Eqns to solve: (delta_1)/a = (1/E)[sigma_x - v(sigma_y + sigma_z)], ...

[sadpanda]

Hi,
I've been having some trouble solving equations for my strength of materials class, I am sure the problem is purely mathematical, but I can't see where I'm making a mistake.
I have the following set of equations:

I have to express sigma z using only deltas, a, v and E. I define the following sum:

And I try to make it sensible either by getting sigma z from the upper equation or by putting sigma z there instead of v(sigmaX + sigmaY). But I get to weird results that do not suit the correct answer.
The correct answer is the following, divided by a^2:



I will be very much grateful I somebody can help me out with this, it doesn't seem hard at all. And please let me know if I should say more about my own solution.

PS Sorry for pictures rather than script in the post, let me know if I should change it.

 

[tkhunny]

Hi,
I've been having some trouble solving equations for my strength of materials class, I am sure the problem is purely mathematical, but I can't see where I'm making a mistake.
I have the following set of equations:
View attachment 9620
I have to express sigma z using only deltas, a, v and E. I define the following sum:
View attachment 9621
And I try to make it sensible either by getting sigma z from the upper equation or by putting sigma z there instead of v(sigmaX + sigmaY). But I get to weird results that do not suit the correct answer.
The correct answer is the following, divided by a^2:

View attachment 9622

I will be very much grateful I somebody can help me out with this, it doesn't seem hard at all. And please let me know if I should say more about my own solution.

PS Sorry for pictures rather than script in the post, let me know if I should change it.

Which \(\displaystyle \delta_{1}\) in the first two equations is supposed to be \(\displaystyle \delta_{2}\)?

This looks a little tedious, but from your presentation, its not clear where you are struggling.

One way that might make sense is to treat it like any other system of equations in three variables. Rewrite each equation to look like this:

\(\displaystyle something_{1}\sigma_{x} + something_{2}\sigma_{y} + something_{3}\sigma_{z} = something_{4}\)

Maybe you will see it better from there.

 

[Dr.Peterson]

Hi,
I've been having some trouble solving equations for my strength of materials class, I am sure the problem is purely mathematical, but I can't see where I'm making a mistake.
I have the following set of equations:
View attachment 9620
I have to express sigma z using only deltas, a, v and E. I define the following sum:
View attachment 9621
And I try to make it sensible either by getting sigma z from the upper equation or by putting sigma z there instead of v(sigmaX + sigmaY). But I get to weird results that do not suit the correct answer.
The correct answer is the following, divided by a^2:

View attachment 9622

I will be very much grateful I somebody can help me out with this, it doesn't seem hard at all. And please let me know if I should say more about my own solution.

PS Sorry for pictures rather than script in the post, let me know if I should change it.

It seems that you have started in a good direction.

From here, I would solve View attachment 9621for the sum \(\displaystyle \sigma_x+\sigma_y\), and substitute that for the same quantity in the third given equation. Then you can solve that for \(\displaystyle \sigma_z\).

If this doesn't do what you want, please show details of your work, especially your answer, so we can see if it is really correct!