Engineering guide
This module calculates spherical shells and dished ends under internal and external pressure to TRD 303, part of the German Technical Rules for Steam Boilers (TRD). For the internal pressure case, the required wall thickness is determined from the design pressure, the material strength value, the safety factor and the joint efficiency; for the external pressure case, the elastic buckling pressure and the allowable external pressure are verified with their associated safety factors. The code section also covers openings and opening reinforcements, such as nozzles in torispherical (Klöpper) or semi-ellipsoidal (Korbbogen) heads as well as multiple openings.
The calculation is used in steam boiler construction: spherical shell courses, hemispherical heads and dished ends of water-tube and shell boilers must be verified both for the operating condition and for the hydrostatic test pressure. The module runs both load cases in parallel and reports the allowances for wall thickness undertolerance and for corrosion and wear separately.
TRD 303 belongs to the German Technical Rules for Steam Boilers, which were withdrawn at the end of 2012. It remains relevant in practice for recalculation, modifications and recurring inspections of existing plants; for new designs it has been superseded by the European standard series EN 12952 (water-tube boilers) and EN 12953 (shell boilers).
Scope
- Spherical shells and dished heads under internal and external pressure
Typical workflow
Define load cases and temperatures
The design pressure and the test pressure are applied for operation and pressure testing respectively. The design temperature is obtained from the operating temperature plus a temperature margin that accounts for how the component is heated.
Determine material strength values and safety factors
The selected material yields the strength values for operation and testing at the respective temperatures. Together with the safety factors for both conditions, this gives the allowable stress.
Calculate the required wall thickness for internal pressure
The theoretical wall thickness is determined from the outside or inside radius of the spherical shell, the design pressure, the allowable stress and the joint efficiency. Allowances for wall thickness undertolerance and for corrosion and wear then give the required wall thickness including allowances, which is compared against the as-built wall thickness.
Perform the external pressure verification
For spherical shells and heads loaded by external pressure, the elastic buckling pressure is calculated from the geometry and the modulus of elasticity. With the safety factors against elastic buckling and plastic deformation, the allowable external pressure follows, which must exceed the design pressure.
Verify openings and reinforcements
Nozzles and openings are verified using the area replacement (pressure-area) method; for multiple openings, the ligament widths between adjacent openings must also be checked. Reinforcement can be provided by pads, reinforced nozzles or an increased base wall thickness.
Frequently asked questions
May TRD 303 still be used for new designs today?
No. The TRD rules were withdrawn on 31 Dec 2012. New steam boiler components are designed to EN 12952-3 or EN 12953-3 (in conjunction with the Pressure Equipment Directive). However, TRD 303 is still needed for recalculating existing boilers, for repair assessments and for checking old design documentation.
Why are the operating and test conditions calculated separately?
At test pressure, a higher pressure is applied, but at the same time room-temperature strength values and a smaller safety factor apply. Which condition governs the wall thickness depends on the ratio of the strength values at design temperature and at test temperature. The module reports both conditions; the larger wall thickness requirement governs.
In the external pressure check, what is the difference between buckling and deformation?
Against elastic buckling, the elastic buckling pressure of the spherical shell is reduced by a high safety factor, because buckling failure is highly sensitive to shape imperfections. In addition, plastic deformation is limited via the material strength value with its own safety factor. The allowable external pressure is the smaller of the two verification results.
Which allowances enter the required wall thickness?
Allowance c1 covers the permissible wall thickness undertolerance of the semi-finished product (the minus tolerance for plates, often a percentage for tubes). Allowance c2 accounts for corrosion and wear; it can be omitted for corrosion-resistant designs or sufficiently thick walls. Both allowances are added to the theoretical wall thickness before comparison with the as-built wall thickness.
Worked example
For the hemispherical head of a steam generator, determine the required wall thickness to TRD 303 for the operating condition — a typical worked example of a pressure vessel wall thickness calculation. The head is made of P265GH and is welded.
Given
| Outside diameter da | 2,000 mm |
|---|---|
| Design pressure p | 16 bar = 1.6 N/mm² |
| Design temperature | 200 °C |
| Strength value K (P265GH, 200 °C) | 205 N/mm² |
| Safety factor S | 1.5 |
| Joint efficiency v | 0.85 |
| Allowance c1 (wall thickness undertolerance) | 0.3 mm |
| Allowance c2 (corrosion/wear) | 1.0 mm |
Solution
Form the allowable stress term
For a spherical shell under internal pressure, the membrane formula based on the outside diameter applies:
s = da · p / (4 · (K/S) · v + p)
The denominator evaluates to 4 · (205/1.5) · 0.85 + 1.6 = 464.67 + 1.6 = 466.27 N/mm².
Theoretical wall thickness
s = 2,000 mm · 1.6 N/mm² / 466.27 N/mm² = 6.86 mm
Add the allowances
sreq = 6.86 + 0.3 + 1.0 = 8.16 mm
The next available plate thickness is selected, e.g. 10 mm. This also provides sufficient margin for the test pressure condition, which must be verified separately with the test-condition strength values.
Result
| Theoretical wall thickness | 6.86 mm |
|---|---|
| Required wall thickness incl. allowances | 8.16 mm |
| As-built wall thickness | 10 mm |
Technical content source: LV-Solved-Problems-Content 628d313247e7