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This section gives a brief overview of the seismic analysis features of SCIA Engineer. For more details, read also the chapter dedicated to seismic loading.
The response spectrum method is one of the most widely used methods for the seismic analysis of structures. It has many advantages on other methods:
The response spectrum method uses a modal superposition of the relevant eigenmodes of the structure. The method allows to calculate the magnitude of each mode, but not their phase shift. The values of phase shift actually depend on the real accelerogram that will be applied to the structure. As a response spectrum represents the envelope of a family of accelerograms, it is not possible to define unique values of phase shift for each mode: these variables are random.
This is where the concept of modal superposition comes in: various statistical techniques allow to determine envelope values which cover the real behaviour with a reasonable probability of occurrence.
The most widely used techniques are the SRSS (Square Root of Sum of Squares) and CQC (Complete Quadratic Combination).
These methods have the advantage of providing very easily design values of all results (displacements, internal forces…) without knowing the real phase shift values, but only part of the information is available:
The last point above is actually not entirely accurate, as probabilistic correlations can be established between results, but those techniques are currently not commonly used in practice and are beyond the scope of this document.
The loss of concomitance and sign of results is an issue typically when computing resulting forces in shear walls: it is not possible to compute a resultant from internal forces after modal superposition, as typically all raw results are positive.
Computing resultant forces in one of those shear walls would typically give near-zero moments and extremely overestimated axial forces.
To obtain usable values of resulting forces, a possibility is the so-called “signed results” method.
It consists of applying some signature scheme to raw results of the modal superposition. A classical approach uses the sign of the most significant eigenmode.
Applying this to shear walls, it is possible to “sign” the internal forces, making them suitable for computation of resulting forces:
The method of signed results might be seen as a workaround to obtain usable resulting forces. This method will be referred to as “calculation of resultants with modal pre-superposition”. It is convenient from a point of view of computation, because modal superposition needs to be done only once on all local results and the resultant can be computed directly from a unique set of results.
However, the rigorous method for computation of resultants in the context of the response spectrum method can be summarized as follows:
This method will be referred to as “calculation of resultants with modal post-superposition”.
When proceeding so, no result signature is necessary to obtain correct values of resulting forces. Moreover there are cases where the method described in the previous paragraph gives overestimated results of most result components and can therefore only be seen as an approximation. The method described here is clearly more robust and accurate.
As shown in the example below, structures with predominant torsional behaviour are especially sensitive to that phenomenon.
Important discrepancies can be seen on most resultant components when using the calculation of resulting forces from superposed signed results (up to 4 times the reference result).
On the other hand, all values obtained by modal superposition of resulting forces computed in each mode separately are very close to the reference model (max 6% difference).
| Forces at the bottom of the core | Fx | Fy | Fz | Mx | My | Mz |
|---|---|---|---|---|---|---|
| Resultant from results signed after superposition | 518 | 855 | 15 | 2509 | 2732 | 1691 |
| Modal superposition after resultant calculation | 249 | 198 | 26 | 1900 | 2394 | 1614 |
| Reference model (1D member) | 264 | 209 | 25 | 1911 | 2429 | 1640 |
SCIA Engineer offers all methods described above. All related settings are located in the properties of the seismic load case.
The signature of results can be enabled using the setting “Predominant mode”. The eigenmode to be used as reference for the signature can be selected automatically or manually.
Note that the automatic selection of the mode shape will select the mode which has the highest modal mass, regardless of the actual direction of the earthquake. This is most of the time correct for 2D models (2D frames) but often wrong for 3D models! For 3D models, it is highly recommended to select the mode shape manually.
Resultants can be calculated in two different ways: by pre-superposition or post-superposition (see above). The flowcharts below summarize the process for both methods. Note that although the post-superposition method might look much simpler than the pre-superposition method, actually all the part related to local results must be done anyway in order to provide local results for seismic load cases. It is not represented on the flowchart because it is irrelevant in this context.
In the current version of SCIA Engineer, the following result services use the pre-superposition method and their accuracy is therefore affected by the selection of an appropriate predominant mode for results signature:
The following result services use the post-superposition method: