Issue 46

L.U. Argiento et alii, Frattura ed Integrità Strutturale, 46 (2018) 226-239; DOI: 10.3221/IGF-ESIS.46.21 235 hinge from the base of the three-storey wall to the base of the top wall, even if the load multipliers corresponding to the three possible positions are very close to each other (  = 0.576, 0.578 and 0.582 from the top to the bottom, respectively). Variable Set Value  %  Var.  c (deg)  c /  b f 1 0.4 0.519 -10.84% 35.51 0.63 Ref 0.6 0.583 - 40.15 0.71 2 0.8 0.626 7.48% 43.34 0.77 p Ref 0 0.583 - 40.15 0.71 3 2 0.578 -0.75% 40.11 0.71 4 8 0.576 -1.20% 40.12 0.71 o 5 36 0.513 -11.94% 37.42 0.66 6 45 0.585 0.46% 40.16 0.71 Ref 60 0.583 - 40.15 0.71 t Ref 1 0.583 - 40.15 0.71 7 2 0.406 -30.30% 55.64 0.99 8 3 0.290 -50.15% 56.31 1 m Ref 1/3 0.583 - 40.15 0.71 9 1/2 0.451 -22.65% 35.12 0.78 10 1 0.252 -56.72% 26.57 1 Table 5 : Results of sensitivity analysis. A significant influence on the load factor, instead, is due to the wall shape ratio t . In fact, increasing value of t implies increasing slenderness of the wall and decreasing load factors  . In particular, assuming as a reference the load factor related to a square wall ( t = 1),  decreases by about 30% when t = 2 (Set 7) and by about 50% when t = 3 (Set 8). Moreover, it is worth noting that if the slenderness of the wall increases, the geometry of the mechanism changes significantly with respect to the case of square wall, because it results  c >  p , being in particular  p 2 <  c <  p 3 and  c >  p 3 for Sets 7 and 8, respectively. This circumstance can justify the drastic variation of the load factor when going from t =1 to t =2, while from t =2 to t =3 the decrement of the load factor is lower. Finally, Sets 9 and 10 reveal that also the variation of the unit shape ratio m has a relevant effect both on the load factor and the angle  c . In particular, with respect to the reference value related to m = 1/3, the load factor decreases by about 23% for m = 1/2 and by about 57% for m = 1. The same trend is also reported for the inclination angle of the crack line, that decreases with increasing values of m ; in particular when m = 1, it is  c =  b = tan -1 (1/2 m ) pointing out that in this case the frictional resistances are null and the mechanism involves only pure rocking. On the other hand, the increment of m implies the reduction of the overlapping length v of the unit blocks and as a consequence the reduction of the frictional resistances. Validation of the proposed model In this section the results provided by the proposed approach to the analysis of the in-plane rocking-sliding mechanism of a multi-storey masonry wall are compared and validated throughout the comparison with other models available in the literature, such as the micro-block model developed by Orduña [20] and the macro-block models proposed by Buhan and De Felice [29], Orduña [20] and Speranza [28]. The micro-block model, in particular, is here assumed as a reference to evaluate the macro-block models. The non-dimensional parameters accounted in the present analysis are those reported in Tab. 4, except for the friction coefficient which is not included in the analysis and is kept as f = 0.75 for all the sets. The different sets of values assumed