Inelastic Displacement Ratio Research Articles

Constant-ductility inelastic displacement ratio spectra for design of superstructures in seismically isolated buildings

Constant-ductility inelastic displacement ratio (Cμ) spectra can be utilized for the estimation of peak inelastic structural displacements in the seismic design procedure. Currently, suitable analytical estimates of Cμ are lacking for base-isolated buildings with inelastic behavior of superstructures in a beyond design basis earthquake. This paper attempts to fill this research gap and hence conducts parametric studies on the Cμ spectra of base-isolated inelastic superstructures with lead-rubber bearings (LRBs). For that purpose, the inelastic model and equations of motion, boundary conditions of the analytical formulation of Cμ, and controlling parameters for the two-degree-of-freedom (2DF) superstructure-isolator system with LRBs are presented first. Subsequently, by analyzing the parameterized 2DF systems using an ensemble of strong earthquake records representative of a site with stiff soil conditions, the influence of controlling parameters, namely, displacement ductility ratios, superstructure periods, post-yielding stiffness ratios of superstructures, mass ratios, isolation periods and normalized isolator strength, on the mean and dispersion of Cμ are discussed, and the boundary conditions of Cμ are validated based on the calculated data. Comparisons of how the controlling parameters influence the Cμ and earlier investigated CR (i.e. constant-strength inelastic displacement ratio) spectra are also presented. Lastly, a predicting equation with reasonable accuracy is proposed for the mean Cμ using the nonlinear multivariable regression analysis method. The outcome of this study allows the application of displacement-based design via inelastic displacement ratio for new base-isolated structures under beyond design basis earthquakes.

Effects of P-delta and spectral shape of ground motion records on strength reduction factor and inelastic displacement ratio of SDOF systems with deterioration

Force-based design, due to its usefulness and simplicity with reasonable accuracy, is the main core of current seismic design codes. In this method, the behavior factor and deflection amplification factor are major elements that play a key role in linking linear and nonlinear behavior. This article examines the strength reduction factor due to ductility (Rμ) and inelastic displacement ratio (Cμ), which are important parts of the codes coefficients, considering the spectral shape of ground motion records and the P-delta effect. The nonlinear response history analysis (NL-RHA) is conducted for an extensive range of single-degree-of-freedom (SDOF) systems with different periods by categorizing the ground motion records based on ε, SaRatio, and Np. The most important emphasis of the paper, to which attention has not been paid previously, is to study the effect of spectral shape of ground motion records as an input excitation indicator and the P-delta effect as a structural parameter on strength reduction factor and inelastic displacement ratio of SDOF systems. In addition, the effects of some other structural parameters, including the ductility factor, deterioration, post-capping stiffness ratio on strength reduction factor and inelastic displacement ratio are evaluated. The results demonstrate that the values of Rμ and Cμ change by changing ε in the range of short periods than long periods. However, they vary more clearly with the change in SaRatio and Np. Furthermore, with the increase in θ-αs as an index of the P-delta effect, the system requires more design strength, and Cμ increases as well.

Inelastic acceleration ratios for nonstructural components

Non-Structural Components (NSCs) include all the elements that are part of structures but are not typically designed to resist the loads acting on the structures. In recent major earthquakes, the seismic design of NSCs has proved to be a key feature to assure suitable performance of structures. The accelerations experienced on the floors of structures are much higher than those at ground level, and therefore, NSCs located at these levels are highly susceptible to experiencing inelastic responses. However, relatively few studies have investigated the inelastic response of NSCs. Specifically, the inelastic absolute acceleration ratio (IAR) of NSCs is an important inelastic design parameter that has been the subject of little investigation. Therefore, this research aims to investigate the inelastic response of NSCs through its IARs by using seven elastic buildings of three different structural systems and three different sets of far-field seismic ground records. The inelastic response of the NSC is characterized by the yield strength reduction coefficient (R). The results of the study were used to develop an equation for estimating the characteristic period of ground IARs. In general, the characteristic period is equal to the fundamental period of the structure for the floor IARs and floor Inelastic Displacement Ratios (IDRs). In addition, the results helped to identify that the convergence values of the IARs mainly depend on the R factor and the damping ratio of the NSC and show consistency in both the ground IARs and the floor IARs. Furthermore, the trends of the floor IDRs are more unstable and less predictable than those of the IARs. An improved equation for predicting both ground and floor IARs is also proposed.

