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SIMULATION AND ANALYSIS OF RECTANGULAR WALL OF GROUND ELEVATED STEEL BUNKER WITH TRANSVERSE SHEAR DUE TO WIND LOAD

Elavenil S1* and Chaugule Vishal S2,*

1Professor, Structural Engineering Division, SMBS VIT University, Chennai, India

2PG student, Structural Engineering Division, SMBS VIT University, Chennai, India

*Corresponding Author:
Elavenil S
Professor, Structural Engineering Division
SMBS VIT University, Chennai, India
E-mail: s.elavenil@vit.ac.in
Chaugule Vishal S
PG student, Structural Engineering Division
SMBS VIT University, Chennai, India
E-mail: vishalchaugule13@gmail.com

Received Date: 17 June, 2017 Accepted Date: 24 November, 2017

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Abstract

Bunker are tall structures used for store the different types of materials like Portland cement, different granular materials, carbon black, coal, sawdust etc. They are subjected to many different static and dynamic loading. It is very difficult to determine the magnitude and distribution of stresses and their corresponding failure modes. The design and analysis of a hopper for pea collection in a boiler plant is carried out. The hopper collects the pea blown from the boiler soot blowers. The objective is to establish the design load. The design load is decided on the basis of two cases. The first case is hopper full of pea case and second one is hopper full of water. Based on the two cases the maximum pressure is considered as the design load. Also the Hopper has a static head of gas pressure. A typical Hopper is taken and the thickness of the plate is decided. Then a procedure is developed for the spacing and size of the stiffeners. The stiffeners used are wide flange I-beams. The hopper is modeled using ANSYS finite element software and the stresses obtained are compared with analytical work with finite element modeling.

Keywords

Finite element analysis, ANSYS, Load Calculation, Wind load

Introduction

Bunkers are the containers designed for storingand loading granular materials. There are two types of bins namely “shallow bins”, called “bunkers”, and “deep bins” called “bins”. The important difference between the two is the behavior of the stored materials. This behavior is influenced by both bin geometry and the characteristics of stored materials. Material pressure against the walls and bottom are usually determined by one method for bins and by another for bunkers. Bins and bunkers are made from different structural materials and of different shapes in cross-sections.

In this investigation, the objective is to provide to the development of design guidance for steel hoppers considering measures for wind load, seismic load, material load, dead and live load.

The height to depth ratio is considered in the analysis of horizontal pressure at different height.

The stresses are determined in the hopper and a new methods are developed for the design for hopper system. The analysis is carried out manually and using ANSYS analysis approach.

Literature Review

Dr. Alice Mathai In this study they concluded that many different static and dynamic loading conditions, mainly due to the characteristics of stored materials (Sergio and Luis). It is very difficult to determine the magnitude and distribution of stresses. In this study, a steel silo stiffened externally with stiffeners at equal height and length is adopted and a linear static analysis is conducted to find out the stresses and displacement occurring in the steel silo. In this study they are also studied the effect of wind loads on the silo.

Osama Suleiman Saada In this study the problems encountered on a flow obstructions and discontinuous flow resulting in doming and piping in hoppers (Vidal, et al., 2008). This problem is of interest to a variety of industries such as chemical processing, granular, detergents, ceramics and cement. An objective of this study is to use finite element analysis is produce to find out the result. In This study both a numerical and a experimental methods are adopted.

Couto Yáñez In this study they analyzed Different types models have been Proposed for analyzing pressure distributions at the opening of the gate of the hopper (Sadowski and Rotter, 2011). When the grain outlet is eccentric these types of the problem is occured. To solving this type of problem finite element analysis can be applied. many research investigators are now investigating the use of finite element methods in silo design.

C.O.C. Oko This paper presents the design parameters for conical hopper, using MS Excel sheet (Ding, et al., 2011; Shelly, et al., 2014). In thisthis study popular range of the wall friction angles for different food powders in common use. The opening diameter, applied stress, angle and the flow factor are the design parameters used in this study. Also, the physical properties data of the ten food powders served as input parameters

C.O.C. Oko (2011) In This paper they design a spreadsheet is used for the design of mass flow of conical and wedge hoppers (Hotała and Skotny, 2014). The Jenike’s hopper design charts for mass flow were curve fitted. The relationships obtained were used together with other relevant expressions to develop an add-in tool for the determination of the pertinent hopper design parameters.

