ABAQUS USERS' CONFERENCE June 4-6, 1997 Milan, Italy

Transcription

1 ABAQUS USERS' CONFERENCE June 4-6, 1997 Milan, Italy

2 Evaluation of the benefits of the use of high shape memory alloy devices on the seismic response of the buildings Massimo Forni, Alessandro Martelli and Maurizio Indirli, ENEA-ERG-FISS, Bologna, Italy Lorenzo Cavina and Enrico Sobrero, University of Bologna, Italy ABSTRACT In the framework of the development of innovative passive techniques for the mitigation of seismic effects on buildings, two strategies are considered to date: the increment of the period (base isolation) and the increment of energy dissipation. The first strategy aims at reducing the input energy provided by the earthquake in the frequency range characterizing the building, the second one aims at increasing the energy dissipated by the structure. Both strategies aim at reducing the seismic response in terms of absolute accelerations and interstorey drift and can also be applied together. On base isolation tecniques, a paper was presented at the 1996 Newport Conference by Forni et al., The present work focuses on the energy dissipation; in particular, the behaviour of innovative devices based on the use of high shape memory alloys (SMAs) and their effects on the seismic response of civil buildings is analysed. INTRODUCTION This work has been performed at the Energy Department (Nuclear Fission Division) of the Italian National Agency for New Tecnology, Energy and the Environment (ENEA), in the framework of an European Project on the development of innovative techniques for the improvement of stability of cultural heritage, in particular seismic protection (ISTECH, FIP Industriale et al., 1996). Aim of this study is the implementation of simplified finite element models (FEMs) of SMA devices, suitable to be used in the seismic analysis of buildings, and evaluation of the benefits of their utilization. Due to their particular characteristics ( 1), SMA devices are particularly attractive for the antiseismic retrofits of old masonry buildings (cultural heritage). Three different structures, all located in Italy, have been considered in this study ( 2): - a masonry church at San Vito in Caposele (Avellino), which was strongly damaged during the 1980 Campano-Lucano earthquake (Irpinia); - a bell-tower at San Martino in Rio (Reggio Emilia), damaged during the 1996 Modena and Reggio Emilia earthquake; - the bell-tower of the San Giorgio Church at Trignano (Reggio Emilia), also damaged during the aforesaid 1996 earthquake. FEMs of the SMA devices and all analysed structures have been implemented in ABAQUS ( 3) and dynamic calculations executed with the aim of identifying the structural parts which are most suitable for the eventual installation of SMA devices and evaluating their effects on the seismic response of the structures ( 4). 1. SHAPE MEMORY ALLOY DEVICES Figures 1a-b schematically show typical stress-strain curves of a SMA (Graesser & Cozzarelli, 1991). The behaviour is initially elastic, with a Young's modulus similar to that of a normal steel (200,000 MPa); then, when a certain stress is reached (the upper plateau corresponds to MPa, depending on temperature), it becomes hysteretic (that is, independent of velocity), like a sort of 'reversible plasticity': in fact, when the stress decreases, the material returns elastic. The

