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# ASME B 31.4 Thermal Stress in Unrestrained Pipelines

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 dasumit (Mechanical) 16 Apr 12 4:16
 Hi, I have a doubt regarding the clause Clause 402.5.2 of ASME B 31.4 2009 edition . Directly quoting the clause, " The stress range resulting from "thermal expansion" in pipe, fittings, and components in "unrestrained pipeline" is calculated as follows, using the modulus of elasticity at the installed temperature: Se =(Sb^2+4St^2)^0.5Se being the thermal stress due to expansion."Can someone kindly clarify these two doubts1)How thermal stress can develop in an unrestrained  pipe, as there will not be any resistance to thermal  movement? 2)What are the reasons for development of bending(Sb) and torsional moment(St)?I cannot be sure, but I think this clause related to thermal stress in unrestrained pipelines was not there in earlier editions of ASME B 31.4Thanks Sumit
 ione (Mechanical) 16 Apr 12 4:34
 Maybe you're thinking just about an unrestrained straight piece of pipe, and so the statement left you puzzled, but this is kind of unrealistic in a pipeline.
 BigInch (Petroleum) 16 Apr 12 6:35
 Realisticly speaking all "unrestrained" pipes are restrained to some extent at certain points along the longitudinal direction, which tend to develop axial stresses.  I think that you (reasonably) are only considering those stresses due to axial direction restraints.  Now consider lack of restraint.  The pipelines that the code refers to as unrestrained means unrestrained primarily in the directions perpendicular  to the pipe axis.  Restrained (underground) pipelines owe their "restrained" classification to the earth keeping the pipeline from moving in any radial direction as well as in the longitudinal direction.   Underground pipelines are restrained in all directions, hence they only (or primarily) develop axial compressive, or axial tension stresses.  All possibility of bending stress is eliminated, because the pipeline physically cannot bend. No curvature = no bending = no bending strains = no bending stress. Above ground pipelines are a different story.  They may be partially restrained in the axial directions, or may not, the important point being is that, regardless of end restraint conditions, they are free to move and displace in the radial directions, hence points along the pipe axis can become offset from one another.  Offsets, considering as a fixed end beam,  produce fixed end moments of 3EI/L.  Now you have bending stress, Sb.  With bending possible in two distinct planes at any point of direction change, out-of-plane bending in one member produces torsion in the other.  Hence the code requires that you evaluate the combined bending and torsional stresses those with the formula you have shown above.    What would you be doing, if you knew that you could not fail?
 dasumit (Mechanical) 18 Apr 12 0:14
 Thanks BigInch for being as helpful as ever. Sumit

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