Design Calculations for Light Mast

FOUNDATION DESIGN CALCULATIONS

LIGHT MAST 25M HIGH – HMA 9251

2 Contents of report: 1 INTRODUCTION ... 3 1.1 General ... 3 1.2 Objective ... 3 1.3 Design methodology ... 3 1.4 Materials ... 3 1.5 Software applied ... 3 1.6 Loads ... 3 2 DESIGN CALCULATIONS ... 5 2.1 Introduction ... 5 2.2 Design of footing ... 5 List of annexes

Annex 01. Reference data

Annex 02. Footing design for light pole HMA 9251 Annex 03. Drawings

1.1 General

This document presents the design calculations of of HMA 9251 Duo decagon Light pole foundation. HMA 9251 is for light mast of 25m high. It is supported on individual spread footing.

1.2 Objective

The design of reinforced concrete design consists of the following objective:

▪ Determination of working loads, ▪ Foundation design.

1.3 Design methodology 1.3.1 Codes and standards

Following codes shall be considered in the design:

▪ BS8110: Structural use of concrete

1.3.2 Reference Documents

▪ Vendor documents – HMA 9251

1.4 Materials

The material qualities are considered as follows:

▪ Concrete grade : C30

▪ Reinforcement steel : B 460 to BS EN 10080, with min. yield strength of 460 N/mm2. ▪ Anchor bolt : Provided by vendor (M27/ Grade 8.8)

1.5 Soil Safe bearing Capcity

▪ Safe bearing capacity of soil : 160 kN/sq.m

(Refer Geotechnical Site Invesitgation Report SD1400005 from ACES dated 3rd March 2014)

1.6 Software applied

▪ PROKON : Foundation design.

1.7 Loads

4 ▪ Permanent:

- _{Vertical load caused by the self-weight.}

▪ Incidental: - _{Wind load.}

1.7.1 Self-weight

The load case consists of the self-weight of light pole which is provided by vendor and is attached in Annex 01. The load is tabulated below:

Item Vertical load Horizontal load Dead load moment

HMA 9251 16.00 kN 8.00 kN 14.00 kN.m

Table 1.1 Self-weight loads 1.7.2 Wind load (WIND)

Wind load is applied on the exposed area of the steel structure with a design wind pressure of 1.25 kPa. The design wind pressure of 1.25 kPa is calculated for a wind speed of 45 m/sec. The load on the foundation due to wind is provided by the vendor and is attached in Annex 01. The load is tabulated below:

Item Wind load moment

HMA 9251 138.0 kN.m

Table 1.2 Wind load

1.7.3 Load combinations

The load combinations are taken as BS codes and standards

The safety factors are considered

Load characteristics Permanent actions Variable actions

Unfavourable 1.40 1.50

Favourable 1.00 0.00

Subsoil capacity evaluation 1.00 0.00

Table 1.3 Safety factors of the actions The partial factors for materials in ULS are as follows:

Material Material factor

Concrete 1.50

Reinforcing steel 1.15

Structural steel (strength / stability) 1.10

3.1 Introduction

After the evaluation of the working loads presented in Section 1.7, the reinforced concrete footing is modelled in Prokon to check for strength and stability.

3.2 Design of footing

One reinforced concrete footing will be used to support the steel structure of light pole HMA 9251. The forces considered at the top of the pedestal are the supports reactions in SLS (provided by the vendor). The footing has been designed in Prokon.

The summary of the footing design for HMA 9251 is as follows:

▪ Footing size : 2500 mm x 2500 mm x 1000 mm,

▪ Footing reinforcement

- Top reinforcement : T20 - 300 (both ways), - Bottom reinforcement : T20 - 300 (both ways).

▪ Pedestal size : 1200 mm x 1200 mm x 1000 mm,

▪ Pedestal reinforcement

- Vertical reinforcement : 24 T20, - Horizontal reinforcement : T12 - 100.

