Engineering Transactions,

**5**, 1, pp. 99-116, 1957### Wyboczenie Kopul Kulistych w Świetle Badań Modelowych

A description of a method for determining the buckling modes of a shell, and the value of the critical load. On the basis of an analysis of buckling modes of space structures (such as beams, arches, frames and plates), and taking into consideration experimental results obtained by means of model shells, the author assumes that the buckling mode of the system is of the same type as the deflection surface due to the action of a concentrated force. This assumption enables the determination of the deformation, and then the value of the critical load corresponding to the load type assumed. Cylidrical vaults and spherical domes are discussed as examples. Short cylindrical shells (b : l ≤ 1,5) buckle in the form of a series of waves characterized by the dimension L along the curvature of the shell (Fig. 11a). For medium and long shells, in which the length of the shell is equal to several times its span, the form of one half-wave will be of decisive significance (Fig. 11b). For spherical domes, it is assumed that the decisive buckling mode is that of local stability loss. The range of the wave is determined by the radius ro obtained from the diagram of deflection of a shell loaded with a concentrated force (Fig. 16). Assuming now that the element of the shell will buckle under the action of the forces Skr equal to the forces acting on a circular plate of radius o (Fig. 17) clamped along the edge, the author obtains (using the finite difference method for, calculating the shell deflection) the value of the critical load: […], here E is Young's modulus, h shell thickness, R radius of curvature of the dome, and v Poisson's ratio. The value thus obtained of the critical load normal to the shell, and the local buckling mode have been confirmed by experiments with models.

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#### References

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