Comparing response of SDF systems to near‐fault and far‐fault earthquake motions in the context of spectral regions

In spite of important differences in structural response to near‐fault and far‐fault ground motions, this paper aims at extending well‐known concepts and results, based on elastic and inelastic response spectra for far‐fault motions, to near‐fault motions. Compared are certain aspects of the response of elastic and inelastic SDF systems to the two types of motions in the context of the acceleration‐, velocity‐, and displacement‐sensitive regions of the response spectrum, leading to the following conclusions. (1) The velocity‐sensitive region for near‐fault motions is much narrower, and the acceleration‐sensitive and displacement‐sensitive regions are much wider, compared to far‐fault motions; the narrower velocity‐sensitive region is shifted to longer periods. (2) Although, for the same ductility factor, near‐fault ground motions impose a larger strength demand than far‐fault motions—both demands expressed as a fraction of their respective elastic demands—the strength reduction factors R_y for the two types of motions are similar over corresponding spectral regions. (3) Similarly, the ratio u_m/u₀ of deformations of inelastic and elastic systems are similar for the two types of motions over corresponding spectral regions. (4) Design equations for R_y (and for u_m/u₀) should explicitly recognize spectral regions so that the same equations apply to various classes of ground motions as long as the appropriate values of T_a, T_b and T_c are used. (5) The Veletsos–Newmark design equations with T_a=0.04 s, T_b=0.35 s, and T_c=0.79 s are equally valid for the fault‐normal component of near‐fault ground motions. Copyright © 2001 John Wiley & Sons, Ltd.     

Accidental eccentricity in symmetric buildings due to wave passage effects arising from near‐fault pulse‐like ground motions

This article investigates the characteristics of the accidental eccentricity in symmetric buildings due to torsional response arising from wave passage effects in the near‐fault region. The soil–foundation–structure system is modeled as a symmetric cylinder placed on a rigid circular foundation supported on an elastic halfspace and subjected to obliquely incident plane SH waves simulating the action of near‐fault pulse‐like ground motions. The translational response is computed assuming that the superstructure behaves as a shear beam under the action of translational and rocking base excitations, whereas the torsional response is calculated using the mathematical formulation proposed in a previous study. A broad range of properties of the soil–foundation–structure system and ground motion input are considered in the analysis, thus facilitating a detailed parametric investigation of the structural response. It is demonstrated that the normalized accidental eccentricity is most sensitive to the pulse period (T_P) of the near‐fault ground motions and to the uncoupled torsional‐to‐translational fundamental frequency ratio (Ω) of the structure. Furthermore, the normalized accidental eccentricities due to simplified pulse‐like and broadband ground motions in the near‐fault region are computed and compared against each other. The results show that the normalized accidental eccentricity due to the broadband ground motion is well approximated by the simplified pulse for longer period buildings, while it is underestimated for shorter period buildings. For symmetric buildings with values of Ω commonly used in design practice, the normalized accidental eccentricity due to wave passage effects is less than the typical code‐prescribed value of 5%, except for buildings with very large foundation radius. Copyright © 2017 John Wiley & Sons, Ltd.     

Near‐fault ground motions,and the response of elastic and inelastic single‐degree‐of‐freedom (SDOF) systems

In order to investigate the response of structures to near‐fault seismic excitations, the ground motion input should be properly characterized and parameterized in terms of simple, yet accurate and reliable, mathematical models whose input parameters have a clear physical interpretation and scale, to the extent possible, with earthquake magnitude. Such a mathematical model for the representation of the coherent (long‐period) ground motion components has been proposed by the authors in a previous study and is being exploited in this article for the investigation of the elastic and inelastic response of the single‐degree‐of‐freedom (SDOF) system to near‐fault seismic excitations. A parametric analysis of the dynamic response of the SDOF system as a function of the input parameters of the mathematical model is performed to gain insight regarding the near‐fault ground motion characteristics that significantly affect the elastic and inelastic structural performance. A parameter of the mathematical representation of near‐fault motions, referred to as ‘pulse duration’ (T_P), emerges as a key parameter of the problem under investigation. Specifically, T_P is employed to normalize the elastic and inelastic response spectra of actual near‐fault strong ground motion records. Such normalization makes feasible the specification of design spectra and reduction factors appropriate for near‐fault ground motions. The ‘pulse duration’ (T_P) is related to an important parameter of the rupture process referred to as ‘rise time’ (τ) which is controlled by the dimension of the sub‐events that compose the mainshock. Copyright © 2004 John Wiley & Sons, Ltd.     

