Aims. Thin shells in the form of cylindroids are fourth-degree ruled shells for which few works are devoted. In this paper, their geometric modeling is worked out and their middle surface are plotted, using the software MathCAD. Their stress-strain state are instigated with two building material: reinforcement concert and qualitative steel. Methods. This linear investigation is done for fixed and hinged supports and for various thicknesses in the software SCAD. The numerical values of their maximum and minimum displacements of their middle surfaces are given. Based on these displacements, conclusions are made for the whole paper. Results. The linear analysis for reinforced concrete and metallic shells, computed using the software SCAD gives the numerical and graphical results that are presented. Conclusions. The investigations of the stress-strain state are done for shells with the shape of cylindroid with two directrices ellipses and cylindroid Frazer. For the same thickness, loading and span, the reinforced concrete shells has minimum displacements. For thickness, 20 cm the steel shells have the same maximum displacements. For the thickness 30 cm the maximum displacement is more in steel shells. It is more optimal to use reinforced concrete shells than the one in steel. A large span (till 30 m) shells can be designed with reinforced concrete.

Introduction. The seismic stability of bearing structures is one of the main objectives of design and construction of structures in earthquake areas. The co-authors have analyzed the effect of a damper, located at the intersection of structural elements, on the seismic response of the main girder of a steel-concrete bridge exposed to the seismic impact. The purpose of this study is to select optimal values of viscous and elastic elements to ensure the seismic resistance of the bridge. Materials and methods. The finite element method was used to simulate the geometric characteristics of the bridge. The model of the bridge has rod elements to simulate girders and viscous elastic elements to simulate dampers. In the study, different values of elastic and viscous characteristics of the damper were used in pairs. The nonlinear problem statement helped to analyze the bridge structure using the direct dynamic method. Results. As a result, we obtained a graphic chart describing the relationship between horizontal displacements and the time for each pair of values of elastic and viscous characteristics of the damper for Maxwell and Kelvin – Voigt models. The effect of changes in the values of stiffness and damping parameters on the values of the period and eigenfrequencies of this superstructure was also investigated. Conclusions. The co-authors chose the damper parameters to minimize seismic displacements of the bridge girder and optimally suppress the dynamic interaction between the bridge elements. Viscoelastic elements of the Kelvin – Voigt type provide more regular values of horizontal displacements of the girder when the direction of the seismic effect changes. We also recommend to select the pair of values equal to 20 000 kN/m, 800 kN s/m, and to use the Kelvin – Voigt model in the design of a viscoelastic damper.

Aims of research.A surface of revolution is generated by rotation of a plane curve z = f(x) about an axis Oz called the axis of rotation. This paper provides information on hyperboloids of revolution surfaces and their classification. Their geometric modeling, linear and materially nonlinear analysis are worked out.Methods. Hyperboloids of revolution middle surface is plotted using the software MathCAD. The linear and materially nonlinear numerical analyses of thin shells of the shape of an hyperboloid of revolution surfaces on stress-strain state is given in this paper, using the finite elements method in a computer software R-FEM, the material which we use in our model is concrete with isotopic nonlinear 2D/3D stress-strain curve for materially nonlinear analysis and linear stress-strain curve for linear analyses. Comparison is done with the result of the finite elements linear analysis of their strain-stress results.Results. That displacements in the investigated shells subject to self-weight, wind load with materially nonlinear analysis are bigger than which done by linear analysis, in the other side the displacements is similarity subjected to free vibration load case. Based on these results, conclusions are made for the whole paper. For citationGil-oulbé M., Jazzan M., Qbaily J. (2019). Geometric modelling and materially nonlinear numerical analysis of shells in the shape of onesheet hyperboloid of revolution. Structural Mechanics of Engineering Constructions and Buildings, 15(3), 210-218. http://dx.

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The aim of the work - development of one of the possible methods for seismic analysis that considers the inelastic behavior of structures under seismic loads. This requires the development of seismic analysis methods that take into account the change (decrease) in the bearing capacity or the destruction of individual elements until the final loss of the bearing capacity of the structure. Methods. The dependences and algorithms include determining seismic forces using the method of normal forms, which until now is the main one in solving problems of the seismic resistance theory in seismic regions, calculation formulas to calculate seismic forces at each time step are presented in the form of expansions into natural vibration modes, which regard the changes in the design scheme. The calculation is repeated at each time step as a static calculation for the action of seismic forces determined at the previous stage, before the building collapses. Results. The developed dependencies and algorithms allow to consider changes in the design scheme during vibrations at each time step, changes in the dynamic properties of the building and, as a result, the values of seismic forces. The value of the coefficient of inelastic work of structures K 1, which are given in regulatory documents, do not give fully correspond to the actual behavior of the structure under seismic influences. The proposed calculation method allows to determine the estimated values of seismic forces and their distribution taking into account the influence of damage of elements and the appearance of inelastic zones in the design process of fluctuations at each time step and to assess the dynamic behavior of the building.