Deflections of Thin-Walled Storage Tanks with Roof due to ...

Results were obtained for various configurations and amplitudes of settlement patterns u.The pattern change as the settlement is increased, drawing a geometric nonlinear behavior. Thedisplacements shown in Figure 3 were obtained for u max = 1 mm and are shown for twomeridians, one located in coincidence with the meridian of maximum settlement, θ = 0º, and asecond one for a meridian at θ = 30º. For θ = 0º, the radial displacement are positive (outwarddirection) with a maximum at about H/3 and with w/u = 1.2. Larger displacement (inwarddirection) are obtained at θ = 30º, with values in the order of w/u = 6 at an elevation of aboutH/2. Such large displacements are clearly outside a linear theory of shell. The pattern ofdisplacements follow a “V” shape, with a large inward displacement along a diagonal at 45ºwith respect to a horizontal plane, and almost zero displacement at the top of the shell, where theroof restrains the radial deflections.98FEMEXPERIMENTAL98FEMEXPERIMENTAL98FEMEXPERIMENTAL7776665h /H45h /H45h /H433322211100.0 0.5 1.0 1.5RADIAL DISPLACEMENTa) b) c)Fig.3. a) Radial displacement for θ = 0°. b) Radial displacement for θ = 30°. c) Comparison ofmaximum radial displacement in FEM an experimental model (for θ ≅ 18° and u max = 1 mm).FINITE ELEMENT MODEL0-6 -5 -4 -3 -2 -1 0RADIAL DISPLACEMENTThe finite element computer package ABAQUS (Hibbitt, Karlsson and Sorensen 1997) wasused to obtain displacements of the shell under vertical settlement. To build the mesh,quadrilateral shell elements with eight nodes (S8R5) were used to model the cylinder and mostof the shell roof (about 2,640 elements), while triangular elements (STRI65) were required forthe center of the roof (about 60 elements). The finite element mesh used in the model is shown0-6 -5 -4 -3 -2 -1 0RADIAL DISPLACEMENT