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11. Silos and tanksLoading, steel structure of walls and supports.

Design is governed by EN 1993-4.

Silos - for storing granular solids

Tanks - for storing liquid products

Gasholders - for storing gas

bunkers

silos

low-pressure (< 2 kPa)

high-pressure (part. spherical)

of steady volume

of variable volume

dry gasholder

(piston ceiling)

water gasholder

(telescopic)

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OK3 2

Helical water gasholder

(without supporting stanchions)

discharged filled

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OK3 3

Water gasholders with supporting stanchions

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Silos

Serve for storing granular solids. They are divided into:

Actions on silos (EN 1991-4)

z pw

pv pwph

Z Z Z

pvph

unit weight Fk angle of internal friction

internal friction factor

F loading factor

exponential decrement: see Eurocode

Another: wind, snow, discharge loadings,

local loading, temperature, settling ofsupports ...

245tg2Coefficient of active earth pressure:

plan area isA

A,h 51

(angle of internal friction)

A,h 51

>

Bunkers Silos

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Analysis and design of silos (EN 1993-4-1)

3 consequence classes: Class 1, 2, 3

Class 1: Simple structures, up to capacity 100 t, simplified actions.

- membrane theory may be used, with simple formulas for boundary disturbance

and asymetric loading.

Checks for:- global stability and static equilibrium,- strength of the structure and joints,

- stability (global and local formulas given in Eurocode),

- cyclic plastification,

- fatigue,

- SLS (deflections and vibrations ).

Design allowance for corrosion and abrasion min. 2 mm is recommended!

for Class 1 may be ignored

Cylindrical silos (shell):

tph

D = 2r

wall of unstiffened cylinder:

from equilibrium (membrane theory)

dxdndxdrp h =

n

dr

dnph

r

d

n

n

dn

x

membrane circumferential tension force in cylinder wall:

ydhEd, ftrpn

cylinder

hopper

ring

yd

hi.e.f

rpt

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- meridional force (vertical, from weight and friction):

Strength check (Ilyushin yield criterion):

Edx,n

yd2Ed,Ed,Edx,

2Edx, ftnnnn

wall of conical hopper:

from equilibrium of vertical forces in ring the meridional force:

sin2

Ed

dr

Vn

=

pressure from

cyllinder content V1

V2

n n

Approximate check of hopper wall:

udEd, 90,02,1 ftn recommended for asymmetrical loading

Transition junction

supports

stiffening ring

(N, M)

n

loading of the ring:

(for M2 =1,25)

V1 + V2

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tstiffeners

(considers own cross-section

+ effective width of plate 30 t)

det.

Planar-sided silos

Approximate circumferential compressive force in the junction (effective area of

the ringAet is given in Eurocode):

andsinrnN Ed,Ed ydet

Edf

A

N

unstiffened web plates

webs with stiffeners

For Class 1 silos: 1st order analysis is possible.

Resulting internal forces need to be checked for strength

and stability.

Except strength checks the stability (buckling) of the shell need to be assessed:

in vertical direction,

in horizontal direction (due to wind and possible depression at discharge).

Check formulas (critical values of internal forces, stresses) are given in Eurocode.

Complex checks require FE analysis for all kinds of loadings.

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OK3 8

Analysis of supports

frame support columns (needed for free passage):

truss structure:

Lcr

= h

1st order analysis may be used, no sway.

Lcr= 2h

can be considered with infinite () rigidity.

h

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Tanks

Acc. shape: cylindrical vertical, cylindrical horizontal, spherical, rectangular, other.

Acc. internal pressure: low-pressure (up to 20 mbar = 2kPa), high-pressure.

Cylindrical tanks

roof structure with

circumferential (primary)

ring or

floating sealed

piston (for oil), primary ring,

possibly with roof

Horizontally placed cylinders Spherical tank

saddles

rings

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Design (EN 1993-4-2)

3 consequence Classes: Class 1, 2, 3

Class 1: Simple structures for agriculture or tanks containing water.

- membrane theory may be used, with simple formulas for boundary disturbance

and asymetric loading.Checks for (roof, webs, for bottom use FEM):

- global stability and static equilibrium,- strength of the structure and joints,

- stability (global and local formulas given in Eurocode),

- cyclic plastification,

- fatigue,

- SLS (deflections and vibrations ).

Simplified relations

Required thickness of cylindrical tank web:

yd

d

f

rpt= - where design loading by liquid and overpressure:

yd2 f

rpt=

dFd qHp unit weight

design overpressure

above liquid level

For spherical tanks:

Ht

D = 2r

(one half in comparison to the above)