Stability of Bars with Lateral and Axial Loading

Abstract

In this paper a method of calculating critical loads is used which involves applying an auxiliary moment M at one point of the structure, calculating the resulting rotation 0, and equating to zero the derivative dM/dd. This method makes it possible to easily investigate certain modes of buckling that would "otherwise be apt to escape attention, as the unsymmetrical buckling of a uniformly loaded bar of two equal spans with axial load.The critical end load for a one or two span strut with lateral load is found to be independent of the lateral load. For a two span strut, the critical load is found to lie between the Euler loads for the long and short span separately.Two new problems are taken up. One is that of a two-bay strut with rotationally elastic middle support. The critical load varies from the value for a simple two-bay strut when the spring constant is zero to the value for the strut with locked middle joint when the spring constant is infinite. The other new problem is that of a straight bar buckled to an arch and supporting lateral load on the convex side. The ends are held a fixed distance apart, and the problem is to find the lateral load necessary to cause collapse. It is found that L Q CR -23.2 P eu a/L where q CR is the intensity of the critical lateral load, a the initial deflection of the buckled bar, L the length and P eu the Euler load for the bar.The arched bar collapses unsymmetrically.