3 energy dissipation is not due to material degradation but to a change of phase of the alloy, which passes from martensitic to austenitic state at two different stress levels or temperatures. The stress level (or temperature value) at which the change of phase occurs, depends on the particular composition of the alloy. Figure 1a refers to the case of ambient temperature lower than the value at which the alloy microstructure is fully martensitic (T m ). The material is pratically elastic-plastic up to a certain strain level (8% tipically) beyond which it returns elastic (superelasticity). The upper pleteau is nearly 100 MPa. A SMA device working in such a range of temperature, can perform thousands of cycles with negligible variations of the mechanical characteristics. Figure 1b refers to the case of ambient temperature higher than the value at which the microstructure is fully austenitic (T a ). The hysteresis loop has a lower plateau corresponding to a stress level MPa lower than the upper one (200 MPa, tipically). Also in this case, beyond a strain level of about 8%, the material returns elastic. The simplest SMA device working in this range of temperatures can be a wire, post-strained, as an example, at 4% of its total length, connecting two parts of a structure divided by a joint or a crack. The initial post-stress value can be on the upper or lower plateau of the hysteresis loop. In the first case, the device will apply a constant force, independently of any increment of deformation up to 4%; in the second case, it will apply a constant force even if the deformation decreases of 4%. The first solution shall be adopted when a increase of deformation is expected, as in case of opening of a crack due to soil settlements. The second solution shall be chosen when a decrement of deformation is expected, as in the case of creep. In both cases, during cyclic deformations, such as those induced by an earthquake, the device will dissipate energy. Contrary to other energy dissipators (viscous, elastic-plastic, etc.), a SMA device can be very small. Thus, it results to be particularly suitable for the retrofit of cultural heritage, where the intervention must take into account aesthetic aspects, not being invasive. 2. STRUCTURES CONSIDERED 2.1 San Vito in Caposele church The San Vito in Caposele church is a small masonry building which was strongly damaged during the Campano-Lucano earthquake (0.18 g peak acceleration) in 1980, as shown in Figure 2a. It was pratically re-builted in 1996, mostly using original materials. This structure is quite stiff, due to its small sizes (it is only 6 m high) and the thickness of the walls (0.6 m minimum). Figure 2b shows a sketch of the new church, which was initially formed of a main building (6.5 m x 9.8 m), a small sacristy (3 m x 5 m) and a little bell-tower (7.5 m height). The roof is made of wood and has three central chains (12 cm x 16 cm section area). In reality, due to relevant soil problems encountred during the construction phase, the bell-tower and the sacristy were not re-builted. Thus, the structure was quickly completed and there was no time for the utilization of the SMA devices, which were still under preliminar analyses. In spite of this, the church was numerically modeled, included the bell-tower and the sacristy ( 3.2), and its FEM used for parametric analyses aimed at evaluating the best position for the application of the SMA devices ( 4.2). In particular, the possibility of using these devices in series with the three chains of the roof and between the church and the sacristy has been analysed. 2.2 San Martino in Rio Civic Bell-Tower The San Martino in Rio Civic Bell-Tower is 200 years old and was damaged during the 1996 Modena and Reggio Emilia earthqake (0.2 g ground acceleration peak). This earthquake was the strongest known seismic event which struck the area. Figure 3a shows a detail of the cracks opened in the walls due to the excessive tensile stresses produced by bending deformation modes. The

4 tower is 34 m high and has a square base with 5.2 m edge. The masonry walls are 1.1 m thick at the base, 0.8 m in the central part and 0.6 m at bell-cell level (22 m). After the earthquake, the belltower was monitored using accelerometers and the first measurements (based on ambient and trafic excitations) showed a first response frequency of 1.7 Hz. The rehabilitation works are still in progress (February 1997, Figure 3b) and consist in the injection of special mortars into the cracks, aimed at re-establishing the continuity of the damaged masonry, and insertion of 16 post-stressed steel bars into the walls (connecting the bell-cell level to the foundations), in order to increase the bending resistance. The possibility of using SMA devices in series with the reinforcing bars was numerically analysed ( 4.2.2). 2.3 Bell-Tower of the San Giorgio church at Trignano Also the San Giorgio church at Trignano (Figure 4a) was seriously damaged during the 1996 Modena and Reggio Emilia earthquake. For this old structure (XIV century), no constructive or architectural drawings were available and a geometric survey was needed. The bell-tower is 18.5 m high and has a square base with 3 m edge. It is surrounded on three edges by others buildings up to the height of 11 m. The masonry walls are 0.42 m thick close to the corners and 0.3 m in the central part. Four large windows, closed using thin brick walls, are present at 13 m level. Thus, the corresponding section results to be quite weak; in fact it braked during the above-mentioned earthquake. Figure 4b shows the cracks at the windows level, caused by a rotation of about 3 cm of the upper part of the structure. Also this tower was monitored and the first frequency measured (2.7 Hz), by recording both ambient and vibrations and aftershocks (Forni et al., 1997a). Moreover, it was subjected to four aftershocks which were recorded and used in the numerical analyses ( 4.3). The intervention of restoration of this bell-tower is still under design (February 1997), but it should be quite similar to that of the San Martino Civic Bell-Tower: injection of special mortars and insertion of post-stressed steel bars ( 2.2). However, in this case, the utilization of SMA devices has already been foreseen: 4 devices will be placed into the walls at the corners of the tower, in series with the post-stressed bars, in order to guarantee the constancy of the compression force against creep or settling phenomena. 3. FINITE ELEMENT MODELS (FEMs) 3.1 SMA devices The higly non-linear behaviour of the SMA ( 1) has been modeled in ABAQUS by coupling a non-linear spring with an elastic-plastic beam. The non-linear spring describes the elastic part of the curve (Figures 1a-b) then, when SMA change of phase occurs, it provides a constant (or quasiconstant) compression force. The 'thickness' of the hysteresis loop (i.e. the energy dissipated in each cycle) depends on the first yelding point of the elastic-plastic beam (of course, its material is completely arbitrary). An appropriate choice of the geometrical and mechanical characteristics of the beam (Young's modulus, section area and length), allows for the modelization of any hysteresis loop. 3.2 San Vito in Caposele church The FEM of the church is composed by 1,424 nodes and 625 solid elements (8-nodes). The contribution of the stiffness of the roof was neglected, while its mass was distributed into the last layer of solid elements of the walls. The three central chains were modeled using axial spring elements in the linear analyses ( 4.1.1) and couples of springs and elastic-plastic beams in the SMA modelization ( 4.1.2). An artificial joint between the church and the sacristy, not present in the original design ( 2.1) was modeled using GAP elements in order to simulate a crack and analyse the effects of inserting SMA devices ( 4.1.3). In this step of the analysis, the height of the

