Inelastic Displacement Demands Research Articles

Comparative earthquake loss estimations for high-code buildings in Istanbul

The paper presents the probabilistic and scenario based earthquake loss estimations for the case that the hazard and building inventory inputs are kept the same whereas the damage functions as well as the seismic demand estimation method are changed in an earthquake loss model. Spectral acceleration-displacement based damage assessments by alternating damage functions and inelastic demand evaluation methods are performed for high-code buildings in Istanbul. The buildings are mid- and high-rise, reinforced concrete, moment-resisting frames that are assumed to be designed in accordance with the provisions of Turkish Earthquake Resistant Design Code (1998). Three damage models, i.e. structural capacity and fragility curves, are employed for each building class: Expert judgment based capacity and fragility functions; HAZUS's high-code seismic design level capacity and fragility functions; and Capacity and fragility functions derived based on nonlinear analyses of code complying RC frames. Inelastic spectral displacement demands are computed with three methods: Capacity Spectrum Method, Modified Acceleration-Displacement Response Spectrum Method, and Displacement Coefficient Method. Analyses are realized under site-specific ground motions based on a state-of-the-art hazard model for eight return periods ranging from 100 to 2475 years as well as for an Mw = 7.5 scenario earthquake. Probabilistic loss curves for each case are developed. Estimated average annual losses (AAL) and loss ratios (AALR) are compared. Grid and district based maps illustrating the spatial distributions of estimated long term average losses per year and the loss ratios are presented. The estimated annualized loss ratios at district level in the city are compared to the earthquake insurance premium rates.

Definition of inelastic displacement demand spectra for precast industrial facilities with friction and fixed beam-to-column joints

Portal-frame reinforced concrete precast industrial facilities built in Italy between 1960 and 1990 have shown high vulnerability during recent seismic events interesting Emilia region. Post-earthquake damage observations have shown that most of collapses interested portal-frame structures arranged with dry beam-to-column friction joints because of the loss of support due to sliding of beams with respect to columns. At the same time severe damage to column base cross-sections was recognized even in the case of portal-frame systems with beam-column connection devices (fixed joints). The paper investigates the dynamic behaviour of portal-frame precast industrial facilities, especially addressing the inelastic displacement demand as function of the generalized mechanical response of beam-to-column joints. Portal-frames are idealized as 2D inelastic single degree of freedom systems. A framework based on a parametric model developed in OpenSees is defined to build inelastic spectra of maximum relative beam-column displacement demands and maximum column top displacement demands. Inelastic displacement demand spectra are defined for four different sites in Italy (Messina, Mirandola, Naples and Turin), characterized by different seismic hazard. Analytical expressions of spectra approximating numerical results are finally derived to be used for rapid displacement capacity/demand assessments of portal-frame industrial buildings with friction joints or fixed joints. The approach can account vertical component of seismic excitation in a simplified way and can be also used to assess the effectiveness of retrofitting interventions.

Inelastic Displacement Spectra and Its Utilization of DDB Design for Seismic Isolated Bridges Subjected to Near-Fault Pulse-Like Ground Motions

A variety of research has focused on the inelastic displacement demand of a single degree of freedom (SDOF) system when subjected to near-fault pulse-like ground motions, in which the concerned ductility, μ, is typically lower than ten for normal structures. However, for seismic isolated structures that are more prone to large displacement, the corresponding research is limited. The purpose of this paper is to investigate the inelastic displacement spectra of an SDOF system with μ ranging from 5 to 70 and further proposes a direct displacement-based (DDB) design method for seismic isolated bridges. More concretely, a pool of near-fault pulse-like records is assembled, the mean Cμas a function of T/ Tpis developed, and the influences of the ductility, μ, and the post-to-pre-yield ratio, α, on Cμare carefully investigated. Then the corresponding inelastic displacement spectra, Sd, are obtained, and a comprehensive piecewise expression is proposed to fit Sd. After that, the utilization of the spectra for the DDB design of a three-span seismic isolated continuous bridge is performed, and the principal of simplifying the bridge to an SDOF system is carefully explained and verified.

