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# B31.1 102.4.5 Required Wall Thickness

## B31.1 102.4.5 Required Wall Thickness

(OP)
Hi all.
My company makes liquid level gages for boiler trim applications.  I am working on pipe bends that join two gage sections together.  Our current product (designed WAY before my time)has the radius of the bend at 1 5/8" (NPS 3/4 Sch. 160 SA-106 Gr. B pipe)which, according to our testing, results in a wall thickness below 12.5% under nominal thickness.  It was just recently that I noticed the Addenda to B31.1 which includes an alternate way of calculating the minimum wall thickness (Equations 3B-3D of B31.1 102.4.5).  What I am trying to do is work backwards from the equations.  For the value of "tm" I am inserting the minimum allowable wall thickness (12.5% under nominal wall thickness), solving for "I".  I then insert that value of "I" into Equation 3D or 3E and attmept to solve for "R", hence giving me the radius that would be acceptable with our material, OD and ID.  However, the value I obtain for "R" comes out negative for the extrados.  This does not make any sense to me.
According to our testing, the smallest radius we can bend and maintain a wall thickness greater than 12.5% under nominal is 2 3/8" with 3/4 Sch. 160 SA-106 Gr. B steel.  However, the old design, as I said is at a 1 5/8" radius with no problems reported from the field (given at least a 40 year history).
Can anyone comment on what I am seeing here?  Am I using the equations incorrectly?  Is there anything in Code that would explain why the 1 5/8" radius is ok?  I have some test parts on order so that I can measure the wall thickness at the bend.  I will then attempt to do a hoop strength calculation and see what I am getting for a safety factor with that wall thickness.

Any comments or suggestions are most appreciated.
Replies continue below

### RE: B31.1 102.4.5 Required Wall Thickness

You don't state your basis for P you are using in your procedure so it it hard to comment on specifics of what you are doing.  If P is the maximum allowable pressure for the nominal pipe less the 12.5% mill tolerance, it won't work.  This is because the thickness of the intrados always is required to be thicker than the required thickness of straight pipe, per these equations.

A couple points.102,4,5 A and B are options.  You do not need to satisfy both.  If you satisfy A, you do not need to use the equations you are citing.

In forming pipe bends, the intrados normally is thickened by the bending process, so that when you check the actual thickness of the bent pipe, you may find that you satisfy the equations in option B.

### RE: B31.1 102.4.5 Required Wall Thickness

(OP)
cb4,
Just to clarify, I am using a working pressure of 1500 psig.  Given this pressure, I have a safety factor greater than 1.00 at the nominal wall thickness minus 12.5%, so I have plenty of wall thickness to start with.  What I want to determine is my tightest bend radius that I can make with the given material.  Since I know what my minimum thickness is for a straight pipe(nominal-12.5%, I can insert that in equation A and solve for "I", given that I know my pressure=1500 psig, Do=1.050", SE=17100 psi, y=0.4.  After that, I insert the value of "I" obtained in equation A into either equation C or D and solve for "R".  When I try to solve for "R" in equation D, the extrados, the value I get is negative.  Shouldn't I be able to work the equations like that?

### RE: B31.1 102.4.5 Required Wall Thickness

It is perhaps difficult to explain, but it won't work for you doing it that way because you have so much excess thickness.  That is why you have gone to a negative radius.  Consider it being that you are out of bounds.

I suggest you approach it another way, which may be more iterative.  Calculate the required tm for the intrados, based on various radius of bend curvatures, and see that is is less than the available thickness (so you are OK).  It make more sense to you after you run the calcs that way and see what the results are.

### RE: B31.1 102.4.5 Required Wall Thickness

(OP)
I will most certainly try it that way, cb4, thanks for your input.  I'll post an update as soon as I can so that maybe others may benefit as well.
Thanks again.

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