Displacement Ductility Demand Research Articles

Seismic reliability-based design of inelastic base-isolated structures with lead-rubber bearing systems

In this paper, a seismic reliability-based approach is proposed to design inelastic steel moment frame structures isolated by lead-rubber bearing (LRB) systems. An equivalent two-degree-of-freedom system is assumed in which a bilinear behaviour is assigned to both the superstructure and the base. Furthermore, uncertainties associated with the equivalent superstructure mass, stiffness, and yield properties are taken into account by employing proper probability density functions. The proposed design approach is twofold: 1) Reliability curves that return the key design parameters of the inelastic base-isolated structure including: the period of the superstructure, the target base displacement, and the ductility-dependent strength reduction factor for a given target reliability. 2) Regression equations, which estimate the displacement ductility demand of the inelastic superstructure and the optimal design properties of the lead-rubber bearing system including: the total initial stiffness and the total yield force. These regression equations are calibrated against a large set of optimally-designed base-isolated buildings using Genetic Algorithm.

Seismic reliability-based ductility demand for hardening and softening structures isolated by friction pendulum bearings

This study aims at proposing seismic reliability-based relationships between the behavior factors and the displacement demand for nonlinear hardening and softening structures isolated by friction pendulum system devices considering several structural properties. An equivalent 2dof model having both a hardening and softening postyield slope is used to describe the superstructure behavior, whereas a velocity-dependent model is adopted for the friction pendulum system response. The yielding characteristics of the superstructures, related to life safety limit state, are designed according to the seismic hazard of L'Aquila site (Italy) for increasing behavior factors, as provided from NTC08. Considering natural seismic records and several elastic and inelastic building properties, different postyield hardening and softening stiffness values, different seismic intensity levels, and modeling the friction coefficient as a random variable, incremental dynamic analyses are performed to evaluate the seismic fragility of these structural systems. By means of the convolution integral between the fragility curves and the seismic hazard curves corresponding to L'Aquila site (Italy), the reliability curves of the equivalent hardening and softening base-isolated structural systems, with a lifetime of 50 years, are defined. Specifically, seismic reliability-based linear and multilinear regression expressions between the displacement ductility demand and the behavior factors for the superstructure as well as seismic reliability-based design abacuses for the friction pendulum devices are proposed.

Probabilistic Seismic Performance Analysis of RC Bridges

ABSTRACT This paper focuses on the evaluation of the seismic vulnerability of pre-1990 highway concrete bridges, based on the development of analytical fragility curves. The parameters considered are the span length, column height, lap splices, reinforcement yield strength, and concrete compressive strength. Nonlinear response history analyses using 3D models were conducted for each set of bridge samples subjected to earthquake ground motions with different intensities. Moreover, this study analyzes the influence of the earthquake fault type on the seismic vulnerability of the bridges, using as a performance parameter the displacement ductility demand of the piers. Based on this parameter, to support future seismic-risk mitigation efforts fragility curves are utilized to assesses the seismic vulnerability of typical concrete bridge classes in Iran. The selected suite of seismic records originates in strike-slip and reverse fault seismic sources. The bridges subjected to reverse fault records present pier demands and seismic vulnerability larger than the bridges subjected to strike-slip accelerograms. The study shows that the span length, lap splice, column height, and seismic fault type have significant effects on the seismic vulnerability of bridge piers. Additionally, the results are useful to identify and prioritize retrofit actions of the most seismically vulnerable bridges.

Influence of Post-Yield Stiffness on Inelastic Seismic Response: A Stochastic Analysis

The main objective of this study is to evaluate inelastic response spectra conditioned on constant displacement ductility demand for a single degree of freedom system, which has positive post-yield stiffness. To develop this analysis, the nonlinear Bouc–Wen model is used and it is subject to a seismic action modeled by a nonstationary stochastic process. The study utilises stochastic linearisation technique and peak theory to obtain inelastic response spectra. More in detail, inelastic acceleration spectra, response modification factor spectra, strength reduction factor spectra, yield strength spectra, and inelastic displacement ratio spectra are obtained for constant displacement ductility demand. The novelty of the present study with respect to the previous ones in this field is to obtain inelastic response spectra in stochastic terms, starting from a stochastic model of the seismic motion. Results suggest that the effect of post-yield stiffness must be considered when determining inelastic response.

