorm effects

Journal: Acta Polytechnica Vol. 46 No. 6/2006

Author: D. Makovicka,

The paper compares the RC structure of a cooling tower unit under seismic loads and under

strong wind loads. The calculated values of the envelopes of the displacements and the

internal forces due to seismic loading states are compared with the envelopes of the loading

states due to the dead, operational and live loads, wind and temperature actions. The seismic

effect takes into account the seismic area of ground motion 0.3g and the ductility properties

of a relatively rigid structure. The ductility is assessed as the reduction in seismic load.


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Fig 3.1: Aircraft hangar at, Orly, France

3.2 REINFORCED CONCRETE THIN SHEL STRUCTURES:3.2.1 Thin shell:

1. Definition - A thin shell is a curved slab whose thickness h is small compared with its

other dimensions and compared with its principal radius of curvature.

2. Middle surface - The surface that bisects the shell is called the middle surface. It

specifies the form of this surface and the thickness h at every point.

3. Analysis of thin shells consists the following steps:

· Establish equilibrium of a differential element cut from the shell

· Achieve strain compatibility so that each element remains continuous with

each adjacent element after deformation.

4. Stress resultants and stress couples


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3.2.2 Shell theories:

1. The Kirchhoff-Love theory - The first-approximation of shells

Assumptions:

1) The shell thickness is negligibly small in comparison with the least radius of curvature of

the shell middle surface.

2) Strains and displacements that arise within the shells are small.

3) Straight lines that are normal to the middle surface prior to deformation remain straight

and normal to the middle surface during deformation, and experience no change in

length.(Analogous to Navier’s hypothesis for beams - Bernoulli-Euler theory for beams)

4) The direct stress acting in the direction normal to the shell middle surface is negligible.

Results of the assumptions:

1) Normal directions to the reference surface remain straight and normal to the

deformed reference surface.

2) The hypothesis precludes any transverse-shear strain, i.e., no change in the right angle

between the normal and any line in the surface.

3) It is strictly applicable to thin shells.

4) It is not descriptive of the behavior near localized loads or junctions. (Assumption (4)

is not valid in the vicinity of concentrated transverse loads.

2. The Flugge-Byrne theory - The second-approximation of shells

Assumptions:

1) It adopts only assumption (2).

2) It is referred to as “higher-order approximations” of the Kirchhoff-Love assumptions


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3.3 Classification of shells:

Classified by governing equation of geometry:

1. Paraboloid of revolution

2. Hyperboloid of revolution

3. Circular cylinder

4. Elliptic paraboloid

5. Hyperbolic paraboloid

6. Circular cone


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CHAPTER-4

INTRODUCTION TO FEM PACKAGE USED ANSYS:

4.1 FINITE ELEMENT ANALYSIS PROGRAMS:

Computer implementation of finite elements and solution procedures for engineering

analysis is addressed. The end product is a general-purpose finite element analysis program.

For such software to be used as an effective CAE tool, the programming should be hardware

independent. The chosen finite elements and numerical methods must be accurate and reliable.

The program should be executable on a given platform of choice - single processor, multi-

processor, parallel processor, etc. A general purpose FEA program consists of three modules: a preprocessor, a solver, and a postprocessor. Commercial FEA programs can handle very large

number of nodes and nodal degrees of freedom provided a powerful hardware is made available.

User's manual, theoretical manual, and verification problems manual, document a commercial

FEA program. Surveys of general-purpose programs for finite element analysis have been

published [3.1]. At present FEA programs are used rather than written. Understanding of the

organization, capabilities, and limitations of commercial FEA programs is generally more

important than an ability to develop or even modify a FEA code.

The purpose of this chapter is to describe the organization and desirable capabilities of a

general-purpose FEA program. A brief description of widely distributed and extensively used

commercial FEA codes is included so that the reader is aware of their current capabilities.

Benchmark constitutes a standard set of test problems devised to assess the performance of FEA

codes. The practical issue of developing a viable FEA program and its implementation in the PC

environment is a much larger challenge. Typically, it involves hundreds of human year's effort.

4.1.1 FEA PROGRAM: ORGANIZTION

The four components shown in Fig. 4.1 are common to virtually all general-purpose FEA

programs The INPUT phase enables the user to provide information relating to geometric

representation, finite element discretization, support conditions, applied loads, and material

properties. The more sophisticated commercial FEM systems facilitate automated generation of


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nodes and elements and provide access to a material property database. Plotting of the finite

element model is also possible so that errors if any, in the input phase, may be delected and

corrected prior to performing computations. The finite element library comprises the element

matrix generation modules. Herein resides the coded formulative process for the individual

finite elements. Ideally, the element library is open-ended and capable of accommodating new

elements to any degree of complexity. This phase generates the required element matrices

and vectors.

Fig4.1: Component of a general purpose finite element analysis program

The assembly module includes alt matrix operations necessary to position the element

matrices for connection to neighboring elements and the connection process itself. The latter

operation thereby produces the global matrix equation of the finite element model. The

solution phase operates on the governing matrix equation of the problem derived in the

previous phase. In the case of a linear static analysis, this may mean no more than the

solution of a set of linear algebraic equations for a known right-hand side. In the case of

linear vibration and buckling analysis, this may mean the extraction of Eigen values and

Eigen vectors. Transient response analysis will require computations over a time history of

applied load.