Estimation of inelastic displacement ratio for base‐isolated structures

This study develops a straightforward approximate method to estimate inelastic displacement ratio, C₁ for base‐isolated structures subjected to near‐fault and far‐fault ground motions. Taking into account the inelastic behavior of isolator and superstructure, a 2 degrees of freedom model is employed. A total of 90 earthquake ground motions are selected and classified into different clusters according to the frequency content features of records represented by the peak ground acceleration to peak ground velocity ratio, A_p/V_p. A parametric study is conducted, and effective factors in C₁ (i.e., fundamental vibration period of the superstructure, T_s; postyield stiffness ratio of the superstructure, α_s; strength reduction ratio, R; vibration period of the isolator, T_b; strength of the isolator, Q; ratio of superstructure mass to total mass of the system, γ_m) are recognized. The results indicate that the practical range of C₁ values could be expected for base‐isolated structures. Subsequently, effective parameters are included in simple predictive equations. Finally, the accuracy of the proposed approximate equations is evaluated and verified through error measurement, and comparisons are made in the analyses.     

Near‐fault effects on residual displacements of RC structures

Residual displacements of single‐degree‐of‐freedom systems due to ground motions with velocity pulses or fling step displacements are presented as a function of period T and of its ratio to the pulse period T_p. Four hysteretic behaviors are considered: bilinear elastoplastic, stiffness‐degrading with cycling, stiffness‐cum‐strength degrading, with or without pinching. When expressed in terms of T/T_p, peak inelastic and residual displacements due to motions with a pulse or fling appear similar to those due to far‐fault motions, if the response to far‐field records are expressed in terms of the ratio of T to the record's characteristic period. However, as the latter is usually much shorter than the pulse period of motions with fling, the range of periods of interest for common structures becomes a short‐period range under fling motions and exhibits very large amplification of residual and peak inelastic displacements. Similar, but less acute, are the effects of motions with a velocity pulse. Wavelets of different complexity are studied as approximations to near‐fault records. Simple two‐parameter wavelets for fling motions overestimate peak inelastic displacements; those for pulse‐type motions overestimate residual displacements. A more complex four‐parameter wavelet for motions with a velocity pulse predicts overall well residual and peak displacements due to either pulse‐ or fling‐type motions; a hard‐to‐identify parameter of the wavelet impacts little computed residual displacements; another significantly affects them and should be carefully estimated from the record. Even this most successful of wavelets overpredicts residual displacements for the periods of engineering interest. Copyright © 2016 John Wiley & Sons, Ltd.     

Acceleration response modification factors for nonstructural components attached to inelastic moment‐resisting frame structures

A statistical analysis of the peak acceleration demands for nonstructural components (NSCs) supported on a variety of stiff and flexible inelastic regular moment‐resisting frame structures with periods from 0.3 to 3.0 s exposed to 40 far‐field ground motions is presented. Peak component acceleration (PCA) demands were quantified based on the floor response spectrum (FRS) method without considering dynamic interaction effects. This study evaluated the main factors that influence the amplification or decrease of FRS values caused by inelasticity in the primary structure in three distinct spectral regions namely long‐period, fundamental‐period, and short‐period region. The amplification or decrease of peak elastic acceleration demands depends on the location of the NSC in the supporting structure, periods of the component and building, damping ratio of the component, and level of inelasticity of the supporting structure. While FRS values at the initial modal periods of the supporting structure are reduced due to inelastic action in the primary structure, the region between the modal periods experiences an increase in PCA demands. A parameter denoted as acceleration response modification factor (R_acc) was proposed to quantify this reduction/increase in PCA demands. Copyright © 2007 John Wiley & Sons, Ltd.     

