Rm Silo Ocp3

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

A. SILO CONFIGURATION

2.80

1 Material = Raw Meal

0.152 Weight of Material Stored in Storage Silo = 20000 Ton

3 Thickness of RCC Wall of Storage Silo = 400 mm4 Average thickness of Top Slab of Silo = 150 mm

46.1

8

5 thickness of Inverted Cone = 500 mm 0.4

6 EL. of Flat Slab Btoom above GL = 21.02 M7 EL. of Top of Top Slab above GL = 70.00 M 22.508 Max. Level of Filling below Silo Top = 0.15 M9 Height of av. Material Storage from Flat Slab = 46.18 M

10 Internal Diameter of Storage silo D = 22.5 M11 Angle of Repose = 25 0

12 Mean Angle of Internal Friction = 25 0

13.6

7513 = 2.05

14 Silo Type = Slender silo15 Temperature of Hot Material inside = 120

16 Temperature of Outside Atmosphere = -0.6

21.0

1617 Bulk Density of Stored Material l = 1.4 0.50018 Maximum ht of Flat Slab = 0.000 M19 Seismic Zone III Z = 0.1620 Live Loads on Operating Floors = 1 FGL

21 Basic Wind speed = 41 M/sec22 Grade of Conc. for wall (Characteristic Strength) = 2523 El. of Top of Flat Slab above GL = 21.016 M24 Angle of Inverted Cone a = 6025 Thickness of RCC Wall below Cone Support = 500 mm26 Axial Force Imposed on Ftop = 20 Ton27 Yield Stress of Reinfocement = 30028 Grade of Conc. For foundation = 2529 Maximum eccentricity of filling = 0 M

30 Maximum eccentricity of outlet = 0 M

B. CAPACITY CALCULATIONVolume above cone = 18363TOTAL = 18363

Weight of material = 22036 T Considering density of material 1.2 from capacity considerationWeight of material = 25708 T Considering density of material 1.4 for structural design

C. DESIGN OF SILO WALLDesign parameters to determine Silo Forces(a) A = Plan Cross-sectional area of the Silo = 397.6078(b) D = Internal Diameter of the Silo ( Bin ) = 22.50 M(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 = 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 = 46.18 M(i) = Mean angle of internal friction = 25(j) = = 30.50

dc

fr

fm

Slenderness Ratio (hc / dc)

TioC

T0oC

T/M3

T/M2

N/mm2

o

N/mm2

N/mm2

ef

e0

M3

M3

T/M3

T/M3

M2

T/M3

fimO

f (max) Maximum angle of internal friction (af X fim) O

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(k) = = 20.49(l) = Mean lateral pressure ratio = 0.54

(m) K (max) = = 0.648(n) K (min) = = 0.450(o) = Mean wall friction coefficient for solid sliding on the vertical wall = 0.56(p) = = 0.599(q) = = 0.523

(r) = Patch load solid reference factor = 0.5

Note: 1)2)3)

1 Determination of Lateral pressure, Vertical pressure and Frictional traction for Symmetrical filling load condition

= Horizontal pressure at depth Z == Wall friction traction at depth Z == Vertical pressure at depth Z == The resulting characteristic value of the vertical force in the wall after filling at depth Z = T/M= M=== 16.59 M ( for maximum normal pressure calculation )= 14.49 M ( for maximum frictional traction calculation )= 23.88393 M ( for maximum vertical load calculation )= 15.04687 ( for maximum normal pressure calculation )= 13.14 ( for maximum frictional traction calculation )= 15.04687 ( for maximum vertical load calculation )

Z

( M ) Normal Friction Vertical Normal Friction Vertical2.80 0.000 0.000 0.000 0.000 0.000 0.000 0.00 0.00 0.00 0.006.98 0.252 0.289 0.175 0.223 0.251 0.161 3.35 1.97 5.37 3.789.98 0.433 0.496 0.301 0.351 0.391 0.260 5.29 3.08 8.68 10.4412.98 0.614 0.703 0.426 0.459 0.505 0.347 6.90 3.97 11.60 19.7215.98 0.795 0.910 0.552 0.548 0.597 0.424 8.25 4.70 14.18 31.1318.98 0.976 1.117 0.677 0.623 0.673 0.492 9.37 5.30 16.45 44.2621.98 1.156 1.324 0.803 0.685 0.734 0.552 10.31 5.78 18.46 58.7924.98 1.337 1.531 0.929 0.737 0.784 0.605 11.10 6.17 20.23 74.4727.98 1.518 1.738 1.054 0.781 0.824 0.652 11.75 6.49 21.79 91.0730.98 1.699 1.945 1.180 0.817 0.857 0.693 12.30 6.75 23.16 108.4333.98 1.880 2.152 1.305 0.847 0.884 0.729 12.75 6.96 24.37 126.4036.98 2.061 2.359 1.431 0.873 0.906 0.761 13.13 7.13 25.44 144.8739.98 2.242 2.566 1.557 0.894 0.923 0.789 13.45 7.27 26.39 163.7442.98 2.423 2.774 1.682 0.911 0.938 0.814 13.71 7.38 27.22 182.9548.98 2.785 3.188 1.934 0.938 0.959 0.855 14.12 7.55 28.60 222.13

