Rm Silo Ocp3

Design of Raw Meal Silo Based on BS EN 1991-4:2006 for Obajana Cement Line 3, Nigeria

A. SILO SILO CONFIG CONFIGURA URATI TION ON

         0          8   .          2

1. Material = Raw Meal 2. Weight of Material Stored in Storage Silo

=

3. Thickness of RCC Wall of Storage Silo 4. Average thickness of Top Slab of Silo 5. th thickness of Inverted Cone

= = =

400 150 500

6. EL E L. of Flat Slab Btoom above GL 7. EL E L. of Top of Top Slab above GL 8. Max. Level of Filling below Silo Top 9. Heig Height ht of av. av. Mate Materi rial al Stor Storag agee from from Flat Flat Sla Slab 10. Internal Diameter of Storage silo D 11. Angle Angle of Repose Repose fr 

= = = = = =

21.02 70.00 0.15 46.18 22.5 25

12. Mean Angle Angle of Internal Internal Friction Friction

=

25

13. Slenderness Ratio (h c / dc)

=

2.05

14. Silo Type

= Sl S lender silo

fm

Ti

15. Temperature Temperature of Hot Material Material inside

=

C

17. Bulk Density Density of Stored Materia Materiall

l

=

1.4

18. Maximum ht of Flat Slab 19. Seismic Seismic Zone Zone III 20. Li L ive Loads on Operating Floors

Z

= = =

23. El E l. of Top of Flat Slab above GL 24. Angle of Inverted Inverted Cone

= =

a

         8          1   .          6          4

0

C

-0.6

22.50

0

o

=

         5          7          6   .          3          1

3

FGL

41 25

M/sec 2 N/mm 21.016 M o 60

= = =

500 20 300

mm Ton 2 N/mm

28. Grade of Conc. For foundation foundation

=

25

29. Maximum eccentricity eccentricity of filling

ef 

=

0

N/mm M

30. Maximum eccentricity eccentricity of outlet

e0

=

0

M

TOTAL

=

18363 M3 18363 M3

Weight of material

=

22036 T

Weight of material

=

=

25708 T

         6          1          0   .          1          2

0.500

T/M 0 .0 0 0 M 0.16 2 1 T/M

25. Thi Thickne kness of of RCC RCC Wall below Co Cone Su Support 26. Ax Axial Force Imposed on Ftop 27. Yi Y ield Stress of Reinfocement

B. CAPACI CAPACITY TY CALCULA CALCULATI TION ON Volume above cone

dc

0.4

M M M M M

o

T0

= =

mm mm mm

120

16. Temperature Temperature of Outside Atmosphere Atmosphere

21. Basic Wind speed 22. 22. Grad Gradee of Con Conc. c. for for wal walll (Char (Charac acte teri rist stic ic Stre Streng ngth th))

         5          1   .          0

20000 Ton

2

Considering density of material Considering density of material

C. DESIG DESIGN N OF SIL SILO O WALL WALL Design parameters to determine Silo Forces (a) = Plan Cross-sectional area of the Silo  A

1.2 1.4

T/M

3

from capacity consideration

T/M

3

for structural design

=

397.608 M2 22.50 M

(b)

D

= Internal Diameter of the Silo ( Bin )

=

(c)

d

= Max. Dia. of the Circle that can be inscribed in the Bin

=

22.50

M

(d)

h

= Height of the Bin

=

48.98

M

(e)

U

= In Internal perimeter of the Silo

=

70.69

M

(f)

R

= A/U

=

5.63

M

(g)

l

= Bulk Density of Stored Material

=

1.40

(h)

Z

= Maximum depth below the Equivalent Surface of the Solid

=

(i)

fim

= Mean angle of internal friction

=

25

O

(j)

f (max)

= Maximum angle of internal friction (a f X fim)

=

30.50

O

(k)

f (min)

= Minimum angle of internal friction ( fim / af))

=

20.49

O

1 of 7

T/M 46.18 M

3

Design of Raw Meal Silo Based on BS EN 1991-4:2006 for Obajana Cement Line 3, Nigeria

Km

(l)

= Mean lateral pressure ratio

=

0.54

(m) K (max)

= Maximum lateral pressure ratio (K m X ak)

=

0.648

(n)

= Minimum lateral pressure ratio (K m / ak)

=

0.450

= Mean wall friction coefficient for solid sliding on the vertical wall

=

0.56

= Maximum wall friction coefficient ( mm X am)

