## Two equations Two unknowns

## Two equations Two unknowns

(OP)

Hello, I am a new Mathcad user and I am wondering:

I have 2 equations and two unknowns. I want to keep the letters and symbols all the way in my calculations.

epsilon_ys = A/E * [1+3/7*(A/R)^(n-1)]

epsilon_ts = B/E * [1+3/7*(B/R)^(n-1)

So I want to know how the equations looks like for n and R. Those are the 2 unknowns. But I don't want to use values for the other knowns like A, B, E etc. But Mathcad sees the "known" ones A, B etc like unknowns aswell?

So, I have these two equations and I want to know how my unknowns look like (n and R).

Can someone help me?

I have 2 equations and two unknowns. I want to keep the letters and symbols all the way in my calculations.

epsilon_ys = A/E * [1+3/7*(A/R)^(n-1)]

epsilon_ts = B/E * [1+3/7*(B/R)^(n-1)

So I want to know how the equations looks like for n and R. Those are the 2 unknowns. But I don't want to use values for the other knowns like A, B, E etc. But Mathcad sees the "known" ones A, B etc like unknowns aswell?

So, I have these two equations and I want to know how my unknowns look like (n and R).

Can someone help me?

## RE: Two equations Two unknowns

You will have to attach your sheet to show what you really need and want to achieve.

## RE: Two equations Two unknowns

epsilon_ys = A/E * [1+3/7*(A/R)^(n-1)]

epsilon_ts = B/E * [1+3/7*(B/R)^(n-1)

I want to write my two unknowns as functions of the knowns. The unknowns are n and R. Everything else is known. I don't want to use numbers for the knowns. I want it to be letters and symbols all the way. So, 2 equations 2 unknowns, symbols and letters all the way! No numbers! :)

Cheers!

## RE: Two equations Two unknowns

You can either user the symbolic solve command (you provide the two equations in a 2x1 matrix) or as an alternative you can use a solve block with find() which you evaluate symbolically (you should not provide guess values in this case).

BTW, the reason for attaching a worksheet are manyfolds. It usually more clearly shows whats needed or why an attempt went wrong. We see which version of Mathcad you are using (you haven't stated it), MC11, MC15, Prime and last but not least it makes it more convenient for people willing to help to play with a ready made sheet rather than having to type in all from scartch.

## RE: Two equations Two unknowns

http://www.ladda-upp.se/bilder/ruxhykvgezgb/

## RE: Two equations Two unknowns

You have to solve for both variables at the same time, but I am not sure if Mathcad will be able to provide a symbolic solution.

## RE: Two equations Two unknowns

I still think that Mathcad will have difficulties in presenting you are closed symbolic solution because of the involved logarithms but it shouldn't be that difficult to (partly) manual derive that solution with the help of Mathcad's symbolics. I guess you already solved your system manually yourself, though.

Why do you think that you need a symbolic solution? Unless you intend to implement the solution in assembler or C embedded in a small circuit, there might be a better way to get what you want at the end using numerics.

## RE: Two equations Two unknowns

equation. While it would be fantastic to have the equation's n-exponent

be found symbolically. I do not see how such a symbolical solution can be

found.

R is normally a chosen "reference strength" and it is normally taken to

be "The Yield strength, SY"

The second equation has an error because the strain corresponding to

the tensile strength is the tensile strain and not the yield strain.

I propose that the equations be solved numerically choosing R to be

SY the solve for n number

Regards,

Calculus

## RE: Two equations Two unknowns

as follows:

Solve the two (2) equations on two (2) unknown

numerically be setting R = Sy and obtaining the

data for all known parameters to initiate the

iterations.

The solution for a given material at temperature

can be solved at different temperatures resulting

in n(T) and R(T).

Once n(T) and R(T) are determined, one can use

a spline interpolation to create a Ramberg-Osgood

as a function of temperature, T.

Calculus