Structural Analysis of Historical Constructions - Modena, Lourenço & Roca (eds) © 2005 Taylor & Francis Group, London, ISBN 04 1536 379 9

Mechanical models for the seismic vulnerability assessment of churches

S. Lagomarsino, S. Podestà, S. Resemini, E. Curti & s. Parodi Department ofStruetural and Geoteehnieal Engineering, University ofGenoa, ltaly

ABSTRACT: In the paper, the authors present a methodology to evaluate the seismic damage scenario of mon­umental buildings. The method is formulated both on a qualitative approach, based on the observation of seismic damage patterns (macroelement response) and on mechanical evaluations, obtained by the definition of sim­plified models. Moreover, the results of the methodology application to the churches in Catania (ltaly) are described. The particular features of this kind of buildings led to the study of the seismic vulnerability of two collapse mechanisms: the overturning ofthe faça de and the in-plane mechanism ofthe triumphal arch. In both cases, the methodology allows us to take into account the influence oftie-rods and the quality ofthe connection with the lateral walls. Even if an approximation criterion is adopted, taking in consideration the seismic hazard in each ditferent site, a di splacement-based method, using the capacity curves of each single macroelement, represents an adequate tool in order to evaluate the seismic response of churches.

INTRODUCTION

The structural safety evaluation on monumental and historical buildings under seismic action (as remarked in the new Italian seismic code) highlights the need to verify in a quantitative way the etfectiveness of a designed retrofitting intervention. This aspect implies the availabi lity of appropriate verification tools, in order to assure both a realistic estimation of the vul­nerability decrease in lhe building (in terms ofseismic ground acceleration that produces damage, before and after the interventions), and the true applicability of lhe melhod (in terms of time and amount of work).

[n the case of structurally complex buildings, the estimation of the global behaviour may be often unrealistic. Besides, monumental buildings, such as churches, are often made up ofrepetitive architectonic elements, called macroelements, which are charac­teri sed by a mostly autonomous structural behaviour in comparison with that ofthe rest ofthe fabric (Doglioni et aI. 1994). This aspect determined the adoption ofan assessment methodology of seismic damage that tries to analyse the global behaviour, as a sum of every sin­gle contribution of every macroelement present in a church. Using a macroelement approach, we want to analyse the vulnerability and the seismic improvement of particular structural systems, applying to these the Capacity Spectrum Method.

This procedure, adopted for R.C. buildings in some new-conception codes (ATC 40, FEMA 273, HAZUS, New ltalian Seismic Code), involves the idea of the

performance-based design and non-linear static anal­yses play in it an important role (Freeman 1998, Fajfar 2000). This method is based on the comparison between the capacity ofthe structure and the demand due to the seismic event, in terms of ductility and strength .

But the Capacity Spectrum Method is atfected by some troubles if we used it on masonry buildings; in fact , these are characterised by a strongly non-linear behaviour under seismic loading, even for low stress values. The curve itself could be of ditficlllt defini­tion, especially in case of monumental or religious buildings. Generally, these constructions present irreg­ularities in plan and in elevation, in which particular architectonic elements (such as the vaults, the arches, the counterforts, etc.) are included.

Therefore the concept of the macroelement allows us to analyse the most vulnerable parts ofthe chllrch, which are characterized by the activation of partial collapse mechanisms. Moreover, it allows simplified models to be used; these could be based on equilibrium limit analysis on rigid body kinematisms. In this way, the capacity curves could be determined for the most significant damage mechanisms.

2 HISTORICAL SEISMIC EVENTS IN CATANIA (ITALY)

The seismic history in Catania (Azzaro et aI. 1999, Boschi et aI. 2001) highlights that the urbanistic

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growth of the town was strongly influenced by the effects ofmany seismic events.ln fact, in the past 1000 years the city of Catania was almost destroyed by the 1169 and 1693 earthquakes and slightly or severely damaged by other 20 events (1542, 1818, 1848, 1990, etc.). The earthquake of January 1693 was character­ized by two strong shocks in three days; it severely shocked a huge area, causing the ma in seismic disaster in Sicily. Only the most damaged area (South-eastern Sicily) measured 14,000 m2 and the most important towns were involved.

