Upload
cdvreugd
View
189
Download
6
Embed Size (px)
Citation preview
1
The Islamic University of GazaDepartment of Civil Engineering
Analysis of Reinforced Concrete Silos
Dr. Mohammed Arafa
2
Concrete Silos
Dr. Mohammed Arafa
3
Silo or Bunker ?
) 1.5) 1.5 for circular silos
1.5 for rectangular silos
a H Ab H D
H a
>>>
Empirical approximation are preferred by many engineers. Tow such approximation are:
The present ACI 313 Silos standard, however, uses the same method for both silos and bunkers
Dr. Mohammed Arafa
4
Design of Silos
Slipformed silos are constructed using a typically 4 ft. (1.2 m) high continuously moving form.
Jumpformed silos are constructed using three typically 4 ft. (1.2 m) high fixed forms. The bottom lift is jumped to the top position after the concrete hardens sufficiently.
hopper is the sloping, walled portion at the bottom of a silo.
Stave silos are silos assembled from small precast concrete units called “staves,” usually tongued and grooved, and held together by exterior adjustable steel hoops.
Dr. Mohammed Arafa
5
Properties of Granular Materials
Dr. Mohammed Arafa
6
Vertical Pressure
' /' 1 kY RRq ek
µγµ
− = −
WhereR = ratio of area to perimeter of horizontal cross section of storage spaceγ = weight per unit volume for stored materialµ` = coefficient of friction between stored material and wall or hopper surface
1 sink φ= −
Dr. Mohammed Arafa
7
Hydraulic Radius R
For Circular silos R=D/4For polygonal silos R=D/4for a circular shape of equivalent area.
For square silos a or shorter wall of rectangular silos use R=a/4
For the long wall b of rectangular silos use R=a`/4where a` is the length of side of an imaginary square silo
2' abaa b
=+Dr. Mohammed Arafa
8
Horizontal Pressure and Vertical Friction
Horizontal Pressure
p kq=
Vertical friction per unit length of wall perimeter
( )V Y q Rγ= −Note: µ`, k vary, the following combinations shall be used with maximum:(1) Minimum µ` and minimum k for maximum vertical pressure q.(2) Minimum µ` and maximum k for maximum lateral pressure p.(3) Maximum µ` and maximum k for maximum vertical friction force V
Dr. Mohammed Arafa
9
Pressures and loads for hoppers
0y yq q hγ= +
( ) ( )2 2
tantan '
tan tan '
sin cos 1 sin cos
yn n n
n y n y
qP and V P
or
P q k and V q k
θφ
θ φ
θ θ θ θ
= =+
= + = − ⋅
The initial pressure normal to the hopper surface at depth hy
below top of hopper shall be the larger of:
Dr. Mohammed Arafa
10
Square and rectangular siloHorizontal Forces Due to Stored Material
( )( )
,
,
2 for wall
2 for wall a b des
b a des
F p b a
F p a b
=
=
Dr. Mohammed Arafa
11
Regular Polygonal siloHorizontal Forces Due to Stored Material
( ) sin21 cosdesT p a θ
θ = −
Dr. Mohammed Arafa
12
Sections with combined tension and bending
( ) ( )
Smalleccentricity ''2
' '''' ''
u
u
u us s
y y
M he dF
F e F eA Af d d f d dφ φ
= < −
= =− −
Dr. Mohammed Arafa
13
hopper Types
Dr. Mohammed Arafa
14
Properties of Granular Materials
Dr. Mohammed Arafa
15
Over pressure Factor cd
Pdesign = 1.7 x Cd x Pinitial
Dr. Mohammed Arafa
16
Earthquake forces
Earthquake loads may affect stability and strength.
The UBC or IBC may be used. Seismic forces are assumed to act in any horizontal direction, but vertical acceleration forces are usually neglected.
In computing lateral seismic force The reduction of lateral force is allowed because of energy loss through inter-granular movement and particle-to-particle friction in the stored material.
ACI 313 use not less 80% of the weight of the stored material as an effective live load, from which to determine seismic forces.
Dr. Mohammed Arafa
17
Wind forces
Wind may affect the stability of empty silos, particularly tall, narrow silos or silos group.
Foundation pressure and column stresses, however, may be worse with wind acting on the full silo.
Wind load reduction may be applied for cylindrical shape may be applied to single circular for cylindrical
The pressures shall be not less than required by the local building code for the locality and height zone in question.
Wind pressure distributions shall take into account adjacent silos or structures.
