Rack and Process Spans — Companion Article

1. What this tool does

Rack and Process Spans estimates an allowable span from the weight the user builds up and from beam theory. The user enters the outside diameter, wall, corrosion allowance, metal density, modulus, allowable bending stress, contents density, insulation thickness and density, and the end condition. The page reports weight per length, the span limited by bending stress, the span limited by deflection, and the governing span.

2. When to use it

Use it for a designer screening a span on a rack or in a process area. The result is preliminary. It is not a support design.

Pipe Span and Support Span are the chart-based pages. This page does not replace them.

3. Inputs

1. Enter the pipe, the contents, and the insulation. Typical densities and moduli on the page are labelled as not code values and are not preselected.
2. Enter the allowable bending stress. It has no default.
3. Choose the end condition, or a preset. The rack preset is continuous equal spans. The process-area preset is simply supported.
4. The absolute sag field starts at 0.1 in (2.54 mm). The span-fraction field has no default. Changing a unit does not convert the number in the box.

Pressure, wind, seismic, point loads, and stress intensification are excluded. They are not inputs.

4. How it works

The running tool is the calculation. The method already written for version 1.0.0 follows.

Simply supported and fixed-end formulas are the strength-of-materials cases for a uniform load. Continuous equal spans use bending moment wL²/10 and deflection 3.9wL⁴/(384EI). The page cites that approximation from Piping World, Allowable Pipe Support Span Calculation. That article rearranges the deflection with a rounded 98. This page keeps 3.9/384 and does not use the rounded 98. The continuous case is an approximation, not a code formula.

The rack preset uses the continuous coefficients. The process-area preset uses the simply supported coefficients. Both presets are modeling choices, not code classifications.

The stress-limited span comes from setting the bending-stress relationship equal to the allowable stress the user enters. The deflection-limited span comes from the deflection the user enters. If the limit is a fixed sag, L is the fourth root of that sag. If the limit is L/N, L is the cube root. The governing span is the smaller of the two. When they match, both govern.

The page says a tenth of an inch is a screening sag used in published preliminary span notes. It is not an ASME limit and it is not an MSS limit. The page does not treat L/240, or any other fraction, as a piping rule.

5. Understanding the result

Read the weight per length and the two spans. The governing span is the smaller one.

Metal, contents, insulation, and total weight are reported per length. The worked case also states the total as a force per length.

Deflection governs when the deflection-limited span is the smaller one.

6. Engineering considerations

The densities and the modulus are values the user types. The page does not treat them as code values. Allowable stress has no default.

The sag of 2.54 mm is the screening start, not an ASME or MSS limit. The L/N field has no default.

The continuous formula is an approximation, not a code formula. The presets are modeling choices, not code classifications.

Pressure, wind, seismic, point loads, and stress intensification are excluded.

7. Example

Entered on the live page on 3 October 2026: the same NPS 6 Sch 40 pipe, outside diameter 168.3 mm, wall 7.11 mm, steel 7850 kg/m³, E 200000 MPa, water 1000 kg/m³, 50 mm insulation at 80 kg/m³. End condition: continuous equal spans (M = wL²/10, deflection 3.9wL⁴/(384EI)). Allowable bending stress 69 MPa. Sag limit 2.54 mm. The figures were hand-checked. They were not re-run for this remap.

• Metal 28.2636 kg/m
• Contents 18.6459 kg/m
• Insulation 2.74324 kg/m
• Total 49.6527 kg/m (486.926 N/m)
• Stress-limited span 14.0462 m
• Deflection-limited span 5.88998 m

Deflection governs.

The densities and the modulus are the values that were typed. The page does not treat them as code values. The sag of 2.54 mm is the screening start, not an ASME or MSS limit.

8. Standards/references (licensed vs interim)

No catalogue facts are read. No span chart is read. The continuous-span citation is Piping World, Allowable Pipe Support Span Calculation, as printed on the page. This article does not name an ASME or MSS edition. The page says the sag start is not an ASME limit and not an MSS limit.

