# When is Euler's formula applicable?

Q.  Euler's formula is applicable only _________

1. for short columns
2. for long columns
3. if slenderness ratio is greater than √(π2 E / σc)
4. if crushing stress < buckling stress
5. if crushing stress ≥ buckling stress

- Published on 21 Sep 15

a. 1, 2 and 3
b. 2, 3 and 5
c. 3 and 4
d. all of the above

#### Discussion

• Sudhakar   -Posted on 12 Feb 20
Sir why doe's not applicable for short column what is the reason can you please detail explaination
• Sravanthi   -Posted on 25 Nov 15
- Leonhard Euler derived a formula for stability of long columns.

- According to Euler's theory, columns fail due to buckling only. In these columns effect of compressive load is neglected.

- In short columns, direct stress is considered hence Euler's theory is not applicable.

- Critical stress increases when slenderness ratio decreases.

Slenderness ratio: It is defined as the ratio of effective length (Le) of column to least radius of gyration (k)

- Euler's theory is applicable, only if crushing stress (σcr) ≥ buckling stress [π2 E / (Le / k)2]

- (σcr) ≥ [π2 E / (Le / k)2]

(Le / k) ≥ π √(π2 E) / σcr

This means that if slenderness ratio (Le / k) is greater than π √(π2 E / σcr), Euler's formula is applicable.

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