Ductility and ductility reduction factor for MDOF systems

Reyes-Salazar, Alfredo Techno-Press 2002 Structural Engineering and Mechanics, An Int'l Jou Vol.13 No.4

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.

Estimation of Curvature and Displacement Ductility in Reinforced Concrete Buildings

M. Hakan Arslan 대한토목학회 2012 KSCE JOURNAL OF CIVIL ENGINEERING Vol.16 No.5

Ensuring sufficient ductility in building load bearing systems and elements of the load bearing system is quite important for their seismic performance. The Seismic Codes stipulate that certain requirements must be met to maintain ductility values above a certain level. The purpose of this study is to determine how ductility values of both elements and load bearing systems vary as parameters related to the conditions specified in the codes change and as estimates of these values are used. With this aim in mind, the curvature ductility in columns and beams of a four-storey Reinforced Concrete (RC) building differs depending on parameters that include the axial load level, longitudinal reinforcement, transverse reinforcement, compression bar ratio and concrete strength. The value of the curvature ductility was found to vary according to the number of parameters and variance range, which was found to be 60 and 135in the beam section and column section, respectively. Later, a pushover analysis was applied to 540 different statuses of the sample RC system for the same parameters, and the ratio variations and respective displacement (global) ductility of the frames were calculated. The relationship between obtained ductility values with the parameters, as well as the accuracy of the established model,were estimated using regression analyses (Multi-linear and Nonlinear Regression (MLR, NLR)) and 11 various Artificial Neural Networks (ANN) methods. According to the estimation methods, it was found that the test parameters that significantly affect curvature ductility values are not sufficient to explain the displacement ductility values. On the other hand, it was seen that the estimation strength of ANNs proved to be greater than MLR in both curvature ductility and displacement ductility. Outcomes also indicated that the NLR model exhibits superior performance for estimating displacement ductility.

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

이형준 사단법인 한국계산역학회 2013 Computers and Concrete, An International Journal Vol.12 No.6

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.

Ductile capacity study of buckling-restrained braced steel frame with rotational connections

Mingming Jia,Jinzhou He,Dagang Lu 국제구조공학회 2023 Steel and Composite Structures, An International J Vol.46 No.3

The maximum ductility and cumulative ductility of connection joints of Buckling-Restrained Braced Frames (BRBF) are critical to the structural overall performance, which should be matched with the BRB ductility. The two-story and one-span BRBF with a one-third scale was tested under cyclic quasi-static loading, and the top-flange beam splice (TFBS) rotational connections were proposed and adopted in BRBF. The deformation capacity of TFBS connections was observed during the test, and the relationship between structural global ductility and local connection ductility was studied. The rotational capacity of the beam-column connections and the stability performance of the BRBs are highly relevant to the structural overall performance. The hysteretic curves of BRBF are stable and full under large displacement demand imposed up to 2% story drift, and energy is dissipated as the large plastic deformation developed in the structural components. The BRBs acted as fuses and yielded first, and the cumulative plastic ductility (CPD) of BRBs is 972.6 of the second floor and 439.7 of the first floor, indicating the excellent energy dissipation capacity of BRBs. Structural members with good local ductility ensure the large global ductility of BRBF. The ductile capacity and hysteretic behavior of BRBF with TFBS connections were compared with those of BRBF with Reduced Beam Section (RBS) connections in terms of the experimental results.

Deflection ductility of RC beams under mid-span load

Haytham Bouzid,Benferhat Rabia,Tahar Hassaine Daouadji 국제구조공학회 2021 Structural Engineering and Mechanics, An Int'l Jou Vol.80 No.5

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.

Effect of Thermal Cycle and Nitrogen Content on the Hot Ductility of Boron-bearing Steel

Cho, Kyung Chul,Mun, Dong Jun,Kang, Myeong Hun,Lee, Jae Sang,Park, Joong Kil,Koo, Yang Mo The Iron and Steel Institute of Japan 2010 ISIJ international Vol.50 No.6

<P>Hot ductility of Boron (B)-bearing steel has been examined in view of slab corner cracking problem. Addition of B to the low carbon steel reduced its hot ductility under a thermal cycle in which samples were cooled directly to the test temperature before straining. The change in hot ductility of B-bearing steel with deformation temperature showed one trough in the temperature range of 800–1000°C, which covered the lower temperature region of austenite single phase (region (I)), and near the austenite/ferrite transformation temperature (Ae<SUB>3</SUB>) (region (II)). An abrupt temperature decrease and reheating before straining heavily deteriorated the hot ductility of B-bearing steel in the region (I). In all steels, the strain concentration in the film-like ferrite primarily reduced hot ductility in region (II) regardless of the addition of B and the thermal cycles before straining. The ductility reduction of B-bearing steel is caused by the distribution and amount of BN precipitation, which is determined by the thermal cycles and the N content. Increase in the N content remarkably reduced hot ductility of B-bearing steel in region (I), where the behavior of BN precipitates controlled hot ductility. The results shows that the improvement of hot ductility in B-bearing steel can be attained by decreasing the N content and by avoiding an abrupt temperature decrease in the secondary cooling stage of the slab after solidification.</P>

