## B31.1 tm calculation - y coefficient

## B31.1 tm calculation - y coefficient

(OP)

Could someone please explain what the y coefficient is there for? It is explained in the code a coefficient having values as given in the table 104.1.2 (A). It seems to be a safety factor as it reduces the calculated value of tm.

## RE: B31.1 tm calculation - y coefficient

Thanks!

Pete

## RE: B31.1 tm calculation - y coefficient

Redivac Vaccum(visitor)You nailed it Pete, "Y" is a factor to compensate for the non-linear reduction in allowable stress at design temperatures above 900 degrees.

Regards, John.

## RE: B31.1 tm calculation - y coefficient

yhas a clear physical meaning.If you take

y=d/(d+D_{o}) as required by B31.3 for thick pipes at low temperatures, you'll find thatSEequalsexactlythe value for the maximum circumferential stress (at inner face) in cylinders under pressure:S=P(D_{o}^{2}+d^{2})/(D_{o}^{2}-d^{2}).For thin pipes

y=0.5, for thick pipesy<0.50.5 is also the value to be used if one wanted to account for the average circumferential stress, not the peak value.

Hence

yis there because it must be there.Now an expert in the foundations of B31.1 should help, but I suppose that the use of 0.4 (e.g.for all non ferrous metals and cast iron) is a safety value to account for thick pipes.

I can't explain the increasing values at higher temperatures: if it is a safety factor, then it decreases the safety with increasing temperature! Would be curious to know the correct answer.

prex

motori@xcalcsREMOVE.com

http://www.xcalcs.com

Online tools for structural design

## RE: B31.1 tm calculation - y coefficient

Redivac Vaccum(visitor)## RE: B31.1 tm calculation - y coefficient

Poisson's ratio appears only in the relationships for deformations.

Also, if at high temperature creep tends to flatten the stress distribution, this would justify taking

y=0.5, not 0.7 as allowed by the code.Can you give some more highlights on why

yis allowed to go over 0.5, so that the resulting average circumferential stress will be slighly higher than the allowable stress?prex

motori@xcalcsREMOVE.com

http://www.xcalcs.com

Online tools for structural design

## RE: B31.1 tm calculation - y coefficient

Redivac Vaccum(visitor)Increasing Y decreases required thickness (which means the calculated stress is lower for the same thickness). Thus, Y increases from 0.4 to a higher value in the creep regime.

If you are worried about why Y can be greater than 0.5, equilibrium is satisfied (more or less) with Y=1.0 (the pressure acts on the inside diameter, not midwall.

## RE: B31.1 tm calculation - y coefficient

Redivac Vaccum(visitor)The radial stress in a cylinder under internal pressure is equal to the internal gauge pressure on the inside surface and is compressive and is zero on the outside surface.

The meridional or axial strain in a cylinder has to be constant through the thickness, or it will cease to be a cylinder (e.g. if there is a bending strain through the thickness, the cylinder walls would have to roll inward or outward).

The radial compressive stress causes a meridional tensile strain due to Poisson's effect. This meridional strain due to radial stress is proportional to internal pressure on the inside of the cylinder and is zero on the outside.

This difference in meridional strain due to radial stress cannot exist, so something else must happen to cancel it out.

The other thing that happens, is the circumferntial stress becomes nonuniform through the thickness.

The circumferential tension due to internal pressure on the inside is larger than the outside. This larger circumferential stress causes a larger meridional compressive strain (inside relative to outside) which offsets the larger tensile strain caused by radial stress (again inside relative to outside).

Thus, Lame exists.

## RE: B31.1 tm calculation - y coefficient

I had missed this thread.

And thanks to Chuck becht & prex.

Once again thank you very much.

Amit