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70

CHAPTER 4

STEEL LATTICE TOWERS

4.1 TRANSMISSION LINE TOWERS

In the power industry, steel lattice towers are commonly used for

transmission of power through electrical conductors from the place of power

generation to the place of distribution. The transmission line towers support

electrical power conductors and ground-wires at suitable height above ground

to satisfy certain functional requirements. It is reported that transmission line

towers contribute to about 35-45% of the total cost of a transmission line.

Hence optimisation of tower design can therefore result in substantial economy.

Great responsibility thus rests on the design engineer who has to prepare not

only economical, but also safe and reliable design. Structurally the tower should

be adequate to resist loads such as wind load, snow load and self-weight.

4.1.1 Specification of Transmission Line Towers

Transmission line towers are generally specified by voltage, number

of circuits and type. Thus, these parameters become the basic parameters, which

govern structural design of the tower.

71

The voltage classification of transmission line towers is according to

the voltage of the line it carries. The common voltages used in India for power

transmission are 110 kV, 220/230 kV and 440 kV.

The configurations adopted are generally rectangular and square

types. The square type broad based towers are the most commonly used. The

number of circuits the tower can carry is either single, double or multi circuit.

The number of earth wires, right of way, etc. also affect the configuration of the

tower. Along the transmission line route, depending upon the profile along the

centre line of the transmission line, towers are classified into three categories

such as tangent tower, angle tower and dead end tower. Further, transmission

line towers are also classified according to their shape as Barrel, Corset and

Guyed towers.

The Barrel type towers are considered in this study for optimisation as

the generation and geometrical data are modular based. The functional

requirements such as minimum ground clearance, and clearance between

conductor and tower body, are governed by the electrical regulations and they

mainly depend on the voltage carried by the conductor. The number of circuits

decides the number of cross arms on the tower. Parameters such as number of

cross arms, vertical spacing between cross arms, height of ground-wire peak,

minimum ground clearance, maximum sag and other clearances decide the

overall height of the tower. The staging of transmission line tower should be

high enough to provide minimum ground clearance under maximum sag

condition. As transmission line towers have components such as a number of

cross arms and ground-wire peaks, the staging below the bottom cross arm is

more useful for optimisation than the portion above.

72

4.1.2 Transmission Line Tower Configuration

Typical barrel type and corset type transmission line tower

configurations are shown in Figure 4.1. Choosing a preliminary configuration is

pre-requisite for detailed analysis and design of a transmission line tower and

this is to be chosen based on functional and structural requirements. The

geometric parameters of transmission line tower configuration are height of the

tower, base width of the tower, top-hamper width, length and depth of cross-

arm. Some of the parameters governing the geometry of a tower are shown in

Figure 4.2. Approximate structural behaviour of the tower or conventional

practice is taken as the basis for fixing these parameters of the tower. Sag

tension and clearances also play an important role in deciding the configuration.

4.1.3 Tower Configuration Parameters

For optimisation of transmission line towers, it is important to know

various design parameters that control the design of the tower. Some of the

parameters that dictate the configuration of the transmission line towers are

briefly described below:

Tower Height: The height of the tower is determined by parameters

such as number of cross arms, vertical spacing between cross arms, height of

ground-wire peak, minimum ground clearance, maximum sag and other

clearances. The cost of the tower increases with the height of the tower. Hence,

it is desirable to keep the tower height minimum to the extent possible without

sacrificing the structural safety and functional requirement such as ground

clearance and electrical clearance.

73

BARREL TYPE TOWERS

NARROW BASE BARREL TYPE TOWER

CORSET TOWER

Figure 4.1 Typical Barrel and Corset Tower Configurations

74

n

~n

E

ABCD

-- Ground wire peak — Cross arm height ~ Panel height-Vertical spacing between

conductors

E - Staging F -- Base width G -- Panel width H1, H2 - Cross arm length I - Top hamper width

Figure 4.2 Geometric Parameters of a Transmission Line Tower

75

Sag: The conductor wires and ground-wires sag due to self-weight.

The size and type of the conductor, wind and climatic conditions of the region

and span length determine the conductor’s sag and tension. Span length is fixed

from economic considerations. The maximum sag occurs at the maximum

temperature and still wind conditions. Sagging of the conductor cables is

considered in determining the height of the tower. It is essential to have

minimum clearance between the bottom-most conductor and the ground, at the

point where the sag is maximum. Sag tension is the force on the conductor,

which in turn is transferred to the tower. Sag tension is maximum at the time of

maximum temperature and when wind is at maximum. Loads such as self

weight and snow load on the conductors contribute to the sag tension.

Spacing between the towers, ground level difference between tower

locations, the mechanical properties of the conductors and ground-wires decide

the sag distance and sag tension in the cables. The conductors assume catenary

profile and the sag is calculated based on parabolic formulae or procedure given

in codes of practices.

Minimum Ground Clearance: Power conductors along the entire

route of the transmission line should maintain requisite clearance to ground

over open country, national highways, important roads, electrified and

unelectrified railway tracks, navigable and non-navigable rivers,

telecommunication and power lines, etc. as laid down in various national

standards. The maximum sag for the normal span of the conductor should be

added to the minimum ground clearance to get the staging height of the tower,

i.e. the vertical distance from the ground level to the bottom of the lowest cross

arm.

76

Ground-wire peak: Ground-wire peaks are provided to support the

ground-wires, which shield the tower from lightning and provide earthing to the

tower. The height of the ground-wire peak is chosen in such a way that the

cross arm falls within the shield angle. The bottom width of the ground-wire

peak is assumed equal to the top hamper width and is normally 0.75m to lm.

Cross-arm spacing: Cross arms are provided to support the

transmission line power conductors. The number of circuits carried by the tower

determines the number of cross arms. In general three cross arms for single

circuit towers and six cross arms for double circuit towers are required. The

vertical spacing between the cross arms must satisfy the minimum clearance

between circuit lines and other electrical requirements. The minimum

horizontal clearance required between the conductors and the tower steel is

based on the swing conditions, and it determines the length of the cross arm.

The depth of the cross arm is assumed in general such that the angle at the tip of

the arm is in the range of 15 to 20 degrees.

Base Width: The base width of the tower is determined heuristically.

For example, the ratio of base width to total height may vary from one-tenth for

tangent towers to one-fifth for large angle tower. Also, there are formulae for

preliminary determination of economical base width. The widths may be varied

to satisfy other constraints like foundation design and land availability.

Top Hamper Width: Top hamper width is the width of the tower at

lower cross-arm level. The top hamper width is also determined heuristically

and is generally about one third of the base width. Other parameters like

horizontal spacing between conductors and slope of the leg may also be

considered while determining the top hamper width.

77

4.2 MICROWAVE TOWERS

Steel lattice towers are also used in electronic and communication

industries for communication of microwave signals through different types of

antennas. Several antennae are fixed on the tower in different directions at

different heights as per the requirement and usage. The antenna positions decide

the height of the tower. Symmetrical cross sections are preferred for microwave

towers due to reversal of wind direction. Generally steel lattice towers with

square or triangular plan are used for microwave towers. Angle sections and

tubes are commonly used for the fabrication of these towers. Microwave towers

are generally self-supporting steel lattice towers. Guyed towers are also used for

microwave communication, but are least preferred for supporting heavy disc

antennae. Wind load on the tower body and antennae is the major load on the

structure besides the self-weight of the tower. Microwave towers are generally

supported either at ground or at rooftop of some buildings. The tip deflection of

the tower is a governing parameter for the functional requirement. Typical

configuration of a 102-m high microwave tower is shown in Figure 4.3. The

tower is triangular in plan. The two-dimensional and three-dimensional views

of the tower are shown.

4.3 GEOMETRICAL MODELLING OF STEEL LATTICE

TOWERS

The mathematical modelling is an important step in the design of steel

lattice towers. Steel lattice towers are treated as a pin jointed skeletal system.

