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Euler’s formula is valid for-
- a)Short column only
- b)Long column only
- c)Both short and long columns
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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Euler’s formula is valid for-a)Short column onlyb)Long column onlyc)B...
Euler’s formula is valid for long columns only.
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It has been shown that Euler's formula is valid for a long column having an l/k ratio greater than a certain value for a particular material. Euler's formula does not give a reliable result for short columns, and the length of the column intermediate between very long to short.
Hence the option B is correct.
Most Upvoted Answer
Euler’s formula is valid for-a)Short column onlyb)Long column onlyc)B...
Explanation:
Euler's formula is a mathematical equation that relates the critical load of a column to its length and other physical properties. It is given as follows:
Pcr = (π²EI)/L²
where Pcr is the critical load, E is the modulus of elasticity, I is the moment of inertia of the cross-section, and L is the length of the column.
Now, let us consider the different cases of columns based on their lengths.
Short Columns:
Short columns are those columns whose length is less than or equal to the radius of gyration of the cross-section. In this case, the critical load is given by the following equation:
Pcr = σcA
where σc is the compressive stress, and A is the cross-sectional area of the column.
Long Columns:
Long columns are those columns whose length is greater than the radius of gyration of the cross-section. In this case, the critical load is given by Euler's formula mentioned above.
Both Short and Long Columns:
Therefore, we can see that Euler's formula is valid only for long columns, and not for short columns. Short columns follow a different equation altogether. Hence, the correct answer is option 'B' - Long column only.
Euler's formula is a mathematical equation that relates the critical load of a column to its length and other physical properties. It is given as follows:
Pcr = (π²EI)/L²
where Pcr is the critical load, E is the modulus of elasticity, I is the moment of inertia of the cross-section, and L is the length of the column.
Now, let us consider the different cases of columns based on their lengths.
Short Columns:
Short columns are those columns whose length is less than or equal to the radius of gyration of the cross-section. In this case, the critical load is given by the following equation:
Pcr = σcA
where σc is the compressive stress, and A is the cross-sectional area of the column.
Long Columns:
Long columns are those columns whose length is greater than the radius of gyration of the cross-section. In this case, the critical load is given by Euler's formula mentioned above.
Both Short and Long Columns:
Therefore, we can see that Euler's formula is valid only for long columns, and not for short columns. Short columns follow a different equation altogether. Hence, the correct answer is option 'B' - Long column only.
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Euler’s formula is valid for-a)Short column onlyb)Long column onlyc)Both short and long columnsd)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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