2 Determination of Lateral patch pressure in wall for filling patch load condition

Silo Type = Thick walled circular silo= Filling outward patch pressure == Filling inward patch pressure =

f (min) Minimum angle of internal friction (fim / af)) O

Km

Maximum lateral pressure ratio (Km X ak)Minimum lateral pressure ratio (Km / ak)

mm

m (max) Maximum wall friction coefficient (mm X am)

m (min) Minimum wall friction coefficient (mm / am)

cop

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

Phf (z) Pho*Yj(z) (T/M2)

Pwf (z) m*Pho*Yj(z) (T/M2)

Pvf (z) (Pho / K)*Yj(z) (T/M2)

nzSkm*Pho*(z-zo*Yj(z))

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

Phol*K*zo (T/M2)

Yj (z) 1 - e(-Z / Zo)

zo

zo

zo

Pho(T/M2)

Pho(T/M2)

Pho(T/M2)

Z / Z0 Z / Z0 Z / Z0 1 -e(Z/Zo) 1 -e(Z/Zo) 1 -e(Z/Zo) Phf Pwf Pvf nzSk

(T/M2) (T/M2) (T/M2) (T/M)

Ppf Cpf*Phf

Ppfi Ppf/7

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=E = = 0.00

= Maximum eccentricity of surface pole during filling = 0.0 M

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

ef

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= Local filling pressure= Patch load solid reference factor = 0.50

s = The length of the zone on which the patch load is applied = = 4.418 M= Resulting symmetrical horizontal pressure for filling =

ζ = = 1.06

Z s

( M ) Normal (M)2.80 0.083 0.00 0.000 0.000 4.418 0.0006.98 0.083 3.35 0.279 0.040 4.418 3.6499.98 0.083 5.29 0.441 0.063 4.418 5.75512.98 0.083 6.90 0.575 0.082 4.418 7.51315.98 0.083 8.25 0.688 0.098 4.418 8.98018.98 0.083 9.37 0.781 0.112 4.418 10.20421.98 0.083 10.31 0.860 0.123 4.418 11.22624.98 0.083 11.10 0.925 0.132 4.418 12.07927.98 0.083 11.75 0.979 0.140 4.418 12.79030.98 0.083 12.30 1.025 0.146 4.418 13.38433.98 0.083 12.75 1.063 0.152 4.418 13.88036.98 0.083 13.13 1.094 0.156 4.418 14.29339.98 0.083 13.45 1.121 0.160 4.418 14.63942.98 0.083 13.71 1.143 0.163 4.418 14.92748.98 0.083 14.12 1.177 0.168 4.418 15.368

3 Determination of Lateral pressure, Vertical pressure and Frictional traction for Symmetrical discharge load condition

= Horizontal pressure at depth Z == Wall friction traction at depth Z == The resulting characteristic value of the vertical force in the wall during discharge at depth Z == Discharge factor for horizontal pressure = 1.15 = (T/M)= Discharge factor for wall frictional traction = 1.10= Discharge factor for all solids

Z

( M )

2.80 0.00 0.00 0.006.98 3.85 2.17 4.159.98 6.08 3.39 11.4912.98 7.94 4.37 21.7015.98 9.49 5.17 34.2418.98 10.78 5.83 48.6921.98 11.86 6.36 64.6724.98 12.76 6.79 81.9227.98 13.51 7.14 100.1830.98 14.14 7.42 119.2733.98 14.66 7.66 139.0436.98 15.10 7.84 159.3639.98 15.46 8.00 180.1242.98 15.77 8.12 201.2448.98 16.24 8.31 244.35

Phf

Cop

p*dc/16Phf,u Phf,u*(1+ *Cζ pf)

Maximun(0.5+0.01*(dc/t) or 1)

Cpf Phf Ppf Ppfi Phf,u

(T/M2) (T/M2) (T/M2)

Phe (z) Ch*Phf (T/M2)

