8
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 [email protected] P.K. Sen, Ph. D, P.E., Senior Member IEEE Professor of Engineering Colorado School of Mines Golden, Colorado 80401 [email protected]

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Page 1: Environmental Loading of Wood Transmission Structures rev

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

[email protected]

P.K. Sen, Ph. D, P.E., Senior Member IEEE

Professor of Engineering

Colorado School of Mines

Golden, Colorado 80401

[email protected]

Page 2: Environmental Loading of Wood Transmission Structures rev

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]

Page 3: Environmental Loading of Wood Transmission Structures rev

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]

Page 4: Environmental Loading of Wood Transmission Structures rev

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]

Page 5: Environmental Loading of Wood Transmission Structures rev

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

Page 6: Environmental Loading of Wood Transmission Structures rev

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.

Page 7: Environmental Loading of Wood Transmission Structures rev

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.

Page 8: Environmental Loading of Wood Transmission Structures rev

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.