This is an Accepted Manuscript of an article published ...

This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Earthquake Engineering, available online: http://www.tandfonline.com/doi/full/10.1080/13632469.2017.1360223.

DISSIPATIVE ROOF DIAPHRAGM FOR THE SEISMIC RETROFIT OF LISTED MASONRY CHURCHES Marco Preti1, Sara Loda1, Valentino Bolis1, Stefania Cominelli1, Alessandra Marini2 and Ezio Giuriani1 1 Dipartimento DICATAM – Università degli Studi di Brescia. Via Branze 43, 25123 Brescia. [email protected] [email protected] [email protected] [email protected] [email protected] 2 Dipartimento di Ingegneria – Università degli Studi di Bergamo. Viale Marconi 5 - 24044 Dalmine (BG) [email protected]

ABSTRACT In the seismic retrofit of existing masonry buildings, dissipative and deformable roof diaphragms could offer an efficient solution in cases where both the adoption of steel ties or stiff diaphragms would be ineffective. An innovative deformable, dissipative and lightweight roof diaphragm for the seismic retrofit of masonry churches is proposed. Such a diaphragm prevents the overturning of the side walls whilst allowing the onset of a controlled rocking mechanism. The specific diaphragm elasto-plastic response caps the seismic actions transferred by the roof diaphragm to the seismic resistant walls, in contrast with a rigid and with a stiffened diaphragm. This effect is meant to mitigate the overload of the head walls thus preventing their collapse or the need for their strengthening, which could require interventions invasive of the historical structure. The feasibility of the proposed retrofit strategy is assessed through the experimental characterisation of a prototype

1

diaphragm sub-assembly and non-linear dynamic analyses of the global response of two retrofitted reference buildings.

KEYWORDS: Dissipative Diaphragm, Seismic Retrofit, Masonry Wall Rocking, Diaphragm Flexibility, Historical Churches, Out-of-plane, Roof Diaphragm, Listed Building Retrofit.

1. INTRODUCTION The seismic vulnerability of historical unreinforced masonry buildings is often principally related to the outof-plane overturning of the perimeter walls [Giuffre’ 1993; Giuriani and Marini 2008a; Griffith et al. 2003]. Accordingly, seismic strengthening solutions are usually aimed at inhibiting such a mechanism to enable a building to exhibit box-like structural behaviour. In the case of open-bay, oblong, masonry building (namely single nave churches), when the seismic action is oriented along the longitudinal building direction, the building is mainly vulnerable to the overturning of the head walls, which can be easily prevented by tie or roof diaphragm strengthening systems [Giuriani and Marini 2008b; Magenes et al. 2014; Tomaz˘evic˘ et al. 1996]. The lateral walls are usually capable of resisting the consequent seismic in-plane load. The same strengthening approach against overturning of the lateral walls, when the action is transverse to the nave, can produce a head wall overload in excess of their capacity, because of their weaker resisting cross-section, compared to the lateral walls. In such cases, substantial strengthening of the head walls may be required to avoid early in-plane collapse mechanisms, which may jeopardise the structural box-like behaviour. However, such interventions may be unfeasible as they are at conflict with conservation requirements. The post-earthquake surveys showed that in several churches lacking a roof diaphragm, the head walls survived the earthquake practically undamaged despite the activation of an out-of-plane mechanism (rocking) in the lateral walls [Giuriani and Marini 2008a], which in some cases suffered partial or global out-of-plane collapse. This evidence suggests a possible strengthening strategy based on (i) taking advantage of the out-of-plane rocking of the lateral walls to limit the seismic overload on the head walls and (ii) controlling the lateral walls’ rocking amplitude to ensure their safety. These two issues are resolved by adopting a deformable and dissipative roof diaphragm, providing an inelastic constraint for the lateral walls. With respect to a rigid diaphragm, creating a stiff box-like behaviour, the dissipative diaphragm works as an inelastic damper limiting the lateral walls’ rocking amplitude and capping the seismic actions transferred to the head walls, while ensuring an overall compactness of the structure.

2

In single nave churches, the out-of-plane rocking of the lateral walls is typically governed by the in-plane rocking of transverse arches, which subdivide the nave into bays and support the longitudinal roof ridge beams and purlins. In the case of brick masonry transverse-arches, the expected structure deformation capacity can be significant and its response can be predicted with reference to the limit analysis [Brandonisio et al. 2015; De Luca et al. 2004; Giuriani et al. 2009]. This was confirmed in a recent experimental test, where a six-meter height brick masonry transverse-arch subjected to quasi-static cyclic lateral loading and dynamic pull-andrelease tests (Figure 1) remained undamaged up to a 1.5% drift and stable up to a tested 3% drift [Preti et al. 2013], displaying the kinematic mechanism and the force-drift behaviour described in Figure1a. Moreover, theoretical and experimental research on rocking mechanism have proven that the out-of-plane seismic stability of masonry walls is governed by displacement rather than by strength capacity ([Al Shawa et al. 2012; Housner 1963; Liberatore and Spera 2001; Menon and Magenes 2008], among others). This is possible whenever the quality of the masonry is good or very good, otherwise the wall may crumble when subjected to low seismic action, without triggering any rocking behaviour. Some authors focused on the evaluation of the out-of-plane seismic response of walls considering the beneficial and/or detrimental dynamic effects of their interaction with the rest of the building. It was observed that the inelastic response of the primary resisting structure, i.e. in-plane walls and floor diaphragms, significantly affects both the displacement demand and the acceleration pertaining to the out-of-plane unreinforced loaded masonry walls, when they are connected to the diaphragm [Nakamura et al. 2016; Penner and Elwood 2016; Simsir 2004; Simsir et al. 2004; Wilhelm et al. 2007]. In the case of one-sided rocking, due to interaction with the transverse walls, this mechanism is a source of stability for the structure [Al Shawa et al. 2012]. The control of the rocking amplitude was extensively discussed by several authors in the case of reinforced concrete walls [Christopoulos et al. 2006; Kurama et al. 1999; Preti and Meda 2015; Priestley et al. 1999; Restrepo and Rahman 2007]. Researchers investigated the effective reduction of the rocking amplitude enabled by increasing the energy dissipation through additional dampers located at the RC wall base. Such solutions seem unviable in monuments, as they cause the excessive impairment of existing structures. In the case of masonry buildings, the adoption of dissipative perimeter tie systems was proposed in [Indirli and Castellano 2008; Mandara and Mazzolani 2001; Mazzolani and Mandara 1994; Paganoni and D’Ayala 2009] to control perimeter walls out-of-plane overturning displacements and to reduce accelerations in the case of

