August 2nd, 2017, 01:04 PM  #1 
Newbie Joined: Aug 2017 From: birmingham Posts: 4 Thanks: 0  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 (Ïƒ) and direct stress (Ïƒx and Ïƒy) was found to be of the form; Ïƒ= (Ïƒx  Ïƒy)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 (Ïƒy) when the value of the shear stress (Ïƒ) is 25 MNm2, the value of (Ïƒx) is 80 MNm2 and the value of the angle of the plane (Î¸) to the horizontal is 25Â°. 
August 2nd, 2017, 05:23 PM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,878 Thanks: 766 
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 $\displaystyle \sigma_y= \sigma_x \frac{2\sigma}{sin(\theta)}$ 
August 3rd, 2017, 11:08 AM  #3 
Newbie Joined: Aug 2017 From: birmingham Posts: 4 Thanks: 0 
thnx country boy much appreciated, this is how i worked it out but am not sure about the whole thing..

August 5th, 2017, 03:55 AM  #4  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,460 Thanks: 489 Math Focus: Yet to find out.  Quote:
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.  
August 7th, 2017, 09:28 AM  #5 
Newbie Joined: Aug 2017 From: birmingham Posts: 4 Thanks: 0 
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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