The influence of dimension in modelling is presented below:

N> Is

) N>

78

§<-

3 m3 m 3,rff~

JnT

3 m7^3 m

3 ni

7^

3 m7 ~

~?C3 m 3 it?

3 n? 3 n?

6 in

6 m

6 m

6 m

6 m

6 m

6 m

6 m/

6 m

6 m

7^

71~

-7<-n"7 ~

7

7 ~

7^

* 16.5 m

2-D VIEW 3-D VIEW

Figure 4.3 Typical Configuration of a 102 m Triangular Microwave Tower

79

4.3.1 One-Dimensional Modelling

In one-dimensional modelling, the tower is treated as a cantilever

beam-column with varying inertia along the height. The properties of the beam

are calculated assuming that the legs are the flanges of an equivalent I-beam so

that the moment of inertia and area can be used in calculating the forces due to

bending and axial loads. But the effect of bracing and torsion are very difficult

to include mainly because the contribution of each of these in resisting the load

as a beam can be done only by approximations. Further, as the beam is non-

prismatic and skeletal, the approximations completely neglect the integral

action of the members. This brings in disproportionate distribution of loads on

to the various components resulting in either over-design or under-design.

4.3.2 Two-Dimensional Modelling*

Even though one dimensional beam model of a square tower gives an

idea of the general behaviour of the tower, the spatial nature of the system calls

for better modelling, reflecting the response more realistically. Here again,

basic engineering knowledge can be extended to visualise in two-dimension so

that axial, lateral and torsional loads are distributed in an appropriate way on to

the four faces of the tower. Typically lateral and axial loads are transferred

equally on to the two faces of the tower. For torsion, the resisting couple for the

torsional moment is assumed to be provided by shear on four faces. Using this

distribution of the loads on the faces, member forces are determined using

method of joints. Here again conservation in stiffness and absence of integrated

action prevent realistic estimation of forces in all members leading to over-

design.

80

4.3.3 Three-Dimensional Modelling

In three-dimensional modelling, the tower is considered as it is, so

that all the loads can be accounted for simultaneously. The member

participation in the response of the tower for axial, bending and torsional effects

is taken into account. But amenability of three-dimensional model to hand

calculation is very difficult. Hence, the tower has to be modelled and analysed

using one of the numerical techniques and computer programming.

The mathematical model of a steel lattice tower is preferably a space

truss for computer analysis. Hence three-dimensional geometric models are

used to represent the mathematical model of the tower. Geometric modelling

and configuration processing are prerequisites for any lattice tower analysis.

Configuration processing refers to the phase in structural analysis where a

mathematical model of a structure is formulated. For example, mesh generation

in finite element analysis is a special case of configuration processing.

Preparation of input data in tower analysis in three-dimension is a tedious and

time-consuming process. Therefore, it is a general practice to write

configuration generator programs to minimise input. The generator, which

reads the input for the tower geometry, generates the data for the analysis

program. The main features of the configuration generator are: ease and

minimisation of input data, automatic generation of joint co-ordinates,

numbering of nodes and members, and members connectivity. Modification can

be done easily and the chances of making errors in input are minimised. These

types of programs are useful to the structural engineers and designers for

configuration optimisation and to evolve various alternatives for analysis and

design. It will considerably reduce the drudgery of data preparation for the

analysis.

81

4.4 MODULAR GENERATION TECHNIQUE

While writing configuration generator, it is preferable to be more

general rather than specific to a particular configuration. For generating tower

configurations, the methods are not generalised and not many attempts have

been made to establish any technique. In an attempt to do so, a knowledge

based modular generation technique has been developed, as this method helps

in the process of optimisation. The tower configuration is decomposed into

various generic modules as shown in Figure. 4.4. Using various combinations

of these modules, it is possible to generate various transmission line tower

configurations and microwave tower configurations. Various modules for

different panels of tower are encoded in the knowledge and can be assembled to

the required configuration of the tower as shown in Figure 4.5.

The modular generator produces the geometry of the tower from

simple input and the function of the generator is shown in the flow chart given

in Figure 4.6. A 220 kV double circuit tangent transmission line tower

generated using this technique is shown in Figure 4.7. The purpose of

considering modules is to simplify the task of generating the tower

configuration. Also, this will enable to generalise the development of

configuration of a similar nature. The modules can be repeatedly used in

different parts to get the desired configuration. The entire height of the

transmission line tower is divided into different segments, such that the leg

members of the tower in that portion have the same slope along the height.

Hence, the width of the tower at any location along its height can be calculated

by linear variation, when the top width and bottom width of the segment are

known. These segments are considered to have one or more panels and each

panel is represented by some module.

82

Figure 4.4 Typical Modules for Tower Modelling

83

EXPLODED VIEW

Figure 4.5 Tower Assembly

84

Figure 4.6. Flow Chart of Modular Generator

851500

Figure 4.7 Geometric Model OF A 220 kV Double Circuit Transmission Line Tower

86

In a way, modules are the representation of any interchangeable

portion or unit of the tower having a particular type of bracing system. Only the

type of module has to be chosen and depending upon the context, appropriate

data for a module are automatically generated. Different modules can be used

for generating different panels, cross arms, and ground-wire peaks. For each

type, varieties of modules may be built in and stored in the knowledge base. By

this way, numerous combinations can be explored to experiment with radically

new structural configurations without much difficulty. This is the major

advantage of decomposing the tower into modules. The system automatically

generates nodes, spatial co-ordinates, member numbers, member groups and

members connectivity for the module locally. They are independent of the full

tower configuration. Then these data are converted to global format for the

required tower configuration. When connecting one module to the other, the

common variables between modules are properly taken into account to

eliminate repetition. Different types of modules with different patterns can be

generated for a particular section and this adds more flexibility to the choice.

4.4.1 Member Grouping

Member grouping has practical significance in tower design as well

as optimisation. Tower members are grouped into different types such as leg

members, diagonal bracing members, tie bracing members and plan bracing

members. Group numbers are assigned to each member to identify the type and

cross section of the member. Freestanding microwave towers and transmission

line towers are subjected to wind load. Reversal in the direction of wind is

always considered, and hence the members are kept identical in each face of the

tower generally. For design purposes, members of similar type at a particular

height or a panel, at a different face of the tower are grouped together with

87

same area of cross section. For example, the leg members in a panel are

considered to be of the same group. Similarly, the diagonal bracing members in

all the faces of a panel are likely to have same section and considered as a

single group entity. The members are designed for the maximum forces in the

group rather than the force in the member. These group numbers are also useful

in identifying the members for applying the design rules such as slenderness

ratio limitations.

4.4.2 Tower Analysis Data

The geometrical data of the tower are generated by assembling the

modules from top to bottom of the tower. While assembling the geometric

model with modules, some parameters like last node, last member, last group

number in each group, are passed internally from module to module for data

continuity. When the generation is done modularly, the input required for

assembling the tower is minimal. The configuration can be changed easily by

changing the modules or the geometric parameters to get a new configuration.

This not only facilitates the analysis and design, but also enables design

revision and optimisation. The top width, number of slopes, bottom width of

each segment, number of the modules, bracing pattern and height of each

module only are specified as input. A 60m high square microwave tower model

having two slopes assembled with modules using this method is shown in

Figure 4.8. The output of the generator contains all the geometrical co-ordinates

of the nodes, member numbers, members’ connectivity, member group numbers

and restrained nodal data. Bottom-most nodes are assumed to be restrained

against all the degrees of freedom.

88

1250H

3-D VIEWALL DIMENSIONS IN mm

Figure 4.8 Geometric Model of a Square Microwave Communication Tower

89

4.5 LOADS

Transmission line towers are subjected to loads acting in all the three

mutually perpendicular directions namely vertical, normal to the direction of

line, and parallel to the direction of line.

4.5.1 Transverse Loads

The load perpendicular to the direction of the line is known as

transverse load. It acts at the points of conductor, i.e. at the tip of the cross arms

and ground-wire support. In addition to that, a load distributed over the

transverse face of the tower due to wind also acts on the tower. Wind load is

applied horizontally, acting in the direction normal to the transmission line. Angle towers are used where the line makes a horizontal angle greater than 2°.

