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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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.