Euler postulated a theory for columns based on the following assumptions:

  1. Column is very long in proportion to its cross sectional dimensions
  2. Column is initially straight and the compressive load is applied axially
  3. Material of the column is elastic, homogeneous and isotropic
  4. Effect of direct stress is very small in comparison with bending stress.
  5. Column shall fail by buckling alone.
  6. Effect of self-weight of column is negligible

The behavior of a column to resist buckling is very much influenced by the end condition and the flexural rigidity of the column. In turn, the flexural rigidity of the column depends on the minimum I and at the critical load it buckles in that plane about which I is minimum. The expression for crippling ...

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