CALCULATION REPORT - arc-occitanie.fr€¦ · CALCULATION REPORT . SILO MODEL: Nominal diameter:...

CALCULATION REPORT SILO MODEL:

Nominal diameter: 7600 mmCylindrical height: 9120 mm

Total height: 10514 mmCapacity: 452 m3

SBH 760 / 8

Grain γ= 8,17 KN/m3

Wind vb= 0,98 KN/m2 General Method (vb= 145 Km/h)Snow qs= 0,784 KN/m2 General Method (qs= 80 Kg/m2)

Seismic cs=Roof type= nº ref. silos: NO REF. DRAWIN

AGRICONSULT PEV--SYM19-00260 30/01/2020

N.A. N.A.Non-structural roof

ANSI/ASAE EP433 DC1988 (R2011)

STATIC_CALCULATION_SBH_760_8_S0_N80_V100_D834_ANS_rev0

CONTENTS 1 SILO DESIGN .................................................................................................................................................3

1.1 GEOMETRY AND SILO DESCRIPTION ...................................................................................................3

1.2 GENERAL CHARACTERISTICS ................................................................................................................4

1.2.1 LOADS SUMMARY ...........................................................................................................................4

1.2.2 CONSTRUCTION DETAILS .................................................................................................................5

2 ACTIONS .......................................................................................................................................................6

2.1 GRAIN PRESSURES ...............................................................................................................................6

2.1.1 STATIC GRAIN PRESSURES WHILE FILLING ......................................................................................6

2.1.2 DINAMIC GRAIN PRESSURES WHILE UNLOADING ...........................................................................8

2.1.3 SUMMARY OF THE LOADS ON THE WALL AND VERTICAL STIFFENERS OF THE SILO ......................9

2.2 WIND LOAD ...................................................................................................................................... 10

2.3 SNOW LOAD ..................................................................................................................................... 11

2.4 SEISMIC LOAD ................................................................................................................................... 12

2.4.1 SEISMIC LOAD – HORIZONTAL COMPONENT ............................................................................... 12

2.4.2 SEISMIC LOAD – VERTICAL COMPONENT ..................................................................................... 13

2.5 OTHER LOADS ................................................................................................................................... 14

2.5.1 PEAK LOAD .................................................................................................................................... 14

2.5.2 SELF-WEIGHT ................................................................................................................................ 14

3 BODYSHEETS AND STIFFENERS CAPACITY ................................................................................................. 15

3.1 BODYSHEETS CAPACITY .................................................................................................................... 15

3.1.1 CROSS-SECTION RESISTANCE ....................................................................................................... 16

3.1.2 SHEAR RESISTANCE OF THE VERTICAL JOINT ............................................................................... 17

3.1.3 BEARING RESISTANCE OF THE VERTICAL JOINT ........................................................................... 18

3.1.4 SUMMARY OF BODYSHEETS CAPACITY ........................................................................................ 19

3.2 STIFFENERS CAPACITY ...................................................................................................................... 25

3.2.1 GEOMETRIC AND MECHANICAL CHARACTERISTICS ..................................................................... 26

3.2.2 SUMMARY OF STIFFENERS CAPACITY .......................................................................................... 27

4 BODYSHEETS CALCULATION ...................................................................................................................... 28

4.1 BASIS OF DESIGN .............................................................................................................................. 28

4.2 BODYSHEETS VERIFICATION ............................................................................................................. 29

5 STIFFENERS CALCULATION ........................................................................................................................ 30

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5.1 BASIS OF DESIGN .............................................................................................................................. 30

5.2 STIFFENERS VERIFICATION ............................................................................................................... 31

6 ANCHOR PLATE ......................................................................................................................................... 32

7 REFERENCE DRAWINGS ............................................................................................................................. 34

8 NORMATIVE, BIBLIOGRAPHY AND REFERENCES ....................................................................................... 35

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1 SILO DESIGN

1.1 GEOMETRY AND SILO DESCRIPTION The figure below shows a general elevation drawing of the silo.

Main dimensions and silo parameters are summarized below.

Diameter of the silo d c (mm) 7600Overall height of the silo B (mm) 9120Equivalent height surface H (mm) 9765Total height of the top pile of solid h tp (mm) 645Silo slenderness H/d c 1,28Flow type FUNNEL FLOW

Capacity V (m 3 ) 452Roof type Non-structural roofNumber of rings Na 8Number of bodysheets per ring 10Number of stiffeners per ring 30Useful height of bodysheets Δh (m) 1140

SILO GEOMETRY

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1.2 GENERAL CHARACTERISTICS

1.2.1 LOADS SUMMARY

In the following table are shown the main parameters of the different loads considered in the calculation, and the code in which it is based on.

Stored solids WHEAT

Density W (Ton/m 3 ) 0,834Angle of repose Ø r (°) 34Lateral pressure ratio K 0,50Wall friction coefficient μ 0,37Overpressure factor F 1,00

Wind pressure v b (m/s) 40

Snow pressure q s (Kg/m 2 ) 80

Seismic coefficient c s N.A.

SEISMICN.A.

