• Title, Summary, Keyword: ductility factor

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Investigation of dynamic P-Δ effect on ductility factor

  • Han, Sang Whan;Kwon, Oh-Sung;Lee, Li-Hyung
    • Structural Engineering and Mechanics
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    • v.12 no.3
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    • pp.249-266
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    • 2001
  • Current seismic design provisions allow structures to deform into inelastic range during design level earthquakes since the chance to meet such event is quite rare. For this purpose, design base shear is defined in current seismic design provisions as the value of elastic seismic shear force divided by strength reduction factor, R (${\geq}1$). Strength reduction factor generally consists of four different factors, which can account for ductility capacity, overstrength, damping, and redundancy inherent in structures respectively. In this study, R factor is assumed to account for only the ductility rather than overstrength, damping, and redundancy. The R factor considering ductility is called "ductility factor" ($R_{\mu}$). This study proposes ductility factor with correction factor, C, which can account for dynamic P-${\Delta}$ effect. Correction factor, C is established as the functional form since it requires computational efforts and time for calculating this factor. From the statistical study using the results of nonlinear dynamic analysis for 40 earthquake ground motions (EQGM) it is shown that the dependence of C factor on structural period is weak, whereas C factor is strongly dependant on the change of ductility ratio and stability coefficient. To propose the functional form of C factor statistical study is carried out using 79,920 nonlinear dynamic analysis results for different combination of parameters and 40 EQGM.

Predictions of curvature ductility factor of doubly reinforced concrete beams with high strength materials

  • Lee, Hyung-Joon
    • Computers and Concrete
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    • v.12 no.6
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    • pp.831-850
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    • 2013
  • The high strength materials have been more widely used in reinforced concrete structures because of the benefits of the mechanical and durable properties. Generally, it is known that the ductility decreases with an increase in the strength of the materials. In the design of a reinforced concrete beam, both the flexural strength and ductility need to be considered. Especially, when a reinforced concrete structure may be subjected an earthquake, the members need to have a sufficient ductility. So, each design code has specified to provide a consistent level of minimum flexural ductility in seismic design of concrete structures. Therefore, it is necessary to assess accurately the ductility of the beam sections with high strength materials in order to ensure the ductility requirement in design. In this study, the effects of concrete strength, yield strength of reinforcement steel and amount of reinforcement including compression reinforcement on the complete moment-curvature behavior and the curvature ductility factor of doubly reinforcement concrete beam sections have been evaluated and a newly prediction formula for curvature ductility factor of doubly RC beam sections has been developed considering the stress of compression reinforcement at ultimate state. Based on the numerical analysis results, the proposed predictions for the curvature ductility factor are verified by comparisons with other prediction formulas. The proposed formula offers fairly accurate and consistent predictions for curvature ductility factor of doubly reinforced concrete beam sections.

Ductility and ductility reduction factor for MDOF systems

  • Reyes-Salazar, Alfredo
    • Structural Engineering and Mechanics
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    • v.13 no.4
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    • pp.369-385
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    • 2002
  • Ductility capacity is comprehensively studied for steel moment-resisting frames. Local, story and global ductility are being considered. An appropriate measure of global ductility is suggested. A time domain nonlinear seismic response algorithm is used to evaluate several definitions of ductility. It is observed that for one-story structures, resembling a single degree of freedom (SDOF) system, all definitions of global ductility seem to give reasonable values. However, for complex structures it may give unreasonable values. It indicates that using SDOF systems to estimate the ductility capacity may be a very crude approximation. For multi degree of freedom (MDOF) systems some definitions may not be appropriate, even though they are used in the profession. Results also indicate that the structural global ductility of 4, commonly used for moment-resisting steel frames, cannot be justified based on this study. The ductility of MDOF structural systems and the corresponding equivalent SDOF systems is studied. The global ductility values are very different for the two representations. The ductility reduction factor $F_{\mu}$ is also estimated. For a given frame, the values of the $F_{\mu}$ parameter significantly vary from one earthquake to another, even though the maximum deformation in terms of the interstory displacement is roughly the same for all earthquakes. This is because the $F_{\mu}$ values depend on the amount of dissipated energy, which in turn depends on the plastic mechanism, formed in the frames as well as on the loading, unloading and reloading process at plastic hinges. Based on the results of this study, the Newmark and Hall procedure to relate the ductility reduction factor and the ductility parameter cannot be justified. The reason for this is that SDOF systems were used to model real frames in these studies. Higher mode effects were neglected and energy dissipation was not explicitly considered. In addition, it is not possible to observe the formation of a collapse mechanism in the equivalent SDOF systems. Therefore, the ductility parameter and the force reduction factor should be estimated by using the MDOF representation.