5 sacristy was also increased by 1 m, in order to allow for higher deformations. Young's modulus of 3,000 MPa, medium density of 2,400 kg/m 3 and damping ratio of 5% were assumed for the masonry walls (but some calculations were also performed with no damping, see 4.1). These values provide a total weight of the structure of 3,000 kn and a first natural frequency of 10.5 Hz. Figures 5a-d show the first four modal shapes of the structure. 3.3 San Martino in Rio Civic Bell-Tower This structure was modeled using 1,390 nodes and 725 solid elements (8-nodes). The FEM contains the main openings which are present in the structure. The effects of the adjacent buildings, surrounding the tower on two edge up to 11 m height, were neglected both in terms of mass and stiffness. In fact, they are structurally independent of the tower and have quite a lower stiffness, with respect that of the tower walls at the same elevation. The Young's modulus of the masonry walls is 3,000 MPa and their medium density 1,700 kg/m 3 (5,300 kn total weight). The failure limits of the masonry had been assumed equal to 4 MPa and 0.4 MPa for the compression and tension stresses, respectively. Also in this case, damping ratio was assumed equal to 5%. The first natural frequency results 1.5 Hz (Figures 6a-d), 13% lower than the first experimental measurements ( 2.2). This is mainly due to the presence of the cracks, which were not included in the FEM. The reinforcing post-stressed bars were simply represented by axial spring elements, coupled with elastic-plastic beams to model the SMA devices ( 3.1). 3.4 Bell-Tower of the San Giorgio church at Trignano This structure is quite small with respect the San Martino tower, thus the effects of the adjacent buildings are important and cannot be neglected. However, due to the difficulties of modeling the behaviour of the lower part of the structure in detail, this was simply simulated giving an appropriate Young's modulus to the material of the lower part of the tower, in order to fit the experimental frequency ( 2.3). On the contrary, the upper part of the tower was modeled in detail, by reproducing the main openings, floors, etc. 1,910 nodes and 1,267 solid elements (8-nodes) were necessary for the FEM. The mechanical characteristics of the masonry are quite poor, thus a Young's modulus of 1,000 MPa and a medium density of 1,700 kg/m 3 were adopted (the damping ratio was 5% also in this case). The failure limits of the masonry were assumed equal to 1 MPa and 0.1 MPa for the compression and tension stresses, respectively. The total weight of the tower resulted to be 1,200 kn and the first frequency 2.6 Hz (Figures 7a-d). For this structure, again, the reinforcing post-stressed bars were simply represented by non-linear axial spring elements, coupled with elastic-plastic beams to model the SMA devices ( 3.1). 4. NUMERICAL ANALYSES 4.1 San Vito in Caposele church Original design After the evaluation of the first 18 modal frequencies (corresponding to the 75% of the total mass), some linear analyses were performed, in both time (Dynamic) and frequency (Response Spectrum) domains, in order to characterize the behaviour of the church in the design conditions. In particular, the structure was subjected, among others, to the 1980 Campano-Lucano eartquake recorded at Calitri (0.18 g peak acceleration, 80 s long) and to a synthetic earthquake generated based on the EC8 standards for medium soils (class B, 0.29 g peak acceleration, 35 s duration). The church was excitated in the transversal direction, which is the most flexible. Stresses and strains of the central chains and wall deformations were controlled, with the aim of identifying the most suitable locations for the SMA devices and their mechanical features (stiffness, plasticization limit, etc.). In order to evaluate the maximum range of deformations available for the application of