General method based on qw

SNOWGeneral method based on qs

WIND

ANSI/ASAE EP433 DC1988 (R2011)GRAIN

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1.2.2 CONSTRUCTION DETAILS

The body of the silo is a cylinder made up of bolted metal sheets, called “bodysheets”, and U shape profiles, “stiffeners”, bolted to the wall sheets and equally distributed around the silo. While bodysheets will carry the grain component load normal to the surface, friction between grain and silo wall, wind, snow and roof loads eventually lead to vertical forces which are carried by the set of silo stiffeners. Bodysheets are cold-formed corrugated sheets manufactured from galvanized metal coils. The mechanical properties of the steel and type of galvanization used in silo bodysheets are summarized in the table below.

BODYSHEETS

Grade Standard fyb(N/mm2) fu(N/mm2) Galvanization

S 350 GD EN 10346 (2010) 350 420 Z600 MACO

The following table contains the mechanical properties of the material used for manufacturing the silo stiffeners.

STIFFENERS


S 350 GD EN 10346 (2010) 350 420 Z600 MACO

S 355 JR EN 10025 (2006) 355 470-630 Hot Deep Galvanization

Apart from bodysheets and stiffeners the S 350 GD steel grade is also used among others, to manufacture hopper silo sheets and some roof rafters. Roof sheets, on the other hand, are made of S 280 GD steel grade.


S 350 GD EN 10346 (2010) 350 420 Z600 MACO

S 280 GD EN 10346 (2010) 280 360 ZM250 MAC

Many other components such as silo roof collar, base plates or silo rings and legs in case of Big Hopper Silos, are made of S 275 JR


S 275 JR EN 10025 (2006) 275 430-580 Hot Deep Galvanization Note: While Z600 and ZM250 galvanization follow the rules given in EN 10346 (2015), Hot Deep Galvanization process in S 355 JR and S 275 JR grades follow the standard ISO 1461 (2009).

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2 ACTIONS

2.1 GRAIN PRESSURES

2.1.1 STATIC GRAIN PRESSURES WHILE FILLING

The American standard ANSI/ASAE, section 4.1.1, establishes a differentiation in the calculation of pressures on the walls of the body of the silos according to their slenderness. The classification of this slenderness, is a function of the flow and diameter of the silo following the rule below:

- Funnel Flow �HD

< 2 𝑤𝑤ℎ𝑒𝑒𝑒𝑒 𝐷𝐷 > 3; HD

< 1.3 𝑤𝑤ℎ𝑒𝑒𝑒𝑒 𝐷𝐷 < 3�

- Plug Flow �HD

> 2 𝑤𝑤ℎ𝑒𝑒𝑒𝑒 𝐷𝐷 > 3; HD

> 1.3 𝑤𝑤ℎ𝑒𝑒𝑒𝑒 𝐷𝐷 < 3�

Then the flow of the silo precedes to the calculation of three types of pressures: vertical (V (y)), horizontal (L (y)) and friction (Sv (y)), and two load situations: static and dynamic, according to the parameters represented on the left-hand side of the following figure. The types of flow are represented on the right:

Whatever the type of channel and silo classification, the static vertical, horizontal and friction pressures developed in the silo eventually result from the equations given below:

𝑉𝑉(𝑌𝑌)𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 =𝛾𝛾 𝐴𝐴

𝜇𝜇 𝐾𝐾 𝑈𝑈 �1 − 𝑒𝑒−𝜇𝜇 𝐾𝐾 𝑈𝑈

𝐴𝐴 𝑌𝑌�

𝐿𝐿(𝑌𝑌)𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝐾𝐾 𝑉𝑉(𝑌𝑌)𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑆𝑆𝑣𝑣(𝑌𝑌)𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝜇𝜇 𝐿𝐿(𝑌𝑌)𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

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Developing the expression given for the fiction pressure Sv, the vertical wall load per unit length at a height “Y” comes from the following expression:

𝑃𝑃𝑣𝑣 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = ∫ 𝜇𝜇 𝐿𝐿(𝑌𝑌)𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑑𝑑𝑌𝑌 = 𝑑𝑑𝑐𝑐4

[𝛾𝛾 𝑌𝑌 − 𝑉𝑉(𝑌𝑌)]𝑌𝑌0

Where:

A area of the cross section of the silo (m2). dc diameter of the silo (m). U Inside silo perimeter (m). μ Coefficient of friction with silo wall (dimensionless). ɣ Density of the stored material (Kg / m3). K Coefficient of lateral pressures (dimensionless). Y Height of interest in the calculation (m).

The maximum grain pressure values result at the bottom of the silo, considering in the formulation Y=Hc, where Hc is the height from the equivalent grain surface to the bottom of the silo.

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2.1.2 DINAMIC GRAIN PRESSURES WHILE UNLOADING

In the calculation of the dinamic pressures when the silo gets unloaded, while the equations applied for the static pressures calculation remain, an overpressure factor must be taken into account. Depending on the type of flow developed in the silo is shall be taken the following F overprresure factor values:

- Funnel Flow (𝐹𝐹 = 1) - Plug Flow (𝐹𝐹 = 1,4)

Then the expresions for the calculation of grain pressure under dinamic events are shown next:

𝐿𝐿(𝑌𝑌)𝑑𝑑𝑑𝑑𝑑𝑑𝑠𝑠𝑑𝑑𝑠𝑠𝑠𝑠 = 𝐿𝐿(𝑌𝑌)𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝐹𝐹 = 𝐹𝐹 𝐾𝐾 𝑉𝑉(𝑌𝑌)𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑆𝑆𝑣𝑣(𝑌𝑌)𝑑𝑑𝑑𝑑𝑑𝑑𝑠𝑠𝑑𝑑𝑠𝑠𝑠𝑠 = 𝜇𝜇 𝐿𝐿(𝑌𝑌)𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