Mitigation of seismic drift response of braced frames using short yielding-core BRBs

Buckling-restrained braced frames (BRBFs) are commonly used as the lateral force-resisting systems in building structures in the seismic regions. The nearly-symmetric hysteretic response and the delayed brace core fracture of buckling-restrained braces (BRBs) under the axial cyclic loading provide the adequate lateral force and deformation capacity to BRBFs under the earthquake excitation. However, the smaller axial stiffness of BRBs result in the undesirable higher residual drift response of BRBFs in the post-earthquake scenario. Two alternative approaches are investigated in this study to improve the elastic axial stiffness of BRBs, namely, (i) by shortening the yielding cores of BRBs; and (ii) by reducing the BRB assemblies and adding the elastic brace segments in series. In order to obtain the limiting yielding core lengths of BRBs, a modified approach based on Coffin-Manson relationship and the higher mode compression buckling criteria has been proposed in this study. Both non-linear static and dynamic analyses are carried out to analytically evaluate the seismic response of BRBFs fitted with short-core BRBs of two medium-rise building frames. Analysis results showed that the proposed brace systems are effective in reducing the inter-story and residual drift response of braced frames without any significant change in the story shear and the displacement ductility demands.

Seismic reliability‐based ductility demand evaluation for inelastic base‐isolated structures with friction pendulum devices

SummaryThe aim of this work is to propose seismic reliability‐based relationships between the strength reduction factors and the displacement ductility demand of nonlinear structural systems equipped with friction pendulum isolators (FPS) depending on the structural properties. The isolated structures are described by employing an equivalent 2dof model characterized by a perfectly elastoplastic rule to account for the inelastic response of the superstructure, whereas, the FPS behavior is described by a velocity‐dependent model. An extensive parametric study is carried out encompassing a wide range of elastic and inelastic building properties, different seismic intensity levels and considering the friction coefficient as a random variable. Defined a set of natural seismic records and scaled to the seismic intensity corresponding to life safety limit state for L'Aquila site (Italy) according to NTC08, the inelastic characteristics of the superstructures are designed as the ratio between the average elastic responses and increasing strength reduction factors. Incremental dynamic analyses (IDAs) are developed to evaluate the seismic fragility curves of both the inelastic superstructure and the isolation level assuming different values of the corresponding limit states. Integrating the fragility curves with the seismic hazard curves related to L'Aquila site (Italy), the reliability curves of the equivalent inelastic base‐isolated structural systems, with a design life of 50 years, are derived proposing seismic reliability‐based regression expressions between the displacement ductility demand and the strength reduction factors for the superstructure as well as seismic reliability‐based design (SRBD) abacuses useful to define the FPS properties. Copyright © 2016 John Wiley & Sons, Ltd.

Hysteretic Modeling of Unbonded Posttensioned Precast Segmental Bridge Columns with Circular Section Based on Cyclic Loading Test

The seismic performance of unbonded posttensioned (PT) precast segmental bridge columns (PSBCs) with circular sections was investigated. Two precast segmental columns with/without energy dissipation (ED) bars were tested under quasi-static cyclic loading. Their damage patterns and hysteretic curves were compared. Three single-degree-of-freedom hysteretic models were formulated with the key parameters identified from the tests. Cyclic loading analyses of the two tested specimens were conducted using these hysteretic models. Time history analyses were also conducted utilizing the proposed three hysteretic models to observe their applicability in modeling the dynamic responses of PSBCs. Finally, parametric analyses of PSBCs were performed under the excitation of an ensemble of 20 history ground motions to study the influences of relative yield force, elastic period, and energy dissipation coefficient on the earthquake responses of displacement ductility demand, maximum absolute acceleration, and maximum absorbed energy.