=

0.599

= Minimum wall friction coefficient ( mm / am)

=

0.523

= Patch load solid reference factor

=

0.5

K (min) mm

(o)

(p) m (max) (q) m (min)

cop

(r) Note:

1) For maximum normal pressure on vertical wall m (min), K (max) & f (min) shall be used 2) For maximum frictional traction on vertical wall m (max), K (max) & f (min) shall be used 3) For maximum vertical load on silo bottom m (min), K (min) & f (max) shall be used

1. Determination of Lateral pressure, Vertical pressure and Frictional traction for Symmetrical filling load condition 2 = Pho*Y j(z) (T/M ) 2 = m*Pho*Y j(z) (T/M ) = Vertical pressure at depth Z = (Pho / K)*Y j(z) (T/M2) = The resulting characteristic value of the vertical force in the wall after filling at depth Z

Phf  (z)

= Horizontal pressure at depth Z = Wall friction traction at depth Z

Pwf  (z) Pvf  (z) nzSk zo

= (1 / (K* m))*(A / U) = l*K*zo

Pho

M 2

(T/M )

zo

= 1 - e(-Z / Zo) = 16.59 M

( for maximum normal pressure calculation )

zo

=

14.49 M

( for maximum frictional traction calculation )

zo

=

23.8839 M

 Y j (z)

Pho

=

Pho

=

Pho

= Z (M) 2.80 6.98 9.98 12.98 15.98 18.98 21.98 24.98 27.98 30.98 33.98 36.98 39.98 42.98 48.98

( for maximum vertical load calculation ) 2

15.0469 (T/M ) 13.14 (T/M2) 2

15.0469 (T/M ) Z / Z0 Normal 0.000 0.252 0.433 0.614 0.795 0.976 1.156 1.337 1.518 1.699 1.880 2.061 2.242 2.423 2.785

Z / Z0 Friction 0.000 0.289 0.496 0.703 0.910 1.117 1.324 1.531 1.738 1.945 2.152 2.359 2.566 2.774 3.188

( for maximum normal pressure calculation ) ( for maximum frictional traction calculation ) ( for maximum vertical load calculation ) Z / Z0

Z/Zo)

Z/Zo)

Z/Zo)

1 -e( 1 -e( 1 -e( Vertical Normal Friction Vertical 0.000 0.000 0.000 0.000 0.175 0.223 0.251 0.161 0.301 0.351 0.391 0.260 0.426 0.459 0.505 0.347 0.552 0.548 0.597 0.424 0.677 0.623 0.673 0.492 0.803 0.685 0.734 0.552 0.929 0.737 0.784 0.605 1.054 0.781 0.824 0.652 1.180 0.817 0.857 0.693 1.305 0.847 0.884 0.729 1.431 0.873 0.906 0.761 1.557 0.894 0.923 0.789 1.682 0.911 0.938 0.814 1.934 0.938 0.959 0.855

Phf  2

(T/M ) 0.00 3.35 5.29 6.90 8.25 9.37 10.31 11.10 11.75 12.30 12.75 13.13 13.45 13.71 14.12

Pwf  2

(T/M ) 0.00 1.97 3.08 3.97 4.70 5.30 5.78 6.17 6.49 6.75 6.96 7.13 7.27 7.38 7.55

Pvf  2

(T/M ) 0.00 5.37 8.68 11.60 14.18 16.45 18.46 20.23 21.79 23.16 24.37 25.44 26.39 27.22 28.60

2. Determination of Lateral patch pressure in wall for filling patch load condition Silo Type Ppf 

= Thick walled circular silo = Filling outward patch pressure

Ppfi

= Filling inward patch pressure

Cpf 

= 0.21*Cop*(1+2E2)*(1-e(-1.5*((hc/dc)-1))) 0.00 = 2*ef  / dc =

E ef 

= m*Pho*(z-zo*Y j(z)) T/M

= Cpf *Phf  = Ppf /7

= Maximum eccentricity of surface pole during filling

2 of 7

=

0.0

M

nzSk (T/M) 0.00 3.78 10.44 19.72 31.13 44.26 58.79 74.47 91.07 108.43 126.40 144.87 163.74 182.95 222.13

Design of Raw Meal Silo Based on BS EN 1991-4:2006 for Obajana Cement Line 3, Nigeria

