UNITED STATES
DEPARTMENT
OF THE INTERIOR
Water and Power Resources
Service
Denver, Colorado
1980
Transmission Line
Design Manual
bY
Holland H. Farr
A guide for the investigation,
development,
and design of power transmission
A Water Resources Technical
lines.
Publication
As the Nation’s principal conservation agency, the Department of the
Interior has responsibility for most of our nationally owned public lands
and natural resources.
This includes fostering the wisest use of our land and water resources,
protecting our fish and wildlife, preserving the environmental and cultural
values of our national parks and historical places, and providing for the
enjoyment of life through outdoor recreation.
The Department assessesour energy and mineral resources and works
to assure that their development is in the best interests of all our people.
The Department also has a major responsibility for American Indian
reservation communities and for people who live in Island Territories
under U.S. administration.
On November 6, 1979, the Bureau of Reclamation was renamed the
Water and Power Resources Service in the U.S. Department of the
Interior. The new name more closely identifies the agency with its
principal functions - supplying water and power.
The text of this publication was prepared prior to adoption of the new
name; all references to the Bureau of Reclamation or any derivative
thereof are to be considered synonymous with the Water and Power
Resources Service.
SI METRIC
UNITED
STATES
GOVERNMENT
DENVER:
PRINTING
OFFICE
1980
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington DC 20402,
and the Water and Power Resources Service, Engineering and Research Center, Attn D-922,
P 0 Box 25007, Denver Federal Center, Denver CO 80225,
Stock Number 024-003-00135-O
PREFACE
The
purpose
followed
in the
of the
line
Interior.
design,
such
of this
manual
is to outline
design
of power
transmission
Numerous
are included
aspects
protection,
spotting.
of the
National
problems
with
as selection
clearance
structure
design
patterns,
Safety
when
the
sixth
some 16 000 circuit
to properly
distribute
made
other
codes
edition
are made
of NESC
as required.
lightning
charts,
of the
are so noted;
sparce
by
and
Interpretations
Some
and
concerning
guying
construction.
considered
voltages
engineers
of transmission
insulation,
and
to he
Department
is presented
was current,
while
of lines having
power,
Bureau
procedures
U.S.
tensions,
limitation
to wood-pole
the
aspects
Information
sags and
structure
are limited
and
on specific
applications.
of NESC.
of the Bureau,
miles
this
of Reclamation,
been
conductors,
and
for,
Bureau
conductor
examples
most examples
use the 1977 edition
The transmission
line network
encompasses
In addition,
have
of their
Code
requirements
by the
of construction,
design
developed
which
galloping
Structure
various
lines
explanations
of type
Electrical
were
studies,
the
some
up to and including
have also designed
example
however,
standards,
500 kilovolts.
and built
some
300 substations
and switchyards.
This total transmission
system
represents
an installed
transformer
capacity
of approximately
22 million
kilovolt
amperes.
In many areas, a Bureau
line is the only source
of electricity
and, if an outage
occurs,
an area may be completely
without
power.
The vast land area
covered
by
Bureau
lines
offers
almost
every
conceivable
type
large percentage
of lines are in remote
areas-maintenance
Therefore,
the line designs
shown
in this manual
are more
ordinarily
be considered.
The
Bureau
of Reclamation
recognized
the
need
for
this
of climatic
condition,
and
complete
be readily
the manual
available
engineers
designing
new
This manual
contains
manual
and
consequently
initiated
so that the design expertise
gained through
years of practical
to other
organizations
as well as being
a technical
guide
lines and maintaining
the engineering
tools
many years of transmission
line
reference
and guide for Bureau
design by the Bureau.
designers.
In keeping
metric
units have been shown
throughout
the
There are occasional
references
to proprietary
not be construed
in any
processes
of manufacturers
other
facilities.
that have
proven
its
of Energy
in
transmission
to have the
experience
for Bureau
to be successful
over
The manual
is not a textbook,
but a useful
with the Metric
Conversion
Act of 1975, SI
manual
in addition
to U.S. customary
materials
or products
in this publication.
way as an endorsement,
as we cannot
or the services
of commercial
firms
units.
These
must
endorse
proprietary
products
for advertising,
publicity,
sales,
or
or
purposes.
The author,
as an electrical
contributions
Area
the remaining
and concepts
a
is both
difficult
and time consuming.
conservative
than designs which
might
preparation.
With
the advent
of the Western
Area Power Administration,
Department
October
of 1977, many of the electrical
power
features
of the Bureau,
including
most
lines, were transferred
to the jurisdiction
of Energy.
However,
it was deemed
prudent
Bureau
would
because
Power
Mr. Holland
H. Farr, has more than 30 years of transmission
line design experience
engineer
with
the Bureau
of Reclamation.
He gratefully.acknowledges
the many
to this manual
by the personnel
of both the Bureau
of Reclamation
and the Western
Administration.
Special
recognition
to H. J. Kientz
for
suggestions,
and consultation;
R. D. Mohr
who provided
the technical
Bureau
of Reclamation,
U.S. Department
is given
to F. F. Priest
his computer
treatment
continuity.
This
of the Interior,
Cdlorado.
. ..
111
for his encouragement,
of the concepts;
and
manual
was prepared
and
Engineering
and Research
published
Center,
to
by the
Denver,
ABBREVIATIONS
ACSR
aluminum
conductor,
AIEE
Alcoa
American
Institute
Aluminum
AND SYMBOLS
steel
of Electrical
Company
ANSI
American
National
,4WG
American
Wire
BIL
basic
impulse
Standards
insulation
level
International
extra
IEEE
Institute
K
conductor
loading
LP
low
(distance
MS1
NBS
maximum
National
Bureau
NESC
National
Electrical
OGW
SAS
overhead
ground
sum of adjacent
UHV
USBR
ultra
high voltage
U.S. Bureau
of Reclamation
gigapascal
GPa
Hz
kcmil
hertz
thousand
kPa
kV*A
kilopascal
kilovolt
kWh
MPa
kilowatt
N/m
N*m
Institute
Gage
EHV
point
Engineers
of America
CIGRE
high
reinforced
Conference
on Large
Electric
Systems
voltage
of Electrical
and
Electronic
Engineers
constant
between
low
sag increase
of Standards
Safety
wire
spans
circular
mils
ampere
hour
megapascal
newtons
per meter
newton
meter
iv
Code
points
in adjacent
spans)
CONTENTS
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Preface
:\bbrc\
ialions
and
CHAPTER
syn~hols
I. BASIC
Field
data
Safety
Cost
6
7
8
9
10
CHAPTER
.....................................
of type
Single
wood-pole
(b)
H-frame,
(c)
(d)
Single-circuit
Double-circuit
(e)
Structures
(f)
Transpositions
structures
...................
4
steel structures
steel structures
....................
...................
s
...................
long-span
construction
.....................
and effective
spans
.............................
Selection
of conductors
................................
Stress-strain
curves
The parabola
and the catenary
........................
Design
instructions
Transmission
data
II. CONDUCTOR
srnnmary
tension
calculations
19
20
21
9
10
14
21
form
23
...................
2s
................................
charts
Preparation
........................................
of sag template
Inclined
spans
using
Coppcrwcld
sag calculating
29
32
..........................
38
SO
....................................
...............................
conductors
Galloping
Broken
conductors
Insulator
effect
III.
7
SAGS AND TENSIONS
Sag and
Spans
7
................................
line
12
CHAPTER
6
6
Special
ruling,
ion
18
6
..................
special
conditions
..............................
informat
16
17
.4
structures
wood-pole
for
4
.......................
.....................
of construction
(a)
General
1S
2
....................................
11
13
14
1
2
......................................
estimates
(g)
Normal,
with
iv
DATA
codes
Selection
5
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
...
III
56
................................
on sag and
concentrated
tension
in short
spans
...........
........................
loads
77
99
INSULATION,
LIGHTNING
PROTECTION,
AND CLEARANCE
PATTERNS
Insulation
coordination
Lightning
Conductor
protection
clearance
.............................
...............................
.........................
patterns
V
103
106
111
TRANSMISSION
vi
CHAPTER
22
LINE DESIGN MANUAL
IV. STRUCTURE
LIMITATION
GUYING CHARTS
AND
127
127
General
........................................
..............................
Components
of charts
...............................
Preparation
of charts
23
24
CHAPTER
25
V. ADDITIONAL
Stresses
Structure
26
in wood-pole
spotting
266
266
required
....................
...........................
(c)
Determining
...........................
26%
(d)
(e)
Insulator
General
...........................
..........................
268
273
Kight-of-way
Armor
Corona
uplift
sideswing
instructions
and
building
clearance
sag data
(a)
Sag tables
(b)
Sag and
Transmission
274
282
284
......................
.................................
292
.................................
292
292
300
insulator
line
266
.....................
rods and vibration
dampers
........................................
Stringing
Bibliography
213
........................
structures
.................................
Data
and equipment
Process
of spotting
28
31
DATA
(a)
(b)
27
29
30
127
offset
equations
data
for
inclined
spans
........
...........................
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
303
APPENDIXES
A.
A method
for computing
transmission
spans adjacent
to a broken
conductor
B.
Useful
C.
Conductor
Index
figures
and
and
tables
overhead
line
sags and
..................
tensions
307
............................
ground
wire
data
tables
in
............
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..~....
339
441
479
CONTENTS
1
Conductor
for
and
USHR
Mathematical
transpositions
calculation
form
(metric)
tension
calculation
form
(U.S.
Stress-strain
furnished
by
tension
parabolic
and
and
and
and
curve
catenary
showing
length
line data
of standard
13
I-I
Typical
sag template
15
Sag and
tension
origin
16
template
Sag and
form
for
(metric)
form
for
on
example
on
construction
calcldation
span
tension
Sag on inclined
span-parameter
of cxampk
% method
problem
on
22
parameter
Conductor
23
Conductor
24
problem
Overhead
25
example
Overhead
26
IIalf-sag
sag
Zmethod
sag and
(U.S. customary)
tension
calculation
galloping
sag and
conductors
24
33
......
34
sag
36
problem
on
sag
..............
38
..............
................
39
44
using
47
span using
..................
form
(metric)
ellipses
on
for
calculation
on
for
,49
example
................
galloping
example
form
52
example
...........
on
galloping
conductors
(U.S. customary)
ground
wire sag and tension
calculation
form
for
..........
problem
on
galloping
conductors
(metric)
ground
wire sag and tension
calculation
form for
problem
tension
form
problem
an inclined
span
........................
21
example
18
36
method
method
parameter
%method
(metric)
Results
of example
problem
on an inclirled
on
18
......................
span-equivalent
span-average
problem
15
16
17
22
inclined
Sag on inclined
Restllts
as
...................
form
tension
..........................
on
I4
problems
............
curves
(U.S. customary)
percentage
relationship
between
summary
sag and
12
used
example
problems
..................
customary)
Sag
of values
.........................
.........................
calculation
form for example
.................................
(metric)
tension
calculation
form
for example
(U.S.
11
....
..................................
Transmission
Explanation
template
..........
customary)
for an ACSR,
26/7
conductor
.................
Association
curves
calculation
7
........................
equations
equations
catenary
tension
span
illustrating
calculations
calculation
and
parabolic
Catenary
curves
and creep curves
the Almninum
Sag and
Sag and
creep
tension
9
19
20
3
tension
and
criteria
..................
sag and
curve
curve
18
design
sag and
Parabolic
Catenary
17
for
ratenary
Standard
7
8
12
wire
.........................
Standard
in sag and
10
ground
lines
solution
Stress-strain
6
overhead
transmission
vii
conductors
problem
on
for
(U.S.
galloping
customary)
conductors
53
54
....
...
54
55
. ..
VIII
TRANSMISSION
LINE DESIGN
MANUAL
Page
b'igrrw
Profile
28
Sag and
problem
tension
calculation
form for
.................................
(metric)
broken
conductor
29
Sag and
tension
broken
conductor
30
31
of spans
used
for
broken
calculation
form
Curves
for
broken
Sag template
for
33
Conditions
condition
for
problem
problem
conductor
60
61
tension
for equilibrium
before
......................................
(U.S.
to broken
and
after
68
sohltion
of unbalanced
condition
(metric)
Graphical
solution
of unbalanced
condition
(U.S.
36
Nomenclature
37
tension
Sag and
39
40
tension
(U.S.
customary)
calculation
Spans
Graphical
rnethod
43
conductor
Reduction
required
of angle
with
structure
concentrated
height
(metric)
tension
effect
for
insulator
effect
problem
problem
(U.S.
94
........................
determining
additional
100
length
of
..........
for concentrated
load problem
of protection
against
lightning
patterns
according
tension
the
three
types
to
of voltage
112
clearance
pattern
problem
calculation
form
for
.................................
clearance
pattern
problem
form
113
for
side
view
114
of structure
at conductor
121
......................................
structure
49
Clearance
pattern
for a 30s
......................................
tangent
structure
so
conductor
Clearance
pattern
angle
for
101
110
for
pattern
for a 30s tangent
......................................
Clearance
conductor
effect
90
insulator
Clearance
conductor
51
problem
for
47
conductor
problem
85
form
calculation
(U.S. customary)
Assrmled
dimensions
18
effect
.......................................
Sag and
elevation
insulator
..................................
16
76
on sag and
78
insulator
loads
for
Superimposed
clearance
stresses
.............................................
Sag and
for
75
...
81
Tension-temperature
curve
for
customary)
.....................................
42
4.5
form
effect
..........
customary)
.................................
41
44
determining
insulator
..............................
spans
Tension-temperature
curve
for
(metric)
.......................................
Sag and
67
unbalanced
Graphical
38
66
.....
conductor
35
(metric)
.......
customary)
due
34
in short
tension
calculation
.......................................
6.5
.............
(metric)
problem
reduced
for
57
...........................
problem
(U.S. customary)
Curves
for broken
conductor
32
conductor
..........
27
a 30A
with
single
122
with
duplex
123
structure
with
single
124
......................................
pattern
for a 30A angle
.......................................
structure
with
duplex
125
CONTENTS
52
Condnctor
sag and
problem
53
on steel
Condnctor
iX
tension
calcnlation
form
for example
strnctnre
limitation
chart
(metric)
tension
calcnlation
form
for example
structure
limitation
chart
(U.S.
sag and
. . . . . . . . .
13s
. . .
136
54
Center
phase
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
of a steel structure
limitation
chart
(metric)
. . . . . . . . .
137
5s
angle
Example
56
Example
limitation
chart
. .
148
57
Conductor
problem
sag and tension
on wood-structnre
calculation
limitation
form
chart
for example
(metric)
. . . . . . . . .
IS0
58
Conductor
sag and tension
on
wood-structure
calculation
limitation
form
chart
for example
(U.S. customary)
59
Type
HS
Type
HSB
problem
on steel
of a steel
problem
60
61
for
type
structure
wood-pole
3OS steel
structure
(U.S.
no line
customary)
. .
. . . . . . . . . . . . . . . . . . . . . . . . .
wind force
ground
wire
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
sag and tension
calculation
form for
158
example
problem
on
wood-structure
. .
160
Overhead
grourld
wire
example
problem
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
sketch
of one pole of a type FIS wood-pole
161
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
161
wood-pole
structure
sketch
of wood pole
sag and
limitation
tension
chart
calculation
on wood-structure
chart
65
66
Single-line
67
structure
with
X-brace
Force
triangle
showing
68
Force
69
limitation
chart
(U.S.
Force
triangle
showing
70
Type
3A
71
Type
3AB
72
Type
3TA
73
HalfHalf-
and
and
full-sag
full-sag
ellipses
ellipses
for
for
type
type
HS wood-pole
HSB wood-pole
Half-
and
full-sag
ellipses
for
type
3AC
structure
sketch
limitation
chart
triangle
angle
of top
portion
HS
for
(U.S.
wood-pole
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
angle of bias lines for wood-structure
163
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
168
(metric)
showing
of a type
(metric)
form
limitation
customary)
Single-line
angle
of bias
for
wood-strncture
. . . . . . . . . . . . . . . . . . . . . .
conductor
force due to line
168
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . .
169
177
. . . . . . . . . . . . . . . . . . . . . . . .
178
wood-pole
customary)
resnltant
lines
structure
wood-pole
structure
wood-pole
structure
. . . . . . . . . . . . . . . . . . . . . . . .
wood-pole
. . . . .
. . . .
189
structure
. . . .
191
193
F&sag
ellipses
for type 3TA
4267-mm
(14-ft)
pole spacing
wood-pole
structure,
tangent,
. . . . . . . . . . . . . . . . . . . . . . . .
77
Half-sag
wood-pole
4267-mm
Full-sag
angle,
ellipses
for
(14-ft)
ellipses
11 278-mm
type
pole
for
3TA
spacing
type
(37-ft)
3TA
pole
structure,
spacing
structure,
187
tangent,
. . . . . . . . . . . . . . . . . . . . . . . .
wood-pole
180
structure
structure
76
78
151
154
1ss
compute
Overhead
strncture
147
157
63
74
75
with
. . . . . . . . . . . . . . . . . . . . . . . .
62
wood-pole
customary)
strnctnre
. . . . . . . . . . . . . . . . . . . . . . . .
showing
values
needed
to
Type
3AC
Single-line
64
V-string
90°
194
line
. . . . . . . . . . . . . . . . . .
195
TRANSMISSION
X
LINE DESIGN MANUAL
FigUIV
79
Page
Half-sag
ellipses
angle,
80
81
Full-sag
angle,
ellipses
4267-mm
Full-sag
ellipses
angle,
8230-mm
82
Half-sag
ellipses
angle,
4267-mm
83
Half-sag
ellipses
84
angle,
Full-sag
85
86
87
angle,
Half-sag
angle,
88
for
11 278-mm
type
(37-ft)
for type
(14-ft)
for
type
(27-ft)
for
type
(14-ft)
for
3TA
wood-pole
structure,
spacing
..................
pole
3TA
pole
90 O line
196
wood-pole
structure,
spacing
....................
60’
3TA
wood-pole
60°
line
pole
spacing
structure,
60°
line
....................
structure,
60°
line
3TA
pole
line
197
structure,
198
....................
wood-pole
spacing
wood-pole
199
type
3TA
8230-mm
ellipses
(27-ft)
for type
pole
3TA
spacing
....................
wood-pole
structure,
45 o line
angle,
Half-sag
6096-mm
ellipses
(20-ft)
for type
pole
3TA
spacing
....................
wood-pole
structure,
45 o line
angle,
6096-mm
(20-ft)
Full-sag
ellipses
pole
spacing
type
3TA
wood-pole
4572-mm
ellipses
(IS-ft)
for type
pole
3TA
spacing
....................
wood-pole
structure,
4572-mm
(15-ft)
pole
spacing
for
200
201
....................
structure,
202
30 O line
203
30°
....................
limitation
chart
......
chart
(metric)
........
chart
(U.S. customary)
89
Instructive
Example
example
of a wood-structure
of a wood-structure
limitation
90
Example
of a wood-structure
91
Additional
92
93
Example
Example
94
95
Standard
guying
arrangement
for type 3TA structure
29-m type HS 230-kV
structure
with class 2 Douglas
96
95-ft
97
(one X-brace)
29-m type HSB
98
poles (one X-brace)
Free body diagram
99
Free
data
chart
required
limitation
for
the
line
wood-structure
customary)
(one
chart
chart
crosstie
body
HS
structures
structures
class
example
of pole
2)
(one X-brace)
....................................
Free body diagram
of pole above
plane
102
Free
customary
customary
example
of pole
2 Douglas
fir
2 Douglas
209
211
poles
fir
219
of inflection
and
to the
example
between
221
planes
101
diagram
.........
fir poleg
..........................
between
with
(U.S.
class
...............................
of pole above
plane
example
2) .....................................
95-ft
type HSB 230-kV
structure
body
.......
217
with
100
crosstie
(metric)
(U.S.
214
with
...................................
230-kV
structure
diagram
207
210
...................................
230-kV
structure
(metric
206
. .
208
wood-pole
wood-pole
.....................................
X-brace)
type
for
for
205
limitation
.........................................
guying
guying
204
of inflection
(metric
223
class
2 Douglas
fir
poles
232
of inflection
and
to the
2)
....................
planes
of inflection
2) ., .............................
234
(U.S.
235
CONTENTS
29-m
type
poles
104
105
HSB
(two
230-kV
3)
107
(two X-braces)
Free body diagram
type
crosstie
HSR
(U.S.
230-kV
fir
243
customary
109
customary
example
Typical
sag template
110
Typical
plan
and
111
superimposed
Typical
plan
and
diagram
profile
114
Average
and
Sag and
insulator
example
3)
between
bundles
poles
(II)
snow
of inflection
(U.S.
2.59
spotting
conductor
sag template
269
showing
use of sag template
271
284
fair
287
weather
with
different
................................
form
..................
voltages
free running
stringing
120
insulator
offset
Profile
of spans
121
sag correction
...................................
Stationing
equation
for common
survey,
assumption
122
Stationing
equation
123
survey,
Station
assumption
designations
calculation
form
sheaves
insulator
operations
offset
and
...............
for
problem
...............
on
problem
on
.........
sag correction
Sag and
example
(metric)
for
and sag correction
for example
problem
example
(U.S. customary)
on insulator
offset
293
297
298
line
common
point
on a transmission
No. 2 ...........................
when station
back is greater
than
line
1
Station
back
designations
point
...........................
301
for
when
station
.........................................
297
and
on a transmission
No.
...
288
290
293
sag
301
station
ahead .........................................
124
267
......
structures
..........................
119
tension
2S7
....................
with
loss under
for different
when using
and
to the
waves in a conductor
(A) fair weather,
(B) rainfall,
calculation
offset
and
...............
required
for calculating
data during
stringing
tension
of inflection
planes
drawing
of corona
Corona
loss curves
Conductor
tensions
Dimensions
correction
fir
..............................
Schematic
of vibration
Corona
loss curves
for
conductor
1 Douglas
255
plane
...................................
profile
drawing
113
valrles
class
3) ..............................
(plastic)
used for
uplift
hoarfrost,
with
above
of pole
in determining
(C)
247
structure
of pole
Free
body
24.5
..................................
108
118
1 Douglas
.....................................
95-ft
116
117
class
body diagram
of pole above plane of inflection
and to the
crosstie
(metric
example
3) ..........................
Free body diagram
of pole between
planes of inflection
(metric
106
115
with
..............................
Free
example
112
structure
X-braces)
xi
302
ahead is greater
than
stat&n
302
TRANSMISSION
xii
NESC
Functions
P curve
conductor
P curve
conductor
6
H
curve
conductor
7
11 curve
conductor
..................
loading
constants
(K)
.........................
sag template
of % ...................................
27
37
41
for
computations
for example
problem
................................
(metric)
computations
example
problem
..........................
customary)
(U.S.
computations
for
computations
(U.S.
example
problem
..........................
customary)
No.
l-broken
I he
computations
for example
................................
for
No.
2-unbalanced
example
problem
..........................
No.
2-unbalanced
11
P
curve
full-load
computations
condition
13
H curve
computations
14
full-load
II curve
condition
computations
no-load
conditiou
15
H
16
no-load
Insulation
conditiou
selection
17
Insulatiou
selection
18
Insulation
Minimum
curve
(grade
computations
69
No.
2-unbhanced
example
problem
..........................
No.
2-unbalanced
for example
problem
..........................
(metric)
No.
2-unbalanced
problem
No.
....................
2-unbalanced
No.
2-unbalanced
problem
No.
....................
2-unbalanced
customary)
H
69
problem
for
12
64
problem
10
(U.S.
63
for
condition
(U.S. customary)
P curve
computations
for example
................................
condition
(metric)
condition
63
l-broken
9
computations
l-broken
No.
computations
(metric)
curve
No.
................................
Line data
condition
data
l-broken
problem
(metric)
example
No.
62
for
8
I9
MANUAL
conductor
Calculations
5
LINE DESIGN
for
example
70
70
71
(U.S. customary)
for example
problem
...........................
(metric)
for
example
72
73
74
107
(U.S. customary)
for 34s kV ........................
........................
for 230 kV
108
20
Conductor
clearance
surface-wood-pole
to pole ground
wire or crossarm
.......................
construction
21
Angular
of suspension
22
USBK
Minimurn
23
109
........................
selection
for 115 kV
factors
of safety
for wood-pole
construction
R) .......................................
limitations
wood-pole
structures
factors
of safety
for
......................................
California
Conductor
clearance
surface-wood-pole
insulator
swing
for
129
129
standard
129
..........................
wood-pole
construction
to pole ground
wire or crossarm
..............
construction
in California
in
131
131
. ..
CONTENTS
21-
Stttntttary
of loads
lertgths
2s
26
and
Stttntttary
lengths
Stttnrttary
of loads
and
Sttrntnary
Minimum
NESC
29
Mirtirttttrtt
NESC
irt structure
low-point
of loads
lengths
28
tttetnbers
distartces
and
in slrrtctttre
for
for
242
3) . . . . . . . . . .
254
spatt
light,
clearartce
rttedittrn,
and
to buildings-USBR
heavy
loading
. . .
266
startdard
for
. . . . . . . . . . .
275
cxatttple
horizontal
clearance
to buildings-USBR
and heavy
loading
(rttetric)
light,
tnedittrn,
horizontal
standard
(U.S.
2)
span
various
customary
231
. . .
various
exarttple
tttetnbers
(U.S.
span
2) . . . . . . . . . .
for various
span
cttstorttary
exatnple
(metric.
distartces
various
exarttple
rnerttbers
distartces
low-point
for
(rttctric
of loads iii structure
rttetttbers
artd low-point
distartcrs
(U.S.
lengths
27
itt structure
low-point
x111
crtstorttary)
3)
for
. . . .
275
30
Right-of-way
values-NESC
light
. . . . . . . . . . . ,
276
31
32
Right-of-way
Right-of-way
values-NESC
values-NE%:
light loading
(U.S. crtstotttary)
. . . . ,
rnedittrn
loadirtg
(metric.)
. . . . . . . . .
277
278
33
Right-of-way
values-NESC
ntedirtrtt
. . .
279
34
35
Right-of-way
Right-of-way
values-NESC
values-NE%:
heavy
heavy
(metric)
. . . . . . . . . . .
(U.S. rttstotnary)
. . . .
280
36
Data
frottt
correctiott
37
Data
1% I
problettt
(metric)
front
correction
example
example
(U.S.
loading
(metric)
loading
loadirtg
loading
ott insulator
(U.S.
offset
cuslorttary)
and
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
problettt
crtstornary)
281
sag
299
on insulator
offset
artd sag
. . . . . . . . . . . . . . . . . . . . . . . . .
. . . . .
340
341
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
342
township
showing
sectiort
rtttrttbering
lartd section
showing
corner
and l/l6
. . . . . . . . . . . . . .
B-2
Typical
Typical
13-3
Azirttitth
H-4
I~eveloprttertt
of forttirtla
for rnaxirnttrrt
rtiorttertt
of resistance
ort wood poles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
343
13-s
Grottnd
344
chart
resistivity
in the
Urtited
States
desigrtatiotts
. . . . . . . . . . . . . . . . . . .
TRANSMISSION
xiv
LINE DESIGN
TABLES
IN
MANUAL
APPENDIXES
Pa&?
Table
B-l
Maximum
ground
B-2
moment
line-USBR
of resistance
standard
for pole circumferences
.........................
at
moment
of resistance
for pole circumferences
..........................
at
Maximum
ground
line-ANSI
standard
B-3
B-4
Pole
circumferences
for
Douglas
fir
Pole
circumferences
for
western
red
B-5
Permanent
set values
for
Alumoweld
B-6
Permanent
set values
for
steel
B-7
Flashover
characteristics
B-9
Flashover
Relative
B-10
Barometric
B-l
1
B-13
B-14
Pressure
Permanent
c-2
(metric)
Permanent
(U.S.
c-3
c-4
c-5
Conductor
Conductor
Conductor
C-6
Conductor
medium,
medium,
pine
385
...............
strand
....................
strand
of suspension
insulator
351
419
420
strings
and
air
424
Conductor
sag-tension
C-l
southern
yellow
................
cedar
..........................
values
of air gaps
...............
air density
and barometric
pressure
....................
pressure
versus elevation
B-12
Equivalent
Selected
and
423
Mass per unit
species used
B-15
348
...
........................................
gaps..
B-8
345
volume
and relative
mass
..............................
for poles
temperature
computations
area
due
set,
and
and
and
and
and
and
427
to wind
and
for
final
normal
428
velocity
data for standard
electrical
........................
conversions
set, creep,
and initial
.......................................
customary)
of wood
coefficients
of expansion
...........................
on a projected
metric
SI-metric
density
426
426
...........
429
......
conductors
431
moduhts
values
442
creep,
and initial
and
.................................
final
overhead
overhead
overhead
..........
data (metric)
data (U.S. customary)
values
for NESC
light,
....................
heavy
loading
overhead
heavy
ground
ground
ground
loading
wire
wire
wire
(metric)
ground
(U.S.
430
wire
values
customary)
modulus
for
values
NESC
.............
452
462
....
466
470
light,
474
(<Chapter
I
BASIC DATA
1.
Field
necessary
Data.-Before
to gather
construction,
establishment
design
certain
requirements
preliminary
for
a transmission
information
prior
line
can
be formulated,
to establishing
and the desired
conductor
and overhead
ground
wire
of the voltage
on major
transmission
lines, the number
the
sizes and
and type
it is
voltage,
type
of
types.
Usually,
of lines required
the
in
a given area, and the type of construction
to be used depends
on a comprehensive
system study. This
study would include
the size and location
of generators
and loads, and the possibility
of using existing
transmission
facilities.
After
a system study has established
the required
voltages
and the end points
of the transmission
and
lines,
to prepare
a. Operating
b.
Average
the following
designs:
voltage
and peak
information
is required
of the line.
loads to be transmitted
over
the
to establish
line,
or the
the
peak
details
load
of construction
and
estimated
load
factor.
c.
per
Value
in mills per kilowatt
hour of the
month
or year of capacity
to be served.
d.
A summary
of local climatic
(1)
Maximum
and minimum
(2)
(3)
e.
and
muskeg.
A map
showing
substations.
g. The
The
length
velocities
with
of ice expected
general
route
navigation
from
a., b., and
is used
mainly
specifications
clearance
c., is used
to establish
prepare
h.
Whether
i.
Date delivery
of power
is required.
Delivery
points
for Government-furnished
i
material
required
k.
Key map,
1.
Drill
logs
line
and
of the
To
the
will
and
a summary
designs,
the
sheets,
of footing
and
line,
for,
to determine
the
required
following
the
value
special
1
river
most
and
lake
economic
and
per
kilowatt
and
drawings.
for
tower
and
agents,
intermediate
crossings.
conductor
size.
The
requirements
is required:
forces:
the
crossing
corrosive
structural
information
or Governrnent
steel
or other
of terminal
additional
materials,
conditions
alkali
mechanical
by contract
and
sand,
locations
requirements
the
be constructed
at each point.
plan and profile
and
and without
ice.
on the conductors.
smoke or fog atmospheres.
that is, the presence
of rock,
of, and
information
other
information
for the line.
the
to be transmitted,
conditions
including:
temperatures.
(4)
Presence
of corrosive
A summary
of soil conditions,
swamps,
f.
Maximmn
wind
Radial
thickness
energy
proportion
lines
or special
of each
steel
item
structures.
of
TRANSMISSION
2
2.
Safety
National
Codes.-The
Standards
NESC
Institute),
supply
and communication
where
it is not
certain
safety
rules
not
provide
The
from
code
specifies
structures,
circuits,
which
the
However,
design
when
also be taken
those
into
Loading
the latest
by
than
Many
states
states
recognize
lines
in California
been
those
and
prescribed
NESC
code
also
be based
line,
may
general
area.
cover
state
the
force
for
of railroads,
weather
the
The
rules
important
to the
public.
supporting
thoroughfares,
geographic
or heavy
loading
and climatic
the use of heavier
that
construct
and
general
areas
in which
more
and
conductors
the
medium,
We
of NESC.
for crossings
local
indicate
of the
those
open
important
lines.
specifies
on light,
of electric
it is very
work
loadings
requirements
conditions
to
line
(American
over
of these
intended
design
The
shall
for
the
have
as the
should
so noted.
in a code
One
climbing
general
special
standard
be designed
area
rules
in which
regarding
for transmission
in accordance
California
Public
It is imperative
have
clearances
areas
loading
in
conditions.
conditions
lines
the
line
electrical
should
conditions
and
is being
than
designed.
construction;
distribution
Utilities
Commission
however,
circuits.
Rules for Overhead Electric
with
3.
used
Cost
by
to make
the
most
Transmission
Line Construction,
[ 11.’
line,
construction.
They
costs
making
types
of construction
on past
and
also
are also
system
A final Engineers
the line, is prepared
cost
in brackets
general
Preliminary
of various
when
certain
latest
refer
to items
state
at least
a minimum
allowable
and
that
often
types
to determine
used
one
Ensure
of cost
are
the
to compare
of line
that
to assure
is too
that
code
and
NESC
all applicable
design
overlooked,
all structures
in which
estimates
used
data
in the
and
Bibliography.
made,
the
amount
of funds
of construction
the economy
This
on current
are
to determine
the
construction.
are to be determined.
bid
be taken
applicable
that
cost
For
and
example,
feasibility
is especially
Cost Estimate,
based on the cost
for each construction
specification.
and
of the
should
estimates
types
studies
editions
Care
have
factors
will
be met.
is the
the
safe
proper
climbing
codes.
Estimates.-Two
estimate.
transmission
the
lines.
important
factors
of safety,
for linemen
on structures.
prescribed
engineers’
that
of transmission
been
of the most
clearance
’ Numbers
maintenance
are
ANSI
are constructed
by fencing,
transmission
transmission
that
municipalities
for all designs
based
lines
by
maintenance
of the example
problems
in this manual
were developed
using the Sixth Edition
of NESC
[2];
most of the problems
use the current
1977 Edition
[3]. Problems
using the old Sixth Edition
be used
compare
special
lines
for
General Order No. 95 of the
have
rather
to the
circuits.
as local
NESC
issued
and
conditions
and conductor
and overhead
ground
wire tensions
shall be in accordance
with
edition
of NESC
with
exceptions
as shown
on figure
1 or by specific
heavier
loading
conditions
Some
however,
and
a particular
account
prescribed
Code),
installation
public
and
of construction,
communication
designing
the
transmission
construction
but
grades
of transmission
Safety
for
the general
of safety
requirements,
and
MANUAL
unless the regulations
with NESC
constructed
are more stringent
than
standpoint
clearances,
strength
power
from
specifications,
the
rules
overhead
in the
in accordance
line is being
detailed
requirements
them
be observed
Electrical
safety
Because
to isolate
our transmission
lines
particular
transmission
do
(National
contains
lines.
possible
LINE DESIGN
prices
a preliminary
economic
to be requested
these
comparisons
would
at voltages
as quoted
a final
voltages
and
of 230 kV
of a
budget
routes,
of all items involved
Both the preliminary
of materials
in the
on alternate
of different
true
and
feasibility
to
be used
alternate
and
in the construction
and final estimates
by
for
and
manufacturers.
above.
of
are
CHAPTER
CONDUCTOR
AN0
OGW
FOR “SGN
FULL LO.9
Fii
LCunductor
I
CATENARY
DESIGN
TNAUSYISSION
LINES
CONDUCTOR
NO LOAD
and overhead
From Dwg. 40-D-5169.
I-BASIC
ground
I
NO LOAD
I
1
wire’catenary
DATA
CRITERIA
O”ER”El0
FULL LOAD
I
GROUND WIRE
NO LOAD
I
“9
design criteria
for USBR transmission
lines. 104-D-1046.
TRANSMISSION
4
4.
Selection
of Type
a transmission
line,
to be used,
desired
or necessary
in the
according
to
structures
in a transmission
and methods
structures.
function:
lines,
special
are given
All
40-D-
original
structures.
to design
conductor
heights
Brief
data
for specific
are on file
are supplied
Since the
structure
Design
These
special
such
transmission
Bureau’s
Denver
units
associated
with
on the basic
types
wood-pole
as standard
three
classes
of the
hardware,
drawings
All standard
for general
design
limitation
and are given
104-D-
office,
and
reproducible
various
field
offices.
of structures
of materials
into
structures,
design
on
are to be used for all transmission
designs.
and loading
conditions
for transmission
and types are varied
to maintain
efficient
discussions
availability
80 to 90 percent
as sag templates,
lines
in the
the
type
are divided
Usually,
drawings
structural
drawings,
of conductors
and
Standard
and established
ratings.
to be used
size and
line
(3) tension.
class.
of construction
line,
of construction,
tangent
require
type
of the
in a transmission
and
designed
voltage
conditions
developed
drawings
been
for various
numbers.
are usually
drawings
and
where
(2) angle,
the
voltage
costs
used
are of the
have
lines
the
lengths,
structures
line
of installation
except
span
The
MANUAL
en selecting
to consider
(1) tangent,
use on transmission
tables,
of Construction.-Wh
it is necessary
to be used
LINE DESIGN
charts,
or project
prints
drawings
and
sag
numbers.
of applicable
lines are often different,
span lengths
and economical
use of the standard
are presented
in the following
paragraphs.
(a)
Single Wood-Pole Structures .-The Bureau usually uses single wood-pole
structures
for voltages
from
2.3 through
46 kV. In addition,
where
right-of-way
is severely
restricted,
it is sometimes
necessary
to use single wood-pole
construction
for 69- and 115-kV
1ines. For lines up to and including
69 kV, two
conductors,
types of single-pole
structures
are designated
flattop and
are used
conductors
triangular
are supported
by a single crossarm
and are arranged
in the same horizontal
plane. In the
type,
the middle
conductor
is supported
at the top of the pole and the two outside
conductors
are supported
by a crossarm
below
both
single-pole
and H-frame
construction.
construction
is used; however,
crossarm
are used. For 115-kV
types
of single-pole,
which,
with reference
In the flattop
type
triangular.
the
For
top of the pole. Pin-type
insulators
69-kV
lines,
a type
of single-pole
suspension
insulators
with two
lines, a single wishbone-type
single-circuit
structures
and
tangent,
single crossarm
small line angle, double
to the arrangement
of the
of construction,
the three
their
conductors
structure
nomenclature
suspended
is used. The
are used
triangular
from the
common,
=
=
suspension,
suspension,
SA
SAT
=
=
vertical
conductor
attachment
suspension,
medium
line angle (up to 600),
tension,
large line angle (60 ’ to 90 ’ ), vertical
conductor
attachment
ST
STR
=
=
tension,
medium
line angle (0’ to 60 O), vertical
suspension,
transposition
structure
crossarm
H-Frame
tangent
be used
230-kV
structure
which
has a double-plank
crossarm.
Occasionally,
for lower voltages
where
long spans cannot
be avoided;
lines. The use of X-braces
between
the poles is standard
the use of longer
Wood-Pole Structures .-The
conductor
(b)
voltages
69 through
spans
161 kV.
and heavier
The
Bureau
usually
H-frame
designation
conductors,
upper
basic
are:
SS
SD
from
in
and to support
attachment
uses H-frame,
wood-pole
structures
for
originates
from the appearance
of the
this type of construction
must
however,
it is sometimes
used for
on H-frame
structures
to permit
the structures
under
transverse
loading.
The use of wood poles longer
than 27 m (90 ft) is not recommended,
except
for very special
cases,
because
they are not economical
and are difficult
to obtain.
For normal
wood-pole
construction,
it
is preferred
that the majority
of poles on lines with overhead
ground
wires should not exceed 19.8 m
CHAPTER
(65 ft) in length;
and on lines
18.3 m (60 ft).
Although
we normally
arise
(other
than
without
and
to permit
the
substation.
The basic
to obtain
reduced
types
HS
3AC
3A
and
high
(c)
161 kV.
Steel
clearance
for
on conductors
=
two-pole,
suspension,
=
three-pole,
suspension,
=
three-pole,
suspension,
=
three-pole,
tension,
and
H-frame
are also
many
were
transmission
line
types:
(1) tangent,
years
used:
steel
used
for
structures
an SAL-type
climatic
loading.
In 1975, the
the voltage;
system
steel
designate
the
voltages
under
long spans
loadings.
is used
special
type
to their
system
Medium
D =
Double
Heavy
Transposition
a 2 indicates
230
kV.
of the
number
and
The
=
Suspension
X
=
Heavier
suspension
with
ST
=
Heavier
suspension
type,
A
=
phase dead-ended
Angle
(insulators
in suspension)
T
=
Tension
Y
D
=
=
Tension
with large line
Dead end with variable
R
=
Transposition
small
to
for
second
is now
specific
digit
such
used
is a design
as crossings
spans
The
first
designator
designers
to immediately
letters
are added to the
letters
designed
as a basic
into
in three
line. For
identifying
structure
loadings.
above
for
light
designation
digit
for
indicates
for a particular
identify
two-digit
the basic
number
to
structure:
S
with
angle
suspension,
voltages
approach
in which
=
=
Circuit
all
and are designed
function
in the
=
voltage
spans
are:
for
for
H
TR
a two-digit
approach
conditions
are required,
by a nomenclature
system
permits
the steel structure
for any given line. The following
function
construction
M
and
For
angle
Tension
Angle
a specific
towers.
angle
line
T =
A =
for
situations
crossarm
Light
was changed,
exceed
angle
line
a single-circuit,
to use steel
nomenclature
=
was
not
occasional
in the
L
designed
This
used
their
double-plank
medium
designated
wires
Suspension
=
for example,
series of towers.
set of structures
were
structure
a set of structures
ground
and
line
0 ’ to 90 ’
lower
it is necessary
should
183 m (600 ft) of a substation;
therefore,
to permit
large line angles, where required,
overhead
small
of poles
up to 161 kV,
structures
are usually
of the self-supporting
(2) an gl e, and (3) dead end, according
S
Thus,
all lines
where
tangent,
Steel Structures .- Normally,
5
the majority
construction
over navigable
streams
where
high clearance
and
substations
and switchyards,
and for extra-heavy
Steel
general
wires,
for crossings)
for
structures
DATA
to guy any structure
within
are used in these locations
tensions
Single-Circuit
ground
structures
of structures
3AB
3TA
overhead
use wood-pole
example,
it is our policy
not
self-supporting
steel structures
I-BASIC
line
small
line
no line
angle
(0’
angle
angle
to 5 “)
(O’to
5O)
capability,
capability
angle (5’ to 30 “) capability
line angle capability
capability
outside
phases
in suspension,
center
6
TRANSMISSION
Thus,
a type
30s structure
The
limitations
in the
conductors
would
of a given
and
LINE DESIGN
be a 345kV
suspension
set of structures
overhead
ground
wires,
MANUAL
structure
will
depend
and
the
with
upon
a design
conductor
loading
area
designation
size,
where
of zero.
maximum
the
structures
may
be used
tension
are to be
used.
Double-Circuit
(d)
Steel Structures
necessary
to place two
cost of two lines along
are arranged
expected,
vertically
the
on one
conductors
loading
are expected,
contact
between
may
(e)
of the
steel
structure.
be located
the conductors.
directly
to offset
Contact
In
areas
above
the center
can be caused
structures
right-of-way,
structures,
where
one another;
conductor
lines
for Special
which
Conditions
and
however,
by galloping
ice loading
are
where
and
the
conductors
snow
possibility
or uneven
.-Sp ecial conditions
frequently
arise in the
use of special
structures.
Special
structures
the
not
ice
of any
snow
and
to use steel
Transpositions
.- To maintain
structures
to obtain
balanced
sufficient
conditions
phases
of a transmission
line, at least one
terminals.
However,
it has been determined
designing
of
are required
a higher voltage
line, (2) a branch
and (4) long spans, such as those
require
higher than normal
structures
to maintain
navigational
conductors.
Where navigational
clearances
over rivers or lakes
necessary
clearances
are required,
height.
of reactance
and
capacitance
on the
line
of uniform
configuration
three
transposition
barrel
should
be placed
between
major
that for less than 161 km (100 mi) between
terminals,
the unbalance
is not sufficient
to affect the operation
of the transmission
line or the protective
barrel, as used by the Bureau of Reclamation,
refers to a section
of a three-phase
The term
transmission
it is
For example,
if the three conductors
are located
directly
above one
one of the lower conductors
may drop its ice and spring
up into the
steel structures
are constructed
in the same general
types as the
necessitate
for a river or lake crossing,
or wider spacings
between
(f)
snow
to minimize
where: (1) a lower voltage
line is carried
on the same structure
below
line takes off from a main line, (3) switches
are required
in a line,
it is usually
where
or if it is desired
to reduce
the
the conductors
for each circuit
structures.
Structures
transmission
side
it is desirable
ice loading
on the conductors.
another
and covered
with ice,
conductor
above.
Double-circuit
single-circuit
.-Double-circuit
transmission
lines on a restricted
the same route.
On double-circuit
that
is divided
length
by two transpositions
arranged
so that
each
one-third
the length
of the section.
Specific
instructions
the design instructions
for each transmission
line.
into
conductor
regarding
three
parts
of approximately
occupies
each
transpositions
relays.
power
equal
phase position
for
should
be given in
The distances
between
conductors
in a transposition
must be studied
to determine
if adequate
minimum
electrical
clearances
will be obtained
in a given case. If possible,
it is helpful
to set up
model
of the transposition.
A model
will give good results
and will also present
the whole
problem
in perspective.
A problem
thorough
analysis.
A model
must
be made
to scale.
area in a transposition
eliminates
the possibility
A large
to hold the dowels in the desired
an inexpensive
way of duplicating
conductors,
between
conductors
Another
method
that
may
sheet
of plywood
may be difficult
to locate
of selecting
the wrong area.
for a base,
dowels
to support
correctly
The model,
the
without
a
of course,
conductors,
locations,
and adequate
string to represent
the conductors
various
questionable
line situations
‘such as clearances
and structures,
or between
conductors
and guys.
be used
geometry
to the problem.
This method
made and the problem
areas determined.
transposition
problems.
to determine
should
The
be used
formulas
these
clearances
is by
applying
a
screws
provide
between
descriptive
after an analysis
of the whole system
derived
on figure
2 may be applied
has been
to many
CHAPTER
I-BASIC
DATA
Dv v
-=-
First
v= kS$=kD,
dD*
dk =-2D,*+2k(Dv
D”
-=S
Solution
S
kS
SHkS
derivative
7
of
D* with
‘+
respect
to k:
DH2)
of differential
equation:
2
ti=(S-kS@
=D,(I-k)
DH
D2=DH2-2D,*
(h2)*
D,* + D,*
D= ~kDv)2+[DH(I-k)]2
D*=
+ OH2 -2kD,‘+k*D,*
Dv2+DH4
D”*
D*=
D,*
k2(Dv2+
For structures
at different
,/(Span)'+
(difference
13). where
rough
Special Long-Span
terrain,
it is often
solution
Construction .-To
necessary
5.
Normal,
span lengths
Ruling,
and Effective
obtainable
by using
take
to use spans
consideration.
To obtain
the required
spacing
may be used on single
wood-pole
structures,
structures.
For steel construction,
the structures
the
-2DH4+DH4
+ D,.,’
conductors
e
on crossarm)
is the slope angle.
in elevation)*
Figure S.-Mathematical
(g)
+D,*)
elevations:
spacing) (-Ices
Span
D,= V
v
D,*)
Remains the same (spacing between
D,= (Vertical
2
(D
D,*)~
(Dv *+ D,‘)
D* = D,2 -2kDH2+
D,
(D,*+
OH2 (Dv2+DH2)-2DH4+DH4
D*= k* D,* + (D, - kD,)*
D2=k2Dy2
+
for transpositions.
advantage
longer
104-D-1047.
of topographic
than
are
normal
conditions
for-
the
in areas
voltage
under
between
conductors
for long spans, longer
crossarms
and greater
pole spacing
may be used on H-frame
can be designed
for any required
conductor
spacing.
Spans.-Th
e normal span is used to determine
and compare
different
structure
heights.
The normal
span may be defined
of
8
TRANSMISSION
as the maximum
level
span
ground.
seldom
can
The
level,
attainable
with
usefulness
and
the
be calculated
a given
of the
actual
spans
the
following
from
LINE DESIGN
structure
normal
will
span
vary
MANUAL
height
and a given
is limited
because
considerably
from
conductor
the
the
clearance
transmission
normal
above
line
span.
The
profile
normal
is
span
formula:
Normal span in meters (feet) =
where:
P = height of conductor
L = conductor
clearance
C =
ruling
D =
conductor
ruling
The
changes
spans
the
span,
sag for
used
and
preparing
n spans
having
and
lengths
length
template,
ruling
which
level
span
be defined
in temperature
span
for
above
the
ground,
normal
span
is to be calculated,
m (ft)
m (ft)
m (ft)
span may
of varying
support
as that
span
will
most
loading,
between
as a basis
the
C, m (ft)
dead
ends.
nearly
agree
tables.
The
the
with
common
the
in the
average
sags and
ruling
span
dead
tension
definition
the conductor
L 1, L 2, Ls... L, between
of lengths
in which
A more
for calculating
stringing
length
for
ends
tension
is that
tensions,
any
may
conductor,
under
in a series
the
ruling
constructing
section
from
is
the
of transmission
be calculated
of
span
the
sag
line
following
equation:
L,3
Ruling span =
To
use this
is used
as a basis
structures
the
equation,
lengths
the structure
the
line
entire
exceptionally
rough
tensions
due to variations
in sections
In
isolated
the
ruling
a structure.
If the
point
of the
the
conductor.
the other,
support
supports
conductor
In this
the
low
that
spans,
is made
used
for
point
portion
the
case,
with
the
of the
of the
the
middle
span
conductor
conductor
by the
should
usually
and
short
spans
cannot
be avoided
a longer
or shorter
a change
ruling
spans
tensions
of the
end
should
for
of
be used.
because
same
sections
canyons
with
because
occurs
by the
between
each
to the
the
conductor
of a span
and
be closer
between
vary
of
be selected
span
span
do not
result
strength
the
amounts
of different
which
are dead-ended
which
is supported
by
elevation,
the
span.
portion
span
ruling
the
so that
span can be estimated
in ruling
or over
actual
is equal
will
line
span
at each
of the
is limited
span
before
a transmission
the ruling
crossings
to the
length
ruling
be estimated
for
ruling
where
as river
conductor
effective
span
Unbalanced
equal
must
structures
the
One
different
such
span
because
Therefore,
long
point
to designate
is at the
case,
is the
at the
and loading.
long
span
span is the term
low
this
of line
in temperature
end,
then
When
be dead-ended
spans.
Effecthe
will
profile.
must
where
However,
ruling
maximum
are located.
sections
+...L,
be known.
the
The
+ .. . Ln3
+L,
to locate
requirements.
structures
for certain
must
practice
as possible.
the
+L,
sag template,
good
clearance
before
L,
locations
the
It is always
except
conductor
horizontal
than
calculating
and conductor
accuracy
at each
structure
are as uniform
sufficient
ruling
for
are located.
span
The
the
i- L,3 + L,3
are at the
structure
actual
span.
to the lower
structure
will
support
If one
support
and
same
the
one-half
support
and
low
each
point.
is higher
structure
In effect,
of
CHAPTER
considering
the
the
equivalent
low
point
conductor
load
of a level
of the
span
conductor.
To determine
on one
equal
This
the total
spans;
6.
Selection
to consider
voltage
for
minimum
depends
of the
it without
has assumed
no-load
conditions.
the
sag and
initially.
When
values,
ru 1’m g s p an, the initial
(8.5 ft),
and
Bureau,
for
strength
(3954
to 3700
The
use of either
point
the
short
that
shorter
structures
by
The
electrical
the conductor
with
conductor
losses
studies
to twice
it is necessary
on the
line,
corona
conductor
cost,
and is determined
of designs
type
or design
amount
of conductor
before
instructions.
of corona
loss;
Corona
loss
surface.
of 13 832
economical
The
The
wind,
and
mm
(9.53
N (3110
lb) a t mimts
enough
and
using
short
spans
or very
the
tension
sag with
small
For
enough
some
small
are required.
structures
can
standard
height.
The
on a line
be supported
structures
Section
may
15 describes
considerations.
conductivity
to a temperature
of the conductor
that
would
must
cause
be high
annealing
enough
to carry
and consequent
N
no ice and no wind.
structures
to structure
is 17 580
the sag to increase
conductor
that
N/m
the immediate
structures.
of the
are
of 4.3782
and the
size conductor
permissible
in addition
tall
cost
the
ultimate
conditions
lb),
cause
mm
by
of the
loading
18 ’ C with
high
were
be 2594
N (7500
sag of the
increases
to use a larger
maximum
the
they
as determined
will
excessively
will
a constant
ft),
assume
on a 213.4-m
percent
heavy
of 33 362
in the conductor
usually
considerations
NESC
tension
is 2906
without
either
condition,
loading
less than
no wind
is 33-l/3
factor
be high
that
more
load
no wind
spans
limiting
the
initial
it will
conductor
no ice and
loading
for maximum
being
24/7
to
after
under
is unloaded,
tension
conditions
transverse
to a full
must
The
maximum
strength
as specified
the
ice loads
conditions
ultimate
ACSR,
and
urlder
conductor
and
no load.
(4-lb/ft2)
wind,
wind
no-load
of the
the
the
strength
specified
(0 OF) with
lb).
initial,
to carry
kcmil),
loading
the creep
spans.
and
percent
(477
heavy
structures
longer
line,
conductivity,
by the permissible
When
N (4429
or tall
conductor
of power
system
under
18 ‘C
no ice and
sag is so great
spans
galloping
galloping
0.19-kPa
long
from
greater
mm2
40 “F)
installation,
it becomes
limited
the
NESC
conductor
for a transmission
electrical
by ice and
sag being
a 242
19 700
use of reasonably
size conductors,
the
a tension
structure
structure.
of the ultimate
stretched.
be
ft) with
of the
is loaded
the conductor
after
(12.14
the
(3) 33-l/3
sag at minus
(0 ’ F) with
years
strength
to permit
sag, and
under
ice,
loading
18 ‘C
Ten
mm
will
radial
After
lb).
strength
40 OC (minus
(l/2-in)
lb/ft).
sag at minus
the
tension
conductor
at minus
13-mm
(0.30
the
this
is equal
be sufficient
(1) 50 p ercent
with
(700-ft)
must
ultimate
if we string
to consider
given
any
of the
for preparation
sea level,
is permanently
example,
it is necessary
below.
the conductor
conductor
tension
For
its final
selected
designers
conductor
of the
the
conductor.
above
exceeding:
and
for
vahte
determined
and
structure
span.
the sum of the adjacent
side
is usually
altitude
of 46 kV
one-half
to one-half
of the conductor,
line
the
effective
supports
is equal
the conductor
is usually
structure
between
the
spans
on either
in the
each
distance
to be transmitted,
used
line
voltage,
(2) 25 percent
conditions,
final
materials
strength
upon
conductor
load
strength
of conductor
voltages
mechanical
conditions,
line,
the
is called
effective
spans
only,
length
selecting
to the transmission
on the
for
be imposed
adjacent
of the
a transmission
diameter
is negligible
The
of the
of the
is assigned
which
of the
points
mechanical
availability
The
The
voltage
interference,
the
the line
sum
low
9
by any one structure,
supported
of Conductors.-When
the
and radio
and
or the
to twice
supported
The
DATA
structure
span
length
effective
between
in length
conductor
on each side of a structure.
distance
of the
hypothetical
the spans
the
side
I-BASIC
the load
reduction
without
in the
heating
strength
to
on
be
TRANSMISSION
10
of the conductor
voltage
drop
which,
in the line
use of reactors,
transmitted
over
conductor
between
the
line
in greater
be limited
to about
synchronous
Usually,
size than
available
results
and
the line.
value
transmission
must
capacitors,
a larger
various
in turn,
LINE DESIGN
sag and
reduced
of power
to control
to limit
heating
in the
conductor
and
the
will
result.
such
that
types
of conductors
minimum
above
this
the
and voltage
annual
cost
as well
as determining
fixed
(reactive
volt
line is sufficient
drop.
A balance
charges
on
Comparison
the most
the ground.
The
can be controlled
vars
losses in a transmission
is required
of losses
clearances
* however,
10 percent,
condensers
the value
MANUAL
must
to justify
must
the
by the
amperes)
be obtained
investment
be made
economical
in
the
between
the
size of any one type
of conductor.
Since
1945,
has proved
1945,
that
copper
(aluminum
conductor,
economical
than
other
were
that
copper
prices
aluminum
90 percent
ACSR
more
such
conductors
are now
of distribution
It is occasionally
being
steel
several
such
conductor
specified
conductor,
as copper
was more
for nearly
because
of its lower
or Copperweld-copper.
economical
all new
than
ACSR.
transmission
lines,
price,
Prior
Records
and
to
show
for about
lines.
necessary
to consider
the availability
it may be necessary
to complete
the transmission
economical
conductor.
Once the route
and length
of a transmission
conductor
type and size selected
to carry safely
power,
reinforced)
conductors,
mechanical
considerations
line
of the different
in a short
or distribution
and economically
remain
which
may
time
types
of conductors
without
regard
because
to the
most
line have been determined,
and a
the system
voltage,
current,
and
influence
the
choice
of conductor
and
will definitely
influence
the installation
methods.
The designer
must consider
such factors
as structure
and ground
clearances.
Thus,
the
heights
and locations,
span lengths,
conductor
sags and tensions,
designer
must have detailed
knowledge
of conductor
sag and tension
as a function
of span length,
temperature,
and
weight
loading.
Most
of this
information
is supplied
by conductor
manufacturers
in the form of tables and graphs;
however,
the designer
will usually
have to prepare
additional
aids
such as forms,
charts,
diagrams,
and templates,
that are related
to a specific
installation.
Figures
3
and .4 show a standard
form
that USBR
designers
use for conductor
calculations.
This form is a
Pa. [6]. Figure 3 shows metric
variation
of a form designed
by the Copperweld
Steel Co. of Glassport,
calculations
calculations
12, chapter
7.
for the conductor
previously
mentioned,
for the same conductor.
A detailed
description
II.
and figure
4 shows
the U.S. customary
of this calculation
form is given in section
Stress-Strain
calculations
Curves.-Most
of the mechanical
properties
required
are determined
by tensile
testing.
Wires used in the manufacture
conductors
are tested
in full section.
The loads
stresses based on an area of the original
section:
determined
in a tension
for sag and tension
of transmission
line
test
are reported
as unit
Load
Stress = Area
Elongation
elongation
is measured
is then
determined
as the
increase
in length
of a gage-marked
as
(Final Length) - (Original Length)
(Original Length)
length
on a test
specimen.
The
CHAPTER
DCm-578
I-BASIC
11
DATA
(3-78)
:“I’N’:“L’ SAGCALCULATIONS
LOADING
j T5!cp-\ LMST~ESSED LENGTH i
/3InIn
Ice
0. 9/~~kP=Wl~(W”‘)~-/8.0,
Permanent
No Ice.
Set 6 creep
NO Wmd
---.a--InIn
0.d!.#vsakPa
Permanent
(W’)
1
-18
1 -1
15.5
12
__
49
lo.
0.
0.000
15
999
O.RUfl
0,949
(w-y
(W’)
mm 1.3
kPa WwJ (W”‘)
Permanent
set 6 creep
- 5 I
110
,6o6!o.uoo
I
096
16
2594
i
!
114
/fJ , OO/
I/. ouu
!
mm ICO
Set S Crew
91)
,a/
I
O”$
I
m
O,/Ull
u.u/-?
62:
1
I
:
I
2.906
,
I
I
/9/j
I
I
I
/7
590
P.5
I
I 13
833
-,
k&d
I
I
I
m
/Q/ I
003
/aY
oofw
,
Qg
d
n,
/383
&/J/7
34
-7700
/
I
/
/9//
I
I
I
I
I
/ 49
,
I
1
I
I
I
SPANLENGTH(S)
m
I
1
j-18
1
I
I
1 49
1
I
I
I
I
I
I
I
I
I
I
I
SPANLENGTH(S)
I
I
I
m
I
I
I
I
15.5
32
40
.-
I
L
SPANLENGTH(S)
,
I
I
,
m
/
1
,
I
I
I
I
I
-18
-1
I
I
15.5
32 j
I
I
I
49
I/J
I
I
j
I
,
700
&&j
/.
115.5
*I
kPa Wind (W”‘)
Set 6 Crew
NO Wind (WY
I!?.? 462
.3 L
I
I
999
_
!
NO Ice. NO Wind (W’)
NO Ice.
! 5,P45
I
4
I
1
1
-1.9
-1
Permanent
lo.nK7
I
I
mm,ca
Permanent
0.0971
4693
SPANLENGTWS)H(S)
set 6 Creep
NO Wind
L
TENSION,N
1
/Q/
15.5
-18
-t
NO Ice,
m5-
SW,N
99
I
0
(W’)
kPa Wl”d
0./7-5210.02,
I
I
Ice
Permanent
7
1
m
3L
SPANLENGTH(S) 2’3.
32
49
Nmm
/o/
j
I
NO Wmd
999
/o/ ~U.OQU 393
SAG,mm
SIG FLCTOR
Y
I
’
1
-18
-1
NO Ice.
499
I
ice
,
Wind cw”%-/g
Set
?!6
SPANLENGTH(S)213.
1
Figure 3.4tandard
I
sag and tension
calculation
fornl (tnetric).
TRANSMISSION
12
DC-576
LINE DESIGN MANUAL
(S-76)
;;L;FL
CONDUCTOR
~77h’d
-.. I
Code
Name
Weight
Breakutg
Diameter
Load
&&!6
Tensat
inch
Initial.-&OF
Final,
Computed
&%,&!&?-lb
-1/oF
Loaded,
*F
*OF
by -
No Wind
X //300
lb
Area
2
% ti
lb
Temp.
18
% &$&lb
(AI
d
Coeff.
Modulus.
in2
of Linear
(E)
Final
0.000
o/&~
(W’)
No Ice.
NO Wind
(WY
per “F
SPAN LENGTH(S)
Ice.
Wind(W”‘)
6 creep
InitialAE
FEET
0
30
No
Ice.
No Wind
(W’)
60
90
-Inch
Pemlanent
SPAN LENGTH(S)
Ice.
Ib/ft2 Wind(W”‘1
set h creep
FEET
0
30
NO Ice.
No Wind
(W’)
60
90
120
Figure 4.-Standard
sag and tension
calculation
FinaljD.
lnltial
Exp.:
(W’)
No Wind
set
_25-
Date
Ice.
-Inch
-Ib/ft2
Permanent
Factors:
/7alb
Limltatlons:
Final.
No
LOADING h/ecrv
-
Rated
No Ice.
.h?dR 24
SAGCALCULATIONS
form (U.S. customary).
AE
‘/
u
53x
g,epLx
4
L
106
lb/in2
106
lb/in2
24
:i
CHAPTER
I-BASIC
DATA
13
Stress-strain curves are prepared from the data obtained from these tests. As the test specimen
is slowly loaded, readings of elongation are made so that the initial curve may be plotted. As the
specimen is unloaded, elongation readings are again taken so that the fin& curve may be plotted.
A typical, stress-strain curve for a wire has a straight line segment, which in the deformation
is
proportional
to the applied load. The unit stress (load divided by original area) is proportional
to
the unit strain (deformation
divided by original gage length). The numerical value of this ratio
(stress/strain), usually expressed in gigapascals (pounds per square inch), is the modulus of elasticity.
For an ACSR conductor, there is no straight line segment on the initial curve, so a straight line average
of the portion of the curve under use is used for determination
of the modulus of elasticity. The final
curve is always a straight line and has the same slope regardless of the maximum load applied, provided
the yield strength is not exceeded. The slope of this line is the final modulus of the conductor.
Other characteristics
of the test specimen may be determined from the stress-strain test. The
proportionul limitis the stress value at which the deformation ceases to be proportional to the applied
load. The maximum stress which can be applied without causing permanent deformation upon release
of the load is the elastic limit. The yield strength is the stress at which the deformation ceases to be
proportional
to the applied load by a specified percent of elongation (usually 0.2 percent).
Ultimate tensile strength is the maximum tensile stress which a material is capable of sustaining.
Tensile strength is calculated from the maximum load during a tension test which is carried to rupture
with the original cross-sectional area of the specimen. All metals have lower ultimate strength values
when subjected to a fluctuating
stress. The amount of decrease will depend upon the range of the
fluctuating
stress and the number of repetitions. Alcoa (Aluminum
Co. of America) states [7] that
research and experience in transmission line design indicates that if the limits of variation in tensile
stress are approximately
10 percent, the maximum value of the fluctuating stress necessary to produce
fracture will be approximately
70 percent of the ultimate strength. This stress is referred to as the
working limit.
Creep is the plastic deformation
that occurs in metal at stresses below its yield strength. Metal
that is stressed below the yield point will normally return to its original shape and size when unloaded
because of its elasticity. However, if the metal is held under stress for a long period of time, permanent
deformation
will occur. This deformation is in addition to the expected increase in length resulting
from the stress-strain characteristics
of the metal.
Figure 5 shows a stress-strain curve that illustrates the origin of values used in conductor sag and
tension calculations for transmission lines. An explanation of figure 5 is:
l
ADFG represents the initial loading curve plotted from test data taken during the loading of
a specimen in a stress-strain test.
l
The average slope of curve AF has been extended and labeled “Average slope of initial from
zero to full load.” The slope of this line is used for the initial modulus in calculations. The value
in this example is 40 GPa (5.8 x lo6 lb/in2).
l
CGis the final loading curve plotted from test data during the unloading on the test specimen.
The slope of this line is the final modulus.
l
The conductor represented by the curves is to have a maximum stress of 69-MPa (10 000 lb/in2)
under full load conditions.
l
BFis drawn parallel to the final curve CG and between the points for full load and zero load.
l
AB is the permanent elongation and is called the permanent set
l
The lo-year creep line is drawn from previously computed values. The creep value DEis read
horizontally
between a point on the initial curve and a point on the creep curve at the same
stress value.
TRANSMISSION LINE DESIGN MANUAL
14
-
30 000
200
175
2s 000
150
I
20000
/
N
.-E
125
2
5
2 - IS 000
100
/ 68
e:
c”
cn
-Full
10000
v;
c
I
v)
75
SO
I
5 000
D
0
A/
i
b
es
-Creep
-
0.4
0.5
0
0.6
-c
c Permanent Set
UNIT
Fii
S.-Stress-strain
104-D-1048.
STRAIN,
and creep curves illustrating
percent
origin
elongation
of values used in sag and tension calculations.
DE represents the creep value over a lo-year period. We assume that the average
tension over a period of 10 years will he at 15.5 ’ C (60 o F) un d er no load conditions.
limits conductor stress to 18 percent of the ultimate strength at these conditions.
values used for our calculations reflect all of these conditions.
Figure 6 shows stress-strain and creep curves for an ACSR, 26/7 (26 aluminum strands
strands) conductor as furnished by the Aluminum
Association.
l
conductor
The USBR
The creep
and 7 steel
8. The Parabola and the Catenary.-Two
curves, the parabola and the catenary, are generally
used in the calculations for conductor sags on transmission lines. The parabola, an approximate curve,
is often used because it simplifies the calculations.
When a wire or cable is assumed to conform to
the curve of the parabola, the mass of the wire or cable is.assumed to he uniformly distributed along
its horizontal projection (the horizontal span length). For the parabolic solution, it is safe to assume
that the sag will vary as the square of the span length for spans that are at least double the length
of the ruling span.
CHAPTER
I-BASIC
DATA
15
35 000
[I
225
30 000
I75
25 000
N
.E
20 000
2
vi
z
(r
E-I
15 000
IO 000
//
H
5 000
25
U.E
UNIT
Figure 6.-Stress-strain
104-D-1049.
0.3
STRAIN,
and creep curves for an ACSR,
0.4
0.45
percent
2617 conductor
as furnished
by the Aluminum
Association.
The second curve to be considered
is the catenary.
Any perfectly
flexible
material
of uniform
mass
will hang in the shape of a catenary
when suspended
between
two supports.
Although
commercially
available
wires and cables are not truly
flexible,
they will, in very short spans, conform
closer to a
catenary
since
than
they
is assumed
The
to any other
will
similar
catenary
and
in long
is easily
understood
parabolic
of an imaginary
Figures
7 and
equations
the
curve
long,
8 show
the
the
arc
the
the
of the
short
or the
be appreciable
that
For
reasonably
catenary
becomes
conductors
curve.
conductor
more
be considered
the
mass
as truly
of the
flexible
conductor
conductor.
span
parabola.
in heavy
even
may
catenary,
with
no unusually
However,
loading
areas
pronounced
in an inclined
the
sag will
between
a
with-comparatively
if the spans
span
large
difference
is actually
low
are inclined.
a small
This
portion
span.
the
Figures
following
can
realizing
a level,
the
difference
level
spans,
along
for
either
This
by
for each.
for
distributed
using
spans.
In longer
of a catenary
obtained
when
tensions
needed
shape
to be uniformly
sag calculations
be very
curve.
sag in the
parabolic
9 and
example
and
10 show
problems.
catenary
the metric
curves,
respectively,
and
U.S. customary
and also the commonly
sag and tension
used
calculations
TRANSMISSION
LINE DESIGN
MANUAL
Parabola
Directrix
X2
Y=40
w= Force
per unit
length
L = p + $$ = Length
of cable
H = 2aw = w& = Horizontal
'=
w(3p2+8s2)
6p
of cable and load
= Vertical
tension
tension
T=.z
m
= Maximum
S,= $
= Sag at
any point
S= g
= Maximum
tension
sag
Figure 7.-Parabolic
curve and equations.
104-D-1050.
CHAPTER
I-BASIC
17
DATA
Catenary
y=
w = Force
4
) = a cash
(e++e+
per unit length
L = a (e’-e’)
=2a
v=y(e
x
o -%*)=
of cable and load
sinh + = Length
H = aw= T -SW= Horizontal
$
of cable
tension
aw sinh + = Vertical
tens ‘ion
T = yw = aw cash $- = H cash $= Maximum
S= y-a = a(cosh
a=
S
8 -I) = Maximum
tension
sag
= Length of cable whose mass is equal to
horizontal
tension = Parameter of catenary
Figure
8.-Catenary
curve and equations.
104-D-1051.
TRANSMISSION
18
DCm-576
MANUAL
(3-78)
M
;;;;LL
CONDUCTOR f/D3
Code
LINE DESIGN
2
mm
k)psn
"%
SAGCALCULATIONS
LOADIHG~
Linear
Name
Rated
SreJklng
Strength
DLsme,er
aB
Tension
L~m,tat,ons
Force
Dead
/3
mm
Factor.
Load
Force
mm Ice
O./m
hPa
N/m
915-7
/5-;
18.
Wand
Resultant
Area
(rV’)
(w,‘)a
(W’“)
Cc&f.
ad-51
N/m
Total
b/j2
N/m
34.
Modulus.
0.000
of
Linear
NO Wind
O.OOQL/65
0.000~
Final
#d.?ztm
ln~tlal
Final
0 /~perOc
56.
GPa
I/do
GPa
AE34
75-T
-369
N
AE dL
939
318
N
(W’)
Figure 9.-Sag and tension
DC-576
(El
Exp..
lnttaal
NO Ice.
Set O.OOOJb
Creep
(A)&..&--rnd
Temp.
Permanent
N/m
calculation
form
for example
problems
on parabolic
and catenary
curves (metric).
(3.78)
;;;f'
CONDUCTORI+'
Code Name 2
Rated
kfm
TensIon
Load
/.
A
500
31
Final.
+ iz~“.
AF
0
%fO
2
OF 50
E
by -
LOADING
WeIghI
Ice
&lb
33f
Z!&.?F
Factors
Dead
lb
Llmltatlons
Loaded,
Fmal.
fl
Inch
In,t,al.-°F
Computed
d
SAGCALCULATIONS
I
LOADING ~-"J/
Welght
Breaking
Dmmeter
/
26
lb
lb
Area
5.70
lb
Temo.
“1 7
% 6
(AI
1.
2,
Ib/ft
opt/s
Iblft
Creep
0.00dL
lb! It
Total
0.000
7
-0.
(W”‘)
2.
a&?%
Coeff.
o.??o
4-09f7
o.000
UNSTRESSED LENGTH\
Figure lO.-Sag and tension calculation
2
o/D
form for example problems
(E)
Final/o*76
In,t,al$.
Exp:
per OF
5;
Set 0.0003
SAC FACTOR
on parabolic
? 6
3
5
8--
8 f’2
Ib/ft
Modulus.
12
of Linear
Permanent
O’o ~-lb
Date
jT\;“”
Wtnd
Resultant:
c00
(W’)
(W”)
SAG, ft
and catenary
/Z6
x 106
lb/l9
* 106
lb/ln2
Final
AE
7
lb
lnltlal
AE
&$tt
lb
SW,lb
1 TENSIONsIb
curves (U.S. customary).
CHAPTER
Example
Z.-Parabolic
Assume:
366-m
‘C
DATA
19
(metric)
ruling
span
403-mme,
ACSR,
44 482-N
maximum
NESC
15.5
curve
I-BASIC
heavy
26/7
conductor
tension
(13 -mm
loading
sag at no load
=
14 556
ice,
0.19-kPa
wind
plus
constant
at minus
mm
sagRS
Sag,
_
VW2
(Span,
I2
where:
sag in ruling
span,
sagRS
=
Sag,
RS
Span,
= sag in any other
=
ruling
span
= span
length
mm
given
m
of any
other
Sag,=
(sa&S
1200-ft
795
NESC
(Span1 j2,
104m2
SagI = K Gwn1)2,
mm
100
200
300
400
500
600
700
800
900
1000
1
4
9
16
25
36
49
64
81
100
1,
(U.S.
1 087
4 346
9780
17 386
27 166
39 119
53 245
69 544
88 017
108 663
customary)
span
ACSR,
maximum
heavy
60 o F sag at no load
= K (Span, I2
m
ruling
kcmil,
) (Span 1I2
m
1.0866 x 10w4m-’
curve
10 OOO-lb
span,
14 556
span
Assume:
given
L=
= (366)2
K =(Rs)2
Z.-Parabolic
mm
WI2
sagRS
Example
span,
length,
loading
=
47.69
26/7
conductor
tension
(l/2ft
in ice,
4-lb/fts
wind
plus
constant
at 0 OF)
18 ’ C)
TRANSMISSION
20
LINE DESIGN MANUAL
SaRS
-=
(RSY
sa&
(Span,
1’
where:
S%RS
=
sag in ruling
Sag,
=
sag in any
=
ruling
span
=
span
length
RS
Span
1
span,
ft
other
given
span,
length,
ft
of any
other
given
47.69
sagRS
-
K=(RS)Z
105fi2
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000
Assume:
366-m
44 482-N
maximum
15.5
‘C
15.5
o C tension
sag at no load
figure
H =
aw =
a =
H/w
0.4
1.6
1.32
5.30
11.92
21.20
33.12
41.69
64.91
84.78
107.30
132.41
160.29
190.76
223.88
259.65
298.06
2
10.0
14.4
19.6
25.6
32.4
40.0
48.4
57.6
67.6
78.4
90.0
span
ACSR,
heavy
ft
(metric)
403-mm2,
NESC
From
ruling
10-5ft-1
S481= K (Spanl)“,
(Span1j2 I
ft
curve
ft
=3.3118x
=(1200)2
Spanl,
3.-Catenary
span,
(SagRs1 (Span 1I2
= K (Span, >2
WI2
Sag, =
Example
ft
26/7
conductor
tension
(13- mm
loading
=
at no load
14 556
=
ice,
0.19-kPa
wind
at minus
mm
18 638
N
8:
T=
SW =
18 638, - (14.556)
18 405/15.9657
=
1152.7839
(15.9657)
m
=
18 405
N
18 “C)
CHAPTER
x =p/2
Example
= 1/2span,
50
100
150
200
250
300
350
400
450
500
0.043 313
0.086146
0.130 120
0.173 493
0.216 866
0.260240
0.303 613
0.346986
0.390 359
0.433133
curve
795
ruling
kcmil,
10 OOO-lb
NESC
ACSR,
heavy
loading
=
at no load
=
9.
Design
the Regional
by the Denver
may
and
office
4-lb/ft2
4190
curve
curves
.-A
=
(1.0940)
3782.29
at 0 “F)
=
4137.83
lb
ft
Sag=a(c;hz-
z.- 1
cosha
showing
0.000 349 531
0.001 398 367
0.003 147 243
0.005 597738
0.008 750 491
0.012 608 78 1
0.017 174 947
0.022452
180
0.028 444 171
0.035 155 107
0.042589680
0.050753087
0.059 651 036
0.069 289745
0.079 675 954
the
percentage
useful
proportion
seven
the technical
further
of the
regions.
design
in chapter
work
Design
of each
between
a clearance
design
l),
1.322
5.289
11.904
21.172
33.097
47.690
64.961
84.921
107.584
132.967
161.087
191.963
225.618
262.074
301.358
relationship
in determining
are discussed
of the Bureau’s
to cover
wind
lb
- (47.69)
x
a
Instructions
1 084
4 340
9113
17 393
21215
39257
53542
70096
88952
110 144
ft
be particularly
catenary
Directors
in ice,
0.026439
0.052 878
0.079 317
0.105 756
0.132 195
0.158 634
0.185 073
0.211 512
0.237 951
0.264 390
0.290829
0.317 268
0.343707
0.370 146
0.396585
11 is a catenary
Parabolic
0.000940156
0.003 764194
0.008 411558
0.015 087 698
0.023607738
0.034053 971
0.046445 57 1
0.06080607
1
0.077 162 490
0.095 546 05 1
conductor
(l/Z-
47.69
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
relationship
- 1),
mm
tension
x = p/2 = l/2 span,
ft
Figure
Sag =a(cosh;
1
customary)
26/‘7
H = aw = T- SW = 4190
a = H/w = 4137.83/1.0940
This
21
span
maximum
60 OF sag at no load
60 OF tension
(U.S.
DATA
coshz-
a
1200-ft
Assume:
X
m
4.-Catenary
I-BASIC
at any
point
span
length,
in a span.
II.
on transmission
instructions
transmission
sag and
lines
are issued
line
is delegated
to these
and include
directors
the following:
to
TRANSMISSION
I””
0,
lb
LINE DESIGN MANUAL
30
2'0
40
5’0
PERCENT
Figure Il.-Catenary
a.
Design
curve showing
percentage
relationship
70
$0
SPAN
80
90
100
LENGTH
between
sag and span length.
104-D-1052.
data.
(1)
Length
of line
(2)
Voltage
of line
(3)
Number
(4)
Type
(5)
Ruling
(6)
Insulators:
(7)
Conductors
and
(8)
Maximum
tension
(9)
Final
of circuits
of structures
span
number,
tension
size,
overhead
under
at 15.5
and
type
ground
loaded
OC (60
wires:
number,
size,
and
type
conditions
for conductors
and
“F) with no wind for conductors
overhead
ground
wit -es
and overhead
groul nd
wires
(10)
For
steel
towers,
ground
wires
the
horizontal
and
vertical
spacing
between
conductors
and
overhe,
ad
CHAPTER
(11)
For
(12)
Final
steel
towers,
sag at
overhead
the
15.5
conductor
OC (60
ground
(14)
wires
The annual
isoceraunic
level
This number
is calculated
clearance
at 15.5
the
Design
c.
d.
Minimum
Drawings
loading
e.
Number
49
23
to tower
steel
with
OC (120OF)
’ F) between
the
conductors
and the probable
number
either per 100 kilometers
for
coefficent
for
the
and
of power outages
or per 100 miles
“per-lOO-miles”
conductors
vahle
overhead
ground
due to lighting.
of transmission
is 1.6 times
locations
of transpositions.
all pertinent
data concerning
the line
Initial
entries
on the summary
form
charts,
so that
should
a compact,
ready
be made when the
steel
tower
are obtained,
filled
out.
notebook,
records-if
along
they
sheets for other lines, for easy reference.
summary
sheet is simple
in layout,
easy
normally
required,
with summary
are kept. The
has
room
for
any
and by the time
The completed
reference
is available.
design work is assigned.
entries
should be made as data
the form
should
be completely
source.
the
than those given in a.
of structures
to be used.
clearance
A Transmission
Line Data Summary
Transmission
Line
Data
Summary
Form.on figure
12, should be prepared
for each transmission
line designed.
This form should
information
and
conditions.
f. Design data drawings
including
sag templates,
structure
limitation
diagrams,
and conductor
height
tables for wood-pole
structures.
10.
shown
no load
value.
clearances,
other
and characteristics
and
o C (60
mmlerical
“per-IOO-kilometers”
b.
and
DATA
wires
Midspan
length;
clearances
“F)
(13)
line
I-BASIC
additional
data
that
the transmission
form
should
might
form,
as
contain
Additional
line is put into service,
be placed
in a looseleaf
Nothing
is better
than good
to fill out, contains
all data
be useful,
and
is an excellent
24
TRANSMISSION
LINE DESIGN
TRANSMISSION LINE
Region:
Project:
Name of Line:
Length:
Elevation,
min.-max.:
NESC loading:
Type of
km
MANUAL
DATA SUMMARY
Specifications
Voltage:
In service:
Data by:
kPa wind,
lb/ft*
wind,
contractor:
mi
zone,
mm ice,
in ice,
construction:
Insulators
Size: -.
Strength:
Number per
mmx
in x
l-Ql(
N (
in)
Conductor
at 15.5
lb)
No.
+K(O.-),
+K(O.-),
and overhead
ground
wire
to ground clearance
"C (60 "F)
mm
ft
Overhead
ground
wire
_
-
Name :
size:
Type:
Stranding:
Ultimate
strength:
Tension
limitations
50% us at -"C(
OF) initial
33-l/3%
US at -"C(eoF)
initial
25% US at -"C(OF) final
18% US at 15.5 "Cf 60 "F) final
15% US at 15.5 "C( 60 OF; final
Diameter:
Area :
Temp. coeff.
of linear
expansion:
Modulus of elasticity
Final:
Initial:
NESC Force (weight)
per unit
length
Bare:
Iced:
Wind:
Resultant
(with constant):
Ellipse
resultant:
Ruling
span:
sacs
OC
OF
string:
Conductor
Conductor
at
at
mm* --
kcmil
mm
ml*
mm dia.
in dia.
lb
N
lb
lb
lb
lb
lb
N
N
N
lb
lb
lb
N
lb
in
in
in*
-p&C
__
perOF
2
pergc
----Tn*
per"F
GPa
GPa
lb/in*
lb/in2
GPa
GPa
lb/in2
lb/in2
N/m
N/m
N/m
N/m
N/m
m
lblft
lb/ft
lb/ft
lb/ft
lb/ft
lb/ft
lb/ft
lb/ft
lb/ft
lb[ft
ft
N/m
N/m
N/m
N/Ill
N/IO
In
OF) final:
OF) final:
nun
Em
mm
mm
mm
ft
ft
ft
ft
ft
mm
mm
mn
mm
mm
OF) final:
OF) final:
N
N
N
N
N
lb
lb
lb
lb
lb
ft
-
Full load:
Cold curve:
Ellipse:
15.5 "C (60
49 'C (120
Tensions
Full load:
Cold curve:
Ellipse:
15.5 “C (60
49 'C (120
___
-OC
(
OF)
Key map:
Plan-profile
drawings:
sag template:
Stringing
sag tables
Cond"&r;
Overhead ground wire:
Structure
Figure
12.-Transmission
line data summary
Limitation
form.
Chart:
104-D-1053.
ft
ft
ft
ft
ft
lb
lb
lb
lb
lb
<<Chapter
CONDUCTOR
11.
General
conductor
under
line design.
This
Information.-The
SAGS AND TENSIONS
determination
of sags
and
various
conditions
of temperature
and loading
determination
enables
design elements,
such
to be established
and permits
the use of sag templates,
criteria
are in use as a basis for making
sag and tension
parabolic
curve.
If a uniform,
perfectly
flexible
and
inelastic
stringing
calculations:
length
corresponding
tensions
is of basic importance
as the most economical
tables,
and other
(1) the catenary
of material,
such
for
aids. Two general
curve, and (2) the
as a chain
points
of support.
The tension
at any
horizontal
component
which
is uniform
point
in the
throughout
component
which
varies along
along its length.
The vertical
This means that the total tension
of the tension
at the low point
the
If it is assumed
that
points
of support,
curve of the
and parabola)
increasingly
as the span
the mass of the cable is uniformly
instead
of along the cable itself,
cable is that of the
are almost
identical
greater
length
ratios
greater
as the sag increases.
increases.
the
value
of this
less than 0.05, and should
than
0.20,
the catenary
encountered
introduced
stringing
(100
error
where
in practice
will
in sag and
the conductor.
tension
ft) of span length
for spans greater
a portion
of a curve
distributed
the resultant
parabola.
The results
of the two
when the sag is small; however,
Within
a limited
range of values
method
may be used for calculations.
to spans
cable will consist
of two
the length
of the cable,
Since
of the ratio
Generally,
ratio
longer
or cable,
be the method
may present
0.05.
The
used for
difficulty.
a sag-to-span
computations
have
not
components:
(1) a
and (2) a vertical
along a horizontal
line
mathematical
equation
between
for the
methods
of calculation
(catenary
the difference
in results becomes
larger
sags, the
catenary
of less than
be greater
difference
catenary
method
method
ratios
between
Fortunately,
ratio
should
hangs
the mass
minimum
be at the
in the cable will also vary
of the cable is zero.
of sag to span, either
the
the use of the parabolic
is less than
involve
spans
increases
or the parabolic
should
be limited
can
also
be used
0.05 and 0.20. For
most
transmission
0.20.
than
The
the
error
tolerance
for
ratios
lines
inherent
or
allowed
in
In general,
the error
allowed
in stringing
is 12 mm (0.04 ft) per 30.5 m
for spans up to and inchtding
366 m (1200 ft), and 152 mm (0.5 ft) maximum
than 366 m. The curve assumed
by the cable in a steep inclined
span is actually
for a very
large
level
span,
so calculations
for steep
inclined
spans,
even
though
the spans may be short, should be made using the catenary
method.
Computed
sags should
to 3 mm (if in feet, to two decimal
places)
regardless
of the method
used.
Sag and tension
data can be divided
into three categories
according
to the physical
state
conductor,
of time
with
any
in transmission
span length,
in still air between
two fixed supports,
it will take the form of a catenary.
For the catenary,
of the conductor
is assumed
to be uniformly
distributed
along the arc of the conductor.
The
tension
in the cable will be at the lowest point
of the arc, and the maximum
tension
will
the curve.
component
II
reference
to its past
and
present
degree
25
of stressing,
and
the
length
be accurate
of the
the
TRANSMISSION
conductor
has been
(2) final
loading
(1)
a small
this
under
stress.
condition,
and
The initial
percentage
condition
preparing
These
LINE DESIGN
three
(3) final
categories
loading
MANUAL
are referred
condition
to as: (1) initial
with
loading
condition
applies
to conductors
which
of the stress value selected
as the maximum
are
used
as stringing
sag templates,
which
data
are used
for
unstressed
to determine
have not
operating
condition,
been stressed beyond
stress. Sags based on
conductors,
uplift
to determine
maximum
stress conditions.
applies
to conductors
(2) Th e f ina 11 oa d in g condition
loading
creep.
forces
and
as basic
on structures.
data
for
Tensions
are
used
selected
as the
maximum
for only
a short
time.
sag and
tension,
and
maximum
stress
(3)
The final
operating
stress,
Sags and tensions
stringing
data
for
conditions.
1oa d’ m g condition
but
based
where
on this
creep
the
have
stressed
has been
to the value
under
this
are used to determine
conductors.
applies
been
conductor
condition
prestressed
with
which
Tensions
to conductors
are used
which
stress
the full-load
to determine
have
been
in place
for several
years. Creep values are generally
based on a lo-year
period,
since about
95 percent
of the creep has been removed
from the conductor
over this length
of time. Sags based on this
loading
condition
are used for preparing
sag templates
that can be used for spotting
structures
on plan-profile
Sag and
conditions,
drawings.
Corresponding
tensions
are used
in broken
conductor
tension
values for a given span length
and conductor
will vary according
that is, the sag for the final loading
condition
with creep will be greater
calculations.
to the loading
than the sag for
the final loading
condition,
and the sag for the final loading
condition
will be greater
than
for the initial
loading
condition.
The difference
in the sag between
final loading
with creep
final
loading
conditions
is obviously
due to creep.
The value of this creep
is dependent
magnitude
of the average
in the sag between
final
permanent
To compute
tension
and the length
of time
and initial
loading
conditions
set is dependent
upon the magnitude
sags and tensions
based on initial
for the conductor
Likewise,
the final
set must
of the
loading
maximum
conditions,
under
study
must be determined
and
modulus
of elasticity
must be determined
tensions
based on either
the
To relate initial
conditions,
permanent
the tension
has been
is due to permanent
final loading
condition
final conditions,
and
be determined.
To
determine
used in formulas
involving
the
and used in order to compute
values,
the
The
loading
permanent
curve
and
approximating
elongation
the
at zero
set may
the
loading
conditions
unloading
initial
stress
Whenever
electrical
subjected
to the effects
be taken
line.
loading
between
as the difference
In the
curve,
the
case where
the
initial
1 Numbers
as the
in brackets
the
permanent
modulus
line
at zero stress
initial
set
and
modulus
modulus
may
the
may
and recommendations
for
conductor
tensions
requirements
California
Rules for Overhead Line Construction
refer to items in the Bibliography.
[l].t
and
be taken
as
loading
curve
between
the
is the slope of the unloading
be taken
unloading
between
the initial
is represented
as the
by a line
difference
are set forth
in
line.
conductors
or overhead
ground
wires
are strung
above
ground,
of wind, temperature,
and ice, all of which
add load to the wires,
rules have been adopted
as the basic standard
code
the Bureau
of Reclamation
serves, except
California.
is published
in elongation
modulus.
sags and
condition
with creep.
creep, values of creep
initial
the slope of a straight
line which
most closely
approximates
the initial
point of maximum
stress and the point of zero stress. The final modulus
line.
applied.
The difference
set. The value of the
stress attained
by the conductor.
the initial
modulus
of elasticity
or the final loading
final conditions
with
these
the sag
and the
on the
in NESC.
by all of the 17 Western
has established
its own
they are
Standard
These
NESC
States that
code, which
CHAPTER
The
the
standard
loading
NESC[S].
length
NESC
loading
districts
of the
According
of the
horizontal
load
conductor
(ice
determined
per
unit
covered
from
conditions
Uniied
to NESC,
components
total
and
Henry, which
on the
general
loading
load
on a conductor
shall
load
per unit
(ice covered
length
due
a horizontal
to
specified),
length
wind
to which
resultant
apply
map
be the resultant
where
in general
in section
loading
specified)
to
25 of
per unit
and
the
pressure
on the
projected
area
of the
has been
added
a constant
that
can
be
1.
Radial thickness of ice,
mm (in)
Horizontal wind pressure,
kPa (lb/ft* )
Temperature, OC (OF)
Constant K to be added
to the resultant of all
conductors, N/m (lb/ft)
State
Medium,
as shown
vertical
Table 1.-NESC
The
are Light,
States
the
27
SAGS AND TENSIONS
of the
where
table
II-CONDUCTOR
of California
specifies
conductor
loading
constants
(K)
Heavy
Loading
Medium
Light
13 (0.5)
6 (0.25)
0 (0)
0.191 52 (4)
- 18 (0)
0.191 52 (4)
- 9.4 (+ 15)
0.430 92 (9)
- 1 (+30)
4.3782 (0.30)
2.9 188 (0.20)
0.7297 (0.05)
heavy
loading
conditions
of 13-mm
(0.5-in)
radial
thickness
of
ice and 0.29 kPa (6 lb/ft2)
of wind
pressure
on the projected
area of cylindrical
surfaces
at
minus 18 ‘C (0 “F) for all parts of the State where the elevation
exceeds 914 m (3000 ft) above sea
level. Unlike
the NESC,
the California
code does not require
the addition
of conductor
loading
constants.
California
light loading
conditions
of no ice and 0.38-kPa
(8-lb/ft2)
wind pressure
on the
projected
area of cylindrical
where the elevation
above
snow
are likely
to occur
surfaces
at minus 4 ’ C (25 OF) are specified
sea level is 914 m or less. However,
our experience
at elevations
below
914
m in northern
California;
for
all areas
has shown
therefore,
of the State
that ice and
some
Bureau
lines in this part of the State are designed
for NESC
medium
loading
conditions.
This loading
is more
practical
for the expected
weather
conditions
and exceeds
the requirements
of the California
code.
In Montana
and Wyoming,
NESC
medium
loading
is specified
for most of the area covering
these
States. However,
extremely
low temperatures
so we have revised,
for Bureau
use, these
1 in section
Both the
strung
of the
2.
NESC
and
California
been encountered
areas to NESC
recommend
that
conductors
in these states during
the winter
heavy loading
as shown
on figure
and
overhead
ground
wires
be
at tensions
such that the final unloaded
tension
at 15.5 ’ C (60 ’ F) will not exceed 25 percent
ultimate
strength,
and the initial
unloaded
tension
at 15.5 “C will not exceed
35 percent
of
the ultimate
strength.
The NESC
ultimate
strength
under
maximum
percent
For
codes
have
loading
of the ultimate
ACSR
conductors,
permits
tensions
assumed
loading.
strength
under
the Aluminum
maximum
Company
under
The
load that
California
do not exceed 60 percent
of the
code limits
maximum
load to 50
assumed
loading.
of America
recommends
that
the
tension
shall
not exceed 50 percent
unloaded
tension
shall
of the ultimate
strength
under maximum
loading
conditions;
and that the final
not exceed 25 percent
of the ultimate
strength
at minus 18 ’ C (0 OF) in NESC
and
loading
California
heavy
districts,
at minus
9.4
‘C
(15
’ F) in NESC
medium
loading
districts,
2%
TRANSMISSION
and at minus
1 ’ C (30
those recommended
vibration.
Several
years
’ F) in NESC
by
the
light
codes
ago, we installed
and
steel
LINE DESIGN
loading
result
districts.
with
some
of the
overhead
conductors,
25 percent
of the ultimate
strength
at the following
temperatures:
ground
so we now
of both
These
in considerably
tensions
at a final
breaks
for
high-strength
clamps.
Vibration
in one
problems
unloaded
ground
from
of 25 percent
occurred
final
overhead
less than
conductor
tension
to vibration
a maximum
steel
to the
unloaded
due
suspension
design
are substantially
less damage
wires
of the ultimate
strength
at 15.5 ’ C (60 OF). N umerous
more wires of the seven-wire
strand
at the supporting
occurred
MANUAL
wires
or
also
tension
of
and conductors
Temperature
OC
(OFI
District
NESC heavy loading
NESC medium loading
NESC light loading
-40
(- 40)
-29
(- 20)
-18
(0)
When extra-high-strength
steel is used for overhead
ground
wires, we design for a maximum
final
unloaded
tension
of 20 percent
of the ultimate
strength
at the temperatures
shown
above
for the
different
loading
districts.
Bureau
design criteria
for conductors
and overhead
ground
wires should
be in accordance
with
the
data shown
on figure
1; note that there are four limiting
conditions
shown.
Although
the ice and wind loadings
prescribed
by the codes are generally
applicable
for determining
the loading
conditions
to be used in the design of a transmission
line, specific
climatic
and weather
conditions
should
be studied
for each
transmission
and South Dakota
transmission
lines,
38 mm (1.5 in) of ice on the conductors,
was considered
as it did not seem
simultaneously.
Certain
limitations
regarding
in various
local
safety
codes.
applicable
authorities.
of spans,
References
are given
inclined
level
to various
to some
be exceeded,
except
a general
discussion
for which
sag and
methods
(symmetrical)
(asymmetrical)
or group
of lines.
For
example,
on our
North
allowable
sags, tensions,
and span lengths
are set forth in NESC
These
codes or regulations
should
be reviewed
to determine
limitations
which
should
not
In the following
paragraphs,
and special
span combinations,
in such spans.
A perfectly
line
the crossarms
were designed
to support
a vertical
load due to
but no extra wind load for the excess ice above 13 mm (0.5 in)
probable
that
heavy
icing
and high
winds
would
occur
span
degree.
simple treatment
by either the parabolic
for computing
sags and tensions
in level
which
by written
permission
from the proper
is given concerning
the various
types
tension
data are likely
to be required.
are in general
is infrequently
However,
found
the level
and
the
use for
computing
in practice
span problem
since
lends
sags and
almost
itself
tensions
all spans
are
to comparatively
or catenary
relations.
Numerous
methods
have been derived
spans, the majority
of which
are-based
on catenary
relations
in the form of dimensionless
ratios.
Four of these methods
Reference
[6] offers the greatest
facility
in most problems
are described
in references
[4, 5, 6, 71.
and is discussed
further
in the following
section.
be made
the
Before
method,
using
and
then
any
care
method,
should
a careful
study
be given
to the
should
application
of the
to determine
method
As might
be expected,
the computation
of sags and tensions
for inclined
their asymmetry.
Most inclined
spans are supported
by suspension
or pin-type
the
within
limitations
these
of
limits.
spans is complicated
insulators
at both
by
ends,
CHAPTER
or by suspension
A few
or pin-type
inclined
spans
can be designed
purposes,
without
correction.
catenary
solving
can
curves
each
insulators
may
the
For
be used
span
extremely
to theoretical
sag condition
for
at both
or correcting
ruling
the data
determination
work
from
requirements
the
spans,
hillside
of support
proper
at the
level
over
railroad,
special
clearances
to ground
treatment.
discussed
waterway,
such
and
line,
be used
applies
conductor
condition
and
the
and
sag curves
to obstructions.
which
14.
to a broken
under
this
communication
structure
may
support
to provide
A method
in section
end.
span
as extending
as the upper
be made
For
usually
calculations,
other
of inclined
spans.
spans
elevation
should
at the
type
for symmetrical
tensions
in spans adjacent
of assuring
compliance
highway,
insulators
suspended
on symmetrical
same
span,
conductor
the
computed
steep
points
of sags and
standpoint
Usually,
based
spans dead-ended
at both ends also require
special
is given as reference
[S]. Inclined
spans are further
The
design
by dead-end-type
ends.
sag template
as an individual
determining
SAGS AND TENSIONS
at one end and
be dead-ended
by modifying
spotting
II-CONDUCTOR
then
which
Inclined
to this
case
is important
in
with
clearance
powerline
crossings;
and
from the standpoint
of determining
the unbalanced
loads on the structures.
The computation
of sags
and tensions
under
this condition
is quite involved,
due mainly
to the many
variables
introduced.
A method
which applies directly
to this problem
is given as reference
[8]. In addition
to this published
solution,
an unpublished
that offers
as appendix
a margin
A, and
method
of facility
an example
was devised
by
Mr.
over other
methods.
problem
using this
G. R. Wiszneauckas,
former
Bureau
This method
has been included
method
is shown
in section
16.
engineer,
in this
manual
In a series of suspension
spans, where
relatively
short spans occur
adjacent
to a relatively
long
span, it is desirable
to determine
the changes in sags and tensions
which would result from temperature
and loading
changes
and
produce
dangerous
loads
values.
The
consequently,
nature
most
this problem
with
in section
16.
Problems
substation
from unbalanced
on the structures;
of this problem
of the methods
slight
relating
for
to spans
with
An
example
concentrated
approach
In some cases, such changes
clearances
may be reduced
is very similar
handling
the
modification.
or switchyard
loadings.
in others,
spans
to that
of the
broken
conductor
problem
loads
broken
conductor
problem;
problem
can be applied
to
on unbalanced
are relatively
or unbalances
will
below the required
few
conditions
and
is presented
are confined
mainly
to
taps or tie-down arrangements
in which
problems
are complicated
by the elastic effects
No published
method
is known
which adequately
are used. Such
of the tie-down
in addition
to the dead load applied.
treats this problem;
however,
a method
was devised
by
facility,
the
Bureau
Another
dead-ended
in references
handled
12.
that
by one
of the
Sag and
Calculating
Engineers’
published
handles
this
problem
with
methods
Tension
Tables [4] were
Society
in book
given
Calculations
first made
of Western
form by the
in reference
18.
[12].
Using
Copperweld
public
by Mr. James
Pennsylvania
Copperweld
in November
Steel Co. That
then, have been in constant
use by engineers
designing
sags and tensions
by Martin’s
Tables
consist
of filling
interpolating,
tables.
see section
problem
similar
to spans with concentrated
loads appears
in the use of extremely
short
spans with long insulator
strings.
This problem
may be handled
by use of the methods
[S, 10, 111. Problems
where
the concentrated
load consists
of dead load only can be
and
computing
values.
There
Sag Calculating
Charts.-Martin
S. Martin
in a paper he presented
1922.
In 1931,
first edition,
and
the tables
were first
several
editions
since
overhead
transmission
lines.
out a calculation
form by
is a trial-and-error
method
required
‘s Sag
to the
Calculations
of
reading
tables,
in the
use of these
30
TRANSMISSION
The
“Graphic
a series
Method
of correlated
conductor.
Graphical
superimposing
The
for
Sag-Tension
graphs
‘to
methods
graph
Copperweld
upon
are very
graph,
and
for overhead
Tables.
The
as with
Martin’s
lines.
general
procedure
Tables.
charts
for
required
occasion,
sag and
but
values
were
[6]
are based
charts
various
developed
provide
and factors
of
which eliminates
using
is applied
the charts
and
to a wire,
as is done
stretches.
If the tension
of load on a suspended
tables
should
in the wire increases,
wire, the elongation
a conductor
problems
the length
(stretch)
in preparing
the calculation
using
a graphical
that
time
of the catenary
curves,
these
all wire
is the
between
to some
two
same
unstressed
force
of construction
solution.
is elastic
between
in Martin’s
charts
times the vertical
and the trial-and-error
most types
part of the
is strung
of sags and
as given
relationship
SF/ T (span length
the interpolating
be aware
when
employing
of an overhead
conditions.
to simplify
tension
is a system
characteristics
considerable
on the functions
sag and
the
require
for
by Alcoa,
tension
when using the tables.
The range of the charts
covers
it may be necessary
to revert
to Martin’s
Tables
for
Designers
tension
reading
solving
However,
length
factors,
elongation
factors,
conductor
divided
by the tension)
the
satisfactory
Charts
The
developed
Calculations”,
determine
Sag Calculating
tensions
LINE DESIGN MANUAL
of the
methods
but,
extent.
supports,
on
When
the
wire
of the wire increases.
With different
amounts
and the tension
in the wire will change.
A temperature
change
in the wire also changes
its length.
If the temperature
changes
while the
wire is unstressed
(at zero tension)
and the wire is free to change
its length,
the length
changes
but
there is no change
in tension.
When
the wire is suspended
in tension
and the temperature
changes,
the change
in length
the wire. All changes
sags and tensions
The conductor
changeover
the metric
is affected
by both the temperature
change
and the elastic
due to ice, wind, and temperature
are taken into consideration
in conductors
by
sag and tension
this method
calculation
period,
we have both a metric
form to which
we have added
and
item
Item
(1)
(2)
(3)
(4)
(9
(6)
(7)
(8)
(9)
Conductor size
Conductor code name’
Rated breaking strength’
Diameter,’ mm (in)
Radial thickness of ice, mm (in)
Wind, kPa (Ib/ft2 )
Loading
W’, N/m (lb/ft)
W”, N/m (lb/ft)
(10)
Wind, N/m (lb/ft)
(11)
W’
(12)
Area A, mm2 (in2 >
Temperature coefficient
of linear expansion
(13)
“, N/m (lb/ft)l
of charts
and tables.
form
is shown
on figure
a U.S. customary
numbers
to help
13.
characteristics
when computing
During
form for our use.
explain
the form:
Figure
the
of
metric
13 shows
Explanation
Determined from economic studies
From NESC or State codes
From NESC or State codes
From NESC or State codes
Vertical force (weight) of conductor’
Vertical force (weight) of conductor with ice’
(if applicable)
Force of wind on conductor and ice’ (if
applicable)
Resultant force, including applicable constant
if NESC loading’
Cross sectional area of conductor’
Change in length of conductor due to temperature change’
CHAPTER
II-CONDUCTOR
Item
(14)
Final modulus E, GPa (lb/in2 )
(15)
Initial modulus E, GPa (lb/in2 )
(16)
Final AE, N (lb)
(17)
Initial AE, N (lb)
(18)
Span length, m (ft)
(19)
(20)
(21)
Thickness of ice, mm (in); and
force of wind, kPa (lb/ft2 )
Temperature, OC (OF)
Tension, N (lb), initial
(22)
SW, N (lb) (two decimal places)
(23)
(24)
SW/T (four decimal places)
SW/AE (seven decimal places)
(25)
Unstressed length (six decimal
places)
Permanent set and creep’ (six
decimal places)
Unstressed length at -18 OC
(0 OF) (six decimal places)
(26)
(27)
(28) - (3 1)
Unstressed length (six decimal
places)
SAGS AND TENSIONS
31
Explanation
Slope of final (unloading) curve of stress-strain
diagram’
Slope of initial loading curve of stress-strain
diagram’ (average slope between maximum
loading and point where entire conductor
starts to assume loading)
Product of conductor area (12) and final
modulus ( 14)
Product of conductor area (12) and initial
modulus (15)
Length of span for which computations are
to be made
For full-load condition
For full-load condition
Expected or desired tension at full-load conditions (Must not exceed 50 percent of
ultimate strength of conductor. May be
limited by 33-l /3 percent of ultimate
strength of conductor for no-load initial
conditions, or 25 percent of conductor
ultimate strength for no-load final conditions.
At temperatures indicated on fig. 1).
Span length (18) times resultant force per
unit length of conductor (11)
SW (22) divided by full-load tension (21)
SW (22) divided by initial AE (17)
From Copperweld charts [ 61 at intersection of
SW/T (23) and SW/AE (24) values
If value of unstressed length is for initial condition, then only a change for temperature,
number of degrees change times temperature
coefficient of linear expansion (13), need be
made. However, if the value for unstressed
length is to be for the final-condition, then
it will also be necessary to add the permanent
set and creep to the value of unstressed length
(25)
Change in value is equal to the degrees of temperature change times temperature coefficient of linear expansion (13)
TRANSMISSION
32
LINE DESIGN
MANUAL
Item
(32)
(33)
(34) - (38)
Explanation
SW, N (lb) (two decimal
places)
SW/AE (seven decimal places)
SW/T (four decimal places)
(39) - (44)
Sag factors (interpolate to
five decimal places)
(45) - (50)
Sags, mm (ft) (two decimal
places , if in feet)
Tensions, N (lb)
(51) - (55)
’ Available from manufacturers’
Span length (18) times unloaded conductor
force per unit length of conductor (8)
SW (32) divided by final AE (16)
From Copperweld charts [ 61 at intersections
of unstressed length values (27) - (3 1) and
SWlAE(33)
From table at back of Copperweld charts book
[ 61, sag factor for each value of SW/T (23)
and (34) - (38)
Span length (18) times sag factors (39) - (44)
SW (22) and (32) divided by SW/T (23) and
(34) - (38), respectively
catalogs or data in appendixes.
Figure
13 can be used for any combination
of ice, wind, and temperature
conditions
to find the
resulting
sags and tensions
in a conductor.
The procedure
is the same for all cases, but one must be
sure of the basic data and to keep in mind whether
initial
or final conditions
are being computed.
for
13.
Preparation
a specified
loading
lengths,
profile
survey
locating
sag and
conditions
catenary
356used
span
and
longer
of structures
on plan-profile
drawings.
The data required
to prepare
a sag template
tension
values of the conductor
at the ruling
span length
for the temperature
and
desired.
These basic sag values
can be computed
and extended
to corresponding
longer
in this
span lengths
by
chapter.
Whatever
The tension
values
catenary
parameters,
relations.
by 0.635-mm
for plotting
and also a curve
span
The
the
template
is made
temperature
final sag values.
loading
conditions.
to the sag values of the ruling
be known
in order to expand
on
a transparent
(lo- by 14- by 0.025- in ) size.
plan-profile
sheets, represents
at an assumed
minimum
curve
is plotted
or
are the
loading
values
either
the parabolic
or catenary
relations,
or by any of the
method
used should be governed
by the limitations
of that
corresponding
which
must
at 49 OC (120 “F) or 54 ‘C (130 “F),
maximum
sags. The minimum
temperature
1 ‘C (30 “F) and minus
51 ‘C (-60
minimum
ruling
and
and the resulting
sag values
plotted
against
the corresponding
span lengths-a
conductor
curve results.
When this curve is plotted
to the same scale as a transmission
line plan-profile
drawing,
it is commonly
called
a sag template and can be used to facilitate
the spotting
for shorter
and
methods
shown
method.
compute
If sag values for a conductor
at a specified
of Sag Template.are expanded
to give corresponding
values of sag at shorter
sheet
The template,
the conductor
from
initial
Figure
14 shows’a
sag template
Changing
any of these specified
of plastic
approximately
temperature
template,
curve,
if desired,
be drawn
for any temperature
on locality
and climatic
sag values,
prepared
conditions
and
for
254-
by
made to the same scales that were
profile
curve at 15.5 O C (60 O F),
temperature.
A maximum
may also be drawn
on the
curve may
OF), depending
span are required
only to
the basic sag values by the
the other
curves
usually
taken
for checking
between
conditions.
are plotted
minus
The
from
a specific
conductor
under
specific
would
change the shape of the curves,
CHAPTER
DCm-578
II-CONDUCTOR
SAGS AND TENSIONS
(3-73)
!yT:ALL SAG CALCULATIONS
(1)
CONDUCTOR
Rated Breaking
Tension
Lmear Force Factor:
(3)
Strength
Dfalmlero
N
L~m~tat~one.
_cs,
mm ice (W”)
(6)
kPa Wmd
Imtial.~,-?&%--N
Resulranr
Oc
25
h -N
Loaded.v.A%
Flnal.15.5’
N
o.oal
Permanent Set 0.00
Creep 0.00
N/IT
Total 0.00
0
1TEMP../
oc UNSTRESSED
LENGTH
Modulus. (E) FInal (14)
(13)
lmtlal
Exp.:
Final AE
PdC
I
18)
(24)
j
!
49
mm Ice
kPa Wind (W”‘)
(25)
SAG, mm
SW,N
]
/
I
(45)
(22)
TENSION, N
(51)
I
(29)
/
(36)
(30)
31
I
(37)
(521
33
SPANLENGTH(S)
50
(53)
(54)
55)
32
m
I
I
/
-13
-1
15.5
32
49
SPAN LENGTH(S)
mm Ice
m
No Ice. No Wind (W’)
No Ice. No Wind (W’)
m
SPAN LENGTH(S)
mm Ice
kPa Wind (W”‘)
Permanent Set IL Creep
No Ice. No Wind (W’)
N
(21)
(33)
(
h Creep
No Ice. No Wind (w’)
GPa
N
m
(39,
(23)
AE
Gpa
(15)
(16)
(17)
(26)
15.5
32
)
SAG FACTOR (
f
I
SPAN LENGTH(S)
-1i
No Ice. No Wind (W’)
ifi
(26)
N/m
lnllial
Ice
Set
(II)
(W”‘)
N/m
N/m
Date -
kPa Wind (W”‘) j(20)
Permanent Set 6 Creep
1
1-13
Permanent
(IO)
Temp. Coeff. of Linear
.-%-
LOADING
(19) -mm
(9)
Area (A)(12)m&
-N
Computed by
(8)
Dead Load Force (W’)
mm
Final.
(7)
LOADING
(2)
Code Name
I
I
1
I
-13
-1
15.5
32
49
Figure
13.-Explanation
of standard
sag and tension
calculation
form.
I
-
---
TRANSMISSION
34
LINE DESIGN MANUAL
SAG TEMPLATE
242mm2(477kcmil)
ACSR 24/ 7
Ruling Span =213.4m (mft)
Maximum Tension 532 472N (7300 lb)=42% ultimote strength
NESC Heavy Loading=13-mm($-in)ice,O.lS-kPa(4-lb/ft*)
wind + K ot-I8
Scales:
Horlzontal
25.4mm -61m (I in = 200 ft)
Vertical
25.4mm = 12.2m( I in =40 ft)
I
12.2m 1
(4011)
305
244
(1000)
(800)
.
\
I
\
le.3
(600)
they would
the minimum
h
122
(400)
Figure
and
and
I
0 meters
14.-Typical
I
61
122
.._-
construction.
requirements
this specific
job. The 15.5
no-load”
curve are plotted
I
104-D-1054.
’ C (60 OF) “final
no-load”
curve
in the center of the template,
and
The
15.5
’
C
final
no-load
curve
the plastic
material
between
these two curves
should be cut away.
is used for plotting
the conductor
location
on plan and profile
drawings
because this is the temperature
which
are identical
to the 15.5 ‘C curve,
used as a basis for NESC
clearances.
Clearance
curves,
are drawn
below the 15.5 ‘C final no-load
curve.
The amount
of clearance
is determined
from the
following
no longer
be good for
temperature
“initial
sag template
I
OC(O OF)
of NESC:
Assume line voltage
Plus 5 percent overvoltage
115
kV
5.75
120.75 kV
Maximum line voltage
120.75
69.7 kV
Line to ground =
n
Assume 2 13.4-m (700-ft) ruling span.
Clearance from NESC, 1977 edition, Rule 232:
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
232.A. Basic clearance
Table 232-l) Basic clearance for 50-kV, 53.3-m
span, in heavy loading area where equipment
ating height is less than 4.3 m (14 ft) . . . .
232.B. Additional clearances
232.B. 1. Voltages exceeding 50 kV
232.B.l .a. Plus 10.2 mm (0.4 in) for each kilovolt
10.2 (69.7 - 50) = 201 mm
%
(69.7
- 50)
(175-ft)
oper. . . . . .
Clearance
6706 mm
(22.0
ft)
above 50 kV
ft . . . . . . . . . . . . . . . . . . .
= 0.66
35
201 mm
(0.66
ft)
18mm
(0.06
ft)
232.B.l .b. Additional clearance calculated in 232.B. 1.a.
shall be increased 3 percent for each 304.8 m
(1000 ft) over 1005.8-m (3300-ft) elevation. Assume
an elevation of 1920.2 m (6300 ft):
1920;ii
ioo5a8
(0.03)
(201)
= 18 mm
630;o;;300
(0.03)
(0.66)
= 0.06
ft . . . . . . . . . . . . .
232.B.2. Sag increase
232.B.2.c. Span is longer than 53.3 m (175 ft). Assume
line operates below 49 OC (120 OF). Calculate clearances
in 232.B.2.c.( 1) and (3), use smaller clearance of the two.
232.B.2.c.( 1) Clearance specified in table 232-l shall be
increased 0.03 m (0.1 ft) for each 3.05 m (10 ft) over
53.3 m (175 ft).
213j4i553e3
(0.03)
= 1.57
m
7o01; 175 (0.1) = 5.25 ft
232.B.2.c.(3) Limits
Assume difference in final sag at 15.5 OC (60
and49 OC(120OF),nowind=
1.2m(4ft)
Total clearance required by NESC . . . . . .
6706+201+18+1219=8144mm
22 + 0.66 + 0.06 + 4 = 26.72
ft
Plus, for width of profile line on drawing and
in plotting
. . . . . . . . . . . . . . . . . .
Total ground clearance on sag template . . .
For lines in California,
a 54 ’ C (130 ’ F) final
and for locating
the structures
instead
of the 15.5
be in accordance
The sag template
calculation
sheets,
with
reference
1219 mm
8144 mm
(4.0 ft)
(26.72 ft)
small errors
. . . . . . . .
. . . . . . . .
8754
610 mm
mm
(2.0 ft)
(28.72 ft)
no-load
’ C (60
curve should
be used for the sag template
’ F) final no-load
curve.
Clearances
should
[l].
shown
on figure
14 was made
figures
15 and 16:
15.5 ‘C (60 “F), final,
Minus
40 ‘C (-40 OF)
OF), no wind,
. . . . . . .
. . . . . . . .
no-load
initial,
sag for 213.4-m
no-load
sag for
from
the
(700-ft)
213.4-m
data
ruling
ruling
indicated
on the
span
span
=
=
4874
2243
sag and
mm
mm
tension
(15.99
(7.36
ft)
ft)
36
TRANSMISSION
DCm-576
LINE DESIGN MANUAL
(3-73)
;llNT;;'
SAGCALCULATIONS
LOADlUG
Linear
Force
Dead
13
Factor
Load
Force
8.
(W’)
a=kPa
W,“da.
Area
(A,~ammi!
Temp.
Coeff.
0.000
No Wind
Set 0.004
,“:
27 I 3450
Nlm
MOduIus.
01 Linear
(E)
Final
Exp.:
p.
d03
GPa
In,tml_5-j,mGPa
0 ~J.&$.fLyl/wrQC
Final
AE
/?
gm
lnttlal
AE
15
2.31
N
252
N
15.-Sag
and tension
calculation
form for example
problem
on sag template
(metric).
(3-78)
krm;/
CONDUCTOR g,??
Code
Permanent
(W’)
Figure
DC-570
N/m
Rdd
Resultant (W”‘)
NO Ice.
f6ff?
mm Ice (N”)
$-/!fL
v7
hdb?
LOADING -kJ+--
F/!&k
Name
Rated
Diameter
Weight
Load =;7
Breakmg
/7.
Tenston
280
lb
Final.
Final.
Computed
Ice
lb
‘AL
d
%
673.4
-zT
% e$!&?&
lb
Area
OF
50
% 9Lofl
lb
Temp.
-f&L+
18
% &.2&m
lb
LOADING
0.000
Date
! “o”“‘t
lmd
UNSTRESSED LENGTH
(Al
0 /o
B-
D
No Wand
Inch
D.
(W”‘)
87L
.I,
7
Ltnear
o.oo~r/48-~
)b/ft
Total
O.OOC&?&2.-
Modulus.
(E)
Final/O,53
lnrtral
Exp.:
per OF
v
Set O.OOCX-&2creep
lb/0
in2
of
Permanent
Ib/ft
SAG FACTOR
;
SAG,R
Final
AE
lnltial
AE
(
x 10s
8./7,?/
1/
x
SW,Ib
I
16.-Sag and tension
calculation
:E
j
TENSION, lb
%+-FEET
SPAN LENGTI
form for example
problem
on sag template
lb/ln2
106 )b/in2
1/
&
(W’)
Ice.
Figure
lblft
p-f.7
1.
a.
Cc&f.
SPAti LENGTk
NO Ice.
(W’) .e
(W”)
Resultant:
lb
zz&?F
by ___
Weight
+ JIk,,.
Llmttatmns.
In,lial,-&F
Factors
Dead
Inch
Loaded.
SAGCAL,CULATIONS
(U.S. customary).
CHAPTER
Using
the
relationship
from
II-CONDUCTOR
section
SAGS AND TENSIONS
37
8,
sag,
sagRS
-=
UW2
C$an,
j2
where,
SagRs = sag in ruling span, mm (in)
Sag, = sag in any other given span, mm (in)
= ruling span length, m (ft)
span i = span length of any other given span, m (ft)
RS
4.874 m
sagRS
For 15.5 OC final: (RS)Z =
sagRS
60 OF final: (RS)~
=
For - 40
= 1 0707 x 10S4m-’
15.99 ft
= 3.2633 x 10-5ft-’
(700 ft)2
sagRS
=
-40 OF initial:
(RS)~
Assume
values for span lengths
sags as shown
in table 2.
7.36 ft
= 1.502x
(700 ft)2
(x),
square
these
Span length
(Span length) 2
horizontally,
m
ft
m2
60.96
121.92
243.84
365.76
487.68
609.60
200
400
800
1200
1600
2000
3 716.12
14 864.49
59 457.95
133 780.38
237 831.78
371612.16
same
and
scales
25.4
as those
mm
=
multiply
by the
15.5 ‘C (60 OF) Sag
0.4 x
1.6 x
6.4 x
14.4 x
:i:::::i5
used
105
lo5
lo5
10:
on the
m or
m
mm
0.398
1.592
6.366
14.324
25.464
39.788
398
1592
6 366
14 324
25 464
39788
plan-profile
1 in =
template
for the span lengths
shown
in table
sag template
to permit
its use on an entire
extremely
steep span where a special
catenary
Kvalues
to obtain
the
-40 OC (-40 OF) Sag
K,X2
ft2
12.2
and
=K,
for sag template
x2
x
10-5ft-1
(x2),
Table 2.-Calculations
the
=K,
2.243 m
= (213.36 m)2 = 4.9272 x 10-5m-1 =K,
VW2
Using
=K 1
’
sas,S
initial:
OC
(213.36 m)2
K22
m
mm
ft
0.183
0.732
2.930
6.592
11.718
18.310
183
732
2 930
6 592
11 718
18310
0.60
2.40
9.61
21.63
38.45
60.08
ft
1.31
5.22
20.89
46.99
83.54
130.53
sheets
40 ft vertically),
(25.4
mm
plot
=
the
61 m or 1 in =
sag values
on
2. The curves
should
be expanded
far enough
transmission
line, with
the possible
exception
curve
should
be used.
200
the
ft
sag
on the
of an
38
TRANSMISSION
Draw
must
the
but
a vertical
be kept
line
at the center
perfectly
vertical
of the
when
the
LINE DESIGN MANUAL
template
(zero
template
span
is being
Clearance
(conductor
to earth)
curves
should
be located
15.5 OC (60 o F) final sag curve.
The clearance
curves
will
be offset
vertically
,411 curves should
maximum
conductor
be noted
on the
14.
inclined
inclined
spans
spans
it by
the
values
at the
will
of clearance
for a reference
for
laying
specified
Spans.-In
to some
may
may
practice,
degree.
get rather
be classified
end; and (2) inclined
spans
falling
in the first category
require
located
This
distances
to the
final
line
line.
below
sag curve
required.
The conductor
horizontal
and
size and type,
vertical
scales
the ruling
span,
used should
also
nearly
every
span
of
a transmission
layout
be used
to ahnost
is inclined
supported
by
at the other
purposes
sags and
span. Some
vertical,
inclined
computed
spans
for
or spotting
purposes,
the ruling
span sag template
based on
without
correction.
Inclined
spans dead-ended
at both ends
layout
or spotting
A series of spans
for stringing
The method
used for calculating
somewhat
on the steepness
of the
level
spans
insulators
which
are dead-ended
at both ends. Problems
concerning
usually
can be handled
by modifying
or correcting
data
special treatment,
even for
on extremely
steep inclines.
insulator
offset calculations
(sec. 30(b),
ch. V).
line
As might
be suspected,
the computations
for sags and tensions
for
complex,
depending
upon the degree of their asymmetry.
In general,
into two categories
for design purposes:
(1) inclined
spans supported
spans. For structure
spans usually
may
spans, from
extremes.
line.
a transmission
NESC
be identical
by suspension
or pin-type
insulators
at both
ends of the span, and inclined
suspension
or pin-type
insulators
at one end of the span and by dead-end
type
symmetrical
symmetrical
out
template.
Inclined
(asymmetrical)
from
be identified
on the sag template.
tension,
NESC
loading,
and the
length)
used
while
purposes,
if they are fairly
long spans and are
located
on extremely
steep inclines
may require
in order
tensions
to get each
for
successive
a dead-ended,
span
properly
inclined
span
sagged
depends
methods
of calculation
are good for all dead-ended
other
methods
apply
to particular
areas between
these
For a dead-ended
span of normal
length
and a relatively
span with the same horizontal
distance
between
supports
on figure
17, the sag D(for
this case) is measured
vertically
small incline,
the calculations
for a level
may be used. Using
the notation
shown
and is the vertical
distance
between
the
straight
is tangent
line
joining
the
supports
Figure
and
a parallel
17.-Sag on inclined
line
which
span-equivalent
to the
span method.
conductor’s
curvature.
CHAPTER
If the
span
is long,
or if there
II-CONDUCTOR
is a relatively
SAGS AND TENSIONS
large
difference
in elevation
39
of the
end
supports,
some
correction
should be made in the calculations.
Calculations
based on the catenary
are preferred
over
those based on the parabola
because
the conductor
conforms
to a catenary
curve
when suspended
between
supports-the
of a cateriary
as the
The
by using
equivalent
level
span.
is then
spans
Another
sag value.
Thus,
span,
of the
an qrrirulfw/
span
the
calculated
as can
the
greater
horizontal
level
span.
span
in the usual
This
be used
as the slope
equivalent
span
equals
manner.
shown
difference
between
error
between
method,
alt bough
plus
field
the
and
=
may
an average
2SI-S.
between
The
where w is the conductor linear force factor per unit length.
Figure
Tl + T2 2T, - wH
2
=
2
18.~Sag on inclined
span-average
tension
this
method.
gives
can
be
results
limitations.
the slope
sag
span
and
the
D for the equivalent
less than
in the span
18:
portion
11 to be the same
However,
field
be used with
tension
comparable
an approximation,
wilhin
T, - T, = wH
Tav=
the
in assuming
supports.
difference
(SLS)
method
IIWS
on figure
is some
distance
in the
S’ +
This
up to 20 percent.
gives good results,
11ie notation
the
the sag, there
same
ordinarily
is taken
with an incline
method,
which
Using
the
In computing
span
are as accurate
span
for
a parabola.
sag for a level
minimized
which
steeper
and
and
I percent
error
has a corrected
TRANSMISSION
40
T,,.
Use
;2lcoa,
and
or other
A method
Zare
and
included
sags
calculation.
Since
for
calculated
various
sag by
sags and tensions
was developed
staff.
For
[S]. A b rte’ f version
a sample
tensions
the
for calculating
of any incline,
as table
and
Correct
of Reclamation
see reference
procedure,
methods.
intended
to spans
Bureau
formulas,
L t to calculate
acceptable
originally
is applicable
of the
length
LINE DESIGN MANUAL
by Mr.
a full
discussion
of this
the
method
method
conditions
the
in steeply
using
Copperweld,
relationship
SL ,/L.
D =
inclined
spans,
but
which
D. 0. Ehrenburg
while
he was a member
of his method,
including
derivations
follows
is based
showing
nonmenclature,
on a parameter
2, the
of
formulas,
functions
of
3.
