Simplified thermal calculations

[numerical1]

Hello everybody,
I have a steel buried pressurized pipeline with two induction bends (L-shape)and (Z-shape). I need to run a quick calculation to check the stresses induced by temperature differences. I am following Peng's old approach ( paper is attached). According to Peng, we have to calculate 2 things, total DELTA (the thermal expansion or deformation) and the Length over which this deformation should be applied (L in Peng's paper). (DELTA is basically the expansion rate multiplied by a certain length). I have 2 questions:

1- what is the length over which DELTA should be calculated
2- is that the same span of the pipe for which bending moment induced by DELTA needs to be calculated

I am guessing the following:
-For L-shape bend, I am assuming that this is the virtual anchor length (starting from the elbow point where largest movemnet is expected until the point of virtual anchor (in the order of few hundreds feet) which need to be calculated based on soil friction

-For Z-shape bend (which is basically acts like an expansion loop), I am assuming that the DELTA should be calculated over virtual anchor length . The resultant deformation should be applied to the Transsverse length of the bend (leg of the expansion loop) which is only feet in this case.

Thanks alot for your discussion and ideas.

 

[LittleInch]

1) Paper isn't attached
2) The effect of soil friction and resistance to movement of the bend is important, but difficult to assess in a hand calculation.
3) What design code are you using, what is bend radius and what size of pipe.

You are correct in terms of the length, but this should be be simulated in a stress program.

What sort of temperature changes are you talking about from initial installation temp to operating? Generally from circa 20C to circa 60C you don't have a real issue, but higher than 70 you usually do.

The "quick" calculation you can do is the combined stress calculation in B31.4/8 for restrained pipe. That will tell you if you an issue or not.

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