Seismic design of yielding structures on flexible foundations

SummaryThis paper introduces a simple method to consider the effects of inertial soil–structure interaction (SSI) on the seismic demands of a yielding single‐degree‐of‐freedom structure. This involves idealizing the yielding soil–structure system as an effective substitute oscillator having a modified period, damping ratio, and ductility. A parametric study is conducted to obtain the ratio between the displacement ductility demand of a flexible‐base system and that of the corresponding fixed‐base system. It is shown that while additional foundation damping can reduce the overall response, the effects of SSI may also increase the ductility demand of some structures, mostly being ductile and having large structural aspect ratio, up to 15%. Finally, a design procedure is provided for incorporation of the SSI effects on structural response. Copyright © 2015 John Wiley & Sons, Ltd.

Evaluation of Post-Earthquake Axial Load Capacity of Circular Bridge Columns

Objective evaluation of the capacity of a bridge to carry self-weight and traffic loads after an earthquake is essential for a safe and timely reopening of the bridge. The ability of a bridge to function depends directly on the remaining capacity of the bridge columns to carry gravity and lateral loads. An experimental study on models of modern circular reinforced concrete bridge columns was performed to investigate the relationship between earthquake-induced damage in bridge columns and the capacity of the columns to carry axial load in a damaged condition. The earthquake-like damage was induced in the column specimens in bidirectional, quasi-static, lateral load tests. The damaged column specimens were then recentered to eliminate the residual drifts and tested in compression to failure to evaluate their remaining axial load strength. It was found that well-confined modern bridge columns lose approximately 20% of their axial load capacity after sustaining displacement ductility demands of 4.5.

A case study on the P–Δ effect on inelastic seismic behaviour of a bridge pier

The P–delta (P–Δ) effect imposes higher ductility demand during earthquakes, which may not be adequately catered for in the prescribed values of response reduction factors (Rμ). The present work investigates the P–Δ effect on inelastic seismic response of slender bridge piers through a case study. Displacement ductility demands and overturning moments of a typical pier are computed both with and without the P–Δ effect using non-linear dynamic analysis and pushover methods. Response history analysis is carried out for four hysteresis behaviours: elasto-plastic, strength degrading, stiffness degrading, and combined strength and stiffness degrading behaviour. The study shows that the P–Δ effect at the plastic stage is a progressive phenomenon and depends on strength rather than on stiffness. The conventional practice to restrict sway based on first-order analysis to prescribed values for containing the P–Δ effect is ineffective. By using a case study, the research provides a methodology for arriving at acceptable Rμ values to prevent occurrence of any instability due to the P–Δ effect arising from undue low lateral strength.

Curvature ductility of columns and structural displacement ductility in RC frame structures subjected to ground motions

This paper examined the statistical relationship between the curvature ductility demands of columns and the global displacement ductility demands of reinforced concrete (RC) frame structures when subjected to earthquakes. Elements with a designated moment–curvature relationship were adopted for both beam and column elements, and five-story and ten-story RC frame numerical structures were established. Using pushover analysis and earthquake nonlinear dynamic time-history analysis, the maximum global displacement ductility demands of the structure and the maximum curvature ductility demands of the columns were determined. The effects of the spectral acceleration and the strong column factor on ductility demands were analyzed, and the quantitative relationship between the curvature ductility demands of columns and the global displacement ductility demands of frame structures were established. Moreover, the validity of the established relationship was further tested and verified through a real-world application. The results show that the maximum curvature ductility demands of the columns and the maximum displacement ductility demands of the structure were positively associated with the spectral acceleration and negatively associated with the strong column factor. A proposed first-degree linear relationship between curvature ductility of columns and structural displacement ductility in RC frame structures with two parameters was obtained by curve fitting, while considering the effect of the strong column factor. The model was highly correlated with the sampling analysis data. Applying the empirical model established in this study is a simple and effective means to guide the design of ductility and the assessment of RC frame columns.