3

strong earthquakes. These studies proposed the use of either shape memory alloy devices or patented dissipative elements to increase the performance of traditional tie anchors. It is worth noting that the use of ties as retaining systems against the wall out-of-plane overturning is inadequate for slender walls, given that no arching mechanism can effectively develop within the wall thickness. Hysteretic devices were also proposed for the connection of the masonry walls to newly constructed steel rigid diaphragms, allowing for energy dissipation due to the relative displacement of the lateral walls and the diaphragm itself [Mazzolani and Mandara 2004]. In the retrofit solution proposed in this paper, dissipation is triggered by installing special dissipative devices within the roof diaphragm, enabling the “natural” deformation of the structure when subjected to lateral loading, similarly as the solution proposed by [Koliou et al. 2016] in application to rigid wall-flexible diaphragm industrial buildings. The feasibility of the technique of the dissipative roof diaphragm is assessed by designing and testing special dissipative friction dampers. The beneficial effect of the controlled rocking design approach is examined through a preliminary comparative numerical study focusing on the dynamic response of two reference historical churches; the two alternative retrofit solutions with a dissipative diaphragm or a non-dissipative one are compare.

2. RESEARCH MOTIVATION In the retrofit of existing masonry buildings, dissipative and deformable roof diaphragms could offer an efficient solution in cases where both the adoption of steel ties or rigid diaphragms would be ineffective. In detail, in the case of buildings with large open bays devoid of floors and vaults, or oblong buildings, i.e. churches and theatres, the perimeter ties are, in general, unable to constrain effectively the perimeter walls due to the slenderness of the walls. In contrast, the adoption of stiff roof diaphragms to avoid the lateral walls overturning could transfer excessive seismic loads to the head walls, which would require them being strengthened. It is worth noting that massive strengthening of the head walls is often forbidden by European conservation standards; in the case of historical monuments, such interventions cause excessive impairment to the valuable finishing or architectural layout. This paper proposes an innovative roof strengthening technique to obtain a dissipative and deformable diaphragm, in compliance with the conservation requirements of listed buildings.

4

3. CONTROLLED ROCKING DESIGN STRATEGIES APPLIED TO HISTORICAL CHURCHES Traditional wooden floors and roofs of historical masonry buildings are usually not designed and organized to behave as horizontal diaphragms: the non-engineered arrangement of the wooden planks, as well as the poor connection of the wooden beams to the peripheral walls, prevent any reliable seismic action transferring to the shear walls. In order to ensure efficient diaphragm behaviour, different solutions were proposed in [Giuriani et al. 2016; Giuriani and Marini 2008b, 2011] for both the in-plane strengthening and stiffening of existing wooden roofs and for ensuring the effective connections of the roof diaphragm to the lateral walls. Simple detailing of the wall-to-diaphragm connection can reduce the relative deformation at the design action to negligible values (below 1mm [Cominelli et al. 2016]). One example of the application of these solutions is shown in 2. These diaphragms (“non-dissipative diaphragm” in the following) are usually designed to withstand seismic actions by maintaining a substantially rigid in-plane behaviour, and are effective whenever the lateral wall out-ofplane rocking can (or needs) to be prevented. In the proposed retrofit strategy solution, the roof is engineered to be used as a dissipative structural element (Figure 3), hence characterised by large horizontal deformation capacity and stable hysteretic behaviour. To this end, special devices and detailing are necessary to enable substantial ductility of the roof system. For the reference studies discussed below, the dissipative roof diaphragm strengthening technique is developed as an enhancement of the roof retrofit solution presented in [Giuriani and Marini 2008b]. The innovation consists of a different configuration of the two end portions of the diaphragm; those defined by the area delimited in the plan by the nave bays next to the head walls (Figures 3c, e). The central portion of the diaphragm maintains a substantially rigid in-plane behaviour, as in the original non-dissipative diaphragm strengthening technique. Accordingly, the central portion of the diaphragm is made of plywood panels overlaying and nailed to the existing planks and connected to each other by means of nailed steel flanges. In the end portions, the diaphragm plywood panels are replaced by wooden strips, whereas the steel flanges are substituted by dampers (Figure 4). Such devices control the relative sliding of adjoining strips. Special flat steel friction dampers are designed and tested (paragraph 4), as a possible option for application in listed buildings, meeting the requirements for the use of traditional materials, minimum and reversible intervention

