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.

Recent studies have demonstrated that there is a relationship between the structure's susceptibility to second-order effects and its natural vibration period (𝑇) since both properties are fundamentally dependent on the structure's stiffness and mass properties. The main advantage on the use of this characteristic is that for the majority of existing structural analysis software, the natural period of vibration can be easily obtained. In this study, different formulations are developed in order to propose and validate an amplification factor (𝜒 𝑇 ) to multiply first-order analysis results and satisfactorily obtain results due to a second-order analysis. These formulations are based on the D'Alembert's principle, Rayleigh's method, and the use of generalized coordinates to represent the dynamic displacement of flexible structures. Therefore, it is analyzed the bending moment amplification (M2/M1bending moment due to a second-order analysis divided by bending moment due to a first-order analysis) for 122 spatial multistory reinforced-concrete frames, with different number of stories and floor plants. The ratios M2/M1 are plotted against natural vibration period for each building floor plant and each orthogonal direction. It is observed that values of 𝜒 𝑇 lead to values closer to the traditional simplified methods currently used in Brazil and, in fact, more accurate. Thus, it is proposed an amplification factor (𝜒 𝑇 ), based on the natural period of vibration, to be used as: (i) an indicator of the structures' susceptibility to second order effects and (ii) an amplification factor to describe the second-order effects on reinforced concrete frames.