CLASSICAL BUCKLING LOAD OF SPHERICAL DOMES UNDER UNIFORM PRESSURE

The purpose of this paper is to provide the classical buckling load of a spherical dome subjected to a uniformly distributed load and clarify the effect of boundary conditions, conical angles, and radius-thickness ratios on the buckling load. Total potential energy formulation is used in the calculation of the buckling load, with eigen modes of axisymmetric flexural free vibration. In this paper, each eigen mode is given as a finite series of the Legendre polynomials. Calculating the critical load individually for several eigen modes, the buckling load is determined as the minimum of the critical loads for each conical angle and radius-thickness ratio. The final results of the buckling load coefficient Ct are tabulated and are depicted. It has been presumed that this coefficient is larger than that of the complete spherical shell because of boundary constraint. The difference of the Ct, however, between a dome, especially a nonshallow dome, and the complete spherical shell (i.e., Ct = 1.21) is very slight. This coefficient of a dome with fixed end is slightly larger than that of a simply supported dome. And, it is shown that contribution of bending moments to the classical buckling load becomes relatively significant.