Issue 43

P. Zampieri et alii, Frattura ed Integrità Strutturale, 43 (2018) 182-190; DOI: 10.3221/IGF-ESIS.43.14 188 It is interesting to observe from the graph in Fig. 9a that up to a displacement d k equal to approximately eighty percent of the final displacement, the hinges remain unchanged in the final configuration. Their positions in fact change in a range of displacements d k between eighty and ninety percent of the collapse displacement. Fig. 9b shows the curve that correlates the displacement d k with the reaction force R α ,k , which increases continually and exponentially up to the maximum displacement, at which point the tangent of the curve is vertical. It is also important to note that the final displacement obtained from limit analysis is 14.7% higher than the displacement seen in experimental testing (dotted line in Fig. 9b). If the intrinsic geometric irregularities of real arches were able to be taken into account in the calculation procedure developed, the final displacement (in limit analysis) would most likely be closer to the value obtained in experimental testing. Figure 9 : a) Position of hinges as a function of d k b) Capacity curve. C ONCLUSIONS his paper examines the behaviour of a masonry arch subjected to settlement along a direction α. The innovation of this paper lies in analyzing collapse mechanisms for the horizontal settlement condition, despite what other studies have already considered. Other previous studies about horizontal settlement only led to a mechanism classification introducing a FEM simulation analysis. This paper investigates on a different configuration, comparing the simulation in terms of limit analysis and implementing the possibility of a varying collapse mechanism configuration. Using the method of equilibrium limit analysis with the hypothesis of significant displacements, an algorithm is proposed that uses PVW. The purpose was to analyse the thrust line and to identify the different positions of collapse hinges occured on the arch, from the initial configuration corresponding to null displacement of the stringing, up to the final collapse configuration. A real arch was built to conduct an experimental test by subjecting it to springing settlement along an inclined direction of 45° until collapse. As the value of imposed displacement was increased, the various configurations of the deformed arch were continuously recorded. The results of the experimental test confirmed the reliability of the structural model developed. However, there were discrepancies in the position of the cracking hinges under displacement. Such discrepancies can be attributed to the geometrical irregularities of the arch and the inherent uncertainties in real structures. In conclusion, as Fig.8 shows, the limit analysis induces the development of an additional crack at joint 6 in the fourth collapse configuration contrary to what the experimental evidence shows, where the position of hinges is preserved for the same configuration. As Fig. 9 shows, in the limit analysis the last displacement of the springing results greater compared to experimental response. This is considered to be due to the fact that the cracks n 1 and n 2 are located between a different and greater number of voussoirs compared to real case. Therefore, the alignment of the three hinges is verified in conjunction with a greater last displacement. As already stated, this discrepancy can be reduced introducing an inherent uncertainties factor. T