6 the SMA devices, some parametric calculations were also performed by assigning a stiffnesses equal to zero and infinite to the three central chains. The effects of the structural damping of the church were also evaluated: some calculations were repeated using no damping. Table 1 summarizes the results of this step of the analysis. Due to the high frequency of the church, the deformations of the structure result to be quite low everywhere and the SMA devices cannot work properly, as energy dissipators at least. This was one of the reasons why the use of SMAs for the rehabilitation of this church was definitively abandoned. However, before abandoning this structure, some parametric analyses were also performed by assigning a Young's modulus 5 times lower and a density 5 times higher to the walls ( 3.2), in order to take advantage of this study to learn useful lessons for the application of SMA to cultural heritage. In this way, the frequency of the church results to be 5 times lower than the design value and simulates the behaviour of a larger structure with larger deformations. In the following this case is called 'flexible' church SMA devices into the chains The second step of the analysis consisted in introducing SMA devices in series with the three central chains of the church. The devices were modeled as described in 3.1 (Figure 1a), by assuming a stiffness equal to zero for the spring (no pre-tension) and plasticization limits of the beam corresponding to 75% and 50% of the maximum force calculated in the linear analyses for the related chain (see Table 1). The elastic part of the hysteresis loop is characterized, of course, by the axial stiffness of the real wood chain. The accelerations and displacements of two points at the top of the church (external and sacristy edges) and forces and deformations into the chains were controlled, in order to evaluate the effects of the SMA devices on the response of the structure. As examples of the results achieved, Figures 8a-b report the displacements at the top of the flexible church during the application of the EC8 earthquake with and without the SMA devices, while Figures 9a-b report the hysteresis loops of the SMA device located in the central chain in the design and flexible cases, respectively. All the results of this step of the analysis are reported in Table 2. The effects of the SMA devices are different for the two edges of the church: in any case they are negligible for both the real and 'flexible' church, due to the low amount of dissipated energy in comparison with that dissipated by the masonry. In fact, as shown in Table 2, only in the case of structural damping equal to zero the SMA devices provide a significant decrease of the seismic response at the top of the church for both edges SMA devices between church and sacristy The last step of the analysis consisted in simulating the presence of a crack between the church and the sacristy and introducing 2 or 4 SMA devices across it, with the aim of providing a constant closure force and energy dissipation in case of cycling. The devices were modeled as described in 3.1 (Figure 1b). Table 2 shows that, in the case of absence of SMA devices ('open crack', Figure 10 a), both maximum accelerations (Figure 10 b) and displacements at the top of the church are higher than those calculated in the case of absence of the crack (original design, Table 1). The analysis also shows that the presence of SMA devices is useful only if they can provide a constant force sufficient to guarantee the closure of the gap during earthquake, otherwise, the shocks between sacristy and church walls would produce too high acceleration peaks. In fact, in this case again, the amount of energy dissipated by the devices is quite low, due to the limited displacements (Figure 10 a). It is worthwile noting that friction dissipation was not considered in the calculations. 4.2 San Martino in Rio Civic Bell-Tower Restoration of the masonry