6 Annexure – 01

Job Ref: HMA9251 Duodecagon Mast (10xM27). Data and Introduction.

Mast Height m. : 25.00 Across Flats mm. Top : 150 Bottom : 520 mm. Head Load (V) kN. : 8.00 Height of flange above ground level : 0 m.

Head Frame Moment : Dead : 0.00 Live : 0.00 kN.m.

Mast Details: Additional Loads: (Live: S. Dead: M & V.) Factors:

Joint Heights Thickness Shears Moments Vertical Gama Gama Gama

No. m. mm. kN. kN.m. kN. Dead Wind Materials

15 25.00 3.00 1.00 1.25 1.15 14 22.00 3.00 Bolts : 1.15 13 20.37 3.00 12 18.00 4.00 Force Coefficients. 11 17.00 4.00 Head Shaft 10 15.50 4.00 CF CF 9 14.00 4.00 1.00 0.60 8 12.00 4.00 7 10.12 4.00 Shaft Material. 6 9.00 4.00 Grade Yield 5 7.00 4.00 S355 355 4 5.50 4.00 3 2.00 4.00 2 0.40 4.00

1 0 4.00 (Live) (Dead) (Dead)

Head Area Sq.M. : 3.37 Basic Wind Speed : 45 m/sec. Wind Factors S1 : 1.00 Topography Factor.

S2 : 2A Category , based on Table 3. Hourly Factor : 1.70 S3 : 0.95 Statistical Probability Factor.

1

Mean Hourly Wind Speed = Basic Wind Speed / Hourly Factor = 26.5

From tests the Log Decrement is 0.20 and the Nf in hertz is 0.31 (see below) Hence (Natural Frequency) / (Mean Hourly Wind Speed) = 0.012

From the graph in Technical Report No 7, the Beta Factor = 1.40 The Delta Factor is obtained from 1 - 0.006(Mast Height - 3) = 0.87 Hence the Magnification Factor, the product of Delta & Beta = 1.21

Foundation Studs.

Type of stud :- McCall’s High Strength Precision Ties. Flange Yield : 275 N/sq.mm.

Ultimate Tensile : 775 N/sq. mm. Bolt Diameter : 27 mm.

Proof Stress(.2%) : 585 N/sq. mm. Number equispaced : 10 no. Elastic Modulus : 205 kN/sq. mm. Pitch Circle Diameter : 650 mm.

Threads are :- ISO metric coarse pitch to BS3643 Part 2, cold rolled.

V.No. 1*09 Maximum Stud Load :- 259 kN.

Wind loading for a Duodecagon (20 sided) High Mast is in accordance with the ILE Technical Report Number 7, based on BS CP3 Chapter V Part 2. In this Standard the Basic Wind Speed is the 3 second gust speed estimated to be exceeded only once in 50 years. The force coefficient Cf for a 20 sided polygon section with rounded corners from De Havilland wind tunnel investigations has been found to be a worst case of 0.6 when "point into wind". Mean hourly wind speed factor is given in Appendix A , Paragraph A1 for each Category.

CU Lighting Ltd.

Highmast Design (Duo). Version: 1*09

Page No:___________ Initials:___________ Date:__08/12/05__ Job Ref: HMA9251 Duodecagon Mast (10xM27).

Natural Frequency Calculation.

