Issue 76

W. Hanini et alii, Fracture and Structural Integrity, 76 (2026) 183-211; DOI: 10.3221/IGF-ESIS.76.12

Figure 20: Recordings of the Boumerdes earthquake of May 21 st , 2003, at the Dar El Beida station, North-South component. The damping factor, ξ , is one of the most important parameters in a structure under seismic loading. Damping, in ordinary current structures, is mainly ensured by the deformation of the material (elastic and plastic phases), which dissipates the vibration energy, and by mechanical wave radiation through the medium. In general, structural damping is rarely considered in research studies on historic buildings, because their damping is often lower than that of modern buildings. This could underestimate the level of structural failure [29]. The Rayleigh method was used in this study. This method is a damping modeling technique in which the damping matrix (C) is a linear combination of the mass matrix (M) and stiffness matrix (K), as indicated by the following equation:

(4)

M K    

C

with  and  damping factors. The RE structures were modeled using Rayleigh damping factors, which were calculated first based on an overall damping factor of 4%, as determined by [23] for RE walls, and then on the results of modal analyses that take into account the natural frequencies of the main modes. These coefficients are calculated as follows:   2 i / i j j         (5)

  2 / i+ j     

(6)

where ξ is the damping ratio, which is assumed to be equal to 4% in the dynamic analysis, and ω i and ω j are angular vibration frequencies. Tab. 6, given below, summarizes the Rayleigh damping factors for the different structures under study.

Structure

Axis X

Axis Y

Damping factor ( α x)

Damping factor ( β x)

Damping factor ( α y)

Damping factor ( β y)

Structure 01 Structure 02 Structure 03 Structure 04 Structure 05 Structure 06

0.659 0.656 0.646

0.0021 0.0024 0.0025 0.0034 0.0018

0.6767 0.8678 0.4857 0.4413 0.5990 1.2500

0.0022 0.0017 0 .0033 0.0036 0.0023 0.0011

0.4570

0.880

1.0900 0.0012 Table 6: Rayleigh damping factors for the structures considered in this study.

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