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August 2nd, 2017, 12:04 PM   #1
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shear stress

Hi

Am stuck on a question which i thought i figured the answer for but came back wrong.

The relationship between Shear Stress (σ) and direct stress (σx and σy) was found to be of the form;

σ= (σx - σy)sin e (20)
...........2

the dots so i could move the two directly under the fraction....thats all

Find the value of the direct stress (σy) when the value of the shear stress (σ) is 25 MNm-2, the value of (σx) is 80 MNm-2 and the value of the angle of the plane (θ) to the horizontal is 25°.
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August 2nd, 2017, 04:23 PM   #2
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So you mean $\displaystyle \sigma= \frac{(\sigma_x- \sigma_y)sin e(20)}{2}$? But what does that "sin e(20)" mean? Did you mean $\displaystyle sin(\theta)$?

To solve $\displaystyle \sigma= \frac{(\sigma_x- \sigma_y)sin(\theta)}{2}$ for $\displaystyle \sigma_y$ in terms of the other variable, start by multiplying both sides by 2 and dividing by $\displaystyle sin(\theta)$ to get $\displaystyle \frac{2\sigma}{sin(\theta)}= \sigma_x- \sigma_y$. Add $\displaystyle \sigma_y$ from both sides and subtract $\displaystyle \frac{2\sigma}{\sin(\theta)}$ to finally get $\displaystyle \sigma_y= \sigma_x- \frac{2\sigma}{sin(\theta)}$
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August 3rd, 2017, 10:08 AM   #3
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thnx country boy much appreciated, this is how i worked it out but am not sure about the whole thing..
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August 5th, 2017, 02:55 AM   #4
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Quote:
Originally Posted by spiritz View Post
thnx country boy much appreciated, this is how i worked it out but am not sure about the whole thing..
As Country Boy has already pointed out, what's this "$sin e 2\theta$"? Do you mean $\sin(2\theta e)$? Or $\sin(2 \theta)$? I have never seen the use of $e$ in mechanics questions such as this..

Yes, in plain English, the spelling for the sine function is, Sine. But very rarely (never?) does one write $sine(\theta)$.

Anyway.. If it really is $\sin(2\theta e)$, then your algebra and calculations seem fine to me.
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August 7th, 2017, 08:28 AM   #5
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Thnx joppy, I honestly don't know what it's meant by sine but I'll take my chances with the answer iv giving
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