Yielding oscillator subjected to simple pulse waveforms: numerical analysis & closed‐form solutions

Numerical and analytical solutions are presented for the elastic and inelastic response of single‐degree‐of‐freedom yielding oscillators to idealized ground acceleration pulses. These motions are typical of near‐fault earthquake recordings generated by forward rupture directivity and may inflict damage in the absence of substantial structural strength and ductility capacity. Four basic pulse waveforms are examined: (1) triangular; (2) sinusoidal; (3) exponential; and (4) rectangular. In the first part of the article, a numerical study is presented of the effect of oscillator period, strength, damping, post‐yielding stiffness and number of excitation cycles, on inelastic response. Results are presented in the form of dimensionless graphs and regression formulas that elucidate the salient features of the problem. It is shown that conventional R–µ relations may significantly underestimate ductility demand imposed by near‐fault motions. The second part of the article concentrates on elastic‐perfectly plastic oscillators. Closed‐form solutions are derived for post‐yielding response and associated ductility demand. It is shown that all three ground motion histories (i.e. acceleration, velocity, and displacement) control oscillator response—contrary to the widespread view that ground velocity alone is of leading importance. The derived solutions provide insight on the physics of inelastic response, which is often obscured by the complexity of numerical algorithms and actual earthquake motions. The model is evaluated against numerical results from near‐field recordings. A case study is presented. Copyright © 2006 John Wiley & Sons, Ltd.     

Critical response of structures to multicomponent earthquake excitation

This paper aims to develop an improved understanding of the critical response of structures to multicomponent seismic motion characterized by three uncorrelated components that are defined along its principal axes: two horizontal and the vertical component. An explicit formula, convenient for code applications, has been derived to calculate the critical value of structural response to the two principal horizontal components acting along any incident angle with respect to the structural axes, and the vertical component of ground motion. The critical response is defined as the largest value of response for all possible incident angles. The ratio r_cr/r_srss between the critical value of response and the SRSS response—corresponding to the principal components of ground acceleration applied along the structure axes—is shown to depend on three dimensionless parameters: the spectrum intensity ratio γ between the two principal components of horizontal ground motion characterized by design spectra A(T_n) and γA(T_n); the correlation coefficient α of responses r_x and r_y due to design spectrum A(T_n) applied in the x‐ and y‐directions, respectively; and β = r_y/r_x. It is demonstrated that the ratio r_cr/r_srss is bounded by 1 and . Thus the largest value of the ratio is , 1.26, 1.13 and 1.08 for γ = 0, 0.5, 0.75 and 0.85, respectively. This implies that the critical response never exceeds times the result of the SRSS analysis, and this ratio is about 1.13 for typical values of γ, say 0.75. The correlation coefficient α depends on the structural properties but is always bounded between −1 and 1. For a fixed value of γ, the ratio r_cr/r_srss is largest if β = 1 and α = ±1. The parametric variations presented for one‐storey buildings indicate that this condition can be satisfied by axial forces in columns of symmetric‐plan buildings or can be approximated by lateral displacements in resisting elements of unsymmetrical‐plan buildings. Copyright © 2000 John Wiley & Sons, Ltd.     

An energy approach to sliding of single-span simply supported slab-on-girder steel highway bridges with damaged bearings

This paper investigates the non-linear inelastic seismic response of existing single-span simply supported bridges having bearings which can remain stable and slide after their anchor bolts are ruptured. A simplified equivalent model is developed for the inelastic analysis of these single-span simply supported bridges. Non-linear inelastic time-history analyses are conducted for various acceleration inputs. It is found that narrower bridges with longer spans may have considerable sliding displacements and fall off their supports if adequate seat width is not provided. It is also found that for the same ratio of friction coefficient to peak ground acceleration, the sliding displacement of a structural system is linearly proportional to the amplitude of the peak ground acceleration beyond a certain threshold value. This is also demonstrated analytically from an energy approach point of view. The distribution of the energy content of an earthquake, which is related to its velocity time history, can be an indication of the propensity of an earthquake to cause high sliding displacements. Ground motions with high frequency content or high A_p/V_p ratio may produce smaller sliding displacements than ground motions with relatively lower A_p/V_p ratios.     

