Buckling Capacity Curves for Steel Spherical Shells Loaded by the External Pressure

Assessment of buckling resistance of pressurised spherical cap is not an easy task. There exist two different approaches which allow to achieve this goal. The first approach involves performing advanced numerical analyses in which material and geometrical nonlinearities would be taken into account as well as considering the worst imperfections of the defined amplitude. This kind of analysis is customarily called GMNIA and is carried out by means of the computer software based on FEM. The other, comparatively easier approach, relies on the utilisation of earlier prepared procedures which enable determination of the critical resistance pRcr, the plastic resistance pRpl and buckling parameters a, b, h, l 0 needed to the definition of the standard buckling resistance curve. The determination of the buckling capacity curve for the particular class of spherical caps is the principal goal of this work. The method of determination of the critical pressure and the plastic resistance were described by the authors in [1] whereas the worst imperfection mode for the considered class of spherical shells was found in [2]. The determination of buckling parameters defining the buckling capacity curve for the whole class of shells is more complicated task. For this reason the authors focused their attention on spherical steel caps with the radius to thickness ratio of R/t = 500, the semi angle j = 30o and the boundary condition BC2 (the clamped supporting edge). Taking into account all imperfection forms considered in [2] and different amplitudes expressed by the multiple of the shell thickness, sets of buckling parameters defining the capacity curve were determined. These parameters were determined by the methods proposed by Rotter in [3] and [4] where the method of determination of the exponent h by means of additional parameter k was presented. As a result of the performed analyses the standard capacity curves for all considered imperfection modes and amplitudes 0.5t, 1.0t, 1.5t were obtained. Obtained capacity curves were compared with the recommendations for different fabrication quality classes formulated in [5].