Nomenclature and units
Metric
U.S.
customary
T, =
Te =
w =
h =
V =
w’ =
S =
S, =
a =
b =
c =
a’ =
b’ =
A =
E =
a =
d =
2 =
tension at upper support
effective (average) tension of conductor
linear force factor of conductor per unit length
wind load per unit length of conductor
ice load per unit length of conductor
(w + v)~ + h2 = resultant force per unit length of conductor
actual length of conductor
unstressed length of conductor
horizontal spacing of supports
vertical spacing of supports
straight line distance between supports
spacing of supports in plane of w’, at right angles to vector w’
spacing of supports in plane of w’, in direction of vector w’
area of conductor cross section
modulus of elasticity of conductor
coefficient of linear expansion
sag of conductor
parameter
Necessary
given data:
Loading
conditions
(ice,
Size, type,
and stranding
Linear
Linear
force
force
factor
factor
per
per
wind,
and temperature)
of conductor
unit
unit
length
length
of bare
of iced
conductor
conductor
Force on conductor
due to wind
Resultant
force on conductor
Cross-sectional
area
Modulus
of elasticity
Temperature
Maximum
Horizontal
Vertical
of conductor
of conductor
coefficient
of linear
tension
in conductor
spacing
spacing
of supports
of supports
expansion
for
conductor
N
N
N/m
N/m
N/m
N/m
(lb)
(lb)
Wft)
Wft)
Wft)
m
m
m
m
m
m
m
mm2
GPa
w>
(ft)
(ft)
(ft)
(ft)
WI
(ft)
mm
WI
(lb/W
(in2 )
(lb/in2 )
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
Table 3.-Functions
Z
f0
0.010
,020
.030
.040
.oso
0.000 016
,000 066
.ooo 150
.OOO266
.OOO416
67
6
0
7
7
.060
.070
.080
.OOO600 1
,000 8169
.OOl 067
.OOl 351
,001 668
.llO
.120
.130
.140
.150
.002
,002
,002
.003
.003
.160
.170
,180
.190
.200
41
of Z
coth Z
l/Z
23
100.003
50.007
33.343
25.013
20.017
100.000
50 .ooo
33.333 3
25.000 0
20.000 0
0.000 001
,000 008
.OOO027
,000 064
.OOO125
0.000 000
.OOO000
.OOO000
.OOO002
.OOO006
01
16
81
56
25
24
16.687
14.309
12.527
11.141
10.0333
16.666
14.285
12.500
11.111
10.000
7
7
0
1
0
,000 216
.ooo 343
.OOO512
.ooo 729
.OOl 000
.OOO012
.OOO024
.OOO040
.OOO065
.ooo 100
96
01
96
61
0
018
402
819
270
754
9.1275
8.3733
7.7356
7.1895
6.7166
9.090
8.333
7.692
7.142
6.666
9
3
3
9
7
.OOl 331
.OOl 728
,002 197
.002 744
.003 375
.OOO146
.OOO207
,000 285
.OOO 384
,000 506
4
4
6
2
3
.004
.004
.005
,006
.006
272
824
409
028
680
6.3032
5.9389
5.6154
5.3263
5.0665
6.250
5.882
5.555
5.263
5 .ooo
0
4
6
2
0
.004
.004
.005
.006
.008
096
913
832
859
000
,000 655 4
.OOO835 2
,001 050
,001 303
.OOl 600
.205
.210
.215
,220
.225
,007
.007
.007
.008
.008
019
366
722
086
459
4.9462
4.8317
4.7226
4.6186
4.5192
4.878
4.761
4.651
4.545
4.444
05
90
16
45
44
,008
.009
.009
,010
.Oll
615
261
938
648
39
.OOl 766
.OOl 945
,002 137
.002 343
.002 563
.230
.235
.240
,245
.008
.009
.009
.OlO
.OlO
840
230
628
034
449
4.4242
4.3334
4.2464
4.1630
4.0830
4.347
4.255
4.166
4.081
4.000
83
32
67
63
00
,012
,012
.013
,014
.015
17
98
82
71
63
.002
.003
ilO3
.003
.003
798
050
318
603
906
.255
.OlO
.Oll
,011
.012
.012
873
305
745
194
652
4.0062
3.9324
3.8615
3.7933
3.7276
3.921
3.846
3.773
3.703
3.636
57
15
58
70
36
.016
,017
,018
.019
.020
58
58
61
68
80
.004
,004
.004
,005
,005
228
570
932
314
719
.280
.285
,290
.295
.013
.013
.014
.014
.015
118
592
076
567
068
3.6643
3.6033
3.5444
3.4876
3.4327
3.571
3.508
3.448
3.389
3.333
43
77
28
83
33
.021
.023
.024
.025
.027
95
15
39
67
00
.006
.006
.007
.007
.008
147
598
073
573
100
.305
.310
,315
.320
.325
,015
.016
.016
.017
.017
576
094
620
154
697
3.3797
3.3285
3.2789
3.2309
3.1845
3.278
3.225
3.174
3.125
3.076
69
81
60
00
92
.028
.029
.031
.032
.034
37
79
26
77
33
.008
.009
,009
.OlO
.Oll
654
235
846
49
16
.018
.018
.019
.019
.020
249
809
378
956
542
3.1395
3.0959
3.0536
3.0126
2.9729
3.030
2.985
2.941
2.898
2.857
30
07
18
55
14
.035
.037
,039
,041
.042
94
60
30
06
88
.Oll
.012
.013
.014
.015
86
59
36
17
01
.265
,270
.275
TRANSMISSION
42
LINE DESIGN MANUAL
Table 3 .-Functions
z
All
plan-profile
coth Z
l/Z
23
24
0.355
.360
.365
,370
.375
0.021
.021
,022
,022
.023
137
740
352
973
602
2.9343
2.8968
2.8603
2.8249
2.7905
2.816
2.777
2.739
2.702
2.666
90
78
73
70
67
0.043
.046
,048
,050
,052
74
66
63
65
73
0.015
.016
.017
.018
.019
88
80
75
74
78
,380
,385
,390
.395
.400
,024
.024
.025
.026
.026
240
887
543
207
880
2.7570
2.7245
2.6928
2.6620
2.6319
2.631
2.597
2.564
2.531
2.500
58
40
10
65
00
.054
.057
,059
.061
.064
87
07
32
63
00
.020
.021
.023
.024
.025
85
97
13
34
60
.405
.410
.415
.420
.425
.027
.028
,028
.029
.030
562
252
95 1
659
376
2.6027
2.5742
2.5464
2.5193
2.4929
2.469
2.439
2.409
2.380
2.352
14
02
64
95
94
.066
,068
.071
.074
.076
43
92
47
09
77
.026
.028
.029
.031
,032
90
26
66
12
63
.430
,435
.440
,445
.450
.031
,031
.032
.033
.034
102
856
579
331
092
2.4672
2.4421
2.4175
2.3936
2.3702
2.325
2.298
2.272
2.247
2.222
58
85
73
19
22
.079
.082
.085
.088
.091
51
32
18
12
13
.034 19
.035 81
.037 48
.039 21
.04101
,455
,460
,465
.470
,475
.034
.035
.036
.037
.038
861
640
427
223
028
2.3474
2.3251
2.3033
2.2821
2.2613
2.197
2.173
2.150
2.127
2.105
80
91
54
66
26
.094
.097
,100
.103
.107
20
34
5
8
2
.042
.044
.046
,048
,050
86
77
75
80
91
.480
,485
,490
.495
.500
.038
.039
.040
.041
.042
842
665
497
338
188
2.2409
2.2210
2.2016
2.1826
2.1640
2.083
2.061
2.040
2.020
2.000
33
86
82
20
00
.llO
,114
.117
.121
.125
6
1
6
3
0
,053
.055
.057
.060
.062
08
33
65
04
50
The loading
conditions,
other
conductor
data
manufacturers’
f(z)
of Z-Continued
catalogs.
conductor
required
The
horizontal
size, and maximum
may be obtained
and
drawings.
Procedure steps:
1. Determine c from c2 = a2 + b2
2. Determine b’ from 21’= b(w + v)/W’
3. Determine a’ from a’ = dn
vertical
tension
are determined
by previous
studies.
from
tables
shown
in appendix
C or from
spacing
of supports
can be determined
from
the
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
4. Determine coth Z from
coth Z =
1 +O.l67t$y
(-$)
where :
A = T,‘(max) - 0.5 w’b’
0.5 w’c
For short spans,
0.5 w’c
zJ=
A
T,‘(max) - 0.5 w’b’
5. From table 3, determine Z from coth Z found in step 4
6. Determine S, from S, = (S-c) + c where
s-c=$f(Z)+Z
24
Find f(Z) from table 3 or from f(Z) = 0.1 67(Z2 + Z4 /20)
7. Determine values for “No-load Chart”
a. Assume values for Z (usually two values smaller and three or four values larger
than the basic Z value found in step 5)
b. Find S-c (from step 6) for each value of Z assumed in step 7.a.
c. Determine So (from step 6) for each assumed value of Z
d. Determine values for T, and T, by using the assumed values of Z in the formulas:
T, = 0.5 w S, coth Z + 0.5 wb, and T, = 0.5 w S,, i
0
+ 0.5 w s,
e. Determine values for d from
d = 0.25 cZ + ““;,;“’
Z3 for assumed values of Z
f. Find the slope of the temperature lines from slope equals AE/S,
8. Determine values for “Full-load Chart”
a. Find S-c for each value of Z assumed in step 7.a., where
smc = (9
f(z)
+ Cd2
@‘I2
z4
72c3
b. Determine S,, for each assumed value of Z, where S, = (S-c) + c
c. Determine horizontal spacing of the temperature lines from
(Sol) (5.9, for increments of 5..5 OC from minus 7 to 48 OC, or
(Sol) (lo), for increments of 10 OF from 20 to 120 OF.
43
TRANSMISSION
44
LINE DESIGN
MANUAL
9. Prepare graph:
a. Plot the tensions for the assumed values of 2 against the slack S-c. This will give four
curves: T,’ and T,’ for full load, and T, and T, for no load
b. Plot sag d against slack S-c on the same graph
c. Find the maximum average tension at full-load conditions by drawing a vertical line
from the point of maximum tension on the full-load curve T,’ down to the full-load curve
T,
d. Starting at the maximum average tension point found in step 9.c., draw temperature
lines down to the no-load T, curve. The slope of these lines was determined in step 7.e., and
their horizontal spacing was found in step 8.b.
e. Determine the sag at every 5.5 OC from minus 7 to 48 OC or at every 10 OF from 20 to
120 OF by drawing vertical lines from the points where the temperature lines intersect the
no-load T, curve down to the sag curve
f. Label all parts of graph
Figure
19 shows
\
the
inclined
span
used
for
the
following
example
calculations:
support
a=
m
ft)
ft)
c = 583.69 m (1915 ft)
545.59
(1790
b= 207.26 m (680
h
WI
w+v
INSULATOR
STRING.
SWING DUE TO
WIND FORCE
Figure
19.-Sag
on inclined
span-parameter
Zmethod.
104-D-10.55.
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
Example
Metric
Loading = 6-mm ice, 0.38-kPa wind, at minus 9.4 OC
Conductor = 1092 mm’ , ACSR 84/l 9 Bluebird
diameter = 45 mm
area = 1181 mm*
E = 5 1.46 GPa (initial)
a = 0.000 020 7 per OC
w = 36.6453 N/m
h = (45 + 12) (0.38) = 2 1.66 N/m
v=9.1314N/m
w’ z&36.6453
+ 9.1314)2 + (21.66)2 = 50.64 N/m
a = 545.59 m
b = 207.26 m
c = 583.69 m
= 18736m
= 207.26
a’ = dc’2_02
= d(583.69)2
- (1 87.36)2 = 552.80 m
A= T,‘(max) - 0.5 w’b’ = 88 964 - 0.5 (50.64) (187.36) = 5 699
0.5 w’c
’
0.5(50.64) (583.69)
A2 = 32.479
coth 2 = 1 + O.l,,;$r
($)=
1 + 0.167 (5G)2(3+9)
5.699
= 5h729
Z= 0.17822
f(Z) = 0.005 305
(0.005 305) +
(545.59j2 (207.2612 (o 178 2214
.
72(583 69)3
= 2.7054 + 0.0009 = 2.7063
S, = (S-c) + c = 2.7063 + 583.69 = 586.40
For “No-Load Table”
a = 545.59
0.5 w = 18.3226
c/4 = 145.92
b = 207.26
c = 583.69
w = 36.6453
0.5 wb = 3797.55
a2 lc = 509.98
3a2 - 2b2 = 9 6023
*
144c
a2b2 172c3 = 0.8931
b2 /3c2 = 0.0420
45
46
TRANSMISSION
2
s-c
0.16
2.179
585.87
10 735
71462
67 166
23.39
SO
0.5 ws,
T,
Ti?
d
0.17
2.461
586.15
10 740
67 581
63 254
24.85
LINE DESIGN
0.1782
2.706
586.40
10 744
64 747
60 402
26.06
MANUAL
0.18
2.759
586.45
10 74.5
64 135
59 776
26.32
0.19
3.075
586.77
10 751
61061
56 670
27.79
0.20
3.408
587.10
10 757
58 298
53 875
29.26
0.21
3.758
587.45
10 764
55 806
51 352
30.73
AE/S, = 103 640
“Full-Load Table”
For
a’ = 552.80
b’ = 187.36
0.5 w’ = 25.32
0.5 w’b’ = 4743.96
(u’)~ /c = 523.54
(a’)? (b’)* /72c3 = 0.7492
c = 583.69
w’ = 50.64
Z
s-c
1
SO
0.5 ws,
T,’
Te’
0.16
2.237
585.93
14 836
98 258
92 806
0.17
2.526
586.22
14 843
92 895
87 399
AS = &x(5.5) = 586.47(0.000
Results
of these
from nlinus
9.5
U.S.
0.1782
2.778
586.47
14 849
88 981
83 459
0.18
2.833
586.52
14 851
88 138
82 598
metric
calculations
to 48 o C.
are shown
on figure
20 along
Loading = l/4-in ice, 8-lb/ft2 wind, at 15 OF
Conductor = 2 156 kcmil, ACSR 84/ 19 Bluebird
diameter = 1.762 in
area = 1.83 10 in2
E = 7 463 320 lb/in2 (initial)
a = 0.000 011 5 per OF
w = 2.511 lb/ft
h = 1.762 + 0.5
(8) (1) = 1.5080 lb/ft
12
v = 0.6257 lb/ft
w’ = x/(2.51 1 + 0.6257)2 + (1 .5080)2 = 3.480 lb/ft
u= 179oft
b = 680 ft
c= 1915 ft
a’ =,/m
3(~‘)~ - Zb’12 = 1o o7
144c
(b’)2 /3c2 = 0.0343
0.19
3.157
586.85
14 859
83 887
78 303
0.203.498
587.19
14 868
80 073
14 442
0.21
3.858
587.55
14 877
76 62.5
70 950
020 7)(5.5) = 0.066 77
Grstoniarv
b’=b(y)
c/4 = 145.92
=680($$)=612.918ft
=&19;5)2
- (612.918)2 = 1814.265 ft
with
initial
sags for temperatures
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
Temp. Sag
(“Cl
(m)
-9.5
24.8
-7.0
25.0
90 000
In
{
80 000
Ec
zi
5
z
70 000
k
60 000
3
SLACK (S-c),
Figure 20.-Results
104-D-1056.
of example
problem
on
an inclined
meters
span using parameter Zmethod
(metric).
48
TRANSMISSION
A=
T, ‘(max) - 0.5 w’b’
LINE DESIGN MANUAL
= 20 000 - 0.5(3.480) (612.918) = 5.682
0.5(3.480) (1915)
0.5 w’c
A2 = 32.286
’
coth 2 = 1 +0.167 A3
O(
Z= 0.178 75
f(Z) = 0.005 336
=
2
i2
>
1 +0.167
(‘8;;;2565)2
5.682
(0.005 336) +
(179o)2
(j&)
= 5’6558
(680)2
72(1915)3
(0.178
7514
= 8.9280 + 0.002 99 = 8.93 10
so = (S-c) + c = 8.9310 + 1915 = 1923.93
For “No-Load Table”
Z
s-c
a= 1790
0.5 w = 1.2555
c/4 = 478.75
b = 680
c = 1915
0.5 wb = 853.74
a2/c= 1673.16
3~’ - 2b2 = 31 5.
144c
.
w = 2.511
a2 b2 /72c3 = 2.93
b2 /3c2 = 0.04203
I
so
0.5 w&J
Tl
Te
d
0.16
7.15
1 922.15
2 413.26
16 135
15 099
16.73
0.17
8.10
1923.10
2 414.45
15 193
14 220
81.54
0.1788
8.93
1923.93
2 415.49
14511
14 093
85.781
0.18
9.05
1 924.05
2 415.64
14 419
13 439
86.36
0.19
10.09
1 925.09
2 416.95
13 727
12 740
91.18
0.20
11.18
1926.18
2 418.32
13 106
12 112
96.00
0.21
12.33
1 927.33
2 419.76
12 545
11544
100.83
AE/S, = 7 100
For “Full-Load Table”
a’ = 1814.26
b’ = 612.92
c= 1915
w’ = 3.480
Z
S-C
so
0.5 w’s0
7.1’
Te’
AS= &(lO)
0.16
7.34
1 922.34
3 344.87
22 150
20 924
0.5 w’ = 1.740
0.5 w’b’ = 1066.48
(a’)2/c = 1718.82
(u’)~ (b’>2 /72c3 = 2.45
0.17
8.29
1 923.29
3 346.52
20 941
19 705
0.1788
9.17
1 924.17
3 348.06
20 003
18 758
1
3
19
18
= 1924.17(0.000 011 5) (10) = 0.2213
0.18
9.30
924.30
348.28
868
622
c/4 = 478.75
3(a’>2
-
2(b’12
=
33
o8
144c
(b’)3 /3c2 = 0.034 15
0.19
10.36
1 925.36
3 350.13
18 910
17 654
0.20
11.48
1 926.48
3 352.08
18 050
16 783
0.21
12.66
1 927.66
3 354.13
17 273
15 996
CHAPTER
Kes~~lts
15 to
120
of these
calculations
II-CONDUCTOR
are shown
on figure
SAGS AND TENSIONS
21 along
with
initial
49
sags for temperatures
from
OF.
22
20
000
I
\\
!
T
TL
\
000
I
10 000
Temp.
(OF)
Sag
(ft)
70
80
90
loo
110
120
81.2
81.75
82.75
83.7
84.6
85.5
86.4
87.3
88.25
89.2
90. I
91.0
t--
T
16 000
I--
::
El
0
0.
c
I
\Tr
!!E
14 000
000
000
000
8
I
0
SLACK
Figure 21.-Results
of example problem
on an inclined
I
IO
9
(s-c).
II
._
IZ
.-
I3
feet
span using parameter
Zmethod
(U.S. customary).
104-D-1057.
50
TRANSMISSION
15.
Galloping
Conductors.-
LINE DESIGN MANUAL
A galloping
conductor
is a phenomenon
usually
caused
blowing
on an iced conductor.
relatively
light wind of about
48 to 56 km/h
(30 to 35 mi/h)
may be in the form of either rime or glaze. A few cases of galloping
conductors
without
the
of ice have
been
In 1930,
Mr.
noted,
but
A. E. Davison
the
In
by the
reaction
lifting
force.
1932,
Mr.
instructor
at Harvard
temperature
will melt
are extremely
of the Hydroelectric
of wind
J. P. Den
formation
which,
of aerodynamic
cases
and
Hartog,
Power
Commission
School,
conductor,
An airfoil
of about
0 ‘C (32
a portion
of the radial
and a periodic
noted
Engineering
with the
stability.
glaze,
OF)
ice,
research
presented
sun
will
a theory
cross
may
has published
is the
result
several
of the
with
Westinghouse
that
sag of the conductor
galloping
increase)
than
the
articles
conductor
on the
which
Electric
lift
controls
and
CO.
was the result
of a glaze
and a light
and around
wind is blowing.
the conductor,
type
The sun
and then
shade at the bottom
of the conductor
where
takes shape and the possibility
of galloping
at 0 OC (32 OF), with
resultant
presented
aerodynamic
13 mm (l/2
conductors,
This method
in) of ices and a wind
of 48.3 km/h
(30 mi/h)
or a wind pressure
of 0.096 kPa (2 lb/ft2).
This approximates
condition
under
which
most cases of galloping
have occurred.
The path of conductor
approximates
a loop of elliptical
shape. The major
axis of the ellipse is slightly
larger
uses a 6 percent
presence
capable
of causing
a certain
be formed
at a freezing-thawing
conductors
becomes
very real.
Based on numerous
observations
and on several motion
pictures
of galloping
developed
an empirical
method
for determining
the conductor
oscillation
path.
on the stabilized
Canada
of the conductor
section
easily
is shining
run down
the water will be blown
back by the light wind into the
it will again freeze. As this process
continues,
the airfoil
of Ontario,
twisting
engineer
has an airfoil
cross section
when the
the water
a
ice
rare.
and
work
on galloping
conductors,
Mr. Davison
suggested
that galloping
the results
of his pioneer
subject
since that time.
produced
these
by
The
sag under
the
loading
Davison
is based
velocity
the loading
oscillation
(the Bureau
condition
described
above, and is inclined
from the vertical
in a direction
by an angle equal to the angle of sideswing.
In level
a small distance
above the normal
level of the points
opposite
the direction
of the conductor
sideswing
spans, the highest
point of the full ellipse is only
of attachment
of the conductor
to the insulator
string.
overhead
not
As long
overlap,
as the
ellipses
galloping
will
in which
the
for all conductors
not
and
ground
wires
of a transmission
the conductors
to come in contact
with each other
overhead
ground
wires.
Contact
would
re’sult in outages
and possible
damage
to the
Observations
of lines with long spans and heavy conductors
indicate
that the conductors
in two
loops
cause
magnitude
of oscillation,
or size of ellipse,
is approximately
line
do
or with the
conductors.
may dance
half
size; that
is, the major
axis of the ellipse
is approximately
one-half
of the total
conductor
sag in the span.
Application
of this method
to several existing
lines, in regions
subject
to sleet conditions,
has shown
that those lines with sufficient
ground
wires to prevent
overlap
spacing
of the
between
ellipses,
conductors
and between
had no outages
under the
conductors
and
sleet conditions.
overhead
The lines
that showed
an overlap
of the ellipses had a record
of many outages
under
sleet conditions.
There
have also been observations
where iced conductors
have galloped
in a manner
similar
to a skip rope
being turned,
with the midpoint
rising as far above the points of support
as it hangs below those points
when at rest. This
a designer
cannot
There
ellipses.
* For
NFX:
sort of galloping
is rare, fortunately,
economically
be expected
to meet.
is no definite
However,
our
heavy
loading
because
clearance
limits
are indicated
which
length
of span where
galloping
will change
from full-sag
ellipses
to half-sag
experience
indicates
that for our line locations
and conditions,
we should
use
area.
CHAPTER
full-sag
ellipses
to gallop
in spans
in two
be used.
and
ground
overhead
Experience
the ends
a weak
To
spot
and
determine
the
wires
to prevent
ground
conductors
structure
and
with
that
spacing
required
ground
wires,
and
1. For loading
conditions
a temperature
of minus
1 ‘C
for the given span length.
a.
Figures
22 and
conductor,
and figures
steel, 7-wire
overhead
the
wear
of time.
all hardware
conductors
a particular
hardware,
24 and
ground
25 show
wire.
b.
From
the calculations
on
conditions
conducive
to galloping,
the
and
between
For
a 289.5-m
(950-ft)
s p an, based
on the
wires,
proceed
span
ordinarily
in relatively
and
length
overhead
with
span
for
given
a given
as follows:
(2-lb/ft2)
wind pressure,
and overhead
ground
wire
based on a 213.4-m
for a 242 mm2 (477
for a lo-mm
a 213.4-m
(700-ft)
kcmil)
(3/8-in)
(700-ft)
ruling
and
sags
ruling
ACSR
span.
24/7
high-strength
span,
and
for
sag
WI
5255
4386
213.4-m
conductors
check
If galloping
failure
permissible
for
carefully
vibrations,
cause
maximum
mm
Conductor
Overhead ground wire
can
the
sag calculations
these figures,
the sags are:
very
and
span
of
conductors
occurred.
wind
and
of 13 mm (l/2
in) of ice,3 0.096-kPa
(30 OF), d e t ermine
the conductor
Assume a 289.5-m
(950-ft)
23 show the sag calculations
and
condition
or to determine
are likely
to 53 percent
between
to have
spot
loading
ground
conductors
equal
of contact
is known
in the
period
the
axis
reduced.
galloping
weakened
overhead
spans,
major
the probability
on the
between
for
longer
to examine
or excessive
contact,
In
with
is greatly
where
in a short
conductors
overlap,
practice
of a line
concentrate
possibly
in length.
of galloping,
in a conductor
overhead
given
do not
51
SAGS AND TENSIONS
size ellipses,
it is good
part
a failure,
weather
ellipses
as a result
in any
ft)
so one-half
If these
wires,
clamps
in producing
moderate
loops,
has shown
of the
has created
slow
up to 183 m (600
or more
the sag, should
II-CONDUCTOR
(17.24)
(14.39)
ruling
span,
the
sags are:
sag
Conductor
Overhead ground wire
2. Determine
loading
conditions
0, the
given
angle
in l.,
a. Conductor B = tan-l
of sideswing,
and
using
heavy loading
area.
the
force
(ft>
9675
8075
(31.75)
(26.50)
conductors
triangles
4.4898 N/m
21.186 N/m Or
b. Overhead ground wire 13= tan- l
3 For NEST
for
the
mm
3.3079 N/m
11.777 N/m Or
and
shown
overhead
on figures
= 1 lo 58,
ground
wires
for
the
22, 23, 24,
and
25.
52
TRANSMISSION
DCm-576
LINE DESIGN MANUAL
(S-78)
Ltnear
Force
Dead
Area
Temp.
0.000
NO Ice.
No Wind
Figure
Factory
Load
Fwce
(W’)
Creep
0.000
Jag
Total
O.CO,!
003
(A).arn&
C&f.
01 Llnear
Exp.:
0 /9peperOC
(W’)
22.-Conductor
sag and tension
calculation
form
for example
problem
on galloping
conductors
(metric).
CHAPTER
II-CONDUCTOR
;;;tL
SAGS AND TENSIONS
53
SAGCALCULATIONS
LOADING
.d-
Vv
Weight Factors:
Dead Weight (W’)
+ hn.
5i
ICY (w”)
lb Wind
Resultant:
0. L 14%
lb/f1
D, L/53
tb,tt
lb/l1
e/.
(W”‘)
‘F
LOADING
UNSTRESSED
LENGTH
Inch Ice.
Creep o.ooa*-Total O.ooa
I.lb/ft
Modulus. (E) Final/D,fl
Initial&@/-x
FinaIM
{ ~~~
Initial%
3 &q
Area (A) &&.%k
in2
Temp. Coolf. of Linear Exp.:
0.004 o/k
Permanent set 0.00
per OF
SACFlCTOR 1
i!
6
I
SPANLENGTH(S) AFEET
SAG,H
1 SW,lb
x 106 lb/in2
106 lb/i&?
-lb
/I/
lb
1 TENSION,lb
NO Ice. No Wind (W’)
Llb/ft2
SPANLENGTH(S)
-FEET
calculation
for example
Wind(W”’
No Ice. No Wind (W’)
Figure 23.-Conductor
customary).
3.
Construct
at an angle
The major
to one-half
method,
sag and tension
half-sag
of 28 from
ellipses
the
plane
as shown
form
on figure
of the conductor
26.
when
The
the
problem
major
0.096-kPa
axis of the ellipse is equal to one-half
the sag plus 6 percent,
of the major
axis. The easiest way to construct
the ellipses
which
is explained
in numerous
drafting
or related
texts.
on galloping
conductors
axis
ellipse
is inclined
wind
is blowing.
of the
(24b/fta)
(U.S.
and the minor axis is equal
is by the use of the trammel
TRANSMISSION
54
DCm-578
LINE DESIGN
-
(3-78)
;;;pL'
llkili
CONDUCTOR,f&mm
Code
MANUAL
,/d’!‘c %ei:
?-W/b
SAG CALCULATIONS
LOADIME &a+----
Name
Linear
Rated
Breaking
Strength
olamerer~22&!5L
Tension
18
&o
N
mm
kPa
l”~tl~l.-~%,-&-%~N
.-a%
%a!.2
0/o
N
50
-%2o-zoN
F,nal.~%.
/g
O’o g
by
Dare
AL/?
Temp.
Co&f.
o.cm
6.
L/L
N/C?7
17, 88 L5
Ice.
NO Wmd
ground
FIMI
w
GPa
Inttlalfig*5
0 //pePc
Fanal
SAG FACTOR
?
wire sag and tension
9
AE
GPa
Lf? 924
AE k
SAG,mm
:
77
E
SW,N
:
TENSION, N
m
calculation
form for example
problem
on galloping
conductors
(3-78)
!;,fL
/t
CONDUCTOR3 f
Code
00
Q
O.C%.&
(W’)
Figure 24.-Overhead
(metric).
DC-576
(E)
Exp..
SPAN LENGTH(S) 2 1.3. 36
NO
0.00
N/m
lnltial
LENGTH1
o.ooo*
Total
Modulus.
of Linear
SW
E
ser
creep
-
/TEMP.
; oc “UftSTRESSEO
LOADING
N
(A)Amm2
Permanent
N/m
(W”‘)
Area
N/m
(W”)//.
W Ind
Resultant
25
(W’I m,&?8j
ForC2
mm Ice
od$&i?
Fmal.&C.
Computed
Factor.
Load
A
Llmltatlons
Loaded
Force
Dead
i/i!?
.?tee(.
7--w/ re
LOADlNG -LM
Welghl
Name
Rated
SAGCALCULATIONS
Breaking
Diameter
Load
m
Factors:
Dead
/nib
Inch
Wetght
+ L”.
Ice
lb
A
(W’) m,73
Resultant:
Area
(A)
o.ooo
[TEMP..
oF /UNSTRESSED LENGTH
LOADING
No
Ice.
NO Wind
Gc7fl,iis
-lb/@
Permanent
Inch
/)
5.D79
226
ou
creep
0.006--
Ib/ft
Total
O.OO+
Ib/ft
In2
of Linear
Permanen~OO~
Ib/ft
Modulus.
per ?=
SAG FACTOR
Y
B
(E)
Exp.:
1
Final~x
106
lb/in2
lnttlaf~ox
106
lb/in2
Final
AE d!
fb
lntttal
AE
tb
SAG.11
/
1 TENSION, lb
SW,lb
(W’)
120
//3
(W’“)
Coeff.
453
0.
Wind
TemD.
Iblft
5.967
(W”)
lo.999
764 b.am
Qq? 51 0. J/L?
lo&z.
967
~9-7
In.o/L
WindW”“i3o
Figure 25.-Overhead
(U.S. customary).
51
m
97
/ 2 ,229 I 14f. I I
/437
1.3 1
I
f/.24
JqQS
V.
/+f.JP
1
/4/.
I
1
S
~6
SPANLENGTH(S).-FEET
Ice.
Set & creep
l,g,dnn
o.
994
373
IO, 000
llp7
51
0.
/630
1
I
ground
wire sag and tension
calculation
form
for example
problem
I
5%
,
on galloping
conductors
FAal
CHAPTER II-CONDUCTOR
Type HS Structure
289.5-m (950ft) Span
Based on 213.4-m (70%ft)
ruling span
3658-mm (12-ft) Pole spacing
NESCHeavy Loading
Conductor ful I- load tension
= 33 362 N (7500
Conductor:
242
mm*
Sag
Half sag
+6%
Major axis
Minor axis
lb)
OGWful I- load tension
=2l 418 N (4815 lb)
Half-sag ellipses
SAGS AND TENSIONS
OGW:
8= ll”58’
IO-mm
(i-in)
2 9f sag
+6%
Major axis
Minor axis
(477
mm
9675
4835
290
5128
2564
55
kcmil\fPjCSR.
24/7
(3.35)
(15.88)
( 0.95)
(16.83)
( 8.42)
H.S. Steel
Cf_t)
mm
8075
4038
242
4250
2125
(26.50)
(13.25)
( 0.79)
(14.04)
( 7.02)
8 = 15’ 42’
4023
(13.2
Figure 26.-Half-sag
ellipses for example
problem
on galloping
mm
ft)
_
conductors.
104-D-1058.
TRANSMISSION
56
16.
Broken
conductor
Conductors.-The
is important
condition
with
crossings;
structures.
The
the
of the
nature
Using
given
this
work
requirements
and
also
computation
over
from
of sags and
from
the
the
railroad,
waterway,
of determining
tensions
under
in spans
of assuring
highway,
standpoint
of sags and
tensions
standpoint
this
to a broken
under
communication
the
condition
adjacent
compliance
unbalanced
is somewhat
this
line,
loads
and
on the
complex
due
to
variables.
a technique
in
determination
in design
clearance
powerline
LINE DESIGN MANUAL
by G. R. Wiszneauckas
section
for
a 345-kV
shown
in appendix
transmission
line
span
A, a broken
over
conductor
Interstate
Highway
problem
is
No.
25
(Sta. 789 + 95 and 790 + 83) and the Colorado
and Southern
Railroad
crossing
(Sta. 795 + 48), both
located
in Colorado.
Figure
27 shows the profile
portion
of the plan and profile
drawing
for this
example
problem.
Please
note
that
this
figure
is predominately
in U.S.
customary
references
to this figure,
such as stationing,
are also in those units. The conductor
as 644 mm2 (1272 kcmil),
ACSR,
45/7 stranding,
with a full-load
(NESC
heavy)
(13 800 lb). Assuming
a broken
conductor
in the span on the
at Sta. 797+30,
the ruling
span for the three remaining
spans
to be 320.95
m (1053 ft). At 49 OC (120 “F) f’ma 1 conditions,
AE
d
HO
HI
LJ
Ll
P
s
s
basic
nomenclature
used
of cross-sectional
Product
Horizontal
displacement
of insulator
string
Initial
horizontal
tension
in conductor
Horizontal
tension
in conductor
after a change
=
=
Length
Initial
=
=
Final span
Horizontal
=
=
of insulator
span length
length
force
caused
Force
Force
(weight)
(weight)
W
8
4
=
=
Total
Angle
vertical
load,
of deflection
=
Change
The
resulting
values
indicated
-
2.110
+
problem
are
and
modulus
of elasticity
of the
of 4 in span
conductor
length
by
Wwhen
the
insulator
string
is deflected
by an angle
8
string
acting
W = w l/2
of insulator
on insulator
string
+ w2
string
length
by the curves show the suspension
insulator
string on the structure
string on the structure
at Sta. 787 +00
2 110 mm (83 in), and the insulator
(37.5 in). This will result in a new span length
of 312.789
m (1026.21
ft)
6.92
+
3.13
=
1026.21
ft].
The
24
310-N
0.955
= 312.789
m, or 1030 -
at Sta. 797 + 30 will deflect
will deflect
about
955 mm
[313.944
example
sag in conductor
span length
of conductor
of insulator
of conductor
in span
in this
A.
string
=
w2
area
has been assumed
tension
of 61 385 N
is:
=
=
=
=
=
Wl
section
=
General
symbol
for
General
symbol
for
Unit force (weight)
W
in this
therefore,
northwest
side of the steel structure
to a dead-end
structure
is calculated
the tension
for this ruling
span is
24 310 N (5465 lb), with a corresponding
sag of 11 211 mm (36.78
ft).
The calculations,
tables, nomenclature,
and broken
conductor
curves
all in accordance
with the broken
conductor
thesis ‘shown
in appendix
The
units;
CHAPTER
(5465~lb)
the
expanded
been
the
tension
conductor
to make
shown
figs.
28 and
in the
the
as a dashed
adjacent
29) is used
adjacent
sag curve
curve
for
span.
plotting
on figure
to compute
The
I.-Broken
Highway
the
calculated
on the
corresponding
sag is 15 736
plan-profile.
27 to indicate
the
The
expected
centerline
(Sta.
789 +95
and
result
790+83)
795 + 48)
Ruling span =
where
S =
span
length.
Metric
s, m
S3, m3
304.373
341.376
3 13.944
28 198 004
39 783 130
30 942 582
959.693 m
98 923 716 m3
Rulingspan=dz=321.
058m
U.S. Customary
s, ft
s3 ) ft3
998.6
1120
1030
995 805 877
1404928 000
1092727000
3 148.6 ft
3 493 460 877 ft3
Ruling span =dw=
sag in this
mm
sag in the
Conductor Calculations
centerline
(Sta.
Span Calculations:
59
SAGS AND TENSIONS
span.
Example
Railroad
Ruling
(from
broken
II-CONDUCTOR
1053.34 ft
(51.64
ft)
crossing
of a conductor
span
which
span
break
with
is
has
in
TRANSMISSION
DCm-576
LINE DESIGN MANUAL
(3-78)
f;;LL
SAGCALCULATIONS
LOADMG
Linear
VY
Force
maa
-Lz
oa
Factor,
Load
Face
kPa
//.
Wtnd
(W”‘)
(A).zm&
Temp.
Co&f.
TEMP..1
oc
UNSTRESSED LENGTH
LOADING
Lmm
O./q/q2
Permanent
Wind
Set
(W”‘)
h Creep
set
Permanent
creep
N/m
T?P9
43
of Ltnear
N/m
Total
Modulus.
(I3
Fmal
lnltlal
01~perOC
SAG FACTOR
Final
AE
lnltial
AE
SAG,mm
~
44
3)
1 SW,N
Ice.
No Wind
-mm
:/
800
,
7,/L,
/ 0
0,
g
nno
No
Ice.
(W’)
‘5.5
32
I/.
j
49
1
454
002
JR/
Ice.
kPa
Permanenf
No
Ice.
/L5
/
0. ah87
D.03.3
q/E
GPa
f
?zGPa
c//9
009
N
924
827
N
1 TENSI0N.N
//
7 17
g97
I
I
,
SPAN LENGTH(S) 350.59
15.5
19
(W’)
Ice
kPa Wind (W”‘)
Set 6 Creep
No Win4
&!dtk
46,
SPAN LENGTH(S)-m
i-/p
j
/
/
I
1
300
!o.
000
o&j
j/,
no/
3
I/,
-18
No
/
O.OO/
0.1506
I
1z
-mm
0,/q/53
Permanent
3
1
~0.000
mm Ice
No Wind
csf/
’
Ice
/3
46 4
0.000
SPAN LENGTH(S)-m
l-/g
I
No
0.004
N/II7
’
Exp.:
v
K = r/.37$2
f/ESC
N/m
I/of?0
’
ii
Ice
kPa
92.77
L75z,
cw.,ao*
37.
ResulIanl
#. /977
X~=#524/
mm Ice (W”)
Area
o.ow
J
018
m
I
I
I
I
1
I
SPANLENGTH(S)-..&!o,?5
o,oD~
1/J) ;21 0 239-q
i
15,
I
I
I
I
I
1
I
!
1
eon
/gin
I
I
21
(W’)
Wind
(W”‘)
Set 6 Creep
No Wind
(W’)
I
i
1
I-18
-1
I
I
/
I
I
I
I
I
I
I
I-
;
15.5
I
I
73L
!6 SN#LI
I
problem
(metric).
32
I
0.3933
49
Figure 28.-Sag
and tension calculation
w
form for broken
31
conductor
/5
/L
&Jo
CHAPTER
DC-573
II-CONDUCTOR
SAGS AND TENSIONS
(3-78)
;;;tL
CONDUCTOR &&22
Code
kr.&gR
‘-r-A
i
Name
Rated
Breakrng
Load
Diameter/*-qf/‘i
Tenston
Final
Computed
k
No
-Inch
__
Permanent
100
lb
-
~
lb
Area
lb
Temo.
% ___
lb
0.000
Date
UNSTRESSED LENGTH
(A)
*&=a,31
fi
lb/l1
a
SB/L
A:
78/T
.1,
00
(W”)
Wind
(W”‘)
/,
of Linear
o//
NESC
/977
Permanent
:,“:::
73
Set 0.000
o.ooo~ZLJ-
Total
O.Oo/
Modulus.
(E)
Final
?,.-?s
I
SAG FACTOR
z;
/
SAG, f!
1
SW, lb
1
FEET
/ 05;‘i!
(W’)
SPAN LENGTH(S)
Figure
FEET
I
I
29.4ag
1
I
I
and
tension
calculation
I
I
form
x 106
lb/In2
Exp.:
per OF
SPAN LENGTH(S)
Ice.
dA+s
creep
(W’)
Ib/ft2 Wlnd(W”’
Set 6 Creeo
/( = a.30
Ib/ft
1n2
Coeff.
i!
Ice.
No Wind
Vu
J
(W*)~/..
Resultanr:
‘yo ____
To”p”j
No Wind
lb
&
___
Weight
Ice
lb
OF 50
&OF
ha
Factors:
Dead
+&on.
*OF..XI-4c
by
Inch
Ice.
.?1/
‘F&4
LOADING
Ice.
Weight
Llmlratlons:
Inltval.-
No
LOADING
Y$‘$
Inch
Loaded,
Final,
SAG CALCULATIONS
for
broken
conductor
problem
I
(U.S.
customary).
TENSION,
lb
TRANSMISSION
62
Horizontal
Tension
Calculate
the
Then
Ho =
and w is the
linear
T-
LINE DESIGN MANUAL
Calculations:
49 ’ C (120
o F) sag and
SW , where
Ho is the
force factor.
tension
horizontal
on sag calculation
T is
tension,
Metric
and
Tabulate
component
P
full
line
(figs.
28 and
tension,
s is the
29).
sag,
U.S. Customary
H,, = 5465 - (36.78) (1.434)
= 5412 lb
HO = 24 310 - (11.211) (20.9277)
= 24 075 N
H
the
forms
Curves:
the
data
of tension
for
Hand P
the
acting
in the
curves
(tables
conductor.
The
p=-
4, 5, 6, and
Pforce
7). The
H
force
is the
4 W,d
i cos 0
and is the horizontal
force which
resists the movement
of an insulator
string
of length
vertical
to any angle 8 while
a vertical
load
?VTis acting.
Plot the Hand Pcurves
(figs. 30 and 31) from the data in tables 4, 5, 6, and 7.
Table 4.-P curve computations for example
problem No. 1 -broken conductor (metric)
i= 2286 mm
$.=7095N
d,
mm
d/i =
500
1000
1250
1500
1650
1800
1950
2050
2150
0.2187
.4314
.5468
.6562
.7218
.I874
.8530
.8968
.9405
cos e
d/i
cos 0
p,
N
0.9758
.8992
.8313
.I546
.6921
.6164
.5219
.4425
.3398
0.2241
.4864
.6531
.8696
1.0429
1.2174
1.6344
2.0267
2.7678
1 589.99
3 451.01
4633.74
6 169.81
7 399.38
9 063.15
11 596.07
14 379.44
19 637.54
Sill6
’ WT = vertical force at attachment point, which is one-half the
insulator force plus force of conductor.
4 WT has been used in this section
for clarity;
horizontal
is
it is shown as Win appendix
A.
i from
the
CHAPTER
II-CONDUCTOR
63
SAGS AND TENSIONS
Table 5.-P curve computations for example
problem No. l-broken conductor (U.S.
customary)
‘WT=15951b
d,
in
d/i =
sin e
20
40
50
60
65
70
75
80
85
0.2222
.4444
.5555
.6667
.7222
.7778
.8333
.8889
.9444
i=7.5ft=90in
cos
dli
cos e
e
0.9750
.8958
.8315
.7453
.6917
.6285
.5528
.4581
.3288
p,
lb
0.2279
.4961
.6681
.8945
1.0441
1.2375
1.5074
1.9404
2.8723
363.50
791.28
1065.62
1426.73
1665.34
1973.81
2404.30
3094.94
4581.32
1 W, = vertical weight at attachment point, which is one-half
the insulator weight plus weight of conductor.
Table 6.-H curve computations for example problem No. I -broken
H,, = 24 075 N
1
2
3
WLO
HosinhK
N
12
13
14
16
18
20
22
24
000
000
000
000
000
000
000
075
L,, = 321 m
3369.803 431
3369.803 431
3369.803 431
3369.803 431
3369.803 431
3369.803 431
3369.803 431
3369.803 431
'
4
-- HO-H,
(2) (3)
AE
0.999
.999
.999
.999
.999
.999
.999
1.000
w = 20.9277 N/m
728
751
773
818
863
908
953
000
3368.886 844
3368.964 350
3369.038 486
3369.190 127
3369.341 768
3369.493 409
3369.645 050
3369.803 431
Numbers in parenthesis are column numbers.
5
6
(4)
sinh-‘(5)
H,
0.280
.259
.240
.210
.187
.168
.153
.139
741
151
646
574
186
475
166
971
0.277
.256
.238
.209
.186
.167
.152
.139
178
335
382
048
110
688
573
518
conductor (metric)
AE = 44 419 008 N
7
8
9
IHl
w
(6) (7)
L o‘I (8) 1
m
1146.8054
1242.3725
1337.9397
1529.0739
1720.2081
1911.3424
2102.4766
2300.7784
317.869 227
318.463 555
318.940 742
319.649 841
320.147 930
320.509 184
320.781 162
321 .OOO001
3.130
2.536
2.059
1.350
0.852
.490
.218
.ooo
77
45
26
16
07
82
84
00
TRANSMISSION
64
LINE DESIGN
MANUAL
7.-H curve computations for example problem No. l-broken
Table
H,, =54121b
1
Lo =1053
2
3
HL
lb
Ho sinh wA
2700
2900
3200
3500
4000
4500
5000
5412
757.452311
151.452311
757.452311
757.452311
757.452311
757.452311
757.452311
757.452311
4
ft
conductor (U.S. Customary)
w = 1.4340 Ib/ft
5
6
AE = 9 985 800
I
8
10
G9=
HO-HI
1- 7
(2) (3)
gf
0.999 728
.999148
.999178
.999 809
.999 859
.999909
.999959
1 .ooo 000
751.246284
751.261433
151.284 157
757.307 638
751.345 510
757.383383
151.421256
151.452311
0.280462
.261125
.236651
.216 314
,189 336
.168 307
.151484
.139958
ZH1
sinh-1 (5)
0.276910
.258245
.234496
.214120
.188223
,167 522
A50911
.139 505
(6)(7)
w
=fO
3765.5904
4044.6304
4463.0404
4881.4505
5578.8006
6276.1506
6973.5007
7548.1172
1042.1573
1044.5056
1046.5651
1048.1451
1050.0586
1051.3933
1052.3780
1053.0001
Loft
(81,
o=
Lo in
(81,
122.88
101.88
77.16
58.20
35.28
19.32
1.44
0.00
10.24
8.49
6.43
4.85
2.94
1.61
0.62
0.00
Numbers in parenthesis are column numbers.
Read
the
insulator
deflections
from
2110
mm
955 mm
Then,
the
313.944
Read
the
(Sta. 797+30).
corresponding
new
span
length
for
m (1030
ft) - 2.110
horizontal
tension
line
tension,
T =
SIC =
16640
+
crossing
ft)
30 and
over obstructions
in sag and tension
30 and
31:
span
+
is equal
0.955
31)
to:
m (3.13
in the
ft)
=
312.789
m (1026.21
ft).
conductor
at the first
suspension
point
and
figures
28
and
29
to
compute
the
lb),
of tension
in the
conductor
may
now
if desired:
(1.5.736)(20.9277)
difference
in sag due to this
in a slightly
larger sag than
clearances
corrections
on figures
Use this value of tension,
16 640 N (3740
49 ‘C (120 “F) sag. Th e h orizontal
component
to the
The
results
curves
(83 in) at Sta. 797+30
(37.5 in) at Sta. 787+00
m (6.92
(figs.
be corrected
H +
the
completed
=
16969
N, or 3740
+
(51.64)(1.434)
=
3814 lh.
correction
is small, and the use of the corrected
horizontal
would
actually
exist; therefore,
by ignoring
the correction,
will be slightly
greater
are seldom
made.
than
those
computed.
For
these
tension
actual
reasons,
the
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
65
Sag curve for broken conductor:
Metric
K = Sag/Span2
15 736
= L
= 1.6062 x 10-4m-’
(3 13)=
(Span)‘,
span,
m
m2 x lo4
48
96
144
192
240
288
366
0.2304
0.9216
2.0736
3.6864
5.7600
8.2944
11.2896
Sag = (K) (Spanj2,
m
0.370
1.480
3.331
5.921
9.252
13.322
18.133
3000
2500
z 2
aa
emaa
.-EE.- .= 2000
.‘=
EE
0
5000
10000
HORIZONTAL
Figure 30.-Curves
for broken
conductor
15000
FORCE,
problem
20000
newtons
(metric).
104-D-1060.
25000
TRANSMISSION
66
U.S.
LINE DESIGN
MANUAL
Custontnry
K = Sag/Span’
=
51.64
= 4.9056 x lo- 5ft- ’
(1026)=
Span,
ft
(Span)=,
ft= x lo5
200
400
600
800
1000
1200
1400
1600
1800
2000
0.4
1.6
3.6
6.4
10.0
14.4
19.6
25.6
32.4
40.0
d=83 in
sag = (K) (Span)=,
ft
1.96
1.85
17.66
31.40
49.06
70.64
96.15
125.58
158.94
196.22
d,
!
ti Curve
60'
0
1000
2000
HORIZONTAL
Figure 31.-Curves
for broken
conductor
3000
4000
sooo
FORCE, pounds
problem
(U.S. customary).
104-D-1061.
6000
CHAPTER
The
sag template
figure
for
the
II-CONDUCTOR
Span
with
reduced
67
SAGS AND TENSIONS
tension
due
to the
broken
conductor
is shown
on
32.
SAG TEMPLATE FOR EXAMPLE PROBLEM NO. I
U.S. Highway No. 25 Sta. 789+ 95 and 790+83
Sta. 795 +48
Rai I road
Ruling Span = 313 m (1026 ft)
Reduced tension at 49 “C (120 OF), no ice, no wind= I6 640 N (3740 lb)
24.0
14.4
E
c
9.6
:
t47
4.6
0
168
144
120
96
72
46
24
0
24
SPAN,
600
200
400
The
broken
conductor
to the highway
of 9754
clearance
to the railroad
requirements.
Example
Any
2.-Unbalanced
number
template
0
curve
plotted
tension
on figure
96
120
144
168
200
400
600
ft
due to broken
27 indicates
conductor.
there
would
104-D-1062.
be conductor
clearances
mm (32 ft) at Sta. 789+95
and 7925 mm (26 ft) at Sta. 790+83.
would
be 14 326 mm (47 ft). These clearances
all meet NESC
and
The
State
Condition
of real or imaginary
shown
in appendix
involved
solution
for reduced
72
m
SPAN,
Figure 32.-Sag
48
problems
may
be studied
by use of the broken
A. A hypothetical
situation
has been assumed
using the basic broken
conductor
concept:
to illustrate
conductor
the
thesis
use of a more
68
TRANSMISSION
A transmission
and
a series
situation.
All
excepted
span
(4-lb/ft2)
line
spans,
except
plus
before
a bundle
(1150-ft)
is loaded
wind,
equilibrium
with
of 350.5-m
have
NESC
constant
and
after
of two
18 OC
kcmil),
for this
no wind
loading
unbalanced
(1272
assumed
no ice and
heavy
at minus
the
MANUAL
644 mm2
sp ans has been
one,
under
LINE DESIGN
load
conditions
(0 “F).
45/7
conductors,
of an unbalanced
at minus
18 ‘C
of 13-mm
Figure
condition
ACSR,
study
(0 OF).
(l/2-in)
33 shows
load
The
ice, 0.19-kPa
the
conditions
for
exists.
INITIAL
CONDITIONS
(Before unbalance due to ice)
L
L
--c
_
d,
~
L,
L2
d,
Lo
_
_
Conditions
d2
LO
for
L4
L3
d3
_
Lo
L5
3
d4
Lo
_-~-
_
L6
3
LO
Lo
d,
Lo
_
equilibrium:
H, = H,+ P,;
H, =H2+P2;
H,=H,+P,;
H3=H4+P4;
H,=
0, =d,-d,;
L, = Lo-O,;
L, = Lo-2d,
02=d2-d3;
L,=L,-0,;
%=d3-d,-,
L,=L,-0,;
0,=d,-d,;
L,=L,-0,;
0,=d,-d,;
L,=L,-0,;
H,+P,;
H,-
H,+P,
; etc.
0,=d,-d,;
L,=L,-0,;
etc.
etc.
FINAL
CONDITIONS
(After
unbolonce due to ice)
Figure 33.-Conditions
and
for equilibrium
before and after
unbalanced
Conductor
data and data for plotting
the Pand
Hcurves
the graphical
solution
is shown
on figures
34 and 35.
The
1.
procedure
Lay out
for the graphical
the graph
axes
in span length
$ and insulator
horizontal
force. Allow
room
and
2.
fourth
Plot
3.
Plot
quadrants.
the PL 1 curve
PL 2
curve
4. Plot the PL1
simplify
calculations,
+L2
computed.
the
this
solution
is:
using millimeters
(inches)
condition.
are shown
for
the
deflection
a! Use newtons
(pounds)
on the graph
for the development
by
plotting
d versus
PI
P2
by plotting
d versus
curve by plotting
dversus
is taken
as the
average
104-D-1063.
in tables
ordinate
values
table
using
table 10 or 11.
+ P2)/2 using table
force
15,
of change
for the abscissa
of curves
in both
using
(PI
P
8 through
values of
the first
10 or 11.
in the
series
10 or 11. To
of spans
being
CHAPTER
II-CONDUCTOR
69
SAGS AND TENSIONS
Table 8. -Line data computations for example problem No. 2unbalanced condition (metric)
Two 644 mm’, ACSR, 4517 (duplex conductors)
Maximum conductor tension = 61 385 N, initial
Twenty 177 928-N insulator units per suspension string
-18 ‘C, no load
Insulator string vertical force (w,)
1 156.5 N
0.5 WI
578.3N
Conductor vertical force, 350.5-m
span (w,)
w,=o.5
20.9277 N/m (no load) x 2 cond.
43.889 N/m (full load) x 2 cond.
wr +w2
Insulator string length (i)
Tension (7) final
1 156.5 N
578.3 N
14 670.3 N
30 766.2 N
15 248.6 N
31 344.5 N
3 734 mm
3734mm
30 514 N
Conductor vertical force (w)
-18 OC, 13-mm ice,
0.19-kPa wind
20.927 7 N/m
57 403 N
43.889 N/m
Sag (s), 350.5-m span
10 621 mm
11 865 mm
Horizontal
30 292 N
56 882 N
44 419 008 N
44 419 008 N
tension (Ho = T - SW)
Area times final modulus (4E)
Table 9.-Line data computations for example problem No. 2unbalanced condition (U. S. customary)
Two 1272 kcmil, ACSR, 4517 (duplex conductors)
Maximum conductor tension = 13 800 lb, initial
Twenty 40 000-lb insulator units per suspension string
0 OF, no load
0 OF, l/2-in ice,
4-lb/ft2 wind
Insulator string weight (wr)
260 lb
260 lb
0.5 w1
130 lb
130 lb
Conductor
weight, 1150-ft span
b3)
wT=o.5wr+w2
Insulator string length (i)
Tension (7’) final
Conductor
weight (w)
Sag (s), 1150-ft span
Horizontal
tension (Ho = T - SW)
Area times final modulus (.4E)
1.4340 lb/ft (no load) x 2 cond.
3.0073 lb/ft (full load) x 2 cond.
3 298.2 lb
6 916.6 lb
3 428.2 lb
7 046.8 lb
147 in
147 in
6 860 lb
12 904 lb
1.434 lb/ft
34.85 ft
3.007 3 lb/ft
38.93 ft
6 810 lb
12 787 lb
9 985 800 lb
9 985 800 lb
70
TRANSMISSION
LINE DESIGN
MANUAL
Table 1O.-P curve computations for example problem No. 2unbalanced condition (metric)
p=- WTd
i case
WT = 15 248.6 N (no load), 31 344.5 N (full load)
d,
mm
d/i =
sin 6
500
1000
1500
2000
2500
3000
3250
3375
3500
3600
3650
3700
3734
0.133 90
.26181
,401 71
.535 62
.66952
.80343
.870 38
.903 86
.937 33
.964 11
.97750
,990 89
1 .ooo 00
cos e
0.990 99
.96341
.915 17
.84446
.I4279
.59540
.492 38
.427 83
.34844
.265 50
.21094
.134 61
.ooo 00
i = 3734 mm
d/i
cos e
No load
Full load
PI
P2
2
0.135 12
.217 96
.43866
.634 28
.90136
1.349 40
1.767 70
2.112 66
2.690 08
3.631 30
4.63402
7.357 91
2 060.39
4 238.50
6 688.95
9 671.88
13 744.48
20 576.46
26 954.95
32 215.11
41 019.95
55 372.24
70 662.32
112 197.83
4 235.21
8 712.52
13 749.58
19 881.19
28 252.68
42 296.27
55 407.67
66 220.27
84 319.21
113 821.28
145 251.04
230630.01
3 147.84
6415.52
10 219.29
14 716.51
20 998.62
31436.43
41 181.40
49 217.79
62699.72
84 596.94
107956.91
171414.29
p,
+p2
Table 11 .-P curve computations for example problem No. 2unbalanced condition (U. S. customary)
p= -WTd
i cos 0
WT = 3428.2 lb (no load), 7046.8 lb (full load)
d, in
20
40
60
80
100
120
130
135
140
142
144
146
147
d/i =
sin e
cos e
0.136 05
.272 11
.40816
.54422
.68027
.81633
.88435
.91837
.952 38
.965 99
.97959
.99320
1 .ooo 00
0.990 70
.96227
.91291
.83894
.73296
.57759
.46682
.39572
.30491
.25858
.20101
.116 42
.ooo 00
i= 147 in
dli
cos 8
No load
PI
Full load
0.137 33
.28278
.447 10
.64870
.928 11
1.413 34
1.894 41
2.32076
3.123 48
3.735 75
4.873 34
8.531 18
470.79
969.43
1 532.75
2 223.87
3 181.75
4 845.21
6494.42
7 956.03
10 707.91
12 806.90
16 706.78
29 246.59
967.74
1 992.69
3 150.62
4 571.26
6540.21
9 959.52
13 349.53
16 353.93
22010.54
26 325.08
34 341.45
60 117.52
p2
PI
+p2
2
719.27
1481.06
2 341.69
3 397.57
4 860.98
7 402.37
9921.97
12 154.98
16359.23
19565.99
25 524.12
44 682.06
Table 12.-H curve computation for example problem No. 2-unbalanced full-load condition (metric)
H,=56882N
1
Hl,
N
L,=350.5
2
3
Ho sinh “2
HO
I--
4
-H,
AE
WO
m
AE = 44 419 008 N
w = 43.889 N/m
5
6
(4)
(2) (3)
H,
sinh-’
7
(5)
2Hl
W
8
9
(6) (7)
G=
Lo - (8,
m
13500
15 750
18 000
22500
27000
7715.007
734
7 715.007 734
7715.007734
7 715.007'734
7715.007734
0.999 023
.999074
,999 125
.999226
.999 327
7701.470171
7707.863 637
1708.257 102
7 709.036 318
7 709.815 534
0.570 924
.489 388
.428231
.342624
.285 549
0.543 733
.471700
.416123
.336252
.281804
615.1883
717.7197
820.2511
1025.3139
1230.3766
334.50
338.55
341.33
344.76
346.73
16.00
11.95
9.17
5.74
3.77
31500
36000
40500
45 000
50000
7 715.007734
7715.007 734
7 715.001734
7 715.007 734
7715.007 734
.999 429
.999530
.999 631
.999733
.999845
7710.602465
7711.381680
7 712.160 896
7 712.947 827
7 713.811 908
.244781
.214 205
.190424
.171399
.154276
.242400
.212600
.189 292
.170 571
.153 670
1435.4394
1640.5022
1845.5649
2050.6277
2278.4752
347.95
348.77
349.35
349.78
350.13
2.55
1.73
1.15
0.72
0.37
56882
60000
65 000
70000
75 000
7715.007734
7 715.007734
7715.007734
7715.007 734
7715.007734
1 .ooo 000
1 .ooo 070
1 .OOO183
1.000 295
1.000 408
7715.007734
7715.547 785
7 716.419 580
7717.283661
7 718.155457
.135
.128
.118
.110
.102
632
592
714
247
909
.135 220
.128 240
.118 431
.110025
.I02728
2592.0846
2734.1703
2962.0178
3189.8653
3417.7129
350.5017
350.63
350.81
350.96
351.09
0.0085
-0.13
-0.31
-0.46
-0.59
80000
85 000
90 000
95 000
100 000
7 715.007 734
7715.007 734
7715.007734
7115.007734
7715.007 734
1 .OOO5 20
1.000 633
1 .OOO746
1.000 858
1.000 971
7 719.019 538
7 719.891 334
7720.763130
7721.627 211
7 722.499007
.096488
.090822
.085 786
.081280
.077 225
.096 339
.090 698
.085 681
,081 191
.077148
3645.5604
3873.4079
4101.2554
4329.1030
4556.9505
351.21
351.31
351.40
351.48
351.56
-0.71
-0.81
-0.90
-0.98
-1.06
105 000
110 000
113764
115 000
120000
7715.007734
7 715.001734
7715.007734
7715.001734
7715.001734
1.001
1.001
1.001
1.001
1.001
1723.363087
7724.234883
7724.890659
7 725.098964
7 725.970760
.073556
.070220
.067902
.067 175
.064 383
.073490
.070162
.067850
.067 125
.064 339
4784.7980
5012.6455
5184.1692
5240.4931
5468.3406
351.63
351.70
351.75
351.77
351.83
-1.13
-1.20
-1.25
-1.27
-1.33
Numbers in parenthesis are column numbers.
083
196
281
308
421
P
;
2
I
z
i?
:
2
n
g
c,
v,
$
0
-I
1
2
5
Table 13.-H curve computations for example problem No. 2-unbalanced
H,, = 12 787 lb
1
Hl,
lL.
3
WLO
H,sinh-
HO
l-WO
4
5
AE
6
(4)
-H1
sinh-’
(2) (3)
(5)
1
1
1
1
1
734.472
734.472
734.472
734.472
734.472
747
747
747
747
747
0.999
.999
.999
.999
.999
020
070
120
220
320
1 732.772
1732.859
1 732.946
1733.119
1733.293
964
687
411
858
306
0.577
.495
.433
.346
.288
591
103
237
624
882
7 000
8 000
9 000
10 000
11000
1
1
1
1
1
734.472
734.472
734.472
734.472
734.472
747
747
747
747
747
.999
.999
.999
.999
,999
420
521
621
721
821
1733.466
1733.641
1733.815
1 733.988
1734.162
753
935
382
829
276
,247
.216
.192
.173
.157
638
705
646
399
651
.245 174
.215 044
.191474
.172 542
.157 005
12
12
14
15
16
000
787
000
000
000
1 734.472
1 734.472
1734.472
1 734.472
1 734.472
747
747
747
747
747
.999
1 .ooo
1.000
1 .ooo
1.000
921
000
121
222
322
1734.335 724
1 734.472 747
1734.682 618
1734.857 800
1735.031 247
.144
.135
.123
,115
.108
528
643
906
657
439
.144
,135
.123
.115
JO8
17 000
18 000
19 000
20 000
21000
1 734.472
1 734.472
1 734.472
1 734.472
1734.472
747
747
747
747
747
1.000 422
1 .OOO522
1 .OOO622
1.000 722
1 .OOO822
1 735.204
1735.378
1735.551
1735.725
1735.898
694
142
589
036
480
.102
.096
.091
.086
.082
071
410
345
786
662
22
23
24
25
25
1 734.472
1734.472
1 734.472
1 734.472
1 734.472
747
747
747
747
747
1.000
1.001
1.001
1.001
1.001
1 736.073
1 736.247
1736.420
1 736.594
1 736.694
665
113
560
007
607
.078
.075
.072
,069
.067
912
489
351
464
909
923
023
123
223
281
Numbers in parenthesis are column numbers.
7
8
2Hl
y
(6) (7)
-
0.549
.476
.420
.340
.285
5 15
828
715
033
008
10
9
9=
Lo ft
H1
3 000
3 500
4 000
5 000
6 000
000
000
000
000
574
AE=9985 800 lb
w = 3.0073 Ib/ft
Lo= 115oft
2
full-load condition f US. customary)
@h
o=
Lo- W,
in
1995.145 2
2 327.669 3
2 660.193 5
3 325.241 9
3 990.290 3
1096.36
1109.90
1119.18
1130.69
1137.26
53.64
40.10
30.82
19.31
12.74
643.68
481.20
369.84
231.72
152.88
4
5
5
6
7
8.63
5.88
3.94
2.51
1.42
103.56
70.56
47.28
30.12
17.04
655.338
320.387
985.435
650.483
315.532
7
1
4
8
2
1141.37
1144.12
1146.06
1147.49
1148.58
030
230
591
401
228
7 980.580
8 503.973
9 310.677
9 975.725
10 640.774
6
7
4
7
1
1149.44
1149.9924
1150.72
1151.21
1151.63
0.56
0.01
-0.72
-1.21
-1.63
6.72
0.09
-8.64
-14.52
-19.56
.lOl
.096
.091
.086
.082
895
261
218
677
568
11 305.822
11970.870
12 635.919
13 300.967
13 966.016
5
9
3
6
0
1152.01
1152.33
1152.62
1152.89
1153.15
-2.01
-2.33
-2.62
-2.89
-3.15
-24.12
-27.96
-31.44
-34.68
-37.80
.078
.075
.072
,069
.067
830
417
288
408
857
14
15
15
16
17
4
8
2
6
3
1153.37
1153.59
1153.80
1153.99
1154.11
-3.37
-3.59
-3.80
-3.99
-4.11
-40.44
-43.08
-45.60
-47.88
-49.32
631.064
296.112
961.161
626.209
007.947
-----
Table 14.-H curve computations for example problem No. 2-unbalanced
$=LoHo=30292N
1
Hl,
N
2H1
W
sinh -1
L, = 350.5 m
2
3
WLO
HO
Ho sinh 2~
l-0
13 500
15 750
18 000
21 000
25 000
3 616.546418
3 616.546478
3616.546418
3 676.546478
3676.546478.
0.999 622
30292
31500
36000
40500
45 000
AE = 44 419 008 N
w = 20.9211 N/m
4
5
(2) (3)
-(4)
-H1
AE
no-load condition (metric)
6
sinh-’
I
W
Hl
0.268 979
.231287
.202803
.174 155
.146 519
9
(6) (7)
Lo m
@=
-2Hl
(5)
8
.999881
3 675.156143
3 615.344 241
3 675.528 015
3675.778080
3 676.108 969
0.272 234
.233 355
.204 196
.175037
.147044
3 676.546478
3676.546478
3676.546418
3676.546478
3 676.546478
1 .ooo 000
1 .OOO027
1.000 129
1.000 230
1.000 331
3616.546418
3676.645 745
3671.020752
3671.392084
3677.763415
.121370
.116 719
.102 139
.090 800
.081728
.I21 074
.116 456
.101962
.090 676
.081 637
2 894.919
3 010.364
3 440.416
3 870.468
4 300.520
2
3
3
3
4
49500
54000
58500
60584
63000
3676.546478
3 616.546478
3676.546478
3 616.546418
3 676.546 418
1.000.432
1.000 534
1.000 635
1 .OOO682
1.000 736
3 678.134 746
3678.509754
3 678.881085
3679.053883
3679.252416
.074 306
.068 121
.062887
.060 726
.058 401
.074
,068
,062
.060
.058
238
068
846
689
368
4
5
5
5
6
730.572
160.624
590.616
789.838
020.728
4
4
5
3
5
351.19
351.27
351.35
351.38
351.42
67 500
12 000
76 500
81000
85 500
3 616.546
3 676.546
3 676.546
3 676.546
3 676.546
478
478
478
478
478
1.000
1.000
1.001
1.001
1.001
838
939
040
142
243
3 619.621424
3 619.998 755
3 680.310 086
3 680.745 094
3 681.116 425
.054
.051
.048
.045
.043
513
111
109
441
054
.054 486
.05 1 089
.048 090
.045 425
.043 041
6
6
7
7
8
450.780
880.832
310.884
740.936
170.988
5
6
6
7
7
351.48
351.53
351.58
351.63
351.69
-1.03
-1.08
-1.13
-1.19
90 000
3 676.546
3 676.546
3 676.546
3 676.546
3 616.546
3 616.546
478
478
418
478
478
418
1.001
1.001
1.001
1.001
1.001
1.001
344
446
547
648
749
851
3
3
3
3
3
3
.040
.038
.037
.035
.034
.032
905
962
194
581
102
741
.040
.038
.037
.035
.034
.032
8 601.040
9 031.092
9 461.144
9 891.196
10 321.248
10 751.300
7
8
8
8
9
9
351.73
351.78
351.81
351.86
351.90
35 1.94
-1.23
-1.28
-1.31
-1.36
-1.40
-1.44
94
99
103
108
112
500
000
500
000
500
.999673
.999123
.999 791
Numbers in parenthesis are column numbers.
681.487
681.862
682.234
682.605
682.976
683.351
756
764
095
427
758
766
894
952
185
573
095
735
1290.156 1
1505.182 1
1720.208 1
2 006.909 5
2 389.178 0
341.02
348.13
348.86
349.51
350.06
350.4994
(0
3.48
2.37
1.64
0.99
0.44
0.00
350.57
-0.07
350.79
350.96
-0.29
351.08
-0.46
-0.58
-0.69
-0.71
-0.85
-0.88
-0.92
-0.98
Table 1S.-H curve computations for example problem No. 2-unbalanced
2
1
Hl,
lb
4
3
WLO
HO
Hosinh-c
l-0
-ff,
AE
(2) (3)
AE = 9 985 800 lb
w = 1.434 Ib/ft
Lo = 1150 ft
H,, = 6810 lb
no-load condition (U.S. customary)
5
(4)
sinh-’
(5)
T
826.248 383
826.303762
826.331866
826.414522
826.491178
0.275 416
.236087
.206583
.165 283
.137750
0.272048
.233947
.205 141
.164540
.137 318
4184.1004
4881.4505
5 578.8005
6973.5007
8368.2008
6 810
I 000
8000
9000
10 000
826.564130
826.564130
826.564130
826.564130
826.564130
1 .ooo
1.000
1.000
1.000
1.000
826.564130
826.579835
826.662491
826.145 148
826.821804
.121315
.118083
.103333
.091 861
.082683
A21079
.117 810
.103150
.091732
.082589
11000
12000
13000
13620
14000
826.564130
826.564130
826.564130
826.564130
826.564130
1.000 420
1.000 520
1 .OOO620
1.000 682
1 .OOO720
826.911287
826.993943
827.076600
827.121847
827.159256
.075 174
.068916
.063621
.060729
.059083
15 000
16000
17000
18000
19000
826.564130
826.564130
826.564 130
826.564130
826.564130
1.000 820
1 .OOO920
1.001 020
1.001 121
1.001 221
827.241913
827.324569
827.401225
827.490708
827.573 365
20000
21000
22000
23000
24000
826.564130
826.564130
826.564130
826.564130
826.564130
1.001
1.001
1.001
1.001
1.001
827.656021
827.738618
827.821334
827.903990
827.986647
321
421
521
621
721
Numbers in parenthesis are column numbers.
9
G=
Lo - (‘3h
ft
0.999 618
.999 685
.999 719
.999819
.999919
000
019
119
219
319
(6) (7)
H,
826.564130
826.564130
826.564130
826.564 130
826.564130
3000
3500
4000
5 000
6000
8
I
6
10
f#J=
Lo - GO,
in
1138.28
1142.00
1144.44
1147.42
1149.10
11.72
8.00
5.56
2.58
0.90
140.64
96.00
66.72
30.96
10.80
9497.9080
9762.9010
11 157.601 1
12 552.301 3
13947.0014
1149.9972
1150.17
1150.91
1151.45
1151.87
0.00
-0.17
-0.91
-1.45
-1.87
0.00
-2.04
-10.92
-17.40
-22.44
.075 103
.068 862
.063578
.060692
.059049
15 341.7015
16736.4017
18 131.1018
18995.8159
19525.8020
1152.21
1152.50
1152.74
1152.89
1152.98
-2.21
-2.50
-2.74
-2.89
-2.98
-26.52
-30.00
-32.88
-34.68
-35.76
,055 149
.051708
.048671
.045 972
.043556
.055 121
.051685
.048 652
.045 956
.043542
20920.5021
22 315.2022
23709.9024
25 104.602 5
26499.3027
1153.16
1153.36
1153.53
1153.71
1153.83
-3.16
-3.36
-3.53
-3.71
-3.83
-37.92
-40.32
-42.36
-44.52
-45.96
.041383
.039416
.037 628
.035 996
.034499
.041 371
.039406
.037619
.035 988
.034492
27894.002
29288.7029
30683.403
32078.1032
33472.8033
1154.00
1154.15
1154.28
1154.43
1154.54
-4.00
-4.15
-4.28
-4.43
-4.54
-48.00
-49.80
-51.36
-53.16
-54.48
8
1
CHAPTER
UJUJ’(P) NOl133133(3
NVdS NI 39NWH3
SAGS AND TENSIONS
ONV U’W’(@) H19N31
II-CONDUCTOR
~OlVltlSNI
75
-6(
6000
Figure 35.-Graphical
IOOcm
solution
12000
14 000
16 000
HORIZONTAL
FORCE, pounds
of unbalanced
condition
18 ooo
(U.S. customary).
20 000
104-D-1065.
22000
24000
26000
28000
CHAPTER
5.
Plot
unloaded
6.
curve
2d versus
the
end of the
is necessary
II-CONDUCTOR
P curve
using
SAGS AND TENSIONS
table
10 or 11. Since
span with iced conductors,
swing
to read the change
in horizontal
77
the
insulator
a like amount
toward
tension
at the insulator
strings
each other,
between
at each
this curve
loaded
and
spans.
Plot
H, 1 ( no load)
the
is not needed
7.
Plot
the
curve
also
is not
for this
HLz (full
curve
load)
needed
usiug
solution,
for
but
curve
this
table
14 or 15 and
normally
using
solution,
is plotted
table
but
HI
plotting
in the first
12 or 13 and
normally
in the
$ . This
for reference.
HI
plotting
is plotted
versus
quadrant
versus
first
4 . This
quadrant
for
reference.
8.
Plot
fourth
9.
2 HI ,1 curve
the
(for
duplex
10.
Plot
the
point
by point,
2 HL 2 curve.
Ht
the
conductors).
2HL2 - PL1 +
=
abscissa
Plot
quadrant,
2 HL, =
duplex
conductors).
quadrants.
In the fourth
Plot the 2 HL2 curve
(for
values
of the
L2 curve.
PL 1 +
Plot
This
12.
values
13.
of the H2 curve
Plot the Ha =
from
the
ordinate
values
d2 + PL1 + L2 curve.
15.
P10ttheHq.=dg+PLt+L2
is done
L2 curve
of the basic
Add graphically,
curve.
Add
graphically,
17. Plot the Hs = dh + f’~~ + Lo, d5 = ~HL*
d6 =2HL1
- H6 curves in a similar manner.
d curves
converge
accuracy
for this problem;
may continue
until
two
quite
rapidly,
so that
the
in the
first
the
Draw
a reflection
intersection
of the
deflection
at that
Insulator
spans
Effect
for
of the H 1 = 2 HL 2 - pL 1 +
reflected
curve
with the d6 curve
The horizontal
adjacent
no-load
to switchyards
is about
Sag
and
and
by
from
quadrant.
subtracting
the
graphically,
abscissa
values
point
by point,
the abscissa
basic 2 HL 1 = d curve.
point by point,
the ordinate
2 HL1 curve.
point by point,
point
gives
the abscissa
the
by point,
ordinate
the abscissa
the ordinate
- Hg, H6 = d5 +
d6 curve
of the
values
f’~~ +
a satisfactory
Lo, and
degree
as indicated
on
a final value.
figure
16 of the
of
L 2 curve
in the fourth
is taken
as an acceptable
broken
quadrant.
answer
tension
in the conductor
at the structure
between
the full-load
span is indicated
as about
74 800 N (16 800 lb). The insulator
structure
on
first
if more accuracy
is desired,
the plotting
of Hand d curves
d curves
are essentially
the same curve.
If desired,
an
however,
successive
approximation
of the d, curve
may be computed
conductor
thesis in appendix
A, and then plotted
as approach
in both
Of the pL t + L 2 curve to the abscissa
values of the d3 curve.
Plot d4= 2HL
- Ha curve.
Subtract
graphically,
point by point,
Ha curve from :he ordinate
values of the basic 2 HL 1 curve.
va1ues
16.
of the
17.
curve
of the P L t + ~2 curve to the abscissa
values of the dz curve.
Subtract
graphically,
point
by point,
Plot the d3 = 2HL,- H3 curve.
of the H3 curve from the ordinate
values of the basic 2 HL, curve.
values
14.
values
problem.
and the
only
Plot the Hz = d+
PL1 + ~~ curve. Add graphically,
of the PL 1 + L2 curve
to the abscissa
vahtes of the
Subtract
graphically,
Plot the d2 = 2HL1 -Hz curve.
11.
values
The
this
d .
1090
Tension
and substations,
on the sag and tension
in the conductors.
This
reduced
tensions.
Based on the same maximum
in accordance
with applicable
electrical
safety
mm
in
(42.8
Short
the
The
to the
span
string
in).
Spans
insulator
.-In
strings
short,
may
dead-ended
have
spans,
considerable
such
effect
is especially
true when the conductors
are strung
at
tension
at full-load
conditions
(ice and wind loading
codes), the tension
at no-load
conditions
(no ice and
TRANSMISSION
no wind)
may
the insulators.
without
The
taking
A method
point
actually
be as much
total
the
into
of calculating
is outside
the span,
as twice
sag of conductors
insulators
the
that
and
calculated
insulators
will
effect
in reference
equations
for transmission
The
insulators.
For
shows
the
two
lines.
catenaries
equilibrium,
nomenclature
the
used
Nomenclature
The
conductor
are
tangent
horizontal
also be different
inclined
spans,
method
has been
is satisfactory
the insulator
assumes
tensions
the
for determining
one catenary,
point
where
in the
procedure
insulator
two
effect
this
conductor
2M
=
=
=
sag at center
of insulator
catenary,
below end of insulator
sag at center
of insulator
catenary,
below support
point,
conductor
sag, below end of insulator
string,
mm (ft)
inclined
length
04
=
=
=
total sag, insulators
plus conductor,
mm (ft)
SV = arc length
of one-half
the conductor
span,
unstressed
arc length
of L, m (ft)
SP
=
=
length
of insulator
string,
arc length
from insulator
A
=
cross-sectional
E
=
modulus
e
=
=
=
temperature
parameter
parameter
area
of elasticity
of span,
are not inclined
on the catenary
be equal.
m (ft)
m (ft)
catenary
of conductor,
of conductor,
coefficient
of conductor
of the catenary
described
of the catenary
described
center
mm2
GPa
to end
mm
(ft)
m (ft)
of insulator
(in2)
(lb/ft2)
by the
by the
conductor
insulator
string
in short spans.
string,
mm (ft)
string
string,
low
to determine
is attached
must
on sag and tension
=
a2
conductor
method.
Dr
02
0s
a1
the
developed
and the insulator
the
catenaries
for
where
description:
=
considering
the sag calculated
for spans which
effect
is based
C
L
Lu
RS
without
than
Another
at the
in describing
Figure 36.-Nomenclature
104-D-1066.
methods
in steeply
[5].
the insulator
effect for approximately
level spans and
by more than 20 percent.
This method
of calculating
catenary.
by normal
account.
insulator
is given
LINE DESIGN MANUAL
m (ft)
another
to
the
Figure
36
CHAPTER
H
=
T
=
tension
W
=
linear
force
factor
(weight
Wt
=
linear
force
factor
of conductor,
X
=
M -
Xs
=
projected
Steps
horizontal
in the
component
II-CONDUCTOR
in conductor,
Xs
=
one-half
length
procedure
the
in conductor,
N (lb)
N (lb)
the
per
unit
length)
N/m
length
of insulator
of insulator
of conductor
string,
string,
N/m
(lb/ft)
(lb/ft)
span,
m (ft)
m (ft)
are:
Step I.-Calculate
using
of tension
79
SAGS AND TENSIONS
Lu,
following
the
unstressed
arc
length
of
L,
for the
required
loading
condition
by
equations:
a, = H/W, , for conductor catenary
(1)
a, = H/W, for insulator catenary
(2)
a2
x,
x
=7>
for this equation assume X = (M - KS) (1 .OOOS)
Assumption
of an appropriate
a more accurate
value of X. The
calculations
repeated
to obtain
calculations
increase
the
accuracy
value for X at this point
greatly
simplifies
the calculation
of
calculated
value of Xcould
be substituted
in equation
(3) and
a still more accurate
value;
however,
subsequent
repetitive
very
little.
SP = a, sinh 3
(4)
a2
RSP=RS+SP
(5)
X2 = a, sinh-’ y
(6)
x, =x2 - x,
(7)
X=M- x,
(8)
L = a, sinh x
a1
(9)
(10)
>
80
TRANSMISSION
Step Z.-With
LA,
a range
determine
the
of tensions
temperatures
LINE DESIGN
(assume
H
which
the
for
=
MANUAL
5”) and
corresponding
conductor
would
unstressed
have
these
arc
arc
lengths
lengths:
Let:
to
Lu 0
=
=
temperature
unstressed
t1,
=
temperatures
=
unstressed
tz,
.
.
*
t,
LlC,, I,112, . . . Lu,
at known
comluctor
at new
conductor
conditions
arc length
at known
conditions
conditions
arc
lengths
at new
conditions
Lu, = Lu, + Lu,e (tl - t,)
(11)
Lu, =Luo +Lu,e(t,-
to)
(11)
Lu, = Lu, + Lu,e (tn- to)
(11)
Step 3.-Plot
tension
against
temperature
corresponding
to each unstressed
arc length
loading
condition.
From this plot, determine
the tension
at the desired
temperatures.
(1) through
(8).
tension,
calculate
values for X, X I, and X 2 using equations
Step
&The
total
sag of the
D, =a, (cash:
D, =a, (co+
line,
insulators
plus
conductor,
is then
for each
For each
determined:
- I>
(12)
l)
(13)
(14)
Dc, =D,
+D,
-D,
mm2
(951. kcmil),
(15)
Example
Assume:
483
(4000 Ih) under NE:SC
plus constant
at’minus
tension
insulator
strings.
ACSR,
G/7
conductor
with
heavy loading
of 13-1~111~ (I/2-in)
18 ‘C (0 ’ F). U. SC a 45.72-m
maximum
tension
of
ice, 0.19-kI’a
(I-lh/ft*)
(1 SO-ft)
span with
17 793
wind,
1 S-unit
N
CHAPTER
Insulator
II-CONDUCTOR
string data
SAGS AND TENSIONS
Length
15 insulator units
Anchor shackle
Ball-eye fitting
Compression dead end
81
Mass
m
(in)
kg
2.1908
0.0813
.0711
.5842
___
86.25
3.2
2.8
23.0
~
74.84
0.45
.68
10.07
165
1.0
1.5
22.2
2.9274 m
115.25 in
86.04 kg
189.7 lb
(lb)
w = 86.04
= 29.3912 kg/m = 288.2292 N/m
2.9274
w = (189*7) (12) = 19 75 lb/ft
115.25
’
Metric
Figure
DCm-579
37 shows
the
metric
sag and
tension
calculations.
(3-78)
;;c
SAGCALCULATIONS
LOAOIMG
k/e2 vu
Lmear
Factor,
Force
Dead
_L3_
Load
Force
mm Ice
(W”)
O@!,&?.kPa
1-5
-qfl
Lgf
N/m
BD2
N/m
Creep
0.00oloo.
N/m
Total
O.OOn
Wind/d:
Resultant
Area
(A)&m&
Temp.
Cc&f.
0.000
(W’)
(W”‘)~Jd,
Permanent
N/m
Modulus.
of
Linear
+mm
?
2
Permanent
kPa
Set
! TYJ..I
Ice
Wtnd (W”‘)
6 Creep
UHSTRESSED LwCTH
/
Final
1
Ice.
NO Wmd
(W’)
I
AE
23
GPa
.-7/f
*/7?
SW,N
m
543.
TENSION, N
/5!16B8.@/?
I
I
773
I
I
I
!
I
I
15.5
I
1
49
1
I
and tension
calculation
form for insulator
I
effect
T - W, (sag) = 17 793 - 36.93 1 (0.5432) = 17 772.94 N
a1 = E = l7 772*94 = 481 . 2472 m
w1
36.931
N
N
I
32
GPa
AE je
SAG, mm
1
1 -11
Figure 37.Sag
H=
klj.rllL
m
0.0949~~.0~/
!
-1
No
SAC FACTOR
‘;
SPAN LENGTH(S)e&$=3.
L/g
FInal
Irntialr/5.c?0
OGkk.pePC
3
(E)
Exp:
lnitlal
LOADING
Set O.OOOA
problem
(mtric).
ln~t:
TRANSMISSION
82
H
17 772.94=61
a2 =i? = 288.2292
x, =
LINE DESIGN MANUAL
6625 m
*
- RS) (1.0005) = 61.6625(22.86
a,04
a1
SP = a, sinhX1
= 61.6625
- 2.9274)(1.0005)=2
481.2472
5553 m
= 2.5560 m
sinh ii56f:#5
a2
RSP -RS+SP=2.9274+2.5560=
X2 =a,
X,
=X2
X=M-
sinh-1
RSP=
a2
- X,
=5.4762-
6 1.6625 sinh- 1 ~~~~,5
X, =22.86-
L =a1 sinhX
5.4834 m
2.5553
=2.9209
2.9209=
19.9391
= 48 1.2472 sinh 4fi9i4!f32
= 5.4762 m
m
m
= 19.9448
m
4
W, (a, j2
.2/&y
Luo=L-
(
xa, + sinh % cash f
36.93 1 (48 1.2472)’
= 19 9448 _
= 19.9342
Temperature
2(33
318 479)
m
= - 18 OC = t,
T = 13 345 N
Assume
H
13 345
a, = - = -=850.6502
15.688
WI
H
a2 =w
13 345
=288.2292
m
= 46.3000
m
>
19.9391
+ sinh 481.2472
19.9391
'Osh 481.2472 >
CHAPTER
x1 =
a, (M - RS) (l.0005)
a1
SP= a, sinh$
II-CONDUCTOR
SAGS AND TENSIONS
= 46.3000 (22.86 - 2.9274) (1.0005) = 1 0855 m
850.6502
= 46.3000 sinh 41$~~~o = 1.0856 m
RSP = RS + SP = 2.9274 + 1.0856 = 4.0130 m
4.0130
X2 = a, sinh- ’ -RSP = 46.3000 sinh- 1 46.3000 = 4.0080 m
a2
x, =x2 - x,
X=M- x,
= 4.0080 - 1.0855 = 2.9225 m
= 22.86 - 2.9225 = 19.9375 m
L =a, sinhE=
Lu,=L-
850.6502 sinh 8Fi9QJ;b52= 19.9393 m
w12AE
(“l I2
_X + sinh _Xco& -x
a1
= 19.9393 -
a1
15.688 (850.6502)2
2(33318479)
a1
19.9375
19.9375
850.6502 ‘Osh 850.6502
= 19.9313 m
t, =
Lu,Lu,e
- Lu, +t,
19.9342
19.9313-(0.000
19.9342
020 7) +(‘18)=-25030c
=
’
Assume T= 12 010 Nm H(no load)
H
12 010
a, = - = = 765.5533 m
Wl
15.688
H
12 010
= 41.6682 m
a2 = i? = 288.2292
x1 =
a2 (M - RS) (1.0005) = 41.6682 (22.86 - 2.9274) (1 .OOOS) = 1 0855 m
765.5533
a1
83
84
TRANSMISSION
SP = a, sinh?=
LINE DESIGN
MANUAL
41.6682 sinh b;T:852 = 1.0856 m
RSP = RS + SP = 2.9274 + 1.0856 = 4.0130 m
RSP
4.0130
X, =a, sinh-’ ~
= 41.6682 sinh- ’ 41 .6682 = 4.0068 m
a2
X, = X2 - Xl = 4.0068 - 1.0855 = 2.9213 m
X = M - X, = 22.86 - 2.9213 = 19.9387 m
X
L =a, sinh - = 765.5533 sinh 7F59535y3= 19.9410 m
a1
W,
Lu2
=L
-
(a,
1’
2*E
x + sinh x cash _x
a1
a1 >
al
15.688 (765.5533)’
2 (33 318 479)
= 19.9410-
19.9387 +sinh 19.9387 cash 19.9387
765.5533
765.5533
765.5533 >
= 19.9338 m
t, =
Lu, - Lu,
+t,
Lu,e
Similar
=
19-9338 - 19*9342 + (- 18) = _ 18.97 OC
19.9342 (0.000 020 7)
calculations
temperatures
were
made
for
five
additional
assumed
Assumed T = H (no load), N
The
resulting
determine
line.
and
the
resulting
Temperature, OC
10 675
9 341
8 007
6 672
6 227
figure,
of the
tensions,
were:
temperatures
the
tensions
t,
t,
t,
t,
t,
are plotted
for the
against
desired
the
= - 11.94
= -2.23
= 11.58
= 33.13
= 43.31
assumed
temperatures
and
tensions
proceed
on figure
in finding
38. Using
the
total
this
sag
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
0
rn
z
W
I-
-23
-13
-5
0
+5
T EM PERATURE,
Figure 38.-Tension-temperature
At-18OC.T=
H
curve for insulator
11 800N
11 800
a, = - =-z752.1673
15.688
wt
m
H
11 800
a, =~=~~~,~~9~=40.9396
m
+I5
+25
+35
“c
effect
problem
(metric).
104-D-1067.
+45
TRANSMISSION
86
x
1
LINE DESIGN MANUAL
= a, (M - RS) (1.0005) = 40.9396 (22.86 - 2.9274) (1.0005) = 1 0855 m
752.1673
a1
Xl
SP = a, sinh a, = ‘40.9396 sinh 40;0983~6= 1.0856 m
RSP = RS + SP = 2.9274 + 1.0856 = 4.013 m
RSP
X, = a, sinh- ’ -
4.013
= 40.9396 sinh- 1 40.9396 = 4.0066 m
a2
X, = X2 - X, = 4.0066 - 1.0855 = 2.9211 m
X = M - X, = 22.86 - 2.9211 = 19.9389 m
D, =a2 (.osh:-
1) =40.9396(cosh4s6-
1) =O.O144m=
14mm
D, =a, (coshz-
1) =40.9396(cosh~~~f~6-
1) =O.l962m=
196mm
D, =o,(coshc-
l) =752.1673(cosh7!~~q368~~3-
l) =0.2643m=264mm
D, = D, + D, - D, = 264 + 196 - 14 = 446 mm
At-
1 OC, T=9220N
H
9220
a, = - = = 587.7104 m
w,
15.688
H
a2 = k=
9220
= 31.9884m
288.2292
x1 = a, (M - RS) (1.0005) = 3 1.9884 (22.86 - 2.9274) (1.0005) = 1 0855 m
a1
587.7104
SP = a, sinh 2
= 3 1.9884 bnh 31{yii4
= 1.0857 m
CHAPTER
RSP=RS+SP=2.9274+
RSP
X, = a2 sinh- ’ -
a2
II-CONDUCTOR
87
SAGS AND TENSIONS
1.0857=4.0131rn
= 3 1.9884 sinh- ’ 34.y1814 = 4.0026 m
X, = X, - X, = 4.0026 - 1.0855 = 2.9176 m
X = M - X, = 22.86 - 2.9176 = 19.9424 m
D, =a,(cosh:-
1) =31.9884
D, =a2 (coshz-
1) = 31.9884(cosh~~~~~4-
D, =a1 (cash:-
D, =D,
+D,
(cosh31~~~~~4- 1) =O.O184m=
1) =0.2507m=251
l) =587.7104(cosh:89;~7412~4-1)
-D,
=338+251
- 18=571
18mm
mm
=0.3384m=338mm
mm
At 15.5 OC, T = 7740 N
H = ~7740 = 493.3707 m
a’ = w,
15.688
H
7740
= 26.8536 m
a2 = w = 288.2292
=
x
1
a2
(M - RS) (1.0005) = 26.8536 (22.86 - 2.9274) (1 .OOOS)= 1 0855 m
493.3707
al
Xl
SP=a? sinh -
a2
= 26.8536 sinh :ey5y6
= 1.0858 m
RSP=RS+SP= 2.9274+ 1.0858=4.0132m
RSP
X, = a, sinh- ’ -
a2
= 26.8536 sinh- l 2:08:3;?6 = 3.9984 m
88
TRANSMISSION
X,
=X2
X=M
- Xl
= 3.9984
LINE DESIGN MANUAL
- 1.0855 = 2.9129 m
- X, = 22.86 - 2.9129 = 19.9471 m
D,=a,(cosh$-
1) =26.8536(~osh:6p88;;5~-
1) =O.O219m=22mm
D, =a,(cosh$-
l) =26.8536(co~h~~~~~~~-
l) =0.2982m=298mm
D, =a, (,osh~-
1) =493.3707(cosh499;83477d7-
D, =D, +D, -D,
At32
l) =0.4033m=403mm
= 403 + 298 - 22 = 679 mm
OC. T=6760N
H
6760
= ~
= 430.9026 m
a1 = w, 15.688
H
a’ =w=
x1 =
a2
6760
= 23.4536 m
288.2292
(M - RS) (1.0005) = 23.4536 (22.86 - 2.9274) (1 .OOOS)= 1 0855 m
430.9026
a1
SP = a, sinh 2 = 23.4536 sinh
1.0855
= 1.0859 m
23.4536
RSP = RS + SP = 2.9274 + 1.0859 = 4.0133 m
X2 =a, sinh-’ !?!f
= 23.4536 sinh- ’ ~~~,j3~6 = 3.9940 m
a2
X, = X2 - Xl = 3.9940 - 1.0855 = 2.9085 m
X=M-
X, =22.86-
2.9085 = 19.9515 m
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
D, =a, (yxh$--
l) = 23.4536 (cash $jp)&T;6 - $ = 0.0251 m = 25 mm
D, =a2 (c~sh$-
1) = 23.4536 (cash :;:23p6‘
1) =0.3409m =341 mm
D, =a, (cosha$-
1) =430.9026(cosh~~!~~256-
l) =0.4620m=462mm
D, =D,
+D,
- D, =462+341-
25=778mm
At43 OC, T=6260N
H
a1 =w 1
6260
= -=
15.688
399.0311 m
H
6260
= 21.7188 m
az = ii = 288.2292
x, =
a,@f - RS) (1.0005) = 21.7188 (22.86 - 2.9274) (1.0005) = 1 0855 m
399.03 11
a1
SP=a, sinh;
Xl
1.0855
= 21.7188 sinh 21.7188 = 1.0860 m
RSP=RS+SP=2.9274+
1.0860=4.0134m
X, = a, sinh-’ RSP = 2 1.7 188 sinh- l ~~~~~8 = 3.9909 m
a2
X, = X2 - X, = 3.9909 - 1.0855 = 2.9054 m
X =M - X, = 22.86 - 2.9054 = 19.9546 m
D, =a, bosh:-
1) =21.7188
(cosh211f!!f~8-
1) =0.0271 m=27mm
90
TRANSMISSION
D, =a, (&$
1) =21.7188
LINE DESIGN
(cosh;;y;;;8-
MANUAL
1) =0.3677rn=368rnm
D3=al(cosh~-I) =399.0311
(coih;g-f,.,~l
-I) =0.4990m=499rnm
D,
=D,
+D,
=499+368-27=840mm
-D,
U. S. Customary
Figure
DC-576
39 shows
the
U.S.
customary
sag and
tension
computations.
(6-76)
&,tL
SAG CALCULATIONS
LOADINGWeight Factws:
Dead Welpht
(W’)
1, n 750
St.1
0.
Initial.- &m°Fd.2d
Fenal. -&?.e.?FX
Loaded. OF
Final. &OF
-5e
-
Computed by -
4
3/7q
lb
SC,‘&!?&% @&!-lb
Resultant:
lb
0.000 o//
Ib/ft2 Wind(W”‘)/
[
90
.*n
I
Figure 39.-Sag
H = T - W,
H
a2 =r=H
t
8
I
0
60
1
and tension
T>/
7
Permanent Set 0.009
IbItt
Creep
Total
Ib/ft
2.330
T
calculation
form
Modulus. (E) Final-x
initial/,.56x
1 SAGFACTOR
1 SAG,ft
FEET
I 0.09d9
lLuf&LLn//
I
I
I
I
3gg5*53g3 = 202 *3058
19.75
f-t
ft
78
I
/
I
I
I
effect
(sag) = 4000 - 2.5306 (1.78) = 3995.5393 lb
3gg5-53g3 = 1578 8901
2.5306
*
106 lb/i,?
106 lb/in2
Final AE .m
lnttial AE s
150
for insulator
151
o.oo--O.ooa
Ib/ft
per “F
SPAE;LENGTH(S)
tnch Ice.
w
(W’“)
Ib/ft
Area (A) ti
in2
Temp. Coeff. of Linear Exp.:
oF * UNSTRESSED
1TEMP.
LENGTH
No Ice. No Wind (W’)
a,=-=
lb
Date
LOADING
.km
Kfe
Ad.2
o/n
problem
tb
lb
1 SW,Ib
1 TENSION,Ib
I.? 7959
I
I
I
(U.S. customary).
I
JImlo
n;d
CHAPTER
x
1
II-CONDUCTOR
SAGS AND TENSIONS
= a, (M - RS) (1.0005) = 202.3013 (75 - 9.6) (1 .OOOS)= 8 3838 ft
1578.8901
4
Xl= 202.3058
SP=a2
sinhz
8.3838
sinh 202.3058 = 8.3862 ft
RSP = RS + SP = 9.6 + 8.3862 = 17.9862 ft
X2 = a, sinh- ’ E
= 202.3058 sinh- ’ :a’;~~5!8
= 17.9626 ft
a2
X, =X2 - Xl = 17.9626 - 8.3838 = 9.5788 ft
= 75 - 9.5788 = 65.4212 ft
X=M-X,
X
sinh -=
L=a,
1578.8901 sinh l;;;p;;;1
= 65.4399 ft
4
Lu,=L-
w,
b,
2AE
= 65.4399 -
I2
--X+sinh&c&
a1
i 4
a1 )
2.5306 ( 1578.8901)2
2 (7 490 285)
65.4212
65.4212
65.4212
1578.8901 + sinh 1578.8901 ‘Osh 1578.8901
= 65.4050 ft
Temperature = 0 OF = t,
Assume T = 3000 lb w H (no load)
H = ==
1 1.075
al=w
H
3000
= -=
a, = w
19.75
x
1
=
2790.6977 ft
151.8987 ft
a, (M - RSI (1 .OOOS) _ 15 1.8987 (75 - 9.60) (1 .OOOS)
SP=a2 sinh:=
Ql
2790.6977
151.8987 sinh 1;.l5;;;7
.
= 3.5618 ft
= 3.5615 ft
91
‘12
TRANSMISSION
RSP=RStSP=9.6+3.5618=
LINE DESIGN
MANUAL
13.1618ft
x2
RSP
= a, sinh-’ = 151.8987 sinh-’
x,
=x2
~~~~91g87= 13.1454 ft
a2
- x,
= 13.1454 - 3.5615 = 9.5839 ft
X =M - X, = 75 - 9.5839 = 65.4161 ft
L = a, sinh:
65.4161
= 2790.6977 sinh 2790.6977 = 65.4221 ft
wl(al)2
LU, =L - 2AE
= 65.4221
x
( c+sinh-f
1
cosht
1.075 (2790.6977)2
2 (7 490 285)
-
1
65.4161
65.4161
65.4161
2790.6977 + sinh 2790.6977 ‘Osh 2790.6977
= 65.3959 ft
Lu, = Lu, + Lu,e(t,
t, =
- to)
Lu, - Lu,
65.3959 - 65.4050 + o = _ 12.10 OF
Lu, e + to = 65.4050 (0.000 011 5)
Assume T = 2700 lb = H (no load)
H
2700
a, = - = 1075=2511.6279ft
WI
*
H
2700
a, = p = 19.75 = 136.7089 ft
x
1
=a,@4 - RS) (1.0005) _ 136.7089 (75 - 9.6) (1.0005)
= 3.5615 ft
2511.6279
a1
SP = a, sinh:
RSP=RS+SP=
= 136.7089 sinh
3.5615
= 3.5619 ft
136.7089
9.6 + 3.5619 = 13.1619 ft
CHAPTER
X2 =a,
sinh-’
@E=
II-CONDUCTOR
93
SAGS AND TENSIONS
136.7089 sinh- l 1:; y;899 =
13.1417
ft
a2
X,
=X2
- X,
= 13.1417
- 3.5615
= 9.5802
ft
X = M - X, = 75 - 9.5802 = 65.4198 ft
L
=
a,
sinh
Lu, =L-
5
= 25 11.6279
sinh
65.4198
25 11.6279
F!&&?
= 65.4273 ft
cash -x
a1
1.075 (25 11 .6279)2
2 (7 490 285)
= 65.4273 -
65.4198
65.4198
65.4198
2511.6279 + sinh 25 11.6279 ‘Osh 25 11.6279
= 65.4037 ft
t, =
Lu, - Lu,
Lu,e
Similar
temperatures
+t,
=
65.4037 - 65.4050
65.4050 (0.000 011 5) = -1*73 OF
calculations
were:
Assumed
were
made
T-- H (no load), lb
2400
2100
1800
1500
1400
At
The
figure,
resulting
determine
of the
line.
0 OF,
temperatures
the tensions
w,
1.075
five
additional
assumed
tensions,
=
=
=
=
=
the
resulting
11.30
28.72
53.58
92.53
110.88
are plotted
against
the assumed
tensions
for the desired temperatures
and proceed
1 ft
and
Temperature, OF
t,
t,
t,
t,
t,
T = 2645 lb
H
2645
= 2460.465
a, = - = -
for
on figure 40. Using
in finding
the total
this
sag
94
TRANSMISSION
LINE DESIGN MANUAL
2600
2400.
g
2200
;
0v)
z
E
2000
1800.
1600
-20
0
+20
l 40
T EM PERATURE,
Figure 40.-Tension-temperature
curve for insulator
+80 -
+60
effect
+I00
OF
problem
(U.S. customary).
104-D-1068.
+I20
CHAPTER
a2
=-=
x
H
w
2645
-=
19.75
II-CONDUCTOR
SAGS AND TENSIONS
133.9241 ft
- RS) (1.0005)
133.9241 (75 =
9.60) (1.0005) = 3.5615 ft
a1
2460.465 1
=a,(M
1
SP=a2 sinh$
= 133.9241 sinh 3.5615 = 3.5619 ft
133.9241
RSP=RS+SP=9.6+3.5619=
X2 = a, sinh- 1 Q
13.1619ft
= 133.9241 sinh- 1 l:‘; kyll
= 13.1408 ft
a2
X, =X2 - X, = 13.1408 - 3.5615 = 9.5793 ft
X = M - X, = 75 - 9.5793 = 65.4207 ft
D,=a,(cosh:-
D, =D,
l) =133.9241(khll~~~~~)481-
+D,
1)=0.6452ft
- D, = 0.8698 + 0.6452 - 0.0474 = 1.4676 ft
At 30 OF, T = 2075 lb
H
2075
a, = - = = 1930.2326 ft
w, 1.075
H _ 2075
a2 = w- = 105.0633 ft
19.75
x
=a,(M-
1
RS)
Ql
(1.0005) = 105.0433 (75 - 9.60) (1.0005) = 3 5615 ft
1930.2326
95
TRANSMISSION
SP = a, sinh 2 = 105.0633 sinh
RSP=RS+SP=9.60+3.5622
RSP
X, = a, sinh-’ -
LINE DESIGN MANUAL
3.5615
= 3.5622 ft
105.0633
= 13.1622 ft
= 105.0633 sinh”
1~~~6~3 = 13.1280 ft
a2
X, =X2 - Xl = 13.1280 - 3.5615 = 9.5665 ft
X=M-
X, =75- 9.5665 =65.4335 ft
D, =a,(cosh$
1) =105.0633(cosh1;;;;;3-
l)=O.O604ft
D, =a, (ah:
- 1) = 105.0633 (cash ll;;;;;;3
- 1) = 0.8213 ft
D, =a1 (co&:
- 1) = 1930.2326(cash
D, =D,
1;;;;;;6-
1) = 1.1092 ft
+D, - D, = 1.1092 + 0.8213 - 0.0604 = 1.8701 ft
At 60 OF, T = 1733 lb
--
H 1733
a, = - =x=
Wl
.
1612.0930 ft
a, = /f=F5=87.7468
x 1- _ a,
ft
04 - RS) (1 .OOOS) 87.7468
=
(75 9.60) (1 .OOOS) = 3.5615 ft
a1
1612.0930
SP = a, sinh:
= 87.7468 sinh
RSP=RS+SP=9.60+3.5625
3.5615
= 3.5625 ft
87.7468
= 13.1625 ft
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
13.1625
X, = a, sinh-’ RSP = 87.7468 sinh-’ 87.7468
= 13.1136 ft
a2
X, =X2 - X, = 13.1136 - 3.5615 = 9.5521 ft
X = M - X, = 75 - 9.5521 = 65.4479 ft
D, =a,
(cosh$-
l) =87.7468(cosh$~~~~8
D, =a2(ysh2-
$ =87.7468(cosh~~:~~~~-
D, =aI(cosht-
- l) =O.O723ft
I) =0.9817ft
l) =1612.0930(xsh1~~~~~~O-
$ =1.3287ft
D, = D, +D, -- D, = 1.3287 + 0.9817 - 0.0723 = 2.2381 ft
At90°F,T=15131b
H
a, = - = g$
WI
*
= 1407.4419 ft
H
1513
= = 76.6076 ft
a2 =w
19.75
x
1
=
Q-2
(M - RS) (l-0005)
a1
= 76.6076 (75 - 9.60) (1 .OOOS) = 3 56 15 ft
1407.4419
SP = a, sinh x, = 76.6076 sinh 7iyo1756 = 3.5628 ft
a2
RSP=RS+SP=9.60+3.5628
RSP
X2 =a2 sinh-’ -
= 13.1628ft
= 76.6076 sinh- l :i’i$i
a2
X, =X2 - X, = 13.0989 - 3.5615’= 9.5374 ft
= 13.0989 ft
98
TRANSMISSION
X=M-
X, =75-
9.5374=65.4626
LINE DESIGN MANUAL
ft
D, =a, kosh$
1) =76.6076(cosh;;~;;6-
1) =O.O828ft
D, =a+sh$-
1) =76.6076(cosh;~:~;;~-
l)
D, =a1 (cosh$
D, =D,
1) = 1407.4419 kosh lg4;;;g
+D,-
= 1.1306ft
- 1) =1.5227 ft
D, = 1.5227 + 1.1306 - 0.0828 = 2.5705 ft
At 110 OF:, T = 1405 lb
H
a, = - = E
Wl
.
H
a2 = w
x
= 1306.9767 ft
1405
== 71.1392 ft
19.75
=a2(M-
= 71.1392 (75 - 9.60) (1.0005) = 3 5615 ft
Ra(1.0005)
1
1306.9767
a1
SP =a2 sinhs
= 71.1392 sinh ;i5fi12
= 3.5630 ft
a2
RSP=RS+SP=9.60+3.5630=
X2 =a, sinh- l g
13.163Oft
= 71.1392 sinh-’
~~‘:~~~ = 13.0890 ft
a2
X, =X2 - Xl = 13.0890 - 3.5615 = 9.5275 ft
X=M-
X, =75-
D, =a,(cosh~-
9.5275 =65.4725 ft
1) = 71i1392 (cash ~~~1631~2
- 1) = 0.0892 ft
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
99
D, =a,(cosh$ 1) =71.1392(cosh;;~;~;;-1)
= 1.2075ft
65.4725
-
1306.9767
D,
18.
=D,
- D 1 = 1.6403
+D,
Spans
With
Concentrated
infrequent
and
arrangements
in addition
figure 3.1 .
are used.
to the dead
are confined
Such
force
to the
span
1.
2.
string
Assume
a desired
Calculate
that will
relating
or switchyard
problems
applied.
are complicated
A method
which
ft
ft
to spans
spans
with concentrated
in which
loads
taps
are
or tie-down
by the elastic effects
of the tap or tie-down
adequately
treats
this problem
is shown
on
to this problem
than the method
shown on figure 41 would
be to sag
normal
sag for a given temperature
and then add a calculated
length
for
the
force
may be determined
F. F. Priest:
spring
tension
of the
by the
at some
tie-down,
following
given
see figure
procedure
42. The
which
required
was developed
temperature.
the angle that will be formed
by a vertical
result
from the horizontal
tension
in the
to the tie-down
after installation
3. By multiplying
the length
reflected
length
of the insulator
The difference
in the originally
= 1.6403
= 2.7586
to substation
to compensate
additional
length
of conductor
by a former
Bureau
engineer,
- 0.0892
Loads.-Problems
mainly
Probably
a better
approach
the conductors
to the calculated
of conductor
+ 1.2075
1
(0 = tan-’
H/P).
of the insulator
string
string
is obtained
(i,
line and the position
of the insulator
conductor
and the vertical
force due
by the sine of this
= isin 0).
angle,
the horizontal
between
the length
of the insulator
string as it will lay in the near horizontal
sagged span and its calculated
horizontal
reflected
length
after the tie-down
indicates
the additional
amount
of conductor
same characteristics
as the originally
sagged
required
to give the final
span without
the tie-down.
tied-down
span
position
is made,
about
the
Example
Conductor:
Span length
Force
Spring
Length
Calculate
might
short
the
242 mm2 (477 kcmil),
= 45.7 m (150 ft)
of hardware
on tie-down
tension
at 15.5 ‘C (60
of insulator
sags and
string
tensions
be applicable
during
span, such as in the
insulator
effect
=
ASCR
24/7
= 444.8 N (100 lb)
OF) = 889.6 N (200
1829
for the
mm
conductor,
lb)
(6 ft)
without
tie-down,
for a range
of temperatures
that
installation.
If the insulator
force will be appreciable
in a comparatively
example
used here, the original
sags should
be determined
by considering
(see sec.
16).
LOO
TRANSMISSION
LINE DESIGN
MANUAL
P
LeveI' Span
Inclined
Span
s = 2PL + wL2
8H
CONCENTRATED LOAD AT
CENTER OF SPAN
H
H-TeH
t
P
Level Span
Inclined
S=
Span
L, L, (2P + WL)
2LH
LOAD AT ANY POINT ON
SPAN
=Horizontal
span length between conductor support points, m (ft)
= Horizontal tension in conductor, N (lb)
= Sag, from line of supports at concentrated
load, m (ft)
=Concentrated
load, N (lb)
= Linear force factor
(weight) of conductor, N/m (Ib/ft)
;,L*= Horizontal distance from concentrated
load to points of support, m (ft)
L
H
S
P
Figure 41.Spans
with
concentrated
loads. 104-D-1069.
CHAPTER
II-CONDUCTOR
SAGS AND TENSIONS
i = Length of insulator
string, mm (ft)
length of insulator string,
in - Horizontal reflected
ni = i-iH,
mm (ft)
H - Horizontal
tension in conductor, N (lb)
P - Vertical
force added by tie-down
(hardware
tension) , N (lb)
Figure 42.-Graphical
method for determining
concentrated
load problem. 104-D-1070.
Assume the following
length
‘C
(OF)
-18
-1
15.5
(0)
(30)
(60)
mm
625
780
917
1039
1149
For 15.5 OC:
mm
required
by previous
for
calculations:
Tension,
SW,
w
N
(2.05)
(2.56)
(3.01)
(3.41)
(3.77)
3750
3015
2571
2268
2050
(lb)
(843)
(678)
(578)
(510)
(461)
For 60 OF:
2571/1334.4
e = tan-’
578/300
= tan- l 1.926 70
= tan- ’ 1.926 70
= 62.57O
= 62.57O
ih = 1829
(ft)
+ spring
of conductor
sag and tension values have been obtained
Temperature,
e = tan-’
additional
101
Sin
8 = 1829 (0.887 57)
= 1623.37 mm
Ai = 1829 - 1623.37 = 205.63 mm
_
ih = 6 sin 8 = 6 (0.887 57)
= 5.33 ft
Ai = 6 - 5.33 = 0.67 ft = 8 in
TRANSMISSION
102
The
Ai vahle
is the additional
Considering
8 constant
can be made:
for setting
Temperature,
OC
(OFI
-18
-1
15.5
32
49
(0)
(30)
(60)
(90)
(120)
amount
of conductor
the spring
Horizontal
N
3750
3015
2571
2269
2050
LINE DESIGN MANUAL
tension
to be added
at other
to the span after
temperatures,
the
the initial
following
tension,
(lb)
Hardware force,
N
(lb)
Spring tension,
N
(lb)
(843)
(678)
(578)
444.8
444.8
444.8
444.8
444.8
1501
1120
890
733
620
(510)
(461)
(100)
(100)
(100)
(100)
(100)
(337.5)
(251.9)
(200)
(164.7)
(139.3)
sagging.
tabulation
<<Chapter
INSULATION,
19. Insulation
which
will
Coordination.-Insulation
withstand
are three
LIGHTNING
PROTECTION,
CLEARANCEPATTERNS
the
different
voltage
voltage
requirements
(1)
for the
Lightning
(2)
(3)
Switching
coordination
stresses
stresses
to which
to consider
design of high-voltage
voltages,
voltages,
60~HZ voltages,
and
called power
the
AND
is the selection
system
when
transmission
of an insulation
or equipment
determining
III
insulation
structure
will
be subjected.
and
electrical
There
clearance
lines:
frequency
operating
voltages.
The probability
of flashover
must be controlled
so that any system
disturbance
is minor.
Lightning
impulse
voltages
generally
have the highest
values and the highest
rates of voltage
rise.
The time range for these voltages
to crest is about
0.5 to 6 microseconds.
Although
it is impractical
to provide
a sufficiently
high
impulse
conductor
is struck
by an average
This is done by locating
overhead
current
structures
to earth
through
for this purpose.
insulation
strength
ground
Ievel
the steel towers
or through
This diversion
of the current
string
and air gap insulation
values,
and by obtaining
In a region of average
storm intensity
of 30 storm
on the average
of 100 direct
must be used on transmission
The
lightning
current
the tower footing
ground
wire will
l
l
Isoceraunic
Stroke-current
level
clearances
Number
l
Span length
Midspan
clearance
Number
of insulator
If the
tower,
height
footing
(number
magnitude
l
l
the
of tower
Tower
Tower
l
to follow
a path
and
along
conductor
permissible
strokes
and
voltage
developed
may
divert
wires
provided
by coordinating
low footing
a transmission
when
a
be controlled.
the lightning
on
wood
pole
the insulator
resistance.
line will
be struck
mi) of line per year. Overhead
ground
wires
lightning
strokes
and shield the conductors.
the shield
wire,
down
the tower,
and through
top of the tower
and the connected
overhead
of the current
resistance
in the tower footing.
and
lightning
protection
design is based primarily
the lightning
performance
of a transmission
l
l
a sufficiently
days per year,
strokes
per 161 km (100
lines to take these direct
is expected
the
lightning
flashovers
direct
strokes
and
the ground
is accomplished
resistance
to the ground.
The entire
attain
a high voltage,
mainly
because
An evaluation
acceptable
affecting
to withstand
lightning
stroke,
wires to intercept
overhead
ground
on theory
line are:
of lightning
storm
and wave shape
days
wire
configurations
and experience.
to be expected
each
The
for an
major
factors
year)
resistance
location
of overhead
ground
between
units
conductors
current
to midspan
stroke
to midspan
may
cause
tower
wires
and
(shield
overhead
is more
than
flashovers.
103
angles
ground
twice
the
to conductors)
wires
permissible
stroke
current
to
TRANSMISSION
For
transmission
flashover
rate.
or by
the
lines
lightning
considerations
lightning
must
not
and
will
impulse
could
levels,
an increase
in insulation
strength.
by the
insulation
is determined
may
be dictated
345
kV,
control
primarily
by either
switching
the
probability
insulation
strength
length
impulses,
tower
does
surge
surfaces
so switching
not
any
result
design;
that
have
however,
made
considerations
will
against
is a function
The number
of
surges very low.
on simulated
towers
(extra-high
voltage)
increase
in switching
surge
does
result
field
effect This
dictate
in
of insulators
is due to the electric
proximity
the
factor
protection
surge
At EHV
number
lightning
considerations
prime
expected.
switching
been
shape.
in the
This
is called
the
due to a switching
tower
the
surge
become
in a proportional
increase
strength.
and
surge
on tests
almost
a lo-percent
in switching
of the
is based
by
switching
surges
of flashover
to duplicate
example,
increase
to lightning
The
be made
For
proximity
Above
probably
insulation
adjustments
in a lo-percent
line
characteristics
and the magnitude
of the surges
be selected
to keep the probability
of flashover
from
where
withstand
kV,
rate.
be overlooked.
of the line insulation
insulators
used may
surge
to 345
the line insulation
flashover
flashover
Switching
up
At 345 kV,
LINE DESIGN MANUAL
distortion
effect
the insulation
not
caused
does
values
not
apply
at the
EHV
levels.
Wave
shapes
grouped
for
for
lightning
testing
and
impulses
to provide
and
basic
switching
data
surges
for
are infinite
use in insulation.
in number,
Wave
shape
but
have
been
is defined
by
two
impulse
and
the
parameters:
(1)
The
time
instant
that
the
(2)
The
time
the
impulse
crest
to crest
BIL
have
have
Two
a time
resulted
tail
the
beginning
of the
value.
as the
of the
time
impulse,
interval
at which
trapped
charge
The
between
the
system
Restriking
at the
occurs
builds
Resistors
overvoltages
insulation.
when
up at a faster
in momentary
voltages
time
reestablishment
on the
are
for
of a typical
with
50 to 2000
UHV
transmission
impulse
testing
the
voltage
beginning
is one-half
have
BIL.
surge
of
of the
of line
and
in transmission
the
other
there
towers
switching
line
is high-speed
but
opening.
Transformers
connected
to ground
high-speed
voltage
reclosing
varies
with
period,
breaker
and
the
may
will
reclosing
characteristics,
tests
voltages.
coordination.
reclosing
there
BIL
an increasing
These
surge
insulation
to energization,
The
surges,
between
has been
and equipment.
is similar
surge
shape.
of switching
lies somewhere
developed,
insulation
wave
of 0.5 to 6 microseconds,
Coordination
of transmission
voltage;
SO-microsecond
microseconds,
are of concern
no initial
the
by
lightning
operation
in the
switching
on a 1.2-
coordination
with
switching
the previous
energy
for
is based
from
and
operations
of a line
from
energization.
data
flashovers.
coordinated
ranging
surge
affecting
the range
is usually
switching
latter
level)
is within
As EHV
of switching
The
line
insulation
stress
in better
types
energizing
breaker
between
is defined
parameter
to crest
to crest
of outdoor
tripout.
of the
which
on the
principal
withstand.
is the
on the
interval
its peak
value,
instant,
impulse
time
impulse
60-Hz
amount
the
is the
reaches
to half
is the
(basic
so lightning
and
voltage
and
1.2-microsecond
which
which
value.
Time
The
to crest,
One
following
be energy
normally
becomes
line length,
a line
trapped
dissipate
the
the
same
as
and the state
of switching.
lines
rate
are being
than
of the
deenergized
the dielectric
arc
across
and
strength
the
interrupting
the
recovery
voltage
of the interrupting
contacts
across
medium.
and
can
the
circuit
This
results
produce
extreme
system.
incorporated
EHV
lines
in the closing
stroke
of a breaker
to help reduce
switching
which,
in turn,
helps reduce
the switching
surge requirements
for
surge
line
CHAPTER
Some
causes
III-INSULATION,
of switching
l
Normal
l
High-speed
line
l
Switching
capacitor
l
Load
l
Out-of-phase
l
Reinsertion
l
Circuit
l
Current
Power
in the
line
surge
energizing
PROTECTION,
overvoltages
and
CLEARANCE
PATTERNS
105
are:
deenergizing
reclosing
banks,
shunt
reactors,
and
cable
circuits
rejection
switching
of series
breaker
capacitors
restriking
chopping
frequency
system
overvoltages
alters
l
Voltages
l
Load
Open
l
LIGHTNING
are caused
or removes
on the
the
unfaulted
rejection
end of a long
Ferroresonance
Although
the clearance
by
condition,
phases
energized
an abnormal
such
during
line
condition
which
exists
until
a change
as:
a phase-to-ground
(Ferranti
fault
effect)
l
necessary
for power
frequency
voltage
is much
less than
for switching
or lightning,
the clearance
envelope
is very sensitive
to the insulator
swing angle created
Data on extreme
winds during
storms
and their frequency
of occurrence
are necessary
power
frequency
electrical
insulation
clearances.
and
and
surges
by the wind.
to determine
In transmission
line design,
there are two basic insulations
to be considered,
the insulator
string
air. The insulator
swing angle depends
on the diameter-to-force
(weight)
ratio of the conductor,
the ratio
Consideration
(2) switching
of wind
must
surge,
span to low-point
be given to each
and (3) p ower
span.
of the
frequency.
three
of flashover
following
a circuit
breaker
operation.
of tripouts
per 161 km (100 mi) of line per year.
of the mean recurrence
interval.
Bureau
insulators
types
Switching
wood-pole
designs
are based on
with the minimum
air gap between
by a 0.19-kPa
wind
pressure
at 15.5
coordination
the conductor
wires
separation
ground
and
at midspan
wires.
Insulation
included
the
conductors
must
See section
withstand
will
be greater
20 for
must
not
than
minimum
be coordinated
impulse,
on the probability
value
of the
a wind pressure
the impulse
insulation
angle of the suspension
and the air-gap
insulator
strings
sufficient
occur
before
at the structure
midspan
across
so that
flashover
because
flashover
occurs
angle of 30’)
the overhead
between
the
at the
structure.
of the impedance
overhead
The
of the overhead
clearances.
the
insulator
string
and
the
air
gap.
Factors
0
Crest
l
Maximum
l
Strength
of air to switching
surges in relation
to the impulse
strength
of the insulators,
the ratio of critical
impulse
to switching
surge withstand
Percent
allowance
made between
withstand
voltage
and critical
flashover
of air, or ratio
withstand
of an insulator
string
l
l
withstand
or for a sideswing
at midspan
between
in an evaluation
Maximum
system
factor
of the insulation
operating
voltage
(1) lightning
is based
of the impulse
insulation
and the structure
with
o C on the conductors,
the clearance
whichever
is greater.
For complete
coordination,
ground
wires and the conductor
must be made
ground
stress:
performance
Lightning
performance
is measured
by the number
Power frequency
performance
is measured
in terms
of 0.19 kPa (4 lb/ft*)
at 15.5 ‘C (60 ’ F). On steel structures,
clearance
to the structure
are coordinated
for the sideswing
caused
of voltage
surge
are:
of wave
switching
to critical
surge
overvoltage
flashover
or
of
TRANSMISSION
106
l
Contaminated
l
Nonstandard
a
Maximum
this
The
values
the
on unfaulted
phases
factor
switching
that
voltage
can
vary,
of the
wave
is fi
surge
varies
of switching.
is, taking
with
hut
breaker
variation
in the
the surge
magnitude
values
line
surges
length,
for all switching
or two
switching
situations
produce
highest
values.
and
that
barometric
pressure.
The Bureau
surges. Some designers
like
switching
two
extra
units
are
and, on 345-kV
steel
unit and for hot-line
because in addition
transmission
lines
not only frustrating,
original
be included
in the
If a transmission
one
for
construction,
maintenance.
examples
elevation
these
satisfactory
to use
insulation
strengths
test data
surfaces,
as the ratio of the impulse
strength
for
value as a ratio between
withstand
upon
value.
gap length,
wave shape, and
A factor
of 1.1 is used for
examining
the
air
is dependent
fault
voltage
insulation
upon
the
on unfaulted
strength
for
power
one extra insulator
unit is added
to allow
two extra units are added:
for 230-kV
steel
a possible
defective
unit
and
one
for
hot-line
one extra unit is added as a combination
safety unit
These extra units have proven
to be very valuable
calculations
to reduce
shown
initial
in section
Lightning
wrote
in the
basically
costs
as insulation
coordination
is not economical
when
further
of insulation
selection
limit
is governed
by
for three different
the switching
surge
voltages.
impulse
limits
shown
in the tables should
be used for design
discussed
for hot-line
maintenance
and possible
defective
line is to operate
designers,
Westinghouse,
and weighting
design.
The lower of the two elevation
extra insulator
units previously
discussed
of the
by statistical
to the hot-line
maintenance
safety they afford,
they have helped to restrict
Bureau
to minimal
“unexplained”
flashovers
and outages.
Such flashovers
and outages
are
but they are costly to an electrical
entity
and must be taken into consideration
Tables
16, 17, and 18 show
tables show that the permissible
factors
such
Such design
1.175
factor
for nonstandard
sea level.
1.2 for the maximum
atmosphere,
are used when
added,
The
for
to use a 3-sigma
wood-pole
transmission
line construction,
defective
unit. For 115-kV
steel structures,
construction,
maintenance;
for a defective
uses
surge
the state
distributions
determined
from
upon the proximity
of grounded
flashover,
but since sigma is a variable
depending
we have set 17.5 percent
as a coordination
A factor
of 1.5 for contaminated
phases,
and a safety
factor
of 1.25
frequency
overvoltages.
For 115-kV
for a possible
the
and air gaps are described
by strength
These distributions
will vary depending
and
situations
it is probably
strings
tower.
accepted
can he described
conservative,
contaminated
atmosphere.
An added
altitude
elevation
of the given transmission
line above
20.
switching
To be more
the critical
configuration,
Some
characteristics,
The
is generally
of occurrence.
humidity,
air to the
not
overvoltage
frequency
one
in the
a S-percent
by their
of insulator
on a full-scale
and
gap
crest
at the time
distribution;
etc.)
(altitude)
voltage
operating
The
maximum
system
MANUAL
of safety
maximum
limit.
(chemicals,
density
fault
Factor
l
The
atmosphere
air
LINE DESIGN
purposes.
The
units, should
tables.
problem
of lines
These
values.
free,
or because
then
of lack
insulation
of facts,
coordination
have
is a necessity.
chosen
to ignore
some
which
results
in lines that have many
unexplained
outages.
considered
over a period
of time._Insulation
coordination
is
21.
Protectioma series
In 1930, C. L. Fortescue,
a consulting
transmission
line engineer
with
of articles
on lightning
investigations
that were published
in Electrical
Joumm!
He advanced
the theory
strokes
of lightning.
Previous
that
high-voltage
to that
time,
transmission
transmission
lines
lines
should
were
be protected
designed
on
from
the
direct
basis
of
CHAPTER
III-INSULATION,
LIGHTNING
PROTECTION,
Table 16.-Insulation
selection
CLEARANCE
PATTERNS
107
for 345 kV
Switching surge
impulse,
positive critical
Power
frequency,
60-Hz wet
a. Overvoltage
1.05
1.05
b. Crest factor
1.414
c. Switching surge
2.5
d. Ratio of critical impulse to switching surge
1.175
e. Ratio of withstand
1.175
1.175
1.1
1.5
1.15
1.25
f. Contaminated
to critical flashover voltage
atmosphere
g. Factor of safety
h. Rise due to line faults
Total withstand
1.2
multiplying
factor (at sea level). Product of (a) through
Normal line to neutral, 345/G
Total withstand multiplying
neutral voltage
(h)
2.78
1291 kV
554 kV
1585 kV
690 kV
= 199.2 kV
factor (at sea level) times normal line to
Flashover of 18 insulator units, 146 by 267 mm (5-3/4 by 10-l/2 in), from
table B-7 in appendix B
Factor for nonstandard
6.48
1585/1291
air density (altitude)
namely,
that
6901554 = 1.25
2154 m (7068 ft)
From table B-10 in appendix B, permissible elevation limit
induced-stroke assumption;
= 1.23
a charge
cloud
in the vicinity
2362 m (7750 ft)
of the transmission
line,
with
its accompanying
gradient
of voltage
to ground,
would
bind a charge
on the line. The discharge
of
the cloud to any object
other than a transmission
line, would
release this bound
charge,
which
was
then free to travel
along the line seeking
a path
to ground.
However,
induced
voltage
gradients
appearing
on transmission
lines during
account
for the damage
to the lines.
high-voltage
lines. Complete
protection
nearby
lightning
discharges
have proved
to be too low to
The direct-stroke
theory
is now generally
accepted
for
against
direct
strokes
requires
a shield to prevent
lightning
from
striking
the electrical
conductors,
together
with
adequate
adequate
drainage
facilities
so that
the discharge
can drain
conductors.
The shielding
method
does not allow the formation
to ground.
An alternative
nonshielding
method
tubes or ground
fault neutralizers,
does allow
conductors
four basic
but provides
requirements
of protection
an arc to form
a means for quenching
for the design of a line
Adequate
the full
clearance
effectiveness
level
used
in the
must
line
design.
such as protector
structure
and the
the
theory
be locatd
from the line conductor
to the tower or ground
of the insulating
structure
can be obtained.
(3)
Adequate
clearances
from overhead
especially
at midspan,
to prevent
flashover
voltage
strength
of the structures
and
without
affecting
the
from the line conductor
by auxiliary
devices,
between
the ground
the arc without
interrupting
based on the direct-stroke
(1)
Ground
wires with sufficient
mechanical
the line conductors
from direct
strokes.
(2)
so that
insulation
to ground
of an arc
ground
wires to conductors
to the conductors
for voltages
line
are:
circuit.
to adequately
must
The
shield
be maintained
must be maintained,
up to the protective
TRANSMISSION
108
LINE DESIGN
Table 17.-Insulation
MANUAL
selection for 230 kV
Switching surge
impulse,
positive critical
Power
frequency,
60-Hz wet
a. Overvoltage
1.05
1.05
b. Crest factor
1.414
c. Switching surge
2.5
d. Ratio of critical impulse to switching surge
1.175
e. Ratio of withstand to critical flashover voltage
1.175
1.175
f. Contaminated
1.1
1.5
1.2
1.25
atmosphere
g. Factor of safety
h. Rise due to line faults
Total withstand
1.2
multiplying
factor (at sea level). Product of (a) through (h)
Normal line to neutral, 230/a
Total withstand multiplying
neutral voltage
6.76
= 132.8 kV
factor (at sea level) times normal line to
Flashover of 12 insulator units, 146 by 254 mm (S-3/4 by 10 in), from table
B-7 in appendix B
Factor for nonstandard
air density (altitude)
898 kV
369 kV
1105 kV
490 kV
1105/898
From table B-10 in appendix B, permissible elevation limit
overhead
ground
wires are not normally
used
ground
wires are used for a distance
of 0.8 km
the entire
length
of line. On lines of 115 kV
for the entire length of the line. On transmission
(3/8-in),
7-wire,
above
are used.
high-strength
lines,
13-mm
On lines
or for extra
so that the
long
extra
saline fogs occur,
corrosion
resistant
overhead
extended
a straight
where
spans,
heavy
galvanized
(l/2-in),
very
7 -wire,
heavy
line
ice loading,
through
the
overhead
maximum
angle of 30 o with the vertical.
to give a maximum
angle of proteetion
the
angle
steel
strand
radial
is used
for overhead
galvanized
steel
ice thickness
of protection
should
adequately,
ground
strand
of 25 mm
On 230
ground
(1 in) or more,
the
poles
the overhead
the terrain
to maintain
kV
wires
occurs
wires
where
it is desirable
to use a more
wires. In order to locate the
in wood-pole
of protection
at tangent
structures.
ground
wire and the outside
conductor
At steel towers,
of 20 O. Where
be decreased
in order
wires.
overhead
steel for the overhead
ground
sag. In areas near a sea coast,
and in other areas having
a contaminated
atmosphere,
material
such as Alumoweld
for the overhead
ground
drawn
must be obtained.
are used on all lines using
For standard
construction,
and higher,
overhead
ground
wires normally
are used
lines for voltages
up to and including
161 kV, lo-mm
high-strength
the conductors
a 30’
cone
3139 m (10 299 ft)
on lines of 46 kV or less. On 69.kV
lines, overhead
(0.5 mi) in each direction
from the substations
or for
it is desirable
to use extra-high-strength
loads may be carried
without
excessive
ground
wires to shield
high enough
to provide
4901369 = 1.32
= 1.23
2154 m (7068 ft)
(4)
Tower
footing
impedances
as low as economically
justified
To meet the first of these requirements,
two overhead
ground
wires
H-frame
wood-pole
construction
and generally
on all steel tower
lines.
and
2.78
ground
wires
lines
should
be
This means that
should
make a
should
be located
slopes across a transmission
line,
an angle of less than
30’
for
CHAPTER
III-INSULATION,
LIGHTNING
PROTECTION,
Table 18.~Insulation
CLEARANCE
109
PATTERNS
selection for I I5 kV
Switching surge
impulse,
positive critical
Power
frequency,
60-Hz wet
a. Overvoltage
1.05
1.05
b. Crest factor
1.414
c. Switching surge’
2.8
d. Ratio of critical impulse to switching surge
1.175
e. Ratio of withstand
1.175
1.175
1.1
1.5
1.2
1.25
f. Contaminated
to critical flashover voltage
atmosphere
g. Factor of safety
h. Rise due to line faults
Total withstand
1.2
multiplying
factor (at sea level). Product of (a) through
Normal line to neutral, 115/fi=
Total withstand multiplying
neutral voltage
(h)
2.78
503 kV
185 kV
610 kV
255 kV
66.4 kV
factor (at sea level) times normal line to
Flashover of 6 insulator units, 146 by 254 mm (5-3/4 by 10 in), from
table B-7 in appendix B
Factor for nonstandard
7.57
610/503
air density (altitude)
From table B-10 in appendix B, permissible elevation limit
= 1.21
255/185
1946 m (6386 ft)
= 1.38
3864 m (12 676 ft)
’ A switching surge value of 2.8 is a more realistic value for 115-kV lines than the 2.5 value used for 230- and 345-kV lines.
wood-pole
the
lines,
overhead
and
ground
less than
wire
earth.
