## Piw

The overall buckling occurs when a relatively large area of the space frame becomes unstable and a relatively large number of joints are involved in the buckle. For most cases, in overall buckling of a space frame, the wave length is significantly greater than the member length. Local buckling often plays the role of a trigger for overall buckling.

The type of buckling collapse of a space frame is greatly influenced by the following factors: its Gaussian curvature, whether it is single- or double-layer system, the degree of statical indeterminacy, and the manner of supporting and loading. Generally speaking, a shallow shell of positive Gaussian curvature, like a dome, is more prone to overall buckling than a cylindrical shell of zero Gaussian curvature. Recent research reveals that hyperbolic paraboloid shell is less vulnerable to overall buckling and the arrangement of the grids has a considerable influence on the stability and stiffness of the shell. It is best to arrange the members along the direction of compressive forces. Single-layer space frame exhibits greater sensitivity to buckling than the double-layer structure. Moreover, various types of buckling behavior may take place simultaneously in a complicated relation. For double-layer grids, in most cases, it is sufficient to examine the member collapse that may occur in the compressive chord members.

The theoretical analysis of buckling behavior may be approached by two methods: continuum analogy analysis and discrete analysis. Since almost all space frames are constructed from nearly identical units arranged in a regular pattern, it is generally accepted that the analysis on the basis of the equivalent continuum serves as an important tool in the investigation of the buckling behavior of space frames. Numerous analytical and experimental studies on the buckling of continuous shells have been performed, and the results can be applied to the latticed shells.

The buckling formula for a spherical shell subjected to a uniformly distributed load normal to the middle surface can be expressed as qcr — kE(P) 2 (24.15)

where t is the thickness and R is the radius of the shell. Different values of the coefficient k were obtained by various investigators:

1.21 ([13], based on classical linear theory) 0.7 (experiments on very carefully prepared models) 0.366 ([14], based on nonlinear elastic theory) 0.228 and 0.246 ([15], for m — 0 and 0.3, respectively).

For a triangulated dome, where an equivalent thickness is used, Wright [16] derived the formula by using

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