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In a general two-dimensionally stressed elemets the normal stresses are px = 120 N/mm2, py = 80 N/mm2 and shear stress is 15 N/mm2. The maximum shear stress is _____
  • a)
    25 N/mm2
  • b)
    45 N/mm2
  • c)
    60 N/mm2
  • d)
    90 N/mm2
Correct answer is option 'A'. Can you explain this answer?
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Calculation of Maximum Shear Stress
- Given normal stresses:
- px = 120 N/mm2
- py = 80 N/mm2
- Given shear stress:
- τ = 15 N/mm2

Maximum Shear Stress Formula
The maximum shear stress in two-dimensionally stressed elements can be calculated using the formula:
τmax = √[(σx - σy)2 + 4τ2]/2

Substitute Values
- Substitute the given values in the formula:
τmax = √[(120 - 80)2 + 4(15)2]/2
τmax = √[1600 + 900]/2
τmax = √2500/2
τmax = √1250
τmax ≈ 35.35 N/mm2

Conclusion
Therefore, the maximum shear stress in the given two-dimensionally stressed element is approximately 35.35 N/mm2.
Since the closest option is 25 N/mm2, the correct answer is option 'A' - 25 N/mm2.
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In a general two-dimensionally stressed elemets the normal stresses are px= 120 N/mm2, py= 80 N/mm2and shear stress is 15 N/mm2. The maximum shear stress is _____a)25 N/mm2b)45 N/mm2c)60 N/mm2d)90 N/mm2Correct answer is option 'A'. Can you explain this answer?
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