Abubakr E. S. Musa

The buckling stress of axially compressed circular cylindrical shells (CCSs) is highly sensitive to imperfections. Perfect CCSs are an idealization unattainable in reality. In practice, imperfections are always present and significantly reduce the load-carrying capacity. Accordingly, shell designers are encouraged by the Eurocode EN 1993:1-6 to conduct geometric and material nonlinear with imperfections analysis (GMNIA) considering different possible forms of imperfections for the shell under design. As GMNIA type of analysis is difficult and requires highly skilled engineers, knowledge of the upper limit of the buckling stress serves as a guide and prevents overestimation of the shell buckling resistance. It also encourages average skilled designers to attempt GMNIA as far as the maximum possible limit is known. Thus, the objective of this study is to provide the upper bound of the buckling stress of carbon steel CCSs. Geometric and material nonlinear analysis (GMNA) of perfect CCSs for a wide range of R/t ratio is conducted. It has been found that for cases of small and intermediate R/t values the buckling stress can be predicted by GMNA while the elastic buckling controls those of larger R/t values. The limiting R/t values depend on the steel grade and have been derived for the available standard grades of carbon steel. The obtained results are presented in terms of simplified formulas and a design chart to be used by engineers. Application of the proposed upper bound in simplified design approaches using knock down factor (KDFs) has also been discussed.

The stiffened slab-on-grade (SSOG) is known to be an efficient type of foundations for one to three-story buildings constructed on expansive soils. During its structural design, it is required to optimize the sizes and spacings of the stiffening beams to minimize the differential movement and this can best be achieved by developing an accurate continuous solution (in a functional form). In this study, Ritz method-based bending solution for SSOG is developed considering the tensionless behaviour of the subgrade reaction. The SSOG is treated as a beam on elastic foundation and the heave of the soil is introduced to the problem as an upward pressure. Ritz method formulation is developed with assumed deformed shape of the beam containing unknown constants to be determined from the minimization of the potential energy. Due to the central heave (mound shape) of the soil, there are zones near the edges of the beam with no contact between the beam and the supporting soil (i.e.: zero subgrade reaction). The exact locations of the zero-subgrade reaction zones are unknown initially and a systematic iterative approach is developed to determine their locations. The accuracy of the proposed solution is verified through comparison of the obtained deflection, bending moment and shear force of a selected numerical example with the results of a recently developed finite element-based design approach. In addition to its accuracy, the proposed solution has the advantage of being in a functional form which is useful for optimization purposes and facilitates further investigations of SSOG parameters.

Due to their thin-walled characteristics, axially loaded circular cylindrical shells (CCSs) commonly undergo buckling failure. The limiting buckling stress of such shells has not yet been fully developed due to a wide range of influencing parameters such as sensitivity to imperfections, nonlinearity, and buckling mode. It has been proved early, and in this study, that the nonaxisymmetric buckling stress can be one of the remedies that casts into eliminating the overestimation caused by the classical axisymmetric buckling formula. However, the complex nonlinear constrained optimization required to obtain the nonaxisymmetric buckling stress and mode remains to be the main obstacle for practicing engineers to approach the nonaxisymmetric buckling. In this study, the nonaxisymmetric buckling formula has been cast in a compact form and possible approaches to utilize it have been discussed considering the degree of user knowledge and availability of computational tools. Moreover, it has been used to derive a closed-form buckling stress formula that considers the effect of all geometric and material properties. The proposed closed-form formula predicts buckling stress that is always less than that of the classical formula for L/R greater than 0.91 and the amount of reduction increases with the increase of L/R ratio. In comparison with the exact nonaxisymmetric buckling formula, the proposed closed-form formula yields buckling stress within ± 4%. Thus, it shares the simplicity of the classical axisymmetric buckling formula and the accuracy of the nonaxisymmetric buckling formula.