Finally, the results phase provides the analyst with a record of the solution. The record is

commonly a printed list of nodal d.a.f, element strains and stresses, reaction forces

corresponding to constrained degrees of freedom and a host of other requested

information. As in input phase, there is a trend toward graphical output of results such as


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plots of displacement and stress contours, modes of vibration and buckling, etc. A

commercial FEM system therefore consists of three basic modules; pre-processor; solver;

and post-processor. These modules and their functions are illustrated in Fig. 9.2. The pre-

processor allows the user to create geometry or input CAD geometry, and provides the

tools for meshing the geometry. The solver lakes the finite element mode! Provided by the

pre-processor and computes the required response. The post-processor takes the data from

the solver and presents it in a form that the user can understand.

4.2 MATERIAL MODELS:

To cover a large number of metallic and non-metallic materials and a wide range of their

behavior, a general-purpose FEA program should provide a library of material models:

1. Homogeneous, isotropic, linear, elastic

2. Ortho tropic

3. Anisotropic

4. Nonlinear elastic

5. Elastic plastic

6. Viscoelastic

7. Viscoplastic8. Temperature-dependent material properties.

4.3 ELEMENT LIBRARY:

The available elements are for solid, structural, thermal and fluid flow analysis. They can be

classified as follows:

1. One-dimensional elements

Ø 1-D.2-D, 3-D bar elements

Ø Linear/quadratic/cubic in order

2. Two-dimensional elements

Ø Triangular/quadrilateral in shape


Ø With straight/curved edges


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3. Axisymmetric ring elements

Ø Triangular/quadrilateral in shape


ØWith flat/curved surfaces4. Three-dimensional elements

Ø Tetrahedra/hexahedra/pentahedra in shape


Ø With flat/curved faces

5. Beam elements

Ø Euler-Bernouli theory/shear deformation theory

Ø 1-D, 2-D, 3-D beam elements

6. Plate elements

Ø Kirchhoff theory/Mindlin theory

Ø Triangular/quadrilateral shapes


Ø With straight-curved edges

7. Shell elements

Ø Flat shell elements/facet approximation.

Ø Curved shell elements: triangular/quadrilateral shapes; quadratic/cubic orders.

Ø Axisymmetric shell elements: with curved surfaces; linear/quadratic/cubic in

order.

Some of these elements are formulated to handle large displacements, large rotations and

finite strains. Some formulations use reduced integration with hourglass control.

4.4 PROCEDURES LIBRARY:

1. Linear static analysis

2. Linear dynamic analysis: Free vibration, mode superposition, response spectrum


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4.5 FEA PROGRAM:

1. ANSYS

2. MSC.Nastran

3. NISA

4. MARC

5. LS-DYNA

4.5.1 ANSYS V.10: This fem package used for analysis.

ANSYS V.10 is an integrated design analysis tool based on the FEM developed by ANSYS,

Inc. It has its own tightly integrated pre- and post-processor. The ANSYS productdocumentation is excellent and it includes commands reference; operations guide; modeling

and meshing guide; basic analysis procedures guide; advanced analysis guide; element

reference; theory reference; structural analysis guide; thermal analysis guide;

electromagnetic fields analysis guide; fluid dynamics guide; and coupled field analysis

guide. Taken together, these manuals provide descriptions of the procedures, commands,

elements, and theoretical details needed to use the ANSYS program. All of the above

manuals except the ANSYS theory reference are available online through the ANSYS help

system, which can be accessed either as a standalone system or from within the ANSYS

program. A brief description of the information found in each of the manuals follows.

Engineering capabilities of ANSYS products are: structural analysis (linear stress, nonlinear

stress, dynamic, buckling); thermal analysis (steady state, transient, conduction, convention,

radiation, and phase change); CFD analysis (steady state, transient, incompressible,

compressible, laminar, turbulent); electromagnetic fields analysis (Magnetostatics,

electrostatics); field and coupled field analysis (acoustics, fluid-structural, fluid-thermal,

magnetic-fluid, magnetic-structural, magnetic-thermal, piezoelectric, thermal-electric,

thermal-structural, electric-magnetic); sub-modeling; optimization; and parametric design

language.


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Element library in ANSYS lists 189 finite elements, they are broadly grouped into: LINK,

PLANE, BEAM, SOLID, CONTAC, COMBIN, PIPE. MASS, SHELL, FLUID, SOURCE,

MATRIX, HYPER, VISCO, INFIN, INTER, SURF, etc. Under each type, different shapes

and orders complete the list. Obviously ANSYS has the best elements in its library.

Analysis procedures in ANSYS can be grouped into: static analysis; transient analysis;

mode frequency analysis; harmonic response analysis; buckling analysis; sub-structuring

analysis; and spectrum analysis.

4.5.2 BASIC PROGRAM STRUCTURE:

Treatment of engineering problems basically contains three main parts: create a

model, solve the problem, analyse the results. ANSYS, like many other FE-programs, is also

divided into three main parts (processors) which are called preprocessor, solution processor,

postprocessor. During the analysis you will communicate with ANSYS via a Graphical User

Interface (GUI), which is described below and seen in Figure 4.3.

Fig 4.2: ANSYS graphical user interface


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The element mesh can in ANSYS be created in several ways. The most common way is that

it is automatically created, however more or less controlled. For example you can specify a

Certain number of elements in a specific area, or you can force the mesh generator to

maintain a specific element size within an area. Certain element shapes or sizes are not

recommended and if these limits are violated, a warning will be generated in ANSYS. It is up

to the user to create a mesh which is able to generate results with a sufficient degree of

accuracy.

