# Torsion, angle of twist, diameter, load, momentum and find G

1. Jun 4, 2015

http://www.upload.ee/image/4760492/DSC_0002.JPG [Broken] 1. The problem statement, all variables and given/known data
I have given angle of twist, diameter, uniform load, and length of the beam. I need to find the G.The load gives me some trouble and i don't know if i should solve it by using integration or? :)

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 7, 2017
2. Jun 4, 2015

### SteamKing

Staff Emeritus
Why do you need to integrate anything?

1. Is the shaft prismatic along its entire length?

2. Does the polar moment of inertia change w.r.t. the length of the shaft?

3. Are the material properties of the shaft the same along its length?

4. Is the torque distributed evenly w.r.t. the length of the shaft?

If you can answer "Yes" to questions 1-4, integration is not necessary. (BTW, you haven't indicated if this shaft is fixed at one end in your diagram.)

Why wouldn't you check the formula for the angular deflection of this shaft given the known quantities and see if a reasonable value of G is obtained?

Remember, you should always draw a FBD to start your analysis.

3. Jun 4, 2015

Thank you for your response. 1,3,4 are yes (2 dunno). I did a new drawing and wrote all the details i was given. The shaft is fixed at the end. At first i used this formula Θ=TL/GIp but teacher told me it is wrong, because i have distributed torque. After that he asked if i even know how should a stress diagram look like and i drew the same diagram as it is on the first picture.

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4. Jun 4, 2015

### SteamKing

Staff Emeritus
Well, let's start with answering question 2. On what physical property of the shaft does the value of Ip depend? Is it the length? Is it the diameter? Is it something else?

Then ask yourself, does this physical property of the shaft change with length? If it doesn't, then the value of Ip stays constant.

So, dθ / dx = T(x) / [G * Ip], and you want to calculate G. How do you calculate θ given dθ / dx ? Where would the value of θ = 20 mRad be obtained on this shaft?

5. Jun 6, 2015

The value of θ = 20 mRad would be obtained on the right end of the shaft.

6. Jun 6, 2015

### SteamKing

Staff Emeritus
Then, which how do you find θ at the right end of the shaft given that:

dθ / dx = T(x) / [G * Ip]

and θ = 0 at the fixed end?

7. Jun 6, 2015

Does this look right now?

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8. Jun 6, 2015

### SteamKing

Staff Emeritus
You say that T(x) = M x / L, but you only use M x in your integral expression

Also, G has units, which you have neglected to show.

9. Jun 6, 2015

I added L to my formula but the G stays same, which is is 2,5 GPa

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