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Math Help - Manipulation of Formula

  1. #1
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    Manipulation of Formula

    Hi everyone,

    I know this may seem a really easy problem but I'm struggling with it and wondered if anyone could tell me where I'm going wrong.

    We are given a set of formula.

    Stress Ratio R=min/max

    Stress Range = бmax -бmin

    Stress Amplitude = (бmax - бmin)/2

    Mean Stress = (бmax + бmin)/2

    Please note that the thing that looks like a 6 is in fact the greek letter for stress.

    Then given a table with some of the data missing and some of it filled in.

    What I need to know is if I'm given the following information:

    R = 0.7 and mean = 85 How do I find the max, min and amplitude?

    and given

    amplitude = 30 and mean = -50 how do I find max, min and R

    Any help would be much appreciated as I'm pulling my hair out over this.

    Thanks in advance

    Andy
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  2. #2
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    Re: Manipulation of Formula

    You need to select the appropriate formulas and substitute the variables in the formulas for values you are given, then rearrange and solve using simultaneous equations.

    For example,

    R = \frac {min}{max}

    min = Rmax

    M = \frac {Smin + Smax}{2}
    2M = Smin + Smax
    2M = S(Rmax) + Smax
    2M = SRmax + Smax = max(SR + S)
    \therefore max = \frac {2M}{S(R + 1)}

    Then you can go back and get min,
    min = Rmax

    You can use the same method of rearranging equations and substituting with simultaneous equations with the other formulas for your other problem.
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  3. #3
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    Re: Manipulation of Formula

    Thank you for the quick response, I will give them a go and work through them. Thanks again.
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  4. #4
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    Re: Manipulation of Formula

    Hi,

    Many thanks for the quick reply but could you clarify something for me please, I'm assuming that you're using S to signify stress but in the final equation I'm still left with S(R+1), but I can't see what S is, ie what figure is should be.

    Regards

    Andy
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  5. #5
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    Re: Manipulation of Formula

    Ack, sorry about the confusion, I've treated "S" as a separate variable for "stress" (as a coefficient of "max" and "min", which is wrong), when the variables are actually:

    S_{max} and S_{min}, the maximum and minimum values for stress, respectively.

    That is,
    R = \frac {S_{min}}{S_{max}}

    S_{min} = R*S_{max}

    M = \frac {S_{min} + S_{max}}{2}

    2M = S_{min} + S_{max}

    2M = (RS_{max}) + S_{max}

    2M = RS_{max} + S_{max} = S_{max}(R + 1)

    \therefore S_{max} = \frac {2M}{R + 1}

    Again, apologies for the confusion. Silly mistake!
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