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The subject of the thesis is the analysis of steel girders behavior (welded steel I beam) under the influence of the localized load. The girders without longitudinal stiffeners were tested, as well as the girders with the longitudinal stiffeners in the vicinity of the loaded area. The influence of the length of uniform distributed load on the loaded flange, in the plane of the web, known as patch loading was analyzed as well as the behavior of the girder in the non-linear area, as well as the ultimate load which is manifested by buckling in the load application zone. During the bridge assembly procedures, when the bridge is being launched to its definite position over the temporary and permanent supports, the influences which occur may exceed the load of the structure in certain points due to the patch loading. Because of its extreme complexity, a complete theoretical solution for the problem has not been found yet. The solution procedure requires the combination of experiments and numerical analysis. Because of the importance of the numerical simulation of the girders, in this thesis, a special attention was paid to the theoretical foundations and solutions which would contribute to the improvements of efficiency of software packages concerning the onset of singularity points during the simulation. The developed software packages are based primarily on the application of Finite Element Method (FEM) and Boundary Element Method (BEM). In these procedures, algebraic and/or logarithmic problems with singularities of often occur, and one of the goals was to give a contribution towards a more efficient solution of these problems. The research comprised application of numerical procedures where FEM was implemented using most up-to-date software packages; many improvements were made using the analytical methods referring to the singularity problems. Theoretical basis and solutions elaborated here can include an occurrence of singularities, so that it contributes to improving the efficiency of software packages, i.e., it gives a faster and more accurate solution of the problem. A special class of Gaussian quadrature formulas is V derived and it provides improved solutions of certain more complex problems with algebraic and/or logarithmic singularities. An alternative approach with Gaussian quadratures for Müntz systems, developed by Milovanović and Cvetković (SIAM J. Sci. Comput. (2005)) is also mentioned. In the existing literature up to now this area has not been paid due attention. In addition to these solutions and the general theoretical fundamentals, direct answers to the problems of patch loading are provided by presenting the compatible developed numerical model in the software package ANSYS Workbench 15, after the experimental research performed. A large number of the results of the experiments, performed during research, conducted at the Faculty of Civil Engineering in Belgrade under the direction of N. Marković [70], served as a basis for the research and creation of the compatible model in the computer simulation. The goal numerical simulation was to determine the ultimate load and monitor development of deformations and stresses. The actual models for numerical simulation of girder behavior allow inclusion of initial deformations-imperfections into the calculation on the basis of the actual girder model. In the numerical simulations of the model, the form, character and course of deformation process as well as the buckling were identical as in the experiments with actual models, for each concrete sample. Numerical simulations tested the girder model behavior, and the values of the ultimate load of the girder was determined for six material models, and the quantitative analysis of those results was performed. The behavior curve corresponding to the multi linear curve according to EN1993-1-5 [28] gave a very good approximate value of the ultimate load. Because of the topicality of this field, a review of the state-of-affairs is provided, as well as the main course of research in this field. The existing experimental results and standard statistical method, common for these issues were used, for the purpose of result verification, as well as contemporary methods of numerical approximation. The results of the research are applied for the structural design, particularly for the design of steel bridges constructed by launching over the temporary or permanent supports, and in the new versions of the national codes for steel structures design. VI The impact of actual imperfections of the beam web plate was included, and a comparison with the beams without imperfections was performed within the numerical simulation, for the purpose of observing the stress development. The cases of research of impact of actual imperfections on the magnitude of the limit load are present in the literature to some small extent. This thesis contributes to a more realistic modeling of the girders, which provides opportunities for new behavior tests of such or different girder models using numerical simulation. The tests carried out in this way, facilitate beam analyses which would indirectly contribute to the adoption of correct approaches in obtaining the theoretical results.

The subject of this thesis is the numerical modeling of the behavior of plane reinforced concrete frame structures under long-term load with the purpose of qualitative and quantitative analysis of the influence of stiffness changes of these structures, as an effect of the occurrence of cracks, as well as creep and shrinkage of concrete, on the results of static and seismic analysis. The algorithm for the calculation of static influences in reinforced concrete frames, as well as dynamic characteristics and design seismic forces and influences by using multimodal spectral analysis, taking into account the real change of cross section stiffness after cracking of the concrete tensile zone, is formulated. This algorithm effectively solves the problem of determination of the stiffness of reinforced concrete structures under long-term load, and is significantly more precise and more detailed than the current recommendations in the literature. The new algorithm is implemented in the form of a package of computer programs, written in Fortran programming language, for the analysis of reinforced concrete frame systems taking into account the reduction of element stiffness. Application of these programs is simple, but effective, and among other, the real data on the geometrical characteristics of the elements of reinforced concrete structures with cracks is obtained, which can be used in other software for the calculation of reinforced concrete structures modeled by linear elements. In the static analysis of reinforced concrete frames two assumptions of linear theory are kept: the assumption of small deformations and the assumption of small displacements, while the material nonlinearity is taken into account by applying the numerical model with cracks, as well as using the Age - Adjusted Effective Modulus Method for the calculation of stress and strain changes during time. Using newly developed computer programs comparative analysis of results of classical static, as well as classical seismic calculation, in which the stiffness of columns and beams of reinforced concrete structures is calculated for gross concrete cross section, at one side, and the calculation that takes into account the changing of structure geometry due to the appearance of cracks, at the other side, is carried out. Conclusions are drawn that will be useful for the improvement of existing engineering practice.

