Young's Modulus / Force per Area Ques.

In summary, the conversation discusses the calculation of compressive deformation in a system with two rods of different elastic moduli and cross-sectional areas. It is suggested to use the equations connecting stress and strain for each beam and to relate the stresses to the total external load. The relationship between stress and force is also discussed, with the conclusion that the total force applied is the sum of the stress multiplied by the cross-sectional area of both rods.
  • #1
vhariharan
4
0
Hello,

My question in this. If you have a system where two rods (different moduli of elasticity and different cross sectional areas, but equal in length) are compressed uniformally by a load, how do you calculate the compressive deformation in the rods. The compression of both will be identical, and I understand how to calculate the compression if only one of the two rods was present. But how does having another rod with a different elastic modulus and cross sectional area affect the system. I understand that the compression in the two rod system should be less than the compression of just the single rod system. Thanks!
 
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  • #2
Hi vhariharan, welcome to PF. It would be a good idea to write the equation connecting stress and strain for each beam. What can you say about the strains? Can you relate the stresses (in conjunction with the cross-sectional areas) to the total external load?
 
  • #3
I have the equations relating stress, strain, and the modulus of elasticity, and I understand that the strain in each rod is equal. But how would you relate the stress in each rod to the total external load?
 
  • #4
What's the relationship between stress and force?
 
  • #5
force=stress*cross sectional area, but how do you relate the stress in each of the rods to the total force applied? Is it just the sum of the stress*cross sectional area of both rods? But then we have two unknowns again (the stress in each of the rods)
 
  • #6
Got it...Thanks!
 

What is Young's Modulus?

Young's Modulus, also known as the modulus of elasticity, is a measure of the stiffness of a material. It represents the ratio of stress (force per unit area) to strain (change in length per unit length) in a material.

How is Young's Modulus calculated?

You can calculate Young's Modulus by dividing the stress by the strain. This can be represented by the equation E = σ/ε, where E is Young's Modulus, σ is stress, and ε is strain.

What is the unit of measurement for Young's Modulus?

The unit of measurement for Young's Modulus is typically expressed in pascals (Pa) or newtons per square meter (N/m²). In the imperial system, it is sometimes expressed in pounds per square inch (psi).

What is the significance of Young's Modulus in materials science?

Young's Modulus is an important property in materials science as it helps determine the stiffness and elasticity of a material. It is often used in engineering to select materials for specific applications and to predict their behavior under different types of stress.

How does temperature affect Young's Modulus?

The temperature can affect Young's Modulus of a material. In general, as the temperature increases, the Young's Modulus decreases. This is due to the increase in thermal energy causing the material to expand and become less stiff.

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