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Math Help - Plastic modulus

  1. #1
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    Plastic modulus

    Hello I was wondeing if anybody could help me work this out. I am an Structural Engineering student btw so feel free to have a laugh at my mathematical incompetence. I have an exam tomorrow where I will most likely have to find the plastic modulus of a triangle or trapezuim, this is the axis that cuts a shape into two equal areas. If you had a triangle what height below the apex would you draw this line to cut the shape in two? I have tried using similar triangles and some algebra, but I am just going round in circles (or triangles ) Thanks
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  2. #2
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    Quote Originally Posted by gjwo1 View Post
    Hello I was wondeing if anybody could help me work this out. I am an Structural Engineering student btw so feel free to have a laugh at my mathematical incompetence. I have an exam tomorrow where I will most likely have to find the plastic modulus of a triangle or trapezuim, this is the axis that cuts a shape into two equal areas. If you had a triangle what height below the apex would you draw this line to cut the shape in two? I have tried using similar triangles and some algebra, but I am just going round in circles (or triangles ) Thanks
    Hello,

    I've attached a sketch.

    The area of the larger triangle is calculated by:

    A=\frac12 \cdot B \cdot H

    The area of the smaller triangle is calcutlated by:

    a=\frac12 \cdot b \cdot h

    You know that 2a = A. That means:

    \frac12 \cdot B \cdot H= 2\left(\frac12 \cdot b \cdot h \right) . After a few steps of transformation you'll get:

    \frac{b}{B} \cdot \frac{h}{H}=\frac{1}{\sqrt{2}} \cdot \frac{1}{\sqrt{2}}

    That means: Draw a parallel to B with h = \frac{1}{\sqrt{2}}\cdot H
    Attached Thumbnails Attached Thumbnails Plastic modulus-dreieck_streckung.gif  
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  3. #3
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    Thanks ear-b, thats saved me lots of time I think I will take that formulae into the exam in my head. Hopefully they will just give us some sort of symetrical shape

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