Choosing "an idealized model of the structure" in the classical theory of structures, connections between the members of the linear systems are usually adopted as ideally pinned or absolutely rigid. Ideally pinned connection does not allow relative displacement of interfaced sections foci, while sections can freely and independently rotate. The rigid connection does not allow both relative displacement and relative rotation. Numerous studies based on experimental results and numerical simulations, which were conducted over the last forty years, indicate that a large number of the node connections of members of linear systems can be classified neither as an ideally pinned nor as absolutely rigid. Systematization of recent results of scientific research, both theoretical and experimental work in this field in our country and worldwide, especially in the field of reinforced concrete linear systems, is performed in the first part of this doctoral thesis. The Chapter 1 presents an introductory discussion and an overview of the development of methods for analysis of linear girders, while in the Chapter 2 the results of the international project COST C1 ˝Semi- Rigid behavior˝ are analyzed in details, especially within the working groups for prestressed and reinforced concrete structures and seismic design. A special contribution to the study of this problem in our country is given by numerous theoretical and experimental works of the team of researchers from the Faculty of Civil Engineering in Niš under the leadership of Prof. Dr. Milic Milicevic. The theoretical approach to the design of structures with semi-rigid connections using the classical formulation of deformation method was analyzed in these works in details which an overview is given in the Chapter 3. Bearing in mind that the contemporary analysis of stress-strain state of complex engineering structures can not be imagined without a matrix formulation and implementation of electronic computers, the matrix formulation of structural analyzes of systems with semi-rigid connections is presented in the same chapter, which opens wide opportunities for relatively quick and simple analysis of these systems by use of modern methods of structural analysis. Variation formulation of the stiffness matrix and the equivalent load vector determination is shown in the Chapter 4, while the use of computers in the analysis of structures with semi-rigid connections is given in the Chapter 5. The results of the full size experimental analysis of a behavior of prefabricated reinforced concrete structures with semi-rigid connections carried out on the newly designed and constructed buildings Minoma and cold storage Lovopromet in Nis under static load are presented in the Chapter 6. In Chapter 7 is shown the experimental determination of the dynamic characteristics of structures by ambient vibration method which is performed on buildings constructed in structural systems Minoma and Amont in Nis. In the second part of the doctoral thesis experimental study is shown, which was realized in cooperation with the "Institute of Earthquake Engineering and Engineering Seismology" of the University St. Cyril and Methodius, Skopje, Republic of Macedonia, as a part of the static and dynamic stability attesting project of the standardized modulus of prefabricated RC halls program of structural system "AMONT", including analysis of obtained results, numerical modeling and calculation of reinforced concrete linear structures constructed in this system taking into account the real characteristics of connections. Almost all earthquakes that have occurred in the world in recent decades have caused severe damage or total demolition of precast reinforced concrete structures with semi-rigid connections (industrial iv halls and other various structures which differ in number of floors and ground floor typology). The most important is to provide that there are no human casualties during this damage, but the demolition of these buildings during the earthquake causes huge losses. In addition to the losses in terms of the economic value of the building itself, demolition most often has caused destruction of the very expensive industrial equipment. Modern technological lines in contemporary industry may be five to ten times more expensive than the value of the building itself. If the long-term economic consequences of the termination of the production process are taken into account, it is clear that the seismic safety of industrial halls is of vital importance in any seismically vulnerable region, which includes the territory of Serbia. In the second part of the doctoral thesis original results obtained on the basis of extensive theoretical and experimental research are presented with the aim to give adequate contribution in the field of real observation of present problems, in order to define the structural conditions and measures to improve the seismic safety of these specific structural systems. For this purpose primarily real phenomena and causes of damage and demolition of similar buildings during earthquake action are studied (Chapter 8). Based on the selected characteristic prototype of an industrial hall, which is widely present in Serbia, very extensive program of experimental research was carried out. These studies have provided original results and new insights into the real behavior of structural connections based on constructed full size physical models testing under the simulated cyclic load to the point of failure (Chapter 9). Improved methodological concept for nonlinear analysis of integral facilities with semi-rigid connections is formulated on the base of the experimental results by use of totally non-linear mathematical model (Chapter 10). A consistent theoretical procedure applicable for a detailed analysis of nonlinear seismic response of the systems with semi-rigid connections has been formulated and presented in the Chapter 11. The methodological concept of developed computer software used for detailed analysis of nonlinear seismic response of the selected prototypical building is presented in the shortest in the Chapter 12. The analytical part of the specific research includes the realization of extensive analysis of nonlinear seismic response of the selected characteristic prototypical industrial hall, with the aim to show the practical applicability of formulated analytical model and theoretical procedure for nonlinear analysis. The concept of formulated totally nonlinear mathematical model is shown in the Chapter 13, while in the Chapter 14 and the Chapter 15 the most significant results of the performed analysis of nonlinear seismic response of the building in transversal and longitudinal direction due to the effect of real registered earthquakes are presented. The fundamental facts that have been reached on the basis of completed complex analytical research are stated in the Chapter 16. Formulated and implemented detailed nonlinear analyzes enable improved design and wide practical application of standardized industrial halls and other facilities of this type in seismic zones of various intensity.Based on the results of completed integral theoretical, experimental and analytical studies, adequate conclusions and appropriate recommendations for further experimental and analytical research are summarized in the Chapter 17.