To explain the effects of material plasticity and of geometric and structural imperfections on the buckling load resistance of columns.
SUMMARY
The inelastic buckling of an idealised strut, i.e. a perfectly straight strut without residual stresses, is discussed with ideal rigid-plastic, ideal elastic-plastic, and real material behaviours being considered. The influence of geometric imperfections and residual stresses is examined, both separately and in combination.
Real structural members do not behave exactly as elastic bifurcation theory predicts. Firstly, the material is not infinitely elastic; as a result, elasto-plastic behaviour and inelastic buckling occur. Secondly, the structural members are affected by several kinds of imperfections (mainly of geometric and mechanical nature), which may weaken the carrying resistance. The rapid change in deformation with increase in applied load (characteristic of the buckling phenomenon) also gives rise to second order effects which, when combined with material inelasticity, result in overall non-linear behaviour of the structure.
In order to illustrate the main features of real responses, this lecture analyses the simplest type of buckling behaviour, i.e. that of a pin-ended, end loaded strut having a doubly symmetrical cross-section (column flexural buckling).
Elastic Instability Modes lecture identified the parameters that govern the elastic behaviour of a geometrically perfect strut, i.e. one with no initial out-of-straightness or eccentricity of loading. This lecture firstly examines the effect of inelastic material behaviour in the absence of any kind of imperfections. Then, the influence of imperfect geometry and residual stresses are studied in turn. Finally, the effect of all features taken together is analysed.
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