PSI - Issue 44

Gianluca Salamida et al. / Procedia Structural Integrity 44 (2023) 139–146 Gianluca Salamida et al. / Structural Integrity Procedia 00 (2022) 000–000

142

4

4. Analysis methodology

The Structural response of the building under investigation was studied through non-linear static analyses, using the software OpenSees. Capacity curves, i.e. the relationships between the total base shear and the displacement at the roof were computed for both the X and Y directions. Pushover analyses were carried out considering different distributions of horizontal force: storey masses proportional distribution and a first mode proportional distribution. Five capacity levels were defined, corresponding to the achievement of five Damage States (DSs), according to the EMS-98 European Macro-seismic Scale, proposed by Grünthal (1998). In the numerical model, these thresholds level were defined as: i) DS1 (slight damage) - corresponds to the first cracking condition of masonry infills; ii) DS2 (moderate damage) - corresponds to the first condition to occur between the yielding of the RC elements and the reaching of the peak strength in the infills; iii) DS3 (heavy damage) - is reached as a plastic hinge of the frame exceeds 3/4 of the ultimate rotation capacity, or when the infills strength reaches the residual value; iv) DS4 (very heavy damage) - corresponds to a resisting moment degradation in the columns of 20% with respect to the peak resistance; v) DS5 (collapse) - is reached when the base shear falls below 20% of the maximum strength associated with the bare frame. An example of capacity curve for the building under consideration is shown in Fig. 1 in which the considerable loss of stiffness and strength resulting from the infills failure can be seen. Results show that DS2 is predominantly characterized by the infills failure (reaching peak strength) while DS3 is mainly governed by RC members behaviour.

Fig. 1. Example of capacity curve for X direction and force profile proportional to storey masses.

4.1. Displacement demand

Given the capacity curve of a structure, the displacement demand associated with a certain IM is generally evaluated using simplified approaches, like the IN2 method, specifically developed for systems with significant strength degradation, as described by Dol š ek and Fajfar (2005). This method involves the definition of an equivalent SDoF system and the use of a specific R-µ-T relationship proposed by Dol š ek and Fajfar (2004). Simplified approaches, however, although widely used, are unable to capture the possible effects of ground shaking with particular characteristics and limit the IMs that can be used. In this regard, in the present study the displacement demand of the structure was evaluated by means of non-linear dynamic analyses on the equivalent SDoF systems associated with the building, considering recorded accelerograms. These analyses were performed using OpenSees. Pushover curves were linearized taking into account the degrading behaviour of the structure and the parameters of the equivalent SDoF systems were obtained. Based on the model proposed by Dol š ek and Fajfar (2004), a one dimensional model incorporating the characteristics of the RC frame and masonry infills was defined. This system consists of a mass connected to a fixed point by a series of springs representing the RC frame and masonry infills. The overall system backbone curve is such that it corresponds to the capacity curve associated to the equivalent SDoF system. For the spring associated to RC frame, Takeda's hysteretic rules were adopted, assuming an unloading stiffness