Constant-strength inelastic displacement ratio spectra for assessment of superstructures in seismically isolated buildings

A reliable estimation of maximum displacement demands of seismically isolated inelastic superstructures is crucial for assessment of base-isolated buildings under beyond-design earthquakes. Constant-strength inelastic displacement ratio, CR, spectra, as applied in the performance-based seismic assessment procedure, can be used to estimate the inelastic displacement demands of structures. Currently, a suitable analytical expression of CR is lacking for base-isolated structures considering the influencing parameters comprehensively. This paper seeks to fill this gap. The constant-strength spectra are computed from nonlinear dynamic analyses of simplified two-degree-of-freedom models considering the inelastic behavior of the superstructure and isolator system, using a set of earthquake ground motions recorded on stiff soil sites. The effects of strength reduction factor of superstructure, superstructure elastic period, secondary stiffness ratio of superstructure, mass ratio, isolation period, normalized strength of isolation system and superstructure viscous damping on the mean and dispersion of CR are investigated. In particular, the effects of variations in earthquake intensity and isolator strength on CR are taken into account by the normalized strength of isolation system. Besides, limiting values of CR as the superstructure elastic period tends to zero or infinity are discussed and verified using the statistical values of CR. Finally, based on the trends of CR with respect to the design parameters of the superstructure and isolation system, and the boundary conditions to the CR formula, an analytical estimating equation with reasonable accuracy is developed to approximate the mean constant-strength inelastic displacement ratios during seismic assessment of base-isolated building structures built on stiff soil sites.

The damage-based inelastic displacement ratio for performance-based design of fully self-centering systems under pulse-like near-fault earthquake ground motions

In this investigation, the damage-based inelastic displacement ratio (IDR) for fully self-centering (SC) systems with flag-shaped hysteresis behavior is determined under pulse-like earthquake ground motions to use in performance-based design theory. Pulsive earthquakes are known as dangerous natural phenomena due to the location of structures in the vicinity of the fault with forward-directivity and high-velocity amplitude features, which expose the system to high risk. Before this, the IDRs were obtained based on constant-ductility and strength reduction factor intensities for designing new and evaluating existing structures with SC behavior. However, the issue could be extended to an energy-based theory using the Park-Ang damage model as a popular index among researchers, with the ability to consider record amplitude, frequency content, and duration. Therefore, the damage-based IDR was determined under 252 pulse-like records with 126 pairs at four damage levels, 30 periods of vibration, four ultimate ductility factors (µu), four stiffness hardening ratios (α), and three dissipative energy factors (βn) by conducting comprehensive nonlinear dynamic analysis. Then, the influence of the mentioned parameters on obtained IDRs is evaluated to propose a robust equation for estimating target displacement in these systems. Statistical results illustrate that the approximate equation based on normalizing the structural period to the predominated period can predict the target displacement compared to achieved ones from direct time-history analysis, where the difference between estimated and mean target displacements is below 15%.

Ductility demands for stiffness-degrading SDOF systems under pulse-like ground motions of the 2023 Pazarcık (Kahramanmaraş) earthquake

This paper investigates the inelastic displacement ratios (IDRs) and displacement ductility demands of a wide range of single-degree-of-freedom (SDOF) systems subjected to pulse-like ground motions (GMs) of the 2023 Pazarcık (Kahramanmaraş) earthquake. A set of twenty-seven GMs characterized as pulse-like are utilized in the study. As-recorded velocity time histories of horizontal components are rotated over 90° at a step of 1° to attain the waveform with the largest peak ground velocity (PGV) over all horizontal orientations. Inelastic displacement ratio and displacement ductility spectra are computed through nonlinear response history analysis (RHA). Local amplifications of both spectra are observed at some periods. The results of this study show that large inelastic displacement and ductility demands are imposed on certain reinforced concrete (RC) structures. Finally, predictive models of the mean inelastic displacement ratio and mean ductility demand spectra (DDS) are developed based on the Gauss–Newton algorithm (GNA). The model provides a strong correlation between the computed and the estimated data, and sufficient convergence criteria. The results of this study collectively emphasize the necessity of integrating pulse-like GMs into future revisions of earthquake codes.

Seismic response of non-structural components in multi-storey steel frames

This paper investigates the elastic and inelastic seismic response of non-structural components in multi-storey steel moment framed structures and derives predictive relationships for their displacements and spectral accelerations. Within 38 primary structural steel frames, non-structural components characterised by various periods and strength reduction factors, are modelled as single-degree-of-freedom systems which are fixed to individual floors. The primary structures are three, five, and seven-storey steel moment-resisting frames, designed according to the provisions of Eurocode 8. Detailed nonlinear time history analyses are conducted, employing a large set of 100 ground motion records from both far-field and near-field sources. These records are scaled to two distinct levels to simulate the response of primary structures in both elastic and inelastic states. The influence of the ground motion type and the inelasticity level in the non-structural components is examined in detail. The sensitivity to strain hardening and viscous damping considerations is also assessed and discussed. Based on the results, representative relationships for predicting the inelastic displacement ratios are proposed. In addition, various provisions stipulated in European design guidance for determining the spectral accelerations are critically evaluated and improvements are suggested with due consideration for the inelasticity of both the non-structural components and the primary structures.

