Engineering guide
This module verifies cylindrical shells under external pressure to TRD 306, part of the German Technical Rules for Steam Boilers (TRD). Typical applications in steam boiler construction are furnace tubes and other flue-gas-heated tubes and shell courses loaded by external pressure: here the water pressure acts on the outside of the furnace tube, which must be verified against elastic buckling and plastic deformation. From the as-built wall thickness, the module calculates the allowable external overpressures for both failure modes and compares them with the operating overpressure.
The buckling verification uses the outside diameter, the largest unstiffened length between effective stiffeners, the out-of-roundness of the shell, and the modulus of elasticity and Poisson's ratio of the material. The deformation verification is based on the material strength value at design temperature with its own safety factor; for furnace tubes, an additional temperature margin is applied. Stiffeners — such as corrugated sections or attached stiffening rings — shorten the unstiffened length and increase the allowable buckling pressure.
The TRD rules were withdrawn at the end of 2012. TRD 306 remains relevant for recalculating existing fire-tube and smoke-tube boilers; new designs follow EN 12953-3 (shell boilers) or EN 12952-3, which govern the external pressure verification with comparable safety concepts.
Scope
- Cylindrical shells under external pressure
Typical workflow
Define operating conditions and temperature
The operating overpressure acts as external pressure on the shell. The design temperature results from the operating temperature plus a temperature margin; for furnace tubes, an additional temperature margin for the heating is applied.
Record geometry and imperfections
The governing quantities are the outside diameter, the as-built wall thickness minus the allowances for wall thickness undertolerance and corrosion, and the largest unstiffened length between end plates, corrugated sections or stiffening rings. The measured or permissible out-of-roundness enters the verification as an imperfection.
Verification against elastic buckling
Using the modulus of elasticity, Poisson's ratio, the wall-thickness-to-diameter ratio and the unstiffened length, the elastic buckling pressure of the shell is calculated. Divided by the safety factor against buckling, this gives the allowable external overpressure for this failure mode.
Verification against plastic deformation
In parallel, plastic deformation of the out-of-round shell is assessed: from the material strength value, the safety factor against deformation and the out-of-roundness, the allowable external overpressure for yielding failure follows.
Determine the governing allowable pressure
The smaller of the two allowable overpressures (buckling or deformation) must exceed the operating overpressure. If the load-bearing capacity is insufficient, a greater wall thickness or additional stiffeners to shorten the unstiffened length must be provided.
Frequently asked questions
Why is out-of-roundness so important in the external pressure verification?
Under external pressure, even small shape deviations act as initial imperfections that generate local bending stresses and significantly reduce the resistance to deformation. TRD 306 therefore applies the out-of-roundness explicitly in the verification against plastic deformation. When recalculating existing plants, the actually measured out-of-roundness should be used, not the as-new value.
What is the effect of stiffeners and corrugated furnace tubes?
Stiffening rings and corrugations divide the shell into shorter unstiffened lengths. Since the elastic buckling pressure rises sharply as the unstiffened length decreases, a considerably higher allowable external pressure can be achieved at the same wall thickness. Corrugated furnace tubes also increase flexibility with respect to the thermal expansion of the furnace tube.
Why are there two separate safety factors?
Elastic buckling is imperfection-sensitive and occurs suddenly, so the calculated buckling pressure is reduced by a high safety factor. Plastic deformation is more benign and receives a smaller factor. Both verifications must be satisfied independently; which one governs depends on the slenderness (length, diameter, wall thickness).
What does the temperature margin for furnace tubes represent?
Furnace tubes are intensely heated on the flue-gas side; the wall temperature lies well above the saturation temperature of the surrounding water. The temperature margin raises the design temperature so that the strength value and the modulus of elasticity are applied at realistic, lower values.
Technical content source: LV-Solved-Problems-Content 628d313247e7