# When does failure occur in long columns as per Euler's theory?

Q.  In Euler's theory, long columns having the ratio of (Le /LLD) ≥ 12 fail due to _______
- Published on 21 Sep 15

a. crushing
b. buckling
c. both a. and b.
d. none of the above

#### Discussion

• Sravanthi   -Posted on 25 Nov 15
- Buckling of columns is not related to the strength of material but is governed by column stiffness considering both geometrical and material.

- Buckling in long columns is caused when subjected to high compressive stress which is less than ultimate compressive stress at the point of failure. Ultimate compressive stress is the stress which a material withstands.

- A short column fails directly due to direct compression under the action of axial load before buckling can occur.

- In long columns, the effect of axial load is neglected and the columns fail due to bending (buckling) .

- A combination of compressive stress and bending leads to failure are observed in the columns, which has length intermediate between short and long column.

- The ratio of (Le /LLD) ≥ 12 for long columns and (Le /LLD) < 12 for short columns, here Le is the effective length and LLD is the least effective diameter.

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