They must resist a transverse load from components of line tension induced by

this angle in addition to the usual wind, ice and broken conductor loads. They

are located such that the axis of the cross-arms bisects the angle formed by the

conductors. The governing wind direction on conductors for the angle condition

is assumed to be parallel to the cross-arms. Wind load over the wind span on

bare or ice-covered conductors, ground-wire and wind load on insulator strings

contribute transverse load on transmission line tower. The two half spans

adjacent to the tower under consideration is known as wind span.

4.5.2 Longitudinal Loads

Longitudinal load on transmission line tower is due to the unbalanced

conductor tensions. It acts on the tower in a direction parallel to the line. The

unbalanced conductor tension may be due to broken wire condition, unequal

90

adjacent spans of the tower, dead-ending of the tower, etc. The unbalanced pull

due to a broken conductor or ground-wire in the case of tension strings is

assumed equal to the component of the maximum working tension of the

conductor or the ground-wire, as the case may be, in the longitudinal direction

along with its component in the transverse direction.

4.5.3 Vertical Loads

Vertical load on transmission line tower is due to the weight of bare or

ice-covered conductor over the governing weight span, weight of insulator,

hardware, etc., covered with ice, if applicable, and a load equal to the weight of

a line man with tools. This vertical load is applied at the ends of the cross-arms

and on the ground-wire peak. The self-weight of the tower acts vertically and is

calculated approximately as this is unknown until the actual design is complete.

This may be revised, if required, before the final design.

4.6 WIND LOAD CALCULATIONS

Wind load is the major load on all freestanding lattice towers. Wind

load on transmission line tower body has to be calculated and transferred to all

panel points to get more realistic effect. As this involves a number of laborious

and complex calculations, it is the general practice to consider the equivalent

loads. These loads are applied on the conductor and ground wire supports

which are already subjected to certain other transverse, longitudinal and vertical

loads.

The projected area is an unknown quantity, but is required for the

wind load calculation. This can be calculated exactly only after the design

91

process is over and actual sections are known. Therefore, it is necessary to

assume certain area to arrive at the wind load on the structure. Depending on

the spread and size of the structure, 15 to 25% of the gross area is generally

taken as the net area. Gross area is the area bounded by the outside perimeter of

single face of the tower. For accounting the wind force on the leeward side, a

factor of 1.5 is used. The wind load on the tower is assumed to act at selected

nodes, generally at the tip of the cross-arms. Some methods suggested by

Murthy (1990) to determine the magnitude of wind load are given below,

In one method, the wind loads on various parts of the tower or the

members are calculated first. Then the moments about the tower base for all

these loads are added and an equivalent load at selected points for that moment

is calculated. The loads applied on the bottom cross-arms are increased with

corresponding reduction in the loads applied on the upper cross-arms in another

method.

The second method is to divide the tower into a number of parts

corresponding to the ground-wire and conductor support points. Based on

solidity ratio, the wind load on each point is then calculated and the moment

due to this wind load about the base is divided by the corresponding height,

which gives the wind load on two points of support.

In another method, the equivalent loads are applied at a number of

points such as ground-wire peak, cross-arm points and waist level. An

approximate solidity ratio is assumed and wind load on different parts of the

tower are determined. An equivalent load, which can produce the same amount

of moment at the base, is transferred to the upper loading point and the

92

remaining part to the base. This process is repeated for various parts of the

tower.

Even though the design wind load based on the last method is more

logical than the others, it is reported that these loads are lower than the actual.

In microwave towers, which are square in plan, the wind load acting

in the diagonal direction of the tower is generally considered to be critical.

Similarly, face wind is critical in microwave towers that are triangular in plan.

In some cases the wind load on antennae may decide the critical wind direction.

An assumed configuration and bracing pattern are used in the preliminary

design. Based on the preliminary design, approximate member sizes are arrived

at for calculating wind load on towers. Recalculation of wind load, if required,

is done before arriving at the final designs. A realistic approach is to apply the

wind load at each node of the tower and this method is possible with computer

programs. A generic load generator based on the modular approach is

developed to calculate the wind load on the tower. The details are given below:

4.7 SELF-WEIGHT AND WIND LOAD GENERATOR

In the calculation of wind load, the projected area is an unknown

quantity and. in the calculation of self-weight, the section weights are unknown.

Hence, the actual quantities of loads can be calculated only after the design

process is complete. But for design, the analysis needs to be completed based

on the load. Hence, it becomes necessary to do an approximate calculation of

load and revise the load after final design in an iterative manner. Generally,

preliminary design calculations are carried out to find the force in members

approximately and the sections are decided based on the experience. Once the

93

sections are assumed, the wind loads as per codal provisions are calculated.

This process is laborious if it is done manually. A computer based method is

necessary to do the process as it may be required to perform calculations

repeatedly whenever there is a change.

The modular generation technique used for tower geometry is also

found suitable for this process. The load generator program is generic and

isolated from other programs so that it can work independently to give wind

load and self-weight on each panel. The basic tower geometry has to be same as

the analytical model. But the modules developed by this program need not be

same as the analytical model. This may include additional members or bracing

patterns. The secondary bracing can also be included in this program for the

purpose of calculating loads. The tower can have the same input as in the case

of geometric model. In addition to that, the input should include the member

sizes for each group of members. The tower is divided into modules. Each

module may represent a panel. The geometric data of the panel is generated

first. The wind load on each panel and self-weight can be calculated from the

geometry of the tower. The wind loads are calculated according to IS:875

(Part 3) - 1987, “Indian Standard Code of Practice for Design Loads (other than

Earthquake) for Buildings and Structures” and are incorporated in the program.

The panel wise wind load generated by this program for a tower shown in

Figure 4.9 is given in Table 4.1. The self-weight of the panels are calculated

using the length of the members and weight per unit length obtained from the

database. This self-weight is assumed to act at all bottom nodes connecting the

panel to the next panel and distributed equally.

94

Table 4.1 Typical output of load generator

Basic Wind Speed Vb: 50 m/s

Design Life in Years : 100

Terrain Category: 2 Class C

kl Factor : 1.08

k3 Factor : 1.00

Force Coeff. for Square Tower with Angles considered

Wind Pressure Pz = 0.6Vz**2 = 0.6{Vb.kl.k2.k3)**2

Design Wind Pressure ■ 0. 6(Vb.kl ■k3.)**2(k2**2) - 178.26(k2**2) Kg/m2

Pan . Ht k2 PZ SR Cf Pz .Cf Exp.Ar. T.D.L. T.W.L. DL si .2W.L .Ho. cm. Kg/m2 Kg/m2 cm2 Kg Kg YSall Sail

1 5875.0 1.1122 220.52 .1380 3.6102 796.14 7652.01 182.71 609.21 .00 77.54

2 5600.0 1.1084 219.00 .1206 3.6970 809.64 8972.50 212.87 726.45 54.81 170.00

3 5300.0 1.1042 217.34 .1194 3.7030 804.82 9903.74 245.75 797.08 63.86 193.91

4 5000.0 1.1000 215.69 .1359 3.6207 780.96 12430.59 310.61 970.78 73.72 225.01

5 4700.0 1.0910 212.18 .1284 3.6582 776.18 12842.88 354.35 996.84 93.18 250.44

6 4400.0 1.0820 208.69 .1277 3.6616 764.13 13867.07 382.77 1059.63 106.30 261.75

7 4100.0 1.0730 205.23 .1272 3.6640 751.98 14900.43 411.47 1120.49 114.83 277.48

8 3800.0 1.0640 201.80 .1220 3.6898 744.62 15340.42 463.26 1142.28 123.44 288.00

9 3525.0 1.0558 198.69 .1377 3.6117 717.60 15319.53 463.48 1099.32 138.98 285.31

10 3250.0 1.0475 195.59 .1356 3.6220 708.44 19170.38 627.03 1358.11 139.04 312.78

11 2850.0 1.0340 190.59 .1135 3.7325 711.36 28900.64 877.80 2055.87 188.11 434.53

12 2350.0 1.0140 183.28 .1068 3.7660 690.25 29728.63 993.10 2052.03 263.34 522.85

13 1850.0 .9910 175.06 .1012 3.7940 664.19 30576.87 1189.19 2030.87 297.93

519.67

14 1350.0 .9580 163.60 .1060 3.7701 616.78 34536.06 1570.83 2130.13 356.76

529.61

15 550.00 .9300 154.18 .1043 3.7786 582.56 83484.92 4373.11 4863.50 471.25

890.14

Total Weight : 12658.33 Kg.

