# Tensile stress, and youngs modulus.

I'm studying elasticity right now in my chemistry class, and I'm confused as to what exactly tensile stress (and maybe compression stress too ) might mean. It's given in N/m^2. And you're stretching the material.

Is the cypher I'm given indicative of what's happening only one side? Indicative of the pulling force acting on one edge of the material?

Also, I'm curious as to why Young's modulus is independent of an objects dimensions? This is interesting because elasticity does depend on this kind of things (the object's dimensions).

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## Answers and Replies

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Dale
Mentor
Tensile stress is the pulling force per unit cross-sectional area. In other words, it is the "pressure" pulling an object apart.

SteamKing
Staff Emeritus
Homework Helper
I'm studying elasticity right now in my chemistry class, and I'm confused as to what exactly tensile stress (and maybe compression stress too) might mean. It's given in N/m^2. And you're stretching the material.

Is the cypher I'm given indicative of what's happening only one side? Indicative of the pulling force acting on one edge of the material?

Also, I'm curious as to why Young's modulus is independent of an objects dimensions? This is interesting because elasticity does depend on this kind of things (the object's dimensions).
Young's modulus is a property of the material. It is roughly analogous to the spring constant of the material, in that it relates the stress applied to the material to the amount of stretch which the material will undergo as a result. For a material like steel, the Young's modulus remains constant up to the point where the steel deforms permanently. In this region, called the elastic region, if you double the stress, the amount of stretch doubles. When the stress is removed, the material returns to its original length. When steel is stressed beyond the elastic limit, the relationship between applied stress and the resulting stretch is no longer simple, and when the stress is removed, the material retains a certain amount of the stretch.

I don't know what your cypher is.

davidbenari
DaleSpam:

Suppose I hang a fiber from some type of roof. I hang a 1kg weight from it. The cross sectional area of the fiber is 1mm2. Then the tensile stress is ##9.8N/1mm^2## ?

Steamking:

I know how the modulus is defined however, I read that if a material is twice as long then it experiences less deformation, etc (similar relationships like that). If this is the case (that deformation depends on dimensions) then why is it that Young's modulus is inherent to the material? Thanks.

Dale
Mentor
Suppose I hang a fiber from some type of roof. I hang a 1kg weight from it. The cross sectional area of the fiber is 1mm2. Then the tensile stress is ##9.8N/1mm^2## ?
Yes.

davidbenari
Chestermiller
Mentor
I know how the modulus is defined however, I read that if a material is twice as long then it experiences less deformation, etc (similar relationships like that). If this is the case (that deformation depends on dimensions) then why is it that Young's modulus is inherent to the material? Thanks.
Actually, if the material is twice as long, then it experiences more deformation. But, the change in length of the sample is not the key parameter. The Young's modulus is defined as the stress in the material divided by the strain. The strain is equal to the change in length divided by the original length. If the original length is twice as long, the change in length will also be twice as large, the strain will be unchanged; and, as a result, the Young's modulus will be unchanged.

Chet

davidbenari
By the way, I have to calculate Young's modulus from a Strain-Stress graph, but I'm not given the initial length. I'm only given the extension of the material. This is impossible to calculate right? I need to have the initial length.

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Chestermiller
Mentor
By the way, I have to calculate Young's modulus from a Shear-Stress graph, but I'm not given the initial length. I'm only given the extension of the material. This is impossible to calculate right? I need to have the initial length.
This is a homework problem. Please post it in the Homework forums, and be sure to use the homework template. Also, please provide a precise statement of the problem (which is obviously missing here), and please make some effort to show us how you have doped out the problem so far.

Chet

davidbenari
Tensile stress is the pulling force per unit cross-sectional area. In other words, it is the "pressure" pulling an object apart.
If young’s modulus of a material, E = 2 x 10^5 and also the stress also reaches to 2 x 10^5, then it means strain, e = stress/E which means strain is 1. Then strain, e = change in length / original length. Therefore, change in length = strain x original length.

Therefore,

Change in length = 1 x original length
change in length = original length.

How is it possible if the stress of the material is reached to its safe stress and there is no change in length??

Chestermiller
Mentor
If young’s modulus of a material, E = 2 x 10^5 and also the stress also reaches to 2 x 10^5, then it means strain, e = stress/E which means strain is 1. Then strain, e = change in length / original length. Therefore, change in length = strain x original length.

Therefore,

Change in length = 1 x original length
change in length = original length.

How is it possible if the stress of the material is reached to its safe stress and there is no change in length??
You yourself wrote, and I quote, "change in length = original length" So the new length = 2 x (original length).

Incidentally, at a strain of 1, most materials are way beyond the region of linear elasticity where Hooke's law applies.

Chet