PSI - Issue 44

Mauro Mezzina et al. / Procedia Structural Integrity 44 (2023) 566–573 Mauro Mezzina, Alfredo Sollazzo, Giuseppina Uva/ Structural Integrity Procedia 00 (2022) 000–000

567

2

1. Introduction When a building is subject to seismic action, the acceleration produced by the ground motion generates inertia forces at each floor, where the entire associated mass is lumped [Paulay (1996); Paulay and Priestley (1992)]. The point of application of inertia force, called the gravity centre of the accelerated mass at that level, is denoted by CM . If F j is the generic inertia force referred to plane j, the sum of all F j located above the level i is defined as the plane shear V i and is applied at a point, called the shear centre CV . Depending on the position of the point of application of the plane shears V i , the response of the generic floor j will be characterised by different configurations. If the plane exhibits a rigid horizontal translation with respect to the lower floor (along x or y axes), an equal horizontal displacement x' ( y' ) will be imposed on all the vertical resistant elements. Let V ij =V xj (V ij =V yj ) be the horizontal reactions applied to the generic i-th wall panel in the x or y direction, their resultant will be applied at a point known as the centre of stiffness CR . Since the plane shear is applied at CV , which, in general, is not coincident with CR , the plane deformation will consist of a rotation coupled with a translation (Fig. 1) † .

Fig. 1. Rigid translation and rigid torsional rotation. For convenience of discussion, let us replace V j with a force of equal intensity acting at CR and a transport torque T j =V j e . If linear superimposition of effects holds the force applied at CR will generate a pure translation, while the transport torque will induce a pure torsional plane rotation with centre CR , whose angle of rotation is called the plane torsion angle. This angle is defined as the relative torsional rotation with respect to the underlying floor h. 2. The requirement of “box-behaviour” The first requirement for the correct performance of a masonry building is the “box-behaviour”, which prevents the occurrence of first-mode damage mechanisms for masonry piers under out-of-plane loads and allows the transfer of actions to the walls parallel to the seismic action, activating their in-plane resistance (second damage mode) and providing higher resistance. The activation of the box-behaviour, of course, requires that effective vertical connections between intersecting piers are guaranteed, in order to allow the above-mentioned transfer of actions. It should be emphasised that the condition of box-behaviour completely modifies the structural functioning. This mode, in fact, results in a "Bredt-like" torsional stress response between the different resisting elements, which allows to optimize the value of the shear stresses in the different panels, to the advantage of a fully spatial response in which the structure no longer behaves as a set of separate resisting elements connected solely by a rigid plane, but as a solid "multiconnected" vertical section, with undoubted advantages in terms of strength and ductility. It is just worth mentioning that the torsional response in thin-walled elements in a closed box section is approached as "Bredt-like" when, being small by assumption the wall thickness, it is assumed that the tangential stresses can be approximated by their mean value, uniform in the thickness and with a direction orthogonal to the chord (Fig. 2).

† The response of resisting elements positioned at a generic angle is determined on the basis of the usual assumption of extensional non deformability of the plane diaphragm