Young's Modulus / Force per Area Ques.

[vhariharan]

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!

 

[Mapes]

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?

 

[vhariharan]

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?

 

[Mapes]

What's the relationship between stress and force?

 

[vhariharan]

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)

 

[vhariharan]

Got it...Thanks!