Engineering task and calculation objective
Pressure is rarely the only loading on a vessel shell: dead weight, wind moments, earthquakes, piping forces and support reactions generate additional longitudinal forces, bending moments and shear forces in the cylindrical shell. This module verifies cylindrical shells under such global loads to DIN EN 13445-3, clause 16.14 — the code section for the combination of pressure with external section forces.
The core of the procedure is the maximum permitted longitudinal compressive stress to clause 16.14.7: since a thin-walled cylindrical shell under axial compression fails by buckling, the limit compressive stress is determined from the elastic buckling value using the coefficient K, the imperfection-dependent reduction factor α and the parameter Δ. For a given wall thickness, the module then determines the maximum allowable individual loads — tensile force, compressive force and bending moment — to clause 16.14.4 and checks the buckling condition (equation 16.14-4).
The verification is needed for vertical columns under wind and earthquake, for horizontal vessels with shear forces from the supports, and generally wherever the question is: which external forces and moments can this cylindrical shell sustain in addition to the pressure?
Standard and calculation basis: DIN EN 13445-3/16.14: 2018-12
Calculation workflow
- Define shell geometry and load case: The inputs are diameter, wall thickness minus allowances, material and the load case considered (operation, testing, erection). The circumferential stress follows from the internal pressure; for external pressure or vacuum, the interaction with the buckling verification to clause 8 must be observed.
- Compile the section forces: At the shell section considered, the global section forces are applied: the total longitudinal force from weight and external forces, the bending moment from wind, seismic or piping loads, and — for horizontal vessels — the shear force from the support reactions.
- Calculate the existing longitudinal stresses: From longitudinal force and bending moment, the module determines the maximum and minimum longitudinal stress around the circumference — the superposition decides whether tension or compression prevails at the most unfavourable point. The internal pressure contributes a relieving tensile component in the longitudinal direction, whose absence (unpressurized conditions) must be checked separately.
- Determine the limit compressive stress to 16.14.7: The maximum permitted longitudinal compressive stress is determined from the elastic buckling value of the cylindrical shell using the coefficient K, the reduction factor α for imperfections and the parameter Δ. It lies well below the ideal buckling stress, because real shells are sensitively weakened by initial dents and residual stresses.
- Carry out the verifications: On the tension side, the maximum longitudinal stress is checked in combination with the circumferential stress against the allowable stress; on the compression side, the minimum longitudinal stress is checked against the limit compressive stress — expressed in the buckling condition of equation 16.14-4. From this condition, the maximum allowable individual loads (tensile force, compressive force, bending moment) for the available wall thickness follow at the same time.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Calculation temperature | t | °C |
| Internal calculation pressure in MPa | P | MPa |
| Material designation | Werkstoffbezeichnung | – |
| Nominal design stress | f | N/mm² |
| Modulus of elasticity | E | N/mm² |
| Analysis thickness | ea | mm |
| allowable elastic limit (Rp02/Sel or Rp1/Sel) | σe | N/mm² |
| Mean shell diameter | D | mm |
| Deviation from perfect shape | w | mm |
| Length of template for checking shape deviations | l | mm |
| Tolerance | w/l | – |
| Scaled diameter | D/ea | - |
| Factor | (16.14-15) K | – |
| Factor | (16.14-16/17) α | – |
| Factor | (16.14-18/19) Δ | – |
| for | σc,all (16.14-20) | N/mm² |
| Maximum tensile force | (16.14-1) Ft,max | kN |
| Maximum compressive force | (16.14-2) Fc,max | kN |
| Bending moment | (16.14-3) Mmax | kN·m |
| Internal calculation pressure in bar | P | bar |
| Load case | 2=Pruefung) | – |
| Wall thickness mill tolerance | c1 | mm |
| Corrosion allowance | c2 | mm |
| Cylinder length (incl. cylindrical part of head) | L | mm |
Calculation options
Option
Allowable individual loads · Cylinder wall thickness under internal pressure · Cylinder wall thickness under external pressure
Frequently asked questions
Why is the allowable compressive stress so much lower than the allowable tensile stress?
Under longitudinal tension, the material strength limits the load capacity; under longitudinal compression it is shell buckling. The classical elastic buckling stress of thin-walled cylinders is reached by real shells only to a fraction, owing to unavoidable initial dents — the reduction factor α captures exactly this imperfection sensitivity, which increases with growing radius-to-wall-thickness ratio. That is why the limit compressive stress can drop to a fraction of the yield strength.
Does internal pressure act favourably or unfavourably in the verification?
In the longitudinal direction, internal pressure acts favourably: it generates longitudinal tension that partially compensates compressive stresses from weight and moment and additionally reduces the buckling sensitivity. The unpressurized or erection condition, in which this relief is absent, is therefore often governing. At the same time, the circumferential tensile stress from the pressure must be considered in the stress combination on the tension side — the module checks both effects separately.
For which load cases must the verification to 16.14 typically be carried out?
For vertical apparatus, at least for operation with wind, testing with reduced wind, earthquake, and erection conditions without internal pressure; for horizontal vessels, additionally for the support sections with shear force. Since longitudinal force, moment and pressure combine differently in each load case, any of these conditions can become governing — the seemingly harmless unpressurized wind load case is, surprisingly often, the one.
What does the module deliver if the section forces are not yet fixed?
For a given wall thickness, it converts the limit condition of clause 16.14.4 into maximum allowable individual loads: the allowable tensile force, the allowable compressive force and the allowable bending moment of the cylindrical shell. These capacity values are suitable as specifications for piping design and structural steelwork — for instance as an allowable-nozzle-load proxy at apparatus level, or for the quick preliminary sizing of column shell courses.