𝑃𝑃𝑣𝑣 𝑑𝑑𝑑𝑑𝑑𝑑𝑠𝑠𝑑𝑑𝑠𝑠𝑠𝑠 = � 𝜇𝜇 𝐹𝐹 𝐿𝐿(𝑌𝑌)𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑑𝑑𝑌𝑌 = 𝐹𝐹 𝑑𝑑𝑠𝑠

4 [𝛾𝛾 𝑌𝑌 − 𝑉𝑉(𝑌𝑌)]

𝑌𝑌

0

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2.1.3 SUMMARY OF THE LOADS ON THE WALL AND VERTICAL STIFFENERS OF THE SILO

In this silo the maximum values obtained for Y or Zmax = Hc, are the following:

Horizontal filling pressure at the bottom P hf (Tn/m 2 ) 2,63Horizontal emptyng pressure at the bottom P hf (Tn/m 2 ) 2,63Vertical wall filling loads at the bottom P v (Tn) 5,49Vertical wall emptying loads at the bottom P v (Tn) 5,49 Note: The calculation of these values at every ring is presented in section 4.

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2.2 WIND LOAD The general method followed in the calculation of the horizontal action of wind on the vertical stiffeners of the silo considers the total wind pressure over the exposed area of the silo; roof, body and hopper where applicable, applying an eolic coefficient of 0.8. In the calculation of the wind effect over the silo it is assumed that the horizontal wind load is taken by the set of vertical stiffeners around it. In section 4 there is detailed information about load distribution and the mathematical method used in the calculation. Wind pressure design and wind rings silo details are included in the following table:

1000

Profile Φ 60 x 2 mmMaterial E-200 Z275 MACStandard EN 10305-3 (2011)

Wind ring type

Number of wind rings N v

Wind pressure (Kg/m2) Q v

Wind load is obtained for the most loaded stiffener of the system at every ring of the silo. As we go down in the silo the exposed area increases along with the wind effect and stiffener load at last. The expression below provides the maximum value of the vertical loads as a function of the bending moment at each silo ring i:

𝑄𝑄𝑤𝑤𝑠𝑠 = 𝑀𝑀𝑠𝑠 ∙4

𝑑𝑑𝑠𝑠 ∙ 𝑒𝑒𝑛𝑛𝑛𝑛𝑛𝑛𝑒𝑒𝑛𝑛 𝑜𝑜𝑜𝑜 𝑠𝑠𝑠𝑠𝑠𝑠𝑜𝑜𝑜𝑜𝑒𝑒𝑒𝑒𝑒𝑒𝑛𝑛𝑠𝑠= 𝑀𝑀𝑠𝑠 ∙

4

𝑑𝑑𝑠𝑠 ∙ 𝑑𝑑𝑠𝑠 ∙ 𝜋𝜋𝑑𝑑𝑠𝑠𝑠𝑠𝑠𝑠𝑑𝑑𝑒𝑒𝑑𝑑𝑒𝑒 𝑛𝑛𝑒𝑒𝑠𝑠𝑤𝑤𝑒𝑒𝑒𝑒𝑒𝑒 𝑠𝑠𝑠𝑠𝑠𝑠𝑜𝑜𝑜𝑜𝑒𝑒𝑒𝑒𝑒𝑒𝑛𝑛𝑠𝑠

Where: Mi bending moment developed due to wind at silo ring I (Kg m). dc diameter of the silo (m).

Substituting the bending moment term, QWi can be reformulated as follows:

𝑄𝑄𝑤𝑤𝑠𝑠 = 𝑑𝑑𝑠𝑠 ∙ 𝑍𝑍𝑠𝑠 ∙𝑍𝑍𝑠𝑠

2∙ 𝑄𝑄𝑤𝑤𝑠𝑠𝑑𝑑𝑑𝑑 𝑠𝑠 ∙

𝑑𝑑𝑊𝑊

𝑤𝑤

Where:

Zi distance between half of the ring i and ground (m). Qwind i horizontal load due to wind at silo ring i (kg). Positioned at Zi/2 it is obtained as the product between wind pressure and the exposed surface at ring height i. cw eolic coefficient (takes a value of 0,8).

𝑤𝑤 =𝜋𝜋 ∙ 𝑑𝑑𝑠𝑠

2

4 ∙ 𝑑𝑑𝑠𝑠𝑠𝑠𝑠𝑠𝑑𝑑𝑒𝑒𝑑𝑑𝑒𝑒 𝑛𝑛𝑒𝑒𝑠𝑠𝑤𝑤𝑒𝑒𝑒𝑒𝑒𝑒 𝑠𝑠𝑠𝑠𝑠𝑠𝑜𝑜𝑜𝑜𝑒𝑒𝑒𝑒𝑒𝑒𝑛𝑛𝑠𝑠

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2.3 SNOW LOAD This section refers to the snow load acting over the silo roof. Snow weight over the roof rest over their rafters, which eventually reach some of the stiffeners around the silo; precisely one stiffener per bodysheet at the very top ring. The general method calculation considers the snow pressure design given in the table below acting on the equivalent normal surface of the roof:

80Snow load (Kg/m2) Q n

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2.4 SEISMIC LOAD In the following table are summarized the main seismic action characteristics considered in the calculation:

N.A.Seismic rule according with Under the influence of seismic action both horizontal and vertical silo loads will be increased.

