What is Buckling ?
Columns are an important part of machines or even civil structures such as bridges. To differentiate column and Beam, Take the example of the most common case of horizontal beams subjected to load perpendicular to its length (such as simply supported beam or cantilever beam). Those beams undergo bending or flexural stress and deflection. Whereas In case of a column, the load is applied along the length or parallel to the axis. If the column is short then it will fail by crushing or compression (beyond ultimate compressive strength). But if the column is long then it may bend instead of crushing. This bending of the column is defined as Buckling. The load at which a column buckles may be well below the compressive strength. The geometry, size, and end conditions of load will define the amount of critical load at which the column will start buckling (and it happens suddenly).
For designing a column, the Slenderness Ratio Sr is important. This ratio equals the length l of the column in inches divided by the least Radius of gyration k of the cross-section. The column can have various end conditions such as Fixed on both ends, Pinned or rounded at both ends, etc. so the effective length of the column should be considered for the calculation of the Slenderness Ratio. A short column is usually defined as one whose slenderness ratio is less than about 10.
Experiments have shown that the Column design by using only the Euler-column formula may result in failure (sometimes) because there is a failure zone ABDA (Refer to empirical failure zone in the below diagram). J.B. Johnson suggested a Parabolic curve between points A & D. The region below this parabolic curve is safe.
Key Words: Columns Buckling, Slenderness Ratio, Radius of Gyration, Euler Formula, Johnson Formula