5

and minimum modification of the roof thickness. The full diaphragm is framed by perimeter steel chords and is fixed to the roof ridge beam, to the masonry crowning walls and to the transverse arches by means of steel studs and vertical anchored bars [Giuriani and Marini 2008a, 2011; Marini et al. 2016]. For the connection to be effective, preliminary local pre-consolidation of the crowning masonry may be necessary in the case of poor quality masonry. Despite the fact that the nailed connections among neighbouring panels provide the roof diaphragm with a little in-plane flexibility, the main deformation of the diaphragm is provided by the devices’ inelastic behaviour (the relative nailed connection displacement can be smaller than 1mm at yielding [Giuriani and Marini 2008b]). The devices are calibrated so that the dissipative diaphragm: (i) caps the seismic actions transferred to the head walls; (ii) limits the out-of-plane rocking of the side walls to within acceptable values, without preventing it. The maximum allowable out-of-plane wall drift can be regarded as a design parameter to control possible building damage (damage that may occur to ceilings and vaults [Marini et al. 2017], frescos, windows, etc.) and limit the second order effects, where necessary. In the direction of the nave axis, the retrofitted roof offers a rigid diaphragm response, preventing the out of plane mechanism of the head walls by transferring their seismic action to the lateral walls.

3.1. Idealised building structural model and diaphragm proportioning criteria Below, the dynamic response of two reference historical churches retrofitted with either a dissipative or stiffened diaphragm is studied, for seismic action oriented transverse to the nave axis. In non-linear dynamic analysis the buildings are idealised as being subdivided into macro-elements, as first proposed by [Giuffre’ 1993], namely: each transverse-arch together with the adjoining tributary sidewalls (Fig. 3a) (“arch-system” below) and the head walls. The roof diaphragm behaves as a relative-constraint applied to the top of the archsystems, connecting them to each other and to the head walls, as shown in Fig. 5. Given the ductile response of the diaphragm (Fig. 6a), the top constraint can be modelled with elastic-plastic behaviour with calibrated stiffness and yielding strength (𝑘𝑑 , 𝑅𝑑,𝑦 ). The diaphragm reaction is activated by the relative displacement

1-2 (1 and 2 being the top displacements of the transverse arch and the head wall, respectively), and transfers a share of the tributary inertia forces acting on the arch-systems, 𝑅𝑑 ,to the head walls. For the design of an effective dissipative diaphragm, yielding must be triggered at a roof displacement significantly smaller than the maximum acceptable displacement for the structure [Preti et al. 2014]. This requirement involves high initial diaphragm stiffness and small deflection at yielding. Assuming an ideal elastic-plastic response of the

6

diaphragm (Fig. 6a) and a bilinear elastic capacity curve for the single arch-system rocking mechanism (Fig. 6b), the resulting damped arch-system behaviour is described by a flag-shaped capacity curve (Fig. 6c). Coefficients 𝑘𝑅 and 𝐹𝑅 represent the equivalent values of the secant stiffness of the arch system and of the force at the rocking triggering, respectively, when the latter is applied at the arch top. The force 𝐹𝑅 and stiffness 𝑘𝑅 are input data of the structural problem: 𝐹𝑅 can be evaluated using the limit analysis approach considering the onset of the arch-system kinematic mechanism ([Giuriani et al. 2009], among others); 𝑘𝑅 can be calibrated on the drift at the rocking triggering, approximated as the elastic deflection of the abutments at the level of the arch imposts, divided by the impost height. Parameters 𝑘𝑑 and 𝑅𝑑,𝑦 are the only design variables of the retrofit intervention. For design purposes, a parameter is introduced (Eq.1), which is defined as the ratio of twice the strength of the diaphragm (2𝑅𝑑,𝑦 = 𝛥𝐹) over the force activating the arch system rocking: 𝛥𝐹

𝛽=𝐹 = 𝑅

2𝑅𝑑,𝑦 𝐹𝑅

(1)

Parameter  is an index of the energy dissipation supplied by the diaphragm in the arch-system rocking response, and its value is a design choice. The damping effect increases for increasing yielding strength of the diaphragm, thus for increasing values of the parameter . However, in order to allow the self-centering rocking behaviour of the arch-systems, values of lower than 2 are preferable in the design. In fact, values of  partially inhibit the self-centering property of the system, and create an unloading branch in the flag-shaped curve intercepting the x-axis with a remarkable residual displacement. With reference to a performance-based design approach, in order to prevent building damage induced by unconstrained, excessive rocking, the maximum target rocking displacement amplitude 𝛿𝑚𝑎𝑥,𝐿𝑆 should be limited by the accurate selection of the stiffness and the yielding strength of the diaphragm, 𝑘𝑑 and 𝑅𝑑,𝑦 respectively. The retrofit design includes the verification of possible local mechanisms, which are not represented in the modelling with macro-elements, and it is beyond the scope of this paper. In particular, possible activation of local mechanism in the lateral walls or their portions must be prevented. A flowchart describing the retrofitting design process and its applicability is shown in Figure 7.