The constant damage inelastic displacement ratio for performance design of self-centering systems under far-field earthquake ground motions

In this research paper, the inelastic displacement ratio known as maximum nonlinear displacement to maximum elastic displacement is determined at different periods of vibration and constant damage indices based on the Park-Ang model for fully self-centering structures under 216 far-field earthquake ground motions. The effect of ground motion characteristics, including soil classification, magnitude, and source-to-site distance, are evaluated at different period ranges. Moreover, the influence of structural parameters is investigated, including the ultimate ductility of the structural system, the β factor related to the damage model, the stiffness-hardening ratio, and the dissipative-energy factor corresponding to the flag-shaped hysteresis behavior of the self-centering system. Then, a simple equation based on nonlinear regression analysis is proposed to estimate the constant damage inelastic displacement ratio. It is worth mentioning that the bias and standard deviation of the error in the suggested equation are presented for better understanding. Finally, the proposed equation is compared with the nonlinear responses obtained from the direct time history analysis in self-centering flag-shaped models under thirty earthquake records selected corresponding to desired seismic hazard level. The statistical analysis illustrates that the effect of ground motion characteristics on constant inelastic displacement ratio is not prominent, while the influence of some structural parameters like ultimate ductility and dissipative-energy factor is remarkable in higher damage levels.The verification analysis showed that the suggested equation could estimate the target displacement of the self-centering structural systems with a lower than 10% error.

Floor acceleration control of self-centering braced frames using viscous dampers

The self-centering braced frames (SCBFs) have been widely investigated for enhancing the building structures’ post-earthquake repairability by reducing or even eliminating the residual inter-story drifts. Nevertheless, it has been highlighted in recent research that the flag-shaped hysteretic behavior of SCBFs amplifies structural floor acceleration (FA) responses, which may lead to severe nonstructural damage. This paper intends to overcome this critical shortcoming of SCBFs by controlling FA responses using viscous dampers. This paper focuses on proposing a practical performance-based design strategy for designing viscous dampers to control the FA responses of the SCBF to the targeted level. To this end, the parametric dynamic analyses of a single-degree-of-freedom (SDOF) system were conducted to investigate the influence of the hysteretic parameters of self-centering braces (SCBs) and the contribution of viscous dampers (VDs) on the peak acceleration control in the SCBFs. Based on the results from the parametric dynamic analysis, the prediction models of inelastic displacement and acceleration ratios of the SCBF with VDs (denoted as the hybrid self-centering braced frame, HSCBF) were developed using the artificial neural network (ANN). The design steps included in the proposed method were presented, where a formula was proposed for predicting the absolute FAs of the HSCBF. Four demonstration buildings with 3, 6, 9, and 12 stories were designed and simulated to verify the developed performance-based design method. The analysis results show that the VDs can effectively control the FA responses of the SCBFs and the mean FAs of the designed systems can reach the desired performance level. Moreover, the reasons why VDs can reduce the accelerations of self-centering building structures are preliminarily discussed from the perspectives of frequency domain and higher mode effects. The analysis results indicate that compared to the original SCBFs, the HSCBF tends to vibrate with a lower frequency and show smaller high-mode responses.

Effect of Soil–Structure Interaction on Inelastic Displacement Ratios of Bridge Structures Subjected to Pulse-Like Ground Motions

This study aimed to investigate the effect of soil–structure interaction (SSI) on the inelastic displacement ratio of bridge structures subjected to near-fault pulse-like earthquake ground motions. SSI was modeled using a discrete-time recursive filter approach and frequency-dependent foundation–soil impedance functions. A total of 105 near-fault earthquake ground motion records were used for the analysis. The study also compared the soil–foundation–superstructure (SFS) system with a fixed-base system to explore the effects of spectral period normalization, strength reduction factor, earthquake magnitude, site-to-source distance, and peak ground velocity on the inelastic displacement ratio. The findings indicate that both the SFS and fixed-base systems have significant inelastic displacement demand under near-fault earthquakes, with values that can be 2–3 times higher than those predicted by ASCE-41-13, particularly in the short period range. Furthermore, as the structural period approaches the earthquake pulse period, the SFS system generally shows larger inelastic displacement ratios compared to the fixed-base system. The analytical results provide insight into the factors affecting the inelastic displacement ratio for near-fault pulse-like earthquakes.

