Info required on how to calculate expansion loops in a steam line on a pipe rack and also determining forces due to pipe expansion on anchor bay etc.

There are back of fag packet methods and spreadsheet calcs to do this, many incorrect and often with no audit trail. The safe way is to use recognised software to do a proper stress and load analysis, such as Caesar II or Autopipe.

steel pipe expands or contracts at 0.000006 x length /?F

Thus, when the axial growth is fully restrained, the axial stress is 0.000006 x E.  If it is not restrained it is zero.

E = Young's modulus

The basic bending forces in an expansion loop are exactly the same as in a plane inverted "U" frame when you pinch the bottom legs together.  That (maximum-safety valve) pinch distance would be the axial growth of any pipe attached to the bottom of the "U", provided that the other ends of those pipes were fully anchored.

Since axial growth "rigidity" is so much more than the rigidity provided by the loop as it flexes in bending, effectively all axial growth of the horizontal pipe at the bottom is permitted by the loop, as the bottom of the loop moves together.  Axial stresses in the horizontal pipe are reduced from say 100 kips to almost zero (but NOT zero), say 1 or 1.5 kips or so, and that resultant load causes bending stresses to be developed, increasing upwards in the vertical pipes and becoming a maximum at the loop elbows.  That bending moment stays at that maximum bending moment level for the entire length of the top horizontal pipe until it gets to the next elbow and starts reducing until it reaches the bottom pipe on the other side of the loop.


As the loop gets higher, both axial resultant stress in the horizontal pipes and the bending moments in the loop are reduced.

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