Design Calculations for Light Mast

FOUNDATION DESIGN CALCULATIONS LIGHT MAST 25M HIGH – HMA 9251

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. Annex 02. Annex 03.

Reference data Footing design for light pole HMA 9251 Drawings

2

1

INTRODUCTION

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 ▪ 1.4

Reference Documents

Vendor documents – HMA 9251 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 ▪ 1.7

Software applied PROKON : Foundation design. Loads

The structure is exposed to the following loads: 3

▪

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

16.00 kN

Table 1.1 1.7.2

Horizontal load

Vertical load

HMA 9251

Dead load moment

8.00 kN

14.00 kN.m

Self-weight loads

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: Wind load moment

Item HMA 9251

Table 1.2

1.7.3

138.0 kN.m

Wind load

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

Table 1.4

Material factors

4

3 3.1

DESIGN CALCULATIONS 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 ▪ Footing reinforcement Top reinforcement Bottom reinforcement

: 2500 mm x 2500 mm x 1000 mm,

▪ Pedestal size ▪ Pedestal reinforcement Vertical reinforcement Horizontal reinforcement

: 1200 mm x 1200 mm x 1000 mm,

: T20 - 300 (both ways), : T20 - 300 (both ways).

: 24 T20, : T12 - 100.

5

Annexure – 01 Reference Data

6

Page No:___________ Initials:___________ Date:__08/12/05__

CU Lighting Ltd. Highmast Design (Duo). Version: 1*09 Job Ref:

HMA9251 Duodecagon Mast (10xM27). Data and Introduction.

Mast Height m. : Head Load (V) kN. : Mast Details: Joint Heights No. m. 15 25.00 14 22.00 13 20.37 12 18.00 11 17.00 10 15.50 9 14.00 8 12.00 7 10.12 6 9.00 5 7.00 4 5.50 3 2.00 2 0.40 1 0

25.00 8.00

Across Flats mm. Top : 150 Bottom : 520 Height of flange above ground level : 0 Head Frame Moment : Dead : 0.00 Live : 0.00 Additional Loads: (Live: S. Dead: M & V.) Factors: Thickness Shears Moments Vertical Gama Gama mm. kN. kN.m. kN. Dead Wind 3.00 1.00 1.25 3.00 Bolts : 3.00 4.00 Force Coefficients. 4.00 Head Shaft 4.00 CF CF 4.00 1.00 0.60 4.00 4.00 Shaft Material. 4.00 Grade Yield 4.00 S355 355 4.00 4.00 4.00 4.00 (Live) (Dead) (Dead)

mm. m. kN.m. Gama Materials 1.15 1.15

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.

Head Area Sq.M. :

3.37

Wind Factors S1 : S2 : S3 :

1.00 2A 0.95

Basic Wind Speed :

45

m/sec.

Topography Factor. Category , based on Table 3. Hourly Factor : Statistical Probability Factor.

1.70

1 Mean Hourly Wind Speed = Basic Wind Speed / Hourly Factor From tests the Log Decrement is 0.20 and the Nf in hertz is Hence (Natural Frequency) / (Mean Hourly Wind Speed) From the graph in Technical Report No 7, the Beta Factor The Delta Factor is obtained from 1 - 0.006(Mast Height - 3) Hence the Magnification Factor, the product of Delta & Beta

= = = = =

26.5 0.31 0.012 1.40 0.87 1.21

Foundation Studs. Type of stud :- McCall’s High Strength Precision Ties. Flange Yield : Ultimate Tensile : 775 N/sq. mm. Bolt Diameter : Proof Stress(.2%) : 585 N/sq. mm. Number equispaced : Elastic Modulus : 205 kN/sq. mm. Pitch Circle Diameter : Threads are :- ISO metric coarse pitch to BS3643 Part 2, cold rolled. V.No. 1*09 Maximum Stud Load :HMA9251 Design v1_09

(see below)

275 27 10 650

N/sq.mm. mm. no. mm.

259

kN.

Page No:___________ Initials:___________ Date:__08/12/05__

CU Lighting Ltd. Highmast Design (Duo). Version: 1*09 Job Ref:

HMA9251 Duodecagon Mast (10xM27). Natural Frequency Calculation.

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.

JOINT NO

HEIGHT H m

MEMBER LENGTHS m

A/F D mm

THICK T mm

ELASTIC MEMBER MODULUS WEIGHTS cm^3 kg

HEAD FRAME WEIGHT kg. 15

25.00 3.00

14

22.00 1.63

13

20.37

12

18.00

11

17.00

10

15.50

9

14.00

8

12.00

7

10.12

2.37 1.00 1.50 1.50 2.00 1.88 1.12 6

9.00 2.00

5

7.00

4

5.50

1.50 3.50 3

2.00 1.60

2

0.40

1

0

0.40

150 172 194 206 219 236 254 261 268 280 291 302 313 328 342 356 370 379 387 402 416 428 439 465 490 502 514 517 520

3.00 3.00 3.00 3.00 3.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00

49.92 39.36 85.01 25.64 107.97 56.84 192.68 26.52 216.40 42.60 254.55 45.98 295.79 66.57 355.60 68.06 416.85 43.07 455.65 81.60 529.22 65.15 588.01 165.17 737.24 81.64 811.07 21.01 830.08

2 Total Theoretical Tip Deflection : 2648 mm. (See note above.) Natural Frequency : 0.3073 Hertz Natural Period : 3.25 Secs. Note: 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.

