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.

Effect of confinement on flexural ductility design of concrete beams

X.C. Chen,Z.Z. Bai,F.T.K. Au 사단법인 한국계산역학회 2017 Computers and Concrete, An International Journal Vol.20 No.2

Seismic design of reinforced concrete (RC) structures requires a certain minimum level of flexural ductility. For example, Eurocode EN1998-1 directly specifies a minimum flexural ductility for RC beams, while Chinese code GB50011 limits the equivalent rectangular stress block depth ratio at peak resisting moment to achieve a certain nominal minimum flexural ductility indirectly. Although confinement is effective in improving the ductility of RC beams, most design codes do not provide any guidelines due to the lack of a suitable theory. In this study, the confinement for desirable flexural ductility performance of both normal- and high-strength concrete beams is evaluated based on a rigorous full-range moment-curvature analysis. An effective strategy is proposed for flexural ductility design of RC beams taking into account confinement. The key parameters considered include the maximum difference of tension and compression reinforcement ratios, and maximum neutral axis depth ratio at peak resisting moment. Empirical formulae and tables are then developed to provide guidelines accordingly.

Effects of strain hardening of steel reinforcement on flexural strength and ductility of concrete beams

Ho, J.C.M.,Au, F.T.K.,Kwan, A.K.H. Techno-Press 2005 Structural Engineering and Mechanics, An Int'l Jou Vol.19 No.2

In the design of reinforced concrete beams, it is a standard practice to use the yield stress of the steel reinforcement for the evaluation of the flexural strength. However, because of strain hardening, the tensile strength of the steel reinforcement is often substantially higher than the yield stress. Thus, it is a common belief that the actual flexural strength should be higher than the theoretical flexural strength evaluated with strain hardening ignored. The possible increase in flexural strength due to strain hardening is a two-edge sword. In some cases, it may be treated as strength reserve contributing to extra safety. In other cases, it could lead to greater shear demand causing brittle shear failure of the beam or unexpected greater capacity of the beam causing violation of the strong column-weak beam design philosophy. Strain hardening may also have certain effect on the flexural ductility. In this paper, the effects of strain hardening on the post-peak flexural behaviour, particularly the flexural strength and ductility, of reinforced normal- and high-strength concrete beams are studied. The results reveal that the effects of strain hardening could be quite significant when the tension steel ratio is relatively small.

Combined strain gradient and concrete strength effects on flexural strength and ductility design of RC columns

M.T. Chen,J. C. M. Ho 사단법인 한국계산역학회 2015 Computers and Concrete, An International Journal Vol.15 No.4

The stress-strain relationship of concrete in flexure is one of the essential parameters in assessing the flexural strength and ductility of reinforced concrete (RC) columns. An overview of previous research studies revealed that the presence of strain gradient would affect the maximum concrete stress developed in flexure. However, no quantitative model was available to evaluate the strain gradient effect on concrete under flexure. Previously, the authors have conducted experimental studies to investigate the strain gradient effect on maximum concrete stress and respective strain and developed two strain-gradient-dependent factors k3 and ko for modifying the flexural concrete stress-strain curve. As a continued study, the authors herein will extend the investigation of strain gradient effects on flexural strength and ductility of RC columns to concrete strength up to 100 MPa by employing the strain-gradient-dependent concrete stress-strain curve using nonlinear moment-curvature analysis. It was evident from the results that both the flexural strength and ductility of RC columns are improved under strain gradient effect. Lastly, for practical engineering design purpose, a new equivalent rectangular concrete stress block incorporating the combined effects of strain gradient and concrete strength was proposed and validated. Design formulas and charts have also been presented for flexural strength and ductility of RC columns.

철근콘크리트 휨부재의 철근 인장변형률에 따른 곡률연성도 예측

이대형,배수호 한국콘크리트학회 2024 콘크리트학회논문집 Vol.36 No.2

이 연구의 목적은 콘크리트 강도 및 철근의 항복강도, 철근량에 따른 철근콘크리트 휨부재의 연성거동을 예측하기 위한 곡률연성도 관계식을 제안하는 것이다. 철근콘크리트 구조는 극한상태에서 연성파괴를 유도하는 것이 가장 중요한 설계개념으로 이를 위해 개정된 설계기준에서는 철근의 항복강도에 따라 최소허용인장변형률 및 인장지배변형률 한계를 규정하고 있다. 따라서 배근된 철근의 압축 콘크리트 파괴시 인장변형률과 항복변형률의 비를 변수로 곡률연성도 계산식을 제시하였다. 이를 위해 콘크리트 강도 및 철근의 항복강도가 곡률연성에 미치는 영향을 조사하였다. 철근의 인장변형률을 기준으로 한 경우 콘크리트의 강도에 따른 곡률연성도의 차이는 미미하였으며 철근의 항복강도가 클 경우 곡률연성도는 감소하였다. 제안식은 기존 연구결과와 유사하였으며 보다 간편하게 곡률연성도를 예측할 수 있을 것이다. This study proposes a simplified ductility formula for predicting the ductile behavior of reinforced concrete flexural members. The formula takes into account concrete strength, rebar yield strength, and the quantity of reinforcement. In reinforced concrete structures, ensuring ductile failure at the ultimate state is a crucial design concept. To achieve this, revised design standards specify minimum allowable tensile strain and tension-controlled strain limits based on rebar yield strength. Consequently, a formula for calculating curvature ductility is presented, using the ratio of tensile strain at compressive concrete failure to yield strain as a variable. In this context, the influence of concrete strength and yield strength of reinforcement on curvature ductility was investigated. It was found that the difference in curvature ductility based on concrete strength was insignificant when considering tensile strain of rebar as a reference, and with higher yield strength of reinforcement, the curvature ductility decreased. The proposed formula aligns with previous research results and provides a more convenient means to predict curvature ductility.

