• Earthquakes and Structures
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• v.10 no.5
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• pp.989-1012
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• 2016

The structural dynamic behavior and yield strength considering both ductility and strain rate effects are analyzed in this article. For the single-degree-of-freedom (SDOF) system, the relationship between the relative velocity and the strain rate response is deduced and the strain rate spectrum is presented. The ductility factor can be incorporated into the strain rate spectrum conveniently based on the constant-ductility velocity response spectrum. With the application of strain rate spectrum, it is convenient to consider the ductility and strain rate effects in engineering practice. The modal combination method, i.e., square root of the sum of the squares (SRSS) method, is employed to calculate the maximum strain rate of the elastoplastic multiple-degree-of-freedom (MDOF) system under uniform excitation. Considering the spatially varying ground motions, a new response spectrum method is developed by incorporating the ductility factor and strain rate into the conventional response spectrum method. In order to further analyze the effects of strain rate and ductility on structural dynamic behavior and yield strength, the cantilever beam (one-dimensional) and the triangular element (two-dimensional) are taken as numerical examples to calculate their seismic responses in time domain. Numerical results show that the permanent displacements with and without considering the strain rate effect are significantly different from each other. It is not only necessary in theory but also significant in engineering practice to take the ductility and strain rate effects into consideration.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2000.04a
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• pp.367-374
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• 2000

This study investigates the effect of hysteretic characteristics to the Inelastic Demand Spectrum (IDS) which was expressed by an acceleration(Sa) and a displacement response spectrum (Sd). Elasto Perfectly Plastic(EPP) model is used in this study and inelastic demand spectrum (Sa vs, Sd) are obtained from a given target ductility ratio. For a given target ductility ratio IDS can be obtained by using nonlinear time history analysis of single degree of system with forth five recorded earthquake ground motions for stiff soil site. The effect EPP model under demand spectrum is investigated by ductility factor and natural frequency. According to the results obtained in this study IDS has dependency on ductility factor and natural frequency.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.205-210
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• 2007

The existing capacity spectrum method (CSM) is based on the displacement based approach for seismic performance and evaluation. Currently, in the domestic and overseas standard concerning seismic design, the CSM to obtain capacity spectrum from capacity curve and demand spectrum from elastic response spectrum is presented. In the multistory building, collapse is affected more by drift than by displacement, but the existing CSM does not work for story drift. Therefore, this paper proposes an improved CSM to estimate story drift of structures through seismic performance and evaluation. It uses the ductility factor in the A-T domain to obtain constant-ductility response spectrum from earthquake response of inelastic system using the drift and capacity curve from capacity analysis of structure.

• Computers and Concrete
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• v.12 no.4
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• pp.537-552
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• 2013

Computation of flexural ductility of reinforced concrete beam sections has been proposed by taking into account strain rate sensitive constitutive behavior of concrete and steel, confinement of core concrete and degradation of cover concrete during load reversal under earthquake loading. The estimate of flexural ductility of reinforced concrete rectangular sections has been made for a wide range of tension and compression steel ratios for confined and unconfined concrete at a strain rate varying from $3.3{\times}10^{-5}$ to 1.0/sec encountered during normal and earthquake loading. The parametric studies indicated that flexural ductility factor decreases at increasing strain rates. Percentage decrease is more for a richer mix concrete with the similar reinforcement. The confinement effect has marked influence on flexural ductility and increase in ductility is more than twice for confined concrete (0.6 percent volumetric ratio of transverse steel) compared to unconfined concrete. The provisions in various codes for achieving ductility in moment resisting frames have been discussed.

• Structural Engineering and Mechanics
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• v.66 no.2
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• pp.195-201
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• 2018

From the structural safety point of view, ductility is an important parameter, a relatively high level of curvature ductility would provide to the structure an increased chance of survival against accidental impact and seismic attack. The ductility of reinforced concrete beams is very important, because it is the property that allows structures to dissipate energy in seismic zone. This paper presents a revision of an earlier formula for predicting the curvature ductility factor of unconfined HSC beams to make it simpler in the use. The new formula is compared with the earlier formula and other numerical and experimental results. The new formula regroups all parameters can affecting the curvature ductility of unconfined HSC beams and it has the same domain of application as the earlier formula.

• Earthquakes and Structures
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• v.12 no.6
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• pp.643-652
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• 2017

One of the methods to strengthen the structures against the seismic lateral loading is the employment of the composite columns. A concrete-filled tube (CFT) has the cumulative advantages of steel and concrete. Concrete-filled steel tube columns have been widely used in the moment-resisting frame (MRF) structures, located in both non-seismic zones and high-risk seismic zones. In this paper, the results of studies on two important seismic parameters of ductility and the response modification factor (RMF) of the MRFs with CFT columns are submitted. While the studies are carried out, the effects of span length-story height ratio, the strength of materials and seismic behavior of MRFs are considered. In this regard, the ductility, RMF and the strength of 36 models of the steel MRFs with CFTs are analyzed. The fiber plastic hinges numerical simulation and pushover analysis method are used in the calculations. Based on the obtained results, the RMFs suitable for the 5-, 10- and 15- story frames are proposed.

