Inelastic Displacement Ratios for Seismic Assessment of Structures Subjected to Forward-Directivity Near-Fault Ground Motions

This article presents results of a statistical study focused on evaluating inelastic displacement ratios (i.e., ratio of maximum inelastic displacement with respect to maximum elastic displacement demand) of degrading and non degrading single-degree-of-freedom (SDOF) systems subjected to forward-directivity near-fault ground motions. C_R spectra are computed for normalized periods of vibration with respect to the predominant period of the ground motion to provide a better ground motion characterization. This period normalization allows reducing the record-to-record variability in the estimation of C_R. An equation to obtain estimates of C_R for the seismic assessment of structures exposed to forward-directivity near-fault ground motions is proposed.     

Characterization of Ductility and Inelastic Displacement Demand in Base-Isolated Structures Considering Cyclic Degradation

New designed or retrofitted structures with the use of isolation system may exhibit nonlinear deformations during strong ground motions. Inelastic displacement ratio of base-isolated structures is studied in this paper by employing two degree of freedom model taking into account inelastic behavior of isolators and superstructure. Parametric study is conducted to evaluate influence of isolator and superstructure properties on inelastic displacement ratio according to two sets of near-fault and far-fault ground motions. Accuracy of proposed equations in the literature to evaluate inelastic displacement ratio are studied, as well. Furthermore, cyclic degradation effects are investigated by considering stiffness and strength degradation and pinching in hysteresis model of superstructure. Eventually, inelastic responses of isolated structures with two types of isolators (lead rubber bearing and friction pendulum bearing) are compared.     

Inelastic Displacement Demand of Strength-Degraded Structures

This article presents findings from parametric studies involving nonlinear time-history analyses of inelastic systems with and without strength degradation. Results showed that estimates based on the equal-displacement and equal-energy propositions can be exceeded significantly by the inelastic displacement demands in the acceleration and velocity-sensitive regions of the response spectrum. The displacement demand behaviour is sensitive to the strength degradation and the frequency properties of the ground shaking. With a modest strength reduction factor of 2, the inelastic displacement demand would typically be constrained by the Peak Displacement Demand as indicated on the elastic displacement response spectrum for 5% damping.     

THE USE OF SIMPLE PULSES TO ESTIMATE INELASTIC RESPONSE SPECTRA

Inelastic response spectra are estimated for elasto-plastic SDOF systems subjected to strong earthquake ground motions by applying the strength reduction factors determined for a simple pulse to the elastic response spectrum of the ground motion. This approach relies upon similarities in the strength reduction factors computed for earthquake ground motions and for short duration pulses. The accuracy of the estimated inelastic spectra obtained using 24 simple pulse waveforms is assessed in order to identify subsets of just several pulse waveforms that are suited for this purpose. Based upon the ground motions and pulses investigated, this approach appears to be equally applicable to short and long duration ground motions and those having near-fault forward directivity features.     

A Simplified Drift-Based Assessment Procedure for Regular Confined Masonry Buildings in Seismic Regions

This article presents a simplified procedure for assessing the seismic performance of existing low-to-medium rise confined masonry (CM) buildings, which are a typical construction type in Latin-America. The procedure consists of the estimation of the peak roof and first-story inelastic drift demand of CM buildings. The expected peak inelastic displacement demand is related to drift-based fragility curves, which express the probability of being or exceeding two key damage states in the masonry panels, developed from a relatively large experimental database. The proposed procedure could be very useful for obtaining rapid estimates of expected performance during future earthquake events and for assessing the seismic vulnerability of regular confined masonry structures.     

Modification of Ductility Reduction Factor for Strength Eccentric Structures Subjected to Pulse-Like Ground Motions

This article investigates the ductility reduction factors for RC eccentric frame structures subjected to pulse-like ground motions. The structural models are with the strength eccentricities which are much disadvantageous than the stiffness eccentricities during the inelastic response range. A method to determine the ductility reduction factors of the strength eccentric structures is suggested by modifying those of reference symmetric structures through an eccentricity modification factor. The four factors of strength eccentricity ratio, ductility ratio, story number and velocity pulse of ground motions, are investigated to gain insight into this modification factor. It shows that the ductility reduction factors of the eccentric structures are clearly smaller than those of the symmetric structures. The eccentricity modification factor is mainly affected by the strength eccentricity and the ductility ratio, decreasing with the increment of the eccentricity or the decrement of the ductility ratio in a medium eccentricity range. The earthquake pulse-like effect and the eccentricity have coupling influence on the modification factor, while the effect of story number is not apparent. Based on the results of a comprehensive statistical study a simplified expression is suggested, which can estimate the eccentricity modification factors for both pulse-like and nonpulse-like ground motion cases.     

