A round bar 4 m long and 64 mm in diameter is used as a strut with both ends hinged. Determine the crippling load (consider young's modulus = 2 × 105 N/mm2 and π= 31).

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  1. 1,01,580.8 N
  2. 2,03,161.6 N
  3. 50,790.4 N
  4. 4,06,323.2 N

Answer (Detailed Solution Below)

Option 1 : 1,01,580.8 N
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Concept:

Euler's Crippling Load for a strut with both ends hinged is given by:

  • \( L = 4 \, \text{m} = 4000 \, \text{mm} \)
  • \( d = 64 \, \text{mm} \)
  • \( E = 2 \times 10^5 \, \text{N/mm}^2 \)
  • \( I = \frac{\pi d^4}{64} \)

Substituting values and solving gives:

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