• Earthquakes and Structures
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• v.16 no.4
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• pp.469-485
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• 2019

A numerical investigation regarding local (${\mu}_L$) and story (${\mu}_S$) ductility demand evaluation of steel buildings with perimeter moment resisting frames (PMRF) and interior gravity frames (IGF), is conducted in this study. The interior connections are modeled, firstly as perfectly pinned (PP), and then as semi-rigid (SR). Three models used in the SAC steel project, representing steel buildings of low-, mid-, and high-rise, are considered. The story ductility reduction factor ($R_{{\mu}S}$) as well as the ratio ($Q_{GL}$) of $R_{{\mu}S}$ to ${\mu}_L$ are calculated. ${\mu}_L$ and ${\mu}_S$, and consequently structural damage, at the PMRF are significant reduced when the usually neglected effect of SR connections is considered; average reductions larger than 40% are observed implying that the behavior of the models with SR connections is superior and that the ductility detailing of the PMRF doesn't need to be so stringent when SR connections are considered. $R_{{\mu}S}$ is approximately constant through height for low-rise buildings, but for the others it tends to increase with the story number contradicting the same proportion reduction assumed in the Equivalent Static Lateral Method (ESLM). It is implicitly assumed in IBC Code that the overall ductility reduction factor for ductile moment resisting frames is about 4; the results of this study show that this value is non-conservative for low-rise buildings but conservative for mid- and high-rise buildings implying that the ESLM fails evaluating the inelastic interstory demands. If local ductility capacity is stated as the basis for design, a value of 0.4 for $Q_{GL}$ seems to be reasonable for low- and medium-rise buildings.

• Structural Engineering and Mechanics
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• v.68 no.2
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• pp.159-170
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• 2018

This paper aims to develop response modification factors for stiffness degrading structures by incorporating soil-structure interaction effects. A comprehensive parametric study is conducted to investigate the effects of key SSI parameters, natural period of vibration, ductility demand and hysteretic behavior on the response modification factor of soil-structure systems. The nonlinear dynamic response of 6300 soil-structure systems are studied under two ensembles of accelograms including 20 recorded and 7 synthetic ground motions. It is concluded that neglecting the stiffness degradation of structures can results in up to 22% underestimation of inelastic strength demands in soil-structure systems, leading to an unexpected high level of ductility demand in the structures located on soft soil. Nonlinear regression analyses are then performed to derive a simplified expression for estimating ductility-dependent response modification factors for stiffness degrading soil-structure systems. The adequacy of the proposed expression is investigated through sensitivity analyses on nonlinear soil-structure systems under seven synthetic spectrum compatible earthquake ground motions. A good agreement is observed between the results of the predicted and the target ductility demands, demonstrating the adequacy of the expression proposed in this study to estimate the inelastic demands of SSI systems with stiffness degrading structures. It is observed that the maximum differences between the target and average target ductility demands was 15%, which is considered acceptable for practical design purposes.

• Architectural research
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• v.7 no.1
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• pp.39-48
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• 2005

Main objective of this research is to evaluate performance of high-strength concrete (HSC) columns for ductility and strength. Eight one-third scale columns with compressive strength of 69 MPa were subjected to a constant axial load corresponding to 30 % of the column axial load capacity and a cyclic horizontal load-inducing reversed bending moment. The variables studied in this research are the volumetric ratio of transverse reinforcement (${\rho}_s=1.58$, 2.25 %), tie configuration (Type H, Type C and Type D) and tie yield strength ($f_{yh}=549$ and 779 MPa). Test results show that the flexural strength of every column exceeds the calculated flexural capacity based on the equivalent concrete stress block used in the current design code. Columns with 42 % higher amounts of transverse reinforcement than that required by seismic provisions of ACI 318-02 showed ductile behaviour, showing a displacement ductility factor (${\mu}_{{\Delta}u}$) of 3.69 to 4.85, and a curvature ductility factor (${\mu}_{{\varphi}u}$) of over 10.0. With an axial load of 30 % of the axial load capacity, it is recommended that the yield strength of transverse reinforcement be held equal to or below 549 MPa.

• Earthquakes and Structures
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• v.12 no.4
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• pp.397-407
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• 2017

To estimate the structural seismic demand, some methods are based on an equivalent linear system such as the Capacity Spectrum Method, the N2 method and the Equivalent Linearization method. Another category, widely investigated, is based on displacement correction such as the Displacement Coefficient Method and the Coefficient Method. Its basic concept consists in converting the elastic linear displacement of an equivalent Single Degree of Freedom system (SDOF) into a corresponding inelastic displacement. It relies on adequate modifying or reduction coefficient such as the inelastic deformation ratio which is usually developed for systems with known ductility factors ($C_{\mu}$) and ($C_R$) for known yield-strength reduction factor. The present paper proposes a rational approach which estimates this inelastic deformation ratio for SDOF bilinear systems by rigorous nonlinear analysis. It proposes a new inelastic deformation ratio which unifies and combines both $C_{\mu}$ and $C_R$ effects. It is defined by the ratio between the inelastic and elastic maximum lateral displacement demands. Three options are investigated in order to express the inelastic response spectra in terms of: ductility demand, yield strength reduction factor, and inelastic deformation ratio which depends on the period, the post-to-preyield stiffness ratio, the yield strength and the peak ground acceleration. This new inelastic deformation ratio ($C_{\eta}$) is describes the response spectra and is related to the capacity curve (pushover curve): normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), natural period (T), peak ductility factor (${\mu}$), and the yield strength reduction factor ($R_y$). For illustrative purposes, instantaneous ductility demand and yield strength reduction factor for a SDOF system subject to various recorded motions (El-Centro 1940 (N/S), Boumerdes: Algeria 2003). The method accuracy is investigated and compared to classical formulations, for various hysteretic models and values of the normalized yield strength coefficient (${\eta}$), post-to-preyield stiffness ratio (${\alpha}$), and natural period (T). Though the ductility demand and yield strength reduction factor differ greatly for some given T and ${\eta}$ ranges, they remain take close when ${\eta}>1$, whereas they are equal to 1 for periods $T{\geq}1s$.