In a pressure vessel wall containing a circular opening, beyond what approximate radial distance from the hole edge does stress concentration become negligible?

Introduction / Context:Openings in pressure components disturb the membrane stress field and create local stress concentration. Designers need a rule-of-thumb distance beyond which the disturbance is small enough to neglect in primary stress evaluation.

Given Data / Assumptions:

• Thin-wall approximation and linear elasticity.
• Single isolated circular opening.

Concept / Approach:The perturbation caused by a hole decays with distance from the discontinuity. In many handbooks, the disturbed region is considered local, and primary membrane stress can be assumed recovered beyond a few diameters from the edge.

Step-by-Step Solution:1) Define characteristic length: hole diameter, D.2) Recognize decay of stress concentration with radial distance r from the edge.3) Apply common guideline: effects are negligible beyond about 5D.

Verification / Alternative check:Finite-element studies and classic elasticity solutions show steep decay; practical design rules often choose 3–5D. A conservative rounded value used in many texts is roughly five diameters.

Why Other Options Are Wrong:2D can still show noticeable concentration.10D and 20D are overly conservative for typical thin-wall cases.

Common Pitfalls:Applying this rule near multiple closely spaced openings where interactions increase disturbed zones; ignoring reinforcement pads and local thickness changes.

Final Answer:Five times the hole diameter