136652578 Design Examples 1 2 of Circular Silo 1 PDF

7/26/2019 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

kg cm

kg cm

kg m

1.5m

6 0 m

4 0 m

D= 10m

2 0 m

1 0 m

1.5m




Solution

2

Assume angle of response = =25

25 tan 25 2.33 1.53

1 sin 25 0.577

44 10 / 4 2.5

/ 40 /10 4

s sh h m

k

D R D m

D

H D

Overpressure Factor C d

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

us ce

At the bottom of the silos

' 2

2

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

1 7.65 t/m'

4.42 t/m

kY R Rq ek

P kq

Ring Tension

2 2

1.85 1.7 4.42 1069.5

2 2

69.518.4 cm /m ie. 9.2cm /m for each side

0.9 4200

use [email protected]

d u

st

y

C P DT ton

T A

f

cm

If slip forming will be used:

2 269.5

19.4 cm /m ie. 9.7cm /m for each side0.95 0.9 42000.95

st

y

T A

f

Minimum Thickness

4

sh 0.0003 200 10 1680 8 35f f 4.42 10=100f f 100 1680 35 2 s s ct

s ct

ε E nt T =7.5 cm




The thickness of silo walls shall be not less than 150 mm for cast-in-place concrete.

Use Wall thickness t=20cm

Vertical Loads

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 0.15 / 4

DL= =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 /

141.4ver

Dto

ton m

Fric

n m

tion V Y q R

atY V

P to

D

o

n

t n m

Check for Buckling

2

,

'

,

141.4101 kg/cm

0.7 20 100

0.55 0.55 0.7 350 134.75

c vert

nw c c vert P f f

The buckling does not control

20.002 20 100 4 cm /m st

A

Design for the Hopper

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

2

st

1.44sin sin sin

1.5 8.45 2 4.1 84.4 29.51.7 1.4 59.2 ton/m

4sin 60 2 4.1 sin 60 2 4.1 sin 60

59.2A 16.5cm /m

0.9 4200

g L

mu

D W W

D D

F

5.0m

4.1

0.75

5.8m




Hoop Reinforcement

2 2

2

2 2 2

2

2

1.51.7

2sin

sin cos

0.577 8.45 4.87 t/m

4.87 sin 60 8.45 cos 60 5.765t/m

' 25

tan 8.45tan304.67t/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

qor q p

use q p

F

2

st, hopper

765 2 4.159.6ton/m

2sin60

69.6A 19.4cm /m

0.9 4200




Design of the Circular Beam

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 6.24 116.53

2.5 2 4.1 0.2 2 0.75 0.2 5.8 29.5

3

1.7 1.44sin sin sin

1.5 8.1 10 116.51.7

4sin60

y

L

g

y g Lmu

mu

R m

q t m

W ton

W ton

q D W W F

D D

F

x

29.51.4 68.4 ton

10 sin 60 10 sin 60

F cos 68.4cos 60 34.2

0.615 2.5 1.4 68.4sin 60 61.5

mu

y

F ton

F ton

Location Shear Comp. Force

due to Fx

Bending Moment Mt due

to Fydue 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

100cm28.5

32.9

r=467cm

1

1

2

2

100

90100

57

6150

32.9 , 42.3

87.2

74.5

0.285 684 19.5 .

r

t

a

ba

b

A

x cm y cm

a cm

b cm

t m

33cm

90cm

100 R=4.67m

28.5

32.9




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)

2

2

2

3 5 5 0.81.3 t/m

5 LW

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

2

2

2

2 3 5 5 2.5 8.33 t/m5

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




Check for shear on slab

228.4 5 0.35

662 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

Documents

136652578 Design Examples 1 2 of Circular Silo 1 PDF