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7/26/2019 136652578 Design Examples 1 2 of Circular Silo 1 PDF
http://slidepdf.com/reader/full/136652578-design-examples-1-2-of-circular-silo-1-pdf 1/7
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
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ENGC6353 Dr. Mohammed Arafa Page 2
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 12@12.5
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
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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
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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
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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
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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)
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
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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
Recommended