Issue 51

G. Cocchetti et alii, Frattura ed Integrità Strutturale, 51 (2020) 356-375; DOI: 10.3221/IGF-ESIS.51.26 371 ( a ) ( b ) Figure 8 : Trends of characteristic parameters  , h at variable friction coefficient  , obtained by the analytical and numerical analyses: (a) inner hinge angular position  ; (b) non-dimensional horizontal thrust h . Reducing friction  sets a non-linear increase of angular position  of the inner hinge and a linear (for 2  =  ) decrease of non-dimensional horizontal thrust h . Then, at decreasing friction coefficient  , different masonry arch collapse modes have been located as follows (Figs. 1b-d, Tab. 3): • for  >  rm classical purely-rotational collapse (Fig. 1b), with five hinges in the symmetric configuration of the whole arch (one at the crown, two at the haunches and two at the shoulders); • for  ms <  <  rm mixed sliding-rotational collapse (Fig. 1c), with three hinges in the whole arch, one at the crown and two at the haunches, and with two sliding joints at the shoulders; • for  =  ms and  >  ms purely-sliding collapse (Fig. 1d), with four sliding joints in the whole arch, symmetrically placed at the shoulders and at the haunches (at an angle  s ≃ 30° differing from that  m (  ms ) ≃ 60° locating the last inner hinge position in the previous collapse mode at  =  ms ). At two transition instances  =  rm and  =  ms , 2-dof modes obtained as any linear combinations of the two adjacent 1-dof modes above become possible. The reducing friction range in which the newly (analytically) discovered mixed sliding-rotational mode occurs is quite narrow, with friction angles between near 22° and 17°. This result obviously holds true for the ideal case of perfectly holding shoulders (i.e. no abutment settlements). As a crucial feature, at decreasing friction coefficient  , horizontal