Thermal growth of a straight run, the blocked-in anchor force if fully restrained, and a guided-cantilever expansion-loop leg sized (or checked) against the allowable displacement stress range.
e = α·ΔT·10³ (mm/m) · ΔL = e·L
L_leg = √(3·E·D·|ΔL| / S_A)
σ_blocked = E·ε · F = σ·A
S_A = f·(1.25·Sc + 0.25·Sh)
Fixed units (SI):
α ×10⁻⁶/°C · T °C · L m · D, t mm · E, S_A N/mm² · ΔL mm · L_leg m · F kN
Mean-α is a near-ambient screening value. For elevated temperature, enter the total unit expansion from ASME B31.3 Appendix C in the override field. Screening only — confirm with a formal flexibility (stress) analysis.
System checks
- Temperature cases: evaluate the full operating envelope, including startup, shutdown, steam-out, upset, ambient extremes, and differential movement between connected equipment.
- Movement path: confirm anchor-to-anchor length and growth direction. Check guide spacing, support travel, spring movement, gaps, friction, and cold-to-hot clearances.
- Equipment loads: blocked force is a theoretical upper-bound screening value. Verify actual anchor, support, flange, and equipment-nozzle loads with a complete piping model.
- Flexibility analysis: include elbows, branches, reducers, valves, restraints, stress intensification factors, and flexibility factors. A single cantilever leg does not represent the full system stress range.
- Expansion joints: bellows require a manufacturer-qualified design and a defined anchor-and-guide system. Include pressure thrust, spring rate, stability, allowable movements, and installation tolerances.
Recommended values
- Allowable range: S_A = f·(1.25·Sc + 0.25·Sh); use f = 1.0 for ≤ 7 000 cycles.
- Provide flexibility: Absorb growth with loops/offsets/bends — never rigidly anchor a hot line end-to-end.
- Cold spring: Up to 50% is common, but credit it only for reactions/loads, not the stress range.
- Loop legs: Size the offset leg from the guided-cantilever length; add margin for anchor movement.
Limitations
- Screening: Guided-cantilever/simplified check — not a nodal pipe-stress run (CAESAR II) with real supports and SIFs.
- Not included: Sustained + occasional load combination, nozzle allowable loads, and support friction are checked separately.
About the standards
- ASME B31.3: Process Piping.
- ASME B31J: Stress intensification and flexibility factors for metallic piping components.