JOINT HEIGHT MEMBER A/F THICK ELASTIC MEMBER

NO H LENGTHS D T MODULUS WEIGHTS

m m mm mm cm^3 kg

HEAD FRAME WEIGHT kg. 815.49

15 25.00 150 3.00 49.92 3.00 172 3.00 39.36 14 22.00 194 3.00 85.01 1.63 206 3.00 25.64 13 20.37 219 3.00 107.97 2.37 236 4.00 56.84 12 18.00 254 4.00 192.68 1.00 261 4.00 26.52 11 17.00 268 4.00 216.40 1.50 280 4.00 42.60 10 15.50 291 4.00 254.55 1.50 302 4.00 45.98 9 14.00 313 4.00 295.79 2.00 328 4.00 66.57 8 12.00 342 4.00 355.60 1.88 356 4.00 68.06 7 10.12 370 4.00 416.85 1.12 379 4.00 43.07 6 9.00 387 4.00 455.65 2.00 402 4.00 81.60 5 7.00 416 4.00 529.22 1.50 428 4.00 65.15 4 5.50 439 4.00 588.01 3.50 465 4.00 165.17 3 2.00 490 4.00 737.24 1.60 502 4.00 81.64 2 0.40 514 4.00 811.07 0.40 517 4.00 21.01 1 0 520 4.00 830.08 2

Total Theoretical Tip Deflection : 2648 mm. (See note above.) Natural Frequency : 0.3073 Hertz

Natural Period : 3.25 Secs.

Note:

V.No. 1*09

The Natural Frequency is derived from the formula given in the Netherlands Standard NEN 3850 TGB 1972., and is equal to : Squareroot of (0.25 / Tip Deflection ) . The tip deflection is calculated under self weight assuming an Elastic Modulus of 210 kN./sq.mm.

The deflection shown on this page is not the actual deflection under wind load but

the deflection used to calculate natural frequency. (See text at top of page.)

For actual wind load deflection refer to later serviceability calculation.

Job Ref: HMA9251 Duodecagon Mast (10xM27). Mast Data and Wind Pressure.

MEMBER JOINT HEIGHT A/F THICK RATIO FACTOR DESIGN PRESSURE

NO NO H D T D/T S2 SPEED m mm mm m/s N/sq.m HEAD FRAME ! 25.00 1.05 44.89 1235.13 15 25.00 150 3.00 50 14 172 1.05 44.89 1235.13 14 22.00 194 3.00 65 13 206 1.04 44.46 1211.71 13 20.37 219 3.00 73 12 236 1.03 44.03 1188.52 12 18.00 254 4.00 63 11 261 1.02 43.61 1165.56 11 17.00 268 4.00 67 10 280 1.01 43.18 1142.81 10 15.50 291 4.00 73 9 302 1.00 42.75 1120.30 9 14.00 313 4.00 78 8 328 0.99 42.32 1098.00 8 12.00 342 4.00 86 7 356 0.96 41.04 1032.46 7 10.12 370 4.00 93 6 379 0.93 39.76 968.94 6 9.00 387 4.00 97 5 402 0.90 38.48 907.44 5 7.00 416 4.00 104 4 428 0.85 36.34 809.41 4 5.50 439 4.00 110 3 465 0.80 34.20 716.99 3 2.00 490 4.00 123 2 502 0.72 30.78 580.76 2 0.40 514 4.00 129 1 517 0.72 30.78 580.76 1 0 520 4.00 130 3 Taper : 14.80 Max D/T: 130 V.No. 1*09

CU Lighting Ltd.

Highmast Design (Duo). Version: 1*09

Page No:___________ Initials:___________ Date:__08/12/05__ Job Ref: HMA9251 Duodecagon Mast (10xM27).

Ultimate Limit State Calculation.

