On the left: scheme of the 10 horizontal sections, drawn on the front facing Piazza del Campo. On the top right, plan with the local reference system chosen to analyze the relative displacements of the geometric center. On the lower right the graph of displacements of the geometric center with height of the sections at different levels. 

On the left: scheme of the 10 horizontal sections, drawn on the front facing Piazza del Campo. On the top right, plan with the local reference system chosen to analyze the relative displacements of the geometric center. On the lower right the graph of displacements of the geometric center with height of the sections at different levels. 

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The paper presents a synergic and multidisciplinary approach where laser scanner survey, radar interfer-ometric monitoring and finite element (FE) numerical modelling are used for expeditious and no-contact dynamic identification of monumental masonry towers. The methodology is applied to a real case of great historical interest: the "Torre del Man...

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... the base as the soil-structure interaction was considered not significant for the analysis herein developed. Mechanical parameters of the numerical model (mainly the elastic modulus) were parametrically identified in order to com- pare the dynamic simulation with the results of the dynamic measurement experimental campaign according to a procedure also adopted by other authors [19,20] but based on the results of a traditional investigation (i.e. full topographic survey and comparison with the results of accelerometer acquisitions). In particular, to take into account the dynamic effects, the elastic modulus of the masonry materials was varied within an admissible range until the first experimental frequency was reproduced. It is notewor- thy to outline that, due to large number of uncertainties affecting the material parameters (mainly their spatial distribution and the masonry multi-leaf internal texture), the assessment procedure herein followed was mainly devoted to match the first experimental modal frequency. Based on this approach the mean elastic modulus was estimated about 2400 N/mm 2 , which is closer to values already utilized in other works [5] [21]. The Poisson’s ratio was assumed equal to 0.2; however by varying this value to 0 or 0.49 no change appeared in the mode shape, and the corresponding frequency variation was less than 1%, well below the uncertainty level. Specific weight of the material (masonry brick) was assumed equal to about 1500 kg/m 3 . Fig. 8 shows the first three numerical modal shaped of the Tower. The first two are bending mode along (approximately) the two main directions of the tower. The third is again a bending one, but is a superior mode. The first bending mode involves translation mainly in the Y-direction (direction North/East-South/West in Fig. 2) while the second one involves translation in the X-direction (direction North/West-South/East in Fig. 2) with a component of translation also in the Y direction as shown in Fig. 9, where are plotted the results as obtained (output) with the numerical model of the tower. Despite the symmetry of the section of the tower (the section is approximately a square section whose dimension are about 7.0 × 7.1 m with the sustaining walls, with an even thickness of about 2.2 m) the slight asymmetries introduced by the connection with the neighbor Town Hall originates a small difference in the first two frequencies. Numerical frequencies are reported in Table 1 where they are compared with the experimental ones. It is possible to observe that the numerical model substantially confirms the experimental values with respect to the first, third and fourth frequency but it remains uncertain the assessment of the second frequency, experimentally positioned at 0.39 Hz. This difference may be due to different factors, but ...
