STEEL SILO DESIGN
A challenge for designers of steel silos Jim Durack, engineering doctorate doctorate candidate USQ Professor Charlie Tranberg Tranberg – USQ
Jim Durack has a background in both academic and practicing engineering. He has worked with Aurecon (formerly Connell Wagner) Wagner) for the last eight years and is currently on sabbatical leave completing an engineering doctorate through University of Southern Queensland. Jim is a specialist in the design of industrial structures for bulk materials handling facilities. He has also worked internationally on the design and assessment of large inverted cone silos as used primarily in the cement production industry. In 2007 ABHR published Jim’s Jim’s article on the implications for such silos of the then new Eurocode for silo loads, EN1991-4. Since then he has presented three further conferenc conference e papers in this field. Both Jim and Professor Tranberg Tranberg have been involved in the development of the USQ coursework based, Online delivered, Master of Engineering that has a significant emphasis on industrial and marine structures. In preparation for a planned course on silo design, Jim has extended his reinforced concrete silo research to a speculative investigation investigation of a steel solution for large inverted cone silos. His knowledge and experience with concrete silos gives him fresh insight into this complex field. Jim considers that there may be a fundamentally new way of approaching steel silo design that is informed by the Eurocode but not limited by it. This paper provides a relatively informal presentation of his ideas. He hopes that these may challenge steel silo designers to think outside the square.
1. Context and background to research Silos of one form and another are fundamental to the success of most industrial projects. Ideally a silo will do its job with minimal maintenance for many years. When a silo suffers some form of failure this may cause massive disruption of plant operations. There is at least anecdotal evidence that silos suffer severe structural failures more frequently than any other structure type with the possible exception of retaining walls. Such structural failures are still likely l ikely to be much less common than operating problems such as flow interruptions. The operating performance of silos should continue to be of prime concern to plant operators but those who are “unlucky” enough to experience the structural collapse of a key process silo will recognise the fundamental importance of structural reliability. Fundamental to structural design is a rational assessment of the loads that are likely to develop during the lifetime of a proposed structure. In 1895 Janssen developed the Janssen equation that for the first t ime provided a rational method for assessment assessment of one aspect of the loads exerted by stored material on a silo wall. It has always been acknowledged that “real silo loads” are more complex than those predicted by this equation. “Traditional” code methods for silo loads such as those of the ACI code and the now superseded DIN code, used fairly simplistic “fudge factors” to scale up the Janssen equation loads to account for the unknown and perhaps unknowabl unk nowable e complexities complexities of real silo loading. The Eurocode for silo load estimation EN1991 – 4 released in draft form in 1995 is still based on the Janssen equation but specifies a fundamentally funda mentally different loading model. Research undertaken by Durack and others generally concludes that while there remain numerous unanswered questions, there is good evidence to suggest that the Eurocode loading model is substantially correct. For reinforced concrete silos, Durack has shown the Eurocode to be considerably more onerous than earlier codes. More importantly, it forces the designer to consider consider important structu ral issues that are not evident when using earlier code defined loading models. Durack recommends that any contemporary contemporary str uctural designer of reinforced concrete silos should give consideration to the Eurocode even if the final silo design is not strictly compliant with this code. Durack has recently undertaken scholarship and finite element modelling to investigate whether the Eurocode load may
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have similar lessons for the designers of steel silos as he has found it to have for reinforced concrete silos. The following represent some key findings of this research: • For the design of steel silos, the Eurocode for silo loads EN1991 EN1991 - 4 is supplemented by the general design code EN1993 - 1 - 6 Strength and Stability of Shell Structures and the silo specific EN1993 - 4 – 1 Design of Seel Structures - Silos. • There is limited contemporary academic interest in the analysis and design of reinforced concrete silos, but a huge body of academic literature r elating to various aspects of the structural behaviour of steel silos. Much of the literature is highly specialised in nature and of limited direct relevance to practicing designers. • Professor Michael Rotter is apparently the most highly published academic working in the steel silo field. He has played a leading role in the develop development ment of all three th ree Eurocodes relevant to silo design. • Professor Rotter has published a text “Guide for the Economic Design of Circular Metal Silos”. Silos”. This text is specifically di rected to practicing silo designers. First published in 2001 it represents a general guide to steel silo design plus specific guidance related to the application of the three silo Eurocodes. • Durack has reported reported that for for reinforced concrete concrete silos, silos, the EuEurocode for silo loading is more conservative than earlier codes by a factor in excess of 1.5. No such comparative review for steel silos has been identified in the published literature. • Rotter’s text and the codes it supports are typical of code specified design methods. They allow a designer to undertake a design assessment of a proposed steel silo but they provide only limited assistance in developing the form of understanding that a designer needs in order to exercise responsible creativity in achieving a reliable and economic design solution for for a particupart icular steel silo si lo application.