Pwe (z) Cw*Pwf (T/M2)

nzSkCw*m*Pho*(z-zo*Yj(z))

Ch C0

Cw

C0

Phe Pwe nzSk

(T/M2) (T/M2) (T/M)

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

Silo Type = Thick walled circular silo= Discharge outward patch pressure == Discharge inward patch pressure == 2.05=

E = = 0.0e = = 0.0 M

= Local discharge pressure= Patch load solid reference factor = 0.50

s = The length of the zone on which the patch load is applied = = 4.418 M= Resulting symmetrical horizontal pressure for discharge =

ζ = = 1.00

Z s

( M ) Normal (M)2.80 0.167 0.00 0.000 0.000 4.418 0.0006.98 0.167 3.85 0.643 0.092 4.418 4.4979.98 0.167 6.08 1.014 0.145 4.418 7.09412.98 0.167 7.94 1.323 0.189 4.418 9.26015.98 0.167 9.49 1.581 0.226 4.418 11.06818.98 0.167 10.78 1.797 0.257 4.418 12.57721.98 0.167 11.86 1.977 0.282 4.418 13.83724.98 0.167 12.76 2.127 0.304 4.418 14.88827.98 0.167 13.51 2.252 0.322 4.418 15.76530.98 0.167 14.14 2.357 0.337 4.418 16.49733.98 0.167 14.66 2.444 0.349 4.418 17.10836.98 0.167 15.10 2.517 0.360 4.418 17.61739.98 0.167 15.46 2.578 0.368 4.418 18.04342.98 0.167 15.77 2.629 0.376 4.418 18.39848.98 0.167 16.24 2.706 0.387 4.418 18.942

5 Discharge loads for silos with large outlet eccentricities

= 0.0 M= 0.0 M

This procedures is not applicable

6 Pressure due to reduction in ambient atmospheric temperature

120

-0.6Thickness of silo wall (hi) m= 0.4

1.71The thermal resistance Rin (m2K/W)= 0.17Thermal resistance Rout (m2K/W)= 0.04Total thermal resistance (m2K/W)

= 0.4439

Ppe Cpe*Phe

Ppei Ppe / 7hc / dc

Cpe 0.42*Cop*(1+2*E2)*(1-exp(-1.5*((hc/dc)-1)))2*e / dc

Max(ef,e0)Phe

Cop

p*dc/16Phe,u Phe,u*(1+ *Cζ pe)

Maximun(0.5+0.01*(dc/t) or 1)

Cpe Phe Ppe Ppei Phe,u

(T/M2) (T/M2) (T/M2)

e0

ef

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

Material temperature inside silo (Tin) oC=

Minimum temperature of outside environment (Tout) 0C=

The thermal conductivity of concrete (λi) (W/(mK))=

Rtot=Rin+∑(hi/λi)+Rout

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= 0.4439

63.549

h = thickness of wall (m) = 0.4

120

-0.6

1.71

0.17

0

0.04

0.00001

21000

0.0053333

2.25h

+

63.5

a) Tension due to Temperature

= Normal pressure =

= 120 = 15

t = Thickness of silo wall = 0.400 m= Temperature load multiplier = 3.0

= Coefficient of thermal expansion of the silo wall = 0.0000011 per degree centigrade

= Temperature differential = 63.5r = = 11.45 M

= Elastic modulus of the silo wall = = 27500.0v = Poisson's ration = 0.3

= Inloading effective elastic modulus at depth Z = = 10487.8= Vertical stress at the base of the vertical walled section = 28.60

Rtot=Rin+∑(hi/λi)+Rout

Temperature differential [(Tin-Tout)/Rtot]*∑(h/λi) 0C=

Temperature DIFFERENTIAL calculation(Ref. clause 6.10 of Reynolds handbook, 10th edition)

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

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

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

ai = Resistance at the internal face (watt/sqm/0C)

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

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

Co-efficient of linear expansion of concrete (Єc) (/0C) =

Modulus of elasticity of concrete (Ec) (N/mm2) =

Moment of inertia (Ic) of concrete section (m4)

Resistance to the transmission of heat (k) through wall (watt/sqm/0C) =

(k= ai+aa+ao)kc

The change in temperature (T0C) through concrete wall =

T = (TG-TA)*k*hc/kc

PhT CT*aw*DT*Ew/((r / t)+(1-v)*(Ew/EsU))

TioC To

oC

CT

aw

DT oC

Silo radius (dc / 2)Ew 5500*SQRT(fck) N/mm2

EsU χ*Pvft T/M2

Pvft T/M2

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χ = Modulus contiguity coefficient = = 366.68

