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1
Structural Loading Calculations Of Wood Transmission Structures
Abstract: The most critical task in the design of
any structure is to determine the loads that the
structure must withstand. In the case of
transmission line pole structures, currently there
are two available methods commonly utilized to
calculate the environmental loads: wind and ice.
The first method is suggested by the National
Electrical Safety Code (NESC). This is an ultimate
stress method where all factors of safety are
included in the loads. The second option,
recommended by the American Society of Civil
Engineers (ASCE), calculates the forces that must
be resisted by the structure and may be used in an
ultimate strength method, where wood is the pole
construction material. This later technique may also
be used in a load and resistance factor design
(LRFD) with other common materials. This paper
compares the advantages and limitations of the two
methods. Numerical examples will be provided
showing how the design may differ depending upon
which method is employed.
I. INTRODUCTION
There are two available options that may be used to
calculate the design loads for transmissions structures.
The minimum design requirements are provided by the
National Electrical Safety Code. The American
Society of Civil Engineers suggests an alternative
method. Even though, in the 2002 edition of the
NESC, efforts have been made to conform the two
loading methods, differences still exist. The two
methods result in differing design criteria for choosing
structures.
This paper focuses mainly on the transverse loading of
tangent type wood transmission structures due to ice
and wind loads and the numerical results illustrate the
differences between the two methods.
II. NESC METHOD
The NESC has traditionally been an ultimate stress
design method where all factors of safety are included
in the loading conditions by applying applicable
overload factors. Three cases for transverse loading
are considered.
1. General loading due to wind on wire and pole
with ice.
2. Extreme wind on all structures without
conductors or ice. This provision is new in the
2002 NESC.
3. Extreme wind on conductor and pole without
ice if the structure exceeds 60 ft in height.
Case 1:
The NESC defines three general loading areas in the
United States: heavy, medium, and light. Figure 1
defines these loading areas. For each of these loading
areas general wind and ice loads are also defined as
described in Table 1. Wind load is calculated
including ice on the conductor but not on the structure.
Figure 1: Loading Map [1]
Keith Malmedal P.E. Member IEEE
Senior Engineer/Project Manager
NEI Electric Power Engineering
Arvada, Colorado 80001
P.K. Sen, Ph. D, P.E., Senior Member IEEE
Professor of Engineering
Colorado School of Mines
Golden, Colorado 80401
2
Table 1: Loading Per District [1]
Heavy Medium Light
Radial Thickness
of ice (inch)
0.5 0.25 0
Horiz. Wind
Pressure (lb/ft2)
4 4 9
Temp. 0°F 15°F 30°F
Cases 2 and 3:
Load cases 2 and 3 require the extreme wind pressure
to be calculated. The method for making this
calculation is also new in the 2002 NESC. The
following equation is utilized to calculate the force due
to extreme wind.
(1) A C I G k )0.00256(V
poundsin Loading
dRFz
2
mi/h
=
Where:
Vmi/h = Basic Wind Speed at 33 ft above Ground
kz = Velocity Pressure Coefficient
GRF = Gust Response Factor
I = Importance factor (1.0 for utility structures)
Cd = Shape Factor 1.0 for circle or ellipse
A = Projected wind area in ft2
The basic wind speed Vmi/h is taken from Figures 2 or
3.
The thickness of ice is taken as 0 for extreme wind
loading. The velocity pressure coefficient (kz) is
dependent upon conductor height or pole height and is
found by using Table 2.
Table 2: Velocity Pressure Coefficient (kz) [1]
Height (ft) Structure Wire
< 33 0.92 1.00
35-50 1.00 1.10
50-80 1.10 1.20
80-115 1.20 1.30
115-165 1.30 1.40
165-250 1.40 1.50
The gust response factor (GRF) is a function of height
and span length. It may be found from Table 3 for
span lengths of 250-1000 ft.
Table 3: Gust Response Factor GRF
Hgt.
Structure Wire GRF, Span Length (ft)
(ft) GRF <250 250-
500
500-
750
750-
1000
< 33 1.02 0.93 0.86 0.79 0.75
35-50 0.97 0.88 0.82 0.86 0.72
50-80 0.93 0.86 0.80 0.75 0.71
80-115 0.89 0.83 0.78 0.73 0.70
115-165 0.86 0.82 0.77 0.72 0.69
165-250 0.83 0.80 0.71 0.71 0.68
For final loading calculations, two different rules are
described in the NESC. Both rules require multiplying
the loads by an overload factor and multiplying the
ultimate pole strength by a strength factor.
