Mast Design.xlsx

STRUCTURAL CALCULATIONS OF 30 M HIGH MAST DESIGN PARAMETERS: 1 Mast Height , H 2 Top diameter,D2 3 bottom diameter,D1 4 Section thickness 5 Lumineries

= = = = =

30 m 200 mm 600 m 0/0/4/5/6 Type Number BGENF 22R 9 LED AOL 1 6 Shielding factor = 0.6 7 Head Load = 397 kg 8 Head area = 1.11 sqm 9 Force co-efficient Cf, for head frame = 1 10 Mast Cross section = 20 sided polygon 11 Grade of shaft material = S355J0 12 Yield stress of shaft material ( s y ) = 355 Mpa 13 Force coefficient (Cf) for shaft = 0.733 14 Basic wind speed = 47 m /sec 15 Terrain category & structure class = 2B 16 Stastical probability factor (K1) = 0.9 17 Terrain, height & structure size factor (K2) = 1.10 18 Topography factor ( K3) = 1.00 19 Design Wind Speed = 47 x 0.9x1.1 x 1 =

As per Table 2, IS.875

STRUCTURAL CALCULATION OF 30 M HIGH MAST: 1 Method of design = Limit state (Plastic design) (Ultimate & Serviceability limit state) 2 Safety factor for dead load in ultimate limit state ( γdf) = 3 Safety factor for dead load in serviceability limit state (γ df) = 4 Safety factor for wind load in ultimate limit state (γ wf) = 5 Safety factor for wind load in serviceability limit state ( γwf) =

46.53 m /sec

1 1 1.25 1

6 Safety factor for materials (γm) = 1.15 7 Safety factor for bolts (γmb) = 1.25 8 Elastic modulus (E) = 205 KN /sq.mm 9 Wind load on structure to conform = IS.875 -Part 3 -1987 10 General construction to conform Technical Report No. ----------------------By The Institution of Lighting Engineers,High Mas

11 General design procedure to = conform

Technical Report No. --------------------

ANALYSIS OF FORCES 1 CALCULATION OF NATURAL FREQUENCY OF VIBRATION Member Outer Thick Moment of Elastic Member D / T

Joint No

Height H

Member length

(m) 30.0

10

(m) 3.30

9

26.7 3.40

8

23.3 3.30

7

20.0 3.30

6

16.7 3.40

5

13.3 3.30

4

10.0 3.30

3

6.7 3.40

2

3.3 3.30

1

0.0

Outer Dia d1

Thick T

(mm) 200 222 244 267 289 311 333 355 377 400 423 445 467 489 511 533 556 578 600

Inner dia d2

(mm) 4.00 4.00 4.00 4.00 4.00 4.00 5.00 5.00 5.00 5.00 5.00 5.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00

Moment of Inertia I

(mm) 192.00 214.00 236.00 259.00 281.00 303.00 323.00 345.00 367.00 390.00 413.00 435.00 455.00 477.00 499.00 521.00 544.00 566.00 588.00

(cm4) 1183.23

Elastic Modulus Z

Member Weights

(cm3) 118.32

(kg) 70.97

2172.07

178.04 88.21

3636.97

251.69 99.94

6930.30

416.23 142.42

10109.67

536.32 165.60

14342.37

678.13 179.04

23088.06

988.78 235.85

30349.15

1187.83 265.13

39205.85

1410.28 279.31

49387.24

1646.24

Moment of inertia at mid-height = Natural frequency due to weight of mast - ωoc =

12106 cm4

Natural frequency due to weight of luminaires - ω ol =

2.635 radian/sec

2.716 radian/sec

Rayleigh quotient 1 ω o2 ωo

=

1 ωoc2

=

+

1 ωol2

=

0.280

1.890 radian/sec

Combined Natural frequency = no ωo/2π =

0.301 Hz

2 CALCULATION OF MAGNIFICATION FACTOR Mean hourly wind speed = Natural frequency (n0)

28.34 m/s =

0.011

Mean hourly wind speed (V10) Assume log decrement = Response factor (β) = Size reduction factor (δ) = Magnification factor =

3 CALCULATION OF WIND PRESSURE

0.2 1.43 1-0.006

( mast ht - 3) = 1.20

0.838

V=

47 m/s

Joint No.