APPLIED LOAD FACTOR « 1.00

95

Figure 4.9 Details of a 60 m Tower for Wind Load Calculations

96

A general database of all angle sections given in IS:808 - 1989

“Dimensions for Hot Rolled Steel Beam, Column, Channel and Angle

Sections”, and tubular sections from IS: 1161 - 1979 “Specification for Steel

Tubes for Structural purposes” are linked to the program. This database

contains the designation, the size, mass, sectional area, moment of Inertia and

the radius of gyration, which are often used in the design.

The variation of k2 factor and design wind pressure along the height

of the tower is given in Figure 4.10. The variation of wind load and dead load

for panels from top to bottom of the tower is shown in Figure 4.11 Since the

height of the bottom most panel is much greater than the rest of the panels the

self weight drastically increases. Also since heavier sections are provided in the

bottom-most panel, it attracts more wind pressure and hence, there is a drastic

increase in the wind pressure in that panel.

4.8 ANALYTICAL PROCEDURE

Steel lattice towers are highly indeterminate space frames with semi

rigid joints and assumptions are made to simplify the complexities involved in

the analysis of the actual tower. It is reported in literature that the comparison

of space frame analysis with space truss analysis showed insignificant

difference (less than 10%) and also different analyses (plane/space/truss/frame)

with and without secondary bracings ultimately gave same member forces.

Hence, the members are considered as three dimensional truss elements for

modelling of the tower. Secondary members are not considered in the analytical

modelling, as these members are assumed to carry less than 2.5% of the main

leg / bracing members.

97

k2 Factor Design Wind Pressure inkN/Sq.m

Height Vs k2 Height Vs Pz

Figure 4.10 Variation of k2 Factor and Design Wind Pressure

98

Height Vs Dead load Height Vs Wind load

Pane

l Num

ber

Pane

l Num

ber

Figure 4.11 Comparison of Dead Load and Wind Load on Panels

99

Self-supporting towers act basically as a-cantilever structure and the

bending moments at different heights of the tower are useful in the preliminary

calculation of width of the tower for the given load.

Matrix method of structural analysis has been used, as large structural

systems like lattice towers can be analysed using matrix method with high

speed computers. Stiffness method, which is also known as Displacement

method or Equilibrium method, which is commonly employed in the analysis of

lattice towers, is adopted in the analysis program. The equations of equilibrium

is given by

[K] [8] = [P] (4.7)

where

[K] = Global stiffness matrix

[8] = Displacement vector

[P] = Force vector

The analysis program solves the set of linear algebraic equations

formed by the above equation using Choleskey’s Decomposition method.

4.9 DESIGN PROCEDURE

Members of lattice towers are designed for either compression or

tension as axial force is the only force in the members. Reversal of loads may

induce alternate nature of force and hence, these members are designed for both

compression and tension. The calculated tensile or compressive stress in

various members shall not exceed the permissible stress limit as prescribed in

the code. For the design of transmission line tower members IS:802 - 1992 -

100

(part 1 / Section 2) - “Use of Structural Steel in Overhead Transmission Line

Towers - Material, Loads and Permissible Stresses” is used. For the design of

microwave towers, IS:800 - 1984 “Indian Standard Code of Practice for

General Construction in Steel” is adopted.

4.10 SENSITIVITY STUDIES WITH RESPECT TO DESIGN

PARAMETERS IN TOWER DESIGN

In engineering design optimisation problems, most of the proposed

methodologies call for assessment of response for any change in design and

configuration variables. For optimal design problems, the direction and the step

length in the complex design space of different tower configurations are

required in some methods. The influence of design variables on selected

performance requirement can identify the most efficient way of modifying a

design concept to obtain the desired structural performance. Studying the

influence of a selected design parameter on the performance of a group, enables

to determine (a) which performance characteristics will benefit most and (b)

which performance characteristics will be most adversely affected. Structural

optimisation codes require the designer to identify all important constraints, the

constraint bounds and the objective function.

Design variables that are most critical to performance and the

performance requirements that are most critically affected by a particular design

variable are valuable information in optimisation. This can help in selecting the

most critical parameters as design variables in optimisation using genetic

algorithm. Hence, sensitivity studies were carried out to estimate the response

for various design parameter changes.

101

In the design of transmission line towers, optimisation possibilities

are more between waist and ground portion and hence, the change in

performance of the design parameters for panels below the waist height alone

are taken. Sensitivity methods for design changes were developed for member

design parameters. Sensitivity studies are needed for the evaluation of response

of transmission line systems when design parameters are varied. So these

studies were carried out for leg and bracing members at different levels below

the waist level to find out the response in terms of stress. The cross sectional

areas of leg and bracing members are taken as design parameter in this study.

They are varied independently keeping the other variables constant. Necessary

relations are derived for evaluating the response.

4.10.1 Sensitivity of Deflection for Leg Members

A typical elevation of a 132 kV tower with numbering scheme and

member groups is shown in Figure 4.12. A three-dimensional truss model is

considered for analysis. Three typical load cases viz., Load case 1- Normal

condition, Load case 2 - Ground wire broken and Load case - 3 Top conductor

broken condition, are considered in the analysis and these load cases are shown

in Figure.4.13 (a), (b) and (c). The leg members in the panel are grouped from

top to bottom with code numbers 1006 to 1009. The code numbers above 1000

and below 2000 are used to identify leg member group in the generation.

Cantilever moment (M) at the bottom of the tower for normal load case - 1 is

calculated and the initial area of bottom leg member group is assumed based on

this moment.

102

Figure 4.12 Typical Elevation of a 132 kv Single Circuit Tower

103

3.766

Figure 4.13. (a) Load case -1(Normal Load Condition)

2.893

Figure 4.13. (b) Load Case -2(Ground-wire Broken Condition)

104

3.766

Figure 4.13 (c) Load Case -3(Top Conductor Broken Condition)

The approximate area is calculated using the equation given below:

Area required

Where

FOS

W

M*FOS W * 0.67 * Fy

(4.8)

Yield Stress of Steel

Factor of Safety

Width at the top of the bottom panel

The nearest area of the equal angle section, from IS Handbook is

chosen as the initial area for all the leg members. The ratio of actual stress to

allowable stress is known as the criticality ratio. The criticality ratio is high in

Load Case - 2 and this may govern the design for the given set of load

105

conditions and initial sections chosen. Hence, the Load Case - 2 is considered

for the deflection sensitivity study.

The changes in deflection due to the change in area of leg members at

different panels are tabulated. The variations of areas and deflections are given

as ratios to the initial section and initial deflections in order to have non-

dimensional quantities for comparison. The change in area of the leg members

at the bottom panel, which is grouped as 1009 and the corresponding change in

maximum deflection of the tower is given in Table 4.2. The deflection vs. the

area behaviour for leg member group 1009 is shown in Figure 4.14.

Table 4.2 Deflection Variation for Leg member group 1009

Area(mm2)

Deflection (8z)

(mm)x = A/Ao a = 8/5o

116.7 151.50 0.1 2.5250

583.5 70.55 0.5 1.1760

1167.0 60.00 1.0 1.0000

2334.0 54.69 2.0 0.9115

11670.0 50.42 10.0 0.8400

The leg members at the panel immediately above the bottom are

grouped as 1008 and same initial area is chosen. The change in area of the leg

members in this group and the corresponding change in maximum deflection is

given in Table 4.3.

