GRAIN SILO OF SUPERIOR RESISTANCE TO WIND AND DEFORMATION PRESSURES Introduction Cylindrical metallic silos made of corrugated steel sheets and conical roof are the most known and exploited units to grain storage in Brazil.

Due to the great structurai'efficiency of cylindrical form and the high strength of the steel that is used nowadays, these structures are lightweight and slender, although they become susceptible to the local and global buckling of the cylinder, when empty, or not fully loaded, as well as to the total pull out of the structure from basement or to the crumpling of the sheets of the cylinder, after excessive deformation under wind action.

The crumpling of the cylindrical body is a frequent hazard subject to mitigating solutions, and might result in some significant reduction of the lifetime of silos and or in substantial detriment of product stored in them.

Uses for and industrial application of the invention The hereby proposed construction model of grain silo capable of superior resistance to deformation by wind action had its preliminary conception carried out with aerodynamic and aeroelastic models of silos, by which the cylinder displacements and the pressures due to the action of wind and stored products had being studied.

The accomplished studies indicated that the silo assembly according to specific characteristics could lead to a higher stiffening of the external surface of silo, reduce the amount of steel used in the conical roof, and make easier the flow of stored products as well as its maintenance and cleanliness.

So, the silo, besides resisting the internal load exerted by the stored product, has superior resistance to external pressures of the wind.

It is evident that the higher durability and safety of the projected structure as a matter of fact assure economic advantages, in addition to operational ones, to the silos designed and assembled according to the structural technique disclosed in the invention.

State of the art Cylindrical steel silos made of corrugated sheets and conical roofs as well as the

device of structural stiffening by means of rings attached to the body of silos are well known.

The technical literature however do not report any cylindrical structures that combine external stringers with"U"profile connected alongside the perimeter of silo body with a vertical arrangement of stiffening rings, and that simultaneously exploit the funnelling of the top of the silo body, by means of the sloping of the sheets in the region between the body and the roof (Figure 4), as provided in this invention herewith disclosed.

Innovative technical solution The body of the silos, when subjected to the wind action in natural circumstances, exhibits an excessive displacement of the stringers attached to the sheets that constitute the body, leading to the crumpling of those sheets, which such effect is intended to be inhibited with the invented system of structural stiffening as well as with the new adopted configuration of the top of the body.

The positioning of the stiffening rings has not ever been conceived before as by external stringers and with the funnelling of the top of the body, according to the now proposed solution and therefore it has been established through various essays that the external positioning of stringers reduces the wind pressures.

Therefore it has been possible to achieve the stiffening effect of those stringers in the body in view of the pressures which they are submitted to, with clearance of the inside area of the silo as a result, too, becoming completely unobstructed internally, without ridges and notches, and allowing moreover the external visiting for verification of component parts, without need of emptying the bin.

Furthermore, the funnelling of the upper region of the silo, together with those stiffening rings effectively placed in the external stringers, raises the strengthening of the structure, improving its capacity to resist wind pressures, contrary to what might occur without the system of the rings altogether with funnelling of the section of the silo body in the transition part at the top of. silo, which should undergo excessive displacements of the body, as wind tunnel tests have clearly demonstrated.

Tests and assessments to the verification of results Physical tests performed in wind tunnel clarified the attainment of the pressure distribution for a short model (H/D=0.5) and a medium one (H/D=1. 0) of the new silo structure and construction systems disclosed herewith. Similarly, it has been obtained the aerodynamic coefficients in rigid models, or aerodynamics, considering the internal and external positioning of the stringers and the stiffening members in the roof, too.

The intermediary values of H/D, as well as those values above 1. 0 and below 0.5, define which values of pressure coefficients are to be adopted optimally in this invention. Accordingly, it should also be considered that silos with ratios different of 0.5 and 1.0 can be as well built with the same conditionings and parameters established by the essays assessments.

Moreover, a flexible model, aeroelastic, has been tested which had undergone deformations with the wind generated inside the wind tunnel.

