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

[roflpask]

http://www.upload.ee/image/4760492/DSC_0002.JPG

Homework Statement

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? :)

Homework Equations

The Attempt at a Solution

 

[SteamKing]

Homework Statement

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? :)

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.

 

[roflpask]

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/GI_p 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.

 

[SteamKing]

Thank you for your response. 1,3,4 are yes (2 dunno).

Well, let's start with answering question 2. On what physical property of the shaft does the value of I_p 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 I_p stays constant.

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/GI_p but teacher told me it is wrong, because i have distributed torque.

Let's examine your teacher's comment.

So, dθ / dx = T(x) / [G * I_p], 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?

 

[roflpask]

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

 

[SteamKing]

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

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?

 

[roflpask]

Does this look right now?

 

[SteamKing]

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.

 

[roflpask]

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