Member length (m)

Height H (m)

light fitting 10 9 8 7 6 5 4 3 2 1

K1 = 0.9

30 30

Factor K2

K3 =

Design speed Pressure qh VH in m/s N / sq.m

1.00

Effect. Eqh N / sq.m

1.100

46.53

1299.025

1558.83

3.3

1.092

46.192

1280.221

1536.26

3.4

1.075

45.473

1240.676

1488.81

3.3

1.058

44.754

1201.752

1442.10

3.3

1.04

43.992

1161.178

1393.41

3.4

1.02

43.146

1116.946

1340.34

3.3

0.993

42.004

1058.602

1270.32

3.3

0.98

41.454

1031.060

1237.27

3.4

0.98

41.454

1031.060

1237.27

3.3

0.98

41.454

1031.060

1237.27

26.7 23.3 20 16.7 13.3 10 6.7 3.3 0

4 ULTIMATE LIMIT STATE CALCULATION (γwf = 1.25 , γdf = 1) Joint No.

Wind load Total shear KN / m KN

Light Fitting

2.16

10

Horizontal Moment KN.m Mh

Direct load KN

Deflection D mm

3.97

Load Moment KN.m

Total Moment KN.m

ML

M

2.16

0

3.97

1273.62

0

0

3.19

8.82

4.68

924.66

1.14

9.96

4.45

21.81

5.57

757

2.4

24.21

5.84

38.79

6.57

552

3.66

42.45

7.36

60.57

8

380

4.92

65.49

9.06

88.49

9.66

238

6.18

94.67

10.85

121.33

11.46

134

7.28

128.61

12.7

160.19

13.82

60

8.22

168.41

14.74

206.84

16.48

15

8.91

215.75

16.89

259.03

19.28

0

9.18

268.21

0.31 9 0.37 8 0.42 7 0.46 6 0.5 5 0.54 4 0.56 3 0.6 2 0.65 1

5 ULTIMATE LIMIT STATE CALCULATION Joint No.

Steel grade Yield stress Mpa

10 S355J0 9 S355J0 8 S355J0 7 S355J0 6 S355J0 5 S355J0 4 S355J0 3 S355J0 2 S355J0 1 S355J0

Mpa

Plastic modulus cm3

355 355 355 355 355 355 355 355 355 355

153.69 230.42 324.92 537.96 691.96 873.66 1275.20 1530.22 1815.07 2117.09

Plastic restoring M

Constant for M*

KN.m Mp 54.56 81.8 115.35 190.98 245.65 310.15 452.7 543.23 644.36 751.57

1.00 1.00 0.96 0.98 0.95 0.91 0.94 0.91 0.89 0.86

Bending resistance Nm M* 47.44 71.13 96.29 162.75 202.93 245.42 370.03 429.86 498.68 562.04