Studied reinforced concrete cylindrical silo

Desh Bandhu Mukherjee In case of long cylindrical steel silo ring stiffeners are provided at intermediate levels of the cylindrical wall in order to reduce this ovalisation effect due to wind load (Zhao, et al., 2013). But, in case of reinforced concrete silo, ring stiffeners are not normally provided to avoid construction hazards during slip forming. After a brief review of the previous investigations in connection with the same, it has been observed that wind pressure distribution in cylindrical silo wall had been taken into consideration for the purpose of pre-buckling and post-buckling analysis of mainly steel silo.

John Michael Rotter(2012), Elevated light gauge silos usually have a conical discharge hopper at the bottom (Fisher, 1966). Although this hopper often carries much of the total weight of the stored solids. In this paper the "light gauge" term is used here to describe the class of cold-formed silo structure. which is not restricted by a nominal minimum plate thickness requirement ( 6 mm).

Dimensions, Loads and material Properties of stiffened steel silo

Dr. Dolly Thomas, In this study the steel silo adopted for used to storing cementmaterials (Alice, et al., 2015; Adem, et al., 2009). it consist of a cylindrical portion fitted with external stiffeners and in longitudinal directions, a bottom hopper and roof with an opening at the top. The cylindrical portion rest on staging support. The dimensions used in this study are as follows:

Radius of cylindrical portion= 1.75 m

Height of the cylindrical portion=12 m

Silos roof has slope=60°

Material properties of the steel,

Poisson’s ratio=0.3

Specific weight=78.5 Kn/m3

The internal pressure of the silo was determined using Janssen’s theory. silo being a tall structure is also invariably affected by wind loads are important factor to be considered in the design of the silo. The distribution and magnitude of wind pressure on silo structure is to be calculated in accordance with IS875 (part-3)-1987. And the silo model is analyzed by using ANSYS 14.5 Software.

Different methods for the classification of bunkers and bin

The designer must classify the structure as a shallow bin or bunker and a deep bin or bin. For such classification the following two empirical approximations are widely used by designers (Alauddin and Sohrabuddin, 1995; IS 4995 (Part II - 1974 ), 1996).

First method

By Dishinger,

H > 1.5*(A)^0.5

By soviet code,

H > 1.5*a

Where

H= The depth of vertical wall

A= The horizontal cross- section of the inside of the bin

a= The Shorter wall of rectangular bin.

If the bin in question satisfies either of the above, it is considered a deep bin. If it satisfies neither rule, it is considered to be a shallow bin or bunker.

Second method

This method is based on the position of the plane of the rupture of the stored materials.

The plane of the rupture is determined by the coulomb theory. If friction against the wall is neglected considering the case of a vertical wall and horizontal top surface, then the coulomb plane of rupture is midway between the angle of repose φ and the vertical wall. If the rupture plane intersects the top surface of the stored material, the bin is bunker otherwise it is bin (Anand and Hemant, 2013; IS 5503 (Part I-1969), 2005).

However, considering the location of the plane of the rupture, there are different approaches. It is considered that the plane of rupture should start either at the bottom of the hopper.

Structural systems of square and rectangular bunkers and bins

Bunkers and bins may be symmetrical or nonsymmetrical about either, or both, principal axes, according to the location of the discharge opening. Rectangular bunker and bins usually have pyramidal bottoms with one or more square, circular or elongated discharge openings. Flat bottoms are seldom used since the undesirable dead storage reduces the efficiency of the material flow.

The slopes of the bottom parts of the bunkers and bins must be so inclined that the bunker or bin is selfcleaning. And the line of the least slope must not be excessively flat. This bottom part is called a hopper and has pyramidal shape. There are symmetrical hopper, unsymmetrical hopper, and eccentrically hoppers.

Square and rectangular bunkers

Shallow bins or bunker are designed for storage and loading of granular materials. The volume of the bunkers is defined by the technological requirements. Bunkers are designed either as separate structures or they are constructed as parts of the industrial building. In the first case the bunker consists of the storage part, carrying structure and the gallery above the bunker figure. between the transverse frame of the bunker, are placed the longitudinal carrying panels which are simultaneously the walls of the bunker. Also in the planes of transverse frames are placed the transverse panels which constitute the walls of the bunker. The longitudinal and transverse panels are supporting all vertical loadings and horizontal thrust as well as the weight of the suspended hoppers. The spans of the longitudinal panels may be greater than the spans of the transverse panels. In this case the intermediate transverse panels transfer Loadings on the longitudinal panels. In the case bunker installed in the buildings, the bunker is supported by the beams of the structure itself.