After the 1693 earthquake, Catania was newly built, follow ing a reconstruction project. The churches were built in Baroque style, typical of this town, char­acterized by architectonic originality, not found in other ltalian regions, and by scenic visual effects. The façades were often shaped with convex and concave lines, in order to better insert the religious building in the urban texture; moreover, a lot of churches shown a particular complexity in plan, both in order to be archi­tecturally original and because the town was already heavi ly urbanized.

In the first half of the XIX century, Catania exper­imented other seismic events after the reconstruction. The deeply modifi ed urban configuration (new roads, buildings and churches) was strongly shocked by three earthquakes: February 1818, March 1818 and January 1848. The evaluated macroseismic intensity of these events is not so high (VI and VII MCS), but the city shown its vulnerability, being damaged both in the ordinary and monumental buildings.

2.1 Deterministic seismic hazard evaluation

In the ambit of the RISK-UE Project "An advanced approach to earthquake risk scenarios with applica­tions to different European towns" (Contract: EVK4-CT-2000-00014, funded by the European Community within the 5th Framework Programme), the vulnera­bi lity of the monuments in the urban area of Catania was studied (Pessina 2000, Faccioli & Pessina 2003) .

In the case of Catania, where high magnitude earth­quakes are well documented, the choice ofthe scenario earthquake as the maximum historical event is reason­able. Choosing as reference earthquake the M7.3 event of January 11 , 1693 (levei I scenario), many hypothe­ses of source location should have been tested; the location of the source on the offshore lbleo Maltese fault was constrained to structural and morphological features, and referring to the recent seismicity, beca use ofthe historical observations were iH documented. As a leveI 11 scenario the M6.2 event ofFebruary 20, 1818 is chosen: this is less destructive, even if a damaging earthquake.

A simplified geotechnical zonation (resulting from a c\ass if ication into rock, stiff soil and soft soi! con­ditions), was proposed within the RISK-UE Project (Fig. I).

• A -Roek B - 5tiff

O C - 50ft o D - 50ft

Figure 1. Simplified geological map of the urban area of Catania.

amax [9] 0.47

0.20

0.07

.2.

Figure 2. Map of spectral acceleration for peri od T = O (ama, ), including the effects ofsoil conditions for levei! event (l eft) and levei 11 event (right) (Faccioli & Pessina 2003).

The Ambraseys attenuation relationship (Ambraseys et aI. 1996), allow generating shaking ground maps in terms of spectral acceleration, inc\ud­ing the effects of soil conditions. The maps of spectral acceleration for T = O (ama,) are plotted in Figure 2.

3 CAPACITY SPECTRUM METHOD FOR THE SEISMIC VULNERABlLITY ASSESSMENT OF CHURCHES

In order to develop an assessment methodology at a territorial scale, there is the need of simplified analysis methods. The seismic vulnerability is evalu­ated through the Capacity Spectrum Method (Freeman 1998, Fajfar 2000). The damage scenario is defined by the intersection (performance point) between the capacity curve and the response spectrum (AD for­mat - pseudo acceleration vs. displacement) that is

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·A·Rock OB · 5t1rr o C ' 50rt

Figure 3. Overlapping ofthe simplified geological map and lhe urban environment of Catania.

representative of the chosen earthquake (derived by the hazard scenarios previously described). The perfor­mance point has to be correlated to the damage leveis previously defined. The analysis method used to define the capacity curve is based on the Equilibrium Limit Analysis. This approach was applied in other cases, in good agreement with fem non-linear dynamic analyses (Lagomarsino et aI. 2002 , lrizzarry et aI. 2002).

3.1 Seismic demand through earthquake response spectrum

On the basis ofthe hazard scenarios in terms ofspectral acceleration for T = O (amax ), described in the previous section, we evaluated the complete response spectra in the site of each church.

In order to determine them, knowing the PGA values in the urban area ofCatania, a Geographic Infor­mation System (GIS) was used. In the urban environ­ment, the churches to be studied were localized, using a geocoded map to which both the simplified geolog­ical map and the hazard scenarios in terms of spectral acceleration forT = O (amax ) were overlapped (Fig. 3).

So, in each church site, the spectral acceleration values, corresponding to different vibration periods T, were evaluated using the Ambraseys attenuation rela­tionship and taking into account the soil condition (Fig.4).

Taking into account the soil stratigraphy, the earth­quake magnitudo and the epicentral distance, the Ambraseys attenuation relationship (considering a vis­cous damping of 5%) describes in a proper way the response spectra of the two chosen seismic events.

