Engineering task and calculation objective
Module B51F verifies the fatigue strength of the tubesheets of fixed-tubesheet heat exchangers (fixed-fixed construction). The basis is the Richtlinienkatalog Festigkeitsberechnungen (Parts 5 and 6), a German catalogue of strength calculation guidelines with detailed design rules for tubesheet constructions. With tubesheets welded rigidly on both sides and no expansion joint, alternating operating conditions — start-up and shutdown, load changes, cleaning cycles — produce repeated stress ranges in the tubesheet that can limit its service life.
The module accounts for the pressure changes on the tube side and the shell side as well as the influence of the maximum temperature change, which introduces additional forces into the tubesheet via the restrained differential thermal expansion between tube bundle and shell. From the geometry of the tubed area (calculation diameter, tube pitch, tube layout coefficient, untubed rim) and the stiffness ratio of tubes to tubesheet, the existing stress range is determined and the number of allowable load cycles is derived from it.
Being able to calculate such a fatigue assessment for the tubesheet is required whenever a heat exchanger is operated cyclically — typically in batch processes, steam generators with frequent start-ups, or equipment with strongly fluctuating operating pressures.
Standard and calculation basis: Richtlinien Katalog Festigkeit Teil 5 und 6
Calculation workflow
- Define the load cycle: The ranges occurring in service are defined: the pressure changes on the shell side and tube side as well as the maximum temperature change between the operating conditions. From the pressure and temperature components, the change of the fictitious pressure is formed, which describes the combined loading of the tubesheet.
- Form the geometry and stiffness parameters: From the calculation diameter of the tubed area, the effective tube pitch, the tube layout coefficient, the width of the untubed rim and the relative tube cross-section, the weakening of the tubesheet by the perforated field and the stiffness ratio of tubes to tubesheet are determined.
- Evaluate the pressure influence coefficients: The coefficients for the shell-side and tube-side pressure action on the tubesheet distribute the two pressure ranges according to the elastic coupling of tubesheet, bundle and shell. Together with the bracketed terms of the governing equation, this yields the loading of the tubesheet in the perforated field and at the rim.
- Determine the stress range: From the fictitious pressure and the geometry parameters follows the existing stress range in the tubesheet. It captures the combination of bending of the perforated tubesheet and the additional forces introduced via the tubes due to restrained thermal expansion.
- Determine the allowable number of load cycles: With the material-dependent fatigue factors A and B, the number of allowable load cycles is calculated from the stress range and compared with the number of cycles planned over the service life. If the allowable cycle count is insufficient, a thicker tubesheet, a modified operating regime or an expansion joint must be considered.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Shell-side pressure change | DP1 | MPa |
| Tube-side pressure change | DP2 | MPa |
| Material of shell | Mantel | - |
| Material of tubes | Rohre | - |
| Material of tube sheet | Platte | - |
| Austenite Y/N | J/N | - |
| Expansion coefficient of tubes | αT | 1E-6/K |
| Expansion coefficient of shell | αK | 1E-6/K |
| Tensile strength of tube sheet material at 20°C | RM20 | N/mm² |
| Mean tube wall temperature operation | TT | °C |
| Bolting-up temperature | T0 | °C |
| Mean shell wall temperature operation | TK | °C |
| Design temperature of tube sheet | TP | °C |
| Modulus of elasticity of tubes | ET | N/mm² |
| Modulus of elasticity of shell | EK | N/mm² |
| Yield strength of tube sheet material at 20°C | K20P | N/mm² |
| Final thickness of tube sheet | sP | mm |
| Outside diameter of tube | dT | mm |
| Final wall thicknes of tube | sT | mm |
| Inside diameter of shell | DK | mm |
| Outside diameter of shell | DKa | mm |
| Final wall thickness of shell | sK | mm |
| Tube length | lT | mm |
| Total number of tubes | nn | - |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Change of fictitious pressure | DPF | MPa |
| Pressure load coefficient shell - tube sheet | η1 | - |
| Pressure load coefficient tube - tube sheet | η2 | - |
| Characteristic width of untubed tube sheet | λ0 | - |
| Characteristic width of untubed tube sheet | λB | - |
| Ratio of stiffness of tubes/tube sheet | κ | - |
| Characteristic tube diameter | δ | - |
| Width of untubed rim | bb | mm |
| Part of equation Eq(59) | Gl(59) | - |
| Part of equation Eq(59) | Gl(59) | - |
| Actual equivalent stress | ρA | N/mm² |
| Factor A for material fatigue | A | MPa |
| Factor B for material fatigue | B | - |
| Number of allowable load cycles | Nall | - |
| 1st expression in bracket | Klammerausdruck | - |
| 2nd expression in bracket | Klammerausdruck | - |
| 3rd expression in bracket | Klammerausdruck | - |
| Design diameter of tubed area | DR | mm |
| Arithmetic tube pitch | tR | mm |
| Factor for tube arrangement | θA | – |
Frequently asked questions
Why is the fixed-fixed construction particularly prone to fatigue?
With tubesheets welded rigidly on both sides and no expansion joint, tube bundle and shell cannot expand independently. Every temperature difference between tubes and shell produces restraint forces that are introduced into the tubesheets as axial forces through the tubes. Together with the pressure changes, each cycle generates a stress range in the tubesheet — with a floating head or U-tube bundle, this restraint component is largely absent.
What does the 'change of the fictitious pressure' mean?
The three actions — shell-side pressure change, tube-side pressure change and temperature difference — are converted via influence coefficients into an equivalent pressure range acting on the tubesheet. This fictitious pressure makes it possible to evaluate the combined cyclic loading with a single tubesheet equation instead of superimposing each action separately.
Isn't the static strength check of the tubesheet sufficient?
No, not if the unit is operated cyclically. The static check limits the stresses of the governing single load case; fatigue cracks, however, arise from the repeated stress range between the conditions, often at notches such as tube-to-tubesheet welds or the transition to the untubed rim — even if each individual condition is statically acceptable. From a few hundred to a thousand significant load cycles over the service life, a fatigue assessment should be performed.
What role do the factors A and B play for material fatigue?
They parameterize the fatigue curve (S-N curve) of the tubesheet material in the code: from the existing stress range, the endurable number of load cycles follows via the A and B factors. The factors depend on the material, temperature and, where applicable, the surface or weld quality; incorrect factors shift the allowable cycle count by orders of magnitude.