Structural Loading Calculations Of Wood Transmission StructuresKeith 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] II. NESC METHOD 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. 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. 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. Figure 1: Loading Map [1] 1 Table 1: Loading Per District [1] Heavy Medium Light Radial Thickness 0.88 0.86 0.80 250500 0. Both rules require multiplying the loads by an overload factor and multiplying the ultimate pole strength by a strength factor.40 165-250 1.71 0. The thickness of ice is taken as 0 for extreme wind loading.00 35-50 1.73 0. 0°F 15°F 30°F Hgt.68 Loading in pounds = 0. Table 3: Gust Response Factor GRF Structure Wire GRF. The method for making this calculation is also new in the 2002 NESC.86 0. Cases 2 and 3: Load cases 2 and 3 require the extreme wind pressure to be calculated.89 0. Table 2: Velocity Pressure Coefficient (kz) [1] Height (ft) Structure Wire < 33 0.0 for utility structures) Cd = Shape Factor 1.75 0.70 0.92 1.25 0 of ice (inch) 4 4 9 Horiz.10 1. Span Length (ft) (ft) GRF <250 < 33 35-50 50-80 80-115 115-165 165-250 1. The velocity pressure coefficient (kz) is dependent upon conductor height or pole height and is found by using Table 2. Table 5 shows the overload and strength factors if the second allowed rule is applied.02 0.82 0.71 500750 0. For transverse wind loading and wood construction the overload factors and strength factors to be used for the first rule are shown in Table 4.40 1.30 115-165 1. The gust response factor (GRF) is a function of height and span length.93 0.86 0.83 0.20 1.5 0.78 0.0 for circle or ellipse A = Projected wind area in ft2 The basic wind speed Vmi/h is taken from Figures 2 or 3.30 1.80 0.50 Figure 2: Basic Wind Speed [1] For final loading calculations. Wind Pressure (lb/ft2) Temp.69 0.79 0. 2 .00256(Vmi/h ) 2 k z G RF I C d A (1) Where: Vmi/h = Basic Wind Speed at 33 ft above Ground kz = Velocity Pressure Coefficient GRF = Gust Response Factor I = Importance factor (1.77 0. The following equation is utilized to calculate the force due to extreme wind.75 0.97 0.00 1.20 80-115 1.93 0.72 0.72 0. It may be found from Table 3 for span lengths of 250-1000 ft.10 50-80 1.82 0. two different rules are described in the NESC.86 0.83 0.71 7501000 0. The overload and strength factors may be combined into a single overload-multiplying factor that will used to multiply the load.00 F = 0.67 (elsewhere) 4.00 Strength Factor (extreme wind) 1.75 0. Figure 3: Basic Wind Speed [1] Table 4 Rule 1 Overload and Strength Factors (Transverse Loads) Construction Grade B C Wind 2.33 1. Since the strength factors in rule 2 are all 1.00 1.00256(Z v V) 2 GC f A (2) Where: F = Force in lbs Zv = Terrain Factor V = Fastest mile wind speed (from map) in mph G = Gust Response Cf = Force Coefficients (1.00 1. However.33 The overload multipliers thus produced are comparable to the rule 2 multipliers. 2.59 Extreme Wind 1. the overload and strength factors from rule 1 may be combined into the single set multipliers shown in Table 6. Table 5 Rule 2 Overload and Strength Factors (Transverse Loads) Construction Grade B C Wind (at crossings) 4.0 Strength Factor (wind) 0.0 1.0 2.0.2 Extreme Wind 1. Table 6 Rule 1 Overload Multipliers Construction Grade B C Wind 3. ASCE METHOD The ASCE calculation technique is applied to an ultimate stress method of design.5 2.85 2. For transverse loading due to wind and ice.33 1. the multiplying factor for rule 2 is the same as the overload factors in Table 5. 40% of calculated design wind on structure and wire with ice. It also lends itself to a load and resistance factor design.0 Extreme Wind 1.33 Strength Factor (wind) 1.0 is recommended [2]) A = Area exposed normal to the wind direction in ft2 3 . But for comparison purposes the ultimate stress application is only examined. The following equation is suggested for calculation of force due to wind loading [2]. two loading calculations must be examined. Calculated design wind on wire and structure with no ice.75 1. III.85 Strength Factor (extreme wind) 0.0 2.65 0. 30 1.91 1.00 1.40 200 1.09 1.99 1.96 1. For exposure C the gust response factor (Gw) for conductors is shown in Figure 5. exposure C is flat open country.88 1.35 140 0. 