3.2 Capacity curve through simplified mechanical models

From the damage survey, it arises that, in case of a complex typology, the seismic behaviour could not be described properly in a global way. In case of

1.2 .... S. Benedetto Levei J se. - .. S. Nicolô ai Borgo Levei T se.

., - S Sebastiano Levei I se S Benedetto levei 11 se,

!i 0.8 .. ~. - -~ --:.;- \ S Nicoló ai Borgo LevellJ se

! ::~ "" ~'-'''" 0.2 . '''\ ' .::,. '\_.-\, ~ .

-. -\.\-...., O ~--------.---------~--------r-----

O 0.05 0. 1 0. 15

Figure 4. Response spectra (both levei I and 11) for three churches: S. Benedetto (rock), S. Nicolo aI Borgo (stiff soil), S. Sebastiano (soft soil).

some monumental typology (tower, obelisk, etc.), the definition of a capacity curve describing the global behaviour of the monument is conceptually correct, even if of difficult realisation. As regards the churches there is another specific requirement, arising from the consideration that a capacity curve representing the global behaviour of the construction could be not totally correct. In this case, the curve has to be defined for a single macroelement. The damage mechanisms depend on vulnerability characteristics (e.g, the con­structive and material aspects), specific ofa particular building,

The capacity curve of a single macroelement may be determined through a simplified mechanical model , based on few geometric parameters (e.g, in case ofthe triumphal-arch macroelement, we consider the arch thickness in crown, the span and rise of the arch, the pillar height, etc,).

The analysis method used to define the capacity curve is based on the Equilibrium Limit Analysis. It takes into consideration kinematic theorem, applied to the masonry considered as an assemblage of rigid blocks, held together by compressive forces and liable to crack as soon as tensile stresses begin to be devel­oped . This approach is based on the observation of the real behaviour of masonry structures. They are generally characterized by a negligible elastic defor­mation ofthe single parts, although displacements and rotations (due to the crack development) are possible. The earthquake, therefore, is simulated as a horizon­tal static force, proportional to the masses, and the obtained collapse multiplier À represents the spec­trai acceleration. This approach allows us to estimate, with few geometrical and typological parameters, a macroelement capacity curve, estimating the effective­ness of some aseismic devices (tie-rods, buttresses, etc.). The kinematic approach is operatively simpler than the static one. Once defined a set of possible mechanisms (a condition in which the structure may be represented by a kinematic chain of rigid bodies), the

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equilibrium is possible only under particular load con­dition. The value of lhe load multiplier À for which the structure is in equilibrium is defined collapse (kinematic) load multiplier. The effective collapse mechanism is the one for which the load multiplier (that is the effective collapse multiplier) determines an admissible stress state (no tension) in the whole structure. For the limit-analysis kinematic theorem, the effective collapse multiplier is the minimum among ali the kinematic load multipliers.

So, in order to be significant, the selected mecha­nisms have to be realistic and related to the observed damage patterns.

The first point on the capacity curve is defined through the effective collapse multiplier À calculated. In order to determine the other points on the capacity curve, we have to follow the development ofthe bear­ing capacity ofthe structure. A modified configuration of the elements (due to the mechanism evolution) is defined, the new multiplier is evaluated and associ­ated to the correspondent displacement ofthe structure centroid. The last step is repeated until the value ofthe horizontal forces multiplier is equal to zero (displace­ments are such that the structure is not able to bear any horizontal load). In this study, being Su the theoreti ­cal ultimate horizontal displacement of the centroid, Sa the spectral acceleration and Sd the spectral dis­placement, the mean threshold between two different damage Iimit states may be so defined:

- Limit state 1 (no damage): Sa = 0.7 À.

- Limit state 2 (slight damage): S. = À.

- Limit state 3 (moderate damage): Sd = 1/8 Su. Limit state 4 (extensive damage): Sd = 1/4 Su.

- Limit state 5 (complete damage): Sd = 1/2 SUo

3.3 Evalualion oflhe performance poinl

The application of the Capacity Spectrum Method to non-Iinear systems, showing stiffness degradation and hysteretic damping, follows two different ways : (a) an equivalent non-linear sdof system, having secant stiffness and equivalent viscous damping compatible with the maximum displacement, is considered (ATC 40, FEMA 273, HAZUS); (b) the inelastic response spectra are used (Vidic et a!. 1994).

