Shear strain

1. Sep 22, 2016

1. The problem statement, all variables and given/known data
for the stress applied at x direction , the tensile strain εx should be = σx / E , right ?
and for the tensile strain εy should be = -vσx / E , am i right ?

2. Relevant equations

3. The attempt at a solution
I think so because in 1.7.1.3 , εy = σy / E - vσx / E ,
and εx = σx / E - vσy / E

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2. Sep 22, 2016

Refer to the bottom part of picture , σx ,
after rearraging , i didnt get what the author get .. my working is :
Eεx = σx - vσy
σx = Eεx + vσy

= E(εx + (V / E)(Eεy )
= E(εx + vεy )

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3. Sep 23, 2016

Staff: Mentor

This is correct.

4. Sep 23, 2016

Staff: Mentor

You did the algebra wrong.

5. Sep 23, 2016

after rearraging , i didnt get what the author get .. my working is :
Eεx = σx - vσy
σx = Eεx + vσy

= E(εx + (V / E)(Eεy )
= E(εx + vεy )

sorry , for the symbol , you said i am wrong , which part is wrong ?

6. Sep 23, 2016

Staff: Mentor

I'm going to let you figure that out. You have 2 linear algebraic equations in two unknowns, $\sigma_x$ and $\sigma_y$. You should have learned how to solve such equations in first year algebra.

If you continue to have trouble with this, please submit the two equations and your working to the Precalculus Mathematics section of the Homework Forums.

Last edited: Sep 23, 2016
7. Sep 23, 2016

Are you sure ? Can you please look at it again ?

8. Sep 23, 2016

Staff: Mentor

Yes, I'm sure that your answer is wrong, and I'm also sure that the book's answer is wrong? In the book answer, the terms in the numerators should have plus signs, not minus signs. Your answer should have a denominator which matches the book's denominator.

9. Sep 23, 2016

do you mean it should be σx = (Eεx + vσy ) / (1-(v^2)[B]) ?[/B]

10. Sep 23, 2016

Staff: Mentor

It's time for you to learn to use LaTex.$$\sigma_x=\frac{E(\epsilon_x+\nu \epsilon_y)}{(1-\nu^2)}$$

11. Sep 23, 2016

do you mean this ?
why there is $$\{(1-\nu^2)}$$ below it ?

12. Sep 23, 2016

Staff: Mentor

C'mon man. You need to learn algebra.
$$E\epsilon_x=\sigma_x-\nu \sigma_y\tag{1}$$
$$E\epsilon_y=\sigma_y-\nu \sigma_x\tag{2}$$
Multiply Eqn. 2 by $\nu$: $$E\nu \epsilon_y=\nu \sigma_y-\nu^2 \sigma_x\tag{3}$$
Add Eqns. 1 and 3 to eliminate $\sigma_y$:$$E(\epsilon_x+\nu \epsilon_2)=(1-\nu^2)\sigma_x\tag{4}$$
Solve Eqn. 4 for $\sigma_x$

13. Sep 23, 2016

why my working is wrong ? I noticed that in your working , you used 2 equations which is $$E\epsilon_x$$ and $$E\epsilon_y$$

14. Sep 23, 2016

Staff: Mentor

Like I said: Put your working in the Precalculus Mathematics Homework forum and let them help you figure out what you did wrong.
Of course you need to use two equations. There are two unknowns: $\sigma_x$ and $\sigma_y$

15. Oct 6, 2016

sorry , just to verify my concept again... is εy = σy / E ?
From another book, the εy is σx / E ..Which is correct ?

16. Oct 6, 2016

Staff: Mentor

check a third book.

17. Oct 6, 2016

It's really hard for me to get a third source . I already searched thru many websites , but i couldnt find this . I could only get simple explaination of poisson ratio, but not the the explaination about when the force is applied in a direction , find the strain in another direction .
Can you explain the concept ?

18. Oct 6, 2016

here it is

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19. Oct 6, 2016