Stress Concentration around a circular hole on a flat rectangular plate

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Discussion Overview

The discussion focuses on finding the analytical solution for stress concentration around a circular hole in a flat rectangular plate subjected to tensile loads on both sides. It involves theoretical considerations and assumptions related to mechanics of materials.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant seeks assistance with the analytical solution for stress concentration around a circular hole in a flat plate under tensile load.
  • Another participant references standard mechanics of materials texts, suggesting that the stress concentration factor, Kt, is used in calculations and can vary based on the hole size.
  • A participant questions the dependency of Kt on the radius of the hole, implying it might be independent.
  • Another participant counters that Kt actually depends on both the hole diameter and the distance from the hole edge to the plate edge.
  • One participant considers a limit where the hole diameter is small relative to the plate dimensions and suggests starting from that simplification for analytical solutions.
  • A participant expresses gratitude for the assistance received in the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the dependency of the stress concentration factor Kt, with some asserting it varies with hole size and others suggesting it may not. The discussion remains unresolved regarding the exact nature of Kt and its implications for the analytical solution.

Contextual Notes

There are assumptions regarding the plane stress condition and the simplifications made when considering small hole diameters relative to the plate dimensions, which may affect the analysis.

aidiot
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Can anyone help with how to find the analytical solution to problem involving finding the stress concentration around a circular hole in a flat plate.

The plate is has tensile load on both sides.
 
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That's a classic example that is in any Mechanics of Materials text. Have you done any searching? The calculation, assuming plane stress, is the regular stress due to the tensile load multiplied by a stress concentration factor, Kt. That value ranges up to 3.0 depending on the size of the hole.

Chart 4.1 in Peterson's Stress Concentration Factors gives an empirical formula for the Kt value.
 
Last edited:
For a circular hole, I'd have imagined that Kt would be independent of the radius.
 
Kt is dependent on hole diameter and the distance between the hole edge and the plate edge.
 
Oh, I'm thinking of the limit where the hole diameter is small compared to the dimensions of the plate, and small compared to the distance from the nearest edge. If I was looking for an analytical solution to the DEs, I'd have started from that simplification.
 
thanks for your help guys...

much appreciated
 

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