BIZOMAT MAKEOS · Strength
Pipe Support Span Check (Pipe and Contents Weight, Bending Stress, Sag, Longest Span)
How far apart can the supports for this pipe be, given its weight full of liquid, the bending stress and the sag I can accept?
Check of the span between pipe supports: the section area, second moment of area and section modulus of the pipe, the weight per metre of pipe, contents and insulation, then the bending moment, stress and sag for simply supported, fixed or one-end-fixed spans under the uniform load (closed forms, the fixed cases as the beam cases tool), and the longest span that keeps both stress and sag within your limits.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Pipe outside diameter | mm | Outside diameter of the pipe. |
| Wall thickness | mm | Wall thickness (less corrosion allowance for a design check). |
| Pipe density | kg/m³ | Density of the pipe material. |
| Contents density | kg/m³ | Density of the contents (0 for empty gas lines; 1000 for water). |
| Insulation and cladding | kg/m | Mass per metre of insulation, cladding and trace heating. |
| Modulus of elasticity | GPa | Modulus of elasticity of the pipe. |
| Span | ||
| Span treated as | choice | How the span is restrained by the supports and neighbouring spans. |
| Support spacing | mm | Distance between supports. |
| Allowable bending stress | MPa | Allowable bending stress for sustained loads (often well below the material allowable, to leave room for pressure stress). |
| Largest sag | mm | Largest sag at mid-span you accept (small values avoid pockets that do not drain). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Pipe outside diameter
- What it is
- The outside diameter of the pipe, from the pipe size tables for its nominal size.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60.3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the actual outside diameter, not the nominal pipe size, which is not the same number for most sizes.
What this means: Wall thickness
- What it is
- The wall thickness of the pipe. The bore is the outside diameter minus twice this thickness.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3.91 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For a design check deduct the corrosion allowance and any mill tolerance from the nominal wall.
What this means: Pipe density
- What it is
- The density of the pipe material, used to work out the pipe’s own weight per metre.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 25000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7850 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the pipe material data.
What this means: Contents density
- What it is
- The density of the fluid filling the pipe bore, used to add the weight of the contents.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0 kg/m³ to 25000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter 0 for an empty or gas line. Check whether the line is hydrotested full of water, which can govern.
What this means: Insulation and cladding
- What it is
- The mass per metre of everything carried on the pipe besides the pipe and contents: insulation, cladding and trace heating.
- Units and format
- Enter a number in kg/m: kilograms per metre of length. The form accepts 0 kg/m to 10000 kg/m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 kg/m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter mass per metre in kg/m, not weight in N/m.
What this means: Modulus of elasticity
- What it is
- The modulus of elasticity of the pipe material, used for the sag.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 1000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sag falls in proportion to it; stress does not change.
- Get it right
- Enter it in GPa, not MPa; at high temperature use the value for the operating temperature from material data.
Span
What this means: Span treated as
- What it is
- How the span is restrained: a single simply supported span, a span in a long continuous run (fixed both ends), or an end span fixed at one end and supported at the other.
- Units and format
- Choose one of 3 options from the list: Simply supported (single span); Fixed both ends (long continuous run); Fixed one end, supported the other (end span).
- Example
- The form opens with “Simply supported (single span)” selected as a worked example. Choose the option that matches your case.
- Get it right
- Choose simply supported if you are unsure; it gives the largest moment and sag.
What this means: Support spacing
- What it is
- The distance between adjacent pipe supports along the pipe.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Bending stress rises with the square of the span and sag with its fourth power.
- Get it right
- Measure between support centres along the pipe, not in plan if the pipe slopes.
What this means: Allowable bending stress
- What it is
- The highest bending stress you allow from sustained weight, compared with the stress in the span.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 10000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from your piping code; it is for sustained loads only and leaves room for pressure stress.
What this means: Largest sag
- What it is
- The largest sag at mid-span you accept, compared with the sag worked out for the span.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2.5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Set it from your piping standard or drainage needs; a small limit avoids pockets that do not drain.
Method and formulas
- A = π (D² − d²) ÷ 4; I = π (D⁴ − d⁴) ÷ 64; Z = 2I ÷ D; weight w = g (A ρ_pipe + π d² ρ_fluid ÷ 4 + insulation).
- Simply supported: M = wL² ÷ 8, sag = 5wL⁴ ÷ 384EI; fixed both ends and fixed–supported as the beam cases tool for a uniform load.
- Stress grows with L² and sag with L⁴, so the longest spans are L √(σ_allow ÷ σ) and L (δ_allow ÷ δ)^¼.
- Example: 7.6006 kg/m gives 9.1387 MPa and 1.4208 mm sag; the span may be up to 3,455.2 mm.
Limitations
- Straight horizontal span with uniform load; valves, flanges and branches add point loads.
- Sustained weight only; pressure, thermal and seismic stresses are separate.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Space hangers for a water or process line
- Check an existing pipe rack span
- See how insulation or a heavier fluid shortens the span
Who it is for
- Piping designers
- Plant engineers
- Mechanical contractors
What you get
- Pipe section and weight per metre
- Moment, stress and sag
- Longest span for stress and sag
Interpreting the result
- For small pipes the sag limit usually governs; for large pipes the stress does.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 234–246, 257–277. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Useful alongside · BIZOMAT original book
Pipe strain
In Shaft Alignment by the Numbers
What it covers: How connected pipes pull a pump out of alignment, how to support pipe weight and absorb thermal growth so the pump carries neither, and how to measure pipe strain at the coupling.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.