Experimentally Determined Young's Modulus

• jdawg
In summary, in a mechanics of materials lab, Young's modulus was calculated using both a bending force and an axial force applied to a beam. The reason for this is because both forces induce a normal force on the beam. In a bending situation, the stress and strain distribution for the cross section of the beam is not uniform, and the variation of stress over the cross section causes the bending moment. The highest tensile stress and strain are typically found at the outer edges of the beam, while the lowest are at the neutral axis. The lateral direction typically has zero stress and strain.
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!

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.

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?

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?

jdawg said:
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?

We assumed them to be uniform.

jdawg said:
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?

1. What is Young's Modulus and why is it important in science?

Young's Modulus, also known as the modulus of elasticity, is a measure of the stiffness of a material. It describes the relationship between stress and strain in a material and is an important parameter in understanding the mechanical behavior of a material.

2. How is Young's Modulus experimentally determined?

You can determine Young's Modulus by performing a tensile test on a material. This involves stretching a sample of the material until it reaches its breaking point, while measuring the applied force and resulting strain. The slope of the stress-strain curve at the elastic region is equal to Young's Modulus.

3. What factors can affect the accuracy of experimentally determined Young's Modulus?

The accuracy of Young's Modulus can be affected by several factors, such as the size and shape of the sample, the testing environment, and the testing method used. It is important to carefully control these variables to obtain accurate results.

4. How does Young's Modulus vary between different materials?

Young's Modulus varies greatly between different materials, as it is dependent on the atomic and molecular structure of the material. For example, materials with strong intermolecular bonds, such as metals, tend to have higher Young's Modulus values compared to materials with weaker bonds, such as rubber.

5. What are some real-world applications of experimentally determined Young's Modulus?

Young's Modulus has many real-world applications, including predicting the behavior of structures under different loads, designing and testing materials for specific uses, and understanding the elasticity of biological tissues. It is also a crucial parameter in fields such as engineering, materials science, and biomechanics.

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