Engineering task and calculation objective
Piping between two anchor points must be able to absorb elastically the thermal expansion that develops between the initial and final temperatures — otherwise inadmissible stresses arise in the pipe and high loads act on nozzles and supports. Whether a three-dimensional pipe routing has enough flexibility for this can be estimated with the elasticity criterion, without having to run a full pipe stress analysis.
The ELKR module checks the elasticity criterion of three-dimensional piping to AD 2000 HP 100 R of the German AD 2000 code. The input quantities are the developed (stretched-out) length of the line between the supports, the direct distance between the anchor points, the pipe outside diameter, and the initial and final temperatures. From the coefficient of expansion, the modulus of elasticity and the allowable stress of the material (nominal design stress divided by the safety factor), the module forms a material factor and evaluates the criterion: if it is satisfied, the line is considered elastically routed and a detailed flexibility analysis can be omitted.
Typical applications are steam, hot water and process lines in plant engineering, where it must be decided early in the project whether the routing with its bends and legs provides enough expansion compensation, or whether additional expansion legs or expansion joints need to be provided.
Standard and calculation basis: AD 2000 HP 100 R
Calculation workflow
- Enter the piping geometry: The inputs are the developed length of the line between the supports (the sum of all straight sections and bends) and the direct length, i.e. the straight-line distance between the two anchor points. The ratio of the two quantities is a measure of the flexibility contained in the routing.
- Determine the temperature difference: From the initial temperature (installation condition) and the final temperature (operation) follows the governing temperature difference, which together with the coefficient of expansion determines the thermal expansion to be absorbed.
- Apply the material properties: For the pipe material, the modulus of elasticity, the coefficient of expansion, the nominal design stress and the safety factor are required; from these follow the allowable stress and the material factor of the criterion.
- Evaluate the elasticity criterion: The module combines the pipe outside diameter, the thermal expansion, and the developed and direct lengths into the criterion value and compares it with the allowable limit. As a result, it reports whether the piping is routed elastically (Yes/No).
- Draw the consequence for the routing: If the criterion is not satisfied, the line must be made more flexible — longer expansion legs, additional changes of direction or expansion joints — or a detailed pipe stress analysis with determination of the actual stresses and support loads is required.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Elongated distance between supports | L | m |
| Direct distance between supports | a | m |
| Material | Nr | - |
| Modulus of elasticity | E | N/mm² |
| Expansion coefficient | β | m/m°C |
| Start temperature | t1 | °C |
| Final temperature | t2 | °C |
| Temperature difference | DT | °C |
| Ratio | L/a | - |
| Outside diameter of pipe | da | mm |
| Safety factor | S | - |
| Nominal design strength | K | N/mm² |
| Allowable stress | σall | N/mm² |
| Criterion for elasticity | Ekr | - |
| Material factor | fw | - |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| The piping is assembled elastically Y/N | erfüllt | - |
Frequently asked questions
Does the elasticity criterion replace a pipe stress analysis?
No. The criterion is a conservative screening method that only demonstrates that the line has enough flexibility for the thermal expansion. It provides no statements on support loads, nozzle loads or stresses at individual bends. If it is not satisfied, or for large nominal sizes, high temperatures or sensitive connection points (pumps, turbines, equipment nozzles), a detailed flexibility analysis is required.
What conditions must the line meet for the criterion to apply?
The criterion applies to lines between two anchor points without intermediate anchors or rigid guides, with an approximately constant cross-section and without significant concentrated additional loads. Axial and sliding supports that allow the expansion movement are harmless; any intermediate anchor, however, divides the line into sections that must be checked separately.
Why does the ratio of developed to direct length enter the criterion?
A line that is considerably longer than the direct anchor-point distance contains legs and bends transverse to the direction of expansion, which can flex elastically and absorb the expansion. If, on the other hand, the line runs almost straight between the anchor points, this compensation is missing and the thermal expansion produces nearly pure axial compression — the most critical configuration, which the criterion reliably screens out.
Which temperatures should be applied?
Governing is the largest difference occurring in operation relative to the installation temperature — usually the installation temperature versus the maximum operating temperature. Exceptional conditions such as bake-out or steam blowing should also be considered. For cryogenic lines, cooling below the installation temperature must likewise be checked, with the opposite sign.