= 2.72

7

Dead Load Factor = 1.20 live Load Factor = 1.4

Pvft Esu

Design Factored Design Factored Design Factored Design Factored Design Factored

(M)

2.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.006.98 3.35 4.69 3.65 5.11 3.85 5.40 4.50 6.30 5.37 1968.5 0.57 0.809.98 5.29 7.40 5.76 8.06 6.08 8.51 7.09 9.93 8.68 3183.4 0.91 1.2712.98 6.90 9.66 7.51 10.52 7.94 11.11 9.26 12.96 11.60 4254.9 1.20 1.6815.98 8.25 11.55 8.98 12.57 9.49 13.28 11.07 15.50 14.18 5200.0 1.45 2.0218.98 9.37 13.12 10.20 14.29 10.78 15.09 12.58 17.61 16.45 6033.4 1.66 2.3221.98 10.31 14.44 11.23 15.72 11.86 16.60 13.84 19.37 18.46 6768.5 1.84 2.5824.98 11.10 15.53 12.08 16.91 12.76 17.86 14.89 20.84 20.23 7416.8 2.00 2.8027.98 11.75 16.45 12.79 17.91 13.51 18.92 15.76 22.07 21.79 7988.6 2.14 2.9930.98 12.30 17.21 13.38 18.74 14.14 19.80 16.50 23.10 23.16 8492.9 2.26 3.1633.98 12.75 17.85 13.88 19.43 14.66 20.53 17.11 23.95 24.37 8937.7 2.36 3.3136.98 13.13 18.38 14.29 20.01 15.10 21.14 17.62 24.66 25.44 9330.0 2.45 3.4439.98 13.45 18.83 14.64 20.49 15.46 21.65 18.04 25.26 26.39 9675.9 2.53 3.5542.98 13.71 19.20 14.93 20.90 15.77 22.08 18.40 25.76 27.22 9981.1 2.60 3.6548.98 14.12 19.76 15.37 21.51 16.24 22.73 18.94 26.52 28.60 10487.8 2.72 3.81

(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 2763.56 352.099.98 113.71 14.60 4358.92 559.5612.98 148.44 19.22 5690.30 736.6915.98 177.43 23.18 6801.39 888.5618.98 201.62 26.59 7728.64 1019.2621.98 221.80 29.53 8502.47 1132.0924.98 238.65 32.08 9148.26 1229.7527.98 252.71 34.29 9687.20 1314.4930.98 264.44 36.21 10136.96 1388.1733.98 274.23 37.89 10512.31 1452.3436.98 282.41 39.35 10825.55 1508.3139.98 289.23 40.62 11086.97 1557.2142.98 294.92 41.74 11305.12 1599.9748.98 303.63 43.57 11639.31 1670.24

7*l3/2

PhT (T/M2)

Design against Hoop Tension due to Load Ph

Kd Kl

Height from top

Lateral Pressure ( Ph)Symmetrical filling

(Phf)Unsymmetrical

filling (Phf,u)Symmetrical

discharge. (Phe)Unsymmetrical

discharge. (Phe,u)Temperature pressure (PhT)

T/M2 T/M2 T/M2 T/M2 T/M2 T/M2 T/M2 T/M2 T/M2 T/M2 T/M2 T/M2

Height from top

Maximum Hoop Tension

(T = Ph*D/2)

Hoop Tension due to Temperature

(T = PhT*D/2)

Steel Reqd. from Filling &

Discharge

Steel Reqd. from

Temperature

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Level (m)

Check Checkf f(M) mm mm (c/c) mm (c/c) mm mm (c/c) mm (c/c)2.80 22 200 22 150

63.016 6.98 22 275 120 OK 22 219 120 OK9.98 25 225 120 OK 25 179 120 OK

57.016 12.98 25 173 130 OK 25 137 65 OK15.98 25 144 130 OK 25 114 65 OK

51.016 18.98 25 127 110 OK 25 101 55 OK21.98 25 115 110 OK 25 91 55 OK

45.016 24.98 25 107 100 OK 25 85 50 OK27.98 25 101 100 OK 25 80 50 OK

39.016 30.98 25 97 100 Revise 25 76 50 OK33.98 25 93 100 Revise 25 73 50 OK

33.016 36.98 25 91 90 OK 25 71 45 OK39.98 25 89 90 Revise 25 69 45 OK

27.016 42.98 25 87 90 Revise 25 68 45 OK21.016 48.98 25 84 90 Revise 25 66 45 OK

Height from top

Rebars(IF) for hoop tension Rebars(OF) for hoop tensions reqd. s prov. s reqd. s prov.

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Rm Silo Ocp3