Engineering task and calculation objective
The KSTA module handles the structural analysis of vertical cylindrical equipment assembled from several shell courses – typically columns, reactors or slender outdoor vessels. For each course, the outside diameter, wall thickness, insulation thickness, length and dead weight are recorded; together with the height of the course start above ground and the aerodynamic pressure coefficient, the wind and weight loads that vary over the height of the vessel can be built up course by course.
In practice, this course-by-course approach is needed whenever a tall vessel can no longer be idealised as a single cantilever with constant cross-section: wall thicknesses are stepped down towards the top, diameters change, and additional forces from internals, platforms or piping act at individual course ends. The type of support at the start and end of each course – including any existing gap – also enters the structural system.
Engineers who want to calculate the statics of a column or estimate the wind load on a vertical pressure vessel obtain with KSTA the internal-force basis on which the stress and stability checks of the individual courses are subsequently carried out to the applicable pressure vessel code.
Calculation workflow
- Divide the vessel into shell courses: First, the number of courses is defined. Each course is described by its outside diameter, wall thickness, insulation thickness, length and weight; the height of the course start above ground places the sections within the overall system.
- Define supports and boundary conditions: For the start and end of each course, the type of support is specified, including any existing gap. This defines the structural system used to determine support reactions and internal forces.
- Apply loads for each course: In addition to the design pressure and the dead weight of each course, the calculation includes the wind load via the aerodynamic pressure coefficient and the exposed area (outside diameter plus insulation), as well as additional forces at the course end – for example from platforms or connected piping.
- Account for temperature effects: The maximum operating temperature determines the allowable material properties of the courses and thus the basis for the subsequent stress checks.
- Evaluate internal forces and verifications: Superimposing weight, wind and additional loads yields the governing axial forces and bending moments for each course, which are then compared with the allowable stresses from the pressure and stability checks.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Number of shells | N | – |
| Type of support at start of shell Gap | La | – |
| Outside diameter | Da | mm |
| Wall thickness | sa | mm |
| Insulation thickness | ID | mm |
| Length | L | mm |
| Design pressure | P | bar |
| Type of support at end of shell Gap | La | – |
| Outside diameter | Da | mm |
| Wall thickness | sa | mm |
| Insulation thickness | ID | mm |
| Length | L | mm |
| Design pressure | P | bar |
| Type of support at end of shell Gap | La | – |
| Outside diameter | Da | mm |
| Wall thickness | sa | mm |
| Insulation thickness | ID | mm |
| Length | L | mm |
| Design pressure | P | bar |
| Type of support at end of shell Gap | La | – |
| Outside diameter | Da | mm |
| Wall thickness | sa | mm |
| Insulation thickness | ID | mm |
| Length | L | mm |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Start | 1 | N |
| End | Schusses | N |
| Start | 1 | Nm |
| End | Schusses | Nm |
| Start | 1 | mm |
| End | Schusses | mm |
| Start | 1 | N/mm² |
| End | Schusses | N/mm² |
| Start | 2 | N |
| End | Schusses | N |
| Start | 2 | Nm |
| End | Schusses | Nm |
| Start | 2 | mm |
| End | Schusses | mm |
| Start | 2 | N/mm² |
| End | Schusses | N/mm² |
| Start | 3 | N |
| End | Schusses | N |
| Start | 3 | Nm |
| End | Schusses | Nm |
| Start | 3 | mm |
| End | Schusses | mm |
| Start | 3 | N/mm² |
| End | Schusses | N/mm² |
Frequently asked questions
Why is the vessel divided into individual courses instead of being analysed as a single beam?
Tall vessels usually have stepped wall thicknesses, changing diameters and locally applied additional forces. A course-by-course calculation delivers the internal forces exactly at the locations where the cross-section or loading changes – these are the governing verification sections, which an analysis with a constant equivalent cross-section cannot capture.
What role does the insulation thickness play in the structural analysis?
The insulation increases the effective wind-exposed diameter and thus the wind load per metre of height; in addition, it increases the dead weight. Both enter the bending moments over the height of the vessel. The insulation, however, contributes nothing to the stiffness or strength of the shell.
What does the gap in the support type mean?
A support with a gap only transmits forces once the deformation has bridged the gap. Whether an intermediate support carries load or not can significantly change the bending moment distribution – which is why the gap is recorded explicitly for each support location and should match the actual installed conditions.
Does this calculation replace the strength verification to the pressure vessel code?
No. The module delivers the load side – weight, wind and additional loads plus the resulting internal forces. The actual verification of the wall thicknesses against internal pressure, longitudinal stresses and buckling is subsequently performed with the relevant code modules (e.g. the German AD 2000 code or EN 13445).