Standard Methods for Aerospace Stress Analysis

12Elastic Stability and Buckling

12.1 Introduction to Elastic Stability

Typically, a structural member is said to have buckled when the member fails to react to the bending moment generated by a compressive load on it. In this chapter, the buckling of long slender columns and thin plates will be considered. A “long” column may be assumed as the one having a slenderness ratio or length to radius of gyration ratio greater than 200. The radius of gyration is defined as the square root of the column's second moment of area over the cross‐sectional area of the column. Likewise, a plate is called a “thin” plate when its thickness is at least one order of magnitude smaller than the span or diameter of the plate.

12.2 Column Buckling Instability

The following mathematical formulation, as used by Simitses (1976), represents the behavior of a column of length L under an axial loading P. Where loading P is applied parallel to its axis without eccentricity:

(12.1)

where “u” is the lateral deflection of the column perpendicular to the column axis.

Rewriting this equation in a simpler form, one would have:

(12.2)

Introducing the term:

(12.3)

Equation (12.2) reduces to:

(12.4)

The available ...