Silos in the form of a cylindrical metal shell are commonly elevated to provide access to the space beneath. In general, a few discrete column supports at evenly spaced intervals are commonly utilized. The presence of discrete supports results in circumferential non-uniformity in the axial compressive stress above the support. Depending on the size of the structure, several different support arrangements may be chosen. A stiff ring beam is utilized in larger silos to transfer and evenly distribute the discrete forces from the supports into the cylindrical shell wall. A stiffness criterion was developed by Rotter to assess the degree of non-uniformity in axial compressive stresses around the circumference. The stiffness criterion is based on the relative stiffnesses of the ring beam and the cylindrical shell and was verified for loading conditions that produce circumferentially uniform axial stresses around the circumference. A study has been undertaken to investigate the applicability of the stiffness criterion to cylindrical shells under global shear and bending. Pursuant to this goal, extensive finite element analyses were conducted where different ring beam and cylindrical shell combinations are subjected to global shearing and bending actions. The results revealed that the stiffness criterion can be extended to shells under this loading condition. The degree of non-uniformity in axial stresses is quantified and presented as simple formulas that can be readily adopted by design standards.