PSI - Issue 11

Cyrille Denis Tetougueni et al. / Procedia Structural Integrity 11 (2018) 452–459 Tetougueni et al./ Structural Integrity Procedia 00 (2018) 000 – 000

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settlement in various direction. From different studies reviewed on the seismic behaviour of masonry arches, it is clear that very few works have been done to study the effect of the geometric irregularities on the seismic behaviour of arch structures. In order to give an insight of this subject, a parametric analysis has been done to study the influence of arch thickness and height abutment on the collapse mechanism and seismic capacity of arches. 2. Definition of Collapse multiplier In arch structures, the situation leading to the hinging mechanism of arch under arbitrary load is observed when a sufficient number of hinges able to transform the originally redundant structure into kinematical unstable structure is formed. The particular condition through which the mechanism is activated due to self-weight and a set of horizontal forces proportional to self-weight occurs in the case where the thrust line inside the arch thickness is tangent to the arch on four points (Misseri, 2017). The arch is then subdivided in three blocks as seen in Fig.1 due to the creation of four alternated hinges located in both intrados and extrados. In particular, five hinges should be necessary to create the mechanism of the arch in the case of symmetric arches structures under symmetric loads.

Fig. 1. Mechanism before collapse of a circular arch, (Clemente, 1998) Limit analysis have been carried out to find the multiplier of the horizontal loads leading to collapse mechanism. For that, the three Heyman’s hypothesis have been considered. The arch structure is made of n masonry elements as presented in Fig.2 that can not slide or interpenetrate each other, but can split into blocks that will rotated due to the formation of non-dissipative hinges. Under an appropriate reference system, the self-weight of the block is considered as the forces applied in the considered block centroid while the seismic action will be considered as × . The principle of virtual works is then applied to find the collapse load multiplier .

Fig. 2. Structural model of masonry arch

Therefore, the multiplier can be calculated by applying the Principle of Virtual Work to the virtual displacement