Issues Related to the Design of Spatial Structures

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(5) Stability Requirements

For simplicity the spatial structures considered here are assumed to be made of pin-ended components. The stability of these structures is determined by the Maxwell’s equations:

In this equation “m” is the number of structural member, “j” is the number of nodes or joints, and “r” is the number of support reactions.

Since a tripod (based on tetrahedron configuration) having three members with three internal forces is a stable configuration, spatial structures formed by simple addition of tripods to each other are also stable. Therefore, to ensure stability, at least the three members not lying in the same plane have to be connected to a joint. More members connected to a joint create an indeterminate system, and fewer members result in an unstable structure.

For the stability analysis of DLGs, it is conservatively assumed that the allowable buckling load of any member to be approximately equal to ¾ of its tensile capacity.

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