Pipe Stress Screening & Approximate Flexibility Calculator
Screen a line against the ASME B31.3 three-category diagram, then run the guided-cantilever sustained and expansion stress check with utilisation against Sh and Sa.
When to use this calculator
Use early, to decide how much stress engineering a line actually needs, and then to do the approximate check when that is what the category calls for. The page runs two stages. The screening stage is rules-based: it takes the line size, design temperature, material, and a set of condition flags, and places the line in Category A, B, or C against the Figure 9.3-1 diagram, listing every rule that triggered. The approximate flexibility stage then computes real sustained and thermal expansion stresses by the guided-cantilever method and reports each as a utilisation of its allowable.
Required inputs
- Screening — line number, service, NPS, design temperature, material
- Screening — condition flags such as PRV/PSV inlet or outlet, thermal cycles above 7 000, wall thickness ratio outside limits, plus any accepted no-formal-analysis basis
- Flexibility — OD, wall thickness, E, expansion coefficient α, densities and insulation weight
- Flexibility — design pressure and temperature, installation temperature, run length, flexible leg length, support span
- Flexibility — stress intensification factor i, and the allowables Sh and Sa
Expected outputs
- Screening category CAT1, CAT2, or CAT3 with the rules that triggered it
- Whether the line goes on the critical line list
- Sustained stress and its utilisation of Sh
- Expansion stress, thermal growth, anchor reaction, and utilisation of Sa
- Required flexible leg length for Sa, and an overall OK / Review / NG verdict
Formula overview
OD, t, and lengths in mm (run and span entered in m), E and stresses in MPa, α in mm/mm/°C, temperatures in °C, w in N/m, I in mm⁴, Z in mm³, F in N and M in N·mm.
Stage 1 — screening, ASME B31.3 para 319.4.1 / Figure 9.3-1:
CAT1 Category A — comprehensive analysis required
CAT2 Category B — approximate method required
CAT3 Category C — no formal analysis required
Stage 2 — approximate flexibility:
sustained
S_sus = P·OD/(4t) + max(0.75i, 1)·(w·L_span²/c)/Z
c = 8 for a simple span, 10 for a continuous one
thermal expansion, guided cantilever
δ = α · L_run · ΔT
M = 6·E·I·δ / L_flex² F = 12·E·I·δ / L_flex³
S_exp = i · M / Z
L_req = √( 3·i·E·OD·δ / Sa )
verdict: NG above 100% utilisation, Review above 75%, else OK —
and any occasional trigger escalates to comprehensive analysis.Worked example
6" Sch 40 carbon steel, water filled, 16 barg at 250 °C, installed
at 21 °C. OD = 168.3, t = 7.11 mm, E = 200 000 MPa, α = 1.2×10⁻⁵,
L_run = 20 m, L_flex = 9 m, support span 6 m, i = 1.0,
Sh = 100 MPa, Sa = 138 MPa
Section: I = 1.172×10⁷ mm⁴, Z = 139 240 mm³
Weight: w = 277 (pipe) + 183 (water) = 460 N/m
SUSTAINED
S_pressure = 1.6 × 168.3 / (4 × 7.11) = 9.47 MPa
M_weight = 460 × 6² × 1000 / 8 = 2.070×10⁶ N·mm
S_weight = 2.070×10⁶ / 139 240 = 14.87 MPa
S_sus = 24.34 MPa → 24.3% of Sh
EXPANSION
δ = 1.2e−5 × 20 000 × 229 = 54.96 mm
M = 6 × 200 000 × 1.172e7 × 54.96 / 9 000² = 9.54×10⁶ N·mm
F = 12 × 200 000 × 1.172e7 × 54.96 / 9 000³ = 2.12 kN
S_exp = 9.54×10⁶ / 139 240 = 68.5 MPa
→ 49.7% of Sa
L_req = √(3 × 200 000 × 168.3 × 54.96 / 138) = 6.34 m
Governing utilisation 49.7% (expansion) → verdict OK.
The 9 m leg is comfortably above the 6.34 m required; shorten it to
6.34 m and S_exp rises to exactly Sa, at 100%.Common mistakes
- Treating Category C as permission to stop thinking. It means no formal analysis is required, not that the line has no thermal problem — a badly anchored short hot run can still overload a nozzle while screening as Category C.
- Screening on design temperature only. The severity of a thermal case depends on the range between installation and operating metal temperature, and on how many times it cycles, not on the peak alone.
- Using screening output as an analysis result. It sizes the effort, it does not replace it. A Category A line needs a full model, and the utilisations here are indicative figures for triage.
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