Derivation of yield force coefficient for RC frames considering energy balance and P-delta effects

Abstract

Currently, prominent energy balance concept can efficiently be used to calculate the yield base shear force of structures. Energy balance equation is an additional constraint for the balance of seismic input energy by the energy absorption of the structure. This equation can be defined as the sum of elastic and plastic energies of structural systems using elastic and plastic load-deformation characteristics and the total energy dissipation capacity can finally be equated to the seismic energy demand. The objective of this paper is to present a procedure for the determination of energy-based yield force coefficient of reinforced concrete (RC) frame structures considering P-delta effects. The total of elastic and plastic energies are computed by means of elastic spectral velocity and energy modification factor, which is originally derived for structural systems with geometric nonlinearity. Total inelastic energy of single-degree-of-freedom (SDOF) system is transformed into the total inelastic energy of the multi-degree-of-freedom (MDOF) system using the conversion based on structural dynamics. Plastic energy of MDOF system is formulated after total seismic energy demand is obtained. It is accordingly equated to the total work done by inelastic MDOF structure with P-delta effects and consequently, a dimensionless yield force coefficient is derived. Nonlinear static analyses are performed for selected multi-story RC frames and yield force coefficients are compared with the results of the energy-based formulation. The results show that the proposed formulation taking P-delta effects into account can be effectively used to estimate the yield force coefficient of RC frame structures.