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Old Jun 8th 2017, 02:10 PM   #1
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Strength of material

Somebody can help me solve those 2 exercises?please?
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Old Jun 9th 2017, 06:14 AM   #2
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For the first problem I assume you have been provided with a formula for the spring constant of a helical spring - right? It should be expressed in terms of G, s, D and n, where n = number of coils. So first determine the spring constant, then play around with various values for d, D and n that make that formula equal to the spring constant. Once you come up with a possible solution, plug the values of d and D into the equation for shear stress and check that the resulting value is lower than the maximum allowable torsional shear for steel (i.e. using the equation given in the hint).

For the second, start with sum of forces in the horizontal direction = 0, which gives you the value for R_Bx. Then use sum of moments about either the left support or right support = 0; this will give you the vertical reaction force at the other support. Finally sum of forces in the vertical direction = 0 gives the remaining vertical reaction force.
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Old Jun 12th 2017, 01:05 AM   #3
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Hello , Thank you very much for your direct reply,
Unfortunately they haven't give me any formula for the spring constant of a helical spring.What formula should I take?And also could you be a little more analytical? I don't really know anything about strength of material , so it's kinda hard to decode what it is written above.
Thank you very much for your time
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Old Jun 12th 2017, 07:41 AM   #4
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I'm surprised that they haven't given you anything on how to calculate the spring constant. A Google search for "helical spring constant" led me to this:

Helical Springs | Strength of Materials Review

It includes this for calculating the spring constant:

$\displaystyle k = \frac {Gd^4}{8 D^3 N}$

where N = number of turns of the coil.
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Old Jun 12th 2017, 09:14 AM   #5
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..continue

Thanks again for replying
I also found this formula in the internet , but i am not sure if what i ve done is right.
I start with the assumption that Ks=τmax and i calculate the d=diameter
and D=radius and then i found a formula of spring constant k (like your suggestion) but first i use k=P/l (l=elongation) and i found k and then i use the other formula of k to find the N.
Do you think it is right ?
I have d=diameter= 5.64mm
D=R=radius= 56.4mm
N=number of coils =7 (it was 7.13 and i round it at 7 ...should i round it at 8?)
And do i need to find anything else?
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Old Jun 12th 2017, 09:44 AM   #6
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Correction!!!

As i was solving it again , i realize that i use a wrong formula( i put 8 instead of 64) .
The first attempt to solve this i didn't use the k (spring constant) and i found a result N=0.89
The second time , i did this mistake , and now that i solve it again (as you can see in the picture above ) with the correct formula , i find that N=0.89

I am thinking that it make sense not giving me the formula of spring constant , as i can solve it without it .
BUT
my problem is how is possible N=0.89?? let's assume that N=1 , only one coil ? :/ :/
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Old Jun 12th 2017, 11:12 AM   #7
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(1) Convert all dimensions to proper SI units - meters, newtons, etc.
(2) You are forgetting that one megapascal = 1,000,000 Pa = 1,000,000 N/m^2.

Using your approach you should end up with N around 7. But you would never want to design a spring to have so much stress as to reach failure. You need a margin of safety, so I suggest you start by assuming max stress should be half of its yield stress.
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Old Jun 12th 2017, 11:17 AM   #8
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I use MPa because i transform everything to mm
So i use MPa=N/mm^2

I think that in the last picture , which i have n=0.89 is the right one
Do you think that n=0.89 ~=1 is ok ?
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Old Jun 12th 2017, 11:54 AM   #9
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No, n=0.89 is not OK.

Where did you get the formula for elongation that has the factor of 64D^3 in the numerator? Are you sure that the it's not supposed to be 8D^3, which is 64 R^3?

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Old Jun 12th 2017, 12:17 PM   #10
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Helical Springs | Strength of Materials Review
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