Def

lect

ion

Var

iatio

n

106

Figure 4.14 Variation of Deflection Vs Area for Leg Members

Table 4.3 Deflection Variation for Leg member group 1008

Area(mm2)

Deflection (8z)

(mm)x = A/A0 a = 8/6o

116.7 140.50 0.1 2.3417

583.5 69.75 0.5 1.1625

1167.0 60.00 1.0 1.0000

2334.0 55.04 2.0 0.9173

11670.0 51.03 10.0 0.8505

107

Similarly the change in area and corresponding change in deflection

for the leg members at the bottom panel, which is grouped as 1007, is given in

Table 4.4.

Table 4.4 Deflection Variation for Leg Member Group 1007

Area(mm2)

Deflection (8z)

(mm)x = A/A0 a = S/5o

I 116.7 148.1 0.1 2.4683

583.5 72.58 0.5 1.2097

1167.0 60.00 1.0 1.00001 2334.0

53.35 2.0 0.8892

11670.0 47.85 10.0 0.7975

Leg members in fourth panel from the bottom are grouped as 1006

and the change in area and corresponding change in deflection for these leg

members are given in Table 4.5.

Table 4.5 Deflection Variation for Leg Member Group 1006

Area(mm2)

Deflection (8z) 1

(mm)x = AJA0 a = 5/5o

116.7 93.03 0.1 1.5505

583.5 68.53 0.5 1.1422

1167.0 60.00 1.0 1.0000

2334.0 54.32 2.0 0.9053

11670.0 48.79 10.0 0.8132

108

4.10.2 Sensitivity Curves for Deflection

The behaviour is asymptotic and can be divided into three regions.

The first region where the area variation revision is above 10% and below 50%

the deflection can be linearly interpolated. The second region is the centre

portion close to the initial section area, i.e. where the variation of area is

between 50 % and 200% and can be fitted with a curve. A quadratic equation

fitting the curve can be arrived by solving a set of equations satisfying the three

points. The third region where the area revision is above 2.0 times and below 10

times can also be linearly interpolated. For area revisions above 10 times and

below 0.1 time (10%), this fitting is not suitable and it is suggested that the

initial section itself is revised. The quadratic equation for curve fitting is arrived

for values in Table 4.2.

ax2+ bx + c = a (4.9)

0.25a + 0.5 b + c =1.176 (4.10)

a + b + c =1.0 (4.11)

4 a + 2 b + c =0.9115 (4.12)

Solving the above equations, the curve fitting equation is

0.17567 x2-0.61550 x+ 1.43983 =a (4.13)

Where

x = A/A0

a = S/80

8 = Revised Deflection

80 = Initial Deflection

A = Revised Area

A0 = Initial Area

109

Similar equations for other leg member groups in subsequent panels

from bottom to top are also arrived. The quadratic equations for the curves

fitted for the centre three points for all the leg member groups are given in

Table 4.6.

Table 4.6 Equations for Deflection Estimation

Leg

Member Equation

Group

1009 0.17567 x2 - 0.61550 x + 1.43983

1008 0.16153 x2 - 0.56730 x + 1.40577

1007 0.20573 x2 - 0.72800 x + 1.52227

1006 0.12647 x2 - 0.47410 x + 1.34763

4.10.3 Validation of Sensitivity Equations

The validation of the above study can be carried out by finding the

deflection of the tower for an area revision using the above formulation and

compared with the actual deflection by complete analysis with revised area. For

example, the maximum criticality ratio is 1.65 for the bottom panel leg

members. If the area is revised as per this stress ratio, (i.e.) 1.65 times the initial

area, the deflection due to the change in area is calculated without doing a

reanalysis. The new area for this leg member shall be revised as

1.65* A0 = 1.65 * 1167 = 1926 mm2

The deflection using the curve fitted with equation (4.12) is

0.17567 (1.65)2-0.61550 (1.65)+ 1.43983 = a = 8/60 = 0.90251

8 = 0.90251 * 60 = 54.15045 mm

noThe actual deflection calculated by a separate analysis is 55.82 noun.

The sensitivity equation underestimated the actual value of deflection by 3 %.

The estimated value and actual value of deflection for revision of leg

member areas as per stress ratio or criticality ratio are tabulated in Table 4.7. In

all cases the sensitivity equation underestimated the actual value of deflection.

Table 4.7 Comparison of Estimated and Actual Deflection

LegMemberGroup

AreaRevision

A/A0

EstimatedDeflection

(mm)

Actual 1

Deflection(mm)

Difference%

1009 1.65 54.15 55.82 3.00

1008 1.56 54.83 56.44 2.85

1007 1.73 52.71 54.40 3.11

1006 1.42 55.77 56.79 1.80

4.10.4 Sensitivity of Deflection for Bracing Members

The bracing members in the panels are grouped from top to bottom with code numbers. An initial area of 52.7 mm2 is chosen for the member

groups. The analysis is carried out for three typical load cases, viz. Normal

condition, Ground wire broken and Top conductor broken condition. The

criticality ratio is high in the top conductor broken for the given set of load

conditions and the initial sections chosen. Hence this load case is considered

throughout for sensitivity on bracing. Table 4.8 gives the change in deflection

for corresponding change in area of the bottom panel bracing member group.

The deflection and area values are tabulated with variation ratios, which are

normalised with initial section.

Ill

Table 4.8 Deflection Variation for Bottom Bracing Member Group

Area 1 Deflection (5z) 1(mm2) 8 (mm)

x = A/A0 | a = 8/8o

5.27 64.16 0.1 1.00250

26.40 64.03 0.5 1.00047

52.70 64.00 1.0 1.00000

105.40 63.99 2.0 0.99980

527.00 63.98 10.0 0.99970

From the above values, the variation of deflection to the variation of

area is not significant and hence, it can be observed that the sensitivity of

deflection for area change in bracing member is insignificant.

4.10.5 Design Sensitivity

The factors controlling the design of compression members are the

force coming on the member and the allowable stress for the member. But, the

allowable stress depends on the 1/r ratio of the member. The force in the leg

member also changes when the area of the member is changed. Hence, when

the area of the member is revised, both the allowable stress and actual stress on

the member are changed. In order to optimise the design of members, the actual

stress shall be equated to the allowable stress. The allowable stress (aali) is

calculated from the Euler bucking load as below:

crall = n2 El (Ur)2 (4.14)

112

Where

E - Young’s modulus

1 - Length of the member

r - Minimum radius of gyration

The radius of gyration can be approximately defined with a simple

relationship

h - size of the angle leg in mm

For equal angle mild steel sections, the approximate area of the angle

(A) is given by

r = 0.197 h (4.15)

Where

A = 2 t h

h = A / 2t

(4.16)

(4.17)

whereA - Area of the angle section in mm2

t - thickness of the angle in mm

For equal angle sections of thickness 5 mm,

h = 0.1A

and hence,

r = 0.0197 A

aall = 7T2 E/ (1/r)2 = tc2E/( 1/0.0197A)2

(4.18)

(4.19)

113

Substituting E

Gall

2.0 x 105 N/mm2

766.059*A2 /12

Gact = F/A

(4.20)

(4.21)

Equating actual stress to the allowable stress

F/A = 766.059 * A2 /12

V 766.059

Whereaac, - Actual stress in N/mm2

A - Area of the member in mm2

F - Force on the member in N

1 - Length of the member in mm

(4.22)

(4.23)

The forces obtained in the analysis with assumed initial areas can be

used in this expression to arrive at a set of minimum theoretical values of areas.

Using the relationship in equation (4.23), the area required for all the leg

member groups are calculated and given in Table 4.9.