4.5.2.2 SOLUTION:

Here you solve the problem by gathering all specified information about the problem:

1. Apply loads: Boundary conditions are usually applied on nodes or elements. The

prescribed quantity can for example be force, traction, displacement, moment,

rotation. The loads may in ANSYS also be edited from the preprocessor.

2. Obtain solution: The solution to the problem can be obtained if the whole problem is

defined.

4.5.2.3 GENERAL POSTPROCESSOR:

Within this part of the analysis you can for example:

1. Visualize the results: For example plot the deformed shape of the geometry or

stresses.

2. List the results: If you prefer tabular listings or file printouts, it is possible.


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CHAPTER-5

DETAILS OF ELEMENT UTILIZED FOR THIS

ANALYSIS: SHELL93, 8-NODE STRUCTURAL SHELL.

5.1 SHELL93 ELEMENT DESCRIPTION:

SHELL93 is particularly well suited to model curved shells. The element has six

degrees of freedom at each node: translations in the nodal x, y, and z directions and rotations

about the nodal x, y, and z-axes. The deformation shapes are quadratic in both in-plane

directions. The element has plasticity, stress stiffening, large deflection, and large strain

capabilities.

FIG 5.1: SHELL 93 GEOMETRY

5.2 SHELL93 INPUT DATA:

The geometry, node locations, and the coordinate system for this element are shown in FIG-

5.1 the element is defined by eight nodes, four thicknesses, and the orthotropic material

properties. Midside nodes may not be removed from this element. A triangular-shaped

element may be formed by defining the same node number for nodes K, L and O. Orthotropic

material directions correspond to the element coordinate directions. The element coordinate

system orientation is as described in Coordinate Systems. The element x and y-axes are in the


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plane of the element. The x-axis may be rotated an angle THETA (in degrees) toward the y-

axis. The element may have variable thickness. The thickness is assumed to vary smoothly

over the area of the element, with the thickness input at the corner nodes. The thickness at the

Midside nodes is taken as the average of the corresponding corner nodes. If the element has a

constant thickness, only TK (I) need be input. If the thickness is not constant, all four

thicknesses must be input. If the total thickness of any shell element is greater than twice the

radius of curvature, ANSYS issues an error. If the total thickness is greater than one-fifth but

less than twice the radius of curvature, ANSYS issues a warning. ADMSUA is the added

mass per unit area.

Element loads are described in Node and Element Loads. Pressures may be input as surface

loads on the element faces as shown by the circled numbers on Figure 1: "SHELL93

Geometry". Positive pressures act into the element. Edge pressures are input as force per unit

length. Temperatures may be input as element body loads at the "corner" locations (1-8)

shown in Figure 1: "SHELL93 Geometry". The first corner temperature T1 defaults to

TUNIF. If all other temperatures are unspecified, they default to T1. If only T1 and T2 are

input, T1 is used for T1, T2, T3, and T4, while T2 (as input) is used for T5, T6, T7, and T8.

For any other input pattern, unspecified temperatures default to TUNIF. Only the lumped

mass matrix is available.

KEYOPT (8) = 2 is used to store midsurface results in the results file for single or multi-layer

shell elements. If you use SHELL, MID, you will see these calculated values, rather than the

average of the TOP and BOTTOM results. You should use this option to access these correct

midsurface results (membrane results) for those analyses where averaging TOP and

BOTTOM results is inappropriate; examples include midsurface stresses and strains with

nonlinear material behavior, and midsurface results after mode combinations that involve

squaring operations such as in spectrum analyses. A summary of the element input is given in"SHELL93 Input Summary". A general description of element input is given in "SHELL93

Input Summary".


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5.3 SHELL93 INPUT SUMMARY:

1. Nodes: I, J, K, L, M, N, O, P

2. Degrees of Freedom: UX, UY, UZ, ROTX, ROTY, ROTZ

3. Real Constants: TK (I), TK (J), TK (K), TK (L), THETA, ADMSUA.

See Table 1: "SHELL93 Real Constants" for a description of the real constants.

4. Material Properties: EX, EY, EZ, ALPX, ALPY, ALPZ (or CTEX, CTEY, CTEZ or

THSX, THSY, THSZ), (PRXY, PRYZ, PRXZ or NUXY, NUYZ, NUXZ), DENS,

GXY, GYZ, GXZ, DAMP

5. Surface Loads: Pressures - Face 1 (I-J-K-L) (bottom, in +Z direction), face 2 (I-J-K-

L) (top, in -Z direction), face 3 (J-I), Face 4 (K-J), face 5 (L-K), face 6 (I-L)

6. Body Loads: Temperature – T1, T2, T3, T4, T5, T6, T7, T8

7. Special Features: Plasticity, Stress stiffening, large deflection, large strain, birth and

death, Adaptive descent.

TABLE 5.1: SHELL93 Real Constants


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5.4 SHELL93 ASSUMPTION AND RESTRICTIONS:

5.4.1 ASSUMPTION:

Zero area elements are not allowed. This occurs most often whenever the elements are not

numbered properly. Zero thickness elements or elements tapering down to a zero thickness at

any corner are not allowed. The applied transverse thermal gradient is assumed to vary

linearly through the thickness. Shear deflections are included in this element. The out-of-

plane (normal) stress for this element varies linearly through the thickness. The transverse

shear stresses (SYZ and SXZ) are assumed to be constant through the thickness. The

transverse shear strains are assumed to be small in a large strain analysis. This element may produce inaccurate stresses under thermal loads for doubly curved or warped domains.