4 .21 50 0.11 1.18 40 0. one for the conductor and one for the structure. The NESC assumes exposure C for all of its calculations. Table 7: Terrain Factor Zv [2] Height Exposure Exposure Exposure above B C D Ground (ft) 0-33 0.31 100 0. or wooded areas.23 60 0.75 1.16 1.02 1.23 1. The value for Zv may be taken from Table 7. Exposure B is urban. suburban.26 70 0.14 1. and exposure D is country directly exposed to wind flowing over large bodies of water. There are two gust response factors.08 1.32 120 0.28 80 0.72 1.39 180 1.The fastest mile wind speed may be obtained from the map in Figure 4.42 Note: Interpolation is acceptable 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 7.06 1.17 1.79 1.20 1.29 90 0.26 1.28 1.37 160 1. Figure 5:Conductor Gust Response Factor Gw [2] The gust response factor (Gt) for structures is shown in Figure 6.05 1. Figure 4: Fastest Mile Wind Speed [2] The terrain factor Zv is dependent upon the type of terrain. which is divided into three exposure types.82 1.03 1.93 1.85 1. 4 psf for wind on wire and ice and 5.33.S.kips 3 5 . The force acting on the pole is: 31. of radial ice results in an area of 114.33(21.45 ft2. the calculated pressure on the pole is 31. The differences can be better illustrated by using numerical examples. The area of 250 ft of Hawk conductor without ice is 17. Extreme wind loading pressure is calculated from equation (1) where V=90 mph. Consider a transmission line in the central U. The force acting on the three conductors is: General NESC loading (Table 1) would be 4 psf on the pole and the thickness of radial ice will be 0.5 in.85 pounds.38 psf. the pole is required to resist a ground line moment of: Figure 7: Maximum 50-Year Ice [2] 2 918. span of 3 hawk conductors with 0. 27. The ground line moment needed for this load case is: For this example a 250 ft. and all three conductors are mounted 55 ft above ground.9 ft .2 psf for the pole and 19.45) = 1433. and the pole will have an area of 55 ft2.5 inch for heavy loading. and GRF = 0.) and 250 ft. The maximum design ice load for NESC is 0. The pressure on the conductor is calculated to be 27.2.5 in. Lets consider a line constructed with 55 ft.34 pounds.kips 3 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 66.16 and Gt = 1.85 (55) = 143. For 1 inch of radial ice the area of the each conductor 2 1433.838 in. For this height of pole only extreme wind on the pole (without conductors) need be considered.8 for the conductor. class 1 poles (average diameter 12 in.1 ft . Figure 7.96 pounds.87(55) = 1752. shows that most of the United States is subject to ice loads between 1.1 psf for wind on the pole. Using these values design pressures are calculated yielding 21.38 (3)(17.1 for the pole and 1.075.7 ft-kips.0 (4)(55) = 440 pounds. 2 1.0. Whereas. Assuming grade C construction with an overload factor of 2.93 for the pole and 0. This results in a pressure of 4.34 (55) + 1752.96 (55) + 440 (55) = 66.2 inches in radial thickness.9 psf for the conductor. The corresponding force on the pole is: 2.33 (from Table 5) for extreme wind loading this produces a ground line moment of: The first thing that becomes evident when comparing the two methods is the difference in ice loading calculations.7 ft .).kips 3 IV.0 inch. adopted by ASCE. Gw = 1.0 (4)(114.0 to 2. 40% of the design wind velocity (36 mph) is applied to both conductor and ice.2)(55) (55) = 56. in the NESC heavy loading area where the ASCE requires a design ice thickness of 1. the force due to wind on the conductors is: For ASCE load case number two. COMPARISON OF NESC AND ASCE LOADING The second loading case for this example is for extreme wind on the pole only.87 psf. kz = 1. Using the ASCE method and equation (2) where exposure C and grade C construction is assumed and V= 90 mph.87 ft2. Zv = 1. Using an overload factor of 1.87) = 918.2 for the conductor. Assuming that the force on the pole is centered at a distance 2/3 from the pole’s base [2]. spans of Hawk conductor (diameter 0. 90 mph wind.becomes 59. 40 35 30 9 8 7 6 5 4 3 2 1 0 25 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 20 Pole Height (ft) 15 10 NESC ASCE Figure 11: Comparison Between NESC and ASCE. However. and grade C construction.4(3) (59.1(55) (55) = 53. NESC ASCE Figure 8: Comparison Between NESC and ASCE. Wind Pressure on Wire (No Ice) Pressure of Wind on Pole (No Ice extreme wind) 45 Pressure on Pole (psf) 8 Pressure on Pole (psf) 2 4. 6 5 4 3 2 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Pole Height (ft) NESC ASCE Figure 10: Comparison Between NESC and ASCE.1 ft-kips is required.2 ft . assuming an average pole diameter of 12 inches and a wind speed of 90 mph. span of Hawk conductor on Grade C construction. when ice is included in the load case the pressures calculated by the NESC are greater then those calculated by the ASCE method. span of Hawk conductor. 