2.4.1 SEISMIC LOAD – HORIZONTAL COMPONENT

In the first place, when it comes to horizontal loads, there will be an overload represented by the term shown next:

∆𝑃𝑃ℎ = 𝐶𝐶𝑠𝑠 ∙ 𝛾𝛾 ∙ 𝐻𝐻𝑠𝑠 ∙𝐷𝐷2

Where:

Cs seismic coefficient. ɣ density of the material stored in (Kg/m3). Hc height from the equivalent surface to the bottom (m):

𝐻𝐻𝑠𝑠 =13

∙𝐷𝐷2

∙ tan ∅𝑟𝑟 + 𝐴𝐴

Where:

Ør natural slope angle of the storage material (°). A height from the bottom to ceiling (m).

Δh useful height of bodysheets (m). D diameter of the silo (m).

N.A.0,00

Seismic coefficient C s

Increase in pressure ΔP h (Ton) Note: Ør and A have been already calculated in sections 3 and 4 respectively. ΔPh" (Increase of the pressure by the seismic action) in the different sections of heights of bodysheet "Y" (in meters), are presented in section 7.

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2.4.2 SEISMIC LOAD – VERTICAL COMPONENT

As far as the effect of seismic activity over vertical loads, the force of the silo and grain considered an accelerated mass, will result in traction/compression loads acting on the stiffeners. Following the theoretical basis given in 2.2 for wind but considering now Qseismic i as the horizontal force due to seismic load acting at ring I, the formulation can be rewrite as follows:

𝑄𝑄𝑠𝑠𝑠𝑠 = 𝑑𝑑𝑠𝑠 ∙ 𝑍𝑍𝑠𝑠 ∙𝑍𝑍𝑠𝑠

2∙ 𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑑𝑑𝑠𝑠𝑠𝑠 𝑠𝑠 ∙

1𝑤𝑤

Where:

Zi distance between half of the ring i and ground (m). Qseismic i horizontal force positioned at Zi /2. Determined as the product between the total mass of the system (considering silo weight, conveyor and grain weight from the very top to the center of gravity of wing i) and the gravitational constant g (9,8 m/s2) (Kg)

𝑤𝑤 =𝜋𝜋 ∙ 𝑑𝑑𝑠𝑠

2

4 ∙ 𝑑𝑑𝑠𝑠𝑠𝑠𝑠𝑠𝑑𝑑𝑒𝑒𝑑𝑑𝑒𝑒 𝑛𝑛𝑒𝑒𝑠𝑠𝑤𝑤𝑒𝑒𝑒𝑒𝑒𝑒 𝑠𝑠𝑠𝑠𝑠𝑠𝑜𝑜𝑜𝑜𝑒𝑒𝑒𝑒𝑒𝑒𝑛𝑛𝑠𝑠

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2.5 OTHER LOADS

2.5.1 PEAK LOAD

Peak load is the load supported by the roof and eventually transmitted to the silo stiffeners. It includes both conveyor and catwalk weight. The table below shows the total load considered in the calculation:

1000Peak load S m (Kg)

2.5.2 SELF-WEIGHT

In the following table are summarized the different silo weight parts:

068601677619148

Wind Rings (Kg)Screws (Kg)Total self-weight (Kg)

Bodysheets (Kg)Stiffeners (Kg)Roof (Kg)

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3 BODYSHEETS AND STIFFENERS CAPACITY

3.1 BODYSHEETS CAPACITY Hoop tension on the silo wall sheet shall be balance by the design resistance of the bodysheet. Eventually the capacity of any bodysheet will take the minimum value between those given next:

- Cross-section resistance of the bodysheet - Shear resistance of the vertical joint - Bearing resistance of the vertical joint

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3.1.1 CROSS-SECTION RESISTANCE

In accordance with EN 1993-1-3: General rules – Supplementary rules for cold-formed members and sheeting the design resistance of a cross-section shall be determined from:

𝑁𝑁𝑠𝑠,𝑅𝑅𝑑𝑑 = min�𝑁𝑁𝑝𝑝𝑝𝑝,𝑅𝑅𝑑𝑑; 𝐹𝐹𝑢𝑢,𝑅𝑅𝑑𝑑� Where:

Npl,Rd Design plastic resistance to normal forces of the gross-cross section EN 1993-1-3. 6.1.2 (1).

𝑁𝑁𝑝𝑝𝑝𝑝,𝑅𝑅𝑑𝑑 =𝑜𝑜𝑑𝑑𝑠𝑠 ∙ 𝐴𝐴𝑔𝑔

𝛾𝛾𝑀𝑀0

Where:

fya Average yield strength of the bodysheet. Ag Gross area of the cross section. γM0 Partial safety factor equal to 1.

Fu,Rd Net-section resistance EN 1993-1-3. Table 8.4.