Table 4.9 Estimated Minimum Areas for Leg Members

LegMemberGroup

Force in Member(kN)

Area(mm2)

1009 102.70 1245

1008 97.42 1223

1007 107.60 1265

1006 884.50 1185

114

For bottom bracing member group, the maximum force in the

member is 14760 N. Using the relationship in equation (4.23) the area required

for bracing member group is calculated as below:

Using these areas as the revised area of the member groups,

reanalysis is carried out and it gives a criticality ratio of 0.98, which is very

close to 1. This means the members have attained 98% of their load capacity,

which can lead to optimality. The equation (4.23) is useful for obtaining the

minimum theoretical area required for the members of tower, which in turn

helps in fixing the variable bound for area of cross section of members in the

optimisation process. This can form the knowledge base required for

optimisation.

4,10.6 Sensitivity for Base Width

The forces in the leg members are mostly governed by the base width

as it resists the moment due to load. Hence, the variations of forces in the leg

members are studied by varying the base width. The same tower configuration

and loadings are assumed. The base width is increased by 10% and then by

20%. Similarly the base width is reduced by 10% and then by 20%. The

comparison of maximum force in compression and tension on top leg member

group for different load cases are tabulated in Table 4.10. (a) and (b)

respectively. Similarly for other leg member groups, the values are tabulated in

Tables 4.11. to 4.13.

115

Table 4.10 (a) Comparison of Forces (Compression) in Leg Member

Group 1006

SI. BaseLoad Case -1 Load Case - 2 Load Case - 3

No.

1

WidthForce(kN)

Variation(%)

Force

(kN)

Variation(%)

Force(kN)

Variation

(%) 11 Initial0

Width28.78 0.00 71.94 0.00 62.70 0.00

1 + 10% 27.64 -3.95 69.19 -3.83 54.74 -12.7

2 + 20% 26.69 -7.26 66.89 -7.02 47.95 -23.52

3 - 10% 30.15 +4.74 75.26 +4.61 71.84 +14.58

4 -20% 31.82 +10.56 79.32 +10.25 82.10 +30.94

Table 4.10 (b) Comparison of Forces (Tension) in Leg Member

Group 1006


No. WidthForce(kN)

Variation(%)

Force(kN)

Variation(%)

Force(kN)

Variation(%)

Initial0

Width19.72 0.00 63.11 0.00 72.85 0.00

1 + 10% 18.82 -4.57 60.57 -4.02 75.10 +3.08

2 + 20% 18.06 -8.40 58.43 -7.41 77.08 +5.803 - 10 % 20.79 +5.42 66.17 +4.85 70.60 -3.094 -20% 22.10 +12.08 69.89 +10.75 68.72 -5.68

116


Group 1007

SI

No.Base

Width

Load case -1 Load Case - 2 Load Case - 3

Force(kN)

Variation(%)

Force(kN)

Variation(%)

Force(kN)

Variation(%)

■.............—

0Initial

Width49.76 0.00 111.89 0.00 90.66 0.00

1 + 10% 47.33 -4.89 105.72 -5.52 84.34 -6.98

2 + 20% 45.18 -9.20 100.32 -10.34 83.03 -8.42

3 -10% I 52.52 +5.56 118.76 +6.13 101.30 +11.74

4 -20% I 55.67 +11.88 126.70 +13.23 114.05 +25.80

Table 4.11 (b) Comparison of Forces (Tension) in Leg Member

Group 1007

1 SL BaseWidth

Load Case -1 Load Case - 2 Load Case - 3 |

No.Force(kN)

Variation(%)

Force

(kN)

Variation

(%)

Force

(kN)Variation

(%)

0Initial

Width31.04 0.00 93.50 0.00 137.10 0.00

1 + 10% 28.66 -7.65 87.44 -6.48 132.29 -3.51

2 + 20% 26.57 -14.41 82.08 -12.21 127.39 -7.083 - 10% 33.74 +8.72 100.42 +7.41 141.90 +3.51

4 -20% 36.85 +18.74 108.27 +15.80 146.81 +7.08

117


Group 1008


N°. WidthForce(kN)

Variation(%)

Force(kN)

Variation(%)

Force(kN)

Variation(%)

Initial 10Width

43.19 0.00 91.98 0.00 88.50 0.00

1 + 10% 40.54 -6.13 85.67 -6.86 85.57 -3.30

2 + 20% 38.31 -11.29 80.34 -12.66 82.33 -6.97

3 -10% 46.38 +7.38 99.54 +8.22 91.11 +2.96

4 -20% 50.27 +16.39 108.76 +18.24 93.54 +5.70

Table 4.12. (b) Comparison of Forces (Tension) in Leg Member

Group 1008

|S1.Base

Load Case -1 Load Case - 2 Load Case - 3 j

No. WidthForce(kN)

Variation(%)

Force(kN)

Variation(%)

Force(kN)

Variation(%)

0Initial

Width29.00 0.00 77.97 0.00 138.57 0.00

1 + 10% 26.20 -9.64 71.52 -8.28 130.72 -5.66

2 + 20% 23.83 -17.82 66.05 -15.29 123.27 -11.04

3 -10% 32.34 +11.53 85.70 +9.91 147.10 +6.16

I 41-20% 36.40 +25.53 95.11 +21.98 156.61 +13.02

118


Group 1009


No. WidthForce

(mVariation 1

(%) 1Force

(kN)

Variation

(%)

Force

(kN)

Variation

(%)

0Initial

Width48.96 0.00 102.97 0.00 100.81 0.00

1 + 10% 45.46 -7.15 94.81 -7.92 95.61 -5.16

2 + 20% 42.55 -13.10 88.00 -14.53 90.49 -10.24

3 -10% 53.21 +8.67 112.87 +9.62 106.01 +5.16

4 -20% 58.47 +19.41 125.13 +21.52 111.50 +10.60

Table 4.13 (b) Comparison of Forces (Tension) in Leg Member Group 1009


No. WidthForce

(kN)

Variation

(%)

Force

(kN)

Variation

(%)

Force

(kN)

Variation

(%)

0Initial

Width32.12 0.00 86.33 0.00 156.22 0.00

1 + 10% 28.66 -10.75 78.24 -9.37 144.94 -7.22

2 + 20% 25.78 -19.73 71.47 -17.21 134.74 -13.75

3 - 10% 36.29 +13.01 96.16 +11.39 168.87 +8.104 -20% 41.47 +29.13 108.27 +25.41 183.48 +17.45

119

The comparison of maximum force in compression and tension on

top bracing members group for different load cases are tabulated in

Tables 4.14 (a) and (b) respectively. Similarly for other bracing member

groups, the values are tabulated in Tables 4.15 to 4.17.

Table 4.14 (a) Comparison of Forces (Compression) in Bracing Member

Group 2008

SI.

No.

Base

Width

Load Case -1 Load Case - 2 Load Case - 3

Force

(kN)

Variation

(%)

Force

(kN)

Variation

(%)

Force

(kN)

Variation

(%)

0Initial

Width10.87 0.00 23.37 0.00 81.39 0.00

1 + 10% 11.13 +2.44 22.97 -1.72 79.24 -2.64

2 + 20% 11.33 +4.24 22.53 -3.61 76.98 -5.41

3 - 10% 10.48 -3.52 23.67 +1.30 83.31 +2.36

4 -20% 9.94 -8.48 23.83 +1.97 84.91 +4.33

Table 4.14 (b) Comparison of Forces (Tension) in Bracing Member

Group 2008

SI.

No.

Base

Width


Force

(kN)

Variation

(%)

Force

(kN)

Variation

(%)

Force

(kN)

Variation

(%)

0Initial

Width8.02 0.00 19.05 0.00 82.87 0.00

1 + 10% 8.19 +2.12 18.45 -3.19 78.84 -4.86

2 + 20% 8.30 +3.47 17.82 -6.48 74.86 -9.66

3 - 10% 7.76 -3.20 19.60 +2.88 86.89 +4.85

4 -20% 7.38 -8.00 20.04 +5.20 90.83 +9.61

120


Group 2009

SI.No.