Thus, this model had reproduced the interaction of the silo structure with the wind. The performed tests have allowed the determination of the aerodynamic coefficients of pressure, drag and lift, for the designed aerodynamic models, taking into account the external positioning of stringers and external ridges in the roof, as to quantify the alleviation of suction in the body and roof, respectively.

For the aeroelastic model corresponding to that aerodynamic one of a ratio H/D=1.0, the behaviour of the silo structure with external stringers has been acknowledged, in terms of number of deformation waves, with the magnitude of the higher displacements in the windward body region.

It has finally been assumed that silos with external stringers in the body benefit from the pressure alleviation. And that could well be seen as not exact a trivial conclusion or simple expectation.

Comparing the short (H/D=0. 5) and medium (H/D=1.0) models,. it was established that a significant reduction of wind negative pressures in the body (up to 50%) would result and it would also be present in the roof (up to 25%).

This evidence have led to the construction of a flexible model with H/D=1.0 ratio, formed by a cylindrical shell of Melinex@ with D=510mm diameter, roof height of 128 mm, and 36 strips made of PETP (Polyethylene terephtalate), used to

simulate the behaviour of an actual steel silo made of corrugated sheets (D = 21.0 m). And its conception took into account physical similarity laws in terms of geometry, rigidity, aerodynamic and mass scales.

Through tests with the flexible model of H/D=1.0 ratio, evaluation of the configuration of displacements of the cylindrical shell under wind action was enabled, and it was then concluded that the body of the silo requires stiffening rings over the height of the structure, and that was due as a remedy to the verified excessive displacements of the body.

The magnitude used to define the limit of excessive radial displacements of the structure is in agreement with the Brazilian code ABNT NBR 14762 (2001)- Cold formed steel design-Procedure. In this case, the stringers are considered to be of general closing under wind loading and the upper limit is given by U120, where L is the length of a stringer. As the stringers were of L=510 mm, so the maximum radial displacement ought to be 4.25 mm.

The above mentioned statement takes into account the stiffness of the cylindrical body, which was simulated with reference to a wind speed equal to 30 m/s for the prototype, or 15 m/s for the model.

As the first movements of the model were present at 11.2 m/s, with radial displacements around 3 mm, thus the body of the silo built only with external stringers would not resist the wind loading.

The displacement at the wind speed at 5.6 m/s is acceptable in as long as the set of corrugated sheets and stringers would resist to displacements of the order of L/120. Otherwise, being that set susceptible to large displacements (limit given by L/180 = 2.8 mm), there would be then necessary to stiffen the body of the silo all around, that meaning to connect stiffening rings alongside the stringers.

The deflection mode is of one (1) half-wave in the generator of the cylinder to the speeds achieved in the tests performed with the model. To speeds up to 6.0 m/s, occurred two (2) half-waves in the perimeter, and to speeds near to 6.9 m/s there were three half-waves in the perimeter of the flexible cylindrical body.

These are evidences that had led to the development and design of connecting rings of circular section to the stringers, in order to achieve a structure able to

resisting higher wind speeds and continuing stability and steady shape.

Supposing that the silo is built with external stringers but not stiffened with rings, it is assumed that the buckling would occur to a critical pressure equal to 375 N/m2, obtained according to a computational coding, which was based on the formulation of BRUSH & ALMROTH (1975) in Buckling of Bars, Plates and Shells, in the topic of buckling of cylindrical stiffened cylindrical shells, being that pressure equivalent, in the terrain conditions to the prototypes, to a speed equal to 25 m/s.

With the ring stiffeners placed externally, the structure integrity has been assured, making it possible for the prototype (H/D=1.0) to resist to a pressure of 5,500 Pa.

The decrease in negative pressures, or suctions, resulting from the external placement of stiffening, benefits the silo structure stability because reduces the external pressure over itself. Therefore, it were concluded that the external stringers should bring reduction of negative pressures on the structures and such effect would be raised if the stiffening rings also had been externally placed.

