Engineering task and calculation objective
The HPR module calculates the allowable support spans of metallic piping to AD 2000-Merkblatt HP 100 R, part of the German AD 2000 pressure equipment code. Anyone routing piping in plant construction has to decide at what intervals the line may rest on pipe supports without the bending stresses from dead weight, medium fill, insulation and additional loads exceeding the allowable stress, or the deflection becoming unacceptably large. HPR performs exactly this pipe span calculation for straight pipes, pipe bends and tees – optionally for the empty, the medium-filled and the insulated line.
In addition, the module verifies the loading from internal pressure: from the pipe outside diameter, the allowable stress (design strength K and safety factor S), the joint efficiency and the allowances for mill tolerance and wear, it determines the required wall thickness of the pipe and of the 90° and 45° branches, as well as the relative maximum allowable operating pressure. This makes it possible to check in a single run whether the actual wall thickness is sufficient for the design pressure.
The elasticity check of installed piping under thermal stresses is carried out in accordance with Appendix 3 of HP 100 R. The module is therefore suited to the design of steam, hot-water and process lines within the scope of the AD 2000 code – for example whenever you need to calculate pipe support spans and document the wall thickness verification in a single report.
Standard and calculation basis: AD 2000 HP 100 R: 2017-06
Calculation workflow
- Enter geometry and operating data: The pipe outside diameter, the actual wall thickness, the design pressure and the design temperature are entered. From the geometry, the module determines the pipe inside diameter, the section modulus and the moment of inertia of the pipe cross-section.
- Define material properties: For the selected pipe material, the design strength K at design temperature, the safety factor S, the modulus of elasticity and the joint efficiency are applied. From these, the allowable stress for both the pressure check and the span check is obtained.
- Perform the internal pressure verification: Taking the mill tolerance and the wear allowance into account, the module calculates the required wall thickness of the straight pipe and of the 90° and 45° branches, and compares them with the actual wall thickness. In addition, the relative maximum allowable operating pressure is reported.
- Determine distributed loads: From the density of the pipe material, the density of the medium (or 0 for an empty line) and the thickness and density of the insulation, the mass of the pipe per unit length is formed. Additional concentrated masses, such as valves, enter the calculation as point loads with their weight.
- Determine the allowable support span: Using the section modulus, the allowable stress in the piping and the allowable deflection, the module determines the allowable support span – from both the stress condition and the deflection condition; the smaller value governs.
- Elasticity check to Appendix 3: For installed lines under thermal stresses, the simplified elasticity check to Appendix 3 of HP 100 R is finally carried out, assessing the flexibility of the pipe routing.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Additional load | m | kg |
| Density of pipe material | ρR | kg/m³ |
| Density of medium or 0 if empty | ρM | kg/m³ |
| Density of absorption material | ρD | kg/m³ |
| Insulation load | B | kg/m² |
| Thickness of absorption material (or 0) | sD | mm |
| Section modulus | W* | mm³ |
| Moment of inertia | I* | mm^4 |
| Modulus of elasticity | E* | N/mm² |
| Allowable stress in pipe material | σmax* | N/mm² |
| Allowable bending | fmax* | mm |
| Stress intensification factor | i* | - |
| Relative mass of pipe | q* | kg/m |
| Operating temperature | t | °C |
| Operating pressure | P ( ) | bar |
| Operating pressure | P ( ) | MPa |
| Outside diameter of pipe | da | mm |
| Existing wall thickness | se | mm |
| Inside diameter of pipe | di dm | mm |
| Pipe bend and | dm = : r | mm |
| Material of pipe | Werkstoff | – |
| Mill tolerance | c1 | mm |
| Corrosion allowance | c2 | mm |
| Thickness to diameter - ratio | Wanddicken-Durchmesserverhältnis | - |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Coefficient of linear expansion | α | 1/K |
| Welding factor | v | - |
| Compensation length | L1 | m |
| Compensation length | L2 | m |
| Temperature difference to be considered | ΔT | K (diff) |
| Length of pipe segment | L | m |
| Actual equivalent length of pipe | L* | m |
| Expansion of pipe segment at ΔT | f | mm |
| Required minimum pipe length acc. to attachm. 3 | Lmin | m |
| Modulus of elasticity | E | kN/mm² |
| Reduction factor for elastic area 1 for bends R≥ 1.5D | ix | – |
Worked example
The internal pressure verification is to be carried out for a seamless DN 150 steam line (outside diameter Da = 168.3 mm, actual wall thickness se = 4.5 mm). Design pressure p = 16 bar, design temperature 200 °C. The design strength of the pipe material at design temperature is taken as K = 170 N/mm², safety factor S = 1.5, joint efficiency v = 1.0 (seamless pipe). Mill tolerance c1 = 12.5 % of the wall thickness, wear allowance c2 = 1.0 mm.