7 The FEM of the tower defined in 3.3 was subjected to several linear calculations, even three-directional (3D), in both time (Modal Dynamic) and frequency (Response Spectrum) domains, by assuming the complete re-establishment of continuity of the masonry after the injection of the special mortars mentioned in 2.2. The first 12 modes, corresponding to 87% of the total mass, were considered. Aim of these calculations was to evaluate the maximum credible displacement at the bell-cell level of the tower, which was chosen as reference point of the structure. The 1996 Modena and Reggio Emilia earthquake recorded at Novellara (which is a few chilometers distant from San Martino in Rio) and other natural records typical of the site (Novellara 1987) or with similar soil conditions (the 1976 Friuli earthquake recorded at Tolmezzo, and the 1980 Campano-Lucano earthquake recorded at Calitri) but more severe in terms of acceleration peaks, were used in this step of the analysis. Figure 11a shows the displacement calculated at the bell-cell in the West-East (WE) direction caused by the application of the 3D 1996 Modena and Reggio Emilia earthquake, while Figure 11b shows the corresponding absolute acceleration. The maximum displacement is 17 mm while the maximum acceleration is 0.3 g. In the frequency domain, the spectrum of the aforesaid earthquake provided a maximum displacement of 22 mm (Figure 12 a) and a maximum absolute acceleration of 0.27 g (Figure 12 b). The application of the Tolmezzo and Calitri records provided, of course, larger displacements (4 and 5 cm, respectively) and accelerations (0.4 g in both cases), but it is necessary to note that they are characteristic of sites with higher sismicity. Based on the above-mentioned results, a value of 3 cm was assumed for the maximum credible displacement at the bell-cell level. This displacement was applied statically in the WE direction, simultaneously to the dead load of the tower, and the maximum strains and stresses evaluated. Figure 13 shows the σ 33 stress distribution (which is the critical one) in the most stressed section of the tower, which is close to that which really failed. It is evident that the tensile failure limit (0.4 MPa) is exceeded in a large part of the section, while no problems are given by the compression component of the stress (max -1.7 MPa) Effects of the reinforcing bars The strains corresponding to the stresses reported in Figure 13 are quite low (ε 33max = ), thus the reinforcing steel bars used for the restoration ( 2.2) cannot work properly if they are not significantly post-stressed. After some parametric calculations, a value of 100 kn for each bar was adopted. Figure 14 shows the stress distribution, in the same section as that showed in Figure 13, in the case of application of the dead load, total stress force of the steel bars (1,600 kn) and displacement of 3 cm at the bell-cell elevation. The tensile failure limit of the masonry is exceeded only in a negligible part of the section. Due to the very low deformations of the bars during a seimic motion, no SMA device can be used as energy dissipator in this case. In fact, if installed in series with the steel bars, SMA devices would remain in the elastic part of the hysteresis loop. The only possible benefit in using these devices would be that of providing a constant tensile force into the reinforcing steel bars, in order to prevent the effect of creep of the masonry and other temperature or settlement phenomena. But, after the application of the designed stress of 100 kn, the bars, due to their length (22 m), are subjected to an elongation of 18 mm, which can be considered as sufficient to absorb all deformations of the masonry. Thus, no SMA device was used for this application. More information about this study is reported by Forni et al., 1997b. 4.3 Bell-Tower of the San Giorgio church at Trignano The numerical analysis of this structure is still in progress (February 1997): in particular, the characterization of the material and modelization of the boundary conditions is being carried out. To this porpuse, the aftershocks recorded after monitoring of the tower will be particularly usefull.

