# Parametric Analysis of Rotational Effects in Seismic Design of Tall Structures
## 5 Detailed FEM Analyses
Further the following was made: (c1) Calculation of the standard seismic response \(M_{T}\) with consideration of only the translational components of the seismic excitation to calculate the amplitudes of the inertial forces (Equation (5)) at the six points along the height of the building (Table 2); (c2) Calculation of the expanded seismic response \(M_{R}\) considering the rotational components of ground motion (Equation (13)) combined with the standard actions of \(M_{T}\) according to (c1). The seismic effects were replaced by amplitudes of the quasi-static inertial forces, calculated in the case (c1) according to Equation (5). In the case (c2), a combination of the effects of forces according to Equation (5) and the effects of additional forces caused by the rotational components of ground motion according Equation (13) was calculated. From these forces, fictitious bending moments in the fixed end were calculated as the resulting seismic effects for comparison purposes. For the case (c1)  
\[\mathrm{M_{T}}=\sum\mathrm{h_{i}F_{i,u}} \tag{35}\]  
and for the case (c2)  
\[M_{R}=\sqrt{\left(\sum_{i}h_{i}F_{i,u}\right)^{2}+\left(\sum_{i}h_{i}F_{i,rot} \right)^{2}}. \tag{36}\]  
(d) Finally, the ratio of the response parameter was calculated from Equation (2)  
\[\Delta=\frac{\mathrm{M_{R}}}{\mathrm{M_{T}}} \tag{37}\]  
Figure 2 shows the influence of the response parameter \(\Delta\) for different structural types. The results of these complex calculations represent always only certain points identifiable by the height of the building \(H\). The above results show that the variables correspond with the curves for each type of construction and various soil conditions with sufficient accuracy. In Figure 2, the basic shape of the bending vibration is also displayed next to the scheme of the building or the chimney. In case (a), a frame + wall structural system is assumed. The pile foundations have been modeled too. The soil-structure interaction was simply assumed by Winkler's springs applied on the piles in both horizontal directions and on the foundation deck in vertical direction. Small irregularity in the plan has been considered. The total height of the building is 50 m. Three different soil categories (A, B and C) have been assumed. Both translational and rotational seismic inputs have been analyzed according to Eurocode 8, Part 6. It is easy to see that the results of the ratio of the total rocking moments (translational and rotational input) to the rocking moment, assuming translational input only, match well with the estimation factor \(\Delta\) for a height of 50 m. There is a small difference in the soil C result where estimation of \(\Delta\) reaches the value 1.23 and the value from SRSS analyses is 1.26. In case (c), the core structural system is assumed as a tall building with a total height of 280 m. In this case, a building with more irregularity in height is assumed. It is easy to see that the results of the ratio between the total rocking moments (translational and rotational input) to the rocking moment, assuming translational input only, match quite well with the estimation factor \(\Delta\) for height 280 m, especially for soil C.  
The study of irregularity in the plan and height needs to be analyzed in more detail in the future. It can be also stated from the analyses summarized in Figure 2 that the influence of the rotational component mainly depends on the soil category for tall buildings.