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CHAPTER 3

TRANSMISSION LINE TOWER -DESIGN CONCEPTS

3.1 INTRODUCTION

The purpose of a transmission line tower is to support conductors carrying electrical power and one or two ground wires at suitable distances above the ground level and from each other. The transmission line towers cost about 35 to 45 per cent of the total cost of the transmission line. A transmission tower is a space truss and is an indeterminate structure.

This chapter covers certain basic principles and stipulations to be followed in the analysis and design of transmission line towers, incorporating Indian electricity rules (1956), Manual on transmission line towers (1977), IS:802 (1977) and draft revision of IS:802 (1989).

3.2 TOWER CONFIGURATION

Depending upon the requirements of the transmission system, various line configurations have to be considered ranging from single circuit horizontal to double circuit vertical structures and with single or V strings in all phases, as well as any combination of these.

The configuration of a transmission line tower depends on the following factors:

1. The length of the insulator assembly.

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2. The minimum clearances to be maintained between conductors, and between conductor and tower.

3. The location of ground wire or wires with respect to the outermost conductor.

4. The mid-span clearance required from consideration of the dynamic behaviour of conductors and lightning protection of the line.

5. The minimum clearance of the lowest conductor above ground level.

The tower configuration is determined essentially by three factors:

(a) Tower height.(b) Base-width.(c) Top hamper-width.

3.3 DETERMINATION OF TOWER HEIGHT

The factors governing height of a tower are :

1. Minimum permissible ground clearance (hi).2. Maximum sag (h2)•3. Vertical spacing between conductors (h3).4. Vertical clearance between ground wire and top

conductor (h4).

Thus the total height of tower is given by :

H= h1+h2+h3+h4

Figure 3.1 shows the parameters h3, h2, h3 and h4 in a transmission line tower.

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Figure 3.1 - Determination of tower height[Source: Reference(37)J

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3.4 CLEARANCES3.4.1 General Remarks

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 tracks, navigable and non-navigable rivers, telecommunication and power lines etc. as laid down in the various national standards issued by the respective authorities.

3.4.2 Ground Clearance

Indian electricity rules (1956), under Clause 77 (incorporating amendments), stipulates clearance above the ground of the lowest point of the conductor. For Extra High Voltage (EHV) lines, this clause stipulates that the clearance above the ground shall not be less than 5.1 m plus 0.3 m for every 33,000 volts or part thereof by which the voltage of the line exceeds 33,000 volts. The permissible minimum ground clearance for different voltages adopted in India are furnished in Table 3.1, and these are applicable for transmission lines running in the open country.

3.4.3 Horizontal Clearance

Clause 80(2) of Indian electricity rules (1956) stipulates that the horizontal clearance between the nearest conductor and any part of the structure shall be based on maximum deflection due to wind pressure. It should not be less than the values shown in Table 3.2, corresponding to the voltage.

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TABLE 3.1 MINIMUM GROUND CLEARANCE

Voltage of the line (Kv)

Permissible minimum ground Clearance

(mm)

66 5490

132 61001 220 7016| 400 8840

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TABLLE 3.2 HORIZONTAL CLEARANCE

a. For high voltage lines upto and including 11,000 volts

..........

1.219 m

b. For high voltage above 11,000 volts and upto and including 33,000 volts

1.829 m

c. For Extra High Voltage Lines (EHV) (plus 0.305 m for every additional 33,000 volts or part thereof)

1.829 m

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3.5 CRITICAL PARAMETERS OF TOWER

The following aspects are considered essential for fixing the tower outline:

a. Maximum sag of lower conductor.b. Height and location of ground wire.c. Length of cross arm and conductor spacing.d. Minimum mid-span clearance.e. Tower width at base and at top hamper.

