Elastic stability relates to the ability of a member or structure to support a given load without experiencing a sudden change in configuration. Abuckling response leads to instability and collapse of the member. Some designs may thus be governed by the possible instability of a system that commonly arises in buckling of components. Here, we are concerned primarily with the column buckling, which presents but one case of structural stability [1-15]. Critical stresses in rectangular plates are discussed briefly in Section 6.10. The problem of buckling in springs is examined in Section 14.6. Buckling of thin-walled cylinders under axial loading and pressure vessels are taken up in the last section of Chapter 16, after discussing the bending of shells.

Both equilibrium and energy methods are applied in determining the critical load. The choice depends on the particulars of the problem considered. Although the equilibrium approach gives exact solutions, the results obtained by the energy approach (sometimes approximate) usually is preferred due to the physical insight that may be more readily gained. A vast number of other situations involve structural stability, such as the buckling of pressure vessels under combined loading; twist-bend buckling of shafts in torsion; lateral buckling of deep, narrow beams; buckling of thin plates in the form of an angle or channel in compression. Analysis of such problems is mathematically complex and beyond the scope of this text.