Dr. Mohammed Arafa
18
Thermal Loads
Temperature and shrinkage steel requirement of ACI 318 apply to silos. In addition, hot stored materials may cause thermal stresses too high to be ignored. The approximate method illustrated below was developed specifically for cement storage silos. In this method:Tensile strength of the concrete is neglectedWall temperatures are assumed to vary only radially.
Dr. Mohammed Arafa
19
Thermal Loads
In building, the usual practice is to ignore a certain amount of inside-outside temperature difference (80oF or 27oC for silos).
( )2
12 1c c
tE hM Tα
ν= ∆
−
( ) ( )0 080 27
0.084.09 0.08
o oi t i
t
T T T F K T T C K
hKh
∆ = − − = − −
=+
Dr. Mohammed Arafa
20
Additional Steel due to Temperature Gradient
The additional horizontal steel Ast to resist moment due temperature gradient should be located near the colder face.
In singly reinforced walls, it should be added to the main hoop steel, ordinarily near the outer face.
In doubly reinforced walls, the entire amount Ast should be added to the outside layer
Dr. Mohammed Arafa
21
Minimum wall thickness
The thickness of silo or stacking tube walls shall be not less than 6 in. (150 mm) for cast-in-place concrete, nor less than 2 in. (50 mm) for precast concrete. The following formula can also be used in service loading
sh f f=100f f
s s ct
s ct
ε E nt T+ −
Dr. Mohammed Arafa
22
Crack Width
the design crack width computed at 2.5 bar diameter from the center of bar (dc = 2.5 bar diameter ) shall not exceed 0.010 in. (0.25 mm). The design crack width (inch) shall be computed by:
Dr. Mohammed Arafa
30.0001 s cw f d A=
23
Load factors and strength reduction factors
Load factors for silo or stacking tube design shall conform to those specified in ACI 318.
The weight of and pressures due to stored material shall be considered as live load.
For concrete cast in stationary forms, strength reduction factors, φ, shall be as given in ACI 318.
For slip forming, unless continuous inspection is provided, strength reduction factors given in ACI 318 shall be multiplied by 0.95.
Dr. Mohammed Arafa
24
Allowable ultimate Compressive load
The compressive axial load strength per unit area for walls in which buckling (including local buckling) does not control shall be computed by
'0.55nw cP fφ=
Dr. Mohammed Arafa
25
Additional Load at Openings
Flat BottomThe simplest flat bottom is a slab of uniform thickness. The flat bottom may also be a ribbed slab or beam-slab system. For a slab without hopper-forming fill, the design loads are dead load and pressure, qdes computed at the top of the slab..
1.4 1.7u desW DL q= +
With earthquake vertical friction at the wall is assumed to be zero, so that the ultimate vertical pressure on the bottom is:
( )0.75 1.4 1.7uW DL Hγ= +
Slab Shear stresses should be checked. Dr. Mohammed Arafa
26
Additional Load at Openings
2 2
1.7 1.44sin sin sin
1.72sin
sin cos
y gLmu
tu
n
q D WWFD D
q DF
q p P q
α
α
α π α π α
αα α
= + +
=
= = +
Conical hopper
Dr. Mohammed Arafa
27
Additional Load at Openings
Pyramidal hopper
( )
( )
,
,
1.7 1.4sin
1.7 1.4sin
a L a a des b gmau
a
b L b b des b gmbu
b
c W A q c WF
a
c W A q c WF
b
α
α
+ +=
+ +=
, ,1.7 sin and 1.7 sin2 2tau b des a tbu a des bb aF q F qα αα α = =
Dr. Mohammed Arafa
28
Additional Load at Openings
Pyramidal hopper
Dr. Mohammed Arafa
29
Circular Concrete Ring-Beam and Column System Supporting a Steel Hopper
Silo-Bottom: Steel hopper supported on concrete ring Beam
Ring-beam cross Section
Dr. Mohammed Arafa
30
Circular Concrete Ring-Beam and Column System Supporting a Steel Hopper
cos sin1.7 1.7
mu mux y beam
F FF and F wα α= = +
The WSD uniform torsional moment isMt = Fm e The Cross sectional Area of the ring Beam is
2 21 1 2r
b aA a b= −
Dr. Mohammed Arafa
31
Circular Concrete Ring-Beam and Column System Supporting a Steel Hopper
Ring-beam cross Section
2 21 1 2r
b aA a b= −
( )( )
( )( )
21 1 2 2 1 2
21 1 2 2 1 2
/ 2 / 2 / 3
/ 2 / 2 / 3r
r
a b a b b bx
Ab a a b a a
yA
− −=
− −=
2
r
a yb A a
==
The Cross sectional Area of the ring Beam is
Coordinate of the centroid measured from the origin O are:
An equivalent rectangle of height a and b is substituted for the pentagon
Dr. Mohammed Arafa
32
Circular Concrete Ring-Beam and Column System Supporting a Steel Hopper
Dr. Mohammed Arafa
33
Details and placement of reinforcement
Where slipforming is to be used, reinforcement arrangement and details shall be as simple as practical to facilitate placing and inspection during construction.