Inelastic displacement ratio of low- to mid-rise BRBFs designed under variable levels of seismicity

Inelastic displacement ratio of low- to mid-rise BRBFs designed under variable levels of seismicity

Development of inelastic displacement ratio using constant energy-based damage index for performance-based design

Development of inelastic displacement ratio using constant energy-based damage index for performance-based design

Effect of ground motion duration on inelastic displacement ratio of SDOF systems

Effect of ground motion duration on inelastic displacement ratio of SDOF systems

Estimation of the inelastic displacement ratio for structures considering nonlinear soil-structure interaction

Estimation of the inelastic displacement ratio for structures considering nonlinear soil-structure interaction

A New Proxy for Near-Fault Acceleration Pulses and Implications on Inelastic Displacement Ratio

ABSTRACT This study develops new equations for predicting the constant-strength inelastic displacement ratio (C R ) by considering nonlinear single-degree-of-freedom systems subjected to near-fault ground motions. To this aim, an energy-based parameter, the MEA/MEV ratio, is firstly considered for characterizing the properties of pulse-like records. “MEA” and “MEV” represent the Maximum Energy of the half-cycle pulse in Acceleration and Velocity time histories, respectively. The effects of the MEA/MEV ratio on the C R spectra are investigated in terms of elastic-perfectly plastic hysteretic behavior. Finally, a simplified equation for estimating the C R spectra is developed, and its accuracy is evaluated by calculating the error measures.

A statistical study of inelastic displacement ratio spectrum for existing structures

AbstractDisplacement‐based design has gained importance due to the emergence of the performance‐based engineering, and it has now become desirable to estimate maximum (inelastic) displacements of structures for different levels of seismic hazard. Being closely related to damage, displacement (or drift) has become an important parameter necessary to meet various performance goals. It is considered convenient to estimate the inelastic displacement demand in a structure by multiplying the elastic displacement demand of the structure with a ratio called the inelastic displacement ratio. A comprehensive study is conducted for the parametric dependence of the inelastic displacement ratio in single‐degree‐of‐freedom (SDOF) systems with known relative lateral strengths, on strong motion duration, earthquake magnitude, epicentral distance, and geological site conditions. This study is different from the earlier studies of similar types in that other governing parameters are kept fixed while the effects of variations in any particular parameter are studied. This study is based on the generation of ensembles of synthetic accelerograms from a database of 1274 accelerograms recorded in western USA for the pseudospectral acceleration (PSA) spectra of given source and site parameters. It is found that strong motion duration may influence the inelastic displacement ratios, depending on the hysteretic properties of the oscillator, in the case of durations not much longer than 10 s. Earthquake magnitude has a significant influence on these ratios for the SDOF systems of most periods, while site geology appears to be important for the stiff oscillators. A scaling model is also proposed in this study for estimating the inelastic displacement ratio spectrum from a normalized relative velocity spectrum of the ground motion. The proposed model indirectly includes the effects of various governing parameters and is shown to preserve the trends available from the direct study.

Constant ductility inelastic displacement ratio spectra of shape memory alloy-friction self-centering structures based on a hybrid model

Previous researches on the constant ductility inelastic displacement ratio spectra (\({C}_{\upmu }\)) of self-centering structures have been conducted based on the typical flag-shaped self-centering (FS) model. However, the arising shape-memory-alloy-friction self-centering structures (SMAFSs) own their specialized force–displacement relationship different from the typical FS model. In this research, a hybrid force–displacement model composed of the typical FS model and Coulomb friction model is employed and an efficient calculating procedure is proposed to statistically investigate the \({C}_{\upmu }\) of SMAFSs. Comparison with the \({C}_{\upmu }\) of the typical FS system with similar self-centering capacity shows that the \({C}_{\upmu }\) of the SMAFS is significantly different from that of the typical FS system, which explains the necessity of employing the hybrid model for SMAFSs and the effects of the friction. The effects of seismic parameters and structural parameters on the \({C}_{\upmu }\) of SMAFSs are investigated. Furthermore, the formula for estimating the \({C}_{\upmu }\) of SMAFSs is proposed through statistical regression. This proposed formula could estimate the \({C}_{\upmu }\) of SMAFSs and describe the effects of structural parameters more accurately. The research could provide a basis of estimating the \({C}_{\upmu }\) of SMAFSs to obtain reliable seismic design results of the structures.

