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45 degree strain-stress rosette

  1. Nov 16, 2009 #1
    can anyone see where i have gone wrong? i am talking about question 4.17 below

    http://lh5.ggpht.com/_H4Iz7SmBrbk/SwEB0MVvMyI/AAAAAAAAB_Q/Uy80NKhkTOI/Capture.JPG [Broken]

    what i did was define [tex]\epsilon[/tex]1 [tex]\epsilon[/tex]2 and [tex]\epsilon[/tex]3
    [tex]\epsilon[/tex]x=[tex]\epsilon[/tex]1
    [tex]\epsilon[/tex]y=[tex]\epsilon[/tex]3
    2[tex]\epsilon[/tex]xy=2[tex]\epsilon[/tex]2-[tex]\epsilon[/tex]1-[tex]\epsilon[/tex]3

    [tex]\sigma[/tex]x=[tex]\frac{E}{(1+\nu)(1-2\nu)}[/tex]*[(1-[tex]\nu[/tex])[tex]\epsilon[/tex]1+[tex]\nu[/tex][tex]\epsilon[/tex]3]

    [tex]\sigma[/tex]y=[tex]\frac{E}{(1+\nu)(1-2\nu)}[/tex]*[(1-[tex]\nu[/tex])[tex]\epsilon[/tex]3+[tex]\nu[/tex][tex]\epsilon[/tex]1]

    [tex]\sigma[/tex]xy=G*2*[tex]\epsilon[/tex]xy=[tex]\frac{E}{2(1+\nu)}[/tex](2[tex]\epsilon[/tex]2-[tex]\epsilon[/tex]1-[tex]\epsilon[/tex]3)

    ---[tex]\frac{E}{2(1+\nu)}[/tex]=A---


    now to find the principal stresses

    [tex]\sigma[/tex]=[tex]\frac{\sigmax + \sigmay}{2}[/tex] +- [tex]\sqrt{\frac{\sigmax - \sigmay}{2}}^2+[tex]\sigma[/tex]xy^2[/tex]

    after plugging all the sigma's in i get

    =A*([tex]\epsilon[/tex]1+[tex]\epsilon[/tex]3)/(1-2[tex]\nu[/tex]) +- [tex]\sqrt{A^2*(\epsilon1-\epsilon3)^2+(A*((2[tex]\epsilon[/tex]2-[tex]\epsilon[/tex]1-[tex]\epsilon[/tex]3))^2}[/tex]

    which is all perfect except for that in the answer the denominator for the first part is : 2(1-[tex]\nu)[/tex] and i get 2(1+[tex]\nu[/tex] )(1-2[tex]\nu[/tex]) every time, is my algebra off somewhere, am i using the wrong method or could they have a mistake in the answer??
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Nov 16, 2009 #2
    sorry about the LATEX work, i see it now, looks terrible, i will try to fix it
     
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