For transverse wind loading and wood construction the
overload factors and strength factors to be used for the
first rule are shown in Table 4.
Table 5 shows the overload and strength factors if the
second allowed rule is applied.
Figure 2: Basic Wind Speed [1]
3
Table 4
Rule 1 Overload and Strength Factors
(Transverse Loads)
Construction
Grade
B C
Wind 2.5 2.2
Extreme Wind 1.0 1.0
Strength Factor (wind) 0.65 0.85
Strength Factor (extreme wind) 0.75 0.75
Table 5
Rule 2 Overload and Strength Factors
(Transverse Loads)
Construction
Grade
B C
Wind (at crossings)
(elsewhere)
4.0
4.0
2.67
2.0
Extreme Wind 1.33 1.33
Strength Factor (wind) 1.00 1.00
Strength Factor (extreme wind) 1.00 1.00
The overload and strength factors may be combined
into a single overload-multiplying factor that will used
to multiply the load. Since the strength factors in rule
2 are all 1.0, the multiplying factor for rule 2 is the
same as the overload factors in Table 5. However, the
overload and strength factors from rule 1 may be
combined into the single set multipliers shown in Table
6.
Table 6
Rule 1 Overload Multipliers
Construction
Grade
B C
Wind 3.85 2.59
Extreme Wind 1.33 1.33
The overload multipliers thus produced are comparable
to the rule 2 multipliers.
III. ASCE METHOD
The ASCE calculation technique is applied to an
ultimate stress method of design. It also lends itself to
a load and resistance factor design. But for
comparison purposes the ultimate stress application is
only examined. For transverse loading due to wind
and ice, two loading calculations must be examined.
1. Calculated design wind on wire and structure
with no ice.
2. 40% of calculated design wind on structure
and wire with ice.
The following equation is suggested for calculation of
force due to wind loading [2].
(2) A GC V)0.00256(Z F f
2
v=
Where:
F = Force in lbs
Zv = Terrain Factor
V = Fastest mile wind speed (from map) in mph
G = Gust Response
Cf = Force Coefficients (1.0 is recommended [2])
A = Area exposed normal to the wind direction in ft2
Figure 3: Basic Wind Speed [1]
4
The fastest mile wind speed may be obtained from the
map in Figure 4.
The terrain factor Zv is dependent upon the type of
terrain, which is divided into three exposure types.
Exposure B is urban, suburban, or wooded areas,
exposure C is flat open country, and exposure D is
country directly exposed to wind flowing over large
bodies of water. The NESC assumes exposure C for
all of its calculations. The value for Zv may be taken
from Table 7.
Table 7: Terrain Factor Zv [2]
Height
above
Ground
(ft)
Exposure
B
Exposure
C
Exposure
D
0-33 0.72 1.00 1.18
40 0.75 1.03 1.21
50 0.79 1.06 1.23
60 0.82 1.09 1.26
70 0.85 1.11 1.28
80 0.88 1.14 1.29
90 0.91 1.16 1.31
100 0.93 1.17 1.32
120 0.96 1.20 1.35
140 0.99 1.23 1.37
160 1.02 1.26 1.39
180 1.05 1.28 1.40
200 1.08 1.30 1.42
Note: Interpolation is acceptable
There are two gust response factors, one for the
conductor and one for the structure. For exposure C
the gust response factor (Gw) for conductors is shown
in Figure 5.
Figure 5:Conductor Gust Response Factor Gw [2]
The gust response factor (Gt) for structures is shown in
Figure 6.
Figure 6: Gust Response Factor for Structures Gw[2]
The ice loading calculations used in design can be
found using the maximum 50-year ice load shown in
Figure 7.
Figure 4: Fastest Mile Wind Speed [2]
5
Figure 7: Maximum 50-Year Ice [2]
IV. COMPARISON OF NESC AND ASCE
LOADING
The first thing that becomes evident when comparing
the two methods is the difference in ice loading
calculations. The maximum design ice load for NESC
is 0.5 inch for heavy loading. Whereas, Figure 7,
adopted by ASCE, shows that most of the United
States is subject to ice loads between 1.0 to 2.2 inches
in radial thickness.
The differences can be better illustrated by using
numerical examples. Consider a transmission line in
the central U.S. in the NESC heavy loading area where
the ASCE requires a design ice thickness of 1.0 inch.
Lets consider a line constructed with 55 ft. class 1
poles (average diameter 12 in.) and 250 ft. spans of
Hawk conductor (diameter 0.838 in.).
General NESC loading (Table 1) would be 4 psf on the
pole and the thickness of radial ice will be 0.5 in.
