# Seismic dimensioning

## Our expertise

G-MET TECHNOLOGIES performs seismic design calculations for support structures such as metal frames or load-bearing structures. The design under seismic loading concerns the mechanical strength of the structural elements, their assemblies (welds, bolts) and their anchors to the civil engineering.

### Calculation methods :

There are several seismic design methods used in the industry, including:

- The simplified static analysis method consisting in applying uniformly acceleration at the peak of the spectrum to the structure. Depending on the type of structure, this method is not always conservative [1] .
- The spectral modal analysis method which consists in determining the eigen modes of the structure and then performing the spectral response by combining the eigen modes (SRSS or CQC for example).
- The transient analysis method, which, unlike the two previous ones, is concerned with the temporal response of the structure under the effect of seismic loading and not only with an estimate of the maximum forces induced. This method is much heavier in calculation.

[1] : Seismic computation – Non conservatism of the ‘peak’ calculation of the spectrum, Philippe MAUREL 2010.

The most commonly used method is the spectral modal analysis method. However, it is sometimes possible to use a simplified method which use less calculation time but still conservative according to the structure studied.

This method for determining the ESA (Equivalent Static Acceleration) to be applied for each direction of the direct orthonormal coordinate system is as follows:

- If the frequency of the first mode has not been determined or is lower than the peak frequency of the spectrum, the ESA is taken equal to “k” times the acceleration of the peak of the spectrum.
- If the frequency of the first mode is situated between the peak frequency and the cutoff frequency of the spectrum, the ESA is taken equal to “k” times the acceleration read on the spectrum at the frequency of the first mode.
- If the frequency of the first mode is located beyond the cutoff frequency, the ESA is taken equal to the cut-off acceleration of the spectrum.

The value of “k” being :

- For equipment that has only one mode of vibration in the amplification zone of the spectrum, k = 1.
- For others, k = 1.5. The use of the coefficient k = 1.5 on the peak value of the spectra makes it possible to cover a possible unfavorable accumulation of modal responses.

### Sizing criteria

The mechanical dimensioning criteria used by G-MET TECHNOLOGIES come from the recommendations of the EUROCODES, the RCC-M or other criteria specified by the customer.

The verification of the assemblies (welding, bolting, anchoring) is carried out thanks to the calculation of the mechanical torsor at gravity center of the assembly and the analytical dimensioning performed with dedicated Excel spreadsheets.

## Examples studies involving seismic dimensioning

### Seismic dimensioning of an experimental nuclear reactor (RJH) irradiation device

- Calculation of eigenfrequencies.
- Seismic dimensioning of structures and assemblies.
- Pseudo-static method.
- Calculations performed using ANSYS under Workbench environment.

### Seismic dimensioning of a storage hopper

- Seismic dimensioning of structures and assemblies.
- Pseudo-static method.
- Analytical sizing of bolted plates, welds and assemblies.
- Calculations performed using ANSYS under Workbench environment.

### Seismic dimensioning of metal frames cabinet supports

- Seismic dimensioning of structures and assemblies.
- Pseudo-static method.
- Analytical sizing of bolted plates, welds and assemblies.
- Calculations performed using ANSYS under Workbench environment.