Seismic Force Demand on Columns of RC Moment Frames due to Higher Mode Effects

The capacity-based design is the main approach and the basic idea in the recent seismic design regulations. In moment frame systems, the desired mechanism is formed by the formation of plastic hinges at the two ends of the beams and the base of the first story column. To ensure preventing the formation of undesired mechanisms, the capacity design approach is used. For this purpose, the beam plastic moments are considered Displacement-Controlled (DC) actions, and the bending moments and shear forces in the columns (except the bending moment in the base of the first story column) are considered as Force-Controlled (FC) actions. Hence, these FC actions must be designed based on the capacity of DC actions and should remain linear during earthquakes. In order to prevent the formation of plastic hinges and shear failure in columns, two issues should be considered in the design: (1) design of columns on the basis of the bending moment capacity of the beam plastic hinges, and (2) taking dynamic amplification factor into account which is mainly due to the higher mode effects. Although the first issue has been considered in most of the design codes, but the dynamic amplification factor for column internal forces has only been considered in some of them. In this study, the higher mode effects were investigated in three reinforced concrete moment frames. For this purpose, three 8-, 12- and 20-story buildings, which were designed based on U.S. seismic design codes, were subjected to 11 earthquake records. The nonlinear time history analyzes were performed for both Design-Based Earthquake (DBE) and Maximum Credible Earthquake (MCE) levels.The results of the analysis show that the higher mode effect significantly influences the column moment in the columns. Hence, satisfying the strong column-weak beam criterion using the coefficient of 1.2 and ignoring the dynamic amplification factor based on U.S. design code is significantly nonconservative and leads to the formation of plastic hinges in the columns even in DBE earthquakes. However, the New Zealand design code recommendations for moment amplification factor is usually conservative. There is a similar judgement for the U.S. and New Zealand design recommendations in the case of column shear forces. It should be noted that the amplification of column shear forces is generally less than the bending moments, but the column shear failure is brittle and may lead to progressive collapse and catastrophic failure of buildings. Therefore, the design recommendations for the shear dynamic amplification factor are very important and cannot be neglected. Based on the average plus the standard deviation index, the column bending moments amplified about 50% to 60% for DBE earthquakes. This increase for shear forces in the columns reaches about 20% that should be considered in the capacity design of columns. In summary, based on the limited analysis and models used, this study recommends 1.6 and 1.2 for moment and shear amplification factors, respectively. It is notable that the dynamic amplification factor is considerably influenced by the earthquake intensity. Hence, increasing the earthquake intensity from the Design-Based Earthquake (DBE) to the Maximum Credible Earthquake (MCE) levels increase the bending moment and shear force amplification factors about 20% and less than 10%, respectively. Despite some recommendations that decrease the dynamic amplification coefficient in the lower floors and upper floors of the building; the results of this study show that the amplification is significant at these stories. Therefore, a uniform dynamic amplification coefficient is recommended along the building height.