Earthquake analysis by response spectrum superposition

1962 ◽  
Vol 52 (3) ◽  
pp. 647-660
Author(s):  
R. W. Clough
Keyword(s):  
Response Spectrum ◽  
Response Spectra ◽  
Degree Of Freedom ◽  
Maximum Response ◽  
Earthquake Response ◽  
Earthquake Response Spectra

abstract Although earthquake response spectra can be used to determine the maximum response of structures having one degree of freedom, they provide only an approximate indication of the maximum response in multi-degree systems. In this paper, two different methods of approximating the maximum response, both based on superposition of the response spectra, are compared with exact analyses and the errors in the approximations are evaluated. Five different structures, each subjected to three different earthquake motions, are considered.

scholarly journals Earthquake Response Spectra Analysis of Bridges considering Pounding at Bilateral Beam Ends Based on an Improved Precise Pounding Algorithm

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Ruijie Zhang ◽  
Lei Yan ◽  
Kefeng Yue ◽  
Junhong Yin ◽  
Kang An
Keyword(s):  
Response Spectrum ◽  
Response Spectra ◽  
Earthquake Response ◽  
System Matrix ◽  
Ground Acceleration ◽  
Maximum Displacement ◽  
Recovery Coefficient ◽  
Precise Integration ◽  
Spectra Analysis ◽  
Earthquake Response Spectra

Asynchronous vibration was generated between the main bridge and approach spans or abutments due to differences in stiffness and mass during an earthquake, thus further leading to pounding at the bilateral beam ends. By taking a T-shaped rigid frame bridge as an example, the bilateral pounding model was abstracted, and the earthquake response spectra considering pounding at the bilateral beam ends were studied, including the maximum displacement spectrum, the acceleration dynamic coefficient spectrum, the pounding force response spectrum, and the response spectrum for the number of pounding events. An improved precise pounding algorithm was proposed to solve the dynamic equation of the bilateral pounding model. This algorithm is based on the precise integration method for solving the second-order dynamic differential equation and reduces the order thereof by introducing a new velocity vector and uses the series method to find the nonhomogeneous term. The system matrix is simpler, and the inversion of the system matrix can be avoided. On this basis, a multipoint earthquake-induced pounding response spectrum program was developed. A total of 18 seismic waves from Class II sites were selected, and the response spectra of 18 waves were analyzed using this new program. Furthermore, the effects of structural stiffness, mass, stiffness of contact element, pounding recovery coefficient, and peak ground acceleration (PGA) on the earthquake response spectrum were studied. Through the analysis of earthquake response spectra and a parametric study, the phenomenon of earthquake-induced pounding of bridges was clarified to the benefit of the analysis and engineering control of earthquake-induced pounding of bridges.

scholarly journals Design Earthquake Response Spectrum Affected by Shallow Soil Deposit

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Dong-Kwan Kim ◽  
Hong-Gun Park ◽  
Chang-Guk Sun
Keyword(s):  
Soil Depth ◽  
Site Response ◽  
Response Spectrum ◽  
Soft Soil ◽  
Response Spectra ◽  
Earthquake Response ◽  
Ground Acceleration ◽  
Site Class ◽  
Shallow Soil ◽  
Short Period

Site response analyses were performed to investigate the earthquake response of structures with shallow soil depth conditions in Korea. The analysis parameters included the properties of soft soil deposits at 487 sites, input earthquake accelerations, and peak ground-acceleration levels. The response spectra resulting from numerical analyses were compared with the design response spectra (DRS) specified in the 2015 International Building Code. The results showed that the earthquake motion of shallow soft soil was significantly different from that of deep soft soil, which was the basis of the IBC DRS. The responses of the structures were amplified when their dynamic periods were close to those of the site. In the case of sites with dynamic periods less than 0.4 s, the spectral accelerations of short-period structures were greater than those of the DRS corresponding to the site class specified in IBC 2015. On the basis of these results, a new form of DRS and soil factors are proposed.

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