Statistical Study of Ductility Factors for Elastic Perfectly Plastic SDOF Systems (탄소성 단자유도 구조물에 대한 연성계수의 통계적 분석)

  • Kang, Cheol-Kyu;Choi, Byong-Jeong
    • Journal of the Earthquake Engineering Society of Korea
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    • v.7 no.2
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    • pp.39-48
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    • 2003
  • This paper present a summary of the results of statistical study of the ductility factor which is key component of response modification factor(R). To compute the ductility factor, a group of 1,860 ground motions recorded from various earthquake was considered. Based on the local site conditions at the recording station, ground motions were classified into four groups according to average shear wave velocity. Inleastic spectrum were computed for elastic perfectly plastic SDOF systems undergoing different level of inelastic deformation and period. Ductility factors were calculated by deviding elastic response spectrum by inelastic response spectrum. The influence f displacement ductility ratio, site condition, magnitude and epicentral distance on ductility factors were studied. The coefficient of variation was computed to evaluated the dispersion of ductility factors as the defined ratio of the standard deviation to the mean.

Evaluation of the Response Modification Factor for RC Wall-type Structures (철근콘크리트 벽식 구조물의 반응수정계수 평가에 관한 연구)

  • 한상환;이리형;오영훈;천영수
    • Proceedings of the Korea Concrete Institute Conference
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    • pp.433-438
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    • 1998
  • Design lateral strength calculated by current seismic design code is prescribed to be much lower than the force level required for a structure to respond elastically during design level earthquake ground motion. Present procedures for calculating seismic design forces are based on the use of elastic spectra reduced by a strength reduction factor known as "response modification factor, R". This factor accounts for the inherent ductility, overstrength, redundancy, and damping of a structural system. This study considers ductility and overstrength of the wall-type structure for investigating R factor. This means that R factor is determined from the product of "ductility-based R factor($R_$\mu$$) and overstrength factor($R_s$). $R_$\mu$$ factor is calibrated to attain the targer ductility ratio (system ductility capacity) and produced in the from of $R_$\mu$$ spectra considering the influence of target ductility, natural period, and hysteretic model. On the other hand, $R_s$ is more difficult to quantify, since it depends on both material and system-dependent uncertain parameters. In this study Rs factor was determined from the result of push-over analysis.-over analysis.

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Propositions of the Ductility Reduction Factor for Estimating Inelastic Displacement Responses of Bridge Structures (교량구조물의 비탄성변위응답 평가를 위한 연성도감소계수 산정식 제안)

  • Song, Jong-Keol;Kim, Hak-Soo
    • Journal of Industrial Technology
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    • v.26 no.A
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    • pp.153-161
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    • 2006
  • The main objective of this study was to derive a formula of ductility reduction factor, expressed as $R_{\mu}$. To attain this objective, a study comprised reduction factors computed for stiffness degrading systems undergoing different levels of ductility and to investigate an accuracy of the formula. Based on this study, the main conclusions can be summarized :(1) The ductility reduction factor is primarily affected by the period of the system and the displacement ductility ratio. (2) The proposed formula is simpler and the inelastic deformations of bridge structures are better than those by the others formulas we used before.

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Probabilistic models for curvature ductility and moment redistribution of RC beams

  • Baji, Hassan;Ronagh, Hamid Reza
    • Computers and Concrete
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    • v.16 no.2
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    • pp.191-207
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    • 2015
  • It is generally accepted that, in the interest of safety, it is essential to provide a minimum level of flexural ductility, which will allow energy dissipation and moment redistribution as required. If one wishes to be uniformly conservative across all of the design variables, curvature ductility and moment redistribution factor should be calculated using a probabilistic method, as is the case for other design parameters in reinforced concrete mechanics. In this study, simple expressions are derived for the evaluation of curvature ductility and moment redistribution factor, based on the concept of demand and capacity rotation. Probabilistic models are then derived for both the curvature ductility and the moment redistribution factor, by means of central limit theorem and through taking advantage of the specific behaviour of moment redistribution factor as a function of curvature ductility and plastic hinge length. The Monte Carlo Simulation (MCS) method is used to check and verify the results of the proposed method. Although some minor simplifications are made in the proposed method, there is a very good agreement between the MCS and the proposed method. The proposed method could be used in any future probabilistic evaluation of curvature ductility and moment redistribution factors.