5.4.2 RESTRICTIONS:

When used in the product(s) listed below, the stated product-specific restrictions apply to this

element in addition to the general assumptions and restrictions given in the previous section.

ANSYS Professional:

1. The DAMP material property is not allowed.

2. The special features allowed are stress stiffening and large deflection.


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CHAPTER 6:

ANALYSIS PROCEDURE & CALCULATIONS:

6.1 DESCRIPTION OF THE GEOMETRY OF THE

COOLING TOWER:

For the purpose of comparison an existing cooling tower is consider, (BTPS, Karnataka). The

total height of the tower is 143.5 m. As shown in Fig. 6.2, the tower has a base, throat and top

radii of 55 m, 30.5 m and 31.85 m respectively, with the throat located 107.75 m above the

base. It has a shell-wall thickness of 200 mm at throat level and 500 mm at top. For other

models the dimensions and rcc shell thickness is varied with respect to reference tower.

Geometric details of models as shown in Table: 6.1. The boundary condition of the cooling

tower has been top end free and bottom end is fixed. The material properties of the cooling

tower have young modulus 31GPa, poission ratio 0.15 and density of rcc 25 Kg/m3.

X

Y

9.2

98.55

35.75

143.5

Rb=55

Rt=31.85

Rthr=30.5

Figure 6.1: Geometry of BTPS

107.75


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CT 1: Bellary thermal power plant as reference tower.

CT 2: Decrease the dimensions & increase the thickness of cooling tower.

CT 3: Increase the dimensions & decrease the thickness of cooling tower.

Table 6.1: Geometric details of hyperbolic cooling towers

SI

noDescription

S mbols

Parametric value

CT1

(BTPS. Ref)

CT2

(decreased)

CT3

(increased)

1 Total height H 143.5 m 136.2 m 150.67 m

2 Height of throat Hthr 107.75 m 102.36 m 113.13 m

3 Diameter at top Dt 63.6 m 60.5 m 66.8 m

4 Diameter at bottom D b 110 m 104.5 m 115.5 m

5 Diameter at throat

level

Dthr 61 m 57.94 m 64 m

6 Column Height 9.2 m 8.74 m 9.66 m

7 Thickness at throat Tthr 200mm 250mm 150mm

6.1.1 GEOMETRIC CALCULATIONS:

The geometry of the hyperboloid revolution:

………….. (6.1)

In which R o is the horizontal radius at any vertical coordinate, Y with the origin of

coordinates being defined by the center of the tower throat, a o is the radius of the throat & b

is some characteristic dimension of the hyperboloid.


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The dimensions taken for CT2 & CT3 are satisfying the equation 6.1.

All calculation has been calculated using excel program.

1. CT 1: Bellary thermal power plant as reference tower.

At Bottom:

ao = 30.5 m

R o=55 m

Y= -107.75 m

Substitute in equation 6.1 we get b=71.88 m

At Top:

ao = 30.5 m

R o=31.85 m

Y= 35.75 m


Table 6.2: Input Geometry values to create model in ANSYS for CT1

Key

Points

X axis

(mm)

Y axis

(mm)

1 51800 98550

2 45200 78550

3 39350 58500

4 34650 38550

5 31500 18550

6(origin)

0 0

7 30650 10000

8 30950 20000

9 551077 35750


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2. CT 2: Decrease the dimensions & increase the thickness of cooling tower.

At Bottom:

ao = 32.025 m

R o=57.75 m

Y= -113.13 m


At Top:

ao = 32.025 m

R o=33.44 m

Y= 37.53 m



Key

Points

X axis

(mm)

Y axis

(mm)

1 54474.91 103478

2 47859.34 83477.5

3 41932.86 63477.5

4 37027.84 43477.5

5 33354.71 23477.5

6(origin)

0 0

7 32177.6 10000

8 32483.8 20000

9 33492.3 37530


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3. CT3: Increase the dimensions & decrease the thickness of cooling tower.

At Bottom:

ao = 28.975 m

R o=52.975 m

Y= -102.36 m


At Top:

ao = 28.975 m

R o=30.25 m

Y= 33.96 m

Substitute in equation 6.1we get b=113.235 m


Key

Points

X axis

(mm)

Y axis

(mm)

1 492113 93625

2 42637.7 73625

3 36859.2 53625

4 32305.3 33625

5 29547.7 13625

6

(origin)

0 0

7 29087.7 10000

8 29423.4 20000

9 30250.2 33960


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6.2 EARTHQUAKE FORCES:

The seismic analysis will be carried out for 0.5g, 0.6g & 0.7g (g: Gravity acceleration 9810

KN/m2) in accordance with IS: 1893 by modal analysis of the hyperbolic cooling towers, theearthquake analysis of the shell will be carried out by response spectrum method. Earthquake

analysis for the fill supporting structures (RCC frames) will be carried out by response

spectrum method. For the Calculation of the Design Spectrum, the following Factors were

considered as per IS 1893(Part I)-2002.

Zone factor: For Zone III = 0.16, as per table 2, pg16 IS 1893 (part 1):2002

Importance factor I = 1.5, as per table 6, pg 18 IS 1893 (part 1):2002

Response reduction factor R = 3, as per table 7, pg 23 IS 1893 (part 1):2002

Average response acceleration coefficient Sa/g =Soft soil site condition, as per clause 6.4.5,

pp16 IS 1893 (part 1):2002

For Soft soil sites

1+15T, 0.00£T£0.10

Sa/g 2.50 0.10£T£0.67

1.67/T 0.67£T£4.00

The design horizontal seismic coefficient Ah for a structure shall be determined by the

following expression: Maximum considered Earthquake (MCE) of 2% probability

……………. (6.2)

Provided that for any structure with T ≤ 0.1 s, the value of Ah will not be taken less than Z/2

whatever be the value of I/R.