7

4. DISSIPATIVE DIAPHRAGM PROTOTYPE The feasibility of the dissipative diaphragm is substantiated by the results of an experimental study on a dissipative device prototype and by its effective implementation in a dissipative panel. The conceptual design of the whole diaphragm is discussed briefly in order to present the diaphragm components. Further details on the experimentation can be found in [Cominelli et al. 2016]. The proposed dissipative roof diaphragm layout is shown in Figure 4. The dissipative roof diaphragm is conceived as a plywood shell overlaying the existing roof planks or rafters. As in the case of non-dissipative diaphragms [Giuriani and Marini 2008a; b], the dissipative diaphragm must be secured to the peripheral masonry walls to avoid unrestrained out-of-plane mechanisms, whereas the diaphragm web-panels must be connected to the roof rafters to prevent the diaphragm from buckling. In the innovative dissipative diaphragm, dissipation is lumped in special devices controlling relative sliding along the interface between neighbouring plywood strips located at the end portion of the diaphragm. The dissipative devices are nailed to the plywood strips. Possible dissipative device distribution is shown in Figure 4, in which sliding joints are designed to be parallel to the eave lines. The yielding strength of the dissipative portion, which is strictly related to the design parameter , depends on the number and on the strength of the dissipative devices installed along each sliding interface. The system yielding strength is therefore expressed by Equation 2: 𝑉𝑝𝑎𝑛𝑒𝑙 = 𝑛𝑑𝑒𝑣𝑖𝑐𝑒 𝐹𝑑𝑒𝑣𝑖𝑐𝑒 (𝐿𝑦 /𝐿𝑥 )

(2)

where ndevice is the number of devices along each sliding interface, Fdevice is the strength of the single dissipative device, Lx and Ly are the length and width of the dissipative portion of the diaphragm, respectively (Figure 4). The initial stiffness of the different diaphragm portions can be easily evaluated taking into account the stiffness of the nailed connections together with the elastic deformability of the components [Giuriani and Marini 2008b].

4.1. Dissipative device prototype A specific friction-based dissipative device (2 in Figure 4) was designed and tested (Figure 8). The device is made of two steel plates, A and B, which are forced into each other, thus activating an elastic clamping effect of plate B onto plate A (Figure 8b). This clamping effect can be calibrated by referring to the elastic deformation of plate B. Plate B is obtained by welding together the two plates B’ and B’’ represented in Figure

8

8a. The device is then connected to the adjoining strips with nails or screws, as shown in Figure 8c. The material characterisation tests for the device showed a steel yielding strength of 320 MPa and a sliding friction coefficient equal to 0.31. To prevent the alteration of the device response over time, protection must be ensured against corrosion and dust, and the use of stainless steel and/or specific coating should be considered. Figure 8d shows the sliding force versus displacement curves of the dissipative device, as obtained under static and dynamic cyclic loading, respectively. A stable plastic response was observed throughout both tests. A slight increase of the friction strength was observed for increasing sliding velocity; in particular, strength increased from 2.5 to 2.8 kN for sliding velocity varying between 5mm/min (quasi static test) to 36mm/s (dynamic test).

4.2. Dissipative diaphragm sub-assembly: experimental test and discussion of results The structural behaviour of a full-scale 2x2m portion of the prototype dissipative diaphragm was investigated under shear cyclic loading. The sample geometry and test set-up are described in Figure 9. A perimeter steel frame was used to impose shear deformations on the diaphragm sub-assembly. The perimeter steel testing frame was composed of four steel trusses. The plywood strips were fixed to the top and bottom frame beams with a single nail, so as to allow relative rotation at the end sections (Figure 9c). A horizontal point load was applied to the top frame beam using a hydraulic jack. Both the diaphragm shear deformation () and the relative sliding of the wooden strips (Δ) were measured. Figure 10 shows the diaphragm sub-assembly base shear force versus top beam displacement curve obtained in the cyclic quasi-static test. The panel displayed an elastic-nearly-plastic response following the activation of the friction mechanism of each device. This response curve is consistent with the assumption made in the roof diaphragm modelling discussed above. The minor hardening response was mainly due to the stiffness of the bare testing frame. Diaphragm deformation was lumped in the dissipative devices and no damage was measured in either the wooden panel components or in the nailed connections for an imposed drift of up to 3%. The experimental yielding strength (Vexp= 8.1 kN) matches well with the theoretical prediction obtained from Equation 2 (Vth = 7.8 kN, where Fdevice= 2.6 kN, ndevice=3, Lx=Ly).

9

According to Equation 2, the number of dissipative devices to be positioned in the dissipative portion of the roof diaphragm, along the single interface between adjoining plywood strips, is expressed by Equation 3: 𝑛°𝑑𝑒𝑣𝑖𝑐𝑒 = ((𝑅𝑑𝑦 ⁄𝐿𝑦 )𝐿𝑥 )/𝐹𝑑𝑒𝑣𝑖𝑐𝑒

(3)

where Ly is the head wall length and Lx is the length of the dissipative end-portions of the diaphragm.

5. NUMERICAL MODELLING OF THE STRUCTURE AND RESULTS The role of the dissipative diaphragm on the overall structural response, as well as the design choices and the retrofit performance targets are discussed with regard to two reference buildings subjected to seismic action transverse to the nave. 3D simplified structural models are implemented and nonlinear dynamic analyses are undertaken with Opensees FEM code [McKenna et al. 2000] in order to explore the potentiality of the retrofit solution. The macro-elements composing the structure are the arch-systems and the head walls, and the diaphragm portions spanning between them. Provided that the retrofit is designed to maintain the masonry arch-systems undamaged, except for the creation of cracks caused by the rocking mechanisms, such macro-elements are modelled in a simplified manner as elastic beams, with lumped spring elements at their ends, which account for the structure’s rocking behaviour. The lateral walls are not explicitly modelled, but their mass is taken into account in the definition of the macro-elements. The mass is distributed along the vertical elements and each vertical element is made up of its own mass and that of the tributary lateral wall and roof. The arch-system rocking mechanism is modelled using of a bi-linear elastic rotational spring introduced at the pinned support of the column base (Figure 11b). The overturning moment (𝑀𝑅 ) and the rotational stiffness (𝐾𝑟, ) of the spring are calibrated at the onset of the arch-system free rocking. The dynamic and dissipative phenomena connected to the wall impact and foundation uplift are ignored, and thus their beneficial effect on the limitation of the rocking amplitude. The head walls are modelled as linear elastic cantilever beams, fixed at the base; for the sake of simplicity, inplane flexural (𝐸𝑚 , 𝐽𝑚 ) and shear stiffness (𝐺𝑚 ,𝐴𝑚 ) are evaluated by assuming the head walls to be solid walls. Implicitly, it is assumed that they remain undamaged throughout the seismic excitation, thanks to the beneficial effect of the predicted global controlled rocking response; consistency of the assumption is checked after analysis by comparing the internal actions with their nominal strength.