If steel towers
exceed
indicated
on figure 43.
To
maintain
between
voltages
lightning
adequate
20 o for steel
and
the
38.1
m (125
clearance
ft)
in height,
the
These
and
the
angles
a line
angle
structure
would
be between
perpendicular
or protection
and
the
a line
to the
should
conductors,
the
through
surface
of the
be reduced
air-gap
as
distance
any conductor
and the structure
should
be sufficient
to coordinate
the impulse
flashover
of the air gap and the insulation
used on the structures,
under
the conditions
at which
is likely to occur.
Almost
all electrical
storms
occur at temperatures
between
minus
1 and
designs are based
air gap between
15.5 OC (60
is measured
a sideswing
lines.
conductor,
between
32 OC (30 and 90 OF), and are not
insulation
suspension
tower
outside
on coordination
the conductor
likely
to occur
OF). 0 n wood-pole structures
between
the conductor
and
and the
insulator
air-gap
clearance
strings
caused
of 30 O, whichever
between
the overhead
between
the ground
ground
wires
and
simultaneously
of the impulse
insulation
and the structure
with
high
winds.
Therefore,
Bureau
of the insulators
with the minimum
pressure
of 0.19 kPa (4 lb/fta)
at
having
ground
wires running
the pole ground
wire.
On
down the pole,
steel structures,
the clearance
the impulse
to the structure
are coordinated
for the sideswing
angle
by a 0.14kPa
wind pressure
on the conductors
at 15.5 ‘C
is greater.
wires
with
value
a wind
and
For
complete
the conductors
the conductors
will
not
coordination,
must
occur
be made
before
the
great
flashover
clearance
enough
occurs
of the
or for
at midspan
so that
flashover
at the
structure.
TRANSMISSION
LINE DESIGN
MANUAL
-
(50)
15.2
(70)
21.3
(90)
27.4
(130)
39.6
(110)
33.5
(150)
45.7
TOWER HEIGHT, meters
Figure 43.-Reduction
Because
than
of the
at the
length
and
of angle of protection
impedance
structure.
of span,
an outage
shows
the
span
lengths.
and
of the
The
the
structure
probability
minimum
overhead
amount
ground
of separation
footing
clearances
between
voltages
have
very
little
tabulation
is satisfactory
tabulation,
the sag in the overhead
for voltages
80 percent
of the
sag of the
to the
conductor
115
at this
separation
depends
desired
structure
per year,
ground
height.
at midspan
on the
a 15-ohm
of line
wires
and
the
104-D-1071.
must
be greater
protection
footing
level,
resistance
following
tabulation
conductors
for
various
(15)
4.6
6.1
7.3
9.7
11.3
11.9
13.7
15.5
17.4
(800)
wire
to structure
Midspan spacing,
m
w
(1000)
(1150)
(1200)
(1400)
(1600)
(1800)
from
ground
mi)
overhead
(700)
relationship
the
Assuming
(600)
183
213
244
305
350
366
427
488
549
according
wires,
161 km (100
Span length,
m
et)
Line
lightning
(feet)
required
resistance.
of 1 or less per
midspan
against
(feet)
( meters 1
(190)
57.9
(170)
5 I.8
(20)
(24)
(32)
(37)
(3%
(45)
(51)
(57)
required
to 500 kV.
at 15.5
midspan
For
’ C (60
temperature.
spans
_
clearances,
longer
’ F) no load,
than
should
so the
those
preceding
shown
be equal
in the
to about
CHAPTER
Lightning
60-Hz
performance
value
slightly
III-INSULATION,
usually
less than
the
60-Hz
less. For
based
best
on the
All
structures
because
path
pole.
under
The
structures,
between
through
to each
desert
is fastened
protection
centerline
of the
tower
I5
the
PATTERNS
footing,
ohms,
of resistance,
wires
the
resistance
wires
should
111
rather
the
surge
surge
to the
pole
surge
than
the
resistance
resistance
should
is
measures
be estimated,
structures,
to reinforcing
(such
as in rocky,
one on each
305
mm
and
(12
a ground
down
turns
grounding
bars
the
brought
into
each
to 18 in) below
ground
the
of the
S-pole
surface
accomplished
or in sandy,
when
a high
level
of
7.6 m (25 ft) from
structure
earth
2
the reinforcing
terrain
at least
butt
all 2- and
welding
is used
of No.
of the pole,
the
At
mountainous
are placed
wire
is usually
and
at the top
the face
around
staples.
counterpoise
wires
side,
to 457
carried
impedance
together
(18 to 24 in) below
angles
counterpoise
structures,
spiral
grounded
on a low
be tied
of Copperweld
continuous
be adequately
depends
should
wires,
complete
On steel
stub
resistivity
line,
ground
457 to 610 mm
or a double
are buried
they
On wood-pole
by means
on each pole.
two
protection
wires,
five
placed
The
transmission
ground
wrapped
of high
ground
for lightning
to ground.
by welding
is desired.
overhead
wires
and
counterpoise
wires
values
to the overhead
pole,
footings
In areas
counterpoise
of the
up to about
15 ohms,
overhead
connection
the ground
lightning
The
is connected
wire
a radial
having
ground
are two
of the
other.
areas)
lines
butt
the concrete
higher
above
the impedance
an underground
is made
bars
there
wire
for
CLEARANCE
data.
to reduce
ground
but
of these
Where
the
resistance
surge
resistances
resistances
in transmission
Copperweld
passed
on the
footing
value,
available
of each structure
AWG
For
footing
the effectiveness
to ground.
PROTECTION,
is dependent
measured.
considerably
LIGHTNING
and
surface.
the
attached.
Figure
B-5
in appendix
An AIEE
B shows ground
resistivity
values
in ohm-meters
for the United
States.
Committee
Report
published
in 1950 [ 131’ was updated
and expanded
by Clayton
and
in 1964 [14]. Th e method
presented
in these reports
consists of groups of curves that are based
Young
on typical
span
horizontal
lengths,
insulator
to 700 kV.
discussed.
For studying
quantities,
that
21.
Conductor
anticipated
Type
l
Loading
area where
Minimum
conductor
Angle
of protection
l
l
of towers
required
Maximum
line deflection
Ruling
span length
l
Insulation
1 Numbers
vertical,
at each
sum
spans
in brackets
(single
the line
spacing
(against
l
Maximum
adjacent
outages
Patterns.-Before
Longitudinal,
ground
wires
l
these
The
curves
footing
curves,
on
wire
configurations,
cover
a voltage
resistances
use surge
transmission
for
range
a desired
resistance
lines
a range
I I5
performance
values
of 345 kV
from
of
as previously
and
above,
it is
a designer
can design
steel
towers
must
afford
for a transmission
be known:
l
l
using
and
ground
be used.
must
l
When
overhead
resistances.
quantities
lightning
[15]
Clearance
data
and
and footing
the curves.
reference
following
conductor
of insulator
from
the
suggested
the
vertical
Combinations
can be determined
line,
and
or double
circuit)
is to be constructed
lightning)
that
and transverse
loading
attachment
point
of adjacent
the
ground
under
wires
full-load
conditions
the
for
conductors
conductors
and
angle
spans,
and
coordination
refer to items in the Bibliography.
the
maximum
distance
between
low
points
of the
TRANSMISSION
112
It is the
the
20;
responsibility
required
data
and insulation
discussed
To
in section
any
insulation
and
line
designer
clearance
conductor
and
the
considering
power
frequency)
required
for the
indicted
on figure
to provide
The angle
construction
all of the
of protection
of conductor
above
data.
Most
of
is discussed
in section
clearance
patterns,
is
19.
adequate
structure
transmission
can be calculated
or approximated.
coordination,
the basis for the
maintain
between
surge,
of the
LINE DESIGN MANUAL
three
between
structure
each
the
stresses
structure
should
of the three
under
voltage
the
condition
are,
and
be sufficient
types
the
to coordinate
of voltage
at which
in general,
conductors,
each
described
stress
is likely
by the
air-gap
the
(lightning
gap
and
the
impulse,
switching
The
clearances
to govern.
three
air
distance
superimposed
patterns
44.
///////////
/l////
Figure 44Auperimposed
clearance
voltage stresses. 104-D-1072.
patterns
1
Insulator
for the three types of
Bureau
designs for wood-pole
structures
are based on coordination
of the impulse
insulation
value
of the insulators
with the minimum
air gap between
the conductor
and structure,
and a wind pressure
of 0.19 kPa (4 lb/ft2)
at 15.5 ‘C (60° F). On steel structures,
the impulse
insulation
of the insulator
string
and
the
air-gap
clearance
to the
structure
are
coordinated
suspension
insulator
strings
caused by a 0.19-kPa
wind pressure
for a sideswing
angle of 30 O, whichever
is greater.
In the normal
string,
10 percent
is added to the impulse
value of the insulator
used
for clearance
to the
structure.
For
the
power
frequency
for
the
sideswing
clearance,
the
maximum
0.43 to 0.48 kPa (9 to 10 lb/ft2),
in the area where the line is to be located,
swing of the insulator
string.
An air gap equivalent
to the wet 60-Hz flashover
string
is used for the clearance
envelope.
An
example
Example
Assume
644
mm2
problem
on constructing
the
clearance
patterns
angle
wind,
(1272
transmission,
kcmil),
ACSR,
line
45/7
follows.
with:
d u pl ex conductor.
The
following
data
usually
is used to define
the
value of the insulator
Problem
a 345-kV
of the
at 15.5 “C on the conductors
or
or vertical
position
of the insulator
string
and an equivalent
air gap is
is also
assumed:
CHAPTER
Maximum
Ruling
initial
III-INSULATION,
tension
per
LIGHTNING
PROTECTION,
conductor
span
18 insulator
units per string
146 by 267 mm (5-3/4
by
Length
per
(single
10-l/2
=
53 378
=
350.5
N (12 000
=
3099
mm
(122
in)
=
3277
mm
(129
in)
=
1500.8
m (1150
PATTERNS
113
lb)
ft)
in)
string
conductor)
(duplex
conductor)
Vertical
CLEARANCE
force
(weight)
per string
N (337.4
lb)
Wind
Everyday
maximum
=
0.19
kPa
(4 lb/ft2)
Maximum
Design
for
design
a minimum
=
0.43
kPa
(9 lb/ft2)
Calculations
Sag and tension
to be made
calculations
low-point
distance
at 15.5 “C
are shown
L,“ear
I TEMP..,
/ oC
UNSTRESSED LENGTH1
LOADING
/3mm
NO Ice.
-mm
0,kPa
sr
AE
to one-third
45 and
Force
the
sum
of adjacent
46.
I
I
,
?
SAG,mm
SAG FACTOR
350.5
SW.N
m
(W’)
Ice
Wind (W”‘)
Figure 45.-Sag
and tension
calculation
spans.
Factor
SPANLENGTHW
Ice
No W\nd
equal
(60 “F).
on figures
form for clearance
pattern
problem
(metric).
TENSION, N
TRANSMISSION
114
LINE DESIGN MANUAL
;;;FL
SAGCALCULATIONS
L43qpJ
CONDUCTOR /'972
Code
Name
Rated
Breaking
Dmmeter
Load
,!..&&
Tension
+/Am.
Final.
-//DF
AcF
Fml.
6oF
Computed
by ~
“/.I/
366
SC R
lb
Area
50
% 17
lb
TemD.
-
% -lb
TEd”p-I
/.
Wind
(A)
(W”‘)
J!&&!-
Coeff.
0.000
tIllSTRESSED
LEI(CTH(
O//
I
,323
Creep
O.OOQ&2---
/7:
7817
lb/f:
Tolal
0.0009,17
2,
977-3
lblft
Modulus,
(E)
Exp.:
z?
Final
9.35
lnltial
per “F
B
Set 0.000
lb/f1
in2
of Linear
Permanent
Ib/ft
5816
1
Final
1 SAC FACTOR
/
SAG.ft
1
wx
AE
InltialAE
SPAH LENGTH(S) //5D
_ lee__
No Wind
(w’)
(w.‘)
Resultant:
_25_
Inch
Ice.
lb
lb
Date
LOADING
weight
Ice
jL
2&
Facrors.
Dead
Llmltarlons:
Loaded.
No
lb
180
L$k.y
LOADING h
Weight
,?d
Inch
l”8,~4,+F
%
___
ACSR “5
km//
1 ern
4
;
48
x 106
lb/~+?
103
lb/&?
J?Ofl
??/L
SW ih
1
:,”
TENSION. lb
FEET
(W’)
Figure 46.-Sag
and tension
calculation
form
for clearance
pattern
problem
(U.S. customary).
Metric
A 0.191 52-kPa wind per meter of conductor =
A 0.430 92-kPa wind per meter of conductor =
(0.430 92) (1000) = 14.722 N/m
U. S. Customary
A 4-lb/ft’
wind per foot of conductor =
A 9-lb/ft2 wind per foot of conductor =
The
vertical
plus
one-half
load
the
due to conductor
low-point
insulator
per
weight
distance
equal
to one-third
the sum of adjacent
spans
conductor:
Metric
For duplex conductor line: ‘(350*5)
3 (2) (20 .928) + -1500*8 = 4890.2 + 375.2 = 5265.4 N
4
CHAPTER
III-INSULATION,
LIGHTNING
PROTECTION,
CLEARANCE
PATTERNS
For single conductor line: (350.5) (2) (20 928) + -1500.8 = 4890.2 + 750.4 = 5640.6 N
3
*
2
U. S. Customary
For duplex conductor line: (1150)
3 (2) (1 .434) + -337.4 = 1099.4 + 84.3 = 1183.7 lb
4
For single conductor line: (1150)(2)
3
Compute
8 (angle
Metric
(0.191
of insulator
52-kPa
swing)
wind,
0’
line
for
(1 .434)+337.4=
2
the
following
1099.4 + 168.7 = 1268.1 lb
conditions:
angle)
Wind = 350.5 (6.542) = 2293 N
fj = tan- 1 - 2293 = tan- ’ 0.435 48 = 23O32’, for one conductor of duplex
5265.4
/J
=
tan-
1
- 2293
= tan- ’ 0.406 52 = 22OO7’, for single conductor
5640.6
U.S. Customary (4-lb/ft2
wind,
Wind = 1150(0.4483)
0
=
tan-l
O”
line
angle)
= 515.55 lb
515.55
= tan- * 0.435 54 = 23O32’, for one conductor of duplex
1183.7
515.55
0 = tan-’ -1268.1 = tan- ’ 0.406 55 = 22OO7’, for single conductor
Metric (0.430
92-kPa
wind,
0’
line
angle)
Wind = 350.5 (14.722) = 5 160.06 N
~9= tan-’
5 160.06
5265.4 = tan- ’ 0.979 99 = 44’25’,
for one conductor of duplex
0 = tan- l 5516$)boi = tan- ’ 0.9 14 8 1 ‘= 42O27’, for single conductor
115
TRANSMISSION
116
U.S. Customary (9-lb/ft2
wind,
Wind = 1150(1.0088)
(j = tan’ l ‘1116~~lf
0 = tan-
Metric
wind,
5’
line
angle)
= 1160.12 lb
= tan- 1 0.980 08 = 44O25’, for one conductor of duplex
l ‘11~~~ 112 = tan-
(No
0’
LINE DESIGN MANUAL
line
l 0.914 85 = 42O27’, for single conductor
angle)
2T sin 2S” = 2 (23 916) (0.043 62) = 2086.43
2086.43
5265 4 = tan -l 0.396 25 =21’37’,
0 = tan-’
(j = tan” l 2~~&4~
U.S. Customary (No
for one conductor of duplex
= tan- l 0.369 90 = 20’ 18’, for single conductor
wind,
5 O line
angle)
2T sin 2.5’ = 2 (5377) (0.043 62) = 469.09
e
=
tan-
1
469’09
1183.7 = tan
8 = tan-
Metric
l ‘s
(0.191
= tan-
52-kPa
wind,
- ’ 0.396 29 = 21037’, for one conductor of duplex
l 0.369 91 = 20’ 18’, for single conductor
5’
line
angle)
2T sin 2.5’ = 2 (24 985) (0.043 62) = 2179.69
e = tan- l
2179.69 + 2293 = tanl 0.849 45 = 40020’, for one conductor of duplex
5265.4
e = tan- l
2179.69 + 2293 =,tanl 0.792 95 = 38O24’, for single conductor
5640.6
CHAPTER
Customary
U.S.
III-INSULATION,
(4-lb/ft2
wind,
LIGHTNING
5 O line
PROTECTION,
CLEARANCE
PATTERNS
angle)
2T sin 2.5O = 2 (5617) (0.043 62) = 490.03
6 = tan- l
490.03 + 515.55
= tan- 1 0.849 52 = 40020’, for one conductor of duplex
1183.7
e = tan-,
490.03 + 515.55
= tan- 1 0.792 98 = 38”24’, for single conductor
1268.1
Metric
(0.430
92-kPa
wind,
5’
line
angle)
2T sin 2.5O = 2 (28 883) (0.043 62) = 2519.75
e = tan-l
2519.75 + 5160.06
= tan- * 1.4585 = 55O34’, for one conductor of duplex
5265.4
8 = tan- l
2519.75 + 5160.06
= tan- 1 1.36 15 = 53O42’, for single conductor
5640.6
Customary
U.S.
(9-lb/f@
wind,
5 O line
angle)
2T sin 2.5O = 2 (6494) (0.043 62) = 566.54
e = tan-I 566.54+ 1160.12
= tan- 1 1.4587 = 55034’, for one conductor of duplex
1183.7
e = tan- 1 566.54 + 1160.12
= tan-’
1268.1
Metric
(No
wind,
15 ’ line
1.3616 = 53O42’, for single conductor
angle)
2T sin 7.5O = 2 (23 916) (0.130 53) = 6243.51
e
=
tmwl
6243.51
5265.4 = tan
e = b-
- l 1.1858 = 49O5 1’ , for one conductor of duplex
i 6243.51
= tan- 1 1.1069 = 47O 54’, for single conductor
5640.6
117
TRANSMISSION
118
Customary
U.S.
(No
wind,
15 O line
LINE DESIGN MANUAL
angle)
2T sin 7.S” = 2 (5377) (0.130 53) = 1403.72
1403.72 = tan- 1 1.1858 = 4905 1’, for one conductor of duplex
1183.7
8 =tan-’
e = TV- 1 1403.72
= tan- ’ 1.1069 = 47O 54’, for single conductor
1268.1
Metric
(0.191
52-kPa
2T sin 79
e = tan-l
wind,
15’
line
angle)
= 2 (24 985) (0.130 53) = 6522.58
6522.58 + 2293 = tan-’
5265.4
1.6742 = 59OO9’, for one conductor of duplex
e = tan- l 6522.58 + 2293 = tan- 1 1.5629 = 57O23’, for single conductor
5640.6
U.S.
Customary
(4-lb/ft2
wind,
15’
line
angle)
2T sin 7.5’ = 2 (5617) (0.130 53) = 1466.37
e =tan-’
1466.37 + 515.55
= tan’ 1 1.6743 = 59OO9’, for one conductor of duplex
1183.7
8 = tan-’
1466.37 + 515.55 = tan-l
1268.1
Metric
(0.430
92-kPa
wind,
15’
line
1.5629 = $7O23’, for single conductor
angle)
2T sin 7.5O = 2 (28 883) (0.130 53) = 7540.20
I:=Qn
1
7540.20 + 5 160.06
= tan-’
5265.4
e = TV- 1 7540.20 + 5160.06
= tan-’
5640.6
2.4119 = 67O29’, for one conductor of duplex
2.25 16 = 66OO3”, for single conductor
CHAPTER
III-INSULATION,
Customary (9-lb/ft2
U.S.
wind,
LIGHTNING
15O
line
PROTECTION,
CLEARANCE
PATTERNS
angle)
2T sin 7.5O = 2 (6494) (0.130 53) = 1695.32
1695.32 + 1160.12
= tan- 1 2.4 123 = 67O29’, for one conductor of duplex
1183.7
0 = tan-’
1695.32 + 1160.12 = tanl 2.2517 = 66OO3’, for single conductor
1268.1
8 = tan-’
Metric
(-0.191
8 = tan-
5%kPa
f 2179..69
wind,
5’
- 2293
5265.4
8 = tan-,
U.S.
Customary
line
angle)
-0.021 52 = -lo 14’, for one conductor of duplex
= tan”
2179.69 - 2293
= tan- 1 - 0.020 09 = -1’09”, for single conductor
5640.6
(-4-lb/ft2
wind,
5 ’
line
angle)
e = tan- 1
490.03 - 515.55 = tm”
1183.7
-0.021 56 = -lo 14’, for one conductor of duplex
8 = tan”
490.03 - 515.55
ztm-1
1268.1
-0.020 12 = -1’09’, for single conductor
Metric
(-0.430
B = tan-l
9%kPa
2519.75
wind,
5 O line
- 5160.06
5265.4
8 = tan-l
U.S.
Custmmy
B = tm-l
angle)
= tan-l -0.501 44 = -26’38’,
2519.75 - 5160.06
=tm-’
5640.6
(-9-lb/ft2
wind,
5 O line
566.54- 1160.12= tm-l
1183.7
for one conductor of duplex
-0.468 09 = -25OO5 , for single conductor
angle)
-o . 501 46 = -26O38’, for one conductor of duplex
0 = tan- 1 566’54 - ’ ’ 60*1 2 = tan- l k 0.468 09 = -25OOS’ , for single conductor
1268.1
119
120
TRANSMISSION
Metric
(-0.191
52-kPa
wind,
15’
MANUAL
line angle)
e = tan- 1 6522.58 - 2293
= tan-’
5265.4
13= tan-’
LINE DESIGN
0.803 28 = 38O46’, for one conductor of duplex
6522.58 - 2293
= tan- l 0.749 84 = 36O5 l’, for single conductor
5640.6
U.S. Customary (-4-lb/ft2
wind,
15 O line angle)
e =tan-’
- 5 15.55
1466.371183.7
= tan- 1 0.803 26 = 38O46’, for one conductor of duplex
8 =tan-’
1466.37 - 515.55
= tan”
1268.1
Metric
(-0.430
92-kPa
wind,
0.749 80 = 36O51’, for single conductor
15 o line angle)
8 = tan-’
7540.20 - 5 160.06
= tan- ’ 0.452 03 = 24O 19’, for one conductor of duplex
5265.4
e = tan- 1
7540.20 - 5 160.06
= tan- 1 0.421 97 = 22O52’, for single conductor
5640.6
U.S. Customary (-9-lb/fts
8 =twl
e=ta-l
wind,
15 O line angle)
1695.32 - 1160.12 = tan’ 0.452 14 = 24O 19’, for one conductor of duplex
1183.7
1695.32 1160.12 = tan- 1 0.422 05 = 22O52’, for single conductor
1268.1
Determine the critical positive impulse flashover value and the 60-Hz wet flashover value of the
insulator string to be used. Determine the lengths of air gaps that are electrically equivalent to the
critical positive impulse flashover, equivalent to the impulse flashover plus 10 percent, and equivalent
to the 60-Hz wet flashover. These values may be obtained from catalog data or from the tables in
appendix B.
For example:
1. For 18 insulator units, the critical positive impulse flashover is 1585 kV (table B-7,
app. B).
2. 1585 kV plus 10 percent equals 1744 kV.
3. The SO-Hz wet flashover for 18 units is 690 kV (table B-7, app. B).
4. The equivalent air gaps for l., 2., and 3. are 2642,2921, and 2083 mm (104,115, and
82 in), respectively (table B-8, app. B).
CHAPTER
III-INSULATION,
LIGHTNING
PROTECTION,
CLEARANCE
-Bottom
of crossarm
PATTERNS
121
1524 mm (i-6)
Conductor elevation
center of tower
Conductor elevation at
edge of tower, high
side of 1:5 ground
at
Conductor elevation at
edge of tower, level span
Conductor elevation at edge
of tower, low side of
1:5 ground slope
NOTES:
Conductor = 644 mm2 (1272 kcmil), ACSR, 45/ 7.
Sag at 15.5 “C (60 OF)=I3 628 mm (44.71 ft) for a 350.5-m (1150-ft) span.
Conductor elevation
at edge of, cage:
bktriC:
1.219/350.5=0.35%
of span = 1.5% of sag =204 mm.
U.S. Customary: 4/1150 = 0.35 % of span = 1.5% of sog = 0.67 ft= 8.1 in.
Assume ground slope of I in 5 equivalent to 244 mm (0.8 ft=9.6
in) additional
sag at edge of tower.
On low side of tower, total drop of conductor at edge of tower=448 mm (17.7 in).
On high side of tower, assume conductor sag cancels effect of ground slope.
Fire
47.-Assumed
dimensions
for side view of structure
at conductor
elevation.
104-D-1073.
Figure 4’7 shows the assumed dimensions of the sideview of the tower at the conductor elevation.
Clearance patterns for two structure types, a tangent structure and an angle structure capable of
taking line angles between 5 O and 15 O, have been constructed for two cases: (1) for duplex conductor,
and (2) a single conductor. These clearance patterns are shown on figures 48, 49, 50, and 51.
The clearance pattern shown on figure 48 has been noted to illustrate the following discussion on
construction
of the clearance pattern. After selecting a scale, begin constructing
the pattern by
striking a 180° arc with a radius equal to the length of the insulator string as it hangs normally;
the center of the arc represents the attachment point of the insulator string at the tower. By looking
at a side view of the tower (fig. 47), it can be seen that the electrical clearance between the conductor
and steel will be most critical at the edge of the tower because of the sag in the conductor. To account
for this, draw a second arc parallel to the first, but with the radius increased by the amount of the
conductor sag at the edge of the tower. These arcs represent the possible locations of the conductor
(short radius at the centerline of the tower, and long radius at the edge of the tower) at the end of
the insulator string, or the centerline between conductors if duplex conductors are used. Draw radii
representing the insulator string as it hangs normally and at its positions with the different wind
TRANSMISSION
122
pressures
edge
and
of the
strike
line
tower
arcs to form
air gaps
previously
equal
to the
drawn
from
t
angles,
(fig.
as applicable.
47)
for
an envelope
the
the 0.19-kPa
From
the
4331
8662
mm (28: 5”)
0.19152-kPa
0.43092-kPa
-0.19152-kPa
-0.43092-kPa
pattern
value
1I
I
is the
radii
4331
locations
conductor
for these
of the
plus
conductor
adjusted
conductor,
the
The
arc
has a radius
radius
of the
of the insulator
mm (Id-2;“)
,/Insulator
at the
locations,
arcs are the equivalent
10 percent.
air gap equivalent
structure
wind,
wind,
wind,
wind,
wind,
w
string
0” line
0” -line
O” line
0” line
0” line
with single conductor.
angle
angle
angle
angle
angle
104-D-1074.
arc
impulse
Additional clearance for
sloping span due to sloping
ground = 244 mm (9.6 in)
no
(d-lb / ft2)
(g-lb/ ft2)
64-lb /ft2)
(-g-lb/ ft2)
for a 30s tangent
the
these
The
position
impulse
tower =204 mm (8.1 in )
Figure BI.-Clearance
points.
position
(Clearance for upslope
a 00
b 1 22’07’.
C = 42”27’,
b’=-22”07’,
C’ =-42’27’,
showing
From
‘?wind”
mm (I 41-2;‘)
MANUAL
points
“no-wind”
insulator
w
w
the
conditions.
the conductor
of the
(4-lb/f@)
Locate
applicable
around
determined.
air gap equivalent
LINE DESIGN
CHAPTER
III-INSULATION,
LIGHTNING
flashover
value, and the arc radius
of the 60-Hz
wet flashover
value
from the 0.43-kPa
of the insulator
corresponding
values,
No
part
wind
of a steel
and line
structure
angle
is allowed
are shown
to encroach
PROTECTION,
CLEARANCE
PATTERNS
(9-lb/ft2)
wind position
is the air gap equivalent
string.
The angles of insulator
swing, with their
on figures
upon
48,49,50,
a clearance
and
51 for ready
pattern
envelope.
9398 mm (30’~101’)
4699 mm (I 5: 5”)
\457
cl
4699 mm ( I 5: 5”)
mm (18 in) Spacing of duplex conductor
0”
b 123’32’:
O.i9152-kPa (4-lb/ft*)
c = 44’25’. 0.43092-kPa (g-lb /ft*)
b’=-23°32’,-0.19152
-kPa (-4-lb/ft*)
C’ =-44°25’,-0.43092-kPa
(-Wb/ft*)
Figure 49Alearance
pattern
for a 30s tangent
123
structure
no wind,
wind,
wind,
wind,
wind,
with duplex
0”
0”
0”
0”
0”
line
line
line
line
line
conductor.
angle
angle
angle
angle
angle
104-D-1075.
reference.
124
TRANSMISSION
LINE DESIGN MANUAL
8992 mm (291-6”)
l-2
3099 mm (122 in)
-0.4x92-kPa
a =-25’05’,
b =-oIO o9’,-O.I9152-kPa
C = 20” I8’,
d = 22” 52’, -0.43092--kPa
e = 36’51’, -0.19152 -kPa
f = 38’24’,
0.19152-kPa
g = 47”54’,
h = 53’42’,
o.43092-kPa
i = 57O 23’, 0.19152-kPa
j=
66OO3’, 0.43092-kPa
Fire
SO.-Clearance
pattern
(-g-lb /ft2) wind, 5” line
(-4-lb / ft2) wind, 5” line
no wind, 5” line
(-g-lb / ft2) wind, 15” line
(-4-lb /ft2) wind, 15” line
(4-lb /ft2) wind, 5” line
no wind,-l5O line
(g-lb / ft2) wind, 5” line
(4-lb / ft2) wind, 15” line
(g-lb / ft2) wind, 15” line
for a 30A angle structure
with single conductor.
angle
angle
angle
angle
angle
angle
angle
angle
angle
angle
104-D-1076.
CHAPTER
III-INSULATION,
9652
*
c
LIGHTNING
3874
mm (12:8;)
1168
PROTECTION,
CLEARANCE
mm ( 31L8”)
C!
C
5778
mm (18Lll~)
mm (46 in)+
L74fR
3277
mm (129 in)
a =-26’38’,-0.43092-kPa
(-g-lb / ft*)
b =-01” ~4’,-0.~9~52 -kPa (-&lb/ ft*)
c =
d=
e=
f =
9=
h=
i=
j =
wind,
wind,
no wind,
21” 36’.
24” I&-0.43092-kPa
(-9-lb/ft*)
wind,
38” 46’, -0.19152 -kPa (-+lb/ft*)
wind,
40020’,
0.19152-kPa (+lb/ft*)
wind,
49O5l’,
no wind,
55O34, 0.43092-kPa (g-lb / f t*) wind,
5g”W, 0.19152-kPa (+lb/ft*)
wind,
67’29’.
0.43092-kPa (g-lb/ft*)
wind,
Figure Sl.-Clearance
pattern
for a 30A angle structure
125
PATTERNS
with duplex
line
5O line
5” line
15” line
15” line
5” line
15” line
5” line
15” line
15’ line
5”
conductor.
angle
angle
angle
angle
angle
angle
angle
angle
angle
angle
104-D-1077.
<Chapter
STRUCTURE
22.
General.-For
constructed
for
construction
wood-pole
is also
main
transmission
loading
line
conditions,
AND GUYING
under
consideration,
specific
size and
CHARTS
a structure
type
limitation
of conductor,
to be used. The chart
is used to determine
the type of structure
construction
that is required
at any’ given location
in the transmission
constructed
23.
each
the
LIMITATION
to determine
Components
the
nutnber
of Charts.-The
of guys
structure
to be used
limitation
and
IV
with
the
guying
and
is
type
of
for either
steel or
line. A guying
chart
wood-pole
chart
chart
the
structures.
consists
of the following
items:
l
A suspension-type
structure
limitation
chart
that
determines
required
for a given location.
The chart
also determines
points)
which must be provided
by the conductor
to limit
for a particular
location
are outside
the limits
of any
necessary
to use a dead-end-type
is dependent
on the magnitude
between
conductor
low points
at the structure.
l
A guy chart
magnitude
that
determines
of the line angle
self-supporting
steel structures
references
to guys are omitted.
l
A summary
of guying
A table summarizing
l
Notes
l
covering
the
structure.
The
type
of suspension
the number
of angle
and the lengths
of
are to be used
for
materials,
and
of structure
required
guys required
the adjacent
a transmission
the
structure
the amount
of mass (between
low
insulator
sideswing.
If the conditions
suspension-type
structure,
it will be
of the line angle, lengths
of the adjacent
in the adjacent
spans, and the required
data for tension
structures.
the structure
types,
their span
construction
the type
limits,
conditions
and
at any
location
actual spans, distance
conductor
clearances
(dependent
upon
the
actual
spans).
When
line,
the
their
allowable
on which
guy
the
chart
and
line
chart
all
angles.
is based.
24.
Preparation
of Charts.-A
structure
limitation
chart
for steel towers
and a structure
limitation
and guying
chart for H-frame,
wood-pole
transmission
lines are developed
in this section.
The following
numbered
paragraphs
(1 through
7) describe
the procedures
for preparing
these charts.
Paragraph
In order
established:
1.
to establish
a basis
for
preparing
For steel structures,
the permissible
a.
structure
is determined
from
the clearance
clearance
pattern
depends
on the
these
sideswing
pattern
size and’ type
charts,
following
standards
have
been
of each insulator
string
on a suspension-type
established
for the design of the towers.
The
of conductor
127
the
and
loading
conditions
for
which
the
128
TRANSMISSION
transmission
shall
The
and
line
for determining
and
the
following
the strength
minimum
strings
(suspension)
2.5
strings
(tension)
3.0
spans,
the maximum
angle
are established
these
structure
distance
limits
factors
Insulator
to fit
in California,
for important
MANUAL
Insulator
deflection
are designed
b.
Except
voltages
and
Calculations
conditions
sum of adjacent
maximum
towers
designed.
on full-load
maximum
the
steel
line is being
be based
LINE DESIGN
between
as required
for
of insulator
strings
of safety:
low points
the
of adjacent
transmission
line
spans,
and
the
requirements.
the design
of all wood-pole
lines of lower voltages
shall
transmission
be in accordance
lines for 69-kV
and higher
with grade B construction
as shown in the latest edition
of NESC.
Loading
conditions
and conductor
and overhead
ground
wire
tensions
shall also be in accordance
with the latest edition
of the code, except
as modified
by figure
1 or by specific
heavier
loading
conditions
than those prescribed
for the general
area for which
a
line
is being
designed.
The recommended
conductor
ultimate
used on transmission
maximum
design tensions
(full-load
tensions
based on 33-l/3
percent
of the
’
C
(0
’
F)
under
initial
conditions)
for
typical
conductors
strength
at minus
18
lines with H-frame,
wood-pole
structures
are shown in the following
tabulation:
ACSR, 2417 conductors
mm2
RCW
242
282
306
322
403
Maximum
full-load
conductor
Maximum
N
(477)
E)
33362
35 585
31810
40034
44482
(636)
(795)
tension
allowble
on standard
exceed
44 482 N (10 000 lb).
Strength
calculations
for determining
permissible
guying,
and requirements
for double
insulator
strings
USBR
tensions
(lb)
(7 500)
(8000)
(8 500)
(9 000)
(10 000)
H-frame,
wood-pole
structures
should
not
in paragraph
2 and
the
minimum
Selection
of the proper
type
condition
of 0.19-kPa
(4-lb/ft2)
factors
of safety
of suspension
wind pressure
zones. The three axes of the structure
limitation
of this loading
condition.
Table
20 shows the
span lengths,
distance
between
low
shall be based on the full-load
conditions
shown
in table
19.
structure
for any location
shall be based on a loading
on the bare conductor
at 15.5 o C (60 o F) in all loading
chart shall be calibrated
minimum
clearance
from
to correspond
the conductor
ground wire or to the surface of the crossarm; these clearances shall be maintained
condition above.
If a pole ground
wire is not
be maintained
to the centerline
types of structures
are shown
different
types
of wood
points,
shown
to the values
to the pole
under the loading
used, the clearances
specified
to the pole ground
wire in table 20 shall
of the. poles. The limits for permissible
insulator
swing on the different
for, the various
voltage
classes in table 21. Drawings
of some of the
structures
are shown
later
in this
section.
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
Table lg.-Minimum
factors of safety for wood-pole
construction’ (grade B)
At full load
Wood poles
Crossarms
Guys (line)
Guys (transverse)
Insulator strings (suspension)
Insulator strings (tension)
Insulator pins (bending)
Conductor
At 15.5 OC (60 OF), no wind
35.5
35.5
z
22:o
2.61
‘2.5
i-8
2:o
4.0
r Factors of safety are based on ultimate strengths of the different materials to
whith they are applicable.
USBR standard.
3 Based on 8.96-MPa (1300-lb/in*) fiber stress for fii, or 6.89-MPa (lOOO-lb/in*)
fiber stress for western red cedar.
Table 20.-Conductor
clearance to pole ground
wire or crossarm surface-wood-pole
construction
Conductor
Type of construction,
kV
Pole ground wire’
mm
(in)
660
1092
1245
1524
1803
69
115
138
161
230
(26)
(43)
(49)
(60)
(71)
clearance
Crossarm surface’
mm
(in)
508
889
991
1245
1473
(20)
(35)
(39)
(49)
(58)
t USBR standard.
Table 21 .-Angukzr limitations of suspension insulator
swing for standard USBR wood-pole structures
Structure
type
HS
HSB
3A
El
3AD’
69 kV
*54 max.
*54 max.
30 min.
-30
12 min.
to +70
-30 to +70
115 kV
36 max.
36 max.
36 min.
-16
24 min.
to +70
-16 to +70
AnguIar limitation,
138 kV
40 max.
40 max.
39 min.
-28
27 min.
to
+70
-28 to +70
degrees
161 kV
38 max.
38 max.
45 min.
35 min.
-16 to +63
-16 to +63
230 kV
42 max.
42 max.
41 mill.
38 min.
-17 to +60
-17 to +60
’ Structure types 3AC and 3AD should not be used where either a type 3A or 3AB wiIl satisfy the
req$rements of the proposed structure:location.
Extreme care should be exercised inchecking for uplift.
129
TRANSMISSION
130
The
following
conductor
minimum
positions
clearance
on wood-pole
LINE DESIGN MANUAL
between
conductor
and
guy
wire
shall
be maintained
at all
construction:
Typeofconsmction
kV
C1&?llWlCe’
mm
w
69
115
138
161
230
965
1397
1524
1676
1956
(38)
(55)
(60)
(66)
(77)
1 USBR standard.
In
areas
where
conductors
and
length
of a single
span
conductors
and overhead
(600 ft), full-sag
ellipses
should
ground
should
one-half-sag
be used.
ellipses
may
overhead
ground
wires
be limited
to prevent
wires due to galloping
be- used to determine
are subject
to ice loading,
contact
between
conductors
conductors.
For span lengths
the required
clearances.
For
the
maximum
or between
up to‘183
m
longer
spans,
c.
In California,
the design of wood-pole
transmission
lines shall be in accordance
with grade B
construction
as shown
in General
Order
No. 95 of the California
Public
Utilities
Commission
[l],’
except
that grade A construction
is required
for crossings
over railroads
and major
communication
lines.
Loading
conditions
with General
Order
and conductor
No. 95, except
The recommended
conductor
ultimate
maximum
design tensions
(full-load
tensions
based on 33-l/3
percent
of the
strength
at minus
18 o C (0 ’ F) under initial
conditions)
for typical
conductors
lines in California
with H-frame,
wood-pole
structures
are shown in the following
used on transmission
tabulation:
and overhead
ground
as modified
by figure
ACSR, 2417 conductors
Maximum
full-load
mm2
W-1
242
282
306
322
403
(4771
(556.5)
conductor
Maximum
N
33
35
37
40
44
(605)
(636)
(795)
tension
on standard
should
not exceed 44 482 N (10 000 lb).
Strength
calculations
for determining
permissible
guying,
and requirements
for double
insulator
strings
in paragraph
’ Numbers
2 and
in brackets
the
minimum
factors
of safety
refer to items in the Bibliography.
wire
1.
tensions
allowble
362
585
810
034
482
USBR
shall
also be in accordance
tensions
(lb)
(7
(8
(8
(9
(10
500)
000)
500)
000)
000)
H-frame-type
structures
in California
span lengths,
distance
between
low
shall be based on the full-load
conditions
shown
in table
22.
points,
shown
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
131
Table 22.-Minimum
factors of safety for
wood-pole construction in California’
Grade A
Wood poles
Crossarms
Guys, except in light loading
rural areas
Guys in light loading rural areas
Insulator strings (suspension)
Insulator strings (tension)
Insulator pins (bending)
Conductor
Grade B
2t::
24.0
3.0
2.0
2.0
2.0
1.5
22.5
23.0
23.0
2.0
23:o
Ei
2.0
’ Factors of safety are based on ultimate strengths of the different
to Thich they are applicable.
USBR standard.
Selection
at 15.5 ‘C
of the proper
(60 OF) with
type of suspension
a 0.19-kPa
(4-lb/ft2)
crossarm;
these
for any
location
shall
he based
on conditions
wind pressure
in all loading
areas. The three axes of
shall be calibrated
to correspond
to the values at the above conditions.
clearance
from the conductor
to the pole ground
wire or to the surface
the structure
limitation
chart
Table 23 shows the minimum
of the
structure
materials
clearances
shall
be maintained
under
the
above
loading
condition.
Table 23.-Conductor
clearance to pole ground
wire or crossarm surface-wood-pole
construction in cizlifornia
Conductor
Pole ground wire’
mm
(in)
Type of construction,
kV
69
115
138
161
230
(26)
660
1092
1245
1524
1803
(43)
(49)
(60)
(71)
clearance
Crossarm surfacer
mm
(in)
(20)
508
889
991
1245
1473
(35)
(39)
(49)
(58)
r USBR standard.
If a pole
ground
be maintained
The limits
The
conductor
wire
is not
used,
the clearances
specified
to the centerline
of the poles.
for permissible
insulator
swing in California
following
minimum
clearance
between
conductor
to the pole
are the
and
same
guy
positions:
T&e of construction
kV
Clearance ’
mm
(in)
69
965
(38)
115
138
161
230
1524
1397
1676
1956
035)
s USBR standard.
si;
(77)
wire
ground
wire
as shown
shall
in table
in table
be maintained
23 shall
21.
at
all
TRANSMISSION
132
In areas
of California
maximum
length
conductors
(600
ft),
where
of a single
and
overhead
full-sag
ellipses
one-half-sag
ellipses
Paragraph
may
span
conductors
should
LINE DESIGN
and
overhead
be limited
ground
wires
due
should
be used
ground
to prevent
to galloping
to determine
MANUAL
wires
contact
are subject
between
conductors.
the
For
required
to ice loading,
conductors
span
lengths
clearance.
For
the
or between
up to
longer
183 m
spans,
be used.
2.
Full-load
conditions
are as follows:
National Electrical Safety
Code or California General
Order No. 95
Loading for calculations
of strength of structures
and their components
Light loading districts’ :
0.43-kPa (9-lb/ft2) wind
pressure, no ice, plus
constant, at -1 OC (30 OF)
0.57~kPa (1 2-lb/ft2 ) wind
pressure, no ice’
Medium loading districts’ :
0.19-kPa (4-lb/ft2 ) wind
pressure, 6-mm (l/4+1)
ice, plus constant, at
-9.5 OC (15 OF)
0.38-kPa (8-lb/ft2 ) wind
pressure, 6-mm ( l/4&)
ice’
Heavy loading districts’ :
0.19-kPa (4lb/ft2 ) wind
pressure, 13-mm ( l/2+)
ice, plus constant, at
- 18 OC (0 OF)
0.38~kPa (S-lb/ft2 ) wind
pressure, 13-mm (l/2+1)
ice’
California light loading:
0.3 8-kPa ( 8-lb/ft2 ) wind
pressure, no ice, at
-4 OC (25 OF)
0.38~kPa (8-lb/ft2 ) wind
pressure, no ice
California heavy
0.29-kPa (6-lb/ft2
pressure, 13-mm
ice, at - 18 OC (0
0.29-kPa (6-lb/ft2 ) wind
pressure, 13-mm ( l/2&)
ice
loading:
) wind
( l/2-in)
OF)
’ Extreme wind loading as shown on NESC figure 250-2 in reference [ 31 should be u;ed if resultant loading is greater.
Pa ragrap
h 3.
The data
transmission
patterns.
The
required
for construction
of a structure
line are discussed
at the beginning
clearance
patterns
themselves
limitation
of section
are important
chart for the design of a steel structure
21, which
covers
conductor
clearance
because
they
indicate
the maximum
design
CHAPTER
swing
of the suspension
limitation
lines
on the
previously
discussed
maximum
sum
that
shows
Example
Assume
conductor.
insulator
strings
low-point
portion
are basically
of adjacent
the
procedure
Problem
for
(steel
a 345-kV
Assume
obtaining
conditions.
The extreme
data are also assumed:
initial
heavy)
made
30s
=
tangent,
30X
=
tangent
30A
30T
30D
=
=
=
angle,
tangent
tangent
for
each
chart.
steel
structure
for
with
a 644-mm2
swing
The
angles
balance
low-point
An
become
of the
distance
example
and
problem
limitation
force
wind
pressure
data
the
follows
chart.
=
per
extreme
per unit length
N/m
(1.8867
here
for
45/7
wind
duplex
pressure.
for the conductor
lb/ft)
for NESC
example
purposes.
The
(weight)
of steel
transmission
V-string
=
63 165 N (14 200 lb)
350.5 m (1150 ft)
=
3556
mm
=
1628
N (366
=
=
0.19
0.48
string
by
per
10-l/2
in)
string
design
suspension,
ACSR,
(16~lb/ftz)
was assumed
maximum
types
(1272-kcmil),
a 0.77-kPa
because the resultant
force
which
is less than 27.5345
Design
for a minimum
sum of adjacent
spans.
are usually
the
maximum
on the
data
is in an area with
267 mm (5-3/4
per string
Maximum
of the different
the
these
chart.
full-load
tension
per conductor
Ruling
span
20 insulator
units
Drawings
although
are drawn
line
location
not be a factor
(1.285
lb/ft),
Vertical
Wind
Everyday
data,
of structures;
limitation
133
CHARTS
construction)
the line
146 by
Length
structure
the
AND GUYING
types
of the
limitations
transmission
Maximum
(NESC
LIMITATION
on the various
tabled
spans
This wind pressure
will
would
be 18.746
N/m
full-load
following
IV-STRUCTURE
low-point
distance
structures
line.
Steel
on center
to 5 O line angle, suspension
line angle, suspension
5 to 15’
to 5’ line angle, tension
to 30’
line angle, dead end
equal
are not shown
tower
phase
kPa
kPa
(140
in)
lb)
(4 lb/ft2)
(10 lh/fts)
to one-third
the
in this manual
designations
and
types
because
are:
new
designs
TRANSMISSION
134
Tabular
steel
tower
data
LINE DESIGN
MANUAL
follows:
Metric
Tower type
Line angle capability
Ruling span (m)
Maximum single span (m)
Minimum line angle
Maximum line angle
Maximum sum of adjacent spans (m)
Minimum line angle
Maximum line angle
Maximum low point distance (m)
Conductor, minimum line angle
Conductor, maximum line angle
OGW, minimum line angle
OCW, maximum line angle
Maximum uplift (N)
Conductor, minimum line angle
Conductor, maximum line angle
OGW, minimum line angle
OGW, maximum line angle
Body heights (m)
Leg extension range (m), at 0.762-m
intervals
30s
30x
30A
30T
30D
O0
350.5
00-50
350.5
so-150
350.5
00-50
350.5
00-300
350.5
396
396
487.5
396
487.5
396
548.5
487.5
640
792.5
792.5
975.5
792.5
975.5
792.5
1097
975.5
1280
731.5
731.5
853.5
853.5
975.5
792.5
1036.5
853.5
975.5
792.5
1036.5
853.5
19.8
and
25.9
1.524
19.8
and
25.9
1.524
19.8
and
25.9
1.524
10x
lo:607
10x
1280
1280
1524
1524
305
213.5
396
254
16.8
and
22.9
1.524
lo::7
1371.5
1463
305
396
16.8
and
22.9
1.524
lo::7
U. S. Customary
Tower type
Line angle capability
Ruling span (ft)
Maximum single span (ft)
Minimum line angle
Maximum line angle
Maximum sum of adjacent spans (ft)
Minimum line angle
Maximum line angle
Maximum low point distance (ft)
Conductor, minimum line angle
Conductor, maximum line anae
OCW, minimum line angle
OCW, maximum line angle
Maximum uplift (lb)
Conductor, minimum line angle
Conductor, maximum line angle
OGW, minimum line angle
OGW, maximum line angle
Body heights 0%
Leg extension range (ft), at 2.5-ft
intervals
30A
30T
30s
30x
00
1150
00-50
1150
so-150
1150
00-50
1150
00-300
1150
1300
1300
1600
1300
1600
1300
1800
1600
2100
2600
2600
3200
2600
3200
2600
3600
3200
4200
2400
2400
2800
2800
3200
2600
3400
2800
3200
2600
3400
2800
4200
4200
5000
5000
65
and
85
5
65
and
85
5
65
and
85
5
:5”
ii
;:
1000
700
1300
833
55
and
75
5
:z
30D
4500
4800
1000
1300
55
and
75
5
ii
CHAPTER
Calculations
IV-STRUCTURE
for the strength
LIMITATION
requirements
AND GUYING
of insulator
strings
CHARTS
for the various
135
types
of steel
towers
are as follows:
Type
30.5,
0 o Ihe
Maximum
Maximum
Conductor
force
0.38-kPa
(8-lb/ft2)
The
bcm-570
with
conductor
a 0.38-kPa
angle
low-point
distance
= 731.5 m (2400 ft)
sum of adjacent
spans = 792.5 m (2600
13 mm
wind
force
wind
values
are simply
(l/2
on iced
in)
are shown
twice
of radial
conductor
the
=
ft)
ice =
37.676
22.816
N/m
on figures
values
shown
N/m
(2.5816
(1.5634
lb/ft)
52 and
53. The
on these
figures
force
for
lb/ft)
values
shown
a 0.19-kPa
above
for
wind.
(9-78)
Dead Load Force (W’)
/3
mm Ica (W”)&
OakPa
Initial *-%,33%-.-Final .oc
,
Loadad,~~.50%
Final I- 15.5~ ,COIIIPUW~ by
No Ica. *Wind
N
25
K -N
(We”)
I/.
408
,.,,m
j.3.
ff9
N/m
N
o.ooo osw?
Oats -
*I977
Total O.O0/4Jo
Modulus. (I3 Final k&&6-
Area (AlC84md
Temp. Coaff. of Linear
-N
K-
Resultant.
creep o.oooGG2LL
Nh
Wind
Exp.:
initial
Fit?alAE
per%
NEtSC K:r/.374?2
Initial
/1/
&
4//P
GPa
2/
:!
GPa
&,/-‘I
AE 3/
t
(W)
No Ice. Lk Wind (W’)
Fire
52.-Conductor
(metric).
sag and tension
calculation
form
for example
problem
on steel structure
limitation
chart
TRANSMISSION
136
DC-K70
LINE DESIGN
MANUAL
(S-78)
CONOUCTOR
l&U km;/
ACSR
454
33ifem
Code Name
Rated Breaking Load
Diameter
Tension
/U.&I
Dead Weight
-lb
inch
+ hi”.
L~m~tauonr:
Initial.Final,
-
computed
OF%
OFA%-
by -
/. 4340
758
6
lb/f1
AL Lb Wind ..,,:,
‘F33fK
LOrded .FiMl. *OF
(W’)
ICI (W”)
Resultant:
-lb
Y -
lb
lb
Area (A) /.
TemD.‘Cooff.
(W”‘) 3.6073
O.WO On
per ‘?=
Set 0.00
Creap
o.oon~-
lb/f1
Totai
0.001
O./O
4
lb/f1
in2
of Linear Exp.: s,g77
$4 -lb
Date
Permanent
lb/f1
X=0,30
NEsc
Modulus. (E) Final 9 35
Initial~x
Final AE .a
Initial AE
,7 159
x 1OS lb/it-$
106 lb/id
lb
276
lb
No Ice. No Wind (W’)
0
Inch Ice
No Ice. Mm Wind (w’)
Figure 53.-Conductor
customary).
sag and tension calculation
form for example problem
on steel structure
limitation
chart (U.S.
Metric
Maximum
Maximum
Resultant
vertical load = (731.52) (37.676) = 27 560.75 newtons per conductor
wind load = (792.48/2) (22.816) = 9040.61 newtons per conductor
load = [(27 560.75)2 + (9040.61)2]1/2 = 29 005.65 newtons per conductor
= 58 011.30 newtons per phase
= 145 028.25 newtons per phase with a safety factor of 2.5
Use 177 928-N insulator units for suspension strings.
A sketch of a center phase V-string
attachment
for the 30s tower is shown on figure 54.
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
137
For center phase V-string,
b
-=-a
sin A
4
145 028 _
b
sin 80°
sin SO0
50”
b
~(800)
SillB
a
b = 145
028
(0.766 04) = 112 810.85 N
0.984 8 1
‘“B’
Use 133 446-N insulator units.
Figure S4.-Center
phase V-string
structure with no line angle.
for type 30s steel
U.S. Customary
Maximum
vertical
Maximum
Resultant
wind load = (2600/2)
load I = [(6195.84)2
+
load
=
=
Use
40 OOO-lb
=
(2400)
13 041.34
32 603.34
insulator
(2.5816)
pounds
pounds
units
for
=
6195.84
(1.5634)
=
(2032.42)2]r/2
per
per
phase
phase
suspension
pounds
per
conductor
2032.42
pounds
per conductor
= 65’20.67
pounds
per conductor
with
a safety
factor
strings.
For center phase V-string (fig. 54),
-=- a
sinA
32=
sin 80’
b
sinB
b
sin SO0
b = 32 603 (o-766 04) = 25 360 57 I,,
0.984 81
Use 30 OOO-lb insulator units.
Type 30X, 0 O line angle
Maximum
Maximum
low-point
distance
= 975.5 m (3200 ft)
sum of adjacent
spans = 975.5 m (3200
ft)
of 2.5
TRANSMISSION
138
LINE DESIGN MANUAL
Metric
Maximum
vertical
Maximum
wind
Resultant
load
Use
222
load
load
=
=
(975.5)
(975.5/2)
=
[(36
=
76 800
=
192 000
410-N
752)a
+
=
36 752
newtons
per
conductor
=
11 128
newtons
per
conductor
(11
newtons
insulator
(37.676)
(22.816)
128)a]1/2
per
newtons
=
38 400
newtons
per
conductor
phase
per
phase
with
a safety
factor
of 2.5
units.
U. S. Customary
Maximum
vertical
Maximum
wind
Resultant
load
Use
50 OOO-lb
load
load
=
=
=
=
=
(3200)
(3200/2)
[(8261.12)2
17 263.06
43 157.65
insulator
(2.5816)
= 8261.12
(1.5634)
(2501.44)
= 2501.44
pounds
per conductor
2 ] l/2 = 8631.53
pounds
per conductor
+
pounds
pounds
per
per
phase
phase
with
pounds
a safety
per
factor
conductor
of 2.5
units.
Type 30X, 5 o line angle
Maximum
low-point
Maximum
sum
distance
of adjacent
=
spans
792.5
=
m (2600
792.5
ft)
m (2600
ft)
Metric
Maximum
vertical
load
Maximum
wind load
Angle
load = 2 T(sin
Resultant
Use
177
load
928-N
=
=
=
=
=
(792.5)
(37.676)
= 29 858
(792.5/2)
(22.816)
= 9040
a/2)
= 2(63 165) (0.043
62)
[(29 858)a
+ (9040
+ 5510)2]1/2
66 428 newtons
per phase
166 070 newtons
per phase with
insulator
newtons
newtons
= 5510
=
per
33 214
a safety
conductor
per conductor
newtons
per conductor
newtons
factor
per
conductor
of 2.5
units.
U.S. Customary
Maximum
Maximum
vertical
load = (2600)
(2.5816)
=
wind load = (2600/2)
(1.5634)
=
= 2(14 200) (0.043
Angle load = 2 T ( sin a/2)
Resultant
load = [(6712.16)2
+ (2032.42
+
= 14 933.72
pounds
per phase
= 37 334.3 pounds
per phase
Use
40 OOO-lb
insulator
6712.16
2032.42
62) =
1238.81)2]1/2
with
a safety
units.
Type 3OA, 5 ’ line angle
Maximum
low-point
Maximum
sum
distance
of adjacent
=
spans
975.5
=
m (3200
975.5
pounds
pounds
1238.81
ft)
m (3200
ft)
per conductor
per conductor
pounds
per
=
7466.86
factor
of 2.5
conductor
pounds
per
conductor
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
139
Metric
Maximum
vertical
Maximum
Angle
wind
load
Resultant
Use
load
222
=
load
=
2 T(sin
load
=
(37.676)
(975.5/2)
a/2)
=
[(36
=
80 684
=
201
410-N
(975.5)
=
752)2
(22.816)
2(63
+
(11
newtons
710
insulator
newtons
=
36 752
newtons
=
11 128
newtons
165)
(0.043
128
+
per
62)
=
5510)2]r/2
5510
=
per
conductor
per
conductor
newtons
40 342
per
conductor
newtons
per
conductor
phase
per
phase
with
a safety
factor
of 2.5
units.
U. S. Customary
Maximum
vertical
load
=
(3200)
(2.5816)
=
8261.12
Maximum
wind load = (3200/2)
(1.5634)
= 2501.44
Angle
load = 2 T (sin a/2)
= 2(14 200) (0.043
62) =
Resultant
load
Use 50 OOO-lb
=
=
=
[(8261.12)2
I8 136.76
45 341.9
insulator
pounds
per
pounds
1238.81
per conductor
pounds
per
+ (2501.44
+ 1238.81)2]1/2
pounds
per phase
pounds
per phase with a safety
=
conductor
9068.38
factor
conductor
pounds
per
conductor
of 2.5
units.
Type 3OA, 15 ’ line angle
Maximum
Maximum
low-point
distance
= 792.5 m (2600 ft)
sum of adjacent
spans = 792.5 m (2600
ft)
Metric
Maximum
vertical
load = (792.5)
(37.676)
= 29 858 newtons
per conductor
Maximum
wind load = (792.5/2)
(22.816)
= 9040 newtons
per conductor
Angle
load = 2 T (sin a/2)
= 2(63 165) (0.130
53) = 16 489 newtons
per conductor
Resultant
Use 222
load
=
=
=
410-N
[(29 858)2 + (9040
+ 16 489)2]1/2
= 39 284 newtons
78 568 newtons
per, phase
196 420 newtons
per phase with a safety factor
of 2.5
insulator
per
conductor
units.
U. S. Customary
Maximum
vertical
load
=
(2600)
(2.5816)
=
6712.16
pounds
per
conductor
Maximum
wind load = (2600/2)
(1.5634)
= 2032.42
pounds
per conductor
Angle load = 2 T (sin a/2)
= 2(14 200) (0.130 53) = 3707.05
pounds
per conductor
3707.05)
2
]
112
=
8831.46
pounds
per conductor
Resultant
load = [(6712.16)2
+ (2032.42
+
=
Use 50 OOO-lb
17 662.92
pounds
= 44 157.3 pounds
insulator
units.
per
per
phase
phase
with
a safety
factor
of 2.5
TRANSMISSION
140
Type
30T
and
300
tension
LINE DESIGN
MANUAL
structures
Metric
Maximum
tension=
63 165
=
=
Use double
strings
newtons
126 330
378 990
per
newtons
newtons
of 222 ,410-N
conductor
per
per
insulator
phase
phase
with
a safety
factor
of 3.0
units.
U.S. Clrstor?larv
Maximum
tension
Use double
strings
Make
the
construction
a.
I4 200
pounds
per
conductor
=
=
28 400
85 200
pounds
pourlds
per
per
phase
phase
of SO OOO-lb
following
calculations
of the steel structure
Calculate
tabulation.
as follows:
=
The
the
conductor
calculations
insulator
(paragraphs
3.a.
limitation
chart:
tensions
are
with
shown
a safety
factor
of 3.0
through
3.g.)
to obtain
units.
to be used
for the
on figures
52 and
loading
53.
conditions
From
data
shown
these
figures,
use in the
in the
the
following
tensions
are
Tension
Loading condition
N
(lb)
63 165
(14 200)
No ice, 0.19-kPa wind, 15.5 OC (60 OF)
29 289
(6 583)
No ice, 0.48-kPa ( IO-lb/ft2 ) wind, 15.5 OC
34 791
(7 821)
No ice, no wind, 15.5 OC
28 083
(6 314)
13-mm (l/2+)
b.
the
for
ice, 0.19-kPa (4-lb/ft2)
wind, - 18 OC (0 OF)
Assume
a scale to be used for the distance
between
point
of origin),
and compute
the scale factor:
Metric
Let 1 mm = 7.2 m of bare conductor vertical force.
Vertical force of conductor = 20.928 N/m
Then, 1 mm = (7.2) (20.928,) = 150.68 N, and
1 N = l/150.68 = 0.006 636 58 mm (scale factor).
conductor
low
points
(vertical
scale
below
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
141
I/. S. Customary
Let 1 in = 600 ft of bare conductor weight,
Weight of conductor = 1.4340 lb/ft
Then, 1 in = (600) (1.434) = 860.4 lb, and
1 lb = l/860.4 = 0.001 162 25 in (scale factor).
Compute the vertical force of the insulator
C.
phase
factor:
or one-fourth
the insulator
force
string
per conductor
and
convert
to millimeters
one-half
(inches)
the
insulator
using
force
the low-point
per
scale
Metric
Insulator
string
force
=
1628
1628/4
= 407 newtons
(407) (0.006
636 58) =
N
per conductor
2.70 mm
U.S. Customary
Insulator
366/4
(91.5)
string
weight
= 366 lb
= 91.5 pounds
per conductor
(0.001
162 25)=
0.106 in
line deflection
angle scale
d. Compute
calibration
equal to the resultant
tension
at 15.5
pressure
angle:
in one
conductor
due
to the
line
(horizontal
axis to the
o C (60
right
’ F) final
of the origin)
with
with
0.48-kPa
the degree
(lo-lb/ft2)
wind
I;‘, = 2T(sin
a/2)
T = 34 791 N (7821 lb)
2 T = 69 582 N (15 642 lb)
Assume
be the
line
same
angles
as that
and
compute
computed
resultant
in paragraph
tensions
e. Assume
the
point
scale
of origin):
their
scale
2T(sinU/2)
N
(lb)
sina/2
40
50
60
and
values.
The
scale
must
scale
above
SC&
mm
on)
(682)
0.043 62
.087 16
3 035
6 065
(1363)
2)
(0.79)
(1.59)
.173 53
.130
65
.216 44
.300 71
.258
82
129 083
15 060
18 009
20
924
(2042)
(2716)
(3385)
(4704)
(4048)
ii:
100
139
120
:z;
(3:95)
- (4.72)
.342 02
.422 62
.500 00
23 798
29 407
34 791
(5350)
(6610)
(7821)
158
195
231
to be used for the sum.of
factor
3.b.
adjacent
spans
portion
of the chart
E,’
(7:7 1)
(9.12)
(vertical
TRANSMISSION
142
LINE DESIGN MANUAL
Metric
Let
1 mm
Note:
=
6 m of wind
This
scale
sum of adjacent
will
spans
span
= one-half
be doubled
may
the
in marking
be read
directly
sum
the
of adjacent
chart;
instead
that
spans.
is, 1 mm
of reading
will
one-half
equal
12 m so that
the sum
of adjacent
the
spans.
0.48-kPa wind on conductor = 16.357 N/m (from force triangle, fig. 52)
Then, 1 mm = (6) (16.357) = 98.142 N, and
1 N = l/98.142 = 0.010 189 318 mm (scale factor).
U.S. Customary
Let
1 in
=
500
ft of wind
span
= one-half
Note:
This scale will be doubled
the sum of adjacent
spans may
spans.
the
sum
in marking
the
be read directly
of adjacent
spans.
chart;
that is, 1 inch will equal 1000
instead
of reading
one-half
the sum
feet so that
of adjacent
IO-lb/ft2 wind on the conductor = 1.12 1 lb/ft (from force triangle, fig. 53)
Then, 1 in = (500) (1.121) = 560.5 lb, and
1 lb = l/560.5 = 0.001 784 12 in (scale factor).
f.
Calculate
angle
of bias lines
to be drawn
right
bias lines are used to automatically
add or subtract
due to a line deflection
angle. Because
the scale
the
same
as that
used
for
the
low-point
tan 8=
scale,
and left of the deflection
angle
the wind pressure
to or from
factor
used for the deflection
the
slope
of the
bias
lines
may
calibrations.
These
the resultant
angle scale
tension
must be
be determined
by
sum of adjacent spans scale factor
low-point scale factor
where
8 is the angle formed
by the
vary depending
upon the choice
e = tan-l
’ = tan-’
g.
Calculate
wind
with
angle
for
0.010 189 318
= tan-l
0.006 636 58
0.001 784 12
= tan-’
0.001 162 25
the
maximum
each
bias lines with
of scale factors
type
maximum
insulator
permitted
line
of suspension
angle,
tower:
the horizontal
previously
axis. The slope of the
determined
in paragraphs
bias lines will
3.b. and 3.e.
1.5353 = 56O55’ (metric)
1.5351 = 56O55’ (U.S. customary)
swing
angles
and
maximum
in each
negative
direction
wind
by using
with
maximum
minimum
permitted
positive
line
CHAPTER
Vertical
plus
load
one-fourth
IV-STRUCTURE
due to conductor
the
insulator
For one conductor,
LIMITATION
low-point
force
per
distance
equal
to one-third
CHARTS
the
sum of adjacent
conductor:
(20.928)
(350:)(2)
AND GUYING
+ y
= 5297.2
N, or
(’ ’ 50)(2) (1 434) + 366 = 1190 9 lb
3
4
*
Calculate
swing
angles
for
suspension
insulator
strings:
Metric
For
0.48-kPa
wind,
0’
line
angle
(30s
tower
with
positive
wind)
Wind = 350.5 (16.357) = 5733.13 N
e = tm-’
For
-0.48-kPa
8 =tan-’
For
0.48-kPa
5733.13
= tan- l 1.0823 = 47O 15’
5297.2
wind,
O”
line
angle
-5733.13 = tan-’
5297.2
wind,
5’
line
(30s
and
30X
towers
with
negative
_ 1.0823 = -47015
angle
(30X
tower
with
positive
wind)
2T(sin a/2) = 2 (34 791) (0.043 62) = 3035.17 N
8 = tan-1 3035’17 + 5733’13 = tan-1 1 6553 = 58051’
5297.2
For
-0.48-kPa
8 = tan’l
For
0.48-kPa
wind,
5O line
angle
(30A
3035.17 5733.13 = tm-’
5297.2
wind,
15 O line
angle
(30A
tower
with
negative
-0.509 32 = - 261059’
tower
with
positive
2T(sin a/2) = 2 (34 791) (0.130 53) = 9082.28 N
8 =tan-’
wind)
9082.28 + 5733.13
= tan- l 2.7968 = 70°‘19’
5297.2
wind)
wind)
143
spans
TRANSMISSION
144
LINE DESIGN
MANUAL
U.S. Customary
For
IO-lb/ftz
wind,
0’
line
angle
(30s
tower
with
positive
wind)
Wind = 1150 (1.121) = 1289.15 lb
1289.15
8
For
=tan-'
-lo-lb/ft2
8 = tan-’
For
llgog
lo-lb/ft2
wind,
= tan-’
0’
line
1.0825 = 47016’
angle
(30s
and
30X
towers
with
negative
wind)
- 1289.15
llgo.g
= tan-’ - 1.0825 = -47O16’
wind,
5’
line
angle
(30X
tower
with
positive
wind)
2T(sin a/2) = 2(7821) (0.043 62) = 682.30 lb
(j = tan-’
682’30
+ 128g’15
= tan-l
1 6553 = 58051’
1190.9
For
-lO-lb/ft2
8 = tan-’
wind,
5’
682.30-
line
angle
1289.15
(30A
= tan-l
tower
-0
509
with
lo-lb/ft2
wind,
15’
line
angle
(30A
tower
wind)
= _ 27DoO’
32
1190.9
For
negative
with
positive
wind)
2T(sin a/2) = 2 (7821) (0.130 53) = 2041.75 lb
e=tan-'
2041.75+
128g*15=tan-l
27970=7p19'
1190.9
the
The permissible
center
phase.
insulator
swing angle
It is desirable
to keep
the bottom
of the V-string
at all times
would cause wearing
of the metal-to-metal
greater
use in this respect.
With
a 50’
for the 30s
approximately
to prevent
contacts
insulator
steel
tower will
890 N (200
be limited
by the V-string
lb) of extra vertical
force
one leg of the V from becoming
slack, which
in the string.
We use a 100 o V-string
to permit
swing:
Metric
tan0 = 1.191 76=
on
on
5733.13 N (0.48-kPa wind on 350.5 m of conductor)
x
(X = low point in newtons)
CHAPTER
Thus,
a vertical
when a 0.48-kPa
required
force of X =
wind is blowing
to provide
4810
- 407
4403
+
this
(extra
=
means
insulator
252.9
the
percent
of the
line angle,
force
vertical
low
sum
LIMITATION
AND GUYING
CHARTS
4810 N is required
to hold the insulator
on a sum of adjacent
spans equal to
vertical
(one-fourth
890
5293/20.928
This
IV-STRUCTURE
plus
the
force)
force
=
extra
890
4403
on V-string)
145
string
at a SO0 angle
701 m. The conductor
N is:
N
=
5293
N
m of conductor
point
for
the
of adjacent
V-string
spans.
must
Therefore,
8 = tan- ’ (350s5) (*I c;;;;;o.g28)
be at least
for
252.9/(2)(350.5)
a V-string
with
=
a 0.48-kPa
0.36,
or 36
wind
and
0’
+ 407 = tan- l 1.007 87 = 45 “13’.
U. S. Customary
tan0 = 1.191 76=
Thus,
a vertical
when a lo-lb/ft2
to provide
this
1082
1289.15
x
weight
wind
weight
- 91.5
of
X =
is blowing
plus the
(one-fourth
(1 O-lb/ft2 wind on 1150 ft of conductor)
(X = low point in pounds)
1082
lb is required
on a sum of adjacent
extra 200 lb is:
Insulator
weight)
to hold
spans
=
990.5
equal
the
to 2300
(extra
vertical
weight
on V-string)
= 830.2 ft of conductor
This
percent
the low point
for the V-string
must be at least
sum of adjacent
spans. Therefore,
for a V-string
line
string
ft. The
at a 50’
conductor
angle
required
lb
990.5
+ 200
1190.5/1.434
means
of the
insulator
=
1190.5
lb
830.2/(2)(1150)
with a lo-lb/ft2
= 0.36, or 36
wind and a 0’
angle,
1289.15
8 = tan- l ( 1 150) (2) (o.36) ( 1.434) + g 1.5 = tan- l 1.008 05 = 4S” 13’.
Paragraph
To
4.
construct
the
structure
limitation
chart
a. Lay out the axes using the same
vertical
scale (see pars. 3.b. and 3.d.).
provided
b.
the
wind
the
Calibrate
degree
deflection
angle
the
horizontal
calibration
equal
pressure
on one
conductor
bias
right
resultant
to the
of the
tension
line
structures,
proceed:
for the horizontal
scale and the lower part
scale may be used for the sum of adjacent
are adjusted
axis to the
due
steel
scale factor
A different
lines
to the
for
of the
spans
accordingly.
origin
in degrees
at 15.5
’ C (60
deflection
angle
of line
OF)
(par.3.d.).
with
angle
deflection
0.48-kPa
(lo-lb/ft2)
with
TRANSMlSSlON
146
c.
Calibrate
calibrations
on a bare
d.
should
conductor
Calibrate
of the bare
be displaced
(pars.
3.b.
e.
lines
the
axis above
the vertical
and
axis below
due
lay
insulator
swing
g.
angle)
deflection
h.
Add
i.
List
to the
pertinent
notes
Conductor,
l
Conductor
Conductor
l
Ruling
Number
Line
in meters
(feet)
pressure
spans
for the
of adjacent
spans.
at 0.48 kPa
(par. 3.e.).
(10 lb/ft2)
distance
the
low
points
should
string
radial
angles
each
type
of insulator
of structure
swing
draw
in heavy
boundary
angle
spans
bias lines at the computed
angle, dependent
upon scale factors
scale and the distance
between
low points
scale (par. 3.f.). These
add or subtract
the wind
(par.
and
for
lines
chart
(sum
showing
on the
size and
span
and
3.g.).
pressure
to or from
the resultant
tension
of adjacent
steel
chart,
tower
spans,
low-point
distance,
and
line
deflection
data.
including:
type
or heavy,
and
maximum
design
wind)
size of insulators
limitation
problem
structure
Problem
a 115-kV
to be located
charts
for
the
example
problem
on steel
structures
follows
that shows the
limitation
and guying
(wood-pole
transmission
in an area
construction)
line with
with
a 0.77-kPa
procedure
charts.
a 242-mm2
(16~lb/fts)
for obtaining
(477-kcmil),
extreme
the
are shown
on figures
required
to prepare
ACSR,
wind
data
24/7
pressure.
not be a factor because
the resultant
force per unit length
of conductor
of 18.746
for this condition
is less than the 27.5345
N/m
(1.8867
lb/ft)
force for the NESC
The following
data is also assumed:
Maximum
Ruling
between
The
5.
An example
the wood-pole
Example
Assume
the origin
loading
(NESC
light,
medium,
maximum
tension
at full load
The structure
55 and 56.
Paragraph
for the sum
limits
limitation
of structure.
a table
l
l
(feet)
angle.
Draw in heavy
for each type
l
out
are used to automatically
to a line
in meters
equal to the vertical
force of the conductor.
The zero point
by a distance
equal to one-half
the vertical
force of the insulator
f.
Lay out the .deflection
used for the sum of adjacent
bias lines
origin
3.c.).
a protractor,
the
the
MANUAL
be at a distance
above the origin equal to the wind
of length
equal to one-half
the sum of adjacent
(no ice) conductor
below the origin
With
for
vertical
LINE DESIGN
initial
span
conductor
tension
(NESC
heavy)
single
conductor.
However,
this
will
N/m
(1.285 lb/ft)
full-load
condition.
=
33 362
N (7500
=
213.36
m (700
lb)
ft)
STRL TURE DATA
v
lef I&ion
V
Angle.
v
90
(dcp~l
eo
Tower
Type
Lme Angle
Maximum
Single Span (m)
Minimum Lme Angle
Mcxrmum
Line Angle
Mox. Sum of Adjacent
Spans (m
Minimum
Line Angle
Maximum
Line Angle
Mox. Low Point Distance
(m)
Conductor
Minimum
Line Angle
Maximum
Line Angle
Overhead
Ground
Wire
Minimum
Line Angle
Maximum
Line Angle
Maximum
Uphft
(N)
Conductor
Minimum
Line Angle
Maximum
Line Angle
Ovcrhcod
Ground
Mmimum
Line
Maximum
Line
30s
7
3%
30x
65’
30T
a-3i
487.5
396
467.5
3%
975.5
792.5
975.5
792.5
731.5
731.5
975.5
792.5
975.5
792.5
653.5
653.5
1036.5
653.5
036.5
653.5
3%
792.5
792.5
540.5
407.5
640
1097
975.5
1260
1371.5
1524
1524
1463
305
213.5
305
3%
254
3%
t
Wire
Angle
Angle
NOTES
This
chart
is based
on
Conductor
size
Conductor
loodmg
Conductor
tensions
the
Ruling
span
Insulators
following:
644 mmf AC%.
4517 (bundle
of two, 457-mm
spacing)
NESC Heavy. maximum
wind at lS.S*C-0.46
kPo
63 165 N maximum
per conductor,
initiol
conditions
34 790 N %r conductor
with
0.46-kPa
wind at IS.S*C
350.5 m
20 Units (146 ty 267 mm)
4
u
?
I
I i iAi i. i ““1 h
I’/
-*0
----
Id I
- -----
I
-----
I\
I\
$
+taox --I-+-
-10
Insulator
z
:
to
S*ing”Angle
Figure
tdegZesl
55.-Example
of a steel structure
limitation
chart (metric).
104-D-1078.
7
I
x
STRUCTURE
Tower Type
he
Anale
Moorimuk Siqle Span ( ft)
Mimmum Line Angle
Moximum Line Anqle
Max Sum of Adjacent Spans (ft)
Minimum Line Angle
hbximum Line AnpIe
Mar. Low point Dirtonce (ft)
conductor
Minimum Line Angle
Morimum Line Angle
Overhead Ground Wire
Minimum Line Angle
lo
Morimum Line Angle
Maximum Uplift (lb)
Conductor
Minimum Line Angle
lo
Moximum Line Angle
Overhead Ground Wire
Minimum Line Angle
Maximum Line Anole
IO
\
1 3osI 0.
IATA
30X
TT
-lo
lnrulotor
0
. ‘0
Swing Angle (degrees)
Figure
of a steel structure
limitation
30D
535
lb00
I300
I600
I300
I600
1600
2100
2600
2606
3200
2600
3200
2600
3600
3200
4200
2400
2400
3200
2600
3200
2600
4200
4200
4500
2600
2600
3400
2600
3400
20
woo
SW0
4600
1000
700
IO00
1300
633
l3DO
NOTES
This chart is based on the following:
Conductor size
1272 hcmil. ACSR. 4517 (bundle of two. 16% spocimll
NESC Heavy. maximum wind ot 6VF-IOlblft*
Conductor loading
14 200 lb morimum per conductor, initiol conditions
Conductor tensions
lo
7620 lb. per ConductOr with IO- Iblft’ wind ot 6O.F
Ruling spon
I IS0 ft.
lnsulotors
20 Units (5) by IO~ in.)
4
5
z
r
M
56.-Example
301
TF
1300
I300
‘\
-co
30A
Tiv
chart (U.S. customary).
104-D-1079.
CHAPTER
IV-STRUCTURE
units per
mm (S-3/4
string
by 10 in)
Seven insulator
146 by 254
Length
per
Vertical
LIMITATION
AND GUYING
string
force
(weight)
per
string
149
CHARTS
=
1194
mm
=
400
N (90
(47
in)
lb)
Wind
Everyday
Maximum
Design
for
Wood-pole
maximum
=
0.19
kPa
(4 lb/ft2)
with
=
0.38
kPa
(8 lb/ft2)
13-mm
a minimum
structure
(l/2-in)
radial
low-point
distance
designations
and
HS
=
tangent,
HSB
3AC
3A
=
=
=
tangent,
suspension,
large
small line angle, suspension
large line angle, suspension
3AB
=
large
3TA =
Paragraphs
charts.
a.
to one-third
the
sum
of adjacent
are:
line
angle,
vertical
and
load
suspension
tensions
calculations
dead end
the procedure
for the
are shown
loading
on figures
for making
conditions
57 and
the
calculations
shown
in the following
Assume
a scale to be used for the distance
between
point
of origin),
and compute
the scale factor:
Metric
Let
6 m of bare
lmm=
Vertical
Then,
conductor
force of conductor
1 mm = (6)(8.968)
1 N =
l/53.808
=
0.018
=
=
vertical
8.968
53.808
585
mm
force.
N/m.
N, and
(scale
factor).
U. S. Customary
Let
1 in
=
500
feet
of bare
conductor
Weight
of conductor
= 0.6145
Then,
1 in = (500)(0.6145)
=
1 lb = l/307.25
= 0.003
254
weight.
lb/ft.
307.25
lb,
7 in (scale
for
the
tabulation.
Tension
N
(lb)
13-mm (l/2&)
ice, 0.19~kPa (4-lb/ft2 ) wind, - 18 OC (0 OF)
No ice, 0.19~kPa (4-lb/ft2) wind, 15.5 OC (60 OF)
No ice, no wind, 15.5 OC (60 OF)
the
required
58.
Loading condition
b.
spans.
suspension
the conductor
data
equal
types
tangent
to 90’
line angle,
5.a. through
5.~. describe
Calculate
Conductor
ice
and
factor).
conductor
low
33 362
(7500)
11 748
10 872
(2641)
(2444)
points
(vertical
scale
below
TRANSMISSION LINE DESIGN MANUAL
150
DCm-570
(3.78)
Linear Force Factw
Rated Breaking
Slrength ,?l
Diameter.&*
TO,9
N
mm
-&
Teneton Lim~lations:
O&L&Z
Resultant:
Final *-!,25K
-N
Ares (A)&?i%mmd
Loaded,%.so%
-N
Temp. bell.
N
%-
by
o.oa
Date -
s
?*/06
.
7q.zyiJ
kPa Wind
-N
Final.~‘,
N/m
mm Ice CW-,,2/.//xd
htiat.%.33f%
computed
j/.
9. ?6fD
Doad Load FQC* (W’)
8.
(W”‘)
4
Permanent Set 0.00 02
Nhn
creep 0.000
N/m
Total 0.0002
N/m
Modulus. (E) Final m
x-R=
of Litmar hp.:
4’90
v’.52y/
FiM,
GPa
*,,;itiaia~GP:,
o&L&!-per%
/?77
msc
Initial
n’= 4.3782
AE /sr27/
N
1 TENSION. N
No Ice. No Wind (W’)
-
__
I
kPa Wind (W”‘)
No Ice#oWind
999
-
6 gs
0. flno
I
SPA# LEN
/pf
I
(W’)
0-m
D.O?574kPI
wind (WV”)1 - /
Permanent set a creep
1
No Ice. No Wind (W*)
Figure 57.-Conductor
(metric).
c.
force
Compute
the
to millimeters
Insulator
One-half
(200.17)
ha&J
I
432
15.5
32
4!4
sag and tension
vertical
(inches)
I 6.000
I
a33/
I 0.
/959
lo , n.74
/
I
1
/
I
I
I
I
I
I
calculation
s-253
621
I4kw.
I
!
I
I
I
form for example
problem
force (weight)
of the insulator
string
using the low-point
scale factor:
string
force
= 400.34
N (90 lb)
insulator
string
force
= 200.17
N (45 lb)
(0.018
585) = 3.720 mm or, (45) (0.003
254
7) =
on wood-structure
and
0.1465
convert
in
one-half
limitation
the
chart
insulator
CHAPTER
DC-676
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
(W’) -r?&/Js
lblft
Permamnt
/.
Wft
151
(6-76)
Rated Breaking
Load
Diameter
8. -946
Tension
Limitatiom:
1.7
doe
+&in.
Initial ,OF331Y-
ICO (w”)
Set O/XX&
creep
O.ooP~--
Total
0.00~
lb
Final ,!F_2L~Laded
Fiml. XF
Dead Weight
lb
inch
lb
OF -5e
-
Modulus. (E) Fimlmx
Am (A) fl&$ki?i2
in2
Temo. ~oeff. of Linear EXP.: * &=0.3~
41 -lb
K -lb
Fiml
Initial 3.
AE Ijs
10s lb/i&
//3
x lOS lb/i&?
lb
No ICO. No Wind (W’)
SP4N LENGTH(S)--FEET
Wlnd(w”’
Set L Creep
lb/f?
Pernunant
/
’ 2
- 40
1
I n
.na9
ff
6.92
4&O.
/5 \ S43i?
7
I
I
Inch ~~
ICI.
I
SPANLENGTH(S)-?a
FEET
I
I
No Ice. No Wind (W’)
60 I
Figure 58Ahductor
cu6tomary).
sag and tension calculation
ml
d.
Compute
deflection
calibration
equal to the
pressure,
in one conductor
I
I
form for example problem
angle scale (horizontal
resultant
tension
at 15.5
due to the line angle:
r;h
I
=
I
on wood-structure
axis to the right
‘C (60 ’ F) final
2 T(sin
11 748
I
I
limitation
of the origin)
with 0.19-kPa
chart (U.S.
with the
(4-lb/f?)
degree
wind
a/2)
N (2641
T =
lb)
2 T = 23 496 N (5282 lb)
Assume
line angles and compute
resultant
be the same as that computed
in paragraph
tensions
5.b.
and
their
scale
values.
The
scale
factor
must
TRANSMISSION LINE DESIGN MANUAL
152
5
10
0.043
.087
.130
.173
.216
.258
342
.422
.500
ii
25
30
40
50
60
e.
the
Assume
point
62
16
53
65
44
82
02
62
00
(230)
1025
2048
3 067
4 080
5085
6 081
8 036
9 930
11748
(0.75)
:i
(460)
scale to be used for the sum of adjacent
E
(1143)
(1367)
57
76
94
113
:;E;
(2641)
184
149
218
spans
portion
::z;
(2:99)
(3.72)
(4.45)
of the chart
(vertical
scale
above
of origin):
Let
1 mm
=
1 inch
6 m of wind
=
span
500 ft of wind
=
span
one-half
=
the
one-half
sum
the
of adjacent
sum
Note: This scale will be doubled
when marking
the chart,
that
equal 1000 ft, so that the sum of adjacent
spans may be read
will
the
sum
of adjacent
spans,
of adjacent
or
spans.
is, 1 mm will equal 12 m, or 1 inch
directly
instead
of reading
one-half
spans.
Metric
0.19-kPa
wind
on conductor
Then,
1 mm =
1 N = l/24.696
=
(6)(4.116)
= 0.040
4.116
= 24.696
492 mm
N/m
N, and
(scale factor).
U. S. Customary
4-lb/ft2
wind on conductor
= 0.282 lb/ft
Then,
1 in = (500)(0.282)
= 141 lb, and
1 lb = l/141
= 0.007
092 in (scale factor).
f.
Calculate
angle
of bias lines
to be drawn
right
bias lines are used to automatically
add or subtract
due to a line deflection
angle. Because
the scale
the
same
as that
used
for
the
low-point
scale,
and left
of the deflection
angle
the wind pressure
to or from
factor
used for the deflection
the
slope
of the
bias
lines
may
calibrations.
These
the resultant
angle scale
tension
must be
be determined
by
tane= sum of adjacent spans scale factor _
low-point scale factor
where
8 is the angle formed
by the
will vary depending
upon the choice
5.e.
bias lines with
of scale factors
the horizontal
previously
axis. The slope of the
determined
in paragraphs
bias lines
5.b. and
CHAPTER
IV-STRUCTURE
LIMITATION
0.040 492
= tan-’
0.018 585
’ = km-’
Compute
maximum
low-point
153
CHARTS
2.1787 = 65o20’ (metric)
0.007 092
= tan-l
I9 = tan-1 0.003 255
g.
AND GUYING
distance
2.1788 = 65’20’ (U.S. customary)
for
the
type
HS
structure
shown
on figure
59:
Crossarm: 67 by 241 by 7620 mm (2-S/8 by 9-l/2 in by 25 ft)
fbd’
Ultimate load = 6~
where: f = ultimate fiber stress of crossarm
= 5 1 02 1 kPa (7400 lb/in2 ) for Douglas fir
b = width of crossarm = 67 mm (2-S/8 in)
d = depth of crossarm = 241 mm (9-l/2 in)
L = length of crossarm projection = 1829 mm (72 in)
fbd’ _ (51 021) (67) (24w
6L
(6) (1829) (1000)
= 18 OS1 N or
= (7400) (2.625) (9-5)2 = 4058 lb
(6) (72)
Ultimate load for two crossarms = 36 104 N (8 116 lb)
Ultimate load withsafety factor of 4 = 9026 N (2029 lb)
Force of conductor with 13-mm (1/2-m) radial ice = 2 1.186 N/m (1.45 17 lb/ft)
Allowable low-point distance:
==426m
21.186
2029
-=
1.4517
or
1397 ft
At no load,
force of conductor = 8.968 N/m (0.6145 lb/ft)
factor of safety =
h.
Using
Compute
18 905
maximum
N (4250
8116
= 9.45
36 lo4
=
426 (8.968)
(1397) (0.6145)
low-point
lb),
b ased
distance
on test
for
data,
type
for
HSB
metal
structure
fittings
shown
on knee
on figure
braces
60:
at 45’
slope:
TRANSMISSION
154
LINE DESIGN
MANUAL
L
-2
..
2-
..
a
:n
k
“I
/
--
NvAngle
\
\
‘\
/
or side guy
For two X-braces.,
install bolts 457mm
(I8 in) apart.
II:
For 22.9-m (75-ft) structure
and under, install one X-brace.
For 24.4-m (80 ft) structure
and over, instal t two x-braces.
TYPE
Fiie
59,Type
HS
STRUCTURE
HS wood-pole
structure.
104-D-1080.
CHAPTER
IV-STRUCTURE
-I
LIMITATION
PLAN
AND GUYING
CHARTS
155
L-
/Angle
or side guy
For two x&braces, install
bolts 457 mm (I8 in) apart.
Structure
ground wires4
“OKge*
A
For 22.9-m (75-f-t) structure
and under, install one x-brace.
For 24.4-m (80-ft) structure
and over, install two x-braces.
TYP E
Metric
L
2
HSB
STRUCTURE
2490 7 620 3658
7 620 3658
2134 8 839 4267
69
II5
2490
138
I61
2439 IO 668 5182
Fiie
60.-Type
HSB wood-pole
structure.
104-D-1081.
TRANSMISSION
156
LINE DESIGN
MANUAL
Metric
US. Customary
Crossarm load = 18 905 (0.707 1) = 13 367 N
Allowable low-point distance:
4250 (0.7071) = 3005 lb
13 367
= 630.94 m
21.186
i. Compute
maximum
low-point
3005
= 2070 ft
1.4517
distance
for
type
3AC
structure
Metric
(7400) (2.625) (9-5)2 = 4870 lb
6 (60)
1217 lb
Ultimate load with a safety factor of 4 = 5414 N
Allowable low-point distance for double crossarm:
Compute
insulator
to prevent
the
effects
m
21(;;;;)
.
of various
sizes of hold
string
to increase
the effective
excessive
insulator
side swing.
conductor
The first
downs
Assume
18 288-mm
example
because
different
formula
allowable
sum
on the structure:
be attached
to the
bottom
of the
in adjacent
spans, and also
is the low-point
scale factor.
1 lb = 0.003 254 7 in
50-lb weight = 0.163 in
loo-lb weight = 0.325 in
150-lb weight = 0.488 in
of adjacent
(60-ft),
class 2 western
red
this is the lowest
strength
classes of poles are a function
for computing
the wind force
may
= 1676 ft
U.S. Customary
1 N=O.O18585mm
222.4-N force = 4.13 mm
444.8-N force = 8.27 mm
667.2-N force = 12.40 mm
this
that
low-point
distance
value shown below
Metric
k.
Compute
the maximum
determining
the wind loading
61:
2-518 by 9-l/2 in
(51 021.52) (67) (241)2 = 2l 662 N
(1000) (6) (1524)
j.
on figure
U.S. Customary
Crossarm section = 67 by 241 mm
fld=
Ultimate load = 6~
2(5415L511
21.186
shown
cedar
wood
spans
on a type
poles (western
permitted
by
of the pole circumference,
on a pole may be derived
HS
structure
(fig.
59)
by
red cedar data are used for
USBR
specifications).
The
see table B-3 in appendix
using figure 62:
B. The
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
-Structure
ground wires--=
TYPE
3,
Metric,
69
115
STRUCTURE
mm
A
2
YT
1982 3658 1372 343
1982 4267 1524 610
Figure 61.-Type
3AC wood-pole
U.S. Customary, ft-in
A
6-6
6-6
structure.
2
Y
14-O 4-6
14-O 5-O
104-D-1082.
T
l-l&
2-O
157
TRANSMISSION
158
d2
0”
LINE DESIGN
H
AX-
d2- diameter of pole at top
dl - diameter of pole a-t b&tom
H - height of pole
t
dl 1 O
Figure 62.~Single-line
compute wind force.
sketch
For pole,
of wood
pole showing
values
needed
to
Y-Y1
x-x,
=x2 - Xl
Y2 - Yl
General form of equation:
Then
MANUAL
y-H
x-4
=o - H d, - d,
x = (Y - Hi
,
-
d2 1
-H
+d,=(y-
Let the force of wind on dy l X be F in kilopascals
moment
of the wind force on a pole above ground
is:
H)k+d,,wherek=F
(pounds
per
H
c
Fx dy*y,
+ Fx dy*y, + . . .
0
H
=F
yb-H)k+d,ldy
/ 0
=F
H
I
WY2 - kHy + dzy)dy
0
square
4
foot).
-
d2
Then,
the
total
CHAPTER
Substituting (d Imeters
(square
dz)/-Hfor
feet)
IV-STRUCTURE
k,
the
LIMITATION
moment
AND GUYING
in newton-meters
CHARTS
(pound-feet)
on an area
is:
- d,)fi’
=F
(d, - d, )H2 d, H2
2
+ 2
1
1
- d2)H2 - 3(d, - d2)H2 d2.H2
-6
+ 2
1
d,H’
+2
=F
I
=F
=
H= d, +2.d,
-y
3
I(
9
FH 2(d 1 + 2d, )
in lb*ft if diameters are in feet, or
6
= FH2W, + 26,) in Nom if diameters are in millimeters, or
6000
= FH2W, + 24 1.111lb* ft if diameters are in inches.
72
159
in square
TRANSMISSION
160
LINE DESIGN
MANUAL
Metric
Mp =
FHZ’(d, + 26,)
6000
, where
Mp = moment
M =(0.383 04)(1000)(15.850)2
[404.34+2(202.18)]
= 12970N.m
6000
P
U.S. Customary
Mp =
The
maximum
IO-mm
allowable
(3/8-in)
high
SAS (sum
strength
of 21 418-N
(4815~lb)
on figures
63 and 64.
DCm-I70
FH2(d, +2d,) 8(52)2 [ 15.92+2(7.96)1
72
=
72
initial
steel,
of adjacent
7-strand
condition.
spans)
overhead
Sag and
L can now
ground
tension
wires
calculations
= 9566 lb-ft
be found
with
by statics.
a maximum
for
the
ground
Assume
full-load
wire
are shown
(S-78)
M
coN0ucTom /o-mm.
-
.-=hJ
.-/JJ+r
Rotad
Making
Stmngth
Dimeta
.&mm
Tmaim
Limtatiana:
Initial.FINI
d--&--N
9c.33f*
.o,
.-
-N
2s
% -N
LUdDdd.~~.Y)%
Finsl
cawutd
NO I-.
-N
*-,--lS.Sg:
w
bv
Date
No Wind
N
-
(W’)
Figure 63Averhead
chart (metric).
ground wire sag and tension calculation
form for example problem
on wood-structure
two
tension
limitation
CHAPTER
IV-STRUCTURE
LIMITATION
km2
AND GUYING
CHARTS
$A6CKCUUTloM
161
0. #f&f
6=/5'+Q'
LOAOIWGA&;'*
7-wire
Ratad ErakIng Load -lb
Dlamotu &d&L
inch
Tonslat
&b
oFA?L%
Final.
-
LM
Flml.
,-!A%
aO?F
WW-
LOADING
NO la.
bad Weight (W')-d!d;73
+ kin. ~a fw") .p.ld7
Limitation:
Inithl.~
OFAL%
-
tb
Wol@t Fntm:
-
(L -lb
Dam
lb
Am
lb
Tamp. coan.
IbItt
(A)
tw”‘)
/*3/c
of Llnu
In2
Exp.:
Q&Q
o.oooonlPu~
[~[LllwnmlLEwlnJ
lb/n
Wind ,A
Resultant:
-lb
Modulw.
*x:
&.q
bt=
&ac
O.bO
0.00
(E) Flrl3j:x
Initlal~.
0
100 IWid
I l@ lb/Id
Flnl AE ;zInitlaIAE
/a
SMfAcloR 1 SAG,R
7
I
Total
Iblft
*:nn
izIE.
Fumsnont sol O.ooJn~
crap 0.00
lb/h
lb
lb
1 SN,Ib
1 TENSJON,lb
No Wind (w’)
F’iie
64.-Overhead
ground
chart (U.S. customary).
wire sag and tension calculation
Using
base:
the
(2 OGW)
sketch
(wind
shown
force
cond.)
(wind force
allowable
moment
force
on pole)
Figure 65.~Single-line
sketch of one pole of
a type HS wood-pole
structure.
form for example problem
on figure
on iced
65, and
OGW)
taking
(moment
on iced cond.)
(moment
on pole) (2 poles)/(safety
(2 poles)]
on wood-structure
moments
arm)
arm)
(l/2
factor
(l/2
limitation
about
SAS)
the
+
SAS) = [(max.
of 2)] - [(wind
(3.
TRANSMISSION
162
LINE DESIGN MANUAL
Metric
(2) (13.222) (15.70) (L/2) + (3) (17.96) (13.87) (L/2) = (250 5255’ (2)- (2) (12 970)
415.1708 L/2 + 747.208 L/2 = 250 555 - 25 940
L12 = 224 615 = 193.24
1162.379
L = 386.48 m
U. S. Customary
(2) (0.9066) (5 1.5) (L/2) + (3) (1.23 1) (45.5) (L/2) =
(184 8200) (2) _ (2) (9566)
93.380 L/2 + 168.031 L/2 = 184 800 - 19 132
L/2 =
165 668
= 633.74
261.411
L= 1267ft
1.
(fig.
Compute
59)
for
the allowable
various
line
maximum
sum
of adjacent
spans
on a type
HS structure
with
angles:
Metric
FH2(d, +
6000
w2)
= (0.383 04) (1000) (3.51)2 i246.63 + 2(202.1-8)] = 512 Lo1 Nem
6000
U.S. Customary
FH’(d,
+ 2d,) = (8) (1 1.5)2 19.71 + 2(7.96)1 = 376 .6 lbeft
72
72
X-brace
CHAPTER
IV-STRUCTURE
Using
the
LIMITATION
sketch
shown
AND GUYING
on figure
66, and
CHARTS
taking
163
moments
about
the
base:
(2
OGW)(2 Ga,. sin
OGW)
(mbment
(l/2
(moment
arm)
SAS)
factor
=
a/2)
(moment
arm)
(l/2
+ (3 cond.)
[(max.
of 2)] - [( wind
allowable
force
arm)
SAS)
( wind
+
(2 OGW)
(wind
force
+ (3 cond.)
(2 T&,x.
sin
force
on cond.)
(moment
moment
on pole)
on
pole)
on
a/2)
arm)
(2 poles)/(safety
(2 poles)]
Figure 66.-Single-line
sketch of top portion
of a type HS woodpole structure with
X-brace.
Metric
(2) (42 836) (sin a/2) (3.35) + (2) (13.222) (3.35) (L/2)
+ (3) (17.96)(1.52)(L/2)
= (56 870) (2)/2 - (2) (512)
287 001
592 063
592 063
6936.88
Assume
A line
L/2 + 305 062 (sin
L/2 = 55 849
L = 55 849
L = 654.35
(sin a/2)
+
88.587
(sin a/2)
(sin a/2)
+
+
170.700
85.35
(sin a/2)
+
values for L and
solve
for
a/2)
sin a/2
aI2
654.35
300
0
0
0.051 08
0.094 33
0
2’0’55’
5O24’
these
tabulated
82.113
L/2 = 56 870 - 1021
values
should
he drawn
a
0
5050’
10@48’
on the
sum
of adjacent
U. S. Customary
(2) (9630) (sin a/2)
(11)
+ (3) (1.231) (5) (L/2)
22 747.2 (sin a/2)
+
(2) (0.9066)
(11) (L/2)
+ (3) (15
= (41 945) (2)/2 - (2) (376.6)
+
L = 2144.86
(1.52)
a:
L, m
representing
+
+ (3) (66 724) (sin a/2)
’
000)
(sin
a/2)
(5)
spans
chart.
TRANSMISSION
164
Assume
values
for
L and
solve
for
ft
L,
for
a working
western
red cedar:
stress,
at 15.5
a
42
0
0.050 33
0.094 29
fiber
MANUAL
a:
sin a/2
2144.86
1000
0
Assuming
LINE DESIGN
0
2053’
5O24’
’ C (60
o F) with
no wind
load,
$$)
= 5.6 safety factor
ultimate fiber stress = 38.612 MPa
or ($ii
working stress
6.895 MPa
With
(1844
(2
a 15.5
‘C
lb) on the
OGW)
(60
(2 Tsin
moment
OF)
overhead
a/2)
on wood
no wind
tension
of 10 872
ground
wire,
the
moment
(moment
arm)
+
(3 cond.)
(2 poles)/(safety
factor
pole)
0
5O46’
1O”48’
N (2444
lb)
equation
on the
would
(2 Tsin
a/2)
of 6.895
MPa
(1000
conductor,
lb/ins)
and
8205
N
be:
(moment
arm)
=
(max.
allowable
of 5.6)
Metric
(2) (16 410) (sin a/2)
(3.35)
+ (3) (21 744) ( sin Q /2)
109 947 (sin U/2)
+ 99 413.57
(sin a/2)
= 20 310.71
(1.524)
=
(56
870)
(2)/5.6
209 360.57
(sin a/2)
= 20 310.71
sin a/2
= 0.097
01, a/2
= So 34 ’
a = 11’08’
U.S.
Customary
(2) (3688)
(sin a/2)
(11)
sin a/2
= 0.096
99, a/2
a = 11’08’
If this
angle
had
been
+
=
less than
be drawn on the sum of adjacent
using the previously
tabulated
m.
Compute
61) for various
the
two
(3) (4888)
5’34
’
(sin
the
angle
spans
angles.
largest
conductors
Example
: without
(2 cond.)
shear)
(2T,,,.
shear
sin a/2)
are guyed
(5)
=
(41
computed
945)
(2)/5.6
previously,
then
chart at 11 o 08 ’ from 0 to the intersection
This means that the original
line would
the allowable
sum of adjacent
line angles. Assume
conductor
outside
a/2)
from
spans due to bolt
on inside of angle
pole
on outside
a vertical
line
would
with the line drawn
be cut off at 11 o 08 :
shear on a type 3AC structure
is guyed to top of middle
pole,
(fig.
and
of angle.
plates
+
(2. cond.)
(wind
force
on iced
cond.)
(l/2
SAS)
=
(allowable
bolt
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
165
Metric
(2) (2) (33 362) (sin a/2) + (2) (17.959)
(L/2)
133 448 (sin a/2) + 17.959
L = 8123.53
7430.70 (sin a/2) + L = 452.34
Assume
values for L and solve for a:
sin a/2
Lm
452.34
200
0
=
(10 831.37)
aI2
0
0.033 96
0.060 87
0
lO56’
3 O29’
(0.75)*
a
0
3O52’
605 8’
U. S. Customary
(2) (2) (7500)
24 378.35 (sin
Assume
Example
values
(sin
a/2)
a/2)
for
+ L = 1507.92
L and solve for a:
+
(2)
(1.2306)
(L/2)
= (2435) (0.75)*
L, ft
sin a/2
aI2
a
1507.92
1000
0
0
0.020 83
0.061 85
0
1011’
3O32’
0
2022’
7004’
a/2
a
: with
shear
plates
Metric
633 448
7430.70
(sin a/2)
(sin a/2)
Assume
values
for
+
17.959
+
L =
L
and
L = 26 689.2**
1486.12
solve
for
a:
km
sina/
450
225
0
.0.139 44
.169 72
,199 99
8OOl’
9O46’
1 lO32’
16OO2’
19032’
23OO4’
* and l * Data from National
Design Specifications
for Stress-Grade Lumber and Its Fastenings,
1973 Edition,
National Forest Products Association, Washington
D.C.
l Part VI Bolted
Joints:
Paragraph 600-K-3.-The
tabulated loads (table 12 for double shear) shall be used for a main member which
is twice the thickness of the thinnest side members (2-5/8 in x 2 = 5-l/4 in). Permissiile load = 2435 lb =
10 831.37 N.
Paragraph 600.G-2.-When
joints are to be exposed to weather, .75 percent of the tabulated loads apply.
l
* Part V Timber Connector
Joints:
Paragraph 500-B-2.-An
assembly with two connector units of the same size used in contact faces with the
connectors concentric with the same bolt axis, the total allowable connector load shall be the sum of the allowable
connector loads given for each connector unit used (table 9).
TRANSMISSION
166
LINE DESIGN
MANUAL
U.S. Customary
30 000 (sin a/2) +
24 378.35 (sin a/2)
Assume
for
values
for
L, ft
sin a/2
2000
1000
0
0.117 96
.158 98
.200 25
To be practical,
assume
type HS structure.
n.
Compute
Full
load
Find
strength
a/2)
2Tsin
A 60’
tension
for
angle
a safety
35 585 N (8000
Let
points
=
a 60’
on chart
Then’ ’ N
Using
same
line
6046’
9009’
1 l/033’
maximum
sum
of single
insulator
33 362
N (7500
of adjacent
(as computed
spans
string
used
(upper
limit)
on angle
type
3AC
as
structures:
under
or
par.
due to the
5.d.)
=
218 mm
(8.6
in)
1 lb =+j=O.OOl
(20 OOO-lb)
= 21.186
line
angle,
insulator
units
N/m
(1.4517
gives
lb/ft).
and
conductor
V
be the
a working
Then,
HZ + V2 = (35 585 N)2 or (8000 lb)2
H(N)=&35
for
lb)
218
=-=O.O065446mm
33 362
force
131~32’
18O18’
23’OO6’
angle:
factor
of 2.5 on 88 964-N
lb). F orce of iced conductor
H be the horizontal
in adjacent
spans.
a
aI2
= 2(33 362) (0.5) = 33 362 N,
= 2(7500) (0.5) = 7500 lb
30’
line
the
limitation
conductor
2 T(sin
L = 6000**
1.2306
+ L = 4875.67
L and solve for a:
585)2 - Y2 or H(lb) = J(8000)2
- V2
force
maximum
between
of
low
CHAPTER
Solve
for
H by
IV-STRUCTURE
assuming
low-point
LIMITATION
AND GUYING
CHARTS
167
distances:
Metric
Low point,
m
H,
V2
v,
N
N
0
4
8
12
16
21
23t.2
414.4
711.4
948.8
186.0
233
231
226
218
205
187
35 585
35 332
34 561
33 237
31289
28 591
0
200
400
600
800
1000
17 953 864
71815 455
161584 175
287 261821
448846596
U. S. Customary
Low point,
ft
0
500
0
Since
angle
structures
with
0
725.85
1451.70
2177.55
2903.40
3629.25
4355.10
1000
1500
2000
2500
suspension
H,
lb
in
8000
7967
7867
7698
7455
7129
6711
9.17
9.14
9.02
8.83
8.55
8.17
7.70
V2
V,
lb
2
4
8
13
18
insulators
526 858
107 433
741 124
429 732
171456
966 896
are limited
preceding
limitation
will not have much bearing.
To show the
66 723-N
(15 OOO-lb) insulator
units are to be considered.
Then,
have a working
tension
of 26 689 N (6000 lb) and,
H(N)
Solve
for
= &26
H by assuming
- V2
689)2
low-point
to a maximum
effect
with
line
of such calculations,
a 2.5 safety factor,
or H(lb) = J(6000)2
- V2
distances:
Metric
Low point,
m
0
200
400
600
800
1000
v,
N
V2
423$2
8 47414
12 711.6
16 948.8
21 186.0
17 953 8640
71815 455
161584 775
287 261821
448 846 596
H,
-
N
26 689
26
25
23
20
16
350
308
467
617
231
angle
mm
175
172
166
154
135
106
of 60 O, the
assume
we would
TRANSMISSION
168
LINE DESIGN
MANUAL
U. S. Customary
Low point,
lb
0
6000
526858
2107433
4141 124
8429732
13171456
18966 896
5956
0
7250.85
1451.70
2171.55
2903.25
500
1000
1500
2000
2500
3000
o.
Determine
limitation
angle
of single
3629.25
4355.10
of bias lines
insulator
strings
to be drawn
under
H,
V2
17
ft
on the
various
-
6.88
6.83
6.68
6.41
6.02
5.48
4.73
5822
5591
5251
4778
4127
sum of adjacent
combinations
in
spans
chart
for reading
of loadings:
Metric
Sm11 of adjacent
For SAS = 600
spans scale, 1 mm = 6 m (from
par. 5.e.)
m, wind span = l/2 SAS = 300 m, 300/6
Conductor
with
13-mm
ice and 0.38-kPa
The wind load on 300 m of iced conductor
1 N = 50/5387.7
= 0.009
280 4 mm
wind,
=
wind
(300)
=
force
=
(17.959)
50 mm
on chart
17.959
N/m
= 5387.7
N
From figure 67,
tan
0.008 280 4
6 (From
= 0.006
o*oog2804=141802
544 6
’
8 = 54O48’
paro. fin.)
Figure 67.-Force triangle showing angle
of bias lines for wood-structure
limitation
chart (metric).
U. S. Customa fy
Sum of adjacent
spans scale, 1 in = 500 ft (from
par. 5.e.)
= 1000 ft, 1000/500
For SAS = 2000 ft, wind span = l/2 S&I
Conductor
The wind
1 lb
=
with
l/2-in
ice and 8-lb wind,
load on 1000 ft of iced conductor
2/1231
=
0.001
624
wind
=
force
= 1.231
(1000)
(1.231)
=
2 in on chart
lb/ft
= 1231
lb
7 in
From figure 68,
._ 0.001 624 7 = 1 416 85
km8 -0.001 1467
*
0.001 624 7
(From poro. 5.n.)
8 = 54O48’
Figure 68.-Force
triangle
showing
angle of bias tines for wood-structure
limitation
chart (U.S. customary).
the
CHAPTER
p.
Compute
IV-STRUCTURE
conductor
guying
LIMITATION
for H-frame
type
AND GUYING
structures
with
CHARTS
no guys
169
on the overhead
ground
wires:
T
When
a transmission
line
which
must be considered
side of the angle structure,
by the
two
a/2),
legs of the
see figure
wind
blowing
both
spans
case that
also
on the
could
use more
heavy
and
areas,
instead
NESC
loading
in all design
the resultant
work.
force
guying,
conductor.
happen.
We
assumption
values
loading
of the
values
The
This
for
value
that
usually
pressure,
and
0.57
called
for
in NESC
and medium
loading
Where extreme
wind
the
is highly
areas
areas
loading
kPa
force
a force
wind
blows
add
250.B.:
result
of
perpendicular
to the
safety
NESC
0.19
worst
factor.
for
light
kPa
and 0.43 kPa (9 lb/ft2)
on the line (rule 250.C.)
to
it is the
(8 lb/ft2)
for
is 2 T(sin
is the
but
kPa
(12 lb/ft2)
rule
force
that
improbable,
0.38
created
is the same on each
of the angle formed
of the resultant
consider
will
wind
is a horizontal
If the line tension
will be on the split
assume
line.
This
practical
line.
there
we also must
transmission
medium
heavy
areas.
direction,
transmission
69. For
of the
changes
We
NESC
loading
(4 lb/ft2)
in NESC
is greater
for
light
than
the combined
ice and wind load (or wind load alone) prescribed
in rule 250.B.,
then
the proper
values taken from the wind pressure
map (fig. 250-2 of NESC)
should
be used for all structure
and guy loading
computations.
Figure
69.-Force
triangle
showing
resultant
conductor
force due to line angle.
Example
H =
:
2
T (sin
a/2)
+
(wind
force)
(L /2)
Metric
H = 2(33 362) (sin a/2) +
(0.383 04) (1000)
1
L/2
= 66 724 (sin a/2) + 17.961 (L/2)
= 66 724 (sin a/2) + 8.98 L
U. S. Customary
H = 2(7500) (sin a/2) + [(F)
(8;l
L/2
= 15 000 (sin a/2) + 0.6155 L
Using
11-mm
(14 500 lb),
(7/16-in),
a safety
7-wire,
factor
high-strength
of 2.67,
and
steel
guy wire
set at an angle
with
of 45’
a breaking
to the
strength
pole:
of 64 500
N
TRANSMISSION
170
LINE DESIGN
MANUAL
Metric
64 500
267
(0.707 1) = 17 080 N of horizontal pull per guy wire
U. S. Customary
14 500
267
(0.7071) = 3840 lb of horizontal pull per guy wire
.
Then,
guying
structures
(2
of the horizontal
is determined
0-9
by
farces
the
of the
moment
conductors
and overhead
ground
wires
on H-frame
equation:
%,a,.
sin a/2)
(moment
arm)
(2
(l/2
SAS) + (3 cond.)
(2 T,,,. sin a/2)
(moment
arm) (l/2
SAS) = ( a 11owable
+ (2 OGW)
( wind
(moment
arm) +
horizontal
load
force
on OGW)
(3 cond.)
on guy)
(moment
(wind
force
(moment
arm)
- (wind
poles)
Metric
(2)
(2)
+
=
1 344
+
4 120
- For
(21
one
418)
guy:
(sin
(3) (2) (33 362)
(17 080) (12.040)
a/2)
(15.697)
+ (2) (13.231)
(15.697)
(L/2)
(13.868)
+ (3) (17.961)
(13.868)
( sin a/2)
L/2 + 2 775 985.30
793.38
( sin a/2)
+
415.48
L/2 =
179
703.69
+
1162.729
778.68
(sin
a/2)
L/2 =
L = 179
4 120 778.68
(sin a/2)
+ 581.364
7088.12
(sin a/2)
+ L = 309.107
Assume
values for L and solve for
Lm
309.107
150
0
For two guys:
4 120 778.68
(sin
7088.12
(sin
a/2)
Assume
values
for
Lm
662.83
300
0
a/2)
+
L
(L/2)
- 25 939.51
747.249
+
179
(sin
a/2)
703.69
703.69
a:
sin a/2
al2
a
0
0.022 45
.043 61
0
1417’
2030’
0
2O34’
5000’
L = (2)
581.364
(17
080)
(12.040)
- 25 939.51
L = 662.832
and
solve
for
a:
sin
a/2
0
0.046 96
.093 51
a/2
0
2Wl’
5422’
a
0
5O22’
lOO44’
=
385
arm)
on cond.)
346.89
on
CHAPTER
IV-STRUCTURE
U.S. Customary-For
(sin
(2) (2) (4815)
one
a/2)
LIMITATION
AND GUYING
CHARTS
guy:
(51.5) + (2) (0.906) (51.5) (L/2)
(45.5) + (3) (1.231) (45.5) (L/2)
(3) (2) (7500)
( sin a/2)
3840 (39.5) - 19 132
+
=
991 890 (sin a/2)
+ 93.318 L/2 + 2 047 500 ( sin a/2) + 168.032 L/2
a/2) + 261.35 L/2 = 132 548
L = 132 548
3 039 390 (sin a/2) + 130.67
23 260.044
(sin a/2) + L = 1014.372
Assume
values for L and solve for a:
3 039
390
For two guys:
3 039 390 (sin
23 260.044
(sin
values
sin a/2
at2
0
0.022 11
.043 61
1 O16’
ft
1014.372
500
0
Assume
Compute
conductor
conductor
and
on inside
guyed from the outside
overhead
ground
wires
two
conductors,
0
0
2032’
SO00
2”‘30’
at2
a
0
0.050 52
.093 51
0
2O53’
5”22’
0
5046’
10044’
overhead
of angle
ground
is guyed
one
wire
to top
pole. Two conductors
will
will be guyed off together.
guying
of center
be guyed
for
pole,
off
a type
and
together,
arm)
horizontal
+
(2 cond.)
load
( wind
656.86
656.86
7429.88 (sin
(sin
one conductor
on guy)
(moment
arm)
a/2)
(13.868)
+
(2)
(17.961)
(13.868)
(L/2)
a/2)
+ 498.166
L/2 = 205 733.62
a/2) + 249.083 L = 205 733.62
a/2) + L = 825.964
(sin
(fig.
and
on cond.)
= (17 080) (13.564) - (2) (12 969.75)
1 850
structure
outside
force
Metric
(2) (2) (33 362) ( sin
3AC
two
conductors
and
guy:
(moment
(2 c0nd.j (2 Tmax. sin a/2)
(l/2
SAS) = (2 guys) ( a 11owable
1 850
548
a
sin a/2
ft
2175.159
1000
0
For
132
a/2) + 130.67 L = (2) (3840) (39.5) - 19 132
a/2)
+ L = 2175.159
for L and solve for a:
L,
q.
=
(sin
L,
Assume
171
(moment
- (wind
arm)
on poles)
61).
are
two
TRANSMISSION
172
Assume
values
for
L
and
solve
for
LINE DESIGN
MANUAL
a:
La
sin a/2
ai2
600
300
0
0.030 4 1
.070 79
,111 17
1044’
4003’
6O23’
a
3 O28’
8006’
112~46’
U.S. Customary
a/2) (45.5) + (2) (1.231)
+ 112.021
L /2 = 170
1 365 000 (sin a/2)
+ 56.01
L = 151 748
24 370.648 (sin a/2) + L = 2709.302
Assume
values for L and solve for Q:
(2) (2) (7500)
1 365
000
(sin
(sin
a/2)
L, ft
two
conductors,
0.029 10
.070 14
.lll 17
two
(L/2)
= (3840) (44.5) - (2) (9566)
880 - 19 132
sina/
2000
1000
0
For
(45.5)
a/2
a
1040’
4001’
6’23’
3O20’
8002’
12O46’
guys:
Metric
1 850
Assume
(sin a/2)
+ 249.083
L = (2)
a/2) + L = 1756.068
values for L and solve for a:
656.86
7429.88
(17
080)
(13.564)
- (2)
(12 969.75)
(sin
sin a/2
Lm
0.155 60
.195 97
.236 35
600
300
0
aI2
8O57’
11°18’
13O40’
a
17054’
22O36’
27 O20’
U. S. Customary
1 365
000
(sin
a/2)
+
56.01
24 370.648
L =
Assume
solve
(sin a/2)
+
values for L and
L = (2) (3840) (44.5) - (2) (9566)
5760.186
for a:
L, ft
sin a/2
2000
1000
0
0.154 29
.195 32
.236 36
aI2
8O52’
11015’
13O40’
a
17044’
22O30’
27 O20’
CHAPTER
For
one
conductor
and
IV-STRUCTURE
two
overhead
LIMITATION
ground
wires,
AND GUYING
one
CHARTS
guy:
Metric
(1) (2)
(33
362)
+
(2)
(2)
=
(17
080)
6860.892
Assume
(sin
(21
a/2)
418)
(sin
(14.326)
a/2)
(sin
values
(14.326)
a/2)
- (12
+
(1)
(14.326)
(17.961)
+
(2)
(14.326)
(L /2)
(13.2318)
(14.326)
(L/2)
969.75)
+ L = 728.186
L and solve for a:
for
sin, a 12
aI2
0.018 68
.062 41
.106 14
1004’
3O34’
6O05’
Lm
600
300
0
a
2OO8’
7OO8’
12010’
U.S. Customary
(1)
(2)
(7500)
(sin
a/2)
(47)
+
( sin a/2)
+ (2) (‘4 (4815)
(1)
(47)
(L/2)
(0.906)
(47)
(1.231)
(47)
+
(2)
(L/2)
= (3840) (47) - 9566
22 517.410
(sin a/2)
+ L = 2390.071
Assume
values
for L and solve for a:
For
one
L, ft
sin a/2
aI2
a
2000
1000
0
0.017 32
.061 73
.106 14
0°S9’
3032’
6Qo5’
lO58’
7w4’
12010’
conductor
and
two
overhead
a/2)
+
+ L =
318.213
1497.131
ground
wires,
two
guys:
Metric
2 183 225.096
6860.882
(sin
Assume
(sin
a/2)
values
for
L and solve
La
for
L = (2) (17 080)
0.130 76
.174 49
.218 21
42
7030’
lPO3’
12036’
U. S. Customary
1 610 220
22 517.410
(sin a/2)
(sin a/2)
+
L = (2) (3840) (47) - (9566)
L = 4913.914
71.510
+
.- (12 969.75)
a:
sina/
600
300
0
(14.326)
a
1SOOO’
20° 06’
2Pi 2’
173
TRANSMISSION
174
Assume
values
L and solve
for
L,
for
0
762 mm
guy
attachment
(2.5
ft)
two-conductor
a total
load
for
(three
conductors
two
attachment
between
the
two
guy
attachment
guys
and
attachment
The
ground
required
points
overhead
with
ground
for the other
guy attachment
and two overhead
points.
two
very
little
wires
is separated
two conductors
and
points,
it is satisfactory
wires)
number
14O52’
20000’
25012’
guyed
of guys
load
from
an imaginary
(as calculated)
transferred
the
at each
(2 cond.1 (2 T,,,.
(1 cond.)
attachment
(moment
on poles)
sin a/2) (moment
arm) + (2 cond.)
( wind force on cond.)
arm) + (1 cond.)
(wind force
(2 T,,,. sin a/2) (moment
arm)
(l/2
SAS)
(2) (2) (33 362) (sin a/2)
=
(2 guys)
sin a/2) (moment
arm) + (2 OGW)
( a 11owable
horizontal
load per guy)
(2)
(33
362)
(sin
(13.868)
a/2)
+
(2)
(14.326)
(17.961)
4 033 881.960
Assmne
be split
between
+
(1)
(17.961)
(sin
(sin
a/2)
values
for
Lm
600
300
0
(14.326)
(14.326)
(L/2)
(L/2)
a/2)
+ 567.296 L = 437 451.95
L = 771.118
L and solve for a:
+
sina/2
0.024 06
.060 63
.108 44
aI2
1022’
3O28’
6% 3’
arm) (l/2
(moment
(wind force on OGW)
(moment
arm) - (wind
(L/2)
(13.868)
+ (2) (2) (21 418) (sin a/2) (14.326)
+ (2) (13.2318)
= (2) (17 080) (13.945)
- (3) (12 969.75)
7110.718
pole
(moment
on cond.)
Metric
(1)
halfway
then
point):
arm) (l/2 SAS) + (2 OGW) (2 T,,,.
+
only
because
the
to consider
point
could
through
by
points.
(one
SAS ) +
conductor
the guy attachment
is located
between
the, two
the
Example
For two
7O26’
10°00’
12”36’
f rom
load
between
these
one
a
al2
0.129 41
.173 82
.218 22
1000
MANUAL
a:
sin a/2
ft
2000
As the
LINE DESIGN
a
2O44’
6O56’
12O26’
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
U. S. Customary
(2) (2) (7500) (sin a/2)
+ (1) (2) (7500) (sin
+ (2) (2) (4815) ( sin
= (2) (3840) (45.75)
(45.5)
a/2)
a/2)
- (3)
+ (2) (1.231) (45.5) (L/2)
(47) + (1) (1.231) (47) (L/2)
(47) + (2) (0.906) (47) (L /2)
(9566)
2 975 220 (sin a/2) + 127.521 L = 322 662
23 331.216 (sin a/2) + L = 2530.266
Assume values for L and solve for a:
L,
ft
2000
1000
0
sin a/2
aI2
a
0.022 73
.065 59
.108 45
lO18’
3045’
6013’
2036’
7030’
12O26’
For three guys (two at upper guy attachment
and one at lower):
Metric
4 033 881.960 (sin a/2) + 567.296 L = (3) (17 080) (13.945)
7110.718 (sin a/2) + L = 1190.970
Assume values for L and solve for a:
- 38 909.25
L, m
sin a/2
aI2
a
600
300
0
0.083 11
.125 30
.167 49
4p46’
7012’
938’
9”32’
14O24
19O16’
U. S. Customary
2 975 220 (sin a/2) + 127.521 L = (3) (3840)
23 331.216 (sin a/2) + L = 3907.921
Assume values for L and solve for a:
L,
ft
2000
1000
0
(45.75)
- 28 698
sin a/2
42
0.081 78
.124 64
.167 50
4041’
7OO9’
938’
For four guys (two at each attachment
a
9O22’
14Ol8’
19O16’
point):
Metric
+
4 033 881.960 (sin a/2)
+ L =
7110.718 (sin a/2)
567.296
1610.822
L.=
(4)
(17 080) (13.945) - 38 909.25
175
TRANSMISSION
176
Assrmle
values
L
for
and
solve
for
LINE DESIGN
a:
sin a/2
Lm
600
300
0
MANUAL
a
aI2
0.142 15
.184 34
.226 53
8OlO’
10O37’
13005’
16O20’
21O14’
26O 10’
U.S. C11st0maly
2 975
200
(sin
a/2) +
r.
Compute
For one guy
L = (4) (3840) (45.75) - 28 698
L = 5285.576
127.521
23 331.216
(sin a/2) +
Assume
values for L and
solve
for
a:
L, ft
sin a/2
2000
1000
0
0.140 82
.183 68
.226 54
conductor
guying
at each conductor:
for
a
42
structure
16OlO’
21010’
26O 10’
8OO5’
10035’
13005’
types
3A
(fig.
70) and
3AB
(fig.
71).
Metric
2 T(sin
(2) (33
66 724
66 724
a/2)
+
362) (sin
(sin a/2)
(sin a/2)
7430.041
Assume
(sin
a/2)
values
for
L
(wind
force)
(L /2) =
17 080
a/2)
+ [(47/1000)
(0.383
04)
+ 17.9607
L /2 = 17 080
L = 17 080
+ 8.9803
and
sin a/2
m
at2
0.175 23
.215 60
.256 00
lOOO5’
12’27’
14O50’
U. S. Customary
(2) (7500)
(sin a/2)
15 000 (sin a/2)
+
15 000 (sin a/2)
+
+ [(1.846/12)
1.231
L/2
0.6155
L =
24 370.43
+
a/2)
17 080
1901.941
solve for a:
600
300
0
(sin
=
L =
+
L
(lOOO)](L/2)
(8)]
= 3840
3840
L = 6238.83
(L/2)
= 3840
a
2o” 10’
24O54’
29040’
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
177
PLAN
b
‘Minimum clearance
between conductor
and band or guy-
7
TYPE
1
230
Figure 70.-Type
3A
Structure
ground wires’
STRUCTURE
130481762011956 110-O 125-016-5
3A wood-pole
structure.
104-D-1083.
178
TRANSMISSION
LINE DESIGN MANUAL
PLAN
/J
c Minimum clearance
between conductor
and band or guy
l-r
TYPE
Voltage,
kV
1
69
Fii
3AB
/J
:
/
STRUCTURE
Metric, mm “.‘. fCtus~~mory’
AIZIB
AIZIB
130481442Oi 965 hO-Oh4-6
71-Type
3AB wood-pole
structure.
1 3-2 1
104-D-1084.
Assume
values
CHAPTER
IV-STRUCTURE
for
solve
L and
for
sin a/2
2000
0.173 93
.214 97
.256 00
0
two
guys
at each
AND GUYING
CHARTS
179
a:
L, ft
1000
For
LIMITATION
a
aI2
20002
241O48’
29O40’
1OOOl’
12O24’
14050’
conductor:
Metric
66
724
(sin
7430.041
Assume
a/2)
+
(sin
a/2)
values
for
8.9803
+
L =
L =
L and
(2)
(17 080)
3803.882
solve
for
Lm
a:
sin a/2
0.431 21
.471 58
Sll 96
600
300
0
aI2
a
25O32’
28OO8’
30°47’
5 I OO4’
56’O16’
6 l’O34’
aI2
a
U. S. Customary
15 000 (sin a/2)
+
(sin a/2)
24 370.43
Assume
values
s. Compute
for
0.6155
+
L =
L =
L and
(2)
(3840).
12 477.66
solve
for
a:
L, ft
sin a/2
2000
1000
0
0.429 93
.470 97
.512 00
overhead
ground
wire
guying
2S0’27’
281OOS’
3 0047’
for structure
types
on 2 OGW)
=
3A,
50054’
56010’
6 1O’34’
3AB,
and
3TA
(figs.
