14
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
stipulations
transmission
rules
chapter covers certain basic
principles
and
to be followed in the analysis and design of
line towers, incorporating Indian electricity
(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,
ranging
vertical
various line configurations have to be considered
from single circuit horizontal to double circuit
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
the following factors:
1.
The length of the insulator assembly.
on
15
2.
The
minimum clearances to be maintained
3.
conductors, and between conductor and tower.
The location of ground wire or wires with respect
4.
to the outermost conductor.
The
mid-span
clearance
consideration
of
the
dynamic
between
required
from
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:
3.3
(a)
Tower height.
(b)
Base-width.
(c)
Top hamper-width.
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
in a transmission line tower.
h4
16
Figure 3.1 - Determination of tower height
[Source: Reference(37)J
17
3.4
CLEARANCES
3.4.1
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
(incorporating amendments), stipulates clearance above
77
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
stipulates
nearest
based
80(2)
that
the
of Indian electricity
rules
horizontal
between
clearance
conductor and any part of the structure
on
maximum
deflection due to
wind
should not be less than the values shown
corresponding to the voltage.
(1956)
shall
pressure.
in
Table
the
be
It
3.2,
18
TABLE 3.1 MINIMUM GROUND CLEARANCE
Voltage of the line
(Kv)
Permissible minimum ground
Clearance
(mm)
66
5490
132
220
6100
1
|
400
7016
8840
19
TABLLE 3.2 HORIZONTAL CLEARANCE
a.
b.
For high voltage lines upto and
including 11,000 volts
..........
1.219 m
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
20
3.5
CRITICAL PARAMETERS OF TOWER
The following aspects are considered essential
fixing the tower outline:
3.5.1
a.
Maximum sag of lower conductor.
b.
Height and location of ground wire.
c.
d.
Length of cross arm and conductor spacing.
Minimum mid-span clearance.
e.
Tower width at base and at top hamper.
Maximum Sag of Lower Conductor
The
size
and type of
conductor,
wind,
conditions of the region and span determines the
sag
for
and
tension.
consideration.
Span length
is
fixed
climatic
conductor
from
economic
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
external
percentage
tension
load
of
at 32°
shall
Centigrade
not
exceed
the ultimate tensile
conductor.
i)
Initial unloaded tension
ii) Final unloaded tension
(90°F)
the
without
following
strength
of
:
35 percent
:
25 percent
the
21
In
accordance with this stipulation,
the
maximum
working tension under stringent loading condition shall not
exceed 50%
conductor.
of the ultimate tensile
Sag tension computation
strength of
the
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
stroke
direct
Ground wire provides protection against
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
100
is
direct strokes to the phase conductors
approaches
percent, if the shield angle is less than 20°, but
not
advisable
considerations.
conductor
On
spacing,
to keep smaller
angles
extra high voltage lines
the
use of two
earth
from
economic
having
wires
it
wide
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
mid-span during the
span 'flash over'
conductor,
before
propagation of surge current and
may occur from ground wire to
the current is discharged
through
the
22
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
conductor,
at
under all temperature conditions in still
the normal spans, so as to give a mid
greater
span
the
wind
separation
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.
ground
In the case of stroke to mid-span, on one of the
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,
partly
which
are
electrical and partly mechanical. The material
and
diameter of the conductors should also be considered,
deciding
the
spacing,
because
a
smaller
when
conductor,
23
TABLE 3.3 MID-SPAN CLEARANCE
Span
(m)
299
Vertical Clearance permissible at the 1
middle of the span (mm)
|
4000
300
5500
400
7000
600
8500
I
especially
made
of aluminium, having a
small
weight
relation to the area presented to a cross-wind, will
in
swing
out of vertical plane farther than a conductor of larger
cross-section. Usually, conductors will swing synchronously
(in
phase)
wires,
there
swinging
is
always a possibility
non-synchronously,
maximum
are
with the wind, but with long spans
and
the
of
the
and
conductor
conductor
sag at the centre of the span are
small
and
factors,
the
which
taken into account in determining the distance
apart,
at which they are strung.
There
deduced
operated
are a number of empirical formulae
in
use,
from spacings, which have been
successfully
in practice, while research continues on minimum
spacings,
horizontal
which
and
could
be employed.
vertical,
between
The
spacings,
conductors
both
commonly
adopted on typical transmission lines in India are given in
Table 3.4.
3.5.5
width
Tower Width at the Base
Spacing between the tower footings, i.e., the base
at the concrete level (or at the foot of the bottom
panel)
is the distance from the centre of gravity
corner leg to the centre of gravity of the adjacent
leg.
one
corner
This width depends upon the height, magnitude of
physical
size,
of
the
loads imposed upon the tower calculated from
the
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 tower
1.