10

The roof diaphragm is modelled using a series of elastic beam elements, connecting each macro-element to the neighbouring one (Figure 11b). The beam element flexural stiffness is set as equal to the in-plane flexural stiffness (𝐾𝑑,𝑓 ) of the roof diaphragm [Giuriani and Marini 2008b], mainly due to the eave-steel chords. The stiffness, Kconn (Table 1), of the walls- and arch- to-roof diaphragm connections was calibrated on the test response reported in [Giuriani and Marini 2011]. In the proposed retrofit solution, the nonlinear deformation of the diaphragm occurs as the relative sliding of adjacent strips composing the diaphragm end portions: accordingly, diaphragm nonlinearity is modelled as shear deformation (Figure 3c) lumped into an elastic-plastic spring element with stiffness (𝐾𝑑,𝑠 ) and strength (𝑅𝑑,𝑦 ). The strength was calibrated based on the dissipative devices; the stiffness also considered the deformability of the panels and nailed connections.

5.1. Reference building description A preliminary parametric analysis was carried out on two reference buildings (“Santa Maria della Neve” church and “Madonna del Brizzo” church), located in the southern area of Lake Garda (Italy). The reference buildings were selected as representative of a common type of oblong single-nave church. The same set of accelerograms was adopted for the analysis of the two buildings (“Building 1” and “Building 2” below, respectively), properly scaled to comply with the seismic hazard of the site of Building 1 (Sirmione, BS), with a PGA of 0.185g on soil type E ([NTC 2008] Annex A). The geometrical layout is detailed in Figures 11a and 12. Both buildings’ perimeter walls and transverse arches are made of solid brick masonry. The wooden roof is composed of purlins and ridge beams, simply supported on the head walls and on the transverse-arches. In the study aimed at assessing the feasibility of the retrofit approach, the sole main nave was considered, ignoring the role of the annexes. For further simplification, the ground plan was regularised and the triumphal arch was modelled as the façade, hence as a solid shear wall. This choice is motivated by the need to remove the irregularities particular to each structure, also accounting for a substantial stiffening effect provided by the annexes to the triumphal arch in-plane response that is not explicitly modelled. In a more detailed evaluation of the church response, the triumphal arch modelling could consider the possible rocking mechanism of its abutments, with a strategy similar to that adopted for transverse arches. Interaction with the transept, annexes

11

or apses can only be evaluated in detail by performing preliminary finite or distinct element model analysis, that can also be very useful for characterising the façade in-plane response. It is worth noting that the important issues related to a non-symmetric response of the building are beyond scope of this paper. Table 1 summarises the setting values of the structural model parameters. In addition to the dissipative diaphragms, the case of elastic non-dissipative diaphragms is analysed for both buildings, for comparison. In the latter case, structural parameters remain those of Table 1, with the only exception that the shear transverse springs are assumed to be linear elastic (𝑅𝑑,𝑦 →∞), and their stiffness is evaluated according to a denser dowel and nail connection distribution. Note that, throughout the parametric numerical study, the initial diaphragm stiffness is kept constant for both case studies, and the sole variability of the parameter governing the diaphragm strength and deflection at yielding, is considered. With reference to Figure 6, diaphragm yielding occurs in all cases with lateral wall drift, y, lower than the rocking activation driftR,1=0.24%, R,2=0.49%).

5.2. Numerical result discussion The results of the non-linear time history analyses, assuming a 5% viscous damping coefficient for all modes of vibration, are presented below. The choice of proper viscous damping in masonry rocking structures is particularly uncertain. The 5% value, commonly adopted for elastic analysis, was arbitrarily chosen for modelling the energy dissipated in the macro-elements assumed to behave elastically. In fact, the only hysteretic response explicitly modelled is that of the dissipative devices. Figures 13 to 16 show the main results of the dynamic responses of both reference buildings 1 and 2. The influence of the diaphragm yielding strength is investigated by varying parameter . The results are compared in terms of maximum lateral wall drift (Dmax, Figure 13), input and dissipated (hysteretic) energy (Figure 14), maximum shear transferred by the diaphragm to the head walls (Vd,max, Figure 15) and maximum head wall base shear (Vhw,max, Figure 16). Figure 13 shows that the adoption of the dissipative, rather than non-dissipative, diaphragm leads to greater drift of the lateral walls, whilst still preventing lateral wall overturning. Increased values of  are beneficial in reducing the average lateral wall drift from 1.2% and 1% to 0.75% and 0.6%, for the two buildings respectively. These values seem acceptable in comparison with the experimental deformation capacity exhibited by brick