3.5.1 Maximum Sag of Lower Conductor

The size and type of conductor, wind, climatic conditions of the region and span determines the conductor sag and tension. Span length is fixed from economic consideration. The maximum sag for conductor span occurs at the maximum temperature and still wind conditions. The maximum value of sag is taken into consideration in fixing the overall height of the steel tower structure. In regions prone to snowfall, the maximum sag may occur at 0°, with the conductor loaded with ice, in still wind condition. While working out tension for arriving at the maximum sag, the following stipulations laid down in Indian electricity rules (1956) are to be satisfied.

a. The minimum factor of safety shall be two based on their ultimate tensile strength.

b. Conductor tension at 32° Centigrade (90°F) withoutexternal load shall not exceed the followingpercentage of the ultimate tensile strength of the conductor.

i) Initial unloaded tension : 35 percentii) Final unloaded tension : 25 percent

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In accordance with this stipulation, the maximum working tension under stringent loading condition shall not exceed 50% of the ultimate tensile strength of the conductor. Sag tension computation made for final stringing of the conductor therefore must ensure that factor of safety of 2 and 4 is obtainable under respective loading condition.

3.5.2 Height and Location of Ground Wire

Ground wire provides protection against direct stroke of lightening. It intercepts the direct lightning strokes and conducts the charge to the nearest ground connections. The height and location of overhead ground wires shall be such that the line joining the ground wire to the outer most conductor shall make angles of approximately 20 to 30 degrees with the vertical. The angle is called shield angle. The practice is to specify 30° for 66 kV and 110 kV, 25 to 30 degrees for 220 kV. A lower angle of 20° is suggested for 400 kV. The protective value against direct strokes to the phase conductors approaches 100 percent, if the shield angle is less than 20°, but it is not advisable to keep smaller angles from economic considerations. On extra high voltage lines having wide conductor spacing, the use of two earth wires provide better protection.

3.5.3 Minimum Mid-Span Clearance

In case of direct lightning stroke on the mid-span of over head ground wires, the critical condition occurs at the mid-span during the propagation of surge current and mid span 'flash over' may occur from ground wire to conductor, before the current is discharged through the

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tower. The mid-span clearance between the earth wires and conductor is therefore, kept more than the clearance at the tower. The usual practice in this regard is to maintain the sag of ground wire at least 10 % less than that of the conductor, under all temperature conditions in still wind at the normal spans, so as to give a mid span separation greater than that at the supports. However, it is ensured that under the minimum temperature and maximum wind conditions, the sag of the ground wire does not exceed the sag of the power conductor.

In the case of stroke to mid-span, on one of the ground wires, when two ground wires are used, it is preferable, if the striken ground wire flashes over to the second ground wire instead of to the conductor. Therefore it is necessary that the spacing between the two ground wire is less than the mid-span clearance between ground wire and conductor. Mid-span clearance vary with the span length. Increased spans, increases the mid span clearance. The design span normally adopted are 250 m for 66 kV, 305 to 335 m for 110 kV, 350 m for 220 kV, 350 to 400 m for 400 kV lines. The vertical clearance generally adopted at the middle of the span between the ground wires and conductors are given in Table 3.3.

3.5.4 Spacing of Conductors

Considerable differences are found in the conductor spacings adopted in different countries and on different transmission line systems in the same country. The spacing of conductors is determined by considerations, which are partly electrical and partly mechanical. The material and diameter of the conductors should also be considered, when deciding the spacing, because a smaller conductor,

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TABLE 3.3 MID-SPAN CLEARANCE

Span Vertical Clearance permissible at the 1(m) middle of the span (mm) |

299 4000 I

300 5500

400 7000

600 8500

especially made of aluminium, having a small weight in relation to the area presented to a cross-wind, will swing out of vertical plane farther than a conductor of larger cross-section. Usually, conductors will swing synchronously (in phase) with the wind, but with long spans and small wires, there is always a possibility of the conductor swinging non-synchronously, and the conductor and the maximum sag at the centre of the span are factors, which are taken into account in determining the distance apart, at which they are strung.

There are a number of empirical formulae in use, deduced from spacings, which have been successfully operated in practice, while research continues on minimum spacings, which could be employed. The spacings, both horizontal and vertical, between conductors commonly adopted on typical transmission lines in India are given in Table 3.4.

