Stress Concentration around a circular hole on a flat rectangular plate

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SUMMARY

The discussion focuses on finding the analytical solution for stress concentration around a circular hole in a flat rectangular plate subjected to tensile loads. The stress concentration factor, Kt, is crucial and can range up to 3.0, depending on the hole's diameter and its proximity to the plate's edge. Reference is made to Chart 4.1 in Peterson's "Stress Concentration Factors," which provides an empirical formula for calculating Kt. The analysis assumes plane stress conditions and simplifies the problem by considering the limit where the hole diameter is small relative to the plate dimensions.

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  • Understanding of Mechanics of Materials principles
  • Familiarity with stress concentration factors and their significance
  • Knowledge of plane stress assumptions in structural analysis
  • Ability to interpret empirical formulas from engineering texts
NEXT STEPS
  • Study Peterson's "Stress Concentration Factors" for detailed empirical formulas
  • Learn about the derivation of stress concentration factors for various geometries
  • Explore analytical methods for solving differential equations in mechanics
  • Investigate finite element analysis (FEA) techniques for stress concentration problems
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Mechanical engineers, structural analysts, and students studying Mechanics of Materials who are interested in stress analysis and design optimization around holes in structural components.

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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