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Structural Analysis of Masonry Historical Constructions
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300 P Roca et al, tackle the specific problems of ancient constructions con partial information can be collected Additional assumptions. cerning materials structural arrangements and real preser on morphology and material properties may be needed in or. vation condition In fact the difficulties posed by histori der to elaborate a model. cal structures are still very challenging and still reminiscent. of those encountered by the pioneers in spite of significant 1 2 Geometry. progress during the last decades, Some of difficulties encountered are related to the de Historical structures are often characterized by a very com. scription of geometry materials and actions all of which plex geometry They often include straight or curved mem. acquire remarkable singularity in the case of historical con bers They combine curved 1D members arches flying. struction Additional important difficulties are related to the arches with 2D members vaults domes and 3D ones. acquisition of data on material properties internal morphol fillings pendentives They combine slender members. ogy and damage as well as to the adequate interpretation with massive ones massive piers walls buttresses foun. of structural arrangements overall organization and histori dations However today numerical methods such as. cal facts Because of all these difficulties it is generally ac FEM do afford a realistic and accurate description of geom. cepted Icomos Iscarsah Committee 60 that the study of etry Due to it geometry is perhaps one of the least although. a historical structure should not only base on calculations still meaningful challenges to be faced by the analysis. but should integrate as well a variety of complementary ac. tivities involving detailed historical investigation deep in 1 3 Morphology. spection by means of non destructive techniques NDT. and monitoring among other Structural analysis of histor A more significant problem lays in the characterization and. ical structures constitutes in fact a multidisciplinary mul description of the internal morphology of structural mem. tifaceted activity requiring a clever integration of different bers and their connections Structural members are often. approaches and sources of evidence These difficulties are non homogeneous and show complex internal structures in. discussed into more detail in the following paragraphs cluding several layers filling material cavities metal inser. tions and other possible singularities Connections are sin. 1 1 Material gular regions featuring specific geometric and morphologi. cal treats The transference of forces may activate specific. Historical or traditional materials such as earth brick or resisting phenomena contact problems friction eccentric. stone masonry and wood are characterized by very com loading Modeling morphology and connections in detail. plex mechanical and strength phenomena still challenging may be extremely demanding from a computational point of. our modeling abilities In particular masonry is character view Nevertheless the main difficulty is found in physically. ized by its composite character it includes stone or brick characterizing them by means of minor or non destructive. in combination with mortar or day joints a brittle response procedures. in tension with almost null tensile strength a frictional re. sponse in shear once the limited bond between units and 1 4 Actions. mortar is lost and anisotropy for the response is highly sen. sitive to the orientation of loads In spite of the very signif Historical structures may have experienced and keep on ex. icant effort invested to characterize and mathematically de periencing actions of very different nature including the. scribe masonry mechanics and strength the accurate and ef effects of gravity forces in the long term earthquake envi. ficient simulation of masonry response is still a challenge in ronmental effects thermal effects chemical or physical at. need of further experimental and theoretical developments tack and anthropogenic actions such as architectural alter. Important results by Ali and Page 1 Louren o 70 Binda ations intentional destruction inadequate restorations. et al 12 and many others have yielded a very significant Many of these actions are to be characterized in historical. level of understanding time Some are cyclic and repetitive and accumulate signifi. Historical materials including brick or stone masonry cant effect in the long term some develop gradually in very. are normally very heterogeneous even in a single building long time periods and some are associated to long return. or construction member Moreover historical structures of periods In many cases they may be influenced by historical. ten show many additions and repairs done with different ma contingency and uncertain or at least insufficiently known. terials Material characterization is constrained by due re historical facts. spect to the monument and original material Non destruc. tive indirect tests NDT and minor destructive tests MDT 1 5 Damage and Alterations. should be preferred If any only a very limited number of. pits or cores allowing direct observation and laboratory test Existing and general alterations may affect very significantly. ing are normally acceptable In practice only limited and the response of the structure Damage and deformation are to. Structural Analysis of Masonry Historical Constructions Classical and Advanced Approaches 301. Fig 1 Continued, 1 6 History, History is an essential dimension of the building and must. be considered and integrated in the model The following ef. fects linked to history may have had influence on the struc. tural response and existing damage Construction process. architectural alterations additions destruction in occasion. of conflicts wars natural disasters earthquake floods. fires and long term decay or damage phenomena His, tory constitutes a source for knowledge In many occasions. the historical performance of the building can be engineered. to obtain conclusions on the structural performance and. strength For instance the performance shown during past. earthquakes can be considered to improve the understanding. on the seismic capacity The history of the building consti. tutes a unique experiment occurred in true scale of space and. time In a way knowledge of historical performance makes. up for the mentioned data insufficiency, 2 Desirable Features of Methods Applied to Historical.