𝐹𝐹𝑢𝑢,𝑅𝑅𝑑𝑑 = min �1 + 3𝑛𝑛 �𝑑𝑑0

𝑛𝑛− 0.3� ; 1� ∙

𝑜𝑜𝑢𝑢 ∙ 𝐴𝐴𝑑𝑑𝑠𝑠𝑠𝑠

𝛾𝛾𝑀𝑀2

Where:

r = number of bolts at the cross section ⁄total number of bolts in the connection. u = min(2∙e2;p2) Where e2 and p2 are characteristic distances in the connection, see EN 1993-1-3. 8.3. fu Ultimate limit strength of the bodysheet material (MPa). Anet Net area of the cross section (mm2). γM2 Partial safety factor equal to 1,25.

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3.1.2 SHEAR RESISTANCE OF THE VERTICAL JOINT

In accordance with EN 1993-1-8: Design of joints. Table 3.4 the design shear resistance of individual fasteners subjected to shear and/or tension shall be determined from:

𝐹𝐹𝑣𝑣,𝑅𝑅𝑑𝑑 =𝛼𝛼𝑣𝑣 ∙ 𝑜𝑜𝑢𝑢𝑢𝑢 ∙ 𝐴𝐴

𝛾𝛾𝑀𝑀2

Where:

αv Depending on the type of class of the bolt: αv (classes 4.6, 5.6 and 8.8) = 0.6 αv (classes 4.8, 5.8, 6.8 and 10.9) = 0.5

fub Ultimate tensile strength of the bolt (MPa). A Tensile stress area of the bolt (mm2).

Note: remaining factors have been already introduced in previous sections.

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3.1.3 BEARING RESISTANCE OF THE VERTICAL JOINT

In accordance with EN 1993-1-8: Design of joints. Table 3.4. the design bearing resistance of individual fasteners shall be determined from:

𝐹𝐹𝑢𝑢,𝑅𝑅𝑑𝑑 =𝐾𝐾1 ∙ 𝛼𝛼𝑢𝑢 ∙ 𝑜𝑜𝑢𝑢 ∙ 𝑑𝑑 ∙ 𝑠𝑠

𝛾𝛾𝑀𝑀2

Where:

K1 Depending on the position of the bolt perpendicular to the direction of the load transfer:

For edge bolts: 𝐾𝐾1 = min �2.8 ∙ 𝑠𝑠2𝑑𝑑0

− 1,7; 2.5�

For inner bolts: 𝐾𝐾1 = min �1.4 ∙ 𝑝𝑝2𝑑𝑑0

− 1,7; 2.5�

αb Depending on the position of the bolt in the direction of the load transfer:

For end bolts: 𝛼𝛼b = min � 𝑠𝑠13∙𝑑𝑑0

; f𝑢𝑢𝑢𝑢𝑓𝑓𝑢𝑢

; 1�

For inner bolts: 𝛼𝛼b = min � 𝑝𝑝13∙𝑑𝑑0

− 14

; f𝑢𝑢𝑢𝑢𝑓𝑓𝑢𝑢

; 1�

fu Ultimate tensile strength of the bolt (MPa). d Bolt diameter (mm). t Bodysheet thickness (mm).


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3.1.4 SUMMARY OF BODYSHEETS CAPACITY

Type of joint "A" - A2x8.8 - DOUBLE JOINT ( 32 Bolts) - M10 - 8.8

THICKNESS (mm) NET SECTION (kN) SHEAR (kN) BEARING (kN) RESISTANCE (kN)

0,8 284,39 668,16 172,57 172,57

1 355,49 668,16 231,84 231,84

1,2 426,59 668,16 297,56 297,56

1,5 533,23 668,16 378,00 378,00

1,8 639,88 668,16 453,60 453,60

2 710,98 668,16 504,00 504,00

2,2 782,07 668,16 554,40 554,40

2,5 880,32 668,16 630,00 630,00

2,8 985,96 668,16 705,60 668,16

Type of joint "B" -B3x8.8 - TRIPLE JOINT (48 Bolts) - M10 - 8.8

RESISTANCE (kN) NET SECTION (kN) SHEAR (kN) BEARING (kN) RESISTANCE (kN)