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Where

Z= Zone factor is for the Maximum Considered Earthquake (MCE) and service life of

structure in a zone. The factor 2 in the denominator of Z is used so as to reduce the

Maximum Considered Earthquake (MCE) zone factor to the factor for Design Basis

Earthquake (DBE).

I = Importance factor, depending upon the functional use of the structures,

characterized by hazardous consequences of its failure, post- earthquake functional

needs, historical value, or economic importance.

R= Response reduction factor, depending on the perceived seismic damage

performance of the structure, characterized by ductile or brittle deformations.

However, the ratio (I/R) shall not be greater than 1.0. The values of R for buildings

are given in the code.

Sa/g= Average response acceleration coefficient, In case design spectrum is

specifically prepared for a structure at a particular project site, the same may be used

for design at the discretion of the project authorities. For rock and soil sites and based

on appropriate natural periods and damping of the structure. These curves represent

free field ground motion.

The Design acceleration spectrum for vertical motions, when required, may be taken as two-

thirds of the design horizontal acceleration spectrum.

Note: All calculation has been calculated using excel program


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TABLE 6.5: Design spectrum for 0.5G

FREQUENCY(HZ)

AhX &Z

Dircn

AhZ Dircn

0.25 0.0167 0.0111

0.33 0.0223 0.0148

0.5 0.0334 0.0223

1 0.0668 0.0445

1.33 0.0891 0.0594

1.54 0.1 0.0667

1.67 0.1 0.0667

10 0.1 0.0667

11.11 0.094 0.0627

12.5 0.088 0.0587

14.29 0.082 0.0547

16.67 0.076 0.0507

20 0.07 0.0467

25 0.064 0.0427

33.33 0.058 0.0387

40

0.055 0.036750 0.052 0.0347

Fig 6.2: Response spectra graph for 0.5g


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TABLE 6.6: design spectrum for 0.6G

FREQUENCY

(Hz)

Ah

X & Z

DIRN

Ah

Y-DIRN

0.250.02 0.0134

0.330.0267 0.0178

0.50.0401 0.0267

10.0802 0.0534

1.330.1069 0.0713

1.540.12 0.08

1.67

0.12 0.0810 0.12 0.08

11.110.1128 0.0752

12.50.1056 0.0704

14.290.0984 0.0656

16.670.0912 0.0608

200.084 0.056

250.0768 0.0512

33.33 0.0696 0.0464

400.066 0.044

500.0624 0.0416


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TABLE 6.7: Design spectrum for 0.7G

FREQUENCY

(Hz)

Ah

X & Z

DIRN

Ah

Y-DIRN

0.250.0234 0.0156

0.330.0312 0.0208

0.50.0468 0.0312

10.0935 0.0623

1.330.1247 0.0831

1.540.14 0.0933

1.670.14 0.0933

100.14 0.0933

11.110.1316 0.0877

12.50.1232 0.0821

14.290.1148 0.0765

16.670.1064 0.0709

200.098 0.0653

25 0.0896 0.0597


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33.330.0812 0.0541

400.077 0.0513

500.0728 0.0485


6.3 WIND LOADS:

The wind pressure on the towers will be assessed on theoretical basis as given in IS 875

(part 3): 1987. The complete cooling tower will be designed for all possible wind

directions and on the basis of worst load conditions as obtained from the theoretical

methods. The wind pressure at a given height [Pz] will be computed as per the

stipulations of IS: 875 (part 3)-1987. For computing the design wind pressure at a given

height the basic wind speed (V b) will be taken as V b=39 m/s at 9.2m height above mean

ground level. For computing design wind speed (Vz) at a height z, the risk coefficient

K 1=1.06 will be considered. For coefficient K 2 terrain category 2 as per table 2 of IS: 875

(part-3)-1987 will be considered. The wind direction for design purpose will be the one

which world induces worst load condition. Coefficient K 3 will be 1 for the tower under

consideration. The wind pressure at a given height wills b e computed theoretically in

accordance to the IS codal provision. Computation of wind pressure (Pz) along the wind

direction by Gust factor method.


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For estimating the wind load on the tower and other elements, will be based on IS: 875 (part-

3) 1987. Design of the tower will satisfy quasi-static method and GF method.

For the Calculation of the wind pressure, the following Factors were considered as per IS 875

(part 3)-1987.

Variation of Hourly mean wind speed with height: The variation of hourly mean wind speed

with height shall be calculated as follows:

Pz = 0.6 Vz2 N/m

2…………. (6.3)

Vz =V bxK 1xK 2xK 3……………… (6.4)

Where,

Vz = Hurly mean wind speed in m/s at height z,

V b = Regional basic wind speed in m/s, 39m/s as per pp10, fig 1 IS 875 (part 3)-1987.

K 1 = Risk coefficient factor, as per clause 5.3.1, pp8 IS 875 (part 3)-1987.

K 2 = Terrain and height factor, from Table 33 IS 875 (part 3)-1987

K 3 = Topography factor, as per clause 5.3.3, pp8 IS 875 (part 3)-1987.

