# Parametric Analysis of Rotational Effects in Seismic Design of Tall Structures
## 1 Introduction  
It is now generally accepted that, in order to properly assess the structural response, the seismic actions must include, besides the horizontal and vertical translational components, also the rotational components of ground motion [1]. The ground rotations about the horizontal axes, x and y, are usually named rocking, while the rotation about the vertical axis z is called torsion. Even a small contribution of rocking excitations around any horizontal axis may dominate the vibrations of a high slender building, which are additionally magnified by P-A effects. Many authors have contributed to the research on seismic rotational components (see, e.g., [1; 2; 3; 4; 5; 6]). New procedures were developed on how to describe this seismic ground motion and how to quantify its effects on the structural response (see, e.g., [7; 8; 9; 10; 11; 12; 13; 14]). The seismic rotational components can be deduced from:  
(a) Considerations of the seismic source and wave propagation. For example, [PERSON] [15; 16] uses a method of deconstructing the translational time series into body waves, which are in turn reassembled to generate rotational time series. A mathematical model based on a representation of soil impedance and contributions of body waves is presented in [17]. (b) Records of rotational ground motion. A simple yet effective technique is presented to explicitly recover the rotational motions from recorded horizontal accelerograms [18]. Much progress has been made with recent developments in rotation sensors, producing direct measurements that could be compared with theoretical expectations or used to predict the responses of structures [19]. (c) Code approximation. One of the first worldwide standards that codifies these actions is EN 1998-6 [20,21]. These effects have to be taken into account in the case of tall structures situated in regions of high seismicity. The rotational component is defined in this standard as a multiplier of the horizontal response spectra. This simplification depends upon the shear-wave velocity of the top 30 m of the ground and upon the soil compliance and not on the seismological parameters of the expected earthquake and its detailed wave propagation characteristics. It is now acknowledged that it depends also on the waves with higher phase velocities associated with the deeper ground layers [14]. These engineering code formulas should be calibrated and reconciled with the results of the latest empirical research on the rocking component of ground motion. The rocking response spectrum proposed in Eurocode 8 Part 6 for slender structures was compared with seismic time history response analyses of an R/C chimney, yielding its substantial conservatism compared with the time history response computations using real records of 6-DOF strong ground motion [10]. Time-history analyses with real measured seismic records are therefore very important for future calibrations of seismic design codes using response spectrum approach. Studies show, e.g., [13], that the contribution of rotational excitation effects in the response of slender towers is substantial and can be of the same order as horizontal excitations. The primary factors affecting the structural response are coupled translational and rotational motion, the frequency content of these components and their interaction with dynamic characteristics of the structure and soil [18]. The actual interaction of translational and rotational excitations in the structural response of a slender tower depends on the frequency contents and actual signs and directions of these two excitations. The proper proportion of horizontal-to-rotational intensity is crucial to properly assess the contribution of rotational effects in overall seismic structural vibrations [9]. According to some studies [10], the presence of seismic rotations about the horizontal axis sometimes increases the overall response (up to 30%), but sometimes it decreases the combined seismic response.