Youngs Modulus and Elastic Modulus

[Poppy]

I am doing my A2 physics coursework of the bending of cantilevers [zz)] I hung masses on a steel bar and measured the deflection, and then used a formula to calculate the Youngs Modulus of the steel, but the answer I got was way out - 9.6X10^9 instead of 200X10^9. Is this because I calculated the Elastic Modulus instead of the Youngs Modulus? What is the difference between the two?

 

[Chi Meson]

I'm not familiar with the term "elastic modulus." Do you mean elastic constant (as in spring constant) or coefficient of elasticity?
That last one is the percentage of the original speed (or is it kinetic energy?) that an object will keep after a collision. But I don't think this is ever referred to as a "modulus."

I think that the two terms are one and the same. The reason (probably) that your numbers did not work, is that the amount of bend depends on the "shear modulus." Young's is specifically for linear expansion/compression. Sideways strain requires one side of an object to stretch whil the other side compresses.

 

[Poppy]

Thankyou for your help. Could you please clarify the difference between Youngs Modulus and Shear Modulus? Can I find a recorded value for the shear modulus of steel or is this not a property of the material?

 

[Chi Meson]

There are genreally three types of "moduluses" (moduli?) Young's Modulus, bulk modulus and shear modulus.

All three are properties of the material from which the object is made. All three are usually provided in a table in nearly all texbooks. Young's Modulus (Y) is determined by how much object's length will change when subjected to stress.

Bulk modulus (beta) is determined by how the volume of the object will change when subjected to changes in pressure.

Shear modulus is harder to talk about, but easiest to demonstrate: take a thick stack of paper (like a phone book) and with your hand on the top, push horizontally. THe layers of the stack will shear and the top of the stack will move while the bottom stays put. All objects can be thought of as layers of material. HOw easily will these layers separate from each other? THe shear modulus relates how the top layer of a material will move in relation to the bottom layer.

Whenever something is bending , the material is shearing some amount because the inside of the bend gets compressed while the outside of the bend gets stretched. "Layers" of the material have to move laterally to each other.

 

[ShawnD]

Originally posted by Poppy
Is this because I calculated the Elastic Modulus instead of the Youngs Modulus? What is the difference between the two?

Young's Modulus is also referred to as the Modulus of Elasticity. They are the same thing.

 

[Poppy]

Is the Shear Modulus also known as the Bending or Flexural Modulus? Because the formula I used was from a website which called it that, but I thought it was the same as the Youngs Modulus. Silly me.

 

[Chi Meson]

Whoops. LOng weekend.

I'm not certain about that. I never heard of "flexural" modulus. It has been a long time since I did stress/strain, and unfortunately it is not part of any course that I teach.

I am certain that the shear modulus is used to determine "flex" but I seem to recall that the formula in which it is used is slightly different than the one used for simple "shearing." So a "flexural" modulus might be a variation of the shear modulus.

I would take this question to the engineering section of the forum for further information.