2.
3.
4.
5.
6.
7.
I
Vertical spacing
between
conductors
(mm)
Horizontal
spacing between
conductors
(mm)
66 kV single circuit
A(0-2°)
B(2-30°)
C(30-60°)
1030
1030
1220
4040
4270
4880
66 kV Double Circuit
A(0-2°)
B(2-30°)
C(30-60°)
2170
2060
2440
4270
4880
6000
132 kV Single Circuit
A(0-2°)
B(2-15°)
C( 15-30°)
D(30-60°)
4200
4200
4200
4200
7140
6290
7150
8820
132 kV Double circuit
A(0-2°)
B(2-15°)
C( 15-30°)
D(30-60°)
3965
3965
3965
4270
7020
7320
7320
8540
220 kV Single circuit
A(0-2°)
B(2-15°)
C( 15-30°)
D(30-60°)
5200
5250
6700
7800
8500
10500
12600
14000
220 kV Double
Circuit
A(0-2°)
B(2-15°)
C( 15-30°)
D(30-60°)
5200
5200
5200
6750
9900
10100
10500
12600
7800
7800
7800
8100
12760
12640
14000
16200
400 kV Single Circuit
horizontal
configuration
A(0-2°)
B(2-15°)
C( 15-30°)
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
level of the lower cross arm in the case of barrel type
the
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
loading.
decided based on resistance required for
torsional
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
3.6.1
TYPES OF TOWER
Classification according to Number of Circuits
The
transmission
majority of high voltage double
circuit
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
desired.
coverage
27
3.6.2
Classification according to use
Towers are classified according to
independent of the number of conductors they
their use,
support. A
tower has to withstand the loadings ranging from
runs
an
straight-
to varying angles. To simplify the design and
overall economy in cost and maintenance, tower
ensure
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
°
conductor
addition to the wind,
loads.
ice,
If the transmission line
relatively flat, featureless terrain,
of
the
Thus,
and
the
greatest
design
of
tangent
traverses
ninety
line may be composed of this type
tower
broken
percent
of
tower.
provides
opportunity for the structural
the
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
than
2°
(Figure
transverse
tension
load
induced
3.2).
from
As
the
they
must
components
by this angle, in
greater
resist
of
addition
the
a
line
to
the
usual wind, ice and broken conductor loads, they are
necessarily heavier than suspension towers.
Unless
restricted
by
site
conditions,
or
influenced
conductor tensions, angle should be located in such
manner
that
the axis of the cross-arms
angle formed by the conductors.
bisects
by
a
the
28
9
T
P,
m Angle of deflection of line
» Tension in conductor
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)]
29
Theoretically,
different
towers,
different
but
line
angles
for economy there
is
require
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
shownthat the
following angle
suitable for most of the lines:
1. Light
angle - 2 to
towers
are
has
generally
15
degrees line deviation.
2. Medium angle - 15 to 30
degrees line deviation.
3. Heavy
degrees line deviation
angle - 30 to 60
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
classification.
(Part
I)-1977
recommends
the
above
It would be uneconomical to use 30° angle towers in
locations where angles higher than 2“ and smaller than
are
encountered.
There are limitations to the use
of
30°
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
3.7.1
STRUCTURAL ANALYSIS
General Remarks
Transmission
line
tower
consists
of
linear
structural members rigidly connected to one another
welding or bolting. For the purposes of analysis,
it
idealized
as
a
space
truss.
A space
truss
is
a
by
is
3-D
30
assemblage
hinges.
of
Space
line members, each member being
truss idealization lead to
joined
the
by
following
assumptions:
1.
The
influence of gusseted
connection
transmitting moment is neglected.
2.
Leg
members
that are continuous
are
in
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
computer
program.
idealization
Figure
consisting
3.3
of
shows
the
foundation
space
leg
the
truss
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
to
trusses, the stiffness method generally
fewer equations.
Hence, the stiffness method
is
leads
used
for the analysis of transmission line towers.
Let (Xjj and
{8denote the nodal
displacement vector of the ith member in
force and
the local
31
>?1'0h-(6
800416
Figure 3.3 - Space truss idealization
LSource: Referencel37)]
32
co- ordinate system as
shown
in
Figure
3.4. The
member
stiffness equation is written as :
{*i)
=
(3.1)
E*jJ {**£}
Where
{Xi>T = (XiL,
{6L)
ZiL,
(3.2)
= (UiL,ViL,WiL,UiR,ViR,WiR)
(3.3)
and [kj^] is the member stiffness matrix given by
[*]
Ei Ai
10
0-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-10
0
1
0
0
(3.4)
0
0
0
0
0
0
0
0
0
0
0
0
In equation (3.4)
and
indicate the modulus of
elasticity and length of the i*"*1 member respectively.
