Diameter changes in a horizontal cylinder 1

[Metalguy]

I am trying to find the equation for the amount of weight-sag in a large round carbon-steel horizontal cylinder. If a cyl. is round when its axis is vertical, the diameters will change when the axis is horizontal and the bottom of the cyl. is on the floor (cyl. will become shorter vertically and wider horiz.). In my specific case we are making cylinders that are 4675 mm in diameter (OD), from 32 mm thick plates.

I don't think the length of them is a factor-just the wall thickness, dia. and E.

 

[JoeTank]

Roark has this as a standard load case... a ring loaded by self weight. Make sure you review your support condition, as you may have to patch several load cases together by superposition.

Steve Braune
Tank Industry Consultants

http://www.tankindustry.com

 

[Metalguy]

OK, but I don't have a copy of Roark (not being a mech. eng.<g>).

Do you have the equation?

 

[desertfox]

Hi Metalguy

From Roarks these are the formula you need:-

Dh = w*R^4 * (2-(3.142/2)*k3)
-----
E*I

Dv = -w*R^4 * ((3.142)^2/4)*k1-2)
-----
E*I



k1= 1+ alfa + beta
k3= 1+ alfa - beta


alfa= I/(A*R^2)

beta= F*E*I/(G*A*R^2)


where Dh & Dv are changes in horizontal and vertical Dia re
spectively

w= distributed load per inch

I = area moment of inertia of ring cross section

E= material modulus of elasticity

G = shear modulus of elasticity

A= cross sectional area

R= radius to centriod of cross section

F= shape factor = 10/9 for a thin walled hollow circular section

hope this helps

regards desertfox

 

[Metalguy]

Thanks, but this is way too much math for me.

 

[desertfox]

Hi Metalguy

If you post the length of the cylinders I can work the weight out and do the numbers for you.


regards desertfox

 

[JoeTank]

Metalguy, sorry, I just assumed it was available to you.

Desertfox, don't you think the support condition of the cylinder would matter here?

Steve Braune
Tank Industry Consultants

http://www.tankindustry.com

 

[Metalguy]

Guys,

The cylinder is pretty long, about 9,000 mm. But I *think* the length shouldn't make any difference.

For simplicity we can assume the bottom is sitting right on the floor. In actuality it sits on rollers spaced about 2,000 mm apart.

 

[desertfox]

Hi Metalguy,Stevebraune

Thanks for the response.
I assumed that the cylinder was sitting on the floor as the original post stated and therefore I took the formula from that case load.

regards desertfox

 

[desertfox]

Hi Metalguy

According to those formula I have calculated the change in diameter in the vertical and horizontal respectively as follows:- vertically dia reduction = 0.01309869712mm
horizontal dia increase = 0.004662715051mm

hope this helps,

ps if you can measure one in practice which might prove difficult I would be interested to know.

regards desertfox

 

[Metalguy]

We have attempted to measure the differences by measuring in both directions and then rotating the cyl. 90 deg. and remeasuring. We seem to get about a 10 mm change-on the 2,000 mm roller spacing, which I think would be a bit less than the worst case of it sitting right on the bottom.

 

[desertfox]

Hi Metalguy

Thanks for your response and my apologies because I made
two errors during number crunching.
I think I have found and eliminated those errors and have put the formula's in a spreadsheet.
My new figures are as follows and are quite close to your measurements they are as follows:-

decrease in vertical dia = -9.05mm

increase in horizontal dia = 8.65mm

regards desertfox

 

[Metalguy]

Wow, that's real close! Am I correct in thinking that the only inputs required would be the dia., wall thickness, density and E--at least for a simple cyl. shape supported at the very bottom?

Here's another star for you-if I am able to give 2.

 

[desertfox]

Hi Metalguy

Your almost correct you also need the area moment of inertia
for the cross section and the weight per unit length so the overall length in this case was not important.
However the main things that can change are loadings and support which would alter which case study in &quot;Roarks&quot; you
would use, to calculate deflection values.

regards desertfox

 

[prex]

metalguy
I get quite different results from those of desertfox.
Those results may be obtained with forms available on the site below under Pipes -> Long.line loads -> 'Self weight' and '2 radial loads'.
In my opinion this calculation should be conducted as follows:
1)take the case of self weight with pipe sitting on its bottom line. The result is shown in the form (till someone changes the data) and is:
-reduction of vertical diameter with respect to nominal: 58 mm
-increase of horizontal diameter: 53 mm
2)now take the case of two radial loads (the rollers should apply radial loads) placed at distance 2000 and again support on bottom line. The result is (see the form):
-increase of vertical diameter: 21 mm
-reduction of horizontal diameter: 15 mm
3)by superposition one gets:
-reduction of vertical diameter with respect to nominal: 58-21=37 mm
-increase of horizontal diameter: 53-15=38 mm
As you see the effect of the support spacing is quite significant.
Would you be so kind to check the inputs and share a little more measured data, so that we all can understand where we are wrong?

prex

http://www.xcalcs.com

Online tools for structural design

See

http://www.xcalcs.com/docs/symbolinfo.htm

if you want to use symbols on these fora

 

[Metalguy]

I'm not sure what you mean in No.2. The cylinder does rest on 2 sets of rollers (4 rollers total), and the bottom doesn't touch anything. I didn't think there would be much difference between the roller support vs. just resting on the bottom--that's why I said just keep it simple. Guess I was wrong.

I don't know if I'll get another chance to measure it. Right now it is full of a bunch of 12-leg &quot;spiders&quot; in order to keep it round-it's &quot;lumpy&quot; without them. Fortunatel it isn't a pressure-retaining item-it serves as a thermal shield, but also supports a series of &quot;eggcrates&quot;-for tubing support.

 

[prex]

One more thought, metalguy.
At first I didn't realize that of course you are sitting on two sets of rollers (2 point support for your cylinder).
Now this condition is quite far from what is assumed by Roark's formulae, and would lead in my opinion to the following qualitative results:
1)if the rollers were close to tube ends, then those tube ends would display a distortion much larger than what is represented by the formulae (I guess at least the double)
2)if the rollers are, as normal, at some 1/3 and 2/3 of the length, then the pipe sections over the supports would distort still more (50% more?), but the tube ends would distort much less, and this could explain your measurements, if you took them at the ends.
Anyway there are no simple formulae to represent such a situation with localized supports, and to even guess a close approach to the result: only a FEM model (quite simple by the way) could help.

prex

http://www.xcalcs.com

Online tools for structural design

See

http://www.xcalcs.com/docs/symbolinfo.htm

if you want to use symbols on these fora