0,8 284,39 979,97 253,10 253,10

1 355,49 979,97 340,03 340,03

1,2 426,59 979,97 436,42 426,59

1,5 533,23 979,97 554,40 533,23

1,8 639,88 979,97 665,28 639,88

2 710,98 979,97 739,20 710,98

2,2 782,07 979,97 813,12 782,07

2,5 880,32 979,97 924,00 880,32

2,8 985,96 979,97 1034,88 979,97

Type of joint "C" - C4x8.8 - QUADRUPLE JOINT (64 Bolts) - M10 - 8.8


1,5 533,23 1291,78 730,80 533,23 1,8 639,88 1291,78 876,96 639,88

2 710,98 1291,78 974,40 710,98

2,2 782,07 1291,78 1071,84 782,07

2,5 880,32 1291,78 1218,00 880,32

2,8 985,96 1291,78 1364,16 985,96

3 1056,38 1291,78 1450,40 1056,38

3,5 1220,69 1291,78 1692,13 1220,69

4 1395,07 1291,78 1933,87 1291,78

S B H 7 6 0 / 0 8 P a g e 19 | 35


Type of joint "E" - E5x8.8 - QUINTUPLE JOINT (80 Bolts) - M10 - 8.8


2 710,98 1648,13 1243,20 710,98 2,2 782,07 1648,13 1367,52 782,07

2,5 880,32 1648,13 1554,00 880,32

2,8 985,96 1648,13 1740,48 985,96

3 1056,38 1648,13 1853,60 1056,38

3,5 1220,69 1648,13 2162,53 1220,69

4 1395,07 1648,13 2471,47 1395,07

4,4 1564,15 1648,13 2718,61 1564,15

5 1760,64 1648,13 3089,33 1648,13

Type of joint "F" - F5x10.9 - QUINTUPLE JOINT (80 Bolts) - M10 - 10.9


2 710,98 1716,80 1243,20 710,98 2,2 782,07 1716,80 1367,52 782,07

2,5 880,32 1716,80 1554,00 880,32

2,8 985,96 1716,80 1740,48 985,96

3 1056,38 1716,80 1853,60 1056,38

3,5 1220,69 1716,80 2162,53 1220,69

4 1395,07 1716,80 2471,47 1395,07

4,4 1564,15 1716,80 2718,61 1564,15

5 1760,64 1716,80 3089,33 1716,80

Type of joint "H" - H6x10.9 - SEXTUPLE JOINT (96 Bolts) - M10 - 10.9


2,2 782,07 2088,00 1663,20 782,07 2,5 880,32 2088,00 1890,00 880,32

2,8 985,96 2088,00 2116,80 985,96

3 1056,38 2088,00 2256,80 1056,38

3,5 1220,69 2088,00 2632,93 1220,69

4 1395,07 2088,00 3009,07 1395,07

4,4 1564,15 2088,00 3309,97 1564,15

5 1760,64 2088,00 3761,33 1760,64

6 2112,77 2088,00 4513,60 2088,00

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Type of joint "I" - F7x8.8 - SEPTUPLE JOINT (112 Bolts) - M10 – 8.8


2,5 880,32 2360,83 2226,00 880,32 2,8 985,96 2360,83 2493,12 985,96

3 1056,38 2360,83 2660,00 1056,38

3,5 1220,69 2360,83 3103,33 1220,69

4 1395,07 2360,83 3546,67 1395,07

4,4 1564,15 2360,83 3901,33 1564,15

5 1760,64 2360,83 4433,33 1760,64

6 2112,77 2360,83 5320,00 2112,77

7 2441,38 2360,83 6206,67 2360,83

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The following figures show in detail the different bodysheet designs.

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S B H 7 6 0 / 0 8 P a g e 23 | 35


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3.2 STIFFENERS CAPACITY According to EN 1993-1-3: General rules – Supplementary rules for cold-formed members and sheeting. 6.1.3. the design resistance of a cross-section for compression Nc,Rd should be determined from:

𝑁𝑁𝑠𝑠,𝑅𝑅𝑑𝑑 =𝐴𝐴𝑠𝑠𝑓𝑓𝑓𝑓 ∙ 𝑜𝑜𝑑𝑑𝑢𝑢

𝛾𝛾𝑀𝑀0

Where:

Aeff Effective area of the cross-section (mm2). Following the method described in EN 1993-1-3. 5.5.3. fyb Basic yield strength of the stiffener material (MPa).


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3.2.1 GEOMETRIC AND MECHANICAL CHARACTERISTICS

The following table shows dimensions and mechanical characteristics of the vertical stiffeners:

STIFFENER MECHANICAL PROPERTIES

THICKNESS (mm)

A (mm)

B (mm)

Ixx (cm4)

Iyy (cm4)

SECTION (mm2)

1,5 68,6 20,6 23,43 67,53 355

2 67,8 21,0 31,24 89,08 474

2,5 67,0 21,4 39,98 106,90 592

3 66,2 21,8 46,26 128,19 711

3,5 65,4 22,2 53,72 149,20 829

4 64,6 22,6 60,92 170,12 948

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3.2.2 SUMMARY OF STIFFENERS CAPACITY

STEEL THICKNESS (mm) EFFECTIVE AREA (mm2) RESISTANCE (Tn)

S350

GD

- CO

LD F

ORM

ED

1,2 184,47 5,99 1,5 275,63 8,95 1,8 371,87 12,07

2,0 431,11 14,00

2,2 484,20 15,72

2,5 558,91 18,15

2,8 634,12 20,59

3,0 684,00 22,21

3,5 798,00 25,91

4,0 912,00 29,61

4,0+1,5 1187,63 38,56

4,0+2,0 1343,11 43,61

4,0+2,5 1470,91 47,76

4,0+3,0 1596,00 51,82

4,0+3,5 1710,00 55,52

4,0+4,0 1824,00 59,22

4,0+4,0+1,5 2099,63 68,17

4,0+4,0+2,0 2255,11 73,22

4,0+4,0+2,5 2382,91 77,37

4,0+4,0+3,0 2508,00 81,43

4,0+4,0+3,5 2622,00 85,13

4,0+4,0+4,0 2736,00 88,83

S275

JR -

HO

T RO

LLED

UPN 200 3220,00 103,92

UPN 220 3740,00 120,72

UPN 240 4230,00 136,54

UPN260 4830,00 155,88

UPN280 5330,00 172,01

UPN300 5880,00 189,76

UPN320 7580,00 244,63

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4 BODYSHEETS CALCULATION

4.1 BASIS OF DESIGN The equations presented in section 2.1.1 refer to grain pressures inside the silo. In order to compare the exerted loads with the resistance of the silo wall, both horizontal pressures due to grain and seismic load must be transformed into stresses. The resultant stress between bodysheets, as a result of any pressure normal to the silo wall, follows the expression below:

𝑄𝑄 = 𝑃𝑃ℎ ∙𝐷𝐷2

∙ ∆ℎ

Where:

Ph Horizontal pressure (Tn/m2). D Diameter of the silo (m). Δh Bodysheet useful height (m).

