Abstract
Large diameter steel silos usually require a beam structure to support rooftop inspection gangways and resist loads derived from the snow and wind actions. The existence of localized overloads caused by drifted snow on roofs as a consequence of the wind action has been reported in the literature. European standard EN 1991-1-3 also considers the need of taking into account asymmetric patterns for snow loads calculation. However, conical roofs are not included in the specific list of cases considered by this standard. The present work compares the normal stresses and displacements produced in a conical steel silo roof structure by applying balanced loads distributed on the whole roof and unbalanced loads applied on a roof sector. Experimental measurements and a three-dimensional beam model developed by the authors have been used to predict the stresses and vertical displacements of a metal silo roof structure measuring 18.34 m in diameter. The results show that the existence of an asymmetric load pattern produces higher normal stresses (up to 23%) and vertical displacements (up to 50%) than those derived from balanced loads, for any similar load per beam considered.
Introduction
Silos have been used as storage facilities in the agricultural, mining, chemical and pharmaceutical industries since the end of the 19th century (Ayuga, 2008). Cylindrical silos made of steel are probably the most commonly used for agroindustrial purposes (Gallego et al., 2011). There are many design alternatives that can be employed for this type of silos. However, the installation of many consecutive large-diameter silos forming a ‘silo battery’ is very frequent. In this particular design, an inspection gangway is usually placed over all the silos forming the battery. In addition, silo roofs are exposed to the action of wind and snow, which have to be taken into account in their design.
Because of this, the silo roof must have a structure that provides support to rooftop inspection gangways and allows resisting loads derived from the snow and wind actions, covered in Europe by the standards EN 1991-1-3 (2003) and EN 1991-1-4 (2005). Silo roof structure must therefore prevent undesirable stresses on the silo wall, which might result in the denting of the side panels or even their buckling and failure, while allowing all gangways to be held firmly in place (Ayuga, 2008; Briassoulis and Pecknold, 1987; Portela and Godoy, 2005).
The loads derived from most of the actions applied on the structures are usually calculated by considering a uniform load arrangement, despite many research works have shown the negative effects caused by asymmetries in the load distribution (Ma et al., 2013; Manko and Beben, 2006; Studziński et al., 2015; Wang and Li, 2007). Snow loads are responsible of many structural failures in buildings (Wardhana and Hadipriono, 2003). The main cause of structural failures associated with snow loads is the occurrence of exceptional heavy snowfalls that produce snow loads above the limits considered by standards (Krentowski, 2014; Piskoty et al., 2013; Sadovský et al., 2012).
However, the existence of localized significant roof overloads caused by drifted snow as a consequence of the wind action occurs frequently. This is the reason why both wind and snow actions are usually combined to design buildings (Wang and Rosowsky, 2013). According to Tsuchiya et al. (2002), the location and form of snowdrift will depend on many factors, such as wind direction, wind velocity, temperature or roof shapes. Meløysund et al. (2007) indicate that drifting occurs even for light winds (0.3–1.5 m/s), but wind velocities greater than 3.4 m/s will induce the snow to move considerably faster horizontally than vertically, thus producing a significant redistribution of snow.
Biegus and Rykaluk (2009) found that the reason for the collapse of a steel building in Katowice was the localized overloads associated with drifted snow. Snow overloads of more than twice the snow load defined in the Polish standard were measured in some localized areas of the roof. Geis et al. (2012) found more than 1000 snow-induced building failure incidents in the United States between 1989 and 2009, from which localized overloads produced by snowdrift was one of the causes. Thus, it is important to consider drifted snow loads on roofs as one of the possible load arrangements associated with snow actions (Sakla and Elbeltagi, 2003).
The Eurocode standard (EN 1991-1-3, 2003) considers the need of taking into account a specific load arrangement for snow action on roofs with asymmetric drifted snow loads. However, conical roofs are not included in the particular list of cases considered by the standard. None of the roof shapes defined in EN 1991-1-3 (2007) is comparable to the roof shape of cylindrical silos. Silo conical roofs have a constant slope like pitched roofs. However, they have a diiferent plan view: rectangular for pitched roofs and circular for conical roofs. If conical and spherical roofs are compared, it can be found a similar plan view (circular), but spherical roofs do not have a constant slope. Thus, it would be interesting to determine the effect of snow drifts on the conical roof of cylindrical silos.