V.No. 1*09

HMA9251 Design v1_09

815.49

Page No:___________ Initials:___________ Date:__08/12/05__

CU Lighting Ltd. Highmast Design (Duo). Version: 1*09 Job Ref:

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

MEMBER NO

JOINT HEIGHT NO H m

HEAD FRAME !

25.00

15

25.00

14 14

22.00

13

20.37

12

18.00

11

17.00

10

15.50

9

14.00

8

12.00

7

10.12

13 12 11 10 9 8 7 6 6

9.00

5

7.00

4

5.50

5 4 3 3

2.00

2

0.40

1

0

2 1

A/F D mm

150 172 194 206 219 236 254 261 268 280 291 302 313 328 342 356 370 379 387 402 416 428 439 465 490 502 514 517 520

THICK T mm

3.00

RATIO D/T

V.No. 1*09

HMA9251 Design v1_09

DESIGN PRESSURE SPEED m/s N/sq.m

1.05

44.89

1235.13

1.05

44.89

1235.13

1.04

44.46

1211.71

1.03

44.03

1188.52

1.02

43.61

1165.56

1.01

43.18

1142.81

1.00

42.75

1120.30

0.99

42.32

1098.00

0.96

41.04

1032.46

0.93

39.76

968.94

0.90

38.48

907.44

0.85

36.34

809.41

0.80

34.20

716.99

0.72

30.78

580.76

0.72

30.78

580.76

50

3.00

65

3.00

73

4.00

63

4.00

67

4.00

73

4.00

78

4.00

86

4.00

93

4.00

97

4.00

104

4.00

110

4.00

123

4.00

129

4.00

130

Max D/T:

130

3 Taper : 14.80

FACTOR S2

Page No:___________ Initials:___________ Date:__08/12/05__

CU Lighting Ltd. Highmast Design (Duo). Version: 1*09 Job Ref:

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

JOINT EFFECT NO PRESSURE N/sq.m

WIND LOAD kN/m

ELASTIC MODULUS cm^3

1498.17

6.31

15 1498.17

0.19

1469.77

0.23

1441.64

0.26

14 13 12 1413.78

0.28

1386.20

0.29

1358.89

0.31

11 10 9 1331.84

0.33

1252.35

0.33

1175.30

0.33

1100.70

0.33

981.80

0.31

869.69

0.30

704.45

0.27

704.45

0.27

8 7 6 5 4 3 2 1

TOTAL HORIZ. SHEAR MOMENT kN kN.m

DIRECT LOAD TOTAL LOAD MOMENT MOMENT kN kN.m kN.m 8.00

49.92

6.31

0.00

8.00

0.00

0.00

85.01

6.89

19.80

8.38

5.62

25.43

107.97

7.26

31.34

8.63

8.34

39.68

192.68

7.87

49.27

9.18

11.91

61.18

216.40

8.14

57.27

9.43

13.28

70.56

254.55

8.58

69.82

9.84

15.22

85.03

295.79

9.04

83.03

10.29

16.99

100.02

355.60

9.70

101.77

10.93

19.10

120.87

416.85

10.32

120.59

11.58

20.82

141.41

455.65

10.70

132.36

12.00

21.71

154.08

529.22

11.36

154.42

12.79

23.08

177.50

588.01

11.83

171.82

13.42

23.89

195.71

737.24

12.89

215.09

15.01

25.11

240.20

811.07

13.32

236.06

15.80

25.29

261.35

830.08

13.43

241.41

16.00

25.30

266.71

4 Approximate Mast Weight :

V.No. 1*09

HMA9251 Design v1_09

910 kg inc.

Page No:___________ Initials:___________ Date:__08/12/05__

CU Lighting Ltd. Highmast Design (Duo). Version: 1*09 Job Ref:

HMA9251 Duodecagon Mast (10xM27). Ultimate Limit State Calculation. Note: Bending Stress (Elastic, unfactored) for flange bolt designs only.

JOINT NO

DEFLECTION mm.

ROTAT- BENDING ION STRESS RADS. N/sq.mm

STEEL GRADE

YIELD STRESS N/sq.mm

PLASTIC MODULUS cm^3

PL/RES ACCEPMOMENT TANCE 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:

V.No. 1*09

HMA9251 Design v1_09

294 max. (See Note.)

MAX AF:

0.99

Page No:___________ Initials:___________ Date:__08/12/05__

CU Lighting Ltd. Highmast Design (Duo). Version: 1*09 Job Ref:

HMA9251 Duodecagon Mast (10xM27). Serviceability Limit State Calculation.