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... the base as the soil-structure interaction was considered not significant for the analysis herein developed. Mechanical parameters of the numerical model (mainly the elastic modulus) were parametrically identified in order to com- pare the dynamic simulation with the results of the dynamic measurement experimental campaign according to a procedure also adopted by other authors [19,20] but based on the results of a traditional investigation (i.e. full topographic survey and comparison with the results of accelerometer acquisitions). In particular, to take into account the dynamic effects, the elastic modulus of the masonry materials was varied within an admissible range until the first experimental frequency was reproduced. It is notewor- thy to outline that, due to large number of uncertainties affecting the material parameters (mainly their spatial distribution and the masonry multi-leaf internal texture), the assessment procedure herein followed was mainly devoted to match the first experimental modal frequency. Based on this approach the mean elastic modulus was estimated about 2400 N/mm 2 , which is closer to values already utilized in other works [5] [21]. The Poisson’s ratio was assumed equal to 0.2; however by varying this value to 0 or 0.49 no change appeared in the mode shape, and the corresponding frequency variation was less than 1%, well below the uncertainty level. Specific weight of the material (masonry brick) was assumed equal to about 1500 kg/m 3 . Fig. 8 shows the first three numerical modal shaped of the Tower. The first two are bending mode along (approximately) the two main directions of the tower. The third is again a bending one, but is a superior mode. The first bending mode involves translation mainly in the Y-direction (direction North/East-South/West in Fig. 2) while the second one involves translation in the X-direction (direction North/West-South/East in Fig. 2) with a component of translation also in the Y direction as shown in Fig. 9, where are plotted the results as obtained (output) with the numerical model of the tower. Despite the symmetry of the section of the tower (the section is approximately a square section whose dimension are about 7.0 × 7.1 m with the sustaining walls, with an even thickness of about 2.2 m) the slight asymmetries introduced by the connection with the neighbor Town Hall originates a small difference in the first two frequencies. Numerical frequencies are reported in Table 1 where they are compared with the experimental ones. It is possible to observe that the numerical model substantially confirms the experimental values with respect to the first, third and fourth frequency but it remains uncertain the assessment of the second frequency, experimentally positioned at 0.39 Hz. This difference may be due to different factors, but ...
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... on this background, the paper proposes a synergic and multidisciplinary approach composed of laser scanner survey, radar interferometric monitoring and FE numerical modeling for expeditious and no-contact dynamic identification of monumental towers. The methodology is applied to a real case of great historical interest: the “Torre del Mangia” (Mangia’s tower) in Siena (Italy). The paper is organized as follows: in section 2 the main historical and architectonical features of the tower are briefly sketched. In section 3 the laser scanning survey together with the main results is reported, while the experimental dynamic investigation by means of the interferometer radar is described in section 4. Next section 5, finally, describes the identified FE model employed to interpret the results of the experimental investigation and to assess the actual dynamic behavior of the tower. The Mangia’s tower in Siena is famous all over the world together with the shell-shaped square (named “Piazza del Campo”) in front of it. The tower’s curious name comes from the nickname of the first bell-ringer. It is one of the tallest Italian medieval towers, about 88 m height from the ground level on the northern corner, and it has a square section of about 7 m. The tower is substantially a masonry structure with a belfry in white travertine. Over the belfry a metallic structure supports the huge bell named “Campanone” (Big bell). Light rods bring the overall height of the tower up to about 102 m. The technical and executive plan of the tower is attributed to Muccio and Francesco di Rinaldo, masters from Perugia, but there is no definite information about neither the construction stages nor their chronology. What is certain is that the laying of the founda- tion stones took place in 1325, simultaneously at the beginning of the last enlargement phase of the Palace, and it is assumed that the travertine crowning dates back to 1348 [12], at the end of construction works. The tower and the Palace became a model for the later civic buildings, marking the transition from the fortress to the palace; therefore they play a very important role in the history of architecture [13]. During its life, some restoration and maintenance interventions were carried out in order to fix the damages caused by lightning and fires. However, the tower seems to have stood up well over the centuries, even against a disastrous earthquake that hit Siena in 1798, which did not cause substantial damages to the structure. The survey of the tower was carried out through Terrestrial Laser Scanning (TLS) techniques. Three-dimensional scanning techniques combine accuracy and sampling density. This allows the creation of a three-dimensional database from which the needed information can be extracted [14–16]. The tower’s geometry and its position within the historical center required special attentions. The most critical aspect is related to the tower’s height and to the non-availability of enough ele- vated