3.5.5 Tower Width at the Base

Spacing between the tower footings, i.e., the base width at the concrete level (or at the foot of the bottom panel) is the distance from the centre of gravity of one corner leg to the centre of gravity of the adjacent corner leg. This width depends upon the height, magnitude of the physical loads imposed upon the tower calculated from the size, type of conductors and wind loads and also upon the height of application of external loads from ground level. Towers with larger base result in low footing costs and lighter main leg member at the expense of longer bracing members. There is a particular base width, which gives the best compromise for the total cost of the tower to be minimum. Through experience expanded over a number of

TABLE 3.4 SPACING OF CONDUCTORS

Type of towerVertical spacing

between conductors

(mm)

Horizontal spacing between

conductors (mm)

1. 66 kV single circuit A(0-2°) 1030 4040B(2-30°) 1030 4270C(30-60°) 1220 4880

2. 66 kV Double Circuit A(0-2°) 2170 4270B(2-30°) 2060 4880C(30-60°) 2440 6000

3. 132 kV Single Circuit A(0-2°) 4200 7140B(2-15°) 4200 6290C( 15-30°) 4200 7150D(30-60°) 4200 8820

4. 132 kV Double circuit A(0-2°) 3965 7020B(2-15°) 3965 7320C( 15-30°) 3965 7320D(30-60°) 4270 8540

5. 220 kV Single circuit A(0-2°) 5200 8500B(2-15°) 5250 10500C( 15-30°) 6700 12600D(30-60°) 7800 14000

6. 220 kV DoubleCircuitA(0-2°) 5200 9900B(2-15°) 5200 10100C( 15-30°) 5200 10500D(30-60°) 6750 12600

7. 400 kV Single Circuithorizontalconfiguration 7800 12760A(0-2°) 7800 12640B(2-15°) 7800 14000C( 15-30°) 8100 16200I D(30-60°)

2b

years, certain empirical relations have also been developed ■for base widths. The ratio between total height of the tower uptc the lower cross arm and base width is generally between 2.8 and 4.4.

3.5.6 Width at the Top Hamper

Top hamper-width is the width of the tower at the level of the lower cross arm in the case of barrel type of towers (In double circuit towers it may be at middle cross arm level) and waist line in case of towers with horizontal configuration of conductors. The width of the top hamper is mainly decided based on resistance required for torsional loading. The torsional stresses are evenly distributed on the four faces of a square tower.

The top hamper width is generally found to be about one-third to one-half of the base width for tangent and light angle towers and about 1/3.5 of the base width for medium and large angle towers.

3.6 TYPES OF TOWER3.6.1 Classification according to Number of Circuits

The majority of high voltage double circuit transmission lines employ a vertical configuration of conductor and single circuit transmission lines, a triangular arrangement of conductors. Single circuit lines, particularly 400 kV and above, generally employ a horizontal arrangement of conductors. The number of ground wires used on the line depends on the iso-ceraunic level of the area, importance of the line and the angle of coverage desired.

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3.6.2 Classification according to use

Towers are classified according to their use, independent of the number of conductors they support. A tower has to withstand the loadings ranging from straight- runs to varying angles. To simplify the design and ensure an overall economy in cost and maintenance, tower designs are generally confined to a few standard types as follows :

(1) Tangent (suspension) towers

Suspension towers are used primarily on tangents, but often are designed to withstand angles in the line upto 2° in addition to the wind, ice, and broken conductor loads. If the transmission line traverses relatively flat, featureless terrain, ninety percent of the line may be composed of this type of tower. Thus, the design of tangent tower provides the greatest opportunity for the structural engineer to minimize the total weight of steel required.

(2) Angle towers

Angle towers, sometimes called semi-anchor towers, are used where the line makes a horizontal angle greater than 2° (Figure 3.2). As they must resist a transverse load from the components of the line tension induced by this angle, in addition to the usual wind, ice and broken conductor loads, they are necessarily heavier than suspension towers. Unless restricted by site conditions, or influenced by conductor tensions, angle should be located in such a manner that the axis of the cross-arms bisects the angle formed by the conductors.

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9 m Angle of deflection of line T » Tension in conductor P, a Transverse load due to component of

conductor tension = T sin &2 P2 » Longitudinal load due to component of lire

tension = T cos 02

Figure 3.2 - Orientation of tower in an angle

lSource: Reference(37)]

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Theoretically, different line angles require different towers, but for economy there is a limiting number of different types of towers used. This number is a function of all the factors, which make up the total erected cost of a tower line. However, experience hasshown that the following angle towers are generallysuitable for most of the lines:

1. Light angle - 2 to 15 degrees line deviation.2. Medium angle - 15 to 30 degrees line deviation.3. Heavy angle - 30 to 60 degrees line deviation

and dead ends.

