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Anonymous Poster #1

Angle of Twist and Power to Shaft Questions

10/26/2015 1:06 PM

So I'm having difficulty finding how this teacher of mine arrived at his answers and wondered if anyone could be of some help

In this one problem there's a shaft with a diameter of 6 inches that can turn at a rate of 200 rpms, what is the power it can deliver given that the shaft can't exceed a shear stress of 18E3 ksi

So T=P/W (w being rotations) to find the power and T(shear)= Tc/J

Not sure if I should just leave it at 200 rpms or convert to radians per second but given the variables I'm given I solved for torque by inputting the cutting the diameter into half giving me a radius of 3 inches and dividing that over the moment of polar inertia (J) which is pi/2 (radius)^4 and equaling it out to the shear stress it can't exceed. From there I get my torque and can not plug it in to T=P/W and once I get my value for P (power) I convert that into horsepower, which should be 12 but that's not what I'm getting.

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angle of twist given a shaft with counterclockwise and clockwise torques being 14 kn*m to the left separated by 2 meters from a torque going to the right of 22 kn*m separated by another torque going 19 kn*m with a separation of distance of 3.5 meters and a final toruqe separated a distance of 2.5 meters with a 11 kn*m torque value going to the right. G=26GPA the shaft is hollow with an outer diameter of 80 mm and a wall thickness of 40 mm

formula for angle of twist is TL/JG

I keep getting .13 for that but it should be .181 for an angle of twist

I know this was a mouthful but I have no adequate tutors in my area to help me out with this and everyone in my class is clueless about it so if you guys can help me out somehow I would appreciate it. For the latter problem I'm I don't know how I should designate the distance and the torque and whether - or + values should be placed inversely.U

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#1

Re: Angle of Twist and power to shaft questions

10/26/2015 1:37 PM

If you and everyone else in the class is lost on this problem - just asking - why aren't any of you asking the teacher to explain?

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#2
In reply to #1

Re: Angle of Twist and power to shaft questions

10/26/2015 2:13 PM

sounds like its due tomorrow....

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#4
In reply to #2

Re: Angle of Twist and power to shaft questions

10/26/2015 2:44 PM

It's not, but thanks for the input.

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#5
In reply to #1

Re: Angle of Twist and power to shaft questions

10/26/2015 2:47 PM

I kinda want to avoid the teacher's input for now because he might just make the question more difficult if he sees we've grasped the concept. I know what I'm doing I'm just not sure how he's arrived at the numbers he has. I guess I wasn't clear, I'm not having difficulty with concepts I'm having trouble arriving at the same calculations.

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#3

Re: Angle of Twist and power to shaft questions

10/26/2015 2:37 PM

First problem : make your units coherent (lbs : rads : s : in) then you will easily solve the problem. The equations are straight forward.

Second problem : you might have noticed the trick question: hollow shaft outer diameter 80mm with thickness 40mm ? Looks quite solid to me.
The torques seem to add up to 0 which is nice.
Your bar is 8m long I take it ?
So take one end or the other as the fixed point of your bar and apply the equations to the 3 remaining torques. It shouldn't matter which end you take as your starting point, in fact you can do it both ways so that your result is checked.

Hope this helps

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#6
In reply to #3

Re: Angle of Twist and power to shaft questions

10/26/2015 2:49 PM

I actually don't like that the torques add up to zero because it gives me "0" for an answer and apparently that's not the answer.

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#10
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Re: Angle of Twist and power to shaft questions

10/26/2015 6:32 PM

If the torques didn't add up to 0, then you would have a spinning bar. Hence the reason why it is good that they are 0. You can treat one of them as the reaction torque which has no effect on the twist of the bar as it is at the origin. It is your starting point.

Then apply the 3 other torques at the lengths you have been given. The length of bar from the origin to the applied torque contributes to the twist. Maybe you haven't taken that into account ? Angle of twist = TL/GJ. Obviously the L is different for each torque.

It is simple superposition of the different torques and the twists. Note that for every individual torque applied, it has an effect between the torque and the origin but has no further twist effect after it because it is assumed that plane sections remain plane (not exactly true but it is the simplified assumption in this type of analysis and is true for a circular section due to the radial symmetry).

You could calculate the overall torque on each particular length of bar and do the calc for each section. It gives the same result.

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#7

Re: Angle of Twist and power to shaft questions

10/26/2015 2:56 PM

You know what forget I asked. I wish you could delete posts here.

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#8
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Re: Angle of Twist and power to shaft questions

10/26/2015 3:02 PM

Don't give up. You are almost there. I am at work and don't have the time to work it out, but you seem to be on the right track.

Start the problem again on a white board or new paper, begin with the free body diagram and work from there. Make sure that you have visualized the problem clearly and the answer is just a little algebra away.

Drew K

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#11
In reply to #7

Re: Angle of Twist and power to shaft questions

10/27/2015 6:06 AM

Don't give up just yet! As a start, tell us what you got for the 1st part, power from a 6" shaft. If you got that right I (and maybe others) might try to help with the next question.

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#9

Re: Angle of Twist and power to shaft questions

10/26/2015 3:34 PM

this why your teacher is making the big union bucks. consult them prior to a forum of strangers.

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