12

masonry transverse arches and lateral walls system subjected to rocking, which displayed an undamaged response up to 1.5% drift [Al Shawa et al. 2012; Preti et al. 2013]. Note that the introduction of dissipative diaphragms reduces the acceleration on the arch system (including the lateral walls) by about 60%, reducing the possible activation of local mechanisms. In contrast, in order to protect structures featuring elements that are particularly vulnerable to roof deformations, such as single leaf vaults, non-dissipative diaphragms should be adopted to limit the maximum drift within acceptable values, which are one order of magnitude lower. Moreover, in the analyses, for increasing values of corresponding to a reduction of the rocking amplitude, an increase in the percentage of input energy dissipated by the friction devices as hysteretic energy is observed (from 30% to 80% with  ranging from 0.25 to 2 – Figure 14). The average maximum shear action transferred by the dissipative diaphragm to the head walls is shown in Figure 15. As expected, the shear action is linearly dependent on the coefficient , being capped at the dissipative device yielding strength. Accordingly, the diaphragm shear demand can be regarded as a design choice, resulting in the selection of parameter , which only depends on the maximum allowable lateral wall drift. The same Figure 15 shows that the alternative adoption of a non-dissipative diaphragm would result in higher loads being transferred to the head walls. The roof shear action evaluated through linear static analysis is also shown in Figure 15, for the non-dissipative diaphragm. Even assuming a behaviour factor (q) of 2, and thus a reduced design shear action, the load transferred to the head wall is significantly larger (by more than five times) than the action transferred through a dissipative diaphragm. Figure 16 compares the head wall base shear obtained for different values of the dissipative diaphragm yielding strength (i.e. different values of ), with the head wall nominal design strength evaluated according to the codes [EN 2005; NTC 2008]. It can be observed that the adoption of a dissipative diaphragm guarantees the head wall safety against in-plane action: the head wall base shear is always smaller than the nominal resistance and not particularly sensitive to the choice of dissipative device strength, for β ranging from 0 to 2. Therefore, thanks to the beneficial effect of the dissipative diaphragm, the strengthening of the head walls can be avoided. Interestingly, head wall safety would be at risk in the case of non-dissipative diaphragms for both reference buildings, as the base shear action calculated assuming the undamaged response of the head walls (2401 kN and 1075kN, respectively) exceeds the nominal resistance.

13

In addition, the feasibility of the proposed retrofit solution was verified for a set of real accelerograms, typical of Italian high-seismicity regions (Table 2). The range lateral walls’ drift demand does not change significantly, whereas the head wall overload appears to increase with the peak ground acceleration (Figure 17). This testifies to the low sensitivity of the lateral walls’ rocking mechanism to peak ground acceleration, contrary to head walls that are subjected to acceleration similar to the ground, according to their very stiff in-plane response. Based on the simplified analyses performed, in most cases the damage to the head walls seems unavoidable in high seismicity regions, unless specific strengthening is undertaken.

6. CONCLUDING REMARKS The possible use of a dissipative roof-diaphragm in the seismic strengthening of masonry buildings vulnerable to out-of-plane rocking of the peripheral masonry walls and to excessive rocking of possible transverse-arches was investigated in this paper. The benefits of the dissipative diaphragm undergoing non-linear deformation during the earthquake are highlighted with reference to two buildings, selected as representative of the common type of oblong single-nave masonry churches with transverse-arches. An innovative roof diaphragm with dissipative end zones and a central stiff portion was proposed and its feasibility was assessed through experimentation. For design purpose, a parameter  was introduced, which is defined as a function of the ratio of the diaphragm yielding strength and the seismic force activating the isolated arch-system free rocking, and which expresses the strength and dissipation capacity of the innovative diaphragm. The role of the roof diaphragm strength in the seismic response of the building was investigated by varying the value of  and by performing nonlinear dynamic analyses with a set of seven earthquake records, calibrated for an Italian moderate seismicity region. The results highlight the benefit of the proposed solution: compared to a non-dissipative diaphragm, the average maximum roof shear demand is dramatically reduced when a dissipative diaphragm is used, resulting in undamaged behaviour of the head walls for the reference buildings. This solution eliminates the need for impairing retrofit or strengthening interventions on the church facades, which would be nevertheless unviable in listed buildings, according to European conservation standards. A similar analysis for higher seismicity earthquakes showed a certain dependence of the head walls in-plane action on the peak-ground acceleration. For the accelerograms considered, peak-ground acceleration larger

14

than 0.3g jeopardize the possibility of keeping the head walls undamaged. More refined analyses are required to explore the response of the structure when damage in the head walls is taken into account. In the two reference buildings, the average maximum out-of-plane drift demand on the lateral walls depends on the yielding strength of the diaphragm, decreasing from about 1.2% to 0.6% when  increases from 0 to 2. It is worth noting that, in the case of vaulted ceilings, such average maximum drifts may be unacceptable, and stronger and/or stiffer roof diaphragm would be required for controlling their damage. Given the observed drift reduction for increasing , a higher diaphragm yielding strength, greater than the rocking activation load (>2), may be worth investigating in order to further reduce the rocking amplitude; in this case, however, significant residual drift after the earthquake may be expected. The choice of the design parameter  also determines the shear action transferred along the roof diaphragm, thereby affecting the proportioning of the diaphragm components and connections. The choice of  should target both the reduction of the head wall base shear demand and the reduction of the lateral wall drift to within permitted values. However, in the explored range of  the head wall shear demand is not particularly sensitive to the value of the diaphragm yielding strength, so that the drift control governs the design. In the conceptual design of the proposed dissipative roof diaphragm, dissipation is triggered by introducing special devices to the end portions of the diaphragm. Special flat steel friction dampers were designed and tested, as a possible option, and implemented in a full-scale dissipative diaphragm sub-assembly, which displayed stable dissipative behaviour governed by friction, as assumed in the modelling.

