Modelling, analysis and testing of masonry structures
Creators: name: Romano, Alessandra
Publisher: name: Università degli Studi di Napoli Federico II
Year: 2006

description: In this thesis, masonry churches under horizontal actions are studied. Such structures feature strong seismic vulnerability, both because of the mechanical properties of the material and the particular configuration. Besides, uncertainty of the conventional seismic action is detected. Different codes provide different spectra and, subsequently, different total seismic actions. 
In order to assess such difficulties, the four basilicas of SGMR, SI, SGMG and SP have been selected. These study cases are analysed with a two step procedure in which the whole structure is analyzed in the linear field through a complete 3D model, and then the single structural elements are assessed in non linear field through FEA and limit analyses.
The following remarks can be stated:
Certain uniformity in the global plan-altimetric apparatus can be recognised so that the four churches can be regarded as deriving from a sort of three-dimensional global model that changes only for a scale factor. Similarly, a common structural behaviour is expected and in the analyses confirmed.
The modal shapes for the analyzed buildings show low torsional and transversal stiffness and great out of the plane deformation. When rigid diaphragms are inserted to model retrofit interventions, greater global stiffness (especially in terms of torsion) and a more monolithic behaviour is detected. It is noticed, furthermore, a stress concentration in the stiffer elements of the buildings (façade elements and in the transept zone) which absorb a larger amount of the total shear.
Given the already stated uncertainty in the characterisation of seismic actions, assessment of the behaviour at collapse through spectrum-independent analyses is preferable. In this aim, advanced nonlinear analyses using the code ABAQUS are carried out on the single macro-elements constituting the structural complex. This approach is apparently the most accurate methodology for structural analyses. The results, in fact, are reliable only providing that very precise material characterisation is made. This can be very tricky for historical existing structures. Additional difficulties also derive from the complex geometrical configuration of the studied non-conventional structures. Load-displacement curves providing the collapse multiplier, the horizontal stiffness and the maximum displacement of some control points are obtained for all the macro-elements. These curves are compared with the elastic demands derived through global analyses. It has been shown that generally the bearing capacity of these elements is smaller than the strength demand. Therefore, these constructions are prone to damage and retrofit techniques are necessary. The presence of a rigid slab at the height of the roof has not improved at all the seismic behaviour of the study cases. On the contrary, the effective use of such retrofit technique has to be carefully evaluated specially when adopted in ancient constructions.
In the light of the analyses conducted on these complex constructions it is derived that is quite hard following a unique procedure able to define with consistency the most influencing quantities. Therefore, the necessity of defining a handy and suitable methodology for designers is strongly felt. In order to seek a simplified procedure on churches macroelements, a basic structural element in historical buildings, such as the portal frame, has been studied in detail. An analytical exact expression, derived using the kinematic theorem, and an approximate formula have been used for performing a parametric analysis varying geometrical proportions. 
The extension of the single portal frame to the multi-bay frame has been applied in order to perform the comparison between non linear analyses and simplified analyses. The use of approximate expressions derived for the portal frame implies an averaging of the pier widths. When the medium value is taken into account, generally, greater error percentages are encountered in the model with the load condition considering the only self weight: in this case, the non linear analyses give higher values; on the contrary the limit analysis gives small values of the collapse multiplier. In the load condition of self weight plus dead load, the scatters are smaller. When the maximum pier is taken into account, the values of non linear analysis will be the same but limit analysis values will assume greater values, moving on the right side so that are inside the domain. This evidence has been confirmed for the churches of SGMR, SI and SP. On the contrary, in the church of SGMG, medium values have shown a better comparison with non linear procedure.
In the last part of the thesis, the structural behaviour of another typical element in ancient structures is sought: it is the masonry arch. In order to determine the thrust ranges and the minimum thickness, a parametric analysis has been carried out on whole and half arches. A theory for the displacement of the supports has been developed: pointed arches can bear greater displacement than circular arches. This result is confirmed moving one of the supports in any direction into the plane and tracing the domains of possible positions. All the theoretical values have been checked with two different codes and the results agree well. Later, in order to verify these values, an extensive experimental campaign has been held on rigid concrete blocks in small scale representing eight different pointed arches varying eccentricity, the thickness and the angle of embrace. Five types of test were made on the arches: first, friction coefficient measures were taken on the blocks; then moving the supports horizontally apart and together, and vertically up and down. The comparison of theoretical and experimental results has allowed to emphasize the limits of both of them. Perfect hinges, sharp blocks, exactly symmetric structures, absence of friction, all accepted hypothesis in the theory, can never exist in reality; as a consequence the theoretical numerical results are greater than those measured in the experiments. At the same time the presented methods correctly predicted the final collapse mechanisms for the circular and specially the pointed arches. 

In the light of the conducted experiences in this study, in terms of modelling, analysis and testing, it is believed that masonry structures deserve great attention in the design and assessment process. Many mistakes can be made regarding the basic assumptions on the constitutive model of the material, the suitable structural modelling, the choice of the seismic action and an effective retrofit techniques. Furthermore, churches are more sensitive to damages than other “conventional” structures for their characteristic typology. 
The main features of these structures have been drawn throughout this work so that whatever similar building will fairly show the same topics here presented.
About the material properties, only experimental campaigns on the structural constituents of the building under study could provide a good characterization.  
Regarding the suitable analysis types, undoubtedly, a global three-dimensional analysis is necessary to get the general idea of the construction and understand its behaviour. On the other side, a useful quantitative result is the evaluation of the ultimate condition at collapse on bi-dimensional elements. This consideration is also made since the definition of the seismic forces for masonry structures according to different code provisions is not unique.
Simplified approaches do prove their appeal. Though some approximations are unavoidably to be made, in the aim of assessing the structural behaviour of ultimate capacity, such techniques seem to provide a very interesting path to follow in the future