Issue 51

G. Cocchetti et alii, Frattura ed Integrità Strutturale, 51 (2020) 356-375; DOI: 10.3221/IGF-ESIS.51.26

Plots in Fig. 4a represent the variation of local slope t / n of the internal thrust (to the local joint normal) at variable half-opening  of upper portion AB, for fixed values of h ranging from 0.1 to 1, together with the maps of stationary points appearing in the t / n curves at variable h .

(a)

(b)

Figure 4 : Local slope t / n of non-dimensional shear/normal internal force components at variable  for the complete semi-circular arch (  =  /2): (a) curves for different values of non-dimensional horizontal thrust h , with stationary maps; (b) limit situations of collapse mode transition with sliding activation at  =  rm and  =  ms . Two main facts clearly appear from the inspection of Fig. 4a: absolute maxima of thrust slope are always attained at the shoulder (  =  =  /2); relative minima (maxima on negative side) occur at stationary points at intermediate locations 0 ≤  ≤ 0.5, at variable thrust 0 ≤ h ≤ 1. This shows, on one hand, that the first sliding joint, at decreasing  , should appear at the shoulder when t / n = +  , leading to:

cos sin sin cos     + −



(10)

= =



h h





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