2. Focus of the current research To address the last of the previous dot point items, a combination of finite element modelling and relatively simplistic first pri nciples analysis has been undertaken in order to explore structural phenomena exhibited by steel silos in response to the Eurocode load and related analysis and design issues.
STEEL SILO DESIGN
The research focuse s on a 12 500 tonne capacity cement storage inverted cone silo with a diameter of 18 metres and a storage chamber height of 40 metres. This silo is not typical of most steel silos that are likely to use a concentric discharge system and to be smaller and more slender. The case study silo has been chosen because of the author’s interest in reinforced concrete silos of these proportions. It should be noted that applicability of the Eurocode for silo loading specifically excludes the “inverted cone” discharge system that is common in the cement industry. This discharge system uses an inverted cone at the base of the silo that sheds the stored material to sequentially operated discharge points located around the silo perimeter. Despite this, the research is generally relevant to the design of a steel silo of any sort.
3. The case study silo and its Eurocode loading The basic details of the case study silo are shown in Figure 1. This also gives a three dimensional representation of the Eurocode loading. In accordance with the Eurocode EN1991 – 4 Clause 5.2.4.3 and with z measured downwards from the top of the silo, the loadings phse and phse – phce shown in Figure 2, that vary both circumferentially and with height were input as follows: phse = 150.94 x (1 – 2.7813 ^ (-z / 14.56)) kPa phse– phce = 150.94 x (1 – 2.7813 ^ (-z / 14.56)) – 40.4 x (1 – 2.7813 ^(-z / 3.9)) kPa
Figure 1 Basic silo details and a graphic illustration of the internal pressure on the silo walls.
4. Two dimensional structural phenomena Prior to considering a three dimensional silo it is informative to consider the behaviour of a two dimensional ring extracted from such a silo. Figure 3 represents a 1 metre high ring extracted from the case study silo with the loading corresponding to that at a height of 15 metres above the base of t he silo. If the thickness of the 1 metre high ring is set to 25 mm then it is obvious that these loads are very large. Despite this, we may expect that the uniform outward pressure should not create a difficulty because this can only cause a uniform increase in the circumference of the ring without inducing any bending. The axial hoop tension can be calculated using the simple hoop tension equation: T = Uniform pressure x Ring height x Radius (1) = 123 kPa x 1 metre x 9 metres = 1107 kN The corresponding axial hoop stress around the circumference is then: f a = 1107 x 103 / (1000 x 25) = 44.3 MPa The differential pressure of +/- 85 kPa over the 30° (4.71 metre arc length) flow zone and the two adjacent shoulder zone would obviously cause a problem if the load had to be carried by bending action in the flexible 25 mm thick plate. Fortunately this is not the case. The hoop tension equation is commonly applied to uniform pressure situations but may also be applied to situations where the pr essu re varie s around t he per imet er. It may b e put in the form: T( θ ) = p( θ ) x r( θ ) (for unit ring height) (2) Where T( θ ), p ( θ ) and r ( θ ) represent the values of the hoop tension, radial pressure and ring radius at any location θ around the perimeter of the ring. Equation (2) may be algebraically rearranged as: r( θ ) = T( θ ) / p( θ ) It may readily be shown by FE modelling or consideration of a small differential arc element of the ring, that for loading of the type shown in Figure 2, the hoop tension T( θ ) remain s constant at the value given by equation (1). Thus, we may write: r( θ ) = T / p( θ ) And substituting for T from Equation (1) r( θ ) = (Uniform pressure / Pres sure at position θ ) x Initial silo radius (3) Equation (3) may be read as follows: Provided t he ring cha nges its shape in r esponse to the loa d such that at any angular location θ around the ring circumfer- ence, the ring radius equals the ratio of the uniform pressure to the pressure at θ, times the initial silo radius, then the load will be carried by hoop tension action rather than by bending. This shape may be referred to as the “compliant shape”.