AN EVALUATION OF THE STRONG GROUND MOTION RECORDED DURING THE MAY 1, 2003 BINGÖL TURKEY,EARTHQUAKE

An important record of ground motion from a M6.4 earthquake occurring on May 1, 2003, at epicentral and fault distances of about 12 and 9 km, respectively, was obtained at a station near the city of Bingöl, Turkey. The maximum peak ground values of 0.55 g and 36 cm/s are among the largest ground-motion amplitudes recorded in Turkey. From simulations and comparisons with ground motions from other earthquakes of comparable magnitude, we conclude that the ground motion over a range of frequencies is unusually high. Site response may be responsible for the elevated ground motion, as suggested from analysis of numerous aftershock recordings from the same station. The mainshock motions have some interesting seismological features, including ramps between the P-and S-wave that are probably due to near- and intermediate-field elastic motions and strong polarisation oriented at about 39 degrees to the fault (and therefore not in the fault-normal direction). Simulations of motions from an extended rupture explain these features. The N10E component shows a high-amplitude spectral acceleration at a period of 0.15 seconds resulting in a site specific design spectrum that significantly overestimates the actual strength and displacement demands of the record. The pulse signal in the N10E component affects the inelastic spectral displacement and increases the inelastic displacement demand with respect to elastic demand for very long periods.     

Inelastic Displacement Response of RC Systems with Cyclic Deterioration—An Energy Approach

Inelastic displacements of reinforced concrete systems are investigated by employing an energy-based approach. A hysteresis model is developed that accounts for stiffness degradation, strength deterioration and pinching. The model is calibrated by using experimental data from literature. Inelastic displacement ratios are calculated under a specific set of ground motion records with long effective durations. The results reveal the importance of deteriorating behavior under long duration excitations, especially for short and medium period structures. The last part of the study is devoted to the introduction of a simple empirical relationship for estimating the inelastic displacement demands of degrading RC structural systems.     

Displacement-Based Seismic Design Approach for Prestressed Precast Concrete Shear Walls and its Application

ABSTRACT

Prestressed precast concrete shear wall (PPCW) is a new kind of shear wall utilizing a combination of unbonded post-tensioning steel and mild steel for flexural resistance across horizontal joints. A simple procedure of direct displacement-based design approach for PPCW based on concept of inelastic design spectra is proposed. Section design is then carried out according to base overturning moment. A detailed design example demonstrating a step-by-step application of the design procedure is also provided. Nonlinear time-history analysis verified that this approach is applicable to control the target displacement to the performance acceptable limit.     

YIELDING OSCILLATOR UNDER TRIANGULAR GROUND ACCELERATION PULSE

An analytical solution is presented for the response of a bilinear inelastic simple oscillator to a symmetric triangular ground acceleration pulse. This type of motion is typical of near-fault recordings generated by source-directivity effects that may generate severe damage. Explicit closed-form expressions are derived for: (i) the inelastic response of the oscillator during the rising and decaying phases of the excitation as well as the ensuing free oscillations; (ii) the time of structural yielding; (iii) the time of peak response; (iv) the associated ductility demand. It is shown that when the duration of the pulse is long relative to the elastic period of the structure and its amplitude is of the same order as the yielding seismic coefficient, serious damage may occur if significant ductility cannot be supplied. The effect of post-yielding structural stiffness on ductility demand is also examined. Contrary to presently-used numerical algorithms, the proposed analytical solution allows many key response parameters to be evaluated in closed-form expressions and insight to be gained on the'response of inelastic structures to such motions. The model is evaluated against numerical results from actual near-field recorded motions. Illustrative examples are also presented.     

Constant Ductility Energy Factors for the Near-Fault Pulse-Like Ground Motions

This study is focused on the constant ductility energy factors for bilinear system under the near-fault pulse-like ground motions. The variation of energy factors is studied in consideration of the earthquake magnitude, rupture distance, damping ratios, and post-yield stiffness ratios. The results indicate that the near-fault pulse-like ground motions would increase the energy dissipation of structures. The energy factors are significantly influenced by the earthquake magnitude. The damping ratios have more obvious influences on the energy factors than the post-yield stiffness ratios. A predictive model is proposed for the application of constant ductility energy factors for near-fault pulse-like ground motions.     

