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Homework Help: Area Calculations to find Jc energy Parmeter (simple maths)

  1. Jan 14, 2010 #1
    1. The problem statement, all variables and given/known data
    I have been given the following load-displacement plots for the same specimin with two different crack lengths. The lines are identical up to a load od 750N

    1zmi0zl.jpg

    i need to calculate the area of the blue shaded region to obtain a value of Jc using a separate equation.

    2. Relevant equations
    Area of triangle = 0.5(b)(h)
    Area of rectangle = (b)(h)

    3. The attempt at a solution
    I found the area of the largest triangle (tip at 1750)
    Total Area = (0.5)(0.003)(1750)=2.625

    Then split the lower half of the plot into 3 sections labeled 1,2&3. And calculated the areas
    Area 1=(0.5)(0.0012)(750)=0.45
    Area 2=(0.003-0.0012)(750)=1.35
    Area 3=(0.5)(0.003-0.0012)(1740-750)=0.891

    So Total Area - Area 1 -Area 2 - Area 3 = the blue shaded region
    However i get a negative value,

    Blue Shaded region = 2.625-0.45-1.35-0891 = -0.066

    Just by looking at the picture, it shouldnt be a negative value, I cant see the problem in my method. Can any1 see what im doing wrong?

    Any Help is appreciated
    Thanks
     
  2. jcsd
  3. Jan 14, 2010 #2
    Part of your problem is I think the "largest triangle" is not actually a triangle. If (1.2,750) is a point on the line, then (3,a) yields 750 x 2.5 for a, which is not 1750. Can't you just use 10 as the base and 1.8 as the height for a triangle?
     
  4. Jan 15, 2010 #3
    Hi,

    I tried it again by doing what you suggested and splitting the diagram further into 4 triangles and 1 rectangle. I got a positive area and solved the question :D

    Thanks for your help!
     
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