Comparison On The Analytical Methods Of Long-span Lattice Structures Under Multi-dimensional Earthquake

The latticed structure is one of the most widely used long-span spatial structures. The new Code for Seismic Design of Buildings (GB50011-2010) (here after referred to as "the code") has pointed out, analytical methods of long-span lattice structures should consider multi-dimensional seismic effect. Response spectrum method and time history analysis method are in common use in the anti-seismic analysis of structures. However, the former method is too rough when dealing with multi-dimensional earthquake, also lack connections with the latter method on parameter values. So random vibration theory is introduced to build the connection between response spectrum method and time history analysis method. Through investigating cross correlation of the ground motion component, the applicable conditions of multi-dimensional seismic formula in the code is analyzed, and the simulation of multi-dimensional earthquake acceleration time history based on response spectrum is discussed. This article includes two works:(1) Based on the random vibration theory, the rationality about the formula using to combine multi-dimensional seismic is analyzed and discussed. Through the comparison of multi-dimensional seismic power spectrum hypothesis by Penzien and HUANG YuPing, it can be concluded that the theory of HUANG YuPing is not logical, because when the cross-power spectrum equals to the auto-power spectrum, the two-dimensional seismic can be combined into one direction, which is not the real condition. Base on the theory of Penzien, the multi-dimensional seismic formula SEk1=(?) is a more reasonable pattern. Through the calculation of multi-dimensional seismic on the latticed structures, the effectiveness of the formula using to combine multi-dimensional seismic is proved, and the value ofα,βandγis discussed.(2) Simulation of earthquake acceleration time history based on response spectrum of the code is discussed. Time-sequence method is adopted to generate the acceleration time history of ground motion by using the discrete power spectrum, which is directly transformed by the response spectrum. The applicability of AR,MA and ARMA model of time-sequence method are further discussed. Using the developed MATLAB program of time-sequence method, three earthquake acceleration time histories are simulated based on three different response spectra according to the code, and it is pointed out that the AR modal of low level has high accuracy. After that, two-dimensional earthquake is simulated based on different correlation of cross correlation of the ground motion component. By comparing the response spectra re-generated by the simulated time histories to the original response spectra, it reveals that the time-sequence method has high accuracy and validity for the simulation of ground motion time history.