Figure 2 The decomposition of the Eurocode load into uniform and differential components.
Figure 3 Two dimensional ring extracted from the 3D silo model.
For the combination of loads defined in Figure 3 there are three pressure zones and corresponding radii being: The general area with p hse = 123 kPa with: r( θ ) = 123 / 123 x 9 = 9 metres The high pressure shoulders with phse + (phse – phce ) = 208 kPa with: r( θ ) = 123 / 208 x 9 = 5.32 metres The low pressure flow zone with p hse – (p hse – p hce ) = 38 kPa with: r( θ ) = 123 / 38 x 9 = 29.13 metres These compliant radii are dependent only on the pressure ratios and are independent of both the thickness of the r ing and the actual magnitude of the pressures. Thus if the pressures are scaled up by a load factor then there will be no change to the compliant shape and corresponding radii. Figure 4 represents the FE Prediction of the compliant shape for the ring subject to the combination of the uniform and differential components of loading shown in Figure 3.
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STEEL SILO DESIGN
Figure 4 Two representations of the compliant shape.
It may be confirmed from the FE model that the numerically predicted radii in the shoulder and flow zones are very close to those predicted using Equation (3). The maximum radial deformations associated with moving to the compliant shape as predicted by FE modelling are around 380 mm inwards in the flow zone and 70 mm outwards in t he shoulder zones. The full stor y is not as simple as this. Firstly, rather than a stepwise change from one radius to the next there is a small transition length from one radius to the next. Secondly, Graph 1 shows the radial displacement at the centre of the flow channel as predicted by FE modelling for a ring with a 10 mm thickness, as the load factor on the combined loading increases from 0 to 2.5. This represents the development of the compliant shape for increasing load.
1 / r bending = 1 / {[(Uniform phse ) / (Differential p hse – phce )] x initial silo radius} (4) = 1 / (123 / 85) x 9 = 0.0768 m-1 In accordance with the engineers theory of bending, bending strains will develop as a result of this curvature as: εmax = y max / r bending (5) Where y max is the maxi mum distance from the neutral axis of the wall of thickness t. Thus y max = t / 2. The bending stress associated with this bending strain for a material with a modulus of elasticity E is then given as: f max = E x εmax (6) = +/- E x (t/2) / r bending (7) The total stress due to the combination of axial hoop tension and bending necessary to move to the compliant shape is then given as (for a unit ring height): f total.max = T / t +/- E x (t/2) / r bending (8) Table 1 records maximum radial displacements and compares the stress predictions of FE modelling with those of Equation 8 for ring thicknesses varying from 5 mm to 200 mm (with T = 1107 kN and 1/r bending = 0.0768 m-1 and E = 200 x 103 MPa):
FromFE 353 357 350 340 327 293
24
FromFE (327)* 204 210 232 253 276
FromFE (117*) 17 - 99 -143 -179 -221
58
-46
*Examination of the FE output for the very thin 5 mm plate s uggests
Graph 1 The development of the compliant shape as the load increases.