고강도철근이 배근된 철근콘크리트 보의 휨성능 평가

홍건호(Hong Geon-Ho) 대한건축학회 2011 大韓建築學會論文集 : 構造系 Vol.27 No.1

Korean building code requirements provide that the yield strength of longitudinal reinforcement shall not exceed 550 ㎫ in flexural members. The purpose of this paper is to evaluate the possibility of yield strength increase up to 600 ㎫ or 700 ㎫ in flexural reinforcement. Total 8 simple beam specimens divided by 3 groups tested for evaluating the flexural performance. Main test variables were yield strength of longitudinal reinforcement, reinforcement ratio and cover thickness. Test data analyzed in the viewpoint of cracking load, ultimate flexural strength, load-deflection relationship, crack progress, failure aspects and ductility. Test results indicate that flexural capacity of the specimen is similar from a standpoint of unit strength-area of reinforcement, but ductility of the specimens with high strength reinforcing bars was reduced in high reinforcement ratio. Flexural stiffness of the specimens with high strength reinforcing bars was also reduced, and this phenomenon is well agreed with the reduction of effective moment of inertia Ie. This paper concluded that flexural strength can be calculated using the present code provision without any change, but deflection checkup will be needed when the flexural member design with high strength reinforcing bars.

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.

하이브리드 강섬유 보강 초고강도 콘크리트 휨파괴형 부재의 강도 및 연성 평가에 관한 연구

여옥경,배백일 한국구조물진단유지관리공학회 2019 한국구조물진단유지관리공학회 논문집 Vol.23 No.6

In this study, the flexural strength and curvature ductility factor of single and hybrid fiber reinforced ultra high strength concrete flexural members with conventional steel rebar were evaluated by experimental program with 3-UHSC beams. Test specimens were loaded by 4-pointed flexural loading. According to the test results, hybrid fiber reinforced UHPC test specimens had higher moment resisting capacity and ductility. For the safe design of hybrid fiber reinforced UHPC, test specimens were analyzed according to the sectional analysis method with material models suggested by K-UHPC design recommendation. Current K-UHPC design recommendation predict the moment resisting capacity of member conventionally and over-estimated the ductility. 본 연구에서는 단일강섬유와 하이브리드강섬유로 보강된 UHPC의 휨강도 및 연성을 평가하기 위해 세 개의 휨파괴형 보에 대한 4점 가력 실험을 수행하였다. 실험 결과 단일섬유로 보강된 UHPC보다 하이브리드 섬유로 보강된 UHPC가 강도 및 연성 모든 측면에서 더 우수한 구조성능을 보유한 것으로 나타났다. 설계시의 안전성에 대해 평가하기 위하여, K-UHPC 구조설계지침에서 제공하는 방법에 따라 실험체의 강도와 연성을 평가해본 결과 현재의 재료모델은 강도에 대해서는 보수적으로 평가할 수 있으나 연성에 대해서는 과대평가하는 것으로 나타났다.

휨을 받는 압축강도 80 MPa 수준의 고강도 콘크리트 부재의 구조거동 실험 연구

양인환,황철성,김경철,조창빈 한국구조물진단유지관리공학회 2017 한국구조물진단유지관리공학회 논문집 Vol.21 No.4

본 연구에서는 휨을 받는 압축강도 80 MPa 수준의 고강도 콘크리트 부재의 구조거동 실험 연구를 수행하였다. 실험변수는 보통(SD 400) 및 고강도(SD 600)철근, 0.98~1.58%의 종방향 철근비, 200×250, 200×300 mm의 단면크기를 고려하였다. 9개의 보 부재를 제작하여 휨 실 험을 수행하였으며 극한휨강도, 하중-처짐 관계, 균열 형태, 파괴형상 및 연성을 파악하였다. 실험결과는 철근비가 증가함에 따라 휨강도는 증 가하고 연성은 감소한다. 또한, 철근비가 증가함에 따라 균열의 개수가 증가하며 균열폭은 감소하는 경향을 나타내었다. 철근의 강도 등급에 따른 하중-균열폭 관계는 뚜렷한 차이를 나타내지 않는다. 콘크리트 비선형거동 해석을 수행하였으며, 극한하중 예측값과 측정값을 비교하였 다. 고강도 콘크리트의 휨거동 예측 결과는 실험부재의 휨강도를 전반적으로 과소평가하고 있다. This paper concerns the structural behavior of high-strength concrete beams with compressive strength of 80 MPa subjected to flexure. Main test variables were nominal yielding strength of longitudinal rebar including normal strength rebar(SD 400) and high strength rebar(SD 600), reinforcement ratio from 0.98 to 1.58% and beam section size with 200×250, 200×300 mm. The nine beams were cast and tested under flexure. The study investigated ultimate flexural strength, load-deflection relationship, crack patterns, failure patterns and ductility of the test beams. Test results indicate that when rebar ratio increased flexural strength increased and ductility decreased. In addition, the number of cracks increased and the crack width decreased as the reinforcement ratio increased. The yield strength of rebar did not affect significantly load-crack width relationship. Nonlinear analysis of test beams was performed and then test results and analytical results of ultimate load were compared. Analytical results of high-strength concrete beams overall underestimated flexural strength of test beams.