Aim of this work is to propose a methodology for the evaluation of the seismic reliability of historical tall buildings. The evaluation of the seismic reliability of the masonry tower was done by a preliminary static and dynamic characterization of an elastic FEM, performed with respect to a series of “in situ” measures. By this method the identified model is used for the evaluation of the time-history of the global force acting on each sections due to a seismic load. After the evaluation of the time-history of each internal action, for some sections of the tower, the evaluation of the seismic reliability have been carried out by analyzing two limit states: (I) tower over-turning and (II) mechanical collapse of a masonry panel. The aim is to connect, for each of this limit states, an appropriate ground acceleration ag able to assure their respect. The procedure is explained with respect to a case study: the “Torre Grossa” masonry tower. Moreover, the evaluation of structural reliability of towers and similar structures is quite demanding: these structures possess a low safety margin with respect to external actions, because of the high level of stress induced by the self weight if compared with the ultimate resistance of the materials utilized in the construction. The masonry characteristics and the compression level are besides responsible for the very low ductile overall behaviour of the whole construction. In the past years, several examples of sudden collapse of important towers have been experienced: in 1989 the Torre Civica in Pavia felt down (Macchi 1993, Binda et al. 1992), while in 1993 a collapse interested the bell-tower of St. Magdalena Church in Goch. Herein it is proposed an original, to the authors' knowledge, methodology for the evaluation of the seismic reliability of historical tall buildings, with specific reference to medieval masonry towers. The proposed method is illustrated with reference to the seismic behaviour of a specific historical masonry tower: the medieval “Torre Grossa”, in San Gimignano, the world famous town close to Siena (Italy). 2 METODOLOGY The evaluation of the seismic reliability of the masonry tower was done by a preliminary static and dynamic characterization of an elastic FEM, performed with respect to a series of “in situ” measures. The dynamic identification allowed to evaluate the degree of constrain offered by the neighbour buildings, while the results obtained from the static identification have been used to tune up the mechanical properties of the smeared model. After this preliminary identification, the elastic model of the whole structure has been used to evaluate the load acting to every section of the tower due to a specified earthquake (modeled by an appropriate accelerogram acting at the base). Loads acting at every section [z] of the tower were identified in global terms like shear force [T(z; t)], normal force [N(z)] and bending moment [M(z; t)]. After the evaluation of the time-history of each internal action, for a certain section of the tower, the evaluation of the seismic reliability has been carried out by analyzing two limit states: • I limit state: tower over-turning (it is verified when the own weight combined with the seismic loads causes a resultant load which eccentricity is internal with respect to the cross-sectional area); • II limit state: mechanical collapse of an external panel in its plane (it is verified when the seismic load acting on the tower is not able to produce a local cracking/crushing on an external panel of the tower). Although masonry building exhibits a non linear behaviour, especially with respect to the severe stress tensile state induced by a seismic load, nevertheless the number of information (both mechanical and geometric) needed for an accurate and realistic non linear FEM analysis are difficult to obtain (Betti and& Vignoli, 2005a, b). In order to buildt an accurate non linear model of the construction it is important to know mechanical properties of each material, the crack pattern, the material damage map and also the actual distribution of the material along the building. With the proposed methodology, with respect to some “in situ” measurement, a linear elastic model of the building has been done and it has been used in order to evaluate the load acting at each section of the tower. Next, the vulnerability of the construction moved to the analysis of the identified two limit states so that the non linear analyses moved from the whole model of the tower to the model of elementary panels. This is not a difficult task because the behaviour of the masonry panel is a well know problem, and an extensive literature exist for it (Tassios 1988). As a matter of fact, with respect to the elementary panels, it is possible to find in literature an extended series of experimental results that make the evaluation of ultimate load less uncertain, and then to evaluate the collapse surface. The aim is to connect, for each of this limit states, an appropriate ground acceleration ag able to assure their respect. The first limit state has been identified in the whole tower, while the second one is related to the behaviour of a single masonry panel with its actual non linear properties. The respect of this two limit states result by the comparison between the resisting force R (evaluate upon geometrical aspects for the first L.S.; estimate upon the collapse behaviour of a 930 Structural Analysis of Historical Constructions G. Bartoli, M. Betti, P. Spinelli and B. Tordini masonry panel for the second L.S.) and the acting force S (obtained by the seismic load applied like ground acceleration time history). The seismic load acting of the tower’s area is determined with reference to the EuroCode Recommendations [(EC8)]. 3 CASE STUDY The above discussed methodology of analysis is explained with reference to a specific case study: the medieval “Torre Grossa” (see Fig. 1a). This building is a tall masonry tower, dated as thirteenth century. It is the tallest and the most mighty of the towers preserved in the town of San Gimignano (Italy). The cross section is a square one measuring 9.5 x 9.5 meters, with an overall height of about 60 m. The walls are of variable thickness, between 2.6 m and 1.6 m. The sustaining wall is an infilled one (“a sacco” is the Italian term) with the external face made by stone masonry, and the internal layer constituted by brick masonry, with mortar layers nearly a centimetre thick. The internal filling is composed of heterogeneous material (remainders brick tied by a poor mortar). Up to the height of 20 m the tower is incorporated in a previous dated building, “Palazzo Comunale” (Town Hall). The floors have been realized through masonry vaults, while in the upper part of the tower a concrete floor is present, connected to the bottom part of the tower by a steel stair. Figure 1 : (a) View of the tower with the neighbour “Palazzo Comunale” and (b) Section of the tower. A FEM model of the masonry tower has been made taking into account the preliminary historical investigation and a geometrical relief (see Fig. 2a). Moreover, by the results of the “in situ” static and dynamic testing (that has been performed within the framework of the research contract called “San Gimignano Project”, (Bartoli and& Mennucci, 2000) the numerical model has been identified in static and dynamic field. Particularly the dynamic identification has permitted to estimate the restrain degree offered by the neighbour “Palazzo Comunale” (Table 1). Table 1 : Frequency and mode shape of the “in situ” experiment and 3D F.E. model Modes shape Direction Experimental results [Hz] Numerical result [Hz] I East west 1.3060 1.2090 II North south 1.3310 1.3306 III Torsional 3.4100 5.1836 IV Vertical --5.9427 V West east 6.5500 6.2308 VI North south 7.6150 6.6617 C. RILIEVO DEL QUADRO FESSURATIVO B. RILIEVO DEI MATERIALI X
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