Issue 46

L.U. Argiento et alii, Frattura ed Integrità Strutturale, 46 (2018) 226-239; DOI: 10.3221/IGF-ESIS.46.21

The external loadings together with internal frictional resistances and the coordinates of the relative application points are reported in Tab. 2.

Figure 4 : Representation of the external and internal actions involved in the rocking-sliding mechanism of a multi-storey masonry wall.

Thereafter, by applying the Principle of Virtual Work to the system of virtual displacements derived by the rotation around the hinge O of the macro-block identified by the crack line, the following expression of the load factor is obtained (Fig. 4):

N

N

N

N

N

N

N

1             1 1 1 1 1 1 Ai WAi Bi WBi Ci WCi Di WDi i Qi gi Fgi i i i i i i i N N N N N Ai WAi Bi WBi Ci WCi Di WDi i Qi W x W x W x W x Q x F y W y W y W y W y Q y                 

F y

qi Fqi



r 

(10)











i

i

i

i

i

1

1

1

1

1

This load factor, accounting for Eq. (9) is a function of the parameter tan  c mechanism; thus it can be minimized with respect to this parameter, with the following constraint:

which defines the geometry of the

v n h

 

tan tan c b  

(11)

It is worth noting that the minimization process has to take into account the circumstance that the position of the hinge can be located at the edge of each level of the multi-storey wall causing the onset of different mechanisms; thus the load factors related to all possible positions the of the hinge have to be compared in order to choose the minimum value

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