136652578 Design Examples 1 2 of Circular Silo 1 PDF

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ENGC6353 Dr. Mohammed Arafa Page 1

Design Example 1

Design the wall and hopper of a wheat silo with an internal diameter of 10 meter and with the height of cylindrical portion of 40 m. The central hopper is supported by eight

columns monolithic with the lower walls. The Roof load ( DL = 150 kg/m2 and LL= 100 kg/m2)

Use the following parameter

' 2 2 3 ' 350 / 4200 / 800 / 25 0.444 c y o f kg cm f kg cm kg m         1.5m 60 m 40 m D= 10m 20 m 10 m 1.5m

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Solution

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2

Assume angle of response = =25 2 5 tan 25 2.33 1.5 3 1 sin 25 0.577 4 4 10 / 4 2.5 / 40 /10 4 s s h h m k D R D m D H D                  Overpressure Factor Cd d d d 1 / 40 / 10 4 upper H lower 2/3 H Hoop From Table 1 c 1.5 c 1.85 1.5

ACI313-4.4.3.2 allows to use

e

c =1.35 for the Hoo

r per d H D usec     

At the bottom of the silos

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2

At the bottom of the silos Y=40-1.5=38.5m

1 7.65 t/m ' 4.42 t/m kY R R q e k P kq        _  _  

Ring Tension

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2 2 1.85 1.7 4.42 10 69.5 2 2 69.5

18.4 cm /m ie. 9.2 cm /m for each side 0.9 4200 use 12@12.5 d u st y C P D T ton T A f cm           

If slip forming will be used:

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69.5 19.4 cm /m ie. 9.7 cm /m for each side2 2 0.95 0.9 4200 0.95 st y T A f       Minimum Thickness

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sh f f 0.0003 200 10 1680 8 35 4.42 10 = 100f f 100 1680 35 2 s s ct s ct ε E n t   T      _  _    =7.5 cm

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ENGC6353 Dr. Mohammed Arafa Page 3 The thickness of silo walls shall be not less than 150 mm for cast-in-place concrete. Use Wall thickness t=20cm

Vertical Loads

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t 2

Weight of the wall W 2.5 0.2 60 30 /

38.5 0.8 38.5 7.65 2.5 57.9 ton/m Roff DL=0.15 / 4=0.15 10 4 0.375 / LL 0.10 10 / 4 0.2 1.7 57.9 0.375 1.4 30 0.25 5 / 141.4 ver D to ton m Fric n m tion V Y q R atY V P to D o n t n m                        

Check for Buckling

2 , ' , 141.4 101 kg/cm 0.7 20 100 0.55 0.55 0.7 350 134.75 c vert nw c c vert f P f f          

The buckling does not control 2 0.002 20 100 4 cm /m st

A    

Design for the Hopper

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0 2 2 2 1.0 7.65 0.8 1 8.45 t/m

= weight of the material in hopper 0.8 = 4.1 0.75 5.8 84.4 3 2.5 = 2 4.1 0.2 2 0.75 0.2 5.8 29.5 3

Merdional forces and required reinforcing 1.7 y y y y L L g y mu q q h at h m q W W ton W ton q F            _  _         

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2 st 1.4

4 sin sin sin

1.5 8.45 2 4.1 84.4 29.5

1.7 1.4 59.2 ton/m

4 sin 60 2 4.1 sin 60 2 4.1 sin 60 59.2 A 16.5 cm /m 0.9 4200 g L mu D W W D D F                             _  _ _ _          5.0m 4.1 0.75 5.8m

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ENGC6353 Dr. Mohammed Arafa Page 4 Hoop Reinforcement 2 2 2 2 2 2 2 2 1.5 1.7 2 sin sin cos 0.577 8.45 4.87 t/m 4.87 sin 60 8.45 cos 60 5.765t/m ' 25 tan 8.45 tan 30 4.67t/m tan tan ' tan 30 tan 25

4.67t/m 1.5 5. 1.7 tu y n n tu q D F q P q where P kq q assume q or q p use q p F                 _ _                       

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2 st, hopper 765 2 4.1 59.6 ton/m 2 sin 60 69.6 A 19.4 cm /m 0.9 4200            

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Design of the Circular Beam

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2 2 2 5 32.9 /100 4.67 7.65 0.8 100 42.3 /100 8.1 / 0.8 4.67 0.75 6.24 116.5 3 2.5 2 4.1 0.2 2 0.75 0.2 5.8 29.5 3 1.7 1.4

4 sin sin sin

1.5 8.1 10 116.5 1.7 4 sin 60 y L g y _L g mu mu R m q t m W ton W ton q D W W F D D F                                 _  _ _ _        

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x 29.5 1.4 68.4 ton 10 sin 60 10 sin 60 F cos 68.4 cos 60 34.2 0.615 2.5 1.4 68.4 sin 60 61.5 mu y F ton F ton                        

Location Shear Comp. Force

due to Fx

Bending Moment Mt due to Fy due to Mt Due to Fy

Support 112.5

159.4

91

69.4

0 Midspan

0 159.4 91 34.86 0

9 33 form support

64.7

159.4

91

0

5.34

33 90 100cm 28.5 32.9 r=467cm 1 1 2 2 100 90 100 57 6150 32.9 , 42.3 87.2 74.5 0.285 684 19.5 . r t a b a b A x cm y cm a cm b cm M t m             33cm 90cm 100 R=4.67m 28.5 32.9

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Example 2

If the silo’s bottom in Example 1 is a circular slab with central opening on the lower walls and carrying hopper forming concrete fill.

Load on the slab

a) Load from wheat in Hopper (assume uniform)

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2 2 2 3 5 5 0.8 1.3 t/m 5 L W     at y=38.5 m ie. h=40m q=7.65 t/m2 p=kq=4.42 t/m2 Total LL=7.65+1.3=9 t/m2

b) Dead Load

Weight of Hopper forming fill

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2 2 2 2 3 5 5 2.5 8.33 t/m 5 g W    

Slab weight assume 40 cm slab thickness

2 2 2 0.4 2.5 1.0 t/m 8.33 1.0 9.33 t/m 1.7 9 1.4 9.33 28.4 t/m slab total u W DL W           

Design of the slab Holes

Slabs with holes may be designed in two ways

 By computing bending moments for slabs with no holes and reinforcing with a steel member with adequate strength and of stiffness equal to that of removed slab.  By considering the hole and reinforcing for bending moments obtained using

tables or Timoshenko equations.

10m

40m

5m

7m 50cm

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ENGC6353 Dr. Mohammed Arafa Page 7 Check for shear on slab

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2 28.4 5 0.35 66 2 5 0.35 0.53 0.85 300 35 2 5 0.35 798 u c u V ton V ton V            

Total reaction at the bottom wall must includes

From Roof, Material above the Hopper, Material in the Hopper, Hopper filling form, Bottom Slab, Upper Wall, and Lower Wall