Simplified numerical model for global stability of corrugated silos with vertical stiffeners P. Iwicki, K. Rejowski, J. Tejchman ⁎ Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk-Wrzeszcz, Poland abstract article info Article history: Received 15 August 2016 Received in revised form 9 May 2017 Accepted 25 June 2017 Available online xxxx The paper deals with buckling of metal cylindrical silos composed of corrugated sheets and vertical stiff- eners (columns). Comprehensive finite element analyses were carried out for three real perfect silos with a different geometry (two slender silos and one intermediate slender silo) by means of a linear buckling ap- proach. Corrugated walls were simulated as an equivalent orthotropic shell and thin-walled columns as beam elements. Numerical calculations for perfect silos with different numbers of columns made it possible to establish three different ranges of the silo buckling performance. Based on results of three dimensional calculations, an original simplified segment silo wall model was proposed for calculations of silo global buckling for sparsely distributed columns. In addition, a single column resting on the elastic foundation with the improved stiffness was suggested. Both models are shown to produce predictions that are much closer to rigorous FE calculations than the hand calculation procedures of EN 1993-4-1. © 2017 Elsevier Ltd. All rights reserved. Keywords: Eurocode approach Columns Corrugated walls Linear buckling analysis Metal cylindrical silo 1. Introduction Cylindrical thin-walled silos are subjected to buckling failures caused by vertical compressive wall friction forces due to the inter- action between the silo fill and silo wall [1–4], particularly during ec- centric discharges which are difficult to avoid with regard to a non- homogeneous character of bulk solids [5,6]. As a consequence, a non-symmetric distribution of vertical wall compressive forces and horizontal wall pressures is created. At present metal cylindrical silos are mainly built of thin-walled horizontally corrugated curved sheets strengthened by vertical stiff- eners (columns) distributed uniformly around the silo circumfer- ence and connected with screws due to an economical material consumption (small silo weight). Corrugated wall sheets carry cir- cumferential tensile forces caused by horizontal wall pressures of bulk solids and vertical columns carry vertical compressive forces exerted by wall frictional traction from bulk solids [7]. In the engi- neering design practice it is usual to use simple formulae instead of full finite element (FE) analyses of entire 3D silos that requires a huge number of finite elements related to the too long calculation time. Simplified design procedures are available in Eurocode 3 (EC3) (sections 5.3.4.3.3 and 5.3.4.3.4) [8] and in EC3 amendment proposals [9] (section 20) where the silo design is based on formulae for global or local buckling and column plastification. The ap- proaches related to silo global buckling depend upon a column sep- aration. Our 3D FE calculation results [10–16] evidently show that the EC3 approach [8] provides evidently too conservative outcomes for silos with corrugated sheets and columns. The silo design follow- ing the formulae in EC3 [8] indicates 3–5 times differences in the buckling strength for sparsely distributed columns and 1.5 times dif- ferences for densely distributed columns. Furthermore the funda- mental drawback of EC3 [8] is the lack of a continuity between two above mentioned approaches with respect to the column separation [14]. Some improvements of standard buckling formulae for the silo design have been already proposed by our research group [13,14,17, 18] based on numerical 3D finite element (FE) analysis outcomes. In the paper [13] we suggested a formula for the orthotropic shell the- ory for all silos but with a reduction factor depending on the column spacing versus the threshold column spacing d s,max . In the papers [17,18], a new formula for the calculation of the 1D silo column elas- tic foundation stiffness was proposed for silos with very sparsely dis- tributed columns, wherein the wall curvature and components associated with bending and circumferential tension were taken into account (it was comparable to the EC3 amendment proposals [9]). The purpose of our research works is the improvement of EC3 formulae [8] for global buckling. In this paper we focus on Journal of Constructional Steel Research 138 (2017) 93–116 ⁎ Corresponding author. E-mail addresses: piwicki@pg.gda.pl (P. Iwicki), rejowskikarol@wp.pl (K. Rejowski), tejchmk@pg.gda.pl (J. Tejchman). http://dx.doi.org/10.1016/j.jcsr.2017.06.031 0143-974X/© 2017 Elsevier Ltd. All rights reserved. Contents lists available at ScienceDirect Journal of Constructional Steel Research