PSI - Issue 44

Luca Umberto Argiento et al. / Procedia Structural Integrity 44 (2023) 1388–1395 Luca Umberto Argiento et al. / Structural Integrity Procedia 00 (2022) 000 – 000

1390

3

considering a non-linear reduction of the frictional resistances due to the progressive detachment of the rocking façade from the sidewalls. The horizontal action is associated with the gravitational loads through a load factor,   which is related to the horizontal displacement of the centre of gravity of the façade, d CG , assumed as the control point. In particular, considering the generic kinematic configuration of the rocking wall, represented by the finite rotation  in Fig. 1c, the corresponding load factor  is derived from the application of the virtual work principle as: ( ) = ( )+2 ( ) ( ) (1) where: = ( + ) ; = ( + ) ; = −1 ( ℎ ) (2)

a)

b)

c)

Fig. 1. a) Geometric parameters of the block; b) geometric parameters of the façade; c) initial and varied configurations of the rocking façade.

Table 1. Geometric dimensions of the rocking façades

ID church SMC

Denomination of church

Height of façade H [m]

Length of façade L [m]

Thickness of façade s [m]

Thickness of sidewalls, s t [m]

λ f

λ s

λ l

S. Maria Buon Consiglio S. Maria della Pietà S. Antonio di Padova

12.00 10.15 10.65 7.60 8.40 9.50 14.00 8.50 13.00 10.24 7.40 7.20 13.25 9.00

7.60 9.10 9.60 9.10 8.00 7.50

0.91 0.80 0.93 0.80 0.60 0.80 0.85 0.80 1.05 0.90 0.60 0.50 1.00 0.60

0.60 0.80 0.86 0.80 0.75 0.80 0.85 0.80 0.85 0.90 0.60 0.50 0.70 0.60

13.2 20.0 8.4 12.7 12.7 11.4 11.5 12.4 10.3 14.0 11.2 13.3 11.9 11.9 9.4 16.5 16.5 12.9 10.6 10.6 15.0 12.4 15.3 14.3 11.4 11.4 10.8 12.3 12.3 11.7 14.4 14.4 13.0 13.3 18.9 10.5 15.0 15.0 22.3 9.5 9.5 11.4

SMP SAP SPB SRO SOC SFA SMA SD SFS SRE CA SG

S. Pasquale Bylon

S. Rocco

Congrega Assunta

S. Gaetano Soccorso

11.00 12.00 15.00 9.70 7.00 6.50 10.50 13.40

S. Francesco d’Assisi S. Michele Arcangelo

S. Domenico

S. Francesco Saverio

S. Restituta

SL

S. Lucia

In order to compare the capacity and demand for the following checks, it is necessary to convert the ‘ pushover curve ’,  ( d CG ), given by the model into the ‘ capacity curve ’, a ( d ), i.e., the acceleration vs. displacement curve, of an