Engineering task and calculation objective
Module BEBEN determines the base fixing forces and fixing moments from seismic loads for regular structures to DIN EN 1998-1 (Eurocode 8) with the German National Annex, or to the predecessor standard DIN 4149. Typical applications in plant engineering are tower-like structures such as columns, stacks, silos and vessel support frames, whose base loading is needed for anchoring and foundation design.
To calculate seismic loads to Eurocode 8 means: from the seismic zone (horizontal ground acceleration), the ground and subsoil class, the importance factor and the soil parameter, the design spectrum is constructed; with the governing vibration period of the structure this yields the spectral value, and with the effective mass the total horizontal seismic force (base shear). The module distributes the equivalent static forces over the height of the structure — for uniform or variable mass distribution — and delivers the horizontal fixing force and the fixing moment at the base.
This provides the internal-force basis for the stability verification of process equipment and supporting structures in German seismic regions, for example as a load case for the anchoring calculation or for combination with wind loads.
Standard and calculation basis: DIN EN 1998-1 / Eurocode 8: 2010-12 / NA Deutschland
Calculation workflow
- Define site and structure parameters: The seismic zone yields the horizontal ground acceleration, and the ground and subsoil class yields the tabulated soil parameter; the importance factor captures the building category (e.g. increased requirements for plants handling hazardous substances).
- Determine the vibration period: The governing natural vibration period of the structure (T1, T2 or T3) is selected or determined; it decides in which branch of the response spectrum the structure lies.
- Evaluate the design spectrum: With the horizontal ground acceleration, the importance factor, the soil parameter and the behaviour factor, the spectral value of the design spectrum is calculated for the selected vibration period.
- Total seismic force and force distribution: The spectral value multiplied by the effective total mass yields the total horizontal seismic force. This is distributed over the height of the structure as an equivalent static load — proportional to mass and height ordinate, optionally for uniform or variable mass distribution.
- Fixing quantities at the base: The force distribution yields the horizontal fixing force and the fixing moment at the base of the structure as inputs for anchoring, foundation and stability verifications.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Building height (≤80m) | H | m |
| Vibration coefficient | Ct | – |
| Result: Vibration period | T1 = Ct·H^0.75 T1 | s |
| Outside diameter | D | mm |
| Wall thickness | t | mm |
| Cylinder length | Lz | m |
| Density (7850 unalloyed steels, 7760 Ferrite, 7930 kg/m3 Austenite) | ρ | kg/m^3 |
| Mass of the equivalent bar | mz | kg |
| Equally distributed additional weight (medium, additions, ...) | P | N |
| Total weight (for the selected method) | W | N |
| Modulus of elasticity | E | MPa |
| Moment of area | Iy = Pi·(D^4-(D-2t)^4)/64 Iy | m^4 |
| Vibration period | T2 = 2·Pi·Lz2/1.87512/c T2 | s |
| n- | T3 = 1.5· √[Lz/(3·E·I)+1/(Ck*If)]·∑(Wj·zj²) T3 | s |
| Earth quake zone (0-3) | Ez | - |
| Building ground class (Depth < 20m, A,B,C) | BK (A,B,C) | - |
| Geological underground class (Depth > 20m, R,S,T) | UK (R,S,T) | - |
| Building category (I, II, III, IV) | Cat (I - IV) | - |
| Condition for the simplified method: | TA = s, TB = s, TC = s, TD = s | s |
| Selected vibration period | Ts | s |
| Method for the basic vibration period, 1 = High buildings, 2 = Equivalent rod, 3 = Mueller/Keintzel n→∞ | Ei | - |
| Behavior coefficient (max=2 for steel cantilever) | q (q ≥ 1) | - |
| Amplification factor | β0 ≈ 2.5·√7/(2+D) ≥ 1.75 β0 | - |
| Correction factor (0.85, 1) | λ | - |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Total weight (for the selected method) | W | N |
| Horizontal acceleration | ag | m/s² |
| Building and underground class | Untergrundklasse | - |
| Importance factor | γI | - |
| Ground parameter acc. Tab. 4 | S | - |
| TA | TA = s, TB = s, TC = s, TD = s | s |
| TB | TA = s, TB = s, TC = s, TD = s | s |
| Condition for the simplified method: | TA = s, TB = s, TC = s, TD = s | s |
| TD | TA = s, TB = s, TC = s, TD = s | s |
| Selected vibration period | Ts | s |
| zulässig | zulässig | - |
| Rating spectrum | Sd | - |
| Horizontal clamping force | Fb = Sd·W/10·λ Fb | N |
| Clamping moment | M = ∑(Fj·zj) M | Nm |
| Selected building height | H4 | m |
| Grundschwingung | Grundschwingung | - |
| Plateau value of elastic response spectrum | Se,max | m/s² |
Worked example
For a regular, tower-like piece of process equipment (height 12 m, effective mass 60 t, uniformly distributed over the height), the total horizontal seismic force and the fixing moment at the base are to be determined — a worked example of the Eurocode 8 base shear calculation. The natural vibration period lies in the plateau region of the design spectrum.
Given values
| Design ground acceleration ag | 0.8 m/s² |
| Importance factor γI | 1.0 |
| Soil parameter S (subsoil condition B-R) | 1.25 |
| Behaviour factor q | 1.5 |
| Effective total mass m | 60,000 kg |
| Structure height h | 12 m |
| Correction factor λ | 1.0 |
Solution
Spectral value in the plateau region
In the plateau region (TB ≤ T1 ≤ TC) the design spectrum gives:
Sd(T1) = ag · γI · S · 2.5/q = 0.8 · 1.0 · 1.25 · 2.5/1.5 = 1.667 m/s²
Total seismic force
Fb = Sd(T1) · m · λ = 1.667 · 60,000 · 1.0 = 100,000 N = 100 kN
Fixing moment at the base
For uniform mass distribution and a height-proportional (linear) distribution of the equivalent forces, the resultant acts at 2/3 of the height:
M = Fb · (2/3) · h = 100 · 8.0 = 800 kNm
Result
| Spectral value Sd(T1) | 1.667 m/s² |
| Horizontal fixing force Fb | 100 kN |
| Fixing moment M | 800 kNm |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
For which structures does the simplified response spectrum method apply?
For regular structures whose behaviour is dominated by the fundamental mode — i.e. structures without major jumps in stiffness or mass over the height. For strongly irregular structures, or those with significant higher modes, Eurocode 8 requires the multimodal response spectrum method, which goes beyond the approach of this module.
What does the behaviour factor q do?
The behaviour factor reduces the elastic spectral values and thereby accounts for energy dissipation through the plastic deformation capacity of the structure. For steel structures in plants, q = 1.5 (limited ductile behaviour) is frequently assumed as a conservative value. A higher q-value presupposes ductility detailing rules and must not be used without complying with them.
Is DIN 4149 still applicable?
DIN 4149 has been superseded by DIN EN 1998-1 with the German National Annex, but remains relevant for re-assessing existing structures. The module supports both codes. Note that the current National Annex (with the revised seismic hazard maps) can yield different site values than the old seismic zones.
Why is the fixing moment usually more critical than the fixing force?
For slender, tower-like structures the equivalent forces act proportionally to height, so the resultant lies well above half the structure height. The base moment therefore grows more than proportionally with height and generally governs anchoring and foundation — the shear force is rarely design-relevant.