# Young's Modulus, Bulk Modulus, and Shear

#### joel amos

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?
Would the entire surface area be used for bulk stress?

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#### SteamKing

Staff Emeritus
Homework Helper
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.

#### joel amos

So when using F / A to find the stress on a cylinder, what area is to be used? Area of face, area of surface?

#### SteamKing

Staff Emeritus
Homework Helper
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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