Table 6.8: Results of variation of hourly mean wind speed with height for CT1

H Vb K 1 K 2 K 3 Vz Pz(N/m2)

9.2 39 1.06 0.670 1 27.69 460.3

29.2 39 1.06 0.787 1 32.52 634.8

49.2 39 1.06 0.848 1 35.04 736.7

69.2 39 1.06 0.877 1 36.25 788.4

89.2 39 1.06 0.905 1 37.40 839.6

108.475 39 1.06 0.925 1 38.31 880.7

134.33 39 1.06 0.947 1 39.16 920.5


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Table 6.9: Results of variation of hourly mean wind speed with height for CT 2

Height Vb K 1 K 2 K 3 Vz Pz(N/m2)

8.74 39 1.06 0.670 1 27.698 460.3

28.74 39 1.06 0.785 1 32.450 631.8

48.74 39 1.06 0.846 1 34.983 734.3

68.74 39 1.06 0.876 1 36.224 787.3

88.74 39 1.06 0.904 1 37.381 838.4

105.55 39 1.06 0.924 1 38.216 876.3

127.585 39 1.06 0.942 1 38.945 910.0

Table 6.10: Results of variation of hourly mean wind speed with height CT 3

Height Vb K 1 K 2 K 3 Vz Pz(N/m2)

9.66 39 1.06 0.670 1 27.698 460.3

29.66 39 1.06 0.789 1 32.602 637.7

49.66 39 1.06 0.850 1 35.119 740.0

69.66 39 1.06 0.878 1 36.277 789.6

89.66 39 1.06 0.906 1 37.434 840.8

109.66 39 1.06 0.928 1 38.352 882.5

121.39 39 1.06 0.937 1 38.740 900.5

141.1 39 1.06 0.953 1 39.392 931.0


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Along wind load – along wind load on a structure on a strip area (Ae) at any height (z) if

given by:

Fz= Cf Ae Pz G……… (6.5)

Where

Fz = along wind load on the structure at any height z corresponding to strip area Ae

Cf = Force coefficient for the building

Ae = Effective frontal area considered for the structure at height z

Pz = Design pressure at height z due to hourly mean wind obtained as 0.6* (Vz)2

(N/m2)

G = Gust factor (peak load/mean load) and is given by

Where

gf = peak factor defined as the ratio of the expected peak value to the root mean value of

afluctuating load, and

r = roughness factor which is dependent on the size of the structure in relation to the ground

roughness.

The, value of ‘gf r’ is given in Fig. 1,

B = background factor indicating a measure of slowly varying component of fluctuating

wind load and is obtained from, from fig 9, pp50 IS 875 (part 3)-1987

SE/β = measure of the resonant component of the fluctuating wind load,

S = size reduction factor, from fig 10, pp 51 IS 875 (part 3)-1987

………. (6.6)


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E = measure of available energy in the wind stream at the natural frequency of the structure,

from fig 11, pp52 IS 875 (part 3)-1987

β= damping coefficient (as a fraction of critical damping) of the structure , from table 34

pp52 IS 875 (part 3)-1987

ф= And is to be accounted only for buildings less than 75 m high in terrain Category 4 and

for buildings .less than 25 m high in terrain Category 3, and is to be taken as zero in all other

cases.

as per clause 8.3,pg52,IS-875(part3):1987

Where, Cy= Lateral correlation constant which may be taken as 10 in the absence of more

precise load data,

Cz = longitudinal correlation constant which may be taken as 12 in the absence of more

precise load data,

b = breadth of a structure normal to the wind stream

h= height of a structure,

Vb = hourly mean wind speed at height t,

f o = natural frequency of the structure, and

Lh = a measure of turbulence length scale.

GUST FACTOR AND WIND PRESSURE CALCULATIONS:

1. CT 1: Bellary thermal power plant as reference tower.

Cy =10, as per clause 8.3, pp 52 IS 875 (part 3)-1987.

Cz =12m, as per clause 8.3, pp 52 IS 875 (part 3)-1987.

Lh = 1700, from fig 8, pp50 IS 875 (part 3)-1987.


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gfr = 0.85, from fig 8, pp50 IS 875 (part 3)-1987.

f o = natural frequency = 0.8210858, as per clause 7, pp48, IS 875 (part 3)-1987.

Damping Value (β) = 0.016, as per table 34, pp52 IS 875 (part 3)-1987.

Table 6.11: Gust factor results for CT 1

Table 6.12: ANSYS input wind pressure results for CT1

H B λ Fo S

Cz x h/

Lh B Ф

fo x Lh/

Vz

E SE/β GF

9.2 103.6 9.4 3.24 0.04 0.065 0.71 0.1791 49.84 0.04 0.1 1.886

29.2 90.4 2.6 8.75 0.041 0.206 0.7 0.1778 42.44 0.042 0.107 1.883

49.2 78.7 1.3 13.68 0.044 0.347 0.7 0.1778 39.39 0.045 0.123 1.889

69.2 69.3 0.8 18.6 0.045 0.488 0.68 0.1752 38.08 0.047 0.132 1.88

89.2 63 0.6 23.24 0.03 0.63 0.65 0.1713 36.9 0.048 0.09 1.842

108.47 61.9 0.5 27.59 0.025 0.766 0.61 0.166 36.03 0.048 0.075 1.808

134.33 63.7 0.4 33.42 0.03 0.948 0.61 0.166 35.24 0.05 0.093 1.817

F(N/mm )

Degrees

(θ)

Height (m)

