Pipe Leg — Companion Article
1. What this tool does
Pipe Leg estimates the leg that absorbs thermal expansion, for a straight leg, an L-bend, and a Z-bend. The calculation runs in the browser. It does not call the Engineering API and it does not ship material tables.
2. When to use it
Use it for a first check of a leg length. The result is preliminary. It is not a flexibility analysis.
3. Inputs
- Choose straight leg, L-bend, or Z-bend.
- Enter outside diameter, modulus, and allowable stress. Enter the expansion, or let the page compute Δ = α × run length × temperature difference.
- For an L-bend, enter both runs.
- For a Z-bend, enter the two parallel runs and the offset.
E and Sa use the same stress unit. D and Δ use the same length unit. The page converts the units chosen so the pair stays consistent. If L is wanted in feet while D and Δ are in inches and E and Sa are in psi, the textbook form divides by 144 inside the square root. That factor is a unit conversion, and the page does not apply it twice.
The wall is not an input to the leg formula.
4. How it works
The running tool is the calculation. The straight-leg formula is the same as version 1.0.0:
L = sqrt(3 × E × D × Δ / Sa)
S = 3 × E × D × Δ / L²
The source named on the page is the guided cantilever method, M.W. Kellogg, Design of Piping Systems, and standard piping textbooks. E and Sa are entered by the user. A typical modulus on the page is a near-ambient textbook figure, labelled as not a code value, and it is not adjusted for temperature.
For an L-bend, leg A absorbs the expansion of run B. Leg B absorbs the expansion of run A. The corner elbow is assumed to add no flexibility.
For a Z-bend, the offset absorbs the sum of the absolute expansions of the two parallel runs. Anchors are at the far ends. The elbows add no flexibility. Friction is not included. The offset is the only absorbing leg.
5. Understanding the result
The page reports the minimum leg and, where a length is entered, the stress.
The result is preliminary. It needs engineering review before anyone uses it. It does not change a design.
6. Engineering considerations
E, Sa, α, diameter, lengths, and temperatures are what the user types. A typical modulus on the page is not a code value and is not adjusted for temperature.
The elbows are assumed to add no flexibility. Friction is not included.
The page does not name a code edition. This article does not add one.
7. Example
Basis, entered on the live page on 3 October 2026: NPS 6 Sch 40 carbon steel, outside diameter 168.3 mm, wall 7.11 mm, operating temperature 150°C, install temperature 20°C (temperature difference 130°C), α 12.0×10⁻⁶ /°C, E 203000 MPa, Sa 207 MPa, run 30 m. The wall is not an input to the leg formula. The figures were hand-checked. They were not re-run for this remap.
Straight leg. Expansion 46.8 mm. Minimum leg L = sqrt(3 × E × D × Δ / Sa) = 4813.8 mm.
L-bend, runs 30 m and 10 m. Expansions 46.8 mm and 15.6 mm. Leg B minimum 4813.8 mm. Leg A minimum 2779.25 mm.
Z-bend, parallel runs 15 m and 15 m, offset 5000 mm. The offset absorbs 46.8 mm. Minimum offset 4813.8 mm. Stress at 5000 mm = 3 × E × D × Δ / L² = 191.87 MPa, which is below the entered Sa of 207 MPa.
8. Standards/references (licensed vs interim)
No catalogue facts are read. The method citation is M.W. Kellogg, Design of Piping Systems, and standard piping textbooks, as the page states. This article does not name a code edition. The page does not name one.
This draft does not class that citation as licensed standards data or as interim owner-authorised data. The interim pattern in the owner decisions log is ASME B36.10-2022 Table 2-1. This tool does not use that table. Owner engineering review confirms the source classification before publish.
9. Limitations/disclaimer
- The result is preliminary and needs engineering review. It is not a flexibility analysis.
- The elbows are assumed to add no flexibility. Friction is not included.
- A typical modulus on the page is not a code value and is not adjusted for temperature.
- The page does not ship a material table.
A member check is not an engineering fact. The note is under Repository notes.
10. Use the tool
Calculate now: Pipe Leg
Shortcode: Preliminary. This result needs engineering review before anyone uses it. It is not a flexibility analysis and it does not change a design. L = sqrt(3 × E × D × Δ / Sa) S = 3 × E × D × Δ / L² Guided cantilever method, as given in M.W. Kellogg, Design of Piping Systems, and in standard piping textbooks. L is the leg length perpendicular to the movement. E and Sa use the same stress unit. D and Δ use the same length unit. This page converts the units you choose so the pair stays consistent. If L is wanted in feet while D and Δ are in inches and E and Sa are in psi, the textbook form divides by 144 inside the square root. That factor is a unit conversion, and this page does not apply it twice. When you compute an expansion, Δ = α × Lrun × ΔT. α is per degree, in the same degree as ΔT. Δ is in the same unit as the run length. An L-bend uses the same formula on each leg. Leg A is perpendicular to run B and absorbs the expansion of run B. Leg B is perpendicular to run A and absorbs the expansion of run A. A Z-bend uses the same formula on the offset. The offset absorbs the sum of the absolute expansions of the two parallel runs. Anchors are at the far ends. The elbows add no flexibility. Friction is not included. The offset is the only absorbing leg. Limits: the absorbing member is guided (it translates and does not rotate), the movement is perpendicular to that member, and the member has a constant section. Friction, pressure elongation, torsion, intermediate restraints, and multi-plane routing are not in this estimate. E and Sa are the values you enter. A typical modulus is a near-ambient textbook figure, not a code allowable, and it is not adjusted for temperature. Numbers on the result line are rounded for display with six significant figures. Pipe Leg version 1.1.0 This records your check of the tool output. It does not change the tool or the engineering data. . Version 1.1.0. Re-check this article when the tool version changes.Pipe leg
Formula
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How this calculation works: companion path TBD.
That return link is not on the tool page. This draft does not add it. The public article path is TBD because this file is not published.
The article stays public if the tool is restricted. A visitor with no entitlement sees a lock message on the tool, not a bare “Access denied”. The copy is in the Companion Article standard. This draft does not place that lock on the page and does not mark the tool free, Pro, or Enterprise.
Related tools
Pipe Loop, at /tools-training/pipe-loop/, sizes a symmetrical U-loop from the same guided-cantilever length. It is a different page.