72, respectively).
(2
OGV
For one
Metric
(2
G,,,.
sin a/2)
+
(wind
load
horizontal
force
to he guyed
guy:
(2) (2) (21 418) ( sin
+
85 672 (sin a/2)
+
85 672 (sin a/2)
6474.754
(sin a/2)
a/2)
+
26.4634
13.2317
+
L =
[ (34.544/1000)
L /2 = 17 080
L =
1290:839
17 080
I
(0.383
04)
(lOOO)]
(2) (L/2)
=
17 080
70, 71, and
180
TRANSMISSION
LINE DESIGN
MANUAL
mm (14 ft) Withpost insulator
4877 mm (16 ft) With
post insulator
out
Structure
wires y
ground
TYPE
I
I
Figure 72.-Type
3TA
STRUCTURE
POLE
3TA wood-pole
SPACING
structure.
104-D-1085.
I
CHAPTER
Assume
values
L
for
IV-STRUCTURE
and
solve
for
Lm
AND GUYING
CHARTS
a:
sin a/2
600
300
0
U.S.
LIMITATION
a/2
0.106 70
.153 03
.199 36
6007’
8O48’
11030’
a
12O14’
17O36’
23OOO’
Customary
(2) (2) (4815)
(sin a/2) +
[(1.36/12)
(8)]
21 244.209
L = 3840
L = 4235.605
Assume
solve
19 260
For two
Metric
(sin
a/2)
+
(sin a/2)
+
values
for L and
for
(2)
(L/2)
= 3840
a:
L, ft
sin a/2
2000
1000
0
0.105 23
,152 30
.199 37
aI2
6OO2’
8O45’
11030’
a
12OO4’
17030’
23OOO’
guys:
85 672 (sin a/2)
6474.754 (sin a/2)
Assume
0.9066
values
+
13.2317
+
L
for
L =
(2)(17
080)
L =
and
2581.679
solve for a:
La
600
300
0
sin a/2
a/2
a
0.306 06
.352 40
.398 73
17O49’
20°38’
23O30’
35O38’
41O16’
47000’
a/2
a
U. S. Customary
19 260
(sin
a/2)
+
L = (2)(3840)
0.9066
21 244.209
(sin a/2)
+
Assume
values for L and
L
= 8471.211
solve for a:
L, ft
sin a/2
2000
1000
0
0.304 61
.351 68
.398,75
17044’
20°35’
23O30’
35O28’
41010’
47000’
181
TRANSMISSION
182
For
three
LINE DESIGN
MANUAL
guys:
Metric
85 672 (sin a/2)
6474.754 (sin a/2)
Assume
values
+
L
for
L =
13.2317
L =
+
and
(3)(17
080)
3872.518
solve
for
a:
sin a/2
Lm
0.505 43
.551 76
.598 10
600
300
0
a
42
30°21’
33O29’
36O44’
60°42’
66O58’
73O28’
42
a
U.S. Customary
19 260 (sin
21 244.209
Assume
a/2)
+
(sin a/2)
vahtes
0.9066
+ L
L
for
and
L = (3) (3840)
= 12 706.817
solve
for
L, ft
sin a/2
2000
0.503 99
.551 06
.598 13
1000
0
t.
Prepare
Assume
guying
structure
data
for
has 18.3-m
requirements
with
no angle
(OGW)
force
on iced
(wind
(moment
arm)
force on pole)
a:
(l/2
SAS)
structure
(60-ft)
type
30015’
33O26’
36O44’
3TA
western
(fig.
60°30’
66O52’
73O28’
72):
red cedar
poles
without
X-braces.
=
OGW)
(moment
[( max. allowable
arm)
(l/2
SAS)
moment
+ ( cond.)
on wood
(wind
pole)/(safetyLfactor
Metric
(13.232)
(15.697)
+
207.703 L/2
202.383 L =
L =
(L/2)
+ (17.959)
L/2 =
197.064
112 307
554.923
m (maximum
125
(10.973)
277 SAS
(L/2)
= (250 555/Z) -
12 970
without
side
guys)
U.S. Customary
(0.9066) (51.5) (L/2)
46.690 L/2 + 44.316
45.503 L = 82 834
L = 1820.41
+
Compute
side guy
guys:
(36) (L/2)
=
= 92 400 - 9566
(1.231)
L/2
ft (maximum
SAS
without
(184
800/2)
side
guys)
- 9566
12 970
force
on iced
cond.)
of 2)] - (wind
CHAPTER
With
At
IV-STRUCTURE
LIMITATION
AND GUYING
183
CHARTS
X-braces:
5.9436
m (19.5
Circumference
Diameter
=
on pole
(wind
874
mm
mm
SAS)
(34.4
in)
in)
on pole
to wind
on iced
(l/2
of structure:
(10.95
moment
due
force
(moment
arm)
force on pole)
top
=
278
allowable
Moment
from
of pole
of pole
Maximum
(OGW)
ft)
=
81 603
OGW)
(moment
[( max. allowable
=
Nom
(60
187 lb*ft)
force:
arm) (l/2
moment
SAS) +
on wood
(cond.)
(wind
pole)/(safety
force
factor
on iced cond.)
of 2)] - (wind
Metric
FfI’(d,
(13.232)
76.6291
+2d,)
6000
(5.7912)
= [0.38304(1000)(5.9436)21
[278.13 +(2)(202.18)1
6000
(L/2)
+
L /2 + 19.1587
47.894
L = 39 262
m
L = 819.7686
U. S. Customary
(17.959)
(1.0668)
(L/2)
801 - 1539
=
(81
603/2)
-
= 153g 176 Nem
1539
L /2 = 40
(maximum
SAS
without
side
guys)
FH2 Cd, + 26,) _ K%19.5)21 f10.95 + (2) (7.9611 = 1135 25.,5 lbaft
72
72
(0.9066)
17.2254
10.767
The
(19) (L/2)
+ (1.231) (3.5) (L/2) = (60 187/2)
L /2 + 4.3085 L /2 = 30 093 - 1135
L = 28 958
L = 2689.51
ft (maximum
SAS without
side guys)
National
Electrical
Safety
Code
does
not
require
- 1135
angle
guys
structures;
however,
we use one single guy for each conductor
up to 60 ‘. These angle guys will keep the structure
from leaning
for
the
u.
3TA
overhead
Determine
single
ground
wires
span
were
limits
on structures
The following
paragraphs
describe
how
between
conductors
and overhead
ground
and span
permissible
(30
length
span
with given
for a given
For loading
conditions
OF), determine
the
Conductor:
242 mm2 (477
Ruling
span
conductors
structure
of 13-mm
conductor
kcmil),
computed
in paragraph
due
to galloping
to determine
the spacing
wires to prevent
contact
and overhead
ground
with given conductors
(l/2-in)
ice, O.lO-kPa
and overhead
ground
ACSR,
24,/7,
NESC
if line
guys
at tension
for line angles
requirements
5.~.
conductors:
required
between
conductors
and
for a particular
loading
condition
wires; or to determine
and overhead
ground
(2-lb/ft2)
wind pressure,
wire sags for the given
heavy
are used
on tension
structures
into the angle. Guying
the maximum
wires.
and at minus
span length:
1 ‘C
loading
=
213.36
m (700
ft)
TRANSMISSION
184
Maximrun
tension
under
full-load
ice, 0.19-kPa
(4-lb/ftz)
Sag under a load of 13-mm
at -l°C
(30
LINE DESIGN MANUAL
conditions
of
13-mm
(l/2-in)
wind, at -18 o C: (0 o F)
(l/2&1)
ice, O.lO-kPa
(2-lb/ftz)
=
33 362N
(7500
lb)
=
5253
(17.23
=
2 13.36
=
21 118 N (4815
=
4353
wind,
“F)
mm
ft)
OG w:
lo-mm
(3/8-in)
Ruling
span
Maximum
high-strength
tension
under
steel,
full-load
Sag under a load of 13-mm
at -1 OC (30 “F)
Sag and
and
tension
calculation
heavy
loading
conditions
(l/2-in)
forms
NEST
ice, O.lO-kPa
for
this
(0)
for
example
(2-lb/ft2)
were
m (700
ft)
lb)
wind,
shown
previously
mm
(14.28
on figures
57,
ft)
58, 63,
64.
Determine
The
the
angle
couductor
(2-lb/ft2)
wiud
of sideswing
has a force
on the
iced
of 21.186
The
overhead
O.lO-kPa
Therefore,
ground
(2-lb/ft2)
wire
wind
has a force
iced
drawn
at the
ellipses:
locations
structures,
sag valrles
of attachment
the conductors
and
below the attachment
N/m
of 11.773
N/m
ground
or
points
overhead
points.
length
of the suspeusion
hardware
suspension
insulator
string
for the
overhead
with
(0.3077
= tan-’
overhead
to scale to give an accurate
configuration.
respective
angles of sideswing
for the
and
lb/ft)
4.4898
or
e = tan- 1 +f!$i$
Construct
First,
the
conductors
(I.4517
equals
E
on the
the
N/m
conductor
e = tan-’
the
the
7-wire,
for
the
(l/2-in)
ice.
Ib/ft).
Therefore,
with
equals
A O.lO-kPa
13-mm
(l/2+1)
ice.
N/m
(0.227
lb/ft).
3.3079
A
0.280 88 = 1SO42’.
conductors
and
the
are then drawn
and overhead
ground
wires
For suspension
are located
structures,
for the overhead
conductors.
ground
A line which
will be the location
of the major
point at an angle of 28 f ram the line representing
13-mm
lb/ft)
wire
Lines
conductors
wires:
0.211 92 = 1 lO58’.
(0.807
= tan-’
ground
overhead
on these lines
the sag points
wires,
gromld
wires
from the attachment
ground
wires.
For
and
axis of an ellipse is then
the conductor
or overhead
are
points
tension
at their respective
must be extended
extended
the
drawn
through
ground
wire
length
of
each sag
sideswing.
The major
axis of the ellipse is equal to the sag for full-sag
ellipses,
or one-half
the sag for half-sag
ellipses,
plus 6 percent. The minor axis is equal to one-half of the major axis.
The ends and center
of the major
axis are marked
with one end being placed
a distance
below
the
sag point
equal
to 3 percent
of the
applicable
sag or half-sag
value.
The
minor
axis
is marked
perpendicular
to the major axis at its center
point. The ellipses may then be drawn
by any acceptable
method.
There
is no definite
length
of span where
galloping
will change
from
full-sag
ellipses
to
half-sag
ellipses.
However,
our experience
has shown
that, for our line locations
and conditions,
we
should
use full-sag
ellipses
in spans
up to 183 m (600
ft)
in length.
In longer
spans,
the
conductors
CHAPTER
are likely
to gallop
IV-STRUCTURE
in two
or more
percent
of the sag, should be used.
conductors
or between
conductors
reduced
(see sec. 15).
for the longer
must
span
be satisfied
Full-sag
limits
Paragraph
6.
To construct
a.
spans
Lay
the
out
the
scale
provided
in one
the
and
deflection
b. Calibrate
the
the degree calibration
pressure
5.b.
chart
183-m
type
same
scale
A different
bias
horizontal
axis to the
equal to the resultant
due
to the
(600-ft)
of structure
the
for
major
spans
axis
and
wire
of these
ellipses
limitations
limitation
Ellipses
chart
are shown
structures:
the
scale
horizontal
factor
are adjusted
deflection
to 53
between
is greatly
configuration.
scale
may
and
be used
the
for
lower
the
part
sum
of the
of adjacent
accordingly.
right of the origin
in degrees of line angle
tension
at 15.5 o C (60 ’ F) with 0.19-kPa
line
equal
the half-sag
and case. Each
ground
for the structure
wood
factor
lines
with
185
CHARTS
the probability
of contact
as a result
of galloping
and overhead
for
5.d.).
angle
conductor
size ellipses,
do not overlap,
ground
wires
of the conductor
limitation
axes using
the
for each
AND GUYING
and cases to be considered
structure
(see pars.
so one-half
for the maximum
be made
by the dimensions
for the different
structure
types
on figures
‘73 through
87.
vertical
loops
If these ellipses
and overhead
ellipses
should
LIMITATION
angle
(par.
deflection
(4-lb/ft2)
with
wind
5.d.).
c. Calibrate
the vertical
axis above the origin in meters
(feet) for the sum of adjacent
spans. The
calibrations
should be at a distance
above the origin equal to the wind pressure
at 0.19 kPa (4 lb/ft2)
on a bare
d.
conductor
Calibrate
of length
the vertical
equal
to one-half
axis below
of the bare (no ice) conductor
be displaced
below the origin
(pars. 5.b. and 5.c.).
the origin
Lay
out
the
deflection
angle
bias
g.
Layout
lines
showing
h.
Draw
lines
to show
in meters
are offset
the vertical
adjacent
(feet)
for the distance
spans
(par.
5.e.).
between
low
the
maximum
(pars.
of the
the conductor
at the
computed
vertically
from
force of each
swing,
and draw in heavy
(see table 21, par. l.c.).
angle
and the distance
between
add or subtract
the wind
permissible
(dependent
low
point
sum of adjacent
limits
the, insulator
holddown
by
permissible
upon
low points
scale,
pressure
to or from
spans
5.k., 5.1., and S.m.), and maximum
low
structures
(pars.
5.g., 5.h., and 5.i.).
of holddowns
to the bottom
of the insulator
strings
holddown
is drawn
parallel
to the insulator
string swing
These lines
multiplying
of the
angles of insulator
type of structure
lines
used for the sum of adjacent
spans scale
These bias lines are used to automatically
tension
due to a line deflection
angle.
types of suspension
structures
calculated
from the strength
sum
points
equal to the vertical
force of the conductor.
The zero point
by a distance
equal to one-half
the vertical
force of the insulator
e. With
a protractor,
lay out the radial
lines for the insulator
swing limits
for each
f.
the
by the
for class
point
addition
should
string
boundary
scale
factors
see par. 5.f.).
the resultant
2 poles
distance
for all
lines
of various
as
sizes
(par. 5.j.).
A line for each size of insulator
limit line for the type HS and HSB structures.
string
swing
the low point
limit
line by values
obtained
scale factor
(par. 5.j.).
by
TRANSMISSION
186
i.
Plot
the
single
35 585 N (8000
j.
spans
The
Add
lb)
insulator
for
the bias lines
chart
(par.
structure
string
88 965-N
limit
LINE DESIGN
line
(20 OOO-lb)
for determining
at the
units
resultant
under
the limitation
MANUAL
load
on the
maximum
of single
insulator
loading
insulator
string
conditions
strings
equal
(par.
to
5.n.).
to the sum of adjacent
5.0.).
limitation
charts
for
wood
structures
are shown
on figures
88 through
91.
Paragraph 7.
To
construct
a.
Use
b.
Superimpose
calibration
C.
under
the
the
same
(sum
From
angle
guying
line
deflection
the
guying
of adjacent
conditions
for
angle
chart
horizontal
using
for the number
(pars.
suspension
on the
spans)
the calculations
full-load
chart
5.p.,
wood
axis
deflection
the
structures:
as used
angle
bias
same
scale
used
of angle
guys
required
q., r.,
and
s.), plot
for
lines,
for
lines
the
the
structure
limitation
or repeat
structure
the
vertical
limitation
for the various
separating
chart.
the
types
zones
axis
chart..
of structures
for
different
quantities
of guys. Some of the limitations
calculated
may be unnecessary
because
some of the limit
lines may be very close to each other if they are all plotted.
Some of these limitations
may be combined
with others
to keep the chart
clean, but care must be taken
to eliminate
the right lines so that
all
guying
requirements
are satisfied.
required
by various
guy
guys required
to satisfy
indicated
one angle
Standard
arrangements,
the calculated
guying
drawings
and the required
guy requirements.
quantities
The
be checked
coordinated
coordinated
for the number
with the
quantities
of guys
number
should
of
be
on the structure
guying
chart.
No guying
is required
for a line angle up to lo, but at least
guy per suspension
structure
should
be used for all line deflection
angles greater
than lo.
A vertical
line at the 1 o mark should
be drawn
and
an angle guy is not required.
Guying
charts are shown
arrangement
must
drawing
for
the
type
3TA
structure
labeled
to indicate
the area on the chart
on figures
92 and 93. A typical
standard
has been
included
as figure
94.
where
guying
CHAPTER
IV-STRUCTURE
Type HS Structure
289.5 -m (950-ft) Span
Based on 213.4-m (700-ft)
ruling span
3658-mm (12-ft) l%e spacing
NESC Heavy Loading
Conductor full-load tension
= 33 362 N (7500 lb)
OGW f ul I - load tension
= 21 418 N (4815 lb)
Half-sag ellipses
LIMITATION
AND GUYING
CHARTS
Conductor: 242 mm2 (477 kcmil~B~SR. 2417
9%
Sag
Half sag
290
(31.74)
( 15.87)
( 0.95)
5127
2563
(16.82)
( 8.41)
4837
+6%
Major axis
Minor axis
8 = I lo 58’
OGW: IO-mm ( i-in)
So
HaBf saa
+6%
~-=
Major axis
Minor axis
8= 15’42’
H.S. Steel
(tilt)
mm
8016 (26.30)
4008
(I 3.15)
ii0 ( 0.79)
4248
(I 3.94)
2124 ( 6.97)
4023 mm
t=
Fiie
73.~Half-
and full-sag
ellipses for type HS wood-pole
(13.2 ft)
structure
(Sheet 1 of 2). 104-D-1086-1.
187
188
TRANSMISSION
Type HS Structure
183-m (600-ft) Span
Based on 213.4-m (700-ft)
ruling span
3658-mm (12-ft) Pole spacing
NESC Heavy Loading
Conductor ful I- load tension
= 33 362 N (7500 lb)
OGW full-load tension
= 21 418 N (4815 lb)
Full-sag ellipses
LINE DESIGN MANUAL
Conductor: 242 mm2 (477 kcmil) ACSR, 24/7
(if)
m
3852
(12.64)
Sag
+6%
Major axis
Minor axis
231
4083
2042
( 0.76)
(13.40)
( 6.70)
0= IP58’
OGW: lo-mm
( i-in)
Sag
+6%
Major axis
Minor axis
H.S. Steel
mm
(tit)
3 I97 (10.49)
192
3389
1695
( 0.63)
(I 1.12)
( 5.56)
8 = 15“ 42’
Figure
73.~Half-
and full-sag
ellipses for type HS wood-pole
structure
(Sheet 2 of 2). 104-D-1086-2.
CHAPTER
IV-STRUCTURE
Based on 213.4-m (700-ft)
ruling span
3658-mm (i2-ft) Pole spacing
NESC Heavy Loading
Conductor full-load tension
Half-sag
ellipses
AND GUYING
IO?7
5 359
321
5 680
2 840
Sag
Half-sog
+6%
Major axis
Minor axis
9 = I lo 58’
OGW: lo-mm
($-in)
Saa
Haif -sag
+6%
Major axis
Minor axis
189
CHARTS
Conductor: 242 mm2 (477 kcmil)f;XiR,
Type HSB Structure
305.4-m (iooo-ft) Span
= 33 362 N (7500 lb)
OGW full-load tension
= 21 418 N (4815 lb)
LIMITATION
24/7
(3576)
(17.58)
( 1.05)
( 18.63)
( 9.32)
H.S. Steel
(fi)
mm
8882 (29.14)
4441 ( 14.57)
266 ( 0.87)
4707
(15.44)
2353 ( 7.72)
6= 15”42’
F’iie
74.~Half-
and full-sag
ellipses for type HSB wood-pole
structure
(Sheet 1 of 2). 104-D-1087-1.
TRANSMISSION
190
Type HS8 Structure
Conductor:
183-m (600-ft)
Span
Based on 213.4-m (7oo-ft)
ruling
span
3658-mm (l2-ft)
Pole spacing
NESC Heavy Loading
Conductor full- load tension
= 33 362 N (7500 lb)
OGW full-load
tension
= 21 418 N (4815 lb)
Full-sag ellipses
Figure 74.-Half-
and full-sag
LINE DESIGN MANUAL
242 mm* (477 kcmil) ACSR, 2417
CY)
3852 (12.64)
Sag
+6%
231 ( 0.76)
Major axis
4083 ( 13.40)
Minor axis
2042 ( 6.70)
0 = I l”58’
OGW: IO-mm ($-in) H.S. Steel
mm
wt)
3197 (10.49)
Sag
+6%
192 ( 0.63)
Major axis
3389
(11.12)
Minor axis
1695 ( 5.56)
0 = 15’42’
ellipses for type HSB wood-pole
structure
(Sheet 2 of 2). 104-D-1087-2.
CHAPTER
IV-STRUCTURE
Type 3AC Structure
loo Line Angie
304.8-m (IOOO-ft) Span
Based on 213.4-m (7oo-ft)
ruling span
4267~ITIm (l4-ft) Pole spacing
NESC Heavy Loading
Conductor full-load tension
= 33 362 N (7500 lb)
OGW full-load tension
= 21 418 N (4815 lb)
Half-sag ellipses
LIMITATION
AND GUYING
CHARTS
Conductor: 242 mm2 (477 kcmi~ft;LCSR. 24/7
IO?7
WI
(35,16)
Half -sag
+6X
Major axis
Minor axis
8 = 11’58’
OGW: IO-mm (i-in)
sag
Half-sag
+6%
Major axis
Minor axis
0 = 15’ 42’
5 680
2 840
( 18.63)
( 9.32)
H.S. Steel
mm
8882
4441
266
4707
2353
Kt)
(29.14)
(14.57)
( 0.87)
(15.44)
( 1.72)
2(23 586) sin 5’+
Fii
75.~Half-
and full-sag ellipses for type 3AC wood-pole
structure
(Sheet 1 of 2). 104-D-1088-1.
191
TRANSMISSION LINE DESIGN MANUAL
192
Type 3AC Structure
IO0 Line Angle
183-m (600-ft) Span
Based on 213.4-m (7oo-ft)
ruling span
4267-mm (l4-ft) Pole spacing
NESC Heavy Loading
Conductor f uI I - load tension
= 33 362 N (7500 lb)
OGW full-load tension
Conductor: 242 mm2 (477 kcmil) ACSR, 2417
mm
K?)
3852 (I 2.64)
wl
+6%
8 = ll”58’
OGW: IO-t?Im (i-in)
+6%
Full-sag ellipses
2
Fire
75.-Half-
and full-sag
Major axis
Minor axis
8 = 15’ 42’
_
t-
( 0.76)
(13.40)
( 6.70)
H.S. Steel
Hi)
mm
swl
= 21 418 N (4815 lb)
z
231
4083
2042
Major axis
Minor axis
3 197
192
3389
( 10.49)
( 0.63)
(I 1.12)
1695 ( 5.56)
4251 mm
(13.95 ft)
ellipses for type 3AC wood-pole
structure
(Sheet 2 of 2). 104-D-1088-2.
CHAPTER
IV-STRUCTURE
Type 3TA Structure
Tangent, OGW in tension
213-m (700 -ft)
Span
4267-mm (I4 - f t) Pole spacing
NESC Heavy loading
Conductor full-load tension
-33 362 N (7500 lb)
OGW full-load tension
-21 418 N (4815 lb)
Full-sag ellipses
LIMITATION
AND GUYING
193
CHARTS
Conductor : 242 mm2 (477 kcmil) ACSR, 24/7
5g
315
5568
2784
Sag
+6 %
Major axis
Minor axis
0- ll”58’
OGW: ICFmm (&in)
WI
(17.23)
(I .03)
(18.26)
(9.13)
H.S. Steel
Sag
+6 %
Major axis
Minor axis
0= 15’42’
mm
(B)
4353
261
4614
2307
(14.28)
(0.86)
(15.14)
(7.5 7)
3534
mm
(28 ft)
Figure 76.-Full-sag
104-D-1089.
ellipses for type 3TA
wood-pole
structure,
tangent,
4267-mm
(14.ft)
pole spacing.
TRANSMISSION
194
Conductor : 242 mm* (477 kcmil)ACSR,
Sag
Half sag
+6 %
Major
axis
Minor axis
8= 11’58’
OGW: IO-mm (i-in)
Sag
Half
sag
+6 %
Major
Minor
0=
F@e.
axis
axis
mm
I2 966
6483
389
6872
3436
LINE DESIGN MANUAL
Type 3TA Structure
Tangent, OGW in tension
2417
(fa
(42.54)
(21.27)
(1.27)
(22.54)
(I 1.27)
335-m (IIOO-ft)
Span
4267-mm (l4- ft) Pole spacing
NESC Heavy loading
Conductor ful l-load tension
=33 362 N (7500 lb)
OGW full-load tension
-21 418 N (4815 lb)
Half-sag ellipses
H.S. Steel
IO 747
5374
(ti)
(35.26)
(I 7.63)
322
5696
2848
(1.06)
(18.69)
(9.35)
8534 mm
(28 ft)
lS“42’
77.-Half-sag
ellipses for type 3TA wood-pole
structure,
tangent,
4267-mm
(14.ft)
pole spacing.
104-D-1090.
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
195
Type 3TA Structure
90” Line ongle, OGW in tension
Conductor : 242 mm’ (477 kcmil) ACSR. 2417
Cf?)
Without post insulator for jumper
4526
(14.86)
Sag
198-m (650-ft)
Span
II 278-mm (37-ft)
Pole spacing
NESC Heavy loading
+6%
272
4798
2399
Major axis
Minor axis
Conductor full -load tension
0 = Ilo 58’
-33 362 N (7500 lb)
OGW: IO-mm ($-in)
OGW full-load tension
121 418 N (4815 lb)
sag
Full-sag ellipses
+6 %
Only one OGW and two conductors
Major axis
are shown
Minor axis
0s
Fiie
78.-Full-sag
ellipses for type 3TA wood-pole
spacing. 104-D-1091.
(0.89)
(15.75)
(7.88)
H.S. Steel
(ti)
3751
225
3976
1988
(12.31)
(0.74)
(13.05)
(6.53)
l5O42’
structure,
90”
line angle,
11 278~mm
(37.ft)
pole
TRANSMISSION LINE DESIGN MANUAL
196
15 951 mm
(52.33 ft)
Conductor: 242 mm2( 477 kcmil). ACSR, 24/ 7
mm
(ft)
m
Half-sag
+6%
Major ax/s
Minor axis
0
e= 11058’
GW: IO-mm (i-in),
m
Half-sag
+6%
Major axis
Minor axis
II817
5 909
355
6 264
3 I32
(38.77)
(19.39)
( 1.16)
(20.55)
(10.28)
H.S. Steel
!E3
4897
294
5191
2596
Type 3iA Structure
90“ Line Angle
320-m (1050-ftj
Span
II 278-mm (37-ft) Pole spacing
NESC Heavy Loading
Conductor full- load tension
= 33 362 N (7500 lb)
OGW ful I- load tension
= 21 418 N (4815 lb)
Half-sag ellipses
O;to;;e
OGW and two conductors
(ft 1
(3Z)
(I 6.07)
( 0.96)
(17.03)
( 8.52)
0 = 15”42’
Figure 79.-Half-sag
104-D-1092.
ellipses for type 3TA wood-pole
structure,
90’
line angle,
11 278-mm
(37-ft)
pole spacing.
CHAPTER
IV-STRUCTURE
Type 3TA Structure
60’ Line angle, OGWin tension
213-m (700-ft)
Span
4267-mm(l4-ft)
Pole spacing
NESC Heavy loading
Conductor full-load tension
-33 362 N (7500 lb)
OGW full-load tension
=21 418 N (4815 lb)
Full-sag ellipses
LIMITATION
Conductor:
AND GUYING
242mm'
Sag
+6 %
Major axis
Minor axis
8 = I lo 58’
OGW: IO-mm (i-in)
%I
+6 %
Major axis
Minor axis
8= 15’42’
\
Figure 80.-Full-sag
ellipses for type 3TA wood-pole
spacing. 104-D-1093.
197
CHARTS
(477 kcmil)ACSR. 2417
(ft)
5%
(17.23)
315
(I .03)
5568
(18.26)
2784
(9.13)
H.S. Steel
mm
Ki)
4353
(14.28)
261
(0.86)
4614
(15.14)
2307
(7.57)
7366 mm
(24.17f t)
structure,
60’
line angle, 4267-mm
(14-ft)
pole
198
TRANSMISSION
LINE DESIGN MANUAL
Type 3TA Structure
Conductor : 242 mm2 (477 kcmi I) ACSR, 2417
60’ Line angle, OGWin’ tension
w
213-m (700- ft) Span
5z3
(17.23)
sag
8230-mm (27-ft)
Pole spacing
+6 %
315
(I .03)
NESC Heavy loading
Major oxis
5568
(18.26)
Conductor full-load tension
Minor axis
2784
(9.13)
=33 362 N (7500 lb)
0 = I lo 58’
OGW full-load
tension
OGW : IO-mm (i-in)
H. S. Steel
=2l 418 N (4815 lb)
Cfi)
mm
Full-sag ellipses
4353
(14.28)
Sag
Only one OGW and two conductors
+6 %
261
(0.86)
are shown
Major oxis
4614
(15.14)
Minor axis
2307
(7.5 7)
8=
; _
14 249 mm
(46.75 ft)
_ 7125 mm
(23.38 ft)
Figure 81.-Full-sag
104-D-1094.
15O42’
ellipses
7125 mm
(23.38 ft)
for type 3TA
wood-pole
structure,
60’
line angle,
8230-mm
(27-ft)
pole spacing.
CHAPTER IV-STRUCTURE LIMITATION AND GUYING CHARTS
Type 3TA Structure
60” Line angje,OGWin tension
335-m (Iloo-ft)
Span
4267-mm(14-ft)
Pole spacing
NESC Heavy loading
Conductor full-load tension
=33 362 N (7500 lb)
OGW full-load tension
-21 418 N (4815 lb)
Half-sag ellipses
Conductor : 242 mm’ (477 kcmil) ACSR, 2417
snm
(W
12966 (42.54)
sag
Half -sag
6483 (21.27)
+6 %
389
(1.27)
Major axis
6872 (22.54)
Minor axis
3436 (I I. 27)
8 = I I“ 58’
OGW: IO-mm (&in) H.S. Steel
mm
Sag
Half -sag
+6 %
Major axis
Minor axis
8= 15”42’
Figure 82.-Half-sag
104-D-1095.
ellipses for type 3TA woo&pole
199
structure,
60 ’ line angle, 4267-mm
(14.ft)
pole spacing.
200
TRANSMISSION
LINE DESIGN
Conductor: 242 mm2 (477 kcmi I) ACSR, 24/7
4<
(ft)
Sag
Half -sag
+6%
Major axis
Minor axis
0==11”58
OGW: IO-mm (i-in)
Sag
Half-sag
+6%
Major axis
Minor axis
I2%6
6483
389
6872
3436
(4224)
(21.27)
( 1.27)
(22.54)
(I 1.27)
H.S. Steel
mm
IO 747
5374
322
5696
2848
(f_t)
(35.26)
(17.63 )
( 1.06)
(18.69)
( 9.35)
MANUAL
14 249 mm
(46.75 f t)
b
Type 3TA Structure
60’
Line angle, OGW in tension
335-m (IIOO-ft)
Span
8230-mm (27-ft)
Pole spacing
NESC Heavy loading
Conductor full-load tension
= 33 362 N (7500 lb)
OGW full-load
tension
= 21 418 N (4815 lb)
Half-sag ellipses
0= 15’42’
Only one OGW and two conductors
are shown
Figure 83.-Half-sag
104-D-1096.
ellipses for type
3TA
wood-pole
structure,
60’
line angle,
8230-mm
(27.ft)
pole spacing.
CHAPTER
IV-STRUCTURE
Type ETA Structure
LIMITATION
full-
Full-sag
Sag
+6%
Major axis
Minor axis
load tension
= 33 362 N (7500 lb)
OGW full- load tension
= 21 418 N (4815 lb)
CHARTS
201
Conductor: 242 mm2 (477 kcmil) ACSR. 2417
45’ Line angle, OGW in tension
213-m (700-ft)
Span
6096-mm
(20-ft)
Pole spacing
NESC Heavy loading
Conductor
AND GUYING
8= Il”58’
OGW: IO-mm ( i-in)
ellipses
Sag
+6%
Major axis
Minor axis
5E3
315
5568
2784
(ft)
(17.23)
( 1.03)
( 18.26)
( 9.13)
H.S. Steel
mm
4353
261
4614
2307
CD)
(14.28)
( 0.86)
(15.14)
( 7.57)
8 =15’42’
II 278 mm
Figure 84.-Full-sag
ellipses for type 3TA
spacing. 104-D-1097.
wood-pole
structure,
45’
line angle,
6096&n
(20-ft)
pole
202
TRANSMISSION
Conductor: 242 mm2(477
Sag
Half -sag
+6%
Major axis
Minor axis
8= 11’58’
OGW: IO-mm (i-in)
Sag
Half-sag
+6%
Major axis
Minor axis
8 = 15’42’
Figure (IL-Half-sag
104-D-1098.
MANUAL
kcmil ) ACSR, 24/7
mm
I2 966
6483
389
6872
3436
(ti)
(42.54)
(21.27 )
( 1.27)
(22.54)
(11.27)
~~~
Heavy loading
Conductor full-load tension
NESC
H.S. Steel
= 33 362 N (7500 lb)
OGW full-load
tension
= 21 418 N (4815 lb)
(W
I Om7:7 (35.26)
5374 (17.63)
322 ( 1.06 )
5696 (18.69)
2848 ( 9.35)
ellipses
LINE DESIGN
for type 3TA
T
E z
ul
Half-sag ellipses
Only one OGW and two
conductors are shown
B d
e J
/
L
wood-pole
structure,
45 ’ line angle,
6096-mm
(20.ft)
pole spacing.
CHAPTER
IV-STRUCTURE
Type 3TA Structure
30° Line angle. OGW in tension
213-m (700-ft)
Span
4572- mm (l5-ft)
hle spacing
NESC Heavy loading
Conductor full- load tension
=33 362 N (7500 lb)
OGW full-load tension
=2l 418 N (4815 lb)
Full-sag ellipses
LIMITATION
AND GUYING
203
Conductor : 242 mm2 (477 kcmil) ACSR. 24/7
sag
+6%
Major axis
Minor axis
8- 11’58’
OGW: IO-mm (i-in)
Sag
+6%
Major axis
Minor axis
8= l5O 42’
Figure 86.-Full-sag
ellipses for type 3TA
spacing. 104-D-1099.
CHARTS
wood-pole
structure,
30°
mm
5253
315
5568
2784
(-ft)
(17.23)
( 1.03)
(18.26)
(9.13)
H.S. Steel
4%
261
4614
2307
(ftl
(1428)
( 0.86)
(15.14)
( 7.57)
line angle, 4572=mm
(IS-ft)
pole
TRANSMISSION
204
Conductor : 242 mm2 (477 kcmiI)ACSR.
Sag
Half -sag
+6%
Major axis
Minor axis
8 = I I’-’58’
OGW: IO-mm (i-in)
Sag
Half -sag
+ 6 “/o
Major
Minor
e=
axis
axis
mm
I2 966
6483
389
6872
3436
LINE DESIGN MANUAL
Type 3TA Structure
30” Line angle, OGW in tension
335-m (Iloo- f t) Span
4572-mm (15 - ft) Pole spacing
NESC Heavy loading
Conductor ful l-load tension
24/7
(-ft)
(42.54)
(21.27)
(1.27)
(22.54)
(II ,27)
=33 362 N (7500 lb)
OGW full-load tension
=2l 418 N (4815 lb)
H.S. Steel
IO%7
5374
322
5696
2848
Half -sag ellipses
(ft)
(3F26)
(17.63)
(1.06)
(18.69)
(9.35) I
15” 42’
Figure 87.-Half-sag
104-D-1100.
ellipses for type 3TA
wood-pole
structure,
30’
line angle,
4572-mm
(15.ft)
pole spacing.
(4x1~) suodS
-P\
CHAPTER
+lMD!
F
IV-STRUCTURE
8
?
:t
\
lp
\
\y
\
I’
LIMITATION
1
AND GUYING
I
CHARTS
t
f
.
,
4’
\
205
5i
900
\
-60
-70
-60
-50
-40
with 88 965-N units
-30
-20
-10
30
40
50
Angle’of InsuloGr Swing ~~egrees)
Figure 89.-Example
of a wood-structure
limitation
chart (metric).
104-D-1102.
s
e
/
I
/I
I4DG
I \/
3&3AB & 3TA OGW Gu
3 A & 3AB Co\nd. Gu
!c
I /
I/
\‘.
I
\‘I .
I
\
/
I
IY.. \
blY\V
/I
\.
\
\
I
I
/
I
I
//
\
\
\
/
In
n
-10
Angle of"lnsulotor
Figure 90.-Example
king
k&s)
of a wood-structure
limitation
chart
(U.S. customary).
104-D-1103.
STRUCTURE
NOTES
DATA
Voltage
Looding
-wet
HS
HSB
36
269
305
305
3A8
305
3AC
305
O-213
3TA’
13%
2070
213
213-335
0- 213
213-335
0- 213
213-335
o- I96
196-320
lure 94 1
lension. 1 = tension
?i2E&
‘or (tensm)
OGW
mlmul)
OGW (suspension)
Angle guys
Conductor
OGW
S
ted
12
610
60
610
Itit
426
0
S
S
3.6
5.5
S
5.2
I2
I6
I7
I4
I4
I4
I4
I4
Conductor
Ultimate strength
Maximum design tension 33
670
0
4.3
Overhead
ground wire
426
4.3
60
Ultimate
strength
670
60
4.3
Mokimum design tension -21
426
30
4.6
I5
Guy wire
670
4.6
30
I5
Conductor
cteomnce
426
6.1
45
20
to pole ground wire or
670
45
6.1
20
to centerline of pok
1092 mm(43 in)
426
60
6.2
27
to crossarme69
mm(35 in)
670
60
6.2
27
to guy wire
1397 mm(55 in)
396
90
II.3
37
Lightning
protective angle -30
degrees
90
II.3
- 37
Span length limits
by holf sag elkpse method for suspemion structures
Safety fuctws
with l3-mm (i-in) ice, 0.36-kPo (&lb/ft)
wind
Poles
2.0
Cmssorms
4.0
One line double guy per conductor. Total for structure
Insulators
would be three
line double guys each way (3-LDGEW).
suspension
2.5
T mor.= 33 362 N (75oolb).
I siflgle
guy = 22 800 N (5125lb)
tension
3.0
horizontal
pull.
Conductor
2.0
-.._
^
.
.
.
one line OouMe guy per OGW. TOtal for Structure
would
uverneoo grouno wire
2.0
be two line double guys each way (P-LDGEW).
Guy wire
Offset OGW line guys 30. from COnduCtOr t for e IV line
line guys.o
angles. 22 800 N (5125 lb) times cos 3Ov-19 745 N (4436lb.3
transverse
2.67
Omit OGW line guys for OGW in MpenSiOn (O*-60. line angles).
Omit angle guys for 0*-I* and 60*- 90. line ongles.
The oppropriateDnetric
or U.S. customary) data from
Use 3-150 for conductors on line angles up to 60. to keep the
this figure should be placed on the structure
structure
from leaning into the angle.
limitation
chart to make o complete chart.
For OGW in suspension (r- 60’ line angles) or tension ( lV-60v
line angles). mad guying rquimments
on suspemion guying
chart.
1675
-335
O-213
iFi
horl
lMkn
3.6
-0.38
wind
1orrongl
chu-t
213-335
O-213
near4
570
610
610
Design wind on structures
Rles
Ultunote
fiber stress
Crossarms
Ultimate
fiber stress
Insulators
II5 kv
NESC Heavy: l3-mm(+in)
ice. O.l9-kPo (rib/ft’)
mum
plus constant ot -l6Y(O*F)
kPa (6 Ib/fte)
Gloss 2 western red cedar
36.612 MPo(5600 lb/in’)
Douglas fir
51.023 MR (7400 lb/in’)
146 by 254 mm (5{
by IO in). 66 964-N (2oOOo-lb)
stwndord suspension units
242 mm’ (477 kcmil). ACSR. 2417. Flicker
76 509 N(l7 200 lb)
362 N (7500 lb) under full load conditions
IO-mm (i-m) high strength steel, 7 wire
46 040 ND0 600 lb)
416 N (4615 lb) under full load conditions
II-mm (fin)
high strength steel, 7 wire
Figure 91.-Additional
S
S or T
S or T
SorT
Sor T
T
T
T
T
T
T
T
T
data required
4.3
4.3
for the wood-structure
limitation
chart.
104-D-1104.
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
209
NOTES
The required number of guys noted on this chart should be coordinated with
the number of guys required by the standard guying arrangement
drawing for the structure
type used. The coordinated
number
of guys should then be shown an the final guying chart.
The line shown for b. may be omitted because of the small area defined.
The H-frame
(x-braced)
limit and the I-ADG limit far conductors are
about identical,
so only one line is shown at f.
The line shown far g. may be omitted
because it falls outside the
structure
limit ; use structure
limit far guy limit.
Use the same maximum sum of adjacent spans limit for Type 3Ac as
used for the type HS structures.
ASG = Angle single guy
ADG = Angle double guy
7\7
- I.x,i/ I/ i Y,/ I 74 /I
.
IV
.
I /
I/
i ’ \, ‘i
Figure 92.-Example
guying chart
‘\/
Line
for wood-pole
I
DeflectioFAngle
structures
(metric).
/
/
r\
I \
(degreesr
104-D-1105.
/
/
210
TRANSMISSION
LINE DESIGN MANUAL
NOTES
The required number of guys noted on this chart should be coordinated
with the number of guys required by the standard guymg arrangement
drowmg for the structure
type used. The coordinated
number of
guys should then be shown on the final guying chart.
The line shown for b. may be omitted
because of the small area
defined.
The H-frame
(x-braced) limit and the I-ADG limit for conductors ore about
identical.
so only one line is shown ot f.
The line shown for g.moy be omitted because it falls outside the structure
limit;
use structure
limit for guy hmit.
Use the same maximum sum ofadJacentspanslimlt
forType
3AC as
used for the Type HS structures.
ASG = Angle single guy
ADG '- Angle double guy
3000
\
c
\
\
s
r
x
v)
v,
2000
\
\
/
/
/
\
\
\
f!i
.z
Q
\
/
&
/
z
\
\
1000
\
/
‘c
0
/
\
\
\.
OO,
5
101
I5
20
h
2
30
50
Line
Figure 93.-Example
guying
chart
for wood-pole
Deflectmn4c!Angle (degrees)
structures
\
\,
\
s
\
\
\
E
.
(U.S. customary).
104-D-1106.
CHAPTER
IV-STRUCTURE
LIMITATION
AND GUYING
CHARTS
211
<<Chapter
ADDITIONAL
25.
Stresses
H-frame
type
in Wood-Pole
structure
will
DATA
Structures.-There
withstand
when
large
V
is a limit
conductors
to the
and long
amount
spans
of loading
are used.
This
that
the
limitation
becomes
even more pronounced
when strong
winds
and heavy ice loadings
are also present.
Sample
analyses
have been made to determine
the pole strength
in column
loading
for small deflections.
Calculations
of stresses have been made for the following
H-frame
structures:
29-m
29-m
29-m
l
l
l
The
(95-ft)
(95-ft)
(95-ft)
type
type
type
HS 230-kV
structure
HSB 230-kV
structure
HSB 230-kV
structure
calculations
assume:
a The
in a structure
load
Clockwise
,bending
Poles are uniformly
l
a
member
moments
tapered
is positive
with class 2 Douglas
fir poles and one X-brace
with class 2 Douglas
fir poles and one X-brace
with class 1 Douglas
fir poles and two X-braces
if it is in tension,
are positive
with minimum
ANSI
and negative
(American
if it is in compression
National
Standards
Institute)
dimensions
a All
The
bolted
effect
joints
of wind
mass was neglected
be made
in tables
and
This
by using
B-l and
B-4.
on the structures
and
Example
L
M
F
U
R
I
I,
was taken
on all structures.
Similar
the methods
shown in the
B-2, and pole circumferences
Development
figure
Let
are rigid
the
of the
above
I.-Stress
= load
formula
tables
for
maximum
(95.ft)
=
=
bending
extreme
=
=
=
axial reaction
in pole
horizontal
reaction
on pole
account
for
only
any
single
double
prime
sign indicates
prime
sign indicates
V,
Vg
=
=
vertical
vertical
H,
=
horizontal
conductor
overhead
conductor
load
ground,
height
and structure
or voltage
class
may
moment
of resistance
type
HS 230-kV
vertical
load stress
horizontal
load stress
wire
is shown
on figure
B-4.
B.
moment
fiber stress
=
on the HS structure,
structure
following
examples.
Pole resistance
moments
are shown
for different
classes of poles are shown in tables B-3
are in appendix
analysis
for a 29-m
in member
into
analyses
load
load
213
structure
with
class
2 wood
poles:
TRANSMISSION LINE DESIGN MANUAL
214
Hg
=
horizontal
P,
=
pole
LP
=
SAS =
overhead
resisting
distance
sum
ground
wire
load
moment
between
of adjacent
low
points
in adjacent
spans
spans
Metric
Figure
95 shows
the
structure
outline
and
-G
I
other
data.
-
i
L
L
2
x
1
N
---
Q
-
Conductor: 403 mm’, ACSR, 45/7
Diameter - 27 mm
0.38- kPo wind on iced (l3-mm radial)
conductor = 20.07 N/m
Vertical force with 13-mm radial ice =
27.26 N/m
OGW: IO mm, H.S. Steel, ‘I-Wire
Diameter = 9 mm
0.38 - kPa wind on iced (l3-mm radial 1
OGW= 13.23 N/m
Vertical force with l3-mm radial ice =
Ii.79 N/m
Position
8 or D
Ground
K or
M or
P or
R or
dim5
Pole
Circumference,
mm
718
L
N
Q
s
Pr ,
N.m
801
59 778
82 996
983
1148
1326
244 634
376 534
I53 411
Douglas Fir
Working Stress = 51.02 MPa
6.706 m
Figure 95.-29-m
Vertical
loads,
type HS 230-kV
structure
with class 2 Douglas
fir poles (one X-brace).
V,
=
(27.26)(LP)
v-
Hc
=
(20.07)(SAS/2)
Hg =
3 V, +
2 Vg, are shared
equally
by two
=
(11.79)(LP)
(13.23)(SAS/2)
poles:
UK’= U,’ = jyM’fl= UN’= Up’= UQ’= U,’ = U,’ = 1.5v, + vg
104-D-1107.
CHAPTER
For
transverse
H,
loads
and
Hg ,
a plane
Y vhf
)
V-ADDITIONAL
PQ exists.
of inflection
215
DATA
The
location
of the
plane
is found
by:
Y, =
‘rR
vertical
force
due
vu =
Assuming
244-m
The
The
The
For
+ 2Hg(hg) + moment due to wind on poles
pole spacing
0.383(16.464)2
[365.2
6
+(2)(202.2)]
037.60N
force
and
in the
overhead
downward
force
and
overhead
force
Pole
3H,(h,)
6.706
uplift
conductor,
is:
(13.416)+2(13.23)
V”=
conductor,
to uplift
spans:
3(20.07)
=49
+PrM
= 12.649 - 3.662 = 8.987 m
Yl
The
= (12.649) (153 411) = 3 662 m
376534+ 153411
*
in the
braces
bending
windward
ground
in the
X-brace
ground
is
installed
at 45
moments
are:
pole
is
VU minus
leeward
the
vertical
force
of structure,
pole
is
one-half
the
vertical
force
of structure,
VU plus
wire.
0.5 Vu/sin 0 .
O, 0.5 Vu 0.707 = 0.707 Vu.
At K, MK = (1 SH,) (3.048) + H,(5.944)
MK = 4.572(20.07)(243.84)+
+
one-half
wire.
0.383(6.096)2
+ moment due to wind on pole
5.944(13.23)(243.84)
[254.8 + (2) (202.2)l
6
At M, MIM = (1 SH, + H,)y,
= 43 114 M,m
+ moment due to wind on pole
MM = t(1.5) (20.07) + 13.231 (243.8) (3.662)
+ 0.383(12.802)2
1312.7 + (2) (202.2)1 = 46 291 Nam
6
TRANSMISSION
216
LINE DESIGN
MANUAL
At R, MR = (1 .5Hc + H,)y, + moment due to wind on pole
MR = [(1.5) (20.07) + 13.231 (243.8) (8.987)
+ 0.383(25.451)2
Crossarm
For
[421.9 + (2) (202.2)1 = 12g 1 l4 Nmrn
6
strength:’
a 79-
by
267-mm
laminated
arm,
the
ultimate
fiber
stress
S =
13.79
MPa:
where :
W, = ultimate vertical load, N
b
= horizontal thickness of arm, mm
d = vertical thickness of arm, mm
L = length of arm to load (lever arm), mm
w = 13.79(79) (267)2
= 3861 N or 7722 N for a double arm
V
6(3352.8)
For
the
given
Allowable
conductor,
distance
the
between
vertical
low
force
points
is 27.26
is 7722/27.26
N/m
=
(with
13-mm
283.272
m.
radial
ice).
U. S. Customary
Figure
Vertical
96 shows
loads,
the
3
structure
outline
V,
=
H,
= (1.3754)(SAS/2)
V, +
2
and
other
data.
(1.8682)(LP)
V',
are shared
Vg =
(0.8079)(LP)
Hg = (0.9066)(SAS/2)
equally
’ Standard Specifications
for Structural Glued Laminated
Association), table II, combination
E, shows this ultimate
(79- by 267-mm) laminated crossarm.
by
two
poles:
Douglas Fir (Coast Region) Timber (West Coast Lumbermen’s
fiber stress is 2000 lb/ in2 (13.79 MPa) for a 3-l/8- by lo-l/2-in
CHAPTER
,
V-ADDITIONAL
DATA
Conductor: 795 kcmil. ACSR, 45/7
Diameter = 1.063 in
8-lb/ft’
wind on iced (f-in radial)
conductor - I. 3754 Ib/ft
Vertical force with t-in radial
ice = 1.8682 Ib/ft
OGW: B - in H.S. steel, 7-wire
Diameter = 0.360 in
8-Ib/ft*
wind on iced (t-in radial)
OGW = 0.9066 Ib/ft
Vertical force with i-in radial
ice = 0.8079 Ib/ft
F
-
Ground
h
Figure 96.-95.ft
22ft
For
transverse
type HS 230.kV
loads
H,and
Hg,
structure
a plane
Pole
Circumference,
in
Posit ion
8 or cl
K or L
28.26
31.52
44 100
6 I 059
M or N
POT0
R or s
38.69
113244
45.20
180421
52.19
277 731
with class 2 Douglas
of inflection
fir poles (one X-brace).
PQexists.
The
location
by:
Y (PM
1
(41.5) (113 244)
y” =PrR +PrM = 277731+113244
yt
The
vertical
force
due
vu =
= 41.5
to the
3H,(h,)
- 12.02
uplift
= 29.48
Pr,
Ibeft
Douglas Fir
Working stress = 7400 lb/in*
ww-
.
217
= 12 o2 ft
’
ft
is:
+ 2Hg(hg) + moment due to wind on poles
pole spacing
104-D-1108.
of the
plane
is found
TRANSMISSION
218
Assuming
800-ft
LINE DESIGN
spans:
3(1.3754) (F)(
44.02) +2(0.9066)(?)(53.52)
vu =
The
uplift
and
overhead
The
At
force
in the
braces
bending
windward
pole
is
VU minus
one-half
the
weight
of structure,
conductor,
in the
leeward
pole
is VU plus
one-half
the
weight
of structure,
conductor,
wire.
X-brace
is 0.5 VU/sin
8 .
installed
at 45 O, 0.5 VU/O.707
moments
are:
=
0.707
V,
K,M, = (1 SH,) (10) + I&( 19.5) + moment due to wind on pole
MK = 15 (1.3752) (800) + 19.5 (0.9066) (800) +
= 31 799
At
+ 2(7’96)1)
wire.
ground
force
For
in the
ground
downward
Pole
[;38
lb
force
overhead
The
+ 2 ((8)(54’02)’
22
= 11 026.87
and
MANUAL
8(20)2 [ 10.03 + (2) (7.96)]
72
lb*ft
M,MM = (1 .5HC + H,)y,
+ moment due to wind on pole
MM = [( 1.5) (1.3752) + 0.90661, (800) (12.02) + 8t42)2 [ 12’y2+ (2) (7*96)1
= 34 087
lb*ft
At R, MR = (1 .5Hc + H,)y, + moment due to wind on pole
MR = [( 1.5)
(1.3752)
+ 0.90661
(800)
(12.02)
+ 8(83’5)2
[ ‘“‘;;
+ (2)
(7’96)1
= 95 231 lb-ft
Crossarm
For
strength:
a 3-l/8-
by
10-l/2-
in laminated
arm,
the
ultimate
fiber
stress
S =
2000
where :
W,,= ultimate vertical load, lb
b = horizontal thickness of arm, in
d = vertical thickness of arm, in
L = length of arm to load (lever arm), in
w = 2000(3.125) (10.5)2
= 870 lb or 1740 lb for a double arm
V
6(132)
lb/G.
CHAPTER
For
the
Allowable
Example
Metric
Figure
given
conductor,
distance
Z.-Stress
97 shows
the
between
analysis
the
vertical
low
force
points
for a 29-m
structure
V-ADDITIONAL
outline
(95-ft)
and
type
other
1
L
X
1
1
-
is 1.8682
HSB
data.
219
(with
=
931
230-kV
Using
l/2-in
ice).
ft.
structure
the
radial
with
nomenclature
class 2 wood
from
example
Vertical force with l3-mm
ice - 11.79 N/m
Pole
Position
Circumference,
mm
N
(Ground
or D
or L
or N
or Q
’ Or ’
718
801
983
II48
1326
radial
Pr,
N*m
59
82
I53
244
376
Douglas Fir
Working Stress - 51.02 MPa
tan QI =m
sin
cos
Figure 97.-29-m
6.706 m
L
= 0.7727
u = 0.6114
a = 0.7913
u = 37O41’
type HSB 230-kV
1,
OGW = 13.23 N/m
8
K
M
P
,
poles:
Conductor: 403 mm,’ ASCR, 45/7
Diameter = 27 mm
0.38 - kPo wind on iced (l3-mm radial)
E
conductor = 20.07 N/m
Vertical force with l3-mm radial
ice = 27.26 N/m
OGW: IO mm, H.S. Steel, 7-wire
Diameter = 9 mm
0.38 - kPa wind on iced (B-mm radial)
C
._-
lb/ft
is 1740/1.8682
F
:
DATA
structure
with class 2 Douglas
fir poles (one X-brace).
104-D-1109.
778
946
41 I
634
534
220
TRANSMISSION
Load
in adjustable
V,
=
H,
= (20.07)(SAS/2)
(27.26)(LP)
braces
load
in nonadjustable
braces
EF:
force
in crossarm
L,’
For
transverse
FC:
= 0.5Vc/sin a = 0.8181/,
= L,’
Band
I- -L,,’
C and
= - v,/tan
D and
between
C:
u = - 1.294&
GF:
in crosstie
loads,
1.635V,
‘=-vc/tana=-1.294vc
- LDE
between
L,,
Vertical
&/ha=
‘= L,‘=
CC and
L,,’
Load
(11.79)(LP)
Hg = (13.23)(SAS/2)
I-
Compressive
=
in crossarm:
LAB
Load
MANUAL
v-
AC and
LAG
Compression
LINE DESIGN
3
V,
loads
= LAG’
cos
2 Vg, are shared
and
a - L,,’
equally
H, and Hg , a plane
of inflection
cos
a = 0.647 V,
by two
poles:
HJexists.
The
location
by:
x (p,B )
X0 =&
+P,,
Xl
A plane
of inflection
PQalso
3.048W 778)
=82946+59778
= 1 277 m
*
= 3.048 - 1.277 = 1.771 m
=x-x,
exists.
Its
Y (PrM 1
y” = PrR + PrM =
location
is found
by:
12.649(153 411)
376534+153411=3*662m
y1 = y - y. = 12.649 - 3.662 = 8.987 m
^
of this
plane
is found
CHAPTER
When
position
considered
is known,
wind
points
forces
of zero
on conductors
the structure
may
be separated
into
parts
and
each
part
at J caused
reaction
dividing
by the
moment
‘?J
UJ
Taking
and overhead
ground
wires
are resisted
equally
by each
pole
moment.
R,
Axial
221
DATA
separately.
Horizontal
at the
of zero moment
V-ADDITIONAL
moments
f)
by
arm
-- R;’ = Rp” = Rd”=
horizontal
(pole
wind
- ISH,
force
is found
- Hg
by
taking
moments
Hand
about
spacing).
,, _ (3H,) (1.277) + <=Q
6.706
(4.173)
= 0.571H, + 1.244H,
” = - ufy
B
about
in the
pole
above
the
plane
of inflection
(fig.
98),
gives
the
Figure 98.-Free body diagram of pole above plane of inflection
to the crosstie (metric example 2).
force&“:
and
“c +“g
1.277(1.5H,
FG 11--
The
outside
CF, carry
braces,
90 percent.
AC and
Load
L,
,, -0.9FG”
--=
cos a
L,
u --L,”
-
+H,)+
2.591
EF, carry
on the
inner
2.896H,
10 percent
braces
of
1
=-0.739H,
FG” and FHtr
CFis:
while
- 1.611H,
the
inside
CG and
0.9(-0.739H, - 1.611H,)
= -0.841H,
0.7913
- 1.832H,
braces,
CG and
TRANSMISSION
222
The
load
in the
outer
,, _ -O.l&”
The
load
=AG
-
L,"
= -LA;
in the
crossarm
L,,”
LB,
The
load
AG
braces
=
cos a
-O.l(-0.739H,
BC
portions
= l.l65H,
+ 1.448Hg
=A,
- 1.61 lH,)
= O.O934H, + 0.2036H,
0.7913
cot?, a + 0.5&
in the
EFis:
and
= (-J&-G”)
" =-
LINE DESIGN MANUAL
CD is:
and
- (- 0.841H, - 1.832H,) (0.79 13) + OSH,)
=
=CD”
crossarm
AB
portions
” = -(LAG”
and
DE
is:
cos a + H,) = - (O.O934H, + 0.204H,) (0.79 13) - H,
=- l.O74H, - O.l61H,
LAB” = -L&V”
The
moment
at
MD
B and D is
given
by:
+Hg)=
“=-xo(1.5Hc
- 1.277(1.5H,
+Hg) =- 1.915H, - 1.277Hg Nom
MB 1)-MD"
For
the
portion
MK
of the
pole
“=x1(1.5Hc
between
+Hg)=
the
planes
of inflection,
1.771(1.5Hc+Hg)=2.657Hc
the
moment
at K and
L
is:
+ 1.771H, N*m
ML M-MK"
The
area
of the pole
at K and
L
, excluding
the
23.8-mm-diameter
hole
for
mounting
the X-brace
is:
??D2
- 23.80 =;(254.84)2
AK ~4
A, =A,
- 23.8(254.84)
= 5 1 006 - 6065 = 44 941 mm2
CHAPTER
The
section
modulus
L
at K and
V-ADDITIONAL
is:
7TD3 23 Joe2
= $ (254.84)3 - y
32
6
‘,=
223
DATA
(254.84)2 = 1 624 810 - 257 609
= 1 367 201 mm3
The
horizontal
reaction
in the
poles
P and
at
1) -
RP
The
axial
reaction
in the
poles
3H, + 2Hg
‘Q” =
up”
The
force
“=-l.SH,
-RQ
Pand
- Hg
Q is:
(12.139) + 0.571H, + 1.244H, = 6.002Hc + 4.864H,
= - UQ”
K
at
6 . 706
at
Q is:
E
i=
b,’
L
can
be found
-1.5
IH
-
K
by
taking
moments
about
point
M (fig.
99):
H, + Hg
F(
E
E
(d
Figure 99.-Free body diagram
(metric example 2).
E
a
8
tii.-
FK
planes of inflection
i;;--Fi’
P
=-
I.5 H, + Hg
+Hg)+3.662WHc
” =-
FK ”
of pole between
6.706
FM”
+Hg)
1
=- 2.715H, - 1.813H,
224
TRANSMISSION
The
force
KN
in X-braces
2.715H, + 1.813H,
= -3.84OH, - 2.564H,
sin 45O
>
11 -
- -L,,”
L,,
The
net
area
A,
=y
A,
=A,
section
of the
LMis:
and
LKN” = -
The
pole
(less the
X-brace
- 23.80 =%(312.80)’
modulus
LINE DESIGN MANUAL
at Mand
mounting
hole)
- 23.8(312.80)
at
M
and
Nis:
= 76 846 - 7445 = 69 401 mm2
N is:
(312.80)3 - y
(312.80)2 = 3 004 693 - 388 114
= 2 616 579 mm3
z, =z,
Taking
about point
moments
M(fig.
99):
” = -3.662(1.5H,
Ml44
+ Hg) = -5.493H,
- 3.662H,
MM 11--MN”’
By superposition,
and horizontal
by its respective
Stress
At
in the
point
the
loading
total
poles
values
of the
forces
and
can he combined
for total
load
factors
and
safety
bending
loading.
tabulated.
is:
L :
sL=--*--
UL
ML
AL
ZL
where :
UL” = UJ” + 0.707L,,”
kd U, = UL’+ULn
moments
The
strength
computed
of each
separately
member
for vertical
can he divided
CHAPTER
” = 0.571H,+
UL
U,‘=
V-ADDITIONAL
1.244H, + 0.707(3.84OH,
+ 2.564HJ
1.5v, + vg
U, = U,’ + UL” = 1.5 V, + Vg + 3.286H, + 3.057H,
A, = 44 941 mm2
ML” = 2.657H, + 1.771H, N-m
Z, = 1367 201 mm3
s,
+ Vb + 3.286H,
=
44 941
+ 3.057H,
mm2
+
At point N:
uN
sN
MN
=A,%
where :
UN
UN
UN
” = ue”
and
UN
= UN’
+ UN”
‘= 1.5vc + v,
” = 6.002H, + 4.864H,
UN = UN’+ UN ” = 1.5vc + vg + 6.002H, + 4.864H,
AN = 69 401 mm2
MN
” = - 5.493H, - 3.662H, N-m
zN = 2 616 579 mm3
1.5 V, + V8 + 6.002H,
s,
=
69 401
+ 4.864H,
+
225
DATA
= 3.286H, + 3.057H,
226
TRANSMISSION
Adjustable
braces
AG
and
EF:
L AG’ = 1.635 Vc
183-m Spans, LP = 366 m
LINE DESIGN MANUAL
LAG" =0.0934Hc+0.2036Hg
L AG=LAG'+L*G"
16 312
343.06+492.92=836
17 148 N
18 987
399.29 + 573.74 = 973
19 960 N
21750
457.38 + 657.22 = 1115
22865 N
I',=9977 N
2 I ;g ;
H; = 2421 N
213-m Spans, LP = 426 m
V,=ll
613N
V = 5 023N
$=
4275N
Hg= 2818N
244-m Spans, LP = 488 m
V,=13303N
$1 ii;;;
H;= 3228N
274-m Spans, LP = 548 m
24424
513.61+
738.05 = 1252
25 676N
27 188
571.70 + 821.53 = 1393
28 581 N
29 862
627.93 + 902.36 = 1530
31 392 N
32625
686.12 + 985.83 = 1672
34297N
35 300
742.34 + 1066.66 = 1809
37 109 N
vc = 14 938 N
v'= 6 461 N
H,=
5 499N
Hg= 3625N
305-m Spans, LP = 610 m
vc = 16 629 N
vg= 7192N
H,=
6121N
Hg= 4035 N
335-m Spans, LP = 670 m
V,=18264N
v-= 7 899N
Hc= 6723N
Hg= 4432N
366-m Spans, LP = 732 m
vc = 19 954 N
vg= 8630N
H,= 7 346N
f&= 4 842N
396-m Spans, LP = 792 m
vc = 21 590 N
vg= 9338N
H,= 7948N
f$.= 5 239N
CHAPTER
Adjustable
braces
AG
and
V-ADDITIONAL
227
DATA
EF-Continued
LaG”= 0.0934
L AG’= 1.635 Vc
427-m Spans, LP = 854 m
38 063
H, +0.2036 Hg
800.44 + 1150.14 = 1951
L &.=L/&+L*d
40 014 N
v, = 23 280 N
Vg=10069N
ff, = 8 570N
Hg = 5 649 N
Nonadiustable
braces
Spans,
m
LP,
m
-
183
213
244
274
305
335
366
396
427
366
426
488
548
610
670
732
792
854
Crosstie
GC and
L&
FC :
= 0.818 vc,
N
Lee”= 0.841
8
9
10
12
13
14
16
17
19
3088.99
3595.27
4118.38
4624.66
5147.76+
5654.04
6177.99+
6684.27
7207.37
161
499
882
219
603
940
322
661
043
H, + 1.832 Hg,
N
+
+
+
+
4 435.27 = 7 524
5 162.58 = 8 758
5 913.70 = 10 032
6 641.00 = 11 266
7392.12=12540
+ 8 119.42 = 13 773
8 870.54 = 15 049
+ 9 597.85 = 16 282
+ 10 348.97 = 17 556
LGC = LGc) + LGc)
N
15
18
20
23
26
28
31
33
36
685
257
914
485
143
713
371
943
599
GF :
AB
Crossarms
and
DE
w,
366
426
488
548
610
670
732
792
854
= 0.647 Vc,
LP,
m
N
183
213
244
274
305
335
366
396
427
366
426
488
548
610
670
732
792
854
6455
7 514
8 607
9 665
10 759
11 817
12 910
13 969
15 062
-
(compressive):
L &=
-1.294
N
m
183
213
244
274
305
335
366
396
427
L&
Spans,
m
-12
-15
-17
-19
-21
-23
-25
-27
-30
910
027
214
330
518
634
820
937
124
vc,
= -1.074
LABN
-3944.80
-4591.35
-5259.38
-5905.93
-6573.95
-7220.50
-7889.60
-8536.15
-9204.18
-
H, - 0.161 Hg,
N
389.78 =
453.70 =
519.71 =
583.63 =
649.64 =
713.55 =
779.56.=
843.48 =
909.49 =
-4
-5
-5
-6
-7
-7
-8
-9
-10
335
045
779
490
224
934
669
380
114
-17
-20
-22
-25
- -28
-31
-34
-37
-40
245
072
993
820
742
568
489
317
238
TRANSMISSION
228
BC and
Crossarms
spans,
m
-
Poles
LP,
m
LCD) = -1.294
366
426
488
548
610
670
732
792
854
-12
-15
-17
-19
-21
-23
-25
-27
-30
KN and
X-braces
(at
point
MANUAL
CD (compressive):
L ,,“=-l.l65H,-
vc,
N
-
183
213
244
274
305
335
366
396
427
LINE DESIGN
1.448Hg,
N
910
027
214
330
518
634
820
937
124
-4279.05
-4980.38
-5705.01-6406.34
-7130.97
-7832.30
-8558.09
-9259.42
-9984.05
- 3505.61 = -7
- 4080.46 = -9
4674.14 = -10
- 5249.00 = -11
- 5842.68 =-12
- 6417.54 = -14
- 7011.22 =-15
- 7586.07 = -16
- 8179.75 = -18
LCD = LCD’ + L&‘,
N
785
061
379
655
974
250
569
845
163
-20
-24
-27
-30
-34
-37
-41
-44
-48
695
088
593
985
492
884
389
782
287
LM:
Spans,
m
LP,
m
183
213
244
274
305
335
366
396
421
366
426
488
548
610
670
732
792
854
L&l=
- 3.840 H, - 2.564 Hg,
N
-14 104 - 6207=-20311
-164167 225 = -23 641
-18 735 - 8277r-27012
-211129295=-30407
-23505-10346=-33851
-25 816- 11364=-37180
-28209-12415=-40624
-30520-13433=-43953
-32909-14484=-47383
L ):
1.5 Vc t Vg + 3.286H,
+ 3.057H8
+
s, =
44 941 mm*
[
183-m spans, 366-m LP
s
=
L
+ 4315 + 3.286(3673)
+ 3.057(2421)
44 941
+ 2.657(3673)
+ 1.771(2421)
1367.201
1
(1000) = 11 136 kPa
213-m spans, 426-m LP
613) + 5023 + 3.286(4275)+
3.057(2818)
+ 2.657(4275)
44 941
+ 1.771(2818)
1367.201
1
(1000) = 12 962 kPa
244-m spans, 488-m LP
s
L
=
303) + 5754 + 3.286(4897)
44 941
+ 3.057(3228)
+ 2.657(4897)
+ 1.771(3228)
1367.201
1
(1000) = 14 848 kPa
CHAPTER
V-ADDITIONAL
DATA
229
274-m spans, 548-m LP
SL =
c
1.5 (14 938) + 6461+ 3.286(5499)
44 941
+ 3.057(3625)
+ 2.657(5499) + 1.771(3625)
1367.201
1
+ 3.057(4035)
+ 2.657(6121) + 1.771(4035)
1367.201
1
+ 3.057(4432)
+ 2.657(6723) + 1.771(4432)
1367.201
1
+ 3.057(4842)
+ 2.657(7346) + 1.771(4842)
1367.201
1
+ 3.057(5239)
+ 2.657(7948) + 1.771(5239)
1367.201
1
(1000) = 16 673 kPa
305-m spans, 610-m LP
629) + 7192 + 3.286(6121)
44 941
s, =
(1000) = 18 559 kPa
335-m spans, 670-m LP
264) + 7899 + 3.286(6723)
44 941
(1000) = 20 385 kPa
366-m spans, 732-m LP
s
=
(19 954) + 8630 + 3.286(7346)
44 941
L
(1000) = 22 273 kPa
396-m spans, 792-m LP
590) + 9338 + 3.286(7948)
44 941
(1000) = 24 098 kPa
427-m spans, 854-m LP
280) + 10 069 + 3.286@570)
44 941
Poles
(at point
+ 3.057(5649)
+ 2.657(8570) + 1.771(5649)
1367.201
1
(1000) = 25 984 kPa
N):
Vc + Vg' 6.002Hc+4.864Hg
s,=
+
69 401
183-m spans, 366-m LP
s,=
1.5(9977)
[
+4315 + 6.002(3673)
+ 4.864(2421)
69 401
+ 5.493(3673)
+ 3.662(2421)
2616.579
1_
(1000) = 11864 kPa
2 13-m spans, 426-m LP
613) + 5023 + 6.002(4275)
69 401
+ 4.864(2818)
+ 5.493(4275)
+ 3.662(2818)
2616.579
1
(1000) = 13 809 kPa
TRANSMISSION
LINE DESIGN MANUAL
244-m spans, 488-m LP
s
_
(13 303) + 5754 + 6.002(4897)
69 401
N-
+ 4.864(3228)
+ 5.493(4897)
+ 3.662(3228)
2616.579
1
+ 4.864(3625)
+ 5.493 (5499) + 3.662(3625)
2616.579
1
(1000) = 15 818 kPa
274-m spans, 548-m LP
sN =
1.5 (14 938) + 6461+
6.002(5499)
69 401
[
(1000) = 17 763 kPa
305-m spans, 610-m LP
1.5(16 629) + 7192 + 6.002(6121)
69 401
sN=
+ 4.864(4035)
+ 5.493(6121) + 3.662(4035)
2616.579
1
(1000) = 19 772 kPa
335-m spans, 670-m LP
s
=
N
264) + 7899 f 6.002(6723)
69 401
+ 4.864(4432)
+ 5.493(6723)
+ 3.662(4432)
2616.579
+ 4.864(4842)
+ 5.493(7346)
1
(1000) = 21 716 kPa
366-m spans, 732-m LP
sN=
(19 954) + 8630 + 6.002(7346)
+ 3.662(4842)
2616.579
69 401
1
(1000) = 23 728 kPa
396-m spans, 792-m LP
sN=
590) + 9338 + 6.002(7948)
+ 4.864(5239)
+ 5.493(7948)
+ 3.662(5239)
2616.579
69 401
1
(1000) = 25 673 kPa
427-m spans, 854-m LP
sN=
280) + 10 069 + 6.002(8570)
+ 4.864(5649)
+5.493(8570)
69 401
Table 24 shows a summary
point distances.
of loads in the structure
+ 3.662(5649)
2616.579
members
1
(1000) = 27 682 kPa
for various span lengths
and low
CHAPTER
V-ADDITIONAL
DATA
231
Table 24.-Summary of loads in structure members for various span lengths
and low-point distances (metric example 2)
SAS/Z, m
183
Member
213
244
274
305
335
366
396
421
Position
LP, m
Adjustable braces, N
Nonadjustable braces, N
Crosstie, N
Crossarm (compressive), N
Crossarm (compressive), N
X-brace, N
Pole, kPa
Pole, kPa
AC&
CC &
GF
AB &
BC &
KN&
L
N
EF
FC
DE
CD
LM
366
426
488
548
610
670
732
792
854
17 148
15 685
6455
17 245
20 695
20 311
11136
11864
19 960
18257
7514
20012
24088
23 641
12962
13809
22 865
20914
8607
22993
27593
27 012
14848
15818
25 676
23485
9665
25820
30985
30407
16673
11763
28 581
26143
10759
28742
34492
33 851
18559
19172
31 392
28713
11817
31568
31884
37 180
20385
21716
34 291
31371
12910
34489
41389
40 624
22213
23728
37 109
33943
13969
37317
44182
43 953
24098
25673
40 014
36599
15062
40238
48281
47 393
25984
27682
U. S. Customary
Figure
100 shows the structure
Load in adjustable
outline
and other data.
V, = (1.8682)(LP)
Vg = (0.8079)(LP)
H, = (1.3754)(SAS/2)
Hg = (0.9066)(SAS/2)
braces AG and EF:
)-
LAG
Compression
‘= V,/sina=
- LEF
load in crossarm:
L AB’ = L,,’
Load in nonadjustable
force in crossarm
= LF,’ = 0.5 V,/sin a = 0.8 18 V,
between
)-
LB,
Load in crosstie
= - V, /tan a = - 1.294 V,
braces GC and FC :
L,,’
Compressive
1.635T/,
-LDC
B and C and between D and C :
‘=-V,/tana=-1.294Vc
GF:
LGF
’ = LA,’
cos
u - L,,’
cos
a = 0.647Vc
-
232
TRANSMISSION
LINE DESIGN
MANUAL
Conductor: 795 kcmil, ACSR 45/ 7
Diameter = 1.063 in
8-lb/ft’
wind on iced ($-in
radial)
E
conductor = I .3754 lb/f t
Vertical force with $-in radial
ice - 1.8682 I b/ft
OGW: f - in, H.S. Steel, 7-wire
Diameter = 0.360 in
8-lb/ft.’
wind on iced (t-in radial)
OGW= 0.9066 Ib/ft
Vertical force with $-in radial
ice = 0.8079 lb/ft’
\
Position
---
8 or
K or
M or
R or
CCround
w
ton cn = y-
0
L
N
S
Pole
Circumference,
in
28.26
3 1.52
Pr,
lb* ft
44 100
61 059
38.69
52.19
II3 244
277 731
Douglas Fir
Working stress = 7400 lb/in 2
0.7727
sin cy = 0.6114
cos a = 0.7913
a - 37041’
Figure
Vertical
lOO.-95-ft
loads,
3
type HSB 230-kV
V,
and
2
Vg,
structure
are shared
with class 2 Douglas
equally
by
two
fir poles (one X-brace).
poles:
104-D-1110.
CHAPTER
For
transverse
H,
loads
Hg,
and
V-ADDITIONAL
a plane
of inflection
DATA
HJexists.
233
The
location
of this
plane
is found
by:
A plane
PQ also
of inflection
exists.
Its
Y c&f
location
is found
by:
>
41.5 (113 244)
y” =PrR +PrM= 277731+113244=12’02ft
= 41.5 - 12.02 = 29.48 ft
Yl =y-Yo
When
position
of zero moment
is known,
considered
separately.
Horizontal
wind forces on conductors
at the points
of zero moment.
the
and
structure
overhead
R, N -- R;’ = &.,” =
Axial
dividing
reaction
by the
at J caused
moment
arm
by horizontal
(pole spacing).
may
ground
Rd’=-
wind
force
be separated
wires
lSH,
into
are resisted
parts
equally
and each
part
by each
pole
- Hg
is found
by
taking
moments
about
Hand
u ,, _ (3H,) (4.19) + 2Hg (13.69)
= O.S71H, + 1.244H,
J22
Taking
moments
about
B in
the
pole
above
the
plane
4.19 (1.5H, + Hg) + 9.5H,
8.5
&“Z-
of inflection
1
(fig.
= -0.739H,
lOl),
gives
the
force
Fen:
- 1.61 lHg
FF v -F,”
The
Ce
outside
carry
AG
braces,
90 percent.
L,,”
L,
Load
and
EF,
on the
carry
10 percent
inner
braces
CG
Fc” and FH”
and CF is:
of
while
the
inside
0.9FG u 0.9 (- 0.739H, - 1.611HJ
= z=
= - 0.841H, - 1.832H,
0.7913
11 -
- - L,,”
braces,
CG and
234
TRANSMISSION
LINE DESIGN MANUAL
Figure lOl.-Free
body diagram of pole above plane of inflection
crosstie (U.S. customary example 2).
The
load
in the
outer
braces
,, _ -O.l(F,“)
LAG
u --
L,,
The
load
cos a
in the
AG
=
EFis:
and
-O.l(-0.739H,
- 1.61 lHg)
= O.O934H, + 0.2036H,
0.7913
- LAG”
crossarm
portions
BC
and
CD
is:
L,c” = (-LCG”) cosa + OSH, = - (-0.841H,
= l.l65H,
load
- 1.832H,) (0.7913) + OSH,
+ 1.448H,
11 -
- - L,”
L,,
The
and to the
in the
LAB
crossarm
portions
AB
and
DE
is:
" = - (LAG" cos a + H,) = - (O.O934H, + 0.204H,)
(0.7913) - H,
= - l.O74H, - O.l61H,
LAB” = - L,,”
The
moment
at
B
and
D
is given
by:
MD” = - x0 (lSH,
+ Hg> = -6.285H,
- 4.19H, lb*ft
MB 1)--MD”
For
the
portion
of pole
between
the
planes
of inflection,
MK ” =x1 (1.5H, +Hg) = 5.81 (1.5H, +i$)
ML” = MK”
the
moment
at
K and
L is:
= 8.715H, + 5.81J$ lb*ft
CHAPTER
The area of the pole at Kand
V-ADDITIONAL
235
DATA
L , excluding the 15/16-inch-diameter
hole for mounting
the X-brace
is:
- 2 (10.03)=
$I=;(10.03)'
79.06 - 9.40 = 69.66 in2
A, =A,
The section modulus
z,
=g
at K and L is:
_ '~~y+-)03)3
- 0.15625(10.03)2
= 99.06 - 15.72 = 83.34 in3
z, = z,
The horizontal
reaction
in the poles at Pand
RP
The axial reaction
Qis:
f’ -RQ ” = - 1.5H, - Hg
in the poles at P and Q is:
u
Q
(39.83) + 0571H,.
+ 1.244H, = 6.002Hc + 4.864H,
‘P” = - ‘Q ”
The force at K can he found by taking
Q”=-
+H,)+
moments
about point
12.02(1.5H,
22
+Hg)
M (fig. 102):
1
= -2.715H,
- 1.813H,
Figure lOZ.-Free body diagram of pole between planes of inflection
customary example 2).
(U.S.
TRANSMISSION
236
The
force
KN
in X-braces
L,”
LM
and
LINE DESIGN MANUAL
is:
2.715H, + 1.813H,
=-
sin 45’
_
- -3.84OH, - 2.564H,
>
L KN f! -- - LLM"
The
net
area
of the
pole,
less the
AM =‘$
The
section
modulus
at
M
X-brace
- ED
and
mounting
hole,
at
Mand
N is:
= 119.12 - 11.54= 107.58 in2
N is:
183.36 - 23.70 = 159.66 in3
Taking
moments
about
MM
point
M(fig.
102):
“=-
12.02(1.5H,
+Hg)=-
18.11H, - 12.02H,
MM )f -MN"
By superposition,
and horizontal
by its respective
Stress
At
in the
point
the
loading
total
poles
values
of the forces
and
can be combined
for total
load
factors
and
safety
bending
loading.
tabulated.
is:
L:
SL=-f-
moments
The
UL
ML
AL
ZL
strength
computed
separately
of each member
for
vertical
can be divided
CHAPTER
V-ADDITIONAL
DATA
where :
” and U, = U,’ + UL”
UL” = UJ” -I- 0.707L,,
uL” = 0.571H, + 1.244H, + 0.707(3.84OH,
U,’ = l.W,
+ 2.564H,) = 3.286H, + 3.057H,
+ vg
U, = U,’ + UL” = 1.5 V, + Vg + 3.286H, I- 3.057H,
A, = 69.66 in’
ML)) = 8.715H, + 5.81H, lbeft
Z, = 83.34 in3
s, =
1.5& + V’ + 3.286H, f 3.057H,
+
69.66 in2
N:
At point
where :
u “=u
N
“adu
Q
N
=u
N
‘+u
UN
’ = 1.5v, + vg
UN
” = 6.002H, + 4.864H,
N
”
UN = UN’ + UN’) = 1.5 V, + V, + 6.002H, + 4.864H,
AN = 107.58 in2
MN
” = - 18.1 lH, - 12.02H,
ZN = 159.66 in3
s, =
1.5 V, + Vg + 6.002H, + 4.864H,
18.11H, + 12.02H,
+
107.58 in2
159.66 in3
237
238
TRANSMISSION
Adjustable
braces
AG
and
MANUAL
EF:
L ,&
600-ft Spans, LP = 1200 ft
LINE DESIGN
= 1.635 Vc
L /&
= O.O934H, + 0.2036Hg
LAG = LllGl + LAG”
3666
77.06 + 110.76 = 188
3854 lb
4277
89.94 + 129.29 = 219
4496 lb
4887
102.74 + 147.61 = 250
5137 lb
5499
115.63 + 166.14 = 282
5781 lb
6110
128.43 + 184.67 = 313
6423 lb
6720
141.31+
202.99 = 344
7064 lb
7331
154.11 + 221.52 = 376
7707 lb
7941
167.00 + 240.04 = 407
8348 lb
8553
179.89 + 258.37 = 438
8991 lb
Vc = 2242 lb
V = 9701b
I$=
Hg=
825 lb
544Ib
700-ft spans, LP = 1400 ft
Vc = 2616 lb
v =1131lb
g=
9631b
Hg=
6351b
800-ft Spans, LP = 1600 ft
Vc = 2989 Ib
V = 12931b
4
= 1100 lb
725 lb
Hg=
900-ft spans, LP = 1800 ft
V, = 3363 lb
V = 1454 lb
z$ = 1238 lb
8161b
Hg=
lOOO-ft Spans, LP = 2000 ft
Vc = 3737 lb
V =16161b
4
= 1375 lb
Hg = 907 lb
llOO-ft
Spans, LP = 2200 ft
V, = 4110 lb
V = 1777 lb
t(
= 1513 lb
Hg=
997 lb
1200-ft Spans, LP = 2400 ft
Vc = 4484 lb
2:
:;g;
H; = 1088 lb
1300-ft Spans, LP = 2600 ft
Vc = 4857 lb
V = 2101 lb
g
= 1788 lb
Hg = 1179 lb
1400-ft Spans, LP = 2800 ft
Vc = 5231 lb
V =2262 lb
4
= 1926 lb
Hg = 1269 lb
CHAPTER
Nonadiustable
spans,
ft
600
700
800
900
1000
1100
1200
1300
1400
Crosstie
V-ADDITIONAL
DATA
239
braces GC and FC :
LP,
ft
L Gc’= 0.818V,,
1200
1400
1600
1800
2000
2200
2400
2600
2800
1834
2140
2445
2751
3057
3362
3668
3973
4279
-
LGC)) = 0.84111, + 1.832Hg,
lb
lb
694+
996=1690
810+1163=1973
925 + 1328 = 2253
1041+1495=2536
1156+1661=2817
1272+1826=3098
1388+1993=3381
1504+2160=3664
1620 + 2324 = 3944
3524
4113
4698
5287
5874
6460
7049
7637
8223
GF :
LP,
Spans,
ft
600
700
800
900
1000
1100
1200
1300
1400
Crossarm
=1bo.647 Vc,
1200
1400
1600
1800
2000
2200
2400
2600
2800
1451
1693
1934
2176
2418
2659
2901
3142
3384
AB and DE (compressive):
Spans,
ft
600
700
800
900
1000
1100
1200
1300
1400
Crossarm
LG;
ft
LP,
ft
L&’
= -1.294yc
lb
1200
1400
1600
1800
2000
2200
2400
2600
2800
-2901
-3385
-3868
-4352
-4836
-5318
-5802
-6285
-6769
L/
’
= -l.O74H,
lb
- ‘0.161Hg,
-886 - 88 = -974
-1034-102=-1136
-1181-117
=-1298
-1330-131=-1461
-1477146=-1623
-1625-161=-1786
-1772 - 175 = -1947
-1920-190=-2110
-2069-204=-2273
LAB=kg’ +LAB:
-3875
-4521
-5166
-5813
-6459
-7104
-7749
-8395
-9042
BC and CD (compressive):
spans,
ft
LP,
600
700
800
900
1000
1100
1200
1300
1400
12DO
1400
1600
1800
2000
2200
2400
2600
2800
ft
L a’
= -1.294v,,
lb
-2901
-3385
-3868
-4352
-4836
-5318
-5802
-6285
-6769
L cD’ = -l.l65H,
- 1.448H&
lb
-961788 =
-1122 - 919 =
-1282 - 1050 =
-1442 - 1182 =
-1602-1313=-2915
-1763-1444=-3207
-1922-1575=-3497
-2083-1707=-3790
-2244-1838=-4082
-1749
-2041
-2332
-2624
LCD = LC”’
~4
-5
-6
-6
-7
-8
-9
-10
-10
+ LCD:
650
426
200
976
751
525
299
075
851
240
TRANSMISSION
KN
X-braces
LP,
L &’
ft
600
700
800
900
1000
1100
1200
1300
1400
(at point
MANUAL
LM :
and
Spans,
ft
Poles
LINE DESIGN
= -3.84OH,
- 2.564Hg,
lb
1200
1400
1600
1800
2000
2200
2400
2600
2800
-3168-1395=
-3698-1628=
-4224-1859=
-4754-2092=
-5280 - 2326 =
-5810-2556=
-6336-2790=
-6866-3023=
-7396-3254=-10650
-4563
-5326
-6083
-6846
-7 606
-8366
-9126
-9889
L):
1.5 Vc + Vg + 3.286H,
+ 3.057Hg
SL =
+ ~‘715;;;‘8’Hf)(!?)
= lb/i,,2
69.66
600-ft spans, 1200-ft
s, =
LP
1.5 (2242) + 970 + 3.286(825)
+ 3.057 (544)
+
= 1615 lb/in2
69.66
700-ft spans, 1400-ft LP
1.5(2616)+
s, =
1131 + 3.286(963)
+ 3.057(635)
69.66
+
= 1886 lb/in2
800-ft spans, 1600-ft LP
SL =
1.5 (2989) + 1293 + 3.286(1100)
+ 3.057 (725). +
69.66
8.715(1100)
+
83.34
900-ft spans, 1800-ft LP
SL = 1.5(3363)
+ 1454 + 3.286(1238)
+ 3.057(816)
69.66
+
= 2424 lb/in2
lOOO-ft spans, 2000-ft LP
s, =
1.5(3737)
+ 1616 + 3.286(1375)
+ 3.057(907)
69.66
+
= 2693 lb/in2
1 lOO-ft spans, 2200-ft LP
s
= 1.5(4110)
L
+ 1777 + 3.286(1513)
69.66
+ 3.057(997)+
8.715(1513)
+5.81(997)
83.34
12
>( -i >
= 2961 lb/i2
CHAPTER
V-ADDITIONAL
DATA
241
1200-ft spans, 2400-ft LP
SL =
1.5(4484)
+ 1939 + 3.286(1650)
+ 3.057(1088)
+
= 3231 lb/in2
69.66
1300-ft spans, 2600-ft LP
sL=
1.5 (4857) + 2101 + 3.286(1788)
+ 3.057(1179)
+,
69.66
8.715
+
12
(1788)
5.81(1179) )(
> = 3501 lb/i2
83.34
r
1400-ft spans, 2800-ft LP
1.5(5231)
+ 2262 + 3.286(1926)
s, =
Poles
(at
+ 3.057(1269)+
69.66
point
1.5 V;'
N):
Vg+ 6.002H, +4.865Hg
sN=
+
107.58
= lb/in’
600-ft spans, 1200-ft LP
sN=
1.5(2242)+
970 + 6.002(825)+4.865(544)+
18.11(825) + 12.02(544)
12
= 1725 lb/in2
159.66
x -i- >
107.58
700-ft spans, 1400-ft LP
t$,,=
1.5(2616)
+ 1131 + 6.002(963)
+ 4.865(635)
+
= 2013 lb/in2
107.58
800-ft spans, 1600-ft LP
s,= 1.5(2989)
+ 1293 + 6.002(1100)
107.58
+ 4.865(725)+
18.11(1100)
+ 12.02(725)
12
159.66
x T 1 = 2300 lb/in2
900-ft spans, 1800-ft LP
s,=
1.5(3363)
+ 1454 + 6.002(1238)
+ 4.865 (816)
107.58
+
18.11(1238)
+ 12.02(816)
159.66
12
x> 1
= 2589 lb/i2
lOOO-ft spans, 2000-ft LP
sN=
1.5(3737)+
1616 + 6.002(1375)+4.865(907)+,
107.58
= 2876 lb/in’
242
TRANSMISSION
LINE DESIGN MANUAL
1 lOO-ft spans, 2200-ft LP
s,=
1.5(4110)+
1200-ft
spans,
lS(4484)
sN=
1777 + 6.002(1513)+4.865(997)
107.58
18.11(1513)
+
+ 12.02(997)
12
159.66
>( 1 > = 3163 lb/in*
2400-ft LP
+ 1939 + 6.002(1650)
+ 4.865(1088)+
= 345 1 lb/in*
107.58
1300-ft spans, 2600-ft LP
1.5 (4857) + 2101+
s,=
6.002 (1788) + 4.865 (1179)
+
18.11(1788)
107.58
+
12
12.02(1179) >( > = 3739 lb/in*
159.66
r
1400-ft spans, 2800-ft LP
lS(5231)
sN=
Table
point
+ 2262 + 6.002(1926)
18.11(1926)
+ 4.865(1269)+
107.58
25 shows
a summary
+ 12.02(1269)
159.66
of loads
in the
structure
members
12
)( r >
for
various
= 4027 lb/in*
span
lengths
and
low
distances.
Table 25.~Summary of loads in structure members for various spans lengths
and low-point distances (U.S. customary example 2)
SAS/Z, ft
Member
Position
600
700
800
900
1000
1100
1200
1300
1400
2 400
2 600
2 800
8 348
7 637
3 142
8 395
10 075
9 889
3 501
3 739
8 991
8 223
3 384
9 042
10 851
10 650
3 770
4 027
LP, ft
1200
AG&EF
GC&FC
GF
AB&DE
BC&CD
KN&LM
L
N
Adjustable braces, lb
Nonadjustable braces, lb
Crosstie, lb
Crossann (compressive), lb
Crossarm (compressive), lb
X-brace, lb
Pole, lb/in*
Pole, lb/in*
Example
and
double
3.-Stress
analysis
1400
3854
3524
1451
3 875
4650
4 563
1 615
1725
4496
4113
1693
4521
5426
5 326
1 886
2013
for a 29-m
(95-ft)
1600
1800
5137
4 698
1934
5166
6 200
6083
2 154
2300
type
5781
5 287
2 176
5813
6 976
6 846
2424
2589
HSB
2000
2 200
6423
5 874
2418
6459
7751
7 606
2 693
2876
7064
6 460
2659
7 104
8525
8 366
2961
3 163
230-kV
structure
--
7 707
7 049
2 901
7 749
9 299
9 126
3 231
3451
with
class
1 wood
poles
X-brace:
Metric
Figure
103
shows
the
structure
outline
and
other
data.
Using
the
nomenclature
from
example
1,
CHAPTER V-ADDITIONAL
DATA
243
Conductor:
403 mm : ACSR, 45/7
27 mm
0.38-kPo wind on iced (l3-mm radial)
conductor - 20.07 N/m
Vertical force with l3-mm radial ice 27.26 N/m
OGW: IO mm, H.S. Steel, 7-wire
Diometer - 9 mm
0.38- kPo wind on iced (l3-mm radial)
OGW= 13.23 N/m
Vertical force with l3-mm radial ice II.79 N/m
DiOmeter:
I---
1
1
Pole
Circumference,
mm
Position
8 or
K or
M or
R or
Pr,
N*m
771
857
1247
1401
13
L
N
s
74 208
IO1 754
312 751
444 314
Douglas Fir
Working Stress - 51.02 MPa
6,706m
tan
- +j&
= 0.7727
sin a - 0.6114
cos a - 0.7913
a - 37O41’
Figure
103.-29-m
type HSB 230.kV
V,
=
H, =
Load
in adjustable
braces
structure
(27.26)(LP)
vg
(20.07)(SAS/2)
Hg =
AC
and
load
=
fir poles (two X-braces).
(11.79)(LP)
(13.23)(SAS/2)
EF:
LAG’ = L,’
Compression
with class 1 Douglas
= V,/sin a = 1.635Vc
in crossarm:
)-
LAB
- L,’
= - Vc/tan a = - 1.294Vc
104-D-1 111.
244
TRANSMISSION
Load
in nonadjustable
braces
Compressive
force
in crossarm
between
I- -
L,
loads
U,’
For
3 V, and
= U,’
transverse
B and
C and
‘=-V,/tana
‘=L,,
D
between
and
C :
=-1.294V,
GF:
in crosstie
Vertical
= 0.5 V,/sin a = 0.8 18 V,
= L,’
LBC
Load
FC:
CC and
L,,’
LINE DESIGN MANUAL
COS
2 Vg are shared
= UK’
loads
L,,’
H,
= u,
equally
’ = U,’
Hg , a
and
a - L,,’
= UN’
plane
a = 0.647Y,
COS
by two
= Up’
of inflection
poles:
= Ue’
= u,
’ = Us’
HJexists.
The
= 1.5 v,
location
+ vg
of this
plane
parts
and
is found
by:
X(PrB)
3.048(74 208)
+P,B = 101 754+74208
xo =&
Xl
A plane
exists.
Its
location
Y C&M 1
considered
moment
Axial
444314+312751
is known,
points
wind
forces
of zero
’
the structure
may
be separated
into
each
part
on conductors
reaction
by
the
and
overhead
ground
wires
are resisted
equally
by each
pole
moment:
RI;’
dividing
= 2 266 m
separately.
Horizontal
at the
of zero
by:
= 5.486 - 2.266 = 3.220 m
Yl =y-Yo
position
is found
5.486(312 751)
y” =PpR +PrM=
When
’
= 3.048 - 1.285 = 1.763 m
=x-x,
PQ also
of inflection
= 1 285 m
at Jcaused
moment
‘J
UJ”
arm
by
(pole
CR, f) --R/z
horizontal
Rd’=-1.5H,-H,
wind
force
is found
by
,, _ (3H,) (1.285) + Cur,> (4.181)
= 0.575H,
6.706
= q/
taking
moments
spacing):
+ 1.247H,
about
Hand
CHAPTER
Taking
moments
B
about
in the
pole
V-ADDITIONAL
above
the
plane
DATA
245
of inflection
(fig.
104)
gives
force
&“:
Figure 104.-Free body diagram of pole above plane of inflection
and to the crosstie (metric example 3).
-F/
-1.5
Hc + Hg
1.285(1.5H,
FG8)---
+I$)+
1
2.896H,
_
- -0.744H,
2.591
[
- 1.614H,
FF” = FG”
The
outside
( fi’ . carry
carry
on the
FGRand FH”
CF is:
10 percent
of
braces
CG and
inner
cos a
L,,
load
EF,
and
Load
,, _ 0.9FG" 0.9(-0.744H,
--=
L,
The
AG
braces,
90 percent.
- 1.614H,)
0.7913
while
the
inside
braces,
=-0.846H, - 1.836H,
--L,"
8) -
in the
outer
L*(y=
braces
-O.lF&’
cos a
AG
=
and
EFis:
-O.l(-0.744H,
- 1.614H,)
= O.O94OH,+0.204H,
0.7913
L,, e --L,,"
The
load
in the
crossarm
LBc)) =(-L,")
= l.l69H,
LBC
II -
--
LCD”
portions
BC
and
CD
is:
cos.a + O.SH, =-(-0.846H,
+ 1.453H,
- 1.836H,)(O.7913)+
O.SH,
CG and
246
The
load
in the
crossarm
TRANSMISSION
LINE DESIGN MANUAL
portions
DE
AB
and
is:
LAB " = -(LAG ” cos a + H,) = - (O.O94H, + 0.204H,)
L,
The
(0.7913) -H, = -
- O.l61H,
l.O74H,
rt -- -L&
moment
B
at
D is
and
given
by:
MD “=-xo(l.5Hc
+Hg) = - 1.928H, - 1.285H, N-m
MB” = MD”
For
the
portion
of pole
between
the
MK ” =x1 (lSH,
planes
of inflection,
the
moment
at
K
and
L
is:
+ Hg) = 2.645H, + 1.763H, Nom
ML” = MK”
The
area
of the
pole
at
K
and
L,
excluding
the
23.8.mm-diameter
hole
for mounting
the
X-brace
is:
AK=x-
nD2
23.80 =a (272.8)2 - 23.8(272.8) = 58 449 - 6493 = 51 956 mm2
A, =A,
The
section
zK=x-
modulus
at
K
and
L
is:
71D3 23.8D2 = 5 (272.8)3
(j
_ 23’8(;72’8)2
= 1993 118- 295 198= 1 697920mm3
z, =z,
The
horizontal
reaction
in the
poles
RP
The
axial
reaction
‘Q” =
UP
in the
poles
at P and
Q is:
11 -
-RQ ” = - 1 .5Hc - Hg
at P and
Q is:
3H, + 2Hg
(17.898) + 0.575H, + 1.247H, = 8.581H, + 6.585H,
6.706
” = - UQ"
The
force
at K can
he found
CHAPTER
V-ADDITIONAL
by
moments
+H
taking
247
DATA
about
point
M (fig.
105):
9
F lgure 105.-Free body diagram of pole between
(metric example 3).
+H
Q
15.632(1.5H,
" =-
FK
planes of inflection
+I$)+
2.266(1.5&
+Hg)
1
= - 4.003H, - 2.669H,
6.706
FK u --FM”
Since
the
the
division
installation,
VN,
WM
and
of load
assume
L,,
net
area
A,=4A,
The
all load
X-braces
KUand
is taken
by
LTand
one
X-braces
set of braces.
The
VNand
force
WMdepends
in X-braces
of the
nD2
4.003H, + 2.669Hg
Of-
--
sin 45O
M- - L,,
pole
(less
M- L,”
the
X-brace
= -5.662H,
- 3.775H,
)
= -L,,”
mounting
hole)
23.80 = 2 (396.80)2 - 23.8(396.80)
at
Mand
N is:
= 123 661- 9444 = 114 217 mm2
=A,
section
modulus
nD3
ZM=F-
at
Mand
N is:
23.8D2
6
= & (396.80)3 - ‘9
= 5 509 039 mm3
z,
upon
KU, LT,
is:
=KU
The
between
that
= z,
(396.80)2 = 6 133 592 -- 624 553
TRANSMISSION
248
Taking
about point
moments
u
MA4
the
By superposition,
and horizontal
loading
by its respective
Stress
At
in the
point
total
poles
M(fig.
-
- - 2.266
values
LINE DESIGN
105):
(1
.5Hc + HE) = - 3.399H, - 2.266H,
of the forces
and
can be combined
for total
load
factors
and
safety
MANUAL
bending
moments
loading.
The
strength
computed
of each
separately
member
for
tabulated.
is:
L :
SL =-
UL
+-
AL
ML
ZL
where :
UL” = UJ” + 0.707LL,”
UL
and UL = UL’ + UL”
” = 0.575H, + 1.247H, + 0.707 (5.662H, + 3.775H,) = 4.578H, + 3.9 16Hg
U,’ = 1.5v, + vg
u, = U,’ + UL” = 1.5V, + Vg + 4.578H, + 3.916H,
A, =51 956mm’
ML” = 2.645H, + 1.763H, N-m
Z, = 1 697 920 mm3
s
lSV,
L
At
point
+ Vg +4.578H,
51 956 mm*
+ 3.916H,
+
N:
‘N
SN=ANfZN
MN
vertical
can be divided
CHAPTER
V-ADDITIONAL
DATA
249
where :
UN” = Ue” and UN = UN’ + UN”
U,‘=
1.5vc + vg
UN” = 8.58lH,
+ 6.585H,
UN = UN) + UN)) = 1.5 v, + vg + 8.581H, + 6.585H,
A,
= 114217mm2
MN
” = - 3.399H, - 2.266H,
zN = 5 509 039
+ vg + 8.581H, + 6.585H,
114 217 mm2
s, =
Adiustable
mm3
braces
AG
and
1000,,,,,,
+ 3.399Hc+2.266Hg
5 509039 mm3 ) ()](lOO~zmm’)
El;:
L AG’ = 1.635V,
183-m Spans, LP = 366 m
+ 1000 = kPa
LA/'
O.O94OH,+0.204H,
LAG=LAG'+LAGA
16 312
345.26+493.88= 839
17 151 N
18 987
401.85 + 574.87 = 977
19 964 N
21 750
460.32 + 658.51=
22869N
24424
516.91+
V,=9977N
V =4315N
4~3673~
iTI"=
N
213-m Spans, LP = 426 m
V,= 11 613N
V = 5023N
d=
4275N
Hg= 2818N
244-m Spans, LP = 488 m
1119
V,=13303N
2:
ii;;;
H;= 3228N
274-m Spans, LP = 548 m
Vc= 14938N
v-
6461 N
f(= 5499N
Hg= 3625N
739.50 = 1256
-
25680N
250
TRANSMISSION
Adjustable
braces
AG and
LINE DESIGN
MANUAL
IS-Continued
LAG’ = 1.635 Vc
305-m Spans, LP = 610 m
LAG))= O.O94OH,+0.204Hg
LAG=L*Gt+L*G)
27 188
575.37 + 823.14 = 1399
28587N
29862
631.96 + 904.13 = 1536
31 398 N
32625
690.52 + 987.77 = 1678
34 303N
35 300
747.11+
1068.76 = 1816
37 116 N
38063
805.58+ 1152.40 = 1958
40 021 N
V,=16629N
V = 7 192 N
$=
6121N
Hg= 4035N
335-m Spans, LP = 670 m
V,=18264N
V = 7899N
l(=
6723N
I+= 4432N
366-m Spans, LP = 732 m
F= = 1gg54N
8630N
l(=
7346N
Hg= 4842N
396-m Spans, LP = 792 m
V,=21590N
V = 9338N
ig= 7948N
fig= 5239N
427-m Spans, LP = 854 m
V,=23280N
V = 10 069 N
f(= 8570N
Hg= 5649N
Nonadjustable
spans,
m
183
213
244
274
305
335
366
396
427
braces
LP,
m
366
426
488
548
610
670
732
792
854
GC and
FC :
Lee' = O.S18V,,
N
N
8 161
9
10
12
13
14
16
17
19
L Gc"= 0.846H,+ 1.836Hg,
499
882
219
603
940
322
661
043
3107 + 4 445 = 7 552
3617+
5174=
8791
4128+
5927=10055
4652+ 6656=11308
5178+
7408=12586
5688+ 8137=13825
6215 + 8 890 = 15 105
6724+ 9619=16343
7250+10372=17622
LGC = L&
+ L&
15 713
18 290
20937
23572
26 189
28765
31427
34004
36665
CHAPTER
Crosstie
V-ADDITIONAL
DATA
251
GF :
spans,
m
LP,
m
-
183
213
366
426
488
548
610
670
732
192
854
244
214
305
335
366
396
421
Crossarm
183
213
LP,
m
-
11
12
13
15
817
910
969
062
L m” = -l.O74H,
- O.l61H&
N
-12 910
-3945-390=
-4335
-15 021
-4591-454=
-5045
-17 214
-5259-520=
-5906-584=
-6574-650=
-1221-114=
-1890-780=
-8536-843=
-5 719
-6490
-7224
-7935
-8670
-9319
-19 330
-21518
-23634
-25 820
-21937
-30124
-9204-909=-10113
LAB = LAB’ + LAB”
-.
N
’
-17245
-20012
-22993
-25 820
-28142
-31569
-34490
-31316
-40231
BC and CD (compressive):
spans,
m
LP,
m
-
183
366
426
488
548
610
610
132
792
854
244
274
305
335
366
396
427
LAB’ = -1.294 vc,
N
366
426
488
548
610
670
732
192
854
244
214
305
335
366
396
421
213
6455
1514
8607
9665
10 159
AB and DE (compressive):
spans,
m
Crossarm
L ,;=0.64lv,,
N
L&
= -1.294 vc,
N
-12 910
-15 027
L &=
-l.l69H,
- 1.453Hg,
N
-4294-3518=
-4991-40951
-1812
-9092
-5725-4690=-10415
-6428-5267=-11695
-7155-5863=-13018
-7859-6440=-14299
-8587-7035=-15622
-9291-7612=-16903
-10018-8208=-18226
-17 214
-19 330
-21518
-23634
-25 820
-21937
-30124
X-brace:
spans,
m
183
213
244
214
305
335
366
396
427
m,
L,;=-5.662#-
366
426
488
548
610
670
132
192
854
-207969139=-29935
-24205-10638=-34843
-27721-12186=-39913
-31 135 - 13 684 = -44 819
-34 651- 15 232 = -49 889
-38066-16731=-54191
-41593-18219=-59812
3.175Hg,
-m
-45002-19171=-64779
-48523-21325=-69848
LCD = ‘SD’
+ LCD:
-20722
-24 119
-21629
-31025
-34536
-37933
-41442
-44 840
-48350
252
TRANSMISSION
Poles
(at
point
L):
1.5 Vc + Vg + 4.578H,
s,
LINE DESIGN MANUAL
+ 3.916Hg
=
+
51956
mm2
183-m spans, 366-m LP
s
=
1.5(9977)
+ 4315 + 4.578(3673)
L
+ 3.916(2421)+
2.645(3673)
+ 1.763(2421)
(1000) = 9113 kPa
1697.92
51 956
I
2 13-m spans, 426-m LP
SL =
C
1.5(11 613) + 5023 + 4.578(4275)
51956
+ 3.916(2818)
+ 2.645(4275)
1
+ 1.763(2818)
(1000) = 10 607 kPa
1697.92
244-m spans, 488-m LP
s
=
L
1.5 (13 303) + 5754 + 4.578(4897)
51956
+ 3.916(3228)
+ 2.645 (4897) + 1.763 (3228)
1697.92
1
(1000) = 12 150 kPa
274-m spans, 548-m LP
s
=
L
1.5(14 938) + 6461 + 4.578(5499)
51956
+ 3.916(3625)+2.645(5499)
+ 1.763(3625)
1697.92
1
(1000) = 13 644 kPa
305-m spans, 610-m LP
s
L
4.578(6121)
=
+ 3.916(4035)
51956
+ 2.645(6121)
+ 1.763(4035)
1697.92
1
(1000) = 15 187 kPa
335-m spans, 670-m LP
s = 1.5(18 264) + 7899 + 4.578(6723)
L
+ 3.916(4432)
51956
+ 2.645 (6723) + 1.763(4432)
1697.92
1
+ 2.645 (7346) + 1.763(4842)
1697.92
1
(1000) = 16 681 kPa
366-m spans, 732-m LP
(19 954) + 8630 + 4.578(7346)
51956
+ 3.916(4842)
(1000) = 18 225 kPa
396-m spans, 792-m LP
SL =
1.5 (21 590) + 9338 + 4.578(7948)
51’956
+ 3.916(5239)
+ 2.645(7948)
+ 1.763(5239)
1697.92
1
(1000) = 19 719 kPa
CHAPTER
427-m spans, 854-m
l’oles
.-
(at point
253
+ 3.916(5649)
+ 2.645 (8570) + 1.763(5649)
1697.92
1
(1000) = 21262
kPa
N):
I .5 V, + Vg + 8.581H,
+ 6.585Hg
&TN=
3.399H, + 2.266Hg
+
[
DATA
LP
(23 280) + 10 069 + 4.578(8570)
51956
s, =
V-ADDITIONAL
114 217 nun2
5 509 039 mm3
1ooo mm
)(~](looo~~m2)
+lOOO= kPa
183-m spans, 366-m LP
S,=
1.5(9977)
+ 4315 + 8.581(3673)
114 217
+ 6.585(2421)
+ 3.399(3673) + 2.266(2421)
5509.039
1
(1000) = 3846 kPa
213-m spans, 426-m LP
S,=
1.5(11 613) + 5023 + 8.581(4275)
114 217
+ 6.585(2818)
+ 3.399(4275) + 2.266(2818)
5509.039
1
(1000) = 4477 kPa
244-m spans, 488-m LP
sN=
1.5 (13 303) + 5754 + 8.581(4897)
+ 6.585(3228)
+ 3.399(4897)
+ 2.266(3228)
1
(1000) = 5128 kPa
114 217
5509.039
274-m spans, 548-m LP
shl=
1.5(14 938) + 6461 + 8.581(5499)
114 217
+ 6.585(3625)
+ 3.399(5499) + 2.266(3625)
5509.039
1
(1000) = 5759 kPa
305-m spans, 610-m LP
slv=
1.5 (16 629) + 7192 + 8.581(6121)
114 217
+ 6.585 (4035) + 3.399(6121)
+ 2.266(4035)
1
(1000) = 6410 kPa
5509.039
335-m spans, 670-m LP
s,=
1.5(18 264) + 7899 + 8.581(6723)
114 217
+ 3.399(6723) + 2.266(4432)
5509.039
1
+ 6.585 (4842) + 3.399(7346) + 2.266(4842)
5509.039
1
+ 6.585(4432)
(iOO0) = 7040 kPa
366-m spans, 732-m LP
SN’
1.5(19 954) + 8630 + 8.581(7346)
114 217
(1000) = 7693 kPa
254
TRANSMISSION
LINE DESIGN
MANUAL
396-m spans, 792-m LP
(21 590) + 9338 + 8.581(7948)
S,=
+ 6.585 (5239) + 3.399(7948) + 2.266(5239)
5509.039
114 217
1
(1000) = 8323 kPa
427-m spans, 854-m LP
1.5 (23 280) + 10 069 + 8.581(8570)
114 217
SN’
Table
point
26 shows
a summary
of loads
+ 6.585 (5649) + 3.399(8570) + 2.266(5649)
5509.039
in the
structure
members
for
various
1
(1000) = 8974 kPa
span
lengths
and
low
distances.
26.~Summary of loads in structure members for various span lengths
and low-point distances (metric example 3)
Table
SAS/Z, m
213
183
Member
244
274
335
366
396
427
670
732
792
854
34303
31427
12910
34 490
41442
59872
18225
7 693
37116
34004
13969
37 316
44840
64779
19719
8 323
40021
36665
15062
40 237
48350
69848
21262
8 974
LP, m
Position
Adjustable braces, N
Nonadjustable braces, N
Crosstie, N
Crossarm (compressive), N
Crossarm (compressive), N
X-brace, N
Pole, kPa
Pole, kPa
305
AG&EF
GC&FC
%&DE
BC & CD
KN&LM
L
N
366
426
488
548
610
17151
15 713
6 455
17 245
20722
29935
9113
3 846
19964
18 290
22869
20937
8 607
22 993
27629
39913
12150
5 128
25680
23572
9665
25 820
31025
44819
13644
5 759
28587
26 189
10759
28 742
34536
49889
15187
6 410
2: iii
24119
34843
10607
4 477
31398
28765
11817
31569
37933
54797
16681
7040
U. S. Customary
Figure
Load
106
shows
in adjustable
the
structure
outline
and
other
data.
V,
=
(1.8682)(LP)
Vg =
(0.8079)(LP)
H,
= (1.3754)(SAS/2)
Hg =
(0.9066)(SAS/2)
braces
AG and
EF:
LAG’ = LEF) = &/sin a = 1.635Vc
Compression
load
in crossarm:
tLAB
Load
in nonadjustable
braces
- LDE
CC and
L,.’
= L,’
‘=-
K/tana=-1.294V,
FC:
= 0.5 V, /sin a = 0.8 18 V,
CHAPTER
L
V-ADDITIONAL
Conductor: 759 kcmii, ACSR, 45/7
Diameter - 1.063 in
8- lb/f t ’ wind on iced (+-in radial)
conductor - I.3754 lb/ft
Vertical force with i-in radial
ice - 1.8682 Ib/ft
oGw:i-in,
H.S. steel, 7-wire
Diameter - 0.360 in
8-Ib/ft’
wind on iced (i-in radial)
OGW- 0.9066 lb/f t
Vertical force with t-in radial
ice = 0.8079 Ib/ft
I
x
X
1
255
DATA
I
Position
Pole
Circumference,
in
8 or D
KWL
30.37
33.74
M or
49.08
N
ROTS
Pr,
Ib=ft
54
75
230
328
55. I5
730
047
976
655
Douglas Fir
Working stress = 7400 lb/in*
.
tan
a - v
sin
a -
cos
a = 0.7913
- 0.7727
37O 41’
106.-95-ft
Compressive
I
0.6114
a Figure
22 ft
type HSB 230.kV
structure
force in crossarm between
LBC
Load in crosstie
‘=L,,
with class 1 Douglas
B and
‘=-
fir poles (two X-braces).
C and between
V,/tana=-1.294
D and C :
V,
GF:
LcF) = LAG’ 00s a - L,,’
cos a = 0.647 V,
104-D-1112.
256
TRANSMISSION
Vertical
loads
3
&I ’ =
For
transverse
V,
u;
and
2
Vg are
= UK’ = u,’
H,
loads
shared
equally
by
= (j-,’
= UN’
= (J,’
Hg,
and
LINE DESIGN
a plane
two
MANUAL
poles:
= Ue’
of inflection
= U,’
HJexists.
= Us’ = 1.5 v,
The
location
+ vg
of this
plane
parts
and
is found
by:
x (prB1
lO(54
xo =PrK +-Prs =
Xl =x-x()
A plane
of inflection
PQ also
75 047
= lo-
exists.
Its
When
position
considered
Horizontal
at the
of zero
separately.
wind forces
points
of zero
- Y,
moment
Axial
is known,
on conductors
J
reaction
at
by the
moment
moments
= 4*22
ft
655
- 7.43
by:
976)
+ 230
976
= 10.57
ft
the structure
and overhead
may
ground
= 7’43
ft
be separated
wires
into
are resisted
equally
each
part
by each
pole
moment:
caused
arm
about
B
&“=m
Rd’=R$=-l.SH,-
by horizontal
(pole
u ,, = (3H,)
J
Taking
328
= 18.0
Rt;‘=R;=
dividing
is found
18(230
Y(PrM)
=Y
+ 54 730
4.22=5.78ft
location
y” =PrR +PrM =
Yl
730)
(4.22)
+ (*H,)
is found
(13.77)
22
pole
(1
above
the
plane
.5Hc + Hg) + 9.5H,
8.5
FF u -- FG”
force
by
taking
moments
about
107)
force
Hand
spacing):
in the
4.22
wind
Hg
I
= 0.575H, +
1.252H,
of inflection
(fig.
= - 0.745H,
- 1.614H,
gives
Fc”:
CHAPTER
-0
4
1
-In
a6
The
CF,
HC+Hg
AG and E&
braces,
Load
90 percent.
LCG
load
in the
load
LB,”
L,
The
load
braces,
of
F,
CG and
” and
CF,
FH”
while
the
inside
braces,
is:
- 1.6 14H,)
= - 0.847H,
- 1.836H,
0.7913
- LCG”
outer
-
in the
10 percent
0.9 (- 0.745H,
=
AG
braces
,, _- 0. I&”
The
inner
cos a
LAG
L,y,
carry
on the
0.9FG”
rr=-
L CF 1)-The
257
Figure 107.-Free body diagram of pole above plane of inflection
and to the crosstie (U.S. customary example 3).
Fe”
-I.5
outside
carry
DATA
;n#?
9
-
-z
dI
V-ADDITIONAL
-0.1
COSa
and
EF
is:
(-0.745H,
=
-
1.614H,)
= 0.0941Hc
0.7913
0.204H,
+
M -
- - LAG”
crossarm
BC
portions
and
CD
is:
= (-a&“)
cos a + 0.5H, = - (- 0.847H, -
= l.l7OH,
+ 1.453H,
1.836H,)
(0.79
13) +
0.204H,)
(0.7913)-
OSH,
rt -
- - L,”
in the
LAB
crossarm
portions
” =- (LAG”
= - l.O74H,
LABu --
L,,”
cos
AB
and
a + H,) = -
- O.l61H,
DE
is:
(O.O941H,
+
H,
CG and
TRANSMISSION
258
The
moment
B
at
D
and
is given
For
the
portion
of pole
MANUAL
by:
MD ” = - x,, (1 SH,
MB”
LINE DESIGN
+ I$)
= -
6.33H,
- 4.22H,
lb* ft
= MD”
hetween
the
planes
of inflection,
the
moment
at
K and
“=x,(1.5Hc+Hg)=5.78(1.5Hc+Hg)=8.67Hc+5.78Hg
MK
L
is:
lb.0
ML” = MK”
The
area of the pole
L
at Kand
, excluding
the 15/16-inch-diameter
hole
for mounting
the X-brace
is:
.rrD2
A,=TAL
The
‘K
section
=
=t (10.74)2 - E (10.74) = 90.59 - 10.07 = 80.52 in2
=A,
modulus
TD3
-32
15
ED
at
K
15D2/16
6
L
and
is:
= &(10.74)3
- 0.15625(10.74)2
= 121.62-
18.02 = 103.6in3
z, =z,
The
horizontal
reaction
in the
poles
P
at
and
Q is:
Rp” = Rp” = - 1.5Hc - Hg
The
axial
reaction
in the
poles
u*” = (34;2fJ
at
P
and
Q is:
g ) (58.71) + 0.575H, + 1.252Hg = 8.581H, + 6.589Hg
‘P” = - ‘Q ”
The
force
at
FK
FK
K
can be found
”=-
by
51.28(1.5H,
” = - F,”
taking
moments
about
+Hg> + 7.43(1.5H,
22
point
+Hg)
M (fig.
1
108):
= -4.003H,
- 2.669H,
CHAPTER
V-ADDITIONAL
DATA
259
Figure 108.-Free body diagram of pole between
(U.S. customary example 3).
Since
the division
installation,
assume
of load
that
between
all load
X-braces
is taken
KUand
LTand
by one set of braces.
X-braces
The
planes of inflection
VNand
force
WMdepends
in X-braces
KU,
upon
LT, VN,
WMis:
and
4.003H, + 2.669H,
II LKU -L KU ” = The
net
area
of the
pole
The
section
>
n -- - LWM”
X-brace
= $(1~62)~
= - 5.662H, - 3.775H,
mounting
- E
(15.62)
hole)
at
Mand
= 191.62
-
N is:
14.64
= 176.88
= 373.48
- 38.21
in2
=A,
modulus
nD3
at Mand
15D2
/16
6
‘hf=x-
Taking
w -L,
-
LLT
(less the
ED
A,
sin 4S”
(
moments
about
N is:
- 0.15625(15.62)2
= 0.098(15.62)3
point
MM“=-
M (fig.
7.43(1.5H,
MM n --MN”
108):
+Hg)=-
ll.l4H,
-
7.43H,
-
= 335.36
in3
260
TRANSMISSION
By superposition,
and horizontal
by
its respective
Stress
At
the
loading
total
in the
poles
values
of the
LINE DESIGN MANUAL
forces
and
can be combined
for total
load
factors
and
safety
bending
moments
loading.
The
strength
computed
of each
separately
member
for vertic:tl
can be divicl~~ll
tabulated.
is:
L:
point
s, =- UL &-ML
AL
ZL
where :
UL
)) = UJ” + 0.707L,,"
and UL = UL' + UL"
UL" = O.S75H, + 1.252H, +0.707(5.662H,
+3.775H,)=
U,’ = l.SV, + vg
U, = UL'+ UL" = 1.5Vc + Vg + 4.578H, + 3.921H,
A, = 80.52 in2
ML"
=
8.67H,
+
5.78H,
lb*ft
ZL = 103.60 in3
s, =
=
Poles
(at
(%;LuL”
+(~)(ni)
1.5Vc + VK + 4.578H, + 3.921H,
+
80.52 in2
point
N):
‘N
SN=ANfZN
where :
UN
“= UQ" and UN = UN'+ UN"
MN
4.578H, + 3.921H,
CHAPTER
V-ADDITIONAL
DATA
261
UN’ = 1.5vc + vg
UN” = 8.581H, + 6.589H,
UN = UN’ + UNf’ = 1.5 V, + Vg + 8.58 lH, + 6.589H,
AN = 176.98 in2
MN
“=-1l.l4H,
- 7.43H,
ZN = 335.36 in3
s, =
Adjustable
1.5V, + V’ + 8.581H, + 6.589H,
braces
176.98 in2
AC
and
600-ft Spans, LP = 1200 ft
+
11.14Hc + 7.43Hg
335.36 in3
EF:
L AG' = 1.635V,
LAGn = O.O94OH,+ 0.204Hg
LAG = LAG' + LA/
3666
77.63 + 110.98 = 189
3855 lb
4277
90.62 + 129.54= 220
4497 lb
4881
103.51+
147.90 = 251
5138 lb
5499
116.50 + 166.46 = 283
5782 lb
6110
129.39 + 185.03 = 315
6425 lb
Vc = 2242 lb
V = 9701b
f( = 825 lb
Hg=
544Ib
700-ft Spans, LP = 1400 ft
V, = 2616 lb
V = 11311b
g=
9631b
Hg= 635 lb
800-ft Spans, LP = 1600 ft
V, = 2989 lb
V = 12931b
l$=llOOlb
Hg = 725 lb
900-ft Spans, LP = 1800 ft
Vc = 3363 lb
v
I(
= 1454 lb
= 1238 lb
Hg= 8161b
lOOO-ft Spans, LP = 2000 ft
vc = 3737 lb
v = 1616 lb
g=1375lb
Hg= 907 lb
262
TRANSMISSION
LINE DESIGN
MANUAL
Adjustable braces AG and E&Continued
’ + LAG”
L AG’ = 1.635 V,
LAG” = O.O94OH, + 0.204Hg
6720
142.37 + 203.39 = 346
7066 lb
7331
155.27 + 221.95 = 377
7708 lb
1300-ft Spans, LP = 2600 ft
7924
168.25 + 240.43 = 409
8351 lb
1400-ft Spans, LP = 2800 ft
8553
181.20 + 258.92 = 440
8993 lb
1100-ft Spans, LP = 2200 ft
LAG
= LAG
Vc = 4110 lb
v = 1777lb
4=15131b
Hg = 997 lb
1200-ft Spans, LP = 2400 ft
Vc = 4484 lb
2
: ;g
;
H; = 1088 lb
Vc = 5231 lb
V = 2262 lb
I$ = 1926 lb
Hg = 1269 lb
Nonadiustable
Spa%
ft
600
700
800
900
1000
1100
1200
1300
1400
Crosstie
braces
GC and
FC :
LP,
ft
L Gc’= 0.818V,,
lb
lb
1200
1400
1600
1800
2000
2200
2400
2600
2800
1834
2140
2445
2751
3057
3362
3668
3973
4279
699 + 999 = 1698
816+ 1165 = 1981
932+1332=2264
1049 + 1498 = 2547
1165 + 1665 = 2830
1282+1831=3113
1398+1998=3396
1515+2164=3679
1631+2330=3961
-
L cc” = 0.847H,
+ 1.836Hg,
GF :
Spans,
ft
LP,
600
700
800
900
1000
1100
1200
1300
1400
1200
1400
1600
1800
2000
2200
2400
2600
2800
ft
L ‘$
= 0.647 Vc,
lb
1451
1693
1934
2176
2418
2659
2901
3142
3384
3532
4121
4709
5298
5887
6475
7064
7652
8240
CHAPTER
AB
Crossarm
and
DE
LP,
ft
L AB’ = -1.294Vc,
lb
600
700
800
900
1000
1100
1200
1300
1400
1200
1400
1600
1800
2000
2200
2400
2600
2800
-2901
-3385
-3868
-4352
-4836
-5318
-5802
-6285
-6769
BC
and
263
DATA
(compressive):
Spans,
ft
Crossarm
V-ADDITIONAL
L ABn = -l.O74H,
lb
- 0.161Hg,
-88688= -974
-1034-102=-1136
-1181-117=-1298
-1330-131=-1461
-1477-146=-1623
-1625-161=-1786
-1772-175=-1947
-1920-190=-2110
-2069-204=-2273
-3875
-4521
-5166
-5813
-6459
-7104
-7749
-8395
-9042
CD (compressive):
spans,
ft
LP,
ft
L cD’= -1.294Vc,
lb
600
700
800
900
1000
1100
1200
1300
1400
1200
1400
1600
1800
2000
2200
2400
2600
2800
-2901
-3385
-3868
-4352
-4836
-5318
-5802
-6285
-6769
L &=
-l.l7OH,
lb
- 1.453H
8.
-966791=-1757
-1127922=-2049
-1287-1054=-2341
-1448 - 1186 = -2634
-1609-1317=-2926
-1770-1449=-3219
-1931-1581=-3512
-2092-1713=-3805
-2253-1844=-4097
L CD = “7”
-4
-5
-6
-6
-7
-8
-9
-10
-10
+ bD:
658
434
209
986
762
537
314
090
866
X-brace:
Poles
(at
point
spans,
ft
LP,
600
700
800
900
1000
1100
1200
1300
1400
1200
1400
1600
1800
2000
2200
2400
2600
2800
ft
L KG = -5.662Hc
lb
- 3.775Hg,
-4673-2054=
-6727
-5451-2396=
-7847
-6230-2738=
-8968
-7009-3080=-10089
-7788-3422=-11210
-8566-3765=-12331
-9345-41Oi=-13452
-10124-4449=-14573
-10903-4791=-15694
L):
1.5 V, + Vg + 4.578Hc + 3.921Hg
SL =
80.52 ina
600-ft spans, 1200-ft LP
s, =
1.5(2242)
+ 970 + 4.578(825)
80.52
+ 3.921(544)
+
= 1320 lb/in2
264
TRANSMISSION
LINE DESIGN
MANUAL
700-ft spans, 1400-ft LP
1.5(2616)+
S,=
1131+4.578(963)
+ 3.921(635)
+
= 1541 lb/in2
8052
800-ft spans, 1600-ft LP
SL =
1.5(2989)+
1293+4.578(1100)
+ 3.921(725)
+
8.67(1100)
80.52
+ 5.78(725)
103.60
12
>(
T
= 1760 lb/in2
>
900-ft spans, 1800-ft LP
SL =
1.5(3363)
+ 1454 + 4.578(1238)
+ 3.921(816)
+
8.67(1238)
80.52
+ 5.78(816)
103.60
12
I( -7 >
= 1980 lb/in2
lOOO-ft spans, 2000-ft LP
s, =
1.5(3737)
+ 1616 + 4.578(1375)
+ 3.921(907)
80.52
8.67(1375)
+
(
+ 5.78(907)
103.60
12
)O T
= 2200 lb/in2
1 lOO-ft spans, 2200-ft LP
s, =
1.5(4110)+
1777 +4.578(1513)+
3.921(997)
+
8.67(1513)+
80.52
5.78(997)
103.60
12
)O r
= 2420 lb/i2
1200-ft spans, 2400-ft LP
1.5 (4484) + 1939 + 4.578(1650)
s,
=
+ 3.921(1088)
8.67 (1650) + 5.78(1088)
+
80.52
103.60
-12
JO 1
= 2640 lb/in2
1300-ft spans, 2600-ft LP
s
= 1.5(4857)+
2101 +4.578(1788)
L
+ 3.921(1179)
+
= 2861 lb/in2
80.52
1400-ft spans, 2800-ft LP
SL =
Poles
(at
1.5 (5231) + 2262 + 4.578(1926)
80.52
point
N):
l.5Vc+Hg+8.581Hc+6.589Hg
s,=
176.98 in2
+ 3.921(1269)
+
8.67(1926)
+ 5.78(1269)
12
103.60
)O T
= 3081 lb/in2
CHAPTER
V-ADDITIONAL
DATA
265
600-ft spans, 1200-ft LP
S,=
1.50242)
+ 970 + 8.581(825)
+ 6.589(544)
+ 11.14(825)
176.98
+ 7.43(544)
335.36
(
)O
12
= 558 lb/in2
1
700-ft spans, 1400-ft LP
S,-=
1.5(2616)+
1131+ 8.581(963)
+ 6.589(635)
+
176.98
800-ft spans, 1600-ft LP
S,=
1.5(2989)
+ 1293 + 8.581(1100)
+ 6.589(725)
+
176.98
11.14(1100)
(
+ 7.43(725)
335.36
12
)O
r
= 744 lb/in2
900-ft spans, 1800-ft LP
S,=
1.5(3363)+
1454 +8.581(1238)
+ 6.589(816)+
176.98
lOOO-ft spans, 2000-ft LP
s,=
1.5(3737)
+ 1616 + 8.581(1375)
+ 6.589(907)
+
176.98
1 loo-ft spans, 2200-ft LP
s,=
1.5(4110)+
1777+8.581(1513)+6.589(997)+
(
176.98
11.14(1513)+7.43(997)
335.36
12
)O - = 1023 lb/in2
1
1200-ft spans, 2400-ft LP
s,=
1.5 (4484) + 1939 + 8.581(1650)
+ 6.589(1088)
+
176.98
1300-ft spans, 2600-ft LP
SN’
1.5(4857)
+ 2101+ 8.581(1788)+
6.589(1179)
176.98
)O
1400-ft spans, 2800-ft LP
sN=
1.5 (5231) + 2262 + 8.581(1926)
176.98
+ 6.589(1269)
+
12
= 1209 lb/in’
1
TRANSMISSION
266
Table
point
27 shows
a summary
of loads
LINE DESIGN MANUAL
in the
structure
members
for
various
span
lengths
and
low
distances.