In case of collapse mechanisms in which rocking is prevalent, the structure shows an almost elastic non­linear behaviour, low hysteretic damping and limited degradation ; in these cases, the previously mentioned approaches are not completely adequate (Doherty et a!. 2000, Doherty et a!. 2002 , Griffith et a!. 2003). On the basis of previous studies and a wide sensitivity analysis, taking into account severa I accelerograms, having spectral characteristics compatible with differ­ent sites, and various structures, a procedure capable to give results in good accordance with the dynamic analyses is proposed.

0.25 ,---- ---__ ----,----__ - ,

0.2

0.15

0.1

0.05

0 1 02 03 0 4 05 0 6 0 7 08 09

ex

Figure 5. Relationship between the values of a Scc and a .

a.secsu Sd(T s) a Sy

Sd[m]

Figure 6. Determination of the performance point.

In the first step, the secant stiffness, varying in func­tion of the displacement evaluated by the intersection of the capacity curve and the elastic response spectra, is defined. Being aSu the intersection displacement and a Scc Su the displacement on the capacity curve for which the secant stiffness has to be calculated, a relationsh ip (Fig. 5) is proposed:

(1 )

In fact, it can be highlighted that, ifthe maximum displacement ll.max (resulting from the dynamic anal­yses) is higher than O.4Su, the adoption of a constant value of a Scc Su seems to well estimate the actualll.max .

In the range of low displacements (ll.max < O.4Su), in order to have a good accordance, it is necessary to assume lower values of a SccSu .

Subsequently, the secant period Ts may be evalu­ated; the corresponding spectral displacement Sd(Ts)

has to be compared to the mean threshold between the different damage limit states. In Figure 6 the procedure is sketched.

In this way, the damage limit state for a particu­lar macroelement of lhe church is found out and the damage scenario may be evaluated.

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4 APPLICATION OF THE METHODOLOGY IN THE CITY OF CATANIA (ITALY)

A preliminary study was done with the aim offinding out which could be the most vulnerable macroelements in case ofthe churches ofCatania (Lagomarsino et a!. in press). On the basis ofthe seismic history analysis of the religious buildings and on the observat ion of the typ ical constructive features (absence of aseismic devices) ofthe different macroelements, we evaluated that the façade and the triumphal arch (when not com­pletely surrounded by other buildings) are the most vulnerable macroelements.

The façade, unlikely the other parts of the church, is a masonry curtain, made of big squared limestone blocks, generally not well connected to the lateral walls (in which the masonry quality is different) and lacking ofaseismic devices, such as steellongitudinal tie-rods.

A lot of churches, in particular with a single nave, have non-structural vaults, and so the only seismic resistant element, in the transversal direction, (besides the faça de) is the triumphal arch.

4.1 Overturning 01 lhe church laçade

The most vulnerable damage mechanism for a church façade is the out-of-plane overturning.

In the rigid body hypothesis , considering that the faça de may overturns around a cylindrical hinge in the base section, and through the principIe of virtual works, the spectral acceleration value Sa that leads to the kinematism activation may be evaluated. With an explaining purpose, in the following formulas the façade has a simplified geometry. Instead, in the appli­cation to the Catania churches we considered the real complex geometry, using the method proposed in The Catania Project (Cavalieri et a!. 2000).

Therefore, in the simplified geometry, the spectral acceleration that leads to the mechanism activation is the ratio between the base section thickness and the height ofthe façade .

According to the previous definition, the spectral displacement Sd that leads to the complete overturning is half of the section thickness.

The capacity curve may be described as in Figure 7 (dotted line).

If the faça de is not considered like an isolated rigid block, but others constructive and technological aspects are taken into account, the structural response may be modified by those factors. The most recurrent ones are:

- presence of steel longitudinal tie-rods; - connection with the lateral walls, due to clamping

and frictional effects between the blocks.

Even a combination is possible and, certainly, other devices could be effective, but, in this example, only the previous ones are considered.

internai force increase

~/"

___ yielding phase

of lhe lie-rod

failure of lhe /' lie-rod

~ . . Capacity curve wi lhout tie-rod - Capacity curve with tie-rod

Figure 7. Capacity curve (unit of gim) in case of lhe overturning of lhe façade: presence of a tie-rod.

The presence of longitudinal steel tie-rods, at a height equal to h', provides an initial contribution, increasing the static multiplier; this is due to the initial value To of the internaI force in the tie-rod.

