Powierzchnie Graniczne w Teorii Wytężenia

This paper is devoted to the analysis of limit surfaces for the exertion of the material at a point, the exertion of a cross-section and that of the structure as a whole (the idea of «exertion» was introduced in [51]). Such surfaces are constructed in the n-dimensional space of exertion factors. The exertion factors are defined to be any independent quantity influencing in an essential manner the attainment of the dangerous (limit) state at a point, in a cross-section or in a structure.
Particular attention has been devoted to the problem of appropriate selection of the exertion factors. Thus, for instance, the danger of destruction of a closed cylindrical shell filled up with liquid or gas under pressure is considered. In the first case the danger is less because the exertion factors are strains, in the second case they are stresses and it is greater because a given state is as a rule more distant from the dangerous state in the space of strains than in that of stresses (Figs. 1, 2 and 3).
The known limit surfaces for exertion of cross-section and structure are systematized and discussed. As an example the limit surface is constructed for a statically indeterminate beam (Fig. 6) on the basis of the theory of elastic and ultimate load carrying capacity (Fig. 7). The elastic load carrying capacity is also analysed for a thick-walled tube subject to internal pressure and temperature (Fig. 8). In the final section the construction of the limit surface is discussed from the viewpoint of the stability loss of an element. An example of such a surface or a bar loaded with two forces is illustrated by Fig 9.