Table 27.-Summary
of loads in structure members for various span lengths
and low-point distances (U.S. customary example 3)
SAS/Z, ft
600
Member
700
800
900
1000
1100
1200
1 300
1400
2000
2200
2400
2600
2800
6425
5881
2418
6459
7762
11 210
2200
930
7066
6475
2659
7104
8537
12 331
2420
1023
7708
7064
2 901
7749
9 314
13452
2640
1116
8351
7 652
3142
8 395
10090
14573
2861
1209
8993
8240
3 384
9042
10 866
15 694
3081
1 302
Position
LP, ft
Adjustable braces, lb
Nonadjustable braces, lb
Crosstie, lb
Crossarm (compressive), lb
Crossarm (compressive), lb
X-brace, lb
Pole, lb/in2
Pole, lb/in2
26.
Structure
location,
wood-pole
Data
(a)
l
necessary
1800
3855
3532
1451
3875
4658
6727
1320
558
4497
4121
1693
4521
5434
7841
1541
651
5138
5782
4709
5298
1934
2176
5166
5813
6209
6986
8968 10089
1760
1980
744
837
spatting is a term
line structures
and bracing
Required.-The
following
to the
structure
plan-profile
limitation
scales
and
for
guying
for
the
For
and
line:
These
the
process
equipment
drawings
are
required
are prepared
specified
conductor,
and
a conductor
charts,
by the
field
span,
and
ruling
height
table
Process ofSpotting.-Figure
Code
109 shows
or the
the details
plan and profile
drawing
with the sag template
spotting
structures.
Figure
110 also shows the
applicable
State
for the various
or
clearances
over ground,
railroads,
highways,
communication
circuits,
and
These clearances
should be calculated
in accordance
with the latest edition
Safety
at the structure
for
Reqnired
conductor
other power lines.
Electrical
ground
the
the conductor
National
above
of determining
on the plan and profile
drawings.
is also determined
for each location.
template
showing
types and heights.
of the
height
used
data
of structures
on a transmission
drawings
of the transmission
line.
Plan
l
(b)
and Equipment
the locations
and profile
forces.
A sag template
made
loading
conditions.
The
1600
type of transmission
the amount
of guying
l
l
1400
Structure
Spotting.-
height,
and
structures,
determining
AG&EF
GCLFC
GF
AB & DE
BC & CD
KU&LT
L
N
1200
or municipal
of the sag template,
and figure
structure
code.
110 is a typical
superimposed
showing
the method
of using it for
method
of using the 15,5 OC (60 “F) curve
of the
template
to determine
the proper
conductor
and structure
heights.
The curve
labeled
“15.5
‘C
(60 o F) Final”
represents
the conductor
position.
The lower
two curves,
marked
“8.2-m
(27-ft)
are exactly
the same curves as the 15.5 ’ C final curve, but
clearance”
and “8.8-m
(29-ft)
clearance”
displaced
vertically
the corresponding
the
8.8-m
clearance
8.2 and 8.8 m, respectively.
Therefore,
point
on the 8,2-m
clearance
curve
curve.
Referring
again
to figure
110,
any point on the final curve is 8.2 m above
or 8.8 m above the corresponding
point
on
the
8.8-m
clearance
curve
just
touches
the
CHAPTER
ground
the
line
8.8-m
of the
profile.
clearance
line
Therefore,
touches
the
the
V-ADDITIONAL
conductor
ground
DATA
267
is 8.8 m above
the
ground
at the
point
where
line.
Ccnductw: 201 md (387.5 kcmil), ACM, 2W7
Ruling Span =213.4 m (700 f t )
Max. Tension = 32 472 N (7300 lb), 45% Ult.
NESC Heavy Loading: IS-mm (IL&in) ice with
a 0.38-kPa
(8-lb&
wind at -18 OC (0 OFI
cut out to prrmit
drawing
curve on the plan-profile
/
the I
sheetr.
TYPE
low point
span.
Figure
The
process
109.-Typical
of spotting
usually
2083 + 50 on figure
110, and
the position
described
above.
in U.S. customary
span to the right
is selected,
either
the various
types
sag template
(plastic)
progresses
the spans to the
Please note that
used for spotting
from
left
the
left
to right
structures.
on the
of it are spotted
station
numbering
ter of
ES the
in each
21.3
IO.3
15.2
12.2
Ill
m
Ill
Ill
HS
@Ott)@Oft&
QofO{
&oft)-
GROUND -
104-D-1113.
profile.
The
structure
at Sta.
before
the template
is placed in
referred
to in this section
are
units. After
the required
position
of the conductor
has been determined
for the
of the structure
at Sta. 2083+50,
the location
and height
of the next structure
by scaling
or by use of a pole template.
For convenience,
the pole template
for
of structures
is marked
on the margin
of the template.
For
the span
under
discussion,
the structure
location
selected
is at Sta. 2090 +20,
the structure
is a type HS with
18.3-m
(60-ft)
poles, and the span length
is 204 m (670 ft). This information
should
be recorded
on the drawing.
The template
is then moved
to the right and the next span and structure
located
by repeating
the
process.
TRANSMISSION
Although
the process
the profile
of spotting
for several
spans
or railroad
crossings,
powerline
which
require
will
special
structures
ahead
because
ahead
there
to one of the fixed
is a choice
to determine
that
of structure
of equal
heights.
The
points
at each of the
as much
as possible.
transmission
(c)
may
example,
and
high
it is best to examine
angle
or low
of the structure.
points,
points
Such
and
work
backward.
be desirable
desirable
ruling
profile
to make
layout
In the
highway
in the profile
conditions
more
is to have
span,
a smooth
is a sign
of good
sections
often
than
one
of line
layout
spans of nearly
conductor
design.
The
where
in order
uniform
profile,
and
length
structures
conductor
structures
should
lie in a smooth
flowing
curve
to equalize
This is called
grading the line and is an important
part
UplifLUplift,
in a rough
profile
occur
refer
to the three
conductor
sag is drawn
conductor
will contract
60 o F), the conductor
template.
supports
conductor
crossings,
as line
attachment
structure
of the
loading
design
of a
line.
Determining
Uplift
the
left to right,
such
and it is usually
a matter
of determining
the most
these fixed locations.
Sometimes
it is desirable
to
it may
most
less than
smooth
line
locations
The
from
be conditions
the location
structure,
between
locations,
to or slightly
progresses
may
and affect
structure
the best arrangement.
are equal
usually
there
or communication
consideration
fix the location
of a transmission
line
desirable
arrangement
of the structures
move
LINE DESIGN MANUAL
Therefore,
of alternate
or upstrain,
where
the
structures
is a condition
which
conductor
supports
at Sta. 2105+35,2112+40,
should
be avoided,
if possible.
are at different
elevations.
For
and
2121+70
on figure
for a temperature
of 15.5 ‘C (60 ’ F), but as the temperature
and the sag will decrease.
When the temperature
reaches minus
assumes the position
indicated
by the minus 51 ‘C cold curve
minus
51 OC curve
on the template
between
the conductor
2 105 + 35 and 2121+70),
it can be determined
whether
the
support
of the intermediate
structure
(Sta. 2112+40)
is above or below
the cold curve.
21.3-m
(70-ft)
structure
at Sta. 2112 +40,
the conductor
support
is approximately
on the
conductor
For the
by placing
structures
lll.‘The
decreases,
the
51 ‘C (minus
shown
on the
the
(Sta.
cold curve.
Suppose,
however,
that the 21.3-m
(70-ft)
structure
is replaced
by a 19.8-m
(65-ft)
structure.
The conductor
support
would then be below the cold curve and the conductor
would
exert
an upward
pull on the structure-this
upward
pull is the uplift or upstrain. Uplift
at a structure
will
cause the conductor
to pull the insulators
cause the conductor
to pull away from
crossarm.
Uplift
may possibly
be avoided
up into the crossarm,
and with pin-type
insulators
it might
the insulator
and possibly
pull the insulator
pin out of the
by adjusting
structure
locations
on the plan-profile
drawing,
to take advantage
of terrain,
by using a higher structure
at the point of uplift
or by attaching
weights
to the conductor.
If these methods
fail, then the conductor
must be dead-ended.
Structures
should
not be located
at uplift
points
if it can be avoided
because
the only function
of such a structure
is
to hold the conductors
conductors
during
hot
Insulator
(d)
that
tends
from
to swing
the
swinging
force
of the
to the distance
of the
adjacent
wind
pressure
Sideswing.-Suspension
pressure.
Conductor
to limit the sideswing
on the conductor
against
weather.
clearance
in order
an insulator
spans
suspended
adjacent
to the
insulator
between
fall
of the
The
rapidly
away
vertical
conductor
low
the
to sideswing
by insulator
insulation.
is equal
force
structure,
supported
the
caused
length
of the
by horizontal
wind
sideswing,
so it is necessary
The horizontal
wind pressure
tends
by the
of the adjacent
a short
to one-half
that
supported
of conductor
points
from
to support
are subject
is reduced
conductor
The
length
conductor
sometimes
on a structure
spans.
force
string.
the
insulators
to the structure
to maintain
proper
in the two
is equal
and
the
to keep
insulator
by the
spans.
conductor
total
string
insulator
On rough
low
wind
pressure
the insulator
terrain
points,
plus
string
string
one-half
is equal
where
each
as indicated
CHAPTER
by the
conductor
template,
the low points
from
is still
swinging.
the
Too
structure.
distance
To
the
checked
the point
much
insulator
falls
sideswing
might
(e)
the
instructions
allowable,
low-point
distance,
of structure
could
for
extra
proper
angle
be used
In
for
by a broken
conductor
policy
and
of 230
kV
and
When strainextra clearance
on both
sides
adjacent
span
or pin-type
for broken
is not
the
to a special
maximum
the
be added
the
this
If
value
area,
Structure
at the
value
chart.
be used,
outside
the
heights
bottom
lengths
and
structure
heights
used
for
pole
lengths
over.
strength
structure
of 13.7
Class
1 poles
of the
are given
is needed
limitation
number
of guys,
as shown
major
highways,
major
for
any
chart,
on the
m (45 ft)
are used
in
or less;
for extra
reason.
should
guying
be used
charts,
at a
should
adjacent
to the crossing
span. Other states
broken
(1977),
d o not require
required
clearance
for
broken
to maintain
over
the
circuits,
clearance
edition
lines
communication
sufficient
latest
NESC
structures
conductors.
of a crossing,
Whenever
the
under
the outside
The
This
railroads,
conductor
clearance
major
conditions
and
required
are governed
conductor
highways,
major
on transmission
lines
above.
the
enough
it is necessary
be reduced
structure.
with
communication
or lake crossings
one-half
may
falls
is necessary.
could
m (50 ft) and
additional
railroads,
of the spans
in
to provide
major
When
sagged
over
which,
River
than
correction
the
limitation
type
point
or
limits,
be used.
by the
correct
be provided
in either
rules
powerlines,
or where
The
the
hardware,
plan-profile.
structure
structure
weights
the
allowable
structures.
should
considerations.
It is our
of 15.2
as indicated
all crossings
NESC
are normally
line.
some
span
3 poles
structures,
on the
between
the insulator
line.
for lengths
of structure,
wood-pole
powerlines
the
class
in a transmission
California,
major
tall
type
transmission
used
and
insulators,
suspension
If
distance
to hold
is within
is measured
limits.
the
vertically
in the
the specified
prescribed
However,
insulators
on the
regarding
each
lines,
are normally
spans,
The
by
the
more
spans.
a failure
spans
spans
273
as acting
of the
area in which
than
type
for
On all wood-pole
class 2 poles
line
be greater
or another
can cause
adjacent
General Instructions.-Instructions
design
long
the
be within
adjacent
sideswing
of adjacent
within
to provide
strings,
the
of the
sum
will
will
be adjusted
insulator
points
the
of the
DATA
to be considered
distance
whether
low
sideswing
outside
low-point
against
so defined
of insulator
fall
of conductor
determine
between
is then
may
the length
V-ADDITIONAL
ruling
are used on both sides of a crossing,
it is not necessary
For lower voltages,
when suspension-type
structures
increased
involving
span,
decrease
special
to use spans
ruling
sag in the
to seriously
the
crossing
the
structures
longer
than
conductors
or long spans
approximately
should
tension
due
to a broken
in most
cases.
are to be handled
1.7 times
be dead-ended
conductor
as special
the
ruling
span
at both
ends
of the
in an
studies.
or shorter
span
and
span.
terrain
slopes across the right-of-way,
conductor
on the high side to meet
approximately
Other
policies
span
clearance
to allow
are used
in conductors
and
overhead
50 percent
in the
regarding
substations
1. It is Bureau
policy
a substation
or switchyard.
sufficient
clearance
all requirements.
ground
span terminating
and switchyards
to install
self-supporting
In general,
this means
structures
that the
wires
on
are:
under
the
should
full
load
substation
(no guys) within
structure
adjacent
be maintained
should
normally
or switchyard
183 m (600 ft) of
to the substation
274
TRANSMISSION
or switchyard
conductor
2.
will
and
When
is not
the
reduced,
should
he a steel
overhead
may
be varied
and
any special
to meet
The
method
that
is designing
of approach
the
tension
requirements
between
span
structures
before
angle
in the transmission
and
design
roads,
should
proceeding
where
with
the
and
overhead
ground
final
tension
ground
wires
wire
substation
power
tensions
or switchyard
or communication
be discussed
the
in the
conductor
overhead
of the
and
tensions
yard.
conductors
structural
as railroads,
unbalanced
the
in a span
the
or switchyard
steel
the
into
of conductor
of the
such
to the substation
slack
is reduced
of reduction
requirements
of accepting
to the
clearance
amount
the
crossing
due
wire
midspan
The
capable
wire
ground
sufficient
be maintained.
structure
ground
overhead
LINE DESIGN MANUAL
with
design
the
of the
lines.
design
group
transmission
line.
3.
The
be made
deflection
deflection
as small as possible.
angle reduces
the
or switchyard
structure.
On wood-pole
lines
all guyed
structures
27.
Right-of-Way
transmission
line
strings
require
wide enough
clearance
Sufficient
should
sandy
that
imposes
soil or other
have
a separate
and Building
design.
Today’s
soil with
poor
anchorplate
Clearance
higher
this angle
additional
voltages,
obstruction
is essential
that may
to avoid
for
each
.-Right-of-way
wider phase
adjacent
to the right-of-way.
are hanging
in their no-wind
It is legally
possible
for someone
right-of-way,
and occasionally
this
be at the
flashover
or switchyard
characteristics
guy
clearance
should
is encountered,
strand.
is a very
spacings,
important
consideration
in
and unrestrained
insulator
ever before.
A right-of-way
in a high-wind
situation,
edge of the right-of-way
to trees, buildings,
pole
Some of these
position.
structure
be less than
loo
because
a larger
transverse
load on the substation
bearing
a wider right-of-way
and greater
clearances
than
to give adequate
clearance
between
conductors
from any
clearance
obstruction
conductors
where
line at the substation
It is preferred
clearance
and
hazards
on private
lines,
and
are not
obvious
to erect a structure,
such as a building,
at the
is done. The only way we can protect
ourselves
very
and
must be
and also
property.
any other
when
the
edge of our
others
is to
make our right-of-way
wide enough
to provide
a minimum
electrical
clearance
between
the outer
conductor,
at a maximum
wind condition
of 0.43 kPa (9 lb/ft2),
and an imaginary
building
with a
wall on the edge of the right-of-way.
Tables
28 and 29 show the horizontal
distance
required
as
clearance
between
Tables
30 through
ruling
spans.
a conductor
and a building
for various
line voltages
35 show the required
right-of-way
for transmission
Sometimes
there is a tendency
to reduce the right-of-way
require
shorter
spans (to keep the conductors
safely within
would
be more
expensive
than
initially
because
of the
and elevations
above sea level.
lines of different
voltages
and
width
to keep costs down, but this would
the right-of-way)
and the line probably
additional
structures
required.
CHAPTER
V-ADDITIONAL
DATA
275
Table 28 .-Minimum
horizontal clearance to buildings- USBR standard for
NESC light, medium, and heavy loading (metric)
kV
Ruling
span,
m
Conductor
69
84 mm2 ACSR 6/l
115
135 mm2 ACSR 26/7
138
242 mm2 ACSR 2417
161
242 mm2 ACSR 2417
230
483 mm2 ACSR 4517
345
483 mm2 ACSR 4517
duplex
213
305
213
305
213
305
213
305
305
366
427
305
366
427
Basic
clearance,
m
3.048
3.048
3.048
3.048
3.048
3.048
3.048
3.048
3.048
3.048
3.048
3.048
3.048
3.048
Increase for
voltage,’
m
0.2003
.2003
.3420
.3420
.4836
.4836
.9086
.9086
.9086
1.6170
1.6170
1.6170
Increase for
elevation,
m
Minimum horizontal
clearance
to buildings,2
m
3 percent of
‘increase for
voltage” for
each 305 m
of elevation
over 1006 m
3.048
3.048
3.249
3.249
3.389
3.389
3.532
3.532
3.956
3.956
3.956
4.666
4.666
4.666
r The increase for voltage is:
’ At 1006-m elevation and a
Table 29.-Minimum
horizontal clearance to buildings-USBR standard
for NESC light, medium, and heavy loading (U.S. customary)
kV
Conductor
69
No. 4/O AWG ACSR 611
115
266.8 kcmil ACSR 2617
138
477 kcmil ACSR 2417
161
477 kcmil ACSR 2417
230
954 kcmil ACSR 4517
345
954 kcmil ACSR 4517
duplex
Ruling
spa
ft
Basic
clearance,
ft
700
1000
700
1000
700
1000
700
1000
1000
1200
1400
1000
1200
1400
10
10
10
10
10
10
::
10
10
10
:8
10
l The increase for voltage is:
2 At 3300-ft elevation and at 60 “F with a 9-lb/ft’
wind.
Increase
for
voltage,’
ft
0.66
0.66
1.12
1.12
1.59
1.59
2.98
2.98
2.98
5.31
5.31
5.31
Increase for
elevation,
ft
3 percent of ‘increase
for voltage” for each
1000 ft of elevation
over 3300 ft
Minimum
horizontal
clearance
to buildings,2
ft
10.00
10.00
10.66
10.66
11.12
11.12
11.59
11.59
12.98
12.98
12.98
15.31
15.31
15.31
Table 30.-Right-of-way
Maximum
kV’
69
Conductor
Ruling
span,
m
conductor
tension,2
newtons per
conductor
84 mm2 ACSR 6/l
213
a12 900
115
138
135 mm2 ACSR 26/7
242 mm2 ACSR 2417
213
213
305
a24900
a16400
161
242 mm2 ACSR 24/l
213
230
483 mm2 ACSR 4517
305
305
a23 100
a24900
a23 100
a31100
366
427
305
366
a30200
a29 300
a31 100
a30200
427
a29 300
305
305
345
483 mm2 ACSR 4517
duplex
b16 900
Insulator
string
length,
mm
Conductor swing
0.43kPa wind
l/3 low point
Degrees
m
869
869
65O19’
65O19’
1219
1372
1219
3746
7 705
8 964
3745
7576
3460
73746
116
a12900
r 69 through 161 kV are H-frame wood-pole construction;
2 Maximum conductor tensions are limited by:
Conductor
sag at
15.5 oc,
mm
values-NESC Iigh t loading (metric)
Right-of-way,4
m
2
%
63OO2'
57OO9’
63OO2'
3.048
3.048
3.658
4.267
3.658
3.048
3.048
3.249
3.389
3.249
21
28
23
24
29
g
1372
1676
1676
2286
57OO9’
57009’
57OO9’
50°38'
7.6255
4.5550
7.8809
8.6982
4.267
5.182
5.182
7.620
3.389
3.532
3.532
3.956
;;
34
41
Iz
m
u
12851
17676
8 964
12851
2286
2286
3658
3658
50°38'
50°38'
50°38'
50°38'
11.7036
15.4341
9.7590
12.7644
7.620
7.620
9.144
9.144
3.956
3.956
4.666
4.666
47
55
48
54
17676
3658
5OO38'
16.4949
9.144
4.666
61
230 and 345 kV are steel tower construction.
3 At 1006-m elevation, and at 15.5 OC with a 0.43kPa wind.
4 At 1006-m elevation, and rounded off to next highest meter.
Minimum
horizontal
clearance
to buildings,3
m
7.6736
4.1705
4.2996
7.4292
7 705
a 18 percent ultimate strength at 15.5 oC fmal, no load.
b 25 percent ultimate strength at -18 OC final, no load.
4.1925
Outside
phase to
structure
centerline,
m
$
E
n
z
5
z
?
Table 3 1.-Right-of-way
kV’
69
Conductor
No. 4/O AWG ACSR 6/l
115
266.8 kcmil ACSR 2617
138
477 kcmil ACSR 24/l
Ruling
span,
ft
411 kcmil ACSR 2417
230
954 kcmil ACSR 4517
345
954 kcmil ACSR 45/l
duplex
Conductor
sag at
60 OF,
ft
Insulator
string
length,
ft
12.28
24.86
11.34
23.27
12.28
25.25
12.28
25.25
29.31
42.09
57.89
29.37
42.09
57.89
2.5
2.5
4.0
4.0
4.5
4.5
5.5
5.5
7.5
7.5
7.5
12.0
12.0
12.0
700
a2900
a29oo
700
b3800
a3700
a5600
a5200
a5600
a5200
a7000
86800
a66oo
a7000
86800
a66oo
700
1000
161
Maximum
conductor
tension,*
pounds per
conductor
1000
1000
700
1000
1000
1200
1400
1000
1200
1400
values-NESC light loading (US. customary)
r 69 through 161 kV are H-frame wood-pole construction;
* Maximum conductor tensions are limited by:
Conductor swing
9-lb/ft* wind
l/3 low point
Degrees
Et
65O19’
65O19’
63OO2'
63OO2'
57009’
57OO9’
57009’
57009’
50°38'
50°38'
50°38'
50°38'
50°38'
50'38'
230 and 345 kV are steel tower construction.
a 18 percent ultimate strength at 60 OF fmal, no load.
b 25 percent ultimate strength at 0 OF fmal, no load.
’ At 3300-ft elevation, and at 60 OF with a 9-lb/ft* wind.
4 At 3300-ft elevation. and rounded off to next highest 5 feet.
Outside
phase to
structure
centerline,
ft
Minimum
horizontal
clearance
to buildings,3
ft
Right-of-way,4
ft
10
10
10.00
10.00
70
24.86
13.67
24.31
14.10
24.99
90
s
12
12
14
14
10.66
10.66
75
95
80
!z
14.94
17
25.83
28.51
38.34
50.56
:5’
25
25
13.43
31.99
41.82
54.04
i8
30
11.12
11.12
11.59
11.59
12.98
12.98
12.98
15.31
105
90
110
135
155
180
155
15.31
15.31
175
200
7
$
0
=i
5
z
:
2
Table 32.-Right-of-way
kV’
Conductor
69
115
138
84 mm2 ACSR 6/l
213
135 mm2 ACSR 26/7
213
242 mm2 ACSR 24/l
161
242 mm2 ACSR 24/l
230
483 mm2 ACSR 45/l
345
Ruling
span,
m
483 mm2 ACSR 4517
duplex
Maximum
conductor
tension,’
newtons per
conductor
Conductor
sag at
15.5 oc,
mm
a15 500
values-NE,!%7 medium loading (metric)
Insulator
string
length,
mm
Conductor swing
0.43-kPa wind
l/3 low point
Degrees
m
305
bll300
a19 100
4033
7521
3111
305
b21300
a26700
6947
4 111
869
869
1219
1219
1372
305
305
305
366
427
305
366
b28500
a267OO
b28500
b37400
b36900
b36400
b37400
b36900
1655
4 111
7655
8948
12 821
17525
8948
12 821
1372
1676
1676
2286
2286
2286
3658
3658
50038'
50°38'
50°38'
50°38'
50°38'
11.6850
15.3174
427
b36400
17525
3658
50°38'
16.3782
213
213
r 69 through 161 kV are H-frame wood-pole construction;
2 Maximum conductor tensions are limited by:
65O19’
65O19’
3 At 1006-m elevation, and at 15.5 OC with a 0.43-kPa wind.
4 At 1006-m elevation, and rounded off to next highest meter.
3.048
3.048
4.4531
7.6291
3.048
3.048
3.658
63OO2'
1.2185
4.6062
3.658
4.267
7.5835
4.8616
4.267
5.182
5.182
7.620
7.620
7.620
230 and 345 kV are steel tower construction.
a 25 percent ultimate strength at -29 OC final, no load.
b 18 percent ultimate strength at 15.5 OC fmal, no load.
Minimum
horizontal
clearance
to buildings,3
m
63OO2'
57009’
57009’
57009’
57009’
4.4542
Outside
phase to
structure
centerline,
m
7.8389
8.6859
9.7467
12.7458
9.144
9.144
9.144
3.249
3.249
3.389
3.389
Right-of-way ,4
m
z
%
22
28
g
5;
ul
i:
3.532
3532
3:
P
1
z
3.956
3.956
3.956
41
41
0
E
:48
5
4.666
4.666
54
4.666
61
m
5
z
r
Table 33.-Right-of-way
kV’
Conductor
69
No. 4/O AWG ACSR 6/l
115
266.8 kcmil ACSR 2617
138
477 kcmil ACSR 2417
161
477 kcmil ACSR 2417
230
954 kcmil ACSR 4517
345
954 kcmil ACSR 4517
duplex
Ruling
span,
ft
700
1000
700
1000
700
1000
700
1000
1000
1200
1400
1000
1200
1400
Maximum
conductor
tension,2
pounds per
conductor
Conductor
sag at
60 OF,
ft
a3500
b3900
a4300
b4800
a6000
b6400
a6000
b6400
b8400
b8300
b8200
b8400
b8300
b8200
’ 69 through 161 kV are H-frame wood-pole construction;
’ Maximum conductor tensions are limited by:
values-NESCmedium
13.16
24.63
12.37
22.75
13.49
25.15
13.49
25.15
29.38
42.07
57.38
29.38
42.07
57.38
Insulator
string
length,
ft
2.5
2.5
4.0
4.0
4.5
4.5
5.5
5.5
7.5
7.5
7.5
12.0
12.0
12.0
loading (U.S. customary)
Conductor swing
9-lb/ft2 wind
l/3 low point
Degrees
ft
6S019’
65O19’
63OO2’
63OO2’
57009’
57009’
57009’
57OO9’
50°38’
50°38’
50°38’
50’38’
50°38’
50°38’
230 and 345 kV are steel tower construction.
a 25 percent ultimate strength at -20 OF final, no load.
b 18 percent ultimate strength at 60 OF final, no load.
’ At 3300-ft elevation, and at 60 OF with a 9-lb/ft’ wind
4 At 3300-ft elevation, and rounded off to next highest 5’f&.
14.23
24.65
14.59
23.84
15.11
24.91
15.95
25.75
28.51
38.33
50.16
31.99
41.81
53.64
Outside
phase to
structure
centerline,
ft
Minimum
horizontal
clearance
to buildings,3
ft
10
10
12
12
14
14
17
17
25
25
25
30
30
30
10.00
10.00
10.66
10.66
11.12
11.12
11.59
11.59
12.98
12.98
12.98
15.31
15.31
15.31
Right-of-way,4
ft
70
90
;:
85
100
1?8
135
155
180
155
175
200
II
TJ
-F
ZJ
a
=I
5
z
g
2
Table 34.-Right-of-way
values-NESC heavy loading (metric)
84 mm2 ACSR 6/l
213
Maximum
conductor
tension,?
newtons per
conductor
a18 200
115
135 mm2 ACSR 26/l
305
213
a182OO
b24400
12530
4452
869
1219
65O19'
63OO2'
12.1751
5.0547
3.048
3.658
3.048
3.249
138
242
305
9524
4665
8 101
4 665
8 101
8 954
12 844
1219
1372
2286
2286
63OO2'
57009'
57009'
57009'
57009'
50°38'
50°38'
9.5755
5.0716
1.9582
5.3270
8.2186
8.6905
11.6982
3.658
4.267
4.267
5.182
5.182
7.620
7.620
3.249
3.389
3.389
3.532
3.532
3.956
3.956
34
41
41
Rulins
span,
Conductor
kV’
69
m
230
345
Insulator
string
length,
mm
Conductor swing
0.43kPa wind
l/3 low point
Degrees
m
5194
869
65O19'
Outside
phase to
structure
centerline,
m
Minimum
horizontal
clearance
to buildIngs,3
m
6.0544
3.048
3.048
25
is
31
24
f
;z
$
239”
r
z
Rightof-way,4
m
i
242 mm2 ACSR 24/l
213
483 mm2 ACSR 4517
305
305
366
a24900
b33300
a382OO
b33 300
a38200
c51 100
c50700
421
c50 300
11515
2286
50°38'
15.3097
7.620
3.956
54
305
366
421
c51100
c50700
c50 300
128954
844
17515
3658
3658
50'38'
50°38'
50°38'
12.7590
9.7513
16.3705
9.144
9.144
4.666
4.666
54
48
61
mm2ACSR
24/l
213
305
161
Conductor
sag at
15.5 oc,
mm
483
mm2 ACSR 45/l
duplex
: 69 through
Maximum
161 kV are H-frame wood-pole
conductor
construction;
1372
1676
1676
230 and 345 kV are steel tower construction.
tensions are limited by:
a 50 percent ultimate strength at -18 OC initial, full load.
b 33-l/3 percent ultimate strength at -40 OC initial, RO load.
c 18 percent ultimate strength at 15.5 OC final, no load.
3 At 1006-m elevation, and at 15.5 OC with a OA3kPa wind.
4 At 1006-m elevation, and rounded off to next highest meter.
m
0
FJ
s
5
f
r
Table
Conductor
kV’
35 .-Right-of-way
values-NESC heavy loading (U.S. customary)
Ruhng
spa%
ft
Maximum
conductor
tension,2
pounds per
conductor
Conductor
sag at
60 OF,
ft
Insulator
string
length,
ft
a4 100
a4 100
18.95
41.00
2.5
2.5
65O19’
65O19’
19.49
39.53
10
10
10.00
10.00
80
120
12
12
14
14
17
10.66
10.66
11.12
11.12
11.59
11.59
12.98
80
110
85
105
95
115
135
12.98
12.98
155
180
:
=i
6
z
Conductor swing
9-lb/ft’ wind
l/3 low point
Degrees
ft
Outside
phase to
structure
centerline,
ft
Minimum
horizontal
clearance
to buildings,’
ft
Rightof-way,4
ft
69
No. 4/O AWG ACSR 6/l
700
1000
115
266.8 kcmil ACSR 26/7
700
1000
700
1000
700
1000
1000
b5
a5
b7
a8
b7
a8
cl1
500
600
500
600
500
600
500
14.57
31.23
15.47
26.54
15.47
26.54
29.35
4.0
4.0
4.5
4.5
5.5
5.5
7.5
63OO2’
63OO2’
57009’
57009’
57OO9’
57009’
50°38’
16.55
31.40
16.78
26.08
17.62
26.92
28.49
1200
1400
c11 400
cl1 300
42.13
57.51
7.5
7.5
50°38’
50°38’
38.37
50.26
1000
1200
c11 400
500
cl1
29.35
42.13
12.0
50°38’
31.97
41.85
ii
30
15.31
155
175
57.51
12.0
50°38’
1400
c11 300
t 69 through 161 kV are H-frame wood-pole construction; 230 and 345 kV are steel tower construction.
2 Maximum conductor tensions are limited by:
53.74
30
15.31
200
138’
477 kcmil ACSR 2417
161
477 kcmfl ACSR 2417
230
954 kcmil ACSR 4517
345
954duplex
kcmil ACSR 4517
a 50 percent ultimate strength at 0 OF initial, full load.
b 33-l/3 percent ultimate strength at -40 OF initial, no load.
’ 18 percent ultimate strength at 60 OF final, no load.
’ At 3300-ft elevation, and at 60 OF with a g-lb/f? wind.
4 At 3300-ft elevation, and rounded off to next highest 5 feet.
::
25
?
D
:
Y
5
.
:
2
282
TRANSMISSION
28.
Armor
Rods
of vibrations
may
and
produced
well
result
by very
turbulence
steady
on the leeward
1 to possibly
millimeters
aeolian
the
hertz,
reinforced
induces
vibrations
of an inch
the
aluminum
on a clear,
conductor
cold
the conductor
support,
which
and
The
The
a few
light
Therefore,
dampers,
effect on vibration
value is through
range
and
to 200
amplitudes
nodes,
of
tension
force per unit length.
On short spans,
by the humming
sound produced-like
and
is usually
this type
or both.
strung
to fairly
of conductor
requires
and reduce the amplitude
from
the reinforcing
of the conductor
some protection
to the conductor
due to flashovers.
Armor
rods
for
high
special
10 to 20 percent;
at the point
of
against vibration,
the armor
aluminum
conductors
are
to a stranded
cable of larger
diameter-thereby
region
of maximum
bending
stress.
A set of 7 to 13 rods, depending
length
of the rods vary
with
are
eddy
frequencies
between
and consist of a spiral layer of short, round
rods surrounding
conductor
to its support
is made in the middle
of the armored
equivalent
is in the
which
varying
millimeters
frequencies
distance
and
morning.
is comparatively
rods have some damping
their greatest
protective
frequencies
from
types
conductor
periodically
the excitation.
length,
and other
in the
natural
It is the
range
or more.
span
to aeolian
stresses
of the
and the conductor
and is evident
only
Armor
however,
to offering
from burns
those
produces
velocity,
so it is quite
susceptible
to vibration.
by the use of armor
rods, vibration
maximum
stress. In addition
rods protect
the conductor
are subject
bending
normally
inches),
wind
of the conductor,
small amplitude
lines
that
to several
of the
MANUAL
(1 to 30 mi/h).
amplitudes
tensions,
protection
made of aluminum
attachment
of the
are
of 1 to 48 km/h
and
are functions
singing of telephone
Steel
repeated
Aeolian
winds
in the conductor,
diameter
the vibration
is of extremely
the
conductors
which
side of the conductor
100
(a fraction
vibrations
Dampers.-All
wind,
in its failure.
stimulated
from
Vibration
by
LINE DESIGN
the conductor.
length.
This
strengthening
The
makes
it at the
on conductor
size, is required
to armor
a conductor.
The size
the size of the conductor.
Generally,
because
of the ease of
application,
and for both
and removal
if necessary,
preformed
armor rods are used for all sizes of ACSR conductors
steel and Alumoweld
overhead
ground
wires. Formed
rods are manufactured
with a spiral
shape
the
to fit
diameter
of the
conductor
on which
they
are to be used.
The
ends
of each
rod
are
discharge
of armor
or parrot-billed to reduce the chance
of abraiding
the conductor
and the tendency
for corona
at these points.
Clips or clamps
are not required
on this type of armor
rod. Older
types
rods, now seldom
used by the Bureau,
include
the straight
rod and the tapered-rod
types.
Straight
armor
rounded
rods,
having
a constant
diameter
sizes of 15 to 62 mm2 (No. 6 AWG to No.
with long tapered
ends and are used for
straight
at the
and tapered
types
time of installation
for their
full
length,
of rods are furnished
using special armor
straight
and the spiral
rod wrenches.
These
on the conductor
by the installation
of armor
rod clips or clamps
been formed.
Normally,
armor
rod clamps
are used on transmission
and higher,
and armor
mostly
to the possibility
Through
experience,
effective
device
against
are used
l/O AWG),
inclusive.
Tapered
79 mm2 (No. 2/O AWG)
and
has found
and, when
damper
will greatly
reduce
vibration.
We use both armor rods and vibration
dampers
the Stockbridge-type
properly
installed,
for ACSR
conductor
rods are straight
rods
conductors.
Both the
is formed
around
the conductor
types of rods are held in place
at each end after
the spiral
has
lines for voltages
of 115 kilovolts
rod clips are used for voltages
of 69 kilovolts
of corona
loss off the sharper
edges of the
the Bureau
vibration
armor
larger
the
on our transmission
suspension
points
may be eliminated
if sized clamps
are used for the
be an almost
perfect
fit, with extremely
small tolerance,
to provide
strand
breakage
at this stress point.
and
clips.
vibration
latest
lines.
lower.
This
choice
is due
damper
to be a very
models
of this type of
Armor
conductor.
the desired
rods
at conductor
These clamps
must
protection
against
Each
construction
application,
contractor
and
transmission
field office
location
in the
to furnish
DATA
the
dampers
vibration
middle
of the
of possible
A damper
the
problem
loop
centerline
could
formed
frequencies
effective,
however,
absolutely
from
of the
should
be handled
in the
is almost
are
be located
conductor
to be furnished
must
be located
in the
middle
suspension
regardless
of size, span
simply.
and
the
midpoint
point
A vibration
problem
third
another
of a loop
would
becomes
of a loop
for
and
are transmitted
dampers.
The
so the problem
at the
the midpoint
could be a node
no effect
(see fig. 112).
recommendations
conductor
quite
unlimited
283
manufacturer’s
that
or compression
dead end.
vibrated
at the same frequency
the
to be most
wind;
have
is required
of the‘ vibration
distance
of a strain
clamp
If all conductors
number
V-ADDITIONAL
line. The data are checked
and, if found
satisfactory,
as the criteria
to use for installation
of the vibration
at a prescribed
velocity,
CHAPTER
created
frequency,
to be effective.
for size,
installed
on the
to the appropriate
dampers
are installed
clamp
or from
length,
tension,
damper
could
he solved.
more
the
and
Studies
and
wind
be placed
However,
complex.
in the
mouth
conductor
the
the
A damper,
by the
damper
should
would
be made
so that a damper
installed
at the chosen location
will be effective
on as many probable
frequencies
as possible.
Numerous
laboratory
studies have been made by manufacturers
of dampers
over the years.
The new, more sophisticated
dampers
have been developed
through
these laboratory
studies
and
should be applied
as recommended
by the manufacturer.
Formulas
for computing
the frequency
and
loop length
and the basic theory
of vibration
can be found
in most physics
books. Two such formulas
are:
For frequency :
Metric
U.S. Customary
Hz
51.4534
km/h
Hz
3.26
mi/h
mm
in
f&l
d
where f = frequency
k= a constant (for air)
V= velocity of wind
d= outside diameter of
conductor
For loop length:
where L = loop length
f= frequency
T= tension in conductor
g = acceleration due to gravity
W=
force of conductor
A standing
but
of opposite
Reduction
wave,
such
direction
of span
as the vibration
loop,
mm
Hz
N
9.8066 m/s*
N/m
is the result
of two
traveling
of motion.
length
and
tension
reduces
the
severity
of vibration.
in
Hz
lb
32.2 ft/s*
lb/ft
waves
equal
in magnitude
TRANSMISSION
284
LINE DESIGN
MANUAL
Midpoint of loop
f
(Vibration waves are exaggerated vertically for illustmtion)
Figure
Galloping
or dancing
112.-Schematic
conductors
by strong
gusty winds blowing
of eliminating
this phenomenon
melt
it off
as quickly
value.
Corona
are large-amplitude,
after
it forms
loss on a transmission
of conductors
when the
occurs
when
waves in a conductor.
low-frequency
vibrations.
Galloping
the
potential
and
before
damage
occurs
(see sec.
line is the result of the ionization
electric
stress (or voltage
gradient)
of a conductor
in air
is raised
conductors
will
result.
There
is always
a power
When and where will corona
occur on a given
be? What
can be done
to reduce
or eliminate
investigators
have studied
over the years. Three
Rockwell
Peterson
[ 161, and Peterson
formulas
have been
to such
used for calculating
of obtaining
good
the expected
data is to take
This
true
of the
Recent
available
corona
the data
loss for these
from the line
extra-high-voltage
lines,
so care
study
based
In fair
conductor.
up to a voltage
near
voltage
is an indicator
surface
For
the
of a given
same
a smooth
will
increase
size of the
conductor
diameter,
conductor.
approaches
a stranded
Any
corona-and
conductors
distortion
their
the
spacings
line
cylinder,
is good
to the surface
the higher
and
a smooth
conductor
voltage,
also
the
corona.
country.
region,
The
below
Carroll-Rockwell
3.1 kilowatt
higher
voltages.
Actually,
the
being studied
after it has been
a published
is small
disruptive
that
and
per phase
work
has been directed
toward
corona
loss in the
information
for this range should
be explored
and
and the method
of calculation
from
to that which
you propose
using.
weather,
corona
The calculated
a value
tufts or streamers
the odor of ozone.
enough,
corrosion
transmission
line ? How much power
loss will there
it? These
are some of the questions
that
many
methods
of calculation
by Peek [15], Carroll
and
[ 171 are in general
use in this
the most accurate
in the low-loss
kilometer
(5 kilowatt
per phase mile).
extra-high-voltage
range, and the latest
is especially
loss with
14).
process which
takes
exceeds a certain
dielectric
strength
of the surrounding
air is exceeded.
Corona
is visible
as bluish
around
the conductor;
the visible discharge
is accompanied
by a hissing sound and
In the presence
of moisture,
nitrous
acid is produced
and, if the corona
is heavy
of the
is caused
across irregularly
ice-covered
conductors.
The only known
methods
are to either
prevent
the ice from forming
on the conductor,
or to
as possible
29.
Corona.-Corona
place on the surface
of vibration
have
the
be exercised
to select
line
the disruptive
voltage
of corona-performance.
the
for
of the
must
on transmission
higher
about
considerable
the critical
80 to 85 percent
conductor
more
(raised
critical
effect
these
best method
constructed.
strands,
data
test
very
data
similar
for a particular
The closer the
disruptive
voltage.
of the
voltage
burrs,
scratches)
of
rough spots become. The
on corona
loss. Fair
weather,
CHAPTER
rain,
snow,
hoarfrost,
corona
loss.
rain produces
the
same
loss is observed
line
to know
In earlier
When
rates
of rainfall
behavior.
Corona
can
and
and
dimension
instead
between
text
reduce
overvoltage
surge.
for
figures
of the
were
illustrations,
from
we have
are
present,
open-circuited
loss to be expected
an entire
lines,
transmission
because
become
corona
and
in a
be necessary
line.
of energy
more
can
affect
it will
loss.
important.
system
attenuate
both
corona
reference
chosen
along
studying
The presence
of
voltage
at which
do so, it would
has probably
expected
SI metric
To
when
factor.
of the
was avoided-strictly
of corona
the
be considered
of corona
simultaneously
on long
taken
value
switching)
calculating
preferred
peak
corona
aspect
(lightning,
switching
related
and
transmission,
must
to determine.
exist
285
than any other
single
as low as 65 percent
The
could
DATA
temperature
impossible,
influence
voltages
is a procedure
procedure
weather.
that
radio
high
voltage
Following
the
and
loss more
at voltages
if not
of high-voltage
years,
abnormally
lightning
fair
difficult,
years
recent
during
is very
all of the
more
pressure,
Rain probably
affects
corona
corona
loss on a conductor
transmission
In
atmospheric
V-ADDITIONAL
loss on a transmission
line.
is
reference
used
centimeters
Th
[18].
dimension
of millimeters.
To
to present
the
in centimeters:
procedure
ensure
This
as a
compatibility
Nomenclature:
Pk =
corona
loss,
kW/km
P,
=
corona
loss,
kW/mi
E
=
average
surface
critical
visual
Eo=
=
line
to ground
>
=
line
frequency,
6
=
air
n
=
number
r
=
conductor
=
spacing
g
=
mean
g,,
=
surface
;=
density
at 50 Hz
at 60 Hz
voltage
corona
(per
phase)
(per
3-phase)
gradient
gradient
voltage,
kV
Hz
factor
of conductors
radius,
in bundle
cm
of conductors
equivalent
phase
between
spacing,
average
voltage
m = conductor
in bundle,
cm
and
gradient
surface
cm
factor
maximum
surface
gradient,
at which
corona
starts,
(assumed
0.88,
average
kV/cm
kV/cm
weathered
conductor)
Assume:
345-kV
transmission
483-mm2
457-mm
10.06-m
The
basic
line
(954-kcmil)
(18~in)
(33-ft)
formula
for
at 1829-m
ACSR,45/7
spacing
on conductor
flat phase spacing
reading
the
corona
(6000-ft)
conductor
elevation
(duplex)
e =
199.2
r
1.48
=
cm
s = 45.72 cm
bundle
D =
loss from
kV
the
curves
shown
on figures
1005.84
113
cm
and
114
is:
286
TRANSMISSION
LINE DESIGN
MANUAL
pk
g is analogous to E so, y22
g,
= F A.
0go
0
For a duplex conductor,
l+$
(
g=
e
)
(2r) log, A+For a single conductor,
g=
e
r log, f
g=
(1 +~)WW
(2) (1.48) log,
Calculateg,
Results
from
for air density
the two-thirds
a high-altitude
test
205.65
== 14.45 kV/cm
14.23
(1 ;;;;k8p72,
.
fromg,
project
= 21.1 m 6%
at Leadville,
Colo.
0.301
1+ fi >
(
[19]
8 varies as the one-half
power
in lieu of the first power
power
as indicated
by Peterson’s
investigations
[17].
concluded
that
as suggested
the
= 20.72 kV/cm
Calculate
g/go
and
read
corresponding
value
for
14.45
g
-z-z
go 20.72
From
figure
113,
-&
curve
Pk /n
2 r2 at 50 Hz
from
figure
o 7.
’
A :
= 0.04
Pk = 0.04(2)2 (1.48)2 = 0.2368 kW/km at 50 Hz (per phase)
correction
by Peek
113:
[15]
or
CHAPTER
V-ADDITIONAL
287
DATA
‘k
n2r2
0.4
0.6
Figure 113.-Corona
As read
test.
from
Because
should
multiplying
1.0
1.2
0.3
loss curves for (A) fair weather,
figures
113
the corona
be multiplied
by
the
in kilowatts
per
for
~7
QS
(B) rainfall,(C)
for
a 60-Hz
factors,
three
phases
The
0.3 OA Q5 Q6 Q7 0.9 09 1.0 I.1 1.2 13
and(D)
value
phases,
should
60-Hz
snow. 104-D-1116.
From [18].
for each phase from a 50-Hz
the value read from the chart
kilometer
for all three
for
---
per kilometer
to frequency,
system.
the figure
1.1
hoarfrost,
Pk is in kilowatts
is in direct proportion
if the loss is desired
three
mile
~5
114,
60/50
and
Combining
and
loss factor
by 1.6093,
by three.
value
0.9
may
the
be changed
answer
be multiplied
should
by 5.79
to
mile
by
be multiplied
to obtain
a loss
systems:
Pk = 0.2368 kW/km at 50 Hz (per phase)
PC = 5.79 (0.2368) = 1.371 kW/mi at 60 Hz (per 3-phase)
When
curve
the
rainfall
two,
three,
100 percent.
give
is to be considered,
B. Similarly,
the
for hoarfrost
or four
Taking
expected
(whichever
the assigned
corona
loss for
the
or snow,
corona
is applicable)
percentages
the
line
loss due
losses are obtained
values
times
‘in question.
for
to rain
must
from
corona
the corresponding
be read
curves
Cor
loss must
from
figure
ZI, respectively.
be apportioned
losses and
summing
113 using
Then,
to make
these
will
288
TRANSMISSION
LINE DESIGN
MANUAL
1.0
0.8
0.6
0.1
0.08
0.06
0.01
0.5
0.6
0.7
0.8
0.9
1.0
I.1
Figure 114.-Average
values of corona loss under fair weather with different
conductor
bundles. (1) single conductor
(2) two-conductor
bundle
(3) three-conductor
bundle (4) four-conductor
bundle (5) average curve.
104-D-1117.
From [18].
CHAPTER
V-ADDITIONAL
DATA
289
Example:
Assume
that
is fair,
the
line
5 percent
previously
of the
used
time
is located
it rains,
and
such
that
10 percent
85 percent
of the
time
of the
time
it snows-all
the
during
weather
a period
of a year.
pk
-
= 0.04 for fair weather (curve A, fig. 113)
n2 Y2
Pk = 0.04(2)2 (1 .4Q2 = 0.2368 kW/km at 50 Hz (per phase)
PC = 5.79(0.2368)
‘k
-
= 1.37 1 kW/mi at 60 Hz (per 3-phase)
= 0.90 for rainfall (curve B, fig. 113)
n2 r2
Pk = 0.90(2j2(
= 7.885 kW/km at 50 Hz (per phase)
1 .48)2
PC = 5.79(7.885) = 45.654 kW/mi at 60 Hz (per 3-phase)
pk
n2 r2
for snow (curve D, fig. 113)
= 0.15
Pk = 0.1 5(2)2 (1 .48)2 = 1.3 14 kW/km at 50 Hz (per phase)
PC = 5.79(1.314) = 7.608 kW/mi at 60 Hz (Per 3-phase)
Summation of losses times percentages:
(0.85)(1.371)
+ (0.05)(45.654)
+ 0.10 (7.608) = 4.21 kW/mi at 60 Hz (per 3-phase)
This is the average corona loss for the year.
Although
justified
this
method
for practical
due to weather
conductor.
decrease
Factors
conditions.
New
rapidly
Fair
weather
lines
with
various
for
As indicated
transmission
rather
for
of calculation
purposes.
corona
loss is only
in the example,
corona
tend
there
loss depends
to have
higher
an approximation,
mostly
losses;
on the
however,
changes
surface
these
conductors
weather
conditions
conductor
in fog,
mist,
Weathered
conductor
in fair
weather
Corona
loss curves
and
computed
by the
for
ACSR
higher
of the
values
will
are:
in rain
Weathered
elevations
in the losses
condition
time.
Range
All
it is apparently
are substantial
different
conductor
Carroll-Rockwell
and
voltages
sizes-from
method
snow
are shown
which
for
fair
0.47
to 0.60
0.54
0.60
to 0.80
0.70
0.80
to 0.95
0.88
on figure
may
A verage value
115.
Curves
be determined
the
weather
are shown
estimated
at 25 o C (77 o F).
for
corona
different
loss as
TRANSMISSION
290
a
0
LINE DESIGN MANUAL
CHAPTER
V-ADDITIONAL
DATA
291
TRANSMISSION
292
30.
Stringing
Sag
furnished
for stringing
sag data
the
sag and
studies,
tension
data
determination
electrical
For
field
results
installation
for
spans
than
sag table
ruling
conductor
for
to cover
length
a range
increments,
and
from
are not
the
without
high
become
On
free
suspension
from
the
tensions,
and
if the stringing
sags
and
are usually
loading
a temperature
form
lengths
in 5-m
elevation,
range
Spans.-When
conductors
spans.
If the
if the
terrain
however,
sag and
loading
is
use and
F in 10’
are
increments,
above
-18
if
conductor
in field
from
tension
conditions
if the
to 50 percent
should
at a lower
the
ruling
to 49 ‘C
in 5’
increments.
Offset Data for Inclined
low
below
tables
unloaded
0 to 120’
span.
Stringing
for the preparation
conditions
from
span.
generally
for convenience
range
the
but
on initial
loading
in table
sag tables
on the ruling
required
are the
are based
on final
listed
data
to furnish
of each
lengths,
basic
spans
values
50 percent
strings
span
and
of sag in that
sheaves
conductor
hanging
terrain
is not
is quite
conductor
supports
in stringing
sheaves
very
this
steep,
to hang
put
span
to obtain
dead
intermediate
ends
to the
conductor.
the
steep,
the
proper
dead
dead
should
tend
problem
sagging
on adjacent
to run
downhill
can be handled
of the
one
to isolate
be such as to minimize
sag and offset
dead end (the last structure
clipped
the
steep
conductor
see figure
is clipped
a way
that
the amount
the
in, slack
conductors
of slack
in a given
span
the sag while
has been
clipped
dead
ends,
must
be sagged
the
For
either
sagged
structure
from
in one
conductor
purposes
tension
permanent
ahead,
during
the
the
the suspension
between
the
the
clip-in
comparatively
the conductor
the
the
distance
it is necessary
temporary
clamp
dead
sections
dead
will
end
operation.
level
for
since
Where
in one operation,
where
of
is changed,
in. Calculations
operation.
the
be taken
or temporary,
of calculation,
For
components
to change
conductor
116.
must
horizontal
it is necessary
of line being
to maintain
be equal;
the
sagging
ends.
be at least
is snubbed,
ends,
ends
T2 must
in such
Whenever
between
to permit
the
span
sag after
dead
in the section
There
conductor
temporary
great
temporary
be the last structure
where
between
is too
after
upper
correct
of spans
of conductor
establish
the
is also changed-so
the
in a series
between
vertically
into
Tl and
tensions
HI and Hz are equal.
tension
length
these
suspension
These
units,
insulator
are made
shall
level
about
sheaves,
the amount
entire
sags and
based
length
span
The
from
running
the conductor
offsets
on exact
line.
metric
concern;
on
line
and
lengths
the individual
For
the
the
directly
including
it is necessary
of span
lengths
into
final
right,
If
based
complex.
lower
is in the
upon
are also based
conductor.
wires,
range
of span
at the same
spans
much
may
ground
based
as to cover
Sag and Insulator
(b)
for
important.
are not
design
he exactly
increments.
span
extremely
wires
calculations
will
the entire
is unstressed,
an extent
in lo-ft
structures
the
sag values
to such
span
cover
approximately
for
the
strengths,
separately
to be installed
and
complete
calculations
and overhead
which
to a substation
span
Stringing
expanded
line,
used on the rest of the transmission
of a stringing
prestressed.
ground
he disastrous.
spans
values
the
of the
are
overhead
of the
sizes and
None
sag data
and
design
of conductors
spans
that
at the
the
are computed
for approach
Tables-Stringing
conductors
for
may
suspension
Dead-ended
tension
used
is wrong.
far off-the
prepared
Sag
the
of structure
clearances
are too
data
Data.-(u)
LINE DESIGN MANUAL
be clipped
and
The
to
end
the point
selection
of line,
calculations.
The insulator
string ofthe
in) must be held in a vertical
position
last previous
temporary
while the next section
The tension
in the conductor
while
after the suspension
clamp is clipped
in the stringing
to the conductor,
or lower than the tension
insulator
string clipped
in may
the
line
is brought
swing
to the
towards
proper
or away
of
should
of
sag.
from
new
section
sheaves may be higher
so the last suspension
of line
being
brought
to sag if the
insulator
is
CHAPTER
V-ADDITdONAL
DATA
293
Figure 116.-Conductor
tensions
running stringing sheaves.
not properly
held
sagging and clipping
to sheave
a reference
string
clamp
for
sag by
mark
in a vertical
position.
in of the conductor
is equal
to the
and
sag correction
at any point
in a conductor
length
of the
ordinate
data
is given
of uniform
of the
curve
in the
error
in the
is brought
sag plus correction)
of several
spans,
under
the point
where each insulator
following
cross section
at the
using free
vertical,
a serious
After the conductor
Clipping
in is then started
at any structure
by placing
offset distance
and direction
from the reference
mark.
offset
Procedure
The tension
is not held
could occur.
checking
the corrected
sag (stringing
chart
should
be placed
on the conductor
directly
is supported.
at the proper
calculating
If the insulator
in the new section
when
given
the center of the suspension
An explanation
of a method
paragraphs.
suspended
point
in the form
times
the
unit
of a catenary
force
conductor.
At
support
A on figure
117:
Directrix 2
+”
1
Figure 117.-Dimensions
required for calculating
stringing operations.
104-D-1 119.
insulator
offset
and sag correction
data during
of the
294
TRANSMISSION
LINE DESIGN MANUAL
T, = WYA in span 1
+Y, - Y,)inspan2
T, =W(YA
T, - T, = W(Y, - Y,)
where :
W = force of conductor in newtons per meter (pounds per foot)
T, and T, = conductor tensions in newtons (pounds)
= difference in elevation between the directrices of the two
cantenaries, which is also the difference in elevation
between the low points of sag in the two spans, in
meters (feet)
y2 - Yl
A table with the following
column
headings
should
be made:
Column
1: Station
number.
This shows the survey
station
2: Span length
L, in meters (feet)
3: Yz- Yt in meters
(feet). This value
Column
Column
the low points
at the stringing
be essentially
sheets.
Column
4:
of sags in spans adjacent
temperature;
however,
the
same
at any
W(
yZ- Y,),
given
( W)
(col.
shows
the
where
each
difference
structure
in elevation
is located.
Yz- Yl between
to each structure.
These sags should
be the initial
sags
because
the difference
between
sags in the two spans will
Ys- Yr may be measured
on the plan-profile
temperature,
3),
in newtons
(pounds).
This
value
shows
the
Tz-Tl, on the two sides of the structure.
between
the conductor
tensions,
Column
5: Assumed
tension
Hin
newtons
(pounds).
This value shows an assumed
component
Hof the tension (called horizontal tension for convenience)
in the conductor
in the stringing
at the stringing
sheaves.
For
temperature
this assumption,
use the initial
horizontal
as shown
on the sag-tension
calculation
difference
horizontal
as it hangs
tension
of the conductor
form.
Assume
this tension
to be in a certain
span (generally,
it is best to use one of the longer spans) and compute
the tensions
in other
spans by adding
or subtracting
increments
from column
4.
(pounds).
This value shows the difference
between
Column
6: H,H,
(& -col. S), in newtons
the horizontal
H
in each
Column
tension
span with
7: Offset
in the
the
Kin
conductor
conductor
millimeters
at the
ruling
K= lOOOW2 L3
mm/N
12H,,3
This value
in tension.
slack per
Column
in slack
in this
shows the change
The sum of the
column
span
corresponding
is the overall
or K=-
change
and
w2 L3
in slack in a span corresponding
values in this column
gives the
pound)
change
in the tension
8: Trial
offset,
(col. 6) (col.
for each
Ho
span
the assumed
horizontal
tension
hanging
in the stringing
sheaves.
per newton
(inches
per pound).
for the complete
7), in millimeters
to the
of slack
unbalanced
Hl13
in/lb
to a one-newton
(one-pound)
change
total change
in slack per newton
(or
section
of line
(inches).
This
tensions.
for the complete
The
section
being
value
considered.
shows the
algebraic
of line,
based
sum of the
change
values
on the assumed
CHAPTER
tensions.
sum
the
This
is a positive
line.
The
sum
must
he zero
value,
If the
sum
should
sum
of column
be applied
that
to the
Ho-H
9:
Column
10:
Column
11: Modulus
by
Corrected
offset,
of column
(col.
295
has been
he subtracted
sum
he added
to the
7 is the
assumed
in each
from
complete
the
complete
total
span.
section
section
correction
If the
of the
in tension
of
line.
which
of line.
column
correction
must
must
section
corrected,
DATA
tension
amount
the
complete
correct
of slack
that
8 divided
Column
if the
amount
is negative,
V-ADDITIONAL
6 - (2 col.
7)
(col.
8/X
col.
7), in newtons
9), in millimeters
in millimeters
(pounds).
(inches).
(inches)
1OOOL (col. 9) mm or
AE
12L (col. 9) in
AE
where :
A = area of conductor in square millimeters (square inches)
E = modulus of conductor in gigapascals (pounds per square inch)
Column
12: Final
correction
in millimeters
(inches).
(Z col. 10 + x col. 11) (col. 7)
z col. 7
Columns
(col.
9, 10, 11, and
11) is the
in columns
corrections
in length
13: Final
amount
Column
the amount
of the
11 should
proportional
Column
the
change
10 and
12 are used
equal
of offset
(col.
required
14: Sum
of offsets,
necessary
to offset
span.
(running
sum
insulator
change
be made
in column
13),
in millimeters
string
from
the vertical.
in millimeters
modulus
The
sum
correction
of the
values
in either
of these
12 to offset
these
remainders.
(inches).
This
value
shows
(inches).
This
value
shows
12), in millimeters
of col.
spans.
while
in sheaves
The
in tension.
is a remainder
11 + col.
in each
each
of the offsets
in the individual
Column
15: Sag correction
must
col.
in the offsets.
with
If there
length
10 +
corrections
conductor
zero.
to the span
offset,
to make
This
offset
columns,
is the summation
(feet)
(3H, )(col. 10)
(3H,,)(col. 10)
(2W)(col. 2) mm Or (2W)(col. 2) (1/12) ft
This
column
conductors
shows
are in the
the
amount
stringing
that
sheaves
will
be necessary
to obtain
to correct
the
correct
the sag in each
sag after
the
span
while
conductor
the
is clipped
in.
The
long
rough
and
offset
as the
terrain
accurate
and
sag correction
individual
where
offset
the offset
computer
data
as computed
for one span
is not
in any one span
program
should
in such
in excess
in a section
be used
instead
a table
should
of 381 mm
of line
of
may
this
(15 in).
be sufficiently
For
accurate
installations
exceed
381 mm,
simplified
method.
a more
It
as
on very
detailed
is usually
TRANSMISSION
296
unnecessary
in one
to consider
operation,
the
the
offset
and
corrections
LINE DESIGN MANUAL
sag correction
calculated
data
are within
if, in a section
all three
of line
of the
following
Line conductor
mm
w
(1) Maximum summation of offsets at any
structure
(2) Maximum difference between summations of offsets at adjacent structures
(3) Maximum sag correction in any span
The
same
conductors
procedure
should
A sample
as described
he used
problem
for
to calculate
has been
worked
out
in both
kcmil),
ACSR,
sagged
limits:
Overhead ground wire
mm
(id
(6)
76
(3)
76
(3)
51
(2)
305
(12)
305
(12)
the
data
is being
152
calculating
similar
that
for
offset
the
metric
and
overhead
and
U.S.
sag correction
ground
customary
data
for
line
wires.
units
to illustrate
this
procedure:
Example
Conductor:
Full
load
644 mm2
conditions:
Maximum
Initial
tension
tension
(1272
13-mm
under
at 15.5
(l/2-in)
full
‘C
load
(60
45/7
radial
conditions
“F)
(Bittern)
ice with
=
is 26 040
a 0.19-kPa
53 378
N (5854
(4-lh/ft2)
wind
at -18
’ C (0 ’ F)
N (12 OOd lb)
lb) widh
a korresponding
sag of 12 485
mm
(40.96 ft).
Area
of conductor
A =
Initial
modulus
of conductor
689 mm2
AE = 32 162 542 N
H,, = T- Ws = 26 040 -
Initial
E
(1.068
=
(7 230
46.678
Figures
shows
in the
118 and 119
the stationing,
procedure
is shown
GPa
(6.77~10~
lb/in2)
=
N
360 lb)
(20.9277)(12.485)
= 5854 - (1.434)(40.96)
120
in2)
25 778
= 5795 lb
show the sag and tension
calculations
elevations,
and span lengths
for the
in tables
36 and
37.
for the given conductor,
and figure
sample
problem.
The table described
CHAPTER
OCm-678
V-ADDITIONAL
DATA
297
(3-78)
:":nT:"L' SAGCALCULATIONS
Ml
2
CONDUCTORst'jmm
R/7%7"
//3Sf
.4547
LOADING&
Code Nams
Linear Force Fnclor:
@3
Rated Breaking Strength/q
Diameter .A
N
Dead Load Force (W’) i?t&d!
Permanenr set 0.00 Qa.
CreepO.OOQ
*s
Tenston Llmlt*tions:
Initial.-
%.Ai-K-
Final.!.
;;;“y+f$-
N
25
8g9
N
o.ow
Exp.: jc
A=
Initial
+!ZZt//
Final AE
OzL&perOC
Dare ~
Initial
*/977
T~cp-/UNSTRESSEG
LENGTN
LOADING
Ice
HEX.
./
N/l?
Modulus. (E) Final &.c&&-
Temp. Coeff. of Linear
%-
Computed by
yd,
sqj
Total O.CQd6?
Area (A)amd
-N
Final .- 15.5% .-
,“;
(W”‘)
Resultant:
% -N
Loaded.~oC.5oW
/dn?m
N/m
mm
jb.
GPa
/,,79
44I//9
GPa
009
AE .&
,”
x=d3782
SAG, mfn
1 SAGFACTOR /
3
';
I
SPAN LENGTH(S
1
SW,N
1
TENSION, N
NO Ice. No Wind (W’)
Figure
DC-578
118.Sag
and tension
calculation
form for example
problem
on insulator
offset
and sag correction
(metric).
(3.73)
!;,p
CONDUCTOR&J
7
Code Nams
Riftcrn
Rated Breaking
Diameter
Tenston
LOADING k'eavv
14,
Load
J!!.?+
Weight Factors:
,?
,
/ofi
Dead Weight
lb
+ ‘/Lin.
inch
Llmltatlons:
o
lb
Final *OF*%-
Compuled by -
LOADING
IbItt
3,gy
0
Wind
Resultant:
lb
OFa%-
(W’) ./,
Ice (W”)
&lb
Initial ,OF&s.
Loaded, Final. *OF-
SAGCALCULATIONS
jb
Area (A) /,&
in2
Temo. Coeff. of Linear Exp.:
lb
Total
0.000 0 a
jc
TEMP..
oF UNSTRESSED
LFJGTH
i!
per “F
1
Modulus. (E) Final 51.36
Initial mx
f=o.3/
x 103 lb/i&?
105 lb/in2
NE%
lzl
k=O.&7
SAGFACTOR 1
Y
0.00~~.
:iIi:
?R/977
% -lb
Date
7
Creep o.ooni2f-
78/T
3.‘0073
(W”‘)
Permanent Set O.OOti?
Ib/ft
SAG.fl
A”,’ +z?z?-
1
SW,Ib
:,”
1 TENSION,Ib
SPAN LENGTH(S) -FEET
No Ice. No Wind (W)
120
Figure 119.~Sag
customary).
I/,nn3
and tension
922 IO. d/l/3 a
& 7 lo. QQ&&@
calculation
form
/ I
/ 1
for example
I
problem
I
on insulator
i/hi/9.
JL49.
offset
/
I
/
I
and sag correction
(U.S.
298
TRANSMISSION
LINE DESIGN MANUAL
365.76 (1200)
457.2
-I
335.28
(1500)
426.72
(1400)
396.24
(1300)
(1100)
g
+
E
03
\
fcr;
.l”.J.
j
7c
I ”
fImn\
\trvv,
-. -.38 (1225)
304.8 (IqOO)
*.
381 (1250)
\x
L
335.28
(D
g
I
(1100)
\ylooo~
A
2
243.84 ZOO)
I
Y-1
213.36 (700)
182.88 (600:
1 All values shown are in meters (feet)
152.4 (500)
Figure
120.-Profile
of spans for example
problem
on insulator
offset and sag correction.
104-D-1120.
Table 36.-Data from example problem on insulator offset and sag correction (metric)
1
Station
2
SP
k@h
L.
3
4
y, - y, .
In
m
WY2 - Yt)
W(3),
N
5
Asrunltd
H,
N
6
7
Ho-H.
H,
- (5).
N
20+72.64
365.760
24+38.40
28642
-50.597
27583
-41.148
-861
-45.110
-944
-1805
.08030
-944
(6) _ z
(8)
(7)(9),
2:0’N
-
13
Fhul
mnectlon
lOOOL(9)
[Z(lO) + Z(11#7)
AE’
mm
Z(7)
15
14
FiMl
sum of
ofr33t
ofY3et3
(lo)+ (ll)+ (12). “E).
'
mm
.%
cofr3ction
whikln
SiHwus
3Ho
(10)
2wo’
mm
mm
0
-299
-2445
-255
-28
0
-283
-43.5%
-912
-52.121
-1091
358.140
-13%
-145
-111
-14
0
-1288
-125
-612
.11091
-105
-525
-58
-6
0
-287
-64
-472
25778
365.760
38+93.82
0.104 26
-2864
(6) (7).
Corrected Corrected Moduhu
Ho-H
offat
correction
12
-408
26722
381.000
35+28.06
1000 3Ls
3 128s ,
mm/N
Trill
OffwA
11
-283
373.380
31+47.06
K
10
9
-1059
335.280
27+73.68
8
othet
pr
Newton
0
,117
84
0
419
49
5
0
238
54
-418
24 866
912
.I0426
95
1331
139
15
0
154
2003
.09788
196
2422
237
27
0
264
702
-264
23775
42+51.%
1223
0
Tot&
0.615
45
-258
l1
-
-1
Numbers in parentheses are column numbers.
Table 37.-Data from example problem on insulator offset and sag correction (U.S. customary)
1
2
3
4
W(Y,-Y,)
W(3).
lb
5
A33llmd
H,
lh
6
7
8
Ho-H.
0ff33t
po:d
Ho - (5).
K
lb
W2L3
Trial
off3et
(6);)~
10
9
cofaected fim
offmt
Ho-H
(6)-z,
11
Modulur
12
FillsI
13
FiMl
14
Sumof
whikhl
(7) (9h
3heavel
la
Ho3.
lb
in
3Ho
1200
8o+oo
91+00
103+25
1100
1225
1250
115+75
6439
-lag
2W(2)
ft
-194
-148
-212
-171
1175
-549.6
-10.04
.014 06
-5.725
-311.6
-4.38
-117.6
-2.28
26
-1.09
0
0.0017
-11.13
-0.57
.0013
-4.95
6201
-4%
6007
-212
.01942
-4.113
5795
0
.02064
0
-0.24
.0018
-2.52
55%
205
.01826
5345
450
.01714
94.4
1.95
0.20
.cm19
2.15
3.751
299.4
5.47
0.60
.0017
6.07
7.695
544.4
9.33
1.06
.0016
10.39
-205
1200
127+75
-11.785
0.018
-238
-135
-143
-644
-245
139+50
TOti
Numbers in parentheses are column numbers.
-0.107
-78
(10)
-
in
in/lb
68+00
15
SW
w
‘II
-10.177
+a05
-0.04
-11.1
-16.1
-18.6
-16.4
-4.2
-2.0
-0.9
0.8
2.3
-10.4
0
4.0
-1
0 12 ,
300
TRANSMISSION
31.
Transmission
Line Equations.-If
and there are no later reroutes;
in numerical
notation
and there
start
work
on the
equation
will
Assume
crew
the line,
also
that
starts
same
result
two
from
4752
2370+66.4
while
second
this point is Sta. 2370+
66.4Bk
belongs
to the part of the line
that station
in the two
other
crews
(fig.
121).
is surveyed
from
one end to the other,
he one
of a line
ends
meet
or more
after
of a line
station
equations
a survey
and
which
at a common
toward
is the
point
crew
designates
it as Sta.
2374+31.2.
in the
has been
work
on the
line,
the
The
200+364.8
If the station
and the length
If the
length
ahead
line
These
is greater
is shortened
One
length
they
will
common
equation
of
each
point
as
to identify
= Sta. 2374 + 31.2Ah.
The Bk means backand
indicates
that station
behind
the common
point.
Similarly,
Ah means
ahead and indicates
lengths
may
of the common
point.
will be 475 200-364.8
be in meters
or feet,
There is a difference
of 364.8
= 474 835.2 if there are no
depending
= 475 564.8 if there are no other
equations
(fig. 122).
back is greater
than the station
ahead, then there is an overlap
of the line is increased
by the amount
of overlap
(fig. 123).
station
of the
An
other.
on the
units
Assume
the crew which
started
at the beginning
of the line determines
that the meeting
Sta. 2374+31:2,
and the crew starting
at the end of the line says the point
is Sta. 2370+66.4.
equation
will then read Sta. 2374+
31.2Bk
= Sta. 2370+66.4Ah,
and the line length
will
475
line.
completed.
each
approximate
point,
but the values
will be different.
at the beginning
of the line designates
belongs
to the section
of line ahead
designations,
and the length
of line
equations
will
at an assumed
the two
that common
which
started
the
there
at opposite
other
line
equally
spaced stations
will increase
uniformly
in the line. However,
if two or more survey crews
of a portion
start
the
+ 00. When
have a station
value for
Assume
that the crew
Sta.
and
points,
a reroute
crews
0 +00
a transmission
then all successive,
will he no equations
at different
survey
at Sta.
say Sta.
line
LINE DESIGN MANUAL
than
by
the
the
station
value
back,
of the
length
then
there
of the
of station
is a gap in the
gap
(fig.
124).
used.
point
is
The
then be
designations
stationing
and
the
2360+002360+00 -
2370+00 2370+00-
on 2374+31.2Bk
EQUATION
on 2370+66.4Ah
-1
:--I
.J
r ---I
Station
2370+66.4Bk-
EQUATION St&ion
2374+31.2Ah
1
I
1
I
L
---me
I
1--1
2380+00-
2380+00-
TRANSMISSION
302
Figure 123.Station
ahead
Figure
124.-Station
LINE DESIGN
designations
designations
when station
when station
MANUAL
back is greater than station
ahead is greater
than station
back.
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TRANSMISSION
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<<Appendix
A
A METHOD FOR COMPUTING
TRANSMISSION
LINE SAGS AND TENSIONS IN SPANS
ADJACENT
TO A BROKEN CONDUCTOR
A thesis by G. R. Wiszneauckas’
I-INTRODUCTION
Description
of the Problem.-The
determination
of sag and
conductor
or cable under
various
conditions
of temperature
the mechanical
design of a transmission
line. It is of equal
of sag and tension
from
the simple
cases of symmetrical
nonsymmetrical
to a broken
and special
spans, none
conductor.
The determination
special case for the reason
such as railroad,
highway,
national
and/or
Purpose
of the
local
conductor
thesis
which
methods
now
date, several methods
or techniques
have
problem;
however,
in many
of the methods
Study
of Initial
in this
case all such
in
of
adjacent
in this
is to develop
a technique
been proposed
rather
severe
for the solution
limitations
have
assumed
for any particular
problem
without
making
Another
somewhat
undesirable
aspect common
to
procedures.
These factors
set forth
the purpose
or method
by which
the
sags and
while accounting
in essence the
tensions
to some
trial-and-error
in a series
degree for the
aspects of
in use.
II-DEVELOPMENT
OF A TECHNIQUE
STRESSES DUE TO A BROKEN
that is before
the
tensions,
and span
any
of structure
heights
necessary
at critical
points
or power line crossings
in order to comply
with
of spans adjacent
to a broken
conductor
can be computed
asymmetries
present
in any particular
case and eliminating
the
for
codes.
been imposed
in that level, equal spans have been
corrections
to account
for existing
asymmetries.
most methods
is the time consuming
trial-and-error
of this
tension
least of which
is the case of a series of spans
of sags and corresponding
tensions
is important
that it assures the designer
waterway,
telephone
line,
safety
of Thesis.-To
broken
the
corresponding
and loading
is of basic importance
importance
to extend
this determination
spans to the more complicated
cases
and Final
Conditions
.-In
the
broken
conductor
breaks,
is one of static
lengths
known.
The final condition
quantities
are unknown.
The
307
This
conductor
equilibrium
is likewise
diagrams
’ Former Electrical
Engineer with Bureau of Reclamation.
Science from the University
of Colorado in 1949.
FOR ANALYZING
CONDUCTOR
shown
method
problem
the
initial
condition,
with all quantities
such as sags,
one of static equilibrium;
however,
in figures
1 and
2 have
been
given
was his thesis for the degree of Master
of
308
TRANSMISSION
to illustrate in general these initial and final
insulator strings and their deflections have
other elements of the spans shown in order
consideration.
A study of figure 2 reveals the complexity
in order to maintain static equilibrium
after
a method for treating this problem by not
been made temporarily:
(a)
(b)
(c)
(d)
(e)
(f)
LINE DESIGN
MANUAL
conditions. In figures 1 and 2, as in those following, the
been shown somewhat exaggerated as compared to the
to present a more readable picture of the features under
of the conditions which must be satisfied simultaneously
the conductor breaks. To facilitate the development of
complicating
it further, the following assumptions have
Level, equal spans exist before the conductor breaks.
Conductor breaks at mid-span.
No deflection of supporting structure as a result of the conductor breaking.
No slipp in g o f conductor in its clamps as a result of the conductor breaking.
The changes in elevation of the conductor after the conductor breaks are negligible.
The insulator acts as a rigid body.
After a procedure has been established for dealing with the problem under the above assumptions,
criteria will be presented by which assumptions (a), (b), an d (c) can be removed entirely. For most
cases the assumption made under assumption (d) is valid; however, conductor clamps are sometimes
set to slip at a predetermined
tension, in which case this assumption may not be in order. The
assumptions made under assumptions (e) and (f) are reasonable for all but very special cases.
Further study of figure 2 shows that the forces acting as a result of a conductor breaking can be
resolved into two opposing horizontal forces. Herein lies the basis for the technique which has been
developed.
Study of the P Force.-Referring
again to figure 2, the horizontal force designated P is the
force which retards or damps the effects of the broken conductor and may be considered as the equal
and opposite of the force required to deflect an insulator string by any angle 0 while a vertical load
is acting. The relation between this force, P, and the vertical load can be developed from figure 3.
Again, assuming that the insulator string acts as a rigid body and also that its gravity axis is midway
between the conductor
and the attachment
hinge, the following
relations can be written:
For
equilibrium
at any angle 8, Wd = P ‘v or P ‘= Wd/v. Also, cos 8 = v/i and tan 8 =’ d/v = P/W
from which P = Wd/v ; therefore, P = P : Also, P = Wd/i cos 8, which is a form more convenient
for calculation.
Insofar as the broken conductor
problem is concerned, this relation should be
interpreted as: P is the horizontal force which resists the movement of an insulator string of length
i from the vertical to any angle 8 while a vertical load W is acting.
Study of the H Force.-The
horizontal force designated H in figure 2 is the horizontal component
of tension acting in the conductor or cable. Insofar as the broken conductor problem is concerned,
the relation between this force and a change in span length, such as might be caused by the deflection
of an insulator string, is of primary importance and can be developed from figure 4 as follows: The
length of conductor in the initial span is:
I =*fJo
0-
W
WLO
sinh -
*HO
APPENDIX
The
length
of conductor
in the
span
after
a change
309
A
of 4 is:
I, =-24 sinh w(L, -#I
W
The
change
from
Ho
in conductor
HI
to
length
24
due to the elastic
properties
of the conductor
in changing
the tension
is:
U-4,- H,) U,)
AE
Then,
barring
temperature
conductor
length
length
is increased
By substituting
and/or
plus or minus
or decreased,
the
values
loading
changes,
the
change
in the
II
le,
the elastic
i.e.
found
above
for
and
final
conductor
conductor
length
must
depending
equal
on whether
the
the
initial
span
2Hl
sinh
W
w(Lo _ @)
or sinh
2H,
=
HI
and solving for Cp:
k.
$=L,
By way of interpretation,
4, the horizontal
tension
The
forces
Relations
become
of which
will
figure
11.
Consider
which
also
Between
the
aids
from
P
in the
a simple
+, Hoi:J
SinhO’
this means that when
in the cable changes
invaluable
progress
- ‘G
sirthzi(l
and
H
solution
special
a span
from
of length
to
Ho
Forces.-The
of the
L e is
HI.
changed
relations
broken
case as shown
as developed
conductor
in figure
first the case of a conductor
breaking
in a span adjacent
outlines
the conditions
to be satisfied
simultaneously
in length
problem,
5 to a general
by an amount
for
the
the
P
and
H
development
case as shown
in
to a dead end as shown in figure
in order
to maintain
equilibrium.
5,
TRANSMISSION
310
Although
these
common
presented:
conditions
are
trial-and-error
If the
P
and
simple
procedures
H
relations,
and
LINE DESIGN
few,
considerable
to evaluate
previously
MANUAL
them.
developed,
effort
In
could
contrast,
are plotted
the
with
be expanded
following
a common
in using
solution
system
of coordinates
as shown in figure
6, the resulting
curves will intersect
at some point
which,
upon examination,
prove
to be the only point
in the system
which
could
possibly
satisfy
simultaneously
all
necessary
and
sufficient
to demonstrate
lies,
for
this
instance,
conditions
solution
above
which
the
point
must
compare
The
and
value of d will be less than
likewise,
will be greater
than
there
with
are any
Pand
Hcurve.
the
number
value
of points
H curve-which
d which
trial-and-error
procedure
Compute
Knowing
the
to the
value
value
this
of
6 has been
given
Hcurve
which
of the
be apparent
of Hat
to a value
Figure
any point
should
or conditions
for which
P=
also the other
necessary
point,
P which
that
note
the
the
equals
the
solution
value
of 4
value
of
H
H, there
condition
is only
that
one-the
intersection
d = $.
of this more or less special case, consider
next the case of a conductor
dead end as shown
in figure
7. In this case an additional
set of
commonly
(1)
Referring
to figure
which
would be HI. Also,
of P1.
(2)
(3)
by studying
Pcurve-it
corresponds
to maintain
equilibrium.
Pand
Hcurves
no longer
case; however,
these
required
conditions.
procedures
are as follows:
solution.
will
of the
the value of 4 for every point
so selected
above the intersection,
do for every point below the intersection.
Note then, that although
must be satisfied
in order
the intersection
of the basic
as in the previous
satisfy
all of the
the
it is the
satisfies
As a step in the generalization
breaking
two spans away from
conditions
seen that
with
Corresponding
of
hence,
can be substantiated
intersection
and
of the
lie on the
for equilibrium;
the
has been
of
to figure
8, it can easily be
all of the required
conditions
basic curves
can be manipulated
A method
for this manipulation
used
in other
7, assume a value for
based on the assumed
Hz, compute
Referring
satisfies
methods.
essentials
of such
which
from
will
the
a trial-and-error
d 1 and compute
the corresponding
new tension
value for d 1, compute
the corresponding
value
Hz by subtracting
the
The
to obtain
values
can be derived
corresponding
PI from
value
HI.
of 4s.
(4)
From this value of $2, the value of dz can be determined
by the relation:
dz = $2 + d 1.
(5)
Pz can now be evaluated
since it is a function
of dz. If this value for Pz is equal to
the value computed
for H 2, the initial
assumption
for the value of d 1 is correct
and all other
values computed
are correct;
however,
if this is not the case, then a new value must be selected
for
dl and the entire
procedure
repeated.
value of d 1 which
can then be found
for HI, Hz, and d 2 can be computed.
Usually,
by
three
interpolation,
Based on this procedure,
a straightforward
graphical
possible
values
for dl were assumed,
then all possible
from
which
all possible
values
of Hz could
be found.
or four
trials
and
corresponding
the
will
bracket
the
correct
correct
values
analysis
can be developed
as follows:
if all
values for HI and PI could be determined
This can be accomplished
very easily
by
subtracting
graphically,
point
by point,
the abscissa values
of the basic Pcurve
from those of the
basic Hcurve.
The resulting
curve then represents
the locus of all possible
values for Hz with respect
to d 1. In similar manner,
the graphical
addition
of the ordinates
of the newly formed
Hz curve, which
represents
represents
all possible
all possible
also the locus of all possible
all possible
values of 42, will
values
values
values
of d 1 to the ordinates
result
in forming
a new curve
of d2 and also represents
all possible
for Hz with respect
to corresponding
values
values
of the basic H curve,
which
which
represents
the locus of
of Hz with respect
of dl and d2 have
to dz. Now
been defined,
that
all
APPENDIX
that
remains
to be done
conditions.
Referring
is to determine
again
to figure
which
A
311
of the
8, it should
possible
be evident
values
that
some
will
point
satisfy
the
on the
newly
ds curve will satisfy the conditions
required
in the conductor.
As in the previous
case,
at the insulator
it will be found
string immediately
adjacent
that there are any number
this
condition
ds =
curve
which
seen that
which
the
can satisfy
to the break.
can
will
b, note
The
next
step
necessary
simple
Hz
in the
and
for this
required
case that only
in the previous
for
bon
of the
away from
to the two
the
4s
equilibrium
+
dl.
at the
first
Hcurve
at the
second
would
the
only
insulator
string.
be
point
adjacent
point
which
In
regard
from
point
down
H curve.
basic
be to add
only
string
to be the
vertically
to intersect
it can
u) is the
insulator
formed
to the break
of points
on
inspection,
(point
it is determined-project
problem
By
ds curve
the basic
horizontally
generalization
nature
in which
the
is moved
away from
and
for equilibrium
in which
thence
that
Pcurve
point
conditions
make the dead end three spans
interest
to note the similarities
and interrelated
conductor
breaks
prove
manner
curve
basic
conditions
will
necessary
the
the
necessary
of the
inspection
all of the
a to intersect
the
point
all of the
Further
satisfy
to point
satisfy
intersection
required
another
span
in the
series
to
the break
as shown
in figure
9. In this case it will be of
previous
cases. Of special
importance
is the progressive
requirements
the dead end.
for equilibrium
By comparing
occur
as the span in which
the
these requirements,
it will be seen
one set of conditions
is needed
to maintain
equilibrium
in addition
case in which
the conductor
breaks two spans away from the dead
to those
end. Also,
though
it may not be immediately
apparent,
the graphical
analysis
as developed
for the previous
case
can be utilized
in its entirety
and requires
only an additional
step to account
for the additional
requirements
for equilibrium
in order to provide
the complete
solution.
This additional
step is one
which
of the
is in continuation
possible
values
values
H3 with
of
of those
graphically,
point
of the dz curve
found
respect
for
to
taken
d 2, the
in the
previous
corresponding
case,
and
possible
dz can be determined.
This
consists
value
can
and
Based
can
be substantiated
on these
can be outlined
special
from
which
all
all possible
by
subtracting
from the corresponding
all possible
values
of
corresponding
values of da can be determined
by adding
graphically,
ordinates
of the basic Hcurve-thus
of the H3 curve to the corresponding
which
represents
the locus of all possible
values
of H3 with respect
case
from
be accomplished
by point,
the abscissa
values of the basic Pcurve
thus forming
a new curve,
Ha. Then,
knowing
manipulations
have been shown in figure
10. Also indicated
points
a, 6, and c. These points were obtained
in a manner
of determining
of Ps
values
the
Hs,
point
by point,
the ordinates
forming
a new curve,
df,
to da. The results
of these
is the solution
which
is represented
by
similar
to that given for the previous
likewise.
cases,
a procedure
for
solving
a general
case
as represented
by figure
11
as follows:
(I)
Compute
and plot values for the basic P and H curves
as shown
in figure 12.
(2)
Subtract
graphically,
point
by point,
the abscissa values of the basic Pcurve
from the
abscissa
values of the basic H curve to form a new curve,
Hz.
(3)
Add graphically,
point by point,
the ordinate
values of the new Hz curve to the ordinate
of the basic H curve
Subtract
graphically,
values
(4)
abscissa
(5)
values
(6)
values
of the
new
to form a new
point
by point,
dz curve
curve,
dt.
the abscissa
to form
a new
curve,
values
of the
basic
Pcurve
from
the
HS.
Add graphically,
point by point,
the ordinate
values of the new H3 curve to the ordinate
of the basic H curve to form a new curve,
d 3.
Continue
this composition
process
of subtracting
abscissa
values of the basic Pcurve
from
those
these
new
of each
Hcurves
succeeding
d curve
successively
to the ordinate
to form
new
values
H curves,
and
of the basic
add
Hcurve
the
ordinate
to form
values
new
dcurves
of
TRANSMISSION
312
until
the
d,, and
be represented
H,, curves
in which
the
indicates
point
(-)
(7)
The
the d,,curve
adjacent
are established.
symbolically
H-
p=H2
+H=d,
point
point
to the
conductor
to the
curve
and
to the
dn-z
across
Each
intersection
insulator
span
insulator
of each
by point
which
. . .H,
as described
above
can
+H=d,
of abscissa
ordinate
string
which
and
values
values
of curves,
and
the
(+)
of curves.
tension
to the
and
of the
converging
by the
above
horizontal
and
curve
across
down
corresponds
is identified
as described
the
H,, curve
and the tension
in each
span and the corresponding
procedure
+H=d,
subtraction
of the
break
break,
the
procedure
solution
is then found
graphically
by stairstepping
down
from the intersection
with the basic P curve,
which
defines
the deflection
of the insulator
immediately
conductor
of the
composition
- P=H,
addition
to the
is reached.
The
as:
indicates
by
LINE DESIGN MANUAL
to the
H n-z
stairstep
to the
same
in the
dn-l
with
down
etc.
until
the
a d curve
of the
Having
immediately
and
curve,
subscript
subscript.
span
curve
curve
established
defines
of
adjacent
to the
basic
Hn+
Hcurve
the
deflection
the
tension
and
also
the
deflections
in
of each
span from the conductor
break to the dead end, the length
sag can he computed
by any standard
method.
The stairstep
can
be represented
symbolically
as:
0d,,
in which
vertical
d,, X P indicates
projection
down
horizontal
projection,
left
the intersection
from
one curve
to right,
from
of d,, and
to another,
one curve
P curves,
the vertical
and the horizontal
to another.
The
circles
arrows
arrows
indicate
indicate
indicate
a
a
intersection
points
of the stairstep
with d curves,
which
points
describe
insulator
deflections
and conductor
tensions.
From
the procedure
as outlined
to this point,
a question
as to the physical
possibility
of
constructing
all of the indicated
number
of curves for a case in which
the nearest
dead end is a very
great number
immediately
of spans away from
suggests trying
to find
the
the
conductor
limiting
break
might
logically
be raised.
Such
locus of the d, and H, curves.
Fortunately,
be done with a fair degree of accuracy.
By following
the procedure
six d and corresponding
H curves
have been constructed,
a tendency
regarding
the space relations
of the intersection
points of the dcurves
examining
will very
these space relations
closely,
it will be found
that a geometric
closely
describe
this tendency.
Then,
it is but a simple
convergence
point
of the
and find
d,, curve.
its sum which,
The location
a question
this can
as outlined
above until
five or
of convergence
can be noted
with the basic Pcurve.
Upon
series
matter
can be arranged
which
to test the series for
if existent,
will describe
the space relations
of the intersection
can be established
by drawing
a curve
through
this point
and
the Ho point
such that it appears
to be a member
of the family
of curves
thus far established.
many cases, this will be a straight
line for practical
purposes.
From
the d,, curve,
the H, curve
easily established
by subtracting
abscissa values of the basic Pcurve,
point
by point,
from those
the
d,, curve.
By stairstepping
with the basic Pcurve
to the
on the d,, curve,
the insulator
down
between
Ho point,
deflection
these
curves
from
the intersection
and noting
the intersection
points
and tension
value for each span
point
of the
of the converging
progressing
away
In
is
of
d,, curve
stairstep
from the
conductor
break
will be defined.
These points
present
an interesting
relation
in that regardless
of
the distance
to the nearest
dead, end, the effects
of a conductor
breaking
will be damped
out for
practical
purposes
in a very few spans. This is in agreement
with statements
made by other
authors
on this
subject.
Figure
16 illustrates
in detail
a solution
for
a typical
problem
by
this
procedure.
APPENDIX
To substantiate
Since
the validity
d, and
the
of stairstepping
H,, curves
represent
curves,
it should
be evident
that
for practical
purposes
one could
d n-1000
Hn-2,
curve.
Likewise,
curve.
be equally
Therefore,
number
of curves
in the family
purposes,
to operating
between
appear
academic
encountered
from
in practice
the
break
in the
Pcurve
far
and
force
to ensure
scale.
This
be attained
cross-section
cases.
Criteria
adjusting
as the
since
it can represent
for
the
the
case in which
the
H,,
the
H,, curves
previously
this aspect
majority
Hn-l,
the
end
the
to represent
given
of the
such
reduces,
analysis
of preliminary
dead
of
together
that
d,,-2, or even the
for
may
problems
is beyond
a few
spans
conductor.
feature
inspection
that
feature
of this entire
in a manner
is approached
and not some other
the question
of accuracy.
As with the other
curves
drawn
offer sufficient
Assumptions
.-The
far to accommodate
following
problems
spans,
it should
than the exception, and that any method
which
does not recognize
this fact and
the problem.
be realized
for dealing
offers some
that
point
on the horizontal
methods,
accuracy
can
on a standard
llaccuracy
for all but
by 15-inch
very special
is an outline
of procedures
for
with asymmetries,
such as unequal
and with other variables,
such as deflections
break which
were initially
assumed
constant.
nonsymmetrical
the results
can easily be
shown
in figures
4, 6, 8,
the d, intersection
point
with the basic
is, reversing
the process
of composition)
Ho point
the
prompts
spans,
conductor
procedure
is that
such as has been
should
be taken to check
by resolving
them (that
for Removing
Initial
the method
developed
thus
and
for
as follows:
number
close
between
d, and
the
reason
of an unlimited
to be so indescribably
the d,, , the dn-l,
solution
any
H, curves,
positions
to distinguish
to any degree
desired.
With
this method,
sheet as shown in figures
16 or 17, should
and nonsymmetrical
the point of the
unequal
will have
between
d, and
the
that
the stairstep
formula
the d, and H, curves.
While
it serves
connection,
care
d,, and H, curves
the
enough
limiting
difficult
actually
Another
interesting
and useful
checked
either
graphically
or by
10 or 12. In this
only
the
it is possible
a great
practical
only,
between
in theory
these curves
not distinquish
it would
Hn-looo
or the
313
A
such
in supporting
In dealing
a series
of spans
structures
and
with a series of
is the
rule rather
with problems
regarding
such a series of spans
means to account
for it-is not doing justice
to
Two criteria
can be used to adjust the method
developed
thus far to account
for such asymmetries
and variables.
One offers an approximate
correction
at the expense of very little additional
work and
is suitable
for use in making
preliminary
studies and estimates.
The other offers a comparatively
exact
solution
but
requires
much
more
a high degree of accuracy.
The approximate
correction
any series
of random-length
symmetrical
spans
same distance
problem,
the
in a conductor
which
will
work
and
is suitable
for
use in connection
is based on the Ruling
Span Theory
which
symmetrical
spans,
there
can be found
have
the
as the random-length
implications
are then,
and the nearest dead
same
horizontal
tension,
the
same
with
problems
requiring
states, in effect,
that
a series
of equal-length
for
total
the
slack,
and
cover
series of spans. Applying
this theory
to the broken
conductor
that for any series of spans which
might
exist between
a break
end, there will exist one series of equal-length
symmetrical
spans
which
will best describe
the characteristics
of the existing
series of spans. If such-an
equivalent
series
of spans can be established,
the method,
as developed,
can be applied.
In order
to establish
the
equivalent
series of spans, a means for determining
the equivalent
level or symmetrical
span for any
inclined
or nonsymmetrical
and is given by a relation
* Numbers
in brackets
span
as:
will
be required.
refer to items in the Bibliography,
Such
a means
section VI.
has been
developed
by Martin[8]*
TRANSMISSION
314
Equivalent
level
20 percent
This
and
relation
leaves
spans.
span
=
2 (inclined
span
makes
possible
one
can
the
condition
be done
conversion
yet
of any
The
ruling
The
the
more
- (horizontal
span
by using
length
solution
a relation
is then
the
of a typical
exact
correction
series
to be fulfilled-that
span
length).
(Safe
limit
=
by
into
a series
of symmetrical
an equivalent
series
spans
of equal
length
of spans.
Figure
Still[6].
<E
length
problem
of spans
of finding
given
Ruling span length =
16 gives
length)
slope)
only
This
length
LINE DESIGN MANUAL
of each
by
this
is accomplished
span
in the
approximate
equivalent
series
method.
by recognizing
asymmetries
as they
actually
exist
and
treating
them as such without
recourse
to equivalent
arrangements.
Treatment
of a problem
on this
basis requires
a separate
basic Pand
H curve for each span involved,
and while
possible,
undue
difficulties
would be experienced
in computing
the basic Hcurves
for nonsymmetrical
spans. In order
to alleviate
these
difficulties,
on the equivalent
H curve relations
previously
outlined;
but
with
little
or no sacrifice
level span of each nonsymmetrical
as previously
derived.
The basic
however,
for nonsymmetrical
in accuracy,
H curves
the
insulator
must be taken as equal to the weight
of conductor
from low point to low
can be measured
on the plan-profile
sheets describing
the series of spans under
given
to illustrate
a typical
to account
only
of the conductor
conductor
the basic
break
occurs at midspan
of the insulator
for the actual
length
of conductor
from
in the adjacent
span. In this connection,
curves
into
Represented
steps
involved
above
structure
deflection
and the horizontal
deflecting
curve similar
in aspect
to the basic Pcurve
can
the ordinates
of this curve to the basic Pcurve
effects of insulator
and structure
deflections
will
as the P
incorporated
are. By a similar
the basic Pcurves.
in figure
in this
procedure,
14 is a solution
procedure
can
by this
be outlined
into
a basic
span.
H Curve
for
each
the
span
weight
horizontal
the basic
to the low
that if the
were inclined
so
or uplift
would
position
Pcurves
which
if the
is
relation
force is known
to the extent
that a
be drawn.
By adding,
point
by point,
of each span, new curves
describing
the combined
be formed
and can be used in the procedure
exactly
the
criteria
effects
of “hinged”
for the
typical
crossarms
case shown
may
in figure
also
be
13. The
as follows:
(1)
Compute
a basic P curve
for each insulator
string
conductor
weights
as determined
from low-point
distances
such as structure
deflections,
hinged
crossarms,
etc.
(2)
Compute
for each actual
This distance
Figure
13 is
the assumed
break point
it is interesting
to note
string
and if the adjacent
of the span, a negative
act on the insulator
string
which
could cause it to deflect
generally
considered
the limiting
position.
The effects of structure
deflection
can also be incorporated
the
point.
study.
can be generalized
under
this
immediately
adjacent
to the
P curve
conductor
is assumed
to break next to an insulator
that its low point
would
fall sufficiently
far outside
between
descriptive
be based
problem.
The initial
assumption
that the
correction
procedure
by adjusting
break
point
can
span thereby
making
possible
the use of the
P curves required
can be computed
exactly
as
spans, the weight
of conductor
acting
on each
span
involved,
to be considered,
based on actual
and based on other
considerations
based
on the
equivalent
level
span
APPENDIX
(3)
Plot
(4)
Manipulate
these
curves
in the
same
these
curves
graphically
coordinate
H, - pl =H,‘+H,
(5)
The
solution
is given
by
0d,
The
justification
general
case
concerns
the handling
break.
out
for
the
of a problem
practical
depending
purposes
on the
nature
One
the
same
reasoning
as given
could
end is a great
are all that
=d,
0d,
which
the
formula:
formula:
the effects
so that
problem,
symbolic
4 Hz’-,
question
cases considered,
of the
0d,
the dead
spans
following
stairstep
follows
11.
in which
in a few
the
=d, - Pz +H3’+H3
symbolic
solution
in figure
In this case, as in previous
for
the
315
system.
by
X P3 4 H,‘+
above
as represented
A
previously
be raised
distance
away
of the broken
from
6, 8, or 10 spans
need
be considered.
will
away
the
connection
the conductor
conductor
first
for
in this
be damped
from
the
break,
III-SUMMARY
To
summarize,
catenary
relations
the
discussion
for
determining
presented
insulator
outlines
a general
and/or
structure
method
or procedure
deflections
and
based
on special
conductor
tensions
in
spans adjacent
to a broken
conductor.
Knowing
these deflections
and tensions,
the corresponding
conductor
sags can be computed
by the use of standard
catenary
relations.
The method,
while
graphical
in nature,
is capable
of a high degree of accuracy
and is straightforward;
that is, it does
not
involve
conductor
method
the
usual
problem
with those
The Solution
conductor
to facilitate
selected.
tension
By
trial-and-error
procedures.
In
appendix
has been worked
out and a comparison
as obtained
by another
method.
of a Typical
Broken
problem
has been worked
a comparison
of results,
The details
of the problem
in span A if the conductor
A-l
made
IV-APPENDIX
A-l
Conductor
Problem.-In
which
follows,
a typical
of the
results
as obtained
the
following,
a typical
out to illustrate
the techniques
the typical
problem
used by
broken
by
this
broken
presented.
For this purpose
and
Bissiri and Landau[4]
has been
are given in figure
15. The requirement
breaks
next to insulator
No. 6.
is to find
the
sag and
the approximate
method
the procedure
is as follows:
(1)
Using the nomograph
given in figure
18, convert
the series of given spans into a series
of level spans. Since all equivalent
level span lengths
are less than 2 feet more than the horizontal
span lengths
(2)
Using
spans into
series.
(3)
of 4.
a series
Using
These
shown,
all spans
the Ruling
Span
the
values
of level
equal
will be assumed
level without
correction.
Computation
Chart
given in figure
18, convert
spans.
Take
H
force formula,
assume
are given in table A.
(4)
Using the P f orce formula;
P. These values are given in table
assume
B.
970
feet
as the
values
for
HI
values
of
d and
span
length
and
compute
compute
the
series
for the equal
corresponding
corresponding
of level
level
span
values
values
of
TRANSMISSION
316
(5)
Plot
curves
the
computed
according
to the
values
Since
the
dead
(6)
by Bissiri
the
end
he assumed,
For
dead
will
the
the
dead
dead
end
04
The
By
16 and
manipulate
the
resulting
Pand
- P=H,
and
. . .H,, +H=d,
Landau)
first,
does
a great
not
state
distance
away
the
location
and,
of the
second,
nearest
at insulator
end
a great
results
distance
away,
XPJ-H,,+
at insulator
No.
0d,
XP+H,+
are tabulated
in table
the
solution
is given
by the
symbolic
formula:
@H/@...H,,
d
1, the
solution
0d,
J-&-,
is given
by
0d,
rH,+
the
$Hp
symbolic
formula:
0d,
E.
the more exact method,
the procedure
is as follows:
(1)
Compute
an Hcurve
for each span. Assume
that span E is dead ended at insulator
No. 1
and that all spans are level spans without
correction
since the correction
is less than 2 feet for
each span. These
(2)
Compute
values are given in table C.
a P curve
for each suspension
table D.
(3)
Plot the
according
to the
H
HE-P,
The
The
results
Discussion
between
and
symbolic
P
curves
formula:
as shown
+HE)+HD =d3- P3 =HD’+Hc=d,-
(4)
the typical
solution
are tabulated
by the
in table
of Results.-Considering
problem,
the
is given
methods
the results
check
lies in the
insulator
in figure
string.
1’7 and
P., =Hc’+H,=d,
following
symbolic
values
manipulate
are
them
-Ps =HB”HA
given
graphically
=d6 -Ph =HA’
E.
made
by
armor rods, vibration
dampers,
etc., were acting.
Since
several
times that of a conductor,
the effects
of such
relative
magnitudes
of the
tension
in
formula:
the inherent
differences
each other as well as could
assumption
These
Bissiri
between
the methods
used to solve
he expected.
The principal
difference
and
Landau-
that
the
conductor
length
in the span adjacent
to a break is increased
by the length
of the insulator
string immediately
adjacent
to the break. Theoretically,
this would be true only if the weight
distribution
over the insulator
string
were the same as that over the conductor,
and if no concentrated
loads such as holddown
weights,
on the
H
E.
0d,
For
+H=d,
(as given
1 in span
in figure
MANUAL
formula:
program
end,
No.
as shown
symbolic
H- p=H2
LINE DESIGN
in the
system
the unit weight
a discontinuity
to the
total
of an insulator
string
of weight
distribution
weight
of conductor,
is usually
depend
insulators,
APPENDIX
and
concentrated
has a varying
low
loads
effect,
comprising
being
more
the
system.
correct
for
A
Hence,
long
317
the
spans
assumption
with
high
made
tensions
by Bissiri
than
and
for short
Landau
spans
with
tensions.
V-APPENDIX
To
Chart
facilitate
and
are given
Figure
conductor
several
certain
a Sag and
on the
following
20 shows
can
specific
computations
Tension
a typical
be facilitated.
ruling
span
such
Computation
pages
lengths
Chart
as figures
set of data
The
as made
by
by the
in Appendix
have
18 and
span-tension
A-2
which
A-l,
devised.
a Ruling
These
Span
Computation
are self-explanatory
and
19, respectively.
preliminary
curves
approximate
been
have
method
studies
been
of the
plotted
as presented
from
effects
data
herein.
of a broken
computed
for
W
E
Table A.-H curve computation
H,, = 4400 lb; L, = 970 ft; w = 1.57 lb/ft;
1
Hl
2
Ho&h-
3
WLO
l--
Ho-H,
765.2528
765.2528
765.2528
765.2528
5
6
(4)
(2) (3)
AE
WO
2300
2500
3000
4000
4
AE = 6,635,672
slnh-’
7
(5)
H,
0.999638
.999713
.999789
.999939
765.0106
765.0331
765.0913
765.2066
0.33261
.30601
.25500
.19130
0.3268
.3015
.2524
.1902
8
9
4
5
Wl
-r
(6) (7)
2929.936
3184.713
3821.650
5095.540
957.503
959.880
964.584
969.171
Lo - (8)
12.5
10.12
5.42
0.83
zi
z
E
Z
m
Numbers in parenthesis are column numbers.
Table B.-P curve computation
Wd
p=-
ic0sll
W = 1655 lb; i = 12.58 ft = 150.96 in
d
d
A
i
case
ii
0.1987
.3975
0.4803
.9178
0.2027
.4331
335.5
716.8
90
120
130
.5962
.7949
.8611
.8028
.6074
so90
.7426
1.3086
1.6910
1229.0
2165.7
2798.6
ic0se
P
Table C . -2 curve computations
Ho = 4400 lb; w = 1.57 lb/ft; AB = 6,635,672
Lo = 880,910,980,
and 1050 ft
1
880
2
3
4
5
(2) (3)
H,
(4)
6
7
slnh-’ (5)
8
16) (7)
9
Lo -
(‘3)
D
869.350
10.6
:
s
0
z
2200
2500
3000
4000
693.6416
693.6416
693.6416
693.6416
0.999668
.999714
.999789
.999939
693.4116
693.4429
693.4951
693.5996
0.3152
.2774
.2309
.1734
0.3102
.2739
.2289
.1725
2802.548
3184.710
3821.660
5095.540
872.292
874.777
878.981
;:‘2
910
2200
2500
3000
4000
717.4822
711.4822
717.4822
711.4822
.999668
.999714
.999789
.999939
717.2443
717.2768
717.3308
717.4384
.3260
.2869
.2389
.1794
.3205
.2831
.2366
.1783
2802.548
3184.710
3821.660
5095.540
898.216
901.591
904.205
908.980
11.8
8.4
5.8
1.02
980
2300
2500
3000
4000
773.2210
773.2210
773.2210
773.2210
.999683
.999714
.999789
.999939
772.9763
772.9996
773.0579
773.1744
.3361
.3092
.2574
.1933
.3300
.3044
.2547
.1921
2929.936
3184.710
3821.660
5095.540
996.879
969.426
973.377
978.853
13.12
10.6
6.62
1.15
1050
2500
3000
4000
829.0365
829.0365
829.0365
.999714
.999789
.999939
828.7991
828.8616
828.9865
.3315
.2760
.2072
.3258
.2727
.2058
3184.710
3821.660
5095.540
1037.597
1042.166
1048.662
12.4
7.83
1.34
'
Numbers in parenthesis are column numbers.
1.02
D
Table D.-P Curve computations
p=wd
i cosd
i = 12.58 ft = 150.96 in
d
i8
90
120
130
140
142
144
146
-d
i
me
0.1987
.3975
.5962
.7949
.8611
.9274
.9406
.9539
.9671
0.9803
.9178
.8028
.6074
.5090
.3740
.3394
.3002
.2542
d
p2
p3
p4
ps
i cost9
w = 1750
W = 1546
W = 1609
W = 1766
0.2027
0.4331
0.7426
1.3086
1.6910
2.4790
2.7710
3.1770
3.8050
354.7
757.9
1299.6
2290.1
2959.3
313.4
669.6
1148.1
2023.1
2614.3
326.1
696.9
1194.8
2105.5
2720.2
357.9
764.9
1311.4
2310.9
2986.3
Table E.-Tab&
Approximate
Dead end a
great dist.
from break
Item
Tension (lb)-A
-B
-C
-D
-E
Insulator deflection
2920
3590
3930
4120
4230
(in)-6
-5
-2
2 Sag (ft)-A
tion of results
method
Dead end at
insuIat01
No. 1
2900
3550
3870
4050
4120
Exact method
2710
3620
3950
4120
4220
131.2
58.0
31.2
18.0
10.8
131.1
57.8
30.0
16.0
6.9
145.8
67.4
32.8
17.0
7.5
53.0
53.5
57.0
Bissiri and Landau ’
2625
59.0
’ For a final result, Bissiri and Landau give only an interpolated catenary parameter value for the span adjacent to the break. From
this, Tension A = (1670)(1.57) = 2625 lb.
2 Sag values determined by use of Computing Chart given in figure 19.
‘6
w=730
174.9
316.2
542.1
955.3
1234.4
1809.7
2022.8
2319.2
2777.6
INITIAL
3
Lo
= _
Lo
CONDITIONS - Before
_)
“0
LO
LO
FIGURE
c-c----------
G
b-2
LO
LO
Conditions
Break
--
for
equilibrium:
-
b-3
b-3
b-4
--lLO
LO
C.f
Ln-4
b-3
h-2
dn-1
dn
in conductor
I
CONDITIONS - After
h-I
LO
LO
= Horizontal
tension
= Span length
FINAL
Break
---LO
0= Change In span length.
Pn = Hn ; Pn-1 + Hn = “n-1 ; Pn-2 + “n-1 = “n-2 ; Pn-3 + “n-2 = “n-3;
On = dn- dn-1; an-1 = dn-1 -dn-2 ; (dn-2=dn-2
Ln = Lo-0n;
Ln-2 = Lo -0n-2
Ln-1 =Lo -0n-1;
FIGURE 2
104.D-1121
etc.
-dn-4
-dn-3 ; On-3 =dn-3
, Ln-3 = Lo - 0n-3 ; etc.
; etc.
TRANSMISSION
322
di v eWIW2-
WPP’ -
LINE DESIGN MANUAL
Horizontal displacement
of insulator string.
Length of insulator string.
Vertical displacement of
insulator string.
Angle of deflection of
insulator string.
Weight of insulator string.
Weight of conductor acting
on insulator string.
Total vertical load = % + w2.
Horizontal force caused by w when the insulator string
is deflected by an angle 8,
Horizontal force required to deflect the insulator string
by an angle 8 when a load w is acting.
FIGURE
3
Initial span length.
Change in span length.
Final span length.
k
‘0 - Initial conductor length.
‘I - Conductor length after a change of 8 in span length.
Initial horizontal tension in conductor.
HOafter a change of 8
“,- Horizontal tension in conductor
in span length.
WUnit weight of conductor.
Product
of Modulus of elasticity and cross section area.
AE-
LO-
0-
FIGURE
104-D-1122
4
APPENDIX
Conductor
Break
323
A
in a Span Adjacent
to a Dead End
4
//
-ijoJ4
LI
_
Conditions
for equilibrium
after
P,=H,;
0, = d, ; L, = ~~-0,
FIGURE
5
Force
*
c
HO
FIGURE
104-D-1123
conductor
Relations
Horizontal
P, & H,
c
LO
d
P&H
-w--e-
6
breaks:
324
TRANSMISSION
Conductor
LINE DESIGN
MANUAL
Break Two Spans Removed From Dead End
,,
/
----L,
L2
4
_ d2
LO
LO
Conditions for equilibrium after conductor breaks:
P,=H,; P,+H,=H,; 0,=d,-d,;
0,=d,;
L,= Lo-Q12; L,=L,-0,
FIGURE 7
P & H Force
Horizontal
.
Force
p2 &
H2
I
H,
.
Relations
-4
HO
-I
FIGURE
104-D-1124
8
c
APPENDIX
Conductor
Conditions
P3= Hg
8, =d,;
Break
for
Three
Spans
conductor
0,=d3-d,;
P,+Hz=H,;
L,=L,-8,;
FIGURE
P&H
_
Removed From Dead End
equi Ii brium after
P2+ H,=Hz;
L,=L,-8,;
f
325
A
Horizontal
breaks:
02=d2-d,;
L, =~~-a,
9
Force Relations
Force
P,&H,
_
p2
H2
PI
HI
HO
FIGURE
104-D-1125
4
IO
II
P
-A
\to=
APPENDIX A
Conditions for equilibrium
after conductor
P3 = H;; P + H’,=H;;
P, + H;= Hi; 0,=d,-d,;
L$= L,-0,;
L’,=L,-0,
8, = d,; Lf,=L,-03;
FIGURE 13
104-D-1127
327
breaks:
0*=4-d,;
1030’
El. difrb;oq.80’
900’
_ 940’
w:
El. diffT7.89’ El. d~~o~l.50’
d-P-
1040’ _
El. diff=,l8.92’
980
Normal horizontal tension ___________H,
Conductor weight per ft ____________w
AE= cond. area x modulus __________
Insulator length _-----___________ i
Insulator weight----------------------For other details see Reference C4l
FIGURE 15
104-D-1128
380’
El. dif8f=$.07’
=
=
=
=
=
-
4400 lb
1.57 lb
6,635,672
12.58 ft
265 lb
Bibliography
5m
APPENDIX
A
329
gkTT
The determination
of a geometric
the space reloiiars of the ‘II’ curve
intersections with the ‘P’curve :
dtstance d2to dx-4e units
I
Avp mtio=0.277
Since mtio <I. the series, 46+Ii.5*~5...
will converge and the sum will be
approximately : 46
m-64
units
This Sum -64 units - is then the
distance from the i$ 6’~’
intersection t0 the . ‘4 6’P’
I
t
i
i
Requirements for
I
equihbrlum:
“‘Y-Ho’%
‘k”C’%
. . . . . . . . . +4-4
. . . . . . . . . Ld- La+,
i
I
“cb+h
#&-4
Y-Y’S
~4,-d,
Hl’ps
k4-4
L,+LO-&
L&LO-b
L;&-h
Lg - 970’
1
-
I
Horizontal
FIGURE
Force - Pounds
16
104-D-1 129
I
TRANSMISSION
LINE DESIGN
MANUAL
Horizontol Force - Pounds
FIGURE
104-D-1130
I7
APPENDIX
A
331
VI-BIBLIOGRAPHY
Technical
[1]
[2]
[3]
[4]
Technical
[5]
[6]
[7]
[8]
Journals
Brown, R. S., “Stresses Produced in a Transmission Line by Breaking of a Conductor,”
Electrical World, vol. 61,
No. 13, pp. 673-676, March 29, 1913.
September,
Healy, E. S., and Wright, A. J., “Unbalanced
Conductor
Tensions,” Trans. of AIEE, pp. 1064-1070,
1926.
Den Hartog, J. P., “Calculation
of Sags in a Transmission Line With a Broken Conductor,”
The Electric Journal,
vol. XXV, pp. 24-26, January, 1928.
Effect on Sags in Suspension Spans,” Trans. of AIEE, vol, 66, pp.
Bissiri, A., and Landau, M., “Broken Conductor
1181-1188,
1947.
Books
Painton, E. T., “Mechanical
Design of Overhead Electrical Transmission Lines,” D. Van Nostrand Co., New York,
pp. 265-269, 1925.
Third Edition, McGraw-Hill
Book Co., New York, pp. 137-138, 1927.
Still, A., “Electric
Power Transmission,”
Engineers Handbook-Electric
Power,” Third Edition,
Pender, H., Del Mar, W. A., and McIlwain,
K., “Electrical
Section 14, pp. 71-73, 1936.
Martin, J. S., “Sag Calculations by the Use of Martin’s Tables,” Copperweld
Steel Co., Glassport, Pa., pp. 39-40,
1942.
332
TRANSMISSION
LINE DESIGN MANUAL
EOUIVALENT
HORIZONTAL
SPAN
NOMOGRAPH
NOTES
These charts
are designed to facilitate
the computation
of the ruling span length
for any series of suspension spans.
The procedure
for computing the ruling span
length is OS follows:
I. Compute
the Equivalent
Horizontol
Spon
(He) for each span in the series being
considered
by using the nomograph which
is based on J.S. Martin’s
formula: He=ZI-H.
(Use only for spans of 20% slope or less.)
2. The Ruling Span Length
by using the relation:
the solution of which is facilitated
by
using the Ruling Span Computation
Chart.
900
600
5. no-c
8
20
600--
-
500--
z
g
400--
G
z
30
40
50
E
::
=
.u
+
k
5
t
ki 100
k
i3
=
s
300--
200
>
200
300
Z He- 2700:
400
i
EXAMPLE:
Horizontol
span (H)
Vertical span (V)
Correction
K)
Equiv. horiz. span
ZHe’ 0.27 x IO’ line.
4. Project
vertlcolly
down from this point
to the Hrs scale ond read the ruling
span length of 910 ft.
500 I
= 1000’
-100’
= IO’
-1010’
FIGURE
(Sheet
ZH,‘-22.5~10’
3. Enter the auxiliary
bias lines at the
value corresponding
to ZHeL 22.5~ IO’
and read down the bias line to the
intersection
of the horizontal
300
200--
IOO-
EXAMPLE
Fmd the ruling span length for a
SerieS of level spans of lengths,
He=800,
900. 6 1000 ft.
Solution:
(Using the Ruling Span Chart),
I. Enter the equivalent
horizontal
stole
at the span lengths given and read the
corresponding
He3 values.
2. Add the Hd& He values:
Problem:
18
2 of 2)
334
NMS
s
LINE DESIGN MANUAL
NI H19N31
TRANSMISSION
133d
EXPLANATION
The purpose of this chart is to focilitote
the computation
of tronsmission line conductor sags and tensions when
any three of the elements-span
length, unit weight,
sag, or tension ore known and when accuracy beyond the
first decimal place is not required. This chart is based on the
cotenory functions OS derived by J.S. Martin and given in
the pamphlet “Sog Colculotions By The Use Of Mortin’s
Tables” published by the Copperweld Steel Compony,
Glossport. PO.
The procedure for computing o sag value when the span
length, unit weight, and tension ore known is OS follows:
3. Project horizontally from this point to the right or left
to intersect the sag ratio curve.
4. From this potnt project vertically upward to intersect
the Bose Spon Aux. Bios Line.
5. Thence, project horizontally -right or left- to intersect
the bias line correspondtng to the span length used
in step (I) obove.
6. from this point project vertically downward to intersect
the sag scale ond read the corresponding sag value in
feet.
As on exomple, the followmg problem has been worked through:
Find the sag for o conductor which weighs 1.1 lb. per
ft when the span length is II00 ft. and the tension
is 7000 lb.
Answer by chart: 23.9 ft.
Answer by more exact computation: 23.871 ft
I. Enter the span length scale at o point corresponding to
the equivalent level span length of the span under
consideration ond project horizontally to the right to
intersect the bias line which corresponds to the unit
weight of the conductor.
2. Project vertically -up or down- from this point to
intersect the bias line which corresponds to the
tension in tne conductor:
FIGURE I9
(Sheet
2 of 2)
D
:
1
0
Z
D
336
TRANSMISSION
LINE DESIGN MANUAL
1000
RULING
1.
P.
3.
4.
5.
6.
7.
I200
SPAN LENGTH
- F 1.
Dead-end
in first span adjacent
Deod- end in second won odjocrnt
hod-end
in third spon odjocmt
Dood-end
in fourth spon odjocent
Dead-end
in fifth spon odjocrnt
Dead-•d
o great distoncr
from
Tonsion brforr
brook.
FIGURE
20
2)
(Sheet
I of
104-D-1133
to brook.
to brook.
to brook.
to brook.
to brook.
break.
1400
APPENDIX
Theso curves
ot crossings
ore
bosed
ore to be use’?1
which worront
on the following:
Conductor
Looding
Insulators
A
NOTES
in moking preliminary
determinations
compliance
with titionol
o&/or
337
of conductor
h6ights
Loco/ sofety
codes ond
- 195,000
C. M. MS. R. 6617 stronding.
130°F. tinol no load with mox. lood = 7500 Ibs. Q 25% ond #*wind.
- lb, &“x
lOWsuspension
units.
The following
l xomple is given to illustrate
the use of the curves
shown to the left.
PROBLEM:
Determine
conductor
heights
ot crossing
shown below,
moking
provisions
for required
cleoronce
under
broken
conductor
conditions.
PROCEDURE:
FIRSTFrom pertinent
SECOND
- Determine
safety
cod6s determine
required
cleoronce
over crossing.
the ruling
spon from crossing
spon to neorest
deod-end
by:
level spons,
where
the l quivolent
Note: L,, Le, etc. ore l quivolent
l?S=jy:*.
level spon = 2 (Inclined
spon)
- octuol
spon.
THIRD
- ;nter?he
curves
ot the value
of the ruling
spon OS determined
obove
ond
using
the curve
which
best describes
the location
of the neorest
deod-end
reod
For deod-ends
more thon 5 spons
the corresponding
value of horizontol
tension.
from breok use curve No.6.
FOURTH
- Determine
brok6n
conductor
sog and/or
profile
OS required.
In applying
conductor
pro file to transmission
line profil6,
the shift
in the spon due to the conductor
breoC need be consider6d
only for
vrry short spans.
FIFTH
- For o I6vel crossing
spon, conductor
height
= required
clr. +
broken
cond. $09. For on inclined
spon, us6 height
osindicohd
by
intercepts
of the broken
cond. prOfil6
on the StruCtur6
center
lines.
FIGURE 20
(Sheet 2 of 2)
<<Appendix
USEFUL
FIGURES
339
AND TABLES
B
TRANSMISSION
340
t=
II
36 I
---
LINE DESIGN
MANUAL
6 Miles
I
I
line
3’
l
I
32
j
I 5 I
35
33
3
4
1
2
36
j 31
-----
I
E --.--
6
_--
7
8
9
IO
II
12
i I2
cr---
7
---
XL
I3
I8
I6
I7
I5
I4
I3
I8
_--
3L
3r
24
19
20
23
22
21
u
a
.2
u
I9
24
---7
--25
30
29
28
27
26
25
31
32
33
34
35
36
--36
2
30 =
Q,
F
--cz
31
_----
I
6
1
5
I
!
4
3
f
j
2
j
Townshi; I ine J
Figure
B-l.-Typical
township
showing
section
numbering.
104-D-1134.
I
/6
APPENDIX
B
341
I Mile
/FN
\
$ car.
---
‘NW car. Sec.15 /t/6\’
co,
‘%
senter NW$
9\’
VEcar:Sec.15’
(Center NE {
i
0
-;
ai
J r
w
t Center SE i
SECOT.
Set 15.
---
Typical Section of Land Showing Corner Designations
---
-
---l---NW )
of NW;
NE ;
of NW;
SW $
of NW)
SE 4’
of NW $
.
15---I
I
I
Typical $ Section
Figure B-2.-Typical
land section
showing
corner and l/16
designations.
104-D-1135.
tmnsmission line olwoys runs from
left to right on o key mop or on
o plon-profile
drawing. The direction
(beoring) of o line, OS indicated on
the plan-profile
drawing, is related
to the directions given on on
azimuth chart. Examples ore:
N8803O’OO”E
S 62” 36’47” E
+l
E a Indicates the angle
..
turned, and the arrow
In
head indicates the
5
direction of the new
segment of the line
i
in relation to the
segment just before
the angle point.
S 71“15’00” W /
S48’09’OO”W
&
The letters PI (point
of intersection) are
+=
5 8
used OS a prefix to
CD’D a station to denote
eP
on angle and to
q
indicate the exact
;a
location of the angle
point.
Figure B-3.-Azimuth
chart.
104-D-1136.
APPENDIX
B
343
Consider pole as a simple beam
where f =
M=
S=
J =
Y=
r =
C =
stress in outer fiber
maximum moment
section modulus
moment of inertia
distance from center of gravity to outer fiber
radius of pole cross section
circumference of pole cross section
N/mm*
N-mm
mm3
mm4
mm
mm
mm
(Ib/in* )
(lb-in)
(in3)
(in4)
(in)
iin)
(in)
axis of moments through center
then b = 4 7 r
rrd _ rr 4
J =w-7
;Ay3
S = $a$.
=f
!
M = fS=f (y3)
C = 27r
r CL
27T
r3= c3
87r3
M = f ($)($)
=fL-$=0.003
166fc3
If f is in N/mm* and c is in mm, M is in N.mm. Dividing by
1000, M iS in N-m. M =3.166 x 10+fC3 N-m.
If f is in lb/in* and c is in inches, M is in lb-in. Dividing by
12, M is in lb-ft. M=2.638 xIOe4fc3 lb-ft.
Figure B-4.-Development
of formula
for maximum
moment
of resistance
on wood poles. 104-D-1137.
