Expansion Loop Sizing

Method: guided cantilever — the most widely used preliminary sizing method for expansion loops. Treats one leg of the loop as a cantilever beam absorbing the thermal displacement ΔL imposed at its free end.

Variables:

• L = required length of the perpendicular leg of the loop
• E = Young’s modulus of pipe material at design temperature
• D_o = outside diameter of the pipe
• ΔL = thermal expansion to absorb (mm or in)
• Sa = allowable displacement stress range per ASME B31.3 §302.3.5

Sa calculation: Sa = f × (1.25 Sc + 0.25 Sh), where Sc and Sh are allowable stresses at cold and hot temperatures. f is a cycle factor (1.0 for < 7000 cycles).

Conservatism: guided cantilever is conservative (over-sizes by 15-25% vs detailed FEA). Good for layout / quick design. For final design, run a stress analysis in Caesar II or equivalent.

Brownfield tip: when adding a loop in a revamp, double-check that the available space accounts for: (1) physical loop dimensions, (2) supporting structure, (3) maintenance access, (4) insulation thickness if applicable. The L value is just the centerline of the pipe.