Reinforcement shall be provided to resist all bending moments, including those due to continuity at wall intersections, alone or in combination with axial and shear forces.
Horizontal ties shall be provided as required to resist forces that tend to separate adjoining silos of monolithically cast silo groups.
In no case shall the total horizontal reinforcement area be less than 0.0025 times the gross concrete area per unit height of wall.
Dr. Mohammed Arafa
34
Details and placement of reinforcement
Vertical reinforcement in the silo wall shall be (φ10 diameter) bars or larger,
The minimum ratio of vertical reinforcement to gross concrete area shall be not less than 0.0020.
Horizontal spacing of vertical bars shall not exceed 18 in. (450 mm) for exterior walls nor 24 in. (600 mm) for interior walls of monolithically cast silo groups.
Vertical steel shall be provided to resist wall bending moment at the junction of walls with silo roofs and bottoms.
Dr. Mohammed Arafa
35
Miscellaneous Reinforcement Details
Dr. Mohammed Arafa
36
Miscellaneous Reinforcement Details
Dr. Mohammed Arafa
37
Typical Conical hopper Reinforcement with circular Beam
Dr. Mohammed Arafa
38
Design Example
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 /250.444
c
y
o
f kg cmf kg cm
kg mγ
φ
µ
=
=
=
=
=
Dr. Mohammed Arafa
39
Design Example
D= 10m
D=4
0m
60m
D=2
0m
D=10m
1.5m
Dr. Mohammed Arafa
40
Design Example
( )( )
2
Assume angle of response = =2525 tan 25 2.33 1.53
1 sin 25 0.577
44 10 / 4 2.5
/ 40 /10 4
s sh h m
k
DR D m
DH D
ρ φ
π
π
= = ⇒
= − =
= = = =
= =
1 d
d
/ 40 /10 4upper H c 1.35lower 2/3 H c 1.75Hooper 1.5d
H D
c
= ==
==
Overpressure Factor Cd
Dr. Mohammed Arafa
41
Design Example
( )' 2
2
At the bottom of the silos Y=40-1.5=38.5m
1 7.65 t/m'
4.42 t/m
kY RRq ek
P kq
µγµ
− = − =
= =
( )
( )2 2
1.75 1.7 4.42 1065.74
2 265.74 17.4 cm /m ie. 8.7cm /m for each side
0.9 4200
p u
sty
C P DT ton
TAf
cm
φ
φ
× ×= = =
= = =×
At the bottom of the silos
Ring Tension
If slip forming will be used:
( )2 265.74 18.3 cm /m ie. 9.2cm /m for each side
0.95 0.9 42000.95sty
TAfφ
= = =× ×Dr. Mohammed Arafa
42
Design Example
Minimum Thickness
( )( )4sh
0.0003 200 10 1680 8 35f f 4.42 10= 7.5100f f 100 1680 35 2
s s ct
s ct
ε E nt T cm× ⋅ + −+ − × = = × ×
The thickness of silo walls shall be not less than 150 mm for cast-in-place concrete. Use Wall thickness t=20cm
Dr. Mohammed Arafa
43
Design Example
( )( )
( )( )
( ) ( )
t
2
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
Roff DL=0.15 10 4 11.8
LL 0.10 10 4 7.85
1.7 57.9 7.85 1.4 30 11.8 170.3ver
tonFriction V Y q R
atY V
ton
ton
P ton
γ
π
π
= × × =
= −
= = × − × =
× =
= × =
= + + + =
2,
',
170.3 122 kg/cm0.7 20 100
0.55 0.55 0.7 350 134.75
c vert
nw c c vert
f
P f fφ
= =× ×
= = × × = >
20.002 20 100 4 cm /mstA = × × =
Vertical Loads
Check for Buckling
The buckling does not control
Dr. Mohammed Arafa
44
Design Example
Design for the hopper
( ) ( ) ( )
[ ]( )
0
2
2 2
1.0
7.65 0.8 1 8.45 t/m
= weight of the material in hopper0.8= 4.1 0.75 5.8 84.4
32.5= 2 4.1 0.2 2 0.75 0.2 5.8 29.5