Graph 1 demonstrates that the stiffness of the ri ng is highly non linear, exhibiting a huge increase in stif fness as the load increases and the r ing moves to the compliant shape. (Durack has reported on f ield measurement of the radial deformations of a 10 000 tonne reinforced concrete silo during discharge and the use of these measurements to infer the magnitude of the loading necessary to cause such deformations. One consequence of the non linear “tension stiffening” behaviour is that this form of field testing cannot be used to determine un stiffened steel silo wall pressures. As indicated in Graph 1, if the measured radial d isplacement is say between 350 and 360 mm then the pressures causing this displacement could be any where corr espon ding to t hat for a load factor between 0.1 and 2.5. Despite this limitation, the method should be excellent for determining pressure ratios in the di fferent flow zones.) Thirdly, the statement following Equation (3) states that once the ring reaches the compliant shape, the combined load is carried by hoop tension rather than by bending. This is not entirely correct. In moving to the compliant shape, bending curvatures obviously must develop in order for the radii to change to the required values. It may readily be shown that the bending curvatures necessary to establish the compliant radii in the flow and shoulder zones are given as:
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that these values are unreliable. Table 1 Maximum radial displacement and combined ring stresses for differing ring thicknesses.
From Table 1, the following observations may be made: • As the plate thickness increases from 5 mm to 40 mm there is only a marginal 17% reduction in the maximum radial displacement from 353 mm to 293 mm and the corresponding bending curvature remains sensibly constant over this thickness range with a value close to that given by Equation (4) • For feasible thickness plates between 5 and 30 mm, the correlation between Equation 8 and FE Modelling is very good. For a plate thickness of 40 mm Equation 8 is overestimating the maximum and minimum stresses by around 20%. • The bending stress component of Equation (8) increases with t/2. As predicted both by Equation (8) and FE modelling this, perhaps surprisingly, leads to an increase in total stress as the plate thickness is increased! • For a plate thickness of 200 mm it is clear that Equation 8 has little relevance. The ring now has substantial flexural sti ffness (similar to that of a typical reinforced concrete silo wall) and is acting in an entirely different fashion. The small maximum displacement of 24 mm indicates that the ring has not moved to the compliant shape where hoop tension can carry the load. Most of the load is now being carried in flexure with high bending moments and shear forces.
5. Design implications of 2D structural phenomena It is to be expected that the behaviour of a three dimensional silo will include additional phenomena that are not evident in a two dimensional ring extracted from such a silo. Despite this, the findings of the previous section provide a suitable starting point for understanding and have significant design implications as summarised below:
STEEL SILO DESIGN
• For feasible steel plate thicknesses and the non uniform Eurocode loading, there is a good correlation between the predictions of simple hoop tension theory and results obtained from FE modelling. • A steel silo is dependent for its equilibr ium on moving towards the compliant shape. Linear static analysis that assesses equilibrium in the undeformed position (with a perfect circular shape) will not give any meaningful prediction of the actual behaviour of the silo. All of the previous FE results are based on geometry non linear analysis. • The Eurocode loading will cause large radial deformations of an unstiffened steel silo. These large deformations develop at quite low load factors but as the load increases they reach a maximum value beyond which they will not further increase. • Increasing the wall thickness of a silo will not significantly reduce the magnitude of radial deformations (until the thickness reaches very large values more typical of a reinforced concrete silo). • For a given non uniform load combination, increasing the wall thickness of a silo will increase the total combined axial and bending stress. A maximum stress in excess of the yield stress should not be taken as an indication that the silo is approaching failure. It simply means that with thicker plates, some degree of yield may be necessar y to allow the silo to move to the compliant shape. • For low loads a silo will exhibit very low stiffness but as soon as it approaches the compliant shape the stiffness will radically increase. For this reason it may be dif ficult to obtain convergence of an FE solution for the first low increments of loadi ng.
6. Three dimensional case study silo – horizontal effects
• The hoop tension force varies around the perimeter of the silo from 968 to 1252 kN/m. The average of these two figures is very close to the constant hoop tension in the two dimensional ring of 1107 kN/m. • The maximum and minimum plate stresses (at the surface of the plate) are 247 MPa and - 163 MPa compared to those for the two dimensional ring of 236 MPa and – 148 MPa.
Figure 6 Aspects of the behaviour of the Figure 5 silo focussing on the ring level.
