A और B पर तय की गई 5 m की एक बीम 'A' से 2 m पर 50 kN के बिंदु भार का वहन करती है। क्रमशः आलंब 'A' और 'B' पर निश्चित छोर आघूर्ण क्या हैं?

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  1. 24 kNm दक्षिणावर्त और 36 kNm दक्षिणावर्त
  2. 24 kNm वामावर्त और 36 kNm वामावर्त
  3. 36 kNm दक्षिणावर्त और 24 kNm वामावर्त
  4. 36 kNm वामावर्त और 24 kNm दक्षिणावर्त

Answer (Detailed Solution Below)

Option 4 : 36 kNm वामावर्त और 24 kNm दक्षिणावर्त
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Detailed Solution

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अवधारणा:

जब एक बीम को बिंदु भार और स्पष्ट भारण जैसे कि uDL के अधीन किया जाता है तब निश्चित छोर आघूर्णों को नीचे दिया गया है:

F2 Abhishek M 11.2.21 Pallavi D5

 

F2 Abhishek M 11.2.21 Pallavi D6

गणना:

दिया हुआ:

F2 Abhishek M 11.2.21 Pallavi D7

a = 2m

b = 3m

L = a + b = 5m

P = 50 kN

\(M_{AB}^F = - \frac{{P{b^2}a}}{{{L^2}}} = - \frac{{50\; \times\; {{\left( 3 \right)}^2}\; \times \;2}}{{{{\left( 5 \right)}^2}}} = - 36\;kNm\;\left( \uparrow \right)\)

-ve चिह्न का अर्थ है कि \(M_{AB}^F\) वामावर्त में है

\(M_{AB}^F = + \frac{{P{a^2}b}}{{{L^2}}} = \frac{{50\; \times \;{{\left( 2 \right)}^2}\;\times\; 3}}{{{{\left( 5 \right)}^2}}} = + 24\;kN\;M\left( \downarrow \right)\)

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