شکست سیلوهای فولادی استوانه ای شکل ساخته شده از صفحات و ستون های موجدار و روش تعمیر با استفاده از تجزیه و تحلیل حساسیت

The paper deals with failure of large cylindrical steel silos composed of horizontally corrugated sheets with vertical stiffeners. The failure reasons were discussed. A linear buckling and a non-linear analysis with geometric and material non-linearity were carried out with a perfect and an imperfect silo shell (with different initial geometric imperfections) by taking into account axisymmetric and non-axisymmetric loads imposed by a bulk solid following Eurocode 1. The 3D FE calculations were carried out with the commercial finite element code “Abaqus”. The calculated buckling forces were compared with the allowable one given by Eurocode 3. Repair methods of silos against buckling were proposed. A sensitivity analysis was performed for a silo to predict the location and profile type of strengthening elements.

Thin metal cylindrical silo shells are vulnerable to buckling failures caused by the compressive wall friction force, particularly during eccentric discharge (which is usually difficult to avoid with regard to a non-homogeneous character of bulk solids). As a consequence, non-uniform horizontal wall pressures develop which contribute to (except of meridional bending) a non-symmetric distribution of compressive vertical wall forces. The buckling strength of shells depends on many different factors such as: form and amplitude of initial geometric imperfections, loading and material imperfections, type of joints, boundary conditions at ends, level of internal pressurization and stiffness of the stored bulk solid [1], [2], [3] and [4]. Metal silos are frequently built of thin-walled horizontally corrugated curved sheets strengthened by vertical stiffeners (columns) distributed uniformly around the silo circumference and connected with screws due to an economical steel consumption and a small silo weight [1]. In those silos, horizontally corrugated wall sheets carry horizontal tensile forces caused by horizontal wall pressure of a bulk solid and vertical columns carry vertical compressive forces exerted by wall friction stress from a bulk solid. Eurocode 3 [5] gives a simplified formula to calculate the buckling strength of vertical columns around the silo circumference, which does not take into account a real 3D buckling behavior of silo shells containing a silo fill. The aim of the paper is threefold: (a) to describe a failure case of large cylindrical metal silos composed of horizontally corrugated sheets strengthened by vertical columns (which failed by buckling), (b) to compare the calculated buckling strength from FE analyses with that given by Eurocode 3 [5] and (c) to predict the location and profile type of strengthening elements by using a sensitivity analysis. Both a linear buckling analysis and a non-linear FE analysis (with both geometric and material non-linearity) were carried out with a perfect and an imperfect silo shell by taking into account uniform and non-uniform loads exerted by a bulk solid (specified by Eurocode 1 [6]) and different initial wall geometric imperfections along the silo circumference and silo height. The full 3D FE calculations were carried out with the commercial finite element code “Abaqus” [7]. Finally, strengthening methods were proposed to repair the failed silos. In contrast to many buckling analyses performed for metal silo shells with isotropic rolled thin-walled walls [4], [8], [9], [10] and [11], the comprehensive buckling analyses of a cylindrical silo consisted of horizontally corrugated sheets and vertical stiffeners have rarely been carried out [12]. Our preliminary FE studies [12] have shown that the buckling strength proposed by [5] is very conservative.

The following conclusions can be drawn: – The failure of cylindrical metal silos was caused by buckling of vertical columns. The buckling strength of columns was 2–4 times smaller than the allowable one by Eurocode 3. – The initial imperfections in the form of an eigen-mode are obviously the most detrimental for a silo. If the wall amplitude of initial geometric imperfections in silos is limited to about 5 cm, the buckling strength from a 3D analysis is five times higher than this from Eurocode 3. If the wall amplitude of initial geometric imperfections is limited to about 10 cm, the buckling strength based on a 3D analysis is as twice as high as this from Eurocode 3. If it is equal approximately to 13 cm, the calculated 3D buckling strength is similar as this given by Eurocode 3. – The buckling bearing capacity of vertical columns by Eurocode 3 is very conservative to be on the very safe side by assuming the number of buckling half-waves along the circumference equal to the half of the column number. – The sensitivity analysis enables one to describe the influence of the location and size of circumferential stiffeners or column profiles on the buckling vertical force. It is helpful in the column design to place the stiffeners in the most effective way. – Two additional circumferential rings of the stiffness 200 kN/m in the silo with the fixed bottom increase the silo buckling resistance to the design load level. – The bending stiffness of vertical columns should be strengthened 2–3 times mainly at height of 5–9 m to increase the silo buckling resistance to the design load level.