S =À=~+2 h'·To a h h.mg

(2)

As the horizontal displacement x and the rotation () increase, the capacity curve shows a term due to the force i ncrease in the tie-rod, beca use of its elongation and function of its stiffness:

F(x) = À- 2x + L'iT .~ mg h mg h

(3)

When the horizontal displacement makes the tie-rod reach the yield state, the contribution can not increase anymore, and it will remain constant until the displace­ment value that leads to failure . Beyond this leveI there will be no more contribution.

The capacity curve may be described as in Figure 7 (continuous line).

The presence ofthe connection with the lateral walls leads to an increase of the static collapse multiplier, because of the frictional forces between the blocks in the corner.

s "F.z S =À.=_+2-~_i -' -'

a h h.mg (4)

where Fi is the force developed at a height Zi (this is function of the number of frictional-cohesive surfaces per unit ofheight). All the contributions ofthe corner (stone or masonry) elements are summed.

The entity of these forces deals with the friction coefficient and the cohesion, with the width c and the length t of the blocks, and with the horizontal displacement x (Fig. 8).

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h

t

Figure 8. Connection elements between the faça de and the latera l walls.

,

~ ~

~ c

~ c

~ ~

~ ~' ~ 5 or;

'1 'i (a) (b) (c)

Figure 9. Evolution of the loss of connection as the hori­zontal displacement x increases.

. Capacity curve - no contribution - Capacity curve · connection

Figure 10. Capacity curve in case of the overturning of the façade: presence of connection with the lateral wa lls (l inear contri bution in range of displacement 1- 2).

As the horizontal displacement x increases, the con­tribution of the connection has a linear decrease, and the whole height of the lateral wall is involved (Fig. 9-a), unti l, in the upper part, the blocks completely separate, and only the lower part contributes to the stabil ity (Fig. 9-b). As the overturning goes on, the contribution ends (Fig. 9-c).

Figure 11. Church façades in Catania: (a) Church of Santo Cuore di Gesú; (b) Church of Santi Angeli Custodi ; (c) Church of S. Francesco Borgia; (d) Church of S. Francesco dei Cappuccini.

The capacity curve is described in Figure 10: If both the contributions are contemporary present,

the initial increment of the stalic multipl ier and the behaviour of lhe curve, as x, () increase, will be a combination of the two effects.

s L ·F;zi+h '.To S = Â = - + 2 = ''--'---'--_''''::' a h h.mg

(5)

A priori it is not possible to define which is the prevalent one, as it depends on the ratio between many factors.

An application of the method has been developed for the town of Catania; in fact a lot of geometrical data were avai lable, and the information was spread on a wide number of churches.

So, a typological classification ofthe façades could have been carried out. This is based on geometrical proportions and dimensions. Simplifying the criteria adopted, the ratio between height and thickness of the façade makes it slender or squat; the wall thick­ness makes it big or smalL Through the combination of these attributes, four façade typologies have been derived. In Figure 11 some churches in Catania are shown. Their façades are examples of each façade typology: slender and big (Fig. li-a), slender and small (Fig. ll-b), squat and big (Fig. li-c), squat and small (Fig. ll-d).

Generally, these churches present quite complex geometry, the parameters and the values themselves

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Table I. Initial static multiplier (Àoo is referred to a material having infinite compressive strength, À and (, to a material having finite compressive strength).