7. Three dimensional case study silo - vertical effects In addition to the horizontal loading on the silo wall, the stored material also causes vertical loading as the stored material attempts to slide down the inner face of the silo wall. This vertical loading is referred to as the wall traction loadi ng and at any depth and radial position θ is equal to the horizontal pressure times the assessed coefficient of friction between the stored material and the silo wall. As with horizontal loading, traction loading has been decomposed into a uniform traction component that is constant around the perimeter and a differential component that is downwards in the high pressure shoulder zones and upwards in the low pressure flow zone. The load path for these traction loads is straight down the silo wall. Figure 7 shows the analysis res ults for the uni form traction component causing a steady increase in the vertical wall stress from zero at the top to a maximum of - 62 MPa (compression) at the base of the 25 thick wall. The differential traction component produces a more complex stress variation that includes both compression and tension areas but with maximum value of only + 5.4 MPa and – 3.6 MPa this is clear ly of secondary concern.
Figure 5 First three dimensional silo analysis model.
In Figure 5 the wall thickness has been kept constant to simplify interpretation of stress information. There is no suggestion that this thickness is adequate or appropriate for Eurocode loading. Figure 6 illustrates the overall behaviour of the three dimensional silo as assessed using geometry non linear analysis for a load factor of 1.0. There are “end effects” at the base and roof of the silo but in the central region the silo is deforming in a similar fashion to the two dimensional ring – pulling inwards in the low pressure flow zone and pushing outwards in the high pressure shoulder zones. Figure 6 also provides detailed information relating to the ring level where the horizontal loading is identical to that for the two dimensional ring previously considered. Referring back to Table 1 the following comparisons may be made between the 25 mm thick two dimensional ring and the 25 thick ring forming part of the three dimensional silo: • The maximum silo displacement at the ring level of 229 mm in wards is substantially less than the 340 mm for the two dimensional ring. This means that in the two dimensional ring essentially all of the load is carried by circumferential hoop tension, but in the silo, some is being carried by an alternative load path.
Figure 7 Vertical wall stresses due to uniform and differential vertical traction taken separately.
The surprise comes with Figure 8 that shows the vertical wal l stresses a sses sed for the full Eur ocode load ing includi ng the uniform and differential components of both the horizontal pressures and vertical tractions. The view on the left of Figure 8 (a) indicates high stresses at the base of the silo in the region of the non uniform pressures with maximum values of 237 MPa tension and 210 MPa compression. These maxima are nearly four times the vertical stresses due to just the vertical traction loads as shown in Figure 7.
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The view on the right of Figure 8 (a) represents the same stresses but with the plottin g range limited to 50 MPa tension and 100 MPa compression. This shows that high ver tical compression (and tension) stresses exist high up the wall height. The maximum compression region is the low pressur e flow zone. It can be demonstrated that this increase in vertical stresses is a result of the differential horizontal loading. It is difficult to come up with a satisfactory intuitive understanding for this effect. One way of thinking about it is to consider it to be a result of the curved silo wall attempting to carr y the differential horizontal loading by spaning vertically from the base of the silo up to the roof. The very high vert ical stresses at the base of the wall correspond to a rigid base to these vertically spanning wall elements giving rise to high “negative moments” at the base of the wall. Despite the difficulties in understanding the origin of th is increase in vertical stresses, they have to be accepted as being real.
0.0
Figure 8 Vertical wall stresses due to the full Eurocode loading.
The magnitude and extent of vertical stresses shown in Figure 8 is of great design significance as it has already been identified that in the flow zone where the compression stresses are high, the horizontal pressures cause a local increase in the silo wall radius as it moves towards the compliant shape. As discussed below this causes a reduction in the buckling capacity of the wall in this region. Recall that the Euler critical lateral buckling stress for an ideal axially loaded column with length l and radius of gyration r is: σcr = 2E / [ (l/r) 2 ] (9) Now a very tall and slender silo could buckle laterally in this fashion but it is much more common for a silo to exhibit local buckling with a buckling shape as illustrated in Figure 9.
Figure 9 Typical buckling mode shapes for uniform and non uniform loading.
