Issue 51

M. Guadagnuolo et alii, Frattura ed Integrità Strutturale, 51 (2020) 398-409; DOI: 10.3221/IGF-ESIS.51.29 403 , * SLV e SLV q F s e M    (6) q is the behavior factor, SLV F is the lower building shear strength, * e is the mass fraction participant to the first mode of vibration and M is the total seismic mass. The procedure used, in the case in which the mode of collapse is not defined with precision, allows us to assume a triangular modal shape, corresponding to the following values for the mass fraction participant on the first mode and for the coefficient that defines the force at the i-th plane: * 0,75 0, 75 0, 25 e N    (7) The capacity models assumed for the analyzed structures are subject to shear failure at each level [32, 33]. The shear strength of the building is the lowest among those evaluated in two main direction. , , yi yi yi yi di xi xi xi xi di SLV xi SLV yi xi i yi i A A F F               (8) xi A and yi A are shear resistant areas of the i-th floor walls according respectively to x and y direction; xi  and yi  are plan irregularity factors related to the i-th floor; xi  and yi  are coefficients considering, at the i-th floor, the stiffness and strength homogeneity of masonry walls according respectively to x and y direction. The failure mechanisms considered are that expected in masonry walls (Fig. 9): collapse of piers due to shear or bending forces, also depending on the strength of the spandrel beams [14, 34]. In masonry piers, the coefficients of failure mechanisms xi  and yi  assume value of 1 in the case of shear failure and 0.8 in the case of eccentric axial force failure; the coefficients related to the spandrel beams resistance  xi and  yi assume values 1.0 in the case of strong spandrel beams and 0.8 and in the case of weak spandrel beams. Figure 9 : In-plane failure modes of masonry piers subjected to eccentric axial force: (a) flexural, (b) shear diagonal cracking. The coefficients xi  and yi  are related to the spandrel resistance of the i-th floor masonry walls: their values are 1.0 in case of strong spandrel and 0.8 and in case of weak spandrel, while di  is the design value of the masonry piers shear strength at the i-th floor, defined as: 0 0 1 1.5   i di i       (9) where 0 i  is the design shear strength of masonry and 0 i  is the average normal stress on walls at the i-th floor. In the preliminary analysis the structure is examined in its actual state before the intervention, identifying the deficiencies and the seismic level at which the limit state of the collapse mechanism activation is achieved. The reference peak ground accelerations are computed using the following seismic parameters: