If the flexural rigidity of a column whose length is L and the loaded end is free is EI, the critical load will bea)Pc = πEI/(4L2)b)Pc = π2EI/(4L2)c)Pc = πEI2/(4L2)d)None of theseCorrect answer is option 'B'. Can you explain this answer?

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Answer

Critical load refers to the maximum load that a column can carry without undergoing buckling or failure. In the given scenario, the column has a length of L and the loaded end is free. The flexural rigidity of the column is given as EI.

To determine the critical load, we can use the Euler's formula for buckling of columns, which states that the critical load (Pc) is inversely proportional to the square of the length of the column (L) and directly proportional to the flexural rigidity (EI). Mathematically, it can be expressed as:

Pc ∝ (EI)/L^2

Now, let's break down the options given:

a) Pc = πEI/(4L^2)
b) Pc = π^2EI/(4L^2)
c) Pc = πEI^2/(4L^2)
d) None of these

According to Euler's formula, the correct expression for the critical load should have π^2 in the numerator, as it is directly proportional to the flexural rigidity (EI).

In option a, there is no π^2 term in the numerator, so it can be eliminated.

In option b, the critical load expression matches Euler's formula, with π^2 in the numerator, EI in the denominator, and L^2 in the denominator. Therefore, option b is the correct answer.

Option c has EI^2 in the numerator, which is not consistent with Euler's formula, so it can be eliminated.

Option d states that none of the given options are correct, but option b matches Euler's formula and is indeed correct.

Therefore, the correct answer is option b) Pc = π^2EI/(4L^2).

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