Max. A.F =

Acceptance factor M/M* 0.00 0.15 0.24 0.19 0.26 0.35 0.28 0.35 0.40 0.48

0.48 should be < 1 SAFE

6 SERVICEABILITY LIMIT STATE CALCULATION (γwf = 1.0 , γdf = 1) Joint No.

10 9 8 7 6 5 4

Total shear KN 1.73 1.73 2.56 3.56 4.68 5.89 7.25 8.68

Horizomoment KN.m Mh 0 7.06 17.45 31.04 48.46 70.8 97.07

Direct load Deflection D KN 3.97 3.97 4.68 5.57 6.57 8 9.66 11.46

mm 1018.9 739.73 605.6 441.6 304 190.4 107.2

Load Moment

Total Moment

Acceptance factor

KN.m ML

KN.m M

M / M*

0 0.912 1.92 2.928 3.936 4.944 5.824

0 0.912 1.92 2.928 3.936 4.944 5.824

0 0.12 0.2 0.16 0.21 0.29 0.23

3 2 1

10.16 11.8 13.52

128.16 165.48 207.23

13.82 16.48 19.28

48 12 0

6.576 7.128 7.344

6.576 7.128 7.344

Max. A.F =

0.29 0.33 0.39

0.39 should be < 1 SAFE

7 DEFLECTION CHECK AT 2/3 of Design Wind Speed Joint. No.

wind Design qh Heights in Design VH m

m/s

N/sq.m

31.02 10

Total Shear

Horizon. Moment

Deflection D

KN/m

KN

KN.m Mh

mm

577.35

30 30.8

9

26.7

8

23.3

30.32 29.84 7

20

6

16.7

29.33 28.77 5

13.3

4

10

28.01 27.64 3

6.7

2

3.3

27.64 27.64 1

Wind load

569.19

0.65 0.65

0

241.62

0.95

3.3

248.95

1.33

7.17

231.62

1.73

12.22

190.54

2.2

18.7

141.07

2.71

27.05

87.78

3.24

36.87

44.61

3.81

48.49

82.24

4.43

62.49

2.2

5.09

78.2

0

0.09

551.59

0.11

534.26

0.12

516.15

0.14

496.63

0.15

470.74

0.16

458.39

0.17

458.39

0.18

458.39

0.2

0

Deflection at the top of mast

242 mm SAFE

Here deflection is checked at 2/3 of design wind speed Deflection at the top most point is found to be less than 1/ 40 of mast height. 750 mm FOUNDATION BOLT DESIGN Properties of foundation bolt Grade

=

Min.Tensile Strength (fu)

=

600 N/m2

Yield Stress Bolt material factor ( γm)

=

405 N/m2

=

1.15

Safety factor for bolts ( γmb)

= =

1.25 30 mm

= = =

16 nos. 740 mm 3.5 mm

Diameter (φ) Number equally spaced (nn) Pitch Circle diameter (P.C.D) Pitch of bolt (p)

TS-600

As of bolt

=

706.86 mm 26.4 mm 2 546.15 mm

=

600 N/m2

= =

Nominal Diameter of bolt (d) An of bolt Characteristic strength in tension (fu)

2

Ultimate Bolt Capacity In Tension (Tdb = Tnb/γmb _x0001_)

=

235.94 kN

=

196.58 kN

(0.9 ƒu An < ƒy As (γmb/γm)) In Bearing (Vdpb = Vnpb / _x0001_γmb)

(2.5 kb d t ƒu) In Shear (Vdsb = Vnsb / _x0001_γmb)

=

149.53 kN

(ƒu nn An /γ3) Mast section properties Diameter (D1) = Section thickness = Inner diameter D2 =

600 mm 6 mm 588 mm

Section area =

11196.64 mm2

Bending Stress @ mast bottom = Max. Tension in one bolt (Tb) =

160.8 N/m2

Max. Tension in one bolt (Tb) =

59.866 kN THUS, SAFE

Max. Compression in one bolt (Vpb) =

Max. Shear in one bolt (Vsb) =

64.644 kN THUS, SAFE Total Horizontal force on mast nn

Max. Shear in one bolt (Vsb) =

1.06 kN THUS, SAFE = =

FOUNDATION BOLT LENGH Diameter of bolt = Embedded length of bolt = Threaded length = Total length of bolt = Grade of concrete = Permissible bond stress = Permissible bearing stress = Tensile force resisted by bolt = through bond stress

DESIGN OF BASE PLATE Grade of steel = Yeild strength = Max.compressive force /unit length of base plate =

(Vsb/ Tb)2

+ 0.01 THUS, SAFE

30 mm 700 mm 150 mm 850 mm M-20 1.2 N/mm2 9 N/mm2 79.17 kN SAFE

E 250 240 Mpa (4 M / P.C.D +W) / π x P.C.D) 631.92 N/m

Assume base plate size =

840 mm circular

Max.bearing pressure (w) =

2.6 N/m2 OK

Cantilever span = Max. cantilever bending moment = Permisssible bending stress in the plate (s bs) = Thickeness of plate required =

