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If a body is subjected to stresses in xy plane with stresses of 60N/mm² and 80N/mm² acting along x and y axes respectively. Also the shear stress acting is 20N/mm². Find the minimum normal stress.
  • a)
    45.4
  • b)
    47.6
  • c)
    48.2
  • d)
    50.6
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If a body is subjected to stresses in xy plane with stresses of 60N/mm...
Explanation: σ=[σ(x) +σ(y)]/2 – √( [σ(x)-σ(y) ]²/2² + τ²).
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Most Upvoted Answer
If a body is subjected to stresses in xy plane with stresses of 60N/mm...
Given Data
- Normal stress in x direction (σx) = 60 N/mm²
- Normal stress in y direction (σy) = 80 N/mm²
- Shear stress (τxy) = 20 N/mm²
Calculation of Principal Stresses
To find the minimum normal stress, we first calculate the principal stresses using the formula:
σ₁,₂ = (σx + σy)/2 ± √[((σx - σy)/2)² + τ²]
Here, σ₁ and σ₂ are the principal stresses.
Step 1: Calculate the Average Stress
- Average stress (σ_avg) = (σx + σy) / 2
= (60 + 80) / 2
= 70 N/mm²
Step 2: Calculate the Radius
- Radius (R) = √[((σx - σy)/2)² + τ²]
= √[((60 - 80)/2)² + (20)²]
= √[(−10)² + (20)²]
= √[100 + 400]
= √500
= 22.36 N/mm²
Step 3: Calculate Principal Stresses
- Principal stress σ₁ = σ_avg + R
= 70 + 22.36
= 92.36 N/mm²
- Principal stress σ₂ = σ_avg - R
= 70 - 22.36
= 47.64 N/mm²
Conclusion
The minimum normal stress is found to be approximately 47.64 N/mm², which rounds to 47.6 N/mm².
Thus, the correct answer is option b) 47.6 N/mm².
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If a body is subjected to stresses in xy plane with stresses of 60N/mm² and 80N/mm² acting along x and y axes respectively. Also the shear stress acting is 20N/mm². Find the minimum normal stress.a)45.4b)47.6c)48.2d)50.6Correct answer is option 'B'. Can you explain this answer?
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