7. ACKNOWLEDGEMENTS The authors gratefully acknowledge the support of Martino Peretti, Valentina Martinelli, Piergiacomo Mutti, Matteo Sandrini and the technicians of the P.Pisa Lab of the University of Brescia in their assistance in the experimental testing or numerical modelling. This study was partly developed as part of the Reluis research programme funded by the “Presidenza del Consiglio dei Ministri Dipartimento della Protezione Civile”; this publication, however, does not necessarily reproduce the Department’s position or judgments.

8. ANNEX A - SPECTRUM-COMPATIBLE ACCELEROGRAMS CHOICE For the analysed site, 7 natural accelerograms, properly scaled to be spectrum-compatible to the life safety limit state design spectrum, were obtained using “Rexel v 3.5 beta” software (Fig.20). The properties of the

15

site are reported below. Site: Sirmione (PGA=0.185g, F0=2.462, Tc*=0.277), Latitude: 45,4695°, Longitude: 10,6062°, Nominal life: 50 years, Class of use: 3, Ground class: E, Topographic categ.: T1.

9. REFERENCES Al Shawa, O. A., de Felice, G., Mauro, A., and Sorrentino, L. [2012] “Out-of-plane seismic behaviour of rocking masonry walls,” Earthquake Engineering & Structural Dynamics, Vol. 41, No.5, pp. 949–968. Brandonisio, G., Mele, E., and De Luca, A. [2015] “Closed form solution for predicting the horizontal capacity of masonry portal frames through limit analysis and comparison with experimental test results,” Engineering Failure Analysis, Vol. 55, pp. 246–270. Christopoulos, C., Filiatrault, A., and Bertero, V. V. [2006] Principles of passive supplemental damping and seismic isolation, Iuss press. Cominelli, S., Giuriani, E., and Preti, M. [2016] Una nuova tecnica per le coperture scatolari antisismiche dissipative: studio sperimentale e problematiche di dimensionamento, Technical report num. 2/2016, DICATAM-Università degli Studi di Brescia. De Luca, A., Giordano, A., and Mele, E. [2004] “A simplified procedure for assessing the seismic capacity of masonry arches,” Engineering Structures, Vol. 26, No.13, pp. 1915–1929. EN, B. [2005] “Eurocode 6 Design of masonry structures,” British adopted European standard. ISBN, Vol. 940154380. Giuffre’, A. [1993] Sicurezza e Conservazione dei centri storici: il caso Ortigia. Bari, Laterza. Giuriani, E., and Marini, A. [2008a] “Experiences from the Northern Italy 2004 earthquake: vulnerability assessment and strengthening of historic churches.,” Taylor and Francis, London, UK, Bath, England, pp. 13–24. Giuriani, E., and Marini, A. [2008b] “Wooden Roof Box Structure for the Anti-Seismic Strengthening of Historic Buildings,” International Journal of Architectural Heritage, Vol. 2, No.3, pp. 226–246. Giuriani, E., and Marini, A. [2011] “Coperture scatolari antisismiche.,” L’Edilizia. Speciale Legno: progettazione, strutture, sismica, Pinelli printing. Milano, pp. 26–44. Giuriani, E., Marini, A., Porteri, C., and Preti, M. [2009] “Seismic Vulnerability for Churches in Association with Transverse Arch Rocking,” International Journal of Architectural Heritage, Vol. 3, No.3, pp. 212–234. Giuriani, E., Marini, A., and Preti, M. [2016] “Thin-folded Shell for the Renewal of Existing Wooden Roofs,” International Journal of Architectural Heritage, Vol. 10, No.6, pp. 797–816. Griffith, M. C., Magenes, G., Melis, G., and Picchi, L. [2003] “Evaluation of out-of-plane stability of unreinforced masonry walls subjected to seismic excitation,” Journal of Earthquake Engineering, Vol. 7, No.spec01, pp. 141–169. Housner, G. W. [1963] “The behavior of inverted pendulum structures during earthquakes,” Bulletin of the Seismological Society of America, Vol. 53, No.2, pp. 403–417. Indirli, M., and Castellano, M. G. [2008] “Shape memory alloy devices for the structural improvement of masonry heritage structures,” International Journal of Architectural Heritage, Vol. 2, No.2, pp. 93–119. Koliou, M., Filiatrault, A., Kelly, D. J., and Lawson, J. [2016] “Distributed Yielding Concept for Improved Seismic Collapse Performance of Rigid Wall-Flexible Diaphragm Buildings,” Journal of Structural Engineering, Vol. 142, No.2, p. 4015137. Kurama, Y., Pessiki, S., Sause, R., and Lu, L.-W. [1999] “Seismic behavior and design of unbonded post-tensioned precast concrete walls,” PCI journal, Vol. 44, No.3, pp. 72–89. Liberatore, D., and Spera, G. [2001] “Response of slender blocks subjected to seismic motion of the base: description of the experimental investigation,” 5th International Symposium on Computer Methods in Structural Masonry, Rome, pp. 117–124. 16

