Engineering guide
Module 301 calculates cylindrical shells under internal pressure to TRD 301 (edition 1997-10) — the German technical rule for steam boilers that governed the design of boiler drums, headers and cylindrical boiler components in Germany for decades. The TRD codes have been withdrawn following the dissolution of the German Steam Boiler Committee; for new plant their role has been taken over by the harmonized standards DIN EN 12952 (water-tube boilers) and DIN EN 12953 (shell boilers). For existing plant, recurring inspections and re-assessments against the original design code, however, TRD 301 remains highly relevant in practice.
From the design pressure, the allowable stress (strength value divided by safety factor) and the geometry, the module determines the required and the as-built wall thickness, verifies individual and adjacent openings and nozzles using the weakening-factor (ligament efficiency) method, and checks the nominal stress in the hydrostatic test case. A special feature of TRD 301 are the limits on the rate of temperature change during start-up and shutdown, which restrict the thermal stresses in thick-walled components.
Typical applications today include assessing findings on old boiler drums, determining the maximum permissible test pressure for recurring inspections, and deriving allowable start-up gradients for the flexible operation of older plant.
Scope
- Cylindrical shells under internal pressure
Typical workflow
Determine the design values
From the material, the design temperature and the safety factor, the allowable stress for the operating case is formed; for the hydrostatic test case a separate allowable stress applies, with a reduced safety factor against the yield strength at room temperature.
Required wall thickness of the unweakened shell
Using the wall thickness formula of TRD 301, the required wall thickness is calculated from the design pressure, diameter, allowable stress and weld joint efficiency; allowances for thickness undertolerance and wear lead to the as-built wall thickness.
Verify openings and nozzles
Individual openings are verified via the weakening factor and the load-bearing (compensating) lengths of shell and nozzle; for unreinforced openings the rule gives the largest permissible diameter (Figure 11). For adjacent nozzles it is checked whether the ligament width is large enough to dispense with the verification of mutual interaction.
Check nominal stress and test pressure
The nominal stress in the operating condition is compared with the allowable stress; in addition, the maximum permissible test pressure for the recurring inspection is determined so that the hydrostatic test stress does not exceed the allowable stress for the test case.
Determine allowable rates of temperature change
For start-up and shutdown, the allowable rates of temperature change are calculated from the wall thickness, material properties and number of load cycles, so that the superimposed thermal stresses at opening edges do not exceed the endurable stress range.
Frequently asked questions
May I still use TRD 301 for new designs?
No. The TRD rules have been withdrawn; new plant within the scope of the Pressure Equipment Directive is designed to DIN EN 12952-3 (water-tube boilers) or DIN EN 12953-3 (shell boilers). Existing boilers, however, enjoy grandfathering: re-assessments, repair evaluations and recurring inspections are sensibly based on the original design code — which is exactly why the TRD 301 calculation is still needed today.
Why does TRD 301 limit the rate of temperature change during start-up and shutdown?
In thick-walled components, a rapid temperature change produces a radial temperature gradient and hence thermal stresses which, at opening edges (nozzles, water-level bores), superimpose on the pressure stresses. During start-up the thermal stresses at the inner surface act in compression, during shutdown in tension — the latter being more critical for crack initiation. The allowable gradients ensure that the stress range remains endurable over the planned number of load cycles; they are the core of the TRD fatigue assessments (TRD 301 Annex 1).
What does 'largest unreinforced opening' per Figure 11 mean?
Up to a certain diameter, the surrounding shell wall carries an opening on its own, without any credit for nozzle wall thickness or a reinforcing pad. Figure 11 of TRD 301 gives this limiting diameter as a function of geometry and loading — distinguishing between an undisturbed region and regions with adjacent discontinuities. Larger openings require the full weakening-factor verification with load-bearing lengths.
How does the result differ from a calculation to EN 12952-3?
The basic wall thickness formulas are closely related (both built on the mean-diameter formula), but safety factors, strength values (in particular creep rupture values), weakening factors and the treatment of cyclic loading differ in detail. Switching the verification basis from TRD to EN can therefore lead to different utilization ratios and should only be done consistently for the complete component, never by mixing individual formulas.
Worked example
For a seamless cylindrical boiler drum, the required wall thickness is to be determined to TRD 301 (re-assessment of an existing plant) — a worked example of how to calculate the wall thickness of a cylindrical shell to the German TRD code. The allowable stress K/S has already been formed from the strength value and the safety factor.
Given
| Design pressure p | 4.0 MPa (40 bar) |
|---|---|
| Outside diameter da | 800 mm |
| Allowable stress K/S | 147 N/mm² |
| Joint efficiency v (seamless, unweakened) | 1.0 |
| Allowance for thickness undertolerance c1 | 0.5 mm |
| Wear allowance c2 | 1.0 mm |
Solution
Required wall thickness to TRD 301
The wall thickness formula referred to the outside diameter reads:
sv = da · p / (2 · (K/S) · v + p)
sv = 800 · 4.0 / (2 · 147 · 1.0 + 4.0) = 3,200 / 298 = 10.74 mm
Wall thickness including allowances
s = sv + c1 + c2 = 10.74 + 0.5 + 1.0 = 12.24 mm
An as-built wall thickness of 12.5 mm is selected; the nominal stress in operation thus stays below the allowable stress.
Result
| Required wall thickness sv | 10.74 mm |
|---|---|
| Minimum wall thickness incl. allowances | 12.24 mm |
| As-built wall thickness | 12.5 mm |
Technical content source: LV-Solved-Problems-Content 628d313247e7