The height of the vertical walls of the bunker is usually not greater than 1.5 times that of the maximum dimensions of the bunker in plan.

Depending on the locations of the openings, the bunkers may have one or two axes of symmetry or may be unsymmetrical. It is advisable to design the bunker with a symmetrical disposition of the openings.

Square and rectangular bins

Bins of rectangular or square cross-section in plane may be designed either as having a single cell, single row of cells, multiple cells bins.

Sometimes it is necessary to design a bin consisting of a combination of square and rectangular cells. Dimensions in plane of square or rectangular bins are from 14 feet to 18 feet.

The walls of the rectangular cells are under tensile forces and bending moments. For a structural analysis of the multi cell structure it is necessary to consider the influence of a single loaded cell on the distribution of the bending moments.

Multi cell rectangular bins are supported by columns at the corners, their walls act as panels. These panels support the weights of the wall, roof and the load from the hopper.

Functional design of square and rectangular bins Types of bins

In selecting a type and size of bin the following three types are used in industry according to their pattern of flow.

A. Mass-flow.

B. Funnel-flow. and

C. Expanded-flow.

The type of flow pattern which develops when solids are withdrawn from a bin significantly affects the reliability and uniformity of flow and therefore. The bin loads.

Mass – flow bins

Mass–Flow bins of square and rectangular crosssection usually consist of a vertical cylinder and mass-flow hopper figure.

When the gate of a mass- flow bin is opened or its feeder started the total volume of solid is in motion. Mass- flow bins have the following characteristics:

a. The total volume of stored solid is available for process by gravity.

b. Channeling, hang- ups, surging, and flooding do not occur. Provided in case of powder no attempt is made to withdraw it faster than its inherent rate of discharge.

c. flow is relatively uniform, so that steady-state flow can be closely approached and an analysis based on steady- state flow can applied with confidence.

d. A First-in first -out flow pattern, which is desirable for solids that deteriorate during storage and essential in chemical reactors, is readily obtained. This flow pattern is also desirable when segregation must be taken into account.

Funnel-flow bins

Funnel- Flow bins generally may consist of a vertical cylinder of rectangular cross-section and a flatbottom floor or non-mass flow hopper figure.

The solid in a funnel-flow bin flows toward the outlet in a channel formed within the stable solid. The flow channel is typically circular in cross- sections and usually assumes a conical shape widening upward from the outlet. The included angle of the cone for a given material depends on its moisture content, temperature, time of storage, and the sequence and rate of charge and draw. In a tall bin the cone may intersect the bin wall. Funnel-flow bins are useful for storing hard, abrasive, lumpy solids because there is little wear of the hopper walls. Funnel flow bins have the following characteristics:

a. Only a small portion of the stored solid is in motion during the draw.

b. A first-in first-out flow sequence prevails. The solid surrounding the flow channel at the bottom of the bin remains at rest until the flow channel is completely empty. This leads to consolidation,caki ng,deterioration, spontaneous combustion of coal, and oxidation of ores.

c. Any solid which remains at rest under pressure for a long period of time may gain strength and obstruct flow. This may lead to piping.

d. Stress analysis is somewhat unreliable because of the unsteady flow.

Expanded-flow bins

Several mass- flow hopper-feeder units can be placed under one large funnel- flow bin.

The hopper forces the flow channel to expand to a size large enough to eliminate the possibility of ratholing, to reduce the segregation to an acceptable level, and to ensure de-aeration and smooth flow. This type of bin is useful for the storage of large quantities of nondegrading solids such as ores. A low- level indicator can be placed on the mass- flow hopper.

Hoppers

The success of bin operations depends largely on the design of the hopper. The ease with which the material flows and converges towards the opening depends almost entirely on the shape of the hopper and the smoothness of the hopper and the smoothness of its walls.

A symmetrical pyramidal hopper may have four walls inclined, or two walls inclined, or two vertical. There are also eccentric pyramidal hoppers having single vertical and three inclined walls or two vertical and two inclined wall. Hoppers with one or more vertical walls are perfectible. The slotted outlets to prevent funneling and assure mass flow, but a feeder over the full length of the slot is necessary to remove the solid.