Several experimental tests have been carried out on steel structures to validate the results predicted by numerical models in relation with the real behaviour of connections (Iványi, 2000; Wood and Dawe, 2006) or buckling of members (Dubina, 2008; Kim et al., 2003), among some other aspects. Other research works have focused on the stresses and deformations on steel members (Bagheri et al., 2010; Lee and McClure, 2007; Xue and Liu, 2009; Yang and Liu, 2012). However, the experimental design made by the authors (Ramírez-Gómez et al., 2014) for instrumenting and testing the real behaviour of a 18.34-m-diameter steel silo roof is original with respect to this type of structure.
The main objective of this work is to compare the normal stresses and displacements produced in a conical steel silo roof structure by employing non-drifted (balanced) and drifted (unbalanced) snow loads. In addition, the validity of a numerical three-dimensional (3D) model developed by the authors (Ramírez-Gómez et al., 2014) was checked in order to predict the effects of drifted snow loads on the conical silo roof structure.
Description of the silo roof structure
The silo roof used in the present work was 18.34 m in diameter. The structure supporting the roof was composed of 24 radial beams resisting the loads acting on the roof (Figure 1). The same beams also provided a surface for the fixing of the covering panels.
Structure of the silo roof used in the present work (left), details of the beam elements and connections (right).
Circular beams were bolted to the radial beams at a regular distance in order to prevent lateral buckling of radial beams. As it can be seen in Figure 1, each radial beam is bolted to four circular beams. Both radial and circular beams have a sigma-cross section profile (∑). A steel plate was used to connect the circular beams to the radial beams only through the web of both beam types, leaving the flanges to rotate freely. This plate was L-shaped, being one side attached to the web of the circular beam and the other side attached to the web of the radial beam. In both cases, bolts were used to connect the plate with the radial or circular beams. Therefore, this type of union was understood as articulated in the 3D beam model.
A ring stiffener made of a UPN-300 profile was placed at top of the roof structure, in order to increase rigidity of this area for preventing excessive displacements of nodes. Therefore, the radial beams were rigidly joined to the ring stiffener. For this type of union, steel plates are also used to connect the ring stiffener to the radial beams by means of bolts. In this case, the steel plate is joined both to the web and flanges of the radial beam, thus forcing the radial beam and ring stiffener to maintain the angle formed by both elements, even if the structure is loaded. This is the reason why this type of union was supposed to be rigid in the 3D beam model.
Tension plates were placed at the lower part of the roof structure joining radial beams among them to prevent their lateral displacement. In this case, radial beams and tension plates were only joined by bolts placed at the web of the radial beams. Therefore, the flanges of the radial beams can freely move with respect to the tension plate. This is the reason why the union of tension plates to the radial beams was supposed to be articulated in the 3D beam model.
The 3D beam model
A 3D beam model was also developed to predict the behaviour of the silo roof under load using the PowerFrame software by BuildSoft (2006). The numerical model was based on the displacement method and contemplated the following cross sections for the main bar elements of the model (Figure 1), trying to simulate as faithfully as possible the real structure:
Radial beams and circular beams with a sigma-cross section profile (height of 250 mm, thickness of 3 mm);
A top ring stiffener with a European Standard Channel UPN-300 profile;
18-cm-high, 3-mm-thick steel tension plates joining the radial beams at their lower part, close to the vertical wall sheet.
The constrains applied to the model, and the assumptions considered with regard to the joints of the roof structure are widely described and explained in Ramírez-Gómez et al. (2014). The simulation of snow loads in the numerical model was developed by applying static loads at the beam locations corresponding to the loading points in the experimental tests conducted. In addition, it was assumed an elastic and geometrically linear behaviour of the material since the maximum level of stresses in the structure was far from the yield limit of the steel used, and the peak value of the measured vertical displacements was very low (less than D/700, where D is the silo diameter).
Test procedure
Load application system
Displacement inducted loads were applied to the roof structure via the use of slings, which were fixed at one end to a concrete floor slab using bolts (Figure 2), while the other end was wrapped over and anchored to the joints between the radial and circular beams. The number of points where loads were applied depended on the type of test conducted.
System used to apply loads to the structure (left), wrapping and anchoring of the slings (right).
Slings were strained by men using a ratcheting system, and following the instructions given by the responsible of making the test in order to obtain a similar level of strain at every step of loading. The ratcheting of the slings implies the application of a tension force which is later transferred to the roof beam, since the sling was completely wrapped around it.
This procedure does not strictly simulate real snow-induced loads, but it was finally adopted for several reasons. It was important to be able to simultaneously apply a quite similar load increment on all roof beams selected, in order to check the effects produced by progressive loads on strains, displacements and stresses. In addition, it was also important to use a load protocol as safe as possible, because of the size of the structure to be tested.