While the angles of line deviation are for the normal span, the span may be increased upto an optimum limit by reducing the angle of line deviation and vice versa. IS: 802 (Part I)-1977 recommends the aboveclassification.

It would be uneconomical to use 30° angle towers in locations where angles higher than 2“ and smaller than 30° are encountered. There are limitations to the use of 2°

angle towers at higher angles with reduced spans and the use of 30“angle towers with smaller angles and increased spans. The introduction of a 15° tower would effect sizable economy.

3.7 STRUCTURAL ANALYSIS3.7.1 General Remarks

Transmission line tower consists of linear structural members rigidly connected to one another by welding or bolting. For the purposes of analysis, it is idealized as a space truss. A space truss is a 3-D

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assemblage of line members, each member being joined by hinges. Space truss idealization lead to the following assumptions:

1. The influence of gusseted connection in transmitting moment is neglected.

2. Leg members that are continuous are assumed to be hinged at the nodal points.

3. Loads are assumed to act only at the joints.

The use of high speed computers has enabled the analysis of large structural systems to be carried out more easily and accurately. Among the various methods available for the truss analysis, the matrix formulation has the advantage over other methods, since the operation of matrix algebra can be provided in the form of a 'routine' in the computer program. Figure 3.3 shows the space truss idealization consisting of foundation leg members, horizontal and diagonal braces.

3.7.2 Matrix Structural Analysis

Every structure must fulfill the dual requirements of equilibrium and compatibility. The stiffness method maintains the compatibility of the structures and makes use of equilibrium conditions for the solution. For solving pin-jointed trusses, the stiffness method generally leads to fewer equations. Hence, the stiffness method is used for the analysis of transmission line towers.

Let (Xjj and {8denote the nodal force and displacement vector of the ith member in the local

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>?1'0h-(6

800416

Figure 3.3 - Space truss idealizationLSource: Referencel37)]

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co- ordinate system as shown in Figure 3.4. The member stiffness equation is written as :

{*i) = E*jJ {**£}Where

{Xi>T = (XiL, ZiL,{6L) = (UiL,ViL,WiL,UiR,ViR,WiR)

and [kj^] is the member stiffness matrix given by

[*] Ei Ai

10 0-10 0 0 00 0 0 0-10 0 10 0 0 00 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0

(3.1)

(3.2)(3.3)

(3.4)

In equation (3.4) and indicate the modulus of elasticity and length of the i*"*1 member respectively. The stiffness equation of all the members are formed in the similar manner and they are transformed from the local co­ordinate system to the global. Then the total structurestiffness matrix is generated by superimposing theindividual member stiffness matrices. Thus,

[K] {d} = (L) (3.5)Where

{d> = Nodal displacement vector referredto global coordinate system

{L} = Vector of external loads

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Figure 3.4 - The global and local co-ordinate system

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[K] Total structure stiffness matrix

[K] =nS [Ti]T [ki] [

i=lTjJ (3. C)

In equation (3.6), (T±3 is the transformationmatrix and the summation sign denotes superimposing themember stiffness matrices of all the members. SolvingEquation (3.5) with respect to the nodal displacementvector.

(d) —— (K)-1 (L) (3.7)then

(di) [Ki]"1 (L) (3.8)where

(di) = Nodal displacement vector of the ith memberreferred to Global Coordinate Systems (GCS).

[Kjj"1 = Matrix formed by extracting the rows corresponding to the vector {d^} from the matrix [K]”1.

thThe nodal displacement vector {<5^} of the i member referred to the Local Coordinate Systems (LCS) is related to {d^ through the transformation matrix [Tj_].

{Si> = [Ti] {dL) (3.9)

From equations (3.1) and (3.9), the nodal force vector {Xj} of the ith member is given by :

Where{Xj_} = [CL] (L)

[Ci] = [kiHTiHKi]

(3.10)

-1 (3.11)

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3.8 TOWER DESIGN3.8.1 General Remarks

Once the external loads acting on the tower are determined, one proceeds with an analysis of the forces in various members with a view to fixing up their sizes. Axial force is the primary force for a truss element and therefore, the member is designed for either compression or tension. When there are multiple load conditions, certain members may be subjected to both compressive and tensile forces under different loading conditions. Hence, these members are designed for both compression or tension acting separately.

