The linear buckling problem of a cylindrical shell subjected to circumferentially varying axial edge loads or thermal loads is considered. The case of an oscillatory loading having a cosinusidal form with a single arbitrary harmonic index is treated first. Closed-form expressions for the critical eigenvalues are obtained, spanning the entire range of the harmonic index. Buckling modes are also presented. An interaction law among harmonic loadings based on existing numerical evidence is then postulated. This leads to the capability of calculating the buckling load for any given distribution. The method is compared, and good agreement is obtained, with published results on the heating of an axial strip. It is then used to calculate the buckling of a cylindrical shell subjected to a concentrated axial force.

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