The total stress QTij between bodysheets acting on each ring resulting from the combination of the different

loads normal to the silo wall follows the next rule:

𝑄𝑄𝑇𝑇𝑠𝑠𝑗𝑗 = � 𝛾𝛾𝑠𝑠

𝑗𝑗𝑄𝑄𝑠𝑠𝑠𝑠 𝑄𝑄𝑇𝑇𝑠𝑠𝑗𝑗 = 𝛾𝛾𝐺𝐺𝐺𝐺

𝑗𝑗 𝑄𝑄𝐺𝐺𝐺𝐺𝑠𝑠 + 𝛾𝛾𝑆𝑆𝑆𝑆𝑗𝑗 ∆𝑄𝑄𝑆𝑆𝑆𝑆𝑠𝑠

Where:

QGHi Stress between bodysheets due to grain pressures in discharge at the lower end of ring i (Tn). See 2.1.1 for further information.

ΔQSFi Stress between bodysheets due to seismic load at the lower end of ring i (Tn). See 2.4.1 for further information.

γtj Combination value of a design situation t for load combination j.

Along with EN 1990, Annex A in EN 1991-4 provides guidance in the combination of the solid stored load with other actions. Partial and combination factors, γ and ψ respectively, will take the following values.

ACTION COMBINATIONS – BODYSHEET DESIGN

C1 CS

Short title (t) - Design situation γ γ

GH - Grain discharge 1.5 1

SF - Seismic action and full silo 1 1

Note: C1 combination corresponds to an ordinary type of combination while CS represents a seismic combination.

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4.2 BODYSHEETS VERIFICATION

1 0,68 4,44 0,00 4,44 2,96 4,44 0,80 A 2x 8.8 17,61

2 1,06 6,90 0,00 6,90 4,60 6,90 0,80 A 2x 8.8 17,61

3 1,40 9,10 0,00 9,10 6,06 9,10 0,80 A 2x 8.8 17,61

4 1,70 11,06 0,00 11,06 7,38 11,06 0,80 A 2x 8.8 17,61

5 1,97 12,83 0,00 12,83 8,55 12,83 0,80 A 2x 8.8 17,61

6 2,22 14,40 0,00 14,40 9,60 14,40 0,80 A 2x 8.8 17,61

7 2,43 15,81 0,00 15,81 10,54 15,81 0,80 A 2x 8.8 17,61

8 2,63 17,08 0,00 17,08 11,38 17,08 0,80 A 2x 8.8 17,61

Thickness (mm)

Type of joint

Bodysheet capacity (Tn)Ph(Tn/m2) QGH (Tn) ΔQSF (Tn) QT

C1 (Tn) QTCS (Tn) QT

MAX (Tn)Nº

Rings

Note: See section 3.1 to find detailed information about the calculation of bodysheet resistances. QTMAX corresponds to the max value between QT

c1 and QTCS.

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5 STIFFENERS CALCULATION

5.1 BASIS OF DESIGN The total stress resulting from the combination of vertical actions acting on each stiffener QTi

j is determined using the following expression:

𝑄𝑄𝑇𝑇𝑠𝑠𝑗𝑗 = � 𝛾𝛾𝑠𝑠

𝑗𝑗𝜓𝜓𝑠𝑠𝑗𝑗𝑄𝑄𝑠𝑠𝑠𝑠 𝑄𝑄𝑇𝑇𝑠𝑠

𝑗𝑗 = 𝛾𝛾𝐺𝐺𝐺𝐺𝑗𝑗 𝑄𝑄𝐺𝐺𝐺𝐺𝑠𝑠 + 𝛾𝛾𝑊𝑊

𝑗𝑗 𝑄𝑄𝑊𝑊𝑠𝑠 + 𝛾𝛾𝑆𝑆𝑆𝑆𝑗𝑗 𝑄𝑄𝑆𝑆𝑆𝑆𝑠𝑠 + 𝛾𝛾𝑆𝑆𝑆𝑆

𝑗𝑗 ∆𝑄𝑄𝑆𝑆𝑠𝑠 + 𝛾𝛾𝐷𝐷𝐷𝐷𝑗𝑗 𝑄𝑄𝐷𝐷𝐷𝐷𝑠𝑠

Where:

QGVi Vertical load acting on the silo stiffeners due to grain pressures at the lower end of ring I (Tn). See 2.1 for further information.

QWi Vertical load acting on the silo stiffeners due to wind at the lower end of ring i (Tn). See 2.2 for further information.

QSNi Vertical load acting on the silo stiffeners due to snow at the lower end of ring i (Tn). See 2.3 for further information.

ΔQSFi Vertical load acting on the silo stiffeners due to seismic load at the lower end of ring i (Tn). See 2.4.2 for further information.

QDLi Vertical load acting on the silo stiffeners due to dead load at the lower end of ring i (Tn). Dead load includes silo self-weight (bodysheets, stiffeners, roof, bolts plus hopper and silo legs if appropriate) plus the extra weight due to conveyor and catwalk. See 2.5 for further information.