Inelastic displacement spectra for Chinese highway bridges characterized by single-degree-of-freedom bilinear systems

As for the inelastic displacement demand of a single-degree-of-freedom system, previous studies usually focus on the strength reduction factor, R, or the inelastic displacement ratio, C. Only a little literature reports the direct statistical results of the mean inelastic displacement spectra, Sd. Based on 308 earthquake records selected from three types of site soil, differences between the direct mean Sd and the indirect ones that respectively derived from mean R and mean Cμ are investigated, in which Cμ refers to the constant ductility inelastic displacement ratio. It is found the indirect Sd will introduce errors for using mean R and mean Cμ, while the dispersion of the direct spectra need to be reduced before putting into practice. Two methods, the period normalized method and the spectra-matching method, are employed to address the dispersion problem, and the latter one that modified a record to make its acceleration response spectra compatible with the specified standard, Chinese highway bridge seismic design guidelines in this study, works with more acceptable performance. Finally, a comprehensive equation is proposed to characterize the spectra-matching mean Sd, the practicality and efficiency of the identified parameters in the equation are verified. It is advisable to use the proposed equation to assess the inelastic displacement demand of Chinese highway bridges characterized by single-degree-of-freedom bilinear system, and the procedures to obtain the displacement spectra can also be utilized for other corresponding researches.

Ductility demand of bilinear hysteretic systems with large post-yield stiffness: Spectral model and application in the seismic design of dual-systems

A structure designed in a dual-system configuration can help to achieve a damage-control and an earthquake-resilient property. In a dual-system, the primary structural system (PSS) and the replaceable fuse act in parallel, and the entire structure exhibits a multi-stage yielding mechanism under earthquake actions. To ensure the PSS keeps elastic, the dual-system is required to have a sufficient first-yielding stage wherein the fuse yields to dissipate the input energy. Accordingly, prediction of the structural ductility demand (μ) associated with the first-yielding stage is an important issue. In the first-yielding stage, the PSS remains elastic, making the post-yield stiffness ratio (α) much larger than conventional structures. This paper focuses on the ductility demand of bilinear hysteretic systems embedded with the high-α characteristic, which represent the dual-systems behaving within the elastic and the first-yielding stages. A total number of 742 strong earthquake records (490 of them are from stiff soil according to the standard of ASCE/SEI 7-10) are adopted to compute the ductility demand of 19,200 bilinear single-degree-of-freedom hysteretic systems. These systems have different combinations of strength levels (strength reduction factor 1.25 ≤ R ≤ 5.00), post-yield stiffness ratios (0.05 ≤ α ≤ 0.80) and natural periods (0.05 s ≤ T ≤ 5.00 s). It is revealed that for α ≥ 0.30, a larger α would lead to a slightly increased μ. Therefore, improving the value of α would not alleviate the expected inelastic displacement demand associated with the first-yielding stage for a dual-system, even though a larger α could remarkably reduce the dispersion of μ. A probabilistic spectral model for μ is developed, based on which the seismic performance of a dual-system could be checked in a statistic way. A trial-and-error design process for dual-systems is given, and the design-check process of a five-story buckling-restrained-braced frame is illustrated using the spectral model of μ. This study provides instructive results for the seismic design and retrofitting of dual-systems, as the effects of α, R and T on the values of μ for dual-systems are quantified appropriately.

Design and Testing of Ratcheting, Tension-Only Devices for Seismic Energy Dissipation Systems

ABSTRACTA pair of ratcheting, tension-only ‘Grip ‘n’ Grab’ (GnG) devices, for use with a range of seismic energy dissipation systems, have been developed and tested. Pawl and collet mechanisms have been tested with pitch sizes ranging from 3 to 40 mm, with smaller pitch sizes showing an increase in energy dissipation and inelastic displacement demand in the dissipater. Rapid and solid engagement of the two systems was observed during cyclic testing, with a total of 14 yielding steel dissipaters. Peak tension and compression forces were 65 kN and 1.3 kN, respectively, with damage confined to the dissipative element.

Estimation of inelastic displacement ratios for soil-structure systems with embedded foundation considering kinematic and inertial interaction effects

In this research, the simultaneous effects of soil-structure interaction (SSI) and nonlinear behavior of the superstructure on inelastic displacement ratios of soil-structure systems with embedded foundation are parametrically investigated. Results involving both kinematic interaction (KI), including rocking foundation input motion (RFIM), and inertial interaction effects are considered and discussed. The effect of KI on the inelastic displacement ratios is investigated with special focus on the role of rocking foundation input motion. The soil-structure system is modeled by sub-structure method. The foundation is modeled as a rigid cylinder embedded in the soil with different embedment ratios. A large number of soil-structure systems with embedded foundation having various dynamics characteristics and SSI key interacting parameters have been analyzed under an ensemble of 19 earthquake ground motions recorded on alluvium deposits. Results reveal that using the inelastic displacement ratios of fixed-base systems leads to an underestimation of the peak inelastic demands for soil-structure systems. The phenomenon is less intensified as foundation embedment increases. Moreover, the effects of rocking foundation input motion due to KI on inelastic displacement demands are significant for deeply embedded foundation when the SSI effect is predominant. For practical purpose, a simplified expression for estimating inelastic displacement ratios of soil-structure systems with embedded foundation considering KI effects is proposed.