9.2 29.2 49.2 69.2 89.2 108.475 134.33

0 0.000434 0.00023 0.000278 0.000296 0.000773 0.000319 0.000334

15 0.00026 0 0 0 0.000464 0 0

30 -0.00035 -0.00084 -0.00097 -0.00104 -0.00062 -0.00111 -0.00117

45 -0.00104 -0.00179 -0.00209 -0.00222 -0.00186 -0.00239 -0.00251

60 -0.00148 -0.00239 -0.00278 -0.00296 -0.00263 -0.00319 -0.00334

75 -0.00182 -0.00287 -0.00334 -0.00356 -0.00325 -0.00382 -0.00401

90 -0.00191 -0.00299 -0.00348 -0.00371 -0.0034 -0.00398 -0.00418

105 -0.00148 -0.00239 -0.00278 -0.00296 -0.00263 -0.00319 -0.00334


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2. CT 2: Decrease the dimensions & increase the thickness of cooling tower

Cy =10, as per clause 8.3, pp 52 IS 875 (part 3)-1987.

Cz =12, as per clause 8.3, pp 52 IS 875 (part 3)-1987.

L h = 1600, from fig 8, pp50 IS 875 (part 3)-1987.

Gfr = 0.9, from fig 8, pp50 IS 875 (part 3)-1987.

fo = natural frequency = 0.833182481, as per clause 7, pp48, IS 875 (part 3)-1987.

Damping Value (β) = 0.016, as per table 34, pp52 IS 875 (part 3)-1987.


120 -0.00061 -0.0012 -0.00139 -0.00148 -0.00108 -0.00159 -0.00167

135 -0.00087 -0.00155 -0.00181 -0.00193 -0.0015 -0.00207 -0.00217

150 -0.00078 -0.00143 -0.00167 -0.00178 -0.00139 -0.00191 -0.00201

165 -0.00078 -0.00143 -0.00167 -0.00178 -0.00139 -0.00191 -0.00201

180 -0.00078 -0.00143 -0.00167 -0.00178 -0.00139 -0.00191 -0.00201

H b Λ Fo S

Cz x h/

Lh B Ф

fo x Lh/

Vz

E SE/β GF

8.74 104.5 10 3.15 0.045 0.066 0.72 0.1909 48.12 0.04 0.112 1.958

28.74 82.6 2.4 8.85 0.04 0.216 0.71 0.1896 41.07 0.045 0.112 1.951

48.74 73.7 1.3 13.93 0.051 0.366 0.7 0.1882 38.10 0.046 0.146 1.959

68.74 64.6 0.8 18.97 0.045 0.516 0.69 0.1869 36.79 0.047 0.132 1.946

88.74 59 0.6 23.73 0.03 0.666 0.65 0.1814 35.65 0.049 0.091 1.900105.55 58.8 0.5 27.61 0.027 0.792 0.62 0.1772 34.87 0.05 0.084 1.874

127.58 60.5 0.4 32.75 0.032 0.957 0.60 0.1743 34.22 0.05 0.10 1.867


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Table 6.14: ANSYS input wind pressure results for CT 2

Degrees

(θ)

F(N/mm )

Height

8.74 28.74 48.74 68.74 88.74 105.55 127.585

0 0.000451 0.000247 0.000288 0.000306 0.000319 0.000328 0.00034

15 0.00027 0 0 0 0 0 0

30 -0.00108 -0.00086 -0.00101 -0.00107 -0.00111 -0.00115 -0.00119

45 -0.00153 -0.00185 -0.00216 -0.0023 -0.00239 -0.00246 -0.00255

60 -0.00189 -0.00247 -0.00288 -0.00306 -0.00319 -0.00328 -0.0034

75 -0.00198 -0.00296 -0.00345 -0.00368 -0.00382 -0.00394 -0.00408

90 -0.00153 -0.00308 -0.0036 -0.00383 -0.00398 -0.00411 -0.00425

105 -0.0009 -0.00246 -0.00287 -0.00306 -0.00318 -0.00328 -0.00339

120 -0.00063 -0.00161 -0.00187 -0.00199 -0.00207 -0.00214 -0.00221

135 -0.00081 -0.00123 -0.00144 -0.00153 -0.00159 -0.00164 -0.0017

150 -0.00081 -0.00148 -0.00173 -0.00184 -0.00191 -0.00197 -0.00204

165 -0.00081 -0.00148 -0.00173 -0.00184 -0.00191 -0.00197 -0.00204

180 -0.00081 -0.00148 -0.00173 -0.00184 -0.00191 -0.00197 -0.00204


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3. CT 3: Increase the dimensions & decrease the thickness of cooling tower.

Cy =10, as per table 34, pp52 IS 875 (part 3)-1987

Cz =12, as per clause 7, pp48, IS 875 (part 3)-1987

L h = 1750, pp50 IS 875 (part 3)-1987

Gfr = 0.82, from fig 8, pp50 IS 875 (part 3)-1987

fo = natural frequency = 0.7925409, as per clause 8.3, pp 52 IS 875 (part 3)-1987

Damping Value (β) = 0.016, as per clause 8.3, pp 52 IS 875 (part 3)-1987


H b λ Fo S

Cz x h/

Lh B Ф

f o x Lh/

Vz E SE/β GF

9.66108.