8 The FEM described in 3.4 is being used to perform the same calculations as for the San Martino in Rio Civic Bell-Tower: linear analyses in the frequency domain and non-linear analyses in the time domain, aimed at evaluating the correct post-stress to be given to the reinforcing bars. The first preliminary calculations showed that the structure needs to be strongly reinforced: as examples, Figures 15 a-d show the distribution of displacements, accelerations, stresses and strains in the upper part of the tower, due to the application of the 2D spectrum of the 1996 Modena and Reggio Emilia earthquake. In particular, Figure 15 c shows that the tensile failure limit (0.1 MPa, 3.4) is exceeded in large part of the structure. The post-compression stress provided to the structure will be keep constant using SMA devices in series with the bars ( 2.3) and modeled as described in 3.1 (Figure 1b). The force provided by the SMA devices shall be sufficient to avoid overcoming the tensile stress failure limit in the structure ( 3.4). 5. CONCLUSIONS The numerical analyses reported in this study showed that, for the structures considered, at least, SMA devices cannot be used only as energy dissipators but mostly as reinforcing devices. In fact, in spite of its quite high damping coefficient, the total amount of energy dissipated by a SMA device is too low, with respect that dissipated by the whole structure, due to the small mass of the device itself. However, SMA devices can properly work as energy dissipators in structures having low structural damping and high deformations, such as cultural heritage structures formed by superposed blocks or also steel frames (this topic is included in a second European project aimed at developing innovative energy dissipation devices - ENEL et al., 1996). Anyway, the capability to dissipate energy remains, of course, always positive, for example in the case of an earthquake higher than that expected. The best wide-ranging use of SMAs is probably that of reinforcing devices. In fact, their capability of providing constant forces is particularly useful in presence of crack opening, creep deformations or settlement phenomena. These features, together with their limited encumbrance, make SMA devices particularly suitable for the retrofit of cultural heritage. REFERENCES ENEL S.p.A. CRIS, ALGA S.p.A., BOUYGUES SA, ENEA, FIP Industriale S.p.A., GEC Alsthom T&D SA, Instituto Superior Técnico, Lisboa, Joint Research Centre of Ispra, LIN (Università di Bologna), MRPRA", Optimization of Energy Dissipation Devices, Rolling-Systems and Hydraulic Couplers for Reducing Seismic Risk to Structures and Industrial Facilities, EC Project REEDS - BE 1031, FIP Industriale S.p.A., Aristotele University of Thessaloniki, ENEA, Istituto Superior Técnico (Lisboa), Joint Research Centre of Ispra, Università di Roma "La Sapienza", Development of Innovative Techniques for the Improvement of Stability of Cultural Heritage, in Particular Seismic Protection, EC Project ISTECH - PL , Forni M., Indirli M., Dusi A., Brasina A., Carinci M., Diotallevi P., Rebecchi V. and Grassi L., Seismic Analysis of Base-Isolated Structures, Proc. ABAQUS Users Conference, Newport, R.I.,USA, Forni M., Indirli M., Martelli A. et al., Rehabilitation of Cultural Heritage Damaged by the 15th October 1996 Earthquake at San Martino in Rio, Reggio Emilia, Italy, International Post-SMiRT Conference Seminar on Seismic Isolation, Passive Energy Dissipation and Active Control of Vibrations of Structures, Taormina, Sicily, Italy, August 25 to 27, 1997a (to be published).

9 Forni M. and Cavina L., Calcoli di Supporto all'intervento di Messa in Sicurezza della Torre Campanaria Civica di San Martino in Rio a Seguito del Danneggiamento Subito Durante il Sisma del 15 Ottobre 1996, ENEA report AT.FAL.00013, 1997b (in Italian). Graesser E. J. and Cozzarelli F. A., Shape-Memory Alloys as New Materials for Aseismic Isolation, Journal of Engineering Mechanics, Vol. 117, N0. 11, November Table 1. Relative displacements (d) and absolute accelerations (a) calculated at the wall top, and displacements (s) and reaction forces (f) calculated in the central chain of the San Vito in Caposele church (linear analyses) Analysis Sacristy edge External edge Central chain CONDITIONS Type Excit. d (mm) a (m/s 2 ) d (mm) a (m/s 2 ) s (mm) f (kn) Original design Spectrum Calitri No chains " " / Rigid chains " " / 24.8 Original design Dynamic " " " EC No damping " " " " " Flexible church Spectrum Calitri " Dynamic " " " EC Table 2. Relative displacements (d) and absolute accelerations (a) calculated at the wall top, and displacements (s) and reaction forces (f) calculated in the central chain of the San Vito in Caposele church (non-linear analyses) Analysis Sacristy edge External edge Central chain INTERVENTION Type Excit. d (mm) a (m/s 2 ) d (mm) a (m/s 2 ) s (mm) f (kn) 3 SMA 75% original d. Dynamic EC SMA 50% original d. " " Open crack " " SMA church-sacristy " " SMA church-sacristy " " SMA 50% no damp. " " SMA 50% flexible ch. " "