Extreme wind loading pressure is calculated from
equation (1) where V=90 mph, kz = 1.1 for the pole
and 1.2 for the conductor, and GRF = 0.93 for the pole
and 0.8 for the conductor.
Using these values design pressures are calculated
yielding 21.2 psf for the pole and 19.9 psf for the
conductor. For this height of pole only extreme wind
on the pole (without conductors) need be considered.
For this example a 250 ft. span of 3 hawk conductors
with 0.5 in. of radial ice results in an area of 114.87 ft2.
and the pole will have an area of 55 ft2. Assuming
grade C construction with an overload factor of 2.0, the
force due to wind on the conductors is:
.pounds 96.918)87.114)(4( 0.2 =
The corresponding force on the pole is:
.pounds 440)55)(4( 0.2 =
Assuming that the force on the pole is centered at a
distance 2/3 from the pole’s base [2], and all three
conductors are mounted 55 ft above ground, the pole is
required to resist a ground line moment of:
( ) kips-ft 7.66553
2 440 (55) 18.969 =
+
The second loading case for this example is for
extreme wind on the pole only. Using an overload
factor of 1.33 (from Table 5) for extreme wind loading
this produces a ground line moment of:
( ) kips-ft 9.56553
2 (55)1.33(21.2) =
Load case 1 controls the design and according to the
NESC this pole would have to be designed to
withstand a ground line moment of 66.7 ft-kips.
Using the ASCE method and equation (2) where
exposure C and grade C construction is assumed and
V= 90 mph, Zv = 1.075, Gw = 1.16 and Gt = 1.33, the
calculated pressure on the pole is 31.87 psf. The
pressure on the conductor is calculated to be 27.38 psf.
The area of 250 ft of Hawk conductor without ice is
17.45 ft2. The force acting on the three conductors is:
.pounds 34.1433)(3)(17.45 38.27 =
The force acting on the pole is:
.pounds 85.1752)55(87.31 =
The ground line moment needed for this load case is:
( ) kips-ft 1.143553
2 1752.85 (55) 34.1433 =
+
For ASCE load case number two, 40% of the design
wind velocity (36 mph) is applied to both conductor
and ice. This results in a pressure of 4.4 psf for wind
on wire and ice and 5.1 psf for wind on the pole. For 1
inch of radial ice the area of the each conductor
6
becomes 59.1 ft2 which gives a total ground line
moment for this load case of:
( ) kips-ft 2.53553
2 5.1(55) (55) (59.1) 4.4(3) =
+
Load case one controls and according to the ASCE
method a design ground line moment of 143.1 ft-kips
is required. The required ground line moment as
calculated by the ASCE method is more than twice that
calculated by the NESC method. According to the
NESC a class 6 pole would be sufficient for this
example but the ASCE method would require a class 3
pole.
Figures 8 through 11 show a comparison between
pressures calculated by the NESC and ASCE methods
on poles and wire for various pole heights, 250 ft. span
of Hawk conductor, 90 mph wind, and grade C
construction.
Pressure of Wind on Wire (No Ice Extreme Wind)
0
5
10
15
20
25
30
35
40
45
10
30
50
70
90
110
130
150
170
190
Pole Height (ft)
Pre
ssu
re o
n W
ire (
psf)
NESC
ASCE
Figure 8: Comparison Between NESC and ASCE, Wind
Pressure on Wire (No Ice)
Pressure of Wind on Pole (No Ice extreme wind)
0
5
10
15
20
25
30
35
40
45
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
Pole Height (ft)
Pre
ssu
re o
n P
ole
(p
sf)
NESC
ASCE
Figure 9: Comparison Between NESC and ASCE, Wind
Pressure on Pole (No Ice)
Pressure of Wind on Pole (Ice Considered)
0
1
2
3
4
5
6
7
8
9
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
Pole Height (ft)
Pre
ssu
re o
n P
ole
(p
sf)
NESC
ASCE
Figure 10: Comparison Between NESC and ASCE, Wind
Pressure on Pole (Ice Considered)
Pressure of Wind on Wire (Ice Considered)
0
1
2
3
4
5
6
7
8
9
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
Pole Height (ft)
Pre
ssu
re o
n W
ire (
psf)
NESC
ASCE
Figure 11: Comparison Between NESC and ASCE, Wind
Pressure on Wire (Ice Considered)
It is seen from these figures that in load cases where
ice is not considered the ASCE values of pressure
always exceed the NESC values. However, when ice
is included in the load case the pressures calculated by
the NESC are greater then those calculated by the
ASCE method. It must be remembered that the NESC
ice loading is often half or less of the ice loading
recommended by the ASCE and the higher values of
pressure may be offset by the lighter ice loading used
for NESC calculations.