Church Àoo (, À

SS. Sacramento 0.27 \.37 0.21 S. Biagio 0.27 1.28 0.17 SS. Cosma e Damiano 0.24 0.85 0.16 s. Domenico 0.24 1.60 0.16 S.Anna 0.22 1.02 0.17 S. Benedetto 0.22 1.50 0.14 S. Francesco Borgia 0.21 1.73 0.15 S. Maria della Palma 0.20 0.70 0.14 S. Maria di Monserrato 0.19 0.73 0.13 S. Sebastiano 0.19 0.81 0.15 S. Maria di Gesu 0.18 0.70 0.16 S. Cristoforo alie Sciare 0.18 0.82 0.13 S. Francesco (cappucc.) 0.17 0.60 0.12 Sacro Cuore aI Fortino 0.16 0.79 0.12 S. Agrippina 0.15 0.48 0.10 S. Maria Consolazione 0.15 0.52 0.10 S.Orsola 0.15 0.53 0.10 S. Agostino 0.15 0.69 0.10 SS. Bambino 0.15 0.65 0.11 S. Berillo 0.14 0.56 0.10 S. Gaetano alia Marina 0.14 0.85 0.12 SS. Antonio ed Euplio 0.13 0.48 0.10 S. Giuseppe aI Duomo 0.13 0.60 0.09 S. Maria dell' Aiuto 0.13 0.85 0.09 S. Maria deI Carmelo 0.12 0.47 0.10 S. Michele Minore 0.12 0.60 0.09 SS. Cuore di Gesu 0.12 0.85 0.09 S. Marta 0.11 0.44 0.07 SS. Angeli Custodi 0.11 0.55 0.08 SS. Sacramento - Borgo 0.11 0.64 0.08 S. Francesco da Paola 0.11 0.57 0.07 S. Maria della Mecca 0.08 0.47 0.07 S. Vito 0.07 0.30 0.04 S. Agata la Vetere 0.07 0.56 0.05

which pointed out the damage limit states has been re-defined, using the mechanical-based model already described in Lagomarsino & Podestà (2000) and already applied to several (35) churches in Catania. Architectural elements such as arcadings or columns, and convex or concave shapes of the façade, typical ofthe Baroque in Sicily, have an important structural function. The ancient builders were conscious of this problem, because of the catastrophic scenario after the 1693's earthquake. The model takes in account ali these factors, and so the static multiplier is re-defined, through the para meter 8 that is referred to the horizon­tal distance between the centroid and the hinge position and the parameter 1) , which is the height of the mass centroid.

In Table 1 the load multiplier that Ieads to the kine­matism activation is shown in the analyzed churches.

The façade capacity curves (Fig. 12), for each typol­ogy, without any anti-seismic devices, are shown. It

Capacity curve 0.6 ,-----~~--=-----r=========j]

-Church (a) 0.5 - Church (b)

- - Church (c) - - Church (d

o 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Sd[m)

Figure 12. Capacity curves for each typology of façade.

Capacity curve (tie-rod) 0.6

-Church (a) 0 .5 - Church (b)

Cl 0.4 i'I Õ I c: 0 .3 I

- - Church (c) - - Church d

2-0.2 '" In

0.1 ------O +-~-~~~=r~~-r-~~-~~~

O 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2

Sd[m)

Figure 13. Capacity curves for each typology of façade (contribution ofthe tie-rod).

can be noticed that, in general, slender façades have a smaller levei of damage activation (connected with À) than the squat ones; big façades have a higher capacity of standing with a large displacement demand (con­nected with their thickness); the coUapse limit state develops for higher value of spectral displacement Sd·

In Figure 13 we can see how the capacity curves for smaU façades have a higher contribution by the steel tie-rod (typically shorter and stiffer); but for every typology this contribution lasts in the range of low displacements.

As the contribution of connection between the façade and the lateral walls is introduced (Fig. 14), there is an initial increase of the static collapse multi­plier, which is function ofthe ratio between mass, n~ of surfaces, height, etc. Big façades have a contnbutlOn ofthe connection with the lateral waUs, which lasts in a wider range of spectral displacements Sd·

In Figure 15, the capacity curves are drawn consid­ering both contributions.

4.2 Triumphal arch in-plane mechanism

In order to develop a seismic assessment methodol­ogy for the triumphal arches in Catania, the churches in which this macroelement is present and geometncal

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data are available were analysed. The damage mech­anism is possible if the church is not completely surrounded by other buildings. The churches with these characteristics are 21 (17 with a single nave

Capacity curve (connect ion) 0.6i---- -----r=====iI

-Church (a) 0.5

Oi 0.4 Õ :g 0.3

2-Ji 0.2

0.1

- Church (b)

- - Church (c) - - Church d

--- ---0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Sd[m]

Figure 14. Capacity curves for each typology of façade (contribution of connection).

Capac ity curve (tie rod + connecl ion) 0.6i---------,==:=====jl

-Church (a) 0.5 I\. - Church (b)

I \ Oi 0.4 1 - Church (c) Õ - Church d

:g 0.3

" '";;; 0.2 -VI

------O +-~--~~~_+~.---,__.--.---~~~

O 0.2 0.4 0 .6 0.8 1 1.2 1.4 1.6 1.8

Sd[m]

Figure 15. Capacity curves for each typology of façade (contribution of both connection and tie-rod).

o (a)

(b)

Figure 16. Possible kinematisms in triumphal arches: (a) single-nave church; (b) three-nave church.

and 4 with three naves). The evaluation ofthe damage scenarios is based on this stock.

