Modeling of a Vertical Tank on an Elastic Foundation According to Rod and Shell Theory

To evaluate the strength of vertical steel tanks used for the storage of liquid media, two models based on the theory of elastic rods and thin shells are developed. The tank is represented by a cylindrical wall of variable thickness with a welded round bottom. The stress-strain state of the tank under axisymmetric static load is studied. In contrast to the accepted engineering approaches, the wall and the bottom are considered together, which allows us to take into account the mutual influence of their deformations. The models take into account loads from weight, pressure of the contained liquid, and reaction of the soil foundation. The rod model takes into account the extension of the wall; the bottom bends, but does not deform in its plane. The shell model allows us to correctly take into account the bottom extension. The theory of classical thin shells of revolution based on Lagrangian mechanics is used in the paper. The calculations of a typical steel tank for oil and oil products are carried out. The displacements, rotations, and all force factors in the tank are found, and the meridional and circumferential stresses are determined. The range of values of the rigidity of the soil foundation is found, at which the stresses in the tank satisfy the strength criterion. It is shown that the rod model can be used to calculate the strength of a tank on an elastic foundation of high rigidity.