An energy-based approach to determine the yield force coefficient of RC frame structures

This paper proposes an energy-based approach for estimating the yield force coefficient of reinforced concrete (RC) frame structures. The procedure is mainly based on the energy balance concept and it considers the nonlinear behavior of structures. First, an energy modification factor is defined to consistently obtain the total energy of the equivalent elastic-plastic single-degree-of-freedom (SDOF) system. Then, plastic energy is formulated as functions of the several structural parameters such as the natural frequency, the strength reduction factor and the yield displacement. Consequently, the plastic energy formulation is derived for multi-degree-of-freedom (MDOF) systems and the yield force coefficient is determined by equating the plastic energy relation to the work needed to push the structure from the yield displacement up to the maximum displacement monotonically. The validity of the energy-based approach is assessed on several RC frame structures by means of nonlinear static pushover analysis considering both material and geometrical nonlinearity. A modification factor is proposed for the yield force coefficient to consider the strain-hardening effects in lateral forces. Moreover, the modified energy-based yield force coefficients are correlated to practical design by using the ductility ratios imposed by Turky Building Earthquake Code and a quite good agreement is observed.