When evaluating afterwards the displacement behaviour of the stringer applied to the flexible model, it was found the need for reducing the length of the stringer, as the bending depends on its length, as well as caring for not raising a significant reduction in the storage capacity of the silo.

Consequently, funnelling a short extent of the upper portion of the body to achieve a reduction of the length of the stringers was found additionally to promote a smooth transition, making possible to stiffen the upper portion of the body by the frustum form, and so to reduce the size of the roof.

In this way, it is defined the frustum of lower diameter D and upper diameter d, d < D, and height 0. 1H, because it is a relatively more resistant element to the loss of stability than a cylinder of diameter D and height 0. 1H, as tests results show in Gaylord & Gaylord (1984) have confirmed in Design of Steel Bins for the storage of Bulk Solids, Prentice Hall, New Jersey, p. 216.

The structure as conceived herewith in this invention is particularized by the external placement of stringers, which perimeter distance between each two of

them is defined according to the forces of stored product, and by the rings that have their vertical distance due to the wind pressure distribution in the body (Figure 5), which are combined to the upper transition of the body in frustum shape, thus altogether propitiating superior resistance against wind pressures as well as to the horizontal pressures applied internally to the silo body, originated by the stored grain mass.

Figure 5 diagrams show the regions of the silo body where ought to be placed the rings as per the invention herewith disclosed, defined according to the range of height of positive pressure distribution, in darker grey, which goes from 0.3H (100/345 = 0.3 ; H = 345) to H to the silo of H/D = 0.5 ratio or 0.25 : 5 H/D s 0. 75, and that goes from 0.45H (225/510 = 0.45 ; H = 510) to H to the silo of 1.0 : 5 H/D 5 2.5 ratio.

Therefore, where there have been empirically defined the regions to the stiffening with rings in relation to the H/D ratio and the height H of the body, namely, to H/D = 0.5 ratio (and ratios in the range 0.25 : 5 HID : 5 0.75), the region is situated between 0.3 s z/D'1. 0 (Figure 4), and to H/D = 1. 0 ratio (and ratios in the range 1. 0'H/D s 2.5) to 0.45 &lt; z/D &lt; 1.0 (Figure 3), inclusive with the highest ring at the height of the conical roof with the frustum, which is given by H.

In Figures 1 and 2 the dashed lines represent the conical roof of silo without transition in frustum shape and the bold horizontal lines the rings.

Due to the size variety by which a silo can be built, there are considerable variations when considering the wind pressures. Consequently, the dimensioning and the distance between rings is relative to the width, a, of the lateral body sheets, and the distance between stringers, b, which define a cylindrical panel, as delimited part of the steel corrugated sheets forming the wall of the silo, and the wind pressure magnitude. The suggested distances to the rings in the Figures 1 and 2 are empirically defined, according to the measured displacements taken from the aeroelastic model and the pressure distributions observed in the aerodynamic models. Thus, the distances defined in Figure 2 are suitable to silos with 0. 25s H/D s 0.75 and those in Figure 1 are for silos with 1.0 H/D 2. 5.

The forces P on the cylindrical panel of Figure 7 come from wind distribution over the body surface. The calculation of panel stability is done according to procedures consistent with ABDEL-SAYED (1970),"Critical Shear Loading of Curved Panels of Corrugated Sheets", in Journal of Engineering Mechanics Division, ASCE, v. 96, No. EM6, Dec.

In this way, to determine the distance between rings and the dimensions (diameter and thickness of the tube ring stiffener) it is necessary a buckling analysis of the body with stringers and rings. To the proposed analysis, the calculation of the critical load in the body of silo is repeated until the determination of their magnitudes, by which the distance between rings is enough to avoid the loss of stability of the panel, that the height a of the panel (Figure 7) have a initial length given by the equation being v = 0.3 the Poisson's ratio of steel, an t the thickness of an even cylindrical sheil equivalent to a corrugated one, according to formulation described in"General Solution of the Elastic Stability Pressure to Cylinders with Stiffeners", ANDRADE JUNIOR (2000), in"A, cão do Vento em silos cilfnricos de chapas metálicas corrugadas", monograph presented to the School of Engineering of Sao Carlos, of The University of Sao Paulo, as a requirement of the qualify examination, necessary to the obtainment of the title of Doctor in Engineering of Structures.

