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# Length of expansion

## Length of expansion

(OP)
A stainless steel Tube of 16.5 M long is at an initial Temp of -170 C which is heated to +38 C. How to calculate the final length of the Tube after expansion.

### RE: Length of expansion

L= DT x coefficient of expansion. Applies if there are no restraints and no friction on supports

coefficient of expansion might change over that temp range, but depends how accurate you want to be. Each type of stainless steel has a different coefficient...

This is high school physics.....

https://www.engineeringtoolbox.com/linear-expansio...

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Length of expansion

(OP)
Thank you Littleinch.
Please advise how to calculate DT for -170 C to +38 C
Is it
i) 38 - (-170) = 208 C. This gives very high expansion of metal.
or
ii) 38 - Room temp ie 38-21 = 17 C.

### RE: Length of expansion

The delta T is in fact 208C.
The detail here is that the CTE is not linear over this range.
The CTE will decrease as the temp drops, but as some point it starts going back up.
I would just use 17.5 over the whole range.
That gives us 60mm of length change.
This is what I would expect.

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P.E. Metallurgy, Plymouth Tube

### RE: Length of expansion

(OP)
Thanks again.

1) If I use DT = 208 C the expansion is 16500 x 15.48X10^-6 x 208 = 53.12 mm
2) If I use DT = 17 C, the expansion is 16500 x 15.48x10^-6 x 17 = 4.32 mm

The mean coefficient of expansion is between room temp and the final heated temperature above room temperature.
That is , the metal expands above room temperature, (it does not start expanding from -170 C, it starts from room temperature and then expands above). Hence (1) does not appear to be realistic.

### RE: Length of expansion

The difference in size between -170C and +38C will be in the range of 50-60mm.
If you install this at RT, then it will get 5 mm longer at 38C, and it will be 50-55mm shorter when it cools to -170C.

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P.E. Metallurgy, Plymouth Tube

### RE: Length of expansion

(OP)
Thank you EdStainless.

The question is, does the metal expand when it is heated from -170 C to Room temperature and contract when it is cooled from Room temperature to -170 C.

Fundamentally, I presume that the metal expands on heating from room temperature to +38 C and contracts back, when cooled from +38 C to Room temperature and lies stable even if it is further cooled below room temperature to -170 C and even less. The metal may become brittle below room temperature (especially if Carbon Steel) but it will not contract in size.

Am I fundamentally wrong.
Kindly clarify.

### RE: Length of expansion

You are wrong. As it cools it will contract, as it heats it will expand. Always.
It does not matter what temp you start and end with or how many time you do it.
People use austenitic stainless such as 304L for cryo service because ti does not have a DBT.
It does get stronger and less ductile as it cools, but it is usable down to any temperature if you can live with the thermal expansion issues.

In situations where you have large dimension changes like yours you must build the system flexible enough to allow the movement. This is either by building in expansion (contraction) features or simply allowing distortion. IF the system is built tight and rigid the stresses will become great enough to break things.

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P.E. Metallurgy, Plymouth Tube

### RE: Length of expansion

see: http://lss.fnal.gov/archive/2013/conf/fermilab-con... As you can see from figure 4 in the paper, steel continues to contract down to 50 kelvins.

or https://indico.cern.ch/event/90787/sessions/113900... slide 8 shows SS304 CTE asymptote at around 50 kelvins

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

### RE: Length of expansion

(OP)
Thank you EdStainless and IRstuff.

I am still not clear of Metals contracting from original length, if cooled below room temperature. To my understanding, the expansion or contraction of metals takes place from Room temperature and above and back to room temperature and cooling below room temperature does not affect the length to shrink.

If you see TEMA Table D11 and ASME Sec II-D Table TE-1, The coefficients of Thermal Expansions of various metals are given from 20 C to the temperature. What does it mean.

### RE: Length of expansion

So explain the physics of expansion or contraction stopping at an arbitrary temperature.

### RE: Length of expansion

DK44, you are wrong.
The CTE is quoted for various ranges because it is not linear. You can't use a CTE that applies to RT-200C to figure out the size at 500C. You need the CTE for the temperature range of interest. In NIST publications these are usually given as third or forth order equations.
A slight correction to what IR posted. The chart shows that the CTE becomes constant below 50K, not that expansion (contraction) stops. The "Y" isn't the size but the CTE.