For the ‘Balanced Load’ tests, a total of 54 points (Figure 3(a)) were employed, and they were distributed over the entire roof structure in order to simulate a uniform snow load distributed on the whole roof. On the other hand, a second test type referred as ‘Sector Load’ was developed in order to simulate an unbalanced snow load. In this case, loads were applied to the roof structure in nine points placed in three consecutive radial beams (Figure 3(b)).
Loading points: (a) ‘Balanced Load’ test type and (b) ‘Sector Load’ test type.
Equal loads were applied simultaneously to the loading points, in regular increments up to a maximum of 7.2 kN (approximately 80% of the load the roof could resist) using the ratcheting system on each of the slings. A complete test for any of the test types conducted included up to 10 steps for applying the total load of the test. This procedure was adopted for safety reasons, and to allow measuring the displacements and stresses produced in the roof structure for different load levels.
Seven tests were conducted for the ‘Balanced Load’ test type, while three tests were performed for the ‘Sector Load’ test type. Eight dynamometers were used to monitor and register the real loads applied to the roof structure for every test. The location of the eight dynamometers (D1–D8) used to measure the applied loads for the balanced load test type and sector load test type is shown in Figure 4. A detailed description of the technical specifications of the dynamometers installed can be found in Ramírez-Gómez et al. (2014).
Position of the dynamometers: (a) ‘Balanced Load’ test type and (b) ‘Sector Load’ test type.
Table 1 shows detailed information about the loads measured for every step in the different tests conducted. BL1–BL7 refer to different repetitions of the ‘Balanced Load’ test type, while SL1–SL3 refer to the ‘Sector Load’ test type. An average load per beam was calculated for every assay dividing the total load applied during the test by the number of radial beams supporting loads in each test type: 24 for the ‘Balanced Load’ tests and 3 for the ‘Sector Load’ tests.
Loads applied for the different assays conducted.
Instrumentation of the tests
Three fleximeters were installed for measuring vertical displacement (range of 0–100 mm, resolution of ±0.025 mm), one hanging from the ring stiffener and two from the second vein of radial beams 1 and 13. The horizontal displacement at the bottom of the radial beams was measured using four displacement gauges (resolution of 0.01 mm) located on vertical stiffeners. Strains in the radial beams were measured using linear strain gauges (350 Ω) located on four beams opposite one another. The magnitude of the stress was then determined by multiplying this value by the modulus of elasticity of the steel beams (210 GPa). Two strain gauges were placed at each point, thus allowing the distribution of normal stress over the cross section of the beam to be determined, and traction and compression stresses to be identified.
Finally, the readings from the strain gauges were recorded using an ESAM Traveller 1 24-channel datalogger. The readings from the fleximeters were recorded using a DATA-TAKER DT50 datalogger. A more detailed description of the location and the technical specifications of the instrumentation can be found in Ramírez-Gómez et al. (2014).
Results
Nomenclature used in the expression of the results
Results included in section ‘Comparison of the experimental results and those obtained using the 3D beam model’ show the change in normal stress (N/mm2) or vertical displacement (mm), with respect to time ‘t’ (s), at defined points in the roof structure. A positive normal stress value reflects traction stress while a negative value reflects compression stress.
The curves for the normal stresses measured in the radial beams are reflected following the format RiGj_PL, where Ri refers to the radial beam in question (varying from 1 to 4 since four radial beams were chosen for mounting the instruments, between which there was an angular separation of 90°), Gj marks the position on the radial beam where the normal stress was measured (1: gauges on the radial beam nearer to the tension plates or 2: gauges on the radial beam nearer to the top ring stiffener), and PL indicates the position (T: upper or B: lower flange) of the strain gauge at point Gj. The results presented in this article refer only to G1 position, since the findings from Ramírez-Gómez et al. (2014) showed that higher stresses appeared in this point.
The curves showing the change in normal stress obtained by the numerical 3D beam model are identified with the nomenclature PF_Gj_PL, where PF refers to the PowerFrame software used in the calculations, and Gj and PL are those described above. In the results obtained using the numerical model, no Ri value is provided since the distribution of the loads applied was symmetrical (the results would therefore be the same for all the radial beams) for the ‘Balanced Load’ test type, while the results corresponding to R1 were obtained with the 3D beam model for the ‘Sector Load’ test type.
The legend FLk is used to describe the vertical displacements recorded, where k indicates the position of the fleximeter. The displacement curves obtained with the Powerframe 3D beam model are identified with the abbreviation PF (FLk).
Comparison of the experimental results and those obtained using the 3D beam model
Figures 5 and 6 show a comparison between the experimental and numerical normal stresses obtained for the ‘Balanced Load’ and ‘Sector Load’ test types, respectively, in one of the test repetitions conducted (similar behaviours were obtained for the rest). It can be noted that the normal stresses predicted by the 3D beam model agree with those measured for both cases.
