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Math Help - Could anyone help on this one ?

  1. #1
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    Could anyone help on this one ?

    I have to derive two equations in order to get a Merit Index.

    so the question is how you derive the

    m=b^2*l*r , r=density

    and Fy = (b^4/12 /(b/2) * sy/(m/b^2*r)
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Uh... I guess that b is the breadth of a square and l the length of a cuboid with a square face...

    Then from \rho = \dfrac{m}{V}

    We know that the volume is V = b \times b \times l

    Hence, we get:

    \rho = \dfrac{m}{b^2l}

    m = b^2l\rho

    I don't know what you mean by Fy and sy...

    Is that it?

    F_y = \left(\dfrac{\frac{b^4}{12}}{\frac{b}{2}}\right)\l  eft(\dfrac{s_y}{\frac{m}{b^2r}}\right)
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  3. #3
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    well I am in that point , Fy = failure load of a beam equation , sy=yield strees .

    the final Merit index is = sy^2/3 / ρ . I am in the point Fy=b^4/12 / b/2 * σy/(m/b^2*ρ) .

    So the thing is , how you get to that σy^2/3 / ρ ?

    To make it a bit clearer it will be in the end Fy = b^3 *6 * m σy/2^3/ρ . So this σy/2^3/ρ will be in the final equation as it is now . without any mass or length in its function.

    I hope I am clear now .
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  4. #4
    MHF Contributor Unknown008's Avatar
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    So, this is right then and you use this to find the Merit index?

    F_y = \left(\dfrac{b^4/12}{b/2}\right)\left(\dfrac{\sigma y}{m/(b^2\rho)}\right)

    This is strange because some terms cancel out... to become:

    F_y = \dfrac{b^5 \sigma y \rho}{6m}
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  5. #5
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    well thats the thing , i know the answer but i cant get it from these equations
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  6. #6
    MHF Contributor Unknown008's Avatar
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    Well... I don't know those equations... which makes me more in the dark... sorry, I don't think I can help you on this one...
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  7. #7
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    cheers anyway dude
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