Making the simulation of the masonry construction, there are three major groups of analyses: linear analysis, nonlinear analysis and limit analysis. It is also worth mentioning that despite the differences resulting from the fact that various types of methods generate different safety coefficients and different final results, there are no ample reasons for choosing the one particular method over the others - during the researches, it was decided that the simplest type of analysis will be applied, namely the linear analysis. Such a decision was made because of the applicability of this type of analysis in the simple constructing solutions.
A mathematical analysis of the curved brick constructions placed an important position in the deliberations of mathematicians and construction theoreticians for a long time. What is more, many instructions substantially based on the engineering practice were established.
Associating the practical knowledge with the theoretical deliberations, enabled one to the better understanding of the problem of the static work of arches, vaults and domes. Making the analysis of the current state of knowledge about estimating the capacity of arches, vaults and domes, one can easily notice that one of the major problems appearing on the level of the estimation of carrying capacity is accepting the static scheme of the curved brick construction with application of the proper method of calculating the internal forces in constructing elements.
On the way to constructive deliberations about the statistics of the curved masonry constructions, the systematization of those deliberations seems to be intentional. However, this systematization should be different from that which dominates over the historical aspects of the subject. Here, the static scheme of the work of the groups, justifies the division into groups which can be attributed to a certain group. The knowledge of the static scheme enables the calculation of internal forces which are present in elements of the arches, vaults and domes as well it facilitates carrying out the analysis of their work in respect to construction security and in case of a failure in accepting the proper method of strengthening.
However, the static calculations are based on various simplified assumptions which are not truly real. Therefore, such calculations cannot be made with full precision. Uncertainty of the static calculations becomes problematic when weight is taken into consideration. The construction weight (especially in relation to monumental buildings) and snow and wind burdens, are rather unknown and depend on other factors which cannot be precisely calculated. Even model-scale experiment cannot ensure certainty.
The problem which ought to be precisely analysed is the issue of static calculations of the damaged arches, vaults and domes. It must be specified how the various types of damage (i.e. loosening of squinch from arch rib, change of construction geometry) influence the way the internal forces flow through the curved brick constructions and safety of the entire construction. Although not all the mathematical considerations can be easily applied, there are a few considerations which highly influence the analysis of the curved masonry constructions' behaviour. Moreover, further solutions relate to various types of the curved brick constructions, not only to the one described type of construction (i.e. arches).
The group of major analytical methods comprises of:
- graphical method of establishing the line of pressure in the arches,
- three-jointed arches calculation method,
- Heyman's non-moment method applied to vaults and domes.
All of the numerical analyses of the monumental buildings related to the static analysis, are encumbered with a basic error, namely it is very difficult or almost impossible to describe the resistance and deformabil-ity of materials in present masonry constructions. If this was possible, it would enable taking the correct calculation model.
The main problem of such approach is the acceptance of the most precise and efficient model of
Figure 2. arch A2.
Real view of one of the examined arches
Real view of one of the examined arches material. After a profound study of the subject's literary sources, it was decided that the masonry material will be treated as homogenous and isotropic material as it has got the same physical properties in all directions.
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