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P.E. Metallurgy, Plymouth Tube

### RE: Length of expansion

The charts have Y with units of delta L divided by L, no temperature, so it's not a CTE, since CTE is delta L divided by L divided by delta T. It's total expansion or contraction from the starting point; since it flattens out, it does mean CTE approaches zero; which makes sense, since it's not energetically possible to get expansion or contraction close to absolute zero.

@DK44 I agree with EdStainless that CTE is a continuous process, but varies with temperature, because things change over temperature. Did you even look at the articles? Your statement is directly contradicted by published authors, in addition to NIST: https://ws680.nist.gov/publication/get_pdf.cfm?pub... In particular, look at the second to last table in the paper. While it does not show steel in that table, other materials' CTEs approach zero as temperature approaches absolute zero. Note silicon's CTE goes to 4.8E-16/K at 0.1 kelvin and copper CTE is 2.28E-9 at 4 kelvin.

See also page 66 of: https://apps.dtic.mil/dtic/tr/fulltext/u2/438718.p... reproduced below. Note the y-axis title, and the temperature is about 30 F about absolute zero for the end of the curve.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

### RE: Length of expansion

(OP)
Thanks for the elaboration.
Not withstanding what is said,
1. Why ASME Sec II-D and TEMA do not list Coeff. of expansion (linear) at various temperatures below 20 C / 70 F.
2. Does low temperature linear contraction of Steel sections(contraction below room temperature) occur in buildings / structures / Rail rods etc. They are understood to become brittle as per the metallurgical properties but not contract in Length when cooled below room temperature. This is not to contradict contraction occurring on cooling from higher temperatures back to room temperature. I could not find explicit explanation on this specific phenomenon at the internet.

### RE: Length of expansion

DK 44 - If you look at the above graph, the coefficient is the angle of the line. This doesn't really change until about -200F. Not many applications require operation at that temperature so most sources won't bother mentioning it.

1) Does low temperature contraction occur - Yes it does. Basic laws of physics.

2) Now in reality what probably happens is that as the item cools, it is constrained from actually contracting and hence starts to increase axial stress and become very "tight". Until the end fixing comes away from the wall you may never notice it, but it is still happening.

Try searching for "cryogenic contraction of steel"...

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: Length of expansion

(OP)
Thank you LitteleInch for the reference.
Given L(293K) = L(20C) = 16.5m for SS 316L
To calculate the contraction, L(311K) - L(103K) = L(38C)-L(-170C),
can you provide Coefficient of Linear expansion of SS 316 L at 103 K ie. at -170 C.

### RE: Length of expansion

Use some of the references listed already.
Or search for the NIST publications that list the equations.
Or look for design guides for using liquid Ar, N2, or O2.

Like this: https://www.researchgate.net/publication/232380004...

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P.E. Metallurgy, Plymouth Tube

### RE: Length of expansion

(OP)
Thank you EdStainless.
1. Could not understand why Pressure Vessel Codes / Material Standards do not provide Coefficient of Thermal Expansion values below 20 C.
2. Can you help for the requested value at -170 C.

### RE: Length of expansion

(OP)
I could not get to the link mentioned by you.

### RE: Length of expansion

Is there some reason your Google isn't working? There are numerous references on the web for cryogenic properties of materials, including this: http://jamme.acmsse.h2.pl/papers_amme03/1240.pdf and the references I listed earlier. The curve I attached in my previous reply covers -170C for SS304, and the reference from which it came includes an actual table of numerical values, but you could just as easily grab numbers off the graph using something like https://automeris.io/WebPlotDigitizer/

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
FAQ731-376: Eng-Tips.com Forum Policies forum1529: Translation Assistance for Engineers Entire Forum list http://www.eng-tips.com/forumlist.cfm

### RE: Length of expansion

The Code does not contain the low temperature data because it isn't the primary focus of the design rules.
If you don't own a reference book with this data then you need to either acquire the correct resources or hire someone who knows how to handle these designs.

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P.E. Metallurgy, Plymouth Tube

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