+

area of mast x stress x D1 N x pcd x magnification factor

Max. Compression in one bolt (Vpb) =

Check for Combined Stress

-

area of mast x stress x D1 N x pcd x magnification factor

120 mm 18720 N-mm/m 180 N/m2 24.98 mm

(Vdsb/ Tdb)2

<

Thickness provided = Provide 30 mm thick base plate

30 mm

FOUNDATION DESIGN CALCULATIONS OF 30 M HIGH MAST A DESIGN PARAMETERS 1 Gross Soil Bearing Capacity 2 Ground Water Table 3 Grade of concrete

: : :

10.00 T/m2 Ground Level M- 20

B LOADS AT BOTTOM OF MAST AS PER ULTIMATE LIMIT STATE 1 Max.wind pressure (Wp) Wp = 0.06 x Vd x Vd 2 Total wind force on luminaire (Wfl) Wfl = Awt x Wp 3 Unit wind pressure at the top of the mast (Wt) = Sf x d x Wp 4 Unit wind pressure at the bottom of the mast (WB) = Sf x D x Wp 5 Net wind pressure on complete mast (Wnet) = ((Wt + Wb)/2) x Ht 6 Total horizontal force on complete mast 7 Over turning moment at base of the mast

: :

1299.025 N/m2 1441.92 N

:

189.7 N/m

:

568.98 N/m

: : :

Thus various forces acting on the foundation are as follows 1 Downward/ Vertical load of the mast system (Fv) 2 Total horizontal force 3 Moment at the base of the foundation

11380.2 N 13.52 kN 202.8 kN-m

2297.00 kg 2.30 T 1352 kg 19378.67 kg-m

ASSUME A FOUNDATION OF THE FOLLOWING SIZE TOWER BASE PLATE

GL

GL

300

1600

300 100 3300

Size of Pedestal (L1,B1) Height of pedestal (H1) Height of pedestal above ground level(h1) Size of raft (L2,B2) Thickness of raft (H2) depth of foundation above PCC & below FGL

= = = = = =

1.200 m 1.90 m 0.30 m 3.30 m 0.30 m 1.90 m

Check for Soil pressure Density of Concrete Weight of foundation (Wf) = Weight of pedestal + Weight of raft

= =

2.50 T/m3 15.01 T

1.50

Density of soil Weight of soil acting on raft (Ws)

= =

Thus total vertical load acting on the soil below foundation is F' v = Weight of system + weight of foundation + weight of soil = Fv + Wf + Ws =

1.65 T/m3 24.95 T

0.65

42.26 T

The Design verification for safe bearing pressure as follows. Section modulus Z

=

L2 x B2^2/6

Z Soil pressure

= =

5.99 m3 [(P / L 2X B2) +/- (M/Z)]

Pmax

7.12 T/m2

Pmin e (M/P) B x 3(B2/2-e) % of Foundation in contact with ground

0.65 T/m2 0.46 m 7.79 m 93.52 %

(Under submerged condtion)

7.30 T/m2 < 10.00

SAFE

0.65 7.12

Check against overturning Factor of safety = Restoring moment(due to D.L ) / Over turning moment Restoring moment for 50 % of soil weight = F2 v x L2 /2 *0.9 = 62.76 T-m Factor of safety = 3.24 > 1.50

SAFE

Check against sliding Sliding force Coefficient of friction ( tan10 ) Frictional capacity Factor of safety

= = = =

1.352 T 0.176 7.69 T 5.69 > 1.50

SAFE

Check for buoyancy Total Weight Under submerged condition F2 Buoyant force = (L2*B2)*H2 + (L1*B1*H1)*Yw

