A mode contribution ratio method for seismic analysis of large-span spatial structures

The structural forms of large-span spatial structures can be characterized by the dense distribution of their natural frequencies, and their vibration subjected to seismic loads is three-dimensional. There are many modes that contribute to the seismic response. The high-order modes typically dominate. The mode superposition dynamic analysis method used for seismic design of spatial structures requires a criterion to determine the dominant modes. The criterion for tall buildings is not applicable for spatial structures; instead, we have proposed the mode contribution ratio method for the selection of the dominant modes of spatial structures subjected to seismic loads. A set of 18 typical cases of different single-layer spherical lattice shells was used to verify the validity of this method. The following conclusions can be drawn: First, the method for combining the first thirty modes to calculate the seismic responses specified in the Technical Specification for Space Frame Structures is not accurate and is not applicable to spatial structures. Second, the mode contribution ratio method can be used to choose the dominant modes of spatial structures. Third, the mode contribution ratio is physically different from the effective mass ratio. Especially when the structural mass distribution is uneven, the two ratios are different, and the mode contribution ratio is more precise in calculation of the seismic responses of spatial structures.