Hi,
Equivalent viscous damping ratio is an indicator that is often used for the analysis of seismic performance of masonry walls.
Two definitions are frequently used (see attached figure) :
- Definition 1 (Priestley et al. 1996)
- Definition 2 (Magenes G, Calvi GM 1997)
Please, can someone explain the physical meaning and the difference between the two definitions?
Hello Khalil,
The common method for defining Equivalent viscous damping is to equate the energy dissipated in a vibration cycle of an actual structure and the energy dissipated by an equivalent viscous damper.
The energy dissipated in a vibration cycle of an actual structure will be the area under the hysteresis loop. Whereas, the energy dissipated by an equivalent viscous damper will be the area under the ellipse as shown in the attachment. In the attachment, I have assumed symmetrical behaviour in push and pull.
The concept of viscous damping is generally used to represent the energy dissipated by the structure in the elastic range. However, energy dissipated by the structure in the inelastic range have also been modeled as equivalent viscous damping in some research. That's why the definition varies.
Dear Khalil Naciri
Both are equivalent definitions with just changes in notation. If you look at the paper by Magenes and Calvi (1997), W_e (which you have denoted as E_inp), is in fact defined as the elastic energy at peak displacement (Page 1105). This is similar to that stated by Priestley et al. (1996).
If you are looking for a detailed discussion on equivalent viscous damping, you can refer any standard text book on structural dynamics (eg. Section 3 of the book "Dynamics of structures" by AK Chopra). You can also find a discussion in the book "Displacement based seismic design of structures" by Priestley, Calvi and Kowalsky.
Regards
Rohan
The dissipated energy in a cycle of an actual structure will be loop.
Dear Khalil Naciri,
There are no big differences in two approaches. The physical meaning is the dissipated (absorbed) energy due to the non-linear behavior of structures, conditioned (characterized) by the width of the hysteresis loop.
Prof. Dr. Mikayel Melkumyan
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