Wall Thickness on Bend ASME 31.3 para 304.2.1

[GeofI]

According to the calculations related in 304.2.1 the minimum wall thickness on the extrados of the bend can be thinner than the minimum wall thickness required for a straight of the same length (section 304.1.2) , conversely on the introdos the wall is required to be greater than that of the straight for the same design pressure.

Can anyone explain a) why inner wall should be thicker and outer wall can be thinner. Note the calculations are for required thickness not actual thinning that occurs.

Although fairly irrelevant the figures used for the formulas are as below.

Straight minimum wall thickness by Calculation 3a (para 304.1.2)

Bend minimum wall thickness by calculation 3c, using 3d and 3e for intrados and extrados I value.

c = 0
P = 5500 psi
D = 0.75"
S = 16700
E = 1
W = 1
Y = 0.4
R1 = 2.2"

This provides a straight section min wall thickness of 0.1091, Extrados mwt of 0.1079, Intrados MWT 0.126.

How can the required thickness on the outside of the bend require to be less than that for a straight? Conversely opposite is true for inside wall?

 

[BigInch]

Stress concentrations are on the tighter radius, the inner curve, thereby requiring thicker wall there.

Some of the hoop stress is directed into the pipe's axial direction as you go around a curve.

 

[GeofI]

Ok, I see where your going with this.

To confirm I understand; If (imaginary) hoops are at spacing x on a straight as they sweep around the bend the you have >x spacing on the outside and <x spacing on the inside and thus the axial load less per unit (length) outside and greater per unit (length) inside (and at R1 is as per straight) thus requiring less/more material to cope with the axial load outside / inside respectively.

Is that right? Sorry I am electrical engineer by training so trying hard to understand this mechanical magicary!

 

[BigInch]

More or less. Pressure is a radial force against the inside pipe wall. As it goes around a curve, radial forces are countered by forces along the tangents in the axial direction of the pipe. In straight pipe, all radial forces are immediately resisted by only by ring tension, transversely around the pipe (hoop tension).

 

[GeofI]

OK, I think I have it. Certainly enough to be able to satisfy my own curiosity and to explain it to others. I feel a slinky may be useful to explain this to those I have to explain it to!

Thanks for the time explaining this as it seemed completely counter intuitive to me, I did ask some of my Mechanically trained colleages and got no satisfactory answers, but this seems good. I will enlighten them and then move onwards with finding correct sized tubes and fittings!

 

[BigInch]

Well yes I admit it is all a bit of a simplification of a far more complicated process, but in general the tightest bend, most change in angle over the shortest arc length, the shortest bend radius, is always associated with higher stresses. If you can get away with that explanation, so much the better, otherwise you will be forced to dig into these papers, which offer a far better explanation than my measly offering,

https://pure.strath.ac.uk/portal/fi...nding_and_cyclic_thermal_loading_May_2011.pdf

For mitered bends,

https://plasticpipe.org/pdf/mitered-elbow-fea-report.pdf