The advantages of using initial stiffness in direct displacement-based design

The basic Direct Displacement-Based Design (DDBD) approach is based on the “substitute structure” method. The substitute structure is a single-degree-of-freedom (SDOF) representation of a structure that was constructed based on the secant stiffness at peak displacement response and the equivalent viscous damping (EVD). Afterward, the method was modified using displacement reduction factor (ημ) instead of EVD, while the secant stiffness was still employed. The modified method can solve some drawbacks. Nevertheless, using secant stiffness still causes a period shift in the displacement spectrum that inputs significant errors in the method. To overcome these shortcomings, an alternative approach on the basis of initial stiffness and inelastic displacement ratio (Cμ) is proposed here. Using initial stiffness does not lead to a period shift and hence spectral shape dependency in the design. Moreover, it would be a great advantage if the Cμ relationships, which were developed in a wide range of studies, were extended to the calculation of design base shear in the DDBD method. To evaluate the proposed method, first, a comprehensive analysis of elasto-plastic SDOF systems was performed to derive appropriate expressions for both ημ and Cμ parameters. Then, a large number of SDOF systems were designed with the modified and proposed methods. The evaluation of methods for three different ground motion sets indicates the superiority of the proposed method.

Seismic response of acceleration-sensitive nonstructural components in a Thin Lightly-Reinforced Concrete Wall (TLRCW) mid-rise building

Experience in recent earthquakes has shown that Non-Structural Components (NSCs) in multi-story buildings exert a significant influence on economic losses. Different topics about the seismic behavior of NSCs have been investigated; however more research is needed in several areas such as the type of building structural system and the type of seismic hazard. Motivated by this observation, floor accelerations in a novel structural system, namely the Thin and Lightly-Reinforced Concrete Wall (TLRCW) building, are examined in this paper. The TLRCW system comprises thin and slender walls with deficient or nonexistent confinement at the wall edges, and web reinforcements made of welded-wire mesh with limited ductility. In this study, seismic demands on NSCs in a TLRCW building are analytically calculated and compared with current characterizations included in earthquake-resistant building codes and presented in the literature. Comparisons are performed in terms of peak floor accelerations, floor spectra, inelastic displacement ratios, and the still not completely characterized inelastic absolute acceleration ratios. Influence of elastic and inelastic behavior of NSCs as well as of the structure is also evaluated. Since the TLRCW system is becoming common in some South American countries prone (in part or wholly) to subduction earthquakes, possible influence of the type of seismic hazard (i.e., crustal earthquakes or subduction earthquakes) is accounted for. It was found that, under design-level seismic demands, floor accelerations can be very large even though the structure undergoes a significant level of inelastic excursion. It was also found that floor accelerations are, for the most part, reasonably approximated by current characterizations. Finally, the type of seismic hazard has a negligible qualitative influence on floor accelerations (only minor quantitative differences were found).

Machine learning-driven performance-based seismic design of hybrid self-centering braced frames with SMA braces and viscous dampers

A hybrid self-centering braced frame equipped with shape memory alloy-based self-centering braces (SMA-SCBs) and viscous dampers is proposed to achieve enhanced seismic performance. Based on the proposed hybrid strategy combining the contributions of SMA-SCBs and viscous dampers, this paper investigates the advantages of such hybrid self-centering braced frames in achieving the desired maximum inter-story drift under a considered seismic intensity. To this end, the influence of design parameters of SMA-SCBs and viscous dampers on hybrid self-centering braced frames is examined through parametric dynamic analyses of equivalent single-degree-of-freedom systems. The analysis results indicate that the post-yield stiffness ratio α and energy dissipation factor β of SMA-SCB, and the contribution of viscous damper show significant influence on the peak displacement responses of hybrid self-centering braced frames. The constant inelastic displacement ratio prediction model for hybrid self-centering braced frames is developed using machine learning algorithms. A performance-based seismic design method is subsequently proposed for the hybrid self-centering braced frames to achieve the target displacement responses based on the developed machine learning models. Two hybrid self-centering braced frames are designed based on the proposed design method. Nonlinear dynamic analyses are conducted to investigate the seismic performance of the designed structures. To highlight the advantages of the hybrid self-centering braced frames, another six-story self-centering braced frame with SMA-SCBs only is also studied in this paper. The analysis results indicate that all the designed hybrid self-centering braced frames can achieve the desired performance objective. Compared to the self-centering braced frame with SMA-SCBs only, the hybrid self-centering braced frames can achieve much smaller base shear demand and absolute floor acceleration responses.