Engineering task and calculation objective
This module calculates the seismic loads on vertical cylindrical process equipment per DIN 4149-1, the German earthquake design standard. Starting from the seismic zone, the horizontal acceleration is determined and processed via the type of structure, ground factor and reduction factor into the relevant (design) horizontal acceleration. For the cylinder, modeled as a cantilever, the calculation delivers the natural periods of the first three bending mode shapes and, as its result, the horizontal constraining load and the constraining moment at the vessel base.
In practice this verification is needed for columns, reactors and vessels in earthquake-prone regions: the seismic restraint moment competes with the wind load case for sizing the support skirt, anchor bolts and foundation, and it enters the strength and stability check of the vessel wall under supplementary loads. Whether a structure is to be classified as susceptible to vibrations is explicitly queried, since the applicable load level depends on it.
Note: DIN 4149 has since been withdrawn; seismic verifications for new structures are today carried out per DIN EN 1998-1 (Eurocode 8) with its national annex. For existing plants whose structural verification is based on DIN 4149-1, and for comparison calculations, the procedure remains relevant.
Standard and calculation basis: DIN 4149-1
Calculation workflow
- Define the seismic input quantities: The seismic zone of the site is taken from the zone map, and from it the horizontal acceleration. The type of structure (section 4 of the standard), the ground factor (section 7.2.2) and the reduction factor per Table 2 scale this value to the relevant horizontal acceleration.
- Set up the equivalent system of the equipment: The equipment is described as a fixed cantilever with cylinder diameter, wall thickness, cylinder length, total mass and modulus of elasticity. From these the module calculates the moment of inertia Iy of the tubular cross-section.
- Determine the natural periods: Via the oscillation parameter c, the natural periods T1, T2 and T3 of the first three bending mode shapes of the cantilever are determined; the eigenvalues lambda1 to lambda3 of the fixed-free beam enter as constants. The fundamental period T1 decides in which range of the response spectrum the equipment lies.
- Calculate equivalent loads and base internal forces: From the relevant horizontal acceleration and the mass distribution, the horizontal equivalent loads are obtained. The module sums them into the constraining load (shear force at the base) and the constraining moment — the input quantities for the anchorage, foundation and wall verifications.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Seismic zone (see graphic - F3) | Erdbebenzone | – |
| Ground factor (section 7.2.2) | κ = | – |
| Type of stucture (Section 4) | Bauwerksklasse | – |
| Horizontal acceleration | a0 = | m/s² |
| Relevant horizontal acceleration | cal a = | m/s² |
| Mass 1: G1 = | P1 = m1 = | kN |
| Mass 1: G1 = | P1 = m1 = | kN |
| Mass 2: G2 = | P2 = m2 = | kN |
| Mass 2: G2 = | P2 = m2 = | kN |
| Mass 3: G3 = | P3 = m3 = | kN |
| Mass 3: G3 = | P3 = m3 = | kN |
| Mass 4: G4 = | P4 = m4 = | kN |
| Mass 4: G4 = | P4 = m4 = | kN |
| Mass 5: G5 = | P5 = m5 = | kN |
| Mass 5: G5 = | P5 = m5 = | kN |
| Mass 6: G6 = | P6 = m6 = | kN |
| Mass 6: G6 = | P6 = m6 = | kN |
| Mass 7: G7 = | P7 = m7 = | kN |
| Mass 7: G7 = | P7 = m7 = | kN |
| Mass 8: G8 = | P8 = m8 = | kN |
| Mass 8: G8 = | P8 = m8 = | kN |
| Mass 1: G1 = | P1 = m1 = | kg |
| Mass 2: G2 = | P2 = m2 = | kg |
| Mass 3: G3 = | P3 = m3 = | kg |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| approximate procedure is | condition | – |
| Natural period of oscilation (Eq. 5) | T1 | s |
| Oscillation period T2 = T1*(lambda1/lambda2)2 | T2 | s |
| Oscillation period T3 = T1*(lambda1/lambda3)2 | T3 | s |
| Normalized response spectrum coeff. (Fig.2) | β = | – |
| Horizontallast | HE1 = | kN |
| Horizontallast | HE2 = | kN |
| Horizontallast | HE3 = | kN |
| Horizontallast | HE4 = | kN |
| Horizontallast | HE5 = | kN |
| Horizontallast | HE6 = | kN |
| Horizontallast | HE7 = | kN |
| Horizontallast | HE8 = | kN |
| Horizontallast | HE1,1 = HE1,2 = HE1,3 = | kN |
| Horizontallast | HE2,1 = HE2,2 = HE2,3 = | kN |
| Horizontallast | HE3,1 = HE3,2 = HE3,3 = | kN |
| Horizontallast | HE4,1 = HE4,2 = HE4,3 = | kN |
| Horizontallast | HE5,1 = HE5,2 = HE5,3 = | kN |
| Horizontallast | HE6,1 = HE6,2 = HE6,3 = | kN |
| Horizontallast | HE7,1 = HE7,2 = HE7,3 = | kN |
| Horizontallast | HE8,1 = HE8,2 = HE8,3 = | kN |
| Horizontallast | HE1,1 = HE1,2 = HE1,3 = | kN |
| Horizontallast | HE2,1 = HE2,2 = HE2,3 = | kN |
| Horizontallast | HE3,1 = HE3,2 = HE3,3 = | kN |
Frequently asked questions
When is a piece of equipment considered susceptible to vibrations?
The governing criterion is the ratio of the fundamental period T1 to the frequency content of the ground excitation. Slender, tall columns with large masses at the top have long natural periods and can be dynamically amplified by the earthquake; squat, stiff vessels behave quasi-rigidly and essentially experience the ground acceleration. The query in the module controls whether the simplified rigid approach or the vibration-based load level is used.
Is DIN 4149-1 still applicable?
DIN 4149 has been withdrawn and replaced by DIN EN 1998-1 (Eurocode 8) with its national annex; there, updated seismic zone and hazard maps and a behavior-factor-based response spectrum method apply. For new structures, Eurocode 8 must be used. Re-rating of existing equipment whose permit-relevant structural analysis is based on DIN 4149, plus plausibility comparisons, is the remaining field of application of this module.
Why are three natural periods calculated when the first one usually governs?
For slender structures, the fundamental mode contributes by far the largest share of the base internal forces. Higher modes can become relevant, however, when their periods fall into the plateau range of the response spectrum while the fundamental period already lies on the descending branch. Outputting T2 and T3 permits this check without having to carry out a full modal analysis.
How does the seismic load case relate to the wind load case?
Both generate a horizontal force and a bending moment at the restraint point and are not superimposed but treated as separate load cases; design is based on the less favorable one. For low, heavy equipment in higher seismic zones, the earthquake often dominates (mass-proportional); for tall, light columns with a large wind exposure area, the wind does.