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,

$\displaystyle R = \frac {min}{max}$

$\displaystyle min = Rmax$

$\displaystyle M = \frac {Smin + Smax}{2}$

$\displaystyle 2M = Smin + Smax$

$\displaystyle 2M = S(Rmax) + Smax$

$\displaystyle 2M = SRmax + Smax = max(SR + S)$

$\displaystyle \therefore max = \frac {2M}{S(R + 1)}$

Then you can go back and get min,

$\displaystyle min = Rmax$

You can use the same method of rearranging equations and substituting with simultaneous equations with the other formulas for your other problem.

Re: Manipulation of Formula

Thank you for the quick response, I will give them a go and work through them. Thanks again.

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

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:

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

That is,

$\displaystyle R = \frac {S_{min}}{S_{max}}$

$\displaystyle S_{min} = R*S_{max}$

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

$\displaystyle 2M = S_{min} + S_{max}$

$\displaystyle 2M = (RS_{max}) + S_{max}$

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

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

Again, apologies for the confusion. Silly mistake!