Comparison between the normal stresses measured experimentally and predicted by 3D beam model for all the radial beams at position G1 in one repetition of the ‘Balanced Load’ test.
Comparison between the normal stresses measured experimentally and predicted by 3D beam model for all the radial beams at position G1 in one repetition of the ‘Sector Load’ test.
For the ‘Balanced Load’ test type (Figure 5), it is interesting to note that in all the radial beams, the normal stress in the upper flange (T, top) was one of compression, while in the lower flange it was one of traction. In addition, the normal stress of traction was always smaller than the normal stress of compression at any single position and at any moment in time. For the assay repetition shown in Figure 5, a maximum normal stress of compression close to 90 MPa was measured, while a maximum normal stress of traction close to 55 MPa was measured, thus indicating the radial beam was subject to a positive bending moment and a normal compression force.
For either of the flanges (T, top; B, bottom), and at any instant t, Figure 5 shows small differences between the normal stresses measured in the four radial beams. The reason for these differences lie in the fact that the forces applied at each of the 54 loading points were not exactly the same.
For the ‘Sector Load’ test type (Figure 6), it can be seen that normal stresses were registered only for radial beam 1, which was caused by the load pattern followed. This test type was conducted by applying loads only in nine loading points belonging to three consecutive radial beams, being one of them the aforementioned radial beam 1. In this case, the normal stresses measured in both flanges (T, top; B, bottom) were very similar at any instant t: one of compression in the upper flange (T) and one of traction in the lower flange (B). A peak value of 70 MPa was obtained for the assay repetition shown in Figure 6.
Figures 7 and 8 show a comparison between the experimental and numerical vertical displacements obtained for the ‘Balanced Load’ and ‘Sector Load’ test types, respectively. In this case, the values predicted by the numerical 3D beam model are lower than those experimentally measured for both test types. In the case of the ‘Balanced Load’ test type, a maximum vertical displacement of 23 mm was measured, while the value predicted by the numerical model was 20 mm. Displacements measured in positions FL1 and FL3 are quite similar for the ‘Balanced Load’ case (Figure 7), as it was expected because this test type tried to reproduce a uniform snow load distributed all over the roof.
Comparison between the vertical displacement values measured experimentally and those predicted by 3D beam model in one repetition of the ‘Balanced Load’ test.
Comparison between the vertical displacement values measured experimentally and those predicted by 3D beam model in one repetition of the ‘Sector Load’ test.
The results obtained for the ‘Sector Load’ test type also show that measured values are greater than the numerical predictions. In this case, in Figure 8, it can be seen that a downward vertical displacement is produced in the radial beam located in the sector loaded, while the radial beam placed on the opposite part of the silo roof shows an upward vertical displacement. However, the downward vertical displacements are significantly greater than the upward vertical registered displacements.
Regression analyses
The normal stresses predicted by the PowerFrame 3D beam model (Figure 9) and those experimentally measured (Figure 10) were plotted against the average load per beam applied at the different load intervals considered for the different test repetitions (Table 1) conducted in both test types, ‘Balanced Load’ and ‘Sector Load’.
Normal stress values predicted by the numerical 3D beam model (PF) for every load interval used in both test types.
Normal stress values experimentally measured (tests) for every load interval used in both test types.
According to Figure 9, it should be noted that the numerical 3D beam model predicts greater normal stresses when a similar load per beam is applied if the load pattern is asymmetric. A linear regression analysis was conducted to check the relationship existing between the expected normal stress and the average load per beam applied to the radial beams. The regression curves were forced to pass through the origin of coordinates because the peak value of normal stresses (90 MPa) was far from the yield stress limit of the steel used (275 MPa), thus indicating the existence of a linear and elastic behaviour of the structure. The correlation between the normal stresses and the average beam load was very good: the square correlation coefficient (R2) was higher than 0.98 for both load patterns.
If the linear regression equations for both load cases (‘Balanced Load’ and ‘Sector Load’) are compared, it can be obtained that the numerical 3D beam model predicts that normal stresses obtained with the ‘Sector Load’ case are meant to be 17.2% greater than those calculated for a ‘Balanced Load’ case with a similar average load per beam.
A similar analysis was conducted for the actual normal stresses measured for all the assay repetitions and load intervals considered in the experimental tests (Figure 10). Very high correlation between the normal stresses measured and the average beam loads applied was also found in this case, as the square correlation coefficient (R2) was higher than 0.90 for both test types. As it was predicted by the numerical 3D beam model, a greater normal stress is expected if the load pattern is asymmetric. In this case, the experimental results show that normal stresses obtained with an asymmetric load pattern (‘Balanced Load’) are expected to be 23.1% greater than the corresponding to a symmetric load pattern (‘Balanced Load’) if a similar average load per beam is applied to the roof structure.
