Due to the widely use of Rayleigh damping model in structural seismic response and the significant influence of the calculation method for RDC on structural response, it is necessary to develop a rational calculation method for Rayleigh damping coefficients (RDC). With the necessity and reality that the multi-dimensional earthquakes along different directions act on structures simultaneously and the strain energy response can well reflect the structural mechanical behavior, the calculation method of RDC based on strain energy response under multi-dimensional excitation was established. The rational pseudo excitation formula was constructed and used to calculate the strain energy response based on the calculation formula for the response under one direction seismic excitation. By applying the pseudo excitation formula to the system under multi-dimensional excitation, the pseudo excitation method for the strain energy of the system was proposed. Based on the pseudo excitation method, the novel weight coefficient for the error square of the mode damping ratio and the corresponding calculation method for RDC were obtained. Taking three kinds of large-span spatial structures without slab and three kinds of tower structures for examples. The large-span spatial structures included the symmetric structure, the eccentric structure in one direction and the eccentric structure in two directions, while the tower structures included the symmetric double towers building, the eccentric double towers building in one direction and the eccentric three towers building in two directions. The proposed calculation method for RDC and the existed calculation method considering the influence of only two modes were put into the application with four strong ground motions. The results showed that the errors of the structural response of the symmetric large-span spatial structure from both the method for RDC were both small, but for the other spatial structures, the minimum value and the maximum value of the errors of the response from the existed calculation method were 5.89% and 19.64%, while that values from the proposed calculation method were 0 and 6.10%, and for all the tower structures, that values from the existed calculation method were 5.76% and 51.17%, while that values from the proposed calculation method were 0.07% and 4.48%, respectively. The comparison showed the proposed calculation method was rational.
