How Do You Calculate Young's Modulus from Tensile Stress and Strain Data?

[anthonyk2013]

A light alloy bar is observed to increase in length by .35% when subjected to a tenstile stress of 280MN/m^2.
Calculate youngs modulus for the material.

σ=280MN/M^2
x=.35%
ε=?
E=?
L=?

I have too many unknowns where do I start?

 

[SteamKing]

What's the definition of Young's modulus? How is it calculated?

 

[anthonyk2013]

What's the definition of Young's modulus? How is it calculated?

E=σ/ε

to find ε=x/L so think I might have to work of .35% but not sure how.

 

[SteamKing]

What does the 0.35% represent?

 

[anthonyk2013]

The length of the alloy has increased by .35%

 

[SteamKing]

And how would this increase be related to the strain?

 

[anthonyk2013]

Is strain not increase in length/original length ?

 

[SteamKing]

Yes.

 

[anthonyk2013]

I have the increase in length I don't have strain and I don't have original length.
Is it possible to work out length using only .35%?

 

[SteamKing]

Well, let's start with the basics. Assume the original length of the test specimen was L. After the stress was applied, what is the length of the test specimen? What is the strain due to the applied stress?

 

[anthonyk2013]

Strain=.35/L

 

[SteamKing]

Strain=.35/L

From the OP:

"A light alloy bar is observed to increase in length by .35% when subjected to a tenstile stress of 280MN/m^2."

Would you like to revise your answer?

 

[anthonyk2013]

Sorry SK but I'm lost now.

 

[anthonyk2013]

Stress and strain are proportional according to hooks law?

 

[SteamKing]

Yes, but you are avoiding the question about the strain of the test piece after it has the stress applied.

If the length of the test piece increases by 0.35%, what is its new length in terms of its original length?

 

[anthonyk2013]

Sorry SK but I'm still lost. Do I need to convert .35 from a % to measurement by dividing by 100.

 

[SteamKing]

Look, if something increases in length by 25%, what is its new length compared to its original length?

 

[Chestermiller]

If you have D dollars in your account to start with, and you earn 0.35% per year interest (compounded annually), how much money do you have in your account after 1 year? How much has the account value increased?

 

[anthonyk2013]

D+.35%?

 

[Chestermiller]

D+.35%?

.35% is not an amount of money. To verify this, try spending .35% at your local store.

The amount of money you would have after 1 year would be (D+0.0035D), and the amount of money you would have earned would be 0.0035D dollars.

 

[anthonyk2013]

Divide by 100 to get the value. I won't forget that too soon. Sorry guys elementary stuff.

So X=.0035

 

[Chestermiller]

Divide by 100 to get the value. I won't forget that too soon. Sorry guys elementary stuff.

So X=.0035

Actually, the bar getting larger by 0.35% means that ε = 0.0035.

 

[anthonyk2013]

E=280/.0035

So if you multiply strain by 100 you get the percentage it increases by?

 

[Chestermiller]

Yes. The strain is the fraction it increases by. To get the % increase in length, you multiply the strain by 100%.