Young's Modulus / Force per Area Ques.

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To calculate the compressive deformation in two rods with different moduli of elasticity and cross-sectional areas under a uniform load, one must consider the relationship between stress, strain, and the modulus of elasticity for each rod. The strains in both rods are equal, but the stresses will differ due to their varying properties. The total external load can be expressed as the sum of the stresses multiplied by their respective cross-sectional areas. This leads to a system of equations that can be solved to find the individual stresses in each rod. Understanding these relationships is crucial for accurately determining the compressive deformation in the two-rod system.
vhariharan
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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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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?
 
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?
 
What's the relationship between stress and force?
 
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)
 
Got it...Thanks!
 

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