Simplified Approach Based on the Natural Period of Vibration for Considering Second-Order Effects on Reinforced Concrete Frames

Abstract

Recent studies have demonstrated the existence of a relationship between a structures susceptibility to second-order effects and its natural period of vibration ([Formula: see text]) given that both these properties are fundamentally dependent on the structure stiffness and mass properties. The main advantage of the use of this characteristic is that [Formula: see text] can be obtained easily by the existing structural analysis software. In this study, different formulations are developed in order to propose an amplification factor ([Formula: see text]) to multiply first-order analysis results and satisfactorily obtain results of a second-order analysis. These formulations are based on D’Alembert’s principle, Rayleighs method, and the use of generalized coordinates to represent the dynamic displacement of flexible structures. It is observed that [Formula: see text] provides values closer to and in fact, more conservatively than, those obtained by the conventional simplified methods currently used by structural design engineers. Thus, the amplification factor [Formula: see text], which is based on the natural period of vibration, is proposed to be used as (i) an indicator of a structure susceptibility to second-order effects and (ii) an amplification factor to describe the second-order effects on reinforced concrete frames.

Analysis of the global second-order effects on irregular reinforced concrete structures using the natural period of vibration

“…Thus, it is essential, to validate the parameter χ T, that a greater number of analysis are carried out considering structural models with similar characteristics to existing buildings. Furthermore, results obtained by Reis et al [17] presented conservative values for the critical columns on the assessed models. Therefore, an improvement in moment amplification methods due to global secondorder effects must be investigated.…”

“…The χ T parameter was developed by Reis et al [17] aiming to evaluate reinforced concrete structures susceptibility to global secondorder effects; in addition, it is possible to estimate the final internal forces through a simplified first-order analysis. The parameter was developed applying Rayleigh's method [18], in which coordinate generalization and the principle of virtual work were used.…”

“…Based on this, Statler et al [16] have demonstrated that it is possible to evaluate the structure susceptibility to global second order effects using the natural period of vibration in steel structures. Recently, Reis et al [17] presented the development of the simplified χ T parameter. This parameter uses the natural period of vibration to estimate bending moments considering non-linear effects.…”

“…To account for the global second-order effects, first-order moments are amplified in reinforced concrete frames. Analyses carried out by Reis et al [17], however, applied the χ T parameter only in structures with floor plan symmetry and no stiffness variation along its height. These characteristics diverge completely from most constructions.…”

“…Therefore, parameter χ T can be improved considering higher vibration modes. In this context, the current work aims to assess the application of the χ T parameter, developed by Reis et al [17], in reinforced concrete structures with different irregularities on the floor plan and, along its height. The study presented herein is intended to cover the major structures designed in Brazil and, to understand the limitation of the methods.…”