Pressure calculation 1

[vinsce]

Hello all of you !

I need someone to confirm my opinion.
I have a strap of 10 mm thickness and 100 mm width that tightens an element. I know the tension force in the strap (T=30kN)and I want to know the pressure P resulting at the center of the element tightened.

You can see the problem in the attached file.

Thanks for your answer...

 

[rb1957]

if the strap tightens around the "element", can you reverse the hoop stress calc ...

strap stress = T/(wt) = pR/t ... p = T/(WR) ?

 

[Cockroach]

Thin wall pressure vessel theory is only an approximation to the true state of a wall element. I would like to point out that in your situation, an external load is going to be of great influence on wall stresses, of which thin wall pressure vessel theory ignores.

I would suggest the Von Mises-Hencky Theory were shear is rotated out of the model by Mohr's Sphere thus resulting in principle stresses. This can be directly compared to material yield, resulting in a computation on Factor of Safety. The mathematics can be a bit much for regular engineers, who are poor mathematicians at best, but the solution is quite elegant.

Therefore I will append the first of two papers discussing the subject.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[Cockroach]

The second paper as attached, explores the assertion that the boundary value load inputs are of great influence to the pressure vessel tri-axial wall element stress. In other words, one cannot assume that the radial, hoop and longitudinal stress induced from internal loading alone, contribute to wall element stress. The vessel can be considered to be semi-rigid, it is not free to react as if unrestricted. The point here is to mathematically quantify how bad thin wall pressure vessel really is.

You have a restriction in hoop stress were the assumption is that longitudinal stress as the result of end cap reactions to pressure, and radial stress let the pressure vessel respond unrestricted. The hoop stress would introduce a variable term of stress into the equations that would need to be manipulated and isolated very similar to the case I have used for longitudinal boundary conditioning, case 2, page 3. The approach is exactly the same but using hoop stress terms instead of longitudinal.

Unfortunately I only did influence to torque and longitudinal stress restrictions. It is the method for analysis that is of interest to you, not necessarily the closed form solution set.

But this situation is very interesting, none-the-less.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[vinsce]

Thanks a lot cockroach !!

Very interesting documents. Nevertheless I did not succeed to find a real answer to my problem. I didn't give enough information in my first post. I explain my situation again.
I have a stap that tightens a cylinder and a plastic element at the top. The axial load of the stapr is 30kN. It tightens the plastic element over all its surface. I want to calculate the pressure on the plastic material resulting from this tightening force... Is it only a matter of force projection ??
I'm only a trainer in a little French company...
You can see the problem in the attached document.


Thanks a lot for your availability...

 

[vinsce]

Thanks rb1957,

I just want to know what do you call "W" and from where comes your formule... ?

Thanks a lot

 

[Cockroach]

Vinsce,
Your file cannot be opened on my end, "png" is unrecognizable. Can you "pdf" it?

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[zekeman]

If you assume uniform pressure on the plastic, then

integration(wprcos@d@)limits -.5 phi to =.5phi.yields the vertical component of force, viz
2wprsin(phi/2)=2Tsin phi/2. Since the sin terms drop out, we have

T=wpr

which could also be done over an infintesimal arc,d@


wprd@=Td@

T=wpr

w=width strap
phi wrap angle

 

[vinsce]

Thanks both of you!

cockroach, I attach the pdf file to enable you to open the file and see the picture of my problem. If you have any suggestion, I wait for it...

Thanks again !!

Vinsce.

 

[vinsce]

Thanks zeckman for your reply.

Unfortunately, in my case the pressure can't be uniform on the plastic. So if you can tell me how to consider it, it will be great...

Thanks a lot

 

[zekeman]

Then, can you assume the tension in the strap over the arc is constant?

If so, then the solution I propose is eminently correct, since it derives from force equilibrium over an infinitesimal arc, and coincidently is the same solution as a thin walled cylinder.
Moreover, if you don't allow a constant tension, then the solution is still correct for local values of T.

 

[vinsce]

Ok !! Good advice.

I can't apply my tension constantly, I must divide it in ten components since it's important to have a strong effort at the center of the plastic element. The strap is applied on 10 surfaces whose the tangents change of value and the projection angle too. So I don't know by what surface I must divide my tension effort to obtain the consistent pressure on each surface...

I attach a more explicit file to show you the problem.

Thanks !

 

[rb1957]

personally, i don't like your "N" reaction ... i think there is a much more distributed reaction between the plastic piece and the strap.

how is the tension in the strap going to change ? friction ?? you can look at you tangent faces and see if they are a reasonable approximation for an arc.

 

[vinsce]

There is no friction since the stap has a polyethylen film that avoid friction... I only know there are 30kN axial tension in the strap and I want to apply a normal pressure (due to the normal effort N projected from the axial tension T of the strap)on the plastic...

The arc has a 110mm radius...

Have you any suggestion concerning the non constant pressure applied ??

Thanks

 

[rb1957]

draw a free body of the strap ... the tension in the strap is reacted by a radial pressure (as we've posted above).

maybe have the strap apply a radial load to the plastic piece at each facette intersection, ie the resultant of the strap tension on either side of the "kink". and this is reacted by a pressure on the plastic piece. it doesn't have to be uniform, but it does have to be equivalent to the strap force.

clear as mud ?

 

[vinsce]

ok I understand what you mean.

Now my final question is : I apply 10 equivalent radial efforts on the plastic piece resulting from the strap effort. If I want to convert this radial effort to a pressure, do you think I have to divide the radial force by the total plastic surface or by only 1/10 of this total surface (1/10 since I have 10 equivalent efforts on 1/10 of the total surface).

Thanks guy,

It's my ultimate question !!!

 

[rb1957]

how much area do you think reacts each load ?
(10 loads ... 1/10th of the toatl area each sounds reasonable)

does the pressure need to be constant ??
(no, there could be some variation, but the distributions need to be symmetric)

 

[zekeman]

"ok I understand what you mean.

Now my final question is : I apply 10 equivalent radial efforts on the plastic piece resulting from the strap effort. If I want to convert this radial effort to a pressure, do you think I have to divide the radial force by the total plastic surface or by only 1/10 of this total surface (1/10 since I have 10 equivalent efforts on 1/10 of the total surface)."

Frankly, I think you are making a mountain out of a mole hill.
Now since you further simplified the problem by proposing zero friction,the tensile force in the strap along the arc is constant, so it is clear that in any of your slices the general form of the solution still stands

pwr=T
P=T/wr

where w is now the width of the slice and T is the force in the elemental 'strap".
The remaining issue is if there is a gradient of strap tension in the depth direction which would allow different elemental T values at the different slices.

Do you really think that gradient is significant?