• Structural Engineering and Mechanics
• /
• 제12권3호
• /
• pp.249-266
• /
• 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.

• Computers and Concrete
• /
• 제12권6호
• /
• pp.831-850
• /
• 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.

• Structural Engineering and Mechanics
• /
• 제80권5호
• /
• pp.585-594
• /
• 2021

Ductility is very important parameter in seismic design of RC members such as beams where it allows RC beams to dissipate the seismic energy. In this field, the curvature ductility has taken a large part of interest compared to the deflection ductility. For this reason, the present paper aims to propose a general formula for predicting the deflection ductility factor of RC beams under mid-span load. Firstly, the moment area theorem is used to develop a model in order to calculate the yield and the ultimate deflections; then this model is validated by using some results extracted from previous researches. Secondly, a general formula of deflection ductility factor is written based on the developed deflection expressions. The new formula is depended on curvature ductility factor, beam length, and plastic hinge length. To facilitate the use of this formula, a parametric study on the curvature ductility factor is conducted in order to write it in simple manner without the need for curvature calculations. Therefore, the deflection ductility factor can be directly calculated based on beam length, plastic hinge length, concrete strength, reinforcement ratios, and yield strength of steel reinforcement. Finally, the new formula of deflection ductility factor is compared with the model previously developed based on the moment area theorem. The results show the good performance of the new formula.

• Structural Engineering and Mechanics
• /
• 제13권4호
• /
• pp.369-385
• /
• 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.

• 한국지진공학회논문집
• /
• 제7권2호
• /
• pp.39-48
• /
• 2003

반응수정계수의 핵심구성요소인 연성계수에 대하여 통계적 분석을 수행하였다. 연성계수의 체계적인 산정을 위하여 총 1,860개의 지진기록을 수집하였다. 수집된 지진기록을 지반 전단파의 평균속도에 따라 4가지로 분류하고, 탄소성 이력거동을 가지는 단자유도 구조물에 대하여 비탄성 스펙트럼을 작성하였다. 작성된 비탄성 스펙트럼으로부터 연성계수를 구하고, 변위연성비, 토질조건, 규모 및 진앙거리가 연성계수에 미지는 영향을 분석하였다. 토질 조건별로 평균연성계수를 구하고, 산정된 연성계수의 산포도를 검토하기 위하여 변동계수를 산정하였다.

• 한국콘크리트학회:학술대회논문집
• /
• 한국콘크리트학회 1998년도 봄 학술발표회논문집(II)
• /
• pp.433-438
• /
• 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.

• 산업기술연구
• /
• 제26권A호
• /
• pp.153-161
• /
• 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.

• Computers and Concrete
• /
• 제16권2호
• /
• pp.191-207
• /
• 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.

• 한국지진공학회:학술대회논문집
• /
• 한국지진공학회 2003년도 추계 학술발표회논문집
• /
• pp.231-238
• /
• 2003

The overstrength factor and the ductility factor are the two important factors that determines response modification factors used in current seismic codes. The objective of this paper is to obtain the overstrength and ductility factors of special concentric braced frames. For this purpose pushover analysis is performed with model structures until the maximum inter-story drift reaches 2.5% of story height. According to the analysis results, the overstrength factors increase as the height of structures decreases and the span length increases. Ductility factors for mid-story structures turns out to be higher than the other structures and span length does not contribute much to ductility factors.

• 한국지진공학회논문집
• /
• 제8권4호
• /
• pp.11-20
• /
• 2004

반응수정계수의 핵심구성요소인 연성계수를 토질조건에 따라 제시하였다. 47개의 지진에서 얻어진 총 1,860개의 지진기록이 사용되었으며, 지반 전단파의 평균속도에 따라 4가지의 토질조건을 고려하였다. 이러한 분류는 현재 사용되고 있는 UBC(1997), NEHRP(1997) 및 IBC 200(1997)의 토질조건과 일치한다. 통계적 회귀분석으로부터, 토질조건에 따른 연성계수를 평가하기 위한 단순화된 식이 제안되었다. 제안된 식은 상대적으로 간단하면서도 평균연성계수와 잘 일치하는 결과를 보였다. 제안된 식에 근거하여, 현재의 기준과 일치하는 토질조건에 따른 연성계수를 평가할 수 있을 것으로 기대한다