Vertical acceleration demands on column lines of steel moment‐resisting frames

In this paper, vertical peak floor acceleration (PFA_v) demands on elastic multistory buildings are statistically evaluated using recorded ground motions. These demands are applicable to the assessment of nonstructural components that are rigid in the vertical direction and located at column lines or next to columns. Hence, PFA_v demands of the floor system away from column lines and their effects on nonstructural components are not addressed. This study is motivated by the questionable general assumption that typical buildings are considered to be relatively flexible in the horizontal (lateral) direction but relatively rigid in the vertical (longitudinal) direction. Consequently, only few papers address the evaluation of vertical component acceleration demands throughout a building, and there is no consensus on the relevance of vertical accelerations in buildings. The results presented in this study show that the vertical ground acceleration demands are amplified throughout the column line of a steel frame structure. This amplification is in many cases significant, depending on the vertical stiffness of the load‐bearing system, damping ratio, and the location of the nonstructural component in the building. From these outcomes it can be concluded that the perception of a rigid‐body response of the column lines in the vertical direction is highly questionable, and further research on this topic is required. Copyright © 2016 John Wiley & Sons, Ltd.     

A shift approach for the dynamic response of rigid‐plastic systems

A shift approach is presented for evaluating and interpreting the response of rigid‐perfectly plastic single‐degree‐of‐freedom systems to dynamic loading. Scaling laws for such systems are, as the term suggests, multiplicative in nature, relating peak dynamic response to products of key problem parameters such as linear spectral coordinates, force reduction coefficient and peak values of the excitation and its time derivatives. Contrary to classical laws, the proposed approach is additive, imposing a shift in the ordinates and the abscissa of the excitation function by means of a set of parameters uniquely related to the yielding resistance of the system. The dynamic response is then obtained by integrating the modified excitation function in a linear‐like manner within a particular yielding branch, for the nonlinearity is incorporated into the forcing term. The mathematical validity of the approach is demonstrated analytically and its importance is highlighted for systems with symmetric yielding resistance subjected to near‐fault earthquake motions. The modified excitation function may be discontinuous between different yielding branches and relates uniquely to the development of plastic deformation. It is thereby referred to as Plastic Input Motion (PIM). It is shown that the ordinates and the duration of this function may be significantly (yet not necessarily) smaller than those of the original ground motion depending on yield strength. The relationship of the proposed approach to the existing methods and parameters of earthquake engineering such as Newmark's sliding block and relative ground acceleration, is discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Effects of near‐fault ground motions on the nonlinear dynamic response of base‐isolated r.c. framed buildings

Near‐fault ground motions are characterized by long‐period horizontal pulses and high values of the ratio between the peak value of the vertical acceleration, PGA_V, and the analogous value of the horizontal acceleration, PGA_H, which can become critical for base‐isolated (BI) structures. The objective of the present work is to check the effectiveness of the base isolation of framed buildings when using High‐Damping‐Rubber Bearings (HDRBs), taking into consideration the combined effects of the horizontal and vertical components of near‐fault ground motions. To this end, a numerical investigation is carried out with reference to BI reinforced concrete buildings designed according to the European seismic code (Eurocode 8). The design of the test structures is carried out in a high‐risk region considering (besides the gravity loads) the horizontal seismic loads acting alone or in combination with the vertical ones and assuming different values of the ratio between the vertical and horizontal stiffnesses of the HDRBs. The nonlinear seismic analysis is performed using a step‐by‐step procedure based on a two‐parameter implicit integration scheme and an initial‐stress‐like iterative procedure. At each step of the analysis, plastic conditions are checked at the potential critical sections of the girders (i.e. end sections of the sub‐elements in which a girder is discretized) and columns (i.e. end sections), where a bilinear moment–curvature law is adopted; the effect of the axial load on the ultimate bending moment (M‐N interaction) of the columns is also taken into account. The response of an HDRB is simulated by a model with variable stiffness properties in the horizontal and vertical directions, depending on the axial force and lateral deformation, and linear viscous damping. Copyright © 2011 John Wiley & Sons, Ltd.     