For comparison purposes, Figure 12 shows the
controlling ground line moment as calculated for
various pole heights by both methods. This is
calculated for a 250 ft. span of Hawk conductor on
Grade C construction, assuming an average pole
diameter of 12 inches and a wind speed of 90 mph.
7
Groundline Moments
0
200
400
600
800
1000
1200
1400
1600
10
30
50
70
90
110
130
150
170
190
Pole Height (ft)
Gro
un
dlin
e M
om
en
t (f
t-
kip
s)
NESC
ASCE
Figure 12: Required Ground Line Moments as calculated
by NESC Compared with ASCE Methods
Ice is calculated for NESC heavy loading and as
required by the ASCE. All loading cases are
considered and Figure 12 displays the controlling
design case.
V. CONCLUSION
It is seen from this comparison that the ASCE method
of loading calculation results in more conservative
design, more wind and ice load, compared to the NESC
method. This is true even though NESC loads contain
overload factors presumably to include some factor of
safety.
The ASCE calculated loads do not contain any factor
of safety and exceed the NESC loads. If a pole were
chosen so that the ultimate breaking moment of the
pole just equaled the loads calculated by this method it
is expected that some pole failures may result due to
variations in pole strengths if the design conditions
were ever actually applied to the transmission line. To
prevent pole failures under the design condition some
factor of safety should be applied. If load and
resistance factor design methodology were applied to
the design, the loads would be multiplied by some load
factor and the resistance of the pole would be
multiplied by a resistance factor to produce a design
that would prevent pole failures if the design
conditions were ever actually applied to the
transmission line.
The considerable disagreement between loads
calculated using NESC and ASCE data and
recommendations must be resolved by each designer.
Under design conditions a transmission line
constructed using NESC loading would be expected to
suffer more structure failures than a transmission line
constructed using ASCE criteria. This must be weighed
against the additional cost of construction if the line
were built to withstand loads as calculated by ASCE
recommendations.
If minimizing structure failure is the primary design
criteria, caution should be exercised when using the
NESC methodology. Rather than relying on the values
of wind and ice loading recommended by the NESC a
more reliable design will be produced by using local
ice and wind records or by using the ASCE
recommendations in determining design loading.
REFERENCES
[1] National Electrical Safety Code, IEEE Std. C2-
2002, Piscataway, New Jersey.
[2] Guidelines for Electrical Transmission Line
Structural Loading, ASCE Manual of Practice
No. 74, ASCE 1991, New York, New York.
[3] Mechanical Design Manual for Overhead
Distribution Lines, REA Bulletin 160-2, US
Department of Agriculture, 1982, Washington
DC.
[4] Design Manual for High Voltage Transmission
Lines, REA Bulletin 1724E-200, US Department
of Agriculture, 1992, Washington DC.
[5] Reliability of Poles in NESC Grade C
Construction, H.J. Dagher, Proceedings of the
2001 IEEE Rural Electric Power Conference,
IEEE Catalog No. 01CH37214, Little Rock,
Arkansas, May 2001.
[6] Methods of Transmission Line Structure Design,
Keith Malmedal, Masters Report, University of
Colorado at Denver, Denver, Colorado, May
2002.
[7] American National Standard for Wood Poles-
Specification and Dimensions, ANSI 05.1-1992,
New York, New York, 1991.
8
Keith Malmedal received his BSEET degree from
Metropolitan State College of Denver in 1995, a MSEE
degree (Power Option) from the University of
Colorado at Denver in 1998, and a MSCE degree
(structural option) from the University of Colorado at
Denver in 2002. He has over ten years experience in
electrical power design and is presently a senior design
engineer and project manager at NEI Electric Power
Engineering, Arvada, Colorado, specializing in all
aspects of power system design. Mr. Malmedal is a
Registered Professional Engineer several states.
Pankaj K. Sen received his B.S.E.E degree (with
honors) from Jadavpur University, Calcutta, India, and
the M.Eng. and Ph.D. degrees in electrical engineering
from the Technical University of Nova Scotia, Halifax,
NS, Canada. He is currently a Professor of
Engineering at Colorado School of Mines in Golden,
Colorado. His research interests include application
problems in electric machines, power systems, and
power engineering education. He has published more
than 55 articles in various archival journals and
conference proceedings. Dr. Sen is a Registered
Professional Engineer in the State of Colorado.