Phf 

= Local filling pressure

Cop

= Patch load solid reference factor

s Phf,u

= The length of the zone on which the patch load is applied

ζ

(M) 2.80 6.98 9.98 12.98 15.98 18.98 21.98 24.98 27.98 30.98 33.98 36.98 39.98 42.98 48.98

4.418 = p*dc/16 = *(1+ζ*C ) P = hf,u pf 

= Resulting symmetrical horizontal pressure for filling = Maximun(0.5+0.01*(d c/t) or 1) Cpf 

Z

0.50

=

0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083 0.083

Phf  Normal 0.00 3.35 5.29 6.90 8.25 9.37 10.31 11.10 11.75 12.30 12.75 13.13 13.45 13.71 14.12

Ppf  2

(T/M ) 0.000 0.279 0.441 0.575 0.688 0.781 0.860 0.925 0.979 1.025 1.063 1.094 1.121 1.143 1.177

Ppfi 2

(T/M ) 0.000 0.040 0.063 0.082 0.098 0.112 0.123 0.132 0.140 0.146 0.152 0.156 0.160 0.163 0.168

=

s

Phf,u

(M) 4.418 4.418 4.418 4.418 4.418 4.418 4.418 4.418 4.418 4.418 4.418 4.418 4.418 4.418 4.418

(T/M ) 0.000 3.649 5.755 7.513 8.980 10.204 11.226 12.079 12.790 13.384 13.880 14.293 14.639 14.927 15.368

M

1.06

2

3. Determination of Lateral pressure, Vertical pressure and Frictional traction for Symmetrical discharge load condition Phe (z)

= Horizontal pressure at depth Z = Wall friction traction at depth Z

Pwe (z)

= Ch*Phf  = Cw*Pwf 

2

(T/M ) 2

nzSk

(T/M ) = The resulting characteristic value of the vertical force in the wall during discharge at depth Z

Ch

= Discharge factor for horizontal pressure

=

1.15

Cw

= Discharge factor for wall frictional traction

=

1.10

C0

= Discharge factor for all solids Z (M) 2.80 6.98 9.98 12.98 15.98 18.98 21.98 24.98 27.98 30.98 33.98 36.98 39.98 42.98 48.98

Phe 2

(T/M ) 0.00 3.85 6.08 7.94 9.49 10.78 11.86 12.76 13.51 14.14 14.66 15.10 15.46 15.77 16.24

Pwe 2

(T/M ) 0.00 2.17 3.39 4.37 5.17 5.83 6.36 6.79 7.14 7.42 7.66 7.84 8.00 8.12 8.31

nzSk (T/M) 0.00 4.15 11.49 21.70 34.24 48.69 64.67 81.92 100.18 119.27 139.04 159.36 180.12 201.24 244.35

3 of 7

=

C0

= Cw*m*Pho*(z-zo*Y j(z)) (T/M)

Design of Raw Meal Silo Based on BS EN 1991-4:2006 for Obajana Cement Line 3, Nigeria

4. Determination of Lateral patch pressure in wall for discharge patch load condition Silo Type

= Thick walled circular silo

Ppe

= Discharge outward patch pressure

Ppei

= Discharge inward patch pressure 2.05 =

hc / dc

= Cpe*Phe = Ppe / 7

= 0.42*Cop*(1+2*E2)*(1-exp(-1.5*((hc/dc)-1))) 0.0 = 2*e / d c =

Cpe E e Phe

= Max(ef ,e0)

0.0

Cop

= Patch load solid reference factor

=

M

= Local discharge pressure

s

0.50

=

4.418 = p*dc/16 = = Phe,u*(1+ζ*Cpe)

= The length of the zone on which the patch load is applied

Phe,u

= Resulting symmetrical horizontal pressure for discharge = Maximun(0.5+0.01*(d c/t) or 1)

ζ

Cpe

Z (M) 2.80 6.98 9.98 12.98 15.98 18.98 21.98 24.98 27.98 30.98 33.98 36.98 39.98 42.98 48.98

0.167 0.167 0.167 0.167 0.167 0.167 0.167 0.167 0.167 0.167 0.167 0.167 0.167 0.167 0.167

Phe Normal 0.00 3.85 6.08 7.94 9.49 10.78 11.86 12.76 13.51 14.14 14.66 15.10 15.46 15.77 16.24

