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How to solve for the angle of principle stresses

  1. Dec 7, 2012 #1
    Hello everyone,

    I want to start by saying this is my first official visit to the forum, however I have been using the forum for several years to help me through my classes, and I owe a big thanks to all who are involved for getting me through some tough times!

    Now, on to my question.....

    I need some help on how to solve the equation for the angle of principle stress on a stress element. The equation is tan2∅=(shear stress/(stress in X-stress in Y)/2.

    I don't understand how to solve for ∅ in this equation, since I don't understand what to make of the tan2∅ term. How do I punch that into a calculator to solve this equation? I also don't understand how I'm suppose to get two seperate angles out of this equation (one for each of the principle stresses).

    Any help would be much obliged.
  2. jcsd
  3. Dec 7, 2012 #2


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    Science Advisor
    Homework Helper

    welcome to pf!

    hello kfc12piece! welcome to pf! :smile:

    (have a nicer phi: φ :wink:)
    use the tan-1 button …

    that'll give you 2φ :wink:

    eg if tan2φ = √3,

    then 2φ = 60° (or 240° or 420° or …)

    so φ = 30° (or 120°) :smile:
  4. Dec 11, 2012 #3
    The principal stresses are perpendicular to one another. So, once you know one angle, you know the other.
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