Euler's theory assumptions for long columns

Some of the assumptions of Euler's theory for long columns are

1. The geometric and material properties of the column is uniform throughout the section,i.e, flexural rigidity is constant all through.
2. The material is isotropic homogeneous and elastic.
3. The layers of the columns are assumed to be straight before the application of the load.
4. The load on the column is usually applied axially at its ends.
5. Since the slenderness ratio  for the long column is more ,it fails by buckling only.
6. Self weight of the column is neglected during the calculation of failure load on the column.
7. The linear dimension of the long column is much more compared to the lateral dimension.
8. Long column experiences bending stress at a higher extent than compared to the direct stress.