344
TRANSMISSION
LINE DESIGN
MANUAL
APPENDIX
Table B-l .-Maximum
Metric:
345
moment of resistance for pole circumferences at
ground line- USBR standard
M,. = 3.166 x 10s6fc3 (c in mm)
Pole
Circumference
B
U.S. customary:
Western Red Cedar
Pole
Diameter
f= 38.610 88 MPa
M,. = 2.638 x 10w4fc3 (c in inches)
Douglas Fir and Southern Yellow Pine
f= 5600 lb/in2
fz51.021
52 MPa
f= 7400 lb/in2
C
mm
in
mm
in
N-m
lb.ft
N.m
lb-ft
508
521
533
546
559
20.0
20.5
21.0
21.5
22.0
162
166
170
114
178
6.37
6.53
6.68
6.84
7.00
16025
17 287
18509
19 891
21 352
11
12
13
14
15
818
726
681
681
730
21176
22 844
24459
26293
28 216
15 616
16817
18 078
19 400
20186
512
584
597
610
622
22.5
23.0
23.5
24.0
24.5
182
186
190
194
198
7.16
7.32
7.48
1.64
7.80
22871
24 341
26 010
27 746
29416
16 821
17 914
19 171
20421
21125
30230
32173
34 370
36665
38 871
22235
23 751
25 334
26986
28708
635
648
660
673
686
25.0
25.5
26.0
26.5
27.0
202
206
210
214
218
7.96
8.12
8.28
8.44
8.59
31299
33261
35 144
37261
39463
23082
24495
25 964
21491
29 071
41360
43953
46440
49239
52147
30501
32368
34 310
36328
38423
699
711
124
737
749
27.5
28.0
28.5
29.0
29.5
222
226
230
235
238
8.75
8.91
9.07
9.23
9.39
41149
43936
46 391
48935
51364
30122
32429
34 191
36029
37925
55 169
58059
61302
64 664
67 874
40597
42852
45 189
41610
50115
162
115
787
800
813
30.0
30.5
31.0
31.5
32.0
242
247
250
255
259
9.55
9.71
9.87
10.03
10.19
54086
56 901
59586
62587
65 688
39886
41914
44009
46173
48407
71470
15 191
78738
82705
86803
52707
55 386
58155
61015
63967
826
838
851
864
876
32.5
33.0
33.5
34.0
34.5
263
267
271
275
219
10.35
10.50
10.66
10.82
10.98
68890
71937
75 337
78842
82017
50712
53089
55538
58063
60662
91034
95059
99552
104185
108586
67012
70153
73 390
76726
80161
889
902
914
921
940
35.0
35.5
36.0
36.5
37.0
283
287
291
295
299
llJ4
11.30
11.46
11.62
11.78
85
89
93
97
101
886
709
338
377
532
63338
66 091
68923
71835
74 828
113493
118545
123 339
128677
134 167
83691
87 335
91078
94925
98880
953
965
978
991
1003
31.5
38.0
38.5
39.0
39.5
303
307
311
315
319
11.94
12.10
12.25
12.41
13.57
105
109
114
118
123
803
850
350
971
345
17903
81 061
84 303
87 630
91044
139 811
145 159
151105
157 211
162992
102943
107 116
111400
115 797
120 308
1016
1029
1041
1054
1067
40.0
40.5
41.0
41.5
42.0
323
328
331
336
340
12.73
12.89
13.05
13.21
13.37
128
133
137
143
148
204
188
902
133
495
94545
98135
101 815
105 586
109 448
169412
175 999
182228
189141
196226
124
129
134
139
144
935
679
542
524
628
TRANSMISSION
LINE DESIGN MANUAL
Table B-l .-Maximum moment of resistance for pole circumferences at
ground line-USBR standard-Continued
Pole
Circumference
Western Red Cedar
Pole
Diameter
f= 38.610 88 MPa
C
N.m
Douglas Fir and Southern Yellow Pine
f=5600
lb/in2
f= 51.02152
MPa
f = 7400 lb/in2
mm
in
mm
in
1080
1092
1105
1118
1130
42.5
43.0
43.5
44.0
44.5
344
348
352
356
360
13.53
13.69
13.85
14.01
14.16
153
159
164
170
176
989
180
932
822
382
113
117
121
125
130
404
454
599
840
179
203
210
217
225
233
486
345
947
730
077
149
155
160
166
172
855
207
684
289
023
1143
1156
1168
1181
1194
45.0
45.5
46.0
46.5
47.0
364
368
372
376
380
14.32
14.48
14.64
14.80
14.96
182
188
194
201
208
540
840
782
358
081
134
139
143
148
153
617
154
792
532
375
241
249
257
266
274
214
538
390
081
964
177
183
190
196
202
886
882
011
275
674
1207
1219
1232
1245
1257
47.5
48.0
48.5
49.0
49.5
384
388
392
396
400
15.12
15.28
15.44
15.60
15.76
214 952
221427
228 587
235 900
242 787
158
163
168
173
179
322
375
534
800
175
284
292
302
311
320
044
600
062
725
826
209
215
222
229
236
212
888
705
664
767
1270
1283
1295
1308
1321
50.0
50.5
51.0
51.5
52.0
404
408
412
416
420
15.92
16.07
16.23
16.39
16.55
250
258
265
273
281
398
166
478
554
792
184
190
195
201
207
660
255
962
782
717
330 883
341 149
350 811
361482
372 368
244 015
251408
258 950
266 641
274 483
1334
1346
1359
1372
1384
52.5
53.0
53.5
54.0
54.5
425
428
433
437
440
16.71
16.87
17.03
17.19
17.35
290
298
306
315
324
193
095
816
706
062
213
219
226
232
239
767
933
216
618
140
383
393
405
417
428
470
912
436
183
225
282
290
298
307
316
477
625
928
388
006
1397
1410
1422
1435
1448
55.0
55.5
56.0
56.5
57.0
445
449
453
457
461
17.51
17.67
17.83
17.98
18.14
333 280
342 671
351495
361 223
371 130
245
252
259
266
273
782
546
434
445
581
440
452
464
477
490
406
815
475
331
422
324
333
342
352
361
783
722
823
088
518
1461
1473
1486
1499
1511
57.5
58.0
58.5
59.0
59.5
465
469
473
477
481
18.30
18.46
18.62
18.78
18.94
381
390
401
411
421
216
686
122
742
710
280
288
295
303
311
844
235
753
402
181
503
516
530
544
557
749
264
054
088
259
371
380
390
400
411
116
882
817
924
204
1524
1537
1549
1562
1575
60.0
60.5
61.0
61.5
62.0
485
489
493
497
501
19.10
19.26
19.42
19.58
19.74
432
443
454
465
477
688
856
333
868
597
319
327
335
343
352
092
136
314
627
077
571
586
600
615
631
767
524
369
612
111
421
432
443
454
465
657
287
094
079
244
1588
1600
1613
1626
1638
62.5
63.0
63.5
64.0
64.5
506
509
513
518
521
19.89
20.05
20.21
20.37
20.53
489
500
513
525
537
521
703
007
511
232
360
369
378
387
396
664
389
254
260
407
646
661
677
694
709
868
643
902
425
914
476
488
499
511
523
591
121
836
736
824
lb-ft
N-m
lb*ft
APPENDIX
347
B
Table B-l .-Maximum moment of resistance for pole circumferences at
ground line-USBR standard-Continued
Pole
Circumference
Douglas Fir and Southern Yellow Pine
Western Red Cedar
Pole
Diameter
f= 38.610 88 MPa
f= 5600 lb/in2
f=5’1.02152
MPa
f = 7400 lb/in2
C
mm
N.m
lb-ft
N-m
lb-ft
in
mm
in
1651
1664
1676
1689
1702
65.0
65.5
66.0
66.5
67.0
526
530
534
538
542
20.69
20.85
21.01
21.17
21.33
550
563
575
588
602
125
223
496
992
697
405
415
424
434
444
698
132
712
437
311
726
744
760
778
796
951
259
477
311
421
536
548
561
574
587
100
567
226
078
125
1715
1727
1740
1753
1765
67.5
68.0
68.5
69.0
69.5
546
550
554
558
562
21.49
21.65
21.80
21.96
22.12
6i6
629
643
658
672
613
647
974
516
132
454
464
474
485
495
332
504
826
299
926
814
832
850
870
888
810
034
965
181
174
600
613
627
641
655
368
808
448
288
331
1778
1791
1803
1816
1829
70.0
70.5
71.0
71.5
72.0
566
570
574
578
582
22.28
22.44
22.60
22.76
22.92
687
702
716
732
747
093
275
486
096
931
506
517
528
539
551
707
642
734
984
391
907
928
946
967
988
945
006
785
412
337
669
684
698
713
728
577
027
685
550
624
1842
1854
1867
1880
1892
72.5
73.0
73.5
74.0
74.5
586
590
594
598
602
23.08
23.24
23.40
23.55
23.71
763
779
795
812
827
993
022
524
258
911
562
574
586
598
610
959
687
576
629
845
1009
1 029
1051
1073
1094
562
422
228
341
026
743
759
775
791
807
910
407
119
045
189
1905
1918
1930
1943
1956
75.0
75.5
76.0
76.5
77.0
606
610
614
618
623
23.87
24.03
24.19
24.35
24.51
845
862
878
896
914
095
514
805
683
802
623
635
648
661
674
227
775
490
374
427
1 116
1139
1 161
1184
1 208
732
751
278
902
845
823
840
856
873
891
550
131
933
958
207
TRANSMISSION
348
LINE DESIGN
MANUAL
Table B-2.-Maximum moment of resistance for pole circumferences at
ground line-ANSI standard
Mr=2.64x
10-4fc3
Western Larch
Pole
diameter,
20.0
20.5
21.0
21.5
22.0
6.37
6.53
6.68
6.84
7.00
12612
13646
14669
15142
16866
16896
18 195
19 559
20990
22488
17 741
19 105
20537
22039
23613
22.5
23.0
23.5
24.0
24.5
7.16
7.32
7.48
7.64
7.80
18042
19 212
20566
21 897
23294
24057
25 696
21409
29 196
31 059
25 259
26 981
28779
30656
32612
25.0
25.5
26.0
26.5
27.0
7.96
8.12
8.28
8.44
8.59
24750
26264
21840
29477
31177
33000
35 019
37 120
39303
41570
34 650
36170
38976
41268
43649
21.5
28.0
28.5
29.0
29.5
8.75
8.91
9.07
9.23
9.39
32942
34 771
36668
38632
40665
43923
46 362
48890
51509
54220
46 119
48680
51335
54085
56 931
30.0
30.5
31.0
31.5
32.0
9.55
9.71
9.87
10.03
10.19
42768
44942
47188
49 509
51904
57 024
59 922
62 918
66012
69 206
59875
62 919
66064
69313
72666
32.5
33.0
33.5
34.0
34.5
10.35
10.50
10.66
10.82
10.98
54 315
56924
59551
62251
65044
72501
75 898
79401
83 010
86726
76126
79 693
83 371
87160
91 062
35.0
35.5
36.0
36.5
37.0
11.14
11.30
11.46
11.62
11.78
67 914
70866
73903
77025
80234
90552
94488
98531
102700
106979
95 079
99212
103464
107 835
112328
37.5
38.0
38.5
39.0
39.5
11.94
12.10
12.26
12 41
12.57
83531
86 917
90 393
93 961
97 621
111315
115 889
120 524
125 281
130 162
116943
121684
126550
131545
136670
40.0
40.5
41.0
41.5
42.0
12.73
12.89
13.05
13.21
13.37
135 168
140300
145 561
150 951
156 413
141926
147 315
152 839
158 499
164 297
in
f
Western
Red Cedar
= 6000 lb/in2,
lb*ft
Southern
Yellow Pine
f = 8000 lb/in2,
lb*ft
Pole
circumference
c,
in
101
105
109
113
117
376
225
170
213
355
f= 8400 Ib/in2,
lb-ft
APPENDIX
6
Table B-2.-Maximum moment of resistance for pole circumferences at
ground line-ANSIstandard-Continued
Pole
Circumference
c,
in
Pole
Diameter,
42.5
43.0
43.5
44.0
44.5
13.53
13.69
13.85
14.01
14.17
121
125
130
134
139
596
939
383
931
583
162
167
173
179
186
129
918
844
908
111
170
176
182
188
195
235
314
537
904
417
45.0
45.5
46.0
46.5
47.0
14.32
14.48
14.64
14.80
14.96
144
149
154
159
164
342
201
180
262
455
192
198
205
212
219
456
942
573
350
274
202
208
215
222
230
078
889
852
961
237
47.5
48.0
48.5
49.0
49.5
15.12
15.28
15.44
15.60
15.76
169
175
180
186
192
760
177
709
356
119
226
233
240
248
256
347
570
945
474
158
237
245
252
260
268
664
248
992
898
966
50.0
50.5
51.0
51.5
52.0
15.92
16.08
16.23
16.39
16.55
198
203
210
216
222
000
999
119
359
723
264
271
280
288
296
000
999
158
479
964
277 200
285 599
294 166
302 903
311812
52.5
53.0
53.5
54.0
54.5
16.71
16.87
17.03
17.19
17.35
229
235
242
249
256
209
821
558
422
415
305
314
323
332
341
613
428
411
563
887
320
330
339
349
358
893
149
581
192
982
55.0
55.5
56.0
56.5
57.0
17.51
17.67
17.83
17.99
18.14
263
270
278
285
293
538
790
175
693
345
351
361
370
380
391
384
054
900
924
127
368
379
389
399
310
953
107
466
971
683
57.5
58.0
58.5
59.0
59.5
18.30
18.46
18.62
18.78
18.94
301
309
317
325
333
133
057
119
320
661
401511
412 076
422 825
433 760
444 881
421
432
443
455
467
586
680
967
448
126
60.0
60.5
61.0
61.5
62.0
19.10
19.26
19.42
19.58
19.74
342
350
359
368
377
144
769
537
451
511
456
467
479
491
503
192
692
383
268
348
479
491
503
515
528
001
076
353
832
516
62.5
63.0
63.5
64.0
64.5
19.90
20.05
20.21
20.37
20.53
386
396
405
415
425
718
074
579
236
044
515
528
540
553
566
625
099
713
648
725
541
554
567
581
595
506
504
811
330
062
in
f
Western
Red Cedar
= 6000 lb/in2
lb*ft
f
Southern
Yellow Pine
= 8000 lb/in2
lb*ft
Western Larch
= 8400 lb/in2
f
lb-ft
TRANSMISSION
LINE DESIGN MANUAL
Table B-2.-Maximum
moment of resistance for pole circumferences at
ground line-ANSI standard-continued
Western Larch
Pole
Diameter,
65.0
65.5
66.0
66.5
67.0
20.69
20.84
21.00
21.16
21.32
435
445
455
465
476
006
122
393
822
408
580 008
593 496
607 191
621096
635 211
609
623
637
652
666
008
170
551
150
972
67.5
68.0
68.5
69.0
69.5
21.48
21.64
21.80
21.96
22.12
487
498
509
520
531
154
060
127
358
752
649
664
678
693
709
539
080
837
811
003
682
697
712
728
744
015
284
779
501
453
70.0
70.5
71.0
71.5
72.0
22.28
22.44
22.60
22.75
22.91
543
555
566
578
591
312
037
931
992
224
724
740
755
771
788
416
050
908
990
299
760
777
793
810
827
636
052
703
590
714
72.5
73.0
73.5
74.0
74.5
23.07
23.23
23.39
23.55
23.71
603
616
628
641
654
627
202
95 1
874
973
804
821
838
855
873
837
603
602
833
298
845
862
880
898
916
078
684
532
624
963
75.0
75.5
76.0
76.5
77.0
23.87
24.03
24.19
24.35
24.50
668
681
695
709
723
250
704
337
152
148
891
908
927
945
964
000
939
117
536
197
935
954
973
992
1012
550
386
473
813
407
77.5
78.0
78.5
79.0
79.5
24.66
24.82
24.98
25.14
25.30
737
751
766
780
795
327
690
238
973
896
983
1002
1021
1041
1061
103
253
651
298
195
1032
1052
1072
1 093
1114
258
366
734
363
255
80.0
80.5
81.0
81.5
82.0
25.46
25.62
25.78
25.94
26.10
811
826
841
857
873
008
309
802
487
366
1081
1 101
1 122
1 143
1 164
344
746
403
317
489
1
1
1
1
1
135
156
178
200
222
411
833
523
483
713
82.5
83.0
83.5
84.0
84.5
26.26
26.41
26.57
26.73
26.89
889
905
922
938
955
440
710
177
843
708
1185
1 207
1 229
1 251
1 274
921
614
570
790
277
1245
1 267
1 291
1 314
1337
217
994
048
380
991
85.0
85.5
27.05
27.21
972 774
990 041
in
f
Western
Red Cedar
= 6000 lb/in2
lb*ft
Southern
Yellow Pine
= 8000 lb/in2
lb-ft
Pole
Circumference
c,
in
f
1 297 032
1 320 055
f = 8400 lb/in2
lb-ft
1 361 883
1 386 058
APPENDIX
Table B-3.-Pole
SOUTHERN
YELLOW
PINE
AND DOUGLAS
FIR
DISTANCE
CLASS
I
FROM TOP
CIRC.
FEET
INCHES
2
3
4
5
6
7
8
9
10
30
CLASS
CIRC.
INCHES
CLASS
CIRC.
INCHES
2
3
CLASS
CIRC.
INCHES
TOP
1
2
3
4
5
6
7
8
9
10
27.00
27.40
27.79
20.19
28.58
28.98
29.38
29.77
30.17
30.56
30.96
25.00
25.38
25.75
26.13
26.50
26.68
27.25
27.63
28.00
28.38
28.75
23.00
23.38
23.75
24.13
24.50
24.89
25.25
25.63
26.00
26.38
26.75
21 .oo
21.33
21 .67
22.00
22.33
22.67
23.00
23.33
23.67
24.00
24.33
I 1
12
13
14
15
16
17
18
19
20
31.35
31.75
32.15
32.54
32.94
33.33
33.73
34.12
34.52
34.92
29.13
29.50
29.00
30.25
30.63
31 .oo
31.38
31.75
32.13
32.50
27.13
27.50
27.68
28.25
28.63
29.00
29.36
29.75
30.13
30.50
24.67
25.00
25.33
25.67
26.00
26.33
26.67
27.00
27.33
27.61
25
26
27
28
29
30
TOP
351
circumferences for Douglas fir and southern yellow pine
21
22
23
24
SOUTHERN
YELLOW
DISTANCE
FROM TOP
FEET
6
35.31
35.71
36.10
36.50
GROUND
36.90
37.29
37.69
38.08
38.48
38.87
L.INE
PINE
AND DOUGLAS
FIR
CLASS
H-2
CLASS
H-l
CIRC.
CIRC.
INCHES
INCHES
31 .oo
31.43
31.86
32.29
32.72
33.16
33.59
34.02
34.45
34.88
35.31
29.00
29.43
29.86
30.29
30.72
31.16
31.59
32.02
32.45
32.88
33.31
32.88
33.25
33.63
34.00
(5 FEE1
34.38
34.75
35.13
35.50
35.88
36.25
30.88
31 .25
31 .63
32.00
6 INCHESl------32.38
32.75
33.13
33.50
33.68
34.25
CLASS
CIRC.
INCHES
27
27
27
28
28
29
29
29
30
30
31
00
41
83
24
66
07
48
90
31
72
14
1
CLASS
CIRC.
INCHES
25.00
25.40
25.79
26.19
26.59
26.98
27.38
27.78
28.17
28.57
28.97
2
FOOT
POLE
4
28.00
28.33
28.67
29.00
29.33
29.67
30.00
30.33
30.67
31 .oo
CLASS
CIRC.
INCHES
23.00
23.38
23.76
24.14
24.52
24.90
25.28
25.66
26.03
26.41
26.79
35 FOOT
CLASS
4
CIRC.
INCHES
3
_
21 .oo
21 .36
21 .72
22.09
22.45
22.81
23.17
23.53
23.90
24.26
24.62
POLE
TRANSMISSION
352
LINE DESIGN
MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
DISTANCE
FROM TOP
FEET
I I
12
13
14
CLASS
CIRC.
1
CLASS
CIRC.
INCHES
CLASS
CIRC.
INCHES
INCHES
5
FOOT POLE-COII.
CLASS
4
CIRC.
INCHES
17
18
19
20
33.74
34.17
34.60
35 03
35 47
35 90
36 33
36 76
37 19
37 62
31.55
31.97
32.38
32 79
33 21
33 62
34 03
34 45
34 86
35 28
29.36
29.76
30.16
30.55
30.95
31.34
31.74
32.14
32.53
32.93
27.17
27.55
27.93
28.31
28.69
29.07
29.45
29.83
30.21
30.59
24.98
25.34
25.71
26.07
26.43
26.79
27.16
27.52
27.88
28.24
21
22
23
24
25
26
27
28
29
40.05
40.48
40.91
41.34
41 .78
42.21
42.64
43.07
43.50
38
38
38
39
39
40
40
41
41
35
36
36
36
37
37
38
38
39
69
10
52
93
34
76
17
59
00
33.33
33.72
34.12
34.52
34.91
35.31
35.71
36.10
36.50
30.97
31.34
31 .72
32.10
32.48
32.86
33.24
33.62
34.00
--------------34.38
28.60
28.97
29.33
29.69
30.05
30.41
30.78
31.14
31.50
34.76
35.14
35.52
35.90
36.28
32.22
32.59
32.95
33.31
33.67
-----------------GROUND
05
48
91
34
78
21
64
07
50
LINE
(6
FEET
30
43.93
41.93
39.4
31
32
33
34
35
44.36
44.79
45.22
45.66
46.09
42.36
42.79
43.22
43.66
44.09
39
40
40
41
41
YELLOW
CLASS
PINE
H-3
CIRC.
INCHES
AND DOUGLAS
CLASS
H-2
CIRC.
INCHES
0
INCHES)36.90
83
24
66
07
48
37.29
37.69
38.09
38.48
38.88
FIR
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
1 NCHES
33.00
33.46
33.91
34.37
34.82
35.28
35.74
36.19
36.65
37.10
37.56
31 00
31 44
31 88
32 32
32 76
33.21
33.65
34 09
34 53
34 97
35 41
29
29
29
30
30
31
31
31
32
32
33
00
1
2
3
4
5
6
7
8
9
10
43
85
28
71
13
56
99
41
84
26
27
27
27
28
28
29
29
29
30
30
31
82
24
65
06
47
88
29
71
12
11
12
13
14
15
16
17
18
19
20
38.01
38.47
38.93
39.38
39.84
40.29
40.75
41.21
41.66
42.12
35
36
36
37
37
38
38
38
39
39
33
34
34
34
35
35
36
36
37
37
69
12
54
97
40
82
25
68
10
53
31
31
32
32
33
33
34
34
34
35
53
94
35
76
18
59
00
41
82
24
TOP
2
35.74
36.17
36.60
37.03
37.47
37.90
38.33
38.76
39.19
39.62
15
16
SOUTHERN
DISTANCE
FROM TOP
FEET
35
PINE
AND DOUGLAS
FIR
CLASS
H-2
CLASS
H-l
CIRC.
CIRC.
INCHES
INCHES
85
29
74
18
62
06
50
94
38
82
00
41
1
CLASS
2
CLASS
31.86
40 FOOT
POLE
3
CLASS
4
CIRC.
INCHES
CIRC.
INCHES
CIRC.
INCHES
25.00
25.40
25.79
26.19
26.59
26.99
27.38
27.78
28.18
28.57
28.97
23.00
23.38
23.76
24.15
24.53
24.91
25.29
25.68
26.06
26.44
26.82
21.37
21.74
22.10
22.47
22.84
23.21
23.57
23.94
24.31
24.68
29.37
29.76
27.21
27.59
27.97
28.35
28.74
29.12
29.50
29.88
30.26
30.65
25.04
25.41
25.78
26.15
26.51
26.88
27.25
27.62
27.99
28.35
30.16
30.56
30.96
31.35
31.75
32.15
32.54
32.94
21 .oo
APPENDIX
353
6
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
DISTANCE
FROM TOP
FEET
21
22
23
24
25
26
27
28
29
30
31
32
33
--------34
35
36
31
38
39
40
SOUTHERN
DISTANCE
FROM TOP
FEET
YELLOW
PINE
CLASS
H-3
CIRC.
INCHES
AND DOUGLAS
CLASS
H-2
CIRC.
INCHES
42.57
43.03
43.49
43.94
44.40
44.85
45.31
45.76
46.22
46.68
40
40
41
41
42
42
42
43
43
44
47.13
47.59
48.04
---------------GROUND
48.50
48.96
49.41
49.87
50.32
50.78
51 .24
YELLOW
PINE
CLASS
H-3
CIRC.
INCHES
FIR
26
71
15
59
03
47
91
35
79
24
46.00
46.44
46.88
41.32
47.76
48.21
48.65
37.96
38.38
38.81
39.24
39.66
40.09
40.51
40.94
41.37
41.79
35.65
36.06
36.47
36.88
37.29
37.71
38.12
38.53
38.94
39.35
33
33
34
34
34
35
35
36
36
36
34
74
13
53
93
32
72
12
51
91
31.03
31.41
31.79
32.18
32.56
32.94
33.32
33.71
34.09
34.47
28 72
29 09
29 46
29.82
30.19
30 56
30 93
31 29
31 66
32 03
39.76
40.18
40.59
0 INCHES)--41 .oo
41.41
41 .82
42.24
42.65
43.06
43.47
37
37
38
31
71
10
34.85
35.24
35.62
32
32
33
40
76
13
38
38
39
39
40
40
40
50
90
29
69
09
49
88
36.00
36.38
36.76
37.15
37.53
37.91
38.29
33
33
34
34
34
35
35
50
87
24
60
97
34
71
AND DOUGLAS
CLASS
H-2
CIRC.
INCHES
FEET
CLASS
CIRC.
INCHES
2
POLE-con.
CLASS
CIRC.
INCHES
CLASS
CIRC.
INCHES
42.22
42.65
43.07
LINE
(6
43.50
43.93
44.35
44.78
45.21
45.63
46.06
44.68
45.12
45.56
1
40 FOOT
CLASS
3
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
FIR
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
CLASS
CIRC.
INCHES
2
CLASS
CIRC.
INCHES
45 FOOT
POLE
3
CLASS
4
CIRC.
INCHES
3
4
5
6
7
8
9
10
33.00
33.46
33.92
34.38
34.85
35.31
35.71
36.23
36.69
37.15
37.62
31 .oo
31.45
31.90
32.35
32.79
33.24
33.69
34.14
34.59
35.04
35.49
29.00
29.42
29.85
30.27
30.69
31.12
31.54
31 .96
32.38
32.81
33.23
27.00
27.41
27.82
28.23
28.64
29.05
29.46
29.87
30.28
30.69
31.10
25
25
25
26
26
26
21
27
28
28
28
00
40
19
19
59
99
38
78
18
58
97
23.00
23.37
23.14
24. 12
24.49
24.86
25.23
25.60
25.97
26.35
26.72
21
21
21
22
22
22
23
23
23
24
24
00
36
72
08
44
79
15
51
87
23
59
I I
12
13
14
15
16
17
18
19
20
38.08
38.54
39.00
39.46
39.92
40.38
40.85
41.31
41.77
42.23
35
36
36
37
37
38
38
39
39
39
33.65
34.08
34.50
34.92
35.35
35.77
36.19
36.62
37.04
37.46
31.51
31.92
32.33
32.74
33.15
33.56
33.97
34.38
34.79
35.21
29
29
30
30
30
31
31
32
32
32
37
77
17
56
96
36
76
15
55
95
27.09
27.46
27.83
28.21
28.58
28.95
29.32
29.69
3Q. 06
30.44
24
25
25
26
26
26
27
27
27
28
95
31
67
03
38
74
10
46
82
18
TOP
2
94
38
83
28
73
18
63
08
53
97
4
354
TRANSMISSION
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
DISTANCE
FROM TOP
FEET
YELLOW
PINE
CLASS
H-3
CIRC.
INCHES
21
22
23
24
25
26
27
28
29
30
42.69
43.15
43.62
44.08
44.54
45.00
45.46
45.92
46.38
46.85
31
32
33
34
35
36
37
38
--------------.
47.31
47.77
48.23
48.69
49.15
49.62
50.08
50.54
39
40
51 .oo
51 .46
41
42
43
44
45
51.92
52.38
52.85
53.31
53.77
SOUTHERN
DISTANCE
FROM TOP
FEET
YELLOW
PINE
CLASS
H-3
CIRC.
INCHES
AND DOUGLAS
CLASS
H-2
CIRC.
INCHES
40
40
41
41
42
42
43
43
44
44
FIR
42
a7
32
77
22
67
12
56
01
46
44.91
45.36
45.81
46.26
46.71
47.15
47.60
48.05
---GROUND
48.50
48.95
49.40
49.85
50.29
50.74
51.19
AND DOUGLAS
CLASS
H-2
CIRC.
INCHES
2
45 FOOT
CLASS
3
CIRC.
INCHES
POLE-con.
CLASS
CIRC.
INCHES
CLASS
CIRC.
INCHES
37.88
38.31
38.73
39.15
39.58
40.00
40.42
40.85
41 .27
41 .69
35.62
36.03
36.44
36.85
37.26
37.67
38.08
38.49
38.90
39.31
33
33
34
34
34
35
35
36
36
36
35
74
14
54
94
33
73
13
53
92
30.81
31.18
31.55
31.92
32.29
32.67
33.04
33.41
33.78
34.15
28.54
28.90
29.26
29.62
29.97
30.33
30.69
31.05
31.41
31 .I7
39.72
40.13
40.54
40.95
41 .36
41 .I7
42.18
42.59
6 INCHES)--43.00
43.41
37
37
38
38
38
39
39
40
32
72
12
51
91
31
71
10
34.53
34.90
35.27
35.. 64
36.01
36.38
36.76
37.13
32.13
32.49
32.85
33.21
33.56
33.92
34.28
34.64
40
40
50
90
37.50
37.87
35.00
35.36
46.35
46.77
47.19
47.62
48.04
43.82
44.23
44.64
45.05
45.46
41.29
41 .69
42.09
42.49
42.88
38.24
38.62
38.99
39.36
39.73
35.72
36.08
36.44
36.79
37.15
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
42.12
42.54
42.96
43.38
43.81
44.23
44.65
45.08
LINE
(6
45.50
45.92
FEET,
1
CLASS
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
FIR
1
CLASS
CIRC.
INCHES
2
CLASS
CIRC.
INCHES
50
3
4
FOOT POLE
CLASS
4
CIRC.
INCHES
TOP
1
2
3
4
5
6
7
a
9
10
33.00
33.45
33.91
34.36
34.82
35.27
35.73
36.18
36.64
37.09
37.55
31 .oo
31.44
31 .a9
32.33
32.77
33.22
33.66
34.10
34.55
34.99
35.43
29.00
29.42
29.84
30.26
30.68
31.10
31 .52
31.94
32.36
32.78
33.20
27.00
27.41
27.82
28.23
28.64
29.05
29.45
29.86
30.27
30.68
31.09
25.00
25.39
25.77
26.16
26.55
26.93
27.32
27.70
28.09
28.48
28.86
23.00
23.36
23.73
24.09
24.45
24.82
25.18
25.55
25.91
26.27
26.64
21 .oo
21.35
21.70
22.06
22.41
22.76
23.11
23.47
23.82
24.17
24.52
11
12
13
14
15
16
17
18
19
20
38.00
38.45
38.91
39.36
39.82
40.27
40.73
41.18
41 .64
42.09
35.88
36.32
36.76
37.20
37.65
38.09
38.53
38.98
39.42
39.86
33.63
34.05
34.47
34.89
35.31
35.73
36.15
36.57
36.99
37.41
31.50
31.91
32.32
32.73
33.14
33.55
33.95
34.36
34.77
35.18
29.25
29.64
30.02
30.41
30.80
31.18
31.57
31.95
32.34
32.73
27.00
27.36
27.73
28.09
28.45
28.82
29.18
29.55
29.91
30.27
24.87
25.23
25.58
25.93
26.28
26.64
26.99
27.34
27.69
28.05
APPENDIX
355
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
DISTANCE
FROM TOP
FEET
YELLOW
PINE
CLASS
H-3
CIRC.
INCHES
AND DOUGLAS
CLASS
H-2
CIRC.
FIR
CLASS
H-l
CIRC.
INCHES
INCHES
CLASS
CIRC.
INCHES
1
CLASS
CIRC.
INCHES
2
50 FOOT
CLASS
3
CIRC.
INCHES
POLE-con.
CLASS
CIRC.
INCHES
42.55
43.00
43.45
43.91
44.36
44.82
45.27
45.73
46.18
46.64
40.31
40.75
41.19
41 .64
42.08
42.52
42.97
43.41
43.85
44.30
37.83
38.25
38.67
39.09
39.51
39.93
40.35
40.77
41.19
41 .61
35.59
22
23
24
25
26
27
28
29
30
36.00
36.41
36.82
37.23
37.64
38.05
38.45
38.86
39.27
33.11
33.50
33.89
34.27
34.66
35.05
35.43
35.82
36.20
36.59
30.64
31 .oo
31 .36
31.73
32.09
32.45
32.82
33.18
33.55
33.91
28.40
28.75
29.10
29.45
29.81
30.16
30.51
30.86
31.22
31.57
31
32
33
34
35
36
37
38
39
40
47.09
47.55
48.00
48.45
48.91
49.36
49.82
50.27
50.73
51.18
44.74
45.18
45.62
46.07
46.51
46.95
47.40
47.84
48.28
48.73
42.03
42.45
42.87
43.30
43.72
44.14
44.56
44.98
45.40
45.82
39.68
40.09
40.50
40.91
41 .32
41.73
42.14
42.55
42.95
43.36
36.98
37.36
37.75
38.14
38.52
38.91
39.30
39.68
40.07
40.45
34.27
34.64
35.00
35.36
35.73
36.09
36.45
36.82
37.18
37.55
31.92
32.27
32.62
32.98
33.33
33.68
34.03
34.39
34.74
35.09
41
42
51 .64
52.09
49.17
49.61
46.24
46.66
43.77
44.18
40.84
41 .23
35.44
35.80
43
44
45
46
47
48
49
50
52.55
53.00
53.45
53.91
54.36
54.82
55.27
55.73
37.91
38.27
--------------38.64
39.00
39.36
39.73
40.09
40.45
40.82
41.18
21
---GROUND
SOUTHERN
DISTANCE
FROM TOP
FEET
TOP
1
2
3
4
5
6
7
8
9
10
YELLOW
PINE
CLASS
H-3
CIRC.
INCHES
33.00
33.45
33.90
34.35
34.80
35.24
35.69
36. 14
36.59
37.04
37.49
LINE
50.06
50.50
50.94
51.39
51 .83
52.27
52.72
53.16
AND DOUGLAS
CLASS
H-2
CIRC.
INCHES
31 .oo
31.43
31.86
32.29
32.71
33.14
33.57
34.00
34.43
34.86
35.29
(7
FEET
47.08
47.50
47.92
48.34
48.76
49.18
49.60
50.02
0 INCHES)------44.59
41 .61
45.00
45.41
45.82
46.23
46.64
47.05
47.45
42.00
42.39
42.77
43.16
43.55
43.93
44.32
FIR
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
1 NCHES
29.00
29.42
29.84
27.00
27.40
27.80
28.19
28.59
28.99
29.39
29.79
30.18
30.58
30.98
30.26
30.67
31.09
31.51
31.93
32.35
32.77
33.18
1
CLASS
CIRC.
INCHES
25
25
25
26
26
26
27
27
28
28
28
00
38
76
13
51
89
27
64
02
40
78
2
4
36.15
36.50
36.85
37.20
37.56
37.91
38.26
38.61
55 FOOT
POLE
3
CLASS
4
CIRC.
INCHES
1 NCHES
CLASS
CIRC.
23.00
23.36
23.71
24.07
24.43
24.79
25.14
25.50
25.86
26,21
26.57
21 00
21 35
21 69
22 04
22 39
22 73
23 08
23 43
23 78
24 12
24 47
356
TRANSMISSION
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
DISTANCE
FROM TOP
FEET
YELLOW
PINE
CLASS
H-3
CIRC.
INCHES
I I
12
13
14
15
16
17
18
19
20
37.94
38.39
38.84
39.29
39.13
40.18
40.63
41 .08
41.53
41 .98
21
22
23
24
25
26
27
28
29
30
AND DOUGLAS
CLASS
H-2
CIRC.
INCHES
.
FIR
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
I
CLASS
CIRC.
INCHES
2
55 FOOT
CLASS
3
CIRC.
INCHES
POLE-con.
CLASS
CIRC.
INCHES
35.71
36. 14
36.57
37.00
37.43
37.86
38.29
38.71
39.14
39.57
33
34
34
34
35
35
36
36
36
37
60
02
44
86
28
69
11
53
95
37
31 .38
31 .78
32.17
32.57
32.97
33.37
33.77
34.16
34.56
34.96
29.15
29.53
29.91
30.29
30.66
31.04
31 .42
31 .80
32.17
32.55
26.93
27.29
27.64
28.00
28.36
28.71
29.07
29.43
29.79
30.14
24.82
25.16
25.51
25.86
26.20
26.55
26.90
27.24
27.59
27.94
42.43
42.88
43.33
43.78
44.22
44.67
45.12
45.57
46.02
46.47
40.00
40.43
40.86
41 .29
41.71
42.14
42.57
43.00
43.43
43.86
37
38
38
39
39
39
40
40
41
41
79
20
62
04
46
88
30
71
13
55
35.36
35.76
36.15
36.55
36.95
37.35
37.74
38. 14
38.54
38.94
32.93
33.31
33.68
34.06
34.44
34.82
35.19
35.51
35.95
36.33
30.50
30.86
31.21
31.57
31.93
32.29
32.64
33.00
33.36
33.71
28.29
28.63
28.98
29.33
29.67
30.02
30.37
30.71
31 .06
31.41
31
32
33
34
35
36
37
38
39
40
46.92
47.37
47.82
48.27
48.71
49.16
49.61
50.06
50.51
50.96
44.29
44.71
45.14
45.57
46.00
46.43
46.86
47.29
47.71
48.14
41
42
42
43
43
44
44
44
45
45
97
39
81
22
64
06
48
90
32
73
39.34
39.73
40.13
40.53
40.93
41.33
41 .72
42.12
42.52
42.92
36.70
37.08
37.46
37.84
38.21
38.59
38.97
39.35
39.72
40.10
34.07
34.43
34.79
35.14
35.50
35.86
36.21
36.57
36.93
37.29
31 .76
32.10
32.45
32.80
33.14
33.49
33.84
34.18
34.53
34.88
41
42
43
44
45
46
47
51.41
51.86
52.31
52.76
53.20
53.65
54.10
48.57
49.00
49.43
49.86
50.29
50.71
51.14
46
46
46
47
47
48
48
37.64
38.00
38.36
38.71
39.07
39.43
39.79
35.22
35.57
35.92
36.27
36.61
36.96
37.31
------
54.55
55.00
55.45
51.57
52.00
52.43
49
49.50
49.92
43.32
43.71
44.11
44.51
44.91
45.31
45.70
6 INCHES)------46.10
46.50
46.90
40.48
40.86
41 .23
41 .61
41.99
42.37
42.74
48
49
50
15
57
99
41
83
24
66
7 FEET,
08
43.12
43.50
43.88
40.14
40.50
40.86
37.65
38.00
38.35
51
52
53
54
55
55.90
56.35
56.80
57.24
57.69
52.86
53.29
53.71
54.14
54.57
50
50
51
51
52
34
76
17
59
01
47.30
47.69
48.09
48.49
48.89
44.26
44.63
45.01
45.39
45.77
41.21
41.57
41.93
42.29
42.64
38.69
39.04
39.39
39.13
40.08
-----------------------GROUND
LINE
4
APPENDIX
357
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
DISTANCE
FROM TOP
FEET
YELLOW
PINE
CLASS
H-3
CIRC.
INCHES
AND DOUGLAS
CLASS
H-2
CIRC.
INCHES
FIR
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
CLASS
CIRC.
INCHES
2
CLASS
CIRC.
INCHES
60
3
FOOT POLE
CLASS
4
CIRC.
INCHES
33.00
33.44
33.89
34.33
34.78
35.22
35.61
36.11
36.56
37.00
37.44
31 .oo
31.43
31.85
32.28
32.70
33.13
33.56
33.98
34.41
34.83
35.26
29.00
29.41
29.81
30.22
30.63
31.04
31.44
31 .85
32.26
32.67
33.07
27.00
27.39
27.78
28.17
28.56
28.94
29.33
29.72
30.11
30.50
30.89
25.00
25.37
25.74
26.11
26.48
26.85
27.22
27.59
27.96
28.33
28.70
23.00
23.35
23.70
24.06
24.41
24.76
25.11
25.46
25.81
26.17
26.52
21 .oo
21.33
21 .67
22.00
22.33
22.67
23.00
23.33
23.67
24.00
24.33
11
12
13
14
I5
16
17
18
19
20
37.89
38.33
38.78
39.22
39.67
40.11
40.56
41 .oo
41.44
41 .89
35.69
36.11
36.54
36.96
37.39
37.81
38.24
38.61
39.09
39.52
33.48
33.89
34.30
34.70
35.11
35.52
35.93
36.33
36.74
31.15
31 .28
31 .67
32.06
32.44
32.83
33.22
33.61
34.00
34.39
34.78
29.07
29.44
29.81
30.19
30.56
30.93
31.30
31 .67
32.04
32.41
26.87
27.22
27.57
27.93
28.28
28.63
28.98
29.33
29.69
30.04
24.67
25.00
25.33
25.67
26.00
26.33
26.67
27.00
27.33
27.67
21
22
23
24
25
26
27
28
29
30
42.33
42.78
43.22
43.67
44.11
44.56
45.00
45.44
45.89
46.33
39.94
40.37
40.80
41.22
41 .65
42.07
42.50
42.93
43.35
43.78
37.56
37.96
38.37
38.78
39.19
39.59
40.00
40.41
40.81
41.22
35.17
35.56
35.94
36.33
36.72
31.11
37.50
37.89
38.28
38.67
32.78
33.15
33.52
33.89
34.26
34.63
35.00
35.37
35.74
36.11
30.39
30.74
31.09
31.44
31 .80
32.15
32.50
32.85
33.20
33.56
28.00
28.33
28.67
29.00
29.33
29.67
30.00
30.33
30.67
31 .oo
31
32
33
34
35
36
37
38
39
40
46.78
47.22
47.67
48.11
48.56
49.00
49.44
49.89
50.33
50.78
44.20
44.63
45.06
45.48
45.91
46.33
46.76
47.19
47.61
48.04
41 .63
42.04
42.44
42.85
43.26
43.67
44.07
44.48
44.89
45.30
39.06
39.44
39.83
40.22
40.61
41 .oo
41.39
41 .78
42.17
42.56
36.48
36.85
37.22
37.59
37.96
38.33
38.70
39.07
39.44
39.81
33.91
34.26
34.61
34.96
35.31
35.67
36.02
36.37
36.72
37.07
31.33
31 .67
32.00
32.33
32.67
33.00
33.33
33.67
34.00
34.33
Ltl
42
43
44
45
46
47
48
49
50
51.22
51 .67
52.11
52.56
53.00
53.44
53.89
54.33
54.78
55.22
48.46
48.89
49.31
49.74
50.17
50.59
51.02
51.44
51 .87
52.30
45.70
46.11
46.52
46.93
47.33
47.74
48.15
48.56
48.96
49.37
42.94
43.33
43.72
44.11
44.50
44.89
45.28
45.67
46.06
46.44
40.19
40.56
40.93
41.30
41 .67
42.04
42.41
42.78
43.15
43.52
37.43
37.78
38.13
38.48
38.83
39.19
39.54
39.89
40.24
40.59
34.67
35.00
35.33
35.67
36.00
36.33
36.67
37.00
37.33
37.67
TOP
1
2
3
4
5
6
I
8
9
10
TRANSMISSION
358
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
DISTANCE
FROM TOP
FEET
51
52
53
54
55
56
57
58
59
60
SOUTHERN
DISTANCE
FROM TOP
FEET
YELLOW
PINE
CLASS
H-3
CIRC.
INCHES
55.67
56.11
56.56
57.00
57.44
57.89
58.33
58.78
59.22
59.67
YELLOW
PINE
CLASS
H-3
CIRC.
INCHES
AND DOUGLAS
CLASS
H-2
CIRC.
INCHES
52.72
---GROUND
53.15
53.57
54.00
54.43
54.85
55.28
55.70
56.13
56.56
AND DOUGLAS
CLASS
H-2
CIRC.
INCHES
FIR
CLASS
H-l
CIRC.
1 NCHES
49.78
Ll INE
(8 FEET,
50.19
50.59
51 .oo
51.41
51.81
52.22
52.63
53.04
53.44
CLASS
CIRC.
INCHES
46
0
47
47
48
48
48
49
49
49
50
1
83
NCHES
22
61
00
39
78
17
56
94
33
CLASS
CIRC.
INCHES
2
60 FOOT
CLASS
3
CIRC.
INCHES
43.89
40.94
44.26
44.63
45.00
45.37
45.74
46.11
46.48
46.85
47.22
91
41
42
42
42
43
43
43
44
CLASS
CIRC.
INCHES
1
38.00
30
65
00
35
70
06
41
76
11
CLASS
CIRC.
INCHES
2
CLASS
CIRC.
INCHES
38.33
36.67
39.00
39.33
39.67
40.00
40.33
40.67
41 .oo
65 FOOT
POLE
3
CLASS
4
CIRC.
INCHES
33.00
33.43
33.86
34.30
34.73
35.16
35.59
36.03
36.46
36.89
37.32
31
31
31
32
32
33
33
33
34
34
35
00
42
83
25
66
08
49
91
32
74
15
29.00
29.40
29.80
30.19
30.59
30.99
31.39
31 .I9
32.19
32.58
32.98
27.00
27.38
27.76
28.14
28.53
28.91
29.29
29.67
30.05
30.43
30.81
25.00
25.36
25.73
26.09
26.46
26.82
27.19
27.55
27.92
28.28
20.64
23.00
23.35
23.69
24.04
24.39
24.74
25.08
25.43
25.78
26.13
26.47
21 .oo
21.33
21.66
21.99
22.32
22.65
22.98
23.31
23.64
23.97
24.31
11
12
13
14
15
16
17
18
19
20
37.75
38.19
38.62
39.05
39.48
39.92
40.35
40.78
41.21
41 .64
35
35
36
36
37
37
38
38
30
39
57
98
40
81
23
64
06
47
89
31
33.38
33.78
34.18
34.58
34.97
35.37
35.77
36.17
36.57
36.97
31.19
31.58
31 .96
32.34
32.72
33.10
33.48
33.86
34.25
34.63
29.0
1
29.37
29.74
30.10
30.47
30.83
31.19
31 .56
31.92
32.29
26.82
27.17
27.52
27.86
28.21
28.56
28.91
29.25
29.60
29.95
24.64
24.97
25.30
25.63
25.96
26.29
26.62
26.95
27.28
27.61
21
22
23
24
25
26
27
28
29
30
42.08
42.51
42.94
43.37
43.81
44.24
44.67
45.10
45.53
45.97
39
40
40
40
41
41
42
42
43
43
72
14
55
97
38
80
21
63
04
46
37.36
37.76
30.16
30.56
30.96
39.36
39.75
40.15
40.55
40.95
35.01
35.39
35.77
36.15
36.53
36.92
37.30
37.68
38.06
38.44
32.65
33.02
33.38
33.75
34.11
34.47
34.84
35.20
35.57
35.93
30.30
30.64
30.99
31.34
31 .69
32.03
32.38
32.73
33.08
33.42
27.94
28.27
28.60
28.93
29.26
29.59
29.92
30.25
30.58
30.92
TOP
1
2
3
4
5
6
7
8
9
10
4
1
FIR
CLASS
H-l
CIRC.
INCHES
POLE-con.
CLASS
CIRC.
INCHES
APPENDIX
359
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
DISTANCE
FROM TOP
FEET
YELLOW
PINE
CLASS
H-3
CIRC.
INCHES
AND DOUGLAS
CLASS
H-2
CIRC.
INCHES
FIR
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
CLASS
2
CIRC.
1 NCHES
65 FOOT
CLASS
3
CIRC.
INCHES
POLE-Con.
CLASS
CIRC.
INCHES
31
32
33
34
35
36
31
38
39
40
46.40
46.83
47.26
47.69
48.13
40.56
48.99
49.42
49.86
50.29
43.87
44.29
44.70
45.12
45.53
45.95
46.36
46.78
47.19
47.61
41.35
41.75
42.14
42.54
42.94
43.34
43.74
44.14
44.53
44.93
38.82
39.20
39.50
39.97
40.35
40.73
41.11
41.49
41.87
42.25
36.30
36.66
37.03
37.39
37.75
38.12
38.48
38.85
39.21
39.58
33.77
34.12
34.47
34.81
35.16
35.51
35.86
36.20
36.55
36.90
31.25
31.58
31.91
32.24
32.57
32.90
33.23
33.56
33.89
34.22
41
42
43
44
45
46
47
48
49
50
50.72
51.15
51.58
52.02
52.45
52.88
53.31
53.75
54.16
54.61
48.03
48.44
48.86
49.27
49.69
50.10
50.52
50.93
51.35
51 .76
45.33
45.73
46.13
46.53
46.92
47.32
47.72
48.12
48.52
48.92
42.64
43.02
43.40
43.78
44.16
44.54
44.92
45.31
45.69
46.07
39.94
40.31
40.67
41.03
41.40
41 .76
42.13
42.49
42.86
43.22
37.25
37.59
37.94
38.29
38.64
38.98
39.33
39.68
40.03
40.37
34.55
34.88
35.21
35.54
35.87
36.20
36.53
36.86
37.19
37.53
51
52
53
54
55
56
--
55.04
55.41
55.91
56.34
56.77
57.20
40.72
41.07
41 .42
41 .76
42.11
42.46
37.86
38.19
38.52
38.85
39.18
39.51
57.64
58.07
58.50
58.93
46.45
46.83
47.21
47.59
47.97
48.36
6 INCHES)------48.74
49.12
49.50
49.88
43.58
43.95
44.31
44.68
45.04
45.41
57
58
59
60
52.18
52.59
53.01
53.42
53.84
54.25
---GROUND
54.67
55.08
55.50
55.92
45.77
46.14
46.50
46.86
42.81
43.15
43.50
43.85
39.84
40.17
40.50
40.83
61
62
63
64
65
59.36
59.80
60.23
60.66
61 .09
53.30
53.69
54.09
54.49
54.89
50.26
50.64
51.03
51.41
51.79
47.23
47.59
47.96
48.32
48.69
44.19
44.54
44.89
45.24
45.58
41.16
41.49
41.82
42.15
42.48
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
29.00
29.39
29.78
30.17
30.56
30.95
31.34
31.73
32.13
32.52
32.91
27.00
27.38
27.75
28.13
28.50
28.88
29.25
29.63
30.00
30.38
30.75
SOUTHERN
DISTANCE
FROM TOP
FEET
TOP
2
3
4
5
6
7
8
9
10
YELLOW
PINE
CLASS
H-3
CIRC.
INCHES
33
33
33
34
34
35
35
36
36
36
37
00
43
86
29
72
15
58
01
44
87
30
49.31
49.71
50.11
50.51
50.91
51.31
LINE
(6
51.70
52.10
52.50
52.90
56.33
56.75
57.16
57.58
57.99
AND DOUGLAS
CLASS
H-2
CIRC.
INCHES
31 .oo
31.41
31 .I31
32.22
32.63
33.03
33.44
33.84
34.25
34.66
35.06
FEET
FIR
1
CLASS
CIRC.
INCHES
25
25
25
26
26
26
27
27
27
28
28
00
36
72
08
44
80
16
52
88
23
59
2
CLASS
CIRC.
INCHES
70
3
23.00
23.34
23.69
24.03
24: 38
24.72
25.06
25.41
25.75
26.09
26.44
4
FOOT POLE
CLASS
4
CIRC.
INCHES
21
21
21
21
22
22
22
23
23
23
24
00
32
64
96
28
60
92
24
56
88
20
360
TRANSMISSION
LINE DESIGN
MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow @e-Continued
SOUTHERN
DISTANCE
FROM TOP
FEET
YELLOW
PINE
CLASS
H-3
CIRC.
INCHES
AND DOUGLAS
CLASS
H-2
CIRC.
INCHES
FIR
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
I
CLASS
CIRC.
INCHES
2
70 FOOT
CLASS
3
CIRC.
INCHES
POLE-con.
CLASS
CIRC.
INCHES
I I
12
13
14
15
16
17
18
19
20
37.73
38.16
38.59
39.02
39.45
39.88
40.30
40.73
41.16
41.59
35.47
35.88
36.28
36.69
37.09
37.50
37.91
38.31
38.72
39.13
33.30
33.69
34.08
34.47
34.86
35.25
35.64
36.03
36.42
36.81
31.13
31.50
31 .aa
32.25
32.63
33.00
33.38
33.75
34.13
34.50
28.95
29.31
29.67
30.03
30.39
30.75
31.11
31.47
31 .a3
32.19
26.78
27.13
27.47
27.81
28.16
28.50
28.84
29.19
29.53
29.88
24.52
24.84
25.16
25.48
25.80
26.13
26.45
26.71
27.09
27.41
21
22
23
24
25
26
27
28
29
30
42.02
42.45
42.88
43.31
43.74
44.17
44.60
45.03
45.46
45.89
39.53
39.94
40.34
40.75
41.16
41 .56
41.97
42.38
42.78
43.19
37.20
37.59
37.98
38.38
38.77
39.16
39.55
39.94
40.33
40.72
34.88
35.25
35.63
36.00
36.38
36.75
37.13
37.50
37.88
38.25
32.55
32.91
33.27
33.63
33.98
34.34
34.70
35.06
35.42
35.78
30.22
30.56
30.91
31 .25
31.59
31.94
32.28
32.63
32.97
33.31
27.73
28.05
28.37
28.69
29.01
29.33
29.65
29.97
30.29
30.61
31
32
33
34
35
36
37
38
39
40
46.32
46.75
47.18
47.61
48.04
48.47
48.90
49.33
49.76
50.19
43.59
44.00
44.41
44.81
45.22
45.63
46.03
46.44
46.84
47.25
41.11
41.50
41 .a9
42.28
42.67
43.06
43.45
43.84
44.23
44.63
38.63
39.00
39.38
39.75
40.13
40.50
40.88
41 .25
41 .63
42.00
36. 14
36.50
36.86
37.22
37.58
37.94
38.30
38.66
39.02
39.38
33.66
34.00
34.34
34.69
35.03
35.38
35.72
36.06
36.41
36.75
30.93
31.25
31.57
31 .a9
32.21
32.53
32.85
33.17
33.49
33.81
41
42
43
44
45
46
47
48
49
50
50.62
51.05
51.48
51.91
52.34
52.77
53.20
53.63
54.05
54.48
47.66
48.06
48.47
48.88
49.28
49.69
50.09
50.50
50.91
51.31
45.02
45.41
45.80
46.19
46.58
46.97
47.36
47.75
48.14
48.53
42.38
42.15
43.13
43.50
43.88
44.25
44.63
45.00
45.38
45.75
39.73
40.09
40.45
40.81
41.17
41.53
41 .a9
42.25
42.61
42.97
37.09
37.44
37.78
38.13
38.47
38.81
39.16
39.50
39.84
40.19
34.13
34.45
34.77
35.09
35.41
35.73
36.05
36.38
36.70
37.02
51
52
53
54
55
56
57
58
59
60
54.91
55.34
55.77
56.20
56.63
57.06
57.49
57.92
58.35
58.78
51 .72
52.13
52.53
52.94
53.34
53.75
54.16
54.56
54.97
55.38
48.92
49.31
49.70
50.09
50.48
50.88
51 .27
51.66
52.05
52.44
46.13
46.50
46.88
47.25
47.63
48.00
48.38
48.75
49.13
49.50
43.33
43.69
44.05
44.41
44.77
45.13
45.48
45.84
46.20
46.56
40.53
40.88
41.22
41 .56
41.91
42.25
42.59
42.94
43.28
43.63
37.34
37.66
37.98
38.30
38.62
38.94
39.26
39.58
39.90
40.22
+
APPENDIX
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
DISTANCE
FROM TOP
FEET
YELLOW
PINE
CLASS
H-3
CIRC.
INCHES
AND DOUGLAS
CLASS
H-2
CIRC.
INCHES
-----------------------GROUND
51
62
63
64
65
66
67
68
69
70
TOP
1
2
3
4
5
6
CLASS
H-l
CIRC.
INCHES
LINE
59.21
59.64
60.07
60.50
60.93
61 .36
61 .79
62.22
62.65
63.08
SOUTHERN
YELLOW
DISTANCE
FROM TOP
FEET
70
FIR
55.78
56.19
56.59
57.00
57.41
57.81
58.22
58.63
59.03
59.44
PINE
AND
CLASS
H-3
CIRC.
INCHES
(9
CLASS
CIRC.
INCHES
FEET.
52.83
53.22
53.61
54.00
54.39
54.76
55.17
55.56
55.95
56.34
DOUGLAS
FIR
CLASS
H-2
CIRC.
INCHES
0
1
CLASS
CIRC.
INCHES
2
FOOT
CLASS
CIRC.
INCHES
POLE-Con.
3
CLASS
CIRC.
INCHES
INCHES)--------------------------
49.88
50.25
50.63
51 .oo
51.38
51 .I5
52.13
52.50
52.88
53.25
46.92
47.26
47.64
48.00
48.36
48.12
49.08
49.44
49.80
50.16
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
I
43.97
44.31
44.66
45.00
45.34
45.69
46.03
46.38
46.72
47.06
CLASS
CIRC.
INCHES
2
40.54
40.86
41.18
41.50
41 .82
42.14
42.46
42.78
43.10
43.42
75 FOOT
CLASS
3
CIRC.
INCHES
8
9
10
33
33
33
34
34
35
35
35
36
36
37
00
42
84
26
68
10
52
94
36
78
20
31 .oo
31.41
31 .81
32.22
32.62
33.03
33.43
33.84
34.25
34.65
35.06
29.00
29.38
29.77
30.15
30.54
30.92
31.30
31 .69
32.07
32.46
32.84
27.00
27.37
27.74
28.11
28.48
28.85
29.22
29.59
29.96
30.33
30.70
25.00
25.35
25.70
26.04
26.39
26.74
27.09
27.43
27.78
28.13
28.48
23.00
23.33
23.67
24.00
24.33
24.67
25.00
25.33
25.67
26.00
26.33
11
12
13
14
15
16
17
18
19
20
37
38
38
38
39
39
40
40
40
41
62
04
46
88
30
72
14
57
99
41
35.46
35.67
36.28
36.68
37.09
37.49
37.90
38.30
38.71
39.12
33.22
33.61
33.99
34.36
34.76
35.14
35.53
35.91
36.30
36.68
31.07
31.43
31.80
32.17
32.54
32.91
33.28
33.65
34.02
34.39
28.63
29.17
29.52
29.87
30.22
30.57
30.91
31 .26
31 .61
31 .96
26.67
27.00
27.33
27.67
28.00
28.33
28.67
29.00
29.33
29.67
21
22
23
24
25
26
27
28
29
30
41
42
42
43
43
43
44
44
45
45
83
25
67
09
51
93
35
77
19
61
39.52
39.93
40.33
40.74
41. I4
41.55
41 .96
42.36
42.77
43.17
37.07
37.45
37.83
38.22
38.60
38.99
39.37
39.75
40.14
40.52
34.76
35.13
35.50
35.87
36.24
36.61
36.98
37.35
37.12
38.09
32.30
32.65
33.00
33.35
33.70
34.04
34.39
34.14
35.09
35.43
30.00
30.33
30.67
31 .oo
31.33
31 .67
32.00
32.33
32.67
33.00
POLE
4
362
TRANSMISSION
LINE DESIGN
MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
DISTANCE
FROM TOP
FEET
PINE
AND
CLASS
H-3
CIRC.
INCHES
DOUGLAS
FIR
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
75 FOOT
CLASS
2
CIRC.
INCHES
POLE-con.
CLASS
CIRC.
INCHES
31
32
33
34
35
36
37
38
39
40
46.03
46.45
46.87
47.29
47.71
48.13
48.55
48.97
49.39
49.81
43.58
43.99
44.39
44.80
45.20
45.61
46.01
46.42
46.83
47.23
40.91
41.29
41 .67
42.06
42.44
42.83
43.21
43.59
43.98
44.36
38.46
38.83
39.20
39.57
39.93
40.30
40.67
41.04
41.41
41 .78
35.78
36.13
36.48
36.83
37.17
37.52
37.87
38.22
38.57
38.91
33.33
33.67
34.00
34.33
34.67
35.00
35.33
35.67
36.00
36.33
41
42
43
44
45
46
47
48
49
50
50.23
50.65
51.07
51.49
51.91
52.33
52.75
53.17
53.59
54.01
47.64
48.04
48.45
48.86
49.26
49.67
50.07
50.48
50.88
51.29
44.75
45.13
45.51
45.90
46.28
46.67
47.05
47.43
47.82
48.20
42.15
42.52
42.89
43.26
43.63
44.00
44.37
44.74
45.11
45.48
39.26
39.61
39.96
40.30
40.65
41 .oo
41.35
41.70
42.04
42.39
36.67
37.00
37.33
37.67
38.00
38.33
38.67
39.00
39.33
39.67
51
52
53
54
55
56
57
58
59
60
54.43
54.86
55.28
55.70
56.12
56.54
56.96
57.38
57.80
58.22
51.70
52.10
52.51
52.91
53.32
53.72
54.13
54.54
54.94
55.35
48.59
48.97
49.36
49.74
50.12
50.51
50.89
51 .28
51.66
52.04
45.85
46.22
46.59
46.96
47.33
47.70
48.07
48.43
48.80
49.17
42.74
43.09
43.43
43.78
44.13
44.48
44.83
45.17
45.52
45.87
40.00
40.33
40.67
41 .oo
41.33
41 .67
42.00
42.33
42.67
43.00
61
62
63
64
65
---------------
58.64
59.06
59.48
59.90
60.32
43.33
43.67
44.00
44.33
44.67
-----
60.74
61.16
61 .58
62.00
62.42
49.54
49.91
50.28
50.65
51.02
INCHES)
51.39
51 .76
52.13
52.50
52.87
46.22
46.57
46.91
47.26
47.61
66
67
68
69
70
55.75
56.16
56.57
56.97
57.38
GROUND
57.78
58.19
58.59
59.00
59.41
47.96
48.30
48.65
49.00
49.35
45.00
45.33
45.67
46.00
46.33
71
72
73
74
75
62.84
63.26
63.68
64.10
64.52
53.24
53.61
53.98
54.35
54.72
49.70
50.04
50.39
50.74
51.09
46.67
47.00
47.33
47.67
48.00
59.81
60.22
60.62
61 .03
61 .43
LINE
52.43
52.81
53.20
53.58
53.96
9 FEET,
54.35
54.73
55.12
55.50
55.88
56.27
56.65
57.04
57.42
57.80
6
3
APPENDIX
363
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
DISTANCE
FROM TOP
FEET
PINE
AND DOUGLAS
FIR
CLASS
H-2
CLASS
H-3
CIRC.
CIRC.
CLASS
H-l
CIRC.
INCHES
INCHES
INCHES
33.00
33.41
33.82
34.24
34.65
35.06
35.47
35.89
36.30
36.71
37.12
31 .oo
31.39
31.70
32.18
32.57
32.96
33.35
33.74
34.14
34.53
34.92
29.00
29.38
29.76
16
17
18
19
20
37.53
37.95
38.36
38.77
39.18
39.59
40.01
40.42
40.83
41 .24
21
22
23
24
25
26
21
28
29
30
CLASS
CIRC.
INCHES
1
CLASS
CIRC.
INCHES
2
80 FOOT POLE
CLASS
3
CIRC.
INCHES
30.14
30.51
30.89
31 .27
31 .65
32.03
32.41
32.78
27.00
27.36
27.73
28.09
28.46
28.82
29.19
29.55
29.92
30.28
30.65
25.00
25.34
25.69
26.03
26.38
26.72
27.07
27.41
27.76
28. IO
28.45
23.00
23.32
23.65
23.97
24.30
24.62
24.95
25.27
25.59
25.92
26.24
35.31
35.70
36.09
36.49
36.88
37.27
37.66
38.05
38.45
38.84
33.16
33.54
33.92
34.30
34.68
35.05
35.43
35.81
36.19
36.57
31 .Ol
31 .38
31.74
32.11
32.47
32.84
33.20
33.57
33.93
34.30
28.79
29.14
29.48
29.82
30.17
30.51
30.86
31.20
31.55
31 .89
26.57
26.89
27.22
27.54
27.86
28.19
28.51
28.84
29.16
29.49
41.66
42.07
42.48
42.89
43.30
43.72
44.13
44.54
44.95
45.36
39.23
39.62
40.01
40.41
40.80
41.19
41.50
41.97
42.36
42.76
36.95
37.32
37.70
38.08
38.46
38.84
39.22
39.59
39.97
40.35
34.66
35.03
35.39
35.76
36.12
36.49
36.85
37.22
37.58
37.95
32.24
32.58
32.93
33.27
33.61
33.96
34.30
34.65
34.99
35.34
29.81
30.14
30.46
30.78
32.08
32.41
32.73
31
32
33
34
35
36
37
38
39
40
45.78
46.19
46.60
47.01
47.43
47.84
48.25
48.66
49.07
49.49
43.15
43.54
43.93
44.32
44.72
45.11
45.50
45.89
46.28
46.68
40.73
42.24
42.62
43.00
43.38
43.76
44.14
38.31
38.68
39.04
39.41
39.77
40.14
40.50
40.86
41 .23
41.59
35.68
36.03
36.37
36.72
37.06
37.41
37.75
38.09
38.44
38.78
33.05
33.38
33.70
34.03
34.35
34.68
35.00
35.32
35.65
35.97
41
42
43
44
45
46
47
48
49
50
49.90
50.31
50.72
51.14
51.55
51.96
52.37
52.78
53.20
53.61
47.07
47.46
47.85
48.24
48.64
49.03
49.42
49.81
50.20
50.59
44.51
44.89
45.27
45.65
46.03
46.41
46.78
47.16
47.54
47.92
41 .96
42.32
42.69
43.05
43.42
43.78
44.15
44.51
44.88
45.24
39.13
39.47
39.82
40.16
40.51
40.85
41.20
41.54
41 .89
42.23
36.30
36.62
36.95
37.27
37.59
37.92
38.24
38.57
38.89
39.22
TOP
1
2
3
4
5
6
7
El
9
10
11
12
13
14
15
41.11
41.49
41.86
31.11
31.43
31 .76
TRANSMISSION
364
LINE DESIGN
MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
DISTANCE
FROM TOP
FEET
PINE
AND DOUGLAS
FIR
CLASS
H-2
CLASS
H-3
CIRC.
CIRC.
INCHES
INCHES
51
52
53
54
55
56
57
58
59
60
54.02
54.43
54.84
55.26
55.67
56.08
56.49
56.91
57.32
57.73
61
62
63
64
65
66
67
68
69
58.14
58.55
58.91
59.38
59.79
60.20
60.61
61 .03
61 .44
70
61 .85
71
72
73
74
75
76
77
78
79
80
62.26
62.68
63.09
63.50
63.91
64.32
64.74
65.15
65.56
65.9-l
SOUTHERN
YELLOW
DISTANCE
FROM TOP
FEET
TOP
2
3
4
5
6
7
8
9
10
PINE
AND
CLASS
H-3
CIRC.
INCHES
33.00
33.41
33.81
34.22
34.62
35.03
35.43
35.84
36.24
36.65
37.05
50 99
51 38
51 77
52
16
52 55
52 95
53 34
53.73
54.12
54.51
54.91
55.30
55.69
56.08
56.47
56.86
57.26
57.65
58.04
-GROUND
58.43
LINE
58.82
59.22
59.61
60.00
60.39
60.78
61.18
61 .51
61 .96
62.35
DOUGLAS
FIR
CLASS
H-2
CIRC.
INCHES
31
31
31
32
32
32
33
33
34
34
34
00
39
77
16
54
93
32
70
09
47
86
CLASS
CIRC.
INCHES
48.30
48.68
49.05
49.43
49.81
50.19
50.57
50.95
51 .32
51.70
45.61
45.97
46.34
46.70
47.07
47.43
47.80
48.16
48.53
48.89
42.57
42.92
43.26
43.61
43.95
44.30
44.64
44.99
45.33
45.68
39.54
39.86
40.19
40.51
40.84
41.16
41.49
41.81
42.14
42.46
49.26
49.62
49.99
50.35
50.72
51 .08
51.45
51 .81
52.18
INCHES)
52.54
46.02
46.36
46.71
47.05
47.40
47.74
48.09
48.43
48.78
42.78
43.11
43.43
43.76
44.08
44.41
44.73
45.05
45.38
49.12
45.70
55.86
56.24
56.62
57.00
57.38
57.16
58.14
58.51
58.89
59.27
52.91
53.21
53.64
54.00
54.36
54.73
55.09
55.46
55.82
56.19
49.47
49.81
50.16
50.50
50.84
51.19
51.53
51.88
52.22
52.57
46.03
46.35
46.68
47.00
47.32
41.65
47.97
48.30
48.62
48.95
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
29.00
29.37
29.75
30.12
30.49
30.87
31 .24
31 .61
31.99
32.36
32.73
27.00
27.35
27.71
28.06
28.42
28.77
29.13
29.48
29.84
30.19
30.54
52.08
52.46
52.84
53.22
53.59
53.91
54.35
54.73
55.11
(10
FEET
55.49
0
1
80 FOOT POLE-Con.
CLASS
2
CLASS
3
CIRC.
CIRC.
INCHES
INCHES
CLASS
H-l
CIRC.
INCHES
1
CLASS
CIRC.
INCHES
25.00
25.34
25.67
26.01
26.34
26.68
27.01
27.35
21.68
28.02
28.35
2
85 FOOT
CLASS
3
CIRC.
INCHES
23.00
23.32
23.63
23.95
24.27
24.58
24.90
25.22
25.53
25.85
26.16
POLE
APPENDIX
365
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
DISTANCE
FROM TOP
FEET
PINE
AND DOUGLAS
FIR
CLASS
H-3
CLASS
H-2
CIRC.
CIRC.
INCHES
INCHES
85
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
CLASS
CIRC.
INCHES
2
FOOT
POLE-Con.
CLASS
CIRC.
INCHES
11
12
13
14
15
16
17
18
19
20
37.46
37.86
38.27
38.67
39.08
39.48
39.89
40.29
40.70
41.10
35.25
35.63
36.02
36.41
36.79
37.16
37.56
37.95
38.34
38.72
33.11
33.46
33.85
34.23
34.60
34.91
35.35
35.72
36.09
36.47
30.90
31.25
31.61
31.96
32.32
32.67
33.03
33.38
33.73
34.09
28.69
29.03
29.36
29.70
30.03
30.37
30.70
31.04
31.37
31.71
26.48
26.80
27.11
27.43
27.75
28.06
28.38
28.70
29.01
29.33
21
22
23
24
25
26
27
28
29
30
41.51
41.91
42.32
42.72
43.13
43.53
43.94
44.34
44.75
45.15
39.11
39.49
39.88
40.27
40.65
41.04
41.42
41.81
42.20
42.58
36.84
37.22
37.59
37.96
38.34
38.71
39.08
39.46
39.83
40.20
34.44
34.80
35.15
35.51
35.86
36.22
36.57
36.92
37.28
37.63
32.04
32.38
32.72
33.05
33.39
33.72
34.06
34.39
34.73
35.06
29.65
29.96
30.28
30.59
30.91
31.23
31.54
31.86
32.18
32.49
31
32
33
34
35
36
37
38
39
40
45.56
45.96
46.37
46.77
47.16
47.58
47.99
48.39
48.80
49.20
42.97
43.35
43.74
44.13
44.51
44.90
45.28
45.67
46.06
46.44
40.58
40.95
41.32
41.70
42.07
42.44
42.82
43.19
43.56
43.94
37.99
36.34
38.70
39.05
39.41
39.16
40.11
40.47
40.82
41.18
35.40
35.73
36.07
36.41
36.74
37.08
37.41
37.75
38.08
38.42
32.81
33.13
33.44
33.76
34.08
34.39
34.71
35.03
35.34
35.66
41
42
43
44
45
46
47
48
49
50
49.61
50.01
50.42
50.82
51.23
51.63
52.04
52.44
52.85
53.25
46.83
47.22
47.60
47.99
48.37
48.76
49.15
49.53
49.92
50.30
44.31
44.68
45.06
45.43
45.80
46.18
46.55
46.92
47.30
47.67
41.53
41.89
42.24
42.59
42.95
43.30
43.66
44.01
44.37
44.72
38.75
39.09
39.42
39.76
40.09
40.43
40.77
41.10
41.44
41.77
35.97
36.29
36.61
36.92
37.24
37.56
37.87
38.19
38.51
38.82
51
52
53
54
55
56
57
56
59
60
53.66
54.06
54.47
54.87
55.28
55.68
56.09
56.49
56.90
57.30
50.69
51.08
51.46
51.85
52.23
52.62
53.01
53.39
53.78
54.16
48.04
48.42
48.79
49.16
49.54
49.91
50.28
50.66
51.03
51.41
45.08
45.43
45.76
46.14
46.49
46.85
47.20
47.56
47.91
48.27
42.11
42.44
42.78
43.11
43.45
43.78
44.12
44.46
44.79
45.13
39.14
39.46
39.77
40.09
40.41
40.72
41.04
41.35
41.67
41.99
3
TRANSMISSION
366
LINE DESIGN
MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
DISTANCE
FROM TOP
FEET
PINE
AND
CLASS
H-3
CIRC.
INCHES
61
62
63
64
65
66
67
68
69
70
57.71
58.11
58.52
58.92
59.33
59.73
60.14
60.54
60.95
61.35
71
72
73
74
61 .76
62.16
62.57
62.97
75
76
77
78
79
80
63.38
63.78
64.19
64.59
65.00
65.41
81
82
83
84
85
65.81
66.22
66.62
67.03
67.43
SOUTHERN
YELLOW
DISTANCE
FROM TOP
FEET
PINE
AND
CLASS
H-3
CIRC.
INCHES
85
FOOT POLE-con.
CLASS
3
CIRC.
INCHES
DOUGLAS
FIR
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
54
54
55
55
56
56
56
57
57
58
51 .78
52.15
52.53
52.90
53.27
53.65
54.02
54.39
54.77
55.14
48.62
48.97
49.33
49.68
50.04
50.39
50.75
51.10
51 .46
51 .81
45.46
45.80
46.13
46.47
46.80
47.14
47.47
47.81
48.15
48.48
42.30
42.62
42.94
43.25
43.57
43.89
44.20
44.52
44.84
45.15
55.51
55.89
56.26
56.63
(10
FEET,
57.01
57.38
57.75
58.13
58.50
58.87
52.16
52.52
52.87
53.23
INCHESl---53.58
53.94
54.29
54.65
55.00
55.35
48.82
49.15
49.49
49.82
45.47
45.78
46.10
46.42
50.16
50.49
50.83
51.16
51.50
51 .84
46.73
47.05
47.37
47.68
48.00
48.32
52
52
52
53
53
48.63
48.95
49.27
49.58
49.90
55
94
32
71
09
48
87
25
64
03
58 41
58 80
59
18
59 57
-GROUND
LINE
59.96
60.34
60.73
61.11
61 .50
61 .89
62.27
62.66
63.04
63.43
63.82
DOUGLAS
FIR
CLASS
H-2
CIRC.
INCHES
59.25
59.62
59.99
60.37
60.74
CLASS
CIRC.
INCHES
6
1
55.71
56.06
56.42
56.77
57.13
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
CLASS?-CIRC.
INCHES
17
51
84
18
51
CLASS
CIRC.
INCHES
TOP
1
2
3
4
5
6
7
8
9
10
33.00
33.40
33.80
34.20
34.60
34.99
35.39
35.79
36.19
36.59
36.99
31 .oo
31 .38
31 .76
32.14
32.52
32.90
33.29
33.67
34.05
34.43
34.81
29.00
29.36
29.73
30.09
30.45
30.82
31.18
31.54
31.90
32.27
32.63
27.00
27.35
27.69
28.04
28.38
28.73
29.07
29.42
29.76
30.11
30.45
25.00
25.33
25.67
26.00
26.33
26.67
27.00
27.33
27.67
28.00
28.33
11
12
13
14
15
16
17
18
19
20
37.39
37.79
38.18
38.58
38.98
39.38
39.78
40.18
40.58
40.98
35.19
35.57
35.95
36.33
36.71
37.10
37.48
37.86
38.24
38.62
32.99
33.36
33.72
34.08
34.45
34.81
35.17
35.54
35.90
36.26
30.80
31.14
31.49
31 .83
32.18
32.52
32.87
33.21
33.56
33.90
28
29
29
29
30
30
30
31
31
31
2
90 FOOT POLE
CLASS
3
CIRC.
INCHES
23.00
23.31
23.62
23.93
24.24
24.55
24.86
25.17
25.48
25.79
26.10
67
00
33
67
00
33
67
00
33
67
26.40
26.71
27.02
27.33
27.64
27.95
28.26
28.57
28.88
29.19
APPENDIX
367
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
DISTANCE
FROM TOP
FEET
PINE
AND DOUGLAS
FIR
CLASS
H-3
CLASS
H-2
CIRC.
CIRC.
INCHES
INCHES
21
22
23
24
25
26
21
28
29
30
41.37
41.77
42.17
42.57
42.97
43.37
43.77
44.17
44.57
44.96
31
32
33
34
35
36
37
38
39
40
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
INCHES
FOOT POLE-Con.
CLASS
3
CIRC.
INCHES
CLASS
CIRC.
90
2
42.05
42.43
36.62
36.99
37.35
37.71
38.08
38.44
38.80
39.17
39.53
39.89
34.25
34.60
34.94
35.29
35.63
35.98
36.32
36.67
37.01
37.36
32.00
32.33
32.67
33.00
33.33
33.67
34.00
34.33
34.67
35.00
29.81
30.12
30.43
30.74
31.05
31 .36
31 .67
31 .98
32.29
45.36
45.16
46.16
46.56
46.96
47.36
47.76
48.15
48.55
48.95
42.81
43.19
43.57
43.95
44.33
44.71
45.10
45.48
45.86
46.24
40.26
40.62
40.98
41.35
41.71
42.07
42.43
42.80
43.16
43.52
37.70
38.74
39.08
39.43
39.77
40.12
40.46
40.81
35.33
35.67
36.00
36.33
36.67
37.00
37.33
37.67
38.00
38.33
32.60
32.90
33.21
33.52
33.83
34.14
34.45
34.76
35.07
35.38
41
42
43
44
45
46
47
48
49
50
49.35
49.75
50.15
50.55
50.95
51.35
51.74
52. 14
52.54
52.94
46.62
47.00
47.38
47.76
48.14
48.52
48.90
49.29
49.67
50.05
43.89
44.25
44.61
44.98
45.34
45.70
46.07
46.43
46.79
47.15
41.15
41.50
41 .85
42.19
42.54
42.88
43.23
43.57
43.92
44.26
38.67
39.00
39.33
39.67
40.00
40.33
40.67
41 .oo
41.33
41 .67
35.69
36.00
36.31
36.62
36.93
37.24
37.55
37.86
38.17
38.48
51
52
53
54
55
56
57
58
59
60
53.34
53.74
54.14
54.54
54.93
55.33
55.13
56.13
56.53
56.93
50.43
50.81
51.19
51.57
52.33
52.71
53.10
53.48
53.06
47.52
47.88
48.24
48.61
48.97
49.33
49.70
50.06
50.42
50.79
44.61
44.95
45.30
45.64
45.99
46.33
46.68
47.02
47.37
47.71
42.00
42.33
42.67
43.00
43.33
43.67
44.00
44.33
44.67
45.00
38.79
39.10
39.40
39.71
40.02
40.33
40.64
40.95
41 .26
41.57
61
62
63
64
65
66
67
68
69
70
57.33
57.73
58.12
50.52
58.92
59.32
59.72
60.12
60.52
60.92
54.24
54.62
55.00
55.30
55.76
56.14
56.52
56.90
57.29
57.67
51.15
51.51
51 .87
52.24
52.60
52.96
53.33
53.69
54.05
54.42
48.06
48.40
48.75
49.10
49.44
49.79
50.13
50.48
50.82
51.17
45.33
45.67
46.00
46.33
46.67
47.00
47.33
47.67
48.00
48.33
41.88
42.19
42.50
42.81
43.12
43.43
43.74
44.05
44.36
44.67
39.00
39.38
39.76
40.14
40.52
40.90
41.29
Ltl .67
51.95
38.05
38.39
29.50
368
TRANSMISSION
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
DISTANCE
FROM TOP
FEET
SOUTHERN
PINE
AND
CLASS
H-3
CIRC.
1 NCHES
71
61 .32
72
73
74
75
76
77
78
61 .71
62. I I
62.51
62.91
63.31
63.71
64.11
79
80
64.51
64.90
81
82
83
84
85
86
87
88
89
90
65.30
65.70
66.10
66.50
66.90
67.30
67.70
68.10
68.49
68.89
YELLOW
PINE
DISTANCE
FROM TOP
FEET
TOP
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
DOUGLAS
FIR
CLASS
H-2
CIRC.
90
CLASS
CIRC.
CLASS
H-l
CIRC.
INCHES
INCHES
INCHES
58.05
58.43
58.81
59.19
59.57
59.95
60.33
60.71
51.51
51 .86
52.20
52.55
52.89
53.24
53.58
53.93
61 .48
54.78
55.14
55.51
55.87
56.23
56.60
56.96
57.32
(11 FEET,
57.68
58.05
61 .86
62.24
62.62
63.00
63.38
63.76
64.14
64.52
64.90
65.29
58.41
58.77
59.14
59.50
59.86
60.23
60.59
60.95
61 .32
61 .68
-GROUND
61.10
AND DOUGLAS
CLASS
H-3
CIRC.
INCHES
LINE
FIR
CLASS
H-2
CIRC.
INCHES
0
1
CLASS
CIRC.
INCHES
54.27
54.62
45.60
45.90
46.21
46.52
46.83
47.14
----47.45
47.76
54.96
55.31
55.65
56.00
56.35
56.69
57.04
57.38
57.13
58.07
52.00
52.33
52.61
53.00
53.33
53.67
54.00
54.33
54.67
55.00
48.07
48.38
48.69
49.00
49.31
49.62
49.93
50.24
50.55
50.86
CLASS
CIRC.
INCHES
1
44.98
45.29
CLASS
95
2
CIRC.
INCHES
31 .oo
31.38
31.75
32.13
32.51
32.88
33.26
33.63
34.0 1
34.39
34.76
29.00
29.36
29.72
30.08
30.44
30.80
31.16
31 .52
31.88
32.24
32.60
27.00
27.34
27.67
28.01
2’3.35
28.69
29.02
29.36
29.70
30.03
30.37
25.00
25.33
25.65
25.98
26.30
26.63
26.96
27.28
27.61
27.93
28.26
37.26
37.65
38.04
38.43
38.81
39.20
39.59
39.98
40.37
40.75
35.14
35.52
35.89
36.27
36.65
37.02
37.40
37.78
38.15
38.53
32
33
33
34
34
34
35
35
35
36
30
31
31
31
32
32
32
33
33
33
28.58
28.91
29.24
29.56
29.89
30.21
30.54
30.87
31.19
31 .52
31
67
03
39
75
11
47
83
19
71
04
38
72
06
39
73
07
40
74
3
INCHES
33.00
33.39
33.78
34.16
34.55
34.94
35.33
35.71
36.10
36.49
36.88
96
POLE-Con.
CLASS
CIRC.
48.67
49.00
49.33
49.67
50.00
50.33
50.67
51 .oo
_-----51.33
51 .67
INCHES1
CLASS
H-l
CIRC.
INCHES
FOOT
2
FOOT
POLE
APPENDIX
369
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
AND DOUGLAS
CLASS
H-3
CIRC.
INCHES
FIR
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
95 FOOT
CLASS
2
CIRC.
INCHES
21
22
23
24
25
26
27
26
29
30
41.14
41.53
41.92
42.30
42.69
43.08
43.47
43.85
44.24
44.63
38.90
39.28
39.66
40.03
40.41
40.79
41.16
41.54
41.92
42.29
36.55
36.91
37.27
37.63
37.99
38.35
38.71
39.07
39.43
39.79
34.08
34.42
34.75
35.09
35.43
35.76
36.10
36.44
36.76
37.1
31
32
33
34
35
36
37
38
39
40
45.02
45.40
45.79
46. I8
46.57
46.96
47.34
47.73
48.12
48.51
42.67
43.04
43.42
43.80
44.17
44.55
44.93
45.30
45.68
46.06
40.15
40.51
40.67
41.22
41.58
41.94
42.30
42.66
43.02
43.38
37.45
37.79
38.12
38.46
38.80
39.13
39.47
39.81
40.15
40.48
35. IO
35.43
35.75
36 ~08
36.40
36.73
37.06
37.36
37.71
38.03
41
42
43
44
45
46
47
48
49
50
48.89
49.28
49.67
50.06
50.44
50.83
51.22
51 .61
51.99
52.38
46.43
46.81
47.19
47.56
47.94
48.31
48.69
49.07
49.44
49.82
43.74
44. IO
44.46
44.82
45.18
45.54
45.90
46.26
46.62
46.98
40.82
41.16
41.49
41 .83
42.17
42.51
42.84
43.18
43.52
43.85
38.36
38.69
39.01
39.34
39.66
39.99
40.31
40.64
40.97
41.29
51
52
53
54
55
56
57
58
59
60
52.77
53.16
53.54
53.93
54.32
54.71
55.10
55.48
55.87
56.26
50.20
50.57
50.95
51.33
51.70
52.08
52.46
52.83
53.21
53.56
47.34
47.70
48.06
48.42
46.78
49.13
49.49
49.85
50.21
50.57
44.19
44.53
44.87
45.20
45.54
45.88
46.21
46.55
46.89
47.22
41 .62
41.94
42.27
42.60
42.92
43.25
43.57
43.90
44.22
44.55
61
62
63
64
65
66
67
68
69
70
56.65
57.03
57.42
57.81
58.20
58.58
58.97
59.36
59.75
60.13
53.96
54.34
54.71
55.09
55.47
55.84
56.22
56.60
56.97
57.35
50.93
51.29
51 .65
52.01
52.37
52.73
53.09
53.45
53.81
54.17
47.56
47.90
46.24
48.57
48.91
49.25
49.58
49.92
50.26
50.60
44.88
45.20
45.53
45.65
46.18
46.51
46.83
47.16
47.48
47.61
I
31.84
32.17
32.49
32.82
33.15
33.47
33.80
34.12
34.45
34.78
POLE-Con.
TRANSMISSION
370
LINE DESIGN
MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
71
72
73
74
75
76
77
78
79
80
81
82
83
AND DOUGLAS
CLASS
H-3
CIRC.
1NCHES
FIR
CLASS
H-2
CIRC.
CLASS
H-l
CIRC.
INCHES
INCHES
INCHES
61 .69
62.07
62.46
62.85
63.24
63.62
64.01
57.72
58.10
58.48
58.85
59.23
59.61
59.98
60.36
60.74
61.11
54.53
54.89
55.25
55.61
55.97
56.33
56.69
57.04
57.40
57.76
50.93
51 .27
51 .61
51.94
52.28
52.62
52.96
53.29
53.63
53.97
64.40
64.79
65.17
61 .49
61 .87
62.24
58.12
58.48
58.84
54.30
54.64
54.98
60.52
60.91
61 .30
1
95 FOOT
CLASS
2
CIRC.
INCHES
85
86
87
88
89
90
65.56
65.95
66.34
66.72
67.11
67.50
67.89
62.62
62.99
63.37
63.75
64.12
64.50
64.88
59.20
59.56
59.92
60.28
60.64
61 .OO
61 .36
55.31
55.65
55.99
56.33
56.66
57.00
57.34
91
92
93
94
95
68.28
68.66
69.05
69.44
69.83
65.25
65.63
66.01
66.38
66.76
61 .72
62.08
62.44
62.80
63.16
57.67
58.01
58.35
58.69
59.02
54.65
54.98
55.30
55.63
55.96
FIR
CLASS
H-2
CIRC.
CLASS
H-l
CIRC.
CLASS
CIRC.
INCHES
INCHES
INCHES
INCHES
INCHES
1
2
3
4
5
6
7
8
9
10
33.00
33.38
33.77
34.15
34.53
34.91
35.30
35.68
36.06
36.45
36.83
31 .oo
31.37
31.73
32.10
32.47
32.84
33.20
33.57
33.94
34.30
34.67
29.00
29.35
29.70
30.05
30.40
30.76
31.11
31 .46
31 .81
32.16
32.51
27.00
27.34
27.67
28.01
28.34
28.68
29.01
29.35
29.68
30.02
30.35
25.00
25.32
25.64
25.96
26.28
26.60
26.91
27.23
27.55
27.87
28.19
11
12
13
14
15
16
17
18
19
20
37.21
37.60
37.98
38.36
38.74
39.13
39.51
39.89
40.28
40.66
35.04
35.40
35.77
36.14
36.51
36.87
37.24
37.61
37.97
38.34
32.86
33.21
33.56
33.91
34.27
34.62
34.97
35.32
35.67
36.02
30.69
31.02
31 .36
31.69
32.03
32.36
32.70
33.03
33.37
33.70
28.51
28.83
29.15
29.47
29.79
30.11
30.43
30.74
31 .06
31 .38
-----GROUND
YELLOW
PINE
DISTANCE
FROM TOP
FEET
TOP
AND DOUGLAS
CLASS
H-3
CIRC.
LINE
(11
FEET,
0
POLE-con.
48.13
48.46
48.79
49.11
49.44
49.76
50.09
50.42
50.74
51.07
51.39
51 .72
52.04
-----52.37
52.70
53.02
53.35
53.67
54.00
54.33
84
SOUTHERN
CLASS
CIRC.
INCHES)-----
100
1
CLASS
CIRC.
2
FOOT
POLE
APPENDIX
371
6
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
AND DOUGLAS
CLASS
H-3
CIRC.
INCHES
FIR
CLASS
H-2
CIRC.
100
INCHES
CLASS
H-l
CIRC.
1NCHES
CLASS
CIRC.
1
FOOT
CLASS
2
CIRC.
INCHES
INCHES
22
23
24
25
26
27
28
29
30
41.04
41.43
41 .81
42.19
42.57
42.96
43.34
43.72
44.11
44.49
38.71
39.07
39.44
39.81
40.18
40.54
40.91
41 .28
41 .64
42.01
36.37
36.72
37.07
37.43
37.78
38.13
38.48
38.83
39.18
39.53
34.04
34.37
34.71
35.04
35.38
35.71
36.05
36.38
36.72
37.05
31.70
32.02
32.34
32.66
32.98
33.30
33.62
33.94
34.26
34.57
31
32
33
34
35
36
37
38
39
40
44.87
45.26
45.64
46.02
46.40
46.79
47.17
47.55
47.94
48.32
42.38
42.74
43.11
43.48
43.85
44.21
44.58
44.95
45.31
45.68
39.88
40.23
40.59
40.94
41.29
41 .64
41.99
42.34
42.69
43.04
37.39
37.72
38.06
38.39
38.73
39.06
39.40
39.73
40.07
40.40
34.89
35.21
35.53
35.05
36.17
36.49
36.81
37.13
37.45
37.77
41
42
43
44
45
46
47
48
49
50
48.70
49.09
49.47
49.85
50.23
50.62
51 .oo
51 .38
51.77
52.15
46.05
46.41
46.78
47.15
47.52
47.88
48.25
48.62
48.98
49.35
43.39
43.74
44.10
44.45
44.80
45.15
45.50
45.85
46.20
46.55
40.74
41.07
41.41
41.74
42.08
42.41
42.75
43.09
43.42
43.76
38.09
38.40
38.72
39.04
39.36
39.68
40.00
40.32
40.64
40.96
51
52
53
54
55
56
57
58
59
60
52.53
52.91
53.30
53.68
54.06
54.45
54.83
55.21
55.60
55.98
49.72
50.09
50.45
50.82
51.19
51.55
51.92
52.29
52.65
53.02
46.90
47.26
47.61
47.96
48.31
48.66
49.01
49.36
49.71
50.06
44.09
44.43
44.76
45.10
45.43
45.77
46.10
46.44
46.77
47.11
41 .28
41 .60
41.91
42.23
42.55
42.87
43.19
43.51
43.83
44.15
61
62
63
64
65
66
67
68
69
70
56.36
56.74
57.13
57.51
57.89
58.28
58.66
59.04
59.43
59.81
53.39
53.76
54.12
54.49
54.86
55.22
55.59
55.96
56.32
56.69
50.41
50.77
51.12
51.47
51 .82
52.17
52.52
52.87
53.22
53.57
47.44
47.78
48.11
48.45
48.78
49.12
49.45
49.79
50.12
50.46
44.47
44.79
45.11
45.43
45.74
46.06
46.38
46.70
47; 02
47.34
21
POLE-Con.
372
TRANSMISSION
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
71
72
73
74
75
76
77
70
79
80
60.19
60.57
60.96
61 .34
61 .72
62.11
62.49
62.87
63.26
63.64
81
82
83
84
85
86
87
88
64.02
64.40
64.79
65.17
65.55
65.94
66.32
66.70
.-----GROUND
67.09
67.47
89
90
91
92
93
94
95
96
97
98
99
100
SOUTHERN
AND DOUGLAS
CLASS
H-3
CIRC.
INCHES
YELLOW
PINE
DISTANCE
FROM TOP
FEET
TOP
1
2
3
4
5
6
7
8
9
10
67.85
68.23
68.62
69.00
69.38
69.77
70.15
70.53
70.91
71.30
AND DOUGLAS
CLASS
H-3
CIRC.
INCHES
33.00
33.38
33.76
34.14
34.52
34.89
35.27
35.65
36.03
36.41
36.79
FIR
CLASS
H-2
CIRC.
INCHES
57.06
57.43
57.79
58.16
58.53
58.89
59.26
59.63
59.99
60.36
60.73
61.10
61 .46
61 .83
62.20
62.56
62.93
63.30
L INE
(11
‘63.66
64.03
64
64
65
65
65
66
66
66
67
67
40
77
13
50
87
23
60
97
34
70
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
1 NCHES
1
100
FOOT
CLASS
2
CIRC.
INCHES
53.93
54.28
54.63
54.98
55.33
55.68
56.03
56.38
56.73
57.09
50
51
51
51
52
52
52
53
53
53
79
13
46
80
13
47
80
14
47
81
47.66
47.98
48.30
48.62
48.94
49.26
49.57
49.89
50.21
50.53
57.44
57.79
58.14
58.49
58.84
59.19
59.54
59.89
FEET,
0
60.24
60.60
54
54
54
55
55
55
56
56
14
48
81
15
48
82
15
49
50.85
51.17
51.49
51 .81
52.13
52.45
52.77
53.09
56
57
82
16
53.40
53.72
POLE-Con.
INCHES)--
60.95
61 .30
61 .65
62.00
62.35
62.70
63.05
63.40
63.76
64.11
57.49
57.83
58.16
58.50
58.84
59.17
59.51
59.84
60.18
60.51
FIR
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
31 .oo
31 .36
31.73
32.09
32.45
32.82
33.18
33.55
33.91
34.27
34.64
29.00
29.34
29.69
30.03
30.37
30.72
31 .06
31.40
31.75
32.09
32.43
27.00
27.33
27.66
27.98
28.31
28.64
28.97
29.30
29.63
29.95
30.28
54.04
54.36
54.68
55.00
55.32
55.64
55.96
56.28
56.60
56.91
1
105
CLASS
2
CIRC.
INCHES
25.00
25.31
25.63
25.94
26.25
26.57
26.88
27.19
27.51
27.82
28.13
FOOT
POLE
APPENDIX
373
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
AND DOUGLAS
CLASS
H-3
CIRC.
INCHES
FIR
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
I
105
FOOT POLE
CLASS
2
CIRC.
INCHES
I I
12
13
14
15
16
17
18
19
20
37.17
37.55
37.92
38.30
38.68
39.06
39.44
39.02
40.20
40.58
35.00
35.36
35.73
36.09
36.45
36.82
37.18
31.55
37.91
38.27
32.78
33.12
33.46
33.81
34.15
34.49
34.84
35.18
35.53
35.87
30.61
30.94
31 .27
31 .60
31.92
32.25
32.58
32.91
33.24
33.57
28.44
28.76
29.07
29.38
29.70
30.01
30.32
30.64
30.95
31 .26
21
22
23
24
25
26
27
28
29
30
40.95
41.33
41.71
42.09
42.47
42.85
43.23
43.61
43.98
44.36
38.64
39.00
39.36
39.73
40.09
40.45
40.82
41.18
41.55
41.91
36.21
36.56
36.90
37.24
37.59
37.93
38.27
38.62
38.96
39.30
33.89
34.22
34.55
34.88
35.21
35.54
35.86
36. 19
36.52
36.85
31 .58
31 .89
32.20
32.52
32.83
33.14
33.45
33.77
34.08
34.39
31
32
33
34
35
36
37
38
39
40
44.74
45.12
45.50
45.88
46.26
46.64
47.02
47.39
41.71
48.15
42.27
42.64
43.00
43.36
43.73
44.09
44.45
44.82
45.18
45.55
39.65
39.99
40.33
40.68
41.02
41 .36
41.71
42.05
42.39
42.74
37.18
37.51
37.83
38.16
38.49
38.82
39.15
39.47
39.80
40.13
34.71
35.02
35.33
35.65
35.96
36.27
36.59
36.90
37.21
37.53
41
42
43
44
45
46
47
48
49
50
48.53
48.91
49.29
49.67
50.05
50.42
50.80
51.18
51 .56
51.94
45.91
46.27
46.64
47.00
47.36
47.73
48.09
48.45
48.82
49.18
43.08
43.42
43.77
44. I I
44.45
44.80
45.14
45.48
45.83
46.17
40.46
40.79
41.12
41.44
41.77
42.10
42.43
42.76
43.09
43.41
37.84
38.15
38.46
38.78
39.09
39.40
39.72
40.03
40.34
40.66
51
52
53
54
55
56
57
58
59
60
52.32
52.70
53.08
53.45
53.83
54.21
54.59
54.97
55.35
55.73
49.55
49.91
50.27
50.64
51 .oo
51 .36
51.73
52.09
52.45
52.82
46.52
46.86
47.20
47.55
47.89
48.23
48.58
48.92
49.26
49.61
43.74
44.07
44.40
44.73
45.06
45.38
45.71
46.04
46.37
46.70
40.97
41 .28
41 .60
41.91
42.22
42.54
42.85
43.16
43.. 47
43.79
-Con.
374
TRANSMISSION
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
AND DOUGLAS
CLASS
H-3
CIRC.
1 NCHES
FIR
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
105
FOOT
CLASS
2
CIRC.
INCHES
61
62
63
64
65
66
67
68
69
70
56.11
56.46
56.86
57.24
57.62
58.00
58.38
58.76
59.14
59.52
53.18
53.55
53.91
54.27
54.64
55.00
55.36
55.73
56.09
56.45
49.95
50.29
50.64
50.98
51 .32
51 .67
52.01
52.35
52.70
53.04
47.03
47.35
47.68
48.01
48.34
48.67
48.99
49.32
49.65
49.98
44.10
44.41
44.73
45.04
45.35
45.67
45.98
46.29
46.61
46.92
71
72
73
74
75
76
77
78
79
80
59.89
60.27
60.65
61 .03
61 .41
61 .79
62.17
62.55
62.92
63.30
56.82
57.18
57.55
57.91
56.27
56.64
59.00
59.36
59.73
60.09
53.38
53.73
54.07
54.41
54.76
55.10
55.44
55.79
56.13
56.47
50.31
50.64
50.96
51 .29
51 .62
51.95
52.28
52.61
52.93
53.26
47.23
47.55
47.86
48: 17
48.48
48.60
49.11
49.42
49.74
50.05
81
82
83
84
85
86
07
88
69
90
63.68
64.06
64.44
64.82
65.20
65.58
65.95
66.33
66.71
67.09
60.45
60.82
61.18
61 .55
61 .91
62.27
62.64
63.00
63.36
63.73
56.82
57.16
57.51
57.85
58.19
56.54
58.88
59.22
59.57
59.91
53.59
53.92
54.25
54.58
54.90
55.23
55.56
55.89
56.22
56.55
50.36
50.68
50.99
51.30
51 .62
51.93
52.24
52.56
52.87
53.18
67.47
91
92
67.85
-------------GROUND
93
68.23
94
68.61
95
68.98
96
69.36
97
69.74
98
70.12
99
70.50
100
70.88
101
102
103
104
105
71 .26
71 .64
72.02
72.39
72.77
64.09
64.45
LINE
64.62
65.18
65.55
65.91
66.27
66.64
67.00
67.36
67.73
68.09
68.45
68.82
69.18
(12
60.25
56.87
60.60
57.20
FEET,
0 INCHES)----60.94
57.53
61 .28
57.86
61 .63
58.19
61 .97
58.52
62.31
58.84
62.66
59.17
63.00
59.50
63.34
59.83
63.69
64.03
64.37
64.72
65.06
60.16
60.48
60.81
61.14
61 .47
53.49
53.81
54.12
54.43
54.75
55.06
55.37
55.69
56.00
56.31
56.63
56.94
57.25
57.57
57.88
POLE-Con.
APPENDIX
375
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
TOP
AND DOUGLAS
CLASS
H-3
CIRC.
INCHES
FIR
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
110 FOOT
CLASS
2
CIRC.
INCHES
1
2
3
4
5
6
7
8
9
10
33.00
33.37
33.74
34.11
34.48
34.85
35.22
35.59
35.96
36.33
36.70
31.00
31.36
31.71
32.07
32.42
32.78
33.13
33.49
33.85
34.20
34.56
29.00
29.34
29.68
30.02
30.37
30.71
31.05
31.39
31.73
32.07
32.41
27.00
27.32
27.64
27.97
28.29
28.61
28.93
29.25
29.58
29.90
30.22
25.00
25.31
25.62
25.92
26.23
26.54
26.85
27.15
27.46
27.77
28.08
11
12
13
14
15
16
17
18
19
20
37.07
37.44
37.81
38.18
38.55
38.92
39.29
39.66
40.03
40.40
34.91
35.27
35.62
35.98
36.34
36.69
37.05
37.40
37.76
38.12
32.75
33.10
33.44
33.78
34.12
34.46
34.80
35.14
35.49
35.83
30.54
30.87
31.19
31.51
31.83
32.15
32.48
32.80
33.12
33.44
28.38
28.69
29.00
29.31
29.62
29.92
30.23
30.54
30.85
31.15
21
22
23
24
25
26
27
28
29
30
40.77
41.14
41.51
41.88
42.25
42.62
43.00
43.37
43.74
44.11
38.47
38.83
39.18
39.54
39.89
40.25
40.61
40.96
41.32
41.67
36.17
36.51
36.85
37.19
37.53
37.87
38.22
38.56
38.90
39.24
33.76
34.09
34.41
34.73
35.05
35.37
35.70
36.02
36.34
36.66
31.46
31.77
32.08
32.38
32.69
33.00
33.31
33.62
33.92
34.23
31
32
33
34
35
36
37
38
39
40
44.48
44.85
45.22
45.59
45.96
46.33
46.70
47.07
47.44
47.81
42.03
42.38
42.74
43.10
43.45
43.81
44.16
44.52
44.87
45.23
39.58
39.92
40.26
40.61
40.95
41.29
41.63
41.97
42.31
42.65
36.99
37.31
37.63
37.95
38.27
38.60
38.92
39.24
39.56
39.88
34.54
34.65
35.15
35.46
35.77
36.08
36.38
36.69
37.00
37.31
41
42
43
44
45
46
47
48
49
50
48.18
48.55
48.92
49.29
49.66
50.03
50.40
50.77
51.14
51.51
45.59
45.94
46.30
46.65
47.01
47.37
47.72
48.08
48.43
48.79
43.00
43.34
43.68
44.02
44.36
44.70
45.04
45.38
45.73
46.07
40.21
40.53
40.85
41.17
41.50
41.82
42.14
42.46
42.78
43.11
37.62
37.92
38.23
38.54
38.85
39.15
39.46
39.77
40.08
40.38
POLE
TRANSMISSION
376
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
AND DOUGLAS
CLASS
H-3
CIRC.
INCHES
FIR
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
I
110
FOOT
CLASS
2
CIRC.
INCHES
51
52
53
54
55
56
57
58
59
60
51.88
52.25
52.62
52.99
53.36
53.73
54.10
54.47
54.84
55.21
49.14
49.50
49.86
50.21
50.57
50.92
51.28
51.63
51.99
52.35
46.41
46.75
47.09
47.43
47.77
48.12
48.46
48.80
49.14
49.48
43.43
43.75
44.07
44.39
44.72
45.04
45.36
45.68
46.00
46.33
40.69
41.00
41.31
41.62
41.92
42.23
42.54
42.85
43.15
43.46
61
62
63
64
65
66
67
68
69
70
55.56
55.95
56.32
56.69
57.06
57.43
57.80
58.17
58.54
58.91
52.70
53.06
53.41
53.77
54.12
54.48
54.84
55.19
55.55
55.90
49.82
50.16
50.50
50.85
51.19
51.53
51.87
52.21
52.55
52.89
46.65
46.97
47.29
47.62
47.94
48.26
48.58
48.90
49.23
49.55
43.77
44.08
44.38
44.69
45.00
45.31
45.62
45.92
46.23
46.54
71
72
73
74
75
76
77
78
79
80
59.28
59.65
60.02
60.39
60.76
61.13
61.50
61.87
62.25
62.62
56.26
56.62
56.97
57.33
57.60
58.04
58.39
50.75
59.11
59.46
53.24
53.58
53.92
54.26
54.60
54.94
55.28
55.62
55.97
56.31
49.87
50.19
50.51
50.84
51.16
51.48
51.80
52.12
52.45
52.77
46.85
47.15
47.46
47.77
48.08
48.38
48.69
49.00
49.31
49.62
81
82
83
84
85
86
87
88
89
90
62.99
63.36
63.73
64.10
64.47
64.84
65.21
65.58
65.95
66.32
59.82
60.17
60.53
60.88
61.24
61.60
61.95
62.31
62.66
63.02
56.65
56.99
57.33
57.67
58.01
58.36
58.70
59.04
59.38
59.72
53.09
53.41
53.74
54.06
54.38
54.70
55.02
55.35
55.67
55.99
49.92
50.23
50.54
50.05
51.15
51.46
51.77
52.08
52.38
52.69
91
66.69
67.06
92
67.43
93
67.80
94
68.17
95
68.54
96
68.91
97
-------------GROUND
98
69.28
99
69.65
100
70.02
63.37
63.73
64.09
64.44
64.80
65.15
65.51
LINE
65.67
66.22
66.58
60.06
60.40
60.75
61.09
61.43
61.77
62.11
FEET,
0
62.45
62.79
63.13
56.31
56.63
56.96
57.28
57.60
57.92
58.25
53.00
53.31
53.62
53.92
54.23
54.54
54.85
58.57
58.89
59.21
55.15
55.46
55.77
(12
INCHES)------
POLE-con.
APPENDIX
377
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SGUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
101
102
103
104
105
106
107
108
109
1 IO
;OUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
AND DOUGLAS
CLASS
H-3
CIRC.
1 NCHES
70.39
70.76
71.13
71.50
71.87
72.24
72.61
72.98
73.35
73.72
66.93
67.29
67.64
68.00
60.36
68.71
69.07
69.42
69.70
70.13
CLASS
H-i
CIRC.
INCHES
63
63
64
64
64
65
65
65
66
66
48
82
16
50
84
18
52
07
21
55
CLASS
H-l
CIRC.
INCHES
INCHES
INCHES
31 .oo
31.35
31.70
32.05
32.39
32.74
33.09
33.44
33.79
34.14
34.49
29.00
9
10
33.00
33.36
33.72
34.09
34.45
34.81
35.17
35.54
35.90
36.26
36.62
11
12
13
14
15
16
36.99
37.35
37.71
38.07
38.44
38.80
17
39.16
18
19
20
39.52
39.09
40.25
34.83
35.18
35.53
35.88
36.23
36.50
36.93
37.28
37.62
37.97
32.60
33.02
33.35
33.69
34.02
34.36
34.69
35.03
35.36
35.70
21
22
23
24
25
26
27
28
29
30
40.61
40.97
41.33
41.70
42.06
42.42
42.78
43.15
38.32
30.67
39.02
39.37
39.72
40.06
40.41
40.76
41.11
41 .46
36.03
36.37
36.70
37.04
37.37
37.71
38.04
38.38
38.71
39.05
2
3
5
6
8
43.51
43.87
CLASS
CIRC.
1
INCHES
59
59
60
60
60
61
61
61
62
62
110
FOOT
CLASS
2
CIRC.
53
86
18
50
82
14
47
79
11
43
29.33
29.67
30.00
30.34
30.67
31 .Ol
31.34
31 .68
32.01
32.35
CLASS
CIRC.
56.08
56.38
56.69
57.00
57.31
57.62
57.92
58.23
58.54
58.05
1
CLASS
CIRC.
INCHES
INCHES
27.00
27.32
27.63
27.95
25.00
25.30
25.61
25.91
26.21
26.51
26.82
27.12
27.42
27.72
28.03
28.27
28.5’3
28.90
29.22
29.53
29.85
30.17
30.48
30.80
32.06
32.38
32.70
33.01
33.33
28.33
28.63
28.94
29.24
29.54
29.84
30.15
30.45
30.75
31 .06
33.65
33.96
34.28
34.60
34.91
35.23
35.55
35.06
36.18
36.50
31 .36
31.66
31 .96
32.27
32.57
32.07
33.17
33.48
33.78
34.08
31.11
31.43
31.75
POLE-con.
INCHES
115
FIR
CLASS
H-2
CIRC.
TOP
AND DOUGLAS
CLASS
H-3
CIRC.
FIR
CLASS
H-2
CIRC.
INCHES
2
FOOT
POLE
378
TRANSMISSION
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
AND DOUGLAS
CLASS
H-3
CIRC.
INCHES
FIR
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
1 15 FOOT
CLASS
2
CIRC.
INCHES
31
32
33
34
35
36
37
38
39
40
44.23
44.60
44.96
45.32
45.68
46.05
46.41
46.77
47.13
47.50
41.81
42.16
42.50
42.85
43.20
43.55
43.90
44.25
44.60
44.94
39.38
39.72
40.05
40.39
40.72
41 .06
41.39
41 .72
42.06
42.39
36.81
37.13
37.44
37.76
38.08
38.39
38.71
39.03
39.34
39.66
34.39
34.69
34.99
35.29
35.60
35.90
36.20
36.50
36.81
37.11
41
42
43
44
45
46
47
48
49
50
47.96
48.22
48.58
48.94
49.31
49.67
50.03
50.39
50.76
51.12
45.29
45.64
45.99
46.34
46.69
47.04
47.39
47.73
48.08
48.43
42.73
43.06
43.40
43.73
44.07
44.40
44.74
45.07
45.41
45.74
39.98
40.29
40.61
40.93
41 .24
41 .56
41.88
42.19
42.51
42.83
37.41
37.72
38.02
38.32
30.62
38.93
39.23
39.53
39.83
40.14
51
52
53
54
55
56
57
58
59
60
51.48
51.84
52.21
52.57
52.93
53.29
53.66
54.02
54.38
54.74
48.78
49.13
49.48
49.83
50.17
50.52
50.87
51.22
51.57
51.92
46.08
46.41
46.15
47.08
47.42
47.75
48.09
48.42
48.76
49.09
43.14
43.46
43.78
44.09
44.41
44.72
45.04
45.36
45.67
45.99
40.44
40.74
41.05
41.35
41 .65
41.95
42.26
42.56
42.86
43.17
61
62
63
64
65
66
61
68
69
70
55.11
55.47
55.83
56.19
56.56
56.92
57.28
57.64
58.00
58.37
52.27
52.61
52.96
53.31
53.66
54.01
54.36
54.71
55.06
55.40
49.43
49.76
50.10
50.43
50.77
51.10
51.44
51.77
52.11
52.44
46.31
46.62
46.94
47.26
47.57
47.89
48.21
48.52
48.84
49.16
43.47
43.77
44.07
44.38
44.68
44.98
45.28
45.59
45.89
46.19
71
72
73
74
75
76
77
78
79
80
59.73
59.09
59.45
59.82
60.18
60.54
60.90
61 .27
61 .63
61 .99
55.75
56.10
56.45
56.80
57.15
57.50
57.84
58.19
58.54
58.89
52.78
53.11
53.44
53.78
54.11
54.45
54.79
55.12
55.45
55.19
49.47
49.79
50.11
50.42
50.74
51 .06
51.37
51 .69
52.00
52.32
46.50
46.80
47.10
47.40
47.71
48.01
48.31
48.61
48.92
49.22
POLE-con.
APPENDIX
379
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
FIR
CLASS
H-2
CIRC.
INCHES
CLASS
CIRC.
INCHES
56.12
56.46
56.79
57.13
57.46
57.80
58.13
58.47
58.80
59.14
52.64
52.95
53.27
53.59
53.90
54.22
54.54
54.85
55.17
55.49
49.52
49.63
50.13
50.43
50.73
51.04
51.34
51.64
51.94
52.25
62.35
62.72
63.08
63.44
63.80
64.17
64.53
64.89
65.25
65.61
59
59
59
60
60
60
61
61
62
62
91
92
93
94
95
96
97
98
99
100
65.98
66.34
66.70
67.06
67.43
67.19
68.15
68.51
68.88
69.24
62.72
63.07
63.42
63.77
64.12
64.41
64.82
65.17
65.51
65.86
59.47
59.81
60.14
60.48
60.81
61.15
61.48
61.82
62.15
62.49
55.80
56.12
56.44
56.75
57.07
57.39
57.70
58.02
58.33
58.65
52.55
52.85
53.16
53.46
53.76
54.06
54.37
54.67
54.97
55.28
66.21
66.56
LINE
66.91
67.26
67.61
67.95
68.30
68.65
69.00
69.35
62.82
63.16
0
FEE T.
63.49
63.83
64.16
64.50
64.63
65.17
65.50
65.83
58.97
59.28
INCHES)---------------
55.58
55.88
59.60
59.92
60.23
60.55
60.87
61.18
61.50
61.82
56.18
56.49
56.79
57.09
57.39
57.70
58.00
58.30
66.17
66.50
66.84
67.17
67.51
62.13
62.45
62.77
63.06
63.40
58.61
58.91
59.21
59.51
59.82
.-
103
109
105
106
107
108
109
110
111
112
113
114
115
YELLOW
PINE
DISTANCE
FROM TOP
FEET
TOP
2
3
4
5
6
7
8
9
10
69.60
69.96
-----GROUND
70.33
70.69
71.05
71.41
71.78
72.14
72.50
72.86
73.22
73.59
73.95
74.31
74.67
( 12
69.70
70.05
70.39
70.74
71.09
AND DOUGLAS
CLASS
H-3
CIRC.
INCHES
33
33
33
34
34
34
35
35
35
36
36
24
59
94
28
63
98
33
60
03
38
1
1 15 FOOT
CLASS
2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
81
82
83
84
85
06
87
88
89
90
101
102
---
SOUTHERN
AND DOUGLAS
CLASS
H-3
CIRC.
1 NCHES
00
36
72
08
44
80
16
52
88
24
60
FIR
CLASS
H-2
CIRC.
INCHES
31.00
31.34
31.60
32.03
32.37
32.71
33.05
33.39
33.74
34.08
34.42
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
29.00
29.33
29.66
29.99
30.32
30.64
30.97
31.30
31.63
31.96
32.29
27.00
27.31
27.62
27.93
28.25
28.56
28.87
29.18
29.49
29.80
30.11
1
120
CLASS
2
CIRC.
INCHES
25
25
25
25
26
26
26
27
27
27
27
00
30
60
89
19
49
79
09
39
68
98
POLE-con.
FOOT
POLE
380
TRANSMISSION
LINE DESIGN
MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
AND DOUGLAS
CLASS
H-3
CIRC.
INCHES
FIR
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
120 FOOT
CLASS
2
CIRC.
INCHES
I 1
12
13
14
15
16
17
18
19
20
36.96
37.32
37.68
38.04
38.39
38.75
39.11
39.47
39.83
40.19
34.76
35.11
35.45
35.79
36.13
36.47
36.82
37.16
37.50
37.84
32.62
32.95
33.28
33.61
33.93
34.26
34.59
34.92
35.25
35.58
30.43
30.74
31.05
31.36
31.67
31.98
32.29
32.61
32.92
33.23
28.28
28.58
28.88
29.18
29.47
29.77
30.07
30.37
30.67
30.96
21
22
23
24
25
26
27
28
29
30
40.55
40.91
41.27
41.63
41.99
42.35
42.71
43.07
43.43
43.19
38.18
38.53
38.87
39.21
39.55
39.89
40.24
40.58
40.92
41.26
35.91
36.24
36.57
36.89
37.22
37.55
37.88
38.21
38.54
38.87
33.54
33.85
34.16
34.47
34.79
35.10
35.41
35.72
36.03
36.34
31.26
31.56
31.86
32.16
32.46
32.75
33.05
33.35
33.65
33.95
31
32
33
34
35
36
37
38
39
40
44.15
44.51
44.87
45.23
45.59
45.95
46.31
46.67
47.03
47.39
41.61
41.95
42.29
42.63
42.97
43.32
43.66
44.00
44.34
44.68
39.20
39.53
39.86
40.18
40.51
40.84
41.17
41.50
41.83
42.16
36.65
36.96
37.28
37.59
37.90
38.21
38.52
38.83
39.14
39.46
34.25
34.54
34.84
35.14
35.44
35.74
36.04
36.33
36.63
36.93
41
42
43
44
45
46
47
48
49
50
47.75
48.11
48.46
48.82
49.18
49.54
49.90
50.26
50.62
50.98
45.03
45.37
45.71
46.05
46.39
46.74
47.08
47.42
47.76
48.11
42.49
42.82
43.14
43.47
43.60
44.13
44.46
44.79
45.12
45.45
39.77
40.08
40.39
40.70
41.01
41.32
41.64
41.95
42.26
42.57
37.23
37.53
37.82
38.12
38.42
38.72
39.02
39.32
39.61
39.91
51
52
53
54
55
56
57
58
59
60
51.34
51.70
52.06
52.42
52.78
53.14
53.50
53.86
54.22
54.58
48.45
48.79
49.13
49.47
49.82
50.16
50.50
50.84
51.18
51.53
45.78
46.11
46.43
46.76
47.09
47.42
47.75
48.08
48.41
48.74
42.88
43.19
43.50
43.82
44.13
44.44
44.75
45.06
45.37
45.68
40.21
40.51
40.81
41.11
41.40
41.70
42.00
42.30
42.60
42.89
POLE-con.
____._
APPENDIX
!3
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
,UUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
AND DOUGLAS
CLASS
H-3
CIRC.
INCHES
120
FIR
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
FOOT
CLASS
CIRC.
INCHES
61
62
63
64
65
66
67
68
69
70
54.94
55.30
55.66
56.02
56.38
56.74
57.10
57.46
57.82
58.18
51 .87
52.21
52.55
52.89
53.24
53.58
53.92
54.26
54.61
54.95
49.07
49.39
49.72
50.05
50.38
50.71
51.04
51.37
51.70
52.03
46.00
46.31
46.62
46.93
47.24
47.55
47.86
48.18
48.49
48.80
43.19
43.49
43.79
44.09
44.39
44.68
44.98
45.28
45.58
45.88
71
72
73
74
75
76
77
18
79
80
58.54
50.89
59.25
59.61
59.97
60.33
60.69
61 .05
61 .41
61 .77
55.29
55.63
55.97
56.32
56.66
57.00
57.34
57.60
58.03
58.37
52.36
52.68
53.01
53.34
53.67
54.00
54.33
54.66
54.99
55.32
49.11
49.42
49.73
50.04
50.36
50.67
50.98
51 .29
51 .60
51.91
46.18
46.47
46.77
47.07
47.37
47.67
47.96
48.26
48.56
48.86
81
82
83
84
85
86
87
88
89
90
62.13
62.49
62.85
63.21
63.57
63.93
64.29
64.65
65.01
65.37
58.71
59.05
59.39
59.74
60.08
60.42
60.76
61.11
61 .45
61 .79
55.64
55.97
56.30
56.63
56.96
57.29
57.62
57.95
58.28
58.61
52.22
52.54
52.05
53.16
53.47
53.78
54.09
54.40
54.71
55.03
49. 16
49.46
49.75
50.05
50.35
50.65
50.95
51 .25
51.54
51 .84
91
92
93
94
95
96
97
98
99
100
65.73
66.09
66.45
66.81
67.17
67.53
67.89
68.25
68.61
68.96
62.13
62.47
62.82
63.16
63.50
63.84
64.18
64.53
64.87
65.21
58.93
59.26
59.59
59.92
60.25
60.58
60.91
61 .24
61 .57
61 .89
55.34
55.65
55.96
56.27
56.58
56.09
57.21
57.52
57.83
58.14
52. 14
52.44
52.74
53.04
53.33
53.63
53.93
54.23
54.53
54.82
101
102
103
104
105
106
107
69.32
69.68
70.04
70.40
70.76
71.12
71.48
----GROUND
71 .a4
72.20
72.56
58.45
50.76
59.07
59.39
59.70
60.01
60.32
55.12
55.42
55.72
56.02
56.32
56.61
56.91
-----
60.63
60.94
61 .25
57.21
57.51
57.81
108
109
110
65.55
65.09
66.24
66.58
66.92
67.26
67.61
LINE
67.95
68.29
68.63
(12
62.22
62.55
62.88
63.21
63.54
63.87
64.20
FEET.
0
64.53
64.86
65.18
INCHES)------
2
POLE-Con.
TRANSMISSION
382
LINE DESIGN MANUAL
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
111
112
113
114
115
116
117
118
119
120
SOUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
AND DOUGLAS
CLASS
H-3
CIRC.
1 NCHES
72.92
73.28
73.64
74.00
74.36
74.72
75.08
75.44
75.80
76.16
CLASS
H-l
CIRC.
INCHES
68.97
69.32
69.66
70.00
70.34
70.68
71.03
71.37
71.71
72.05
65.51
65.84
66.17
66.50
66.83
67.16
67.49
67.82
68.14
68.47
CLASS
CIRC.
INCHES
1
FOOT
CLASS
CIRC.
INCHES
61 .57
61 .88
62.19
62.50
62.81
63.12
63.43
63.75
64.06
64.37
58.11
58.40
58.70
59.00
59.30
59.60
59.89
60.19
60.49
60.79
125
2
CLASS
H-l
CIRC.
INCHES
INCHES
INCHES
INCHES
INCHES
1
2
3
4
5
6
7
8
9
10
33.00
33.35
33.71
34.06
34.41
34.76
35.12
35.47
35.82
36.18
36.53
31 .oo
31.34
31 .67
32.01
32.34
32.68
33.02
33.35
33.69
34.03
34.36
29.00
29.32
29.65
29.97
30.29
27.00
27.31
27.61
27.92
28.23
28.53
28.84
29.15
29.45
29.76
30.07
25.00
25.29
25.58
25.87
26.16
26.45
26.74
27.03
27.32
27.61
27.90
11
12
13
14
15
16
17
18
19
20
36.88
37.24
37.59
37.94
38.29
38.65
39.00
39.35
39.71
40.06
34.70
35.03
35.37
35.71
36.04
36.38
36.71
37.05
37.39
37.72
32.56
32.88
33.53
33.85
34.18
34.50
34.82
35.15
35.47
30.37
30.68
30.99
31.29
31 .60
31.91
32.21
32.52
32.83
33.13
28.19
28.48
28.77
29.06
29.35
29.64
29.93
30.22
30.51
30.80
21
22
23
24
25
26
27
28
29
30
40.41
40.76
41.12
41.47
41 .82
42.18
42.53
42.88
43.24
43.59
38.06
38.39
38.73
39.07
35.79
36.12
36.44
36.76
37.09
37.41
37.74
38.06
38.38
38.71
33.44
33.75
34.05
34.36
34.67
34.97
35.28
35.59
35.89
36.20
31.09
31 .38
31 .67
31 .96
32.25
32.54
32.83
33.12
33.41
33.70
39.40
39.74
40.08
40.41
40.75
41 .08
30.62
30.94
31 .26
31.59
31.91
32.24
33.21
CLASS
CIRC.
POLE-Con.
2
FIR
CLASS
H-2
CIRC.
TOP
AND DOUGLAS
CLASS
H-3
CIRC.
120
FIR
CLASS
H-2
CIRC.
INCHES
1
CLASS
CIRC.
FOOT
POLE
APPENDIX
383
B
Table B-3.-Pole circumferences for Douglas fir and southern yellow pine-Continued
SOUTHERN
YELLOW
PINE
DISTANCE
FROM TOP
FEET
AND DOUGLAS
CLASS
H-3
CIRC.
INCHES
FIR
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
125
FOOT
CLASS
2
CIRC.
INCHES
31
32
33
34
35
36
37
38
39
40
43.94
44.29
44.65
45.00
45.35
45.71
46.06
46.41
46.76
47.12
41 .42
41 .76
42.09
42.43
42.76
43. IO
43.44
43.77
44.11
44.45
39.03
39.35
39.68
40.00
40.32
40.65
40.97
41.29
41 .62
41.94
36.51
36.82
37.12
37.43
37.74
38.04
38.35
38.66
38.96
39.27
33.99
34.28
34.57
34.86
35.15
35.44
35.73
36.02
36.31
36.60
41
42
43
44
45
46
47
48
49
50
47.47
47.82
48.18
48.53
48.88
49.24
49.59
49.94
50.29
50.65
44.78
45.12
45.45
45.79
46.13
46.46
46.80
47.13
47.47
47.81
42.26
42.59
42.91
43.24
43.56
43.88
44.21
44.53
44.85
45.18
39.58
39.88
40.19
40.50
40.80
41.11
41 .42
41 .72
42.03
42.34
36.89
37.18
37.47
37.16
38.05
38.34
38.63
38.92
39.21
39.50
51
52
53
54
55
56
57
58
59
60
51 .oo
51.35
51.71
52.06
52.41
52.76
53.12
53.47
53.82
54.18
48.14
48 ‘48
48.82
49.15
49.49
49.82
50.16
50.50
50.83
51.17
45.50
45.82
46.15
46.47
46.79
47.12
47.44
47.76
48.09
48.41
42.64
42.95
43.26
43.56
43.87
44.18
44.48
44.79
45.10
45.40
39.79
40.08
40.37
40.66
40.95
41 .24
41.53
41.82
42.11
42.39
61
62
63
64
65
66
67
68
69
70
54.53
54.88
55.24
55.59
55.94
56.29
56.65
57.00
57.35
57.71
51.50
51.84
52.18
52.51
52.85
53.18
53.52
53.86
54.19
54.53
48.74
49.06
49.38
49.71
50.03
50.35
50.68
51 .oo
51 .32
51 .65
45.71
46.02
46.32
46.63
46.94
47.24
47.55
47.86
48.16
48.47
42.68
42.97
43.26
43.55
43.84
44.13
44.42
44.71
45.00
45.29
71
72
73
74
75
76
77
78
79
80
58.06
58.41
58.76
59.12
59.47
59.82
60.18
60.53
60.88
61 .24
54.87
55.20
55.54
55.87
56.21
56.55
56.88
57.22
57.55
57.89
51.97
52.29
52.62
52.94
53.26
53.59
53.91
54.24
54.56
54.88
48.78
49.08
49.39
49.70
50.00
50.31
50.62
50.92
51 .23
51.54
45.58
45.87
46.16
46.45
46.74
47.03
47.32
47.61
47.90
48.19
POLE-con.
APPENDIX
385
B
Table B-4.-Pole circumferences for western red cedar
rlESTERN
RED
30
CEDAR
DISTANCE
FROM TOP
FEET
CLASS
CIRC.
INCHES
TOP
WESTERN
1
2
3
4
5
6
7
8
9
10
CLASS
CIRC.
INCHES
2
CLASS
CIRC.
INCHES
3
CLASS
CIRC.
INCHES
2
3
4
5
6
I
8
9
10
27
27
28
28
29
29
30
30
31
31
32
00
54
08
63
17
71
25
79
33
88
42
25.00
25.52
26.04
26.56
27.08
27.60
28.13
28.65
29.17
29.69
30.21
23.00
23.50
24.00
24.50
25.00
25.50
26.00
26.50
21.00
27.50
28.00
21 .oo
21 .48
21 .96
22.44
22.92
23.40
23.88
24.35
24.83
25.31
25.79
I I
12
13
14
15
16
17
18
19
20
32
33
34
34
35
35
36
36
37
31
96
50
04
58
12
67
21
75
29
83
30.73
31 .25
31 .-II
32.29
32.81
33.33
33.85
34.37
34.90
35.42
28.50
29.00
29.50
30.00
30.50
31 .oo
31.50
32.00
32.50
33.00
26.27
26.75
27.23
27.71
28.19
28.61
29.15
29.63
30.10
30.58
21
22
23
24
------GROUND
25
26
27
28
29
30
38
38
39
40
37
92
46
00
35.94
36.46
36.98
37.50
(5 FEET,
38.02
38.54
39.06
39.58
40.10
40.62
RED CEDAR
DISTANCE
CLASS
H-2
FROM TOP
CIRC.
FEET
INCHES
TOP
1
31 .oo
31.59
32.17
32.76
33.34
33.93
34.52
35.10
35.69
36.28
36.86
LINE
40.54
41 .08
41 .62
42.17
42.71
43.25
CLASS
H-l
CIRC.
INCHES
29.00
29.57
30.14
30.71
31 .28
31 .84
32.41
32.98
33.55
34.12
34.69
CLASS
CIRC.
INCHES
27.00
27.53
28.07
28.60
29.14
29.67
30.21
30.74
31 .28
31 .81
32.34
33.50
34.00
34.50
35.00
6 INCHE!S------35.50
36.00
36.50
37.00
37.50
38.00
I
CLASS
CIRC.
INCHES
25
25
26
26
27
27
28
28
29
29
30
00
52
03
55
07
59
10
62
14
66
17
2
FOOT
POLE
35 FOOT
CLASS
4
CIRC.
INCHES
POLE
4
31 .06
31.54
32.02
32.50
32.98
33.46
33.94
34.42
34.90
35.37
CLASS
CIRC.
INCHES
23.00
23.50
24.00
24.50
25.00
25.50
26.00
26.50
27.00
27.50
28.00
3
-
21 .oo
21.47
21.93
22.40
22.86
23.33
23.79
24.26
24.72
25.19
25.66
386
TRANSMISSION
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
CLASS
H-2
FROM TOP
CIRC.
FEET
INCHES
11
12
13
I4
15
16
17
19
19
20
21
22
23
24
25
26
27
28
29
--30
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
33
33
34
34
35
36
36
37
37
38
39
39
40
40
41
42
42
43
43
44
45
30.69
31.21
31 .72
32.24
32.76
33.28
33.79
32
33
33
34
35
35
36
36
37
37
43.31
43.90
44.4E
45.07
45.66
46.24
46.83
47.41
48.00
40
41
42
42
43
43
44
44
45
95
38.22
38.76
39.29
39.83
40.36
40.90
41.43
41.97
42.50
LINE
(6
CLASS
CIRC.
INCHES
88
26
83
40
97
53
IO
67
24
81
30
52
09
66
22
79
36
93
50
1
41
95
48
02
55
09
62
16
69
35
35
36
36
37
30
30
39
39
40
FEET.
CLASS
CIRC.
INCHES
FOOT POLE-con.
CLASS
4
CIRC.
1 NCHES
34.83
35.34
26.12
26.59
27.05
27.52
27.98
28.45
28.91
29.38
29.84
30.31
35.86
36.38
36.90
37.41
37.93
39.45
38.97
39.48
40.00
33.50
34.00
34.50
35.00
35.50
36.00
36.50
37.00
37.50
30.78
31 .24
31.71
32.17
32.64
33.10
33.57
34.03
34.50
34.31
0
35
3
28.50
29.00
29.50
30.00
30.50
31 .oo
31.50
32.00
32.50
33.00
INCHES)-
46 07
43.03
40.52
38.00
34.97
49.17
49.76
46
47
47
48
48
43 57
44 10
44 64
45 17
45 71
41.03
41.55
42.07
42.59
43.10
38.50
39.00
39.50
40.00
40.50
35.43
35.90
36.36
36.03
37.29
CLASS
H-2
CIRC.
INCHES
64
21
70
34
91
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
60
21
81
41
01
62
22
82
43
03
31 .oo
31.59
32.18
32.76
33.35
33.94
34.53
35.12
35.71
36.29
36.88
30.12
30.68
31 .24
31.79
32.35
32.91
33.47
34.03
34.59
27.00
27.53
28.06
28.59
29.12
29.65
30.18
30.71
31 .24
31 .76
32.29
63
24
84
44
04
65
25
85
46
06
37.47
38.06
38.65
39.24
39.82
40.41
41 .oo
41.59
42.18
42.76
35.15
35.71
36.26
36.82
37.38
37.94
38.50
39.06
39.62
40.18
32.92
33.35
33.88
34.41
34.94
35.47
36.00
36.53
37.06
37.59
00
2
40.59
50.34
50.93
51.52
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
CLASS
CIRC.