Having observed the real damage patterns, it is pos­sible to define the most probable mechanisms, and so the kinematic approach of the Equilibrium Limit Analysis was developed.

For the triumphal arches ofthe single-nave churches were recognised two mechanisms (Fig. 16-a), involv­ing the rotation of both the pillars (mechanism A) or only one pillar (mechanism B). For the triumphal arches of the three-nave churches the most probable mechanism (figure 16-b) was defined considering the kinematism of7 rigid blocks (lO hinges).

In order to quantify the effectiveness of the steel transversal tie-rod in the arch, the collapse multiplier and the capacity curve were evaluated both with and without this aseismic device (Table 2). Several values of internai force in the tie-rod were considered. The results highlighted that the introduction of a tie-rod increased the load multiplier that activates the kine­matism (due to the initial value ofthe internai force),

Table 2. Initial static multiplier with and without tie-rod.

Collapse multiplier U,)

Without T (kN)

tie-rod 10 20 50

1 nave

S. Agostino 0.102 0.110 0.1 17 0.126 S. Cristo foro 0.116 0. 126 0.135 0. 146 alie Sciare

S.S. Cuore di Gesu 0.163 0.168 0.174 0.189 S. Maria del la 0.177 0.194 0.203 0.226 Provvidenza

S. Biagio 0.179 0.184 0.189 0.201 S. Berillo 0.187 0.200 0.210 0.226 S. Filippo Neri 0.191 0.199 0.205 0.221 S. Martino 0.196 0.198 0.201 0.207 ai Bianchi

S. Sebastiano 0.205 0.22 1 0.234 0.260 S. Agata ai Borgo 0.206 0.21 1 0.216 0.229 S.M. di Monserrato 0.208 0.222 0.233 0.258 S. Giuseppe 0.231 0.236 0.241 0.253 ai Duomo

S.S. Angeli Custodi 0.240 0.246 0.251 0.266 S. Nicolõ ai Borgo 0.248 0.255 0.262 0.279 S. Agata la Vetere 0.268 0.269 0.270 0.273 S. Benedetto 0.300 0.302 0.304 0.309 S. Maria dei Carmelo 0.321 0.332 0.341 0.365

3 naves

S. Maria di Ognina 0.080 0.102 0.117 0.153 S. Maria 0.090 0.093 0.097 0.107

dell 'Elemosina Basilica Cattedrale 0.104 0.104 0.104 0.105 S. Maria 0.107 0.11 1 0.115 0.126

dell ' Indirizzo

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even if in different percentage in relation to the shape of the arches.

In Figures 17- 19 the capacity curves of three churches are shown.

4.3 Damage scenarios

Using the previously defined thresholds and the proposed procedure to evaluate the damage limit state using a displacement-based method, the damage

0.35

03

_ 025 .. .. ~ 02

'= ~ 0.15

rIS 0.1 .

005

Capacity curve (Church of S. Benedetto)

0.5 1 5

- Wlthout t1e-rod

- .. T lc·rod T= IOkN .... T le-rod T=20k::-.r

- - Tic·rod T=50kN

2.5

Figure 17. Capacity curves for the triumphal arch of the Church of S. Benedetto (with and without tie-rod) .

0.35

0.3

_ 0.25 .., .. ~ 02

'= ~ 0.15

rIS 0.1

0.05

Capacity curve (Church of S. Nicoló ai Borgo)

0.2 0 4

, , ,

0.6 08

Sdlml

- Without tie-rod

- .. Tie·rod T= I OkN .

. . . . Tio·rod T=20kN

- - Tie·rod T=50kN

1.2 14

Figure 18. Capacity curves for the triumphal arch of the Church ofS. Nicolo aI Borgo (with and without tie-rod).

0.35

0.3

_ 0.25 OI) ..

. : 02

1 0.15

rIS O I

0.05

"

Capacity curve (Church of S. Sebastiano)

0.2 0.4 0.6 0.8 Sd[m)

""'] - Without tie-rod

-"Tie·rodT= IOkN . .. . Tio·rod T=20kN

- - Tie·rod T=50kN

1.2

Figure 19. Capacity curves for the triumphal arch of the Church of S. Sebastiano (with and without tie-rod).

scenarios for the overturning of the façades and the in-plane mechanism of the triumphal arches were determined in case of 1693 and 1818 earthquakes.