The
stiffness
in
the
similar manner and they are transformed from the local
co­
ordinate
stiffness
equation
of all the members are formed
system to the global.
matrix is
Then
generated
the total
structure
bysuperimposing
the
individual member stiffness matrices. Thus,
[K]
{d} =
(L)
(3.5)
Where
{d>
=Nodal
displacement
vector
to global coordinate system
{L}
=
Vector of external loads
referred
33
Figure 3.4 - The global and local co-ordinate system
34
Total structure stiffness matrix
[K]
[K]
In
=
equation
matrix
and
member
stiffness
Equation
n
S
i=l
[Ti]T [ki]
(3.6),
(T±3
[ TjJ
the
is
the summation sign denotes
matrices of all
(3.5)
with
(d)
——
the
respect to
(3. C)
transformation
superimposing
members.
nodal
the
the
Solving
displacement
vector.
(K)-1 (L)
(3.7)
[Ki]"1 (L)
(3.8)
then
(di)
where
(di)
= Nodal
displacement
vector
of
the
ith
member
referred to Global Coordinate Systems (GCS).
[Kjj"1 = Matrix formed by extracting the rows corresponding
to the vector {d^} from the matrix [K]”1.
The
member
nodal
displacement
vector {<5^}
of
referred to the Local Coordinate Systems
i th
the
(LCS)
is
related to {d^ through the transformation matrix [Tj_].
{Si> = [Ti]
From equations (3.1) and (3.9),
the
vector {Xj} of the ith member is given by :
{Xj_} =
(3.9)
{dL)
[CL] (L)
nodal
force
(3.10)
Where
[Ci]
= [kiHTiHKi] -1
(3.11)
35
3.8
TOWER DESIGN
3.8.1
General Remarks
Once the external loads acting on the tower are
determined, one proceeds with an analysis of the forces in
various
Axial
members
with
a view to fixing
up
their
sizes.
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
and for portal type of towers. Except for
single circuit towers, this system has
girders
66 kV
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.
diagonal braces are connected at cross
Since the shear per face is carried by two
The
points.
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
adopted
small towers and
can
be
economically
throughout the shaft except in
the
one or two panels, where diamond or portal
of braces is more suitable.
(iii)
lower
system
Pratt system
This
system shown in Figure 3.5 (c) also
diagonal
horizontal
cross
braces
and in
contains
addition,
struts. These struts are
it
has
subjected
to
compression and the shear is taken entirely by
diagonal
redundant
Pratt
one
in tension. The other diagonal acts as
member.
braces
It is often economical
for bottom two or three
a
to
use
panels
and
Warren system for the rest of the tower.
(iv)
Portal system
The diagonals are necessarily designed for
tension
and compression, and therefore,
arrangement provides more stiffness than the
both
this
Pratt
system. The advantage of this system is that the
horizontal struts are supported at mid-length by
37
the
diagonals
[Figure 3.5 (d)].
Like
the
Pratt
system, this arrangement is also used for
bottom two or three panels in conjunction with
Warren
system for the other panels.
It
the
the
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
transverse
face consist of staggered
and the
bracing
arrangement
The
as shown in Figure 3.5 (e).
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
angle sizes and minimum thickness of steel members
in
the
designs, based on experience
and
minimum
adopted
judgement,
are
briefly described below:
(a)
Minimum angle size
The
present
practice is not to
allow
angle
leg
38
(a) Single web
system
(d) Portal system
Longitudinal face
Transverse face
(e) Offset or staggered bracing system
Figure 3.5 - Bracing systems
[Source:
Reference(37)3
39
width less than 45 nun through which a bolt of 16 nun
diameter passes.
braces,
This results in a number of
cross-arm
braces
and
almost
all
redundant members of the tower being of this
even
though
a smaller size may be
stress requirements.
main
the
size,
adequate
from
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
specifies
overhead
the
transmission
minimum
line
thicknesses
towers,
which
is
reproduced in Table 3.5. The limiting values of the
slenderness
ratio for the design
tower members is shown in Table
3.9
of
transmission
3.6.
CONCLUSION
The various aspects described in this chapter
have
been incorporated in the expert system program. The minimum
requirements
based
on experience and practice
used
as constraints in the optimization
the
implementation
of
these
have
program.
practical
been
Without
requirements,
optimization of tower weight will at best be, a theoretical
exercise.
40
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
41
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