एक गोल छड़ जिसकी लंबाई 4 मीटर और व्यास 64 मिमी है, का उपयोग दोनों सिरों पर टिका हुआ स्ट्रट के रूप में किया जाता है। क्रिपलिंग लोड निर्धारित करें (यंग मापांक = 2 x 105 N/mm2 और π3 = 31 मान लें)।

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BHEL Engineer Trainee Civil 24 Aug 2023 Official Paper
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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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संप्रत्यय:

दोनों सिरों पर टिका हुआ स्ट्रट के लिए ऑयलर का क्रिपलिंग लोड इस प्रकार दिया गया है:

\( P = \frac{\pi^2 \cdot E \cdot I}{L^2} \)

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

मानों को प्रतिस्थापित करने और हल करने पर प्राप्त होता है:

\( P \approx 101601.6 \, \text{N} \)

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