4.3. 1 Overlurning 01 lhe church laçade The results of the damage scenario in case of the out­plane mechanism are shown in Figure 20. It is possible to notice how, for both the scenarios, ali the façades suffer a certain leveI of damage.

This aspect remarks the high vulnerability of this kind of mechanism, especially when aseismic devices are not present (e.g. tie-rods). Nevertheless, it worth noticing that the peak of damage distribution, also for the 1693 scenario, is located on the third grade: this aspect can be correlated to the particular shape of the façades ofCatania, with arcadings and colurnns, which reduce the collapse vulnerability of these structures.

4.3.2 Triumphal arch in-plane mechanism The damage scenarios in case ofthe in-plane mecha­nism ofthe triumphal arch are presented; (without the tie-rod and with tie-rod differently pre-stressed). The results are shown in Figures 21 - 23.

100%

~ ~ 80% OI ~ ~ 60% '" oS ~

40% OI CJl ~

5 20% !li

~

0%

Figure 20. façades.

~I OO%

'" ~ 800/0 ... " .ã 60% c.. E '" 40% :s ~ 20%

'" E

lo 1 81 8 Scenario • 1693 Scenario I

n o 2 3 4 5

Damage levei

Damage scenarios for the overturning of the

lo I 818 Scenario • 1693 Scenario I

A OOM~~--~----~--a,--~~--~~----, o 2 3 4 5

Damage leveI

Figure 21. Damage scenarios for triumpha1 arches: without the tie-rod.

1099

~100%

'" lo 1818 Scenario 11 1693 Scenario I

<li 80% ..c

" ... .. -; 60% ..c c. E .:: 40%

.i:: "tl

'" 20% 0Jl .. E ..

0% Q O 2 3 4 5

Damage levei

Figure 22. Damage scenarios for triumphal arches: with the tie-rod (T = 1000 kN).

~ 100% ~

'" lO 1818 Scenario 1693 Scenario I

'" 80% ..c " ... .. -; 60% ..c c. E '" 40% 'i: ....

"tl <li 20% 0Jl

" E " 0% Q

O 2 3 4 5 Damage levei

Figure 23. Damage scenarios for triumphal arches: with the ti e-rod (T = 5000 kN).

We can notice tha1 the tie-rod represents an effi­cient retrofitting intervention, both in order to contrast the kinematism activation and, if the mechanism is activated by the earthquake, to limit the damage leveI.

5 FINAL REMARKS

This research allows us to carry out a double result. First of ali , in the paper, a methodology developed in order to make applicable the performance-based design to masonry monumental buildings is described. In fact, these are a kind of structures strongly different from those for which the Capacity Spectrum Method was proposed (reinforced concrete or steel structures). Secondly, through the methodology presented, a dam­age scenario for some macroelements ofthe churches ofCatania was determined for the main seismic events that shocked this area: 1693 and 1818 earthquakes.

Moreover, it is worth noticing that this approach allows us to calculate the capacity curves through the definition of a mechanical model of simple formu­lation. It is based, in fac t, on the Equilibrium Limit

Analysis of rigid bodies, and its evaluation is not subordinate to the use of a sophisticate numerical code.

It is important to highlight how the proposed methodology shows some aspects that should be deep­ened. For example, after a detailed analysis of the macroelements, the evaluation of a parameter able to summarize in a total judgement the seismic vulnera­bility ofthe whole church may be very significant. In case of the previously described two damage mech­anisms, the risk threshold could be correctly corre­lated to the kinematism with the minor value of the collapse multipl ier; in case of other collapse mecha­nisms (e.g. activated in the same direction or which involve simultaneously two or more macroelements), this observation seems to be less adequate. Ifthe defi­nition of a capacity curve for a complex building (e.g. a church) can lose its structural meaning, the need to define a parameter that allows us to compare different structures, in terms of dimensions or architectonical elements, is fundamental in case of a territorial scale analysis. In this case, the correlation between the par­tial results, evaluated on different macroelements, and those carried out through a global finite element analy­sis could help us to define a useful parameter in order to compare the damage levei in churches that, generally, could be extremely different.

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