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.1) (55) + 5. 250 ft.1 ft2 which gives a total ground line moment for this load case of: Pressure of Wind on Pole (Ice Considered) 9 Load case one controls and according to the ASCE method a design ground line moment of 143. The required ground line moment as calculated by the ASCE method is more than twice that calculated by the NESC method. This is calculated for a 250 ft. Wind Pressure on Pole (No Ice) 6 . Wind Pressure on Pole (Ice Considered) Pressure on Wire (psf) Pressure of Wind on Wire (Ice Considered) Pressure of Wind on Wire (No Ice Extreme Wind) 45 Pressure on Wire (psf) 7 1 Figures 8 through 11 show a comparison between pressures calculated by the NESC and ASCE methods on poles and wire for various pole heights. According to the NESC a class 6 pole would be sufficient for this example but the ASCE method would require a class 3 pole.kips 3 40 35 30 25 20 For comparison purposes. Wind Pressure on Wire (Ice Considered) 5 Pole Height (ft) 19 0 17 0 15 0 13 0 11 0 90 70 50 30 10 0 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. 15 10 5 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Pole Height (ft) NESC ASCE Figure 9: Comparison Between NESC and ASCE. Figure 12 shows the controlling ground line moment as calculated for various pole heights by both methods. New York. If load and resistance factor design methodology were applied to the design. May 2002. REFERENCES [1] National Electrical Safety Code. Guidelines for Electrical Transmission Line Structural Loading. C22002. compared to the NESC method. 1992. 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. New York. Denver. 01CH37214. The considerable disagreement between loads calculated using NESC and ASCE data and recommendations must be resolved by each designer. CONCLUSION [2] It is seen from this comparison that the ASCE method of loading calculation results in more conservative design. Dagher. 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. V. Arkansas. To prevent pole failures under the design condition some factor of safety should be applied. IEEE Catalog No. This is true even though NESC loads contain overload factors presumably to include some factor of safety. ANSI 05. Proceedings of the 2001 IEEE Rural Electric Power Conference. [3] Mechanical Design Manual for Overhead Distribution Lines. 1991. Little Rock. ASCE Manual of Practice No. Washington DC. [6] Methods of Transmission Line Structure Design. The ASCE calculated loads do not contain any factor of safety and exceed the NESC loads. New York.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. University of Colorado at Denver. Under design conditions a transmission line 7 . Groundline Moments Groundline Moment (ftkips) 1600 1400 1200 1000 800 600 If minimizing structure failure is the primary design criteria. Masters Report. IEEE Std. REA Bulletin 1724E-200. REA Bulletin 160-2. [4] Design Manual for High Voltage Transmission Lines. All loading cases are considered and Figure 12 displays the controlling design case. H. 400 200 Pole Height (ft) 19 0 17 0 15 0 13 0 11 0 90 70 50 30 10 0 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. Colorado. May 2001. US Department of Agriculture. Keith Malmedal. US Department of Agriculture. [5] Reliability of Poles in NESC Grade C Construction.J.1-1992. Washington DC. New York. caution should be exercised when using the NESC methodology. ASCE 1991. Piscataway. [7] American National Standard for Wood PolesSpecification and Dimensions. 1982. more wind and ice load. New Jersey. 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. 74. specializing in all aspects of power system design.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.S. Halifax. and power engineering education. Pankaj K. Sen received his B. Colorado. Malmedal is a Registered Professional Engineer several states. Calcutta. and the M. India. Colorado.E degree (with honors) from Jadavpur University. Arvada. 8 . He has published more than 55 articles in various archival journals and conference proceedings. His research interests include application problems in electric machines. NS. Mr.D. Canada. 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.E. Dr. and Ph. Sen is a Registered Professional Engineer in the State of Colorado. degrees in electrical engineering from the Technical University of Nova Scotia. He is currently a Professor of Engineering at Colorado School of Mines in Golden. and a MSCE degree (structural option) from the University of Colorado at Denver in 2002. power systems.Eng.