Free rocking response of a regular stone masonry wall with equivalent block approach: experimental and analytical evaluation

SUMMARYIn modern unreinforced masonry buildings with stiff RC slabs, walls of the top floor are most susceptible to out-of-plane failure. The out-of-plane response depends not only on the acceleration demand and wall geometry but also on the static and kinematic boundary conditions of the walls. This paper discusses the influence of these boundary conditions on the out-of-plane response through evaluation of shake table test results and numerical modelling. As a novum, it shows that the in-plane response of flanking elements, which are orthogonal to the wall whose out-of-plane response is studied, has a significant influence on the vertical restraint at the top of the walls. The most critical configuration exists if the flanking elements are unreinforced masonry walls that rock. In this case, the floor slabs can uplift, and the out-of-plane loadbearing walls loose the vertical restraint at the top. Numerical modelling confirms this experimentally observed behaviour and shows that slab uplift and the difference in base and top excitation have a strong influence on the out-of-plane response of the walls analysed.

Section: Sensitivity With Regard To the Assumed Block Roundingmentioning

confidence: 99%

Influence of boundary conditions on the out‐of‐plane response of brick masonry walls in buildings with RC slabs

Tondelli

Beyer

DeJong

2016

“…[9][10][11][12][13] The CR was largely adopted for the study of the dynamic behaviour of rigid blocks under trigonometric pulses [14][15][16] and earthquake excitations. [9][10][11][12][13] The CR was largely adopted for the study of the dynamic behaviour of rigid blocks under trigonometric pulses [14][15][16] and earthquake excitations.…”

Section: Introductionmentioning

confidence: 99%

Modelling rocking response via equivalent viscous damping

Tomassetti

Graziotti

Sorrentino

et al. 2019

Self Cite

Summary The assessment of the out‐of‐plane response of masonry structures has been largely investigated in literature assuming that walls respond as rigid or semi‐rigid bodies, and relevant equations of motion of single‐degree‐of‐freedom and multi‐degree of freedom systems have been proposed. Therein, energy dissipation has been usually modelled resorting to the classical hypotheses of impulsive dynamics, delivering a velocity‐reduction coefficient of restitution applied at impact. In fewer works, a velocity‐proportional damping force has been introduced, by means of a viscous coefficient being constant or variable. A review of such models is presented, a criterion for equivalence of dissipated energy is proposed, equations predicting equivalent viscous damping ratios are derived and compared with experimental responses. Finally, predictive equations are examined in terms of incremental dynamic analyses for large sets of natural ground motions.

“…In this case, it is thus perhaps more realistic to use a flexible Winkler‐type foundation, which models the interface as a set of springs with a stiffness k n . While most of the analytical studies previously conducted on these flexible interfaces assume pure elastic behaviour, recent work by Roh and Reinhorn, Costa et al, Costa, and Penna and Galasco assumes a bilinear elastic representation of the compressive behaviour of the interface, and thus also accounts for crushing effects. Nonetheless, in both cases, the rocking equation of motion now includes an additional term a f ( θ ) which accounts for the moment due to the reaction from the elastic/elastoplastic joint, and is a function of the rotation θ of the structure, as illustrated by Equation :

\overset{θ}{true} = - \frac{{italicWR}_{0}}{I_{O'} ((), θ)} ([], sin ((), α_{0} sgn ((), θ) - θ) - \frac{a_{f} ((), θ)}{R_{0}} + \frac{{\overset{u}{true}}_{g}}{g} cos ((), α_{0} sgn ((), θ) - θ))

where

\overset{θ}{true}

is the angular acceleration, W is the weight, R 0 is the distance between the centre of the mass and the axis of rotation, α 0 is the slenderness,

{\ddot{u}}_{g}

is the input ground acceleration, g is the acceleration due to gravity, and θ is the corresponding rotation of the structure.…”

Section: Introductionmentioning

confidence: 99%

The influence of interface geometry, stiffness, and crushing on the dynamic response of masonry collapse mechanisms

Mehrotra

DeJong

2018

Summary Failure of masonry structures generally occurs via specific collapse mechanisms which have been well documented. Using rocking dynamics, equations of motion have been derived for a number of different failure mechanisms ranging from the simple overturning of a single block to more complicated mechanisms. However, most of the equations of motion derived thus far assume that the structures can be modelled as rigid bodies rocking on rigid interfaces with an infinite compressive strength—which is not always the case. In fact, crushing of masonry—commonly observed in larger scale constructions and vertically restrained walls—can lead to a reduction in the dynamic capacity of these structures. This paper rederives the rocking equation of motion to account for the influence of flexible interfaces, characterized by a specific interface stiffness as well as finite compressive strength. The interface now includes a continually shifting rotation point, the location of which depends not only on the material properties of the interface but also on its geometry. Expressions have thus also been derived for interfaces of different geometries, and parametric studies conducted to gauge their influence on dynamic response. The new interface formulations are also implemented within a new analytical modelling tool that provides a novel approach to the dynamic analysis of masonry collapse mechanisms. Finally, this tool is exemplified, along with the importance of the interface formulation, by evaluating the collapse of the Dharahara Tower in Kathmandu, which was almost completely destroyed during the 2015 Gorkha earthquake.