Engineering Transactions, 11, 3, pp. 435-448, 1963

### Stateczność Sprężyście Utwierdzonego Pręta Ściskanego w Ogólnym Przypadku Zachowania się Obciążenia

Z. Kordas
Politechnika Krakowska
Poland

This is a study of the stability of a bar elastically clamped and loaded on the free end. with a force which changes during buckling its direction and its attachment point (produces an additional moment). Such a load acting on the end surface of a bar may be produced, for instance by a fluid flowing past the bar. The position of the force after the stability loss has been determined by means of the angle X (that is the angle between the direction of the force with the direction of the tangent to the axis of the bar at the end) and the eccentricity e (that e is the distance of the point of attachment of the force from the centre of gravity of the cross-section of the bar). It is assumed that the cross-section of the bar has at least one symmetry axis. The considerations are confined to the buckling in this symmetry plane. The functions e and X are assumed to be analytic functions of the end deflection f = y (I) and deflection angle Pi = y'(N). Confining ourselves to an analysis of infinitely small deflections and introducing dimensionless parameters a, ß, y, ò the expressions for e and x are written in the form (1.2). The assumption (1.2) and the condition of elastic clamping lead to very general boundary conditions (1.4) for which the stability of the bar is discussed.
The aim of this paper is to derive an equation determining the critical force in function of 1 five parameters a, p, y, S, p characterising the elastic properties of the clamping and the position of the load vector after stability loss, on the basis of the static and kinetic criterion of elastic (p.2) and (p.5) respectively. In Section 3 the limits of applicability of the static criterion are determined. The Section 4 is devoted to a detailed investigation of some particular cases.

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