Ductility-based design approach of tall buildings under wind loads

Fouad Elezaby,Ashraf El Damatty 한국풍공학회 2020 Wind and Structures, An International Journal (WAS Vol.31 No.2

The wind design of buildings is typically based on strength provisions under ultimate loads. This is unlike the ductility-based approach used in seismic design, which allows inelastic actions to take place in the structure under extreme seismic events. This research investigates the application of a similar concept in wind engineering. In seismic design, the elastic forces resulting from an extreme event of high return period are reduced by a load reduction factor chosen by the designer and accordingly a certain ductility capacity needs to be achieved by the structure. Two reasons have triggered the investigation of this ductility-based concept under wind loads. Firstly, there is a trend in the design codes to increase the return period used in wind design approaching the large return period used in seismic design. Secondly, the structure always possesses a certain level of ductility that the wind design does not benefit from. Many technical issues arise when applying a ductility-based approach under wind loads. The use of reduced design loads will lead to the design of a more flexible structure with larger natural periods. While this might be beneficial for seismic response, it is not necessarily the case for the wind response, where increasing the flexibility is expected to increase the fluctuating response. This particular issue is examined by considering a case study of a sixty-five-story high-rise building previously tested at the Boundary Layer Wind Tunnel Laboratory at the University of Western Ontario using a pressure model. A three-dimensional finite element model is developed for the building. The wind pressures from the tested rigid model are applied to the finite element model and a time history dynamic analysis is conducted. The time history variation of the straining actions on various structure elements of the building are evaluated and decomposed into mean, background and fluctuating components. A reduction factor is applied to the fluctuating components and a modified time history response of the straining actions is calculated. The building components are redesigned under this set of reduced straining actions and its fundamental period is then evaluated. A new set of loads is calculated based on the modified period and is compared to the set of loads associated with the original structure. This is followed by non-linear static pushover analysis conducted individually on each shear wall module after redesigning these walls. The ductility demand of shear walls with reduced cross sections is assessed to justify the application of the load reduction factor “R”.

On the Ductility of High-Strength Concrete Beams

장일영,박훈규,김성수,김종회,김용곤 한국콘크리트학회 2008 International Journal of Concrete Structures and M Vol.2 No.2

Ductility is important in the design of reinforced concrete structures. In seismic design of reinforced concrete members, it is necessary to allow for relatively large ductility so that the seismic energy is absorbed to avoid shear failure or significant degradation of strength even after yielding of reinforcing steels in the concrete member occurs. Therefore, prediction of the ductility should be as accurate as possible. The principal aim of this paper is to present the basic data for the ductility evaluation of reinforced high-strength concrete beams. Accordingly, 23 flexural tests were conducted on full-scale structural concrete beam specimens having concrete compressive strength of 40, 60, and 70 MPa. The test results were then reviewed in terms of flexural capacity and ductility. The effect of concrete compressive strength, web reinforcement ratio, tension steel ratio, and shear span to beam depth ratio on ductility were investigated experimentally.

On the Ductility of High-Strength Concrete Beams

Jang, Il-Young,Park, Hoon-Gyu,Kim, Sung-Soo,Kim, Jong-Hoe,Kim, Yong-Gon Korea Concrete Institute 2008 International Journal of Concrete Structures and M Vol.2 No.2

Ductility is important in the design of reinforced concrete structures. In seismic design of reinforced concrete members, it is necessary to allow for relatively large ductility so that the seismic energy is absorbed to avoid shear failure or significant degradation of strength even after yielding of reinforcing steels in the concrete member occurs. Therefore, prediction of the ductility should be as accurate as possible. The principal aim of this paper is to present the basic data for the ductility evaluation of reinforced high-strength concrete beams. Accordingly, 23 flexural tests were conducted on full-scale structural concrete beam specimens having concrete compressive strength of 40, 60, and 70MPa. The test results were then reviewed in terms of flexural capacity and ductility. The effect of concrete compressive strength, web reinforcement ratio, tension steel ratio, and shear span to beam depth ratio on ductility were investigated experimentally.

Flexural ductility and deformability of reinforced and prestressed concrete sections

Francis T.K. Au,Cliff C.Y. Leung,Albert K.H. Kwan 사단법인 한국계산역학회 2011 Computers and Concrete, An International Journal Vol.8 No.4

In designing a flexural member for structural safety, both the flexural strength and ductility have to be considered. For this purpose, the flexural ductility of reinforced concrete sections has been studied quite extensively. As there have been relatively few studies on the flexural ductility of prestressed concrete sections, it is not well understood how various structural parameters affect the flexural ductility. In the present study, the full-range flexural responses of reinforced and prestressed concrete sections are analyzed taking into account the nonlinearity and stress-path dependence of constitutive materials. From the numerical results, the effects of steel content, yield strength and degree of prestressing on the yield curvature and ultimate curvature are evaluated. It is found that whilst the concept of flexural ductility in terms of the ductility factor works well for reinforced sections, it can be misleading when applied to prestressed concrete sections. For prestressed concrete sections, the concept of flexural deformability in terms of ultimate curvature times overall depth of section may be more appropriate.