دانلود رایگان مقاله کمانش گنبد مدور با پشتیبانی لبه حلقه

ABSTRACT

Spherical dome roofs are widely used on large diameter tanks and silos, as they provide high strength for very limited amounts of material: buckling normally controls the design. Their design is currently based on very simple rules that were devised many decades ago. In particular, existing design is based on very simple boundary condition assumptions that cannot be realised in practice. This paper presents the first thorough study of the in- fluence of realistic boundary conditions, in the form of a ring at the eaves, on the linear bifurcation of these domes. The outcome is a clear documentation of one of the key reference resistances required for a design description in the terminology of the Eurocode on shell buckling EN 1993-1-6. The complete study explored a very wide range of parameters, so only a sample of the findings is presented here. The complete results are expected to form the basis of future rules in the ECCS Recommendations on Buckling of Shells.

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.