JOINT NO

TOTAL HORIZ. SHEAR MOMENT kN kN.m 5.05

DIRECT LOAD TOTAL LOAD MOMENT MOMENT kN kN.m kN.m

DEFLECTION mm.

ROTATION rads.

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

Page No:___________ Initials:___________ Date:__08/12/05__

CU Lighting Ltd. Highmast Design (Duo). Version: 1*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 : Proof Stress (0.2%) : Elastic Modulus : Bolt Material Factor :

775 N/sq. mm. 585 N/sq. mm. 205 kN/sq. mm. 1.15

Threads are :- ISO metric coarse pitch to BS3643 Part 2, cold rolled. Diameter (maximum) : Number equispaced : Pitch Circle Diameter :

27 mm. 10 no. 650 mm.

Maximum Stud Load :-

259 kN.

Mast Section Analysed. Diameter (across flats) : Section Thickness : Section Area : Section stress (inc. LF) :

520 4 6535 257.04

mm. mm. sq. mm. 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 = Foundation Loading. 7 Using a Beta factor of :Vertical load : Horizontal shear : Dead load bending moment : Wind bending moment : NOTE: The above loads are all unfactored.

V.No. 1*09

HMA9251 Design v1_09

0.75 Must be less than unity.

1.40 16 8 14 138

kN. kN. kN.M. kN.M.

Annexure –02 Design of foundation (using Prokon)

7

Job Number

Sheet

Job Title Software Consultants (Pty) Ltd Internet: http://www.prokon.com E-Mail : [email protected]

Client Calcs by

Checked by

Date

Column Base Design : C15

Input Data Base length A (m) Base width B (m) Column(s) Col 1 C (m) 1.20 D (m) 1.20 E (m) F (m) 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)

Sketch of Base

2.50 2.50 Col 2

Load Case DL DL+WLx DL+WLy

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

Col no. 1 1 1

LF ovt

LF ULS

1.5 1.5 1.5

1.5 1.5 1.5

P (kN) 16 16 16

Unfactored Loads Hx Hy (kN) (kN) 8 8

Mx (kNm)

My (kNm)

14 138 8

138

Job Number

Sheet

Job Title Software Consultants (Pty) Ltd Internet: http://www.prokon.com E-Mail : [email protected]

Client Calcs by

Checked by

BS8110 - 1997

Date

Y

C1 X B

D1

A Y

Mx P

Z

Hx X

Y

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. Cost 0.00

Job Number

Sheet

Job Title Software Consultants (Pty) Ltd Internet: http://www.prokon.com E-Mail : [email protected]

Client Calcs by

Checked by

Date

Load Case:DL

Legend

BS8110 - 1997

Y

1.20

1.20 1.20

X

2.50

2.50

X

1.20

2.50

2.50

Y

Y

Mx

Mx P

P

1.20 0.75

54.98 kN/m²

Soil Pressures at SLS

Output for Load Case DL+WLx

1.00

Hx 1.00

Hx

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. vc (MPa) N.A. Cost 0.00

Max M (+) Max M (-) Max Shear

Y

1.20 0.75

78.36 kN/m²

Soil Pressures at ULS

Job Number

Sheet

Job Title Software Consultants (Pty) Ltd Internet: http://www.prokon.com E-Mail : [email protected]

Client Calcs by

Checked by

Date

Load Case:DL+WLx BS8110 - 1997

Legend

Y

1.20

1.20 1.20

X

2.50

X

2.50

Max M (+) Max M (-) Max Shear

Y

1.20

2.50

2.50

Y

Y

Mx

Mx P

P

1.20 0.75

105.88 kN/m²

Soil Pressures at SLS

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. Cost 0.00

1.00

Hx 1.00

Hx

1.20 0.75

157.51 kN/m²

Soil Pressures at ULS

Job Number

Sheet

Job Title Software Consultants (Pty) Ltd Internet: http://www.prokon.com E-Mail : [email protected]

Client Calcs by

Checked by

Date

Legend

Load Case:DL+WLy BS8110 - 1997

Y

1.20

1.20 1.20

X

2.50

X

2.50

Max M (+) Max M (-) Max Shear

Y

1.20

2.50

2.50

Y

Y

Mx

Mx P

P

1.00

Hx 1.00

Hx 1.20

1.20

0.75

105.88 kN/m²

Soil Pressures at SLS

0.75

157.51 kN/m²

Soil Pressures at ULS

9T20-C-300 ABR (T1) 9T20-A-300 (B1)

R12-H E

GGGGG

E

F F F F E col1

9T20-B-300 (B2) PLAN

4T20-E + 8T20-F + 10T20-G 3R12-H

B

B

B

B

GGGGG

E

SECTION: col1

9T20-D-300 ABR (T2)

B

F F F F

B

SECTION

B

B

B

Annexure –03 Design Drawings

8