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Finding the maximum stress

  1. Dec 5, 2009 #1
    in the below question

    Capture.JPG
    2 identical boards are glued together at their centers, the strength of the glue is 10Mpa shearing and 20Mpa normal, the strength of the boards is 10Mpa shearing and 30Mpa normal


    i found the stress on the system and found

    [tex]\sigma[/tex]xx= 5P
    [tex]\sigma[/tex]yy= P
    [tex]\sigma[/tex]xy= 0

    this meaning that [tex]\theta[/tex]=0 is the principal plane and that
    [tex]\sigma[/tex]s max=+-2P


    now the question asks what the maximum value of P can be,
    i clearly need to compare the values of the principal stresses to the strengths of the wood and glue,
    my question is whether i need to compare the principal normal stress to the glues strength even though it is at 45 degrees to the plane where the glue lies??

    meaning: the glue lies on the x axis but the maximum stress is at 45 degrees so do i need to compare the normal strength at 90 degrees (P) or the maximum stress (5P)??
    same goes for the shear stress?

    at first i thought i just need to compare it to the stress perpindicular to the x axis, and the shear stress parallel to it, but someone told me that since the "stress cube" is tiny and the glue does have some volume, i need to compare the maximum stresses to the glues strength


    therefore i would get P<=4

    whereas had i not done that ii would have P<=5
     
  2. jcsd
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