Square and rectangular bins in which cohesive and non-flowing materials are stored may require an eccentric hopper, figure stable arches are less likely to form in these hoppers because the solids tend to slide down the vertical wall. Rectangular gravity –flow bins with flat bottom and multiple circular openings are commonly used to store granular solids. Such bins are low in cost and occupy less vertical space than bins with a single hopper outlet. To maximize the live storage the openings should be spaced as to permit the flow patterns above the openings to intersect.

Outlets of hopper

The outlets of hopper must be large enough to assure an unobstructed flow at the required rate. Unless the outlet for granular materials is larger than several particle sizes, the flow may be obstructed by the interlocking of large particles. Furthermore, certain minimum dimensions are necessary to prevent cohesive doming and piping figure.

It is important distinguish between the actual area of an outlet of a hopper, bin, or storage pile and the effective area, which is the area through which the solid flows. In the particular case of rectangular outlets, the effective area may be only a small part of the actual area.

Archings

The solid in-a-flow channel may form an arch if the channel is wedge-shaped and a dome if it is conical figure.

The stress S1 at the abutment must be less than the unconfined compressive strength Fc of the solid if the arch is stable.

Analytical Investigations

Design considerations

Loads

In the design of bins and bunkers the following loads are considered:

1. Dead load of the structure itself and items supported by the structure.

2. Live loads as follows :

a. Forces from stored materials.

b. Changes in the above due to filling and emptying.

c. Wind.

d. Snow, and

e. Seismic forces on structure and stored material.

3. Thermal stresses due to stored materials (especially important in long bin groups).

Bin loading from stored material

Material stored in the bin applies lateral forces to the side walls, vertical forces due to friction, to the side walls, vertical forces to horizontal bottoms and both normal and extension-al forces to inclined surfaces. The static values of these forces, resulting from materials at rest, are all modified during withdrawal of the material. In general all forces will increase, so that loads during withdrawal tend to control design.

Forces applied by stored materials may also be affected by moisture changes, by compaction, and by settling which may accompany alternate expansion and contraction of the walls during daily or seasonal temperature changes

Details of Structure

According to the typical design properties of granular materials the height of the bunker should vary. If Specific weight of the granular material is less than 50 lb/ft3,the height of the bunker is above 10 m and the specific weight of the granular material is more than 50 lb/ft3 the height of the bunker is below 10 m. The material details are shown in Table 1. The dimension of the bunker is shown in (Figure. 1).

icontrolpollution-Dimensions

Figure 1: Dimensions of bunker.

Material Specific weight ? lb/ft3 Coefficient of friction against steel Angle of repose f
Cement 100 0.300 250
Peas 50 0.263 250
Wheat 50 0.414 250
Iron ore 165 0.364 400
Lime 75 0.300 350

Table 1. Material details

Selection of material:

Specific Weight of the materials = 7.855 kN/m3

Coefficient of friction against steel = 0.263

Angle of repose = 25°

Dimensions of the bunker:

H=Height of the bunker = 12.192 m

H1=Height of the hopper = 2.6212 m

H2=height of the column below bunker = 6.096 m

B= Width of the longer wall = 6.096 m

A= width of the shorter wall = 3.6578 m

Calculation of loadings

In the calculation of loadings the following design load are calculated manually Design of Bin wall forces (horizontal forces and vertical forces are calculated), material load at the opening of the hopper, vertical wall load due to friction, shear and bending moments, compressive and tensile stresses Design pressure, design of side wall, hopper, vertical and horizontal stiffeners, Wind load etc. (Tables 2 and 3).

Depth Y m Coefficient Cd Static Pressure Kn/m2 Design Pressure
Kn/m2
1.53 1.5 4.41 6.615
3.05 1.5 8.02 12.03
6.10 1.65 13.40 22.11
9.14 1.65 17.10 28.215
12.20 1.65 19.40 32.01
13.42 1.65 20.20 33.33
14.79 1.65 20.90 34.49

Table 2. Calculation vertical load

Depth Y m Coefficient Cd Static Pressure Kn/m2 Design Pressure
Kn/m2
1.53 1.5 4.45 6.6795
3.05 1.5 8.4526 12.679
6.10 1.65 14.8012 24.422
9.14 1.65 19.5836 32.313
12.20 1.65 23.1490 38.196
13.42 1.65 24.3181 40.125
14.79 1.65 25.4806 42.043

Table 3. Calculation of horizontal forces

Horizontal pressures on bin walls

For shorter wall A=3.657 m

Design pressure = Cd * Static pressure

For longer wall B=6.096 m

Calculation vertical load acting on hopper openings

Load is acting on prismatic section:

W1 = 7.9*12.192*2.79=268.72 Kn

Load is acting on hopper section:

W2 = (1/2)*7.9*12.192*2.79*2.79=134 Kn

Load is immediately above the bottom plate or gate:

W3 = (12.192+6.096)*7.9*1.5= 216.7128 Kn

Calculation of horizontal forces

At B,

Kϒh = (1/3)*7.9*12.192=32.1056Kn/m2

At C,

Kϒh=(1/3)*7.9*(12.192+6.096) =48.1584Kn/m2

L1=(1/2)*32.1056*12.196=195.77Kn/m

L2=32.1056*6.096=195.71Kn/m

L3=(1/2)*16.05*6.096=48.92Kn/m

HA’=(48.92/3)=16.3068Kn/m

HB’ = (2/3)*48.92 =32.6136Kn/m

Taking moment at point ‘o’

HB=(1/12.192)*(268*1.29+134*1.72+216.7128*3.048-195.77*3.04-48.92*2.032) =41.77Kn/m

Vertical reactions at point B,

RB = 268.72+134+216.7128=619.4328Kn

(Figure. 2) shows the Diagrammatic representation of the Loading of the horizontal and vertical forces acting on a bunker due to material load. The lateral pressure is separated into two components: A constants lateral pressure between B and C of 32.10 Kn/m2 plus a varying pressure, maximum at C.

Bending moment values at support and mid span

The bending moment values are tabulated in Table 4 and the pressure calculations are tabulated in Table 5. The vertical and horizontal loadings are shown in (Figure. 2).

icontrolpollution-horizontal-loadings

Figure 2: Vertical and horizontal loadings.

Depth Y m For shorter wall A For Longer Wall B
SupportkN/m Mid
kN/m
Support
kN/m
Mid
kN/m
14.79 -95.828 +38.10 -95.828 +38.10

Table 4. Bending moment for shorter and longer wall

Height Upto (m) Coefficient K2 Pressure Kn/m2
30 1.06 1.708
20 1.01 1.550
15 0.97 1.430
10 0.91 1.259

Table 5. Pressure calculations for various height

Wind load calculations

The basic wind pressure, which varies along the height of the Bunker at Solapur hasbeen calculated as per IS 875 – 1987 (Part III) with Basic wind speed (Vb) = 47 m/s. Risk coefficient (K1) and Topography factor (K3) are taken as 1.07 and 1.00 respectively, whereas Terrain height factor (K2) varies with the height of the bunker wall. Now the design wind speed, (Vdes) becomes equal to K1K2K3Vb and design wind pressure (p) = 0.60 (Vdes)2= 1.52(K2)2Kn/m2. This variation wind pressure along the height is calculated in below Table 5.

Analytical investigations

The typical model of the Bunker shown in (Figure. 3a) the mesh generatedis shown in (Figure. 3b) and aFinite Element analysis has been performed using ANSYS. The material properties of all the parts have been simulated as homogeneous, isotropic, elastic with Young’s modulus = 25000 N/mm2, Poisson’s ratio = 0.17 and density = 7850 Kg/m3.

icontrolpollution-model

Figure 3a: Typical model of the bunker.

icontrolpollution-generated

Figure 3b: Mesh generated in bunker model.

After the assembly of all the parts a complete silo model has been generated. Then the wind load in the Bunker wall has been applied. (Figure. 3c) indicates the loading diagram of the Bunker. Also the design pressure, Horizontal and vertical force due to material load, and bending moments has been applied.

icontrolpollution-Load-acted

Figure 3c: Load acted on bunker model.

In meshing operation all components (Bunker side wall, Column, Horizontal and vertical Stiffener) except hopper are meshed using hexagonal meshing. The behaviour of the bunker under the following load combinations were considered;

Case 1: 1.5 *( DL + LL )

Case 2: 1.2 *( DL+LL+WL )

Case 3: 1.5 *( DL +WL )

Results and Discussion

The deformation pattern is observed on the application of the wind pressure on the rectangular wall of the steel bunker. The summary of critical values of Von mises stress (Vvon) and vertical stress (Vvert) due to the wind load acting along the Bunker wall at various levels have been summarizedis shown in (Figures. 4a and 4b). The stress values due to the wind loading effect have been taken from ANSYS 15.0 output for windward side, leeward side (Yasuiko and Jin, 1988).

icontrolpollution-vertical-stress-acted

Figure 4a: Vertical stress.

icontrolpollution-Misses-stress-acted

Figure 4b: Von Misses stress.

