# The Torsional Response of Civil Engineering Structures during Earthquake from an Observational Point of View

^{*}

## Abstract

**:**

## 1. Introduction

- rotations around the vertical axis (or torsion) due to the symmetric or asymmetric design of the building;
- rotations around the horizontal axis (or rocking) due to the inertial translational response of structures under earthquake loading, coupled with soil–structure interaction.

^{−6}μrad/s for a tele-seismic event) and the ability to record the uncoupled rotation [17]. The seismological community has been aware of the importance of this field for some time now. Over the past three decades, seismologists have invested in the observation and interpretation of the rotation components of the seismic wave field, thanks to the development of dense networks (among others [18,19,20,21]), and the emergence of new rotation sensors (e.g., [22,23,24,25,26,27]). These sensors have gradually become more sensitive and broadband to record earthquake-induced rotational ground motion in the near field and far field. Since the seminal numerical study of Bouchon and Aki [28] on ground motion rotation, this renewed interest has been encouraged by experimental observation and associated signal processing and inversion schemes. That includes new rotational and strain observables to improve our understanding of earthquake processes and the structure of the Earth’s crust [29]. Two monographs [30,31] have been published, several working groups have been formed [32,33], and special issues on rotation have been published in seismological and earth science journals [29,34,35]. In spite of their evocative titles, these special issues contain very few papers related to the field of earthquake engineering, even though all the authors argue the need for earthquake-resistant structures. A few examples of buildings instrumented with sensors allowing rotation analysis do exist, but they are still marginal. Similar to seismology, progress in instrument deployment in structures could provide new observations supported by the development of innovative signal processing methods to improve the understanding of rotational structural response. This may result in new perspectives to refine the principles and foundations of the rotational dynamics of structures, addressing the fields of earthquake engineering and Seismic Structural Health Monitoring (S

^{2}HM, [36,37]).

## 2. The Primary Origin of Torsional Motion in Buildings Linked to Static Eccentricity

_{s}to be taken into account by applying additional equivalent lateral forces at a distance e

_{s}from the centre of stiffness [4,42]. The resulting torque along the height of the structure, in addition to shear and overturning forces, has a direct effect on the peak ductility demand of the resisting elements and the maximum lateral floor displacement [43]. In his review, Rutenberg [4] also noted many conflicting conclusions in almost all referenced studies due to model dependence. This is also confirmed by Paulay’s works [44,45] related to (among others) the elastic/ductile building behaviour considered in earthquake code design. Rutenberg [4] concluded on the absence of experimental confirmation of the rotation and a lack of instrumentation.

## 3. Accidental Eccentricity

_{a}, which may be multiple and difficult to separate with any degree of precision. Modern codes (e.g., [7]) introduce design eccentricity e

_{d}, considering other terms in addition to static eccentricity, as follows:

_{a}is a general term to include any other source of eccentricity. The adjective “accidental” suggests that this eccentricity is the result of discrepancies between the design and the construction of the structure, implying that a building whose plane is nominally symmetric is in fact asymmetric to an unknown degree and undergoes torsional vibrations when subjected to pure translational ground motion. Accidental eccentricity is given as follows:

#### 3.1. Discrepancies between the Calculated and the Actual Values of the Stiffness and Mass of Structural Elements

#### 3.2. The Synchronised Orthogonal Components of Horizontal Ground Motion

#### 3.3. Rotation of Ground Motion at the Base

## 4. Experimental and Numerical Observation of Torsion

#### 4.1. Experimental Observation

#### 4.2. Numerical Observation

_{a}, Equation (2)) provided in codes (as suggested also by [105]). They also showed the strong influence of site conditions for symmetric and asymmetric designs, which are related to soil–structure interactions. When Ω increases (>1), the effect of torsion decreases.

#### 4.3. Array-Derived Rotation

^{2}HM.

## 5. Rotational Structural Response for a Wide Range of Earthquakes

#### 5.1. Data

^{−7}to 10

^{−3}.

^{-3}to 42.4cm/s and from 7.3 × 10

^{−3}to 159.6cm/s, respectively.

#### 5.2. Rotation Rate

_{8NE}), 8FE-8FS ($\theta $

_{8ES}), and 8FS-8FN ($\theta $

_{8SN}), and at the bottom BFN-BFE ($\theta $

_{BNE}), BFE-BFS ($\theta $

_{BES}), and BFS-BFN ($\theta $

_{BSN}), respectively. For example, at the top of the building, rotation rates were calculated as follows:

#### 5.3. Comparison of Rotations and Translations

^{2}and rotations in mrad/s. Without further information on the relations between rotations and translations, a function of the form y=ax+b is fitted to the data. At the bottom of the building (7a), the ratio between rotational rate and acceleration is 0.716 with a σ (standard deviation of the residues) value of 0.045, confirming a simple linear relationship. Compared with Takeo [132] and Liu et al. [25], who reported a ratio around 1 in free field, this ratio is lower. In our case, the rotation rate is calculated at the base of the foundations, with definite soil–structure interaction effects. Analysis of the inertial interaction of a structure with shallow embedded foundations is traditionally performed by imposing that the input motion of the foundations is simply that of the free field, thus neglecting the kinematic interaction generated by the travel of seismic waves. This leads to excessive conservatism, because it has been proved that free field motion can be completely filtered by the foundations. With rigid foundations, the kinematic effect is observed if the dimensions of the foundation are equal to or greater than the apparent wavelength in the frequency range of interest, showing reduced motion at the foundation with respect to the corresponding free field [133]. As a result of the high-frequency content of the rotation compared to the translation motion, the kinematic effect may also have bigger effects on rotational motion that could be explored in further analysis thanks to the design of the ANX array.

