Discussion
At which of the following internal pressures will the cylindrical vessel yield as per the Tresca criterion if the yield strength of the material in tension is 320 MPa
Answer: A
The vessel yields at an internal pressure of about 3.55 MPa.
In a thin cylinder the principal stresses are the hoop stress, the axial stress (half of it) and a negligible radial stress. Tresca says yield occurs when the largest difference of principal stresses reaches the tensile yield strength; here that is hoop minus radial:
\[ \begin{aligned} \sigma_{h} &= \frac{pr}{t} = \frac{p(1800)}{20} = 90p \\ 90p &= 320 \Rightarrow p = 3.55\ \text{MPa} \end{aligned} \]
7.1 MPa uses the hoop-minus-axial difference (45p) as if the radial stress were not the minimum. 1.775 MPa is half the correct value, and 4.0 MPa does not follow from the hoop stress.
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