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Stress problem, units? (some calculation inside)

  1. Oct 16, 2012 #1

    n13

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    1. The problem statement, all variables and given/known data

    The stress of a particular material, σ, is a function of x and y, where x is stress in the x-direction and y is stress in the y direction. the stress function is given by:

    σ(x,y)= [itex]e^{y}[/itex] ln(2x+3y)
    when x=2cm @ 3cm/s​
    y=3cm @ 1cm/s​



    2. Relevant equations


    [itex]\frac{dσ}{dt}[/itex]=[itex]\frac{∂σ}{∂u}\frac{dx}{dt}+\frac{∂σ}{∂y}\frac{dy}{dt}[/itex]

    ∴[itex]\frac{dx}{dt}[/itex] = 3cm/s
    and [itex]\frac{dy}{dt}[/itex] = 1cm/s


    3. The attempt at a solution
    1. The problem statement, all variables and given/known data

    I have:

    [itex]\frac{∂σ}{∂y}[/itex] = [itex]\frac{3}{2x+3y}[/itex]

    and

    [itex]\frac{∂σ}{∂x}[/itex] = [itex]\frac{2}{2x+3y}[/itex]


    2. Relevant equations

    Im not sure if these partial differentiations are correct.

    3. The attempt at a solution
    1. The problem statement, all variables and given/known data

    carrying on asif they were:

    [itex]\frac{dσ}{dt}[/itex]= [itex]\frac{3}{2x+3y}[/itex] (3) + [itex]\frac{2}{2x+3y}[/itex] (2)

    sub rates in for x and y:

    [itex]\frac{dσ}{dt}[/itex]= [itex]\frac{9}{2(3)+3(1)}[/itex] + [itex]\frac{4}{2(3)+3(1)}[/itex] (2)

    2. Relevant equations

    so summing up i end up with:

    [itex]\frac{dσ}{dt}[/itex]= 1.44

    I was wondering what the units would be? considering that the original problem states stress, I cant figure out what the units are?
     
    Last edited: Oct 16, 2012
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