JOINT EFFECT WIND ELASTIC TOTAL HORIZ. DIRECT LOAD TOTAL

NO PRESSURE LOAD MODULUS SHEAR MOMENT LOAD MOMENT MOMENT

N/sq.m kN/m cm^3 kN kN.m kN kN.m kN.m 1498.17 6.31 8.00 15 49.92 6.31 0.00 8.00 0.00 0.00 1498.17 0.19 14 85.01 6.89 19.80 8.38 5.62 25.43 1469.77 0.23 13 107.97 7.26 31.34 8.63 8.34 39.68 1441.64 0.26 12 192.68 7.87 49.27 9.18 11.91 61.18 1413.78 0.28 11 216.40 8.14 57.27 9.43 13.28 70.56 1386.20 0.29 10 254.55 8.58 69.82 9.84 15.22 85.03 1358.89 0.31 9 295.79 9.04 83.03 10.29 16.99 100.02 1331.84 0.33 8 355.60 9.70 101.77 10.93 19.10 120.87 1252.35 0.33 7 416.85 10.32 120.59 11.58 20.82 141.41 1175.30 0.33 6 455.65 10.70 132.36 12.00 21.71 154.08 1100.70 0.33 5 529.22 11.36 154.42 12.79 23.08 177.50 981.80 0.31 4 588.01 11.83 171.82 13.42 23.89 195.71 869.69 0.30 3 737.24 12.89 215.09 15.01 25.11 240.20 704.45 0.27 2 811.07 13.32 236.06 15.80 25.29 261.35 704.45 0.27 1 830.08 13.43 241.41 16.00 25.30 266.71 4

Approximate Mast Weight : 910 kg inc.

V.No. 1*09

Job Ref: HMA9251 Duodecagon Mast (10xM27). Ultimate Limit State Calculation.

Note: Bending Stress (Elastic, unfactored) for flange bolt designs only.

JOINT DEFLEC- ROTAT- BENDING STEEL YIELD PLASTIC PL/RES

ACCEP-NO TION ION STRESS GRADE STRESS MODULUS MOMENT TANCE

mm. RADS. N/sq.mm N/sq.mm cm^3 kN.m FACTOR 15 2637 0.2403 0 S355 355 66.13 20.41 INFINITY 14 1948 0.2085 239 S355 355 112.11 34.61 0.73 13 1627 0.1830 294 S355 355 142.15 42.45 0.93 12 1225 0.1541 254 S355 355 254.21 78.47 0.78 11 1077 0.1423 261 S355 355 285.24 87.47 0.81 10 876 0.1254 267 S355 355 335.15 100.17 0.85 9 699 0.1094 271 S355 355 389.08 113.55 0.88 8 500 0.0897 272 S355 355 467.24 132.41 0.91 7 347 0.0726 271 S355 355 547.23 151.19 0.94 6 271 0.0630 271 S355 355 597.89 162.83 0.95 5 160 0.0471 268 S355 355 693.92 184.48 0.96 4 98 0.0359 266 S355 355 770.64 201.42 0.97 3 12 0.0122 261 S355 355 965.29 243.18 0.99 2 0 0.0024 258 S355 355 1061.56 263.30 0.99 1 0 0.0000 257 S355 355 1086.35 268.43 0.99 5

STRESS: 294 max. (See Note.) MAX AF: 0.99

CU Lighting Ltd.

Highmast Design (Duo). Version: 1*09

Page No:___________ Initials:___________ Date:__08/12/05__ Job Ref: HMA9251 Duodecagon Mast (10xM27).

Serviceability Limit State Calculation.

JOINT TOTAL HORIZ. DIRECT LOAD TOTAL DEFLEC-

ROTAT-NO SHEAR MOMENT LOAD MOMENT MOMENT TION ION

kN kN.m kN kN.m kN.m mm. rads. 5.05 8.00 15 5.05 0.00 8.00 0.00 0.00 2110 0.1923 14 5.51 15.84 8.38 4.50 20.34 1558 0.1668 13 5.81 25.07 8.63 6.67 31.74 1302 0.1464 12 6.29 39.41 9.18 9.53 48.94 980 0.1232 11 6.52 45.82 9.43 10.63 56.45 862 0.1138 10 6.86 55.85 9.84 12.17 68.03 701 0.1003 9 7.23 66.43 10.29 13.59 80.02 559 0.0876 8 7.76 81.42 10.93 15.28 96.70 400 0.0717 7 8.26 96.47 11.58 16.65 113.13 277 0.0581 6 8.56 105.89 12.00 17.37 123.26 217 0.0504 5 9.09 123.54 12.79 18.46 142.00 128 0.0376 4 9.47 137.46 13.42 19.12 156.57 78 0.0287 3 10.32 172.07 15.01 20.09 192.16 10 0.0098 2 10.66 188.85 15.80 20.23 209.08 0 0.0019 1 10.74 193.13 16.00 20.24 213.37 0 0.0000 6 V.No. 1*09 HMA9251 Design v1_09

Job Ref: HMA9251 Duodecagon Mast (10xM27). Foundation Stud Design.

