Figure 18. Inner face of shell elements. Tensile stresses due to self-weight of the structure.
One of the major steps of the assessment of an existing structure is the analytical reproduction of its pathological image. In the case of the Katholikon, preliminary linear parameter analyses were performed (Miltiadou-Fezans et al. 2004), as a means for selecting adequate emergency interventions. Those analyses provided a quite satisfactory numerical verification of the pathological image of the monument. For the preliminary analytical study, using the computer code ACORD, the structure was modeled by shell elements (Fig. 17), whereas the mechanical properties ofelements belonging to various parts of the structures were assumed on the basis of the available data for the construction materials. Linear elastic analyses were performed for various combinations of actions (self weight alone or combined with seismic action). Both static and dynamic analyses were performed.
Figure 18 shows the calculated stresses for the inner face of shell elements, due to vertical loads. Irrespectively of the accuracy of numerical values of stresses, one may clearly distinguish the vulnerability of the region of arches and domes (especially in the west part), even for the self-weight of the monument alone. As expected, tensile stresses are developed in the apex of several arches, in the groin vaults of the narthex, in the base of the cupola and that of its drum, as well as in the four squinches. The obtained results are conform with the qualitative interpretation of the pathology of the monument and they prove the inherent vulnerability of the structural system, in which (a) a stiff central cupola is resting (through the drum) on four major arches parallel to the two main axes of the church (see Figures 3, 4), as well as on four arches oblique in respect with the longitudinal and the transverse axis, (b) the vertical, as well as the horizontal component of the self weight of the whole system of (intersecting) groin vaults arranged around the central dome, are transferred to rather flexible stone masonry piers, and (c) there are not currently ties in the arches and vaults, or other elements to confine critical structural elements or link the various parts among them. Therefore, the tendency of the structural system to deform laterally in its upper region is expected to be apparent even under self-weight alone.
This working hypothesis seems to be confirmed by the deformed shape of the structure in-plan, shown in Figure 19. One can even observe the more pronounced lateral deformation along the N-S axis of the
Figure 20. Deformed shape of the structure looking from the N. Dynamic analysis; seismic action along the longitudinal axis.
monument, as well as the out of plane deformation of the perimeter walls of the narthex, which historically has been proved to be a vulnerable part of the structure, already reconstructed in 1896 and deformed again as measured after the 1999 earthquake. On the same Figure, the excessive out-of-plane deformation of the exonarhtex is also apparent.
Expectedly, this behaviour is deteriorating when a seismic event occurs. In Figure 20, the out of phase movement of the east and west parts of the monument is shown. Such a movement can explain the severe damages occurred to the drum of the dome, as well as to the arches and vaults supporting the dome. In general, the analyses for loading combinations including the seismic action have shown a critical concentration of tensile stresses in arches at various levels, as well as in the piers of the drum. In addition, extensive damages in vertical elements (masonry in the perimeter of the monument, as well as piers) were confirmed.
Furthermore, in the framework of this preliminary work, the plots of principal tensile stresses were compared with the respective drawings on which observed cracks were reported (Miltiadou et al. 2004). This comparison proved to be quite satisfactory, as, in general, the observed crack pattern (location and inclination of cracks) seems to be confirmed by the analytical results in all regions of the monument.
Although this preliminary analytical work allowed for a better understanding of the structural behaviour of this important monument, it was judged that a more accurate assessment of its seismic behaviour was of primordial importance for the design of optimum interventions.
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