Differences in the Determination of Seismic Loads for Pressure Vessels and Pipelines According to EC8

Why are different seismic acceleration values used for horizontal pressure vessels and pipelines?

Why one seismic acceleration for all components is often too conservative

Employees at IBL and LES GmbH are frequently asked why they use different seismic accelerations in seismic analyses for pressure vessels and piping, even though these are located within the same plant, while other companies often use a uniform horizontal equivalent acceleration in the seismic design of plant components.

The main reason lies not in the ground acceleration itself, but in the dynamic behavior of the components. Piping and horizontal pressure vessels differ in their natural frequencies and thus in their dominant vibration periods. It is precisely this period that determines which value from the design spectrum should be applied.

Key point: Pipelines, with their characteristic periods, often fall within the plateau region of the design spectrum. Horizontal pressure vessels, on the other hand, are generally much stiffer and often fall within the short-period initial region of the spectrum. It follows that the design seismic acceleration for vessels can be significantly lower than the plateau acceleration assumed for pipelines.

1- Piping is usually flexible; pressure vessels are usually stiff

Horizontal piping systems normally have significantly lower natural frequencies than pressure vessels. Long pipe runs, expansion loops, offsets, guides, sliding supports and elastic restraints often result in governing natural frequencies of only a few hertz.

A typical order of magnitude is:

fpiping ≈ 1 … 10 Hz

The corresponding vibration periods are:

T = 1/f ≈ 0,1 … 1,0 s

Horizontal pressure vessels on saddles, in contrast, are compact and relatively stiff structural systems. The mass is concentrated, the span is usually small compared with the shell stiffness, and the global horizontal displacement is limited. Their natural frequencies are therefore often much higher.

A typical order of magnitude is:

fvessel ≈ 15 … 50 Hz
Tvessel ≈ 0,02 … 0,07 s

As a consequence, piping systems often fall within the plateau region of the design response spectrum, while horizontal pressure vessels are often located at the very beginning of the spectrum.

2 – The design response spectrum is not constant

The horizontal design response spectrum first increases in the short-period range and reaches its plateau only after the corner period T_B. In simplified form, the initial branch may be written as:

Sd(T) = ag · S · [ 2/3 + T/TB · (2,5/q − 2/3) ]

For the plateau range, the acceleration is approximately:

Sd(T) = ag · S · 2,5/q

For non-dissipative design of plant components, a behaviour factor of q = 1.0 is often used. The plateau value then becomes:

Sd,Plateau = 2,5 · ag · S

At the beginning of the spectrum, however, the spectral acceleration is considerably lower. At T = 0, the above spectrum gives:

Sd(0) = 2/3 · ag · S

This is only about 27% of the plateau acceleration.

3 – Example

Assume:

TB = 0,10 s, q = 1,0

A pipe with a natural frequency of 3 Hz has a vibration period of::

T = 1/3 = 0,33 s

It is therefore typically located in the plateau region of the response spectrum. The applicable spectral acceleration is then:

Sd = 2,5 · ag · S

In comparison, a horizontal vessel with a natural frequency of 25 Hz has:

T = 1/25 = 0,04 s

It is still located in the increasing initial branch of the spectrum. For T_B = 0.10 s and q = 1.0.
This gives approximately:

Sd(0,04) = ag · S · [ 2/3 + 0,04/0,10 · (2,5 − 2/3) ]
Sd(0,04) ≈ 1,40 · ag · S

Compared with the plateau value:

1,40 / 2,50 ≈ 0,56

In this example, the pressure vessel would therefore be designed with only about 56% of the plateau acceleration.
If, however, the plateau acceleration is applied across the board, this results in correspondingly higher horizontal inertial forces, greater saddle forces, and often excessive local shell stresses in the support area, which must be compensated for by increasing the thickness of the shell and/or saddle plates.

4 -Consequence for design

For piping systems, it generally makes sense to use plateau acceleration because, based on the experience of the staff at LES GmbH and the IBL, their dominant natural modes are usually in the range of the maximum spectral value. While using the maximum equivalent acceleration within the plateau region may still be a conservative approach, the potential savings from conducting additional vibration analyses to determine the natural frequencies are generally relatively small. Furthermore, the natural frequencies depend heavily on the support concept and the stiffnesses of the supports, the vessel, and the pipe ends, and would therefore need to be re-evaluated each time there are changes to the support concept and/or the pipeline route.

For horizontal pressure vessels, however, the same approach may be unnecessarily conservative. A stiff vessel with a very short vibration period behaves closer to a quasi-rigid body following the ground motion. Its seismic inertia load should therefore not automatically be based on the plateau acceleration, but on the spectral acceleration corresponding to its actual natural period.

The horizontal equivalent seismic force should therefore be evaluated as:

Fh = m · Sd(T)

and not automatically as:

Fh = m · Sd,plateau

Depending on the component, the natural period can be determined using a modal FEA, a simplified equivalent system, or a conservative estimate. It is crucial that the dynamic behavior of the specific component not be replaced by a generic plant acceleration if this would result in a spectral value that is clearly too high.

5 – Important engineering limitations

The argument above applies to the global horizontal vibration mode of a vessel on saddles or similar supports. It does not eliminate the need to consider local or system-related effects, such as:

• flexibility of saddles, steel support structures or foundations;
• local shell stresses in the saddle region;
• nozzle and piping interaction loads;
• elevated vessels or vessels on very flexible supporting structures;
• liquid sloshing in partly filled vessels.

If the vessel is installed on a flexible supporting structure, the relevant period is not only the vessel period itself, but the period of the coupled system consisting of vessel, supports and structure.
In this case, the relevant period may become significantly longer, and the spectral value must be recalculated accordingly.

6 – Conclusion

Anyone seeking to reduce material usage and manufacturing costs—and thus offer more cost-effective systems—should avoid analyzing piping and horizontal pressure vessels for seismic effects using the same maximum replacement acceleration during the basic engineering phase.

Pipelines are usually flexible. Their natural periods often fall within the plateau region of the design spectrum. Using the maximum acceleration within the plateau region is therefore, for most pipelines, an approximation that may be somewhat too conservative but reduces the computational effort.

Horizontal pressure vessels supported on saddles, on the other hand, are usually significantly stiffer. Their natural periods are therefore often at the beginning of the spectrum. The corresponding spectral acceleration can thus be significantly smaller than the maximum value in the plateau region.

A period-based determination of seismic acceleration therefore often leads to more realistic and cost-effective results for pressure vessels without compromising the safety of the design.