• Structural Engineering and Mechanics
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• v.90 no.5
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• pp.505-515
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• 2024

In this study, obtaining theoretical stress-strain curves and determining the parameters defining the equivalent rectangular stress block were aimed for 3 and 4-layered rectangular Reinforced Concrete (RC) cross-sections subjected to flexure. For these aims, the analytical stress-strain model proposed by Hognestad was chosen for the concrete grades (20 MPa≤fck≤60 MPa) used in this study. The tensile strength of the concrete was neglected and the thickness of the concrete layers in the compression zone of the concrete cross-section was taken as equal. In addition, while concrete strength was kept constant within each layer, concrete strengths belonging to separate layers were increased from the neutral axis towards the outer face of the compression zone of the concrete cross-section. After the equivalent rectangular stress block parameters were determined by numerical iterations, variations of these parameters depending on concrete strength in layers and layer numbers were obtained. Finally, some analytical equations have been proposed to predict the equivalent stress block parameters for the 3 and 4-layered RC cross-sections and validities of these proposed equations were shown by different metrics in this study.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.05a
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• pp.915-920
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• 2001

This study was conducted to analysis the distribution of the rectangular stress block for high-strength polymer concrete beam. C-shaped specimens were produced and tested to compute parameters of the rectangular stress block. They were $\kappa_{1}$ = 0.73, $\kappa_{3}$ = 0.94 and $\gamma$= 0.845, respectively. Experimental value of flexural strength of beam was same to be compared with theoretical value. But there is desirable to need many experimental data in order to exact design of polymer concrete structure.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.11a
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• pp.248-251
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• 2003

The ACI 318 stress block parameters have been closely examined for validity of their values in evaluation of flexural strength and deformability. For this the conventional definition of stress block has been used. The comparison of parameter values between ACI stress blocks and the exact approach implies that an alternative idealization other than the rectangular stress block may be required.

• Journal of The Korean Society of Agricultural Engineers
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• v.50 no.5
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• pp.29-37
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• 2008

Stress-strain relation and stress block parameters of polymer concrete flexural compression members were experimentally investigated. For these purposes, a series of C-shaped polymer concrete specimens subjected to axial compressive load was tested. Based on the test results, we proposed an equation by which the stress-strain relation of polymer concrete can be predicted. In this model, we took account the slope of descending branch beyond the peak stress point of single curve. The proposed equation was numerically integrated to compute the rectangular stress block parameters. Computed ${\beta}_1$ was greater than the values prescribed in ACI 318 Code for cement concrete, and $\gamma$ was about 0.85 that is similar to the value regulated in the ACI.

• Journal of the Korea Concrete Institute
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• v.15 no.2
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• pp.335-343
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• 2003

In the previous experimental study, it is verified that the ultimate strain of concrete (${\varepsilon}$$_{cu}$=0.003) and coefficient of equivalent stress block (${\beta}$$_1$) can be used for the analysis of RC beams under biaxial and uniaxial bending moment. However, the characteristics of stress distribution of non rectangular compressed area in the RC columns are different to those of rectangular compressed area. The properties of compressive stress distribution of concrete have minor effect on the pure bending moment such as beams, but for the columns subjected to combined axial load and biaxial bending moment, the properties of compressive stress distribution are influencing factors. Nevertheless, in ACI 318-99 code, the design tables for columns subjected to axial loads with bidirectional eccentricities are based on the parameters recommended for rectangular stress block(RSB) of rectangular compressed areas. In this study the characteristics of stress distribution through both angle and depth of neutral axis are observed and formulated rationally. And the modified parameters of rectangular stress block(MRSB) for non rectangular compressed area is proposed. And the computer program using MRSB for the biaxial bending analysis of RC columns is developed and the results of MRSB are compared to RSB and experimental results respectively.