Foundation Stud Properties.

Type of stud :- McCall’s High Strength Precision Ties.

Ultimate Tensile Strength : 775 N/sq. mm. Proof Stress (0.2%) : 585 N/sq. mm. Elastic Modulus : 205 kN/sq. mm. Bolt Material Factor : 1.15

Threads are :- ISO metric coarse pitch to BS3643 Part 2, cold rolled. Diameter (maximum) : 27 mm.

Number equispaced : 10 no. Pitch Circle Diameter : 650 mm.

Maximum Stud Load :- 259 kN. Mast Section Analysed.

Diameter (across flats) : 520 mm. Section Thickness : 4 mm.

Section Area : 6535 sq. mm. Section stress (inc. LF) : 257.04 N/sq. mm.

Stud Acceptance Factor.

AF = ( Diameter * Mast Area * Stress* gamma f * gamma mb ) ( PCD * No of Studs * Max Stud Load *10^3)

AF = 0.75 Must be less than unity. Foundation Loading.

7

Using a Beta factor of :- 1.40

Vertical load : 16 kN.

Horizontal shear : 8 kN.

Dead load bending moment : 14 kN.M.

Wind bending moment : 138 kN.M.

NOTE: The above loads are all unfactored.

7 Annexure –02

Design of foundation (using Prokon)

C15

Input Data

Stub column height X (m) Base depth Y (m) Soil cover Z (m) Concrete density (kN/m3₎ Soil density (kN/m3₎ Soil friction angle (°) Base friction constant Rebar depth top X (mm) Rebar depth top Y (mm) Rebar depth bottom X (mm) Rebar depth bottom Y (mm) Ovt. load factor: Self weight ULS load factor: Self weight Max. SLS bearing pr. (kN/m²) S.F. Overturning (ULS) S.F. Slip (ULS)

fcu base (MPa)

fcu columns (MPa)

fy (MPa) 2.50 2.50 Col 1 Col 2 1.20 1.20 1.2 0.75 1.0 25 20 30 0.3 75 75 75 75 0.9 1.4 160 1 1.5 30 30 460 Unfactored Loads Load Case Col no. LF ovt LF ULS P (kN) Hx (kN) Hy (kN) Mx (kNm) My (kNm) DL 1 1.5 1.5 16 8 14 DL+WLx 1 1.5 1.5 16 8 138 DL+WLy 1 1.5 1.5 16 8 138

Sketch of Base

Sheet Job Number

Job Title

Client

Calcs by Checked by Date

Software Consultants (Pty) Ltd Internet: http://www.prokon.com E-Mail : [email protected] A X Y Y B C1 D1 P Mx Z Hx Y X BS8110 - 1997

Output for Load Case DL

Output for Load Case DL Soil pressure (ULS) (kN/m²) 78.36 Soil pressure (SLS) (kN/m²) 54.98 SF overturning (SLS) 11.51 SF overturning (ULS) 7.18 Safety Factor slip (ULS) 26.77 Safety Factor uplift (ULS) >100

Bottom Design moment X (kNm/m) 4.47 Reinforcement X (mm²/m) 16 Design moment Y (kNm/m) 1.49 Reinforcement Y (mm²/m) 5 Top Design moment X (kNm/m) -1.48 Reinforcement X (mm²/m) 5 Design moment Y (kNm/m) 0.00 Reinforcement Y (mm²/m) 0 Linear Shear X (MPa) 0.000

vc (MPa) 0.357

Linear Shear Y (MPa) 0.000

vc (MPa) 0.357

Linear Shear Other (MPa) 0.000 Punching Shear (MPa) N.A.

vc (MPa) N.A.