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

ABSTRACTNew 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.

Seismic structural demands and inelastic deformation ratios: Sensitivity analysis and simplified models

Modern seismic codes rely on performance-based seismic design methodology which requires that the structures withstand inelastic deformation. Many studies have focused on the inelastic deformation ratio evaluation (ratio between the inelastic and elastic maximum lateral displacement demands) for various inelastic spectra. This paper investigates the inelastic response spectra through the ductility demand µ, the yield strength reduction factor Ry, and the inelastic deformation ratio. They depend on the vibration period T, the post-to-preyield stiffness ratio α, the peak ground acceleration (PGA), and the normalized yield strength coefficient η (ratio of yield strength coefficient divided by the PGA). A new inelastic deformation ratio Cη is defined; it is related to the capacity curve (pushover curve) through the coefficient (η) and the ratio (α) that are used as control parameters. A set of 140 real ground motions is selected. The structures are bilinear inelastic single degree of freedom systems (SDOF). The sensitivity of the resulting inelastic deformation ratio mean values is discussed for different levels of normalized yield strength coefficient. The influence of vibration period T, post-to-preyield stiffness ratio α, normalized yield strength coefficient η, earthquake magnitude, ruptures distance (i.e., to fault rupture) and site conditions is also investigated. A regression analysis leads to simplified expressions of this inelastic deformation ratio. These simplified equations estimate the inelastic deformation ratio for structures, which is a key parameter for design or evaluation. The results show that, for a given level of normalized yield strength coefficient, these inelastic displacement ratios become non sensitive to none of the rupture distance, the earthquake magnitude or the site class. Furthermore, they show that the post-to-preyield stiffness has a negligible effect on the inelastic deformation ratio if the normalized yield strength coefficient is greater than unity.

Inelastic Displacement Ratios for Evaluation of Degrading Peak – Oriented SDOF Systems

Estimation of the inelastic displacement demand (IDD) is an important part of the performance-based design. Coefficient method is one of the methods for the estimation of IDD and in this method, IDD is determined by multiplying elastic displacement demand with inelastic displacement ratio (CR ). Previous researches showed that structures deteriorate and also exhibit dynamic instability under severe earthquakes and these behaviors should be considered in the estimation of CR to estimate a reliable IDD. In this study, CR of the non-degrading bilinear hysteretic model and the degrading peak-oriented hysteretic model with collapse potential were determined and effects of degradation on IDD were investigated. Nonlinear time history analysis of SDOF systems were performed using considered hysteretic models. Furthermore a new equation is proposed for the mean CR of degrading SDOF systems. Also, effect of local site conditions and post-yield stiffness on the mean CR of degrading SDOF systems were investigated.

Improved evaluation of inelastic displacement demands for short‐period masonry structures

SummaryThis work discusses the simplified estimation of earthquake‐induced nonlinear displacement demands as required by nonlinear static procedures, with particular attention on short‐period masonry structures. The study focuses on systems with fundamental periods between 0.1 and 0.5 s, for which inelastic amplification of the elastic displacement demand is more pronounced; hysteretic force‐displacement relationships characteristic of masonry structures are adopted, because these structures are more commonly found within the considered period range. Referring to the results of nonlinear dynamic analyses of single‐degree‐of‐freedom oscillators, some limitations of the Eurocode 8 and Italian Building Code formulations are first discussed, then an improved equation is calibrated that relates inelastic and elastic displacement demands. Numerical values of the equation parameters are obtained, considering the amount of hysteretic energy dissipation associated with various damage mechanisms observed in masonry structures. Safety factors are also calculated to determine several percentiles of the displacement demand. It is shown that the proposed equation can be extended to more dissipative systems. Finally, the same formulation is adapted to the estimation of seismic displacements when elastic analysis procedures are employed. Copyright © 2017 John Wiley & Sons, Ltd.

