Discharge buckling assessment of example cylindrical steel flat-sheet silos with depressions in circumferential welded joints

Steel cylindrical silos are key storages in many industries. They can be composed of flat or corrugated sheets. To construct these structures, steel sheets may be welded or bolted to each other. This study addresses steel welded silos with flat sheets. Different loads, such as, filling and discharge loads, wind load, seismic load and thermal loads should be considered in design of silos. 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 primarily considered for structural design of silos.
Due to small wall thickness, buckling resistance is of vital importance in steel silos design. Ensiled materials exert normal pressures and frictional tractions on silo walls. Accordingly, during discharge process, meridional buckling resistance of shell walls concurrent with internal pressures should be assessed. It is well known that buckling strength is very sensitive to geometric imperfections in shell structures. In welded silos, the most regular and well-defined imperfection is local depressions existing in circumferential welded joints due to the plate rolling process and shrinkage of the weld. The assumed shape given for this type of imperfection in the literature were adopted throughout the paper.
Eurocode as the most advanced and pioneering standard on the design of steel silos, provides a hand design procedure for buckling evaluation of steel silos under discharge loads. To assess the procedure, a full suite of computational shell buckling calculations was performed with special emphasis on the effect of aforementioned geometric imperfection. A slender, an intermediate slender and a squat silo were considered for the assessments. Linear elastic Bifurcation Analysis with Imperfections (LBIA) and Geometrically and Materially Non-linear Analysis with Imperfections (GMNIA) were carried out for each structure. Sample silos were loaded in accordance to the pressure distribution proposed in the Eurocode. By assuming strake’s height of 2 meters, uniform depressions were simulated in circumferential welded joints of each silo. Three different Fabrication Quality Classes (FQCs) denoted by FQC A, B and C in a descending order from Excellent to Normal Class were introduced in the Standard. The imposed depression amplitudes were calculated in accordance to FQCs of the silos.
Considering the results obtained, the LBIA buckling modes show several circumferential buckling waves at the first welded joint of each silo from the base. Lowering the FQC leads to the decrease in number of circumferential waves and to the development of buckling waves at the location of second and third welded joints. Nevertheless, the more sophisticated GMNIA analyses predict elastic-plastic buckling mode in the form of diamond pattern concentered at the first welded joint of the silos from the base, irrespective of selected FCQ. However, for the slender silo the two upper welded joints are also interact during buckling. With respect to the design buckling resistance ratios (rRd</sub></em>) obtained by hand calculations and through non-linear analyses, the former method has predicted rRd</sub></em> values in the range from 13% to 32% lower than those of GMNIA. Therefore, hand design procedure of Eurocode produced satisfactory results, without high conservatism. However, more researches on this issue can enhance the reliability of conclusions made with respect to the Eurocode provisions.