3Merdional forces and required reinforcing
1.7
y y
y
y
L
L
g
ymu
q q hat h m
qW
W ton
W ton
qF
γ
π
π
= +
=
= + × =
+ =
× × + × × =
=
( )( ) ( )
2st
1.44sin sin sin
1.5 8.45 2 4.1 84.4 29.51.7 1.4 59.2 ton/m4sin 60 2 4.1 sin 60 2 4.1 sin 60
59.2A 16.5cm /m0.9 4200
gL
mu
D WWD D
F
α π α π α
π π
+ +
× ×
= + + = × ×
= =×
5.0m
4.1
0.75
5.8m
Dr. Mohammed Arafa
45
Design Example
Hoop Reinforcement
2 2
2
2 2 2
2
2
1.51.72sin
sin cos
0.577 8.45 4.87 t/m4.87sin 60 8.45cos 60 5.765t/m
' 25tan 8.45 tan 30 4.67t/m
tan tan ' tan 30 tan 254.67t/m
1.5 5.1.7
tu
yn
n
tu
q DF
q P qwhere P kqqassume
qor q p
use q p
F
α
α
α
α
α
αα α
φθ
θ φ
× = = +
= = × =
= + =
=
= = = =+ +
= =
×=
( )
2st, hopper
765 2 4.159.6 ton/m
2sin 6069.6A 19.4cm /m
0.9 4200
× × =
= =×
Dr. Mohammed Arafa
46
Design Example
Design of the Circular Beam
33
90
100cm28.5
32.9r=467cm
33cm
90cm
90cm R=4.67m28.5
32.9
1
1
2
2
10090100576150
32.9 , 42.387.274.5
0.285 684 19.5 .
r
t
ababAx cm y cma cmb cmM t m
=====
= ===
= × =
Dr. Mohammed Arafa
47
Design Example
Design of the Circular Beam
33cm
90cm
90cm R=4.67m28.5
32.9
( )
( )
( )
2
2 2
5 32.9 /100 4.677.65 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 29.53
1.7 1.44sin sin sin
1.5 8.1 10 116.51.74sin 60
y
L
g
y gLmu
mu
R mq t m
W ton
W ton
q D WWFD D
F
π
π
α π α π α
π
= − =
= + − =
= + × =
= × × + × × × =
= + +
× ×= +
( ) ( )x
29.51.4 68.4 ton10 sin 60 10 sin 60
F cos 68.4cos 60 34.20.615 2.5 1.4 68.4sin 60 61.5
mu
y
F tonF ton
π
α
+ =
= = == × × + =
Dr. Mohammed Arafa
48
Design Example
Design of the Circular Beam
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
Dr. Mohammed Arafa
49
Design Example 2
10m
40m
5m
7m
φ50cm
( ) ( )( )( )
22
2
3 5 5 0.81.3 t/m
5LWπ
π= =
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.
at y=38.5 m ie. h=40mq=7.65 t/m2
p=kq=4.42 t/m2
Total LL=7.65+1.3=9 t/m2
Load on the slabLoad from wheat in hopper
Dr. Mohammed Arafa
50
Design Example 2
( ) ( )( )( )
22
2
2 3 5 5 2.58.33 t/m
5gWπ
π= =
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
WDLW
= × =
= + =
= × + × =
Dead LoadWeight of hopper forming fill
Slab weight assume 40 cm slab thickness
Dr. Mohammed Arafa
51
Design Example 2
Design of the slab HolesSlabs 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.
Dr. Mohammed Arafa
52
Design Example 2
Check for shear on slab
( )( )( ) ( ) ( )( )
228.4 5 0.3566
2 5 0.35
0.53 0.85 300 35 2 5 0.35 798
u
c u
V ton
V ton V
ππ
φ π
−= =
−
= − = >
Total ReactionTotal reaction at the bottom wall must includesFrom Roof, Material above the hopper, Material in the hopper, hopper filling form, Bottom Slab, Upper Wall, and Lower Wall
Dr. Mohammed Arafa
53
Design Example 2 Design a single rectangular concrete silo for storing peas. The bottom is a symmetrical pyramidal Hopper. The silo walls rest on the Hopper base which is supported by four columns. The Roof load ( DL = 150 kg/m2 and LL= 100 kg/m2).
Dr. Mohammed Arafa
Openning0.5x0.5m
30m
5m
7m3m
b=6m
a=4m
An Above Hopperb=6m
a=6m
Ground Floor Plan
' 2
2
3
'
350 /
4200 /
800 /250.296
c
y
o
f kg cmf kg cm
kg mγ
φ
µ
=
=
=
=
=