Ugięcie Pręta Ściskanego Mimośrodowo pod Działaniem Siły Krytycznej

An approximate analysis of eccentric compression indicates an infinite increase of deflection under the action of the critical force. This result is evidently erroneous, which has been pointed out by many investigators. Starting from the exact equation of the deflection curve, we obtain a result in terms of a non-elementary function of two variables, difficult to be represented by means of tables.
The paper presents the derivation of an approximate formula, expressing the dependence of the deflection upon the compression force P and its eccentricity e. The formula is based on the exact solution, certain functions being expanded in corresponding power series. The first few terms are accepted, others neglected as small.
Starting from the general case, an analysis is given of the particular
cases of e = 0 (buckling under axial load) and P = P (deflection of a beam compressed eccentrically by the critical force). In the last .case we obtain a particularly simple and exact formula for the deflection in terms of eccentricity.
It is shown that in the case of eccentric compression the concept of critical force has no reason. Speaking of the critical force of a certain
shaft, the Eulerian force alone should be meant, i.e. the force which
would be critical in the case of axial compression.