= =

21.14 T 6.003 T Safe in Buoyancy

DESIGN OF PEDESTAL Pedestal size = Check for L/D = Design as Pedestal Load on pedestal -P = Moment @ bottom of pedestal -M = Assume Cover = Pu / fck bd =

1200 2.75 9.14 T 20.108 T-m 50 mm 0.01

X

1200

Mu / fck bd2 = d' /D Refer design aids of concrete, Chart 43 = p / fck = pt (Provide a min of 0.15% steel.) = Consider diameter of bar = Assume Pt = Nos of Bar Required = ptACt = 8 Tor Rings at c/c of = 190 c/c

0.01 0.04 negligible negligible % 12 mm 0.27 % 36 0.28% 190 c/c

Provide 36 tor 12 mm steel as longitudinal reinforcement & tor 8 mm ties @ 190 c/c.

Z of pedestal = 1/6 * B^3 Direct Stress Due to P (P/A) scc,cal Bending Stress due to M (M/Z) scbc,cal Combined Stress = (scc,cal / scc + scbc,cal / scbc ) =

= = scc = scbc

2.88E+08 mm3 0.01 N/m2 <5

SAFE

6.98E-01 N/m2 < 6.5

SAFE

1.09E-01 N/m2 <1 SAFE

DESIGN OF RAFT 1050

1200

0.65

1050

Critical Section

7.12 6.47

SOIL PRESSURE DIAGRAM

Effective cantilever span

1.05 m

Soil Pressure @ critical section Net Max. Cantilever moment @ bottom 5.12*1.05^2/2+0.5*(7.3-5.124)*1.05*1.05*2/3-2.64*1.05^2/2 Mu = Assume Cover = d = 300-50-10/2 =

4.41 T/m2 2.17 T-m/m 32.55 kN-m/m 50 mm 245 mm

Mu / bd2 = Pt = Pt act =

0.542 N/mm2 0.163 % 0.210 %

Ast/m = Consider diameter of bar = Spacing of bars =

398 mm2 10 mm 160 mm

21 tor 10 bothways @ bottom Soil Pressure from top = Max. Cantilever moment on top = Mu at top =

2.64 T/m2 0.73 T-m/m 10.91 kN-m/m

Mu / bd2 = Pt = Pt act =

0.182 0.055 % 0.140 %

Ast/m (Provide Ptmin=0.12%) = Consider diameter of bar = Spacing of bars =

360 m2 10 mm 250 mm

14 tor 10 bothways @ top CHECK FOR ONE WAY SHEAR Critical section is at 'd ' from face of column.

1200 1050

1050

0.65

critical section 7.12

SOIL PRESSURE DIAGRAM Distance of critical section for one way shear from edge =

0.805 m

Soil Pressure at the critical section = Max. shear force = Factored shear force =

5.38 T/m2 4.33 T/m 64.96 kN/m

Shear stress = b=

0.27 N/mm2 11.038

Permissible shear stress =

0.333 N/mm2

SAFE

CHECK FOR TWO WAY SHEAR Critical section is at 'd/2 ' from face of column.

1200

1050

1050 0.65

critical section

5.378

7.12

2.382

SOIL PRESSURE DIAGRAM Distance of critical section for two way shear from edge = Soil Pressure at the critical section Max. shear force = Factored shear force = B0 =

0.93 m 5.12 T/m2 34.15 T 512.25 kN 1425.00 mm

Shear stress = Permissible shear stress = k

13.44

0.25 N/mm2 = =

k s √Tc 0.25 x 20^0.5 1.12 N/mm2

SAFE

---------------By The Institution of Lighting Engineers,High Mast Lighting

D/T 50.00 61.00 72.25 66.60 75.40 84.60 77.83 85.17 92.67 100.00

W N W N

1.0

30 3.3 26.7 3.4

3.3

23.3

3.3

20

3.4

16.7

3.3

13.3

3.3

10

3.4

6.7

3.3

3.3

Md = fy = D/t

βbZpfd 355

ε=

50 0.84

42ε2

29.64

52ε2

36.7

146ε2

103.02

N/mm2