A criterion for the development of the full plastic moment at one end of a uniform strut prior to instability

Abstract

Plastic design methods for steel-framed structures involve an assumption that members do not become unstable prior to the development of sufficient hinges to form a mechanism. Some check on this assumption is desirable and a basic problem is that of a member subjected to combined axial stress and unequal major-axis bending moments at its ends; the question is then whether the full plastic moment can be developed at one end without prior instability. In previous theories, Horne has tackled this problem indirectly by considering an ‘equivalent’ problem in which the major-axis bending moment is uniform along the member. The actual loading problem is now analysed directly and a criterion of critical slenderness ratio is developed which can be linked to physically plausible causes of instability. The theory is in reasonable agreement with relevant published experimental data except in one instance; but the data are very limited and many more are needed before any theory can be verified or disproved with confidence.