Evaluation of ASCE 7 equations for designing acceleration‐sensitive nonstructural components using data from instrumented buildings

This study uses instrumented buildings and models of code‐based designed buildings to validate the results of previous studies that highlighted the need to revise the ASCE 7 F_p equation for designing nonstructural components (NSCs) through utilizing oversimplified linear and nonlinear models. The evaluation of floor response spectra of a large number of instrumented buildings illustrates that, unlike the ASCE 7 approach, the in‐structure and the component amplification factors are a function of the ratio of NSC period to the supporting building modal periods, the ground motion intensity, and the NSC location. It is also shown that the recorded ground motions at the base of instrumented buildings in most cases are significantly lower than design earthquake (DE) ground motions. Because ASCE 7 is meant to provide demands at a DE level, for a more reliable evaluation of the F_p equation, 2 representative archetype buildings are designed based on the ASCE 7‐16 seismic provisions and exposed to various ground motion intensity levels (including those consistent with the ones experienced by instrumented buildings and the DE). Simulation results of the archetype buildings, consistent with previous numerical studies, illustrate the tendency of the ASCE 7 in‐structure amplification factor, [1 + 2(z/h)] , to significantly overestimate demands at all floor levels and the ASCE 7 limit of to in many cases underestimate the calculated NSC amplification factors. Furthermore, the product of these 2 amplification factors (that represents the normalized peak NSC acceleration) in some cases exceeds the ASCE 7 equation by a factor up to 1.50.     

Seismic response analysis of multidrum classical columns

This paper presents a numerical investigation on the seismic response of multidrum classical columns. The motivation for this study originates from the need to understand: (a) the level of ground shaking that classical multidrum columns can survive, and (b) the possible advantages or disadvantages of retrofitting multidrum columns with metallic shear links that replace the wooden poles that were installed in ancient times. The numerical study presented in this paper is conducted with the commercially available software Working Model 2D?, which can capture with fidelity the sliding, rocking, and slide‐rocking response of rigid‐body assemblies. This paper validates the software Working Model by comparing selected computed responses with scarce analytical solutions and the results from in‐house numerical codes initially developed at the University of California, Berkeley, to study the seismic response of electrical transformers and heavy laboratory equipment. The study reveals that relative sliding between drums happens even when the g‐value of the ground acceleration is less than the coefficient of friction, µ, of the sliding interfaces and concludes that: (a) typical multidrum classical columns can survive the ground shaking from strong ground motions recorded near the causative faults of earthquakes with magnitudes M_w=6.0–7.4; (b) in most cases multidrum classical columns free to dislocate at the drum interfaces exhibit more controlled seismic response than the monolithic columns with same size and slenderness; (c) the shear strength of the wooden poles has a marginal effect on the sliding response of the drums; and (d) stiff metallic shear links in‐between column drums may have an undesirable role on the seismic stability of classical columns and should be avoided. Copyright © 2005 John Wiley & Sons, Ltd.     

Evaluation of combination rules for peak response calculation in three‐component seismic analysis

The responses, r_e, given by several multicomponent combination rules used in seismic codes for determining peak responses to three ground motion components are evaluated for elastic systems and compared with the critical response r_cr; this is defined as the largest response for all possible incident angles of the seismic components and obtained by means of the CQC3‐rule when a principal seismic component is vertical, or the GCQC3‐rule when it departs from the vertical direction. The combination rules examined are the SRSS‐, 30%‐, 40%‐ and IBC‐rules, considering different alternatives for the design horizontal spectrum. Assuming that a principal seismic component is along the vertical direction, the upper and lower bounds of the ratio r_e/r_cr for each combination rule are determined as a function of the spectral intensity ratio of the horizontal seismic components and of the responses to one seismic component acting alternately along each structural axis. Underestimations and overestimations of the critical response are identified for each combination rule and each design spectrum. When a component departs from the vertical direction, the envelopes of the bounds of the ratio r_e/r_cr for each combination rule are calculated, considering all possible values of the spectral intensity ratios. It is shown that the inclination of a principal component with respect to the vertical axis can significantly reduce the values of r_e/r_cr with respect to the case when the component is vertical. Copyright © 2003 John Wiley & Sons, Ltd.     