Given values
| Outside diameter Da | 168.3 mm |
| Actual wall thickness se | 4.5 mm |
| Design pressure p | 16 bar |
| Design temperature | 200 °C |
| Design strength K (assumed) | 170 N/mm² |
| Safety factor S | 1.5 |
| Joint efficiency v | 1.0 |
| Mill tolerance c1 | 12.5 % of se |
| Wear allowance c2 | 1.0 mm |
Solution
Calculated wall thickness from internal pressure
For pipes with Da/Di ≤ 1.2, the wall thickness formula of the AD 2000 calculation applies:
s0 = Da · p / (20 · (K/S) · v + p)
s0 = 168.3 · 16 / (20 · (170/1.5) · 1.0 + 16) = 2,692.8 / 2,282.7 = 1.18 mm
Allowances and required wall thickness
Mill tolerance: c1 = 0.125 · 4.5 mm = 0.56 mm; wear allowance c2 = 1.0 mm.
sreq = s0 + c1 + c2 = 1.18 + 0.56 + 1.0 = 2.74 mm
The actual wall thickness of 4.5 mm is greater than 2.74 mm – the internal pressure verification is satisfied.
Relative maximum allowable operating pressure
With the wall thickness reduced by the allowances, s = 4.5 − 0.56 − 1.0 = 2.94 mm, it follows that:
pallow = 20 · (K/S) · v · s / (Da − s) = 20 · 113.33 · 2.94 / (168.3 − 2.94) ≈ 40.3 bar
The design pressure of 16 bar is well below this value; the margin is available, for example, for the branch verification.
Result
| Calculated wall thickness s0 | 1.18 mm |
| Required wall thickness sreq | 2.74 mm |
| Actual wall thickness se | 4.5 mm (verification satisfied) |
| Allowable operating pressure pallow | approx. 40.3 bar |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
What limits the support span first: stress or deflection?
Both are checked. For thin-walled, medium-filled and insulated lines, the allowable deflection is frequently governing, because excessive sag causes drainage problems (pocket formation) and unacceptable changes in slope. For short spans with heavy point loads – such as valves between two supports – the bending stress can become decisive instead. The module reports both conditions.
Does the span calculation to HP 100 R replace a pipe stress analysis?
No. HP 100 R provides allowable support spans for the weight loads and a simplified elasticity check for thermal expansion in accordance with Appendix 3. For complex piping systems with large temperature differences, anchor forces or nozzle loads on equipment, a full flexibility and stress analysis (e.g. to EN 13480-3) is additionally required.
How do insulation and medium enter the calculation?
The mass of the line per unit length is formed from the density of the medium (0 for an empty line), the density of the insulation material and the insulation thickness. The load case "filled and insulated" usually yields the shortest allowable support span; the "empty" load case is relevant, among other things, for the erection condition and for the hydrostatic pressure test with water fill, which should be considered separately.
Why are required wall thicknesses also reported for 90° and 45° branches?
At branches (tees), the opening weakens the main body, so a greater wall thickness may be required there than in the undisturbed straight pipe. The module therefore determines the required wall thicknesses separately for the straight pipe, the 90° branch and the 45° branch, together with the associated relative maximum allowable operating pressure.