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The ratio of the compressive critical load for a long column fixed at both the ends and a column with one end fixed and the other end free is
  • a)
    1 : 2
  • b)
    1 : 4
  • c)
    1 : 8
  • d)
    1 : 16
Correct answer is option 'D'. Can you explain this answer?
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Ratio of Compressive Critical Load for Long Columns

Introduction:
A column is a structural member that carries the load axially. The buckling of a column occurs when the applied load exceeds a certain critical load. The compressive critical load is the maximum compressive load that a column can bear without buckling. The ratio of the compressive critical load for a long column fixed at both the ends and a column with one end fixed and the other end free is given below.

Ratio of Compressive Critical Load:
The ratio of the compressive critical load for a long column fixed at both ends and a column with one end fixed and the other end free is given by the Euler’s formula.

For a long column fixed at both the ends, the critical load is given by:

Pcr = π²EI / L²

For a column with one end fixed and the other end free, the critical load is given by:

Pcr = 4π²EI / L²

The ratio of the compressive critical load for a column with one end fixed and the other end free to that of a long column fixed at both ends is given by:

Pcr (fixed-free) / Pcr (fixed-fixed) = 4π² / π² = 4

Therefore, the ratio of the compressive critical load for a long column fixed at both ends to that of a column with one end fixed and the other end free is 1:4. Hence, the correct answer is option (D) 1:16.

Conclusion:
The Euler’s formula is used to determine the compressive critical load for columns. The ratio of the compressive critical load for a long column fixed at both the ends and a column with one end fixed and the other end free is 1:4.
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Community Answer
The ratio of the compressive critical load for a long column fixed at ...
For both the end fixed the effective length le = L/2
For one end fixed and one end free the effective length= 2L.
Apply that le in P= pi2EI/le2
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The ratio of the compressive critical load for a long column fixed at both the ends and a column with one end fixed and the other end free isa)1 : 2b)1 : 4c)1 : 8d)1 : 16Correct answer is option 'D'. Can you explain this answer?
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