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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 kmalmedal@neiengineering.com

P.K. Sen, Ph. D, P.E., Senior Member IEEE Professor of Engineering Colorado School of Mines Golden, Colorado 80401 psen@mines.edu

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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

dRFz2

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]

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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 f2

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]

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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]

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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 7.665532 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 9.565532 (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 1.1435532 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

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becomes 59.1 ft2 which gives a total ground line moment for this load case of:

( ) kips-ft 2.535532 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)

Pres

sure

on

Wire

(psf

)

NESCASCE

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)

Pres

sure

on

Pole

(psf

)

NESCASCE

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)

Pres

sure

on

Pole

(psf

)

NESCASCE

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)

Pres

sure

on

Wire

(psf

)

NESCASCE

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.

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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

undl

ine

Mom

ent (

ft-ki

ps)

NESCASCE

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.

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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.