Enter material, size, temperatures and anchor spacing. The page computes how much the pipe grows, what would happen with the line restrained, the U-loop size and the axial expansion joint alternative.
Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.
U-loop by guided cantilever; the dashed line is the available height entered.
Logarithmic scale: fully restrained line, axial joint (pressure thrust) and loop.
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ΔL = L × α × ΔT. Carbon steel grows about 0.8 in per 100 ft for every 100 °F; in the example, 200 ft of steel heated from 70 °F to 350 °F grows 4.49 in (2.25 in per 100 ft). Stainless steel and copper expand about 40% more than carbon steel, and aluminum nearly twice as much.
Pipe stress becomes E × α × ΔT, whatever the length: in the example, 55 ksi, 2.8 times the allowable, with a force of about 300,000 lbf on the anchors. In practice the pipe buckles, bends supports, leaks at flanges or tears out anchors. That is why every hot line needs flexibility: elbows, loops or expansion joints.
By the guided cantilever method, the required leg length is L = √(3 × E × D × ΔL ÷ SA), split as 2H + W with H = 2W. In the example, 6" pipe with 4.49 in of growth needs 30 ft: a loop 12.1 ft high by 6 ft wide. The method is conservative; a software flexibility analysis usually gives somewhat smaller loops.
A loop is just pipe and elbows, has no wearing part and barely loads the anchors (about 940 lbf in the example), but it takes space. A bellows joint fits in the straight run, yet pressure pushes the main anchors with the pressure thrust (6,840 lbf at 150 psig in the example), it needs close guides and it must be inspected. Use joints where there is no room for loops.
It depends on the loop size that fits on site. In the example, with loops up to 13 ft high the anchors can be up to 231 ft apart; with 3 in travel expansion joints, up to 134 ft. Between anchors, use guides and sliding supports that let the pipe move axially.
ASME B31.3 defines SA = f × (1.25 Sc + 0.25 Sh), from the cold and hot allowable stresses of the material. For A106 Gr. B steel, 20 ksi is a common conservative value in this method; copper and aluminum are much lower. When in doubt, follow the governing code (ASME B31.1, B31.3 or B31.9).
Whenever the line carries steam or a hazardous fluid, is large, connects to sensitive equipment nozzles (pumps, turbines, vessels) or has a complex layout. This calculator gives a preliminary size: the final design needs a flexibility analysis and anchor design by a licensed engineer.
Important notice: Indus Metrics tools produce estimates and pre-sizing results from the data you enter and from published engineering methods. They do not replace design, calculations or reports signed by a licensed professional engineer (PE), nor verification against the applicable codes, standards and regulations, such as OSHA rules and the ASME codes. Material and fuel properties vary: check manufacturer data or your own process analyses before deciding. By using this site you agree to the Terms of Use.
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