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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2

Nomenclature f

rise of the arch L net span of the arch S thickness of the arch H Height of the higher abutment h Height of the lower abutment β Angle of development of the arch S Greater arch thickness S Smaller arch thickness β

Angle of development of the arch with thickness S Angle of development of the arch with thickness

β

1. Introduction Masonry bricks have been widely used around the world for the construction of buildings and infrastructures. The Roman Empire took profit to the high compressive strength that the material provide to design and built important buildings and bridges. Most of these buildings still exist and are now considered as cultural heritage for many countries. Since almost all the existing masonry constructions built very long time ago are now facing either higher load intensity or higher dynamic load that had not been taken into account, these structures are suffering important deterioration and damage. For this reason, studies on arches behaviour under static and or seismic loads are intensively done nowadays to understand the collapse mode of masonry structure and to propose solution for the retrofit of existing damaged structures. Limit analysis is considered as the simplest and basic method for seismic assessment of masonry arches. It provides excellent results that describe pretty well the arch structure even if it is based on simple structural calculation. The limit analysis has been firstly applied by Heyman [(1966), (1969)]; the method provides an effective tool to estimate the collapse load of structure through upper and lower bound of the horizontal capacity as presented by De Luca et al. (2004). Three assumptions defined by Heyman (1982) should be made when using the limit analysis: the masonry has an infinite compressive strength, the tensile strength of the masonry is neglected and sliding within masonry elements is not allowed. The masonry arch is then considered as the assembling of rigid elements maintained altogether by mutual pressure and the collapse occurs by the formation of sufficient non-dissipative hinges that transforms the structure into mechanism. Clemente (1998) is the first to provide an idea on the seismic behaviour of masonry arch. He used the limit analysis to evaluate the seismic acceleration and the position of the four plastic hinges developed on two different semi-circular arches. Raithel (1998) conducted parametric investigations on circular arches subjected to constant acceleration. He evaluated the thrust forces through successive iterations of the solution of the mechanism problem. The same work has been done on non-circular arches by Dimitri and Tornabene, (2015) and Cavalagli et al. (2016). Several studies describing the collapse mechanism of arch structures with slender abutments (Zampieri et al., 2015), assessing the seismic capacity of arch bridges and studying both the in-plane and out of plane mechanisms of arch bridges (Da Porto et al., 2016) have been done the last decade through limit analysis method. The influence of geometric uncertainty of the arches in the evaluation of the collapse multiplier of seismic loads have also been studied recently. Severini et al. (2018) performed a parametric analysis to study the effect of the irregularity from geometric point of view on the dynamic response of circular arch bridges. They found that the uncertainties on the arch geometry might reduce the seismic capacity of the arch. Paolo et al. (2016) studied through limit analysis the consequence that reduction of arches thickness can lead on the seismic capacity of masonry arches. According to the various studies using non-linear static and dynamic analysis done by Moazam et al. (2018) and Marefat et al. (2017), the dynamic behaviour of the arch structure observed during an earthquake event is well described by the non-linear dynamic analysis. Finally, an interesting work has been done by Paolo et al. (2017) to evaluate the effects of settlement springing on the collapse mechanisms of masonry arch while in 2018, the same author used the principle of virtual works to study the structural behaviour masonry arches under the effects of