Ppe 2

(T/M ) 0.000 0.643 1.014 1.323 1.581 1.797 1.977 2.127 2.252 2.357 2.444 2.517 2.578 2.629 2.706

Ppei 2

(T/M ) 0.000 0.092 0.145 0.189 0.226 0.257 0.282 0.304 0.322 0.337 0.349 0.360 0.368 0.376 0.387

s

Phe,u

(M) 4.418 4.418 4.418 4.418 4.418 4.418 4.418 4.418 4.418 4.418 4.418 4.418 4.418 4.418 4.418

(T/M ) 0.000 4.497 7.094 9.260 11.068 12.577 13.837 14.888 15.765 16.497 17.108 17.617 18.043 18.398 18.942

=

1.00

2

5. Discharge loads for silos with large outlet eccentricities e0

=

0.0

M ef  0.0 M = This procedures is not applicable 6. Pressure due to reduction in ambient atmospheric temperature

Temperature DIFFERENTIAL calculation (Ref. Annex D of BS EN 1991-1-5-: 2003 o

120 -0.6 0.4 1.71 0.17 0.04

Material temperature inside silo (Tin) C= 0 Minimum temperature of outside environment (Tout) C= Thickness of silo wall (hi) m= The thermal conductivity of concrete ( λi) (W/(mK))= The thermal resistance Rin (m2K/W)= Thermal resistance Rout (m2K/W)= Total thermal resistance (m2K/W) Rtot=Rin+∑(hi/λi)+Rout

=

0

0.444 63.55

Temperature differential [(Tin-Tout)/Rtot]* ∑(h/λi) C=

4 of 7

M

Design of Raw Meal Silo Based on BS EN 1991-4:2006 for Obajana Cement Line 3, Nigeria

Temperature DIFFERENTIAL calculation (Ref. clause 6.10 of Reynolds handbook, 10th edition) h = thickness of wall (m) =

0.4 120

0

Inside material/hot liquid/flue gas (T G) temperature ( C) = 0

-0.6

External air temperature/temperature (T A)at other face of wall ( C) = 0

1.71

ai = Resistance at the internal face (watt/sqm/ C)

0.17

Thermal conductivity (k c) of RCC wall(watt/sqm/ C) = 0

0

0

aa = Resistance due to cavity (watt/sqm/ C) 0

0.04

ao = Resistance at the external face (watt/sqm/ C) 0

0.00001

Co-efficient of linear expansion of concrete ( Єc) (/ C) = 2

21000

Modulus of elasticity of concrete (Ec) (N/mm ) = 4 Moment of inertia (I c) of concrete section (m )

0.0053333 0

2.25

Resistance to the transmission of heat (k) through wall (watt/sqm/ C) = h + k= ai+aa+ao kc

(

)

0

63.5

The change in temperature (T C) through concrete wall = T = (T G-T A)*k*hc/kc

a) Tension due to Temperature PhT = Normal pressure o

= CT*aw*DT*Ew/((r / t)+(1-v)*(E w/EsU)) o 15 To = C

CT

120 = C = Thickness of silo wall = = Temperature load multiplier

aw

= Coefficient of thermal expansion of the silo wall

Ti

t

DT

r 

= Elastic modulus of the silo wall

v

= Poisson's ration

Pvft

m = =

= Temperature differential = Silo radius (dc / 2)

Ew EsU

0.400

=

3.0 0.0000011

63.5

per degree centigrade

o

C 11.45 M = = 5500*SQRT(f ck) 0.3 =

= χ*Pvft 28.60 = Vertical stress at the base of the vertical walled section = = Inloading effective elastic modulus at depth Z

5 of 7

T/M

2

=

27500.0 N/mm2

=

10487.8 T/M2

Design of Raw Meal Silo Based on BS EN 1991-4:2006 for Obajana Cement Line 3, Nigeria

= 7*l3/2

= Modulus contiguity coefficient

χ

PhT

=

=

366.68

2

2.72

(T/M )

7. Design against Hoop Tension due to Load P h Dead Load Factor 

Kd

=

Height Symmetrical filling (Phf ) from top

1.20

Kl = 1.4 live Load Factor  Lateral Pressure ( P h) Unsymmetrical Symmetrical Unsymmetrical filling (Phf,u) discharge. (Phe) discharge. (Phe,u)

Pvft

Esu

Design Factored Design Factored Design Factored Design Factored 2

(M)

T/M

2.80 6.98 9.98 12.98 15.98 18.98 21.98 24.98 27.98 30.98 33.98 36.98 39.98 42.98 48.98