Inelastic deformation ratio for seismic demands assessment of structures

Modern seismic codes rely on performance-based seismic design methodology which requires from the structures to withstand inelastic deformation. Many studies have focused on the inelastic deformation ratio evaluation for various inelastic spectra. The purpose is to investigate the ratio between the inelastic and elastic maximum lateral displacement demands. Three options are considered in the present work to express the inelastic response spectra in terms of the ductility demand, yield strength reduction factor and inelastic deformation ratio. This later, a new non dimensional parameter called inelastic deformation ratio (Cη), depends on the natural period (T), the post-to-preyield stiffness ratio (a), the normalized yield strength coefficient (t) and the peak ground acceleration (PGA). The inelastic deformation ratio (Cη), is not evaluated for a fixed ductility ratio or for a fixed strength reduction factor. Though the ductility demand and yield strength reduction factor differ greatly for given ranges of T and r“ they take close values for systems for any T value when η > 1. It confirms also previous studies stating that they take unity value for periods T ≥ 1sec.

Empirical Correlation between Inelastic and Elastic Spectral Displacement Demands

Inelastic spectral displacement demand is arguably one of the most effective, simplified means of relating earthquake intensity to building damage. However, seismic hazard assessment is typically conducted using empirical ground-motion prediction equations (GMPEs) that only provide indications of elastic spectral response quantities, which an engineer subsequently relates to inelastic demands using empirical relationships such as the equal-displacement rule. An alternative approach is to utilize relationships for the inelastic spectral displacement demand directly within the seismic hazard assessment process. Such empirical relationships are developed in this work, as a function of magnitude, distance, building period, and yield strength coefficient, for four different hysteretic models that are representative of a wide range of possible structural typologies found in practice. The new relationships are likely to be particularly useful for performance-based seismic design and assessment.

Seismic Assessment of Reinforced Concrete Frameworks through Advanced Pushover Analysis and Nonlinear Response of a SDOF Oscillator

This paper presents an integrated system for advanced structural analysis and seismic performance evaluation of 2D reinforced concrete frameworks. The advanced non-linear inelastic static analysis employed herein uses the accuracy of the fibre elements approach for large deflection inelastic frame analysis and address its efficiency and modelling shortcomings both to element level, through the use of only one element to model each physical member of the frame, and to cross-sectional level through the use of path integral approach for numerical integration of the cross-sectional nonlinear characteristics. Evaluation of the seismic performance is achieved with an approach that uses nonlinear time-history analysis (NTHA) of a single degree-of-freedom (SDOF) oscillator. The inelastic ductility and displacement demand is determined directly from accelerograms, without graphical or numerical approximations. Several computational examples are given to validate the effectiveness of the proposed method, the reliability and time saving of the code. The influence of the accuracy of the second-order nonlinear inelastic analysis methods involved in the modelling of the selected RC frame in conjunction with the distributions of the pushover lateral loads is pointed out. The proposed procedure is developed in the framework of Eurocode 8 design methodology, as reliable tool ready to be implemented into everyday design practice for advanced analysis, pushover analysis, and seismic performance evaluation of RC frame structures.

Influence of Displacement Ductility on Concrete Contribution to Shear Strength

Shear strength of reinforced concrete (RC) members is composed of the contributions of the nominal shear strength provided by transverse reinforcement and concrete. The shear strength of RC members under cyclic lateral loading degrades much faster than the flexural strength. Based on this state, Seismic Codes tend to be excessively conservative and do not take into account the contribution of concrete in certain cases. The aim of this study is to investigate the influence of displacement ductility on concrete contribution to shear strength using finite element analyses (FEA). Based on the agreement between the FEA and experimental results selected from literature, a simple relation is proposed for the prediction of the concrete contribution to shear strength of RC beams. The relation proposed takes into account a reduction of the normalized concrete contribution for increasing inelastic displacement demands, with a small residual strength at large ductility levels.

Estimation of inelastic displacement demands of flexible-based structures on soft soils

This study aims to develop efficient tools for performance-based seismic design of soil-structure interaction (SSI) systems on soft soils. To simulate the SSI effects, linear and nonlinear 'equivalent fixed-base single-degree-of-freedom' (EFSDOF) oscillators as well as a sway-rocking SSI model were adopted. The nonlinear dynamic response of around 10,000 SSI models and EFSDOF oscillators having a wide range of fundamental periods, target ductility demands, and damping ratios were obtained under a total of 20 seismic records on soft soil sites. Based on the results of this study, a practical method is developed for estimating the base shear and maximum displacement demands of a nonlinear single-degree-of-freedom structure on soft soil deposits. In the proposed procedure, the effect of frequency content of ground motions is considered by normalising the period of vibration by the spectral predominant periods, while the nonlinear EFSDOF models are used to improve the computational efficiency.