3.8.2 Bracing Systems

Once the width of the tower at the top and also the level at which the batter should start are determined, the next step is to select the system of braces. The following bracing systems are usually adopted for transmission line towers.

(i) Single web system

This system shown in Figure 3.5(a) is particularly used for narrow-based towers, in cross arm girders and for portal type of towers. Except for 66 kV single circuit towers, this system has little application for towers at higher voltages.

(ii) Double web or Warren system

This system shown in Figure 3.5(b), is made up of

3b

diagonal cross braces. Shear is equally distributed between the two diagonals, one in compression and tne other in tension. Both the diagonals are designed for compression and tension in order to permit reversal of externally applied shears. The diagonal braces are connected at cross points. Since the shear per face is carried by two members and critical length is approximately half that of a corresponding single web system, it is apparent that the individual members will be smaller than in the single web system. This system is used for both large and small towers and can be economically adopted throughout the shaft except in the lower one or two panels, where diamond or portal system of braces is more suitable.

(iii) Pratt system

This system shown in Figure 3.5 (c) also contains diagonal cross braces and in addition, it has horizontal struts. These struts are subjected to compression and the shear is taken entirely by one diagonal in tension. The other diagonal acts as a redundant member. It is often economical to use Pratt braces for bottom two or three panels and Warren system for the rest of the tower.

(iv) Portal system

The diagonals are necessarily designed for both tension and compression, and therefore, this arrangement provides more stiffness than the Pratt system. The advantage of this system is that the horizontal struts are supported at mid-length by

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the diagonals [Figure 3.5 (d)]. Like the Pratt system, this arrangement is also used for the bottom two or three panels in conjunction with the Warren system for the other panels. It is especially useful for heavy river crossing towers.

(v) Offset or Staggered bracing system

This bracing arrangement can be derived from the Portal system and Warren system. The longitudinal face is similar to that of Warren system and the transverse face consist of staggered bracing arrangement as shown in Figure 3.5 (e). The leg members are thus supported at alternate points in two directions. All diagonals are designed for tension and compression and they share the web shear. This arrangement has the advantage that the struts carry no primary loads and are designed as redundant members. The increased efficiency in the legs, however, is obtained at the expense of increasing the number of different diagonals and correspondingly reducing the advantages of mass production methods.

3.8.3 Determination of Member Sizes

The practices followed with regard to the minimum angle sizes and minimum thickness of steel members adopted in the designs, based on experience and judgement, are briefly described below:

(a) Minimum angle size

The present practice is not to allow angle leg

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(a) Single web

system

(d) Portal system

Figure 3.5

Longitudinal face Transverse face

(e) Offset or staggered bracing system

- Bracing systems

[Source: Reference(37)3

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width less than 45 nun through which a bolt of 16 nun diameter passes. This results in a number of main braces, cross-arm braces and almost all the redundant members of the tower being of this size, even though a smaller size may be adequate from stress requirements. Unequal angle size 45 x 30 x 5 nun can be used in place of equal angle 45 x 45 x 5 nun for a number of braces and for almost all the redundant members.

(b) Minimum thickness and Slenderness ratio

IS:802-1977, code of practice for use of structural steel in overhead transmission line towers, specifies the minimum thicknesses which is reproduced in Table 3.5. The limiting values of the slenderness ratio for the design of transmission tower members is shown in Table 3.6.

3.9 CONCLUSION

The various aspects described in this chapter have been incorporated in the expert system program. The minimum requirements based on experience and practice have been used as constraints in the optimization program. Without the implementation of these practical requirements, optimization of tower weight will at best be, a theoreticalexercise.

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TABLE 3.5 MINIMUM THICKNESS OF TOWER MEMBERS

Minimum thickness (mm)Galvanised Painted

Leg members and lower members of cross arms in compression

5 6

Other members 4 5

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TABLE 3.6 SLENDERNESS RATIO-LIMITING VALUES

Leg members and main members in the cross-arm in compression

150

Members carrying computed stresses

200

Redundant members and those carrying nominal stresses

250

Tension members 350