Box Structure

f1yLx

f1yLx

8Ly z fz head gable wall

2 I 2cosa I Ly ndy

8Ly g head gable f z fz head gable wall

Figure 16. Structural behavior: a) Frame action and b) box-structure undergoing horizontal ridge loads.

lateral wall. These possible tensile forces must be balanced by the wall self-weight, through anchored bars suitably embedded and distributed along the crowning masonries.

In the second step, the additional ridge constraint reactions were backed out with forces of equal intensity and opposite sign (fiy, fiz in Figure 16). Provided that Frame A would be a free mechanism with respect to the horizontal force f1y, for the balance to be restored, the roof box-structure must sustain these forces (case B, Figure 16).

According to Giuriani and Marini (2008), the roof box structure behavior was interpreted by reference to the classical analysis of the ribbed panels, which is based on the assumption that the in-plane bending moment and the shear force be decoupled and resisted by the chords and panels, respectively (Bruhn 1973). Considering a gable roof, the ribbed panels box structure is assumed to behave like a simply supported beam undergoing distributed forces f1y, in which the eaves chords withstand the global horizontal bending moment, and the pitch panels resist to the shear forces induced by the horizontal load (Figure 17).

The structure proportioning was based on the resistance criteria, by enforcing the elastic behavior throughout the design seismic event. It is worth noting, however, that ductility was guaranteed at the ultimate

Figure 17. Simplified schemes for the evaluation of the force distribution in the box structure.

limit state by the ductile behavior of the nailed connections (Giuriani and Marini 2008), which are the weakest link of the structure.

The expressions of the most significant internal forces are shown in Figures 16 and 17. The eaves chord cross section was proportioned to resist the eaves chord maximum axial forces (F13); whereas the pitch panel thickness, the panel mutual connection, and the diaphragm connections to both the head gables and the eaves chords were proportioned to resist the maximum shear flow q1.

Horizontal and vertical steel stud connections were adopted to allow shear transferring to the shear resisting head gable and longitudinal walls, respectively (Figure 18). For the proportioning of the stud connection, mindful attention was paid to the reduced shear resistance of the masonry wall crown caused by the lack of vertical confining load. To increase the stud connection resistance, strengthening of the masonry wall crown was sometime necessary. To this end, injections of clay mortar along the perimeter wall crown served the purpose in most cases. Alternatively, the whole masonry crown was replaced, or a thin 20 ^ 40 mm slab of high performance clay mortar stiffened by means of plaster meshes was cast on top of the masonry walls. Experimental results proving the effectiveness of these techniques are available in the literature (Gattesco and Del Piccolo 1998; Giuriani 2004; Tengattini etal. 2006).

Distributed vertical deep anchor rebars, embedded along the head gable crowning masonries, were needed h stud connections head gable chord stud connections head gable chord

facade head gable

plywood panels eaves chord a)

plywood panels eaves chord

deep anchorages

Figure 18. Detail of the connection a) to the facade head gable and b) to the longitudinal walls.

top perimeter masonry strengthened by means of injected clay masonry deep anchorages b)

Figure 19. General view of the anti-seismic plywood roof box structure in San Pietro Church (Roe Volciano, Bresica, Italy) and detail of the eaves chord connected to the underlying masonry by means of steel studs and deep anchorages.

Figure 18. Detail of the connection a) to the facade head gable and b) to the longitudinal walls.

in some restoration works to confine the uplift traction forces per unit length nA and fz induced by the horizontal loadings (Figure 16). The tensile forces must be balanced by the self-weight of the "lifted masonry". The distributed anchor bar embedment length was carefully proportioned for the weight of the "lifted masonry" to be sufficiently larger than the traction forces.

Besides the structure bearing capacity, the appraisal of the roof structure deformability was sometime necessary. Unlike perimeter walls, which can usually endure large out-of-plane displacements with little damage, excessive in-plane shear deformability of the masonry vaults and unconstrained drift of the diaphragm arch pillars were shown to be responsible of serious damages and even partial collapses in some churches. To this end, restrictions were enforced that the roof box structure lateral deflection ye was smaller than the maximum allowable drift of the diaphragm arch pillars; and the slope of the box structure transverse deflection at the head gable ye was smaller than the maximum shear deformation y* allowed by the vaults.

For the evaluation of the horizontal deformability of the plywood box structure, the analytical model based on the principle of virtual works proposed in Giuri-ani and Marini (2008) was adopted. In the model, in order to account for the nailed connection shear slip, which largely affect the global deformability,

Figure 19. General view of the anti-seismic plywood roof box structure in San Pietro Church (Roe Volciano, Bresica, Italy) and detail of the eaves chord connected to the underlying masonry by means of steel studs and deep anchorages.

reduced equivalent young and shear elastic moduli are entered.

The lightweight wooden box structure applied for the anti-seismic retrofit of the San Pietro church is shown in Figure 19.

3.3 Light spandrel ribs

In San Pietro Church (Roe Volciano, Brescia), covered by a single leave masonry vault, the strengthening of the structure against the differential deflection of the groin vault was necessary (Table 1).

In masonry vaults, which are incapable to resist tensile stresses, equilibrium is guaranteed by the ideal arch developing within the vault thickness. The ideal arch corresponds to the anti-funicular of the set of applied loads. After cracking, the ideal arch must cross the solid part ofeach cracked sections, both at the vault key and at the springing. Single leave vaults are usually very thin, thus the ideal resisting arch has little possibility to shift and modify within the vault thickness to adapt to different unsymmetrical load distributions. As a result, the structure is often quite vulnerable with respect to seismic load distributions, which require pronounced deviation of the ideal arch.

In order to enhance the structure resistance, spandrel masonry walls are traditionally proposed. The structure resistance is increased by increasing the thickness of the vaults, thus allowing the ideal resisting arch to adjust within the spandrel wall thickness.

In the case of single leave thin vaults, such as in San Pietro church, attention was paid to avoid dead load increase, which in turn could result in additional seismic actions. Accordingly, lightweight spandrel ribs were proposed as a new vault strengthening technique.

Spandrel ribs were designed to resist both compres-sive axial forces and bending moment. This way, the flexural stiffness of the structure was greatly enhanced.

The lightweight spandrel ribs tubular cross section is shown in Figure 20. The resisting cross section is made of clay mortar reinforced with plaster meshes.

lightweight spandrel ribs polystyrene ribs cross section ^lay plaster plaster meshes

single leave vault

single leave vault

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