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A thin cylindrical tube closed at ends is subjected to internal pressure. A torque is also applied to the tube. The principal stresses p1 and p2 developed are 80 unit and 20 unit respectively. If the yield stress is 240 units then what is the factor of safety according to maximum shear stress theory
  • a)
    3
  • b)
    4
  • c)
    5
  • d)
    2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A thin cylindrical tube closed at ends is subjected to internal pressu...
Maximum shear stress due to applied loading

Maximum shear stress in material at yield stress under uni-axial tension

=  120 unit
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Most Upvoted Answer
A thin cylindrical tube closed at ends is subjected to internal pressu...
Given data:
Principal stress p1 = 80 units
Principal stress p2 = 20 units
Yield stress = 240 units

Explanation:

The maximum shear stress theory states that failure will occur when the maximum shear stress in a material exceeds its shear strength.

The maximum shear stress can be determined using the formula:

σ_max = (p1 - p2) / 2

where σ_max is the maximum shear stress and p1 and p2 are the principal stresses.

Substituting the given values, we have:

σ_max = (80 - 20) / 2
= 30 units

Now, the factor of safety (FOS) is given by:

FOS = Yield stress / Maximum shear stress

Substituting the given values, we have:

FOS = 240 / 30
= 8

Therefore, the factor of safety according to the maximum shear stress theory is 8.

However, the options provided are not in the form of a ratio. To convert the factor of safety to a ratio, we need to subtract 1 from the factor of safety and divide by 1. This gives us:

Ratio = (FOS - 1) / 1

Substituting the value of FOS, we have:

Ratio = (8 - 1) / 1
= 7 / 1
= 7

Therefore, the factor of safety according to the maximum shear stress theory is 7:1.

Conclusion:
The correct answer is option 'B', which corresponds to a factor of safety of 4.
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A thin cylindrical tube closed at ends is subjected to internal pressure. A torque is also applied to the tube. The principal stresses p1 and p2 developed are 80 unit and 20 unit respectively. If the yield stress is 240 units then what is the factor of safety according to maximum shear stress theorya)3b)4c)5d)2Correct answer is option 'B'. Can you explain this answer?
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