• Earthquakes and Structures
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• v.3 no.1
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• pp.59-81
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• 2012

A ductility inverse-mapping method for SDOF systems including passive dampers is proposed which enables one to find the maximum acceleration of ground motion for the prescribed maximum response deformation. In the conventional capacity spectrum method, the maximum response deformation is computed through iterative procedures for the prescribed maximum acceleration of ground motion. This is because the equivalent linear model for response evaluation is described in terms of unknown maximum deformation. While successive calculations are needed, no numerically unstable iterative procedure is required in the proposed method. This ductility inverse-mapping method is applied to an SDOF model of bilinear hysteresis. The SDOF models without and with passive dampers (viscous, viscoelastic and hysteretic dampers) are taken into account to investigate the effectiveness of passive dampers for seismic retrofitting of building structures. Since the maximum response deformation is the principal parameter and specified sequentially, the proposed ductility inverse-mapping method is suitable for the implementation of the performance-based design.

• Smart Structures and Systems
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• v.21 no.4
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• pp.389-395
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• 2018

This paper presents the application of a semi-active fuzzy based control system for seismic response reduction of a single degree-of-freedom (SDOF) framed structure using a Magnetorheological (MR) damper. Semi-active vibration control with MR dampers has been shown to be a viable approach to protect building structures from earthquake excitation. Moreover, intelligent damping systems based on soft-computing techniques such as fuzzy logic models have the inherent robustness to deal with typical uncertainties and non-linearities present in civil engineering structures. Thus, the proposed semi-active control system uses fuzzy logic based models to simulate the behavior of MR damper and also to develop the control algorithm that computes the required control signal to command the actuator. The results of the numerical simulations show the effectiveness of the suggested semi-active control system in reducing the response of the SDOF structure.

• Earthquakes and Structures
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• v.9 no.3
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• pp.455-480
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• 2015

In the last decade, displacement-based (DB) methods have become established design procedures for reinforced concrete (RC) structures. They use strain and displacement measures as seismic performance control parameters. As for other simplified seismic design methods, it is of great interest to prove if they are usually conservative in respect to more refined, nonlinear, time history analyses, and can estimate design parameters with acceptable accuracy. In this paper, the current Direct Displacement-Based Design (DDBD) procedure is evaluated for designing simple single degree of freedom (SDOF) systems with specific reference to simply supported RC bridge piers. Using different formulations proposed in literature for the equivalent viscous damping and spectrum reduction factor, a parametric study is carried out on a comprehensive set of SDOF systems, and an average error chart of the method is derived allowing prediction of the expected error for an ample range of design cases. Following the chart, it can be observed that, for the design of actual RC bridge piers, underestimation errors of the DDBD method are very low, while the overestimation range of the simplified displacement-based procedure is strongly dependent on design ductility.

• Structural Engineering and Mechanics
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• v.38 no.2
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• pp.211-229
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• 2011

In this paper, we present a new explicit procedure using periodic cubic B-spline interpolation polynomials to solve linear and nonlinear dynamic equation of motion governing single degree of freedom (SDOF) systems. In the proposed approach, a straightforward formulation was derived from the approximation of displacement with B-spline basis in a fluent manner. In this way, there is no need to use a special pre-starting procedure to commence solving the problem. Actually, this method lies in the case of conditionally stable methods. A simple step-by-step algorithm is implemented and presented to calculate dynamic response of SDOF systems. The validity and effectiveness of the proposed method is demonstrated with four examples. The results were compared with those from the numerical methods such as Duhamel integration, Linear Acceleration and also Exact method. The comparison shows that the proposed method is a fast and simple procedure with trivial computational effort and acceptable accuracy exactly like the Linear Acceleration method. But its power point is that its time consumption is notably less than the Linear Acceleration method especially in the nonlinear analysis.

• Earthquakes and Structures
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• v.16 no.4
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• pp.487-499
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• 2019

Energy-based seismic design of structures has gradually become prominent in today's structural engineering investigations because of being more rational and reliable when it is compared to traditional force-based and displacement-based methods. Energy-based approaches have widely taken place in many previous studies and investigations and undoubtedly, they are going to play more important role in future seismic design codes, too. This paper aims to compute the maximum earthquake energy input to elastic single-degree-of-freedom (SDOF) systems for selected real ground motion records. A data set containing 100 real ground motion records which have the same site soil profiles has been selected from Pacific Earthquake Research (PEER) database. Response time history (RTH) analyses have been conducted for elastic SDOF systems having a constant damping ratio and natural periods of 0.1 s to 3.0 s. Totally 3000 RTH analyses have been performed and the maximum mass normalized earthquake input energy values for all records have been computed. Previous researchers' approaches have been compared to the results of RTH analyses and an approach which considers the pseudo-spectral velocity with Arias Intensity has been proposed. Graphs of the maximum earthquake input energy versus the maximum pseudo-spectral velocity have been obtained. The results show that there is a good agreement between the maximum input energy demands of RTH analysis and the other approaches and the maximum earthquake input energy is a relatively stable response parameter to be used for further seismic design and evaluations.