Seismic response analysis of a nuclear reactor structure considering nonlinear soil-structure interaction

This study focuses on the seismic response analysis of an internal shearwall of a typical Indian reactor resting on a medium dense sandy silty soil, incorporating the nonlinear behavior of the soil-foundation interface. The modeling is done in an open-source finite element framework, OpenSees, where the soil-structure interaction (SSI) is modeled using a Beam-on-Nonlinear-Winkler-Foundation (BNWF) approach. Static pushover analysis and cyclic analysis are performed followed by an incremental dynamic analysis (IDA) with 30 recorded ground motions. For performing IDA, the spectral acceleration of each motion corresponding to the fundamental period, Sa(T1)is incremented from 0.1g to 1.0g with an increment step of 0.1g. It is observed from the cyclic analysis that the equivalent viscous damping of the system increases upto twice upon incorporation of inelastic SSI. The IDA results demonstrate that the average peak base shear, base moment and displacement ductility demand reduces as much as 62%, 40%, and 35%, respectively, whereas the roof drift demand increases up to 25% upon consideration of foundation nonlinearity for the highest intensity motion. These observations indicate the need of critical consideration of nonlinear soil-structure interaction as any deficient modeling of the same may lead to an inaccurate estimation of the seismic demands of the structure.

Performance-based plastic design of steel plate shear walls

The existing codes and design guidelines for steel plate shear walls (SPSWs) fail to utilise the excellent ductility capacity of SPSW systems to its fullest extent, because these methods do not consider the inelastic displacement demand or ductility demand as their design objective. A performance-based plastic design method for SPSW systems with rigid beam-to-column connections is proposed in this work, which sets a specific ductility demand and a preferred yield mechanism as its performance targets. The effectiveness of the proposed method in achieving these targets is illustrated through sample case studies of four- and eight-storey SPSW systems for varied design scenarios. A comparison with the existing AISC method for the same design scenario shows that the proposed method consistently performs better, in achieving these performance-based targets. The proposed method is modified to account for P-Delta effects, wherever necessary. This modified method is found to be more effective than the original proposal, whenever P-Delta effects are significant.

Dynamics of inelastic base‐isolated structures subjected to analytical pulse ground motions

SUMMARYStructural design code provisions worldwide prescribe relatively small seismic force reduction factors for seismically base‐isolated structures, making their response to design‐level earthquake excitation essentially elastic. This paper uses the method of dimensional analysis to prove that; in most cases, this is not a conservative design approach but a necessity that emerges from the dynamics of base‐isolated structures. It is shown that allowing typical base‐isolated structures to yield results in large displacement ductility demands for the structure. This phenomenon is caused by the change in the nature of the ground motion excitation as it is transmitted to the structure through the seismic base isolation system as well as by the change in the distribution of displacements between the structure and the isolation bearings caused by yielding of the isolated structure. Copyright © 2013 John Wiley & Sons, Ltd.

Ductility demand of partially self-centering structures under seismic loading: SDOF systems

In this paper, a numerical simulation study was conducted on the seismic behavior and ductility demand of single-degree-of-freedom (SDOF) systems with partially self-centering hysteresis. Unlike fully self-centering systems, partially self-centering systems display noticeable residual displacement after unloading is completed. Such partially self-centering behavior has been observed in a number of recently researched self-centering structural systems with energy dissipation devices. It is thus of interest to examine the seismic performance such as ductility demand of partially self-centering systems. In this study, a modified flag-shaped hysteresis model with residual displacement is proposed to represent the hysteretic behavior of partially self-centering structural systems. A parametric study considering the effect of variations in post-yield stiffness ratio, energy dissipation coefficient, and residual displacement ratio on the displacement ductility demand of partially self-centering systems was conducted using a suite of 192 scaled ground motions. The results of this parametric study reveal that increasing the post-yield stiffness, energy dissipation coefficient or residual displacement ratio of the partially self-centering systems generally leads to reduced ductility demand, especially for systems with lower yield strength.

Seismic health monitoring of RC frame structures using smart aggregates

Structural health monitoring of RC structures under seismic loads has recently attracted much attention in the earthquake engineering research community. In this study, a piezoceramic-based device called “smart aggregate” was used for the health monitoring of RC frame structures under earthquake excitations. Three RC moment frames instrumented with smart aggregates were tested using a shaketable with different ground excitation intensities. Distributed piezoceramic-based smart aggregates were embedded in the RC structures and used to monitor their health condition during the tests. The sensitivity and effectiveness of the proposed piezoceramic-based approach were investigated and evaluated by analyzing the measured responses. The displacement ductility demand of the structural members was calculated and compared with the damage index determined from the health monitoring system. The comparison shows that the damage index is compatible with the calculated ductility demand.