The funnelling from a certain height, z = 0.9H, relative to the base, of body transition, by means of the sloping of the sheets in the region 0.9 s z/H s 1. 0, guarantees the efficient stiffening of the structure in the upper portion of the body, and the structure built in this manner doesn't show an abrupt transition between the body and the roof, what also represents a factor of increase of strength that the body structure presents to the wind action. Any changes in the initial height of transition, due to a requirement of project, nearby z =, 0. 9H, still continues to typify the invention.

By other means, also in the case that it is necessary to place internally the stringers, but the rings are used in combination with the funnelling of the top of the body, even in this case this is in the scope of the invention here proposed, as it expresses the concomitant use of funnelling and rings.

Procedure of execution of the silo The silos to be built according to the invention (Figure 1 or 2) comprehend structural stringers executed in U profiles (Figure 2) placed externally to that set because propitiate the alleviation of wind suction, arranged in a circular base, and in those being connected corrugated steel sheets that will form the body of the silo and the lateral closing of the structure, oriented by the geometry of the circular base and the placement of the structural stringers.

The U profiles can, inclusive, optionally, be composed by an element of predefined length d, namely lip stiffener (Figure 6).

The U profiles can also have the flanges with a pitch different of 90g, but should have the two parameters bw and bf defined as shown in Figure 6.

The stringers are elements coupled with the body of the silo capable of transmitting the vertical friction stresses exerted by the grain mass stored in its interior, as well as of supporting the closing surfaces of the structure that bear the stresses produced laterally by the same mass stored and by the wind, depending on the situation that the silo might be submitted to.

At this point, it is worth mentioning that, when the silo is fully or partially loaded, the principal actions it is subject to are the forces exerted on it or on its wall by the load of grain and, when the silo is empty or almost empty, the principal actions it would be subject to is are the wind forces outside. In both conditions, the silo building system according to the invention will show regularly the remarked stability characteristics and superior resistance to those pressures exerted over its walls or body, originating from its construction and structural system and from the designed devices incorporated to it as herewith disclosed.

The structures of the silos executed according to the invention will also be composed of a base, by which there will be transmitted the vertical loads of the silo to the foundation and/or soil over which it have been placed and/or erected or have been anchored the structures forming the silo body.

The base can be implemented as of flat bottom, whenever the lower closing of the silo body is composed of a flat surface; or having an elevated bottom, when the lower closing is situated on a higher level over the soil level.

In this manner it conforms a set presenting a cylindrical arrangement composed

by structural profiles, sheets for lateral closing of the body of the silo and base.

The set of cylindrical arrangement thus produced is completed by stiffening rings, or of reinforcement (Figure 3), and by the frustum conformation due to the funnelling of the top of the body, from a transition volume proportionally determined (Figures 1 or 2) in relation to the diameter of the silo (D), to the diameter of the top of the frustum in the top body of silo (d), to the height of the body of the silo (H) measured from base to top of body, to the total volume (V), equivalent to the volume of the body added to the volume of roof, to the volume of cylinder (Vi) of diameter (D) and from a defined height according to expression H/10, considering an index (i), equivalent to 1 or 2, which indicates two preferential reductions, namely 1 and 2, to buildings in which H=D and H = D/2, and an ordinate z, used to indicate the height in relation to the silo base (Figures 1 and 2), to a dimensionless volume (Vad) given in relation to the volume of cylinder (i) of reference, to a volume of covering (Vcob) given by the volume of covering, of height d/4, over the body (Figures 1 and 2).

The slope of the conical roof of the cylindrical silo, measured from the horizontal section of silo, has its internal angle given by the generator of the silo roof and its horizontal.

The slope angle of the roof should be preferentially between 272 and 302, due to the repose angle of stored grain.