A similar analysis was also conducted for the vertical displacements suffered by the radial beams of the roof structure. Figure 11 shows again that the peak vertical displacements predicted by the 3D beam model are greater for an asymmetric load pattern (‘Sector Load’) than those corresponding to the ‘Balanced Load’ case. In this case, it is quite significant to observe that the differences between both load patterns are significantly greater than those observed for the normal stresses. Thus, vertical displacements would be 42.1% higher if a ‘Sector Load’ pattern is followed, for a certain value of average load per beam.
Vertical displacements predicted by 3D beam model (PF) for every load interval used in both test types.
The experimental regression curves obtained for the vertical displacements (Figure 12) are again in good agreement with the conclusions derived from the numerical analysis. Now, vertical displacements would be 50.6% higher if a ‘Sector Load’ pattern is followed, for a certain value of average load per beam.
Vertical displacements experimentally measured (tests) for every load interval used in both test types.
Discussion
Table 2 shows all the linear regression equations obtained for both sets of results (‘Numerical model’ and ‘Experimental tests’) and test types considered in this research (‘Balanced Load’ and ‘Sector Load’) with respect to the normal stresses and vertical displacements, where q is the average load per beam applied, as defined in section ‘Regression analyses’.
Linear regression equations obtained for normal stresses (σ) and vertical displacements (δ) against the average beam load (q, in kN/beam) applied to the radial beam for both sets of results and test types.
The regression equations obtained for both sets of results are very similar for the normal stresses, with independence of the type of test considered. Thus, a maximum difference of only 2.99% between the experimental tests and the numerical 3D beam model results is observed for the ‘Sector Load’ case, and the differences for the ‘Balanced Load’ case are even lower. On the other hand, greater differences appear when vertical displacements are compared. In this case, the experimentally measured results are 21.6% greater than those predicted by the numerical 3D beam model for the ‘Sector Load’ case, and 16.9% greater for the ‘Balanced Load’ case.
An important fact can be derived from the results shown in Table 2. If the results obtained in the experimental assays are considered, then the existence of an asymmetric load pattern (‘Sector Load’) can produce up to 23.1% higher normal stresses and 50.6% higher vertical displacements than the ones measured for a symmetric load pattern (‘Balanced Load’) for any similar beam load considered.
The regression equations obtained (Table 2) also corroborate that the 3D beam model developed by Ramírez-Gómez et al. (2014) satisfactorily predicts the maximum normal stresses expected in a roof structure, even for an asymmetric load pattern. However, the vertical displacements predicted by the 3D beam model are slightly underestimated, thus indicating the need of adjusting the numerical predicted values to those that would appear in a real roof structure.
Conclusions
Snow loads are responsible of some structural failures in buildings. Many of those failures are associated with exceptional heavy snowfalls that produce snow loads above the limits considered by standards. Other frequent cause is the existence of localized significant roof overloads on roofs caused by drifted snow as a consequence of the wind action. The European standard EN 1991-1-3 considers the need of taking into account an asymmetric distribution of snow load, but conical roofs are not included in the specific list of cases considered by this standard.
The present research analyses the effects of applying balanced or unbalanced sectorial loads on 18.34-m-diameter steel silo conical roof. Experimental measurements and a numerical 3D beam model developed by the authors allow the following conclusions to be drawn:
The regression equations obtained corroborate that the numerical model developed satisfactorily predicts the maximum normal stresses expected in a roof structure, even for an asymmetric load pattern. However, the vertical displacements predicted by the 3D beam model were slightly underestimated.
A high square correlation coefficient (R2), greater than 0.92 in every case, was obtained for the linear regression equations derived to relate normal stresses (σ) or vertical displacements (δ) with the average beam load (q, in kN/beam) applied to the radial beams. A very good relationship was found for both sets of results (experimental tests and numerical model) and test types (balanced load and sector load), as shown in Table 2.
The experimental measurements and numerical results show that the existence of an asymmetric sector load produces higher normal stresses (up to 23.1%) and vertical displacements (up to 50.6%) than those derived from balanced loads, for any similar load per beam considered. The values of the higher stresses and vertical displacements measured for the sector load test type could have slightly varied if another load protocol would have been used. Therefore, it could be interesting to analyse different load protocols in future research works.
According to the results obtained, it would be recommended that a drifted snow load arrangement should also be considered for conical roofs in Eurocode standards.
Footnotes
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship and/or publication of this article.