Stability of Half-Barrel Orthotropic Shells

The overall buckling of half-barrel shells made of corrugated steel sheets is studied in this paper. This type of buckling is recognized as a prime factor in defining ultimate load carrying capacity of such shells. The mathematical formulations are based on the linear theory or orthotropic cylindrical shells. The stability conditions are governed by two linear simultaneous differential equations in the deflection and a stress function. The series presentation of the deflection and the stress function yield a set of homogeneous linear simultaneous algebraic equations in the unknown deflection coefficients. The eigenvalues of this system are calculated with different load distributions representing the cases of snow and wind loads, as well as combined loading. Note that the magnitude of critical load as well as the mode of buckling are dependent on the ratio of length to radius of shell and the ratios between the rigidities in the longitudinal and circumferential directions.