Young's Modulus, Bulk Modulus, and Shear

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Discussion Overview

The discussion revolves around the concepts of Young's Modulus, Bulk Modulus, and Shear Modulus in relation to stress calculations for a cylinder. Participants explore the appropriate areas to use in the stress formula (Force / Area) for different types of modulus and stress conditions.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether the area for Young's Modulus stress should be the area of the circular face of the cylinder.
  • Another participant clarifies that Young's Modulus and Shear Modulus are ratios of stress to strain, not conventional stresses, and mentions their relationship through Poisson's ratio.
  • A participant seeks clarification on which area to use in the F / A formula for stress on a cylinder, asking if it should be the area of the face or the surface area.
  • One response indicates that the area to be used depends on the type of stress being analyzed, suggesting that different loading conditions (axial force, bending moment, torsional moment) may require different approaches.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate areas to use in stress calculations for different moduli, indicating that there is no consensus on the matter.

Contextual Notes

The discussion highlights the dependence on specific loading conditions and the definitions of stress types, which may not be universally applicable across different scenarios.

joel amos
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I'm dealing with a cylinder. The equation for the stress of each is Force / Area. What are the different areas for the equation in regard to young's modulus, bulk modulus, and shear modulus?

Is the area Young's Modulus stress the area of circle face?
What about for shear stress?
Would the entire surface area be used for bulk stress?
 
Last edited:
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Although Young's modulus and the Shear modulus have units of stress, they are not stresses in the conventional meaning of force divided by area. Young's modulus represents the ratio of tensile stress to tensile strain, and the strain is non-dimensional. Similarly, the shear modulus represents the ratio of shear stress to shear strain. Young's modulus is related to shear modulus by a parameter known as Poisson's ration. The bulk modulus is also related to Young's and the shear moduli.

See: http://en.wikipedia.org/wiki/Bulk_modulus
http://en.wikipedia.org/wiki/Shear_modulus
http://en.wikipedia.org/wiki/Young's_modulus

There are a bunch of handy formulas at the bottom of the bulk modulus article.
 
So when using F / A to find the stress on a cylinder, what area is to be used? Area of face, area of surface?
 
It depends on what kind of stress you are analyzing. Is the cylinder loaded with an axial force? Is a bending moment or torsional moment being applied? Not all stresses have the formula F / A.
 

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