Evaluation of Site-dependent Ductility Factors for Elastic Perfectly Plastic SDOF Systems (토질조건에 따른 탄소성 단자유도 구조물의 연성계수 평가)

  • Kang, Cheol-Kyu;Choi, Byong-Jeong
    • Journal of the Earthquake Engineering Society of Korea
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    • v.8 no.4
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    • pp.11-20
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    • 2004
  • This paper suggests the site-dependent ductility factor which is a key component of response modification factor(R). To compute the ductility factor, a group of 1,860 ground motions recorded from 47 earthquake was considered. Based on the local site conditions at the recording station, ground motions were classified into four groups according to average shear wave velocity. This site classification was consistent with site categories of the UBC(1997), NEHRP(1997) and IBC 2000(1997). Based on the results of regression analysis, a simplified equations were proposed to compute site-dependent ductility factors. The proposed equations were relatively simple and provide a good estimation of mean ductility factors. Based on the proposed equation, ductility factors considering the site conditions can be evaluated in accordance with the present building codes.

Evaluation of Ductility Factors for MDOF Systems in Special Steel Moment Resisting Frames (철골 연성 모멘트 골조에 대한 다자유도 시스템의 연성계수 평가)

  • Kang, Cheol-Kyu;Han, Young-Cheol
    • Journal of the Earthquake Engineering Society of Korea
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    • v.8 no.6
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    • pp.13-22
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    • 2004
  • Ductiluty factor has played an important role in seismic design as it is key component of response modification factor(R). In this stuty, ductility factors() are calculated by multiplying ductility factor for SDOF systems() and MDOF modification factors(). Ductility factors() for SDOF systems are computed from nonlinear dynamic analysis undergoing different level of displacement ductiluty demands and period when subjected to a large number of recorded earthquake ground motions. The MDOF modification factors() are proposed to account for the MDOF systems, based on previous studies. A total of 108 prototype steel frames are designed to investigate the ductility factors considering the number of stories(4, 8 and 16-stories), framing system(Perimeter Frames, PF and Distributed Frames, DF), failure mechanism(Strong-Column Weak-Beam, SCWB and Weak-Column Strong-Beam, WCSB), soil profiles(SA, SC and SE in UBC 1997) and seismic zone factors(Z=0.075, 0.2 and 0.4 in UBC 1997). It is shown that the number of stories, failure mechanisms (SCWB, WCSB), and soil profiles have great influence on the ductility factors, however, the structural system(Perimeter frames, Distributed frames), and seismic zones have no influence on the ductility factors.

Prediction of curvature ductility factor for FRP strengthened RHSC beams using ANFIS and regression models

  • Komleh, H. Ebrahimpour;Maghsoudi, A.A.
    • Computers and Concrete
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    • v.16 no.3
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    • pp.399-414
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    • 2015
  • Nowadays, fiber reinforced polymer (FRP) composites are widely used for rehabilitation, repair and strengthening of reinforced concrete (RC) structures. Also, recent advances in concrete technology have led to the production of high strength concrete, HSC. Such concrete due to its very high compression strength is less ductile; so in seismic areas, ductility is an important factor in design of HSC members (especially FRP strengthened members) under flexure. In this study, the Adaptive Neuro-Fuzzy Inference System (ANFIS) and multiple regression analysis are used to predict the curvature ductility factor of FRP strengthened reinforced HSC (RHSC) beams. Also, the effects of concrete strength, steel reinforcement ratio and externally reinforcement (FRP) stiffness on the complete moment-curvature behavior and the curvature ductility factor of the FRP strengthened RHSC beams are evaluated using the analytical approach. Results indicate that the predictions of ANFIS and multiple regression models for the curvature ductility factor are accurate to within -0.22% and 1.87% error for practical applications respectively. Finally, the effects of height to wide ratio (h/b) of the cross section on the proposed models are investigated.