ONE-SIDED rocking analysis of corner mechanisms in masonry structures: Influence of geometry, energy dissipation, boundary conditions

Abstract

The corner mechanism in masonry structures is one of the out-of-plane modes that may frequently occur under dynamic actions such as earthquakes. The three dimensional motion, in principle complex to treat, can be simplified into a two-dimensional problem, where a prismatic equivalent block is associated to the corner mechanism. This paper provides a method to treat the corner mechanism in two dimensional rocking analysis, taking into account the roof actions -especially the roof thrust that acts as destabilizing force in the preliminary phases of motion -and the boundary conditions such as the transverse walls. A case study is taken as benchmark to perform rocking non-linear analyses and discuss the role of geometry, energy dissipation and boundary conditions. It is shown the relevant influence of the geometry and of the coefficient of restitution on the stability conditions, whenever the oscillation produce horizontal displacement values of some cm. The results of the case study, subjected to the Central Italy earthquake, are compared to the actual response of the corner mechanism, which collapsed during this seismic swarm, showing that the rocking analysis on the equivalent block correctly predicts the collapse occurred.

Nonlinear Static and Dynamic Analysis of Rocking Masonry Corners Using Rigid Macro-Block Modeling

“…The geometry of the rocking corner de¯ned by the nonlinear static analysis is assumed to be the same for the application of nonlinear dynamic analysis, with the aim of comparing the results of the two modeling approaches. This assumption was also validated through a parametric analysis performed by Giresini et al 21 Based on this geometry, the rocking analysis is performed by considering an equivalent prismatic block characterized by an equivalent radius vector R eq , between 3.41 m and 3.64 m and slenderness angle between 0.193 and 0.404 according to the rotation axis ( Table 1). The corresponding coe±cients of restitution, calculated according to Housner, 6 are between 0.77 and 0.95.…”

“…6(c)). 21 More in detail, when the rotation axis is X (Y ), only the sti®ness K 0 Y ðK 0 X Þ is considered. Again, the steel tie-rods, if present, can be considered with a spring of sti®ness K acting in the actual application point.…”

“…Seismic capacity for the three limit states LS0 (mechanism activation), LS1 (moderate rocking) and LS2 (near-collapse). 21 This is due to the fact that the e®ective length of the transverse wall in X direction is lower because of the presence of the opening. Moreover, null tension spring bed sti®ness is assumed in accordance with the non-activation of frictional resistances obtained by the static analysis.…”

“…[15][16][17] In particular, the corner failure involving a complex three-dimensional motion is still poorly investigated. In fact, although this kind of failure has frequently been observed in seismic scenarios, only few analytical works [18][19][20][21] and experimental investigation 22 devoted to it were found in the literature. Generally, it can occur when at least one corner of the building is free, without any adjacent structures, i.e.…”

Reinforced Concrete Slab Optimization with Simulated Annealing

“…This aspect is particularly relevant in structural retrofitting. Examples dealing with reinforced concrete structures under seismic loads are reported in [17,18], while masonry structure cases are reviewed in [19][20][21].…”