γtj Combination value of a design situation t for load combination j.

Partial and combination factors, γ and ψ respectively, will take the following values.

ACTION COMBINATIONS – STIFFENERS DESIGN

C1 CS

Short title (t) - Design situation γ γ

GV - Grain discharge 1.5 1,5

W – Wind 1,5 0,3

SN - Snow 1,5 1

SF - Seismic action and full silo 0 1

DL – Dead load 1,35 1

Note: C1 combination corresponds to an ordinary type of combination while CS represents an seismic combination.

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5.2 STIFFENERS VERIFICATION

1 0,18 0,03 0,36 0,00 0,18 1,25 0,47 1,25 1,5 8,95

2 0,48 0,07 0,36 0,00 0,20 2,00 0,94 2,00 1,5 8,95

3 0,89 0,13 0,36 0,00 0,22 3,04 1,59 3,04 1,5 8,95

4 1,41 0,22 0,36 0,00 0,23 4,37 2,42 4,37 1,5 8,95

5 2,03 0,32 0,36 0,00 0,25 5,94 3,39 5,94 1,8 12,07

6 2,74 0,45 0,36 0,00 0,26 7,73 4,50 7,73 1,8 12,07

7 3,52 0,60 0,36 0,00 0,28 9,73 5,73 9,73 2,5 18,15

8 4,37 0,76 0,36 0,00 0,30 11,92 7,07 11,92 2,5 18,15

Thickness (mm)

Stiffener capacity (Tn)QSN (Tn) ΔQsF (Tn) QDL (Tn) QT

C1 (Tn) QTCS (Tn) QT

MAX (Tn)Nº

Rings QGV (Tn) QW (Tn)

Note: see section 3.2 for detailed information about the calculation of bodysheet resistances. QTMAX corresponds to the max value between QT

c1 and QTCS.

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6 ANCHOR PLATE

Details about the anchor plate and design load applied for its calculation is provided in the table below:

BF28800

18016025

11,92

tDESIGN LOAD

FEdMAX (Ton)

PLATE DIMENSIONS

AB

Type of anchor plate

A BASE PLATE (mm 2 )

To following figure provides information about the notation of the parameters applied in the calculation, for both standard stiffeners plates and UPN type of stiffeners plates:

The following expression provides the bearing width of the base plate (EN 1993-1-8: 2005):

𝑑𝑑 = 𝑠𝑠 �𝑜𝑜𝑑𝑑

3 𝑜𝑜𝑗𝑗𝑑𝑑𝛾𝛾𝑀𝑀𝑀𝑀

Where: t Thickness of the anchor plate (mm). fy Yield strength of the anchor plate. 275 N/mm2. γMo Partial safety factor EN 1993-1-1. γMo = 1.1.

C

A

A'

C

cA

SECTION A-A

A(mm²)

C

A'

<c <cC

SECTION A'-A'

B

A(mm²)

B

c

A

A

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fjd Bearing resistance. Represents the maximum concrete resistance and it is given by the following expression:

𝑜𝑜𝑗𝑗𝑑𝑑 = 3 𝛽𝛽𝑗𝑗𝑜𝑜𝑠𝑠𝑑𝑑 Where:

β Foundation joint material coefficient. β = 2/3. fcd Compressive strength design value for concrete EN 1992 1-1. 3.1.6.

𝑜𝑜𝑠𝑠𝑑𝑑 =𝑜𝑜𝑠𝑠𝑐𝑐

𝛾𝛾𝑠𝑠

Where: fck Characteristic value of the compressive concrete resistance.

γc Partial safety factor for concrete. γc=1,5. Working on the expressions above, we can obtain the bearing width factor c and eventually the effective area Aeff of the base plate. The following table provides the intermediate and final results of the expressions previously introduced.

CONCRETE C20/25fck (N/mm 2 ) 25fcd (N/mm 2 ) 16,67fjd (N/mm 2 ) 33,33

c (mm) 40Aeff (mm 2 ) 14799

Finally the design compressive resistance provided by the anchor plate follow the expression below:

𝐹𝐹𝐶𝐶,𝑅𝑅𝑑𝑑 = 𝑜𝑜𝑗𝑗𝑑𝑑 𝐴𝐴𝑠𝑠𝑓𝑓𝑓𝑓

It shall be verified the following:

𝐹𝐹𝐶𝐶,𝑅𝑅𝑑𝑑 ≥ 𝐹𝐹𝐸𝐸𝑑𝑑𝑀𝑀𝐴𝐴𝑀𝑀

F C,Rd (Ton) 50,34FEd

MAX (Ton) 11,92OK

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7 REFERENCE DRAWINGS NO REF. DRAWINGS AVAILABLE

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8 NORMATIVE, BIBLIOGRAPHY AND REFERENCES - ANSI/ASAE EP433 DEC01 - EN 1993-1-8 - Eurocode 3 - Design of steel structures - Part 1-8: Design of joints - EN 1993-1-1 - Eurocode 3 - Design of steel structures - Part 1-1: General rules and rules for buildings - EN 1993-1-3 - Eurocode 3 - Design of steel structures - Part 1-3: General rules. Supplementary rules for cold-formed members and sheeting - http://www.symaga.com

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http://www.symaga.com/

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