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 support design.
• The continuous formula is an approximation, not a code formula. The presets are modeling choices, not code classifications.
• Pressure, wind, seismic, point loads, and stress intensification are excluded.
• Allowable stress has no default. The L/N field has no default.
• This page does not replace the chart-based Pipe Span Calculator or Support Span Calculator.

A member check is not an engineering fact. The note is under Repository notes.

10. Use the tool

Calculate now: Rack and Process Spans

Shortcode:

Rack and process spans

Preliminary. This result needs engineering review before anyone uses it. It is a beam-theory screen. It is not a support design.

This page calculates an allowable span from beam theory and the weight you build up. The Pipe Span Calculator and the Support Span Calculator on this site are chart-based. This page does not replace them and it does not read their charts.

Formula

Remaining wall t = wall − corrosion allowance

Di = OD − 2t

Am = π/4 × (OD² − Di²)

I = π/64 × (OD⁴ − Di⁴)

Z = I / (OD/2)

w = (metal + contents + insulation) × g

Metal mass per length is Am times the density you enter. Contents mass per length is the internal area times the contents density. Insulation mass per length is the annulus outside the pipe times the insulation density. No cladding is added unless you include it in the insulation thickness and density. g is standard gravity, 9.80665 m/s². The beam formulas use w in force per length.

Simply supported, uniform load, from strength of materials: bending moment wL²/8, mid-span deflection 5wL⁴/(384EI). Fixed ends, uniform load, from strength of materials: bending moment wL²/12, mid-span deflection wL⁴/(384EI).

Continuous equal spans are placed between those two cases. This page uses the published approximation bending moment wL²/10 and deflection 3.9wL⁴/(384EI), from Piping World, Allowable Pipe Support Span Calculation (https://www.piping-world.com/allowable-pipe-support-span-calculation). That article rearranges the deflection with a rounded 98. This page keeps 3.9/384 and does not use the rounded 98. The continuous case is an approximation, not a code formula.

The rack preset uses the continuous coefficients, as a model of repeated spans. The process-area preset uses the simply supported coefficients, as a model of a single span that can rotate. Both presets are modeling choices. They are not code classifications. Simply supported, continuous, and fixed are also listed on their own so the presets are defined.

The stress-limited span comes from setting the bending stress Z relationship equal to the allowable stress you enter. The deflection-limited span comes from the deflection you enter. If the limit is a fixed sag, L is the fourth root of that sag. If the limit is L/N, L is the cube root. The governing span is the smaller of the two. When they match, both govern.

The absolute deflection field starts at 0.1 in, which is 2.54 mm. A tenth of an inch is a screening sag used in published preliminary span notes. It is not an ASME limit and it is not an MSS limit. Change it to the limit you accept. The span-fraction field has no default. This page does not treat L/240, or any other fraction, as a piping rule. Changing a unit does not convert the number in the box.

A typical modulus and a typical density are near-ambient textbook figures, not code values. Carbon steel 200000 MPa and 7850 kg/m³. Austenitic stainless 193000 MPa and 8000 kg/m³. The lists do not preselect a material. Allowable stress has no default and is not filled from a code table. Pressure, wind, seismic, point loads, and stress intensification are excluded. Numbers on the result line are rounded for display with six significant figures.

Outside diameter mmin Wall thickness mmin Corrosion allowance mmin Metal density kg/m³lb/ft³ Modulus E MPapsi Allowable bending stress MPapsi Contents density, empty means no contents kg/m³lb/ft³ Insulation thickness, empty means none mmin Insulation density kg/m³lb/ft³ End condition Choose the end condition Rack preset — continuous equal spans Process-area preset — simply supported Simply supported Continuous equal spans Fixed ends

Deflection limit

Absolute sag Span fraction L/N

Sag limit inmm

Calculate

Check this tool

Rack Process Spans version 1.0.0

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. Version 1.0.0. Re-check this article when the tool version changes.

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.

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Related tools

Pipe Span, at /tools-training/pipe-span-calculator/, and Support Span, at /tools-training/support-span-calculator/, are the chart-based pages. This page does not read their charts and does not replace them.