10 Stress (MPa) Strees (MPa) Strain (%) Strain (%) Figure 1a. Sketch of SMA hysteresis loop at ambient temperature lower than T m Figure 1b. Sketch of SMA hysteresis loop at ambient temperature higher than T a Figure 2a. San Vito in Caposele church after the 1980 earthquake Figure 2b. Sketch of the original restoration design of the San Vito in Caposele church Figure 3a. Cracks in the San Martino in Rio Civic Bell-Tower after the 1996 earthquake Figure 3b. Civic Bell-Tower at San Martino in Rio during the restoration works

11 Figure 4a. San Giorgio church at Trignano and its bell-tower Figure 4b. Craks caused in the Trignano bell-tower by the 1996 earthquake Figure 5a. First modal shape of the San Vito in Caposele church (10.5 Hz) Figure 5b. Second modal shape of the San Vito in Caposele church (13.5 Hz) Figure 5c. Third modal shape of the San Vito in Caposele church (14.6 Hz) Figure 5d. Fourth modal shape of the San Vito in Caposele church (15.9 Hz)

12 Figure 6a. First modal shape of the San Martino in Rio bell-tower (1.5 Hz) Figure 6b. Second modal shape of the San Martino in Rio bell-tower (1.5 Hz) Figure 6c. Third modal shape of the San Martino in Rio bell-tower (6.6 Hz) Figure 6d. Fourth modal shape of the San Martino in Rio bell-tower (6.6 Hz)

13 Figure 7a. First modal shape of the Trignano bell-tower (2.61 Hz) Figure 7b. Second modal shape of the Trignano bell-tower (2.63 Hz) Figure 7c. Third modal shape of the Trignano bell-tower (6.18 Hz) Figure 7d. Fourth modal shape of the Trignano bell-tower (9.65 Hz)

14 3 mm 3 mm 0 0 m Figure 8a. Displacement at the top of the San Vito church in the design conditions (EC8 earthquake - transversal direction) s Figure 8b. Displacement at the top of the San Vito church with 3 SMA devices (EC8 earthquake - transversal direction) s 20 kn 150 kn 0 mm mm Figure 9a. Hysteresys loops of a SMA device installed in the central chain of the San Vito church (EC8 earthquake) -150 Figure 9b. Hysteresys loops of a SMA device installed in the central chain of the San Vito church (flexible church, EC8 earthquake) 2,5 mm 15 m/s*s 1,5 0 0,5-0, Figure 10a. Opening of the crack between San Vito church and sacristy in the case of absence of SMA devices (EC8 earthquake) s Figure 10b. Acceleration at the top of the San Vito church in the case of absence of SMA devices across the crack (EC8 earthquake) s

15 0,02 m 4,00 m/s*s 2,00 0,00 0,00-0, Figure 11a. WE displacement at the bell-cell of the San Martino tower in the original conditions (1996 Novellara 3D record) s -2,00-4, Figure 11b. WE acceleration at the bell-cell of the San Martino tower in the original conditions (1996 Novellara 3D record) s Figure 12a. WE displacement distribution of the San Martino tower in the original conditions (1996 Novellara 2D spectrum) Figure 12b. WE acceleration distribution of the San Martino tower in the original conditions (1996 Novellara 2D spectrum)

16 Figure 13. Stress distribution in the most stressed section of the San Martino tower in the original conditions (dead load plus 3 cm deflection at the bell-cell level) Figure 14. Stress distribution in the most stressed section of the San Martino tower after the intervention (dead load plus 3 cm deflection at the bell-cell level)

17 Figure 15a. Displacement distribution in the Trignano tower due to the application of the 1996 Novellara 2D spectrum Figure 15b. Acceleration distribution in the Trignano tower due to the application of the 1996 Novellara 2D spectrum Figure 15c. Stress distribution in the Trignano tower due to the application of the 1996 Novellara 2D spectrum Figure 15d. Strain distribution in the Trignano tower due to the application of the 1996 Novellara 2D spectrum