Structures are designed using current seismic design codes which are mostly based on Force-Based Design approach. The aim of the work is to implement the Performance-Based Seismic Design (PBSD) approach in concrete buildings. PBSD, which is a new concept in seismic design of structures, is a reliable approach capable of providing more detailed information on the performance levels of both structural and non-structural elements. Methods. In this study Performance-Based Seismic Design has been utilized on reinforced concrete irregular frame. In order to do this pushover analysis was done. Story drift ratios were chosen as deformation limits to define the performance levels for specific earthquake hazard levels. The results of this study show that Performance-Based Seismic Design gives a structure with better seismic load carrying capacity, thereby achieving the objective of performance as well as economy. It is also possible to conclude that PBSD obtained by above procedure satisfies the acceptance criteria for immediate occupancy and life safety limit states for various intensities of earthquakes.

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.

Geometers have proposed more than 600 analytical surfaces for implementation. The largest number of these surfaces is used in architecture and mechanical engineering. Although digital architecture and free form architecture are now increasingly influencing the design of long-span shell structures and curved buildings, the research and application of analytical surfaces continues on an increasing scale. The purpose of the research is to study the state of affairs in the application of analytical surfaces in the construction and engineering industries and to clarify the classes of surfaces that have found application in the study of physical phenomena or in solving purely mathematical problems, but not used in other areas of human activity. Another goal is to find analytical surfaces promising for application in architecture and mechanical engineering, which are still little known to architects and engineers. It has been established that, as before, designers take new analytical surfaces to implement their creative ideas from well-studied classes of surfaces of revolution, transfer and umbrella, minimal, ruled, wavy surfaces.

There are more and more needs of new forms in the world architecture. The thin shells theory and the surfaces theory give enough materials to scientifics and designers. This article is devoted to the geometric investigation of carved Monge surfaces. The geometry of these surfaces is inner and outer. For this, the coefficients of their fundamental forms are found and allow the classification of these surfaces. The kinetic method is used for their geometric investigation and classification. The parametric definitions of these multitude forms of carved Monge surfaces allow the 3D plotting of these surfaces by mean of the software MathCAD. The results obtained by this investigation are their vector, implicite, explicite and parametric definitions, the mathematic modelling of their inner and outer geometry, their 3D plotting and their classification. This variety of carved Monge surfaces can be used as the median surface of thin elastic shells design from them. The geometry these elastic shells, because their thin is the one of the carved Monge surfaces. The multitude of the designed thin elastic shells are expressive, durable and cover large spans. The multitude of their forms can find applications in the architecture of civil and industrial buildings and also in mechanical engineering.