• Journal of the Korea Concrete Institute
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• v.23 no.3
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• pp.365-376
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• 2011

The current Concrete Structural Design Code (2007) prescribe the equivalent rectangular stress block of the ACI 318 Building Code as concrete compressive stress distribution for design of concrete structures. The rectangular stress block may be enough for flexural strength calculation, but realistic stress-strain relationship is required for performance verification at selected limit state in performance-based design. Moreover, the ACI rectangular stress block provides non-conservative flexural strength for high strength concrete columns. Therefore a new stress distribution model is required for development of performance-based design code. This paper proposes a concrete compressive stress-strain distribution model for design and performance verification. The proposed model has a parabolic-rectangular shape, which is adopted by Eurocode 2 and Japanese Code (JSCE). It was developed by investigation of experimental test results conducted by the authors and other researchers. The test results cover high strength concrete as well as normal strength concrete. The stress distribution parameters of the proposed models are compared to those of the ACI 318 Building Code, Eurocode 2, Japanese Code (JSCE) and Canadian Code (CSA) as well as the test results.

• 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.

• Magazine of the Korea Concrete Institute
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• v.11 no.1
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• pp.149-160
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• 1999

This paper is a part of a research aimed at the verification of basic design rules of high-strength concrete columns. A total of 32 column specimens were tested to investigate structural behavior and strength of eccentrically loaded reinforced concrete tied columns. Main variables included in this test program were concrete compressive strength. steel amount, eccentricity, and slenderness ratio. The concrete compressive strength varied from 356 kg/$cm^2$ to 951 kg/$cm^2$ and the longitudinal steel ratios were between 1.13 % and 5.51 %. Test results of column sectional strength are compared with the results of analyses by ACI rectangular stress block, trapezoidal stress block, and modified rectangular stress block. Axial force-moment-curvature analysis is also performed for predicting axial load-moment strength and compared with the test results. The ACI rectangular stress block provides over-estimated column strengths for the lightly reinforced high strength column specimens. The calculated strengths by moment-curvature analyses are highly affected by $k_3$ values of the concrete stress-strain curve. Observed failure mode. concrete ultimate strain, and stress block parameters are discussed.

• Structural Engineering and Mechanics
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• v.47 no.2
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• pp.185-207
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• 2013

In flexural strength design of normal-strength concrete (NSC) beams, it is commonly accepted that the distribution of concrete stress within the compression zone can be reasonably represented by an equivalent rectangular stress block. The stress block it governed by two parameters, which are normally denoted by ${\alpha}$ and ${\beta}$ to stipulate the width and depth of the stress block. Currently in most of the reinforced concrete (RC) design codes, ${\alpha}$ and ${\beta}$ are usually taken as 0.85 and 0.80 respectively for NSC. Nonetheless, in an experimental study conducted earlier by the authors on NSC columns, it was found that ${\alpha}$ increases significantly with strain gradient, which means that larger concrete stress can be developed in flexure. Consequently, less tension steel will be required for a given design flexural strength, which improves the ductility performance. In this study, the authors' previously proposed strain-gradient-dependent concrete stress block will be adopted to produce a series of design charts showing the maximum design limits of flexural strength and ductility of singly-and doubly-NSC beams. Through the design charts, it can be verified that the consideration of strain gradient effect can improve significantly the flexural strength and ductility design limits of NSC beams.

• Journal of the Korea Concrete Institute
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• v.14 no.5
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• pp.638-644
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• 2002

The stress-strain relationship of polymer concrete flexural member was evaluated using C-shaped polyester concrete specimen, the compressive strength of which is 1400 kgf/$\textrm{cm}^2$. Eccentric compression test was performed to estimate the parameters, ${\alpha}$, ${\beta}$1, ${\gamma}$ for equivalent rectangular stress block. The ultimate moment strength ware obtained from the bending test on reinforced polymer concrete beams which were prepared with S different tensile steel ratios with a shear span ratio of 4.0. These values were compared with theoretical ultimate moment strengths, which were obtained using the parameters ${\alpha}$=0.61 and ${\beta}$1=0.73 from stress-stain curves of C-shaped specimens. The results showed that, when tensile steel ratio was over 0.50 $\rho$b, the experimentally obtained moment strengths were well matched with theoretically calculated values. In order to develop accurate criteria for polymer concrete flexural members, however, many other expermental studies for parameter determination are necessary using C-shaped specimens which have various compressive strengths and different sizes.