# Discrete Field Stability Analysis of X-Braced Lattices

*by*Raja R. A. Issa, (M.ASCE), Univ of Florida, Gainesville, United States,

R. Richard Avent, (M.ASCE), Univ of Florida, Gainesville, United States,

**Document Type:**Proceeding Paper

**Part of:**Spatial, Lattice and Tension Structures

**Abstract:**

The three-dimensional X-braced lattice is used as a compression member in structures ranging from the long span roof of buildings to radio and television antennas. In such cases the design is often controlled by the stability of the overall system as opposed to local member buckling. The purpose of this paper is to present applications of discrete field mechanics techniques in the elastic stability analysis of three dimensional X-braced lattices. The use of discrete field mechanics offers several advantages over alternative approaches for the structural analysis of latticed systems. The foremost of these advantages is that the discrete mathematical model is usually 'exact' in the sense of linear elastic, small deflection theory, thus yielding very accurate results. Moreover, the solution to the resulting difference equation model quite often lends itself to a field solution which usually leads to closed form analytical formulas. Finally, the solution forms are independent of the number of joints in the system thus allowing the user to avoid having to solve large systems of equations for eigenvalues as is usually the case with other elastic stability analysis methods. Thus, the critical buckling load for any given X-braced lattice can be determined without a huge computational effort.

**Subject Headings:**Bracing | Lattices | Three-dimensional analysis | System analysis | Model accuracy | Structural stability | Elastic analysis | Roofs

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