5. Summary of results#
Comparison with CASTEM 2000:
The differences in the natural frequencies calculated with CASTEM 2000 and Aster are less than \(\text{1,4 \%}\). The dual mode has been separated into two close modes (6 and 7), one of which is a predominant mode along the \(y\) axis (mode 6) and the other along \(x\) (mode 7); the very high difference in effective modal masses (in \(\text{\%}\)) according to \(x\) for mode 6 and according to \(y\) for mode 7, is not relevant given the low weight of these directions in the modes considered.
The differences obtained on the calculation with the spectral method, for the displacements remain generally less than \(\text{8 \%}\), the differences in the reactions to the embedment of the columns B and E are generally less than \(\text{11 \%}\) (without taking into account the moment of reaction along z), and the differences in the generalized forces remain generally less than \(\text{7 \%}\) (without taking into account the moment of twisting).
Strong tolerances are allowed for certain calculated fields whose values are several orders of magnitude lower.
Comparison to SAMCEF :
The resolution method adopted in SAMCEF is based on the so-called earth node method. This method consists in linking all the nodes that are integral to the foundation to a single node. This node has a translational mass that is equal to 1000 times the mass of the structure. The displacements reported in the tables are not corrected for the effects of residual masses, which are results that are also available.
The differences in the natural frequencies calculated with SAMCEF and Aster are less than \(\text{3,2 \%}\). The type of shell element used (deformable or not deformable by shear force) influences the result, as does the fineness of the floor mesh. Differences in natural frequencies up to \(\text{10 \%}\) were observed by initially using a coarser mesh for the floors, consisting of 345 knots and 516 elements including 108 Timoshenko straight beam elements and 408 DKT shell elements. Modes 6 and 7 represent a dual mode whose percentage of effective modal mass does not exceed \(\text{4 \%}\) in the \(x\) direction and \(\text{2 \%}\) in the \(y\) direction.
The differences obtained on the calculation with the spectral method, for the displacements in the direction of the excitation remain generally less than \(\text{10,5 \%}\). For the reactions to the embedding of column \(B\), these differences are generally less than \(\text{30 \%}\). They reach \(\text{80 \%}\) for column \(E\), however for the reaction along the \(x\) axis and the moment along the \(y\) axis, they remain less than \(\text{18 \%}\). The torsional reaction of the columns is not zero. The differences in generalized efforts in the direction of arousal remain generally less than \(\text{26 \%}\). On the other hand, a different coupling between the directions of excitation introduces significant differences in the forces in the directions transverse to the excitation.
Strong tolerances are allowed for certain calculated fields whose values are several orders of magnitude lower.
Notes:
the form of the function describing the spectrum in motion depends strongly on the natural frequencies \({f}_{i}\) for which the displacement peaks are given. Consequently, a shift in the calculated natural frequencies disrupts the seismic response at the input of the data and does not allow an effective comparison of the calculations,
the results of generalized efforts are expressed in the local coordinate system of the beams and corrected for static effects.