How is required shell thickness for internal pressure calculated?

How is required shell thickness for internal pressure calculated?

• A. t = PR/SE
• B. t = P R S E
• C. t = (P × R) / S
• D. t = P/(R E S)

Answer: (A)

The main idea here is how internal pressure sets up a hoop (circumferential) stress in a thin-walled shell and how thickness is chosen to keep that stress below what the material and joints can safely carry. For a thin-walled cylinder under internal pressure, the hoop stress is approximately σ = P R / t. To be safe, this hoop stress must not exceed the allowable stress of the material, reduced by joint efficiency, so the available design stress is S × E. Setting σ = S×E and solving for thickness gives t = P R / (S E). This is why the correct form places SE in the denominator; it accounts for both material strength and any reduction in effective strength due to joints or welds. If the seam is perfectly efficient (E = 1), it reduces to t = PR/S. If a corrosion allowance is needed, you add that after calculating t. The other forms misplace S or E or invert the relationship, leading to incorrect thickness.

The main idea here is how internal pressure sets up a hoop (circumferential) stress in a thin-walled shell and how thickness is chosen to keep that stress below what the material and joints can safely carry. For a thin-walled cylinder under internal pressure, the hoop stress is approximately σ = P R / t. To be safe, this hoop stress must not exceed the allowable stress of the material, reduced by joint efficiency, so the available design stress is S × E. Setting σ = S×E and solving for thickness gives t = P R / (S E). This is why the correct form places SE in the denominator; it accounts for both material strength and any reduction in effective strength due to joints or welds. If the seam is perfectly efficient (E = 1), it reduces to t = PR/S. If a corrosion allowance is needed, you add that after calculating t. The other forms misplace S or E or invert the relationship, leading to incorrect thickness.