Response Sensitivity of Highway Bridges to Randomly Oriented Multi-Component Earthquake Excitation

In two-dimensional and single axis three-dimensional finite element analyses, the ground motion incidence angle can play a significant role in structural response. The effect of incidence angle for three-dimensional excitation and response is investigated in this paper for response of highway bridges. Single-degree-of-freedom elastic and inelastic mean spectra were computed from various orientation techniques and found indistinguishable for combinations of orthogonal horizontal components. Probabilistic seismic demand models were generated for the nonlinear response of five different bridge models. The negligible effect of incidence angle on mean ensemble response was confirmed with a stochastic representation of the ground motions.     

A PROCEDURE FOR ESTIMATING INPUT ENERGY SPECTRA FOR SEISMIC DESIGN

In this paper, the damage potential of an earthquake ground motion is evaluated in terms of the total power of the acceleration of the ground motion. By assuming an appropriate spectral shape for the input energy spectrum, and using the well-known Parseval theorem for evaluating the total power of a random signal, the peak amplification factor for the equivalent input energy velocity spectrum can be determined. It is shown that the peak amplification factor for the input energy spectrum depends on the peak-ground-acceleration to peak-ground-velocity ratio and duration of the strong motion phase of the ground motion. Values for the equivalent input energy velocity amplification factor vary from about 2 to 10 for most of the recorded ground motions used in this study. Although a considerable scatter of data is observed in this study, the peak amplification factor predicted by the Fourier amplitude spectrum of the ground acceleration provides a fairly good estimate of the mean value of the peak input energy compared to that determined from inelastic dynamic time history analyses, particularly for systems with high damping and low lateral strength. The peak amplification factor derived in this paper provides a more consistent approach for estimation of seismic demand when compared to an earlier empirical expression used for the formulation of duration-dependent inelastic seismic design spectra, even though only a slight difference in the required lateral strength results from the use of the new formula.     

Inelastic Displacement Ratios for Nonstructural Components Subjected to Floor Accelerations

This paper describes a study on the characterization of the Inelastic Displacement Ratios (IDRs) of inelastic acceleration-sensitive nonstructural components subjected to floor accelerations obtained from the linear analysis of multistory building structures under far-field ground accelerations. Several building models having different structural systems and a number of stories were considered. IDRs were obtained from the displacement response of elastic and inelastic single-degree-of-freedom systems subjected to floor accelerations. Similarities and differences between floor acceleration IDRs and ground acceleration IDRs were identified, and efforts were made to explain the differences. Finally, a predicting equation for floor acceleration IDRs is proposed and validated.     

Definition of Seismic Input for Out-of-Plane Response of Masonry Walls: I. Parametric Study

Response of masonry walls to out-of-plane excitation is a complex, yet inadequately addressed theme in seismic analysis. The seismic input expected on an out-of-plane wall (or a generic “secondary system”) in a masonry building is the ground excitation filtered by the in-plane response of the walls and the floor diaphragm response. More generally, the dynamic response of the primary structure, which can be nonlinear, contributes to the filtering phenomenon. The current article delves into the details and results of several nonlinear dynamic time-history analyses executed within a parametric framework. The study addresses masonry structures with rigid diaphragm response to lateral loads. The scope of the parametric study is to demonstrate the influence of inelastic structural response on the seismic response of secondary systems and eventually develop an expression to estimate the seismic input on secondary systems that explicitly accounts for the level of inelasticity in the primary structure in terms of the displacement ductility demand. The proposed formulation is discussed in the companion article.     