INCHES
37.45
38.03
38.62
39.21
39.79
40.38
40.97
41.55
42.14
42.72
.-GROUND
31
32
33
34
35
TOP
CLASS
H-l
CIRC.
1 NCHES
29.00
29.56
1
CLASS
CIRC.
2
40 FOOT POLE
3
CLASS
4
CIRC.
INCHES
CLASS
CIRC.
INCHES
25.00
25.51
26.03
26.54
27.06
27.57
28.09
28.60
29.12
29.63
30.15
23.00
23.49
23.97
24.46
24.94
25.43
25.91
26.40
26.88
27.37
27.85
21 .oo
21 .46
21.91
22.37
22.82
23.28
23.74
24.19
24.65
25.10
25.56
30.66
31.18
31 .69
32.21
32.72
33.24
33.75
34.26
34.78
35.29
28
28
29
29
30
30
31
31
32
32
26.01
26.47
26.93
27.38
27.84
28.29
28.75
29.21
29.66
30.12
34
82
31
79
28
76
25
74
22
71
INCHES
APPENDIX
387
B
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
45.66
46.26
46.87
47.47
48.07
48.68
49.28
49.88
50.49
51.09
51 .69
52.29
52.90
____--------_
53.50
54.10
54.71
55.31
55.91
56.51
57.12
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
TOP
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
40
CLASS
H-2
CIRC.
INCHES
43
43
44
45
45
46
46
47
48
48
35
94
53
12
71
29
88
47
06
65
49.24
49.82
50.41
.--GROUND
51 .oo
51.59
52.18
52.76
53.35
53.94
54.53
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
40.74
41.29
41.85
42.41
42.97
43.53
44.09
44.65
45.21
45.76
46.32
46.88
47.44
LINE
(6
48.00
48.56
49.12
49.68
50.24
50.79
51.35
FEET,
CLASS
CIRC.
INCHES
1
CLASS
CIRC.
INCHES
38.12
38.65
39.18
39.71
40.24
40.76
41.29
41 .82
42.35
42.88
35
36
36
37
37
38
38
39
39
40
43.41
43.94
44.47
0 INCHES)------45.00
45.53
46.06
46.59
47.12
47.65
48.18
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
2
81
32
84
35
87
38
90
41
93
44
FOOT
CLASS
CIRC.
INCHES
3
POLE-con.
CLASS
CIRC.
INCHES
33.19
33.68
34.16
34.65
35.13
35.62
36.10
36.59
37.07
37.56
30
31
31
31
32
32
33
33
34
34
57
03
49
94
40
85
31
76
22
68
40.96
41.47
41.99
38.04
38.53
39.01
35
35
36
13
59
04
42.50
43.01
43.53
44.04
44.56
45.07
45.59
39.50
39.99
40.47
40.96
41.44
41.93
42.41
36
36
37
37
38
38
39
50
96
41
87
32
78
24
CLASS
CIRC.
INCHES
33.00
33.59
34.18
34.77
35.36
35.95
36.54
37.13
37.72
38.31
38.90
31
31
32
32
33
33
34
35
35
36
36
00
58
15
73
31
88
46
04
62
19
77
29.00
29.55
30.10
30.65
31.21
31 .76
32.31
32.86
33.41
33.96
34.51
27.00
27.53
28.05
28.58
29.10
29.63
30.15
30.68
31.21
31.73
32.26
25
25
26
26
27
27
28
28
29
29
30
00
50
00
50
00
50
00
50
00
50
00
39.49
40.08
40.67
41 .26
41 .85
42.44
43.03
43.62
44.21
44.79
37
37
38
39
39
40
40
41
41
42
35
92
50
08
65
23
81
38
96
54
35.06
35.62
36.17
36.72
37.27
37.82
38.37
38.92
39.47
40.03
32.78
33.31
33.83
34.36
34.88
35.41
35.94
36.46
36.99
37.51
30.50
31 .oo
31.50
32.00
32.50
33.00
33.50
34.00
34.50
35.00
2
CLASS
CIRC.
INCHES
4
45 FOOT
POLE
3
CLASS
4
CIRC.
INCHES
23.00
23.47
23.95
24.42
24.90
25.37
25.85
26.32
26.79
27.27
27.74
21
21
21
22
22
23
23
24
24
25
25
28.22
28.69
29.17
29.64
30.12
30.59
31 .06
31.54
32.01
32.49
25.94
26.38
26.83
27.28
27.73
28.18
28.63
29.08
29.53
29.97
00
45
90
35
79
24
69
14
59
04
49
TRANSMISSION
LINE DESIGN
MANUAL
Table B-4.-Pole circumferences for western red cedar-continued
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
21
22
23
24
25
26
27
28
29
30
CLASS
H-2
CIRC.
INCHES
45.38
45.91
46 56
47
15
47 74
48 33
48 92
49 51
50.10
50.69
43.12
43.69
44.27
44.85
45.42
46.00
46.58
47.15
47.73
48.31
31
51.28
32
51.87
33
52.46
34
53.05
35
53.64
36
54.23
37
54.82
38
55.41
-----------------------GROUND
39
56.00
40
56.59
48.66
49.46
50.04
50.62
51.19
51.77
52.35
52.92
41
42
43
44
45
54.65
55.23
55.81
56.38
56.96
57.18
57.77
58.36
58.95
59.54
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
53.50
54.08
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
40.58
41.13
41.68
42.23
42.70
43.33
43.88
44.44
44.99
45.54
38.04
30.56
39.09
39.62
40.14
40.67
41.19
41.72
42.24
42.77
35.50
36.00
36.50
37.00
37.50
38.00
38.50
39.00
39.50
40.00
43.29
43.82
44.35
44.87
45.40
45.92
46.45
46.97
6 INCHES)--47.50
48.03
40
41
41
42
42
43
43
44
48.55
49.08
49.60
50.13
50.65
46.09
46.64
47.19
47.74
48.29
48.85
49.40
49.95
LINE
(6
50.50
51.05
FEET,
51.60
52.15
52.71
53.26
53.81
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
1
CLASS
CIRC.
INCHES
2
45 FOOT
POLE-Con.
CLASS
CLASS
3~
CIRC.
CIRC.
INCHES
INCHES
32.96
33.44
33.91
34.36
34.86
35.33
35.81
36.28
36.76
37.23
30.42
30.87
31.32
31.77
32.22
32.67
33.12
33.56
34.01
34.46
50
00
50
00
50
00
50
00
--
37.71
38.18
38.65
39.13
39.60
40.08
40.55
41.03
---_---
34.91
35.36
35.81
36.26
36.71
37.15
37.60
38.05
44
45
50
00
41.50
41.97
38.50
38.95
45
46
46
47
47
50
00
50
00
50
42.45
42.92
43.40
43.87
44.35
39.40
39.05
40.29
40.74
41.19
CLASS
CIRC.
INCHES
.oo
2
CLASS
CIRC.
INCHES
50
3
FOOT POLE
CLASS
4
CIRC.
INCHES
;
6
7
8
9
IO
35
36
37
37
38
38
00
58
16
74
32
90
48
06
64
22
80
31.00
31.56
32.11
32.67
33.23
33.78
34.34
34.90
35.45
36.01
36.57
29.00
29.53
30.07
30.60
31.14
31.67
32.20
32.74
33.27
33.81
34.34
27.00
27.51
28.02
28.53
29.05
29.56
30.07
30.58
31.09
31.60
32.11
25
25
25
26
26
27
27
28
28
29
29
.49
.98
.47
.95
44
:93
.42
.91
40
:89
23.00
23.47
23.93
24.40
24.86
25.33
25.80
26.26
26.73
27.19
27.66
21.00
21.43
21.86
22.30
22.73
23.16
23.59
24.02
24.45
24.89
25.32
11
12
13
14
15
16
17
18
19
20
39.37
39.95
40.53
41
11
41 69
42 27
42.85
43.43
44 01
44 59
37.12
37.68
38.24
38.80
39.35
39.91
40.47
41.02
41.58
42.14
34.87
35.41
35.94
36.48
37.01
37.55
38.08
38.61
39.15
39.68
32.63
33.14
33.65
34.16
34.67
35.18
35.69
36.20
36.72
37.23
30.37
30.86
31.35
31.84
32.33
32.82
33.31
33.80
34 28
34 77
26.12
28.59
29.06
29.52
29.99
30.45
30.92
31.39
31.65
32.32
25.75
26.18
26.61
27.05
27.48
27.91
28.34
28.77
29.20
29.64
TOP
1
2
3
33
33
34
34
4
APPENDIX
B
Table B-4.-Pole circumferences for western red cedar-Continued
HESTERN
RED CEDAR
DISTANCE
CLASS
H-3
f-ROM TOP
CIRC.
FEET
INCHES
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
CLASS
CIRC.
INCHES
2
50 FOOT
CLASS
3
CIRC.
INCHES
Pot-E-con.
CIASS
CIRC.
INCHES
21
22
23
24
25
26
27
28
29
30
45.17
45.15
46.33
46.91
47.49
48.07
48.65
49.23
49.81
50.39
42.69
43.25
43.81
44.36
44.92
45.48
46.03
46.59
47.15
47.70
40.22
40.75
41 .28
41.62
42.35
42.89
43.42
43.95
44.49
45.02
37.74
38.25
38.76
39.27
39.78
40.30
40.81
41 .32
41 .83
42.34
35.26
35.75
36.24
36.73
37.22
37.70
38.19
36.68
39.17
39.66
32.78
33.25
33.72
34.18
34.65
35.11
35.58
36.05
36.51
36.98
30.07
30.50
30.93
31 .36
31 .80
32.23
32.66
33.09
33.52
33.95
31
32
33
34
35
36
31
38
39
40
50.97
51.55
52.12
52.70
53.28
53.86
54.44
55.02
55.60
56.18
48.26
48.82
49.37
49.93
50.49
51.05
51 .60
52.16
52.72
53.27
45.56
46.09
46.62
47.16
47.69
48.23
48.76
49.30
49.83
50.36
42.85
43.36
43.87
44.39
44.90
45.41
45.92
46.43
46.94
47.45
40.15
40.64
41.12
41 .61
42.10
42.59
43.08
43.57
44.06
44.55
37.44
37.91
38.37
36’. 84
39.31
39.77
40.24
40.70
41.17
41 .64
34.39
34.82
35.25
35.68
36.11
36.55
36.98
37.41
37.84
38.27
41
42
56.76
57.34
42.10
42.57
38.70
39.14
51.92
58.50
59.08
59.66
60.24
60.82
61 .40
61 .98
47.97
48.48
0 INCHES)------48.99
45.50
50.01
50.52
51.03
51.55
52.06
52.57
45.03
45.52
43
44
45
46
47
48
49
50
53.83
54.39
---GROUND
54.94
55.50
56.06
56.61
57.17
57.13
58.28
58.84
46.01
46.50
46.99
47.48
47.97
48.45
48.94
49.43
43.03
43.50
43.97
44.43
44.90
45.36
45.83
46.30
39.57
40.00
40.43
40.86
41.30
41.73
42.16
42.59
IHESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
TOP
2
3
4
5
6
7
8
9
10
33
33
34
34
35
35
36
37
37
38
38
00
57
14
71
29
86
43
00
57
14
71
50.90
51.43
LINE
(7
51.97
52.50
53.03
53.57
54.10
54.64
55.17
55.70
FEET
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
31 .oo
31.54
32.08
32.62
33.16
33.70
34.24
34.79
35.33
35.87
36.41
29.00
29.52
30.04
30.56
31 .08
31 .60
32.12
32.64
33.16
33.68
34.20
CLASS
CIRC.
INCHES
27.00
27.50
28.00
28.50
29.00
29.50
30.00
30.50
31 .oo
31.50
32.00
1
CLASS
CIRC.
INCHES
25
25
25
26
26
27
27
28
26
29
29
00
48
96
44
92
40
88
36
84
32
80
2
CLASS
CIRC.
INCHES
23.00
23.45
23.90
24.35
24.80
25.24
25.69
26.14
26.59
27.04
27.49
4
55 FOOT
POLE
3
CLASS
4
CIRC.
INCHES
21 .oo
21.43
21.86
22.29
22.71
23.14
23.57
24.00
24.43
24.86
25.29
390
TRANSMISSION
LINE DESIGN
MANUAL
Table B-4.-Pole circumferences for western red cedar-continued
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
i NCHES
CLASS
CIRC.
INCHES
I
CLASS
2
CIRC.
1 NCHES
55 FOOT
CLASS
3
CIRC.
INCHES
POLE-Con.
CLASS
CIRC.
INCHES
11
12
13
14
15
I6
17
18
19
20
39.29
39.86
40.43
41 .oo
41.57
42.14
42.71
43.29
43.86
44.43
36.95
37.49
38.03
38.57
39.11
39.65
40.19
40.73
41.28
41 .82
34.72
35.24
35.77
36.29
36.81
37.33
37.85
38.37
38.89
39.41
32.50
33.00
33.50
34.00
34.50
35.00
35.50
36.00
36.50
37.00
30.28
30.76
31 .23
31.71
32.19
32.67
33.15
33.63
34.1
I
34.59
27.94
28.39
28.84
29.29
29.73
30.18
30.63
31 .oa
31.53
31.98
25.71
26.14
26.57
27.00
27.43
27.86
28.29
28.71
29.14
29.57
21
22
23
24
25
26
27
28
29
30
45.00
45.57
46.14
46.71
47.29
47.86
48.43
49.00
49.57
50.14
42.36
42.90
43.44
43.98
44.52
45.06
45.60
46.14
46.68
47.22
39.93
40.45
40.97
41.49
42.01
42.53
43.05
43.57
44.09
44.61
37.50
38.00
38.50
39.00
39.50
40.00
40.50
41 .oo
41.50
42.00
35.07
35.55
36.03
36.51
36.99
37.47
37.95
38.43
38.91
39.39
32.43
32.88
33.33
33.78
34.22
34.67
35.12
35.57
36.02
36.47
30.00
30.43
30.86
31.29
31.71
32.14
32.57
33.00
33.43
33.86
31
32
33
34
35
36
37
38
39
40
50.71
51.29
51 .86
52.43
53.00
53.57
54.14
54.71
55.29
55.86
47.77
48.31
48.85
49.39
49.93
50.47
51 .Ol
51.55
52.09
52.63
45.13
45.65
46.17
46.69
47.21
47.73
48.26
48.78
49.30
49.82
42.50
43.00
43.50
44.00
44.50
45.00
45.50
46.00
46.50
47.00
39.07
40.35
40.83
41.31
41.79
42.27
42.74
43.22
43.70
44.18
36.92
37.37
37.82
38.27
38.71
39.16
39.61
40.06
40.51
40.96
34.29
34.71
35.14
35.57
36.00
36.43
36.86
37.29
37.71
38.14
41
42
43
44
45
46
47
---
56.43
57.00
57.57
58.14
58.71
59.29
59.86
-----
44.66
45.14
45.62
46.10
46.58
47.06
47.54
41.41
41 .86
42.31
42.76
43.20
43.65
44.10
-----
38.57
39.00
39.43
39.86
40.29
40.71
41.14
48
49
50
60.43
61 .OO
61 .57
47.50
48.00
48.50
49.00
49.50
50.00
50.50
6 INCHES)------51 .oo
51.50
52.00
48.02
48.50
48.98
44.55
45.00
45.45
41.57
42.00
42.43
51
52
53
54
55
62.14
62.71
63.29
63.86
64.43
52.50
53.00
53.50
54.00
54.50
49.46
49.94
50.42
50.90
51.38
45.90
46.35
46.80
47.24
47.69
42.86
43.29
43.71
44.14
44.57
53.17
53.71
54.26
54.80
55.34
55.88
56.42
---GROUND
56.96
57.50
58.04
58.58
59.12
59.66
60.20
60.74
50.34
50.86
51.38
51.90
52.42
52.94
53.46
LINE
(7
53.98
54.50
55.02
55.54
56.06
56.58
57.10
57.62
FEET,
Lt
APPENDIX
391
6
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
1
CLASS
CIRC.
INCHES
2
CLASS
CIRC.
INCHES
FOOT POLE
CLASS
Lt
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
33.00
33.56
34.11
34.67
35.22
35.76
36.33
36.89
37.44
38.00
38.56
31 .oo
31.53
32.06
32.58
33.11
33.64
34.17
34.69
35.22
35.75
36.28
29.00
29.51
30.02
30.53
31.04
31.55
32.06
32.56
33.07
33.58
34.09
27.00
27.49
27.98
28.47
28.96
29.45
29.94
30.44
30.93
31 .42
31.91
25.00
25.47
25.94
26.42
26.89
27.36
27.83
28.31
28.78
29.25
29.72
23.00
23.44
23.87
24.31
24.74
25.18
25.61
26.05
26.48
26.92
27.35
21 .oo
21.42
21 .83
22.25
22.67
23.08
23.50
23.92
24.33
24.75
25.17
11
12
13
14
15
16
17
18
19
20
39.11
39.67
40.22
40.78
41.33
41 .89
42.44
43.00
43.56
44.11
36.81
37.33
37.86
38.39
38.92
39.44
39.97
40.50
41.03
41 .56
34.60
35.11
35.62
36.13
36.64
37.15
37.66
38.17
38.68
39.19
32.40
32.89
33.38
33.87
34.36
34.85
35.34
35.63
36.32
36.81
30.19
30.67
31.14
31 .61
32.08
32.56
33.03
33.50
33.97
34.44
27.79
28.22
28.66
29.09
29.53
29.96
30.40
30.83
31 .27
31.70
25.56
26.00
26.42
26.83
27.25
27.67
28.08
28.50
28.92
29.33
21
22
23
24
25
26
27
28
29
30
44.67
45.22
45.78
46.33
46.89
47.44
48.00
48.56
49.11
49.67
42.08
42.61
43.14
43.67
44.19
44.72
45.25
45.78
46.31
46.83
39.69
40.20
40.71
41.22
41.73
42.24
42.75
43.26
43.77
44.28
37.31
37.80
38.29
30.78
39.27
39.76
40.25
40.74
41 .23
41 .72
34.92
35.39
35.86
36.33
36.81
37.28
37.75
38.22
38.69
39.17
32.14
32.57
33.01
33.44
33.08
34.31
34.75
35.19
35.62
36.06
29.75
30.17
30.58
31 .oo
31.42
31 .83
32.25
32.67
33.08
33.50
31
32
33
34
35
36
37
38
39
40
50.22
50.78
51.33
51 .89
52.44
53.00
53.56
54. I1
54.61
55.22
47.36
47.89
48.42
48.94
49.47
50.00
50.53
51 .06
51 .58
52.1
I
44.79
45.30
45.81
46.31
46.82
47.33
47.84
48.35
48.86
49.37
42.21
42.70
43.19
43.69
44.18
44.67
45.16
45.65
46.14
46.63
39.64
40.11
40.58
41 .06
41.53
42.00
42.47
42.94
43.92
43.89
36.49
36.93
37.36
37.80
38.23
38.67
39.10
39.54
39.97
40.41
33.92
34.33
34.75
35.17
35.58
36.00
36.42
36.83
37.25
37.67
41
42
43
44
45
46
47
48
49
50
55.18
56.33
56.89
57.44
58.00
58.56
59.11
59.67
60.22
60.78
52.64
53.17
53.69
54.22
54.75
55.28
55.81
56.33
56.86
57.39
49.88
50.39
50.90
51.41
51.92
52.43
52.94
53.44
53.95
54.46
47.12
47.61
48.10
48.59
49.08
49.57
50.06
50.56
51.05
51.54
44.36
44.83
45.31
45.78
46.25
46.72
47.19
47.67
48.14
48.61
40.84
41 .28
41.71
42.15
42.58
43.02
43.45
43.89
44.32
44.76
38.08
38.50
38.92
39.33
39.75
40.17
40.58
41 .oo
41 .42
41 .83
TOP
1
2
3
4
5
6
7
8
9
10
CLASS
CIRC.
INCHES
60
3
CLASS
H-2
CIRC.
INCHES
TRANSMISSION
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
CLASS
H-2
CIRC.
INCHES
51
61.33
-----------------------GROUND
57.92
52
53
54
55
56
57
58
59
60
58.44
58.97
59.50
60.03
60.56
61 .08
61 .61
62.14
62.67
61 .89
62.44
63.00
63.56
64.1
I
64.67
65.22
65.78
66.33
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
TOP
CLASS
H-l
CIRC.
INCHES
1
CLASS
CIRC.
INCHES
2
60 FOOT
CLASS
3
CIRC.
1 NCHES
52.03
49.08
0 INCHES)-------
45.19
55.48
55.99
56.50
57.01
57.52
58.03
58.54
59.05
59.56
52.52
53.01
53.50
53.99
54.48
54.97
55.46
55.95
56.44
45.63
46.06
46.50
46.94
47.37
47.81
48.24
48.68
49.11
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
LINE
54.97
CLASS
CIRC.
INCHES
(8
FEET,
49.56
50.03
50.50
50.97
51.44
51 .92
52.39
52.86
53.33
1
CLASS
CIRC.
INCHES
2
CLASS
CIRC.
INCHES
POLE-Con.
CLASS
CIRC.
INCHES
--------
4
42.25
42.67
43.08
43.50
43.92
44.33
44.75
45.17
45.58
46.00
65
3
FOOT POLE
CLASS
4
CIRC.
INCHES
1
2
3
4
5
6
7
8
9
10
33.00
33.54
34.08
34.63
35.17
35.71
36.25
36.80
37.34
37.88
38.42
31 .oo
31 .52
32.03
32.55
33.07
33.58
34.10
34.62
35.14
35.65
36.17
29.00
29.50
30.00
30.50
31 .oo
31.50
32.00
32.50
33.00
33.50
34.00
27.00
27.47
27.95
28.42
28.90
29.37
29.85
30.32
30.80
31 .27
31.75
25.00
25.45
25.90
26.35
26.80
27.25
27.69
28.14
28.59
29.04
29.49
23.00
23.42
23.85
24.27
24.69
25.12
25.54
25.97
26.39
26.81
27.24
21 .oo
21.41
21 .81
22.22
22.63
23.03
23.44
23.85
24.25
24.66
25.07
11
12
13
14
15
16
17
18
19
20
38.97
39.51
40.05
40.59
41.14
41.68
42.22
42.76
43.31
43.85
36.69
37.20
37.72
38.24
38.75
39.27
39.79
40.31
40.82
41.34
34.50
35.00
35.50
36.00
36.50
37.00
37.50
38.00
38.50
39.00
32.22
32.69
33.17
33.64
34.12
34.59
35.07
35.54
36.02
36.49
29.94
30.39
30.84
31 .29
31.74
32.19
32.64
33.08
33.53
33.98
27.66
28.08
28.51
28.93
29.36
29.78
30.20
30.63
31.05
31.47
25.47
25.88
26.29
26.69
27.10
27.51
27.92
28.32
28.73
29.14
21
22
23
24
25
26
27
28
29
30
44.39
44.93
45.47
46.02
46.56
47.10
47.64
48.19
48.73
49.27
41.86
42.37
42.89
43.41
43.92
44.44
44.96
45.47
45.99
46.51
39.50
40.00
40.50
41 .oo
41.50
42.00
42.50
43.00
43.50
44.00
36.97
37.44
37.92
38.39
38.86
39.34
39.81
40.29
40.76
41 .24
34.43
34.88
35.33
35.78
36.23
36.68
37.13
37.58
38.03
38.47
31.90
32.32
32.75
33.17
33.59
34.02
34.44
34.86
35.29
35.71
29.54
29.95
30.36
30.76
31.17
31 .58
31 .98
32.39
32.80
33.20
APPENDIX
393
B
Table B-4.-Pole circumferences for western red cedar-continued
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
CLASS
H-2
CIRC.
1 NCHES
CLASS
H-l
CIRC.
1 NCHES
CLASS
CIRC.
INCHES
1
CLASS
CIRC.
INCHES
2
65 FOOT
CLASS
3
CIRC.
INCHES
POLE--Con.
CLASS
CIRC.
INCHES
31
32
33
34
35
36
3-I
38
39
40
49.81
50.36
50.90
51.44
51.98
52.53
53.07
53.61
54.15
54.69
47.03
47.54
48.06
48.58
49.09
49.61
50.13
50.64
51.16
51 .68
44.50
45.00
45.50
46.00
46.50
47.00
47.50
48.00
48.50
49.00
41.71
42.19
42.66
43.14
43.61
44.08
44.56
45.03
45.51
45.98
38.92
39.37
39.82
40.27
40.72
41.17
41 .62
42.07
42.52
42.97
36. 14
36.56
36.98
37.41
37.83
38.25
38.68
39.10
39.53
39.95
33.61
34.02
34.42
34.83
35.24
35.64
36.05
36.46
36.86
37.27
41
42
43
44
45
46
47
4a
49
50
55.24
55.78
56.32
56.06
57.41
57.95
58.49
59.03
59.58
60.12
52.19
52.71
53.23
53.75
54.26
54.78
55.30
55.81
56.33
56.85
49.50
50.00
50.50
51 .oo
51.50
52.00
52.50
53.00
53.50
54.00
46.46
46.93
47.41
47.88
48.36
48.83
49.31
49.78
50.25
50.73
43.42
43.86
44.31
44.76
45.21
45.66
46.11
46.56
47.01
47.46
40.37
40.80
41.22
41 .64
42.07
42.49
42.92
43.34
43.76
44.19
37.68
30.08
38.49
38.90
39.31
39.71
40.12
40.53
40.93
41.34
51
52
53
54
55
56
60.66
61 .20
61 .75
62.29
62.03
63.37
------
47.91
48.36
48.81
49.25
49.70
50.15
44.61
45.03
45.46
45.88
46.31
46.73
-----
41.75
42.15
42.56
42.97
43.37
43.78
57
58
59
60
63.92
64.46
65.00
65.54
51.20
51.68
52.15
52.63
53.10
53.58
6 INCHES)------54.05
54.53
55.00
55.47
50.60
51.05
51.50
51.95
47.15
47.58
48.00
48.42
44.19
44.59
45.00
45.41
61
62
63
64
65
66.08
66.63
67.17
67.71
68.25
55.95
56.42
56.90
57.37
57.85
52.40
52.85
53.30
53.75
54.19
48.85
49.27
49.69
50.12
50.54
45.81
46.22
46.63
47.03
47.44
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
INCHES
FEET
TOP
2
3
4
5
6
7
8
9
10
33.00
33.53
34.06
34.59
35.13
35.66
36.19
36.72
37.25
37.70
38.31
57.36
57.88
58.40
58.92
59.43
59.95
---GROUND
60.47
60.98
61 .50
62.02
62.53
63.05
63.57
64.08
64.60
54.50
55.00
55.50
56.00
56.50
57.00
LINE
(a
57.50
58.00
58.50
59.00
FEE1
59.50
60.00
60.50
61 .OO
61 .50
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
31 .oo
31.51
32.02
32.52
33.03
33.54
34.05
34.55
35.06
35.57
36.08
29.00
29.48
29.97
30.45
30.94
31 .42
31.91
32.39
32.88
33.36
33.84
CLASS
CIRC.
INCHES
27
27
27
28
28
29
29
30
30
31
31
00
46
92
38
a4
30
77
23
69
15
61
1
CLASS
CIRC.
INCHES
25.00
25.44
25.88
26.31
26.75
27.19
27.63
28.06
28.50
28.94
29.38
2
CLASS
CIRC.
INCHES
23
23
23
24
24
25
25
25
26
26
27
70
3
00
41
a3
24
66
07
48
90
31
73
14
4
FOOT POLE
CLASS
4
CIRC.
INCHES
21 .oo
21.39
21.78
22.17
22.56
22.95
23.34
23.73
24.13
24.52
24.91
394
TRANSMISSION
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
70
18
19
20
38.84
39.38
39.91
40.44
40.97
41.50
42.03
42.56
43.09
43.63
36.59
37.09
37.60
38.11
38.62
39.13
39.63
40.14
40.65
41.16
34.33
34.81
35.30
35.78
36.27
36.75
37.23
37.72
38.20
38.69
32.07
32.53
32.99
33.45
33.91
34.38
34.84
35.30
35.76
36.22
29.81
30.25
30.69
31.13
31 .56
32.00
32.44
32.88
33.31
33.75
27.55
27.97
28.38
28.80
29.21
29.63
30.04
30.45
30.87
31 .28
25.30
25.69
26.08
26.47
26.86
27.25
27.64
28.03
28.42
28.81
21
22
23
24
25
26
27
28
29
30
44.16
44.69
45.22
45.75
46.28
46.81
47.34
47.88
48.41
48.94
41.66
42.17
42.68
43.19
43.70
44.20
44.71
45.22
45.73
46.23
39.17
39.66
40.14
40.63
42.08
42.56
43.05
43.53
36.68
37.14
37.60
38.06
38.52
38.98
39.45
39.91
40.37
40.83
34.19
34.63
35.06
35.50
35.94
36.38
36.81
37.25
37.69
38.13
31.70
32.11
32.52
32: 94
33.35
33.77
34.18
34.59
35.01
35.42
29.20
29.59
29.98
30.38
30.77
31.16
31.55
31.94
32.33
32.72
31
32
33
34
35
36
37
38
39
40
49.47
50.00
50.53
51 .06
51.59
52.13
52.66
53.19
53.72
54.25
46.74
47.25
47.76
48.27
48.77
49.28
49.79
50.30
50.80
51.31
44.02
44.50
44.98
45.47
45.95
46.44
46.92
47.41
47.89
48.38
41.29
41.75
42.21
42.67
43.13
43.59
44.05
44.52
44.98
45.44
38.56
39.00
39.44
39.88
40.31
40.75
41.19
41 .63
42.06
42.50
35.84
36.25
36.66
37.08
37.49
37.91
38.32
38.73
39.15
39.56
33.11
33.50
33.89
34.28
34.67
35.06
35.45
35.84
36.23
36.63
41
42
43
44
45
46
47
48
49
50
54.78
55.31
55.84
56.38
56.91
57.44
57.97
58.50
59.03
59.56
51 .82
52.33
52.84
53.34
53.85
54.36
54.87
55.38
55.88
56.39
48.86
49.34
49.83
50.31
50.80
51 .28
51.77
52.25
52.73
53.22
45.90
46.36
46.82
47.28
47.74
48.20
48.66
49.13
49.59
50.05
42.94
43.38
43.81
44.25
44.69
45.13
45.56
46.00
46.44
46.88
39.98
40.39
40.80
41.22
41 .63
42.05
42.46
42.88
43.29
43.70
37.02
37.41
37.80
38.19
38.58
38.97
39.36
39.75
40.14
40.53
51
52
53
54
55
56
57
58
59
60
60.09
60.63
61.16
61 .69
62.22
62.75
63.28
63.81
64.34
64.88
56.90
57.41
57.91
56.42
58.93
59.44
59.95
60.45
60.96
61.47
53.70
54.19
54.67
55.16
55.64
56.13
56.61
57.09
57.58
58.06
50.51
50.97
51.43
51.89
52.35
52.81
53.27
53.73
54.20
54.66
47.31
47.75
48. 19
48.63
49.06
49.50
49.94
50.38
50.81
51 .25
44.12
44.53
44.95
45.36
45.77
46.19
46.60
47.02
47.43
47.84
40.92
41.31
41.70
42.09
42.48
42.88
43.27
43.66
44.05
44.44
11
12
13
14
15
16
17
41.11
41.59
1
CLASS
CIRC.
INCHES
2
CLASS
CIRC.
INCHES
3
POLE-con.
CLASS
H-l
ClRC.
INCHES
CLASS
CIRC.
INCHES
FOOT
CLASS
H-2
CIRC.
INCHES
CLASS
CIRC.
INCHES
4
APPENDIX
395
I3
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
70
CLASS
H-2
CIRC.
-----------------------GROUND
51
65.41
62
65.94
63
66.41
64
67.00
65
67.53
66
68.06
67
68.59
68
69.13
69
69.66
70
70.19
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
CLASS
H-l
CIRC.
INCHES
INCHES
LINE
(9
CLASS
ClRC.
INCHES
FEET,
58.55
59.03
59.52
60.00
60.48
60.97
61 .45
61 .9’t
62.42
62.91
61 .98
62.48
62.99
63.50
64.01
64.52
65.02
65.53
66.04
66.55
0
1
INCHES)
55.12
55.58
56.04
56.50
56.96
57.42
57.88
58.34
58.80
59.27
CLASS
CIRC.
INCHES
2
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
POLE--con.
3
CLASS
CIRC.
INCHES
---------
1
48.26
48.67
49.09
49.50
49.91
50.33
50.74
51.16
51.57
51.98
CLASS
CIRC.
2
44.83
45.22
45.61
46.00
46.39
46.78
47.17
47.56
47.95
48.34
75 FOOT
CLASS
3
CIRC.
INCHES
INCHES
1
2
3
4
5
6
7
8
9
10
33.00
33.51
34.03
34.54
35.06
35.57
36.09
36.60
37.12
37.63
38.14
31 .oo
31.49
31.99
32.48
32.97
33.46
33.96
34.45
34.94
35.43
35.93
29.00
29.47
29.94
30.41
30.88
31 .36
31 .83
32.30
32.77
33.24
33.71
27.00
27.45
27.90
28.35
28.80
29.25
29.70
30.14
30.59
31.04
31.49
25.00
25.43
25.86
26.28
26.71
27.14
27.57
27.99
28.42
28.85
29.28
23.00
23.41
23.81
24.22
24.62
25.03
25.43
25.84
26.25
26.65
27.06
11
12
13
14
15
16
17
18
19
20
38.66
39.17
39.69
40.20
40.72
41.23
41.75
42.26
42.78
43.29
36.42
36.91
37.41
37.90
38.39
38.88
39.38
39.87
40.36
40.86
34.18
34.65
35.12
35.59
36.07
36.54
37.01
37.48
37.95
38.42
31.94
32.39
32.84
33.29
33.74
34.19
34.64
35.09
35.54
35.99
29.70
30.13
30.56
30.99
31.41
31 .84
32.27
32.70
33.12
33.55
27.46
27.87
28.28
28.68
29.09
29.49
29.90
30.30
30.71
31.12
21
22
23
24
25
26
27
28
29
30
43.80
44.32
44.83
45.35
45.86
46.38
46.89
47.41
47.92
48.43
41.35
41 .84
42.33
42.83
43.32
43.81
44.30
44.80
45.29
45.78
38.89
39.36
39.83
40.30
40.78
41 .25
41 .72
42.19
42.66
43.13
36.43
36.88
37.33
37.78
38.23
38.68
39.13
39.58
40.03
40.48
33.98
34.41
34.83
35.26
35.69
36.12
36.54
36.97
37.40
37.83
31 .52
31.93
32.33
32.74
33.14
33.55
33.96
34.36
34.77
35.17
TOP
‘-t
.-----
51.69
52.13
52.56
53.00
53.44
53.88
54.31
54.75
55.19
55.63
CLASS
H-2
CIRC.
INCHES
FOOT
CLASS
CIRC.
INCHES
POLE
TRANSMISSION
396
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
ClRC.
INCHES
CLASS
CIRC.
INCHES
1
CLASS
ClRC.
INCHES
75
2
FOOT POLE-con.
CLASS
3
CIRC.
INCHES
31
32
33
34
35
36
37
38
39
40
48.95
49.46
49.98
50.49
51.01
51.52
52.04
52.55
53.07
53.50
46
46
47
47
48
48
49
49
50
50
28
77
26
75
25
74
23
72
22
71
43.60
44.07
44.54
45.01
45.49
45.96
46.43
46.90
47.37
47.84
40.93
41.38
41.83
42.28
42.72
43.17
43.62
44.07
44.52
44.97
38.25
30.60
39.11
39.54
39.96
40.39
40.82
41.25
41.67
42.10
35.50
35.99
36.39
36.80
37.20
37.61
38.01
38.42
38.83
39.23
41
42
43
44
45
46
47
48
49
50
54.09
54.61
55.12
55.64
56.15
56.67
57.18
57.70
58.21
50.72
51
51
52
52
53
53
54
54
55
55
20
70
19
68
17
67
16
65
14
64
48.31
48.78
49.25
49.72
50.20
50.67
51.14
51.61
52.08
52.55
45.42
45.87
46.32
46.77
47.22
47.67
48.12
48.57
49.01
49.46
42.53
42.96
43.38
43.81
44.24
44.67
45.09
45.52
45.95
46.38
39.64
40.04
40.45
40.86
41.26
41.67
42.07
42.48
42.88
43.29
51
52
53
54
55
56
57
58
59
60
59.24
59.75
60.27
60.78
61.30
61.81
62.33
62.84
63.36
63.87
56
56
57
57
58
58
59
59
60
60
13
62
12
61
10
59
09
58
07
57
53.02
53.49
53.96
54.43
54.91
55.38
55.85
56.32
56.79
57.26
49.91
50.36
50.81
51.26
51.71
52.16
52.61
53.06
53.51
53.96
46.80
47.23
47.66
48.09
48.51
48.94
49.37
49.80
50.22
50.65
43.70
44.10
44.51
44.91
45.32
45.72
46.13
46.54
46.94
47.35
61
62
63
64
65
---
64.38
64.90
65.41
65.93
66.44
_------__-
51.08
51.51
51.93
52.36
52.79
47.75
48.16
48.57
48.97
49.38
66
67
68
69
70
66.96
67.47
67.99
68.50
69.01
56.65
57.10
57.55
58.00
58.45
53.22
53.64
54.07
54.50
54.93
49.78
50.19
50.59
51.00
51.41
71
72
73
74
75
69.53
70.04
70.56
71.07
71.59
58.90
59.35
59.80
60.25
60.70
55.36
55.78
56.21
56.64
57.07
51.81
52.22
52.62
53.03
53.43
____
61 06
61 55
62 04
62 54
63 03
GROUND LINE
63.52
64.01
64.51
65.00
65.49
65.99
66.48
66.97
67.46
67.96
(
57.73
58.20
58.67
59.14
59.62
9 FEET,
60.09
60.56
61.03
61.50
61.97
62.44
62.91
63.38
63.06
64.33
6
54.41
54.86
55.30
55.75
56.20
*NCHES)---------.
APPENDIX
B
397
Table B-4.-Pole circumferences for western red cedar-continued
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
TOP
I
2
3
4
5
6
7
8
9
10
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
1
CLASS
CIRC.
2
80 FOOT
CLASS
3
CIRC.
INCHES
INCHES
INCHES
25.00
25.42
25.84
26.26
26.68
27.09
27.51
27.93
28.35
28.77
29.19
23.00
23.39
23.78
24.18
24.57
24.96
25.35
25.74
26.14
26.53
26.92
33.00
33.51
34.01
34.52
35.03
35.53
36.04
36.55
37.05
37.56
38.07
31 .oo
31.49
31.97
32.46
32.95
33.43
33.92
34.41
34.89
35.38
35.86
29.00
29.46
29.92
30.38
30.84
31.30
31 .76
32.22
32.68
33.14
33.59
27.00
27.44
27.88
20.32
28.76
29.20
29.64
30.07
30.51
30.95
31.39
38.57
39.08
39.59
40.09
40.60
34.05
34.51
34.97
35.43
35.89
36.35
36.81
37.27
37.73
38.19
31 .83
32.27
32.71
33.15
33.59
34.03
34.47
34.91
35.34
35.78
29.61
30.03
30.45
30.86
31.28
31.70
32.12
32.54
32.96
33.38
27.31
27.70
28.09
28.49
28.88
29.27
29.66
30.05
30.45
30.84
15
16
17
41.11
41 .61
18
19
20
42.12
42.63
43.14
36.35
36.84
37.32
37.81
38.30
38.78
39.27
39.76
40.24
40.73
21
22
23
24
25
26
27
28
29
30
43.64
44.15
44.66
45.16
45.67
46.18
46.68
47.19
47.70
48.20
41.22
41.70
42.19
42.68
43.16
43.65
44.14
44.62
45.11
45.59
38.65
39.11
39.57
40.03
40.49
40.95
41.41
41.86
42.32
42.78
36.22
36.66
37.10
37.54
37.98
38.42
38.86
39.30
39.74
40.18
33.80
34.22
34.64
35.05
35.47
35.89
36.31
36.73
37.15
37.57
31 .23
31 .62
32.01
32.41
32.80
33.19
33.58
33.97
34.36
34.76
31
32
33
34
35
36
37
38
39
40
48.71
49.22
49.72
50.23
50.74
51 .24
51.75
52.26
52.76
53.27
46.08
46.57
47.05
47.54
48.03
48.51
49.00
49.49
49.97
50.46
43.24
43.70
44.16
44.62
45.08
45.54
46.00
46.46
46.92
47.38
40.61
41.05
41.49
41.93
42.37
42.81
43.25
43.69
44.13
44.57
37.99
38.41
38.82
39.24
39.66
40.08
40.50
40.92
41.34
41 .76
35.15
35.54
35.93
36.32
36.72
37.11
37.50
37.89
38.28
38.68
41
42
43
44
45
46
47
48
49
50
53.78
54.28
54.79
55.30
55.80
56.31
56.02
57.32
57.83
58.34
50.95
51.43
51.92
52.41
52.89
53.38
53.86
54.35
54.84
55.32
47.84
48.30
48.76
49.22
49.68
50.14
50.59
51.05
51.51
51.97
45.01
45.45
45.89
46.32
46.76
47.20
47.64
48.08
48.52
48.96
42.18
42.59
43.01
43.43
43.85
44.27
44.69
45.11
45.53
45.95
39.07
39.46
39.85
40.24
40.64
41.03
41 .42
41 .81
42.20
42.59
11
12
13
14
POLE
398
TRANSMISSION
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
51
52
53
54
55
56
57
58
59
60
58.84
59.35
59.86
60.36
60.87
61.38
61 .89
62.39
62.90
63.41
61
::
64
65
66
67
68
69
__------
63.91
64.42
64.93
65.43
65.94
66.45
66.95
67.46
67.97
-----------
70
68.47
71
72
73
74
75
76
77
78
79
80
68.98
69.49
69.99
70.50
71 .Ol
71.51
72.02
72.53
73.03
73.54
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
INCHES
FEET
TOP
1
2
3
4
5
6
7
8
9
10
33.00
33.49
33.99
34.46
34.97
35.47
35.96
36.46
36.95
37.44
37.94
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
52.43
52.89
53.35
53.81
54.27
54.73
55.19
55.65
56.11
56.57
49.40
49.84
50.28
50.72
51.16
51.59
52.03
52.47
1
INCHES
80
2
CLASS
CIRC.
INCHES
FOOT POLE-Con.
CLASS
3
CIRC.
1NCHES
53.35
46.36
46.78
47.20
47.62
48.04
48.46
48.86
49.30
49.72
50.14
53.79
54.23
54.67
55.11
55.55
55.99
56.43
56.86
57.30
50.55
50.97
51 .39
51.81
52.23
52.65
53.07
53.49
53.91
57.74
54.32
50.43
61 .62
62.08
62.54
63.00
63.46
63.92
64.38
64.84
65.30
65.76
58.18
58.62
59.06
59.50
59.94
60.38
60.82
61 .26
61 .70
62.14
54.74
55.16
55.58
56.00
56.42
56.84
57.26
57.68
58.09
58.51
50.82
51.22
51 .61
52.00
52.39
52.78
53.18
53.57
53.96
54.35
CLASS
CIRC.
INCHES
CLASS
H-l
CIRC.
1 NCHES
31 .oo
31.47
31.95
32.42
32.90
33.37
33.85
34.32
34.80
35.27
35.75
29.00
29.45
29.90
30.35
30.80
31 .25
31.70
32.15
32.59
33.04
33.49
27.00
27.43
27.86
28.29
28.72
29.15
29.58
30.01
30.44
30.87
31.30
55.81
56.30
56.78
57.27
57.76
58.24
58.73
59.22
59.70
60.19
60.68
61.16
61.65
62.14
62.62
63.11
63.59
64.08
64.57
-GROUND
65.05
L INE
65.54
66.03
66.51
67.00
67.49
67.97
68.46
68.95
69.43
69.92
CLASS
H-2
CIRC.
57.03
57.49
57.95
58.41
58.86
59.32
59.78
60.24
60.70
( 10 FEET
61.16
52.91
0
INCHES )------------
INCHES
1
42.99
43.38
43.77
44.16
44.55
44.95
45.34
45.73
46.12
46.51
CLASS
CIRC.
INCHES
25
25
25
26
26
27
27
27
28
28
29
00
41
81
22
62
03
43
84
24
65
05
46.91
47.30
47.69
48.08
48.47
48.86
49.26
49.65
50.04
----_--
2
85 FOOT POLE
CLASS
3
CIRC.
INCHES
23.00
23.39
23.77
24.16
24.54
24.93
25.32
25.70
26.09
26.47
26.86
APPENDIX
399
B
Table B-4.-Pole circumferences for western red cedar-continued
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
CLASS
CIRC.
INCHES
85
2
FOOT POLE-Con.
CLASS
3
CIRC.
INCHES
11
12
13
I4
15
16
17
18
19
20
38.43
30.92
39.42
39.91
40.41
40.90
41.39
41.69
42.36
42.87
36.22
36.70
37.17
37.65
39.12
38.59
39.07
39.54
40.02
40.49
33.94
34.39
34.84
35.29
35.74
36.19
36.64
37.09
37.54
37.99
31.73
32.16
32.59
33.03
33.46
33.89
34.32
34.75
35.18
35.61
29.46
29.86
30.27
30.67
31.08
31.48
31.89
32.29
32.70
33.10
27.25
27.63
28.02
28.41
28.79
29.18
29.56
29.95
30.34
30.72
21
22
23
24
25
26
:i
29
30
43.37
43.06
44.35
44.85
45.34
45.84
46.33
46.82
47.32
47.81
40.97
41.44
41.92
42.39
42.87
43.34
43.82
44.29
44.77
45.24
38.44
38.89
39.34
39.78
40.23
40.68
41.13
41.58
42.03
42.48
36.04
36.47
36.90
37.33
37.76
38.19
38.62
39.05
39.48
39.91
33.51
33.91
34.32
34.72
35.13
35.53
35.94
36.34
36.75
37.15
31.11
31.49
31.88
32.27
32.65
33.04
33.42
33.81
34.20
34.58
31
32
33
34
35
36
37
38
39
40
48.30
48.80
49.29
49.78
50.28
50.77
51.27
51.76
52.25
52.75
45.72
46.19
46.66
47.14
47.61
48.09
48.56
49.04
49.51
49.99
42.93
43.38
43.83
44.28
44.73
45.18
45.63
46.08
46.53
46.97
40.34
40.77
41.20
41.63
42.06
42.49
42.92
43.35
43.78
44.22
37.56
37.96
38.37
38.77
39.18
39.58
39.99
40.39
40.80
41.20
34.97
35.35
35.74
36.13
36.51
36.90
37.28
37.67
38.06
38.44
41
42
43
44
45
46
47
40
49
50
53.24
53.73
54.23
54.72
55.22
55.71
56.20
56.70
57.19
51.68
50.46
50.94
51.41
51.89
52.36
52.84
53.31
53.78
54.26
54.73
47.42
47.87
48.32
48.77
49.22
49.67
50.12
50.57
51.02
51.37
44.65
45.08
45.51
45.94
46.37
46.80
47.23
47.66
48.09
48.52
41.61
42.01
42.42
42.82
43.23
43.63
44.04
44.44
44.85
45.25
38.83
39.22
39.60
39.99
40.37
40.76
41.15
41.53
41.92
42.30
51
52
53
54
55
56
57
58
59
60
58.18
58.61
59.16
59.66
60.15
60.65
61.14
61.63
62.13
62.62
55.21
55.68
56.16
56.63
51.11
51.58
58.06
58.53
59.01
59.48
51.92
52.37
52.82
53.27
53.72
54.16
54.61
55.06
55.51
55.96
48.95
49.38
49.81
50.24
50.67
51.10
51.53
51.96
52.39
52.82
45.66
46.06
46.47
46.87
47.28
47.68
48.09
48.49
48.90
49.30
42.69
43.08
43.46
43.85
't4.23
44.62
45.01
45.39
45.78
46.16
TRANSMISSION
400
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
61
62
63
64
65
66
61
68
69
70
71
72
13
74
75
76
77
78
79
80
81
82
83
84
63.11
63.61
64. IO
64.59
65.09
65.58
66.08
66.51
67.06
67.56
68.05
68.54
69.04
69.53
----------_
70.03
70.52
71 .Ol
71.51
72.00
72.49
72.99
73.48
73.97
74.47
74.96
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
TOP
1
2
33.00
33.48
33.96
34.45
34.93
35.41
35.89
36.37
36.86
37.34
37.82
11
38.30
12
13
14
15
16
17
18
19
38.79
20
39.27
39.75
40.23
40.71
41.20
41.68
42.16
42.64
CLASS
H-2
CIRC.
CLASS
H-l
CIRC.
INCHES
INCHES
59.96
60.43
60.91
61 .38
61 .a5
62.33
56.41
56.86
57.31
63.28
63.75
64.23
57.76
58.21
58.66
59.11
59.56
60.01
60.46
64.70
65.18
65.65
66.13
60.91
61 .35
61 .80
62.25
62.80
-GROUND
L INE
66.60
67.08
61.55
68.03
68.50
68.97
69.45
69.92
70.40
( 10
FEET
62.70
63.15
63.60
64.05
64.50
64.95
CLASS
CIRC.
1
INCHES
53.25
53.68
54.11
54.54
54.97
55.41
85
CLASS
2
CIRC.
1 NCHES
FOOT
POLE-Con.
CLASS
3
CIRC.
INCHES
49.71
50.11
50.52
50.92
51.33
51.73
52.14
52.54
52.95
53.35
46.55
46.94
47.32
47.71
53.76
54.16
54.57
58.85
54.97
6 INCHES I---------59.28
55.38
55.78
59.71
56.19
60.14
56.59
60.57
57.00
61 .OO
61 .43
57.41
50.41
50.80
51.18
51.51
----51.96
52.34
52.73
53.11
53.50
55.84
56.27
56.70
57.13
48.09
48.48
48.87
49.25
49.64
50.03
57.56
57.99
58.42
61 .86
62.29
62.72
63.15
63.58
53.89
57.81
58.22
54.27
54.66
55.04
55.43
70.87
71.35
65.40
65.85
66.30
66.75
67.20
CLASS
H-2
CIRC.
CLASS
H-l
CIRC.
INCHES
INCHES
INCHES
INCHES
31 .oo
31 .46
31.93
29.00
29.44
29.88
30.32
30.76
31.20
31 .64
27.00
21.42
25.00
25.40
23.00
27.85
28.27
28.69
29.11
25.80
23.75
24.13
24.50
24.88
25.25
25.63
26.00
32.39
32.86
33.32
33.79
34.25
34.71
35.18
35.64
36.11
36.57
37.04
37.50
37.96
38.43
38.89
39.36
39.82
40.29
CLASS
CIRC.
58.62
59.03
59.43
1
CLASS
CIRC.
32.08
29.54
29.96
26.20
26.60
26.99
21.39
27.79
32.52
32.96
33.40
30.38
30.80
31 .23
28.19
28.59
28.99
31 .65
29.39
29.79
30.18
33.85
34.29
34.73
35.17
35.61
36.05
36.49
36.93
37.31
37.81
32.07
32.49
32.92
33.34
33.76
34.18
34.61
35.03
35.45
30.58
30.98
31.38
31.78
32. la
32.58
32.98
55.82
2
90 FOOT
CLASS
3
CIRC.
1 NCHES
23.38
26.38
26.75
27.13
27.50
27.88
28.25
28.63
29.00
29.38
29.75
30.13
30.50
POLE
APPENDIX
401
B
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
CLASS
H-2
CIRC.
1NCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
SO FOOT
POLE-Con.
2
CLASS
3
CIRC.
INCHES
INCHES
CLASS
CIRC.
22
23
24
25
26
27
28
29
30
43.12
43.61
44.09
44.57
45.05
45.54
46.02
46.50
46.98
47.46
40.75
41.21
41 .68
42.14
42.61
43.07
43.54
44.00
44.46
44.93
38.25
30.69
39.13
39.57
40.01
40.45
40.89
41.33
41.77
42.21
35.88
36.30
36.72
37.14
37.57
37.99
38.41
38.83
39.26
39.68
33.38
33.77
34.17
34.57
34.97
35.37
35.77
36.17
36.57
36.96
30.88
31.25
31 .63
32.00
32.38
32.75
33.13
33.50
33.88
34.25
31
32
33
34
35
36
37
38
39
40
41.95
48.43
48.91
49.39
49.87
50.36
50.84
51 .32
51 .80
52.29
45.39
45.86
46.32
46.79
47.25
47.71
48.18
48.64
49.11
49.57
42.65
43.10
43.54
43.98
44.42
44.86
45.30
45.74
46.18
46.62
40.10
40.52
40.95
41.37
41 .I9
42.21
42.64
43.06
43.48
43.90
31.36
37.76
38.16
38.56
38.96
39.36
39.76
40.15
40.55
40.95
34.63
35.00
35.38
35.75
36.13
36.50
36.88
37.25
37.63
38.00
41
52.77
53.25
53.73
54.21
54.70
55.18
55.66
56.14
56.62
57.11
50.04
50.50
50.96
51.43
51 .89
52.36
52.82
53.29
53.75
54.21
47.06
47.50
47.94
48.38
48.82
49.26
49.70
50.14
50.58
51.02
44.33
44.75
45.17
45.60
46.02
46.44
46.86
47.29
47.71
48.13
41.35
41.75
42.15
42.55
42.95
43.35
43.74
44.14
44.54
44.94
38.38
38.75
39.13
39.50
39.88
40.25
40.63
41 .oo
41 .38
41.75
57
58
59
60
57.59
58.07
50.55
59.04
59.52
60.00
60.48
60.96
61 .45
61 .93
54.68
55.14
55.61
56.07
56.54
57.00
57.46
57.93
58.39
58.06
51 .46
51.90
52.35
52.79
53.23
53.67
54.11
54.55
54.99
55.43
48.55
48.98
49.40
49.82
50.24
50.67
51.09
51.51
51.93
52.36
45.34
45.74
46.14
46.54
46.93
47.33
47.73
48.13
48.53
40.93
42.13
42.50
42.88
43.25
43.63
44.00
44.38
44.75
45.13
45.50
61
62
63
64
65
66
67
68
69
70
62.41
62.89
63.37
63.66
64.34
64.82
65.30
65.79
66.27
66.75
59.32
59.79
60.25
60.71
61.18
61 .64
62.11
62.57
63.04
63.50
55.87
56.31
56.75
57.19
57.63
58.07
58.51
58.95
59.39
59.83
52.78
53.20
53.62
54.05
54.47
54.89
55.32
55.74
56.16
56.58
49.33
49.73
50.12
50.52
50.92
51 .32
51 .72
52.12
52.52
52.92
45.88
46.25
46.63
47.00
47.38
47.75
48.13
48.50
48.88
49.25
21
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
TRANSMISSION
402
LINE DESIGN
MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
CLASS
H-3
FROM TOP
CIRC.
FEET
INCHES
WESTERN
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
63.96
64.43
64.89
65.36
65.82
66.29
66.75
67.21
INCHES
71
72
73
74
75
76
77
78
----79
80
67.23
67.71
68.20
68.68
69.16
69.64
70.12
70.61
71.09
71.57
67.68
68.14
60.27
60.71
61.15
61 .60
62.04
62.48
62.92
63.36
( 1 1 FEET
63.80
64.24
81
82
83
84
85
86
87
88
89
so
72.05
72.54
73.02
73.50
73.98
74.46
74.95
75.43
75.91
76.39
68.61
69.07
69.54
70.00
70.46
70.93
71.39
71.86
72.32
72.79
64.68
65.12
65.56
66.00
66.44
66.88
67.32
67.76
68.20
68.64
.-GROUND
RED CEDAR
DISTANCE
FROM TOP
FEET
L INE
CLASS
H-3
CIRC.
INCHES
CLASS
H-2
CIRC.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
TOP
CLASS
CIRC.
INCHES
1
57.01
57.43
57.85
58.27
58.70
59.12
59.54
59.96
0
SO FOOT POLE -Con.
2
CLASS
3
CIRC.
INCHES
I TiCHiS
CLASS
CIRC.
53.32
53.71
54.11
54.51
54.91
55.31
55.71
56.11
49.63
50.00
50.38
50.75
51.13
51.50
51.88
60.39
60.81
56.51
56.90
52.25
-----52.63
53.00
61 .23
61 .65
62.08
62.50
62.92
63.35
63.77
64.19
64.61
65.04
57.30
57.70
58.10
58.50
58.90
59.30
59.70
60.10
60.49
60.89
53.38
53.75
54.13
54.50
54.88
55.25
55.63
56.00
56.38
56.75
INCHESl---
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
1 NCHES
33.00
33.47
33.94
34.42
34.89
35.36
35.83
36.30
36.78
37.25
37.72
31 .oo
31 .46
31.91
32.37
32.82
33.28
33.73
34.19
34.64
35.10
35.55
29.00
29.43
29.87
30.30
30.73
31.16
31 .60
32.03
32.46
32.89
33.33
27.00
27.41
27.82
28.23
28.64
29.05
29.46
29.87
30.28
30.69
31.10
25.00
25.39
25.78
26.16
26.55
26.94
27.33
27.71
28.10
28.49
28.88
38.19
38.66
39.13
39.61
40.08
40.55
41.02
41.49
41.97
42.44
36
36
36
37
37
38
38
39
39
40
33.76
34.19
34.62
35.06
35.49
35.92
36.35
36.79
37.22
37.65
31.51
31 .92
32.33
32.74
33.15
33.56
33.97
34.38
34.79
35.20
29.26
29.65
30.04
30.43
30.81
31.20
31.59
31 .98
32.37
32.75
01
46
92
37
83
28
74
19
65
10
I
CLASS
CIRC.
95
2
INCHES
FOOT
POLE
APPENDIX
403
B
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
CLASS
H-3
CIRC.
CLASS
H-2
CIRC.
CLASS
H-l
CIRC.
1 NCHES
CLASS
CIRC.
INCHES
INCHES
INCHES
21
42.91
22
23
24
25
26
27
28
29
30
43.38
43.85
44.33
44.80
45.27
45.74
46.21
46.69
47.16
40.56
41 .Ol
41.47
41.92
42.38
42.83
43.29
43.74
44.20
44.65
38.08
38.52
38.95
39.38
39.81
40.25
40.68
35.61
31
32
33
34
35
36
37
38
39
40
47.63
48.10
48.57
49.04
49.52
49.99
50.46
50.93
51.40
51.88
45.11
45.56
46.02
46.47
46.93
47.38
47.84
48.29
48.75
49.20
42.41
41
42
43
44
45
46
47
48
49
50
52.35
52.82
53.29
53.76
54.24
54.71
55.18
55.65
56.12
56.60
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
1
95 FOOT
CLASS
2
CIRC.
INCHES
36.02
36.43
36.84
37.25
37.66
38.07
38.48
38.89
39.30
33.14
33.53
33.92
34.30
34.69
35.08
35.47
35.85
36.24
36.63
42.84
43.28
43.71
44.14
44.57
45.01
45.44
45.87
46.30
39.71
40.12
40.53
40.94
41.35
41 .76
42.17
42.58
42.99
43.40
37.02
37.40
37.79
38.18
38.57
38.96
39.34
39.73
40.12
40.51
49.66
50.11
50.57
51.02
51.48
51.93
52.39
52.84
53.30
53.75
46.74
47.17
47.60
48.03
48.47
48.90
49.33
49.76
50.20
50.63
43.81
44.22
44.63
45.04
45.46
45.87
46.28
46.69
47.10
47.51
40.89
41 .28
41 .67
42.06
42.44
42.83
43.22
43.61
43.99
44.38
57.07
57.54
58.01
58.48
58.96
59.43
59.90
60.37
60.84
61 .31
54.21
54.66
55.12
55.57
56.03
56.48
56.94
57.39
57.85
58.30
51 .06
51.49
51.93
52.36
52.79
53.22
53.66
54.09
54.52
54.96
47.92
48.33
48.74
49.15
49.56
49.97
50.38
50.79
51.20
51.61
44.77
45.16
45.54
45.93
46.32
46.71
47.10
47.48
47.87
48.26
61 .79
62.26
62.73
63.20
63.67
64.15
64.62
65.09
65.56
66.03
58.76
59.21
59.67
60.12
60.58
61.03
61 .49
61.94
62.40
62.65
55.39
55.82
56.25
56.69
57.12
57.55
57.98
58.42
58.85
59.28
52.02
52.43
52.84
53.25
53.66
54.07
54.48
54.89
55.30
55.71
48.65
49.03
49.42
49.81
50.20
50.58
50.97
51 .36
51.75
5‘2.13
41.11
41.54
41.98
POLE-Cot-I.
TRANSMISSION
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
CLASS
H-3
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
95 FOOT
CLASS
2
CIRC.
66.51
63.31
72
73
74
75
76
77
78
79
80
66.98
67.45
67.92
68.39
68.87
69.34
69.81
70.28
70.75
63.76
64.22
64.67
65.13
65.50
66.04
66.49
66.95
67.40
59 71
60 15
60 58
61 01
61 44
61 98
62 31
62.74
63.17
63.61
56 12
56 53
56 94
57 35
57 76
59 17
58 58
58 99
59 40
59 81
52.52
52.91
53.30
53.69
54.07
54.46
54.85
55.24
55.62
56.01
81
82
83
71.22
71.70
72.17
67.86
68.31
68.77
64.04
64.47
64.90
60
60
61
22
63
04
56.40
56.79
57.17
LINE
(11
FEET.
0
INCHES)--
84
85
06
87
08
89
90
72.64
73.11
73.58
74.06
74.53
75.00
75.47
69.22
69.60
70.13
70.59
71.04
71.50
71 .96
65.34
65.77
66 20
66 63
67 07
67.50
67.93
61
61
62
62
63
63
63
45
86
27
68
09
50
91
57.56
57.95
58.34
58.72
59.11
59.50
59.89
91
92
93
94
95
75.94
76.42
76.89
77.36
77.83
72.41
72.87
73.32
73.78
74.23
68
68
69
69
70
37
80
23
66
10
64
64
65
65
65
32
73
14
55
96
60.28
60.66
61 .05
61 .44
61 .83
RED CEDAR
DISTANCE
FROM TOP
FEET
TOP
2
3
4
5
6
8
9
10
11
12
13
14
15
16
17
ia
19
20
100
CLASS
H-3
CIRC.
INCHES
33.00
33.46
33.93
34.39
34.85
35.31
35.78
36.24
36.70
37.16
37.63
38.09
38.55
39.02
39.48
39.94
40.40
40.87
41.33
41.79
42.26
CLASS
H-2
CIRC.
INCHES
31 .oo
POLE-Con.
INCHES
71
-------------GROUND
WESTERN
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
29 00
29 43
29.85
31.44
31.88
32.32
32.77
33.21
33.65
34.09
34.53
34.97
35.41
30.28
30 70
31 13
31 55
31.98
32.40
32.83
33.26
35.96
36.30
36.74
37.18
37.62
38.06
38.51
38.95
39.39
39.83
33
34
34
34
35
35
36
36
37
37
68
11
53
96
38
81
23
66
09
51
CLASS
CIRC.
1
CLASS
CIRC.
INCHES
INCHES
27.00
27.40
27.81
29.21
28.62
29.02
29.43
30.23
30.64
31.04
25.00
25.39
25.77
26.15
26.53
26.91
27.30
27.68
28.06
20.45
28.83
31.45
31 .85
32.26
32.66
33.06
33.47
33.97
34.28
34.68
35.09
29.21
29.60
29.98
30.36
30.74
31.13
31.51
31 .89
32.28
32.66
29.83
2
FOOT
POLE
APPENDIX
405
B
Table B-4.-Pole circumferences for western red cedar-continued
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
100
FOOT
CLASS
2
CIRC.
CLASS
H-3
CIRC.
INCHES
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
22
23
24
25
26
27
28
29
30
42.72
43.18
43.64
44.11
44.57
45.03
45.49
45.96
46.42
46.88
40.27
40.71
41.15
41 .60
42.04
42.48
42.92
43.36
43.80
44.24
37.94
38.36
38.79
39.21
39.64
40.06
40.49
40.91
41.34
41.77
35.49
35.89
36.30
36.70
37.11
37.51
37.91
38.32
38.72
39.13
33.04
33.43
33.81
34.19
34.57
34.96
35.34
35.72
36.11
36.49
31
32
33
34
35
36
37
38
39
40
47.35
47.81
48.27
48.73
49.20
49.66
50.12
50.59
51.05
51.51
44.69
45.13
45.57
46.01
46.45
46.89
47.34
47.78
48.22
48.66
42.19
42.62
43.04
43.47
43.89
44.32
44.74
45.17
45.60
46.02
39.53
39.94
40.34
40.74
41.15
41.55
41 .96
42.36
42.77
43.17
36.87
37.26
37.64
38.02
38.40
38.79
39.17
39.55
39.94
40.32
41
42
43
44
45
46
47
48
49
50
51.97
52.44
52.90
53.36
53.82
54.29
54.75
55.21
55.68
56. 14
49.10
49.54
43.57
43.98
44.38
44.79
45.19
45.60
46.00
46.40
46.81
47.21
40.70
41.09
50.43
50.87
51.31
51.75
52.19
52.63
53.07
46.45
46.87
47.30
47.72
48.15
48.57
49.00
49.43
49.85
50.28
42.23
42.62
43.00
43.38
43.77
44.15
51
52
53
54
55
56
57
58
59
60
56.60
57.06
57.53
57.99
58.45
58.91
59.38
59.84
60.30
60.77
53.52
53.96
54.40
54.84
55.28
55.72
56.16
56.61
57.05
57.49
50.70
51.13
51.55
51 .98
52.40
52.83
53.26
53.68
54.11
54.53
47.62
48.02
48.43
48.83
49.23
49.64
50.04
50.45
50.85
51 .26
44.53
44.91
45.30
45.68
46.06
46.45
46.83
47.21
47.60
47.98
61
62
63
64
65
66
67
68
69
70
61 .23
61 .69
62.15
62.62
63.08
63.54
64.01
64.47
64.93
65.39
57.93
58.37
58.81
59.26
59.70
60.14
60.58
61 .02
61 .46
61.90
54.96
55.38
55.81
56.23
56.66
57.09
57.51
57.94
58.36
58.79
51.66
52.06
52.47
52.87
53.28
53.68
54.09
54.49
54.89
55.30
48.36
48.74
49.13
49.51
21
49.98
1
INCHES
41.47
41.85
49.89
50.28
50.66
51.04
5 l_. 43
51 .a1
POLE-Con.
406
TRANSMISSION
LINE DESIGN
MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
71
72
73
74
75
76
77
78
79
80
81
82
83
04
05
86
87
88
------89
so
91
92
93
94
95
96
97
98
99
100
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
TOP
1
2
3
4
5
6
7
8
9
10
100
CLASS
H-3
CIRC.
INCHES
CLASS
H-2
CIRC.
INCHES
65.06
66.32
66.78
67.24
67.71
68.17
68.63
69.10
69.56
70.02
62.35
62.79
63.23
63.67
64.11
64.55
64.99
65.44
65.88
66.32
59 21
59 64
60 06
60 49
60 91
61 34
61 77
62 19
62 62
63 04
55.70
56.11
56.51
56.91
57.32
57.72
58.13
58.53
58.94
59.34
70.48
70.95
71.41
71.87
72.34
72.80
73.26
73.72
66.76
67.20
67.64
68.09
68.53
60.97
69.41
69.85
63
63
64
64
65
65
66
66
59.74
60.15
60.55
60.96
61 .36
61 .77
62.17
62.57
CLASS
H-l
CIRC.
INCHES
1
INCHES
FOOT
CLASS
CIRC.
INCHES
74.19
74.65
70.29
70.73
66.87
67.30
62.98
63.38
75.11
75.57
76.04
76.50
76.96
77.43
77.89
78.35
78.81
79.28
71.18
71 .62
72.06
72.50
72.94
73.38
73.82
74.27
74.71
75.15
67.72
68.15
68.51
69.00
69.43
69.85
70.28
70.70
71.13
71.55
63.79
64.19
64.60
65.00
65.40
65.81
66.21
66.62
67.02
67.43
59.85
60.23
60.62
61 .OO
61 .38
61 .77
62.15
62.53
62.91
63.30
CLASS
H-3
CIRC.
CLASS
H-2
CIRC.
CLASS
H-l
CIRC.
INCHES
INCHES
INCHES
CIRC.
INCHES
CIRC.
INCHES
33.00
33.45
33.91
34.36
34.82
35.27
35.73
36.18
36.64
37.09
37.55
31 .oo
31.43
31 .87
32.30
32.74
33.17
33.61
34.04
34.47
34.91
35.34
29.00
29.41
29.83
30.24
30.66
31.07
31.48
31.90
32.31
32.73
33.14
27.00
27.39
27.79
28.18
28.58
28.97
29.36
29.76
30.15
30.55
30.94
25.00
25.37
25.75
26.12
26.49
26.87
27.24
27.62
27.99
20.36
28.74
LINE
(11
FEET,
0
INCHES)
------
CLASS
POLE-Con.
2
52.19
52.57
52.96
53.34
53.72
54.11
54.49
54.87
55.26
55.64
56.02
56.40
56.79
5-l. 17
57.55
57.94
58.32
58.70
-----59.09
59.47
-----GROUND
47
89
32
74
17
60
02
45
CLASS
CIRC.
1
CLASS
105
2
FOOT
POLE
APPENDIX
407
B
Table B-4.-Pole circumferences for western red cedar-continued
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
35.78
36.21
36.65
37.08
37.52
37.95
38.38
38.82
39.25
39.69
33.56
33.97
34.38
14
15
16
17
18
19
20
38.00
38.45
38.91
39.36
39.82
40.27
40.73
41.18
41 .64
42.09
31.33
31.73
32.12
32.52
32.91
33.30
33.70
34.09
34.48
34.88
29.11
29.48
29.86
30.23
30.61
30.98
31.35
31.73
32.10
32.47
21
22
23
24
25
26
27
28
29
30
42.55
43.00
43.45
43.91
44.36
44.82
45.27
45.73
46.18
46.64
40.12
40.56
40.99
41 .42
41.86
42.29
42.73
43.16
43.60
44.03
37.70
38.11
40. la
40.60
41 .Ol
41 .42
35.27
35.67
36.06
36.45
36.85
37.24
37.64
38.03
38.42
38.82
32.85
33.22
33.60
33.97
34.34
34.72
35.09
35.46
35.84
36.21
31
32
33
34
35
36
37
38
39
40
47.09
47.55
48.00
48.45
48.91
49.36
49.82
50.27
50.73
51.18
44.46
44.90
45.33
45.77
46.20
46.64
47.07
47.51
47.94
48.37
41 .84
42.25
42.67
43.08
43.49.
43.91
44.32
44.74
45.15
45.57
39.21
39.61
40.00
40.39
40.79
41.18
41.58
41.97
42.36
42.76
36.59
36.96
37.33
37.71
38.08
38.45
38.83
39.20
39.58
39.95
41
42
43
44
45
46
47
48
49
50
51 .64
52.09
52.55
53.00
53.45
53.91
54.36
54.82
55.27
55.73
48.81
49.24
49.68
50.11
50.55
50.98
51.41
51 .a5
52.28
52.72
45.98
46.39
46.81
47.22
47.64
48.05
48.46
48.88
49.29
49.71
43.15
43.55
43.94
44.33
44.73
45.12
45.52
45.91
46.30
46.70
40.32
40.70
41.07
41.44
41 .82
42.19
42.57
42.94
43.31
43.69
51
52
53
54
55
56
57
58
59
60
56.18
56.64
57.09
57.55
58.00
58.45
58.91
59.36
59.82
60.27
53.15
53.59
54.02
54.45
54.89
55.32
55.76
56.19
56.63
57.06
50.12
50.54
50.95
51 .36
51 .78
52.19
52.61
53.02
53.43
53.85
47.09
47.48
47.88
48.27
48.67
49.06
49.45
49.85
50.24
50.64
44.06
44.43
44.81
45. la
45.56
45.93
46.30
46.68
47.05
47.42
34.80
35.21
35.63
36.04
36.45
36.87
37.28
38.53
38.94
39.35
39.77
1
105
FOOT
CLASS
2
CIRC.
INCHES
CLASS
H-2
CIRC.
INCHES
I I
12
13
CLASS
H-3
CIRC.
POLE-Con.
408
TRANSMISSION
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-continued
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
CLASS
H-3
CIRC.
INCHES
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
I
105
FOOT
CLASS
2
CIRC.
INCHES
61
62
63
64
65
66
67
68
69
70
60.73
61.18
61 .64
62.09
62.55
63.00
63.45
63.91
64.36
64.82
57
57
58
58
59
59
60
60
60
61
49
93
36
80
23
67
10
54
97
40
54.26
54.68
55.09
55.51
55.92
56.33
56.75
57.16
57.58
57.99
51.03
51.42
51 .82
52.21
52.61
53.00
53.39
53.79
54.18
54.58
47.80
48.17
48.55
48.92
49.29
49.67
50.04
50.41
50.79
51.16
71
72
73
74
75
76
77
78
79
80
65.27
65.73
66.18
66.64
67.09
67.55
68.00
68.45
68.91
69.36
61
62
62
63
63
64
64
64
65
65
84
27
71
14
58
01
44
88
31
75
58.40
58.82
59.23
59.65
60.06
60.47
60.89
61 .30
61 .72
62.13
54.97
55.36
55.76
56.15
56.55
56.94
57.33
57.73
58.12
58.52
51.54
51.91
52.28
52.66
53.03
53.40
53.78
54.15
54.53
54.90
81
82
83
84
85
86
87
88
89
90
69.82
70.27
70.73
71.18
71 .64
72.09
72.55
73.00
73.45
73.91
66
66
67
67
67
68
68
69
69
70
18
62
05
48
92
35
79
22
66
09
62.55
62.96
63.37
63.79
64.20
64.62
65.03
65.44
65.86
66.27
58.91
59.30
59.70
60.09
60.48
60.88
61 .27
61 .67
62.06
62.45
55.27
55.65
56.02
56.39
56.77
57.14
57.52
57.89
58.26
58.64
91
92
-------93
94
95
96
97
98
99
100
101
102
103
104
105
74.36
74.82
-----GROUND
75.27
75.73
76.18
76.64
77.09
77.55
78.00
78.45
78.91
79.36
79.82
80.27
80.73
70 53
70.96
LINE
(12
71.39
71 .83
72.26
72.70
73.13
73.57
74.00
74.43
74
75
75
76
76
87
30
74
17
61
66.69
62.85
67. IO
63.24
FEET,
0 INCHES)----67.52
63.64
67.93
64.03
68.34
64.42
68.76
64.82
69.17
65.21
69.59
65.61
70.00
66.00
70.41
66.39
70.83
71 .24
71.66
72.07
72.48
66.79
67.18
67.58
67.97
68.36
59.01
59.38
59.76
60.13
60.51
60.88
61 .25
61 .63
62.00
62.37
62.75
63.12
63.49
63.87
64.24
POLE-Con.
APPENDIX
409
B
Table B-4.-Pole circumferences for western red cedar-continued
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
CLASS
H-3
CIRC.
INCHES
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
33.00
33.45
33.09
34.34
34.79
35.24
35.68
36.13
36.58
37.02
31.47
31 .oo
31.43
31 .86
29.00
CLASS
CIRC.
INCHES
1
CLASS
CIRC.
110
2
INCHES
32.28
32.71
33.14
33.57
34.00
34.42
34.65
35.20
29.41
29.82
30.23
30.63
31.04
31.45
31.86
32.27
32.68
33.09
27.00
27.39
27.70
26.17
28.56
28.95
29.34
29.73
30.12
30.50
30.89
25.00
25.37
25.73
26.10
26.46
26.93
27.19
27.56
27.92
28.29
28.65
16
19
20
37.92
38.37
38.81
39.26
39.71
40.15
40.60
41.05
41.50
41.94
35.71
36.13
36.56
36.99
37.42
37.95
36.27
38.70
39.13
39.56
33.50
33.90
34.31
34.72
35.13
35.54
35.95
36.36
36.76
37.17
31 .28
31 .67
32.06
32.45
32.04
33.23
33.62
34.01
34.40
34.79
29.02
29.38
29.75
30.12
30.48
30.65
31.21
31.58
31.94
32.31
21
22
23
24
25
26
27
29
29
30
42.39
42.04
43.26
43.73
44.18
44.62
45.07
45.52
45.97
46.41
39.99
40.41
40.94
41 .27
41.70
42.12
42.55
42.98
43.41
43.84
37.58
37.99
38.40
38.81
39.22
39.63
40.03
40.44
40.85
41 .26
35.18
35.57
35.96
36.35
36.74
37.12
37.51
37.90
38.29
38.66
32.67
33.04
33.40
33.77
34.13
34.50
34.87
35.23
35.60
35.96
31
32
33
34
35
36
37
38
39
40
46.06
47.31
47.75
48.20
40.65
49.10
49.54
49.99
50.44
50.88
44.26
44.69
45.12
45.55
45.98
46.40
46.83
47.26
47.69
48.12
41.67
42.08
42.49
42.09
43.30
43.71
44.12
44.53
44.94
45.35
39.07
39.46
39.85
40.24
40.63
41.02
41.41
41.80
42.19
42.58
36.33
36.69
37.06
37.42
37.79
36.15
39.52
38.88
39.25
39.62
91
42
43
44
45
46
47
48
49
50
51.33
51.78
52.23
52.67
53.12
53.57
54.01
54.46
54.91
55.36
49.54
48.97
49.40
49.83
50.25
50.68
45.75
46.16
46.57
46.98
47.39
47.80
48.21
46.62
49.02
49.43
42.97
43.36
43.75
44.13
44.52
44.91
45.30
45.69
46.08
46.47
39.98
40.35
40.71
41.08
41.44
41 .81
42.17
42.54
42.90
43.27
TOP
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
51.11
51.54
51.97
52.39
FOOT
POLE
410
TRANSMISSION
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-continued
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
110 FOOT
CLASS
H-3
CIRC.
1 NCHES
CLASS
H-2
CIRC.
INCHES
51
52
53
54
55
56
57
58
59
60
55.80
56.25
56.70
57.14
57.59
58.04
58.49
58.93
59.38
59.83
52.82
53.25
53.68
54.11
54.53
54.96
55.39
55.82
56.25
56.67
49.84
50.25
50.66
51.07
51.48
51.88
52.29
52.70
53.1 I
53.52
46.86
47.25
47.64
48.03
48.42
48.81
49.20
49.59
49.98
50.37
43.63
44.00
44.37
44.73
45.10
45.46
45.83
46.19
46.56
46.92
61
62
63
64
65
66
67
68
69
70
60.27
60.72
61.17
61 .62
62.06
62.51
62.96
63.40
63.85
64.30
57.10
57.53
57.96
58.38
58.81
59.24
59.67
60.10
60.52
60.95
53.93
54.34
54.75
55.15
55.56
55.97
56.38
56.79
57.20
57.61
50.75
51.14
51.53
51.92
52.31
52.70
53.09
53.48
53.87
54.26
47.29
47.65
48.02
48.38
48.75
49.12
49.48
49.85
50.21
50.58
71
72
73
74
75
76
77
78
79
80
64.75
65.19
65.64
66.09
66.53
66.98
67.43
67.87
68.32
68.77
61.38
61.81
62.24
62.66
63.09
63.52
63.95
64.37
64.80
65.23
58.01
58.42
58.83
59.24
59.65
60.06
60.47
60.87
61 .28
61 .69
54.65
55.04
55.43
55.82
56.21
56.60
56.99
57.37
57.76
58.15
50.94
51.31
51 .67
52.04
52.40
52.77
53.13
53.50
53.87
54.23
81
82
83
84
85
86
87
88
89
90
69.22
69.66
70.11
70.56
71 .oo
71.45
71.90
72.35
72.79
73.24
65.66
66.09
66.51
66.94
67.37
67.80
68.23
68.65
69.08
69.51
62.10
62.51
62.92
63.33
63.74
64.14
64.55
64.96
65.37
65.78
58.54
58.93
59.32
59.71
60.10
60.49
60.88
61 .27
61 .66
62.05
54.60
54.96
55.33
55.69
56.06
56.42
56.79
57.15
57.52
57.88
73.69
74.13
74.58
75.03
75.48
75.92
76.37
69.94
70.37
70.79
71.22
71 .65
72.08
72.50
66.19
66.60
67.00
67.41
67.82
68.23
68.64
62.44
62.83
63.22
63.61
64.00
64.38
64.77
58.25
58.62
58.98
59.35
59.71
60.08
60.44
----60.81
61.17
61 .54
91
92
93
94
95
96
97
--98
99
100
----GROUND
76.82
77.26
77.71
LINE
72.93
73.36
73.79
(12
CLASS
H-l
CIRC.
INCHES
FEET,
0
69.05
69.46
69.87
CLASS
CIRC.
INCHES
INCHES)------
65.16
65.55
65.94
1
CLASS
CIRC.
INCHES
2
POLE-Con.
APPENDIX
411
6
Table B-4.-Pole circumferences for western red cedar-continued
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
101
102
103
104
105
106
107
108
109
110
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
110
CLASS
H-3
CIRC.
CLASS
H-2
CIRC.
INCHES
INCHES
CLASS
H-l
CIRC.
INCHES
78.16
78.61
79.05
79.50
79.95
80.39
80.84
81.29
81.74
82.18
74.22
74.64
75.07
75.50
75.93
76.36
76.78
77.21
77.64
78.07
70.27
70.68
71.09
71.50
71.91
72.32
72.73
73.13
73.54
73.95
CLASS
H-3
CIRC.
CLASS
H-2
CIRC.
CLASS
H-l
CIRC.
INCHES
INCHES
INCHES
1
2
3
4
5
6
7
8
9
10
33.00
33.44
33.87
34.31
34.74
35.18
35.61
36.05
36.49
36.92
37.36
31 .oo
31.42
31.83
32.25
32.67
33.09
33.50
33.92
34.34
34.76
35.17
29.00
29.40
29.80
11
12
13
14
15
16
17
18
19
20
37.79
38.23
38.67
39.10
39.54
39.97
40.41
40.84
41.28
41.72
21
22
23
24
25
26
27
28
29
30
42.15
42.59
43.02
43.46
43.89
44.33
44.77
45.20
45.64
46.07
TOP
CLASS
1
CIRC.
INCHES
POLE-Con.
INCHES
66.33
66.72
67.11
67.50
67.09
68.28
68.67
69.06
69.45
69.84
CLASS
CIRC.
FOOT
CLASS
2
CIRC.
61.90
62.27
62.63
63.00
63.37
63.73
64.10
64.46
64.83
65.19
1
CLASS
CIRC.
115
2
INCHES
INCHES
30.20
30.60
31 .oo
31.39
31.79
32.19
32.59
32.99
27.00
27.38
27.76
28.14
28.52
28.90
29.28
29.67
30.05
30.43
30.81
25.00
25.36
25.72
26.07
26.43
26.79
27.15
27.50
27.86
28.22
28.58
35.59
36.01
36.43
36.84
37.26
37.68
38.10
38.51
38.93
39.35
33.39
33.79
34.19
34.59
34.99
35.39
35.76
36.18
36.58
36.98
31.19
31.57
31.95
32.33
32.71
33.09
33.47
33.85
34.23
34.61
28.94
29.29
29.65
30.01
30.37
30.72
31.08
31.44
31.80
32.16
39.77
40.18
40.60
41.02
41.44
41.85
42.27
42.69
43.1 I
43.52
37.38
37.78
38.18
38.58
38.98
39.38
39.78
40.17
40.57
40.97
35.00
35.38
35.76
36.14
36.52
36.90
37.28
37.66
38.04
38.42
32.51
32.87
33.23
33.59
33.94
34 * 30
34.66
35.02
35.38
35.73
FOOT
POLE
TRANSMISSION
412
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red cedar-continued
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
CLASS
H-3
CIRC.
INCHES
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
115
FOOT
CLASS
2
CIRC.
INCHES
31
32
33
34
35
36
37
38
39
40
46.51
46.94
47.38
47.82
48.25
48.69
49.12
49.56
50.00
50.43
43.94
44.36
44.78
45.19
45.61
46.03
46.44
46.86
47.28
47.70
41.37
41.77
42.17
42.57
42.97
43.37
43.77
44.17
44.56
44.96
38.80
39.18
39.56
39.94
40.33
40.71
41.09
41.47
41 .85
42.23
36.09
36.45
36.81
37.17
37.52
37.88
38.24
38.60
38.95
39.31
41
42
43
44
45
46
47
48
49
50
50.87
51.30
51.74
52.17
52.61
53.05
53.48
53.92
54.35
54.79
48.11
48.53
48.95
49.37
49.78
50.20
50.62
51.04
51.45
51 .81
45.36
45.16
46.16
46.56
46.96
47.36
47.76
48.16
48.56
48.95
42.61
42.99
43.37
43.75
44.13
44.51
44.89
45.28
45.66
46.04
39.67
40.03
40.39
40.74
41.10
41 .46
41 .82
42.17
42.53
42.89
51
52
53
54
55
56
57
58
59
60
55.22
55.66
56.10
56.53
56.97
57.40
57.84
58.28
58.71
59.15
52.29
52.71
53.12
53.54
53.96
54.38
54.79
55.21
55.63
56.05
49.35
49.75
50.15
50.55
50.95
51.35
51.75
52.15
52.55
52.94
46.42
46.80
47.18
47.56
47.94
48.32
48.70
49.08
49.46
49.84
43.25
43.61
43.96
44.32
44.68
45.04
45.39
45.75
46.11
46.47
61
62
63
64
65
66
67
68
69
70
59.58
60.02
60.45
60.89
61 .33
61 .76
62.20
62.63
63.07
63.50
56.46
56.88
57.30
57.72
58.13
58.55
58.97
59.39
59.80
60.22
53.34
53.74
54.14
54.54
54.94
55.34
55.74
56.14
56.54
56.94
50.22
50.61
50.99
51.37
51.75
52.13
52.51
52.89
53.27
53.65
46.83
47.18
47.54
47.90
48.26
48.61
48.97
49.33
49.69
50.05
71
72
73
74
75
76
77
78
79
80
63.94
64.38
64.81
65.25
65.68
66.12
66.56
66.99
67.43
67.86
60.64
61 .06
61 .47
61 .89
62.31
62.72
63.14
63.56
63.98
64.39
57.33
57.73
58.13
58.53
58.93
59.33
59.73
60.13
60.53
60.93
54.03
54.41
54.79
55.17
55.56
55.94
56.32
56.70
57.08
57.46
50.40
50.76
51.12
51 .48
51 .83
52.19
52.55
52.91
53.27
53.62
POLE-Con.
APPENDIX
6
413
Table B-4.-Pole circumferences for western red cechr-Continued
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
1
115
FOOT
CLASS
2
CIRC.
INCHES
81
62
83
84
85
86
87
88
89
90
68.30
68.73
69.17
69.61
70.04
70.48
70.91
71.35
71.78
72.22
64 81
65 23
65 65
66.06
66.48
66 90
67 32
67 73
15
68
68 57
61 33
61 72
12
62
62.52
62.92
63 32
63 72
64
12
64 52
64 92
57 84
58 22
58 60
58.98
59.36
59 74
60
12
60 50
60 89
61 27
53.98
54.34
54.70
55.06
55.41
55.77
56.13
56.49
56.84
57.20
91
92
93
94
95
96
97
98
99
100
72.66
73.09
73.53
73.96
74.40
74.83
75.27
75.71
76.14
76.58
68 99
69 40
69 82
70.24
70.66
71 07
71 49
71 91
72 33
72 74
65 32
65 72
66
11
66.51
66.91
67.31
67.71
68.11
68.51
68.91
61 65
62 03
62 41
62.79
63.17
63 55
63 93
64 31
64 69
65 07
57.56
57.92
58.28
58.63
58.99
59.35
59.71
60.06
60.42
60.78
65.45
65.83
61.14
61.50
66 22
66 60
66 98
67 36
67 74
68.12
68.50
68 88
61.85
62.21
62.57
62.93
63.28
63.64
64.00
64.36
26
64
02
40
78
64.72
65.07
65.43
65.19
66.15
101
102
-103
104
105
106
107
108
109
110
111
112
113
114
115
WESTERN
CLASS
H-3
CIRC.
INCHES
RED CEDAR
DISTANCE
FROM TOP
FEET
TOP
1
2
3
4
5
6
7
8
9
10
77.01
77.45
-----GROUND
77.89
78.32
78.76
79.19
79.63
80.06
80.50
80.94
81.37
81.81
82.24
82.68
83.11
CLASS
H-3
CIRC.
INCHES
33.00
33.43
33.86
34.29
34.72
35.15
35.58
36.01
36.44
36.81
37.30
73.16
73.58
LINE
(12
74.00
74.41
74.83
75.25
75.67
76.08
76.50
76 92
77
77
78
78
79
33
75
17
59
00
69.31
69.71
FEET,
0 INCHES)-70.11
70.50
70.90
71.30
71.70
72.10
72.50
72 90
73
73
74
74
74
30
70
10
50
89
.--
69
69
70
70
70
CLASS
H-2
CIRC.
INCHES
CLASS
H-l
CIRC.
INCHES
CLASS
CIRC.
INCHES
31 00
31 41
31 82
32 24
32 65
33.06
33.47
33 89
34 30
34 71
35
12
29.00
29.39
29.79
30.18
30.58
30.97
31.37
31.76
32.16
32.55
32.95
27.00
27.37
27.75
28.12
28.49
28.86
29.24
29.61
29.98
30.36
30.73
1
120
CLASS
2
CIRC.
INCHES
25.00
25.35
25.70
26.05
26.40
26.75
27.11
27.46
27.81
28.16
28.51
POLE-con.
FOOT
POLE
414
TRANSMISSION
LINE DESIGN
MANUAL
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
CLASS
H-2
CIRC.
INCHES
18
19
20
37.73
38.16
38.59
39.02
39.45
39.88
40.31
40.74
41.17
41.60
35.54
35.95
36.36
36.77
37.18
37.60
38.01
38.42
38.83
39.25
33.34
33.74
34.13
34.53
34.92
35.32
35.71
36.1 I
36.50
36.89
31.47
31 .85
32.22
32.59
32.96
33.34
33.71
34.08
34.46
28.86
29.21
29.56
29.91
30.26
30.61
30.96
31.32
31.67
32.02
21
22
23
24
25
26
27
28
29
30
42.03
42.46
42.89
43.32
43.75
44.18
44.61
45.04
45.46
45.89
39.66
40.07
40.48
40.89
41.31
41 .72
42.13
42.54
42.96
43.37
37.29
37.68
38.08
38.47
38.87
39.26
39.66
40.05
40.45
40.84
34.83
35.20
35.57
35.95
36.32
36.69
37.07
37.44
37.81
38.18
32.37
32.72
33.07
33.. 42
33.77
34.12
34.47
34.82
35.18
35.53
31
32
33
34
35
36
37
38
39
40
46.32
46.75
47.18
47.61
48.04
48.47
48.90
49.33
49.76
50.19
43.78
44.19
44.61
45.02
45.43
45.84
46.25
46.67
47.08
47.49
41.24
41 .63
42.03
42.42
42.82
43.21
43.61
44.00
44.39
44.79
38.56
38.93
39.30
39.68
40.05
40.42
40.79
41.17
41.54
41.91
35.88
36.23
36.58
36.93
37.28
37.63
37.98
38.33
38.68
39.04
41
42
43
44
45
46
47
48
49
50
50.62
51.05
51.48
51.91
52.34
52.77
53.20
53.63
54.06
54.49
47.90
48.32
48.73
49.14
49.55
49.96
50.38
50.79
51.20
51.61
45.18
45.58
45.97
46.37
46.76
47.16
47.55
47.95
48.34
48.74
42.29
42.66
43.03
43.40
43.78
44.15
44.52
44.89
45.27
45.64
39.39
39.74
40.09
40.44
40.79
41.14
41.49
41 .84
42.19
42.54
51
52
53
54
55
56
57
58
59
60
54.92
55.35
55.78
56.21
56.64
57.07
57.50
57.93
58.36
58.79
52.03
52.44
52.85
53.26
53.68
54.09
54.50
54.91
55.32
55.74
49.13
49.53
49.92
50.32
50.71
46.01
46.39
46.76
47.13
47.50
47.88
48.25
48.62
49.00
49.37
42.89
43.25
43.60
43.95
44.30
44.65
45.00
45.35
45.70
46.05
11
12
13
I4
15
16
17
CLASS
H-l
CIRC.
INCHES
51.11
51.50
51.89
52.29
52.68
CLASS
CIRC.
INCHES
31.10
1
120
FOOT
CLASS
2
CIRC.
CLASS
H-3
CIRC.
1 NCHES
INCHES
POLE-Con.
APPENDIX
415
B
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
CLASS
H-l
CIRC.
INCHES
60.08
60.51
60.94
61.37
61.80
62.23
62.66
63.09
56.15
56.56
56.97
57.39
57.80
58.21
50.62
59.04
59.45
59.06
53.08
53.47
53.87
54.26
54.66
55.05
55.45
55.04
56.24
56.63
50.11
50.49
50.86
51 .23
51 .61
51.98
52.35
52.72
53.10
46.40
46.75
Lt7.11
47.46
47.81
48.16
48.51
48.06
49.21
49.56
71
72
73
74
75
76
77
78
79
80
63.52
63.95
64.30
64.81
65.24
65.67
66.10
66.53
66.96
67.39
60.27
60.68
61.10
61.51
61.92
62.33
62.75
63.16
63.57
63.90
57.03
57.42
57.02
58.21
58.61
59.00
59.39
59.79
60.18
60.50
53.47
53.04
54.21
54.59
54.96
55.33
55.71
56.08
56.45
56.02
49.91
50.26
50.61
50.96
51 .32
51 .67
52.02
52.37
52.72
53.07
81
02
83
84
85
86
87
80
89
90
67.02
60.25
60.60
69.11
69.54
69.96
70.39
70.82
71 .25
71.60
64.39
64.81
65.22
65.63
66.04
66.46
66.07
67.20
67.69
68.11
60.97
61 .37
61 .76
62.16
62.55
62.95
63.34
63.74
64.13
64.53
57.20
57.57
57.94
50.32
50.69
59.06
59.43
59.81
60.18
60.55
53.42
53.77
54.12
54.47
54.02
55.18
55.53
55.80
56.23
56.50
91
92
93
94
95
96
97
98
99
72.11
72.54
72.97
73.40
73.03
74.26
74.69
75.12
75.55
75.90
60.52
68.93
69.34
69.75
70.17
70.58
70.99
71.40
71.02
72.23
64.92
65.32
65.71
66.11
66.50
66.09
67.29
67.60
68.08
68.47
60.93
61.30
61 .67
62.04
62.42
62.79
63.16
63.54
63.91
64.28
56.93
57.20
57.63
57.90
50.33
50.60
59.04
59.39
59.74
60.09
76.41
76.04
77.27
77.70
70.13
70.56
70.99
72.64
73.05
73.46
73.80
74.29
74 .‘70
75.11
68.87
69.26
69.66
70.05
70.45
70.84
71 .24
64.65
65.03
65.40
65.77
66.14
66.52
60.44
60.79
61.14
61 .49
61 .84
62.19
62.54
62
63
64
65
66
67
68
69
70
100
101
102
103
104
105
106
107
59.22
59.65
-------------GROUND
108
109
110
79.42
79.85
80.28
LINE
75.53
75.94
76.35
(12
FEET,
0
71.63
72.03
72.42
CLASS
CIRC.
INCHES
49.74
66.09
INCHES)---------------
67.26
67.64
68.01
1
120
FOOT
CLASS
2
CIRC.
INCHES
CLASS
H-2
CIRC.
INCHES
61
CLASS
H-3
CIRC.
INCHES
62.89
63.25
63.60
POLE-con.
416
TRANSMISSION
LINE DESIGN MANUAL
Table B-4.-Pole circumferences for western red Cedar-Continued
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
111
112
113
114
115
116
117
118
119
120
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
CLASS
H-3
CIRC.
1 NCHES
80.71
81.14
81.57
82.00
82.43
82.86
83.29
83.72
84.15
84.58
CLASS
H-2
CIRC.
CLASS
H-l
CIRC.
INCHES
INCHES
76
77
77
78
78
78
79
79
80
80
72.82
73.21
73.61
74.00
74.39
74.79
75.18
75.58
75.97
76.37
1
12_p FOOT
POLE
CLASS
2
CIRC.
INCHES
CLASS
H-2
CIRC.
INCHES
33.00
33.42
33.84
34.26
34.68
35.10
35.52
35.94
36.36
36.78
37.20
31
31
31
32
32
33
33
33
34
34
35
1I
12
13
14
15
16
17
18
19
20
37.62
38.04
38.46
38.88
39.30
39.72
40.14
40.56
40.98
41.40
21
22
23
24
25
26
27
28
29
30
41.82
42.24
42.66
43.08
43.50
43.92
44.34
44.76
45.18
45.61
00
40
81
21
61
02
42
82
23
63
03
CLASS
H-l
CIRC.
68 38
68 75
69 13
69 50
69 87
70 25
70 62
70 99
71 36
71 74
INCHES
CLASS
CIRC.
INCHES
63.95
64.30
64.65
65.00
65.35
65.70
66.05
66.40
66.75
67.11
1
CLASS
CIRC.
INCHES
30.16
30.55
30.93
31 .32
31.71
32.09
32.48
32.87
27.00
27.37
27.73
28.10
28.46
28.83
29.19
29.56
29.92
30.29
30.66
25.00
25.34
25.69
26.03
26.38
26.72
27.07
27.41
27.76
28.10
28.45
35.44
35.84
36.24
36.65
37.05
37.45
37.86
38.26
38.66
39.07
33.25
33.64
34.03
34.41
34.80
35.18
35.57
35.96
36.34
36.73
31.02
31.39
31.75
32.12
32.48
32.85
33.21
33.58
33.95
34.31
28.79
29.13
29.48
29.82
30.17
30.51
30.86
31.20
31.55
31 .89
39.47
39.87
40.28
40.68
41 .08
41.49
41 .89
42.29
42.70
43.10
37.12
37.50
34.68
35.04
35.41
35.77
36.14
36.50
36.87
37.24
37.60
37.97
32.24
32.58
32.92
33.27
33.61
33.96
34.30
34.65
34.99
35.34
29.00
29.39
29.77
37.89
38.28
38.66
39.05
39.44
39.82
40.21
40.60
-Con.
INCHES
125
CLASS
H-3
CIRC.
1
2
3
4
5
6
7
8
9
10
TOP
76
18
59
00
41
82
24
65
06
47
CLASS
CIRC.
1 NCHES
FOOT
POLE
APPENDIX
B
417
Table B-4.-Pole circumferences for western red cedar-Continued
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
CLASS
H-3
CIRC.
CLASS
H-2
CIRC.
CLASS
H-l
CIRC.
INCHES
INCHES
INCHES
31
32
33
34
35
36
37
38
39
40
46.03
46.45
46.87
47.29
47.71
48.13
48.55
48.97
49.39
49.81
43.50
43.91
44.31
44.71
45.12
45.52
45.92
46.33
46.73
47.13
40.98
41.37
41 .I6
41
42
43
44
45
46
41
48
49
50
50.23
50.65
51.07
51.49
51.91
52.33
52.75
53.17
53.59
54.01
51
52
53
54
55
56
57
58
59
60
CLASS
CIRC.
INCHES
I
125 FOOT
CLASS
2
CIRC.
INCHES
42.14
42.53
42.92
43.30
43.69
44.08
44.46
38.33
38.70
39.06
39.43
39.79
40.16
40.53
40.89
41 .26
41 .62
35.68
36.03
36.37
36.71
37.06
37.40
37.75
38.09
38.44
38.78
47.54
47.94
48.34
48.75
49.15
49.55
49.96
50.36
50.76
51.17
44.85
45.24
45.62
46.01
46.39
46.78
47.17
47.55
47.94
48.33
41.99
42.35
42.72
43.08
43.45
43.82
44.18
44.55
44.91
45.28
39.13
39.47
39.82
40.16
40.50
40.85
41.19
41.54
41.88
42.23
54.43
54.85
55.27
55.69
56.11
56.53
56.95
57.37
57.79
58.21
51.57
51.97
52.38
52.78
53.18
53.59
53.99
54.39
54.80
55.20
48.71
49.10
49.49
49.87
50.26
50.65
51.03
51 .42
51 .81
52.19
45.64
46.01
46.37
46.74
47.1 I
47.47
47.84
48.20
48.57
48.93
42.57
42.92
43.26
43.61
43.95
44.29
44.64
44.98
45.33
45.67
61
62
63
64
65
66
67
68
69
70
58.63
59.05
59.47
59.89
60.31
60.73
61.15
61 .57
61 .99
62.41
55.61
56.01
56.41
56.82
57.22
57.62
58.03
58.43
58.83
59.24
52.58
52.97
53.35
53.74
54.13
54.51
54.90
55.29
55.67
56.06
49.30
49.66
50.03
50.39
50.76
51.13
51.49
51.86
52.22
52.59
46.02
46.36
46.71
47.05
47.39
47.74
48.08
48.43
48.77
49.12
71
72
73
74
75
76
77
78
79
80
62.83
63.25
63.67
64.09
64.51
64.93
65.35
65.77
66.19
66.61
59.64
60.04
60.45
60.85
61 .25
61.66
62.06
62.46
62.87
63.27
56.45
56.83
57.22
57.61
57.99
58.38
58.76
59.15
59.>4
59.92
52.95
53.32
53.68
54.05
54.42
54.78
55.15
55.51
55.88
56.24
49.46
49.81
50.15
50.50
50.84
51.18
51.53
51 .87
52.22
52.56
POLE-con.
418
TRANSMISSION
LINE DESIGN
MANUAL
Table B-4.-Pole circumferences for western red Cedar-Continued
WESTERN
RED CEDAR
DISTANCE
FROM TOP
FEET
125
CLASS
H-2
CIRC.
CLASS
H-l
CIRC.
INCHES
INCHES
INCHES
81
82
83
84
85
86
87
88
89
90
67.03
67.45
67.87
68.29
68.71
69.13
69.55
69.97
70.39
70.82
63.67
64.08
64.48
64.88
65.29
65.69
66.09
66.50
66.90
67.30
60
60
61
61
61
62
62
63
63
63
31
70
08
47
86
24
63
02
40
79
56
56
57
57
58
58
58
59
59
59
61
97
34
71
07
44
80
17
53
90
52.91
53.25
53.60
53.94
54.29
54.63
54.97
55.32
55.66
56.01
91
92
93
94
95
96
97
98
99
100
71.24
71.66
72.08
72.50
72.92
73.34
73.76
74.18
74.60
75.02
67.71
68.11
68.51
68.92
69.32
69.72
70.13
70.53
70.93
71.34
64
64
64
65
65
66
66
66
67
67
18
56
95
34
72
11
50
88
27
66
60
60
61
61
61
62
62
62
63
63
26
63
00
36
73
09
46
82
19
55
56.35
56.70
57.04
5%. 39
57.73
58.08
58.42
58.76
59.11
59.45
101
102
103
104
105
106
107
108
109
110
75.44
75.86
76.28
76.70
77.12
77.54
77.96
78.38
78.80
79.22
71.74
72.14
72.55
72.95
73.35
73.76
74.16
74.56
74.97
75.37
68
68
68
69
69
69
70
70
71
71
04
43
82
20
59
97
36
75
13
52
63
64
64
65
65
65
66
66
66
67
92
29
65
02
38
75
11
48
84
21
59.80
60.14
60.49
60.83
61.18
61.52
61.87
62.21
62.55
62.90
111
112
-------113
114
115
116
117
118
119
120
79.64
80.06
75.77
76.18
71.91
72.29
121
122
123
124
125
-----GROUND
LINE
I12
FEET,
0
CLASS
CIRC.
INCHES
67.58
67.94
INCHES)-----
80.48
80.90
81 .32
81.74
82.16
82.58
83.00
83.42
76.58
76.98
77.39
77.79
78.19
78.60
79.00
79.40
72.68
73.07
73.45
73.84
74.23
74.61
75.00
75.39
68.31
68.67
69.04
69.40
69.77
70.13
70.50
70.87
83.84
84.26
84.68
85.10
85.52
79.81
80.21
80.61
81.02
81 .42
75 77
76 16
76 55
76 93
77.32
71 23
71 60
71 96
72 33
72.69
1
FOOT
CLASS
H-3
CIRC.
CLASS
CIRC.
INCHES
63.24
63.59
-. _------_63.93
64.28
64.62
64.97
65.31
65.66
66.00
66.34
66.69
67.03
67.38
67.72
68.07
2
POLE-Con.
APPENDIX
Table B-S.-Permanent
Maximum conductor tension
Percent of rated strength
419
B
set values for Alumoweld strand
Permanent set
mm/mm or in/in
Maximum conductor tension
Percent of rated strength
Permanent set
mm/mm 01 in/in
096
104
112
120
129
40
41
42
43
44
15
16
17
18
19
.ooo 138
.OOO 148
.ooo 159
.ooo 171
.OOO183
45
46
47
48
49
.OOO600
.OOO622
.OOO645
.ooo 668
.OOO691
:i
.OOO206
.ooo
195
22
23
24
.OOO217
.OOO228
.OOO240
50
51
52
53
54
.ooo 714
.ooo 737
.OOO760
.OOO783
.OOO807
25
26
27
.OOO253
.OOO267
.OOO282
ii
.ooo 298
.OOO
314
55
56
57
58
59
.OOO832
.OOO858
.OOO885
.ooo 912
.ooo 940
30
.ooo 330
:Y
62
63
64
.OOO968
.ooo 997
.001027
.001057
.001087
10
11
12
13
14
0.000
.ooo
.ooo
.ooo
.ooo
i:
33
34
.ooo 347
.OOO
364
.OOO381
.OOO398
ii
.OOO415
.ooo
432
2
39
.ooo 449
.OOO
466
.OOO484
65
Initial modulus:
Final modulus:
148.238 GPa (21.5 x 10” lb/in2)
158.580 GPa (23 x 10” lb/in2)
0.000
.ooo
.ooo
.ooo
.ooo
502
521
540
559
5 79
zt
.OOl
.OOl
.OOl
.OOl
.OOl
118
149
181
214
248
70
.OOl 283
420
TRANSMISSION
Table B-6.-Permanent
Tension
LINE DESIGN MANUAL
set values for steel strand
10 mm (3/8 in)
13 mm (l/2 in)
11 mm (7/16 in)
HS’
EHS2
lb
HS’
EHS’
8 896
9 341
9 786
10 231
10 657
2 000
2 100
2 200
2 300
2 400
0.000 136
.OOO142
.ooo 147
.ooo 154
.OOO162
0.000 036
.ooo 037
.OOO038
.ooo 039
.ooo 040
0.000 091
.OOO096
.ooo 100
.ooo 105
.ooo 110
0.000 019
.ooo 020
.ooo 021
.ooo 022
.OOO023
0.000 060
.OOO063
.ooo 066
.ooo 070
.ooo 074
0.000 012
.ooo 013
.ooo 014
.ooo 015
.OOO016
11
11
12
12
12
121
565
010
455
900
2 500
2 600
2 700
2 800
2 900
.ooo 170
.ooo 179
.ooo 188
.OOO198
.OOO208
.ooo 041
.OOO042
.ooo 043
.ooo 045
.ooo 047
.ooo 115
.ooo 120
.OOO125
.ooo 130
.ooo 135
.OOO024
.OOO025
.OOO026
.OOO027
.OOO028
.OOO078
.OOO082
.ooo 086
.ooo 090
.ooo 094
.ooo 017
.OOO018
xl00 019
.ooo 020
.ooo 021
13
13
14
14
15
345
789
234
679
124
3 000
3 100
3 200
3 300
3 400
.ooo 219
.OOO230
.OOO242
.OOO253
.OOO264
.ooo 049
.OOO052
.ooo 055
.OOO058
.OOO061
.ooo 140
.ooo 145
.ooo 150
.ooo 155
.OOO 160
.ooo 029
.ooo 030
.ooo 031
.OOO032
.ooo 033
.OOO098
.ooo 102
.OOO 106
.ooo 111
.ooo 115
.ooo 022
.OOO023
.OOO024
.OOO025
.OOO026
15
16
16
16
17
569
014
458
903
348
3 500
3 600
3 700
3 800
3 900
.OOO275
.OOO287
.ooo 299
.ooo 311
.OOO323
,000 064
.ooo 068
.OOO072
.OOO076
.OOO081
.OOO165
.ooo 170
.ooo 175
.OOO180
.OOO 185
.ooo 034
.ooo 035
.OOO036
.ooo 037
.OOO038
.ooo 119
.OOO123
.OOO127
.ooo 131
.ooo 135
.OOO027
,000 028
.ooo 029
.ooo 030
.ooo 031
17
18
18
19
19
793
238
682
127
572
4 000
4 100
4,200
4 300
4 400
.OOO336
.ooo 350
.OOO365
.OOO381
.OOO398
.ooo 086
.ooo 092
.OOO098
.ooo 104
.ooo 110
.ooo 190
.ooo 195
.ooo 202
.OOO208
.OOO214
.ooo
.ooo
.ooo
.ooo
.ooo
040
04 1
043
045
047
.ooo 139
.ooo 143
.OOO148
.OOO152
.OOO156
.OOO032
.ooo 033
.ooo 034
.ooo 035
.OOO036
20
20
20
21
21
017
462
907
351
796
4
4
4
4
4
500
600
700
800
900
.OOO416
.ooo 435
.ooo 455
.ooo 475
.OOO496
.ooo 117
.OOO124
.ooo 131
.OOO138
.OOO146
.ooo 220
.OOO227
.OOO234
.OOO242
.OOO250
.ooo 049
.ooo 05 1
.ooo 053
.OOO056
.OOO05 8
.OOO160
.OOO164
.ooo 168
.OOO172
.OOO176
.ooo 037
.OOO038
.ooo 039
.ooo 040
.ooo 041
22
22
23
23
24
241
686
131
575
020
5 000
5 100
5 200
5 300
5 400
.ooo 519
.ooo 544
.ooo 571
.OOO600
.OOO631
.ooo 154
.OOO162
.ooo 171
.OOO180
‘:OOO189
.ooo 259
.OOO268
.OOO277
.OOO286
,000 295
.OOO062
.OOO065
.ooo 068
.ooo 07 1
.ooo 074
.OOO180
.OOO185
.ooo 190
.ooo 195
.ooo 200
.OOO042
.ooo 043
.ooo 044
.ooo 045
.OOO046
24
24
25
25
26
465
910
355
800
244
5
5
5
5
5
500
600
700
800
900
.ooo 199
.ooo 209
.ooo 219
.OOO230
.OOO241
.ooo 305
.ooo 315
.OOO325
.ooo 335
.ooo 347
.ooo 077
.OOO080
.OOO083
.ooo 086
.OOO089
.OOO205
.ooo 210
.OOO215
.ooo 220
.OOO225
.ooo 047
.OOO048
.ooo 049
.ooo 050
.ooo 05 1
26
27
27
28
28
689
134
576
024
468
6 000
6 100
6 200
6 300
6 400
.OOO252
.OOO263
.OOO275
.OOO287
.ooo 299
.ooo
.ooo
,000
.ooo
.ooo
.ooo
.ooo
.ooo
.ooo
.ooo
092
095
099
103
107
.OOO230
.OOO236
.OOO243
.OOO250
.OOO257
.OOO052
.ooo 053
.ooo 054
.OOO056
.OOO058
28
29
29
30
30
913
358
803
248
693
6 500
6 600
6 700
6 800
6 900
.ooo 311
.OOO324
.ooo 337
.ooo 351
.OOO365
.ooo 417
.ooo 429
.ooo 441
.ooo 453
.OOO465
.ooo 111
.ooo 115
.ooo 119
.OOO123
.OOO128
.OOO264
.OOO271
.OOO278
.OOO285
.ooo 292
.OOO060
.OOO062
.OOO064
.OOO067
.ooo 070
359
371
382
393
405
EHS2
HS’
N
APPENDIX
Table B-6.-Permanent
Tension
421
6
set values for steel strand-continued
10 mm (3/8 in)
EHS2
HS'
N
lb
31 137
31 582
32 027
32 472
32 917
7 000
7 100
7 200
7 300
7 400
0.000 380
.OOO396
.ooo 413
.ooo 431
.ooo 45 1
33 362
33 806
34 251
34 696
35 141
7 500
7 600
7 700
7 800
7 900
.OOO472
.ooo 493
.ooo 515
35 586
36 030
36 475
36 920
37 365
11 mm (7/16 in)
HS'
EHS2
0.000 477
.OOO489
.ooo 501
.ooo 513
13 mm (l/2 in)
HS'
EHS2
0.000 133
,000 139
,000 146
.OOO152
.ooo 159
0.000 299
.OOO306
.ooo 313
.OOO320
.OOO327
0.000073
.ooo075
.OOO
078
.OOO
081
.OOO
083
.OOO165
.OOO172
.OOO178
.OOO185
.ooo 191
.ooo 334
.ooo 341
.OOO348
.ooo 355
.OOO363
.OOO085
.OOO087
.ooo 090
.ooo 093
.OOO096
8 000
8 100
8 200
8 300
8 400
.OOO198
.OOO204
.ooo 211
.OOO217
,000 224
.ooo 371
.OOO378
.OOO387
.OOO396
.ooo 405
.ooo 099
.ooo 102
.ooo 105
.OOO108
.ooo 111
37 810
38 255
38 699
39 144
39 589
8 500
8 600
8 700
8 800
8 900
.OOO230
.OOO237
.OOO243
.ooo 249
.OOO256
.ooo 414
.OOO424
.ooo 434
.ooo 444
.ooo 454
.ooo 114
.OOO118
.ooo 122
.OOO126
.ooo 130
40 034
40 479
40 923
41 368
41 813
9 000
9 100
9 200
9 300
9 400
.OOO262
.OOO268
.OOO274
.OOO280
.OOO287
.OOO464
,000 474
.OOO484
.ooo 495
.OOO506
.ooo 135
.ooo 139
.ooo 143
.ooo 147
.ooo 151
42 258
42 703
43 148
43 592
44 037
9 500
9 600
9 700
9 800
9 900
.ooo 295
.OOO306
.OOO318
,000 329
.ooo 341
.ooo 155
.ooo 159
.OOO164
.ooo 168
.ooo 173
44 482
44 927
45 372
45 816
46 261
10 000
10 100
10 200
10 300
10 400
.OOO352
.OOO364
.ooo 375
.OOO387
.ooo 403
.OOO178
.OOO183
.ooo 188
.ooo 192
.ooo 197
46 706
47 151
47 596
48 041
48 485
10 500
10 600
10 700
10 800
10 900
.ooo 201
.OOO205
.ooo 209
.OOO213
.OOO218
48 930
49 375
49 820
50 265
50 709
11000
11 100
11 200
11300
11400
.OOO223
.OOO228
.OOO233
.OOO238
,000 243
51 154
51599
52 044
52 489
52 934
11500
11 600
11700
11 800
11900
.OOO255
.OOO261
.OOO267
.OOO273
.ooo 249
422
TRANSMISSION
Table B-6.-Permanent
Tension
10
N
lb
HS’
mm (3/8
LINE DESIGN MANUAL
set values for steel strand-Continued
in)
EHS’
11
HS’
mm (7/16
in)
F2-d
13 mm (l/2 in)
HS’
EHS2
53
53
54
54
55
378
823
268
713
158
12
12
12
12
12
000
100
200
300
400
0.000 280
.OOO287
.ooo 295
.OOO302
.ooo 309
55
56
56
56
57
603
047
492
937
382
12
12
12
12
12
500
600
700
800
900
.ooo 317
.OOO325
.ooo 333
.ooo 341
.ooo 350
57
58
58
59
59
827
271
716
161
606
13
13
13
13
13
000
100
200
300
400
.ooo 359
.OOO368
.ooo 377
.OOO386
.OOO396
Ultimate
strength
48 040 N
(10 800 lb)
68 500 N
(15 400 lb)
64 500 N
(14 500 lb)
92 520 N
(20 800 lb)
83 625 N
(18 800 lb)
119 655 N
(26 900 lb)
t High strength. Initial modulus = 158.580 GPa (23 x lo6 lb/in2). Final modulus = 177.885 GPa (25.8 x lo6 lb/in2).
’ Extra-high strength. Initial modulus = 162.028 GPa (23.5 x lo6 lb/in2). Final modulus = 177.885 GPa (25.8 x 10 6 lb/in2).
APPENDIX
423
B
Table B- 7.-Flashover characteristics of suspension insulator strings
and air gaps
Impulse air gap,
in
mm
8
Impulse
flashover
(positive
critical),
kV
Number of
insulator
units’
Wet 6082
flashover,
Wet 60-Hz air gap,
kV
mm
in
130
170
215
254
305
406
508
660
10
12
16
20
26
762
889
991
1118
1245
;t
39
44
49
203
356
533
660
813
150
255
355
440
525
965
1092
1245
1397
1524
610
695
780
860
945
5
9
10
255
295
335
375
415
1025
1105
1185
1265
1345
11
12
13
14
15
455
490
525
565
600
1346
1473
1575
1676
1778
53
58
I;
88
1676
1803
1956
2083
2235
;3
104
110
115
2362
2515
2642
2794
2921
1425
1505
1585
1665
1745
16
17
18
630
660
690
720
750
1880
1981
2083
2184
2286
74
78
82
86
90
121
126
132
137
143
3073
3200
3353
3480
3632
1825
1905
1985
2065
2145
21
22
23
780
810
840
870
900
2388
2464
2565
2692
2794
94
97
101
106
110
148
154
159
165
171
3759
3912
4039
4191
4343
2225
2305
2385
2465
2550
26
27
930
960
990
1020
1050
2921
3023
3124
3251
3353
115
119
123
128
132
14
21
26
32
38
43
49
z;
66
71
6
:Fl
z
ii
30
ifi
70
1 Insulator units are 146 by 254 mm (5-3/4 by 10 in) or 146 by 267 mm (5-3/4 by 10-l/2 in).
424
TRANSMISSION
LINE DESIGN
Table B-8.-Flashover
_
Ahgap
mm
in
Flashover
60-Hz wet,
Pos. critical
kV
impulse, kV
MANUAL
values of air gaps
AirgaP
mm
in
Flashover
60-Hz wet,
Pos. critical
kV
impulse, kV
25
51
76
102
127
1
2
3
4
5
38
60
75
91-95
106-114
1295
1321
1346
1372
1397
51
52
53
54
55
438
447
455
464
472
814
829
843
858
872
152
178
203
229
254
6
7
8
9
10
80
128-141
141-15’5
159-166
175-178
190
1422
1448
1473
1499
1524
56
57
58
59
60
481
489
498
506
515
887
901
916
930
945
279
305
330
356
381
11
12
13
14
15
89
98
107
116
125
207
224
241
258
275
1549
1575
1600
1626
1651
::
63
64
65
523
532
540
549
557
960
975
990
1005
1020
406
432
457
483
508
16
17
18
19
20
134
143
152
161
170
290
305
320
335
350
1676
1702
1727
1753
1778
66
z’8
69
70
566
574
583
591
600
1035
1050
1065
1080
1095
533
559
584
610
635
21
22
23
24
25
178
187
195
204
212
365
381
396
412
427
1803
1829
1854
1880
1905
71
72
73
74
75
607
615
622
630
637
1109
1124
1138
1153
1167
660
686
711
737
762
26
27
28
29
30
221
229
238
246
255
443
458
474
489
505
1930
1956
1981
2007
2032
76
77
78
79
80
645
652
660
667
675
1182
1196
1211
1225
1240
787
813
838
864
889
31
32
33
34
35
264
273
282
291
300
519
534
548
563
577
2057
2083
2108
2134
2159
81
82
83
84
85
683
691
699
707
715
1254
1269
1283
1298
1312
914
940
965
991
1016
36
;;:
39
40
309
318
327
336
345
592
606
621
635
650
2184
2210
2235
2261
2286
86
87
88
89
90
723
731
739
747
755
1327
1341
1356
1370
1385
1041
1067
1092
1118
1143
41
42
43
44
45
353
362
370
379
387
665
680
695
710
725
2311
2337
2362
2388
2413
91
92
93
;:
763
771
779
787
795
1399
1414
1428
1443
1457
1168
1194
1219
1245
1270
46
47
48
49
50
396
404
413
421
430
740
755
770
785
800
2438
2464
2489
2515
2540
;4
98
99
100
803
811
819
827
835
1472
1486
1501
1515
1530
APPENDIX
Table B-8.-Flashover
bc gap
Flashover
60-Hz wet,
Pos. critical
kV
imuulse. kV
mm
in
2565
2591
2616
2642
2667
101
102
103
104
105
842
848
855
862
869
2692
2718
2743
2769
2794
106
107
108
109
110
2819
2845
2870
2896
2921
425
B
values of air gaps-Continued
Air gap
Flashover
60-Hz wet,
Pos. critical
kV
impulse, kV
mm
in
1544
1559
1573
1588
1602
3835
3861
3886
3912
3937
15:
152
153
154
155
1176
1182
1188
1194
1200
2269
2284
2298
2313
2327
875
882
889
896
902
1617
1631
1646
1660
1675
3962
3988
4013
4039
4064
156
157
158
159
160
1206
1212
1218
1224
1230
2342
2356
2371
2385
2400
111
112
113
114
115
909
916
923
929
936
1689
1704
1718
1733
1747
4089
4115
4140
4166
4191
161
162
163
164
165
1236
1242
1248
1254
1260
2414
2429
2443
2458
2472
2946
2972
2997
3023
3048
116
117
118
119
120
943
950
956
963
970
1762
1776
1791
1805
1820
4216
4242
4267
4293
4318
166
167
168
169
170
1266
1272
1278
1284
1290
2487
2501
2516
2530
2545
3073
3099
3124
3150
3175
121
122
123
124
125
977
984
991
998
1005
1834
1849
1863
1878
1892
4343
4369
4394
4420
4445
171
172
173
174
175
1296
1302
1308
1314
1320
2559
2574
2588
2603
2617
3200
3226
3251
3277
3302
126
127
128
129
130
1012
1019
1026
1033
1040
1907
1921
1936
1950
1965
4470
4496
4521
4547
4572
176
177
178
179
180
1326
1332
1338
1344
1350
2632
2646
2661
2675
2690
3327
3353
3378
3404
3429
131
132
133
134
135
1047
1054
1061
1068
1075
1979
1994
2008
2023
2037
4597
4623
4648
4674
4699
181
182
183
184
185
1355
1361
1366
1372
1377
2704
2719
2733
2748
2762
3454
3480
3505
3531
3556
136
137
138
139
140
1082
1089
1096
1103
1110
2052
2066
2081
2095
2110
4724
4750
4775
4801
4826
186
187
188
189
190
1383
1388
1394
1399
1405
2777
2791
2806
2820
2835
3581
3607
3632
3658
3683
141
142
143
144
145
1116
1122
1128
1134
1140
2124
2139
2153
2168
2182
4851
4877
4902
4928
4953
191
192
193
194
195
1410
1416
1421
1427
1432
2849
2864
2878
2893
2907
3708
3734
3759
3785
3810
146
147
148
149
150
1146
1152
1158
1164
1170
2197
2211
2226
2240
2255
4978
5004
5029
5055
5080
196
197
198
199
200
1438
1443
1449
1454
1460
2922
2936
2951
2965
2980
426
TRANSMISSION
Table B-9.-Relative
Elevation
m
LINE DESIGN
air density and barometric pressure
Barometric
mm
ft
pressure
in
Relative air density
at 25 OC
at II OF
0
328.08
656.17
984.25
1312.34
1
2
3
4
0
000
000
000
000
760
733
107
681
656
29.92
28.86
21.82
26.81
25.84
1 .oo
0.96
.93
.90
.86
1.00
0.96
.93
.90
.86
1640.42
1968.>0
2296.59
2624.67
2952.16
5
6
I
8
9
000
000
000
000
000
632
609
581
564
544
24.89
23.98
23.10
22.22
21.40
.83
.80
.77
.I4
.I2
.83
.80
.I1
.I4
.I2
3280.84
3608.92
3937.01
4265.09
4593.18
10 000
11000
12 000
13 000
14 000
523
503
484
465
447
20.58
19.81
19.05
18.31
17.58
.69
.66
.64
.61
.59
.69
.66
.64
.61
.59
4921.26
5249.34
15 000
16 000
429
412
16.88
16.21
.56
.54
.56
.54
Table B- 1O.-Barometric
Nonstandard
air factor
MANUAL
Barometric
mm of
mercury
pressure
inches of
mercury r
Elevation
m
ft
pressure versus elevation
Nonstandard
air factor
Barometric
mm of
mercury
pressure
inchesof
mercury 1
m
Elevation
ft
1 .oo
1.01
1.02
1.03
1.04
760
152
145
131
730
29.92
29.62
29.32
29.02
28.12
8:
171
256
343
0
280
561
841
1126
1.23
1.24
1.25
1.26
1.27
585
578
570
562
555
23.04
22.74
22.44
22.14
21.84
2154
2258
2362
2468
2580
1.05
1.06
1.07
1.08
1.09
722
114
101
699
692
28.42
28.12
27.83
27.53
21.23
432
521
609
691
788
1417
1709
1999
2287
2584
1.28
1.29
1.30
1.31
1.32
547
540
532
524
517
21.54
21.24
20.94
20.64
20.35
2691
2803
2914
3026
3139
8
9
9
9
10
1.10
1.11
1.12
1.13
1.14
684
676
669
661
654
26.93
26.63
26.33
26.03
25.13
878
971
1065
1159
1253
2881
3186
3495
3804
4112
1.33
1.34
1.35
1.36
1.37
509
502
494
486
419
20.05
19.75
19.45
19.15
18.85
3258
3317
3491
3617
3740
10 688
11079
11414
11 868
12 270
1.15
1.16
1.17
1.18
1.19
646
638
631
623
616
25.43
25.13
24.83
24.53
24.24
1347
1440
1534
1638
1739
4418
4724
5034
5375
5705
1.38
1.39
1.40
1.41
1.42
471
464
456
448
441
18.55
18.25
17.95
17.65
17.35
3864
3987
4113
4238
4369
12
13
13
13
14
1.20
1.21
1.22
608
600
593
23.94
23.64
23.34
1843
1946
2050
6045
6386
6727
1.43
1.44
1.45
433
426
418
17.05
16.76
16.46
4501
4630
4765
14 768
15 191
15 632
r Barometric
pressure = (29.92) (2 minus nonstandard
air factor).
7 068
7 409
I 750
8 098
8 463
829
195
561
921
299
676
082
493
904
333
APPENDIX
427
B
Table B-l 1.-Mass per unit volume and relative mass density of
wood species used for poles 1
Green
Air-dry
(15 percent moisture content)
Species
k/m3
Bald cypress
lb/ft3
kg/m3
lb/ft3
Relative
mass
density 2
512
32
0.42
801
Douglas-fn
Coast type
Rocky Mountain
625
657
39
41
545
480
34
30
.45
.40
Hemlock, western
657
41
464
29
.38
Larch, western
801
50
609
38
.51
Pine
Jack
Loblolly 3
Lodgepole
Longleaf’
Ponderosa
Red
Shortleaf
641
849
625
881
721
785
833
40
53
39
55
45
49
52
480
577
464
657
448
496
561
30
;;
41
28
31
35
.40
.47
.38
.54
.38
.41
.46
Red cedar
Eastern
Western
593
432
37
27
529
368
33
23
.44
.31
Redwood
801
50
400
25
.38
Spruce (red, sitka, and white)
545
34
448
28
.37
White cedar
Atlantic
Northern
400
432
25
27
368
352
23
22
.31
.29
type
r From “Wood Handbook,”
Agriculture.
Forest Products Laboratory,
U.S. Forest Service, Department
of
2 Based on volume when green, and mass when oven dry.
3 Part of southern yellow pine group.
Volume of pole
Metric
V= 2.616 x lo-‘h(d,’
+ d,d2)m3
where, h = length of pole, m
dr = diameter of pole at top, mm
di = diameter of pole at bottom, mm
U.S. Customary
V= 1.818 x lo-’ h(d12 +d,d2)ft3
where, h = length of pole, ft
dr = diameter of pole at top,-in
d2 = diameter of pole at bottom,
in
428
TRANSMISSION
LINE DESIGN MANUAL
Table B- 12 .-Conductor
temperature coefficients of expansion
for normal sag-tension computations
Temperature
coefficient
of expansion
Conductor
Stranding
InitialJOF
x 1o-6
Final/OF
x 1o-6
Initial/OC
x lo+
Final/OC
x 1o-6
EC aluminum
Steel
ACSR 1
ACSR
ACSR
ACSR
ACSR
ACSR
ACSR
ACSR
ACSR
ACSR
all
all
12.8
12.8
6.4
23.0
11.5
18.3
23.0
6/l
l/l
18/l
24/i'
26/l
30/l
45/l
54/l
54119
84119
6.4
10.2
9.5
11.6
10.5
9.9
9.5
11.2
10.2
10.4
11.2
10.5
9.8
11.1
10.8
10.5
9.9
11.5
10.1
10.8
11.5
11.1
20.8
18.9
11.8
11.0
20.2
18.3
18.8
20.1
11.5
18.9
11.1
21.1
19.5
18.9
11.8
20.7
19.3
19.5
20.6
’ For ACSR conductors, the values shown apply only when the stress is borne by both
the steel and aluminum strands.
