Abstract
A model is presented for pushover analysis of reinforced concrete (RC) beam-column joints in soft-first-story frames. In such frames, the sections of first-story columns are usually much larger than those of second-story columns to prevent story collapse (Fig. 1). Based on the experimental results of specimens O-1 and O-1t (Fig. 2a), which are reported in Reference 3, this study proposes new equations for calculating the strength and the yield deformation of such frames with columns extended toward outside of frames and subjected to opening load.
Figure 1a shows the column failure mode, which is considered in the conventional model. Figure 1b shows the beam failure mode, which is proposed in this paper. To represent these two modes, the proposed model includes a rotational spring of first-story column and that of beam (Fig. 2b). Taking the result of strut-and-tie analysis (Fig. 9) into account, we determine the non-linear characteristics of these two springs which may be applied to actual design.
The strength of column spring, yMc1, mainly consists of the moment capacity of the first-story column of which depth is lb, where lb is the development length of the beam bottom bars. Moreover, adding the contribution of the hoops in the joint, yMc1 is calculated from Eq. 3. The column spring is located at the center of the beam bottom bars (Fig. 2b). The strength of beam spring, yMj, is evaluated as the sum of the flexural resistance of the beam (yMb) and that of the second-story column (yMc2) (Fig. 11). yMb is calculated as the moment capacity of the section shown by hatched lines in Fig. 11 (Eq. 4). The beam spring is located at the center of the joint (Fig. 2b).
The yield deformation of each spring is determined based on the observed strain distribution. Figures 14d and 14f show the deformations related to the column and beam spring, respectively. It is assumed that the strains of the bars in the dark regions in Figs. 14d and 14f reach the yield strain when the column or beam spring reaches the yield deformation. Considering the elongations of the longitudinal bars caused by the rotational deformations (Figs. 14d and 14f), the yield rotations of the column spring is given by Eq. 13, and that of the beam spring is given by Eq. 14.
The model defined in Fig. 2b is integrated into the model as shown in Fig. 2d with a single spring at the end of the column.
The load-drift relationships obtained from the proposed model (the chain lines in Figs. 4 and 5) agreed with the test results much better than the conventional model (the broken lines). The ultimate strengths and the yield deformations given by the new model accurately correspond to the test results with the ratio of 1.02 to 1.21 (Figs. 16 and 17). It is indicated that the conventional model may provide the higher strength than the observed value and less than a half of the observed deformation due to neglecting the beam failure mode.
