Analysis Of Seismic Effects Of Frames Based On Elastic Wave Theory

Along with the widespread application of the large span trusses, frames, spatial trusses and grid structures in civil engineering, offshore engineering as well as space station, the dynamic analysis of these structures has received afresh attention of engineers and researchers. Nowadays, the dynamic analysis in engineering design is carried out by numerical methods such as finite element method. However, the finite element method is mainly suitable for analysis of low frequency movement of the structure, moreover, the number of degrees of freedom and computation efforts are large. If the dynamic response is caused by impact load, the transient response of initial stage contains rich high frequency components, the analysis of elastic wave method in frequency domain is appropriate. Method of Reverberation Ray Matrix (MRRM) is a novel analytical method for the transient response of trusses and frames in frequency domain proposed by Pao[1] and his collaborators. The method has been verified to be accurate with experiments.Based on Bernulli beam theory, the present study extends the MRRM to the dynamic analysis of structures subjected to ground acceleration load. MRRM is used to analyze earthquake effects of frames. A square cross section beam which is simply supported at the left end and subjected to step displacementδH(t) at the right end is analyzed. The solution for this beam with MRRM is compared with that of Mindlin theory. The analysis and computer code of MRRM are verified for the case of the structure subjected to displacement load. The acceleration of El Centro earthquake is transformed to obtain velocity and displacement in frequency domain. The dynamic responses of a frame composed of five steel beams subjected to ground movement of El Centro earthquake are calculated with MRRM. Furthermore, a steel bridge with 29 beams subjected to El Centro earthquake is also analyzed. The cases of dynamic responses of the bridge with or without travelling wave effect (the case of right support receives the earthquake wave later than the left support and the case of both supports receive the earthquake wave at the same time) are calculated and compared.Calculations show that MRRM can analyze the earthquake effect due to ground movement efficiently. The calculations for the travelling wave effect of the bridge show that for some elements the maximum stresses with the travelling wave effect are obviously larger than that without travelling wave effect. These results can be used as reference in engineering design. MRRM provides a novel approach for the analysis of earthquake effects in engineering.