Estimation of inelastic displacement demands of flexible-based structures on soft soils

This study aims to develop efficient tools for performance-based seismic design of soil-structure interaction (SSI) systems on soft soils. To simulate the SSI effects, linear and nonlinear 'equivalent fixed-base single-degree-of-freedom' (EFSDOF) oscillators as well as a sway-rocking SSI model were adopted. The nonlinear dynamic response of around 10,000 SSI models and EFSDOF oscillators having a wide range of fundamental periods, target ductility demands, and damping ratios were obtained under a total of 20 seismic records on soft soil sites. Based on the results of this study, a practical method is developed for estimating the base shear and maximum displacement demands of a nonlinear single-degree-of-freedom structure on soft soil deposits. In the proposed procedure, the effect of frequency content of ground motions is considered by normalising the period of vibration by the spectral predominant periods, while the nonlinear EFSDOF models are used to improve the computational efficiency.

Use of the conditional spectrum to incorporate record‐to‐record variability in simplified seismic assessment of RC wall buildings

SummaryA procedure for incorporating record‐to‐record variability into the simplified seismic assessment of RC wall buildings is presented. The procedure relies on the use of the conditional spectrum to randomly sample spectral ordinates at relevant periods of vibration. For inelastic response, displacement reduction factors are then used to relate inelastic displacement demand to the spectral displacement at the effective period for single‐degree‐of‐freedom systems. Simple equations are used to convert back and forth between multi‐degree‐of‐freedom RC wall buildings and equivalent single‐degree‐of‐systems so that relevant engineering demand parameters can be obtained. Consideration is also given to higher‐mode effects by adapting existing modal combination rules. The proposed method is applied to several case study buildings, showing promising results in the examination of inter‐storey drift ratio and shear forces. The proposed method captures the variation in the distribution of structural response parameters that occurs with variations in structural configuration, intensity, engineering demand parameter of interest and site characteristics. Discussion is provided on possible ways to improve the accuracy of the procedure and suggestions for additional future work. Copyright © 2015 John Wiley & Sons, Ltd.

On the improvement of inelastic displacement demands for near-fault ground motions considering various faulting mechanisms

This paper investigates inelastic seismic demands of the normal component of near-fault pulse-like ground motions, which differ considerably from those of far-fault ground motions and also parallel component of near-fault ones. The results are utilized to improve the nonlinear static procedure (NSP) called Displacement Coefficient Method (DCM). 96 near-fault and 20 far-fault ground motions and the responses of various single degree of freedom (SDOF) systems constitute the dataset. Nonlinear Dynamic Analysis (NDA) is utilized as the benchmark for comparison with nonlinear static analysis results. Considerable influences of different faulting mechanisms are observed on inelastic seismic demands. The demands are functions of the strength ratio and also the pulse period to structural period ratio. Simple mathematical expressions are developed to consider the effects of near-fault motion and fault type on nonlinear responses. Modifications are presented for the DCM by introducing a near-fault modification factor, . In locations, where the fault type is known, the modifications proposed in this paper help to obtain a more precise estimate of seismic demands in structures.

Seismic performance of shear wall buildings with gravity-induced lateral demands

Architectural features and other irregularities in the gravity system which apply gravity-induced lateral demands to the seismic force resisting system are being incorporated in new buildings. These gravity-induced demands have raised concerns due to the perceived potential for a ratcheting effect to occur during seismic loading. This paper summarizes the results of a study to identify if there are behavioral trends not recognized within the scope of current building codes. To this end, a nonlinear, parametric study was conducted in OpenSees to investigate the inelastic response of concrete shear wall buildings with a range of design characteristics, including gravity-induced lateral demands. The results demonstrated that a seismic ratcheting effect can develop and amplify inelastic displacement demands. The effect is significantly more prevalent in coupled shear walls compared with cantilevered shear walls. An irregularity class to address buildings with gravity-induced lateral demands on the seismic force resisting system is proposed for the 2015 National Building Code of Canada.