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Equal area axis

  1. Jun 14, 2017 #1
    1. The problem statement, all variables and given/known data
    For this shape , it's clear that the centroid and the horizontal line of equal axis lies on the same horizontal line , am i right ????

    2. Relevant equations


    3. The attempt at a solution
    I'm not sure . correct me if i am wrong .
     

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  3. Jun 14, 2017 #2

    Mark44

    Staff: Mentor

    Do you mean "line of equal area"?
    Anyway, yes, symmetry should convince you that you're right if there's no other information given.
     
  4. Jun 14, 2017 #3
    Are you familiar with plastic analysis ? Zp here is the plastic modulus .

    I use another method to do , but i get different answer , why ?

    Here's my working : , Zp = Sum of area x ( difference between centroid of particluar area and the equal area axis )

    Zp = [ (130)(20)(150-10) + (150)(20)(150/2) ] x 2 = 1178000 , but the ans provided is only 929040
     
  5. Jun 14, 2017 #4

    Mark44

    Staff: Mentor

    No, I'm not, but I am familiar with the concept of centroids.
    My answer is based on the fact that the shape in the drawing is symmetric about its horizontal midline.
    If you had a rectangular piece of some uniform, rigid material 150 mm by 300 mm, its centroid would be at the center of the piece, at a point 75 mm to the right of the left edge, and 150 mm above the lower edge. If you cut out a rectangle 130 mm by 260 mm to form a "C" shape as in your drawing, the centroid of the piece you remove would be at its center, and the centroid of the remaining C-shaped piece would be along the horizontal midline, but a bit right of where it was for the original uncut piece of material.
     
  6. Jun 21, 2017 #5

    PhanthomJay

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Your number looks correct for the plastic section modulus perhaps the book is looking for the elastic section modulus you'll have to run the numbers
     
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