# Stability of Spaceframes

*by*Mehdi S. Zarghamee,

Jayant M. Shah,

**Serial Information**:

*Journal of the Engineering Mechanics Division*, 1968, Vol. 94, Issue 2, Pg. 371-384

**Document Type:**Journal Paper

**Abstract:**Nonlinear equations governing the behavior of spaceframes whose members undergo finite deflections and moderate chord rotations are presented. The beam-column effect including the effect of flexural shortening is taken into account, while twist due to torsion is assumed to be small. The method of solution is based upon the Newton method, and the corresponding tangent stiffness matrix is given. The solution for a particular loading is obtained by applying successive corrections to the approximate solution by means of the tangent stiffness matrix. A tangent stiffness matrix which is not positive, definitely implies that the potential energy of the corresponding equilibrium configuration is not at a minimum, and thus the configuration is unstable. Therefore, the lowest value of the load for which the determinant of the tangent stiffness matrix vanishes gives the critical buckling load for the structure. The formulation may be used for predicting the buckling loads and the load-deformation history for arches or shell-like spaceframes. Buckling of a shallow arch is investigated as an illustration. The first two branching points on the load-deflection curve, indicating the asymmetric modes of buckling, are determined.

**Subject Headings:**Stiffening | Matrix (mathematics) | Displacement (mechanics) | Load factors | Critical loads | Arches

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