Young's Modulus, Bulk Modulus, and Shear

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SUMMARY

This discussion focuses on the application of Young's Modulus, Bulk Modulus, and Shear Modulus in the context of stress analysis for a cylinder. The stress is calculated using the formula Force / Area, but the specific area used varies depending on the type of stress being analyzed. Young's Modulus relates tensile stress to tensile strain, while Shear Modulus relates shear stress to shear strain, with both moduli connected through Poisson's ratio. The Bulk Modulus is also interrelated with these moduli, emphasizing the importance of understanding the type of loading (axial, bending, or torsional) when determining the appropriate area for stress calculations.

PREREQUISITES
  • Understanding of Young's Modulus and its application in tensile stress analysis
  • Knowledge of Shear Modulus and its relationship to shear stress
  • Familiarity with Bulk Modulus and its role in volumetric stress analysis
  • Basic grasp of Poisson's ratio and its significance in material mechanics
NEXT STEPS
  • Research the specific formulas for calculating stress in axial, bending, and torsional loading scenarios
  • Study the relationship between Young's Modulus, Shear Modulus, and Poisson's ratio in detail
  • Explore practical applications of Bulk Modulus in engineering materials
  • Examine case studies involving stress analysis of cylindrical structures under various loading conditions
USEFUL FOR

Mechanical engineers, materials scientists, and students studying material mechanics who seek to deepen their understanding of stress analysis in cylindrical structures.

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?
 
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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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