# Manipulation of Formula

• Oct 10th 2011, 07:54 AM
Rastanking
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.

Andy
• Oct 10th 2011, 08:49 AM
FrameOfMind
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.
• Oct 10th 2011, 10:33 AM
Rastanking
Re: Manipulation of Formula
Thank you for the quick response, I will give them a go and work through them. Thanks again.
• Oct 10th 2011, 10:51 AM
Rastanking
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
• Oct 10th 2011, 11:30 AM
FrameOfMind
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!