Magenes, G., Penna, A., Senaldi, I. E., Rota, M., and Galasco, A. [2014] “Shaking Table Test of a Strengthened Full-Scale Stone Masonry Building with Flexible Diaphragms,” International Journal of Architectural Heritage, Vol. 8, No.3, pp. 349–375. Mandara, A., and Mazzolani, F. M. [2001] “Energy dissipation devices in seismic up-grading of monumental buildings,” Proc. of III Seminar on Historical Constructions, Guimaraes, Portugal. Marini, A., Belleri, A., Preti, M., Riva, P., and Giuriani, E. [2017] “Lightweight extrados restraining elements for the anti-seismic retrofit of single leaf vaults,” Engineering Structures, Vol. 141, pp. 543–554. Marini, A., Giuriani, E., Lugoboni, M., Cominelli, S., and Belleri, A. [2016] Le connessioni tra le coperture scatolari sismiche e le pareti perimetrali degli edifici storici, Technical report num. 3/2016, DICATAM-Università degli Studi di Brescia. Mazzolani, F. M., and Mandara, A. [1994] “Seismic upgrading of churches by means of dissipative devices,” 1st STESSA Conference, Timisoara (Romania). Mazzolani, F. M., and Mandara, A. [2004] “Copertura dissipativa in acciaio per un edificio industrial murario di grande luce.,” Proc. Of the 11° ANIDIS National Congress 2004, Genova, Italy. McKenna, F., Fenves, G. L., Scott, M. H., and others. [2000] “Open system for earthquake engineering simulation,” University of California, Berkeley, CA. Menon, A., and Magenes, G. [2008] Out-of-plane seismic response of unreinforced masonry: definition of seismic input, Rose School, IUSS Press. Nakamura, Y., Derakhshan, H., Magenes, G., and Griffith, M. C. [2016] “Influence of Diaphragm Flexibility on Seismic Response of Unreinforced Masonry Buildings,” Journal of Earthquake Engineering, Vol. 0, No.0, pp. 1–26. NTC. [2008] Ministry Decree, January 14th, 2008. Nuove norme tecniche per le costruzioni (New technical codes for construction) [in Italian]. Paganoni, S., and D’Ayala, D. [2009] “Development and testing of dissipative anchor devices for the seismic protection of heritage buildings,” ANCER Workshop 2009, University of Bath. Penner, O., and Elwood, K. J. [2016] “Out-of-Plane Dynamic Stability of Unreinforced Masonry Walls in One-Way Bending: Shake Table Testing,” Earthquake Spectra, Vol. 32, No.3, pp. 1675–1697. Preti, M., Bolis, V., Marini, A., and Giuriani, E. [2014] “Example of benefits of a dissipative roof diaphragm in the seismic response of masonry buildings,” Proceedings of SAHC2014 – 9th International Conference on Structural Analysis of Historical Constructions, F. Peña & M. Chávez (eds.), Mexico City, Mexico. Preti, M., Marini, A., Bolis, V., and Giuriani, E. [2013] “Experimental response of a large scale transverse-arch subjected to horizontal cyclic loading,” Proc. Conf. “XV convegno ANIDIS, Ingegneria sismica in Italia” 2013, Padova. Preti, M., and Meda, A. [2015] “RC structural wall with unbonded tendons strengthened with highperformance fiber-reinforced concrete,” Materials and Structures, Vol. 48, No.1–2, pp. 249– 260. Priestley, M. N., Sritharan, S., Conley, J. R., and Pampanin, S. [1999] “Preliminary results and conclusions from the PRESSS five-story precast concrete test building,” PCI journal, Vol. 44, No.6, pp. 42–67. Restrepo, J. I., and Rahman, A. [2007] “Seismic Performance of Self-Centering Structural Walls Incorporating Energy Dissipators,” Journal of Structural Engineering, Vol. 133, No.11, pp. 1560–1570. Simsir, C. C. [2004] “Influence of diaphragm flexibility on the out-of-plane dynamic response of unreinforced masonry walls,” University of Illinois at Urbana-Champaign. Simsir, C. C., Aschheim, M. A., and Abrams, D. P. [2004] “Out-of-plane dynamic response of unreinforced masonry bearing walls attached to flexible diaphragms,” 13th World Conference on Earthquake Engineering, pp. 1–6. 17

Tomaz˘evic˘, M., Lutman, M., and Weiss, P. [1996] “Seismic Upgrading of Old Brick‐Masonry Urban Houses: Tying of Walls with Steel Ties,” Earthquake Spectra, Vol. 12, No.3, pp. 599– 622. Wilhelm, M., Mojsilović, N., and Dazio, A. [2007] “Out-of-plane shaking table tests on unreinforced masonry walls,” 10th North American Masonry Conference, pp. 671–682.

18

40

FR

30

Force [kN]

20

10 0 -10 -20 -30

FR

-40 -3%

-2%

-1%

0%

1%

2%

3%

Drift [%] (a) (b) Figure 1. Results of the test on a large scale masonry transverse-arch presented in [Preti et al. 2013]: force-vs.-drift curve (a) and crack pattern at 3% drift (b).

(a) view of the building (S. Maria Assunta, Bione, XVII century)

(b) view of non-dissipative roof diaphragm

(c) dowel connection shear-vs.-displacement response and test set-up

(d) detail of the diaphragm to wall connection (vertical cross-section) and view of the in-situ test set-up Figure 2. Roof-diaphragm strengthening of a church in northern Italy, and typical results of in-situ shear tests on the stud connections securing the diaphragm to the crowning masonries [Marini et al. 2016].

19

Figure 3. Retrofit concept description: building macro-elements (a), behaviour of non-dissipative (b) and dissipative (c, e) diaphragms, and kinematic mechanism of the transverse arch (d).

(a) overall view of the plane (b) detail of the dissipative and stiffened portions Figure 4. Possible layout of the dissipative roof diaphragm.

Figure 5. Diagram of the dissipative roof diaphragm allowing the controlled rocking of the transverse-arches and lateral walls (a). Idealized non-linear behaviour of the dissipative portion of the roof diaphragm (b).

20

(a) elastic-plastic diaphragm (b) ideal elastic-bilinear free rocking (c) dissipative rocking response response response Figure 6. Idealized force-vs.-displacement curves of the roof diaphragm (a) and of the transverse-arch (b) free and controlled rocking (assuming δ2