For uniform vertical loading only, applied to a cylinder of radius r the formula to predict the development of the form of buckling illustrated in Figure 9(a) with Poisson’s ratio of 0.25 is: σcr = 0.6 x E x t / r (10) = 0.6 x 200 x 103 x 25 / 9000 (for the 25 thick wall and the original 9 metre silo radius) = 333 MPa Figure 9 (a) shows the FE buckling prediction for uni form vertical traction loading only applied to the per fect circular silo. The buckling stress prediction of 319 MPa shows excellent correlation to Equation (10).
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The situation for non uniform loading is more complex. It has already been noted that proper assessment of silo behaviour requires non linear analysis – but finite element buckling analysis by definition, is linear and thus cannot directly predict the onset of buckling due to non uniform loading with its inherently non linear characteristics. The analytical Equation (10) is strictly speaking only applicable to uniform loading but it is informative to apply it in the flow zone region where, for non uniform loading, the silo moves (almost) to the compliant shape. The FE model predicts a final silo radius in this region of 24.8 metres. We then have: σcr = 0.6 x 200 x 103 x 25 / 24 800 = 121 MPa Figure 9(b) represents the FE buckling prediction, again for uniform traction loading only but for a model that is initially deformed to the shape illustrated in Figure (6) with the final geometry non linear, 24.8 metre silo radius in the critical region. The FE prediction of 132 MPa buckling stress is very close to that of Equation (10) with some increase due to averaging of the peak stress and the stabilising effect of the adjacent small radius shoulder regions. Thus it appears that for this silo, the non uniform Eurocode loading is causing: • High vertical stresses near the base of the silo • Vertical compression stresses around 100 MPa reaching well up the height of the silo (compared to a • maximum of 62 MPa at the base of the silo for the uniform traction loading only) • A substantial reduction in the buckling capacity of the wall in the flow zone as evidenced by a reduction in the critical buckling stress from 319 MPa down to 132 MPa due to the increase in the silo radius as it moves towards the compliant shape.
8. Working around the problem It appears that the Eurocode load, when applied to steel silos, may be considerably more onerous in comparison to earlier codes that considered only uniform loading. It can probably be shown that while there have been an unacceptable number of failures of steel silos, there are many that are performing well but do not comply with the requirements of the new loading code. It would be easy to start criticising the Eurocode for silo loading that could be seen as being unnecessarily conservative. The author’s research on reinforced concrete silos indicates that the Eurocode for silo loading probably represents a good model of actual silo loads. A more creative way around the problem is to consider whether some modification to the traditional silo structural system may allow the development of a Eurocode conforming silo without the need for significant additional cost while providi ng signif icantly enhanced structural reliabilit y. One possibility is the use of some form of corrugated walling or of multiple vertical or circumferential s tiffeners - or both. The author considers that this approach may have its applications in some areas but that in general is un likely to produce significant benefits. The structural efficiency of a steel silo comes largely from the flexibility of the thin steel wall and its ability to move to the compliant shape. Stiffeners wil l inevitably cause high stress concentrations as they attempt to fight against the flexibility of the wall. A second possibility is illustr ated in Figure 10 (b). This makes use of a single relatively massive stiffener at about one third height. The idea behind this stiffener started with an acceptance of the tendency of the silo to attempt to carry some of the non uniform load by spaning vertically, resulting in high compression stresses in the high radius flow zone. The stiffener represents an attempt to provide an internal support for this vertical load path thus increasing its efficiency in carrying some of the non uniform components of the load.
STEEL SILO DESIGN
the heavier unsti ffened one. Despite this, exami nation of the Von Mises stress at the mid plane shows no yield for the heavier silo and only limited regions of yield for the stiffened silo. It may be concluded that more detailed investigation is likely to confirm that both silos are code compliant as assessed using design by advanced analysis - probably with a considerable margin of safety and some possibility of reductions in plate thicknesses. No attempt has been made to identify whether either or both of these silos comply with the design requirements of EN1993 - 4 - 1 Design of Seel Structures – Silos.
Figure 10 A modified structural system for a steel silo.
