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Thin-walled cylindrical steel silos are one of the major storage structures in most of industrial and agricultural sectors. There are different load cases that should be considered in design of silos, such as, filling and discharge loads, wind load, seismic load and thermal loads. Nevertheless, during the life cycle of a silo, filling and discharge of particulate solids exert the most frequent loads on the silo walls. Due to larger values of discharge pressures as compared with those of filling pressures, discharge loads are considered for structural design of silos. Considering small wall thickness of steel silos, they are susceptible to buckling failure. Under discharge pressures, high meridional (axial) compression and internal pressure form at the base of silos that can lead to elastic-plastic elephant’s foot buckling mode. Therefore, it is deemed as the main buckling failure mode under discharge loads of silos. 
The wall friction coefficient of silos mainly depends on the wall surface characteristic and type of the ensiled material. This coefficient is a key variable in determination of magnitude and distribution of discharge pressures. To assess the effect of this variable on buckling capacity of steel silos, three example silos with different aspect ratios were considered. Each silo was loaded by the concentric discharge pressures in accordance to Eurocode. Subsequently, 3D linear and non-linear buckling analyses (i.e., LBA and GMNA analyses, respectively) were performed for different amounts of wall friction coefficient that varied between 0.2 and 0.6.  
Considering the results obtained, LBA analyses predicted an elastic axial compression buckling mode in the upper edge of base strake, where there is a change in shell wall thickness. Also, an elastic-plastic elephant’s foot buckling mode at the base strake of each silo was predicted by the GMNA analyses. Moreover, the load-path curves of example silos extracted from the GMNA analyses showed a bifurcation buckling that was followed by a dramatic reduction in post-buckling resistance. This held true for all three silos and all different values of wall friction coefficient considered in this study. 
The discharge buckling resistances estimated by the LBA were up to three times larger than those predicted by the GMNA. Therefore, including non-linearity in discharge buckling assessment of silos is urgently required. The effect of wall friction coefficient on buckling capacities of steel silos was significant for the LBA analyses that governed by axial compression. However, the elephant’s foot buckling mode observed under discharge load is affected by the both axial and internal pressures. As a result, adopting more sophisticated analyzing procedure that includes geometrically and materially non-linearity in the calculations (i.e., GMNA analyses) showed quite marginal effects for this coefficient (with the maximum difference of 8% in buckling capacity). 
As an extra investigation, the Eurocode provisions on stress design of steel silos under meridional compression with coexistent of internal pressure have also been examined. Eurocode recommends a reduction in critical axial buckling stress due to accompanying internal pressure, in terms of the plastic pressurised imperfection reduction factor αpp. As compared with the finite element results, for all the cases considered in this paper, the critical axial membrane stress calculated with respect to the Eurocode provisions yielded satisfactory predictions. 

Keywords: Steel cylindrical silos, Buckling, Eurocode, Discharge pressure, Abaqus

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