2.50 X Y Y 2 .5 0 1.20 1.20 P Mx 1 .0 0 Hx 0.75 1.20 54.98 kN/m² 2.50 X Y Y 2 .5 0 1.20 1.20 P Mx 1 .0 0 Hx 0.75 1.20 78.36 kN/m² Soil Pressures at ULS Soil Pressures at SLS Legend Max M (+) Max M (-) Max Shear Load Case:DL BS8110 - 1997

Output for Load Case DL+WLx

Output for Load Case DL+WLx Soil pressure (ULS) (kN/m²) 157.51 Soil pressure (SLS) (kN/m²) 105.88 SF overturning (SLS) 2.22 SF overturning (ULS) 1.38 Safety Factor slip (ULS) 26.77 Safety Factor uplift (ULS) >100

Bottom Design moment X (kNm/m) 18.10 Reinforcement X (mm²/m) 65 Design moment Y (kNm/m) 1.49 Reinforcement Y (mm²/m) 5 Top Design moment X (kNm/m) -11.45 Reinforcement X (mm²/m) 41 Design moment Y (kNm/m) 0.00 Reinforcement Y (mm²/m) 0 Linear Shear X (MPa) 0.000

vc (MPa) 0.357

Linear Shear Y (MPa) 0.000

vc (MPa) 0.357

Linear Shear Other (MPa) 0.000 Punching Shear (MPa) N.A.

Sheet Job Number

Job Title

Client

Calcs by Checked by Date

Software Consultants (Pty) Ltd Internet: http://www.prokon.com E-Mail : [email protected] 2.50 X Y Y 2 .5 0 1.20 1.20 P Mx 1 .0 0 Hx 0.75 1.20 105.88 kN/m² 2.50 X Y Y 2 .5 0 1.20 1.20 P Mx 1 .0 0 Hx 0.75 1.20 157.51 kN/m² Soil Pressures at ULS Soil Pressures at SLS Legend Max M (+) Max M (-) Max Shear Load Case:DL+WLx BS8110 - 1997

Output for Load Case DL+WLy

Output for Load Case DL+WLy Soil pressure (ULS) (kN/m²) 157.51 Soil pressure (SLS) (kN/m²) 105.88 SF overturning (SLS) 2.22 SF overturning (ULS) 1.38 Safety Factor slip (ULS) 26.77 Safety Factor uplift (ULS) >100

Bottom Design moment X (kNm/m) 1.49 Reinforcement X (mm²/m) 5 Design moment Y (kNm/m) 18.10 Reinforcement Y (mm²/m) 65 Top Design moment X (kNm/m) 0.00 Reinforcement X (mm²/m) 0 Design moment Y (kNm/m) -11.45 Reinforcement Y (mm²/m) 41 Linear Shear X (MPa) 0.000

vc (MPa) 0.357

Linear Shear Y (MPa) 0.000

vc (MPa) 0.357

Linear Shear Other (MPa) 0.000 Punching Shear (MPa) N.A.

vc (MPa) N.A.

2.50 X Y Y 2 .5 0 1.20 1.20 P Mx 1 .0 0 Hx 0.75 1.20 105.88 kN/m² 2.50 X Y Y 2 .5 0 1.20 1.20 P Mx 1 .0 0 Hx 0.75 1.20 157.51 kN/m²

Soil Pressures at ULS Soil Pressures at SLS Legend Max M (+) Max M (-) Max Shear Load Case:DL+WLy BS8110 - 1997

9T20-B-300 (B2)

9T20-A-300 (B1)

9T20-D-300 ABR (T2)

9T20-C-300 ABR (T1)

col1

PLAN

SECTION

B

B

B

B

B

B

B

B

B

3R12-H

R12-H

10T20-G

8T20-F +

4T20-E +

E

E

E

E

F

F

F

F

F

F

F

F

G

G

G

G

G

G

G

G

G

G

SECTION: col1

Annexure –03