Amplification Factor for Estimation of Maximum Inelastic Lateral Displacement of Reinforced Concrete Moment Resisting Frames

Abstract: In seismic design of structures, estimating maximum inelastic lateral displacement of the structure occurring in the sever earthquake is of grate importance. Although by conducting nonlinear time history analysis good estimates of inelastic displacements can be obtained, but this method is relatively expensive and needs high expert in this field and its use is impractical in most of the design offices. So in most seismic design provisions, maximum inelastic displacement of the structure is estimated by amplifying the lateral displacement computed from an elastic analysis with a displacement amplification factor (C_d). Reviewing several seismic design provisions indicates that in most of them C_d is only dependent on the earthquake force resisting system. In this paper in addition to the earthquake force resisting system, the effect of some important parameters such as number of stories of the structure, story number, characteristic of the earthquake ground motion and number of bays on C_d is investigated. For this research 32 reinforced concrete moment resisting frames with high and moderate ductility which have 3 or 5 bays and 2, 3, 4, 5, 6, 8, 10 and 12 stories are considered. For determination of real displacements occurring in major earthquake (inelastic displacements), nonlinear time history analysis using IDARC program is performed. In nonlinear analyses, 7 earthquake ground motions consistent with soil type II of Standard no. 2800 are used. These records are scaled according to Standard no. 2800 directions. For linear analyses, equivalent static procedure is employed using ETABS program. The inelastic displacements which are computed by averaging the results of 7 ground motions, are then divided by elastic displacements and so C_d for each story of 32 frames is determined. In this research, like most researches and provisions, C_d is considered as a function of R (structural behavior factor) and for simplicity C_d/R is shown by DF and the following results are presented for DF. The first important result is that DF in high ductility frames are more than corresponding ones in moderate ductility frames especially in low frames and lower stories of tall frames. Furthermore in more than 97% cases, this factor decreases by increasing story number showing that inelastic deformations and damages are mostly concentrated in lower stories. Also it was observed that in low frames and lower stories of tall frames, the response of structure is more sensitive to the characteristic of the earthquake ground motion. Another conclusion is that in all frames, DF is almost independent of the number of bays. Then by recognizing the most affecting parameters and conducting nonlinear regression, an equation for computing displacement amplification factor in special and intermediate reinforced concrete moment frames is suggested. In the proposed equation, DF has been recognized as a function of lateral load resisting system, story number and height of frame (natural period of frame). Finally, results are compared with Standard no. 2800 formula (DF=0.7) for estimating inelastic displacements. It is concluded that inelastic lateral displacement of frames obtained from nonlinear time history analysis are largely different from those calculated by Standard no. 2800 formula especially at upper stories. This difference is originated from the fact that considering a unique DF (0.7) for all stories results in a deformed shape in nonlinear domain similar to that in linear domain which is true only if damages and inelastic deformations occur monotonous in height of structure; but this assumption is not consistent with real response of structures during the sever earthquake.