Fig 1 Some pioneering FEM studies on historical structures. a Tower of Pisa FEM model and substructuring of the colonnade sys Structures. tem Macchi et al 79 b Mexico City Cathedral Meli and S nchez. Ram rez 88 c The Colosseum in Rome Tensile horizontal stresses Because of the aforementioned challenges attempts to. due to the seismic action Croci 34 model and simulate the response of a historical structure. should try to satisfy some basic requirements Firstly any. modelling technique should be able to adequately describe. the geometry and morphology of the real construction in. be modeled as present features of any existing structure to cluding the structural form internal composition connec. grant adequate realism and accuracy in the prediction of the tions and support conditions An accurate description of the. actual performance and capacity Damage encompasses me distribution of mass and external forces is essential for both. chanical cracking material decay due to chemical or phys gravity and seismic analyses. ical attack or whatever phenomena influencing on the orig Secondly constitutive equations should be adopted al. inal capacity of materials and structural members lowing an adequate description of the essential mechanical. 302 P Roca et al, and strength features of the different materials existing in the necessary In turn the use of such constitutive equations. building It is important to highlight that simple linear elas will require the availability of non linear properties to be ob. tic analysis fails to simulate essential features of non tension tained by means of different laboratory or in situ mechanical. resisting materials such as stone and masonry More sophis tests. ticated non linear constitutive equations will normally be Actions mechanical physical chemical are also to. be modelled by means of mathematical formulations de. scribing their mechanical effect in terms for forces on the. structure imposed movements or deformations or possible. variations of the material properties, An accurate model of the structure should also afford the. description of damage and alterations existing in the struc. ture including cracks disconnections crushing deforma. tion and out of plumb and construction defects Some dam. age types can be modelled indirectly as a disconnection be. tween elements or a local reduction of material properties In. order to characterize the actual capacity in the present con. dition of a building the analysis should be carried out on the. model accounting for its real damaged and deformed state. As the analysis of historical structures will normally be. oriented to identify needs for restoration and strengthening. analysis methods should able to incorporate and model pos. sible stabilization repair or strengthening measures In some. cases these can be taken into account in an indirect way. by adequately modifying material properties modifying the. sectional dimensions or configuration or by adding forces. to represent their mechanical effect, The interaction of the structure with the soil is also to be. taken into account except in cases it is judged to be irrele. vant Taking it into account will often require the inclusion. of a large portion of foundation soil as part of the entire FEM. model as done in the analysis of San Marcos Basilica by. Fig 2 The finite element model of the St Mark s Basilica Top global. discretization Bottom soil foundation discretization including defor Mola and Vitaliani 93 or the modal analysis of a masonry. mation Mola and Vitaliani 93 tower by Fanelli 44 Figs 2 and 3. Fig 3 Examples of graphical rendering for a FE mathematical model of a masonry tower discretized geometry including the soil foundation. and first two vibration modal shapes Fanelli 44, Structural Analysis of Masonry Historical Constructions Classical and Advanced Approaches 303. Fig 4 Different stages of the, model a to d and successive.
boundary conditions variation, Casarin 21 The surrounding. buildings are taken into account, by directly modelling their walls. or by simulating them with, translational springs, Fig 5 Deformed meshes and. maximum displacements in, grey scale for seismic load. acting along the longitudinal, direction of the building.
Monastery of Jer nimos, Louren o and Mour o 72, Fig 6 Detailed modelling of Mallorca cathedral in Spain including the different parts of the structure which can influence on the modal analysis. tower fa ade choir and first modal shapes Roca et al 126. Certain types of analyses as in particular dynamic one account the real contact conditions which requires a pre. may require the inclusion of neighboring buildings into the vious detailed inspection and investigation The agreement. model with an adequate description of existing connections between numerical and experimental vibration modes and. This is so because of their possible effect on the modal frequencies may be considered as a way to validate the de. shapes and overall dynamic response Modelling accurately scription of connection among different parts in the struc. the dynamic response will often require to construct a global ture. model incorporating all the distinct parts of a complex struc Studies on different historical structures Roca 121. ture as in the analysis of Reggio Emilia Cathedral Casarin Roca et al 123 have shown that real deformations are nor. 21 Casarin and Modena 22 of the Monastery of Jer n mally much larger one or even two orders of magnitude. imos Louren o and Mour o 72 or of Mallorca Cathedral than those predicted by conventional instantaneous calcu. Roca et al 126 Figs 4 6 The connection between the lations This is due to the fact that these analysis neglect. different parts should be modelled accurately by taking into history related aspects such as 1 deformations occurred. 304 P Roca et al, Fig 7 Color online Analysis of Tarazona Cathedral for different his of lateral vaults during late Middle Age c tensile stresses N m2. torical configurations Roca 121 by FEM isotropic damage model after thinning of piers 16th c tensile damage during momentary. a Distribution of tensile damage at the initial condition after con dismantling of flying arches for restoration purposes 20th c. struction 12th 13th c b compression damage after overloading. during the construction process as those due to the deflec iercio 108 Binda et al 11 13 14 the effect of creep. tion of centerings and forms and the deformation of struc under constant stress at the long term may induce signifi. tural members during intermediate and incomplete config cant cumulative damage in rock like materials The investi. urations of the structure 2 initial and historical soil set gation of specimens cut from the walls of the Pavia Tower. tlements 3 architectural alterations 4 the non reversible after its collapse allowed to Anzani et al 4 the formula. effect of multiple thermal and hygrometric cycles and 4 tion for the first time on ancient masonry of the hypothesis. Structural Analysis of Masonry Historical Constructions Classical and Advanced Approaches 301 a b Fig 1 Some pioneering FEM studies on historical structures

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