• Structural Engineering and Mechanics
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• v.6 no.5
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• pp.473-484
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• 1998

The first and second moments of response variables for SDOF systems with hysteretic nonlinearity are obtained by a direct linearization procedure. This adaptation in the implementation of well-known statistical linearization methods, provides concise, model-independent linearization coefficients that are well-suited for numerical solution. The method may be applied to systems which incorporate any hysteresis model governed by a differential constitutive equation, and may be used for zero or non-zero mean random vibration. The implementation eliminates the effort of analytically deriving specific linearization coefficients for new hysteresis models. In doing so, the procedure of stochastic analysis is made independent from the task of physical modeling of hysteretic systems. In this study, systems with three different hysteresis models are analyzed under various zero and non-zero mean Gaussian White noise inputs. Results are shown to be in agreement with previous linearization studies and Monte Carlo Simulation.

• Structural Engineering and Mechanics
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• v.46 no.6
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• pp.755-773
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• 2013

One of the main requirements of the seismic design codes must be its easy application by structural engineers. The use of practically-applicable models or simplified models as single-degree-of-freedom (SDOF) systems is a good alternative to achieve this condition. In this study, deterministic and probabilistic response transformation factors are obtained to evaluate the response in terms of maximum ductility and maximum interstory drifts of multi-degree-of-freedom (MDOF) systems based on the response of equivalent SDOF systems. For this aim, five steel frames designed with the Mexican City Building Code (MCBC) as well as their corresponding equivalent SDOF systems (which represent the characteristics of the frames) are analyzed. Both structural systems are subjected to ground motions records. For the MDOF and the simplified systems, incremental dynamic analyses IDAs are developed in first place, then, structural demand hazard curves are obtained. The ratio between the IDAs curves corresponding to the MDOF systems and the curves corresponding to the simplified models are used to obtain deterministic response transformation factors. On the other hand, demand hazard curves are used to calculate probabilistic response transformation factors. It was found that both approaches give place to similar results.

• Earthquakes and Structures
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• v.7 no.6
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• pp.1283-1301
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• 2014

Ground motion modification is extensively used in seismic design of civil infrastructure, especially where few or no recorded ground motions representative of the design scenario are available. A site in Los Angeles, California is used as a study site and 28 ground motions consistent with the design earthquake scenario are selected. The suite of 28 ground motions is scaled and modified in the time domain (TD) and frequency domain (FD) before being used as input to a bilinear SDOF system. The median structural responses to the suites of scaled, TD-modified, and FD-modified motions, along with ratios of he modified-to-scaled responses, are investigated for SDOF systems with different periods, strength ratios, and post-yield stiffness ratios. Overall, little difference (less than 20%) is observed in the peak structural accelerations, velocities, and displacements; displacement ductility; and absolute accelerations caused by the TD-modified and FD-modified motions when compared to the responses caused by the scaled motions. The energy absorbed by the system when the modified motions are used as input is more than 20% greater than when scaled motions are used as input. The observed trends in the structural response are predominantly the result of changes in the ground motion characteristics caused by modification.

• Structural Engineering and Mechanics
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• v.85 no.5
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• pp.655-664
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• 2023

Reinforced concrete (RC) shear wall structures are one of the most widely used structural systems to resist seismic loading all around the world. Although there have been several efforts to provide conceptually simple procedures to reasonably assess the seismic demands of structures over recent decades, it seems that lesser effort has been put on a number of structural forms such as RC shear wall structures. Therefore, this study aims to represent a simple linear response spectrum-based method which can acceptably predict the nonlinear displacements of a non-ductile RC shear wall structure subjected to an individual ground motion record. An effective period and an equivalent damping ratio are introduced as the dynamic characteristics of an equivalent linear SDOF system relevant to the main structure. By applying the fundamental mode participation factor of the original MDOF structure to the linear spectral response of the equivalent SDOF system, an acceptable estimation of the nonlinear displacement response is obtained. Subsequently, the accuracy of the proposed method is evaluated by comparison with another approximate method which is based on linear response spectrum. Results show that the proposed method has better estimations for maximum nonlinear responses and is more utilizable and applicable than the other one.

• Earthquakes and Structures
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• v.4 no.4
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• pp.365-381
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• 2013

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.