Simple-beam model — pipe (D) on two supports, span L, uniform load W, mid-span sag δ.
Computes the allowable simple-beam support span (L) for a horizontal pipe run as the minimum of three independent limits, then reports the governing span.
L₁ = √(160·I·f_max / (D·W))
L₂ = (384·E·I·δ_max / (5·W·10⁵))^¼
L₃ = S·(d+b)·t² / (0.644·W·√(R·t))
L = min(L₁, L₂, L₃)
Units (fixed):
• D, t, b, d, δ_max — mm
• W — N/m · I — cm⁴
• E, S, f_max — N/mm²
• Output L — metres
Only E is set from the pipe material. S, f_max and δ_max are project / temperature-dependent design criteria — adjust them for your material grade and design temperature.
Recommended values
- Deflection limit: Keep mid-span sag ≤ 2.5 mm (MSS SP-69) so lines drain and look level.
- Stress limit: Bending stress ≤ ~½ allowable leaves margin for pressure + occasional loads.
- Drainage slope: For gravity/drain lines add ~1:100 slope — this shortens the practical span.
- Concentrated loads: Support valves, flanges and branch weights directly; do not average them into the span.
Limitations
- Static beam: Uniform simple/continuous-beam screening — no slug, wind, or seismic dynamic loads.
- Not included: Support friction, guide/anchor spacing, and thermal-movement clearances are separate.
About the standards
- MSS SP-69: Pipe Hangers and Supports.