The critical angle of seismic incidence and the maximum structural response

Abstract

SUMMARYA simple method which can be applied in seismic codes to determine the critical angle of seismic incidence and the corresponding peak response of structures subjected to two horizontal components applied along any arbitrary directions and to the vertical component of earthquake ground motion, is proposed in this paper. The seismic components are given in terms of response spectra that may be equal or have different spectral shapes. The structures are discrete, linear systems with viscous damping. The method, which is based on the response spectrum method of analysis, requires the solution of standard cases of seismic analysis and therefore can be easily implemented in standard computer programs. For the general case of three arbitrary response spectra, the method requires the solution of five seismic loading cases, two for each horizontal component and one for the vertical component. If the horizontal response spectra have the same shape or if there is only one horizontal component, it is then required to solve just two seismic loading cases for the horizontal components and one for the vertical component. It can be shown that the formulas derived for the critical angles and the peak response are essentially identical to the ones obtained earlier by Smeby and Der Kiureghian using random vibration theory.The application and the accuracy of the method is illustrated by means of numerical analysis of buildings, comparing the results with those obtained using other proposed methods. For the specific case of two horizontal spectra with identical shape and an arbitrary vertical spectra, the critical angle neither depends on the spectral ratio of the two horizontal components nor on the vertical spectrum. For the special case of equal horizontal spectra, the structural response does not vary with the angle of incidence and it is an upper bound for all possible responses.

The impact of the earthquake incident angle on the seismic loss estimation

“…In the work by Wilson et al [16] it was proposed an alternative code approved method that results in structural designs having equal resistance to seismic motions from all directions. Lopez and Torres [17] proposed a simple method which can be employed by the seismic codes to determine the critical angle of seismic incidence and the corresponding peak response of structures subjected to two horizontal components applied along any arbitrary directions and to the vertical component of earthquake ground motion. The CQC3 response spectrum rule for combining the contributions from three orthogonal components of ground motion to the maximum value of a response quantity is presented in the work by Menun and Der Kiureghian [18].…”

Study of Effect of Seismic Excitation Angle for the Analysis of Regular and Irregular RC Frame

“…Lopez and Torres (1997) have tried to present a simple method, which can be applied to determine the critical angle of seismic incidence and the corresponding peak response of structures. In their method the seismic components are given in terms of response spectra that may be equal or have different spectral shapes.…”

Combination rule for critical structural response in soft soil

“…This rule explicitly takes into account the correlation between the modal responses, as well as the correlation between the horizontal components of the ground motion. In addition, the CQC3 rule provides an equation to calculate the response as a function of the earthquake incident angle and a formula for evaluating the critical angle, which is defined as the incident angle that produces the largest response value [13].…”