Response Spectrum Method for the Earthquake Check According to SIA 261

For any given beam or shell structure, the soil acceleration and the calculation coefficients are specified according to SIA 261 for the specified earthquake zone, foundation and structure class. For the check the reactions of the structure corresponding to the resonant frequencies are calculated and statistically superposed according to the response spectrum method. The resulting internal forces are available for further superposition with the static load cases and subsequent design.

To allow for the evaluation of the relevant modes of vibration, the program outputs the applied as well as the effective modal masses:

Sum of the applied masses (global)

                  Mx [t]      My [t]     Mz [t]
-----------------------------------------------
Dead weights:      0.000       0.000      0.000
Point masses:   1500.000     1500.000      0.000
-----------------------------------------------
Sum:         1500.000     1500.000      0.000

Effective modal masses (global)

Eigenmode    Mx eff [t]  My eff [t]  Mz eff [t]
------------------------------------------------
   1           935.135       0.000       0.000
   2             0.000     935.135       0.000
   3             0.000     287.137       0.000
   4           287.137       0.000       0.000
   5            98.544       0.168       0.000
   6             0.168     98.548       0.000
   7            47.342       3.197       0.000
   8             3.201      47.258       0.000
------------------------------------------------
Sum:         1371.526    1371.443       0.000

According to section 16.5.3.5 of the standard, the sum of the effective modal masses should be at least 90% of the total weight of the structure.

Example: 3D reinforced concrete frame

1st eigenmode	Corresponding internal forces My from the response spectrum
Statistically superposed internal forces My from all eigenmodes