A close inspection of the stress values along the wind ward direction states that it is critical at almost middle one-half height of the bunker wall i.e., at (+)5.2m to (+)12.20m level, whereas the same along the leeward direction is critical only at the intersection.

Conclusion

Analysis indicates that the values of vertical stress are critical in windward side and thesame occur at about middle half height (i.e., around H/3 to 2*H/3) of the bunker wall.

Von Mises stresses are critical at the junction in leeward side as well as mid height of the wall in windward side.

For the different load cases 1, 2, 3, the stiffener found to perform its reinforcing action perfectly. And the deflection and stress value was found to be minimal at the location of stiffeners and progressively increases away from it.

This work is carried out to check the behavior of bunker in wind load condition. A typical model of bunkeris used for analysis and checked for static design criteria. For software data validation, manual analysis is carried out. It is concluded that both results are very close for stresses.

References

  1. Adem, D., Zeki, K., Ahmet, D. and Hali, S. (2009). Cause of damage and failures in silico structures. Journal of Performance of Constructed Facilities. 65-71.
  2. Alauddin, M. and Sohrabuddin, A. (1995). Design forces and moments in circular silos based on finite elemeent analysis. Journal of Civil Engineering Division, The Institution of Engineers, Bangladesh. 23.
  3. Alice, M., Ann, S.S., Elizabeth, T., Neethu, K. and Shema, S.M. (2015). Finite elment Analysis of a Stiffened Steel Silo. International Journal of Civil and Structural Engg. Research. 3 : 1-5.
  4. Anand, A. and Hemant, L.S. (2013). Parametric Study on Dynamic Response Of Silo. International Journal of Engineering Research & Technology (IJERT). 2.
  5. Ding, S., Rotter, J.M., Ooi, J.Y., Enstad, G. and Xu, D. (2011). Normal pressures and frictional tractionson shallow conical hopper walls after concentric filling: Predictions and experiments, PhD Thesis, University of Adger, Norway.
  6. Fisher.W. (1966). Silos and Bunkersinstahlbau. VEB Verlag Fur Bauwesen, Berlin.
  7. Hotała, E. and Skotny, Ł. (2014). Experimental investigations on the stability of stiffened cylindrical shells of steel silos. Journal of Constructional Steel Research. 96 : 81-94.
  8. IS 4995 (Part II - 1974 ). (1996). Criteria for design of reinforced concrete bins for storage of grainular and powdery materials. Bureau of Indian Standards.
  9. IS 5503 (Part I-1969). (2005). General requirement for silos for grain storage. Reaffirmed.
  10. Sadowski, A.J. and Rotter, J.M. (2011). Buckling of very slender metal silos under eccentric discharge. Engineering Structures. 33(4) : 1187-1194.
  11. Sergio, A.E. and Luis A.G. Effect of geometric distortions on wall pressures in silos during gravity discharge, PhD Thesis, University of Cordoba, Argentina.
  12. Shelly, T., Jaya, V. and Manju, M. (2014). Non-linear analysis of reinforced concrete chimney. International Journal of Civil Engineering and Technology. 5 : 107-116.
  13. Standard IS Codes. Criteria for Design of Steel Bins for Storage of Bulk Materials. (1979). (IS 9178 Part 1 1979 and IS 4155 Part 1 and 2). Bureau of Indian Standards.
  14. Vidal, P., Gallego, E., Guaita, M. and Ayuga, F. (2008). Finite element analysis under different boundary conditions of the filling of cylindrical steel silos having an eccentric hopper. Journal of Constructional Steel Research. 64 : 480-492.
  15. Yasuiko, S, and Jin, Y. (1988). Seismic response of concrete stave silos with structural discontinuity. Proceedings of ninth world conference on earthquake Engineering. Tokyo-Kyoto, Japan. 4.
  16. Zhao, Y., Cao, Q.S. and Su, L. (2013). Buckling design of large circular steel silos subject to wind pressure. Thin-Walled Structures. 73 : 337-349.

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