## 6. Conclusions and Perspectives

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Examples of operational modal building responses using ambient vibrations by Frequency Domain Decomposition. (

**a**) City-Hall building in Grenoble (France). (

**b**) Taipo Tower in Taipei (Taiwan). Singular value decomposition and examples of experimental mode shapes including torsion are given with resonance frequencies in translation and in torsion (in bold).

**Figure 3.**Schematic view of the ANX building and the positions of the sensors deployed at the top and bottom used in this study.

**Figure 4.**—Example of translational motion recorded during the 2011 Mw 9.0 Tohoku (Japan) earthquake and the array-derived rotational motion (

**a**) at the top and (

**b**) at the bottom of the ANX building.

**Figure 5.**Comparison of the array-derived rotational rate for the ANX earthquake dataset. (

**a**) at the bottom (the colour scale corresponds to the peak bottom acceleration (PBA) in cm/s

^{2}). (

**b**) at the top (the colour scale corresponds to the peak top acceleration (PTA) in cm/s

^{2}). X-label corresponds to the bottom or top rotation rate computed with Equations (6) and (7).

**Figure 6.**Attenuation of the rotation rate at the bottom of the ANX building with respect to the epicentral distance for several magnitude bins.

**Figure 7.**Comparison of the translational (cm/s

^{2}) and rotational rates (mrad/s) observed in the ANX building: (

**a**) at the bottom, (

**b**) at the top, (

**c**) comparison of bottom and top rotational rates. Thick lines correspond to a linear function (y = ax + b) fitted to the data. $\sigma $ is the standard deviation of the residual values (observed–predicted).

**Figure 8.**Fourier spectra of the rotational rate computed at the top of the structure. Bold line corresponds to the mean Fourier spectra of earthquakes with PBA < 6 cm/s

^{2}. Thin lines correspond to the +/− standard deviation Fourier spectra.

**Table 1.**Qualitative description of the torsion effects. LR, MR, HR: low-rise, mid-rise, high-rise building. CM: centre of mass. CR: centre of rigidity. e

_{s}: static eccentricity. e

_{d}: dynamic eccentricity. e

_{a}: accidental eccentricity. L: dimension perpendicular to the direction of the seismic motion. Ty: resonance period in translation. Ω: torsion-to-translation frequency ratio. Bldg: building.

Description | Building Features | Qualitative Effect | Refs. | |
---|---|---|---|---|

Static e_{s} −CM/CR Shift | asym | Max for Ty | [40,41] | |

Dynamic e_{d} − e_{d} =α e_{s} with α = 1.5 in EC8 | asym Ω = 1 | Amplification of e_{s} | [46,53] | |

Accidental e_{a} − e_{a} =βL with β = 0.05 to 0.10 in EC8 | CM/CR uncertainties | asym/sym | smaller than β value | [60,61] |

2D trans. ground motion | asym/sym | [61,62] | ||

Ground motion rotation | ||||

Differential trans. motion | asym/sym | strong when site effects | [64,65] | |

Rotational component | ||||

Bldg features consideration | ||||

MR-to-HR bldg | Ty > 0.5s | small | [60] | |

HR building | Ty > 1.5 s | strong (up to 20%) | [87] | |

sym/asym torsionally stiff bldg | Ω>1 | small | [107] | |

tall and torsionally stiff bldg | Ω > 1 all Ty | increase | [11] | |

tall asym. bldg | Ty < 1 | decrease | [11] | |

LR-to-MR, short period and torsionally flexible bldg | Ty < 1 s – Ω < 1 | more prevalent for sym. | [107] | |

LR-to-MR, short period and torsionally flexible bldg | Ty < 0.5 to 1s – Ω < 2/3 to 1 | strong | [60,105] | |

β consideration | ||||

LR-to-MR sym. bldg | Ty>0.2 | β = 0.05 significant | [60,108,109] | |

LR-to-MR, short period and torsionally flexible bldg | Ty < 0.3 – Ω < 2/3 | β > 0.05 for sym. bldg | [105,110] | |

torsionally stiff bldg | Ω > 1 all Ty | β < 0.05 | [107] | |

torsionally flexible bldg | Ω < 1 all Ty | β > 0.05 | [107] | |

asym. bldg | β = 0.05 conservative | [11] |

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Guéguen, P.; Astorga, A.
The Torsional Response of Civil Engineering Structures during Earthquake from an Observational Point of View. *Sensors* **2021**, *21*, 342.
https://doi.org/10.3390/s21020342

**AMA Style**

Guéguen P, Astorga A.
The Torsional Response of Civil Engineering Structures during Earthquake from an Observational Point of View. *Sensors*. 2021; 21(2):342.
https://doi.org/10.3390/s21020342

**Chicago/Turabian Style**

Guéguen, Philippe, and Ariana Astorga.
2021. "The Torsional Response of Civil Engineering Structures during Earthquake from an Observational Point of View" *Sensors* 21, no. 2: 342.
https://doi.org/10.3390/s21020342