Investigation of 30% rule for the combination of component response with the unidirectional principal and critical response spectrum

The ground motion caused by an earthquake can be considered as the resultant of three orthogonal translation components along three Cartesian coordinates x, y, and z; and three rotational components about these three co-ordinate axes. Though it is well recognized that the response of important structures like nuclear reactor components, dams, tall buildings, and long-span bridges, may be dependent on all the three translational components of motion, due to the complexity of the three-dimensional analysis and various uncertainness in spatial combination procedures, most of the studies in the past considered only one component of earthquake motion. Many investigators have recognized the necessity of finding the response of structures under multi-component earthquake excitation. The vertical component of the ground motion is excluded, assuming that the horizontal components are the governing components for building analysis. In the present study, the validity of the [Max +30%] rule of combining bi-directional response is investigated by comparing the results with the exact results based on the response spectrum in the principal direction [SAXP] and, the critical response spectrum [SACRIT] providing an upper bound to the multi-directional component response. A typical six-story steel building is modeled as a shear building with lateral and torsional degrees-of-freedom at each floor. Dynamic analysis of the building is performed using CSI SAP2000. Three different sets of real earthquake ground motions, with widely differing characteristics used in the study, are Uttarkashi(1991) earthquake, Sikkim (2011) earthquake, and Nepal (2015) earthquake. After analysis, it has been found that the [Max +30%] rule of combining bi-directional response, which is included in IS 1893 (2016) may not lead to realistic results in all the cases. [Max+30%] rule may not work equally well in all cases and it may lead to higher or lower estimates of response when compared with the desired estimate in the principal directional response spectrum. However, in no case, the 30% combination rule exceeds the estimate based on the critical response spectrum [SACRIT]. It may be found that estimation of the response of the multi-directional excitation can be performed in a much simpler and efficient way, using unidirectional principal response spectrum analysis. Thus, it can be stated that the Ground Motion Prediction Equations (GMPE) must be developed for the principal as well as the critical response spectrum