BaseLoad Case -1 | Load Case - 2 Load Case - 3

WidthForce(kN)

Variation 1 (%) 1

Force(kN)

Variation(%)

Force(kN)

Variation

(%) 1Initial I0Width

3.73 0.00 8.86 0.00 38.52 0.00

1 + 10% 3.58 -4.10 8.05 -9.07 34.42 -10.64

2 + 20% 3.42 -8.21 7.35 -17.05 30.87 -19.86

3 -10% 3.87 +3.73 9.77 +10.26 43.29 +12.37

4 -20% 3.97 +6.50 10.79 +21.80 48.88 +26.88

Table 4.15. (b) Comparison of Forces (Tension) in Bracing Member

Group 2009


No. WidthForce(kN)

Variation(%)

Force j (kN))

Variation(%)

Force(kN)

Variation(%)

0Initial

Width5.05 0.00 10.87 0.00 37.83 0.00

1 + 10% 4.86 -3.71 10.03 -7.67 34.60 -8.55

2 + 20% 4.67 -7.46 9.29 -14.52 31.74 -16.10

3 -10% 5.22 +3.40 11.80 +8.66 41.51 +9.72

4 -20% 5.35 +5.94 12.83 +18.05 45.69 +20.76====

121


Group 2010

SI. 1 Base Load Case -1 Load Case - 2 Load Case - 3

No. WidthForce(kN)

Variation(%)

Force(kN)

Variation(%)

Force(kN)

Variation(%)

0Initial

Width3.07 0.00 6.61 0.00 23.04 0.00

1 + 10% 2.90 -5.58 5.99 -9.47 20.65 -10.34

2 + 20% 2.75 -10.65 5.46 -17.45 18.66 -18.99

3 -10% 3.26 +6.03 7.37 +11.36 25.92 +12.52

4 -20% 3.45 +12.22 8.27 +25.06 29.47 +27.93


Group 2010

SI.

No.Base

Width


Force(kN)

Variation(%)

Force(kN)

Variation(%)

Force(kN)

Variation(%)

0Initial

Width2.27 0.00 5.39 0.00 23.46 0.00

1 + 10% 2.13 -5.96 4.81 -10.84 20.55 -12.37

2 + 20% 2.01 -11.36 4.32 -19.91 18.15 -22.62

3 -10% 2.42 +6.39 6.10 +13.08 27.03 +15.22

4 -20% 2.56 +12.79 6.95 +28.97 31.52 +34.36

122


Group 2011

1 SL BaseLoad Case -1 Load Case - 2 Load Case - 3

No. Width Force(kN)

Variation(%)

Force(kN)

Variation(%)

Force(kN)

Variation(%)

0Initial

Width1.59 0.00 3.78 0.00 16.44 0.00

1 + 10% 1.49 -6.53 3.35 -11.36 14.32 -12.892 + 20% 1.40 -12.26 3.00 -20.68 12.60 -23.333 -10% 1.71 +7.33 4.31 +14.14 19.12 +16.354 -20% 1.84 +15.47 4.99 +32.02 22.61 +37.59


Group 2011

SI.No.

BaseWidth

Load Case -1sssssss=sss=sass=ssss=s=ssss==a

Load Case - 2 Load Case - 3

Force

(kN)

Variatio

n (%)

Force

(kN)

Variatio

n (%)

Force

(kN)

Variatio

n (%)

0Initial

Width2.15 0.00 i 4.64 0.00 16.14 0.00

1 + 10% 2.02 -6.14 4.17 -10.03 14.39 -10.87

2 + 20% 1.91 -11.47 | 3.79 -18.25 12.95 -19.74

3 - 10% 2.31 +7.06 5.21 +12.37 18.34 +13.614 -20% 2.48 +14.88 5.93 +27.98 21.14 +30.98

123

Figure 4.15 (a) Variation of Maximum Compression in Leg Members for Load Case -1

LOAD CASE - 1 Tension in Leg Members

Base Variation in %

The percentage variation of maximum force in compression and

tension with respect to percentage variation in base width in different leg

member groups for Load Case 1 is plotted in Figures 4.15 (a) and (b).

LOAD CASE -1 Compression in Leg Members

Base Variation in %

Figure 4.15 (b) Variation of Maximum Tension in Leg Members for Load Case -1

I <2 <2

& <2

sill

(O 00

~sl 0)

124

LOAD CASE - 1 Tension in Bracing Members

Base Variation in %

LOAD CASE -1 Compression in Bracing Members

Base Variation in %

Figure 4.16 (a) Variation of Maximum Compression m Bracing Members for Load Case -1

Similarly, the variation of maximum force in compression and

tension in different bracing member groups for Load Case 1 is shown in

Figures 4. 16 (a) and (b).O

Figure 4.16 (b) Variation of Maximum Tension in Bracing Members for Load Case * 1

125

Figure 4.17 (a) Variation of Maximum Compression m Leg Members for Load Case -2


Base Width Variation in %

LOAD CASE - 2 Compression in Leg Members

Base Width Variation in %H-------------------- 1

------- 2P

Figure 4.17 (b) Variation of Maximum Tension in Leg Members for Load Case - 2

Similarly for load case 2 and load case3 the variation of maximum

forces in different member groups are given in Figures 4.17 to 4.20.-f

x OForc

e Var

iatio

n in %

126

—•— Bracing 2008- - - Bracing 2009- ■» - Bracing 2010 —*— Bracing 2011

— Bracing 2008 Bracing 2009

— •* — Bracing 2010 —*—Bracing 2011



LOAD CASE - 2 Compression in Bracing Members


Figure 4.18 (a) Variation of Maximum Compression m Bracing Members for Load Case - 2

Forc

e Var

iatio

n in %

4 &

h.©

o ©

©

oCM

OCO

O

Forc

e Var

iatio

n in %

oCM

Figure 4.18 (b) Variation of Maximum Tension in Bracing Members for Load Case - 2

127

Figure 4.19 (a) Variation of Maximum Compression in Leg Members for Load Case - 3

40 T

30

20


LOAD CASE - 3 Compression in Leg Members


Figure 4.19. (b) Variation of Maximum Tension in Leg Members for Load Case - 3

128

— Bracing 2008 Bracing 2009

— -» — Bracing 2010 —*— Bracing 2011

— — Bracing 2008— - - Bracing 2009— •* — Bracing 2010 —*— Bracing 2011



LOAD CASE - 3 Compression in Bracing Members


Figure 4.20 (a) Variation of Maximum Compression in Bracing Members for Load Case - 3

OCOOFo

rce V

aria

tion i

n %

_i__

___I

____

_i__

___L

oCMoCO

oForc

e Var

iatio

n in %

oCM

Figure 4.20 (b) Variation of Maximum Tension in Bracing Members for Load Case - 3

129

4.10.7 Sensitivity for Bracing Patterns

The same tower configuration is considered for sensitivity of member

forces in leg members and bracing members for different bracing patterns.

Three dimensional truss analysis was carried out for all the load cases with

different bracing patterns. The bracing pattern of the tower below waist level

alone is considered. There are four panels below the waist level. Two bracing

patterns, viz. X - bracing and K - bracing for these panels are considered in this

study. A schematic diagram of five different combinations of bracing patterns is

shown in Figure 4.21.

The comparison of maximum force in compression and tension on

top leg member group for different load cases due to the change in bracing

pattern are tabulated in Table 4.18. Similarly for other leg member groups, the

values are tabulated in Tables 4.19 to 4.21. Similar comparison tables of

maximum force in compression and tension on bracing member groups for

different load cases due to the change in bracing pattern are tabulated in

Tables 4.22 to 4.25.

It is observed that there is a considerable amount of change in

member forces due to bracing pattern, but the changes are not having any

decisive pattern. During this process, sensitivity of deflection to bracing pattern

is also found. The maximum deflection values and ratios of the deflections to

the maximum deflection of the X X X X pattern as datum are given in

Table 4.26. For normal load case, the maximum deflection occurs in

X-direction and in broken ground wire and top conductor broken condition, the

maximum deflection occurs in Z-direction. Also, it is observed that the change

in deflection due to change in bracing pattern is not significant.

