## Introduction

1 With refernce to Fig. 14.1, we distinguish different levels of analysis:

Displacement

Figure 14.1: Level of Analysis

Displacement

Figure 14.1: Level of Analysis

First Level elastic which excludes anly nonlinearities. This is usually acceptable for service loads.

Elastic Critical load is usually determined from an eigenvalue analysis resulting in the buckling load.

Secon-order elastic accounts for the effects of finite deformation and displacements, equilibrium equations are written in terms of the geometry of the deformed shape, does not account for material non-linearilties, may be able to detect bifurcation and or increased stiffness (when a member is subjected to a tensile axial load).

First-order inelastic equilibrium equations written in terms of the geometry of the unde-formed structure, accounts for material non-linearity.

Second-order inelastic equations of equilibrium written in terms of the geometry of the deformed shape, can account for both geometric and material nonlinearities. Most suitable to determine failure or ultimate loads.

2 This chapter will focus on elastic critical load determination. We will begin by reviewing the derivation of some of the fundamental equations in stability analysis. We will examine both the strong form, and the weak formulation.

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