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?
What about for shear stress?
Would the entire surface area be used for bulk stress?

 

[SteamKing]

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]

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.

 

[pmacias]

Young's Modulus, Bulk Modulus, and Shear Modulus are all measures of a material's response to stress or strain. Each of these moduli has a different area associated with it in the stress equation, depending on the type of stress being applied.

For Young's Modulus, which measures a material's resistance to changes in length or volume, the area in the stress equation is the cross-sectional area of the cylinder. This is the area of the circular face of the cylinder, as you mentioned.

For Shear Modulus, which measures a material's resistance to shearing forces, the area in the stress equation is the area of the surface that is being sheared. In the case of a cylinder, this would be the curved surface area.

For Bulk Modulus, which measures a material's resistance to changes in volume under pressure, the area in the stress equation is the entire surface area of the cylinder. This is because the pressure is being applied uniformly to the entire surface of the cylinder, rather than just one specific area.

It is important to note that the stress equation for each of these moduli is a simplification and does not take into account the complex internal structure and properties of the material. However, in many engineering applications, these equations provide a good approximation of the material's behavior under stress.