PSI - Issue 44

2

Matteo Marra et al. / Structural Integrity Procedia 00 (2022) 000–000

Matteo Marra et al. / Procedia Structural Integrity 44 (2023) 1482–1489

1483

1. Introduction Fluid viscous dampers have already proven to be effective in the mitigation of the seismic effects in building structures [1,2]. However, their application is still limited. This is also due the lack of specific code indications and prescriptions. For instance, the Italian code (NTC 2018 [3]) does not explicitly consider damper systems. The normative point §7.10.4 deals only with isolation devices. The corresponding point §C.7.10.4 of the Circular [4] distinguishes between velocity-dependent dissipation devices and displacement-dependent devices, underlining the common goal of reducing deformations to contain damage and avoid collapse of the structure, and highlighting the importance of a preliminary analysis of the structure in the event that an intervention is carried out on an existing building. Nevertheless, the Circular does not suggest either pre-dimensioning/design formulas for the different types of dampers, or practical indications of how the ductile capacities of the existing structure could be taken into account. A simplified procedure called "direct five-step procedure" was developed for the design of viscous dampers to be placed in new buildings in the last years by some of the authors [5,6,7]. This design procedure, which must be then followed by appropriate verification of the seismic behaviour through non-linear dynamic analyses, consists of 5 steps and is based on a prefixed seismic performance, such as a target damping ratio. The procedure aims at the full definition of the mechanical characteristics of the commercial fluid viscous dampers characterized by the non-linear force velocity relationship ( ), and at the estimation of the maximum forces both in the dampers and in the structural elements (columns). In particular, it provides the following formula for estimating the damping coefficient, , for the commercial non-linear devices (assuming they are inserted according to the classical inter-storey placement and they are all equal to each other): (1) The procedure also recommends a minimum value for the axial stiffness of the device (fluid + support rod): (2) In the case of new buildings, the objective of sizing the viscous dampers in such a way as to keep the structural elements within the linear elastic range even for "rare" earthquakes of high intensity is easily achievable. In the case of existing buildings designed for vertical loads only, the introduction of a damper system is not generally sufficient to keep the structural elements in the elastic range. Thus, it might be necessary to accept local plastic excursion of the structural elements, by taking into account the ductility capacity (albeit probably limited) of the existing building (hysteretic dissipations associated with damage in beams and columns). In this paper the "direct five-step procedure for existing buildings" is introduced for the first time and an applicative example is carried out. NL F c v a = × NL c ( ) 1 1 visc 2 1 1 , 2 1 1 2 0.8 cos 2 1 cos e NL S T W N c T g n T N a h p x q p q - æ ö + æ ö = × × × × × × × × ç ÷ ç ÷ + è ø è ø 2 visc 2 1 2 1 1 10 cos axial W N k T g n p x q æ ö + æ ö ³ × × × × × ç ÷ ç ÷ è ø è ø

Nomenclature F

dissipative force developed by the fluid viscous damper damping coefficient of the non-linear damper damping exponent of the non-linear damper target damping ratio provided by the fluid viscous dampers velocity between the two damper ends

NL c

v

a = 0.15

visc x

fundamental period of the structure total seismic weight of the building gravity acceleration (9.81 m/s 2 )

T 1 W

g N n

total number of storeys of the building structure total number of dampers at each storey for each direction