PSI - Issue 44

P. Sorrentino et al. / Procedia Structural Integrity 44 (2023) 1656–1663 P. Sorrentino et al./ Structural Integrity Procedia 00 (2022) 000 – 000

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1. Introduction Nowadays, the evaluation of seismic safety of historical buildings and the retrofitting design still deserve attention from the international scientific community, due to wide heritage of existing masonry buildings. In fact, the historical buildings were constructed according to ancient rules of art, without performing any explicit structural analysis. Furthermore, the assessment of masonry structures is a complex task due to the anisotropic and non homogeneous material properties, as well as frequent modifications of the static scheme, occurring over the centuries because of e.g. elevations, openings in the bearing walls. In this regard, the Italian technical code explicitly requires the evaluation of the structural safety, that must be included in the structural report with the safety level achieved through the retrofitting and/or the possible limitations to be imposed for the building use. For these assessments, the Italian technical code recommends the use of linear, non-linear kinematic, and pushover analysis. In the framework of limit analysis approach, several studies have been conducted by the authors (Brandonisio et al., 2015; Brandonisio et al., 2017; Brandonisio and De Luca, 2019; Brandonisio et al., 2020; Brandonisio and De Luca, 2021). In this paper a simple expression for predicting the horizontal capacity of multistorey unreinforced masonry frames only depending on geometrical parameters and external loads is proposed, extending the results already obtained regarding the single span portal. In the previous studies on the single portal frame conducted by the authors (Giordano et al., 2005) a simplified expression to predict the horizontal capacity (1) was proposed: = 2 ℎ (1 + ) (0.50 + ) (1) where: F/W tot is the collapse multiplier; The formula defines the collapse multiplier as a function of three factors that mainly influenced the failure modes: the first term represents the pier overturning load; the second one the stabilizing effect of the beam weight; the third one the opening percentage effect. It was used to perform an extensive parametric analysis on 80 structural schemes characterized by varying geometrical proportions, providing excellent results, with less than 6% scatters. 2. Proposal of a simple formula The application of Limit Analysis to single portal frames can be extended to generic walls. The global collapse mechanism has been hypothesized as generally it provides the smaller value of load multiplier and a proportional to mass distribution of forces has been considered. To draw the kinematic chain the following assumptions have been done: • the piers have the same angle of rotation with respect to the hinges at the base; as consequence there is a geometrical compenetration in the zone that mutually rotate in the deformed shape. This hypothesis also is on the basis of the methodology adopted by Como and Grimaldi (1983). • as the facades are characterized by low values of the A spandrel /A tot ratio, variable in the range 10%-16%, the contribution of the spandrels to horizontal capacity is neglected and the spandrels are considered as a pendulum without weight. For n bays, the proposed simple formula, i.e. the expression of the collapse multiplier for the considered mechanism, derives from the application of the principle of virtual work and is defined as follows: = = ∑ =1 2 ∑ =1 2 1 (2) where: H eq is the height of application of the resultant of the horizontal forces and is equal to: B is the pier width; h is the pier height; W b is the weight of the beam; W tot is the total weight of the portal; D is the length of two piers with the central opening.