Rocking analysis of masonry walls interacting with roofs

Abstract

This paper investigates the out-of-plane behavior of masonry walls interacting with roofs. Often, collapses of masonry portions supporting roofs may occur due to the roof thrust, which generates a destabilizing effect over motion. Nevertheless, the roof weight can produce a positive stabilizing effect for rotation amplitudes smaller than the critical value. The dynamics of a rocking masonry block interacting with roofs is discussed, by properly modifying the Housner equation of motion of the free-standing single degree-of-freedom block. The dependence of the restoring moment on the rotation angle is investigated and the minimum horizontal stiffness is calculated so that the same ultimate displacement as the system without roof thrust is obtained. Two case studies are presented as applicative examples of the proposed method: an unreinforced masonry structure tested on shaking table and a spandrel beam subjected to roof thrust that survived the Emilia Romagna earthquake. Inertia moments and radius vectors of different failure mechanisms are also provided to solve the equation of motion for different block shapes. Finally, a parametric analysis of a trapezoidal rocking block has been carried out by changing its geometrical shape. This analysis shows that the influence of the shape is relevant for the calculation of the failure load, although is not possible to determine an a priori most critical shape

Rocking and Kinematic Approaches for Rigid Block Analysis of Masonry Walls: State of the Art and Recent Developments

“…A mass placed at the top of the block could simulate a roof mass, whose effect is one of changing the centroid of the composed system block + mass (Figure 1b). Thus, the inertia moment accordingly changes, with multiple values of radius and slenderness, but the equation of motion is basically the same as that of Housner's model (see Section 3) [17].…”

“…Due to the eccentricity of the roof mass, the radius vector changes depending on the rotation sign, R r.cw for clockwise and R r.cc for counterclockwise rotations, respectively ( Figure 2, [17]). However, for slender blocks, the difference between R r.cw and R r.cc is negligible, and the radius vector can be assumed as the double of the radius vector R.…”

Rocking Resonance Conditions of Large and Slender Rigid Blocks Under the Intense Phase of an Earthquake

“…Moreover, the response of a rocking block is extremely sensitive to boundary conditions, very relevant for masonry panels. In that sense, some methods were recently proposed to consider the interaction with transverse walls [10], roofs [11], or vertical restrainers [12].…”

Production procedures and mechanical behaviour of interlocking stabilized compressed earth blocks (ISCEBs) manufactured using float ram 1.0 press

“…Recent investigations on the behaviour of walls made using interlocking stabilized compressed earth blocks (ISCEBs) (Laursen et al, 2015;Qu et al, 2015 a,b) and the role of the compaction force (Bruno et al, 2017) have been carried out; in particular, the adoption of interlocking dry-stack blocks (Sturm et al, 2015) can simplify the execution phases. When this type of building exhibits box-type behaviour, the role of the out-of-plane behaviour must be evaluated in the seismic context (Qu et al, 2015 a,b;Andreini et al, 2013) or with regard to rocking phenomena in masonry walls (Giresini & Sassu, 2017;Giresini et al, 2016). Indeed, earth block walls behave as rigid blocks that can rotate in the case of dynamic actions.…”