The reduction in the total volume of silo is a consequence of funnelling the top of body of silo, obtained by means of two reductions being calculated. The reductions in the body and the covering are calculated separately and the percentages of reduction are demonstrated individually, as shown in Tables 1 and 2, which follows, respectively.

Further, the total reductions between the silos to be built without (initial) and with the frustum device are calculated as per Table 3, below, and the reductions in the height and the projected area of the roof are given respectively in Tables 4 and 5, either indicated below.

Body

Vdisp = (Vl-V2)/2 d=D-H/10 V. =C ? HD _ 1D2 _d2lJ H 14 4 2110 Reduction 1 (H = D) 2 3 Vdisp =-D D- (9 D ) I-==> Vdisp :,--D-+ Vdisp 0. 905 4 C 10 2 I O 40 C 2 200 40 Vcos-1 = Vcos + Vdisp V D3 9 + D3 0. 905. . V D3 9. 905 4 10 40 4 10 y-+Q905-V-J Reduction 2 (H = D/2) 2 19 2 _1 _D 1 _t 3 _l 3 61 1 nD 3 Vaap = 4 D D 10 D 2 20 aisP 2 40 D 2 + 800'. Vasp-2 40 0. 95125 Vcos 2 = Vcos +'Vdisp D 2 9 D D 3 0. 95125 D 3 9. 95125 Vcos2 = Vcos + Vdisp 4 10 2 40 2 4 20 cos2- .'. cos2- TABLE 1-Reductions of volume of body relative to the initial body Case Ratio Ratio between Vad = 1-Vad height/diameter diameters d and Vcosj/ (D/4) % D Vad = VCOS_2/D3l8) 1 H=D d = (9/10) D 0. 990500 0. 95 2 H=D/2 d = (19120) D 0. 995125 0. 4875-0. 49 Covering Reduction 1 (H = D)

Reduction 2 (H = D/2) TABLE 2-Reductions in the covering volume relative to the initial covering Case Ratio Ratio between Vad=Vcob i/ (nD3/48) 1-Vad height/diamet diameters d and i = 1, 2 % er D 1 H=D d = (9/10) D 0. 729 27. 1 2 H=D/2 d = (19/20) D 0. 857 14. 3 The total volumetric reduction is given by the difference between the total initial volume and the total volume of the silo with device, divided by the total initial volume.

TABLE 3-Total volumetric reductions Case Total initial Total reduced volume Reduction, volume % 3l3. 0. 9905 0. 729. 312. 615 48 (4 48 48 48 4 48 J 48 3 7 3 0. 995125 0. 857 3 6. 82775 2 icD-r-) 2. 46 48 8 48 48 TABLE 4-Reductions in the height of covering Case Initial height Final height Reduction, % 1 D/4 d/4 = 0. 9D/4 10. 0 2 D/4 d/4 = 0. 95/4 5. 0 TABLE 5-Reductions of the projected area of covering Case Initial area Total reduced volume Reduction, % 1 (0. 9D) =-D 0. 81 19. 0 4 4 4 4

2 2 2 icd= (0. 95D) 2=D20. 9025 9. 75 4 4 4'4 Referenced figures The figures attached to this report are: Figure 1-lateral schematic view of silo of ratio H/D = 1.0 and of the positioning of the stiffening rings; Figure 2-lateral schematic view of silo of ratio H/D = 0.5 and of the positioning of the stiffening rings; Figure 3-detail of the connection of the stiffening ring to a vertical stringer; Figure 4-detail of the transition device in the upper portion of a vertical stringer; Figure 5-distribution of external pressure coefficients in silos with outside stringers; Figure 6-example of U section of stringer with option of lip stiffening; Figure 7-cylindrical panel defined by stringers and by the distance between rings.

In Figures 1 and 2 the dashed lines represent the conical covering of silo without a frustum transition. The bold lines represent the rings, with the suggested heights in function of height H that are dependent of the positive pressure distributions, shown in Figure 5.