APPENDIX
429
6
Table B-l 3.-Pressure on a projected area due to wind velocity
Indicated velocity
Actual velocity
Cylindrical
m/s
0.894
1.788
2.682
3.576
4.470
mi/h
:
6
8
10
12
14
16
m/s
mi/h
kPa
Pressure on projected area
surface
Flat surface
lblft=
kPa
lb/ft2
0.894
1.743
2.593
3.442
4.291
2.0
3.9
5.8
7.7
9.6
0.000 48
.OOl 82
.004 03
.007 10
.01103
0.01
.c4
.08
.15
.23
0.0008
.0031
.0068
.0119
.0185
0.02
.06
.14
.25
.39
11.2
12.9
14.5
16.2
17.8
.015 01
.019 91
.025 17
.03141
.037 92
.31
.42
.53
.66
.79
.0252
.0335
.0423
.0528
.0637
.53
.70
.88
1.10
1.33
5.364
6.258
7.152
8.046
8.940
to8
5.006
5.766
6.482
7.241
7.951
11.175
13.410
15.645
17.880
20.115
25
30
35
40
45
9.745
11.488
13.231
14.930
16.584
21.8
25.7
29.6
33.4
37.1
.056
.079
.104
.133
.164
88
05
86
51
73
1.19
1.65
2.19
2.79
3.44
.0956
.1328
.1762
.2243
.2768
2.00
2.77
3.68
4.68
5.78
22.350
24.585
26.820
29.055
31.290
50
55
60
65
70
18.238
19.892
21.500
23.065
24.630
40.8
44.5
48.1
51.6
55.1
.199
,237
.276
.318
.363
23
01
87
65
36
4.16
4.95
5.78
6.66
7.59
.3347
.3982
.4652
.5353
.6104
6.99
8.32
9.72
11.18
12.75
33.525
35.760
37.995
40.230
42.465
75
8”:
90
95
26.194
27.893
29.368
30.971
32.542
58.6
62.4
65.7
69.3
72.8
.410
.466
.516
.574
.634
97
01
60
76
30
8.58
9.73
10.79
12.01
13.25
.6904
.7829
.8679
.9656
1.0656
14.42
16.25
18.13
20.17
22.26
44.700
46.935
49.170
51.405
53.640
100
105
110
115
120
34.061
35.626
37.190
38.755
40.319
76.2
79.7
83.2
86.7
90.2
.694
.760
.828
.899
.973
90
22
43
62
70
14.52
15.88
17.31
18.79
20.34
1.1674
1.2772
1.3918
1.5114
1.6358
24.39
26.68
29.07
31.57
34.17
55.875
58.110
60.345
62.580
64.815
125
130
135
140
145
41.884
43.448
45.013
46.622
48.187
93.7
97.2
100.7
104.3
107.8
1.050
1.130
1.213
1.301
1.390
75
69
62
93
80
21.95
23.62
25.35
27.20
29.05
1.7653
1.8996
2.0389
2.1872
2.3365
36.87
39.68
42.59
45.69
48.81
67.050
71.520
75.990
80.460
84.930
150
160
170
180
190
49.751
52.835
55.964
59.093
62.178
111.3
118.2
125.2
132.2
139.1
1.482
1.672
1.875
2.091
2.315
55
05
96
59
68
30.97
34.93
39.19
43.69
48.37
2.4907
2.8090
3.1516
3.5139
3.8903
52.03
58.68
65.84
73.40
81.26
430
TRANSMISSION
Table B-14.-Equivalent
LINE DESIGN
MANUAL
metric data for standard electrical conductors
U.S. customary
Code word
Stranding
Turkey
swan
sparrow
Robin
Raven
6/l
611
6/l
6/l
6/l
Quail
Pigeon
Penguin
Partridge
Ostrich
6/l
6/l
6/l
z;::
Size of conductor
Thousand
AWG
circular
No.
mlls
@mill
6
4
2
Diameter,
in
0.198
Metric
Area, in2
Aluminum
Total
13.29
21.16
33.61
42.39
10.11
53.48
15.48
24.11
39.23
49.48
62.39
0.1219
0.1538
0.1939
11.35
0.2436
0.2140
16.31
11.21
61.42
85.03
101.23
135.16
152.00
18.65
99.23
125.10
151.16
116.17
0.2642
0.3122
0.3122
0.3146
0.3146
0.3012
0.3630
0.3850
0.4232
0.4356
18.31
20.41
198.19
234.19
248.39
21.19
110.45
201.42
201.42
241.68
241.68
213.03
281.03
0.4938
0.5083
0.5368
0.5526
0.5643
23.22
23.55
24.21
24.54
24.82
282.00
282.00
306.58
306.58
322.26
318.58
321.93
346.32
356.52
364.06
322.26
331.14
402.84
402.84
483.42
314.11
381.55
468.45
430.11
516.84
546.06
559.81
0.0206
0.0328
0.0521
0.0651
0.0829
0.0240
0.0383
0.0608
0.0161
0.0961
266.8
300.0
0.441
0.502
0.563
0.642
0.680
0.1045
0.1318
0.1662
0.2095
0.2356
0.721
0.183
0.806
0.846
0.858
0.914
210
3/o
4/o
Area, mm2
Aluminum
Total
5.03
6.35
8.03
9.02
0.250
0.316
0.355
0.398
If0
Diameter,
mm
12.15
14.30
Linnet
Ibis
Lark
Flicker
Hawk
2617
26/l
30/l
WI
26/l
336.4
391.5
397.5
411.0
411.0
Parakeet
Dove
Peacock
Squab
Rook
24/l
26/l
24/l
26/l
24/l
556.5
556.5
605.0
605.0
636.0
0.911
0.4311
0.4311
0.4152
0.4152
0.4955
Grosbeak
Flamingo
Drake
Tern
Rail
26/l
24/l
26/l
45/l
45/l
636.0
666.0
195.0
195.0
954.0
0.990
1.000
1.108
1.063
1.165
0.4995
0.5235
0.6244
0.6244
0.1493
0.5809
0.1261
0.6676
0.8011
25.15
25.40
28.14
21.00
29.59
C~dilld
Ortolan
Curlew
Bluejay
Finch
54/l
954.0
1033.5
30.38
30.81
1033.5
1113.0
1113.0
0.1493
0.8111
0.8117
0.8141
0.8141
0.8464
0.8618
2;:
45/l
54119
1.196
1.213
1.246
1.259
1.293
0.9169
0.9346
0.9849
31.65
31.98
32.84
483.42
523.68
523.68
563.93
563.93
45/l
1212.0
1212.0
1.345
1.382
1431.0
1431.0
1590.0
1.421
1.465
1.502
0.9990
0.9990
1.124
1.124
1.068
1.126
1.202
1.266
1.335
34.16
35.10
36.25
31.21
38.15
644.51
644.51
125.16
125.16
805.80
689.03
126.45
115.48
816.17
1590.0
1.545
1.602
1.762
1.131
1.401
1.512
1.831
1.116
39.24
40.69
44.15
44.12
805.80
901.93
1092.26
1098.06
901.74
915.48
Bittern
Pheasant
Bobolink
Plover
Lapwing
Falcon
ChUkiU
Bluebird
Kiwi
54119
45/l
54119
45/l
54119
84119
84119
1217
1180.0
2156.0
2161.0
0.921
0.953
0.966
1.249
1.249
1.398
1.693
1.102
0.5914
19.89
21.49
591.55
602.91
635.42
861.29
1181.29
1145.80
APPENDIX
Table B-15.-Selected
B
431
U-metric conversions. From /20/
Area
To convert
from
To
acre (U.S. survey1
are
barn
circular mil (cmil)
hectare (ha)
section [U.S. survey]
square centimeter
(cm’ )
square chain
square foot [International
(ft2 1
square foot [U.S. survey]
ut* 1
square inch (in* )
square kilometer
(km* )
square mile [International
(mi*)
square mile [U.S. survey]
(mi* )
square rod [U.S. survey]
hd*
1
square yard (yd*)
township
l
Exact
square
square
square
square
square
square
square
square
square
meter
meter
meter
meter
meter
meter
meter
meter
meter
______ Multiply
(m*)
(m*)
(m* )
(m*)
(m* )
(m*
(m*
(m*
(m*
f
4.046
* 1 .ooo
l 1 .ooo
5.067
“I .ooo
2.589
*I .ooo
* 1.562
“9.290
by
873
500
304
E+03
E+02
E- 28
E-10
E+04
E+06
E- 04
E- 04
E-02
341
E- 02
“6.451 600
1 .ooo
2.589 988
E- 04
E+OG
E+06
075
998
square meter
(m*
square meter
square meter
square meter
(m*
(m*
(m2
square meter
(m*
2.589
998
E+06
square meter
(m*
2.529
295
E+Ol
square meter
square meter
(m*
(m*
8.361
9.323
274
993
--
E-01
E+07
9.290
l
conversion.
Force
To convert
from
---
To
---
crinal
dyne (dyn)
kilogram force
(kgf)
kilopond
kip
ounce force
pound force (Ibf)
poundal
(pdl)
ton force
Exact
l
I
newton
newton
newton
newton
newton
newton
newton
newton
newton
Multiply
(N)
(N)
(N)
(N)
(N)
(N)
(N)
(N)
(N)
*1 .ooo
“I ,000
“9.806
“9.806
4.448
2.780
4.448
1.382
8.896
by
E-01
E- 05
650
650
222
139
222
550
444
E+03
E-01
E-01
E+03
conversion.
Force per length
To convert
from
dyne per centimeter
(dyn/cm)
kilogram force per meter
(W/m)
pound per foot (Ib/ft)
pound per inch (lb/in)
l
Exact
conversion.
To
Multiolv
newton
per meter
(N/m)
* 1 .ooo
newton
per meter
(N/m)
“9.806
newton
newton
per meter
per meter
(N/m)
(N/m)
1.459
1.751
bv
E- 03
650
390
268
E+Ol
E+O2
TRANSMISSION
432
LINE DESIGN MANUAL
Table B-15. -Selected X-metric conversions-Continued
Density-Mass
To convert
from
gram per cubic centimeter
(g/cm3 1
gram per liter (g/L)
megagram per cubic meter
&b/m3 1
metric ton per cubic meter
(t/m3 1
milligram
per liter (mg/L)
ounce per cubic inch
(oz/in3 )
ounce per gallon (oz/gal)
ounce per pint (oz/pt)
pound per
(Ib/in3)
pound per
(Ib/ft3)
pound per
(I b/yd3 1
pound per
cubic
inch
cubic foot
cubic yard
gallon
(lb/gall
slug per cubic foot
(slug/ft3 )
ton [short]
per cubic yard
(ton/yd3 1
l
Exact
capacity
To
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
per cubic
(kg/m3 1
per cubic
(kg/m3 1
per cubic
(kg/m3 1
per cubic
(kg/m3 l
per cubic
(kg/m3 1
per cubic
(kg/m3 1
per cubic
(kg/m3 1
per cubic
(kg/m3 1
per cubic
(kg/m3 l
per cubic
(kg/m’ 1
per cubic
(kg/m3 1
per cubic
(kg/m31
per cubic
(kg/m3 1
per cubic
(kg/m3 1
Multiply
by
“1 .ooo
E+03
*I .ooo
*I .ooo
E+03
*I a00
E+03
*I .ooo
E-03
1.729 994
E+03
7.489
152
9.361
440
E-01
2.767
990
E+04
1.601
846
E+OI
5.932
764
E-01
1.198
264
E+02
5.153
788
E+02
1.186
553
E+03
conversion.
Time
To convert
from
day [mean solar1 (dl
day [sidereal]
hour [mean solar] (hr)
hour [sidereal]
minute [mean solar] (min)
minute [sidereal]
month [mean calendar]
(mol
second [sidereal]
week 17 days1 (wkl
year [calendar]
(al
year [sidereal]
l
Exact
conversion.
Multiply
To
second
second
second
second
second
second
second
second
second
second
second
(s)
(sl
(s)
(s)
(s)
(sl
(sl
(sl
(sl
(s)
(sl
“8.640
8.616
“3.600
3.590
l 6.000
5.983
l 2.628
9.972
“6.048
l 3. I53
3.155
409
170
617
696
600
815
by
E+O4
E+O4
E+03
E+03
E+Ol
E+OI
E+O6
E-01
E+05
E+07
E+07
APPENDIX
B
433
Table B- 15 .-Selected SI-metric conversions-Continued
Length
-To convert
from
To
angstrom unit (A)
astronomical
unit (AU)
caliber
centimeter
(cm)
chain, surveyor’s
chain, engineer’s
chain, nautical
fathom
fermi [obsolete replaced by
femtometer]
femtometer
(fm)
foot [U.S. survey] (ft)
foot [International]
(ft)
furlong (fur)
inch (in)
kilometer
(km)
league
link, surveyor’s
light year (Iv)
microinch
(pin)
micrometer
@m)
micron [obsolete,
replaced by
micrometer]
mil (mil)
mile [International]
(mi
mile [Statute]
(mi)
mile [U.S. survey]
(mi)
nautical mile (nmi)
parsec
pica, printer’s
point, printer’s
rod
spat
vard (vd)
meter
meter
meter
meter
meter
meter
meter
meter
(m)
(m)
(m)
(m)
(m)
(m)
(m)
(m)
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
(m)
(m)
(m)
(m)
(m)
(m)
(m)
(m)
(m)
(m)
(m)
(m)
l 1 .ooo
* 1 .ooo
3.048
“3.048
2.011
l 2.540
l 1 .ooo
4.828
2.011
9.460
“2.540
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
(m)
(m)
(m)
(m)
(m)
(m)
(m)
(m)
(m)
(m)
(m)
(m)
“1.000
“2.540
* 1.609
1.609
1.609
l 1 .852
3.085
4.217
3.514
5.029
* 1.000
Exact conversion.
l
Linear
~
l
Exact conversion.
Multiply
density
l
1 .ooo
1.495979
“2.540
l 1 .ooo
2.011 680
“3.048
4.572
l 1.828
800
006
680
032
680
900
l 1.ooo
l 9.144
344
300
347
678
518
598
210
by
E-10
E+l 1
E- 02
E-02
E+Ol
E+Ol
E-15
E-15
E-01
E-01
E+02
E-02
E+03
E- 03
E-01
E+l5
E-08
E- 06
E-06
E- 05
E+03
E+03
E+03
E+03
E+16
E- 03
E- 04
E+12
E-01
TRANSMISSION
434
Table B-15.-Selected
LINE DESIGN MANUAL
N-metric
conversions-Continued
Load concentration
To convert
from
To
gram per square centimeter
(s/cm2 1
megagram per square metet
(Mg/m2 ]
metric ton per square mete1
(t/m2 ]
ounce per square inch
(ozlin2)
ounce per square foot
(oz/ft2 )
ounce per square yard
(o&d2
]
pound per square inch
(I b/in2 ]
pound per square foot
(Ib/ft2)
pound per square yard
(I b&d2 ]
ton per square foot
(ton/ft2 )
Exact
l
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
kilogram
meter
Multiply
per square
(kg/m’ )
per square
(kg/m2 )
per square
(kg/m’)
per square
(kg/m’ ]
per square
(kg/m21
per square
(kg/m’ )
per square
(kg/m2 )
per square
(kg/m2 )
per square
( kg/m2 )
per square
(kg/m2 )
by
*I .ooo
E+Ol
*I .ooo
E+03
*I .ooo
E+03
2.119
109
E-03
3.051
517
E-01
3.390
575
E- 02
7.030
696
E+02
4.882
428
5.424
920
E-01
9.071
a47
E+02
conversion.
Power
To convert
British thermal
(Btu,,/h
]
British thermal
(Btu,,/h
]
British thermal
(Btul,/min)
British thermal
unit [IT]
per hour
unit
per hour
[rc]
unit [tc]
per minute
unit
per second
[tcl
(Btu&
calorie [tc] per minute (cal,,/min)
calorie [tcl per second (calt,/s)
erg per second (erg/s]
foot-pound
per hour (ftlb/h)
foot-pound
per minute (ftlb/min)
foot-pound
per second (ft*lb/s)
horsepower
(hp)
horsepower
[boiler]
horsepower
[electric]
horsepower
[metric]
(hpM)
horsepower
[water]
ton [refrigeration]
l
Exact
conversion.
To
from
Multiolv
bv
watt
(W]
2.930
711
E-01
watt
(WI
2.928
751
E-01
watt
(WI
1.757
250
E+Ol
watt
watt
watt
watt
watt
watt
watt
watt
watt
watt
watt
watt
watt
(WI
(WI
(WI
(W]
(W]
(W]
(WI
(WI
(WI
(WI
(WI
(WI
(WI
1.054
6.973
l 4.lB4
350
333
E+03
E-02
l
1
.ooo
3.766 161
2.259 697
1.355 ala
7.456 999
9.809 500
“7.460
7.354 990
7.460 430
3.516 BOO
E-07
E- 04
E-02
E+02
E+03
E+02
E+O2
E+02
E+03
APPENDIX
B
435
Table B- 15 .-Selected S&metric conversions-Continued
Mass
To convert
barrel of cement
carat [metric]
carat (kt)
cental
centner
centner [metric]
grain
from
[376
To
lb]
gram (9)
hundredweight
[gross or long] (cwt)
hundredweight
[net or short]
(cwt)
kilogram
force-second
squared per
meter (kgfx* /m)
kilotonne
(kt)
ounce [avoirdupois]
(oz)
ounce [troy/apothecary]
(oz)
megagram
(Mg)
metric grain
metric ton (t)
milligram
(mg)
pennyweight
pound [avoirdupois]
(lb)
pound [troy/apothecary]
quintal
sack of cement 194 Ibs]
slug
ton [assay]
ton [long]
ton [ short]
tonne (t)
Exact
l
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
1.705
“2.000
2.591
4.535
4.535
1 .ooo
6.479
* 1 .ooo
5.080
4.535
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
kilogram
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
(kg)
“9.806
* 1 .ooo
2.834
3.110
* 1 .ooo
“5.000
* 1 .ooo
* 1 .ooo
1.555
4.535
3.732
“1.000
4.263
1.459
2.916
1 .016
9.071
“1.000
507
956
924
924
891
235
924
by
E+02
E- 04
E-04
E+Ol
E+Ol
E+02a
E- 05
E- 03
E+Ol
E+Ol
650
952
348
174
924
417
767
390
667
047
847
E+06
E-02
E- 02
E+03
E-05
E+03
E- 06
E-03
E-01
E-01
E+02
E+Ol
E+Ol
E-02
E+03
E+02
E+03
conversion.
a European
applies
Multiply
metric centner
to the centner
is 50 percent
of
this
value;
conversion
factor
presented
as used in the U.S.S.R
Frequency
I
To convert
from
To
Multiply
by
hertz
(Hz)
2.777
778
f- 04
cycle per minute
(c/min)
hertz
(Hz)
1.666
667
E-02
cycle per second
(c/s)
hertz
(Hz)
* 1 .ooo
hertz
(Hz)
“1.000
cycle per hour
(c/h)
fresnel
l
Exact
conversion.
E+12
436
TRANSMISSION
Table B-15.4elected
LINE DESIGN MANUAL
S-metric conversions-Continued
Pressure-Stress
To convert
from
atmosphere
[standard]
(atm)
bar
barye
dyne per square centimeter
(dyn/crr?)
foot of water 14 “Cl
gram force per square centimeter
(gf/cm’ )
inch of mercury
[O “Cl
inch of mercury
[ I6 “Cl
inch of water [4 “C]
inch of water [ I6 “C]
kilogram force per square meter
(kgf/m2 )
kilogram force per square centimeter
(kgf/cm’)
To
Multiply
by
Pascal (Pa)
Pascal (Pa)
Pascal (Pa)
1.013 250
“1.000
*I .ooo
E+05
E+05
E-01
Pascal (Pa)
Pascal (Pa)
“I .ooo
2.988 980
E-01
E+03
Pascal
Pascal
Pascal
Pascal
Pascal
(Pa)
(Pa)
(Pa)
(Pa)
(Pa)
“9.806
3.386
3.376
2.490
2.488
650
380
850
817
400
E+Ol
E+03
E+03
E+02
E+02
Pascal (Pa)
l 9.806
650
Pascal (Pa)
“9.806
650
E+04
kip per square inch (kip/in2)
kip per square foot (kip/ft2 )
megapascal (MPa)
meter-head
[meter of water, 4 “C]
millibar
(mbar)
millimeter
of mercury
[0 “C]
Pascal
Pascal
Pascal
Pascal
Pascal
Pascal
6.894 757
4.788 026
*I .ooo
9.806 365
“1.000
I .333 220
E+06
E+04
E+06
E+03
E+02
E+02
(mm(W)
millimeter
Pascal (Pa)
of water
[4 “C]
(Pa)
(Pa)
(Pa)
(Pa)
(Pa)
(Pa)
9.806
365
hm(H20))
newton per square meter (N/m2 )
pound per square foot (Ib/ft2 )
pound per square inch (lb/in2 )
poundal per square foot (pdl/ft2 )
tor
torr (mm(Hg))
l
Exact
conversion.
Pascal
Pascal
Pascal
Pascal
Pascal
Pascal
(Pa)
(Pa)
(Pa)
(Pa)
(Pa)
(Pa)
“I .ooo
4.788 026
6.894 757
I .488 164
* 1 .ooo
I .333 220
E+OI
E+03
E+02
APPENDIX
437
B
Table B-15. -Selected SI-metric conversions--Continued
Tempera
we
Scale
values
Degrees
Celsius
“C
Degrees
Fahrenheit
OF
-
x “c=
X OF=
$(x-
X K=
x-
x “R=
; (x-
X Or=
x + 273.15
:x+32
-
32)
273.15
fx-
491.67)
fx
+ 491.67
459.67
%x+32
Degrees
Reaumur
Or
%X
x + 459.67
t (x + 459.67)
$(x-
;(x
;X
x - 459.67
$X
Degrees
Rankine
“R
Kelvins
K
-
fX
$x
+ 273.15
$x
$(x-
K
OF
OR
Or
l”C=l
K=
1
9
5
4
5
IoF=
“R=
5
9
1
4
s
5
4
9
4
1 Or=
- 273.15)
491.67)
-
+491.67
Intervals:
“C
32)
1
TRANSMISSION
438
LINE DESIGN MANUAL
Table B- 15 .-Selected S-metric conversions-Continued
Velocity-Speed
To convert
Angular
from
revolution
(r/min)
revolution
(r/s)
per minute
per second
by
radian per second
(rad/s)
radian per second
(rad/s)
radian per second
(rad/s)
1.745
329
E-02
1.047
198
E-01
6.283
185
(L/T):
foot per second (ft/s)
foot per minute (ft/min)
foot per hour (ft/h)
foot per day (ft/d)
foot per year (ft/a)
inch per second (in/s)
inch per hour (in/h)
kilometer
per hour (km/h
knot [nautical miles per
hour1 (kn)
mile per hour (mi/h)
meter per hour (m/h)
meter per year (m/a)
millimeter
per second
(mm/s)
speed of light (c)
l
Multiply
(e/r):
degree per second
Linear
To
Exact
meter
meter
meter
meter
meter
meter
meter
meter
per
per
per
per
per
per
per
per
second
second
second
second
second
second
second
second
(m/s)
(m/s)
(m/s)
(m/s)
(m/s)
(m/s)
(m/s)
(m/s)
“3.048
“5.080
8.466
3.527
9.695
“2.540
7.055
2.777
meter
meter
meter
meter
per
per
per
per
second
second
second
second
(m/s)
(m/s)
(m/s)
(m/s)
5.144
4.470
2.777
3.170
meter
meter
per second
per second
(m/s)
(m/s)
*I .ooo
2.997
556
778
E-01
E- 03
E-05
E- 06
E- 09
E-02
E-06
E-01
444
400
778
979
E-01
E-01
E- 04
E-08
925
E-03
E+08
667
778
890
conversion.
Torque-Bending
To convert
from
dyne centimeter
(dyncm)
kilogram force
meter (kgfem)
kip-foot
(kip.ft)
ounce inch (oz.in)aS b
pound-foot
(Ib*ft) aSb
pound-inch
(Ib*in)aS b
moment
Multiply
To
newton
meter
(N-m)
l 1.ooo
newton
newton
newton
newton
newton
meter
meter
meter
meter
meter
(N.m)
(N*m)
(N*m)
(N-m)
(N-m)
“9.806 650
1.355 818
7.061 552
1.355 818
1.129848
l
Exact conversion.
iThe
addition
of the force designator
Most USBR
engipeers
reverse the
equivalent
terminology.
may be desirable,
torque
units, for
e.g., Ibf-ft.
example,
foot-pound;
by
E- 07
E+02
E- 03
E-01
this
is
APPENDIX
B
439
Table B- 15 .-Selected S&metric conversions-Continued
Volume-Capacity
To convert
from
To
Multiply
acre-foot
[U.S. survey1 (acre-ft)
barrel [oil] (bbl)
barrel [water]
(bbl)
board foot [l ft x 1 ft x 1 in]
cubic
cubic
cubic
meter
meter
meter
(m3)
(m3)
(m3 1
(fbm)
bushel [U.S., dry] (bu)
cord
cubic centimeter
(cm3)
cubic decimeter
(dm3)
cubic dekameter
(dam3 )
cubic foot (ft3)
cubic inch (in3 )
cubic kilometer
(km3)
cubic mile (mi3)
cubic millimeter
(mm3)
cubic yard (yd3 )
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
cubic
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
meter
(m3)
(m3
(m3)
(m3
(m3)
(m3)
(m3)
(m3
(m3)
(m3
(m3)
(m3
(m3
(m3
(m3
(m3
(m3
(m3)
(m3
(m3
(m3)
(m3
(m3
(m3
(m3)
(m3)
(m3
(m3)
(m3)
(m3
(m3
(m3
cubic
cubic
cubic
cubic
cubic
cup
firkin
fluid dram
fluid ounce [U.S.]
(fl.oz.)
gallon Ilmperiall
gallon [U.S., dry1
gallon [U.S., liquid]
(gal)
gill [U.S.]
kiloliter
(kL)
liter (L)
megaliter
(ML)
milliliter
(mL)
peck [U.S.]
pint [U.S., dry1
pint [U.S., liquid]
quart [U.S., dry1
quart [U.S., liquid]
stere [timber]
tablespoon
teaspoon
ton [sea freight or shipping
capacity]
ton [internal
cap. of ships or
register ton]
ton [vol. of oil]
ton [timber]
tun [U.S., liquid]
l
Exact conversion.
1
1
1.233
1.589
1.192
489
873
405
E+O3
E-01
E-01
2.359 737
3.523 907
3.624 556
* 1 .ooo
E-03
E- 02
549
737
871
691
353
060
884
412
941
E- 06
E-03
E+03
E-02
E- 05
E+09
E+09
E-09
E-01
E- 03
E-02
E- 06
E- 05
E-03
E- 03
E- 03
E-04
l 1.ooo
)
)
)
)
)
1
)
)
1
)
by
*1 .ooo
2.831
1.638
*1 .ooo
4.168
l 1 .ooo
7.645
2.359
3.406
3.696
2.957
4.546
4.404
3.785
1.182
“1.000
“1 .ooo
685
706
182
768
105
765
221
529
)
)
)
*1 .ooo
8.809
5.506
4.731
1.101
9.463
*1 .ooo
1.478
4.928
E-03
E+03
E-06
E- 03
E-04
E-04
E-03
E-04
676
922
E-05
E-06
meter
(m3 1
1.132
674
meter
meter
meter
meter
(m3)
(m3 1
(m3)
(m3 1
2.831
6.700
1.415
9.539
685
179
842
238
1
)
)
)
l 1.ooo
E-O!
<<Appendix
C
CONDUCTORANDOVERHEADGROUNDWIREDATATABLES
The
tables
in this
and stress-strain
and
based on information
and
Wire
Initial
loading
Co.
(U.S.
appendix
creep
from
Steel)
have
catalog
modulus
values shown
curve between
the point
at 50 percent
of the
ultimate
been
prepared
for
ACSR
curves prepared
by the Aluminum
Copperweld
Steel Co., and the
conductor
based
upon
conductor
data
Association.
The Alumoweld
data are
steel data are based on American
Steel
information.
in the
where
tables were determined
the entire
conductor
from
starts
the
average
the
to share
slope
load
of the initial
the point
and
strength.
Permanent
set values
were determined
at 50 percent
of the conductor
ultimate
strength
as it
represents
the maximum
stress permitted
under
full load conditions.
Creep values were determined
at 18 percent
of the ultimate
strength
of the conductor
because
ma
no-load
tension
on
a
conductor.
this would
be about
equal to the 15.5 ‘C (60 OF) f
1
441
442
TRANSMISSION
LINE DESIGN
MANUAL
Table C-l .-Permanent set, creep, and initial and final
modulus values (metric)
103.42
110.32
117.21
124.11
131 .oo
137.90
144.79
151.69
158.58
165.48
172.37
179.26
186.16
193.05
199.95
206.84
.00070146
.00123350
’ Calculated at 18 percent of ultimate strength.
APPENDIX
443
C
Table C-l .-Permanent set, creep, and initial and final
modulus values (metric&Continued
DS AND
Code
word
Size,
mm2
WANATE
PARATE
21.13
33.64
1 STFFI
1O-year
creep’
S
Tension’ ,
N
I
1
1.00048932
.00047536
1
1889.6
AND
Final
modulus,
GPa
87.012
87.012
L
Stress,
MPa
6.89
13.79
20.68
27.58
34.47
41.37
48.26
55.16
62.05
68.95
75.84
82.74
89.63
96.53
103.42
110.32
117.21
124.11
131 .oo
137.90
144.79
151.69
158.58
165.48
172.37
i79.26
186.16
193.05
199.95
206.84
213.74
220.63
227.53
234.42
Permanent
set
.00002236
.00003009
.00003766
.00004518
.00005282
.00006070
.00006896
.00007776
.00008723
.00009751
.00010874
.00012106
.00013462
.00014955
.00016600
.00018410
.00020401
to0022585
.00024977
.00027591
.00030442
.00033543
.00036908
.00040552
.00044488
.00048731
.00053295
.00058194
.00063441
.00069052
.00075040
.00081419
.00088204
.00095408
Calculatedat 18 percentof ultimate strength.
Initial
modulus,
GPa
79.271
79.351
79.389
79.383
79.335
79.244
79.112
78.939
78.726
78.474
78.186
77.862
77.505
77.115
76.696
76.249
75.776
75.280
74.761
74.223
73.666
73.094
72.507
71.909
71.299
70.680
70.054
69.421
68.784
68.143
67.500
66.856
66.211
444
TRANSMISSION
LINE DESIGN
MANUAL
Table C-l .-Permanent set, creep, and initial and final
modulus values (metric&Continued
r
STRANDS
Code
word
Size,
mm2
135.19
170.45
201.41
241.70
‘AXW I NG
IERL IN
HICKADEE
‘ELICAN
SPREY
INGBIRD
287.05
322.26
Stress,
MPa
6.89
13.79
20.68
27.58
34.47
41.37
48.26
55.16
62.05
68.95
75.84
82.74
89.63
96.53
103.42
110.32
117.21
124.11
131 .oo
137.90
144.79
151.69
158.58
165.48
’ Calculated at 18 &ent
AN
1O-year
creep’
Tension’,
N
.00058691
.00058702
.00056698
.00056019
.00055702
.00055886
5508.7
6949.9
7958.7
9448.0
10969.3
12570.6
Permanent
set
.00007997
.00011682
.00015029
.00018134
.00021094
.00024002
.00026954
.00030046
.00033374
.00037032
.00041116
.00045722
.00050944
.00056879
.00063621
.00071266
.00079909
.00089647
.00100573
.00112784
.00126375
.00141442
.00158079
.00176383
of ultimate
1
1 STE!=l S
strength.
Final
modulus,
GPa
68.031
68.031
68.031
68.031
68.031
68.031
Initial
modulus,
GPa
49.893
50.516
51.036
51.441
51.725
51.885
51.919
51.831
51.627
51.313
50.900
50.400
49.824
49.183
48.489
47.754
46.985
46.194
45.387
44.570
43.751
42.933
42.120
APPENDIX
C
445
Table C-l .-Permanent set, creep, and initial and final
modulus values (metric&Continued
r
7 STFFI
Code
word
Size,
mm2
7ANT
I CKER
~RAKEET
IACOCK
IOK
-AM I NGO
JCKOO
201.41
241.70
281 .98
306.81
322.26
337.46
402.83
1O-year
creep’
Tension’,
N
11689.9
13771.6
15853.4
17294.6
17614.9
18976.0
22338.9
.00050955
.00049932
.00049191
.00049382
.00047682
.00049160
.0004845a
S’ LBANDS
Final
modulus,
GPa
72.602
72.602
72.602
72.602
72.602
72.602
72.602
L
Stress,
MPa
6.89
13.79
20.68
27.58
34.47
41.37
48.26
55.16
62.05
68.95
75.84
82.74
89.63
96.53
103.42
110.32
117.21
124.11
131 .oo
137.90
144.79
151.69
158.58
165.48
172.37
i79.26
186.16
193.05
199.95
’ Calculated
at 18 percent
Permanent
set
.0000444
I
.00007736
,000 I 0696
.00013378
.OOOI 5840
.00018138
.000203
30
.00022474
.00024627
.00026846
.00029
I 89
.00031713
.00034475
.00037532
.00040943
.ooO44764
.00049053
.00053867
.00059263
.00065299
,00072033
.0007952
I
.0008782
i
.00096990
. 00 I 07086
.OOl 18166
.00130287
.00143507
.00157883
of ultimate
strength.
Initial
modulus,
GPa
53 .900
54.625
55.288
55.880
56.395
56.827
57.170
57.422
57.581
57 646
57.620
57.506
57.307
57 .029
56.678
56 .262
55.787
55.259
54.687
54.077
53.435
52.767
52.079
51.375
50.660
49.939
49.213
48.487
TRANSMISSION
446
LINE DESIGN
MANUAL
Table C-l .-Permanent set, creep, and initial and final
modulus values (metric&Continued
r
STRANDSAM2
Code
word
4RTR I DGE
STR I CH
I NNET
31s
4WK
IJVE
IJUAB
?OSBEAK
TARL I NG
?AKE
Size,
mm2
135.19
152.01
170.45
201.41
241.70
281.98
306.55
322.26
362.54
402.83
1O-year
creep’
10168.6
11289.5
13051 .o
15613.2
18095.3
19456.4
20177.0
22739.2
25221.3
-1
L
6.89
13.79
.00007464
.00010656
206.84
.00013679
.00016568
.00019357
.00022078
.00024767
.00027456
.00030180
.00032973
.00035868
.00038900
.00042101
.00045507
.00049150
.00053065
.00057285
.00061844
.00066777
.00072116
.00077897
.00084152
.00090915
.00098221
.00106103
.00114595
.00123731
.00133544
.00144069
.00155340
’ Calculated at 18 Ijercent of ultimate
74.188
74.188
74.188
74.188
74.188
74.188
74.188
74.188
74.188
74.188
9047.6
.00050213
.00050168
.00049623
.00048422
.00048255
.00047888
.00047298
.00046581
.00046675
.00046583
Permanent
set
137.90
144.79
151.69
158.58
165.48
172.37
i79.26
186.16
193.05
199.95
Final
modulus,
GPa
Tension’
N
Stress,
MPa
20.68
27.58
34.47
41.37
48.26
55.16
62.05
68.95
75.84
82.74
89.63
96.53
103.42
110.32
117.21
124.11
131 .oo
ANDS
strength.
L
Initial
modulus,
GPa
55.223
55.600
55.932
56.215
56.449
56.631
56.761
56.837
56.860
56.831
56.750
56.619
56.440
56.216
55.948
55.640
55.295
54.915
54.505
54.067
53.604
53.119
52.615
52.096
51.562
51.018
50.465
49.905
49.340
1
APPENDIX
C
447
Table C-l .-Permanent set, creep, and initial and final
inodulus values (metric&-Continued
30
AI MUJ.M
Size,
mm*
Code
word
RIOLE
ARK
EN
AGLE
170.45
201.41
241.70
281.98
Stress,
MPa
6.89
13.79
20.68
27.58
34.47
41.37
48.26
55.16
62.05
68.95
75.84
82.74
89.63
96.53
103.42
110.32
117.21
124.11
131 .oo
137.90
144.79
151.69
158.58
165.48
172.37
i79.26
186.16
193.05
199.95
206.84
213.74
STRANDS
AND
1O-year
creep’
7 STFFL
SIjXANDS
Tension’ ,
N
.00041719
.00041419
.00040398
.00040442
Permanent
set
.00004619
.00006826
.00008940
.00010977
.00012958
.00014901
.00016823
.00018745
.00020683
.00022657
.00024684
.00026785
.00028976
.00031276
.00033705
.00036280
.00039020
.00041943
.00045068
.00048413
.00051997
.00055839
.00059956
.00064367
.00069091
.00074147
.00079552
.00085325
.00091485
.00098050
.00105038
’ Calculated at 18 percent of ultimate strength.
13851.7
16253.7
19056.1
22258.8
Final
modulus,
GPa
78.187
78.187
78.187
78.187
Initial
modulus,
GPa
62.536
62.804
63.040
63.241
63.407
63.538
63.633
63.691
63.713
63.698
63.648
63.563
63.444
63.291
63.106
62.890
62.645
62.372
62.072
61.748
61.401
61.033
60.645
60.240
59.818
59.382
58.933
58.472
58.001
57.522
448
TRANSMISSION
LINE DESIGN MANUAL
Table C-l .-Permanent
set, creep, and initial and final
modulus values (metric&Continued
IlWNDs AND
4
Code
word
T ERN
RUDDY
RAIL
0 RTOLAN
B LUEJAY
B UNT I NG
B I TTERN
D I PPER
BOBOL I NK
NNUTHATCH
L APWI NG
1O-year
creep’
Size,
mm2
402.83
456.03
483.39
523.67
563.96
604.24
644.52
684.81
725.09
765.37
805.65
00057764
00056147
00056215
00055394
00055325
00055490
00055412
00055343
00055282
00054804
00054776
Tension’
N
L
Stress,
MPa
Permanent
set
6.89
.00007248
.00012961
.00017972
,00022409
.00026402
.00030081
.00033576
.00037017
.00040532
.00044251
.00048305
.00052822
.00057932
.00063765
.00070450
.00078118
.00086897
.00096917
.00108308
.00121199
.00135721
.00152002
.00170172
17694.9
19536.5
20737.5
22178.7
23860.1
25621.6
27303.1
28984.5
30665.9
32107.1
33788.5
- -
-
Final
modulus,
GPa
64.466
64.466
64.466
64.466
64.466
64.466
64.466
64.466
64.466
64.466
64.466
Initial
modulus,
GPa
-
13.79
20.68
27.58
34.47
41.37
48.26
55.16
62.05
68.95
75.84
82.74
89.63
96.53
103.42
110.32
117.21
124.11
131 .oo
137.90
144.79
151.69
158.58
Calculated at 18percentofultimate
strength.
42.020
42.961
43.828
44.606
45.278
45.830
46.251
46.534
46.679
46.686
46.562
46.317
45.963
45.513
44.982
44.384
43.731
43.036
42.309
41.561
40.799
40.030
APPENDIX
C
449
Table C-l .-Permanent
set, creep, and initial and final
modulus values (metric&Continued
Code
word
Size,
mm*
402.83
456.03
483.39
523.67
ONDOR
ANARY
ARD I NAL
URLEW
I;_;
I
1O-year
creep’
00046434
00046390
00046369
00046347
Tension’ ,
N
22579.1
25541.6
27062.8
29304.7
67.114
67.114
67.114
67.114
-
Stress,
MPa
6.89
13.79
20.68
27.58
34.47
41.37
48.26
55.16
62.05
68.95
75.84
82.74
89.63
96.53
103.42
110.32
117.21
124.11
131 .oo
137.90
144.79
151.69
158.58
165.48
172.37
179.26
Permanent
set
00005753
00010350
00014543
00018402
00021994
00025388
00028652
00031856
00035066
00038352
00041782
00045425
00049348
00053621
00058311
00063487
00069218
00075571
00082615
00090420
00099052
00108580
00119074
00130600
00143228
00157026
Calculated at 18 percent of ultimate
strength.
Final
modulus,
GPa
1
Initial
modulus,
GPa
46.368
47.014
47.606
48.136
48.598
48.987
49.297
49.527
49.674
49.738
49.721
49.624
49.453
49.212
48.907
48.543
48.126
47.665
47.163
46.629
46.066
45.482
44.879
44.264
43.639
450
TRANSMISSION
LINE DESIGN MANUAL
Table C-l .-Permanent set, creep, and initial and final
modulus values (metric)-Continued
r
9 STFFl
Code
word
Size,
mm2
563.96
604.24
644.52
684.81
725.09
765.37
805.65
I NCH
RACKLE
HEASANT
ARTIN
LOVER
ARROT
ALCON
1O-year
creep’
00050022
00050043
0004877 1
00048760
00048851
00048704
00048789
S
Tension’ ,
N
31306.4
33548.3
34909.5
37071.3
39313.2
41394.9
43636.8
Final
modulus,
GPa
69.706
69.706
69.706
69.706
69.706
69.706
69.706
Stress,
MPa
6.89
13.79
20.68
27.58
34.47
41.37
48.26
55.16
62.05
68.95
75.84
82.74
89.63
96.53
103.42
110.32
117.21
124.11
131 .oo
137.90
144.79
151.69
158.58
165.48
172.37
179.26
186.16
Permanent
set
Initial
modulus,
GPa
.00002892
.00006013
.00008941
.00011729
.00014431
.00017099
.00019788
.00022551
.00025441
.00028512
.00031817
.00035409
.00039342
.00043669
.00048444
.00053719
.00059549
.00065987
.00073086
.00080900
.00089482
.00098885
.00109163
.00120369
.00132557
.00145779
.00160090
’ Calculated at 18 percent of ultimate
strength.
52.987
53.386
53.717
53.976
54.159
54.267
54.299
54.254
54.136
53.948
53.692
53.374
52.999
52.571
52.097
51.582
51.031
50.451
49.845
49.219
48.577
47.923
47.260
46.592
45.922
45.251
APPENDIX
451
C
Table C-l .-Permanent set, creep, and initial and final
modulus values (metric&-Continued
9 STFFL S
Size,
mm2
Code
word
901.93
092.45
552.53
HUCKAR
LUEBIRD
1O-year
creep’
Tension’,
N
00071310
00069677
00069663
40834.5
48280.8
68617.9
LANDS
Final
modulus,
GPa
66.811
66.811
66.811
L
Stress,
MPa
6.89
13.79
20.68
27.58
34.47
41.37
48.26
55.16
62.05
68.95
75.84
82.74
89.63
96.53
103.42
110.32
117.21
124.11
131.00
137.90
144.79
151.69
158.58
165.48
Initial
modulus,
GPa
Permanent
set
0.00000000
.00003350
.00006531
.00009538
.00012455
.00015366
.00018356
.00021507
.00024904
.00028631
.00032772
.00037411
.00042632
.00048519
.00055156
.00062627
.00071016
.00080407
.00090885
.00102532
.00115433
.00129672
.00145333
.00162500
50.111
50.590
50.972
51.251
51.423
51.487
51.443
51.296
51.050
50.713
50.293
49.799
49.241
48.628
47.970
47.275
46.551
45.807
45.048
44.280
43.509
42.737
41.970
1t Calculated at 18 percent of .ultimate strength.
TRANSMISSION
452
LINE DESIGN MANUAL
Table C-2.-Permanent set, creep, and initial and final
modulus values (U.S. customary)
r
1
1 STFFL S
L
Code
word
TURKEY
SWAN
SPARROW
ROBIN
RAVEN
QUAIL
PI GEON
PENGU I N
Size,
AWG 01
kcmil
6
4
2
1
l/O
2/o
3/o
4/o
1O-year
creep’
214.
335.
513.
639.
788.
956.
1192.
1503.
.00046458
.00045465
.00043810
.00043228
.00042251
.00040529
.00040014
.00040034
L
Stress,
lb/in’
Final
modulus,
lb/in2
Tension’ ,
lb
Permanent
set
11460000.
11460000.
11460000.
11460000.
11460000.
11460000.
11460000.
11460000.
-
1
Initial
modulus,
lb/in2
1000.
2000.
3000.
4000.
5000.
6000.
7000.
8000.
9000.
10000.
11000.
12000.
13000.
14000.
15000.
16000.
17000.
18000.
19000.
20000.
21000.
22000.
23000.
24000.
25000.
26000.
27000.
28000.
29000.
30000.
.00005034
.00006347
.00007589
.00008791
.00009981
.00011190
.00012448
.00013784
.00015228
.00016810
.00018560
.00020507
.00022682
.00025114
.00027834
.00030870
.00034253
.00038012
.00042178
.00046780
.00051848
.00057412
.00063501
.00070146
.00077376
.00085221
.00093712
.00102877
.00112746
.00123350
L
’ Calculated at 18 percent of ultimate
strength.
9960963.
9996316.
10021891.
10037502.
10043072.
10038633.
10024321.
10000376.
9967127.
9924989.
9874445.
9816035.
9750342.
9677978.
9599568.
9515745.
9427132.
9334340.
9237955.
9138534.
9036604.
8932655.
8827140.
8720474.
8613037.
8505170.
8397179.
8289339.
8181890.
APPENDIX
453
C
Table C-2.-Permanent set, creep, and initial and final
modulus values (U.S. customary&Continued
.00007776
.00009751
.00010874
.00014955
.00016600
.00020401
.00036908
.00044488
t Calculated at 18 percent of ultimate
strength.
11497226.
11508882.
11514317.
11513518.
11506512.
11493358.
11474154.
11449026.
11418134.
11381666.
11339833.
11292869.
11241027.
11184574.
11123789.
11058958.
10990372.
10918326.
10843111.
10765016.
10684325.
10601313.
10516247.
10429384.
454
TRANSMISSION
LINE DESIGN
MANUAL
Table C-2.-Permanent
set, creep, and initial and final
modulus values (U.S. customary)-Continued
1
1 STFFL S
Code
word
Size,
AWG or
kcmil
WAXWI NG
MERL IN
CHICKADEE
PEL I CAN
OSPREY
KINGBIRD
266.8
336.4
397.5
477.0
566.5
636.0
Stress,
lb/in2
1000.
2000.
3000.
4000.
5000.
6000.
7000.
8000.
9000.
10000.
11000.
12000.
13000.
14000.
15000.
16000.
17000.
18000.
19000.
20000.
21000.
22000.
23000.
24000.
1O-year
creep’
.00058691
.00058702
.00056698
.00056019
.00055702
.00055886
Permanent
set
.00007997
.00011682
.00015029
.00018134
.00021094
.00024002
.00026954
.00030046
.00033374
.00037032
.00041116
.00045722
.00050944
.00056879
.00063621
.00071266
.00079909
.00089647
.00100573
.00112784
.00126375
.00141442
.00158079
.00176383
Calculated at 18 percent of ultimate
lb
Final
modulus,
lb/in2
1238.
1562.
1789.
2124.
2466.
2826.
9867000.
9867000.
9867000.
9867000.
9867000.
9867000.
Tension’,
strength.
Initial
modulus,
lb/in2
7236257,
7326749.
7402066.
7460835.
7502070.
7525224.
7530226.
7517466.
7487760.
7442273.
7382441.
7309875.
7226273.
7133343.
7032742.
6926027.
6814624.
6699814.
6582724.
6464328.
6345457.
6226811.
6108966.
APPENDIX
C
455
Table C-2.-Permanent set, creep, and initial and .final
modulus values (U.S. customary)-Continued
TRANDS
Size
AWG or
kcmil
Code
word
AJYR
7
1O-year
creep’
STFFL
S‘
ANDS
Final
modulus,
lb/in*
Tension’,
lb
~~
IRANT
L I CKER
IARAKEET
‘EACOCK
!OOK
LAM I NGO
:UCKOO
397.5
477.0
556.5
605.5
636.0
666.0
795.0
.00050955
.00049932
.00049191
.00049302
.00047682
.00049160
.00048458
1
Stress,
lb/in2
Permanent
set
1000.
.0000444
.00007736
.00010696
.00013378
.00015840
.00018138
.00020330
.00022474
2000.
3000.
4000.
5000.
6000.
7000.
8000.
9000.
10000.
11000.
12000.
13000.
14000.
15000.
16000.
17000.
18000.
19000.
20000.
21000.
22000.
23000.
24000.
25000.
26000.
27000.
28000.
29000.
L
Initial
modulus,
lb/in2
I
.00024627
.00026846
.00029
I89
.00031713
00034475
: 00037532
.00040943
.00044764
.00049053
00053867
: 00059263
.00065299
.00072033
.0007952
I
.0008782
I
.00096990
.00107086
.OOll8166
. 00 I 30287
. 00 I43507
.00157883
Calculated at 18 percent qf ultimate
10530000.
10530000.
10530000.
10530000.
10530000.
10530000.
10530000.
2628.
3096.
3564.
3888.
3960.
4266.
5022.
strength.
7817435
7922641
8018775.
8 I 04704
8179403.
.
.
824 I 996
829 I796
8328327.
8351347
8360853
8357070.
8340441
a31 1590.
827 I299
8220464.
8 I60059
8091 IO3
.
8014626
793 I642
7843128.
7750010.
7653 I47
7553330.
745 I274
73476 I 9
7242933
7137716.
7032400.
.
.
.
.
.
.
.
.
.
.
.
.
456
TRANSMISSION
LINE DESIGN MANUAL
Table C-2.-Permanent
set, creep, and initial and final
modulus values (U.S. customary)-Continued
1000.
2000.
3000.
4000.
5000.
6000.
7000.
8000.
9000.
10000.
11000.
12000.
13000.
14000.
15000.
16000.
17000.
18000.
19000.
20000.
21000.
22000.
23000.
24000.
25000.
26000.
27000.
28000.
29000.
30000.
at 18 percentofultimate
.00007464
.00010656
.00013679
.00016568
.00019357
.00022078
.00024767
.00027456
.00030180
.00032973
.00035868
.00038900
.00042101
.00045507
.00049150
.00053065
.00057285
.00061844
.00066777
.00072116
.00077897
.00084152
.00090915
.00098221
.00106103
.00114595
.00123731
.00133544
.00144069
.00155340
strength.
8009304.
8064029.
8112144.
8153295.
8187189.
8213600.
8232378.
8243448.
8246813.
8242554.
8230825.
8211848.
8185905.
8153331.
8114503.
8069834.
8019760.
7964731.
7905206.
7841642.
7774488.
7704182.
7631143.
7555770.
7478440.
7399503.
7319286.
7238088.
7156184.
APPENDIX
457
C
Table C-2.-Permament set, creep, and initial and final
modulus values (U.S. customary)-Continued
1000.
2000.
3000.
4000.
5000.
6000.
7000.
8000.
9000.
10000.
11000.
12000.
13000.
14000.
15000.
16000.
17000.
18000.
19000.
20000.
21000.
22000.
23000.
24000.
25000.
26000.
27000.
28000.
29000.
30000.
31000.
.00004619
.00006826
.00008940
.00010977
.00012958
.00014901
.00016823
.00018745
.00020683
.00022657
.00024684
.00026785
.00028976
.00031276
.00033705
.00036280
.00039020
.00041943
.00045068
.00048413
.00051997
.00055839
.00059956
.00064367
.00069091
.00074147
.00079552
.00085325
.00091485
.00098050
.00105038
Calculated at 18 percent o$ ultimate strength.
9069999.
9108929.
9143072..
9172274.
9196403.
9215362.
9229082.
9237528.
9240698.
9238620.
9231356.
9218997.
9201662.
9179498.
9152671.
9121373.
9085809.
9046200.
9002779.
8955785.
8905464.
8852064.
8795831.
8737012.
8675847.
8612572.
8547413.
8480591.
8412314.
8342782.
458
TRANSMISSION
LINE DESIGN
MANUAL
Table C-2.-Permanent
set, creep, and initial and final
modulus values (U.S. customary&-Continued
r
AND
Code
word
TERN
RUCDY
RAIL
ORTOLAN
BLUE JAY
BUNT I NG
B I TTERN
D I PPER
BOBOL I NK
NUTHATCH
LAPW I NG
Size,
AWG 01
kcmil
795.0
900.0
954.0
1,033.5
1,113.0
1,192.5
1,272.0
1,351.5
1,431.0
1,510.5
1.590.0
1O-year
creel.9
7 STFF’
Tension’,
lb
.00057764
.00056147
.00056215
.00055394
.00055325
.00055490
.00055412
.00055343
.00055282
.00054804
eOOO54776
Stress,
lb/in2
Permanent
set
1000.
2000.
3000.
4000.
5000.
6000.
7000.
8000.
9000.
10000.
11000.
12000.
13000.
14000.
15000.
16000.
17000.
18000.
19000.
20000.
21000.
22000.
23000.
.00007248
.00012961
.00017972
.00022409
.00026402
.00030081
.00033576
.00037017
.00040532
.00044251
.00048305
.00052822
.00057932
.00063765
.00070450
.00078118
.00086897
.00096917
.00108308
.00121199
.00135721
.00152002
.00170172
1 Calculated at 18’percent of ultimate
strength.
S
3978.
4392.
4662.
4986.
5364.
5760.
6138.
6516.
6894.
7218.
7598.
-
Final
modulus,
lb/in2
9350000.
9350000.
9350000.
9350000.
9350000.
9350000.
9350000.
9350000.
9350000.
9350000.
9350000.
Initial
modulus,
lb/in2
6094514.
6230875.
6356725.
6469544.
6566978.
6647001.
6708064.
6749205.
6770117.
6771136.
6753185.
6717665.
6666327.
6601128.
6524109.
6437290.
6342586.
6241760.
6136388.
6027851.
5917333.
5805834.
APPENDIX
459
C
Table C-2.-Permanent
set, creep, and initial and final
modulus values (US. customary&-Continued
Size,
AWG or
kcmil
Code
word
CONDOR
CANARY
CARDINAL
CURLEW
795.0
900.0
954.0
1.033.5
1O-year
creep’
.00046434
.00046390
.00046369
.00046347
5076.
5742.
6084.
6588.
9734000.
9734000.
9734000.
9734000.
Stress,
lb/in’
Permanent
set
1000.
2000.
3000.
4000.
5000.
6000.
7000.
8000.
9000.
10000.
11000.
12000.
13000.
.00005753
.00010350
.00014543
.00018402
.00021994
.00025388
.00028652
.00031856
.00035066
.00038352
.00041782
.00045425
.00049348
.00053621
.00058311
.00063487
.00069218
.00075571
.00082615
.00090420
.00099052
.00108580
.00119074
.00130600
.00143228
.00157026
14000.
15000.
16000.
17000.
18000.
19000.
20000.
21000.
22000.
23000.
24000.
25000.
26000.
Calculatedat
percentofultimate
strength.
Final
modulus,
lb/in2
Tension’,
lb
1
Initial
modulus,
lb/in2
6725040.
6818757.
6904585.
6981488.
7048526.
7104893.
7149946.
7183242.
7204543.
7213835.
7211311.
7197364.
7172554.
7137584.
7093261.
7040465.
6980111.
6913128.
6840425.
6762878.
6681315.
6596501.
6509140.
6419866.
6329243.
,
460
TRANSMISSION
LINE DESIGN MANUAL
Table C-2.-Permanent
set, creep, and initial and final
modulus values (U.S. customary&Continued
1000.
2000.
3000.
4000.
5000.
6000.
7000.
8000.
9000.
10000.
11000.
12000.
13000.
14000.
15000.
16000.
17000.
18000.
19000.
20000.
21000.
22000.
23000.
24000.
25000.
26000.
27000.
.00002892
.00006013
.0000894 1
.00011729
.00014431
.00017099
.00019788
.00022551
.00025441
.00028512
.00031817
.00035409
.00039342
.00043669
.00048444
.00053719
.00059549
.00065987
.00073086
.00080900
.00089482
.00098885
.00109163
.00120369
.00132557
.00145779
.00160090
’ Calculated at 18 percent of ultimate strength.
7685036.
7742948.
7790922.
7828437.
7855119.
7870755.
7875301.
7868880.
7851773.
7824407.
7787332.
7741200.
7686737.
7624723.
7555962.
7481264.
7401427.
7317221.
7229375.
7138573.
7045445.
6950565.
6854451.
6757566.
6660319.
6563070.
APPENDIX
461
C
Table C-2.-Permanent set, creep, and initial and final
modulus values (U.S. customary&Continued
1000.
2000.
3000.
4000.
5000.
6000.
7000.
8000.
9000.
10000.
11000.
12000.
13000.
14000.
15000.
16000.
17000.
18000.
19000.
20000.
21000.
22000.
23000.
24000.
0.00000000
.00003350
.00006531
.00009538
.00012455
.00015366
.00018356
.00021507
.00024904
.00028631
.00032772
.00037411
.00042632
.00048519
.00055156
.00062627
.00071016
.00080407
.00090885
.00102532
.00115433
.00129672
.00145333
.00162500
Calculated at 18 percent of ultimate strength.
7267970.
7337414.
7392798.
7433244.
7458197.
7467449.
7461150.
7439784.
7404137.
7355238.
7294302.
7222659.
7141699.
7052811.
6957345.
6856575.
6751677.
6643716.
6533641.
6422281.
6310355.
6198473.
6087152.
Table C-3.-Conductor
Code
word
TURKEY
SWAN
SWANATE
SPARROW
SPARATE
ROBIN
RAVEN
QUAIL
PIGEON
PENGU I N
GROUSE
PETREL
M I NORCA
LEGHORN
GUINEA
DOTTEREL
DORK I NG
COCH I N
OWL
WAXWI NG
PARTR I DGE
OSTR I CH
MERLIN
LINNET
ORIOLE
CH I CKADEE
BRANT
IBIS
Size,
mm2
13.28
21.13
21..13
33 864
33.64
42.41
53.46
67.44
85.02
107.22
40.54
51.58
56.14
68.20
80.57
89.64
96.68
107.07
135.19
135.19
135.19
152.01
170.45
170.45
170.45
201.41
201.41
201.41
’ Does not include NEW constant.
Stranding!
Xameter,
hminum,
mm
steel
6/
6/
7/
6/
7/
6/
6/
6/
6/
6/
8/
12/
12/
12/
12/
12/
12/
12/
6/
18/
26/
26/
18/
26/
30/
18/
24/
26/
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
1
7
7
1
7
7
1
7
7
5.03
6.35
6.53
8.03
8.26
9.02
10.11
11.35
12.75
14.30
9.32
11.71
12.22
13.46
14.63
15.42
16.03
16.84
16.08
15.47
16.31
17.27
17.37
18.31
18.82
18.87
19.61
19.89
and overhead ground wire data (metric)
Area,
mm2
15.5
24.7
26.5
39.2
42.1
49.5
62.4
78.6
99.2
125.1
54.6
81.7
88.9
108.0
127.5
141.9
153.1
169.5
152.8
142.6
157.2
176.8
179.9
198.2
210.3
212.6
227.5
234.2
Ultimate
strength,
N
5293
4715
10497
12677
16191
15791
19483
23619
29447
37142
23130
46261
50264
60495
71171
76953
83181
126328
43058
30603
50264
56492
38610
62719
76953
44215
64943
72505
Coeff. of
linear
expansion,
per “C
.0000189
.0000189
.0000176
.0000189
.0000176
.0000189
.0000189
.0000189
.0000189
.0000189
.0000153
.0000153
.0000153
.0000153
.0000153
.0000153
.0000153
.0000153
.0000194
.0000211
.0000189
.0000189
.0000211
.0000189
.0000178
.0000211
.0000194
.0000189
Force,
N/m
.5268
.8377
.9778
1.3324
1.5572
1.6812
2.1190
2.6721
3.3697
4.2483
2.1745
3.7083
4.0367
4.9036
5.7909
6.4417
6.9511
7.6983
4.9970
4.2235
5.3603
6.0229
5.3312
6.7570
7.6924
6.2987
7.4735
7.9814
I. 192-kPa Resultant,
force’ ,
wind,
N/m
N/m
.963
1.216
1.250
1.537
1.581
1.727
1.936
2.174
2.442
2.739
1.785
2.243
2.340
2.578
2.802
2.953
3.070
3.225
3.079
2.963
3.123
3.308
3.327
3.507
3.605
3.614
3.755
3.809
1.0979
1.4767
1.5872
2.0343
2.2191
2.4102
2.8703
3.4451
4.1616
5.0546
2.8135
4.3337
4.6658
5.5401
6.4332
7.0863
7.5987
8.3466
5.8696
5.1589
6.2038
6.8715
6.2843
7.6131
8.4951
7.2621
8.3641
8.8437
Table C-3 .-Conductor
Code
word
LARK
PEL I CAN
FLICKER
HAWK
HEN
OSPREY
PARAKEET
DO.VE
EAGLE
PEACOCK
SQUAB
TEAL
KINGBIRD
ROOK
GROSBEAK
EGRET
SWIFT
FLAMINGO
STARLING
REDW I NG
CUCKOO
DRAKE
MALLARD
COOT
TERN
CONDOR
RUDDY
Size,
mm2
201.41
241.70
241.70
241.70
241.70
281.98
281.98
281.98
281.98
306.55
306.55
306.55
322.26
322.26
322.26
322.26
322.26
331.33
337.46
362.54
362.54
402.83
402.83
402.83
402.83
402.83
402.83
456.03
l Does not include NESC constant.
Stranding!
luminum,
steel
Diameter,
mm
30/ 7
18/ 1
24/ 7
26/ 7
30/ 7
18/ 1
24/ 7
26/ 7
30/ 7
24/ 7
26/ 7
30/19
18/ 1
24/ 7
26/ 7
30/19
36/ 1
18/ 3
24/ 7
26/ 7
30/19
24/ 7
26/ 7
30/19
36/ 1
45/ 7
54/ 7
45/ 7
20.47
20.68
21.49
21.79
22.43
22.33
23.22
23.55
24.21
24.21
24.54
25.25
23.88
24.82
25.15
25.88
23.62
24.21
25.40
26.70
27.46
27.74
28.14
28.96
26.42
27.00
27.76
28.73
and .overhead ground wire data (metric&Continued
Area,
mm2
248.4
255.1
273.0
281.0
298.1
297.7
318.6
327.9
347.8
346.3
356.5
376.5
340.1
364.1
374.8
395.7
331.2
343.3
381.5
421.6
445.2
455.0
468.5
494.7
413.9
430.7
455.0
487.4
Ultimate
strength,
N
90298
52488
76509
86739
105867
60940
88074
100529
123659
96081
108091
133446
69836
97860
112094
140118
61385
65833
105422
126328
153907
124104
14011.8
170810
74729
98305
125439
108536
Coeff. of
linear
expansion,
per “C
.0000178
.0000211
.0000194
.0000189
.0000178
.0000211
.0000194
.0000189
.0000178
.0000194
.0000189
.0000207
.0000211
.0000194
.0000189
.0000207
.0000220
.0000218
.0000194
.0000189
.0000207
.0000194
.0000189
.0000207
.0000220
.0000207
.0000193
.0000207
Force,
N/m
9.0891
7.5596
8.9680
9.5882
10.9016
8.8147
10.4638
11.1789
12.7259
11.3832
12.1567
13.7183
10.0844
11.9524
12.7697
14.4188
9.3941
9.8684
12.5362
14.3750
16.2138
14.9442
15.9657
18.0235
11.7437
13.0761
14.9442
14.8128
3.192-kPa
wind,
N/m
3.921
3.960
4.115
4.174
4.295
4.276
4.446
4.510
4.636
4.636
4.699
4.835
4.573
4.753
4.816
4.957
4.524
4.636
4.865
5.113
5.259
5.312
5.390
5.546
5.059
5.171
5.317
5.502
Resultant
force’ ,
N/m
9.8987
8.5339
9.8672
10.4573
11.7174
9.7971
11.3693
12.0542
13.5440
12.2911
13.0334
14.5455
11.0727
12.8627
13.6476
15.2471
10.4267
10.9031
13.4469
15.2571
17.0453
15.8602
16.8510
18.8574
12.7871
14.0615
15.8619
15.8016
Table C-3.-Conductor
Code
word
CANARY
CATB I RD
RAIL
CARDINAL
ORTOLAN
CURLEW
BLUEJAY
FINCH
BUNT I NG
GRACKLE
BITTERN
PHEASANT
D I PPER
MART I N
BOBOLINK
PLOVER
NUTHATCH
PARROT
LAPW I NG
FALCON
CHUKAR
BLUEBIRD
KIWI
THRASHER
JOREE
Size,
mm*
456.03
483.39
483.39
483.39
523.67
523.67
563.96
563.96
604.24
604.24
644.52
644.52
684.81
684.81
725.09
725.09
765.37
765.37
805.65
805.65
901.93
.030.63
.092.45
.098.02
.165.41
.171.49
274.35
552.53
’ Does not include NESC constant.
Stranding
’ 1Xameter,
Juminum I
mm
steel
541 7
361 1
451 7
541 7
451 7
541 7
451 7
54/19
451 7
54/19
451 7
54/19
451 7
54/19
451 7
54/19
451 7
54/19
451 7
54/19
84/19
72/ 7
84/19
721 7
96/19
76/19
76/19
84/19
29.51
28.96
29.59
30.38
30.81
31.65
31.98
32.84
33.07
33.99
34.16
35.10
35.20
36.17
36.25
37.21
37.24
38.25
38.15
39.24
40.69
42.70
44.75
44.12
47.17
45.77
47.75
53.37
and overhead ground wire data (metric&Continued
Area,
mm*
515.2
496.9
516.8
546.1
559.9
591.5
603.0
635.4
645.8
680.6
689.0
726.5
732.3
771.6
775.5
816.8
818.1
862.6
861.3
907.7
975.5
1075.4
1181.3
1145.8
1313.5
1235.1
1343.6
1679.2
Ultimate
strength,
N
141897
88074
115208
150349
123215
162804
132556
173924
142342
186379
151683
193941
161024
20595 1
170366
218406
178372
229971
187714
242426
226858
208175
268226
221520
355856
252212
274453
381210
Coeff. of
linear
expansion,
per “C
.0000193
.0000220
.0000207
.0000193
.0000207
.0000193
.0000207
.0000194
.0000207
.0000194
.0000207
.0000194
.0000207
.0000194
.0000207
.0000194
.0000207
.0000194
.0000207
.0000194
.0000207
.0000216
.0000207
.0000216
.0000194
.0000211
.0000211
.0000207
Force,
N/m
16.9143
14.0977
15.6884
17.9359
17.0019
19.4245
18.3153
20.8839
19.6142
22.3724
20.9277
23.8610
22.2119
25.3496
23.5400
26.8528
24.8388
28.3414
26.1523
29.8299
30.2677
31.5520
36.6453
33.6098
43.3147
36.8642
40.1186
52.1002
0.192-kPa
wind,
N/m
Resultant
force’ ,
5.653
5.546
5.667
5.818
5.901
6.061
6.125
6.290
6.334
6.509
6.543
6.723
6.742
6.927
6.942
7.127
7.132
7.326
7.307
7.516
7.793
8.177
8.571
8.450
9.034
8.766
9.146
10.221
17.8339
15.1493
16.6807
18.8560
17.9968
20.3482
19.3122
21.8105
20.6115
23.3000
21.9266
24.7900
23.2127
26.2791
24.5422
27.7824
25.8423
29.2729
27.1538
30.7622
31.2549
32.5945
37.6344
34.6557
44.2467
37.8921
41.1478
53.0933
N/m
Table C-3.-Conductor
and overhead ground wire data (metric)-Continued
Diameter,
mm
Wire type
and size
STEEL
3.525
3.525
II.113
II.113
12.7
12.7
HIGH
EXTRA HIGH
HIGH
EXTRA HIGH
HIGH
EXTRA HIGH
mm
mm
mm
mm
mm
mm
STRENGTH
STRENGTH
STRENGTH
STRENGTH
STRENGTH
STRENGTH
9.14
9.14
11.05
11.05
12.57
12.57
Area,
mm2
Ultimate
strength,
N
Coeff. of
linear
expansion,
per “C
Force,
N/m
0.192~kpa
wind,
N/m
Resultant
force’ ,
N/m
STRAND OVERHEAD GROUND WIRE (7-WIRE)
51.1
51.1
74.6
74.6
96.6
96.6
48040
68502
64498
92522
83626
119656
.0000115
.0000115
.0000115
.0000115
.0000115
.0000115
3.9841
3.9841
5.8230
5.8230
7.5450
7.5450
ALUMOWELD STRAND OVERHEAD GROUND WIRE
7
7
7
7
7
7
7
7
8M
10M
12.5M
14M
16M
18M
20M
25M
NO. 12
NO. 11
NO. 10
NO.
9
NO.
8
NO.
7
NO.
6
NO.
5
AWG
AWG
AWG
AWG
AWG
AWG
AWG
AWG
’ Does not include NESC constant.
6.91
7.77
8.71
9.22
9.80
10.59
11.28
13.18
6.15
6.91
7.77
8.71
9.78
11 .oo
12.34
13.87
29.4
36.9
46.1
51.9
58.1
68.5
77.7
106.1
23.2
29.2
36.8
46.5
58.6
73.9
93.1
117.4
35585
44482
55602
62274
71171
80067
88964
111205
28028
35340
44570
56180
70859
84782
101107
120234
.0000130
.0000130
.0000130
.0000130
.0000130
.0000130
.0000130
.0000130
.0000130
.0000130
.0000130
.0000130
.0000130
.0000130
.0000130
.0000130
1.9118
2.4080
3.0355
3.3858
3.8236
4.4657
5.0641
6.9321
1.5119
1.9060
2.4036
3.0297
3.8207
4.8160
6.0754
7.6603
1.323
1.489
1.669
1.766
1.878
2.029
2.160
2.525
1.177
1.323
1.489
1.669
1.873
2.106
2.364
2.656
2.3250
2.8310
3.4639
3.8186
4.2598
4.9049
5.5055
7.3776
1.9162
2.3202
2.8272
3.4588
4.2550
5.2565
6.5192
8.1077
Table C-4.-Conductor
Code
word
‘URKEY
iWAN
;WANATE
iPARROW
;PARATE
lOBIN
!AVEN
!UAlL
’ I GEON
‘ENGU I N
iROUSE
‘ETREL
I I NORCA
.EGHORN
iU I NEA
IOTTEREL
lORK I NG
:OCHI N
IWL
‘AXW I NG
‘ARTR I DGE
lSTR I CH
IERLIN
I NNET
#RlOLE
HICKADEE
RANT
BIS
Size,
AWG
or
kcmil
6
4
4
2
2
1
l/O
2/o
3/o
4/o
80.0
101.8
110.8
134.6
159.0
176.9
190.8
211.3
266.8
266.8
266.8
300.0
336.4
336.4
336.4
397.5
397.5
397.5
Does not include NESC constant.
Stranding
duminum
steel
6/
6/
7/
6/
7/
6/
6/
6/
6/
6/
8/
12/
12/
12/
12/
12/
12/
12/
6/
18/
26/
26/
18/
26/
30/
18/
24/
26/
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
1
7
7
1
7
7
1
7
7
Diameter:
in
198
: 250
.257
.316
.325
.355
.398
.447
.502
.563
.367
.461
.481
.530
.576
.607
.631
.663
.633
.609
.642
.680
.684
.721
.741
.743
.772
.783
and overhead ground wire data (U.S. customary)
Area,
in2
.0240
.0383
.0411
.0608
.0653
.0767
.0967
.1219
.1538
.1939
.0847
.1266
.1378
.1674
1977
: 2200
.2373
.2628
.2368
.2211
.2436
.2740
.2789
.3072
.3259
.3295
.3527
.3630
Ultimate
strength,
lb
Coeff. of
linear
expansion,
per OF
Weight,
lb/ft
4-lb/ft2
wind,
lb/ft
Resultant
weight,’
lb/ft
1,190
1,860
2,360
2,850
3,640
3,550
4,380
5,310
6,620
8,350
5,200
10,400
11,300
13,600
16,000
17,300
18,700
28,400
9,680
6,880
11,300
12,700
8,680
14,100
17,300
9,940
14,600
16,300
.0000105
.0000105
.0000098
.0000105
.0000098
.0000105
.0000105
.0000105
.0000105
.0000105
.0000085
.0000085
.0000085
.0000085
.0000085
.0000085
.0000085
.0000085
.0000108
.0000117
.0000105
.0000105
.0000117
.0000105
.0000099
.0000117
.0000108
.0000105
.03610
.05740
.06700
.09130
10670
: 11520
.14520
18310
: 23090
.29110
14900
: 25410
.27660
.33600
.39680
.44140
.47630
.52750
.34240
.28940
.36730
.41270
.36530
.46300
.52710
.43160
.51210
.54690
.06600
.08333
.08567
.10533
.10833
.11833
.13267
.14900
.16733
18767
: 12233
.15367
.16033
.17667
19200
: 20233
.21033
.22100
.21100
.20300
21400
: 22667
.22800
.24033
.24700
.24767
.25733
.26100
.07523
.10119
.10876
.13939
.15206
.16515
19668
: 23606
.28516
.34635
19279
: 29695
.31971
.37961
.44081
.48556
.52067
.57192
.40219
.35350
.42509
.47085
.43061
.52166
.58210
.49761
.57312
.60599
Table C-4.-Conductor
Code
word
LARK
PEL I CAN
FLICKER
HAWK
HEN
OSPREY
PARAKEET
DOVE
EAGLE
PEACOCK
SQUAB
TEAL
KINGBIRD
ROOK
GROSBEAK
EGRET
SWIFT
FLAMINGO
STARLING
REDW I NG
CUCKOO
DRAKE
MALLARD
COOT
TERN
CONDOR
RUDDY
Size,
AWG
or
kcmil
397.5
477.0
477.0
477.0
477.0
556.5
556.5
556.5
556.5
605.0
605.0
605.0
636.0
636.0
636.0
636.0
636.0
653.9
666.0
715.5
715.5
795.0
795.0
795.0
795.0
795.0
795.0
900.0
’ Does not include NESC constant.
Stranding
.luminum
steel
30/ 7
18/ 1
24/ 7
26/ 7
30/ 7
18/ 1
24/ 7
26/ 7
30/ 7
24/ 7
26/ 7
30/19
18/ 1
24/ 7
26/ 7
30/19
36/ 1
18/ 3
24/ 7
26/ 7
30/19
24/ 7
26/ 7
30/19
36/ 1
45/ 7
54/ 7
45/ 7
and overhead ground wire data (U.S. customary&Continued
Diameter ,
in
Area,
in2
.806
.3850
.3954
.4232
.4356
.4620
.814
.846
.858
.883
.879
.914
.927
.953
.953
.966
.994
.940
.977
.990
1.019
.930
.953
1 .ooo
1.051
1.081
1.092
1.108
1.140
1.040
1.063
1.093
1.131
.4614
.4938
.5083
.5391
.5368
.5526
.5835
.5272
.5643
.5809
.6134
.5133
.5321
.5914
.6535
.6901
.7053
7261
: 7668
.6416
.6676
.7053
.7555
Ultimate
strength,
lb
20,300
11,800
17,200
19,500
23,800
13,700
19,800
22,600
27,800
21,600
24,300
30,000
15,700
22 ) 000
25,200
31,500
13,800
14,800
23,700
28,400
34,600
27,900
31,500
38,400
16,800
22) 100
28,200
24,400
Coeff. of
linear
expansion,
per OF
.0000099
.0000117
.0000108
.0000105
.0000099
.0000117
.0000108
.0000105
.0000099
.0000108
.0000105
.0000115
.0000117
.0000108
.0000105
.0000115
.0000122
.0000121
.0000108
.0000105
.0000115
.0000108
.0000105
.0000115
.0000122
.0000115
.0000107
.0000115
Weight,
lb/ft
.62280
.51800
.61450
.65700
74700
: 60400
.71700
76600
: 87200
.78000
.83300
.94000
.69100
.81900
.87500
.98800
.64370
.67620
.85900
.98500
1.11100
1.02400
1.09400
1.23500
.80470
.89600
1.02400
1.01500
4-lb/ft2
wind,
Ib/ft
Resultant
weight,’
Ib/ft
.26867
.27133
.28200
.28600
.29433
.29300
.30467
.30900
.31767
.31767
.32200
.33133
.31333
.32567
.33000
.33967
.31000
.31767
.33333
.35033
.36033
.36400
.36933
.38000
.34667
.35433
.36433
.37700
.67828
.58476
.67612
.71655
.80290
.67132
.77904
.82598
.92806
.84221
.89307
.99669
.75872
.88137
.93516
1.04476
71446
: 74710
.92141
1.04545
1.16797
1.08677
1.15466
1.29214
.87620
.96352
1.08688
1.08275
Table @I.-Conductor
Code
word
CANARY
CATB I RD
RAIL
CARDINAL
ORTOLAN
CURLEW
BLUE JAY
FINCH
BUNT I NG
GRACKLE
B I TTERN
PHEASANT
D I PPER
MART I N
BOBOLINK
PLOVER
NUTHATCH
PARROT
LAPW I NG
FALCON
CHUKAR
BLUEBIRD
KIWI
THRASHER
JOREE
Size,
AWG
or
kcmil
900.0
954.0
954.0
954.0
1,033.5
1,033.5
1,113.0
1,113.0
1,192.5
1,192.5
1,272.0
1,272.0
1,351.5
1,351.5
1,431.0
1,431.0
1,510.5
1,510.5
1,590.o
1,590.o
1,780.O
2,034.o
2,156.0
2,167.O
2,300.O
2,312.0
2,515.0
3,064.O
’ Does not include NESC constant.
Stranding
.luminum,
steel
54/ 7
36/ 1
45/ 7
54/ 7
45/ 7
54/ 7
45/ 7
54/19
45/ 7
54/19
45/ 7
54/19
45/ 7
54/19
45/ 7
54/19
45/ 7
54119
45/ 7
54/19
84/19
721 7
84/19
72/ 7
96/19
76119
76/19
84/19
and overhead ground wire data (U.S. customary&Continued
Diameter.
in
1.162
1.140
1.165
1.196
1.213
1.246
1.259
1.293
1.302
1.338
1.345
1.382
1.386
1.424
1.427
1.465
1.466
1.506
1.502
1.545
1.602
1.681
1.762
1.737
1.857
1.802
1.880
2.101
Area,
in2
7985
: 7702
.8011
.8464
.8678
.9169
.9346
.9849
1 .OOlO
1.0550
1.0680
1.1260
1.1350
1.1960
1.2020
1.2660
1.2680
1.3370
1.3350
1.4070
1.5120
1.6669
1.8310
1.7760
2.0359
1.9144
2.0826
2.6028
Ultimate
strength,
lb
Coeff. of
linear
expansion,
per OF
31,900
19,800
25,900
33,800
27,700
36,600
29,800
39,100
32,000
41,900
34,100
43,600
36,200
46,300
38,300
49,100
40,100
51,700
42,200
54,500
51,000
46,800
60,300
49,800
80,000
56,700
61,700
85,700
.0000107
.0000122
.0000115
.0000107
.0000115
.0000107
.0000115
.0000108
.0000115
.0000108
.0000115
.0000108
.0000115
.0000108
.0000115
.0000108
.0000115
.0000108
.0000115
.0000108
.0000115
.0000120
.0000115
.0000120
.0000108
.0000117
.0000117
.0000115
Weight,
lb/ft
4-lb/ft2
wind,
lb/ft
Resultant
weight,’
lb/ft
1.15900
.96600
1.07500
1.22900
1.16500
1.33100
1.25500
1.43100
1.34400
1.53300
1.43400
1.63500
1.52200
1.73700
1.61300
1.84000
1.70200
1.94200
1.79200
2.04400
2.07400
2.16200
2.51100
2.30300
2.96800
2.52600
2.74900
3.57000
.38733
.38000
.38833
.39867
.40433
.41533
.41967
.43100
.43400
.44600
.44833
.46067
.46200
.47467
.47567
148833
.48867
.50200
.50067
.51500
.53400
.56033
.58733
.57900
.61900
.60067
.62667
.70033
1.22201
1.03805
1.14299
1.29204
1.23317
1.39430
1.32331
1.49450
1.41234
1.59656
1.50245
1.69866
1.59057
1.80069
1.68167
1.90370
1.77076
2.00583
1.86063
2.10788
2.14164
2.23343
2.57878
2.37467
3.03186
2.59644
2.81952
3.63804
Table C-4.-Conductor
Wire type
and size
and overhead ground wire data (U.S. customary&Continued
Diameter,
in
Area,
in2
Ultimate
strength,
lb
Coeff. of
linear
expansion,
per OF
I
Weight,
lb/ft
4-lb/ft2
wind,
lb/ft
Resultant
weight ,l
lb/ft
STEEL STRAND OVERHEAD GROUND WIRE (7 WIRE)
3/8
3/8
7/16
7/16
l/2
i/2
HIGH STRENGTH
INCH
INCH EXTRA HIGH STRENGTH
INCH
HIGH STRENGTH
INCH EXTRA HIGH STRENGTH
INCH
HIGH STRENGTH
INCH EXTRA HIGH STRENGTH
.360
.360
.435
.435
.495
.495
.0792
.0792
.1156
.1156
1497
:1497
10,800
15,400
14,500
20,800
18,800
26.900
.0000064
.0000064
.0000064
.0000064
.0000064
.0000064
ALUMOWELD STRAND OVERHEAD GROUND WIRE
8M
10M
12.5M
14M
7
7
7
7
7
7
7
7
16M
18M
20M
25M
NO. 12
NO. 11
NO. 10
NO.
9
NO.
8
NO.
7
NO.
6
NO.
5
AWG
AWG
AWG
AWG
AWG
AWG
AWG
AWG
* Does not include NESC constant.
.272
.306
.343
.363
.386
.417
.444
.519
.242
.272
.306
.343
.385
.433
.486
.546
.0455
.0572
.0714
.oco5
.0901
.1062
.1204
1645
: 0359
.0453
.0571
.0720
.0908
.1145
.1443
.1820
8,000
10,000
12,500
14,000
16,000
18,000
20,000
25,000
6,301
7,945
10,020
12,630
15,930
19,060
22,730
27.030
.0000072
.0000072
.0000072
.0000072
.0000072
.0000072
.0000072
.0000072
.0000072
.0000072
.0000072
.0000072
.0000072
.0000072
.0000072
.0000072
.27300
.27300
.39900
.39900
.51700
.51700
.12000
.12000
.14500
.14500
.16500
.16500
.29821
.29821
.42453
.42453
.54269
.54269
.13100
16500
:20800
.23200
.26200
.30600
.34700
.47500
.10360
.13060
16470
:20760
.26180
.33000
.41630
.52490
.09067
.10200
.11433
.12100
.12867
.13900
.14800
.17300
.08067
.09067
.10200
.11433
.12833
.14433
.16200
.18200
.15932
19398
:23735
.26166
.29189
.33609
.37724
.50552
.13130
.15899
19373
:23700
.29156
.36018
.44671
.55556
Table C-5.-Conductor
and overhead ground wire values for NESC
light, medium, and heavy loading (metric)
Code
word
TURKEY
SWAN
SWANATE
SPARROW
SPARATE
ROBIN
RAVEN
QUAIL
PIGEON
PENGU I N
GROUSE
PETREL
M I NORCA
LEGHORN
GUINEA
DOTTEREL
DORK I NG
COCH I N
OWL
WAXW I NG
PARTR I DGE
OSTR I CH
MERLIN
L I NNET
ORIOLE
CH I CKADEE
BRANT
IBIS
F
NATIONAL
LIGHT
Force
with no
ice
.5268
.8377
.9778
1.3324
1.5572
1.6812
2.1190
2.6721
3.3697
4.2483
2.1745
3.7083
4.0367
4.9036
5.7909
6.4417
6.9511
7.6983
4.9970
4.2235
5.3603
6.0229
5.3312
6.7570
7.6924
6.2987
7.4735
7.9814
’ Includes 0.7297 NESC constant.
* Includes 2.9188 NESC constant.
3 Includes 4.3782 NESC constant.
ELECTRICAL
SAFETY
T
LOADING
MEDIUM
0.43 1-kPa Resultant
wind
force’
7orce with
6.35-mm
ice
2.1672
2.7364
2.8130
3.4588
3.5573
3.8856
4.3563
4.8926
5.4946
6.1623
4.0170
5.0458
5.2647
5.8011
6.3046
6.6439
6.9066
7.2568
6.9285
6.6658
7.0270
7.4429
7.4867
7.8917
8.1106
8.1325
8.4499
8.5703
2.5602
3.1070
3.2789
3.9013
4.1669
4.4271
5.0601
5.8356
6.7828
7.9382
4.9749
6.9353
7.3545
8.4437
9.5398
10.3314
10.9497
11.8421
9.0046
8.1222
9.4089
10.2439
9.5703
2.9600
3.5914
3.7078
4.4362
4.6129
4.9634
5.5740
6.3045
7.1753
8.2144
5.2975
6.9916
7.3639
8.3256
9.2902
9.9837
10.5286
11.3092
9.2721
8.6208
9.5678
10.3042
9.9205
11.1189
11.9080
11.0161
12.0104
12.4409
11.1641
12.1903
10.8057
12.1121
12.6699
CODE
T
LOADING
0.192-kPa
wind
3.3955
3.6485
3.6825
3.9695
4.0133
4.1593
4.3684
4.6068
4.8744
5.1711
4.2176
4.6749
4.7722
5.0106
5.2343
5.3851
5.5019
5.6576
5.5116
5.3949
5.5554
5.7403
5.7597
5.9397
‘6.0370
6.0467
6.1878
6.2413
1977
Resultant
force2
7.1713
7.7110
7.8495
8.4845
8.7041
8.9932
9.6037
10.3536
11.2714
12.3928
9.4409
11.2826
11.6859
12.7373
13.8003
14.5694
15.1730
16.0430
13.4763
12.6694
13.8453
14.6614
14.0886
15.5646
16.5220
15.3012
16.5199
17.0425
ALL VALUES
1
EDITION
HEAVY
Force witk
12.7-mm
ice
6.8629
7.6457
7.8494
8.7396
9.0460
9.4424
10.2705
11.2684
12.4653
13.8976
10.0446
12.4317
12.9416
14.2533
15.5581
16.4904
17.2176
18.2553
15.2817
14.2903
15.7267
16.7342
16.0788
17.8405
18.9575
17.5819
19.0200
19.6277
LOADING
0.192~kPa
wind
5.8278
6.0808
6.1148
6.4019
6.4456
6.5916
6.8008
7.0391
7.3067
7.6034
6.6500
7.1072
7.2045
7.4429
7.6667
7.8175
7.9342
8.0899
7.9439
7.8272
7.9877
8.1726
8.1920
8.3720
8.4693
8.4791
8.6201
8.6736
Resultant
force3
13.3816
14.1472
14.3283
15.2116
15.4857
15.8937
16.6962
17.6645
18.8271
20.2197
16.4246
18.6981
19.1900
20.4577
21.7227
22.6278
23.3360
24.3457
21.6013
20.6717
22.0172
23.0014
22.4236
24.0854
25.1415
23.8979
25.2604
25.8370
ARE IN NEWTONS PER METER.
Table C-S.-Conductor
and overhead ground wire values for NESC
light, medium, and heavy loading (metric&Continued
NATIONAL
Code
word
-LARK
PEL I CAN
FLICKER
HAWK
HEN
OSPREY
PARAKEET
DOVE
EAGLE
PEACOCK
SQUAB
TEAL
KINGBIRD
ROOK
GROSBEAK
EGRET
SWIFT
FLAM I NGO
STARLING
REDWING
CUCKOO
DRAKE
MALLARD
COOT
TERN
CONDOR
RUDDY
L I GHT
ELECTRICAL
SAFETY
T
LOADING
MEDIUM
T
LOADING
9.0891
7.5596
8.9680
9.5882
10.9016
8.8147
10.4638
11.1789
12.7259
11.3832
12.1567
13.7183
10.0844
11.9524
12.7697
14.4188
9.3941
9.8684
12.5362
14.3750
16.2138
14.9442
15.9657
18.0235
11.7437
13.0761
14.9442
14.8128
1 Includes 0.7297 NESC constant.
’ Includes 2.9188 NESC constant.
3 Includes 4.3782 NESC constant.
0.43 1-kPa
wind
8.8220
8.9096
9.2598
9.3912
9.6648
9.6210
10.0041
10.1464
10.4310
10.4310
LO. 5733
LO.8798
LO.2887
LO.6937
10.8360
11.1534
LO. 1792
10.4310
10.9454
11.5036
11.8320
11.9524
12.1275
12.4778
11.3832
11.6350
11.9633
12.3793
Resultant
force’
13.3962
12.4142
13.6203
14.1509
15.2986
13.7782
15.2064
15.8266
17.1843
16.1694
16.8412
18.2385
15.1364
16.7676
17.4773
18.9588
14.5813
15.0890
17.3717
19.1409
20.8017
19.8657
20.7792
22.6509
17.0849
18.2328
19.8726
20.0342
1by;
.
;Nll
-
ice
13.8820
12.3888
13.9424
14.6171
16.0440
13.9389
15.7469
16.5210
18.1859
16.8433
17.6758
19.3644
15.4854
17.5214
18.3977
20.1784
14.7498
15.3285
18.2095
20.2798
22.2548
21.0351
22.1293
24.3323
17.5986
19.0355
21.0396
21.0808
0.192-kPa
wind
Resultant
force2
6.3532
6.3921
6.5478
6.6062
6.7278
6.7083
6.8786
6.9418
7.0683
7.0683
7.1316
7.2678
.7.0051
7.1851
7.2483
7.3894
6.9564
7.0683
7.2970
7.5450
7.6910
7.7445
7.8223
7.9780
7.4915
7.6034
7.7494
7.9342
18.185516.8594
18.3221
18.9594
20.3163
18.3879
20.1025
20.8389
22.4300
21.1851
21.9790
23.6021
19.9150
21.8562
22.6928
24.4076
19.2267
19.7984
22.5359
24.5567
26.4651
25.3342
26.3899
28.5256
22.0456
23.4166
25.3402
25.4432
ALLVALUES
EDITION
HEAVY
L
L
Force
with no
ice
1977
CODE
I Torte
LOADING
with
12.7-mm
ice
0.192~kPa Resultant
force3
wind
20.9442
19.4874
21.1861
21.9153
23.4557
21.3325
23.2993
24.1324
25.9154
24.5727
25.4642
27.2799
23.1558
25.3597
26.2950
28.2074
22.3748
23.0579
26.1523
28.4540
30.5652
29.3954
30.5622
32.9104
25.7229
27.2641
29.4045
29.6181
8.7855
8.8244
8.9801
9.0385
9.1601
9.1406
9.3109
9.3741
9.5006
9.5006
9.5639
9.7001
9.4374
9.6174
9.6806
9.8217
9.3887
9.5006
9.7293
9.9774
10.1233
10.1768
10.2546
10.4103
9.9239
10.0357
10.1817
10.3665
ARE IN
27.0904
25.7704
27.3889
28.0842
29.5591
27.5865
29.4690
30.2673
31.9801
30.7236
31.5791
33.3313
29.3833
31.5003
32.3985
34.2466
28.6429
29.3166
32.2816
34.5308
36.5762
35.4853
36.6149
38.8958
31.9490
33.4307
35.4955
35.7580
D
:
2
0
x
0
E7NTONS PER METER.
2
Table C-5.-Conductor
and overhead ground wire values for NESC
light, medium, and heavy loading (met&)-Continued
NATIONAL
Code
word
CANARY
CATB I RD
RAIL
CARDINAL
ORTOLAN
CURLEW
BLUEJAY
FINCH
BUNT I NG
GRACKLE
B I TTERN
PHEASANT
D I PPER
MART I N
BOBOL I NK
PLOVER
NUTHATCH
PARROT
LAPW I NG
FALCON
CHUKAR
BLUEBIRD
KIWI
THRASHER
JOREE
LIGHT
Force
with no
ice
16.9143
14.0977
15.6884
17.9359
17.9019
19.4245
18.3153
20.8839
19.6142
22.3724
20.9277
23.8610
22.2119
25.3496
23.5400
26.8528
24.8388
28.3414
26.1523
29.8299
30.2677
31.5520
36.6453
33.6098
13.3147
36.8642
10.1186
52.1002
’ Includes 0.7297 NESC constant.
’ Includes 2.9188 NESC constant.
3 Includes 4.3782 NESC constant.
SAFETY
ELECTRICAL
T
LOADING
MEDIUM
CODE
LOADING
0.43 1-kPa Resultant
wind
force’
Force with
6.35-mm
ice
0.192-kPa
wind
12.7186
12.4778
12.7514
13.0907
13.2768
13.6380
13.7803
14.1524
14.2509
14.6450
14.7216
15.1266
15.1704
15.5863
15.6191
16.0350
16.0460
16.4838
16.4400
16.9107
17.5346
18.3993
19.2858
19.0122
20.3257
19.7237
20.5774
22.9963
23.3230
20.4065
22.1107
24.4989
23.6420
26.2144
25.1642
27.8871
26.6583
29.5799
28.1669
31.2682
29.6372
32.9474
31.1514
34.6367
32.6272
36.3113
34.1041
37.9769
38.6734
40.3162
45.7772
42.6282
52.8777
46.1776
49.7861
62.7707
8.0850
7.9780
8.0996
8.2504
8.3331
8.4936
8.5569
8.7223
8.7661
8.9412
8.9752
9.1552
9.1747
9.3596
9.3741
9.5590
9.5639
9.7585
9.7390
9.9482
10.2255
10.6098
11.0038
10.8822
11.4659
11.1984
11.5778
12.6529
21.8923
19.5563
20.9467
22.9347
22.3014
24.4638
23.6502
25.9572
24.9744
27.4692
26.3166
28.9815
27.6278
30.4876
28.9801
32.0058
30.3006
33.5161
31.6201
35.0196
35.7097
37.2545
42.1401
39.3442
48.5763
42.5387
45.8178
57.6794
1
1977
T
1
EDITION
HEAVY
LOADING
Resultant
force2
Force with
12.7-mm
ice
0.192-kPa
wind
Resultant
force3
27.6034
24.8294
26.4663
28.7696
27.9864
30.4748
29.4981
32.1381
30.9813
33.8205
32.4811
35.4997
33.9436
37.1698
35.4500
38.8503
36.9188
40.5185
38.3862
42.1770
42.9212
44.6077
49.9999
46.9140
57.0254
50.4348
54.0333
66.9520
32.0010
28.9847
30.8023
33.3312
32.5515
35.2736
34.2825
37.1597
35.9717
39.0567
37.6755
40.9447
39.3319
42.8145
41.0321
44.6899
42.6850
46.5506
44.3252
48.3932
49.3485
51.3498
57.1784
53.9159
64.7101
57.7604
61.7229
75.7106
10.5173
10.4103
10.5319
10.6827
10.7654
10.9260
10.9892
11.1546
11.1984
11.3735
11.4076
11.5876
11.6070
11.7919
11.8065
11.9913
11.9962
12.1908
12.1713
12.3805
12.6578
13.0421
13.4361
13.3145
13.8983
13.6307
14.0101
15.0852
38.0631
35.1756
36.9313
39.3794
38.6636
41.3052
40.3789
43.1759
42.0526
45.0572
43.7428
46.9310
45.3870
48.7869
47.0751
50.6489
48.7168
52.4986
50.3441
54.3300
55.3241
57.3584
63.1140
59.9138
70.5640
63.7251
67.6711
81.5770
ALL VALUES
ARE IN NEWTONS PER METER.
Table C-5.-Conductor
and overhead ground wire values for NESC
light, medium, and heavy loading (metric)-Continued
NATIONAL
Wire type
and size
0.43 l-kPa
wind
3.9841
3.9841
mm HS
mm EHS
mm HS
mm EHS
mm HS
mm EHS
5.8230
5.8230
7.5450
7.5450
3.9404
3.9404
4.7613
4.7613
5.4180
5.4180
Resultant
force’
1.9118
8M
12.5M
14M
16M
18M
20M
25M
7 NO.
7 NO.
7 NO.
7N0.
7N0.
7N0.
7N0.
7N0.
2.4080
3.0355
3.3858
3.8236
4.4657
5.0641
6.9321
1.5119
1.9060
12
11
10
9
8
7
6
5
/
2.4036
3.0297
3.8207
4.8160
6.0754
7.6603
1 Includes 0.7297 NESC constant.
’ Includes 2.9188 NESC constant.
3 Includes 4.3782 NESC constant.
2.9772
3.3493
3.7543
3.9732
4.2249
4.5642
4.8598
5.6807
2.6488
2.9772
3.3493
3.7543
4.2140
4.7394
5.3195
5.9762
FtT<zgh
* ice
STRAND
4.2678
4.8548
5.5576
5.9498
6.4279
7.1152
7.7484
9.6921
3.7796
4.2647
4.8522
5.5540
6.4179
7.4866
8.8048
.0.4454
GROUND
OVERHEAD
4.2810
4.. 9315
5.7270
6.1680
6.7102
7.4930
8.2139
10.4224
3.7450
4.2752
4.9271
5.7211
6.7028
7.9159
9.4159
11.2731
EDITION
HEAVY
0.192-kPa
wind
WIRE
4.3101
4.4609
4.5922
4.9571
3.6096
~~.~~~”
ice
LOADING
0.192-kPa
wind
Resultant
force3
(7-WIRE)
11.7907
11.7907
14.3103
14.3103
16.5771
16.5771
6.6159
6.6159
6.9807
6.9807
8.6136
9.2190
9.9626
10.3799
10.8940
11.6392
12.3293
14.4599
8.9196
9.7244
10.6878
11.2196
11.8662
12.7897
13.6332
16.1820
6.1878
6.3532
6.5332
6.6305
6.7424
6.8932
7.0245
7.3894
8.1201
8.6092
8.2474
GROUND
3.7555
3.9209
4.1009
4.1982
3.7555
3.9209
4.1009
4.3052
4.5387
4.7965
5.0884
Resultant
force2
10.8625
10.8625
12.9422
12.9422
14.8693
14.8693
4.1836
4.1836
4.5484
4.5484
4.8403
4.8403
STRAND
1977
LOADING
OVERHEAD
6.3332
6.3332
8.2514
8.2514
10.0185
10.0185
ALUMOWELD
10M
CODE
MEDIUM
STEEL
I.525
I.525
I.11
I.11
12.7
12.7
SAFETY
LOADING
LIGHT
Force
with no
ice
ELECTRICAL
7.2726
7.2726
17.8982
17.8982
20.3004
20.3004
22.4804
22.4804
WIRE
9.2156
9.9579
10.8851
12.0436
13.4860
15.2871
8.9137
9.7200
10.6819
11.8542
13.2852
15.0258
17.1553
6.0419
6.1878
6.3532
6.5332
6.7375
6.9710
7.2288
7.5207
15.2339
15.9940
16.9046
17.4105
18.0261
18.9072
19.7146
22.1675
14.6018
15.2291
15.9903
16.8996
18.0133
19.3812
21.0524
23.1096
ALL VALUES ARE IN NEWTONS PER METER.
Table C-&-Conductor
and overhead ground wire values for NESC
light, medium, and heavy loading (U.S. customary)
Code
word
TURKEY
SWAN
SWANATE
SPARROW
SPARATE
ROBIN
RAVEN
QUAIL
PIGEON
PENGU I N
GROUSE
PETREL
M I NORCA
LEGHORN
GUINEA
OOTTEREL
DORK I NG
COW I N
OWL
WAXWI NG
PARTR I DGE
OSTR I CH
MERLIN
L I NNET
ORIOLE
CH I CKADEE
BRANT
IBIS
F
NAT
LIGHT
IONAL
ELECTRICAL
r
LOADING
SAFETY
MEDIUM
Weight
with
no ice
9-lb/ft2
wind
Resultant
weight’
Weight
with
l/4-in ice
.0361
.0574
.0670
.0913
.1067
.1152
.1452
1831
: 2309
.2911
1490
: 2541
.2766
.3360
.3968
.4414
.4763
.5275
.3424
.2894
.3673
.4127
.3653
.4630
.5271
.4316
.5121
15469
.1485
.1875
1928
: 2370
.2438
.2663
.2985
.3353
.3765
.4223
.2753
.3458
.3608
.3975
.4320
.4553
.4733
.4973
.4748
.4568
.4815
.5100
.5130
.5408
.5558
.5573
.5790
.5873
.2028
.2461
.2541
.3040
.3161
.3401
.3819
14320
.4917
.5629
.3630
.4791
.5046
.5705
.6366
.6841
.7214
.7749
.6353
.5907
.6556
.7061
.6798
.7619
.8160
17548
.8230
.8525
1754
: 2129
.2247
.2673
.2855
.3034
.3467
.3999
.4648
.5439
.3409
.4752
.5039
.5786
.6537
.7079
.7503
.8114
.6170
.5565
.6447
.7019
.6558
.7650
.8353
.7404
.8299
.8682
1 Includes 0.05 NESC constant.
’ Includes 0.20 NESC constant.
3 Includes 0.30 NEW constant.
1977
CODE
EDITION
T-
LOADING
4-lb/ft2
wind
Resultant
weight’
.2327
.2500
.2523
.2720
.2750
.2850
.2993
.3157
.3340
.3543
.2890
.3203
.3270
.3433
.3587
.3690
.3770
.3877
.3777
.3697
.3807
.3933
.3947
.4070
.4137
.4143
.4240
.4277
.4914
.5284
.5379
.5814
.5964
.6162
.6581
.7094
.7723
.8492
.6469
.7731
.8007
.8728
.9456
.9983
1.0397
1.0993
.9234
.8681
.9487
1.0046
.9654
1.0665
1.1321
1.0485
1.1320
1.1678
HEAVY
Weight
with
l/2-in ice
.4703
.5239
.5379
.5989
.6199
.6470
.7038
.7721
.8541
.9523
.6883
.8518
.8868
.9767
1.0661
1.1300
1.1798
1.2509
1.0471
.9792
1.0776
1.1467
1.1017
1.2225
1.2990
1.2047
1.3033
I 1.3449
ALL VALUES
LOADING
4-lb/ft2
wind
.3993
.4167
.4190
.4387
.4417
.4517
.4660
.4823
.5007
.5210
.4557
.4870
.4937
.5100
.5253
.5357
.5437
.5543
.5443
.5363
.5473
.5600
.5613
.5737
.5803
.5810
.5907
.5943
ARE IB POUNDS
Resultant
weight3
.9169
.9694
.9818
1.0423
1.0611
1.0891
1.1441
1.2104
1.2901
1.3855
1.1254
1.2812
1.3149
1.4018
1.4885
1.5505
1.5990
1.6682
1.4802
1.4165
1.5087
1.5761
1.5365
1.6504
1.7227
1.6375
1.7309
1.7704
ER FOOT
Table C-k-Conductor
and overhead ground wire values for NESC
light, medium, and heavy loading (U.S. customary)-Continued
Code
word
LARK
PEL I CAN
FLICKER
HAWK
HEN
OSPREY
PARAKEET
DOVE
EAGLE
PEACOCK
SQUAB
TEAL
KINGBIRD
ROOK
GROSBEAK
EGRET
SWIFT
FLAMINGO
STARLING
REDWI NG
CUCKOO
DRAKE
MALLARD
COOT
TERN
CONDOR
RUDDY
F
NATIONAL
LIGHT
Weight
with
no ice
.6228
.5180
.6145
.6570
.7470
.6040
.7170
.7660
.8720
.7800
.8330
.9400
.6910
.8190
.8750
.9880
.6437
.6762
.8590
.9850
1.1110
1.0240
1.0940
1.2350
.8047
.8960
1.0240
1.0150
’ Includes 0.05 NESC constant.
* Includes 0.20 NESC constant.
3 Includes 0.30 NESC constant.
ELECTRICAL
T
LOADING
9-lb/ft*
wind
Resultant
weight’
.6045
.6105
.6345
.6435
.6623
.6593
.6855
.6953
.7148
.7148
.7245
.7455
.7050
.7328
.7425
.7643
.6975
.7148
.7500
.7883
.8108
.8190
.8310
.8550
.7800
.7973
.8198
.8483
.9179
.8506
.9333
.9696
1.0483
.9441
1.0420
1.0845
1.1775
1.1080
1.1540
1.2497
1.0372
1.1489
1.1976
1.2991
.9991
1.0339
1.1903
1.3116
1.4254
1.3612
1.4238
1.5521
1.1707
1.2493
1.3617
1.3728
SAFETY
MEDIUM
Weight
with
l/4-in ice
.9512
.8489
.9554
1.0016
1.0994
.9551
1.0790
1.1320
1.2461
1.1541
1.2112
1.3269
1.0611
1.2006
1.2606
1.3827
1.0107
1.0503
1.2478
1.3896
1.5249
1.4414
1.5163
1.6673
1.2059
1.3043
1.4417
1.4445
CODE
LOADING
4-lb/ft*
wind
.4353
.4380
.4487
.4527
.4610
.4597
.4713
.4757
.4843
.4843
.4887
.4980
.4800
.4923
.4967
.5063
.4767
.4843
.5000
.5170
.5270
.5307
.5360
.5467
.5133
.5210
.5310
.5437
1977
HEAVY
Resultant
weight*
1.2461
1.1552
1.2555
1.2991
1.3921
1.2600
1.3775
1.4279
1.5369
1.4516
1.5060
1.6173
1.3646
1.4976
1.5550
1.6725
1.3174
1.3566
1.5442
1.6827
1.8134
1.7359
1.8083
1.9546
1.5106
1.6045
1.7364
1.7434
ALL VALUES
1
EDITION
Weight
with
l/2-in ice
1.4351
1.3353
1.4517
1.5017
1.6072
1.4617
1.5965
1.6536
1.7758
1.6838
1.7449
1.8693
1.5867
1.7377
1.8018
1.9328
1.5332
1.5800
1.7920
1.9497
2.0944
2.0142
2.0942
2.2551
1.7626
1.8682
2.0148
2.0295
LOADING
4-lb/ft*
wind
.6020
.6047
.6153
.6193
.6277
.6263
.6380
.6423
.6510
.6510
.6553
.6647
.6467
.6590
.6633
.6730
.6433
.6510
.6667
.6837
.6937
.6973
.7027
.7133
.6800
.6877
.6977
.7103
Resultant
weight3
1.8563
1.7658
1.8767
1.9244
2.0254
1.8903
2.0193
2.0740
2.1913
2.1052
2.1639
2.2839
2.0134
2.1585
2.2200
2.3466
1.9627
2.0088
2.2120
2.3661
2.5063
2.4315
2.5089
2.6652
2.1892
2.2907
2.4322
2.4502
ARE IN POUNDS PER FOOT.
Table C-&-Conductor
and overhead ground wire values for NESC
light, medium, and heavy loading (U.S. customary)-Continued
Code
word
CANARY
CATB I RD
RAIL
CARDINAL
ORTOLAN
CURLEW
BLUEJAY
FINCH
BUNT I NG
GRACKLE
B I TTERN
PHEASANT
D I PPER
MART I N
BOBOLINK
PLOVER
NUTHATCH
PARROT
LAPW I NG
FALCON
CHUKAR
BLUEBIRD
KIWI
THRASHER
JOREE
F
NATIONAL
LIGHT
Weight
with
no ice
1.1590
.9660
1.0750
1.2290
1.1650
1.3310
1.2550
1.4310
1.3440
1.5330
1.4340
1.6350
1.5220
1.7370
1.6130
1.8400
1.7020
1.9420
1.7920
2.0440
2.0740
2.1620
2.5110
2.3030
2.9680
2.5260
2.7490
3.5700
’ Includes 0.05 NESC constant.
2 Includes 0.20 NESC constant.
3 Includes 0.30 NESC constant.
l-
LOADING
9-lb/ft2
wind
.8715
.8550
.8738
.8970
.9098
.9345
.9443
.9698
.9765
1.0035
1.0088
1.0365
1.0395
1.0680
1.0703
1.0988
1.0995
1.1295
1.1265
1.1588
1.2015
1.2608
1.3215
1.3028
1.3928
1.3515
1.4100
1.5758
SAFETY
ELECTRICAL
Resultant
weight l
1.5001
1.3400
1.4353
1.5715
1.5281
1.6763
1.6206
1.7786
1.7113
1.8822
1.8033
1.9859
1.8931
2.0891
1.9858
2.1931
2.0763
2.2966
2.1667
2.3996
2.4469
2.5527
2.8875
2.6959
3.3285
2.9148
3.1395
3.9523
MEDIUM
Weight
with
l/4-in ice
1.5981
1.3983
1.5151
1.6787
1.6200
1.7963
1.7243
1.9109
1.8267
2.0269
1.9300
2.1426
2.0308
2.2576.
2.1345
2.3734
2.2357
2.4881
2.3369
2.6022
2.6500
2.7625
3.1367
2.9210
3.6233
3.1642
3.4114
4.3012
1977
CODE
l-
LOADING
4-lb/ft2
wind
.5540
.5467
.5550
.5653
.5710
.5820
.5863.
.5977
.6007
.6127
.6150
.6273
.6287
.6413
.6423
.6550
.6553
.6687
.6673
.6817
.7007
.7270
.7540
.7457
.7857
.7673
.7933
.8670
Resultant
weight2
1.8914
1.7014
1.8135
1.9713
1.9177
2.0882
2.0213
2.2022
2.1229
2.3174
2.2257
2.4325
2.3259
2.5469
2.4291
2.6621
2.5297
2.7764
2.6303
2.8900
2.9410
3.0566
3.4261
3.2146
3.9075
3.4559
3.7025
4.5877
ALL VALUES
1
EDITION
HEAVY
LOADING
Weight
with
l/2-in ice
4-lb/ft2
wind
Resultatlt
weight’
2.1928
1.9861
2.1106
2.2839
2.2305
2.4170
2.3491
2.5462
2.4648
2.6762
2.5816
2.8056
2.6951
2.9337
2.8116
3.0622
2.9249
3.1897
3.0372
3.3160
3.3814
3.5186
3.9180
3.6944
4.4341
3.9578
4.2294
5.1878
.7207
.7133
97217
.7320
.7377
.7487
.7530
.7643
.7673
.7793
.7817
.7940
.7953
.8080
.8090
.8217
.8220
.8353
.8340
-8483
.8673
.8937
.9207
.9123
.9523
.9340
.9600
1.0337
2.6082
2.4103
2.5306
2.6983
2.6493
2.8303
2.7668
2.9585
2.8815
3.0874
2.9973
3.2158
3.1100
3.3430
3.2257
3.4706
3.3382
3.5973
3.4497
3.7228
3.7909
3.9303
4.3247
4.1054
4.8352
4.3666
4.6369
5.5898
ARE IN POUNDS PER FOOT.
Table Cd.-Conductor
and overhead ground wire values for NESC
light, medium, and heavy loading f U.S. customary&Continued
I
Wire type
and size
NATIONAL
I. I GHT
Weight
with
no ice
ELECTRICAL
MEDIUM
LOADING
9-lb/ft2
wind
Resultant
weight l
STEEL
3/8
3/8
‘/I6
‘46
l/2
y/2
INCH
INCH
INCH
INCH
INCH
INCH
HS
EHS
HS
EHS
HS
EHS
.2730
.2730
.3990
.3990
.5170
.5170
.2700
.2700
.3263
.3263
.3713
.3713
.1310
8M
16M
18M
20M
25M
7 NO.
7 NO.
7 NO.
7N0.
7N0.
7N0.
7N0.
7N0.
12
11
10
9
8
7
6
5
1650
: 2080
.2320
.2620
.3060
.3470
.4750
.1036
.1306
1647
: 2076
.2618
.3300
.4163
.5249
’ Includes 0.05 NESC constant.
2 Includes 0.20 NESC constant.
3 Includes 0.30 NESC constant.
.2040
.2295
.2573
.2723
.2895
.3128
.3330
.3893
1815
: 2040
.2295
.2573
.2888
.3248
.3645
.4095
Weight
with
l/4-in ice
STRAND
.2924
.3327
.3808
.4077
.4405
.4875
.5309
.6641
.2590
.2922
.3325
.3806
.4398
.5130
.6033
.7157
1977
CODE
LOADING
4-lb/ft2
wind
OVERHEAD
.4340
.4340
.5654
.5654
.6865
.6865
ALUMOWELD
10M
12.5M
14M
SAFETY
GROUND
HEAVY
Resultant
weight’
WIRE
.3117
.3117
.3317
.3317
OVERHEAD
.2933
.3379
.3924
.4226
.4598
.5134
.5628
.7142
.2566
.2929
.3376
.3920
.4593
.5424
.6452
.7725
.2573
.2687
.2810
.2877
.2953
.3057
.3147
.3397
.2473
.2573
.2687
.2810
.2950
.3110
.3287
.3487
Weight
with
l/2-in ice
4-lb/ft2
wind
Resultant
weight”
.8079
.8079
99806
.9806
.4533
.4533
.4783
.4783
.4983
.4983
1.2264
1.2264
1.3910
1.3910
1.5404
1.5404
.4240
.4353
.4477
.4543
.4620
.4723
1.0439
1.0959
1.1583
1.1930
1.2352
1 h2956
1.3509
1.5190
1.0005
1.0435
1.0957
1.1580
1.2343
1.3280
1.4425
1.5835
1.1359
1.1359
GROUND
LOADING
(7-WIRE)
.2867
.2867
STRAND
EDITION
WIRE
.5902
.6317
.6827
.7113
.7465
.7975
.8448
.9908
.5564
.5899
.6315
.6823
.7459
.8252
.9241
1.0475
ALL VALUES
.6112
.6663
.7323
.7688
.8131
.8764
.9342
1.1088
.5651
.6108
.6660
.7319
.8123
.9103
1.0296
1.1755
.4813
.5063
.4140
.4240
.4353
.4477
.4617
.4777
.4953
.5153
ARE IN POUNDS PER FOOT.
<<Index
ACSR conductors
creep, 9, 13, 26. 442, 452
data tables, 462, 466
ice and wind load, 27, 470, 474
initial and final modulus,
13, 15, 26, 442, 452
loading conditions,
2, 26, 128
loading constants,
27
loading tables, 470, 474
permanent
set, 14, 26, 442, 45?
sags and tensions (see Sags and tensions)
stress-strain
curves, 10
Adjacent
spans
distance between low points of, 128
maximum
sum of, 128
Air gap, 103. 112
flashover
values, 423, 424
Aluminum
conductor
tables, 462
Alumoweld
strand
data tables, 465. 469
ice and wind load, 27, 473, 477
initial and final modulus,
13, 26, 419
loading conditions,
2, 26
loading constants,
27
loading tables, 473, 477
permanent
set, 419
sags and tensions (see Sags and tensions)
stress-strain
curves, 14
Angle
insulator
swing, 105, 112, 123, 129, 133, 142
maximum
line deflection,
128
of bias lines for single insulator
string limit, 168
of bias lines on structure
limitation
chart, 152
of line deflection
scale, 141 (wood),
151 (steel)
of protection,
108
of sideswing,
51, 127
ANSI.
2, 213
moment
of resistance for wood poles, 348
Armor
rods, 282
Aaiiutb
chart, 342
Barometric
pressure, 426
Basic impulse insulation
level,
Broken conductor,
56
sags and tensions, 29
thesis, 307
unbalanced
condition,
67
Building
clearances,
274
104
California
safety code (see Safety codes)
Carroll,
J. S., 284
catenary
curve. 14, 17, 22, 25, 28
charts
azimuth,
342
pyiw.
127
structure
limitation,
127
Circumference
tables for wood
Class of poles, 156
by pole lengths, 273
Clayton,
J. M.. 111
Clearance
patterns.
103, 111
construction
of, 121
poles,
351
Clearances
air-gap,
103, 109, 112
at conductor
transposition,
7
between conductors,
51
climbing,
2
conductor
to building,
274
conductor
to ground,
34, 38, 266
conductor
to guy, 130, 131 (Calif.)
conductor
to steel structure,
112
conductor
to wood structure,
129, 131 (Calif.)
crossings, 273
curves for spotting,
266
midspan,
110
models for, 6
NESC, 34
patterns,
103, 111
right-of-way,
274
Codes (see Safety codes)
Concentrated
loads, 29, 99
Conductor
broken,
29, 56, 307
clearance
patterns,
103, 111
clearances
(see Clearances)
creep, 9, 13, 26, 442, 452
data tables, 430, 442, 452, 462, 466, 470, 474
effect of temperature
change, 30
elastic limit, 13
electrical
conductivity,
9
elongation,
10
galloping,
50, 284
ice and wind load, 27, 470, 474
lightning
protection,
103
loading conditions
(see Loading
conditions)
loading constants,
27
mechanical
strength,
9
modulus of elasticity,
13
proportional
limit, 13
sags and tensions (see Sags and tensions)
sag template,
32
selection
of, 9
stress-strain
curves, 10
ultimate
tensile strength,
13
uplift, 268
vibration,
282
working
limit, 13
yield strength,
13
Cone of protection,
108
Construction
single wood-pole,
4
type of, 4, 128
Copperweld
sag charts, 29
Corona,
284
loss, 9
with armor rods, 282
Cost estimates, 2
Creep, 9, 442, 452
defdtion,
13
in final loading condition,
26
Crossings, 273
Dancing
conductors
(see Galloping
Data summary
form. 23
Davison,
A. E., 50
479
conductors)
480
TRANSMISSION
Den Hat-tog, J. P., 50
Density, 426, 427
Department
of Energy,
iii
Design instructions,
21
Design tensions (conductor),
128
Distance between low points, 128
Double-circuit
steel structures.
6
Douglas fir pole circumferences,
351
Drawings
guying chart, 209
plan and profile, 32, 266
project,
4
sag template,
32, 266
standard,
4
steel structure
limitation
chart, 147
wood structure
limitation
chart, 205
clearance
to conductor,
130,
in poor hearing soil, 274
Factor of safety
California,
13 1
insulation
withstand,
105
steel construction,
127
wood construction,
129
Farr. Holland
H., iii
Field data, 1
Final loading condition,
26
Final modulus of elasticity,
13, 26, 442, 452
Flashover,
103
characteristics
of insulators
and air gaps, 423
critical
impulse, 120
lightning,
107
60-He wet, 120
surge,
104
switching
values of air gaps, 424
Flattop
construction,
4
Footing
resistance,
103, 111
surge resistance,
111
Fortescue,
C. L., 106
GUYS
calculations
for,
169
131 (Calif.)
H-frame
wood-pole
structures,
4
guying,
169
maximum
design tensions, 128
maximum
low-point
distance.
153
maximum
sum of adjacent
spans, 156,
stresses, 213
Effective
span, 8
Ehrenburg,
D. O., 40
Elastic limit, 13
Electrical
conductivity,
9
Ellipses,
130, 184
Elongation,
10, 26
Engineers
cost estimate, 2
Equations
(survey),
300
Galloping
conductors,
50
half- and full-sag ellipses, 130
vibrations,
284
Grading
the transmission
line, 268
Graphic
method for sag-tension
calculations,
Ground
clearances,
34, 38
on side slopes, 273
Ground
resistivity.
111, 344
Guying chart. 127
eonstrnction
of. 186
LINE DESIGN MANUAL
30
162
Ice loading,
27, 470, 474
Impulse insulation
level (value), 104, 112, 423
Inclined
spans, 38
sags and tensions, 28
stringing,
292
Initial
loading condition,
26
Initial
modulus of elasticity,
13, 26, 442, 452
Insulation,
103
air-gap,
103, 112, 423
basic impulse level, 104
safety factors, 106
selection tables, 107
withstand,
105
Insulator
effect, 77
extra units, 106
factor of safety, 128
flashover
characteristics,
423
impulse insulation
value, 104, 112. 423
offset, 292
sideswing,
51, 268
strength
requirement
for steel structures,
135
swing angle, 105. 112, 129, 131, 133, 142
vertical
force, 141
Isoceraunic
level. 103
Kientz,
H. J., iii
Land sections, 340, 341
Level spans
sags and tensions, 28
Lightning
direct-stroke
theory,
106
impulse voltages, 103
protection,
103, 106
Line deflection
angle, 128
near a substation,
274
resultant
force, 169
Loading
conditions,
2, 128
ACSR, 27
California,
3, 27, 130
final, 26
for galloping,
50
full load, 132
initial.
26
NESC. 9.26
overhead
ground wire, 28
Loading
constants,
27
INDEX
Locating
structures
(see Structure
Long-span
construction,
7
Losses
corona, 284
Martin,
J. S., 29
Martin’s
Sag Calculating
Tables,
Mass per volume (wood species),
Metric conversions,
431
Midspan
clearances,
110
Models for clearances,
6
Modulus
of elasticity,
13, 26
Mohr, R. D., iii
Moment
of resistance
ANSI standard,
348
formula,
343
USBR standard,
345
spotting)
29
427
NESC, 2.93
clearances,
34, 273
loading conditions,
27, 132
Nomenclature
steel structures,
5, 133
wood-pole
structures,
4, 149
Normal
span, 7
Oscillations
(see Galloping
conductors)
Outages
lightning,
111
Overhead
ground wires, 108
data tables, 462, 466, 470, 474
loading conditions,
3, 27
midspan clearances,
110
Overvoltage6
causes, 105
liihtuing,
103
power frequency,
103
switching
surges, 103
Parabola.
14, 25, 28
Peek, F. W., 284
Permanent
set, 10, 26
definition,
13
values for ACSR, 442, 452
values for Alumoweld
strand, 419
values for steel strand, 420
Peterson,
W. S., 284
Pole circumferences
Douglas fir, 351
southern
yellow pine, 351
western red cedar, 385
Pole ground wire. 128
Power frequency
operating
voltages, 103
causes of overvoltages,
105
Power loss. 284
Pressure due to wind, 429
Priest, F. F.. iii, 99
Proportional
limit, 13
Protection
lightning,
103
Proximity
effect, 104
Relative
air density, 426
Relative
mass density (wood), 427
Resistance
maximum
moment
of, 343
Resistivity,
111, 344
Restriking,
104
Right-of-way,
274
Rockwell,
M. M., 284
Ruling span
definition,
8
for stringing,
292
Safety codes, 2, 28
California,
2, 26, 35, 130, 273
NESC, 2,26,
132, 273, 275
Safety factor (see Factor of safety)
Sags and tensions, 25, 29
calculation
form, 33
calculations
for, 30, 38
catenary
versus parabola,
14, 25, 28
Copperweld
charts, 30
Ehrenburg’s
method.
40
inclined
spans, 28, 38, 292
initial
and final loading conditions,
26
insulator
effect on, 29, 77
level spans, 28
loading conditions,
2, 27
loading constants,
27
Martin’s
tables, 29
maximum
tensions, 3, 27
spans adjacent
to a broken conductor,
29, 56
spans with concentrated
loads, 29, 99
stringing,
292
temperature
for loading
conditions,
3, 27
Sag template,
32
broken conductor,
67
for structure
spotting,
266
inclined
span, 38
Scale factors for structure
limitation
charts
line deflection
angle, 141 (steel), 151 (wood)
low point, 140 (steel), 149 (wood)
sum of adjacent
spans, 141 (steel), 152 (wood)
Section numbering,
340
Selection
of
conductor,
9
ruling span, 8
type of construction,
4
Sheaves
for stringing,
292
Shield angle, 103, 108
Sideswing,
51, 268
angle, 105, 112, 129, 131, 133, 142
SI metric, 431
Single-circuit
steel structure,
5, 133
Single span limits on structures,
183
Single wood-pole
structure,
4
Southern
yellow pine
pole circumferences,
351
481
482
TRANSMISSION
Spacing
between conductors,
51
SpaDS
adjacent
to broken conductor,
29, 56
effective,
8
inclined,
28, 38
level, 28
maximum
permissable,
51
normal,
7
~lins,
8
substation
approach,
273
with concentrated
loads, 29, 99
with unbalanced
loads, 29, 67
Standards
for preparing
structure
limitation
chart, 127
Station equations,
300
Steel strand, 7-wire
data tables, 465. 469
ice and wind load. 27,473,477
initial and foal modulus,
13, 26, 422
loading conditions,
2, 26
loading constants,
27
loading tables, 473, 477
permanent
set, 420
sags and tensions (see Sags and tensions)
stress-strain
mtrves, 14
Steel structures
(see Structures)
Strength
basis for calculation,
128
determining
low-point
distance,
153
determining
span length,
183
determiniq
sum of adjacent
spans, 156, 162
limitation
of single insulator
string, 166
requirements
of insulator
string, 135 (steel)
Stresses
conductor,
10
voltage,
103, 112
wood-pole
structures,
213
Stress-strain
curves, 10, 15
Stringing,
25
sag data, 292
Stroke current,
103
Structure
limitation
chart, 127
angle of bias lines, 142 (steel), 152 (wood)
angle of bias lines for insulators,
168
basis for strength
calculations,
128
clearance
patterns,
111
conductor
calcuhxtions,
135 (steel), 150 (wood)
conductor
clearances,
129, 131 (Cahf.)
construction
of, 145 (steel), 185 (wood)
data required
for construction
of, 132 (steel), 146 (wood)
effect of hold downs, 156
full-load
conditions,
132
guying, 169, 176, 179, 182
insulator
swing angles, 142 (steel)
insulator
swing limits, 129, 131
insulator
vertical
force, 141 (steel), 150 (wood)
line deflection
angle scale, 141 (steel), 151 (wood)
loading conditions,
3, 128
low-point
distance,
153
low-point
scale, 140 (steel), 149 (wood)
maximum
design tensions, 128
safety factors, 128, 131
single span limits, 183
standards
to follow, 127
LINE DESIGN MANUAL
strength of insulators,
105 (wood),
135 (steel)
structure
design, 130 (Cahf.)
sum of adjacent
spans, 156, 162, 164
sum of adjacent
spans scale, 141 (steel), 152 (wood)
wind force on pole, 156
Structures
adjacent
to substation.
273
basic types of, 4
double-circuit
steel, 6
for special conditions,
4, 6
functional
classes of. 4
gr0”miing
of, 111
H-frame
wood-pole,
4, 149
insulation
for, 103
liihtning
protection,
103
single-circuit
steel, 5. 133
single wood-pole,
4
spotting,
266
stresses in wood-pole,
213
Structure
spotting,
29, 266
sag template,
32
uplift,
268
Substations,
29, 273
Summary
form, 23
Sum of adjacent
spans, 128 (steel), 156, 162 (wood)
Survey equations,
300
Suspension
clamp, 292
Suspension
insulator
string
flashover
characteristics,
423
switching
surges, 103
Switchyards
(see Substations)
Taps, 29, 99
Temperature
coefficients
of expansion,
428
for loading conditions,
3, 27
Template
(see Sag template)
Tensile testing, 10
Tension
(see also Sags and tensions)
calculation
of, 29
conductor,
3, 25
maximum
design. 128, 130
overhead
ground wire, 28
Tie-downs,
29, 99
Township,
340
Transmission
lie
data summary
form, 23
equations,
300
grading the line, 268
Transpositions,
6
Triangular
construction,
4
Types of construction
double-circuit
steel, 6
H-frame
wood-pole,
4
selection of, 4
single-circuit
steel, 5
single wood-pole,
4
ultimate
tensile strength,
defhtion,
13
Uplift (upstrain).
268
422,
462,
466
INDEX
USBR standards
augle of protection,
110
clearance
patterns,
111
conductor
and overhead
ground wire design criteria,
3
conductor
clearance
to buildiugs,
275
conductor
clearance
to guy wire, 130, 131 (Calif.)
conductor
clearance
to structure,
129, 131 (Calif.)
wowings,
273
ellipses, 50
factors of safety for wood construction,
129, 131 (Calif.)
full-load
conditions.
132
insulation
coordination,
105
insulator
swing limitations,
129 (wood)
maximum
moment of resistance
for wood poles, 345
structure
limitation
chart, 127
structures
and spans near substations,
273
Vibration
dampers, 282
Voltagc
stress, 112
lightning
impulse,
103, 105
power frequency,
103, 105
switching
surge. 103
Wave shape, 103
Western Area Power Administration,
iii
Western red cedar
pole circumferences,
385
Wind
force on ~004 pole, i56
loadiug on conductor,
3
pressure on projected
area, 429
Wiieauckas,
G. R., 29, 56, 307
Wood-pole
structures
basis for strcugth
calculation,
128
classes of poles, 156, 273
483
climbii
clearance,
2
conductor
calculations,
149
conductor
clearance
to guy wire, 130, 131 (Calif.)
conductor
clearance
to structure,
129, 131 (Calif.)
designations
and types, 149
effect of hold downs, 156
full-load
conditions,
133
guying, 169;171,
176, 179, 182
H-frame,
4, 128, 149
insulator
string strength,
166
insulator
swing limits, 129, 131
insulator
vertical
force, 150
loading conditions,
3, 128
low-point
distance,
153
mass per volume of wood, 427
moment of resistance,
343
pole circumferences,
351, 385
relative
mass density of wood, 427
safety factors, 129, 131 (Calif.)
single, 4
single span limits, 183
stresses in, 213
structure
limitation
chart, 146, 185
sum of adjacent
spans, 156, 162, 164
tensions (design),
128
type of construction,
128
wind force on pole, 156
Wood species
mass and density of, 427
Working
limit, 13
X-braces,
4
Yield strength,
13
Young,
F. S., 111