The paper points out to the differences of the First order theory and Second order theory and of the significance in practical calculations. The paper presents theoretical foundations and expressions of calculations of impacts on the stability of structure, that is, review of the Second order theory in a bridge with members semi-rigid connections in joints. In the real structures in general and the especially in the prefabricated structures the connection of members in the nodes can be partially rigid which can be very significant for the changes in tension and deformation. If the influence of the normal forces is significant and the structure is slender then it is necessary to carry out a calculation according to the Second order theory because the balance between internal and external forces really established on the deformed configuration and displacements in strict formation are also unreal. The importance and significance of the calculations and distribution of impact according to the Second order theory were presented in numerical examples as well as the calculation of critical load as well as the buckling length of members with semi-rigid connections in joint
The structures with semi-rigid connections comprise systems with the connections in joints which are not absolutely rigid, but allow, in general, some relative movements in directions of generalized displacements. Such type of connections is considered very little, or not at all, in designing of structures in today's engineering practice. If the influence of rigidity of semi-rigid connections is underestimated, and they are treated in the design as pinned, it has a negative impact on cost of a structure. But if it is overstated, the calculation results are not on the side of safety, what is reflected on bearing capacity, durability and stability, especially in the case of precast structures. Therefore Eurocodes take due account to the structures with semi-rigid connections. Matrix formulation of the analysis of systems with semi-rigid connections opens wide possibilities for relatively easy calculation by use of computers that is shown by example of seismic design. The interpolation functions, stiffness matrix, equivalent load vectors, and the consistent mass matrix are presented in this paper, particularly with an emphasis on systems with semi-rigid connection
It is natural the people should be most interested in the behavior of buildings during earthquakes, as they spend the most of their time in them. The times when the buildings were designed and constructed for unknown customers have passed. Apart from the static stability, which must not be endangered, care must be taken of functional and esthetic features. The buildings are long-lasting and expensive human property, more so in the seismic areas, so by their quality they must guarantee safety to their users. Regarding high seismicity and frequency of earthquakes on the territory of our country, safety of social resources and human lives must be harmonized with the development degree and future needs of the society and the users. Through seismic safety and reduction of risks, we protect ourselves from collapse and damage of the structures, from injuries and human casualties, and from direct and indirect, economic and functional, social and other damage. For these reasons building in seismically active areas is a complex task. Complete protection from the earthquake action is not possible, and for this reason the level of seismic risk represents an acceptable vulnerability for the corresponding period and probability of excitation. Structures are protected from collapse and seismic damage if the appropriate regulations are applied. Seismic division in micro-regions represents a good approach to defining an uniform criterion of protection of structures and protection of equipment in them
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