| ProjectSample Project — Demonstration Only | Job No.SAMPLE-001 | Client— |
| CalculationPipe Support Spacing Calculator — Maximum Deflection-Limited Span | Calc byPiping Toolset (calc-core) | Checked byUNCHECKED — sample |
| Date2026-10-12 | Rev0 | BasisDeflection-limited support span (beam form) |
4 in FRP process line, 4.5 in OD × 4.0 in ID structural laminate, long-term flexural modulus 1,000,000 psi. Operating load (pipe + contents) 2 lb/in, owner's sag limit 0.5 in, single simply supported span (c = 5/384).
| Flexural modulus E | 1,000,000 | psi |
| Outside diameter OD | 4.5 | in |
| Inside diameter ID | 4.0 | in |
| Uniform load w | 2 | lb/in |
| Deflection limit δ | 0.5 | in |
| Coefficient c (5/384) | 0.0130208 | — |
Mid-span deflection of a uniformly loaded prismatic beam, solved for length:
δ = c · w · L⁴ / (E · I)
L = ( δ · E · I / (c · w) )1/4
I = π/64 · (OD⁴ − ID⁴)
where δ is the allowable mid-span deflection (owner's spec, commonly 0.5 in), E the flexural or elastic modulus at design temperature, w the uniform load per unit length (pipe + contents + insulation), I the section moment of inertia of the bare pipe wall, and c the end-condition coefficient in the deflection equation — 5/384 for a single simply supported span, roughly 1/185 for the interior spans of a continuous equal-span run. Because L varies as the fourth root, span is insensitive to load and modulus: quadrupling E buys only about 41% more span. Units must be consistent (E psi, OD/ID in, w lb/in, δ in → L in inches).
When you also enter an allowable bending stress S, the matched bending-stress span is computed from the moment coefficient k in M = w·L²/k, giving Z = I/(OD/2) and:
Lstress = ( k · Z · S / w )1/2
k has no default — it must match the same boundary condition c was built on: k=8 pairs with c=5/384 (simple span, M=wL²/8), k=12 pairs with c=1/384 (fixed-fixed, M=wL²/12). ASME B31.1-2024 Table 121.5-1 General Note (c) is the Code precedent for pairing a bending-stress limit with a sag limit on a fixed-beam model (2,300 psi and a 0.1 in sag), though that table's own span values are not used here. The governing span is min(L, Lstress); leaving S blank returns only the deflection span, as the calculator always has.
| I — section moment of inertia | 7.56253 | in⁴ |
| Maximum deflection-limited span | 109.772 | in |
The result values above are locked as fixture support-span.json, case
“FRP 4in, E=1e6 psi, w=2 lb/in, delta=0.5 in, simple span (c=5/384)”, tolerance 0.001, in the calc-core continuous
verification gate (see https://pipingtoolset.com/trust/validation.html). Allowable-stress and factor data are
user-supplied inputs; citations: ASME B31.3, Process Piping — ¶321.1.1, support spacing and design to prevent excessive sag, stress and joint leakage; the Code sets the objective, not a span table. · ASME B31.3, Process Piping — Chapter VII ¶A321, support of nonmetallic piping; spacing follows the manufacturer's published deflection and stress limits. · ASME B31.1-2024, Power Piping — §121 Piping Support, including the suggested support-spacing table for standard-wall steel pipe in water/steam service (values user-supplied, not reproduced here). · ASME B31.1-2024, Table 121.5-1, General Note (c) — the Code precedent for pairing a bending-stress limit (2,300 psi) with a sag limit (0.1 in) on a fixed-beam model; cited here as the basis for the optional bending-stress span, not as a source of span values (this module computes both criteria from your own inputs). · MSS SP-58, Pipe Hangers and Supports — Materials, Design, Manufacture, Selection, Application, and Installation; tabulated maximum spans referenced only, never reproduced. · Elastic beam theory (Roark, Table 8.1, simply supported and continuous uniformly loaded spans) — the source of the end-condition coefficient c and the matched moment coefficient k. · PIP PNC00004 §3.2.11.1 gives a deflection (sag) limit for B31.3 metallic piping spans only — it is not a source for the bending-stress span and is not cited as one.