Concurrent Design Forces in Structures under Three-Component Orthotropic Seismic Excitation

Abstract

According to the model of Penzien and Watabe, the three translational ground motion components on a specific point of the ground are statistically noncorrelated along a well-defined orthogonal system of axes p, w, and v, whose orientation remains reasonably stable over time during the strong motion phase of an earthquake. This orthotropic ground motion is described by three generally independent response spectra Sa, Sb, and Sc, respectively. The paper presents an antiseismic design procedure for structures according to the above seismic motion model. This design includes a) determination of the critical orientation of the seismic input, i.e., the orientation that gives the largest response, b) calculation of the maximum and the minimum values of any response quantity, and c) application of either the Extreme Stress Method or the Extreme Force Method for determining the most unfavorable combinations of several stress resultants (or sectional forces) acting concurrently at a specified section of a structural member.

Time History Seismic Analysis

“…In the work by Menun and Der Kiureghian (2000), a response spectrum-based procedure for predicting the envelope that bounds two or more responses in a linear structure is developed. In the work by Encyclopedia of Earthquake Engineering DOI 10.1007/978-3-642-36197-5_134-1 # Springer-Verlag Berlin Heidelberg 2013 Anastassiadis et al (2002), a seismic design procedure for structures is proposed where the three translational ground motion components on a specific point of the ground are statistically noncorrelated.…”

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

“…In two works by Menun and Der Kiureghian [21,22] a response spectrum based procedure for predicting the envelope that bounds two or more responses in a linear structure is developed. In the work by Anastassiadis et al [23] a seismic design procedure for structures is proposed based on the model of Penzien and Watabe [15].…”

Response to three‐component seismic motion of arbitrary direction

“…Let u = {u x u y u z } T be a unit vector in space along which a seismic component is applied, which has a spectrum intensity u relative to spectrum S. Following the same line of reasoning as used above to derive Equation (13), the quadratic response is …”

“…If we also consider another seismic component along unit vector v = {v x v y v z } T , which has spectrum intensity v and is fully correlated with the seismic component along u, it is a matter From Equation (26), the quadratic response to the principal seismic component along the principal direction u k , Equation (13), can be rewritten as…”