Young's Modulus / Force per Area Ques.

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Discussion Overview

The discussion revolves around calculating the compressive deformation of two rods with different elastic moduli and cross-sectional areas when subjected to a uniform load. Participants explore the relationships between stress, strain, and the modulus of elasticity, as well as how these factors interact in a system with multiple rods.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant questions how to calculate the compressive deformation in two rods with different properties when compressed uniformly.
  • Another participant suggests writing the equations that connect stress and strain for each rod and inquires about the relationship between strains.
  • A participant acknowledges understanding the relationship between stress, strain, and modulus of elasticity, but seeks clarification on relating stress in each rod to the total external load.
  • There is a discussion about the relationship between stress and force, with a participant stating the equation force = stress * cross-sectional area.
  • One participant expresses confusion about how to relate the stress in each rod to the total force applied, noting the presence of unknowns in the system.

Areas of Agreement / Disagreement

Participants generally agree on the need to relate stress and strain in the context of the problem, but there is no consensus on how to approach the calculation of stress in each rod relative to the total force applied.

Contextual Notes

Participants have not fully resolved how to handle the unknowns in the stress calculations for each rod, and there are assumptions regarding the uniformity of compression and the relationship between stress and external load that remain unaddressed.

Who May Find This Useful

This discussion may be useful for students or individuals studying mechanics of materials, particularly those interested in understanding the behavior of composite systems under load.

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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