Time-Related Procedure to Structural Column Failure

Abstract

Based on a thought experiment, a slender column is loaded to the Euler column buckling load by bringing the platen of a testing machine down at a uniform rate. The shortening of the column y is proportional to the time t. Bending, that is, bowing out of the column, starts as soon as the compressive load P > 0. Every column to be tested has an initial accidental eccentricity, either because it is not perfectly straight or the mean resistance internally of the random arrangement of the crystalline structure of the grains of structural steel (or other metal) does not coincide with the central column axis. For a solid rectangular cross-section, the eccentricity e falls within a certain interval. The value of e is always greater than zero, but also has an upper bound so that the maximum compressive stress due to compression plus bending does not exceed the proportional limit σ pl . Euler's formula for critical buckling P cr when divided by the cross-sectional column area A does not yield a meaningful average stress. Only the maximum compressive fiber stress, at the midlength of the column is significant as it approaches σ pl . The coordinates of the bowed column are solved for at any time t at the column midlength, until the column fails at time t cr . It is also demonstrated that P = f(y) is not a straight line, although it may come close. Adopting a convenient rate of compression of the column C 1 the time to failure t cr can also be predicted for the corresponding, computed y cr .