PSI - Issue 44

Sara S. Lucchini et al. / Procedia Structural Integrity 44 (2023) 2286–2293 Lucchini et al. / Structural Integrity Procedia 00 (2022) 000–000

2287

2

1. Introduction Retrofitting or repairing existing masonry building represents one of the main challenges of structural engineering that has involved several research studies worldwide. Among the different techniques available in the literature to improve the in-plane resistance of Un-Reinforced Masonry (URM) elements, particular attention has been recently devoted to the development of techniques based on the use of reinforced coatings such as those adopting Engineered Cementitious Composites (ECC) (Lin et al. 2014), Fiber Reinforced Cementitious Mortar (FRCM) (Giaretton et al. 2018) and Steel Fiber Reinforced Mortar (SFRM) (Sevil et al. 2011; Lucchini et al.2021). The latter is the subject of the present research. Since the studies focusing on masonry retrofitted with SFRM coting are still limited, the complete understanding of the resisting mechanisms affecting the flexural and shear behavior of retrofitted walls is still far to be fully achieved. The application of this technique to real existing buildings is still far from an extensive and widespread use. Some structural codes, such as the Italian standard NTC (2018), have introduced, in the recent past years, design recommendations concerning steel fiber reinforced cementitious materials for structural use. Based on the practically oriented analytical model described by the Authors in the technical report DPC-ReLUIS 2019 21:WP14, the present work reports some case studies aiming at determining the in-plane capacity of masonry building strengthened with SFRM coating. The validation of the model prediction is based on the comparison with the experimental results obtained from a full-scale building tested at the University of Brescia and with the finite element (FE) analysis of a real two-story residential building. As discussed in detail in the technical report DPC-ReLUIS 2019-21:WP14, the shear failure of coating may be governed either by the formation of diagonal shear cracks (V R,t ) or by the attainment of the shear resistance along potential sliding sections (V R,s ). The weakest of these mechanisms governs the total shear resistance (V R ) of masonry. Diagonal shear resistance Assuming the perfect bond condition between masonry and SFRM coating, the total in-plane diagonal shear capacity of reinforced masonry (V R,t ) is obtained by adding the two resisting components and assuming the upper limit V R,max as the shear force causing diagonal crushing of masonry: V R,t =min(V t,m +V t,coat ; V R,max ) ; V R,max =0.25∙k∙f m ∙ ( t m +n∙t coat ) ∙z (1) where k≥1 is a factor considering the increase of masonry compressive strength after retrofitting; f m is the compressive strength of URM; t m and t coat are respectively the thickness of masonry and of the single SFRM coating layer; n=1,2 is the number of coating layers and z is the lever arm between compression and tensile forces. The capacity of URM (V t,m ) can be calculated by the traditional equation proposed by Turnšek and Cačovic: V t,m =L∙t m ∙ 1.5 τ 0 b ∙  1+ σ 0 1.5 τ 0 with σ 0 =N/(L·t m ) (2) where L is the wall length; N is the axial load; b=h/L is a factor lower than 1 and higher than 1.5; τ 0 is the shear strength of URM from diagonal tension test. The shear resistance of coating (V t,coat ) can be calculated as follows: V t,coat =m∙f Ft ∙nt coat ∙ h 2∙sin 2 (θ) (3) where m=[1;(2·L/h-1)] is a redundancy factor; h is the height of the wall; f Ft =max(0.9·f ct ;f Ft-0.25 ) is the residual tensile strength of SFRM; f ct is the tensile strength corresponding to first cracking; f Ft-0.25 is the residual tensile strength corresponding to a crack width of 0.25 mm and θ is the average slope of the struts: 2. Analytical model 2.1. Shear resistance