Palm Frond Calculations

Palm Frond Calculations 250 E. Broad Street Suite 500 Columbus, Ohio 43215 Paul J. Ford and Company Job # 33201-0014 Reference PJF Drawing # 33201-0014 Sheet S-3, Dated 02/06/2001

PAGE 1 OF 6 FORMULAS Gusted Wind Pressure = Gh qz = Gh [0.00256 Kz Vˆˆ2] (TIA/EIA 2.3.3 & 2.3.4) Gh = 1.69 (TIA/EIA 2.3.4.2) Kz = [z/33]ˆ(2/7) (TIA/EIA 2.3.3) Calculate design wind pressure at 33 ft. above grade. Therefore, Kz = 1.0. V = Design Wind Velocity (mph) TESTING COMPLETED BY INNOVATIVE SITE SOLUTIONS Innovative Site Solutions performed load testing of the palm fronds, and have provided the results to Paul J. Ford and Company. The palm fronds were tested to determine the applied wind force at various wind velocities. The wind load was measured by a strain gauge placed at a distance (38") from the pivot point. The resulting wind force on the palm frond is calculated from statics. Below is a free body diagram of the test model. TEST RESULTS Wind Velocity (mph) 50 60 70 80 Gage Tension Force Wind Into Frond Profile Wind Into Front Face of Frond (lbs) (lbs) 14 19 20 30 29 40 36 50

PAGE 2 OF 6 CALCULATION OF WIND FORCE Resolve moment about pivot point to obtain wind force Sum of moment about pivot = 0 = (51" * Wind Force) - (38" * Tension Gage Force) Wind Force = 38" * Tension Gage Force 51" Wind Velocity Gage Tension / Profile Wind Force / Profile Gage Tension / Face Wind Force / Face (mph) (lbs) (lbs) (lbs) (lbs) 50 14 10.43 19 14.16 60 20 14.90 30 22.35 70 29 21.61 40 29.80 80 36 26.82 50 37.25 CALCULATION OF FACTORED PROJECTED AREA Factored Wind Area = CaA = Tested Wind Force Gusted Wind Pressure (Gh * qz) Wind Velocity Gh Gh * qz Wind Force / Profile CaA / Profile (mph) psf (lbs) (square feet, sf) 50 1.69 10.82 10.43 0.96 60 1.69 15.58 14.90 0.96 70 1.69 21.20 21.61 1.02 80 1.69 27.69 26.82 0.97 0.98 Average of CaA Wind Velocity Gh Gh * qz Wind Force / Profile CaA / Profile (mph) psf (lbs) (square feet, sf) 50 1.69 10.82 14.16 1.31 60 1.69 15.58 22.35 1.44 70 1.69 21.20 29.80 1.41 80 1.69 27.69 37.25 1.35 1.37 Average of CaA Since palm fronds will be mounted in the profile view, the CaA used for pole calculations could be 1.0 square feet. Due to dynamic and cyclical nature of wind, use a CaA of 1.3 square feet.

PAGE 3 OF 6 ANTENNA AND PALM FROND AREA Gross Area of Antennas, T-Arms and Palm Frond = Area of 17-ft diameter circle = 227 Square Feet (SF) Total Front Area of Palm Fronds, Antennas and Platforms Area of Pam Fronds = (30) Palm Fronds @ 1.3 Square Feet = 39 SF (1/2 of Palm Fronds in front view, 1/2 in back view) Frontal Areas of 1-ft x 4-ft Panel Antennas = 4 x [ 1-ft x 4-ft x 1.4 ] = 22.4 SF (Shape factor, Cf = 1.4) Area of 12-ft T-Arm Mounts = (4-in / 12-in/ft) x 12-ft x 2 = 8 SF (T-Arm Mount is constructed of 4" square tube with a front face width of 12-ft) (Shape factor, Cf = 1.4) Total Frontal Area of Palm Fronds, Antennas and Platforms = 69.4 SF 69.4 Solidity Ratio of Total Frontal Area / Gross Area = = 0.31 227 Use a Solidity Ratio of 0.60 for calculating areas of palm fronds, to account for back areas of fronds Area of Palm Frond used in Pole Calculations Palm Frond Area = [ 60 palm fronds ] x 1.3 sf x [ Solidity Ratio = 0.60 ] 46.800 SF

PAGE 4 OF 6 PALM BRANCH CONNECTION TO CLAMP BRACKET Dead_Load := 7lb (Weight of Branch) Wind_Load := 50lb (Ref. Attached Test Data/ Calcs.) Branch_Length := 7.5 ft. Moment_Arm := 0.6 Branch_Length + 16in Moment_Arm := 5.833 ft Calculated Moment at the base of the Receiver Stubs M := (Wind_Load Moment_Arm) + (Dead_Load Moment_Arm) M = 332.5 ft lb Calculate Moment Capacity of Tube Tube is 1 1/2 x 1 1/2 x 0.188 x 24 long ASTM A500 Grade B (46 KSI) Tube Width = B Tube Depth = D Inside Tube Width = B1 Inside Tube Depth = D1 Wall Thickness = 0.188 in Thk := 0.188in B := 1.25IN D := 1.25IN Fy := 46ksi B1 := B - (2 Thk) D1 := D - (2 Thk)

