Mechanics of Materials - Part 54 (Columns)|Strength of Materials | BME301

Column is a structural member mainly designed to take axial compressive loads. A short column when subjected to axial load fails when the direct normal compressive stress exceeds the permissible stress of the material. A long column may fail due to buckling, and this leads to failure of a column at a very low value of load compared to the load usually found to fail a short columns.
Euler's formula gives the buckling load at which a slender long column fails for different end conditions.
A short column usually fails by crushing whereas a long column fails due to buckling.
To check the validity of Euler's formula we have to compare the slenderness ratio of the given column with the critical value of slenderness ratio for the material of the column. If the slenderness ratio of the given column is less than the critical value, it can be considered as a short column and Euler's formula is not valid. If slenderness ratio is greater than the critical value the column is a long column and we can safely use the Euler's formula to calculate the buckling or crippling load.
In this class, I have worked out few numerical examples to calculate the buckling load for columns with different end conditions.