Statistical analysis of the second order effects variation with the stories height of reinforced concrete buildings
Resumo In this paper the simplified method to evaluate final efforts using γz coefficient is studied considering the variation of the second order effects with the height of the buildings. With this purpose, several reinforced concrete buildings of medium height are analyzed in first and second order using ANSYS software. Initially, it was checked that the γz coefficient should be used as magnifier of first order moments to evaluate final second order moments. Therefore, the study is developed considering the relation (final second order moments/ first order moments), calculated for each story of the structures. This moments relation is called magnifier of first order moments, “γ”, and, in the ideal situation, it must coincide with the γz value. However, it is observed that the reason γ / γz varies with the height of the buildings. Furthermore, using an statistical analysis, it was checked that γ / γz relation is generally lower than 1,05 and varies significantly in accordance with the considered building and with the presence or not of symmetry in the structure.
Evaluation of second order moments in reinforced concrete structures using the γz and B2 coefficients
This paper presents an alternative to estimate the magnifier of first order moments to be applied on each storey of reinforced concrete structures, from the values obtained for the γz and B2 coefficients, used to evaluate second order effects in reinforced concrete structures and in steel structures, respectively. In order to develop the study, initially several reinforced concrete buildings of medium height are processed, in first order and in second order, using the ANSYS software. Next, γz, B2 and the increase in first order moments, when considering the second order effects along the height of the buildings, are calculated. Finally, from the results obtained, the magnifier of the first order moments, differentiated for each storey of the structure and calculated from both γz and B2 coefficients, is estimated and the efficiency of the simplified method of obtaining final moments using the magnifier proposed is evaluated.
Mechanics of deformable directed surfaces
Abstract The paper develops a simple, yet complete and consistent non-linear dynamic thermo-elastic shell theory based on the concepts of a two-dimensional directed continuum. The constitutive equations are postulated in a general form. Stress-strain relations are derived using the equation of energy balance and the two entropy production inequalities, which are rewritten in a special form. The linear theory is discussed in detail. The structure of the stress-strain relations is presented in the most general form and then specialized to concrete examples, in particular, to the classical shell theory, using their invariance properties with respective to certain symmetry groups. The elastic moduli are determined by demanding the coincidence of the frequency dispersion surfaces obtained using the two-dimensional theory with the lowest foils of the corresponding surfaces resulting from the three-dimensional theory of elasticity.