• Computers and Concrete
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• v.15 no.4
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• pp.607-642
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• 2015

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.

• Structural Engineering and Mechanics
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• v.19 no.2
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• pp.185-198
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• 2005

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.

• Journal of the Korea institute for structural maintenance and inspection
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• v.4 no.3
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• pp.197-204
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• 2000

Tensile strength (stress) of bar splice is important in the research of mechanical behavior of reinforced concrete structures-beam, column etc.- with bar splice. The purpose of this research is to evaluate the flexural behavior - deflection of beam specimens, strain of main bars - of reinforced concrete beam with Lock Joint Coupler. To make a comparative research, reinforced concrete beam specimens with normal deformed bar and lap splice are tested and analyzed. Test results, Comparing a deflection of three types flexural specimens, a flexural specimen with Lock Joint Coupler is 40% greater than the other flexural specimens. At the center of flexural specimen, the strain of main bar(D29) with lock joint coupler is 50% less, and vice versa, at the point of 14cm far from the center of flexural specimen, the strain of main bar(D29) with lock joint coupler is 9% larger than the strain of main bar(D29) which calculated using the classical flexure theory. A discords, between a deflection behavior of the flexural specimens and a strain of the main bar, are caused by the difference of strain between the lock joint coupler and main bar, near the lock joint coupler. So, additional research is need to verify as stated above discords.

• 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.

• Proceedings of the Korean Society For Composite Materials Conference
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• 1999.11a
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• pp.95-100
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• 1999

A FEA(finite element analysis model) was proposed to study stress and strain distributions in thick composites with fiber waviness and initial curvature under flexural loading. Three types of model with initial curvature were considered in this study: flat, concave and concave models. In the analysis, both material and geometrical nonlinearities were incorporated. Four point flexural tests were conducted on the flat specimens to obtain the flexural behavior of thick composites experimentally. It was concluded that the predictions from the models were in good agreement with the experimental results. It was shown that the stress and strain distributions as well as nonlinear flexural behaviors of thick composites were significantly affected by the fiber waviness and initial curvature.

• Computers and Concrete
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• v.8 no.2
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• pp.207-227
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• 2011

In flexural strength design of unconfined reinforced concrete (RC) members, the concrete compressive stress-strain curve is scaled down from the uni-axial stress-strain curve such that the maximum concrete stress adopted in design is less than the uni-axial strength to account for the strain gradient effect. It has been found that the use of this smaller maximum concrete stress will underestimate the flexural strength of unconfined RC members although the safety factors for materials are taken as unity. Herein, in order to investigate the effect of strain gradient on the maximum concrete stress that can be developed in unconfined flexural RC members, several pairs of plain concrete (PC) and RC inverted T-shaped specimens were fabricated and tested under concentric and eccentric loads. From the test results, the maximum concrete stress developed in the eccentric specimens under strain gradient is determined by the modified concrete stress-strain curve obtained from the counterpart concentric specimens based on axial load and moment equilibriums. Based on that, a pair of equivalent rectangular concrete stress block parameters for the purpose of flexural strength design of unconfined RC members is determined.

• International Journal of Concrete Structures and Materials
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• v.6 no.2
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• pp.79-85
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• 2012

This paper presents the differences in growth of time-dependent strain values in reinforced cement concrete (RCC) and pre-stressed concrete (PSC) flexural members through experiment. It was observed that at any particular age, the time-dependent strain values were less in RCC beams than in PSC beams of identical size and grade of concrete. Variables considered in the study were percentage area of reinforcement, span of members for RCC beams and eccentricity of applied pre-stress force for PSC beams. In RCC beams the time-dependent strain values increases with reduction in percentage area of reinforcement and in PSC beams eccentricity directly influences the growth of time-dependent strain. With increase in age, a non-uniform strain develops across the depth of beams which influence the growth of concave curvature in RCC beams and convex curvature in PSC beams. The experimentally obtained strain values were compared with predicted strain values of similar size and grade of plane concrete (PC) beam using ACI 318 Model Code and found more than RCC beams but less than PSC beams.

• Journal of the Korean Recycled Construction Resources Institute
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• v.7 no.2
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• pp.158-165
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• 2019

The purpose of this study is to investigate analytically the flexural behavior of beam reinforced by an alkali-activated slag-based fiber-reinforced composite. The materials and mixture proportion were selected to manufacture an alkali-activated slag-based fiber-reinforced composite with high tensile strain capacity over 7% and compressive strength and tension tests were performed. The composite showed a compressive strength of 32.7MPa, a tensile strength of 8.43MPa, and a tensile strain capacity of 7.52%. In order to analyze the flexural behavior of beams reinforced by ultra-high-ductile composite, nonlinear sectional analysis was peformed for four types of beams. Analysis showed that the flexural strength of beam reinforced partially by ultra-high-ductile composite increased by 8.0%, and the flexural strength of beam reinforced fully by ultra-high-ductile composite increased by 24.7%. It was found that the main reason of low improvement in flexural strength is the low tensile strain at the bottom of beam. The tensile strain at bottom corresponding to the flexural strength was 1.38% which was 18.4% of tensile strain capacity of the composite.

• Proceedings of the Korea Concrete Institute Conference
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• 2006.11a
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• pp.129-132
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• 2006

It is generally reported that most of RC beams strengthened with simply bonded FRP composite is failed by FRP debonding. Also, the flexural performance of RC member strengthened with FRP composite can be calculated using the effective strain of FRP. The effective strain as a result of the debonding failure depends on many variables, such as FRP stiffness including the thickness($t_f$) and modulus of elasticity($E_f$), the amount of FRP but the FRP stiffness is reportedly the most influential. The purpose of this paper, therefore, is to examine effects of FRP stiffness on the flexural strengthening of RC beams. 4 different stiffness of CFRP composite including CFRP sheet and laminae were selected. From the tests, it was found that the flexural performance of RC beams strengthened with CFRP composite can be calculated based on the effective strain of the CFRP composite and the effective strain is inversely proportional to the CFRP stiffness.

• Journal of Korean Society of Steel Construction
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• v.29 no.1
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• pp.1-12
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• 2017

This paper proposes nominal flexural strength considering strain-hardening effect of HSB600 high performance steel for compact composite I-girders in positive bending. Unlike conventional steels, HSB600 undergoes strain-hardening just after yielding without going through yield plateau. However, because the nominal flexural strength specified in domestic and foreign bridge design specifications has been developed for the conventional steel composite girders, the nominal flexural strength does not appropriately consider the strain-hardening of HSB600. Therefore, plastic moment considering a strain-hardening is proposed so as to consider effect of the strain-hardening of HSB600 on flexural strength and then moment-curvature analysis is performed to a wide range of cross-sections. From results of the analysis, a parameter representing the effect of the strain-hardening on the flexural strength of HSB600 composite girders is proposed. Furthermore, by using this parameter, the nominal flexural strength considering the strain-hardening effect for HSB600 composite I-girders in positive bending is proposed and then evaluated by comparing with the current AASHTO LRFD bridge design specifications.