accessible places from which data could be acquired. The tower’s sides overlooking the market square and the City Hall are within the buildings up to about 20 m in height while the visible part is about 68 m high. The other two tower’s sides are outside the buildings and they are about 88 m high (towards Piazza del Campo and via Salicotto). These conditions led to use two different instruments: a phase-based scanner (Leica HDS6000) for the lower sides and a pulse-based scanner (RIEGL LMS-Z420i) for the taller ones (Fig. 1). The range of the first is not enough to reach the top of the higher sides, but the later has lower resolution. The phase-based scanner has a nominal accuracy on positioning of ± 10 mm (up to 50 m distance, 1sigma) and sampling density of about 1.5 cm (at 100 m distance). The pulse-based scanner has a nominal accuracy on positioning ranging from ± 5 mm to ± 10 mm ( ± 20 ppm up to 100 m distance) while the sampling density is about 5 cm (at 100 m distance). Data have been referred to a local reference system determined by a topographic network. The alignment was solved at first with an automatic procedure using topographic targets as reference points. After that, an ICP algorithm was performed to add constraints between scans couples. The root mean square error of the alignment is lower than 1 cm. The overlapping percentage between point clouds is dependent on the scan positions, as we can identify two groups of point clouds–the one in the square and the one on the reverse side of the tower. The overlapping percentage is about 70% between scans belonging to the same group. We made this choice in order to guarantee the completeness of data and to reduce lacks of information. The overlapping between the two data sets is whereas about 10%. This difference is due to the conformation of the site. A first analysis of the fronts showed that the exterior surfaces are out of plumb and the tower is tilted towards North. These preliminary results had led to perform more detailed analyses. From the 3D points model of the tower’s upper part — located on top of the building — ten horizontal sections were extracted from every 4 m vertical distance. Once imported into a CAD-software, maintaining their referencing, the geometric center of each one was positioned, in order to observe its relative displacement between different levels. The obtained graph is shown on Fig. 2. The detected out-of-plumb, although interesting from a geometrical point of view, is very small: 18 cm in the North/East-South/West direction, 8 cm in the North/West-South/East direction. This corresponds to about 0.31 ◦ that, taking into account the aim of the structural analyses herein developed, can be considered as not significant. Nevertheless the possibility to have instruments that expeditiously and precisely allow for the correct evaluation of the actual tilt of such typology of structures can be very important in those cases where it becomes significant from a structural point of view. In order to detect the dynamic characteristics of the tower under environmental loads (mainly a light wind as downtown is closed to vehicular traffic), a radar survey was planned in May 2012 to record ambient vibrations. The measurements were carried out by placing the radar in Piazza del Campo, facing the Mangia’s Tower, at the three positions indicated with the letters A, B, C in Fig. 3. The aim of the measurement is to observe the movement of the structure at several heights, along both the direction orthogonal to the faces of the structure and one of the two diagonals. Each measurement position provides information about a projection of the real movement and by combining all information an estimate of the mode shape and the direction of the movement at each resonance frequency can be obtained. As measurements from different points of view were carried out at different times, possible changes on the environmental conditions (noise sources, weather ...
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... the tower's upper part -located on top of the building -ten horizontal sections were extracted from every 4 m vertical distance. Once imported into a CAD-software, maintaining their referencing, the geometric center of each one was positioned, in order to observe its relative displacement between different levels. The obtained graph is shown on Fig. 2. The detected out-of-plumb, although interesting from a geometrical point of view, is very small: 18 cm in the North/East-South/West direction, 8 cm in the North/West-South/East direction. This corresponds to about 0.31 • that, taking into account the aim of the structural analyses herein developed, can be considered as not ...
Context 5
... to about 1500 kg/m 3 . Fig. 8 shows the first three numerical modal shaped of the Tower. The first two are bending mode along (approximately) the two main directions of the tower. The third is again a bending one, but is a superior mode. The first bending mode involves transla- tion mainly in the Y-direction (direction North/East-South/West in Fig. 2) while the second one involves translation in the X-direction (direction North/West-South/East in Fig. 2) with a component of translation also in the Y direction as shown in Fig. 9, where are plotted the results as obtained (output) with the numerical model of the ...
Context 6
... are bending mode along (approximately) the two main directions of the tower. The third is again a bending one, but is a superior mode. The first bending mode involves transla- tion mainly in the Y-direction (direction North/East-South/West in Fig. 2) while the second one involves translation in the X-direction (direction North/West-South/East in Fig. 2) with a component of translation also in the Y direction as shown in Fig. 9, where are plotted the results as obtained (output) with the numerical model of the ...

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