0.00 3.35 5.29 6.90 8.25 9.37 10.31 11.10 11.75 12.30 12.75 13.13 13.45 13.71 14.12

T/M

2

0.00 4.69 7.40 9.66 11.55 13.12 14.44 15.53 16.45 17.21 17.85 18.38 18.83 19.20 19.76

T/M

2

T/M

0.00 3.65 5.76 7.51 8.98 10.20 11.23 12.08 12.79 13.38 13.88 14.29 14.64 14.93 15.37

2

0.00 5.11 8.06 10.52 12.57 14.29 15.72 16.91 17.91 18.74 19.43 20.01 20.49 20.90 21.51

T/M

2

T/M

0.00 3.85 6.08 7.94 9.49 10.78 11.86 12.76 13.51 14.14 14.66 15.10 15.46 15.77 16.24

2

0.00 5.40 8.51 11.11 13.28 15.09 16.60 17.86 18.92 19.80 20.53 21.14 21.65 22.08 22.73

T/M

2

0.00 4.50 7.09 9.26 11.07 12.58 13.84 14.89 15.76 16.50 17.11 17.62 18.04 18.40 18.94

Hoop Tension due Steel Reqd. Steel Reqd. to Temperature from Filling & from (T = P hT*D/2) Discharge Temperature

Height from top

Maximum Hoop Tension (T = P h*D/2)

(M)

T/M of Height

T/M of Height

mm2/m

mm2/m

2.80

0.00

0.00

0.00

0.00

6.98

72.09

9.18

2763.56

352.09

9.98

113.71

14.60

4358.92

559.56

12.98

148.44

19.22

5690.30

736.69

15.98

177.43

23.18

6801.39

888.56

18.98

201.62

26.59

7728.64

1019.26

21.98

221.80

29.53

8502.47

1132.09

24.98

238.65

32.08

9148.26

1229.75

27.98

252.71

34.29

9687.20

1314.49

30.98

264.44

36.21

10136.96

1388.17

33.98

274.23

37.89

10512.31

1452.34

36.98

282.41

39.35

10825.55

1508.31

39.98

289.23

40.62

11086.97

1557.21

42.98

294.92

41.74

11305.12

1599.97

48.98

303.63

43.57

11639.31

1670.24

6 of 7

T/M

2

0.00 6.30 9.93 12.96 15.50 17.61 19.37 20.84 22.07 23.10 23.95 24.66 25.26 25.76 26.52

Temperature pressure (PhT) Design Factored

T/M

2

0.00 5.37 8.68 11.60 14.18 16.45 18.46 20.23 21.79 23.16 24.37 25.44 26.39 27.22 28.60

T/M

2

0.00 1968.5 3183.4 4254.9 5200.0 6033.4 6768.5 7416.8 7988.6 8492.9 8937.7 9330.0 9675.9 9981.1 10487.8

T/M

2

0.57 0.91 1.20 1.45 1.66 1.84 2.00 2.14 2.26 2.36 2.45 2.53 2.60 2.72

T/M

2

0.80 1.27 1.68 2.02 2.32 2.58 2.80 2.99 3.16 3.31 3.44 3.55 3.65 3.81

Design of Raw Meal Silo Based on BS EN 1991-4:2006 for Obajana Cement Line 3, Nigeria

Level (m) Height Rebars(IF) for hoop tension from top s reqd. s prov. f (M) mm mm (c/c) mm (c/c) 2.80 22 200 6.98 22 275 120 63.016 9.98 25 225 120 12.98 25 173 130 57.016 15.98 25 144 130 18.98 25 127 110 51.016 21.98 25 115 110 24.98 25 107 100 45.016 27.98 25 101 100 30.98 25 97 100 39.016 33.98 25 93 100 36.98 25 91 90 33.016 39.98 25 89 90 42.98 25 87 90 27.016 48.98 25 84 90 21.016

Rebars(OF) for hoop tension Check

OK OK OK OK OK OK OK OK Revise Revise OK Revise Revise Revise

f mm

22 22 25 25 25 25 25 25 25 25 25 25 25 25 25

s reqd. s prov. Check mm (c/c) mm (c/c) 150 OK 219 120 OK 179 120 OK 137 65 OK 114 65 OK 101 55 91 55 OK OK 85 50 OK 80 50 OK 76 50 OK 73 50 OK 71 45 OK 69 45 OK 68 45 OK 66 45

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