Effects of near-fault ground motions on the nonlinear behaviour of reinforced concrete framed buildings

The design provisions of current seismic codes are generally not very accurate for assessing effects of near-fault ground motions on reinforced concrete(r.c.)spatial frames,because only far-fault ground motions are considered in the seismic codes.Strong near-fault earthquakes are characterized by long-duration(horizontal)pulses and high values of the ratio α_(PGA)of the peak value of the vertical acceleration,PGA_V,to the analogous value of the horizontal acceleration,PGA_H,which can become critical for girders and columns.In this work,six- and twelve-storey r.c.spatial frames are designed according to the provisions of the Italian seismic code,considering the horizontal seismic loads acting(besides the gravity loads)alone or in combination with the vertical ones.The nonlinear seismic analysis of the test structures is performed using a step-by-step procedure based on a two-parameter implicit integration scheme and an initial stress-like iterative procedure.A lumped plasticity model based on the Haar-Karman principle is adopted to model the inelastic behaviour of the frame members.For the numerical investigation,five near-fault ground motions with high values of the acceleration ratio α_(PGA) are considered.Moreover,following recent seismological studies,which allow the extraction of the largest(horizontal) pulse from a near-fault ground motion,five pulse-type(horizontal)ground motions are selected by comparing the original ground motion with the residual motion after the pulse has been extracted.The results of the nonlinear dynamic analysis carried out on the test structures highlighted that horizontal and vertical components of near-fault ground motions may require additional consideration in the seismic codes.     

Generation of probabilistic displacement response spectra for displacement-based design

Displacement response spectrum (DRS), as the input, is of great significance to the displacement-based design just like the acceleration response spectrum to the traditional force-based design. Although the procedure of performance-based, in particular the displacement-based design has achieved considerable development, there is not a general DRS covering an enough long period range for common seismic design yet. This paper develops a systematic ground motion data processing procedure for the purpose of correcting the noise in the earthquake records and generating consistent DRS for seismic design. An adaptive algorithm is proposed to determine the cutoff frequency of the high-pass digital filter. The DRS of more than 500 recorded earthquake ground motions are generated and they are classified into three groups according to the ratio of the peak ground acceleration to the peak ground velocity (A/V) and/or the ratio of the peak ground velocity to the peak ground displacement (V/D). In each group, all the ground motions are normalized with respect to a selected scaling factor. Their corresponding DRS are obtained and then averaged to get the mean and standard deviation DRS, which can be used for both deterministic and probabilistic displacement-based design.     

Estimation of seismic demands on isolators in asymmetric buildings using non‐linear analysis

A procedure based on rigorous non‐linear analysis is presented that estimates the peak deformation among all isolators in an asymmetric building due to strong ground motion. The governing equations are reduced to a form such that the median normalized deformation due to an ensemble of ground motions with given corner period T_d depends primarily on four global parameters of the isolation system: the isolation period T_b, the normalized strength η, the torsional‐to‐lateral frequency ratio Ω_θ, and the normalized stiffness eccentricity e_b/r. The median ratio of the deformations of the asymmetric and corresponding symmetric systems is shown to depend only weakly on T_b, η, and Ω_θ, but increases with e_b/r. The equation developed to estimate the largest ratio among all isolators depends only on the stiffness eccentricity and the distance from the center of mass to the outlying isolator. This equation, multiplied by an earlier equation for the deformation of the corresponding symmetric system, provides a design equation to estimate the deformations of asymmetric systems. This design equation conservatively estimates the peak deformation among all isolators, but is generally within 10% of the ‘exact’ value. Relative to the non‐linear procedure presented, the peak isolator deformation is shown to be significantly underestimated by the U.S. building code procedures. Copyright © 2003 John Wiley & Sons, Ltd.     

Ground motion directionality in the 2010–2011 Canterbury earthquakes

This paper examines the observed directionality of ground motions in the Christchurch urban area during the 2010–2011 Canterbury, New Zealand earthquakes. A dataset of ground motions recorded at 20 strong motion stations over 10 different earthquake events is utilized to examine the ratios of various response spectral directionality definitions and the orientation of the maximum direction. Because the majority of previous related studies have utilized overlapping ground motion datasets from the NGA database, the results of this study provide a largely independent assessment of these ground motion aspects. It is found that the directionality ratio between the maximum (100th percentile) and 50th percentile orientation‐independent spectral acceleration is similar to that obtained from recent studies. Ground motions from the 4 September 2010 Darfield earthquake are shown to exhibit strong directionality for source‐to‐site distances up to R_rup = 30 km, notably further than results from a previous study, which suggests that such effects are generally limited to R_rup < 5 km. The adopted dataset also offers the unique potential to consider site‐specific effects on directionality ratios and maximum direction orientations; however, in both cases, site‐specific effects are found not to be significant in the observed empirical results. Copyright © 2014 John Wiley & Sons, Ltd.