Use of sliding multirotational devices of an irregular bridge in a zone of high seismicity

The 525 meters long Infiernillo II bridge crosses the Infiernillo Dam and it is the first isolated bridge built in Mexico. It is located in the Morelia-Lazaro Cardenas highway that connects the central cities of the country to the Pacific Coast. Arch steel trusses compose the superstructure of the five simple supported spans. The substructure consists of reinforced concrete abutments and piers supported on cylinders and piles. The total cylinder-pier subsystem height is in the range of 46 m to 71 m, causing a strong irregularity in the transverse and longitudinal directions. The bridge was subjected to an assembly of real strong motion movements recorded close to the Pacific Coast in Mexico, site where the most severe earthquakes occur in the country. The study started by evaluating the analytical model with environmental vibration measurements previously taken. Based on the similarity of the results, none adjustment was required for the numerical model. The results show the importance of the isolator dynamic characteristics on the expected seismic behavior of the bridge. Special emphasis is dedicated to analyze the effectiveness of the isolation system for avoiding concentration of strength and displacement ductility demands on an irregular bridge substructure.

Cyclic Performance of Glued Laminated Guadua Bamboo-Sheathed Shear Walls

AbstractThis paper presents a study aimed to determine the cyclic performance of wood-frame shear walls sheathed with glued laminated Guadua bamboo (GLG) panels as a first step to evaluate their potential application. GLG-sheathed walls having 2:1 and 1:1 aspect ratios and three different sheathing nail spacing were tested under cyclic conditions. Parameters, such as peak shear strength, shear modulus, displacement ductility demand, and energy dissipation of the walls, were examined. Values for peak shear strength were then compared with those of walls sheathed with wood or wood-based panels. The wall aspect ratio was found to be a parameter with lesser impact than nail spacing. It was also found that the reduction in nail spacing increases to some extent the strength, stiffness, and energy dissipation, but lowers the ductility of the wall. The peak cyclic shear strength of shear walls sheathed with GLG panels was found to be within the shear strength reported for wood or wood-based panels and the tested ...

Seismic fragility analysis of reinforced concrete continuous span bridges with irregular configuration

A set of fragility curves of a class of reinforced concrete bridges with different degrees of irregularity has been generated. Eighteen bridge configurations have been identified, from regular to so-called highly irregular models. The geometric irregularity in this class of bridges is assumed to vary with the height of the piers. Using non-linear analytical models and an appropriate suite of 60 ground motions, analytical fragility curves have been generated for the individual piers of each of these 18 bridge models. Discussions have been made about the imposition of the displacement ductility demand of the piers versus the earthquake intensity as well as the bridge regularity. Comparison of the fragility curves shows that the most vulnerable bridges are the irregular bridges and high damage probability is expected for the short piers of this class of bridges. It was found that the fragility curves may be used for categorisation of regular and irregular bridges.

Risk-Based Approach for Optimum Maintenance of Bridges under Traffic and Earthquake Loads

Structures deteriorate as a result of material aging, aggressive environmental conditions, and increasing loads. During their lifetime, structures are also possibly exposed to some extreme events. The associated consequences of failure caused by progressive deterioration or extreme events can be devastating. Therefore, risk assessment and risk mitigation are necessary to keep structural performance within tolerable levels. This paper proposes an approach for assessing the time-dependent risks caused by traffic and earthquake loads and establishing the optimal preventive and essential maintenance strategies of bridges. The efficiency of the proposed approach is demonstrated using a highway bridge. Socioeconomic and environmental losses are investigated in a consequence-based framework. The vulnerability analysis under traffic loads is performed using time-dependent deterioration and traffic load models. The time-dependent failure probability for given earthquake loads is computed by comparing displacement ductility capacity and demand obtained via nonlinear dynamic analysis. The risks from 196 earthquake scenarios associated with four magnitudes and 49 earthquake strike locations are compared, and the highest one is selected as representative of the seismic risk. Based on the available maintenance options and the associated costs, the optimal lifetime essential/preventive maintenance strategies for total risk mitigation are developed.