## 2 Structural Typology and Arrangement of Circular Silos
### Buckling Types and Analysis
On this topic, the European standard EN 1991-4 [71] suggests a unique approach (mentioned in Section 5.5) to characterize the unsymmetric pressure exerted by eccentricities in silo filling/discharging. [PERSON] and [PERSON] [67] introduced a study addressing the buckling behavior and imperfection sensitivity of a moderately slender silo, considering the real-life conditions and more realistic situations by taking into consideration the eccentric solids flow and the associated unsymmetrical pressure on the silo wall. The study adopted the approach suggested by the European Standard EN 1991-4 [71] to characterize the unsymmetric pressure exerted by the eccentric discharge. The study defined the critical regions of the highest compressive axial membrane stresses, where the silo may buckle, providing a dissertation on the phenomenon of the mid-height buckling failure that was frequently observed in the practice. In this phenomenon, a very high membrane stress developed in the thin wall coinciding with the lower bulk-induced internal pressures in the flow channel leads to eliminate the elastic restraint provided by the solids. The study mainly stated that a silo designed for symmetrical filling/discharging conditions only (according to EN 1991-4 [71]) may encounter a disastrous failure if eccentric discharging develops. In addition, this work was resumed by [PERSON] and [PERSON] [16] for very slender silos, taking into consideration the imperfection sensitivity of the buckling failure mode. Similarly, this study characterized the unsymmetric pressure induced by the eccentric discharge in accordance with the description provided by EN 1991-4 [71]. Then, the geometric and material nonlinearities were considered for buckling calculations according to the European standards EN 1993-1-6 [72]. Authors concluded that the approach of EN 1991-4 [71]. For unsymmetrical pressure modelling (induced by eccentric discharge) is highly damaging for a very slender stepped-wall metal silo if it is designed only for symmetric pressure. The nonlinear FE model yielded that the European provisions EN 1993-1-6 [72] should be re-edited as they are formulated, considering experiments under axisymmetric conditions only. However, the vulnerability of cylindrical shells to the different buckling modes could be reduced and the structural efficiency could be enhanced by adopting alternative structural arrangements, such as a closely stiffened shell, a cylindrical shell reinforced by stringers/corrugations [73] and rings [18], or even fiber reinforced polymers [19]. In other words, the basic idea is to use a higher efficient material in silos construction. In practice, the shell body of the silo could be combined with ring or vertical stiffeners, aiming to reduce the thickness of the shell without decreasing the buckling resistance of the silo. Corrugated walls could also be used in combination with different stiffeners, as for example, shown in Figure 5. One of the first studies addressing the stiffened shell buckling behavior were conducted by [PERSON] [74], pursuing to produce lightweight structures, in order to meet the demand of the aerospace and ship industry. A few decades later, [PERSON] [75] developed an extensive experimental program and provided a remarkable approach (used until today) to simply analyze stiffened shells. In the recent scientific literature, a huge research work is introduced addressing meanly the stiffened shells used for aerospace applications, for example [76,77]. In the last few years, several researchers reactivated the research about stiffened shells used in the field of civil engineering. Some research directions approached the interaction of different strengthening techniques with corrugated shells. For instance, [PERSON] and [PERSON] [73] introduced a study in which they investigated the buckling behavior of vertical stiffeners attached to the shell body of a corrugated silo. The considered stiffeners have the characteristics of cold-formed steel sections.