130

Figure 4.21 Bracing Patterns for Sensitivity

131

Table 4.18 Comparison of Forces in Leg Member Group 1006 for Different Bracing Patterns

SI.No. Pattern

Compression Tension

L.C.-1(kN)

L.C.-2(kN)

L.C.-3(kN)

L.C. -1 (kN)

L.C.-2(kN)

L.C.-3(kN)

1 xxxx 35.02 86.74 74.10 23.09 75.10 88.36

2 XXXK 33.23 83.13 70.82 22.20 72.37 84.05

3 XXKK 35.36 87.37 77.24 23.37 75.69 87.02

4 XKKK 28.64 72.78 58.06 20.21 64.57 78.36

5 KKKK 38.56 101.60 80.57 22.75 86.17 89.11


SI.No. Pattern

Compression Tension

L.C. -1 (kN)

L.C. - 2 (kN)

L.C. — 3 (kN)

L.C. -1 (kN)

L.C. - 2 (kN)

L.C. - 3 (kN)

1 XXXX 47.07 105.52 83.86 29.59 88.32 133.66

2 XXXK 47.84 107.09 84.77 29.97 89.50 135.23

3 XXKK 46.92 105.23 87.22 29.47 88.06 136.80

4 XKKK 43.44 99.83 83.93 27.63 84.31 130.13

5 KKKK 43.43 99.73 102.58 27.63 84.40 97.41

132


SI.No. Pattern

Compression Tension

L.C.-1(kN)

L.C.-2(kN)

L.C.-3(kN)

L.C. -1 (kN)

L.C. - 2 (kN)

L.C.-3(kN)

1 xxxx 44.69 95.54 91.00 29.81 80.86 142.39

2 X X X K 44.27 94.67 91.13 29.60 80.20 142.10

3 XXKK 45.54 99.15 93.68 29.73 83.51 144.45

4 XKKK 45.54 99.05 96.89 29.73 83.58 116.21

5 KKKK 45.54 99.05 111.89 29.73 83.62 101.20


SI.No. Pattern

Compression Tension

L.C. -1 (kN)

L.C. - 2 (kN)

L.C.-3(kN)

L.C. -1 (kN)

L.C. - 2 (kN)

L.C.-3(kN)

1 XXXX 48.00 100.71 100.22 31.60 84.49 154.85

2 X X X K 46.72 98.65 97.37 30.90 83.07 150.73

3 XXKK 46.72 98.65 89.52 30.90 83.13 130.23

4 XKKK 46.72 98.56 107.48 30.90 83.17 112.87

5 KKKK 46.72 98.56 116.40 30.90 83.19 103.95

133

Table 4.22 Comparison of Forces in Bracing Member Group 2008 for Different Bracing Patterns

No. PatternCompression Tension

L.C. -1 (kN)

L.C.-2(kN)

L.C.-3(kN)

L.C. -1 (kN)

L.C. - 2 (kN)

L.C.-3(kN)

1 xxxx 4.97 13.08 70.01 3.66 10.26 72.95

2 X X X K 6.62 15.37 73.43 4.85 12.05 75.88

3 XXKK 4.54 12.83 71.55 3.41 9.87 74.36

4 XKKK 10.71 22.60 85.38 7.79 17.66 86.26 1

5 KKKK 4.99 7.12 119.64 4.99 7.12 119.64


SI.No. Pattern

Compression Tension

L.C. -1 (kN)

L.C. - 2 (kN)

L.C. - 3 (kN)

L.C. -1 (kN)

L.C. - 2 (kN)

L.C. - 3 (kN)

1 XXXX 1.70 4.77 33.91 2.31 6.08 32.55

2 X X X K 2.26 5.60 35.27 3.08 7.14 34.14

3 XXKK 1.59 4.59 34.57 2.11 5.96 33.26

4 XKKK 2.21 3.17 62.12 2.21 3.17 62.12

5 KKKK 2.21 3.15 52.80 2.21 3.15 52.80

134


SI.No. Pattern

Compression Tension

L.C. -1 (kN)

L.C. - 2 (kN)

L.C. - 3 (kN)

L.C. -1 (kN)

L.C. - 2 (kN)

L.C. - 3 (kN)

1 xxxx 1.41 3.70 19.82 1.03 2.90 20.65

2 X X X K 1.87 4.35 20.79 1.37 3.41 21.48

3 XXKK 1.27 1.84 39.27 1.27 1.84 39.27

4 XKKK 1.27 1.82 33.34 1.27 1.82 33.34

5 KKKK 1.27 1.81 30.06 1.27 1.81 30.06


SI.No. Pattern

Compression Tension

L.C. -1 (kN)

L.C. - 2 (kN)

L.C.-3 (kN)

L.C. -1 (kN)

L.C. - 2 (kN)

L.C.-3(kN)

1 XXXX 0.73 2.03 14.47 0.98 2.60 13.89

2 X X X K 0.84 1.20 19.46 0.84 1.20 19.46

3 XXKK 0.84 1.20 19.82 0.84 1.20 19.82

4 XKKK 0.84 1.20 19.67 0.84 1.20 19.67

5 KKKK 0.84 1.20 19.58 0.84 1.20 19.58

135

Table 4.26 Comparison of Maximum Deflection for Different Bracing Patterns

SI.No. Pattern

Load Case -1X Deflections

Load Case - 2Z Deflections

Load Case - 3 8 Z Deflections

(mm) Ratio (mm) Ratio (mm) Ratio

1 xxxx 35.33 1.0000 60.00 1.0000 64.00 1.0000

2 X X X K 34.97 0.9898 59.63 0.9938 63.31 0.9892

3 XXKK 35.42 1.0025 60.74 1.0123 64.19 1.0029

4 XKKK 33.96 0.9612 58.92 0.9820 61.36 0.9588

5 KKKK 35.48 1.0042 64.30 1.0717 64.31 1.0048

The weight of the towers due to the change in bracing patterns is also

compared in Table 4.27. It is observed that there is 18.9% increase in weight of

the tower if X- bracings are completely replaced by K-bracings. Figure 4.22

shows the comparison of the weight of the tower with different bracing

patterns.

Table 4.27 Weight of the Tower for Different Bracing Patterns

SI. No. PATTERN WEIGHT(kN) % Change

1 XXXX 18.29306 100.0

2 X X X K 19.54017 106.8

3 XXKK 20.49228 112.0

4 XKKK 21.29292 116.4

5 | KKKK 21.76466 118.9

136

Bracing pattern

Figure 4.22 Comparison of weight for different bracing patterns

4.10.8 Knowledge Obtained from Sensitivity Studies

The following observations are obtained from the sensitivity studies

carried out on the tower.

> The deflection behaviour of the tower is asymptotic and the

variation in the cross sectional area of leg members in the range

of 10% to 50% of preliminary area calculated by cantilever

moments are more sensitive. Hence, it is useful to vary the area

in this range to control the deflection.

The sensitivity studies carried out on a sample tower show the

behaviour and response of the tower to various design parameters. The

observations are useful in optimisation for selecting the variable as well as

fixing the upper bound and lower bound values of the variables.

137

> The expected deflection for a change in area of the leg members

can be estimated using equations formulated, without

performing analysis.

> The deflection is less sensitive to bracing members cross

sectional area and hence the control of deflection is difficult to

achieve by varying the area of bracing members.

> Design sensitivity equations are useful in fixing the required

area of a member from the force. This can help in fixing the

range in which the area of the member has to be selected.

> The forces in bottom leg members are more sensitive than the

top leg members to the base width of tower. Similar trend is for

observed in the bracing members also.

> Bracing pattern affects the member forces but no decisive trend

could be obtained.

Sensitivity studies give knowledge about the behaviour of the tower,

which is useful in optimisation in many ways. Based on the knowledge

obtained from the above observation the upper and lower bound values for the

optimisation are fixed. The values of variables for sensitive parameters are

allowed to select from a wider range of data than for less sensitive parameters.

Thus the knowledge gained in this study is used in the optimisation.

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