9 9.4 3.3 0.049 0.06 0.71 0.1727 50.07 0.039 0.11 1.858

29.66 95.6 2.7 8.7 0.04 0.2 0.69 0.1703 42.54 0.041 0.1 1.839

49.66 83.9 1.4 13.4 0.045 0.34 0.69 0.1703 39.49 0.045 0.12 1.849

69.66 74.1 0.9 18.3 0.039 0.47 0.68 0.169 38.23 0.046 0.11 1.837

89.66 67.2 0.6 22.8 0.035 0.61 0.65 0.1653 37.05 0.047 0.1 1.814

109.6 64.2 0.5 27.2 0.03 0.75 0.62 0.1614 36.16 0.047 0.08 1.788

121.9 64.9 0.5 24.8 0.032 0.69 0.62 0.1614 35.8 0.049 0.09 1.793

141.1 66.9 0.4 34.1 0.25 0.96 0.61 0.1601 35.2 0.049 0.76 2.033

Table 6.16: ANSYS input wind pressure results for CT 3

Degrees

(θ)

F(N/mm )

Height (M)

9.66 29.66 49.66 69.66 89.66 109.66 121.39 141.1

0 0.000428 0.000235 0.000274 0.00029 0.00030 0.000316 0.00032 0.00037

15 0.000257 0 0 0 0 0 0 0

30 -0.00034 -0.00082 -0.00096 -0.00107 -0.0010 -0.0011 -0.0011 -0.0013

45 -0.00103 -0.00176 -0.00205 -0.00218 -0.0022 -0.00237 -0.00242 -0.0028

60 -0.00145 -0.00235 -0.00274 -0.0029 -0.0030 -0.00316 -0.00323 -0.0379


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6.4 ANALYSIS STEPS INVOLVED IN FINITE ELEMENT

MODELLING:

6.4.1 PREPROCESSING: DEFINING THE PROBLEM

1. Give example a Title

Utility Menu > File > Change Title ...

/title, CT

2. Create Key points

Preprocessor > Modeling > Create > Key points > In Active CS

3. Define Lines

Preprocessor > Modeling > Create > Lines > Lines > splines Line

4. Symmetrical model

Preprocessor> Modeling>Operate>Extrude>line>About Axis

5. Define Element Types

For modeling we have used 8 noded shell93.

75 -0.0018 -0.00282 -0.00328 -0.00348 -0.0036 -0.00379 -0.00387 -0.0045

90 -0.00188 -0.00293 -0.00342 -0.00363 -0.0038 -0.00395 -0.00404 -0.0047

105 -0.00145 -0.00234 -0.00273 -0.00290 -0.0030 -0.00315 -0.00322 -0.0037

120 -0.00086 -0.00152 -0.00178 -0.00189 -0.0019 -0.00205 -0.0021 -0.0024

135 -0.0006 -0.00117 -0.00137 -0.00145 -0.0015 -0.00158 -0.00161 -0.0018

150 -0.00077 -0.00141 -0.00164 -0.00174 -0.0018 -0.00189 -0.00194 -0.0022

165 -0.00077 -0.00141 -0.00164 -0.00174 -0.0018 -0.00189 -0.00194 -0.0022

180 -0.00077 -0.00141 -0.00164 -0.00174 -0.0018 -0.00189 -0.00194 -0.0022


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6.4.2 DEFINE REAL CONSTANT

Preprocessor > Real Constants... > Add...

6.4.3 DEFINE ELEMENT MATERIAL PROPERTIES

Preprocessor > Material Props > Material Models > Structural >

Linear > Elastic > Isotropic

In the window that appears, enter the following geometric properties

Young's modulus EX:

Poisson's Ratio PRXY:

Density:

6.4.4 MESH

1. Define Mesh Size

Preprocessor > Meshing > Manual Size > Size Controls > Lines > picked Lines...

2. Mesh the frame

Preprocessor > Meshing > Mesh > Area > click 'Pick All'.

6.4.5 SOLUTION: ASSIGNING LOADS & SOLVING

1. Define Analysis Type

For Static analysis:

Solution > New Analysis > Static

For Modal analysis:

Solution > New Analysis > modal

For Spectrum analysis:

Solution > New Analysis > spectrum


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2. Apply Constraints

Solution > Define Loads > Apply > Structural > Displacement > On Nodes

3. Apply Loads

Solution > Define Loads > Apply > Structural > Force/Moment > Inertia

force> Gravity> Global

4. Apply Pressure

Solution > Define Loads > Apply > Structural > Pressure > Elements

5. Solve the System

Solution > Solve > Current LS

6.4.6 GENEREL POSTPROCESSING: VIEWING THE RESULTS

1. To view the element in 3D rather than a line:

Utility Menu > Plot Ctrls > Style > Size and Shape

2. View the deflection contour plot.

3. View the stress and strain in contour plot


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CHAPTER-7

TABULATION AND RESULTS:

1. CT 1: Reference cooling tower.

2. CT 2: Decrease the Dimensions of cooling tower & Increase the thickness.

3. CT 3: Increase the Dimension of cooling tower & Decrease the thickness.

7.1 STATIC ANALYSIS:

Ø Creating geometric model:

Fig 7.1: Key points to create CT model Fig 7.2: Geometric model

Fig 7.3 Boundary condition Fig 7.4: Thickness of rcc shell


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Fig 7.5: Element number in model Fig 7.6: Nodes number in model

Ø Static analysis:

First we create the geometry of the model in ANSYS by using key points & we have to input

material models, shell element & make mesh to model in Preprocessor. By assigning the

loads to the model and selecting Static analysis and solve the problem in solution & read the

results in General post processor.

Fig 7.7: Deflection for CT 1


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DEPT. OF CIVIL, GCE

Study the Effects of Seismic and Wind Loads on Hyperbolic Cooling Tower

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Transcript of Study the Effects of Seismic and Wind Loads on Hyperbolic Cooling Tower