PAGE 5 OF 6 CALCULATED SECTION MODULUS OF TUBE [(B D 3 ) - (B1 D1 3 )] Sx := Sx = 0.248 in 3 6 D Allowable Moment Capacity in Tube Momentallow := 0.6 Fy Sx 1.33 Momentallow := 757.775 ft lb The Allowable Moment in the Tube is greater than the Calculated Moment in the tube. Therefore, the bending stresses in the tube are okay. Check the 1/4 Fillet Weld Section Modulus of Weld = Sx W D 2 SxW := B D + SxW := 2.083in 2 3 Actual Force in the Weld = Fw M Fw := Fw = 1915.2 SxW lb in Allowable Force in the Weld 3 Fyw := 70ksi W := in 16 Fillet Weld size = W (in) Fw_allow := (0.3) (Fyw) (0.707) (W) (1.33) Fw_allow :3702.471 lb in The Allowable Force in the Weld is greater than the Calculated Force in the Weld. Therefore, the stresses in the weld are okay.

PAGE 6 OF 6 FORCES IN CLAMP PLATE Tension in Clamp Bolts from Wind Load (worst case) Wind_Load Moment_Arm 60 = 17500 ft lb Wind_Load Moment_Arm 60 1.5ft = 11666.667lb 1.5 ft is the distance from the center of the pole to the bolts (worst case). Bolt_Tensionw := Wind_Load Moment_Arm 60 1.5ft Bolt_Tensionw := 3888.889lb 3 3 bolts assumes that all the force is carried in tension (no bearing occurs on the pole shaft). This is very conservative. Tension in Clamp Bolts from Dead Load (worst case) Dead_Load Moment_Arm 60 = 2450 ft lb Dead_Load Moment_Arm 60 4in = 7350 lb 4 in is half the distance of the clamp height. Bolt_Tensiond := Bolt_Tensiond = 2450lb Dead_Load Moment_Arm 60 4in 3 3 bolts assumes that all the force is carried in tension in the top (3) bolts only (no bearing occurs on the pole shaft). This is very conservative. Combined_Tension := Bolt_Tensionw + Bolt_Tensiond Combined_Tension = 6338.889 lb Tension Capacity of a 3/4 Diameter A307 Bolt = 8800 lbs

Panel Components Impact ABS Finishing: SP-932 can be sawed, drilled, routed, punched and die-cut with conventional tooling. Painting, silk-screen, and other decorative techniques are easily done, and SP-932 can be joined to itself or other materials by adhesive or solvent bonding. Mechanical fastening with screws, rivets, etc. is often successful depending on specific end use. PHYSICAL PROPERTY SUMMARY Property Test Method Value Unit Specific Gravity ASTM D-792 1.05 g/cc Tensile Modulus ASTM D-638 290,000 psi Tensile Strength @ Yield ASTM D-638 4,500 psi Flexural Modulus ASTM D-790 310,000 psi Flexural Strength @ Yield ASTM D-790 8,000 psi Izon Impact ASTM D-256 (73 F) 6.0 ft-lbs/in (-40 F) 1.4 ft-lbs/in Falling Dart Impact ASTM D-3029 (73 F) 19 ft-lbs/in (-40 F) 8 ft-lbs/in Heat Deflection Temperature ASTM D-648 (264 pis, unannealed) 190 F Coefficient of Thermal Expansion ASTM D-696 5.3 x 10-5 in/in/ F Hardness ASTM D-785 105 Rockwell R Flammability UL Subject 94 HB.062 Gardner Gloss ASTM D-523 95 % These typical results are based on test procedures which are believed to be reliable. Due to variable conditions or methods of processing, NO GUARANTEES OR WARRANTIES ARE EXPRESSED OR IMPLIED INCLUDING THE IMPLIED WARRANTY OF MERCHANTABILITY AND FITNESS FOR PARTICULAR PURPOSE, nor any recommendations made to infringe on patents. Extruded Polystyrene Meets Cal. QUAL. STAND. REG. # CA-T064, BOCA 90-11, ICBO 2257, SBCCI 9161, ASTM C578, HUD UMB-71, NYC BSA 912-52-SM, UND LAB. INC. CLASSIFIED. SEE CLASSIFICATION CERTIFICATE D-369 Surface Burning Characteristics for STYROFOAM Brand Insulation Flame Spread 5(1) Smoke Developed 165(1) (1) These numerical flame spread and smoke ratings are not intended to reflect hazards presented by this material under actual fire conditions.