Inelastic Demand Spectra of Bi-Linear Models for Capacity Spectrum Method and Response of Simple Structures under Near-Source Records

A very useful tool for the preliminary design of structures is the elastic demand spectrum that can be used in the capacity spectrum method. A pseudo-acceleration relationship has to be assumed when constructing a demand spectrum. This assumption results in large errors for long period structures with large damping ratios and the conventional demand spectra require a substitute elastic structure. In the present study, the conventional demand spectra are extended to bi-linear models. Pseudo-acceleration is still assumed but results in acceptably small errors, when a constant viscous damping coefficient for a single-degree-of-freedom (SDF) structure is calculated from the tangent stiffness and the damping ratio is set at 5% in both elastic and yield phases. For nonlinear structures, tangent stiffness dependency of damping force could be acceptable because energy absorption is primarily the result of structural nonlinear deformation. To extend the conventional demand spectra to a bi-linear model, effective period calculated from the secant stiffness has to be used. The use of effective period introduces no approximation because the peak displacement of the SDF structure is computed from nonlinear analysis in the time domain. The method presented in this study is also valid if damping coefficient proportional to initial elastic spectra is used. In this case, the pseudo-acceleration is defined as the base shear coefficient that is required to produce the peak displacement of the SDF structure in a static manner. We present demand spectra of bi-linear models for a number of near-source records from large earthquakes, and spectral ratios of two horizontal components. The effects of different types of ground motion on the response reduction factor due to inelastic deformation are investigated.     

A Single-Run Dynamic-Based Approach for Pushover Analysis of Structures Subjected to Near-Fault Pulse-Like Ground Motions

In this paper, a fairly effective procedure called dynamic load pattern (DLP), is proposed to account for the effects of near-fault ground motions in estimating the seismic demands of structures from pushover analyses. The seismic demands are obtained by enveloping the results of single-run conventional first-mode and single-run DLP pushover analyses. Improving the estimation of target displacement is another objective, implemented by performing response-spectrum analysis. Three special steel moment-resisting frames are considered and the seismic demands resulting from DLP are compared to those from the nonlinear time-history analysis as a benchmark solution, as well as to those predicted from modal pushover analysis.     

An Improved Displacement-Based Adaptive Pushover Procedure for the Analysis of Frame Buildings

The main purpose of this article is to develop an alternative adaptive pushover method in which multiple inelastic response spectra proportional to the instantaneous ductility ratio of the structure are employed to reflect the actual energy dissipation characteristic of the structure at a given deformation level. Based on the proposed methodology, two load patterns are independently applied to the structure and the envelope of the demand values is computed. The obtained results demonstrate that the proposed method provides improved predictions of the peak interstory and total drift profiles of the structure.     

Direct Displacement-Based Seismic Design of Eccentrically Braced Steel Frames

A series of eccentrically braced frames (EBF) are designed and subjected to nonlinear analyses to highlight ambiguities and differences in current seismic design provisions for EBF structures. This provides motivation to implement better guidance for the checking of local displacement demand considerations and move towards a displacement-based design approach. A recently proposed direct displacement-based design (DDBD) procedure for EBFs is then described and further developed in this article through the calibration of a spectral displacement reduction factors that relate the displacement of an inelastically responding structure to that of the equivalent linear representation used in the DDBD of EBFs. Such an expression is calibrated as part of this study using an experimentally validated numerical model also proposed here for the EBF links such that the actual hysteretic behavior of the links is well represented. The DDBD guidelines are applied to EBF systems from 1–15 stories in height and their performance is verified via nonlinear dynamic analyses using two different sets of design spectrum compatible ground motions. The results of the study indicate the robustness of the proposed DDBD method in limiting the interstory drifts to design limits for a variety of EBF systems with short links, thus demonstrating that the proposed DDBD method is an effective tool for seismic design of EBFs.     

Predicting the Seismic Response of Capacity-Designed Structures by Equivalent Linearization

An equivalent linearization procedure is developed for predicting the inelastic deformations and internal forces of capacity-designed structures under earthquake excitations. The procedure employs response spectrum analysis, and mainly consists of the construction of an equivalent linear system by reducing the stiffness of structural members that are expected to respond in the inelastic range. These members are well defined in structures designed with capacity principles. Maximum modal displacement demands of the equivalent linear system are determined either from the equal displacement rule, or from independent nonlinear response history analysis of SDOF systems representing inelastic modes.

Predictions obtained from the proposed equivalent linearization procedure are evaluated comparatively by using the results of nonlinear response history analysis as benchmark, linear elastic response spectrum analysis and conventional pushover analysis. The deformations and capacity controlled actions of a 12-story symmetrical plan concrete frame and a 6-story unsymmetrical plan concrete frame are obtained by each method under 96 strong ground motions. It is observed that the proposed procedure results in better accuracy in estimating the inelastic seismic displacement response parameters and capacity controlled forces than the other two approximate methods.