9. Design comparison To explore the potential advantages of the silo illustrated in Figure 10 (b) compared to the simpler reference silo of Figure 10 (a), a design assessment was undertaken for the two silos. Both silos were taken as being of Grade 450 steel with elastic plastic behaviour using the Von Mises yield criterion and with E = 200 x 103 MPa and Poisson’s ratio = 0.25. Both silos were of identical geometry and subject to the same loading defined in Figure 2. A decision was made to use a form of design by advanced analysis using geometry and material non linear analysis. The primary decisions necessary for such design assessment involve setting the magnitude and shape of the imperfections to be incorporated in the analysis model and the choice of an appropriate failure criterion to identify the collapse load. Such decisions require extensive sensitivity analyses and comparative trialling against other accepted design methods. The following decisions were adopted with l imited trialling and are intended only to allow for rational comparison of the stiffened and unstiffened silos on an equal basis. The nominal geometric construction tolerance on the silo radius was taken as being +/- 30 mm with a magnifier of 3.0 to include for non geometric imperfections such as residual stresses. Thus the maximum deviation from a perfect cylinder prior to load application was 90 mm. The deformat ion due to the non uniform loads is not included as an imperfection as this deformation is determined directly by the geometry and material non linear analysis. The shape of the imperfections was different for each silo being set to that corresponding to the lowest mode buckling shape for each silo subject to the uniform traction load only but with an initially deformed shape corresponding to the full Eurocode load. The failure criterion was taken as the load beyond which a convergent solution was no longer obtained. This represents a non conservative failure criterion and some might argue for a more conservative criterion such as first yield – but it has already been identified that for steel silos that must adopt their compliant shape, yield is not a good indicator of an approaching failure mechanism. It was found that both silos reached convergence for Load Factors up to 3.2 with no convergent solutions beyond thi s point. Figure 11 compares the Von Mises strain at the outer surface of the silo for load factors of 1.67 and 3.2. The plotting range for strain is limited to the yield strain for Grade 450 steel so white regions represents reg ions where yield has developed at the plate surface. In principle, a load factor of 1.5 / 0.9 = 1.67 represents the minimum necessary load factor for code compliance. At this load factor there is no yield in the heavier unstiffened silo and only small regions of yield for the lighter stiffened silo. With this slight exception, both silos achieve the necessary collapse load as assessed using the very conservative first yield failure criterion. At a load factor of 3.2 as must be expected, the thinner sti ffened silo, with extensive regions of yield, is working harder than
Figure 11 Comparative design assessment for the two silos.
10. Disclaimer and overall conclusions This paper has simplified some matters and omitted consideration of significant design issues other than those central to its focus. The paper is not intended to demonstrate a definitive design approach for steel silos. It is hoped that this paper will provide some general understanding of steel silo behaviour and design for interested engineers and that specialist steel silo designers may find it to be pro vocative of discussion and perhaps robust criticism. Some will continue to question the credibility of the Eurocode silo loading. As has been shown, field measurements of steel silo wall deformations allowing determination of pressure ratios in flow and shoulder zones could readily provide further proof or otherwise as to the correctness of the Eurocode load. It is not claimed that the silo system incorporating a single relatively massive stiffener necessarily represents a step forward with regard to the design of steel silos. It is suggested that steel silo designers should accept the challenge of considering new options for achieving more reliable and economical steel silo designs based on a solid understanding of the implications of the Eurocode loading.
KEY REFERENCES Durack, J. McKay, H. 2007. Implications of the new Eurocode EN1991-4 to cement and raw meal silo design. Austra lian Bu lk Handl ing Revie w Vol 12 Nos 2 and 3. Durack, J. McKay, H. 2007. Measured wall movements during discharge compared to Eurocode predictions for an inverted cone silo. Intern ationa l Bulk Materi als Handling Conferen ce. University of Newcastle. Durack, J. 2008. Observations of the performance of existing inverted cone silos. Bulk Materials Handli ng Conference, Brisbane. Durack, J. 2008. The analysis and design of reinforced concrete silos. 20th Austr alian Conferen ce on the Mechanic s of Stru cture s and Materi als . University of Southern Queensland.
Contact: James Durack, email –
[email protected]
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