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1 The Islamic University of Gaza Department of Civil Engineering Analysis of Reinforced Concrete Silos Dr. Mohammed Arafa

# Conc Silos 20101

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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

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Properties of Granular Materials

Dr. Mohammed Arafa

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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

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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

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

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Regular Polygonal siloHorizontal Forces Due to Stored Material

( ) sin21 cosdesT p a θ

θ = −

Dr. Mohammed Arafa

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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

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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

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

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

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

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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

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

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

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

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

Pyramidal hopper

Dr. Mohammed Arafa

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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 = × × =

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

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

= × =

= + =

= × + × =

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

=

=

=

=

=