Issue 46

L.U. Argiento et alii, Frattura ed Integrità Strutturale, 46 (2018) 226-239; DOI: 10.3221/IGF-ESIS.46.21 234 Storey W Ai W Bi W Ci W Di Q i 1 1 1 n b hv  1 1 ( ) n L v hb    - - Lq 1 2 2 2 n b hv  2 2 2 ( ) ( ) c n n L v hb     * 2 2 2 3 tan c c n h b n     2 * 2 2 tan 2 c c n h b    Lq 2 3 3 3 n b hv  - -   2 * 3 3 tan 2 c c n h b    3 3 tan c n h q  Table 3 : Expressions of the external actions for three-storey masonry wall, when  p 2 <  c <  p 3 . S ENSITIVITY ANALYSIS AND VALIDATION OF THE PROPOSED MODEL Sensitivity analysis numerical analysis is here reported in order to test the sensitivity of the results obtained from the proposed model with respect to the main geometrical parameters, the overloading and the friction coefficient. The dimensionless definition of such parameters is reported in Tab. 4, together with their reference values. All the results of the numerical analysis of this and subsequent section have been obtained by using the SOLVER tool from Microsoft EXCEL to calculate the minimum of Eq. (10). Parameter Variable Definition Reference value Wall shape ratio t H / L 1 Unit shape ratio m h / l 1/3 Number of rows o H / h 60 Overloading ratio p q /( Hb  ) 0 Friction coefficient f f 0.6 Table 4 : Non-dimensional parameters accounted by numerical analysis. The sensitivity analysis has been performed by varying only one parameter at a time, while keeping the others as reference values. For each parameter, three values are considered as representative of most recurrent cases. The analyzed model is a three-storey wall, with constant inter-storey height and equal overloading condition at each level. In Tab. 5 the results in terms of load factor  and inclination angle  c of the crack line are reported, highlighting the percentage variation of  for each set with respect to that corresponding to the reference value of the same parameter. This table also reports the  c /  b ratio for each set which is useful to indicate the prevalence of a mechanism over the other; in fact, according to Eq. (8), when  c /  b → 1 F W → 0 and only rocking occurs, while when  c /  b → 0 F W → F and only sliding may take place. Overall, a relevant trend of the position of the rotational hinge emerges from the analysis. In fact, for all the accounted combinations of parameters, except for Set 4 only, the hinge is always located at the base vertex of the entire wall, defining a mechanism that always involves three levels. This also means that the load factor corresponding to such a position is always lower than those obtained if the hinge is located at the upper levels. Set 4 is the only case with the hinge at the base of the top level. Then, looking at the results related to Set 1 and 2 in Tab. 5, it arises that increasing friction coefficient implies the increment of the load factor and also of the inclination angle of the crack line with a bigger portion of the wall involved into the mechanism. The results related to the parameters p (Sets 3 and 4) and o (Sets 5 and 6), show that the variation of the overloading ratio and the number of rows are substantially irrelevant both on the load factor and the angle  c . However, as previously mentioned, the only effect observed for Set 4, corresponding to overloading ratio p = 8, is the shift of the position of the A