6. Conclusions
An outline has been given of a wide-ranging study of perfect spherical dome shells with eaves rings under uniform external pressure, exploring both the stresses that develop and the linear bifurcation buckling resistance. A thorough investigation has investigated the effect on the linear bifurcation pressure of the shell thickness, the dome subtended angle and the cross-sectional size of the eaves ring. This study has been undertaken to provide a basis for the development of further rules for the Eurocode on shell buckling EN 1993-1-6 [8]. The size of the eaves ring has been shown to have a very significant effect on the membrane and bending stresses in the shell, but surprisingly little on the elastic critical buckling pressure. This finding runs counter to accepted wisdom on shell buckling, where peak membrane stresses are normally expected to control the buckling resistance. It is clear that the elastic critical buckling pressure may be conservatively estimated at 0.81 of the classical elastic critical pressure [11] for almost all geometries and ring sizes. The increased resistances above this value when larger (or smaller) rings are used are relatively small, so they may not justify the complexity that an additional calculation would require. Current buckling design recommendations [3,4] do not allow for a ring at all, but simply name the support conditions identified in Fig. 1. Moreover, the API standard [1] does not address the issue of the effect of an eaves ring or curb angle on buckling resistance. Thus, this paper is the first source to give advice on the sizing of practically useful rings to influence both the stress state and the buckling resistance of the dome. It is evident that rings with cross-sectional areas in the range 0.1 b ArND b 2 can usefully affect the stress state, but that these do not significantly affect the buckling resistance.
