Accounting for directionality as a function of structural typology in performance‐based earthquake engineering design

Abstract

For the seismic design of a structure, horizontal ground shaking is usually considered in two perpendicular directions, even though real horizontal ground motions are complex two-dimensional phenomena that impose different demands at different orientations. While the issue of ground motion dependence on the orientation of the recording devices has been the focus of many significant developments during the last decade, the effects of directionality on the characteristics of the structure have received less attention. This work presents a proposal to calculate the probability of exceedance of elastic spectral displacements accounting for structural typology and illustrates its relevance by means of its application to two case-study buildings. In order to ease its implementation in seismic design codes, a simplification is developed by means of a detailed statistical analysis of the results obtained using four sets of real hazard curves. The framework presented herein is considered to represent an important contribution to the field of performance-based earthquake engineering, permitting improved treatment of directionality effects within seismic risk design and assessment.

A multidirectional conditional spectrum

“…Having worked within the context of the NGA‐West2 research programme, coordinated by the Pacific Earthquake Engineering Research Center, Shahi and Baker use S a R o t D 50 ( T ), while the present work is built upon S a R o t D 100 ( T ) instead. S a R o t D 100 ( T ) is preferred herein for two reasons: firstly, because it is relevant for azimuth‐independent structures (e.g., Grant, Stewart et al, and Nievas and Sullivan()) and secondly, because its relation with the spectral demand at other orientations appears more intuitive. As S a R o t D 100 ( T ) is the largest demand at all possible orientations, the ratio S a ( T , θ )/ S a R o t D 100 ( T ) can only lie in the range [0.0,1.0] and has a lower bound at each angle θ equal to .…”

“…Having worked within the context of the NGA-West2 research programme, 21 coordinated by the Pacific Earthquake Engineering Research Center, Shahi and Baker 8 use Sa RotD50 (T), while the present work is built upon Sa RotD100 (T) instead. Sa RotD100 (T) is preferred herein for two reasons: firstly, because it is relevant for azimuth-independent structures (e.g., Grant, Stewart et al, and Nievas and Sullivan 1,7,9 ) and secondly, because its relation with the spectral demand…”

“…However, the use of S a R o t D 100 to define seismic hazard is advantageous over other metrics because of its relevance to azimuth‐independent structures() and the elegance of the behaviour of the ratio of the spectral demand at an arbitrary orientation with respect to it, η ( T , ξ , θ ). ()…”

“…[2][3][4][5] If, on top of this, the UHS is defined in terms of the maximum response component Sa RotD100 , i.e., the rotationally dependent 100th percentile, 6 the situation worsens, as pointed out by Stewart et al, 7 as it is clear that the maximum response direction tends to not be the same for different oscillator (building) periods, 8 and the main structural axes of buildings are unlikely to be oriented in the same direction at which Sa RotD100 of their fundamental period occurs. However, the use of Sa RotD100 to define seismic hazard is advantageous over other metrics because of its relevance to azimuth-independent structures 1,7,9 and the elegance of the behaviour of the ratio of the spectral demand at an arbitrary orientation with respect to it, (T, , ). 9,10 With this in mind, this paper presents a procedure to generate multidirectional conditional spectra (MDCS), defined herein as sets of mean response spectra and their associated dispersions corresponding to different orientations with respect to the direction of maximum response at the anchoring period T * .…”

“…However, the use of Sa RotD100 to define seismic hazard is advantageous over other metrics because of its relevance to azimuth-independent structures 1,7,9 and the elegance of the behaviour of the ratio of the spectral demand at an arbitrary orientation with respect to it, (T, , ). 9,10 With this in mind, this paper presents a procedure to generate multidirectional conditional spectra (MDCS), defined herein as sets of mean response spectra and their associated dispersions corresponding to different orientations with respect to the direction of maximum response at the anchoring period T * . The three main components needed for their generation are first outlined, and new developments associated with two components are then reported.…”