Experimentally Determined Young's Modulus

[jdawg]

Homework Statement

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So in my mechanics of materials lab, we calculated Young's modulus after measuring the strain and applying force to a beam. What I'm trying to figure out is, why are you able to use both a bending force and an axial force when calculating Young's modulus?

Homework Equations

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Young's modulus = stress/strain

The Attempt at a Solution

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Is it because they both induce a normal force on the beam?

Thanks for any help!

 

[Chestermiller]

Is this a beam bending situation, or is it a situation where you are applying a tensile force along the beam axis?

 

[jdawg]

Sorry I forgot to include that, its a bending situation. We had a beam placed into a cantilever flexure frame and loaded weights on one end of the beam.

 

[Chestermiller]

Please describe your understanding of the axial stress distribution and the axial strain distribution on an arbitrary cross section of the beam, say half way along the length of the beam. What is your understanding of the kinematics of the deformation?

 

[jdawg]

The stress and strain distribution for the cross section was assumed to be uniaxial, so does that mean in the lateral direction the stress and strain is zero?

 

[Chestermiller]

The stress and strain distribution for the cross section was assumed to be uniaxial, so does that mean in the lateral direction the stress and strain is zero?

Are these stress and strain distributions uniform over the cross section of the beam, or do they vary with position over the cross section?

 

[jdawg]

We assumed them to be uniform.

 

[Chestermiller]

We assumed them to be uniform.

You need to go back and review beam bending. They are definitely not uniform. The variation of stress over the cross section is what causes the bending moment. Where over the cross section of the beam would your intuition tell you that the tensile stress (and strain) are highest? Lowest? Zero?