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3D Solid Deformation Problem

  1. Mar 29, 2015 #1
    Hi all,
    Having some trouble getting the final answer on the question below, the fact that the cube doesn't have a force in the x direction is throwing me off. Once I fine the force(??) in the x-direction, I can just use the generalized Hooke's law to obtain strain? Any help is appreciated.

    1. The problem statement, all variables and given/known data
    Capture_zpsav4w8qd6.jpg

    2. Equations in upload of solution.

    See my solution for relevant equations.
    http://[ATTACH=full]199721[/ATTACH]
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Mar 29, 2015 #2
    In the block is constrained in the x-direction, what is the strain in the x-direction? What does your first equation give you in this case?

    Chet
     
  4. Mar 29, 2015 #3
    So I am assuming Sigma(x) = 0, therefore, Strain(x) = -1.00005 x10^-4

    However the question says to find the stress in the x-direction, which I have taken as 0?

    Or, do I sub Epsilon(x) as 0 and therefore would be able to find Sigma(x) from the first equation? After second thought I think this is correct due to 0 deformation in the x direction hence strain is 0?
     
  5. Mar 29, 2015 #4
    How can you say that the strain in the x direction is not zero, when the problem statement says that strain in the x direction is zero? What does the word "constrained" mean to you?

    Chet
     
  6. Mar 29, 2015 #5
    I realised this soon after I posted my previous response and edited it soon afterwards, it make sense now.

    Due to the tensile force in the y direction and the compressive force in the z direction the block obviously expands in the z direction and contracts in the y direction? Therefore, shouldn't Epsilon(y) be negative and Epsilon(z) be positive. Is this done by changing the sign (+ or -) for the Sigma values in the generalised Hooke's law? I.E. Sigma(y) should in fact be -50MPa?

    You can see the two different answers on either side of my page.
    717d3a72-5a50-4632-aa33-2d243fc07cc9_zpscik2qcsj.jpg
     
  7. Mar 29, 2015 #6
    You have a sign error in the calculation of the stress in the y direction. It should be negative.

    Chet
     
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