Rack and Process Spans

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 converts 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.

It is a beam-theory screen. It is not a support design.